LMFDB - Embedded newform 385.2.i.c.221.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, degree $2$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 $ x^16 - 3x^15 + 17x^14 - 28x^13 + 127x^12 - 178x^11 + 612x^10 - 527x^9 + 1556x^8 - 1065x^7 + 2812x^6 - 1224x^5 + 2359x^4 - 1154x^3 + 1351x^2 - 333*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.6
Root			$-0.531161 - 0.919997i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.c.331.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.531161 + 0.919997i) q^{2} +(1.35728 - 2.35087i) q^{3} +(0.435737 - 0.754718i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88373 q^{6} +(0.964079 + 2.46385i) q^{7} +3.05043 q^{8} +(-2.18440 - 3.78348i) q^{9} +O(q^{10})$	\(q+(0.531161 + 0.919997i) q^{2} +(1.35728 - 2.35087i) q^{3} +(0.435737 - 0.754718i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88373 q^{6} +(0.964079 + 2.46385i) q^{7} +3.05043 q^{8} +(-2.18440 - 3.78348i) q^{9} +(0.531161 - 0.919997i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.18283 - 2.04872i) q^{12} -2.49133 q^{13} +(-1.75465 + 2.19565i) q^{14} -2.71455 q^{15} +(0.748794 + 1.29695i) q^{16} +(-2.74672 + 4.75745i) q^{17} +(2.32053 - 4.01928i) q^{18} +(0.108012 + 0.187082i) q^{19} -0.871473 q^{20} +(7.10071 + 1.07770i) q^{21} +1.06232 q^{22} +(-2.17693 - 3.77055i) q^{23} +(4.14027 - 7.17116i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.32330 - 2.29202i) q^{26} -3.71566 q^{27} +(2.27960 + 0.345982i) q^{28} +4.41251 q^{29} +(-1.44186 - 2.49738i) q^{30} +(-2.01220 + 3.48524i) q^{31} +(2.25497 - 3.90572i) q^{32} +(-1.35728 - 2.35087i) q^{33} -5.83579 q^{34} +(1.65172 - 2.06684i) q^{35} -3.80729 q^{36} +(-0.495349 - 0.857970i) q^{37} +(-0.114743 + 0.198741i) q^{38} +(-3.38142 + 5.85680i) q^{39} +(-1.52521 - 2.64175i) q^{40} -10.0228 q^{41} +(2.78014 + 7.10507i) q^{42} +9.68882 q^{43} +(-0.435737 - 0.754718i) q^{44} +(-2.18440 + 3.78348i) q^{45} +(2.31260 - 4.00554i) q^{46} +(6.02364 + 10.4333i) q^{47} +4.06528 q^{48} +(-5.14110 + 4.75069i) q^{49} -1.06232 q^{50} +(7.45611 + 12.9144i) q^{51} +(-1.08556 + 1.88025i) q^{52} +(-0.217362 + 0.376481i) q^{53} +(-1.97361 - 3.41839i) q^{54} -1.00000 q^{55} +(2.94085 + 7.51579i) q^{56} +0.586407 q^{57} +(2.34375 + 4.05950i) q^{58} +(3.02161 - 5.23359i) q^{59} +(-1.18283 + 2.04872i) q^{60} +(2.54706 + 4.41164i) q^{61} -4.27521 q^{62} +(7.21601 - 9.02960i) q^{63} +7.78618 q^{64} +(1.24567 + 2.15756i) q^{65} +(1.44186 - 2.49738i) q^{66} +(-0.192937 + 0.334177i) q^{67} +(2.39369 + 4.14599i) q^{68} -11.8188 q^{69} +(2.77882 + 0.421750i) q^{70} -12.7026 q^{71} +(-6.66334 - 11.5412i) q^{72} +(-5.72195 + 9.91070i) q^{73} +(0.526220 - 0.911440i) q^{74} +(1.35728 + 2.35087i) q^{75} +0.188259 q^{76} +(2.61580 + 0.397008i) q^{77} -7.18432 q^{78} +(4.67342 + 8.09461i) q^{79} +(0.748794 - 1.29695i) q^{80} +(1.51002 - 2.61543i) q^{81} +(-5.32370 - 9.22093i) q^{82} -7.72963 q^{83} +(3.90740 - 4.88944i) q^{84} +5.49343 q^{85} +(5.14632 + 8.91369i) q^{86} +(5.98899 - 10.3732i) q^{87} +(1.52521 - 2.64175i) q^{88} +(-7.97496 - 13.8130i) q^{89} -4.64106 q^{90} +(-2.40184 - 6.13826i) q^{91} -3.79427 q^{92} +(5.46223 + 9.46086i) q^{93} +(-6.39904 + 11.0835i) q^{94} +(0.108012 - 0.187082i) q^{95} +(-6.12123 - 10.6023i) q^{96} +6.56206 q^{97} +(-7.10137 - 2.20642i) q^{98} -4.36879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.531161	+	0.919997i	0.375587	+	0.650536i	0.990415	−	0.138125i	$-0.0441077\pi$
$2$	0.531161	+	0.919997i	0.375587	+	0.650536i	−0.614827	+	0.788662i	$0.710774\pi$
$3$	1.35728	−	2.35087i	0.783624	−	1.35728i	−0.146194	−	0.989256i	$-0.546702\pi$
$3$	1.35728	−	2.35087i	0.783624	−	1.35728i	0.929818	−	0.368020i	$-0.119964\pi$
$4$	0.435737	−	0.754718i	0.217868	−	0.377359i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	2.88373			1.17728
$7$	0.964079	+	2.46385i	0.364388	+	0.931247i
$7$	0.964079	+	2.46385i	0.364388	+	0.931247i
$8$	3.05043			1.07849
$9$	−2.18440	−	3.78348i	−0.728132	−	1.26116i
$10$	0.531161	−	0.919997i	0.167968	−	0.290929i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.18283	−	2.04872i	−0.341454	−	0.591415i
$13$	−2.49133			−0.690971			−0.345485	−	0.938424i	$-0.612286\pi$
$13$	−2.49133			−0.690971			−0.345485	+	0.938424i	$0.612286\pi$
$14$	−1.75465	+	2.19565i	−0.468951	+	0.586812i
$15$	−2.71455			−0.700894
$16$	0.748794	+	1.29695i	0.187198	+	0.324237i
$17$	−2.74672	+	4.75745i	−0.666177	+	1.15385i	0.312788	+	0.949823i	$0.398737\pi$
$17$	−2.74672	+	4.75745i	−0.666177	+	1.15385i	−0.978965	+	0.204029i	$0.934596\pi$
$18$	2.32053	−	4.01928i	0.546954	−	0.947353i
$19$	0.108012	+	0.187082i	0.0247796	+	0.0429195i	0.878149	−	0.478387i	$-0.158778\pi$
$19$	0.108012	+	0.187082i	0.0247796	+	0.0429195i	−0.853370	+	0.521306i	$0.825445\pi$
$20$	−0.871473			−0.194867
$21$	7.10071	+	1.07770i	1.54950	+	0.235173i
$22$	1.06232			0.226488
$23$	−2.17693	−	3.77055i	−0.453921	−	0.786215i	0.544704	−	0.838628i	$-0.316642\pi$
$23$	−2.17693	−	3.77055i	−0.453921	−	0.786215i	−0.998625	+	0.0524135i	$0.983309\pi$
$24$	4.14027	−	7.17116i	0.845129	−	1.46381i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.32330	−	2.29202i	−0.259520	−	0.449502i
$27$	−3.71566			−0.715078
$28$	2.27960	+	0.345982i	0.430803	+	0.0653844i
$29$	4.41251			0.819382			0.409691	−	0.912224i	$-0.365636\pi$
$29$	4.41251			0.819382			0.409691	+	0.912224i	$0.365636\pi$
$30$	−1.44186	−	2.49738i	−0.263247	−	0.455957i
$31$	−2.01220	+	3.48524i	−0.361402	+	0.625967i	−0.988192	−	0.153221i	$-0.951035\pi$
$31$	−2.01220	+	3.48524i	−0.361402	+	0.625967i	0.626790	+	0.779189i	$0.284369\pi$
$32$	2.25497	−	3.90572i	0.398626	−	0.690440i
$33$	−1.35728	−	2.35087i	−0.236271	−	0.409234i
$34$	−5.83579			−1.00083
$35$	1.65172	−	2.06684i	0.279191	−	0.349360i
$36$	−3.80729			−0.634548
$37$	−0.495349	−	0.857970i	−0.0814349	−	0.141049i	0.822432	−	0.568864i	$-0.192617\pi$
$37$	−0.495349	−	0.857970i	−0.0814349	−	0.141049i	−0.903866	+	0.427815i	$0.859284\pi$
$38$	−0.114743	+	0.198741i	−0.0186138	+	0.0322401i
$39$	−3.38142	+	5.85680i	−0.541461	+	0.937838i
$40$	−1.52521	−	2.64175i	−0.241157	−	0.417697i
$41$	−10.0228			−1.56529			−0.782647	−	0.622465i	$-0.786131\pi$
$41$	−10.0228			−1.56529			−0.782647	+	0.622465i	$0.786131\pi$
$42$	2.78014	+	7.10507i	0.428985	+	1.09634i
$43$	9.68882			1.47753			0.738766	−	0.673962i	$-0.235409\pi$
$43$	9.68882			1.47753			0.738766	+	0.673962i	$0.235409\pi$
$44$	−0.435737	−	0.754718i	−0.0656898	−	0.113778i
$45$	−2.18440	+	3.78348i	−0.325631	+	0.564009i
$46$	2.31260	−	4.00554i	0.340974	−	0.590585i
$47$	6.02364	+	10.4333i	0.878638	+	1.52185i	0.852836	+	0.522179i	$0.174881\pi$
$47$	6.02364	+	10.4333i	0.878638	+	1.52185i	0.0258025	+	0.999667i	$0.491786\pi$
$48$	4.06528			0.586773
$49$	−5.14110	+	4.75069i	−0.734443	+	0.678670i
$50$	−1.06232			−0.150235
$51$	7.45611	+	12.9144i	1.04406	+	1.80837i
$52$	−1.08556	+	1.88025i	−0.150541	+	0.260744i
$53$	−0.217362	+	0.376481i	−0.0298569	+	0.0517137i	−0.880568	−	0.473920i	$-0.842838\pi$
$53$	−0.217362	+	0.376481i	−0.0298569	+	0.0517137i	0.850711	+	0.525634i	$0.176172\pi$
$54$	−1.97361	−	3.41839i	−0.268574	−	0.465185i
$55$	−1.00000			−0.134840
$56$	2.94085	+	7.51579i	0.392988	+	1.00434i
$57$	0.586407			0.0776715
$58$	2.34375	+	4.05950i	0.307750	+	0.533038i
$59$	3.02161	−	5.23359i	0.393381	−	0.681355i	−0.599512	−	0.800366i	$-0.704639\pi$
$59$	3.02161	−	5.23359i	0.393381	−	0.681355i	0.992893	+	0.119010i	$0.0379721\pi$
$60$	−1.18283	+	2.04872i	−0.152703	+	0.264489i
$61$	2.54706	+	4.41164i	0.326118	+	0.564852i	0.981738	−	0.190238i	$-0.0609261\pi$
$61$	2.54706	+	4.41164i	0.326118	+	0.564852i	−0.655620	+	0.755091i	$0.727593\pi$
$62$	−4.27521			−0.542953
$63$	7.21601	−	9.02960i	0.909131	−	1.13762i
$64$	7.78618			0.973272
$65$	1.24567	+	2.15756i	0.154506	+	0.267612i
$66$	1.44186	−	2.49738i	0.177481	−	0.307406i
$67$	−0.192937	+	0.334177i	−0.0235710	+	0.0408262i	−0.877570	−	0.479448i	$-0.840837\pi$
$67$	−0.192937	+	0.334177i	−0.0235710	+	0.0408262i	0.853999	+	0.520274i	$0.174170\pi$
$68$	2.39369	+	4.14599i	0.290278	+	0.502776i
$69$	−11.8188			−1.42281
$70$	2.77882	+	0.421750i	0.332132	+	0.0504087i
$71$	−12.7026			−1.50752			−0.753762	−	0.657147i	$-0.771763\pi$
$71$	−12.7026			−1.50752			−0.753762	+	0.657147i	$0.771763\pi$
$72$	−6.66334	−	11.5412i	−0.785282	−	1.36015i
$73$	−5.72195	+	9.91070i	−0.669703	+	1.15996i	0.308284	+	0.951294i	$0.400245\pi$
$73$	−5.72195	+	9.91070i	−0.669703	+	1.15996i	−0.977987	+	0.208666i	$0.933088\pi$
$74$	0.526220	−	0.911440i	0.0611718	−	0.105953i
$75$	1.35728	+	2.35087i	0.156725	+	0.271455i
$76$	0.188259			0.0215948
$77$	2.61580	+	0.397008i	0.298098	+	0.0452432i
$78$	−7.18432			−0.813464
$79$	4.67342	+	8.09461i	0.525801	+	0.910714i	0.999548	+	0.0300534i	$0.00956774\pi$
$79$	4.67342	+	8.09461i	0.525801	+	0.910714i	−0.473747	+	0.880661i	$0.657099\pi$
$80$	0.748794	−	1.29695i	0.0837177	−	0.145003i
$81$	1.51002	−	2.61543i	0.167780	−	0.290603i
$82$	−5.32370	−	9.22093i	−0.587905	−	1.01828i
$83$	−7.72963			−0.848437			−0.424219	−	0.905560i	$-0.639451\pi$
$83$	−7.72963			−0.848437			−0.424219	+	0.905560i	$0.639451\pi$
$84$	3.90740	−	4.88944i	0.426332	−	0.533482i
$85$	5.49343			0.595847
$86$	5.14632	+	8.91369i	0.554942	+	0.961188i
$87$	5.98899	−	10.3732i	0.642087	−	1.11213i
$88$	1.52521	−	2.64175i	0.162588	−	0.281611i
$89$	−7.97496	−	13.8130i	−0.845344	−	1.46418i	−0.885323	−	0.464977i	$-0.846062\pi$
$89$	−7.97496	−	13.8130i	−0.845344	−	1.46418i	0.0399790	−	0.999201i	$-0.487271\pi$
$90$	−4.64106			−0.489211
$91$	−2.40184	−	6.13826i	−0.251781	−	0.643465i
$92$	−3.79427			−0.395580
$93$	5.46223	+	9.46086i	0.566407	+	0.981045i
$94$	−6.39904	+	11.0835i	−0.660011	+	1.14317i
$95$	0.108012	−	0.187082i	0.0110818	−	0.0191942i
$96$	−6.12123	−	10.6023i	−0.624745	−	1.08209i
$97$	6.56206			0.666277			0.333138	−	0.942878i	$-0.391892\pi$
$97$	6.56206			0.666277			0.333138	+	0.942878i	$0.391892\pi$
$98$	−7.10137	−	2.20642i	−0.717347	−	0.222882i
$99$	−4.36879			−0.439080
$100$	0.435737	+	0.754718i	0.0435737	+	0.0754718i
$101$	8.91539	−	15.4419i	0.887114	−	1.53653i	0.0438427	−	0.999038i	$-0.486040\pi$
$101$	8.91539	−	15.4419i	0.887114	−	1.53653i	0.843271	−	0.537488i	$-0.180627\pi$
$102$	−7.92078	+	13.7192i	−0.784274	+	1.35840i
$103$	4.92258	+	8.52616i	0.485037	+	0.840108i	0.999852	−	0.0171930i	$-0.00547296\pi$
$103$	4.92258	+	8.52616i	0.485037	+	0.840108i	−0.514816	+	0.857301i	$0.672140\pi$
$104$	−7.59962			−0.745204
$105$	−2.61704	−	6.68825i	−0.255397	−	0.652706i
$106$	−0.461816			−0.0448555
$107$	−5.65447	−	9.79383i	−0.546638	−	0.946805i	−0.998502	−	0.0547181i	$-0.982574\pi$
$107$	−5.65447	−	9.79383i	−0.546638	−	0.946805i	0.451864	−	0.892087i	$-0.350759\pi$
$108$	−1.61905	+	2.80427i	−0.155793	+	0.269841i
$109$	−5.16643	+	8.94852i	−0.494854	+	0.857112i	−0.999982	−	0.00593188i	$-0.998112\pi$
$109$	−5.16643	+	8.94852i	−0.494854	+	0.857112i	0.505128	+	0.863044i	$0.331445\pi$
$110$	−0.531161	−	0.919997i	−0.0506442	−	0.0877183i
$111$	−2.68930			−0.255257
$112$	−2.47359	+	3.09528i	−0.233732	+	0.292476i
$113$	14.7643			1.38891			0.694457	−	0.719535i	$-0.255645\pi$
$113$	14.7643			1.38891			0.694457	+	0.719535i	$0.255645\pi$
$114$	0.311476	+	0.539493i	0.0291724	+	0.0505281i
$115$	−2.17693	+	3.77055i	−0.203000	+	0.351606i
$116$	1.92269	−	3.33020i	0.178517	−	0.309201i
$117$	5.44205	+	9.42591i	0.503118	+	0.871426i
$118$	6.41985			0.590995
$119$	−14.3697	−	2.18094i	−1.31727	−	0.199926i
$120$	−8.28054			−0.755907
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−2.70580	+	4.68658i	−0.244971	+	0.424303i
$123$	−13.6037	+	23.5623i	−1.22660	+	2.12454i
$124$	1.75358	+	3.03729i	0.157476	+	0.272757i
$125$	1.00000			0.0894427
$126$	12.1401	+	1.84254i	1.08152	+	0.164146i
$127$	−2.10124			−0.186455			−0.0932275	−	0.995645i	$-0.529718\pi$
$127$	−2.10124			−0.186455			−0.0932275	+	0.995645i	$0.529718\pi$
$128$	−0.374225	−	0.648176i	−0.0330771	−	0.0572912i
$129$	13.1504	−	22.7772i	1.15783	−	2.00542i
$130$	−1.32330	+	2.29202i	−0.116061	+	0.201023i
$131$	−7.66720	−	13.2800i	−0.669886	−	1.16028i	−0.977936	−	0.208906i	$-0.933010\pi$
$131$	−7.66720	−	13.2800i	−0.669886	−	1.16028i	0.308050	−	0.951370i	$-0.400324\pi$
$132$	−2.36566			−0.205904
$133$	−0.356810	+	0.446486i	−0.0309393	+	0.0387153i
$134$	−0.409922			−0.0354119
$135$	1.85783	+	3.21785i	0.159896	+	0.276949i
$136$	−8.37866	+	14.5123i	−0.718464	+	1.24442i
$137$	−2.27859	+	3.94663i	−0.194673	+	0.337183i	−0.946793	−	0.321842i	$-0.895698\pi$
$137$	−2.27859	+	3.94663i	−0.194673	+	0.337183i	0.752120	+	0.659026i	$0.229031\pi$
$138$	−6.27767	−	10.8732i	−0.534391	−	0.925592i
$139$	−13.8225			−1.17241			−0.586203	−	0.810164i	$-0.699378\pi$
$139$	−13.8225			−1.17241			−0.586203	+	0.810164i	$0.699378\pi$
$140$	−0.840169	−	2.14718i	−0.0710072	−	0.181470i
$141$	32.7030			2.75409
$142$	−6.74714	−	11.6864i	−0.566207	−	0.980699i
$143$	−1.24567	+	2.15756i	−0.104168	+	0.180424i
$144$	3.27132	−	5.66610i	0.272610	−	0.472175i
$145$	−2.20625	−	3.82134i	−0.183219	−	0.317345i
$146$	−12.1571			−1.00613
$147$	4.19036	+	18.5341i	0.345615	+	1.52866i
$148$	−0.863367			−0.0709683
$149$	−4.80504	−	8.32257i	−0.393644	−	0.681812i	0.599283	−	0.800537i	$-0.295452\pi$
$149$	−4.80504	−	8.32257i	−0.393644	−	0.681812i	−0.992927	+	0.118726i	$0.962119\pi$
$150$	−1.44186	+	2.49738i	−0.117728	+	0.203910i
$151$	0.153369	−	0.265643i	0.0124810	−	0.0216177i	−0.859717	−	0.510770i	$-0.829360\pi$
$151$	0.153369	−	0.265643i	0.0124810	−	0.0216177i	0.872198	+	0.489152i	$0.162694\pi$
$152$	0.329482	+	0.570680i	0.0267245	+	0.0462882i
$153$	23.9997			1.94026
$154$	1.02416	+	2.61740i	0.0825293	+	0.210916i
$155$	4.02441			0.323248
$156$	2.94682	+	5.10404i	0.235934	+	0.408650i
$157$	8.19997	−	14.2028i	0.654429	−	1.13350i	−0.327608	−	0.944814i	$-0.606243\pi$
$157$	8.19997	−	14.2028i	0.654429	−	1.13350i	0.982037	−	0.188690i	$-0.0604241\pi$
$158$	−4.96468	+	8.59907i	−0.394969	+	0.684106i
$159$	0.590039	+	1.02198i	0.0467932	+	0.0810481i
$160$	−4.50994			−0.356542
$161$	7.19134	−	8.99874i	0.566757	−	0.709200i
$162$	3.20825			0.252064
$163$	−5.06695	−	8.77621i	−0.396874	−	0.687406i	0.596464	−	0.802640i	$-0.296572\pi$
$163$	−5.06695	−	8.77621i	−0.396874	−	0.687406i	−0.993338	+	0.115233i	$0.963238\pi$
$164$	−4.36729	+	7.56437i	−0.341028	+	0.590678i
$165$	−1.35728	+	2.35087i	−0.105664	+	0.183015i
$166$	−4.10568	−	7.11124i	−0.318662	−	0.551939i
$167$	11.3927			0.881590			0.440795	−	0.897608i	$-0.354697\pi$
$167$	11.3927			0.881590			0.440795	+	0.897608i	$0.354697\pi$
$168$	21.6602	+	3.28744i	1.67112	+	0.253631i
$169$	−6.79327			−0.522559
$170$	2.91790	+	5.05395i	0.223792	+	0.387620i
$171$	0.471881	−	0.817322i	0.0360856	−	0.0625022i
$172$	4.22177	−	7.31233i	0.321907	−	0.557560i
$173$	0.0832416	+	0.144179i	0.00632874	+	0.0109617i	0.869172	−	0.494509i	$-0.164652\pi$
$173$	0.0832416	+	0.144179i	0.00632874	+	0.0109617i	−0.862844	+	0.505471i	$0.831319\pi$
$174$	12.7245			0.964639
$175$	−2.61580	−	0.397008i	−0.197736	−	0.0300110i
$176$	1.49759			0.112885
$177$	−8.20233	−	14.2069i	−0.616525	−	1.06785i
$178$	8.47197	−	14.6739i	0.635001	−	1.09985i
$179$	−8.27771	+	14.3374i	−0.618705	+	1.07163i	0.371018	+	0.928626i	$0.379009\pi$
$179$	−8.27771	+	14.3374i	−0.618705	+	1.07163i	−0.989722	+	0.143002i	$0.954324\pi$
$180$	1.90364	+	3.29721i	0.141889	+	0.245759i
$181$	12.2225			0.908493			0.454247	−	0.890876i	$-0.349909\pi$
$181$	12.2225			0.908493			0.454247	+	0.890876i	$0.349909\pi$
$182$	4.37142	−	5.47009i	0.324031	−	0.405470i
$183$	13.8283			1.02221
$184$	−6.64057	−	11.5018i	−0.489549	−	0.847924i
$185$	−0.495349	+	0.857970i	−0.0364188	+	0.0630792i
$186$	−5.80264	+	10.0505i	−0.425470	+	0.736936i
$187$	2.74672	+	4.75745i	0.200860	+	0.347899i
$188$	10.4989			0.765710
$189$	−3.58219	−	9.15482i	−0.260566	−	0.665915i
$190$	0.229486			0.0166487
$191$	−5.50460	−	9.53425i	−0.398299	−	0.689874i	0.595217	−	0.803565i	$-0.297066\pi$
$191$	−5.50460	−	9.53425i	−0.398299	−	0.689874i	−0.993516	+	0.113691i	$0.963733\pi$
$192$	10.5680	−	18.3043i	0.762679	−	1.32100i
$193$	−9.48367	+	16.4262i	−0.682649	+	1.18238i	0.291520	+	0.956565i	$0.405839\pi$
$193$	−9.48367	+	16.4262i	−0.682649	+	1.18238i	−0.974169	+	0.225819i	$0.927494\pi$
$194$	3.48551	+	6.03708i	0.250245	+	0.433437i
$195$	6.76285			0.484297
$196$	1.34526	+	5.95013i	0.0960903	+	0.425010i
$197$	15.3718			1.09519			0.547596	−	0.836743i	$-0.315543\pi$
$197$	15.3718			1.09519			0.547596	+	0.836743i	$0.315543\pi$
$198$	−2.32053	−	4.01928i	−0.164913	−	0.285638i
$199$	4.00279	−	6.93304i	0.283750	−	0.491470i	−0.688555	−	0.725184i	$-0.741755\pi$
$199$	4.00279	−	6.93304i	0.283750	−	0.491470i	0.972305	+	0.233714i	$0.0750880\pi$
$200$	−1.52521	+	2.64175i	−0.107849	+	0.186800i
$201$	0.523738	+	0.907140i	0.0369416	+	0.0639847i
$202$	18.9420			1.33276
$203$	4.25401	+	10.8718i	0.298573	+	0.763048i
$204$	12.9956			0.909874
$205$	5.01139	+	8.67998i	0.350010	+	0.606236i
$206$	−5.22937	+	9.05753i	−0.364347	+	0.631068i
$207$	−9.51055	+	16.4728i	−0.661029	+	1.14494i
$208$	−1.86549	−	3.23113i	−0.129349	−	0.224038i
$209$	0.216024			0.0149427
$210$	4.76310	−	5.96021i	0.328685	−	0.411293i
$211$	−11.3174			−0.779123			−0.389561	−	0.921001i	$-0.627373\pi$
$211$	−11.3174			−0.779123			−0.389561	+	0.921001i	$0.627373\pi$
$212$	0.189425	+	0.328093i	0.0130098	+	0.0225335i
$213$	−17.2410	+	29.8622i	−1.18133	+	2.04613i
$214$	6.00686	−	10.4042i	0.410621	−	0.711216i
$215$	−4.84441	−	8.39076i	−0.330386	−	0.572245i
$216$	−11.3343			−0.771204
$217$	−10.5270	−	1.59772i	−0.714621	−	0.108460i
$218$	−10.9768			−0.743444
$219$	15.5325	+	26.9031i	1.04959	+	1.81794i
$220$	−0.435737	+	0.754718i	−0.0293774	+	0.0508831i
$221$	6.84298	−	11.8524i	0.460309	−	0.797278i
$222$	−1.42845	−	2.47415i	−0.0958714	−	0.166054i
$223$	24.4418			1.63674			0.818370	−	0.574691i	$-0.194878\pi$
$223$	24.4418			1.63674			0.818370	+	0.574691i	$0.194878\pi$
$224$	11.7971	+	1.79048i	0.788225	+	0.119631i
$225$	4.36879			0.291253
$226$	7.84224	+	13.5832i	0.521658	+	0.903538i
$227$	2.28274	−	3.95383i	0.151511	−	0.262425i	−0.780272	−	0.625440i	$-0.784919\pi$
$227$	2.28274	−	3.95383i	0.151511	−	0.262425i	0.931783	+	0.363015i	$0.118253\pi$
$228$	0.255519	−	0.442572i	0.0169222	−	0.0293100i
$229$	−2.59273	−	4.49073i	−0.171332	−	0.296756i	0.767554	−	0.640985i	$-0.221474\pi$
$229$	−2.59273	−	4.49073i	−0.171332	−	0.296756i	−0.938886	+	0.344229i	$0.888140\pi$
$230$	−4.62520			−0.304977
$231$	4.48367	−	5.61055i	0.295004	−	0.369147i
$232$	13.4600			0.883695
$233$	−2.46327	−	4.26650i	−0.161374	−	0.279508i	0.773988	−	0.633201i	$-0.218259\pi$
$233$	−2.46327	−	4.26650i	−0.161374	−	0.279508i	−0.935362	+	0.353693i	$0.884926\pi$
$234$	−5.78121	+	10.0133i	−0.377929	+	0.654593i
$235$	6.02364	−	10.4333i	0.392939	−	0.680590i
$236$	−2.63326	−	4.56093i	−0.171410	−	0.296892i
$237$	25.3725			1.64812
$238$	−5.62617	−	14.3785i	−0.364690	−	0.932021i
$239$	−19.0096			−1.22963			−0.614813	−	0.788673i	$-0.710769\pi$
$239$	−19.0096			−1.22963			−0.614813	+	0.788673i	$0.710769\pi$
$240$	−2.03264	−	3.52064i	−0.131206	−	0.227256i
$241$	−0.839349	+	1.45379i	−0.0540672	+	0.0936471i	−0.891792	−	0.452445i	$-0.850552\pi$
$241$	−0.839349	+	1.45379i	−0.0540672	+	0.0936471i	0.837725	+	0.546092i	$0.183885\pi$
$242$	0.531161	−	0.919997i	0.0341443	−	0.0591397i
$243$	−9.67250	−	16.7533i	−0.620491	−	1.07472i
$244$	4.43939			0.284203
$245$	6.68477	+	2.07698i	0.427074	+	0.132693i
$246$	−28.9029			−1.84278
$247$	−0.269093	−	0.466083i	−0.0171220	−	0.0296561i
$248$	−6.13808	+	10.6315i	−0.389768	+	0.675099i
$249$	−10.4912	+	18.1714i	−0.664856	+	1.15156i
$250$	0.531161	+	0.919997i	0.0335936	+	0.0581857i
$251$	−24.8596			−1.56912			−0.784562	−	0.620051i	$-0.787112\pi$
$251$	−24.8596			−1.56912			−0.784562	+	0.620051i	$0.787112\pi$
$252$	−3.67052	−	9.38058i	−0.231221	−	0.590921i
$253$	−4.35386			−0.273725
$254$	−1.11610	−	1.93314i	−0.0700301	−	0.121296i
$255$	7.45611	−	12.9144i	0.466920	−	0.808728i
$256$	8.18372	−	14.1746i	0.511483	−	0.885914i
$257$	−12.4603	−	21.5819i	−0.777252	−	1.34624i	−0.933520	−	0.358525i	$-0.883280\pi$
$257$	−12.4603	−	21.5819i	−0.777252	−	1.34624i	0.156269	−	0.987715i	$-0.450053\pi$
$258$	27.9399			1.73946
$259$	1.63635	−	2.04762i	0.101678	−	0.127233i
$260$	2.17113			0.134648
$261$	−9.63867	−	16.6947i	−0.596618	−	1.03337i
$262$	8.14503	−	14.1076i	0.503201	−	0.871570i
$263$	−0.530769	+	0.919318i	−0.0327286	+	0.0566876i	−0.881926	−	0.471388i	$-0.843753\pi$
$263$	−0.530769	+	0.919318i	−0.0327286	+	0.0566876i	0.849197	+	0.528076i	$0.177086\pi$
$264$	−4.14027	−	7.17116i	−0.254816	−	0.441354i
$265$	0.434723			0.0267048
$266$	−0.600290	−	0.0911079i	−0.0368061	−	0.00558618i
$267$	−43.2969			−2.64972
$268$	0.168139	+	0.291226i	0.0102708	+	0.0177895i
$269$	−5.13660	+	8.89685i	−0.313184	+	0.542450i	−0.979050	−	0.203621i	$-0.934729\pi$
$269$	−5.13660	+	8.89685i	−0.313184	+	0.542450i	0.665866	+	0.746071i	$0.268062\pi$
$270$	−1.97361	+	3.41839i	−0.120110	+	0.208037i
$271$	4.27575	+	7.40582i	0.259733	+	0.449872i	0.966170	−	0.257904i	$-0.0830320\pi$
$271$	4.27575	+	7.40582i	0.259733	+	0.449872i	−0.706437	+	0.707776i	$0.749699\pi$
$272$	−8.22690			−0.498829
$273$	−17.6902	−	2.68490i	−1.07066	−	0.162498i
$274$	−4.84119			−0.292467
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$	−5.14988	+	8.91985i	−0.309986	+	0.536912i
$277$	3.65586	−	6.33213i	0.219659	−	0.380461i	−0.735045	−	0.678019i	$-0.762839\pi$
$277$	3.65586	−	6.33213i	0.219659	−	0.380461i	0.954704	+	0.297558i	$0.0961722\pi$
$278$	−7.34195	−	12.7166i	−0.440341	−	0.762693i
$279$	17.5818			1.05259
$280$	5.03844	−	6.30475i	0.301104	−	0.376781i
$281$	23.2429			1.38655			0.693276	−	0.720672i	$-0.256167\pi$
$281$	23.2429			1.38655			0.693276	+	0.720672i	$0.256167\pi$
$282$	17.3705	+	30.0866i	1.03440	+	1.79163i
$283$	−1.08598	+	1.88097i	−0.0645546	+	0.111812i	−0.896496	−	0.443051i	$-0.853896\pi$
$283$	−1.08598	+	1.88097i	−0.0645546	+	0.111812i	0.831942	+	0.554863i	$0.187229\pi$
$284$	−5.53500	+	9.58690i	−0.328442	+	0.568878i
$285$	−0.293204	−	0.507843i	−0.0173679	−	0.0300821i
$286$	−2.64659			−0.156496
$287$	−9.66275	−	24.6946i	−0.570374	−	1.45768i
$288$	−19.7030			−1.16101
$289$	−6.58891	−	11.4123i	−0.387583	−	0.671314i
$290$	2.34375	−	4.05950i	0.137630	−	0.238382i
$291$	8.90653	−	15.4266i	0.522110	−	0.904321i
$292$	4.98652	+	8.63691i	0.291814	+	0.505437i
$293$	−12.1315			−0.708727			−0.354364	−	0.935108i	$-0.615302\pi$
$293$	−12.1315			−0.708727			−0.354364	+	0.935108i	$0.615302\pi$
$294$	−14.8255	+	13.6997i	−0.864643	+	0.798982i
$295$	−6.04323			−0.351850
$296$	−1.51103	−	2.61717i	−0.0878266	−	0.152120i
$297$	−1.85783	+	3.21785i	−0.107802	+	0.186719i
$298$	5.10450	−	8.84125i	0.295695	−	0.512160i
$299$	5.42345	+	9.39370i	0.313646	+	0.543251i
$300$	2.36566			0.136581
$301$	9.34079	+	23.8718i	0.538394	+	1.37595i
$302$	0.325855			0.0187508
$303$	−24.2013	−	41.9178i	−1.39033	−	2.40812i
$304$	−0.161757	+	0.280172i	−0.00927741	+	0.0160689i
$305$	2.54706	−	4.41164i	0.145844	−	0.252610i
$306$	12.7477	+	22.0796i	0.728737	+	1.26221i
$307$	−31.0266			−1.77078			−0.885390	−	0.464848i	$-0.846109\pi$
$307$	−31.0266			−1.77078			−0.885390	+	0.464848i	$0.846109\pi$
$308$	1.43943	−	1.80120i	0.0820189	−	0.102633i
$309$	26.7252			1.52034
$310$	2.13761	+	3.70244i	0.121408	+	0.210285i
$311$	−3.32841	+	5.76497i	−0.188737	+	0.326902i	−0.944829	−	0.327563i	$-0.893773\pi$
$311$	−3.32841	+	5.76497i	−0.188737	+	0.326902i	0.756093	+	0.654465i	$0.227106\pi$
$312$	−10.3148	+	17.8657i	−0.583960	+	1.01145i
$313$	−12.2931	−	21.2923i	−0.694849	−	1.20351i	−0.970231	−	0.242180i	$-0.922138\pi$
$313$	−12.2931	−	21.2923i	−0.694849	−	1.20351i	0.275382	−	0.961335i	$-0.411196\pi$
$314$	17.4220			0.983181
$315$	−11.4279	−	1.73444i	−0.643887	−	0.0977248i
$316$	8.14553			0.458222
$317$	14.7259	+	25.5060i	0.827087	+	1.43256i	0.900313	+	0.435242i	$0.143337\pi$
$317$	14.7259	+	25.5060i	0.827087	+	1.43256i	−0.0732261	+	0.997315i	$0.523329\pi$
$318$	−0.626811	+	1.08567i	−0.0351498	+	0.0608813i
$319$	2.20625	−	3.82134i	0.123527	−	0.213954i
$320$	−3.89309	−	6.74303i	−0.217630	−	0.376947i
$321$	−30.6987			−1.71343
$322$	12.0986	+	1.83624i	0.674227	+	0.102330i
$323$	−1.18671			−0.0660304
$324$	−1.31594	−	2.27927i	−0.0731077	−	0.126626i
$325$	1.24567	−	2.15756i	0.0690971	−	0.119680i
$326$	5.38273	−	9.32316i	0.298122	−	0.516362i
$327$	14.0245	+	24.2912i	0.775559	+	1.34331i
$328$	−30.5737			−1.68815
$329$	−19.8987	+	24.8998i	−1.09705	+	1.37277i
$330$	−2.88373			−0.158744
$331$	−2.38001	−	4.12229i	−0.130817	−	0.226582i	0.793175	−	0.608994i	$-0.208427\pi$
$331$	−2.38001	−	4.12229i	−0.130817	−	0.226582i	−0.923992	+	0.382412i	$0.875093\pi$
$332$	−3.36808	+	5.83369i	−0.184848	+	0.320165i
$333$	−2.16408	+	3.74829i	−0.118591	+	0.205405i
$334$	6.05133	+	10.4812i	0.331114	+	0.573506i
$335$	0.385874			0.0210826
$336$	3.91925	+	10.0162i	0.213813	+	0.546430i
$337$	23.2559			1.26683			0.633416	−	0.773811i	$-0.281652\pi$
$337$	23.2559			1.26683			0.633416	+	0.773811i	$0.281652\pi$
$338$	−3.60832	−	6.24979i	−0.196267	−	0.339944i
$339$	20.0393	−	34.7091i	1.08839	−	1.88514i
$340$	2.39369	−	4.14599i	0.129816	−	0.224848i
$341$	2.01220	+	3.48524i	0.108967	+	0.188736i
$342$	1.00258			0.0542132
$343$	−16.6614	−	8.08686i	−0.899632	−	0.436650i
$344$	29.5550			1.59350
$345$	5.90939	+	10.2354i	0.318151	+	0.551053i
$346$	−0.0884294	+	0.153164i	−0.00475399	+	0.00823416i
$347$	−0.262030	+	0.453849i	−0.0140665	+	0.0243639i	−0.872973	−	0.487769i	$-0.837811\pi$
$347$	−0.262030	+	0.453849i	−0.0140665	+	0.0243639i	0.858906	+	0.512132i	$0.171144\pi$
$348$	−5.21925	−	9.04000i	−0.279781	−	0.484595i
$349$	26.7599			1.43242			0.716211	−	0.697884i	$-0.245875\pi$
$349$	26.7599			1.43242			0.716211	+	0.697884i	$0.245875\pi$
$350$	−1.02416	−	2.61740i	−0.0547437	−	0.139906i
$351$	9.25693			0.494098
$352$	−2.25497	−	3.90572i	−0.120190	−	0.208176i
$353$	−5.03405	+	8.71922i	−0.267935	+	0.464077i	−0.968328	−	0.249680i	$-0.919675\pi$
$353$	−5.03405	+	8.71922i	−0.267935	+	0.464077i	0.700393	+	0.713757i	$0.253008\pi$
$354$	8.71351	−	15.0922i	0.463118	−	0.802144i
$355$	6.35131	+	11.0008i	0.337093	+	0.583862i
$356$	−13.8999			−0.736694
$357$	−24.6307	+	30.8212i	−1.30360	+	1.63123i
$358$	−17.5872			−0.929511
$359$	−0.737897	−	1.27808i	−0.0389447	−	0.0674542i	0.845896	−	0.533348i	$-0.179066\pi$
$359$	−0.737897	−	1.27808i	−0.0389447	−	0.0674542i	−0.884841	+	0.465894i	$0.845733\pi$
$360$	−6.66334	+	11.5412i	−0.351189	+	0.608277i
$361$	9.47667	−	16.4141i	0.498772	−	0.863898i
$362$	6.49212	+	11.2447i	0.341219	+	0.591008i
$363$	−2.71455			−0.142477
$364$	−5.67923	−	0.861954i	−0.297672	−	0.0451787i
$365$	11.4439			0.599001
$366$	7.34502	+	12.7220i	0.383931	+	0.664987i
$367$	−9.02127	+	15.6253i	−0.470907	+	0.815634i	−0.999446	−	0.0332744i	$-0.989406\pi$
$367$	−9.02127	+	15.6253i	−0.470907	+	0.815634i	0.528540	+	0.848909i	$0.322740\pi$
$368$	3.26014	−	5.64673i	0.169947	−	0.294356i
$369$	21.8937	+	37.9210i	1.13974	+	1.97409i
$370$	−1.05244			−0.0547137
$371$	−1.13715	−	0.172588i	−0.0590377	−	0.00896034i
$372$	9.52037			0.493608
$373$	4.52968	+	7.84563i	0.234538	+	0.406231i	0.959138	−	0.282938i	$-0.0913090\pi$
$373$	4.52968	+	7.84563i	0.234538	+	0.406231i	−0.724600	+	0.689169i	$0.757976\pi$
$374$	−2.91790	+	5.05395i	−0.150881	+	0.261333i
$375$	1.35728	−	2.35087i	0.0700894	−	0.121398i
$376$	18.3747	+	31.8259i	0.947602	+	1.64129i
$377$	−10.9930			−0.566169
$378$	6.51969	−	8.15828i	0.335337	−	0.419617i
$379$	−10.1597			−0.521868			−0.260934	−	0.965357i	$-0.584030\pi$
$379$	−10.1597			−0.521868			−0.260934	+	0.965357i	$0.584030\pi$
$380$	−0.0941294	−	0.163037i	−0.00482874	−	0.00836361i
$381$	−2.85196	+	4.93975i	−0.146111	+	0.253071i
$382$	5.84766	−	10.1284i	0.299192	−	0.518216i
$383$	−8.66656	−	15.0109i	−0.442841	−	0.767022i	0.555058	−	0.831811i	$-0.312696\pi$
$383$	−8.66656	−	15.0109i	−0.442841	−	0.767022i	−0.997899	+	0.0647890i	$0.979363\pi$
$384$	−2.03170			−0.103680
$385$	−0.964079	−	2.46385i	−0.0491340	−	0.125569i
$386$	−20.1494			−1.02558
$387$	−21.1642	−	36.6575i	−1.07584	−	1.86341i
$388$	2.85933	−	4.95251i	0.145161	−	0.251426i
$389$	−0.182248	+	0.315663i	−0.00924036	+	0.0160048i	−0.870609	−	0.491976i	$-0.836275\pi$
$389$	−0.182248	+	0.315663i	−0.00924036	+	0.0160048i	0.861368	+	0.507981i	$0.169608\pi$
$390$	3.59216	+	6.22180i	0.181896	+	0.315053i
$391$	23.9176			1.20957
$392$	−15.6826	+	14.4916i	−0.792089	+	0.731938i
$393$	−41.6260			−2.09975
$394$	8.16487	+	14.1420i	0.411340	+	0.712462i
$395$	4.67342	−	8.09461i	0.235145	−	0.407284i
$396$	−1.90364	+	3.29721i	−0.0956616	+	0.165691i
$397$	1.51468	+	2.62351i	0.0760197	+	0.131670i	0.901529	−	0.432718i	$-0.142445\pi$
$397$	1.51468	+	2.62351i	0.0760197	+	0.131670i	−0.825510	+	0.564388i	$0.809112\pi$
$398$	8.50450			0.426292
$399$	0.565343	+	1.44482i	0.0283025	+	0.0723314i
$400$	−1.49759			−0.0748794
$401$	−13.9773	−	24.2094i	−0.697994	−	1.20896i	−0.969161	−	0.246429i	$-0.920743\pi$
$401$	−13.9773	−	24.2094i	−0.697994	−	1.20896i	0.271167	−	0.962532i	$-0.412590\pi$
$402$	−0.556378	+	0.963674i	−0.0277496	+	0.0480637i
$403$	5.01306	−	8.68288i	0.249718	−	0.432525i
$404$	−7.76952	−	13.4572i	−0.386548	−	0.669521i
$405$	−3.02003			−0.150067
$406$	−7.74242	+	9.68832i	−0.384250	+	0.480823i
$407$	−0.990698			−0.0491071
$408$	22.7443	+	39.3943i	1.12601	+	1.95031i
$409$	3.17712	−	5.50294i	0.157099	−	0.272103i	−0.776723	−	0.629843i	$-0.783119\pi$
$409$	3.17712	−	5.50294i	0.157099	−	0.272103i	0.933821	+	0.357740i	$0.116453\pi$
$410$	−5.32370	+	9.22093i	−0.262919	+	0.455389i
$411$	6.18535	+	10.7133i	0.305101	+	0.528450i
$412$	8.57980			0.422696
$413$	15.8079	+	2.39921i	0.777854	+	0.118057i
$414$	−20.2065			−0.993097
$415$	3.86482	+	6.69406i	0.189716	+	0.328598i
$416$	−5.61787	+	9.73044i	−0.275439	+	0.477074i
$417$	−18.7609	+	32.4948i	−0.918725	+	1.59128i
$418$	0.114743	+	0.198741i	0.00561227	+	0.00972074i
$419$	13.4218			0.655700			0.327850	−	0.944730i	$-0.393676\pi$
$419$	13.4218			0.655700			0.327850	+	0.944730i	$0.393676\pi$
$420$	−6.18808	−	0.939185i	−0.301947	−	0.0458275i
$421$	−9.40394			−0.458320			−0.229160	−	0.973389i	$-0.573598\pi$
$421$	−9.40394			−0.458320			−0.229160	+	0.973389i	$0.573598\pi$
$422$	−6.01136	−	10.4120i	−0.292629	−	0.506847i
$423$	26.3160	−	45.5807i	1.27953	−	2.21621i
$424$	−0.663046	+	1.14843i	−0.0322003	+	0.0557726i
$425$	−2.74672	−	4.75745i	−0.133235	−	0.230770i
$426$	−36.6309			−1.77477
$427$	−8.41404	+	10.5287i	−0.407184	+	0.509521i
$428$	−9.85544			−0.476381
$429$	3.38142	+	5.85680i	0.163257	+	0.282769i
$430$	5.14632	−	8.91369i	0.248178	−	0.429856i
$431$	−5.63874	+	9.76659i	−0.271609	+	0.470440i	−0.969274	−	0.245984i	$-0.920889\pi$
$431$	−5.63874	+	9.76659i	−0.271609	+	0.470440i	0.697665	+	0.716424i	$0.254222\pi$
$432$	−2.78226	−	4.81902i	−0.133862	−	0.231855i
$433$	30.4381			1.46276			0.731381	−	0.681969i	$-0.238876\pi$
$433$	30.4381			1.46276			0.731381	+	0.681969i	$0.238876\pi$
$434$	−4.12164	−	10.5335i	−0.197845	−	0.505623i
$435$	−11.9780			−0.574300
$436$	4.50240	+	7.79839i	0.215626	+	0.373475i
$437$	0.470268	−	0.814528i	0.0224960	−	0.0389642i
$438$	−16.5005	+	28.5798i	−0.788426	+	1.36559i
$439$	−6.40632	−	11.0961i	−0.305757	−	0.529586i	0.671673	−	0.740848i	$-0.265576\pi$
$439$	−6.40632	−	11.0961i	−0.305757	−	0.529586i	−0.977430	+	0.211262i	$0.932243\pi$
$440$	−3.05043			−0.145423
$441$	29.2044	+	9.07390i	1.39068	+	0.432090i
$442$	14.5389			0.691544
$443$	17.8347	+	30.8906i	0.847353	+	1.46766i	0.883562	+	0.468313i	$0.155138\pi$
$443$	17.8347	+	30.8906i	0.847353	+	1.46766i	−0.0362099	+	0.999344i	$0.511528\pi$
$444$	−1.17183	+	2.02966i	−0.0556125	+	0.0963236i
$445$	−7.97496	+	13.8130i	−0.378049	+	0.654800i
$446$	12.9825	+	22.4863i	0.614739	+	1.06476i
$447$	−26.0871			−1.23388
$448$	7.50649	+	19.1840i	0.354648	+	0.906357i
$449$	40.4845			1.91058			0.955290	−	0.295671i	$-0.0955431\pi$
$449$	40.4845			1.91058			0.955290	+	0.295671i	$0.0955431\pi$
$450$	2.32053	+	4.01928i	0.109391	+	0.189471i
$451$	−5.01139	+	8.67998i	−0.235977	+	0.408724i
$452$	6.43337	−	11.1429i	0.302600	−	0.524119i
$453$	−0.416329	−	0.721103i	−0.0195608	−	0.0338804i
$454$	4.85002			0.227623
$455$	−4.11497	+	5.14919i	−0.192913	+	0.241398i
$456$	1.78879			0.0837679
$457$	−14.7080	−	25.4750i	−0.688012	−	1.19167i	−0.972480	−	0.232986i	$-0.925150\pi$
$457$	−14.7080	−	25.4750i	−0.688012	−	1.19167i	0.284468	−	0.958685i	$-0.408183\pi$
$458$	2.75431	−	4.77060i	0.128700	−	0.222916i
$459$	10.2059	−	17.6771i	0.476369	−	0.825095i
$460$	1.89714	+	3.28594i	0.0884544	+	0.153208i
$461$	−18.9682			−0.883436			−0.441718	−	0.897154i	$-0.645631\pi$
$461$	−18.9682			−0.883436			−0.441718	+	0.897154i	$0.645631\pi$
$462$	7.54324	+	1.14486i	0.350943	+	0.0532638i
$463$	−15.8564			−0.736910			−0.368455	−	0.929646i	$-0.620113\pi$
$463$	−15.8564			−0.736910			−0.368455	+	0.929646i	$0.620113\pi$
$464$	3.30406	+	5.72280i	0.153387	+	0.265674i
$465$	5.46223	−	9.46086i	0.253305	−	0.438737i
$466$	2.61678	−	4.53239i	0.121220	−	0.209959i
$467$	6.70450	+	11.6125i	0.310247	+	0.537364i	0.978416	−	0.206646i	$-0.0662548\pi$
$467$	6.70450	+	11.6125i	0.310247	+	0.537364i	−0.668168	+	0.744010i	$0.732921\pi$
$468$	9.48521			0.438454
$469$	−1.00937	−	0.153195i	−0.0466083	−	0.00707389i
$470$	12.7981			0.590332
$471$	−22.2592	−	38.5541i	−1.02565	−	1.77648i
$472$	9.21722	−	15.9647i	0.424257	−	0.734834i
$473$	4.84441	−	8.39076i	0.222746	−	0.385808i
$474$	13.4769	+	23.3426i	0.619013	+	1.07216i
$475$	−0.216024			−0.00991184
$476$	−7.90740	+	9.89476i	−0.362435	+	0.453526i
$477$	1.89922			0.0869591
$478$	−10.0971	−	17.4887i	−0.461832	−	0.799917i
$479$	−6.17215	+	10.6905i	−0.282013	+	0.488460i	−0.971880	−	0.235475i	$-0.924335\pi$
$479$	−6.17215	+	10.6905i	−0.282013	+	0.488460i	0.689868	+	0.723936i	$0.257669\pi$
$480$	−6.12123	+	10.6023i	−0.279395	+	0.483925i
$481$	1.23408	+	2.13749i	0.0562691	+	0.0974610i
$482$	−1.78332			−0.0812278
$483$	−11.3942	−	29.1197i	−0.518456	−	1.32499i
$484$	−0.871473			−0.0396124
$485$	−3.28103	−	5.68291i	−0.148984	−	0.258048i
$486$	10.2753	−	17.7974i	0.466097	−	0.807304i
$487$	18.4642	−	31.9809i	0.836691	−	1.44919i	−0.0559547	−	0.998433i	$-0.517820\pi$
$487$	18.4642	−	31.9809i	0.836691	−	1.44919i	0.892646	−	0.450758i	$-0.148846\pi$
$488$	7.76962	+	13.4574i	0.351714	+	0.609187i
$489$	−27.5090			−1.24400
$490$	1.63987	+	7.25318i	0.0740818	+	0.327665i
$491$	17.0641			0.770092			0.385046	−	0.922897i	$-0.374186\pi$
$491$	17.0641			0.770092			0.385046	+	0.922897i	$0.374186\pi$
$492$	11.8552	+	20.5339i	0.534475	+	0.925738i
$493$	−12.1199	+	20.9923i	−0.545853	+	0.945446i
$494$	0.285863	−	0.495130i	0.0128616	−	0.0222769i
$495$	2.18440	+	3.78348i	0.0981813	+	0.170055i
$496$	−6.02690			−0.270616
$497$	−12.2463	−	31.2974i	−0.549323	−	1.40388i
$498$	−22.2901			−0.998845
$499$	−6.00532	−	10.4015i	−0.268835	−	0.465636i	0.699726	−	0.714411i	$-0.253305\pi$
$499$	−6.00532	−	10.4015i	−0.268835	−	0.465636i	−0.968561	+	0.248775i	$0.919972\pi$
$500$	0.435737	−	0.754718i	0.0194867	−	0.0337520i
$501$	15.4630	−	26.7827i	0.690835	−	1.19656i
$502$	−13.2044	−	22.8708i	−0.589343	−	1.02077i
$503$	35.3880			1.57787			0.788936	−	0.614476i	$-0.210632\pi$
$503$	35.3880			1.57787			0.788936	+	0.614476i	$0.210632\pi$
$504$	22.0119	−	27.5441i	0.980488	−	1.22691i
$505$	−17.8308			−0.793459
$506$	−2.31260	−	4.00554i	−0.102808	−	0.178068i
$507$	−9.22034	+	15.9701i	−0.409490	+	0.709257i
$508$	−0.915588	+	1.58584i	−0.0406226	+	0.0703605i
$509$	−11.1528	−	19.3171i	−0.494337	−	0.856218i	0.505641	−	0.862744i	$-0.331256\pi$
$509$	−11.1528	−	19.3171i	−0.494337	−	0.856218i	−0.999979	+	0.00652626i	$0.997923\pi$
$510$	15.8416			0.701476
$511$	−29.9349	−	4.54331i	−1.32424	−	0.200984i
$512$	15.8906			0.702271
$513$	−0.401335	−	0.695132i	−0.0177194	−	0.0306908i
$514$	13.2368	−	22.9269i	0.583852	−	1.01126i
$515$	4.92258	−	8.52616i	0.216915	−	0.375708i
$516$	−11.4602	−	19.8497i	−0.504508	−	0.873834i
$517$	12.0473			0.529839
$518$	2.75297	+	0.417827i	0.120958	+	0.0183582i
$519$	0.451927			0.0198374
$520$	3.79981	+	6.58147i	0.166633	+	0.288616i
$521$	−0.728723	+	1.26219i	−0.0319259	+	0.0552973i	−0.881547	−	0.472096i	$-0.843497\pi$
$521$	−0.728723	+	1.26219i	−0.0319259	+	0.0552973i	0.849621	+	0.527394i	$0.176831\pi$
$522$	10.2394	−	17.7351i	0.448165	−	0.776244i
$523$	−6.60891	−	11.4470i	−0.288987	−	0.500541i	0.684581	−	0.728937i	$-0.259985\pi$
$523$	−6.60891	−	11.4470i	−0.288987	−	0.500541i	−0.973568	+	0.228396i	$0.926652\pi$
$524$	−13.3635			−0.583788
$525$	−4.48367	+	5.61055i	−0.195683	+	0.244864i
$526$	−1.12769			−0.0491698
$527$	−11.0539	−	19.1459i	−0.481516	−	0.834010i
$528$	2.03264	−	3.52064i	0.0884593	−	0.153216i
$529$	2.02195	−	3.50212i	0.0879109	−	0.152266i
$530$	0.230908	+	0.399944i	0.0100300	+	0.0173725i
$531$	−26.4016			−1.14573
$532$	0.181496	+	0.463841i	0.00786886	+	0.0201101i
$533$	24.9700			1.08157
$534$	−22.9976	−	39.8330i	−0.995203	−	1.72374i
$535$	−5.65447	+	9.79383i	−0.244464	+	0.423424i
$536$	−0.588540	+	1.01938i	−0.0254211	+	0.0440306i
$537$	22.4703	+	38.9196i	0.969663	+	1.67951i
$538$	−10.9134			−0.470512
$539$	1.54367	+	6.82767i	0.0664904	+	0.294089i
$540$	3.23810			0.139345
$541$	19.1421	+	33.1552i	0.822985	+	1.42545i	0.903450	+	0.428694i	$0.141026\pi$
$541$	19.1421	+	33.1552i	0.822985	+	1.42545i	−0.0804649	+	0.996757i	$0.525640\pi$
$542$	−4.54222	+	7.86736i	−0.195105	+	0.337932i
$543$	16.5893	−	28.7336i	0.711917	−	1.23308i
$544$	12.3875	+	21.4558i	0.531110	+	0.919910i
$545$	10.3329			0.442611
$546$	−6.92625	−	17.7011i	−0.296416	−	0.757536i
$547$	−17.7989			−0.761027			−0.380513	−	0.924775i	$-0.624253\pi$
$547$	−17.7989			−0.761027			−0.380513	+	0.924775i	$0.624253\pi$
$548$	1.98573	+	3.43938i	0.0848261	+	0.146923i
$549$	11.1276	−	19.2735i	0.474913	−	0.822574i
$550$	−0.531161	+	0.919997i	−0.0226488	+	0.0392288i
$551$	0.476603	+	0.825500i	0.0203040	+	0.0351675i
$552$	−36.0523			−1.53449
$553$	−15.4383	+	19.3184i	−0.656505	+	0.821504i
$554$	7.76739			0.330005
$555$	1.34465	+	2.32900i	0.0570772	+	0.0988607i
$556$	−6.02295	+	10.4321i	−0.255430	+	0.442418i
$557$	9.63588	−	16.6898i	0.408285	−	0.707171i	−0.586412	−	0.810013i	$-0.699460\pi$
$557$	9.63588	−	16.6898i	0.408285	−	0.707171i	0.994698	+	0.102842i	$0.0327935\pi$
$558$	9.33876	+	16.1752i	0.395341	+	0.684751i
$559$	−24.1381			−1.02093
$560$	3.91738	+	0.594554i	0.165540	+	0.0251245i
$561$	14.9122			0.629594
$562$	12.3457	+	21.3834i	0.520771	+	0.902003i
$563$	−8.94276	+	15.4893i	−0.376892	+	0.652797i	−0.990608	−	0.136730i	$-0.956341\pi$
$563$	−8.94276	+	15.4893i	−0.376892	+	0.652797i	0.613716	+	0.789527i	$0.289674\pi$
$564$	14.2499	−	24.6815i	0.600028	−	1.03928i
$565$	−7.38217	−	12.7863i	−0.310570	−	0.537924i
$566$	−2.30731			−0.0969836
$567$	7.89979	+	1.19898i	0.331760	+	0.0503523i
$568$	−38.7484			−1.62585
$569$	7.91130	+	13.7028i	0.331659	+	0.574450i	0.982837	−	0.184475i	$-0.0590583\pi$
$569$	7.91130	+	13.7028i	0.331659	+	0.574450i	−0.651178	+	0.758925i	$0.725725\pi$
$570$	0.311476	−	0.539493i	0.0130463	−	0.0225969i
$571$	3.47272	−	6.01493i	0.145329	−	0.251717i	−0.784167	−	0.620550i	$-0.786909\pi$
$571$	3.47272	−	6.01493i	0.145329	−	0.251717i	0.929496	+	0.368833i	$0.120243\pi$
$572$	1.08556	+	1.88025i	0.0453897	+	0.0786173i
$573$	−29.8851			−1.24847
$574$	17.5865	−	22.0065i	0.734046	−	0.918534i
$575$	4.35386			0.181569
$576$	−17.0081	−	29.4589i	−0.708671	−	1.22745i
$577$	−19.8086	+	34.3095i	−0.824643	+	1.42832i	0.0775490	+	0.996989i	$0.475291\pi$
$577$	−19.8086	+	34.3095i	−0.824643	+	1.42832i	−0.902192	+	0.431335i	$0.858043\pi$
$578$	6.99954	−	12.1236i	0.291143	−	0.504274i
$579$	25.7439	+	44.5898i	1.06988	+	1.85309i
$580$	−3.84538			−0.159671
$581$	−7.45198	−	19.0446i	−0.309160	−	0.790105i
$582$	18.9232			0.784392
$583$	0.217362	+	0.376481i	0.00900220	+	0.0155923i
$584$	−17.4544	+	30.2319i	−0.722268	+	1.25100i
$585$	5.44205	−	9.42591i	0.225001	−	0.389713i
$586$	−6.44375	−	11.1609i	−0.266189	−	0.461053i
$587$	7.62489			0.314713			0.157356	−	0.987542i	$-0.449703\pi$
$587$	7.62489			0.314713			0.157356	+	0.987542i	$0.449703\pi$
$588$	15.8139	+	4.91343i	0.652154	+	0.202626i
$589$	−0.869366			−0.0358216
$590$	−3.20993	−	5.55976i	−0.132151	−	0.228891i
$591$	20.8637	−	36.1370i	0.858218	−	1.48648i
$592$	0.741829	−	1.28488i	0.0304890	−	0.0528084i
$593$	23.9263	+	41.4416i	0.982536	+	1.70180i	0.652411	+	0.757866i	$0.273758\pi$
$593$	23.9263	+	41.4416i	0.982536	+	1.70180i	0.330125	+	0.943937i	$0.392909\pi$
$594$	−3.94722			−0.161956
$595$	5.29610	+	13.5350i	0.217119	+	0.554881i
$596$	−8.37493			−0.343050
$597$	−10.8658	−	18.8201i	−0.444707	−	0.770255i
$598$	−5.76145	+	9.97912i	−0.235603	+	0.408077i
$599$	−5.71176	+	9.89307i	−0.233376	+	0.404220i	−0.958800	−	0.284083i	$-0.908311\pi$
$599$	−5.71176	+	9.89307i	−0.233376	+	0.404220i	0.725423	+	0.688303i	$0.241644\pi$
$600$	4.14027	+	7.17116i	0.169026	+	0.292761i
$601$	35.8382			1.46187			0.730936	−	0.682446i	$-0.239084\pi$
$601$	35.8382			1.46187			0.730936	+	0.682446i	$0.239084\pi$
$602$	−17.0005	+	21.2733i	−0.692890	+	0.867033i
$603$	1.68580			0.0686512
$604$	−0.133657	−	0.231501i	−0.00543843	−	0.00941964i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$	25.7095	−	44.5302i	1.04438	−	1.80892i
$607$	−7.13392	−	12.3563i	−0.289557	−	0.501527i	0.684147	−	0.729344i	$-0.260175\pi$
$607$	−7.13392	−	12.3563i	−0.289557	−	0.501527i	−0.973704	+	0.227817i	$0.926841\pi$
$608$	0.974252			0.0395111
$609$	31.3320	+	4.75535i	1.26963	+	0.192697i
$610$	5.41159			0.219109
$611$	−15.0069	−	25.9927i	−0.607113	−	1.05155i
$612$	10.4575	−	18.1130i	0.422721	−	0.732174i
$613$	3.57146	−	6.18595i	0.144250	−	0.249848i	−0.784843	−	0.619695i	$-0.787256\pi$
$613$	3.57146	−	6.18595i	0.144250	−	0.249848i	0.929093	+	0.369846i	$0.120590\pi$
$614$	−16.4801	−	28.5444i	−0.665083	−	1.15196i
$615$	27.2073			1.09711
$616$	7.97929	+	1.21104i	0.321495	+	0.0487943i
$617$	−38.3359			−1.54335			−0.771673	−	0.636019i	$-0.780580\pi$
$617$	−38.3359			−1.54335			−0.771673	+	0.636019i	$0.780580\pi$
$618$	14.1954	+	24.5871i	0.571022	+	0.989039i
$619$	12.2549	−	21.2261i	0.492567	−	0.853151i	−0.507397	−	0.861713i	$-0.669392\pi$
$619$	12.2549	−	21.2261i	0.492567	−	0.853151i	0.999963	+	0.00856198i	$0.00272540\pi$
$620$	1.75358	−	3.03729i	0.0704255	−	0.121981i
$621$	8.08872	+	14.0101i	0.324589	+	0.562205i
$622$	−7.07168			−0.283549
$623$	26.3447	−	32.9659i	1.05548	−	1.32075i
$624$	−10.1280			−0.405443
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	13.0593	−	22.6193i	0.521953	−	0.904050i
$627$	0.293204	−	0.507843i	0.0117094	−	0.0202813i
$628$	−7.14605	−	12.3773i	−0.285159	−	0.493909i
$629$	5.44234			0.217000
$630$	−4.47435	−	11.4349i	−0.178262	−	0.455576i
$631$	27.2067			1.08308			0.541540	−	0.840675i	$-0.317841\pi$
$631$	27.2067			1.08308			0.541540	+	0.840675i	$0.317841\pi$
$632$	14.2559	+	24.6920i	0.567071	+	0.982195i
$633$	−15.3608	+	26.6058i	−0.610539	+	1.05748i
$634$	−15.6436	+	27.0955i	−0.621287	+	1.07610i
$635$	1.05062	+	1.81973i	0.0416926	+	0.0722137i
$636$	1.02841			0.0407790
$637$	12.8082	−	11.8355i	0.507479	−	0.468941i
$638$	4.68750			0.185580
$639$	27.7476	+	48.0602i	1.09768	+	1.90123i
$640$	−0.374225	+	0.648176i	−0.0147925	+	0.0256214i
$641$	−0.152815	+	0.264684i	−0.00603584	+	0.0104544i	−0.869028	−	0.494764i	$-0.835255\pi$
$641$	−0.152815	+	0.264684i	−0.00603584	+	0.0104544i	0.862992	+	0.505218i	$0.168588\pi$
$642$	−16.3059	−	28.2427i	−0.643544	−	1.11465i
$643$	30.0896			1.18662			0.593309	−	0.804974i	$-0.297821\pi$
$643$	30.0896			1.18662			0.593309	+	0.804974i	$0.297821\pi$
$644$	−3.65798	−	9.34852i	−0.144145	−	0.368383i
$645$	−26.3008			−1.03559
$646$	−0.630334	−	1.09177i	−0.0248002	−	0.0429552i
$647$	−3.27311	+	5.66919i	−0.128679	+	0.222879i	−0.923165	−	0.384404i	$-0.874407\pi$
$647$	−3.27311	+	5.66919i	−0.128679	+	0.222879i	0.794486	+	0.607283i	$0.207740\pi$
$648$	4.60620	−	7.97816i	0.180948	−	0.313412i
$649$	−3.02161	−	5.23359i	−0.118609	−	0.205436i
$650$	2.64659			0.103808
$651$	−18.0441	+	22.5791i	−0.707204	+	0.884946i
$652$	−8.83142			−0.345865
$653$	4.44049	+	7.69116i	0.173770	+	0.300978i	0.939735	−	0.341904i	$-0.111072\pi$
$653$	4.44049	+	7.69116i	0.173770	+	0.300978i	−0.765965	+	0.642882i	$0.777738\pi$
$654$	−14.8986	+	25.8051i	−0.582580	+	1.00906i
$655$	−7.66720	+	13.2800i	−0.299582	+	0.518892i
$656$	−7.50499	−	12.9990i	−0.293021	−	0.507527i
$657$	49.9960			1.95053
$658$	−33.4772	−	5.08094i	−1.30508	−	0.198076i
$659$	44.0609			1.71637			0.858185	−	0.513341i	$-0.171592\pi$
$659$	44.0609			1.71637			0.858185	+	0.513341i	$0.171592\pi$
$660$	1.18283	+	2.04872i	0.0460416	+	0.0797464i
$661$	−10.5785	+	18.3226i	−0.411457	+	0.712665i	−0.995049	−	0.0993821i	$-0.968313\pi$
$661$	−10.5785	+	18.3226i	−0.411457	+	0.712665i	0.583592	+	0.812047i	$0.301647\pi$
$662$	2.52833	−	4.37920i	0.0982664	−	0.170202i
$663$	−18.5756	−	32.1739i	−0.721418	−	1.24953i
$664$	−23.5787			−0.915030
$665$	0.565073	+	0.0857630i	0.0219126	+	0.00332575i
$666$	−4.59789			−0.178165
$667$	−9.60572	−	16.6376i	−0.371935	−	0.644210i
$668$	4.96420	−	8.59824i	0.192071	−	0.332676i
$669$	33.1742	−	57.4594i	1.28259	−	2.22151i
$670$	0.204961	+	0.355003i	0.00791834	+	0.0137150i
$671$	5.09412			0.196656
$672$	20.2211	−	25.3032i	0.780044	−	0.976093i
$673$	14.7120			0.567107			0.283554	−	0.958956i	$-0.408487\pi$
$673$	14.7120			0.567107			0.283554	+	0.958956i	$0.408487\pi$
$674$	12.3526	+	21.3954i	0.475806	+	0.824120i
$675$	1.85783	−	3.21785i	0.0715078	−	0.123855i
$676$	−2.96008	+	5.12700i	−0.113849	+	0.197192i
$677$	9.80674	+	16.9858i	0.376904	+	0.652816i	0.990610	−	0.136718i	$-0.0436555\pi$
$677$	9.80674	+	16.9858i	0.376904	+	0.652816i	−0.613706	+	0.789534i	$0.710322\pi$
$678$	42.5763			1.63513
$679$	6.32635	+	16.1679i	0.242783	+	0.620468i
$680$	16.7573			0.642614
$681$	−6.19663	−	10.7329i	−0.237455	−	0.411285i
$682$	−2.13761	+	3.70244i	−0.0818532	+	0.141774i
$683$	−24.1152	+	41.7687i	−0.922742	+	1.59824i	−0.127590	+	0.991827i	$0.540724\pi$
$683$	−24.1152	+	41.7687i	−0.922742	+	1.59824i	−0.795152	+	0.606410i	$0.792609\pi$
$684$	−0.411232	−	0.712274i	−0.0157238	−	0.0272345i
$685$	4.55718			0.174121
$686$	−1.41000	−	19.6239i	−0.0538339	−	0.749243i
$687$	−14.0762			−0.537040
$688$	7.25493	+	12.5659i	0.276592	+	0.479071i
$689$	0.541520	−	0.937939i	0.0206303	−	0.0357326i
$690$	−6.27767	+	10.8732i	−0.238987	+	0.413937i
$691$	18.8030	+	32.5677i	0.715300	+	1.23894i	0.962844	+	0.270059i	$0.0870432\pi$
$691$	18.8030	+	32.5677i	0.715300	+	1.23894i	−0.247544	+	0.968877i	$0.579623\pi$
$692$	0.145086			0.00551533
$693$	−4.21186	−	10.7640i	−0.159995	−	0.408892i
$694$	−0.556720			−0.0211328
$695$	6.91123	+	11.9706i	0.262158	+	0.454071i
$696$	18.2690	−	31.6428i	0.692484	−	1.19942i
$697$	27.5297	−	47.6829i	1.04276	−	1.80612i
$698$	14.2138	+	24.6190i	0.538000	+	0.931843i
$699$	−13.3733			−0.505825
$700$	−1.43943	+	1.80120i	−0.0544052	+	0.0680788i
$701$	38.1263			1.44001			0.720005	−	0.693969i	$-0.244140\pi$
$701$	38.1263			1.44001			0.720005	+	0.693969i	$0.244140\pi$
$702$	4.91692	+	8.51635i	0.185577	+	0.321429i
$703$	0.107007	−	0.185342i	0.00403585	−	0.00699029i
$704$	3.89309	−	6.74303i	0.146726	−	0.254137i
$705$	−16.3515	−	28.3216i	−0.615833	−	1.06665i
$706$	−10.6955			−0.402532
$707$	46.6416	+	7.07895i	1.75414	+	0.266231i
$708$	−14.2962			−0.537285
$709$	1.43440	+	2.48445i	0.0538699	+	0.0933054i	0.891703	−	0.452621i	$-0.149511\pi$
$709$	1.43440	+	2.48445i	0.0538699	+	0.0933054i	−0.837833	+	0.545927i	$0.816178\pi$
$710$	−6.74714	+	11.6864i	−0.253215	+	0.438582i
$711$	20.4172	−	35.3637i	0.765705	−	1.32624i
$712$	−24.3270	−	42.1356i	−0.911694	−	1.57910i
$713$	17.5217			0.656193
$714$	−41.4383	−	6.28922i	−1.55079	−	0.235368i
$715$	2.49133			0.0931705
$716$	7.21380	+	12.4947i	0.269592	+	0.466948i
$717$	−25.8012	+	44.6890i	−0.963564	+	1.66894i
$718$	0.783884	−	1.35773i	0.0292543	−	0.0506699i
$719$	5.47759	+	9.48747i	0.204280	+	0.353823i	0.949903	−	0.312545i	$-0.101181\pi$
$719$	5.47759	+	9.48747i	0.204280	+	0.353823i	−0.745623	+	0.666368i	$0.767848\pi$
$720$	−6.54265			−0.243830
$721$	−16.2614	+	20.3484i	−0.605607	+	0.757814i
$722$	20.1345			0.749330
$723$	2.27846	+	3.94640i	0.0847367	+	0.146768i
$724$	5.32580	−	9.22456i	0.197932	−	0.342828i
$725$	−2.20625	+	3.82134i	−0.0819382	+	0.141921i
$726$	−1.44186	−	2.49738i	−0.0535126	−	0.0926865i
$727$	−36.6999			−1.36112			−0.680562	−	0.732691i	$-0.738264\pi$
$727$	−36.6999			−1.36112			−0.680562	+	0.732691i	$0.738264\pi$
$728$	−7.32664	−	18.7243i	−0.271543	−	0.693970i
$729$	−43.4529			−1.60937
$730$	6.07855	+	10.5284i	0.224977	+	0.389672i
$731$	−26.6124	+	46.0941i	−0.984297	+	1.70485i
$732$	6.02548	−	10.4364i	0.222708	−	0.385742i
$733$	2.09665	+	3.63151i	0.0774416	+	0.134133i	0.902145	−	0.431432i	$-0.141992\pi$
$733$	2.09665	+	3.63151i	0.0774416	+	0.134133i	−0.824704	+	0.565565i	$0.808658\pi$
$734$	−19.1670			−0.707466
$735$	13.9558	−	12.8960i	0.514767	−	0.475676i
$736$	−19.6356			−0.723779
$737$	0.192937	+	0.334177i	0.00710693	+	0.0123096i
$738$	−23.2582	+	40.2843i	−0.856145	+	1.48289i
$739$	−19.6231	+	33.9883i	−0.721849	+	1.25028i	0.238409	+	0.971165i	$0.423374\pi$
$739$	−19.6231	+	33.9883i	−0.721849	+	1.25028i	−0.960258	+	0.279114i	$0.909959\pi$
$740$	0.431683	+	0.747698i	0.0158690	+	0.0274859i
$741$	−1.46093			−0.0536688
$742$	−0.445227	−	1.13784i	−0.0163448	−	0.0417716i
$743$	−31.7254			−1.16389			−0.581946	−	0.813227i	$-0.697708\pi$
$743$	−31.7254			−1.16389			−0.581946	+	0.813227i	$0.697708\pi$
$744$	16.6621	+	28.8597i	0.610863	+	1.05805i
$745$	−4.80504	+	8.32257i	−0.176043	+	0.304915i
$746$	−4.81197	+	8.33458i	−0.176179	+	0.305151i
$747$	16.8846	+	29.2449i	0.617774	+	1.07002i
$748$	4.78738			0.175044
$749$	18.6792	−	23.3738i	0.682522	−	0.854059i
$750$	2.88373			0.105299
$751$	24.4512	+	42.3507i	0.892236	+	1.54540i	0.837189	+	0.546914i	$0.184197\pi$
$751$	24.4512	+	42.3507i	0.892236	+	1.54540i	0.0550467	+	0.998484i	$0.482469\pi$
$752$	−9.02093	+	15.6247i	−0.328959	+	0.569775i
$753$	−33.7413	+	58.4417i	−1.22960	+	2.12973i
$754$	−5.83906	−	10.1135i	−0.212646	−	0.368314i
$755$	−0.306738			−0.0111634
$756$	−8.47020	−	1.28555i	−0.308058	−	0.0467550i
$757$	−45.1542			−1.64116			−0.820578	−	0.571535i	$-0.806348\pi$
$757$	−45.1542			−1.64116			−0.820578	+	0.571535i	$0.806348\pi$
$758$	−5.39642	−	9.34688i	−0.196007	−	0.339494i
$759$	−5.90939	+	10.2354i	−0.214497	+	0.371520i
$760$	0.329482	−	0.570680i	0.0119516	−	0.0207007i
$761$	−6.91929	−	11.9846i	−0.250824	−	0.434440i	0.712929	−	0.701236i	$-0.247368\pi$
$761$	−6.91929	−	11.9846i	−0.250824	−	0.434440i	−0.963753	+	0.266796i	$0.914035\pi$
$762$	−6.05941			−0.219509
$763$	−27.0286	−	4.10222i	−0.978502	−	0.148510i
$764$	−9.59423			−0.347107
$765$	−11.9998	−	20.7843i	−0.433855	−	0.751459i
$766$	9.20667	−	15.9464i	0.332651	−	0.576168i
$767$	−7.52784	+	13.0386i	−0.271815	+	0.470797i
$768$	−22.2151	−	38.4778i	−0.801620	−	1.38845i
$769$	18.2700			0.658832			0.329416	−	0.944185i	$-0.393148\pi$
$769$	18.2700			0.658832			0.329416	+	0.944185i	$0.393148\pi$
$770$	1.75465	−	2.19565i	0.0632333	−	0.0791257i
$771$	−67.6482			−2.43629
$772$	8.26476	+	14.3150i	0.297455	+	0.515208i
$773$	−17.1015	+	29.6207i	−0.615099	+	1.06538i	0.375268	+	0.926916i	$0.377551\pi$
$773$	−17.1015	+	29.6207i	−0.615099	+	1.06538i	−0.990367	+	0.138466i	$0.955783\pi$
$774$	22.4832	−	38.9420i	0.808142	−	1.39974i
$775$	−2.01220	−	3.48524i	−0.0722805	−	0.125193i
$776$	20.0171			0.718572
$777$	−2.59270	−	6.62603i	−0.0930126	−	0.237708i
$778$	−0.387213			−0.0138822
$779$	−1.08258	−	1.87508i	−0.0387874	−	0.0671817i
$780$	2.94682	−	5.10404i	0.105513	−	0.182754i
$781$	−6.35131	+	11.0008i	−0.227268	+	0.393639i
$782$	12.7041	+	22.0042i	0.454298	+	0.786868i
$783$	−16.3954			−0.585923
$784$	−10.0110	−	3.11046i	−0.357537	−	0.111088i
$785$	−16.3999			−0.585339
$786$	−22.1101	−	38.2958i	−0.788641	−	1.36597i
$787$	−15.1229	+	26.1936i	−0.539073	+	0.933701i	0.459882	+	0.887980i	$0.347892\pi$
$787$	−15.1229	+	26.1936i	−0.539073	+	0.933701i	−0.998954	+	0.0457209i	$0.985442\pi$
$788$	6.69804	−	11.6013i	0.238608	−	0.413281i
$789$	1.44080	+	2.49554i	0.0512938	+	0.0888435i
$790$	9.92935			0.353271
$791$	14.2340	+	36.3771i	0.506103	+	1.29342i
$792$	−13.3267			−0.473543
$793$	−6.34557	−	10.9908i	−0.225338	−	0.390296i
$794$	−1.60908	+	2.78701i	−0.0571041	+	0.0989072i
$795$	0.590039	−	1.02198i	0.0209265	−	0.0362458i
$796$	−3.48833	−	6.04196i	−0.123640	−	0.214151i
$797$	3.77585			0.133748			0.0668738	−	0.997761i	$-0.478698\pi$
$797$	3.77585			0.133748			0.0668738	+	0.997761i	$0.478698\pi$
$798$	−1.02894	+	1.28754i	−0.0364241	+	0.0455786i
$799$	−66.1810			−2.34131
$800$	2.25497	+	3.90572i	0.0797251	+	0.138088i
$801$	−34.8409	+	60.3462i	−1.23104	+	2.13223i
$802$	14.8484	−	25.7182i	0.524315	−	0.908141i
$803$	5.72195	+	9.91070i	0.201923	+	0.349741i
$804$	0.912847			0.0321936
$805$	−11.3888	−	1.72852i	−0.401403	−	0.0609222i
$806$	10.6510			0.375164
$807$	13.9436	+	24.1510i	0.490837	+	0.850154i
$808$	27.1957	−	47.1044i	0.956743	−	1.65713i
$809$	−8.29353	+	14.3648i	−0.291585	+	0.505040i	−0.974185	−	0.225753i	$-0.927516\pi$
$809$	−8.29353	+	14.3648i	−0.291585	+	0.505040i	0.682600	+	0.730792i	$0.260849\pi$
$810$	−1.60412	−	2.77842i	−0.0563631	−	0.0976238i
$811$	15.7522			0.553135			0.276567	−	0.960995i	$-0.410803\pi$
$811$	15.7522			0.553135			0.276567	+	0.960995i	$0.410803\pi$
$812$	10.0587	+	1.52665i	0.352992	+	0.0535748i
$813$	23.2135			0.814133
$814$	−0.526220	−	0.911440i	−0.0184440	−	0.0319459i
$815$	−5.06695	+	8.77621i	−0.177488	+	0.307417i
$816$	−11.1662	+	19.3404i	−0.390894	+	0.677049i
$817$	1.04651	+	1.81260i	0.0366126	+	0.0634149i
$818$	6.75025			0.236017
$819$	−17.9775	+	22.4957i	−0.628183	+	0.786064i
$820$	8.73458			0.305025
$821$	−4.14441	−	7.17833i	−0.144641	−	0.250525i	0.784598	−	0.620005i	$-0.212869\pi$
$821$	−4.14441	−	7.17833i	−0.144641	−	0.250525i	−0.929239	+	0.369479i	$0.879536\pi$
$822$	−6.57083	+	11.3810i	−0.229184	+	0.396958i
$823$	−10.2160	+	17.6946i	−0.356107	+	0.616795i	−0.987307	−	0.158825i	$-0.949229\pi$
$823$	−10.2160	+	17.6946i	−0.356107	+	0.616795i	0.631200	+	0.775620i	$0.282563\pi$
$824$	15.0160	+	26.0084i	0.523107	+	0.906047i
$825$	2.71455			0.0945086
$826$	6.18924	+	15.8175i	0.215351	+	0.550363i
$827$	47.3196			1.64546			0.822732	−	0.568429i	$-0.192449\pi$
$827$	47.3196			1.64546			0.822732	+	0.568429i	$0.192449\pi$
$828$	8.28819	+	14.3556i	0.288035	+	0.498891i
$829$	18.4475	−	31.9520i	0.640708	−	1.10974i	−0.344567	−	0.938762i	$-0.611974\pi$
$829$	18.4475	−	31.9520i	0.640708	−	1.10974i	0.985275	−	0.170977i	$-0.0546924\pi$
$830$	−4.10568	+	7.11124i	−0.142510	+	0.246835i
$831$	−9.92401	−	17.1889i	−0.344260	−	0.596276i
$832$	−19.3979			−0.672503
$833$	−8.48003	−	37.5074i	−0.293816	−	1.29955i
$834$	−39.8602			−1.38025
$835$	−5.69633	−	9.86633i	−0.197130	−	0.341438i
$836$	0.0941294	−	0.163037i	0.00325553	−	0.00563875i
$837$	7.47666	−	12.9499i	0.258431	−	0.447616i
$838$	7.12916	+	12.3481i	0.246273	+	0.426557i
$839$	13.3898			0.462269			0.231134	−	0.972922i	$-0.425756\pi$
$839$	13.3898			0.462269			0.231134	+	0.972922i	$0.425756\pi$
$840$	−7.98310	−	20.4020i	−0.275443	−	0.703936i
$841$	−9.52977			−0.328613
$842$	−4.99500	−	8.65159i	−0.172139	−	0.298154i
$843$	31.5470	−	54.6409i	1.08654	−	1.88193i
$844$	−4.93141	+	8.54145i	−0.169746	+	0.294009i
$845$	3.39664	+	5.88315i	0.116848	+	0.202386i
$846$	55.9122			1.92230
$847$	1.65172	−	2.06684i	0.0567536	−	0.0710175i
$848$	−0.651036			−0.0223567
$849$	2.94794	+	5.10598i	0.101173	+	0.175237i
$850$	2.91790	−	5.05395i	0.100083	−	0.173349i
$851$	−2.15668	+	3.73548i	−0.0739301	+	0.128051i
$852$	15.0250	+	26.0241i	0.514750	+	0.891572i
$853$	25.6968			0.879841			0.439920	−	0.898037i	$-0.355007\pi$
$853$	25.6968			0.879841			0.439920	+	0.898037i	$0.355007\pi$
$854$	−14.1556	−	2.14844i	−0.484395	−	0.0735182i
$855$	−0.943762			−0.0322760
$856$	−17.2485	−	29.8754i	−0.589543	−	1.02112i
$857$	8.52030	−	14.7576i	0.291048	−	0.504110i	−0.683010	−	0.730409i	$-0.739329\pi$
$857$	8.52030	−	14.7576i	0.291048	−	0.504110i	0.974058	+	0.226299i	$0.0726627\pi$
$858$	−3.59216	+	6.22180i	−0.122634	+	0.212409i
$859$	−8.55013	−	14.8093i	−0.291727	−	0.505285i	0.682491	−	0.730894i	$-0.260896\pi$
$859$	−8.55013	−	14.8093i	−0.291727	−	0.505285i	−0.974218	+	0.225608i	$0.927563\pi$
$860$	−8.44355			−0.287923
$861$	−71.1688	−	10.8015i	−2.42543	−	0.368115i
$862$	−11.9803			−0.408051
$863$	−13.3342	−	23.0955i	−0.453902	−	0.786181i	0.544722	−	0.838616i	$-0.316635\pi$
$863$	−13.3342	−	23.0955i	−0.453902	−	0.786181i	−0.998624	+	0.0524353i	$0.983302\pi$
$864$	−8.37869	+	14.5123i	−0.285049	+	0.493719i
$865$	0.0832416	−	0.144179i	0.00283030	−	0.00490222i
$866$	16.1675	+	28.0030i	0.549395	+	0.951580i
$867$	−35.7719			−1.21488
$868$	−5.79284	+	7.24875i	−0.196622	+	0.246039i
$869$	9.34685			0.317070
$870$	−6.36223	−	11.0197i	−0.215700	−	0.373603i
$871$	0.480670	−	0.832545i	0.0162869	−	0.0282097i
$872$	−15.7598	+	27.2968i	−0.533695	+	0.924386i
$873$	−14.3341	−	24.8275i	−0.485137	−	0.840283i
$874$	0.999152			0.0337968
$875$	0.964079	+	2.46385i	0.0325918	+	0.0832933i
$876$	27.0724			0.914690
$877$	24.8907	+	43.1120i	0.840499	+	1.45579i	0.889473	+	0.456987i	$0.151071\pi$
$877$	24.8907	+	43.1120i	0.840499	+	1.45579i	−0.0489742	+	0.998800i	$0.515595\pi$
$878$	6.80557	−	11.7876i	0.229677	−	0.397812i
$879$	−16.4657	+	28.5195i	−0.555375	+	0.961938i
$880$	−0.748794	−	1.29695i	−0.0252418	−	0.0437201i
$881$	12.6033			0.424615			0.212307	−	0.977203i	$-0.431902\pi$
$881$	12.6033			0.424615			0.212307	+	0.977203i	$0.431902\pi$
$882$	7.16425	+	31.6876i	0.241233	+	1.06698i
$883$	3.37550			0.113595			0.0567973	−	0.998386i	$-0.481911\pi$
$883$	3.37550			0.113595			0.0567973	+	0.998386i	$0.481911\pi$
$884$	−5.96348	−	10.3290i	−0.200573	−	0.347403i
$885$	−8.20233	+	14.2069i	−0.275718	+	0.477558i
$886$	−18.9462	+	32.8158i	−0.636510	+	1.10247i
$887$	−20.8175	−	36.0570i	−0.698983	−	1.21067i	−0.968819	−	0.247769i	$-0.920303\pi$
$887$	−20.8175	−	36.0570i	−0.698983	−	1.21067i	0.269836	−	0.962906i	$-0.413031\pi$
$888$	−8.20352			−0.275292
$889$	−2.02576	−	5.17714i	−0.0679419	−	0.173636i
$890$	−16.9439			−0.567962
$891$	−1.51002	−	2.61543i	−0.0505875	−	0.0876200i
$892$	10.6502	−	18.4466i	0.356594	−	0.617639i
$893$	−1.30125	+	2.25383i	−0.0435446	+	0.0754215i
$894$	−13.8564	−	24.0000i	−0.463428	−	0.802681i
$895$	16.5554			0.553386
$896$	1.23623	−	1.54693i	0.0412994	−	0.0516792i
$897$	29.4445			0.983123
$898$	21.5038	+	37.2456i	0.717590	+	1.24290i
$899$	−8.87886	+	15.3786i	−0.296127	+	0.512906i
$900$	1.90364	−	3.29721i	0.0634548	−	0.109907i
$901$	−1.19406	−	2.06818i	−0.0397800	−	0.0689009i
$902$	−10.6474			−0.354520
$903$	68.7975	+	10.4416i	2.28944	+	0.347475i
$904$	45.0376			1.49793
$905$	−6.11126	−	10.5850i	−0.203145	−	0.351858i
$906$	0.442275	−	0.766043i	0.0146936	−	0.0254501i
$907$	14.9492	−	25.8929i	0.496382	−	0.859758i	−0.503610	−	0.863931i	$-0.667995\pi$
$907$	14.9492	−	25.8929i	0.496382	−	0.859758i	0.999991	+	0.00417321i	$0.00132838\pi$
$908$	−1.98935	−	3.44566i	−0.0660189	−	0.114348i
$909$	−77.8989			−2.58374
$910$	−6.92295	−	1.05072i	−0.229493	−	0.0348310i
$911$	27.2007			0.901199			0.450599	−	0.892726i	$-0.351210\pi$
$911$	27.2007			0.901199			0.450599	+	0.892726i	$0.351210\pi$
$912$	0.439098	+	0.760540i	0.0145400	+	0.0251840i
$913$	−3.86482	+	6.69406i	−0.127907	+	0.221541i
$914$	15.6246	−	27.0627i	0.516817	−	0.895153i
$915$	−6.91413	−	11.9756i	−0.228574	−	0.395902i
$916$	−4.51898			−0.149311
$917$	25.3281	−	31.6938i	0.836406	−	1.04662i
$918$	21.6838			0.715672
$919$	−6.57532	−	11.3888i	−0.216900	−	0.375682i	0.736959	−	0.675938i	$-0.236261\pi$
$919$	−6.57532	−	11.3888i	−0.216900	−	0.375682i	−0.953859	+	0.300256i	$0.902928\pi$
$920$	−6.64057	+	11.5018i	−0.218933	+	0.379203i
$921$	−42.1116	+	72.9395i	−1.38763	+	2.40344i
$922$	−10.0752	−	17.4507i	−0.331808	−	0.574708i
$923$	31.6464			1.04166
$924$	−2.28068	−	5.82863i	−0.0750289	−	0.191748i
$925$	0.990698			0.0325740
$926$	−8.42230	−	14.5879i	−0.276774	−	0.479387i
$927$	21.5057	−	37.2490i	0.706341	−	1.22342i
$928$	9.95006	−	17.2340i	0.326627	−	0.565734i
$929$	−26.6328	−	46.1294i	−0.873794	−	1.51346i	−0.858042	−	0.513580i	$-0.828319\pi$
$929$	−26.6328	−	46.1294i	−0.873794	−	1.51346i	−0.0157522	−	0.999876i	$-0.505014\pi$
$930$	11.6053			0.380552
$931$	−1.44407	−	0.448677i	−0.0473274	−	0.0147048i
$932$	−4.29334			−0.140633
$933$	9.03514	+	15.6493i	0.295797	+	0.512336i
$934$	−7.12234	+	12.3362i	−0.233050	+	0.403654i
$935$	2.74672	−	4.75745i	0.0898273	−	0.155585i
$936$	16.6006	+	28.7531i	0.542607	+	0.939823i
$937$	15.8292			0.517119			0.258559	−	0.965995i	$-0.416752\pi$
$937$	15.8292			0.517119			0.258559	+	0.965995i	$0.416752\pi$
$938$	−0.395197	−	1.00999i	−0.0129037	−	0.0329772i
$939$	−66.7407			−2.17800
$940$	−5.24944	−	9.09230i	−0.171218	−	0.296558i
$941$	26.0421	−	45.1063i	0.848949	−	1.47042i	−0.0331985	−	0.999449i	$-0.510569\pi$
$941$	26.0421	−	45.1063i	0.848949	−	1.47042i	0.882147	−	0.470974i	$-0.156097\pi$
$942$	23.6465	−	40.9569i	0.770443	−	1.33445i
$943$	21.8189	+	37.7914i	0.710521	+	1.23066i
$944$	9.05027			0.294561
$945$	−6.13721	+	7.67967i	−0.199643	+	0.249820i
$946$	10.2926			0.334643
$947$	18.3116	+	31.7166i	0.595047	+	1.03065i	0.993540	+	0.113481i	$0.0362000\pi$
$947$	18.3116	+	31.7166i	0.595047	+	1.03065i	−0.398493	+	0.917171i	$0.630467\pi$
$948$	11.0557	−	19.1491i	0.359073	−	0.621933i
$949$	14.2553	−	24.6908i	0.462745	−	0.801499i
$950$	−0.114743	−	0.198741i	−0.00372276	−	0.00644801i
$951$	79.9483			2.59250
$952$	−43.8337	−	6.65279i	−1.42066	−	0.215618i
$953$	37.9581			1.22958			0.614791	−	0.788690i	$-0.289240\pi$
$953$	37.9581			1.22958			0.614791	+	0.788690i	$0.289240\pi$
$954$	1.00879	+	1.74727i	0.0326607	+	0.0565700i
$955$	−5.50460	+	9.53425i	−0.178125	+	0.308521i
$956$	−8.28316	+	14.3469i	−0.267897	+	0.464011i
$957$	−5.98899	−	10.3732i	−0.193597	−	0.335319i
$958$	−13.1136			−0.423682
$959$	−11.9206	−	1.80923i	−0.384938	−	0.0584232i
$960$	−21.1360			−0.682161
$961$	7.40208	+	12.8208i	0.238777	+	0.413573i
$962$	−1.31099	+	2.27070i	−0.0422679	+	0.0732102i
$963$	−24.7032	+	42.7872i	−0.796049	+	1.37880i
$964$	0.731470	+	1.26694i	0.0235591	+	0.0408055i
$965$	18.9673			0.610580
$966$	20.7379	−	25.9499i	0.667230	−	0.834924i
$967$	−1.62261			−0.0521796			−0.0260898	−	0.999660i	$-0.508306\pi$
$967$	−1.62261			−0.0521796			−0.0260898	+	0.999660i	$0.508306\pi$
$968$	−1.52521	−	2.64175i	−0.0490222	−	0.0849090i
$969$	−1.61069	+	2.78980i	−0.0517430	+	0.0896214i
$970$	3.48551	−	6.03708i	0.111913	−	0.193839i
$971$	19.1378	+	33.1476i	0.614161	+	1.06376i	0.990531	+	0.137288i	$0.0438386\pi$
$971$	19.1378	+	33.1476i	0.614161	+	1.06376i	−0.376371	+	0.926469i	$0.622828\pi$
$972$	−16.8587			−0.540742
$973$	−13.3259	−	34.0565i	−0.427210	−	1.09180i
$974$	39.2298			1.25700
$975$	−3.38142	−	5.85680i	−0.108292	−	0.187568i
$976$	−3.81445	+	6.60681i	−0.122097	+	0.211479i
$977$	−8.97617	+	15.5472i	−0.287173	+	0.497398i	−0.973134	−	0.230240i	$-0.926049\pi$
$977$	−8.97617	+	15.5472i	−0.287173	+	0.497398i	0.685961	+	0.727638i	$0.259382\pi$
$978$	−14.6117	−	25.3082i	−0.467231	−	0.809267i
$979$	−15.9499			−0.509761
$980$	4.48033	−	4.14010i	0.143119	−	0.132251i
$981$	45.1421			1.44128
$982$	9.06378	+	15.6989i	0.289237	+	0.500973i
$983$	2.55908	−	4.43245i	0.0816219	−	0.141373i	−0.822325	−	0.569018i	$-0.807323\pi$
$983$	2.55908	−	4.43245i	0.0816219	−	0.141373i	0.903947	+	0.427645i	$0.140657\pi$
$984$	−41.4970	+	71.8749i	−1.32288	+	2.29129i
$985$	−7.68588	−	13.3123i	−0.244892	−	0.424166i
$986$	−25.7505			−0.820063
$987$	31.5282	+	80.5752i	1.00356	+	2.56474i
$988$	−0.469015			−0.0149213
$989$	−21.0919	−	36.5322i	−0.670683	−	1.16166i
$990$	−2.32053	+	4.01928i	−0.0737513	+	0.127741i
$991$	−29.7549	+	51.5371i	−0.945197	+	1.63713i	−0.189840	+	0.981815i	$0.560797\pi$
$991$	−29.7549	+	51.5371i	−0.945197	+	1.63713i	−0.755357	+	0.655314i	$0.772536\pi$
$992$	9.07491	+	15.7182i	0.288129	+	0.499053i
$993$	−12.9213			−0.410045
$994$	22.2887	−	27.8905i	0.706955	−	0.884634i
$995$	−8.00558			−0.253794
$996$	9.14284	+	15.8359i	0.289702	+	0.501778i
$997$	−22.2085	+	38.4663i	−0.703351	+	1.21824i	0.263933	+	0.964541i	$0.414980\pi$
$997$	−22.2085	+	38.4663i	−0.703351	+	1.21824i	−0.967283	+	0.253698i	$0.918353\pi$
$998$	6.37958	−	11.0498i	0.201942	−	0.349774i
$999$	1.84055	+	3.18792i	0.0582323	+	0.100861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.c.221.6	✓	16
7.2	even	3	inner	385.2.i.c.331.6	yes	16
7.3	odd	6		2695.2.a.s.1.3		8
7.4	even	3		2695.2.a.t.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.c.221.6	✓	16	1.1	even	1	trivial
385.2.i.c.331.6	yes	16	7.2	even	3	inner
2695.2.a.s.1.3		8	7.3	odd	6
2695.2.a.t.1.3		8	7.4	even	3

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.531161 + 0.919997i) q^{2} +(1.35728 - 2.35087i) q^{3} +(0.435737 - 0.754718i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88373 q^{6} +(0.964079 + 2.46385i) q^{7} +3.05043 q^{8} +(-2.18440 - 3.78348i) q^{9} +O(q^{10})\)	\(q+(0.531161 + 0.919997i) q^{2} +(1.35728 - 2.35087i) q^{3} +(0.435737 - 0.754718i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.88373 q^{6} +(0.964079 + 2.46385i) q^{7} +3.05043 q^{8} +(-2.18440 - 3.78348i) q^{9} +(0.531161 - 0.919997i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.18283 - 2.04872i) q^{12} -2.49133 q^{13} +(-1.75465 + 2.19565i) q^{14} -2.71455 q^{15} +(0.748794 + 1.29695i) q^{16} +(-2.74672 + 4.75745i) q^{17} +(2.32053 - 4.01928i) q^{18} +(0.108012 + 0.187082i) q^{19} -0.871473 q^{20} +(7.10071 + 1.07770i) q^{21} +1.06232 q^{22} +(-2.17693 - 3.77055i) q^{23} +(4.14027 - 7.17116i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.32330 - 2.29202i) q^{26} -3.71566 q^{27} +(2.27960 + 0.345982i) q^{28} +4.41251 q^{29} +(-1.44186 - 2.49738i) q^{30} +(-2.01220 + 3.48524i) q^{31} +(2.25497 - 3.90572i) q^{32} +(-1.35728 - 2.35087i) q^{33} -5.83579 q^{34} +(1.65172 - 2.06684i) q^{35} -3.80729 q^{36} +(-0.495349 - 0.857970i) q^{37} +(-0.114743 + 0.198741i) q^{38} +(-3.38142 + 5.85680i) q^{39} +(-1.52521 - 2.64175i) q^{40} -10.0228 q^{41} +(2.78014 + 7.10507i) q^{42} +9.68882 q^{43} +(-0.435737 - 0.754718i) q^{44} +(-2.18440 + 3.78348i) q^{45} +(2.31260 - 4.00554i) q^{46} +(6.02364 + 10.4333i) q^{47} +4.06528 q^{48} +(-5.14110 + 4.75069i) q^{49} -1.06232 q^{50} +(7.45611 + 12.9144i) q^{51} +(-1.08556 + 1.88025i) q^{52} +(-0.217362 + 0.376481i) q^{53} +(-1.97361 - 3.41839i) q^{54} -1.00000 q^{55} +(2.94085 + 7.51579i) q^{56} +0.586407 q^{57} +(2.34375 + 4.05950i) q^{58} +(3.02161 - 5.23359i) q^{59} +(-1.18283 + 2.04872i) q^{60} +(2.54706 + 4.41164i) q^{61} -4.27521 q^{62} +(7.21601 - 9.02960i) q^{63} +7.78618 q^{64} +(1.24567 + 2.15756i) q^{65} +(1.44186 - 2.49738i) q^{66} +(-0.192937 + 0.334177i) q^{67} +(2.39369 + 4.14599i) q^{68} -11.8188 q^{69} +(2.77882 + 0.421750i) q^{70} -12.7026 q^{71} +(-6.66334 - 11.5412i) q^{72} +(-5.72195 + 9.91070i) q^{73} +(0.526220 - 0.911440i) q^{74} +(1.35728 + 2.35087i) q^{75} +0.188259 q^{76} +(2.61580 + 0.397008i) q^{77} -7.18432 q^{78} +(4.67342 + 8.09461i) q^{79} +(0.748794 - 1.29695i) q^{80} +(1.51002 - 2.61543i) q^{81} +(-5.32370 - 9.22093i) q^{82} -7.72963 q^{83} +(3.90740 - 4.88944i) q^{84} +5.49343 q^{85} +(5.14632 + 8.91369i) q^{86} +(5.98899 - 10.3732i) q^{87} +(1.52521 - 2.64175i) q^{88} +(-7.97496 - 13.8130i) q^{89} -4.64106 q^{90} +(-2.40184 - 6.13826i) q^{91} -3.79427 q^{92} +(5.46223 + 9.46086i) q^{93} +(-6.39904 + 11.0835i) q^{94} +(0.108012 - 0.187082i) q^{95} +(-6.12123 - 10.6023i) q^{96} +6.56206 q^{97} +(-7.10137 - 2.20642i) q^{98} -4.36879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 16 q - 3 q^{2} - q^{3} - 9 q^{4} - 8 q^{5} - 6 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} - 3 q^{10} + 8 q^{11} - 9 q^{12} + 28 q^{13} - 9 q^{14} + 2 q^{15} - 7 q^{16} - 5 q^{17} - 27 q^{18} - q^{19} + 18 q^{20} - 18 q^{21} - 6 q^{22} + 2 q^{23} + 24 q^{24} - 8 q^{25} - 21 q^{26} - 10 q^{27} + 32 q^{28} + 52 q^{29} + 3 q^{30} - 2 q^{31} - 16 q^{32} + q^{33} - 52 q^{34} + 5 q^{35} + 108 q^{36} + q^{37} + 31 q^{38} - 19 q^{39} - 9 q^{40} - 6 q^{41} + 44 q^{42} + 8 q^{43} + 9 q^{44} - 19 q^{45} - 10 q^{46} - q^{47} - 42 q^{48} + 17 q^{49} + 6 q^{50} - 3 q^{51} - 37 q^{52} - 26 q^{53} + 5 q^{54} - 16 q^{55} + 40 q^{57} + q^{58} + 19 q^{59} - 9 q^{60} - 52 q^{62} - 21 q^{63} + 2 q^{64} - 14 q^{65} - 3 q^{66} + 13 q^{67} - 15 q^{68} - 28 q^{69} + 15 q^{70} - 18 q^{71} - 32 q^{72} - 11 q^{73} - 24 q^{74} - q^{75} - 36 q^{76} + 4 q^{77} - 66 q^{78} + 8 q^{79} - 7 q^{80} - 52 q^{81} - 41 q^{82} + 64 q^{83} + 138 q^{84} + 10 q^{85} - 28 q^{86} + 16 q^{87} + 9 q^{88} - 5 q^{89} + 54 q^{90} + 13 q^{91} + 60 q^{92} + 14 q^{93} + 5 q^{94} - q^{95} - q^{96} + 18 q^{97} + 22 q^{98} - 38 q^{99}+O(q^{100}) \) 16 * q - 3 * q^2 - q^3 - 9 * q^4 - 8 * q^5 - 6 * q^6 - q^7 + 18 * q^8 - 19 * q^9 - 3 * q^10 + 8 * q^11 - 9 * q^12 + 28 * q^13 - 9 * q^14 + 2 * q^15 - 7 * q^16 - 5 * q^17 - 27 * q^18 - q^19 + 18 * q^20 - 18 * q^21 - 6 * q^22 + 2 * q^23 + 24 * q^24 - 8 * q^25 - 21 * q^26 - 10 * q^27 + 32 * q^28 + 52 * q^29 + 3 * q^30 - 2 * q^31 - 16 * q^32 + q^33 - 52 * q^34 + 5 * q^35 + 108 * q^36 + q^37 + 31 * q^38 - 19 * q^39 - 9 * q^40 - 6 * q^41 + 44 * q^42 + 8 * q^43 + 9 * q^44 - 19 * q^45 - 10 * q^46 - q^47 - 42 * q^48 + 17 * q^49 + 6 * q^50 - 3 * q^51 - 37 * q^52 - 26 * q^53 + 5 * q^54 - 16 * q^55 + 40 * q^57 + q^58 + 19 * q^59 - 9 * q^60 - 52 * q^62 - 21 * q^63 + 2 * q^64 - 14 * q^65 - 3 * q^66 + 13 * q^67 - 15 * q^68 - 28 * q^69 + 15 * q^70 - 18 * q^71 - 32 * q^72 - 11 * q^73 - 24 * q^74 - q^75 - 36 * q^76 + 4 * q^77 - 66 * q^78 + 8 * q^79 - 7 * q^80 - 52 * q^81 - 41 * q^82 + 64 * q^83 + 138 * q^84 + 10 * q^85 - 28 * q^86 + 16 * q^87 + 9 * q^88 - 5 * q^89 + 54 * q^90 + 13 * q^91 + 60 * q^92 + 14 * q^93 + 5 * q^94 - q^95 - q^96 + 18 * q^97 + 22 * q^98 - 38 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more