LMFDB - Embedded newform 441.2.h.d.214.1

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			214.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.d.373.1

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.930742\pi$
$5$	−0.673648	+	1.16679i	−0.301265	+	0.521806i	0.675158	+	0.737673i	$0.264075\pi$
$6$	−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	0.714137	−	0.700006i	$-0.246819\pi$
$11$	−0.826352	−	1.43128i	−0.249154	−	0.431548i	−0.963291	+	0.268458i	$0.913486\pi$
$12$	−2.09240	−	0.368946i	−0.604023	−	0.106506i
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	0.999301	−	0.0373813i	$-0.0119016\pi$
$13$	1.68479	+	2.91815i	0.467277	+	0.809348i	−0.532024	+	0.846729i	$0.678568\pi$
$14$		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	$-0.851405\pi$
$17$	−0.233956	+	0.405223i	−0.0567426	+	0.0982810i	0.836259	+	0.548335i	$0.184738\pi$
$18$	−2.47906	−	0.902302i	−0.584319	−	0.212675i
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	0.989585	−	0.143953i	$-0.0459813\pi$
$19$	1.61334	+	2.79439i	0.370126	+	0.641077i	−0.619459	+	0.785029i	$0.712648\pi$
$20$	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	−0.153279	+	0.988183i	$0.548983\pi$
$23$	−4.47178	+	7.74535i	−0.932431	+	1.61502i	−0.779152	+	0.626835i	$0.784350\pi$
$24$	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	0.413217	+	0.910632i	$0.364405\pi$
$29$	−3.13429	+	5.42874i	−0.582022	+	1.00809i	−0.995239	+	0.0974595i	$0.968928\pi$
$30$	1.31908	−	1.57202i	0.240830	−	0.287010i
$31$	9.23442			1.65855			0.829276	−	0.558840i	$-0.188753\pi$
$31$	9.23442			1.65855			0.829276	+	0.558840i	$0.188753\pi$
$32$	−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	−0.943328	−	0.331862i	$-0.892323\pi$
$37$	−4.61721	−	7.99724i	−0.759065	−	1.31474i	0.184263	−	0.982877i	$-0.441010\pi$
$38$	−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	$-0.252498\pi$
$41$	−1.70574	−	2.95442i	−0.266391	−	0.461403i	−0.967927	+	0.251231i	$0.919165\pi$
$42$		0			0
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	−0.647376	−	0.762171i	$-0.724133\pi$
$43$	2.20574	−	3.82045i	0.336372	−	0.582613i	0.983747	+	0.179558i	$0.0574668\pi$
$44$	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	$-0.260986\pi$
$47$	9.35504			1.36457			0.682286	+	0.731085i	$0.260986\pi$
$48$	−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	−0.845642	−	0.533751i	$-0.820782\pi$
$53$	0.286989	−	0.497079i	0.0394210	−	0.0682791i	0.885063	+	0.465472i	$0.154115\pi$
$54$	−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	$-0.736626\pi$
$59$	−10.3969			−1.35356			−0.676782	+	0.736183i	$0.736626\pi$
$60$	1.84002	−	2.19285i	0.237546	−	0.283096i
$61$	7.63816			0.977966			0.488983	−	0.872293i	$-0.337368\pi$
$61$	7.63816			0.977966			0.488983	+	0.872293i	$0.337368\pi$
$62$	−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	$-0.871605\pi$
$73$	−1.02481	+	1.77503i	−0.119946	+	0.207752i	0.799800	+	0.600266i	$0.204939\pi$
$74$	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	−0.0752309	−	0.997166i	$-0.523969\pi$
$83$	7.52481	−	13.0334i	0.825956	−	1.43060i	0.901187	−	0.433431i	$-0.142697\pi$
$84$		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	$-0.326604\pi$
$89$	−4.54323	−	7.86911i	−0.481582	−	0.834124i	−0.999777	+	0.0211385i	$0.993271\pi$
$90$	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	$-0.802598\pi$
$97$	0.949493	−	1.64457i	0.0964064	−	0.166981i	0.910195	+	0.414181i	$0.135932\pi$
$98$		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	$-0.139567\pi$
$101$	0.854570	+	1.48016i	0.0850329	+	0.147281i	−0.820372	+	0.571830i	$0.806234\pi$
$102$	0.458111	−	0.545955i	0.0453597	−	0.0540576i
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	−0.762381	−	0.647128i	$-0.775970\pi$
$103$	1.81908	−	3.15074i	0.179239	−	0.310451i	0.941620	+	0.336677i	$0.109303\pi$
$104$	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	0.640712	−	0.767781i	$-0.278639\pi$
$107$	−3.56418	−	6.17334i	−0.344562	−	0.596799i	−0.985274	+	0.170982i	$0.945306\pi$
$108$	−5.52007	−	3.18701i	−0.531169	−	0.306670i
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	−0.875531	−	0.483162i	$-0.839488\pi$
$109$	−0.201867	+	0.349643i	−0.0193353	+	0.0334898i	0.856196	+	0.516651i	$0.172822\pi$
$110$	−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	−0.976208	−	0.216835i	$-0.930427\pi$
$113$	−7.18479	−	12.4444i	−0.675888	−	1.17067i	0.300320	−	0.953839i	$-0.402907\pi$
$114$	−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	$-0.731995\pi$
$131$	3.58260	−	6.20524i	0.313013	−	0.542154i	0.979013	+	0.203797i	$0.0653284\pi$
$132$	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	0.805925	−	0.592017i	$-0.201668\pi$
$137$	−1.28446	−	2.22475i	−0.109739	−	0.190074i	−0.915665	+	0.401943i	$0.868335\pi$
$138$	8.75624	−	10.4353i	0.745381	−	0.888310i
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	0.966272	−	0.257523i	$-0.0829064\pi$
$139$	3.06670	+	5.31169i	0.260114	+	0.450531i	−0.706158	+	0.708055i	$0.749573\pi$
$140$		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	−0.874719	−	0.484630i	$-0.838954\pi$
$149$	−0.215537	+	0.373321i	−0.0176575	+	0.0305837i	0.857062	+	0.515214i	$0.172288\pi$
$150$	−1.65910	−	4.55834i	−0.135465	−	0.372187i
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	0.911902	−	0.410408i	$-0.134614\pi$
$151$	1.23530	+	2.13960i	0.100527	+	0.174118i	−0.811375	+	0.584526i	$0.801280\pi$
$152$	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	$-0.367492\pi$
$157$	10.1334			0.808734			0.404367	+	0.914597i	$0.367492\pi$
$158$	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	0.912376	−	0.409353i	$-0.134246\pi$
$163$	1.29813	+	2.24843i	0.101678	+	0.176111i	−0.810698	+	0.585464i	$0.800912\pi$
$164$	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	0.831337	+	0.555769i	$0.187576\pi$
$167$	11.5915	+	20.0771i	0.896979	+	1.55361i	0.0656422	+	0.997843i	$0.479090\pi$
$168$		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	$-0.557818\pi$
$173$	−4.75196			−0.361285			−0.180643	+	0.983549i	$0.557818\pi$
$174$	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	−0.661391	−	0.750041i	$-0.730034\pi$
$179$	4.26604	−	7.38901i	0.318859	−	0.552280i	0.980250	+	0.197761i	$0.0633670\pi$
$180$	3.79813	−	3.18701i	0.283096	−	0.237546i
$181$	−17.2344			−1.28102			−0.640512	−	0.767948i	$-0.721278\pi$
$181$	−17.2344			−1.28102			−0.640512	+	0.767948i	$0.721278\pi$
$182$		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	$-0.792172\pi$
$199$	1.81908	−	3.15074i	0.128951	−	0.223350i	0.923270	+	0.384151i	$0.125506\pi$
$200$	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	0.748234	−	0.663435i	$-0.230902\pi$
$211$	−2.91147	−	5.04282i	−0.200434	−	0.347162i	−0.948668	+	0.316273i	$0.897569\pi$
$212$	−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	$-0.909557\pi$
$223$	−3.54189	+	6.13473i	−0.237182	+	0.410812i	0.722722	+	0.691139i	$0.242891\pi$
$224$		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	$-0.0369395\pi$
$227$	5.97178	+	10.3434i	0.396361	+	0.686517i	−0.596913	+	0.802306i	$0.703606\pi$
$228$	−2.34477	−	6.44220i	−0.155286	−	0.426645i
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	−0.415529	−	0.909580i	$-0.636403\pi$
$229$	8.77631	−	15.2010i	0.579955	−	1.00451i	0.995484	−	0.0949315i	$-0.0302632\pi$
$230$	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	−0.999284	−	0.0378470i	$-0.987950\pi$
$233$	−8.12701	−	14.0764i	−0.532418	−	0.922175i	0.466865	−	0.884328i	$-0.345383\pi$
$234$	−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	0.999910	−	0.0134062i	$-0.00426745\pi$
$239$	7.54963	+	13.0763i	0.488345	+	0.845838i	−0.511565	+	0.859244i	$0.670934\pi$
$240$	0.0628336	−	0.0748822i	0.00405589	−	0.00483362i
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	0.999991	+	0.00424420i	$0.00135097\pi$
$241$	7.81908	+	13.5430i	0.503671	+	0.872384i	−0.496320	+	0.868140i	$0.665316\pi$
$242$	−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	$-0.294494\pi$
$251$	19.0651			1.20338			0.601690	+	0.798730i	$0.294494\pi$
$252$		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	0.0697146	+	0.997567i	$0.477791\pi$
$257$	−13.2909	+	23.0204i	−0.829061	+	1.43598i	−0.898776	+	0.438409i	$0.855542\pi$
$258$	−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	0.877120	−	0.480270i	$-0.159461\pi$
$263$	0.367059	+	0.635765i	0.0226338	+	0.0392029i	−0.854487	+	0.519473i	$0.826128\pi$
$264$	−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	−0.350749	−	0.936470i	$-0.614073\pi$
$269$	10.4251	−	18.0569i	0.635632	−	1.10095i	0.986381	−	0.164478i	$-0.0525939\pi$
$270$	5.33157	−	3.07818i	0.324469	−	0.187332i
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	0.740796	−	0.671730i	$-0.234449\pi$
$271$	−3.47906	−	6.02590i	−0.211338	−	0.366047i	−0.952133	+	0.305683i	$0.901115\pi$
$272$	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	−0.999067	−	0.0431811i	$-0.986251\pi$
$277$	−8.93629	−	15.4781i	−0.536930	−	0.929989i	0.462138	−	0.886808i	$-0.347083\pi$
$278$	−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	0.313694	+	0.949524i	$0.398433\pi$
$281$	−11.1552	+	19.3214i	−0.665465	+	1.15262i	−0.979159	+	0.203095i	$0.934900\pi$
$282$	−14.0326	−	2.47432i	−0.835627	−	0.147344i
$283$	−18.5945			−1.10533			−0.552665	−	0.833404i	$-0.686389\pi$
$283$	−18.5945			−1.10533			−0.552665	+	0.833404i	$0.686389\pi$
$284$	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	$-0.291572\pi$
$293$	−6.54576	−	11.3376i	−0.382407	−	0.662349i	−0.991406	+	0.130822i	$0.958238\pi$
$294$		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	$-0.442365\pi$
$307$	6.31046			0.360157			0.180078	+	0.983652i	$0.442365\pi$
$308$		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	$-0.587036\pi$
$311$	−9.52435			−0.540076			−0.270038	+	0.962850i	$0.587036\pi$
$312$	5.66401	+	15.5617i	0.320661	+	0.881010i
$313$	−17.6287			−0.996431			−0.498215	−	0.867053i	$-0.666011\pi$
$313$	−17.6287			−0.996431			−0.498215	+	0.867053i	$0.666011\pi$
$314$	−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	−0.925659	−	0.378359i	$-0.876489\pi$
$337$	−14.5116	−	25.1348i	−0.790498	−	1.36918i	0.135161	−	0.990824i	$-0.456845\pi$
$338$	−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	$-0.845799\pi$
$349$	−0.731429	+	1.26687i	−0.0391525	+	0.0678141i	0.845785	+	0.533524i	$0.179132\pi$
$350$		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	$-0.291234\pi$
$353$	−7.16637	−	12.4125i	−0.381428	−	0.660652i	−0.991267	+	0.131873i	$0.957901\pi$
$354$	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	0.998093	+	0.0617224i	$0.0196594\pi$
$359$	10.4684	+	18.1318i	0.552500	+	0.956958i	−0.445593	+	0.895235i	$0.647007\pi$
$360$	−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	$-0.0647645\pi$
$367$	6.02869	+	10.4420i	0.314695	+	0.545067i	−0.664678	+	0.747130i	$0.731431\pi$
$368$	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	−0.855738	−	0.517410i	$-0.826896\pi$
$373$	0.390530	−	0.676417i	0.0202209	−	0.0350235i	0.875959	+	0.482386i	$0.160230\pi$
$374$	−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	$-0.896633\pi$
$383$	−3.86618	+	6.69642i	−0.197553	+	0.342171i	0.750182	+	0.661232i	$0.229966\pi$
$384$	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	0.789431	−	0.613840i	$-0.210376\pi$
$389$	−2.69981	−	4.67620i	−0.136886	−	0.237093i	−0.926316	+	0.376747i	$0.877043\pi$
$390$	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	0.955328	+	0.295549i	$0.0955026\pi$
$397$	14.6172	+	25.3178i	0.733617	+	1.27066i	−0.221711	+	0.975112i	$0.571164\pi$
$398$	−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	−0.289629	−	0.957139i	$-0.593532\pi$
$401$	13.6989	−	23.7272i	0.684092	−	1.18488i	0.973721	−	0.227743i	$-0.0731346\pi$
$402$	−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	$-0.571627\pi$
$409$	−9.02498			−0.446256			−0.223128	+	0.974789i	$0.571627\pi$
$410$	−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	$-0.168030\pi$
$419$	−0.0876485	−	0.151812i	−0.00428191	−	0.00741649i	−0.868158	+	0.496287i	$0.834696\pi$
$420$		0			0
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	−0.390490	−	0.920607i	$-0.627694\pi$
$421$	12.3525	−	21.3952i	0.602025	−	1.04274i	0.992514	−	0.122130i	$-0.0389724\pi$
$422$	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	−0.260157	−	0.965566i	$-0.583774\pi$
$431$	14.6596	−	25.3911i	0.706126	−	1.22305i	0.966283	−	0.257481i	$-0.0828924\pi$
$432$	−0.188501	−	0.108831i	−0.00906925	−	0.00523613i
$433$	19.6554			0.944578			0.472289	−	0.881444i	$-0.343428\pi$
$433$	19.6554			0.944578			0.472289	+	0.881444i	$0.343428\pi$
$434$		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	$-0.675310\pi$
$439$	−21.9299			−1.04666			−0.523330	+	0.852130i	$0.675310\pi$
$440$	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	$-0.826173\pi$
$461$	0.482926	−	0.836452i	0.0224921	−	0.0389575i	0.877052	+	0.480395i	$0.159507\pi$
$462$		0			0
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	0.871156	−	0.491006i	$-0.163371\pi$
$463$	0.222811	+	0.385920i	0.0103549	+	0.0179352i	−0.860802	+	0.508941i	$0.830037\pi$
$464$	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	0.924953	+	0.380081i	$0.124104\pi$
$467$	17.1074	+	29.6309i	0.791637	+	1.37115i	−0.133317	+	0.991074i	$0.542563\pi$
$468$	−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	$-0.000781622\pi$
$479$	10.8965	+	18.8732i	0.497872	+	0.862339i	−0.502125	+	0.864795i	$0.667448\pi$
$480$	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	−0.997642	−	0.0686297i	$-0.978137\pi$
$487$	−9.69640	+	16.7947i	−0.439386	+	0.761039i	0.558256	+	0.829669i	$0.311471\pi$
$488$	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	−0.994203	−	0.107519i	$-0.965709\pi$
$491$	−13.0783	−	22.6523i	−0.590216	−	1.02228i	0.403987	−	0.914765i	$-0.367624\pi$
$492$	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	−0.660403	−	0.750911i	$-0.729615\pi$
$499$	7.15064	−	12.3853i	0.320107	−	0.554441i	0.980510	+	0.196470i	$0.0629479\pi$
$500$	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	$-0.363092\pi$
$503$	18.7033			0.833937			0.416969	+	0.908921i	$0.363092\pi$
$504$		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	−0.429257	−	0.903183i	$-0.641224\pi$
$509$	12.8045	−	22.1781i	0.567551	−	0.983027i	0.996807	−	0.0798442i	$-0.0254423\pi$
$510$	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	$-0.679510\pi$
$521$	10.6061	−	18.3702i	0.464660	−	0.804815i	0.999186	+	0.0403370i	$0.0128431\pi$
$522$	12.6684	−	10.6301i	0.554482	−	0.465266i
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	0.543796	−	0.839217i	$-0.316986\pi$
$523$	−10.4029	−	18.0183i	−0.454885	−	0.787884i	−0.998682	+	0.0513330i	$0.983653\pi$
$524$	−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	−0.996085	−	0.0884001i	$-0.971825\pi$
$541$	−13.3648	−	23.1486i	−0.574599	−	0.995235i	0.421486	−	0.906835i	$-0.361509\pi$
$542$	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	0.142523	+	0.989792i	$0.454479\pi$
$547$	−18.3812	+	31.8372i	−0.785923	+	1.36126i	−0.928446	+	0.371467i	$0.878855\pi$
$548$	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	0.288282	+	0.957546i	$0.406916\pi$
$557$	−16.1694	+	28.0062i	−0.685118	+	1.18666i	−0.973400	+	0.229114i	$0.926417\pi$
$558$	−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	$-0.621968\pi$
$563$	−17.7419			−0.747730			−0.373865	+	0.927483i	$0.621968\pi$
$564$	−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	−0.288274	−	0.957548i	$-0.593082\pi$
$577$	16.4572	−	28.5048i	0.685124	−	1.18667i	0.973398	−	0.229121i	$-0.0735852\pi$
$578$	−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	$-0.732649\pi$
$587$	7.53643	−	13.0535i	0.311062	−	0.538774i	0.978592	+	0.205808i	$0.0659821\pi$
$588$		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	−0.888326	−	0.459213i	$-0.848131\pi$
$593$	−20.5005	−	35.5079i	−0.841853	−	1.45813i	0.0464729	−	0.998920i	$-0.485202\pi$
$594$			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	$-0.740246\pi$
$601$	7.06758	−	12.2414i	0.288293	−	0.499338i	0.973402	+	0.229102i	$0.0735791\pi$
$602$		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	−0.161377	+	0.986893i	$0.551594\pi$
$607$	−23.0449	+	39.9149i	−0.935363	+	1.62010i	−0.773986	+	0.633203i	$0.781740\pi$
$608$	−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	−0.464124	−	0.885770i	$-0.653631\pi$
$613$	13.2469	−	22.9443i	0.535038	−	0.926712i	0.999162	−	0.0409421i	$-0.0130359\pi$
$614$	−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	0.887781	−	0.460266i	$-0.152246\pi$
$617$	1.12495	+	1.94847i	0.0452889	+	0.0784426i	−0.842492	+	0.538708i	$0.818913\pi$
$618$	−3.56196	+	4.24497i	−0.143283	+	0.170758i
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	0.797090	−	0.603861i	$-0.206372\pi$
$619$	−3.09539	−	5.36137i	−0.124414	−	0.215492i	−0.921504	+	0.388369i	$0.873038\pi$
$620$	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	0.813705	−	0.581278i	$-0.197447\pi$
$641$	−2.44444	−	4.23389i	−0.0965496	−	0.167229i	−0.910254	+	0.414050i	$0.864114\pi$
$642$	3.71348	+	10.2027i	0.146559	+	0.402668i
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	0.922218	+	0.386671i	$0.126375\pi$
$643$	20.1839	+	34.9596i	0.795976	+	1.37867i	−0.126242	+	0.992000i	$0.540291\pi$
$644$		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	$-0.819058\pi$
$647$	1.14038	−	1.97519i	0.0448329	−	0.0776528i	0.887571	+	0.460671i	$0.152391\pi$
$648$	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	−0.998930	−	0.0462542i	$-0.985272\pi$
$653$	−11.7396	+	20.3336i	−0.459407	+	0.795717i	0.539522	+	0.841971i	$0.318605\pi$
$654$	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	0.158073	−	0.987427i	$-0.449472\pi$
$659$	23.9812	−	41.5366i	0.934174	−	1.61804i	0.776101	−	0.630609i	$-0.217195\pi$
$660$	−4.65910	−	0.821525i	−0.181355	−	0.0319778i
$661$	29.3090			1.13999			0.569995	−	0.821648i	$-0.306945\pi$
$661$	29.3090			1.13999			0.569995	+	0.821648i	$0.306945\pi$
$662$	−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	0.492719	+	0.870189i	$0.336003\pi$
$673$	−13.1591	+	22.7922i	−0.507246	+	0.878576i	−0.999965	+	0.00838731i	$0.997330\pi$
$674$	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	$-0.257744\pi$
$677$	35.8907			1.37939			0.689697	+	0.724098i	$0.257744\pi$
$678$	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	0.306818	+	0.951768i	$0.400736\pi$
$683$	−17.5321	+	30.3665i	−0.670847	+	1.16194i	−0.977664	+	0.210172i	$0.932597\pi$
$684$	−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	$-0.487483\pi$
$691$	2.06687			0.0786273			0.0393136	+	0.999227i	$0.487483\pi$
$692$	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	$-0.00586678\pi$
$719$	12.9768	+	22.4765i	0.483954	+	0.838233i	−0.515876	+	0.856663i	$0.672533\pi$
$720$	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	$-0.773000\pi$
$727$	5.08007	−	8.79894i	0.188409	−	0.326335i	0.944720	+	0.327878i	$0.106333\pi$
$728$		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	0.196441	+	0.980516i	$0.437062\pi$
$733$	−20.3307	+	35.2138i	−0.750931	+	1.30065i	−0.947372	+	0.320135i	$0.896272\pi$
$734$	−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	−0.532791	−	0.846247i	$-0.678857\pi$
$739$	12.6809	−	21.9640i	0.466475	−	0.807959i	0.999267	+	0.0382877i	$0.0121903\pi$
$740$	−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	0.995076	−	0.0991184i	$-0.0316023\pi$
$743$	11.2221	+	19.4372i	0.411699	+	0.713083i	−0.583377	+	0.812202i	$0.698269\pi$
$744$	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	−0.997827	−	0.0658924i	$-0.979011\pi$
$751$	−12.1086	+	20.9727i	−0.441849	+	0.765305i	0.555978	+	0.831197i	$0.312344\pi$
$752$	−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	$-0.725886\pi$
$761$	9.13610	−	15.8242i	0.331183	−	0.573626i	0.982744	+	0.184970i	$0.0592188\pi$
$762$	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	$-0.275097\pi$
$769$	−9.26470	−	16.0469i	−0.334094	−	0.578667i	−0.983310	+	0.181936i	$0.941764\pi$
$770$		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	$-0.816376\pi$
$773$	1.48040	−	2.56413i	0.0532463	−	0.0922253i	0.891420	+	0.453178i	$0.149710\pi$
$774$	−8.91534	+	7.48086i	−0.320455	+	0.268894i
$775$	14.7049	+	25.4696i	0.528214	+	0.914894i
$776$	2.69418	−	4.66646i	0.0967155	−	0.167516i
$777$		0			0
$778$	2.37417	+	4.11218i	0.0851181	+	0.147429i
$779$	5.50387	−	9.53298i	0.197197	−	0.341555i
$780$	9.49912	+	1.67495i	0.340123	+	0.0599729i
$781$	0.458111	+	0.793471i	0.0163925	+	0.0283926i
$782$	1.84002	+	3.18701i	0.0657991	+	0.113967i
$783$	−28.2086	+	16.2862i	−1.00809	+	0.582022i
$784$		0			0
$785$	−6.82635	+	11.8236i	−0.243643	+	0.422002i
$786$	−7.01512	+	8.36030i	−0.250221	+	0.298202i
$787$	−33.4020			−1.19065			−0.595326	−	0.803484i	$-0.702977\pi$
$787$	−33.4020			−1.19065			−0.595326	+	0.803484i	$0.702977\pi$
$788$	−14.0401			−0.500159
$789$	0.434889	+	1.19485i	0.0154824	+	0.0425377i
$790$	−1.42396	+	2.46638i	−0.0506623	+	0.0877497i
$791$		0			0
$792$	−2.44299	−	13.8549i	−0.0868079	−	0.492312i
$793$	12.8687	+	22.2893i	0.456981	+	0.791515i
$794$	−12.8542	−	22.2641i	−0.456177	−	0.790122i
$795$	0.458111	+	1.25865i	0.0162475	+	0.0446397i
$796$	−2.23143	+	3.86495i	−0.0790909	+	0.136989i
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.857772	−	0.514031i	$-0.828152\pi$
$797$	−24.6755	−	42.7391i	−0.874050	−	1.51390i	−0.0162779	−	0.999868i	$-0.505182\pi$
$798$		0			0
$799$	−2.18866	+	3.79088i	−0.0774293	+	0.134112i
$800$	−8.97818	−	15.5507i	−0.317427	−	0.549799i
$801$	−4.73355	−	26.8453i	−0.167252	−	0.948531i
$802$	−12.0466	+	20.8654i	−0.425382	+	0.736782i
$803$	3.38743			0.119540
$804$	−1.24763	−	0.219990i	−0.0440004	−	0.00775845i
$805$		0			0
$806$	−13.6816	−	23.6971i	−0.481912	−	0.834696i
$807$	23.2135	−	27.6647i	0.817153	−	0.973845i
$808$	2.42484	+	4.19995i	0.0853056	+	0.147754i
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	−0.985993	−	0.166784i	$-0.946662\pi$
$809$	−9.91400	+	17.1716i	−0.348558	+	0.603720i	0.637436	+	0.770503i	$0.279995\pi$
$810$	10.0201	−	3.64701i	0.352069	−	0.128143i
$811$	−23.8557			−0.837686			−0.418843	−	0.908059i	$-0.637564\pi$
$811$	−23.8557			−0.837686			−0.418843	+	0.908059i	$0.637564\pi$
$812$		0			0
$813$	−4.12196	−	11.3250i	−0.144563	−	0.397185i
$814$	6.71048	−	11.6229i	0.235202	−	0.407382i
$815$	−3.49794			−0.122528
$816$	0.0218219	−	0.0260063i	0.000763919	−	0.000910403i
$817$	14.2344			0.497999
$818$	7.93643			0.277491
$819$		0			0
$820$	−5.63816			−0.196893
$821$	−50.9427			−1.77791			−0.888957	−	0.457991i	$-0.848569\pi$
$821$	−50.9427			−1.77791			−0.888957	+	0.457991i	$0.848569\pi$
$822$	1.33827	+	3.67686i	0.0466774	+	0.128245i
$823$	13.6149			0.474587			0.237293	−	0.971438i	$-0.423740\pi$
$823$	13.6149			0.474587			0.237293	+	0.971438i	$0.423740\pi$
$824$	5.16163	−	8.94020i	0.179814	−	0.311447i
$825$	5.86009	−	6.98378i	0.204022	−	0.243144i
$826$		0			0
$827$	36.2158			1.25935			0.629673	−	0.776861i	$-0.283189\pi$
$827$	36.2158			1.25935			0.629673	+	0.776861i	$0.283189\pi$
$828$	25.2126	−	21.1559i	0.876198	−	0.735218i
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	−0.997674	−	0.0681664i	$-0.978285\pi$
$829$	−12.6630	+	21.9329i	−0.439803	+	0.761761i	0.557871	+	0.829928i	$0.311618\pi$
$830$	−8.91534	−	15.4418i	−0.309456	−	0.535994i
$831$	−10.5876	−	29.0893i	−0.367281	−	1.00910i
$832$	8.49454	+	14.7130i	0.294495	+	0.510080i
$833$		0			0
$834$	−3.19517	−	8.77864i	−0.110640	−	0.303980i
$835$	−31.2344			−1.08091
$836$	−3.27079	+	5.66518i	−0.113123	+	0.195934i
$837$	41.5549	+	23.9917i	1.43635	+	0.829276i
$838$	0.0770768	+	0.133501i	0.00266257	+	0.00461171i
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	−0.931383	−	0.364040i	$-0.881397\pi$
$839$	−4.35710	+	7.54671i	−0.150424	+	0.260541i	0.780960	+	0.624582i	$0.214730\pi$
$840$		0			0
$841$	−5.14749	−	8.91571i	−0.177500	−	0.307438i
$842$	−10.8626	+	18.8146i	−0.374350	+	0.648394i
$843$	−24.8391	+	29.6021i	−0.855506	+	1.01955i
$844$	3.57145	+	6.18594i	0.122934	+	0.212929i
$845$	1.10876	+	1.92042i	0.0381423	+	0.0660645i
$846$	−23.1917	−	8.44107i	−0.797346	−	0.290210i
$847$		0			0
$848$	−0.0120217	+	0.0208222i	−0.000412827	+	0.000715037i
$849$	−31.7173	−	5.59262i	−1.08854	−	0.191938i
$850$	1.31046			0.0449484
$851$	82.5886			2.83110
$852$	1.15998	+	0.204535i	0.0397402	+	0.00700727i
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	−0.745053	−	0.667005i	$-0.767576\pi$
$853$	5.99067	−	10.3761i	0.205117	−	0.355272i	0.950170	+	0.311733i	$0.100909\pi$
$854$		0			0
$855$	−12.2554	−	4.46059i	−0.419125	−	0.152549i
$856$	−10.1133	−	17.5168i	−0.345667	−	0.598713i
$857$	−3.25015	−	5.62943i	−0.111023	−	0.192298i	0.805160	−	0.593058i	$-0.202079\pi$
$857$	−3.25015	−	5.62943i	−0.111023	−	0.192298i	−0.916183	+	0.400760i	$0.868746\pi$
$858$	−5.45229	+	6.49778i	−0.186138	+	0.221831i
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.104652	−	0.994509i	$-0.466627\pi$
$859$	26.7763	−	46.3779i	0.913596	−	1.58239i	0.808944	−	0.587886i	$-0.200040\pi$
$860$	−3.64543	−	6.31407i	−0.124308	−	0.215308i
$861$		0			0
$862$	−12.8914	+	22.3286i	−0.439083	+	0.760514i
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	0.832822	−	0.553540i	$-0.186723\pi$
$863$	−1.84982	−	3.20399i	−0.0629687	−	0.109065i	−0.895791	+	0.444475i	$0.853390\pi$
$864$	−25.3717	−	14.6484i	−0.863163	−	0.498347i
$865$	3.20115	−	5.54456i	0.108842	−	0.188521i
$866$	−17.2847			−0.587357
$867$	9.94104	+	27.3128i	0.337615	+	0.927590i
$868$		0			0
$869$	1.98633	+	3.44042i	0.0673816	+	0.116708i
$870$	4.39970	+	12.0881i	0.149164	+	0.409824i
$871$	1.00459	+	1.73999i	0.0340391	+	0.0589574i
$872$	−0.572796	+	0.992112i	−0.0193973	+	0.0335971i
$873$	4.36412	−	3.66193i	0.147703	−	0.123938i
$874$	25.3773			0.858401
$875$		0			0
$876$	2.79921	−	3.33597i	0.0945765	−	0.112712i
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	−0.749178	−	0.662369i	$-0.769551\pi$
$877$	5.89440	−	10.2094i	0.199040	−	0.344747i	0.948217	+	0.317622i	$0.102884\pi$
$878$	19.2849			0.650833
$879$	−7.75537	−	21.3077i	−0.261582	−	0.718691i
$880$	−0.0932736			−0.00314425
$881$	49.4858			1.66722			0.833609	−	0.552355i	$-0.186271\pi$
$881$	49.4858			1.66722			0.833609	+	0.552355i	$0.186271\pi$
$882$		0			0
$883$	−21.5357			−0.724734			−0.362367	−	0.932035i	$-0.618031\pi$
$883$	−21.5357			−0.724734			−0.362367	+	0.932035i	$0.618031\pi$
$884$	1.93407			0.0650497
$885$	15.5954	−	18.5859i	0.524233	−	0.624757i
$886$	16.4534			0.552762
$887$	−5.94238	+	10.2925i	−0.199526	+	0.345589i	−0.948375	−	0.317152i	$-0.897273\pi$
$887$	−5.94238	+	10.2925i	−0.199526	+	0.345589i	0.748849	+	0.662741i	$0.230607\pi$
$888$	−15.5223	−	42.6473i	−0.520896	−	1.43115i
$889$		0			0
$890$	−10.7656			−0.360863
$891$	2.58290	−	14.6484i	0.0865304	−	0.490738i
$892$	4.34477	−	7.52536i	0.145474	−	0.251968i
$893$	15.0929	+	26.1416i	0.505063	+	0.874795i
$894$	0.422046	−	0.502975i	0.0141153	−	0.0168220i
$895$	5.74763	+	9.95518i	0.192122	+	0.332765i
$896$		0			0
$897$	−51.4043	−	9.06396i	−1.71634	−	0.302637i
$898$	−5.87433			−0.196029
$899$	−28.9433	+	50.1313i	−0.965314	+	1.67197i
$900$	−2.03519	−	11.5421i	−0.0678396	−	0.384737i
$901$	0.134285	+	0.232589i	0.00447369	+	0.00774866i
$902$	2.47906	−	4.29385i	0.0825435	−	0.142970i
$903$		0			0
$904$	−20.3868	−	35.3110i	−0.678056	−	1.17443i
$905$	11.6099	−	20.1090i	0.385927	−	0.668446i
$906$	−1.28705	−	3.53613i	−0.0427592	−	0.117480i
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	0.997047	−	0.0767980i	$-0.0244697\pi$
$907$	13.0107	+	22.5353i	0.432014	+	0.748271i	−0.565032	+	0.825069i	$0.691136\pi$
$908$	−7.32547	−	12.6881i	−0.243104	−	0.421069i
$909$	0.890367	+	5.04952i	0.0295316	+	0.167482i
$910$		0			0
$911$	2.01636	−	3.49244i	0.0668050	−	0.115710i	−0.830688	−	0.556738i	$-0.812053\pi$
$911$	2.01636	−	3.49244i	0.0668050	−	0.115710i	0.897493	+	0.441028i	$0.145386\pi$
$912$	−0.0800699	−	0.219990i	−0.00265138	−	0.00728460i
$913$	−24.8726			−0.823162
$914$	17.0853			0.565132
$915$	−11.4572	+	13.6542i	−0.378764	+	0.451394i
$916$	−10.7657	+	18.6468i	−0.355710	+	0.616108i
$917$		0			0
$918$	1.85163	−	1.06904i	0.0611130	−	0.0352836i
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	0.546167	−	0.837677i	$-0.316087\pi$
$919$	−13.7135	−	23.7524i	−0.452366	−	0.783521i	−0.998532	+	0.0541559i	$0.982753\pi$
$920$	−17.0954	−	29.6101i	−0.563618	−	0.976216i
$921$	10.7640	+	1.89798i	0.354685	+	0.0625406i
$922$	−0.424678	+	0.735564i	−0.0139860	+	0.0242245i
$923$	−0.934011	−	1.61775i	−0.0307434	−	0.0532491i
$924$		0			0
$925$	14.7049	−	25.4696i	0.483493	−	0.837434i
$926$	−0.195937	−	0.339373i	−0.00643889	−	0.0111525i
$927$	8.36097	−	7.01568i	0.274610	−	0.230425i
$928$	17.6716	−	30.6081i	0.580098	−	1.00476i
$929$	7.67675			0.251866			0.125933	−	0.992039i	$-0.459808\pi$
$929$	7.67675			0.251866			0.125933	+	0.992039i	$0.459808\pi$
$930$	12.1809	−	14.5167i	0.399428	−	0.476020i
$931$		0			0
$932$	9.96926	+	17.2673i	0.326554	+	0.565608i
$933$	−16.2460	−	2.86461i	−0.531871	−	0.0937833i
$934$	−15.0440	−	26.0570i	−0.492255	−	0.852610i
$935$	−0.520945	+	0.902302i	−0.0170367	+	0.0295084i
$936$	4.98085	+	28.2478i	0.162804	+	0.923308i
$937$	−2.02465			−0.0661425			−0.0330713	−	0.999453i	$-0.510529\pi$
$937$	−2.02465			−0.0661425			−0.0330713	+	0.999453i	$0.510529\pi$
$938$		0			0
$939$	−30.0699	−	5.30213i	−0.981293	−	0.173028i
$940$	7.73055	−	13.3897i	0.252143	−	0.436724i
$941$	−6.13928			−0.200135			−0.100067	−	0.994981i	$-0.531906\pi$
$941$	−6.13928			−0.200135			−0.100067	+	0.994981i	$0.531906\pi$
$942$	−15.2001	−	2.68019i	−0.495246	−	0.0873253i
$943$	30.5107			0.993566
$944$	0.435518			0.0141749
$945$		0			0
$946$	6.41147			0.208455
$947$	5.56448			0.180821			0.0904107	−	0.995905i	$-0.471182\pi$
$947$	5.56448			0.180821			0.0904107	+	0.995905i	$0.471182\pi$
$948$	5.02956	+	0.886848i	0.163353	+	0.0288035i
$949$	−6.90640			−0.224191
$950$	4.51842	−	7.82613i	0.146597	−	0.253913i
$951$	13.7772	+	2.42929i	0.446756	+	0.0787751i
$952$		0			0
$953$	−8.72018			−0.282474			−0.141237	−	0.989976i	$-0.545108\pi$
$953$	−8.72018			−0.282474			−0.141237	+	0.989976i	$0.545108\pi$
$954$	−1.15998	+	0.973337i	−0.0375557	+	0.0315129i
$955$	−8.69640	+	15.0626i	−0.281409	+	0.487415i
$956$	−9.26099	−	16.0405i	−0.299522	−	0.518787i
$957$	17.6716	+	3.11598i	0.571241	+	0.100725i
$958$	−9.58219	−	16.5968i	−0.309586	−	0.536219i
$959$		0			0
$960$	−7.56283	+	9.01303i	−0.244089	+	0.290894i
$961$	54.2746			1.75079
$962$	−13.6816	+	23.6971i	−0.441111	+	0.764027i
$963$	−3.71348	−	21.0602i	−0.119665	−	0.678655i
$964$	−9.59152	−	16.6130i	−0.308922	−	0.535069i
$965$	0.429892	−	0.744596i	0.0138387	−	0.0239694i
$966$		0			0
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.785206	+	0.619235i	$0.212557\pi$
$967$	28.8849	+	50.0301i	0.928876	+	1.60886i	0.143670	+	0.989626i	$0.454110\pi$
$968$	11.7310	−	20.3187i	0.377049	−	0.653068i
$969$	−2.57532	−	0.454099i	−0.0827313	−	0.0145878i
$970$	−1.12495	−	1.94847i	−0.0361200	−	0.0625617i
$971$	15.3596	+	26.6036i	0.492914	+	0.853752i	0.999967	−	0.00816326i	$-0.00259847\pi$
$971$	15.3596	+	26.6036i	0.492914	+	0.853752i	−0.507053	+	0.861915i	$0.669265\pi$
$972$	−12.2914	−	14.6484i	−0.394248	−	0.469846i
$973$		0			0
$974$	8.52687	−	14.7690i	0.273219	−	0.473229i
$975$	−11.9477	+	14.2388i	−0.382634	+	0.456005i
$976$	−0.319955			−0.0102415
$977$	10.3000			0.329527			0.164764	−	0.986333i	$-0.447314\pi$
$977$	10.3000			0.329527			0.164764	+	0.986333i	$0.447314\pi$
$978$	−1.35251	−	3.71599i	−0.0432485	−	0.118824i
$979$	−7.50862	+	13.0053i	−0.239976	+	0.415651i
$980$		0			0
$981$	−0.927833	+	0.778544i	−0.0296234	+	0.0248570i
$982$	11.5009	+	19.9201i	0.367008	+	0.635676i
$983$	−6.84817	−	11.8614i	−0.218423	−	0.378319i	0.735903	−	0.677087i	$-0.236758\pi$
$983$	−6.84817	−	11.8614i	−0.218423	−	0.378319i	−0.954326	+	0.298767i	$0.903425\pi$
$984$	−5.73442	−	15.7552i	−0.182807	−	0.502257i
$985$	−7.71032	+	13.3547i	−0.245671	+	0.425515i
$986$	1.28968	+	2.23379i	0.0410717	+	0.0711383i
$987$		0			0
$988$	6.66860	−	11.5503i	0.212156	−	0.367465i
$989$	19.7271	+	34.1684i	0.627287	+	1.08649i
$990$	−5.52007	−	2.00914i	−0.175439	−	0.0638547i
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.122922	+	0.992416i	$0.539227\pi$
$991$	−28.9907	+	50.2133i	−0.920919	+	1.59508i	−0.797997	+	0.602662i	$0.794107\pi$
$992$	−52.0651			−1.65307
$993$	39.3166	+	6.93258i	1.24767	+	0.219999i
$994$		0			0
$995$	2.45084	+	4.24497i	0.0776968	+	0.134575i
$996$	−20.5535	+	24.4947i	−0.651263	+	0.776145i
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	0.708578	−	0.705633i	$-0.249337\pi$
$997$	−8.10876	−	14.0448i	−0.256807	−	0.444803i	−0.965385	+	0.260830i	$0.916004\pi$
$998$	−6.28817	+	10.8914i	−0.199049	+	0.344762i
$999$		−	47.9835i		−	1.51813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.d.214.1		6
3.2	odd	2		1323.2.h.c.802.3		6
7.2	even	3		441.2.g.c.79.3		6
7.3	odd	6		441.2.f.c.295.3		6
7.4	even	3		63.2.f.a.43.3	yes	6
7.5	odd	6		441.2.g.b.79.3		6
7.6	odd	2		441.2.h.e.214.1		6
9.4	even	3		441.2.g.c.67.3		6
9.5	odd	6		1323.2.g.d.361.1		6
21.2	odd	6		1323.2.g.d.667.1		6
21.5	even	6		1323.2.g.e.667.1		6
21.11	odd	6		189.2.f.b.127.1		6
21.17	even	6		1323.2.f.d.883.1		6
21.20	even	2		1323.2.h.b.802.3		6
28.11	odd	6		1008.2.r.h.673.2		6
63.4	even	3		63.2.f.a.22.3	✓	6
63.5	even	6		1323.2.h.b.226.3		6
63.11	odd	6		567.2.a.c.1.3		3
63.13	odd	6		441.2.g.b.67.3		6
63.23	odd	6		1323.2.h.c.226.3		6
63.25	even	3		567.2.a.h.1.1		3
63.31	odd	6		441.2.f.c.148.3		6
63.32	odd	6		189.2.f.b.64.1		6
63.38	even	6		3969.2.a.l.1.3		3
63.40	odd	6		441.2.h.e.373.1		6
63.41	even	6		1323.2.g.e.361.1		6
63.52	odd	6		3969.2.a.q.1.1		3
63.58	even	3	inner	441.2.h.d.373.1		6
63.59	even	6		1323.2.f.d.442.1		6
84.11	even	6		3024.2.r.k.2017.2		6
252.11	even	6		9072.2.a.bs.1.2		3
252.67	odd	6		1008.2.r.h.337.2		6
252.95	even	6		3024.2.r.k.1009.2		6
252.151	odd	6		9072.2.a.ca.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.3	✓	6	63.4	even	3
63.2.f.a.43.3	yes	6	7.4	even	3
189.2.f.b.64.1		6	63.32	odd	6
189.2.f.b.127.1		6	21.11	odd	6
441.2.f.c.148.3		6	63.31	odd	6
441.2.f.c.295.3		6	7.3	odd	6
441.2.g.b.67.3		6	63.13	odd	6
441.2.g.b.79.3		6	7.5	odd	6
441.2.g.c.67.3		6	9.4	even	3
441.2.g.c.79.3		6	7.2	even	3
441.2.h.d.214.1		6	1.1	even	1	trivial
441.2.h.d.373.1		6	63.58	even	3	inner
441.2.h.e.214.1		6	7.6	odd	2
441.2.h.e.373.1		6	63.40	odd	6
567.2.a.c.1.3		3	63.11	odd	6
567.2.a.h.1.1		3	63.25	even	3
1008.2.r.h.337.2		6	252.67	odd	6
1008.2.r.h.673.2		6	28.11	odd	6
1323.2.f.d.442.1		6	63.59	even	6
1323.2.f.d.883.1		6	21.17	even	6
1323.2.g.d.361.1		6	9.5	odd	6
1323.2.g.d.667.1		6	21.2	odd	6
1323.2.g.e.361.1		6	63.41	even	6
1323.2.g.e.667.1		6	21.5	even	6
1323.2.h.b.226.3		6	63.5	even	6
1323.2.h.b.802.3		6	21.20	even	2
1323.2.h.c.226.3		6	63.23	odd	6
1323.2.h.c.802.3		6	3.2	odd	2
3024.2.r.k.1009.2		6	252.95	even	6
3024.2.r.k.2017.2		6	84.11	even	6
3969.2.a.l.1.3		3	63.38	even	6
3969.2.a.q.1.1		3	63.52	odd	6
9072.2.a.bs.1.2		3	252.11	even	6
9072.2.a.ca.1.2		3	252.151	odd	6

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

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