LMFDB - Embedded newform 392.3.g.m.99.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(99,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("392.99");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.g (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.292213762624.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} - 2x^{5} + 24x^{4} - 8x^{3} - 32x^{2} - 64x + 256 $ x^8 - x^7 - 2x^6 - 2x^5 + 24x^4 - 8x^3 - 32x^2 - 64x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.2
Root			$-1.67467 - 1.09337i$ of defining polynomial
Character	$\chi$	$=$	392.99
Dual form			392.3.g.m.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67467 + 1.09337i) q^{2} -4.56747 q^{3} +(1.60906 - 3.66209i) q^{4} +5.73252i q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +11.8618 q^{9} +O(q^{10})$	\(q+(-1.67467 + 1.09337i) q^{2} -4.56747 q^{3} +(1.60906 - 3.66209i) q^{4} +5.73252i q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +11.8618 q^{9} +(-6.26779 - 9.60010i) q^{10} -1.40065 q^{11} +(-7.34935 + 16.7265i) q^{12} -19.0821i q^{13} -26.1831i q^{15} +(-10.8218 - 11.7851i) q^{16} +32.2699 q^{17} +(-19.8646 + 12.9694i) q^{18} -12.5675 q^{19} +(20.9930 + 9.22398i) q^{20} +(2.34563 - 1.53143i) q^{22} -15.8893i q^{23} +(-5.98058 - 36.0470i) q^{24} -7.86180 q^{25} +(20.8639 + 31.9563i) q^{26} -13.0712 q^{27} +3.29194i q^{29} +(28.6280 + 43.8482i) q^{30} +22.6705i q^{31} +(31.0085 + 7.90382i) q^{32} +6.39741 q^{33} +(-54.0415 + 35.2831i) q^{34} +(19.0864 - 43.4390i) q^{36} +54.1537i q^{37} +(21.0464 - 13.7410i) q^{38} +87.1569i q^{39} +(-45.2417 + 7.50608i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(-2.25373 + 5.12930i) q^{44} +67.9980i q^{45} +(17.3729 + 26.6094i) q^{46} +21.6384i q^{47} +(49.4284 + 53.8280i) q^{48} +(13.1659 - 8.59589i) q^{50} -147.392 q^{51} +(-69.8804 - 30.7043i) q^{52} -0.356667i q^{53} +(21.8900 - 14.2917i) q^{54} -8.02924i q^{55} +57.4016 q^{57} +(-3.59933 - 5.51293i) q^{58} -26.8583 q^{59} +(-95.8850 - 42.1303i) q^{60} +86.2287i q^{61} +(-24.7873 - 37.9656i) q^{62} +(-60.5710 + 20.6676i) q^{64} +109.389 q^{65} +(-10.7136 + 6.99477i) q^{66} +114.523 q^{67} +(51.9243 - 118.175i) q^{68} +72.5739i q^{69} +104.792i q^{71} +(15.5317 + 93.6147i) q^{72} +24.3974 q^{73} +(-59.2103 - 90.6898i) q^{74} +35.9085 q^{75} +(-20.2218 + 46.0232i) q^{76} +(-95.2952 - 145.959i) q^{78} -117.128i q^{79} +(67.5582 - 62.0364i) q^{80} -47.0539 q^{81} +(-12.7209 + 8.30535i) q^{82} -79.2706 q^{83} +184.988i q^{85} +(34.9133 - 22.7945i) q^{86} -15.0359i q^{87} +(-1.83399 - 11.0541i) q^{88} -2.66078 q^{89} +(-74.3473 - 113.874i) q^{90} +(-58.1880 - 25.5669i) q^{92} -103.547i q^{93} +(-23.6589 - 36.2373i) q^{94} -72.0433i q^{95} +(-141.631 - 36.1005i) q^{96} +52.0930 q^{97} -16.6142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	$ 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 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} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 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} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * 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 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * 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 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.67467	+	1.09337i	−0.837337	+	0.546687i
$2$	−1.67467	+	1.09337i	−0.837337	+	0.546687i
$3$	−4.56747			−1.52249			−0.761245	−	0.648464i	$-0.775412\pi$
$3$	−4.56747			−1.52249			−0.761245	+	0.648464i	$0.775412\pi$
$4$	1.60906	−	3.66209i	0.402266	−	0.915523i
$5$			5.73252i			1.14650i	0.819379	+	0.573252i	$0.194318\pi$
$5$			5.73252i			1.14650i	−0.819379	+	0.573252i	$0.805682\pi$
$6$	7.64902	−	4.99396i	1.27484	−	0.832327i
$7$		0			0
$7$		0			0
$8$	1.30939	+	7.89212i	0.163673	+	0.986515i
$9$	11.8618			1.31798
$10$	−6.26779	−	9.60010i	−0.626779	−	0.960010i
$11$	−1.40065			−0.127332			−0.0636658	−	0.997971i	$-0.520279\pi$
$11$	−1.40065			−0.127332			−0.0636658	+	0.997971i	$0.520279\pi$
$12$	−7.34935	+	16.7265i	−0.612446	+	1.39388i
$13$		−	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
$16$	−10.8218	−	11.7851i	−0.676365	−	0.736567i
$17$	32.2699			1.89823			0.949114	−	0.314932i	$-0.101982\pi$
$17$	32.2699			1.89823			0.949114	+	0.314932i	$0.101982\pi$
$18$	−19.8646	+	12.9694i	−1.10359	+	0.720522i
$19$	−12.5675			−0.661446			−0.330723	−	0.943728i	$-0.607293\pi$
$19$	−12.5675			−0.661446			−0.330723	+	0.943728i	$0.607293\pi$
$20$	20.9930	+	9.22398i	1.04965	+	0.461199i
$21$		0			0
$22$	2.34563	−	1.53143i	0.106619	−	0.0696105i
$23$		−	15.8893i		−	0.690839i	−0.938448	−	0.345419i	$-0.887737\pi$
$23$		−	15.8893i		−	0.690839i	0.938448	−	0.345419i	$-0.112263\pi$
$24$	−5.98058	−	36.0470i	−0.249191	−	1.50196i
$25$	−7.86180			−0.314472
$26$	20.8639	+	31.9563i	0.802457	+	1.22909i
$27$	−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	$0.981924\pi$
$30$	28.6280	+	43.8482i	0.954266	+	1.46161i
$31$			22.6705i			0.731306i	0.930751	+	0.365653i	$0.119154\pi$
$31$			22.6705i			0.731306i	−0.930751	+	0.365653i	$0.880846\pi$
$32$	31.0085	+	7.90382i	0.969017	+	0.246994i
$33$	6.39741			0.193861
$34$	−54.0415	+	35.2831i	−1.58946	+	1.03774i
$35$		0			0
$36$	19.0864	−	43.4390i	0.530177	−	1.20664i
$37$			54.1537i			1.46361i	0.681512	+	0.731807i	$0.261323\pi$
$37$			54.1537i			1.46361i	−0.681512	+	0.731807i	$0.738677\pi$
$38$	21.0464	−	13.7410i	0.553853	−	0.361604i
$39$			87.1569i			2.23479i
$40$	−45.2417	+	7.50608i	−1.13104	+	0.187652i
$41$	7.59607			0.185270			0.0926350	−	0.995700i	$-0.470471\pi$
$41$	7.59607			0.185270			0.0926350	+	0.995700i	$0.470471\pi$
$42$		0			0
$43$	−20.8478			−0.484833			−0.242417	−	0.970172i	$-0.577940\pi$
$43$	−20.8478			−0.484833			−0.242417	+	0.970172i	$0.577940\pi$
$44$	−2.25373	+	5.12930i	−0.0512211	+	0.116575i
$45$			67.9980i			1.51107i
$46$	17.3729	+	26.6094i	0.377673	+	0.578465i
$47$			21.6384i			0.460392i	0.973144	+	0.230196i	$0.0739367\pi$
$47$			21.6384i			0.460392i	−0.973144	+	0.230196i	$0.926063\pi$
$48$	49.4284	+	53.8280i	1.02976	+	1.12142i
$49$		0			0
$50$	13.1659	−	8.59589i	0.263319	−	0.171918i
$51$	−147.392			−2.89004
$52$	−69.8804	−	30.7043i	−1.34385	−	0.590467i
$53$		−	0.356667i		−	0.00672957i	−0.999994	−	0.00336479i	$-0.998929\pi$
$53$		−	0.356667i		−	0.00672957i	0.999994	−	0.00336479i	$-0.00107105\pi$
$54$	21.8900	−	14.2917i	0.405370	−	0.264661i
$55$		−	8.02924i		−	0.145986i
$56$		0			0
$57$	57.4016			1.00705
$58$	−3.59933	−	5.51293i	−0.0620574	−	0.0950505i
$59$	−26.8583			−0.455226			−0.227613	−	0.973752i	$-0.573092\pi$
$59$	−26.8583			−0.455226			−0.227613	+	0.973752i	$0.573092\pi$
$60$	−95.8850	−	42.1303i	−1.59808	−	0.702171i
$61$			86.2287i			1.41359i	0.707420	+	0.706793i	$0.249859\pi$
$61$			86.2287i			1.41359i	−0.707420	+	0.706793i	$0.750141\pi$
$62$	−24.7873	−	37.9656i	−0.399796	−	0.612349i
$63$		0			0
$64$	−60.5710	+	20.6676i	−0.946422	+	0.322932i
$65$	109.389			1.68290
$66$	−10.7136	+	6.99477i	−0.162327	+	0.105981i
$67$	114.523			1.70929			0.854646	−	0.519211i	$-0.173774\pi$
$67$	114.523			1.70929			0.854646	+	0.519211i	$0.173774\pi$
$68$	51.9243	−	118.175i	0.763592	−	1.73787i
$69$			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	$0.735785\pi$
$72$	15.5317	+	93.6147i	0.215718	+	1.30020i
$73$	24.3974			0.334211			0.167106	−	0.985939i	$-0.446558\pi$
$73$	24.3974			0.334211			0.167106	+	0.985939i	$0.446558\pi$
$74$	−59.2103	−	90.6898i	−0.800140	−	1.22554i
$75$	35.9085			0.478781
$76$	−20.2218	+	46.0232i	−0.266077	+	0.605569i
$77$		0			0
$78$	−95.2952	−	145.959i	−1.22173	−	1.87127i
$79$		−	117.128i		−	1.48263i	−0.671157	−	0.741315i	$-0.734202\pi$
$79$		−	117.128i		−	1.48263i	0.671157	−	0.741315i	$-0.265798\pi$
$80$	67.5582	−	62.0364i	0.844477	−	0.775455i
$81$	−47.0539			−0.580913
$82$	−12.7209	+	8.30535i	−0.155133	+	0.101285i
$83$	−79.2706			−0.955067			−0.477534	−	0.878614i	$-0.658469\pi$
$83$	−79.2706			−0.955067			−0.477534	+	0.878614i	$0.658469\pi$
$84$		0			0
$85$			184.988i			2.17633i
$86$	34.9133	−	22.7945i	0.405969	−	0.265052i
$87$		−	15.0359i		−	0.172826i
$88$	−1.83399	−	11.0541i	−0.0208408	−	0.125614i
$89$	−2.66078			−0.0298964			−0.0149482	−	0.999888i	$-0.504758\pi$
$89$	−2.66078			−0.0298964			−0.0149482	+	0.999888i	$0.504758\pi$
$90$	−74.3473	−	113.874i	−0.826081	−	1.26527i
$91$		0			0
$92$	−58.1880	−	25.5669i	−0.632479	−	0.277901i
$93$		−	103.547i		−	1.11341i
$94$	−23.6589	−	36.2373i	−0.251691	−	0.385503i
$95$		−	72.0433i		−	0.758350i
$96$	−141.631	−	36.1005i	−1.47532	−	0.376046i
$97$	52.0930			0.537042			0.268521	−	0.963274i	$-0.413465\pi$
$97$	52.0930			0.537042			0.268521	+	0.963274i	$0.413465\pi$
$98$		0			0
$99$	−16.6142			−0.167820
$100$	−12.6501	+	28.7906i	−0.126501	+	0.287906i
$101$			91.4742i			0.905685i	0.891591	+	0.452842i	$0.149590\pi$
$101$			91.4742i			0.905685i	−0.891591	+	0.452842i	$0.850410\pi$
$102$	246.833	−	161.154i	2.41993	−	1.57995i
$103$			39.7891i			0.386302i	0.981169	+	0.193151i	$0.0618708\pi$
$103$			39.7891i			0.386302i	−0.981169	+	0.193151i	$0.938129\pi$
$104$	150.598	−	24.9858i	1.44806	−	0.240248i
$105$		0			0
$106$	0.389971	+	0.597301i	0.00367897	+	0.00563492i
$107$	82.6631			0.772552			0.386276	−	0.922383i	$-0.373761\pi$
$107$	82.6631			0.772552			0.386276	+	0.922383i	$0.373761\pi$
$108$	−21.0323	+	47.8679i	−0.194744	+	0.443221i
$109$			29.4719i			0.270384i	0.990819	+	0.135192i	$0.0431652\pi$
$109$			29.4719i			0.270384i	−0.990819	+	0.135192i	$0.956835\pi$
$110$	8.77897	+	13.4463i	0.0798088	+	0.122240i
$111$		−	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	$0.251337\pi$
$114$	−96.1289	+	62.7614i	−0.843236	+	0.550539i
$115$	91.0857			0.792049
$116$	12.0554	+	5.29694i	0.103926	+	0.0456633i
$117$		−	226.348i		−	1.93460i
$118$	44.9789	−	29.3662i	0.381177	−	0.248866i
$119$		0			0
$120$	206.640	−	34.2838i	1.72200	−	0.285698i
$121$	−119.038			−0.983787
$122$	−94.2803	−	144.405i	−0.772790	−	1.18365i
$123$	−34.6948			−0.282072
$124$	83.0214	+	36.4782i	0.669527	+	0.294179i
$125$			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	$-0.0201690\pi$
$128$	78.8392	−	100.838i	0.615931	−	0.787800i
$129$	95.2219			0.738154
$130$	−183.190	+	119.603i	−1.40915	+	0.920021i
$131$	118.136			0.901799			0.450899	−	0.892575i	$-0.351103\pi$
$131$	118.136			0.901799			0.450899	+	0.892575i	$0.351103\pi$
$132$	10.2938	−	23.4279i	0.0779836	−	0.177484i
$133$		0			0
$134$	−191.788	+	125.216i	−1.43125	+	0.934448i
$135$		−	74.9308i		−	0.555043i
$136$	42.2537	+	254.678i	0.310689	+	1.87263i
$137$	−19.1708			−0.139933			−0.0699664	−	0.997549i	$-0.522289\pi$
$137$	−19.1708			−0.139933			−0.0699664	+	0.997549i	$0.522289\pi$
$138$	−79.3505	−	121.538i	−0.575003	−	0.880707i
$139$	−104.954			−0.755062			−0.377531	−	0.925997i	$-0.623227\pi$
$139$	−104.954			−0.755062			−0.377531	+	0.925997i	$0.623227\pi$
$140$		0			0
$141$		−	98.8329i		−	0.700942i
$142$	−114.577	−	175.492i	−0.806877	−	1.23586i
$143$			26.7273i			0.186904i
$144$	−128.366	−	139.792i	−0.891434	−	0.970779i
$145$	−18.8711			−0.130146
$146$	−40.8577	+	26.6755i	−0.279847	+	0.182709i
$147$		0			0
$148$	198.316	+	87.1367i	1.33997	+	0.588762i
$149$			82.3906i			0.552957i	0.961020	+	0.276478i	$0.0891674\pi$
$149$			82.3906i			0.552957i	−0.961020	+	0.276478i	$0.910833\pi$
$150$	−60.1351	+	39.2615i	−0.400901	+	0.261743i
$151$			57.7395i			0.382381i	0.981553	+	0.191190i	$0.0612347\pi$
$151$			57.7395i			0.382381i	−0.981553	+	0.191190i	$0.938765\pi$
$152$	−16.4557	−	99.1840i	−0.108261	−	0.652526i
$153$	382.779			2.50182
$154$		0			0
$155$	−129.959			−0.838445
$156$	319.177	+	140.241i	2.04600	+	0.898981i
$157$			3.72975i			0.0237564i	0.999929	+	0.0118782i	$0.00378104\pi$
$157$			3.72975i			0.0237564i	−0.999929	+	0.0118782i	$0.996219\pi$
$158$	128.065	+	196.151i	0.810536	+	1.24146i
$159$			1.62907i			0.0102457i
$160$	−45.3088	+	177.757i	−0.283180	+	1.11098i
$161$		0			0
$162$	78.8000	−	51.4476i	0.486420	−	0.317578i
$163$	77.7069			0.476729			0.238365	−	0.971176i	$-0.423389\pi$
$163$	77.7069			0.476729			0.238365	+	0.971176i	$0.423389\pi$
$164$	12.2225	−	27.8175i	0.0745277	−	0.169619i
$165$			36.6733i			0.222262i
$166$	132.752	−	86.6724i	0.799713	−	0.522123i
$167$			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
$170$	−202.261	−	309.794i	−1.18977	−	1.82232i
$171$	−149.073			−0.871771
$172$	−33.5455	+	76.3467i	−0.195032	+	0.443876i
$173$		−	195.614i		−	1.13072i	−0.824846	−	0.565358i	$-0.808738\pi$
$173$		−	195.614i		−	1.13072i	0.824846	−	0.565358i	$-0.191262\pi$
$174$	16.4398	+	25.1801i	0.0944818	+	0.144713i
$175$		0			0
$176$	15.1576	+	16.5067i	0.0861225	+	0.0937882i
$177$	122.675			0.693077
$178$	4.45594	−	2.90923i	0.0250334	−	0.0163440i
$179$	72.2099			0.403407			0.201704	−	0.979447i	$-0.435352\pi$
$179$	72.2099			0.403407			0.201704	+	0.979447i	$0.435352\pi$
$180$	249.015	+	109.413i	1.38342	+	0.607850i
$181$		−	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
$184$	125.400	−	20.8052i	0.681522	−	0.113072i
$185$	−310.437			−1.67804
$186$	113.215	+	173.407i	0.608685	+	0.932296i
$187$	−45.1987			−0.241704
$188$	79.2419	+	34.8176i	0.421499	+	0.185200i
$189$		0			0
$190$	78.7703	+	120.649i	0.414581	+	0.634995i
$191$			284.473i			1.48939i	0.667407	+	0.744693i	$0.267404\pi$
$191$			284.473i			1.48939i	−0.667407	+	0.744693i	$0.732596\pi$
$192$	276.656	−	94.3989i	1.44092	−	0.491661i
$193$	−123.850			−0.641710			−0.320855	−	0.947128i	$-0.603970\pi$
$193$	−123.850			−0.641710			−0.320855	+	0.947128i	$0.603970\pi$
$194$	−87.2388	+	56.9572i	−0.449685	+	0.293594i
$195$	−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	$-0.0884662\pi$
$198$	27.8233	−	18.1655i	0.140522	−	0.0917451i
$199$			331.854i			1.66761i	0.552060	+	0.833804i	$0.313842\pi$
$199$			331.854i			1.66761i	−0.552060	+	0.833804i	$0.686158\pi$
$200$	−10.2941	−	62.0462i	−0.0514706	−	0.310231i
$201$	−523.079			−2.60238
$202$	−100.016	−	153.189i	−0.495127	−	0.758363i
$203$		0			0
$204$	−237.163	+	539.762i	−1.16256	+	2.64589i
$205$			43.5446i			0.212413i
$206$	−43.5044	−	66.6338i	−0.211187	−	0.323465i
$207$		−	188.476i		−	0.910510i
$208$	−224.884	+	206.503i	−1.08117	+	0.992805i
$209$	17.6026			0.0842229
$210$		0			0
$211$	26.3950			0.125095			0.0625475	−	0.998042i	$-0.480078\pi$
$211$	26.3950			0.125095			0.0625475	+	0.998042i	$0.480078\pi$
$212$	−1.30615	−	0.573900i	−0.00616108	−	0.00270708i
$213$		−	478.633i		−	2.24710i
$214$	−138.434	+	90.3818i	−0.646887	+	0.422345i
$215$		−	119.511i		−	0.555864i
$216$	−17.1152	−	103.159i	−0.0792371	−	0.477589i
$217$		0			0
$218$	−32.2238	−	49.3558i	−0.147816	−	0.226403i
$219$	−111.434			−0.508833
$220$	−29.4038	−	12.9195i	−0.133654	−	0.0587252i
$221$		−	615.777i		−	2.78632i
$222$	270.442	+	414.223i	1.21821	+	1.86587i
$223$		−	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
$226$	−266.497	+	173.993i	−1.17919	+	0.769879i
$227$	171.279			0.754533			0.377266	−	0.926105i	$-0.376864\pi$
$227$	171.279			0.754533			0.377266	+	0.926105i	$0.376864\pi$
$228$	92.3627	−	210.210i	0.405100	−	0.921973i
$229$			229.251i			1.00110i	0.865709	+	0.500548i	$0.166868\pi$
$229$			229.251i			1.00110i	−0.865709	+	0.500548i	$0.833132\pi$
$230$	−152.539	+	99.5908i	−0.663212	+	0.433003i
$231$		0			0
$232$	−25.9804	+	4.31042i	−0.111984	+	0.0185794i
$233$	−270.154			−1.15946			−0.579730	−	0.814808i	$-0.696842\pi$
$233$	−270.154			−1.15946			−0.579730	+	0.814808i	$0.696842\pi$
$234$	247.483	+	379.059i	1.05762	+	1.61991i
$235$	−124.043			−0.527841
$236$	−43.2167	+	98.3576i	−0.183122	+	0.416770i
$237$			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	$0.893364\pi$
$240$	−308.570	+	283.350i	−1.28571	+	1.18062i
$241$	97.7124			0.405445			0.202723	−	0.979236i	$-0.435021\pi$
$241$	97.7124			0.405445			0.202723	+	0.979236i	$0.435021\pi$
$242$	199.350	−	130.153i	0.823761	−	0.537824i
$243$	332.558			1.36855
$244$	315.778	+	138.747i	1.29417	+	0.568637i
$245$		0			0
$246$	58.1025	−	37.9345i	0.236189	−	0.154205i
$247$			239.814i			0.970906i
$248$	−178.918	+	29.6844i	−0.721444	+	0.119695i
$249$	362.066			1.45408
$250$	−107.419	−	164.528i	−0.429675	−	0.658114i
$251$	313.145			1.24759			0.623796	−	0.781587i	$-0.285590\pi$
$251$	313.145			1.24759			0.623796	+	0.781587i	$0.285590\pi$
$252$		0			0
$253$			22.2553i			0.0879655i
$254$	17.5852	+	26.9345i	0.0692331	+	0.106041i
$255$		−	844.927i		−	3.31344i
$256$	−21.7757	+	255.072i	−0.0850614	+	0.996376i
$257$	348.855			1.35741			0.678707	−	0.734409i	$-0.262541\pi$
$257$	348.855			1.35741			0.678707	+	0.734409i	$0.262541\pi$
$258$	−159.466	+	104.113i	−0.618084	+	0.403540i
$259$		0			0
$260$	176.013	−	400.591i	0.676973	−	1.54073i
$261$			39.0484i			0.149611i
$262$	−197.839	+	129.167i	−0.755109	+	0.493002i
$263$			384.364i			1.46146i	0.682667	+	0.730729i	$0.260820\pi$
$263$			384.364i			1.46146i	−0.682667	+	0.730729i	$0.739180\pi$
$264$	8.37668	+	50.4891i	0.0317299	+	0.191247i
$265$	2.04460			0.00771548
$266$		0			0
$267$	12.1530			0.0455170
$268$	184.274	−	419.392i	0.687589	−	1.56490i
$269$		−	37.7613i		−	0.140376i	−0.997534	−	0.0701882i	$-0.977640\pi$
$269$		−	37.7613i		−	0.140376i	0.997534	−	0.0701882i	$-0.0223600\pi$
$270$	81.9275	+	125.485i	0.303435	+	0.464758i
$271$			308.730i			1.13922i	0.821914	+	0.569612i	$0.192907\pi$
$271$			308.730i			1.13922i	−0.821914	+	0.569612i	$0.807093\pi$
$272$	−349.219	−	380.303i	−1.28389	−	1.39817i
$273$		0			0
$274$	32.1048	−	20.9609i	0.117171	−	0.0764995i
$275$	11.0116			0.0400422
$276$	265.772	+	116.776i	0.962943	+	0.423101i
$277$			244.210i			0.881623i	0.897600	+	0.440812i	$0.145309\pi$
$277$			244.210i			0.881623i	−0.897600	+	0.440812i	$0.854691\pi$
$278$	175.763	−	114.754i	0.632241	−	0.412783i
$279$			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	$0.342693\pi$
$282$	108.061	+	165.513i	0.383196	+	0.586925i
$283$	−165.605			−0.585177			−0.292589	−	0.956238i	$-0.594517\pi$
$283$	−165.605			−0.585177			−0.292589	+	0.956238i	$0.594517\pi$
$284$	383.757	+	168.616i	1.35126	+	0.593719i
$285$			329.056i			1.15458i
$286$	−29.2229	−	44.7595i	−0.102178	−	0.156502i
$287$		0			0
$288$	367.817	+	93.7535i	1.27714	+	0.325533i
$289$	752.346			2.60327
$290$	31.6030	−	20.6332i	0.108976	−	0.0711490i
$291$	−237.933			−0.817641
$292$	39.2570	−	89.3456i	0.134442	−	0.305978i
$293$		−	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
$296$	−427.388	+	70.9081i	−1.44388	+	0.239554i
$297$	18.3081			0.0616434
$298$	−90.0838	−	137.977i	−0.302295	−	0.463011i
$299$	−303.201			−1.01405
$300$	57.7791	−	131.500i	0.192597	−	0.438335i
$301$		0			0
$302$	−63.1309	−	96.6947i	−0.209043	−	0.320181i
$303$		−	417.806i		−	1.37890i
$304$	136.003	+	148.109i	0.447379	+	0.487199i
$305$	−494.308			−1.62068
$306$	−641.030	+	418.521i	−2.09487	+	1.36772i
$307$	222.934			0.726170			0.363085	−	0.931756i	$-0.381724\pi$
$307$	222.934			0.726170			0.363085	+	0.931756i	$0.381724\pi$
$308$		0			0
$309$		−	181.736i		−	0.588141i
$310$	217.639	−	142.094i	0.702061	−	0.458367i
$311$		−	419.934i		−	1.35027i	−0.737694	−	0.675135i	$-0.764085\pi$
$311$		−	419.934i		−	1.35027i	0.737694	−	0.675135i	$-0.235915\pi$
$312$	−687.853	+	114.122i	−2.20466	+	0.365776i
$313$	293.869			0.938878			0.469439	−	0.882965i	$-0.344456\pi$
$313$	293.869			0.938878			0.469439	+	0.882965i	$0.344456\pi$
$314$	−4.07802	−	6.24612i	−0.0129873	−	0.0198921i
$315$		0			0
$316$	−428.933	−	188.466i	−1.35738	−	0.596411i
$317$			423.461i			1.33584i	0.744234	+	0.667919i	$0.232815\pi$
$317$			423.461i			1.33584i	−0.744234	+	0.667919i	$0.767185\pi$
$318$	−1.78118	−	2.72816i	−0.00560120	−	0.00857911i
$319$		−	4.61085i		−	0.0144541i
$320$	−118.478	−	347.225i	−0.370243	−	1.08508i
$321$	−377.561			−1.17620
$322$		0			0
$323$	−405.551			−1.25558
$324$	−75.7127	+	172.316i	−0.233681	+	0.531839i
$325$			150.020i			0.461599i
$326$	−130.134	+	84.9627i	−0.399183	+	0.260622i
$327$		−	134.612i		−	0.411658i
$328$	9.94618	+	59.9491i	0.0303237	+	0.182772i
$329$		0			0
$330$	−40.0977	−	61.4158i	−0.121508	−	0.186109i
$331$	−126.666			−0.382678			−0.191339	−	0.981524i	$-0.561283\pi$
$331$	−126.666			−0.382678			−0.191339	+	0.981524i	$0.561283\pi$
$332$	−127.551	+	290.296i	−0.384191	+	0.874386i
$333$			642.361i			1.92901i
$334$	−67.8807	−	103.970i	−0.203236	−	0.311287i
$335$			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	$0.351898\pi$
$338$	326.773	−	213.346i	0.966785	−	0.631202i
$339$	−726.838			−2.14406
$340$	677.442	+	297.657i	1.99248	+	0.875462i
$341$		−	31.7533i		−	0.0931183i
$342$	249.648	−	162.992i	0.729966	−	0.476586i
$343$		0			0
$344$	−27.2979	−	164.534i	−0.0793542	−	0.478295i
$345$	−416.031			−1.20589
$346$	213.879	+	327.589i	0.618148	+	0.946790i
$347$	320.532			0.923724			0.461862	−	0.886952i	$-0.347182\pi$
$347$	320.532			0.923724			0.461862	+	0.886952i	$0.347182\pi$
$348$	−55.0627	−	24.1936i	−0.158226	−	0.0695219i
$349$		−	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
$352$	−43.4320	−	11.0705i	−0.123386	−	0.0314502i
$353$	364.369			1.03221			0.516104	−	0.856526i	$-0.327382\pi$
$353$	364.369			1.03221			0.516104	+	0.856526i	$0.327382\pi$
$354$	−205.440	+	134.129i	−0.580339	+	0.378896i
$355$	−600.720			−1.69217
$356$	−4.28137	+	9.74403i	−0.0120263	+	0.0273709i
$357$		0			0
$358$	−120.928	+	78.9525i	−0.337788	+	0.220538i
$359$			111.995i			0.311965i	0.987760	+	0.155982i	$0.0498543\pi$
$359$			111.995i			0.311965i	−0.987760	+	0.155982i	$0.950146\pi$
$360$	−536.648	+	89.0356i	−1.49069	+	0.247321i
$361$	−203.059			−0.562489
$362$	154.144	+	236.096i	0.425812	+	0.652198i
$363$	543.704			1.49781
$364$		0			0
$365$			139.859i			0.383174i
$366$	430.623	+	659.566i	1.17657	+	1.80209i
$367$			439.042i			1.19630i	0.801384	+	0.598150i	$0.204097\pi$
$367$			439.042i			1.19630i	−0.801384	+	0.598150i	$0.795903\pi$
$368$	−187.256	+	171.951i	−0.508849	+	0.467259i
$369$	90.1030			0.244182
$370$	519.881	−	339.424i	1.40508	−	0.917363i
$371$		0			0
$372$	−379.198	−	166.613i	−1.01935	−	0.447885i
$373$		−	254.996i		−	0.683637i	−0.939766	−	0.341818i	$-0.888957\pi$
$373$		−	254.996i		−	0.683637i	0.939766	−	0.341818i	$-0.111043\pi$
$374$	75.6931	−	49.4191i	0.202388	−	0.132137i
$375$		−	448.732i		−	1.19662i
$376$	−170.773	+	28.3330i	−0.454183	+	0.0753538i
$377$	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	$0.207167\pi$
$380$	−263.829	−	115.922i	−0.694287	−	0.305058i
$381$			73.4605i			0.192810i
$382$	−311.035	−	476.399i	−0.814229	−	1.24712i
$383$			73.3855i			0.191607i	0.995400	+	0.0958035i	$0.0305420\pi$
$383$			73.3855i			0.191607i	−0.995400	+	0.0958035i	$0.969458\pi$
$384$	−360.096	+	460.577i	−0.937749	+	1.19942i
$385$		0			0
$386$	207.408	−	135.415i	0.537328	−	0.350815i
$387$	−247.293			−0.639000
$388$	83.8209	−	190.769i	0.216033	−	0.491674i
$389$		−	340.800i		−	0.876092i	−0.898953	−	0.438046i	$-0.855671\pi$
$389$		−	340.800i		−	0.876092i	0.898953	−	0.438046i	$-0.144329\pi$
$390$	836.715	−	546.282i	2.14542	−	1.40072i
$391$		−	512.745i		−	1.31137i
$392$		0			0
$393$	−539.581			−1.37298
$394$	118.192	+	181.029i	0.299979	+	0.459465i
$395$	671.438			1.69984
$396$	−26.7333	+	60.8427i	−0.0675082	+	0.153643i
$397$		−	111.540i		−	0.280957i	−0.990084	−	0.140478i	$-0.955136\pi$
$397$		−	111.540i		−	0.280957i	0.990084	−	0.140478i	$-0.0448640\pi$
$398$	−362.841	−	555.747i	−0.911661	−	1.39635i
$399$		0			0
$400$	85.0791	+	92.6518i	0.212698	+	0.231630i
$401$	340.535			0.849215			0.424607	−	0.905378i	$-0.360412\pi$
$401$	340.535			0.849215			0.424607	+	0.905378i	$0.360412\pi$
$402$	875.986	−	571.921i	2.17907	−	1.42269i
$403$	432.600			1.07345
$404$	334.987	+	147.188i	0.829175	+	0.364326i
$405$		−	269.738i		−	0.666019i
$406$		0			0
$407$		−	75.8502i		−	0.186364i
$408$	−192.993	−	1163.23i	−0.473021	−	2.85106i
$409$	−666.959			−1.63071			−0.815354	−	0.578963i	$-0.803457\pi$
$409$	−666.959			−1.63071			−0.815354	+	0.578963i	$0.803457\pi$
$410$	−47.6106	−	72.9230i	−0.116123	−	0.177861i
$411$	87.5620			0.213046
$412$	145.711	+	64.0232i	0.353669	+	0.155396i
$413$		0			0
$414$	206.074	+	315.635i	0.497764	+	0.762403i
$415$		−	454.420i		−	1.09499i
$416$	150.821	−	591.708i	0.362552	−	1.42238i
$417$	479.373			1.14958
$418$	−29.4786	+	19.2462i	−0.0705229	+	0.0460436i
$419$	200.191			0.477783			0.238891	−	0.971046i	$-0.423216\pi$
$419$	200.191			0.477783			0.238891	+	0.971046i	$0.423216\pi$
$420$		0			0
$421$			15.9136i			0.0377996i	0.999821	+	0.0188998i	$0.00601636\pi$
$421$			15.9136i			0.0377996i	−0.999821	+	0.0188998i	$0.993984\pi$
$422$	−44.2031	+	28.8597i	−0.104747	+	0.0683878i
$423$			256.671i			0.606786i
$424$	2.81486	−	0.467015i	0.00663882	−	0.00110145i
$425$	−253.699			−0.596940
$426$	523.325	+	801.554i	1.22846	+	1.88158i
$427$		0			0
$428$	133.010	−	302.720i	0.310771	−	0.707290i
$429$		−	122.076i		−	0.284560i
$430$	130.670	+	200.141i	0.303884	+	0.465445i
$431$		−	628.013i		−	1.45711i	−0.684989	−	0.728553i	$-0.740193\pi$
$431$		−	628.013i		−	1.45711i	0.684989	−	0.728553i	$-0.259807\pi$
$432$	141.454	+	154.045i	0.327440	+	0.356585i
$433$	−789.232			−1.82271			−0.911353	−	0.411625i	$-0.864961\pi$
$433$	−789.232			−1.82271			−0.911353	+	0.411625i	$0.864961\pi$
$434$		0			0
$435$	86.1933			0.198146
$436$	107.929	+	47.4221i	0.247543	+	0.108766i
$437$			199.688i			0.456952i
$438$	186.616	−	121.840i	0.426065	−	0.278173i
$439$		−	665.570i		−	1.51610i	−0.652194	−	0.758052i	$-0.726151\pi$
$439$		−	665.570i		−	1.51610i	0.652194	−	0.758052i	$-0.273849\pi$
$440$	63.3677	−	10.5134i	0.144017	−	0.0238940i
$441$		0			0
$442$	673.275	+	1031.23i	1.52325	+	2.33309i
$443$	507.152			1.14481			0.572406	−	0.819970i	$-0.306010\pi$
$443$	507.152			1.14481			0.572406	+	0.819970i	$0.306010\pi$
$444$	−905.802	−	397.995i	−2.04010	−	0.896384i
$445$		−	15.2530i		−	0.0342764i
$446$	176.234	+	269.930i	0.395143	+	0.605224i
$447$		−	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	$0.600571\pi$
$450$	156.172	−	101.963i	0.347048	−	0.226584i
$451$	−10.6394			−0.0235907
$452$	256.056	−	582.761i	0.566495	−	1.28930i
$453$		−	263.723i		−	0.582171i
$454$	−286.836	+	187.272i	−0.631798	+	0.412494i
$455$		0			0
$456$	75.1608	+	453.020i	0.164826	+	0.993465i
$457$	−720.881			−1.57742			−0.788710	−	0.614765i	$-0.789251\pi$
$457$	−720.881			−1.57742			−0.788710	+	0.614765i	$0.789251\pi$
$458$	−250.657	−	383.921i	−0.547287	−	0.838255i
$459$	−421.805			−0.918966
$460$	146.563	−	333.564i	0.318614	−	0.725139i
$461$		−	483.262i		−	1.04829i	−0.851629	−	0.524145i	$-0.824385\pi$
$461$		−	483.262i		−	1.04829i	0.851629	−	0.524145i	$-0.175615\pi$
$462$		0			0
$463$		−	39.6326i		−	0.0855995i	−0.999084	−	0.0427997i	$-0.986372\pi$
$463$		−	39.6326i		−	0.0855995i	0.999084	−	0.0427997i	$-0.0136277\pi$
$464$	38.7958	−	35.6249i	0.0836116	−	0.0767777i
$465$	593.584			1.27652
$466$	452.420	−	295.380i	0.970859	−	0.633863i
$467$	−17.7868			−0.0380874			−0.0190437	−	0.999819i	$-0.506062\pi$
$467$	−17.7868			−0.0380874			−0.0190437	+	0.999819i	$0.506062\pi$
$468$	−828.907	−	364.208i	−1.77117	−	0.778222i
$469$		0			0
$470$	207.731	−	135.625i	0.441981	−	0.288564i
$471$		−	17.0355i		−	0.0361689i
$472$	−35.1679	−	211.969i	−0.0745083	−	0.449087i
$473$	29.2005			0.0617346
$474$	−584.932	−	895.914i	−1.23403	−	1.89011i
$475$	98.8029			0.208006
$476$		0			0
$477$		−	4.23072i		−	0.00886943i
$478$	−171.829	−	263.183i	−0.359475	−	0.550592i
$479$			668.616i			1.39586i	0.716166	+	0.697930i	$0.245895\pi$
$479$			668.616i			1.39586i	−0.716166	+	0.697930i	$0.754105\pi$
$480$	206.947	−	811.901i	0.431139	−	1.69146i
$481$	1033.37			2.14837
$482$	−163.636	+	106.836i	−0.339494	+	0.221652i
$483$		0			0
$484$	−191.540	+	435.929i	−0.395744	+	0.900679i
$485$			298.624i			0.615720i
$486$	−556.926	+	363.611i	−1.14594	+	0.748170i
$487$			418.484i			0.859311i	0.902993	+	0.429656i	$0.141365\pi$
$487$			418.484i			0.859311i	−0.902993	+	0.429656i	$0.858635\pi$
$488$	−680.527	+	112.907i	−1.39452	+	0.231366i
$489$	−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	$0.373161\pi$
$492$	−55.8261	+	127.056i	−0.113468	+	0.258243i
$493$			106.231i			0.215478i
$494$	−262.206	−	401.610i	−0.530782	−	0.812975i
$495$		−	95.2412i		−	0.192406i
$496$	267.173	−	245.336i	0.538656	−	0.494629i
$497$		0			0
$498$	−606.342	+	395.874i	−1.21756	+	0.794928i
$499$	−438.392			−0.878541			−0.439271	−	0.898355i	$-0.644763\pi$
$499$	−438.392			−0.878541			−0.439271	+	0.898355i	$0.644763\pi$
$500$	359.783	+	158.083i	0.719565	+	0.316165i
$501$		−	283.565i		−	0.565999i
$502$	−524.416	+	342.385i	−1.04465	+	0.682043i
$503$			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
$506$	−24.3334	−	37.2703i	−0.0480896	−	0.0736568i
$507$	891.235			1.75786
$508$	−58.8989	−	25.8792i	−0.115943	−	0.0509433i
$509$		−	494.029i		−	0.970588i	−0.874351	−	0.485294i	$-0.838713\pi$
$509$		−	494.029i		−	0.970588i	0.874351	−	0.485294i	$-0.161287\pi$
$510$	923.822	+	1414.98i	1.81141	+	2.77446i
$511$		0			0
$512$	−242.422	−	450.972i	−0.473481	−	0.880804i
$513$	164.272			0.320218
$514$	−584.219	+	381.430i	−1.13661	+	0.742081i
$515$	−228.092			−0.442897
$516$	153.218	−	348.711i	0.296934	−	0.675797i
$517$		−	30.3078i		−	0.0586224i
$518$		0			0
$519$			893.460i			1.72150i
$520$	143.232	+	863.307i	0.275446	+	1.66021i
$521$	32.8747			0.0630993			0.0315496	−	0.999502i	$-0.489956\pi$
$521$	32.8747			0.0630993			0.0315496	+	0.999502i	$0.489956\pi$
$522$	−42.6945	−	65.3932i	−0.0817902	−	0.125274i
$523$	28.2755			0.0540640			0.0270320	−	0.999635i	$-0.491394\pi$
$523$	28.2755			0.0540640			0.0270320	+	0.999635i	$0.491394\pi$
$524$	190.088	−	432.624i	0.362763	−	0.825617i
$525$		0			0
$526$	−420.254	−	643.684i	−0.798961	−	1.22373i
$527$			731.574i			1.38819i
$528$	−69.2318	−	75.3940i	−0.131121	−	0.142792i
$529$	276.531			0.522742
$530$	−3.42404	+	2.23552i	−0.00646046	+	0.00421796i
$531$	−318.588			−0.599977
$532$		0			0
$533$		−	144.949i		−	0.271949i
$534$	−20.3524	+	13.2878i	−0.0381131	+	0.0248836i
$535$			473.868i			0.885735i
$536$	149.954	+	903.825i	0.279765	+	1.68624i
$537$	−329.817			−0.614183
$538$	41.2872	+	63.2378i	0.0767420	+	0.117542i
$539$		0			0
$540$	−274.404	−	120.568i	−0.508155	−	0.223275i
$541$		−	1071.59i		−	1.98077i	−0.138352	−	0.990383i	$-0.544180\pi$
$541$		−	1071.59i		−	1.98077i	0.138352	−	0.990383i	$-0.455820\pi$
$542$	−337.558	−	517.022i	−0.622800	−	0.953915i
$543$			643.922i			1.18586i
$544$	1000.64	+	255.055i	1.83942	+	0.468852i
$545$	−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	$0.857968\pi$
$548$	−30.8470	+	70.2052i	−0.0562901	+	0.128112i
$549$			1022.83i			1.86307i
$550$	−18.4408	+	12.0398i	−0.0335288	+	0.0218906i
$551$		−	41.3714i		−	0.0750842i
$552$	−572.761	+	95.0272i	−1.03761	+	0.172151i
$553$		0			0
$554$	−267.013	−	408.971i	−0.481972	−	0.738215i
$555$	1417.91			2.55480
$556$	−168.877	+	384.350i	−0.303736	+	0.691277i
$557$			483.550i			0.868133i	0.900881	+	0.434067i	$0.142922\pi$
$557$			483.550i			0.868133i	−0.900881	+	0.434067i	$0.857078\pi$
$558$	−294.022	−	450.341i	−0.526922	−	0.807062i
$559$			397.821i			0.711665i
$560$		0			0
$561$	206.444			0.367993
$562$	−446.417	+	291.460i	−0.794336	+	0.518613i
$563$	−520.893			−0.925210			−0.462605	−	0.886564i	$-0.653085\pi$
$563$	−520.893			−0.925210			−0.462605	+	0.886564i	$0.653085\pi$
$564$	−361.935	−	159.028i	−0.641729	−	0.281965i
$565$			912.236i			1.61458i
$566$	277.334	−	181.068i	0.489990	−	0.319909i
$567$		0			0
$568$	−827.028	+	137.213i	−1.45603	+	0.241572i
$569$	−732.959			−1.28815			−0.644077	−	0.764961i	$-0.722758\pi$
$569$	−732.959			−1.28815			−0.644077	+	0.764961i	$0.722758\pi$
$570$	−359.781	−	551.061i	−0.631195	−	0.966773i
$571$	−999.584			−1.75058			−0.875292	−	0.483595i	$-0.839331\pi$
$571$	−999.584			−1.75058			−0.875292	+	0.483595i	$0.839331\pi$
$572$	97.8777	+	43.0059i	0.171115	+	0.0751851i
$573$		−	1299.32i		−	2.26758i
$574$		0			0
$575$			124.918i			0.217249i
$576$	−718.481	+	245.155i	−1.24736	+	0.425617i
$577$	−465.859			−0.807381			−0.403690	−	0.914896i	$-0.632273\pi$
$577$	−465.859			−0.807381			−0.403690	+	0.914896i	$0.632273\pi$
$578$	−1259.93	+	822.596i	−2.17982	+	1.42318i
$579$	565.682			0.976998
$580$	−30.3648	+	69.1078i	−0.0523531	+	0.119151i
$581$		0			0
$582$	398.461	−	260.150i	0.684641	−	0.446994i
$583$			0.499565i			0.000856887i
$584$	31.9456	+	192.547i	0.0547014	+	0.329704i
$585$	1297.54			2.21803
$586$	37.5741	+	57.5506i	0.0641196	+	0.0982092i
$587$	574.851			0.979303			0.489651	−	0.871918i	$-0.337124\pi$
$587$	574.851			0.979303			0.489651	+	0.871918i	$0.337124\pi$
$588$		0			0
$589$		−	284.911i		−	0.483719i
$590$	168.342	+	257.843i	0.285326	+	0.437021i
$591$			493.735i			0.835423i
$592$	638.205	−	586.043i	1.07805	−	0.989937i
$593$	−943.055			−1.59031			−0.795156	−	0.606405i	$-0.792611\pi$
$593$	−943.055			−1.59031			−0.795156	+	0.606405i	$0.792611\pi$
$594$	−30.6601	+	20.0176i	−0.0516163	+	0.0336997i
$595$		0			0
$596$	301.722	+	132.572i	0.506245	+	0.222436i
$597$		−	1515.73i		−	2.53892i
$598$	507.763	−	331.512i	0.849101	−	0.554368i
$599$		−	9.26699i		−	0.0154708i	−0.999970	−	0.00773538i	$-0.997538\pi$
$599$		−	9.26699i		−	0.0154708i	0.999970	−	0.00773538i	$-0.00246227\pi$
$600$	47.0181	+	283.394i	0.0783635	+	0.472324i
$601$	−57.7003			−0.0960072			−0.0480036	−	0.998847i	$-0.515286\pi$
$601$	−57.7003			−0.0960072			−0.0480036	+	0.998847i	$0.515286\pi$
$602$		0			0
$603$	1358.44			2.25281
$604$	211.447	+	92.9064i	0.350078	+	0.153819i
$605$		−	682.389i		−	1.12792i
$606$	456.818	+	699.688i	0.753825	+	1.15460i
$607$		−	1024.68i		−	1.68810i	−0.536264	−	0.844050i	$-0.680165\pi$
$607$		−	1024.68i		−	1.68810i	0.536264	−	0.844050i	$-0.319835\pi$
$608$	−389.699	−	99.3310i	−0.640952	−	0.163373i
$609$		0			0
$610$	827.805	−	540.464i	1.35706	−	0.886007i
$611$	412.906			0.675788
$612$	615.915	−	1401.77i	1.00640	−	2.29048i
$613$			404.818i			0.660389i	0.943913	+	0.330195i	$0.107114\pi$
$613$			404.818i			0.660389i	−0.943913	+	0.330195i	$0.892886\pi$
$614$	−373.342	+	243.750i	−0.608048	+	0.396988i
$615$		−	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	$0.242005\pi$
$618$	198.705	+	304.348i	0.321530	+	0.492472i
$619$	779.388			1.25911			0.629554	−	0.776957i	$-0.283238\pi$
$619$	779.388			1.25911			0.629554	+	0.776957i	$0.283238\pi$
$620$	−209.112	+	475.922i	−0.337278	+	0.767616i
$621$			207.692i			0.334447i
$622$	459.145	+	703.252i	0.738176	+	1.13063i
$623$		0			0
$624$	1027.15	−	943.198i	1.64607	−	1.51154i
$625$	−759.737			−1.21558
$626$	−492.134	+	321.309i	−0.786157	+	0.513273i
$627$	−80.3993			−0.128229
$628$	13.6587	+	6.00140i	0.0217495	+	0.00955638i
$629$			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	$0.787855\pi$
$632$	924.387	−	153.366i	1.46264	−	0.242667i
$633$	−120.559			−0.190456
$634$	−463.001	−	709.158i	−0.730286	−	1.11855i
$635$	92.1985			0.145194
$636$	5.96580	+	2.62127i	0.00938018	+	0.00412150i
$637$		0			0
$638$	5.04139	+	7.72166i	0.00790186	+	0.0121029i
$639$			1243.02i			1.94525i
$640$	578.058	+	451.947i	0.903216	+	0.706168i
$641$	−23.3139			−0.0363712			−0.0181856	−	0.999835i	$-0.505789\pi$
$641$	−23.3139			−0.0363712			−0.0181856	+	0.999835i	$0.505789\pi$
$642$	632.292	−	412.816i	0.984879	−	0.643016i
$643$	−530.706			−0.825360			−0.412680	−	0.910876i	$-0.635407\pi$
$643$	−530.706			−0.825360			−0.412680	+	0.910876i	$0.635407\pi$
$644$		0			0
$645$			545.862i			0.846297i
$646$	679.165	−	443.419i	1.05134	−	0.686407i
$647$		−	213.435i		−	0.329883i	−0.986303	−	0.164942i	$-0.947256\pi$
$647$		−	213.435i		−	0.329883i	0.986303	−	0.164942i	$-0.0527436\pi$
$648$	−61.6117	−	371.355i	−0.0950799	−	0.573079i
$649$	37.6190			0.0579646
$650$	−164.028	−	251.234i	−0.252350	−	0.386514i
$651$		0			0
$652$	125.035	−	284.570i	0.191772	−	0.436457i
$653$		−	274.874i		−	0.420941i	−0.977600	−	0.210470i	$-0.932500\pi$
$653$		−	274.874i		−	0.420941i	0.977600	−	0.210470i	$-0.0674995\pi$
$654$	147.181	+	225.431i	0.225048	+	0.344696i
$655$			677.215i			1.03392i
$656$	−82.2034	−	89.5202i	−0.125310	−	0.136464i
$657$	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	$0.113925\pi$
$660$	134.301	+	59.0096i	0.203486	+	0.0894085i
$661$		−	582.733i		−	0.881593i	−0.897607	−	0.440797i	$-0.854696\pi$
$661$		−	582.733i		−	0.881593i	0.897607	−	0.440797i	$-0.145304\pi$
$662$	212.125	−	138.494i	0.320430	−	0.209205i
$663$			2812.54i			4.24215i
$664$	−103.796	−	625.613i	−0.156319	−	0.942188i
$665$		0			0
$666$	−702.341	−	1075.74i	−1.05457	−	1.61523i
$667$	52.3066			0.0784207
$668$	227.356	+	99.8965i	0.340353	+	0.149546i
$669$			736.201i			1.10045i
$670$	−717.804	−	1099.43i	−1.07135	−	1.64094i
$671$		−	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	$0.595833\pi$
$674$	−506.428	+	330.641i	−0.751377	+	0.490565i
$675$	102.763			0.152241
$676$	−313.971	+	714.571i	−0.464454	+	1.05706i
$677$			754.467i			1.11443i	0.830369	+	0.557214i	$0.188130\pi$
$677$			754.467i			1.11443i	−0.830369	+	0.557214i	$0.811870\pi$
$678$	1217.22	−	794.706i	1.79530	−	1.17213i
$679$		0			0
$680$	−1459.95	+	242.220i	−2.14698	+	0.356206i
$681$	−782.312			−1.14877
$682$	34.7183	+	53.1765i	0.0509066	+	0.0779713i
$683$	288.264			0.422055			0.211028	−	0.977480i	$-0.432319\pi$
$683$	288.264			0.422055			0.211028	+	0.977480i	$0.432319\pi$
$684$	−239.867	+	545.918i	−0.350683	+	0.798126i
$685$		−	109.897i		−	0.160433i
$686$		0			0
$687$		−	1047.10i		−	1.52416i
$688$	225.612	+	245.693i	0.327924	+	0.357112i
$689$	−6.80596			−0.00987803
$690$	696.716	−	454.878i	1.00973	−	0.659244i
$691$	156.692			0.226761			0.113380	−	0.993552i	$-0.463832\pi$
$691$	156.692			0.226761			0.113380	+	0.993552i	$0.463832\pi$
$692$	−716.356	−	314.755i	−1.03520	−	0.454848i
$693$		0			0
$694$	−536.787	+	350.462i	−0.773468	+	0.504988i
$695$		−	601.649i		−	0.865682i
$696$	118.665	−	19.6877i	0.170495	−	0.0282870i
$697$	245.124			0.351685
$698$	416.224	+	637.512i	0.596310	+	0.913341i
$699$	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	$0.702970\pi$
$702$	−272.716	−	417.706i	−0.388484	−	0.595023i
$703$		−	680.575i		−	0.968102i
$704$	84.8386	−	28.9481i	0.120509	−	0.0411194i
$705$	566.562			0.803633
$706$	−610.200	+	398.392i	−0.864306	+	0.564295i
$707$		0			0
$708$	197.391	−	449.246i	0.278801	−	0.634528i
$709$			1096.17i			1.54608i	0.634356	+	0.773041i	$0.281266\pi$
$709$			1096.17i			1.54608i	−0.634356	+	0.773041i	$0.718734\pi$
$710$	1006.01	−	656.812i	1.41692	−	0.925088i
$711$		−	1389.35i		−	1.95407i
$712$	−3.48399	−	20.9992i	−0.00489325	−	0.0294933i
$713$	360.218			0.505214
$714$		0			0
$715$	−153.215			−0.214286
$716$	116.190	−	264.439i	0.162277	−	0.369328i
$717$		−	717.800i		−	1.00112i
$718$	−122.453	−	187.556i	−0.170547	−	0.261220i
$719$			605.362i			0.841949i	0.907072	+	0.420975i	$0.138312\pi$
$719$			605.362i			0.841949i	−0.907072	+	0.420975i	$0.861688\pi$
$720$	801.361	−	735.863i	1.11300	−	1.02203i
$721$		0			0
$722$	340.057	−	222.019i	0.470993	−	0.307506i
$723$	−446.298			−0.617287
$724$	−516.282	−	226.846i	−0.713097	−	0.313323i
$725$		−	25.8806i		−	0.0356974i
$726$	−910.526	+	594.472i	−1.25417	+	0.818832i
$727$		−	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
$730$	−152.918	−	234.218i	−0.209477	−	0.320846i
$731$	−672.757			−0.920325
$732$	−1442.31	−	633.725i	−1.97036	−	0.865744i
$733$			750.026i			1.02323i	0.859216	+	0.511614i	$0.170952\pi$
$733$			750.026i			1.02323i	−0.859216	+	0.511614i	$0.829048\pi$
$734$	−480.038	−	735.252i	−0.654002	−	1.00171i
$735$		0			0
$736$	125.586	−	492.704i	0.170633	−	0.669434i
$737$	−160.406			−0.217647
$738$	−150.893	+	98.5164i	−0.204462	+	0.133491i
$739$	619.293			0.838015			0.419007	−	0.907983i	$-0.362378\pi$
$739$	619.293			0.838015			0.419007	+	0.907983i	$0.362378\pi$
$740$	−499.513	+	1136.85i	−0.675018	+	1.53628i
$741$		−	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	$0.993461\pi$
$744$	817.203	−	135.583i	1.09839	−	0.182235i
$745$	−472.306			−0.633967
$746$	278.807	+	427.036i	0.373736	+	0.572434i
$747$	−940.291			−1.25876
$748$	−72.7275	+	165.522i	−0.0972293	+	0.221286i
$749$		0			0
$750$	490.632	+	751.479i	0.654176	+	1.00197i
$751$		−	968.214i		−	1.28923i	−0.764506	−	0.644616i	$-0.777017\pi$
$751$		−	968.214i		−	1.28923i	0.764506	−	0.644616i	$-0.222983\pi$
$752$	255.010	−	234.167i	0.339109	−	0.311393i
$753$	−1430.28			−1.89945
$754$	−105.198	+	68.6827i	−0.139520	+	0.0910911i
$755$	−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	$-0.281521\pi$
$758$	−1009.91	+	659.357i	−1.33233	+	0.869865i
$759$		−	101.650i		−	0.133927i
$760$	568.574	−	94.3325i	0.748124	−	0.124122i
$761$	−235.996			−0.310113			−0.155057	−	0.987906i	$-0.549556\pi$
$761$	−235.996			−0.310113			−0.155057	+	0.987906i	$0.549556\pi$
$762$	−80.3199	−	123.022i	−0.105407	−	0.161447i
$763$		0			0
$764$	1041.77	+	457.734i	1.36357	+	0.599129i
$765$			2194.29i			2.86835i
$766$	−80.2379	−	122.897i	−0.104749	−	0.160440i
$767$			512.513i			0.668205i
$768$	99.4599	−	1165.03i	0.129505	−	1.51697i
$769$	124.257			0.161582			0.0807912	−	0.996731i	$-0.474255\pi$
$769$	124.257			0.161582			0.0807912	+	0.996731i	$0.474255\pi$
$770$		0			0
$771$	−1593.39			−2.06665
$772$	−199.283	+	453.550i	−0.258138	+	0.587501i
$773$		−	178.223i		−	0.230560i	−0.993333	−	0.115280i	$-0.963224\pi$
$773$		−	178.223i		−	0.230560i	0.993333	−	0.115280i	$-0.0367765\pi$
$774$	414.135	−	270.384i	0.535058	−	0.349333i
$775$		−	178.231i		−	0.229975i
$776$	68.2099	+	411.124i	0.0878993	+	0.529799i
$777$		0			0
$778$	372.622	+	570.728i	0.478948	+	0.733584i
$779$	−95.4634			−0.122546
$780$	−803.934	+	1829.69i	−1.03068	+	2.34575i
$781$		−	146.776i		−	0.187933i
$782$	560.623	+	858.681i	0.716909	+	1.09806i
$783$		−	43.0296i		−	0.0549548i
$784$		0			0
$785$	−21.3809			−0.0272368
$786$	903.622	−	589.964i	1.14965	−	0.750591i
$787$	1107.90			1.40775			0.703873	−	0.710326i	$-0.251453\pi$
$787$	1107.90			1.40775			0.703873	+	0.710326i	$0.251453\pi$
$788$	−395.865	−	173.937i	−0.502367	−	0.220732i
$789$		−	1755.57i		−	2.22506i
$790$	−1124.44	+	734.133i	−1.42334	+	0.929283i
$791$		0			0
$792$	−21.7544	−	131.121i	−0.0274676	−	0.165557i
$793$	1645.43			2.07494
$794$	121.955	+	186.793i	0.153595	+	0.235255i
$795$	−9.33867			−0.0117468
$796$	1215.28	+	533.974i	1.52673	+	0.670821i
$797$			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
$800$	−243.783	−	62.1382i	−0.304729	−	0.0776728i
$801$	−31.5617			−0.0394028
$802$	−570.285	+	372.332i	−0.711079	+	0.464255i
$803$	−34.1722			−0.0425556
$804$	−841.666	+	1915.56i	−1.04685	+	2.38254i
$805$		0			0
$806$	−724.464	+	472.994i	−0.898839	+	0.586842i
$807$			172.473i			0.213722i
$808$	−721.925	+	119.775i	−0.893471	+	0.148236i
$809$	−1386.75			−1.71416			−0.857079	−	0.515185i	$-0.827723\pi$
$809$	−1386.75			−1.71416			−0.857079	+	0.515185i	$0.827723\pi$
$810$	294.924	+	451.723i	0.364104	+	0.557682i
$811$	312.204			0.384962			0.192481	−	0.981301i	$-0.438347\pi$
$811$	312.204			0.384962			0.192481	+	0.981301i	$0.438347\pi$
$812$		0			0
$813$		−	1410.11i		−	1.73446i
$814$	82.9328	+	127.024i	0.101883	+	0.156050i
$815$			445.456i			0.546572i
$816$	1595.05	+	1737.02i	1.95472	+	2.12870i
$817$	262.005			0.320691
$818$	1116.94	−	729.237i	1.36545	−	0.891487i
$819$		0			0
$820$	159.464	+	70.0660i	0.194469	+	0.0854464i
$821$		−	1092.89i		−	1.33117i	−0.746324	−	0.665583i	$-0.768183\pi$
$821$		−	1092.89i		−	1.33117i	0.746324	−	0.665583i	$-0.231817\pi$
$822$	−146.638	+	95.7381i	−0.178391	+	0.116470i
$823$		−	907.162i		−	1.10226i	−0.834419	−	0.551131i	$-0.814196\pi$
$823$		−	907.162i		−	1.10226i	0.834419	−	0.551131i	$-0.185804\pi$
$824$	−314.020	+	52.0993i	−0.381093	+	0.0632273i
$825$	−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	$0.619641\pi$
$828$	−690.215	−	303.269i	−0.833593	−	0.366267i
$829$			427.969i			0.516247i	0.966112	+	0.258124i	$0.0831042\pi$
$829$			427.969i			0.516247i	−0.966112	+	0.258124i	$0.916896\pi$
$830$	496.852	+	761.005i	0.598616	+	0.916874i
$831$		−	1115.42i		−	1.34226i
$832$	394.382	+	1155.82i	0.474017	+	1.38921i
$833$		0			0
$834$	−802.793	+	524.134i	−0.962581	+	0.628458i
$835$	−355.896			−0.426223
$836$	28.3237	−	64.4623i	0.0338800	−	0.0771080i
$837$		−	296.330i		−	0.354038i
$838$	−335.255	+	218.884i	−0.400065	+	0.261198i
$839$			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
$842$	−17.3996	−	26.6502i	−0.0206646	−	0.0316510i
$843$	−1217.55			−1.44430
$844$	42.4712	−	96.6610i	0.0503214	−	0.114527i
$845$		−	1118.57i		−	1.32375i
$846$	−280.637	−	429.839i	−0.331722	−	0.508084i
$847$		0			0
$848$	−4.20335	+	3.85980i	−0.00495678	+	0.00455165i
$849$	756.397			0.890927
$850$	424.864	−	277.388i	0.499839	−	0.326339i
$851$	860.464			1.01112
$852$	−1752.80	−	770.150i	−2.05727	−	0.903932i
$853$			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
$856$	108.238	+	652.387i	0.126446	+	0.762134i
$857$	234.079			0.273138			0.136569	−	0.990631i	$-0.456393\pi$
$857$	234.079			0.273138			0.136569	+	0.990631i	$0.456393\pi$
$858$	133.475	+	204.438i	0.155565	+	0.238272i
$859$	−894.342			−1.04114			−0.520571	−	0.853818i	$-0.674281\pi$
$859$	−894.342			−1.04114			−0.520571	+	0.853818i	$0.674281\pi$
$860$	−437.659	−	192.300i	−0.508906	−	0.223605i
$861$		0			0
$862$	686.654	+	1051.72i	0.796582	+	1.22009i
$863$			778.580i			0.902178i	0.892479	+	0.451089i	$0.148964\pi$
$863$			778.580i			0.902178i	−0.892479	+	0.451089i	$0.851036\pi$
$864$	−405.318	−	103.312i	−0.469118	−	0.119574i
$865$	1121.36			1.29637
$866$	1321.71	−	862.927i	1.52622	−	0.996451i
$867$	−3436.32			−3.96346
$868$		0			0
$869$			164.055i			0.188786i
$870$	−144.346	+	94.2416i	−0.165915	+	0.108324i
$871$		−	2185.33i		−	2.50899i
$872$	−232.596	+	38.5901i	−0.266738	+	0.0442547i
$873$	617.917			0.707809
$874$	−218.334	−	334.412i	−0.249810	−	0.382623i
$875$		0			0
$876$	−179.305	+	408.083i	−0.204686	+	0.465849i
$877$			17.2780i			0.0197013i	0.999951	+	0.00985064i	$0.00313561\pi$
$877$			17.2780i			0.0197013i	−0.999951	+	0.00985064i	$0.996864\pi$
$878$	727.717	+	1114.61i	0.828835	+	1.26949i
$879$			156.962i			0.178569i
$880$	−94.6251	+	86.8911i	−0.107529	+	0.0987399i
$881$	−770.918			−0.875049			−0.437524	−	0.899207i	$-0.644145\pi$
$881$	−770.918			−0.875049			−0.437524	+	0.899207i	$0.644145\pi$
$882$		0			0
$883$	776.362			0.879232			0.439616	−	0.898186i	$-0.355114\pi$
$883$	776.362			0.879232			0.439616	+	0.898186i	$0.355114\pi$
$884$	−2255.03	−	990.824i	−2.55094	−	1.12084i
$885$			703.235i			0.794616i
$886$	−849.313	+	554.507i	−0.958593	+	0.625854i
$887$		−	1630.80i		−	1.83856i	−0.393603	−	0.919280i	$-0.628772\pi$
$887$		−	1630.80i		−	1.83856i	0.393603	−	0.919280i	$-0.371228\pi$
$888$	1952.08	−	323.871i	2.19829	−	0.364719i
$889$		0			0
$890$	16.6772	+	25.5438i	0.0187385	+	0.0287009i
$891$	65.9059			0.0739685
$892$	−590.269	−	259.354i	−0.661736	−	0.290756i
$893$		−	271.940i		−	0.304524i
$894$	411.455	+	630.207i	0.460241	+	0.704930i
$895$			413.945i			0.462508i
$896$		0			0
$897$	1384.86			1.54388
$898$	467.283	−	305.084i	0.520360	−	0.339737i
$899$	−74.6299			−0.0830144
$900$	−150.053	+	341.509i	−0.166726	+	0.379454i
$901$		−	11.5096i		−	0.0127743i
$902$	17.8175	−	11.6329i	0.0197534	−	0.0128967i
$903$		0			0
$904$	208.367	+	1255.90i	0.230495	+	1.38927i
$905$	808.171			0.893007
$906$	288.349	+	441.650i	0.318265	+	0.487473i
$907$	−953.863			−1.05167			−0.525834	−	0.850587i	$-0.676247\pi$
$907$	−953.863			−1.05167			−0.525834	+	0.850587i	$0.676247\pi$
$908$	275.598	−	627.239i	0.303523	−	0.690792i
$909$			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	$-0.374017\pi$
$912$	−621.190	−	676.481i	−0.681130	−	0.741756i
$913$	111.030			0.121610
$914$	1207.24	−	788.194i	1.32083	−	0.862356i
$915$	2257.74			2.46747
$916$	839.538	+	368.879i	0.916527	+	0.402707i
$917$		0			0
$918$	706.386	−	461.192i	0.769484	−	0.502387i
$919$		−	504.991i		−	0.549500i	−0.961516	−	0.274750i	$-0.911405\pi$
$919$		−	504.991i		−	0.549500i	0.961516	−	0.274750i	$-0.0885952\pi$
$920$	119.266	+	718.859i	0.129637	+	0.781368i
$921$	−1018.24			−1.10559
$922$	528.387	+	809.306i	0.573088	+	0.877773i
$923$	1999.64			2.16646
$924$		0			0
$925$		−	425.746i		−	0.460266i
$926$	43.3333	+	66.3716i	0.0467962	+	0.0716756i
$927$			471.971i			0.509138i
$928$	−26.0189	+	102.078i	−0.0280376	+	0.109998i
$929$	−983.851			−1.05904			−0.529521	−	0.848297i	$-0.677628\pi$
$929$	−983.851			−1.05904			−0.529521	+	0.848297i	$0.677628\pi$
$930$	−994.059	+	649.010i	−1.06888	+	0.697860i
$931$		0			0
$932$	−434.695	+	989.330i	−0.466411	+	1.06151i
$933$			1918.04i			2.05577i
$934$	29.7871	−	19.4476i	0.0318919	−	0.0208219i
$935$		−	259.103i		−	0.277115i
$936$	1786.36	−	296.377i	1.90851	−	0.316642i
$937$	389.648			0.415846			0.207923	−	0.978145i	$-0.433330\pi$
$937$	389.648			0.415846			0.207923	+	0.978145i	$0.433330\pi$
$938$		0			0
$939$	−1342.24			−1.42943
$940$	−199.592	+	454.256i	−0.212332	+	0.483251i
$941$			875.465i			0.930356i	0.885217	+	0.465178i	$0.154010\pi$
$941$			875.465i			0.930356i	−0.885217	+	0.465178i	$0.845990\pi$
$942$	18.6262	+	28.5290i	0.0197731	+	0.0302855i
$943$		−	120.696i		−	0.127992i
$944$	290.656	+	316.527i	0.307899	+	0.335304i
$945$		0			0
$946$	−48.9012	+	31.9270i	−0.0516926	+	0.0337495i
$947$	−1251.29			−1.32132			−0.660661	−	0.750685i	$-0.729724\pi$
$947$	−1251.29			−1.32132			−0.660661	+	0.750685i	$0.729724\pi$
$948$	1959.14	+	860.813i	2.06660	+	0.908031i
$949$		−	465.554i		−	0.490573i
$950$	−165.463	+	108.029i	−0.174171	+	0.113714i
$951$		−	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	$0.653161\pi$
$954$	4.62576	+	7.08507i	0.00484880	+	0.00742670i
$955$	−1630.75			−1.70759
$956$	575.515	+	252.872i	0.602003	+	0.264510i
$957$			21.0599i			0.0220062i
$958$	−731.049	−	1119.71i	−0.763099	−	1.16880i
$959$		0			0
$960$	541.144	+	1585.94i	0.563691	+	1.65202i
$961$	447.049			0.465192
$962$	−1730.55	+	1129.86i	−1.79891	+	1.17449i
$963$	980.533			1.01821
$964$	157.225	−	357.832i	0.163097	−	0.371195i
$965$		−	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	$-0.260099\pi$
$968$	−155.867	−	939.463i	−0.161020	−	0.970520i
$969$	1852.34			1.91160
$970$	−326.508	−	500.098i	−0.336607	−	0.515565i
$971$	−678.550			−0.698815			−0.349408	−	0.936971i	$-0.613617\pi$
$971$	−678.550			−0.698815			−0.349408	+	0.936971i	$0.613617\pi$
$972$	535.107	−	1217.86i	0.550521	−	1.25294i
$973$		0			0
$974$	−457.560	−	700.825i	−0.469775	−	0.719533i
$975$		−	685.210i		−	0.702780i
$976$	1016.21	−	933.153i	1.04120	−	0.956100i
$977$	111.815			0.114447			0.0572235	−	0.998361i	$-0.481775\pi$
$977$	111.815			0.114447			0.0572235	+	0.998361i	$0.481775\pi$
$978$	594.382	−	388.065i	0.607752	−	0.396794i
$979$	3.72682			0.00380676
$980$		0			0
$981$			349.590i			0.356360i
$982$	−638.102	+	416.609i	−0.649798	+	0.424246i
$983$		−	202.226i		−	0.205723i	−0.994696	−	0.102862i	$-0.967200\pi$
$983$		−	202.226i		−	0.205723i	0.994696	−	0.102862i	$-0.0327999\pi$
$984$	−45.4289	−	273.816i	−0.0461676	−	0.278268i
$985$	619.675			0.629111
$986$	−116.150	−	177.902i	−0.117799	−	0.180428i
$987$		0			0
$988$	878.220	+	385.875i	0.888887	+	0.390562i
$989$			331.257i			0.334942i
$990$	104.134	+	159.498i	0.105186	+	0.161109i
$991$		−	189.064i		−	0.190781i	−0.995440	−	0.0953907i	$-0.969590\pi$
$991$		−	189.064i		−	0.190781i	0.995440	−	0.0953907i	$-0.0304100\pi$
$992$	−179.183	+	702.978i	−0.180628	+	0.708648i
$993$	578.546			0.582624
$994$		0			0
$995$	−1902.36			−1.91192
$996$	582.587	−	1325.92i	0.584927	−	1.33124i
$997$		−	1632.91i		−	1.63783i	−0.573917	−	0.818914i	$-0.694577\pi$
$997$		−	1632.91i		−	1.63783i	0.573917	−	0.818914i	$-0.305423\pi$
$998$	734.164	−	479.327i	0.735635	−	0.480288i
$999$		−	707.853i		−	0.708562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.g.m.99.2		8
4.3	odd	2		1568.3.g.m.687.8		8
7.2	even	3		392.3.k.n.67.7		16
7.3	odd	6		392.3.k.o.275.5		16
7.4	even	3		392.3.k.n.275.5		16
7.5	odd	6		392.3.k.o.67.7		16
7.6	odd	2		56.3.g.b.43.2	yes	8
8.3	odd	2	inner	392.3.g.m.99.1		8
8.5	even	2		1568.3.g.m.687.7		8
21.20	even	2		504.3.g.b.379.7		8
28.27	even	2		224.3.g.b.15.1		8
56.3	even	6		392.3.k.o.275.7		16
56.11	odd	6		392.3.k.n.275.7		16
56.13	odd	2		224.3.g.b.15.2		8
56.19	even	6		392.3.k.o.67.5		16
56.27	even	2		56.3.g.b.43.1	✓	8
56.51	odd	6		392.3.k.n.67.5		16
84.83	odd	2		2016.3.g.b.1135.7		8
112.13	odd	4		1792.3.d.j.1023.13		16
112.27	even	4		1792.3.d.j.1023.14		16
112.69	odd	4		1792.3.d.j.1023.4		16
112.83	even	4		1792.3.d.j.1023.3		16
168.83	odd	2		504.3.g.b.379.8		8
168.125	even	2		2016.3.g.b.1135.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.g.b.43.1	✓	8	56.27	even	2
56.3.g.b.43.2	yes	8	7.6	odd	2
224.3.g.b.15.1		8	28.27	even	2
224.3.g.b.15.2		8	56.13	odd	2
392.3.g.m.99.1		8	8.3	odd	2	inner
392.3.g.m.99.2		8	1.1	even	1	trivial
392.3.k.n.67.5		16	56.51	odd	6
392.3.k.n.67.7		16	7.2	even	3
392.3.k.n.275.5		16	7.4	even	3
392.3.k.n.275.7		16	56.11	odd	6
392.3.k.o.67.5		16	56.19	even	6
392.3.k.o.67.7		16	7.5	odd	6
392.3.k.o.275.5		16	7.3	odd	6
392.3.k.o.275.7		16	56.3	even	6
504.3.g.b.379.7		8	21.20	even	2
504.3.g.b.379.8		8	168.83	odd	2
1568.3.g.m.687.7		8	8.5	even	2
1568.3.g.m.687.8		8	4.3	odd	2
1792.3.d.j.1023.3		16	112.83	even	4
1792.3.d.j.1023.4		16	112.69	odd	4
1792.3.d.j.1023.13		16	112.13	odd	4
1792.3.d.j.1023.14		16	112.27	even	4
2016.3.g.b.1135.2		8	168.125	even	2
2016.3.g.b.1135.7		8	84.83	odd	2

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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67467 + 1.09337i) q^{2} -4.56747 q^{3} +(1.60906 - 3.66209i) q^{4} +5.73252i q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +11.8618 q^{9} +O(q^{10})\)	\(q+(-1.67467 + 1.09337i) q^{2} -4.56747 q^{3} +(1.60906 - 3.66209i) q^{4} +5.73252i q^{5} +(7.64902 - 4.99396i) q^{6} +(1.30939 + 7.89212i) q^{8} +11.8618 q^{9} +(-6.26779 - 9.60010i) q^{10} -1.40065 q^{11} +(-7.34935 + 16.7265i) q^{12} -19.0821i q^{13} -26.1831i q^{15} +(-10.8218 - 11.7851i) q^{16} +32.2699 q^{17} +(-19.8646 + 12.9694i) q^{18} -12.5675 q^{19} +(20.9930 + 9.22398i) q^{20} +(2.34563 - 1.53143i) q^{22} -15.8893i q^{23} +(-5.98058 - 36.0470i) q^{24} -7.86180 q^{25} +(20.8639 + 31.9563i) q^{26} -13.0712 q^{27} +3.29194i q^{29} +(28.6280 + 43.8482i) q^{30} +22.6705i q^{31} +(31.0085 + 7.90382i) q^{32} +6.39741 q^{33} +(-54.0415 + 35.2831i) q^{34} +(19.0864 - 43.4390i) q^{36} +54.1537i q^{37} +(21.0464 - 13.7410i) q^{38} +87.1569i q^{39} +(-45.2417 + 7.50608i) q^{40} +7.59607 q^{41} -20.8478 q^{43} +(-2.25373 + 5.12930i) q^{44} +67.9980i q^{45} +(17.3729 + 26.6094i) q^{46} +21.6384i q^{47} +(49.4284 + 53.8280i) q^{48} +(13.1659 - 8.59589i) q^{50} -147.392 q^{51} +(-69.8804 - 30.7043i) q^{52} -0.356667i q^{53} +(21.8900 - 14.2917i) q^{54} -8.02924i q^{55} +57.4016 q^{57} +(-3.59933 - 5.51293i) q^{58} -26.8583 q^{59} +(-95.8850 - 42.1303i) q^{60} +86.2287i q^{61} +(-24.7873 - 37.9656i) q^{62} +(-60.5710 + 20.6676i) q^{64} +109.389 q^{65} +(-10.7136 + 6.99477i) q^{66} +114.523 q^{67} +(51.9243 - 118.175i) q^{68} +72.5739i q^{69} +104.792i q^{71} +(15.5317 + 93.6147i) q^{72} +24.3974 q^{73} +(-59.2103 - 90.6898i) q^{74} +35.9085 q^{75} +(-20.2218 + 46.0232i) q^{76} +(-95.2952 - 145.959i) q^{78} -117.128i q^{79} +(67.5582 - 62.0364i) q^{80} -47.0539 q^{81} +(-12.7209 + 8.30535i) q^{82} -79.2706 q^{83} +184.988i q^{85} +(34.9133 - 22.7945i) q^{86} -15.0359i q^{87} +(-1.83399 - 11.0541i) q^{88} -2.66078 q^{89} +(-74.3473 - 113.874i) q^{90} +(-58.1880 - 25.5669i) q^{92} -103.547i q^{93} +(-23.6589 - 36.2373i) q^{94} -72.0433i q^{95} +(-141.631 - 36.1005i) q^{96} +52.0930 q^{97} -16.6142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * q^8 + 48 * q^9	\( 8 q + q^{2} + 8 q^{3} + 5 q^{4} + 22 q^{6} + 13 q^{8} + 48 q^{9} - 16 q^{10} - 32 q^{11} - 30 q^{12} - 71 q^{16} + 80 q^{17} - 29 q^{18} - 56 q^{19} + 108 q^{20} + 66 q^{22} - 22 q^{24} - 16 q^{25} - 24 q^{26} + 32 q^{27} + 96 q^{30} - 19 q^{32} - 32 q^{33} - 74 q^{34} - 33 q^{36} + 14 q^{38} - 84 q^{40} - 128 q^{41} + 50 q^{44} - 152 q^{46} - 134 q^{48} + 33 q^{50} - 368 q^{51} - 132 q^{52} + 228 q^{54} + 56 q^{57} + 24 q^{58} - 104 q^{59} + 192 q^{60} - 120 q^{62} - 55 q^{64} - 72 q^{65} + 276 q^{66} + 304 q^{67} + 190 q^{68} - 209 q^{72} + 112 q^{73} + 8 q^{74} - 72 q^{75} - 70 q^{76} - 304 q^{78} - 124 q^{80} + 48 q^{81} - 450 q^{82} - 72 q^{83} + 210 q^{86} - 486 q^{88} + 512 q^{89} + 184 q^{90} - 472 q^{92} - 472 q^{94} - 558 q^{96} - 64 q^{97} + 256 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 5 * q^4 + 22 * q^6 + 13 * 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 + 108 * q^20 + 66 * q^22 - 22 * q^24 - 16 * q^25 - 24 * q^26 + 32 * q^27 + 96 * q^30 - 19 * q^32 - 32 * q^33 - 74 * q^34 - 33 * q^36 + 14 * q^38 - 84 * q^40 - 128 * q^41 + 50 * q^44 - 152 * q^46 - 134 * q^48 + 33 * q^50 - 368 * q^51 - 132 * q^52 + 228 * q^54 + 56 * q^57 + 24 * q^58 - 104 * q^59 + 192 * q^60 - 120 * q^62 - 55 * 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 - 70 * q^76 - 304 * q^78 - 124 * q^80 + 48 * q^81 - 450 * q^82 - 72 * q^83 + 210 * q^86 - 486 * q^88 + 512 * q^89 + 184 * q^90 - 472 * q^92 - 472 * q^94 - 558 * q^96 - 64 * q^97 + 256 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more