LMFDB - Embedded newform 605.2.g.l.251.2

Newspace parameters

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$-1.14412 + 0.831254i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.l.511.2

$q$-expansion

$f(q)$	$=$	$q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} +O(q^{10})$	\(q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} -0.414214 q^{10} -5.17157 q^{12} +(2.11010 - 6.49422i) q^{13} +(-0.670212 + 0.486937i) q^{14} +(2.28825 + 1.66251i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-0.362036 - 1.11423i) q^{17} +(-1.67553 - 1.21734i) q^{18} +(0.565015 - 1.73894i) q^{20} +5.65685 q^{21} +2.82843 q^{23} +(-1.38603 + 4.26576i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.28825 - 1.66251i) q^{26} +(1.74806 + 5.37999i) q^{27} +(-1.13003 - 3.47788i) q^{28} +(6.19453 + 4.50059i) q^{29} +(0.947822 - 0.688633i) q^{30} +4.41421 q^{32} -0.485281 q^{34} +(-0.618034 + 1.90211i) q^{35} +(7.39614 - 5.37361i) q^{36} +(-2.95846 - 2.14944i) q^{37} +(5.96826 + 18.3684i) q^{39} +(-1.28293 - 0.932102i) q^{40} +(4.85410 - 3.52671i) q^{41} +(0.724072 - 2.22846i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(0.362036 - 1.11423i) q^{46} +(2.28825 - 1.66251i) q^{47} +(-6.86474 - 4.98752i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(0.127999 + 0.393941i) q^{50} +(2.68085 + 1.94775i) q^{51} +(10.1008 - 7.33866i) q^{52} +(0.106038 - 0.326351i) q^{53} +2.34315 q^{54} -3.17157 q^{56} +(2.56586 - 1.86420i) q^{58} +(7.81256 + 5.67616i) q^{59} +(1.59810 + 4.91846i) q^{60} +(-4.11416 - 12.6621i) q^{61} +(-8.09017 + 5.87785i) q^{63} +(-1.28909 + 3.96740i) q^{64} -6.82843 q^{65} -4.48528 q^{67} +(0.661956 - 2.03729i) q^{68} +(-6.47214 + 4.70228i) q^{69} +(0.670212 + 0.486937i) q^{70} +(-3.49613 - 10.7600i) q^{71} +(-2.45017 - 7.54086i) q^{72} +(-5.52431 - 4.01365i) q^{73} +(-1.22543 + 0.890329i) q^{74} +(0.874032 - 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 + 3.80423i) q^{79} +(2.42705 - 1.76336i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.767994 - 2.36364i) q^{82} +(1.85410 + 5.70634i) q^{83} +(8.36778 + 6.07955i) q^{84} +(-0.947822 + 0.688633i) q^{85} +(0.767994 - 2.36364i) q^{86} -21.6569 q^{87} +9.31371 q^{89} +(-0.639995 + 1.96970i) q^{90} +(-11.0486 + 8.02730i) q^{91} +(4.18389 + 3.03977i) q^{92} +(-0.362036 - 1.11423i) q^{94} +(-10.1008 + 7.33866i) q^{96} +(-2.36610 + 7.28210i) q^{97} -1.24264 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.127999	−	0.393941i	0.0905090	−	0.278558i	−0.895548	−	0.444964i	$-0.853216\pi$
$2$	0.127999	−	0.393941i	0.0905090	−	0.278558i	0.986057	+	0.166406i	$0.0532163\pi$
$3$	−2.28825	+	1.66251i	−1.32112	+	0.959849i	−0.321202	+	0.947011i	$0.604087\pi$
$3$	−2.28825	+	1.66251i	−1.32112	+	0.959849i	−0.999918	+	0.0128385i	$0.995913\pi$
$4$	1.47923	+	1.07472i	0.739614	+	0.537361i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	0.362036	+	1.11423i	0.147801	+	0.454883i
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	0.238404	−	0.971166i	$-0.423376\pi$
$7$	−1.61803	−	1.17557i	−0.611559	−	0.444324i	−0.849963	+	0.526842i	$0.823376\pi$
$8$	1.28293	−	0.932102i	0.453584	−	0.329548i
$9$	1.54508	−	4.75528i	0.515028	−	1.58509i
$10$	−0.414214			−0.130986
$11$		0			0
$11$		0			0
$12$	−5.17157			−1.49290
$13$	2.11010	−	6.49422i	0.585236	−	1.80117i	−0.0130823	−	0.999914i	$-0.504164\pi$
$13$	2.11010	−	6.49422i	0.585236	−	1.80117i	0.598319	−	0.801258i	$-0.295836\pi$
$14$	−0.670212	+	0.486937i	−0.179122	+	0.130139i
$15$	2.28825	+	1.66251i	0.590822	+	0.429258i
$16$	0.927051	+	2.85317i	0.231763	+	0.713292i
$17$	−0.362036	−	1.11423i	−0.0878066	−	0.270241i	0.897506	−	0.441003i	$-0.145377\pi$
$17$	−0.362036	−	1.11423i	−0.0878066	−	0.270241i	−0.985312	+	0.170762i	$0.945377\pi$
$18$	−1.67553	−	1.21734i	−0.394926	−	0.286931i
$19$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$19$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$20$	0.565015	−	1.73894i	0.126341	−	0.388838i
$21$	5.65685			1.23443
$22$		0			0
$23$	2.82843			0.589768			0.294884	−	0.955533i	$-0.404719\pi$
$23$	2.82843			0.589768			0.294884	+	0.955533i	$0.404719\pi$
$24$	−1.38603	+	4.26576i	−0.282922	+	0.870744i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−2.28825	−	1.66251i	−0.448762	−	0.326045i
$27$	1.74806	+	5.37999i	0.336415	+	1.03538i
$28$	−1.13003	−	3.47788i	−0.213556	−	0.657257i
$29$	6.19453	+	4.50059i	1.15029	+	0.835738i	0.988520	−	0.151090i	$-0.0482783\pi$
$29$	6.19453	+	4.50059i	1.15029	+	0.835738i	0.161774	+	0.986828i	$0.448278\pi$
$30$	0.947822	−	0.688633i	0.173048	−	0.125727i
$31$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$31$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$32$	4.41421			0.780330
$33$		0			0
$34$	−0.485281			−0.0832251
$35$	−0.618034	+	1.90211i	−0.104467	+	0.321516i
$36$	7.39614	−	5.37361i	1.23269	−	0.895602i
$37$	−2.95846	−	2.14944i	−0.486367	−	0.353367i	0.317418	−	0.948286i	$-0.397184\pi$
$37$	−2.95846	−	2.14944i	−0.486367	−	0.353367i	−0.803786	+	0.594919i	$0.797184\pi$
$38$		0			0
$39$	5.96826	+	18.3684i	0.955687	+	2.94130i
$40$	−1.28293	−	0.932102i	−0.202849	−	0.147378i
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	−0.140238	−	0.990118i	$-0.544787\pi$
$41$	4.85410	−	3.52671i	0.758083	−	0.550780i	0.898322	+	0.439338i	$0.144787\pi$
$42$	0.724072	−	2.22846i	0.111727	−	0.343859i
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$		0			0
$45$	−5.00000			−0.745356
$46$	0.362036	−	1.11423i	0.0533793	−	0.164285i
$47$	2.28825	−	1.66251i	0.333775	−	0.242502i	−0.408256	−	0.912868i	$-0.633863\pi$
$47$	2.28825	−	1.66251i	0.333775	−	0.242502i	0.742031	+	0.670366i	$0.233863\pi$
$48$	−6.86474	−	4.98752i	−0.990839	−	0.719887i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	0.127999	+	0.393941i	0.0181018	+	0.0557116i
$51$	2.68085	+	1.94775i	0.375394	+	0.272739i
$52$	10.1008	−	7.33866i	1.40073	−	1.01769i
$53$	0.106038	−	0.326351i	0.0145654	−	0.0448278i	−0.943510	−	0.331345i	$-0.892498\pi$
$53$	0.106038	−	0.326351i	0.0145654	−	0.0448278i	0.958075	+	0.286517i	$0.0924976\pi$
$54$	2.34315			0.318862
$55$		0			0
$56$	−3.17157			−0.423819
$57$		0			0
$58$	2.56586	−	1.86420i	0.336913	−	0.244782i
$59$	7.81256	+	5.67616i	1.01711	+	0.738973i	0.965688	−	0.259704i	$-0.0836251\pi$
$59$	7.81256	+	5.67616i	1.01711	+	0.738973i	0.0514204	+	0.998677i	$0.483625\pi$
$60$	1.59810	+	4.91846i	0.206314	+	0.634970i
$61$	−4.11416	−	12.6621i	−0.526764	−	1.62121i	−0.760800	−	0.648986i	$-0.775193\pi$
$61$	−4.11416	−	12.6621i	−0.526764	−	1.62121i	0.234036	−	0.972228i	$-0.424807\pi$
$62$		0			0
$63$	−8.09017	+	5.87785i	−1.01927	+	0.740540i
$64$	−1.28909	+	3.96740i	−0.161136	+	0.495925i
$65$	−6.82843			−0.846962
$66$		0			0
$67$	−4.48528			−0.547964			−0.273982	−	0.961735i	$-0.588341\pi$
$67$	−4.48528			−0.547964			−0.273982	+	0.961735i	$0.588341\pi$
$68$	0.661956	−	2.03729i	0.0802740	−	0.247058i
$69$	−6.47214	+	4.70228i	−0.779154	+	0.566088i
$70$	0.670212	+	0.486937i	0.0801056	+	0.0582001i
$71$	−3.49613	−	10.7600i	−0.414914	−	1.27697i	−0.912328	−	0.409461i	$-0.865717\pi$
$71$	−3.49613	−	10.7600i	−0.414914	−	1.27697i	0.497414	−	0.867513i	$-0.334283\pi$
$72$	−2.45017	−	7.54086i	−0.288756	−	0.888699i
$73$	−5.52431	−	4.01365i	−0.646572	−	0.469762i	0.215530	−	0.976497i	$-0.430852\pi$
$73$	−5.52431	−	4.01365i	−0.646572	−	0.469762i	−0.862102	+	0.506735i	$0.830852\pi$
$74$	−1.22543	+	0.890329i	−0.142454	+	0.103499i
$75$	0.874032	−	2.68999i	0.100925	−	0.310614i
$76$		0			0
$77$		0			0
$78$	8.00000			0.905822
$79$	−1.23607	+	3.80423i	−0.139069	+	0.428009i	−0.996201	−	0.0870877i	$-0.972244\pi$
$79$	−1.23607	+	3.80423i	−0.139069	+	0.428009i	0.857132	+	0.515097i	$0.172244\pi$
$80$	2.42705	−	1.76336i	0.271353	−	0.197149i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.767994	−	2.36364i	−0.0848108	−	0.261021i
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	0.999771	+	0.0213936i	$0.00681031\pi$
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	−0.796257	+	0.604959i	$0.793190\pi$
$84$	8.36778	+	6.07955i	0.913000	+	0.663333i
$85$	−0.947822	+	0.688633i	−0.102806	+	0.0746928i
$86$	0.767994	−	2.36364i	0.0828149	−	0.254878i
$87$	−21.6569			−2.32186
$88$		0			0
$89$	9.31371			0.987251			0.493626	−	0.869675i	$-0.335671\pi$
$89$	9.31371			0.987251			0.493626	+	0.869675i	$0.335671\pi$
$90$	−0.639995	+	1.96970i	−0.0674614	+	0.207625i
$91$	−11.0486	+	8.02730i	−1.15821	+	0.841489i
$92$	4.18389	+	3.03977i	0.436201	+	0.316918i
$93$		0			0
$94$	−0.362036	−	1.11423i	−0.0373412	−	0.114924i
$95$		0			0
$96$	−10.1008	+	7.33866i	−1.03091	+	0.748999i
$97$	−2.36610	+	7.28210i	−0.240241	+	0.739385i	0.756142	+	0.654408i	$0.227082\pi$
$97$	−2.36610	+	7.28210i	−0.240241	+	0.739385i	−0.996383	+	0.0849778i	$0.972918\pi$
$98$	−1.24264			−0.125526
$99$		0			0
$100$	−1.82843			−0.182843
$101$	4.11416	−	12.6621i	0.409374	−	1.25992i	−0.507812	−	0.861468i	$-0.669546\pi$
$101$	4.11416	−	12.6621i	0.409374	−	1.25992i	0.917187	−	0.398457i	$-0.130454\pi$
$102$	1.11044	−	0.806784i	0.109950	−	0.0798835i
$103$	−0.947822	−	0.688633i	−0.0933917	−	0.0678531i	0.540109	−	0.841595i	$-0.318383\pi$
$103$	−0.947822	−	0.688633i	−0.0933917	−	0.0678531i	−0.633501	+	0.773742i	$0.718383\pi$
$104$	−3.34617	−	10.2984i	−0.328119	−	1.00985i
$105$	−1.74806	−	5.37999i	−0.170594	−	0.525033i
$106$	−0.114990	−	0.0835452i	−0.0111688	−	0.00811463i
$107$	−2.95846	+	2.14944i	−0.286005	+	0.207795i	−0.721532	−	0.692381i	$-0.756562\pi$
$107$	−2.95846	+	2.14944i	−0.286005	+	0.207795i	0.435527	+	0.900175i	$0.356562\pi$
$108$	−3.19621	+	9.83692i	−0.307555	+	0.946558i
$109$	−3.65685			−0.350263			−0.175132	−	0.984545i	$-0.556035\pi$
$109$	−3.65685			−0.350263			−0.175132	+	0.984545i	$0.556035\pi$
$110$		0			0
$111$	10.3431			0.981728
$112$	1.85410	−	5.70634i	0.175196	−	0.539198i
$113$	−6.74975	+	4.90398i	−0.634963	+	0.461327i	−0.858116	−	0.513456i	$-0.828365\pi$
$113$	−6.74975	+	4.90398i	−0.634963	+	0.461327i	0.223153	+	0.974783i	$0.428365\pi$
$114$		0			0
$115$	−0.874032	−	2.68999i	−0.0815039	−	0.250843i
$116$	4.32624	+	13.3148i	0.401681	+	1.23625i
$117$	−27.6216	−	20.0682i	−2.55361	−	1.85531i
$118$	3.23607	−	2.35114i	0.297904	−	0.216440i
$119$	−0.724072	+	2.22846i	−0.0663756	+	0.204283i
$120$	4.48528			0.409448
$121$		0			0
$122$	−5.51472			−0.499279
$123$	−5.24419	+	16.1400i	−0.472853	+	1.45529i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	1.27999	+	3.93941i	0.114031	+	0.350950i
$127$	−4.83823	−	14.8906i	−0.429324	−	1.32132i	−0.898793	−	0.438374i	$-0.855555\pi$
$127$	−4.83823	−	14.8906i	−0.429324	−	1.32132i	0.469469	−	0.882949i	$-0.344445\pi$
$128$	8.54027	+	6.20487i	0.754860	+	0.548438i
$129$	−13.7295	+	9.97505i	−1.20881	+	0.878254i
$130$	−0.874032	+	2.68999i	−0.0766577	+	0.235928i
$131$	−11.3137			−0.988483			−0.494242	−	0.869325i	$-0.664554\pi$
$131$	−11.3137			−0.988483			−0.494242	+	0.869325i	$0.664554\pi$
$132$		0			0
$133$		0			0
$134$	−0.574112	+	1.76693i	−0.0495957	+	0.152640i
$135$	4.57649	−	3.32502i	0.393882	−	0.286172i
$136$	−1.50304	−	1.09203i	−0.128885	−	0.0936404i
$137$	7.09829	+	21.8463i	0.606448	+	1.86646i	0.486512	+	0.873674i	$0.338269\pi$
$137$	7.09829	+	21.8463i	0.606448	+	1.86646i	0.119937	+	0.992782i	$0.461731\pi$
$138$	1.02399	+	3.15152i	0.0871680	+	0.268276i
$139$	−3.23607	−	2.35114i	−0.274480	−	0.199421i	0.442026	−	0.897002i	$-0.354260\pi$
$139$	−3.23607	−	2.35114i	−0.274480	−	0.199421i	−0.716506	+	0.697581i	$0.754260\pi$
$140$	−2.95846	+	2.14944i	−0.250035	+	0.181661i
$141$	−2.47214	+	7.60845i	−0.208191	+	0.640747i
$142$	−4.68629			−0.393265
$143$		0			0
$144$	15.0000			1.25000
$145$	2.36610	−	7.28210i	0.196494	−	0.604746i
$146$	−2.28825	+	1.66251i	−0.189377	+	0.137590i
$147$	6.86474	+	4.98752i	0.566194	+	0.411364i
$148$	−2.06618	−	6.35904i	−0.169839	−	0.522710i
$149$	−3.60217	−	11.0863i	−0.295101	−	0.908227i	−0.983188	−	0.182599i	$-0.941549\pi$
$149$	−3.60217	−	11.0863i	−0.295101	−	0.908227i	0.688087	−	0.725629i	$-0.258451\pi$
$150$	−0.947822	−	0.688633i	−0.0773894	−	0.0562267i
$151$	−9.70820	+	7.05342i	−0.790042	+	0.573999i	−0.907976	−	0.419022i	$-0.862373\pi$
$151$	−9.70820	+	7.05342i	−0.790042	+	0.573999i	0.117934	+	0.993021i	$0.462373\pi$
$152$		0			0
$153$	−5.85786			−0.473580
$154$		0			0
$155$		0			0
$156$	−10.9125	+	33.5853i	−0.873702	+	2.68898i
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	−0.0355408	−	0.999368i	$-0.511315\pi$
$157$	11.3262	−	8.22899i	0.903932	−	0.656745i	0.939473	+	0.342623i	$0.111315\pi$
$158$	1.34042	+	0.973874i	0.106638	+	0.0774773i
$159$	0.299920	+	0.923060i	0.0237852	+	0.0732034i
$160$	−1.36407	−	4.19817i	−0.107839	−	0.331894i
$161$	−4.57649	−	3.32502i	−0.360678	−	0.262048i
$162$	−0.335106	+	0.243469i	−0.0263284	+	0.0191287i
$163$	−0.149960	+	0.461530i	−0.0117458	+	0.0361498i	−0.956758	−	0.290886i	$-0.906050\pi$
$163$	−0.149960	+	0.461530i	−0.0117458	+	0.0361498i	0.945012	+	0.327036i	$0.106050\pi$
$164$	10.9706			0.856657
$165$		0			0
$166$	2.48528			0.192895
$167$	−3.39009	+	10.4336i	−0.262333	+	0.807378i	0.729963	+	0.683487i	$0.239537\pi$
$167$	−3.39009	+	10.4336i	−0.262333	+	0.807378i	−0.992296	+	0.123891i	$0.960463\pi$
$168$	7.25734	−	5.27276i	0.559916	−	0.406803i
$169$	−27.2052	−	19.7657i	−2.09270	−	1.52044i
$170$	0.149960	+	0.461530i	0.0115014	+	0.0353977i
$171$		0			0
$172$	8.87537	+	6.44833i	0.676741	+	0.491681i
$173$	4.96909	−	3.61026i	0.377793	−	0.274483i	−0.382642	−	0.923897i	$-0.624986\pi$
$173$	4.96909	−	3.61026i	0.377793	−	0.274483i	0.760435	+	0.649414i	$0.224986\pi$
$174$	−2.77206	+	8.53151i	−0.210149	+	0.646772i
$175$	2.00000			0.151186
$176$		0			0
$177$	−27.3137			−2.05302
$178$	1.19215	−	3.66905i	0.0893551	−	0.275007i
$179$	1.34042	−	0.973874i	0.100188	−	0.0727908i	−0.536563	−	0.843860i	$-0.680278\pi$
$179$	1.34042	−	0.973874i	0.100188	−	0.0727908i	0.636751	+	0.771069i	$0.280278\pi$
$180$	−7.39614	−	5.37361i	−0.551276	−	0.400525i
$181$	−0.405958	−	1.24941i	−0.0301746	−	0.0928680i	0.934835	−	0.355082i	$-0.115547\pi$
$181$	−0.405958	−	1.24941i	−0.0301746	−	0.0928680i	−0.965010	+	0.262214i	$0.915547\pi$
$182$	1.74806	+	5.37999i	0.129575	+	0.398791i
$183$	30.4650	+	22.1341i	2.25204	+	1.63620i
$184$	3.62867	−	2.63638i	0.267509	−	0.194357i
$185$	−1.13003	+	3.47788i	−0.0830815	+	0.255698i
$186$		0			0
$187$		0			0
$188$	5.17157			0.377176
$189$	3.49613	−	10.7600i	0.254306	−	0.782673i
$190$		0			0
$191$	15.6251	+	11.3523i	1.13059	+	0.821425i	0.985781	−	0.168035i	$-0.0537420\pi$
$191$	15.6251	+	11.3523i	1.13059	+	0.821425i	0.144813	+	0.989459i	$0.453742\pi$
$192$	−3.64609	−	11.2215i	−0.263134	−	0.809842i
$193$	2.11010	+	6.49422i	0.151888	+	0.467464i	0.997832	−	0.0658075i	$-0.0209623\pi$
$193$	2.11010	+	6.49422i	0.151888	+	0.467464i	−0.845944	+	0.533272i	$0.820962\pi$
$194$	2.56586	+	1.86420i	0.184218	+	0.133842i
$195$	15.6251	−	11.3523i	1.11894	−	0.812956i
$196$	1.69505	−	5.21681i	0.121075	−	0.372629i
$197$	5.17157			0.368459			0.184230	−	0.982883i	$-0.441021\pi$
$197$	5.17157			0.368459			0.184230	+	0.982883i	$0.441021\pi$
$198$		0			0
$199$	21.6569			1.53521			0.767607	−	0.640921i	$-0.221447\pi$
$199$	21.6569			1.53521			0.767607	+	0.640921i	$0.221447\pi$
$200$	−0.490035	+	1.50817i	−0.0346507	+	0.106644i
$201$	10.2634	−	7.45682i	0.723926	−	0.525963i
$202$	−4.46150	−	3.24147i	−0.313910	−	0.228069i
$203$	−4.73220	−	14.5642i	−0.332135	−	1.02221i
$204$	1.87230	+	5.76233i	0.131087	+	0.403444i
$205$	−4.85410	−	3.52671i	−0.339025	−	0.246316i
$206$	−0.392601	+	0.285241i	−0.0273538	+	0.0198737i
$207$	4.37016	−	13.4500i	0.303747	−	0.934838i
$208$	20.4853			1.42040
$209$		0			0
$210$	−2.34315			−0.161692
$211$	4.94427	−	15.2169i	0.340378	−	1.04757i	−0.623634	−	0.781716i	$-0.714345\pi$
$211$	4.94427	−	15.2169i	0.340378	−	1.04757i	0.964012	−	0.265859i	$-0.0856555\pi$
$212$	0.507591	−	0.368786i	0.0348615	−	0.0253284i
$213$	25.8885	+	18.8091i	1.77385	+	1.28878i
$214$	0.468074	+	1.44058i	0.0319969	+	0.0984762i
$215$	−1.85410	−	5.70634i	−0.126449	−	0.389169i
$216$	7.25734	+	5.27276i	0.493799	+	0.358766i
$217$		0			0
$218$	−0.468074	+	1.44058i	−0.0317020	+	0.0975686i
$219$	19.3137			1.30510
$220$		0			0
$221$	−8.00000			−0.538138
$222$	1.32391	−	4.07458i	0.0888552	−	0.273468i
$223$	4.18389	−	3.03977i	0.280174	−	0.203558i	−0.438819	−	0.898575i	$-0.644603\pi$
$223$	4.18389	−	3.03977i	0.280174	−	0.203558i	0.718993	+	0.695017i	$0.244603\pi$
$224$	−7.14235	−	5.18922i	−0.477218	−	0.346719i
$225$	1.54508	+	4.75528i	0.103006	+	0.317019i
$226$	1.06791	+	3.28670i	0.0710366	+	0.218628i
$227$	2.17326	+	1.57896i	0.144244	+	0.104799i	0.657567	−	0.753396i	$-0.271586\pi$
$227$	2.17326	+	1.57896i	0.144244	+	0.104799i	−0.513323	+	0.858196i	$0.671586\pi$
$228$		0			0
$229$	−6.58630	+	20.2705i	−0.435235	+	1.33952i	0.457611	+	0.889153i	$0.348705\pi$
$229$	−6.58630	+	20.2705i	−0.435235	+	1.33952i	−0.892846	+	0.450363i	$0.851295\pi$
$230$	−1.17157			−0.0772512
$231$		0			0
$232$	12.1421			0.797170
$233$	−6.84230	+	21.0584i	−0.448254	+	1.37958i	0.430622	+	0.902532i	$0.358294\pi$
$233$	−6.84230	+	21.0584i	−0.448254	+	1.37958i	−0.878876	+	0.477051i	$0.841706\pi$
$234$	−11.4412	+	8.31254i	−0.747936	+	0.543408i
$235$	−2.28825	−	1.66251i	−0.149269	−	0.108450i
$236$	5.45627	+	16.7927i	0.355173	+	1.09311i
$237$	−3.49613	−	10.7600i	−0.227098	−	0.698936i
$238$	0.785202	+	0.570482i	0.0508971	+	0.0369789i
$239$	−0.555221	+	0.403392i	−0.0359143	+	0.0260933i	−0.605598	−	0.795771i	$-0.707066\pi$
$239$	−0.555221	+	0.403392i	−0.0359143	+	0.0260933i	0.569683	+	0.821864i	$0.307066\pi$
$240$	−2.62210	+	8.06998i	−0.169256	+	0.520915i
$241$	−6.00000			−0.386494			−0.193247	−	0.981150i	$-0.561902\pi$
$241$	−6.00000			−0.386494			−0.193247	+	0.981150i	$0.561902\pi$
$242$		0			0
$243$	−14.1421			−0.907218
$244$	7.52245	−	23.1517i	0.481575	−	1.48214i
$245$	−2.42705	+	1.76336i	−0.155059	+	0.112657i
$246$	5.68693	+	4.13180i	0.362586	+	0.263434i
$247$		0			0
$248$		0			0
$249$	−13.7295	−	9.97505i	−0.870070	−	0.632143i
$250$	0.335106	−	0.243469i	0.0211940	−	0.0153983i
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	−0.763185	−	0.646180i	$-0.776365\pi$
$251$	3.70820	−	11.4127i	0.234060	−	0.720362i	0.997245	−	0.0741818i	$-0.0236345\pi$
$252$	−18.2843			−1.15180
$253$		0			0
$254$	−6.48528			−0.406923
$255$	1.02399	−	3.15152i	0.0641249	−	0.197356i
$256$	−3.21225	+	2.33384i	−0.200766	+	0.145865i
$257$	−10.7710	−	7.82560i	−0.671878	−	0.488148i	0.198776	−	0.980045i	$-0.436304\pi$
$257$	−10.7710	−	7.82560i	−0.671878	−	0.488148i	−0.870653	+	0.491897i	$0.836304\pi$
$258$	2.17222	+	6.68539i	0.135236	+	0.416214i
$259$	2.26006	+	6.95575i	0.140433	+	0.432209i
$260$	−10.1008	−	7.33866i	−0.626425	−	0.455125i
$261$	30.9726	−	22.5029i	1.91716	−	1.39290i
$262$	−1.44814	+	4.45693i	−0.0894666	+	0.275350i
$263$	−22.9706			−1.41643			−0.708213	−	0.705999i	$-0.750498\pi$
$263$	−22.9706			−1.41643			−0.708213	+	0.705999i	$0.750498\pi$
$264$		0			0
$265$	−0.343146			−0.0210793
$266$		0			0
$267$	−21.3121	+	15.4841i	−1.30428	+	0.947612i
$268$	−6.63476	−	4.82043i	−0.405282	−	0.294455i
$269$	−1.64203	−	5.05364i	−0.100116	−	0.308126i	0.888437	−	0.458998i	$-0.151792\pi$
$269$	−1.64203	−	5.05364i	−0.100116	−	0.308126i	−0.988553	+	0.150873i	$0.951792\pi$
$270$	−0.724072	−	2.22846i	−0.0440656	−	0.135620i
$271$	−12.3891	−	9.00117i	−0.752581	−	0.546782i	0.144045	−	0.989571i	$-0.453989\pi$
$271$	−12.3891	−	9.00117i	−0.752581	−	0.546782i	−0.896626	+	0.442789i	$0.853989\pi$
$272$	2.84347	−	2.06590i	0.172411	−	0.125264i
$273$	11.9365	−	36.7369i	0.722432	−	2.22342i
$274$	9.51472			0.574805
$275$		0			0
$276$	−14.6274			−0.880467
$277$	−0.362036	+	1.11423i	−0.0217526	+	0.0669477i	−0.961344	−	0.275352i	$-0.911206\pi$
$277$	−0.362036	+	1.11423i	−0.0217526	+	0.0669477i	0.939591	+	0.342299i	$0.111206\pi$
$278$	−1.34042	+	0.973874i	−0.0803932	+	0.0584091i
$279$		0			0
$280$	0.980070	+	3.01635i	0.0585704	+	0.180261i
$281$	1.64203	+	5.05364i	0.0979551	+	0.301475i	0.988013	−	0.154374i	$-0.0493359\pi$
$281$	1.64203	+	5.05364i	0.0979551	+	0.301475i	−0.890057	+	0.455848i	$0.849336\pi$
$282$	2.68085	+	1.94775i	0.159642	+	0.115987i
$283$	−10.2158	+	7.42221i	−0.607266	+	0.441205i	−0.848451	−	0.529275i	$-0.822464\pi$
$283$	−10.2158	+	7.42221i	−0.607266	+	0.441205i	0.241185	+	0.970479i	$0.422464\pi$
$284$	6.39242	−	19.6738i	0.379320	−	1.16743i
$285$		0			0
$286$		0			0
$287$	−12.0000			−0.708338
$288$	6.82034	−	20.9908i	0.401892	−	1.23690i
$289$	12.6428	−	9.18557i	0.743697	−	0.540327i
$290$	−2.56586	−	1.86420i	−0.150672	−	0.109470i
$291$	−6.69234	−	20.5969i	−0.392312	−	1.20741i
$292$	−3.85816	−	11.8742i	−0.225782	−	0.694885i
$293$	−11.9964	−	8.71593i	−0.700840	−	0.509190i	0.179366	−	0.983782i	$-0.442595\pi$
$293$	−11.9964	−	8.71593i	−0.700840	−	0.509190i	−0.880206	+	0.474592i	$0.842595\pi$
$294$	2.84347	−	2.06590i	0.165834	−	0.120486i
$295$	2.98413	−	9.18421i	0.173743	−	0.534726i
$296$	−5.79899			−0.337059
$297$		0			0
$298$	−4.82843			−0.279703
$299$	5.96826	−	18.3684i	0.345154	−	1.06227i
$300$	4.18389	−	3.03977i	0.241557	−	0.175501i
$301$	−9.70820	−	7.05342i	−0.559572	−	0.406553i
$302$	1.53599	+	4.72729i	0.0883862	+	0.272025i
$303$	11.6366	+	35.8138i	0.668506	+	2.05745i
$304$		0			0
$305$	−10.7710	+	7.82560i	−0.616747	+	0.448093i
$306$	−0.749801	+	2.30765i	−0.0428633	+	0.131920i
$307$	27.6569			1.57846			0.789230	−	0.614098i	$-0.210480\pi$
$307$	27.6569			1.57846			0.789230	+	0.614098i	$0.210480\pi$
$308$		0			0
$309$	3.31371			0.188510
$310$		0			0
$311$	−22.0973	+	16.0546i	−1.25302	+	0.910373i	−0.998393	−	0.0566667i	$-0.981953\pi$
$311$	−22.0973	+	16.0546i	−1.25302	+	0.910373i	−0.254627	+	0.967039i	$0.581953\pi$
$312$	24.7781	+	18.0023i	1.40278	+	1.01918i
$313$	6.58630	+	20.2705i	0.372280	+	1.14576i	0.945296	+	0.326215i	$0.105773\pi$
$313$	6.58630	+	20.2705i	0.372280	+	1.14576i	−0.573016	+	0.819544i	$0.694227\pi$
$314$	−1.79199	−	5.51517i	−0.101128	−	0.311239i
$315$	8.09017	+	5.87785i	0.455829	+	0.331179i
$316$	−5.91691	+	4.29889i	−0.332852	+	0.241831i
$317$	6.58630	−	20.2705i	0.369923	−	1.13851i	−0.576917	−	0.816803i	$-0.695744\pi$
$317$	6.58630	−	20.2705i	0.369923	−	1.13851i	0.946840	−	0.321704i	$-0.104256\pi$
$318$	0.402020			0.0225442
$319$		0			0
$320$	4.17157			0.233198
$321$	3.19621	−	9.83692i	0.178395	−	0.549043i
$322$	−1.89564	+	1.37727i	−0.105640	+	0.0767521i
$323$		0			0
$324$	−0.565015	−	1.73894i	−0.0313897	−	0.0966076i
$325$	2.11010	+	6.49422i	0.117047	+	0.360235i
$326$	0.162621	+	0.118151i	0.00900672	+	0.00654377i
$327$	8.36778	−	6.07955i	0.462739	−	0.336200i
$328$	2.94021	−	9.04904i	0.162346	−	0.499649i
$329$	−5.65685			−0.311872
$330$		0			0
$331$	15.3137			0.841718			0.420859	−	0.907126i	$-0.361729\pi$
$331$	15.3137			0.841718			0.420859	+	0.907126i	$0.361729\pi$
$332$	−3.39009	+	10.4336i	−0.186055	+	0.572620i
$333$	−14.7923	+	10.7472i	−0.810612	+	0.588944i
$334$	3.67630	+	2.67099i	0.201158	+	0.146150i
$335$	1.38603	+	4.26576i	0.0757268	+	0.233063i
$336$	5.24419	+	16.1400i	0.286094	+	0.880507i
$337$	−2.84347	−	2.06590i	−0.154894	−	0.112537i	0.507639	−	0.861570i	$-0.330518\pi$
$337$	−2.84347	−	2.06590i	−0.154894	−	0.112537i	−0.662533	+	0.749033i	$0.730518\pi$
$338$	−11.2687	+	8.18722i	−0.612939	+	0.445326i
$339$	7.29218	−	22.4430i	0.396057	−	1.21894i
$340$	−2.14214			−0.116174
$341$		0			0
$342$		0			0
$343$	−6.18034	+	19.0211i	−0.333707	+	1.02704i
$344$	7.69757	−	5.59261i	0.415025	−	0.301533i
$345$	6.47214	+	4.70228i	0.348448	+	0.253162i
$346$	−0.786187	−	2.41964i	−0.0422657	−	0.130080i
$347$	7.09829	+	21.8463i	0.381056	+	1.17277i	0.939301	+	0.343095i	$0.111475\pi$
$347$	7.09829	+	21.8463i	0.381056	+	1.17277i	−0.558244	+	0.829677i	$0.688525\pi$
$348$	−32.0354	−	23.2751i	−1.71728	−	1.24768i
$349$	−5.63930	+	4.09719i	−0.301865	+	0.219318i	−0.728398	−	0.685154i	$-0.759735\pi$
$349$	−5.63930	+	4.09719i	−0.301865	+	0.219318i	0.426533	+	0.904472i	$0.359735\pi$
$350$	0.255998	−	0.787881i	0.0136837	−	0.0421140i
$351$	38.6274			2.06178
$352$		0			0
$353$	−1.31371			−0.0699216			−0.0349608	−	0.999389i	$-0.511131\pi$
$353$	−1.31371			−0.0699216			−0.0349608	+	0.999389i	$0.511131\pi$
$354$	−3.49613	+	10.7600i	−0.185817	+	0.571886i
$355$	−9.15298	+	6.65003i	−0.485790	+	0.352947i
$356$	13.7771	+	10.0097i	0.730185	+	0.530510i
$357$	−2.04798	−	6.30305i	−0.108391	−	0.333593i
$358$	−0.212076	−	0.652702i	−0.0112086	−	0.0344964i
$359$	18.8612	+	13.7035i	0.995455	+	0.723241i	0.961109	−	0.276169i	$-0.0890651\pi$
$359$	18.8612	+	13.7035i	0.995455	+	0.723241i	0.0343464	+	0.999410i	$0.489065\pi$
$360$	−6.41464	+	4.66051i	−0.338081	+	0.245630i
$361$	−5.87132	+	18.0701i	−0.309017	+	0.951057i
$362$	−0.544156			−0.0286002
$363$		0			0
$364$	−24.9706			−1.30881
$365$	−2.11010	+	6.49422i	−0.110448	+	0.339923i
$366$	12.6190	−	9.16826i	0.659607	−	0.479233i
$367$	−6.86474	−	4.98752i	−0.358336	−	0.260347i	0.394022	−	0.919101i	$-0.371084\pi$
$367$	−6.86474	−	4.98752i	−0.358336	−	0.260347i	−0.752358	+	0.658755i	$0.771084\pi$
$368$	2.62210	+	8.06998i	0.136686	+	0.420677i
$369$	−9.27051	−	28.5317i	−0.482603	−	1.48530i
$370$	1.22543	+	0.890329i	0.0637072	+	0.0462860i
$371$	−0.555221	+	0.403392i	−0.0288257	+	0.0209431i
$372$		0			0
$373$	3.79899			0.196704			0.0983521	−	0.995152i	$-0.468643\pi$
$373$	3.79899			0.196704			0.0983521	+	0.995152i	$0.468643\pi$
$374$		0			0
$375$	−2.82843			−0.146059
$376$	1.38603	−	4.26576i	0.0714789	−	0.219990i
$377$	42.2989	−	30.7319i	2.17850	−	1.58277i
$378$	−3.79129	−	2.75453i	−0.195003	−	0.141678i
$379$	6.90441	+	21.2496i	0.354656	+	1.09152i	0.956209	+	0.292685i	$0.0945489\pi$
$379$	6.90441	+	21.2496i	0.354656	+	1.09152i	−0.601553	+	0.798833i	$0.705451\pi$
$380$		0			0
$381$	35.8267	+	26.0296i	1.83546	+	1.33354i
$382$	6.47214	−	4.70228i	0.331143	−	0.240590i
$383$	−10.5505	+	32.4711i	−0.539105	+	1.65920i	0.195502	+	0.980703i	$0.437366\pi$
$383$	−10.5505	+	32.4711i	−0.539105	+	1.65920i	−0.734607	+	0.678492i	$0.762634\pi$
$384$	−29.8579			−1.52368
$385$		0			0
$386$	2.82843			0.143963
$387$	9.27051	−	28.5317i	0.471246	−	1.45035i
$388$	−11.3262	+	8.22899i	−0.575003	+	0.417764i
$389$	19.9240	+	14.4756i	1.01019	+	0.733944i	0.964248	−	0.265001i	$-0.0853721\pi$
$389$	19.9240	+	14.4756i	1.01019	+	0.733944i	0.0459386	+	0.998944i	$0.485372\pi$
$390$	−2.47214	−	7.60845i	−0.125181	−	0.385269i
$391$	−1.02399	−	3.15152i	−0.0517855	−	0.159379i
$392$	−3.84878	−	2.79631i	−0.194393	−	0.141235i
$393$	25.8885	−	18.8091i	1.30590	−	0.948795i
$394$	0.661956	−	2.03729i	0.0333489	−	0.102637i
$395$	4.00000			0.201262
$396$		0			0
$397$	13.3137			0.668196			0.334098	−	0.942538i	$-0.391568\pi$
$397$	13.3137			0.668196			0.334098	+	0.942538i	$0.391568\pi$
$398$	2.77206	−	8.53151i	0.138951	−	0.427646i
$399$		0			0
$400$	−2.42705	−	1.76336i	−0.121353	−	0.0881678i
$401$	5.35023	+	16.4663i	0.267178	+	0.822289i	0.991184	+	0.132495i	$0.0422988\pi$
$401$	5.35023	+	16.4663i	0.267178	+	0.822289i	−0.724006	+	0.689794i	$0.757701\pi$
$402$	−1.62383	−	4.99764i	−0.0809894	−	0.249260i
$403$		0			0
$404$	19.6940	−	14.3085i	0.979814	−	0.711877i
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−6.34315			−0.314805
$407$		0			0
$408$	5.25483			0.260153
$409$	−10.8065	+	33.2590i	−0.534347	+	1.64455i	0.210709	+	0.977549i	$0.432423\pi$
$409$	−10.8065	+	33.2590i	−0.534347	+	1.64455i	−0.745056	+	0.667002i	$0.767577\pi$
$410$	−2.01063	+	1.46081i	−0.0992982	+	0.0721443i
$411$	−52.5623	−	38.1887i	−2.59271	−	1.88371i
$412$	−0.661956	−	2.03729i	−0.0326122	−	0.100370i
$413$	−5.96826	−	18.3684i	−0.293679	−	0.903851i
$414$	−4.73911	−	3.44317i	−0.232915	−	0.169222i
$415$	4.85410	−	3.52671i	0.238278	−	0.173119i
$416$	9.31443	−	28.6669i	0.456678	−	1.40551i
$417$	11.3137			0.554035
$418$		0			0
$419$	−14.3431			−0.700709			−0.350354	−	0.936617i	$-0.613939\pi$
$419$	−14.3431			−0.700709			−0.350354	+	0.936617i	$0.613939\pi$
$420$	3.19621	−	9.83692i	0.155959	−	0.479992i
$421$	4.85410	−	3.52671i	0.236574	−	0.171881i	−0.463181	−	0.886264i	$-0.653292\pi$
$421$	4.85410	−	3.52671i	0.236574	−	0.171881i	0.699756	+	0.714382i	$0.253292\pi$
$422$	−5.36169	−	3.89550i	−0.261003	−	0.189630i
$423$	−4.37016	−	13.4500i	−0.212484	−	0.653960i
$424$	−0.168153	−	0.517523i	−0.00816625	−	0.0251331i
$425$	0.947822	+	0.688633i	0.0459761	+	0.0334036i
$426$	10.7234	−	7.79100i	0.519550	−	0.377475i
$427$	−8.22832	+	25.3242i	−0.398197	+	1.22552i
$428$	−6.68629			−0.323194
$429$		0			0
$430$	−2.48528			−0.119851
$431$	−3.49613	+	10.7600i	−0.168403	+	0.518290i	−0.999271	−	0.0381792i	$-0.987844\pi$
$431$	−3.49613	+	10.7600i	−0.168403	+	0.518290i	0.830868	+	0.556469i	$0.187844\pi$
$432$	−13.7295	+	9.97505i	−0.660560	+	0.479925i
$433$	−2.95846	−	2.14944i	−0.142174	−	0.103296i	0.514425	−	0.857536i	$-0.328006\pi$
$433$	−2.95846	−	2.14944i	−0.142174	−	0.103296i	−0.656599	+	0.754240i	$0.728006\pi$
$434$		0			0
$435$	6.69234	+	20.5969i	0.320873	+	0.987545i
$436$	−5.40932	−	3.93010i	−0.259060	−	0.188218i
$437$		0			0
$438$	2.47214	−	7.60845i	0.118123	−	0.363546i
$439$	16.0000			0.763638			0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000			0.763638			0.381819	+	0.924237i	$0.375298\pi$
$440$		0			0
$441$	−15.0000			−0.714286
$442$	−1.02399	+	3.15152i	−0.0487063	+	0.149903i
$443$	17.1282	−	12.4443i	0.813784	−	0.591248i	−0.101142	−	0.994872i	$-0.532249\pi$
$443$	17.1282	−	12.4443i	0.813784	−	0.591248i	0.914925	+	0.403624i	$0.132249\pi$
$444$	15.2999	+	11.1160i	0.726100	+	0.527543i
$445$	−2.87809	−	8.85786i	−0.136435	−	0.419903i
$446$	−0.661956	−	2.03729i	−0.0313445	−	0.0964686i
$447$	26.6737	+	19.3796i	1.26162	+	0.916624i
$448$	6.74975	−	4.90398i	0.318896	−	0.231691i
$449$	−5.13815	+	15.8136i	−0.242484	+	0.746291i	0.753555	+	0.657384i	$0.228337\pi$
$449$	−5.13815	+	15.8136i	−0.242484	+	0.746291i	−0.996040	+	0.0889063i	$0.971663\pi$
$450$	2.07107			0.0976311
$451$		0			0
$452$	−15.2548			−0.717527
$453$	10.4884	−	32.2799i	0.492787	−	1.51664i
$454$	0.900192	−	0.654028i	0.0422481	−	0.0306950i
$455$	11.0486	+	8.02730i	0.517968	+	0.376326i
$456$		0			0
$457$	5.09423	+	15.6784i	0.238298	+	0.733406i	0.996667	+	0.0815803i	$0.0259967\pi$
$457$	5.09423	+	15.6784i	0.238298	+	0.733406i	−0.758369	+	0.651826i	$0.774003\pi$
$458$	7.14235	+	5.18922i	0.333740	+	0.242476i
$459$	5.36169	−	3.89550i	0.250262	−	0.181826i
$460$	1.59810	−	4.91846i	0.0745120	−	0.229324i
$461$	32.6274			1.51961			0.759805	−	0.650151i	$-0.225294\pi$
$461$	32.6274			1.51961			0.759805	+	0.650151i	$0.225294\pi$
$462$		0			0
$463$	22.1421			1.02903			0.514516	−	0.857481i	$-0.327972\pi$
$463$	22.1421			1.02903			0.514516	+	0.857481i	$0.327972\pi$
$464$	−7.09829	+	21.8463i	−0.329530	+	1.01419i
$465$		0			0
$466$	7.41996	+	5.39092i	0.343723	+	0.249729i
$467$	−2.83417	−	8.72268i	−0.131150	−	0.403638i	0.863821	−	0.503798i	$-0.168064\pi$
$467$	−2.83417	−	8.72268i	−0.131150	−	0.403638i	−0.994971	+	0.100160i	$0.968064\pi$
$468$	−19.2908	−	59.3710i	−0.891718	−	2.74443i
$469$	7.25734	+	5.27276i	0.335113	+	0.243474i
$470$	−0.947822	+	0.688633i	−0.0437198	+	0.0317643i
$471$	−12.2364	+	37.6599i	−0.563826	+	1.73528i
$472$	15.3137			0.704871
$473$		0			0
$474$	−4.68629			−0.215248
$475$		0			0
$476$	−3.46605	+	2.51823i	−0.158866	+	0.115423i
$477$	−1.38805	−	1.00848i	−0.0635546	−	0.0461751i
$478$	0.0878446	+	0.270358i	0.00401792	+	0.0123659i
$479$	11.1246	+	34.2380i	0.508296	+	1.56438i	0.795157	+	0.606403i	$0.207388\pi$
$479$	11.1246	+	34.2380i	0.508296	+	1.56438i	−0.286861	+	0.957972i	$0.592612\pi$
$480$	10.1008	+	7.33866i	0.461037	+	0.334963i
$481$	−20.2016	+	14.6773i	−0.921114	+	0.669229i
$482$	−0.767994	+	2.36364i	−0.0349812	+	0.107661i
$483$	16.0000			0.728025
$484$		0			0
$485$	7.65685			0.347680
$486$	−1.81018	+	5.57116i	−0.0821114	+	0.252713i
$487$	6.07954	−	4.41704i	0.275490	−	0.200155i	−0.441458	−	0.897282i	$-0.645539\pi$
$487$	6.07954	−	4.41704i	0.275490	−	0.200155i	0.716948	+	0.697127i	$0.245539\pi$
$488$	−17.0805	−	12.4097i	−0.773199	−	0.561762i
$489$	−0.424151	−	1.30540i	−0.0191808	−	0.0590324i
$490$	0.383997	+	1.18182i	0.0173472	+	0.0533893i
$491$	−18.8612	−	13.7035i	−0.851193	−	0.618428i	0.0742814	−	0.997237i	$-0.476334\pi$
$491$	−18.8612	−	13.7035i	−0.851193	−	0.618428i	−0.925475	+	0.378809i	$0.876334\pi$
$492$	−25.1033	+	18.2386i	−1.13175	+	0.822262i
$493$	2.77206	−	8.53151i	0.124847	−	0.384240i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.99226	+	21.5200i	−0.313646	+	0.965302i
$498$	−5.68693	+	4.13180i	−0.254838	+	0.185150i
$499$	1.34042	+	0.973874i	0.0600056	+	0.0435966i	0.617384	−	0.786662i	$-0.288193\pi$
$499$	1.34042	+	0.973874i	0.0600056	+	0.0435966i	−0.557378	+	0.830259i	$0.688193\pi$
$500$	0.565015	+	1.73894i	0.0252682	+	0.0777677i
$501$	−9.58862	−	29.5107i	−0.428388	−	1.31844i
$502$	−4.02127	−	2.92162i	−0.179478	−	0.130398i
$503$	−23.1601	+	16.8268i	−1.03266	+	0.750269i	−0.968839	−	0.247693i	$-0.920328\pi$
$503$	−23.1601	+	16.8268i	−1.03266	+	0.750269i	−0.0638177	+	0.997962i	$0.520328\pi$
$504$	−4.90035	+	15.0817i	−0.218279	+	0.671793i
$505$	−13.3137			−0.592452
$506$		0			0
$507$	95.1127			4.22410
$508$	8.84636	−	27.2263i	0.392494	−	1.20797i
$509$	−7.53495	+	5.47446i	−0.333981	+	0.242651i	−0.742118	−	0.670269i	$-0.766179\pi$
$509$	−7.53495	+	5.47446i	−0.333981	+	0.242651i	0.408137	+	0.912921i	$0.366179\pi$
$510$	−1.11044	−	0.806784i	−0.0491712	−	0.0357250i
$511$	4.22020	+	12.9884i	0.186691	+	0.574575i
$512$	7.03241	+	21.6435i	0.310792	+	0.956518i
$513$		0			0
$514$	−4.46150	+	3.24147i	−0.196788	+	0.142975i
$515$	−0.362036	+	1.11423i	−0.0159532	+	0.0490989i
$516$	−31.0294			−1.36599
$517$		0			0
$518$	3.02944			0.133106
$519$	−5.36842	+	16.5223i	−0.235648	+	0.725249i
$520$	−8.76038	+	6.36479i	−0.384168	+	0.279114i
$521$	−2.17326	−	1.57896i	−0.0952121	−	0.0691756i	0.539161	−	0.842203i	$-0.318742\pi$
$521$	−2.17326	−	1.57896i	−0.0952121	−	0.0691756i	−0.634373	+	0.773027i	$0.718742\pi$
$522$	−4.90035	−	15.0817i	−0.214482	−	0.660109i
$523$	−11.6184	−	35.7578i	−0.508038	−	1.56358i	−0.795603	−	0.605818i	$-0.792846\pi$
$523$	−11.6184	−	35.7578i	−0.508038	−	1.56358i	0.287565	−	0.957761i	$-0.407154\pi$
$524$	−16.7356	−	12.1591i	−0.731096	−	0.531173i
$525$	−4.57649	+	3.32502i	−0.199734	+	0.145116i
$526$	−2.94021	+	9.04904i	−0.128199	+	0.394557i
$527$		0			0
$528$		0			0
$529$	−15.0000			−0.652174
$530$	−0.0439223	+	0.135179i	−0.00190786	+	0.00587180i
$531$	39.0628	−	28.3808i	1.69518	−	1.23162i
$532$		0			0
$533$	−12.6606	−	38.9653i	−0.548391	−	1.68778i
$534$	3.37190	+	10.3776i	0.145916	+	0.449084i
$535$	2.95846	+	2.14944i	0.127905	+	0.0929286i
$536$	−5.75429	+	4.18074i	−0.248548	+	0.180580i
$537$	−1.44814	+	4.45693i	−0.0624920	+	0.192331i
$538$	−2.20101			−0.0948923
$539$		0			0
$540$	10.3431			0.445098
$541$	−1.85410	+	5.70634i	−0.0797141	+	0.245335i	−0.982970	−	0.183768i	$-0.941170\pi$
$541$	−1.85410	+	5.70634i	−0.0797141	+	0.245335i	0.903255	+	0.429103i	$0.141170\pi$
$542$	−5.13171	+	3.72841i	−0.220426	+	0.160149i
$543$	3.00609	+	2.18405i	0.129004	+	0.0937266i
$544$	−1.59810	−	4.91846i	−0.0685181	−	0.210877i
$545$	1.13003	+	3.47788i	0.0484052	+	0.148976i
$546$	−12.9443	−	9.40456i	−0.553964	−	0.402478i
$547$	−27.5066	+	19.9847i	−1.17610	+	0.854484i	−0.991726	−	0.128373i	$-0.959025\pi$
$547$	−27.5066	+	19.9847i	−1.17610	+	0.854484i	−0.184370	+	0.982857i	$0.559025\pi$
$548$	−12.9787	+	39.9444i	−0.554423	+	1.70634i
$549$	−66.5685			−2.84108
$550$		0			0
$551$		0			0
$552$	−3.92028	+	12.0654i	−0.166858	+	0.513537i
$553$	6.47214	−	4.70228i	0.275223	−	0.199961i
$554$	0.392601	+	0.285241i	0.0166800	+	0.0121187i
$555$	−3.19621	−	9.83692i	−0.135671	−	0.417554i
$556$	−2.26006	−	6.95575i	−0.0958479	−	0.294990i
$557$	30.8576	+	22.4194i	1.30748	+	0.949940i	0.999999	−	0.00161430i	$-0.000513849\pi$
$557$	30.8576	+	22.4194i	1.30748	+	0.949940i	0.307481	+	0.951554i	$0.400514\pi$
$558$		0			0
$559$	12.6606	−	38.9653i	0.535486	−	1.64806i
$560$	−6.00000			−0.253546
$561$		0			0
$562$	2.20101			0.0928440
$563$	−3.60217	+	11.0863i	−0.151813	+	0.467233i	−0.997824	−	0.0659327i	$-0.978998\pi$
$563$	−3.60217	+	11.0863i	−0.151813	+	0.467233i	0.846011	+	0.533166i	$0.178998\pi$
$564$	−11.8338	+	8.59778i	−0.498294	+	0.362032i
$565$	6.74975	+	4.90398i	0.283964	+	0.206312i
$566$	1.61630	+	4.97445i	0.0679380	+	0.209092i
$567$	0.618034	+	1.90211i	0.0259550	+	0.0798812i
$568$	−14.5147	−	10.5455i	−0.609022	−	0.442481i
$569$	16.4580	−	11.9574i	0.689953	−	0.501280i	−0.186692	−	0.982419i	$-0.559776\pi$
$569$	16.4580	−	11.9574i	0.689953	−	0.501280i	0.876645	+	0.481138i	$0.159776\pi$
$570$		0			0
$571$	−45.9411			−1.92258			−0.961288	−	0.275545i	$-0.911142\pi$
$571$	−45.9411			−1.92258			−0.961288	+	0.275545i	$0.911142\pi$
$572$		0			0
$573$	−54.6274			−2.28209
$574$	−1.53599	+	4.72729i	−0.0641109	+	0.197313i
$575$	−2.28825	+	1.66251i	−0.0954264	+	0.0693314i
$576$	16.8744	+	12.2599i	0.703099	+	0.510831i
$577$	2.15402	+	6.62940i	0.0896731	+	0.275985i	0.985829	−	0.167754i	$-0.0536515\pi$
$577$	2.15402	+	6.62940i	0.0896731	+	0.275985i	−0.896156	+	0.443740i	$0.853651\pi$
$578$	−2.00029	−	6.15627i	−0.0832013	−	0.256067i
$579$	−15.6251	−	11.3523i	−0.649358	−	0.471786i
$580$	11.3262	−	8.22899i	0.470296	−	0.341690i
$581$	3.70820	−	11.4127i	0.153842	−	0.473478i
$582$	−8.97056			−0.371842
$583$		0			0
$584$	−10.8284			−0.448084
$585$	−10.5505	+	32.4711i	−0.436209	+	1.34251i
$586$	−4.96909	+	3.61026i	−0.205271	+	0.149138i
$587$	−21.1494	−	15.3660i	−0.872930	−	0.634221i	0.0584412	−	0.998291i	$-0.481387\pi$
$587$	−21.1494	−	15.3660i	−0.872930	−	0.634221i	−0.931372	+	0.364070i	$0.881387\pi$
$588$	4.79431	+	14.7554i	0.197714	+	0.608501i
$589$		0			0
$590$	−3.23607	−	2.35114i	−0.133227	−	0.0967949i
$591$	−11.8338	+	8.59778i	−0.486779	+	0.353665i
$592$	3.39009	−	10.4336i	0.139332	−	0.428819i
$593$	−20.4853			−0.841230			−0.420615	−	0.907239i	$-0.638186\pi$
$593$	−20.4853			−0.841230			−0.420615	+	0.907239i	$0.638186\pi$
$594$		0			0
$595$	2.34315			0.0960596
$596$	6.58630	−	20.2705i	0.269785	−	0.830314i
$597$	−49.5562	+	36.0047i	−2.02820	+	1.47357i
$598$	−6.47214	−	4.70228i	−0.264665	−	0.192291i
$599$	1.74806	+	5.37999i	0.0714240	+	0.219820i	0.980396	−	0.197036i	$-0.0631317\pi$
$599$	1.74806	+	5.37999i	0.0714240	+	0.219820i	−0.908972	+	0.416857i	$0.863132\pi$
$600$	−1.38603	−	4.26576i	−0.0565844	−	0.174149i
$601$	−35.5491	−	25.8279i	−1.45008	−	1.05354i	−0.985813	−	0.167848i	$-0.946318\pi$
$601$	−35.5491	−	25.8279i	−1.45008	−	1.05354i	−0.464266	−	0.885696i	$-0.653682\pi$
$602$	−4.02127	+	2.92162i	−0.163895	+	0.119076i
$603$	−6.93014	+	21.3288i	−0.282217	+	0.868575i
$604$	−21.9411			−0.892772
$605$		0			0
$606$	15.5980			0.633625
$607$	5.65015	−	17.3894i	0.229333	−	0.705813i	−0.768490	−	0.639861i	$-0.778992\pi$
$607$	5.65015	−	17.3894i	0.229333	−	0.705813i	0.997823	−	0.0659515i	$-0.0210083\pi$
$608$		0			0
$609$	35.0415	+	25.4592i	1.41995	+	1.03166i
$610$	1.70414	+	5.24481i	0.0689987	+	0.212356i
$611$	−5.96826	−	18.3684i	−0.241450	−	0.743107i
$612$	−8.66512	−	6.29558i	−0.350267	−	0.254484i
$613$	20.5942	−	14.9626i	0.831792	−	0.604333i	−0.0882735	−	0.996096i	$-0.528135\pi$
$613$	20.5942	−	14.9626i	0.831792	−	0.604333i	0.920066	+	0.391764i	$0.128135\pi$
$614$	3.54005	−	10.8952i	0.142865	−	0.439693i
$615$	16.9706			0.684319
$616$		0			0
$617$	11.6569			0.469287			0.234644	−	0.972081i	$-0.424608\pi$
$617$	11.6569			0.469287			0.234644	+	0.972081i	$0.424608\pi$
$618$	0.424151	−	1.30540i	0.0170619	−	0.0525111i
$619$	20.7568	−	15.0807i	0.834287	−	0.606145i	−0.0864816	−	0.996253i	$-0.527562\pi$
$619$	20.7568	−	15.0807i	0.834287	−	0.606145i	0.920769	+	0.390108i	$0.127562\pi$
$620$		0			0
$621$	4.94427	+	15.2169i	0.198407	+	0.610633i
$622$	3.49613	+	10.7600i	0.140182	+	0.431436i
$623$	−15.0699	−	10.9489i	−0.603763	−	0.438659i
$624$	−46.8754	+	34.0569i	−1.87652	+	1.36337i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	8.82843			0.352855
$627$		0			0
$628$	25.5980			1.02147
$629$	−1.32391	+	4.07458i	−0.0527879	+	0.162464i
$630$	3.35106	−	2.43469i	0.133509	−	0.0970002i
$631$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$631$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$632$	1.96014	+	6.03269i	0.0779702	+	0.239968i
$633$	13.9845	+	43.0399i	0.555834	+	1.71068i
$634$	−7.14235	−	5.18922i	−0.283659	−	0.206090i
$635$	−12.6667	+	9.20287i	−0.502661	+	0.365205i
$636$	−0.548383	+	1.68775i	−0.0217448	+	0.0669236i
$637$	−20.4853			−0.811656
$638$		0			0
$639$	−56.5685			−2.23782
$640$	3.26209	−	10.0397i	0.128945	−	0.396853i
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.952832	−	0.303500i	$-0.901845\pi$
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.00579592	+	0.999983i	$0.501845\pi$
$642$	−3.46605	−	2.51823i	−0.136794	−	0.0993867i
$643$	15.2827	+	47.0353i	0.602691	+	1.85489i	0.511947	+	0.859017i	$0.328924\pi$
$643$	15.2827	+	47.0353i	0.602691	+	1.85489i	0.0907436	+	0.995874i	$0.471076\pi$
$644$	−3.19621	−	9.83692i	−0.125948	−	0.387629i
$645$	13.7295	+	9.97505i	0.540597	+	0.392767i
$646$		0			0
$647$	−10.8504	+	33.3942i	−0.426574	+	1.31286i	0.474905	+	0.880037i	$0.342482\pi$
$647$	−10.8504	+	33.3942i	−0.426574	+	1.31286i	−0.901479	+	0.432823i	$0.857518\pi$
$648$	−1.58579			−0.0622956
$649$		0			0
$650$	2.82843			0.110940
$651$		0			0
$652$	−0.717842	+	0.521543i	−0.0281129	+	0.0204252i
$653$	−0.277611	−	0.201696i	−0.0108637	−	0.00789297i	0.582340	−	0.812945i	$-0.302137\pi$
$653$	−0.277611	−	0.201696i	−0.0108637	−	0.00789297i	−0.593204	+	0.805052i	$0.702137\pi$
$654$	−1.32391	−	4.07458i	−0.0517691	−	0.159329i
$655$	3.49613	+	10.7600i	0.136605	+	0.420427i
$656$	14.5623	+	10.5801i	0.568563	+	0.413085i
$657$	−27.6216	+	20.0682i	−1.07762	+	0.782937i
$658$	−0.724072	+	2.22846i	−0.0282273	+	0.0868746i
$659$	21.9411			0.854705			0.427352	−	0.904085i	$-0.359446\pi$
$659$	21.9411			0.854705			0.427352	+	0.904085i	$0.359446\pi$
$660$		0			0
$661$	−0.627417			−0.0244037			−0.0122018	−	0.999926i	$-0.503884\pi$
$661$	−0.627417			−0.0244037			−0.0122018	+	0.999926i	$0.503884\pi$
$662$	1.96014	−	6.03269i	0.0761830	−	0.234467i
$663$	18.3060	−	13.3001i	0.710945	−	0.516532i
$664$	7.69757	+	5.59261i	0.298724	+	0.217035i
$665$		0			0
$666$	2.34037	+	7.20292i	0.0906875	+	0.279107i
$667$	17.5208	+	12.7296i	0.678407	+	0.492891i
$668$	−16.2280	+	11.7903i	−0.627879	+	0.456181i
$669$	−4.52012	+	13.9115i	−0.174758	+	0.537850i
$670$	1.85786			0.0717756
$671$		0			0
$672$	24.9706			0.963260
$673$	−1.38603	+	4.26576i	−0.0534275	+	0.164433i	−0.974210	−	0.225644i	$-0.927551\pi$
$673$	−1.38603	+	4.26576i	−0.0534275	+	0.164433i	0.920782	+	0.390077i	$0.127551\pi$
$674$	−1.17780	+	0.855724i	−0.0453673	+	0.0329612i
$675$	−4.57649	−	3.32502i	−0.176149	−	0.127980i
$676$	−19.0000	−	58.4760i	−0.730769	−	2.24908i
$677$	−5.30631	−	16.3311i	−0.203938	−	0.627657i	−0.999755	−	0.0221198i	$-0.992958\pi$
$677$	−5.30631	−	16.3311i	−0.203938	−	0.627657i	0.795817	−	0.605537i	$-0.207042\pi$
$678$	−7.90782	−	5.74537i	−0.303698	−	0.220650i
$679$	12.3891	−	9.00117i	0.475448	−	0.345433i
$680$	−0.574112	+	1.76693i	−0.0220162	+	0.0677588i
$681$	−7.59798			−0.291155
$682$		0			0
$683$	31.7990			1.21675			0.608377	−	0.793648i	$-0.291821\pi$
$683$	31.7990			1.21675			0.608377	+	0.793648i	$0.291821\pi$
$684$		0			0
$685$	18.5836	−	13.5018i	0.710042	−	0.515876i
$686$	6.70212	+	4.86937i	0.255888	+	0.185914i
$687$	−18.6289	−	57.3337i	−0.710736	−	2.18742i
$688$	5.56231	+	17.1190i	0.212061	+	0.652656i
$689$	−1.89564	−	1.37727i	−0.0722183	−	0.0524697i
$690$	2.68085	−	1.94775i	0.102058	−	0.0741495i
$691$	−5.15635	+	15.8696i	−0.196157	+	0.603708i	0.803804	+	0.594894i	$0.202806\pi$
$691$	−5.15635	+	15.8696i	−0.196157	+	0.603708i	−0.999961	+	0.00881465i	$0.997194\pi$
$692$	11.2304			0.426918
$693$		0			0
$694$	9.51472			0.361174
$695$	−1.23607	+	3.80423i	−0.0468867	+	0.144303i
$696$	−27.7842	+	20.1864i	−1.05316	+	0.765163i
$697$	−5.68693	−	4.13180i	−0.215408	−	0.156503i
$698$	0.892225	+	2.74599i	0.0337712	+	0.103937i
$699$	−19.3529	−	59.5622i	−0.731995	−	2.25285i
$700$	2.95846	+	2.14944i	0.111819	+	0.0812414i
$701$	26.3961	−	19.1779i	0.996968	−	0.724340i	0.0355322	−	0.999369i	$-0.488687\pi$
$701$	26.3961	−	19.1779i	0.996968	−	0.724340i	0.961436	+	0.275029i	$0.0886874\pi$
$702$	4.94427	−	15.2169i	0.186610	−	0.574325i
$703$		0			0
$704$		0			0
$705$	8.00000			0.301297
$706$	−0.168153	+	0.517523i	−0.00632854	+	0.0194772i
$707$	−21.5420	+	15.6512i	−0.810172	+	0.588624i
$708$	−40.4032	−	29.3547i	−1.51845	−	1.10322i
$709$	−6.37422	−	19.6178i	−0.239389	−	0.736763i	−0.996509	−	0.0834875i	$-0.973394\pi$
$709$	−6.37422	−	19.6178i	−0.239389	−	0.736763i	0.757120	−	0.653276i	$-0.226606\pi$
$710$	1.44814	+	4.45693i	0.0543479	+	0.167266i
$711$	16.1803	+	11.7557i	0.606810	+	0.440873i
$712$	11.9488	−	8.68133i	0.447801	−	0.325346i
$713$		0			0
$714$	−2.74517			−0.102735
$715$		0			0
$716$	3.02944			0.113215
$717$	0.599841	−	1.84612i	0.0224015	−	0.0689446i
$718$	7.81256	−	5.67616i	0.291562	−	0.211832i
$719$	−23.9929	−	17.4319i	−0.894784	−	0.650099i	0.0423368	−	0.999103i	$-0.486520\pi$
$719$	−23.9929	−	17.4319i	−0.894784	−	0.650099i	−0.937121	+	0.349005i	$0.886520\pi$
$720$	−4.63525	−	14.2658i	−0.172746	−	0.531657i
$721$	0.724072	+	2.22846i	0.0269658	+	0.0829923i
$722$	6.36701	+	4.62590i	0.236956	+	0.172158i
$723$	13.7295	−	9.97505i	0.510605	−	0.370976i
$724$	0.742265	−	2.28446i	0.0275861	−	0.0849012i
$725$	−7.65685			−0.284368
$726$		0			0
$727$	−36.4853			−1.35316			−0.676582	−	0.736367i	$-0.736540\pi$
$727$	−36.4853			−1.35316			−0.676582	+	0.736367i	$0.736540\pi$
$728$	−6.69234	+	20.5969i	−0.248034	+	0.763372i
$729$	34.7877	−	25.2748i	1.28843	−	0.936102i
$730$	2.28825	+	1.66251i	0.0846918	+	0.0615322i
$731$	−2.17222	−	6.68539i	−0.0803423	−	0.247268i
$732$	21.2767	+	65.4829i	0.786409	+	2.42032i
$733$	27.0663	+	19.6649i	0.999718	+	0.726338i	0.962028	−	0.272952i	$-0.0879999\pi$
$733$	27.0663	+	19.6649i	0.999718	+	0.726338i	0.0376905	+	0.999289i	$0.488000\pi$
$734$	−2.84347	+	2.06590i	−0.104954	+	0.0762538i
$735$	2.62210	−	8.06998i	0.0967175	−	0.297666i
$736$	12.4853			0.460214
$737$		0			0
$738$	−12.4264			−0.457422
$739$	11.7245	−	36.0842i	0.431291	−	1.32738i	−0.465549	−	0.885022i	$-0.654143\pi$
$739$	11.7245	−	36.0842i	0.431291	−	1.32738i	0.896840	−	0.442355i	$-0.145857\pi$
$740$	−5.40932	+	3.93010i	−0.198851	+	0.144473i
$741$		0			0
$742$	0.0878446	+	0.270358i	0.00322488	+	0.00992516i
$743$	−9.14628	−	28.1494i	−0.335544	−	1.03270i	−0.966453	−	0.256843i	$-0.917318\pi$
$743$	−9.14628	−	28.1494i	−0.335544	−	1.03270i	0.630909	−	0.775857i	$-0.282682\pi$
$744$		0			0
$745$	−9.43059	+	6.85173i	−0.345510	+	0.251028i
$746$	0.486267	−	1.49658i	0.0178035	−	0.0547935i
$747$	30.0000			1.09764
$748$		0			0
$749$	7.31371			0.267237
$750$	−0.362036	+	1.11423i	−0.0132197	+	0.0406860i
$751$	12.9443	−	9.40456i	0.472343	−	0.343177i	−0.326011	−	0.945366i	$-0.605705\pi$
$751$	12.9443	−	9.40456i	0.472343	−	0.343177i	0.798354	+	0.602189i	$0.205705\pi$
$752$	6.86474	+	4.98752i	0.250331	+	0.181876i
$753$	10.4884	+	32.2799i	0.382218	+	1.17635i
$754$	−6.69234	−	20.5969i	−0.243721	−	0.750095i
$755$	9.70820	+	7.05342i	0.353318	+	0.256700i
$756$	16.7356	−	12.1591i	0.608666	−	0.442222i
$757$	−2.87809	+	8.85786i	−0.104606	+	0.321945i	−0.989638	−	0.143586i	$-0.954137\pi$
$757$	−2.87809	+	8.85786i	−0.104606	+	0.321945i	0.885032	+	0.465531i	$0.154137\pi$
$758$	9.25483			0.336151
$759$		0			0
$760$		0			0
$761$	9.27051	−	28.5317i	0.336056	−	1.03427i	−0.630144	−	0.776478i	$-0.717004\pi$
$761$	9.27051	−	28.5317i	0.336056	−	1.03427i	0.966200	−	0.257795i	$-0.0829959\pi$
$762$	14.8399	−	10.7818i	0.537593	−	0.390585i
$763$	5.91691	+	4.29889i	0.214207	+	0.155630i
$764$	10.9125	+	33.5853i	0.394802	+	1.21507i
$765$	1.81018	+	5.57116i	0.0654472	+	0.201426i
$766$	11.4412	+	8.31254i	0.413388	+	0.300344i
$767$	53.3475	−	38.7592i	1.92627	−	1.39951i
$768$	3.47040	−	10.6808i	0.125227	−	0.385410i
$769$	−14.9706			−0.539852			−0.269926	−	0.962881i	$-0.586999\pi$
$769$	−14.9706			−0.539852			−0.269926	+	0.962881i	$0.586999\pi$
$770$		0			0
$771$	37.6569			1.35618
$772$	−3.85816	+	11.8742i	−0.138858	+	0.427362i
$773$	24.5005	−	17.8006i	0.881221	−	0.640245i	−0.0523529	−	0.998629i	$-0.516672\pi$
$773$	24.5005	−	17.8006i	0.881221	−	0.640245i	0.933574	+	0.358384i	$0.116672\pi$
$774$	−10.0532	−	7.30406i	−0.361354	−	0.262539i
$775$		0			0
$776$	3.75213	+	11.5479i	0.134693	+	0.414544i
$777$	−16.7356	−	12.1591i	−0.600385	−	0.436205i
$778$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} +O(q^{10})\)	\(q+(0.127999 - 0.393941i) q^{2} +(-2.28825 + 1.66251i) q^{3} +(1.47923 + 1.07472i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(0.362036 + 1.11423i) q^{6} +(-1.61803 - 1.17557i) q^{7} +(1.28293 - 0.932102i) q^{8} +(1.54508 - 4.75528i) q^{9} -0.414214 q^{10} -5.17157 q^{12} +(2.11010 - 6.49422i) q^{13} +(-0.670212 + 0.486937i) q^{14} +(2.28825 + 1.66251i) q^{15} +(0.927051 + 2.85317i) q^{16} +(-0.362036 - 1.11423i) q^{17} +(-1.67553 - 1.21734i) q^{18} +(0.565015 - 1.73894i) q^{20} +5.65685 q^{21} +2.82843 q^{23} +(-1.38603 + 4.26576i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.28825 - 1.66251i) q^{26} +(1.74806 + 5.37999i) q^{27} +(-1.13003 - 3.47788i) q^{28} +(6.19453 + 4.50059i) q^{29} +(0.947822 - 0.688633i) q^{30} +4.41421 q^{32} -0.485281 q^{34} +(-0.618034 + 1.90211i) q^{35} +(7.39614 - 5.37361i) q^{36} +(-2.95846 - 2.14944i) q^{37} +(5.96826 + 18.3684i) q^{39} +(-1.28293 - 0.932102i) q^{40} +(4.85410 - 3.52671i) q^{41} +(0.724072 - 2.22846i) q^{42} +6.00000 q^{43} -5.00000 q^{45} +(0.362036 - 1.11423i) q^{46} +(2.28825 - 1.66251i) q^{47} +(-6.86474 - 4.98752i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(0.127999 + 0.393941i) q^{50} +(2.68085 + 1.94775i) q^{51} +(10.1008 - 7.33866i) q^{52} +(0.106038 - 0.326351i) q^{53} +2.34315 q^{54} -3.17157 q^{56} +(2.56586 - 1.86420i) q^{58} +(7.81256 + 5.67616i) q^{59} +(1.59810 + 4.91846i) q^{60} +(-4.11416 - 12.6621i) q^{61} +(-8.09017 + 5.87785i) q^{63} +(-1.28909 + 3.96740i) q^{64} -6.82843 q^{65} -4.48528 q^{67} +(0.661956 - 2.03729i) q^{68} +(-6.47214 + 4.70228i) q^{69} +(0.670212 + 0.486937i) q^{70} +(-3.49613 - 10.7600i) q^{71} +(-2.45017 - 7.54086i) q^{72} +(-5.52431 - 4.01365i) q^{73} +(-1.22543 + 0.890329i) q^{74} +(0.874032 - 2.68999i) q^{75} +8.00000 q^{78} +(-1.23607 + 3.80423i) q^{79} +(2.42705 - 1.76336i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.767994 - 2.36364i) q^{82} +(1.85410 + 5.70634i) q^{83} +(8.36778 + 6.07955i) q^{84} +(-0.947822 + 0.688633i) q^{85} +(0.767994 - 2.36364i) q^{86} -21.6569 q^{87} +9.31371 q^{89} +(-0.639995 + 1.96970i) q^{90} +(-11.0486 + 8.02730i) q^{91} +(4.18389 + 3.03977i) q^{92} +(-0.362036 - 1.11423i) q^{94} +(-10.1008 + 7.33866i) q^{96} +(-2.36610 + 7.28210i) q^{97} -1.24264 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{8} - 10 q^{9} + 8 q^{10} - 64 q^{12} - 8 q^{13} + 4 q^{14} - 6 q^{16} + 8 q^{17} + 10 q^{18} + 2 q^{20} - 8 q^{24} - 2 q^{25} - 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{32} + 64 q^{34} + 4 q^{35} - 10 q^{36} + 4 q^{37} - 16 q^{39} - 6 q^{40} + 12 q^{41} - 16 q^{42} + 48 q^{43} - 40 q^{45} - 8 q^{46} + 6 q^{49} + 2 q^{50} - 16 q^{51} + 8 q^{52} - 12 q^{53} + 64 q^{54} - 48 q^{56} + 12 q^{58} + 8 q^{59} - 16 q^{60} + 4 q^{61} - 20 q^{63} + 14 q^{64} - 32 q^{65} + 32 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} + 30 q^{72} - 8 q^{73} - 20 q^{74} + 64 q^{78} + 8 q^{79} + 6 q^{80} - 2 q^{81} - 12 q^{82} - 12 q^{83} + 32 q^{84} - 8 q^{85} + 12 q^{86} - 128 q^{87} - 16 q^{89} - 10 q^{90} - 16 q^{91} + 16 q^{92} + 8 q^{94} - 8 q^{96} + 4 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^8 - 10 * q^9 + 8 * q^10 - 64 * q^12 - 8 * q^13 + 4 * q^14 - 6 * q^16 + 8 * q^17 + 10 * q^18 + 2 * q^20 - 8 * q^24 - 2 * q^25 - 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^32 + 64 * q^34 + 4 * q^35 - 10 * q^36 + 4 * q^37 - 16 * q^39 - 6 * q^40 + 12 * q^41 - 16 * q^42 + 48 * q^43 - 40 * q^45 - 8 * q^46 + 6 * q^49 + 2 * q^50 - 16 * q^51 + 8 * q^52 - 12 * q^53 + 64 * q^54 - 48 * q^56 + 12 * q^58 + 8 * q^59 - 16 * q^60 + 4 * q^61 - 20 * q^63 + 14 * q^64 - 32 * q^65 + 32 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 + 30 * q^72 - 8 * q^73 - 20 * q^74 + 64 * q^78 + 8 * q^79 + 6 * q^80 - 2 * q^81 - 12 * q^82 - 12 * q^83 + 32 * q^84 - 8 * q^85 + 12 * q^86 - 128 * q^87 - 16 * q^89 - 10 * q^90 - 16 * q^91 + 16 * q^92 + 8 * q^94 - 8 * q^96 + 4 * q^97 + 24 * q^98

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