LMFDB - Embedded newform 392.3.k.n.275.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 $ x^16 - x^15 + 3x^14 + 6x^13 - 22x^12 + 44x^11 - 20x^10 - 112x^9 + 368x^8 - 448x^7 - 320x^6 + 2816x^5 - 5632x^4 + 6144x^3 + 12288x^2 - 16384x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			275.5
Root			$-1.78423 + 0.903622i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.n.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.109554 - 1.99700i) q^{2} +(2.28374 + 3.95555i) q^{3} +(-3.97600 + 0.437557i) q^{4} +(-4.96451 - 2.86626i) q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +O(q^{10})$	\(q+(-0.109554 - 1.99700i) q^{2} +(2.28374 + 3.95555i) q^{3} +(-3.97600 + 0.437557i) q^{4} +(-4.96451 - 2.86626i) q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +(-5.18003 + 10.2281i) q^{10} +(0.700323 + 1.21300i) q^{11} +(-10.8109 - 14.7280i) q^{12} -19.0821i q^{13} -26.1831i q^{15} +(15.6171 - 3.47945i) q^{16} +(-16.1349 - 27.9465i) q^{17} +(21.1641 + 10.7186i) q^{18} +(6.28374 - 10.8837i) q^{19} +(20.9930 + 9.22398i) q^{20} +(2.34563 - 1.53143i) q^{22} +(13.7605 + 7.94464i) q^{23} +(-28.2273 + 23.2028i) q^{24} +(3.93090 + 6.80852i) q^{25} +(-38.1069 + 2.09052i) q^{26} -13.0712 q^{27} +3.29194i q^{29} +(-52.2876 + 2.86846i) q^{30} +(19.6332 - 11.3352i) q^{31} +(-8.65936 - 30.8061i) q^{32} +(-3.19871 + 5.54032i) q^{33} +(-54.0415 + 35.2831i) q^{34} +(19.0864 - 43.4390i) q^{36} +(-46.8985 - 27.0769i) q^{37} +(-22.4232 - 11.3562i) q^{38} +(75.4801 - 43.5785i) q^{39} +(16.1204 - 42.9335i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(-3.31524 - 4.51643i) q^{44} +(58.8880 - 33.9990i) q^{45} +(14.3579 - 28.3501i) q^{46} +(-18.7394 - 10.8192i) q^{47} +(49.4284 + 53.8280i) q^{48} +(13.1659 - 8.59589i) q^{50} +(73.6959 - 127.645i) q^{51} +(8.34951 + 75.8703i) q^{52} +(-0.308883 + 0.178334i) q^{53} +(1.43200 + 26.1031i) q^{54} -8.02924i q^{55} +57.4016 q^{57} +(6.57400 - 0.360645i) q^{58} +(13.4292 + 23.2600i) q^{59} +(11.4566 + 104.104i) q^{60} +(-74.6763 - 43.1144i) q^{61} +(-24.7873 - 37.9656i) q^{62} +(-60.5710 + 20.6676i) q^{64} +(-54.6943 + 94.7333i) q^{65} +(11.4144 + 5.78085i) q^{66} +(-57.2613 - 99.1794i) q^{67} +(76.3807 + 104.055i) q^{68} +72.5739i q^{69} +104.792i q^{71} +(-88.8385 - 33.3565i) q^{72} +(-12.1987 - 21.1288i) q^{73} +(-48.9345 + 96.6226i) q^{74} +(-17.9543 + 31.0977i) q^{75} +(-20.2218 + 46.0232i) q^{76} +(-95.2952 - 145.959i) q^{78} +(101.436 + 58.5639i) q^{79} +(-87.5042 - 27.4889i) q^{80} +(23.5270 + 40.7499i) q^{81} +(-0.832178 - 15.1693i) q^{82} -79.2706 q^{83} +184.988i q^{85} +(2.28396 + 41.6331i) q^{86} +(-13.0214 + 7.51793i) q^{87} +(-8.65611 + 7.11531i) q^{88} +(1.33039 - 2.30431i) q^{89} +(-74.3473 - 113.874i) q^{90} +(-58.1880 - 25.5669i) q^{92} +(89.6741 + 51.7734i) q^{93} +(-19.5530 + 38.6079i) q^{94} +(-62.3913 + 36.0216i) q^{95} +(102.079 - 104.605i) q^{96} +52.0930 q^{97} -16.6142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	$ 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) $ 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.109554	−	1.99700i	−0.0547769	−	0.998499i
$2$	−0.109554	−	1.99700i	−0.0547769	−	0.998499i
$3$	2.28374	+	3.95555i	0.761245	+	1.31852i	0.942209	+	0.335026i	$0.108745\pi$
$3$	2.28374	+	3.95555i	0.761245	+	1.31852i	−0.180964	+	0.983490i	$0.557922\pi$
$4$	−3.97600	+	0.437557i	−0.993999	+	0.109389i
$5$	−4.96451	−	2.86626i	−0.992902	−	0.573252i	−0.0867614	−	0.996229i	$-0.527652\pi$
$5$	−4.96451	−	2.86626i	−0.992902	−	0.573252i	−0.906140	+	0.422977i	$0.860985\pi$
$6$	7.64902	−	4.99396i	1.27484	−	0.832327i
$7$		0			0
$7$		0			0
$8$	1.30939	+	7.89212i	0.163673	+	0.986515i
$9$	−5.93090	+	10.2726i	−0.658989	+	1.14140i
$10$	−5.18003	+	10.2281i	−0.518003	+	1.02281i
$11$	0.700323	+	1.21300i	0.0636658	+	0.110272i	0.896101	−	0.443849i	$-0.146388\pi$
$11$	0.700323	+	1.21300i	0.0636658	+	0.110272i	−0.832436	+	0.554122i	$0.813054\pi$
$12$	−10.8109	−	14.7280i	−0.900909	−	1.22733i
$13$		−	19.0821i		−	1.46785i	−0.679228	−	0.733927i	$-0.737685\pi$
$13$		−	19.0821i		−	1.46785i	0.679228	−	0.733927i	$-0.262315\pi$
$14$		0			0
$15$		−	26.1831i		−	1.74554i
$16$	15.6171	−	3.47945i	0.976068	−	0.217466i
$17$	−16.1349	−	27.9465i	−0.949114	−	1.64391i	−0.747296	−	0.664491i	$-0.768648\pi$
$17$	−16.1349	−	27.9465i	−0.949114	−	1.64391i	−0.201818	−	0.979423i	$-0.564685\pi$
$18$	21.1641	+	10.7186i	1.17579	+	0.595477i
$19$	6.28374	−	10.8837i	0.330723	−	0.572829i	−0.651931	−	0.758278i	$-0.726041\pi$
$19$	6.28374	−	10.8837i	0.330723	−	0.572829i	0.982654	+	0.185449i	$0.0593741\pi$
$20$	20.9930	+	9.22398i	1.04965	+	0.461199i
$21$		0			0
$22$	2.34563	−	1.53143i	0.106619	−	0.0696105i
$23$	13.7605	+	7.94464i	0.598284	+	0.345419i	0.768366	−	0.640011i	$-0.221070\pi$
$23$	13.7605	+	7.94464i	0.598284	+	0.345419i	−0.170082	+	0.985430i	$0.554403\pi$
$24$	−28.2273	+	23.2028i	−1.17614	+	0.966785i
$25$	3.93090	+	6.80852i	0.157236	+	0.272341i
$26$	−38.1069	+	2.09052i	−1.46565	+	0.0804045i
$27$	−13.0712			−0.484118
$28$		0			0
$29$			3.29194i			0.113515i	0.998388	+	0.0567576i	$0.0180762\pi$
$29$			3.29194i			0.113515i	−0.998388	+	0.0567576i	$0.981924\pi$
$30$	−52.2876	+	2.86846i	−1.74292	+	0.0956153i
$31$	19.6332	−	11.3352i	0.633329	−	0.365653i	−0.148711	−	0.988881i	$-0.547512\pi$
$31$	19.6332	−	11.3352i	0.633329	−	0.365653i	0.782040	+	0.623228i	$0.214179\pi$
$32$	−8.65936	−	30.8061i	−0.270605	−	0.962690i
$33$	−3.19871	+	5.54032i	−0.0969305	+	0.167889i
$34$	−54.0415	+	35.2831i	−1.58946	+	1.03774i
$35$		0			0
$36$	19.0864	−	43.4390i	0.530177	−	1.20664i
$37$	−46.8985	−	27.0769i	−1.26753	−	0.731807i	−0.293008	−	0.956110i	$-0.594656\pi$
$37$	−46.8985	−	27.0769i	−1.26753	−	0.731807i	−0.974519	+	0.224303i	$0.927990\pi$
$38$	−22.4232	−	11.3562i	−0.590085	−	0.298849i
$39$	75.4801	−	43.5785i	1.93539	−	1.11740i
$40$	16.1204	−	42.9335i	0.403010	−	1.07334i
$41$	7.59607			0.185270			0.0926350	−	0.995700i	$-0.470471\pi$
$41$	7.59607			0.185270			0.0926350	+	0.995700i	$0.470471\pi$
$42$		0			0
$43$	−20.8478			−0.484833			−0.242417	−	0.970172i	$-0.577940\pi$
$43$	−20.8478			−0.484833			−0.242417	+	0.970172i	$0.577940\pi$
$44$	−3.31524	−	4.51643i	−0.0753463	−	0.102646i
$45$	58.8880	−	33.9990i	1.30862	−	0.755533i
$46$	14.3579	−	28.3501i	0.312129	−	0.616306i
$47$	−18.7394	−	10.8192i	−0.398711	−	0.230196i	0.287217	−	0.957866i	$-0.407270\pi$
$47$	−18.7394	−	10.8192i	−0.398711	−	0.230196i	−0.685928	+	0.727670i	$0.740603\pi$
$48$	49.4284	+	53.8280i	1.02976	+	1.12142i
$49$		0			0
$50$	13.1659	−	8.59589i	0.263319	−	0.171918i
$51$	73.6959	−	127.645i	1.44502	−	2.50284i
$52$	8.34951	+	75.8703i	0.160567	+	1.45905i
$53$	−0.308883	+	0.178334i	−0.00582798	+	0.00336479i	−0.502911	−	0.864338i	$-0.667738\pi$
$53$	−0.308883	+	0.178334i	−0.00582798	+	0.00336479i	0.497083	+	0.867703i	$0.334404\pi$
$54$	1.43200	+	26.1031i	0.0265185	+	0.483391i
$55$		−	8.02924i		−	0.145986i
$56$		0			0
$57$	57.4016			1.00705
$58$	6.57400	−	0.360645i	0.113345	−	0.00621801i
$59$	13.4292	+	23.2600i	0.227613	+	0.394237i	0.957100	−	0.289757i	$-0.0935746\pi$
$59$	13.4292	+	23.2600i	0.227613	+	0.394237i	−0.729487	+	0.683994i	$0.760241\pi$
$60$	11.4566	+	104.104i	0.190944	+	1.73507i
$61$	−74.6763	−	43.1144i	−1.22420	−	0.706793i	−0.258390	−	0.966041i	$-0.583192\pi$
$61$	−74.6763	−	43.1144i	−1.22420	−	0.706793i	−0.965811	+	0.259248i	$0.916525\pi$
$62$	−24.7873	−	37.9656i	−0.399796	−	0.612349i
$63$		0			0
$64$	−60.5710	+	20.6676i	−0.946422	+	0.322932i
$65$	−54.6943	+	94.7333i	−0.841450	+	1.45743i
$66$	11.4144	+	5.78085i	0.172946	+	0.0875886i
$67$	−57.2613	−	99.1794i	−0.854646	−	1.48029i	−0.876973	−	0.480539i	$-0.840441\pi$
$67$	−57.2613	−	99.1794i	−0.854646	−	1.48029i	0.0223272	−	0.999751i	$-0.492892\pi$
$68$	76.3807	+	104.055i	1.12325	+	1.53023i
$69$			72.5739i			1.05180i
$70$		0			0
$71$			104.792i			1.47594i	0.674834	+	0.737969i	$0.264215\pi$
$71$			104.792i			1.47594i	−0.674834	+	0.737969i	$0.735785\pi$
$72$	−88.8385	−	33.3565i	−1.23387	−	0.463285i
$73$	−12.1987	−	21.1288i	−0.167106	−	0.289435i	0.770295	−	0.637687i	$-0.220109\pi$
$73$	−12.1987	−	21.1288i	−0.167106	−	0.289435i	−0.937401	+	0.348252i	$0.886775\pi$
$74$	−48.9345	+	96.6226i	−0.661277	+	1.30571i
$75$	−17.9543	+	31.0977i	−0.239390	+	0.414636i
$76$	−20.2218	+	46.0232i	−0.266077	+	0.605569i
$77$		0			0
$78$	−95.2952	−	145.959i	−1.22173	−	1.87127i
$79$	101.436	+	58.5639i	1.28400	+	0.741315i	0.977576	−	0.210581i	$-0.0675356\pi$
$79$	101.436	+	58.5639i	1.28400	+	0.741315i	0.306420	+	0.951897i	$0.400869\pi$
$80$	−87.5042	−	27.4889i	−1.09380	−	0.343611i
$81$	23.5270	+	40.7499i	0.290456	+	0.503085i
$82$	−0.832178	−	15.1693i	−0.0101485	−	0.184992i
$83$	−79.2706			−0.955067			−0.477534	−	0.878614i	$-0.658469\pi$
$83$	−79.2706			−0.955067			−0.477534	+	0.878614i	$0.658469\pi$
$84$		0			0
$85$			184.988i			2.17633i
$86$	2.28396	+	41.6331i	0.0265577	+	0.484106i
$87$	−13.0214	+	7.51793i	−0.149672	+	0.0864130i
$88$	−8.65611	+	7.11531i	−0.0983649	+	0.0808558i
$89$	1.33039	−	2.30431i	0.0149482	−	0.0258911i	−0.858455	−	0.512890i	$-0.828575\pi$
$89$	1.33039	−	2.30431i	0.0149482	−	0.0258911i	0.873403	+	0.486999i	$0.161908\pi$
$90$	−74.3473	−	113.874i	−0.826081	−	1.26527i
$91$		0			0
$92$	−58.1880	−	25.5669i	−0.632479	−	0.277901i
$93$	89.6741	+	51.7734i	0.964238	+	0.556703i
$94$	−19.5530	+	38.6079i	−0.208010	+	0.410722i
$95$	−62.3913	+	36.0216i	−0.656751	+	0.379175i
$96$	102.079	−	104.605i	1.06333	−	1.08964i
$97$	52.0930			0.537042			0.268521	−	0.963274i	$-0.413465\pi$
$97$	52.0930			0.537042			0.268521	+	0.963274i	$0.413465\pi$
$98$		0			0
$99$	−16.6142			−0.167820
$100$	−18.6084	−	25.3506i	−0.186084	−	0.253506i
$101$	79.2189	−	45.7371i	0.784346	−	0.452842i	−0.0536223	−	0.998561i	$-0.517077\pi$
$101$	79.2189	−	45.7371i	0.784346	−	0.452842i	0.837968	+	0.545719i	$0.183743\pi$
$102$	−262.980	−	133.187i	−2.57824	−	1.30575i
$103$	−34.4584	−	19.8946i	−0.334548	−	0.193151i	0.323311	−	0.946293i	$-0.395204\pi$
$103$	−34.4584	−	19.8946i	−0.334548	−	0.193151i	−0.657858	+	0.753142i	$0.728537\pi$
$104$	150.598	−	24.9858i	1.44806	−	0.240248i
$105$		0			0
$106$	0.389971	+	0.597301i	0.00367897	+	0.00563492i
$107$	−41.3316	+	71.5884i	−0.386276	+	0.669050i	−0.991945	−	0.126667i	$-0.959572\pi$
$107$	−41.3316	+	71.5884i	−0.386276	+	0.669050i	0.605669	+	0.795717i	$0.292906\pi$
$108$	51.9710	−	5.71939i	0.481213	−	0.0529573i
$109$	25.5234	−	14.7359i	0.234160	−	0.135192i	−0.378330	−	0.925671i	$-0.623501\pi$
$109$	25.5234	−	14.7359i	0.234160	−	0.135192i	0.612490	+	0.790479i	$0.290168\pi$
$110$	−16.0344	+	0.879633i	−0.145767	+	0.00799666i
$111$		−	247.346i		−	2.22834i
$112$		0			0
$113$	159.133			1.40826			0.704130	−	0.710071i	$-0.251337\pi$
$113$	159.133			1.40826			0.704130	+	0.710071i	$0.251337\pi$
$114$	−6.28856	−	114.631i	−0.0551628	−	1.00553i
$115$	−45.5428	−	78.8825i	−0.396025	−	0.685935i
$116$	−1.44041	−	13.0887i	−0.0124174	−	0.112834i
$117$	196.023	+	113.174i	1.67541	+	0.967299i
$118$	44.9789	−	29.3662i	0.381177	−	0.248866i
$119$		0			0
$120$	206.640	−	34.2838i	1.72200	−	0.285698i
$121$	59.5191	−	103.090i	0.491893	−	0.851984i
$122$	−77.9182	+	153.852i	−0.638674	+	1.26108i
$123$	17.3474	+	30.0466i	0.141036	+	0.244281i
$124$	−73.1017	+	53.6595i	−0.589530	+	0.432738i
$125$			98.2451i			0.785961i
$126$		0			0
$127$		−	16.0834i		−	0.126641i	−0.997993	−	0.0633205i	$-0.979831\pi$
$127$		−	16.0834i		−	0.126641i	0.997993	−	0.0633205i	$-0.0201690\pi$
$128$	47.9090	+	118.696i	0.374289	+	0.927312i
$129$	−47.6110	−	82.4646i	−0.369077	−	0.639260i
$130$	195.174	+	98.8459i	1.50134	+	0.760353i
$131$	−59.0678	+	102.308i	−0.450899	+	0.780981i	−0.998442	−	0.0557972i	$-0.982230\pi$
$131$	−59.0678	+	102.308i	−0.450899	+	0.780981i	0.547543	+	0.836778i	$0.315563\pi$
$132$	10.2938	−	23.4279i	0.0779836	−	0.177484i
$133$		0			0
$134$	−191.788	+	125.216i	−1.43125	+	0.934448i
$135$	64.8920	+	37.4654i	0.480681	+	0.277522i
$136$	199.431	−	163.932i	1.46640	−	1.20538i
$137$	9.58539	+	16.6024i	0.0699664	+	0.121185i	0.898886	−	0.438182i	$-0.144377\pi$
$137$	9.58539	+	16.6024i	0.0699664	+	0.121185i	−0.828920	+	0.559367i	$0.811044\pi$
$138$	144.930	−	7.95074i	1.05022	−	0.0576141i
$139$	−104.954			−0.755062			−0.377531	−	0.925997i	$-0.623227\pi$
$139$	−104.954			−0.755062			−0.377531	+	0.925997i	$0.623227\pi$
$140$		0			0
$141$		−	98.8329i		−	0.700942i
$142$	209.269	−	11.4803i	1.47372	−	0.0808473i
$143$	23.1465	−	13.3636i	0.161864	−	0.0934520i
$144$	−56.8803	+	181.065i	−0.395002	+	1.25739i
$145$	9.43556	−	16.3429i	0.0650729	−	0.112709i
$146$	−40.8577	+	26.6755i	−0.279847	+	0.182709i
$147$		0			0
$148$	198.316	+	87.1367i	1.33997	+	0.588762i
$149$	−71.3523	−	41.1953i	−0.478875	−	0.276478i	0.241073	−	0.970507i	$-0.422501\pi$
$149$	−71.3523	−	41.1953i	−0.478875	−	0.276478i	−0.719947	+	0.694029i	$0.755834\pi$
$150$	64.0690	+	32.4478i	0.427127	+	0.216318i
$151$	50.0038	−	28.8697i	0.331151	−	0.191190i	−0.325201	−	0.945645i	$-0.605432\pi$
$151$	50.0038	−	28.8697i	0.331151	−	0.191190i	0.656352	+	0.754455i	$0.272099\pi$
$152$	94.1237	+	35.3410i	0.619235	+	0.232506i
$153$	382.779			2.50182
$154$		0			0
$155$	−129.959			−0.838445
$156$	−281.041	+	206.295i	−1.80154	+	1.32240i
$157$	3.23006	−	1.86488i	0.0205736	−	0.0118782i	−0.489678	−	0.871903i	$-0.662886\pi$
$157$	3.23006	−	1.86488i	0.0205736	−	0.0118782i	0.510252	+	0.860025i	$0.329552\pi$
$158$	105.839	−	208.983i	0.669869	−	1.32268i
$159$	−1.41081	−	0.814534i	−0.00887305	−	0.00512286i
$160$	−45.3088	+	177.757i	−0.283180	+	1.11098i
$161$		0			0
$162$	78.8000	−	51.4476i	0.486420	−	0.317578i
$163$	−38.8534	+	67.2961i	−0.238365	+	0.412860i	−0.960245	−	0.279158i	$-0.909945\pi$
$163$	−38.8534	+	67.2961i	−0.238365	+	0.412860i	0.721881	+	0.692018i	$0.243278\pi$
$164$	−30.2019	+	3.32371i	−0.184158	+	0.0202665i
$165$	31.7600	−	18.3367i	0.192485	−	0.111131i
$166$	8.68439	+	158.303i	0.0523156	+	0.953633i
$167$			62.0837i			0.371759i	0.982573	+	0.185879i	$0.0595133\pi$
$167$			62.0837i			0.371759i	−0.982573	+	0.185879i	$0.940487\pi$
$168$		0			0
$169$	−195.127			−1.15459
$170$	369.420	−	20.2661i	2.17306	−	0.119212i
$171$	74.5364	+	129.101i	0.435885	+	0.754976i
$172$	82.8909	−	9.12212i	0.481924	−	0.0530356i
$173$	169.407	+	97.8069i	0.979228	+	0.565358i	0.902037	−	0.431659i	$-0.142071\pi$
$173$	169.407	+	97.8069i	0.979228	+	0.565358i	0.0771913	+	0.997016i	$0.475405\pi$
$174$	16.4398	+	25.1801i	0.0944818	+	0.144713i
$175$		0			0
$176$	15.1576	+	16.5067i	0.0861225	+	0.0937882i
$177$	−61.3373	+	106.239i	−0.346538	+	0.600222i
$178$	−4.74744	−	2.40434i	−0.0266710	−	0.0135075i
$179$	−36.1049	−	62.5356i	−0.201704	−	0.349361i	0.747374	−	0.664404i	$-0.231314\pi$
$179$	−36.1049	−	62.5356i	−0.201704	−	0.349361i	−0.949077	+	0.315043i	$0.897981\pi$
$180$	−219.262	+	160.947i	−1.21812	+	0.894149i
$181$		−	140.980i		−	0.778895i	−0.921049	−	0.389448i	$-0.872666\pi$
$181$		−	140.980i		−	0.778895i	0.921049	−	0.389448i	$-0.127334\pi$
$182$		0			0
$183$		−	393.847i		−	2.15217i
$184$	−44.6822	+	119.002i	−0.242838	+	0.646752i
$185$	155.219	+	268.847i	0.839020	+	1.45323i
$186$	93.5672	−	184.751i	0.503049	−	0.993285i
$187$	22.5994	−	39.1432i	0.120852	−	0.209322i
$188$	79.2419	+	34.8176i	0.421499	+	0.185200i
$189$		0			0
$190$	78.7703	+	120.649i	0.414581	+	0.634995i
$191$	−246.361	−	142.236i	−1.28985	−	0.744693i	−0.311219	−	0.950338i	$-0.600737\pi$
$191$	−246.361	−	142.236i	−1.28985	−	0.744693i	−0.978627	+	0.205645i	$0.934071\pi$
$192$	−220.080	−	192.392i	−1.14625	−	1.00204i
$193$	61.9251	+	107.257i	0.320855	+	0.555738i	0.980665	−	0.195695i	$-0.0626964\pi$
$193$	61.9251	+	107.257i	0.320855	+	0.555738i	−0.659810	+	0.751433i	$0.729363\pi$
$194$	−5.70699	−	104.030i	−0.0294175	−	0.536235i
$195$	−499.629			−2.56220
$196$		0			0
$197$		−	108.098i		−	0.548721i	−0.961627	−	0.274361i	$-0.911534\pi$
$197$		−	108.098i		−	0.548721i	0.961627	−	0.274361i	$-0.0884662\pi$
$198$	1.82015	+	33.1785i	0.00919266	+	0.167568i
$199$	287.394	−	165.927i	1.44419	−	0.833804i	0.446065	−	0.895000i	$-0.352825\pi$
$199$	287.394	−	165.927i	1.44419	−	0.833804i	0.998126	+	0.0611961i	$0.0194915\pi$
$200$	−48.5865	+	39.9381i	−0.242933	+	0.199690i
$201$	261.539	−	452.999i	1.30119	−	2.25373i
$202$	−100.016	−	153.189i	−0.495127	−	0.758363i
$203$		0			0
$204$	−237.163	+	539.762i	−1.16256	+	2.64589i
$205$	−37.7107	−	21.7723i	−0.183955	−	0.106206i
$206$	−35.9543	+	70.9928i	−0.174536	+	0.344625i
$207$	−163.225	+	94.2378i	−0.788525	+	0.455255i
$208$	−66.3952	−	298.007i	−0.319208	−	1.43273i
$209$	17.6026			0.0842229
$210$		0			0
$211$	26.3950			0.125095			0.0625475	−	0.998042i	$-0.480078\pi$
$211$	26.3950			0.125095			0.0625475	+	0.998042i	$0.480078\pi$
$212$	1.15009	−	0.844208i	0.00542494	−	0.00398211i
$213$	−414.508	+	239.316i	−1.94605	+	1.12355i
$214$	147.490	+	74.6962i	0.689205	+	0.349048i
$215$	103.499	+	59.7553i	0.481392	+	0.277932i
$216$	−17.1152	−	103.159i	−0.0792371	−	0.477589i
$217$		0			0
$218$	−32.2238	−	49.3558i	−0.147816	−	0.226403i
$219$	55.7172	−	96.5051i	0.254417	−	0.440663i
$220$	3.51325	+	31.9242i	0.0159693	+	0.145110i
$221$	−533.279	+	307.889i	−2.41303	+	1.39316i
$222$	−493.949	+	27.0976i	−2.22499	+	0.122061i
$223$		−	161.183i		−	0.722796i	−0.932412	−	0.361398i	$-0.882300\pi$
$223$		−	161.183i		−	0.722796i	0.932412	−	0.361398i	$-0.117700\pi$
$224$		0			0
$225$	−93.2551			−0.414467
$226$	−17.4337	−	317.789i	−0.0771401	−	1.40615i
$227$	−85.6395	−	148.332i	−0.377266	−	0.653445i	0.613397	−	0.789775i	$-0.289803\pi$
$227$	−85.6395	−	148.332i	−0.377266	−	0.653445i	−0.990663	+	0.136330i	$0.956469\pi$
$228$	−228.228	+	25.1165i	−1.00100	+	0.110160i
$229$	−198.537	−	114.626i	−0.866975	−	0.500548i	−0.000632973	−	1.00000i	$-0.500201\pi$
$229$	−198.537	−	114.626i	−0.866975	−	0.500548i	−0.866342	+	0.499452i	$0.833535\pi$
$230$	−152.539	+	99.5908i	−0.663212	+	0.433003i
$231$		0			0
$232$	−25.9804	+	4.31042i	−0.111984	+	0.0185794i
$233$	135.077	−	233.961i	0.579730	−	1.00412i	−0.415780	−	0.909465i	$-0.636491\pi$
$233$	135.077	−	233.961i	0.579730	−	1.00412i	0.995510	−	0.0946571i	$-0.0301755\pi$
$234$	204.533	−	403.856i	0.874073	−	1.72588i
$235$	62.0214	+	107.424i	0.263921	+	0.457124i
$236$	−63.5718	−	86.6056i	−0.269372	−	0.366973i
$237$			534.978i			2.25729i
$238$		0			0
$239$			157.155i			0.657551i	0.944408	+	0.328776i	$0.106636\pi$
$239$			157.155i			0.657551i	−0.944408	+	0.328776i	$0.893364\pi$
$240$	−91.1029	−	408.904i	−0.379595	−	1.70377i
$241$	−48.8562	−	84.6214i	−0.202723	−	0.351126i	0.746682	−	0.665181i	$-0.231646\pi$
$241$	−48.8562	−	84.6214i	−0.202723	−	0.351126i	−0.949405	+	0.314055i	$0.898312\pi$
$242$	−212.391	−	107.566i	−0.877649	−	0.444486i
$243$	−166.279	+	288.004i	−0.684276	+	1.18520i
$244$	315.778	+	138.747i	1.29417	+	0.568637i
$245$		0			0
$246$	58.1025	−	37.9345i	0.236189	−	0.154205i
$247$	−207.685	−	119.907i	−0.840829	−	0.485453i
$248$	115.166	+	140.105i	0.464381	+	0.564941i
$249$	−181.033	−	313.558i	−0.727040	−	1.25927i
$250$	196.195	−	10.7631i	0.784781	−	0.0430525i
$251$	313.145			1.24759			0.623796	−	0.781587i	$-0.285590\pi$
$251$	313.145			1.24759			0.623796	+	0.781587i	$0.285590\pi$
$252$		0			0
$253$			22.2553i			0.0879655i
$254$	−32.1185	+	1.76200i	−0.126451	+	0.00693700i
$255$	−731.728	+	422.463i	−2.86952	+	1.65672i
$256$	231.787	−	108.678i	0.905417	−	0.424523i
$257$	−174.428	+	302.118i	−0.678707	+	1.17555i	0.296664	+	0.954982i	$0.404126\pi$
$257$	−174.428	+	302.118i	−0.678707	+	1.17555i	−0.975371	+	0.220573i	$0.929207\pi$
$258$	−159.466	+	104.113i	−0.618084	+	0.403540i
$259$		0			0
$260$	176.013	−	400.591i	0.676973	−	1.54073i
$261$	−33.8169	−	19.5242i	−0.129567	−	0.0748053i
$262$	210.781	+	106.750i	0.804507	+	0.407443i
$263$	332.869	−	192.182i	1.26566	−	0.730729i	0.291496	−	0.956572i	$-0.405847\pi$
$263$	332.869	−	192.182i	1.26566	−	0.730729i	0.974164	+	0.225843i	$0.0725135\pi$
$264$	−47.9132	−	17.9901i	−0.181489	−	0.0681445i
$265$	2.04460			0.00771548
$266$		0			0
$267$	12.1530			0.0455170
$268$	271.067	+	369.282i	1.01145	+	1.37792i
$269$	−32.7022	+	18.8806i	−0.121570	+	0.0701882i	−0.559552	−	0.828795i	$-0.689027\pi$
$269$	−32.7022	+	18.8806i	−0.121570	+	0.0701882i	0.437982	+	0.898984i	$0.355693\pi$
$270$	67.7092	−	133.694i	0.250775	−	0.495161i
$271$	−267.368	−	154.365i	−0.986597	−	0.569612i	−0.0823420	−	0.996604i	$-0.526240\pi$
$271$	−267.368	−	154.365i	−0.986597	−	0.569612i	−0.904255	+	0.426992i	$0.859573\pi$
$272$	−349.219	−	380.303i	−1.28389	−	1.39817i
$273$		0			0
$274$	32.1048	−	20.9609i	0.117171	−	0.0764995i
$275$	−5.50580	+	9.53633i	−0.0200211	+	0.0346775i
$276$	−31.7552	−	288.553i	−0.115055	−	1.04548i
$277$	211.492	−	122.105i	0.763508	−	0.440812i	−0.0670458	−	0.997750i	$-0.521357\pi$
$277$	211.492	−	122.105i	0.763508	−	0.440812i	0.830554	+	0.556938i	$0.188024\pi$
$278$	11.4981	+	209.592i	0.0413600	+	0.753929i
$279$			268.913i			0.963845i
$280$		0			0
$281$	266.569			0.948646			0.474323	−	0.880351i	$-0.342693\pi$
$281$	266.569			0.948646			0.474323	+	0.880351i	$0.342693\pi$
$282$	−197.369	+	10.8275i	−0.699890	+	0.0383954i
$283$	82.8026	+	143.418i	0.292589	+	0.506778i	0.974421	−	0.224730i	$-0.0721501\pi$
$283$	82.8026	+	143.418i	0.292589	+	0.506778i	−0.681833	+	0.731508i	$0.738817\pi$
$284$	−45.8523	−	416.651i	−0.161452	−	1.46708i
$285$	−284.971	−	164.528i	−0.999897	−	0.577291i
$286$	−29.2229	−	44.7595i	−0.102178	−	0.156502i
$287$		0			0
$288$	367.817	+	93.7535i	1.27714	+	0.325533i
$289$	−376.173	+	651.550i	−1.30164	+	2.25450i
$290$	−33.6704	−	17.0524i	−0.116105	−	0.0588013i
$291$	118.967	+	206.056i	0.408820	+	0.708098i
$292$	57.7471	+	78.6703i	0.197764	+	0.269419i
$293$		−	34.3652i		−	0.117288i	−0.998279	−	0.0586438i	$-0.981322\pi$
$293$		−	34.3652i		−	0.117288i	0.998279	−	0.0586438i	$-0.0186776\pi$
$294$		0			0
$295$		−	153.966i		−	0.521918i
$296$	152.286	−	405.583i	0.514478	−	1.37021i
$297$	−9.15405	−	15.8553i	−0.0308217	−	0.0533848i
$298$	−74.4500	+	147.004i	−0.249832	+	0.493300i
$299$	151.600	−	262.580i	0.507025	−	0.878193i
$300$	57.7791	−	131.500i	0.192597	−	0.438335i
$301$		0			0
$302$	−63.1309	−	96.6947i	−0.209043	−	0.320181i
$303$	361.830	+	208.903i	1.19416	+	0.689448i
$304$	60.2642	−	191.836i	0.198237	−	0.631041i
$305$	247.154	+	428.083i	0.810341	+	1.40355i
$306$	−41.9349	−	764.408i	−0.137042	−	2.49807i
$307$	222.934			0.726170			0.363085	−	0.931756i	$-0.381724\pi$
$307$	222.934			0.726170			0.363085	+	0.931756i	$0.381724\pi$
$308$		0			0
$309$		−	181.736i		−	0.588141i
$310$	14.2375	+	259.528i	0.0459274	+	0.837186i
$311$	−363.673	+	209.967i	−1.16937	+	0.675135i	−0.953531	−	0.301294i	$-0.902581\pi$
$311$	−363.673	+	209.967i	−1.16937	+	0.675135i	−0.215837	+	0.976429i	$0.569248\pi$
$312$	442.759	+	538.637i	1.41910	+	1.72640i
$313$	−146.934	+	254.498i	−0.469439	+	0.813092i	−0.999390	−	0.0349363i	$-0.988877\pi$
$313$	−146.934	+	254.498i	−0.469439	+	0.813092i	0.529950	+	0.848029i	$0.322211\pi$
$314$	−4.07802	−	6.24612i	−0.0129873	−	0.0198921i
$315$		0			0
$316$	−428.933	−	188.466i	−1.35738	−	0.596411i
$317$	−366.728	−	211.730i	−1.15687	−	0.667919i	−0.206318	−	0.978485i	$-0.566148\pi$
$317$	−366.728	−	211.730i	−1.15687	−	0.667919i	−0.950552	+	0.310566i	$0.899481\pi$
$318$	−1.47206	+	2.90663i	−0.00462913	+	0.00914034i
$319$	−3.99311	+	2.30542i	−0.0125176	+	0.00722703i
$320$	359.944	+	71.0076i	1.12483	+	0.221899i
$321$	−377.561			−1.17620
$322$		0			0
$323$	−405.551			−1.25558
$324$	−111.374	−	151.727i	−0.343745	−	0.468293i
$325$	129.921	−	75.0098i	0.399756	−	0.230799i
$326$	138.647	+	70.2177i	0.425297	+	0.215392i
$327$	116.577	+	67.3060i	0.356506	+	0.205829i
$328$	9.94618	+	59.9491i	0.0303237	+	0.182772i
$329$		0			0
$330$	−40.0977	−	61.4158i	−0.121508	−	0.186109i
$331$	63.3332	−	109.696i	0.191339	−	0.331409i	−0.754355	−	0.656467i	$-0.772050\pi$
$331$	63.3332	−	109.696i	0.191339	−	0.331409i	0.945694	+	0.325057i	$0.105384\pi$
$332$	315.179	−	34.6854i	0.949336	−	0.104474i
$333$	556.301	−	321.180i	1.67057	−	0.964505i
$334$	123.981	−	6.80150i	0.371200	−	0.0203638i
$335$			656.503i			1.95971i
$336$		0			0
$337$	302.404			0.897341			0.448671	−	0.893697i	$-0.351898\pi$
$337$	302.404			0.897341			0.448671	+	0.893697i	$0.351898\pi$
$338$	21.3768	+	389.667i	0.0632451	+	1.15286i
$339$	363.419	+	629.460i	1.07203	+	1.85681i
$340$	−80.9427	−	735.511i	−0.238067	−	2.16327i
$341$	27.4992	+	15.8767i	0.0806428	+	0.0465591i
$342$	249.648	−	162.992i	0.729966	−	0.476586i
$343$		0			0
$344$	−27.2979	−	164.534i	−0.0793542	−	0.478295i
$345$	208.016	−	360.294i	0.602944	−	1.04433i
$346$	176.761	−	349.019i	0.510870	−	1.00873i
$347$	−160.266	−	277.589i	−0.461862	−	0.799969i	0.537192	−	0.843460i	$-0.319485\pi$
$347$	−160.266	−	277.589i	−0.461862	−	0.799969i	−0.999054	+	0.0434916i	$0.986152\pi$
$348$	48.4836	−	35.5889i	0.139321	−	0.102267i
$349$		−	380.678i		−	1.09077i	−0.838186	−	0.545385i	$-0.816384\pi$
$349$		−	380.678i		−	1.09077i	0.838186	−	0.545385i	$-0.183616\pi$
$350$		0			0
$351$			249.426i			0.710614i
$352$	31.3033	−	32.0780i	0.0889298	−	0.0911307i
$353$	−182.185	−	315.553i	−0.516104	−	0.893918i	−0.999825	−	0.0186962i	$-0.994048\pi$
$353$	−182.185	−	315.553i	−0.516104	−	0.893918i	0.483721	−	0.875222i	$-0.339285\pi$
$354$	218.879	+	110.852i	0.618303	+	0.313140i
$355$	300.360	−	520.239i	0.846085	−	1.46546i
$356$	−4.28137	+	9.74403i	−0.0120263	+	0.0273709i
$357$		0			0
$358$	−120.928	+	78.9525i	−0.337788	+	0.220538i
$359$	−96.9908	−	55.9977i	−0.270169	−	0.155982i	0.358795	−	0.933416i	$-0.383188\pi$
$359$	−96.9908	−	55.9977i	−0.270169	−	0.155982i	−0.628965	+	0.777434i	$0.716521\pi$
$360$	345.431	+	420.233i	0.959531	+	1.16731i
$361$	101.529	+	175.854i	0.281245	+	0.487130i
$362$	−281.537	+	15.4449i	−0.777726	+	0.0426655i
$363$	543.704			1.49781
$364$		0			0
$365$			139.859i			0.383174i
$366$	−786.512	+	43.1475i	−2.14894	+	0.117889i
$367$	380.222	−	219.521i	1.03603	−	0.598150i	0.117321	−	0.993094i	$-0.462569\pi$
$367$	380.222	−	219.521i	1.03603	−	0.598150i	0.918705	+	0.394944i	$0.129236\pi$
$368$	242.542	+	76.1931i	0.659082	+	0.207047i
$369$	−45.0515	+	78.0315i	−0.122091	+	0.211468i
$370$	519.881	−	339.424i	1.40508	−	0.917363i
$371$		0			0
$372$	−379.198	−	166.613i	−1.01935	−	0.447885i
$373$	220.833	+	127.498i	0.592047	+	0.341818i	0.765906	−	0.642952i	$-0.222291\pi$
$373$	220.833	+	127.498i	0.592047	+	0.341818i	−0.173860	+	0.984770i	$0.555624\pi$
$374$	−80.6448	−	40.8426i	−0.215628	−	0.109205i
$375$	−388.613	+	224.366i	−1.03630	+	0.598309i
$376$	60.8493	−	162.060i	0.161833	−	0.431011i
$377$	62.8172			0.166624
$378$		0			0
$379$	603.048			1.59116			0.795578	−	0.605852i	$-0.207167\pi$
$379$	603.048			1.59116			0.795578	+	0.605852i	$0.207167\pi$
$380$	232.306	−	170.522i	0.611332	−	0.448741i
$381$	63.6187	−	36.7303i	0.166978	−	0.0964049i
$382$	−257.056	+	507.564i	−0.672921	+	1.32870i
$383$	−63.5537	−	36.6927i	−0.165937	−	0.0958035i	0.414732	−	0.909944i	$-0.363875\pi$
$383$	−63.5537	−	36.6927i	−0.165937	−	0.0958035i	−0.580668	+	0.814140i	$0.697209\pi$
$384$	−360.096	+	460.577i	−0.937749	+	1.19942i
$385$		0			0
$386$	207.408	−	135.415i	0.537328	−	0.350815i
$387$	123.646	−	214.162i	0.319500	−	0.553390i
$388$	−207.122	+	22.7937i	−0.533819	+	0.0587466i
$389$	−295.141	+	170.400i	−0.758718	+	0.438046i	−0.828835	−	0.559493i	$-0.810996\pi$
$389$	−295.141	+	170.400i	−0.758718	+	0.438046i	0.0701174	+	0.997539i	$0.477663\pi$
$390$	54.7362	+	997.758i	0.140349	+	2.55835i
$391$		−	512.745i		−	1.31137i
$392$		0			0
$393$	−539.581			−1.37298
$394$	−215.872	+	11.8426i	−0.547898	+	0.0300572i
$395$	−335.719	−	581.482i	−0.849921	−	1.47211i
$396$	66.0579	−	7.26966i	0.166813	−	0.0183577i
$397$	96.5963	+	55.7699i	0.243316	+	0.140478i	0.616700	−	0.787199i	$-0.288469\pi$
$397$	96.5963	+	55.7699i	0.243316	+	0.140478i	−0.373384	+	0.927677i	$0.621803\pi$
$398$	−362.841	−	555.747i	−0.911661	−	1.39635i
$399$		0			0
$400$	85.0791	+	92.6518i	0.212698	+	0.231630i
$401$	−170.268	+	294.912i	−0.424607	+	0.735441i	−0.996384	−	0.0849681i	$-0.972921\pi$
$401$	−170.268	+	294.912i	−0.424607	+	0.735441i	0.571776	+	0.820410i	$0.306254\pi$
$402$	−933.291	−	472.665i	−2.32162	−	1.17578i
$403$	−216.300	−	374.643i	−0.536725	−	0.929635i
$404$	−294.962	+	216.513i	−0.730103	+	0.535924i
$405$		−	269.738i		−	0.666019i
$406$		0			0
$407$		−	75.8502i		−	0.186364i
$408$	1103.89	+	414.480i	2.70560	+	1.01588i
$409$	333.480	+	577.604i	0.815354	+	1.41223i	0.909074	+	0.416635i	$0.136791\pi$
$409$	333.480	+	577.604i	0.815354	+	1.41223i	−0.0937202	+	0.995599i	$0.529876\pi$
$410$	−39.3479	+	77.6935i	−0.0959705	+	0.189496i
$411$	−43.7810	+	75.8309i	−0.106523	+	0.184503i
$412$	145.711	+	64.0232i	0.353669	+	0.155396i
$413$		0			0
$414$	206.074	+	315.635i	0.497764	+	0.762403i
$415$	393.539	+	227.210i	0.948288	+	0.547494i
$416$	−587.845	+	165.239i	−1.41309	+	0.397209i
$417$	−239.686	−	415.149i	−0.574788	−	0.995561i
$418$	−1.92843	−	35.1523i	−0.00461347	−	0.0840965i
$419$	200.191			0.477783			0.238891	−	0.971046i	$-0.423216\pi$
$419$	200.191			0.477783			0.238891	+	0.971046i	$0.423216\pi$
$420$		0			0
$421$			15.9136i			0.0377996i	0.999821	+	0.0188998i	$0.00601636\pi$
$421$			15.9136i			0.0377996i	−0.999821	+	0.0188998i	$0.993984\pi$
$422$	−2.89167	−	52.7108i	−0.00685231	−	0.124907i
$423$	222.283	−	128.335i	0.525492	−	0.303393i
$424$	−1.81188	−	2.20423i	−0.00427330	−	0.00519866i
$425$	126.850	−	219.710i	0.298470	−	0.516965i
$426$	523.325	+	801.554i	1.22846	+	1.88158i
$427$		0			0
$428$	133.010	−	302.720i	0.310771	−	0.707290i
$429$	105.721	+	61.0380i	0.246436	+	0.142280i
$430$	107.993	−	213.234i	0.251145	−	0.495893i
$431$	−543.875	+	314.006i	−1.26189	+	0.728553i	−0.973440	−	0.228941i	$-0.926474\pi$
$431$	−543.875	+	314.006i	−1.26189	+	0.728553i	−0.288451	+	0.957495i	$0.593140\pi$
$432$	−204.134	+	45.4805i	−0.472532	+	0.105279i
$433$	−789.232			−1.82271			−0.911353	−	0.411625i	$-0.864961\pi$
$433$	−789.232			−1.82271			−0.911353	+	0.411625i	$0.864961\pi$
$434$		0			0
$435$	86.1933			0.198146
$436$	−95.0331	+	69.7580i	−0.217966	+	0.159995i
$437$	172.935	−	99.8441i	0.395732	−	0.228476i
$438$	−198.824	−	100.695i	−0.453937	−	0.229897i
$439$	576.400	+	332.785i	1.31298	+	0.758052i	0.982589	−	0.185791i	$-0.0594846\pi$
$439$	576.400	+	332.785i	1.31298	+	0.758052i	0.330395	+	0.943843i	$0.392818\pi$
$440$	63.3677	−	10.5134i	0.144017	−	0.0238940i
$441$		0			0
$442$	673.275	+	1031.23i	1.52325	+	2.33309i
$443$	−253.576	+	439.206i	−0.572406	+	0.991436i	0.423912	+	0.905703i	$0.360656\pi$
$443$	−253.576	+	439.206i	−0.572406	+	0.991436i	−0.996318	+	0.0857327i	$0.972677\pi$
$444$	108.228	+	983.445i	0.243756	+	2.21497i
$445$	−13.2095	+	7.62650i	−0.0296842	+	0.0171382i
$446$	−321.883	+	17.6583i	−0.721711	+	0.0395925i
$447$		−	376.317i		−	0.841872i
$448$		0			0
$449$	−279.029			−0.621446			−0.310723	−	0.950501i	$-0.600571\pi$
$449$	−279.029			−0.621446			−0.310723	+	0.950501i	$0.600571\pi$
$450$	10.2164	+	186.230i	0.0227032	+	0.413845i
$451$	5.31970	+	9.21400i	0.0117954	+	0.0204301i
$452$	−632.714	+	69.6300i	−1.39981	+	0.154049i
$453$	228.391	+	131.862i	0.504175	+	0.291085i
$454$	−286.836	+	187.272i	−0.631798	+	0.412494i
$455$		0			0
$456$	75.1608	+	453.020i	0.164826	+	0.993465i
$457$	360.441	−	624.302i	0.788710	−	1.36609i	−0.138047	−	0.990426i	$-0.544082\pi$
$457$	360.441	−	624.302i	0.788710	−	1.36609i	0.926757	−	0.375661i	$-0.122584\pi$
$458$	−207.156	+	409.036i	−0.452306	+	0.893091i
$459$	210.903	+	365.294i	0.459483	+	0.795848i
$460$	215.594	+	293.709i	0.468682	+	0.638498i
$461$		−	483.262i		−	1.04829i	−0.851629	−	0.524145i	$-0.824385\pi$
$461$		−	483.262i		−	1.04829i	0.851629	−	0.524145i	$-0.175615\pi$
$462$		0			0
$463$		−	39.6326i		−	0.0855995i	−0.999084	−	0.0427997i	$-0.986372\pi$
$463$		−	39.6326i		−	0.0855995i	0.999084	−	0.0427997i	$-0.0136277\pi$
$464$	11.4542	+	51.4106i	0.0246857	+	0.110799i
$465$	−296.792	−	514.059i	−0.638262	−	1.10550i
$466$	−482.017	−	244.118i	−1.03437	−	0.523857i
$467$	8.89340	−	15.4038i	0.0190437	−	0.0329846i	−0.856347	−	0.516402i	$-0.827271\pi$
$467$	8.89340	−	15.4038i	0.0190437	−	0.0329846i	0.875390	+	0.483417i	$0.160605\pi$
$468$	−828.907	−	364.208i	−1.77117	−	0.778222i
$469$		0			0
$470$	207.731	−	135.625i	0.441981	−	0.288564i
$471$	14.7532	+	8.51777i	0.0313232	+	0.0180844i
$472$	−165.987	+	136.441i	−0.351666	+	0.289069i
$473$	−14.6002	−	25.2883i	−0.0308673	−	0.0534637i
$474$	1068.35	−	58.6089i	2.25390	−	0.123647i
$475$	98.8029			0.208006
$476$		0			0
$477$		−	4.23072i		−	0.00886943i
$478$	313.837	−	17.2169i	0.656564	−	0.0360186i
$479$	579.039	−	334.308i	1.20885	−	0.697930i	0.246341	−	0.969183i	$-0.420772\pi$
$479$	579.039	−	334.308i	1.20885	−	0.697930i	0.962508	+	0.271254i	$0.0874382\pi$
$480$	−806.600	+	226.729i	−1.68042	+	0.472353i
$481$	−516.683	+	894.922i	−1.07419	+	1.86054i
$482$	−163.636	+	106.836i	−0.339494	+	0.221652i
$483$		0			0
$484$	−191.540	+	435.929i	−0.395744	+	0.900679i
$485$	−258.616	−	149.312i	−0.533230	−	0.307860i
$486$	593.359	+	300.507i	1.22090	+	0.618327i
$487$	362.418	−	209.242i	0.744185	−	0.429656i	−0.0794038	−	0.996843i	$-0.525302\pi$
$487$	362.418	−	209.242i	0.744185	−	0.429656i	0.823589	+	0.567187i	$0.191968\pi$
$488$	242.484	−	645.807i	0.496893	−	1.32338i
$489$	−354.924			−0.725816
$490$		0			0
$491$	381.031			0.776030			0.388015	−	0.921653i	$-0.373161\pi$
$491$	381.031			0.776030			0.388015	+	0.921653i	$0.373161\pi$
$492$	−82.1204	−	111.875i	−0.166911	−	0.227388i
$493$	91.9984	−	53.1153i	0.186609	−	0.107739i
$494$	−216.701	+	427.882i	−0.438666	+	0.866158i
$495$	82.4813	+	47.6206i	0.166629	+	0.0962032i
$496$	267.173	−	245.336i	0.538656	−	0.494629i
$497$		0			0
$498$	−606.342	+	395.874i	−1.21756	+	0.794928i
$499$	219.196	−	379.659i	0.439271	−	0.760839i	−0.558363	−	0.829597i	$-0.688570\pi$
$499$	219.196	−	379.659i	0.439271	−	0.760839i	0.997633	+	0.0687578i	$0.0219036\pi$
$500$	−42.9878	−	390.622i	−0.0859757	−	0.781244i
$501$	−245.575	+	141.783i	−0.490169	+	0.282999i
$502$	−34.3063	−	625.351i	−0.0683392	−	1.24572i
$503$			754.754i			1.50050i	0.661151	+	0.750252i	$0.270068\pi$
$503$			754.754i			1.50050i	−0.661151	+	0.750252i	$0.729932\pi$
$504$		0			0
$505$	−524.378			−1.03837
$506$	44.4437	−	2.43815i	0.0878334	−	0.00481848i
$507$	−445.617	−	771.832i	−0.878930	−	1.52235i
$508$	7.03741	+	63.9476i	0.0138532	+	0.125881i
$509$	427.842	+	247.015i	0.840554	+	0.485294i	0.857452	−	0.514563i	$-0.172046\pi$
$509$	427.842	+	247.015i	0.840554	+	0.485294i	−0.0168985	+	0.999857i	$0.505379\pi$
$510$	923.822	+	1414.98i	1.81141	+	2.77446i
$511$		0			0
$512$	−242.422	−	450.972i	−0.473481	−	0.880804i
$513$	−82.1358	+	142.263i	−0.160109	+	0.277317i
$514$	622.437	+	315.233i	1.21097	+	0.613295i
$515$	114.046	+	197.533i	0.221449	+	0.383560i
$516$	225.384	+	307.046i	0.436791	+	0.595051i
$517$		−	30.3078i		−	0.0586224i
$518$		0			0
$519$			893.460i			1.72150i
$520$	−819.262	−	307.611i	−1.57550	−	0.591560i
$521$	−16.4374	−	28.4704i	−0.0315496	−	0.0546456i	0.849819	−	0.527074i	$-0.176711\pi$
$521$	−16.4374	−	28.4704i	−0.0315496	−	0.0546456i	−0.881369	+	0.472428i	$0.843378\pi$
$522$	−35.2850	+	69.6711i	−0.0675957	+	0.133470i
$523$	−14.1377	+	24.4873i	−0.0270320	+	0.0468208i	−0.879225	−	0.476407i	$-0.841939\pi$
$523$	−14.1377	+	24.4873i	−0.0270320	+	0.0468208i	0.852193	+	0.523228i	$0.175272\pi$
$524$	190.088	−	432.624i	0.362763	−	0.825617i
$525$		0			0
$526$	−420.254	−	643.684i	−0.798961	−	1.22373i
$527$	−633.561	−	365.787i	−1.20220	−	0.694093i
$528$	−30.6772	+	97.6534i	−0.0581008	+	0.184950i
$529$	−138.265	−	239.482i	−0.261371	−	0.452708i
$530$	−0.223994	−	4.08307i	−0.000422630	−	0.00770390i
$531$	−318.588			−0.599977
$532$		0			0
$533$		−	144.949i		−	0.271949i
$534$	−1.33141	−	24.2696i	−0.00249328	−	0.0454487i
$535$	410.382	−	236.934i	0.767069	−	0.442867i
$536$	707.759	−	581.777i	1.32045	−	1.08540i
$537$	164.908	−	285.629i	0.307092	−	0.531898i
$538$	41.2872	+	63.2378i	0.0767420	+	0.117542i
$539$		0			0
$540$	−274.404	−	120.568i	−0.508155	−	0.223275i
$541$	928.028	+	535.797i	1.71539	+	0.990383i	0.926873	+	0.375375i	$0.122486\pi$
$541$	928.028	+	535.797i	1.71539	+	0.990383i	0.788521	+	0.615008i	$0.210847\pi$
$542$	−278.975	+	550.844i	−0.514714	+	1.01632i
$543$	557.653	−	321.961i	1.02699	−	0.592930i
$544$	−721.205	+	739.054i	−1.32575	+	1.35855i
$545$	−168.948			−0.309997
$546$		0			0
$547$	−986.888			−1.80418			−0.902091	−	0.431545i	$-0.857968\pi$
$547$	−986.888			−1.80418			−0.902091	+	0.431545i	$0.857968\pi$
$548$	−45.3760	−	61.8169i	−0.0828029	−	0.112805i
$549$	885.795	−	511.414i	1.61347	−	0.931537i
$550$	19.6472	+	9.95033i	0.0357222	+	0.0180915i
$551$	35.8287	+	20.6857i	0.0650248	+	0.0375421i
$552$	−572.761	+	95.0272i	−1.03761	+	0.172151i
$553$		0			0
$554$	−267.013	−	408.971i	−0.481972	−	0.738215i
$555$	−708.957	+	1227.95i	−1.27740	+	2.21252i
$556$	417.295	−	45.9232i	0.750531	−	0.0825957i
$557$	418.767	−	241.775i	0.751826	−	0.434067i	−0.0745276	−	0.997219i	$-0.523745\pi$
$557$	418.767	−	241.775i	0.751826	−	0.434067i	0.826353	+	0.563152i	$0.190412\pi$
$558$	537.018	−	29.4604i	0.962397	−	0.0527964i
$559$			397.821i			0.711665i
$560$		0			0
$561$	206.444			0.367993
$562$	−29.2037	−	532.338i	−0.0519639	−	0.947221i
$563$	260.447	+	451.107i	0.462605	+	0.801256i	0.999090	−	0.0426543i	$-0.0135814\pi$
$563$	260.447	+	451.107i	0.462605	+	0.801256i	−0.536485	+	0.843910i	$0.680248\pi$
$564$	43.2450	+	392.959i	0.0766756	+	0.696736i
$565$	−790.020	−	456.118i	−1.39826	−	0.807289i
$566$	277.334	−	181.068i	0.489990	−	0.319909i
$567$		0			0
$568$	−827.028	+	137.213i	−1.45603	+	0.241572i
$569$	366.480	−	634.761i	0.644077	−	1.11557i	−0.340437	−	0.940267i	$-0.610575\pi$
$569$	366.480	−	634.761i	0.644077	−	1.11557i	0.984514	−	0.175306i	$-0.0560916\pi$
$570$	−297.342	+	587.110i	−0.521653	+	1.03002i
$571$	499.792	+	865.665i	0.875292	+	1.51605i	0.856451	+	0.516228i	$0.172664\pi$
$571$	499.792	+	865.665i	0.875292	+	1.51605i	0.0188408	+	0.999822i	$0.494002\pi$
$572$	−86.1830	+	63.2617i	−0.150670	+	0.110597i
$573$		−	1299.32i		−	2.26758i
$574$		0			0
$575$			124.918i			0.217249i
$576$	146.930	−	744.801i	0.255086	−	1.29306i
$577$	232.929	+	403.445i	0.403690	+	0.699212i	0.994168	−	0.107842i	$-0.0343940\pi$
$577$	232.929	+	403.445i	0.403690	+	0.699212i	−0.590478	+	0.807054i	$0.701061\pi$
$578$	1342.36	+	679.836i	2.32241	+	1.17619i
$579$	−282.841	+	489.895i	−0.488499	+	0.846105i
$580$	−30.3648	+	69.1078i	−0.0523531	+	0.119151i
$581$		0			0
$582$	398.461	−	260.150i	0.684641	−	0.446994i
$583$	−0.432636	−	0.249782i	−0.000742086	−	0.000428443i
$584$	150.778	−	123.939i	0.258181	−	0.212225i
$585$	−648.772	−	1123.71i	−1.10901	−	1.92087i
$586$	−68.6273	+	3.76484i	−0.117111	+	0.00642465i
$587$	574.851			0.979303			0.489651	−	0.871918i	$-0.337124\pi$
$587$	574.851			0.979303			0.489651	+	0.871918i	$0.337124\pi$
$588$		0			0
$589$		−	284.911i		−	0.483719i
$590$	−307.469	+	16.8675i	−0.521135	+	0.0285891i
$591$	427.587	−	246.868i	0.723498	−	0.417712i
$592$	−826.631	−	259.681i	−1.39634	−	0.438650i
$593$	471.528	−	816.710i	0.795156	−	1.37725i	−0.127584	−	0.991828i	$-0.540722\pi$
$593$	471.528	−	816.710i	0.795156	−	1.37725i	0.922740	−	0.385423i	$-0.125945\pi$
$594$	−30.6601	+	20.0176i	−0.0516163	+	0.0336997i
$595$		0			0
$596$	301.722	+	132.572i	0.506245	+	0.222436i
$597$	1312.66	+	757.867i	2.19877	+	1.26946i
$598$	−540.979	−	273.979i	−0.904648	−	0.458159i
$599$	−8.02545	+	4.63349i	−0.0133981	+	0.00773538i	−0.506684	−	0.862132i	$-0.669129\pi$
$599$	−8.02545	+	4.63349i	−0.0133981	+	0.00773538i	0.493286	+	0.869867i	$0.335796\pi$
$600$	−268.936	−	100.978i	−0.448226	−	0.168297i
$601$	−57.7003			−0.0960072			−0.0480036	−	0.998847i	$-0.515286\pi$
$601$	−57.7003			−0.0960072			−0.0480036	+	0.998847i	$0.515286\pi$
$602$		0			0
$603$	1358.44			2.25281
$604$	−186.183	+	136.665i	−0.308250	+	0.226267i
$605$	−590.966	+	341.194i	−0.976804	+	0.563958i
$606$	377.538	−	745.460i	0.623001	−	1.23013i
$607$	887.396	+	512.339i	1.46194	+	0.844050i	0.999101	−	0.0423930i	$-0.0134982\pi$
$607$	887.396	+	512.339i	1.46194	+	0.844050i	0.462837	+	0.886443i	$0.346831\pi$
$608$	−389.699	−	99.3310i	−0.640952	−	0.163373i
$609$		0			0
$610$	827.805	−	540.464i	1.35706	−	0.886007i
$611$	−206.453	+	357.588i	−0.337894	+	0.585250i
$612$	−1521.93	+	167.488i	−2.48681	+	0.273673i
$613$	350.583	−	202.409i	0.571914	−	0.330195i	−0.186000	−	0.982550i	$-0.559552\pi$
$613$	350.583	−	202.409i	0.571914	−	0.330195i	0.757913	+	0.652355i	$0.226219\pi$
$614$	−24.4233	−	445.199i	−0.0397773	−	0.725079i
$615$		−	198.889i		−	0.323396i
$616$		0			0
$617$	894.209			1.44928			0.724642	−	0.689125i	$-0.242005\pi$
$617$	894.209			1.44928			0.724642	+	0.689125i	$0.242005\pi$
$618$	−362.926	+	19.9098i	−0.587258	+	0.0322166i
$619$	−389.694	−	674.970i	−0.629554	−	1.09042i	−0.987641	−	0.156731i	$-0.949904\pi$
$619$	−389.694	−	674.970i	−0.629554	−	1.09042i	0.358087	−	0.933688i	$-0.383429\pi$
$620$	516.716	−	56.8645i	0.833414	−	0.0917169i
$621$	−179.866	−	103.846i	−0.289640	−	0.167224i
$622$	459.145	+	703.252i	0.738176	+	1.13063i
$623$		0			0
$624$	1027.15	−	943.198i	1.64607	−	1.51154i
$625$	379.869	−	657.952i	0.607790	−	1.05272i
$626$	524.329	+	265.546i	0.837586	+	0.424196i
$627$	40.1997	+	69.6278i	0.0641143	+	0.111049i
$628$	−12.0267	+	8.82808i	−0.0191508	+	0.0140574i
$629$			1747.53i			2.77827i
$630$		0			0
$631$			780.191i			1.23644i	0.786007	+	0.618218i	$0.212145\pi$
$631$			780.191i			1.23644i	−0.786007	+	0.618218i	$0.787855\pi$
$632$	−329.375	+	877.225i	−0.521163	+	1.38801i
$633$	60.2793	+	104.407i	0.0952279	+	0.164940i
$634$	−382.648	+	755.550i	−0.603546	+	1.19172i
$635$	−46.0992	+	79.8462i	−0.0725972	+	0.125742i
$636$	5.96580	+	2.62127i	0.00938018	+	0.00412150i
$637$		0			0
$638$	5.04139	+	7.72166i	0.00790186	+	0.0121029i
$639$	−1076.48	−	621.509i	−1.68464	−	0.972627i
$640$	102.369	−	726.587i	0.159951	−	1.13529i
$641$	11.6570	+	20.1905i	0.0181856	+	0.0314984i	0.874975	−	0.484168i	$-0.160878\pi$
$641$	11.6570	+	20.1905i	0.0181856	+	0.0314984i	−0.856789	+	0.515667i	$0.827544\pi$
$642$	41.3633	+	753.989i	0.0644288	+	1.17444i
$643$	−530.706			−0.825360			−0.412680	−	0.910876i	$-0.635407\pi$
$643$	−530.706			−0.825360			−0.412680	+	0.910876i	$0.635407\pi$
$644$		0			0
$645$			545.862i			0.846297i
$646$	44.4296	+	809.884i	0.0687765	+	1.25369i
$647$	−184.840	+	106.717i	−0.285687	+	0.164942i	−0.635995	−	0.771693i	$-0.719410\pi$
$647$	−184.840	+	106.717i	−0.285687	+	0.164942i	0.350308	+	0.936635i	$0.386077\pi$
$648$	−290.797	+	239.035i	−0.448761	+	0.368881i
$649$	−18.8095	+	32.5790i	−0.0289823	+	0.0501988i
$650$	−164.028	−	251.234i	−0.252350	−	0.386514i
$651$		0			0
$652$	125.035	−	284.570i	0.191772	−	0.436457i
$653$	238.048	+	137.437i	0.364545	+	0.210470i	0.671073	−	0.741392i	$-0.265834\pi$
$653$	238.048	+	137.437i	0.364545	+	0.210470i	−0.306528	+	0.951862i	$0.599167\pi$
$654$	121.638	−	240.178i	0.185991	−	0.367245i
$655$	586.485	−	338.607i	0.895397	−	0.516958i
$656$	118.628	−	26.4301i	0.180836	−	0.0402899i
$657$	289.397			0.440483
$658$		0			0
$659$	1234.48			1.87327			0.936633	−	0.350313i	$-0.113925\pi$
$659$	1234.48			1.87327			0.936633	+	0.350313i	$0.113925\pi$
$660$	−118.254	+	86.8033i	−0.179173	+	0.131520i
$661$	−504.662	+	291.367i	−0.763482	+	0.440797i	−0.830545	−	0.556952i	$-0.811971\pi$
$661$	−504.662	+	291.367i	−0.763482	+	0.440797i	0.0670625	+	0.997749i	$0.478637\pi$
$662$	−226.002	−	114.459i	−0.341392	−	0.172898i
$663$	−2435.74	−	1406.27i	−3.67381	−	2.12107i
$664$	−103.796	−	625.613i	−0.156319	−	0.942188i
$665$		0			0
$666$	−702.341	−	1075.74i	−1.05457	−	1.61523i
$667$	−26.1533	+	45.2989i	−0.0392104	+	0.0679143i
$668$	−27.1652	−	246.844i	−0.0406664	−	0.369528i
$669$	637.569	−	368.101i	0.953018	−	0.550225i
$670$	1311.03	−	71.9224i	1.95677	−	0.107347i
$671$		−	120.776i		−	0.179994i
$672$		0			0
$673$	−399.145			−0.593083			−0.296542	−	0.955020i	$-0.595833\pi$
$673$	−399.145			−0.593083			−0.296542	+	0.955020i	$0.595833\pi$
$674$	−33.1295	−	603.900i	−0.0491536	−	0.895994i
$675$	−51.3815	−	88.9953i	−0.0761207	−	0.131845i
$676$	775.822	−	85.3790i	1.14767	−	0.126300i
$677$	−653.388	−	377.234i	−0.965123	−	0.557214i	−0.0673768	−	0.997728i	$-0.521463\pi$
$677$	−653.388	−	377.234i	−0.965123	−	0.557214i	−0.897746	+	0.440514i	$0.854796\pi$
$678$	1217.22	−	794.706i	1.79530	−	1.17213i
$679$		0			0
$680$	−1459.95	+	242.220i	−2.14698	+	0.356206i
$681$	391.156	−	677.502i	0.574384	−	0.994863i
$682$	28.6930	−	56.6552i	0.0420719	−	0.0830721i
$683$	−144.132	−	249.644i	−0.211028	−	0.365511i	0.741009	−	0.671495i	$-0.234348\pi$
$683$	−144.132	−	249.644i	−0.211028	−	0.365511i	−0.952036	+	0.305985i	$0.901014\pi$
$684$	−352.845	−	480.690i	−0.515856	−	0.702764i
$685$		−	109.897i		−	0.160433i
$686$		0			0
$687$		−	1047.10i		−	1.52416i
$688$	−325.583	+	72.5390i	−0.473230	+	0.105435i
$689$	3.40298	+	5.89414i	0.00493901	+	0.00855462i
$690$	−742.294	−	375.935i	−1.07579	−	0.544833i
$691$	−78.3458	+	135.699i	−0.113380	+	0.196380i	−0.917131	−	0.398586i	$-0.869501\pi$
$691$	−78.3458	+	135.699i	−0.113380	+	0.196380i	0.803751	+	0.594966i	$0.202835\pi$
$692$	−716.356	−	314.755i	−1.03520	−	0.454848i
$693$		0			0
$694$	−536.787	+	350.462i	−0.773468	+	0.504988i
$695$	521.043	+	300.824i	0.749703	+	0.432841i
$696$	−76.3824	−	92.9228i	−0.109745	−	0.133510i
$697$	−122.562	−	212.284i	−0.175842	−	0.304568i
$698$	−760.214	+	41.7048i	−1.08913	+	0.0597489i
$699$	1233.92			1.76527
$700$		0			0
$701$			1126.50i			1.60700i	0.595307	+	0.803498i	$0.297030\pi$
$701$			1126.50i			1.60700i	−0.595307	+	0.803498i	$0.702970\pi$
$702$	498.102	−	27.3255i	0.709547	−	0.0389252i
$703$	−589.396	+	340.288i	−0.838401	+	0.484051i
$704$	−67.4891	−	58.9983i	−0.0958651	−	0.0838045i
$705$	−283.281	+	490.657i	−0.401817	+	0.695967i
$706$	−610.200	+	398.392i	−0.864306	+	0.564295i
$707$		0			0
$708$	197.391	−	449.246i	0.278801	−	0.634528i
$709$	−949.313	−	548.086i	−1.33895	−	0.773041i	−0.352296	−	0.935889i	$-0.614599\pi$
$709$	−949.313	−	548.086i	−1.33895	−	0.773041i	−0.986651	+	0.162847i	$0.947932\pi$
$710$	−1071.82	−	542.824i	−1.50961	−	0.764541i
$711$	−1203.21	+	694.673i	−1.69228	+	0.977037i
$712$	19.9278	+	7.48238i	0.0279885	+	0.0105090i
$713$	360.218			0.505214
$714$		0			0
$715$	−153.215			−0.214286
$716$	170.916	+	232.843i	0.238709	+	0.325200i
$717$	−621.633	+	358.900i	−0.866991	+	0.500558i
$718$	−101.201	+	199.825i	−0.140949	+	0.278308i
$719$	−524.259	−	302.681i	−0.729150	−	0.420975i	0.0889614	−	0.996035i	$-0.471645\pi$
$719$	−524.259	−	302.681i	−0.729150	−	0.420975i	−0.818111	+	0.575060i	$0.804979\pi$
$720$	801.361	−	735.863i	1.11300	−	1.02203i
$721$		0			0
$722$	340.057	−	222.019i	0.470993	−	0.307506i
$723$	223.149	−	386.506i	0.308643	−	0.534586i
$724$	61.6868	+	560.536i	0.0852028	+	0.774221i
$725$	−22.4132	+	12.9403i	−0.0309148	+	0.0178487i
$726$	−59.5648	−	1085.77i	−0.0820451	−	1.49556i
$727$		−	443.659i		−	0.610260i	−0.952311	−	0.305130i	$-0.901300\pi$
$727$		−	443.659i		−	0.610260i	0.952311	−	0.305130i	$-0.0986999\pi$
$728$		0			0
$729$	−1095.46			−1.50269
$730$	279.297	−	15.3220i	0.382599	−	0.0209891i
$731$	336.379	+	582.625i	0.460162	+	0.797025i
$732$	172.331	+	1565.94i	0.235424	+	2.13926i
$733$	−649.541	−	375.013i	−0.886141	−	0.511614i	−0.0134626	−	0.999909i	$-0.504285\pi$
$733$	−649.541	−	375.013i	−0.886141	−	0.511614i	−0.872678	+	0.488296i	$0.837619\pi$
$734$	−480.038	−	735.252i	−0.654002	−	1.00171i
$735$		0			0
$736$	125.586	−	492.704i	0.170633	−	0.669434i
$737$	80.2028	−	138.915i	0.108823	−	0.188488i
$738$	160.764	+	81.4191i	0.217838	+	0.110324i
$739$	−309.646	−	536.323i	−0.419007	−	0.725742i	0.576833	−	0.816862i	$-0.304288\pi$
$739$	−309.646	−	536.323i	−0.419007	−	0.725742i	−0.995840	+	0.0911205i	$0.970955\pi$
$740$	−734.785	−	1001.02i	−0.992952	−	1.35272i
$741$		−	1095.34i		−	1.47819i
$742$		0			0
$743$			30.5255i			0.0410842i	0.999789	+	0.0205421i	$0.00653921\pi$
$743$			30.5255i			0.0410842i	−0.999789	+	0.0205421i	$0.993461\pi$
$744$	−291.184	+	775.510i	−0.391376	+	1.04235i
$745$	236.153	+	409.029i	0.316984	+	0.549032i
$746$	230.420	−	454.972i	0.308875	−	0.609882i
$747$	470.146	−	814.316i	0.629378	−	1.09012i
$748$	−72.7275	+	165.522i	−0.0972293	+	0.221286i
$749$		0			0
$750$	490.632	+	751.479i	0.654176	+	1.00197i
$751$	838.498	+	484.107i	1.11651	+	0.644616i	0.940507	−	0.339773i	$-0.110350\pi$
$751$	838.498	+	484.107i	1.11651	+	0.644616i	0.176001	+	0.984390i	$0.443684\pi$
$752$	−330.300	−	103.762i	−0.439229	−	0.137981i
$753$	715.142	+	1238.66i	0.949723	+	1.64497i
$754$	−6.88186	−	125.446i	−0.00912713	−	0.166374i
$755$	−330.993			−0.438401
$756$		0			0
$757$		−	1171.15i		−	1.54710i	−0.633736	−	0.773550i	$-0.718479\pi$
$757$		−	1171.15i		−	1.54710i	0.633736	−	0.773550i	$-0.281521\pi$
$758$	−66.0662	−	1204.28i	−0.0871585	−	1.58877i
$759$	−88.0318	+	50.8252i	−0.115984	+	0.0669633i
$760$	−365.981	−	445.233i	−0.481554	−	0.585833i
$761$	117.998	−	204.379i	0.155057	−	0.268566i	−0.778023	−	0.628236i	$-0.783777\pi$
$761$	117.998	−	204.379i	0.155057	−	0.268566i	0.933080	+	0.359670i	$0.117111\pi$
$762$	−80.3199	−	123.022i	−0.105407	−	0.161447i
$763$		0			0
$764$	1041.77	+	457.734i	1.36357	+	0.599129i
$765$	−1900.31	−	1097.14i	−2.48406	−	1.43418i
$766$	−66.3128	+	130.936i	−0.0865702	+	0.170935i
$767$	443.849	−	256.257i	0.578682	−	0.334102i
$768$	959.220	+	668.652i	1.24898	+	0.870641i
$769$	124.257			0.161582			0.0807912	−	0.996731i	$-0.474255\pi$
$769$	124.257			0.161582			0.0807912	+	0.996731i	$0.474255\pi$
$770$		0			0
$771$	−1593.39			−2.06665
$772$	−293.145	−	399.359i	−0.379721	−	0.517304i
$773$	−154.345	+	89.1114i	−0.199671	+	0.115280i	−0.596502	−	0.802612i	$-0.703443\pi$
$773$	−154.345	+	89.1114i	−0.199671	+	0.115280i	0.396831	+	0.917892i	$0.370110\pi$
$774$	−441.227	−	223.459i	−0.570060	−	0.288707i
$775$	154.352	+	89.1154i	0.199164	+	0.114988i
$776$	68.2099	+	411.124i	0.0878993	+	0.529799i
$777$		0			0
$778$	372.622	+	570.728i	0.478948	+	0.733584i
$779$	47.7317	−	82.6737i	0.0612730	−	0.106128i
$780$	1986.52	−	218.616i	2.54682	−	0.280277i
$781$	−127.112	+	73.3880i	−0.162755	+	0.0939667i
$782$	−1023.95	+	56.1732i	−1.30940	+	0.0718327i
$783$		−	43.0296i		−	0.0549548i
$784$		0			0
$785$	−21.3809			−0.0272368
$786$	59.1131	+	1077.54i	0.0752076	+	1.37092i
$787$	−553.948	−	959.466i	−0.703873	−	1.21914i	−0.967097	−	0.254409i	$-0.918119\pi$
$787$	−553.948	−	959.466i	−0.703873	−	1.21914i	0.263224	−	0.964735i	$-0.415214\pi$
$788$	47.2991	+	429.798i	0.0600242	+	0.545429i
$789$	1520.37	+	877.785i	1.92696	+	1.11253i
$790$	−1124.44	+	734.133i	−1.42334	+	0.929283i
$791$		0			0
$792$	−21.7544	−	131.121i	−0.0274676	−	0.165557i
$793$	−822.713	+	1424.98i	−1.03747	+	1.79695i
$794$	100.790	−	199.012i	0.126939	−	0.250645i
$795$	4.66933	+	8.08752i	0.00587338	+	0.0101730i
$796$	−1070.08	+	785.477i	−1.34432	+	0.986780i
$797$			1094.69i			1.37351i	0.726889	+	0.686755i	$0.240966\pi$
$797$			1094.69i			1.37351i	−0.726889	+	0.686755i	$0.759034\pi$
$798$		0			0
$799$			698.269i			0.873929i
$800$	175.705	−	180.053i	0.219631	−	0.225066i
$801$	15.7808	+	27.3332i	0.0197014	+	0.0341238i
$802$	607.592	+	307.715i	0.757596	+	0.383685i
$803$	17.0861	−	29.5940i	0.0212778	−	0.0368542i
$804$	−841.666	+	1915.56i	−1.04685	+	2.38254i
$805$		0			0
$806$	−724.464	+	472.994i	−0.898839	+	0.586842i
$807$	−149.366	−	86.2367i	−0.185089	−	0.106861i
$808$	464.691	+	565.318i	0.575112	+	0.699651i
$809$	693.377	+	1200.96i	0.857079	+	1.48450i	0.874703	+	0.484659i	$0.161056\pi$
$809$	693.377	+	1200.96i	0.857079	+	1.48450i	−0.0176240	+	0.999845i	$0.505610\pi$
$810$	−538.665	+	29.5508i	−0.665019	+	0.0364824i
$811$	312.204			0.384962			0.192481	−	0.981301i	$-0.438347\pi$
$811$	312.204			0.384962			0.192481	+	0.981301i	$0.438347\pi$
$812$		0			0
$813$		−	1410.11i		−	1.73446i
$814$	−151.473	+	8.30968i	−0.186084	+	0.0102085i
$815$	385.776	−	222.728i	0.473345	−	0.273286i
$816$	706.781	−	2249.86i	0.866153	−	2.75719i
$817$	−131.002	+	226.903i	−0.160346	+	0.277727i
$818$	1116.94	−	729.237i	1.36545	−	0.891487i
$819$		0			0
$820$	159.464	+	70.0660i	0.194469	+	0.0854464i
$821$	946.469	+	546.444i	1.15282	+	0.665583i	0.949574	−	0.313544i	$-0.101516\pi$
$821$	946.469	+	546.444i	1.15282	+	0.665583i	0.203250	+	0.979127i	$0.434850\pi$
$822$	156.231	+	79.1230i	0.190061	+	0.0962567i
$823$	−785.625	+	453.581i	−0.954587	+	0.551131i	−0.894503	−	0.447062i	$-0.852470\pi$
$823$	−785.625	+	453.581i	−0.954587	+	0.551131i	−0.0600842	+	0.998193i	$0.519137\pi$
$824$	111.891	−	297.999i	0.135790	−	0.361650i
$825$	−50.2952			−0.0609638
$826$		0			0
$827$	−607.144			−0.734152			−0.367076	−	0.930191i	$-0.619641\pi$
$827$	−607.144			−0.734152			−0.367076	+	0.930191i	$0.619641\pi$
$828$	607.746	−	446.109i	0.733993	−	0.538779i
$829$	370.632	−	213.984i	0.447083	−	0.258124i	−0.259514	−	0.965739i	$-0.583562\pi$
$829$	370.632	−	213.984i	0.447083	−	0.258124i	0.706598	+	0.707616i	$0.250229\pi$
$830$	410.624	−	810.789i	0.494728	−	0.976854i
$831$	965.982	+	557.710i	1.16243	+	0.671131i
$832$	394.382	+	1155.82i	0.474017	+	1.38921i
$833$		0			0
$834$	−802.793	+	524.134i	−0.962581	+	0.628458i
$835$	177.948	−	308.215i	0.213111	−	0.369120i
$836$	−69.9878	+	7.70214i	−0.0837175	+	0.00921308i
$837$	−256.629	+	148.165i	−0.306606	+	0.177019i
$838$	−21.9317	−	399.781i	−0.0261715	−	0.477066i
$839$			1133.09i			1.35053i	0.737575	+	0.675265i	$0.235971\pi$
$839$			1133.09i			1.35053i	−0.737575	+	0.675265i	$0.764029\pi$
$840$		0			0
$841$	830.163			0.987114
$842$	31.7795	−	1.74340i	0.0377429	−	0.00207055i
$843$	608.774	+	1054.43i	0.722152	+	1.25080i
$844$	−104.947	+	11.5493i	−0.124344	+	0.0136840i
$845$	968.707	+	559.283i	1.14640	+	0.661874i
$846$	−280.637	−	429.839i	−0.331722	−	0.508084i
$847$		0			0
$848$	−4.20335	+	3.85980i	−0.00495678	+	0.00455165i
$849$	−378.198	+	655.059i	−0.445463	+	0.771565i
$850$	−452.657	−	229.248i	−0.532538	−	0.269704i
$851$	−430.232	−	745.184i	−0.505561	−	0.875657i
$852$	1543.37	−	1132.89i	1.81146	−	1.32969i
$853$			169.502i			0.198712i	0.995052	+	0.0993562i	$0.0316783\pi$
$853$			169.502i			0.198712i	−0.995052	+	0.0993562i	$0.968322\pi$
$854$		0			0
$855$		−	854.563i		−	0.999489i
$856$	−619.103	−	232.457i	−0.723251	−	0.271562i
$857$	−117.039	−	202.718i	−0.136569	−	0.236544i	0.789627	−	0.613587i	$-0.210274\pi$
$857$	−117.039	−	202.718i	−0.136569	−	0.236544i	−0.926196	+	0.377043i	$0.876941\pi$
$858$	110.311	−	217.811i	0.128567	−	0.253860i
$859$	447.171	−	774.523i	0.520571	−	0.901656i	−0.479143	−	0.877737i	$-0.659052\pi$
$859$	447.171	−	774.523i	0.520571	−	0.901656i	0.999714	−	0.0239189i	$-0.00761436\pi$
$860$	−437.659	−	192.300i	−0.508906	−	0.223605i
$861$		0			0
$862$	686.654	+	1051.72i	0.796582	+	1.22009i
$863$	−674.270	−	389.290i	−0.781309	−	0.451089i	0.0555850	−	0.998454i	$-0.482298\pi$
$863$	−674.270	−	389.290i	−0.781309	−	0.451089i	−0.836894	+	0.547365i	$0.815631\pi$
$864$	113.188	+	402.672i	0.131005	+	0.466056i
$865$	−560.680	−	971.126i	−0.648185	−	1.12269i
$866$	86.4633	+	1576.09i	0.0998422	+	1.81997i
$867$	−3436.32			−3.96346
$868$		0			0
$869$			164.055i			0.188786i
$870$	−9.44281	−	172.128i	−0.0108538	−	0.197848i
$871$	−1892.55	+	1092.67i	−2.17285	+	1.25450i
$872$	149.718	+	182.139i	0.171695	+	0.208875i
$873$	−308.959	+	535.132i	−0.353904	+	0.612980i
$874$	−218.334	−	334.412i	−0.249810	−	0.382623i
$875$		0			0
$876$	−179.305	+	408.083i	−0.204686	+	0.465849i
$877$	−14.9632	−	8.63901i	−0.0170618	−	0.00985064i	0.491445	−	0.870909i	$-0.336469\pi$
$877$	−14.9632	−	8.63901i	−0.0170618	−	0.00985064i	−0.508507	+	0.861058i	$0.669802\pi$
$878$	601.424	−	1187.53i	0.684993	−	1.35254i
$879$	135.933	−	78.4811i	0.154645	−	0.0892846i
$880$	−27.9373	−	125.393i	−0.0317470	−	0.142492i
$881$	−770.918			−0.875049			−0.437524	−	0.899207i	$-0.644145\pi$
$881$	−770.918			−0.875049			−0.437524	+	0.899207i	$0.644145\pi$
$882$		0			0
$883$	776.362			0.879232			0.439616	−	0.898186i	$-0.355114\pi$
$883$	776.362			0.879232			0.439616	+	0.898186i	$0.355114\pi$
$884$	1985.60	−	1457.50i	2.24615	−	1.64876i
$885$	609.019	−	351.617i	0.688157	−	0.397308i
$886$	904.874	+	458.273i	1.02130	+	0.517239i
$887$	1412.32	+	815.402i	1.59224	+	0.919280i	0.992922	+	0.118770i	$0.0378950\pi$
$887$	1412.32	+	815.402i	1.59224	+	0.919280i	0.599319	+	0.800511i	$0.295438\pi$
$888$	1952.08	−	323.871i	2.19829	−	0.364719i
$889$		0			0
$890$	16.6772	+	25.5438i	0.0187385	+	0.0287009i
$891$	−32.9530	+	57.0762i	−0.0369842	+	0.0640586i
$892$	70.5270	+	640.865i	0.0790661	+	0.718458i
$893$	−235.507	+	135.970i	−0.263726	+	0.152262i
$894$	−751.503	+	41.2269i	−0.840608	+	0.0461151i
$895$			413.945i			0.462508i
$896$		0			0
$897$	1384.86			1.54388
$898$	30.5687	+	557.221i	0.0340409	+	0.620513i
$899$	37.3150	+	64.6314i	0.0415072	+	0.0718925i
$900$	370.782	−	40.8044i	0.411980	−	0.0453382i
$901$	9.96762	+	5.75481i	0.0110628	+	0.00638713i
$902$	17.8175	−	11.6329i	0.0197534	−	0.0128967i
$903$		0			0
$904$	208.367	+	1255.90i	0.230495	+	1.38927i
$905$	−404.086	+	699.897i	−0.446503	+	0.773367i
$906$	238.306	−	470.542i	0.263031	−	0.519362i
$907$	476.931	+	826.069i	0.525834	+	0.910771i	0.999547	+	0.0300919i	$0.00958001\pi$
$907$	476.931	+	826.069i	0.525834	+	0.910771i	−0.473713	+	0.880679i	$0.657087\pi$
$908$	405.406	+	552.295i	0.446482	+	0.608254i
$909$			1085.05i			1.19367i
$910$		0			0
$911$		−	1681.15i		−	1.84539i	−0.385534	−	0.922694i	$-0.625983\pi$
$911$		−	1681.15i		−	1.84539i	0.385534	−	0.922694i	$-0.374017\pi$
$912$	896.445	−	199.726i	0.982944	−	0.218998i
$913$	−55.5150	−	96.1548i	−0.0608051	−	0.105317i
$914$	−1286.22	−	651.404i	−1.40724	−	0.712696i
$915$	−1128.87	+	1955.26i	−1.23374	+	2.13689i
$916$	839.538	+	368.879i	0.916527	+	0.402707i
$917$		0			0
$918$	706.386	−	461.192i	0.769484	−	0.502387i
$919$	437.335	+	252.495i	0.475881	+	0.274750i	0.718698	−	0.695322i	$-0.244738\pi$
$919$	437.335	+	252.495i	0.475881	+	0.274750i	−0.242817	+	0.970072i	$0.578071\pi$
$920$	562.917	−	462.717i	0.611866	−	0.502953i
$921$	509.122	+	881.826i	0.552793	+	0.957466i
$922$	−965.073	+	52.9432i	−1.04672	+	0.0574221i
$923$	1999.64			2.16646
$924$		0			0
$925$		−	425.746i		−	0.460266i
$926$	−79.1461	+	4.34190i	−0.0854710	+	0.00468887i
$927$	408.739	−	235.985i	0.440926	−	0.254569i
$928$	101.412	−	28.5061i	0.109280	−	0.0307178i
$929$	491.925	−	852.040i	0.529521	−	0.917158i	−0.469886	−	0.882727i	$-0.655705\pi$
$929$	491.925	−	852.040i	0.529521	−	0.917158i	0.999407	−	0.0344306i	$-0.0109618\pi$
$930$	−994.059	+	649.010i	−1.06888	+	0.697860i
$931$		0			0
$932$	−434.695	+	989.330i	−0.466411	+	1.06151i
$933$	−1661.07	−	959.018i	−1.78035	−	1.02789i
$934$	−31.7357	−	16.0725i	−0.0339782	−	0.0172083i
$935$	−224.389	+	129.551i	−0.239989	+	0.138558i
$936$	−636.513	+	1695.23i	−0.680035	+	1.81114i
$937$	389.648			0.415846			0.207923	−	0.978145i	$-0.433330\pi$
$937$	389.648			0.415846			0.207923	+	0.978145i	$0.433330\pi$
$938$		0			0
$939$	−1342.24			−1.42943
$940$	−293.601	−	399.980i	−0.312341	−	0.425511i
$941$	758.175	−	437.732i	0.805712	−	0.465178i	−0.0397529	−	0.999210i	$-0.512657\pi$
$941$	758.175	−	437.732i	0.805712	−	0.465178i	0.845464	+	0.534032i	$0.179324\pi$
$942$	15.3937	−	30.3953i	0.0163415	−	0.0322667i
$943$	104.526	+	60.3481i	0.110844	+	0.0639958i
$944$	290.656	+	316.527i	0.307899	+	0.335304i
$945$		0			0
$946$	−48.9012	+	31.9270i	−0.0516926	+	0.0337495i
$947$	625.646	−	1083.65i	0.660661	−	1.14430i	−0.319781	−	0.947491i	$-0.603609\pi$
$947$	625.646	−	1083.65i	0.660661	−	1.14430i	0.980442	−	0.196807i	$-0.0630572\pi$
$948$	−234.083	−	2127.07i	−0.246923	−	2.24375i
$949$	−403.181	+	232.777i	−0.424849	+	0.245287i
$950$	−10.8242	−	197.309i	−0.0113939	−	0.207694i
$951$		−	1934.14i		−	2.03380i
$952$		0			0
$953$	−882.129			−0.925633			−0.462817	−	0.886454i	$-0.653161\pi$
$953$	−882.129			−0.925633			−0.462817	+	0.886454i	$0.653161\pi$
$954$	−8.44873	+	0.463491i	−0.00885611	+	0.000485839i
$955$	815.373	+	1412.27i	0.853793	+	1.47881i
$956$	−68.7642	−	624.846i	−0.0719290	−	0.653605i
$957$	−18.2384	−	10.5300i	−0.0190579	−	0.0110031i
$958$	−731.049	−	1119.71i	−0.763099	−	1.16880i
$959$		0			0
$960$	541.144	+	1585.94i	0.563691	+	1.65202i
$961$	−223.525	+	387.156i	−0.232596	+	0.402868i
$962$	1843.76	+	933.773i	1.91659	+	0.970658i
$963$	−490.267	−	849.167i	−0.509103	−	0.881793i
$964$	231.279	+	315.077i	0.239916	+	0.326843i
$965$		−	709.973i		−	0.735724i
$966$		0			0
$967$		−	1410.24i		−	1.45836i	−0.684320	−	0.729182i	$-0.739901\pi$
$967$		−	1410.24i		−	1.45836i	0.684320	−	0.729182i	$-0.260099\pi$
$968$	891.533	+	334.747i	0.921005	+	0.345813i
$969$	−926.171	−	1604.18i	−0.955801	−	1.65550i
$970$	−269.844	+	532.814i	−0.278189	+	0.549293i
$971$	339.275	−	587.641i	0.349408	−	0.605192i	−0.636737	−	0.771081i	$-0.719716\pi$
$971$	339.275	−	587.641i	0.349408	−	0.605192i	0.986144	+	0.165889i	$0.0530495\pi$
$972$	535.107	−	1217.86i	0.550521	−	1.25294i
$973$		0			0
$974$	−457.560	−	700.825i	−0.469775	−	0.719533i
$975$	593.410	+	342.605i	0.608625	+	0.351390i
$976$	−1316.24	−	413.488i	−1.34861	−	0.423656i
$977$	−55.9074	−	96.8344i	−0.0572235	−	0.0991141i	0.835995	−	0.548738i	$-0.184891\pi$
$977$	−55.9074	−	96.8344i	−0.0572235	−	0.0991141i	−0.893218	+	0.449624i	$0.851558\pi$
$978$	38.8833	+	708.782i	0.0397579	+	0.724726i
$979$	3.72682			0.00380676
$980$		0			0
$981$			349.590i			0.356360i
$982$	−41.7434	−	760.917i	−0.0425085	−	0.774865i
$983$	−175.133	+	101.113i	−0.178162	+	0.102862i	−0.586429	−	0.810001i	$-0.699467\pi$
$983$	−175.133	+	101.113i	−0.178162	+	0.102862i	0.408267	+	0.912863i	$0.366133\pi$
$984$	−214.417	+	176.250i	−0.217903	+	0.179116i
$985$	−309.837	+	536.654i	−0.314556	+	0.544826i
$986$	−116.150	−	177.902i	−0.117799	−	0.180428i
$987$		0			0
$988$	878.220	+	385.875i	0.888887	+	0.390562i
$989$	−286.877	−	165.629i	−0.290068	−	0.167471i
$990$	86.0620	−	169.932i	0.0869314	−	0.171648i
$991$	−163.735	+	94.5322i	−0.165222	+	0.0953907i	−0.580331	−	0.814381i	$-0.697077\pi$
$991$	−163.735	+	94.5322i	−0.165222	+	0.0953907i	0.415109	+	0.909772i	$0.363743\pi$
$992$	−519.206	−	506.667i	−0.523393	−	0.510753i
$993$	578.546			0.582624
$994$		0			0
$995$	−1902.36			−1.91192
$996$	856.986	+	1167.49i	0.860428	+	1.17218i
$997$	−1414.14	+	816.457i	−1.41840	+	0.818914i	−0.996158	−	0.0875699i	$-0.972090\pi$
$997$	−1414.14	+	816.457i	−1.41840	+	0.818914i	−0.422241	+	0.906483i	$0.638757\pi$
$998$	−782.191	−	396.141i	−0.783759	−	0.396935i
$999$	613.019	+	353.927i	0.613632	+	0.354281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.n.275.5		16
7.2	even	3		392.3.g.m.99.2		8
7.3	odd	6		392.3.k.o.67.7		16
7.4	even	3	inner	392.3.k.n.67.7		16
7.5	odd	6		56.3.g.b.43.2	yes	8
7.6	odd	2		392.3.k.o.275.5		16
8.3	odd	2	inner	392.3.k.n.275.7		16
21.5	even	6		504.3.g.b.379.7		8
28.19	even	6		224.3.g.b.15.1		8
28.23	odd	6		1568.3.g.m.687.8		8
56.3	even	6		392.3.k.o.67.5		16
56.5	odd	6		224.3.g.b.15.2		8
56.11	odd	6	inner	392.3.k.n.67.5		16
56.19	even	6		56.3.g.b.43.1	✓	8
56.27	even	2		392.3.k.o.275.7		16
56.37	even	6		1568.3.g.m.687.7		8
56.51	odd	6		392.3.g.m.99.1		8
84.47	odd	6		2016.3.g.b.1135.7		8
112.5	odd	12		1792.3.d.j.1023.4		16
112.19	even	12		1792.3.d.j.1023.3		16
112.61	odd	12		1792.3.d.j.1023.13		16
112.75	even	12		1792.3.d.j.1023.14		16
168.5	even	6		2016.3.g.b.1135.2		8
168.131	odd	6		504.3.g.b.379.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.1	✓	8	56.19	even	6
56.3.g.b.43.2	yes	8	7.5	odd	6
224.3.g.b.15.1		8	28.19	even	6
224.3.g.b.15.2		8	56.5	odd	6
392.3.g.m.99.1		8	56.51	odd	6
392.3.g.m.99.2		8	7.2	even	3
392.3.k.n.67.5		16	56.11	odd	6	inner
392.3.k.n.67.7		16	7.4	even	3	inner
392.3.k.n.275.5		16	1.1	even	1	trivial
392.3.k.n.275.7		16	8.3	odd	2	inner
392.3.k.o.67.5		16	56.3	even	6
392.3.k.o.67.7		16	7.3	odd	6
392.3.k.o.275.5		16	7.6	odd	2
392.3.k.o.275.7		16	56.27	even	2
504.3.g.b.379.7		8	21.5	even	6
504.3.g.b.379.8		8	168.131	odd	6
1568.3.g.m.687.7		8	56.37	even	6
1568.3.g.m.687.8		8	28.23	odd	6
1792.3.d.j.1023.3		16	112.19	even	12
1792.3.d.j.1023.4		16	112.5	odd	12
1792.3.d.j.1023.13		16	112.61	odd	12
1792.3.d.j.1023.14		16	112.75	even	12
2016.3.g.b.1135.2		8	168.5	even	6
2016.3.g.b.1135.7		8	84.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.109554 - 1.99700i) q^{2} +(2.28374 + 3.95555i) q^{3} +(-3.97600 + 0.437557i) q^{4} +(-4.96451 - 2.86626i) q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +O(q^{10})\)	\(q+(-0.109554 - 1.99700i) q^{2} +(2.28374 + 3.95555i) q^{3} +(-3.97600 + 0.437557i) q^{4} +(-4.96451 - 2.86626i) q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +(-5.18003 + 10.2281i) q^{10} +(0.700323 + 1.21300i) q^{11} +(-10.8109 - 14.7280i) q^{12} -19.0821i q^{13} -26.1831i q^{15} +(15.6171 - 3.47945i) q^{16} +(-16.1349 - 27.9465i) q^{17} +(21.1641 + 10.7186i) q^{18} +(6.28374 - 10.8837i) q^{19} +(20.9930 + 9.22398i) q^{20} +(2.34563 - 1.53143i) q^{22} +(13.7605 + 7.94464i) q^{23} +(-28.2273 + 23.2028i) q^{24} +(3.93090 + 6.80852i) q^{25} +(-38.1069 + 2.09052i) q^{26} -13.0712 q^{27} +3.29194i q^{29} +(-52.2876 + 2.86846i) q^{30} +(19.6332 - 11.3352i) q^{31} +(-8.65936 - 30.8061i) q^{32} +(-3.19871 + 5.54032i) q^{33} +(-54.0415 + 35.2831i) q^{34} +(19.0864 - 43.4390i) q^{36} +(-46.8985 - 27.0769i) q^{37} +(-22.4232 - 11.3562i) q^{38} +(75.4801 - 43.5785i) q^{39} +(16.1204 - 42.9335i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(-3.31524 - 4.51643i) q^{44} +(58.8880 - 33.9990i) q^{45} +(14.3579 - 28.3501i) q^{46} +(-18.7394 - 10.8192i) q^{47} +(49.4284 + 53.8280i) q^{48} +(13.1659 - 8.59589i) q^{50} +(73.6959 - 127.645i) q^{51} +(8.34951 + 75.8703i) q^{52} +(-0.308883 + 0.178334i) q^{53} +(1.43200 + 26.1031i) q^{54} -8.02924i q^{55} +57.4016 q^{57} +(6.57400 - 0.360645i) q^{58} +(13.4292 + 23.2600i) q^{59} +(11.4566 + 104.104i) q^{60} +(-74.6763 - 43.1144i) q^{61} +(-24.7873 - 37.9656i) q^{62} +(-60.5710 + 20.6676i) q^{64} +(-54.6943 + 94.7333i) q^{65} +(11.4144 + 5.78085i) q^{66} +(-57.2613 - 99.1794i) q^{67} +(76.3807 + 104.055i) q^{68} +72.5739i q^{69} +104.792i q^{71} +(-88.8385 - 33.3565i) q^{72} +(-12.1987 - 21.1288i) q^{73} +(-48.9345 + 96.6226i) q^{74} +(-17.9543 + 31.0977i) q^{75} +(-20.2218 + 46.0232i) q^{76} +(-95.2952 - 145.959i) q^{78} +(101.436 + 58.5639i) q^{79} +(-87.5042 - 27.4889i) q^{80} +(23.5270 + 40.7499i) q^{81} +(-0.832178 - 15.1693i) q^{82} -79.2706 q^{83} +184.988i q^{85} +(2.28396 + 41.6331i) q^{86} +(-13.0214 + 7.51793i) q^{87} +(-8.65611 + 7.11531i) q^{88} +(1.33039 - 2.30431i) q^{89} +(-74.3473 - 113.874i) q^{90} +(-58.1880 - 25.5669i) q^{92} +(89.6741 + 51.7734i) q^{93} +(-19.5530 + 38.6079i) q^{94} +(-62.3913 + 36.0216i) q^{95} +(102.079 - 104.605i) q^{96} +52.0930 q^{97} -16.6142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9	\( 16 q - q^{2} - 8 q^{3} - 5 q^{4} + 44 q^{6} + 26 q^{8} - 48 q^{9} + 16 q^{10} + 32 q^{11} + 30 q^{12} + 71 q^{16} - 80 q^{17} + 29 q^{18} + 56 q^{19} + 216 q^{20} + 132 q^{22} + 22 q^{24} + 16 q^{25} + 24 q^{26} + 64 q^{27} - 96 q^{30} + 19 q^{32} + 32 q^{33} - 148 q^{34} - 66 q^{36} - 14 q^{38} + 84 q^{40} - 256 q^{41} - 50 q^{44} + 152 q^{46} - 268 q^{48} + 66 q^{50} + 368 q^{51} + 132 q^{52} - 228 q^{54} + 112 q^{57} - 24 q^{58} + 104 q^{59} - 192 q^{60} - 240 q^{62} - 110 q^{64} + 72 q^{65} - 276 q^{66} - 304 q^{67} - 190 q^{68} + 209 q^{72} - 112 q^{73} - 8 q^{74} + 72 q^{75} - 140 q^{76} - 608 q^{78} + 124 q^{80} - 48 q^{81} + 450 q^{82} - 144 q^{83} - 210 q^{86} + 486 q^{88} - 512 q^{89} + 368 q^{90} - 944 q^{92} + 472 q^{94} + 558 q^{96} - 128 q^{97} + 512 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 5 * q^4 + 44 * q^6 + 26 * q^8 - 48 * q^9 + 16 * q^10 + 32 * q^11 + 30 * q^12 + 71 * q^16 - 80 * q^17 + 29 * q^18 + 56 * q^19 + 216 * q^20 + 132 * q^22 + 22 * q^24 + 16 * q^25 + 24 * q^26 + 64 * q^27 - 96 * q^30 + 19 * q^32 + 32 * q^33 - 148 * q^34 - 66 * q^36 - 14 * q^38 + 84 * q^40 - 256 * q^41 - 50 * q^44 + 152 * q^46 - 268 * q^48 + 66 * q^50 + 368 * q^51 + 132 * q^52 - 228 * q^54 + 112 * q^57 - 24 * q^58 + 104 * q^59 - 192 * q^60 - 240 * q^62 - 110 * q^64 + 72 * q^65 - 276 * q^66 - 304 * q^67 - 190 * q^68 + 209 * q^72 - 112 * q^73 - 8 * q^74 + 72 * q^75 - 140 * q^76 - 608 * q^78 + 124 * q^80 - 48 * q^81 + 450 * q^82 - 144 * q^83 - 210 * q^86 + 486 * q^88 - 512 * q^89 + 368 * q^90 - 944 * q^92 + 472 * q^94 + 558 * q^96 - 128 * q^97 + 512 * q^99

Introduction

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