LMFDB - Embedded newform 126.3.n.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,3,Mod(19,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("126.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	126.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43325133094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	126.19
Dual form			126.3.n.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.24264 - 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.24264 - 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} -2.82843 q^{8} +(-6.00000 + 3.46410i) q^{10} +(-8.48528 - 14.6969i) q^{11} +1.73205i q^{13} +(-4.94975 - 8.57321i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(25.5000 + 14.7224i) q^{19} +9.79796i q^{20} -24.0000 q^{22} +(-4.24264 + 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.12132 + 1.22474i) q^{26} -14.0000 q^{28} +33.9411 q^{29} +(-10.5000 + 6.06218i) q^{31} +(2.82843 + 4.89898i) q^{32} -6.92820i q^{34} +(-29.6985 + 17.1464i) q^{35} +(23.5000 - 40.7032i) q^{37} +(36.0624 - 20.8207i) q^{38} +(12.0000 + 6.92820i) q^{40} +68.5857i q^{41} +31.0000 q^{43} +(-16.9706 + 29.3939i) q^{44} +(6.00000 + 10.3923i) q^{46} +(72.1249 + 41.6413i) q^{47} +(-24.5000 - 42.4352i) q^{49} -1.41421 q^{50} +(3.00000 - 1.73205i) q^{52} +(-38.1838 - 66.1362i) q^{53} +83.1384i q^{55} +(-9.89949 + 17.1464i) q^{56} +(24.0000 - 41.5692i) q^{58} +(72.1249 - 41.6413i) q^{59} +(-72.0000 - 41.5692i) q^{61} +17.1464i q^{62} +8.00000 q^{64} +(4.24264 - 7.34847i) q^{65} +(15.5000 + 26.8468i) q^{67} +(-8.48528 - 4.89898i) q^{68} +48.4974i q^{70} -59.3970 q^{71} +(-70.5000 + 40.7032i) q^{73} +(-33.2340 - 57.5630i) q^{74} -58.8897i q^{76} -118.794 q^{77} +(-20.5000 + 35.5070i) q^{79} +(16.9706 - 9.79796i) q^{80} +(84.0000 + 48.4974i) q^{82} -4.89898i q^{83} -24.0000 q^{85} +(21.9203 - 37.9671i) q^{86} +(24.0000 + 41.5692i) q^{88} +(-50.9117 - 29.3939i) q^{89} +(10.5000 + 6.06218i) q^{91} +16.9706 q^{92} +(102.000 - 58.8897i) q^{94} +(-72.1249 - 124.924i) q^{95} -41.5692i q^{97} -69.2965 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 14 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 + 14 * q^7	$ 4 q - 4 q^{4} + 14 q^{7} - 24 q^{10} - 8 q^{16} + 102 q^{19} - 96 q^{22} - 2 q^{25} - 56 q^{28} - 42 q^{31} + 94 q^{37} + 48 q^{40} + 124 q^{43} + 24 q^{46} - 98 q^{49} + 12 q^{52} + 96 q^{58} - 288 q^{61} + 32 q^{64} + 62 q^{67} - 282 q^{73} - 82 q^{79} + 336 q^{82} - 96 q^{85} + 96 q^{88} + 42 q^{91} + 408 q^{94}+O(q^{100}) $ 4 * q - 4 * q^4 + 14 * q^7 - 24 * q^10 - 8 * q^16 + 102 * q^19 - 96 * q^22 - 2 * q^25 - 56 * q^28 - 42 * q^31 + 94 * q^37 + 48 * q^40 + 124 * q^43 + 24 * q^46 - 98 * q^49 + 12 * q^52 + 96 * q^58 - 288 * q^61 + 32 * q^64 + 62 * q^67 - 282 * q^73 - 82 * q^79 + 336 * q^82 - 96 * q^85 + 96 * q^88 + 42 * q^91 + 408 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	−4.24264	−	2.44949i	−0.848528	−	0.489898i	0.0116258	−	0.999932i	$-0.496299\pi$
$5$	−4.24264	−	2.44949i	−0.848528	−	0.489898i	−0.860154	+	0.510034i	$0.829633\pi$
$6$		0			0
$7$	3.50000	−	6.06218i	0.500000	−	0.866025i
$7$	3.50000	−	6.06218i	0.500000	−	0.866025i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−6.00000	+	3.46410i	−0.600000	+	0.346410i
$11$	−8.48528	−	14.6969i	−0.771389	−	1.33609i	−0.936802	−	0.349861i	$-0.886229\pi$
$11$	−8.48528	−	14.6969i	−0.771389	−	1.33609i	0.165412	−	0.986224i	$-0.447104\pi$
$12$		0			0
$13$			1.73205i			0.133235i	0.997779	+	0.0666173i	$0.0212207\pi$
$13$			1.73205i			0.133235i	−0.997779	+	0.0666173i	$0.978779\pi$
$14$	−4.94975	−	8.57321i	−0.353553	−	0.612372i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	4.24264	−	2.44949i	0.249567	−	0.144088i	−0.369999	−	0.929032i	$-0.620642\pi$
$17$	4.24264	−	2.44949i	0.249567	−	0.144088i	0.619566	+	0.784945i	$0.287309\pi$
$18$		0			0
$19$	25.5000	+	14.7224i	1.34211	+	0.774865i	0.987116	−	0.160006i	$-0.0511512\pi$
$19$	25.5000	+	14.7224i	1.34211	+	0.774865i	0.354989	+	0.934870i	$0.384485\pi$
$20$			9.79796i			0.489898i
$21$		0			0
$22$	−24.0000			−1.09091
$23$	−4.24264	+	7.34847i	−0.184463	+	0.319499i	−0.943395	−	0.331670i	$-0.892388\pi$
$23$	−4.24264	+	7.34847i	−0.184463	+	0.319499i	0.758933	+	0.651169i	$0.225721\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$26$	2.12132	+	1.22474i	0.0815892	+	0.0471056i
$27$		0			0
$28$	−14.0000			−0.500000
$29$	33.9411			1.17038			0.585192	−	0.810895i	$-0.301019\pi$
$29$	33.9411			1.17038			0.585192	+	0.810895i	$0.301019\pi$
$30$		0			0
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	−0.659701	−	0.751528i	$-0.729317\pi$
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	0.320992	+	0.947082i	$0.395984\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$		−	6.92820i		−	0.203771i
$35$	−29.6985	+	17.1464i	−0.848528	+	0.489898i
$36$		0			0
$37$	23.5000	−	40.7032i	0.635135	−	1.10009i	−0.351351	−	0.936244i	$-0.614278\pi$
$37$	23.5000	−	40.7032i	0.635135	−	1.10009i	0.986486	−	0.163843i	$-0.0523889\pi$
$38$	36.0624	−	20.8207i	0.949012	−	0.547912i
$39$		0			0
$40$	12.0000	+	6.92820i	0.300000	+	0.173205i
$41$			68.5857i			1.67282i	0.548103	+	0.836411i	$0.315350\pi$
$41$			68.5857i			1.67282i	−0.548103	+	0.836411i	$0.684650\pi$
$42$		0			0
$43$	31.0000			0.720930			0.360465	−	0.932773i	$-0.382618\pi$
$43$	31.0000			0.720930			0.360465	+	0.932773i	$0.382618\pi$
$44$	−16.9706	+	29.3939i	−0.385695	+	0.668043i
$45$		0			0
$46$	6.00000	+	10.3923i	0.130435	+	0.225920i
$47$	72.1249	+	41.6413i	1.53457	+	0.885986i	0.999142	+	0.0414059i	$0.0131837\pi$
$47$	72.1249	+	41.6413i	1.53457	+	0.885986i	0.535430	+	0.844580i	$0.320150\pi$
$48$		0			0
$49$	−24.5000	−	42.4352i	−0.500000	−	0.866025i
$50$	−1.41421			−0.0282843
$51$		0			0
$52$	3.00000	−	1.73205i	0.0576923	−	0.0333087i
$53$	−38.1838	−	66.1362i	−0.720448	−	1.24785i	−0.960820	−	0.277172i	$-0.910603\pi$
$53$	−38.1838	−	66.1362i	−0.720448	−	1.24785i	0.240372	−	0.970681i	$-0.422731\pi$
$54$		0			0
$55$			83.1384i			1.51161i
$56$	−9.89949	+	17.1464i	−0.176777	+	0.306186i
$57$		0			0
$58$	24.0000	−	41.5692i	0.413793	−	0.716711i
$59$	72.1249	−	41.6413i	1.22246	−	0.705785i	0.257015	−	0.966407i	$-0.417261\pi$
$59$	72.1249	−	41.6413i	1.22246	−	0.705785i	0.965441	+	0.260622i	$0.0839277\pi$
$60$		0			0
$61$	−72.0000	−	41.5692i	−1.18033	−	0.681463i	−0.224237	−	0.974535i	$-0.571989\pi$
$61$	−72.0000	−	41.5692i	−1.18033	−	0.681463i	−0.956090	+	0.293072i	$0.905322\pi$
$62$			17.1464i			0.276555i
$63$		0			0
$64$	8.00000			0.125000
$65$	4.24264	−	7.34847i	0.0652714	−	0.113053i
$66$		0			0
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	0.958204	−	0.286087i	$-0.0923546\pi$
$67$	15.5000	+	26.8468i	0.231343	+	0.400698i	−0.726860	+	0.686785i	$0.759021\pi$
$68$	−8.48528	−	4.89898i	−0.124784	−	0.0720438i
$69$		0			0
$70$			48.4974i			0.692820i
$71$	−59.3970			−0.836577			−0.418289	−	0.908314i	$-0.637370\pi$
$71$	−59.3970			−0.836577			−0.418289	+	0.908314i	$0.637370\pi$
$72$		0			0
$73$	−70.5000	+	40.7032i	−0.965753	+	0.557578i	−0.897939	−	0.440120i	$-0.854936\pi$
$73$	−70.5000	+	40.7032i	−0.965753	+	0.557578i	−0.0678144	+	0.997698i	$0.521603\pi$
$74$	−33.2340	−	57.5630i	−0.449108	−	0.777878i
$75$		0			0
$76$		−	58.8897i		−	0.774865i
$77$	−118.794			−1.54278
$78$		0			0
$79$	−20.5000	+	35.5070i	−0.259494	+	0.449456i	−0.966106	−	0.258144i	$-0.916889\pi$
$79$	−20.5000	+	35.5070i	−0.259494	+	0.449456i	0.706613	+	0.707601i	$0.250222\pi$
$80$	16.9706	−	9.79796i	0.212132	−	0.122474i
$81$		0			0
$82$	84.0000	+	48.4974i	1.02439	+	0.591432i
$83$		−	4.89898i		−	0.0590238i	−0.999564	−	0.0295119i	$-0.990605\pi$
$83$		−	4.89898i		−	0.0590238i	0.999564	−	0.0295119i	$-0.00939530\pi$
$84$		0			0
$85$	−24.0000			−0.282353
$86$	21.9203	−	37.9671i	0.254887	−	0.441478i
$87$		0			0
$88$	24.0000	+	41.5692i	0.272727	+	0.472377i
$89$	−50.9117	−	29.3939i	−0.572041	−	0.330268i	0.185923	−	0.982564i	$-0.440473\pi$
$89$	−50.9117	−	29.3939i	−0.572041	−	0.330268i	−0.757964	+	0.652296i	$0.773806\pi$
$90$		0			0
$91$	10.5000	+	6.06218i	0.115385	+	0.0666173i
$92$	16.9706			0.184463
$93$		0			0
$94$	102.000	−	58.8897i	1.08511	−	0.626486i
$95$	−72.1249	−	124.924i	−0.759209	−	1.31499i
$96$		0			0
$97$		−	41.5692i		−	0.428549i	−0.976774	−	0.214274i	$-0.931261\pi$
$97$		−	41.5692i		−	0.428549i	0.976774	−	0.214274i	$-0.0687387\pi$
$98$	−69.2965			−0.707107
$99$		0			0
$100$	−1.00000	+	1.73205i	−0.0100000	+	0.0173205i
$101$	152.735	−	88.1816i	1.51223	−	0.873085i	0.512331	−	0.858788i	$-0.328782\pi$
$101$	152.735	−	88.1816i	1.51223	−	0.873085i	0.999898	−	0.0142971i	$-0.00455107\pi$
$102$		0			0
$103$	−25.5000	−	14.7224i	−0.247573	−	0.142936i	0.371080	−	0.928601i	$-0.378988\pi$
$103$	−25.5000	−	14.7224i	−0.247573	−	0.142936i	−0.618652	+	0.785665i	$0.712321\pi$
$104$		−	4.89898i		−	0.0471056i
$105$		0			0
$106$	−108.000			−1.01887
$107$	−72.1249	+	124.924i	−0.674064	+	1.16751i	0.302677	+	0.953093i	$0.402120\pi$
$107$	−72.1249	+	124.924i	−0.674064	+	1.16751i	−0.976741	+	0.214421i	$0.931214\pi$
$108$		0			0
$109$	−84.5000	−	146.358i	−0.775229	−	1.34274i	−0.934665	−	0.355528i	$-0.884301\pi$
$109$	−84.5000	−	146.358i	−0.775229	−	1.34274i	0.159436	−	0.987208i	$-0.449032\pi$
$110$	101.823	+	58.7878i	0.925667	+	0.534434i
$111$		0			0
$112$	14.0000	+	24.2487i	0.125000	+	0.216506i
$113$	59.3970			0.525637			0.262818	−	0.964845i	$-0.415348\pi$
$113$	59.3970			0.525637			0.262818	+	0.964845i	$0.415348\pi$
$114$		0			0
$115$	36.0000	−	20.7846i	0.313043	−	0.180736i
$116$	−33.9411	−	58.7878i	−0.292596	−	0.506791i
$117$		0			0
$118$		−	117.779i		−	0.998131i
$119$		−	34.2929i		−	0.288175i
$120$		0			0
$121$	−83.5000	+	144.626i	−0.690083	+	1.19526i
$122$	−101.823	+	58.7878i	−0.834618	+	0.481867i
$123$		0			0
$124$	21.0000	+	12.1244i	0.169355	+	0.0977771i
$125$			127.373i			1.01899i
$126$		0			0
$127$	209.000			1.64567			0.822835	−	0.568281i	$-0.192391\pi$
$127$	209.000			1.64567			0.822835	+	0.568281i	$0.192391\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.00000	−	10.3923i	−0.0461538	−	0.0799408i
$131$	50.9117	+	29.3939i	0.388639	+	0.224381i	0.681570	−	0.731753i	$-0.261297\pi$
$131$	50.9117	+	29.3939i	0.388639	+	0.224381i	−0.292931	+	0.956133i	$0.594631\pi$
$132$		0			0
$133$	178.500	−	103.057i	1.34211	−	0.774865i
$134$	43.8406			0.327169
$135$		0			0
$136$	−12.0000	+	6.92820i	−0.0882353	+	0.0509427i
$137$	76.3675	+	132.272i	0.557427	+	0.965492i	0.997710	+	0.0676333i	$0.0215448\pi$
$137$	76.3675	+	132.272i	0.557427	+	0.965492i	−0.440283	+	0.897859i	$0.645122\pi$
$138$		0			0
$139$			195.722i			1.40807i	0.710165	+	0.704035i	$0.248620\pi$
$139$			195.722i			1.40807i	−0.710165	+	0.704035i	$0.751380\pi$
$140$	59.3970	+	34.2929i	0.424264	+	0.244949i
$141$		0			0
$142$	−42.0000	+	72.7461i	−0.295775	+	0.512297i
$143$	25.4558	−	14.6969i	0.178013	−	0.102776i
$144$		0			0
$145$	−144.000	−	83.1384i	−0.993103	−	0.573369i
$146$			115.126i			0.788534i
$147$		0			0
$148$	−94.0000			−0.635135
$149$	25.4558	−	44.0908i	0.170845	−	0.295912i	−0.767871	−	0.640605i	$-0.778684\pi$
$149$	25.4558	−	44.0908i	0.170845	−	0.295912i	0.938715	+	0.344693i	$0.112017\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.0331126	−	0.0573527i	0.848994	−	0.528402i	$-0.177209\pi$
$151$	−5.00000	−	8.66025i	−0.0331126	−	0.0573527i	−0.882107	+	0.471049i	$0.843875\pi$
$152$	−72.1249	−	41.6413i	−0.474506	−	0.273956i
$153$		0			0
$154$	−84.0000	+	145.492i	−0.545455	+	0.944755i
$155$	59.3970			0.383206
$156$		0			0
$157$	36.0000	−	20.7846i	0.229299	−	0.132386i	−0.380949	−	0.924596i	$-0.624403\pi$
$157$	36.0000	−	20.7846i	0.229299	−	0.132386i	0.610249	+	0.792210i	$0.291069\pi$
$158$	28.9914	+	50.2145i	0.183490	+	0.317814i
$159$		0			0
$160$		−	27.7128i		−	0.173205i
$161$	29.6985	+	51.4393i	0.184463	+	0.319499i
$162$		0			0
$163$	−43.0000	+	74.4782i	−0.263804	+	0.456921i	−0.967250	−	0.253828i	$-0.918310\pi$
$163$	−43.0000	+	74.4782i	−0.263804	+	0.456921i	0.703446	+	0.710749i	$0.251644\pi$
$164$	118.794	−	68.5857i	0.724353	−	0.418206i
$165$		0			0
$166$	−6.00000	−	3.46410i	−0.0361446	−	0.0208681i
$167$			181.262i			1.08540i	0.839926	+	0.542701i	$0.182598\pi$
$167$			181.262i			1.08540i	−0.839926	+	0.542701i	$0.817402\pi$
$168$		0			0
$169$	166.000			0.982249
$170$	−16.9706	+	29.3939i	−0.0998268	+	0.172905i
$171$		0			0
$172$	−31.0000	−	53.6936i	−0.180233	−	0.312172i
$173$	38.1838	+	22.0454i	0.220715	+	0.127430i	0.606281	−	0.795250i	$-0.292660\pi$
$173$	38.1838	+	22.0454i	0.220715	+	0.127430i	−0.385566	+	0.922680i	$0.625994\pi$
$174$		0			0
$175$	−7.00000			−0.0400000
$176$	67.8823			0.385695
$177$		0			0
$178$	−72.0000	+	41.5692i	−0.404494	+	0.233535i
$179$	−4.24264	−	7.34847i	−0.0237019	−	0.0410529i	0.853931	−	0.520386i	$-0.174212\pi$
$179$	−4.24264	−	7.34847i	−0.0237019	−	0.0410529i	−0.877633	+	0.479333i	$0.840879\pi$
$180$		0			0
$181$		−	43.3013i		−	0.239234i	−0.992820	−	0.119617i	$-0.961833\pi$
$181$		−	43.3013i		−	0.239234i	0.992820	−	0.119617i	$-0.0381666\pi$
$182$	14.8492	−	8.57321i	0.0815892	−	0.0471056i
$183$		0			0
$184$	12.0000	−	20.7846i	0.0652174	−	0.112960i
$185$	−199.404	+	115.126i	−1.07786	+	0.622303i
$186$		0			0
$187$	−72.0000	−	41.5692i	−0.385027	−	0.222295i
$188$		−	166.565i		−	0.885986i
$189$		0			0
$190$	−204.000			−1.07368
$191$	38.1838	−	66.1362i	0.199915	−	0.346263i	−0.748586	−	0.663038i	$-0.769267\pi$
$191$	38.1838	−	66.1362i	0.199915	−	0.346263i	0.948501	+	0.316775i	$0.102600\pi$
$192$		0			0
$193$	143.500	+	248.549i	0.743523	+	1.28782i	0.950882	+	0.309555i	$0.100180\pi$
$193$	143.500	+	248.549i	0.743523	+	1.28782i	−0.207358	+	0.978265i	$0.566487\pi$
$194$	−50.9117	−	29.3939i	−0.262431	−	0.151515i
$195$		0			0
$196$	−49.0000	+	84.8705i	−0.250000	+	0.433013i
$197$	−127.279			−0.646087			−0.323044	−	0.946384i	$-0.604706\pi$
$197$	−127.279			−0.646087			−0.323044	+	0.946384i	$0.604706\pi$
$198$		0			0
$199$	180.000	−	103.923i	0.904523	−	0.522226i	0.0258579	−	0.999666i	$-0.491768\pi$
$199$	180.000	−	103.923i	0.904523	−	0.522226i	0.878665	+	0.477439i	$0.158435\pi$
$200$	1.41421	+	2.44949i	0.00707107	+	0.0122474i
$201$		0			0
$202$		−	249.415i		−	1.23473i
$203$	118.794	−	205.757i	0.585192	−	1.01358i
$204$		0			0
$205$	168.000	−	290.985i	0.819512	−	1.41944i
$206$	−36.0624	+	20.8207i	−0.175060	+	0.101071i
$207$		0			0
$208$	−6.00000	−	3.46410i	−0.0288462	−	0.0166543i
$209$		−	499.696i		−	2.39089i
$210$		0			0
$211$	82.0000			0.388626			0.194313	−	0.980940i	$-0.437752\pi$
$211$	82.0000			0.388626			0.194313	+	0.980940i	$0.437752\pi$
$212$	−76.3675	+	132.272i	−0.360224	+	0.623927i
$213$		0			0
$214$	102.000	+	176.669i	0.476636	+	0.825557i
$215$	−131.522	−	75.9342i	−0.611730	−	0.353182i
$216$		0			0
$217$			84.8705i			0.391108i
$218$	−239.002			−1.09634
$219$		0			0
$220$	144.000	−	83.1384i	0.654545	−	0.377902i
$221$	4.24264	+	7.34847i	0.0191975	+	0.0332510i
$222$		0			0
$223$			41.5692i			0.186409i	0.995647	+	0.0932045i	$0.0297110\pi$
$223$			41.5692i			0.186409i	−0.995647	+	0.0932045i	$0.970289\pi$
$224$	39.5980			0.176777
$225$		0			0
$226$	42.0000	−	72.7461i	0.185841	−	0.321886i
$227$	−330.926	+	191.060i	−1.45782	+	0.841675i	−0.998904	−	0.0468029i	$-0.985097\pi$
$227$	−330.926	+	191.060i	−1.45782	+	0.841675i	−0.458920	+	0.888478i	$0.651763\pi$
$228$		0			0
$229$	−70.5000	−	40.7032i	−0.307860	−	0.177743i	0.338108	−	0.941107i	$-0.390213\pi$
$229$	−70.5000	−	40.7032i	−0.307860	−	0.177743i	−0.645969	+	0.763364i	$0.723546\pi$
$230$		−	58.7878i		−	0.255599i
$231$		0			0
$232$	−96.0000			−0.413793
$233$	114.551	−	198.409i	0.491636	−	0.851539i	−0.508317	−	0.861170i	$-0.669732\pi$
$233$	114.551	−	198.409i	0.491636	−	0.851539i	0.999954	+	0.00963059i	$0.00306556\pi$
$234$		0			0
$235$	−204.000	−	353.338i	−0.868085	−	1.50357i
$236$	−144.250	−	83.2827i	−0.611228	−	0.352893i
$237$		0			0
$238$	−42.0000	−	24.2487i	−0.176471	−	0.101885i
$239$	67.8823			0.284026			0.142013	−	0.989865i	$-0.454642\pi$
$239$	67.8823			0.284026			0.142013	+	0.989865i	$0.454642\pi$
$240$		0			0
$241$	−396.000	+	228.631i	−1.64315	+	0.948675i	−0.663451	+	0.748220i	$0.730909\pi$
$241$	−396.000	+	228.631i	−1.64315	+	0.948675i	−0.979703	+	0.200455i	$0.935758\pi$
$242$	118.087	+	204.532i	0.487962	+	0.845175i
$243$		0			0
$244$			166.277i			0.681463i
$245$			240.050i			0.979796i
$246$		0			0
$247$	−25.5000	+	44.1673i	−0.103239	+	0.178815i
$248$	29.6985	−	17.1464i	0.119752	−	0.0691388i
$249$		0			0
$250$	156.000	+	90.0666i	0.624000	+	0.360267i
$251$		−	347.828i		−	1.38577i	−0.721050	−	0.692884i	$-0.756340\pi$
$251$		−	347.828i		−	1.38577i	0.721050	−	0.692884i	$-0.243660\pi$
$252$		0			0
$253$	144.000			0.569170
$254$	147.785	−	255.972i	0.581832	−	1.00776i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−140.007	−	80.8332i	−0.544775	−	0.314526i	0.202237	−	0.979337i	$-0.435179\pi$
$257$	−140.007	−	80.8332i	−0.544775	−	0.314526i	−0.747012	+	0.664811i	$0.768512\pi$
$258$		0			0
$259$	−164.500	−	284.922i	−0.635135	−	1.10009i
$260$	−16.9706			−0.0652714
$261$		0			0
$262$	72.0000	−	41.5692i	0.274809	−	0.158661i
$263$	127.279	+	220.454i	0.483951	+	0.838228i	0.999830	−	0.0184332i	$-0.00586781\pi$
$263$	127.279	+	220.454i	0.483951	+	0.838228i	−0.515879	+	0.856662i	$0.672534\pi$
$264$		0			0
$265$			374.123i			1.41178i
$266$		−	291.489i		−	1.09582i
$267$		0			0
$268$	31.0000	−	53.6936i	0.115672	−	0.200349i
$269$	−16.9706	+	9.79796i	−0.0630876	+	0.0364236i	−0.531212	−	0.847239i	$-0.678263\pi$
$269$	−16.9706	+	9.79796i	−0.0630876	+	0.0364236i	0.468124	+	0.883663i	$0.344930\pi$
$270$		0			0
$271$	36.0000	+	20.7846i	0.132841	+	0.0766960i	0.564948	−	0.825127i	$-0.308896\pi$
$271$	36.0000	+	20.7846i	0.132841	+	0.0766960i	−0.432107	+	0.901823i	$0.642230\pi$
$272$			19.5959i			0.0720438i
$273$		0			0
$274$	216.000			0.788321
$275$	−8.48528	+	14.6969i	−0.0308556	+	0.0534434i
$276$		0			0
$277$	168.500	+	291.851i	0.608303	+	1.05361i	0.991520	+	0.129954i	$0.0414829\pi$
$277$	168.500	+	291.851i	0.608303	+	1.05361i	−0.383217	+	0.923658i	$0.625184\pi$
$278$	239.709	+	138.396i	0.862263	+	0.497828i
$279$		0			0
$280$	84.0000	−	48.4974i	0.300000	−	0.173205i
$281$	−246.073			−0.875705			−0.437853	−	0.899047i	$-0.644261\pi$
$281$	−246.073			−0.875705			−0.437853	+	0.899047i	$0.644261\pi$
$282$		0			0
$283$	−169.500	+	97.8609i	−0.598940	+	0.345798i	−0.768624	−	0.639700i	$-0.779058\pi$
$283$	−169.500	+	97.8609i	−0.598940	+	0.345798i	0.169685	+	0.985498i	$0.445725\pi$
$284$	59.3970	+	102.879i	0.209144	+	0.362248i
$285$		0			0
$286$		−	41.5692i		−	0.145347i
$287$	415.779	+	240.050i	1.44871	+	0.836411i
$288$		0			0
$289$	−132.500	+	229.497i	−0.458478	+	0.794106i
$290$	−203.647	+	117.576i	−0.702230	+	0.405433i
$291$		0			0
$292$	141.000	+	81.4064i	0.482877	+	0.278789i
$293$			97.9796i			0.334401i	0.985923	+	0.167201i	$0.0534728\pi$
$293$			97.9796i			0.334401i	−0.985923	+	0.167201i	$0.946527\pi$
$294$		0			0
$295$	−408.000			−1.38305
$296$	−66.4680	+	115.126i	−0.224554	+	0.388939i
$297$		0			0
$298$	−36.0000	−	62.3538i	−0.120805	−	0.209241i
$299$	−12.7279	−	7.34847i	−0.0425683	−	0.0245768i
$300$		0			0
$301$	108.500	−	187.928i	0.360465	−	0.624344i
$302$	−14.1421			−0.0468283
$303$		0			0
$304$	−102.000	+	58.8897i	−0.335526	+	0.193716i
$305$	203.647	+	352.727i	0.667694	+	1.15648i
$306$		0			0
$307$			71.0141i			0.231316i	0.993289	+	0.115658i	$0.0368977\pi$
$307$			71.0141i			0.231316i	−0.993289	+	0.115658i	$0.963102\pi$
$308$	118.794	+	205.757i	0.385695	+	0.668043i
$309$		0			0
$310$	42.0000	−	72.7461i	0.135484	−	0.234665i
$311$	−186.676	+	107.778i	−0.600245	+	0.346552i	−0.769138	−	0.639083i	$-0.779314\pi$
$311$	−186.676	+	107.778i	−0.600245	+	0.346552i	0.168893	+	0.985634i	$0.445981\pi$
$312$		0			0
$313$	253.500	+	146.358i	0.809904	+	0.467598i	0.846923	−	0.531716i	$-0.178453\pi$
$313$	253.500	+	146.358i	0.809904	+	0.467598i	−0.0370184	+	0.999315i	$0.511786\pi$
$314$		−	58.7878i		−	0.187222i
$315$		0			0
$316$	82.0000			0.259494
$317$	−118.794	+	205.757i	−0.374744	+	0.649076i	−0.990289	−	0.139026i	$-0.955603\pi$
$317$	−118.794	+	205.757i	−0.374744	+	0.649076i	0.615544	+	0.788102i	$0.288936\pi$
$318$		0			0
$319$	−288.000	−	498.831i	−0.902821	−	1.56373i
$320$	−33.9411	−	19.5959i	−0.106066	−	0.0612372i
$321$		0			0
$322$	84.0000			0.260870
$323$	144.250			0.446594
$324$		0			0
$325$	1.50000	−	0.866025i	0.00461538	−	0.00266469i
$326$	60.8112	+	105.328i	0.186537	+	0.323092i
$327$		0			0
$328$		−	193.990i		−	0.591432i
$329$	504.874	−	291.489i	1.53457	−	0.885986i
$330$		0			0
$331$	92.5000	−	160.215i	0.279456	−	0.484032i	−0.691794	−	0.722095i	$-0.743179\pi$
$331$	92.5000	−	160.215i	0.279456	−	0.484032i	0.971250	+	0.238063i	$0.0765125\pi$
$332$	−8.48528	+	4.89898i	−0.0255581	+	0.0147560i
$333$		0			0
$334$	222.000	+	128.172i	0.664671	+	0.383748i
$335$		−	151.868i		−	0.453338i
$336$		0			0
$337$	−359.000			−1.06528			−0.532641	−	0.846341i	$-0.678800\pi$
$337$	−359.000			−1.06528			−0.532641	+	0.846341i	$0.678800\pi$
$338$	117.380	−	203.308i	0.347277	−	0.601502i
$339$		0			0
$340$	24.0000	+	41.5692i	0.0705882	+	0.122262i
$341$	178.191	+	102.879i	0.522554	+	0.301697i
$342$		0			0
$343$	−343.000			−1.00000
$344$	−87.6812			−0.254887
$345$		0			0
$346$	54.0000	−	31.1769i	0.156069	−	0.0901067i
$347$	233.345	+	404.166i	0.672465	+	1.16474i	0.977203	+	0.212307i	$0.0680976\pi$
$347$	233.345	+	404.166i	0.672465	+	1.16474i	−0.304738	+	0.952436i	$0.598569\pi$
$348$		0			0
$349$		−	581.969i		−	1.66753i	−0.552117	−	0.833767i	$-0.686180\pi$
$349$		−	581.969i		−	1.66753i	0.552117	−	0.833767i	$-0.313820\pi$
$350$	−4.94975	+	8.57321i	−0.0141421	+	0.0244949i
$351$		0			0
$352$	48.0000	−	83.1384i	0.136364	−	0.236189i
$353$	−250.316	+	144.520i	−0.709110	+	0.409405i	−0.810731	−	0.585418i	$-0.800930\pi$
$353$	−250.316	+	144.520i	−0.709110	+	0.409405i	0.101621	+	0.994823i	$0.467597\pi$
$354$		0			0
$355$	252.000	+	145.492i	0.709859	+	0.409837i
$356$			117.576i			0.330268i
$357$		0			0
$358$	−12.0000			−0.0335196
$359$	169.706	−	293.939i	0.472718	−	0.818771i	−0.526795	−	0.849992i	$-0.676606\pi$
$359$	169.706	−	293.939i	0.472718	−	0.818771i	0.999512	+	0.0312215i	$0.00993973\pi$
$360$		0			0
$361$	253.000	+	438.209i	0.700831	+	1.21387i
$362$	−53.0330	−	30.6186i	−0.146500	−	0.0845818i
$363$		0			0
$364$		−	24.2487i		−	0.0666173i
$365$	398.808			1.09263
$366$		0			0
$367$	133.500	−	77.0763i	0.363760	−	0.210017i	−0.306969	−	0.951720i	$-0.599315\pi$
$367$	133.500	−	77.0763i	0.363760	−	0.210017i	0.670729	+	0.741703i	$0.265981\pi$
$368$	−16.9706	−	29.3939i	−0.0461157	−	0.0798747i
$369$		0			0
$370$			325.626i			0.880069i
$371$	−534.573			−1.44090
$372$		0			0
$373$	144.500	−	250.281i	0.387399	−	0.670996i	−0.604699	−	0.796454i	$-0.706707\pi$
$373$	144.500	−	250.281i	0.387399	−	0.670996i	0.992099	+	0.125458i	$0.0400401\pi$
$374$	−101.823	+	58.7878i	−0.272255	+	0.157187i
$375$		0			0
$376$	−204.000	−	117.779i	−0.542553	−	0.313243i
$377$			58.7878i			0.155936i
$378$		0			0
$379$	7.00000			0.0184697			0.00923483	−	0.999957i	$-0.497060\pi$
$379$	7.00000			0.0184697			0.00923483	+	0.999957i	$0.497060\pi$
$380$	−144.250	+	249.848i	−0.379605	+	0.657495i
$381$		0			0
$382$	−54.0000	−	93.5307i	−0.141361	−	0.244845i
$383$	−428.507	−	247.398i	−1.11882	−	0.645949i	−0.177718	−	0.984081i	$-0.556871\pi$
$383$	−428.507	−	247.398i	−1.11882	−	0.645949i	−0.941099	+	0.338132i	$0.890205\pi$
$384$		0			0
$385$	504.000	+	290.985i	1.30909	+	0.755804i
$386$	405.879			1.05150
$387$		0			0
$388$	−72.0000	+	41.5692i	−0.185567	+	0.107137i
$389$	−114.551	−	198.409i	−0.294476	−	0.510048i	0.680387	−	0.732853i	$-0.261812\pi$
$389$	−114.551	−	198.409i	−0.294476	−	0.510048i	−0.974863	+	0.222805i	$0.928479\pi$
$390$		0			0
$391$			41.5692i			0.106315i
$392$	69.2965	+	120.025i	0.176777	+	0.306186i
$393$		0			0
$394$	−90.0000	+	155.885i	−0.228426	+	0.395646i
$395$	173.948	−	100.429i	0.440375	−	0.254251i
$396$		0			0
$397$	70.5000	+	40.7032i	0.177582	+	0.102527i	0.586156	−	0.810198i	$-0.300641\pi$
$397$	70.5000	+	40.7032i	0.177582	+	0.102527i	−0.408574	+	0.912725i	$0.633974\pi$
$398$		−	293.939i		−	0.738540i
$399$		0			0
$400$	4.00000			0.0100000
$401$	−46.6690	+	80.8332i	−0.116382	+	0.201579i	−0.918331	−	0.395813i	$-0.870463\pi$
$401$	−46.6690	+	80.8332i	−0.116382	+	0.201579i	0.801950	+	0.597392i	$0.203796\pi$
$402$		0			0
$403$	−10.5000	−	18.1865i	−0.0260546	−	0.0451279i
$404$	−305.470	−	176.363i	−0.756114	−	0.436543i
$405$		0			0
$406$	−168.000	−	290.985i	−0.413793	−	0.716711i
$407$	−797.616			−1.95975
$408$		0			0
$409$	−361.500	+	208.712i	−0.883863	+	0.510299i	−0.871930	−	0.489630i	$-0.837132\pi$
$409$	−361.500	+	208.712i	−0.883863	+	0.510299i	−0.0119329	+	0.999929i	$0.503798\pi$
$410$	−237.588	−	411.514i	−0.579483	−	1.00369i
$411$		0			0
$412$			58.8897i			0.142936i
$413$		−	582.979i		−	1.41157i
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.0289157	+	0.0500834i
$416$	−8.48528	+	4.89898i	−0.0203973	+	0.0117764i
$417$		0			0
$418$	−612.000	−	353.338i	−1.46411	−	0.845307i
$419$			19.5959i			0.0467683i	0.999727	+	0.0233842i	$0.00744408\pi$
$419$			19.5959i			0.0467683i	−0.999727	+	0.0233842i	$0.992556\pi$
$420$		0			0
$421$	407.000			0.966746			0.483373	−	0.875415i	$-0.339412\pi$
$421$	407.000			0.966746			0.483373	+	0.875415i	$0.339412\pi$
$422$	57.9828	−	100.429i	0.137400	−	0.237984i
$423$		0			0
$424$	108.000	+	187.061i	0.254717	+	0.441183i
$425$	−4.24264	−	2.44949i	−0.00998268	−	0.00576351i
$426$		0			0
$427$	−504.000	+	290.985i	−1.18033	+	0.681463i
$428$	288.500			0.674064
$429$		0			0
$430$	−186.000	+	107.387i	−0.432558	+	0.249738i
$431$	−80.6102	−	139.621i	−0.187031	−	0.323946i	0.757228	−	0.653150i	$-0.226553\pi$
$431$	−80.6102	−	139.621i	−0.187031	−	0.323946i	−0.944259	+	0.329204i	$0.893220\pi$
$432$		0			0
$433$			168.009i			0.388011i	0.981000	+	0.194006i	$0.0621480\pi$
$433$			168.009i			0.388011i	−0.981000	+	0.194006i	$0.937852\pi$
$434$	103.945	+	60.0125i	0.239504	+	0.138278i
$435$		0			0
$436$	−169.000	+	292.717i	−0.387615	+	0.671368i
$437$	−216.375	+	124.924i	−0.495137	+	0.285867i
$438$		0			0
$439$	−468.000	−	270.200i	−1.06606	−	0.615490i	−0.138957	−	0.990298i	$-0.544375\pi$
$439$	−468.000	−	270.200i	−1.06606	−	0.615490i	−0.927102	+	0.374809i	$0.877708\pi$
$440$		−	235.151i		−	0.534434i
$441$		0			0
$442$	12.0000			0.0271493
$443$	63.6396	−	110.227i	0.143656	−	0.248819i	−0.785215	−	0.619224i	$-0.787447\pi$
$443$	63.6396	−	110.227i	0.143656	−	0.248819i	0.928871	+	0.370404i	$0.120781\pi$
$444$		0			0
$445$	144.000	+	249.415i	0.323596	+	0.560484i
$446$	50.9117	+	29.3939i	0.114152	+	0.0659056i
$447$		0			0
$448$	28.0000	−	48.4974i	0.0625000	−	0.108253i
$449$	−110.309			−0.245676			−0.122838	−	0.992427i	$-0.539200\pi$
$449$	−110.309			−0.245676			−0.122838	+	0.992427i	$0.539200\pi$
$450$		0			0
$451$	1008.00	−	581.969i	2.23503	−	1.29040i
$452$	−59.3970	−	102.879i	−0.131409	−	0.227607i
$453$		0			0
$454$			540.400i			1.19031i
$455$	−29.6985	−	51.4393i	−0.0652714	−	0.113053i
$456$		0			0
$457$	−12.5000	+	21.6506i	−0.0273523	+	0.0473756i	−0.879378	−	0.476125i	$-0.842041\pi$
$457$	−12.5000	+	21.6506i	−0.0273523	+	0.0473756i	0.852025	+	0.523501i	$0.175374\pi$
$458$	−99.7021	+	57.5630i	−0.217690	+	0.125683i
$459$		0			0
$460$	−72.0000	−	41.5692i	−0.156522	−	0.0903679i
$461$		−	78.3837i		−	0.170030i	−0.996380	−	0.0850148i	$-0.972906\pi$
$461$		−	78.3837i		−	0.170030i	0.996380	−	0.0850148i	$-0.0270938\pi$
$462$		0			0
$463$	521.000			1.12527			0.562635	−	0.826705i	$-0.309788\pi$
$463$	521.000			1.12527			0.562635	+	0.826705i	$0.309788\pi$
$464$	−67.8823	+	117.576i	−0.146298	+	0.253395i
$465$		0			0
$466$	−162.000	−	280.592i	−0.347639	−	0.602129i
$467$	190.919	+	110.227i	0.408820	+	0.236032i	0.690283	−	0.723540i	$-0.257486\pi$
$467$	190.919	+	110.227i	0.408820	+	0.236032i	−0.281463	+	0.959572i	$0.590820\pi$
$468$		0			0
$469$	217.000			0.462687
$470$	−576.999			−1.22766
$471$		0			0
$472$	−204.000	+	117.779i	−0.432203	+	0.249533i
$473$	−263.044	−	455.605i	−0.556118	−	0.963224i
$474$		0			0
$475$		−	29.4449i		−	0.0619892i
$476$	−59.3970	+	34.2929i	−0.124784	+	0.0720438i
$477$		0			0
$478$	48.0000	−	83.1384i	0.100418	−	0.173930i
$479$	759.433	−	438.459i	1.58545	−	0.915363i	0.591412	−	0.806370i	$-0.298571\pi$
$479$	759.433	−	438.459i	1.58545	−	0.915363i	0.994043	−	0.108993i	$-0.0347626\pi$
$480$		0			0
$481$	70.5000	+	40.7032i	0.146570	+	0.0846220i
$482$			646.665i			1.34163i
$483$		0			0
$484$	334.000			0.690083
$485$	−101.823	+	176.363i	−0.209945	+	0.363636i
$486$		0			0
$487$	−63.5000	−	109.985i	−0.130390	−	0.225842i	0.793437	−	0.608653i	$-0.208290\pi$
$487$	−63.5000	−	109.985i	−0.130390	−	0.225842i	−0.923827	+	0.382810i	$0.874956\pi$
$488$	203.647	+	117.576i	0.417309	+	0.240933i
$489$		0			0
$490$	294.000	+	169.741i	0.600000	+	0.346410i
$491$	627.911			1.27884			0.639420	−	0.768857i	$-0.279174\pi$
$491$	627.911			1.27884			0.639420	+	0.768857i	$0.279174\pi$
$492$		0			0
$493$	144.000	−	83.1384i	0.292089	−	0.168638i
$494$	36.0624	+	62.4620i	0.0730009	+	0.126441i
$495$		0			0
$496$		−	48.4974i		−	0.0977771i
$497$	−207.889	+	360.075i	−0.418289	+	0.724497i
$498$		0			0
$499$	116.500	−	201.784i	0.233467	−	0.404377i	−0.725359	−	0.688371i	$-0.758326\pi$
$499$	116.500	−	201.784i	0.233467	−	0.404377i	0.958826	+	0.283994i	$0.0916596\pi$
$500$	220.617	−	127.373i	0.441235	−	0.254747i
$501$		0			0
$502$	−426.000	−	245.951i	−0.848606	−	0.489943i
$503$			538.888i			1.07135i	0.844425	+	0.535674i	$0.179942\pi$
$503$			538.888i			1.07135i	−0.844425	+	0.535674i	$0.820058\pi$
$504$		0			0
$505$	−864.000			−1.71089
$506$	101.823	−	176.363i	0.201232	−	0.348544i
$507$		0			0
$508$	−209.000	−	361.999i	−0.411417	−	0.712596i
$509$	−275.772	−	159.217i	−0.541791	−	0.312803i	0.204013	−	0.978968i	$-0.434601\pi$
$509$	−275.772	−	159.217i	−0.541791	−	0.312803i	−0.745805	+	0.666165i	$0.767935\pi$
$510$		0			0
$511$			569.845i			1.11516i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	−198.000	+	114.315i	−0.385214	+	0.222403i
$515$	72.1249	+	124.924i	0.140048	+	0.242571i
$516$		0			0
$517$		−	1413.35i		−	2.73376i
$518$	−465.276			−0.898217
$519$		0			0
$520$	−12.0000	+	20.7846i	−0.0230769	+	0.0399704i
$521$	492.146	−	284.141i	0.944619	−	0.545376i	0.0532135	−	0.998583i	$-0.483054\pi$
$521$	492.146	−	284.141i	0.944619	−	0.545376i	0.891405	+	0.453207i	$0.149720\pi$
$522$		0			0
$523$	457.500	+	264.138i	0.874761	+	0.505043i	0.868927	−	0.494939i	$-0.164810\pi$
$523$	457.500	+	264.138i	0.874761	+	0.505043i	0.00583355	+	0.999983i	$0.498143\pi$
$524$		−	117.576i		−	0.224381i
$525$		0			0
$526$	360.000			0.684411
$527$	−29.6985	+	51.4393i	−0.0563539	+	0.0976078i
$528$		0			0
$529$	228.500	+	395.774i	0.431947	+	0.748154i
$530$	458.205	+	264.545i	0.864538	+	0.499141i
$531$		0			0
$532$	−357.000	−	206.114i	−0.671053	−	0.387432i
$533$	−118.794			−0.222878
$534$		0			0
$535$	612.000	−	353.338i	1.14393	−	0.660446i
$536$	−43.8406	−	75.9342i	−0.0817922	−	0.141668i
$537$		0			0
$538$			27.7128i			0.0515108i
$539$	−415.779	+	720.150i	−0.771389	+	1.33609i
$540$		0			0
$541$	−167.500	+	290.119i	−0.309612	+	0.536263i	−0.978277	−	0.207300i	$-0.933532\pi$
$541$	−167.500	+	290.119i	−0.309612	+	0.536263i	0.668666	+	0.743563i	$0.266866\pi$
$542$	50.9117	−	29.3939i	0.0939330	−	0.0542322i
$543$		0			0
$544$	24.0000	+	13.8564i	0.0441176	+	0.0254713i
$545$			827.928i			1.51913i
$546$		0			0
$547$	−658.000			−1.20293			−0.601463	−	0.798901i	$-0.705415\pi$
$547$	−658.000			−1.20293			−0.601463	+	0.798901i	$0.705415\pi$
$548$	152.735	−	264.545i	0.278714	−	0.482746i
$549$		0			0
$550$	12.0000	+	20.7846i	0.0218182	+	0.0377902i
$551$	865.499	+	499.696i	1.57078	+	0.906889i
$552$		0			0
$553$	143.500	+	248.549i	0.259494	+	0.449456i
$554$	476.590			0.860271
$555$		0			0
$556$	339.000	−	195.722i	0.609712	−	0.352018i
$557$	−135.765	−	235.151i	−0.243742	−	0.422174i	0.718035	−	0.696007i	$-0.245042\pi$
$557$	−135.765	−	235.151i	−0.243742	−	0.422174i	−0.961777	+	0.273833i	$0.911708\pi$
$558$		0			0
$559$			53.6936i			0.0960529i
$560$		−	137.171i		−	0.244949i
$561$		0			0
$562$	−174.000	+	301.377i	−0.309609	+	0.536258i
$563$	12.7279	−	7.34847i	0.0226073	−	0.0130523i	−0.488654	−	0.872478i	$-0.662512\pi$
$563$	12.7279	−	7.34847i	0.0226073	−	0.0130523i	0.511261	+	0.859425i	$0.329179\pi$
$564$		0			0
$565$	−252.000	−	145.492i	−0.446018	−	0.257508i
$566$			276.792i			0.489032i
$567$		0			0
$568$	168.000			0.295775
$569$	−424.264	+	734.847i	−0.745631	+	1.29147i	0.204268	+	0.978915i	$0.434519\pi$
$569$	−424.264	+	734.847i	−0.745631	+	1.29147i	−0.949899	+	0.312556i	$0.898815\pi$
$570$		0			0
$571$	−224.500	−	388.845i	−0.393170	−	0.680990i	0.599696	−	0.800228i	$-0.295288\pi$
$571$	−224.500	−	388.845i	−0.393170	−	0.680990i	−0.992866	+	0.119238i	$0.961955\pi$
$572$	−50.9117	−	29.3939i	−0.0890064	−	0.0513879i
$573$		0			0
$574$	588.000	−	339.482i	1.02439	−	0.591432i
$575$	8.48528			0.0147570
$576$		0			0
$577$	−253.500	+	146.358i	−0.439341	+	0.253654i	−0.703318	−	0.710875i	$-0.748299\pi$
$577$	−253.500	+	146.358i	−0.439341	+	0.253654i	0.263977	+	0.964529i	$0.414966\pi$
$578$	187.383	+	324.557i	0.324193	+	0.561518i
$579$		0			0
$580$			332.554i			0.573369i
$581$	−29.6985	−	17.1464i	−0.0511162	−	0.0295119i
$582$		0			0
$583$	−648.000	+	1122.37i	−1.11149	+	1.92516i
$584$	199.404	−	115.126i	0.341445	−	0.197134i
$585$		0			0
$586$	120.000	+	69.2820i	0.204778	+	0.118229i
$587$		−	529.090i		−	0.901345i	−0.892689	−	0.450673i	$-0.851184\pi$
$587$		−	529.090i		−	0.901345i	0.892689	−	0.450673i	$-0.148816\pi$
$588$		0			0
$589$	−357.000			−0.606112
$590$	−288.500	+	499.696i	−0.488982	+	0.846942i
$591$		0			0
$592$	94.0000	+	162.813i	0.158784	+	0.275022i
$593$	907.925	+	524.191i	1.53107	+	0.883964i	0.999313	+	0.0370681i	$0.0118018\pi$
$593$	907.925	+	524.191i	1.53107	+	0.883964i	0.531758	+	0.846896i	$0.321531\pi$
$594$		0			0
$595$	−84.0000	+	145.492i	−0.141176	+	0.244525i
$596$	−101.823			−0.170845
$597$		0			0
$598$	−18.0000	+	10.3923i	−0.0301003	+	0.0173784i
$599$	−322.441	−	558.484i	−0.538298	−	0.932360i	−0.998996	−	0.0448028i	$-0.985734\pi$
$599$	−322.441	−	558.484i	−0.538298	−	0.932360i	0.460698	−	0.887557i	$-0.347599\pi$
$600$		0			0
$601$		−	458.993i		−	0.763716i	−0.924221	−	0.381858i	$-0.875284\pi$
$601$		−	458.993i		−	0.763716i	0.924221	−	0.381858i	$-0.124716\pi$
$602$	−153.442	−	265.770i	−0.254887	−	0.441478i
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.0165563	+	0.0286763i
$605$	708.521	−	409.065i	1.17111	−	0.676140i
$606$		0			0
$607$	910.500	+	525.677i	1.50000	+	0.866025i	1.00000			$0$
$607$	910.500	+	525.677i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$608$			166.565i			0.273956i
$609$		0			0
$610$	576.000			0.944262
$611$	−72.1249	+	124.924i	−0.118044	+	0.204458i
$612$		0			0
$613$	−145.000	−	251.147i	−0.236542	−	0.409702i	0.723178	−	0.690662i	$-0.242681\pi$
$613$	−145.000	−	251.147i	−0.236542	−	0.409702i	−0.959720	+	0.280960i	$0.909347\pi$
$614$	86.9741	+	50.2145i	0.141652	+	0.0817826i
$615$		0			0
$616$	336.000			0.545455
$617$	729.734			1.18271			0.591357	−	0.806410i	$-0.298593\pi$
$617$	729.734			1.18271			0.591357	+	0.806410i	$0.298593\pi$
$618$		0			0
$619$	−709.500	+	409.630i	−1.14620	+	0.661761i	−0.947959	−	0.318392i	$-0.896857\pi$
$619$	−709.500	+	409.630i	−1.14620	+	0.661761i	−0.198244	+	0.980153i	$0.563524\pi$
$620$	−59.3970	−	102.879i	−0.0958016	−	0.165933i
$621$		0			0
$622$			304.841i			0.490098i
$623$	−356.382	+	205.757i	−0.572041	+	0.330268i
$624$		0			0
$625$	299.500	−	518.749i	0.479200	−	0.829999i
$626$	358.503	−	206.982i	0.572689	−	0.330642i
$627$		0			0
$628$	−72.0000	−	41.5692i	−0.114650	−	0.0661930i
$629$		−	230.252i		−	0.366060i
$630$		0			0
$631$	−58.0000			−0.0919176			−0.0459588	−	0.998943i	$-0.514634\pi$
$631$	−58.0000			−0.0919176			−0.0459588	+	0.998943i	$0.514634\pi$
$632$	57.9828	−	100.429i	0.0917449	−	0.158907i
$633$		0			0
$634$	168.000	+	290.985i	0.264984	+	0.458966i
$635$	−886.712	−	511.943i	−1.39640	−	0.806210i
$636$		0			0
$637$	73.5000	−	42.4352i	0.115385	−	0.0666173i
$638$	−814.587			−1.27678
$639$		0			0
$640$	−48.0000	+	27.7128i	−0.0750000	+	0.0433013i
$641$	−479.418	−	830.377i	−0.747923	−	1.29544i	−0.948817	−	0.315827i	$-0.897718\pi$
$641$	−479.418	−	830.377i	−0.747923	−	1.29544i	0.200894	−	0.979613i	$-0.435615\pi$
$642$		0			0
$643$			760.370i			1.18254i	0.806475	+	0.591268i	$0.201372\pi$
$643$			760.370i			1.18254i	−0.806475	+	0.591268i	$0.798628\pi$
$644$	59.3970	−	102.879i	0.0922313	−	0.159749i
$645$		0			0
$646$	102.000	−	176.669i	0.157895	−	0.273482i
$647$	−305.470	+	176.363i	−0.472133	+	0.272586i	−0.717132	−	0.696937i	$-0.754546\pi$
$647$	−305.470	+	176.363i	−0.472133	+	0.272586i	0.244999	+	0.969523i	$0.421212\pi$
$648$		0			0
$649$	−1224.00	−	706.677i	−1.88598	−	1.08887i
$650$		−	2.44949i		−	0.00376845i
$651$		0			0
$652$	172.000			0.263804
$653$	220.617	−	382.120i	0.337852	−	0.585177i	−0.646177	−	0.763188i	$-0.723633\pi$
$653$	220.617	−	382.120i	0.337852	−	0.585177i	0.984028	+	0.178011i	$0.0569664\pi$
$654$		0			0
$655$	−144.000	−	249.415i	−0.219847	−	0.380787i
$656$	−237.588	−	137.171i	−0.362177	−	0.209103i
$657$		0			0
$658$		−	824.456i		−	1.25297i
$659$	161.220			0.244644			0.122322	−	0.992490i	$-0.460966\pi$
$659$	161.220			0.244644			0.122322	+	0.992490i	$0.460966\pi$
$660$		0			0
$661$	−721.500	+	416.558i	−1.09153	+	0.630194i	−0.933983	−	0.357318i	$-0.883691\pi$
$661$	−721.500	+	416.558i	−1.09153	+	0.630194i	−0.157545	+	0.987512i	$0.550358\pi$
$662$	−130.815	−	226.578i	−0.197605	−	0.342263i
$663$		0			0
$664$			13.8564i			0.0208681i
$665$	−1009.75			−1.51842
$666$		0			0
$667$	−144.000	+	249.415i	−0.215892	+	0.373936i
$668$	313.955	−	181.262i	0.469993	−	0.271351i
$669$		0			0
$670$	−186.000	−	107.387i	−0.277612	−	0.160279i
$671$			1410.91i			2.10269i
$672$		0			0
$673$	−263.000			−0.390788			−0.195394	−	0.980725i	$-0.562598\pi$
$673$	−263.000			−0.390788			−0.195394	+	0.980725i	$0.562598\pi$
$674$	−253.851	+	439.683i	−0.376634	+	0.652349i
$675$		0			0
$676$	−166.000	−	287.520i	−0.245562	−	0.425326i
$677$	432.749	+	249.848i	0.639216	+	0.369052i	0.784313	−	0.620366i	$-0.213016\pi$
$677$	432.749	+	249.848i	0.639216	+	0.369052i	−0.145096	+	0.989418i	$0.546349\pi$
$678$		0			0
$679$	−252.000	−	145.492i	−0.371134	−	0.214274i
$680$	67.8823			0.0998268
$681$		0			0
$682$	252.000	−	145.492i	0.369501	−	0.213332i
$683$	−479.418	−	830.377i	−0.701930	−	1.21578i	−0.967788	−	0.251767i	$-0.918988\pi$
$683$	−479.418	−	830.377i	−0.701930	−	1.21578i	0.265858	−	0.964012i	$-0.414345\pi$
$684$		0			0
$685$		−	748.246i		−	1.09233i
$686$	−242.538	+	420.087i	−0.353553	+	0.612372i
$687$		0			0
$688$	−62.0000	+	107.387i	−0.0901163	+	0.156086i
$689$	114.551	−	66.1362i	0.166257	−	0.0959887i
$690$		0			0
$691$	1069.50	+	617.476i	1.54776	+	0.893598i	0.998313	+	0.0580674i	$0.0184938\pi$
$691$	1069.50	+	617.476i	1.54776	+	0.893598i	0.549444	+	0.835530i	$0.314839\pi$
$692$		−	88.1816i		−	0.127430i
$693$		0			0
$694$	660.000			0.951009
$695$	479.418	−	830.377i	0.689811	−	1.19479i
$696$		0			0
$697$	168.000	+	290.985i	0.241033	+	0.417481i
$698$	−712.764	−	411.514i	−1.02115	−	0.589562i
$699$		0			0
$700$	7.00000	+	12.1244i	0.0100000	+	0.0173205i
$701$	−975.807			−1.39202			−0.696011	−	0.718031i	$-0.745044\pi$
$701$	−975.807			−1.39202			−0.696011	+	0.718031i	$0.745044\pi$
$702$		0			0
$703$	1198.50	−	691.954i	1.70484	−	0.984288i
$704$	−67.8823	−	117.576i	−0.0964237	−	0.167011i
$705$		0			0
$706$			408.764i			0.578986i
$707$		−	1234.54i		−	1.74617i
$708$		0			0
$709$	553.000	−	957.824i	0.779972	−	1.35095i	−0.151986	−	0.988383i	$-0.548567\pi$
$709$	553.000	−	957.824i	0.779972	−	1.35095i	0.931957	−	0.362568i	$-0.118100\pi$
$710$	356.382	−	205.757i	0.501946	−	0.289799i
$711$		0			0
$712$	144.000	+	83.1384i	0.202247	+	0.116767i
$713$		−	102.879i		−	0.144290i
$714$		0			0
$715$	−144.000			−0.201399
$716$	−8.48528	+	14.6969i	−0.0118510	+	0.0205265i
$717$		0			0
$718$	−240.000	−	415.692i	−0.334262	−	0.578958i
$719$	−593.970	−	342.929i	−0.826105	−	0.476952i	0.0264120	−	0.999651i	$-0.491592\pi$
$719$	−593.970	−	342.929i	−0.826105	−	0.476952i	−0.852517	+	0.522699i	$0.824925\pi$
$720$		0			0
$721$	−178.500	+	103.057i	−0.247573	+	0.142936i
$722$	715.592			0.991125
$723$		0			0
$724$	−75.0000	+	43.3013i	−0.103591	+	0.0598084i
$725$	−16.9706	−	29.3939i	−0.0234077	−	0.0405433i
$726$		0			0
$727$			427.817i			0.588468i	0.955733	+	0.294234i	$0.0950646\pi$
$727$			427.817i			0.588468i	−0.955733	+	0.294234i	$0.904935\pi$
$728$	−29.6985	−	17.1464i	−0.0407946	−	0.0235528i
$729$		0			0
$730$	282.000	−	488.438i	0.386301	−	0.669094i
$731$	131.522	−	75.9342i	0.179920	−	0.103877i
$732$		0			0
$733$	34.5000	+	19.9186i	0.0470668	+	0.0271741i	0.523349	−	0.852119i	$-0.324682\pi$
$733$	34.5000	+	19.9186i	0.0470668	+	0.0271741i	−0.476282	+	0.879293i	$0.658016\pi$
$734$		−	218.005i		−	0.297009i
$735$		0			0
$736$	−48.0000			−0.0652174
$737$	263.044	−	455.605i	0.356911	−	0.618189i
$738$		0			0
$739$	243.500	+	421.754i	0.329499	+	0.570710i	0.982413	−	0.186723i	$-0.0597867\pi$
$739$	243.500	+	421.754i	0.329499	+	0.570710i	−0.652913	+	0.757433i	$0.726453\pi$
$740$	398.808	+	230.252i	0.538930	+	0.311151i
$741$		0			0
$742$	−378.000	+	654.715i	−0.509434	+	0.882366i
$743$	509.117			0.685218			0.342609	−	0.939478i	$-0.388689\pi$
$743$	509.117			0.685218			0.342609	+	0.939478i	$0.388689\pi$
$744$		0			0
$745$	−216.000	+	124.708i	−0.289933	+	0.167393i
$746$	−204.354	−	353.951i	−0.273933	−	0.474466i
$747$		0			0
$748$			166.277i			0.222295i
$749$	504.874	+	874.468i	0.674064	+	1.16751i
$750$		0			0
$751$	272.500	−	471.984i	0.362850	−	0.628474i	−0.625579	−	0.780161i	$-0.715137\pi$
$751$	272.500	−	471.984i	0.362850	−	0.628474i	0.988429	+	0.151687i	$0.0484706\pi$
$752$	−288.500	+	166.565i	−0.383643	+	0.221496i
$753$		0			0
$754$	72.0000	+	41.5692i	0.0954907	+	0.0551316i
$755$			48.9898i			0.0648871i
$756$		0			0
$757$	−770.000			−1.01717			−0.508587	−	0.861011i	$-0.669832\pi$
$757$	−770.000			−1.01717			−0.508587	+	0.861011i	$0.669832\pi$
$758$	4.94975	−	8.57321i	0.00653001	−	0.0113103i
$759$		0			0
$760$	204.000	+	353.338i	0.268421	+	0.464919i
$761$	−148.492	−	85.7321i	−0.195128	−	0.112657i	0.399253	−	0.916841i	$-0.369270\pi$
$761$	−148.492	−	85.7321i	−0.195128	−	0.112657i	−0.594381	+	0.804184i	$0.702603\pi$
$762$		0			0
$763$	−1183.00			−1.55046
$764$	−152.735			−0.199915
$765$		0			0
$766$	−606.000	+	349.874i	−0.791123	+	0.456755i
$767$	72.1249	+	124.924i	0.0940351	+	0.162874i
$768$		0			0
$769$		−	704.945i		−	0.916703i	−0.888771	−	0.458352i	$-0.848440\pi$
$769$		−	704.945i		−	0.916703i	0.888771	−	0.458352i	$-0.151560\pi$
$770$	712.764	−	411.514i	0.925667	−	0.534434i
$771$		0			0
$772$	287.000	−	497.099i	0.371762	−	0.643910i
$773$	−797.616	+	460.504i	−1.03185	+	0.595736i	−0.917513	−	0.397706i	$-0.869806\pi$
$773$	−797.616	+	460.504i	−1.03185	+	0.595736i	−0.114333	+	0.993443i	$0.536473\pi$
$774$		0			0
$775$	10.5000	+	6.06218i	0.0135484	+	0.00782216i
$776$			117.576i			0.151515i
$777$		0			0
$778$	−324.000			−0.416452
$779$	−1009.75	+	1748.94i	−1.29621	+	2.24510i
$780$		0			0
$781$	504.000	+	872.954i	0.645327	+	1.11774i
$782$	50.9117	+	29.3939i	0.0651045	+	0.0375881i
$783$		0			0
$784$	196.000			0.250000
$785$	−203.647			−0.259423
$786$		0			0
$787$	396.000	−	228.631i	0.503177	−	0.290509i	−0.226848	−	0.973930i	$-0.572842\pi$
$787$	396.000	−	228.631i	0.503177	−	0.290509i	0.730024	+	0.683421i	$0.239509\pi$
$788$	127.279	+	220.454i	0.161522	+	0.279764i
$789$		0			0
$790$		−	284.056i		−	0.359565i
$791$	207.889	−	360.075i	0.262818	−	0.455215i
$792$		0			0
$793$	72.0000	−	124.708i	0.0907945	−	0.157261i
$794$	99.7021	−	57.5630i	0.125569	−	0.0724975i
$795$		0			0
$796$	−360.000	−	207.846i	−0.452261	−	0.261113i
$797$		−	14.6969i		−	0.0184403i	−0.999957	−	0.00922016i	$-0.997065\pi$
$797$		−	14.6969i		−	0.0184403i	0.999957	−	0.00922016i	$-0.00293491\pi$
$798$		0			0
$799$	408.000			0.510638
$800$	2.82843	−	4.89898i	0.00353553	−	0.00612372i
$801$		0			0
$802$	66.0000	+	114.315i	0.0822943	+	0.142538i
$803$	1196.42	+	690.756i	1.48994	+	0.860219i
$804$		0			0
$805$		−	290.985i		−	0.361471i
$806$	−29.6985			−0.0368468
$807$		0			0
$808$	−432.000	+	249.415i	−0.534653	+	0.308682i
$809$	470.933	+	815.680i	0.582118	+	1.00826i	0.995228	+	0.0975763i	$0.0311090\pi$
$809$	470.933	+	815.680i	0.582118	+	1.00826i	−0.413110	+	0.910681i	$0.635558\pi$
$810$		0			0
$811$			498.831i			0.615081i	0.951535	+	0.307540i	$0.0995059\pi$
$811$			498.831i			0.615081i	−0.951535	+	0.307540i	$0.900494\pi$
$812$	−475.176			−0.585192
$813$		0			0
$814$	−564.000	+	976.877i	−0.692875	+	1.20009i
$815$	364.867	−	210.656i	0.447690	−	0.258474i
$816$		0			0
$817$	790.500	+	456.395i	0.967564	+	0.558623i
$818$			590.327i			0.721671i
$819$		0			0
$820$	−672.000			−0.819512
$821$	301.227	−	521.741i	0.366903	−	0.635495i	−0.622176	−	0.782877i	$-0.713751\pi$
$821$	301.227	−	521.741i	0.366903	−	0.635495i	0.989080	+	0.147382i	$0.0470847\pi$
$822$		0			0
$823$	−19.0000	−	32.9090i	−0.0230863	−	0.0399866i	0.854251	−	0.519860i	$-0.174016\pi$
$823$	−19.0000	−	32.9090i	−0.0230863	−	0.0399866i	−0.877338	+	0.479873i	$0.840683\pi$
$824$	72.1249	+	41.6413i	0.0875302	+	0.0505356i
$825$		0			0
$826$	−714.000	−	412.228i	−0.864407	−	0.499065i
$827$	687.308			0.831086			0.415543	−	0.909574i	$-0.363592\pi$
$827$	687.308			0.831086			0.415543	+	0.909574i	$0.363592\pi$
$828$		0			0
$829$	−721.500	+	416.558i	−0.870326	+	0.502483i	−0.867456	−	0.497513i	$-0.834247\pi$
$829$	−721.500	+	416.558i	−0.870326	+	0.502483i	−0.00286924	+	0.999996i	$0.500913\pi$
$830$	16.9706	+	29.3939i	0.0204465	+	0.0354143i
$831$		0			0
$832$			13.8564i			0.0166543i
$833$	−207.889	−	120.025i	−0.249567	−	0.144088i
$834$		0			0
$835$	444.000	−	769.031i	0.531737	−	0.920995i
$836$	−865.499	+	499.696i	−1.03529	+	0.597722i
$837$		0			0
$838$	24.0000	+	13.8564i	0.0286396	+	0.0165351i
$839$		−	244.949i		−	0.291953i	−0.989288	−	0.145977i	$-0.953368\pi$
$839$		−	244.949i		−	0.291953i	0.989288	−	0.145977i	$-0.0466325\pi$
$840$		0			0
$841$	311.000			0.369798
$842$	287.792	−	498.471i	0.341796	−	0.592009i
$843$		0			0
$844$	−82.0000	−	142.028i	−0.0971564	−	0.168280i
$845$	−704.278	−	406.615i	−0.833466	−	0.481202i
$846$		0			0
$847$	584.500	+	1012.38i	0.690083	+	1.19526i
$848$	305.470			0.360224
$849$		0			0
$850$	−6.00000	+	3.46410i	−0.00705882	+	0.00407541i
$851$	199.404	+	345.378i	0.234317	+	0.405850i
$852$		0			0
$853$			1245.34i			1.45996i	0.683469	+	0.729979i	$0.260470\pi$
$853$			1245.34i			1.45996i	−0.683469	+	0.729979i	$0.739530\pi$
$854$			823.029i			0.963734i
$855$		0			0
$856$	204.000	−	353.338i	0.238318	−	0.412778i
$857$	1060.66	−	612.372i	1.23764	−	0.714554i	0.269031	−	0.963131i	$-0.413297\pi$
$857$	1060.66	−	612.372i	1.23764	−	0.714554i	0.968612	+	0.248578i	$0.0799632\pi$
$858$		0			0
$859$	216.000	+	124.708i	0.251455	+	0.145178i	0.620430	−	0.784262i	$-0.286958\pi$
$859$	216.000	+	124.708i	0.251455	+	0.145178i	−0.368975	+	0.929439i	$0.620291\pi$
$860$			303.737i			0.353182i
$861$		0			0
$862$	−228.000			−0.264501
$863$	−330.926	+	573.181i	−0.383460	+	0.664172i	−0.991554	−	0.129693i	$-0.958601\pi$
$863$	−330.926	+	573.181i	−0.383460	+	0.664172i	0.608094	+	0.793865i	$0.291934\pi$
$864$		0			0
$865$	−108.000	−	187.061i	−0.124855	−	0.216256i
$866$	205.768	+	118.800i	0.237607	+	0.137183i
$867$		0			0
$868$	147.000	−	84.8705i	0.169355	−	0.0977771i
$869$	695.793			0.800682
$870$		0			0
$871$	−46.5000	+	26.8468i	−0.0533869	+	0.0308229i
$872$	239.002	+	413.964i	0.274085	+	0.474729i
$873$		0			0
$874$			353.338i			0.404277i
$875$	772.161	+	445.807i	0.882469	+	0.509494i
$876$		0			0
$877$	287.000	−	497.099i	0.327252	−	0.566817i	−0.654714	−	0.755877i	$-0.727211\pi$
$877$	287.000	−	497.099i	0.327252	−	0.566817i	0.981966	+	0.189060i	$0.0605441\pi$
$878$	−661.852	+	382.120i	−0.753818	+	0.435217i
$879$		0			0
$880$	−288.000	−	166.277i	−0.327273	−	0.188951i
$881$		−	161.666i		−	0.183503i	−0.995782	−	0.0917516i	$-0.970753\pi$
$881$		−	161.666i		−	0.183503i	0.995782	−	0.0917516i	$-0.0292466\pi$
$882$		0			0
$883$	1735.00			1.96489			0.982446	−	0.186546i	$-0.0597294\pi$
$883$	1735.00			1.96489			0.982446	+	0.186546i	$0.0597294\pi$
$884$	8.48528	−	14.6969i	0.00959873	−	0.0166255i
$885$		0			0
$886$	−90.0000	−	155.885i	−0.101580	−	0.175942i
$887$	−169.706	−	97.9796i	−0.191325	−	0.110462i	0.401277	−	0.915957i	$-0.368566\pi$
$887$	−169.706	−	97.9796i	−0.191325	−	0.110462i	−0.592603	+	0.805495i	$0.701900\pi$
$888$		0			0
$889$	731.500	−	1267.00i	0.822835	−	1.42519i
$890$	407.294			0.457633
$891$		0			0
$892$	72.0000	−	41.5692i	0.0807175	−	0.0466023i
$893$	1226.12	+	2123.71i	1.37304	+	2.37817i
$894$		0			0
$895$			41.5692i			0.0464461i
$896$	−39.5980	−	68.5857i	−0.0441942	−	0.0765466i
$897$		0			0
$898$	−78.0000	+	135.100i	−0.0868597	+	0.150445i
$899$	−356.382	+	205.757i	−0.396420	+	0.228873i
$900$		0			0
$901$	−324.000	−	187.061i	−0.359600	−	0.207615i
$902$		−	1646.06i		−	1.82490i
$903$		0			0
$904$	−168.000			−0.185841
$905$	−106.066	+	183.712i	−0.117200	+	0.202996i
$906$		0			0
$907$	−375.500	−	650.385i	−0.414002	−	0.717073i	0.581321	−	0.813674i	$-0.302536\pi$
$907$	−375.500	−	650.385i	−0.414002	−	0.717073i	−0.995323	+	0.0966015i	$0.969203\pi$
$908$	661.852	+	382.120i	0.728912	+	0.420837i
$909$		0			0
$910$	−84.0000			−0.0923077
$911$	−1247.34			−1.36919			−0.684597	−	0.728921i	$-0.740022\pi$
$911$	−1247.34			−1.36919			−0.684597	+	0.728921i	$0.740022\pi$
$912$		0			0
$913$	−72.0000	+	41.5692i	−0.0788609	+	0.0455304i
$914$	17.6777	+	30.6186i	0.0193410	+	0.0334996i
$915$		0			0
$916$			162.813i			0.177743i
$917$	356.382	−	205.757i	0.388639	−	0.224381i
$918$		0			0
$919$	−507.500	+	879.016i	−0.552231	+	0.956492i	0.445883	+	0.895091i	$0.352890\pi$
$919$	−507.500	+	879.016i	−0.552231	+	0.956492i	−0.998113	+	0.0614001i	$0.980443\pi$
$920$	−101.823	+	58.7878i	−0.110678	+	0.0638997i
$921$		0			0
$922$	−96.0000	−	55.4256i	−0.104121	−	0.0601146i
$923$		−	102.879i		−	0.111461i
$924$		0			0
$925$	−47.0000			−0.0508108
$926$	368.403	−	638.092i	0.397843	−	0.689084i
$927$		0			0
$928$	96.0000	+	166.277i	0.103448	+	0.179178i
$929$	−946.109	−	546.236i	−1.01842	−	0.587983i	−0.104772	−	0.994496i	$-0.533411\pi$
$929$	−946.109	−	546.236i	−1.01842	−	0.587983i	−0.913645	+	0.406513i	$0.866744\pi$
$930$		0			0
$931$		−	1442.80i		−	1.54973i
$932$	−458.205			−0.491636
$933$		0			0
$934$	270.000	−	155.885i	0.289079	−	0.166900i
$935$	203.647	+	352.727i	0.217804	+	0.377248i
$936$		0			0
$937$		−	1747.64i		−	1.86514i	−0.360985	−	0.932572i	$-0.617559\pi$
$937$		−	1747.64i		−	1.86514i	0.360985	−	0.932572i	$-0.382441\pi$
$938$	153.442	−	265.770i	0.163584	−	0.283337i
$939$		0			0
$940$	−408.000	+	706.677i	−0.434043	+	0.751784i
$941$	−1073.39	+	619.721i	−1.14069	+	0.658577i	−0.946601	−	0.322407i	$-0.895508\pi$
$941$	−1073.39	+	619.721i	−1.14069	+	0.658577i	−0.194088	+	0.980984i	$0.562175\pi$
$942$		0			0
$943$	−504.000	−	290.985i	−0.534464	−	0.308573i
$944$			333.131i			0.352893i
$945$		0			0
$946$	−744.000			−0.786469
$947$	602.455	−	1043.48i	0.636172	−	1.10188i	−0.350093	−	0.936715i	$-0.613850\pi$
$947$	602.455	−	1043.48i	0.636172	−	1.10188i	0.986266	−	0.165168i	$-0.0528165\pi$
$948$		0			0
$949$	−70.5000	−	122.110i	−0.0742887	−	0.128672i
$950$	−36.0624	−	20.8207i	−0.0379605	−	0.0219165i
$951$		0			0
$952$			96.9948i			0.101885i
$953$	−1026.72			−1.07735			−0.538677	−	0.842512i	$-0.681076\pi$
$953$	−1026.72			−1.07735			−0.538677	+	0.842512i	$0.681076\pi$
$954$		0			0
$955$	−324.000	+	187.061i	−0.339267	+	0.195876i
$956$	−67.8823	−	117.576i	−0.0710065	−	0.122987i
$957$		0			0
$958$		−	1240.15i		−	1.29452i
$959$	1069.15			1.11485
$960$		0			0
$961$	−407.000	+	704.945i	−0.423517	+	0.733553i
$962$	99.7021	−	57.5630i	0.103640	−	0.0598368i
$963$		0			0
$964$	792.000	+	457.261i	0.821577	+	0.474338i
$965$		−	1406.01i		−	1.45700i
$966$		0			0
$967$	−895.000			−0.925543			−0.462771	−	0.886478i	$-0.653145\pi$
$967$	−895.000			−0.925543			−0.462771	+	0.886478i	$0.653145\pi$
$968$	236.174	−	409.065i	0.243981	−	0.422588i
$969$		0			0
$970$	144.000	+	249.415i	0.148454	+	0.257129i
$971$	182.434	+	105.328i	0.187882	+	0.108474i	0.590991	−	0.806678i	$-0.298737\pi$
$971$	182.434	+	105.328i	0.187882	+	0.108474i	−0.403109	+	0.915152i	$0.632070\pi$
$972$		0			0
$973$	1186.50	+	685.026i	1.21942	+	0.704035i
$974$	−179.605			−0.184400
$975$		0			0
$976$	288.000	−	166.277i	0.295082	−	0.170366i
$977$	−627.911	−	1087.57i	−0.642693	−	1.11318i	−0.984829	−	0.173526i	$-0.944484\pi$
$977$	−627.911	−	1087.57i	−0.642693	−	1.11318i	0.342136	−	0.939650i	$-0.388849\pi$
$978$		0			0
$979$			997.661i			1.01906i
$980$	415.779	−	240.050i	0.424264	−	0.244949i
$981$		0			0
$982$	444.000	−	769.031i	0.452138	−	0.783127i
$983$	−1022.48	+	590.327i	−1.04016	+	0.600536i	−0.919878	−	0.392204i	$-0.871713\pi$
$983$	−1022.48	+	590.327i	−1.04016	+	0.600536i	−0.120281	+	0.992740i	$0.538379\pi$
$984$		0			0
$985$	540.000	+	311.769i	0.548223	+	0.316517i
$986$		−	235.151i		−	0.238490i
$987$		0			0
$988$	102.000			0.103239
$989$	−131.522	+	227.803i	−0.132985	+	0.230336i
$990$		0			0
$991$	−327.500	−	567.247i	−0.330474	−	0.572398i	0.652131	−	0.758107i	$-0.273875\pi$
$991$	−327.500	−	567.247i	−0.330474	−	0.572398i	−0.982605	+	0.185708i	$0.940542\pi$
$992$	−59.3970	−	34.2929i	−0.0598760	−	0.0345694i
$993$		0			0
$994$	294.000	+	509.223i	0.295775	+	0.512297i
$995$	−1018.23			−1.02335
$996$		0			0
$997$	397.500	−	229.497i	0.398696	−	0.230187i	−0.287225	−	0.957863i	$-0.592733\pi$
$997$	397.500	−	229.497i	0.398696	−	0.230187i	0.685921	+	0.727676i	$0.259399\pi$
$998$	−164.756	−	285.366i	−0.165086	−	0.285937i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.3.n.b.19.2	yes	4
3.2	odd	2	inner	126.3.n.b.19.1	✓	4
4.3	odd	2		1008.3.cg.i.145.1		4
7.2	even	3		882.3.c.c.685.2		4
7.3	odd	6	inner	126.3.n.b.73.2	yes	4
7.4	even	3		882.3.n.c.325.2		4
7.5	odd	6		882.3.c.c.685.1		4
7.6	odd	2		882.3.n.c.19.2		4
12.11	even	2		1008.3.cg.i.145.2		4
21.2	odd	6		882.3.c.c.685.3		4
21.5	even	6		882.3.c.c.685.4		4
21.11	odd	6		882.3.n.c.325.1		4
21.17	even	6	inner	126.3.n.b.73.1	yes	4
21.20	even	2		882.3.n.c.19.1		4
28.3	even	6		1008.3.cg.i.577.1		4
84.59	odd	6		1008.3.cg.i.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.n.b.19.1	✓	4	3.2	odd	2	inner
126.3.n.b.19.2	yes	4	1.1	even	1	trivial
126.3.n.b.73.1	yes	4	21.17	even	6	inner
126.3.n.b.73.2	yes	4	7.3	odd	6	inner
882.3.c.c.685.1		4	7.5	odd	6
882.3.c.c.685.2		4	7.2	even	3
882.3.c.c.685.3		4	21.2	odd	6
882.3.c.c.685.4		4	21.5	even	6
882.3.n.c.19.1		4	21.20	even	2
882.3.n.c.19.2		4	7.6	odd	2
882.3.n.c.325.1		4	21.11	odd	6
882.3.n.c.325.2		4	7.4	even	3
1008.3.cg.i.145.1		4	4.3	odd	2
1008.3.cg.i.145.2		4	12.11	even	2
1008.3.cg.i.577.1		4	28.3	even	6
1008.3.cg.i.577.2		4	84.59	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	126.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.24264 - 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-4.24264 - 2.44949i) q^{5} +(3.50000 - 6.06218i) q^{7} -2.82843 q^{8} +(-6.00000 + 3.46410i) q^{10} +(-8.48528 - 14.6969i) q^{11} +1.73205i q^{13} +(-4.94975 - 8.57321i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(4.24264 - 2.44949i) q^{17} +(25.5000 + 14.7224i) q^{19} +9.79796i q^{20} -24.0000 q^{22} +(-4.24264 + 7.34847i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(2.12132 + 1.22474i) q^{26} -14.0000 q^{28} +33.9411 q^{29} +(-10.5000 + 6.06218i) q^{31} +(2.82843 + 4.89898i) q^{32} -6.92820i q^{34} +(-29.6985 + 17.1464i) q^{35} +(23.5000 - 40.7032i) q^{37} +(36.0624 - 20.8207i) q^{38} +(12.0000 + 6.92820i) q^{40} +68.5857i q^{41} +31.0000 q^{43} +(-16.9706 + 29.3939i) q^{44} +(6.00000 + 10.3923i) q^{46} +(72.1249 + 41.6413i) q^{47} +(-24.5000 - 42.4352i) q^{49} -1.41421 q^{50} +(3.00000 - 1.73205i) q^{52} +(-38.1838 - 66.1362i) q^{53} +83.1384i q^{55} +(-9.89949 + 17.1464i) q^{56} +(24.0000 - 41.5692i) q^{58} +(72.1249 - 41.6413i) q^{59} +(-72.0000 - 41.5692i) q^{61} +17.1464i q^{62} +8.00000 q^{64} +(4.24264 - 7.34847i) q^{65} +(15.5000 + 26.8468i) q^{67} +(-8.48528 - 4.89898i) q^{68} +48.4974i q^{70} -59.3970 q^{71} +(-70.5000 + 40.7032i) q^{73} +(-33.2340 - 57.5630i) q^{74} -58.8897i q^{76} -118.794 q^{77} +(-20.5000 + 35.5070i) q^{79} +(16.9706 - 9.79796i) q^{80} +(84.0000 + 48.4974i) q^{82} -4.89898i q^{83} -24.0000 q^{85} +(21.9203 - 37.9671i) q^{86} +(24.0000 + 41.5692i) q^{88} +(-50.9117 - 29.3939i) q^{89} +(10.5000 + 6.06218i) q^{91} +16.9706 q^{92} +(102.000 - 58.8897i) q^{94} +(-72.1249 - 124.924i) q^{95} -41.5692i q^{97} -69.2965 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 14 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 + 14 * q^7	\( 4 q - 4 q^{4} + 14 q^{7} - 24 q^{10} - 8 q^{16} + 102 q^{19} - 96 q^{22} - 2 q^{25} - 56 q^{28} - 42 q^{31} + 94 q^{37} + 48 q^{40} + 124 q^{43} + 24 q^{46} - 98 q^{49} + 12 q^{52} + 96 q^{58} - 288 q^{61} + 32 q^{64} + 62 q^{67} - 282 q^{73} - 82 q^{79} + 336 q^{82} - 96 q^{85} + 96 q^{88} + 42 q^{91} + 408 q^{94}+O(q^{100}) \) 4 * q - 4 * q^4 + 14 * q^7 - 24 * q^10 - 8 * q^16 + 102 * q^19 - 96 * q^22 - 2 * q^25 - 56 * q^28 - 42 * q^31 + 94 * q^37 + 48 * q^40 + 124 * q^43 + 24 * q^46 - 98 * q^49 + 12 * q^52 + 96 * q^58 - 288 * q^61 + 32 * q^64 + 62 * q^67 - 282 * q^73 - 82 * q^79 + 336 * q^82 - 96 * q^85 + 96 * q^88 + 42 * q^91 + 408 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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