LMFDB - Embedded newform 588.2.o.e.31.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [24,-4,-12,4,0,8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	588.31
Dual form			588.2.o.e.19.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22355 - 0.709180i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.994127 + 1.73543i) q^{4} +(-3.15890 + 1.82379i) q^{5} +(1.22594 - 0.705031i) q^{6} +(0.0143727 - 2.82839i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.15845 + 0.00873760i) q^{10} +(-5.25694 - 3.03510i) q^{11} +(-1.99999 - 0.00677535i) q^{12} +0.483253i q^{13} -3.64758i q^{15} +(-2.02342 + 3.45047i) q^{16} +(2.21053 + 1.27625i) q^{17} +(-0.00239545 + 1.41421i) q^{18} +(0.609546 + 1.05577i) q^{19} +(-6.30540 - 3.66896i) q^{20} +(4.27968 + 7.44170i) q^{22} +(3.00269 - 1.73360i) q^{23} +(2.44227 + 1.42664i) q^{24} +(4.15242 - 7.19220i) q^{25} +(0.342713 - 0.591282i) q^{26} +1.00000 q^{27} +8.21857 q^{29} +(-2.58679 + 4.46298i) q^{30} +(3.15625 - 5.46678i) q^{31} +(4.92276 - 2.78684i) q^{32} +(5.25694 - 3.03510i) q^{33} +(-1.79959 - 3.12921i) q^{34} +(1.00586 - 1.72865i) q^{36} +(-0.595080 - 1.03071i) q^{37} +(0.00292028 - 1.72405i) q^{38} +(-0.418509 - 0.241626i) q^{39} +(5.11299 + 8.96081i) q^{40} +6.59422i q^{41} -3.51184i q^{43} +(0.0411277 - 12.1403i) q^{44} +(3.15890 + 1.82379i) q^{45} +(-4.90336 - 0.00830552i) q^{46} +(-5.83110 - 10.0998i) q^{47} +(-1.97648 - 3.47757i) q^{48} +(-10.1812 + 5.85517i) q^{50} +(-2.21053 + 1.27625i) q^{51} +(-0.838651 + 0.480414i) q^{52} +(-1.31391 + 2.27576i) q^{53} +(-1.22355 - 0.709180i) q^{54} +22.1415 q^{55} -1.21909 q^{57} +(-10.0558 - 5.82845i) q^{58} +(-0.580801 + 1.00598i) q^{59} +(6.33011 - 3.62616i) q^{60} +(0.180530 - 0.104229i) q^{61} +(-7.73874 + 4.45050i) q^{62} +(-7.99959 - 0.0813030i) q^{64} +(-0.881351 - 1.52655i) q^{65} +(-8.58454 - 0.0145409i) q^{66} +(-1.53820 - 0.888083i) q^{67} +(-0.0172941 + 5.10497i) q^{68} +3.46720i q^{69} -9.13166i q^{71} +(-2.45664 + 1.40175i) q^{72} +(-5.23883 - 3.02464i) q^{73} +(-0.00285097 + 1.68314i) q^{74} +(4.15242 + 7.19220i) q^{75} +(-1.22624 + 2.10739i) q^{76} +(0.340708 + 0.592439i) q^{78} +(2.75342 - 1.58969i) q^{79} +(0.0988539 - 14.5900i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.67649 - 8.06832i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(-2.49052 + 4.29689i) q^{86} +(-4.10928 + 7.11749i) q^{87} +(-8.66000 + 14.8251i) q^{88} +(10.6411 - 6.14362i) q^{89} +(-2.57166 - 4.47172i) q^{90} +(5.99359 + 3.48753i) q^{92} +(3.15625 + 5.46678i) q^{93} +(-0.0279362 + 16.4928i) q^{94} +(-3.85099 - 2.22337i) q^{95} +(-0.0479085 + 5.65665i) q^{96} -11.8376i q^{97} +6.07019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

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 $

$2$	−1.22355	−	0.709180i	−0.865177	−	0.501466i
$2$	−1.22355	−	0.709180i	−0.865177	−	0.501466i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.994127	+	1.73543i	0.497063	+	0.867714i
$5$	−3.15890	+	1.82379i	−1.41270	+	0.815624i	−0.995642	−	0.0932558i	$-0.970273\pi$
$5$	−3.15890	+	1.82379i	−1.41270	+	0.815624i	−0.417059	+	0.908879i	$0.636939\pi$
$6$	1.22594	−	0.705031i	0.500488	−	0.287828i
$7$		0			0
$7$		0			0
$8$	0.0143727	−	2.82839i	0.00508150	−	0.999987i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	5.15845	+	0.00873760i	1.63124	+	0.00276307i
$11$	−5.25694	−	3.03510i	−1.58503	−	0.915116i	−0.994109	−	0.108385i	$-0.965432\pi$
$11$	−5.25694	−	3.03510i	−1.58503	−	0.915116i	−0.590919	−	0.806731i	$-0.701235\pi$
$12$	−1.99999	−	0.00677535i	−0.577347	−	0.00195588i
$13$			0.483253i			0.134030i	0.997752	+	0.0670151i	$0.0213476\pi$
$13$			0.483253i			0.134030i	−0.997752	+	0.0670151i	$0.978652\pi$
$14$		0			0
$15$		−	3.64758i		−	0.941801i
$16$	−2.02342	+	3.45047i	−0.505856	+	0.862618i
$17$	2.21053	+	1.27625i	0.536132	+	0.309536i	0.743510	−	0.668725i	$-0.233160\pi$
$17$	2.21053	+	1.27625i	0.536132	+	0.309536i	−0.207378	+	0.978261i	$0.566493\pi$
$18$	−0.00239545	+	1.41421i	−0.000564613	+	0.333333i
$19$	0.609546	+	1.05577i	0.139840	+	0.242209i	0.927436	−	0.373983i	$-0.122008\pi$
$19$	0.609546	+	1.05577i	0.139840	+	0.242209i	−0.787596	+	0.616192i	$0.788675\pi$
$20$	−6.30540	−	3.66896i	−1.40993	−	0.820405i
$21$		0			0
$22$	4.27968	+	7.44170i	0.912430	+	1.58658i
$23$	3.00269	−	1.73360i	0.626103	−	0.361481i	−0.153138	−	0.988205i	$-0.548938\pi$
$23$	3.00269	−	1.73360i	0.626103	−	0.361481i	0.779241	+	0.626724i	$0.215605\pi$
$24$	2.44227	+	1.42664i	0.498527	+	0.291212i
$25$	4.15242	−	7.19220i	0.830483	−	1.43844i
$26$	0.342713	−	0.591282i	0.0672116	−	0.115960i
$27$	1.00000			0.192450
$28$		0			0
$29$	8.21857			1.52615			0.763075	−	0.646310i	$-0.223689\pi$
$29$	8.21857			1.52615			0.763075	+	0.646310i	$0.223689\pi$
$30$	−2.58679	+	4.46298i	−0.472281	+	0.814825i
$31$	3.15625	−	5.46678i	0.566878	−	0.981862i	−0.429994	−	0.902832i	$-0.641484\pi$
$31$	3.15625	−	5.46678i	0.566878	−	0.981862i	0.996872	−	0.0790304i	$-0.0251824\pi$
$32$	4.92276	−	2.78684i	0.870229	−	0.492648i
$33$	5.25694	−	3.03510i	0.915116	−	0.528343i
$34$	−1.79959	−	3.12921i	−0.308627	−	0.536655i
$35$		0			0
$36$	1.00586	−	1.72865i	0.167644	−	0.288109i
$37$	−0.595080	−	1.03071i	−0.0978305	−	0.169447i	0.812956	−	0.582325i	$-0.197857\pi$
$37$	−0.595080	−	1.03071i	−0.0978305	−	0.169447i	−0.910786	+	0.412878i	$0.864524\pi$
$38$	0.00292028	−	1.72405i	0.000473731	−	0.279679i
$39$	−0.418509	−	0.241626i	−0.0670151	−	0.0386912i
$40$	5.11299	+	8.96081i	0.808434	+	1.41683i
$41$			6.59422i			1.02984i	0.857237	+	0.514922i	$0.172179\pi$
$41$			6.59422i			1.02984i	−0.857237	+	0.514922i	$0.827821\pi$
$42$		0			0
$43$		−	3.51184i		−	0.535550i	−0.963481	−	0.267775i	$-0.913712\pi$
$43$		−	3.51184i		−	0.535550i	0.963481	−	0.267775i	$-0.0862884\pi$
$44$	0.0411277	−	12.1403i	0.00620023	−	1.83022i
$45$	3.15890	+	1.82379i	0.470900	+	0.271875i
$46$	−4.90336	−	0.00830552i	−0.722961	−	0.00122458i
$47$	−5.83110	−	10.0998i	−0.850553	−	1.47320i	−0.880710	−	0.473656i	$-0.842934\pi$
$47$	−5.83110	−	10.0998i	−0.850553	−	1.47320i	0.0301567	−	0.999545i	$-0.490399\pi$
$48$	−1.97648	−	3.47757i	−0.285281	−	0.501944i
$49$		0			0
$50$	−10.1812	+	5.85517i	−1.43984	+	0.828046i
$51$	−2.21053	+	1.27625i	−0.309536	+	0.178711i
$52$	−0.838651	+	0.480414i	−0.116300	+	0.0666215i
$53$	−1.31391	+	2.27576i	−0.180479	+	0.312600i	−0.942044	−	0.335490i	$-0.891098\pi$
$53$	−1.31391	+	2.27576i	−0.180479	+	0.312600i	0.761564	+	0.648089i	$0.224432\pi$
$54$	−1.22355	−	0.709180i	−0.166503	−	0.0965072i
$55$	22.1415			2.98556
$56$		0			0
$57$	−1.21909			−0.161473
$58$	−10.0558	−	5.82845i	−1.32039	−	0.765313i
$59$	−0.580801	+	1.00598i	−0.0756138	+	0.130967i	−0.901353	−	0.433085i	$-0.857425\pi$
$59$	−0.580801	+	1.00598i	−0.0756138	+	0.130967i	0.825739	+	0.564052i	$0.190758\pi$
$60$	6.33011	−	3.62616i	0.817214	−	0.468135i
$61$	0.180530	−	0.104229i	0.0231145	−	0.0133451i	−0.488398	−	0.872621i	$-0.662419\pi$
$61$	0.180530	−	0.104229i	0.0231145	−	0.0133451i	0.511513	+	0.859276i	$0.329085\pi$
$62$	−7.73874	+	4.45050i	−0.982821	+	0.565215i
$63$		0			0
$64$	−7.99959	−	0.0813030i	−0.999948	−	0.0101629i
$65$	−0.881351	−	1.52655i	−0.109318	−	0.189345i
$66$	−8.58454	−	0.0145409i	−1.05668	−	0.00178986i
$67$	−1.53820	−	0.888083i	−0.187922	−	0.108497i	0.403088	−	0.915161i	$-0.367937\pi$
$67$	−1.53820	−	0.888083i	−0.187922	−	0.108497i	−0.591009	+	0.806665i	$0.701270\pi$
$68$	−0.0172941	+	5.10497i	−0.00209721	+	0.619068i
$69$			3.46720i			0.417402i
$70$		0			0
$71$		−	9.13166i		−	1.08373i	−0.840466	−	0.541864i	$-0.817719\pi$
$71$		−	9.13166i		−	1.08373i	0.840466	−	0.541864i	$-0.182281\pi$
$72$	−2.45664	+	1.40175i	−0.289518	+	0.165198i
$73$	−5.23883	−	3.02464i	−0.613159	−	0.354007i	0.161042	−	0.986948i	$-0.448515\pi$
$73$	−5.23883	−	3.02464i	−0.613159	−	0.354007i	−0.774201	+	0.632940i	$0.781848\pi$
$74$	−0.00285097	+	1.68314i	−0.000331418	+	0.195661i
$75$	4.15242	+	7.19220i	0.479480	+	0.830483i
$76$	−1.22624	+	2.10739i	−0.140659	+	0.241734i
$77$		0			0
$78$	0.340708	+	0.592439i	0.0385776	+	0.0670805i
$79$	2.75342	−	1.58969i	0.309784	−	0.178854i	−0.337046	−	0.941488i	$-0.609428\pi$
$79$	2.75342	−	1.58969i	0.309784	−	0.178854i	0.646830	+	0.762634i	$0.276094\pi$
$80$	0.0988539	−	14.5900i	0.0110522	−	1.63121i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	4.67649	−	8.06832i	0.516432	−	0.890997i
$83$	−7.49842			−0.823059			−0.411529	−	0.911396i	$-0.635005\pi$
$83$	−7.49842			−0.823059			−0.411529	+	0.911396i	$0.635005\pi$
$84$		0			0
$85$	−9.31044			−1.00986
$86$	−2.49052	+	4.29689i	−0.268560	+	0.463346i
$87$	−4.10928	+	7.11749i	−0.440562	+	0.763075i
$88$	−8.66000	+	14.8251i	−0.923159	+	1.58036i
$89$	10.6411	−	6.14362i	1.12795	−	0.651222i	0.184531	−	0.982827i	$-0.440923\pi$
$89$	10.6411	−	6.14362i	1.12795	−	0.651222i	0.943419	+	0.331604i	$0.107590\pi$
$90$	−2.57166	−	4.47172i	−0.271076	−	0.471360i
$91$		0			0
$92$	5.99359	+	3.48753i	0.624875	+	0.363600i
$93$	3.15625	+	5.46678i	0.327287	+	0.566878i
$94$	−0.0279362	+	16.4928i	−0.00288140	+	1.70110i
$95$	−3.85099	−	2.22337i	−0.395103	−	0.228113i
$96$	−0.0479085	+	5.65665i	−0.00488964	+	0.577330i
$97$		−	11.8376i		−	1.20192i	−0.799277	−	0.600962i	$-0.794784\pi$
$97$		−	11.8376i		−	1.20192i	0.799277	−	0.600962i	$-0.205216\pi$
$98$		0			0
$99$			6.07019i			0.610077i
$100$	16.6096	+	0.0562682i	1.66096	+	0.00562682i
$101$	−4.95940	−	2.86331i	−0.493479	−	0.284910i	0.232538	−	0.972587i	$-0.425297\pi$
$101$	−4.95940	−	2.86331i	−0.493479	−	0.284910i	−0.726016	+	0.687677i	$0.758630\pi$
$102$	3.60977	+	0.00611438i	0.357421	+	0.000605414i
$103$	−2.47654	−	4.28949i	−0.244020	−	0.422656i	0.717835	−	0.696213i	$-0.245133\pi$
$103$	−2.47654	−	4.28949i	−0.244020	−	0.422656i	−0.961856	+	0.273557i	$0.911800\pi$
$104$	1.36683	+	0.00694562i	0.134028	+	0.000681074i
$105$		0			0
$106$	3.22155	−	1.85270i	0.312905	−	0.179950i
$107$	11.8888	−	6.86398i	1.14933	−	0.663566i	0.200606	−	0.979672i	$-0.435709\pi$
$107$	11.8888	−	6.86398i	1.14933	−	0.663566i	0.948724	+	0.316107i	$0.102376\pi$
$108$	0.994127	+	1.73543i	0.0956599	+	0.166992i
$109$	6.82537	−	11.8219i	0.653752	−	1.13233i	−0.328453	−	0.944520i	$-0.606527\pi$
$109$	6.82537	−	11.8219i	0.653752	−	1.13233i	0.982205	−	0.187812i	$-0.0601394\pi$
$110$	−27.0911	−	15.7023i	−2.58304	−	1.49716i
$111$	1.19016			0.112965
$112$		0			0
$113$	−7.11968			−0.669764			−0.334882	−	0.942260i	$-0.608696\pi$
$113$	−7.11968			−0.669764			−0.334882	+	0.942260i	$0.608696\pi$
$114$	1.49162	+	0.864556i	0.139703	+	0.0809731i
$115$	−6.32345	+	10.9525i	−0.589665	+	1.02133i
$116$	8.17030	+	14.2627i	0.758593	+	1.32426i
$117$	0.418509	−	0.241626i	0.0386912	−	0.0223384i
$118$	1.42406	−	0.818966i	0.131095	−	0.0753919i
$119$		0			0
$120$	−10.3168	−	0.0524254i	−0.941789	−	0.00478576i
$121$	12.9236	+	22.3844i	1.17487	+	2.03494i
$122$	−0.294803		0.000499351i	−0.0266903		4.52091e-5i
$123$	−5.71076	−	3.29711i	−0.514922	−	0.297290i
$124$	12.6249	+	0.0427693i	1.13375	+	0.00384080i
$125$			12.0546i			1.07820i
$126$		0			0
$127$		−	3.03609i		−	0.269409i	−0.990886	−	0.134705i	$-0.956991\pi$
$127$		−	3.03609i		−	0.269409i	0.990886	−	0.134705i	$-0.0430086\pi$
$128$	9.73020	+	5.77263i	0.860036	+	0.510233i
$129$	3.04134	+	1.75592i	0.267775	+	0.154600i
$130$	−0.00422247	+	2.49283i	−0.000370335	+	0.218636i
$131$	7.23328	+	12.5284i	0.631974	+	1.09461i	0.987148	+	0.159811i	$0.0510885\pi$
$131$	7.23328	+	12.5284i	0.631974	+	1.09461i	−0.355173	+	0.934800i	$0.615578\pi$
$132$	10.4933	+	6.10578i	0.913321	+	0.531440i
$133$		0			0
$134$	1.25225	+	2.17747i	0.108178	+	0.188105i
$135$	−3.15890	+	1.82379i	−0.271875	+	0.156967i
$136$	3.64150	−	6.23389i	0.312256	−	0.534552i
$137$	−5.78134	+	10.0136i	−0.493933	+	0.855517i	−0.999976	−	0.00699157i	$-0.997774\pi$
$137$	−5.78134	+	10.0136i	−0.493933	+	0.855517i	0.506043	+	0.862508i	$0.331108\pi$
$138$	2.45887	−	4.24228i	0.209313	−	0.361127i
$139$	−17.6203			−1.49453			−0.747266	−	0.664525i	$-0.768634\pi$
$139$	−17.6203			−1.49453			−0.747266	+	0.664525i	$0.768634\pi$
$140$		0			0
$141$	11.6622			0.982134
$142$	−6.47599	+	11.1730i	−0.543453	+	0.937617i
$143$	1.46672	−	2.54043i	0.122653	−	0.212442i
$144$	3.99991	+	0.0271012i	0.333326	+	0.00225844i
$145$	−25.9616	+	14.9889i	−2.15599	+	1.24476i
$146$	4.26493	+	7.41606i	0.352968	+	0.613757i
$147$		0			0
$148$	1.19714	−	2.05737i	0.0984040	−	0.169115i
$149$	−3.05734	−	5.29546i	−0.250467	−	0.433821i	0.713188	−	0.700973i	$-0.247251\pi$
$149$	−3.05734	−	5.29546i	−0.250467	−	0.433821i	−0.963654	+	0.267152i	$0.913917\pi$
$150$	0.0198938	−	11.7448i	0.00162432	−	0.958958i
$151$	12.3346	+	7.12137i	1.00377	+	0.579529i	0.909363	−	0.416004i	$-0.136570\pi$
$151$	12.3346	+	7.12137i	1.00377	+	0.579529i	0.0944112	+	0.995533i	$0.469903\pi$
$152$	2.99488	−	1.70886i	0.242917	−	0.138607i
$153$		−	2.55250i		−	0.206357i
$154$		0			0
$155$			23.0253i			1.84944i
$156$	0.00327421	−	0.966500i	0.000262146	−	0.0773819i
$157$	−18.2706	−	10.5485i	−1.45815	−	0.841865i	−0.459232	−	0.888316i	$-0.651875\pi$
$157$	−18.2706	−	10.5485i	−1.45815	−	0.841865i	−0.998921	+	0.0464518i	$0.985209\pi$
$158$	−4.49632	−	0.00761605i	−0.357708	−	0.000605901i
$159$	−1.31391	−	2.27576i	−0.104200	−	0.180479i
$160$	−10.4679	+	17.7814i	−0.827559	+	1.40574i
$161$		0			0
$162$	1.22594	−	0.705031i	0.0963190	−	0.0553925i
$163$	−16.5731	+	9.56851i	−1.29811	+	0.749464i	−0.980077	−	0.198617i	$-0.936355\pi$
$163$	−16.5731	+	9.56851i	−1.29811	+	0.749464i	−0.318032	+	0.948080i	$0.603022\pi$
$164$	−11.4438	+	6.55549i	−0.893610	+	0.511898i
$165$	−11.0708	+	19.1751i	−0.861857	+	1.49278i
$166$	9.17466	+	5.31773i	0.712092	+	0.412736i
$167$	7.69624			0.595553			0.297776	−	0.954636i	$-0.403755\pi$
$167$	7.69624			0.595553			0.297776	+	0.954636i	$0.403755\pi$
$168$		0			0
$169$	12.7665			0.982036
$170$	11.3917	+	6.60278i	0.873707	+	0.506410i
$171$	0.609546	−	1.05577i	0.0466132	−	0.0807364i
$172$	6.09454	−	3.49121i	0.464704	−	0.266202i
$173$	−0.713055	+	0.411682i	−0.0542125	+	0.0312996i	−0.526861	−	0.849951i	$-0.676631\pi$
$173$	−0.713055	+	0.411682i	−0.0542125	+	0.0312996i	0.472649	+	0.881251i	$0.343298\pi$
$174$	10.0755	−	5.79435i	0.763820	−	0.439268i
$175$		0			0
$176$	21.1095	−	11.9976i	1.59119	−	0.904356i
$177$	−0.580801	−	1.00598i	−0.0436557	−	0.0756138i
$178$	−17.3767	−	0.0294335i	−1.30244	−	0.00220613i
$179$	8.20383	+	4.73649i	0.613183	+	0.354022i	0.774210	−	0.632928i	$-0.218147\pi$
$179$	8.20383	+	4.73649i	0.613183	+	0.354022i	−0.161027	+	0.986950i	$0.551481\pi$
$180$	−0.0247136	+	7.29512i	−0.00184204	+	0.543746i
$181$		−	2.06119i		−	0.153207i	−0.997062	−	0.0766034i	$-0.975592\pi$
$181$		−	2.06119i		−	0.153207i	0.997062	−	0.0766034i	$-0.0244075\pi$
$182$		0			0
$183$			0.208458i			0.0154096i
$184$	−4.86015	−	8.51769i	−0.358295	−	0.627932i
$185$	3.75959	+	2.17060i	0.276411	+	0.159586i
$186$	0.0151213	−	8.92720i	0.00110875	−	0.654574i
$187$	−7.74708	−	13.4183i	−0.566522	−	0.981245i
$188$	11.7306	−	20.1599i	0.855539	−	1.47031i
$189$		0			0
$190$	3.13509	+	5.45144i	0.227443	+	0.395489i
$191$	9.40191	−	5.42820i	0.680298	−	0.392770i	−0.119669	−	0.992814i	$-0.538183\pi$
$191$	9.40191	−	5.42820i	0.680298	−	0.392770i	0.799967	+	0.600043i	$0.204850\pi$
$192$	4.07020	−	6.88719i	0.293742	−	0.497040i
$193$	−4.85673	+	8.41210i	−0.349595	+	0.605517i	−0.986178	−	0.165692i	$-0.947014\pi$
$193$	−4.85673	+	8.41210i	−0.349595	+	0.605517i	0.636582	+	0.771209i	$0.280348\pi$
$194$	−8.39498	+	14.4838i	−0.602725	+	1.03988i
$195$	1.76270			0.126230
$196$		0			0
$197$	−15.9300			−1.13496			−0.567481	−	0.823386i	$-0.692082\pi$
$197$	−15.9300			−1.13496			−0.567481	+	0.823386i	$0.692082\pi$
$198$	4.30486	−	7.42716i	0.305933	−	0.527825i
$199$	5.02859	−	8.70978i	0.356467	−	0.617420i	−0.630901	−	0.775864i	$-0.717314\pi$
$199$	5.02859	−	8.70978i	0.356467	−	0.617420i	0.987368	+	0.158444i	$0.0506477\pi$
$200$	−20.2827	−	11.8480i	−1.43420	−	0.837782i
$201$	1.53820	−	0.888083i	0.108497	−	0.0626405i
$202$	4.03745	+	7.02050i	0.284074	+	0.493961i
$203$		0			0
$204$	−4.41238	−	2.56746i	−0.308929	−	0.179758i
$205$	−12.0265	−	20.8304i	−0.839965	−	1.45486i
$206$	−0.0118648	+	7.00469i	−0.000826663	+	0.488040i
$207$	−3.00269	−	1.73360i	−0.208701	−	0.120494i
$208$	−1.66745	−	0.977825i	−0.115617	−	0.0678000i
$209$		−	7.40013i		−	0.511878i
$210$		0			0
$211$			1.03227i			0.0710647i	0.999369	+	0.0355324i	$0.0113127\pi$
$211$			1.03227i			0.0710647i	−0.999369	+	0.0355324i	$0.988687\pi$
$212$	−5.25561	−	0.0178044i	−0.360957	−	0.00122281i
$213$	7.90825	+	4.56583i	0.541864	+	0.312846i
$214$	−19.4142	−	0.0328846i	−1.32713	−	0.00224795i
$215$	6.40485	+	11.0935i	0.436807	+	0.756572i
$216$	0.0143727	−	2.82839i	0.000977935	−	0.192448i
$217$		0			0
$218$	−16.7350	+	9.62420i	−1.13344	+	0.651833i
$219$	5.23883	−	3.02464i	0.354007	−	0.204386i
$220$	22.0115	+	38.4250i	1.48401	+	2.59061i
$221$	−0.616751	+	1.06824i	−0.0414871	+	0.0718578i
$222$	−1.45621	−	0.844038i	−0.0977347	−	0.0566481i
$223$	−9.57250			−0.641022			−0.320511	−	0.947245i	$-0.603855\pi$
$223$	−9.57250			−0.641022			−0.320511	+	0.947245i	$0.603855\pi$
$224$		0			0
$225$	−8.30483			−0.553656
$226$	8.71126	+	5.04914i	0.579464	+	0.335864i
$227$	5.57692	−	9.65951i	0.370153	−	0.641124i	−0.619436	−	0.785048i	$-0.712638\pi$
$227$	5.57692	−	9.65951i	0.370153	−	0.641124i	0.989589	+	0.143923i	$0.0459718\pi$
$228$	−1.21193	−	2.11565i	−0.0802622	−	0.140112i
$229$	8.77151	−	5.06423i	0.579637	−	0.334654i	−0.181352	−	0.983418i	$-0.558047\pi$
$229$	8.77151	−	5.06423i	0.579637	−	0.334654i	0.760989	+	0.648764i	$0.224714\pi$
$230$	15.5043	−	8.91646i	1.02233	−	0.587934i
$231$		0			0
$232$	0.118123	−	23.2453i	0.00775513	−	1.52613i
$233$	−6.32072	−	10.9478i	−0.414084	−	0.717215i	0.581248	−	0.813727i	$-0.302565\pi$
$233$	−6.32072	−	10.9478i	−0.414084	−	0.717215i	−0.995332	+	0.0965119i	$0.969231\pi$
$234$	−0.683422	−	0.00115761i	−0.0446767	−	7.56752e-5i
$235$	36.8397	+	21.2694i	2.40316	+	1.38746i
$236$	−2.32319	−	0.00787026i	−0.151227	−	0.000512310i
$237$			3.17938i			0.206523i
$238$		0			0
$239$		−	5.46050i		−	0.353211i	−0.984282	−	0.176605i	$-0.943488\pi$
$239$		−	5.46050i		−	0.353211i	0.984282	−	0.176605i	$-0.0565116\pi$
$240$	12.5859	+	7.38060i	0.812414	+	0.476416i
$241$	11.8106	+	6.81887i	0.760790	+	0.439242i	0.829579	−	0.558389i	$-0.188580\pi$
$241$	11.8106	+	6.81887i	0.760790	+	0.439242i	−0.0687894	+	0.997631i	$0.521914\pi$
$242$	0.0619158	−	36.5535i	0.00398010	−	2.34975i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.360351	+	0.209680i	0.0230691	+	0.0134234i
$245$		0			0
$246$	4.64913	+	8.08412i	0.296418	+	0.515425i
$247$	−0.510201	+	0.294565i	−0.0324633	+	0.0187427i
$248$	−15.4168	−	9.00567i	−0.978969	−	0.571860i
$249$	3.74921	−	6.49383i	0.237597	−	0.411529i
$250$	8.54892	−	14.7494i	0.540681	−	0.932834i
$251$	−28.2425			−1.78265			−0.891324	−	0.453367i	$-0.850223\pi$
$251$	−28.2425			−1.78265			−0.891324	+	0.453367i	$0.850223\pi$
$252$		0			0
$253$	−21.0466			−1.32319
$254$	−2.15313	+	3.71479i	−0.135100	+	0.233087i
$255$	4.65522	−	8.06307i	0.291521	−	0.504929i
$256$	−7.81151	−	13.9635i	−0.488219	−	0.872721i
$257$	17.4613	−	10.0813i	1.08920	−	0.628852i	0.155840	−	0.987782i	$-0.450192\pi$
$257$	17.4613	−	10.0813i	1.08920	−	0.628852i	0.933364	+	0.358930i	$0.116858\pi$
$258$	−2.47595	−	4.30530i	−0.154146	−	0.268036i
$259$		0			0
$260$	1.77304	−	3.04710i	0.109959	−	0.188973i
$261$	−4.10928	−	7.11749i	−0.254358	−	0.440562i
$262$	0.0346539	−	20.4588i	0.00214093	−	1.26395i
$263$	−10.8326	−	6.25419i	−0.667965	−	0.385650i	0.127340	−	0.991859i	$-0.459356\pi$
$263$	−10.8326	−	6.25419i	−0.667965	−	0.385650i	−0.795305	+	0.606209i	$0.792689\pi$
$264$	−8.50888	−	14.9123i	−0.523686	−	0.917789i
$265$		−	9.58518i		−	0.588813i
$266$		0			0
$267$			12.2872i			0.751967i
$268$	0.0120341	−	3.55231i	0.000735102	−	0.216992i
$269$	11.3057	+	6.52738i	0.689324	+	0.397981i	0.803359	−	0.595496i	$-0.203044\pi$
$269$	11.3057	+	6.52738i	0.689324	+	0.397981i	−0.114035	+	0.993477i	$0.536378\pi$
$270$	5.15845	+	0.00873760i	0.313933	+	0.000531753i
$271$	−5.14672	−	8.91437i	−0.312641	−	0.541510i	0.666292	−	0.745691i	$-0.267880\pi$
$271$	−5.14672	−	8.91437i	−0.312641	−	0.541510i	−0.978933	+	0.204181i	$0.934547\pi$
$272$	−8.87650	+	5.04497i	−0.538217	+	0.305896i
$273$		0			0
$274$	14.1752	−	8.15205i	0.856352	−	0.492483i
$275$	−43.6580	+	25.2060i	−2.63268	+	1.51998i
$276$	−6.01708	+	3.44684i	−0.362186	+	0.207475i
$277$	9.48111	−	16.4218i	0.569665	−	0.986689i	−0.426934	−	0.904283i	$-0.640406\pi$
$277$	9.48111	−	16.4218i	0.569665	−	0.986689i	0.996599	−	0.0824058i	$-0.0262604\pi$
$278$	21.5592	+	12.4960i	1.29304	+	0.749458i
$279$	−6.31249			−0.377919
$280$		0			0
$281$	17.5144			1.04482			0.522412	−	0.852693i	$-0.325032\pi$
$281$	17.5144			1.04482			0.522412	+	0.852693i	$0.325032\pi$
$282$	−14.2692	−	8.27060i	−0.849720	−	0.492507i
$283$	9.47095	−	16.4042i	0.562990	−	0.975127i	−0.434244	−	0.900795i	$-0.642984\pi$
$283$	9.47095	−	16.4042i	0.562990	−	0.975127i	0.997234	−	0.0743313i	$-0.0236822\pi$
$284$	15.8473	−	9.07803i	0.940367	−	0.538682i
$285$	3.85099	−	2.22337i	0.228113	−	0.131701i
$286$	−3.59622	+	2.06816i	−0.212649	+	0.122293i
$287$		0			0
$288$	−4.87485	−	2.86982i	−0.287253	−	0.169106i
$289$	−5.24238	−	9.08007i	−0.308375	−	0.534122i
$290$	42.3951	+	0.0718106i	2.48952	+	0.00421686i
$291$	10.2517	+	5.91879i	0.600962	+	0.346966i
$292$	0.0409860	−	12.0985i	0.00239852	−	0.708010i
$293$		−	25.2760i		−	1.47664i	−0.674451	−	0.738320i	$-0.735620\pi$
$293$		−	25.2760i		−	1.47664i	0.674451	−	0.738320i	$-0.264380\pi$
$294$		0			0
$295$		−	4.23703i		−	0.246690i
$296$	−2.92380	+	1.66830i	−0.169942	+	0.0969682i
$297$	−5.25694	−	3.03510i	−0.305039	−	0.176114i
$298$	−0.0146474	+	8.64744i	−0.000848501	+	0.500933i
$299$	0.837768	+	1.45106i	0.0484494	+	0.0839167i
$300$	−8.35352	+	14.3562i	−0.482290	+	0.828854i
$301$		0			0
$302$	−10.0416	−	17.4608i	−0.577828	−	1.00475i
$303$	4.95940	−	2.86331i	0.284910	−	0.164493i
$304$	−4.87626	−	0.0330389i	−0.279673	−	0.00189491i
$305$	−0.380183	+	0.658497i	−0.0217692	+	0.0377054i
$306$	−1.81018	+	3.12310i	−0.103481	+	0.178536i
$307$	−10.2457			−0.584750			−0.292375	−	0.956304i	$-0.594446\pi$
$307$	−10.2457			−0.584750			−0.292375	+	0.956304i	$0.594446\pi$
$308$		0			0
$309$	4.95307			0.281770
$310$	16.3291	−	28.1725i	0.927430	−	1.60009i
$311$	−15.1919	+	26.3131i	−0.861451	+	1.49208i	0.00907691	+	0.999959i	$0.497111\pi$
$311$	−15.1919	+	26.3131i	−0.861451	+	1.49208i	−0.870528	+	0.492119i	$0.836223\pi$
$312$	−0.689429	+	1.18023i	−0.0390312	+	0.0668176i
$313$	−14.8277	+	8.56075i	−0.838108	+	0.483882i	−0.856621	−	0.515946i	$-0.827440\pi$
$313$	−14.8277	+	8.56075i	−0.838108	+	0.483882i	0.0185123	+	0.999829i	$0.494107\pi$
$314$	14.8741	+	25.8638i	0.839394	+	1.45958i
$315$		0			0
$316$	5.49605	+	3.19802i	0.309177	+	0.179903i
$317$	6.18286	+	10.7090i	0.347264	+	0.601478i	0.985762	−	0.168145i	$-0.0537775\pi$
$317$	6.18286	+	10.7090i	0.347264	+	0.601478i	−0.638499	+	0.769623i	$0.720444\pi$
$318$	−0.00629482	+	3.71629i	−0.000352996	+	0.208399i
$319$	−43.2045	−	24.9442i	−2.41899	−	1.39660i
$320$	25.4181	−	14.3327i	1.42092	−	0.801224i
$321$			13.7280i			0.766220i
$322$		0			0
$323$			3.11173i			0.173141i
$324$	−1.99999	−	0.00677535i	−0.111110	−	0.000376408i
$325$	3.47565	+	2.00667i	0.192794	+	0.111310i
$326$	27.0638	+	0.0458418i	1.49892	+	0.00253894i
$327$	6.82537	+	11.8219i	0.377444	+	0.653752i
$328$	18.6510	+	0.0947764i	1.02983	+	0.00523315i
$329$		0			0
$330$	27.1442	−	15.6105i	1.49424	−	0.859327i
$331$	6.65278	−	3.84098i	0.365670	−	0.211120i	−0.305895	−	0.952065i	$-0.598956\pi$
$331$	6.65278	−	3.84098i	0.365670	−	0.211120i	0.671565	+	0.740946i	$0.265622\pi$
$332$	−7.45438	−	13.0130i	−0.409112	−	0.714180i
$333$	−0.595080	+	1.03071i	−0.0326102	+	0.0564825i
$334$	−9.41670	−	5.45802i	−0.515259	−	0.298650i
$335$	6.47871			0.353969
$336$		0			0
$337$	−13.3863			−0.729201			−0.364600	−	0.931164i	$-0.618794\pi$
$337$	−13.3863			−0.729201			−0.364600	+	0.931164i	$0.618794\pi$
$338$	−15.6204	−	9.05373i	−0.849635	−	0.492458i
$339$	3.55984	−	6.16583i	0.193344	−	0.334882i
$340$	−9.25575	−	16.1576i	−0.501964	−	0.876269i
$341$	−33.1844	+	19.1590i	−1.79704	+	1.03752i
$342$	−1.49454	+	0.859498i	−0.0808152	+	0.0464763i
$343$		0			0
$344$	−9.93284	−	0.0504744i	−0.535543	−	0.00272140i
$345$	−6.32345	−	10.9525i	−0.340443	−	0.589665i
$346$	1.16441	+	0.00197233i	0.0625992	+	0.000106033i
$347$	27.6076	+	15.9393i	1.48206	+	0.855666i	0.999793	−	0.0203606i	$-0.00648144\pi$
$347$	27.6076	+	15.9393i	1.48206	+	0.855666i	0.482264	+	0.876026i	$0.339815\pi$
$348$	−16.4370	−	0.0556837i	−0.881118	−	0.00298496i
$349$		−	9.51634i		−	0.509398i	−0.967020	−	0.254699i	$-0.918024\pi$
$349$		−	9.51634i		−	0.509398i	0.967020	−	0.254699i	$-0.0819764\pi$
$350$		0			0
$351$			0.483253i			0.0257941i
$352$	−34.3370	−	0.290814i	−1.83017	−	0.0155004i
$353$	12.2392	+	7.06628i	0.651425	+	0.376100i	0.789002	−	0.614391i	$-0.210598\pi$
$353$	12.2392	+	7.06628i	0.651425	+	0.376100i	−0.137577	+	0.990491i	$0.543931\pi$
$354$	−0.00278256	+	1.64275i	−0.000147891	+	0.0873112i
$355$	16.6542	+	28.8460i	0.883915	+	1.53099i
$356$	21.2404	+	12.3593i	1.12574	+	0.655040i
$357$		0			0
$358$	−6.67874	−	11.6133i	−0.352982	−	0.613782i
$359$	−19.4557	+	11.2328i	−1.02684	+	0.592843i	−0.916076	−	0.401004i	$-0.868661\pi$
$359$	−19.4557	+	11.2328i	−1.02684	+	0.592843i	−0.110759	+	0.993847i	$0.535328\pi$
$360$	5.20379	−	8.90838i	0.274264	−	0.469513i
$361$	8.75691	−	15.1674i	0.460890	−	0.798285i
$362$	−1.46175	+	2.52196i	−0.0768280	+	0.132551i
$363$	−25.8472			−1.35663
$364$		0			0
$365$	22.0652			1.15495
$366$	0.147834	−	0.255058i	0.00772742	−	0.0133321i
$367$	−5.99956	+	10.3915i	−0.313174	+	0.542434i	−0.979048	−	0.203631i	$-0.934726\pi$
$367$	−5.99956	+	10.3915i	−0.313174	+	0.542434i	0.665873	+	0.746065i	$0.268059\pi$
$368$	−0.0939655	+	13.8685i	−0.00489829	+	0.722945i
$369$	5.71076	−	3.29711i	0.297290	−	0.171641i
$370$	−3.06068	−	5.32206i	−0.159117	−	0.276680i
$371$		0			0
$372$	−6.34949	+	10.9121i	−0.329206	+	0.565766i
$373$	−2.81380	−	4.87365i	−0.145693	−	0.252348i	0.783938	−	0.620839i	$-0.213208\pi$
$373$	−2.81380	−	4.87365i	−0.145693	−	0.252348i	−0.929631	+	0.368491i	$0.879875\pi$
$374$	−0.0371155	+	21.9120i	−0.00191920	+	1.13304i
$375$	−10.4396	−	6.02732i	−0.539100	−	0.311250i
$376$	−28.6499	+	16.3475i	−1.47750	+	0.843056i
$377$			3.97165i			0.204550i
$378$		0			0
$379$			21.3356i			1.09594i	0.836500	+	0.547968i	$0.184598\pi$
$379$			21.3356i			1.09594i	−0.836500	+	0.547968i	$0.815402\pi$
$380$	0.0301282	−	8.89342i	0.00154554	−	0.456223i
$381$	2.62933	+	1.51804i	0.134705	+	0.0777718i
$382$	−15.3532	−	0.0260060i	−0.785540	−	0.00133058i
$383$	3.77595	+	6.54013i	0.192942	+	0.334185i	0.946224	−	0.323513i	$-0.104864\pi$
$383$	3.77595	+	6.54013i	0.192942	+	0.334185i	−0.753282	+	0.657698i	$0.771530\pi$
$384$	−9.86434	+	5.54029i	−0.503388	+	0.282727i
$385$		0			0
$386$	11.9081	−	6.84829i	0.606108	−	0.348569i
$387$	−3.04134	+	1.75592i	−0.154600	+	0.0892583i
$388$	20.5433	−	11.7681i	1.04293	−	0.597433i
$389$	1.32531	−	2.29550i	0.0671957	−	0.116386i	−0.830470	−	0.557063i	$-0.811928\pi$
$389$	1.32531	−	2.29550i	0.0671957	−	0.116386i	0.897666	+	0.440677i	$0.145261\pi$
$390$	−2.15675	−	1.25007i	−0.109211	−	0.0633000i
$391$	8.85003			0.447565
$392$		0			0
$393$	−14.4666			−0.729741
$394$	19.4910	+	11.2972i	0.981944	+	0.569145i
$395$	−5.79852	+	10.0433i	−0.291755	+	0.505335i
$396$	−10.5344	+	6.03454i	−0.529373	+	0.303247i
$397$	16.1515	−	9.32508i	0.810621	−	0.468012i	−0.0365505	−	0.999332i	$-0.511637\pi$
$397$	16.1515	−	9.32508i	0.810621	−	0.468012i	0.847171	+	0.531320i	$0.178304\pi$
$398$	−12.3295	+	7.09063i	−0.618023	+	0.355421i
$399$		0			0
$400$	16.4144	+	28.8807i	0.820718	+	1.44403i
$401$	11.9242	+	20.6533i	0.595464	+	1.03137i	0.993481	+	0.113996i	$0.0363652\pi$
$401$	11.9242	+	20.6533i	0.595464	+	1.03137i	−0.398017	+	0.917378i	$0.630302\pi$
$402$	−2.51187	−	0.00425472i	−0.125281	−	0.000212206i
$403$	2.64184	+	1.52526i	0.131599	+	0.0759788i
$404$	0.0387999	−	11.4532i	0.00193037	−	0.569817i
$405$		−	3.64758i		−	0.181250i
$406$		0			0
$407$			7.22450i			0.358105i
$408$	3.57796	+	6.27058i	0.177135	+	0.310440i
$409$	−15.0922	−	8.71346i	−0.746259	−	0.430853i	0.0780817	−	0.996947i	$-0.475121\pi$
$409$	−15.0922	−	8.71346i	−0.746259	−	0.430853i	−0.824341	+	0.566094i	$0.808454\pi$
$410$	−0.0576176	+	34.0159i	−0.00284553	+	1.67993i
$411$	−5.78134	−	10.0136i	−0.285172	−	0.493933i
$412$	4.98211	−	8.56215i	0.245451	−	0.421827i
$413$		0			0
$414$	2.44449	+	4.25059i	0.120140	+	0.208905i
$415$	23.6867	−	13.6755i	1.16274	−	0.671306i
$416$	1.34675	+	2.37894i	0.0660297	+	0.116637i
$417$	8.81014	−	15.2596i	0.431434	−	0.747266i
$418$	−5.24802	+	9.05439i	−0.256689	+	0.442865i
$419$	26.6148			1.30022			0.650109	−	0.759841i	$-0.274723\pi$
$419$	26.6148			1.30022			0.650109	+	0.759841i	$0.274723\pi$
$420$		0			0
$421$	17.2196			0.839234			0.419617	−	0.907701i	$-0.362164\pi$
$421$	17.2196			0.839234			0.419617	+	0.907701i	$0.362164\pi$
$422$	0.732069	−	1.26303i	0.0356366	−	0.0614836i
$423$	−5.83110	+	10.0998i	−0.283518	+	0.491067i
$424$	6.41785	+	3.74896i	0.311678	+	0.182066i
$425$	18.3581	−	10.5990i	0.890497	−	0.514129i
$426$	−6.43811	−	11.1949i	−0.311927	−	0.542394i
$427$		0			0
$428$	23.7309	+	13.8084i	1.14707	+	0.667455i
$429$	1.46672	+	2.54043i	0.0708138	+	0.122653i
$430$	0.0306850	−	18.1156i	0.00147976	−	0.873613i
$431$	−17.0459	−	9.84148i	−0.821074	−	0.474047i	0.0297126	−	0.999558i	$-0.490541\pi$
$431$	−17.0459	−	9.84148i	−0.821074	−	0.474047i	−0.850787	+	0.525511i	$0.823874\pi$
$432$	−2.02342	+	3.45047i	−0.0973521	+	0.166011i
$433$		−	6.43311i		−	0.309156i	−0.987981	−	0.154578i	$-0.950598\pi$
$433$		−	6.43311i		−	0.309156i	0.987981	−	0.154578i	$-0.0494017\pi$
$434$		0			0
$435$		−	29.9779i		−	1.43733i
$436$	27.3013	+	0.0924886i	1.30750	+	0.00442940i
$437$	3.66055	+	2.11342i	0.175108	+	0.101099i
$438$	−8.55496	−	0.0144908i	−0.408772	−	0.000692395i
$439$	3.47675	+	6.02190i	0.165936	+	0.287410i	0.936987	−	0.349363i	$-0.113602\pi$
$439$	3.47675	+	6.02190i	0.165936	+	0.287410i	−0.771051	+	0.636773i	$0.780269\pi$
$440$	0.318232	−	62.6248i	0.0151711	−	2.98552i
$441$		0			0
$442$	1.51220	−	0.869657i	0.0719280	−	0.0413654i
$443$	6.74126	−	3.89207i	0.320287	−	0.184918i	−0.331234	−	0.943549i	$-0.607465\pi$
$443$	6.74126	−	3.89207i	0.320287	−	0.184918i	0.651520	+	0.758631i	$0.274132\pi$
$444$	1.18317	+	2.06544i	0.0561507	+	0.0980213i
$445$	−22.4093	+	38.8141i	−1.06230	+	1.83996i
$446$	11.7124	+	6.78863i	0.554598	+	0.321451i
$447$	6.11467			0.289214
$448$		0			0
$449$	−13.4404			−0.634290			−0.317145	−	0.948377i	$-0.602724\pi$
$449$	−13.4404			−0.634290			−0.317145	+	0.948377i	$0.602724\pi$
$450$	10.1613	+	5.88962i	0.479010	+	0.277640i
$451$	20.0141	−	34.6654i	0.942427	−	1.63233i
$452$	−7.07787	−	12.3557i	−0.332915	−	0.581163i
$453$	−12.3346	+	7.12137i	−0.579529	+	0.334591i
$454$	−13.6740	+	7.86381i	−0.641750	+	0.369067i
$455$		0			0
$456$	−0.0175216	+	3.44807i	−0.000820524	+	0.161471i
$457$	0.581825	+	1.00775i	0.0272166	+	0.0471406i	0.879313	−	0.476244i	$-0.158002\pi$
$457$	0.581825	+	1.00775i	0.0272166	+	0.0471406i	−0.852096	+	0.523385i	$0.824669\pi$
$458$	−14.3238	−	0.0242622i	−0.669307	−	0.00113370i
$459$	2.21053	+	1.27625i	0.103179	+	0.0595702i
$460$	−25.2937	−	0.0856872i	−1.17932	−	0.00399518i
$461$		−	21.4211i		−	0.997678i	−0.866695	−	0.498839i	$-0.833760\pi$
$461$		−	21.4211i		−	0.997678i	0.866695	−	0.498839i	$-0.166240\pi$
$462$		0			0
$463$		−	14.4408i		−	0.671119i	−0.942019	−	0.335560i	$-0.891075\pi$
$463$		−	14.4408i		−	0.671119i	0.942019	−	0.335560i	$-0.108925\pi$
$464$	−16.6297	+	28.3579i	−0.772012	+	1.31648i
$465$	−19.9405	−	11.5127i	−0.924719	−	0.533887i
$466$	−0.0302820	+	17.8777i	−0.00140278	+	0.828167i
$467$	−14.8830	−	25.7780i	−0.688701	−	1.19287i	−0.972258	−	0.233910i	$-0.924848\pi$
$467$	−14.8830	−	25.7780i	−0.688701	−	1.19287i	0.283557	−	0.958955i	$-0.408485\pi$
$468$	0.835376	+	0.486085i	0.0386153	+	0.0224693i
$469$		0			0
$470$	−29.9912	−	52.1500i	−1.38339	−	2.40550i
$471$	18.2706	−	10.5485i	0.841865	−	0.486051i
$472$	2.83695	+	1.65719i	0.130581	+	0.0762784i
$473$	−10.6588	+	18.4615i	−0.490090	+	0.848861i
$474$	2.25475	−	3.89012i	0.103564	−	0.178679i
$475$	10.1244			0.464538
$476$		0			0
$477$	2.62782			0.120320
$478$	−3.87248	+	6.68117i	−0.177123	+	0.305590i
$479$	14.1776	−	24.5563i	0.647790	−	1.12201i	−0.335859	−	0.941912i	$-0.609027\pi$
$479$	14.1776	−	24.5563i	0.647790	−	1.12201i	0.983649	−	0.180094i	$-0.0576401\pi$
$480$	−10.1652	−	17.9561i	−0.463976	−	0.819582i
$481$	0.498093	−	0.287574i	0.0227111	−	0.0131122i
$482$	−9.61504	−	16.7191i	−0.437953	−	0.761533i
$483$		0			0
$484$	−25.9988	+	44.6809i	−1.18176	+	2.03095i
$485$	21.5893	+	37.3937i	0.980318	+	1.69796i
$486$	−0.00239545	+	1.41421i	−0.000108660	+	0.0641499i
$487$	8.28601	+	4.78393i	0.375475	+	0.216781i	0.675848	−	0.737041i	$-0.263778\pi$
$487$	8.28601	+	4.78393i	0.375475	+	0.216781i	−0.300373	+	0.953822i	$0.597111\pi$
$488$	−0.292205	−	0.512107i	−0.0132275	−	0.0231820i
$489$		−	19.1370i		−	0.865406i
$490$		0			0
$491$		−	17.7521i		−	0.801141i	−0.916266	−	0.400571i	$-0.868812\pi$
$491$		−	17.7521i		−	0.801141i	0.916266	−	0.400571i	$-0.131188\pi$
$492$	0.0446781	−	13.1884i	0.00201425	−	0.594577i
$493$	18.1674	+	10.4889i	0.818217	+	0.472398i
$494$	0.833154	+	0.00141123i	0.0374854	+	6.34943e-5i
$495$	−11.0708	−	19.1751i	−0.497593	−	0.861857i
$496$	12.4765	+	21.9521i	0.560213	+	0.985681i
$497$		0			0
$498$	−9.19262	+	5.28662i	−0.411931	+	0.236899i
$499$	−8.14160	+	4.70056i	−0.364468	+	0.210426i	−0.671039	−	0.741422i	$-0.734152\pi$
$499$	−8.14160	+	4.70056i	−0.364468	+	0.210426i	0.306571	+	0.951848i	$0.400818\pi$
$500$	−20.9200	+	11.9838i	−0.935570	+	0.535934i
$501$	−3.84812	+	6.66514i	−0.171921	+	0.297776i
$502$	34.5559	+	20.0290i	1.54231	+	0.893938i
$503$	40.9278			1.82488			0.912440	−	0.409211i	$-0.134196\pi$
$503$	40.9278			1.82488			0.912440	+	0.409211i	$0.134196\pi$
$504$		0			0
$505$	20.8883			0.929517
$506$	25.7515	+	14.9258i	1.14479	+	0.663534i
$507$	−6.38323	+	11.0561i	−0.283489	+	0.491018i
$508$	5.26891	−	3.01826i	0.233770	−	0.133913i
$509$	−12.4798	+	7.20520i	−0.553156	+	0.319365i	−0.750394	−	0.660991i	$-0.770136\pi$
$509$	−12.4798	+	7.20520i	−0.553156	+	0.319365i	0.197238	+	0.980356i	$0.436803\pi$
$510$	−11.4140	+	6.56415i	−0.505422	+	0.290665i
$511$		0			0
$512$	−0.344932	+	22.6248i	−0.0152440	+	0.999884i
$513$	0.609546	+	1.05577i	0.0269121	+	0.0466132i
$514$	−28.5141	−	0.0482984i	−1.25770	−	0.00213035i
$515$	15.6462	+	9.03336i	0.689456	+	0.398058i
$516$	−0.0237939	+	7.02363i	−0.00104747	+	0.309198i
$517$			70.7918i			3.11342i
$518$		0			0
$519$		−	0.823365i		−	0.0361417i
$520$	−4.33033	+	2.47087i	−0.189898	+	0.108355i
$521$	9.18855	+	5.30501i	0.402558	+	0.232417i	0.687587	−	0.726102i	$-0.258670\pi$
$521$	9.18855	+	5.30501i	0.402558	+	0.232417i	−0.285029	+	0.958519i	$0.592003\pi$
$522$	−0.0196872	+	11.6228i	−0.000861685	+	0.508716i
$523$	−18.1358	−	31.4121i	−0.793022	−	1.37355i	−0.924088	−	0.382181i	$-0.875173\pi$
$523$	−18.1358	−	31.4121i	−0.793022	−	1.37355i	0.131066	−	0.991374i	$-0.458160\pi$
$524$	−14.5514	+	25.0077i	−0.635679	+	1.09246i
$525$		0			0
$526$	8.81880	+	15.3345i	0.384518	+	0.668618i
$527$	13.9539	−	8.05631i	0.607843	−	0.350938i
$528$	−0.164510	+	24.2802i	−0.00715937	+	1.05666i
$529$	−5.48925	+	9.50766i	−0.238663	+	0.413377i
$530$	−6.79762	+	11.7279i	−0.295270	+	0.509428i
$531$	1.16160			0.0504092
$532$		0			0
$533$	−3.18667			−0.138030
$534$	8.71386	−	15.0340i	0.377086	−	0.650584i
$535$	−25.0369	+	43.3652i	−1.08244	+	1.87484i
$536$	−2.53395	+	4.33788i	−0.109450	+	0.187368i
$537$	−8.20383	+	4.73649i	−0.354022	+	0.204394i
$538$	−9.20401	−	16.0044i	−0.396813	−	0.689997i
$539$		0			0
$540$	−6.30540	−	3.66896i	−0.271341	−	0.157887i
$541$	11.8173	+	20.4682i	0.508065	+	0.879995i	0.999956	+	0.00933811i	$0.00297245\pi$
$541$	11.8173	+	20.4682i	0.508065	+	0.879995i	−0.491891	+	0.870657i	$0.663694\pi$
$542$	−0.0246574	+	14.5571i	−0.00105913	+	0.625281i
$543$	1.78504	+	1.03059i	0.0766034	+	0.0442270i
$544$	14.4386	+	0.122286i	0.619049	+	0.00524298i
$545$			49.7922i			2.13286i
$546$		0			0
$547$			40.9096i			1.74917i	0.484875	+	0.874583i	$0.338865\pi$
$547$			40.9096i			1.74917i	−0.484875	+	0.874583i	$0.661135\pi$
$548$	−23.1252	−	0.0783412i	−0.987860	−	0.00334657i
$549$	−0.180530	−	0.104229i	−0.00770482	−	0.00444838i
$550$	71.2932	+	0.120759i	3.03995	+	0.00514920i
$551$	5.00960	+	8.67688i	0.213416	+	0.369647i
$552$	9.80661	+	0.0498329i	0.417397	+	0.00212103i
$553$		0			0
$554$	−23.2466	+	13.3690i	−0.987652	+	0.567993i
$555$	−3.75959	+	2.17060i	−0.159586	+	0.0921369i
$556$	−17.5168	−	30.5787i	−0.742877	−	1.29683i
$557$	19.1391	−	33.1498i	0.810948	−	1.40460i	−0.101254	−	0.994861i	$-0.532285\pi$
$557$	19.1391	−	33.1498i	0.810948	−	1.40460i	0.912202	−	0.409742i	$-0.134381\pi$
$558$	7.72362	+	4.47669i	0.326967	+	0.189514i
$559$	1.69710			0.0717799
$560$		0			0
$561$	15.4942			0.654164
$562$	−21.4297	−	12.4209i	−0.903957	−	0.523944i
$563$	−2.28008	+	3.94921i	−0.0960939	+	0.166439i	−0.910065	−	0.414466i	$-0.863968\pi$
$563$	−2.28008	+	3.94921i	−0.0960939	+	0.166439i	0.813971	+	0.580906i	$0.197302\pi$
$564$	11.5937	+	20.2389i	0.488183	+	0.852212i
$565$	22.4903	−	12.9848i	0.946176	−	0.546275i
$566$	−23.2216	+	13.3546i	−0.976079	+	0.561337i
$567$		0			0
$568$	−25.8279	−	0.131246i	−1.08371	−	0.00550697i
$569$	−21.9078	−	37.9455i	−0.918425	−	1.59076i	−0.801808	−	0.597581i	$-0.796129\pi$
$569$	−21.9078	−	37.9455i	−0.918425	−	1.59076i	−0.116616	−	0.993177i	$-0.537205\pi$
$570$	−6.28863	−	0.0106519i	−0.263402	−	0.000446161i
$571$	−7.32046	−	4.22647i	−0.306352	−	0.176872i	0.338941	−	0.940808i	$-0.389931\pi$
$571$	−7.32046	−	4.22647i	−0.306352	−	0.176872i	−0.645293	+	0.763935i	$0.723265\pi$
$572$	5.86684	+	0.0198751i	0.245305	+	0.000831018i
$573$			10.8564i			0.453532i
$574$		0			0
$575$		−	28.7945i		−	1.20082i
$576$	3.92938	+	6.96850i	0.163724	+	0.290354i
$577$	−21.8371	−	12.6076i	−0.909089	−	0.524863i	−0.0289511	−	0.999581i	$-0.509217\pi$
$577$	−21.8371	−	12.6076i	−0.909089	−	0.524863i	−0.880138	+	0.474718i	$0.842550\pi$
$578$	−0.0251157	+	14.8277i	−0.00104468	+	0.616750i
$579$	−4.85673	−	8.41210i	−0.201839	−	0.349595i
$580$	−51.8214	−	30.1536i	−2.15176	−	1.25206i
$581$		0			0
$582$	−8.34587	−	14.5122i	−0.345947	−	0.601549i
$583$	13.8143	−	7.97569i	0.572130	−	0.330319i
$584$	−8.63016	+	14.7740i	−0.357118	+	0.611352i
$585$	−0.881351	+	1.52655i	−0.0364394	+	0.0631149i
$586$	−17.9252	+	30.9263i	−0.740485	+	1.27755i
$587$	−3.61615			−0.149254			−0.0746272	−	0.997212i	$-0.523777\pi$
$587$	−3.61615			−0.149254			−0.0746272	+	0.997212i	$0.523777\pi$
$588$		0			0
$589$	7.69551			0.317088
$590$	−3.00482	+	5.18420i	−0.123707	+	0.213430i
$591$	7.96498	−	13.7957i	0.327635	−	0.567481i
$592$	4.76053	+	0.0322548i	0.195657	+	0.00132566i
$593$	7.35701	−	4.24757i	0.302116	−	0.174427i	−0.341277	−	0.939963i	$-0.610859\pi$
$593$	7.35701	−	4.24757i	0.302116	−	0.174427i	0.643393	+	0.765536i	$0.277526\pi$
$594$	4.27968	+	7.44170i	0.175597	+	0.305337i
$595$		0			0
$596$	6.15052	−	10.5702i	0.251935	−	0.432970i
$597$	5.02859	+	8.70978i	0.205807	+	0.356467i
$598$	0.00401366	−	2.36956i	0.000164131	−	0.0968986i
$599$	−16.0128	−	9.24497i	−0.654264	−	0.377739i	0.135824	−	0.990733i	$-0.456632\pi$
$599$	−16.0128	−	9.24497i	−0.654264	−	0.377739i	−0.790088	+	0.612994i	$0.789965\pi$
$600$	20.4020	−	11.6413i	0.832909	−	0.475254i
$601$			31.5493i			1.28692i	0.765479	+	0.643461i	$0.222502\pi$
$601$			31.5493i			1.28692i	−0.765479	+	0.643461i	$0.777498\pi$
$602$		0			0
$603$			1.77617i			0.0723311i
$604$	−0.0964996	+	28.4853i	−0.00392651	+	1.15905i
$605$	−81.6488	−	47.1399i	−3.31949	−	1.91651i
$606$	−8.09865	−	0.0137178i	−0.328985	−	0.000557249i
$607$	7.76045	+	13.4415i	0.314987	+	0.545573i	0.979435	−	0.201761i	$-0.0646665\pi$
$607$	7.76045	+	13.4415i	0.314987	+	0.545573i	−0.664448	+	0.747335i	$0.731333\pi$
$608$	5.94289	+	3.49857i	0.241016	+	0.141886i
$609$		0			0
$610$	0.932164	−	0.536082i	0.0377422	−	0.0217053i
$611$	4.88074	−	2.81789i	0.197453	−	0.114000i
$612$	4.42968	−	2.53751i	0.179059	−	0.102573i
$613$	2.77406	−	4.80481i	0.112043	−	0.194064i	−0.804551	−	0.593884i	$-0.797594\pi$
$613$	2.77406	−	4.80481i	0.112043	−	0.194064i	0.916594	+	0.399820i	$0.130927\pi$
$614$	12.5360	+	7.26602i	0.505913	+	0.293233i
$615$	24.0529			0.969908
$616$		0			0
$617$	−32.3633			−1.30290			−0.651448	−	0.758693i	$-0.725838\pi$
$617$	−32.3633			−1.30290			−0.651448	+	0.758693i	$0.725838\pi$
$618$	−6.06031	−	3.51262i	−0.243781	−	0.141298i
$619$	−1.04453	+	1.80918i	−0.0419832	+	0.0727171i	−0.886253	−	0.463201i	$-0.846701\pi$
$619$	−1.04453	+	1.80918i	−0.0419832	+	0.0727171i	0.844270	+	0.535918i	$0.180034\pi$
$620$	−39.9588	+	22.8901i	−1.60478	+	0.919288i
$621$	3.00269	−	1.73360i	0.120494	−	0.0695670i
$622$	37.2486	−	21.4215i	1.49353	−	0.858923i
$623$		0			0
$624$	1.68055	−	0.955141i	0.0672757	−	0.0382362i
$625$	−1.22305	−	2.11839i	−0.0489220	−	0.0847354i
$626$	24.2134	+	0.0410137i	0.967763	+	0.00163924i
$627$	6.40870	+	3.70006i	0.255939	+	0.147766i
$628$	0.142940	−	42.1939i	0.00570393	−	1.68372i
$629$		−	3.03788i		−	0.121128i
$630$		0			0
$631$		−	37.2258i		−	1.48194i	−0.671541	−	0.740968i	$-0.734367\pi$
$631$		−	37.2258i		−	1.48194i	0.671541	−	0.740968i	$-0.265633\pi$
$632$	−4.45669	−	7.81061i	−0.177278	−	0.310689i
$633$	−0.893976	−	0.516137i	−0.0355324	−	0.0205146i
$634$	0.0296215	−	17.4877i	0.00117642	−	0.694526i
$635$	5.53719	+	9.59069i	0.219737	+	0.380595i
$636$	2.64322	−	4.54259i	0.104811	−	0.180125i
$637$		0			0
$638$	35.1728	+	61.1601i	1.39250	+	2.42135i
$639$	−7.90825	+	4.56583i	−0.312846	+	0.180621i
$640$	−41.2647	−	0.489294i	−1.63113	−	0.0193411i
$641$	5.78071	−	10.0125i	0.228324	−	0.395469i	−0.728987	−	0.684527i	$-0.760009\pi$
$641$	5.78071	−	10.0125i	0.228324	−	0.395469i	0.957312	+	0.289058i	$0.0933420\pi$
$642$	9.73559	−	16.7968i	0.384233	−	0.662916i
$643$	−5.82948			−0.229892			−0.114946	−	0.993372i	$-0.536670\pi$
$643$	−5.82948			−0.229892			−0.114946	+	0.993372i	$0.536670\pi$
$644$		0			0
$645$	−12.8097			−0.504381
$646$	2.20678	−	3.80734i	0.0868245	−	0.149798i
$647$	−23.1386	+	40.0772i	−0.909671	+	1.57560i	−0.0951507	+	0.995463i	$0.530333\pi$
$647$	−23.1386	+	40.0772i	−0.909671	+	1.57560i	−0.814521	+	0.580134i	$0.803000\pi$
$648$	2.44227	+	1.42664i	0.0959415	+	0.0560438i
$649$	6.10647	−	3.52557i	0.239700	−	0.138391i
$650$	−2.82953	−	4.92011i	−0.110983	−	0.192983i
$651$		0			0
$652$	−33.0813	−	19.2492i	−1.29556	−	0.753857i
$653$	−11.7881	−	20.4175i	−0.461303	−	0.798999i	0.537724	−	0.843121i	$-0.319284\pi$
$653$	−11.7881	−	20.4175i	−0.461303	−	0.798999i	−0.999026	+	0.0441218i	$0.985951\pi$
$654$	0.0326997	−	19.3050i	0.00127866	−	0.754887i
$655$	−45.6983	−	26.3839i	−1.78558	−	1.03091i
$656$	−22.7532	−	13.3429i	−0.888362	−	0.520953i
$657$			6.04928i			0.236005i
$658$		0			0
$659$		−	20.7935i		−	0.810001i	−0.914316	−	0.405001i	$-0.867271\pi$
$659$		−	20.7935i		−	0.810001i	0.914316	−	0.405001i	$-0.132729\pi$
$660$	−44.2828	−	0.150016i	−1.72370	−	0.00583938i
$661$	28.8226	+	16.6407i	1.12107	+	0.647249i	0.941674	−	0.336528i	$-0.109253\pi$
$661$	28.8226	+	16.6407i	1.12107	+	0.647249i	0.179395	+	0.983777i	$0.442586\pi$
$662$	−10.8639	−	0.0184018i	−0.422238	−	0.000715205i
$663$	−0.616751	−	1.06824i	−0.0239526	−	0.0414871i
$664$	−0.107772	+	21.2085i	−0.00418237	+	0.823048i
$665$		0			0
$666$	1.45907	−	0.839100i	0.0565376	−	0.0325144i
$667$	24.6778	−	14.2477i	0.955528	−	0.551674i
$668$	7.65104	+	13.3563i	0.296028	+	0.516770i
$669$	4.78625	−	8.29003i	0.185047	−	0.320511i
$670$	−7.92699	−	4.59457i	−0.306246	−	0.177504i
$671$	−1.26538			−0.0488494
$672$		0			0
$673$	−13.1796			−0.508037			−0.254019	−	0.967199i	$-0.581752\pi$
$673$	−13.1796			−0.508037			−0.254019	+	0.967199i	$0.581752\pi$
$674$	16.3788	+	9.49334i	0.630888	+	0.365670i
$675$	4.15242	−	7.19220i	0.159827	−	0.276828i
$676$	12.6915	+	22.1553i	0.488134	+	0.852127i
$677$	38.0749	−	21.9825i	1.46334	−	0.844858i	0.464173	−	0.885745i	$-0.346352\pi$
$677$	38.0749	−	21.9825i	1.46334	−	0.844858i	0.999164	+	0.0408865i	$0.0130182\pi$
$678$	−8.72831	+	5.01960i	−0.335209	+	0.192777i
$679$		0			0
$680$	−0.133816	+	26.3336i	−0.00513160	+	1.00985i
$681$	5.57692	+	9.65951i	0.213708	+	0.370153i
$682$	54.1898	+	0.0917890i	2.07504	+	0.00351478i
$683$	−10.3341	−	5.96637i	−0.395422	−	0.228297i	0.289085	−	0.957303i	$-0.406649\pi$
$683$	−10.3341	−	5.96637i	−0.395422	−	0.228297i	−0.684507	+	0.729007i	$0.739982\pi$
$684$	2.43817	+	0.00825978i	0.0932258	+	0.000315821i
$685$		−	42.1758i		−	1.61145i
$686$		0			0
$687$			10.1285i			0.386425i
$688$	12.1175	+	7.10593i	0.461975	+	0.270911i
$689$	−1.09977	−	0.634951i	−0.0418978	−	0.0241897i
$690$	−0.0302950	+	17.8854i	−0.00115331	+	0.680885i
$691$	18.6375	+	32.2811i	0.709003	+	1.22803i	0.965227	+	0.261412i	$0.0841882\pi$
$691$	18.6375	+	32.2811i	0.709003	+	1.22803i	−0.256224	+	0.966617i	$0.582478\pi$
$692$	−1.42331	−	0.828191i	−0.0541062	−	0.0314831i
$693$		0			0
$694$	−22.4754	−	39.0812i	−0.853154	−	1.48350i
$695$	55.6606	−	32.1357i	2.11133	−	1.21898i
$696$	20.0720	+	11.7250i	0.760826	+	0.444433i
$697$	−8.41586	+	14.5767i	−0.318773	+	0.552132i
$698$	−6.74880	+	11.6437i	−0.255446	+	0.440720i
$699$	12.6414			0.478143
$700$		0			0
$701$	−30.9151			−1.16765			−0.583823	−	0.811881i	$-0.698444\pi$
$701$	−30.9151			−1.16765			−0.583823	+	0.811881i	$0.698444\pi$
$702$	0.342713	−	0.591282i	0.0129349	−	0.0223165i
$703$	0.725457	−	1.25653i	0.0273611	−	0.0473909i
$704$	41.8066	+	24.7069i	1.57565	+	0.931177i
$705$	−36.8397	+	21.2694i	−1.38746	+	0.801052i
$706$	−9.96390	−	17.3257i	−0.374996	−	0.652061i
$707$		0			0
$708$	1.16841	−	2.00801i	0.0439116	−	0.0754655i
$709$	4.32776	+	7.49590i	0.162532	+	0.281514i	0.935776	−	0.352594i	$-0.114700\pi$
$709$	4.32776	+	7.49590i	0.162532	+	0.281514i	−0.773244	+	0.634109i	$0.781367\pi$
$710$	0.0797888	−	47.1052i	0.00299442	−	1.76783i
$711$	−2.75342	−	1.58969i	−0.103261	−	0.0596180i
$712$	−17.2236	−	30.1854i	−0.645482	−	1.13124i
$713$		−	21.8867i		−	0.819663i
$714$		0			0
$715$			10.6999i			0.400155i
$716$	−0.0641827	+	18.9458i	−0.00239862	+	0.708039i
$717$	4.72894	+	2.73025i	0.176605	+	0.101963i
$718$	31.7711	+	0.0538152i	1.18569	+	0.00200836i
$719$	−13.8268	−	23.9487i	−0.515653	−	0.893137i	−0.999835	−	0.0181697i	$-0.994216\pi$
$719$	−13.8268	−	23.9487i	−0.515653	−	0.893137i	0.484182	−	0.874967i	$-0.339117\pi$
$720$	−12.6847	+	7.20938i	−0.472732	+	0.268678i
$721$		0			0
$722$	−21.4709	+	12.3478i	−0.799064	+	0.459537i
$723$	−11.8106	+	6.81887i	−0.439242	+	0.253597i
$724$	3.57704	−	2.04908i	0.132940	−	0.0761535i
$725$	34.1269	−	59.1096i	1.26744	−	2.19527i
$726$	31.6253	+	18.3304i	1.17372	+	0.680303i
$727$	31.3975			1.16447			0.582235	−	0.813021i	$-0.302178\pi$
$727$	31.3975			1.16447			0.582235	+	0.813021i	$0.302178\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−26.9978	−	15.6482i	−0.999233	−	0.579167i
$731$	4.48198	−	7.76301i	0.165772	−	0.287125i
$732$	−0.361764	+	0.207233i	−0.0133712	+	0.00765957i
$733$	16.8834	−	9.74763i	0.623602	−	0.360037i	−0.154668	−	0.987966i	$-0.549431\pi$
$733$	16.8834	−	9.74763i	0.623602	−	0.360037i	0.778270	+	0.627930i	$0.216097\pi$
$734$	14.7102	−	8.45975i	0.542964	−	0.312255i
$735$		0			0
$736$	9.95023	−	16.9021i	0.366771	−	0.623019i
$737$	5.39083	+	9.33720i	0.198574	+	0.343940i
$738$	−9.32562	−	0.0157961i	−0.343281	−	0.000581463i
$739$	−34.2166	−	19.7550i	−1.25868	−	0.726698i	−0.285861	−	0.958271i	$-0.592280\pi$
$739$	−34.2166	−	19.7550i	−1.25868	−	0.726698i	−0.972818	+	0.231573i	$0.925613\pi$
$740$	−0.0294132	+	8.68235i	−0.00108125	+	0.319170i
$741$		−	0.589130i		−	0.0216422i
$742$		0			0
$743$			10.9193i			0.400590i	0.979736	+	0.200295i	$0.0641901\pi$
$743$			10.9193i			0.400590i	−0.979736	+	0.200295i	$0.935810\pi$
$744$	15.5075	−	8.84852i	0.568534	−	0.324403i
$745$	19.3156	+	11.1519i	0.707670	+	0.408573i
$746$	−0.0134807	+	7.95862i	−0.000493562	+	0.291386i
$747$	3.74921	+	6.49383i	0.137176	+	0.237597i
$748$	15.5850	−	26.7840i	0.569843	−	0.979321i
$749$		0			0
$750$	8.49890	+	14.7783i	0.310336	+	0.539627i
$751$	−26.2548	+	15.1582i	−0.958050	+	0.553130i	−0.895572	−	0.444916i	$-0.853233\pi$
$751$	−26.2548	+	15.1582i	−0.958050	+	0.553130i	−0.0624774	+	0.998046i	$0.519900\pi$
$752$	46.6477	+	0.316060i	1.70107	+	0.0115255i
$753$	14.1212	−	24.4587i	0.514606	−	0.891324i
$754$	2.81661	−	4.85949i	0.102575	−	0.176972i
$755$	−51.9515			−1.89071
$756$		0			0
$757$	18.4211			0.669526			0.334763	−	0.942302i	$-0.391344\pi$
$757$	18.4211			0.669526			0.334763	+	0.942302i	$0.391344\pi$
$758$	15.1308	−	26.1051i	0.549574	−	0.948178i
$759$	10.5233	−	18.2269i	0.381971	−	0.661594i
$760$	−6.34390	+	10.8601i	−0.230118	+	0.393939i
$761$	−29.0996	+	16.8007i	−1.05486	+	0.609023i	−0.924006	−	0.382379i	$-0.875105\pi$
$761$	−29.0996	+	16.8007i	−1.05486	+	0.609023i	−0.130853	+	0.991402i	$0.541772\pi$
$762$	−2.14054	−	3.72206i	−0.0775435	−	0.134836i
$763$		0			0
$764$	18.7669	+	10.9200i	0.678964	+	0.395073i
$765$	4.65522	+	8.06307i	0.168310	+	0.291521i
$766$	0.0180902	−	10.6800i	0.000653625	−	0.385883i
$767$	−0.486141	−	0.280674i	−0.0175535	−	0.0101345i
$768$	15.9985	+	0.216805i	0.577297	+	0.00782328i
$769$		−	0.776682i		−	0.0280079i	−0.999902	−	0.0140039i	$-0.995542\pi$
$769$		−	0.776682i		−	0.0280079i	0.999902	−	0.0140039i	$-0.00445774\pi$
$770$		0			0
$771$			20.1625i			0.726136i
$772$	−19.4268	−	0.0658121i	−0.699186	−	0.00236863i
$773$	17.6333	+	10.1806i	0.634225	+	0.366170i	0.782387	−	0.622793i	$-0.214002\pi$
$773$	17.6333	+	10.1806i	0.634225	+	0.366170i	−0.148161	+	0.988963i	$0.547335\pi$
$774$	4.96648	+	0.00841243i	0.178516	+	0.000302379i
$775$	−26.2121	−	45.4007i	−0.941566	−	1.63084i
$776$	−33.4813	−	0.170138i	−1.20191	−	0.00610758i
$777$		0			0
$778$	−3.24949	+	1.86876i	−0.116500	+	0.0669984i
$779$	−6.96194	+	4.01948i	−0.249438	+	0.144013i
$780$	1.75235	+	3.05904i	0.0627442	+	0.109531i
$781$	−27.7155	+	48.0046i	−0.991738	+	1.71774i
$782$	−10.8284	−	6.27626i	−0.387223	−	0.224439i
$783$	8.21857			0.293708
$784$		0			0
$785$	76.9532			2.74658
$786$	17.7005	+	10.2594i	0.631355	+	0.365940i
$787$	−24.3908	+	42.2461i	−0.869437	+	1.50591i	−0.00686444	+	0.999976i	$0.502185\pi$
$787$	−24.3908	+	42.2461i	−0.869437	+	1.50591i	−0.862573	+	0.505933i	$0.831148\pi$
$788$	−15.8364	−	27.6453i	−0.564148	−	0.984823i
$789$	10.8326	−	6.25419i	0.385650	−	0.222655i
$790$	14.2173	−	8.17628i	0.505828	−	0.290899i
$791$		0			0
$792$	17.1689	+	0.0872448i	0.610070	+	0.00310011i
$793$	0.0503689	+	0.0872415i	0.00178865	+	0.00309804i
$794$	−26.3753	−	0.0446755i	−0.936023	−	0.00158548i
$795$	8.30101	+	4.79259i	0.294407	+	0.169976i
$796$	20.1143	+	0.0681409i	0.712931	+	0.00241519i
$797$		−	5.84706i		−	0.207113i	−0.994624	−	0.103557i	$-0.966978\pi$
$797$		−	5.84706i		−	0.207113i	0.994624	−	0.103557i	$-0.0330223\pi$
$798$		0			0
$799$		−	29.7677i		−	1.05311i
$800$	0.397872	−	46.9776i	0.0140669	−	1.66091i
$801$	−10.6411	−	6.14362i	−0.375983	−	0.217074i
$802$	0.0571275	−	33.7266i	0.00201724	−	1.19093i
$803$	18.3601	+	31.8007i	0.647915	+	1.12222i
$804$	3.07037	+	1.78658i	0.108284	+	0.0630077i
$805$		0			0
$806$	−2.15072	−	3.73977i	−0.0757558	−	0.131728i
$807$	−11.3057	+	6.52738i	−0.397981	+	0.229775i
$808$	−8.16984	+	13.9860i	−0.287414	+	0.492025i
$809$	−12.5937	+	21.8130i	−0.442772	+	0.766903i	−0.997894	−	0.0648654i	$-0.979338\pi$
$809$	−12.5937	+	21.8130i	−0.442772	+	0.766903i	0.555122	+	0.831769i	$0.312672\pi$
$810$	−2.58679	+	4.46298i	−0.0908906	+	0.156813i
$811$	12.4012			0.435465			0.217733	−	0.976008i	$-0.430134\pi$
$811$	12.4012			0.435465			0.217733	+	0.976008i	$0.430134\pi$
$812$		0			0
$813$	10.2934			0.361006
$814$	5.12347	−	8.83950i	0.179578	−	0.309824i
$815$	34.9019	−	60.4519i	1.22256	−	2.11754i
$816$	0.0691759	−	10.2098i	0.00242164	−	0.357413i
$817$	3.70767	−	2.14063i	0.129715	−	0.0748910i
$818$	12.2865	+	21.3644i	0.429588	+	0.746988i
$819$		0			0
$820$	24.1939	−	41.5792i	0.844889	−	1.45201i
$821$	−7.13932	−	12.3657i	−0.249164	−	0.431564i	0.714130	−	0.700013i	$-0.246822\pi$
$821$	−7.13932	−	12.3657i	−0.249164	−	0.431564i	−0.963294	+	0.268448i	$0.913489\pi$
$822$	−0.0276978	+	16.3521i	−0.000966072	+	0.570344i
$823$	12.2752	+	7.08709i	0.427887	+	0.247040i	0.698446	−	0.715663i	$-0.253875\pi$
$823$	12.2752	+	7.08709i	0.427887	+	0.247040i	−0.270559	+	0.962703i	$0.587209\pi$
$824$	−12.1679	+	6.94296i	−0.423890	+	0.241870i
$825$		−	50.4119i		−	1.75512i
$826$		0			0
$827$			25.5816i			0.889559i	0.895640	+	0.444779i	$0.146718\pi$
$827$			25.5816i			0.889559i	−0.895640	+	0.444779i	$0.853282\pi$
$828$	0.0234915	−	6.93437i	0.000816387	−	0.240986i
$829$	35.2159	+	20.3319i	1.22310	+	0.706156i	0.965577	−	0.260117i	$-0.0837611\pi$
$829$	35.2159	+	20.3319i	1.22310	+	0.706156i	0.257521	+	0.966273i	$0.417094\pi$
$830$	−38.6802	−	0.0655182i	−1.34261	−	0.00227417i
$831$	9.48111	+	16.4218i	0.328896	+	0.569665i
$832$	0.0392899	−	3.86582i	0.00136213	−	0.134023i
$833$		0			0
$834$	−21.6014	+	12.4228i	−0.747996	+	0.430168i
$835$	−24.3116	+	14.0363i	−0.841338	+	0.485747i
$836$	12.8424	−	7.35666i	0.444163	−	0.254436i
$837$	3.15625	−	5.46678i	0.109096	−	0.188959i
$838$	−32.5644	−	18.8747i	−1.12492	−	0.652016i
$839$	24.4293			0.843394			0.421697	−	0.906737i	$-0.361435\pi$
$839$	24.4293			0.843394			0.421697	+	0.906737i	$0.361435\pi$
$840$		0			0
$841$	38.5449			1.32913
$842$	−21.0690	−	12.2118i	−0.726086	−	0.420848i
$843$	−8.75722	+	15.1679i	−0.301615	+	0.522412i
$844$	−1.79144	+	1.02621i	−0.0616639	+	0.0353237i
$845$	−40.3279	+	23.2833i	−1.38732	+	0.800972i
$846$	14.2972	−	8.22221i	0.491547	−	0.282686i
$847$		0			0
$848$	−5.19384	−	9.13844i	−0.178357	−	0.313815i
$849$	9.47095	+	16.4042i	0.325042	+	0.562990i
$850$	−29.9786	−	0.0507789i	−1.02826	−	0.00174170i
$851$	−3.57368	−	2.06326i	−0.122504	−	0.0707277i
$852$	−0.0618702	+	18.2632i	−0.00211964	+	0.625687i
$853$			21.6039i			0.739705i	0.929091	+	0.369852i	$0.120592\pi$
$853$			21.6039i			0.739705i	−0.929091	+	0.369852i	$0.879408\pi$
$854$		0			0
$855$			4.44674i			0.152075i
$856$	−19.2431	−	33.7247i	−0.657717	−	1.15269i
$857$	−2.05943	−	1.18901i	−0.0703487	−	0.0406159i	0.464413	−	0.885619i	$-0.346265\pi$
$857$	−2.05943	−	1.18901i	−0.0703487	−	0.0406159i	−0.534762	+	0.845003i	$0.679599\pi$
$858$	0.00702691	−	4.14850i	0.000239895	−	0.141627i
$859$	20.9336	+	36.2580i	0.714244	+	1.23711i	0.963250	+	0.268605i	$0.0865626\pi$
$859$	20.9336	+	36.2580i	0.714244	+	1.23711i	−0.249007	+	0.968502i	$0.580104\pi$
$860$	−12.8848	+	22.1435i	−0.439368	+	0.755088i
$861$		0			0
$862$	13.8771	+	24.1301i	0.472656	+	0.821876i
$863$	−34.4456	+	19.8872i	−1.17254	+	0.676967i	−0.954277	−	0.298923i	$-0.903373\pi$
$863$	−34.4456	+	19.8872i	−1.17254	+	0.676967i	−0.218263	+	0.975890i	$0.570039\pi$
$864$	4.92276	−	2.78684i	0.167476	−	0.0948101i
$865$	1.50164	−	2.60092i	0.0510574	−	0.0884341i
$866$	−4.56224	+	7.87120i	−0.155031	+	0.267474i
$867$	10.4848			0.356081
$868$		0			0
$869$	−19.2995			−0.654689
$870$	−21.2597	+	36.6793i	−0.720772	+	1.24354i
$871$	0.429168	−	0.743342i	0.0145418	−	0.0251872i
$872$	−33.3388	−	19.4747i	−1.12900	−	0.659498i
$873$	−10.2517	+	5.91879i	−0.346966	+	0.200321i
$874$	−2.98006	−	5.18186i	−0.100802	−	0.175279i
$875$		0			0
$876$	10.4571	+	6.08474i	0.353313	+	0.205584i
$877$	−13.3590	−	23.1385i	−0.451102	−	0.781331i	0.547353	−	0.836902i	$-0.315635\pi$
$877$	−13.3590	−	23.1385i	−0.451102	−	0.781331i	−0.998455	+	0.0555709i	$0.982302\pi$
$878$	0.0166568	−	9.83371i	0.000562138	−	0.331872i
$879$	21.8897	+	12.6380i	0.738320	+	0.426269i
$880$	−44.8017	+	76.3987i	−1.51026	+	2.57540i
$881$			39.2357i			1.32188i	0.750437	+	0.660942i	$0.229843\pi$
$881$			39.2357i			1.32188i	−0.750437	+	0.660942i	$0.770157\pi$
$882$		0			0
$883$		−	57.7837i		−	1.94458i	−0.233783	−	0.972289i	$-0.575111\pi$
$883$		−	57.7837i		−	1.94458i	0.233783	−	0.972289i	$-0.424889\pi$
$884$	−2.46699	−	0.00835740i	−0.0829738	−	0.000281090i
$885$	3.66938	+	2.11852i	0.123345	+	0.0712132i
$886$	−11.0084	−	0.0186465i	−0.369835	−	0.000626442i
$887$	−24.9877	−	43.2800i	−0.839005	−	1.45320i	−0.890727	−	0.454538i	$-0.849804\pi$
$887$	−24.9877	−	43.2800i	−0.839005	−	1.45320i	0.0517223	−	0.998662i	$-0.483529\pi$
$888$	0.0171057	−	3.36624i	0.000574031	−	0.112963i
$889$		0			0
$890$	54.9450	−	31.5986i	1.84176	−	1.05919i
$891$	5.25694	−	3.03510i	0.176114	−	0.101680i
$892$	−9.51628	−	16.6124i	−0.318629	−	0.556224i
$893$	7.10865	−	12.3125i	0.237882	−	0.412023i
$894$	−7.48158	−	4.33641i	−0.250222	−	0.145031i
$895$	−34.5534			−1.15499
$896$		0			0
$897$	−1.67554			−0.0559445
$898$	16.4449	+	9.53164i	0.548773	+	0.318075i
$899$	25.9398	−	44.9291i	0.865141	−	1.49847i
$900$	−8.25606	−	14.4124i	−0.275202	−	0.480415i
$901$	−5.80887	+	3.35375i	−0.193522	+	0.111730i
$902$	−49.0722	+	28.2211i	−1.63392	+	0.939660i
$903$		0			0
$904$	−0.102329	+	20.1372i	−0.00340340	+	0.669755i
$905$	3.75917	+	6.51107i	0.124959	+	0.216435i
$906$	20.1423	+	0.0341178i	0.669182	+	0.00113349i
$907$	13.4055	+	7.73965i	0.445121	+	0.256991i	0.705768	−	0.708444i	$-0.250602\pi$
$907$	13.4055	+	7.73965i	0.445121	+	0.256991i	−0.260646	+	0.965434i	$0.583936\pi$
$908$	22.3076	+	0.0755712i	0.740302	+	0.00250792i
$909$			5.72662i			0.189940i
$910$		0			0
$911$			2.22992i			0.0738807i	0.999317	+	0.0369403i	$0.0117612\pi$
$911$			2.22992i			0.0738807i	−0.999317	+	0.0369403i	$0.988239\pi$
$912$	2.46674	−	4.20644i	0.0816820	−	0.139289i
$913$	39.4188	+	22.7584i	1.30457	+	0.753194i
$914$	0.00278747	−	1.64565i	9.22013e−5	−	0.0544332i
$915$	−0.380183	−	0.658497i	−0.0125685	−	0.0217692i
$916$	17.5086	+	10.1878i	0.578500	+	0.336616i
$917$		0			0
$918$	−1.79959	−	3.12921i	−0.0593953	−	0.103279i
$919$	−26.1682	+	15.1082i	−0.863211	+	0.498375i	−0.865086	−	0.501623i	$-0.832736\pi$
$919$	−26.1682	+	15.1082i	−0.863211	+	0.498375i	0.00187547	+	0.999998i	$0.499403\pi$
$920$	30.8872	+	18.0426i	1.01832	+	0.594847i
$921$	5.12283	−	8.87300i	0.168803	−	0.292375i
$922$	−15.1914	+	26.2096i	−0.500302	+	0.863169i
$923$	4.41290			0.145252
$924$		0			0
$925$	−9.88408			−0.324986
$926$	−10.2411	+	17.6689i	−0.336544	+	0.580637i
$927$	−2.47654	+	4.28949i	−0.0813401	+	0.140885i
$928$	40.4580	−	22.9038i	1.32810	−	0.751854i
$929$	2.41731	−	1.39564i	0.0793095	−	0.0457894i	−0.459821	−	0.888012i	$-0.652086\pi$
$929$	2.41731	−	1.39564i	0.0793095	−	0.0457894i	0.539130	+	0.842222i	$0.318753\pi$
$930$	16.2336	+	28.2277i	0.532320	+	0.925622i
$931$		0			0
$932$	12.7155	−	21.8527i	0.416511	−	0.715808i
$933$	−15.1919	−	26.3131i	−0.497359	−	0.861451i
$934$	−0.0713028	+	42.0953i	−0.00233310	+	1.37740i
$935$	48.9444	+	28.2581i	1.60065	+	0.924138i
$936$	−0.677399	−	1.18718i	−0.0221415	−	0.0388042i
$937$			13.5645i			0.443133i	0.975145	+	0.221566i	$0.0711169\pi$
$937$			13.5645i			0.443133i	−0.975145	+	0.221566i	$0.928883\pi$
$938$		0			0
$939$		−	17.1215i		−	0.558739i
$940$	−0.288215	+	85.0771i	−0.00940054	+	2.77491i
$941$	22.7548	+	13.1375i	0.741787	+	0.428271i	0.822719	−	0.568449i	$-0.192456\pi$
$941$	22.7548	+	13.1375i	0.741787	+	0.428271i	−0.0809319	+	0.996720i	$0.525790\pi$
$942$	−29.8357	−	0.0505370i	−0.972100	−	0.00164658i
$943$	11.4317	+	19.8004i	0.372269	+	0.644789i
$944$	−2.29589	−	4.03956i	−0.0747248	−	0.131476i
$945$		0			0
$946$	26.1340	−	15.0295i	0.849690	−	0.488652i
$947$	7.80904	−	4.50855i	0.253760	−	0.146508i	−0.367725	−	0.929935i	$-0.619863\pi$
$947$	7.80904	−	4.50855i	0.253760	−	0.146508i	0.621485	+	0.783426i	$0.286530\pi$
$948$	−5.51759	+	3.16071i	−0.179203	+	0.102655i
$949$	1.46167	−	2.53168i	0.0474477	−	0.0821818i
$950$	−12.3876	−	7.18000i	−0.401907	−	0.232950i
$951$	−12.3657			−0.400986
$952$		0			0
$953$	5.49448			0.177984			0.0889918	−	0.996032i	$-0.471636\pi$
$953$	5.49448			0.177984			0.0889918	+	0.996032i	$0.471636\pi$
$954$	−3.21526	−	1.86360i	−0.104098	−	0.0603362i
$955$	−19.7998	+	34.2942i	−0.640706	+	1.10973i
$956$	9.47631	−	5.42843i	0.306486	−	0.175568i
$957$	43.2045	−	24.9442i	1.39660	−	0.806330i
$958$	−34.7618	+	19.9913i	−1.12310	+	0.645889i
$959$		0			0
$960$	−0.296559	+	29.1791i	−0.00957140	+	0.941752i
$961$	−4.42377	−	7.66220i	−0.142702	−	0.247168i
$962$	−0.813381	−	0.00137774i	−0.0262244	−	4.44201e-5i
$963$	−11.8888	−	6.86398i	−0.383110	−	0.221189i
$964$	−0.0924005	+	27.2753i	−0.00297602	+	0.878479i
$965$		−	35.4306i		−	1.14055i
$966$		0			0
$967$			45.1993i			1.45351i	0.686896	+	0.726756i	$0.258973\pi$
$967$			45.1993i			1.45351i	−0.686896	+	0.726756i	$0.741027\pi$
$968$	63.4975	−	36.2313i	2.04089	−	1.16452i
$969$	−2.69484	−	1.55587i	−0.0865707	−	0.0499816i
$970$	0.103432	−	61.0636i	0.00332100	−	1.96063i
$971$	−20.5279	−	35.5554i	−0.658772	−	1.14103i	−0.980934	−	0.194342i	$-0.937743\pi$
$971$	−20.5279	−	35.5554i	−0.658772	−	1.14103i	0.322162	−	0.946685i	$-0.395591\pi$
$972$	1.00586	−	1.72865i	0.0322630	−	0.0554466i
$973$		0			0
$974$	−6.74564	−	11.7296i	−0.216144	−	0.375842i
$975$	−3.47565	+	2.00667i	−0.111310	+	0.0642648i
$976$	−0.00564947	+	0.833812i	−0.000180835	+	0.0266897i
$977$	−28.6096	+	49.5532i	−0.915301	+	1.58535i	−0.108842	+	0.994059i	$0.534714\pi$
$977$	−28.6096	+	49.5532i	−0.915301	+	1.58535i	−0.806459	+	0.591289i	$0.798619\pi$
$978$	−13.5716	+	23.4150i	−0.433972	+	0.748730i
$979$	−74.5859			−2.38378
$980$		0			0
$981$	−13.6507			−0.435835
$982$	−12.5894	+	21.7205i	−0.401745	+	0.693129i
$983$	26.1872	−	45.3575i	0.835241	−	1.44668i	−0.0585929	−	0.998282i	$-0.518661\pi$
$983$	26.1872	−	45.3575i	0.835241	−	1.44668i	0.893834	−	0.448398i	$-0.148005\pi$
$984$	−9.40759	+	16.1049i	−0.299903	+	0.513405i
$985$	50.3211	−	29.0529i	1.60336	−	0.925702i
$986$	−14.7901	−	25.7176i	−0.471011	−	0.819016i
$987$		0			0
$988$	−1.01840	−	0.592583i	−0.0323997	−	0.0188526i
$989$	−6.08812	−	10.5449i	−0.193591	−	0.335310i
$990$	−0.0530389	+	31.3128i	−0.00168569	+	0.995185i
$991$	51.5895	+	29.7852i	1.63879	+	0.946158i	0.981249	+	0.192743i	$0.0617383\pi$
$991$	51.5895	+	29.7852i	1.63879	+	0.946158i	0.657545	+	0.753415i	$0.271595\pi$
$992$	0.302422	−	35.7076i	0.00960190	−	1.13372i
$993$			7.68197i			0.243780i
$994$		0			0
$995$			36.6844i			1.16297i
$996$	14.9968	+	0.0508044i	0.475191	+	0.00160980i
$997$	−28.0159	−	16.1750i	−0.887274	−	0.512268i	−0.0142239	−	0.999899i	$-0.504528\pi$
$997$	−28.0159	−	16.1750i	−0.887274	−	0.512268i	−0.873050	+	0.487631i	$0.837861\pi$
$998$	13.2952	+	0.0225199i	0.420851	+	0.000712855i
$999$	−0.595080	−	1.03071i	−0.0188275	−	0.0326102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.e.31.3		24
4.3	odd	2		588.2.o.f.31.8		24
7.2	even	3	inner	588.2.o.e.19.8		24
7.3	odd	6		588.2.b.c.391.9	✓	12
7.4	even	3		588.2.b.d.391.9	yes	12
7.5	odd	6		588.2.o.f.19.8		24
7.6	odd	2		588.2.o.f.31.3		24
21.11	odd	6		1764.2.b.m.1567.4		12
21.17	even	6		1764.2.b.l.1567.4		12
28.3	even	6		588.2.b.d.391.10	yes	12
28.11	odd	6		588.2.b.c.391.10	yes	12
28.19	even	6	inner	588.2.o.e.19.3		24
28.23	odd	6		588.2.o.f.19.3		24
28.27	even	2	inner	588.2.o.e.31.8		24
84.11	even	6		1764.2.b.l.1567.3		12
84.59	odd	6		1764.2.b.m.1567.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.9	✓	12	7.3	odd	6
588.2.b.c.391.10	yes	12	28.11	odd	6
588.2.b.d.391.9	yes	12	7.4	even	3
588.2.b.d.391.10	yes	12	28.3	even	6
588.2.o.e.19.3		24	28.19	even	6	inner
588.2.o.e.19.8		24	7.2	even	3	inner
588.2.o.e.31.3		24	1.1	even	1	trivial
588.2.o.e.31.8		24	28.27	even	2	inner
588.2.o.f.19.3		24	28.23	odd	6
588.2.o.f.19.8		24	7.5	odd	6
588.2.o.f.31.3		24	7.6	odd	2
588.2.o.f.31.8		24	4.3	odd	2
1764.2.b.l.1567.3		12	84.11	even	6
1764.2.b.l.1567.4		12	21.17	even	6
1764.2.b.m.1567.3		12	84.59	odd	6
1764.2.b.m.1567.4		12	21.11	odd	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 $\F_{q}$
Belyi maps

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+(-1.22355 - 0.709180i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.994127 + 1.73543i) q^{4} +(-3.15890 + 1.82379i) q^{5} +(1.22594 - 0.705031i) q^{6} +(0.0143727 - 2.82839i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(5.15845 + 0.00873760i) q^{10} +(-5.25694 - 3.03510i) q^{11} +(-1.99999 - 0.00677535i) q^{12} +0.483253i q^{13} -3.64758i q^{15} +(-2.02342 + 3.45047i) q^{16} +(2.21053 + 1.27625i) q^{17} +(-0.00239545 + 1.41421i) q^{18} +(0.609546 + 1.05577i) q^{19} +(-6.30540 - 3.66896i) q^{20} +(4.27968 + 7.44170i) q^{22} +(3.00269 - 1.73360i) q^{23} +(2.44227 + 1.42664i) q^{24} +(4.15242 - 7.19220i) q^{25} +(0.342713 - 0.591282i) q^{26} +1.00000 q^{27} +8.21857 q^{29} +(-2.58679 + 4.46298i) q^{30} +(3.15625 - 5.46678i) q^{31} +(4.92276 - 2.78684i) q^{32} +(5.25694 - 3.03510i) q^{33} +(-1.79959 - 3.12921i) q^{34} +(1.00586 - 1.72865i) q^{36} +(-0.595080 - 1.03071i) q^{37} +(0.00292028 - 1.72405i) q^{38} +(-0.418509 - 0.241626i) q^{39} +(5.11299 + 8.96081i) q^{40} +6.59422i q^{41} -3.51184i q^{43} +(0.0411277 - 12.1403i) q^{44} +(3.15890 + 1.82379i) q^{45} +(-4.90336 - 0.00830552i) q^{46} +(-5.83110 - 10.0998i) q^{47} +(-1.97648 - 3.47757i) q^{48} +(-10.1812 + 5.85517i) q^{50} +(-2.21053 + 1.27625i) q^{51} +(-0.838651 + 0.480414i) q^{52} +(-1.31391 + 2.27576i) q^{53} +(-1.22355 - 0.709180i) q^{54} +22.1415 q^{55} -1.21909 q^{57} +(-10.0558 - 5.82845i) q^{58} +(-0.580801 + 1.00598i) q^{59} +(6.33011 - 3.62616i) q^{60} +(0.180530 - 0.104229i) q^{61} +(-7.73874 + 4.45050i) q^{62} +(-7.99959 - 0.0813030i) q^{64} +(-0.881351 - 1.52655i) q^{65} +(-8.58454 - 0.0145409i) q^{66} +(-1.53820 - 0.888083i) q^{67} +(-0.0172941 + 5.10497i) q^{68} +3.46720i q^{69} -9.13166i q^{71} +(-2.45664 + 1.40175i) q^{72} +(-5.23883 - 3.02464i) q^{73} +(-0.00285097 + 1.68314i) q^{74} +(4.15242 + 7.19220i) q^{75} +(-1.22624 + 2.10739i) q^{76} +(0.340708 + 0.592439i) q^{78} +(2.75342 - 1.58969i) q^{79} +(0.0988539 - 14.5900i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.67649 - 8.06832i) q^{82} -7.49842 q^{83} -9.31044 q^{85} +(-2.49052 + 4.29689i) q^{86} +(-4.10928 + 7.11749i) q^{87} +(-8.66000 + 14.8251i) q^{88} +(10.6411 - 6.14362i) q^{89} +(-2.57166 - 4.47172i) q^{90} +(5.99359 + 3.48753i) q^{92} +(3.15625 + 5.46678i) q^{93} +(-0.0279362 + 16.4928i) q^{94} +(-3.85099 - 2.22337i) q^{95} +(-0.0479085 + 5.65665i) q^{96} -11.8376i q^{97} +6.07019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 12 q^{3} + 4 q^{4} + 8 q^{6} + 8 q^{8} - 12 q^{9} + 4 q^{12} + 4 q^{16} - 4 q^{18} - 48 q^{20} - 4 q^{24} + 12 q^{25} - 24 q^{26} + 24 q^{27} + 64 q^{29} - 16 q^{31} - 4 q^{32} + 64 q^{34}+ \cdots - 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 - 12 * q^3 + 4 * q^4 + 8 * q^6 + 8 * q^8 - 12 * q^9 + 4 * q^12 + 4 * q^16 - 4 * q^18 - 48 * q^20 - 4 * q^24 + 12 * q^25 - 24 * q^26 + 24 * q^27 + 64 * q^29 - 16 * q^31 - 4 * q^32 + 64 * q^34 - 8 * q^36 - 32 * q^37 + 24 * q^38 + 32 * q^40 + 24 * q^44 - 24 * q^46 - 8 * q^48 - 56 * q^50 - 32 * q^52 + 32 * q^53 - 4 * q^54 + 32 * q^55 - 16 * q^58 + 16 * q^59 + 24 * q^60 + 16 * q^62 - 8 * q^64 + 8 * q^68 - 4 * q^72 + 32 * q^74 + 12 * q^75 - 64 * q^76 + 48 * q^78 + 16 * q^80 - 12 * q^81 - 32 * q^82 - 32 * q^83 + 32 * q^85 + 24 * q^86 - 32 * q^87 - 24 * q^88 - 16 * q^93 - 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

Properties

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