LMFDB - Embedded newform 392.3.k.o.67.7

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			67.7
Root			$-1.78423 - 0.903622i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.o.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.78423 + 0.903622i) q^{2} +(-2.28374 + 3.95555i) q^{3} +(2.36693 + 3.22453i) q^{4} +(-4.96451 + 2.86626i) q^{5} +(-7.64902 + 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 - 10.2726i) q^{9} +O(q^{10})$	\(q+(1.78423 + 0.903622i) q^{2} +(-2.28374 + 3.95555i) q^{3} +(2.36693 + 3.22453i) 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} +(-11.4478 + 0.628019i) q^{10} +(0.700323 - 1.21300i) q^{11} +(-18.1602 + 1.99853i) q^{12} +19.0821i q^{13} -26.1831i q^{15} +(-4.79525 + 15.2645i) q^{16} +(16.1349 - 27.9465i) q^{17} +(-1.29950 - 23.6880i) 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} +(-34.2079 - 12.8442i) q^{24} +(3.93090 - 6.80852i) q^{25} +(-17.2430 + 34.0468i) q^{26} +13.0712 q^{27} +3.29194i q^{29} +(23.6597 - 46.7166i) q^{30} +(19.6332 + 11.3352i) q^{31} +(-22.3492 + 22.9023i) 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} +(-1.37681 - 25.0972i) q^{38} +(-75.4801 - 43.5785i) q^{39} +(-29.1213 - 35.4274i) q^{40} -7.59607 q^{41} -20.8478 q^{43} +(5.56897 - 0.612863i) q^{44} +(58.8880 + 33.9990i) q^{45} +(-31.7309 + 1.74073i) 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} +(-61.5309 + 45.1661i) q^{52} +(0.308883 + 0.178334i) q^{53} +(23.3220 + 11.8114i) q^{54} +8.02924i q^{55} +57.4016 q^{57} +(-2.97467 + 5.87357i) q^{58} +(-13.4292 + 23.2600i) q^{59} +(84.4284 - 61.9737i) 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} +(0.700861 + 12.7756i) q^{66} +(-57.2613 + 99.1794i) q^{67} +(128.305 - 14.1199i) q^{68} -72.5739i q^{69} +104.792i q^{71} +(73.3069 - 60.2582i) q^{72} +(12.1987 - 21.1288i) q^{73} +(108.145 - 5.93274i) 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} +(-19.9460 - 89.5253i) q^{80} +(23.5270 - 40.7499i) q^{81} +(-13.5531 - 6.86398i) q^{82} +79.2706 q^{83} +184.988i q^{85} +(-37.1973 - 18.8386i) q^{86} +(-13.0214 - 7.51793i) q^{87} +(10.4901 + 3.93875i) 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} +(-43.2119 + 2.37057i) q^{94} +(62.3913 + 36.0216i) q^{95} +(-39.5514 - 140.706i) 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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.78423	+	0.903622i	0.892114	+	0.451811i
$2$	1.78423	+	0.903622i	0.892114	+	0.451811i
$3$	−2.28374	+	3.95555i	−0.761245	+	1.31852i	0.180964	+	0.983490i	$0.442078\pi$
$3$	−2.28374	+	3.95555i	−0.761245	+	1.31852i	−0.942209	+	0.335026i	$0.891255\pi$
$4$	2.36693	+	3.22453i	0.591733	+	0.806134i
$5$	−4.96451	+	2.86626i	−0.992902	+	0.573252i	−0.906140	−	0.422977i	$-0.860985\pi$
$5$	−4.96451	+	2.86626i	−0.992902	+	0.573252i	−0.0867614	+	0.996229i	$0.527652\pi$
$6$	−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
$10$	−11.4478	+	0.628019i	−1.14478	+	0.0628019i
$11$	0.700323	−	1.21300i	0.0636658	−	0.110272i	−0.832436	−	0.554122i	$-0.813054\pi$
$11$	0.700323	−	1.21300i	0.0636658	−	0.110272i	0.896101	+	0.443849i	$0.146388\pi$
$12$	−18.1602	+	1.99853i	−1.51335	+	0.166544i
$13$			19.0821i			1.46785i	0.679228	+	0.733927i	$0.262315\pi$
$13$			19.0821i			1.46785i	−0.679228	+	0.733927i	$0.737685\pi$
$14$		0			0
$15$		−	26.1831i		−	1.74554i
$16$	−4.79525	+	15.2645i	−0.299703	+	0.954032i
$17$	16.1349	−	27.9465i	0.949114	−	1.64391i	0.201818	−	0.979423i	$-0.435315\pi$
$17$	16.1349	−	27.9465i	0.949114	−	1.64391i	0.747296	−	0.664491i	$-0.231352\pi$
$18$	−1.29950	−	23.6880i	−0.0721947	−	1.31600i
$19$	−6.28374	−	10.8837i	−0.330723	−	0.572829i	0.651931	−	0.758278i	$-0.273959\pi$
$19$	−6.28374	−	10.8837i	−0.330723	−	0.572829i	−0.982654	+	0.185449i	$0.940626\pi$
$20$	−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	$-0.778930\pi$
$23$	−13.7605	+	7.94464i	−0.598284	+	0.345419i	0.170082	+	0.985430i	$0.445597\pi$
$24$	−34.2079	−	12.8442i	−1.42533	−	0.535174i
$25$	3.93090	−	6.80852i	0.157236	−	0.272341i
$26$	−17.2430	+	34.0468i	−0.663193	+	1.30949i
$27$	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	$0.981924\pi$
$30$	23.6597	−	46.7166i	0.788655	−	1.55722i
$31$	19.6332	+	11.3352i	0.633329	+	0.365653i	0.782040	−	0.623228i	$-0.214179\pi$
$31$	19.6332	+	11.3352i	0.633329	+	0.365653i	−0.148711	+	0.988881i	$0.547512\pi$
$32$	−22.3492	+	22.9023i	−0.698412	+	0.715696i
$33$	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	$-0.405344\pi$
$37$	46.8985	−	27.0769i	1.26753	−	0.731807i	0.974519	+	0.224303i	$0.0720105\pi$
$38$	−1.37681	−	25.0972i	−0.0362319	−	0.660453i
$39$	−75.4801	−	43.5785i	−1.93539	−	1.11740i
$40$	−29.1213	−	35.4274i	−0.728033	−	0.885686i
$41$	−7.59607			−0.185270			−0.0926350	−	0.995700i	$-0.529529\pi$
$41$	−7.59607			−0.185270			−0.0926350	+	0.995700i	$0.529529\pi$
$42$		0			0
$43$	−20.8478			−0.484833			−0.242417	−	0.970172i	$-0.577940\pi$
$43$	−20.8478			−0.484833			−0.242417	+	0.970172i	$0.577940\pi$
$44$	5.56897	−	0.612863i	0.126567	−	0.0139287i
$45$	58.8880	+	33.9990i	1.30862	+	0.755533i
$46$	−31.7309	+	1.74073i	−0.689801	+	0.0378420i
$47$	−18.7394	+	10.8192i	−0.398711	+	0.230196i	−0.685928	−	0.727670i	$-0.740603\pi$
$47$	−18.7394	+	10.8192i	−0.398711	+	0.230196i	0.287217	+	0.957866i	$0.407270\pi$
$48$	−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
$52$	−61.5309	+	45.1661i	−1.18329	+	0.868578i
$53$	0.308883	+	0.178334i	0.00582798	+	0.00336479i	0.502911	−	0.864338i	$-0.332262\pi$
$53$	0.308883	+	0.178334i	0.00582798	+	0.00336479i	−0.497083	+	0.867703i	$0.665596\pi$
$54$	23.3220	+	11.8114i	0.431888	+	0.218730i
$55$			8.02924i			0.145986i
$56$		0			0
$57$	57.4016			1.00705
$58$	−2.97467	+	5.87357i	−0.0512875	+	0.101269i
$59$	−13.4292	+	23.2600i	−0.227613	+	0.394237i	−0.957100	−	0.289757i	$-0.906425\pi$
$59$	−13.4292	+	23.2600i	−0.227613	+	0.394237i	0.729487	+	0.683994i	$0.239759\pi$
$60$	84.4284	−	61.9737i	1.40714	−	1.03290i
$61$	−74.6763	+	43.1144i	−1.22420	+	0.706793i	−0.965811	−	0.259248i	$-0.916525\pi$
$61$	−74.6763	+	43.1144i	−1.22420	+	0.706793i	−0.258390	+	0.966041i	$0.583192\pi$
$62$	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
$66$	0.700861	+	12.7756i	0.0106191	+	0.193570i
$67$	−57.2613	+	99.1794i	−0.854646	+	1.48029i	0.0223272	+	0.999751i	$0.492892\pi$
$67$	−57.2613	+	99.1794i	−0.854646	+	1.48029i	−0.876973	+	0.480539i	$0.840441\pi$
$68$	128.305	−	14.1199i	1.88684	−	0.207646i
$69$		−	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	$0.735785\pi$
$72$	73.3069	−	60.2582i	1.01815	−	0.836919i
$73$	12.1987	−	21.1288i	0.167106	−	0.289435i	−0.770295	−	0.637687i	$-0.779891\pi$
$73$	12.1987	−	21.1288i	0.167106	−	0.289435i	0.937401	+	0.348252i	$0.113225\pi$
$74$	108.145	−	5.93274i	1.46142	−	0.0801722i
$75$	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	$-0.932464\pi$
$79$	−101.436	+	58.5639i	−1.28400	+	0.741315i	−0.306420	+	0.951897i	$0.599131\pi$
$80$	−19.9460	−	89.5253i	−0.249325	−	1.11907i
$81$	23.5270	−	40.7499i	0.290456	−	0.503085i
$82$	−13.5531	−	6.86398i	−0.165282	−	0.0837070i
$83$	79.2706			0.955067			0.477534	−	0.878614i	$-0.341531\pi$
$83$	79.2706			0.955067			0.477534	+	0.878614i	$0.341531\pi$
$84$		0			0
$85$			184.988i			2.17633i
$86$	−37.1973	−	18.8386i	−0.432526	−	0.219053i
$87$	−13.0214	−	7.51793i	−0.149672	−	0.0864130i
$88$	10.4901	+	3.93875i	0.119206	+	0.0447586i
$89$	−1.33039	−	2.30431i	−0.0149482	−	0.0258911i	0.858455	−	0.512890i	$-0.171425\pi$
$89$	−1.33039	−	2.30431i	−0.0149482	−	0.0258911i	−0.873403	+	0.486999i	$0.838092\pi$
$90$	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
$94$	−43.2119	+	2.37057i	−0.459701	+	0.0252188i
$95$	62.3913	+	36.0216i	0.656751	+	0.379175i
$96$	−39.5514	−	140.706i	−0.411994	−	1.46569i
$97$	−52.0930			−0.537042			−0.268521	−	0.963274i	$-0.586535\pi$
$97$	−52.0930			−0.537042			−0.268521	+	0.963274i	$0.586535\pi$
$98$		0			0
$99$	−16.6142			−0.167820
$100$	31.2585	−	3.43999i	0.312585	−	0.0343999i
$101$	79.2189	+	45.7371i	0.784346	+	0.452842i	0.837968	−	0.545719i	$-0.183743\pi$
$101$	79.2189	+	45.7371i	0.784346	+	0.452842i	−0.0536223	+	0.998561i	$0.517077\pi$
$102$	16.1473	+	294.341i	0.158307	+	2.88570i
$103$	−34.4584	+	19.8946i	−0.334548	+	0.193151i	−0.657858	−	0.753142i	$-0.728537\pi$
$103$	−34.4584	+	19.8946i	−0.334548	+	0.193151i	0.323311	+	0.946293i	$0.395204\pi$
$104$	−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	0.605669	−	0.795717i	$-0.292906\pi$
$107$	−41.3316	−	71.5884i	−0.386276	−	0.669050i	−0.991945	+	0.126667i	$0.959572\pi$
$108$	30.9386	+	42.1485i	0.286469	+	0.390264i
$109$	−25.5234	−	14.7359i	−0.234160	−	0.135192i	0.378330	−	0.925671i	$-0.376499\pi$
$109$	−25.5234	−	14.7359i	−0.234160	−	0.135192i	−0.612490	+	0.790479i	$0.709832\pi$
$110$	−7.25540	+	14.3260i	−0.0659582	+	0.130236i
$111$			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	$0.251337\pi$
$114$	102.417	+	51.8693i	0.898399	+	0.454994i
$115$	45.5428	−	78.8825i	0.396025	−	0.685935i
$116$	−10.6150	+	7.79181i	−0.0915085	+	0.0671708i
$117$	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
$122$	−172.199	+	9.44668i	−1.41146	+	0.0774318i
$123$	17.3474	−	30.0466i	0.141036	−	0.244281i
$124$	9.91963	+	90.1377i	0.0799970	+	0.726917i
$125$		−	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	$-0.0201690\pi$
$128$	−126.748	−	17.8575i	−0.990220	−	0.139512i
$129$	47.6110	−	82.4646i	0.369077	−	0.639260i
$130$	−11.9839	−	218.449i	−0.0921840	−	1.68037i
$131$	59.0678	+	102.308i	0.450899	+	0.780981i	0.998442	−	0.0557972i	$-0.0177700\pi$
$131$	59.0678	+	102.308i	0.450899	+	0.780981i	−0.547543	+	0.836778i	$0.684437\pi$
$132$	−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
$136$	241.684	+	90.7461i	1.77709	+	0.667250i
$137$	9.58539	−	16.6024i	0.0699664	−	0.121185i	−0.828920	−	0.559367i	$-0.811044\pi$
$137$	9.58539	−	16.6024i	0.0699664	−	0.121185i	0.898886	+	0.438182i	$0.144377\pi$
$138$	65.5794	−	129.488i	0.475213	−	0.938321i
$139$	104.954			0.755062			0.377531	−	0.925997i	$-0.376773\pi$
$139$	104.954			0.755062			0.377531	+	0.925997i	$0.376773\pi$
$140$		0			0
$141$		−	98.8329i		−	0.700942i
$142$	−94.6920	+	186.972i	−0.666845	+	1.31670i
$143$	23.1465	+	13.3636i	0.161864	+	0.0934520i
$144$	185.247	−	41.2725i	1.28644	−	0.286615i
$145$	−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	$-0.577499\pi$
$149$	71.3523	−	41.1953i	0.478875	−	0.276478i	0.719947	+	0.694029i	$0.244166\pi$
$150$	3.93392	+	71.7093i	0.0262261	+	0.478062i
$151$	−50.0038	−	28.8697i	−0.331151	−	0.191190i	0.325201	−	0.945645i	$-0.394568\pi$
$151$	−50.0038	−	28.8697i	−0.331151	−	0.191190i	−0.656352	+	0.754455i	$0.727901\pi$
$152$	77.6680	−	63.8430i	0.510974	−	0.420020i
$153$	−382.779			−2.50182
$154$		0			0
$155$	−129.959			−0.838445
$156$	−38.1361	−	346.536i	−0.244462	−	2.22138i
$157$	3.23006	+	1.86488i	0.0205736	+	0.0118782i	0.510252	−	0.860025i	$-0.329552\pi$
$157$	3.23006	+	1.86488i	0.0205736	+	0.0118782i	−0.489678	+	0.871903i	$0.662886\pi$
$158$	−233.904	+	12.8318i	−1.48040	+	0.0812139i
$159$	−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	0.721881	−	0.692018i	$-0.243278\pi$
$163$	−38.8534	−	67.2961i	−0.238365	−	0.412860i	−0.960245	+	0.279158i	$0.909945\pi$
$164$	−17.9794	−	24.4938i	−0.109630	−	0.149352i
$165$	−31.7600	−	18.3367i	−0.192485	−	0.111131i
$166$	141.437	+	71.6306i	0.852028	+	0.431510i
$167$		−	62.0837i		−	0.371759i	−0.982573	−	0.185879i	$-0.940487\pi$
$167$		−	62.0837i		−	0.371759i	0.982573	−	0.185879i	$-0.0595133\pi$
$168$		0			0
$169$	−195.127			−1.15459
$170$	−167.159	+	330.060i	−0.983289	+	1.94153i
$171$	−74.5364	+	129.101i	−0.435885	+	0.754976i
$172$	−49.3454	−	67.2246i	−0.286892	−	0.390841i
$173$	169.407	−	97.8069i	0.979228	−	0.565358i	0.0771913	−	0.997016i	$-0.475405\pi$
$173$	169.407	−	97.8069i	0.979228	−	0.565358i	0.902037	+	0.431659i	$0.142071\pi$
$174$	−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
$178$	−0.291499	−	5.31358i	−0.00163763	−	0.0298515i
$179$	−36.1049	+	62.5356i	−0.201704	+	0.349361i	−0.949077	−	0.315043i	$-0.897981\pi$
$179$	−36.1049	+	62.5356i	−0.201704	+	0.349361i	0.747374	+	0.664404i	$0.231314\pi$
$180$	29.7530	+	270.360i	0.165295	+	1.50200i
$181$			140.980i			0.778895i	0.921049	+	0.389448i	$0.127334\pi$
$181$			140.980i			0.778895i	−0.921049	+	0.389448i	$0.872666\pi$
$182$		0			0
$183$		−	393.847i		−	2.15217i
$184$	−80.7179	−	98.1971i	−0.438684	−	0.533680i
$185$	−155.219	+	268.847i	−0.839020	+	1.45323i
$186$	−206.783	+	11.3439i	−1.11173	+	0.0609889i
$187$	−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	$-0.399263\pi$
$191$	246.361	−	142.236i	1.28985	−	0.744693i	0.978627	+	0.205645i	$0.0659293\pi$
$192$	56.5764	−	286.791i	0.294669	−	1.49370i
$193$	61.9251	−	107.257i	0.320855	−	0.555738i	−0.659810	−	0.751433i	$-0.729363\pi$
$193$	61.9251	−	107.257i	0.320855	−	0.555738i	0.980665	+	0.195695i	$0.0626964\pi$
$194$	−92.9458	−	47.0724i	−0.479102	−	0.242641i
$195$	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	$-0.0884662\pi$
$198$	−29.6435	−	15.0129i	−0.149715	−	0.0758230i
$199$	287.394	+	165.927i	1.44419	+	0.833804i	0.998126	−	0.0611961i	$-0.0194915\pi$
$199$	287.394	+	165.927i	1.44419	+	0.833804i	0.446065	+	0.895000i	$0.352825\pi$
$200$	58.8807	+	22.1081i	0.294403	+	0.110541i
$201$	−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
$206$	−79.4588	+	4.35905i	−0.385722	+	0.0211604i
$207$	163.225	+	94.2378i	0.788525	+	0.455255i
$208$	−291.279	−	91.5035i	−1.40038	−	0.439920i
$209$	−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	$0.480078\pi$
$212$	0.156062	+	1.41811i	0.000736143	+	0.00668919i
$213$	−414.508	−	239.316i	−1.94605	−	1.12355i
$214$	−9.05606	−	165.078i	−0.0423180	−	0.771393i
$215$	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
$220$	−25.8906	+	19.0047i	−0.117684	+	0.0863849i
$221$	533.279	+	307.889i	2.41303	+	1.39316i
$222$	−223.507	+	441.321i	−1.00679	+	1.98793i
$223$			161.183i			0.722796i	0.932412	+	0.361398i	$0.117700\pi$
$223$			161.183i			0.722796i	−0.932412	+	0.361398i	$0.882300\pi$
$224$		0			0
$225$	−93.2551			−0.414467
$226$	283.930	+	143.797i	1.25633	+	0.636268i
$227$	85.6395	−	148.332i	0.377266	−	0.653445i	−0.613397	−	0.789775i	$-0.710197\pi$
$227$	85.6395	−	148.332i	0.377266	−	0.653445i	0.990663	+	0.136330i	$0.0435308\pi$
$228$	135.866	+	185.093i	0.595902	+	0.811813i
$229$	−198.537	+	114.626i	−0.866975	+	0.500548i	−0.866342	−	0.499452i	$-0.833535\pi$
$229$	−198.537	+	114.626i	−0.866975	+	0.500548i	−0.000632973		1.00000i	$0.500201\pi$
$230$	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	0.995510	+	0.0946571i	$0.0301755\pi$
$233$	135.077	+	233.961i	0.579730	+	1.00412i	−0.415780	+	0.909465i	$0.636491\pi$
$234$	452.016	−	24.7973i	1.93169	−	0.105971i
$235$	62.0214	−	107.424i	0.263921	−	0.457124i
$236$	−106.789	+	11.7520i	−0.452494	+	0.0497968i
$237$		−	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	$0.893364\pi$
$240$	399.673	+	125.555i	1.66530	+	0.523144i
$241$	48.8562	−	84.6214i	0.202723	−	0.351126i	−0.746682	−	0.665181i	$-0.768354\pi$
$241$	48.8562	−	84.6214i	0.202723	−	0.351126i	0.949405	+	0.314055i	$0.101688\pi$
$242$	13.0411	+	237.719i	0.0538888	+	0.982310i
$243$	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
$248$	−63.7516	+	169.790i	−0.257063	+	0.684636i
$249$	−181.033	+	313.558i	−0.727040	+	1.25927i
$250$	88.7765	−	175.292i	0.355106	−	0.701166i
$251$	−313.145			−1.24759			−0.623796	−	0.781587i	$-0.714410\pi$
$251$	−313.145			−1.24759			−0.623796	+	0.781587i	$0.714410\pi$
$252$		0			0
$253$			22.2553i			0.0879655i
$254$	14.5333	−	28.6965i	0.0572178	−	0.112978i
$255$	−731.728	−	422.463i	−2.86952	−	1.65672i
$256$	−210.011	−	146.394i	−0.820356	−	0.571853i
$257$	174.428	+	302.118i	0.678707	+	1.17555i	0.975371	+	0.220573i	$0.0707926\pi$
$257$	174.428	+	302.118i	0.678707	+	1.17555i	−0.296664	+	0.954982i	$0.595874\pi$
$258$	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
$262$	12.9422	+	235.917i	0.0493977	+	0.900445i
$263$	−332.869	−	192.182i	−1.26566	−	0.730729i	−0.291496	−	0.956572i	$-0.594153\pi$
$263$	−332.869	−	192.182i	−1.26566	−	0.730729i	−0.974164	+	0.225843i	$0.927486\pi$
$264$	−39.5365	+	32.4990i	−0.149760	+	0.123102i
$265$	−2.04460			−0.00771548
$266$		0			0
$267$	12.1530			0.0455170
$268$	−455.341	+	50.1102i	−1.69903	+	0.186978i
$269$	−32.7022	−	18.8806i	−0.121570	−	0.0701882i	0.437982	−	0.898984i	$-0.355693\pi$
$269$	−32.7022	−	18.8806i	−0.121570	−	0.0701882i	−0.559552	+	0.828795i	$0.689027\pi$
$270$	−149.637	+	8.20895i	−0.554210	+	0.0304035i
$271$	−267.368	+	154.365i	−0.986597	+	0.569612i	−0.904255	−	0.426992i	$-0.859573\pi$
$271$	−267.368	+	154.365i	−0.986597	+	0.569612i	−0.0823420	+	0.996604i	$0.526240\pi$
$272$	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
$276$	234.017	−	171.778i	0.847888	−	0.622382i
$277$	−211.492	−	122.105i	−0.763508	−	0.440812i	0.0670458	−	0.997750i	$-0.478643\pi$
$277$	−211.492	−	122.105i	−0.763508	−	0.440812i	−0.830554	+	0.556938i	$0.811976\pi$
$278$	187.261	+	94.8385i	0.673601	+	0.341146i
$279$		−	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	$0.342693\pi$
$282$	89.3076	−	176.340i	0.316694	−	0.625320i
$283$	−82.8026	+	143.418i	−0.292589	+	0.506778i	−0.974421	−	0.224730i	$-0.927850\pi$
$283$	−82.8026	+	143.418i	−0.292589	+	0.506778i	0.681833	+	0.731508i	$0.261183\pi$
$284$	−337.904	+	248.035i	−1.18980	+	0.873362i
$285$	−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
$290$	−2.06740	−	37.6856i	−0.00712898	−	0.129950i
$291$	118.967	−	206.056i	0.408820	−	0.708098i
$292$	97.0040	−	10.6753i	0.332206	−	0.0365591i
$293$			34.3652i			0.117288i	0.998279	+	0.0586438i	$0.0186776\pi$
$293$			34.3652i			0.117288i	−0.998279	+	0.0586438i	$0.981322\pi$
$294$		0			0
$295$		−	153.966i		−	0.521918i
$296$	275.102	+	334.674i	0.929399	+	1.13066i
$297$	9.15405	−	15.8553i	0.0308217	−	0.0533848i
$298$	164.534	−	9.02620i	0.552127	−	0.0302893i
$299$	−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
$304$	196.267	−	43.7279i	0.645616	−	0.143842i
$305$	247.154	−	428.083i	0.810341	−	1.40355i
$306$	−682.964	−	345.888i	−2.23191	−	1.13035i
$307$	−222.934			−0.726170			−0.363085	−	0.931756i	$-0.618276\pi$
$307$	−222.934			−0.726170			−0.363085	+	0.931756i	$0.618276\pi$
$308$		0			0
$309$		−	181.736i		−	0.588141i
$310$	−231.876	−	117.434i	−0.747988	−	0.378819i
$311$	−363.673	−	209.967i	−1.16937	−	0.675135i	−0.215837	−	0.976429i	$-0.569248\pi$
$311$	−363.673	−	209.967i	−1.16937	−	0.675135i	−0.953531	+	0.301294i	$0.902581\pi$
$312$	245.094	−	652.759i	0.785557	−	2.09218i
$313$	146.934	+	254.498i	0.469439	+	0.813092i	0.999390	−	0.0349363i	$-0.0111228\pi$
$313$	146.934	+	254.498i	0.469439	+	0.813092i	−0.529950	+	0.848029i	$0.677789\pi$
$314$	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	$-0.433852\pi$
$317$	366.728	−	211.730i	1.15687	−	0.667919i	0.950552	+	0.310566i	$0.100519\pi$
$318$	−3.25324	+	0.178471i	−0.0102303	+	0.000561228i
$319$	3.99311	+	2.30542i	0.0125176	+	0.00722703i
$320$	241.466	−	276.217i	0.754583	−	0.863178i
$321$	377.561			1.17620
$322$		0			0
$323$	−405.551			−1.25558
$324$	187.086	−	20.5888i	0.577427	−	0.0635456i
$325$	129.921	+	75.0098i	0.399756	+	0.230799i
$326$	−8.51308	−	155.180i	−0.0261137	−	0.476014i
$327$	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	0.945694	−	0.325057i	$-0.105384\pi$
$331$	63.3332	+	109.696i	0.191339	+	0.331409i	−0.754355	+	0.656467i	$0.772050\pi$
$332$	187.628	+	255.611i	0.565145	+	0.769912i
$333$	−556.301	−	321.180i	−1.67057	−	0.964505i
$334$	56.1002	−	110.771i	0.167965	−	0.331651i
$335$		−	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	$0.351898\pi$
$338$	−348.150	−	176.321i	−1.03003	−	0.521659i
$339$	−363.419	+	629.460i	−1.07203	+	1.85681i
$340$	−596.500	+	437.854i	−1.75441	+	1.28781i
$341$	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
$346$	390.640	−	21.4302i	1.12902	−	0.0619371i
$347$	−160.266	+	277.589i	−0.461862	+	0.799969i	−0.999054	−	0.0434916i	$-0.986152\pi$
$347$	−160.266	+	277.589i	−0.461862	+	0.799969i	0.537192	+	0.843460i	$0.319485\pi$
$348$	−6.57904	−	59.7825i	−0.0189053	−	0.171789i
$349$			380.678i			1.09077i	0.838186	+	0.545385i	$0.183616\pi$
$349$			380.678i			1.09077i	−0.838186	+	0.545385i	$0.816384\pi$
$350$		0			0
$351$			249.426i			0.710614i
$352$	12.1287	+	43.1485i	0.0344566	+	0.122581i
$353$	182.185	−	315.553i	0.516104	−	0.893918i	−0.483721	−	0.875222i	$-0.660715\pi$
$353$	182.185	−	315.553i	0.516104	−	0.893918i	0.999825	−	0.0186962i	$-0.00595153\pi$
$354$	−13.4395	−	244.981i	−0.0379646	−	0.692036i
$355$	−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	$-0.616812\pi$
$359$	96.9908	−	55.9977i	0.270169	−	0.155982i	0.628965	+	0.777434i	$0.283479\pi$
$360$	−191.217	+	509.269i	−0.531158	+	1.41464i
$361$	101.529	−	175.854i	0.281245	−	0.487130i
$362$	−127.393	+	251.540i	−0.351914	+	0.694863i
$363$	−543.704			−1.49781
$364$		0			0
$365$			139.859i			0.383174i
$366$	355.889	−	702.713i	0.972375	−	1.91998i
$367$	380.222	+	219.521i	1.03603	+	0.598150i	0.918705	−	0.394944i	$-0.129236\pi$
$367$	380.222	+	219.521i	1.03603	+	0.598150i	0.117321	+	0.993094i	$0.462569\pi$
$368$	−55.2860	−	248.144i	−0.150234	−	0.674305i
$369$	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	$-0.777709\pi$
$373$	−220.833	+	127.498i	−0.592047	+	0.341818i	0.173860	+	0.984770i	$0.444376\pi$
$374$	−4.95169	−	90.2617i	−0.0132398	−	0.241341i
$375$	388.613	+	224.366i	1.03630	+	0.598309i
$376$	−109.924	−	133.727i	−0.292350	−	0.355657i
$377$	−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	$0.207167\pi$
$380$	31.5231	+	286.444i	0.0829554	+	0.753800i
$381$	63.6187	+	36.7303i	0.166978	+	0.0964049i
$382$	568.091	−	31.1651i	1.48715	−	0.0815839i
$383$	−63.5537	+	36.6927i	−0.165937	+	0.0958035i	−0.580668	−	0.814140i	$-0.697209\pi$
$383$	−63.5537	+	36.6927i	−0.165937	+	0.0958035i	0.414732	+	0.909944i	$0.363875\pi$
$384$	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
$388$	−123.301	−	167.976i	−0.317785	−	0.432927i
$389$	295.141	+	170.400i	0.758718	+	0.438046i	0.828835	−	0.559493i	$-0.189004\pi$
$389$	295.141	+	170.400i	0.758718	+	0.438046i	−0.0701174	+	0.997539i	$0.522337\pi$
$390$	891.452	+	451.476i	2.28577	+	1.15763i
$391$			512.745i			1.31137i
$392$		0			0
$393$	−539.581			−1.37298
$394$	97.6799	−	192.872i	0.247918	−	0.489522i
$395$	335.719	−	581.482i	0.849921	−	1.47211i
$396$	−39.3247	−	53.5730i	−0.0993047	−	0.135285i
$397$	96.5963	−	55.7699i	0.243316	−	0.140478i	−0.373384	−	0.927677i	$-0.621803\pi$
$397$	96.5963	−	55.7699i	0.243316	−	0.140478i	0.616700	+	0.787199i	$0.288469\pi$
$398$	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	0.571776	−	0.820410i	$-0.306254\pi$
$401$	−170.268	−	294.912i	−0.424607	−	0.735441i	−0.996384	+	0.0849681i	$0.972921\pi$
$402$	−57.3052	−	1044.59i	−0.142550	−	2.59847i
$403$	−216.300	+	374.643i	−0.536725	+	0.929635i
$404$	40.0252	+	363.701i	0.0990722	+	0.900250i
$405$			269.738i			0.666019i
$406$		0			0
$407$		−	75.8502i		−	0.186364i
$408$	−910.893	+	748.753i	−2.23258	+	1.83518i
$409$	−333.480	+	577.604i	−0.815354	+	1.41223i	0.0937202	+	0.995599i	$0.470124\pi$
$409$	−333.480	+	577.604i	−0.815354	+	1.41223i	−0.909074	+	0.416635i	$0.863209\pi$
$410$	86.9585	−	4.77048i	0.212094	−	0.0116353i
$411$	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
$416$	−437.024	−	426.469i	−1.05054	−	1.02517i
$417$	−239.686	+	415.149i	−0.574788	+	0.995561i
$418$	−31.4070	−	15.9061i	−0.0751364	−	0.0380528i
$419$	−200.191			−0.477783			−0.238891	−	0.971046i	$-0.576784\pi$
$419$	−200.191			−0.477783			−0.238891	+	0.971046i	$0.576784\pi$
$420$		0			0
$421$			15.9136i			0.0377996i	0.999821	+	0.0188998i	$0.00601636\pi$
$421$			15.9136i			0.0377996i	−0.999821	+	0.0188998i	$0.993984\pi$
$422$	47.0947	+	23.8511i	0.111599	+	0.0565193i
$423$	222.283	+	128.335i	0.525492	+	0.303393i
$424$	−1.00298	+	2.67125i	−0.00236553	+	0.00630011i
$425$	−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
$430$	238.662	−	13.0928i	0.555029	−	0.0304485i
$431$	543.875	+	314.006i	1.26189	+	0.728553i	0.973440	−	0.228941i	$-0.0735264\pi$
$431$	543.875	+	314.006i	1.26189	+	0.728553i	0.288451	+	0.957495i	$0.406860\pi$
$432$	−62.6796	+	199.525i	−0.145092	+	0.461864i
$433$	789.232			1.82271			0.911353	−	0.411625i	$-0.135039\pi$
$433$	789.232			1.82271			0.911353	+	0.411625i	$0.135039\pi$
$434$		0			0
$435$	86.1933			0.198146
$436$	−12.8956	−	117.180i	−0.0295771	−	0.268762i
$437$	172.935	+	99.8441i	0.395732	+	0.228476i
$438$	12.2081	+	222.534i	0.0278723	+	0.508069i
$439$	576.400	−	332.785i	1.31298	−	0.758052i	0.330395	−	0.943843i	$-0.392818\pi$
$439$	576.400	−	332.785i	1.31298	−	0.758052i	0.982589	+	0.185791i	$0.0594846\pi$
$440$	−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	−0.996318	−	0.0857327i	$-0.972677\pi$
$443$	−253.576	−	439.206i	−0.572406	−	0.991436i	0.423912	−	0.905703i	$-0.360656\pi$
$444$	−797.575	+	585.451i	−1.79634	+	1.31858i
$445$	13.2095	+	7.62650i	0.0296842	+	0.0171382i
$446$	−145.649	+	287.588i	−0.326567	+	0.644816i
$447$			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	$0.600571\pi$
$450$	−166.388	−	84.2673i	−0.369752	−	0.187261i
$451$	−5.31970	+	9.21400i	−0.0117954	+	0.0204301i
$452$	376.658	+	513.131i	0.833315	+	1.13525i
$453$	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	0.926757	+	0.375661i	$0.122584\pi$
$457$	360.441	+	624.302i	0.788710	+	1.36609i	−0.138047	+	0.990426i	$0.544082\pi$
$458$	−457.814	+	25.1153i	−0.999593	+	0.0548369i
$459$	210.903	−	365.294i	0.459483	−	0.795848i
$460$	362.156	−	39.8552i	0.787296	−	0.0866417i
$461$			483.262i			1.04829i	0.851629	+	0.524145i	$0.175615\pi$
$461$			483.262i			1.04829i	−0.851629	+	0.524145i	$0.824385\pi$
$462$		0			0
$463$		−	39.6326i		−	0.0855995i	−0.999084	−	0.0427997i	$-0.986372\pi$
$463$		−	39.6326i		−	0.0855995i	0.999084	−	0.0427997i	$-0.0136277\pi$
$464$	−50.2499	−	15.7857i	−0.108297	−	0.0340209i
$465$	296.792	−	514.059i	0.638262	−	1.10550i
$466$	29.5964	+	539.498i	0.0635116	+	1.15772i
$467$	−8.89340	−	15.4038i	−0.0190437	−	0.0329846i	0.856347	−	0.516402i	$-0.172729\pi$
$467$	−8.89340	−	15.4038i	−0.0190437	−	0.0329846i	−0.875390	+	0.483417i	$0.839395\pi$
$468$	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
$472$	−201.154	−	75.5282i	−0.426175	−	0.160017i
$473$	−14.6002	+	25.2883i	−0.0308673	+	0.0534637i
$474$	483.418	−	954.522i	1.01987	−	2.01376i
$475$	−98.8029			−0.208006
$476$		0			0
$477$		−	4.23072i		−	0.00886943i
$478$	−142.008	+	280.400i	−0.297089	+	0.586610i
$479$	579.039	+	334.308i	1.20885	+	0.697930i	0.962508	−	0.271254i	$-0.0874382\pi$
$479$	579.039	+	334.308i	1.20885	+	0.697930i	0.246341	+	0.969183i	$0.420772\pi$
$480$	599.653	+	585.171i	1.24928	+	1.21911i
$481$	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
$486$	36.4330	+	664.118i	0.0749650	+	1.36650i
$487$	−362.418	−	209.242i	−0.744185	−	0.429656i	0.0794038	−	0.996843i	$-0.474698\pi$
$487$	−362.418	−	209.242i	−0.744185	−	0.429656i	−0.823589	+	0.567187i	$0.808032\pi$
$488$	−438.044	−	532.901i	−0.897631	−	1.09201i
$489$	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	$0.373161\pi$
$492$	137.946	−	15.1810i	0.280379	−	0.0308556i
$493$	91.9984	+	53.1153i	0.186609	+	0.107739i
$494$	478.907	−	26.2725i	0.969448	−	0.0531832i
$495$	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	0.997633	−	0.0687578i	$-0.0219036\pi$
$499$	219.196	+	379.659i	0.439271	+	0.760839i	−0.558363	+	0.829597i	$0.688570\pi$
$500$	316.795	−	232.540i	0.633590	−	0.465079i
$501$	245.575	+	141.783i	0.490169	+	0.282999i
$502$	−558.723	−	282.965i	−1.11299	−	0.563676i
$503$		−	754.754i		−	1.50050i	−0.661151	−	0.750252i	$-0.729932\pi$
$503$		−	754.754i		−	1.50050i	0.661151	−	0.750252i	$-0.270068\pi$
$504$		0			0
$505$	−524.378			−1.03837
$506$	−20.1104	+	39.7085i	−0.0397438	+	0.0784752i
$507$	445.617	−	771.832i	0.878930	−	1.52235i
$508$	51.8615	−	38.0684i	0.102090	−	0.0749377i
$509$	427.842	−	247.015i	0.840554	−	0.485294i	−0.0168985	−	0.999857i	$-0.505379\pi$
$509$	427.842	−	247.015i	0.840554	−	0.485294i	0.857452	+	0.514563i	$0.172046\pi$
$510$	−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
$514$	38.2184	+	696.663i	0.0743549	+	1.35538i
$515$	114.046	−	197.533i	0.221449	−	0.383560i
$516$	378.602	−	41.6650i	0.733725	−	0.0807462i
$517$			30.3078i			0.0586224i
$518$		0			0
$519$			893.460i			1.72150i
$520$	676.030	−	555.696i	1.30006	−	1.06865i
$521$	16.4374	−	28.4704i	0.0315496	−	0.0546456i	−0.849819	−	0.527074i	$-0.823289\pi$
$521$	16.4374	−	28.4704i	0.0315496	−	0.0546456i	0.881369	+	0.472428i	$0.156622\pi$
$522$	77.9795	−	4.27789i	0.149386	−	0.00819520i
$523$	14.1377	+	24.4873i	0.0270320	+	0.0468208i	0.879225	−	0.476407i	$-0.158061\pi$
$523$	14.1377	+	24.4873i	0.0270320	+	0.0468208i	−0.852193	+	0.523228i	$0.824728\pi$
$524$	−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
$528$	−99.9090	+	22.2595i	−0.189222	+	0.0421581i
$529$	−138.265	+	239.482i	−0.261371	+	0.452708i
$530$	−3.64804	−	1.84755i	−0.00688309	−	0.00348594i
$531$	318.588			0.599977
$532$		0			0
$533$		−	144.949i		−	0.271949i
$534$	21.6838	+	10.9818i	0.0406064	+	0.0205651i
$535$	410.382	+	236.934i	0.767069	+	0.442867i
$536$	−857.713	−	322.049i	−1.60021	−	0.600837i
$537$	−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	−0.788521	+	0.615008i	$0.789153\pi$
$541$	−928.028	+	535.797i	−1.71539	+	0.990383i	−0.926873	+	0.375375i	$0.877514\pi$
$542$	−616.533	+	33.8225i	−1.13751	+	0.0624032i
$543$	−557.653	−	321.961i	−1.02699	−	0.592930i
$544$	279.437	+	994.109i	0.513670	+	1.82741i
$545$	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	$0.857968\pi$
$548$	76.2230	−	8.38831i	0.139093	−	0.0153071i
$549$	885.795	+	511.414i	1.61347	+	0.931537i
$550$	−1.20636	−	21.9901i	−0.00219339	−	0.0399821i
$551$	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
$556$	248.418	+	338.427i	0.446796	+	0.608681i
$557$	−418.767	−	241.775i	−0.751826	−	0.434067i	0.0745276	−	0.997219i	$-0.476255\pi$
$557$	−418.767	−	241.775i	−0.751826	−	0.434067i	−0.826353	+	0.563152i	$0.809588\pi$
$558$	242.995	−	479.801i	0.435476	−	0.859859i
$559$		−	397.821i		−	0.711665i
$560$		0			0
$561$	206.444			0.367993
$562$	475.620	+	240.878i	0.846300	+	0.428609i
$563$	−260.447	+	451.107i	−0.462605	+	0.801256i	−0.999090	−	0.0426543i	$-0.986419\pi$
$563$	−260.447	+	451.107i	−0.462605	+	0.801256i	0.536485	+	0.843910i	$0.319752\pi$
$564$	318.690	−	233.931i	0.565053	−	0.414771i
$565$	−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	0.984514	+	0.175306i	$0.0560916\pi$
$569$	366.480	+	634.761i	0.644077	+	1.11557i	−0.340437	+	0.940267i	$0.610575\pi$
$570$	−657.123	+	36.0493i	−1.15285	+	0.0632444i
$571$	499.792	−	865.665i	0.875292	−	1.51605i	0.0188408	−	0.999822i	$-0.494002\pi$
$571$	499.792	−	865.665i	0.875292	−	1.51605i	0.856451	−	0.516228i	$-0.172664\pi$
$572$	11.6947	+	106.268i	0.0204453	+	0.185782i
$573$			1299.32i			2.26758i
$574$		0			0
$575$			124.918i			0.217249i
$576$	571.551	+	499.645i	0.992277	+	0.867440i
$577$	−232.929	+	403.445i	−0.403690	+	0.699212i	−0.994168	−	0.107842i	$-0.965606\pi$
$577$	−232.929	+	403.445i	−0.403690	+	0.699212i	0.590478	+	0.807054i	$0.298939\pi$
$578$	−82.4223	−	1502.43i	−0.142599	−	2.59936i
$579$	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
$584$	182.724	+	68.6079i	0.312883	+	0.117479i
$585$	−648.772	+	1123.71i	−1.10901	+	1.92087i
$586$	−31.0532	+	61.3154i	−0.0529918	+	0.104634i
$587$	−574.851			−0.979303			−0.489651	−	0.871918i	$-0.662876\pi$
$587$	−574.851			−0.979303			−0.489651	+	0.871918i	$0.662876\pi$
$588$		0			0
$589$		−	284.911i		−	0.483719i
$590$	139.127	−	274.710i	0.235808	−	0.465610i
$591$	427.587	+	246.868i	0.723498	+	0.417712i
$592$	188.425	+	845.724i	0.318286	+	1.42859i
$593$	−471.528	−	816.710i	−0.795156	−	1.37725i	−0.922740	−	0.385423i	$-0.874055\pi$
$593$	−471.528	−	816.710i	−0.795156	−	1.37725i	0.127584	−	0.991828i	$-0.459278\pi$
$594$	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
$598$	−33.2168	−	605.491i	−0.0555465	−	1.01253i
$599$	8.02545	+	4.63349i	0.0133981	+	0.00773538i	0.506684	−	0.862132i	$-0.330871\pi$
$599$	8.02545	+	4.63349i	0.0133981	+	0.00773538i	−0.493286	+	0.869867i	$0.664204\pi$
$600$	−221.918	+	182.416i	−0.369863	+	0.304027i
$601$	57.7003			0.0960072			0.0480036	−	0.998847i	$-0.484714\pi$
$601$	57.7003			0.0960072			0.0480036	+	0.998847i	$0.484714\pi$
$602$		0			0
$603$	1358.44			2.25281
$604$	−25.2643	−	229.572i	−0.0418283	−	0.380086i
$605$	−590.966	−	341.194i	−0.976804	−	0.563958i
$606$	−834.357	+	45.7722i	−1.37683	+	0.0755316i
$607$	887.396	−	512.339i	1.46194	−	0.844050i	0.462837	−	0.886443i	$-0.346831\pi$
$607$	887.396	−	512.339i	1.46194	−	0.844050i	0.999101	+	0.0423930i	$0.0134982\pi$
$608$	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
$612$	−906.012	−	1234.28i	−1.48041	−	2.01680i
$613$	−350.583	−	202.409i	−0.571914	−	0.330195i	0.186000	−	0.982550i	$-0.440448\pi$
$613$	−350.583	−	202.409i	−0.571914	−	0.330195i	−0.757913	+	0.652355i	$0.773781\pi$
$614$	−397.765	−	201.448i	−0.647826	−	0.328091i
$615$			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	$0.242005\pi$
$618$	164.220	−	324.258i	0.265729	−	0.524689i
$619$	389.694	−	674.970i	0.629554	−	1.09042i	−0.358087	−	0.933688i	$-0.616571\pi$
$619$	389.694	−	674.970i	0.629554	−	1.09042i	0.987641	−	0.156731i	$-0.0500957\pi$
$620$	−307.604	−	419.057i	−0.496136	−	0.675899i
$621$	−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
$626$	32.1944	+	586.855i	0.0514288	+	0.937469i
$627$	40.1997	−	69.6278i	0.0641143	−	0.111049i
$628$	1.63198	+	14.8295i	0.00259869	+	0.0236138i
$629$		−	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	$0.787855\pi$
$632$	−595.012	−	723.859i	−0.941474	−	1.14535i
$633$	−60.2793	+	104.407i	−0.0952279	+	0.164940i
$634$	845.650	−	46.3917i	1.33383	−	0.0731730i
$635$	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
$640$	680.427	−	274.639i	1.06317	−	0.429124i
$641$	11.6570	−	20.1905i	0.0181856	−	0.0314984i	−0.856789	−	0.515667i	$-0.827544\pi$
$641$	11.6570	−	20.1905i	0.0181856	−	0.0314984i	0.874975	+	0.484168i	$0.160878\pi$
$642$	673.655	+	341.173i	1.04931	+	0.531422i
$643$	530.706			0.825360			0.412680	−	0.910876i	$-0.364593\pi$
$643$	530.706			0.825360			0.412680	+	0.910876i	$0.364593\pi$
$644$		0			0
$645$			545.862i			0.846297i
$646$	−723.595	−	366.465i	−1.12012	−	0.567283i
$647$	−184.840	−	106.717i	−0.285687	−	0.164942i	0.350308	−	0.936635i	$-0.386077\pi$
$647$	−184.840	−	106.717i	−0.285687	−	0.164942i	−0.635995	+	0.771693i	$0.719410\pi$
$648$	352.409	+	132.320i	0.543841	+	0.204198i
$649$	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	$-0.734166\pi$
$653$	−238.048	+	137.437i	−0.364545	+	0.210470i	0.306528	+	0.951862i	$0.400833\pi$
$654$	268.820	−	14.7473i	0.411039	−	0.0225493i
$655$	−586.485	−	338.607i	−0.895397	−	0.516958i
$656$	36.4251	−	115.950i	0.0555260	−	0.176754i
$657$	−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	$0.113925\pi$
$660$	−16.0467	−	145.813i	−0.0243131	−	0.220929i
$661$	−504.662	−	291.367i	−0.763482	−	0.440797i	0.0670625	−	0.997749i	$-0.478637\pi$
$661$	−504.662	−	291.367i	−0.763482	−	0.440797i	−0.830545	+	0.556952i	$0.811971\pi$
$662$	13.8768	+	252.953i	0.0209619	+	0.382104i
$663$	−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
$668$	200.191	−	146.948i	0.299687	−	0.219982i
$669$	−637.569	−	368.101i	−0.953018	−	0.550225i
$670$	593.231	−	1171.35i	0.885419	−	1.74828i
$671$			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	$0.595833\pi$
$674$	539.558	+	273.259i	0.800530	+	0.405429i
$675$	51.3815	−	88.9953i	0.0761207	−	0.131845i
$676$	−461.851	−	629.192i	−0.683212	−	0.930758i
$677$	−653.388	+	377.234i	−0.965123	+	0.557214i	−0.897746	−	0.440514i	$-0.854796\pi$
$677$	−653.388	+	377.234i	−0.965123	+	0.557214i	−0.0673768	+	0.997728i	$0.521463\pi$
$678$	−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
$682$	63.4113	−	3.47870i	0.0929785	−	0.00510073i
$683$	−144.132	+	249.644i	−0.211028	+	0.365511i	−0.952036	−	0.305985i	$-0.901014\pi$
$683$	−144.132	+	249.644i	−0.211028	+	0.365511i	0.741009	+	0.671495i	$0.234348\pi$
$684$	−592.713	+	65.2279i	−0.866539	+	0.0953624i
$685$			109.897i			0.160433i
$686$		0			0
$687$		−	1047.10i		−	1.52416i
$688$	99.9706	−	318.232i	0.145306	−	0.462547i
$689$	−3.40298	+	5.89414i	−0.00493901	+	0.00855462i
$690$	45.5778	+	830.813i	0.0660548	+	1.20408i
$691$	78.3458	+	135.699i	0.113380	+	0.196380i	0.917131	−	0.398586i	$-0.130499\pi$
$691$	78.3458	+	135.699i	0.113380	+	0.196380i	−0.803751	+	0.594966i	$0.797165\pi$
$692$	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
$696$	42.2823	−	112.611i	0.0607504	−	0.161797i
$697$	−122.562	+	212.284i	−0.175842	+	0.304568i
$698$	−343.990	+	679.217i	−0.492822	+	0.973090i
$699$	−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	$0.702970\pi$
$702$	−225.386	+	445.032i	−0.321063	+	0.633949i
$703$	−589.396	−	340.288i	−0.838401	−	0.484051i
$704$	−17.3495	+	87.9464i	−0.0246442	+	0.124924i
$705$	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	$-0.385401\pi$
$709$	949.313	−	548.086i	1.33895	−	0.773041i	0.986651	+	0.162847i	$0.0520678\pi$
$710$	−65.8112	−	1199.64i	−0.0926918	−	1.68963i
$711$	1203.21	+	694.673i	1.69228	+	0.977037i
$712$	16.4439	−	13.5168i	0.0230953	−	0.0189843i
$713$	−360.218			−0.505214
$714$		0			0
$715$	−153.215			−0.214286
$716$	−287.106	+	31.5959i	−0.400986	+	0.0441284i
$717$	−621.633	−	358.900i	−0.866991	−	0.500558i
$718$	223.654	−	12.2695i	0.311496	−	0.0170885i
$719$	−524.259	+	302.681i	−0.729150	+	0.420975i	−0.818111	−	0.575060i	$-0.804979\pi$
$719$	−524.259	+	302.681i	−0.729150	+	0.420975i	0.0889614	+	0.996035i	$0.471645\pi$
$720$	−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
$724$	−454.595	+	333.690i	−0.627894	+	0.460898i
$725$	22.4132	+	12.9403i	0.0309148	+	0.0178487i
$726$	−970.091	−	491.303i	−1.33621	−	0.676725i
$727$			443.659i			0.610260i	0.952311	+	0.305130i	$0.0986999\pi$
$727$			443.659i			0.610260i	−0.952311	+	0.305130i	$0.901300\pi$
$728$		0			0
$729$	−1095.46			−1.50269
$730$	−126.379	+	249.540i	−0.173123	+	0.341835i
$731$	−336.379	+	582.625i	−0.460162	+	0.797025i
$732$	1269.97	−	932.210i	1.73494	−	1.27351i
$733$	−649.541	+	375.013i	−0.886141	+	0.511614i	−0.872678	−	0.488296i	$-0.837619\pi$
$733$	−649.541	+	375.013i	−0.886141	+	0.511614i	−0.0134626	+	0.999909i	$0.504285\pi$
$734$	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
$738$	9.87113	+	179.935i	0.0133755	+	0.243815i
$739$	−309.646	+	536.323i	−0.419007	+	0.725742i	−0.995840	−	0.0911205i	$-0.970955\pi$
$739$	−309.646	+	536.323i	−0.419007	+	0.725742i	0.576833	+	0.816862i	$0.304288\pi$
$740$	−1234.30	+	135.834i	−1.66797	+	0.183560i
$741$			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	$0.993461\pi$
$744$	−526.020	−	639.927i	−0.707016	−	0.860117i
$745$	−236.153	+	409.029i	−0.316984	+	0.549032i
$746$	−509.227	+	27.9358i	−0.682610	+	0.0374475i
$747$	−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	$-0.889650\pi$
$751$	−838.498	+	484.107i	−1.11651	+	0.644616i	−0.176001	+	0.984390i	$0.556316\pi$
$752$	−75.2898	−	337.929i	−0.100119	−	0.449374i
$753$	715.142	−	1238.66i	0.949723	−	1.64497i
$754$	−112.080	−	56.7630i	−0.148647	−	0.0752825i
$755$	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	$-0.281521\pi$
$758$	1075.97	+	544.927i	1.41949	+	0.718902i
$759$	−88.0318	−	50.8252i	−0.115984	−	0.0669633i
$760$	−202.593	+	539.566i	−0.266569	+	0.709955i
$761$	−117.998	−	204.379i	−0.155057	−	0.268566i	0.778023	−	0.628236i	$-0.216223\pi$
$761$	−117.998	−	204.379i	−0.155057	−	0.268566i	−0.933080	+	0.359670i	$0.882889\pi$
$762$	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
$766$	−146.551	+	8.03966i	−0.191319	+	0.0104956i
$767$	−443.849	−	256.257i	−0.578682	−	0.334102i
$768$	1058.68	−	496.383i	1.37849	−	0.646332i
$769$	−124.257			−0.161582			−0.0807912	−	0.996731i	$-0.525745\pi$
$769$	−124.257			−0.161582			−0.0807912	+	0.996731i	$0.525745\pi$
$770$		0			0
$771$	−1593.39			−2.06665
$772$	492.428	−	54.1915i	0.637859	−	0.0701962i
$773$	−154.345	−	89.1114i	−0.199671	−	0.115280i	0.396831	−	0.917892i	$-0.370110\pi$
$773$	−154.345	−	89.1114i	−0.199671	−	0.115280i	−0.596502	+	0.802612i	$0.703443\pi$
$774$	27.0919	+	493.843i	0.0350024	+	0.638040i
$775$	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
$780$	1182.59	+	1611.07i	1.51614	+	2.06548i
$781$	127.112	+	73.3880i	0.162755	+	0.0939667i
$782$	−463.328	+	914.854i	−0.592491	+	1.16989i
$783$			43.0296i			0.0549548i
$784$		0			0
$785$	−21.3809			−0.0272368
$786$	−962.735	−	487.578i	−1.22485	−	0.620328i
$787$	553.948	−	959.466i	0.703873	−	1.21914i	−0.263224	−	0.964735i	$-0.584786\pi$
$787$	553.948	−	959.466i	0.703873	−	1.21914i	0.967097	−	0.254409i	$-0.0818808\pi$
$788$	348.566	−	255.861i	0.442343	−	0.324697i
$789$	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
$794$	222.745	−	12.2196i	0.280535	−	0.0153899i
$795$	4.66933	−	8.08752i	0.00587338	−	0.0101730i
$796$	145.205	+	1319.45i	0.182418	+	1.65760i
$797$		−	1094.69i		−	1.37351i	−0.726889	−	0.686755i	$-0.759034\pi$
$797$		−	1094.69i		−	1.37351i	0.726889	−	0.686755i	$-0.240966\pi$
$798$		0			0
$799$			698.269i			0.873929i
$800$	68.0782	+	242.191i	0.0850977	+	0.302739i
$801$	−15.7808	+	27.3332i	−0.0197014	+	0.0341238i
$802$	−37.3069	−	680.048i	−0.0465173	−	0.847940i
$803$	−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
$808$	−257.234	+	685.093i	−0.318359	+	0.847887i
$809$	693.377	−	1200.96i	0.857079	−	1.48450i	−0.0176240	−	0.999845i	$-0.505610\pi$
$809$	693.377	−	1200.96i	0.857079	−	1.48450i	0.874703	−	0.484659i	$-0.161056\pi$
$810$	−243.741	+	481.273i	−0.300915	+	0.594165i
$811$	−312.204			−0.384962			−0.192481	−	0.981301i	$-0.561653\pi$
$811$	−312.204			−0.384962			−0.192481	+	0.981301i	$0.561653\pi$
$812$		0			0
$813$		−	1410.11i		−	1.73446i
$814$	68.5400	−	135.334i	0.0842014	−	0.166258i
$815$	385.776	+	222.728i	0.473345	+	0.273286i
$816$	−2301.83	+	512.842i	−2.82087	+	0.628483i
$817$	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	$-0.898484\pi$
$821$	−946.469	+	546.444i	−1.15282	+	0.665583i	−0.203250	+	0.979127i	$0.565150\pi$
$822$	9.59275	+	174.861i	0.0116700	+	0.212726i
$823$	785.625	+	453.581i	0.954587	+	0.551131i	0.894503	−	0.447062i	$-0.147530\pi$
$823$	785.625	+	453.581i	0.954587	+	0.551131i	0.0600842	+	0.998193i	$0.480863\pi$
$824$	−202.130	−	245.900i	−0.245303	−	0.298422i
$825$	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	$0.619641\pi$
$828$	82.4688	+	749.378i	0.0996000	+	0.905046i
$829$	370.632	+	213.984i	0.447083	+	0.258124i	0.706598	−	0.707616i	$-0.250229\pi$
$829$	370.632	+	213.984i	0.447083	+	0.258124i	−0.259514	+	0.965739i	$0.583562\pi$
$830$	−907.476	+	49.7834i	−1.09334	+	0.0599800i
$831$	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
$836$	−41.6642	−	56.7602i	−0.0498375	−	0.0678949i
$837$	256.629	+	148.165i	0.306606	+	0.177019i
$838$	−357.186	−	180.897i	−0.426237	−	0.215868i
$839$		−	1133.09i		−	1.35053i	−0.737575	−	0.675265i	$-0.764029\pi$
$839$		−	1133.09i		−	1.35053i	0.737575	−	0.675265i	$-0.235971\pi$
$840$		0			0
$841$	830.163			0.987114
$842$	−14.3799	+	28.3936i	−0.0170783	+	0.0337216i
$843$	−608.774	+	1054.43i	−0.722152	+	1.25080i
$844$	62.4753	+	85.1117i	0.0740228	+	0.100843i
$845$	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
$850$	−27.7937	−	506.637i	−0.0326985	−	0.596043i
$851$	−430.232	+	745.184i	−0.505561	+	0.875657i
$852$	−209.429	−	1903.04i	−0.245809	−	2.23362i
$853$		−	169.502i		−	0.198712i	−0.995052	−	0.0993562i	$-0.968322\pi$
$853$		−	169.502i		−	0.198712i	0.995052	−	0.0993562i	$-0.0316783\pi$
$854$		0			0
$855$		−	854.563i		−	0.999489i
$856$	510.865	−	419.930i	0.596805	−	0.490573i
$857$	117.039	−	202.718i	0.136569	−	0.236544i	−0.789627	−	0.613587i	$-0.789726\pi$
$857$	117.039	−	202.718i	0.136569	−	0.236544i	0.926196	+	0.377043i	$0.123059\pi$
$858$	−243.786	+	13.3739i	−0.284132	+	0.0155873i
$859$	−447.171	−	774.523i	−0.520571	−	0.901656i	−0.999714	−	0.0239189i	$-0.992386\pi$
$859$	−447.171	−	774.523i	−0.520571	−	0.901656i	0.479143	−	0.877737i	$-0.340948\pi$
$860$	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	$-0.517702\pi$
$863$	674.270	−	389.290i	0.781309	−	0.451089i	0.836894	+	0.547365i	$0.184369\pi$
$864$	−292.130	+	299.360i	−0.338114	+	0.346481i
$865$	−560.680	+	971.126i	−0.648185	+	1.12269i
$866$	1408.17	+	713.168i	1.62606	+	0.823519i
$867$	3436.32			3.96346
$868$		0			0
$869$			164.055i			0.188786i
$870$	153.789	+	77.8862i	0.176768	+	0.0895244i
$871$	−1892.55	−	1092.67i	−2.17285	−	1.25450i
$872$	82.8778	−	220.729i	0.0950434	−	0.253129i
$873$	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	$-0.663531\pi$
$877$	14.9632	−	8.63901i	0.0170618	−	0.00985064i	0.508507	+	0.861058i	$0.330198\pi$
$878$	1329.14	−	72.9157i	1.51383	−	0.0830475i
$879$	−135.933	−	78.4811i	−0.154645	−	0.0892846i
$880$	−122.562	−	38.5022i	−0.139275	−	0.0437525i
$881$	770.918			0.875049			0.437524	−	0.899207i	$-0.355855\pi$
$881$	770.918			0.875049			0.437524	+	0.899207i	$0.355855\pi$
$882$		0			0
$883$	776.362			0.879232			0.439616	−	0.898186i	$-0.355114\pi$
$883$	776.362			0.879232			0.439616	+	0.898186i	$0.355114\pi$
$884$	269.438	+	2448.33i	0.304794	+	2.76960i
$885$	609.019	+	351.617i	0.688157	+	0.397308i
$886$	−55.5604	−	1012.78i	−0.0627092	−	1.14309i
$887$	1412.32	−	815.402i	1.59224	−	0.919280i	0.599319	−	0.800511i	$-0.295438\pi$
$887$	1412.32	−	815.402i	1.59224	−	0.919280i	0.992922	−	0.118770i	$-0.0378950\pi$
$888$	−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
$892$	−519.742	+	381.511i	−0.582670	+	0.427702i
$893$	235.507	+	135.970i	0.263726	+	0.152262i
$894$	−340.048	+	671.434i	−0.380367	+	0.751045i
$895$		−	413.945i		−	0.462508i
$896$		0			0
$897$	1384.86			1.54388
$898$	−497.852	−	252.137i	−0.554400	−	0.280776i
$899$	−37.3150	+	64.6314i	−0.0415072	+	0.0718925i
$900$	−220.729	−	300.704i	−0.245254	−	0.334116i
$901$	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
$906$	526.655	−	28.8919i	0.581297	−	0.0318895i
$907$	476.931	−	826.069i	0.525834	−	0.910771i	−0.473713	−	0.880679i	$-0.657087\pi$
$907$	476.931	−	826.069i	0.525834	−	0.910771i	0.999547	−	0.0300919i	$-0.00958001\pi$
$908$	681.004	−	74.9443i	0.750005	−	0.0825378i
$909$		−	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	$-0.374017\pi$
$912$	−275.255	+	876.207i	−0.301815	+	0.960754i
$913$	55.5150	−	96.1548i	0.0608051	−	0.105317i
$914$	78.9753	+	1439.60i	0.0864062	+	1.57505i
$915$	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	$-0.755262\pi$
$919$	−437.335	+	252.495i	−0.475881	+	0.274750i	0.242817	+	0.970072i	$0.421929\pi$
$920$	682.183	+	256.142i	0.741503	+	0.278415i
$921$	509.122	−	881.826i	0.552793	−	0.957466i
$922$	−436.686	+	862.249i	−0.473630	+	0.935195i
$923$	−1999.64			−2.16646
$924$		0			0
$925$		−	425.746i		−	0.460266i
$926$	35.8129	−	70.7135i	0.0386748	−	0.0763645i
$927$	408.739	+	235.985i	0.440926	+	0.254569i
$928$	−75.3930	−	73.5722i	−0.0812424	−	0.0792804i
$929$	−491.925	−	852.040i	−0.529521	−	0.917158i	−0.999407	−	0.0344306i	$-0.989038\pi$
$929$	−491.925	−	852.040i	−0.529521	−	0.917158i	0.469886	−	0.882727i	$-0.344295\pi$
$930$	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
$934$	−1.94861	−	35.5202i	−0.00208631	−	0.0380302i
$935$	224.389	+	129.551i	0.239989	+	0.138558i
$936$	1149.85	+	1398.85i	1.22847	+	1.49450i
$937$	−389.648			−0.415846			−0.207923	−	0.978145i	$-0.566670\pi$
$937$	−389.648			−0.415846			−0.207923	+	0.978145i	$0.566670\pi$
$938$		0			0
$939$	−1342.24			−1.42943
$940$	493.193	−	54.2758i	0.524674	−	0.0577402i
$941$	758.175	+	437.732i	0.805712	+	0.465178i	0.845464	−	0.534032i	$-0.179324\pi$
$941$	758.175	+	437.732i	0.805712	+	0.465178i	−0.0397529	+	0.999210i	$0.512657\pi$
$942$	−34.0199	+	1.86631i	−0.0361146	+	0.00198122i
$943$	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	0.980442	+	0.196807i	$0.0630572\pi$
$947$	625.646	+	1083.65i	0.660661	+	1.14430i	−0.319781	+	0.947491i	$0.603609\pi$
$948$	1725.06	−	1266.26i	1.81968	−	1.33571i
$949$	403.181	+	232.777i	0.424849	+	0.245287i
$950$	−176.287	−	89.2805i	−0.185565	−	0.0939795i
$951$			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	$0.653161\pi$
$954$	3.82297	−	7.54856i	0.00400731	−	0.00791254i
$955$	−815.373	+	1412.27i	−0.853793	+	1.47881i
$956$	−506.751	+	371.975i	−0.530074	+	0.389095i
$957$	−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
$962$	113.209	+	2063.63i	0.117681	+	2.14515i
$963$	−490.267	+	849.167i	−0.509103	+	0.881793i
$964$	388.504	−	42.7547i	0.403012	−	0.0443514i
$965$			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	$-0.260099\pi$
$968$	−735.666	+	604.716i	−0.759985	+	0.624707i
$969$	926.171	−	1604.18i	0.955801	−	1.65550i
$970$	596.352	−	32.7154i	0.614796	−	0.0337272i
$971$	−339.275	−	587.641i	−0.349408	−	0.605192i	0.636737	−	0.771081i	$-0.280284\pi$
$971$	−339.275	−	587.641i	−0.349408	−	0.605192i	−0.986144	+	0.165889i	$0.946951\pi$
$972$	−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
$976$	−300.029	−	1346.64i	−0.307406	−	1.37976i
$977$	−55.9074	+	96.8344i	−0.0572235	+	0.0991141i	−0.893218	−	0.449624i	$-0.851558\pi$
$977$	−55.9074	+	96.8344i	−0.0572235	+	0.0991141i	0.835995	+	0.548738i	$0.184891\pi$
$978$	633.265	+	320.717i	0.647510	+	0.327932i
$979$	−3.72682			−0.00380676
$980$		0			0
$981$			349.590i			0.356360i
$982$	679.845	+	344.308i	0.692307	+	0.350619i
$983$	−175.133	−	101.113i	−0.178162	−	0.102862i	0.408267	−	0.912863i	$-0.366133\pi$
$983$	−175.133	−	101.113i	−0.178162	−	0.102862i	−0.586429	+	0.810001i	$0.699467\pi$
$984$	259.846	+	97.5652i	0.264071	+	0.0991517i
$985$	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
$990$	190.196	−	10.4340i	0.192118	−	0.0105394i
$991$	163.735	+	94.5322i	0.165222	+	0.0953907i	0.580331	−	0.814381i	$-0.302923\pi$
$991$	163.735	+	94.5322i	0.165222	+	0.0953907i	−0.415109	+	0.909772i	$0.636257\pi$
$992$	−698.389	+	196.312i	−0.704021	+	0.197895i
$993$	−578.546			−0.582624
$994$		0			0
$995$	−1902.36			−1.91192
$996$	−1439.57	+	158.425i	−1.44535	+	0.159061i
$997$	−1414.14	−	816.457i	−1.41840	−	0.818914i	−0.422241	−	0.906483i	$-0.638757\pi$
$997$	−1414.14	−	816.457i	−1.41840	−	0.818914i	−0.996158	+	0.0875699i	$0.972090\pi$
$998$	48.0275	+	875.468i	0.0481238	+	0.877222i
$999$	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.o.67.7		16
7.2	even	3	inner	392.3.k.o.275.5		16
7.3	odd	6		392.3.g.m.99.2		8
7.4	even	3		56.3.g.b.43.2	yes	8
7.5	odd	6		392.3.k.n.275.5		16
7.6	odd	2		392.3.k.n.67.7		16
8.3	odd	2	inner	392.3.k.o.67.5		16
21.11	odd	6		504.3.g.b.379.7		8
28.3	even	6		1568.3.g.m.687.8		8
28.11	odd	6		224.3.g.b.15.1		8
56.3	even	6		392.3.g.m.99.1		8
56.11	odd	6		56.3.g.b.43.1	✓	8
56.19	even	6		392.3.k.n.275.7		16
56.27	even	2		392.3.k.n.67.5		16
56.45	odd	6		1568.3.g.m.687.7		8
56.51	odd	6	inner	392.3.k.o.275.7		16
56.53	even	6		224.3.g.b.15.2		8
84.11	even	6		2016.3.g.b.1135.7		8
112.11	odd	12		1792.3.d.j.1023.14		16
112.53	even	12		1792.3.d.j.1023.4		16
112.67	odd	12		1792.3.d.j.1023.3		16
112.109	even	12		1792.3.d.j.1023.13		16
168.11	even	6		504.3.g.b.379.8		8
168.53	odd	6		2016.3.g.b.1135.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.1	✓	8	56.11	odd	6
56.3.g.b.43.2	yes	8	7.4	even	3
224.3.g.b.15.1		8	28.11	odd	6
224.3.g.b.15.2		8	56.53	even	6
392.3.g.m.99.1		8	56.3	even	6
392.3.g.m.99.2		8	7.3	odd	6
392.3.k.n.67.5		16	56.27	even	2
392.3.k.n.67.7		16	7.6	odd	2
392.3.k.n.275.5		16	7.5	odd	6
392.3.k.n.275.7		16	56.19	even	6
392.3.k.o.67.5		16	8.3	odd	2	inner
392.3.k.o.67.7		16	1.1	even	1	trivial
392.3.k.o.275.5		16	7.2	even	3	inner
392.3.k.o.275.7		16	56.51	odd	6	inner
504.3.g.b.379.7		8	21.11	odd	6
504.3.g.b.379.8		8	168.11	even	6
1568.3.g.m.687.7		8	56.45	odd	6
1568.3.g.m.687.8		8	28.3	even	6
1792.3.d.j.1023.3		16	112.67	odd	12
1792.3.d.j.1023.4		16	112.53	even	12
1792.3.d.j.1023.13		16	112.109	even	12
1792.3.d.j.1023.14		16	112.11	odd	12
2016.3.g.b.1135.2		8	168.53	odd	6
2016.3.g.b.1135.7		8	84.11	even	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)

\(f(q)\)	\(=\)	\(q+(1.78423 + 0.903622i) q^{2} +(-2.28374 + 3.95555i) q^{3} +(2.36693 + 3.22453i) q^{4} +(-4.96451 + 2.86626i) q^{5} +(-7.64902 + 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +(-5.93090 - 10.2726i) q^{9} +O(q^{10})\)	\(q+(1.78423 + 0.903622i) q^{2} +(-2.28374 + 3.95555i) q^{3} +(2.36693 + 3.22453i) 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} +(-11.4478 + 0.628019i) q^{10} +(0.700323 - 1.21300i) q^{11} +(-18.1602 + 1.99853i) q^{12} +19.0821i q^{13} -26.1831i q^{15} +(-4.79525 + 15.2645i) q^{16} +(16.1349 - 27.9465i) q^{17} +(-1.29950 - 23.6880i) 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} +(-34.2079 - 12.8442i) q^{24} +(3.93090 - 6.80852i) q^{25} +(-17.2430 + 34.0468i) q^{26} +13.0712 q^{27} +3.29194i q^{29} +(23.6597 - 46.7166i) q^{30} +(19.6332 + 11.3352i) q^{31} +(-22.3492 + 22.9023i) 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} +(-1.37681 - 25.0972i) q^{38} +(-75.4801 - 43.5785i) q^{39} +(-29.1213 - 35.4274i) q^{40} -7.59607 q^{41} -20.8478 q^{43} +(5.56897 - 0.612863i) q^{44} +(58.8880 + 33.9990i) q^{45} +(-31.7309 + 1.74073i) 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} +(-61.5309 + 45.1661i) q^{52} +(0.308883 + 0.178334i) q^{53} +(23.3220 + 11.8114i) q^{54} +8.02924i q^{55} +57.4016 q^{57} +(-2.97467 + 5.87357i) q^{58} +(-13.4292 + 23.2600i) q^{59} +(84.4284 - 61.9737i) 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} +(0.700861 + 12.7756i) q^{66} +(-57.2613 + 99.1794i) q^{67} +(128.305 - 14.1199i) q^{68} -72.5739i q^{69} +104.792i q^{71} +(73.3069 - 60.2582i) q^{72} +(12.1987 - 21.1288i) q^{73} +(108.145 - 5.93274i) 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} +(-19.9460 - 89.5253i) q^{80} +(23.5270 - 40.7499i) q^{81} +(-13.5531 - 6.86398i) q^{82} +79.2706 q^{83} +184.988i q^{85} +(-37.1973 - 18.8386i) q^{86} +(-13.0214 - 7.51793i) q^{87} +(10.4901 + 3.93875i) 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} +(-43.2119 + 2.37057i) q^{94} +(62.3913 + 36.0216i) q^{95} +(-39.5514 - 140.706i) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more