LMFDB - Embedded newform 675.2.l.g.151.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [66,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	675.151
Dual form			675.2.l.g.76.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.70314 - 1.42910i) q^{2} +(0.320463 - 1.70215i) q^{3} +(0.511048 + 2.89830i) q^{4} +(-2.97833 + 2.44102i) q^{6} +(0.653660 - 3.70709i) q^{7} +(1.04829 - 1.81569i) q^{8} +(-2.79461 - 1.09095i) q^{9} +(5.03989 - 1.83437i) q^{11} +(5.09710 + 0.0589180i) q^{12} +(4.69294 - 3.93784i) q^{13} +(-6.41109 + 5.37954i) q^{14} +(1.15085 - 0.418876i) q^{16} +(1.40339 + 2.43075i) q^{17} +(3.20052 + 5.85182i) q^{18} +(1.71412 - 2.96894i) q^{19} +(-6.10054 - 2.30061i) q^{21} +(-11.2051 - 4.07833i) q^{22} +(0.155686 + 0.882941i) q^{23} +(-2.75464 - 2.36621i) q^{24} -13.6203 q^{26} +(-2.75252 + 4.40722i) q^{27} +11.0783 q^{28} +(1.61238 + 1.35294i) q^{29} +(0.576073 + 3.26707i) q^{31} +(-6.49896 - 2.36543i) q^{32} +(-1.50727 - 9.16647i) q^{33} +(1.08362 - 6.14550i) q^{34} +(1.73372 - 8.65714i) q^{36} +(-1.73247 - 3.00072i) q^{37} +(-7.16230 + 2.60687i) q^{38} +(-5.19887 - 9.25000i) q^{39} +(-1.85735 + 1.55850i) q^{41} +(7.10225 + 12.6366i) q^{42} +(6.42421 - 2.33822i) q^{43} +(7.89217 + 13.6696i) q^{44} +(0.996658 - 1.72626i) q^{46} +(-0.626080 + 3.55068i) q^{47} +(-0.344183 - 2.09315i) q^{48} +(-6.73741 - 2.45222i) q^{49} +(4.58723 - 1.60982i) q^{51} +(13.8114 + 11.5891i) q^{52} -7.07162 q^{53} +(10.9863 - 3.57247i) q^{54} +(-6.04572 - 5.07296i) q^{56} +(-4.50426 - 3.86912i) q^{57} +(-0.812603 - 4.60850i) q^{58} +(-5.74383 - 2.09058i) q^{59} +(0.0966336 - 0.548037i) q^{61} +(3.68785 - 6.38754i) q^{62} +(-5.87097 + 9.64675i) q^{63} +(6.46348 + 11.1951i) q^{64} +(-10.5327 + 17.7658i) q^{66} +(-12.1326 + 10.1805i) q^{67} +(-6.32784 + 5.30969i) q^{68} +(1.55279 + 0.0179489i) q^{69} +(7.71778 + 13.3676i) q^{71} +(-4.91040 + 3.93052i) q^{72} +(-6.47229 + 11.2103i) q^{73} +(-1.33771 + 7.58652i) q^{74} +(9.48088 + 3.45076i) q^{76} +(-3.50580 - 19.8824i) q^{77} +(-4.36480 + 23.1837i) q^{78} +(7.60758 + 6.38352i) q^{79} +(6.61966 + 6.09755i) q^{81} +5.39058 q^{82} +(-3.66133 - 3.07222i) q^{83} +(3.55019 - 18.8569i) q^{84} +(-14.2829 - 5.19854i) q^{86} +(2.81962 - 2.31093i) q^{87} +(1.95262 - 11.0738i) q^{88} +(-1.45438 + 2.51905i) q^{89} +(-11.5304 - 19.9712i) q^{91} +(-2.47946 + 0.902451i) q^{92} +(5.74565 + 0.0664147i) q^{93} +(6.14058 - 5.15256i) q^{94} +(-6.10898 + 10.3042i) q^{96} +(5.99345 - 2.18144i) q^{97} +(7.97026 + 13.8049i) q^{98} +(-16.0857 - 0.371923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) $ 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.70314	−	1.42910i	−1.20430	−	1.01053i	−0.999497	−	0.0317247i	$-0.989900\pi$
$2$	−1.70314	−	1.42910i	−1.20430	−	1.01053i	−0.204803	−	0.978803i	$-0.565656\pi$
$3$	0.320463	−	1.70215i	0.185019	−	0.982735i
$3$	0.320463	−	1.70215i	0.185019	−	0.982735i
$4$	0.511048	+	2.89830i	0.255524	+	1.44915i
$5$		0			0
$5$		0			0
$6$	−2.97833	+	2.44102i	−1.21590	+	0.996541i
$7$	0.653660	−	3.70709i	0.247060	−	1.40115i	−0.568598	−	0.822615i	$-0.692514\pi$
$7$	0.653660	−	3.70709i	0.247060	−	1.40115i	0.815659	−	0.578534i	$-0.196375\pi$
$8$	1.04829	−	1.81569i	0.370627	−	0.641945i
$9$	−2.79461	−	1.09095i	−0.931536	−	0.363650i
$10$		0			0
$11$	5.03989	−	1.83437i	1.51958	−	0.553083i	0.558539	−	0.829478i	$-0.311362\pi$
$11$	5.03989	−	1.83437i	1.51958	−	0.553083i	0.961044	+	0.276396i	$0.0891400\pi$
$12$	5.09710	+	0.0589180i	1.47141	+	0.0170082i
$13$	4.69294	−	3.93784i	1.30159	−	1.09216i	0.311718	−	0.950175i	$-0.399096\pi$
$13$	4.69294	−	3.93784i	1.30159	−	1.09216i	0.989869	−	0.141986i	$-0.0453489\pi$
$14$	−6.41109	+	5.37954i	−1.71343	+	1.43774i
$15$		0			0
$16$	1.15085	−	0.418876i	0.287713	−	0.104719i
$17$	1.40339	+	2.43075i	0.340373	+	0.589544i	0.984502	−	0.175373i	$-0.0561133\pi$
$17$	1.40339	+	2.43075i	0.340373	+	0.589544i	−0.644129	+	0.764917i	$0.722780\pi$
$18$	3.20052	+	5.85182i	0.754370	+	1.37929i
$19$	1.71412	−	2.96894i	0.393246	−	0.681122i	−0.599630	−	0.800278i	$-0.704685\pi$
$19$	1.71412	−	2.96894i	0.393246	−	0.681122i	0.992876	+	0.119156i	$0.0380187\pi$
$20$		0			0
$21$	−6.10054	−	2.30061i	−1.33125	−	0.502034i
$22$	−11.2051	−	4.07833i	−2.38894	−	0.869503i
$23$	0.155686	+	0.882941i	0.0324628	+	0.184106i	0.996728	−	0.0808349i	$-0.0257587\pi$
$23$	0.155686	+	0.882941i	0.0324628	+	0.184106i	−0.964265	+	0.264941i	$0.914648\pi$
$24$	−2.75464	−	2.36621i	−0.562289	−	0.483001i
$25$		0			0
$26$	−13.6203			−2.67116
$27$	−2.75252	+	4.40722i	−0.529724	+	0.848170i
$28$	11.0783			2.09360
$29$	1.61238	+	1.35294i	0.299411	+	0.251235i	0.780099	−	0.625656i	$-0.215169\pi$
$29$	1.61238	+	1.35294i	0.299411	+	0.251235i	−0.480688	+	0.876892i	$0.659613\pi$
$30$		0			0
$31$	0.576073	+	3.26707i	0.103466	+	0.586784i	0.991822	+	0.127629i	$0.0407366\pi$
$31$	0.576073	+	3.26707i	0.103466	+	0.586784i	−0.888356	+	0.459155i	$0.848152\pi$
$32$	−6.49896	−	2.36543i	−1.14887	−	0.418153i
$33$	−1.50727	−	9.16647i	−0.262382	−	1.59568i
$34$	1.08362	−	6.14550i	0.185839	−	1.05394i
$35$		0			0
$36$	1.73372	−	8.65714i	0.288953	−	1.44286i
$37$	−1.73247	−	3.00072i	−0.284816	−	0.493316i	0.687749	−	0.725949i	$-0.258599\pi$
$37$	−1.73247	−	3.00072i	−0.284816	−	0.493316i	−0.972565	+	0.232633i	$0.925266\pi$
$38$	−7.16230	+	2.60687i	−1.16188	+	0.422889i
$39$	−5.19887	−	9.25000i	−0.832486	−	1.48119i
$40$		0			0
$41$	−1.85735	+	1.55850i	−0.290069	+	0.243397i	−0.776196	−	0.630491i	$-0.782854\pi$
$41$	−1.85735	+	1.55850i	−0.290069	+	0.243397i	0.486127	+	0.873888i	$0.338409\pi$
$42$	7.10225	+	12.6366i	1.09590	+	1.94986i
$43$	6.42421	−	2.33822i	0.979683	−	0.356576i	0.197966	−	0.980209i	$-0.436566\pi$
$43$	6.42421	−	2.33822i	0.979683	−	0.356576i	0.781717	+	0.623633i	$0.214344\pi$
$44$	7.89217	+	13.6696i	1.18979	+	2.06078i
$45$		0			0
$46$	0.996658	−	1.72626i	0.146949	−	0.254523i
$47$	−0.626080	+	3.55068i	−0.0913232	+	0.517919i	0.904489	+	0.426497i	$0.140252\pi$
$47$	−0.626080	+	3.55068i	−0.0913232	+	0.517919i	−0.995812	+	0.0914225i	$0.970859\pi$
$48$	−0.344183	−	2.09315i	−0.0496785	−	0.302120i
$49$	−6.73741	−	2.45222i	−0.962487	−	0.350316i
$50$		0			0
$51$	4.58723	−	1.60982i	0.642341	−	0.225420i
$52$	13.8114	+	11.5891i	1.91529	+	1.60712i
$53$	−7.07162			−0.971362			−0.485681	−	0.874136i	$-0.661428\pi$
$53$	−7.07162			−0.971362			−0.485681	+	0.874136i	$0.661428\pi$
$54$	10.9863	−	3.57247i	1.49505	−	0.486151i
$55$		0			0
$56$	−6.04572	−	5.07296i	−0.807893	−	0.677903i
$57$	−4.50426	−	3.86912i	−0.596604	−	0.512477i
$58$	−0.812603	−	4.60850i	−0.106700	−	0.605126i
$59$	−5.74383	−	2.09058i	−0.747782	−	0.272171i	−0.0601101	−	0.998192i	$-0.519145\pi$
$59$	−5.74383	−	2.09058i	−0.747782	−	0.272171i	−0.687672	+	0.726021i	$0.741367\pi$
$60$		0			0
$61$	0.0966336	−	0.548037i	0.0123727	−	0.0701689i	−0.977996	−	0.208622i	$-0.933102\pi$
$61$	0.0966336	−	0.548037i	0.0123727	−	0.0701689i	0.990369	+	0.138453i	$0.0442131\pi$
$62$	3.68785	−	6.38754i	0.468357	−	0.811219i
$63$	−5.87097	+	9.64675i	−0.739673	+	1.21538i
$64$	6.46348	+	11.1951i	0.807935	+	1.39938i
$65$		0			0
$66$	−10.5327	+	17.7658i	−1.29649	+	2.18682i
$67$	−12.1326	+	10.1805i	−1.48224	+	1.24375i	−0.578484	+	0.815694i	$0.696356\pi$
$67$	−12.1326	+	10.1805i	−1.48224	+	1.24375i	−0.903754	+	0.428052i	$0.859200\pi$
$68$	−6.32784	+	5.30969i	−0.767363	+	0.643894i
$69$	1.55279	+	0.0179489i	0.186934	+	0.00216079i
$70$		0			0
$71$	7.71778	+	13.3676i	0.915933	+	1.58644i	0.805530	+	0.592555i	$0.201881\pi$
$71$	7.71778	+	13.3676i	0.915933	+	1.58644i	0.110402	+	0.993887i	$0.464786\pi$
$72$	−4.91040	+	3.93052i	−0.578696	+	0.463216i
$73$	−6.47229	+	11.2103i	−0.757524	+	1.31207i	0.186585	+	0.982439i	$0.440258\pi$
$73$	−6.47229	+	11.2103i	−0.757524	+	1.31207i	−0.944110	+	0.329632i	$0.893075\pi$
$74$	−1.33771	+	7.58652i	−0.155505	+	0.881915i
$75$		0			0
$76$	9.48088	+	3.45076i	1.08753	+	0.395829i
$77$	−3.50580	−	19.8824i	−0.399523	−	2.26581i
$78$	−4.36480	+	23.1837i	−0.494216	+	2.62504i
$79$	7.60758	+	6.38352i	0.855920	+	0.718202i	0.961085	−	0.276253i	$-0.0890927\pi$
$79$	7.60758	+	6.38352i	0.855920	+	0.718202i	−0.105165	+	0.994455i	$0.533537\pi$
$80$		0			0
$81$	6.61966	+	6.09755i	0.735517	+	0.677506i
$82$	5.39058			0.595289
$83$	−3.66133	−	3.07222i	−0.401884	−	0.337220i	0.419338	−	0.907830i	$-0.362262\pi$
$83$	−3.66133	−	3.07222i	−0.401884	−	0.337220i	−0.821221	+	0.570610i	$0.806707\pi$
$84$	3.55019	−	18.8569i	0.387357	−	2.05746i
$85$		0			0
$86$	−14.2829	−	5.19854i	−1.54016	−	0.560573i
$87$	2.81962	−	2.31093i	0.302295	−	0.247758i
$88$	1.95262	−	11.0738i	0.208150	−	1.18048i
$89$	−1.45438	+	2.51905i	−0.154164	+	0.267019i	−0.932754	−	0.360513i	$-0.882602\pi$
$89$	−1.45438	+	2.51905i	−0.154164	+	0.267019i	0.778591	+	0.627532i	$0.215935\pi$
$90$		0			0
$91$	−11.5304	−	19.9712i	−1.20871	−	2.09355i
$92$	−2.47946	+	0.902451i	−0.258502	+	0.0940870i
$93$	5.74565	+	0.0664147i	0.595796	+	0.00688688i
$94$	6.14058	−	5.15256i	0.633353	−	0.531446i
$95$		0			0
$96$	−6.10898	+	10.3042i	−0.623496	+	1.05166i
$97$	5.99345	−	2.18144i	0.608543	−	0.221491i	−0.0193229	−	0.999813i	$-0.506151\pi$
$97$	5.99345	−	2.18144i	0.608543	−	0.221491i	0.627865	+	0.778322i	$0.283929\pi$
$98$	7.97026	+	13.8049i	0.805118	+	1.39451i
$99$	−16.0857	−	0.371923i	−1.61667	−	0.0373797i
$100$		0			0
$101$	0.799294	−	4.53302i	0.0795328	−	0.451053i	−0.918870	−	0.394560i	$-0.870897\pi$
$101$	0.799294	−	4.53302i	0.0795328	−	0.451053i	0.998403	−	0.0564928i	$-0.0179918\pi$
$102$	−10.1133	−	3.81388i	−1.00136	−	0.377630i
$103$	8.40172	+	3.05797i	0.827846	+	0.301311i	0.720974	−	0.692962i	$-0.243695\pi$
$103$	8.40172	+	3.05797i	0.827846	+	0.301311i	0.106871	+	0.994273i	$0.465917\pi$
$104$	−2.23035	−	12.6490i	−0.218704	−	1.24033i
$105$		0			0
$106$	12.0439	+	10.1061i	1.16981	+	0.981589i
$107$	16.5248			1.59751			0.798754	−	0.601657i	$-0.205493\pi$
$107$	16.5248			1.59751			0.798754	+	0.601657i	$0.205493\pi$
$108$	−14.1801	−	5.72534i	−1.36448	−	0.550921i
$109$	−6.79600			−0.650939			−0.325469	−	0.945553i	$-0.605522\pi$
$109$	−6.79600			−0.650939			−0.325469	+	0.945553i	$0.605522\pi$
$110$		0			0
$111$	−5.66286	+	1.98729i	−0.537495	+	0.188626i
$112$	−0.800545	−	4.54011i	−0.0756444	−	0.429000i
$113$	−16.1944	−	5.89428i	−1.52344	−	0.554487i	−0.561436	−	0.827520i	$-0.689751\pi$
$113$	−16.1944	−	5.89428i	−1.52344	−	0.554487i	−0.962005	+	0.273033i	$0.911973\pi$
$114$	2.14201	+	13.0267i	0.200618	+	1.22006i
$115$		0			0
$116$	−3.09723	+	5.36457i	−0.287571	+	0.498088i
$117$	−17.4109	+	5.88496i	−1.60964	+	0.544065i
$118$	6.79487	+	11.7691i	0.625518	+	1.08343i
$119$	9.92836	−	3.61363i	0.910131	−	0.331261i
$120$		0			0
$121$	13.6090	−	11.4193i	1.23719	−	1.03812i
$122$	−0.947781	+	0.795282i	−0.0858080	+	0.0720015i
$123$	2.05758	+	3.66092i	0.185526	+	0.330094i
$124$	−9.17456	+	3.33927i	−0.823899	+	0.299875i
$125$		0			0
$126$	23.7853	−	8.03953i	2.11896	−	0.716218i
$127$	−2.40782	+	4.17046i	−0.213659	+	0.370069i	−0.952857	−	0.303420i	$-0.901872\pi$
$127$	−2.40782	+	4.17046i	−0.213659	+	0.370069i	0.739198	+	0.673489i	$0.235205\pi$
$128$	2.58879	−	14.6818i	0.228819	−	1.29770i
$129$	−1.92128	−	11.6843i	−0.169159	−	1.02874i
$130$		0			0
$131$	0.969287	+	5.49710i	0.0846870	+	0.480284i	0.997424	+	0.0717355i	$0.0228538\pi$
$131$	0.969287	+	5.49710i	0.0846870	+	0.480284i	−0.912737	+	0.408548i	$0.866035\pi$
$132$	25.7969	−	9.05302i	2.24533	−	0.787965i
$133$	−9.88569	−	8.29508i	−0.857198	−	0.719274i
$134$	35.2125			3.04190
$135$		0			0
$136$	5.88467			0.504606
$137$	3.18283	+	2.67071i	0.271927	+	0.228174i	0.768546	−	0.639795i	$-0.220981\pi$
$137$	3.18283	+	2.67071i	0.271927	+	0.228174i	−0.496618	+	0.867969i	$0.665425\pi$
$138$	−2.61896	−	2.24966i	−0.222941	−	0.191504i
$139$	−1.48337	−	8.41259i	−0.125817	−	0.713546i	−0.980819	−	0.194921i	$-0.937555\pi$
$139$	−1.48337	−	8.41259i	−0.125817	−	0.713546i	0.855002	−	0.518625i	$-0.173556\pi$
$140$		0			0
$141$	5.84314	+	2.20354i	0.492081	+	0.185572i
$142$	5.95921	−	33.7964i	0.500086	−	2.83613i
$143$	16.4284	−	28.4549i	1.37381	−	2.37951i
$144$	−3.67315	−	0.0849281i	−0.306096	−	0.00707734i
$145$		0			0
$146$	27.0439	−	9.84318i	2.23817	−	0.814627i
$147$	−6.33312	+	10.6822i	−0.522347	+	0.881054i
$148$	7.81162	−	6.55472i	0.642111	−	0.538795i
$149$	8.62380	−	7.23622i	0.706489	−	0.592815i	−0.217123	−	0.976144i	$-0.569667\pi$
$149$	8.62380	−	7.23622i	0.706489	−	0.592815i	0.923612	+	0.383330i	$0.125223\pi$
$150$		0			0
$151$	−15.9706	+	5.81283i	−1.29967	+	0.473042i	−0.896890	−	0.442255i	$-0.854179\pi$
$151$	−15.9706	+	5.81283i	−1.29967	+	0.473042i	−0.402781	+	0.915296i	$0.631957\pi$
$152$	−3.59380	−	6.22464i	−0.291495	−	0.504885i
$153$	−1.27011	−	8.32403i	−0.102682	−	0.672958i
$154$	−22.4431	+	38.8726i	−1.80851	+	3.13244i
$155$		0			0
$156$	24.1524	−	19.7951i	1.93374	−	1.58488i
$157$	11.7281	+	4.26867i	0.936002	+	0.340677i	0.764586	−	0.644522i	$-0.222944\pi$
$157$	11.7281	+	4.26867i	0.936002	+	0.340677i	0.171416	+	0.985199i	$0.445166\pi$
$158$	−3.83406	−	21.7440i	−0.305021	−	1.72986i
$159$	−2.26619	+	12.0369i	−0.179721	+	0.954592i
$160$		0			0
$161$	3.37491			0.265980
$162$	−2.56016	−	19.8451i	−0.201145	−	1.55918i
$163$	−7.49060			−0.586709			−0.293354	−	0.956004i	$-0.594772\pi$
$163$	−7.49060			−0.586709			−0.293354	+	0.956004i	$0.594772\pi$
$164$	−5.46620	−	4.58668i	−0.426838	−	0.358160i
$165$		0			0
$166$	1.84523	+	10.4648i	0.143218	+	0.812229i
$167$	11.7621	+	4.28105i	0.910177	+	0.331277i	0.754324	−	0.656503i	$-0.227965\pi$
$167$	11.7621	+	4.28105i	0.910177	+	0.331277i	0.155854	+	0.987780i	$0.450187\pi$
$168$	−10.5724	+	8.66501i	−0.815675	+	0.668520i
$169$	4.25964	−	24.1576i	0.327664	−	1.85828i
$170$		0			0
$171$	−8.02926	+	6.42701i	−0.614013	+	0.491486i
$172$	10.0600	+	17.4243i	0.767064	+	1.32859i
$173$	−14.2477	+	5.18574i	−1.08323	+	0.394264i	−0.821110	−	0.570771i	$-0.806645\pi$
$173$	−14.2477	+	5.18574i	−1.08323	+	0.394264i	−0.262122	+	0.965035i	$0.584422\pi$
$174$	−8.10475	−	0.0936838i	−0.614420	−	0.00710215i
$175$		0			0
$176$	5.03179	−	4.22217i	0.379285	−	0.318258i
$177$	−5.39916	+	9.10688i	−0.405826	+	0.684515i
$178$	6.07699	−	2.21184i	0.455490	−	0.165785i
$179$	−4.06134	−	7.03445i	−0.303559	−	0.525780i	0.673380	−	0.739296i	$-0.264842\pi$
$179$	−4.06134	−	7.03445i	−0.303559	−	0.525780i	−0.976939	+	0.213517i	$0.931508\pi$
$180$		0			0
$181$	7.95939	−	13.7861i	0.591617	−	1.02471i	−0.402398	−	0.915465i	$-0.631823\pi$
$181$	7.95939	−	13.7861i	0.591617	−	1.02471i	0.994015	−	0.109245i	$-0.0348434\pi$
$182$	−8.90305	+	50.4917i	−0.659938	+	3.74269i
$183$	−0.901871	−	0.340110i	−0.0666682	−	0.0251417i
$184$	1.76636	+	0.642901i	0.130218	+	0.0473953i
$185$		0			0
$186$	−9.69072	−	8.32423i	−0.710558	−	0.610362i
$187$	11.5318	+	9.67636i	0.843292	+	0.707606i
$188$	−10.6109			−0.773878
$189$	14.5388	+	13.0847i	1.05754	+	0.951771i
$190$		0			0
$191$	−13.7721	−	11.5562i	−0.996516	−	0.836176i	−0.0100183	−	0.999950i	$-0.503189\pi$
$191$	−13.7721	−	11.5562i	−0.996516	−	0.836176i	−0.986498	+	0.163773i	$0.947633\pi$
$192$	21.1270	−	7.41418i	1.52471	−	0.535073i
$193$	0.168689	+	0.956681i	0.0121425	+	0.0688634i	0.990277	−	0.139110i	$-0.0444243\pi$
$193$	0.168689	+	0.956681i	0.0121425	+	0.0688634i	−0.978134	+	0.207974i	$0.933313\pi$
$194$	−13.3252	−	4.84996i	−0.956691	−	0.348207i
$195$		0			0
$196$	3.66411	−	20.7802i	0.261722	−	1.48430i
$197$	4.61678	−	7.99649i	0.328932	−	0.569727i	−0.653368	−	0.757040i	$-0.726645\pi$
$197$	4.61678	−	7.99649i	0.328932	−	0.569727i	0.982300	+	0.187313i	$0.0599780\pi$
$198$	26.8646	+	23.6215i	1.90919	+	1.67871i
$199$	8.81540	+	15.2687i	0.624907	+	1.08237i	0.988559	+	0.150836i	$0.0481966\pi$
$199$	8.81540	+	15.2687i	0.624907	+	1.08237i	−0.363651	+	0.931535i	$0.618470\pi$
$200$		0			0
$201$	13.4406	+	23.9140i	0.948029	+	1.68676i
$202$	−7.83946	+	6.57809i	−0.551583	+	0.462833i
$203$	6.06943	−	5.09286i	0.425991	−	0.357449i
$204$	7.01003	+	12.4725i	0.490800	+	0.873248i
$205$		0			0
$206$	−9.93912	−	17.2151i	−0.692491	−	1.19943i
$207$	0.528162	−	2.63732i	0.0367098	−	0.183306i
$208$	3.75141	−	6.49763i	0.260113	−	0.450530i
$209$	3.19283	−	18.1075i	0.220853	−	1.25252i
$210$		0			0
$211$	−4.23225	−	1.54041i	−0.291360	−	0.106046i	0.192205	−	0.981355i	$-0.438436\pi$
$211$	−4.23225	−	1.54041i	−0.291360	−	0.106046i	−0.483565	+	0.875308i	$0.660658\pi$
$212$	−3.61394	−	20.4957i	−0.248207	−	1.40765i
$213$	25.2269	−	8.85298i	1.72852	−	0.606596i
$214$	−28.1439	−	23.6156i	−1.92388	−	1.61433i
$215$		0			0
$216$	5.11672	+	9.61780i	0.348149	+	0.654408i
$217$	12.4879			0.847734
$218$	11.5745	+	9.71218i	0.783926	+	0.657792i
$219$	17.0075	+	14.6093i	1.14926	+	0.987204i
$220$		0			0
$221$	16.1580	+	5.88101i	1.08690	+	0.395600i
$222$	12.4847	+	4.70817i	0.837917	+	0.315992i
$223$	−4.26645	+	24.1963i	−0.285703	+	1.62030i	0.417061	+	0.908878i	$0.363060\pi$
$223$	−4.26645	+	24.1963i	−0.285703	+	1.62030i	−0.702764	+	0.711423i	$0.748051\pi$
$224$	−13.0170	+	22.5461i	−0.869733	+	1.50642i
$225$		0			0
$226$	19.1578	+	33.1822i	1.27435	+	2.20725i
$227$	−15.9741	+	5.81410i	−1.06024	+	0.385895i	−0.812518	−	0.582936i	$-0.801904\pi$
$227$	−15.9741	+	5.81410i	−1.06024	+	0.385895i	−0.247721	+	0.968831i	$0.579682\pi$
$228$	8.91197	−	15.0320i	0.590210	−	0.995519i
$229$	−11.2404	+	9.43183i	−0.742788	+	0.623273i	−0.933585	−	0.358356i	$-0.883337\pi$
$229$	−11.2404	+	9.43183i	−0.742788	+	0.623273i	0.190797	+	0.981630i	$0.438893\pi$
$230$		0			0
$231$	−34.9662	−	0.404179i	−2.30061	−	0.0265930i
$232$	4.14677	−	1.50930i	0.272249	−	0.0990905i
$233$	12.7753	+	22.1275i	0.836939	+	1.44962i	0.892442	+	0.451162i	$0.148990\pi$
$233$	12.7753	+	22.1275i	0.836939	+	1.44962i	−0.0555035	+	0.998458i	$0.517676\pi$
$234$	38.0634	+	14.8591i	2.48828	+	0.971367i
$235$		0			0
$236$	3.12376	−	17.7157i	0.203339	−	1.15319i
$237$	13.3036	−	10.9035i	0.864164	−	0.708261i
$238$	−22.0736	−	8.03413i	−1.43082	−	0.520776i
$239$	−1.11927	−	6.34771i	−0.0723998	−	0.410599i	−0.999371	−	0.0354667i	$-0.988708\pi$
$239$	−1.11927	−	6.34771i	−0.0723998	−	0.410599i	0.926971	−	0.375133i	$-0.122403\pi$
$240$		0			0
$241$	2.05438	+	1.72383i	0.132334	+	0.111042i	0.706552	−	0.707661i	$-0.250249\pi$
$241$	2.05438	+	1.72383i	0.132334	+	0.111042i	−0.574218	+	0.818702i	$0.694694\pi$
$242$	−39.4975			−2.53900
$243$	12.5003	−	9.31359i	0.801893	−	0.597467i
$244$	1.63776			0.104847
$245$		0			0
$246$	1.72748	−	9.17555i	0.110140	−	0.585012i
$247$	−3.64697	−	20.6830i	−0.232051	−	1.31603i
$248$	6.53590	+	2.37887i	0.415030	+	0.151059i
$249$	−6.40270	+	5.24759i	−0.405754	+	0.332553i
$250$		0			0
$251$	9.83460	−	17.0340i	0.620755	−	1.07518i	−0.368591	−	0.929592i	$-0.620160\pi$
$251$	9.83460	−	17.0340i	0.620755	−	1.07518i	0.989345	−	0.145587i	$-0.0465070\pi$
$252$	−30.9595	−	12.0859i	−1.95027	−	0.761339i
$253$	2.40428	+	4.16434i	0.151156	+	0.261810i
$254$	10.0609	−	3.66186i	0.631275	−	0.229765i
$255$		0			0
$256$	−5.58555	+	4.68683i	−0.349097	+	0.292927i
$257$	−4.25190	+	3.56777i	−0.265226	+	0.222551i	−0.765696	−	0.643203i	$-0.777605\pi$
$257$	−4.25190	+	3.56777i	−0.265226	+	0.222551i	0.500469	+	0.865754i	$0.333161\pi$
$258$	−13.4258	+	22.6456i	−0.835855	+	1.40985i
$259$	−12.2564	+	4.46096i	−0.761575	+	0.277191i
$260$		0			0
$261$	−3.02996	−	5.53997i	−0.187550	−	0.342915i
$262$	6.20509	−	10.7475i	0.383352	−	0.663985i
$263$	−2.44722	+	13.8789i	−0.150902	+	0.855808i	0.811535	+	0.584303i	$0.198632\pi$
$263$	−2.44722	+	13.8789i	−0.150902	+	0.855808i	−0.962437	+	0.271504i	$0.912479\pi$
$264$	−18.2236	−	6.87240i	−1.12158	−	0.422967i
$265$		0			0
$266$	4.98217	+	28.2553i	0.305477	+	1.73244i
$267$	3.82173	+	3.28283i	0.233886	+	0.200906i
$268$	−35.7065	−	29.9613i	−2.18112	−	1.83018i
$269$	10.6489			0.649278			0.324639	−	0.945838i	$-0.394757\pi$
$269$	10.6489			0.649278			0.324639	+	0.945838i	$0.394757\pi$
$270$		0			0
$271$	−18.7000			−1.13595			−0.567973	−	0.823047i	$-0.692272\pi$
$271$	−18.7000			−1.13595			−0.567973	+	0.823047i	$0.692272\pi$
$272$	2.63328	+	2.20958i	0.159666	+	0.133976i
$273$	−37.6889	+	13.2263i	−2.28104	+	0.800495i
$274$	−1.60408	−	9.09717i	−0.0969058	−	0.549580i
$275$		0			0
$276$	0.741528	+	4.50961i	0.0446347	+	0.271447i
$277$	−1.27693	+	7.24183i	−0.0767233	+	0.435119i	0.922114	+	0.386918i	$0.126460\pi$
$277$	−1.27693	+	7.24183i	−0.0767233	+	0.435119i	−0.998838	+	0.0482019i	$0.984651\pi$
$278$	−9.49607	+	16.4477i	−0.569536	+	0.986466i
$279$	1.95431	−	9.75865i	0.117002	−	0.584235i
$280$		0			0
$281$	−15.3253	+	5.57797i	−0.914233	+	0.332754i	−0.755942	−	0.654639i	$-0.772821\pi$
$281$	−15.3253	+	5.57797i	−0.914233	+	0.332754i	−0.158291	+	0.987392i	$0.550599\pi$
$282$	−6.80258	−	12.1034i	−0.405088	−	0.720745i
$283$	−0.413729	+	0.347160i	−0.0245936	+	0.0206365i	−0.655002	−	0.755627i	$-0.727332\pi$
$283$	−0.413729	+	0.347160i	−0.0245936	+	0.0206365i	0.630408	+	0.776264i	$0.282888\pi$
$284$	−34.7991	+	29.1999i	−2.06495	+	1.73270i
$285$		0			0
$286$	−68.6447	+	24.9846i	−4.05905	+	1.47737i
$287$	4.56343	+	7.90409i	0.269371	+	0.466564i
$288$	15.5815	+	13.7005i	0.918148	+	0.807309i
$289$	4.56097	−	7.89983i	0.268292	−	0.464696i
$290$		0			0
$291$	−1.79245	−	10.9008i	−0.105075	−	0.639016i
$292$	−35.7986	−	13.0296i	−2.09495	−	0.762500i
$293$	−3.01350	−	17.0904i	−0.176051	−	0.998432i	−0.936924	−	0.349532i	$-0.886340\pi$
$293$	−3.01350	−	17.0904i	−0.176051	−	0.998432i	0.760874	−	0.648900i	$-0.224771\pi$
$294$	26.0521	−	9.14260i	1.51939	−	0.533207i
$295$		0			0
$296$	−7.26453			−0.422242
$297$	−5.78794	+	27.2610i	−0.335850	+	1.58185i
$298$	−25.0288			−1.44988
$299$	4.20751	+	3.53052i	0.243327	+	0.204175i
$300$		0			0
$301$	−4.46875	−	25.3435i	−0.257575	−	1.46078i
$302$	35.5073	+	12.9236i	2.04322	+	0.743670i
$303$	−7.45973	−	2.81318i	−0.428550	−	0.161613i
$304$	0.729079	−	4.13481i	0.0418156	−	0.237148i
$305$		0			0
$306$	−9.73271	+	15.9921i	−0.556382	+	0.914206i
$307$	2.22842	+	3.85973i	0.127182	+	0.220287i	0.922584	−	0.385796i	$-0.126073\pi$
$307$	2.22842	+	3.85973i	0.127182	+	0.220287i	−0.795401	+	0.606083i	$0.792740\pi$
$308$	55.8334	−	20.3217i	3.18140	−	1.15794i
$309$	7.89756	−	13.3210i	0.449276	−	0.757804i
$310$		0			0
$311$	−9.04919	+	7.59317i	−0.513133	+	0.430569i	−0.862230	−	0.506517i	$-0.830933\pi$
$311$	−9.04919	+	7.59317i	−0.513133	+	0.430569i	0.349097	+	0.937086i	$0.386488\pi$
$312$	−22.2451	−	0.257134i	−1.25938	−	0.0145574i
$313$	3.33057	−	1.21223i	0.188255	−	0.0685191i	−0.246173	−	0.969226i	$-0.579173\pi$
$313$	3.33057	−	1.21223i	0.188255	−	0.0685191i	0.434427	+	0.900707i	$0.356951\pi$
$314$	−13.8741	−	24.0307i	−0.782964	−	1.35613i
$315$		0			0
$316$	−14.6135	+	25.3113i	−0.822074	+	1.42387i
$317$	0.675236	−	3.82945i	0.0379250	−	0.215084i	−0.959956	−	0.280151i	$-0.909615\pi$
$317$	0.675236	−	3.82945i	0.0379250	−	0.215084i	0.997881	+	0.0650679i	$0.0207264\pi$
$318$	21.0617	−	17.2619i	1.18108	−	0.968002i
$319$	10.6080	+	3.86099i	0.593933	+	0.216174i
$320$		0			0
$321$	5.29557	−	28.1276i	0.295570	−	1.56993i
$322$	−5.74793	−	4.82309i	−0.320320	−	0.268780i
$323$	9.62234			0.535402
$324$	−14.2896	+	22.3019i	−0.793865	+	1.23899i
$325$		0			0
$326$	12.7575	+	10.7048i	0.706573	+	0.592886i
$327$	−2.17787	+	11.5678i	−0.120436	+	0.639700i
$328$	0.882718	+	5.00614i	0.0487399	+	0.276418i
$329$	12.7534	+	4.64187i	0.703120	+	0.255915i
$330$		0			0
$331$	3.47191	−	19.6902i	0.190833	−	1.08227i	−0.727395	−	0.686219i	$-0.759269\pi$
$331$	3.47191	−	19.6902i	0.190833	−	1.08227i	0.918228	−	0.396051i	$-0.129620\pi$
$332$	7.03311	−	12.1817i	0.385992	−	0.668557i
$333$	1.56793	+	10.2759i	0.0859220	+	0.563114i
$334$	−13.9144	−	24.1004i	−0.761362	−	1.31872i
$335$		0			0
$336$	−7.98448	−	0.0922937i	−0.435589	−	0.00503503i
$337$	19.9104	−	16.7068i	1.08459	−	0.910078i	0.0882954	−	0.996094i	$-0.471858\pi$
$337$	19.9104	−	16.7068i	1.08459	−	0.910078i	0.996294	+	0.0860160i	$0.0274136\pi$
$338$	−41.7784	+	35.0563i	−2.27245	+	1.90681i
$339$	−15.2226	+	25.6763i	−0.826779	+	1.39455i
$340$		0			0
$341$	8.89636	+	15.4089i	0.481765	+	0.834441i
$342$	22.8598	+	0.528549i	1.23612	+	0.0285806i
$343$	−0.319584	+	0.553536i	−0.0172559	+	0.0298881i
$344$	2.48895	−	14.1155i	0.134195	−	0.761059i
$345$		0			0
$346$	31.6767	+	11.5294i	1.70295	+	0.619824i
$347$	3.62567	+	20.5622i	0.194636	+	1.10384i	0.912936	+	0.408102i	$0.133809\pi$
$347$	3.62567	+	20.5622i	0.194636	+	1.10384i	−0.718300	+	0.695733i	$0.755080\pi$
$348$	8.13873	+	6.99109i	0.436282	+	0.374762i
$349$	−8.83183	−	7.41078i	−0.472757	−	0.396690i	0.375042	−	0.927008i	$-0.377628\pi$
$349$	−8.83183	−	7.41078i	−0.472757	−	0.396690i	−0.847799	+	0.530318i	$0.822073\pi$
$350$		0			0
$351$	4.43752	+	31.5218i	0.236857	+	1.68251i
$352$	−37.0931			−1.97707
$353$	−8.10550	−	6.80132i	−0.431412	−	0.361998i	0.401072	−	0.916047i	$-0.368638\pi$
$353$	−8.10550	−	6.80132i	−0.431412	−	0.361998i	−0.832484	+	0.554049i	$0.813082\pi$
$354$	22.2102	−	7.79432i	1.18046	−	0.414263i
$355$		0			0
$356$	−8.04423	−	2.92786i	−0.426343	−	0.155176i
$357$	−2.96925	−	18.0576i	−0.157150	−	0.955707i
$358$	−3.13592	+	17.7847i	−0.165739	+	0.939951i
$359$	9.71352	−	16.8243i	0.512660	−	0.887953i	−0.487232	−	0.873272i	$-0.661994\pi$
$359$	9.71352	−	16.8243i	0.512660	−	0.887953i	0.999892	−	0.0146804i	$-0.00467310\pi$
$360$		0			0
$361$	3.62359	+	6.27624i	0.190715	+	0.330328i
$362$	−33.2576	+	12.1048i	−1.74798	+	0.636213i
$363$	−15.0762	−	26.8241i	−0.791296	−	1.40790i
$364$	51.9898	−	43.6247i	2.72501	−	2.28655i
$365$		0			0
$366$	1.04996	+	1.86812i	0.0548822	+	0.0976482i
$367$	−11.2289	+	4.08698i	−0.586143	+	0.213339i	−0.618032	−	0.786153i	$-0.712070\pi$
$367$	−11.2289	+	4.08698i	−0.586143	+	0.213339i	0.0318889	+	0.999491i	$0.489848\pi$
$368$	0.549014	+	0.950921i	0.0286194	+	0.0495702i
$369$	6.89080	−	2.32912i	0.358721	−	0.121249i
$370$		0			0
$371$	−4.62244	+	26.2152i	−0.239985	+	1.36102i
$372$	2.74381	+	16.6865i	0.142260	+	0.865157i
$373$	26.1774	+	9.52781i	1.35542	+	0.493331i	0.914634	−	0.404283i	$-0.132479\pi$
$373$	26.1774	+	9.52781i	1.35542	+	0.493331i	0.440782	+	0.897614i	$0.354701\pi$
$374$	−5.81180	−	32.9603i	−0.300521	−	1.70434i
$375$		0			0
$376$	5.79063	+	4.85892i	0.298629	+	0.250579i
$377$	12.8945			0.664098
$378$	−6.06216	−	43.0624i	−0.311804	−	2.21489i
$379$	19.6724			1.01050			0.505251	−	0.862973i	$-0.331400\pi$
$379$	19.6724			1.01050			0.505251	+	0.862973i	$0.331400\pi$
$380$		0			0
$381$	6.32713	+	5.43494i	0.324148	+	0.278440i
$382$	6.94086	+	39.3636i	0.355125	+	2.01401i
$383$	4.85629	+	1.76754i	0.248145	+	0.0903173i	0.463098	−	0.886307i	$-0.346738\pi$
$383$	4.85629	+	1.76754i	0.248145	+	0.0903173i	−0.214953	+	0.976624i	$0.568960\pi$
$384$	−24.1609	−	9.11146i	−1.23296	−	0.464967i
$385$		0			0
$386$	1.07989	−	1.87043i	0.0549652	−	0.0952025i
$387$	−20.5040	−	0.474081i	−1.04228	−	0.0240989i
$388$	9.38540	+	16.2560i	0.476472	+	0.825273i
$389$	−8.84157	+	3.21807i	−0.448285	+	0.163162i	−0.556291	−	0.830988i	$-0.687776\pi$
$389$	−8.84157	+	3.21807i	−0.448285	+	0.163162i	0.108005	+	0.994150i	$0.465554\pi$
$390$		0			0
$391$	−1.92772	+	1.61755i	−0.0974890	+	0.0818030i
$392$	−11.5152	+	9.66244i	−0.581608	+	0.488027i
$393$	9.66749	+	0.111748i	0.487660	+	0.00563693i
$394$	−19.2908	+	7.02128i	−0.971857	+	0.353727i
$395$		0			0
$396$	−7.14263	−	46.8113i	−0.358931	−	2.35235i
$397$	−4.01712	+	6.95786i	−0.201614	+	0.349205i	−0.949048	−	0.315130i	$-0.897952\pi$
$397$	−4.01712	+	6.95786i	−0.201614	+	0.349205i	0.747435	+	0.664335i	$0.231285\pi$
$398$	6.80673	−	38.6029i	0.341190	−	1.93499i
$399$	−17.2874	+	14.1686i	−0.865454	+	0.709319i
$400$		0			0
$401$	−1.68169	−	9.53732i	−0.0839794	−	0.476271i	−0.997572	−	0.0696405i	$-0.977815\pi$
$401$	−1.68169	−	9.53732i	−0.0839794	−	0.476271i	0.913593	−	0.406630i	$-0.133296\pi$
$402$	11.2843	−	59.9369i	0.562810	−	2.98938i
$403$	15.5687	+	13.0637i	0.775532	+	0.650749i
$404$	13.5465			0.673965
$405$		0			0
$406$	−17.6153			−0.874232
$407$	−14.2359	−	11.9453i	−0.705646	−	0.592107i
$408$	1.88582	−	10.0166i	0.0933619	−	0.495894i
$409$	2.41577	+	13.7005i	0.119452	+	0.677446i	0.984449	+	0.175669i	$0.0562089\pi$
$409$	2.41577	+	13.7005i	0.119452	+	0.677446i	−0.864997	+	0.501776i	$0.832680\pi$
$410$		0			0
$411$	5.56592	−	4.56178i	0.274546	−	0.225016i
$412$	−4.56924	+	25.9135i	−0.225110	+	1.27666i
$413$	−11.5045	+	19.9264i	−0.566099	+	0.980512i
$414$	−4.66853	+	3.73692i	−0.229446	+	0.183660i
$415$		0			0
$416$	−39.8139	+	14.4911i	−1.95204	+	0.710484i
$417$	−14.7948	−	0.171015i	−0.724505	−	0.00837465i
$418$	−31.3152	+	26.2766i	−1.53168	+	1.28523i
$419$	−23.8549	+	20.0166i	−1.16539	+	0.977876i	−0.999965	−	0.00834704i	$-0.997343\pi$
$419$	−23.8549	+	20.0166i	−1.16539	+	0.977876i	−0.165422	+	0.986223i	$0.552899\pi$
$420$		0			0
$421$	−14.6085	+	5.31705i	−0.711974	+	0.259137i	−0.672515	−	0.740084i	$-0.734786\pi$
$421$	−14.6085	+	5.31705i	−0.711974	+	0.259137i	−0.0394593	+	0.999221i	$0.512564\pi$
$422$	5.00670	+	8.67186i	0.243722	+	0.422139i
$423$	5.62326	−	9.23972i	0.273412	−	0.449251i
$424$	−7.41313	+	12.8399i	−0.360013	+	0.623561i
$425$		0			0
$426$	−55.6167	−	20.9739i	−2.69464	−	1.01619i
$427$	−1.96846	−	0.716460i	−0.0952603	−	0.0346719i
$428$	8.44495	+	47.8937i	0.408202	+	2.31503i
$429$	−43.1696	−	37.0823i	−2.08425	−	1.79035i
$430$		0			0
$431$	5.10872			0.246078			0.123039	−	0.992402i	$-0.460736\pi$
$431$	5.10872			0.246078			0.123039	+	0.992402i	$0.460736\pi$
$432$	−1.32167	+	6.22502i	−0.0635888	+	0.299502i
$433$	−9.22565			−0.443356			−0.221678	−	0.975120i	$-0.571153\pi$
$433$	−9.22565			−0.443356			−0.221678	+	0.975120i	$0.571153\pi$
$434$	−21.2686	−	17.8465i	−1.02093	−	0.856658i
$435$		0			0
$436$	−3.47308	−	19.6968i	−0.166331	−	0.943308i
$437$	2.88827	+	1.05124i	0.138165	+	0.0502878i
$438$	−8.08797	−	49.1871i	−0.386458	−	2.35025i
$439$	−2.32033	+	13.1592i	−0.110743	+	0.628057i	0.878027	+	0.478612i	$0.158860\pi$
$439$	−2.32033	+	13.1592i	−0.110743	+	0.628057i	−0.988770	+	0.149445i	$0.952251\pi$
$440$		0			0
$441$	16.1532	+	14.2032i	0.769198	+	0.676340i
$442$	−19.1147	−	33.1075i	−0.909191	−	1.57477i
$443$	7.23777	−	2.63433i	0.343877	−	0.125161i	−0.164308	−	0.986409i	$-0.552539\pi$
$443$	7.23777	−	2.63433i	0.343877	−	0.125161i	0.508184	+	0.861248i	$0.330317\pi$
$444$	−8.65377	−	15.3971i	−0.410690	−	0.730712i
$445$		0			0
$446$	41.8453	−	35.1124i	1.98143	−	1.66262i
$447$	−9.55351	−	16.9979i	−0.451865	−	0.803973i
$448$	45.7261	−	16.6429i	2.16035	−	0.786305i
$449$	16.9493	+	29.3570i	0.799886	+	1.38544i	0.919690	+	0.392645i	$0.128440\pi$
$449$	16.9493	+	29.3570i	0.799886	+	1.38544i	−0.119805	+	0.992797i	$0.538227\pi$
$450$		0			0
$451$	−6.50196	+	11.2617i	−0.306165	+	0.530294i
$452$	8.80726	−	49.9485i	0.414259	−	2.34938i
$453$	4.77630	+	29.0471i	0.224410	+	1.36475i
$454$	35.5151	+	12.9264i	1.66680	+	0.606667i
$455$		0			0
$456$	−11.7469	+	4.12240i	−0.550100	+	0.193049i
$457$	19.6509	+	16.4891i	0.919230	+	0.771325i	0.973852	−	0.227182i	$-0.0729511\pi$
$457$	19.6509	+	16.4891i	0.919230	+	0.771325i	−0.0546225	+	0.998507i	$0.517396\pi$
$458$	32.6230			1.52437
$459$	−14.5757	−	0.505628i	−0.680337	−	0.0236007i
$460$		0			0
$461$	11.2323	+	9.42502i	0.523140	+	0.438967i	0.865725	−	0.500520i	$-0.166858\pi$
$461$	11.2323	+	9.42502i	0.523140	+	0.438967i	−0.342585	+	0.939487i	$0.611302\pi$
$462$	58.9746	+	50.6586i	2.74375	+	2.35685i
$463$	0.0945229	+	0.536066i	0.00439285	+	0.0249131i	0.986925	−	0.161178i	$-0.0515292\pi$
$463$	0.0945229	+	0.536066i	0.00439285	+	0.0249131i	−0.982533	+	0.186091i	$0.940418\pi$
$464$	2.42232	+	0.881652i	0.112453	+	0.0409297i
$465$		0			0
$466$	9.86433	−	55.9434i	0.456956	−	2.59153i
$467$	20.5859	−	35.6559i	0.952604	−	1.64996i	0.212845	−	0.977086i	$-0.431727\pi$
$467$	20.5859	−	35.6559i	0.952604	−	1.64996i	0.739759	−	0.672872i	$-0.234940\pi$
$468$	−25.9542	−	47.4545i	−1.19973	−	2.19359i
$469$	29.8094	+	51.6314i	1.37647	+	2.38412i
$470$		0			0
$471$	11.0243	−	18.5949i	0.507973	−	0.856810i
$472$	−9.81706	+	8.23749i	−0.451867	+	0.379161i
$473$	28.0881	−	23.5687i	1.29149	−	1.08369i
$474$	−38.2402	−	0.442023i	−1.75643	−	0.0203028i
$475$		0			0
$476$	15.5472	+	26.9286i	0.712607	+	1.23427i
$477$	19.7624	+	7.71479i	0.904859	+	0.353236i
$478$	−7.16525	+	12.4106i	−0.327731	+	0.567647i
$479$	1.02370	−	5.80571i	0.0467742	−	0.265270i	−0.952448	−	0.304701i	$-0.901443\pi$
$479$	1.02370	−	5.80571i	0.0467742	−	0.265270i	0.999222	+	0.0394312i	$0.0125546\pi$
$480$		0			0
$481$	−19.9467	−	7.26002i	−0.909493	−	0.331028i
$482$	−1.03536	−	5.87183i	−0.0471595	−	0.267455i
$483$	1.08153	−	5.74459i	0.0492115	−	0.261388i
$484$	40.0516	+	33.6073i	1.82053	+	1.52760i
$485$		0			0
$486$	−34.5998	−	2.00186i	−1.56948	−	0.0908060i
$487$	11.9102			0.539704			0.269852	−	0.962902i	$-0.413025\pi$
$487$	11.9102			0.539704			0.269852	+	0.962902i	$0.413025\pi$
$488$	−0.893767	−	0.749960i	−0.0404589	−	0.0339491i
$489$	−2.40046	+	12.7501i	−0.108552	+	0.576579i
$490$		0			0
$491$	−35.0462	−	12.7558i	−1.58161	−	0.575661i	−0.606060	−	0.795419i	$-0.707251\pi$
$491$	−35.0462	−	12.7558i	−1.58161	−	0.575661i	−0.975554	+	0.219758i	$0.929473\pi$
$492$	−9.55892	+	7.83440i	−0.430949	+	0.353202i
$493$	−1.02587	+	5.81800i	−0.0462029	+	0.262029i
$494$	−23.3468	+	40.4379i	−1.05042	+	1.81939i
$495$		0			0
$496$	2.03147	+	3.51861i	0.0912158	+	0.157990i
$497$	54.5997	−	19.8727i	2.44913	−	0.891411i
$498$	18.4040	+	0.212734i	0.824704	+	0.00953286i
$499$	−14.2032	+	11.9179i	−0.635821	+	0.533517i	−0.902732	−	0.430204i	$-0.858442\pi$
$499$	−14.2032	+	11.9179i	−0.635821	+	0.533517i	0.266911	+	0.963721i	$0.413997\pi$
$500$		0			0
$501$	11.0563	−	18.6489i	0.493958	−	0.833170i
$502$	−41.0930	+	14.9566i	−1.83407	+	0.667548i
$503$	17.2340	+	29.8502i	0.768428	+	1.33096i	0.938415	+	0.345510i	$0.112294\pi$
$503$	17.2340	+	29.8502i	0.768428	+	1.33096i	−0.169987	+	0.985446i	$0.554373\pi$
$504$	11.3611	+	20.7725i	0.506062	+	0.925281i
$505$		0			0
$506$	1.85644	−	10.5284i	0.0825289	−	0.468044i
$507$	−39.7547	−	14.9921i	−1.76557	−	0.665824i
$508$	−13.3178	−	4.84727i	−0.590880	−	0.215063i
$509$	4.38600	+	24.8743i	0.194406	+	1.10253i	0.913262	+	0.407373i	$0.133555\pi$
$509$	4.38600	+	24.8743i	0.194406	+	1.10253i	−0.718856	+	0.695159i	$0.755334\pi$
$510$		0			0
$511$	37.3271	+	31.3211i	1.65125	+	1.38556i
$512$	−13.6056			−0.601287
$513$	8.36663	+	15.7266i	0.369396	+	0.694346i
$514$	12.3403			0.544307
$515$		0			0
$516$	32.8826	−	11.5397i	1.44758	−	0.508005i
$517$	3.35788	+	19.0435i	0.147679	+	0.837531i
$518$	27.2495	+	9.91801i	1.19727	+	0.435772i
$519$	4.26103	+	25.9135i	0.187038	+	1.13748i
$520$		0			0
$521$	5.72752	−	9.92036i	0.250927	−	0.434619i	−0.712854	−	0.701312i	$-0.752598\pi$
$521$	5.72752	−	9.92036i	0.250927	−	0.434619i	0.963781	+	0.266693i	$0.0859311\pi$
$522$	−2.75674	+	13.7655i	−0.120659	+	0.602497i
$523$	−14.4630	−	25.0507i	−0.632424	−	1.09539i	−0.987055	−	0.160384i	$-0.948727\pi$
$523$	−14.4630	−	25.0507i	−0.632424	−	1.09539i	0.354631	−	0.935006i	$-0.384607\pi$
$524$	−15.4369	+	5.61857i	−0.674364	+	0.245448i
$525$		0			0
$526$	24.0023	−	20.1403i	1.04655	−	0.878158i
$527$	−7.13298	+	5.98528i	−0.310718	+	0.260723i
$528$	−5.57425	−	9.91789i	−0.242588	−	0.431621i
$529$	20.8576	−	7.59154i	0.906851	−	0.330067i
$530$		0			0
$531$	13.7710	+	12.1086i	0.597611	+	0.525468i
$532$	18.9896	−	32.8909i	0.823302	−	1.42600i
$533$	−2.57929	+	14.6279i	−0.111722	+	0.633604i
$534$	−1.81743	−	11.0527i	−0.0786480	−	0.478299i
$535$		0			0
$536$	5.76612	+	32.7013i	0.249059	+	1.41248i
$537$	−13.2752	+	4.65872i	−0.572866	+	0.201039i
$538$	−18.1366	−	15.2184i	−0.781925	−	0.656113i
$539$	−38.4540			−1.65633
$540$		0			0
$541$	13.9635			0.600338			0.300169	−	0.953886i	$-0.402957\pi$
$541$	13.9635			0.600338			0.300169	+	0.953886i	$0.402957\pi$
$542$	31.8487	+	26.7242i	1.36802	+	1.14790i
$543$	−20.9152	−	17.9660i	−0.897558	−	0.770994i
$544$	−3.37084	−	19.1170i	−0.144524	−	0.819634i
$545$		0			0
$546$	83.0912	+	31.3350i	3.55597	+	1.34101i
$547$	−3.30929	+	18.7679i	−0.141495	+	0.802457i	0.828620	+	0.559811i	$0.189126\pi$
$547$	−3.30929	+	18.7679i	−0.141495	+	0.802457i	−0.970115	+	0.242646i	$0.921985\pi$
$548$	−6.11394	+	10.5897i	−0.261174	+	0.452367i
$549$	−0.867933	+	1.42612i	−0.0370425	+	0.0608655i
$550$		0			0
$551$	6.78062	−	2.46794i	0.288864	−	0.105138i
$552$	1.66036	−	2.80057i	0.0706698	−	0.119200i
$553$	28.6371	−	24.0294i	1.21777	−	1.02183i
$554$	12.5241	−	10.5090i	0.532098	−	0.446483i
$555$		0			0
$556$	23.6241	−	8.59848i	1.00189	−	0.364657i
$557$	−14.6962	−	25.4546i	−0.622700	−	1.07855i	−0.988981	−	0.148044i	$-0.952702\pi$
$557$	−14.6962	−	25.4546i	−0.622700	−	1.07855i	0.366281	−	0.930504i	$-0.380631\pi$
$558$	−17.2746	+	13.8274i	−0.731291	+	0.585361i
$559$	20.9409	−	36.2707i	0.885705	−	1.53409i
$560$		0			0
$561$	20.1661	−	16.5280i	0.851414	−	0.697811i
$562$	34.0727	+	12.4014i	1.43727	+	0.523123i
$563$	−4.42830	−	25.1141i	−0.186631	−	1.05844i	−0.923842	−	0.382773i	$-0.874969\pi$
$563$	−4.42830	−	25.1141i	−0.186631	−	1.05844i	0.737212	−	0.675662i	$-0.236142\pi$
$564$	−3.40039	+	18.0613i	−0.143182	+	0.760517i
$565$		0			0
$566$	1.20076			0.0504719
$567$	26.9312	−	20.5539i	1.13100	−	0.863185i
$568$	32.3620			1.35788
$569$	−7.32350	−	6.14515i	−0.307017	−	0.257618i	0.476241	−	0.879315i	$-0.341999\pi$
$569$	−7.32350	−	6.14515i	−0.307017	−	0.257618i	−0.783258	+	0.621697i	$0.786444\pi$
$570$		0			0
$571$	5.37062	+	30.4583i	0.224754	+	1.27464i	0.863156	+	0.504938i	$0.168485\pi$
$571$	5.37062	+	30.4583i	0.224754	+	1.27464i	−0.638402	+	0.769703i	$0.720404\pi$
$572$	90.8664	+	33.0727i	3.79931	+	1.38284i
$573$	−24.0838	+	19.7389i	−1.00611	+	0.824603i
$574$	3.52360	−	19.9834i	0.147072	−	0.834089i
$575$		0			0
$576$	−5.84962	−	38.3372i	−0.243734	−	1.59738i
$577$	−18.1993	−	31.5221i	−0.757647	−	1.31228i	−0.944047	−	0.329810i	$-0.893015\pi$
$577$	−18.1993	−	31.5221i	−0.757647	−	1.31228i	0.186400	−	0.982474i	$-0.440318\pi$
$578$	−19.0576	+	6.93641i	−0.792692	+	0.288516i
$579$	1.68247	+	0.0194479i	0.0699211	+	0.000808226i
$580$		0			0
$581$	−13.7823	+	11.5647i	−0.571785	+	0.479785i
$582$	−12.5256	+	21.1272i	−0.519202	+	0.875749i
$583$	−35.6402	+	12.9720i	−1.47607	+	0.537244i
$584$	13.5697	+	23.5034i	0.561518	+	0.972578i
$585$		0			0
$586$	−19.2915	+	33.4139i	−0.796926	+	1.38032i
$587$	7.01686	−	39.7946i	0.289617	−	1.64250i	−0.398696	−	0.917083i	$-0.630537\pi$
$587$	7.01686	−	39.7946i	0.289617	−	1.64250i	0.688312	−	0.725415i	$-0.258352\pi$
$588$	−34.1968	−	12.8961i	−1.41025	−	0.531828i
$589$	10.6872	+	3.88983i	0.440359	+	0.160278i
$590$		0			0
$591$	−12.1317	−	10.4210i	−0.499032	−	0.428663i
$592$	−3.25074	−	2.72770i	−0.133605	−	0.112108i
$593$	−11.8336			−0.485946			−0.242973	−	0.970033i	$-0.578123\pi$
$593$	−11.8336			−0.485946			−0.242973	+	0.970033i	$0.578123\pi$
$594$	48.8165	−	38.1577i	2.00296	−	1.56563i
$595$		0			0
$596$	25.3799	+	21.2963i	1.03960	+	0.872330i
$597$	28.8146	−	10.1121i	1.17930	−	0.413859i
$598$	−2.12049	−	12.0259i	−0.0867135	−	0.491776i
$599$	8.76898	+	3.19165i	0.358291	+	0.130407i	0.514893	−	0.857255i	$-0.327832\pi$
$599$	8.76898	+	3.19165i	0.358291	+	0.130407i	−0.156602	+	0.987662i	$0.550054\pi$
$600$		0			0
$601$	3.42397	−	19.4183i	0.139667	−	0.792088i	−0.831829	−	0.555032i	$-0.812706\pi$
$601$	3.42397	−	19.4183i	0.139667	−	0.792088i	0.971496	−	0.237057i	$-0.0761827\pi$
$602$	−28.6076	+	49.5498i	−1.16596	+	2.01950i
$603$	45.0124	−	15.2144i	1.83305	−	0.619578i
$604$	−25.0091	−	43.3170i	−1.01761	−	1.76254i
$605$		0			0
$606$	8.68462	+	15.4519i	0.352788	+	0.627692i
$607$	−27.6671	+	23.2154i	−1.12297	+	0.942285i	−0.998751	−	0.0499698i	$-0.984087\pi$
$607$	−27.6671	+	23.2154i	−1.12297	+	0.942285i	−0.124221	+	0.992255i	$0.539643\pi$
$608$	−18.1628	+	15.2404i	−0.736600	+	0.618081i
$609$	−6.72376	−	11.9631i	−0.272461	−	0.484771i
$610$		0			0
$611$	11.0439	+	19.1285i	0.446786	+	0.773857i
$612$	23.4764	−	7.93514i	0.948978	−	0.320759i
$613$	1.95873	−	3.39263i	0.0791125	−	0.137027i	−0.823755	−	0.566946i	$-0.808125\pi$
$613$	1.95873	−	3.39263i	0.0791125	−	0.137027i	0.902867	+	0.429919i	$0.141458\pi$
$614$	1.72065	−	9.75829i	0.0694398	−	0.393813i
$615$		0			0
$616$	−39.7754	−	14.4771i	−1.60260	−	0.583298i
$617$	−6.36880	−	36.1192i	−0.256398	−	1.45411i	−0.792458	−	0.609926i	$-0.791199\pi$
$617$	−6.36880	−	36.1192i	−0.256398	−	1.45411i	0.536060	−	0.844180i	$-0.319912\pi$
$618$	−32.4877	+	11.4011i	−1.30685	+	0.458618i
$619$	8.22380	+	6.90059i	0.330543	+	0.277358i	0.792921	−	0.609325i	$-0.208559\pi$
$619$	8.22380	+	6.90059i	0.330543	+	0.277358i	−0.462378	+	0.886683i	$0.653004\pi$
$620$		0			0
$621$	−4.31985	−	1.74417i	−0.173350	−	0.0699912i
$622$	26.2634			1.05307
$623$	8.38770	+	7.03811i	0.336046	+	0.281976i
$624$	−9.85773	−	8.46770i	−0.394625	−	0.338979i
$625$		0			0
$626$	−7.40481	−	2.69513i	−0.295956	−	0.107719i
$627$	−29.7984	−	11.2374i	−1.19003	−	0.448780i
$628$	−6.37827	+	36.1729i	−0.254521	+	1.44346i
$629$	4.86267	−	8.42239i	0.193887	−	0.335823i
$630$		0			0
$631$	−1.62045	−	2.80670i	−0.0645090	−	0.111733i	0.831967	−	0.554825i	$-0.187215\pi$
$631$	−1.62045	−	2.80670i	−0.0645090	−	0.111733i	−0.896476	+	0.443092i	$0.853881\pi$
$632$	19.5655	−	7.12126i	0.778273	−	0.283268i
$633$	−3.97829	+	6.71027i	−0.158123	+	0.266709i
$634$	−6.62270	+	5.55711i	−0.263021	+	0.220701i
$635$		0			0
$636$	−36.0448	−	0.416646i	−1.42927	−	0.0165211i
$637$	−41.2747	+	15.0228i	−1.63536	+	0.595223i
$638$	−12.5491	−	21.7357i	−0.496824	−	0.860524i
$639$	−6.98480	−	45.7769i	−0.276314	−	1.81091i
$640$		0			0
$641$	0.522380	−	2.96256i	0.0206328	−	0.117014i	−0.972752	−	0.231849i	$-0.925523\pi$
$641$	0.522380	−	2.96256i	0.0206328	−	0.117014i	0.993385	+	0.114834i	$0.0366337\pi$
$642$	−49.2162	+	40.3372i	−1.94241	+	1.59198i
$643$	35.5666	+	12.9452i	1.40261	+	0.510509i	0.928952	−	0.370200i	$-0.120711\pi$
$643$	35.5666	+	12.9452i	1.40261	+	0.510509i	0.473659	+	0.880708i	$0.342933\pi$
$644$	1.72474	+	9.78150i	0.0679644	+	0.385445i
$645$		0			0
$646$	−16.3882	−	13.7513i	−0.644784	−	0.541038i
$647$	−13.1670			−0.517650			−0.258825	−	0.965924i	$-0.583335\pi$
$647$	−13.1670			−0.517650			−0.258825	+	0.965924i	$0.583335\pi$
$648$	18.0106	−	5.62726i	0.707524	−	0.221060i
$649$	−32.7831			−1.28685
$650$		0			0
$651$	4.00191	−	21.2562i	0.156847	−	0.833097i
$652$	−3.82806	−	21.7100i	−0.149918	−	0.850229i
$653$	−18.4773	−	6.72520i	−0.723074	−	0.263177i	−0.0458437	−	0.998949i	$-0.514598\pi$
$653$	−18.4773	−	6.72520i	−0.723074	−	0.263177i	−0.677230	+	0.735771i	$0.736820\pi$
$654$	20.2408	−	16.5891i	0.791476	−	0.648687i
$655$		0			0
$656$	−1.48471	+	2.57160i	−0.0579683	+	0.100404i
$657$	30.3174	−	24.2675i	1.18280	−	0.946767i
$658$	−15.0872	−	26.1317i	−0.588158	−	1.01872i
$659$	17.4856	−	6.36425i	0.681143	−	0.247916i	0.0218050	−	0.999762i	$-0.493059\pi$
$659$	17.4856	−	6.36425i	0.681143	−	0.247916i	0.659338	+	0.751846i	$0.270836\pi$
$660$		0			0
$661$	−26.9451	+	22.6096i	−1.04804	+	0.879412i	−0.992886	−	0.119066i	$-0.962010\pi$
$661$	−26.9451	+	22.6096i	−1.04804	+	0.879412i	−0.0551562	+	0.998478i	$0.517566\pi$
$662$	−34.0524	+	28.5734i	−1.32348	+	1.11054i
$663$	15.1884	−	25.6186i	0.589868	−	0.994943i
$664$	−9.41637	+	3.42728i	−0.365426	+	0.133004i
$665$		0			0
$666$	12.0149	−	19.7420i	0.465567	−	0.764985i
$667$	−0.943545	+	1.63427i	−0.0365342	+	0.0632791i
$668$	−6.39677	+	36.2779i	−0.247498	+	1.40363i
$669$	39.8183	+	15.0161i	1.53947	+	0.580557i
$670$		0			0
$671$	−0.518279	−	2.93930i	−0.0200079	−	0.113471i
$672$	34.2053	+	29.3820i	1.31950	+	1.13343i
$673$	−17.6455	−	14.8063i	−0.680183	−	0.570741i	0.235877	−	0.971783i	$-0.424204\pi$
$673$	−17.6455	−	14.8063i	−0.680183	−	0.570741i	−0.916060	+	0.401042i	$0.868648\pi$
$674$	−57.7859			−2.22583
$675$		0			0
$676$	72.1928			2.77665
$677$	−9.49900	−	7.97061i	−0.365076	−	0.306335i	0.441734	−	0.897146i	$-0.354364\pi$
$677$	−9.49900	−	7.97061i	−0.365076	−	0.306335i	−0.806810	+	0.590811i	$0.798808\pi$
$678$	62.6203	−	21.9756i	2.40492	−	0.843970i
$679$	−4.16911	−	23.6442i	−0.159996	−	0.907380i
$680$		0			0
$681$	4.77734	+	29.0535i	0.183068	+	1.11333i
$682$	6.86923	−	38.9574i	0.263037	−	1.49175i
$683$	2.90926	−	5.03898i	0.111320	−	0.192811i	−0.804983	−	0.593298i	$-0.797826\pi$
$683$	2.90926	−	5.03898i	0.111320	−	0.192811i	0.916303	+	0.400487i	$0.131159\pi$
$684$	−22.7307	−	19.9867i	−0.869131	−	0.764210i
$685$		0			0
$686$	1.33535	−	0.486029i	0.0509841	−	0.0185567i
$687$	12.4522	+	22.1554i	0.475082	+	0.845281i
$688$	6.41389	−	5.38189i	0.244527	−	0.205183i
$689$	−33.1867	+	27.8469i	−1.26431	+	1.06088i
$690$		0			0
$691$	−4.15074	+	1.51075i	−0.157902	+	0.0574715i	−0.419762	−	0.907634i	$-0.637886\pi$
$691$	−4.15074	+	1.51075i	−0.157902	+	0.0574715i	0.261860	+	0.965106i	$0.415664\pi$
$692$	−22.3111	−	38.6439i	−0.848140	−	1.46902i
$693$	−11.8933	+	59.3881i	−0.451790	+	2.25597i
$694$	23.2104	−	40.2017i	0.881057	−	1.52603i
$695$		0			0
$696$	−1.24017	−	7.54209i	−0.0470084	−	0.285882i
$697$	−6.39492	−	2.32756i	−0.242225	−	0.0881626i
$698$	4.45105	+	25.2432i	0.168475	+	0.955468i
$699$	41.7583	−	14.6544i	1.57944	−	0.554281i
$700$		0			0
$701$	45.9990			1.73736			0.868678	−	0.495376i	$-0.164970\pi$
$701$	45.9990			1.73736			0.868678	+	0.495376i	$0.164970\pi$
$702$	37.4902	−	60.0277i	1.41498	−	2.26560i
$703$	−11.8786			−0.448011
$704$	53.1111	+	44.5655i	2.00170	+	1.67962i
$705$		0			0
$706$	4.08500	+	23.1672i	0.153741	+	0.871908i
$707$	−16.2819	−	5.92611i	−0.612343	−	0.222874i
$708$	−29.1537	−	10.9943i	−1.09566	−	0.413192i
$709$	−1.65171	+	9.36728i	−0.0620311	+	0.351796i	0.937956	+	0.346754i	$0.112716\pi$
$709$	−1.65171	+	9.36728i	−0.0620311	+	0.351796i	−0.999987	+	0.00504202i	$0.998395\pi$
$710$		0			0
$711$	−14.2961	−	26.1389i	−0.536146	−	0.980286i
$712$	3.04922	+	5.28141i	0.114274	+	0.197929i
$713$	−2.79495	+	1.01728i	−0.104672	+	0.0380973i
$714$	−20.7490	+	34.9979i	−0.776513	+	1.30976i
$715$		0			0
$716$	18.3124	−	15.3659i	0.684367	−	0.574252i
$717$	−11.1634	−	0.129039i	−0.416906	−	0.00481907i
$718$	−40.5871	+	14.7725i	−1.51470	+	0.551305i
$719$	−9.60533	−	16.6369i	−0.358218	−	0.620452i	0.629445	−	0.777045i	$-0.283282\pi$
$719$	−9.60533	−	16.6369i	−0.358218	−	0.620452i	−0.987663	+	0.156593i	$0.949949\pi$
$720$		0			0
$721$	16.8281	−	29.1471i	0.626710	−	1.08549i
$722$	2.79792	−	15.8678i	0.104128	−	0.590537i
$723$	3.59256	−	2.94443i	0.133609	−	0.109505i
$724$	44.0238	+	16.0233i	1.63613	+	0.595503i
$725$		0			0
$726$	−12.6575	+	67.2305i	−0.469763	+	2.49516i
$727$	26.9901	+	22.6474i	1.00101	+	0.839944i	0.987124	−	0.159960i	$-0.0511364\pi$
$727$	26.9901	+	22.6474i	1.00101	+	0.839944i	0.0138826	+	0.999904i	$0.495581\pi$
$728$	−48.3487			−1.79192
$729$	−11.8472	−	24.2620i	−0.438786	−	0.898592i
$730$		0			0
$731$	14.6993	+	12.3342i	0.543675	+	0.456197i
$732$	0.524841	−	2.78771i	0.0193987	−	0.103037i
$733$	−2.68164	−	15.2083i	−0.0990485	−	0.561732i	−0.993431	−	0.114430i	$-0.963496\pi$
$733$	−2.68164	−	15.2083i	−0.0990485	−	0.561732i	0.894383	−	0.447302i	$-0.147615\pi$
$734$	24.9651	+	9.08654i	0.921477	+	0.335390i
$735$		0			0
$736$	1.07673	−	6.10647i	0.0396890	−	0.225087i
$737$	−42.4724	+	73.5643i	−1.56449	+	2.70977i
$738$	−15.0645	−	5.88085i	−0.554533	−	0.216477i
$739$	−6.55875	−	11.3601i	−0.241268	−	0.417888i	0.719808	−	0.694173i	$-0.244230\pi$
$739$	−6.55875	−	11.3601i	−0.241268	−	0.417888i	−0.961076	+	0.276285i	$0.910896\pi$
$740$		0			0
$741$	−36.3742	−	0.420454i	−1.33624	−	0.0154458i
$742$	45.3368	−	38.0421i	1.66437	−	1.39657i
$743$	−11.2392	+	9.43078i	−0.412325	+	0.345982i	−0.825234	−	0.564790i	$-0.808957\pi$
$743$	−11.2392	+	9.43078i	−0.412325	+	0.345982i	0.412909	+	0.910772i	$0.364513\pi$
$744$	6.14371	−	10.3627i	0.225239	−	0.379916i
$745$		0			0
$746$	−30.9676	−	53.6374i	−1.13380	−	1.96380i
$747$	6.88035	+	12.5800i	0.251739	+	0.460278i
$748$	−22.1517	+	38.3678i	−0.809945	+	1.40287i
$749$	10.8016	−	61.2588i	0.394681	−	2.23835i
$750$		0			0
$751$	−13.7050	−	4.98820i	−0.500101	−	0.182022i	0.0796384	−	0.996824i	$-0.474623\pi$
$751$	−13.7050	−	4.98820i	−0.500101	−	0.182022i	−0.579739	+	0.814802i	$0.696846\pi$
$752$	0.766767	+	4.34855i	0.0279611	+	0.158575i
$753$	−25.8428	−	22.1987i	−0.941764	−	0.808966i
$754$	−21.9610	−	18.4275i	−0.799774	−	0.671090i
$755$		0			0
$756$	−30.4933	+	48.8246i	−1.10903	+	1.77573i
$757$	−13.5259			−0.491607			−0.245803	−	0.969320i	$-0.579052\pi$
$757$	−13.5259			−0.491607			−0.245803	+	0.969320i	$0.579052\pi$
$758$	−33.5047	−	28.1138i	−1.21695	−	1.02114i
$759$	7.85879	−	2.75792i	0.285256	−	0.100106i
$760$		0			0
$761$	−31.9148	−	11.6160i	−1.15691	−	0.421081i	−0.308918	−	0.951089i	$-0.599967\pi$
$761$	−31.9148	−	11.6160i	−1.15691	−	0.421081i	−0.847993	+	0.530008i	$0.822189\pi$
$762$	−3.00888	−	18.2986i	−0.109000	−	0.662887i
$763$	−4.44227	+	25.1934i	−0.160821	+	0.912062i
$764$	26.4551	−	45.8215i	0.957111	−	1.65776i
$765$		0			0
$766$	−5.74493	−	9.95050i	−0.207573	−	0.359526i
$767$	−35.1878	+	12.8073i	−1.27056	+	0.462445i
$768$	6.18771	+	11.0094i	0.223280	+	0.397267i
$769$	−1.51739	+	1.27324i	−0.0547184	+	0.0459142i	−0.669737	−	0.742599i	$-0.733593\pi$
$769$	−1.51739	+	1.27324i	−0.0547184	+	0.0459142i	0.615018	+	0.788513i	$0.289149\pi$
$770$		0			0
$771$	4.71029	+	8.38070i	0.169637	+	0.301824i
$772$	−2.68654	+	0.977821i	−0.0966907	+	0.0351925i
$773$	−26.8597	−	46.5224i	−0.966077	−	1.67329i	−0.706694	−	0.707519i	$-0.749814\pi$
$773$	−26.8597	−	46.5224i	−0.966077	−	1.67329i	−0.259382	−	0.965775i	$-0.583519\pi$
$774$	34.2437	+	30.1098i	1.23086	+	1.08227i
$775$		0			0
$776$	2.32206	−	13.1691i	0.0833571	−	0.472742i
$777$	3.66549	+	22.2918i	0.131499	+	0.799712i
$778$	19.6574	+	7.15469i	0.704750	+	0.256508i
$779$	1.44338	+	8.18582i	0.0517145	+	0.293287i
$780$		0			0
$781$	63.4178	+	53.2139i	2.26927	+	1.90414i
$782$	5.59482			0.200070
$783$	−10.4008	+	3.38209i	−0.371695	+	0.120866i
$784$	−8.78093			−0.313605
$785$		0			0
$786$	−16.3054	−	14.0062i	−0.581593	−	0.499583i
$787$	2.94262	+	16.6884i	0.104893	+	0.594877i	0.991263	+	0.131900i	$0.0421078\pi$
$787$	2.94262	+	16.6884i	0.104893	+	0.594877i	−0.886370	+	0.462977i	$0.846781\pi$
$788$	25.5356	+	9.29421i	0.909669	+	0.331093i
$789$	22.8396	+	8.61319i	0.813112	+	0.306638i
$790$		0			0
$791$	−32.4363	+	56.1812i	−1.15330	+	1.99757i
$792$	−17.5378	+	28.8168i	−0.623179	+	1.02396i
$793$	−1.70459	−	2.95243i	−0.0605316	−	0.104844i
$794$	16.7852	−	6.10931i	0.595684	−	0.216811i
$795$		0			0
$796$	−39.7482	+	33.3527i	−1.40884	+	1.18216i
$797$	−0.124410	+	0.104393i	−0.00440684	+	0.00369778i	−0.644988	−	0.764192i	$-0.723138\pi$
$797$	−0.124410	+	0.104393i	−0.00440684	+	0.00369778i	0.640582	+	0.767890i	$0.278693\pi$
$798$	49.6913	+	0.574388i	1.75905	+	0.0203331i
$799$	−9.50945	+	3.46116i	−0.336420	+	0.122447i
$800$		0			0
$801$	6.81257	−	5.45312i	0.240710	−	0.192676i
$802$	−10.7657	+	18.6467i	−0.380149	+	0.658437i
$803$	−12.0557	+	68.3714i	−0.425437	+	2.41277i
$804$	−62.4411	+	51.1762i	−2.20213	+	1.80485i
$805$		0			0
$806$	−7.84629	−	44.4985i	−0.276374	−	1.56739i
$807$	3.41259	−	18.1261i	0.120129	−	0.638068i
$808$	−7.39269	−	6.20321i	−0.260074	−	0.218228i
$809$	−24.6513			−0.866695			−0.433347	−	0.901227i	$-0.642668\pi$
$809$	−24.6513			−0.866695			−0.433347	+	0.901227i	$0.642668\pi$
$810$		0			0
$811$	−9.59786			−0.337026			−0.168513	−	0.985699i	$-0.553897\pi$
$811$	−9.59786			−0.337026			−0.168513	+	0.985699i	$0.553897\pi$
$812$	17.8624	+	14.9883i	0.626847	+	0.525987i
$813$	−5.99266	+	31.8302i	−0.210172	+	1.11633i
$814$	7.17457	+	40.6890i	0.251469	+	1.42615i
$815$		0			0
$816$	4.60491	−	3.77414i	0.161204	−	0.132121i
$817$	4.06982	−	23.0811i	0.142385	−	0.807506i
$818$	15.4650	−	26.7862i	0.540722	−	0.936557i
$819$	10.4353	+	68.3906i	0.364638	+	2.38976i
$820$		0			0
$821$	−7.75048	+	2.82094i	−0.270493	+	0.0984516i	−0.473706	−	0.880683i	$-0.657084\pi$
$821$	−7.75048	+	2.82094i	−0.270493	+	0.0984516i	0.203212	+	0.979135i	$0.434862\pi$
$822$	−15.9988	−	0.184932i	−0.558021	−	0.00645024i
$823$	−3.30870	+	2.77633i	−0.115334	+	0.0967768i	−0.698631	−	0.715482i	$-0.746207\pi$
$823$	−3.30870	+	2.77633i	−0.115334	+	0.0967768i	0.583297	+	0.812259i	$0.301763\pi$
$824$	14.3598	−	12.0493i	0.500247	−	0.419757i
$825$		0			0
$826$	48.0705	−	17.4962i	1.67259	−	0.608772i
$827$	−5.71421	−	9.89730i	−0.198703	−	0.344163i	0.749405	−	0.662111i	$-0.230339\pi$
$827$	−5.71421	−	9.89730i	−0.198703	−	0.344163i	−0.948108	+	0.317948i	$0.897006\pi$
$828$	7.91366	+	0.182974i	0.275019	+	0.00635880i
$829$	−14.4282	+	24.9904i	−0.501113	+	0.867954i	0.498886	+	0.866668i	$0.333743\pi$
$829$	−14.4282	+	24.9904i	−0.501113	+	0.867954i	−0.999999	+	0.00128593i	$0.999591\pi$
$830$		0			0
$831$	11.9175	+	4.49426i	0.413412	+	0.155904i
$832$	74.4171	+	27.0856i	2.57995	+	0.939025i
$833$	−3.49452	−	19.8184i	−0.121078	−	0.686666i
$834$	24.9532	+	21.4346i	0.864059	+	0.742219i
$835$		0			0
$836$	54.1125			1.87152
$837$	−15.9844	−	6.45382i	−0.552501	−	0.223077i
$838$	69.2339			2.39165
$839$	−14.9031	−	12.5052i	−0.514513	−	0.431728i	0.348201	−	0.937420i	$-0.386793\pi$
$839$	−14.9031	−	12.5052i	−0.514513	−	0.431728i	−0.862714	+	0.505692i	$0.831237\pi$
$840$		0			0
$841$	−4.26650	−	24.1965i	−0.147121	−	0.834363i
$842$	32.4789	+	11.8213i	1.11930	+	0.407390i
$843$	4.58332	+	27.8735i	0.157858	+	0.960015i
$844$	2.30169	−	13.0536i	0.0792276	−	0.449322i
$845$		0			0
$846$	−22.7817	+	7.70031i	−0.783251	+	0.264742i
$847$	−33.4369	−	57.9144i	−1.14890	−	1.98996i
$848$	−8.13839	+	2.96213i	−0.279473	+	0.101720i
$849$	0.458332	+	0.815479i	0.0157299	+	0.0279872i
$850$		0			0
$851$	2.37974	−	1.99684i	0.0815764	−	0.0684507i
$852$	38.5508	+	68.5907i	1.32073	+	2.34988i
$853$	0.706049	−	0.256981i	0.0241746	−	0.00879885i	−0.329905	−	0.944014i	$-0.607017\pi$
$853$	0.706049	−	0.256981i	0.0241746	−	0.00879885i	0.354079	+	0.935215i	$0.384794\pi$
$854$	2.32866	+	4.03335i	0.0796850	+	0.138019i
$855$		0			0
$856$	17.3228	−	30.0039i	0.592080	−	1.02551i
$857$	−6.32595	+	35.8762i	−0.216090	+	1.22551i	0.662914	+	0.748695i	$0.269319\pi$
$857$	−6.32595	+	35.8762i	−0.216090	+	1.22551i	−0.879005	+	0.476813i	$0.841792\pi$
$858$	20.5294	+	124.850i	0.700863	+	4.26231i
$859$	−27.3052	−	9.93826i	−0.931640	−	0.339089i	−0.168781	−	0.985654i	$-0.553983\pi$
$859$	−27.3052	−	9.93826i	−0.931640	−	0.339089i	−0.762859	+	0.646564i	$0.776205\pi$
$860$		0			0
$861$	14.9163	−	5.23466i	0.508347	−	0.178397i
$862$	−8.70085	−	7.30088i	−0.296352	−	0.248669i
$863$	2.49689			0.0849951			0.0424975	−	0.999097i	$-0.486469\pi$
$863$	2.49689			0.0849951			0.0424975	+	0.999097i	$0.486469\pi$
$864$	28.3135	−	22.1315i	0.963246	−	0.752928i
$865$		0			0
$866$	15.7125	+	13.1844i	0.533934	+	0.448024i
$867$	−11.9850	−	10.2950i	−0.407034	−	0.349638i
$868$	6.38192	+	36.1937i	0.216616	+	1.22849i
$869$	50.0511	+	18.2171i	1.69787	+	0.617973i
$870$		0			0
$871$	−16.8486	+	95.5529i	−0.570891	+	3.23769i
$872$	−7.12419	+	12.3395i	−0.241256	+	0.417867i
$873$	−19.1292	−	0.442292i	−0.647424	−	0.0149693i
$874$	−3.41678	−	5.91804i	−0.115574	−	0.200181i
$875$		0			0
$876$	−33.6504	+	56.7589i	−1.13694	+	1.91771i
$877$	27.7487	−	23.2839i	0.937006	−	0.786241i	−0.0400561	−	0.999197i	$-0.512754\pi$
$877$	27.7487	−	23.2839i	0.937006	−	0.786241i	0.977062	+	0.212956i	$0.0683092\pi$
$878$	22.7577	−	19.0960i	0.768037	−	0.644459i
$879$	−30.0561	−	0.347422i	−1.01377	−	0.0117183i
$880$		0			0
$881$	−5.21700	−	9.03610i	−0.175765	−	0.304434i	0.764661	−	0.644433i	$-0.222907\pi$
$881$	−5.21700	−	9.03610i	−0.175765	−	0.304434i	−0.940426	+	0.339999i	$0.889573\pi$
$882$	−7.21330	−	47.2744i	−0.242885	−	1.59181i
$883$	13.5036	−	23.3890i	0.454434	−	0.787102i	−0.544222	−	0.838941i	$-0.683175\pi$
$883$	13.5036	−	23.3890i	0.454434	−	0.787102i	0.998655	+	0.0518393i	$0.0165084\pi$
$884$	−8.78745	+	49.8361i	−0.295554	+	1.67617i
$885$		0			0
$886$	−16.0916	−	5.85688i	−0.540609	−	0.196766i
$887$	2.12762	+	12.0663i	0.0714384	+	0.405148i	0.999467	+	0.0326390i	$0.0103912\pi$
$887$	2.12762	+	12.0663i	0.0714384	+	0.405148i	−0.928029	+	0.372509i	$0.878498\pi$
$888$	−2.32801	+	12.3653i	−0.0781229	+	0.414952i
$889$	13.8864	+	11.6521i	0.465735	+	0.390798i
$890$		0			0
$891$	44.5475	+	18.5881i	1.49240	+	0.622724i
$892$	−72.3084			−2.42106
$893$	9.46858	+	7.94508i	0.316854	+	0.265872i
$894$	−8.02081	+	42.6027i	−0.268256	+	1.42485i
$895$		0			0
$896$	−52.7344	−	19.1938i	−1.76173	−	0.641218i
$897$	7.35781	−	6.03040i	0.245670	−	0.201349i
$898$	13.0872	−	74.2212i	0.436726	−	2.47679i
$899$	−3.49132	+	6.04714i	−0.116442	+	0.201684i
$900$		0			0
$901$	−9.92428	−	17.1894i	−0.330626	−	0.572660i
$902$	27.1679	−	9.88830i	0.904592	−	0.329244i
$903$	−44.5705	−	0.515196i	−1.48321	−	0.0171446i
$904$	−27.6787	+	23.2252i	−0.920578	+	0.772457i
$905$		0			0
$906$	33.3766	−	56.2971i	1.10886	−	1.87035i
$907$	−4.25762	+	1.54965i	−0.141372	+	0.0514552i	−0.411737	−	0.911303i	$-0.635078\pi$
$907$	−4.25762	+	1.54965i	−0.141372	+	0.0514552i	0.270365	+	0.962758i	$0.412856\pi$
$908$	−25.0146	−	43.3265i	−0.830137	−	1.43784i
$909$	−7.17901	+	11.7960i	−0.238113	+	0.391250i
$910$		0			0
$911$	2.98118	−	16.9071i	0.0987710	−	0.560158i	−0.894755	−	0.446557i	$-0.852650\pi$
$911$	2.98118	−	16.9071i	0.0987710	−	0.560158i	0.993526	−	0.113601i	$-0.0362387\pi$
$912$	−6.80442	−	2.56605i	−0.225317	−	0.0849706i
$913$	−24.0883	−	8.76742i	−0.797206	−	0.290159i
$914$	−9.90363	−	56.1663i	−0.327583	−	1.85781i
$915$		0			0
$916$	−33.0807	−	27.7580i	−1.09302	−	0.917150i
$917$	21.0118			0.693872
$918$	24.1019	+	21.6914i	0.795481	+	0.715922i
$919$	−42.1043			−1.38889			−0.694447	−	0.719544i	$-0.744351\pi$
$919$	−42.1043			−1.38889			−0.694447	+	0.719544i	$0.744351\pi$
$920$		0			0
$921$	7.28395	−	2.55619i	0.240014	−	0.0842294i
$922$	−5.66084	−	32.1042i	−0.186430	−	1.05730i
$923$	88.8586	+	32.3419i	2.92482	+	1.06455i
$924$	−16.6980	−	101.549i	−0.549323	−	3.34072i
$925$		0			0
$926$	0.605108	−	1.04808i	0.0198851	−	0.0344420i
$927$	−20.1434	−	17.7117i	−0.661596	−	0.581728i
$928$	−7.27848	−	12.6067i	−0.238928	−	0.413835i
$929$	24.1410	−	8.78662i	0.792042	−	0.288280i	0.0858572	−	0.996307i	$-0.472637\pi$
$929$	24.1410	−	8.78662i	0.792042	−	0.288280i	0.706185	+	0.708028i	$0.250415\pi$
$930$		0			0
$931$	−18.8292	+	15.7996i	−0.617102	+	0.517810i
$932$	−57.6033	+	48.3349i	−1.88686	+	1.58326i
$933$	10.0248	+	17.8364i	0.328196	+	0.583937i
$934$	−86.0166	+	31.3075i	−2.81455	+	1.02441i
$935$		0			0
$936$	−7.56641	+	37.7821i	−0.247316	+	1.23495i
$937$	22.2421	−	38.5244i	0.726617	−	1.25854i	−0.231688	−	0.972790i	$-0.574425\pi$
$937$	22.2421	−	38.5244i	0.726617	−	1.25854i	0.958305	−	0.285748i	$-0.0922419\pi$
$938$	23.0170	−	130.536i	0.751533	−	4.26215i
$939$	−0.996066	−	6.05759i	−0.0325054	−	0.197682i
$940$		0			0
$941$	−3.84491	−	21.8056i	−0.125341	−	0.710842i	−0.981105	−	0.193476i	$-0.938024\pi$
$941$	−3.84491	−	21.8056i	−0.125341	−	0.710842i	0.855764	−	0.517366i	$-0.173087\pi$
$942$	−45.3500	+	15.9149i	−1.47758	+	0.518535i
$943$	−1.66523	−	1.39729i	−0.0542273	−	0.0455021i
$944$	−7.48598			−0.243648
$945$		0			0
$946$	−81.5201			−2.65045
$947$	−21.0838	−	17.6914i	−0.685131	−	0.574894i	0.232369	−	0.972628i	$-0.425352\pi$
$947$	−21.0838	−	17.6914i	−0.685131	−	0.574894i	−0.917501	+	0.397734i	$0.869797\pi$
$948$	38.4005	+	32.9857i	1.24719	+	1.07133i
$949$	13.7705	+	78.0963i	0.447009	+	2.53511i
$950$		0			0
$951$	−6.30190	−	2.37655i	−0.204353	−	0.0770649i
$952$	3.84657	−	21.8150i	0.124668	−	0.707028i
$953$	−2.54376	+	4.40592i	−0.0824005	+	0.142722i	−0.904281	−	0.426939i	$-0.859592\pi$
$953$	−2.54376	+	4.40592i	−0.0824005	+	0.142722i	0.821880	+	0.569661i	$0.192925\pi$
$954$	−22.6329	−	41.3818i	−0.732767	−	1.33979i
$955$		0			0
$956$	17.8256	−	6.48798i	0.576520	−	0.209836i
$957$	9.97144	−	16.8190i	0.322331	−	0.543682i
$958$	−10.0405	+	8.42495i	−0.324393	+	0.272198i
$959$	11.9811	−	10.0533i	0.386888	−	0.324638i
$960$		0			0
$961$	18.7886	−	6.83848i	0.606083	−	0.220596i
$962$	23.5967	+	40.8707i	0.760789	+	1.31773i
$963$	−46.1802	−	18.0277i	−1.48814	−	0.580934i
$964$	−3.94628	+	6.83516i	−0.127101	+	0.220146i
$965$		0			0
$966$	−10.0516	+	8.23821i	−0.323405	+	0.265060i
$967$	10.9900	+	4.00003i	0.353414	+	0.128632i	0.512626	−	0.858612i	$-0.328673\pi$
$967$	10.9900	+	4.00003i	0.353414	+	0.128632i	−0.159211	+	0.987245i	$0.550895\pi$
$968$	−6.46780	−	36.6807i	−0.207883	−	1.17896i
$969$	3.08360	−	16.3786i	0.0990596	−	0.526158i
$970$		0			0
$971$	9.40243			0.301738			0.150869	−	0.988554i	$-0.451793\pi$
$971$	9.40243			0.301738			0.150869	+	0.988554i	$0.451793\pi$
$972$	33.3818	+	31.4699i	1.07072	+	1.00940i
$973$	−32.1558			−1.03087
$974$	−20.2848	−	17.0209i	−0.649966	−	0.545386i
$975$		0			0
$976$	−0.118348	−	0.671186i	−0.00378823	−	0.0214841i
$977$	−35.6014	−	12.9578i	−1.13899	−	0.414558i	−0.297441	−	0.954740i	$-0.596133\pi$
$977$	−35.6014	−	12.9578i	−1.13899	−	0.414558i	−0.841548	+	0.540182i	$0.818355\pi$
$978$	22.3095	−	18.2847i	0.713379	−	0.584679i
$979$	−2.70902	+	15.3636i	−0.0865806	+	0.491023i
$980$		0			0
$981$	18.9921	+	7.41409i	0.606373	+	0.236714i
$982$	41.4592	+	71.8095i	1.32302	+	2.29153i
$983$	53.9418	−	19.6332i	1.72048	−	0.626202i	0.722595	−	0.691271i	$-0.242949\pi$
$983$	53.9418	−	19.6332i	1.72048	−	0.626202i	0.997881	+	0.0650694i	$0.0207269\pi$
$984$	8.80406	+	0.101767i	0.280663	+	0.00324422i
$985$		0			0
$986$	10.0617	−	8.44278i	0.320430	−	0.268873i
$987$	11.9882	−	20.2207i	0.381587	−	0.643631i
$988$	58.0817	−	21.1400i	1.84783	−	0.672554i
$989$	3.06467	+	5.30817i	0.0974510	+	0.168790i
$990$		0			0
$991$	13.9592	−	24.1781i	0.443430	−	0.768043i	−0.554512	−	0.832176i	$-0.687095\pi$
$991$	13.9592	−	24.1781i	0.443430	−	0.768043i	0.997941	+	0.0641332i	$0.0204282\pi$
$992$	3.98415	−	22.5952i	0.126497	−	0.717400i
$993$	−32.4030	−	12.2197i	−1.02828	−	0.387780i
$994$	−121.391	−	44.1827i	−3.85029	−	1.40139i
$995$		0			0
$996$	−18.4812	−	15.8752i	−0.585599	−	0.503024i
$997$	15.1219	+	12.6888i	0.478916	+	0.401858i	0.850034	−	0.526727i	$-0.176581\pi$
$997$	15.1219	+	12.6888i	0.478916	+	0.401858i	−0.371118	+	0.928586i	$0.621026\pi$
$998$	41.2218			1.30485
$999$	17.9935	+	0.624190i	0.569289	+	0.0197485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.g.151.2	yes	66
5.2	odd	4		675.2.u.e.124.20		132
5.3	odd	4		675.2.u.e.124.3		132
5.4	even	2		675.2.l.f.151.10	yes	66
27.22	even	9	inner	675.2.l.g.76.2	yes	66
135.22	odd	36		675.2.u.e.49.3		132
135.49	even	18		675.2.l.f.76.10	✓	66
135.103	odd	36		675.2.u.e.49.20		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.10	✓	66	135.49	even	18
675.2.l.f.151.10	yes	66	5.4	even	2
675.2.l.g.76.2	yes	66	27.22	even	9	inner
675.2.l.g.151.2	yes	66	1.1	even	1	trivial
675.2.u.e.49.3		132	135.22	odd	36
675.2.u.e.49.20		132	135.103	odd	36
675.2.u.e.124.3		132	5.3	odd	4
675.2.u.e.124.20		132	5.2	odd	4

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70314 - 1.42910i) q^{2} +(0.320463 - 1.70215i) q^{3} +(0.511048 + 2.89830i) q^{4} +(-2.97833 + 2.44102i) q^{6} +(0.653660 - 3.70709i) q^{7} +(1.04829 - 1.81569i) q^{8} +(-2.79461 - 1.09095i) q^{9} +(5.03989 - 1.83437i) q^{11} +(5.09710 + 0.0589180i) q^{12} +(4.69294 - 3.93784i) q^{13} +(-6.41109 + 5.37954i) q^{14} +(1.15085 - 0.418876i) q^{16} +(1.40339 + 2.43075i) q^{17} +(3.20052 + 5.85182i) q^{18} +(1.71412 - 2.96894i) q^{19} +(-6.10054 - 2.30061i) q^{21} +(-11.2051 - 4.07833i) q^{22} +(0.155686 + 0.882941i) q^{23} +(-2.75464 - 2.36621i) q^{24} -13.6203 q^{26} +(-2.75252 + 4.40722i) q^{27} +11.0783 q^{28} +(1.61238 + 1.35294i) q^{29} +(0.576073 + 3.26707i) q^{31} +(-6.49896 - 2.36543i) q^{32} +(-1.50727 - 9.16647i) q^{33} +(1.08362 - 6.14550i) q^{34} +(1.73372 - 8.65714i) q^{36} +(-1.73247 - 3.00072i) q^{37} +(-7.16230 + 2.60687i) q^{38} +(-5.19887 - 9.25000i) q^{39} +(-1.85735 + 1.55850i) q^{41} +(7.10225 + 12.6366i) q^{42} +(6.42421 - 2.33822i) q^{43} +(7.89217 + 13.6696i) q^{44} +(0.996658 - 1.72626i) q^{46} +(-0.626080 + 3.55068i) q^{47} +(-0.344183 - 2.09315i) q^{48} +(-6.73741 - 2.45222i) q^{49} +(4.58723 - 1.60982i) q^{51} +(13.8114 + 11.5891i) q^{52} -7.07162 q^{53} +(10.9863 - 3.57247i) q^{54} +(-6.04572 - 5.07296i) q^{56} +(-4.50426 - 3.86912i) q^{57} +(-0.812603 - 4.60850i) q^{58} +(-5.74383 - 2.09058i) q^{59} +(0.0966336 - 0.548037i) q^{61} +(3.68785 - 6.38754i) q^{62} +(-5.87097 + 9.64675i) q^{63} +(6.46348 + 11.1951i) q^{64} +(-10.5327 + 17.7658i) q^{66} +(-12.1326 + 10.1805i) q^{67} +(-6.32784 + 5.30969i) q^{68} +(1.55279 + 0.0179489i) q^{69} +(7.71778 + 13.3676i) q^{71} +(-4.91040 + 3.93052i) q^{72} +(-6.47229 + 11.2103i) q^{73} +(-1.33771 + 7.58652i) q^{74} +(9.48088 + 3.45076i) q^{76} +(-3.50580 - 19.8824i) q^{77} +(-4.36480 + 23.1837i) q^{78} +(7.60758 + 6.38352i) q^{79} +(6.61966 + 6.09755i) q^{81} +5.39058 q^{82} +(-3.66133 - 3.07222i) q^{83} +(3.55019 - 18.8569i) q^{84} +(-14.2829 - 5.19854i) q^{86} +(2.81962 - 2.31093i) q^{87} +(1.95262 - 11.0738i) q^{88} +(-1.45438 + 2.51905i) q^{89} +(-11.5304 - 19.9712i) q^{91} +(-2.47946 + 0.902451i) q^{92} +(5.74565 + 0.0664147i) q^{93} +(6.14058 - 5.15256i) q^{94} +(-6.10898 + 10.3042i) q^{96} +(5.99345 - 2.18144i) q^{97} +(7.97026 + 13.8049i) q^{98} +(-16.0857 - 0.371923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 6 q^{2} - 6 q^{6} + 6 q^{7} + 12 q^{8} - 6 q^{9} + 15 q^{11} + 18 q^{12} + 15 q^{14} + 18 q^{16} + 30 q^{17} - 12 q^{18} + 12 q^{19} + 12 q^{21} - 45 q^{22} + 36 q^{23} - 39 q^{24} + 6 q^{26} + 51 q^{27}+ \cdots - 48 q^{99}+O(q^{100}) \) 66 * q + 6 * q^2 - 6 * q^6 + 6 * q^7 + 12 * q^8 - 6 * q^9 + 15 * q^11 + 18 * q^12 + 15 * q^14 + 18 * q^16 + 30 * q^17 - 12 * q^18 + 12 * q^19 + 12 * q^21 - 45 * q^22 + 36 * q^23 - 39 * q^24 + 6 * q^26 + 51 * q^27 - 36 * q^28 - 15 * q^29 + 3 * q^31 + 27 * q^32 - 3 * q^33 + 30 * q^36 + 6 * q^37 - 12 * q^38 - 15 * q^39 + 39 * q^41 + 48 * q^42 + 12 * q^43 + 51 * q^44 + 9 * q^46 + 30 * q^47 - 132 * q^48 - 6 * q^49 + 9 * q^52 - 24 * q^53 + 75 * q^54 + 144 * q^56 + 33 * q^57 + 27 * q^58 + 45 * q^59 - 54 * q^61 + 66 * q^62 - 120 * q^63 - 24 * q^64 + 48 * q^66 + 9 * q^67 - 69 * q^68 + 51 * q^69 - 15 * q^71 + 9 * q^72 - 15 * q^73 + 96 * q^74 - 48 * q^76 - 36 * q^77 - 18 * q^78 + 48 * q^79 - 54 * q^81 - 36 * q^82 + 30 * q^83 + 57 * q^84 - 111 * q^86 - 33 * q^87 + 36 * q^88 - 12 * q^89 + 9 * q^91 - 219 * q^92 + 63 * q^93 + 36 * q^94 - 249 * q^96 + 57 * q^97 + 75 * q^98 - 48 * q^99

Introduction

L-functions

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