LMFDB - Embedded newform 675.2.l.g.76.2

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			76.2
Character	$\chi$	$=$	675.76
Dual form			675.2.l.g.151.2

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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	−0.204803	+	0.978803i	$0.565656\pi$
$2$	−1.70314	+	1.42910i	−1.20430	+	1.01053i	−0.999497	+	0.0317247i	$0.989900\pi$
$3$	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	0.815659	+	0.578534i	$0.196375\pi$
$7$	0.653660	+	3.70709i	0.247060	+	1.40115i	−0.568598	+	0.822615i	$0.692514\pi$
$8$	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	0.961044	−	0.276396i	$-0.0891400\pi$
$11$	5.03989	+	1.83437i	1.51958	+	0.553083i	0.558539	+	0.829478i	$0.311362\pi$
$12$	5.09710	−	0.0589180i	1.47141	−	0.0170082i
$13$	4.69294	+	3.93784i	1.30159	+	1.09216i	0.989869	+	0.141986i	$0.0453489\pi$
$13$	4.69294	+	3.93784i	1.30159	+	1.09216i	0.311718	+	0.950175i	$0.399096\pi$
$14$	−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	−0.644129	−	0.764917i	$-0.722780\pi$
$17$	1.40339	−	2.43075i	0.340373	−	0.589544i	0.984502	+	0.175373i	$0.0561133\pi$
$18$	3.20052	−	5.85182i	0.754370	−	1.37929i
$19$	1.71412	+	2.96894i	0.393246	+	0.681122i	0.992876	−	0.119156i	$-0.0380187\pi$
$19$	1.71412	+	2.96894i	0.393246	+	0.681122i	−0.599630	+	0.800278i	$0.704685\pi$
$20$		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	−0.964265	−	0.264941i	$-0.914648\pi$
$23$	0.155686	−	0.882941i	0.0324628	−	0.184106i	0.996728	+	0.0808349i	$0.0257587\pi$
$24$	−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	−0.480688	−	0.876892i	$-0.659613\pi$
$29$	1.61238	−	1.35294i	0.299411	−	0.251235i	0.780099	+	0.625656i	$0.215169\pi$
$30$		0			0
$31$	0.576073	−	3.26707i	0.103466	−	0.586784i	−0.888356	−	0.459155i	$-0.848152\pi$
$31$	0.576073	−	3.26707i	0.103466	−	0.586784i	0.991822	−	0.127629i	$-0.0407366\pi$
$32$	−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	−0.972565	−	0.232633i	$-0.925266\pi$
$37$	−1.73247	+	3.00072i	−0.284816	+	0.493316i	0.687749	+	0.725949i	$0.258599\pi$
$38$	−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	0.486127	−	0.873888i	$-0.338409\pi$
$41$	−1.85735	−	1.55850i	−0.290069	−	0.243397i	−0.776196	+	0.630491i	$0.782854\pi$
$42$	7.10225	−	12.6366i	1.09590	−	1.94986i
$43$	6.42421	+	2.33822i	0.979683	+	0.356576i	0.781717	−	0.623633i	$-0.214344\pi$
$43$	6.42421	+	2.33822i	0.979683	+	0.356576i	0.197966	+	0.980209i	$0.436566\pi$
$44$	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	−0.995812	−	0.0914225i	$-0.970859\pi$
$47$	−0.626080	−	3.55068i	−0.0913232	−	0.517919i	0.904489	−	0.426497i	$-0.140252\pi$
$48$	−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	−0.687672	−	0.726021i	$-0.741367\pi$
$59$	−5.74383	+	2.09058i	−0.747782	+	0.272171i	−0.0601101	+	0.998192i	$0.519145\pi$
$60$		0			0
$61$	0.0966336	+	0.548037i	0.0123727	+	0.0701689i	0.990369	−	0.138453i	$-0.0442131\pi$
$61$	0.0966336	+	0.548037i	0.0123727	+	0.0701689i	−0.977996	+	0.208622i	$0.933102\pi$
$62$	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	−0.903754	−	0.428052i	$-0.859200\pi$
$67$	−12.1326	−	10.1805i	−1.48224	−	1.24375i	−0.578484	−	0.815694i	$-0.696356\pi$
$68$	−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	0.110402	−	0.993887i	$-0.464786\pi$
$71$	7.71778	−	13.3676i	0.915933	−	1.58644i	0.805530	−	0.592555i	$-0.201881\pi$
$72$	−4.91040	−	3.93052i	−0.578696	−	0.463216i
$73$	−6.47229	−	11.2103i	−0.757524	−	1.31207i	−0.944110	−	0.329632i	$-0.893075\pi$
$73$	−6.47229	−	11.2103i	−0.757524	−	1.31207i	0.186585	−	0.982439i	$-0.440258\pi$
$74$	−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	−0.105165	−	0.994455i	$-0.533537\pi$
$79$	7.60758	−	6.38352i	0.855920	−	0.718202i	0.961085	+	0.276253i	$0.0890927\pi$
$80$		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	−0.821221	−	0.570610i	$-0.806707\pi$
$83$	−3.66133	+	3.07222i	−0.401884	+	0.337220i	0.419338	+	0.907830i	$0.362262\pi$
$84$	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	0.778591	−	0.627532i	$-0.215935\pi$
$89$	−1.45438	−	2.51905i	−0.154164	−	0.267019i	−0.932754	+	0.360513i	$0.882602\pi$
$90$		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	0.627865	−	0.778322i	$-0.283929\pi$
$97$	5.99345	+	2.18144i	0.608543	+	0.221491i	−0.0193229	+	0.999813i	$0.506151\pi$
$98$	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	0.998403	+	0.0564928i	$0.0179918\pi$
$101$	0.799294	+	4.53302i	0.0795328	+	0.451053i	−0.918870	+	0.394560i	$0.870897\pi$
$102$	−10.1133	+	3.81388i	−1.00136	+	0.377630i
$103$	8.40172	−	3.05797i	0.827846	−	0.301311i	0.106871	−	0.994273i	$-0.465917\pi$
$103$	8.40172	−	3.05797i	0.827846	−	0.301311i	0.720974	+	0.692962i	$0.243695\pi$
$104$	−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	−0.962005	−	0.273033i	$-0.911973\pi$
$113$	−16.1944	+	5.89428i	−1.52344	+	0.554487i	−0.561436	+	0.827520i	$0.689751\pi$
$114$	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	0.739198	−	0.673489i	$-0.235205\pi$
$127$	−2.40782	−	4.17046i	−0.213659	−	0.370069i	−0.952857	+	0.303420i	$0.901872\pi$
$128$	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	−0.912737	−	0.408548i	$-0.866035\pi$
$131$	0.969287	−	5.49710i	0.0846870	−	0.480284i	0.997424	−	0.0717355i	$-0.0228538\pi$
$132$	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	−0.496618	−	0.867969i	$-0.665425\pi$
$137$	3.18283	−	2.67071i	0.271927	−	0.228174i	0.768546	+	0.639795i	$0.220981\pi$
$138$	−2.61896	+	2.24966i	−0.222941	+	0.191504i
$139$	−1.48337	+	8.41259i	−0.125817	+	0.713546i	0.855002	+	0.518625i	$0.173556\pi$
$139$	−1.48337	+	8.41259i	−0.125817	+	0.713546i	−0.980819	+	0.194921i	$0.937555\pi$
$140$		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	0.923612	−	0.383330i	$-0.125223\pi$
$149$	8.62380	+	7.23622i	0.706489	+	0.592815i	−0.217123	+	0.976144i	$0.569667\pi$
$150$		0			0
$151$	−15.9706	−	5.81283i	−1.29967	−	0.473042i	−0.402781	−	0.915296i	$-0.631957\pi$
$151$	−15.9706	−	5.81283i	−1.29967	−	0.473042i	−0.896890	+	0.442255i	$0.854179\pi$
$152$	−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	0.171416	−	0.985199i	$-0.445166\pi$
$157$	11.7281	−	4.26867i	0.936002	−	0.340677i	0.764586	+	0.644522i	$0.222944\pi$
$158$	−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	0.155854	−	0.987780i	$-0.450187\pi$
$167$	11.7621	−	4.28105i	0.910177	−	0.331277i	0.754324	+	0.656503i	$0.227965\pi$
$168$	−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	−0.262122	−	0.965035i	$-0.584422\pi$
$173$	−14.2477	−	5.18574i	−1.08323	−	0.394264i	−0.821110	+	0.570771i	$0.806645\pi$
$174$	−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	−0.976939	−	0.213517i	$-0.931508\pi$
$179$	−4.06134	+	7.03445i	−0.303559	+	0.525780i	0.673380	+	0.739296i	$0.264842\pi$
$180$		0			0
$181$	7.95939	+	13.7861i	0.591617	+	1.02471i	0.994015	+	0.109245i	$0.0348434\pi$
$181$	7.95939	+	13.7861i	0.591617	+	1.02471i	−0.402398	+	0.915465i	$0.631823\pi$
$182$	−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	−0.986498	−	0.163773i	$-0.947633\pi$
$191$	−13.7721	+	11.5562i	−0.996516	+	0.836176i	−0.0100183	+	0.999950i	$0.503189\pi$
$192$	21.1270	+	7.41418i	1.52471	+	0.535073i
$193$	0.168689	−	0.956681i	0.0121425	−	0.0688634i	−0.978134	−	0.207974i	$-0.933313\pi$
$193$	0.168689	−	0.956681i	0.0121425	−	0.0688634i	0.990277	+	0.139110i	$0.0444243\pi$
$194$	−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	0.982300	−	0.187313i	$-0.0599780\pi$
$197$	4.61678	+	7.99649i	0.328932	+	0.569727i	−0.653368	+	0.757040i	$0.726645\pi$
$198$	26.8646	−	23.6215i	1.90919	−	1.67871i
$199$	8.81540	−	15.2687i	0.624907	−	1.08237i	−0.363651	−	0.931535i	$-0.618470\pi$
$199$	8.81540	−	15.2687i	0.624907	−	1.08237i	0.988559	−	0.150836i	$-0.0481966\pi$
$200$		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	−0.483565	−	0.875308i	$-0.660658\pi$
$211$	−4.23225	+	1.54041i	−0.291360	+	0.106046i	0.192205	+	0.981355i	$0.438436\pi$
$212$	−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	−0.702764	−	0.711423i	$-0.748051\pi$
$223$	−4.26645	−	24.1963i	−0.285703	−	1.62030i	0.417061	−	0.908878i	$-0.363060\pi$
$224$	−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	−0.247721	−	0.968831i	$-0.579682\pi$
$227$	−15.9741	−	5.81410i	−1.06024	−	0.385895i	−0.812518	+	0.582936i	$0.801904\pi$
$228$	8.91197	+	15.0320i	0.590210	+	0.995519i
$229$	−11.2404	−	9.43183i	−0.742788	−	0.623273i	0.190797	−	0.981630i	$-0.438893\pi$
$229$	−11.2404	−	9.43183i	−0.742788	−	0.623273i	−0.933585	+	0.358356i	$0.883337\pi$
$230$		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	−0.0555035	−	0.998458i	$-0.517676\pi$
$233$	12.7753	−	22.1275i	0.836939	−	1.44962i	0.892442	−	0.451162i	$-0.148990\pi$
$234$	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	0.926971	+	0.375133i	$0.122403\pi$
$239$	−1.11927	+	6.34771i	−0.0723998	+	0.410599i	−0.999371	+	0.0354667i	$0.988708\pi$
$240$		0			0
$241$	2.05438	−	1.72383i	0.132334	−	0.111042i	−0.574218	−	0.818702i	$-0.694694\pi$
$241$	2.05438	−	1.72383i	0.132334	−	0.111042i	0.706552	+	0.707661i	$0.250249\pi$
$242$	−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	0.989345	+	0.145587i	$0.0465070\pi$
$251$	9.83460	+	17.0340i	0.620755	+	1.07518i	−0.368591	+	0.929592i	$0.620160\pi$
$252$	−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	0.500469	−	0.865754i	$-0.333161\pi$
$257$	−4.25190	−	3.56777i	−0.265226	−	0.222551i	−0.765696	+	0.643203i	$0.777605\pi$
$258$	−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	−0.962437	−	0.271504i	$-0.912479\pi$
$263$	−2.44722	−	13.8789i	−0.150902	−	0.855808i	0.811535	−	0.584303i	$-0.198632\pi$
$264$	−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	−0.998838	−	0.0482019i	$-0.984651\pi$
$277$	−1.27693	−	7.24183i	−0.0767233	−	0.435119i	0.922114	−	0.386918i	$-0.126460\pi$
$278$	−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	−0.158291	−	0.987392i	$-0.550599\pi$
$281$	−15.3253	−	5.57797i	−0.914233	−	0.332754i	−0.755942	+	0.654639i	$0.772821\pi$
$282$	−6.80258	+	12.1034i	−0.405088	+	0.720745i
$283$	−0.413729	−	0.347160i	−0.0245936	−	0.0206365i	0.630408	−	0.776264i	$-0.282888\pi$
$283$	−0.413729	−	0.347160i	−0.0245936	−	0.0206365i	−0.655002	+	0.755627i	$0.727332\pi$
$284$	−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	0.760874	+	0.648900i	$0.224771\pi$
$293$	−3.01350	+	17.0904i	−0.176051	+	0.998432i	−0.936924	+	0.349532i	$0.886340\pi$
$294$	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	−0.795401	−	0.606083i	$-0.792740\pi$
$307$	2.22842	−	3.85973i	0.127182	−	0.220287i	0.922584	+	0.385796i	$0.126073\pi$
$308$	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	0.349097	−	0.937086i	$-0.386488\pi$
$311$	−9.04919	−	7.59317i	−0.513133	−	0.430569i	−0.862230	+	0.506517i	$0.830933\pi$
$312$	−22.2451	+	0.257134i	−1.25938	+	0.0145574i
$313$	3.33057	+	1.21223i	0.188255	+	0.0685191i	0.434427	−	0.900707i	$-0.356951\pi$
$313$	3.33057	+	1.21223i	0.188255	+	0.0685191i	−0.246173	+	0.969226i	$0.579173\pi$
$314$	−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	0.997881	−	0.0650679i	$-0.0207264\pi$
$317$	0.675236	+	3.82945i	0.0379250	+	0.215084i	−0.959956	+	0.280151i	$0.909615\pi$
$318$	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	0.918228	+	0.396051i	$0.129620\pi$
$331$	3.47191	+	19.6902i	0.190833	+	1.08227i	−0.727395	+	0.686219i	$0.759269\pi$
$332$	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	0.996294	−	0.0860160i	$-0.0274136\pi$
$337$	19.9104	+	16.7068i	1.08459	+	0.910078i	0.0882954	+	0.996094i	$0.471858\pi$
$338$	−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	−0.718300	−	0.695733i	$-0.755080\pi$
$347$	3.62567	−	20.5622i	0.194636	−	1.10384i	0.912936	−	0.408102i	$-0.133809\pi$
$348$	8.13873	−	6.99109i	0.436282	−	0.374762i
$349$	−8.83183	+	7.41078i	−0.472757	+	0.396690i	−0.847799	−	0.530318i	$-0.822073\pi$
$349$	−8.83183	+	7.41078i	−0.472757	+	0.396690i	0.375042	+	0.927008i	$0.377628\pi$
$350$		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	−0.832484	−	0.554049i	$-0.813082\pi$
$353$	−8.10550	+	6.80132i	−0.431412	+	0.361998i	0.401072	+	0.916047i	$0.368638\pi$
$354$	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	0.999892	+	0.0146804i	$0.00467310\pi$
$359$	9.71352	+	16.8243i	0.512660	+	0.887953i	−0.487232	+	0.873272i	$0.661994\pi$
$360$		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	0.0318889	−	0.999491i	$-0.489848\pi$
$367$	−11.2289	−	4.08698i	−0.586143	−	0.213339i	−0.618032	+	0.786153i	$0.712070\pi$
$368$	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	0.440782	−	0.897614i	$-0.354701\pi$
$373$	26.1774	−	9.52781i	1.35542	−	0.493331i	0.914634	+	0.404283i	$0.132479\pi$
$374$	−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	−0.214953	−	0.976624i	$-0.568960\pi$
$383$	4.85629	−	1.76754i	0.248145	−	0.0903173i	0.463098	+	0.886307i	$0.346738\pi$
$384$	−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	0.108005	−	0.994150i	$-0.465554\pi$
$389$	−8.84157	−	3.21807i	−0.448285	−	0.163162i	−0.556291	+	0.830988i	$0.687776\pi$
$390$		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	0.747435	−	0.664335i	$-0.231285\pi$
$397$	−4.01712	−	6.95786i	−0.201614	−	0.349205i	−0.949048	+	0.315130i	$0.897952\pi$
$398$	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	0.913593	+	0.406630i	$0.133296\pi$
$401$	−1.68169	+	9.53732i	−0.0839794	+	0.476271i	−0.997572	+	0.0696405i	$0.977815\pi$
$402$	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	−0.864997	−	0.501776i	$-0.832680\pi$
$409$	2.41577	−	13.7005i	0.119452	−	0.677446i	0.984449	−	0.175669i	$-0.0562089\pi$
$410$		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	−0.165422	−	0.986223i	$-0.552899\pi$
$419$	−23.8549	−	20.0166i	−1.16539	−	0.977876i	−0.999965	+	0.00834704i	$0.997343\pi$
$420$		0			0
$421$	−14.6085	−	5.31705i	−0.711974	−	0.259137i	−0.0394593	−	0.999221i	$-0.512564\pi$
$421$	−14.6085	−	5.31705i	−0.711974	−	0.259137i	−0.672515	+	0.740084i	$0.734786\pi$
$422$	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	−0.988770	−	0.149445i	$-0.952251\pi$
$439$	−2.32033	−	13.1592i	−0.110743	−	0.628057i	0.878027	−	0.478612i	$-0.158860\pi$
$440$		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	0.508184	−	0.861248i	$-0.330317\pi$
$443$	7.23777	+	2.63433i	0.343877	+	0.125161i	−0.164308	+	0.986409i	$0.552539\pi$
$444$	−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	−0.119805	−	0.992797i	$-0.538227\pi$
$449$	16.9493	−	29.3570i	0.799886	−	1.38544i	0.919690	−	0.392645i	$-0.128440\pi$
$450$		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	−0.0546225	−	0.998507i	$-0.517396\pi$
$457$	19.6509	−	16.4891i	0.919230	−	0.771325i	0.973852	+	0.227182i	$0.0729511\pi$
$458$	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	−0.342585	−	0.939487i	$-0.611302\pi$
$461$	11.2323	−	9.42502i	0.523140	−	0.438967i	0.865725	+	0.500520i	$0.166858\pi$
$462$	58.9746	−	50.6586i	2.74375	−	2.35685i
$463$	0.0945229	−	0.536066i	0.00439285	−	0.0249131i	−0.982533	−	0.186091i	$-0.940418\pi$
$463$	0.0945229	−	0.536066i	0.00439285	−	0.0249131i	0.986925	+	0.161178i	$0.0515292\pi$
$464$	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	0.739759	+	0.672872i	$0.234940\pi$
$467$	20.5859	+	35.6559i	0.952604	+	1.64996i	0.212845	+	0.977086i	$0.431727\pi$
$468$	−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	0.999222	−	0.0394312i	$-0.0125546\pi$
$479$	1.02370	+	5.80571i	0.0467742	+	0.265270i	−0.952448	+	0.304701i	$0.901443\pi$
$480$		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	−0.975554	−	0.219758i	$-0.929473\pi$
$491$	−35.0462	+	12.7558i	−1.58161	+	0.575661i	−0.606060	+	0.795419i	$0.707251\pi$
$492$	−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	0.266911	−	0.963721i	$-0.413997\pi$
$499$	−14.2032	−	11.9179i	−0.635821	−	0.533517i	−0.902732	+	0.430204i	$0.858442\pi$
$500$		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	−0.169987	−	0.985446i	$-0.554373\pi$
$503$	17.2340	−	29.8502i	0.768428	−	1.33096i	0.938415	−	0.345510i	$-0.112294\pi$
$504$	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	−0.718856	−	0.695159i	$-0.755334\pi$
$509$	4.38600	−	24.8743i	0.194406	−	1.10253i	0.913262	−	0.407373i	$-0.133555\pi$
$510$		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	0.963781	−	0.266693i	$-0.0859311\pi$
$521$	5.72752	+	9.92036i	0.250927	+	0.434619i	−0.712854	+	0.701312i	$0.752598\pi$
$522$	−2.75674	−	13.7655i	−0.120659	−	0.602497i
$523$	−14.4630	+	25.0507i	−0.632424	+	1.09539i	0.354631	+	0.935006i	$0.384607\pi$
$523$	−14.4630	+	25.0507i	−0.632424	+	1.09539i	−0.987055	+	0.160384i	$0.948727\pi$
$524$	−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	−0.970115	−	0.242646i	$-0.921985\pi$
$547$	−3.30929	−	18.7679i	−0.141495	−	0.802457i	0.828620	−	0.559811i	$-0.189126\pi$
$548$	−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	0.366281	+	0.930504i	$0.380631\pi$
$557$	−14.6962	+	25.4546i	−0.622700	+	1.07855i	−0.988981	+	0.148044i	$0.952702\pi$
$558$	−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	0.737212	+	0.675662i	$0.236142\pi$
$563$	−4.42830	+	25.1141i	−0.186631	+	1.05844i	−0.923842	+	0.382773i	$0.874969\pi$
$564$	−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	−0.783258	−	0.621697i	$-0.786444\pi$
$569$	−7.32350	+	6.14515i	−0.307017	+	0.257618i	0.476241	+	0.879315i	$0.341999\pi$
$570$		0			0
$571$	5.37062	−	30.4583i	0.224754	−	1.27464i	−0.638402	−	0.769703i	$-0.720404\pi$
$571$	5.37062	−	30.4583i	0.224754	−	1.27464i	0.863156	−	0.504938i	$-0.168485\pi$
$572$	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	0.186400	+	0.982474i	$0.440318\pi$
$577$	−18.1993	+	31.5221i	−0.757647	+	1.31228i	−0.944047	+	0.329810i	$0.893015\pi$
$578$	−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	0.688312	+	0.725415i	$0.258352\pi$
$587$	7.01686	+	39.7946i	0.289617	+	1.64250i	−0.398696	+	0.917083i	$0.630537\pi$
$588$	−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	−0.156602	−	0.987662i	$-0.550054\pi$
$599$	8.76898	−	3.19165i	0.358291	−	0.130407i	0.514893	+	0.857255i	$0.327832\pi$
$600$		0			0
$601$	3.42397	+	19.4183i	0.139667	+	0.792088i	0.971496	+	0.237057i	$0.0761827\pi$
$601$	3.42397	+	19.4183i	0.139667	+	0.792088i	−0.831829	+	0.555032i	$0.812706\pi$
$602$	−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	−0.124221	−	0.992255i	$-0.539643\pi$
$607$	−27.6671	−	23.2154i	−1.12297	−	0.942285i	−0.998751	+	0.0499698i	$0.984087\pi$
$608$	−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	0.902867	−	0.429919i	$-0.141458\pi$
$613$	1.95873	+	3.39263i	0.0791125	+	0.137027i	−0.823755	+	0.566946i	$0.808125\pi$
$614$	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	0.536060	+	0.844180i	$0.319912\pi$
$617$	−6.36880	+	36.1192i	−0.256398	+	1.45411i	−0.792458	+	0.609926i	$0.791199\pi$
$618$	−32.4877	−	11.4011i	−1.30685	−	0.458618i
$619$	8.22380	−	6.90059i	0.330543	−	0.277358i	−0.462378	−	0.886683i	$-0.653004\pi$
$619$	8.22380	−	6.90059i	0.330543	−	0.277358i	0.792921	+	0.609325i	$0.208559\pi$
$620$		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	−0.896476	−	0.443092i	$-0.853881\pi$
$631$	−1.62045	+	2.80670i	−0.0645090	+	0.111733i	0.831967	+	0.554825i	$0.187215\pi$
$632$	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	0.993385	−	0.114834i	$-0.0366337\pi$
$641$	0.522380	+	2.96256i	0.0206328	+	0.117014i	−0.972752	+	0.231849i	$0.925523\pi$
$642$	−49.2162	−	40.3372i	−1.94241	−	1.59198i
$643$	35.5666	−	12.9452i	1.40261	−	0.510509i	0.473659	−	0.880708i	$-0.342933\pi$
$643$	35.5666	−	12.9452i	1.40261	−	0.510509i	0.928952	+	0.370200i	$0.120711\pi$
$644$	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	−0.677230	−	0.735771i	$-0.736820\pi$
$653$	−18.4773	+	6.72520i	−0.723074	+	0.263177i	−0.0458437	+	0.998949i	$0.514598\pi$
$654$	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	0.659338	−	0.751846i	$-0.270836\pi$
$659$	17.4856	+	6.36425i	0.681143	+	0.247916i	0.0218050	+	0.999762i	$0.493059\pi$
$660$		0			0
$661$	−26.9451	−	22.6096i	−1.04804	−	0.879412i	−0.0551562	−	0.998478i	$-0.517566\pi$
$661$	−26.9451	−	22.6096i	−1.04804	−	0.879412i	−0.992886	+	0.119066i	$0.962010\pi$
$662$	−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	−0.916060	−	0.401042i	$-0.868648\pi$
$673$	−17.6455	+	14.8063i	−0.680183	+	0.570741i	0.235877	+	0.971783i	$0.424204\pi$
$674$	−57.7859			−2.22583
$675$		0			0
$676$	72.1928			2.77665
$677$	−9.49900	+	7.97061i	−0.365076	+	0.306335i	−0.806810	−	0.590811i	$-0.798808\pi$
$677$	−9.49900	+	7.97061i	−0.365076	+	0.306335i	0.441734	+	0.897146i	$0.354364\pi$
$678$	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	0.916303	−	0.400487i	$-0.131159\pi$
$683$	2.90926	+	5.03898i	0.111320	+	0.192811i	−0.804983	+	0.593298i	$0.797826\pi$
$684$	−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	0.261860	−	0.965106i	$-0.415664\pi$
$691$	−4.15074	−	1.51075i	−0.157902	−	0.0574715i	−0.419762	+	0.907634i	$0.637886\pi$
$692$	−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	−0.999987	−	0.00504202i	$-0.998395\pi$
$709$	−1.65171	−	9.36728i	−0.0620311	−	0.351796i	0.937956	−	0.346754i	$-0.112716\pi$
$710$		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	−0.987663	−	0.156593i	$-0.949949\pi$
$719$	−9.60533	+	16.6369i	−0.358218	+	0.620452i	0.629445	+	0.777045i	$0.283282\pi$
$720$		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	0.0138826	−	0.999904i	$-0.495581\pi$
$727$	26.9901	−	22.6474i	1.00101	−	0.839944i	0.987124	+	0.159960i	$0.0511364\pi$
$728$	−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	0.894383	+	0.447302i	$0.147615\pi$
$733$	−2.68164	+	15.2083i	−0.0990485	+	0.561732i	−0.993431	+	0.114430i	$0.963496\pi$
$734$	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	−0.961076	−	0.276285i	$-0.910896\pi$
$739$	−6.55875	+	11.3601i	−0.241268	+	0.417888i	0.719808	+	0.694173i	$0.244230\pi$
$740$		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	0.412909	−	0.910772i	$-0.364513\pi$
$743$	−11.2392	−	9.43078i	−0.412325	−	0.345982i	−0.825234	+	0.564790i	$0.808957\pi$
$744$	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	−0.579739	−	0.814802i	$-0.696846\pi$
$751$	−13.7050	+	4.98820i	−0.500101	+	0.182022i	0.0796384	+	0.996824i	$0.474623\pi$
$752$	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	−0.847993	−	0.530008i	$-0.822189\pi$
$761$	−31.9148	+	11.6160i	−1.15691	+	0.421081i	−0.308918	+	0.951089i	$0.599967\pi$
$762$	−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	0.615018	−	0.788513i	$-0.289149\pi$
$769$	−1.51739	−	1.27324i	−0.0547184	−	0.0459142i	−0.669737	+	0.742599i	$0.733593\pi$
$770$		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	−0.259382	+	0.965775i	$0.583519\pi$
$773$	−26.8597	+	46.5224i	−0.966077	+	1.67329i	−0.706694	+	0.707519i	$0.749814\pi$
$774$	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	−0.886370	−	0.462977i	$-0.846781\pi$
$787$	2.94262	−	16.6884i	0.104893	−	0.594877i	0.991263	−	0.131900i	$-0.0421078\pi$
$788$	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	0.640582	−	0.767890i	$-0.278693\pi$
$797$	−0.124410	−	0.104393i	−0.00440684	−	0.00369778i	−0.644988	+	0.764192i	$0.723138\pi$
$798$	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	0.203212	−	0.979135i	$-0.434862\pi$
$821$	−7.75048	−	2.82094i	−0.270493	−	0.0984516i	−0.473706	+	0.880683i	$0.657084\pi$
$822$	−15.9988	+	0.184932i	−0.558021	+	0.00645024i
$823$	−3.30870	−	2.77633i	−0.115334	−	0.0967768i	0.583297	−	0.812259i	$-0.301763\pi$
$823$	−3.30870	−	2.77633i	−0.115334	−	0.0967768i	−0.698631	+	0.715482i	$0.746207\pi$
$824$	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	−0.948108	−	0.317948i	$-0.897006\pi$
$827$	−5.71421	+	9.89730i	−0.198703	+	0.344163i	0.749405	+	0.662111i	$0.230339\pi$
$828$	7.91366	−	0.182974i	0.275019	−	0.00635880i
$829$	−14.4282	−	24.9904i	−0.501113	−	0.867954i	−0.999999	−	0.00128593i	$-0.999591\pi$
$829$	−14.4282	−	24.9904i	−0.501113	−	0.867954i	0.498886	−	0.866668i	$-0.333743\pi$
$830$		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	−0.862714	−	0.505692i	$-0.831237\pi$
$839$	−14.9031	+	12.5052i	−0.514513	+	0.431728i	0.348201	+	0.937420i	$0.386793\pi$
$840$		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	0.354079	−	0.935215i	$-0.384794\pi$
$853$	0.706049	+	0.256981i	0.0241746	+	0.00879885i	−0.329905	+	0.944014i	$0.607017\pi$
$854$	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	−0.879005	−	0.476813i	$-0.841792\pi$
$857$	−6.32595	−	35.8762i	−0.216090	−	1.22551i	0.662914	−	0.748695i	$-0.269319\pi$
$858$	20.5294	−	124.850i	0.700863	−	4.26231i
$859$	−27.3052	+	9.93826i	−0.931640	+	0.339089i	−0.762859	−	0.646564i	$-0.776205\pi$
$859$	−27.3052	+	9.93826i	−0.931640	+	0.339089i	−0.168781	+	0.985654i	$0.553983\pi$
$860$		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	0.977062	−	0.212956i	$-0.0683092\pi$
$877$	27.7487	+	23.2839i	0.937006	+	0.786241i	−0.0400561	+	0.999197i	$0.512754\pi$
$878$	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	−0.940426	−	0.339999i	$-0.889573\pi$
$881$	−5.21700	+	9.03610i	−0.175765	+	0.304434i	0.764661	+	0.644433i	$0.222907\pi$
$882$	−7.21330	+	47.2744i	−0.242885	+	1.59181i
$883$	13.5036	+	23.3890i	0.454434	+	0.787102i	0.998655	−	0.0518393i	$-0.0165084\pi$
$883$	13.5036	+	23.3890i	0.454434	+	0.787102i	−0.544222	+	0.838941i	$0.683175\pi$
$884$	−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	−0.928029	−	0.372509i	$-0.878498\pi$
$887$	2.12762	−	12.0663i	0.0714384	−	0.405148i	0.999467	−	0.0326390i	$-0.0103912\pi$
$888$	−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	0.270365	−	0.962758i	$-0.412856\pi$
$907$	−4.25762	−	1.54965i	−0.141372	−	0.0514552i	−0.411737	+	0.911303i	$0.635078\pi$
$908$	−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	0.993526	+	0.113601i	$0.0362387\pi$
$911$	2.98118	+	16.9071i	0.0987710	+	0.560158i	−0.894755	+	0.446557i	$0.852650\pi$
$912$	−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	0.706185	−	0.708028i	$-0.250415\pi$
$929$	24.1410	+	8.78662i	0.792042	+	0.288280i	0.0858572	+	0.996307i	$0.472637\pi$
$930$		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	0.958305	+	0.285748i	$0.0922419\pi$
$937$	22.2421	+	38.5244i	0.726617	+	1.25854i	−0.231688	+	0.972790i	$0.574425\pi$
$938$	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	0.855764	+	0.517366i	$0.173087\pi$
$941$	−3.84491	+	21.8056i	−0.125341	+	0.710842i	−0.981105	+	0.193476i	$0.938024\pi$
$942$	−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	−0.917501	−	0.397734i	$-0.869797\pi$
$947$	−21.0838	+	17.6914i	−0.685131	+	0.574894i	0.232369	+	0.972628i	$0.425352\pi$
$948$	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	0.821880	−	0.569661i	$-0.192925\pi$
$953$	−2.54376	−	4.40592i	−0.0824005	−	0.142722i	−0.904281	+	0.426939i	$0.859592\pi$
$954$	−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	−0.159211	−	0.987245i	$-0.550895\pi$
$967$	10.9900	−	4.00003i	0.353414	−	0.128632i	0.512626	+	0.858612i	$0.328673\pi$
$968$	−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	−0.841548	−	0.540182i	$-0.818355\pi$
$977$	−35.6014	+	12.9578i	−1.13899	+	0.414558i	−0.297441	+	0.954740i	$0.596133\pi$
$978$	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	0.997881	−	0.0650694i	$-0.0207269\pi$
$983$	53.9418	+	19.6332i	1.72048	+	0.626202i	0.722595	+	0.691271i	$0.242949\pi$
$984$	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	0.997941	−	0.0641332i	$-0.0204282\pi$
$991$	13.9592	+	24.1781i	0.443430	+	0.768043i	−0.554512	+	0.832176i	$0.687095\pi$
$992$	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	−0.371118	−	0.928586i	$-0.621026\pi$
$997$	15.1219	−	12.6888i	0.478916	−	0.401858i	0.850034	+	0.526727i	$0.176581\pi$
$998$	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.76.2	yes	66
5.2	odd	4		675.2.u.e.49.3		132
5.3	odd	4		675.2.u.e.49.20		132
5.4	even	2		675.2.l.f.76.10	✓	66
27.16	even	9	inner	675.2.l.g.151.2	yes	66
135.43	odd	36		675.2.u.e.124.3		132
135.97	odd	36		675.2.u.e.124.20		132
135.124	even	18		675.2.l.f.151.10	yes	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.l.f.76.10	✓	66	5.4	even	2
675.2.l.f.151.10	yes	66	135.124	even	18
675.2.l.g.76.2	yes	66	1.1	even	1	trivial
675.2.l.g.151.2	yes	66	27.16	even	9	inner
675.2.u.e.49.3		132	5.2	odd	4
675.2.u.e.49.20		132	5.3	odd	4
675.2.u.e.124.3		132	135.43	odd	36
675.2.u.e.124.20		132	135.97	odd	36

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

Modular forms

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Database

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