LMFDB - Embedded newform 605.2.j.i.9.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [605,2,Mod(9,605)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(605, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("605.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,6,3,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	16.0.343361479062744140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 3 x^{14} - 8 x^{13} + 8 x^{12} + 7 x^{11} + 6 x^{10} + 56 x^{9} - 137 x^{8} + \cdots + 6561 $ x^16 - x^15 + 3x^14 - 8x^13 + 8x^12 + 7x^11 + 6x^10 + 56x^9 - 137x^8 + 168x^7 + 54x^6 + 189x^5 + 648x^4 - 1944x^3 + 2187x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.4
Root			$-0.833856 + 1.51812i$ of defining polynomial
Character	$\chi$	$=$	605.9
Dual form			605.2.j.i.269.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.40079 + 0.780063i) q^{2} +(0.465695 + 0.640974i) q^{3} +(3.53725 + 2.56996i) q^{4} +(-1.81200 + 1.31021i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-2.03615 + 2.80252i) q^{7} +(3.51992 + 4.84475i) q^{8} +(0.733075 - 2.25617i) q^{9} +(-5.37228 + 1.73205i) q^{10} +3.46410i q^{12} +(-7.07450 + 5.13992i) q^{14} +(-1.68365 - 0.551291i) q^{15} +(1.96914 + 6.06040i) q^{16} +(1.50702 - 0.489660i) q^{17} +(3.51992 - 4.84475i) q^{18} +(3.23607 - 2.35114i) q^{19} +(-9.77669 - 0.0222534i) q^{20} -2.74456 q^{21} +0.792287i q^{23} +(-1.46615 + 4.51235i) q^{24} +(1.56672 - 4.74820i) q^{25} +(4.04807 - 1.31530i) q^{27} +(-14.4047 + 4.68038i) q^{28} +(7.07450 + 5.13992i) q^{29} +(-3.61204 - 2.63688i) q^{30} +(1.04209 - 3.20723i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(0.0176311 - 7.74595i) q^{35} +(8.39135 - 6.09667i) q^{36} +(0.639064 - 0.879596i) q^{37} +(9.60315 - 3.12025i) q^{38} +(-12.7257 - 4.16689i) q^{40} +(-7.07450 + 5.13992i) q^{41} +(-6.58911 - 2.14093i) q^{42} +3.46410i q^{43} +(1.62772 + 5.04868i) q^{45} +(-0.618034 + 1.90211i) q^{46} +(-3.89893 - 5.36641i) q^{47} +(-2.96754 + 4.08446i) q^{48} +(-1.54508 - 4.75528i) q^{49} +(7.46525 - 10.1773i) q^{50} +(1.01567 + 0.737928i) q^{51} +(9.60315 + 3.12025i) q^{53} +10.7446 q^{54} -20.7446 q^{56} +(3.01404 + 0.979321i) q^{57} +(12.9749 + 17.8584i) q^{58} +(-5.96430 - 4.33332i) q^{59} +(-4.53869 - 6.27697i) q^{60} +(-0.230083 - 0.708121i) q^{61} +(5.00368 - 6.88698i) q^{62} +(4.83032 + 6.64836i) q^{63} +(0.733075 - 2.25617i) q^{64} -9.30506i q^{67} +(6.58911 + 2.14093i) q^{68} +(-0.507835 + 0.368964i) q^{69} +(6.08466 - 18.5826i) q^{70} +(-3.12628 - 9.62169i) q^{71} +(13.5110 - 4.38998i) q^{72} +(-4.07230 + 5.60503i) q^{73} +(2.22040 - 1.61321i) q^{74} +(3.77308 - 1.20699i) q^{75} +17.4891 q^{76} +(-0.387951 + 1.19399i) q^{79} +(-11.5085 - 8.40148i) q^{80} +(-3.02941 - 2.20100i) q^{81} +(-20.9938 + 6.82131i) q^{82} +(-6.30860 + 2.04979i) q^{83} +(-9.70820 - 7.05342i) q^{84} +(-2.08917 + 2.86177i) q^{85} +(-2.70222 + 8.31657i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-0.0304791 + 13.3905i) q^{90} +(-2.03615 + 2.80252i) q^{92} +(2.54105 - 0.825636i) q^{93} +(-5.17435 - 15.9250i) q^{94} +(-2.78329 + 8.50019i) q^{95} +(-2.63370 + 1.91350i) q^{96} +(-5.55509 - 1.80496i) q^{97} -12.6217i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} + 3 q^{5} - 8 q^{6} + 2 q^{9} - 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} + 16 q^{19} + 12 q^{20} + 48 q^{21} - 4 q^{24} - q^{25} + 12 q^{29} + 6 q^{30} - 2 q^{31} + 64 q^{34} - 18 q^{35}+ \cdots - 36 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 + 3 * q^5 - 8 * q^6 + 2 * q^9 - 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 + 16 * q^19 + 12 * q^20 + 48 * q^21 - 4 * q^24 - q^25 + 12 * q^29 + 6 * q^30 - 2 * q^31 + 64 * q^34 - 18 * q^35 + 30 * q^36 - 28 * q^40 - 12 * q^41 + 72 * q^45 + 8 * q^46 + 20 * q^49 + 18 * q^50 + 28 * q^51 + 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 - 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 - 12 * q^74 - 15 * q^75 + 96 * q^76 + 28 * q^79 - 6 * q^80 + 8 * q^81 - 48 * q^84 - 2 * q^85 + 12 * q^86 + 24 * q^89 + 28 * q^90 + 44 * q^94 - 12 * q^95 - 36 * q^96

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 $

$2$	2.40079	+	0.780063i	1.69761	+	0.551588i	0.988195	−	0.153200i	$-0.0489578\pi$
$2$	2.40079	+	0.780063i	1.69761	+	0.551588i	0.709418	+	0.704788i	$0.248958\pi$
$3$	0.465695	+	0.640974i	0.268869	+	0.370066i	0.922007	−	0.387172i	$-0.126548\pi$
$3$	0.465695	+	0.640974i	0.268869	+	0.370066i	−0.653139	+	0.757238i	$0.726548\pi$
$4$	3.53725	+	2.56996i	1.76862	+	1.28498i
$5$	−1.81200	+	1.31021i	−0.810353	+	0.585942i
$5$	−1.81200	+	1.31021i	−0.810353	+	0.585942i
$6$	0.618034	+	1.90211i	0.252311	+	0.776534i
$7$	−2.03615	+	2.80252i	−0.769592	+	1.05925i	0.226764	+	0.973950i	$0.427186\pi$
$7$	−2.03615	+	2.80252i	−0.769592	+	1.05925i	−0.996355	+	0.0853021i	$0.972814\pi$
$8$	3.51992	+	4.84475i	1.24448	+	1.71288i
$9$	0.733075	−	2.25617i	0.244358	−	0.752058i
$10$	−5.37228	+	1.73205i	−1.69886	+	0.547723i
$11$		0			0
$11$		0			0
$12$			3.46410i			1.00000i
$13$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$13$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$14$	−7.07450	+	5.13992i	−1.89074	+	1.37370i
$15$	−1.68365	−	0.551291i	−0.434716	−	0.142343i
$16$	1.96914	+	6.06040i	0.492286	+	1.51510i
$17$	1.50702	−	0.489660i	0.365506	−	0.118760i	−0.120505	−	0.992713i	$-0.538451\pi$
$17$	1.50702	−	0.489660i	0.365506	−	0.118760i	0.486011	+	0.873953i	$0.338451\pi$
$18$	3.51992	−	4.84475i	0.829652	−	1.14192i
$19$	3.23607	−	2.35114i	0.742405	−	0.539389i	−0.151058	−	0.988525i	$-0.548268\pi$
$19$	3.23607	−	2.35114i	0.742405	−	0.539389i	0.893463	+	0.449136i	$0.148268\pi$
$20$	−9.77669	−	0.0222534i	−2.18613	−	0.00497602i
$21$	−2.74456			−0.598913
$22$		0			0
$23$			0.792287i			0.165203i	0.996583	+	0.0826016i	$0.0263229\pi$
$23$			0.792287i			0.165203i	−0.996583	+	0.0826016i	$0.973677\pi$
$24$	−1.46615	+	4.51235i	−0.299277	+	0.921079i
$25$	1.56672	−	4.74820i	0.313343	−	0.949640i
$26$		0			0
$27$	4.04807	−	1.31530i	0.779051	−	0.253129i
$28$	−14.4047	+	4.68038i	−2.72224	+	0.884509i
$29$	7.07450	+	5.13992i	1.31370	+	0.954460i	0.999988	+	0.00494253i	$0.00157326\pi$
$29$	7.07450	+	5.13992i	1.31370	+	0.954460i	0.313714	+	0.949518i	$0.398427\pi$
$30$	−3.61204	−	2.63688i	−0.659466	−	0.481427i
$31$	1.04209	−	3.20723i	0.187165	−	0.576036i	−0.812814	−	0.582524i	$-0.802065\pi$
$31$	1.04209	−	3.20723i	0.187165	−	0.576036i	0.999979	+	0.00648824i	$0.00206529\pi$
$32$			4.10891i			0.726360i
$33$		0			0
$34$	4.00000			0.685994
$35$	0.0176311	−	7.74595i	0.00298020	−	1.30930i
$36$	8.39135	−	6.09667i	1.39856	−	1.01611i
$37$	0.639064	−	0.879596i	0.105061	−	0.144605i	−0.753249	−	0.657736i	$-0.771514\pi$
$37$	0.639064	−	0.879596i	0.105061	−	0.144605i	0.858310	+	0.513131i	$0.171514\pi$
$38$	9.60315	−	3.12025i	1.55784	−	0.506172i
$39$		0			0
$40$	−12.7257	−	4.16689i	−2.01211	−	0.658843i
$41$	−7.07450	+	5.13992i	−1.10485	+	0.802721i	−0.981845	−	0.189684i	$-0.939253\pi$
$41$	−7.07450	+	5.13992i	−1.10485	+	0.802721i	−0.123006	+	0.992406i	$0.539253\pi$
$42$	−6.58911	−	2.14093i	−1.01672	−	0.330353i
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$		0			0
$45$	1.62772	+	5.04868i	0.242646	+	0.752612i
$46$	−0.618034	+	1.90211i	−0.0911241	+	0.280451i
$47$	−3.89893	−	5.36641i	−0.568717	−	0.782772i	0.423685	−	0.905810i	$-0.360736\pi$
$47$	−3.89893	−	5.36641i	−0.568717	−	0.782772i	−0.992402	+	0.123038i	$0.960736\pi$
$48$	−2.96754	+	4.08446i	−0.428327	+	0.589542i
$49$	−1.54508	−	4.75528i	−0.220726	−	0.679326i
$50$	7.46525	−	10.1773i	1.05575	−	1.43929i
$51$	1.01567	+	0.737928i	0.142222	+	0.103331i
$52$		0			0
$53$	9.60315	+	3.12025i	1.31909	+	0.428600i	0.882184	−	0.470905i	$-0.156073\pi$
$53$	9.60315	+	3.12025i	1.31909	+	0.428600i	0.436911	+	0.899505i	$0.356073\pi$
$54$	10.7446			1.46215
$55$		0			0
$56$	−20.7446			−2.77211
$57$	3.01404	+	0.979321i	0.399219	+	0.129714i
$58$	12.9749	+	17.8584i	1.70369	+	2.34493i
$59$	−5.96430	−	4.33332i	−0.776486	−	0.564150i	0.127436	−	0.991847i	$-0.459325\pi$
$59$	−5.96430	−	4.33332i	−0.776486	−	0.564150i	−0.903922	+	0.427697i	$0.859325\pi$
$60$	−4.53869	−	6.27697i	−0.585942	−	0.810353i
$61$	−0.230083	−	0.708121i	−0.0294590	−	0.0906656i	0.935246	−	0.353999i	$-0.115178\pi$
$61$	−0.230083	−	0.708121i	−0.0294590	−	0.0906656i	−0.964705	+	0.263333i	$0.915178\pi$
$62$	5.00368	−	6.88698i	0.635469	−	0.874648i
$63$	4.83032	+	6.64836i	0.608563	+	0.837614i
$64$	0.733075	−	2.25617i	0.0916344	−	0.282022i
$65$		0			0
$66$		0			0
$67$		−	9.30506i		−	1.13679i	−0.822754	−	0.568397i	$-0.807564\pi$
$67$		−	9.30506i		−	1.13679i	0.822754	−	0.568397i	$-0.192436\pi$
$68$	6.58911	+	2.14093i	0.799047	+	0.259626i
$69$	−0.507835	+	0.368964i	−0.0611362	+	0.0444180i
$70$	6.08466	−	18.5826i	0.727256	−	2.22105i
$71$	−3.12628	−	9.62169i	−0.371021	−	1.14188i	−0.946124	−	0.323804i	$-0.895038\pi$
$71$	−3.12628	−	9.62169i	−0.371021	−	1.14188i	0.575103	−	0.818081i	$-0.304962\pi$
$72$	13.5110	−	4.38998i	1.59228	−	0.517364i
$73$	−4.07230	+	5.60503i	−0.476626	+	0.656020i	−0.977852	−	0.209297i	$-0.932883\pi$
$73$	−4.07230	+	5.60503i	−0.476626	+	0.656020i	0.501226	+	0.865316i	$0.332883\pi$
$74$	2.22040	−	1.61321i	0.258116	−	0.187532i
$75$	3.77308	−	1.20699i	0.435678	−	0.139371i
$76$	17.4891			2.00614
$77$		0			0
$78$		0			0
$79$	−0.387951	+	1.19399i	−0.0436480	+	0.134335i	−0.970506	−	0.241078i	$-0.922499\pi$
$79$	−0.387951	+	1.19399i	−0.0436480	+	0.134335i	0.926858	+	0.375413i	$0.122499\pi$
$80$	−11.5085	−	8.40148i	−1.28669	−	0.939314i
$81$	−3.02941	−	2.20100i	−0.336602	−	0.244555i
$82$	−20.9938	+	6.82131i	−2.31838	+	0.753288i
$83$	−6.30860	+	2.04979i	−0.692458	+	0.224993i	−0.634042	−	0.773299i	$-0.718605\pi$
$83$	−6.30860	+	2.04979i	−0.692458	+	0.224993i	−0.0584167	+	0.998292i	$0.518605\pi$
$84$	−9.70820	−	7.05342i	−1.05925	−	0.769592i
$85$	−2.08917	+	2.86177i	−0.226602	+	0.310403i
$86$	−2.70222	+	8.31657i	−0.291388	+	0.896799i
$87$			6.92820i			0.742781i
$88$		0			0
$89$	−1.37228			−0.145462			−0.0727308	−	0.997352i	$-0.523171\pi$
$89$	−1.37228			−0.145462			−0.0727308	+	0.997352i	$0.523171\pi$
$90$	−0.0304791	+	13.3905i	−0.00321278	+	1.41149i
$91$		0			0
$92$	−2.03615	+	2.80252i	−0.212283	+	0.292183i
$93$	2.54105	−	0.825636i	0.263494	−	0.0856145i
$94$	−5.17435	−	15.9250i	−0.533694	−	1.64254i
$95$	−2.78329	+	8.50019i	−0.285559	+	0.872102i
$96$	−2.63370	+	1.91350i	−0.268801	+	0.195296i
$97$	−5.55509	−	1.80496i	−0.564033	−	0.183266i	0.0131018	−	0.999914i	$-0.495829\pi$
$97$	−5.55509	−	1.80496i	−0.564033	−	0.183266i	−0.577135	+	0.816649i	$0.695829\pi$
$98$		−	12.6217i		−	1.27498i
$99$		0			0
$100$	17.7446	−	12.7692i	1.77446	−	1.27692i
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	−0.815449	−	0.578829i	$-0.803510\pi$
$101$	1.85410	−	5.70634i	0.184490	−	0.567802i	0.999939	+	0.0110267i	$0.00350999\pi$
$102$	1.86278	+	2.56389i	0.184443	+	0.253863i
$103$	−6.10844	+	8.40755i	−0.601883	+	0.828421i	−0.995879	−	0.0906914i	$-0.971092\pi$
$103$	−6.10844	+	8.40755i	−0.601883	+	0.828421i	0.393996	+	0.919112i	$0.371092\pi$
$104$		0			0
$105$	4.97316	−	3.59594i	0.485331	−	0.350928i
$106$	20.6211	+	14.9821i	2.00290	+	1.45519i
$107$	−3.89893	−	5.36641i	−0.376923	−	0.518791i	0.577843	−	0.816148i	$-0.303895\pi$
$107$	−3.89893	−	5.36641i	−0.376923	−	0.518791i	−0.954766	+	0.297358i	$0.903895\pi$
$108$	17.6993	+	5.75085i	1.70311	+	0.553375i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	0.861407			0.0817611
$112$	−20.9938	−	6.82131i	−1.98373	−	0.644553i
$113$	0.292325	+	0.402351i	0.0274996	+	0.0378500i	0.822545	−	0.568699i	$-0.192553\pi$
$113$	0.292325	+	0.402351i	0.0274996	+	0.0378500i	−0.795046	+	0.606549i	$0.792553\pi$
$114$	6.47214	+	4.70228i	0.606171	+	0.440409i
$115$	−1.03806	−	1.43563i	−0.0967996	−	0.133873i
$116$	11.8149	+	36.3624i	1.09698	+	3.37616i
$117$		0			0
$118$	−10.9388	−	15.0559i	−1.00699	−	1.38601i
$119$	−1.69623	+	5.22047i	−0.155493	+	0.478560i
$120$	−3.25544	−	10.0974i	−0.297179	−	0.921758i
$121$		0			0
$122$		−	1.87953i		−	0.170164i
$123$	−6.58911	−	2.14093i	−0.594120	−	0.193041i
$124$	11.9286	−	8.66664i	1.07122	−	0.778287i
$125$	3.38223	+	10.6565i	0.302516	+	0.953144i
$126$	6.41042	+	19.7293i	0.571086	+	1.75762i
$127$	−7.81561	+	2.53945i	−0.693524	+	0.225339i	−0.634507	−	0.772917i	$-0.718797\pi$
$127$	−7.81561	+	2.53945i	−0.693524	+	0.225339i	−0.0590171	+	0.998257i	$0.518797\pi$
$128$	8.35023	−	11.4931i	0.738063	−	1.01586i
$129$	−2.22040	+	1.61321i	−0.195495	+	0.142036i
$130$		0			0
$131$	−2.74456			−0.239794			−0.119897	−	0.992786i	$-0.538256\pi$
$131$	−2.74456			−0.239794			−0.119897	+	0.992786i	$0.538256\pi$
$132$		0			0
$133$			13.8564i			1.20150i
$134$	7.25854	−	22.3395i	0.627042	−	1.92984i
$135$	−5.61180	+	7.68713i	−0.482987	+	0.661602i
$136$	7.67686	+	5.57757i	0.658286	+	0.478273i
$137$	13.6512	−	4.43555i	1.16630	−	0.378955i	0.339041	−	0.940772i	$-0.389898\pi$
$137$	13.6512	−	4.43555i	1.16630	−	0.378955i	0.827261	+	0.561817i	$0.189898\pi$
$138$	−1.50702	+	0.489660i	−0.128286	+	0.0416827i
$139$	−13.1333	−	9.54192i	−1.11395	−	0.809335i	−0.130673	−	0.991426i	$-0.541714\pi$
$139$	−13.1333	−	9.54192i	−1.11395	−	0.809335i	−0.983282	+	0.182090i	$0.941714\pi$
$140$	19.9692	−	27.3540i	1.68770	−	2.31184i
$141$	1.62402	−	4.99822i	0.136767	−	0.420926i
$142$		−	25.5383i		−	2.14313i
$143$		0			0
$144$	15.1168			1.25974
$145$	−19.5534	−	0.0445068i	−1.62382	−	0.00369609i
$146$	−14.1490	+	10.2798i	−1.17098	+	0.850766i
$147$	2.32847	−	3.20487i	0.192049	−	0.264333i
$148$	4.52106	−	1.46898i	0.371629	−	0.120749i
$149$	3.55033	+	10.9268i	0.290855	+	0.895159i	0.984582	+	0.174921i	$0.0559672\pi$
$149$	3.55033	+	10.9268i	0.290855	+	0.895159i	−0.693728	+	0.720237i	$0.744033\pi$
$150$	9.99990	+	0.0455232i	0.816488	+	0.00371695i
$151$	9.89726	−	7.19078i	0.805428	−	0.585177i	−0.107074	−	0.994251i	$-0.534148\pi$
$151$	9.89726	−	7.19078i	0.805428	−	0.585177i	0.912501	+	0.409074i	$0.134148\pi$
$152$	22.7814	+	7.40212i	1.84781	+	0.600391i
$153$		−	3.75906i		−	0.303902i
$154$		0			0
$155$	2.31386	+	7.17687i	0.185854	+	0.576460i
$156$		0			0
$157$	−14.3720	−	19.7813i	−1.14701	−	1.57872i	−0.750752	−	0.660584i	$-0.770309\pi$
$157$	−14.3720	−	19.7813i	−1.14701	−	1.57872i	−0.396258	−	0.918139i	$-0.629691\pi$
$158$	−1.86278	+	2.56389i	−0.148195	+	0.203972i
$159$	2.47214	+	7.60845i	0.196053	+	0.603390i
$160$	−5.38352	−	7.44536i	−0.425605	−	0.588608i
$161$	−2.22040	−	1.61321i	−0.174992	−	0.127139i
$162$	−5.55606	−	7.64727i	−0.436526	−	0.600826i
$163$	−3.29456	−	1.07047i	−0.258050	−	0.0838454i	0.177135	−	0.984187i	$-0.443317\pi$
$163$	−3.29456	−	1.07047i	−0.258050	−	0.0838454i	−0.435185	+	0.900341i	$0.643317\pi$
$164$	−38.2337			−2.98555
$165$		0			0
$166$	−16.7446			−1.29963
$167$	14.9658	+	4.86267i	1.15809	+	0.376285i	0.824183	−	0.566323i	$-0.191635\pi$
$167$	14.9658	+	4.86267i	1.15809	+	0.376285i	0.333902	+	0.942608i	$0.391635\pi$
$168$	−9.66063	−	13.2967i	−0.745334	−	1.02586i
$169$	−10.5172	−	7.64121i	−0.809017	−	0.587785i
$170$	−7.24802	+	5.24083i	−0.555897	+	0.401953i
$171$	−2.93230	−	9.02469i	−0.224239	−	0.690136i
$172$	−8.90261	+	12.2534i	−0.678818	+	0.934312i
$173$	5.00368	+	6.88698i	0.380423	+	0.523608i	0.955697	−	0.294354i	$-0.0951044\pi$
$173$	5.00368	+	6.88698i	0.380423	+	0.523608i	−0.575273	+	0.817961i	$0.695104\pi$
$174$	−5.40444	+	16.6331i	−0.409709	+	1.26096i
$175$	10.1168	+	14.0588i	0.764762	+	1.06274i
$176$		0			0
$177$		−	5.84096i		−	0.439034i
$178$	−3.29456	−	1.07047i	−0.246937	−	0.0802348i
$179$	10.4051	−	7.55975i	0.777713	−	0.565042i	−0.126578	−	0.991957i	$-0.540400\pi$
$179$	10.4051	−	7.55975i	0.777713	−	0.565042i	0.904292	+	0.426915i	$0.140400\pi$
$180$	−7.21726	+	22.0416i	−0.537943	+	1.64288i
$181$	7.45251	+	22.9365i	0.553941	+	1.70486i	0.698724	+	0.715392i	$0.253752\pi$
$181$	7.45251	+	22.9365i	0.553941	+	1.70486i	−0.144783	+	0.989464i	$0.546248\pi$
$182$		0			0
$183$	0.346739	−	0.477245i	0.0256317	−	0.0352790i
$184$	−3.83843	+	2.78878i	−0.282973	+	0.205592i
$185$	−0.00553368	+	2.43114i	−0.000406845	+	0.178741i
$186$	6.74456			0.494535
$187$		0			0
$188$		−	29.0024i		−	2.11522i
$189$	−4.55632	+	14.0229i	−0.331424	+	1.02002i
$190$	−13.3128	+	18.2360i	−0.965810	+	1.32298i
$191$	15.6725	+	11.3867i	1.13402	+	0.823916i	0.986275	−	0.165109i	$-0.0527977\pi$
$191$	15.6725	+	11.3867i	1.13402	+	0.823916i	0.147747	+	0.989025i	$0.452798\pi$
$192$	1.78754	−	0.580806i	0.129004	−	0.0419161i
$193$	15.6312	−	5.07889i	1.12516	−	0.365587i	0.313426	−	0.949613i	$-0.398523\pi$
$193$	15.6312	−	5.07889i	1.12516	−	0.365587i	0.811735	+	0.584026i	$0.198523\pi$
$194$	−11.9286	−	8.66664i	−0.856424	−	0.622228i
$195$		0			0
$196$	6.75555	−	20.7914i	0.482539	−	1.48510i
$197$		−	8.51278i		−	0.606510i	−0.952909	−	0.303255i	$-0.901927\pi$
$197$		−	8.51278i		−	0.606510i	0.952909	−	0.303255i	$-0.0980734\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	28.5185	−	9.12292i	2.01657	−	0.645088i
$201$	5.96430	−	4.33332i	0.420689	−	0.305649i
$202$	8.90261	−	12.2534i	0.626386	−	0.862146i
$203$	−28.8095	+	9.36076i	−2.02203	+	0.656997i
$204$	1.69623	+	5.22047i	0.118760	+	0.365506i
$205$	6.08466	−	18.5826i	0.424971	−	1.29787i
$206$	−21.2235	+	15.4198i	−1.47871	+	1.07435i
$207$	1.78754	+	0.580806i	0.124242	+	0.0403688i
$208$		0			0
$209$		0			0
$210$	14.7446	−	4.75372i	1.01747	−	0.328038i
$211$	0.460165	−	1.41624i	0.0316791	−	0.0974981i	−0.933967	−	0.357360i	$-0.883677\pi$
$211$	0.460165	−	1.41624i	0.0316791	−	0.0974981i	0.965646	+	0.259862i	$0.0836770\pi$
$212$	25.9498	+	35.7169i	1.78224	+	2.45304i
$213$	4.71136	−	6.48463i	0.322817	−	0.444320i
$214$	−5.17435	−	15.9250i	−0.353712	−	1.08861i
$215$	−4.53869	−	6.27697i	−0.309536	−	0.428086i
$216$	20.6211	+	14.9821i	1.40309	+	1.01940i
$217$	6.86646	+	9.45088i	0.466126	+	0.641567i
$218$	−24.0079	−	7.80063i	−1.62602	−	0.528326i
$219$	−5.48913			−0.370921
$220$		0			0
$221$		0			0
$222$	2.06805	+	0.671952i	0.138799	+	0.0450984i
$223$	1.39708	+	1.92292i	0.0935557	+	0.128768i	0.853229	−	0.521537i	$-0.174641\pi$
$223$	1.39708	+	1.92292i	0.0935557	+	0.128768i	−0.759673	+	0.650305i	$0.774641\pi$
$224$	−11.5153	−	8.36635i	−0.769398	−	0.559000i
$225$	−9.56424	−	7.01557i	−0.637616	−	0.467705i
$226$	0.387951	+	1.19399i	0.0258061	+	0.0794232i
$227$	−9.83400	+	13.5353i	−0.652706	+	0.898372i	−0.999213	−	0.0396753i	$-0.987368\pi$
$227$	−9.83400	+	13.5353i	−0.652706	+	0.898372i	0.346507	+	0.938047i	$0.387368\pi$
$228$	8.14459	+	11.2101i	0.539389	+	0.742405i
$229$	−4.52021	+	13.9118i	−0.298704	+	0.919317i	0.683248	+	0.730187i	$0.260567\pi$
$229$	−4.52021	+	13.9118i	−0.298704	+	0.919317i	−0.981952	+	0.189130i	$0.939433\pi$
$230$	−1.37228	−	4.25639i	−0.0904856	−	0.280658i
$231$		0			0
$232$			52.3663i			3.43801i
$233$	−3.57507	−	1.16161i	−0.234211	−	0.0760997i	0.189560	−	0.981869i	$-0.439294\pi$
$233$	−3.57507	−	1.16161i	−0.234211	−	0.0760997i	−0.423771	+	0.905769i	$0.639294\pi$
$234$		0			0
$235$	14.0960	+	4.61556i	0.919520	+	0.301086i
$236$	−9.96076	−	30.6561i	−0.648390	−	1.99554i
$237$	−0.945984	+	0.307369i	−0.0614483	+	0.0199658i
$238$	−8.14459	+	11.2101i	−0.527935	+	0.726641i
$239$	−11.9286	+	8.66664i	−0.771597	+	0.560598i	−0.902445	−	0.430804i	$-0.858230\pi$
$239$	−11.9286	+	8.66664i	−0.771597	+	0.560598i	0.130848	+	0.991402i	$0.458230\pi$
$240$	0.0256960	−	11.2892i	0.00165867	−	0.728712i
$241$	16.7446			1.07861			0.539306	−	0.842110i	$-0.318687\pi$
$241$	16.7446			1.07861			0.539306	+	0.842110i	$0.318687\pi$
$242$		0			0
$243$		−	15.7359i		−	1.00946i
$244$	1.00599	−	3.09610i	0.0644016	−	0.198208i
$245$	9.03010	+	6.59221i	0.576912	+	0.421161i
$246$	−14.1490	−	10.2798i	−0.902107	−	0.655419i
$247$		0			0
$248$	19.2063	−	6.24051i	1.21960	−	0.396273i
$249$	−4.25174	−	3.08907i	−0.269443	−	0.195762i
$250$	−0.192719	+	28.2223i	−0.0121886	+	1.78493i
$251$	−6.83448	+	21.0344i	−0.431389	+	1.32768i	0.465354	+	0.885125i	$0.345927\pi$
$251$	−6.83448	+	21.0344i	−0.431389	+	1.32768i	−0.896742	+	0.442553i	$0.854073\pi$
$252$			35.9306i			2.26342i
$253$		0			0
$254$	−20.7446			−1.30163
$255$	−2.80724	−	0.00638975i	−0.175796	−	0.000400142i
$256$	25.1741	−	18.2900i	1.57338	−	1.14313i
$257$	−6.28181	+	8.64617i	−0.391849	+	0.539334i	−0.958675	−	0.284504i	$-0.908171\pi$
$257$	−6.28181	+	8.64617i	−0.391849	+	0.539334i	0.566826	+	0.823837i	$0.308171\pi$
$258$	−6.58911	+	2.14093i	−0.410220	+	0.133289i
$259$	1.16385	+	3.58198i	0.0723184	+	0.222573i
$260$		0			0
$261$	16.7827	−	12.1933i	1.03882	−	0.754749i
$262$	−6.58911	−	2.14093i	−0.407077	−	0.132267i
$263$			27.4179i			1.69066i	0.534246	+	0.845329i	$0.320595\pi$
$263$			27.4179i			1.69066i	−0.534246	+	0.845329i	$0.679405\pi$
$264$		0			0
$265$	−21.4891	+	6.92820i	−1.32007	+	0.425596i
$266$	−10.8089	+	33.2663i	−0.662735	+	2.03969i
$267$	−0.639064	−	0.879596i	−0.0391101	−	0.0538304i
$268$	23.9137	−	32.9143i	1.46076	−	2.01056i
$269$	3.55033	+	10.9268i	0.216468	+	0.666219i	0.999046	+	0.0436672i	$0.0139041\pi$
$269$	3.55033	+	10.9268i	0.216468	+	0.666219i	−0.782578	+	0.622552i	$0.786096\pi$
$270$	−19.4692	+	14.0776i	−1.18486	+	0.856735i
$271$	−10.9129	−	7.92871i	−0.662913	−	0.481635i	0.204732	−	0.978818i	$-0.434368\pi$
$271$	−10.9129	−	7.92871i	−0.662913	−	0.481635i	−0.867646	+	0.497183i	$0.834368\pi$
$272$	5.93507	+	8.16893i	0.359867	+	0.495314i
$273$		0			0
$274$	36.2337			2.18896
$275$		0			0
$276$	−2.74456			−0.165203
$277$	11.1102	+	3.60991i	0.667545	+	0.216899i	0.623135	−	0.782115i	$-0.285859\pi$
$277$	11.1102	+	3.60991i	0.667545	+	0.216899i	0.0444110	+	0.999013i	$0.485859\pi$
$278$	−24.0870	−	33.1530i	−1.44464	−	1.98838i
$279$	−6.47214	−	4.70228i	−0.387477	−	0.281518i
$280$	37.5892	−	27.1797i	2.24639	−	1.62430i
$281$	−0.157869	−	0.485871i	−0.00941767	−	0.0289846i	0.946237	−	0.323473i	$-0.104851\pi$
$281$	−0.157869	−	0.485871i	−0.00941767	−	0.0289846i	−0.955655	+	0.294489i	$0.904851\pi$
$282$	7.79785	−	10.7328i	0.464355	−	0.639130i
$283$	−8.90261	−	12.2534i	−0.529205	−	0.728389i	0.457804	−	0.889053i	$-0.348636\pi$
$283$	−8.90261	−	12.2534i	−0.529205	−	0.728389i	−0.987009	+	0.160665i	$0.948636\pi$
$284$	13.6690	−	42.0687i	0.811104	−	2.49632i
$285$	−6.74456	+	2.17448i	−0.399513	+	0.128805i
$286$		0			0
$287$		−	30.2921i		−	1.78808i
$288$	9.27042	+	3.01214i	0.546265	+	0.177492i
$289$	−11.7219	+	8.51649i	−0.689526	+	0.500970i
$290$	−46.9088	−	15.3597i	−2.75458	−	0.901954i
$291$	−1.43004	−	4.40122i	−0.0838306	−	0.258004i
$292$	−28.8095	+	9.36076i	−1.68595	+	0.547797i
$293$	1.86278	−	2.56389i	0.108825	−	0.149784i	−0.751131	−	0.660153i	$-0.770491\pi$
$293$	1.86278	−	2.56389i	0.108825	−	0.149784i	0.859955	+	0.510369i	$0.170491\pi$
$294$	8.09017	−	5.87785i	0.471828	−	0.342803i
$295$	16.4849	+	0.0375224i	0.959787	+	0.00218464i
$296$	6.51087			0.378437
$297$		0			0
$298$			29.0024i			1.68007i
$299$		0			0
$300$	16.4482	+	5.42727i	0.949640	+	0.313343i
$301$	−9.70820	−	7.05342i	−0.559572	−	0.406553i
$302$	29.3705	−	9.54305i	1.69008	−	0.549141i
$303$	4.52106	−	1.46898i	0.259728	−	0.0843907i
$304$	20.6211	+	14.9821i	1.18270	+	0.859284i
$305$	1.34470	+	0.981663i	0.0769970	+	0.0562098i
$306$	2.93230	−	9.02469i	0.167628	−	0.515907i
$307$		−	31.5817i		−	1.80246i	−0.433340	−	0.901231i	$-0.642665\pi$
$307$		−	31.5817i		−	1.80246i	0.433340	−	0.901231i	$-0.357335\pi$
$308$		0			0
$309$	−8.23369			−0.468398
$310$	−0.0433271	+	19.0351i	−0.00246082	+	1.08112i
$311$	−4.44080	+	3.22643i	−0.251814	+	0.182954i	−0.706531	−	0.707683i	$-0.749741\pi$
$311$	−4.44080	+	3.22643i	−0.251814	+	0.182954i	0.454716	+	0.890636i	$0.349741\pi$
$312$		0			0
$313$	20.8014	−	6.75877i	1.17576	−	0.382028i	0.344972	−	0.938613i	$-0.387888\pi$
$313$	20.8014	−	6.75877i	1.17576	−	0.382028i	0.830791	+	0.556585i	$0.187888\pi$
$314$	−19.0734	−	58.7019i	−1.07637	−	3.31274i
$315$	−17.4633	−	5.71814i	−0.983944	−	0.322181i
$316$	−4.44080	+	3.22643i	−0.249814	+	0.181501i
$317$	−31.3505	−	10.1864i	−1.76082	−	0.572125i	−0.763535	−	0.645767i	$-0.776538\pi$
$317$	−31.3505	−	10.1864i	−1.76082	−	0.572125i	−0.997285	+	0.0736417i	$0.976538\pi$
$318$			20.1947i			1.13246i
$319$		0			0
$320$	1.62772	+	5.04868i	0.0909922	+	0.282230i
$321$	1.62402	−	4.99822i	0.0906439	−	0.278973i
$322$	−4.07230	−	5.60503i	−0.226940	−	0.312356i
$323$	3.72556	−	5.12779i	0.207296	−	0.285318i
$324$	−5.05931	−	15.5710i	−0.281073	−	0.865054i
$325$		0			0
$326$	−7.07450	−	5.13992i	−0.391820	−	0.284674i
$327$	−4.65695	−	6.40974i	−0.257530	−	0.354459i
$328$	−49.8033	−	16.1821i	−2.74993	−	0.893505i
$329$	22.9783			1.26683
$330$		0			0
$331$	−14.1168			−0.775932			−0.387966	−	0.921674i	$-0.626822\pi$
$331$	−14.1168			−0.775932			−0.387966	+	0.921674i	$0.626822\pi$
$332$	−27.5830	−	8.96224i	−1.51381	−	0.491867i
$333$	−1.51604	−	2.08665i	−0.0830785	−	0.114348i
$334$	32.1364	+	23.3485i	1.75843	+	1.27757i
$335$	12.1916	+	16.8608i	0.666096	+	0.921205i
$336$	−5.40444	−	16.6331i	−0.294836	−	0.907413i
$337$	19.0834	−	26.2660i	1.03954	−	1.43080i	0.141996	−	0.989867i	$-0.454648\pi$
$337$	19.0834	−	26.2660i	1.03954	−	1.43080i	0.897541	−	0.440932i	$-0.145352\pi$
$338$	−19.2890	−	26.5490i	−1.04918	−	1.44408i
$339$	−0.121762	+	0.374746i	−0.00661321	+	0.0203534i
$340$	−14.7446	+	4.75372i	−0.799636	+	0.257807i
$341$		0			0
$342$		−	23.9538i		−	1.29527i
$343$	−6.58911	−	2.14093i	−0.355779	−	0.115599i
$344$	−16.7827	+	12.1933i	−0.904863	+	0.657421i
$345$	0.436780	−	1.33393i	0.0235155	−	0.0718165i
$346$	6.64050	+	20.4374i	0.356996	+	1.09872i
$347$	−21.5549	+	7.00360i	−1.15713	+	0.375973i	−0.823823	−	0.566847i	$-0.808163\pi$
$347$	−21.5549	+	7.00360i	−1.15713	+	0.375973i	−0.333303	+	0.942820i	$0.608163\pi$
$348$	−17.8052	+	24.5068i	−0.954460	+	1.31370i
$349$	12.5310	−	9.10428i	0.670767	−	0.487341i	−0.199515	−	0.979895i	$-0.563937\pi$
$349$	12.5310	−	9.10428i	0.670767	−	0.487341i	0.870282	+	0.492554i	$0.163937\pi$
$350$	13.3217	+	41.6439i	0.712072	+	2.22596i
$351$		0			0
$352$		0			0
$353$			25.0410i			1.33280i	0.745595	+	0.666399i	$0.232165\pi$
$353$			25.0410i			1.33280i	−0.745595	+	0.666399i	$0.767835\pi$
$354$	4.55632	−	14.0229i	0.242166	−	0.745309i
$355$	18.2712	+	13.3385i	0.969736	+	0.707933i
$356$	−4.85410	−	3.52671i	−0.257267	−	0.186915i
$357$	−4.13611	+	1.34390i	−0.218906	+	0.0711269i
$358$	30.8775	−	10.0327i	1.63193	−	0.530245i
$359$	23.8572	+	17.3333i	1.25914	+	0.914815i	0.998715	−	0.0506802i	$-0.0161389\pi$
$359$	23.8572	+	17.3333i	1.25914	+	0.914815i	0.260420	+	0.965495i	$0.416139\pi$
$360$	−18.7301	+	25.6568i	−0.987165	+	1.35223i
$361$	−0.927051	+	2.85317i	−0.0487922	+	0.150167i
$362$			60.8791i			3.19973i
$363$		0			0
$364$		0			0
$365$	0.0352622	−	15.4919i	0.00184571	−	0.810883i
$366$	1.20473	−	0.875286i	0.0629721	−	0.0457519i
$367$	−15.1300	+	20.8247i	−0.789780	+	1.08704i	0.204355	+	0.978897i	$0.434490\pi$
$367$	−15.1300	+	20.8247i	−0.789780	+	1.08704i	−0.994135	+	0.108142i	$0.965510\pi$
$368$	−4.80158	+	1.56013i	−0.250299	+	0.0813272i
$369$	6.41042	+	19.7293i	0.333713	+	1.02706i
$370$	−1.90973	+	5.83233i	−0.0992819	+	0.303208i
$371$	−28.2980	+	20.5597i	−1.46916	+	1.06741i
$372$	11.1102	+	3.60991i	0.576036	+	0.187165i
$373$		−	11.6819i		−	0.604867i	−0.953170	−	0.302434i	$-0.902201\pi$
$373$		−	11.6819i		−	0.604867i	0.953170	−	0.302434i	$-0.0977990\pi$
$374$		0			0
$375$	−5.25544	+	7.13058i	−0.271390	+	0.368222i
$376$	12.2750	−	37.7786i	0.633036	−	1.94828i
$377$		0			0
$378$	−21.8775	+	30.1118i	−1.12526	+	1.54878i
$379$	0.193976	+	0.596996i	0.00996386	+	0.0306656i	0.955915	−	0.293644i	$-0.0948680\pi$
$379$	0.193976	+	0.596996i	0.00996386	+	0.0306656i	−0.945951	+	0.324310i	$0.894868\pi$
$380$	−31.6904	+	22.9144i	−1.62568	+	1.17548i
$381$	−5.26741	−	3.82700i	−0.269858	−	0.196063i
$382$	28.7440	+	39.5627i	1.47067	+	2.02420i
$383$	−10.3567	−	3.36508i	−0.529201	−	0.171948i	0.0322161	−	0.999481i	$-0.489744\pi$
$383$	−10.3567	−	3.36508i	−0.529201	−	0.171948i	−0.561417	+	0.827533i	$0.689744\pi$
$384$	11.2554			0.574377
$385$		0			0
$386$	41.4891			2.11174
$387$	7.81561	+	2.53945i	0.397290	+	0.129087i
$388$	−15.0111	−	20.6609i	−0.762071	−	1.04890i
$389$	15.2592	+	11.0865i	0.773672	+	0.562106i	0.903073	−	0.429487i	$-0.141305\pi$
$389$	15.2592	+	11.0865i	0.773672	+	0.562106i	−0.129401	+	0.991592i	$0.541305\pi$
$390$		0			0
$391$	0.387951	+	1.19399i	0.0196195	+	0.0603828i
$392$	17.5996	−	24.2237i	0.888913	−	1.22348i
$393$	−1.27813	−	1.75919i	−0.0644730	−	0.0887395i
$394$	6.64050	−	20.4374i	0.334544	−	1.02962i
$395$	−0.861407	−	2.67181i	−0.0433421	−	0.134434i
$396$		0			0
$397$			16.4356i			0.824881i	0.910984	+	0.412441i	$0.135324\pi$
$397$			16.4356i			0.824881i	−0.910984	+	0.412441i	$0.864676\pi$
$398$	19.2063	+	6.24051i	0.962725	+	0.312808i
$399$	−8.88159	+	6.45285i	−0.444636	+	0.323047i
$400$	31.8611	+	0.145043i	1.59305	+	0.00725216i
$401$	−3.55033	−	10.9268i	−0.177295	−	0.545659i	0.822436	−	0.568858i	$-0.192615\pi$
$401$	−3.55033	−	10.9268i	−0.177295	−	0.545659i	−0.999731	+	0.0231995i	$0.992615\pi$
$402$	17.6993	−	5.75085i	0.882760	−	0.286826i
$403$		0			0
$404$	21.2235	−	15.4198i	1.05591	−	0.767162i
$405$	8.37307	+	0.0190585i	0.416061	+	0.000947027i
$406$	−76.4674			−3.79501
$407$		0			0
$408$			7.51811i			0.372202i
$409$	−8.49461	+	26.1437i	−0.420031	+	1.29272i	0.487641	+	0.873044i	$0.337857\pi$
$409$	−8.49461	+	26.1437i	−0.420031	+	1.29272i	−0.907672	+	0.419679i	$0.862143\pi$
$410$	29.1036	−	39.8665i	1.43732	−	1.96887i
$411$	9.20037	+	6.68446i	0.453821	+	0.329720i
$412$	−43.2142	+	14.0411i	−2.12901	+	0.691757i
$413$	24.2884	−	7.89178i	1.19515	−	0.388329i
$414$	3.83843	+	2.78878i	0.188649	+	0.137061i
$415$	8.74555	−	11.9798i	0.429302	−	0.588065i
$416$		0			0
$417$		−	12.8617i		−	0.629842i
$418$		0			0
$419$	22.9783			1.12256			0.561280	−	0.827626i	$-0.310309\pi$
$419$	22.9783			1.12256			0.561280	+	0.827626i	$0.310309\pi$
$420$	26.8327	+	0.0610759i	1.30930	+	0.00298020i
$421$	−6.88544	+	5.00257i	−0.335576	+	0.243810i	−0.742793	−	0.669521i	$-0.766499\pi$
$421$	−6.88544	+	5.00257i	−0.335576	+	0.243810i	0.407217	+	0.913331i	$0.366499\pi$
$422$	2.20952	−	3.04114i	0.107558	−	0.148040i
$423$	−14.9658	+	4.86267i	−0.727660	+	0.236431i
$424$	18.6854	+	57.5079i	0.907446	+	2.79283i
$425$	0.0360674	−	7.92279i	0.00174953	−	0.384312i
$426$	16.3694	−	11.8931i	0.793100	−	0.576221i
$427$	2.45300	+	0.797029i	0.118709	+	0.0385709i
$428$		−	29.0024i		−	1.40189i
$429$		0			0
$430$	−6.00000	−	18.6101i	−0.289346	−	0.897460i
$431$	−7.94879	+	24.4638i	−0.382880	+	1.17838i	0.555127	+	0.831765i	$0.312670\pi$
$431$	−7.94879	+	24.4638i	−0.382880	+	1.17838i	−0.938007	+	0.346617i	$0.887330\pi$
$432$	15.9424	+	21.9429i	0.767031	+	1.05573i
$433$	17.1662	−	23.6272i	0.824953	−	1.13545i	−0.163889	−	0.986479i	$-0.552404\pi$
$433$	17.1662	−	23.6272i	0.824953	−	1.13545i	0.988842	−	0.148971i	$-0.0475962\pi$
$434$	9.11264	+	28.0458i	0.437421	+	1.34624i
$435$	−9.07738	−	12.5539i	−0.435227	−	0.601915i
$436$	−35.3725	−	25.6996i	−1.69404	−	1.23079i
$437$	1.86278	+	2.56389i	0.0891088	+	0.122648i
$438$	−13.1782	−	4.28187i	−0.629680	−	0.204595i
$439$	−21.4891			−1.02562			−0.512810	−	0.858502i	$-0.671395\pi$
$439$	−21.4891			−1.02562			−0.512810	+	0.858502i	$0.671395\pi$
$440$		0			0
$441$	−11.8614			−0.564829
$442$		0			0
$443$	18.6177	+	25.6250i	0.884552	+	1.21748i	0.975139	+	0.221592i	$0.0711254\pi$
$443$	18.6177	+	25.6250i	0.884552	+	1.21748i	−0.0905879	+	0.995888i	$0.528875\pi$
$444$	3.04701	+	2.21378i	0.144605	+	0.105061i
$445$	2.48658	−	1.79797i	0.117875	−	0.0852321i
$446$	1.85410	+	5.70634i	0.0877943	+	0.270203i
$447$	−5.35042	+	7.36423i	−0.253066	+	0.348316i
$448$	4.83032	+	6.64836i	0.228211	+	0.314105i
$449$	−2.12029	+	6.52559i	−0.100063	+	0.307961i	−0.988540	−	0.150959i	$-0.951764\pi$
$449$	−2.12029	+	6.52559i	−0.100063	+	0.307961i	0.888477	+	0.458921i	$0.151764\pi$
$450$	−17.4891	−	24.3036i	−0.824445	−	1.14568i
$451$		0			0
$452$			2.17448i			0.102279i
$453$	9.21820	+	2.99518i	0.433109	+	0.140726i
$454$	−34.1678	+	24.8243i	−1.60357	+	1.16506i
$455$		0			0
$456$	5.86460	+	18.0494i	0.274635	+	0.845240i
$457$	−19.7673	+	6.42280i	−0.924677	+	0.300446i	−0.732384	−	0.680892i	$-0.761592\pi$
$457$	−19.7673	+	6.42280i	−0.924677	+	0.300446i	−0.192293	+	0.981338i	$0.561592\pi$
$458$	−21.7041	+	29.8732i	−1.01417	+	1.39588i
$459$	5.45647	−	3.96435i	0.254686	−	0.185040i
$460$	0.0176311	−	7.74595i	0.000822054	−	0.361157i
$461$	2.23369			0.104033			0.0520166	−	0.998646i	$-0.483435\pi$
$461$	2.23369			0.104033			0.0520166	+	0.998646i	$0.483435\pi$
$462$		0			0
$463$		−	30.0897i		−	1.39839i	−0.714933	−	0.699193i	$-0.753543\pi$
$463$		−	30.0897i		−	1.39839i	0.714933	−	0.699193i	$-0.246457\pi$
$464$	−17.2193	+	52.9955i	−0.799386	+	2.46026i
$465$	−3.52263	+	4.82535i	−0.163358	+	0.223770i
$466$	−7.67686	−	5.57757i	−0.355624	−	0.258376i
$467$	−7.34262	+	2.38576i	−0.339776	+	0.110400i	−0.473935	−	0.880560i	$-0.657167\pi$
$467$	−7.34262	+	2.38576i	−0.339776	+	0.110400i	0.134159	+	0.990960i	$0.457167\pi$
$468$		0			0
$469$	26.0776	+	18.9465i	1.20415	+	0.874867i
$470$	30.2410	+	22.0767i	1.39491	+	1.01832i
$471$	5.98636	−	18.4241i	0.275837	−	0.848939i
$472$		−	44.1485i		−	2.03210i
$473$		0			0
$474$	−2.51087			−0.115328
$475$	−6.09369	−	19.0491i	−0.279597	−	0.874031i
$476$	−19.4164	+	14.1068i	−0.889950	+	0.646586i
$477$	14.0797	−	19.3790i	0.644664	−	0.887303i
$478$	−35.3986	+	11.5017i	−1.61909	+	0.526075i
$479$	1.69623	+	5.22047i	0.0775029	+	0.238529i	0.982300	−	0.187313i	$-0.0599779\pi$
$479$	1.69623	+	5.22047i	0.0775029	+	0.238529i	−0.904797	+	0.425842i	$0.859978\pi$
$480$	2.26520	−	6.91796i	0.103392	−	0.315760i
$481$		0			0
$482$	40.2001	+	13.0618i	1.83107	+	0.594950i
$483$		−	2.17448i		−	0.0989423i
$484$		0			0
$485$	12.4307	−	4.00772i	0.564449	−	0.181981i
$486$	12.2750	−	37.7786i	0.556806	−	1.71367i
$487$	−4.19125	−	5.76876i	−0.189924	−	0.261408i	0.703427	−	0.710767i	$-0.251652\pi$
$487$	−4.19125	−	5.76876i	−0.189924	−	0.261408i	−0.893351	+	0.449360i	$0.851652\pi$
$488$	2.62080	−	3.60722i	0.118638	−	0.163291i
$489$	−0.848116	−	2.61023i	−0.0383532	−	0.118039i
$490$	16.5370	+	22.8706i	0.747067	+	1.03319i
$491$	−5.26741	−	3.82700i	−0.237715	−	0.172710i	0.462550	−	0.886593i	$-0.346935\pi$
$491$	−5.26741	−	3.82700i	−0.237715	−	0.172710i	−0.700265	+	0.713883i	$0.746935\pi$
$492$	−17.8052	−	24.5068i	−0.802721	−	1.10485i
$493$	13.1782	+	4.28187i	0.593517	+	0.192846i
$494$		0			0
$495$		0			0
$496$	21.4891			0.964890
$497$	33.3305	+	10.8297i	1.49508	+	0.485780i
$498$	−7.79785	−	10.7328i	−0.349430	−	0.480949i
$499$	−16.1803	−	11.7557i	−0.724331	−	0.526258i	0.163434	−	0.986554i	$-0.447743\pi$
$499$	−16.1803	−	11.7557i	−0.724331	−	0.526258i	−0.887765	+	0.460297i	$0.847743\pi$
$500$	−15.4230	+	46.3868i	−0.689736	+	2.07448i
$501$	3.85263	+	11.8572i	0.172123	+	0.529740i
$502$	−32.8163	+	45.1677i	−1.46466	+	2.01593i
$503$	−7.97122	−	10.9714i	−0.355419	−	0.489193i	0.593446	−	0.804874i	$-0.297767\pi$
$503$	−7.97122	−	10.9714i	−0.355419	−	0.489193i	−0.948865	+	0.315681i	$0.897767\pi$
$504$	−15.2073	+	46.8033i	−0.677388	+	2.08479i
$505$	4.11684	+	12.7692i	0.183197	+	0.568220i
$506$		0			0
$507$		−	10.2997i		−	0.457427i
$508$	−34.1721	−	11.1032i	−1.51614	−	0.492624i
$509$	18.3062	−	13.3002i	0.811408	−	0.589523i	−0.102830	−	0.994699i	$-0.532790\pi$
$509$	18.3062	−	13.3002i	0.811408	−	0.589523i	0.914239	+	0.405176i	$0.132790\pi$
$510$	−6.73459	−	2.20516i	−0.298213	−	0.0976462i
$511$	−7.41641	−	22.8254i	−0.328083	−	1.00973i
$512$	47.6830	−	15.4932i	2.10731	−	0.684707i
$513$	10.0074	−	13.7740i	0.441836	−	0.608135i
$514$	−21.8259	+	15.8574i	−0.962698	+	0.699441i
$515$	0.0528933	−	23.2378i	0.00233076	−	1.02398i
$516$	−12.0000			−0.528271
$517$		0			0
$518$			9.50744i			0.417733i
$519$	−2.08418	+	6.41446i	−0.0914855	+	0.281564i
$520$		0			0
$521$	17.4796	+	12.6997i	0.765795	+	0.556383i	0.900682	−	0.434478i	$-0.143067\pi$
$521$	17.4796	+	12.6997i	0.765795	+	0.556383i	−0.134887	+	0.990861i	$0.543067\pi$
$522$	49.8033	−	16.1821i	2.17983	−	0.708270i
$523$	−27.5830	+	8.96224i	−1.20612	+	0.391892i	−0.842008	−	0.539464i	$-0.818627\pi$
$523$	−27.5830	+	8.96224i	−1.20612	+	0.391892i	−0.364110	+	0.931356i	$0.618627\pi$
$524$	−9.70820	−	7.05342i	−0.424105	−	0.308130i
$525$	−4.29995	+	13.0317i	−0.187665	+	0.568751i
$526$	−21.3877	+	65.8245i	−0.932547	+	2.87008i
$527$		−	5.34363i		−	0.232772i
$528$		0			0
$529$	22.3723			0.972708
$530$	−56.9953	−	0.129731i	−2.47572	−	0.00563515i
$531$	−14.1490	+	10.2798i	−0.614014	+	0.446107i
$532$	−35.6104	+	49.0136i	−1.54391	+	2.12501i
$533$		0			0
$534$	−0.848116	−	2.61023i	−0.0367016	−	0.112956i
$535$	14.0960	+	4.61556i	0.609422	+	0.199548i
$536$	45.0807	−	32.7530i	1.94719	−	1.41472i
$537$	9.69119	+	3.14886i	0.418206	+	0.135883i
$538$			29.0024i			1.25038i
$539$		0			0
$540$	−39.6060	+	12.7692i	−1.70437	+	0.549497i
$541$	10.5788	−	32.5582i	0.454818	−	1.39979i	−0.416531	−	0.909121i	$-0.636754\pi$
$541$	10.5788	−	32.5582i	0.454818	−	1.39979i	0.871349	−	0.490664i	$-0.163246\pi$
$542$	−20.0147	−	27.5479i	−0.859707	−	1.18328i
$543$	−11.2311	+	15.4583i	−0.481972	+	0.663377i
$544$	2.01197	+	6.19221i	0.0862625	+	0.265489i
$545$	18.1200	−	13.1021i	0.776177	−	0.561231i
$546$		0			0
$547$	−17.0472	−	23.4635i	−0.728886	−	1.00323i	−0.999182	−	0.0404479i	$-0.987122\pi$
$547$	−17.0472	−	23.4635i	−0.728886	−	1.00323i	0.270296	−	0.962777i	$-0.412878\pi$
$548$	59.6870	+	19.3935i	2.54970	+	0.828448i
$549$	−1.76631			−0.0753844
$550$		0			0
$551$	34.9783			1.49012
$552$	−3.57507	−	1.16161i	−0.152165	−	0.0494415i
$553$	−2.55626	−	3.51838i	−0.108703	−	0.149617i
$554$	23.8572	+	17.3333i	1.01360	+	0.736420i
$555$	−1.56087	+	1.12862i	−0.0662553	+	0.0479073i
$556$	−21.9335	−	67.5043i	−0.930187	−	2.86282i
$557$	0.584650	−	0.804702i	0.0247724	−	0.0340963i	−0.796451	−	0.604703i	$-0.793292\pi$
$557$	0.584650	−	0.804702i	0.0247724	−	0.0340963i	0.821224	+	0.570607i	$0.193292\pi$
$558$	−11.8701	−	16.3379i	−0.502503	−	0.691637i
$559$		0			0
$560$	46.9783	−	15.1460i	1.98519	−	0.640036i
$561$		0			0
$562$		−	1.28962i		−	0.0543994i
$563$	−17.9798	−	5.84199i	−0.757758	−	0.246211i	−0.0954420	−	0.995435i	$-0.530426\pi$
$563$	−17.9798	−	5.84199i	−0.757758	−	0.246211i	−0.662316	+	0.749224i	$0.730426\pi$
$564$	18.5898	−	13.5063i	0.782772	−	0.568717i
$565$	−1.05686	−	0.346055i	−0.0444623	−	0.0145587i
$566$	−11.8149	−	36.3624i	−0.496616	−	1.52843i
$567$	12.3367	−	4.00843i	0.518092	−	0.168338i
$568$	35.6104	−	49.0136i	1.49418	−	2.05656i
$569$	−22.0501	+	16.0203i	−0.924389	+	0.671608i	−0.944613	−	0.328188i	$-0.893562\pi$
$569$	−22.0501	+	16.0203i	−0.924389	+	0.671608i	0.0202237	+	0.999795i	$0.493562\pi$
$570$	−17.8885	−	0.0407173i	−0.749267	−	0.00170546i
$571$	1.48913			0.0623180			0.0311590	−	0.999514i	$-0.490080\pi$
$571$	1.48913			0.0623180			0.0311590	+	0.999514i	$0.490080\pi$
$572$		0			0
$573$			15.3484i			0.641189i
$574$	23.6297	−	72.7248i	0.986285	−	3.03547i
$575$	3.76194	+	1.24129i	0.156884	+	0.0517653i
$576$	−4.55292	−	3.30789i	−0.189705	−	0.137829i
$577$	20.8014	−	6.75877i	0.865972	−	0.281371i	0.157852	−	0.987463i	$-0.449543\pi$
$577$	20.8014	−	6.75877i	0.865972	−	0.281371i	0.708121	+	0.706091i	$0.249543\pi$
$578$	−34.7853	+	11.3024i	−1.44688	+	0.470119i
$579$	10.5348	+	7.65399i	0.437812	+	0.318089i
$580$	−69.0508	−	50.4089i	−2.86718	−	2.09312i
$581$	7.10067	−	21.8536i	0.294585	−	0.906641i
$582$		−	11.6819i		−	0.484231i
$583$		0			0
$584$	−41.4891			−1.71683
$585$		0			0
$586$	6.47214	−	4.70228i	0.267361	−	0.194249i
$587$	24.2604	−	33.3916i	1.00133	−	1.37822i	0.0768307	−	0.997044i	$-0.475520\pi$
$587$	24.2604	−	33.3916i	1.00133	−	1.37822i	0.924503	−	0.381174i	$-0.124480\pi$
$588$	16.4728	−	5.35233i	0.679326	−	0.220726i
$589$	−4.16837	−	12.8289i	−0.171755	−	0.528606i
$590$	39.5474	+	12.9493i	1.62814	+	0.533116i
$591$	5.45647	−	3.96435i	0.224449	−	0.163072i
$592$	6.58911	+	2.14093i	0.270811	+	0.0879918i
$593$		−	22.7739i		−	0.935214i	−0.883937	−	0.467607i	$-0.845116\pi$
$593$		−	22.7739i		−	0.935214i	0.883937	−	0.467607i	$-0.154884\pi$
$594$		0			0
$595$	−3.76631	−	11.6819i	−0.154404	−	0.478912i
$596$	−15.5231	+	47.7751i	−0.635849	+	1.95694i
$597$	3.72556	+	5.12779i	0.152477	+	0.209866i
$598$		0			0
$599$	−3.39247	−	10.4409i	−0.138612	−	0.426605i	0.857522	−	0.514447i	$-0.172003\pi$
$599$	−3.39247	−	10.4409i	−0.138612	−	0.426605i	−0.996134	+	0.0878422i	$0.972003\pi$
$600$	19.1285	+	14.0311i	0.780917	+	0.572819i
$601$	31.1208	+	22.6106i	1.26944	+	0.922304i	0.999180	−	0.0404830i	$-0.0128897\pi$
$601$	31.1208	+	22.6106i	1.26944	+	0.922304i	0.270262	+	0.962787i	$0.412890\pi$
$602$	−17.8052	−	24.5068i	−0.725687	−	0.998822i
$603$	−20.9938	−	6.82131i	−0.854935	−	0.277785i
$604$	53.4891			2.17644
$605$		0			0
$606$	12.0000			0.487467
$607$	−3.29456	−	1.07047i	−0.133722	−	0.0434489i	0.241391	−	0.970428i	$-0.422396\pi$
$607$	−3.29456	−	1.07047i	−0.133722	−	0.0434489i	−0.375113	+	0.926979i	$0.622396\pi$
$608$	9.66063	+	13.2967i	0.391790	+	0.539253i
$609$	−19.4164	−	14.1068i	−0.786793	−	0.571638i
$610$	2.46257	+	3.40571i	0.0997065	+	0.137893i
$611$		0			0
$612$	9.66063	−	13.2967i	0.390508	−	0.537488i
$613$	2.55626	+	3.51838i	0.103246	+	0.142106i	0.857514	−	0.514461i	$-0.172008\pi$
$613$	2.55626	+	3.51838i	0.103246	+	0.142106i	−0.754268	+	0.656567i	$0.772008\pi$
$614$	24.6357	−	75.8209i	0.994216	−	3.05988i
$615$	14.7446	−	4.75372i	0.594558	−	0.191689i
$616$		0			0
$617$			17.0256i			0.685423i	0.939441	+	0.342712i	$0.111345\pi$
$617$			17.0256i			0.685423i	−0.939441	+	0.342712i	$0.888655\pi$
$618$	−19.7673	−	6.42280i	−0.795159	−	0.258363i
$619$	11.4208	−	8.29767i	0.459039	−	0.333512i	−0.334115	−	0.942532i	$-0.608437\pi$
$619$	11.4208	−	8.29767i	0.459039	−	0.333512i	0.793154	+	0.609021i	$0.208437\pi$
$620$	−10.2596	+	31.3329i	−0.412035	+	1.25836i
$621$	1.04209	+	3.20723i	0.0418177	+	0.128702i
$622$	−13.1782	+	4.28187i	−0.528399	+	0.171687i
$623$	2.79417	−	3.84584i	0.111946	−	0.154080i
$624$		0			0
$625$	−20.0908	−	14.8782i	−0.803632	−	0.595127i
$626$	55.2119			2.20671
$627$		0			0
$628$		−	106.907i		−	4.26606i
$629$	0.532379	−	1.63849i	0.0212273	−	0.0653310i
$630$	−37.4651	−	27.3505i	−1.49265	−	1.08967i
$631$	−19.0976	−	13.8752i	−0.760265	−	0.552365i	0.138727	−	0.990331i	$-0.455699\pi$
$631$	−19.0976	−	13.8752i	−0.760265	−	0.552365i	−0.898991	+	0.437966i	$0.855699\pi$
$632$	−7.15015	+	2.32322i	−0.284418	+	0.0924129i
$633$	1.12207	−	0.364583i	0.0445983	−	0.0144909i
$634$	−67.3199	−	48.9108i	−2.67361	−	1.94249i
$635$	10.8347	−	14.8416i	0.429963	−	0.588969i
$636$	−10.8089	+	33.2663i	−0.428600	+	1.31909i
$637$		0			0
$638$		0			0
$639$	−24.0000			−0.949425
$640$	−0.0723050	+	31.7661i	−0.00285811	+	1.25566i
$641$	20.5266	−	14.9135i	0.810752	−	0.589046i	−0.103296	−	0.994651i	$-0.532939\pi$
$641$	20.5266	−	14.9135i	0.810752	−	0.589046i	0.914049	+	0.405605i	$0.132939\pi$
$642$	7.79785	−	10.7328i	0.307757	−	0.423591i
$643$	29.0019	−	9.42330i	1.14372	−	0.371619i	0.324948	−	0.945732i	$-0.394653\pi$
$643$	29.0019	−	9.42330i	1.14372	−	0.371619i	0.818776	+	0.574113i	$0.194653\pi$
$644$	−3.70820	−	11.4127i	−0.146124	−	0.449723i
$645$	1.90973	−	5.83233i	0.0751954	−	0.229648i
$646$	12.9443	−	9.40456i	0.509286	−	0.370018i
$647$	20.9058	+	6.79271i	0.821892	+	0.267049i	0.689626	−	0.724166i	$-0.257775\pi$
$647$	20.9058	+	6.79271i	0.821892	+	0.267049i	0.132265	+	0.991214i	$0.457775\pi$
$648$		−	22.4241i		−	0.880901i
$649$		0			0
$650$		0			0
$651$	−2.86009	+	8.80244i	−0.112096	+	0.344995i
$652$	−8.90261	−	12.2534i	−0.348653	−	0.479880i
$653$	−18.0975	+	24.9091i	−0.708212	+	0.974770i	0.291622	+	0.956534i	$0.405805\pi$
$653$	−18.0975	+	24.9091i	−0.708212	+	0.974770i	−0.999834	+	0.0182362i	$0.994195\pi$
$654$	−6.18034	−	19.0211i	−0.241670	−	0.743785i
$655$	4.97316	−	3.59594i	0.194317	−	0.140505i
$656$	−45.0807	−	32.7530i	−1.76011	−	1.27879i
$657$	9.66063	+	13.2967i	0.376897	+	0.518754i
$658$	55.1659	+	17.9245i	2.15059	+	0.698769i
$659$	−21.2554			−0.827994			−0.413997	−	0.910278i	$-0.635868\pi$
$659$	−21.2554			−0.827994			−0.413997	+	0.910278i	$0.635868\pi$
$660$		0			0
$661$	−16.3505			−0.635962			−0.317981	−	0.948097i	$-0.603005\pi$
$661$	−16.3505			−0.635962			−0.317981	+	0.948097i	$0.603005\pi$
$662$	−33.8915	−	11.0120i	−1.31723	−	0.427995i
$663$		0			0
$664$	−32.1364	−	23.3485i	−1.24714	−	0.906097i
$665$	−18.1548	−	25.1079i	−0.704011	−	0.973641i
$666$	−2.01197	−	6.19221i	−0.0779623	−	0.239943i
$667$	−4.07230	+	5.60503i	−0.157680	+	0.217028i
$668$	40.4408	+	55.6619i	1.56470	+	2.15362i
$669$	−0.581927	+	1.79099i	−0.0224986	+	0.0692436i
$670$	16.1168	+	49.9894i	0.622648	+	1.93126i
$671$		0			0
$672$		−	11.2772i		−	0.435026i
$673$	17.6993	+	5.75085i	0.682257	+	0.221679i	0.629583	−	0.776933i	$-0.283226\pi$
$673$	17.6993	+	5.75085i	0.682257	+	0.221679i	0.0526739	+	0.998612i	$0.483226\pi$
$674$	66.3042	−	48.1728i	2.55394	−	1.85555i
$675$	0.0968822	−	21.2817i	0.00372900	−	0.819134i
$676$	−17.5644	−	54.0577i	−0.675555	−	2.07914i
$677$	47.6308	−	15.4762i	1.83060	−	0.594798i	0.831364	−	0.555728i	$-0.187560\pi$
$677$	47.6308	−	15.4762i	1.83060	−	0.594798i	0.999236	−	0.0390703i	$-0.0124396\pi$
$678$	−0.584650	+	0.804702i	−0.0224534	+	0.0309044i
$679$	16.3694	−	11.8931i	0.628200	−	0.456414i
$680$	−21.2183	−	0.0482964i	−0.813684	−	0.00185208i
$681$	−13.2554			−0.507949
$682$		0			0
$683$			17.9104i			0.685323i	0.939459	+	0.342661i	$0.111328\pi$
$683$			17.9104i			0.685323i	−0.939459	+	0.342661i	$0.888672\pi$
$684$	12.8208	−	39.4585i	0.490217	−	1.50873i
$685$	−18.9246	+	25.9232i	−0.723071	+	0.990473i
$686$	−14.1490	−	10.2798i	−0.540211	−	0.392486i
$687$	−11.0221	+	3.58131i	−0.420520	+	0.136635i
$688$	−20.9938	+	6.82131i	−0.800383	+	0.260060i
$689$		0			0
$690$	2.08917	−	2.86177i	0.0795333	−	0.108946i
$691$	13.8629	−	42.6657i	0.527371	−	1.62308i	−0.232208	−	0.972666i	$-0.574595\pi$
$691$	13.8629	−	42.6657i	0.527371	−	1.62308i	0.759579	−	0.650415i	$-0.225405\pi$
$692$			37.2203i			1.41490i
$693$		0			0
$694$	−57.2119			−2.17174
$695$	36.2995	+	0.0826239i	1.37692	+	0.00313410i
$696$	−33.5654	+	24.3867i	−1.27229	+	0.924375i
$697$	−8.14459	+	11.2101i	−0.308498	+	0.424612i
$698$	37.1861	−	12.0825i	1.40751	−	0.457329i
$699$	−0.920330	−	2.83248i	−0.0348101	−	0.107134i
$700$	−0.344748	+	75.7293i	−0.0130302	+	2.86230i
$701$	10.1215	−	7.35371i	0.382284	−	0.277746i	−0.380002	−	0.924986i	$-0.624077\pi$
$701$	10.1215	−	7.35371i	0.382284	−	0.277746i	0.762286	+	0.647240i	$0.224077\pi$
$702$		0			0
$703$		−	4.34896i		−	0.164024i
$704$		0			0
$705$	3.60597	+	11.1846i	0.135809	+	0.421236i
$706$	−19.5336	+	60.1181i	−0.735155	+	2.26258i
$707$	12.2169	+	16.8151i	0.459463	+	0.632397i
$708$	15.0111	−	20.6609i	0.564150	−	0.776486i
$709$	−7.38030	−	22.7142i	−0.277173	−	0.853051i	−0.988636	−	0.150328i	$-0.951967\pi$
$709$	−7.38030	−	22.7142i	−0.277173	−	0.853051i	0.711463	−	0.702723i	$-0.248033\pi$
$710$	33.4605	+	46.2756i	1.25575	+	1.73669i
$711$	2.40946	+	1.75057i	0.0903616	+	0.0656516i
$712$	−4.83032	−	6.64836i	−0.181024	−	0.249158i
$713$	2.54105	+	0.825636i	0.0951629	+	0.0309203i
$714$	−10.9783			−0.410851
$715$		0			0
$716$	56.2337			2.10155
$717$	−11.1102	−	3.60991i	−0.414917	−	0.134815i
$718$	43.7550	+	60.2236i	1.63292	+	2.24753i
$719$	−24.5541	−	17.8396i	−0.915713	−	0.665305i	0.0267400	−	0.999642i	$-0.491487\pi$
$719$	−24.5541	−	17.8396i	−0.915713	−	0.665305i	−0.942453	+	0.334338i	$0.891487\pi$
$720$	−27.3918	+	19.8062i	−1.02083	+	0.738133i
$721$	−11.1246	−	34.2380i	−0.414302	−	1.27509i
$722$	−4.45131	+	6.12670i	−0.165660	+	0.228012i
$723$	7.79785	+	10.7328i	0.290005	+	0.399158i
$724$	−32.5845	+	100.285i	−1.21099	+	3.72705i
$725$	35.4891	−	25.5383i	1.31803	−	0.948470i
$726$		0			0
$727$		−	14.0588i		−	0.521412i	−0.965418	−	0.260706i	$-0.916045\pi$
$727$		−	14.0588i		−	0.521412i	0.965418	−	0.260706i	$-0.0839552\pi$
$728$		0			0
$729$	0.998075	−	0.725144i	0.0369657	−	0.0268572i
$730$	12.1693	−	37.1652i	0.450407	−	1.37555i
$731$	1.69623	+	5.22047i	0.0627374	+	0.193086i
$732$	2.45300	−	0.797029i	0.0906656	−	0.0294590i
$733$	−5.58834	+	7.69168i	−0.206410	+	0.284099i	−0.899654	−	0.436604i	$-0.856181\pi$
$733$	−5.58834	+	7.69168i	−0.206410	+	0.284099i	0.693244	+	0.720703i	$0.256181\pi$
$734$	−52.5685	+	38.1933i	−1.94034	+	1.40974i
$735$	−0.0201624	+	8.85801i	−0.000743700	+	0.326733i
$736$	−3.25544			−0.119997
$737$		0			0
$738$			52.3663i			1.92763i
$739$	3.32025	−	10.2187i	0.122137	−	0.375900i	−0.871231	−	0.490873i	$-0.836678\pi$
$739$	3.32025	−	10.2187i	0.122137	−	0.375900i	0.993369	+	0.114972i	$0.0366780\pi$
$740$	−6.26751	+	8.58532i	−0.230398	+	0.315603i
$741$		0			0
$742$	−83.9754	+	27.2852i	−3.08283	+	1.00167i
$743$	−10.8297	+	3.51877i	−0.397301	+	0.129091i	−0.500852	−	0.865533i	$-0.666980\pi$
$743$	−10.8297	+	3.51877i	−0.397301	+	0.129091i	0.103550	+	0.994624i	$0.466980\pi$
$744$	12.9443	+	9.40456i	0.474560	+	0.344788i
$745$	−20.7496	−	15.1477i	−0.760206	−	0.554970i
$746$	9.11264	−	28.0458i	0.333637	−	1.02683i
$747$			15.7359i			0.575748i
$748$		0			0
$749$	22.9783			0.839607
$750$	−18.1795	+	13.0194i	−0.663821	+	0.475403i
$751$	−22.1446	+	16.0890i	−0.808069	+	0.587097i	−0.913270	−	0.407354i	$-0.866451\pi$
$751$	−22.1446	+	16.0890i	−0.808069	+	0.587097i	0.105201	+	0.994451i	$0.466451\pi$
$752$	24.8451	−	34.1963i	0.906006	−	1.24701i
$753$	−16.6653	+	5.41487i	−0.607316	+	0.197329i
$754$		0			0
$755$	−8.51247	+	25.9972i	−0.309800	+	0.946134i
$756$	−52.1552	+	37.8930i	−1.89687	+	1.37815i
$757$	−37.8516	−	12.2987i	−1.37574	−	0.447005i	−0.474473	−	0.880270i	$-0.657361\pi$
$757$	−37.8516	−	12.2987i	−1.37574	−	0.447005i	−0.901266	+	0.433266i	$0.857361\pi$
$758$			1.58457i			0.0575543i
$759$		0			0
$760$	−50.9783	+	16.4356i	−1.84918	+	0.596184i
$761$	10.1186	−	31.1419i	0.366800	−	1.12889i	−0.582046	−	0.813156i	$-0.697748\pi$
$761$	10.1186	−	31.1419i	0.366800	−	1.12889i	0.948846	−	0.315738i	$-0.102252\pi$
$762$	−9.66063	−	13.2967i	−0.349968	−	0.481689i
$763$	20.3615	−	28.0252i	0.737135	−	1.01458i
$764$	26.1741	+	80.5555i	0.946945	+	2.91440i
$765$	4.92514	+	6.81142i	0.178069	+	0.246268i
$766$	−22.2392	−	16.1577i	−0.803534	−	0.583802i
$767$		0			0
$768$	23.4468	+	7.61834i	0.846065	+	0.274903i
$769$	−29.2119			−1.05341			−0.526705	−	0.850048i	$-0.676573\pi$
$769$	−29.2119			−1.05341			−0.526705	+	0.850048i	$0.676573\pi$
$770$		0			0
$771$	−8.46738			−0.304945
$772$	68.3441	+	22.2064i	2.45976	+	0.799224i
$773$	10.3541	+	14.2512i	0.372411	+	0.512580i	0.953554	−	0.301221i	$-0.0973943\pi$
$773$	10.3541	+	14.2512i	0.372411	+	0.512580i	−0.581143	+	0.813802i	$0.697394\pi$
$774$	16.7827	+	12.1933i	0.603242	+	0.438281i
$775$	−13.5959	−	9.97288i	−0.488379	−	0.358237i
$776$	−10.8089	−	33.2663i	−0.388016	−	1.19419i
$777$	−1.75395	+	2.41411i	−0.0629226	+	0.0866056i
$778$	27.9860	+	38.5194i	1.00335	+	1.38099i
$779$	−10.8089	+	33.2663i	−0.387268	+	1.19189i
$780$		0			0
$781$		0			0
$782$			3.16915i			0.113328i
$783$	35.3986	+	11.5017i	1.26504	+	0.411037i
$784$	25.7764	−	18.7277i	0.920586	−	0.668845i
$785$	51.9598	+	17.0136i	1.85452	+	0.607241i
$786$	−1.69623	−	5.22047i	−0.0605026	−	0.186208i
$787$	−14.4047	+	4.68038i	−0.513473	+	0.166838i	−0.554281	−	0.832329i	$-0.687007\pi$
$787$	−14.4047	+	4.68038i	−0.513473	+	0.166838i	0.0408081	+	0.999167i	$0.487007\pi$
$788$	21.8775	−	30.1118i	0.779354	−	1.07269i
$789$	−17.5741	+	12.7683i	−0.625655	+	0.454565i
$790$	0.0161299	−	7.08641i	0.000573876	−	0.252123i
$791$	−1.72281			−0.0612562
$792$		0			0
$793$		0			0
$794$	−12.8208	+	39.4585i	−0.454995	+	1.40033i
$795$	−14.4482	−	10.5475i	−0.512424	−	0.374083i
$796$	28.2980	+	20.5597i	1.00300	+	0.728719i
$797$	4.99405	−	1.62267i	0.176898	−	0.0574778i	−0.219229	−	0.975674i	$-0.570354\pi$
$797$	4.99405	−	1.62267i	0.176898	−	0.0574778i	0.396127	+	0.918196i	$0.370354\pi$
$798$	−26.3565	+	8.56373i	−0.933008	+	0.303153i
$799$	−8.50348	−	6.17814i	−0.300831	−	0.218567i
$800$	19.5099	+	6.43750i	0.689780	+	0.227600i
$801$	−1.00599	+	3.09610i	−0.0355447	+	0.109395i
$802$		−	29.0024i		−	1.02411i
$803$		0			0
$804$	32.2337			1.13679
$805$	6.13701	+	0.0139689i	0.216301	+	0.000492339i
$806$		0			0
$807$	−5.35042	+	7.36423i	−0.188344	+	0.259233i
$808$	34.1721	−	11.1032i	1.20217	−	0.390608i
$809$	10.1186	+	31.1419i	0.355752	+	1.09489i	0.955572	+	0.294757i	$0.0952388\pi$
$809$	10.1186	+	31.1419i	0.355752	+	1.09489i	−0.599820	+	0.800135i	$0.704761\pi$
$810$	20.0871	+	6.57728i	0.705789	+	0.231102i
$811$	0.189058	−	0.137358i	0.00663871	−	0.00482330i	−0.584461	−	0.811422i	$-0.698694\pi$
$811$	0.189058	−	0.137358i	0.00663871	−	0.00482330i	0.591100	+	0.806599i	$0.298694\pi$
$812$	−125.963	−	40.9279i	−4.42044	−	1.43629i
$813$		−	10.6873i		−	0.374819i
$814$		0			0
$815$	7.37228	−	2.37686i	0.258240	−	0.0832578i
$816$	−2.47214	+	7.60845i	−0.0865421	+	0.266349i
$817$	8.14459	+	11.2101i	0.284943	+	0.392191i
$818$	−40.7875	+	56.1392i	−1.42610	+	1.96286i
$819$		0			0
$820$	69.2796	−	50.0940i	2.41935	−	1.74936i
$821$	14.5623	+	10.5801i	0.508228	+	0.369249i	0.812151	−	0.583447i	$-0.198297\pi$
$821$	14.5623	+	10.5801i	0.508228	+	0.369249i	−0.303923	+	0.952697i	$0.598297\pi$
$822$	16.8738	+	23.2248i	0.588543	+	0.810059i
$823$	53.2903	+	17.3151i	1.85758	+	0.603566i	0.995265	+	0.0972005i	$0.0309888\pi$
$823$	53.2903	+	17.3151i	1.85758	+	0.603566i	0.862319	+	0.506365i	$0.169011\pi$
$824$	−62.2337			−2.16801
$825$		0			0
$826$	64.4674			2.24311
$827$	−27.0219	−	8.77995i	−0.939644	−	0.305309i	−0.201144	−	0.979562i	$-0.564466\pi$
$827$	−27.0219	−	8.77995i	−0.939644	−	0.305309i	−0.738501	+	0.674253i	$0.764466\pi$
$828$	4.83032	+	6.64836i	0.167865	+	0.231046i
$829$	−16.4639	−	11.9617i	−0.571816	−	0.415448i	0.263949	−	0.964537i	$-0.414975\pi$
$829$	−16.4639	−	11.9617i	−0.571816	−	0.415448i	−0.835764	+	0.549088i	$0.814975\pi$
$830$	30.3412	−	21.9388i	1.05316	−	0.761508i
$831$	2.86009	+	8.80244i	0.0992153	+	0.305353i
$832$		0			0
$833$	−4.65695	−	6.40974i	−0.161354	−	0.222084i
$834$	10.0330	−	30.8783i	0.347413	−	1.06923i
$835$	−33.4891	+	10.7971i	−1.15894	+	0.373648i
$836$		0			0
$837$		−	14.3537i		−	0.496138i
$838$	55.1659	+	17.9245i	1.90567	+	0.619191i
$839$	−8.18470	+	5.94653i	−0.282567	+	0.205297i	−0.720036	−	0.693936i	$-0.755875\pi$
$839$	−8.18470	+	5.94653i	−0.282567	+	0.205297i	0.437469	+	0.899233i	$0.355875\pi$
$840$	34.9266	+	11.4363i	1.20508	+	0.394589i
$841$	14.6682	+	45.1442i	0.505801	+	1.55670i
$842$	−20.4328	+	6.63902i	−0.704161	+	0.228796i
$843$	0.237912	−	0.327457i	0.00819411	−	0.0112782i
$844$	5.26741	−	3.82700i	0.181312	−	0.131731i
$845$	29.0688	+	0.0661656i	0.999997	+	0.00227617i
$846$	−39.7228			−1.36570
$847$		0			0
$848$			64.3432i			2.20955i
$849$	3.70820	−	11.4127i	0.127265	−	0.391682i
$850$	6.26687	−	18.9928i	0.214952	−	0.651448i
$851$	0.696893	+	0.506322i	0.0238892	+	0.0173565i
$852$	33.3305	−	10.8297i	1.14188	−	0.371021i
$853$	−33.3305	+	10.8297i	−1.14122	+	0.370803i	−0.817828	−	0.575463i	$-0.804822\pi$
$853$	−33.3305	+	10.8297i	−1.14122	+	0.370803i	−0.323387	+	0.946267i	$0.604822\pi$
$854$	5.26741	+	3.82700i	0.180247	+	0.130957i
$855$	17.1376	+	12.5109i	0.586092	+	0.427862i
$856$	12.2750	−	37.7786i	0.419552	−	1.29125i
$857$			23.9538i			0.818245i	0.912480	+	0.409122i	$0.134165\pi$
$857$			23.9538i			0.818245i	−0.912480	+	0.409122i	$0.865835\pi$
$858$		0			0
$859$	6.11684			0.208704			0.104352	−	0.994540i	$-0.466723\pi$
$859$	6.11684			0.208704			0.104352	+	0.994540i	$0.466723\pi$
$860$	0.0770881	−	33.8675i	0.00262868	−	1.15487i
$861$	19.4164	−	14.1068i	0.661709	−	0.480760i
$862$	−38.1667	+	52.5320i	−1.29996	+	1.78925i
$863$	2.73352	−	0.888175i	0.0930501	−	0.0302338i	−0.262122	−	0.965035i	$-0.584422\pi$
$863$	2.73352	−	0.888175i	0.0930501	−	0.0302338i	0.355172	+	0.934801i	$0.384422\pi$
$864$	5.40444	+	16.6331i	0.183863	+	0.565871i
$865$	−18.0901	−	5.92338i	−0.615081	−	0.201401i
$866$	59.6430	−	43.3332i	2.02675	−	1.47252i
$867$	−10.9177	−	3.54737i	−0.370784	−	0.120475i
$868$			51.0767i			1.73365i
$869$		0			0
$870$	−12.0000	−	37.2203i	−0.406838	−	1.26188i
$871$		0			0
$872$	−35.1992	−	48.4475i	−1.19199	−	1.64064i
$873$	−8.14459	+	11.2101i	−0.275653	+	0.379403i
$874$	2.47214	+	7.60845i	0.0836212	+	0.257360i
$875$	−36.7517	−	12.2194i	−1.24243	−	0.413092i
$876$	−19.4164	−	14.1068i	−0.656020	−	0.476626i
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$	−51.5908	−	16.7629i	−1.74111	−	0.565720i
$879$	2.51087			0.0846897
$880$		0			0
$881$	−6.86141			−0.231167			−0.115583	−	0.993298i	$-0.536874\pi$
$881$	−6.86141			−0.231167			−0.115583	+	0.993298i	$0.536874\pi$
$882$	−28.4767	−	9.25265i	−0.958861	−	0.311553i
$883$	−14.2530	−	19.6176i	−0.479653	−	0.660185i	0.498785	−	0.866726i	$-0.333780\pi$
$883$	−14.2530	−	19.6176i	−0.479653	−	0.660185i	−0.978438	+	0.206540i	$0.933780\pi$
$884$		0			0
$885$	7.65287	+	10.5838i	0.257248	+	0.355772i
$886$	24.7079	+	76.0432i	0.830079	+	2.55472i
$887$	16.1158	−	22.1815i	0.541116	−	0.744782i	−0.447657	−	0.894205i	$-0.647742\pi$
$887$	16.1158	−	22.1815i	0.541116	−	0.744782i	0.988773	+	0.149423i	$0.0477416\pi$
$888$	3.03208	+	4.17330i	0.101750	+	0.140047i
$889$	8.79690	−	27.0741i	0.295039	−	0.908036i
$890$	7.37228	−	2.37686i	0.247119	−	0.0796726i
$891$		0			0
$892$			10.3923i			0.347960i
$893$	−25.2344	−	8.19915i	−0.844436	−	0.274374i
$894$	−18.5898	+	13.5063i	−0.621736	+	0.451717i
$895$	−8.94925	+	27.3311i	−0.299140	+	0.913578i
$896$	15.2073	+	46.8033i	0.508041	+	1.56359i
$897$		0			0
$898$	−10.1807	+	14.0126i	−0.339736	+	0.467606i
$899$	23.8572	−	17.3333i	0.795682	−	0.578097i
$900$	−15.8014	−	49.3956i	−0.526712	−	1.64652i
$901$	16.0000			0.533037
$902$		0			0
$903$		−	9.50744i		−	0.316388i
$904$	−0.920330	+	2.83248i	−0.0306097	+	0.0942070i
$905$	−43.5555	−	31.7967i	−1.44783	−	1.05696i
$906$	19.7945	+	14.3816i	0.657629	+	0.477795i
$907$	−18.9258	+	6.14936i	−0.628420	+	0.204186i	−0.605875	−	0.795560i	$-0.707177\pi$
$907$	−18.9258	+	6.14936i	−0.628420	+	0.204186i	−0.0225451	+	0.999746i	$0.507177\pi$
$908$	−69.5706	+	22.6049i	−2.30878	+	0.750169i
$909$	−11.5153	−	8.36635i	−0.381938	−	0.277494i
$910$		0			0
$911$	−16.5290	+	50.8712i	−0.547632	+	1.68544i	0.167017	+	0.985954i	$0.446587\pi$
$911$	−16.5290	+	50.8712i	−0.547632	+	1.68544i	−0.714649	+	0.699483i	$0.753413\pi$
$912$			20.1947i			0.668713i
$913$		0			0
$914$	−52.4674			−1.73547
$915$	−0.00300243	+	1.31907i	−9.92572e−5	+	0.0436071i
$916$	−51.7419	+	37.5927i	−1.70960	+	1.24210i
$917$	5.58834	−	7.69168i	0.184543	−	0.254002i
$918$	16.1923	−	5.26119i	0.534424	−	0.173645i
$919$	8.72469	+	26.8518i	0.287801	+	0.885760i	0.985545	+	0.169413i	$0.0541872\pi$
$919$	8.72469	+	26.8518i	0.287801	+	0.885760i	−0.697744	+	0.716347i	$0.745813\pi$
$920$	3.30137	−	10.0824i	0.108843	−	0.332408i
$921$	20.2430	−	14.7074i	0.667030	−	0.484626i
$922$	5.36261	+	1.74242i	0.176608	+	0.0573835i
$923$		0			0
$924$		0			0
$925$	−3.17527	−	4.41248i	−0.104402	−	0.145081i
$926$	23.4718	−	72.2389i	0.771333	−	2.37392i
$927$	14.4909	+	19.9451i	0.475945	+	0.655082i
$928$	−21.1195	+	29.0685i	−0.693281	+	0.954220i
$929$	2.16984	+	6.67808i	0.0711901	+	0.219101i	0.980321	−	0.197410i	$-0.0632529\pi$
$929$	2.16984	+	6.67808i	0.0711901	+	0.219101i	−0.909131	+	0.416510i	$0.863253\pi$
$930$	−12.2212	+	8.83677i	−0.400748	+	0.289769i
$931$	−16.1803	−	11.7557i	−0.530289	−	0.385278i
$932$	−9.66063	−	13.2967i	−0.316444	−	0.435548i
$933$	−4.13611	−	1.34390i	−0.135410	−	0.0439974i
$934$	−19.4891			−0.637704
$935$		0			0
$936$		0			0
$937$	−51.0298	−	16.5806i	−1.66707	−	0.541664i	−0.684735	−	0.728792i	$-0.740082\pi$
$937$	−51.0298	−	16.5806i	−1.66707	−	0.541664i	−0.982336	+	0.187128i	$0.940082\pi$
$938$	47.8273	+	65.8287i	1.56162	+	2.14938i
$939$	14.0193	+	10.1856i	0.457502	+	0.332395i
$940$	37.9992	+	52.5525i	1.23940	+	1.71407i
$941$	−18.0674	−	55.6058i	−0.588981	−	1.81270i	−0.582659	−	0.812717i	$-0.697988\pi$
$941$	−18.0674	−	55.6058i	−0.588981	−	1.81270i	−0.00632159	−	0.999980i	$-0.502012\pi$
$942$	28.7440	−	39.5627i	0.936530	−	1.28902i
$943$	−4.07230	−	5.60503i	−0.132612	−	0.182525i
$944$	14.5171	−	44.6790i	0.472491	−	1.45418i
$945$	−10.1168	−	31.3793i	−0.329101	−	1.02077i
$946$		0			0
$947$			26.7354i			0.868783i	0.900724	+	0.434392i	$0.143037\pi$
$947$			26.7354i			0.868783i	−0.900724	+	0.434392i	$0.856963\pi$
$948$	−4.13611	−	1.34390i	−0.134335	−	0.0436480i
$949$		0			0
$950$	0.229832	−	50.4862i	0.00745673	−	1.63799i
$951$	−8.07055	−	24.8386i	−0.261705	−	0.805447i
$952$	−31.2625	+	10.1578i	−1.01322	+	0.329216i
$953$	18.3899	−	25.3115i	0.595706	−	0.819920i	−0.399600	−	0.916689i	$-0.630851\pi$
$953$	18.3899	−	25.3115i	0.595706	−	0.819920i	0.995307	+	0.0967699i	$0.0308511\pi$
$954$	48.9191	−	35.5418i	1.58382	−	1.15071i
$955$	−43.3176	−	0.0985983i	−1.40173	−	0.00319057i
$956$	−64.4674			−2.08502
$957$		0			0
$958$			13.8564i			0.447680i
$959$	−15.3652	+	47.2892i	−0.496168	+	1.52705i
$960$	−2.47805	+	3.39447i	−0.0799787	+	0.109556i
$961$	15.8792	+	11.5369i	0.512231	+	0.372158i
$962$		0			0
$963$	−14.9658	+	4.86267i	−0.482265	+	0.156697i
$964$	59.2297	+	43.0329i	1.90766	+	1.38600i
$965$	−21.6694	+	29.6831i	−0.697564	+	0.955533i
$966$	1.69623	−	5.22047i	0.0545754	−	0.167966i
$967$			26.4232i			0.849713i	0.905261	+	0.424856i	$0.139675\pi$
$967$			26.4232i			0.849713i	−0.905261	+	0.424856i	$0.860325\pi$
$968$		0			0
$969$	5.02175			0.161322
$970$	32.9698	+	0.0750448i	1.05860	+	0.00240954i
$971$	7.35809	−	5.34596i	0.236132	−	0.171560i	−0.463426	−	0.886136i	$-0.653380\pi$
$971$	7.35809	−	5.34596i	0.236132	−	0.171560i	0.699558	+	0.714575i	$0.253380\pi$
$972$	40.4408	−	55.6619i	1.29714	−	1.78536i
$973$	53.4828	−	17.3776i	1.71458	−	0.557101i
$974$	−5.56231	−	17.1190i	−0.178228	−	0.548529i
$975$		0			0
$976$	3.83843	−	2.78878i	0.122865	−	0.0892668i
$977$	48.1038	+	15.6299i	1.53898	+	0.500044i	0.951094	−	0.308902i	$-0.0999615\pi$
$977$	48.1038	+	15.6299i	1.53898	+	0.500044i	0.587883	+	0.808946i	$0.299962\pi$
$978$		−	6.92820i		−	0.221540i
$979$		0			0
$980$	15.0000	+	46.5253i	0.479157	+	1.48620i
$981$	−7.33075	+	22.5617i	−0.234053	+	0.720341i
$982$	−9.66063	−	13.2967i	−0.308283	−	0.424315i
$983$	−14.5454	+	20.0200i	−0.463925	+	0.638538i	−0.975317	−	0.220810i	$-0.929130\pi$
$983$	−14.5454	+	20.0200i	−0.463925	+	0.638538i	0.511392	+	0.859348i	$0.329130\pi$
$984$	−12.8208	−	39.4585i	−0.408714	−	1.25789i
$985$	11.1535	+	15.4252i	0.355380	+	0.491487i
$986$	28.2980	+	20.5597i	0.901192	+	0.654754i
$987$	10.7008	+	14.7285i	0.340612	+	0.468812i
$988$		0			0
$989$	−2.74456			−0.0872720
$990$		0			0
$991$	18.9783			0.602864			0.301432	−	0.953488i	$-0.402535\pi$
$991$	18.9783			0.602864			0.301432	+	0.953488i	$0.402535\pi$
$992$	13.1782	+	4.28187i	0.418409	+	0.135949i
$993$	−6.57414	−	9.04852i	−0.208624	−	0.287146i
$994$	71.5716	+	51.9998i	2.27011	+	1.64933i
$995$	−14.4960	+	10.4817i	−0.459555	+	0.332291i
$996$	−7.10067	−	21.8536i	−0.224993	−	0.692458i
$997$	−1.27813	+	1.75919i	−0.0404787	+	0.0557142i	−0.828777	−	0.559580i	$-0.810963\pi$
$997$	−1.27813	+	1.75919i	−0.0404787	+	0.0557142i	0.788298	+	0.615294i	$0.210963\pi$
$998$	−29.6754	−	40.8446i	−0.939357	−	1.29291i
$999$	1.43004	−	4.40122i	0.0452446	−	0.139249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.i.9.4		16
5.4	even	2	inner	605.2.j.i.9.1		16
11.2	odd	10		605.2.j.j.124.4		16
11.3	even	5	inner	605.2.j.i.444.4		16
11.4	even	5		55.2.b.a.34.4	yes	4
11.5	even	5	inner	605.2.j.i.269.1		16
11.6	odd	10		605.2.j.j.269.4		16
11.7	odd	10		605.2.b.c.364.1		4
11.8	odd	10		605.2.j.j.444.1		16
11.9	even	5	inner	605.2.j.i.124.1		16
11.10	odd	2		605.2.j.j.9.1		16
33.26	odd	10		495.2.c.a.199.1		4
44.15	odd	10		880.2.b.h.529.3		4
55.4	even	10		55.2.b.a.34.1	✓	4
55.7	even	20		3025.2.a.ba.1.4		4
55.9	even	10	inner	605.2.j.i.124.4		16
55.14	even	10	inner	605.2.j.i.444.1		16
55.18	even	20		3025.2.a.ba.1.1		4
55.19	odd	10		605.2.j.j.444.4		16
55.24	odd	10		605.2.j.j.124.1		16
55.29	odd	10		605.2.b.c.364.4		4
55.37	odd	20		275.2.a.h.1.1		4
55.39	odd	10		605.2.j.j.269.1		16
55.48	odd	20		275.2.a.h.1.4		4
55.49	even	10	inner	605.2.j.i.269.4		16
55.54	odd	2		605.2.j.j.9.4		16
165.59	odd	10		495.2.c.a.199.4		4
165.92	even	20		2475.2.a.bi.1.4		4
165.158	even	20		2475.2.a.bi.1.1		4
220.59	odd	10		880.2.b.h.529.2		4
220.103	even	20		4400.2.a.cc.1.2		4
220.147	even	20		4400.2.a.cc.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.b.a.34.1	✓	4	55.4	even	10
55.2.b.a.34.4	yes	4	11.4	even	5
275.2.a.h.1.1		4	55.37	odd	20
275.2.a.h.1.4		4	55.48	odd	20
495.2.c.a.199.1		4	33.26	odd	10
495.2.c.a.199.4		4	165.59	odd	10
605.2.b.c.364.1		4	11.7	odd	10
605.2.b.c.364.4		4	55.29	odd	10
605.2.j.i.9.1		16	5.4	even	2	inner
605.2.j.i.9.4		16	1.1	even	1	trivial
605.2.j.i.124.1		16	11.9	even	5	inner
605.2.j.i.124.4		16	55.9	even	10	inner
605.2.j.i.269.1		16	11.5	even	5	inner
605.2.j.i.269.4		16	55.49	even	10	inner
605.2.j.i.444.1		16	55.14	even	10	inner
605.2.j.i.444.4		16	11.3	even	5	inner
605.2.j.j.9.1		16	11.10	odd	2
605.2.j.j.9.4		16	55.54	odd	2
605.2.j.j.124.1		16	55.24	odd	10
605.2.j.j.124.4		16	11.2	odd	10
605.2.j.j.269.1		16	55.39	odd	10
605.2.j.j.269.4		16	11.6	odd	10
605.2.j.j.444.1		16	11.8	odd	10
605.2.j.j.444.4		16	55.19	odd	10
880.2.b.h.529.2		4	220.59	odd	10
880.2.b.h.529.3		4	44.15	odd	10
2475.2.a.bi.1.1		4	165.158	even	20
2475.2.a.bi.1.4		4	165.92	even	20
3025.2.a.ba.1.1		4	55.18	even	20
3025.2.a.ba.1.4		4	55.7	even	20
4400.2.a.cc.1.2		4	220.103	even	20
4400.2.a.cc.1.3		4	220.147	even	20

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.40079 + 0.780063i) q^{2} +(0.465695 + 0.640974i) q^{3} +(3.53725 + 2.56996i) q^{4} +(-1.81200 + 1.31021i) q^{5} +(0.618034 + 1.90211i) q^{6} +(-2.03615 + 2.80252i) q^{7} +(3.51992 + 4.84475i) q^{8} +(0.733075 - 2.25617i) q^{9} +(-5.37228 + 1.73205i) q^{10} +3.46410i q^{12} +(-7.07450 + 5.13992i) q^{14} +(-1.68365 - 0.551291i) q^{15} +(1.96914 + 6.06040i) q^{16} +(1.50702 - 0.489660i) q^{17} +(3.51992 - 4.84475i) q^{18} +(3.23607 - 2.35114i) q^{19} +(-9.77669 - 0.0222534i) q^{20} -2.74456 q^{21} +0.792287i q^{23} +(-1.46615 + 4.51235i) q^{24} +(1.56672 - 4.74820i) q^{25} +(4.04807 - 1.31530i) q^{27} +(-14.4047 + 4.68038i) q^{28} +(7.07450 + 5.13992i) q^{29} +(-3.61204 - 2.63688i) q^{30} +(1.04209 - 3.20723i) q^{31} +4.10891i q^{32} +4.00000 q^{34} +(0.0176311 - 7.74595i) q^{35} +(8.39135 - 6.09667i) q^{36} +(0.639064 - 0.879596i) q^{37} +(9.60315 - 3.12025i) q^{38} +(-12.7257 - 4.16689i) q^{40} +(-7.07450 + 5.13992i) q^{41} +(-6.58911 - 2.14093i) q^{42} +3.46410i q^{43} +(1.62772 + 5.04868i) q^{45} +(-0.618034 + 1.90211i) q^{46} +(-3.89893 - 5.36641i) q^{47} +(-2.96754 + 4.08446i) q^{48} +(-1.54508 - 4.75528i) q^{49} +(7.46525 - 10.1773i) q^{50} +(1.01567 + 0.737928i) q^{51} +(9.60315 + 3.12025i) q^{53} +10.7446 q^{54} -20.7446 q^{56} +(3.01404 + 0.979321i) q^{57} +(12.9749 + 17.8584i) q^{58} +(-5.96430 - 4.33332i) q^{59} +(-4.53869 - 6.27697i) q^{60} +(-0.230083 - 0.708121i) q^{61} +(5.00368 - 6.88698i) q^{62} +(4.83032 + 6.64836i) q^{63} +(0.733075 - 2.25617i) q^{64} -9.30506i q^{67} +(6.58911 + 2.14093i) q^{68} +(-0.507835 + 0.368964i) q^{69} +(6.08466 - 18.5826i) q^{70} +(-3.12628 - 9.62169i) q^{71} +(13.5110 - 4.38998i) q^{72} +(-4.07230 + 5.60503i) q^{73} +(2.22040 - 1.61321i) q^{74} +(3.77308 - 1.20699i) q^{75} +17.4891 q^{76} +(-0.387951 + 1.19399i) q^{79} +(-11.5085 - 8.40148i) q^{80} +(-3.02941 - 2.20100i) q^{81} +(-20.9938 + 6.82131i) q^{82} +(-6.30860 + 2.04979i) q^{83} +(-9.70820 - 7.05342i) q^{84} +(-2.08917 + 2.86177i) q^{85} +(-2.70222 + 8.31657i) q^{86} +6.92820i q^{87} -1.37228 q^{89} +(-0.0304791 + 13.3905i) q^{90} +(-2.03615 + 2.80252i) q^{92} +(2.54105 - 0.825636i) q^{93} +(-5.17435 - 15.9250i) q^{94} +(-2.78329 + 8.50019i) q^{95} +(-2.63370 + 1.91350i) q^{96} +(-5.55509 - 1.80496i) q^{97} -12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} + 3 q^{5} - 8 q^{6} + 2 q^{9} - 40 q^{10} - 12 q^{14} - q^{15} - 14 q^{16} + 16 q^{19} + 12 q^{20} + 48 q^{21} - 4 q^{24} - q^{25} + 12 q^{29} + 6 q^{30} - 2 q^{31} + 64 q^{34} - 18 q^{35}+ \cdots - 36 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 + 3 * q^5 - 8 * q^6 + 2 * q^9 - 40 * q^10 - 12 * q^14 - q^15 - 14 * q^16 + 16 * q^19 + 12 * q^20 + 48 * q^21 - 4 * q^24 - q^25 + 12 * q^29 + 6 * q^30 - 2 * q^31 + 64 * q^34 - 18 * q^35 + 30 * q^36 - 28 * q^40 - 12 * q^41 + 72 * q^45 + 8 * q^46 + 20 * q^49 + 18 * q^50 + 28 * q^51 + 80 * q^54 - 240 * q^56 - 18 * q^59 + 18 * q^60 - 20 * q^61 + 2 * q^64 - 14 * q^69 - 24 * q^70 + 6 * q^71 - 12 * q^74 - 15 * q^75 + 96 * q^76 + 28 * q^79 - 6 * q^80 + 8 * q^81 - 48 * q^84 - 2 * q^85 + 12 * q^86 + 24 * q^89 + 28 * q^90 + 44 * q^94 - 12 * q^95 - 36 * q^96

Introduction

L-functions

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