LMFDB - Embedded newform 392.3.k.o.275.7

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			275.7
Root			$-1.78423 + 0.903622i$ of defining polynomial
Character	$\chi$	$=$	392.275
Dual form			392.3.k.o.67.7

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	−0.942209	−	0.335026i	$-0.891255\pi$
$3$	−2.28374	−	3.95555i	−0.761245	−	1.31852i	0.180964	−	0.983490i	$-0.442078\pi$
$4$	2.36693	−	3.22453i	0.591733	−	0.806134i
$5$	−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
$10$	−11.4478	−	0.628019i	−1.14478	−	0.0628019i
$11$	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	$0.813054\pi$
$12$	−18.1602	−	1.99853i	−1.51335	−	0.166544i
$13$		−	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
$16$	−4.79525	−	15.2645i	−0.299703	−	0.954032i
$17$	16.1349	+	27.9465i	0.949114	+	1.64391i	0.747296	+	0.664491i	$0.231352\pi$
$17$	16.1349	+	27.9465i	0.949114	+	1.64391i	0.201818	+	0.979423i	$0.435315\pi$
$18$	−1.29950	+	23.6880i	−0.0721947	+	1.31600i
$19$	−6.28374	+	10.8837i	−0.330723	+	0.572829i	−0.982654	−	0.185449i	$-0.940626\pi$
$19$	−6.28374	+	10.8837i	−0.330723	+	0.572829i	0.651931	+	0.758278i	$0.273959\pi$
$20$	−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	0.170082	−	0.985430i	$-0.445597\pi$
$23$	−13.7605	−	7.94464i	−0.598284	−	0.345419i	−0.768366	+	0.640011i	$0.778930\pi$
$24$	−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	$-0.981924\pi$
$29$		−	3.29194i		−	0.113515i	0.998388	−	0.0567576i	$-0.0180762\pi$
$30$	23.6597	+	46.7166i	0.788655	+	1.55722i
$31$	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	$0.214179\pi$
$32$	−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	0.974519	−	0.224303i	$-0.0720105\pi$
$37$	46.8985	+	27.0769i	1.26753	+	0.731807i	0.293008	+	0.956110i	$0.405344\pi$
$38$	−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	0.287217	−	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
$52$	−61.5309	−	45.1661i	−1.18329	−	0.868578i
$53$	0.308883	−	0.178334i	0.00582798	−	0.00336479i	−0.497083	−	0.867703i	$-0.665596\pi$
$53$	0.308883	−	0.178334i	0.00582798	−	0.00336479i	0.502911	+	0.864338i	$0.332262\pi$
$54$	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	0.729487	−	0.683994i	$-0.239759\pi$
$59$	−13.4292	−	23.2600i	−0.227613	−	0.394237i	−0.957100	+	0.289757i	$0.906425\pi$
$60$	84.4284	+	61.9737i	1.40714	+	1.03290i
$61$	−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
$66$	0.700861	−	12.7756i	0.0106191	−	0.193570i
$67$	−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	$-0.492892\pi$
$68$	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	$-0.735785\pi$
$71$		−	104.792i		−	1.47594i	0.674834	−	0.737969i	$-0.264215\pi$
$72$	73.3069	+	60.2582i	1.01815	+	0.836919i
$73$	12.1987	+	21.1288i	0.167106	+	0.289435i	0.937401	−	0.348252i	$-0.113225\pi$
$73$	12.1987	+	21.1288i	0.167106	+	0.289435i	−0.770295	+	0.637687i	$0.779891\pi$
$74$	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	−0.306420	−	0.951897i	$-0.599131\pi$
$79$	−101.436	−	58.5639i	−1.28400	−	0.741315i	−0.977576	+	0.210581i	$0.932464\pi$
$80$	−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	−0.873403	−	0.486999i	$-0.838092\pi$
$89$	−1.33039	+	2.30431i	−0.0149482	+	0.0258911i	0.858455	+	0.512890i	$0.171425\pi$
$90$	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	−0.0536223	−	0.998561i	$-0.517077\pi$
$101$	79.2189	−	45.7371i	0.784346	−	0.452842i	0.837968	+	0.545719i	$0.183743\pi$
$102$	16.1473	−	294.341i	0.158307	−	2.88570i
$103$	−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	$0.292906\pi$
$108$	30.9386	−	42.1485i	0.286469	−	0.390264i
$109$	−25.5234	+	14.7359i	−0.234160	+	0.135192i	−0.612490	−	0.790479i	$-0.709832\pi$
$109$	−25.5234	+	14.7359i	−0.234160	+	0.135192i	0.378330	+	0.925671i	$0.376499\pi$
$110$	−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	$0.0201690\pi$
$127$			16.0834i			0.126641i	−0.997993	+	0.0633205i	$0.979831\pi$
$128$	−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	−0.547543	−	0.836778i	$-0.684437\pi$
$131$	59.0678	−	102.308i	0.450899	−	0.780981i	0.998442	+	0.0557972i	$0.0177700\pi$
$132$	−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	0.898886	−	0.438182i	$-0.144377\pi$
$137$	9.58539	+	16.6024i	0.0699664	+	0.121185i	−0.828920	+	0.559367i	$0.811044\pi$
$138$	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	0.719947	−	0.694029i	$-0.244166\pi$
$149$	71.3523	+	41.1953i	0.478875	+	0.276478i	−0.241073	+	0.970507i	$0.577499\pi$
$150$	3.93392	−	71.7093i	0.0262261	−	0.478062i
$151$	−50.0038	+	28.8697i	−0.331151	+	0.191190i	−0.656352	−	0.754455i	$-0.727901\pi$
$151$	−50.0038	+	28.8697i	−0.331151	+	0.191190i	0.325201	+	0.945645i	$0.394568\pi$
$152$	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	−0.489678	−	0.871903i	$-0.662886\pi$
$157$	3.23006	−	1.86488i	0.0205736	−	0.0118782i	0.510252	+	0.860025i	$0.329552\pi$
$158$	−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	−0.960245	−	0.279158i	$-0.909945\pi$
$163$	−38.8534	+	67.2961i	−0.238365	+	0.412860i	0.721881	+	0.692018i	$0.243278\pi$
$164$	−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	$0.0595133\pi$
$167$			62.0837i			0.371759i	−0.982573	+	0.185879i	$0.940487\pi$
$168$		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	0.902037	−	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
$178$	−0.291499	+	5.31358i	−0.00163763	+	0.0298515i
$179$	−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	$0.897981\pi$
$180$	29.7530	−	270.360i	0.165295	−	1.50200i
$181$		−	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
$184$	−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	0.978627	−	0.205645i	$-0.0659293\pi$
$191$	246.361	+	142.236i	1.28985	+	0.744693i	0.311219	+	0.950338i	$0.399263\pi$
$192$	56.5764	+	286.791i	0.294669	+	1.49370i
$193$	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	$0.729363\pi$
$194$	−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	$0.0884662\pi$
$197$			108.098i			0.548721i	−0.961627	+	0.274361i	$0.911534\pi$
$198$	−29.6435	+	15.0129i	−0.149715	+	0.0758230i
$199$	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	$0.0194915\pi$
$200$	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	$-0.882300\pi$
$223$		−	161.183i		−	0.722796i	0.932412	−	0.361398i	$-0.117700\pi$
$224$		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	0.990663	−	0.136330i	$-0.0435308\pi$
$227$	85.6395	+	148.332i	0.377266	+	0.653445i	−0.613397	+	0.789775i	$0.710197\pi$
$228$	135.866	−	185.093i	0.595902	−	0.811813i
$229$	−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	$-0.0301755\pi$
$234$	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	$-0.893364\pi$
$239$		−	157.155i		−	0.657551i	0.944408	−	0.328776i	$-0.106636\pi$
$240$	399.673	−	125.555i	1.66530	−	0.523144i
$241$	48.8562	+	84.6214i	0.202723	+	0.351126i	0.949405	−	0.314055i	$-0.101688\pi$
$241$	48.8562	+	84.6214i	0.202723	+	0.351126i	−0.746682	+	0.665181i	$0.768354\pi$
$242$	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	−0.296664	−	0.954982i	$-0.595874\pi$
$257$	174.428	−	302.118i	0.678707	−	1.17555i	0.975371	−	0.220573i	$-0.0707926\pi$
$258$	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	−0.974164	−	0.225843i	$-0.927486\pi$
$263$	−332.869	+	192.182i	−1.26566	+	0.730729i	−0.291496	+	0.956572i	$0.594153\pi$
$264$	−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	−0.559552	−	0.828795i	$-0.689027\pi$
$269$	−32.7022	+	18.8806i	−0.121570	+	0.0701882i	0.437982	+	0.898984i	$0.355693\pi$
$270$	−149.637	−	8.20895i	−0.554210	−	0.0304035i
$271$	−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
$276$	234.017	+	171.778i	0.847888	+	0.622382i
$277$	−211.492	+	122.105i	−0.763508	+	0.440812i	−0.830554	−	0.556938i	$-0.811976\pi$
$277$	−211.492	+	122.105i	−0.763508	+	0.440812i	0.0670458	+	0.997750i	$0.478643\pi$
$278$	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	0.681833	−	0.731508i	$-0.261183\pi$
$283$	−82.8026	−	143.418i	−0.292589	−	0.506778i	−0.974421	+	0.224730i	$0.927850\pi$
$284$	−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	$-0.981322\pi$
$293$		−	34.3652i		−	0.117288i	0.998279	−	0.0586438i	$-0.0186776\pi$
$294$		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	−0.953531	−	0.301294i	$-0.902581\pi$
$311$	−363.673	+	209.967i	−1.16937	+	0.675135i	−0.215837	+	0.976429i	$0.569248\pi$
$312$	245.094	+	652.759i	0.785557	+	2.09218i
$313$	146.934	−	254.498i	0.469439	−	0.813092i	−0.529950	−	0.848029i	$-0.677789\pi$
$313$	146.934	−	254.498i	0.469439	−	0.813092i	0.999390	+	0.0349363i	$0.0111228\pi$
$314$	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	0.950552	−	0.310566i	$-0.100519\pi$
$317$	366.728	+	211.730i	1.15687	+	0.667919i	0.206318	+	0.978485i	$0.433852\pi$
$318$	−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	−0.754355	−	0.656467i	$-0.772050\pi$
$331$	63.3332	−	109.696i	0.191339	−	0.331409i	0.945694	+	0.325057i	$0.105384\pi$
$332$	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	0.537192	−	0.843460i	$-0.319485\pi$
$347$	−160.266	−	277.589i	−0.461862	−	0.799969i	−0.999054	+	0.0434916i	$0.986152\pi$
$348$	−6.57904	+	59.7825i	−0.0189053	+	0.171789i
$349$		−	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
$352$	12.1287	−	43.1485i	0.0344566	−	0.122581i
$353$	182.185	+	315.553i	0.516104	+	0.893918i	0.999825	+	0.0186962i	$0.00595153\pi$
$353$	182.185	+	315.553i	0.516104	+	0.893918i	−0.483721	+	0.875222i	$0.660715\pi$
$354$	−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	0.628965	−	0.777434i	$-0.283479\pi$
$359$	96.9908	+	55.9977i	0.270169	+	0.155982i	−0.358795	+	0.933416i	$0.616812\pi$
$360$	−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	0.117321	−	0.993094i	$-0.462569\pi$
$367$	380.222	−	219.521i	1.03603	−	0.598150i	0.918705	+	0.394944i	$0.129236\pi$
$368$	−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	0.173860	−	0.984770i	$-0.444376\pi$
$373$	−220.833	−	127.498i	−0.592047	−	0.341818i	−0.765906	+	0.642952i	$0.777709\pi$
$374$	−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	0.414732	−	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
$388$	−123.301	+	167.976i	−0.317785	+	0.432927i
$389$	295.141	−	170.400i	0.758718	−	0.438046i	−0.0701174	−	0.997539i	$-0.522337\pi$
$389$	295.141	−	170.400i	0.758718	−	0.438046i	0.828835	+	0.559493i	$0.189004\pi$
$390$	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	0.616700	−	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	$0.306254\pi$
$402$	−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	−0.909074	−	0.416635i	$-0.863209\pi$
$409$	−333.480	−	577.604i	−0.815354	−	1.41223i	0.0937202	−	0.995599i	$-0.470124\pi$
$410$	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	$-0.993984\pi$
$421$		−	15.9136i		−	0.0377996i	0.999821	−	0.0188998i	$-0.00601636\pi$
$422$	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	0.288451	−	0.957495i	$-0.406860\pi$
$431$	543.875	−	314.006i	1.26189	−	0.728553i	0.973440	+	0.228941i	$0.0735264\pi$
$432$	−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	0.982589	−	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	$0.972677\pi$
$444$	−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	−0.138047	−	0.990426i	$-0.544082\pi$
$457$	360.441	−	624.302i	0.788710	−	1.36609i	0.926757	−	0.375661i	$-0.122584\pi$
$458$	−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	$-0.824385\pi$
$461$		−	483.262i		−	1.04829i	0.851629	−	0.524145i	$-0.175615\pi$
$462$		0			0
$463$			39.6326i			0.0855995i	0.999084	+	0.0427997i	$0.0136277\pi$
$463$			39.6326i			0.0855995i	−0.999084	+	0.0427997i	$0.986372\pi$
$464$	−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	−0.875390	−	0.483417i	$-0.839395\pi$
$467$	−8.89340	+	15.4038i	−0.0190437	+	0.0329846i	0.856347	+	0.516402i	$0.172729\pi$
$468$	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	0.246341	−	0.969183i	$-0.420772\pi$
$479$	579.039	−	334.308i	1.20885	−	0.697930i	0.962508	+	0.271254i	$0.0874382\pi$
$480$	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	−0.823589	−	0.567187i	$-0.808032\pi$
$487$	−362.418	+	209.242i	−0.744185	+	0.429656i	0.0794038	+	0.996843i	$0.474698\pi$
$488$	−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	−0.558363	−	0.829597i	$-0.688570\pi$
$499$	219.196	−	379.659i	0.439271	−	0.760839i	0.997633	+	0.0687578i	$0.0219036\pi$
$500$	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	$0.270068\pi$
$503$			754.754i			1.50050i	−0.661151	+	0.750252i	$0.729932\pi$
$504$		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	0.857452	−	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
$514$	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	0.881369	−	0.472428i	$-0.156622\pi$
$521$	16.4374	+	28.4704i	0.0315496	+	0.0546456i	−0.849819	+	0.527074i	$0.823289\pi$
$522$	77.9795	+	4.27789i	0.149386	+	0.00819520i
$523$	14.1377	−	24.4873i	0.0270320	−	0.0468208i	−0.852193	−	0.523228i	$-0.824728\pi$
$523$	14.1377	−	24.4873i	0.0270320	−	0.0468208i	0.879225	+	0.476407i	$0.158061\pi$
$524$	−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	−0.926873	−	0.375375i	$-0.877514\pi$
$541$	−928.028	−	535.797i	−1.71539	−	0.990383i	−0.788521	−	0.615008i	$-0.789153\pi$
$542$	−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	−0.826353	−	0.563152i	$-0.809588\pi$
$557$	−418.767	+	241.775i	−0.751826	+	0.434067i	0.0745276	+	0.997219i	$0.476255\pi$
$558$	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	0.536485	−	0.843910i	$-0.319752\pi$
$563$	−260.447	−	451.107i	−0.462605	−	0.801256i	−0.999090	+	0.0426543i	$0.986419\pi$
$564$	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	−0.340437	−	0.940267i	$-0.610575\pi$
$569$	366.480	−	634.761i	0.644077	−	1.11557i	0.984514	−	0.175306i	$-0.0560916\pi$
$570$	−657.123	−	36.0493i	−1.15285	−	0.0632444i
$571$	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	$0.494002\pi$
$572$	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	0.590478	−	0.807054i	$-0.298939\pi$
$577$	−232.929	−	403.445i	−0.403690	−	0.699212i	−0.994168	+	0.107842i	$0.965606\pi$
$578$	−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	0.127584	+	0.991828i	$0.459278\pi$
$593$	−471.528	+	816.710i	−0.795156	+	1.37725i	−0.922740	+	0.385423i	$0.874055\pi$
$594$	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	−0.493286	−	0.869867i	$-0.664204\pi$
$599$	8.02545	−	4.63349i	0.0133981	−	0.00773538i	0.506684	+	0.862132i	$0.330871\pi$
$600$	−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	0.999101	−	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
$612$	−906.012	+	1234.28i	−1.48041	+	2.01680i
$613$	−350.583	+	202.409i	−0.571914	+	0.330195i	−0.757913	−	0.652355i	$-0.773781\pi$
$613$	−350.583	+	202.409i	−0.571914	+	0.330195i	0.186000	+	0.982550i	$0.440448\pi$
$614$	−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	0.987641	+	0.156731i	$0.0500957\pi$
$619$	389.694	+	674.970i	0.629554	+	1.09042i	−0.358087	+	0.933688i	$0.616571\pi$
$620$	−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	$-0.787855\pi$
$631$		−	780.191i		−	1.23644i	0.786007	−	0.618218i	$-0.212145\pi$
$632$	−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	0.874975	−	0.484168i	$-0.160878\pi$
$641$	11.6570	+	20.1905i	0.0181856	+	0.0314984i	−0.856789	+	0.515667i	$0.827544\pi$
$642$	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	−0.635995	−	0.771693i	$-0.719410\pi$
$647$	−184.840	+	106.717i	−0.285687	+	0.164942i	0.350308	+	0.936635i	$0.386077\pi$
$648$	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	0.306528	−	0.951862i	$-0.400833\pi$
$653$	−238.048	−	137.437i	−0.364545	−	0.210470i	−0.671073	+	0.741392i	$0.734166\pi$
$654$	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	−0.830545	−	0.556952i	$-0.811971\pi$
$661$	−504.662	+	291.367i	−0.763482	+	0.440797i	0.0670625	+	0.997749i	$0.478637\pi$
$662$	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	−0.0673768	−	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
$682$	63.4113	+	3.47870i	0.0929785	+	0.00510073i
$683$	−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	$0.901014\pi$
$684$	−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	−0.803751	−	0.594966i	$-0.797165\pi$
$691$	78.3458	−	135.699i	0.113380	−	0.196380i	0.917131	+	0.398586i	$0.130499\pi$
$692$	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	$-0.702970\pi$
$701$		−	1126.50i		−	1.60700i	0.595307	−	0.803498i	$-0.297030\pi$
$702$	−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	0.986651	−	0.162847i	$-0.0520678\pi$
$709$	949.313	+	548.086i	1.33895	+	0.773041i	0.352296	+	0.935889i	$0.385401\pi$
$710$	−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	0.0889614	−	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
$724$	−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	$-0.901300\pi$
$727$		−	443.659i		−	0.610260i	0.952311	−	0.305130i	$-0.0986999\pi$
$728$		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	−0.0134626	−	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
$738$	9.87113	−	179.935i	0.0133755	−	0.243815i
$739$	−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	$0.970955\pi$
$740$	−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	$-0.993461\pi$
$743$		−	30.5255i		−	0.0410842i	0.999789	−	0.0205421i	$-0.00653921\pi$
$744$	−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	−0.176001	−	0.984390i	$-0.556316\pi$
$751$	−838.498	−	484.107i	−1.11651	−	0.644616i	−0.940507	+	0.339773i	$0.889650\pi$
$752$	−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	$0.281521\pi$
$757$			1171.15i			1.54710i	−0.633736	+	0.773550i	$0.718479\pi$
$758$	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	−0.933080	−	0.359670i	$-0.882889\pi$
$761$	−117.998	+	204.379i	−0.155057	+	0.268566i	0.778023	+	0.628236i	$0.216223\pi$
$762$	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	−0.596502	−	0.802612i	$-0.703443\pi$
$773$	−154.345	+	89.1114i	−0.199671	+	0.115280i	0.396831	+	0.917892i	$0.370110\pi$
$774$	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	0.967097	+	0.254409i	$0.0818808\pi$
$787$	553.948	+	959.466i	0.703873	+	1.21914i	−0.263224	+	0.964735i	$0.584786\pi$
$788$	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	$0.240966\pi$
$797$			1094.69i			1.37351i	−0.726889	+	0.686755i	$0.759034\pi$
$798$		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	0.874703	+	0.484659i	$0.161056\pi$
$809$	693.377	+	1200.96i	0.857079	+	1.48450i	−0.0176240	+	0.999845i	$0.505610\pi$
$810$	−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	−0.203250	−	0.979127i	$-0.565150\pi$
$821$	−946.469	−	546.444i	−1.15282	−	0.665583i	−0.949574	+	0.313544i	$0.898484\pi$
$822$	9.59275	−	174.861i	0.0116700	−	0.212726i
$823$	785.625	−	453.581i	0.954587	−	0.551131i	0.0600842	−	0.998193i	$-0.480863\pi$
$823$	785.625	−	453.581i	0.954587	−	0.551131i	0.894503	+	0.447062i	$0.147530\pi$
$824$	−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	−0.259514	−	0.965739i	$-0.583562\pi$
$829$	370.632	−	213.984i	0.447083	−	0.258124i	0.706598	+	0.707616i	$0.250229\pi$
$830$	−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	$0.235971\pi$
$839$			1133.09i			1.35053i	−0.737575	+	0.675265i	$0.764029\pi$
$840$		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	$0.0316783\pi$
$853$			169.502i			0.198712i	−0.995052	+	0.0993562i	$0.968322\pi$
$854$		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	0.926196	−	0.377043i	$-0.123059\pi$
$857$	117.039	+	202.718i	0.136569	+	0.236544i	−0.789627	+	0.613587i	$0.789726\pi$
$858$	−243.786	−	13.3739i	−0.284132	−	0.0155873i
$859$	−447.171	+	774.523i	−0.520571	+	0.901656i	0.479143	+	0.877737i	$0.340948\pi$
$859$	−447.171	+	774.523i	−0.520571	+	0.901656i	−0.999714	+	0.0239189i	$0.992386\pi$
$860$	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	0.836894	−	0.547365i	$-0.184369\pi$
$863$	674.270	+	389.290i	0.781309	+	0.451089i	−0.0555850	+	0.998454i	$0.517702\pi$
$864$	−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	0.508507	−	0.861058i	$-0.330198\pi$
$877$	14.9632	+	8.63901i	0.0170618	+	0.00985064i	−0.491445	+	0.870909i	$0.663531\pi$
$878$	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	0.992922	+	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
$892$	−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	0.999547	+	0.0300919i	$0.00958001\pi$
$907$	476.931	+	826.069i	0.525834	+	0.910771i	−0.473713	+	0.880679i	$0.657087\pi$
$908$	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	$0.374017\pi$
$911$			1681.15i			1.84539i	−0.385534	+	0.922694i	$0.625983\pi$
$912$	−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	0.242817	−	0.970072i	$-0.421929\pi$
$919$	−437.335	−	252.495i	−0.475881	−	0.274750i	−0.718698	+	0.695322i	$0.755262\pi$
$920$	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	0.469886	+	0.882727i	$0.344295\pi$
$929$	−491.925	+	852.040i	−0.529521	+	0.917158i	−0.999407	+	0.0344306i	$0.989038\pi$
$930$	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	−0.0397529	−	0.999210i	$-0.512657\pi$
$941$	758.175	−	437.732i	0.805712	−	0.465178i	0.845464	+	0.534032i	$0.179324\pi$
$942$	−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	−0.319781	−	0.947491i	$-0.603609\pi$
$947$	625.646	−	1083.65i	0.660661	−	1.14430i	0.980442	−	0.196807i	$-0.0630572\pi$
$948$	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	$0.260099\pi$
$967$			1410.24i			1.45836i	−0.684320	+	0.729182i	$0.739901\pi$
$968$	−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	−0.986144	−	0.165889i	$-0.946951\pi$
$971$	−339.275	+	587.641i	−0.349408	+	0.605192i	0.636737	+	0.771081i	$0.280284\pi$
$972$	−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	0.835995	−	0.548738i	$-0.184891\pi$
$977$	−55.9074	−	96.8344i	−0.0572235	−	0.0991141i	−0.893218	+	0.449624i	$0.851558\pi$
$978$	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	−0.586429	−	0.810001i	$-0.699467\pi$
$983$	−175.133	+	101.113i	−0.178162	+	0.102862i	0.408267	+	0.912863i	$0.366133\pi$
$984$	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	−0.415109	−	0.909772i	$-0.636257\pi$
$991$	163.735	−	94.5322i	0.165222	−	0.0953907i	0.580331	+	0.814381i	$0.302923\pi$
$992$	−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	−0.996158	−	0.0875699i	$-0.972090\pi$
$997$	−1414.14	+	816.457i	−1.41840	+	0.818914i	−0.422241	+	0.906483i	$0.638757\pi$
$998$	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.275.7		16
7.2	even	3		56.3.g.b.43.1	✓	8
7.3	odd	6		392.3.k.n.67.5		16
7.4	even	3	inner	392.3.k.o.67.5		16
7.5	odd	6		392.3.g.m.99.1		8
7.6	odd	2		392.3.k.n.275.7		16
8.3	odd	2	inner	392.3.k.o.275.5		16
21.2	odd	6		504.3.g.b.379.8		8
28.19	even	6		1568.3.g.m.687.7		8
28.23	odd	6		224.3.g.b.15.2		8
56.3	even	6		392.3.k.n.67.7		16
56.5	odd	6		1568.3.g.m.687.8		8
56.11	odd	6	inner	392.3.k.o.67.7		16
56.19	even	6		392.3.g.m.99.2		8
56.27	even	2		392.3.k.n.275.5		16
56.37	even	6		224.3.g.b.15.1		8
56.51	odd	6		56.3.g.b.43.2	yes	8
84.23	even	6		2016.3.g.b.1135.2		8
112.37	even	12		1792.3.d.j.1023.3		16
112.51	odd	12		1792.3.d.j.1023.4		16
112.93	even	12		1792.3.d.j.1023.14		16
112.107	odd	12		1792.3.d.j.1023.13		16
168.107	even	6		504.3.g.b.379.7		8
168.149	odd	6		2016.3.g.b.1135.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.1	✓	8	7.2	even	3
56.3.g.b.43.2	yes	8	56.51	odd	6
224.3.g.b.15.1		8	56.37	even	6
224.3.g.b.15.2		8	28.23	odd	6
392.3.g.m.99.1		8	7.5	odd	6
392.3.g.m.99.2		8	56.19	even	6
392.3.k.n.67.5		16	7.3	odd	6
392.3.k.n.67.7		16	56.3	even	6
392.3.k.n.275.5		16	56.27	even	2
392.3.k.n.275.7		16	7.6	odd	2
392.3.k.o.67.5		16	7.4	even	3	inner
392.3.k.o.67.7		16	56.11	odd	6	inner
392.3.k.o.275.5		16	8.3	odd	2	inner
392.3.k.o.275.7		16	1.1	even	1	trivial
504.3.g.b.379.7		8	168.107	even	6
504.3.g.b.379.8		8	21.2	odd	6
1568.3.g.m.687.7		8	28.19	even	6
1568.3.g.m.687.8		8	56.5	odd	6
1792.3.d.j.1023.3		16	112.37	even	12
1792.3.d.j.1023.4		16	112.51	odd	12
1792.3.d.j.1023.13		16	112.107	odd	12
1792.3.d.j.1023.14		16	112.93	even	12
2016.3.g.b.1135.2		8	84.23	even	6
2016.3.g.b.1135.7		8	168.149	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)

\(f(q)\)	\(=\)	\(q+(1.78423 - 0.903622i) q^{2} +(-2.28374 - 3.95555i) q^{3} +(2.36693 - 3.22453i) q^{4} +(-4.96451 - 2.86626i) q^{5} +(-7.64902 - 4.99396i) q^{6} +(1.30939 - 7.89212i) q^{8} +(-5.93090 + 10.2726i) q^{9} +O(q^{10})\)	\(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

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