LMFDB - Embedded newform 675.2.l.f.151.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(76,675)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			151.10
Character	$\chi$	$=$	675.151
Dual form			675.2.l.f.76.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70314 + 1.42910i) q^{2} +(-0.320463 + 1.70215i) q^{3} +(0.511048 + 2.89830i) q^{4} +(-2.97833 + 2.44102i) q^{6} +(-0.653660 + 3.70709i) q^{7} +(-1.04829 + 1.81569i) q^{8} +(-2.79461 - 1.09095i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$0.0101000\pi$
$2$	1.70314	+	1.42910i	1.20430	+	1.01053i	0.204803	+	0.978803i	$0.434344\pi$
$3$	−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	$0.307486\pi$
$7$	−0.653660	+	3.70709i	−0.247060	+	1.40115i	−0.815659	+	0.578534i	$0.803625\pi$
$8$	−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	$0.600904\pi$
$13$	−4.69294	+	3.93784i	−1.30159	+	1.09216i	−0.989869	+	0.141986i	$0.954651\pi$
$14$	−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	$-0.277220\pi$
$17$	−1.40339	−	2.43075i	−0.340373	−	0.589544i	−0.984502	+	0.175373i	$0.943887\pi$
$18$	−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	0.964265	−	0.264941i	$-0.0853524\pi$
$23$	−0.155686	−	0.882941i	−0.0324628	−	0.184106i	−0.996728	+	0.0808349i	$0.974241\pi$
$24$	−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	0.972565	−	0.232633i	$-0.0747342\pi$
$37$	1.73247	+	3.00072i	0.284816	+	0.493316i	−0.687749	+	0.725949i	$0.741401\pi$
$38$	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	−0.781717	−	0.623633i	$-0.785656\pi$
$43$	−6.42421	+	2.33822i	−0.979683	+	0.356576i	−0.197966	+	0.980209i	$0.563434\pi$
$44$	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	$-0.859748\pi$
$47$	0.626080	−	3.55068i	0.0913232	−	0.517919i	0.995812	−	0.0914225i	$-0.0291414\pi$
$48$	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	$-0.338572\pi$
$53$	7.07162			0.971362			0.485681	+	0.874136i	$0.338572\pi$
$54$	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	$-0.303644\pi$
$67$	12.1326	−	10.1805i	1.48224	−	1.24375i	0.903754	−	0.428052i	$-0.140800\pi$
$68$	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	$-0.559742\pi$
$73$	6.47229	−	11.2103i	0.757524	−	1.31207i	0.944110	−	0.329632i	$-0.106925\pi$
$74$	−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	0.821221	−	0.570610i	$-0.193293\pi$
$83$	3.66133	+	3.07222i	0.401884	+	0.337220i	−0.419338	+	0.907830i	$0.637738\pi$
$84$	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	−0.627865	−	0.778322i	$-0.716071\pi$
$97$	−5.99345	+	2.18144i	−0.608543	+	0.221491i	0.0193229	+	0.999813i	$0.493849\pi$
$98$	−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	−0.106871	−	0.994273i	$-0.534083\pi$
$103$	−8.40172	−	3.05797i	−0.827846	−	0.301311i	−0.720974	+	0.692962i	$0.756305\pi$
$104$	−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	$-0.794507\pi$
$107$	−16.5248			−1.59751			−0.798754	+	0.601657i	$0.794507\pi$
$108$	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	$-0.0880270\pi$
$113$	16.1944	+	5.89428i	1.52344	+	0.554487i	0.561436	+	0.827520i	$0.310249\pi$
$114$	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	$-0.764795\pi$
$127$	2.40782	−	4.17046i	0.213659	−	0.370069i	0.952857	+	0.303420i	$0.0981284\pi$
$128$	−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	0.496618	−	0.867969i	$-0.334575\pi$
$137$	−3.18283	−	2.67071i	−0.271927	−	0.228174i	−0.768546	+	0.639795i	$0.779019\pi$
$138$	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	−0.171416	−	0.985199i	$-0.554834\pi$
$157$	−11.7281	−	4.26867i	−0.936002	−	0.340677i	−0.764586	+	0.644522i	$0.777056\pi$
$158$	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	$-0.405228\pi$
$163$	7.49060			0.586709			0.293354	+	0.956004i	$0.405228\pi$
$164$	−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	$-0.549813\pi$
$167$	−11.7621	−	4.28105i	−0.910177	−	0.331277i	−0.754324	+	0.656503i	$0.772035\pi$
$168$	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	$-0.415578\pi$
$173$	14.2477	−	5.18574i	1.08323	−	0.394264i	0.821110	+	0.570771i	$0.193355\pi$
$174$	−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	0.978134	−	0.207974i	$-0.0666869\pi$
$193$	−0.168689	−	0.956681i	−0.0121425	−	0.0688634i	−0.990277	+	0.139110i	$0.955576\pi$
$194$	−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	$-0.940022\pi$
$197$	−4.61678	+	7.99649i	−0.328932	+	0.569727i	0.653368	+	0.757040i	$0.273355\pi$
$198$	−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	$-0.636940\pi$
$223$	4.26645	−	24.1963i	0.285703	−	1.62030i	0.702764	−	0.711423i	$-0.251949\pi$
$224$	−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	$-0.420318\pi$
$227$	15.9741	−	5.81410i	1.06024	−	0.385895i	0.812518	+	0.582936i	$0.198096\pi$
$228$	−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	$-0.851010\pi$
$233$	−12.7753	−	22.1275i	−0.836939	−	1.44962i	0.0555035	−	0.998458i	$-0.482324\pi$
$234$	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	−0.500469	−	0.865754i	$-0.666839\pi$
$257$	4.25190	−	3.56777i	0.265226	−	0.222551i	0.765696	+	0.643203i	$0.222395\pi$
$258$	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	$-0.801368\pi$
$263$	2.44722	−	13.8789i	0.150902	−	0.855808i	0.962437	−	0.271504i	$-0.0875211\pi$
$264$	−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	$-0.873540\pi$
$277$	1.27693	−	7.24183i	0.0767233	−	0.435119i	0.998838	−	0.0482019i	$-0.0153491\pi$
$278$	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	−0.630408	−	0.776264i	$-0.717112\pi$
$283$	0.413729	−	0.347160i	0.0245936	−	0.0206365i	0.655002	+	0.755627i	$0.272668\pi$
$284$	−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	$0.113660\pi$
$293$	3.01350	+	17.0904i	0.176051	+	0.998432i	−0.760874	+	0.648900i	$0.775229\pi$
$294$	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	$-0.207260\pi$
$307$	−2.22842	−	3.85973i	−0.127182	−	0.220287i	−0.922584	+	0.385796i	$0.873927\pi$
$308$	−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	−0.434427	−	0.900707i	$-0.643049\pi$
$313$	−3.33057	+	1.21223i	−0.188255	+	0.0685191i	0.246173	+	0.969226i	$0.420827\pi$
$314$	−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	$-0.979274\pi$
$317$	−0.675236	+	3.82945i	−0.0379250	+	0.215084i	0.959956	+	0.280151i	$0.0903847\pi$
$318$	−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	−0.996294	−	0.0860160i	$-0.972586\pi$
$337$	−19.9104	+	16.7068i	−1.08459	+	0.910078i	−0.0882954	+	0.996094i	$0.528142\pi$
$338$	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	$-0.866191\pi$
$347$	−3.62567	−	20.5622i	−0.194636	−	1.10384i	0.718300	−	0.695733i	$-0.244920\pi$
$348$	−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	0.832484	−	0.554049i	$-0.186918\pi$
$353$	8.10550	+	6.80132i	0.431412	+	0.361998i	−0.401072	+	0.916047i	$0.631362\pi$
$354$	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	−0.0318889	−	0.999491i	$-0.510152\pi$
$367$	11.2289	−	4.08698i	0.586143	−	0.213339i	0.618032	+	0.786153i	$0.287930\pi$
$368$	−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	$-0.645299\pi$
$373$	−26.1774	−	9.52781i	−1.35542	−	0.493331i	−0.914634	+	0.404283i	$0.867521\pi$
$374$	−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	$-0.431040\pi$
$383$	−4.85629	−	1.76754i	−0.248145	−	0.0903173i	−0.463098	+	0.886307i	$0.653262\pi$
$384$	−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	−0.747435	−	0.664335i	$-0.768715\pi$
$397$	4.01712	−	6.95786i	0.201614	−	0.349205i	0.949048	+	0.315130i	$0.102048\pi$
$398$	−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	$-0.428847\pi$
$433$	9.22565			0.443356			0.221678	+	0.975120i	$0.428847\pi$
$434$	−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	−0.508184	−	0.861248i	$-0.669683\pi$
$443$	−7.23777	+	2.63433i	−0.343877	+	0.125161i	0.164308	+	0.986409i	$0.447461\pi$
$444$	−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	0.0546225	−	0.998507i	$-0.482604\pi$
$457$	−19.6509	−	16.4891i	−0.919230	−	0.771325i	−0.973852	+	0.227182i	$0.927049\pi$
$458$	−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	0.982533	−	0.186091i	$-0.0595819\pi$
$463$	−0.0945229	−	0.536066i	−0.00439285	−	0.0249131i	−0.986925	+	0.161178i	$0.948471\pi$
$464$	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	$0.568273\pi$
$467$	−20.5859	+	35.6559i	−0.952604	+	1.64996i	−0.739759	+	0.672872i	$0.765060\pi$
$468$	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	$-0.586975\pi$
$487$	−11.9102			−0.539704			−0.269852	+	0.962902i	$0.586975\pi$
$488$	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	$-0.887706\pi$
$503$	−17.2340	−	29.8502i	−0.768428	−	1.33096i	0.169987	−	0.985446i	$-0.445627\pi$
$504$	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	$0.0512732\pi$
$523$	14.4630	+	25.0507i	0.632424	+	1.09539i	−0.354631	+	0.935006i	$0.615393\pi$
$524$	−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	$-0.810874\pi$
$547$	3.30929	−	18.7679i	0.141495	−	0.802457i	0.970115	−	0.242646i	$-0.0780153\pi$
$548$	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	$0.0472976\pi$
$557$	14.6962	+	25.4546i	0.622700	+	1.07855i	−0.366281	+	0.930504i	$0.619369\pi$
$558$	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	$0.125031\pi$
$563$	4.42830	+	25.1141i	0.186631	+	1.05844i	−0.737212	+	0.675662i	$0.763858\pi$
$564$	−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	$0.106985\pi$
$577$	18.1993	+	31.5221i	0.757647	+	1.31228i	−0.186400	+	0.982474i	$0.559682\pi$
$578$	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	$0.369463\pi$
$587$	−7.01686	+	39.7946i	−0.289617	+	1.64250i	−0.688312	+	0.725415i	$0.741648\pi$
$588$	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	$-0.421877\pi$
$593$	11.8336			0.485946			0.242973	+	0.970033i	$0.421877\pi$
$594$	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	0.124221	−	0.992255i	$-0.460357\pi$
$607$	27.6671	−	23.2154i	1.12297	−	0.942285i	0.998751	+	0.0499698i	$0.0159125\pi$
$608$	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	$-0.858542\pi$
$613$	−1.95873	+	3.39263i	−0.0791125	+	0.137027i	0.823755	+	0.566946i	$0.191875\pi$
$614$	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	$0.208801\pi$
$617$	6.36880	+	36.1192i	0.256398	+	1.45411i	−0.536060	+	0.844180i	$0.680088\pi$
$618$	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	−0.473659	−	0.880708i	$-0.657067\pi$
$643$	−35.5666	−	12.9452i	−1.40261	−	0.510509i	−0.928952	+	0.370200i	$0.879289\pi$
$644$	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	$-0.416665\pi$
$647$	13.1670			0.517650			0.258825	+	0.965924i	$0.416665\pi$
$648$	−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	$-0.263180\pi$
$653$	18.4773	+	6.72520i	0.723074	+	0.263177i	0.0458437	+	0.998949i	$0.485402\pi$
$654$	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	0.916060	−	0.401042i	$-0.131352\pi$
$673$	17.6455	+	14.8063i	0.680183	+	0.570741i	−0.235877	+	0.971783i	$0.575796\pi$
$674$	−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	$-0.201192\pi$
$677$	9.49900	+	7.97061i	0.365076	+	0.306335i	−0.441734	+	0.897146i	$0.645636\pi$
$678$	−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	$-0.868841\pi$
$683$	−2.90926	+	5.03898i	−0.111320	+	0.192811i	0.804983	+	0.593298i	$0.202174\pi$
$684$	−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	−0.0138826	−	0.999904i	$-0.504419\pi$
$727$	−26.9901	−	22.6474i	−1.00101	−	0.839944i	−0.987124	+	0.159960i	$0.948864\pi$
$728$	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	$0.0365040\pi$
$733$	2.68164	+	15.2083i	0.0990485	+	0.561732i	−0.894383	+	0.447302i	$0.852385\pi$
$734$	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	−0.412909	−	0.910772i	$-0.635487\pi$
$743$	11.2392	−	9.43078i	0.412325	−	0.345982i	0.825234	+	0.564790i	$0.191043\pi$
$744$	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	$-0.420948\pi$
$757$	13.5259			0.491607			0.245803	+	0.969320i	$0.420948\pi$
$758$	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	$0.250186\pi$
$773$	26.8597	+	46.5224i	0.966077	+	1.67329i	0.259382	+	0.965775i	$0.416481\pi$
$774$	34.2437	+	30.1098i	1.23086	+	1.08227i
$775$		0			0
$776$	2.32206	−	13.1691i	0.0833571

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.70314 + 1.42910i) q^{2} +(-0.320463 + 1.70215i) q^{3} +(0.511048 + 2.89830i) q^{4} +(-2.97833 + 2.44102i) q^{6} +(-0.653660 + 3.70709i) q^{7} +(-1.04829 + 1.81569i) q^{8} +(-2.79461 - 1.09095i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 66 * q - 6 * q^2 - 6 * q^6 - 6 * q^7 - 12 * q^8 - 6 * q^9	\( 66 q - 6 q^{2} - 6 q^{6} - 6 q^{7} - 12 q^{8} - 6 q^{9} + 15 q^{11} - 18 q^{12} + 15 q^{14} + 18 q^{16} - 30 q^{17} + 12 q^{18} + 12 q^{19} + 12 q^{21} + 45 q^{22} - 36 q^{23} - 39 q^{24} + 6 q^{26} - 51 q^{27} + 36 q^{28} - 15 q^{29} + 3 q^{31} - 27 q^{32} + 3 q^{33} + 30 q^{36} - 6 q^{37} + 12 q^{38} - 15 q^{39} + 39 q^{41} - 48 q^{42} - 12 q^{43} + 51 q^{44} + 9 q^{46} - 30 q^{47} + 132 q^{48} - 6 q^{49} - 9 q^{52} + 24 q^{53} + 75 q^{54} + 144 q^{56} - 33 q^{57} - 27 q^{58} + 45 q^{59} - 54 q^{61} - 66 q^{62} + 120 q^{63} - 24 q^{64} + 48 q^{66} - 9 q^{67} + 69 q^{68} + 51 q^{69} - 15 q^{71} - 9 q^{72} + 15 q^{73} + 96 q^{74} - 48 q^{76} + 36 q^{77} + 18 q^{78} + 48 q^{79} - 54 q^{81} + 36 q^{82} - 30 q^{83} + 57 q^{84} - 111 q^{86} + 33 q^{87} - 36 q^{88} - 12 q^{89} + 9 q^{91} + 219 q^{92} - 63 q^{93} + 36 q^{94} - 249 q^{96} - 57 q^{97} - 75 q^{98} - 48 q^{99}+O(q^{100}) \) 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

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