LMFDB - Embedded newform 441.2.h.e.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	441.373
Dual form			441.2.h.e.214.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.879385 q^{2} +(-1.70574 + 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})$	\(q-0.879385 q^{2} +(-1.70574 + 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +(-0.592396 - 1.02606i) q^{10} +(-0.826352 + 1.43128i) q^{11} +(2.09240 - 0.368946i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} -0.0418891 q^{16} +(0.233956 + 0.405223i) q^{17} +(-2.47906 + 0.902302i) q^{18} +(-1.61334 + 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(-4.84002 + 0.853427i) q^{24} +(1.59240 - 2.75811i) q^{25} +(1.48158 - 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(1.31908 + 1.57202i) q^{30} -9.23442 q^{31} -5.63816 q^{32} +(0.979055 - 2.68993i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 + 7.99724i) q^{37} +(1.41875 - 2.45734i) q^{38} +(1.99613 - 5.48432i) q^{39} +(1.91147 + 3.31077i) q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 - 1.75573i) q^{44} +(3.09627 + 2.59808i) q^{45} +(3.93242 + 6.81115i) q^{46} -9.35504 q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(-0.520945 - 0.620838i) q^{51} +(2.06670 - 3.57964i) q^{52} +(0.286989 + 0.497079i) q^{53} +(3.95723 - 2.28471i) q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} +10.3969 q^{59} +(1.84002 + 2.19285i) q^{60} -7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} -4.53983 q^{65} +(-0.860967 + 2.36549i) q^{66} +0.596267 q^{67} +(-0.286989 - 0.497079i) q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(7.99912 - 2.91144i) q^{72} +(1.02481 + 1.77503i) q^{73} +(4.06031 - 7.03266i) q^{74} +(-1.88666 + 5.18355i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} -2.40373 q^{79} +(-0.0282185 - 0.0488759i) q^{80} +(6.89440 - 5.78509i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(6.97906 + 8.31731i) q^{87} +(-2.34477 + 4.06126i) q^{88} +(4.54323 - 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(15.7515 - 2.77741i) q^{93} +8.22668 q^{94} -4.34730 q^{95} +(9.61721 - 1.69577i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} - 9 q^{24} + 6 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} + 6 q^{31} + 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} + 6 q^{38} + 36 q^{39} - 9 q^{40} + 3 q^{43} - 15 q^{44} - 9 q^{45} - 6 q^{47} + 6 q^{50} - 21 q^{52} - 6 q^{53} - 27 q^{54} - 9 q^{57} + 9 q^{58} + 6 q^{59} - 9 q^{60} - 12 q^{61} + 60 q^{62} + 24 q^{64} + 30 q^{65} + 18 q^{66} - 24 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 9 q^{72} - 21 q^{73} + 30 q^{74} - 18 q^{75} + 15 q^{76} + 54 q^{78} - 42 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} + 45 q^{87} - 27 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} + 54 q^{93} + 36 q^{94} - 24 q^{95} + 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 - 9 * q^24 + 6 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 + 6 * q^31 + 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 + 6 * q^38 + 36 * q^39 - 9 * q^40 + 3 * q^43 - 15 * q^44 - 9 * q^45 - 6 * q^47 + 6 * q^50 - 21 * q^52 - 6 * q^53 - 27 * q^54 - 9 * q^57 + 9 * q^58 + 6 * q^59 - 9 * q^60 - 12 * q^61 + 60 * q^62 + 24 * q^64 + 30 * q^65 + 18 * q^66 - 24 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 9 * q^72 - 21 * q^73 + 30 * q^74 - 18 * q^75 + 15 * q^76 + 54 * q^78 - 42 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 + 45 * q^87 - 27 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 + 54 * q^93 + 36 * q^94 - 24 * q^95 + 27 * q^96 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.879385			−0.621819			−0.310910	−	0.950439i	$-0.600634\pi$
$2$	−0.879385			−0.621819			−0.310910	+	0.950439i	$0.600634\pi$
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$3$	−1.70574	+	0.300767i	−0.984808	+	0.173648i
$4$	−1.22668			−0.613341
$5$	0.673648	+	1.16679i	0.301265	+	0.521806i	0.976423	−	0.215867i	$-0.0692579\pi$
$5$	0.673648	+	1.16679i	0.301265	+	0.521806i	−0.675158	+	0.737673i	$0.735925\pi$
$6$	1.50000	−	0.264490i	0.612372	−	0.107978i
$7$		0			0
$7$		0			0
$8$	2.83750			1.00321
$9$	2.81908	−	1.02606i	0.939693	−	0.342020i
$10$	−0.592396	−	1.02606i	−0.187332	−	0.324469i
$11$	−0.826352	+	1.43128i	−0.249154	+	0.431548i	−0.963291	−	0.268458i	$-0.913486\pi$
$11$	−0.826352	+	1.43128i	−0.249154	+	0.431548i	0.714137	+	0.700006i	$0.246819\pi$
$12$	2.09240	−	0.368946i	0.604023	−	0.106506i
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	−0.999301	−	0.0373813i	$-0.988098\pi$
$13$	−1.68479	+	2.91815i	−0.467277	+	0.809348i	0.532024	+	0.846729i	$0.321432\pi$
$14$		0			0
$15$	−1.50000	−	1.78763i	−0.387298	−	0.461564i
$16$	−0.0418891			−0.0104723
$17$	0.233956	+	0.405223i	0.0567426	+	0.0982810i	0.893001	−	0.450054i	$-0.148595\pi$
$17$	0.233956	+	0.405223i	0.0567426	+	0.0982810i	−0.836259	+	0.548335i	$0.815262\pi$
$18$	−2.47906	+	0.902302i	−0.584319	+	0.212675i
$19$	−1.61334	+	2.79439i	−0.370126	+	0.641077i	−0.989585	−	0.143953i	$-0.954019\pi$
$19$	−1.61334	+	2.79439i	−0.370126	+	0.641077i	0.619459	+	0.785029i	$0.287352\pi$
$20$	−0.826352	−	1.43128i	−0.184778	−	0.320045i
$21$		0			0
$22$	0.726682	−	1.25865i	0.154929	−	0.268345i
$23$	−4.47178	−	7.74535i	−0.932431	−	1.61502i	−0.779152	−	0.626835i	$-0.784350\pi$
$23$	−4.47178	−	7.74535i	−0.932431	−	1.61502i	−0.153279	−	0.988183i	$-0.548983\pi$
$24$	−4.84002	+	0.853427i	−0.987965	+	0.174205i
$25$	1.59240	−	2.75811i	0.318479	−	0.551622i
$26$	1.48158	−	2.56617i	0.290562	−	0.503268i
$27$	−4.50000	+	2.59808i	−0.866025	+	0.500000i
$28$		0			0
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	−0.995239	−	0.0974595i	$-0.968928\pi$
$29$	−3.13429	−	5.42874i	−0.582022	−	1.00809i	0.413217	−	0.910632i	$-0.364405\pi$
$30$	1.31908	+	1.57202i	0.240830	+	0.287010i
$31$	−9.23442			−1.65855			−0.829276	−	0.558840i	$-0.811247\pi$
$31$	−9.23442			−1.65855			−0.829276	+	0.558840i	$0.811247\pi$
$32$	−5.63816			−0.996695
$33$	0.979055	−	2.68993i	0.170432	−	0.468257i
$34$	−0.205737	−	0.356347i	−0.0352836	−	0.0611130i
$35$		0			0
$36$	−3.45811	+	1.25865i	−0.576352	+	0.209775i
$37$	−4.61721	+	7.99724i	−0.759065	+	1.31474i	0.184263	+	0.982877i	$0.441010\pi$
$37$	−4.61721	+	7.99724i	−0.759065	+	1.31474i	−0.943328	+	0.331862i	$0.892323\pi$
$38$	1.41875	−	2.45734i	0.230151	−	0.398634i
$39$	1.99613	−	5.48432i	0.319637	−	0.878194i
$40$	1.91147	+	3.31077i	0.302231	+	0.523479i
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	−0.701536	−	0.712634i	$-0.747502\pi$
$41$	1.70574	−	2.95442i	0.266391	−	0.461403i	0.967927	+	0.251231i	$0.0808353\pi$
$42$		0			0
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	0.983747	−	0.179558i	$-0.0574668\pi$
$43$	2.20574	+	3.82045i	0.336372	+	0.582613i	−0.647376	+	0.762171i	$0.724133\pi$
$44$	1.01367	−	1.75573i	0.152817	−	0.264686i
$45$	3.09627	+	2.59808i	0.461564	+	0.387298i
$46$	3.93242	+	6.81115i	0.579803	+	1.00425i
$47$	−9.35504			−1.36457			−0.682286	−	0.731085i	$-0.739014\pi$
$47$	−9.35504			−1.36457			−0.682286	+	0.731085i	$0.739014\pi$
$48$	0.0714517	−	0.0125989i	0.0103132	−	0.00181849i
$49$		0			0
$50$	−1.40033	+	2.42544i	−0.198037	+	0.343009i
$51$	−0.520945	−	0.620838i	−0.0729468	−	0.0869346i
$52$	2.06670	−	3.57964i	0.286600	−	0.496406i
$53$	0.286989	+	0.497079i	0.0394210	+	0.0682791i	0.885063	−	0.465472i	$-0.154115\pi$
$53$	0.286989	+	0.497079i	0.0394210	+	0.0682791i	−0.845642	+	0.533751i	$0.820782\pi$
$54$	3.95723	−	2.28471i	0.538511	−	0.310910i
$55$	−2.22668			−0.300246
$56$		0			0
$57$	1.91147	−	5.25173i	0.253181	−	0.695609i
$58$	2.75624	+	4.77396i	0.361913	+	0.626851i
$59$	10.3969			1.35356			0.676782	−	0.736183i	$-0.263374\pi$
$59$	10.3969			1.35356			0.676782	+	0.736183i	$0.263374\pi$
$60$	1.84002	+	2.19285i	0.237546	+	0.283096i
$61$	−7.63816			−0.977966			−0.488983	−	0.872293i	$-0.662632\pi$
$61$	−7.63816			−0.977966			−0.488983	+	0.872293i	$0.662632\pi$
$62$	8.12061			1.03132
$63$		0			0
$64$	5.04189			0.630236
$65$	−4.53983			−0.563097
$66$	−0.860967	+	2.36549i	−0.105978	+	0.291171i
$67$	0.596267			0.0728456			0.0364228	−	0.999336i	$-0.488404\pi$
$67$	0.596267			0.0728456			0.0364228	+	0.999336i	$0.488404\pi$
$68$	−0.286989	−	0.497079i	−0.0348025	−	0.0602797i
$69$	9.95723	+	11.8666i	1.19871	+	1.42857i
$70$		0			0
$71$	−0.554378			−0.0657925			−0.0328963	−	0.999459i	$-0.510473\pi$
$71$	−0.554378			−0.0657925			−0.0328963	+	0.999459i	$0.510473\pi$
$72$	7.99912	−	2.91144i	0.942706	−	0.343117i
$73$	1.02481	+	1.77503i	0.119946	+	0.207752i	0.919746	−	0.392514i	$-0.128395\pi$
$73$	1.02481	+	1.77503i	0.119946	+	0.207752i	−0.799800	+	0.600266i	$0.795061\pi$
$74$	4.06031	−	7.03266i	0.472001	−	0.817530i
$75$	−1.88666	+	5.18355i	−0.217853	+	0.598545i
$76$	1.97906	−	3.42782i	0.227013	−	0.393198i
$77$		0			0
$78$	−1.75537	+	4.82283i	−0.198756	+	0.546078i
$79$	−2.40373			−0.270441			−0.135221	−	0.990816i	$-0.543174\pi$
$79$	−2.40373			−0.270441			−0.135221	+	0.990816i	$0.543174\pi$
$80$	−0.0282185	−	0.0488759i	−0.00315492	−	0.00546449i
$81$	6.89440	−	5.78509i	0.766044	−	0.642788i
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	−0.901187	−	0.433431i	$-0.857303\pi$
$83$	−7.52481	−	13.0334i	−0.825956	−	1.43060i	0.0752309	−	0.997166i	$-0.476031\pi$
$84$		0			0
$85$	−0.315207	+	0.545955i	−0.0341891	+	0.0592172i
$86$	−1.93969	−	3.35965i	−0.209162	−	0.362280i
$87$	6.97906	+	8.31731i	0.748233	+	0.891710i
$88$	−2.34477	+	4.06126i	−0.249953	+	0.432932i
$89$	4.54323	−	7.86911i	0.481582	−	0.834124i	−0.518195	−	0.855263i	$-0.673396\pi$
$89$	4.54323	−	7.86911i	0.481582	−	0.834124i	0.999777	+	0.0211385i	$0.00672911\pi$
$90$	−2.72281	−	2.28471i	−0.287010	−	0.240830i
$91$		0			0
$92$	5.48545	+	9.50108i	0.571898	+	0.990556i
$93$	15.7515	−	2.77741i	1.63335	−	0.288004i
$94$	8.22668			0.848517
$95$	−4.34730			−0.446023
$96$	9.61721	−	1.69577i	0.981553	−	0.173074i
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	0.813788	−	0.581161i	$-0.197402\pi$
$97$	−0.949493	−	1.64457i	−0.0964064	−	0.166981i	−0.910195	+	0.414181i	$0.864068\pi$
$98$		0			0
$99$	−0.860967	+	4.88279i	−0.0865304	+	0.490738i
$100$	−1.95336	+	3.38332i	−0.195336	+	0.338332i
$101$	−0.854570	+	1.48016i	−0.0850329	+	0.147281i	−0.905405	−	0.424548i	$-0.860433\pi$
$101$	−0.854570	+	1.48016i	−0.0850329	+	0.147281i	0.820372	+	0.571830i	$0.193766\pi$
$102$	0.458111	+	0.545955i	0.0453597	+	0.0540576i
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	0.762381	−	0.647128i	$-0.224030\pi$
$103$	−1.81908	−	3.15074i	−0.179239	−	0.310451i	−0.941620	+	0.336677i	$0.890697\pi$
$104$	−4.78059	+	8.28023i	−0.468776	+	0.811943i
$105$		0			0
$106$	−0.252374	−	0.437124i	−0.0245127	−	0.0424573i
$107$	−3.56418	+	6.17334i	−0.344562	+	0.596799i	−0.985274	−	0.170982i	$-0.945306\pi$
$107$	−3.56418	+	6.17334i	−0.344562	+	0.596799i	0.640712	+	0.767781i	$0.278639\pi$
$108$	5.52007	−	3.18701i	0.531169	−	0.306670i
$109$	−0.201867	−	0.349643i	−0.0193353	−	0.0334898i	0.856196	−	0.516651i	$-0.172822\pi$
$109$	−0.201867	−	0.349643i	−0.0193353	−	0.0334898i	−0.875531	+	0.483162i	$0.839488\pi$
$110$	1.95811			0.186699
$111$	5.47044	−	15.0299i	0.519231	−	1.42658i
$112$		0			0
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	0.300320	+	0.953839i	$0.402907\pi$
$113$	−7.18479	+	12.4444i	−0.675888	+	1.17067i	−0.976208	+	0.216835i	$0.930427\pi$
$114$	−1.68092	+	4.61830i	−0.157433	+	0.432543i
$115$	6.02481	−	10.4353i	0.561817	−	0.973095i
$116$	3.84477	+	6.65934i	0.356978	+	0.618304i
$117$	−1.75537	+	9.95518i	−0.162284	+	0.920357i
$118$	−9.14290			−0.841672
$119$		0			0
$120$	−4.25624	−	5.07239i	−0.388540	−	0.463044i
$121$	4.13429	+	7.16079i	0.375844	+	0.650981i
$122$	6.71688			0.608118
$123$	−2.02094	+	5.55250i	−0.182222	+	0.500652i
$124$	11.3277			1.01726
$125$	11.0273			0.986315
$126$		0			0
$127$	−20.7716			−1.84318			−0.921589	−	0.388167i	$-0.873108\pi$
$127$	−20.7716			−1.84318			−0.921589	+	0.388167i	$0.873108\pi$
$128$	6.84255			0.604802
$129$	−4.91147	−	5.85327i	−0.432431	−	0.515351i
$130$	3.99226			0.350144
$131$	−3.58260	−	6.20524i	−0.313013	−	0.542154i	0.666000	−	0.745952i	$-0.268005\pi$
$131$	−3.58260	−	6.20524i	−0.313013	−	0.542154i	−0.979013	+	0.203797i	$0.934672\pi$
$132$	−1.20099	+	3.29969i	−0.104533	+	0.287201i
$133$		0			0
$134$	−0.524348			−0.0452968
$135$	−6.06283	−	3.50038i	−0.521806	−	0.301265i
$136$	0.663848	+	1.14982i	0.0569245	+	0.0985961i
$137$	−1.28446	+	2.22475i	−0.109739	+	0.190074i	−0.915665	−	0.401943i	$-0.868335\pi$
$137$	−1.28446	+	2.22475i	−0.109739	+	0.190074i	0.805925	+	0.592017i	$0.201668\pi$
$138$	−8.75624	−	10.4353i	−0.745381	−	0.888310i
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	−0.966272	−	0.257523i	$-0.917094\pi$
$139$	−3.06670	+	5.31169i	−0.260114	+	0.450531i	0.706158	+	0.708055i	$0.250427\pi$
$140$		0			0
$141$	15.9572	−	2.81369i	1.34384	−	0.236956i
$142$	0.487511			0.0409111
$143$	−2.78446	−	4.82283i	−0.232848	−	0.403305i
$144$	−0.118089	+	0.0429807i	−0.00984071	+	0.00358173i
$145$	4.22281	−	7.31412i	0.350685	−	0.607405i
$146$	−0.901207	−	1.56094i	−0.0745844	−	0.129184i
$147$		0			0
$148$	5.66385	−	9.81007i	0.465565	−	0.806383i
$149$	−0.215537	−	0.373321i	−0.0176575	−	0.0305837i	0.857062	−	0.515214i	$-0.172288\pi$
$149$	−0.215537	−	0.373321i	−0.0176575	−	0.0305837i	−0.874719	+	0.484630i	$0.838954\pi$
$150$	1.65910	−	4.55834i	0.135465	−	0.372187i
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	−0.811375	−	0.584526i	$-0.801280\pi$
$151$	1.23530	−	2.13960i	0.100527	−	0.174118i	0.911902	+	0.410408i	$0.134614\pi$
$152$	−4.57785	+	7.92907i	−0.371313	+	0.643132i
$153$	1.07532	+	0.902302i	0.0869346	+	0.0729468i
$154$		0			0
$155$	−6.22075	−	10.7747i	−0.499663	−	0.865441i
$156$	−2.44862	+	6.72752i	−0.196046	+	0.538632i
$157$	−10.1334			−0.808734			−0.404367	−	0.914597i	$-0.632508\pi$
$157$	−10.1334			−0.808734			−0.404367	+	0.914597i	$0.632508\pi$
$158$	2.11381			0.168166
$159$	−0.639033	−	0.761570i	−0.0506786	−	0.0603964i
$160$	−3.79813	−	6.57856i	−0.300269	−	0.520081i
$161$		0			0
$162$	−6.06283	+	5.08732i	−0.476341	+	0.399698i
$163$	1.29813	−	2.24843i	0.101678	−	0.176111i	−0.810698	−	0.585464i	$-0.800912\pi$
$163$	1.29813	−	2.24843i	0.101678	−	0.176111i	0.912376	+	0.409353i	$0.134246\pi$
$164$	−2.09240	+	3.62414i	−0.163389	+	0.282998i
$165$	3.79813	−	0.669713i	0.295684	−	0.0521371i
$166$	6.61721	+	11.4613i	0.513595	+	0.889573i
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.0656422	+	0.997843i	$0.520910\pi$
$167$	−11.5915	+	20.0771i	−0.896979	+	1.55361i	−0.831337	+	0.555769i	$0.812424\pi$
$168$		0			0
$169$	0.822948	+	1.42539i	0.0633037	+	0.109645i
$170$	0.277189	−	0.480105i	0.0212594	−	0.0368224i
$171$	−1.68092	+	9.53298i	−0.128543	+	0.729005i
$172$	−2.70574	−	4.68647i	−0.206311	−	0.357340i
$173$	4.75196			0.361285			0.180643	−	0.983549i	$-0.442182\pi$
$173$	4.75196			0.361285			0.180643	+	0.983549i	$0.442182\pi$
$174$	−6.13728	−	7.31412i	−0.465266	−	0.554482i
$175$		0			0
$176$	0.0346151	−	0.0599551i	0.00260921	−	0.00451929i
$177$	−17.7344	+	3.12706i	−1.33300	+	0.235044i
$178$	−3.99525	+	6.91998i	−0.299457	+	0.518674i
$179$	4.26604	+	7.38901i	0.318859	+	0.552280i	0.980250	−	0.197761i	$-0.0633670\pi$
$179$	4.26604	+	7.38901i	0.318859	+	0.552280i	−0.661391	+	0.750041i	$0.730034\pi$
$180$	−3.79813	−	3.18701i	−0.283096	−	0.237546i
$181$	17.2344			1.28102			0.640512	−	0.767948i	$-0.278722\pi$
$181$	17.2344			1.28102			0.640512	+	0.767948i	$0.278722\pi$
$182$		0			0
$183$	13.0287	−	2.29731i	0.963108	−	0.169822i
$184$	−12.6887	−	21.9774i	−0.935421	−	1.62020i
$185$	−12.4415			−0.914718
$186$	−13.8516	+	2.44242i	−1.01565	+	0.179087i
$187$	−0.773318			−0.0565506
$188$	11.4757			0.836948
$189$		0			0
$190$	3.82295			0.277346
$191$	12.9094			0.934092			0.467046	−	0.884233i	$-0.345318\pi$
$191$	12.9094			0.934092			0.467046	+	0.884233i	$0.345318\pi$
$192$	−8.60014	+	1.51644i	−0.620661	+	0.109439i
$193$	−0.638156			−0.0459355			−0.0229677	−	0.999736i	$-0.507311\pi$
$193$	−0.638156			−0.0459355			−0.0229677	+	0.999736i	$0.507311\pi$
$194$	0.834970	+	1.44621i	0.0599473	+	0.103832i
$195$	7.74376	−	1.36543i	0.554542	−	0.0977807i
$196$		0			0
$197$	11.4456			0.815467			0.407733	−	0.913101i	$-0.366319\pi$
$197$	11.4456			0.815467			0.407733	+	0.913101i	$0.366319\pi$
$198$	0.757122	−	4.29385i	0.0538063	−	0.305151i
$199$	−1.81908	−	3.15074i	−0.128951	−	0.223350i	0.794319	−	0.607500i	$-0.207828\pi$
$199$	−1.81908	−	3.15074i	−0.128951	−	0.223350i	−0.923270	+	0.384151i	$0.874494\pi$
$200$	4.51842	−	7.82613i	0.319500	−	0.553391i
$201$	−1.01707	+	0.179338i	−0.0717389	+	0.0126495i
$202$	0.751497	−	1.30163i	0.0528751	−	0.0915824i
$203$		0			0
$204$	0.639033	+	0.761570i	0.0447413	+	0.0533206i
$205$	4.59627			0.321017
$206$	1.59967	+	2.77071i	0.111454	+	0.193045i
$207$	−20.5535	−	17.2464i	−1.42857	−	1.19871i
$208$	0.0705744	−	0.122238i	0.00489345	−	0.00847571i
$209$	−2.66637	−	4.61830i	−0.184437	−	0.319454i
$210$		0			0
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	−0.948668	−	0.316273i	$-0.897569\pi$
$211$	−2.91147	+	5.04282i	−0.200434	+	0.347162i	0.748234	+	0.663435i	$0.230902\pi$
$212$	−0.352044	−	0.609758i	−0.0241785	−	0.0418784i
$213$	0.945622	−	0.166739i	0.0647930	−	0.0114248i
$214$	3.13429	−	5.42874i	0.214255	−	0.371101i
$215$	−2.97178	+	5.14728i	−0.202674	+	0.351041i
$216$	−12.7687	+	7.37203i	−0.868802	+	0.501603i
$217$		0			0
$218$	0.177519	+	0.307471i	0.0120231	+	0.0208246i
$219$	−2.28194	−	2.71951i	−0.154199	−	0.183767i
$220$	2.73143			0.184153
$221$	−1.57667			−0.106058
$222$	−4.81062	+	13.2171i	−0.322868	+	0.887072i
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	0.959905	−	0.280327i	$-0.0904428\pi$
$223$	3.54189	+	6.13473i	0.237182	+	0.410812i	−0.722722	+	0.691139i	$0.757109\pi$
$224$		0			0
$225$	1.65910	−	9.40923i	0.110607	−	0.627282i
$226$	6.31820	−	10.9434i	0.420280	−	0.727947i
$227$	−5.97178	+	10.3434i	−0.396361	+	0.686517i	−0.993274	−	0.115789i	$-0.963060\pi$
$227$	−5.97178	+	10.3434i	−0.396361	+	0.686517i	0.596913	+	0.802306i	$0.296394\pi$
$228$	−2.34477	+	6.44220i	−0.155286	+	0.426645i
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	−0.995484	−	0.0949315i	$-0.969737\pi$
$229$	−8.77631	−	15.2010i	−0.579955	−	1.00451i	0.415529	−	0.909580i	$-0.363597\pi$
$230$	−5.29813	+	9.17664i	−0.349349	+	0.605089i
$231$		0			0
$232$	−8.89352	−	15.4040i	−0.583888	−	1.01132i
$233$	−8.12701	+	14.0764i	−0.532418	+	0.922175i	0.466865	+	0.884328i	$0.345383\pi$
$233$	−8.12701	+	14.0764i	−0.532418	+	0.922175i	−0.999284	+	0.0378470i	$0.987950\pi$
$234$	1.54364	−	8.75444i	0.100911	−	0.572296i
$235$	−6.30200	−	10.9154i	−0.411097	−	0.712042i
$236$	−12.7537			−0.830196
$237$	4.10014	−	0.722965i	0.266333	−	0.0469616i
$238$		0			0
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	−0.511565	−	0.859244i	$-0.670934\pi$
$239$	7.54963	−	13.0763i	0.488345	−	0.845838i	0.999910	+	0.0134062i	$0.00426745\pi$
$240$	0.0628336	+	0.0748822i	0.00405589	+	0.00483362i
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	0.496320	+	0.868140i	$0.334684\pi$
$241$	−7.81908	+	13.5430i	−0.503671	+	0.872384i	−0.999991	+	0.00424420i	$0.998649\pi$
$242$	−3.63563	−	6.29710i	−0.233707	−	0.404793i
$243$	−10.0201	+	11.9415i	−0.642788	+	0.766044i
$244$	9.36959			0.599826
$245$		0			0
$246$	1.77719	−	4.88279i	0.113309	−	0.311315i
$247$	−5.43629	−	9.41593i	−0.345903	−	0.599121i
$248$	−26.2026			−1.66387
$249$	16.7554	+	19.9683i	1.06183	+	1.26544i
$250$	−9.69728			−0.613310
$251$	−19.0651			−1.20338			−0.601690	−	0.798730i	$-0.705506\pi$
$251$	−19.0651			−1.20338			−0.601690	+	0.798730i	$0.705506\pi$
$252$		0			0
$253$	14.7811			0.929277
$254$	18.2662			1.14612
$255$	0.373455	−	1.02606i	0.0233867	−	0.0642544i
$256$	−16.1010			−1.00631
$257$	13.2909	+	23.0204i	0.829061	+	1.43598i	0.898776	+	0.438409i	$0.144458\pi$
$257$	13.2909	+	23.0204i	0.829061	+	1.43598i	−0.0697146	+	0.997567i	$0.522209\pi$
$258$	4.31908	+	5.14728i	0.268894	+	0.320455i
$259$		0			0
$260$	5.56893			0.345370
$261$	−14.4060	−	12.0881i	−0.891710	−	0.748233i
$262$	3.15048	+	5.45680i	0.194637	+	0.337122i
$263$	0.367059	−	0.635765i	0.0226338	−	0.0392029i	−0.854487	−	0.519473i	$-0.826128\pi$
$263$	0.367059	−	0.635765i	0.0226338	−	0.0392029i	0.877120	+	0.480270i	$0.159461\pi$
$264$	2.77807	−	7.63267i	0.170978	−	0.469759i
$265$	−0.386659	+	0.669713i	−0.0237523	+	0.0411402i
$266$		0			0
$267$	−5.38279	+	14.7891i	−0.329421	+	0.905078i
$268$	−0.731429			−0.0446792
$269$	−10.4251	−	18.0569i	−0.635632	−	1.10095i	−0.986381	−	0.164478i	$-0.947406\pi$
$269$	−10.4251	−	18.0569i	−0.635632	−	1.10095i	0.350749	−	0.936470i	$-0.385927\pi$
$270$	5.33157	+	3.07818i	0.324469	+	0.187332i
$271$	3.47906	−	6.02590i	0.211338	−	0.366047i	−0.740796	−	0.671730i	$-0.765551\pi$
$271$	3.47906	−	6.02590i	0.211338	−	0.366047i	0.952133	+	0.305683i	$0.0988847\pi$
$272$	−0.00980018	−	0.0169744i	−0.000594223	−	0.00102922i
$273$		0			0
$274$	1.12954	−	1.95642i	0.0682379	−	0.118191i
$275$	2.63176	+	4.55834i	0.158701	+	0.274878i
$276$	−12.2144	−	14.5565i	−0.735218	−	0.876198i
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	0.462138	+	0.886808i	$0.347083\pi$
$277$	−8.93629	+	15.4781i	−0.536930	+	0.929989i	−0.999067	+	0.0431811i	$0.986251\pi$
$278$	2.69681	−	4.67102i	0.161744	−	0.280149i
$279$	−26.0326	+	9.47508i	−1.55853	+	0.567258i
$280$		0			0
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	−0.979159	−	0.203095i	$-0.934900\pi$
$281$	−11.1552	−	19.3214i	−0.665465	−	1.15262i	0.313694	−	0.949524i	$-0.398433\pi$
$282$	−14.0326	+	2.47432i	−0.835627	+	0.147344i
$283$	18.5945			1.10533			0.552665	−	0.833404i	$-0.313611\pi$
$283$	18.5945			1.10533			0.552665	+	0.833404i	$0.313611\pi$
$284$	0.680045			0.0403532
$285$	7.41534	−	1.30753i	0.439247	−	0.0774511i
$286$	2.44862	+	4.24113i	0.144790	+	0.250783i
$287$		0			0
$288$	−15.8944	+	5.78509i	−0.936587	+	0.340890i
$289$	8.39053	−	14.5328i	0.493561	−	0.854872i
$290$	−3.71348	+	6.43193i	−0.218063	+	0.377696i
$291$	2.11422	+	2.51963i	0.123938	+	0.147703i
$292$	−1.25712	−	2.17740i	−0.0735675	−	0.127423i
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	−0.608998	−	0.793171i	$-0.708428\pi$
$293$	6.54576	−	11.3376i	0.382407	−	0.662349i	0.991406	+	0.130822i	$0.0417618\pi$
$294$		0			0
$295$	7.00387	+	12.1311i	0.407781	+	0.706298i
$296$	−13.1013	+	22.6922i	−0.761499	+	1.31895i
$297$		−	8.58770i		−	0.498309i
$298$	0.189540	+	0.328293i	0.0109798	+	0.0190175i
$299$	30.1361			1.74282
$300$	2.31433	−	6.35857i	0.133618	−	0.367112i
$301$		0			0
$302$	−1.08630	+	1.88153i	−0.0625098	+	0.108270i
$303$	1.01249	−	2.78179i	0.0581659	−	0.159810i
$304$	0.0675813	−	0.117054i	0.00387606	−	0.00671353i
$305$	−5.14543	−	8.91215i	−0.294626	−	0.510308i
$306$	−0.945622	−	0.793471i	−0.0540576	−	0.0453597i
$307$	−6.31046			−0.360157			−0.180078	−	0.983652i	$-0.557635\pi$
$307$	−6.31046			−0.360157			−0.180078	+	0.983652i	$0.557635\pi$
$308$		0			0
$309$	4.05051	+	4.82721i	0.230425	+	0.274610i
$310$	5.47044	+	9.47508i	0.310700	+	0.538148i
$311$	9.52435			0.540076			0.270038	−	0.962850i	$-0.412964\pi$
$311$	9.52435			0.540076			0.270038	+	0.962850i	$0.412964\pi$
$312$	5.66401	−	15.5617i	0.320661	−	0.881010i
$313$	17.6287			0.996431			0.498215	−	0.867053i	$-0.333989\pi$
$313$	17.6287			0.996431			0.498215	+	0.867053i	$0.333989\pi$
$314$	8.91117			0.502886
$315$		0			0
$316$	2.94862			0.165873
$317$	8.07697			0.453648			0.226824	−	0.973936i	$-0.427166\pi$
$317$	8.07697			0.453648			0.226824	+	0.973936i	$0.427166\pi$
$318$	0.561956	+	0.669713i	0.0315129	+	0.0375557i
$319$	10.3601			0.580054
$320$	3.39646	+	5.88284i	0.189868	+	0.328861i
$321$	4.22281	−	11.6021i	0.235694	−	0.647565i
$322$		0			0
$323$	−1.50980			−0.0840075
$324$	−8.45723	+	7.09646i	−0.469846	+	0.394248i
$325$	5.36571	+	9.29369i	0.297636	+	0.515521i
$326$	−1.14156	+	1.97724i	−0.0632251	+	0.109509i
$327$	0.449493	+	0.535685i	0.0248570	+	0.0296234i
$328$	4.84002	−	8.38316i	0.267246	−	0.462883i
$329$		0			0
$330$	−3.34002	+	0.588936i	−0.183862	+	0.0324199i
$331$	23.0496			1.26692			0.633461	−	0.773775i	$-0.281634\pi$
$331$	23.0496			1.26692			0.633461	+	0.773775i	$0.281634\pi$
$332$	9.23055	+	15.9878i	0.506592	+	0.877444i
$333$	−4.81062	+	27.2824i	−0.263620	+	1.49507i
$334$	10.1934	−	17.6555i	0.557759	−	0.966066i
$335$	0.401674	+	0.695720i	0.0219458	+	0.0380112i
$336$		0			0
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	0.135161	+	0.990824i	$0.456845\pi$
$337$	−14.5116	+	25.1348i	−0.790498	+	1.36918i	−0.925659	+	0.378359i	$0.876489\pi$
$338$	−0.723689	−	1.25347i	−0.0393635	−	0.0681795i
$339$	8.51249	−	23.3879i	0.462335	−	1.27025i
$340$	0.386659	−	0.669713i	0.0209695	−	0.0363203i
$341$	7.63088	−	13.2171i	0.413235	−	0.715745i
$342$	1.47818	−	8.38316i	0.0799307	−	0.453310i
$343$		0			0
$344$	6.25877	+	10.8405i	0.337450	+	0.584481i
$345$	−7.13816	+	19.6119i	−0.384305	+	1.05587i
$346$	−4.17881			−0.224654
$347$	12.9463			0.694991			0.347496	−	0.937682i	$-0.387032\pi$
$347$	12.9463			0.694991			0.347496	+	0.937682i	$0.387032\pi$
$348$	−8.56108	−	10.2027i	−0.458922	−	0.546922i
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	0.884938	−	0.465710i	$-0.154201\pi$
$349$	0.731429	+	1.26687i	0.0391525	+	0.0678141i	−0.845785	+	0.533524i	$0.820868\pi$
$350$		0			0
$351$		−	17.5089i		−	0.934555i
$352$	4.65910	−	8.06980i	0.248331	−	0.430122i
$353$	7.16637	−	12.4125i	0.381428	−	0.660652i	−0.609839	−	0.792525i	$-0.708766\pi$
$353$	7.16637	−	12.4125i	0.381428	−	0.660652i	0.991267	+	0.131873i	$0.0420992\pi$
$354$	15.5954	−	2.74989i	0.828886	−	0.146155i
$355$	−0.373455	−	0.646844i	−0.0198210	−	0.0343309i
$356$	−5.57310	+	9.65289i	−0.295374	+	0.511602i
$357$		0			0
$358$	−3.75150	−	6.49778i	−0.198273	−	0.343418i
$359$	10.4684	−	18.1318i	0.552500	−	0.956958i	−0.445593	−	0.895235i	$-0.647007\pi$
$359$	10.4684	−	18.1318i	0.552500	−	0.956958i	0.998093	−	0.0617224i	$-0.0196594\pi$
$360$	8.78564	+	7.37203i	0.463044	+	0.388540i
$361$	4.29426	+	7.43788i	0.226014	+	0.391467i
$362$	−15.1557			−0.796566
$363$	−9.20574	−	10.9710i	−0.483176	−	0.575827i
$364$		0			0
$365$	−1.38073	+	2.39149i	−0.0722707	+	0.125176i
$366$	−11.4572	+	2.02022i	−0.598879	+	0.105599i
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	−0.979373	−	0.202063i	$-0.935236\pi$
$367$	−6.02869	+	10.4420i	−0.314695	+	0.545067i	0.664678	+	0.747130i	$0.268569\pi$
$368$	0.187319	+	0.324446i	0.00976466	+	0.0169129i
$369$	1.77719	−	10.0789i	0.0925168	−	0.524689i
$370$	10.9409			0.568789
$371$		0			0
$372$	−19.3221	+	3.40700i	−1.00180	+	0.176645i
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	0.875959	−	0.482386i	$-0.160230\pi$
$373$	0.390530	+	0.676417i	0.0202209	+	0.0350235i	−0.855738	+	0.517410i	$0.826896\pi$
$374$	0.680045			0.0351643
$375$	−18.8097	+	3.31667i	−0.971331	+	0.171272i
$376$	−26.5449			−1.36895
$377$	21.1225			1.08786
$378$		0			0
$379$	−6.92396			−0.355660			−0.177830	−	0.984061i	$-0.556908\pi$
$379$	−6.92396			−0.355660			−0.177830	+	0.984061i	$0.556908\pi$
$380$	5.33275			0.273564
$381$	35.4308	−	6.24741i	1.81518	−	0.320065i
$382$	−11.3523			−0.580837
$383$	3.86618	+	6.69642i	0.197553	+	0.342171i	0.947734	−	0.319061i	$-0.103367\pi$
$383$	3.86618	+	6.69642i	0.197553	+	0.342171i	−0.750182	+	0.661232i	$0.770034\pi$
$384$	−11.6716	+	2.05802i	−0.595613	+	0.105023i
$385$		0			0
$386$	0.561185			0.0285636
$387$	10.1382	+	8.50692i	0.515351	+	0.432431i
$388$	1.16473	+	2.01736i	0.0591300	+	0.102416i
$389$	−2.69981	+	4.67620i	−0.136886	+	0.237093i	−0.926316	−	0.376747i	$-0.877043\pi$
$389$	−2.69981	+	4.67620i	−0.136886	+	0.237093i	0.789431	+	0.613840i	$0.210376\pi$
$390$	−6.80974	+	1.20074i	−0.344825	+	0.0608019i
$391$	2.09240	−	3.62414i	0.105817	−	0.183280i
$392$		0			0
$393$	7.97730	+	9.50698i	0.402402	+	0.479564i
$394$	−10.0651			−0.507073
$395$	−1.61927	−	2.80466i	−0.0814743	−	0.141118i
$396$	1.05613	−	5.98962i	0.0530726	−	0.300990i
$397$	−14.6172	+	25.3178i	−0.733617	+	1.27066i	0.221711	+	0.975112i	$0.428836\pi$
$397$	−14.6172	+	25.3178i	−0.733617	+	1.27066i	−0.955328	+	0.295549i	$0.904497\pi$
$398$	1.59967	+	2.77071i	0.0801842	+	0.138883i
$399$		0			0
$400$	−0.0667040	+	0.115535i	−0.00333520	+	0.00577674i
$401$	13.6989	+	23.7272i	0.684092	+	1.18488i	0.973721	+	0.227743i	$0.0731346\pi$
$401$	13.6989	+	23.7272i	0.684092	+	1.18488i	−0.289629	+	0.957139i	$0.593532\pi$
$402$	0.894400	−	0.157707i	0.0446086	−	0.00786570i
$403$	15.5581	−	26.9474i	0.775003	−	1.34235i
$404$	1.04829	−	1.81568i	0.0521542	−	0.0903337i
$405$	11.3944	+	4.14722i	0.566192	+	0.206077i
$406$		0			0
$407$	−7.63088	−	13.2171i	−0.378249	−	0.655146i
$408$	−1.47818	−	1.76162i	−0.0731807	−	0.0872134i
$409$	9.02498			0.446256			0.223128	−	0.974789i	$-0.428373\pi$
$409$	9.02498			0.446256			0.223128	+	0.974789i	$0.428373\pi$
$410$	−4.04189			−0.199615
$411$	1.52182	−	4.18117i	0.0750659	−	0.206242i
$412$	2.23143	+	3.86495i	0.109935	+	0.190412i
$413$		0			0
$414$	18.0744	+	15.1663i	0.888310	+	0.745381i
$415$	10.1382	−	17.5598i	0.497662	−	0.861977i
$416$	9.49912	−	16.4530i	0.465733	−	0.806673i
$417$	3.63341	−	9.98271i	0.177929	−	0.488855i
$418$	2.34477	+	4.06126i	0.114686	+	0.198643i
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	−0.863877	−	0.503704i	$-0.831970\pi$
$419$	0.0876485	−	0.151812i	0.00428191	−	0.00741649i	0.868158	+	0.496287i	$0.165304\pi$
$420$		0			0
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	0.992514	+	0.122130i	$0.0389724\pi$
$421$	12.3525	+	21.3952i	0.602025	+	1.04274i	−0.390490	+	0.920607i	$0.627694\pi$
$422$	2.56031	−	4.43458i	0.124634	−	0.215872i
$423$	−26.3726	+	9.59883i	−1.28228	+	0.466711i
$424$	0.814330	+	1.41046i	0.0395474	+	0.0684980i
$425$	1.49020			0.0722853
$426$	−0.831566	+	0.146628i	−0.0402895	+	0.00710413i
$427$		0			0
$428$	4.37211	−	7.57272i	0.211334	−	0.366041i
$429$	6.20011	+	7.38901i	0.299344	+	0.356745i
$430$	2.61334	−	4.52644i	0.126026	−	0.218284i
$431$	14.6596	+	25.3911i	0.706126	+	1.22305i	0.966283	+	0.257481i	$0.0828924\pi$
$431$	14.6596	+	25.3911i	0.706126	+	1.22305i	−0.260157	+	0.965566i	$0.583774\pi$
$432$	0.188501	−	0.108831i	0.00906925	−	0.00523613i
$433$	−19.6554			−0.944578			−0.472289	−	0.881444i	$-0.656572\pi$
$433$	−19.6554			−0.944578			−0.472289	+	0.881444i	$0.656572\pi$
$434$		0			0
$435$	−5.00316	+	13.7461i	−0.239883	+	0.659073i
$436$	0.247626	+	0.428901i	0.0118591	+	0.0205406i
$437$	28.8580			1.38047
$438$	2.00670	+	2.39149i	0.0958839	+	0.114270i
$439$	21.9299			1.04666			0.523330	−	0.852130i	$-0.324690\pi$
$439$	21.9299			1.04666			0.523330	+	0.852130i	$0.324690\pi$
$440$	−6.31820			−0.301208
$441$		0			0
$442$	1.38650			0.0659489
$443$	−18.7101			−0.888942			−0.444471	−	0.895793i	$-0.646608\pi$
$443$	−18.7101			−0.888942			−0.444471	+	0.895793i	$0.646608\pi$
$444$	−6.71048	+	18.4369i	−0.318466	+	0.874977i
$445$	12.2422			0.580334
$446$	−3.11468	−	5.39479i	−0.147485	−	0.255451i
$447$	0.479933	+	0.571962i	0.0227000	+	0.0270529i
$448$		0			0
$449$	6.68004			0.315251			0.157625	−	0.987499i	$-0.449616\pi$
$449$	6.68004			0.315251			0.157625	+	0.987499i	$0.449616\pi$
$450$	−1.45899	+	8.27433i	−0.0687774	+	0.390056i
$451$	2.81908	+	4.88279i	0.132745	+	0.229921i
$452$	8.81345	−	15.2653i	0.414550	−	0.718022i
$453$	−1.46357	+	4.02114i	−0.0687647	+	0.188929i
$454$	5.25150	−	9.09586i	0.246465	−	0.426890i
$455$		0			0
$456$	5.42380	−	14.9018i	0.253993	−	0.697839i
$457$	−19.4287			−0.908837			−0.454418	−	0.890788i	$-0.650153\pi$
$457$	−19.4287			−0.908837			−0.454418	+	0.890788i	$0.650153\pi$
$458$	7.71776	+	13.3676i	0.360627	+	0.624625i
$459$	−2.10560	−	1.21567i	−0.0982810	−	0.0567426i
$460$	−7.39053	+	12.8008i	−0.344585	+	0.596839i
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	0.854560	−	0.519352i	$-0.173827\pi$
$461$	−0.482926	−	0.836452i	−0.0224921	−	0.0389575i	−0.877052	+	0.480395i	$0.840493\pi$
$462$		0			0
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	−0.860802	−	0.508941i	$-0.830037\pi$
$463$	0.222811	−	0.385920i	0.0103549	−	0.0179352i	0.871156	+	0.491006i	$0.163371\pi$
$464$	0.131292	+	0.227405i	0.00609509	+	0.0105570i
$465$	13.8516	+	16.5077i	0.642354	+	0.765528i
$466$	7.14677	−	12.3786i	0.331068	−	0.573426i
$467$	−17.1074	+	29.6309i	−0.791637	+	1.37115i	0.133317	+	0.991074i	$0.457437\pi$
$467$	−17.1074	+	29.6309i	−0.791637	+	1.37115i	−0.924953	+	0.380081i	$0.875896\pi$
$468$	2.15328	−	12.2118i	0.0995352	−	0.564492i
$469$		0			0
$470$	5.54189	+	9.59883i	0.255628	+	0.442761i
$471$	17.2849	−	3.04780i	0.796448	−	0.140435i
$472$	29.5012			1.35790
$473$	−7.29086			−0.335234
$474$	−3.60560	+	0.635765i	−0.165611	+	0.0292016i
$475$	5.13816	+	8.89955i	0.235755	+	0.408339i
$476$		0			0
$477$	1.31908	+	1.10684i	0.0603964	+	0.0506786i
$478$	−6.63903	+	11.4991i	−0.303662	+	0.525959i
$479$	−10.8965	+	18.8732i	−0.497872	+	0.862339i	−0.999997	−	0.00245553i	$-0.999218\pi$
$479$	−10.8965	+	18.8732i	−0.497872	+	0.862339i	0.502125	+	0.864795i	$0.332552\pi$
$480$	8.45723	+	10.0789i	0.386018	+	0.460038i
$481$	−15.5581	−	26.9474i	−0.709388	−	1.22870i
$482$	6.87598	−	11.9095i	0.313192	−	0.542465i
$483$		0			0
$484$	−5.07145	−	8.78401i	−0.230521	−	0.399273i
$485$	1.27925	−	2.21572i	0.0580877	−	0.100611i
$486$	8.81150	−	10.5011i	0.399698	−	0.476341i
$487$	−9.69640	−	16.7947i	−0.439386	−	0.761039i	0.558256	−	0.829669i	$-0.311471\pi$
$487$	−9.69640	−	16.7947i	−0.439386	−	0.761039i	−0.997642	+	0.0686297i	$0.978137\pi$
$488$	−21.6732			−0.981101
$489$	−1.53802	+	4.22567i	−0.0695516	+	0.191091i
$490$		0			0
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	0.403987	+	0.914765i	$0.367624\pi$
$491$	−13.0783	+	22.6523i	−0.590216	+	1.02228i	−0.994203	+	0.107519i	$0.965709\pi$
$492$	2.47906	−	6.81115i	0.111764	−	0.307070i
$493$	1.46657	−	2.54017i	0.0660509	−	0.114403i
$494$	4.78059	+	8.28023i	0.215089	+	0.372545i
$495$	−6.27719	+	2.28471i	−0.282139	+	0.102690i
$496$	0.386821			0.0173688
$497$		0			0
$498$	−14.7344	−	17.5598i	−0.660265	−	0.786873i
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	0.980510	−	0.196470i	$-0.0629479\pi$
$499$	7.15064	+	12.3853i	0.320107	+	0.554441i	−0.660403	+	0.750911i	$0.729615\pi$
$500$	−13.5270			−0.604947
$501$	13.7335	−	37.7326i	0.613570	−	1.68577i
$502$	16.7656			0.748284
$503$	−18.7033			−0.833937			−0.416969	−	0.908921i	$-0.636908\pi$
$503$	−18.7033			−0.833937			−0.416969	+	0.908921i	$0.636908\pi$
$504$		0			0
$505$	−2.30272			−0.102470
$506$	−12.9982			−0.577842
$507$	−1.83244	−	2.18382i	−0.0813817	−	0.0969869i
$508$	25.4801			1.13050
$509$	−12.8045	−	22.1781i	−0.567551	−	0.983027i	−0.996807	−	0.0798442i	$-0.974558\pi$
$509$	−12.8045	−	22.1781i	−0.567551	−	0.983027i	0.429257	−	0.903183i	$-0.358776\pi$
$510$	−0.328411	+	0.902302i	−0.0145423	+	0.0399546i
$511$		0			0
$512$	0.473897			0.0209435
$513$		−	16.7663i		−	0.740252i
$514$	−11.6878	−	20.2438i	−0.515526	−	0.892917i
$515$	2.45084	−	4.24497i	0.107997	−	0.187056i
$516$	6.02481	+	7.18009i	0.265228	+	0.316086i
$517$	7.73055	−	13.3897i	0.339989	−	0.588879i
$518$		0			0
$519$	−8.10560	+	1.42924i	−0.355796	+	0.0627365i
$520$	−12.8817			−0.564902
$521$	−10.6061	−	18.3702i	−0.464660	−	0.804815i	0.534526	−	0.845152i	$-0.320490\pi$
$521$	−10.6061	−	18.3702i	−0.464660	−	0.804815i	−0.999186	+	0.0403370i	$0.987157\pi$
$522$	12.6684	+	10.6301i	0.554482	+	0.465266i
$523$	10.4029	−	18.0183i	0.454885	−	0.787884i	−0.543796	−	0.839217i	$-0.683014\pi$
$523$	10.4029	−	18.0183i	0.454885	−	0.787884i	0.998682	+	0.0513330i	$0.0163470\pi$
$524$	4.39470	+	7.61185i	0.191984	+	0.332525i
$525$		0			0
$526$	−0.322786	+	0.559082i	−0.0140741	+	0.0243771i
$527$	−2.16044	−	3.74200i	−0.0941104	−	0.163004i
$528$	−0.0410117	+	0.112679i	−0.00178481	+	0.00490371i
$529$	−28.4937	+	49.3525i	−1.23885	+	2.14576i
$530$	0.340022	−	0.588936i	0.0147696	−	0.0255817i
$531$	29.3097	−	10.6679i	1.27193	−	0.462946i
$532$		0			0
$533$	5.74763	+	9.95518i	0.248957	+	0.431207i
$534$	4.73355	−	13.0053i	0.204841	−	0.562795i
$535$	−9.60401			−0.415217
$536$	1.69190			0.0730791
$537$	−9.49912	−	11.3206i	−0.409917	−	0.488521i
$538$	9.16772	+	15.8790i	0.395248	+	0.684590i
$539$		0			0
$540$	7.43717	+	4.29385i	0.320045	+	0.184778i
$541$	−13.3648	+	23.1486i	−0.574599	+	0.995235i	0.421486	+	0.906835i	$0.361509\pi$
$541$	−13.3648	+	23.1486i	−0.574599	+	0.995235i	−0.996085	+	0.0884001i	$0.971825\pi$
$542$	−3.05943	+	5.29909i	−0.131414	+	0.227615i
$543$	−29.3974	+	5.18355i	−1.26156	+	0.222448i
$544$	−1.31908	−	2.28471i	−0.0565550	−	0.0979561i
$545$	0.271974	−	0.471073i	0.0116501	−	0.0201786i
$546$		0			0
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	−0.928446	−	0.371467i	$-0.878855\pi$
$547$	−18.3812	−	31.8372i	−0.785923	−	1.36126i	0.142523	−	0.989792i	$-0.454479\pi$
$548$	1.57563	−	2.72907i	0.0673074	−	0.116580i
$549$	−21.5326	+	7.83721i	−0.918987	+	0.334484i
$550$	−2.31433	−	4.00854i	−0.0986834	−	0.170925i
$551$	20.2267			0.861686
$552$	28.2536	+	33.6713i	1.20255	+	1.43315i
$553$		0			0
$554$	7.85844	−	13.6112i	0.333873	−	0.578285i
$555$	21.2219	−	3.74200i	0.900821	−	0.158839i
$556$	3.76187	−	6.51575i	0.159539	−	0.276329i
$557$	−16.1694	−	28.0062i	−0.685118	−	1.18666i	−0.973400	−	0.229114i	$-0.926417\pi$
$557$	−16.1694	−	28.0062i	−0.685118	−	1.18666i	0.288282	−	0.957546i	$-0.406916\pi$
$558$	22.8926	−	8.33224i	0.969123	−	0.352732i
$559$	−14.8648			−0.628716
$560$		0			0
$561$	1.31908	−	0.232589i	0.0556915	−	0.00981992i
$562$	9.80974	+	16.9910i	0.413799	+	0.716721i
$563$	17.7419			0.747730			0.373865	−	0.927483i	$-0.378032\pi$
$563$	17.7419			0.747730			0.373865	+	0.927483i	$0.378032\pi$
$564$	−19.5744	+	3.45150i	−0.824233	+	0.145334i
$565$	−19.3601			−0.814485
$566$	−16.3517			−0.687315
$567$		0			0
$568$	−1.57304			−0.0660035
$569$	−26.6013			−1.11519			−0.557593	−	0.830115i	$-0.688275\pi$
$569$	−26.6013			−1.11519			−0.557593	+	0.830115i	$0.688275\pi$
$570$	−6.52094	+	1.14982i	−0.273132	+	0.0481606i
$571$	−10.0172			−0.419208			−0.209604	−	0.977786i	$-0.567218\pi$
$571$	−10.0172			−0.419208			−0.209604	+	0.977786i	$0.567218\pi$
$572$	3.41565	+	5.91608i	0.142815	+	0.247364i
$573$	−22.0201	+	3.88273i	−0.919902	+	0.162203i
$574$		0			0
$575$	−28.4834			−1.18784
$576$	14.2135	−	5.17328i	0.592228	−	0.215553i
$577$	−16.4572	−	28.5048i	−0.685124	−	1.18667i	−0.973398	−	0.229121i	$-0.926415\pi$
$577$	−16.4572	−	28.5048i	−0.685124	−	1.18667i	0.288274	−	0.957548i	$-0.406918\pi$
$578$	−7.37851	+	12.7800i	−0.306905	+	0.531576i
$579$	1.08853	−	0.191936i	0.0452376	−	0.00797661i
$580$	−5.18004	+	8.97210i	−0.215090	+	0.372546i
$581$		0			0
$582$	−1.85921	−	2.21572i	−0.0770668	−	0.0918447i
$583$	−0.948615			−0.0392876
$584$	2.90791	+	5.03665i	0.120330	+	0.208418i
$585$	−12.7981	+	4.65814i	−0.529138	+	0.192590i
$586$	−5.75624	+	9.97011i	−0.237788	+	0.411861i
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	0.667531	−	0.744582i	$-0.267351\pi$
$587$	−7.53643	−	13.0535i	−0.311062	−	0.538774i	−0.978592	+	0.205808i	$0.934018\pi$
$588$		0			0
$589$	14.8983	−	25.8046i	0.613873	−	1.06326i
$590$	−6.15910	−	10.6679i	−0.253566	−	0.439189i
$591$	−19.5232	+	3.44247i	−0.803078	+	0.141604i
$592$	0.193411	−	0.334997i	0.00794913	−	0.0137683i
$593$	20.5005	−	35.5079i	0.841853	−	1.45813i	−0.0464729	−	0.998920i	$-0.514798\pi$
$593$	20.5005	−	35.5079i	0.841853	−	1.45813i	0.888326	−	0.459213i	$-0.151869\pi$
$594$			7.55190i			0.309858i
$595$		0			0
$596$	0.264396	+	0.457947i	0.0108301	+	0.0187582i
$597$	4.05051	+	4.82721i	0.165776	+	0.197564i
$598$	−26.5012			−1.08372
$599$	6.07367			0.248164			0.124082	−	0.992272i	$-0.460401\pi$
$599$	6.07367			0.248164			0.124082	+	0.992272i	$0.460401\pi$
$600$	−5.35339	+	14.7083i	−0.218551	+	0.600464i
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	0.685110	−	0.728440i	$-0.259754\pi$
$601$	−7.06758	−	12.2414i	−0.288293	−	0.499338i	−0.973402	+	0.229102i	$0.926421\pi$
$602$		0			0
$603$	1.68092	−	0.611806i	0.0684524	−	0.0249147i
$604$	−1.51532	+	2.62461i	−0.0616575	+	0.106794i
$605$	−5.57011	+	9.64771i	−0.226457	+	0.392235i
$606$	−0.890367	+	2.44626i	−0.0361687	+	0.0993727i
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.773986	+	0.633203i	$0.218260\pi$
$607$	23.0449	+	39.9149i	0.935363	+	1.62010i	0.161377	+	0.986893i	$0.448406\pi$
$608$	9.09627	−	15.7552i	0.368902	−	0.638958i
$609$		0			0
$610$	4.52481	+	7.83721i	0.183204	+	0.317319i
$611$	15.7613	−	27.2994i	0.637634	−	1.10441i
$612$	−1.31908	−	1.10684i	−0.0533206	−	0.0447413i
$613$	13.2469	+	22.9443i	0.535038	+	0.926712i	0.999162	+	0.0409421i	$0.0130359\pi$
$613$	13.2469	+	22.9443i	0.535038	+	0.926712i	−0.464124	+	0.885770i	$0.653631\pi$
$614$	5.54933			0.223953
$615$	−7.84002	+	1.38241i	−0.316140	+	0.0557440i
$616$		0			0
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	−0.842492	−	0.538708i	$-0.818913\pi$
$617$	1.12495	−	1.94847i	0.0452889	−	0.0784426i	0.887781	+	0.460266i	$0.152246\pi$
$618$	−3.56196	−	4.24497i	−0.143283	−	0.170758i
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	−0.797090	−	0.603861i	$-0.793628\pi$
$619$	3.09539	−	5.36137i	0.124414	−	0.215492i	0.921504	+	0.388369i	$0.126962\pi$
$620$	7.63088	+	13.2171i	0.306464	+	0.530811i
$621$	40.2460	+	23.2361i	1.61502	+	0.932431i
$622$	−8.37557			−0.335830
$623$		0			0
$624$	−0.0836160	+	0.229733i	−0.00334732	+	0.00919668i
$625$	−0.533433	−	0.923933i	−0.0213373	−	0.0369573i
$626$	−15.5024			−0.619600
$627$	5.93717	+	7.07564i	0.237108	+	0.282574i
$628$	12.4305			0.496030
$629$	−4.32089			−0.172285
$630$		0			0
$631$	26.1661			1.04166			0.520829	−	0.853661i	$-0.325623\pi$
$631$	26.1661			1.04166			0.520829	+	0.853661i	$0.325623\pi$
$632$	−6.82058			−0.271308
$633$	3.44949	−	9.47740i	0.137105	−	0.376693i
$634$	−7.10277			−0.282087
$635$	−13.9927	−	24.2361i	−0.555284	−	0.961781i
$636$	0.783890	+	0.934204i	0.0310833	+	0.0370436i
$637$		0			0
$638$	−9.11051			−0.360689
$639$	−1.56283	+	0.568825i	−0.0618247	+	0.0225024i
$640$	4.60947	+	7.98384i	0.182205	+	0.315589i
$641$	−2.44444	+	4.23389i	−0.0965496	+	0.167229i	−0.910254	−	0.414050i	$-0.864114\pi$
$641$	−2.44444	+	4.23389i	−0.0965496	+	0.167229i	0.813705	+	0.581278i	$0.197447\pi$
$642$	−3.71348	+	10.2027i	−0.146559	+	0.402668i
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	0.126242	+	0.992000i	$0.459709\pi$
$643$	−20.1839	+	34.9596i	−0.795976	+	1.37867i	−0.922218	+	0.386671i	$0.873625\pi$
$644$		0			0
$645$	3.52094	−	9.67372i	0.138637	−	0.380902i
$646$	1.32770			0.0522375
$647$	−1.14038	−	1.97519i	−0.0448329	−	0.0776528i	0.842738	−	0.538324i	$-0.180942\pi$
$647$	−1.14038	−	1.97519i	−0.0448329	−	0.0776528i	−0.887571	+	0.460671i	$0.847609\pi$
$648$	19.5628	−	16.4152i	0.768501	−	0.644849i
$649$	−8.59152	+	14.8809i	−0.337247	+	0.584128i
$650$	−4.71853	−	8.17273i	−0.185076	−	0.320561i
$651$		0			0
$652$	−1.59240	+	2.75811i	−0.0623631	+	0.108016i
$653$	−11.7396	−	20.3336i	−0.459407	−	0.795717i	0.539522	−	0.841971i	$-0.318605\pi$
$653$	−11.7396	−	20.3336i	−0.459407	−	0.795717i	−0.998930	+	0.0462542i	$0.985272\pi$
$654$	−0.395277	−	0.471073i	−0.0154566	−	0.0184204i
$655$	4.82682	−	8.36030i	0.188599	−	0.326664i
$656$	−0.0714517	+	0.123758i	−0.00278972	+	0.00483194i
$657$	4.71032	+	3.95243i	0.183767	+	0.154199i
$658$		0			0
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.776101	+	0.630609i	$0.217195\pi$
$659$	23.9812	+	41.5366i	0.934174	+	1.61804i	0.158073	+	0.987427i	$0.449472\pi$
$660$	−4.65910	+	0.821525i	−0.181355	+	0.0319778i
$661$	−29.3090			−1.13999			−0.569995	−	0.821648i	$-0.693055\pi$
$661$	−29.3090			−1.13999			−0.569995	+	0.821648i	$0.693055\pi$
$662$	−20.2695			−0.787797
$663$	2.68938	−	0.474210i	0.104447	−	0.0184168i
$664$	−21.3516	−	36.9821i	−0.828604	−	1.43518i
$665$		0			0
$666$	4.23039	−	23.9917i	0.163924	−	0.929661i
$667$	−28.0317	+	48.5523i	−1.08539	+	1.87995i
$668$	14.2191	−	24.6282i	0.550154	−	0.952894i
$669$	−7.88666	−	9.39895i	−0.304916	−	0.363385i
$670$	−0.353226	−	0.611806i	−0.0136463	−	0.0236361i
$671$	6.31180	−	10.9324i	0.243664	−	0.422039i
$672$		0			0
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	−0.999965	−	0.00838731i	$-0.997330\pi$
$673$	−13.1591	−	22.7922i	−0.507246	−	0.878576i	0.492719	−	0.870189i	$-0.336003\pi$
$674$	12.7613	−	22.1032i	0.491547	−	0.851384i
$675$			16.5487i			0.636959i
$676$	−1.00950	−	1.74850i	−0.0388267	−	0.0672499i
$677$	−35.8907			−1.37939			−0.689697	−	0.724098i	$-0.742256\pi$
$677$	−35.8907			−1.37939			−0.689697	+	0.724098i	$0.742256\pi$
$678$	−7.48576	+	20.5669i	−0.287489	+	0.789869i
$679$		0			0
$680$	−0.894400	+	1.54915i	−0.0342987	+	0.0594070i
$681$	7.07532	−	19.4393i	0.271127	−	0.744915i
$682$	−6.71048	+	11.6229i	−0.256958	+	0.445064i
$683$	−17.5321	−	30.3665i	−0.670847	−	1.16194i	−0.977664	−	0.210172i	$-0.932597\pi$
$683$	−17.5321	−	30.3665i	−0.670847	−	1.16194i	0.306818	−	0.951768i	$-0.400736\pi$
$684$	2.06196	−	11.6939i	0.0788409	−	0.447129i
$685$	−3.46110			−0.132242
$686$		0			0
$687$	19.5421	+	23.2893i	0.745576	+	0.888543i
$688$	−0.0923963	−	0.160035i	−0.00352257	−	0.00610128i
$689$	−1.93407			−0.0736821
$690$	6.27719	−	17.2464i	0.238968	−	0.656561i
$691$	−2.06687			−0.0786273			−0.0393136	−	0.999227i	$-0.512517\pi$
$691$	−2.06687			−0.0786273			−0.0393136	+	0.999227i	$0.512517\pi$
$692$	−5.82915			−0.221591
$693$		0			0
$694$	−11.3847			−0.432159
$695$	−8.26352			−0.313453
$696$	19.8030	+	23.6003i	0.750632	+	0.894569i
$697$	1.59627			0.0604629
$698$	−0.643208	−	1.11407i	−0.0243458	−	0.0421681i
$699$	9.62882	−	26.4550i	0.364196	−	1.00062i
$700$		0			0
$701$	−7.36009			−0.277987			−0.138993	−	0.990293i	$-0.544387\pi$
$701$	−7.36009			−0.277987			−0.138993	+	0.990293i	$0.544387\pi$
$702$			15.3970i			0.581124i
$703$	−14.8983	−	25.8046i	−0.561899	−	0.973237i
$704$	−4.16637	+	7.21637i	−0.157026	+	0.271977i
$705$	14.0326	+	16.7233i	0.528497	+	0.629838i
$706$	−6.30200	+	10.9154i	−0.237179	+	0.410806i
$707$		0			0
$708$	21.7545	−	3.83590i	0.817584	−	0.144162i
$709$	9.10876			0.342086			0.171043	−	0.985264i	$-0.445286\pi$
$709$	9.10876			0.342086			0.171043	+	0.985264i	$0.445286\pi$
$710$	0.328411	+	0.568825i	0.0123251	+	0.0213476i
$711$	−6.77631	+	2.46638i	−0.254132	+	0.0924963i
$712$	12.8914	−	22.3286i	0.483126	−	0.836799i
$713$	41.2943	+	71.5239i	1.54648	+	2.67859i
$714$		0			0
$715$	3.75150	−	6.49778i	0.140298	−	0.243003i
$716$	−5.23308	−	9.06396i	−0.195569	−	0.338736i
$717$	−8.94475	+	24.5755i	−0.334048	+	0.917788i
$718$	−9.20574	+	15.9448i	−0.343555	+	0.595055i
$719$	−12.9768	+	22.4765i	−0.483954	+	0.838233i	−0.999830	−	0.0184300i	$-0.994133\pi$
$719$	−12.9768	+	22.4765i	−0.483954	+	0.838233i	0.515876	+	0.856663i	$0.327467\pi$
$720$	−0.129700	−	0.108831i	−0.00483362	−	0.00405589i
$721$		0			0
$722$	−3.77631	−	6.54076i	−0.140540	−	0.243422i
$723$	9.26399	−	25.4526i	0.344531	−	0.946592i
$724$	−21.1411			−0.785705
$725$	−19.9641			−0.741448
$726$	8.09539	+	9.64771i	0.300448	+	0.358060i
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	0.756311	−	0.654213i	$-0.227000\pi$
$727$	−5.08007	−	8.79894i	−0.188409	−	0.326335i	−0.944720	+	0.327878i	$0.893667\pi$
$728$		0			0
$729$	13.5000	−	23.3827i	0.500000	−	0.866025i
$730$	1.21419	−	2.10304i	0.0449393	−	0.0778372i
$731$	−1.03209	+	1.78763i	−0.0381732	+	0.0661179i
$732$	−15.9820	+	2.81807i	−0.590714	+	0.104159i
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	0.947372	+	0.320135i	$0.103728\pi$
$733$	20.3307	+	35.2138i	0.750931	+	1.30065i	−0.196441	+	0.980516i	$0.562938\pi$
$734$	5.30154	−	9.18253i	0.195683	−	0.338933i
$735$		0			0
$736$	25.2126	+	43.6695i	0.929349	+	1.60968i
$737$	−0.492726	+	0.853427i	−0.0181498	+	0.0314364i
$738$	−1.56283	+	8.86327i	−0.0575287	+	0.326261i
$739$	12.6809	+	21.9640i	0.466475	+	0.807959i	0.999267	−	0.0382877i	$-0.0121903\pi$
$739$	12.6809	+	21.9640i	0.466475	+	0.807959i	−0.532791	+	0.846247i	$0.678857\pi$
$740$	15.2618			0.561034
$741$	12.1049	+	14.4260i	0.444684	+	0.529954i
$742$		0			0
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	−0.583377	−	0.812202i	$-0.698269\pi$
$743$	11.2221	−	19.4372i	0.411699	−	0.713083i	0.995076	+	0.0991184i	$0.0316023\pi$
$744$	44.6948	−	7.88090i	1.63859	−	0.288928i
$745$	0.290393	−	0.502975i	0.0106392	−	0.0184276i
$746$	−0.343426	−	0.594831i	−0.0125737	−	0.0217783i
$747$	−34.5861	−	29.0211i	−1.26544	−	1.06183i
$748$	0.948615			0.0346848
$749$		0			0
$750$	16.5410	−	2.91663i	0.603992	−	0.106500i
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	0.555978	−	0.831197i	$-0.312344\pi$
$751$	−12.1086	−	20.9727i	−0.441849	−	0.765305i	−0.997827	+	0.0658924i	$0.979011\pi$
$752$	0.391874			0.0142902
$753$	32.5201	−	5.73417i	1.18510	−	0.208965i
$754$	−18.5748			−0.676454
$755$	3.32863			0.121141
$756$		0			0
$757$	9.11793			0.331397			0.165698	−	0.986176i	$-0.447012\pi$
$757$	9.11793			0.331397			0.165698	+	0.986176i	$0.447012\pi$
$758$	6.08883			0.221156
$759$	−25.2126	+	4.44566i	−0.915159	+	0.161367i
$760$	−12.3354			−0.447453
$761$	−9.13610	−	15.8242i	−0.331183	−	0.573626i	0.651561	−	0.758596i	$-0.274114\pi$
$761$	−9.13610	−	15.8242i	−0.331183	−	0.573626i	−0.982744	+	0.184970i	$0.940781\pi$
$762$	−31.1573	+	5.49388i	−1.12871	+	0.199022i
$763$		0			0
$764$	−15.8357			−0.572917
$765$	−0.328411	+	1.86251i	−0.0118737	+	0.0673393i
$766$	−3.39986	−	5.88874i	−0.122842	−	0.212769i
$767$	−17.5167	+	30.3398i	−0.632490	+	1.09550i
$768$	27.4641	−	4.84266i	0.991025	−	0.174744i
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	−0.649217	−	0.760604i	$-0.724903\pi$
$769$	9.26470	−	16.0469i	0.334094	−	0.578667i	0.983310	+	0.181936i	$0.0582365\pi$
$770$		0			0
$771$	−29.5945	−	35.2694i	−1.06582	−	1.27020i
$772$	0.782814			0.0281741
$773$	−1.48040	−	2.56413i	−0.0532463	−	0.0922253i	0.838174	−	0.545403i

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.879385 q^{2} +(-1.70574 + 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\)	\(q-0.879385 q^{2} +(-1.70574 + 0.300767i) q^{3} -1.22668 q^{4} +(0.673648 + 1.16679i) q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +(-0.592396 - 1.02606i) q^{10} +(-0.826352 + 1.43128i) q^{11} +(2.09240 - 0.368946i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} -0.0418891 q^{16} +(0.233956 + 0.405223i) q^{17} +(-2.47906 + 0.902302i) q^{18} +(-1.61334 + 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(-4.84002 + 0.853427i) q^{24} +(1.59240 - 2.75811i) q^{25} +(1.48158 - 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(1.31908 + 1.57202i) q^{30} -9.23442 q^{31} -5.63816 q^{32} +(0.979055 - 2.68993i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 + 7.99724i) q^{37} +(1.41875 - 2.45734i) q^{38} +(1.99613 - 5.48432i) q^{39} +(1.91147 + 3.31077i) q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 - 1.75573i) q^{44} +(3.09627 + 2.59808i) q^{45} +(3.93242 + 6.81115i) q^{46} -9.35504 q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(-0.520945 - 0.620838i) q^{51} +(2.06670 - 3.57964i) q^{52} +(0.286989 + 0.497079i) q^{53} +(3.95723 - 2.28471i) q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} +10.3969 q^{59} +(1.84002 + 2.19285i) q^{60} -7.63816 q^{61} +8.12061 q^{62} +5.04189 q^{64} -4.53983 q^{65} +(-0.860967 + 2.36549i) q^{66} +0.596267 q^{67} +(-0.286989 - 0.497079i) q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(7.99912 - 2.91144i) q^{72} +(1.02481 + 1.77503i) q^{73} +(4.06031 - 7.03266i) q^{74} +(-1.88666 + 5.18355i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} -2.40373 q^{79} +(-0.0282185 - 0.0488759i) q^{80} +(6.89440 - 5.78509i) q^{81} +(-1.50000 + 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(6.97906 + 8.31731i) q^{87} +(-2.34477 + 4.06126i) q^{88} +(4.54323 - 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(15.7515 - 2.77741i) q^{93} +8.22668 q^{94} -4.34730 q^{95} +(9.61721 - 1.69577i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} - 9 q^{24} + 6 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} + 6 q^{31} + 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} + 6 q^{38} + 36 q^{39} - 9 q^{40} + 3 q^{43} - 15 q^{44} - 9 q^{45} - 6 q^{47} + 6 q^{50} - 21 q^{52} - 6 q^{53} - 27 q^{54} - 9 q^{57} + 9 q^{58} + 6 q^{59} - 9 q^{60} - 12 q^{61} + 60 q^{62} + 24 q^{64} + 30 q^{65} + 18 q^{66} - 24 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 9 q^{72} - 21 q^{73} + 30 q^{74} - 18 q^{75} + 15 q^{76} + 54 q^{78} - 42 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} + 45 q^{87} - 27 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} + 54 q^{93} + 36 q^{94} - 24 q^{95} + 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 - 9 * q^24 + 6 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 + 6 * q^31 + 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 + 6 * q^38 + 36 * q^39 - 9 * q^40 + 3 * q^43 - 15 * q^44 - 9 * q^45 - 6 * q^47 + 6 * q^50 - 21 * q^52 - 6 * q^53 - 27 * q^54 - 9 * q^57 + 9 * q^58 + 6 * q^59 - 9 * q^60 - 12 * q^61 + 60 * q^62 + 24 * q^64 + 30 * q^65 + 18 * q^66 - 24 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 9 * q^72 - 21 * q^73 + 30 * q^74 - 18 * q^75 + 15 * q^76 + 54 * q^78 - 42 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 + 45 * q^87 - 27 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 + 54 * q^93 + 36 * q^94 - 24 * q^95 + 27 * q^96 - 3 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more