LMFDB - Embedded newform 588.2.o.a.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(19,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("588.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.432972864.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{6} + 4x^{5} - 6x^{4} + 8x^{3} + 4x^{2} - 8x + 16 $ x^8 - x^7 + x^6 + 4x^5 - 6x^4 + 8x^3 + 4x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$1.15972 - 0.809347i$ of defining polynomial
Character	$\chi$	$=$	588.31
Dual form			588.2.o.a.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15972 + 0.809347i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.689916 + 1.87724i) q^{4} +(-2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.15972 + 0.809347i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.689916 + 1.87724i) q^{4} +(-2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.69928 - 0.403728i) q^{10} +(-0.810969 - 0.468213i) q^{11} +(-1.97069 - 0.341134i) q^{12} -1.87285i q^{13} -3.33513i q^{15} +(-3.04803 + 2.59027i) q^{16} +(-4.51025 - 2.60399i) q^{17} +(0.121053 - 1.40902i) q^{18} +(3.56155 + 6.16879i) q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +(-0.810969 + 0.468213i) q^{23} +(-2.00936 - 1.99059i) q^{24} +(3.06155 - 5.30277i) q^{25} +(1.51579 - 2.17199i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(2.69928 - 3.86783i) q^{30} +(-5.63130 + 0.537082i) q^{32} +(0.810969 - 0.468213i) q^{33} +(-3.12311 - 6.67026i) q^{34} +(1.28078 - 1.53610i) q^{36} +(-0.561553 - 0.972638i) q^{37} +(-0.862275 + 10.0366i) q^{38} +(1.62194 + 0.936426i) q^{39} +(-2.48421 - 9.10019i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(0.319446 - 1.84541i) q^{44} +(2.88831 + 1.66757i) q^{45} +(-1.31945 - 0.113357i) q^{46} +(3.12311 + 5.40938i) q^{47} +(-0.719224 - 3.93481i) q^{48} +(7.84233 - 3.67188i) q^{50} +(4.51025 - 2.60399i) q^{51} +(3.51579 - 1.29211i) q^{52} +(-6.12311 + 10.6055i) q^{53} +(1.15972 + 0.809347i) q^{54} +3.12311 q^{55} -7.12311 q^{57} +(-2.31945 - 1.61869i) q^{58} +(2.00000 - 3.46410i) q^{59} +(6.26083 - 2.30096i) q^{60} +(-4.15468 + 2.39871i) q^{61} +(-6.96543 - 3.93481i) q^{64} +(3.12311 + 5.40938i) q^{65} +(1.31945 + 0.113357i) q^{66} +(9.47590 + 5.47091i) q^{67} +(1.77662 - 10.2633i) q^{68} -0.936426i q^{69} -3.86098i q^{71} +(2.72859 - 0.744862i) q^{72} +(5.77662 + 3.33513i) q^{73} +(0.135956 - 1.58248i) q^{74} +(3.06155 + 5.30277i) q^{75} +(-9.12311 + 10.9418i) q^{76} +(1.12311 + 2.39871i) q^{78} +(-2.07734 + 1.19935i) q^{79} +(4.48421 - 12.5643i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.18349 + 1.69584i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(-7.33994 + 10.5175i) q^{86} +(1.00000 - 1.73205i) q^{87} +(1.86404 - 1.88162i) q^{88} +(-1.26637 + 0.731140i) q^{89} +(2.00000 + 4.27156i) q^{90} +(-1.43845 - 1.19935i) q^{92} +(-0.756124 + 8.80106i) q^{94} +(-20.5737 - 11.8782i) q^{95} +(2.35052 - 5.14539i) q^{96} +10.4160i q^{97} +0.936426i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	$ 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) $ 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.15972	+	0.809347i	0.820048	+	0.572295i
$2$	1.15972	+	0.809347i	0.820048	+	0.572295i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.689916	+	1.87724i	0.344958	+	0.938618i
$5$	−2.88831	+	1.66757i	−1.29169	+	0.745758i	−0.978954	−	0.204082i	$-0.934579\pi$
$5$	−2.88831	+	1.66757i	−1.29169	+	0.745758i	−0.312737	+	0.949840i	$0.601246\pi$
$6$	−1.28078	+	0.599676i	−0.522875	+	0.244817i
$7$		0			0
$7$		0			0
$8$	−0.719224	+	2.73546i	−0.254284	+	0.967130i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−4.69928	−	0.403728i	−1.48604	−	0.127670i
$11$	−0.810969	−	0.468213i	−0.244516	−	0.141172i	0.372734	−	0.927938i	$-0.378420\pi$
$11$	−0.810969	−	0.468213i	−0.244516	−	0.141172i	−0.617251	+	0.786766i	$0.711754\pi$
$12$	−1.97069	−	0.341134i	−0.568890	−	0.0984768i
$13$		−	1.87285i		−	0.519436i	−0.965685	−	0.259718i	$-0.916370\pi$
$13$		−	1.87285i		−	0.519436i	0.965685	−	0.259718i	$-0.0836296\pi$
$14$		0			0
$15$		−	3.33513i		−	0.861127i
$16$	−3.04803	+	2.59027i	−0.762008	+	0.647568i
$17$	−4.51025	−	2.60399i	−1.09390	−	0.631561i	−0.159285	−	0.987233i	$-0.550919\pi$
$17$	−4.51025	−	2.60399i	−1.09390	−	0.631561i	−0.934611	+	0.355672i	$0.884252\pi$
$18$	0.121053	−	1.40902i	0.0285325	−	0.332110i
$19$	3.56155	+	6.16879i	0.817076	+	1.41522i	0.907827	+	0.419344i	$0.137740\pi$
$19$	3.56155	+	6.16879i	0.817076	+	1.41522i	−0.0907512	+	0.995874i	$0.528927\pi$
$20$	−5.12311	−	4.27156i	−1.14556	−	0.955149i
$21$		0			0
$22$	−0.561553	−	1.19935i	−0.119723	−	0.255703i
$23$	−0.810969	+	0.468213i	−0.169099	+	0.0976292i	−0.582161	−	0.813074i	$-0.697793\pi$
$23$	−0.810969	+	0.468213i	−0.169099	+	0.0976292i	0.413062	+	0.910703i	$0.364459\pi$
$24$	−2.00936	−	1.99059i	−0.410159	−	0.406328i
$25$	3.06155	−	5.30277i	0.612311	−	1.06055i
$26$	1.51579	−	2.17199i	0.297270	−	0.425962i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	2.69928	−	3.86783i	0.492819	−	0.706166i
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	−5.63130	+	0.537082i	−0.995483	+	0.0949435i
$33$	0.810969	−	0.468213i	0.141172	−	0.0815055i
$34$	−3.12311	−	6.67026i	−0.535608	−	1.14394i
$35$		0			0
$36$	1.28078	−	1.53610i	0.213463	−	0.256017i
$37$	−0.561553	−	0.972638i	−0.0923187	−	0.159901i	0.816168	−	0.577815i	$-0.196095\pi$
$37$	−0.561553	−	0.972638i	−0.0923187	−	0.159901i	−0.908486	+	0.417914i	$0.862761\pi$
$38$	−0.862275	+	10.0366i	−0.139879	+	1.62815i
$39$	1.62194	+	0.936426i	0.259718	+	0.149948i
$40$	−2.48421	−	9.10019i	−0.392789	−	1.43887i
$41$			1.46228i			0.228370i	0.993460	+	0.114185i	$0.0364256\pi$
$41$			1.46228i			0.228370i	−0.993460	+	0.114185i	$0.963574\pi$
$42$		0			0
$43$			9.06897i			1.38300i	0.722374	+	0.691502i	$0.243051\pi$
$43$			9.06897i			1.38300i	−0.722374	+	0.691502i	$0.756949\pi$
$44$	0.319446	−	1.84541i	0.0481584	−	0.278206i
$45$	2.88831	+	1.66757i	0.430564	+	0.248586i
$46$	−1.31945	−	0.113357i	−0.194542	−	0.0167136i
$47$	3.12311	+	5.40938i	0.455552	+	0.789039i	0.998720	−	0.0505852i	$-0.0161087\pi$
$47$	3.12311	+	5.40938i	0.455552	+	0.789039i	−0.543168	+	0.839624i	$0.682775\pi$
$48$	−0.719224	−	3.93481i	−0.103811	−	0.567941i
$49$		0			0
$50$	7.84233	−	3.67188i	1.10907	−	0.519283i
$51$	4.51025	−	2.60399i	0.631561	−	0.364632i
$52$	3.51579	−	1.29211i	0.487552	−	0.179184i
$53$	−6.12311	+	10.6055i	−0.841073	+	1.45678i	0.0479149	+	0.998851i	$0.484742\pi$
$53$	−6.12311	+	10.6055i	−0.841073	+	1.45678i	−0.888988	+	0.457930i	$0.848591\pi$
$54$	1.15972	+	0.809347i	0.157818	+	0.110138i
$55$	3.12311			0.421119
$56$		0			0
$57$	−7.12311			−0.943478
$58$	−2.31945	−	1.61869i	−0.304558	−	0.212545i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	6.26083	−	2.30096i	0.808270	−	0.297053i
$61$	−4.15468	+	2.39871i	−0.531952	+	0.307123i	−0.741811	−	0.670609i	$-0.766033\pi$
$61$	−4.15468	+	2.39871i	−0.531952	+	0.307123i	0.209859	+	0.977732i	$0.432700\pi$
$62$		0			0
$63$		0			0
$64$	−6.96543	−	3.93481i	−0.870679	−	0.491851i
$65$	3.12311	+	5.40938i	0.387374	+	0.670951i
$66$	1.31945	+	0.113357i	0.162413	+	0.0139533i
$67$	9.47590	+	5.47091i	1.15766	+	0.668378i	0.950743	−	0.309979i	$-0.100322\pi$
$67$	9.47590	+	5.47091i	1.15766	+	0.668378i	0.206922	+	0.978358i	$0.433655\pi$
$68$	1.77662	−	10.2633i	0.215447	−	1.24461i
$69$		−	0.936426i		−	0.112732i
$70$		0			0
$71$		−	3.86098i		−	0.458215i	−0.973401	−	0.229107i	$-0.926419\pi$
$71$		−	3.86098i		−	0.458215i	0.973401	−	0.229107i	$-0.0735807\pi$
$72$	2.72859	−	0.744862i	0.321567	−	0.0877828i
$73$	5.77662	+	3.33513i	0.676102	+	0.390348i	0.798385	−	0.602148i	$-0.205688\pi$
$73$	5.77662	+	3.33513i	0.676102	+	0.390348i	−0.122283	+	0.992495i	$0.539021\pi$
$74$	0.135956	−	1.58248i	0.0158045	−	0.183960i
$75$	3.06155	+	5.30277i	0.353518	+	0.612311i
$76$	−9.12311	+	10.9418i	−1.04649	+	1.25511i
$77$		0			0
$78$	1.12311	+	2.39871i	0.127167	+	0.271600i
$79$	−2.07734	+	1.19935i	−0.233719	+	0.134938i	−0.612287	−	0.790636i	$-0.709750\pi$
$79$	−2.07734	+	1.19935i	−0.233719	+	0.134938i	0.378568	+	0.925574i	$0.376417\pi$
$80$	4.48421	−	12.5643i	0.501350	−	1.40473i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.18349	+	1.69584i	−0.130695	+	0.187274i
$83$	10.2462			1.12467			0.562334	−	0.826910i	$-0.309904\pi$
$83$	10.2462			1.12467			0.562334	+	0.826910i	$0.309904\pi$
$84$		0			0
$85$	17.3693			1.88397
$86$	−7.33994	+	10.5175i	−0.791486	+	1.13413i
$87$	1.00000	−	1.73205i	0.107211	−	0.185695i
$88$	1.86404	−	1.88162i	0.198708	−	0.200581i
$89$	−1.26637	+	0.731140i	−0.134235	+	0.0775006i	−0.565614	−	0.824670i	$-0.691361\pi$
$89$	−1.26637	+	0.731140i	−0.134235	+	0.0775006i	0.431379	+	0.902171i	$0.358027\pi$
$90$	2.00000	+	4.27156i	0.210819	+	0.450262i
$91$		0			0
$92$	−1.43845	−	1.19935i	−0.149968	−	0.125041i
$93$		0			0
$94$	−0.756124	+	8.80106i	−0.0779882	+	0.907760i
$95$	−20.5737	−	11.8782i	−2.11082	−	1.21868i
$96$	2.35052	−	5.14539i	0.239899	−	0.525149i
$97$			10.4160i			1.05758i	0.848752	+	0.528791i	$0.177354\pi$
$97$			10.4160i			1.05758i	−0.848752	+	0.528791i	$0.822646\pi$
$98$		0			0
$99$			0.936426i			0.0941144i
$100$	12.0668	+	2.08880i	1.20668	+	0.208880i
$101$	11.9088	+	6.87555i	1.18497	+	0.684143i	0.957159	−	0.289562i	$-0.0935098\pi$
$101$	11.9088	+	6.87555i	1.18497	+	0.684143i	0.227811	+	0.973705i	$0.426843\pi$
$102$	7.33817	+	0.630443i	0.726587	+	0.0624232i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	5.12311	+	1.34700i	0.502362	+	0.132084i
$105$		0			0
$106$	−15.6847	+	7.34376i	−1.52343	+	0.713289i
$107$	−8.20953	+	4.73977i	−0.793645	+	0.458211i	−0.841244	−	0.540655i	$-0.818176\pi$
$107$	−8.20953	+	4.73977i	−0.793645	+	0.458211i	0.0475993	+	0.998867i	$0.484843\pi$
$108$	0.689916	+	1.87724i	0.0663872	+	0.180637i
$109$	4.12311	−	7.14143i	0.394922	−	0.684025i	−0.598169	−	0.801370i	$-0.704105\pi$
$109$	4.12311	−	7.14143i	0.394922	−	0.684025i	0.993091	+	0.117345i	$0.0374383\pi$
$110$	3.62194	+	2.52768i	0.345338	+	0.241004i
$111$	1.12311			0.106600
$112$		0			0
$113$	−4.24621			−0.399450			−0.199725	−	0.979852i	$-0.564005\pi$
$113$	−4.24621			−0.399450			−0.199725	+	0.979852i	$0.564005\pi$
$114$	−8.26083	−	5.76506i	−0.773698	−	0.539948i
$115$	1.56155	−	2.70469i	0.145616	−	0.252214i
$116$	−1.37983	−	3.75447i	−0.128114	−	0.348594i
$117$	−1.62194	+	0.936426i	−0.149948	+	0.0865726i
$118$	5.12311	−	2.39871i	0.471620	−	0.220819i
$119$		0			0
$120$	9.12311	+	2.39871i	0.832822	+	0.218971i
$121$	−5.06155	−	8.76687i	−0.460141	−	0.796988i
$122$	−6.75966	−	0.580742i	−0.611991	−	0.0525779i
$123$	−1.26637	−	0.731140i	−0.114185	−	0.0659246i
$124$		0			0
$125$			3.74571i			0.335026i
$126$		0			0
$127$		−	9.89012i		−	0.877606i	−0.898583	−	0.438803i	$-0.855403\pi$
$127$		−	9.89012i		−	0.877606i	0.898583	−	0.438803i	$-0.144597\pi$
$128$	−4.89335	−	10.2007i	−0.432515	−	0.901627i
$129$	−7.85396	−	4.53448i	−0.691502	−	0.399239i
$130$	−0.756124	+	8.80106i	−0.0663164	+	0.771904i
$131$	2.87689	+	4.98293i	0.251355	+	0.435360i	0.963899	−	0.266267i	$-0.0857904\pi$
$131$	2.87689	+	4.98293i	0.251355	+	0.435360i	−0.712544	+	0.701628i	$0.752457\pi$
$132$	1.43845	+	1.19935i	0.125201	+	0.104390i
$133$		0			0
$134$	6.56155	+	14.0140i	0.566832	+	1.21063i
$135$	−2.88831	+	1.66757i	−0.248586	+	0.143521i
$136$	10.3670	−	10.4647i	0.888961	−	0.897343i
$137$	−0.123106	+	0.213225i	−0.0105176	+	0.0182171i	−0.871236	−	0.490864i	$-0.836681\pi$
$137$	−0.123106	+	0.213225i	−0.0105176	+	0.0182171i	0.860719	+	0.509081i	$0.170015\pi$
$138$	0.757894	−	1.08600i	0.0645162	−	0.0924461i
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$		0			0
$141$	−6.24621			−0.526026
$142$	3.12488	−	4.47767i	0.262234	−	0.375758i
$143$	−0.876894	+	1.51883i	−0.0733296	+	0.127011i
$144$	3.76726	+	1.34454i	0.313938	+	0.112045i
$145$	5.77662	−	3.33513i	0.479722	−	0.276968i
$146$	4.00000	+	8.54312i	0.331042	+	0.707033i
$147$		0			0
$148$	1.43845	−	1.72521i	0.118240	−	0.141811i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$	−0.741222	+	8.62760i	−0.0605205	+	0.704440i
$151$	7.85396	+	4.53448i	0.639146	+	0.369011i	0.784286	−	0.620400i	$-0.213030\pi$
$151$	7.85396	+	4.53448i	0.639146	+	0.369011i	−0.145139	+	0.989411i	$0.546363\pi$
$152$	−19.4360	+	5.30573i	−1.57647	+	0.430352i
$153$			5.20798i			0.421041i
$154$		0			0
$155$		0			0
$156$	−0.638893	+	3.69082i	−0.0511524	+	0.295502i
$157$	−18.9518	−	10.9418i	−1.51252	−	0.873252i	−0.999893	−	0.0146398i	$-0.995340\pi$
$157$	−18.9518	−	10.9418i	−1.51252	−	0.873252i	−0.512625	−	0.858613i	$-0.671327\pi$
$158$	−3.37983	−	0.290371i	−0.268885	−	0.0231007i
$159$	−6.12311	−	10.6055i	−0.485594	−	0.841073i
$160$	15.3693	−	10.9418i	1.21505	−	0.865027i
$161$		0			0
$162$	−1.28078	+	0.599676i	−0.100627	+	0.0471150i
$163$	13.6306	−	7.86962i	1.06763	−	0.616396i	0.140096	−	0.990138i	$-0.455259\pi$
$163$	13.6306	−	7.86962i	1.06763	−	0.616396i	0.927533	+	0.373742i	$0.121925\pi$
$164$	−2.74504	+	1.00885i	−0.214352	+	0.0787779i
$165$	−1.56155	+	2.70469i	−0.121567	+	0.210560i
$166$	11.8828	+	8.29274i	0.922282	+	0.643641i
$167$	−14.2462			−1.10240			−0.551202	−	0.834372i	$-0.685831\pi$
$167$	−14.2462			−1.10240			−0.551202	+	0.834372i	$0.685831\pi$
$168$		0			0
$169$	9.49242			0.730186
$170$	20.1436	+	14.0578i	1.54494	+	1.07818i
$171$	3.56155	−	6.16879i	0.272359	−	0.471739i
$172$	−17.0246	+	6.25683i	−1.29811	+	0.477078i
$173$	14.4415	−	8.33783i	1.09797	−	0.633913i	0.162283	−	0.986744i	$-0.448114\pi$
$173$	14.4415	−	8.33783i	1.09797	−	0.633913i	0.935687	+	0.352831i	$0.114781\pi$
$174$	2.56155	−	1.19935i	0.194191	−	0.0909227i
$175$		0			0
$176$	3.68466	−	0.673500i	0.277742	−	0.0507670i
$177$	2.00000	+	3.46410i	0.150329	+	0.260378i
$178$	−2.06039	−	0.177014i	−0.154432	−	0.0132677i
$179$	13.9861	+	8.07490i	1.04537	+	0.603547i	0.921351	−	0.388733i	$-0.127087\pi$
$179$	13.9861	+	8.07490i	1.04537	+	0.603547i	0.124023	+	0.992279i	$0.460420\pi$
$180$	−1.13773	+	6.57252i	−0.0848010	+	0.489887i
$181$			1.87285i			0.139208i	0.997575	+	0.0696040i	$0.0221736\pi$
$181$			1.87285i			0.139208i	−0.997575	+	0.0696040i	$0.977826\pi$
$182$		0			0
$183$		−	4.79741i		−	0.354635i
$184$	−0.697508	−	2.55512i	−0.0514210	−	0.188366i
$185$	3.24388	+	1.87285i	0.238495	+	0.137695i
$186$		0			0
$187$	2.43845	+	4.22351i	0.178317	+	0.308854i
$188$	−8.00000	+	9.59482i	−0.583460	+	0.699774i
$189$		0			0
$190$	−14.2462	−	30.4268i	−1.03353	−	2.20739i
$191$	2.43291	−	1.40464i	0.176039	−	0.101636i	−0.409391	−	0.912359i	$-0.634259\pi$
$191$	2.43291	−	1.40464i	0.176039	−	0.101636i	0.585430	+	0.810723i	$0.300926\pi$
$192$	6.89036	−	4.06484i	0.497269	−	0.293355i
$193$	7.68466	−	13.3102i	0.553154	−	0.958091i	−0.444891	−	0.895585i	$-0.646758\pi$
$193$	7.68466	−	13.3102i	0.553154	−	0.958091i	0.998045	−	0.0625057i	$-0.0199092\pi$
$194$	−8.43013	+	12.0796i	−0.605248	+	0.867268i
$195$	−6.24621			−0.447300
$196$		0			0
$197$	−16.2462			−1.15749			−0.578747	−	0.815507i	$-0.696458\pi$
$197$	−16.2462			−1.15749			−0.578747	+	0.815507i	$0.696458\pi$
$198$	−0.757894	+	1.08600i	−0.0538612	+	0.0771783i
$199$	−1.56155	+	2.70469i	−0.110696	+	0.191730i	−0.916051	−	0.401062i	$-0.868641\pi$
$199$	−1.56155	+	2.70469i	−0.110696	+	0.191730i	0.805355	+	0.592792i	$0.201975\pi$
$200$	12.3035	+	12.1886i	0.869991	+	0.861865i
$201$	−9.47590	+	5.47091i	−0.668378	+	0.385888i
$202$	8.24621	+	17.6121i	0.580201	+	1.23918i
$203$		0			0
$204$	8.00000	+	6.67026i	0.560112	+	0.467012i
$205$	−2.43845	−	4.22351i	−0.170309	−	0.294983i
$206$	0.968426	−	11.2722i	0.0674734	−	0.785370i
$207$	0.810969	+	0.468213i	0.0563662	+	0.0325431i
$208$	4.85119	+	5.70852i	0.336370	+	0.395814i
$209$		−	6.67026i		−	0.461392i
$210$		0			0
$211$			12.8147i			0.882199i	0.897458	+	0.441099i	$0.145411\pi$
$211$			12.8147i			0.882199i	−0.897458	+	0.441099i	$0.854589\pi$
$212$	−24.1335	−	4.17759i	−1.65750	−	0.286918i
$213$	3.34371	+	1.93049i	0.229107	+	0.132275i
$214$	−13.3569	−	1.14753i	−0.913059	−	0.0784435i
$215$	−15.1231	−	26.1940i	−1.03139	−	1.78642i
$216$	−0.719224	+	2.73546i	−0.0489370	+	0.186124i
$217$		0			0
$218$	10.5616	−	4.94506i	0.715319	−	0.334922i
$219$	−5.77662	+	3.33513i	−0.390348	+	0.225367i
$220$	2.15468	+	5.86281i	0.145268	+	0.395270i
$221$	−4.87689	+	8.44703i	−0.328055	+	0.568209i
$222$	1.30249	+	0.908982i	0.0874175	+	0.0610069i
$223$	−27.1231			−1.81630			−0.908149	−	0.418648i	$-0.862504\pi$
$223$	−27.1231			−1.81630			−0.908149	+	0.418648i	$0.862504\pi$
$224$		0			0
$225$	−6.12311			−0.408207
$226$	−4.92443	−	3.43666i	−0.327568	−	0.228603i
$227$	−8.24621	+	14.2829i	−0.547320	+	0.947987i	0.451137	+	0.892455i	$0.351019\pi$
$227$	−8.24621	+	14.2829i	−0.547320	+	0.947987i	−0.998457	+	0.0555316i	$0.982315\pi$
$228$	−4.91434	−	13.3718i	−0.325460	−	0.885566i
$229$	−4.86581	+	2.80928i	−0.321542	+	0.185642i	−0.652080	−	0.758150i	$-0.726103\pi$
$229$	−4.86581	+	2.80928i	−0.321542	+	0.185642i	0.330538	+	0.943793i	$0.392770\pi$
$230$	4.00000	−	1.87285i	0.263752	−	0.123492i
$231$		0			0
$232$	1.43845	−	5.47091i	0.0944387	−	0.359183i
$233$	−11.2462	−	19.4790i	−0.736764	−	1.27611i	−0.953945	−	0.299981i	$-0.903020\pi$
$233$	−11.2462	−	19.4790i	−0.736764	−	1.27611i	0.217181	−	0.976131i	$-0.430314\pi$
$234$	−2.63889	−	0.226715i	−0.172510	−	0.0148208i
$235$	−18.0410	−	10.4160i	−1.17686	−	0.679463i
$236$	7.88277	+	1.36453i	0.513125	+	0.0888236i
$237$		−	2.39871i		−	0.155813i
$238$		0			0
$239$			16.1498i			1.04464i	0.852748	+	0.522322i	$0.174934\pi$
$239$			16.1498i			1.04464i	−0.852748	+	0.522322i	$0.825066\pi$
$240$	8.63889	+	10.1656i	0.557638	+	0.656186i
$241$	20.5737	+	11.8782i	1.32527	+	0.765145i	0.984564	−	0.175024i	$-0.0560005\pi$
$241$	20.5737	+	11.8782i	1.32527	+	0.765145i	0.340706	+	0.940170i	$0.389334\pi$
$242$	1.22543	−	14.2637i	0.0787739	−	0.916905i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−7.36932	−	6.14441i	−0.471772	−	0.393356i
$245$		0			0
$246$	−0.876894	−	1.87285i	−0.0559087	−	0.119409i
$247$	11.5532	−	6.67026i	0.735115	−	0.424419i
$248$		0			0
$249$	−5.12311	+	8.87348i	−0.324664	+	0.562334i
$250$	−3.03157	+	4.34398i	−0.191734	+	0.274738i
$251$	5.75379			0.363176			0.181588	−	0.983375i	$-0.441876\pi$
$251$	5.75379			0.363176			0.181588	+	0.983375i	$0.441876\pi$
$252$		0			0
$253$	0.876894			0.0551299
$254$	8.00453	−	11.4698i	0.502249	−	0.719679i
$255$	−8.68466	+	15.0423i	−0.543854	+	0.941983i
$256$	2.58100	−	15.7905i	0.161313	−	0.986903i
$257$	−1.97751	+	1.14171i	−0.123353	+	0.0712181i	−0.560407	−	0.828217i	$-0.689355\pi$
$257$	−1.97751	+	1.14171i	−0.123353	+	0.0712181i	0.437054	+	0.899435i	$0.356022\pi$
$258$	−5.43845	−	11.6153i	−0.338583	−	0.723138i
$259$		0			0
$260$	−8.00000	+	9.59482i	−0.496139	+	0.595046i
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	−0.696515	+	8.10722i	−0.0430308	+	0.500866i
$263$	21.3847	+	12.3465i	1.31864	+	0.761315i	0.983509	−	0.180857i	$-0.0578872\pi$
$263$	21.3847	+	12.3465i	1.31864	+	0.761315i	0.335128	+	0.942173i	$0.391221\pi$
$264$	0.697508	+	2.55512i	0.0429287	+	0.157257i
$265$		−	40.8427i		−	2.50895i
$266$		0			0
$267$		−	1.46228i		−	0.0894900i
$268$	−3.73262	+	21.5630i	−0.228006	+	1.31717i
$269$	−9.37606	−	5.41327i	−0.571669	−	0.330053i	0.186147	−	0.982522i	$-0.440400\pi$
$269$	−9.37606	−	5.41327i	−0.571669	−	0.330053i	−0.757815	+	0.652469i	$0.773733\pi$
$270$	−4.69928	−	0.403728i	−0.285989	−	0.0245701i
$271$	−14.2462	−	24.6752i	−0.865396	−	1.49891i	−0.866654	−	0.498910i	$-0.833734\pi$
$271$	−14.2462	−	24.6752i	−0.865396	−	1.49891i	0.00125803	−	0.999999i	$-0.499600\pi$
$272$	20.4924	−	3.74571i	1.24254	−	0.227117i
$273$		0			0
$274$	−0.315342	+	0.147647i	−0.0190505	+	0.00891969i
$275$	−4.96565	+	2.86692i	−0.299440	+	0.172882i
$276$	1.75789	−	0.646055i	0.105813	−	0.0388880i
$277$	2.56155	−	4.43674i	0.153909	−	0.266578i	−0.778752	−	0.627331i	$-0.784147\pi$
$277$	2.56155	−	4.43674i	0.153909	−	0.266578i	0.932661	+	0.360754i	$0.117480\pi$
$278$	13.9167	+	9.71216i	0.834667	+	0.582497i
$279$		0			0
$280$		0			0
$281$	16.2462			0.969168			0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462			0.969168			0.484584	+	0.874745i	$0.338971\pi$
$282$	−7.24388	−	5.05535i	−0.431367	−	0.301042i
$283$	4.43845	−	7.68762i	0.263838	−	0.456981i	−0.703420	−	0.710774i	$-0.748345\pi$
$283$	4.43845	−	7.68762i	0.263838	−	0.456981i	0.967259	+	0.253793i	$0.0816781\pi$
$284$	7.24798	−	2.66375i	0.430089	−	0.158065i
$285$	20.5737	−	11.8782i	1.21868	−	0.703607i
$286$	−2.24621	+	1.05171i	−0.132821	+	0.0621887i
$287$		0			0
$288$	3.28078	+	4.60831i	0.193322	+	0.271547i
$289$	5.06155	+	8.76687i	0.297738	+	0.515698i
$290$	9.39856	+	0.807457i	0.551902	+	0.0474155i
$291$	−9.02049	−	5.20798i	−0.528791	−	0.305297i
$292$	−2.27545	+	13.1450i	−0.133161	+	0.769255i
$293$		−	13.7511i		−	0.803348i	−0.915783	−	0.401674i	$-0.868429\pi$
$293$		−	13.7511i		−	0.803348i	0.915783	−	0.401674i	$-0.131571\pi$
$294$		0			0
$295$			13.3405i			0.776716i
$296$	3.06449	−	0.836559i	0.178120	−	0.0486240i
$297$	−0.810969	−	0.468213i	−0.0470572	−	0.0271685i
$298$	−1.21053	+	14.0902i	−0.0701242	+	0.816225i
$299$	0.876894	+	1.51883i	0.0507121	+	0.0878360i
$300$	−7.84233	+	9.40572i	−0.452777	+	0.543039i
$301$		0			0
$302$	5.43845	+	11.6153i	0.312947	+	0.668387i
$303$	−11.9088	+	6.87555i	−0.684143	+	0.394990i
$304$	−26.8346	−	9.57729i	−1.53907	−	0.549295i
$305$	8.00000	−	13.8564i	0.458079	−	0.793416i
$306$	−4.21507	+	6.03982i	−0.240959	+	0.345274i
$307$	−19.6155			−1.11952			−0.559759	−	0.828656i	$-0.689106\pi$
$307$	−19.6155			−1.11952			−0.559759	+	0.828656i	$0.689106\pi$
$308$		0			0
$309$	8.00000			0.455104
$310$		0			0
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$	−3.72809	+	3.76324i	−0.211061	+	0.213051i
$313$	19.8626	−	11.4677i	1.12270	−	0.648191i	0.180611	−	0.983555i	$-0.442192\pi$
$313$	19.8626	−	11.4677i	1.12270	−	0.648191i	0.942089	+	0.335363i	$0.108859\pi$
$314$	−13.1231	−	28.0281i	−0.740580	−	1.58171i
$315$		0			0
$316$	−3.68466	−	3.07221i	−0.207278	−	0.172825i
$317$	7.24621	+	12.5508i	0.406988	+	0.704923i	0.994551	−	0.104255i	$-0.0332458\pi$
$317$	7.24621	+	12.5508i	0.406988	+	0.704923i	−0.587563	+	0.809179i	$0.699912\pi$
$318$	1.48244	−	17.2552i	0.0831313	−	0.967623i
$319$	1.62194	+	0.936426i	0.0908111	+	0.0524298i
$320$	26.6799	−	0.250380i	1.49145	−	0.0139966i
$321$		−	9.47954i		−	0.529097i
$322$		0			0
$323$		−	37.0970i		−	2.06413i
$324$	−1.97069	−	0.341134i	−0.109483	−	0.0189519i
$325$	−9.93130	−	5.73384i	−0.550889	−	0.318056i
$326$	22.1769	+	1.90528i	1.22827	+	0.105524i
$327$	4.12311	+	7.14143i	0.228008	+	0.394922i
$328$	−4.00000	−	1.05171i	−0.220863	−	0.0580707i
$329$		0			0
$330$	−4.00000	+	1.87285i	−0.220193	+	0.103097i
$331$	−15.2525	+	8.80604i	−0.838354	+	0.484024i	−0.856704	−	0.515808i	$-0.827492\pi$
$331$	−15.2525	+	8.80604i	−0.838354	+	0.484024i	0.0183504	+	0.999832i	$0.494159\pi$
$332$	7.06902	+	19.2346i	0.387963	+	1.05563i
$333$	−0.561553	+	0.972638i	−0.0307729	+	0.0533002i
$334$	−16.5217	−	11.5301i	−0.904025	−	0.630900i
$335$	−36.4924			−1.99379
$336$		0			0
$337$	8.24621			0.449200			0.224600	−	0.974451i	$-0.427892\pi$
$337$	8.24621			0.449200			0.224600	+	0.974451i	$0.427892\pi$
$338$	11.0086	+	7.68266i	0.598788	+	0.417882i
$339$	2.12311	−	3.67733i	0.115311	−	0.199725i
$340$	11.9834	+	32.6063i	0.649889	+	1.76833i
$341$		0			0
$342$	9.12311	−	4.27156i	0.493321	−	0.230979i
$343$		0			0
$344$	−24.8078	−	6.52262i	−1.33754	−	0.351676i
$345$	1.56155	+	2.70469i	0.0840712	+	0.145616i
$346$	23.4964	+	2.01864i	1.26317	+	0.108523i
$347$	−17.4297	−	10.0630i	−0.935675	−	0.540212i	−0.0470729	−	0.998891i	$-0.514989\pi$
$347$	−17.4297	−	10.0630i	−0.935675	−	0.540212i	−0.888602	+	0.458679i	$0.848323\pi$
$348$	3.94138	+	0.682267i	0.211280	+	0.0365734i
$349$			21.8836i			1.17140i	0.810526	+	0.585702i	$0.199181\pi$
$349$			21.8836i			1.17140i	−0.810526	+	0.585702i	$0.800819\pi$
$350$		0			0
$351$		−	1.87285i		−	0.0999655i
$352$	4.81828	+	2.20109i	0.256815	+	0.117319i
$353$	−25.0840	−	14.4822i	−1.33509	−	0.770812i	−0.349011	−	0.937119i	$-0.613483\pi$
$353$	−25.0840	−	14.4822i	−1.33509	−	0.770812i	−0.986074	+	0.166307i	$0.946816\pi$
$354$	−0.484213	+	5.63609i	−0.0257356	+	0.299555i
$355$	6.43845	+	11.1517i	0.341717	+	0.591872i
$356$	−2.24621	−	1.87285i	−0.119049	−	0.0992610i
$357$		0			0
$358$	9.68466	+	20.6843i	0.511850	+	1.09320i
$359$	19.7628	−	11.4100i	1.04304	−	0.602199i	0.122346	−	0.992487i	$-0.460958\pi$
$359$	19.7628	−	11.4100i	1.04304	−	0.602199i	0.920692	+	0.390289i	$0.127625\pi$
$360$	−6.63889	+	6.70149i	−0.349900	+	0.353199i
$361$	−15.8693	+	27.4865i	−0.835227	+	1.44666i
$362$	−1.51579	+	2.17199i	−0.0796680	+	0.114157i
$363$	10.1231			0.531325
$364$		0			0
$365$	−22.2462			−1.16442
$366$	3.88277	−	5.56367i	0.202956	−	0.290818i
$367$	−16.6847	+	28.8987i	−0.870932	+	1.50850i	−0.00989821	+	0.999951i	$0.503151\pi$
$367$	−16.6847	+	28.8987i	−0.870932	+	1.50850i	−0.861034	+	0.508548i	$0.830183\pi$
$368$	1.25906	−	3.52776i	0.0656331	−	0.183897i
$369$	1.26637	−	0.731140i	0.0659246	−	0.0380616i
$370$	2.24621	+	4.79741i	0.116775	+	0.249406i
$371$		0			0
$372$		0			0
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	−0.590364	+	6.87166i	−0.0305270	+	0.355325i
$375$	−3.24388	−	1.87285i	−0.167513	−	0.0967137i
$376$	−17.0433	+	4.65256i	−0.878942	+	0.239938i
$377$			3.74571i			0.192914i
$378$		0			0
$379$		−	25.1035i		−	1.28948i	−0.764402	−	0.644740i	$-0.776966\pi$
$379$		−	25.1035i		−	1.28948i	0.764402	−	0.644740i	$-0.223034\pi$
$380$	8.10414	−	46.8167i	0.415733	−	2.40165i
$381$	8.56509	+	4.94506i	0.438803	+	0.253343i
$382$	3.95834	+	0.340072i	0.202526	+	0.0173996i
$383$	−4.87689	−	8.44703i	−0.249198	−	0.431623i	0.714106	−	0.700038i	$-0.246834\pi$
$383$	−4.87689	−	8.44703i	−0.249198	−	0.431623i	−0.963303	+	0.268415i	$0.913500\pi$
$384$	11.2808	+	0.862603i	0.575670	+	0.0440195i
$385$		0			0
$386$	19.6847	−	9.21662i	1.00192	−	0.469113i
$387$	7.85396	−	4.53448i	0.399239	−	0.230501i
$388$	−19.5532	+	7.18614i	−0.992665	+	0.364821i
$389$	8.12311	−	14.0696i	0.411858	−	0.713359i	−0.583235	−	0.812303i	$-0.698213\pi$
$389$	8.12311	−	14.0696i	0.411858	−	0.713359i	0.995093	+	0.0989447i	$0.0315467\pi$
$390$	−7.24388	−	5.05535i	−0.366808	−	0.255988i
$391$	4.87689			0.246635
$392$		0			0
$393$	−5.75379			−0.290240
$394$	−18.8411	−	13.1488i	−0.949201	−	0.662428i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$	−1.75789	+	0.646055i	−0.0883375	+	0.0324655i
$397$	−15.7079	+	9.06897i	−0.788358	+	0.455159i	−0.839384	−	0.543539i	$-0.817084\pi$
$397$	−15.7079	+	9.06897i	−0.788358	+	0.455159i	0.0510263	+	0.998697i	$0.483751\pi$
$398$	−4.00000	+	1.87285i	−0.200502	+	0.0938776i
$399$		0			0
$400$	4.40388	+	24.0932i	0.220194	+	1.20466i
$401$	−4.12311	−	7.14143i	−0.205898	−	0.356626i	0.744520	−	0.667600i	$-0.232678\pi$
$401$	−4.12311	−	7.14143i	−0.205898	−	0.356626i	−0.950418	+	0.310974i	$0.899345\pi$
$402$	−15.4173	−	1.32454i	−0.768944	−	0.0660622i
$403$		0			0
$404$	−4.69096	+	27.0992i	−0.233384	+	1.34824i
$405$		−	3.33513i		−	0.165724i
$406$		0			0
$407$			1.05171i			0.0521311i
$408$	3.87923	+	14.2104i	0.192050	+	0.703521i
$409$	−0.711134	−	0.410574i	−0.0351633	−	0.0203016i	0.482315	−	0.875998i	$-0.339796\pi$
$409$	−0.711134	−	0.410574i	−0.0351633	−	0.0203016i	−0.517479	+	0.855696i	$0.673129\pi$
$410$	0.590364	−	6.87166i	0.0291560	−	0.339367i
$411$	−0.123106	−	0.213225i	−0.00607235	−	0.0105176i
$412$	10.2462	−	12.2888i	0.504795	−	0.605427i
$413$		0			0
$414$	0.561553	+	1.19935i	0.0275988	+	0.0589450i
$415$	−29.5942	+	17.0862i	−1.45272	+	0.838730i
$416$	1.00587	+	10.5466i	0.0493171	+	0.517089i
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$	5.39856	−	7.73566i	0.264052	−	0.378363i
$419$	16.4924			0.805708			0.402854	−	0.915264i	$-0.368018\pi$
$419$	16.4924			0.805708			0.402854	+	0.915264i	$0.368018\pi$
$420$		0			0
$421$	10.8769			0.530107			0.265054	−	0.964234i	$-0.414610\pi$
$421$	10.8769			0.530107			0.265054	+	0.964234i	$0.414610\pi$
$422$	−10.3715	+	14.8615i	−0.504877	+	0.723445i
$423$	3.12311	−	5.40938i	0.151851	−	0.263013i
$424$	−24.6071	−	24.3772i	−1.19503	−	1.18386i
$425$	−27.6167	+	15.9445i	−1.33961	+	0.773423i
$426$	2.31534	+	4.94506i	0.112179	+	0.239589i
$427$		0			0
$428$	−14.5616	−	12.1412i	−0.703859	−	0.586866i
$429$	−0.876894	−	1.51883i	−0.0423369	−	0.0733296i
$430$	3.66140	−	42.6176i	0.176568	−	2.05520i
$431$	4.05485	+	2.34107i	0.195315	+	0.112765i	0.594468	−	0.804119i	$-0.297363\pi$
$431$	4.05485	+	2.34107i	0.195315	+	0.112765i	−0.399153	+	0.916884i	$0.630696\pi$
$432$	−3.04803	+	2.59027i	−0.146649	+	0.124624i
$433$			13.3405i			0.641105i	0.947231	+	0.320552i	$0.103869\pi$
$433$			13.3405i			0.641105i	−0.947231	+	0.320552i	$0.896131\pi$
$434$		0			0
$435$			6.67026i			0.319815i
$436$	16.2507	+	2.81306i	0.778270	+	0.134721i
$437$	−5.77662	−	3.33513i	−0.276333	−	0.159541i
$438$	−9.39856	−	0.807457i	−0.449080	−	0.0385818i
$439$	−3.31534	−	5.74234i	−0.158233	−	0.274067i	0.775999	−	0.630734i	$-0.217246\pi$
$439$	−3.31534	−	5.74234i	−0.158233	−	0.274067i	−0.934231	+	0.356667i	$0.883913\pi$
$440$	−2.24621	+	8.54312i	−0.107084	+	0.407277i
$441$		0			0
$442$	−12.4924	+	5.84912i	−0.594204	+	0.278214i
$443$	16.3192	−	9.42190i	0.775349	−	0.447648i	−0.0594302	−	0.998232i	$-0.518928\pi$
$443$	16.3192	−	9.42190i	0.775349	−	0.447648i	0.834780	+	0.550584i	$0.185595\pi$
$444$	0.774848	+	2.10833i	0.0367727	+	0.100057i
$445$	2.43845	−	4.22351i	0.115593	−	0.200214i
$446$	−31.4553	−	21.9520i	−1.48945	−	1.03946i
$447$	−10.0000			−0.472984
$448$		0			0
$449$	11.7538			0.554696			0.277348	−	0.960770i	$-0.410545\pi$
$449$	11.7538			0.554696			0.277348	+	0.960770i	$0.410545\pi$
$450$	−7.10111	−	4.95572i	−0.334749	−	0.233615i
$451$	0.684658	−	1.18586i	0.0322393	−	0.0558401i
$452$	−2.92953	−	7.97114i	−0.137793	−	0.374931i
$453$	−7.85396	+	4.53448i	−0.369011	+	0.213049i
$454$	−21.1231	+	9.89012i	−0.991356	+	0.464166i
$455$		0			0
$456$	5.12311	−	19.4849i	0.239911	−	0.912466i
$457$	−0.123106	−	0.213225i	−0.00575864	−	0.00997425i	0.863132	−	0.504979i	$-0.168500\pi$
$457$	−0.123106	−	0.213225i	−0.00575864	−	0.00997425i	−0.868890	+	0.495005i	$0.835166\pi$
$458$	−7.91668	−	0.680144i	−0.369922	−	0.0317811i
$459$	−4.51025	−	2.60399i	−0.210520	−	0.121544i
$460$	6.15468	+	1.06540i	0.286963	+	0.0496743i
$461$			6.25969i			0.291543i	0.989318	+	0.145771i	$0.0465664\pi$
$461$			6.25969i			0.291543i	−0.989318	+	0.145771i	$0.953434\pi$
$462$		0			0
$463$			39.2652i			1.82481i	0.409292	+	0.912404i	$0.365776\pi$
$463$			39.2652i			1.82481i	−0.409292	+	0.912404i	$0.634224\pi$
$464$	6.09606	−	5.18054i	0.283003	−	0.240501i
$465$		0			0
$466$	2.72278	−	31.6923i	0.126130	−	1.46812i
$467$	17.1231	+	29.6581i	0.792363	+	1.37241i	0.924500	+	0.381181i	$0.124483\pi$
$467$	17.1231	+	29.6581i	0.792363	+	1.37241i	−0.132137	+	0.991231i	$0.542184\pi$
$468$	−2.87689	−	2.39871i	−0.132984	−	0.110880i
$469$		0			0
$470$	−12.4924	−	26.6811i	−0.576232	−	1.23071i
$471$	18.9518	−	10.9418i	0.873252	−	0.504173i
$472$	8.03745	+	7.96237i	0.369954	+	0.366498i
$473$	4.24621	−	7.35465i	0.195241	−	0.338167i
$474$	1.94138	−	2.78183i	0.0891707	−	0.127774i
$475$	43.6155			2.00122
$476$		0			0
$477$	12.2462			0.560715
$478$	−13.0708	+	18.7293i	−0.597844	+	0.856659i
$479$	6.24621	−	10.8188i	0.285397	−	0.494322i	−0.687309	−	0.726366i	$-0.741208\pi$
$479$	6.24621	−	10.8188i	0.285397	−	0.494322i	0.972705	+	0.232044i	$0.0745413\pi$
$480$	1.79124	+	18.7811i	0.0817584	+	0.857237i
$481$	−1.82161	+	1.05171i	−0.0830582	+	0.0479537i
$482$	14.2462	+	30.4268i	0.648897	+	1.38590i
$483$		0			0
$484$	12.9654	−	15.5501i	0.589338	−	0.706824i
$485$	−17.3693	−	30.0845i	−0.788700	−	1.36607i
$486$	0.121053	−	1.40902i	0.00549108	−	0.0639146i
$487$	1.36621	+	0.788779i	0.0619087	+	0.0357430i	0.530635	−	0.847601i	$-0.321954\pi$
$487$	1.36621	+	0.788779i	0.0619087	+	0.0357430i	−0.468726	+	0.883344i	$0.655287\pi$
$488$	−3.57341	−	13.0901i	−0.161761	−	0.592563i
$489$			15.7392i			0.711753i
$490$		0			0
$491$			11.3524i			0.512326i	0.966634	+	0.256163i	$0.0824585\pi$
$491$			11.3524i			0.512326i	−0.966634	+	0.256163i	$0.917542\pi$
$492$	0.498832	−	2.88170i	0.0224891	−	0.129917i
$493$	9.02049	+	5.20798i	0.406263	+	0.234556i
$494$	18.7971	+	1.61491i	0.845722	+	0.0726584i
$495$	−1.56155	−	2.70469i	−0.0701866	−	0.121567i
$496$		0			0
$497$		0			0
$498$	−13.1231	+	6.14441i	−0.588060	+	0.275338i
$499$	−12.0086	+	6.93319i	−0.537580	+	0.310372i	−0.744098	−	0.668071i	$-0.767120\pi$
$499$	−12.0086	+	6.93319i	−0.537580	+	0.310372i	0.206517	+	0.978443i	$0.433787\pi$
$500$	−7.03157	+	2.58422i	−0.314462	+	0.115570i
$501$	7.12311	−	12.3376i	0.318237	−	0.551202i
$502$	6.67280	+	4.65681i	0.297822	+	0.207844i
$503$	26.7386			1.19222			0.596108	−	0.802904i	$-0.296713\pi$
$503$	26.7386			1.19222			0.596108	+	0.802904i	$0.296713\pi$
$504$		0			0
$505$	−45.8617			−2.04082
$506$	1.01695	+	0.709712i	0.0452092	+	0.0315505i
$507$	−4.74621	+	8.22068i	−0.210787	+	0.365093i
$508$	18.5661	−	6.82335i	0.823737	−	0.302737i
$509$	2.88831	−	1.66757i	0.128022	−	0.0739136i	−0.434621	−	0.900613i	$-0.643118\pi$
$509$	2.88831	−	1.66757i	0.128022	−	0.0739136i	0.562643	+	0.826700i	$0.309784\pi$
$510$	−22.2462	+	10.4160i	−0.985079	+	0.461227i
$511$		0			0
$512$	15.7732	−	16.2236i	0.697083	−	0.716990i
$513$	3.56155	+	6.16879i	0.157246	+	0.272359i
$514$	−3.21740	−	0.276416i	−0.141913	−	0.0121922i
$515$	23.1065	+	13.3405i	1.01819	+	0.587854i
$516$	3.09373	−	17.8721i	0.136194	−	0.786777i
$517$		−	5.84912i		−	0.257244i
$518$		0			0
$519$			16.6757i			0.731980i
$520$	−17.0433	+	4.65256i	−0.747399	+	0.204028i
$521$	25.7951	+	14.8928i	1.13010	+	0.652466i	0.943961	−	0.330057i	$-0.107068\pi$
$521$	25.7951	+	14.8928i	1.13010	+	0.652466i	0.186143	+	0.982523i	$0.440401\pi$
$522$	−0.242106	+	2.81805i	−0.0105967	+	0.123343i
$523$	16.2462	+	28.1393i	0.710397	+	1.23044i	0.964708	+	0.263322i	$0.0848180\pi$
$523$	16.2462	+	28.1393i	0.710397	+	1.23044i	−0.254311	+	0.967123i	$0.581849\pi$
$524$	−7.36932	+	8.83841i	−0.321930	+	0.386108i
$525$		0			0
$526$	14.8078	+	31.6261i	0.645649	+	1.37896i
$527$		0			0
$528$	−1.25906	+	3.52776i	−0.0547936	+	0.153526i
$529$	−11.0616	+	19.1592i	−0.480937	+	0.833007i
$530$	33.0559	−	47.3663i	1.43586	−	2.05746i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	2.73863			0.118623
$534$	1.18349	−	1.69584i	0.0512147	−	0.0733861i
$535$	15.8078	−	27.3799i	0.683429	−	1.18373i
$536$	−21.7807	+	21.9861i	−0.940784	+	0.949654i
$537$	−13.9861	+	8.07490i	−0.603547	+	0.348458i
$538$	−6.49242	−	13.8664i	−0.279908	−	0.597822i
$539$		0			0
$540$	−5.12311	−	4.27156i	−0.220463	−	0.183819i
$541$	−1.43845	−	2.49146i	−0.0618437	−	0.107116i	0.833446	−	0.552601i	$-0.186365\pi$
$541$	−1.43845	−	2.49146i	−0.0618437	−	0.107116i	−0.895290	+	0.445485i	$0.853031\pi$
$542$	3.44910	−	40.1465i	0.148151	−	1.72444i
$543$	−1.62194	−	0.936426i	−0.0696040	−	0.0401859i
$544$	26.7971	+	12.2415i	1.14892	+	0.524850i
$545$			27.5022i			1.17806i
$546$		0			0
$547$		−	16.7909i		−	0.717929i	−0.933351	−	0.358964i	$-0.883130\pi$
$547$		−	16.7909i		−	0.717929i	0.933351	−	0.358964i	$-0.116870\pi$
$548$	−0.485207	−	0.0839909i	−0.0207270	−	0.00358791i
$549$	4.15468	+	2.39871i	0.177317	+	0.102374i
$550$	−8.07911	−	0.694099i	−0.344494	−	0.0295965i
$551$	−7.12311	−	12.3376i	−0.303455	−	0.525599i
$552$	2.56155	+	0.673500i	0.109027	+	0.0286661i
$553$		0			0
$554$	6.56155	−	3.07221i	0.278774	−	0.130526i
$555$	−3.24388	+	1.87285i	−0.137695	+	0.0794982i
$556$	8.27899	+	22.5268i	0.351107	+	0.955351i
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	−0.975356	−	0.220638i	$-0.929186\pi$
$557$	−7.00000	+	12.1244i	−0.296600	+	0.513725i	0.678756	+	0.734364i	$0.262519\pi$
$558$		0			0
$559$	16.9848			0.718382
$560$		0			0
$561$	−4.87689			−0.205903
$562$	18.8411	+	13.1488i	0.794764	+	0.554649i
$563$	1.12311	−	1.94528i	0.0473333	−	0.0819836i	−0.841388	−	0.540431i	$-0.818261\pi$
$563$	1.12311	−	1.94528i	0.0473333	−	0.0819836i	0.888721	+	0.458448i	$0.151594\pi$
$564$	−4.30936	−	11.7256i	−0.181457	−	0.493737i
$565$	12.2644	−	7.08084i	0.515966	−	0.297893i
$566$	11.3693	−	5.32326i	0.477888	−	0.223753i
$567$		0			0
$568$	10.5616	+	2.77691i	0.443153	+	0.116517i
$569$	15.4924	+	26.8337i	0.649476	+	1.12493i	0.983248	+	0.182272i	$0.0583451\pi$
$569$	15.4924	+	26.8337i	0.649476	+	1.12493i	−0.333772	+	0.942654i	$0.608322\pi$
$570$	33.4735	+	2.87580i	1.40205	+	0.120454i
$571$	7.65429	+	4.41921i	0.320322	+	0.184938i	0.651536	−	0.758618i	$-0.274125\pi$
$571$	7.65429	+	4.41921i	0.320322	+	0.184938i	−0.331214	+	0.943556i	$0.607458\pi$
$572$	−3.45618	−	0.598276i	−0.144510	−	0.0250152i
$573$			2.80928i			0.117359i
$574$		0			0
$575$			5.73384i			0.239118i
$576$	0.0750734	+	7.99965i	0.00312806	+	0.333319i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	−1.22543	+	14.2637i	−0.0509713	+	0.593291i
$579$	7.68466	+	13.3102i	0.319364	+	0.553154i
$580$	10.2462	+	8.54312i	0.425451	+	0.354734i
$581$		0			0
$582$	−6.24621	−	13.3405i	−0.258914	−	0.552983i
$583$	9.93130	−	5.73384i	0.411312	−	0.237471i
$584$	−13.2778	+	13.4030i	−0.549439	+	0.554619i
$585$	3.12311	−	5.40938i	0.129125	−	0.223650i
$586$	11.1294	−	15.9475i	0.459752	−	0.658784i
$587$	21.7538			0.897875			0.448937	−	0.893563i	$-0.351803\pi$
$587$	21.7538			0.897875			0.448937	+	0.893563i	$0.351803\pi$
$588$		0			0
$589$		0			0
$590$	−10.7971	+	15.4713i	−0.444510	+	0.636944i
$591$	8.12311	−	14.0696i	0.334140	−	0.578747i
$592$	4.23103	+	1.51006i	0.173894	+	0.0620630i
$593$	22.5512	−	13.0200i	0.926068	−	0.534666i	0.0405023	−	0.999179i	$-0.487104\pi$
$593$	22.5512	−	13.0200i	0.926068	−	0.534666i	0.885566	+	0.464514i	$0.153771\pi$
$594$	−0.561553	−	1.19935i	−0.0230408	−	0.0492100i
$595$		0			0
$596$	−12.8078	+	15.3610i	−0.524626	+	0.629212i
$597$	−1.56155	−	2.70469i	−0.0639101	−	0.110696i
$598$	−0.212302	+	2.47113i	−0.00868166	+	0.101052i
$599$	14.8969	+	8.60076i	0.608673	+	0.351417i	0.772446	−	0.635081i	$-0.219033\pi$
$599$	14.8969	+	8.60076i	0.608673	+	0.351417i	−0.163773	+	0.986498i	$0.552366\pi$
$600$	−16.7074	+	4.56087i	−0.682078	+	0.186197i
$601$			17.0862i			0.696962i	0.937316	+	0.348481i	$0.113302\pi$
$601$			17.0862i			0.696962i	−0.937316	+	0.348481i	$0.886698\pi$
$602$		0			0
$603$		−	10.9418i		−	0.445585i
$604$	−3.09373	+	17.8721i	−0.125882	+	0.727207i
$605$	29.2387	+	16.8809i	1.18872	+	0.686308i
$606$	−19.3756	−	1.66461i	−0.787081	−	0.0676204i
$607$	3.80776	+	6.59524i	0.154552	+	0.267693i	0.932896	−	0.360146i	$-0.117273\pi$
$607$	3.80776	+	6.59524i	0.154552	+	0.267693i	−0.778344	+	0.627839i	$0.783940\pi$
$608$	−23.3693	−	32.8255i	−0.947751	−	1.33125i
$609$		0			0
$610$	20.4924	−	9.59482i	0.829714	−	0.388483i
$611$	10.1310	−	5.84912i	0.409855	−	0.236630i
$612$	−9.77662	+	3.59307i	−0.395196	+	0.145241i
$613$	−4.36932	+	7.56788i	−0.176475	+	0.305664i	−0.940671	−	0.339321i	$-0.889803\pi$
$613$	−4.36932	+	7.56788i	−0.176475	+	0.305664i	0.764196	+	0.644984i	$0.223136\pi$
$614$	−22.7486	−	15.8758i	−0.918058	−	0.640694i
$615$	4.87689			0.196655
$616$		0			0
$617$	32.2462			1.29818			0.649092	−	0.760710i	$-0.275149\pi$
$617$	32.2462			1.29818			0.649092	+	0.760710i	$0.275149\pi$
$618$	9.27779	+	6.47477i	0.373207	+	0.260454i
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$	−0.810969	+	0.468213i	−0.0325431	+	0.0187887i
$622$	10.2462	−	4.79741i	0.410836	−	0.192359i
$623$		0			0
$624$	−7.36932	+	1.34700i	−0.295009	+	0.0539232i
$625$	9.06155	+	15.6951i	0.362462	+	0.627803i
$626$	32.3164	+	2.77640i	1.29162	+	0.110967i
$627$	5.77662	+	3.33513i	0.230696	+	0.133192i
$628$	7.46524	−	43.1259i	0.297896	−	1.72091i
$629$			5.84912i			0.233220i
$630$		0			0
$631$		−	40.3169i		−	1.60499i	−0.596659	−	0.802495i	$-0.703506\pi$
$631$		−	40.3169i		−	1.60499i	0.596659	−	0.802495i	$-0.296494\pi$
$632$	−1.78670	−	6.54507i	−0.0710713	−	0.260349i
$633$	−11.0978	−	6.40734i	−0.441099	−	0.254669i
$634$	−1.75435	+	20.4202i	−0.0696743	+	0.810988i
$635$	16.4924	+	28.5657i	0.654482	+	1.13360i
$636$	15.6847	−	18.8114i	0.621937	−	0.745922i
$637$		0			0
$638$	1.12311	+	2.39871i	0.0444642	+	0.0949657i
$639$	−3.34371	+	1.93049i	−0.132275	+	0.0763691i
$640$	31.1439	+	21.3029i	1.23107	+	0.842071i
$641$	21.2462	−	36.7995i	0.839175	−	1.45349i	−0.0514106	−	0.998678i	$-0.516372\pi$
$641$	21.2462	−	36.7995i	0.839175	−	1.45349i	0.890585	−	0.454816i	$-0.150295\pi$
$642$	7.67224	−	10.9936i	0.302799	−	0.433885i
$643$	11.6155			0.458072			0.229036	−	0.973418i	$-0.426443\pi$
$643$	11.6155			0.458072			0.229036	+	0.973418i	$0.426443\pi$
$644$		0			0
$645$	30.2462			1.19094
$646$	30.0244	−	43.0223i	1.18129	−	1.69269i
$647$	−16.4924	+	28.5657i	−0.648384	+	1.12303i	0.335125	+	0.942174i	$0.391222\pi$
$647$	−16.4924	+	28.5657i	−0.648384	+	1.12303i	−0.983509	+	0.180860i	$0.942112\pi$
$648$	−2.00936	−	1.99059i	−0.0789352	−	0.0781979i
$649$	−3.24388	+	1.87285i	−0.127333	+	0.0735159i
$650$	−6.87689	−	14.6875i	−0.269734	−	0.576092i
$651$		0			0
$652$	24.1771	+	20.1584i	0.946848	+	0.789465i
$653$	−8.36932	−	14.4961i	−0.327517	−	0.567276i	0.654502	−	0.756060i	$-0.272878\pi$
$653$	−8.36932	−	14.4961i	−0.327517	−	0.567276i	−0.982018	+	0.188785i	$0.939545\pi$
$654$	−0.998230	+	11.6191i	−0.0390339	+	0.454343i
$655$	−16.6187	−	9.59482i	−0.649347	−	0.374901i
$656$	−3.78770	−	4.45707i	−0.147885	−	0.174020i
$657$		−	6.67026i		−	0.260232i
$658$		0			0
$659$			26.7963i			1.04384i	0.852995	+	0.521919i	$0.174783\pi$
$659$			26.7963i			1.04384i	−0.852995	+	0.521919i	$0.825217\pi$
$660$	−6.15468	−	1.06540i	−0.239571	−	0.0414705i
$661$	7.39856	+	4.27156i	0.287770	+	0.166144i	0.636936	−	0.770917i	$-0.280202\pi$
$661$	7.39856	+	4.27156i	0.287770	+	0.166144i	−0.349165	+	0.937061i	$0.613535\pi$
$662$	−24.8158	−	2.13200i	−0.964495	−	0.0828625i
$663$	−4.87689	−	8.44703i	−0.189403	−	0.328055i
$664$	−7.36932	+	28.0281i	−0.285985	+	1.08770i
$665$		0			0
$666$	−1.43845	+	0.673500i	−0.0557387	+	0.0260976i
$667$	1.62194	−	0.936426i	0.0628017	−	0.0362586i
$668$	−9.82869	−	26.7435i	−0.380283	−	1.03474i
$669$	13.5616	−	23.4893i	0.524320	−	0.908149i
$670$	−42.3211	−	29.5350i	−1.63501	−	1.14104i
$671$	4.49242			0.173428
$672$		0			0
$673$	−27.8617			−1.07399			−0.536996	−	0.843585i	$-0.680441\pi$
$673$	−27.8617			−1.07399			−0.536996	+	0.843585i	$0.680441\pi$
$674$	9.56332	+	6.67404i	0.368365	+	0.257075i
$675$	3.06155	−	5.30277i	0.117839	−	0.204104i
$676$	6.54897	+	17.8195i	0.251884	+	0.685366i
$677$	−7.95379	+	4.59212i	−0.305689	+	0.176490i	−0.644996	−	0.764186i	$-0.723141\pi$
$677$	−7.95379	+	4.59212i	−0.305689	+	0.176490i	0.339307	+	0.940676i	$0.389808\pi$
$678$	5.43845	−	2.54635i	0.208862	−	0.0977921i
$679$		0			0
$680$	−12.4924	+	47.5130i	−0.479063	+	1.82204i
$681$	−8.24621	−	14.2829i	−0.315996	−	0.547320i
$682$		0			0
$683$	−27.8725	−	16.0922i	−1.06651	−	0.615750i	−0.139284	−	0.990252i	$-0.544480\pi$
$683$	−27.8725	−	16.0922i	−1.06651	−	0.615750i	−0.927226	+	0.374503i	$0.877813\pi$
$684$	14.0374	+	2.42993i	0.536735	+	0.0929107i
$685$		−	0.821147i		−	0.0313744i
$686$		0			0
$687$		−	5.61856i		−	0.214361i
$688$	−23.4911	−	27.6425i	−0.895589	−	1.05386i
$689$	19.8626	+	11.4677i	0.756705	+	0.436884i
$690$	−0.378062	+	4.40053i	−0.0143926	+	0.167525i
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	0.957290	−	0.289130i	$-0.0933661\pi$
$691$	6.00000	+	10.3923i	0.228251	+	0.395342i	−0.729039	+	0.684472i	$0.760033\pi$
$692$	25.6155	+	21.3578i	0.973756	+	0.811901i
$693$		0			0
$694$	−12.0691	−	25.7770i	−0.458138	−	0.978481i
$695$	−34.6597	+	20.0108i	−1.31472	+	0.759053i
$696$	4.01872	+	3.98119i	0.152329	+	0.150907i
$697$	3.80776	−	6.59524i	0.144229	−	0.249813i
$698$	−17.7115	+	25.3790i	−0.670388	+	0.960608i
$699$	22.4924			0.850742
$700$		0			0
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	1.51579	−	2.17199i	0.0572097	−	0.0819765i
$703$	4.00000	−	6.92820i	0.150863	−	0.261302i
$704$	3.80642	+	6.45232i	0.143460	+	0.243181i
$705$	18.0410	−	10.4160i	0.679463	−	0.392288i
$706$	−17.3693	−	37.0970i	−0.653703	−	1.39616i
$707$		0			0
$708$	−5.12311	+	6.14441i	−0.192538	+	0.230921i
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	0.804178	−	0.594389i	$-0.202606\pi$
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	−0.916845	+	0.399244i	$0.869273\pi$
$710$	−1.55879	+	18.1438i	−0.0585003	+	0.680926i
$711$	2.07734	+	1.19935i	0.0779063	+	0.0449792i
$712$	−1.08920	−	3.98995i	−0.0408194	−	0.149530i
$713$		0			0
$714$		0			0
$715$		−	5.84912i		−	0.218745i
$716$	−5.50924	+	31.8263i	−0.205890	+	1.18940i
$717$	−13.9861	−	8.07490i	−0.522322	−	0.301563i
$718$	32.1540	+	2.76244i	1.19998	+	0.103093i
$719$	14.2462	+	24.6752i	0.531294	+	0.920228i	0.999333	+	0.0365204i	$0.0116274\pi$
$719$	14.2462	+	24.6752i	0.531294	+	0.920228i	−0.468039	+	0.883708i	$0.655039\pi$
$720$	−13.1231	+	2.39871i	−0.489069	+	0.0893945i
$721$		0			0
$722$	−40.6501	+	19.0329i	−1.51284	+	0.708332i
$723$	−20.5737	+	11.8782i	−0.765145	+	0.441757i
$724$	−3.51579	+	1.29211i	−0.130663	+	0.0480209i
$725$	−6.12311	+	10.6055i	−0.227406	+	0.393879i
$726$	11.7400	+	8.19310i	0.435712	+	0.304075i
$727$	−32.9848			−1.22334			−0.611670	−	0.791113i	$-0.709502\pi$
$727$	−32.9848			−1.22334			−0.611670	+	0.791113i	$0.709502\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−25.7994	−	18.0049i	−0.954880	−	0.666391i
$731$	23.6155	−	40.9033i	0.873452	−	1.51286i
$732$	9.00587	−	3.30981i	0.332867	−	0.122334i
$733$	−31.2162	+	18.0227i	−1.15300	+	0.665682i	−0.949615	−	0.313418i	$-0.898526\pi$
$733$	−31.2162	+	18.0227i	−1.15300	+	0.665682i	−0.203380	+	0.979100i	$0.565193\pi$
$734$	−42.7386	+	20.0108i	−1.57751	+	0.738612i
$735$		0			0
$736$	4.31534	−	3.07221i	0.159066	−	0.113243i
$737$	−5.12311	−	8.87348i	−0.188712	−	0.326859i
$738$	2.06039	+	0.177014i	0.0758438	+	0.00651596i
$739$	−31.6716	−	18.2856i	−1.16506	−	0.672646i	−0.212547	−	0.977151i	$-0.568176\pi$
$739$	−31.6716	−	18.2856i	−1.16506	−	0.672646i	−0.952511	+	0.304505i	$0.901509\pi$
$740$	−1.27779	+	7.38163i	−0.0469723	+	0.271354i
$741$			13.3405i			0.490077i
$742$		0			0
$743$		−	35.1089i		−	1.28802i	−0.765017	−	0.644010i	$-0.777269\pi$
$743$		−	35.1089i		−	1.28802i	0.765017	−	0.644010i	$-0.222731\pi$
$744$		0			0
$745$	−28.8831	−	16.6757i	−1.05819	−	0.610949i
$746$	−1.21053	+	14.0902i	−0.0443207	+	0.515880i
$747$	−5.12311	−	8.87348i	−0.187445	−	0.324664i
$748$	−6.24621	+	7.49141i	−0.228384	+	0.273913i
$749$		0			0
$750$	−2.24621	−	4.79741i	−0.0820200	−	0.175177i
$751$	24.9841	−	14.4246i	0.911684	−	0.526361i	0.0307116	−	0.999528i	$-0.490223\pi$
$751$	24.9841	−	14.4246i	0.911684	−	0.526361i	0.880973	+	0.473167i	$0.156889\pi$
$752$	−23.5311	−	8.39827i	−0.858090	−	0.306253i
$753$	−2.87689	+	4.98293i	−0.104840	+	0.181588i
$754$	−3.03157	+	4.34398i	−0.110403	+	0.158198i
$755$	−30.2462			−1.10077
$756$		0			0
$757$	−34.9848			−1.27155			−0.635773	−	0.771876i	$-0.719319\pi$
$757$	−34.9848			−1.27155			−0.635773	+	0.771876i	$0.719319\pi$
$758$	20.3174	−	29.1131i	0.737962	−	1.05744i
$759$	−0.438447	+	0.759413i	−0.0159146	+	0.0275649i
$760$	47.2895	−	47.7354i	1.71537	−	1.73155i
$761$	25.7951	−	14.8928i	0.935072	−	0.539864i	0.0466599	−	0.998911i	$-0.485142\pi$
$761$	25.7951	−	14.8928i	0.935072	−	0.539864i	0.888412	+	0.459047i	$0.151809\pi$
$762$	5.93087	+	12.6670i	0.214853	+	0.458878i
$763$		0			0
$764$	4.31534	+	3.59806i	0.156124	+	0.130173i
$765$	−8.68466	−	15.0423i	−0.313994	−	0.543854i
$766$	1.18073	−	13.7433i	0.0426614	−	0.496566i
$767$	−6.48775	−	3.74571i	−0.234259	−	0.135250i
$768$	12.3844	+	10.1304i	0.446885	+	0.365551i
$769$			32.5302i			1.17307i	0.809925	+	0.586534i	$0.199508\pi$
$769$			32.5302i			1.17307i	−0.809925	+	0.586534i	$0.800492\pi$
$770$		0			0
$771$		−	2.28343i		−	0.0822356i
$772$	30.2882	+	5.24299i	1.09010	+	0.188699i
$773$	2.88831	+	1.66757i	0.103885	+	0.0599782i	0.551042	−	0.834477i	$-0.314230\pi$
$773$	2.88831	+	1.66757i	0.103885	+	0.0599782i	−0.447157	+	0.894455i	$0.647564\pi$
$774$	12.7784	+	1.09783i	0.459310	+	0.0394606i
$775$		0			0
$776$	−28.4924	−	7.49141i	−1.02282	−	0.268926i
$777$		0			0
$778$	20.8078	−	9.74247i	0.745994	−	0.349284i
$779$	−9.02049	+	5.20798i	−0.323193	+	0.186595i
$780$	−4.30936	−	11.7256i	−0.154300	−	0.419844i
$781$	−1.80776	+	3.13114i	−0.0646869	+	0.112041i
$782$	5.65585	+	3.94710i	0.202253	+	0.141148i
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	72.9848			2.60494
$786$	−6.67280	−	4.65681i	−0.238011	−	0.166103i
$787$	−22.4924	+	38.9580i	−0.801768	+	1.38870i	0.116683	+	0.993169i	$0.462774\pi$
$787$	−22.4924	+	38.9580i	−0.801768	+	1.38870i	−0.918451	+	0.395534i	$0.870559\pi$
$788$	−11.2085	−	30.4980i	−0.399287	−	1.08645i
$789$	−21.3847	+	12.3465i	−0.761315	+	0.439546i
$790$	10.2462	−	4.79741i	0.364544	−	0.170684i
$791$		0			0
$792$	−2.56155	−	0.673500i	−0.0910208	−	0.0239318i
$793$	4.49242	+	7.78110i	0.159531	+	0.276315i
$794$	−25.5568	−	2.19566i	−0.906976	−	0.0779209i
$795$	35.3708	+	20.4214i	1.25447	+	0.724271i
$796$	−6.15468	−	1.06540i	−0.218147	−	0.0377620i
$797$		−	39.6110i		−	1.40309i	−0.712623	−	0.701547i	$-0.752493\pi$
$797$		−	39.6110i		−	1.40309i	0.712623	−	0.701547i	$-0.247507\pi$
$798$		0			0
$799$		−	32.5302i		−	1.15083i
$800$	−14.3925	+	31.5058i	−0.508852	+	1.11390i
$801$	1.26637	+	0.731140i	0.0447450	+	0.0258335i
$802$	0.998230	−	11.6191i	0.0352487	−	0.410285i
$803$	−3.12311	−	5.40938i	−0.110212	−	0.190893i
$804$	−16.8078	−	14.0140i	−0.592764	−	0.494237i
$805$		0			0
$806$		0			0
$807$	9.37606	−	5.41327i	0.330053	−	0.190556i
$808$	−27.3729	+	27.6309i	−0.962974	+	0.972053i
$809$	−11.2462	+	19.4790i	−0.395396	+	0.684845i	−0.993152	−	0.116833i	$-0.962726\pi$
$809$	−11.2462	+	19.4790i	−0.395396	+	0.684845i	0.597756	+	0.801678i	$0.296059\pi$
$810$	2.69928	−	3.86783i	0.0948430	−	0.135902i
$811$	−0.492423			−0.0172913			−0.00864565	−	0.999963i	$-0.502752\pi$
$811$	−0.492423			−0.0172913			−0.00864565	+	0.999963i	$0.502752\pi$
$812$		0			0
$813$	28.4924			0.999273
$814$	−0.851195	+	1.21969i	−0.0298344	+	0.0427500i
$815$	−26.2462	+	45.4598i	−0.919365	+	1.59239i
$816$	−7.00234	+	19.6198i	−0.245131	+	0.686831i
$817$	−55.9446	+	32.2996i	−1.95725	+	1.13002i
$818$	−0.492423	−	1.05171i	−0.0172171	−	0.0367720i
$819$		0			0
$820$	6.24621	−	7.49141i	0.218127	−	0.261611i
$821$	28.6155	+	49.5635i	0.998689	+	1.72978i	0.543678	+	0.839294i	$0.317031\pi$
$821$	28.6155	+	49.5635i	0.998689	+	1.72978i	0.455011	+	0.890486i	$0.349635\pi$
$822$	0.0298047	−	0.346917i	0.00103956	−	0.0121001i
$823$	−11.2975	−	6.52262i	−0.393806	−	0.227364i	0.290002	−	0.957026i	$-0.406344\pi$
$823$	−11.2975	−	6.52262i	−0.393806	−	0.227364i	−0.683808	+	0.729662i	$0.739677\pi$
$824$	21.8287	−	5.95890i	0.760438	−	0.207588i
$825$		−	5.73384i		−	0.199627i
$826$		0			0
$827$			55.9408i			1.94525i	0.232373	+	0.972627i	$0.425351\pi$
$827$			55.9408i			1.94525i	−0.232373	+	0.972627i	$0.574649\pi$
$828$	−0.319446	+	1.84541i	−0.0111015	+	0.0641324i
$829$	18.2407	+	10.5312i	0.633524	+	0.365765i	0.782116	−	0.623133i	$-0.214141\pi$
$829$	18.2407	+	10.5312i	0.633524	+	0.365765i	−0.148591	+	0.988899i	$0.547474\pi$
$830$	−48.1498	−	4.13669i	−1.67130	−	0.143586i
$831$	2.56155	+	4.43674i	0.0888593	+	0.153909i
$832$	−7.36932	+	13.0452i	−0.255485	+	0.452262i
$833$		0			0
$834$	−15.3693	+	7.19612i	−0.532196	+	0.249181i
$835$	41.1475	−	23.7565i	1.42397	−	0.822128i
$836$	12.5217	−	4.60192i	0.433071	−	0.159161i
$837$		0			0
$838$	19.1266	+	13.3481i	0.660719	+	0.461102i
$839$	42.7386			1.47550			0.737751	−	0.675073i	$-0.235888\pi$
$839$	42.7386			1.47550			0.737751	+	0.675073i	$0.235888\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	12.6142	+	8.80318i	0.434714	+	0.303378i
$843$	−8.12311	+	14.0696i	−0.279775	+	0.484584i
$844$	−24.0562	+	8.84105i	−0.828048	+	0.304321i
$845$	−27.4170	+	15.8292i	−0.943175	+	0.544542i
$846$	8.00000	−	3.74571i	0.275046	−	0.128780i
$847$		0			0
$848$	−8.80776	−	48.1865i	−0.302460	−	1.65473i
$849$	4.43845	+	7.68762i	0.152327	+	0.263838i
$850$	−44.9324	−	3.86027i	−1.54117	−	0.132406i
$851$	0.910804	+	0.525853i	0.0312220	+	0.0180260i
$852$	−1.31711	+	7.60881i	−0.0451235	+	0.260674i
$853$		−	50.2070i		−	1.71905i	−0.511090	−	0.859527i	$-0.670758\pi$
$853$		−	50.2070i		−	1.71905i	0.511090	−	0.859527i	$-0.329242\pi$
$854$		0			0
$855$			23.7565i			0.812455i
$856$	−7.06095	−	25.8657i	−0.241338	−	0.884073i
$857$	−48.9016	−	28.2333i	−1.67045	−	0.964433i	−0.967388	−	0.253301i	$-0.918484\pi$
$857$	−48.9016	−	28.2333i	−1.67045	−	0.964433i	−0.703059	−	0.711132i	$-0.748183\pi$
$858$	0.212302	−	2.47113i	0.00724786	−	0.0843629i
$859$	−12.9309	−	22.3969i	−0.441196	−	0.764173i	0.556583	−	0.830792i	$-0.312112\pi$
$859$	−12.9309	−	22.3969i	−0.441196	−	0.764173i	−0.997778	+	0.0666189i	$0.978779\pi$
$860$	38.7386	−	46.4613i	1.32098	−	1.58432i
$861$		0			0
$862$	2.80776	+	5.99676i	0.0956328	+	0.204251i
$863$	7.49839	−	4.32920i	0.255248	−	0.147368i	−0.366917	−	0.930254i	$-0.619587\pi$
$863$	7.49839	−	4.32920i	0.255248	−	0.147368i	0.622165	+	0.782886i	$0.286253\pi$
$864$	−5.63130	+	0.537082i	−0.191581	+	0.0182719i
$865$	−27.8078	+	48.1645i	−0.945492	+	1.63764i
$866$	−10.7971	+	15.4713i	−0.366901	+	0.525737i
$867$	−10.1231			−0.343799
$868$		0			0
$869$	2.24621			0.0761975
$870$	−5.39856	+	7.73566i	−0.183028	+	0.262263i
$871$	10.2462	−	17.7470i	0.347180	−	0.601333i
$872$	16.5696	+	16.4149i	0.561118	+	0.555877i
$873$	9.02049	−	5.20798i	0.305297	−	0.176264i
$874$	−4.00000	−	8.54312i	−0.135302	−	0.288975i
$875$		0			0
$876$	−10.2462	−	8.54312i	−0.346187	−	0.288645i
$877$	−18.1231	−	31.3901i	−0.611974	−	1.05997i	−0.990907	−	0.134546i	$-0.957042\pi$
$877$	−18.1231	−	31.3901i	−0.611974	−	1.05997i	0.378934	−	0.925424i	$-0.376291\pi$
$878$	0.802665	−	9.34279i	0.0270886	−	0.315304i
$879$	11.9088	+	6.87555i	0.401674	+	0.231907i
$880$	−9.51933	+	8.08969i	−0.320896	+	0.272703i
$881$		−	46.8719i		−	1.57915i	−0.613652	−	0.789577i	$-0.710300\pi$
$881$		−	46.8719i		−	1.57915i	0.613652	−	0.789577i	$-0.289700\pi$
$882$		0			0
$883$			18.6638i			0.628087i	0.949409	+	0.314043i	$0.101684\pi$
$883$			18.6638i			0.628087i	−0.949409	+	0.314043i	$0.898316\pi$
$884$	−19.2217	−	3.32734i	−0.646496	−	0.111911i
$885$	−11.5532	−	6.67026i	−0.388358	−	0.224218i
$886$	26.5514	+	2.28110i	0.892010	+	0.0766352i
$887$	−13.3693	−	23.1563i	−0.448898	−	0.777514i	0.549417	−	0.835548i	$-0.314850\pi$
$887$	−13.3693	−	23.1563i	−0.448898	−	0.777514i	−0.998315	+	0.0580347i	$0.981517\pi$
$888$	−0.807764	+	3.07221i	−0.0271068	+	0.103096i
$889$		0			0
$890$	6.24621	−	2.92456i	0.209373	−	0.0980314i
$891$	0.810969	−	0.468213i	0.0271685	−	0.0156857i
$892$	−18.7127	−	50.9165i	−0.626546	−	1.70481i
$893$	−22.2462	+	38.5316i	−0.744441	+	1.28941i
$894$	−11.5972	−	8.09347i	−0.387869	−	0.270686i
$895$	−53.8617			−1.80040
$896$		0			0
$897$	−1.75379			−0.0585573
$898$	13.6311	+	9.51289i	0.454877	+	0.317449i
$899$		0			0
$900$	−4.22443	−	11.4945i	−0.140814	−	0.383151i
$901$	55.2334	−	31.8890i	1.84009	−	1.06238i
$902$	1.75379	−	0.821147i	0.0583948	−	0.0273412i
$903$		0			0
$904$	3.05398	−	11.6153i	0.101574	−	0.386320i
$905$	−3.12311	−	5.40938i	−0.103816	−	0.179814i
$906$	−12.7784	−	1.09783i	−0.424534	−	0.0364729i
$907$	33.2935	+	19.2220i	1.10549	+	0.638256i	0.937658	−	0.347559i	$-0.112989\pi$
$907$	33.2935	+	19.2220i	1.10549	+	0.638256i	0.167834	+	0.985815i	$0.446323\pi$
$908$	−32.5015	−	5.62612i	−1.07860	−	0.186709i
$909$		−	13.7511i		−	0.456095i
$910$		0			0
$911$			5.73384i			0.189971i	0.995479	+	0.0949853i	$0.0302804\pi$
$911$			5.73384i			0.189971i	−0.995479	+	0.0949853i	$0.969720\pi$
$912$	21.7115	−	18.4508i	0.718938	−	0.610966i
$913$	−8.30936	−	4.79741i	−0.275000	−	0.158771i
$914$	0.0298047	−	0.346917i	0.000985851	−	0.0114750i
$915$	8.00000	+	13.8564i	0.264472	+	0.458079i
$916$	−8.63068	−	7.19612i	−0.285166	−	0.237766i
$917$		0			0
$918$	−3.12311	−	6.67026i	−0.103078	−	0.220152i
$919$	−7.85396	+	4.53448i	−0.259078	+	0.149579i	−0.623914	−	0.781493i	$-0.714458\pi$
$919$	−7.85396	+	4.53448i	−0.259078	+	0.149579i	0.364836	+	0.931072i	$0.381125\pi$
$920$	6.27545	+	6.21683i	0.206895	+	0.204963i
$921$	9.80776	−	16.9875i	0.323177	−	0.559759i
$922$	−5.06626	+	7.25951i	−0.166848	+	0.239079i
$923$	−7.23106			−0.238013
$924$		0			0
$925$	−6.87689			−0.226111
$926$	−31.7791	+	45.5367i	−1.04433	+	1.49643i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	11.2626	−	1.07416i	0.369713	−	0.0352611i
$929$	3.08798	−	1.78285i	0.101313	−	0.0584933i	−0.448487	−	0.893789i	$-0.648037\pi$
$929$	3.08798	−	1.78285i	0.101313	−	0.0584933i	0.549801	+	0.835296i	$0.314704\pi$
$930$		0			0
$931$		0			0
$932$	28.8078	−	34.5507i	0.943630	−	1.13174i
$933$	4.00000	+	6.92820i	0.130954	+	0.226819i
$934$	−4.14561	+	48.2537i	−0.135649	+	1.57891i
$935$	−14.0860	−	8.13254i	−0.460661	−	0.265963i
$936$	−1.39502	−	5.11024i	−0.0455975	−	0.167033i
$937$		−	28.7845i		−	0.940348i	−0.882574	−	0.470174i	$-0.844191\pi$
$937$		−	28.7845i		−	0.940348i	0.882574	−	0.470174i	$-0.155809\pi$
$938$		0			0
$939$			22.9354i			0.748467i
$940$	7.10647	−	41.0533i	0.231788	−	1.33901i
$941$	−46.5685	−	26.8863i	−1.51809	−	0.876470i	−0.999774	−	0.0212809i	$-0.993226\pi$
$941$	−46.5685	−	26.8863i	−1.51809	−	0.876470i	−0.518317	−	0.855189i	$-0.673441\pi$
$942$	30.8346	+	2.64909i	1.00464	+	0.0863119i
$943$	−0.684658	−	1.18586i	−0.0222955	−	0.0386170i
$944$	2.87689	+	15.7392i	0.0936349	+	0.512268i
$945$		0			0
$946$	10.8769	−	5.09271i	0.353638	−	0.165578i
$947$	−42.1581	+	24.3400i	−1.36995	+	0.790943i	−0.990922	−	0.134440i	$-0.957076\pi$
$947$	−42.1581	+	24.3400i	−1.36995	+	0.790943i	−0.379032	+	0.925383i	$0.623743\pi$
$948$	4.50294	−	1.65491i	0.146249	−	0.0537488i
$949$	6.24621	−	10.8188i	0.202761	−	0.351192i
$950$	50.5819	+	35.3001i	1.64109	+	1.14529i
$951$	−14.4924			−0.469949
$952$		0			0
$953$	−21.2311			−0.687741			−0.343871	−	0.939017i	$-0.611738\pi$
$953$	−21.2311			−0.687741			−0.343871	+	0.939017i	$0.611738\pi$
$954$	14.2022	+	9.91143i	0.459814	+	0.320894i
$955$	−4.68466	+	8.11407i	−0.151592	+	0.262565i
$956$	−30.3170	+	11.1420i	−0.980522	+	0.360358i
$957$	−1.62194	+	0.936426i	−0.0524298	+	0.0302704i
$958$	16.0000	−	7.49141i	0.516937	−	0.242037i
$959$		0			0
$960$	−13.1231	+	23.2306i	−0.423546	+	0.749766i
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−2.96376	−	0.254625i	−0.0955553	−	0.00820943i
$963$	8.20953	+	4.73977i	0.264548	+	0.152737i
$964$	−8.10414	+	46.8167i	−0.261017	+	1.50787i
$965$			51.2587i			1.65008i
$966$		0			0
$967$			8.83841i			0.284224i	0.989851	+	0.142112i	$0.0453893\pi$
$967$			8.83841i			0.284224i	−0.989851	+	0.142112i	$0.954611\pi$
$968$	27.6218	−	7.54032i	0.887797	−	0.242355i
$969$	32.1270	+	18.5485i	1.03207	+	0.595864i
$970$	4.20522	−	48.9475i	0.135022	−	1.57161i
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	0.753545	−	0.657396i	$-0.228342\pi$
$971$	−6.00000	−	10.3923i	−0.192549	−	0.333505i	−0.946094	+	0.323891i	$0.895009\pi$
$972$	1.28078	−	1.53610i	0.0410809	−	0.0492705i
$973$		0			0
$974$	0.946025	+	2.02050i	0.0303126	+	0.0647410i
$975$	9.93130	−	5.73384i	0.318056	−	0.183630i
$976$	6.45030	−	18.0731i	0.206469	−	0.578505i
$977$	5.63068	−	9.75263i	0.180142	−	0.312014i	−0.761787	−	0.647827i	$-0.775678\pi$
$977$	5.63068	−	9.75263i	0.180142	−	0.312014i	0.941929	+	0.335813i	$0.109011\pi$
$978$	−12.7385	+	18.2532i	−0.407332	+	0.583672i
$979$	1.36932			0.0437636
$980$		0			0
$981$	−8.24621			−0.263281
$982$	−9.18802	+	13.1656i	−0.293202	+	0.420132i
$983$	2.63068	−	4.55648i	0.0839058	−	0.145329i	−0.821019	−	0.570901i	$-0.806594\pi$
$983$	2.63068	−	4.55648i	0.0839058	−	0.145329i	0.904924	+	0.425572i	$0.139927\pi$
$984$	2.91080	−	2.93825i	0.0927930	−	0.0936679i
$985$	46.9241	−	27.0916i	1.49513	−	0.863211i
$986$	6.24621	+	13.3405i	0.198920	+	0.424849i
$987$		0			0
$988$	20.4924	+	17.0862i	0.651951	+	0.543586i
$989$	−4.24621	−	7.35465i	−0.135022	−	0.233864i
$990$	0.378062	−	4.40053i	0.0120156	−	0.139858i
$991$	−0.455402	−	0.262926i	−0.0144663	−	0.00835213i	0.492749	−	0.870171i	$-0.335992\pi$
$991$	−0.455402	−	0.262926i	−0.0144663	−	0.00835213i	−0.507216	+	0.861819i	$0.669325\pi$
$992$		0			0
$993$		−	17.6121i		−	0.558903i
$994$		0			0
$995$		−	10.4160i		−	0.330208i
$996$	−20.1921	−	3.49533i	−0.639812	−	0.110754i
$997$	−17.1302	−	9.89012i	−0.542518	−	0.313223i	0.203581	−	0.979058i	$-0.434742\pi$
$997$	−17.1302	−	9.89012i	−0.542518	−	0.313223i	−0.746099	+	0.665835i	$0.768075\pi$
$998$	−19.5381	−	1.67857i	−0.618466	−	0.0531342i
$999$	−0.561553	−	0.972638i	−0.0177667	−	0.0307729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.a.31.4		8
4.3	odd	2		588.2.o.c.31.2		8
7.2	even	3	inner	588.2.o.a.19.2		8
7.3	odd	6		84.2.b.a.55.2	yes	4
7.4	even	3		84.2.b.b.55.2	yes	4
7.5	odd	6		588.2.o.c.19.2		8
7.6	odd	2		588.2.o.c.31.4		8
21.11	odd	6		252.2.b.d.55.3		4
21.17	even	6		252.2.b.e.55.3		4
28.3	even	6		84.2.b.b.55.1	yes	4
28.11	odd	6		84.2.b.a.55.1	✓	4
28.19	even	6	inner	588.2.o.a.19.4		8
28.23	odd	6		588.2.o.c.19.4		8
28.27	even	2	inner	588.2.o.a.31.2		8
56.3	even	6		1344.2.b.e.895.1		4
56.11	odd	6		1344.2.b.f.895.4		4
56.45	odd	6		1344.2.b.f.895.1		4
56.53	even	6		1344.2.b.e.895.4		4
84.11	even	6		252.2.b.e.55.4		4
84.59	odd	6		252.2.b.d.55.4		4
168.11	even	6		4032.2.b.n.3583.1		4
168.53	odd	6		4032.2.b.j.3583.1		4
168.59	odd	6		4032.2.b.j.3583.4		4
168.101	even	6		4032.2.b.n.3583.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.b.a.55.1	✓	4	28.11	odd	6
84.2.b.a.55.2	yes	4	7.3	odd	6
84.2.b.b.55.1	yes	4	28.3	even	6
84.2.b.b.55.2	yes	4	7.4	even	3
252.2.b.d.55.3		4	21.11	odd	6
252.2.b.d.55.4		4	84.59	odd	6
252.2.b.e.55.3		4	21.17	even	6
252.2.b.e.55.4		4	84.11	even	6
588.2.o.a.19.2		8	7.2	even	3	inner
588.2.o.a.19.4		8	28.19	even	6	inner
588.2.o.a.31.2		8	28.27	even	2	inner
588.2.o.a.31.4		8	1.1	even	1	trivial
588.2.o.c.19.2		8	7.5	odd	6
588.2.o.c.19.4		8	28.23	odd	6
588.2.o.c.31.2		8	4.3	odd	2
588.2.o.c.31.4		8	7.6	odd	2
1344.2.b.e.895.1		4	56.3	even	6
1344.2.b.e.895.4		4	56.53	even	6
1344.2.b.f.895.1		4	56.45	odd	6
1344.2.b.f.895.4		4	56.11	odd	6
4032.2.b.j.3583.1		4	168.53	odd	6
4032.2.b.j.3583.4		4	168.59	odd	6
4032.2.b.n.3583.1		4	168.11	even	6
4032.2.b.n.3583.4		4	168.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.15972 + 0.809347i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.689916 + 1.87724i) q^{4} +(-2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.15972 + 0.809347i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.689916 + 1.87724i) q^{4} +(-2.88831 + 1.66757i) q^{5} +(-1.28078 + 0.599676i) q^{6} +(-0.719224 + 2.73546i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.69928 - 0.403728i) q^{10} +(-0.810969 - 0.468213i) q^{11} +(-1.97069 - 0.341134i) q^{12} -1.87285i q^{13} -3.33513i q^{15} +(-3.04803 + 2.59027i) q^{16} +(-4.51025 - 2.60399i) q^{17} +(0.121053 - 1.40902i) q^{18} +(3.56155 + 6.16879i) q^{19} +(-5.12311 - 4.27156i) q^{20} +(-0.561553 - 1.19935i) q^{22} +(-0.810969 + 0.468213i) q^{23} +(-2.00936 - 1.99059i) q^{24} +(3.06155 - 5.30277i) q^{25} +(1.51579 - 2.17199i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(2.69928 - 3.86783i) q^{30} +(-5.63130 + 0.537082i) q^{32} +(0.810969 - 0.468213i) q^{33} +(-3.12311 - 6.67026i) q^{34} +(1.28078 - 1.53610i) q^{36} +(-0.561553 - 0.972638i) q^{37} +(-0.862275 + 10.0366i) q^{38} +(1.62194 + 0.936426i) q^{39} +(-2.48421 - 9.10019i) q^{40} +1.46228i q^{41} +9.06897i q^{43} +(0.319446 - 1.84541i) q^{44} +(2.88831 + 1.66757i) q^{45} +(-1.31945 - 0.113357i) q^{46} +(3.12311 + 5.40938i) q^{47} +(-0.719224 - 3.93481i) q^{48} +(7.84233 - 3.67188i) q^{50} +(4.51025 - 2.60399i) q^{51} +(3.51579 - 1.29211i) q^{52} +(-6.12311 + 10.6055i) q^{53} +(1.15972 + 0.809347i) q^{54} +3.12311 q^{55} -7.12311 q^{57} +(-2.31945 - 1.61869i) q^{58} +(2.00000 - 3.46410i) q^{59} +(6.26083 - 2.30096i) q^{60} +(-4.15468 + 2.39871i) q^{61} +(-6.96543 - 3.93481i) q^{64} +(3.12311 + 5.40938i) q^{65} +(1.31945 + 0.113357i) q^{66} +(9.47590 + 5.47091i) q^{67} +(1.77662 - 10.2633i) q^{68} -0.936426i q^{69} -3.86098i q^{71} +(2.72859 - 0.744862i) q^{72} +(5.77662 + 3.33513i) q^{73} +(0.135956 - 1.58248i) q^{74} +(3.06155 + 5.30277i) q^{75} +(-9.12311 + 10.9418i) q^{76} +(1.12311 + 2.39871i) q^{78} +(-2.07734 + 1.19935i) q^{79} +(4.48421 - 12.5643i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.18349 + 1.69584i) q^{82} +10.2462 q^{83} +17.3693 q^{85} +(-7.33994 + 10.5175i) q^{86} +(1.00000 - 1.73205i) q^{87} +(1.86404 - 1.88162i) q^{88} +(-1.26637 + 0.731140i) q^{89} +(2.00000 + 4.27156i) q^{90} +(-1.43845 - 1.19935i) q^{92} +(-0.756124 + 8.80106i) q^{94} +(-20.5737 - 11.8782i) q^{95} +(2.35052 - 5.14539i) q^{96} +10.4160i q^{97} +0.936426i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9	\( 8 q + q^{2} - 4 q^{3} - q^{4} - 2 q^{6} - 14 q^{8} - 4 q^{9} - 8 q^{10} - q^{12} + 7 q^{16} + q^{18} + 12 q^{19} - 8 q^{20} + 12 q^{22} + 7 q^{24} + 8 q^{25} + 12 q^{26} + 8 q^{27} - 16 q^{29} - 8 q^{30} - 9 q^{32} + 8 q^{34} + 2 q^{36} + 12 q^{37} - 20 q^{38} - 20 q^{40} - 14 q^{44} + 6 q^{46} - 8 q^{47} - 14 q^{48} + 38 q^{50} + 28 q^{52} - 16 q^{53} + q^{54} - 8 q^{55} - 24 q^{57} - 2 q^{58} + 16 q^{59} + 4 q^{60} + 2 q^{64} - 8 q^{65} - 6 q^{66} - 32 q^{68} + 7 q^{72} + 14 q^{74} + 8 q^{75} - 40 q^{76} - 24 q^{78} + 36 q^{80} - 4 q^{81} + 20 q^{82} + 16 q^{83} + 40 q^{85} + 30 q^{86} + 8 q^{87} + 2 q^{88} + 16 q^{90} - 28 q^{92} - 32 q^{94} - 9 q^{96}+O(q^{100}) \) 8 * q + q^2 - 4 * q^3 - q^4 - 2 * q^6 - 14 * q^8 - 4 * q^9 - 8 * q^10 - q^12 + 7 * q^16 + q^18 + 12 * q^19 - 8 * q^20 + 12 * q^22 + 7 * q^24 + 8 * q^25 + 12 * q^26 + 8 * q^27 - 16 * q^29 - 8 * q^30 - 9 * q^32 + 8 * q^34 + 2 * q^36 + 12 * q^37 - 20 * q^38 - 20 * q^40 - 14 * q^44 + 6 * q^46 - 8 * q^47 - 14 * q^48 + 38 * q^50 + 28 * q^52 - 16 * q^53 + q^54 - 8 * q^55 - 24 * q^57 - 2 * q^58 + 16 * q^59 + 4 * q^60 + 2 * q^64 - 8 * q^65 - 6 * q^66 - 32 * q^68 + 7 * q^72 + 14 * q^74 + 8 * q^75 - 40 * q^76 - 24 * q^78 + 36 * q^80 - 4 * q^81 + 20 * q^82 + 16 * q^83 + 40 * q^85 + 30 * q^86 + 8 * q^87 + 2 * q^88 + 16 * q^90 - 28 * q^92 - 32 * q^94 - 9 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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