LMFDB - Embedded newform 925.2.bb.e.151.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(151,925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("925.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			151.13
Character	$\chi$	$=$	925.151
Dual form			925.2.bb.e.876.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07021 - 1.27542i) q^{2} +(1.97419 - 1.65654i) q^{3} +(-0.134064 - 0.760312i) q^{4} -4.29076i q^{6} +(0.133008 + 0.0484108i) q^{7} +(1.77057 + 1.02224i) q^{8} +(0.632347 - 3.58622i) q^{9} +(0.715450 - 1.23920i) q^{11} +(-1.52415 - 1.27892i) q^{12} +(1.85629 - 0.327315i) q^{13} +(0.204090 - 0.117831i) q^{14} +(4.64963 - 1.69233i) q^{16} +(-0.482371 - 0.0850551i) q^{17} +(-3.89720 - 4.64450i) q^{18} +(-1.87580 - 2.23549i) q^{19} +(0.342776 - 0.124760i) q^{21} +(-0.814818 - 2.23869i) q^{22} +(-7.07485 + 4.08466i) q^{23} +(5.18883 - 0.914931i) q^{24} +(1.56915 - 2.71785i) q^{26} +(-0.826667 - 1.43183i) q^{27} +(0.0189758 - 0.107617i) q^{28} +(3.23140 + 1.86565i) q^{29} +1.31432i q^{31} +(1.41912 - 3.89901i) q^{32} +(-0.640345 - 3.63158i) q^{33} +(-0.624718 + 0.524201i) q^{34} -2.81142 q^{36} +(-5.86718 - 1.60505i) q^{37} -4.85869 q^{38} +(3.12246 - 3.72121i) q^{39} +(-1.00565 - 5.70332i) q^{41} +(0.207719 - 0.570704i) q^{42} +11.0186i q^{43} +(-1.03809 - 0.377834i) q^{44} +(-2.36187 + 13.3948i) q^{46} +(-5.09207 - 8.81972i) q^{47} +(6.37584 - 11.0433i) q^{48} +(-5.34696 - 4.48664i) q^{49} +(-1.09319 + 0.631153i) q^{51} +(-0.497723 - 1.36748i) q^{52} +(1.41611 - 0.515423i) q^{53} +(-2.71089 - 0.478003i) q^{54} +(0.186012 + 0.221681i) q^{56} +(-7.40637 - 1.30594i) q^{57} +(5.83775 - 2.12477i) q^{58} +(4.60589 + 12.6546i) q^{59} +(-6.91487 + 1.21928i) q^{61} +(1.67631 + 1.40659i) q^{62} +(0.257719 - 0.446382i) q^{63} +(1.49391 + 2.58753i) q^{64} +(-5.31709 - 3.06982i) q^{66} +(14.5595 + 5.29924i) q^{67} +0.378156i q^{68} +(-7.20066 + 19.7837i) q^{69} +(-2.86044 + 2.40019i) q^{71} +(4.78560 - 5.70326i) q^{72} -2.49025 q^{73} +(-8.32621 + 5.76539i) q^{74} +(-1.44820 + 1.72589i) q^{76} +(0.155151 - 0.130187i) q^{77} +(-1.40443 - 7.96491i) q^{78} +(4.55510 - 12.5150i) q^{79} +(6.26191 + 2.27915i) q^{81} +(-8.35039 - 4.82110i) q^{82} +(-1.44890 + 8.21712i) q^{83} +(-0.140811 - 0.243891i) q^{84} +(14.0533 + 11.7922i) q^{86} +(9.46991 - 1.66980i) q^{87} +(2.53351 - 1.46273i) q^{88} +(1.86850 + 5.13365i) q^{89} +(0.262747 + 0.0463293i) q^{91} +(4.05410 + 4.83149i) q^{92} +(2.17722 + 2.59471i) q^{93} +(-16.6984 - 2.94438i) q^{94} +(-3.65725 - 10.0482i) q^{96} +(0.475449 - 0.274500i) q^{97} +(-11.4447 + 2.01801i) q^{98} +(-3.99161 - 3.34936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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 $

$2$	1.07021	−	1.27542i	0.756750	−	0.901859i	−0.240888	−	0.970553i	$-0.577439\pi$
$2$	1.07021	−	1.27542i	0.756750	−	0.901859i	0.997638	+	0.0686936i	$0.0218831\pi$
$3$	1.97419	−	1.65654i	1.13980	−	0.956404i	0.140366	−	0.990100i	$-0.455172\pi$
$3$	1.97419	−	1.65654i	1.13980	−	0.956404i	0.999432	+	0.0336957i	$0.0107277\pi$
$4$	−0.134064	−	0.760312i	−0.0670318	−	0.380156i
$5$		0			0
$5$		0			0
$6$		−	4.29076i		−	1.75170i
$7$	0.133008	+	0.0484108i	0.0502721	+	0.0182976i	0.367034	−	0.930208i	$-0.380373\pi$
$7$	0.133008	+	0.0484108i	0.0502721	+	0.0182976i	−0.316762	+	0.948505i	$0.602596\pi$
$8$	1.77057	+	1.02224i	0.625993	+	0.361417i
$9$	0.632347	−	3.58622i	0.210782	−	1.19541i
$10$		0			0
$11$	0.715450	−	1.23920i	0.215716	−	0.373631i	−0.737778	−	0.675044i	$-0.764125\pi$
$11$	0.715450	−	1.23920i	0.215716	−	0.373631i	0.953494	+	0.301412i	$0.0974581\pi$
$12$	−1.52415	−	1.27892i	−0.439985	−	0.369192i
$13$	1.85629	−	0.327315i	0.514843	−	0.0907807i	0.0898107	−	0.995959i	$-0.471374\pi$
$13$	1.85629	−	0.327315i	0.514843	−	0.0907807i	0.425032	+	0.905178i	$0.360263\pi$
$14$	0.204090	−	0.117831i	0.0545453	−	0.0314917i
$15$		0			0
$16$	4.64963	−	1.69233i	1.16241	−	0.423082i
$17$	−0.482371	−	0.0850551i	−0.116992	−	0.0206289i	0.114845	−	0.993383i	$-0.463363\pi$
$17$	−0.482371	−	0.0850551i	−0.116992	−	0.0206289i	−0.231838	+	0.972754i	$0.574474\pi$
$18$	−3.89720	−	4.64450i	−0.918579	−	1.09472i
$19$	−1.87580	−	2.23549i	−0.430338	−	0.512857i	0.506682	−	0.862133i	$-0.330872\pi$
$19$	−1.87580	−	2.23549i	−0.430338	−	0.512857i	−0.937020	+	0.349276i	$0.886428\pi$
$20$		0			0
$21$	0.342776	−	0.124760i	0.0747999	−	0.0272250i
$22$	−0.814818	−	2.23869i	−0.173720	−	0.477291i
$23$	−7.07485	+	4.08466i	−1.47521	+	0.851711i	−0.999609	−	0.0279514i	$-0.991102\pi$
$23$	−7.07485	+	4.08466i	−1.47521	+	0.851711i	−0.475598	+	0.879663i	$0.657768\pi$
$24$	5.18883	−	0.914931i	1.05917	−	0.186760i
$25$		0			0
$26$	1.56915	−	2.71785i	0.307736	−	0.533014i
$27$	−0.826667	−	1.43183i	−0.159092	−	0.275556i
$28$	0.0189758	−	0.107617i	0.00358610	−	0.0203378i
$29$	3.23140	+	1.86565i	0.600056	+	0.346442i	0.769063	−	0.639172i	$-0.220723\pi$
$29$	3.23140	+	1.86565i	0.600056	+	0.346442i	−0.169008	+	0.985615i	$0.554056\pi$
$30$		0			0
$31$			1.31432i			0.236059i	0.993010	+	0.118029i	$0.0376577\pi$
$31$			1.31432i			0.236059i	−0.993010	+	0.118029i	$0.962342\pi$
$32$	1.41912	−	3.89901i	0.250868	−	0.689254i
$33$	−0.640345	−	3.63158i	−0.111470	−	0.632176i
$34$	−0.624718	+	0.524201i	−0.107138	+	0.0898996i
$35$		0			0
$36$	−2.81142			−0.468570
$37$	−5.86718	−	1.60505i	−0.964558	−	0.263869i
$37$	−5.86718	−	1.60505i	−0.964558	−	0.263869i
$38$	−4.85869			−0.788183
$39$	3.12246	−	3.72121i	0.499994	−	0.595870i
$40$		0			0
$41$	−1.00565	−	5.70332i	−0.157056	−	0.890709i	−0.956882	−	0.290477i	$-0.906186\pi$
$41$	−1.00565	−	5.70332i	−0.157056	−	0.890709i	0.799826	−	0.600232i	$-0.204925\pi$
$42$	0.207719	−	0.570704i	0.0320518	−	0.0880615i
$43$			11.0186i			1.68032i	0.542340	+	0.840159i	$0.317539\pi$
$43$			11.0186i			1.68032i	−0.542340	+	0.840159i	$0.682461\pi$
$44$	−1.03809	−	0.377834i	−0.156498	−	0.0569606i
$45$		0			0
$46$	−2.36187	+	13.3948i	−0.348239	+	1.97496i
$47$	−5.09207	−	8.81972i	−0.742754	−	1.28649i	−0.951237	−	0.308462i	$-0.900186\pi$
$47$	−5.09207	−	8.81972i	−0.742754	−	1.28649i	0.208482	−	0.978026i	$-0.433148\pi$
$48$	6.37584	−	11.0433i	0.920273	−	1.59396i
$49$	−5.34696	−	4.48664i	−0.763852	−	0.640948i
$50$		0			0
$51$	−1.09319	+	0.631153i	−0.153077	+	0.0883791i
$52$	−0.497723	−	1.36748i	−0.0690217	−	0.189636i
$53$	1.41611	−	0.515423i	0.194518	−	0.0707988i	−0.242924	−	0.970045i	$-0.578107\pi$
$53$	1.41611	−	0.515423i	0.194518	−	0.0707988i	0.437442	+	0.899246i	$0.355884\pi$
$54$	−2.71089	−	0.478003i	−0.368906	−	0.0650480i
$55$		0			0
$56$	0.186012	+	0.221681i	0.0248569	+	0.0296233i
$57$	−7.40637	−	1.30594i	−0.980997	−	0.172976i
$58$	5.83775	−	2.12477i	0.766534	−	0.278996i
$59$	4.60589	+	12.6546i	0.599636	+	1.64749i	0.752001	+	0.659162i	$0.229089\pi$
$59$	4.60589	+	12.6546i	0.599636	+	1.64749i	−0.152365	+	0.988324i	$0.548689\pi$
$60$		0			0
$61$	−6.91487	+	1.21928i	−0.885358	+	0.156113i	−0.597795	−	0.801649i	$-0.703956\pi$
$61$	−6.91487	+	1.21928i	−0.885358	+	0.156113i	−0.287563	+	0.957762i	$0.592845\pi$
$62$	1.67631	+	1.40659i	0.212892	+	0.178637i
$63$	0.257719	−	0.446382i	0.0324695	−	0.0562389i
$64$	1.49391	+	2.58753i	0.186739	+	0.323441i
$65$		0			0
$66$	−5.31709	−	3.06982i	−0.654489	−	0.377869i
$67$	14.5595	+	5.29924i	1.77873	+	0.647405i	0.999794	+	0.0203035i	$0.00646323\pi$
$67$	14.5595	+	5.29924i	1.77873	+	0.647405i	0.778937	+	0.627102i	$0.215759\pi$
$68$			0.378156i			0.0458581i
$69$	−7.20066	+	19.7837i	−0.866858	+	2.38167i
$70$		0			0
$71$	−2.86044	+	2.40019i	−0.339472	+	0.284850i	−0.796546	−	0.604578i	$-0.793342\pi$
$71$	−2.86044	+	2.40019i	−0.339472	+	0.284850i	0.457074	+	0.889428i	$0.348897\pi$
$72$	4.78560	−	5.70326i	0.563989	−	0.672136i
$73$	−2.49025			−0.291462			−0.145731	−	0.989324i	$-0.546553\pi$
$73$	−2.49025			−0.291462			−0.145731	+	0.989324i	$0.546553\pi$
$74$	−8.32621	+	5.76539i	−0.967902	+	0.670213i
$75$		0			0
$76$	−1.44820	+	1.72589i	−0.166119	+	0.197973i
$77$	0.155151	−	0.130187i	0.0176811	−	0.0148362i
$78$	−1.40443	−	7.96491i	−0.159020	−	0.901849i
$79$	4.55510	−	12.5150i	0.512489	−	1.40805i	−0.366146	−	0.930557i	$-0.619323\pi$
$79$	4.55510	−	12.5150i	0.512489	−	1.40805i	0.878635	−	0.477494i	$-0.158455\pi$
$80$		0			0
$81$	6.26191	+	2.27915i	0.695768	+	0.253239i
$82$	−8.35039	−	4.82110i	−0.922146	−	0.532401i
$83$	−1.44890	+	8.21712i	−0.159037	+	0.901946i	0.795964	+	0.605344i	$0.206964\pi$
$83$	−1.44890	+	8.21712i	−0.159037	+	0.901946i	−0.955001	+	0.296602i	$0.904147\pi$
$84$	−0.140811	−	0.243891i	−0.0153637	−	0.0266107i
$85$		0			0
$86$	14.0533	+	11.7922i	1.51541	+	1.27158i
$87$	9.46991	−	1.66980i	1.01528	−	0.179021i
$88$	2.53351	−	1.46273i	0.270074	−	0.155927i
$89$	1.86850	+	5.13365i	0.198060	+	0.544166i	0.998471	−	0.0552865i	$-0.0176072\pi$
$89$	1.86850	+	5.13365i	0.198060	+	0.544166i	−0.800410	+	0.599453i	$0.795385\pi$
$90$		0			0
$91$	0.262747	+	0.0463293i	0.0275433	+	0.00485663i
$92$	4.05410	+	4.83149i	0.422669	+	0.503717i
$93$	2.17722	+	2.59471i	0.225767	+	0.269059i
$94$	−16.6984	−	2.94438i	−1.72231	−	0.303690i
$95$		0			0
$96$	−3.65725	−	10.0482i	−0.373266	−	1.02554i
$97$	0.475449	−	0.274500i	0.0482745	−	0.0278713i	−0.475669	−	0.879625i	$-0.657794\pi$
$97$	0.475449	−	0.274500i	0.0482745	−	0.0278713i	0.523943	+	0.851753i	$0.324460\pi$
$98$	−11.4447	+	2.01801i	−1.15609	+	0.203850i
$99$	−3.99161	−	3.34936i	−0.401172	−	0.336624i
$100$		0			0
$101$	4.75004	+	8.22731i	0.472647	+	0.818648i	0.999510	−	0.0313019i	$-0.00996534\pi$
$101$	4.75004	+	8.22731i	0.472647	+	0.818648i	−0.526863	+	0.849950i	$0.676632\pi$
$102$	−0.364951	+	2.06974i	−0.0361355	+	0.204935i
$103$	−12.0110	−	6.93455i	−1.18348	−	0.683282i	−0.226662	−	0.973973i	$-0.572781\pi$
$103$	−12.0110	−	6.93455i	−1.18348	−	0.683282i	−0.956817	+	0.290692i	$0.906115\pi$
$104$	3.62130	+	1.31805i	0.355098	+	0.129245i
$105$		0			0
$106$	0.858150	−	2.35775i	0.0833509	−	0.229005i
$107$	1.04059	+	5.90147i	0.100597	+	0.570516i	0.992888	+	0.119054i	$0.0379863\pi$
$107$	1.04059	+	5.90147i	0.100597	+	0.570516i	−0.892290	+	0.451462i	$0.850903\pi$
$108$	−0.977812	+	0.820482i	−0.0940900	+	0.0789509i
$109$	−3.59687	+	4.28658i	−0.344517	+	0.410580i	−0.910283	−	0.413986i	$-0.864136\pi$
$109$	−3.59687	+	4.28658i	−0.344517	+	0.410580i	0.565766	+	0.824566i	$0.308581\pi$
$110$		0			0
$111$	−14.2418	+	6.55054i	−1.35177	+	0.621750i
$112$	0.700363			0.0661781
$113$	6.59430	−	7.85878i	0.620339	−	0.739292i	−0.360789	−	0.932647i	$-0.617493\pi$
$113$	6.59430	−	7.85878i	0.620339	−	0.739292i	0.981129	+	0.193356i	$0.0619371\pi$
$114$	−9.59196	+	8.04861i	−0.898370	+	0.753822i
$115$		0			0
$116$	0.985263	−	2.70699i	0.0914793	−	0.251337i
$117$		−	6.86405i		−	0.634582i
$118$	21.0692	+	7.66856i	1.93958	+	0.705948i
$119$	−0.0600415	−	0.0346650i	−0.00550399	−	0.00317773i
$120$		0			0
$121$	4.47626	+	7.75312i	0.406933	+	0.704829i
$122$	−5.84524	+	10.1243i	−0.529203	+	0.916607i
$123$	−11.4331	−	9.59353i	−1.03089	−	0.865019i
$124$	0.999293	−	0.176202i	0.0897391	−	0.0158234i
$125$		0			0
$126$	−0.293513	−	0.806421i	−0.0261482	−	0.0718417i
$127$	−8.69159	+	3.16348i	−0.771254	+	0.280713i	−0.697521	−	0.716565i	$-0.745713\pi$
$127$	−8.69159	+	3.16348i	−0.771254	+	0.280713i	−0.0737330	+	0.997278i	$0.523491\pi$
$128$	13.0714	+	2.30484i	1.15536	+	0.203721i
$129$	18.2527	+	21.7528i	1.60706	+	1.91522i
$130$		0			0
$131$	3.01089	+	0.530901i	0.263063	+	0.0463850i	0.303624	−	0.952792i	$-0.401803\pi$
$131$	3.01089	+	0.530901i	0.263063	+	0.0463850i	−0.0405611	+	0.999177i	$0.512915\pi$
$132$	−2.67528	+	0.973724i	−0.232854	+	0.0847518i
$133$	−0.141274	−	0.388146i	−0.0122500	−	0.0336566i
$134$	22.3405	−	12.8983i	1.92992	−	1.11424i
$135$		0			0
$136$	−0.767128	−	0.643697i	−0.0657807	−	0.0551965i
$137$	−8.54190	+	14.7950i	−0.729784	+	1.26402i	0.227191	+	0.973850i	$0.427046\pi$
$137$	−8.54190	+	14.7950i	−0.729784	+	1.26402i	−0.956975	+	0.290172i	$0.906287\pi$
$138$	17.5263	+	30.3565i	1.49194	+	2.58411i
$139$	3.99733	−	22.6700i	0.339049	−	1.92284i	−0.0438178	−	0.999040i	$-0.513952\pi$
$139$	3.99733	−	22.6700i	0.339049	−	1.92284i	0.382867	−	0.923804i	$-0.374937\pi$
$140$		0			0
$141$	−24.6629	−	8.97657i	−2.07699	−	0.755963i
$142$			6.21697i			0.521716i
$143$	0.922478	−	2.53449i	0.0771415	−	0.211944i
$144$	−3.12888	−	17.7447i	−0.260740	−	1.47873i
$145$		0			0
$146$	−2.66508	+	3.17612i	−0.220564	+	0.262858i
$147$	−17.9882			−1.48364
$148$	−0.433767	+	4.67607i	−0.0356554	+	0.384370i
$149$	8.41279			0.689203			0.344601	−	0.938749i	$-0.388014\pi$
$149$	8.41279			0.689203			0.344601	+	0.938749i	$0.388014\pi$
$150$		0			0
$151$	11.8521	−	9.94510i	0.964511	−	0.809321i	−0.0171699	−	0.999853i	$-0.505466\pi$
$151$	11.8521	−	9.94510i	0.964511	−	0.809321i	0.981681	+	0.190532i	$0.0610212\pi$
$152$	−1.03603	−	5.87563i	−0.0840333	−	0.476576i
$153$	−0.610053	+	1.67611i	−0.0493198	+	0.135505i
$154$		−	0.337209i		−	0.0271731i
$155$		0			0
$156$	−3.24789	−	1.87517i	−0.260039	−	0.150134i
$157$	0.272586	−	1.54591i	0.0217548	−	0.123377i	−0.971996	−	0.234996i	$-0.924492\pi$
$157$	0.272586	−	1.54591i	0.0217548	−	0.123377i	0.993751	+	0.111618i	$0.0356034\pi$
$158$	−11.0871	−	19.2033i	−0.882038	−	1.52774i
$159$	1.94185	−	3.36339i	0.153999	−	0.266734i
$160$		0			0
$161$	−1.13875	+	0.200792i	−0.0897461	+	0.0158247i
$162$	9.60842	−	5.54742i	0.754908	−	0.435847i
$163$	3.81604	+	10.4845i	0.298896	+	0.821209i	0.994685	+	0.102963i	$0.0328324\pi$
$163$	3.81604	+	10.4845i	0.298896	+	0.821209i	−0.695790	+	0.718246i	$0.744945\pi$
$164$	−4.20148	+	1.52921i	−0.328081	+	0.119412i
$165$		0			0
$166$	8.92967	+	10.6420i	0.693077	+	0.825976i
$167$	2.11545	+	2.52109i	0.163698	+	0.195088i	0.841658	−	0.540011i	$-0.181580\pi$
$167$	2.11545	+	2.52109i	0.163698	+	0.195088i	−0.677960	+	0.735099i	$0.737136\pi$
$168$	0.734446	+	0.129503i	0.0566638	+	0.00999135i
$169$	−8.87731	+	3.23108i	−0.682870	+	0.248544i
$170$		0			0
$171$	−9.20313	+	5.31343i	−0.703781	+	0.406328i
$172$	8.37756	−	1.47719i	0.638783	−	0.112635i
$173$	−13.9089	−	11.6710i	−1.05747	−	0.887327i	−0.0636151	−	0.997975i	$-0.520263\pi$
$173$	−13.9089	−	11.6710i	−1.05747	−	0.887327i	−0.993860	+	0.110648i	$0.964707\pi$
$174$	8.00505	−	13.8652i	0.606861	−	1.05111i
$175$		0			0
$176$	1.22945	−	6.97258i	0.0926735	−	0.525578i
$177$	30.0557	+	17.3527i	2.25913	+	1.30431i
$178$	8.54725	+	3.11094i	0.640643	+	0.233175i
$179$		−	19.3372i		−	1.44533i	−0.691199	−	0.722665i	$-0.742917\pi$
$179$		−	19.3372i		−	1.44533i	0.691199	−	0.722665i	$-0.257083\pi$
$180$		0			0
$181$	−1.66427	−	9.43854i	−0.123704	−	0.701561i	−0.982069	−	0.188522i	$-0.939630\pi$
$181$	−1.66427	−	9.43854i	−0.123704	−	0.701561i	0.858365	−	0.513040i	$-0.171481\pi$
$182$	0.340282	−	0.285531i	0.0252234	−	0.0211650i
$183$	−11.6315	+	13.8618i	−0.859823	+	1.02470i
$184$	−16.7021			−1.23129
$185$		0			0
$186$	5.63943			0.413503
$187$	−0.450512	+	0.536900i	−0.0329447	+	0.0392620i
$188$	−6.02308	+	5.05396i	−0.439278	+	0.368598i
$189$	−0.0406370	−	0.230464i	−0.00295591	−	0.0167638i
$190$		0			0
$191$			1.26320i			0.0914017i	0.998955	+	0.0457008i	$0.0145521\pi$
$191$			1.26320i			0.0914017i	−0.998955	+	0.0457008i	$0.985448\pi$
$192$	7.23560	+	2.63354i	0.522184	+	0.190060i
$193$	−19.3761	−	11.1868i	−1.39472	−	0.805243i	−0.400888	−	0.916127i	$-0.631298\pi$
$193$	−19.3761	−	11.1868i	−1.39472	−	0.805243i	−0.993833	+	0.110885i	$0.964632\pi$
$194$	0.158724	−	0.900169i	0.0113957	−	0.0646284i
$195$		0			0
$196$	−2.69441	+	4.66686i	−0.192458	+	0.333347i
$197$	−12.0523	−	10.1131i	−0.858694	−	0.720530i	0.102993	−	0.994682i	$-0.467158\pi$
$197$	−12.0523	−	10.1131i	−0.858694	−	0.720530i	−0.961686	+	0.274153i	$0.911603\pi$
$198$	−8.54370	+	1.50648i	−0.607174	+	0.107061i
$199$	12.1930	−	7.03961i	0.864336	−	0.499024i	−0.00112613	−	0.999999i	$-0.500358\pi$
$199$	12.1930	−	7.03961i	0.864336	−	0.499024i	0.865462	+	0.500975i	$0.167025\pi$
$200$		0			0
$201$	37.5217	−	13.6568i	2.64658	−	0.963275i
$202$	15.5768	+	2.74661i	1.09598	+	0.193251i
$203$	0.339483	+	0.404580i	0.0238270	+	0.0283959i
$204$	0.626430	+	0.746550i	0.0438589	+	0.0522690i
$205$		0			0
$206$	−21.6987	+	7.89769i	−1.51182	+	0.550258i
$207$	10.1747	+	27.9549i	0.707194	+	1.94300i
$208$	8.07716	−	4.66335i	0.560050	−	0.323345i
$209$	−4.11225	+	0.725101i	−0.284450	+	0.0501563i
$210$		0			0
$211$	7.11706	−	12.3271i	0.489958	−	0.848633i	−0.509975	−	0.860189i	$-0.670345\pi$
$211$	7.11706	−	12.3271i	0.489958	−	0.848633i	0.999933	+	0.0115566i	$0.00367866\pi$
$212$	−0.581731	−	1.00759i	−0.0399535	−	0.0692014i
$213$	−1.67103	+	9.47686i	−0.114497	+	0.649344i
$214$	8.64050	+	4.98860i	0.590653	+	0.341013i
$215$		0			0
$216$		−	3.38022i		−	0.229995i
$217$	−0.0636272	+	0.174814i	−0.00431930	+	0.0118672i
$218$	1.61781	+	9.17504i	0.109572	+	0.621412i
$219$	−4.91622	+	4.12520i	−0.332208	+	0.278755i
$220$		0			0
$221$	−0.923263			−0.0621054
$222$	−6.88690	+	25.1747i	−0.462219	+	1.68961i
$223$	4.00304			0.268064			0.134032	−	0.990977i	$-0.457208\pi$
$223$	4.00304			0.268064			0.134032	+	0.990977i	$0.457208\pi$
$224$	0.377508	−	0.449897i	0.0252233	−	0.0300600i
$225$		0			0
$226$	−2.96600	−	16.8210i	−0.197295	−	1.11892i
$227$	−0.694757	+	1.90883i	−0.0461126	+	0.126693i	−0.960611	−	0.277895i	$-0.910363\pi$
$227$	−0.694757	+	1.90883i	−0.0461126	+	0.126693i	0.914499	+	0.404589i	$0.132585\pi$
$228$			5.80623i			0.384527i
$229$	−1.24369	−	0.452667i	−0.0821854	−	0.0299131i	0.300600	−	0.953750i	$-0.402813\pi$
$229$	−1.24369	−	0.452667i	−0.0821854	−	0.0299131i	−0.382786	+	0.923837i	$0.625035\pi$
$230$		0			0
$231$	0.0906368	−	0.514027i	0.00596346	−	0.0338205i
$232$	3.81429	+	6.60654i	0.250420	+	0.433741i
$233$	−3.08024	+	5.33513i	−0.201793	+	0.349516i	−0.949106	−	0.314956i	$-0.898010\pi$
$233$	−3.08024	+	5.33513i	−0.201793	+	0.349516i	0.747313	+	0.664472i	$0.231344\pi$
$234$	−8.75456	−	7.34595i	−0.572304	−	0.480220i
$235$		0			0
$236$	9.00395	−	5.19843i	0.586107	−	0.338389i
$237$	−11.7390	−	32.2527i	−0.762532	−	2.09504i
$238$	−0.108469	+	0.0394795i	−0.00703101	+	0.00255908i
$239$	10.0252	+	1.76771i	0.648477	+	0.114344i	0.488205	−	0.872729i	$-0.337652\pi$
$239$	10.0252	+	1.76771i	0.648477	+	0.114344i	0.160272	+	0.987073i	$0.448763\pi$
$240$		0			0
$241$	8.50467	+	10.1355i	0.547834	+	0.652883i	0.966925	−	0.255061i	$-0.0820955\pi$
$241$	8.50467	+	10.1355i	0.547834	+	0.652883i	−0.419091	+	0.907944i	$0.637651\pi$
$242$	14.6790	+	2.58831i	0.943603	+	0.166383i
$243$	20.7986	−	7.57006i	1.33423	−	0.485620i
$244$	1.85406	+	5.09400i	0.118694	+	0.326110i
$245$		0			0
$246$	−24.4716	+	4.31500i	−1.56025	+	0.275114i
$247$	−4.21375	−	3.53575i	−0.268114	−	0.224975i
$248$	−1.34355	+	2.32710i	−0.0853156	+	0.147771i
$249$	10.7516	+	18.6223i	0.681354	+	1.18014i
$250$		0			0
$251$	18.2560	+	10.5401i	1.15231	+	0.665286i	0.949449	−	0.313922i	$-0.101643\pi$
$251$	18.2560	+	10.5401i	1.15231	+	0.665286i	0.202860	+	0.979208i	$0.434976\pi$
$252$	−0.373940	−	0.136103i	−0.0235560	−	0.00857369i
$253$			11.6895i			0.734912i
$254$	−5.26702	+	14.4710i	−0.330482	+	0.907992i
$255$		0			0
$256$	12.3511	−	10.3638i	0.771944	−	0.647738i
$257$	−3.82429	+	4.55761i	−0.238553	+	0.284296i	−0.872017	−	0.489476i	$-0.837188\pi$
$257$	−3.82429	+	4.55761i	−0.238553	+	0.284296i	0.633464	+	0.773772i	$0.281632\pi$
$258$	47.2781			2.94341
$259$	−0.702677	−	0.497519i	−0.0436622	−	0.0309143i
$260$		0			0
$261$	8.73399	−	10.4088i	0.540621	−	0.644287i
$262$	3.89939	−	3.27198i	0.240905	−	0.202144i
$263$	0.559408	+	3.17256i	0.0344945	+	0.195628i	0.997185	−	0.0749754i	$-0.0238878\pi$
$263$	0.559408	+	3.17256i	0.0344945	+	0.195628i	−0.962691	+	0.270604i	$0.912777\pi$
$264$	2.57857	−	7.08456i	0.158700	−	0.436025i
$265$		0			0
$266$	−0.646242	−	0.235213i	−0.0396237	−	0.0144218i
$267$	12.1929	+	7.03955i	0.746191	+	0.430814i
$268$	2.07717	−	11.7802i	0.126884	−	0.719592i
$269$	3.59295	+	6.22317i	0.219066	+	0.379433i	0.954523	−	0.298138i	$-0.0963657\pi$
$269$	3.59295	+	6.22317i	0.219066	+	0.379433i	−0.735457	+	0.677572i	$0.763032\pi$
$270$		0			0
$271$	−18.3340	−	15.3841i	−1.11371	−	0.934516i	−0.115443	−	0.993314i	$-0.536829\pi$
$271$	−18.3340	−	15.3841i	−1.11371	−	0.934516i	−0.998270	+	0.0587978i	$0.981273\pi$
$272$	−2.38679	+	0.420856i	−0.144720	+	0.0255181i
$273$	0.595458	−	0.343788i	0.0360387	−	0.0208070i
$274$	9.72828	+	26.7282i	0.587707	+	1.61471i
$275$		0			0
$276$	16.0071	+	2.82248i	0.963514	+	0.169894i
$277$	3.09419	+	3.68751i	0.185912	+	0.221561i	0.850948	−	0.525250i	$-0.176028\pi$
$277$	3.09419	+	3.68751i	0.185912	+	0.221561i	−0.665036	+	0.746811i	$0.731584\pi$
$278$	−24.6358	−	29.3598i	−1.47756	−	1.76089i
$279$	4.71344	+	0.831106i	0.282186	+	0.0497570i
$280$		0			0
$281$	6.02089	+	16.5422i	0.359176	+	0.986828i	0.979316	+	0.202337i	$0.0648535\pi$
$281$	6.02089	+	16.5422i	0.359176	+	0.986828i	−0.620140	+	0.784491i	$0.712924\pi$
$282$	−37.8433	+	21.8488i	−2.25354	+	1.30108i
$283$	1.53397	−	0.270480i	0.0911850	−	0.0160784i	−0.127869	−	0.991791i	$-0.540814\pi$
$283$	1.53397	−	0.270480i	0.0911850	−	0.0160784i	0.219055	+	0.975713i	$0.429703\pi$
$284$	2.20838	+	1.85305i	0.131043	+	0.109958i
$285$		0			0
$286$	−2.24530	−	3.88897i	−0.132767	−	0.229960i
$287$	0.142343	−	0.807269i	0.00840226	−	0.0476516i
$288$	−13.0853	−	7.55482i	−0.771060	−	0.445172i
$289$	−15.7493	−	5.73229i	−0.926431	−	0.337193i
$290$		0			0
$291$	0.483904	−	1.32952i	0.0283670	−	0.0779376i
$292$	0.333852	+	1.89337i	0.0195372	+	0.110801i
$293$	−19.1667	+	16.0828i	−1.11973	+	0.939565i	−0.998591	−	0.0530700i	$-0.983099\pi$
$293$	−19.1667	+	16.0828i	−1.11973	+	0.939565i	−0.121140	+	0.992635i	$0.538655\pi$
$294$	−19.2511	+	22.9425i	−1.12275	+	1.33804i
$295$		0			0
$296$	−8.74753	−	8.83954i	−0.508440	−	0.513788i
$297$	−2.36576			−0.137275
$298$	9.00342	−	10.7299i	0.521554	−	0.621564i
$299$	−11.7960	+	9.89804i	−0.682181	+	0.572418i
$300$		0			0
$301$	−0.533419	+	1.46556i	−0.0307457	+	0.0844732i
$302$		−	25.7597i		−	1.48231i
$303$	23.0063	+	8.37363i	1.32168	+	0.481052i
$304$	−12.5050	−	7.21975i	−0.717209	−	0.414081i
$305$		0			0
$306$	1.48486	+	2.57185i	0.0848838	+	0.147023i
$307$	10.3146	−	17.8655i	0.588688	−	1.01964i	−0.405717	−	0.913999i	$-0.632978\pi$
$307$	10.3146	−	17.8655i	0.588688	−	1.01964i	0.994405	−	0.105638i	$-0.0336885\pi$
$308$	−0.119783	−	0.100510i	−0.00682525	−	0.00572707i
$309$	−35.1993	+	6.20659i	−2.00242	+	0.353081i
$310$		0			0
$311$	−3.49371	−	9.59890i	−0.198110	−	0.544303i	0.800365	−	0.599514i	$-0.204639\pi$
$311$	−3.49371	−	9.59890i	−0.198110	−	0.544303i	−0.998475	+	0.0552103i	$0.982417\pi$
$312$	9.33252	−	3.39676i	0.528350	−	0.192304i
$313$	12.6318	+	2.22732i	0.713990	+	0.125896i	0.518832	−	0.854876i	$-0.326367\pi$
$313$	12.6318	+	2.22732i	0.713990	+	0.125896i	0.195158	+	0.980772i	$0.437478\pi$
$314$	−1.67997	−	2.00211i	−0.0948062	−	0.112986i
$315$		0			0
$316$	−10.1260	−	1.78549i	−0.569632	−	0.100442i
$317$	−18.2324	+	6.63605i	−1.02403	+	0.372717i	−0.798806	−	0.601589i	$-0.794535\pi$
$317$	−18.2324	+	6.63605i	−1.02403	+	0.372717i	−0.225227	+	0.974306i	$0.572312\pi$
$318$	−2.21156	−	6.07620i	−0.124018	−	0.340736i
$319$	4.62381	−	2.66956i	0.258883	−	0.149466i
$320$		0			0
$321$	11.8303	+	9.92683i	0.660305	+	0.554062i
$322$	−0.962602	+	1.66728i	−0.0536437	+	0.0929136i
$323$	0.714693	+	1.23788i	0.0397666	+	0.0688777i
$324$	0.893371	−	5.06656i	0.0496317	−	0.281476i
$325$		0			0
$326$	17.4561	+	6.35350i	0.966804	+	0.351888i
$327$			14.4209i			0.797475i
$328$	4.04959	−	11.1262i	0.223601	−	0.614340i
$329$	−0.250314	−	1.41960i	−0.0138002	−	0.0782651i
$330$		0			0
$331$	−7.11270	+	8.47659i	−0.390950	+	0.465916i	−0.925238	−	0.379387i	$-0.876135\pi$
$331$	−7.11270	+	8.47659i	−0.390950	+	0.465916i	0.534289	+	0.845302i	$0.320580\pi$
$332$	6.44182			0.353541
$333$	−9.46617	+	20.0261i	−0.518743	+	1.09742i
$334$	5.47942			0.299820
$335$		0			0
$336$	1.38265	−	1.16018i	0.0754297	−	0.0632930i
$337$	−1.52587	−	8.65362i	−0.0831193	−	0.471393i	−0.997747	−	0.0670948i	$-0.978627\pi$
$337$	−1.52587	−	8.65362i	−0.0831193	−	0.471393i	0.914627	−	0.404298i	$-0.132484\pi$
$338$	−5.37957	+	14.7802i	−0.292610	+	0.803939i
$339$		−	26.4384i		−	1.43594i
$340$		0			0
$341$	1.62870	+	0.940329i	0.0881989	+	0.0509217i
$342$	−3.07238	+	17.4243i	−0.166135	+	0.942200i
$343$	−0.989388	−	1.71367i	−0.0534219	−	0.0925295i
$344$	−11.2637	+	19.5092i	−0.607296	+	1.05187i
$345$		0			0
$346$	−29.7708	+	5.24939i	−1.60049	+	0.282209i
$347$	−11.7848	+	6.80394i	−0.632639	+	0.365254i	−0.781774	−	0.623562i	$-0.785685\pi$
$347$	−11.7848	+	6.80394i	−0.632639	+	0.365254i	0.149134	+	0.988817i	$0.452351\pi$
$348$	−2.53914	−	6.97623i	−0.136112	−	0.373965i
$349$	4.49791	−	1.63711i	0.240768	−	0.0876323i	−0.218818	−	0.975766i	$-0.570220\pi$
$349$	4.49791	−	1.63711i	0.240768	−	0.0876323i	0.459586	+	0.888133i	$0.347998\pi$
$350$		0			0
$351$	−2.00320	−	2.38732i	−0.106923	−	0.127426i
$352$	−3.81632	−	4.54811i	−0.203411	−	0.242415i
$353$	−17.0344	−	3.00362i	−0.906648	−	0.159867i	−0.299167	−	0.954201i	$-0.596709\pi$
$353$	−17.0344	−	3.00362i	−0.906648	−	0.159867i	−0.607481	+	0.794334i	$0.707820\pi$
$354$	54.2978	−	19.7628i	2.88590	−	1.05038i
$355$		0			0
$356$	3.65268	−	2.10888i	0.193592	−	0.111770i
$357$	−0.175957	+	0.0310260i	−0.00931263	+	0.00164207i
$358$	−24.6631	−	20.6948i	−1.30348	−	1.09375i
$359$	−3.84231	+	6.65508i	−0.202789	+	0.351242i	−0.949426	−	0.313990i	$-0.898334\pi$
$359$	−3.84231	+	6.65508i	−0.202789	+	0.351242i	0.746637	+	0.665232i	$0.231667\pi$
$360$		0			0
$361$	1.82052	−	10.3247i	0.0958167	−	0.543404i
$362$	−13.8192	−	7.97854i	−0.726323	−	0.419343i
$363$	21.6803	+	7.89100i	1.13792	+	0.414170i
$364$		−	0.205981i		−	0.0107963i
$365$		0			0
$366$	5.23163	+	29.6701i	0.273462	+	1.55088i
$367$	−13.6648	+	11.4661i	−0.713295	+	0.598525i	−0.925522	−	0.378695i	$-0.876373\pi$
$367$	−13.6648	+	11.4661i	−0.713295	+	0.598525i	0.212227	+	0.977220i	$0.431928\pi$
$368$	−25.9828	+	30.9651i	−1.35445	+	1.61417i
$369$	−21.0893			−1.09786
$370$		0			0
$371$	0.213306			0.0110743
$372$	1.68091	−	2.00323i	0.0871509	−	0.103862i
$373$	20.6590	−	17.3349i	1.06968	−	0.897568i	0.0746570	−	0.997209i	$-0.476214\pi$
$373$	20.6590	−	17.3349i	1.06968	−	0.897568i	0.995023	+	0.0996408i	$0.0317694\pi$
$374$	0.202633	+	1.14919i	0.0104779	+	0.0594230i
$375$		0			0
$376$		−	20.8213i		−	1.07378i
$377$	6.60908	+	2.40551i	0.340385	+	0.123890i
$378$	−0.337429	−	0.194814i	−0.0173555	−	0.0100202i
$379$	−2.12764	+	12.0664i	−0.109290	+	0.619812i	0.880130	+	0.474732i	$0.157455\pi$
$379$	−2.12764	+	12.0664i	−0.109290	+	0.619812i	−0.989420	+	0.145080i	$0.953656\pi$
$380$		0			0
$381$	−11.9184	+	20.6433i	−0.610598	+	1.05759i
$382$	1.61111	+	1.35188i	0.0824314	+	0.0691682i
$383$	−4.00699	+	0.706540i	−0.204747	+	0.0361025i	−0.275081	−	0.961421i	$-0.588705\pi$
$383$	−4.00699	+	0.706540i	−0.204747	+	0.0361025i	0.0703337	+	0.997524i	$0.477594\pi$
$384$	29.6234	−	17.1031i	1.51171	−	0.872788i
$385$		0			0
$386$	−35.0043	+	12.7405i	−1.78167	+	0.648475i
$387$	39.5151	+	6.96757i	2.00866	+	0.354182i
$388$	−0.272446	−	0.324689i	−0.0138314	−	0.0164836i
$389$	−2.86804	−	3.41799i	−0.145415	−	0.173299i	0.688420	−	0.725312i	$-0.258304\pi$
$389$	−2.86804	−	3.41799i	−0.145415	−	0.173299i	−0.833836	+	0.552013i	$0.813860\pi$
$390$		0			0
$391$	3.76012	−	1.36857i	0.190158	−	0.0692117i
$392$	−4.88077	−	13.4098i	−0.246516	−	0.677298i
$393$	6.82352	−	3.93956i	0.344201	−	0.198725i
$394$	−25.7970	+	4.54870i	−1.29963	+	0.229160i
$395$		0			0
$396$	−2.01143	+	3.48390i	−0.101078	+	0.175073i
$397$	1.54768	+	2.68067i	0.0776760	+	0.134539i	0.902247	−	0.431220i	$-0.141917\pi$
$397$	1.54768	+	2.68067i	0.0776760	+	0.134539i	−0.824571	+	0.565759i	$0.808583\pi$
$398$	4.07051	−	23.0850i	0.204036	−	1.15715i
$399$	−0.921881	−	0.532248i	−0.0461518	−	0.0266457i
$400$		0			0
$401$		−	11.6167i		−	0.580111i	−0.957010	−	0.290056i	$-0.906326\pi$
$401$		−	11.6167i		−	0.580111i	0.957010	−	0.290056i	$-0.0936739\pi$
$402$	22.7378	−	62.4715i	1.13406	−	3.11580i
$403$	0.430196	+	2.43976i	0.0214296	+	0.121533i
$404$	5.61852	−	4.71450i	0.279532	−	0.234555i
$405$		0			0
$406$	0.879327			0.0436402
$407$	−6.18665	+	6.12225i	−0.306661	+	0.303468i
$408$	−2.58076			−0.127767
$409$	15.1640	−	18.0718i	0.749813	−	0.893592i	−0.247346	−	0.968927i	$-0.579558\pi$
$409$	15.1640	−	18.0718i	0.749813	−	0.893592i	0.997158	+	0.0753355i	$0.0240028\pi$
$410$		0			0
$411$	7.64520	+	43.3581i	0.377110	+	2.13870i
$412$	−3.66219	+	10.0618i	−0.180423	+	0.495708i
$413$			1.90613i			0.0937945i
$414$	46.5433	+	16.9404i	2.28748	+	0.832575i
$415$		0			0
$416$	1.35811	−	7.70220i	0.0665866	−	0.377632i
$417$	−29.6623	−	51.3765i	−1.45257	−	2.51592i
$418$	−3.47615	+	6.02086i	−0.170024	+	0.294490i
$419$	−24.7248	−	20.7466i	−1.20789	−	1.01354i	−0.999369	−	0.0355171i	$-0.988692\pi$
$419$	−24.7248	−	20.7466i	−1.20789	−	1.01354i	−0.208516	−	0.978019i	$-0.566863\pi$
$420$		0			0
$421$	−21.2520	+	12.2699i	−1.03576	+	0.597997i	−0.918630	−	0.395119i	$-0.870703\pi$
$421$	−21.2520	+	12.2699i	−1.03576	+	0.597997i	−0.117131	+	0.993116i	$0.537370\pi$
$422$	−8.10554	−	22.2698i	−0.394571	−	1.08408i
$423$	−34.8494	+	12.6841i	−1.69444	+	0.616724i
$424$	3.03422	+	0.535015i	0.147355	+	0.0259826i
$425$		0			0
$426$	10.2987	+	12.2735i	0.498971	+	0.594651i
$427$	−0.978756	−	0.172581i	−0.0473653	−	0.00835179i
$428$	4.34745	−	1.58234i	0.210142	−	0.0764854i
$429$	−2.37734	−	6.53168i	−0.114779	−	0.315352i
$430$		0			0
$431$	28.1831	−	4.96943i	1.35753	−	0.239369i	0.552951	−	0.833214i	$-0.313502\pi$
$431$	28.1831	−	4.96943i	1.35753	−	0.239369i	0.804580	+	0.593845i	$0.202391\pi$
$432$	−6.26682	−	5.25849i	−0.301513	−	0.252999i
$433$	−5.88773	+	10.1979i	−0.282946	+	0.490077i	−0.972109	−	0.234529i	$-0.924645\pi$
$433$	−5.88773	+	10.1979i	−0.282946	+	0.490077i	0.689163	+	0.724607i	$0.257979\pi$
$434$	0.154868	+	0.268239i	0.00743389	+	0.0128759i
$435$		0			0
$436$	3.74134	+	2.16007i	0.179178	+	0.103448i
$437$	22.4022	+	8.15375i	1.07164	+	0.390047i
$438$			10.6851i			0.510553i
$439$	−4.76177	+	13.0829i	−0.227267	+	0.624411i	−0.999946	−	0.0103862i	$-0.996694\pi$
$439$	−4.76177	+	13.0829i	−0.227267	+	0.624411i	0.772679	+	0.634797i	$0.218916\pi$
$440$		0			0
$441$	−19.4712	+	16.3383i	−0.927200	+	0.778013i
$442$	−0.988081	+	1.17755i	−0.0469982	+	0.0560103i
$443$	30.0591			1.42815			0.714075	−	0.700069i	$-0.246847\pi$
$443$	30.0591			1.42815			0.714075	+	0.700069i	$0.246847\pi$
$444$	6.88976	+	9.94999i	0.326973	+	0.472206i
$445$		0			0
$446$	4.28408	−	5.10557i	0.202857	−	0.241756i
$447$	16.6084	−	13.9361i	0.785552	−	0.659156i
$448$	0.0734370	+	0.416482i	0.00346957	+	0.0196769i
$449$	5.99840	−	16.4805i	0.283082	−	0.777761i	−0.713909	−	0.700239i	$-0.753077\pi$
$449$	5.99840	−	16.4805i	0.283082	−	0.777761i	0.996991	−	0.0775221i	$-0.0247008\pi$
$450$		0			0
$451$	−7.78702	−	2.83424i	−0.366676	−	0.133459i
$452$	−6.85918	−	3.96015i	−0.322629	−	0.186270i
$453$	6.92383	−	39.2670i	0.325310	−	1.84492i
$454$	1.69103	+	2.92895i	0.0793639	+	0.137462i
$455$		0			0
$456$	−11.7785	−	9.88337i	−0.551581	−	0.462831i
$457$	−0.964804	+	0.170121i	−0.0451316	+	0.00795793i	−0.196168	−	0.980570i	$-0.562850\pi$
$457$	−0.964804	+	0.170121i	−0.0451316	+	0.00795793i	0.151037	+	0.988528i	$0.451739\pi$
$458$	−1.90835	+	1.10178i	−0.0891712	+	0.0514830i
$459$	0.276976	+	0.760986i	0.0129281	+	0.0355198i
$460$		0			0
$461$	−32.8802	−	5.79767i	−1.53139	−	0.270025i	−0.656489	−	0.754335i	$-0.727959\pi$
$461$	−32.8802	−	5.79767i	−1.53139	−	0.270025i	−0.874896	+	0.484311i	$0.839070\pi$
$462$	−0.558601	−	0.665714i	−0.0259885	−	0.0309718i
$463$	−20.9329	−	24.9468i	−0.972834	−	1.15938i	−0.987201	−	0.159481i	$-0.949018\pi$
$463$	−20.9329	−	24.9468i	−0.972834	−	1.15938i	0.0143674	−	0.999897i	$-0.495427\pi$
$464$	18.1821	+	3.20599i	0.844083	+	0.148835i
$465$		0			0
$466$	3.50805	+	9.63829i	0.162507	+	0.446485i
$467$	9.79223	−	5.65355i	0.453130	−	0.261615i	−0.256021	−	0.966671i	$-0.582412\pi$
$467$	9.79223	−	5.65355i	0.453130	−	0.261615i	0.709151	+	0.705056i	$0.249078\pi$
$468$	−5.21882	+	0.920219i	−0.241240	+	0.0425372i
$469$	1.67999	+	1.40968i	0.0775747	+	0.0650929i
$470$		0			0
$471$	−2.02273	−	3.50348i	−0.0932026	−	0.161432i
$472$	−4.78097	+	27.1142i	−0.220062	+	1.24803i
$473$	13.6542	+	7.88324i	0.627820	+	0.362472i
$474$	−53.6990	−	19.5448i	−2.46648	−	0.897725i
$475$		0			0
$476$	−0.0183068	+	0.0502976i	−0.000839092	+	0.00230538i
$477$	−0.952945	−	5.40442i	−0.0436323	−	0.247451i
$478$	12.9836	−	10.8945i	0.593857	−	0.498305i
$479$	9.79890	−	11.6779i	0.447723	−	0.533576i	−0.494225	−	0.869334i	$-0.664548\pi$
$479$	9.79890	−	11.6779i	0.447723	−	0.533576i	0.941948	+	0.335758i	$0.108993\pi$
$480$		0			0
$481$	−11.4166	−	1.05904i	−0.520551	−	0.0482879i
$482$	22.0288			1.00338
$483$	−1.91549	+	2.28279i	−0.0871576	+	0.103870i
$484$	5.29468	−	4.44277i	0.240667	−	0.201944i
$485$		0			0
$486$	12.6037	−	34.6285i	0.571717	−	1.57078i
$487$		−	34.2072i		−	1.55008i	−0.631914	−	0.775039i	$-0.717730\pi$
$487$		−	34.2072i		−	1.55008i	0.631914	−	0.775039i	$-0.282270\pi$
$488$	−13.4897	−	4.90985i	−0.610650	−	0.222258i
$489$	24.9016	+	14.3769i	1.12609	+	0.650147i
$490$		0			0
$491$	−13.4367	−	23.2731i	−0.606392	−	1.05030i	−0.991830	−	0.127568i	$-0.959283\pi$
$491$	−13.4367	−	23.2731i	−0.606392	−	1.05030i	0.385438	−	0.922734i	$-0.374050\pi$
$492$	−5.76131	+	9.97888i	−0.259740	+	0.449883i
$493$	−1.40005	−	1.17478i	−0.0630551	−	0.0529095i
$494$	−9.01915	+	1.59032i	−0.405791	+	0.0715519i
$495$		0			0
$496$	2.22426	+	6.11110i	0.0998721	+	0.274396i
$497$	−0.496655	+	0.180768i	−0.0222780	+	0.00810854i
$498$	35.2577	+	6.21688i	1.57993	+	0.278585i
$499$	2.77216	+	3.30373i	0.124099	+	0.147895i	0.824516	−	0.565838i	$-0.191447\pi$
$499$	2.77216	+	3.30373i	0.124099	+	0.147895i	−0.700418	+	0.713733i	$0.747003\pi$
$500$		0			0
$501$	8.35258	+	1.47279i	0.373166	+	0.0657992i
$502$	32.9808	−	12.0040i	1.47200	−	0.535766i
$503$	9.31032	+	25.5799i	0.415127	+	1.14055i	0.954429	+	0.298439i	$0.0964659\pi$
$503$	9.31032	+	25.5799i	0.415127	+	1.14055i	−0.539302	+	0.842112i	$0.681312\pi$
$504$	0.912621	−	0.526902i	0.0406514	−	0.0234701i
$505$		0			0
$506$	14.9090	+	12.5102i	0.662787	+	0.556144i
$507$	−12.1731	+	21.0844i	−0.540625	+	0.936390i
$508$	3.57046	+	6.18421i	0.158413	+	0.274380i
$509$	3.15689	−	17.9036i	0.139927	−	0.793564i	−0.831375	−	0.555712i	$-0.812446\pi$
$509$	3.15689	−	17.9036i	0.139927	−	0.793564i	0.971301	−	0.237852i	$-0.0764433\pi$
$510$		0			0
$511$	−0.331222	−	0.120555i	−0.0146524	−	0.00533304i
$512$		−	0.298219i		−	0.0131795i
$513$	−1.65018	+	4.53384i	−0.0728573	+	0.200174i
$514$	1.72010	+	9.75517i	0.0758703	+	0.430282i
$515$		0			0
$516$	14.0919	−	16.7940i	0.620360	−	0.739316i
$517$	−14.5725			−0.640897
$518$	−1.38656	+	0.363762i	−0.0609218	+	0.0159828i
$519$	−46.7922			−2.05395
$520$		0			0
$521$	−23.5688	+	19.7766i	−1.03257	+	0.866427i	−0.991154	−	0.132715i	$-0.957630\pi$
$521$	−23.5688	+	19.7766i	−1.03257	+	0.866427i	−0.0414132	+	0.999142i	$0.513186\pi$
$522$	−3.92840	−	22.2790i	−0.171941	−	0.975127i
$523$	11.5829	−	31.8237i	0.506484	−	1.39155i	−0.378358	−	0.925659i	$-0.623511\pi$
$523$	11.5829	−	31.8237i	0.506484	−	1.39155i	0.884841	−	0.465893i	$-0.154267\pi$
$524$		−	2.36039i		−	0.103114i
$525$		0			0
$526$	4.64503	+	2.68181i	0.202533	+	0.116932i
$527$	0.111790	−	0.633990i	0.00486963	−	0.0276170i
$528$	−9.12318	−	15.8018i	−0.397036	−	0.687686i
$529$	21.8690	−	37.8782i	0.950824	−	1.64688i
$530$		0			0
$531$	48.2947	−	8.51565i	2.09581	−	0.369548i
$532$	−0.276173	+	0.159448i	−0.0119736	+	0.00691297i
$533$	−3.73356	−	10.2579i	−0.161718	−	0.444318i
$534$	22.0273	−	8.01727i	0.953213	−	0.346941i
$535$		0			0
$536$	20.3617	+	24.2661i	0.879489	+	1.04813i
$537$	−32.0328	−	38.1752i	−1.38232	−	1.64738i
$538$	11.7824	+	2.07755i	0.507974	+	0.0895695i
$539$	−9.38530	+	3.41597i	−0.404254	+	0.147136i
$540$		0			0
$541$	5.47663	−	3.16193i	0.235459	−	0.135942i	−0.377629	−	0.925957i	$-0.623261\pi$
$541$	5.47663	−	3.16193i	0.235459	−	0.135942i	0.613088	+	0.790015i	$0.289927\pi$
$542$	−39.2424	+	6.91949i	−1.68560	+	0.297218i
$543$	−18.9209	−	15.8765i	−0.811974	−	0.681327i
$544$	−1.01617	+	1.76007i	−0.0435681	+	0.0754622i
$545$		0			0
$546$	0.198788	−	1.12738i	0.00850734	−	0.0482475i
$547$	20.5463	+	11.8624i	0.878498	+	0.507201i	0.870163	−	0.492764i	$-0.164013\pi$
$547$	20.5463	+	11.8624i	0.878498	+	0.507201i	0.00833519	+	0.999965i	$0.497347\pi$
$548$	12.3940	+	4.51104i	0.529444	+	0.192702i
$549$			25.5693i			1.09127i
$550$		0			0
$551$	−1.89082	−	10.7233i	−0.0805515	−	0.456830i
$552$	−32.9730	+	27.6676i	−1.40342	+	1.17761i
$553$	1.21173	−	1.44408i	0.0515278	−	0.0614085i
$554$	8.01455			0.340505
$555$		0			0
$556$	−17.7722			−0.753708
$557$	−27.4465	+	32.7094i	−1.16294	+	1.38594i	−0.254953	+	0.966953i	$0.582060\pi$
$557$	−27.4465	+	32.7094i	−1.16294	+	1.38594i	−0.907991	+	0.418989i	$0.862385\pi$
$558$	6.10436	−	5.12217i	0.258418	−	0.216839i
$559$	3.60654	+	20.4537i	0.152541	+	0.865101i
$560$		0			0
$561$			1.80623i			0.0762592i
$562$	27.5419	+	10.0244i	1.16179	+	0.422856i
$563$	−14.2880	−	8.24917i	−0.602167	−	0.347661i	0.167727	−	0.985834i	$-0.446357\pi$
$563$	−14.2880	−	8.24917i	−0.602167	−	0.347661i	−0.769894	+	0.638172i	$0.779691\pi$
$564$	−3.51859	+	19.9549i	−0.148160	+	0.840255i
$565$		0			0
$566$	1.29669	−	2.24593i	0.0545038	−	0.0944034i
$567$	0.722547	+	0.606289i	0.0303441	+	0.0254617i
$568$	−7.51820	+	1.32566i	−0.315457	+	0.0556235i
$569$	−30.4520	+	17.5815i	−1.27662	+	0.737055i	−0.976225	−	0.216762i	$-0.930451\pi$
$569$	−30.4520	+	17.5815i	−1.27662	+	0.737055i	−0.300391	+	0.953816i	$0.597117\pi$
$570$		0			0
$571$	10.1706	−	3.70179i	0.425626	−	0.154915i	−0.120321	−	0.992735i	$-0.538392\pi$
$571$	10.1706	−	3.70179i	0.425626	−	0.154915i	0.545947	+	0.837820i	$0.316170\pi$
$572$	−2.05067	−	0.361589i	−0.0857429	−	0.0151188i
$573$	2.09254	+	2.49379i	0.0874169	+	0.104179i
$574$	−0.877272	−	1.04549i	−0.0366166	−	0.0436380i
$575$		0			0
$576$	10.2241	−	3.72127i	0.426005	−	0.155053i
$577$	−12.0161	−	33.0140i	−0.500237	−	1.37439i	−0.891044	−	0.453917i	$-0.850026\pi$
$577$	−12.0161	−	33.0140i	−0.500237	−	1.37439i	0.390807	−	0.920473i	$-0.372196\pi$
$578$	−24.1661	+	13.9523i	−1.00518	+	0.580339i
$579$	−56.7834	+	10.0124i	−2.35984	+	0.416103i
$580$		0			0
$581$	−0.590512	+	1.02280i	−0.0244986	+	0.0424327i
$582$	−1.17782	−	2.04004i	−0.0488220	−	0.0845622i
$583$	0.374448	−	2.12360i	0.0155080	−	0.0879505i
$584$	−4.40918	−	2.54564i	−0.182453	−	0.105339i
$585$		0			0
$586$			41.6575i			1.72086i
$587$	4.57687	−	12.5748i	0.188907	−	0.519019i	−0.808695	−	0.588229i	$-0.799826\pi$
$587$	4.57687	−	12.5748i	0.188907	−	0.519019i	0.997602	+	0.0692097i	$0.0220477\pi$
$588$	2.41156	+	13.6766i	0.0994512	+	0.564016i
$589$	2.93815	−	2.46540i	0.121064	−	0.101585i
$590$		0			0
$591$	−40.5464			−1.66785
$592$	−29.9965	+	2.46628i	−1.23285	+	0.101364i
$593$	−34.2551			−1.40669			−0.703344	−	0.710850i	$-0.748310\pi$
$593$	−34.2551			−1.40669			−0.703344	+	0.710850i	$0.748310\pi$
$594$	−2.53185	+	3.01734i	−0.103883	+	0.123803i
$595$		0			0
$596$	−1.12785	−	6.39635i	−0.0461985	−	0.262005i
$597$	12.4098	−	34.0956i	0.507899	−	1.39544i
$598$			25.6378i			1.04841i
$599$	26.5603	+	9.66717i	1.08523	+	0.394990i	0.821850	−	0.569704i	$-0.192942\pi$
$599$	26.5603	+	9.66717i	1.08523	+	0.394990i	0.263375	+	0.964693i	$0.415164\pi$
$600$		0			0
$601$	6.66964	−	37.8254i	0.272060	−	1.54293i	−0.476088	−	0.879398i	$-0.657946\pi$
$601$	6.66964	−	37.8254i	0.272060	−	1.54293i	0.748148	−	0.663532i	$-0.230943\pi$
$602$	1.29833	+	2.24878i	0.0529161	+	0.0916534i
$603$	28.2109	−	48.8628i	1.14884	−	1.98985i
$604$	−9.15032	−	7.67803i	−0.372321	−	0.312415i
$605$		0			0
$606$	35.3014	−	20.3813i	1.43402	−	0.827933i
$607$	10.0230	+	27.5379i	0.406820	+	1.11773i	0.958852	+	0.283907i	$0.0916306\pi$
$607$	10.0230	+	27.5379i	0.406820	+	1.11773i	−0.552031	+	0.833823i	$0.686147\pi$
$608$	−11.3782	+	4.14132i	−0.461447	+	0.167953i
$609$	1.34041	+	0.236350i	0.0543160	+	0.00957737i
$610$		0			0
$611$	−12.3392	−	14.7053i	−0.499190	−	0.594912i
$612$	1.35615	+	0.239126i	0.0548191	+	0.00966609i
$613$	0.184458	−	0.0671373i	0.00745019	−	0.00271165i	−0.338292	−	0.941041i	$-0.609849\pi$
$613$	0.184458	−	0.0671373i	0.00745019	−	0.00271165i	0.345743	+	0.938329i	$0.387627\pi$
$614$	−11.7472	−	32.2753i	−0.474080	−	1.30252i
$615$		0			0
$616$	0.407788	−	0.0719041i	0.0164303	−	0.00289710i
$617$	10.7347	+	9.00749i	0.432163	+	0.362628i	0.832767	−	0.553623i	$-0.186755\pi$
$617$	10.7347	+	9.00749i	0.432163	+	0.362628i	−0.400604	+	0.916251i	$0.631200\pi$
$618$	−29.7545	+	51.5363i	−1.19690	+	2.07310i
$619$	0.294985	+	0.510928i	0.0118564	+	0.0205359i	0.871893	−	0.489697i	$-0.162893\pi$
$619$	0.294985	+	0.510928i	0.0118564	+	0.0205359i	−0.860036	+	0.510233i	$0.829559\pi$
$620$		0			0
$621$	11.6971	+	6.75332i	0.469388	+	0.271001i
$622$	−15.9816	−	5.81684i	−0.640805	−	0.233234i
$623$			0.773270i			0.0309804i
$624$	8.22080	−	22.5865i	0.329095	−	0.904182i
$625$		0			0
$626$	16.3594	−	13.7271i	0.653852	−	0.548647i
$627$	−6.91720	+	8.24360i	−0.276246	+	0.329218i
$628$	−1.21192			−0.0483609
$629$	2.69364	+	1.27327i	0.107403	+	0.0507684i
$630$		0			0
$631$	3.32127	−	3.95813i	0.132218	−	0.157571i	−0.695873	−	0.718164i	$-0.744983\pi$
$631$	3.32127	−	3.95813i	0.132218	−	0.157571i	0.828091	+	0.560594i	$0.189427\pi$
$632$	20.8585	−	17.5024i	0.829708	−	0.696208i
$633$	−6.36994	−	36.1257i	−0.253182	−	1.43587i
$634$	−11.0487	+	30.3559i	−0.438798	+	1.20559i
$635$		0			0
$636$	−2.81756	−	1.02551i	−0.111723	−	0.0406640i
$637$	−11.3941	−	6.57837i	−0.451450	−	0.260645i
$638$	1.54362	−	8.75428i	0.0611123	−	0.346585i
$639$	6.79883	+	11.7759i	0.268958	+	0.465848i
$640$		0			0
$641$	−6.86879	−	5.76360i	−0.271301	−	0.227648i	0.496979	−	0.867763i	$-0.334443\pi$
$641$	−6.86879	−	5.76360i	−0.271301	−	0.227648i	−0.768280	+	0.640114i	$0.778887\pi$
$642$	25.3218	−	4.46491i	0.999371	−	0.176216i
$643$	−15.2005	+	8.77601i	−0.599449	+	0.346092i	−0.768825	−	0.639459i	$-0.779158\pi$
$643$	−15.2005	+	8.77601i	−0.599449	+	0.346092i	0.169376	+	0.985552i	$0.445825\pi$
$644$	0.305330	+	0.838886i	0.0120317	+	0.0330568i
$645$		0			0
$646$	2.34369	+	0.413256i	0.0922113	+	0.0162593i
$647$	14.0258	+	16.7153i	0.551411	+	0.657147i	0.967705	−	0.252083i	$-0.0811158\pi$
$647$	14.0258	+	16.7153i	0.551411	+	0.657147i	−0.416294	+	0.909230i	$0.636671\pi$
$648$	8.75734	+	10.4366i	0.344021	+	0.409988i
$649$	18.9768	+	3.34612i	0.744904	+	0.131347i
$650$		0			0
$651$	0.163975	+	0.450518i	0.00642669	+	0.0176572i
$652$	7.45990	−	4.30697i	0.292152	−	0.168674i
$653$	2.58253	−	0.455370i	0.101062	−	0.0178200i	−0.122888	−	0.992421i	$-0.539216\pi$
$653$	2.58253	−	0.455370i	0.101062	−	0.0178200i	0.223951	+	0.974600i	$0.428105\pi$
$654$	18.3927	+	15.4333i	0.719211	+	0.603489i
$655$		0			0
$656$	−14.3278	−	24.8164i	−0.559406	−	0.968919i
$657$	−1.57470	+	8.93059i	−0.0614351	+	0.348416i
$658$	−2.07848	−	1.20001i	−0.0810274	−	0.0467812i
$659$	−11.2804	−	4.10573i	−0.439422	−	0.159937i	0.112829	−	0.993614i	$-0.464009\pi$
$659$	−11.2804	−	4.10573i	−0.439422	−	0.159937i	−0.552251	+	0.833678i	$0.686231\pi$
$660$		0			0
$661$	2.99497	−	8.22862i	0.116491	−	0.320056i	−0.867721	−	0.497052i	$-0.834416\pi$
$661$	2.99497	−	8.22862i	0.116491	−	0.320056i	0.984212	+	0.176996i	$0.0566380\pi$
$662$	3.19917	+	18.1434i	0.124339	+	0.705163i
$663$	−1.82269	+	1.52942i	−0.0707876	+	0.0593978i
$664$	−10.9653	+	13.0679i	−0.425535	+	0.507133i
$665$		0			0
$666$	15.4109	+	33.5054i	0.597160	+	1.29831i
$667$	−30.4822			−1.18028
$668$	1.63321	−	1.94639i	0.0631909	−	0.0753080i
$669$	7.90276	−	6.63120i	0.305538	−	0.256377i
$670$		0			0
$671$	−3.43632	+	9.44121i	−0.132658	+	0.364474i
$672$		−	1.51354i		−	0.0583860i
$673$	41.2226	+	15.0038i	1.58902	+	0.578354i	0.977140	−	0.212599i	$-0.0681928\pi$
$673$	41.2226	+	15.0038i	1.58902	+	0.578354i	0.611876	+	0.790953i	$0.290415\pi$
$674$	−12.6700	−	7.31503i	−0.488030	−	0.281765i
$675$		0			0
$676$	3.64675	+	6.31636i	0.140260	+	0.242937i
$677$	−6.19238	+	10.7255i	−0.237993	+	0.412215i	−0.960138	−	0.279526i	$-0.909823\pi$
$677$	−6.19238	+	10.7255i	−0.237993	+	0.412215i	0.722146	+	0.691741i	$0.243156\pi$
$678$	−33.7201	−	28.2946i	−1.29501	−	1.08665i
$679$	0.0765271	−	0.0134938i	0.00293684	−	0.000517844i
$680$		0			0
$681$	1.79047	+	4.91928i	0.0686110	+	0.188507i
$682$	2.94236	−	1.07093i	0.112669	−	0.0410081i
$683$	9.00116	+	1.58715i	0.344420	+	0.0607305i	0.343183	−	0.939269i	$-0.388495\pi$
$683$	9.00116	+	1.58715i	0.344420	+	0.0607305i	0.00123733	+	0.999999i	$0.499606\pi$
$684$	5.27367	+	6.28491i	0.201644	+	0.240310i
$685$		0			0
$686$	−3.24450	−	0.572093i	−0.123876	−	0.0218426i
$687$	−3.20514	+	1.16658i	−0.122284	+	0.0445076i
$688$	18.6471	+	51.2324i	0.710912	+	1.95322i
$689$	2.46001	−	1.42029i	0.0937191	−	0.0541087i
$690$		0			0
$691$	−8.52471	−	7.15308i	−0.324295	−	0.272116i	0.466075	−	0.884745i	$-0.345668\pi$
$691$	−8.52471	−	7.15308i	−0.324295	−	0.272116i	−0.790371	+	0.612629i	$0.790112\pi$
$692$	−7.00890	+	12.1398i	−0.266438	+	0.461485i
$693$	−0.368770	−	0.638728i	−0.0140084	−	0.0242633i
$694$	−3.93424	+	22.3122i	−0.149342	+	0.846958i
$695$		0			0
$696$	18.4741	+	6.72403i	0.700260	+	0.254874i
$697$			2.83665i			0.107446i
$698$	2.72569	−	7.48877i	0.103169	−	0.283454i
$699$	2.75689	+	15.6351i	0.104275	+	0.591373i
$700$		0			0
$701$	−24.3830	+	29.0585i	−0.920934	+	1.09753i	0.0740265	+	0.997256i	$0.476415\pi$
$701$	−24.3830	+	29.0585i	−0.920934	+	1.09753i	−0.994960	+	0.100270i	$0.968029\pi$
$702$	−5.18867			−0.195834
$703$	7.41757	+	16.1268i	0.279759	+	0.608234i
$704$	4.27527			0.161130
$705$		0			0
$706$	−22.0612	+	18.5115i	−0.830283	+	0.696690i
$707$	0.233501	+	1.32425i	0.00878170	+	0.0498035i
$708$	9.16408	−	25.1781i	0.344407	−	0.946251i
$709$		−	10.5625i		−	0.396682i	−0.980133	−	0.198341i	$-0.936445\pi$
$709$		−	10.5625i		−	0.396682i	0.980133	−	0.198341i	$-0.0635553\pi$
$710$		0			0
$711$	−42.0013	−	24.2494i	−1.57517	−	0.909425i
$712$	−1.93952	+	10.9996i	−0.0726866	+	0.412226i
$713$	−5.36855	−	9.29860i	−0.201054	−	0.348235i
$714$	−0.148739	+	0.257624i	−0.00556642	+	0.00964132i
$715$		0			0
$716$	−14.7023	+	2.59241i	−0.549451	+	0.0968830i
$717$	22.7199	−	13.1174i	0.848491	−	0.489877i
$718$	4.37597	+	12.0229i	0.163310	+	0.448690i
$719$	33.2531	−	12.1032i	1.24013	−	0.451372i	0.363077	−	0.931759i	$-0.381726\pi$
$719$	33.2531	−	12.1032i	1.24013	−	0.451372i	0.877056	+	0.480388i	$0.159504\pi$
$720$		0			0
$721$	−1.26185	−	1.50381i	−0.0469936	−	0.0560048i
$722$	−11.2200	−	13.3715i	−0.417564	−	0.497634i
$723$	33.5796	+	5.92100i	1.24884	+	0.220204i
$724$	−6.95312	+	2.53073i	−0.258411	+	0.0940538i
$725$		0			0
$726$	33.2668	−	19.2066i	1.23465	−	0.712823i
$727$	24.7348	−	4.36141i	0.917362	−	0.161756i	0.305018	−	0.952347i	$-0.401338\pi$
$727$	24.7348	−	4.36141i	0.917362	−	0.161756i	0.612345	+	0.790591i	$0.290227\pi$
$728$	0.417853	+	0.350620i	0.0154867	+	0.0129948i
$729$	18.5245	−	32.0854i	0.686093	−	1.18835i
$730$		0			0
$731$	0.937187	−	5.31505i	0.0346631	−	0.196584i
$732$	12.0987	+	6.98518i	0.447180	+	0.258180i
$733$	30.0840	+	10.9497i	1.11118	+	0.404435i	0.831425	−	0.555637i	$-0.187526\pi$
$733$	30.0840	+	10.9497i	1.11118	+	0.404435i	0.279752	+	0.960072i	$0.409748\pi$
$734$			29.6994i			1.09623i
$735$		0			0
$736$	5.88606	+	33.3815i	0.216963	+	1.23046i
$737$	16.9834	−	14.2508i	0.625592	−	0.524934i
$738$	−22.5699	+	26.8977i	−0.830808	+	0.990119i
$739$	38.8950			1.43078			0.715388	−	0.698727i	$-0.246250\pi$
$739$	38.8950			1.43078			0.715388	+	0.698727i	$0.246250\pi$
$740$		0			0
$741$	−14.1758			−0.520763
$742$	0.228281	−	0.272055i	0.00838046	−	0.00998744i
$743$	−9.06927	+	7.61002i	−0.332719	+	0.279185i	−0.793807	−	0.608170i	$-0.791904\pi$
$743$	−9.06927	+	7.61002i	−0.332719	+	0.279185i	0.461088	+	0.887355i	$0.347459\pi$
$744$	1.20251	+	6.81978i	0.0440862	+	0.250025i
$745$		0			0
$746$		−	44.9008i		−	1.64394i
$747$	28.5522	+	10.3921i	1.04467	+	0.380229i
$748$	0.468609	+	0.270551i	0.0171340	+	0.00989234i
$749$	−0.147289	+	0.835315i	−0.00538181	+	0.0305218i
$750$		0			0
$751$	4.64115	−	8.03870i	0.169358	−	0.293336i	−0.768836	−	0.639446i	$-0.779164\pi$
$751$	4.64115	−	8.03870i	0.169358	−	0.293336i	0.938194	+	0.346109i	$0.112497\pi$
$752$	−38.6021	−	32.3910i	−1.40767	−	1.18118i
$753$	53.5009	−	9.43365i	1.94968	−	0.343781i
$754$	10.1411	−	5.85497i	0.369317	−	0.213226i
$755$		0			0
$756$	−0.169777	+	0.0617936i	−0.00617471	+	0.00224741i
$757$	34.5555	+	6.09307i	1.25594	+	0.221456i	0.761735	−	0.647888i	$-0.224348\pi$
$757$	34.5555	+	6.09307i	1.25594	+	0.221456i	0.494206	+	0.869345i	$0.335459\pi$
$758$	13.1128	+	15.6272i	0.476278	+	0.567606i
$759$	19.3641	+	23.0772i	0.702873	+	0.837651i
$760$		0			0
$761$	34.5513	−	12.5756i	1.25248	−	0.455866i	0.371243	−	0.928536i	$-0.378932\pi$
$761$	34.5513	−	12.5756i	1.25248	−	0.455866i	0.881240	+	0.472670i	$0.156710\pi$
$762$	13.5737	+	37.2935i	0.491724	+	1.35100i
$763$	−0.685927	+	0.396020i	−0.0248322	+	0.0143369i
$764$	0.960423	−	0.169349i	0.0347469	−	0.00612681i
$765$		0			0
$766$	−3.38716	+	5.86674i	−0.122383	+	0.211974i
$767$	12.6919	+	21.9830i	0.458279	+	0.793762i
$768$	7.21534	−	40.9202i	0.260361	−	1.47658i
$769$	−18.5544	−	10.7124i	−0.669088	−	0.386298i	0.126643	−	0.991948i	$-0.459580\pi$
$769$	−18.5544	−	10.7124i	−0.669088	−	0.386298i	−0.795731	+	0.605650i	$0.792913\pi$
$770$		0			0
$771$			15.3327i			0.552193i
$772$	−5.90782	+	16.2316i	−0.212627	+	0.584188i
$773$	−4.32849	−	24.5481i	−0.155685	−	0.882933i	−0.958157	−	0.286243i	$-0.907593\pi$
$773$	−4.32849	−	24.5481i	−0.155685	−	0.882933i	0.802472	−	0.596690i	$-0.203518\pi$
$774$	51.1759	−	42.9417i	1.83948	−	1.54351i
$775$		0			0
$776$	1.12242			0.0402926
$777$	−2.21138	+	0.181817i	−0.0793327	+	0.00652265i
$778$	−7.42878			−0.266335
$779$	−10.8633	+	12.9464i	−0.389219	+	0.463853i
$780$		0			0
$781$	0.927808	+	5.26186i	0.0331996	+	0.188284i
$782$	2.27860	−	6.26040i	0.0814826	−	0.223871i
$783$		−	6.16908i		−	0.220465i
$784$	−32.4543	−	11.8124i	−1.15908	−	0.421871i
$785$		0			0
$786$	2.27797	−	12.9190i	0.0812525	−	0.460806i
$787$	3.48911	+	6.04331i	0.124373	+	0.215421i	0.921488	−	0.388407i	$-0.126975\pi$
$787$	3.48911	+	6.04331i	0.124373	+	0.215421i	−0.797115	+	0.603828i	$0.793641\pi$
$788$	−6.07334	+	10.5193i	−0.216354	+	0.374736i
$789$	6.35985	+	5.33654i	0.226417	+	0.189986i
$790$		0			0
$791$	1.25754	−	0.726042i	0.0447130	−	0.0258151i
$792$	−3.64359	−	10.0107i	−0.129469	−	0.355714i
$793$	−12.4369	+	4.52668i	−0.441649	+	0.160747i
$794$	5.07532	+	0.894916i	0.180116	+	0.0317594i
$795$		0			0
$796$	−6.98693	−	8.32670i	−0.247645	−	0.295132i
$797$	15.2324	+	2.68588i	0.539558	+	0.0951386i	0.436784	−	0.899566i	$-0.356117\pi$
$797$	15.2324	+	2.68588i	0.539558	+	0.0951386i	0.102773	+	0.994705i	$0.467228\pi$
$798$	−1.66544	+	0.606172i	−0.0589561	+	0.0214583i
$799$	1.70611	+	4.68749i	0.0603577	+	0.165831i
$800$		0			0
$801$	19.5919	−	3.45459i	0.692247	−	0.122062i
$802$	−14.8162	−	12.4323i	−0.523179	−	0.438999i
$803$	−1.78165	+	3.08591i	−0.0628731	+	0.108899i
$804$	−15.4137	−	26.6973i	−0.543599	−	0.941542i
$805$		0			0
$806$	3.57212	+	2.06237i	0.125823	+	0.0726438i
$807$	17.4021	+	6.33384i	0.612583	+	0.222962i
$808$			19.4228i			0.683290i
$809$	−6.87030	+	18.8760i	−0.241547	+	0.663644i	0.758383	+	0.651809i	$0.225990\pi$
$809$	−6.87030	+	18.8760i	−0.241547	+	0.663644i	−0.999930	+	0.0118353i	$0.996233\pi$
$810$		0			0
$811$	14.0793	−	11.8140i	0.494393	−	0.414845i	−0.361205	−	0.932487i	$-0.617634\pi$
$811$	14.0793	−	11.8140i	0.494393	−	0.414845i	0.855597	+	0.517642i	$0.173190\pi$
$812$	0.262095	−	0.312352i	0.00919772	−	0.0109614i
$813$	−61.6792			−2.16318
$814$	1.18746	+	14.4426i	0.0416204	+	0.506215i
$815$		0			0
$816$	−4.01481	+	4.78466i	−0.140546	+	0.167497i
$817$	24.6320	−	20.6687i	0.861763	−	0.723105i
$818$	−6.82051	−	38.6810i	−0.238474	−	1.35245i
$819$	0.332294	−	0.912971i	0.0116113	−	0.0319018i
$820$		0			0
$821$	−26.5318	−	9.65679i	−0.925967	−	0.337024i	−0.165357	−	0.986234i	$-0.552878\pi$
$821$	−26.5318	−	9.65679i	−0.925967	−	0.337024i	−0.760610	+	0.649209i	$0.775100\pi$
$822$	63.4818	+	36.6512i	2.21418	+	1.27836i
$823$	−5.33259	+	30.2426i	−0.185882	+	1.05419i	0.738934	+	0.673778i	$0.235329\pi$
$823$	−5.33259	+	30.2426i	−0.185882	+	1.05419i	−0.924817	+	0.380414i	$0.875782\pi$
$824$	−14.1776	−	24.5563i	−0.493899	−	0.855459i
$825$		0			0
$826$	2.43112	+	2.03995i	0.0845895	+	0.0709790i
$827$	−3.05719	+	0.539066i	−0.106309	+	0.0187452i	−0.226550	−	0.974000i	$-0.572745\pi$
$827$	−3.05719	+	0.539066i	−0.106309	+	0.0187452i	0.120241	+	0.992745i	$0.461633\pi$
$828$	19.8904	−	11.4837i	0.691238	−	0.399087i
$829$	−15.5915	−	42.8373i	−0.541516	−	1.48780i	−0.844895	−	0.534933i	$-0.820337\pi$
$829$	−15.5915	−	42.8373i	−0.541516	−	1.48780i	0.303379	−	0.952870i	$-0.401885\pi$
$830$		0			0
$831$	12.2170	+	2.15419i	0.423803	+	0.0747280i
$832$	3.62007	+	4.31423i	0.125503	+	0.149569i
$833$	2.19761	+	2.61901i	0.0761427	+	0.0907434i
$834$	−97.2715	−	17.1516i	−3.36824	−	0.593911i
$835$		0			0
$836$	1.10261	+	3.02939i	0.0381344	+	0.104774i
$837$	1.88188	−	1.08650i	0.0650473	−	0.0375551i
$838$	−52.9212	+	9.33144i	−1.82813	+	0.322349i
$839$	−30.6988	−	25.7593i	−1.05984	−	0.889311i	−0.0657454	−	0.997836i	$-0.520943\pi$
$839$	−30.6988	−	25.7593i	−1.05984	−	0.889311i	−0.994094	+	0.108526i	$0.965387\pi$
$840$		0			0
$841$	−7.53871	−	13.0574i	−0.259956	−	0.450256i
$842$	−7.09480	+	40.2366i	−0.244503	+	1.38664i
$843$	39.2893	+	22.6837i	1.35319	+	0.781267i
$844$	−10.3266	−	3.75857i	−0.355456	−	0.129375i
$845$		0			0
$846$	−21.1184	+	58.0223i	−0.726066	+	1.99485i
$847$	0.220042	+	1.24792i	0.00756075	+	0.0428791i
$848$	5.71214	−	4.79305i	0.196156	−	0.164594i
$849$	2.58028	−	3.07506i	0.0885551	−	0.105536i
$850$		0			0
$851$	48.0655	−	12.6100i	1.64766	−	0.432264i
$852$	7.42940			0.254527
$853$	19.4716	−	23.2054i	0.666695	−	0.794536i	−0.321635	−	0.946864i	$-0.604232\pi$
$853$	19.4716	−	23.2054i	0.666695	−	0.794536i	0.988330	+	0.152327i	$0.0486768\pi$
$854$	−1.26758	+	1.06363i	−0.0433758	+	0.0363967i
$855$		0			0
$856$	−4.19029	+	11.5127i	−0.143221	+	0.393497i
$857$			13.8821i			0.474202i	0.971485	+	0.237101i	$0.0761973\pi$
$857$			13.8821i			0.474202i	−0.971485	+	0.237101i	$0.923803\pi$
$858$	−10.8749	−	3.95813i	−0.371262	−	0.135128i
$859$	38.8870	+	22.4514i	1.32681	+	0.766033i	0.984805	−	0.173666i	$-0.0555614\pi$
$859$	38.8870	+	22.4514i	1.32681	+	0.766033i	0.342003	+	0.939699i	$0.388895\pi$
$860$		0			0
$861$	−1.05626	−	1.82950i	−0.0359973	−	0.0623491i
$862$	23.8236	−	41.2636i	0.811433	−	1.40544i
$863$	−6.47395	−	5.43229i	−0.220376	−	0.184917i	0.525915	−	0.850537i	$-0.323723\pi$
$863$	−6.47395	−	5.43229i	−0.220376	−	0.184917i	−0.746291	+	0.665620i	$0.768167\pi$
$864$	−6.75586	+	1.19124i	−0.229839	+	0.0405268i
$865$		0			0
$866$	6.70548	+	18.4231i	0.227861	+	0.626044i
$867$	−40.5879	+	14.7728i	−1.37844	+	0.501710i
$868$	0.141444	+	0.0249403i	0.00480091	+	0.000846530i
$869$	−12.2496	−	14.5985i	−0.415540	−	0.495221i
$870$		0			0
$871$	28.7613	+	5.07139i	0.974540	+	0.171838i
$872$	−10.7504	+	3.91284i	−0.364056	+	0.132505i
$873$	−0.683770	−	1.87864i	−0.0231421	−	0.0635824i
$874$	34.3745	−	19.8461i	1.16273	−	0.671305i
$875$		0			0
$876$	3.79553	+	3.18483i	0.128239	+	0.107605i
$877$	−2.65387	+	4.59663i	−0.0896147	+	0.155217i	−0.907348	−	0.420380i	$-0.861897\pi$
$877$	−2.65387	+	4.59663i	−0.0896147	+	0.155217i	0.817734	+	0.575597i	$0.195230\pi$
$878$	11.5901	+	20.0746i	0.391146	+	0.677485i
$879$	−11.1969	+	63.5008i	−0.377662	+	2.14183i
$880$		0			0
$881$	4.90636	+	1.78577i	0.165299	+	0.0601640i	0.423344	−	0.905969i	$-0.360856\pi$
$881$	4.90636	+	1.78577i	0.165299	+	0.0601640i	−0.258045	+	0.966133i	$0.583078\pi$
$882$			42.3193i			1.42497i
$883$	−7.98529	+	21.9394i	−0.268726	+	0.738320i	0.729780	+	0.683682i	$0.239623\pi$
$883$	−7.98529	+	21.9394i	−0.268726	+	0.738320i	−0.998506	+	0.0546374i	$0.982600\pi$
$884$	0.123776	+	0.701968i	0.00416303	+	0.0236097i
$885$		0			0
$886$	32.1694	−	38.3380i	1.08075	−	1.28799i
$887$	−2.77215			−0.0930797			−0.0465398	−	0.998916i	$-0.514819\pi$
$887$	−2.77215			−0.0930797			−0.0465398	+	0.998916i	$0.514819\pi$
$888$	−31.9123	−	2.96029i	−1.07091	−	0.0993408i
$889$	−1.30919			−0.0439089
$890$		0			0
$891$	7.30440	−	6.12912i	0.244707	−	0.205333i
$892$	−0.536662	−	3.04356i	−0.0179688	−	0.101906i
$893$	−10.1647	+	27.9273i	−0.340149	+	0.934552i
$894$		−	36.0973i		−	1.20727i
$895$		0			0
$896$	1.62701	+	0.939357i	0.0543547	+	0.0313817i
$897$	−6.89106	+	39.0812i	−0.230086	+	1.30488i
$898$	−14.6000	−	25.2880i	−0.487209	−	0.843870i
$899$	−2.45206	+	4.24709i	−0.0817807	+	0.141648i
$900$		0			0
$901$	−0.726931	+	0.128178i	−0.0242176	+	0.00427022i
$902$	−11.9486	+	6.89851i	−0.397844	+	0.229695i
$903$	1.37468	+	3.77691i	0.0457466	+	0.125688i
$904$	19.7093	−	7.17359i	0.655521	−	0.238590i
$905$		0			0
$906$	−42.6721	−	50.8546i	−1.41768	−	1.68953i
$907$	−3.54938	−	4.22999i	−0.117855	−	0.140455i	0.703891	−	0.710308i	$-0.251444\pi$
$907$	−3.54938	−	4.22999i	−0.117855	−	0.140455i	−0.821746	+	0.569854i	$0.807000\pi$
$908$	1.54445	+	0.272328i	0.0512543	+	0.00903751i
$909$	32.5086	−	11.8322i	1.07824	−	0.392448i
$910$		0			0
$911$	−27.3320	+	15.7801i	−0.905549	+	0.522819i	−0.878996	−	0.476829i	$-0.841786\pi$
$911$	−27.3320	+	15.7801i	−0.905549	+	0.522819i	−0.0265524	+	0.999647i	$0.508453\pi$
$912$	−36.6470	+	6.46185i	−1.21350	+	0.213973i
$913$	9.14600	+	7.67440i	0.302688	+	0.253986i
$914$	−0.815563	+	1.41260i	−0.0269764	+	0.0467246i
$915$		0			0
$916$	−0.177434	+	1.00628i	−0.00586259	+	0.0332484i
$917$	0.374770	+	0.216373i	0.0123760	+	0.00714528i
$918$	1.26700	+	0.461150i	0.0418172	+	0.0152202i
$919$			49.9236i			1.64683i	0.567442	+	0.823413i	$0.307933\pi$
$919$			49.9236i			1.64683i	−0.567442	+	0.823413i	$0.692067\pi$
$920$		0			0
$921$	−9.23185	−	52.3564i	−0.304200	−	1.72520i
$922$	−42.5831	+	35.7315i	−1.40240	+	1.17675i
$923$	−4.52419	+	5.39173i	−0.148916	+	0.177471i
$924$	−0.402972			−0.0132568
$925$		0			0
$926$	−54.2202			−1.78179
$927$	−32.4640	+	38.6890i	−1.06626	+	1.27071i
$928$	11.8599	−	9.95166i	0.389321	−	0.326679i
$929$	8.44767	+	47.9091i	0.277159	+	1.57185i	0.732019	+	0.681284i	$0.238578\pi$
$929$	8.44767	+	47.9091i	0.277159	+	1.57185i	−0.454860	+	0.890563i	$0.650311\pi$
$930$		0			0
$931$			20.3691i			0.667571i
$932$	4.46931	+	1.62670i	0.146397	+	0.0532842i
$933$	−22.7982	−	13.1625i	−0.746380	−	0.430922i
$934$	3.26905	−	18.5397i	0.106966	−	0.606637i
$935$		0			0
$936$	7.01672	−	12.1533i	0.229349	−	0.397244i
$937$	−33.1957	−	27.8545i	−1.08446	−	0.909967i	−0.0881730	−	0.996105i	$-0.528103\pi$
$937$	−33.1957	−	27.8545i	−1.08446	−	0.909967i	−0.996283	+	0.0861384i	$0.972547\pi$
$938$	3.59587	−	0.634049i	0.117409	−	0.0207024i
$939$	28.6272	−	16.5279i	0.934212	−	0.539367i
$940$		0			0
$941$	−4.62180	+	1.68220i	−0.150666	+	0.0548381i	−0.416253	−	0.909249i	$-0.636657\pi$
$941$	−4.62180	+	1.68220i	−0.150666	+	0.0548381i	0.265586	+	0.964087i	$0.414435\pi$
$942$	−6.63315	−	1.16960i	−0.216120	−	0.0381077i
$943$	30.4110	+	36.2424i	0.990317	+	1.18021i
$944$	42.8314	+	51.0445i	1.39404	+	1.66136i
$945$		0			0
$946$	24.6672	−	8.97814i	0.802001	−	0.291905i
$947$	12.1253	+	33.3140i	0.394019	+	1.08256i	0.965150	+	0.261699i	$0.0842827\pi$
$947$	12.1253	+	33.3140i	0.394019	+	1.08256i	−0.571131	+	0.820859i	$0.693495\pi$
$948$	−22.9484	+	13.2492i	−0.745328	+	0.430316i
$949$	−4.62264	+	0.815096i	−0.150057	+	0.0264591i
$950$		0			0
$951$	−25.0013	+	43.3035i	−0.810722	+	1.40421i
$952$	−0.0708719	−	0.122754i	−0.00229697	−	0.00397847i
$953$	−6.55823	+	37.1936i	−0.212442	+	1.20482i	0.672849	+	0.739780i	$0.265070\pi$
$953$	−6.55823	+	37.1936i	−0.212442	+	1.20482i	−0.885291	+	0.465038i	$0.846041\pi$
$954$	−7.91276	−	4.56843i	−0.256185	−	0.147908i
$955$		0			0
$956$		−	7.85927i		−	0.254187i
$957$	4.70603	−	12.9297i	0.152124	−	0.417959i
$958$	−4.40737	−	24.9955i	−0.142396	−	0.807567i
$959$	−1.85237	+	1.55433i	−0.0598163	+	0.0501918i
$960$		0			0
$961$	29.2726			0.944276
$962$	−13.5688	+	13.4275i	−0.437476	+	0.432922i
$963$	21.8220			0.703203
$964$	6.56596	−	7.82500i	0.211475	−	0.252026i
$965$		0			0
$966$	0.861552	+	4.88610i	0.0277200	+	0.157208i
$967$	−12.4664	+	34.2510i	−0.400891	+	1.10144i	0.560955	+	0.827846i	$0.310434\pi$
$967$	−12.4664	+	34.2510i	−0.400891	+	1.10144i	−0.961846	+	0.273592i	$0.911788\pi$
$968$			18.3033i			0.588290i
$969$	3.46154	+	1.25990i	0.111201	+	0.0404738i
$970$		0			0
$971$	−7.63372	+	43.2930i	−0.244978	+	1.38934i	0.575567	+	0.817755i	$0.304782\pi$
$971$	−7.63372	+	43.2930i	−0.244978	+	1.38934i	−0.820544	+	0.571583i	$0.806330\pi$
$972$	−8.54394	−	14.7985i	−0.274047	−	0.474664i
$973$	1.62915	−	2.82177i	0.0522281	−	0.0904617i
$974$	−43.6286	−	36.6088i	−1.39795	−	1.17302i
$975$		0			0
$976$	−30.0882	+	17.3714i	−0.963099	+	0.556046i
$977$	−7.20878	−	19.8060i	−0.230629	−	0.633649i	0.769357	−	0.638819i	$-0.220577\pi$
$977$	−7.20878	−	19.8060i	−0.230629	−	0.633649i	−0.999987	+	0.00517002i	$0.998354\pi$
$978$	44.9865	−	16.3737i	1.43851	−	0.523574i
$979$	7.69841	+	1.35744i	0.246042	+	0.0433839i
$980$		0			0
$981$	13.0981	+	15.6098i	0.418191	+	0.498381i
$982$	−44.0631	−	7.76952i	−1.40611	−	0.247935i
$983$	39.0806	−	14.2242i	1.24648	−	0.453680i	0.367267	−	0.930116i	$-0.380294\pi$
$983$	39.0806	−	14.2242i	1.24648	−	0.453680i	0.879210	+	0.476435i	$0.158071\pi$
$984$	−10.4363	−	28.6735i	−0.332697	−	0.914077i
$985$		0			0
$986$	−2.99669	+	0.528397i	−0.0954339	+	0.0168276i
$987$	−2.84579	−	2.38790i	−0.0905825	−	0.0760078i
$988$	−2.12337	+	3.67778i	−0.0675533	+	0.117006i
$989$	−45.0072	−	77.9548i	−1.43115	−	2.47882i
$990$		0			0
$991$	−16.0941	−	9.29195i	−0.511247	−	0.295168i	0.222099	−	0.975024i	$-0.428709\pi$
$991$	−16.0941	−	9.29195i	−0.511247	−	0.295168i	−0.733346	+	0.679856i	$0.762042\pi$
$992$	5.12454	+	1.86518i	0.162704	+	0.0592195i
$993$			28.5169i			0.904955i
$994$	−0.300968	+	0.826904i	−0.00954613	+	0.0262278i
$995$		0			0
$996$	12.7174	−	10.6711i	0.402965	−	0.338128i
$997$	9.51853	−	11.3437i	0.301455	−	0.359260i	−0.593959	−	0.804496i	$-0.702436\pi$
$997$	9.51853	−	11.3437i	0.301455	−	0.359260i	0.895413	+	0.445236i	$0.146880\pi$
$998$	7.18043			0.227293
$999$	2.55204	+	9.72765i	0.0807430	+	0.307769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bb.e.151.13		96
5.2	odd	4		185.2.v.a.114.13	yes	96
5.3	odd	4		185.2.v.a.114.4	yes	96
5.4	even	2	inner	925.2.bb.e.151.4		96
37.25	even	18	inner	925.2.bb.e.876.13		96
185.62	odd	36		185.2.v.a.99.4	✓	96
185.99	even	18	inner	925.2.bb.e.876.4		96
185.173	odd	36		185.2.v.a.99.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.v.a.99.4	✓	96	185.62	odd	36
185.2.v.a.99.13	yes	96	185.173	odd	36
185.2.v.a.114.4	yes	96	5.3	odd	4
185.2.v.a.114.13	yes	96	5.2	odd	4
925.2.bb.e.151.4		96	5.4	even	2	inner
925.2.bb.e.151.13		96	1.1	even	1	trivial
925.2.bb.e.876.4		96	185.99	even	18	inner
925.2.bb.e.876.13		96	37.25	even	18	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07021 - 1.27542i) q^{2} +(1.97419 - 1.65654i) q^{3} +(-0.134064 - 0.760312i) q^{4} -4.29076i q^{6} +(0.133008 + 0.0484108i) q^{7} +(1.77057 + 1.02224i) q^{8} +(0.632347 - 3.58622i) q^{9} +(0.715450 - 1.23920i) q^{11} +(-1.52415 - 1.27892i) q^{12} +(1.85629 - 0.327315i) q^{13} +(0.204090 - 0.117831i) q^{14} +(4.64963 - 1.69233i) q^{16} +(-0.482371 - 0.0850551i) q^{17} +(-3.89720 - 4.64450i) q^{18} +(-1.87580 - 2.23549i) q^{19} +(0.342776 - 0.124760i) q^{21} +(-0.814818 - 2.23869i) q^{22} +(-7.07485 + 4.08466i) q^{23} +(5.18883 - 0.914931i) q^{24} +(1.56915 - 2.71785i) q^{26} +(-0.826667 - 1.43183i) q^{27} +(0.0189758 - 0.107617i) q^{28} +(3.23140 + 1.86565i) q^{29} +1.31432i q^{31} +(1.41912 - 3.89901i) q^{32} +(-0.640345 - 3.63158i) q^{33} +(-0.624718 + 0.524201i) q^{34} -2.81142 q^{36} +(-5.86718 - 1.60505i) q^{37} -4.85869 q^{38} +(3.12246 - 3.72121i) q^{39} +(-1.00565 - 5.70332i) q^{41} +(0.207719 - 0.570704i) q^{42} +11.0186i q^{43} +(-1.03809 - 0.377834i) q^{44} +(-2.36187 + 13.3948i) q^{46} +(-5.09207 - 8.81972i) q^{47} +(6.37584 - 11.0433i) q^{48} +(-5.34696 - 4.48664i) q^{49} +(-1.09319 + 0.631153i) q^{51} +(-0.497723 - 1.36748i) q^{52} +(1.41611 - 0.515423i) q^{53} +(-2.71089 - 0.478003i) q^{54} +(0.186012 + 0.221681i) q^{56} +(-7.40637 - 1.30594i) q^{57} +(5.83775 - 2.12477i) q^{58} +(4.60589 + 12.6546i) q^{59} +(-6.91487 + 1.21928i) q^{61} +(1.67631 + 1.40659i) q^{62} +(0.257719 - 0.446382i) q^{63} +(1.49391 + 2.58753i) q^{64} +(-5.31709 - 3.06982i) q^{66} +(14.5595 + 5.29924i) q^{67} +0.378156i q^{68} +(-7.20066 + 19.7837i) q^{69} +(-2.86044 + 2.40019i) q^{71} +(4.78560 - 5.70326i) q^{72} -2.49025 q^{73} +(-8.32621 + 5.76539i) q^{74} +(-1.44820 + 1.72589i) q^{76} +(0.155151 - 0.130187i) q^{77} +(-1.40443 - 7.96491i) q^{78} +(4.55510 - 12.5150i) q^{79} +(6.26191 + 2.27915i) q^{81} +(-8.35039 - 4.82110i) q^{82} +(-1.44890 + 8.21712i) q^{83} +(-0.140811 - 0.243891i) q^{84} +(14.0533 + 11.7922i) q^{86} +(9.46991 - 1.66980i) q^{87} +(2.53351 - 1.46273i) q^{88} +(1.86850 + 5.13365i) q^{89} +(0.262747 + 0.0463293i) q^{91} +(4.05410 + 4.83149i) q^{92} +(2.17722 + 2.59471i) q^{93} +(-16.6984 - 2.94438i) q^{94} +(-3.65725 - 10.0482i) q^{96} +(0.475449 - 0.274500i) q^{97} +(-11.4447 + 2.01801i) q^{98} +(-3.99161 - 3.34936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} + 6 q^{9} - 30 q^{11} + 36 q^{14} + 18 q^{19} - 24 q^{21} - 96 q^{24} + 48 q^{26} + 18 q^{29} + 54 q^{34} + 24 q^{36} + 36 q^{39} + 72 q^{41} + 84 q^{44} - 18 q^{46} + 6 q^{49} - 18 q^{51}+ \cdots + 24 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 + 6 * q^9 - 30 * q^11 + 36 * q^14 + 18 * q^19 - 24 * q^21 - 96 * q^24 + 48 * q^26 + 18 * q^29 + 54 * q^34 + 24 * q^36 + 36 * q^39 + 72 * q^41 + 84 * q^44 - 18 * q^46 + 6 * q^49 - 18 * q^51 - 24 * q^54 + 90 * q^56 - 18 * q^59 - 144 * q^61 - 66 * q^64 - 36 * q^66 + 6 * q^69 - 30 * q^71 + 6 * q^74 - 54 * q^76 - 60 * q^79 - 18 * q^81 - 48 * q^84 - 72 * q^86 - 108 * q^89 - 54 * q^91 - 6 * q^94 + 24 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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