LMFDB - Embedded newform 361.2.e.a.28.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-3,-6,9,3,-6,0,-6,12,9,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$6$
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:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	361.28
Dual form			361.2.e.a.245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.152704 - 0.866025i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(1.15270 - 0.419550i) q^{4} +(2.37939 + 0.866025i) q^{5} +(0.358441 + 0.300767i) q^{6} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +(0.386659 - 2.19285i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(-0.326352 + 0.565258i) q^{12} +(4.05303 + 3.40090i) q^{13} +(-1.55303 - 0.565258i) q^{14} +(-1.26604 + 0.460802i) q^{15} +(-0.0320889 + 0.0269258i) q^{16} +(0.286989 + 1.62760i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(0.173648 + 0.984808i) q^{21} +(-2.29813 + 1.92836i) q^{22} +(-1.65270 + 0.601535i) q^{23} +(1.41875 + 0.516382i) q^{24} +(1.08125 + 0.907278i) q^{25} +(2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(0.400330 - 2.27038i) q^{28} +(0.602196 - 3.41523i) q^{29} +(0.592396 + 1.02606i) q^{30} +(0.971782 - 1.68317i) q^{31} +(-4.31908 - 3.62414i) q^{32} +(1.70574 + 0.620838i) q^{33} +(1.36571 - 0.497079i) q^{34} +(3.64543 - 3.05888i) q^{35} +(0.578726 + 3.28212i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(-1.24763 - 7.07564i) q^{40} +(3.43969 - 2.88624i) q^{41} +(0.826352 - 0.300767i) q^{42} +(-4.51114 - 1.64192i) q^{43} +(-3.20574 - 2.68993i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(0.773318 + 1.33943i) q^{46} +(0.124485 - 0.705990i) q^{47} +(0.00387039 - 0.0219501i) q^{48} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(-0.673648 - 0.565258i) q^{51} +(6.09879 + 2.21978i) q^{52} +(-5.73783 + 2.08840i) q^{53} +(-2.04916 + 1.71945i) q^{54} +(-1.50000 - 8.50692i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(1.86824 + 10.5953i) q^{59} +(-1.26604 + 1.06234i) q^{60} +(-4.12449 + 1.50119i) q^{61} +(-1.60607 - 0.584561i) q^{62} +(3.91147 + 3.28212i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(0.277189 - 1.57202i) q^{66} +(-2.46791 + 13.9962i) q^{67} +(1.01367 + 1.75573i) q^{68} +(0.467911 - 0.810446i) q^{69} +(-3.20574 - 2.68993i) q^{70} +(-12.9290 - 4.70578i) q^{71} +(7.24422 - 2.63668i) q^{72} +(-5.75877 + 4.83218i) q^{73} +(-0.127889 - 0.725293i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(0.429892 + 2.43804i) q^{78} +(5.33409 - 4.47584i) q^{79} +(-0.0996702 + 0.0362770i) q^{80} +(-6.13816 - 2.23411i) q^{81} +(-3.02481 - 2.53812i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(0.613341 + 1.06234i) q^{84} +(-0.726682 + 4.12122i) q^{85} +(-0.733078 + 4.15749i) q^{86} +(0.922618 + 1.59802i) q^{87} +(-4.84002 + 8.38316i) q^{88} +(1.74897 + 1.46756i) q^{89} +(5.68479 + 2.06910i) q^{90} +(9.34389 - 3.40090i) q^{91} +(-1.65270 + 1.38678i) q^{92} +(0.179578 + 1.01844i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(0.316552 + 1.79525i) q^{97} +(2.33615 - 1.96026i) q^{98} +(8.70961 - 3.17004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25}+ \cdots + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.152704	−	0.866025i	−0.107978	−	0.612372i	−0.989989	−	0.141144i	$-0.954922\pi$
$2$	−0.152704	−	0.866025i	−0.107978	−	0.612372i	0.882011	−	0.471228i	$-0.156189\pi$
$3$	−0.407604	+	0.342020i	−0.235330	+	0.197465i	−0.752825	−	0.658221i	$-0.771309\pi$
$3$	−0.407604	+	0.342020i	−0.235330	+	0.197465i	0.517495	+	0.855686i	$0.326865\pi$
$4$	1.15270	−	0.419550i	0.576352	−	0.209775i
$5$	2.37939	+	0.866025i	1.06409	+	0.387298i	0.813965	−	0.580914i	$-0.197305\pi$
$5$	2.37939	+	0.866025i	1.06409	+	0.387298i	0.250129	+	0.968213i	$0.419527\pi$
$6$	0.358441	+	0.300767i	0.146333	+	0.122788i
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	−0.631977	−	0.774987i	$-0.717756\pi$
$7$	0.939693	−	1.62760i	0.355170	−	0.615173i	0.987147	+	0.159814i	$0.0510895\pi$
$8$	−1.41875	−	2.45734i	−0.501603	−	0.868802i
$9$	−0.471782	+	2.67561i	−0.157261	+	0.891869i
$10$	0.386659	−	2.19285i	0.122272	−	0.693441i
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	−0.999862	−	0.0165906i	$-0.994719\pi$
$11$	−1.70574	−	2.95442i	−0.514299	−	0.890792i	0.485563	−	0.874202i	$-0.338615\pi$
$12$	−0.326352	+	0.565258i	−0.0942097	+	0.163176i
$13$	4.05303	+	3.40090i	1.12411	+	0.943240i	0.998805	−	0.0488787i	$-0.0155648\pi$
$13$	4.05303	+	3.40090i	1.12411	+	0.943240i	0.125304	+	0.992118i	$0.460009\pi$
$14$	−1.55303	−	0.565258i	−0.415066	−	0.151072i
$15$	−1.26604	+	0.460802i	−0.326891	+	0.118979i
$16$	−0.0320889	+	0.0269258i	−0.00802222	+	0.00673144i
$17$	0.286989	+	1.62760i	0.0696051	+	0.394750i	0.999629	+	0.0272501i	$0.00867503\pi$
$17$	0.286989	+	1.62760i	0.0696051	+	0.394750i	−0.930024	+	0.367500i	$0.880214\pi$
$18$	2.38919			0.563136
$19$		0			0
$19$		0			0
$20$	3.10607			0.694538
$21$	0.173648	+	0.984808i	0.0378931	+	0.214903i
$22$	−2.29813	+	1.92836i	−0.489964	+	0.411128i
$23$	−1.65270	+	0.601535i	−0.344613	+	0.125429i	−0.508527	−	0.861046i	$-0.669810\pi$
$23$	−1.65270	+	0.601535i	−0.344613	+	0.125429i	0.163915	+	0.986474i	$0.447588\pi$
$24$	1.41875	+	0.516382i	0.289601	+	0.105406i
$25$	1.08125	+	0.907278i	0.216250	+	0.181456i
$26$	2.32635	−	4.02936i	0.456235	−	0.790222i
$27$	−1.52094	−	2.63435i	−0.292706	−	0.506982i
$28$	0.400330	−	2.27038i	0.0756552	−	0.429062i
$29$	0.602196	−	3.41523i	0.111825	−	0.634192i	−0.876448	−	0.481496i	$-0.840094\pi$
$29$	0.602196	−	3.41523i	0.111825	−	0.634192i	0.988273	−	0.152695i	$-0.0487953\pi$
$30$	0.592396	+	1.02606i	0.108156	+	0.187332i
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	−0.765464	−	0.643479i	$-0.777490\pi$
$31$	0.971782	−	1.68317i	0.174537	−	0.302307i	0.940001	+	0.341172i	$0.110824\pi$
$32$	−4.31908	−	3.62414i	−0.763512	−	0.640663i
$33$	1.70574	+	0.620838i	0.296931	+	0.108074i
$34$	1.36571	−	0.497079i	0.234218	−	0.0852484i
$35$	3.64543	−	3.05888i	0.616190	−	0.517045i
$36$	0.578726	+	3.28212i	0.0964543	+	0.547019i
$37$	0.837496			0.137684			0.0688418	−	0.997628i	$-0.478070\pi$
$37$	0.837496			0.137684			0.0688418	+	0.997628i	$0.478070\pi$
$38$		0			0
$39$	−2.81521			−0.450794
$40$	−1.24763	−	7.07564i	−0.197267	−	1.11876i
$41$	3.43969	−	2.88624i	0.537190	−	0.450756i	−0.333386	−	0.942790i	$-0.608191\pi$
$41$	3.43969	−	2.88624i	0.537190	−	0.450756i	0.870576	+	0.492035i	$0.163747\pi$
$42$	0.826352	−	0.300767i	0.127509	−	0.0464094i
$43$	−4.51114	−	1.64192i	−0.687943	−	0.250391i	−0.0256888	−	0.999670i	$-0.508178\pi$
$43$	−4.51114	−	1.64192i	−0.687943	−	0.250391i	−0.662254	+	0.749279i	$0.730400\pi$
$44$	−3.20574	−	2.68993i	−0.483283	−	0.405523i
$45$	−3.43969	+	5.95772i	−0.512759	+	0.888125i
$46$	0.773318	+	1.33943i	0.114020	+	0.197488i
$47$	0.124485	−	0.705990i	0.0181580	−	0.102979i	−0.974382	−	0.224900i	$-0.927794\pi$
$47$	0.124485	−	0.705990i	0.0181580	−	0.102979i	0.992540	+	0.121921i	$0.0389055\pi$
$48$	0.00387039	−	0.0219501i	0.000558643	−	0.00316822i
$49$	1.73396	+	3.00330i	0.247708	+	0.429043i
$50$	0.620615	−	1.07494i	0.0877682	−	0.152019i
$51$	−0.673648	−	0.565258i	−0.0943296	−	0.0791519i
$52$	6.09879	+	2.21978i	0.845750	+	0.307828i
$53$	−5.73783	+	2.08840i	−0.788151	+	0.286864i	−0.704567	−	0.709637i	$-0.748859\pi$
$53$	−5.73783	+	2.08840i	−0.788151	+	0.286864i	−0.0835838	+	0.996501i	$0.526637\pi$
$54$	−2.04916	+	1.71945i	−0.278856	+	0.233988i
$55$	−1.50000	−	8.50692i	−0.202260	−	1.14707i
$56$	−5.33275			−0.712618
$57$		0			0
$58$	−3.04963			−0.400436
$59$	1.86824	+	10.5953i	0.243224	+	1.37939i	0.824581	+	0.565744i	$0.191411\pi$
$59$	1.86824	+	10.5953i	0.243224	+	1.37939i	−0.581356	+	0.813649i	$0.697478\pi$
$60$	−1.26604	+	1.06234i	−0.163446	+	0.137147i
$61$	−4.12449	+	1.50119i	−0.528086	+	0.192208i	−0.592284	−	0.805730i	$-0.701773\pi$
$61$	−4.12449	+	1.50119i	−0.528086	+	0.192208i	0.0641974	+	0.997937i	$0.479551\pi$
$62$	−1.60607	−	0.584561i	−0.203971	−	0.0742393i
$63$	3.91147	+	3.28212i	0.492799	+	0.413508i
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	6.69846	+	11.6021i	0.830842	+	1.43906i
$66$	0.277189	−	1.57202i	0.0341196	−	0.193502i
$67$	−2.46791	+	13.9962i	−0.301503	+	1.70991i	0.338020	+	0.941139i	$0.390243\pi$
$67$	−2.46791	+	13.9962i	−0.301503	+	1.70991i	−0.639524	+	0.768772i	$0.720868\pi$
$68$	1.01367	+	1.75573i	0.122926	+	0.212913i
$69$	0.467911	−	0.810446i	0.0563299	−	0.0975662i
$70$	−3.20574	−	2.68993i	−0.383159	−	0.321508i
$71$	−12.9290	−	4.70578i	−1.53439	−	0.558473i	−0.569700	−	0.821853i	$-0.692940\pi$
$71$	−12.9290	−	4.70578i	−1.53439	−	0.558473i	−0.964692	+	0.263380i	$0.915163\pi$
$72$	7.24422	−	2.63668i	0.853740	−	0.310736i
$73$	−5.75877	+	4.83218i	−0.674013	+	0.565564i	−0.914250	−	0.405150i	$-0.867219\pi$
$73$	−5.75877	+	4.83218i	−0.674013	+	0.565564i	0.240237	+	0.970714i	$0.422775\pi$
$74$	−0.127889	−	0.725293i	−0.0148668	−	0.0843136i
$75$	−0.751030			−0.0867214
$76$		0			0
$77$	−6.41147			−0.730655
$78$	0.429892	+	2.43804i	0.0486757	+	0.276054i
$79$	5.33409	−	4.47584i	0.600132	−	0.503571i	−0.291356	−	0.956615i	$-0.594106\pi$
$79$	5.33409	−	4.47584i	0.600132	−	0.503571i	0.891488	+	0.453044i	$0.149662\pi$
$80$	−0.0996702	+	0.0362770i	−0.0111435	+	0.00405589i
$81$	−6.13816	−	2.23411i	−0.682017	−	0.248234i
$82$	−3.02481	−	2.53812i	−0.334035	−	0.280289i
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	−0.926698	−	0.375807i	$-0.877366\pi$
$83$	−1.25624	+	2.17588i	−0.137891	+	0.238834i	0.788807	+	0.614641i	$0.210699\pi$
$84$	0.613341	+	1.06234i	0.0669210	+	0.115911i
$85$	−0.726682	+	4.12122i	−0.0788197	+	0.447009i
$86$	−0.733078	+	4.15749i	−0.0790499	+	0.448314i
$87$	0.922618	+	1.59802i	0.0989151	+	0.171326i
$88$	−4.84002	+	8.38316i	−0.515948	+	0.893648i
$89$	1.74897	+	1.46756i	0.185390	+	0.155561i	0.730760	−	0.682635i	$-0.239166\pi$
$89$	1.74897	+	1.46756i	0.185390	+	0.155561i	−0.545369	+	0.838196i	$0.683611\pi$
$90$	5.68479	+	2.06910i	0.599230	+	0.218102i
$91$	9.34389	−	3.40090i	0.979506	−	0.356511i
$92$	−1.65270	+	1.38678i	−0.172306	+	0.144582i
$93$	0.179578	+	1.01844i	0.0186214	+	0.105607i
$94$	−0.630415			−0.0650223
$95$		0			0
$96$	3.00000			0.306186
$97$	0.316552	+	1.79525i	0.0321409	+	0.182280i	0.996652	−	0.0817628i	$-0.0260550\pi$
$97$	0.316552	+	1.79525i	0.0321409	+	0.182280i	−0.964511	+	0.264043i	$0.914944\pi$
$98$	2.33615	−	1.96026i	0.235987	−	0.198017i
$99$	8.70961	−	3.17004i	0.875348	−	0.318601i
$100$	1.62701	+	0.592184i	0.162701	+	0.0592184i
$101$	−6.06805	−	5.09170i	−0.603793	−	0.506643i	0.288869	−	0.957369i	$-0.406721\pi$
$101$	−6.06805	−	5.09170i	−0.603793	−	0.506643i	−0.892662	+	0.450726i	$0.851165\pi$
$102$	−0.386659	+	0.669713i	−0.0382850	+	0.0663115i
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	0.865667	−	0.500621i	$-0.166895\pi$
$103$	−0.00727396	−	0.0125989i	−0.000716725	−	0.00124140i	−0.866384	+	0.499379i	$0.833561\pi$
$104$	2.60694	−	14.7847i	0.255632	−	1.44976i
$105$	−0.439693	+	2.49362i	−0.0429096	+	0.243352i
$106$	2.68479	+	4.65020i	0.260770	+	0.451667i
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	−0.939052	−	0.343776i	$-0.888294\pi$
$107$	−1.77719	+	3.07818i	−0.171807	+	0.297579i	0.767244	+	0.641355i	$0.221627\pi$
$108$	−2.85844	−	2.39852i	−0.275054	−	0.230797i
$109$	6.92514	+	2.52055i	0.663309	+	0.241425i	0.651664	−	0.758508i	$-0.274071\pi$
$109$	6.92514	+	2.52055i	0.663309	+	0.241425i	0.0116444	+	0.999932i	$0.496293\pi$
$110$	−7.13816	+	2.59808i	−0.680596	+	0.247717i
$111$	−0.341367	+	0.286441i	−0.0324011	+	0.0271877i
$112$	0.0136706	+	0.0775297i	0.00129175	+	0.00732587i
$113$	−7.37733			−0.694000			−0.347000	−	0.937865i	$-0.612800\pi$
$113$	−7.37733			−0.694000			−0.347000	+	0.937865i	$0.612800\pi$
$114$		0			0
$115$	−4.45336			−0.415278
$116$	−0.738703	−	4.18939i	−0.0685869	−	0.388976i
$117$	−11.0116	+	9.23984i	−1.01802	+	0.854223i
$118$	8.89053	−	3.23589i	0.818440	−	0.297888i
$119$	2.91875	+	1.06234i	0.267561	+	0.0973843i
$120$	2.92855	+	2.45734i	0.267339	+	0.224324i
$121$	−0.319078	+	0.552659i	−0.0290071	+	0.0502417i
$122$	1.92989	+	3.34267i	0.174724	+	0.302631i
$123$	−0.414878	+	2.35289i	−0.0374083	+	0.212153i
$124$	0.414000	−	2.34791i	0.0371783	−	0.210849i
$125$	−4.54323	−	7.86911i	−0.406359	−	0.703835i
$126$	2.24510	−	3.88863i	0.200009	−	0.346426i
$127$	0.0773815	+	0.0649308i	0.00686650	+	0.00576168i	0.646214	−	0.763156i	$-0.276351\pi$
$127$	0.0773815	+	0.0649308i	0.00686650	+	0.00576168i	−0.639348	+	0.768918i	$0.720796\pi$
$128$	−6.42989	−	2.34029i	−0.568328	−	0.206854i
$129$	2.40033	−	0.873649i	0.211337	−	0.0769205i
$130$	9.02481	−	7.57272i	0.791529	−	0.664171i
$131$	−0.527341	−	2.99070i	−0.0460740	−	0.261299i	0.953066	−	0.302763i	$-0.0979089\pi$
$131$	−0.527341	−	2.99070i	−0.0460740	−	0.261299i	−0.999140	+	0.0414639i	$0.986798\pi$
$132$	2.22668			0.193808
$133$		0			0
$134$	12.4979			1.07966
$135$	−1.33750	−	7.58532i	−0.115113	−	0.652840i
$136$	3.59240	−	3.01438i	0.308045	−	0.258481i
$137$	−18.3614	+	6.68302i	−1.56872	+	0.570969i	−0.972714	−	0.232009i	$-0.925470\pi$
$137$	−18.3614	+	6.68302i	−1.56872	+	0.570969i	−0.596009	+	0.802977i	$0.703248\pi$
$138$	−0.773318	−	0.281465i	−0.0658292	−	0.0239599i
$139$	11.7947	+	9.89695i	1.00042	+	0.839449i	0.987042	−	0.160462i	$-0.0512984\pi$
$139$	11.7947	+	9.89695i	1.00042	+	0.839449i	0.0133739	+	0.999911i	$0.495743\pi$
$140$	2.91875	−	5.05542i	0.246679	−	0.427261i
$141$	0.190722	+	0.330341i	0.0160617	+	0.0278197i
$142$	−2.10101	+	11.9154i	−0.176313	+	0.999922i
$143$	3.13429	−	17.7754i	0.262102	−	1.48645i
$144$	−0.0569038	−	0.0985603i	−0.00474198	−	0.00821336i
$145$	4.39053	−	7.60462i	0.364614	−	0.631529i
$146$	5.06418	+	4.24935i	0.419114	+	0.351679i
$147$	−1.73396	−	0.631108i	−0.143014	−	0.0520529i
$148$	0.965385	−	0.351371i	0.0793541	−	0.0288825i
$149$	−2.88532	+	2.42107i	−0.236374	+	0.198342i	−0.753278	−	0.657702i	$-0.771529\pi$
$149$	−2.88532	+	2.42107i	−0.236374	+	0.198342i	0.516904	+	0.856043i	$0.327084\pi$
$150$	0.114685	+	0.650411i	0.00936399	+	0.0531058i
$151$	14.5963			1.18783			0.593914	−	0.804529i	$-0.297582\pi$
$151$	14.5963			1.18783			0.593914	+	0.804529i	$0.297582\pi$
$152$		0			0
$153$	−4.49020			−0.363011
$154$	0.979055	+	5.55250i	0.0788945	+	0.447433i
$155$	3.76991	−	3.16333i	0.302807	−	0.254085i
$156$	−3.24510	+	1.18112i	−0.259816	+	0.0945653i
$157$	9.74897	+	3.54834i	0.778053	+	0.283188i	0.700360	−	0.713789i	$-0.253023\pi$
$157$	9.74897	+	3.54834i	0.778053	+	0.283188i	0.0776922	+	0.996977i	$0.475245\pi$
$158$	−4.69072	−	3.93598i	−0.373174	−	0.313130i
$159$	1.62449	−	2.81369i	0.128830	−	0.223140i
$160$	−7.13816	−	12.3636i	−0.564321	−	0.977432i
$161$	−0.573978	+	3.25519i	−0.0452358	+	0.256545i
$162$	−0.997474	+	5.65695i	−0.0783689	+	0.444452i
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	0.902905	−	0.429841i	$-0.141430\pi$
$163$	1.01114	+	1.75135i	0.0791989	+	0.137177i	−0.823706	+	0.567018i	$0.808097\pi$
$164$	2.75402	−	4.77011i	0.215053	−	0.372483i
$165$	3.52094	+	2.95442i	0.274105	+	0.230002i
$166$	2.07620	+	0.755675i	0.161144	+	0.0586517i
$167$	−21.8542	+	7.95426i	−1.69113	+	0.615519i	−0.994767	−	0.102174i	$-0.967420\pi$
$167$	−21.8542	+	7.95426i	−1.69113	+	0.615519i	−0.696359	+	0.717694i	$0.745198\pi$
$168$	2.17365	−	1.82391i	0.167701	−	0.140718i
$169$	2.60354	+	14.7654i	0.200272	+	1.13580i
$170$	3.68004			0.282247
$171$		0			0
$172$	−5.88888			−0.449023
$173$	−0.155697	−	0.883000i	−0.0118374	−	0.0671332i	0.978317	−	0.207114i	$-0.0664071\pi$
$173$	−0.155697	−	0.883000i	−0.0118374	−	0.0671332i	−0.990154	+	0.139981i	$0.955296\pi$
$174$	1.24304	−	1.04303i	0.0942347	−	0.0790723i
$175$	2.49273	−	0.907278i	0.188432	−	0.0685838i
$176$	0.134285	+	0.0488759i	0.0101221	+	0.00368416i
$177$	−4.38532	−	3.67972i	−0.329620	−	0.276584i
$178$	1.00387	−	1.73875i	0.0752433	−	0.130325i
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	−0.921755	−	0.387773i	$-0.873245\pi$
$179$	−10.6591	−	18.4621i	−0.796699	−	1.37992i	0.125056	−	0.992150i	$-0.460089\pi$
$180$	−1.46538	+	8.31061i	−0.109223	+	0.619436i
$181$	2.79561	−	15.8547i	0.207796	−	1.17847i	−0.685183	−	0.728371i	$-0.740278\pi$
$181$	2.79561	−	15.8547i	0.207796	−	1.17847i	0.892979	−	0.450098i	$-0.148611\pi$
$182$	−4.37211	−	7.57272i	−0.324082	−	0.561327i
$183$	1.16772	−	2.02255i	0.0863202	−	0.149511i
$184$	3.82295	+	3.20783i	0.281831	+	0.236485i
$185$	1.99273	+	0.725293i	0.146508	+	0.0533246i
$186$	0.854570	−	0.311038i	0.0626601	−	0.0228064i
$187$	4.31908	−	3.62414i	0.315842	−	0.265023i
$188$	−0.152704	−	0.866025i	−0.0111371	−	0.0631614i
$189$	−5.71688			−0.415842
$190$		0			0
$191$	18.9486			1.37107			0.685537	−	0.728038i	$-0.259568\pi$
$191$	18.9486			1.37107			0.685537	+	0.728038i	$0.259568\pi$
$192$	−0.465852	−	2.64198i	−0.0336200	−	0.190668i
$193$	−9.88326	+	8.29304i	−0.711412	+	0.596946i	−0.924995	−	0.379979i	$-0.875931\pi$
$193$	−9.88326	+	8.29304i	−0.711412	+	0.596946i	0.213583	+	0.976925i	$0.431487\pi$
$194$	1.50640	−	0.548284i	0.108153	−	0.0393645i
$195$	−6.69846	−	2.43804i	−0.479687	−	0.174592i
$196$	3.25877	+	2.73443i	0.232769	+	0.195317i
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	−0.0743108	−	0.997235i	$-0.523676\pi$
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	0.900786	−	0.434263i	$-0.142991\pi$
$198$	−4.07532	−	7.05866i	−0.289621	−	0.501637i
$199$	1.60132	−	9.08153i	0.113515	−	0.643773i	−0.873960	−	0.485997i	$-0.838457\pi$
$199$	1.60132	−	9.08153i	0.113515	−	0.643773i	0.987475	−	0.157776i	$-0.0504323\pi$
$200$	0.695470	−	3.94421i	0.0491772	−	0.278898i
$201$	−3.78106	−	6.54899i	−0.266695	−	0.461930i
$202$	−3.48293	+	6.03260i	−0.245058	+	0.424453i
$203$	−4.99273	−	4.18939i	−0.350421	−	0.294038i
$204$	−1.01367	−	0.368946i	−0.0709711	−	0.0258314i
$205$	10.6839	−	3.88863i	0.746197	−	0.271593i
$206$	−0.00980018	+	0.00822333i	−0.000682811	+	0.000572946i
$207$	−0.829755	−	4.70578i	−0.0576720	−	0.327074i
$208$	−0.221629			−0.0153672
$209$		0			0
$210$	2.22668			0.153656
$211$	−2.53936	−	14.4014i	−0.174817	−	0.991436i	−0.938355	−	0.345673i	$-0.887651\pi$
$211$	−2.53936	−	14.4014i	−0.174817	−	0.991436i	0.763538	−	0.645763i	$-0.223461\pi$
$212$	−5.73783	+	4.81461i	−0.394076	+	0.330669i
$213$	6.87939	−	2.50389i	0.471368	−	0.171564i
$214$	2.93717	+	1.06904i	0.200781	+	0.0730781i
$215$	−9.31180	−	7.81353i	−0.635060	−	0.532878i
$216$	−4.31567	+	7.47497i	−0.293644	+	0.508607i
$217$	−1.82635	−	3.16333i	−0.123981	−	0.214741i
$218$	1.12536	−	6.38225i	0.0762192	−	0.432260i
$219$	0.694593	−	3.93923i	0.0469362	−	0.266189i
$220$	−5.29813	−	9.17664i	−0.357200	−	0.618689i
$221$	−4.37211	+	7.57272i	−0.294100	+	0.509396i
$222$	0.300193	+	0.251892i	0.0201476	+	0.0169059i
$223$	−2.83275	−	1.03104i	−0.189695	−	0.0690433i	0.245426	−	0.969415i	$-0.421072\pi$
$223$	−2.83275	−	1.03104i	−0.189695	−	0.0690433i	−0.435121	+	0.900372i	$0.643294\pi$
$224$	−9.95723	+	3.62414i	−0.665296	+	0.242148i
$225$	−2.93763	+	2.46497i	−0.195842	+	0.164331i
$226$	1.12654	+	6.38895i	0.0749366	+	0.424987i
$227$	13.7219			0.910757			0.455378	−	0.890298i	$-0.349504\pi$
$227$	13.7219			0.910757			0.455378	+	0.890298i	$0.349504\pi$
$228$		0			0
$229$	9.41416			0.622105			0.311053	−	0.950393i	$-0.399318\pi$
$229$	9.41416			0.622105			0.311053	+	0.950393i	$0.399318\pi$
$230$	0.680045	+	3.85673i	0.0448408	+	0.254305i
$231$	2.61334	−	2.19285i	0.171945	−	0.144279i
$232$	−9.24675	+	3.36554i	−0.607079	+	0.220959i
$233$	22.7271	+	8.27201i	1.48890	+	0.541917i	0.953161	−	0.302463i	$-0.0978090\pi$
$233$	22.7271	+	8.27201i	1.48890	+	0.541917i	0.535744	+	0.844380i	$0.320031\pi$
$234$	9.68345	+	8.12538i	0.633027	+	0.531173i
$235$	0.907604	−	1.57202i	0.0592055	−	0.102547i
$236$	6.59879	+	11.4294i	0.429545	+	0.743993i
$237$	−0.643370	+	3.64873i	−0.0417914	+	0.237011i
$238$	0.474308	−	2.68993i	0.0307448	−	0.174362i
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	0.945665	+	0.325143i	$0.105413\pi$
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	−0.191250	+	0.981541i	$0.561254\pi$
$240$	0.0282185	−	0.0488759i	0.00182150	−	0.00315492i
$241$	−0.228026	−	0.191336i	−0.0146884	−	0.0123251i	0.635414	−	0.772172i	$-0.280830\pi$
$241$	−0.228026	−	0.191336i	−0.0146884	−	0.0123251i	−0.650102	+	0.759847i	$0.725274\pi$
$242$	0.527341	+	0.191936i	0.0338988	+	0.0123381i
$243$	11.8414	−	4.30990i	0.759624	−	0.276481i
$244$	−4.12449	+	3.46085i	−0.264043	+	0.221558i
$245$	1.52481	+	8.64766i	0.0974169	+	0.552478i
$246$	2.10101			0.133956
$247$		0			0
$248$	−5.51485			−0.350193
$249$	−0.232145	−	1.31656i	−0.0147116	−	0.0834334i
$250$	−6.12108	+	5.13620i	−0.387131	+	0.324842i
$251$	15.2208	−	5.53990i	0.960725	−	0.349675i	0.186408	−	0.982472i	$-0.440315\pi$
$251$	15.2208	−	5.53990i	0.960725	−	0.349675i	0.774318	+	0.632797i	$0.218093\pi$
$252$	5.88578	+	2.14225i	0.370769	+	0.134949i
$253$	4.59627	+	3.85673i	0.288965	+	0.242470i
$254$	0.0444153	−	0.0769295i	0.00278686	−	0.00482699i
$255$	−1.11334	−	1.92836i	−0.0697201	−	0.120759i
$256$	−2.79591	+	15.8564i	−0.174744	+	0.991025i
$257$	−2.66637	+	15.1218i	−0.166324	+	0.943269i	0.781365	+	0.624074i	$0.214524\pi$
$257$	−2.66637	+	15.1218i	−0.166324	+	0.943269i	−0.947689	+	0.319195i	$0.896587\pi$
$258$	−1.12314	−	1.94534i	−0.0699237	−	0.121111i
$259$	0.786989	−	1.36310i	0.0489011	−	0.0846992i
$260$	12.5890	+	10.5634i	0.780736	+	0.655115i
$261$	8.85369	+	3.22248i	0.548030	+	0.199467i
$262$	−2.50950	+	0.913382i	−0.155037	+	0.0564289i
$263$	7.38713	−	6.19853i	0.455510	−	0.382218i	−0.385966	−	0.922513i	$-0.626132\pi$
$263$	7.38713	−	6.19853i	0.455510	−	0.382218i	0.841476	+	0.540295i	$0.181687\pi$
$264$	−0.894400	−	5.07239i	−0.0550465	−	0.312184i
$265$	−15.4611			−0.949768
$266$		0			0
$267$	−1.21482			−0.0743459
$268$	3.02734	+	17.1689i	0.184924	+	1.04876i
$269$	14.0025	−	11.7495i	0.853749	−	0.716381i	−0.106863	−	0.994274i	$-0.534081\pi$
$269$	14.0025	−	11.7495i	0.853749	−	0.716381i	0.960612	+	0.277893i	$0.0896361\pi$
$270$	−6.36484	+	2.31661i	−0.387352	+	0.140984i
$271$	−17.8204	−	6.48610i	−1.08251	−	0.394003i	−0.261671	−	0.965157i	$-0.584274\pi$
$271$	−17.8204	−	6.48610i	−1.08251	−	0.394003i	−0.820843	+	0.571154i	$0.806496\pi$
$272$	−0.0530334	−	0.0445003i	−0.00321562	−	0.00269823i
$273$	−2.64543	+	4.58202i	−0.160109	+	0.277316i
$274$	8.59152	+	14.8809i	0.519033	+	0.898991i
$275$	0.836152	−	4.74205i	0.0504219	−	0.285957i
$276$	0.199340	−	1.13052i	0.0119989	−	0.0680491i
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	0.581775	−	0.813350i	$-0.302358\pi$
$277$	−6.88191	−	11.9198i	−0.413494	−	0.716193i	−0.995269	+	0.0971571i	$0.969025\pi$
$278$	6.76991	−	11.7258i	0.406033	−	0.703269i
$279$	4.04504	+	3.39420i	0.242170	+	0.203205i
$280$	−12.6887	−	4.61830i	−0.758293	−	0.275996i
$281$	12.3204	−	4.48427i	0.734975	−	0.267509i	0.0527057	−	0.998610i	$-0.483215\pi$
$281$	12.3204	−	4.48427i	0.734975	−	0.267509i	0.682269	+	0.731101i	$0.260993\pi$
$282$	0.256959	−	0.215615i	0.0153017	−	0.0128397i
$283$	−3.01754	−	17.1133i	−0.179374	−	1.01728i	−0.932973	−	0.359947i	$-0.882795\pi$
$283$	−3.01754	−	17.1133i	−0.179374	−	1.01728i	0.753599	−	0.657335i	$-0.228316\pi$
$284$	−16.8776			−1.00150
$285$		0			0
$286$	−15.8726			−0.938565
$287$	−1.46538	−	8.31061i	−0.0864989	−	0.490560i
$288$	11.7344	−	9.84635i	0.691457	−	0.580202i
$289$	13.4081	−	4.88014i	0.788710	−	0.287067i
$290$	−7.25624	−	2.64106i	−0.426101	−	0.155088i
$291$	−0.743041	−	0.623485i	−0.0435578	−	0.0365493i
$292$	−4.61081	+	7.98617i	−0.269828	+	0.467355i
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	0.998734	−	0.0503091i	$-0.0160206\pi$
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	−0.542936	+	0.839774i	$0.682687\pi$
$294$	−0.281774	+	1.59802i	−0.0164334	+	0.0931985i
$295$	−4.73055	+	26.8283i	−0.275423	+	1.56200i
$296$	−1.18820	−	2.05802i	−0.0690625	−	0.119620i
$297$	−5.18866	+	8.98703i	−0.301077	+	0.521480i
$298$	2.53730	+	2.12905i	0.146982	+	0.123333i
$299$	−8.74422	−	3.18264i	−0.505691	−	0.184057i
$300$	−0.865715	+	0.315094i	−0.0499821	+	0.0181920i
$301$	−6.91147	+	5.79942i	−0.398371	+	0.334273i
$302$	−2.22890	−	12.6407i	−0.128259	−	0.727393i
$303$	4.21482			0.242135
$304$		0			0
$305$	−11.1138			−0.636375
$306$	0.685670	+	3.88863i	0.0391971	+	0.222298i
$307$	−16.4855	+	13.8329i	−0.940874	+	0.789487i	−0.977737	−	0.209833i	$-0.932708\pi$
$307$	−16.4855	+	13.8329i	−0.940874	+	0.789487i	0.0368628	+	0.999320i	$0.488264\pi$
$308$	−7.39053	+	2.68993i	−0.421115	+	0.153273i
$309$	0.00727396	+	0.00264750i	0.000413801	+	0.000150611i
$310$	−3.31521	−	2.78179i	−0.188291	−	0.157995i
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	−0.994997	−	0.0999083i	$-0.968145\pi$
$311$	−7.24763	+	12.5533i	−0.410975	+	0.711830i	0.584021	+	0.811738i	$0.301478\pi$
$312$	3.99407	+	6.91793i	0.226120	+	0.391651i
$313$	3.38935	−	19.2219i	0.191577	−	1.08649i	−0.725632	−	0.688083i	$-0.758453\pi$
$313$	3.38935	−	19.2219i	0.191577	−	1.08649i	0.917209	−	0.398406i	$-0.130436\pi$
$314$	1.58424	−	8.98470i	0.0894041	−	0.507036i
$315$	6.46451	+	11.1969i	0.364234	+	0.630871i
$316$	4.27079	−	7.39723i	0.240251	−	0.416127i
$317$	−21.7153	−	18.2213i	−1.21965	−	1.02341i	−0.998843	−	0.0480926i	$-0.984686\pi$
$317$	−21.7153	−	18.2213i	−1.21965	−	1.02341i	−0.220809	−	0.975317i	$-0.570870\pi$
$318$	−2.68479	−	0.977185i	−0.150556	−	0.0547978i
$319$	−11.1172	+	4.04633i	−0.622444	+	0.226551i
$320$	−9.77972	+	8.20616i	−0.546703	+	0.458738i
$321$	−0.328411	−	1.86251i	−0.0183301	−	0.103955i
$322$	2.90673			0.161986
$323$		0			0
$324$	−8.01279			−0.445155
$325$	1.29679	+	7.35446i	0.0719329	+	0.407952i
$326$	1.36231	−	1.14311i	0.0754514	−	0.0633113i
$327$	−3.68479	+	1.34115i	−0.203769	+	0.0741660i
$328$	−11.9726	−	4.35765i	−0.661074	−	0.240611i
$329$	−1.03209	−	0.866025i	−0.0569009	−	0.0477455i
$330$	2.02094	−	3.50038i	0.111249	−	0.192690i
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	0.841570	−	0.540148i	$-0.181632\pi$
$331$	−0.855037	−	1.48097i	−0.0469971	−	0.0814014i	−0.888567	+	0.458747i	$0.848298\pi$
$332$	−0.535188	+	3.03520i	−0.0293722	+	0.166578i
$333$	−0.395115	+	2.24081i	−0.0216522	+	0.122796i
$334$	10.2258	+	17.7116i	0.559531	+	0.969136i
$335$	−17.9932	+	31.1651i	−0.983073	+	1.70273i
$336$	−0.0320889	−	0.0269258i	−0.00175059	−	0.00146892i
$337$	23.9047	+	8.70059i	1.30217	+	0.473951i	0.897703	−	0.440601i	$-0.145235\pi$
$337$	23.9047	+	8.70059i	1.30217	+	0.473951i	0.404467	+	0.914552i	$0.367457\pi$
$338$	12.3897	−	4.50946i	0.673908	−	0.245283i
$339$	3.00703	−	2.52319i	0.163319	−	0.137041i
$340$	0.891407	+	5.05542i	0.0483433	+	0.274169i
$341$	−6.63041			−0.359057
$342$		0			0
$343$	19.6732			1.06225
$344$	2.36541	+	13.4149i	0.127534	+	0.723283i
$345$	1.81521	−	1.52314i	0.0977275	−	0.0820031i
$346$	−0.740925	+	0.269675i	−0.0398324	+	0.0144978i
$347$	−7.23783	−	2.63435i	−0.388547	−	0.141419i	0.140358	−	0.990101i	$-0.455175\pi$
$347$	−7.23783	−	2.63435i	−0.388547	−	0.141419i	−0.528904	+	0.848681i	$0.677397\pi$
$348$	1.73396	+	1.45496i	0.0929498	+	0.0779941i
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	0.382315	+	0.924032i	$0.375127\pi$
$349$	−11.3785	+	19.7082i	−0.609078	+	1.05495i	−0.991393	+	0.130921i	$0.958206\pi$
$350$	−1.16637	−	2.02022i	−0.0623453	−	0.107985i
$351$	2.79473	−	15.8497i	0.149172	−	0.845994i
$352$	−3.34002	+	18.9422i	−0.178024	+	1.00962i
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	0.977171	−	0.212454i	$-0.0681457\pi$
$353$	5.72281	+	9.91220i	0.304595	+	0.527573i	−0.672576	+	0.740028i	$0.734812\pi$
$354$	−2.51707	+	4.35970i	−0.133781	+	0.231715i
$355$	−26.6878	−	22.3937i	−1.41644	−	1.18853i
$356$	2.63176	+	0.957882i	0.139483	+	0.0507676i
$357$	−1.55303	+	0.565258i	−0.0821952	+	0.0299166i
$358$	−14.3610	+	12.0503i	−0.759001	+	0.636877i
$359$	1.80319	+	10.2264i	0.0951685	+	0.539727i	0.994696	+	0.102862i	$0.0328001\pi$
$359$	1.80319	+	10.2264i	0.0951685	+	0.539727i	−0.899527	+	0.436865i	$0.856089\pi$
$360$	19.5202			1.02881
$361$		0			0
$362$	−14.1575			−0.744099
$363$	−0.0589632	−	0.334397i	−0.00309477	−	0.0175513i
$364$	9.34389	−	7.84046i	0.489753	−	0.410952i
$365$	−17.8871	+	6.51038i	−0.936255	+	0.340769i
$366$	−1.92989	−	0.702423i	−0.100877	−	0.0367163i
$367$	−24.9217	−	20.9118i	−1.30090	−	1.09159i	−0.989988	−	0.141151i	$-0.954920\pi$
$367$	−24.9217	−	20.9118i	−1.30090	−	1.09159i	−0.310916	−	0.950437i	$-0.600636\pi$
$368$	0.0368366	−	0.0638029i	0.00192024	−	0.00332596i
$369$	6.09967	+	10.5649i	0.317536	+	0.549989i
$370$	0.323826	−	1.83651i	0.0168349	−	0.0954754i
$371$	−1.99273	+	11.3013i	−0.103457	+	0.586735i
$372$	0.634285	+	1.09861i	0.0328862	+	0.0569605i
$373$	15.2429	−	26.4014i	0.789246	−	1.36701i	−0.137183	−	0.990546i	$-0.543805\pi$
$373$	15.2429	−	26.4014i	0.789246	−	1.36701i	0.926429	−	0.376469i	$-0.122862\pi$
$374$	−3.79813	−	3.18701i	−0.196397	−	0.164796i
$375$	4.54323	+	1.65360i	0.234612	+	0.0853916i
$376$	−1.91147	+	0.695720i	−0.0985768	+	0.0358790i
$377$	14.0556	−	11.7940i	0.723898	−	0.607423i
$378$	0.872989	+	4.95096i	0.0449017	+	0.254650i
$379$	−17.8598			−0.917396			−0.458698	−	0.888592i	$-0.651684\pi$
$379$	−17.8598			−0.917396			−0.458698	+	0.888592i	$0.651684\pi$
$380$		0			0
$381$	−0.0537486			−0.00275363
$382$	−2.89352	−	16.4100i	−0.148045	−	0.839608i
$383$	17.9684	−	15.0773i	0.918141	−	0.770412i	−0.0555091	−	0.998458i	$-0.517678\pi$
$383$	17.9684	−	15.0773i	0.918141	−	0.770412i	0.973650	+	0.228046i	$0.0732337\pi$
$384$	3.42127	−	1.24524i	0.174591	−	0.0635460i
$385$	−15.2554	−	5.55250i	−0.777485	−	0.282982i
$386$	8.69119	+	7.29277i	0.442370	+	0.371192i
$387$	6.52141	−	11.2954i	0.331502	−	0.574178i
$388$	1.11809	+	1.93659i	0.0567623	+	0.0983153i
$389$	0.678863	−	3.85002i	0.0344197	−	0.195204i	−0.962749	−	0.270395i	$-0.912846\pi$
$389$	0.678863	−	3.85002i	0.0344197	−	0.195204i	0.997169	+	0.0751913i	$0.0239568\pi$
$390$	−1.08853	+	6.17334i	−0.0551197	+	0.312599i
$391$	−1.45336	−	2.51730i	−0.0734997	−	0.127305i
$392$	4.92009	−	8.52185i	0.248502	−	0.430418i
$393$	1.23783	+	1.03866i	0.0624401	+	0.0523934i
$394$	−19.1716	−	6.97789i	−0.965851	−	0.351541i
$395$	16.5680	−	6.03028i	0.833629	−	0.303416i
$396$	8.70961	−	7.30823i	0.437674	−	0.367252i
$397$	1.55572	+	8.82294i	0.0780794	+	0.442810i	0.998637	+	0.0522024i	$0.0166241\pi$
$397$	1.55572	+	8.82294i	0.0780794	+	0.442810i	−0.920557	+	0.390608i	$0.872265\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	0.352044	+	1.99654i	0.0175802	+	0.0997025i	0.992335	−	0.123574i	$-0.0394357\pi$
$401$	0.352044	+	1.99654i	0.0175802	+	0.0997025i	−0.974755	+	0.223277i	$0.928325\pi$
$402$	−5.09421	+	4.27455i	−0.254076	+	0.213195i
$403$	9.66297	−	3.51703i	0.481347	−	0.175196i
$404$	−9.13088	−	3.32337i	−0.454278	−	0.165344i
$405$	−12.6702	−	10.6316i	−0.629590	−	0.528288i
$406$	−2.86571	+	4.96356i	−0.142223	+	0.246338i
$407$	−1.42855	−	2.47432i	−0.0708105	−	0.122647i
$408$	−0.433296	+	2.45734i	−0.0214513	+	0.121657i
$409$	5.59286	−	31.7187i	0.276549	−	1.56839i	−0.457448	−	0.889236i	$-0.651236\pi$
$409$	5.59286	−	31.7187i	0.276549	−	1.56839i	0.733997	−	0.679152i	$-0.237653\pi$
$410$	−4.99912	−	8.65873i	−0.246889	−	0.427624i
$411$	5.19846	−	9.00400i	0.256421	−	0.444135i
$412$	−0.0136706	−	0.0114710i	−0.000673501	−	0.000565134i
$413$	19.0005	+	6.91560i	0.934952	+	0.340295i
$414$	−3.94862	+	1.43718i	−0.194064	+	0.0706335i
$415$	−4.87346	+	4.08931i	−0.239229	+	0.200737i
$416$	−5.18004	−	29.3775i	−0.253973	−	1.44035i
$417$	−8.19253			−0.401190
$418$		0			0
$419$	−23.2499			−1.13583			−0.567916	−	0.823086i	$-0.692250\pi$
$419$	−23.2499			−1.13583			−0.567916	+	0.823086i	$0.692250\pi$
$420$	0.539363	+	3.05888i	0.0263182	+	0.149258i
$421$	−4.94356	+	4.14814i	−0.240935	+	0.202168i	−0.755257	−	0.655429i	$-0.772488\pi$
$421$	−4.94356	+	4.14814i	−0.240935	+	0.202168i	0.514322	+	0.857597i	$0.328043\pi$
$422$	−12.0842	+	4.39831i	−0.588252	+	0.214106i
$423$	1.83022	+	0.666146i	0.0889884	+	0.0323891i
$424$	13.2724	+	11.1369i	0.644567	+	0.540856i
$425$	−1.16637	+	2.02022i	−0.0565775	+	0.0979950i
$426$	−3.21894	−	5.57537i	−0.155958	−	0.270128i
$427$	−1.43242	+	8.12365i	−0.0693196	+	0.393131i
$428$	−0.757122	+	4.29385i	−0.0365969	+	0.207551i
$429$	4.80200	+	8.31731i	0.231843	+	0.401564i
$430$	−5.34477	+	9.25741i	−0.257748	+	0.446432i
$431$	10.7226	+	8.99730i	0.516488	+	0.433385i	0.863405	−	0.504511i	$-0.168327\pi$
$431$	10.7226	+	8.99730i	0.516488	+	0.433385i	−0.346918	+	0.937896i	$0.612772\pi$
$432$	0.119737	+	0.0435809i	0.00576087	+	0.00209678i
$433$	−26.9624	+	9.81353i	−1.29573	+	0.471608i	−0.895605	−	0.444851i	$-0.853257\pi$
$433$	−26.9624	+	9.81353i	−1.29573	+	0.471608i	−0.400128	+	0.916459i	$0.631034\pi$
$434$	−2.46064	+	2.06472i	−0.118114	+	0.0991097i
$435$	0.811337	+	4.60132i	0.0389006	+	0.220616i
$436$	9.04013			0.432944
$437$		0			0
$438$	−3.51754			−0.168075
$439$	2.31686	+	13.1395i	0.110578	+	0.627116i	0.988845	+	0.148947i	$0.0475884\pi$
$439$	2.31686	+	13.1395i	0.110578	+	0.627116i	−0.878268	+	0.478169i	$0.841301\pi$
$440$	−18.7763	+	15.7552i	−0.895126	+	0.751099i
$441$	−8.85369	+	3.22248i	−0.421604	+	0.153451i
$442$	7.22580	+	2.62998i	0.343696	+	0.125095i
$443$	25.9559	+	21.7796i	1.23320	+	1.03478i	0.998024	+	0.0628264i	$0.0200114\pi$
$443$	25.9559	+	21.7796i	1.23320	+	1.03478i	0.235177	+	0.971953i	$0.424433\pi$
$444$	−0.273318	+	0.473401i	−0.0129711	+	0.0224666i
$445$	2.89053	+	5.00654i	0.137024	+	0.237333i
$446$	−0.460332	+	2.61068i	−0.0217974	+	0.123619i
$447$	0.348012	−	1.97367i	0.0164604	−	0.0933515i
$448$	4.73783	+	8.20616i	0.223841	+	0.387704i
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	−0.553460	−	0.832876i	$-0.686693\pi$
$449$	9.42009	−	16.3161i	0.444562	−	0.770003i	0.998022	+	0.0628725i	$0.0200261\pi$
$450$	2.58331	+	2.16766i	0.121778	+	0.102184i
$451$	−14.3944	−	5.23913i	−0.677806	−	0.246701i
$452$	−8.50387	+	3.09516i	−0.399988	+	0.145584i
$453$	−5.94949	+	4.99222i	−0.279532	+	0.234555i
$454$	−2.09539	−	11.8835i	−0.0983415	−	0.557722i
$455$	25.1780			1.18036
$456$		0			0
$457$	14.2790			0.667943			0.333972	−	0.942583i	$-0.391611\pi$
$457$	14.2790			0.667943			0.333972	+	0.942583i	$0.391611\pi$
$458$	−1.43758	−	8.15290i	−0.0671736	−	0.380960i
$459$	3.85117	−	3.23151i	0.179757	−	0.150834i
$460$	−5.13341	+	1.86841i	−0.239346	+	0.0871150i
$461$	13.0881	+	4.76368i	0.609574	+	0.221867i	0.628317	−	0.777957i	$-0.283744\pi$
$461$	13.0881	+	4.76368i	0.609574	+	0.221867i	−0.0187427	+	0.999824i	$0.505966\pi$
$462$	−2.29813	−	1.92836i	−0.106919	−	0.0897156i
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	−0.844816	−	0.535056i	$-0.820290\pi$
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	0.885781	+	0.464104i	$0.153624\pi$
$464$	0.0726338	+	0.125805i	0.00337194	+	0.00584037i
$465$	−0.454707	+	2.57877i	−0.0210865	+	0.119588i
$466$	3.69325	−	20.9455i	0.171086	−	0.970279i
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	−0.999933	−	0.0115724i	$-0.996316\pi$
$467$	−11.0209	−	19.0888i	−0.509988	−	0.883326i	0.489945	−	0.871754i	$-0.337017\pi$
$468$	−8.81655	+	15.2707i	−0.407545	+	0.705889i
$469$	20.4611	+	17.1689i	0.944806	+	0.792786i
$470$	−1.50000	−	0.545955i	−0.0691898	−	0.0251830i
$471$	−5.18732	+	1.88803i	−0.239019	+	0.0869958i
$472$	23.3858	−	19.6230i	1.07642	−	0.903222i
$473$	2.84389	+	16.1285i	0.130762	+	0.741590i
$474$	3.25814			0.149651
$475$		0			0
$476$	3.81016			0.174638
$477$	−2.88073	−	16.3374i	−0.131900	−	0.748039i
$478$	15.7135	−	13.1852i	0.718718	−	0.603076i
$479$	23.9217	−	8.70680i	1.09301	−	0.397824i	0.268276	−	0.963342i	$-0.413546\pi$
$479$	23.9217	−	8.70680i	1.09301	−	0.397824i	0.824736	+	0.565518i	$0.191324\pi$
$480$	7.13816	+	2.59808i	0.325811	+	0.118585i
$481$	3.39440	+	2.84824i	0.154771	+	0.129869i
$482$	−0.130882	+	0.226694i	−0.00596150	+	0.0103256i
$483$	−0.879385	−	1.52314i	−0.0400134	−	0.0693053i
$484$	−0.135934	+	0.770921i	−0.00617883	+	0.0350419i
$485$	−0.801537	+	4.54574i	−0.0363959	+	0.206411i
$486$	−5.54071	−	9.59679i	−0.251332	−	0.435319i
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	0.489903	+	0.871777i	$0.337032\pi$
$487$	−11.2554	+	19.4949i	−0.510029	+	0.883397i	−0.999932	+	0.0116199i	$0.996301\pi$
$488$	9.54054	+	8.00547i	0.431880	+	0.362390i
$489$	−1.01114	−	0.368026i	−0.0457255	−	0.0166427i
$490$	7.25624	−	2.64106i	0.327804	−	0.119311i
$491$	11.9764	−	10.0494i	0.540486	−	0.453522i	−0.331218	−	0.943554i	$-0.607460\pi$
$491$	11.9764	−	10.0494i	0.540486	−	0.453522i	0.871704	+	0.490033i	$0.163015\pi$
$492$	0.508923	+	2.88624i	0.0229440	+	0.130122i
$493$	5.73143			0.258131
$494$		0			0
$495$	23.4688			1.05485
$496$	0.0141374	+	0.0801772i	0.000634788	+	0.00360006i
$497$	−19.8084	+	16.6212i	−0.888528	+	0.745564i
$498$	−1.10472	+	0.402086i	−0.0495038	+	0.0180179i
$499$	26.8910	+	9.78752i	1.20381	+	0.438150i	0.864551	−	0.502545i	$-0.167603\pi$
$499$	26.8910	+	9.78752i	1.20381	+	0.438150i	0.339255	+	0.940694i	$0.389825\pi$
$500$	−8.53849	−	7.16464i	−0.381853	−	0.320412i
$501$	6.18732	−	10.7168i	0.276429	−	0.478789i
$502$	−7.12196	−	12.3356i	−0.317869	−	0.550565i
$503$	−4.34911	+	24.6650i	−0.193917	+	1.09976i	0.720035	+	0.693937i	$0.244126\pi$
$503$	−4.34911	+	24.6650i	−0.193917	+	1.09976i	−0.913952	+	0.405821i	$0.866986\pi$
$504$	2.51589	−	14.2683i	0.112067	−	0.635562i
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$	2.63816	−	4.56942i	0.117280	−	0.203135i
$507$	−6.11128	−	5.12797i	−0.271412	−	0.227741i
$508$	0.116440	+	0.0423806i	0.00516617	+	0.00188033i
$509$	31.4996	−	11.4649i	1.39619	−	0.508173i	0.469148	−	0.883119i	$-0.344561\pi$
$509$	31.4996	−	11.4649i	1.39619	−	0.508173i	0.927047	+	0.374946i	$0.122339\pi$
$510$	−1.50000	+	1.25865i	−0.0664211	+	0.0557339i
$511$	2.45336	+	13.9137i	0.108530	+	0.615506i
$512$	0.473897			0.0209435
$513$		0			0
$514$	13.5030			0.595591
$515$	−0.00639661	−	0.0362770i	−0.000281868	−	0.00159856i
$516$	2.40033	−	2.01412i	0.105669	−	0.0886665i
$517$	−2.29813	+	0.836452i	−0.101072	+	0.0367871i
$518$	−1.30066	−	0.473401i	−0.0571477	−	0.0208001i
$519$	0.365466	+	0.306663i	0.0160422	+	0.0134610i
$520$	19.0069	−	32.9209i	0.833506	−	1.44367i
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	−0.992530	−	0.122005i	$-0.961068\pi$
$521$	−13.7392	−	23.7969i	−0.601924	−	1.04256i	0.390606	−	0.920558i	$-0.372266\pi$
$522$	1.43876	−	8.15961i	0.0629728	−	0.357136i
$523$	1.79854	−	10.2000i	0.0786448	−	0.446017i	−0.919903	−	0.392146i	$-0.871733\pi$
$523$	1.79854	−	10.2000i	0.0786448	−	0.446017i	0.998548	−	0.0538712i	$-0.0171560\pi$
$524$	−1.86262	−	3.22615i	−0.0813687	−	0.140935i
$525$	−0.705737	+	1.22237i	−0.0308009	+	0.0533487i
$526$	−6.49613	−	5.45090i	−0.283245	−	0.237671i
$527$	3.01842	+	1.09861i	0.131484	+	0.0478564i
$528$	−0.0714517	+	0.0260063i	−0.00310954	+	0.00113178i
$529$	−15.2494	+	12.7958i	−0.663019	+	0.556339i
$530$	2.36097	+	13.3897i	0.102554	+	0.581612i
$531$	−29.2303			−1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$	0.185508	+	1.05207i	0.00802771	+	0.0455274i
$535$	−6.89440	+	5.78509i	−0.298071	+	0.250111i
$536$	37.8949	−	13.7926i	1.63681	−	0.595750i
$537$	10.6591	+	3.87960i	0.459974	+	0.167417i
$538$	−12.3136	−	10.3323i	−0.530878	−	0.445459i
$539$	5.91534	−	10.2457i	0.254792	−	0.441313i
$540$	−4.72416	−	8.18248i	−0.203295	−	0.352118i
$541$	0.438348	−	2.48600i	0.0188461	−	0.106881i	−0.973934	−	0.226833i	$-0.927163\pi$
$541$	0.438348	−	2.48600i	0.0188461	−	0.106881i	0.992780	+	0.119952i	$0.0382739\pi$
$542$	−2.89589	+	16.4234i	−0.124389	+	0.705445i
$543$	4.28312	+	7.41858i	0.183806	+	0.318362i
$544$	4.65910	−	8.06980i	0.199757	−	0.345990i
$545$	14.2947	+	11.9947i	0.612319	+	0.513797i
$546$	4.37211	+	1.59132i	0.187109	+	0.0681021i
$547$	7.21213	−	2.62500i	0.308369	−	0.112237i	−0.183201	−	0.983076i	$-0.558646\pi$
$547$	7.21213	−	2.62500i	0.308369	−	0.112237i	0.491569	+	0.870839i	$0.336424\pi$
$548$	−18.3614	+	15.4071i	−0.784362	+	0.658158i
$549$	−2.07074	−	11.7437i	−0.0883769	−	0.501210i
$550$	−4.23442			−0.180556
$551$		0			0
$552$	−2.65539			−0.113021
$553$	−2.27244	−	12.8877i	−0.0966340	−	0.548039i
$554$	−9.27197	+	7.78011i	−0.393928	+	0.330545i
$555$	−1.06031	+	0.385920i	−0.0450075	+	0.0163814i
$556$	17.7481	+	6.45978i	0.752687	+	0.273956i
$557$	2.49407	+	2.09277i	0.105677	+	0.0886737i	0.694095	−	0.719883i	$-0.255805\pi$
$557$	2.49407	+	2.09277i	0.105677	+	0.0886737i	−0.588418	+	0.808557i	$0.700249\pi$
$558$	2.32177	−	4.02142i	0.0982882	−	0.170240i
$559$	−12.6998	−	21.9967i	−0.537145	−	0.930362i
$560$	−0.0346151	+	0.196312i	−0.00146276	+	0.00829570i
$561$	−0.520945	+	2.95442i	−0.0219943	+	0.124736i
$562$	−5.76486	−	9.98503i	−0.243176	−	0.421193i
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	−0.805280	−	0.592895i	$-0.797985\pi$
$563$	2.62954	−	4.55449i	0.110822	−	0.191949i	0.916102	+	0.400946i	$0.131318\pi$
$564$	0.358441	+	0.300767i	0.0150931	+	0.0126646i
$565$	−17.5535	−	6.38895i	−0.738481	−	0.268785i
$566$	−14.3598	+	5.22653i	−0.603587	+	0.219688i
$567$	−9.40420	+	7.89106i	−0.394939	+	0.331393i
$568$	6.77930	+	38.4473i	0.284453	+	1.61321i
$569$	29.9564			1.25584			0.627918	−	0.778280i	$-0.283907\pi$
$569$	29.9564			1.25584			0.627918	+	0.778280i	$0.283907\pi$
$570$		0			0
$571$	−16.7101			−0.699295			−0.349647	−	0.936881i	$-0.613699\pi$
$571$	−16.7101			−0.699295			−0.349647	+	0.936881i	$0.613699\pi$
$572$	−3.84477	−	21.8048i	−0.160758	−	0.911703i
$573$	−7.72353	+	6.48081i	−0.322655	+	0.270740i
$574$	−6.97343	+	2.53812i	−0.291065	+	0.105939i
$575$	−2.33275	−	0.849051i	−0.0972823	−	0.0354079i
$576$	−10.4934	−	8.80504i	−0.437227	−	0.366877i
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	−0.687796	−	0.725904i	$-0.741421\pi$
$577$	6.84002	−	11.8473i	0.284754	−	0.493208i	0.972549	+	0.232696i	$0.0747548\pi$
$578$	−6.27379	−	10.8665i	−0.260955	−	0.451987i
$579$	1.19207	−	6.76055i	0.0495406	−	0.280959i
$580$	1.87046	−	10.6079i	0.0776667	−	0.440470i
$581$	2.36097	+	4.08931i	0.0979494	+	0.169653i
$582$	−0.426489	+	0.738700i	−0.0176785	+	0.0306201i
$583$	15.9572	+	13.3897i	0.660881	+	0.554545i
$584$	20.0446	+	7.29563i	0.829451	+	0.301895i
$585$	−34.2028	+	12.4488i	−1.41411	+	0.514695i
$586$	10.5116	−	8.82029i	0.434231	−	0.364363i
$587$	−4.17395	−	23.6717i	−0.172277	−	0.977034i	−0.941240	−	0.337740i	$-0.890338\pi$
$587$	−4.17395	−	23.6717i	−0.172277	−	0.977034i	0.768962	−	0.639294i	$-0.220773\pi$
$588$	−2.26352			−0.0933459
$589$		0			0
$590$	23.9564			0.986268
$591$	2.14362	+	12.1571i	0.0881767	+	0.500075i
$592$	−0.0268743	+	0.0225502i	−0.00110453	+	0.000926809i
$593$	3.98545	−	1.45059i	0.163663	−	0.0595684i	−0.258889	−	0.965907i	$-0.583357\pi$
$593$	3.98545	−	1.45059i	0.163663	−	0.0595684i	0.422552	+	0.906339i	$0.361134\pi$
$594$	8.57532	+	3.12116i	0.351850	+	0.128063i
$595$	6.02481	+	5.05542i	0.246993	+	0.207252i
$596$	−2.31016	+	4.00131i	−0.0946276	+	0.163900i
$597$	2.45336	+	4.24935i	0.100409	+	0.173914i
$598$	−1.42097	+	8.05872i	−0.0581078	+	0.329546i
$599$	4.56242	−	25.8748i	0.186416	−	1.05722i	−0.737708	−	0.675120i	$-0.764092\pi$
$599$	4.56242	−	25.8748i	0.186416	−	1.05722i	0.924123	−	0.382095i	$-0.124797\pi$
$600$	1.06552	+	1.84554i	0.0434998	+	0.0753438i
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	0.00899659	+	0.999960i	$0.497136\pi$
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	−0.870489	+	0.492188i	$0.836197\pi$
$602$	6.07785	+	5.09992i	0.247715	+	0.207857i
$603$	−36.2841	−	13.2063i	−1.47760	−	0.537803i
$604$	16.8252	−	6.12386i	0.684606	−	0.249176i
$605$	−1.23783	+	1.03866i	−0.0503248	+	0.0422275i
$606$	−0.643619	−	3.65014i	−0.0261452	−	0.148277i
$607$	22.0969			0.896885			0.448443	−	0.893812i	$-0.351979\pi$
$607$	22.0969			0.896885			0.448443	+	0.893812i	$0.351979\pi$
$608$		0			0
$609$	3.46791			0.140527
$610$	1.69712	+	9.62484i	0.0687143	+	0.389698i
$611$	2.90554	−	2.43804i	0.117546	−	0.0986326i
$612$	−5.17587	+	1.88386i	−0.209222	+	0.0761506i
$613$	−6.74422	−	2.45470i	−0.272397	−	0.0991442i	0.202210	−	0.979342i	$-0.435188\pi$
$613$	−6.74422	−	2.45470i	−0.272397	−	0.0991442i	−0.474607	+	0.880198i	$0.657410\pi$
$614$	14.4971	+	12.1645i	0.585054	+	0.490918i
$615$	−3.02481	+	5.23913i	−0.121972	+	0.211262i
$616$	9.09627	+	15.7552i	0.366499	+	0.634795i
$617$	−8.57351	+	48.6228i	−0.345157	+	1.95748i	−0.0634261	+	0.997987i	$0.520203\pi$
$617$	−8.57351	+	48.6228i	−0.345157	+	1.95748i	−0.281730	+	0.959494i	$0.590908\pi$
$618$	0.00118205	−	0.00670372i	4.75489e−5	−	0.000269663i
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	−0.999279	−	0.0379684i	$-0.987911\pi$
$619$	−13.2490	−	22.9479i	−0.532521	−	0.922354i	0.466758	−	0.884385i	$-0.345422\pi$
$620$	3.01842	−	5.22805i	0.121223	−	0.209964i
$621$	4.09833	+	3.43890i	0.164460	+	0.137998i
$622$	11.9782	+	4.35970i	0.480281	+	0.174808i
$623$	4.03209	−	1.46756i	0.161542	−	0.0587966i
$624$	0.0903369	−	0.0758016i	0.00361637	−	0.00303449i
$625$	−5.22075	−	29.6084i	−0.208830	−	1.18433i
$626$	−17.1643			−0.686022
$627$		0			0
$628$	12.7264			0.507838
$629$	0.240352	+	1.36310i	0.00958347	+	0.0543506i
$630$	8.70961	−	7.30823i	0.346999	−	0.291167i
$631$	−31.3114	+	11.3964i	−1.24649	+	0.453684i	−0.879213	−	0.476429i	$-0.841931\pi$
$631$	−31.3114	+	11.3964i	−1.24649	+	0.453684i	−0.367274	+	0.930113i	$0.619709\pi$
$632$	−18.5664	−	6.75762i	−0.738532	−	0.268804i
$633$	5.96064	+	5.00157i	0.236914	+	0.198794i
$634$	−12.4641	+	21.5884i	−0.495013	+	0.857387i
$635$	0.127889	+	0.221510i	0.00507511	+	0.00879035i
$636$	0.692066	−	3.92490i	0.0274422	−	0.155633i
$637$	−3.18614	+	18.0695i	−0.126239	+	0.715939i
$638$	5.20187	+	9.00990i	0.205944	+	0.356705i
$639$	18.6905	−	32.3729i	0.739384	−	1.28065i
$640$	−13.2724	−	11.1369i	−0.524639	−	0.440225i
$641$	−0.127889	−	0.0465477i	−0.00505130	−	0.00183852i	0.339493	−	0.940608i	$-0.389744\pi$
$641$	−0.127889	−	0.0465477i	−0.00505130	−	0.00183852i	−0.344545	+	0.938770i	$0.611967\pi$
$642$	−1.56283	+	0.568825i	−0.0616801	+	0.0224497i
$643$	36.9065	−	30.9682i	1.45545	−	1.22127i	0.526970	−	0.849884i	$-0.323328\pi$
$643$	36.9065	−	30.9682i	1.45545	−	1.22127i	0.928480	−	0.371383i	$-0.121116\pi$
$644$	0.704088	+	3.99308i	0.0277450	+	0.157349i
$645$	6.46791			0.254674
$646$		0			0
$647$	−36.9718			−1.45351			−0.726756	−	0.686895i	$-0.758973\pi$
$647$	−36.9718			−1.45351			−0.726756	+	0.686895i	$0.758973\pi$
$648$	3.21853	+	18.2532i	0.126436	+	0.717053i
$649$	28.1163	−	23.5924i	1.10366	−	0.926083i
$650$	6.17112	−	2.24610i	0.242051	−	0.0880995i
$651$	1.82635	+	0.664738i	0.0715804	+	0.0260531i
$652$	1.90033	+	1.59457i	0.0744227	+	0.0624480i
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	1.72416	+	2.98632i	0.0674198	+	0.116775i
$655$	1.33527	−	7.57272i	0.0521735	−	0.295891i
$656$	−0.0326615	+	0.185233i	−0.00127522	+	0.00723212i
$657$	−10.2121	−	17.6879i	−0.398413	−	0.690072i
$658$	−0.592396	+	1.02606i	−0.0230940	+	0.0400000i
$659$	−14.4590	−	12.1326i	−0.563244	−	0.472618i	0.316152	−	0.948709i	$-0.397609\pi$
$659$	−14.4590	−	12.1326i	−0.563244	−	0.472618i	−0.879396	+	0.476090i	$0.842054\pi$
$660$	5.29813	+	1.92836i	0.206230	+	0.0750614i
$661$	−28.7656	+	10.4698i	−1.11885	+	0.407229i	−0.834234	−	0.551411i	$-0.814090\pi$
$661$	−28.7656	+	10.4698i	−1.11885	+	0.407229i	−0.284620	+	0.958640i	$0.591867\pi$
$662$	−1.15199	+	0.966633i	−0.0447733	+	0.0375693i
$663$	−0.807934	−	4.58202i	−0.0313775	−	0.177951i
$664$	7.12918			0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	1.05913	+	6.00660i	0.0410095	+	0.232576i
$668$	−21.8542	+	18.3378i	−0.845563	+	0.709511i
$669$	1.50727	−	0.548603i	0.0582746	−	0.0212102i
$670$	29.7374	+	10.8235i	1.14886	+	0.418150i
$671$	11.4704	+	9.62484i	0.442811	+	0.371563i
$672$	2.81908	−	4.88279i	0.108748	−	0.188358i
$673$	5.95471	+	10.3139i	0.229537	+	0.397570i	0.957671	−	0.287865i	$-0.0929454\pi$
$673$	5.95471	+	10.3139i	0.229537	+	0.397570i	−0.728134	+	0.685435i	$0.759612\pi$
$674$	3.88460	−	22.0307i	0.149629	−	0.848589i
$675$	0.745567	−	4.22832i	0.0286969	−	0.162748i
$676$	9.19594	+	15.9278i	0.353690	+	0.612609i
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	−0.805119	−	0.593114i	$-0.797898\pi$
$677$	2.89053	−	5.00654i	0.111092	−	0.192417i	0.916211	+	0.400696i	$0.131232\pi$
$678$	−2.64433	−	2.21886i	−0.101555	−	0.0852148i
$679$	3.21941	+	1.17177i	0.123550	+	0.0449683i
$680$	11.1582	−	4.06126i	0.427898	−	0.155742i
$681$	−5.59311	+	4.69318i	−0.214328	+	0.179843i
$682$	1.01249	+	5.74211i	0.0387702	+	0.219877i
$683$	−21.0496			−0.805442			−0.402721	−	0.915323i	$-0.631935\pi$
$683$	−21.0496			−0.805442			−0.402721	+	0.915323i	$0.631935\pi$
$684$		0			0
$685$	−49.4766			−1.89040
$686$	−3.00418	−	17.0375i	−0.114700	−	0.650496i
$687$	−3.83725	+	3.21983i	−0.146400	+	0.122844i
$688$	0.188968	−	0.0687786i	0.00720432	−	0.00262216i
$689$	−30.3580	−	11.0494i	−1.15655	−	0.420949i
$690$	−1.59627	−	1.33943i	−0.0607688	−	0.0509911i
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	−0.361744	−	0.932278i	$-0.617818\pi$
$691$	16.4688	−	28.5249i	0.626504	−	1.08514i	0.988248	−	0.152860i	$-0.0488483\pi$
$692$	−0.549935	−	0.952515i	−0.0209054	−	0.0362092i
$693$	3.02481	−	17.1546i	0.114903	−	0.651649i
$694$	−1.17617	+	6.67042i	−0.0446470	+	0.253206i
$695$	19.4932	+	33.7632i	0.739419	+	1.28071i
$696$	2.61793	−	4.53438i	0.0992322	−	0.171875i
$697$	5.68479	+	4.77011i	0.215327	+	0.180681i
$698$	18.8053	+	6.84457i	0.711791	+	0.259071i
$699$	−12.0929	+	4.40144i	−0.457394	+	0.166478i
$700$	2.49273	−	2.09165i	0.0942162	−	0.0790568i
$701$	3.70867	+	21.0329i	0.140075	+	0.794403i	0.971191	+	0.238304i	$0.0765914\pi$
$701$	3.70867	+	21.0329i	0.140075	+	0.794403i	−0.831116	+	0.556099i	$0.812297\pi$
$702$	−14.1530			−0.534171
$703$		0			0
$704$	17.2003			0.648260
$705$	0.167718	+	0.951178i	0.00631664	+	0.0358234i
$706$	7.71032	−	6.46973i	0.290182	−	0.243491i
$707$	−13.9893	+	5.09170i	−0.526123	+	0.191493i
$708$	−6.59879	−	2.40176i	−0.247998	−	0.0902638i
$709$	−12.0810	−	10.1372i	−0.453712	−	0.380709i	0.387099	−	0.922038i	$-0.373477\pi$
$709$	−12.0810	−	10.1372i	−0.453712	−	0.380709i	−0.840811	+	0.541329i	$0.817921\pi$
$710$	−15.3182	+	26.5319i	−0.574882	+	0.995725i
$711$	9.45904	+	16.3835i	0.354742	+	0.614431i
$712$	1.12495	−	6.37992i	0.0421594	−	0.239098i
$713$	−0.593578	+	3.36635i	−0.0222297	+	0.126071i
$714$	0.726682	+	1.25865i	0.0271954	+	0.0471038i
$715$	22.8516	−	39.5802i	0.854603	−	1.48022i
$716$	−20.0326	−	16.8093i	−0.748652	−	0.628193i
$717$	−11.6630	−	4.24497i	−0.435562	−	0.158531i
$718$	8.58095	−	3.12321i	0.320238	−	0.116557i
$719$	−27.0631	+	22.7086i	−1.00928	+	0.846888i	−0.988243	−	0.152891i	$-0.951142\pi$
$719$	−27.0631	+	22.7086i	−1.00928	+	0.846888i	−0.0210385	+	0.999779i	$0.506697\pi$
$720$	−0.0500404	−	0.283793i	−0.00186489	−	0.0105763i
$721$	−0.0273411			−0.00101824
$722$		0			0
$723$	0.158385			0.00589040
$724$	−3.42932	−	19.4486i	−0.127450	−	0.722803i
$725$	3.74969	−	3.14636i	0.139260	−	0.116853i
$726$	−0.280592	+	0.102127i	−0.0104138	+	0.00379030i
$727$	−37.9839	−	13.8250i	−1.40874	−	0.512741i	−0.477983	−	0.878369i	$-0.658632\pi$
$727$	−37.9839	−	13.8250i	−1.40874	−	0.512741i	−0.930761	+	0.365629i	$0.880854\pi$
$728$	−21.6138	−	18.1361i	−0.801061	−	0.672170i
$729$	6.44562	−	11.1641i	0.238727	−	0.413487i
$730$	8.36959	+	14.4965i	0.309772	+	0.536541i
$731$	1.37774	−	7.81353i	0.0509574	−	0.288994i
$732$	0.497474	−	2.82131i	0.0183872	−	0.104279i
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	0.977918	+	0.208988i	$0.0670170\pi$
$733$	18.1382	+	31.4162i	0.669948	+	1.16038i	−0.307970	+	0.951396i	$0.599650\pi$
$734$	−14.3045	+	24.7762i	−0.527990	+	0.914505i
$735$	−3.57919	−	3.00330i	−0.132021	−	0.110778i
$736$	9.31820	+	3.39155i	0.343473	+	0.125014i
$737$	45.5604	−	16.5826i	1.67824	−	0.610829i
$738$	8.21806	−	6.89577i	0.302511	−	0.253837i
$739$	−3.59034	−	20.3618i	−0.132073	−	0.749021i	−0.976854	−	0.213909i	$-0.931380\pi$
$739$	−3.59034	−	20.3618i	−0.132073	−	0.749021i	0.844781	−	0.535112i	$-0.179731\pi$
$740$	2.60132			0.0956264
$741$		0			0
$742$	10.0915			0.370471
$743$	−1.16415	−	6.60224i	−0.0427086	−	0.242213i	0.955979	−	0.293436i	$-0.0947989\pi$
$743$	−1.16415	−	6.60224i	−0.0427086	−	0.242213i	−0.998687	+	0.0512238i	$0.983688\pi$
$744$	2.24787	−	1.88619i	0.0824111	−	0.0691511i
$745$	−8.96198	+	3.26189i	−0.328342	+	0.119507i
$746$	−25.1920	−	9.16912i	−0.922343	−	0.335705i
$747$	−5.22912	−	4.38775i	−0.191324	−	0.160540i
$748$	3.45811	−	5.98962i	0.126441	−	0.219002i
$749$	3.34002	+	5.78509i	0.122042	+	0.211383i
$750$	0.738293	−	4.18707i	0.0269586	−	0.152890i
$751$	−1.85932	+	10.5447i	−0.0678475	+	0.384782i	0.931909	+	0.362693i	$0.118143\pi$
$751$	−1.85932	+	10.5447i	−0.0678475	+	0.384782i	−0.999756	+	0.0220888i	$0.992968\pi$
$752$	0.0150147	+	0.0260063i	0.000547531	+	0.000948352i
$753$	−4.30928	+	7.46389i	−0.157039	+	0.271999i
$754$	−12.3603	−	10.3715i	−0.450134	−	0.377707i
$755$	34.7301	+	12.6407i	1.26396	+	0.460044i
$756$	−6.58987	+	2.39852i	−0.239671	+	0.0872332i
$757$	−3.11200	+	2.61128i	−0.113107	+	0.0949084i	−0.697587	−	0.716500i	$-0.745743\pi$
$757$	−3.11200	+	2.61128i	−0.113107	+	0.0949084i	0.584480	+	0.811408i	$0.301299\pi$
$758$	2.72725	+	15.4670i	0.0990583	+	0.561788i
$759$	−3.19253			−0.115882
$760$		0			0
$761$	−11.0077			−0.399030			−0.199515	−	0.979895i	$-0.563937\pi$
$761$	−11.0077			−0.399030			−0.199515	+	0.979895i	$0.563937\pi$
$762$	0.00820761	+	0.0465477i	0.000297330	+	0.00168624i
$763$	10.6099	−	8.90279i	0.384106	−	0.322303i
$764$	21.8421	−	7.94989i	0.790221	−	0.287617i
$765$	−10.6839	−	3.88863i	−0.386278	−	0.140594i
$766$	−15.8011	−	13.2587i	−0.570918	−	0.479057i
$767$	−28.4616	+	49.2969i	−1.02769	+	1.78001i
$768$	−4.28359	−	7.41939i	−0.154571	−	0.267724i
$769$	3.70692	−	21.0230i	0.133675	−	0.758108i	−0.842098	−	0.539324i	$-0.818680\pi$
$769$	3.70692	−	21.0230i	0.133675	−	0.758108i	0.975773	−	0.218784i	$-0.0702091\pi$
$770$	−2.47906	+	14.0594i	−0.0893390	+	0.506666i
$771$	−4.08512	−	7.07564i	−0.147122	−	0.254823i
$772$	−7.91312	+	13.7059i	−0.284800	+	0.493287i
$773$	−13.7253	−	11.5169i	−0.493666	−	0.414235i	0.361672	−	0.932305i	$-0.382206\pi$
$773$	−13.7253	−	11.5169i	−0.493666	−	0.414235i	−0.855338	+	0.518070i	$0.826651\pi$
$774$	−10.7780	−	3.92286i	−0.387406	−	0.141004i
$775$	2.57785	−	0.938260i	0.0925990	−	0.0337033i
$776$	3.96245	−	3.32489i	0.142244	−	0.119357i
$777$	0.145430	+	0.824773i	0.00521726	+	0.0295886i
$778$	−3.43788			−0.123254
$779$		0			0
$780$	−8.74422			−0.313093
$781$	8.15064	+	46.2246i	0.291653	+	1.65405i
$782$	−1.95811	+	1.64305i	−0.0700219	+	0.0587554i
$783$	−9.91282	+	3.60797i	−0.354255	+	0.128938i
$784$	−0.136507	−	0.0496844i	−0.00487524	−	0.00177444i
$785$	20.1236	+	16.8857i	0.718242	+	0.602677i
$786$	0.710485	−	1.23060i	0.0253422	−	0.0438939i
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.861656	+	0.507493i	$0.169428\pi$
$787$	24.4158	+	42.2894i	0.870330	+	1.50746i	0.00867371	+	0.999962i	$0.497239\pi$
$788$	4.94191	−	28.0270i	0.176048	−	0.998420i
$789$	−0.890996	+	5.05309i	−0.0317203	+	0.179895i
$790$	−7.75237	−	13.4275i	−0.275817	−	0.477729i
$791$	−6.93242	+	12.0073i	−0.246488	+	0.426930i
$792$	−20.1466	−	16.9050i	−0.715879	−	0.600694i
$793$	−21.8221	−	7.94258i	−0.774924	−	0.282049i
$794$	7.40332	−	2.69459i	0.262734	−	0.0956274i
$795$	6.30200	−	5.28801i	0.223509	−	0.187546i
$796$	−1.96431	−	11.1401i	−0.0696231	−	0.394852i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	−1.38191	−	7.83721i	−0.0488579	−	0.277087i
$801$	−4.75174	+	3.98719i	−0.167895	+	0.140880i
$802$	1.67530	−	0.609758i	0.0591568	−	0.0215313i
$803$	24.0993	+	8.77141i	0.850444	+	0.309536i
$804$	−7.10607	−	5.96270i	−0.250612	−	0.210288i
$805$	−4.18479	+	7.24827i	−0.147495	+	0.255468i
$806$	−4.52141	−	7.83131i	−0.159260	−	0.275846i
$807$	−1.68891	+	9.57829i	−0.0594525	+	0.337172i
$808$	−3.90302	+	22.1351i	−0.137308	+	0.778711i
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	0.966459	−	0.256822i	$-0.0826755\pi$
$809$	7.41834	+	12.8489i	0.260815	+	0.451745i	−0.705644	+	0.708567i	$0.749342\pi$
$810$	−7.27244	+	12.5962i	−0.255528	+	0.442587i
$811$	6.41740	+	5.38484i	0.225346	+	0.189087i	0.748469	−	0.663169i	$-0.230789\pi$
$811$	6.41740	+	5.38484i	0.225346	+	0.189087i	−0.523124	+	0.852257i	$0.675234\pi$
$812$	−7.51279	−	2.73443i	−0.263647	−	0.0959598i
$813$	9.48205	−	3.45118i	0.332550	−	0.121038i
$814$	−1.92468	+	1.61500i	−0.0674599	+	0.0566056i
$815$	0.889185	+	5.04282i	0.0311468	+	0.176642i
$816$	0.0368366			0.00128954
$817$		0			0
$818$	−28.3233			−0.990299
$819$	4.69119	+	26.6051i	0.163923	+	0.929656i
$820$	10.6839	−	8.96487i	0.373099	−	0.313067i
$821$	−5.90033	+	2.14754i	−0.205923	+	0.0749498i	−0.442922	−	0.896560i	$-0.646058\pi$
$821$	−5.90033	+	2.14754i	−0.205923	+	0.0749498i	0.236999	+	0.971510i	$0.423836\pi$
$822$	−8.59152	−	3.12706i	−0.299664	−	0.109069i
$823$	8.44672	+	7.08764i	0.294434	+	0.247060i	0.778023	−	0.628236i	$-0.216223\pi$
$823$	8.44672	+	7.08764i	0.294434	+	0.247060i	−0.483589	+	0.875295i	$0.660667\pi$
$824$	−0.0206398	+	0.0357492i	−0.000719023	+	0.00124538i
$825$	1.28106	+	2.21886i	0.0446008	+	0.0772508i
$826$	3.08765	−	17.5109i	0.107433	−	0.609283i
$827$	−5.89289	+	33.4203i	−0.204916	+	1.16214i	0.692656	+	0.721268i	$0.256440\pi$
$827$	−5.89289	+	33.4203i	−0.204916	+	1.16214i	−0.897572	+	0.440868i	$0.854671\pi$
$828$	−2.93077	−	5.07624i	−0.101851	−	0.176412i
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	−0.986892	−	0.161381i	$-0.948405\pi$
$829$	−10.1834	+	17.6382i	−0.353686	+	0.612602i	0.633206	+	0.773983i	$0.281738\pi$
$830$	4.28564	+	3.59608i	0.148757	+	0.124822i
$831$	6.88191	+	2.50481i	0.238731	+	0.0868909i
$832$	−25.0672	+	9.12370i	−0.869048	+	0.316308i
$833$	−4.39053	+	3.68409i	−0.152123	+	0.127646i
$834$	1.25103	+	7.09494i	0.0433196	+	0.245678i
$835$	−58.8881			−2.03791
$836$		0			0
$837$	−5.91210			−0.204352
$838$	3.55035	+	20.1350i	0.122645	+	0.695552i
$839$	−12.1107	+	10.1620i	−0.418106	+	0.350833i	−0.827442	−	0.561551i	$-0.810205\pi$
$839$	−12.1107	+	10.1620i	−0.418106	+	0.350833i	0.409336	+	0.912384i	$0.365760\pi$
$840$	6.75150	−	2.45734i	0.232949	−	0.0847864i
$841$	15.9500	+	5.80531i	0.549999	+	0.200183i
$842$	4.34730	+	3.64781i	0.149818	+	0.125712i
$843$	−3.48814	+	6.04164i	−0.120138	+	0.208085i
$844$	−8.96926	−	15.5352i	−0.308734	−	0.534744i
$845$	−6.59240	+	37.3873i	−0.226785	+	1.28616i
$846$	0.297418	−	1.68674i	0.0102254	−	0.0579914i
$847$	0.599670	+	1.03866i	0.0206049	+	0.0356888i
$848$	0.127889	−	0.221510i	0.00439172	−	0.00760668i
$849$	7.08306	+	5.94340i	0.243090	+	0.203977i
$850$	1.92767	+	0.701615i	0.0661186	+	0.0240652i
$851$	−1.38413	+	0.503783i	−0.0474475	+	0.0172695i
$852$	6.87939	−	5.77249i	0.235684	−	0.197762i
$853$	−9.14244	−	51.8493i	−0.313031	−	1.77529i	−0.583054	−	0.812433i	$-0.698142\pi$
$853$	−9.14244	−	51.8493i	−0.313031	−	1.77529i	0.270023	−	0.962854i	$-0.412969\pi$
$854$	7.25402			0.248228
$855$		0			0
$856$	10.0855			0.344716
$857$	3.99866	+	22.6775i	0.136591	+	0.774649i	0.973738	+	0.227670i	$0.0731109\pi$
$857$	3.99866	+	22.6775i	0.136591	+	0.774649i	−0.837147	+	0.546978i	$0.815778\pi$
$858$	6.46972	−	5.42874i	0.220873	−	0.185334i
$859$	−8.37211	+	3.04720i	−0.285653	+	0.103969i	−0.480873	−	0.876790i	$-0.659680\pi$
$859$	−8.37211	+	3.04720i	−0.285653	+	0.103969i	0.195220	+	0.980759i	$0.437458\pi$
$860$	−14.0119	−	5.09992i	−0.477802	−	0.173906i
$861$	3.43969	+	2.88624i	0.117224	+	0.0983630i
$862$	6.15451	−	10.6599i	0.209624	−	0.363079i
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	0.999970	+	0.00773998i	$0.00246374\pi$
$863$	14.8849	+	25.7814i	0.506688	+	0.877609i	−0.493282	+	0.869869i	$0.664203\pi$
$864$	−2.97818	+	16.8901i	−0.101320	+	0.574612i
$865$	0.394238	−	2.23583i	0.0134045	−	0.0760206i
$866$	12.6160	+	21.8516i	0.428710	+	0.742548i
$867$	−3.79607	+	6.57499i	−0.128921	+	0.223298i
$868$	−3.43242	−	2.88014i	−0.116504	−	0.0977584i
$869$	−22.3221	−	8.12457i	−0.757224	−	0.275607i
$870$	3.86097	−	1.40528i	0.130899	−	0.0476434i
$871$	−57.6023	+	48.3340i	−1.95178	+	1.63774i
$872$	−3.63119	−	20.5935i	−0.122967	−	0.697383i
$873$	−4.95273			−0.167625
$874$		0			0
$875$	−17.0770			−0.577307
$876$	−0.852044	−	4.83218i	−0.0287879	−	0.163264i
$877$	19.1741	−	16.0890i	0.647464	−	0.543287i	−0.258836	−	0.965921i	$-0.583339\pi$
$877$	19.1741	−	16.0890i	0.647464	−	0.543287i	0.906300	+	0.422635i	$0.138895\pi$
$878$	11.0254	−	4.01291i	0.372089	−	0.135429i
$879$	−7.80200	−	2.83970i	−0.263155	−	0.0957806i
$880$	0.277189	+	0.232589i	0.00934403	+	0.00784057i
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	−0.985095	−	0.172014i	$-0.944973\pi$
$881$	−10.1980	+	17.6634i	−0.343579	+	0.595097i	0.641515	+	0.767110i	$0.278306\pi$
$882$	4.14274	+	7.17544i	0.139493	+	0.241610i
$883$	−1.84554	+	10.4666i	−0.0621074	+	0.352229i	0.937879	+	0.346963i	$0.112787\pi$
$883$	−1.84554	+	10.4666i	−0.0621074	+	0.352229i	−0.999986	+	0.00526542i	$0.998324\pi$
$884$	−1.86262	+	10.5634i	−0.0626465	+	0.355286i
$885$	−7.24763	−	12.5533i	−0.243626	−	0.421973i
$886$	14.8981	−	25.8043i	0.500512	−	0.866912i
$887$	43.1580	+	36.2138i	1.44910	+	1.21594i	0.933231	+	0.359276i	$0.116976\pi$
$887$	43.1580	+	36.2138i	1.44910	+	1.21594i	0.515872	+	0.856666i	$0.327468\pi$
$888$	1.18820	+	0.432468i	0.0398733	+	0.0145127i
$889$	0.178396	−	0.0649308i	0.00598321	−	0.00217771i
$890$	3.89440	−	3.26779i	0.130541	−	0.109537i
$891$	3.86959	+	21.9455i	0.129636	+	0.735202i
$892$	−3.69789			−0.123815
$893$		0			0
$894$	−1.76239			−0.0589432
$895$	−9.37346	−	53.1595i	−0.313320	−	1.77693i
$896$	−9.85117	+	8.26611i	−0.329104	+	0.276151i
$897$	4.65270	−	1.69345i	0.155349	−	0.0565425i
$898$	−15.5686	−	5.66651i	−0.519532	−	0.189094i
$899$	−5.16322	−	4.33246i	−0.172203	−	0.144495i
$900$	−2.35204	+	4.07386i	−0.0784015	+	0.135795i
$901$	−5.04576	−	8.73951i	−0.168099	−	0.291155i
$902$	−2.33915	+	13.2660i	−0.0778850	+	0.441708i
$903$	0.833626	−	4.72773i	0.0277413	−	0.157329i
$904$	10.4666	+	18.1286i	0.348113	+	0.602949i
$905$	20.3824	−	35.3033i	0.677533	−	1.17352i
$906$	5.23190	+	4.39008i	0.173818	+	0.145851i
$907$	−5.56640	−	2.02600i	−0.184829	−	0.0672723i	0.247948	−	0.968773i	$-0.420244\pi$
$907$	−5.56640	−	2.02600i	−0.184829	−	0.0672723i	−0.432777	+	0.901501i	$0.642466\pi$
$908$	15.8173	−	5.75703i	0.524916	−	0.191054i
$909$	16.4862	−	13.8335i	0.546812	−	0.458829i
$910$	−3.84477	−	21.8048i	−0.127453	−	0.722821i
$911$	34.0591			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$911$	34.0591			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$912$		0			0
$913$	8.57129			0.283668
$914$	−2.18046	−	12.3660i	−0.0721231	−	0.409030i
$915$	4.53003	−	3.80115i	0.149758	−	0.125662i
$916$	10.8517	−	3.94971i	0.358552	−	0.130502i
$917$	−5.36319	−	1.95204i	−0.177108	−	0.0644621i
$918$	−3.38666	−	2.84174i	−0.111776	−	0.0937915i
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	−0.809637	−	0.586931i	$-0.800336\pi$
$919$	3.13697	−	5.43340i	0.103479	−	0.179231i	0.913116	+	0.407700i	$0.133669\pi$
$920$	6.31820	+	10.9434i	0.208305	+	0.360795i
$921$	1.98839	−	11.2767i	0.0655196	−	0.371580i
$922$	2.12687	−	12.0621i	0.0700447	−	0.397243i
$923$	−36.3979	−	63.0429i	−1.19805	−	2.07508i
$924$	2.09240	−	3.62414i	0.0688348	−	0.119225i
$925$	0.905544	+	0.759842i	0.0297741	+	0.0249834i
$926$	−1.45677	−	0.530220i	−0.0478723	−	0.0174241i
$927$	0.0371413	−	0.0135183i	0.00121988	−	0.000444000i
$928$	−14.9782	+	12.5682i	−0.491683	+	0.412571i
$929$	4.91828	+	27.8930i	0.161364	+	0.915138i	0.952735	+	0.303803i	$0.0982563\pi$
$929$	4.91828	+	27.8930i	0.161364	+	0.915138i	−0.791371	+	0.611336i	$0.790633\pi$
$930$	2.30272			0.0755091
$931$		0			0
$932$	29.6682			0.971814
$933$	−1.33931	−	7.59559i	−0.0438469	−	0.248668i
$934$	−14.8485	+	12.4594i	−0.485857	+	0.407682i
$935$	13.4153	−	4.88279i	0.438729	−	0.159684i
$936$	38.3282	+	13.9503i	1.25280	+	0.455980i
$937$	−15.3760	−	12.9020i	−0.502311	−	0.421489i	0.356103	−	0.934447i	$-0.384105\pi$
$937$	−15.3760	−	12.9020i	−0.502311	−	0.421489i	−0.858414	+	0.512958i	$0.828550\pi$
$938$	11.7442	−	20.3416i	0.383462	−	0.664176i
$939$	5.19278	+	8.99416i	0.169460	+	0.293513i
$940$	0.386659	−	2.19285i	0.0126114	−	0.0715230i
$941$	−0.936862	+	5.31321i	−0.0305408	+	0.173206i	−0.996263	−	0.0863726i	$-0.972472\pi$
$941$	−0.936862	+	5.31321i	−0.0305408	+	0.173206i	0.965722	+	0.259578i	$0.0835835\pi$
$942$	2.42720	+	4.20404i	0.0790826	+	0.136975i
$943$	−3.94862	+	6.83920i	−0.128585	+	0.222715i
$944$	−0.345237	−	0.289688i	−0.0112365	−	0.00942855i
$945$	−13.6027	−	4.95096i	−0.442495	−	0.161055i
$946$	13.5334	−	4.92577i	0.440010	−	0.160150i
$947$	5.08899	−	4.27017i	0.165370	−	0.138762i	−0.556347	−	0.830950i	$-0.687798\pi$
$947$	5.08899	−	4.27017i	0.165370	−	0.138762i	0.721717	+	0.692188i	$0.243353\pi$
$948$	0.789210	+	4.47584i	0.0256324	+	0.145368i
$949$	−39.7743			−1.29113
$950$		0			0
$951$	15.0833			0.489109
$952$	−1.53044	−	8.67956i	−0.0496018	−	0.281306i
$953$	11.3558	−	9.52861i	0.367849	−	0.308662i	−0.440061	−	0.897968i	$-0.645043\pi$
$953$	11.3558	−	9.52861i	0.367849	−	0.308662i	0.807910	+	0.589306i	$0.200599\pi$
$954$	−13.7087	+	4.98957i	−0.443837	+	0.161543i
$955$	45.0861	+	16.4100i	1.45895	+	0.531015i
$956$	21.9192	+	18.3924i	0.708918	+	0.594853i
$957$	3.14749	−	5.45161i	0.101744	−	0.176226i
$958$	−11.1932	−	19.3873i	−0.361637	−	0.626374i
$959$	−6.37686	+	36.1650i	−0.205920	+	1.16783i
$960$	1.17958	−	6.68972i	0.0380707	−	0.215910i
$961$	13.6113	+	23.5754i	0.439074	+	0.760498i
$962$	1.94831	−	3.37457i	0.0628161	−	0.108801i
$963$	−7.39756	−	6.20729i	−0.238383	−	0.200027i
$964$	−0.343121	−	0.124886i	−0.0110512	−	0.00402230i
$965$	−30.6981	+	11.1732i	−0.988205	+	0.359677i
$966$	−1.18479	+	0.994159i	−0.0381201	+	0.0319865i
$967$	3.68510	+	20.8992i	0.118505	+	0.672074i	0.984955	+	0.172811i	$0.0552848\pi$
$967$	3.68510	+	20.8992i	0.118505	+	0.672074i	−0.866450	+	0.499263i	$0.833604\pi$
$968$	1.81076			0.0582002
$969$		0			0
$970$	4.05913			0.130331
$971$	6.53033	+	37.0354i	0.209568	+	1.18852i	0.890087	+	0.455791i	$0.150643\pi$
$971$	6.53033	+	37.0354i	0.209568	+	1.18852i	−0.680519	+	0.732731i	$0.738245\pi$
$972$	11.8414	−	9.93609i	0.379812	−	0.318700i
$973$	27.1917	−	9.89695i	0.871724	−	0.317282i
$974$	18.6018	+	6.77050i	0.596040	+	0.216941i
$975$	−3.04395	−	2.55418i	−0.0974844	−	0.0817991i
$976$	0.0919294	−	0.159226i	0.00294259	−	0.00509671i
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	−0.954204	−	0.299156i	$-0.903295\pi$
$977$	−23.0107	−	39.8558i	−0.736179	−	1.27510i	0.218026	−	0.975943i	$-0.430038\pi$
$978$	−0.164315	+	0.931876i	−0.00525421	+	0.0297981i
$979$	1.35251	−	7.67047i	0.0432264	−	0.245149i
$980$	5.38578	+	9.32845i	0.172042	+	0.297986i
$981$	−10.0111	+	17.3398i	−0.319631	+	0.553618i
$982$	−10.5318	−	8.83726i	−0.336085	−	0.282008i
$983$	56.9420	+	20.7252i	1.81617	+	0.661031i	0.996046	+	0.0888404i	$0.0283161\pi$
$983$	56.9420	+	20.7252i	1.81617	+	0.661031i	0.820121	+	0.572190i	$0.193906\pi$
$984$	6.37046	−	2.31866i	0.203083	−	0.0739161i
$985$	45.0014	−	37.7607i	1.43386	−	1.20315i
$986$	−0.875210	−	4.96356i	−0.0278724	−	0.158072i
$987$	0.716881			0.0228186
$988$		0			0
$989$	8.44326			0.268480
$990$	−3.58378	−	20.3246i	−0.113900	−	0.645959i
$991$	−32.0959	+	26.9316i	−1.01956	+	0.855511i	−0.989572	−	0.144039i	$-0.953991\pi$
$991$	−32.0959	+	26.9316i	−1.01956	+	0.855511i	−0.0299865	+	0.999550i	$0.509546\pi$
$992$	−10.2973	+	3.74789i	−0.326938	+	0.118996i
$993$	0.855037	+	0.311208i	0.0271338	+	0.00987589i
$994$	17.4192	+	14.6165i	0.552504	+	0.463606i
$995$	11.6750	−	20.2217i	0.370122	−	0.641070i
$996$	−0.819955	−	1.42020i	−0.0259813	−	0.0450009i
$997$	5.85457	−	33.2029i	0.185416	−	1.05155i	−0.740004	−	0.672603i	$-0.765176\pi$
$997$	5.85457	−	33.2029i	0.185416	−	1.05155i	0.925420	−	0.378944i	$-0.123713\pi$
$998$	4.36989	−	24.7829i	0.138326	−	0.784488i
$999$	−1.27379	−	2.20626i	−0.0403008	−	0.0698030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.a.28.1		6
19.2	odd	18		361.2.e.g.245.1		6
19.3	odd	18		19.2.e.a.5.1	yes	6
19.4	even	9		361.2.c.h.68.3		6
19.5	even	9		361.2.e.b.54.1		6
19.6	even	9		361.2.a.h.1.1		3
19.7	even	3		361.2.e.h.99.1		6
19.8	odd	6		361.2.e.f.234.1		6
19.9	even	9		361.2.c.h.292.3		6
19.10	odd	18		361.2.c.i.292.1		6
19.11	even	3		361.2.e.b.234.1		6
19.12	odd	6		19.2.e.a.4.1	✓	6
19.13	odd	18		361.2.a.g.1.3		3
19.14	odd	18		361.2.e.f.54.1		6
19.15	odd	18		361.2.c.i.68.1		6
19.16	even	9		361.2.e.h.62.1		6
19.17	even	9	inner	361.2.e.a.245.1		6
19.18	odd	2		361.2.e.g.28.1		6
57.32	even	18		3249.2.a.z.1.1		3
57.41	even	18		171.2.u.c.100.1		6
57.44	odd	18		3249.2.a.s.1.3		3
57.50	even	6		171.2.u.c.118.1		6
76.3	even	18		304.2.u.b.81.1		6
76.31	even	6		304.2.u.b.289.1		6
76.51	even	18		5776.2.a.br.1.1		3
76.63	odd	18		5776.2.a.bi.1.3		3
95.3	even	36		475.2.u.a.24.2		12
95.12	even	12		475.2.u.a.99.2		12
95.22	even	36		475.2.u.a.24.1		12
95.44	even	18		9025.2.a.x.1.3		3
95.69	odd	6		475.2.l.a.251.1		6
95.79	odd	18		475.2.l.a.176.1		6
95.88	even	12		475.2.u.a.99.1		12
95.89	odd	18		9025.2.a.bd.1.1		3
133.3	even	18		931.2.x.b.765.1		6
133.12	even	6		931.2.x.b.802.1		6
133.31	even	6		931.2.v.a.422.1		6
133.41	even	18		931.2.w.a.442.1		6
133.60	odd	18		931.2.x.a.765.1		6
133.69	even	6		931.2.w.a.99.1		6
133.79	odd	18		931.2.v.b.214.1		6
133.88	odd	6		931.2.v.b.422.1		6
133.107	odd	6		931.2.x.a.802.1		6
133.117	even	18		931.2.v.a.214.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	19.12	odd	6
19.2.e.a.5.1	yes	6	19.3	odd	18
171.2.u.c.100.1		6	57.41	even	18
171.2.u.c.118.1		6	57.50	even	6
304.2.u.b.81.1		6	76.3	even	18
304.2.u.b.289.1		6	76.31	even	6
361.2.a.g.1.3		3	19.13	odd	18
361.2.a.h.1.1		3	19.6	even	9
361.2.c.h.68.3		6	19.4	even	9
361.2.c.h.292.3		6	19.9	even	9
361.2.c.i.68.1		6	19.15	odd	18
361.2.c.i.292.1		6	19.10	odd	18
361.2.e.a.28.1		6	1.1	even	1	trivial
361.2.e.a.245.1		6	19.17	even	9	inner
361.2.e.b.54.1		6	19.5	even	9
361.2.e.b.234.1		6	19.11	even	3
361.2.e.f.54.1		6	19.14	odd	18
361.2.e.f.234.1		6	19.8	odd	6
361.2.e.g.28.1		6	19.18	odd	2
361.2.e.g.245.1		6	19.2	odd	18
361.2.e.h.62.1		6	19.16	even	9
361.2.e.h.99.1		6	19.7	even	3
475.2.l.a.176.1		6	95.79	odd	18
475.2.l.a.251.1		6	95.69	odd	6
475.2.u.a.24.1		12	95.22	even	36
475.2.u.a.24.2		12	95.3	even	36
475.2.u.a.99.1		12	95.88	even	12
475.2.u.a.99.2		12	95.12	even	12
931.2.v.a.214.1		6	133.117	even	18
931.2.v.a.422.1		6	133.31	even	6
931.2.v.b.214.1		6	133.79	odd	18
931.2.v.b.422.1		6	133.88	odd	6
931.2.w.a.99.1		6	133.69	even	6
931.2.w.a.442.1		6	133.41	even	18
931.2.x.a.765.1		6	133.60	odd	18
931.2.x.a.802.1		6	133.107	odd	6
931.2.x.b.765.1		6	133.3	even	18
931.2.x.b.802.1		6	133.12	even	6
3249.2.a.s.1.3		3	57.44	odd	18
3249.2.a.z.1.1		3	57.32	even	18
5776.2.a.bi.1.3		3	76.63	odd	18
5776.2.a.br.1.1		3	76.51	even	18
9025.2.a.x.1.3		3	95.44	even	18
9025.2.a.bd.1.1		3	95.89	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.152704 - 0.866025i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(1.15270 - 0.419550i) q^{4} +(2.37939 + 0.866025i) q^{5} +(0.358441 + 0.300767i) q^{6} +(0.939693 - 1.62760i) q^{7} +(-1.41875 - 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +(0.386659 - 2.19285i) q^{10} +(-1.70574 - 2.95442i) q^{11} +(-0.326352 + 0.565258i) q^{12} +(4.05303 + 3.40090i) q^{13} +(-1.55303 - 0.565258i) q^{14} +(-1.26604 + 0.460802i) q^{15} +(-0.0320889 + 0.0269258i) q^{16} +(0.286989 + 1.62760i) q^{17} +2.38919 q^{18} +3.10607 q^{20} +(0.173648 + 0.984808i) q^{21} +(-2.29813 + 1.92836i) q^{22} +(-1.65270 + 0.601535i) q^{23} +(1.41875 + 0.516382i) q^{24} +(1.08125 + 0.907278i) q^{25} +(2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(0.400330 - 2.27038i) q^{28} +(0.602196 - 3.41523i) q^{29} +(0.592396 + 1.02606i) q^{30} +(0.971782 - 1.68317i) q^{31} +(-4.31908 - 3.62414i) q^{32} +(1.70574 + 0.620838i) q^{33} +(1.36571 - 0.497079i) q^{34} +(3.64543 - 3.05888i) q^{35} +(0.578726 + 3.28212i) q^{36} +0.837496 q^{37} -2.81521 q^{39} +(-1.24763 - 7.07564i) q^{40} +(3.43969 - 2.88624i) q^{41} +(0.826352 - 0.300767i) q^{42} +(-4.51114 - 1.64192i) q^{43} +(-3.20574 - 2.68993i) q^{44} +(-3.43969 + 5.95772i) q^{45} +(0.773318 + 1.33943i) q^{46} +(0.124485 - 0.705990i) q^{47} +(0.00387039 - 0.0219501i) q^{48} +(1.73396 + 3.00330i) q^{49} +(0.620615 - 1.07494i) q^{50} +(-0.673648 - 0.565258i) q^{51} +(6.09879 + 2.21978i) q^{52} +(-5.73783 + 2.08840i) q^{53} +(-2.04916 + 1.71945i) q^{54} +(-1.50000 - 8.50692i) q^{55} -5.33275 q^{56} -3.04963 q^{58} +(1.86824 + 10.5953i) q^{59} +(-1.26604 + 1.06234i) q^{60} +(-4.12449 + 1.50119i) q^{61} +(-1.60607 - 0.584561i) q^{62} +(3.91147 + 3.28212i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(6.69846 + 11.6021i) q^{65} +(0.277189 - 1.57202i) q^{66} +(-2.46791 + 13.9962i) q^{67} +(1.01367 + 1.75573i) q^{68} +(0.467911 - 0.810446i) q^{69} +(-3.20574 - 2.68993i) q^{70} +(-12.9290 - 4.70578i) q^{71} +(7.24422 - 2.63668i) q^{72} +(-5.75877 + 4.83218i) q^{73} +(-0.127889 - 0.725293i) q^{74} -0.751030 q^{75} -6.41147 q^{77} +(0.429892 + 2.43804i) q^{78} +(5.33409 - 4.47584i) q^{79} +(-0.0996702 + 0.0362770i) q^{80} +(-6.13816 - 2.23411i) q^{81} +(-3.02481 - 2.53812i) q^{82} +(-1.25624 + 2.17588i) q^{83} +(0.613341 + 1.06234i) q^{84} +(-0.726682 + 4.12122i) q^{85} +(-0.733078 + 4.15749i) q^{86} +(0.922618 + 1.59802i) q^{87} +(-4.84002 + 8.38316i) q^{88} +(1.74897 + 1.46756i) q^{89} +(5.68479 + 2.06910i) q^{90} +(9.34389 - 3.40090i) q^{91} +(-1.65270 + 1.38678i) q^{92} +(0.179578 + 1.01844i) q^{93} -0.630415 q^{94} +3.00000 q^{96} +(0.316552 + 1.79525i) q^{97} +(2.33615 - 1.96026i) q^{98} +(8.70961 - 3.17004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 6 q^{3} + 9 q^{4} + 3 q^{5} - 6 q^{6} - 6 q^{8} + 12 q^{9} + 9 q^{10} - 3 q^{12} + 12 q^{13} + 3 q^{14} - 3 q^{15} + 9 q^{16} - 6 q^{17} + 6 q^{18} - 6 q^{20} - 12 q^{23} + 6 q^{24} + 9 q^{25}+ \cdots + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 6 * q^3 + 9 * q^4 + 3 * q^5 - 6 * q^6 - 6 * q^8 + 12 * q^9 + 9 * q^10 - 3 * q^12 + 12 * q^13 + 3 * q^14 - 3 * q^15 + 9 * q^16 - 6 * q^17 + 6 * q^18 - 6 * q^20 - 12 * q^23 + 6 * q^24 + 9 * q^25 + 15 * q^26 - 6 * q^27 - 12 * q^28 + 3 * q^29 - 9 * q^31 - 9 * q^32 + 18 * q^34 + 6 * q^35 + 21 * q^36 - 24 * q^39 + 9 * q^40 + 15 * q^41 + 6 * q^42 - 21 * q^43 - 9 * q^44 - 15 * q^45 + 18 * q^46 - 12 * q^47 - 24 * q^48 + 15 * q^49 + 15 * q^50 - 3 * q^51 - 6 * q^52 - 15 * q^53 - 24 * q^54 - 9 * q^55 + 6 * q^56 + 36 * q^58 + 6 * q^59 - 3 * q^60 - 12 * q^61 + 15 * q^62 + 3 * q^63 - 12 * q^64 + 12 * q^65 - 9 * q^66 - 24 * q^67 - 15 * q^68 + 12 * q^69 - 9 * q^70 - 12 * q^71 - 15 * q^72 - 12 * q^73 - 30 * q^74 - 30 * q^75 - 18 * q^77 - 6 * q^78 - 15 * q^79 - 15 * q^80 - 3 * q^81 + 9 * q^82 - 3 * q^84 + 9 * q^85 + 48 * q^86 - 21 * q^87 - 9 * q^88 - 15 * q^89 + 27 * q^90 + 12 * q^91 - 12 * q^92 + 27 * q^93 - 18 * q^94 + 18 * q^96 + 18 * q^98 + 18 * q^99

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