LMFDB - Embedded newform 294.3.b.e.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,3,Mod(197,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("294.197");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	294.b (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:	$8.01091977219$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 11x^{2} - 10x + 3 $ x^4 - 2x^3 + 11x^2 - 10*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.1
Root			$0.500000 + 0.244099i$ of defining polynomial
Character	$\chi$	$=$	294.197
Dual form			294.3.b.e.197.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421i q^{2} +(-2.84521 - 0.951206i) q^{3} -2.00000 q^{4} +6.14505i q^{5} +(-1.34521 + 4.02373i) q^{6} +2.82843i q^{8} +(7.19042 + 5.41276i) q^{9} +O(q^{10})$	\(q-1.41421i q^{2} +(-2.84521 - 0.951206i) q^{3} -2.00000 q^{4} +6.14505i q^{5} +(-1.34521 + 4.02373i) q^{6} +2.82843i q^{8} +(7.19042 + 5.41276i) q^{9} +8.69042 q^{10} -17.9973i q^{11} +(5.69042 + 1.90241i) q^{12} -1.38083 q^{13} +(5.84521 - 17.4840i) q^{15} +4.00000 q^{16} -6.14505i q^{17} +(7.65479 - 10.1688i) q^{18} +15.0712 q^{19} -12.2901i q^{20} -25.4521 q^{22} -26.4826i q^{23} +(2.69042 - 8.04746i) q^{24} -12.7617 q^{25} +1.95279i q^{26} +(-15.3096 - 22.2400i) q^{27} -19.0241i q^{29} +(-24.7260 - 8.26637i) q^{30} -18.4521 q^{31} -5.65685i q^{32} +(-17.1192 + 51.2062i) q^{33} -8.69042 q^{34} +(-14.3808 - 10.8255i) q^{36} -1.00000 q^{37} -21.3140i q^{38} +(3.92875 + 1.31345i) q^{39} -17.3808 q^{40} -11.4145i q^{41} +54.1425 q^{43} +35.9947i q^{44} +(-33.2617 + 44.1855i) q^{45} -37.4521 q^{46} -53.6897i q^{47} +(-11.3808 - 3.80482i) q^{48} +18.0477i q^{50} +(-5.84521 + 17.4840i) q^{51} +2.76166 q^{52} -40.9618i q^{53} +(-31.4521 + 21.6510i) q^{54} +110.595 q^{55} +(-42.8808 - 14.3359i) q^{57} -26.9042 q^{58} -54.5654i q^{59} +(-11.6904 + 34.9679i) q^{60} +71.7617 q^{61} +26.0952i q^{62} -8.00000 q^{64} -8.48528i q^{65} +(72.4165 + 24.2102i) q^{66} +21.9754 q^{67} +12.2901i q^{68} +(-25.1904 + 75.3486i) q^{69} +109.433i q^{71} +(-15.3096 + 20.3376i) q^{72} +14.2383 q^{73} +1.41421i q^{74} +(36.3096 + 12.1390i) q^{75} -30.1425 q^{76} +(1.85751 - 5.55610i) q^{78} +92.7371 q^{79} +24.5802i q^{80} +(22.4042 + 77.8399i) q^{81} -16.1425 q^{82} -35.6924i q^{83} +37.7617 q^{85} -76.5691i q^{86} +(-18.0958 + 54.1276i) q^{87} +50.9042 q^{88} -160.360i q^{89} +(62.4877 + 47.0391i) q^{90} +52.9652i q^{92} +(52.5000 + 17.5517i) q^{93} -75.9288 q^{94} +92.6136i q^{95} +(-5.38083 + 16.0949i) q^{96} -118.904 q^{97} +(97.4152 - 129.408i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9	$ 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9} + 16 q^{10} + 4 q^{12} + 32 q^{13} + 14 q^{15} + 16 q^{16} + 40 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} + 24 q^{25} - 80 q^{27} - 52 q^{30} + 20 q^{31} - 106 q^{33} - 16 q^{34} - 20 q^{36} - 4 q^{37} + 72 q^{39} - 32 q^{40} + 104 q^{43} - 58 q^{45} - 56 q^{46} - 8 q^{48} - 14 q^{51} - 64 q^{52} - 32 q^{54} + 236 q^{55} - 134 q^{57} + 80 q^{58} - 28 q^{60} + 212 q^{61} - 32 q^{64} + 224 q^{66} - 156 q^{67} - 82 q^{69} - 80 q^{72} + 132 q^{73} + 164 q^{75} - 8 q^{76} + 120 q^{78} + 52 q^{79} - 98 q^{81} + 48 q^{82} + 76 q^{85} - 260 q^{87} + 16 q^{88} + 128 q^{90} + 210 q^{93} - 360 q^{94} + 16 q^{96} - 288 q^{97} - 70 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9 + 16 * q^10 + 4 * q^12 + 32 * q^13 + 14 * q^15 + 16 * q^16 + 40 * q^18 + 4 * q^19 - 8 * q^22 - 8 * q^24 + 24 * q^25 - 80 * q^27 - 52 * q^30 + 20 * q^31 - 106 * q^33 - 16 * q^34 - 20 * q^36 - 4 * q^37 + 72 * q^39 - 32 * q^40 + 104 * q^43 - 58 * q^45 - 56 * q^46 - 8 * q^48 - 14 * q^51 - 64 * q^52 - 32 * q^54 + 236 * q^55 - 134 * q^57 + 80 * q^58 - 28 * q^60 + 212 * q^61 - 32 * q^64 + 224 * q^66 - 156 * q^67 - 82 * q^69 - 80 * q^72 + 132 * q^73 + 164 * q^75 - 8 * q^76 + 120 * q^78 + 52 * q^79 - 98 * q^81 + 48 * q^82 + 76 * q^85 - 260 * q^87 + 16 * q^88 + 128 * q^90 + 210 * q^93 - 360 * q^94 + 16 * q^96 - 288 * q^97 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$	−2.84521	−	0.951206i	−0.948403	−	0.317069i
$3$	−2.84521	−	0.951206i	−0.948403	−	0.317069i
$4$	−2.00000			−0.500000
$5$			6.14505i			1.22901i	0.788913	+	0.614505i	$0.210644\pi$
$5$			6.14505i			1.22901i	−0.788913	+	0.614505i	$0.789356\pi$
$6$	−1.34521	+	4.02373i	−0.224201	+	0.670622i
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$	7.19042	+	5.41276i	0.798935	+	0.601417i
$10$	8.69042			0.869042
$11$		−	17.9973i		−	1.63612i	−0.575132	−	0.818061i	$-0.695049\pi$
$11$		−	17.9973i		−	1.63612i	0.575132	−	0.818061i	$-0.304951\pi$
$12$	5.69042	+	1.90241i	0.474201	+	0.158534i
$13$	−1.38083			−0.106218			−0.0531089	−	0.998589i	$-0.516913\pi$
$13$	−1.38083			−0.106218			−0.0531089	+	0.998589i	$0.516913\pi$
$14$		0			0
$15$	5.84521	−	17.4840i	0.389681	−	1.16560i
$16$	4.00000			0.250000
$17$		−	6.14505i		−	0.361474i	−0.983531	−	0.180737i	$-0.942152\pi$
$17$		−	6.14505i		−	0.361474i	0.983531	−	0.180737i	$-0.0578482\pi$
$18$	7.65479	−	10.1688i	0.425266	−	0.564932i
$19$	15.0712			0.793224			0.396612	−	0.917986i	$-0.370186\pi$
$19$	15.0712			0.793224			0.396612	+	0.917986i	$0.370186\pi$
$20$		−	12.2901i		−	0.614505i
$21$		0			0
$22$	−25.4521			−1.15691
$23$		−	26.4826i		−	1.15142i	−0.817655	−	0.575709i	$-0.804726\pi$
$23$		−	26.4826i		−	1.15142i	0.817655	−	0.575709i	$-0.195274\pi$
$24$	2.69042	−	8.04746i	0.112101	−	0.335311i
$25$	−12.7617			−0.510467
$26$			1.95279i			0.0751073i
$27$	−15.3096	−	22.2400i	−0.567022	−	0.823703i
$28$		0			0
$29$		−	19.0241i		−	0.656004i	−0.944677	−	0.328002i	$-0.893625\pi$
$29$		−	19.0241i		−	0.656004i	0.944677	−	0.328002i	$-0.106375\pi$
$30$	−24.7260	−	8.26637i	−0.824201	−	0.275546i
$31$	−18.4521			−0.595228			−0.297614	−	0.954686i	$-0.596191\pi$
$31$	−18.4521			−0.595228			−0.297614	+	0.954686i	$0.596191\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−17.1192	+	51.2062i	−0.518763	+	1.55170i
$34$	−8.69042			−0.255600
$35$		0			0
$36$	−14.3808	−	10.8255i	−0.399468	−	0.300709i
$37$	−1.00000			−0.0270270			−0.0135135	−	0.999909i	$-0.504302\pi$
$37$	−1.00000			−0.0270270			−0.0135135	+	0.999909i	$0.504302\pi$
$38$		−	21.3140i		−	0.560894i
$39$	3.92875	+	1.31345i	0.100737	+	0.0336783i
$40$	−17.3808			−0.434521
$41$		−	11.4145i		−	0.278402i	−0.990264	−	0.139201i	$-0.955547\pi$
$41$		−	11.4145i		−	0.278402i	0.990264	−	0.139201i	$-0.0444534\pi$
$42$		0			0
$43$	54.1425			1.25913			0.629564	−	0.776949i	$-0.283234\pi$
$43$	54.1425			1.25913			0.629564	+	0.776949i	$0.283234\pi$
$44$			35.9947i			0.818061i
$45$	−33.2617	+	44.1855i	−0.739148	+	0.981900i
$46$	−37.4521			−0.814176
$47$		−	53.6897i		−	1.14233i	−0.820834	−	0.571167i	$-0.806491\pi$
$47$		−	53.6897i		−	1.14233i	0.820834	−	0.571167i	$-0.193509\pi$
$48$	−11.3808	−	3.80482i	−0.237101	−	0.0792671i
$49$		0			0
$50$			18.0477i			0.360954i
$51$	−5.84521	+	17.4840i	−0.114612	+	0.342823i
$52$	2.76166			0.0531089
$53$		−	40.9618i		−	0.772864i	−0.922318	−	0.386432i	$-0.873707\pi$
$53$		−	40.9618i		−	0.772864i	0.922318	−	0.386432i	$-0.126293\pi$
$54$	−31.4521	+	21.6510i	−0.582446	+	0.400945i
$55$	110.595			2.01081
$56$		0			0
$57$	−42.8808	−	14.3359i	−0.752295	−	0.251506i
$58$	−26.9042			−0.463865
$59$		−	54.5654i		−	0.924837i	−0.886662	−	0.462418i	$-0.846982\pi$
$59$		−	54.5654i		−	0.924837i	0.886662	−	0.462418i	$-0.153018\pi$
$60$	−11.6904	+	34.9679i	−0.194840	+	0.582798i
$61$	71.7617			1.17642			0.588210	−	0.808708i	$-0.299833\pi$
$61$	71.7617			1.17642			0.588210	+	0.808708i	$0.299833\pi$
$62$			26.0952i			0.420890i
$63$		0			0
$64$	−8.00000			−0.125000
$65$		−	8.48528i		−	0.130543i
$66$	72.4165	+	24.2102i	1.09722	+	0.366821i
$67$	21.9754			0.327991			0.163996	−	0.986461i	$-0.447562\pi$
$67$	21.9754			0.327991			0.163996	+	0.986461i	$0.447562\pi$
$68$			12.2901i			0.180737i
$69$	−25.1904	+	75.3486i	−0.365078	+	1.09201i
$70$		0			0
$71$			109.433i			1.54131i	0.637252	+	0.770655i	$0.280071\pi$
$71$			109.433i			1.54131i	−0.637252	+	0.770655i	$0.719929\pi$
$72$	−15.3096	+	20.3376i	−0.212633	+	0.282466i
$73$	14.2383			0.195046			0.0975229	−	0.995233i	$-0.468908\pi$
$73$	14.2383			0.195046			0.0975229	+	0.995233i	$0.468908\pi$
$74$			1.41421i			0.0191110i
$75$	36.3096	+	12.1390i	0.484128	+	0.161853i
$76$	−30.1425			−0.396612
$77$		0			0
$78$	1.85751	−	5.55610i	0.0238142	−	0.0712320i
$79$	92.7371			1.17389			0.586943	−	0.809628i	$-0.300331\pi$
$79$	92.7371			1.17389			0.586943	+	0.809628i	$0.300331\pi$
$80$			24.5802i			0.307253i
$81$	22.4042	+	77.8399i	0.276595	+	0.960987i
$82$	−16.1425			−0.196860
$83$		−	35.6924i		−	0.430029i	−0.976611	−	0.215014i	$-0.931020\pi$
$83$		−	35.6924i		−	0.430029i	0.976611	−	0.215014i	$-0.0689799\pi$
$84$		0			0
$85$	37.7617			0.444255
$86$		−	76.5691i		−	0.890338i
$87$	−18.0958	+	54.1276i	−0.207998	+	0.622156i
$88$	50.9042			0.578456
$89$		−	160.360i		−	1.80180i	−0.434025	−	0.900901i	$-0.642907\pi$
$89$		−	160.360i		−	1.80180i	0.434025	−	0.900901i	$-0.357093\pi$
$90$	62.4877	+	47.0391i	0.694308	+	0.522657i
$91$		0			0
$92$			52.9652i			0.575709i
$93$	52.5000	+	17.5517i	0.564516	+	0.188728i
$94$	−75.9288			−0.807753
$95$			92.6136i			0.974880i
$96$	−5.38083	+	16.0949i	−0.0560503	+	0.167655i
$97$	−118.904			−1.22582			−0.612908	−	0.790154i	$-0.710000\pi$
$97$	−118.904			−1.22582			−0.612908	+	0.790154i	$0.710000\pi$
$98$		0			0
$99$	97.4152	−	129.408i	0.983992	−	1.30715i
$100$	25.5233			0.255233
$101$			31.9032i			0.315873i	0.987449	+	0.157936i	$0.0504841\pi$
$101$			31.9032i			0.315873i	−0.987449	+	0.157936i	$0.949516\pi$
$102$	24.7260	+	8.26637i	0.242412	+	0.0810429i
$103$	−187.499			−1.82038			−0.910188	−	0.414195i	$-0.864063\pi$
$103$	−187.499			−1.82038			−0.910188	+	0.414195i	$0.864063\pi$
$104$		−	3.90558i		−	0.0375537i
$105$		0			0
$106$	−57.9288			−0.546498
$107$			25.6070i			0.239318i	0.992815	+	0.119659i	$0.0381801\pi$
$107$			25.6070i			0.239318i	−0.992815	+	0.119659i	$0.961820\pi$
$108$	30.6192	+	44.4800i	0.283511	+	0.411851i
$109$	47.6192			0.436873			0.218437	−	0.975851i	$-0.429904\pi$
$109$	47.6192			0.436873			0.218437	+	0.975851i	$0.429904\pi$
$110$		−	156.404i		−	1.42186i
$111$	2.84521	+	0.951206i	0.0256325	+	0.00856942i
$112$		0			0
$113$			100.374i			0.888269i	0.895960	+	0.444134i	$0.146489\pi$
$113$			100.374i			0.888269i	−0.895960	+	0.444134i	$0.853511\pi$
$114$	−20.2740	+	60.6427i	−0.177842	+	0.531953i
$115$	162.737			1.41510
$116$			38.0482i			0.328002i
$117$	−9.92875	−	7.47410i	−0.0848611	−	0.0638812i
$118$	−77.1671			−0.653958
$119$		0			0
$120$	49.4521	+	16.5327i	0.412101	+	0.137773i
$121$	−202.904			−1.67689
$122$		−	101.486i		−	0.831855i
$123$	−10.8575	+	32.4765i	−0.0882724	+	0.264037i
$124$	36.9042			0.297614
$125$			75.2052i			0.601642i
$126$		0			0
$127$	−40.6192			−0.319836			−0.159918	−	0.987130i	$-0.551123\pi$
$127$	−40.6192			−0.319836			−0.159918	+	0.987130i	$0.551123\pi$
$128$			11.3137i			0.0883883i
$129$	−154.047	−	51.5006i	−1.19416	−	0.399230i
$130$	−12.0000			−0.0923077
$131$			64.5308i			0.492602i	0.969193	+	0.246301i	$0.0792152\pi$
$131$			64.5308i			0.492602i	−0.969193	+	0.246301i	$0.920785\pi$
$132$	34.2383	−	102.412i	0.259381	−	0.775851i
$133$		0			0
$134$		−	31.0779i		−	0.231925i
$135$	136.666	−	94.0782i	1.01234	−	0.696875i
$136$	17.3808			0.127800
$137$			59.4126i			0.433668i	0.976208	+	0.216834i	$0.0695731\pi$
$137$			59.4126i			0.433668i	−0.976208	+	0.216834i	$0.930427\pi$
$138$	106.559	+	35.6246i	0.772166	+	0.258149i
$139$	59.6658			0.429251			0.214625	−	0.976696i	$-0.431147\pi$
$139$	59.6658			0.429251			0.214625	+	0.976696i	$0.431147\pi$
$140$		0			0
$141$	−51.0700	+	152.758i	−0.362198	+	1.08339i
$142$	154.762			1.08987
$143$			24.8513i			0.173785i
$144$	28.7617	+	21.6510i	0.199734	+	0.150354i
$145$	116.904			0.806236
$146$		−	20.1360i		−	0.137918i
$147$		0			0
$148$	2.00000			0.0135135
$149$			1.46459i			0.00982948i	0.999988	+	0.00491474i	$0.00156442\pi$
$149$			1.46459i			0.00982948i	−0.999988	+	0.00491474i	$0.998436\pi$
$150$	17.1671	−	51.3495i	0.114447	−	0.342330i
$151$	171.975			1.13891			0.569455	−	0.822023i	$-0.307154\pi$
$151$	171.975			1.13891			0.569455	+	0.822023i	$0.307154\pi$
$152$			42.6279i			0.280447i
$153$	33.2617	−	44.1855i	0.217396	−	0.288794i
$154$		0			0
$155$		−	113.389i		−	0.731542i
$156$	−7.85751	−	2.62691i	−0.0503686	−	0.0168392i
$157$	1.00000			0.00636943			0.00318471	−	0.999995i	$-0.498986\pi$
$157$	1.00000			0.00636943			0.00318471	+	0.999995i	$0.498986\pi$
$158$		−	131.150i		−	0.830063i
$159$	−38.9631	+	116.545i	−0.245051	+	0.732987i
$160$	34.7617			0.217260
$161$		0			0
$162$	110.082	−	31.6843i	0.679520	−	0.195582i
$163$	−249.926			−1.53329			−0.766645	−	0.642071i	$-0.778075\pi$
$163$	−249.926			−1.53329			−0.766645	+	0.642071i	$0.778075\pi$
$164$			22.8289i			0.139201i
$165$	−314.665	−	105.198i	−1.90706	−	0.637565i
$166$	−50.4767			−0.304076
$167$			26.9048i			0.161107i	0.996750	+	0.0805534i	$0.0256688\pi$
$167$			26.9048i			0.161107i	−0.996750	+	0.0805534i	$0.974331\pi$
$168$		0			0
$169$	−167.093			−0.988718
$170$		−	53.4031i		−	0.314136i
$171$	108.369	+	81.5770i	0.633734	+	0.477058i
$172$	−108.285			−0.629564
$173$			91.3001i			0.527746i	0.964557	+	0.263873i	$0.0850001\pi$
$173$			91.3001i			0.527746i	−0.964557	+	0.263873i	$0.915000\pi$
$174$	76.5479	+	25.5914i	0.439931	+	0.147077i
$175$		0			0
$176$		−	71.9894i		−	0.409030i
$177$	−51.9029	+	155.250i	−0.293237	+	0.877118i
$178$	−226.784			−1.27407
$179$		−	241.575i		−	1.34958i	−0.738009	−	0.674791i	$-0.764234\pi$
$179$		−	241.575i		−	1.34958i	0.738009	−	0.674791i	$-0.235766\pi$
$180$	66.5233	−	88.3710i	0.369574	−	0.490950i
$181$	19.9067			0.109982			0.0549909	−	0.998487i	$-0.482487\pi$
$181$	19.9067			0.109982			0.0549909	+	0.998487i	$0.482487\pi$
$182$		0			0
$183$	−204.177	−	68.2601i	−1.11572	−	0.373006i
$184$	74.9042			0.407088
$185$		−	6.14505i		−	0.0332165i
$186$	24.8219	−	74.2462i	0.133451	−	0.399173i
$187$	−110.595			−0.591415
$188$			107.379i			0.571167i
$189$		0			0
$190$	130.975			0.689344
$191$			99.3476i			0.520145i	0.965589	+	0.260072i	$0.0837464\pi$
$191$			99.3476i			0.520145i	−0.965589	+	0.260072i	$0.916254\pi$
$192$	22.7617	+	7.60964i	0.118550	+	0.0396336i
$193$	−384.852			−1.99405			−0.997027	−	0.0770527i	$-0.975449\pi$
$193$	−384.852			−1.99405			−0.997027	+	0.0770527i	$0.975449\pi$
$194$			168.156i			0.866783i
$195$	−8.07125	+	24.1424i	−0.0413910	+	0.123807i
$196$		0			0
$197$		−	105.628i		−	0.536184i	−0.963393	−	0.268092i	$-0.913607\pi$
$197$		−	105.628i		−	0.536184i	0.963393	−	0.268092i	$-0.0863931\pi$
$198$	−183.011	−	137.766i	−0.924298	−	0.695787i
$199$	−41.2137			−0.207104			−0.103552	−	0.994624i	$-0.533021\pi$
$199$	−41.2137			−0.207104			−0.103552	+	0.994624i	$0.533021\pi$
$200$		−	36.0954i		−	0.180477i
$201$	−62.5246	−	20.9031i	−0.311068	−	0.103996i
$202$	45.1179			0.223356
$203$		0			0
$204$	11.6904	−	34.9679i	0.0573060	−	0.171411i
$205$	70.1425			0.342159
$206$			265.163i			1.28720i
$207$	143.344	−	190.421i	0.692483	−	0.919908i
$208$	−5.52333			−0.0265545
$209$		−	271.242i		−	1.29781i
$210$		0			0
$211$	249.858			1.18416			0.592079	−	0.805880i	$-0.298307\pi$
$211$	249.858			1.18416			0.592079	+	0.805880i	$0.298307\pi$
$212$			81.9236i			0.386432i
$213$	104.093	−	311.360i	0.488701	−	1.46178i
$214$	36.2137			0.169223
$215$			332.708i			1.54748i
$216$	62.9042	−	43.3020i	0.291223	−	0.200472i
$217$		0			0
$218$		−	67.3437i		−	0.308916i
$219$	−40.5110	−	13.5436i	−0.184982	−	0.0618429i
$220$	−221.189			−1.00541
$221$			8.48528i			0.0383949i
$222$	1.34521	−	4.02373i	0.00605949	−	0.0181249i
$223$	−170.427			−0.764249			−0.382124	−	0.924111i	$-0.624807\pi$
$223$	−170.427			−0.764249			−0.382124	+	0.924111i	$0.624807\pi$
$224$		0			0
$225$	−91.7617	−	69.0758i	−0.407830	−	0.307003i
$226$	141.951			0.628101
$227$		−	343.096i		−	1.51144i	−0.654897	−	0.755718i	$-0.727288\pi$
$227$		−	343.096i		−	1.51144i	0.654897	−	0.755718i	$-0.272712\pi$
$228$	85.7617	+	28.6717i	0.376148	+	0.125753i
$229$	269.806			1.17819			0.589096	−	0.808063i	$-0.299484\pi$
$229$	269.806			1.17819			0.589096	+	0.808063i	$0.299484\pi$
$230$		−	230.145i		−	1.00063i
$231$		0			0
$232$	53.8083			0.231932
$233$		−	313.971i		−	1.34752i	−0.738952	−	0.673758i	$-0.764679\pi$
$233$		−	313.971i		−	1.34752i	0.738952	−	0.673758i	$-0.235321\pi$
$234$	−10.5700	+	14.0414i	−0.0451708	+	0.0600059i
$235$	329.926			1.40394
$236$			109.131i			0.462418i
$237$	−263.856	−	88.2120i	−1.11332	−	0.372203i
$238$		0			0
$239$		−	59.6992i		−	0.249788i	−0.992170	−	0.124894i	$-0.960141\pi$
$239$		−	59.6992i		−	0.249788i	0.992170	−	0.124894i	$-0.0398590\pi$
$240$	23.3808	−	69.9358i	0.0974201	−	0.291399i
$241$	309.285			1.28334			0.641670	−	0.766981i	$-0.278242\pi$
$241$	309.285			1.28334			0.641670	+	0.766981i	$0.278242\pi$
$242$			286.950i			1.18574i
$243$	10.2973	−	242.782i	0.0423757	−	0.999102i
$244$	−143.523			−0.588210
$245$		0			0
$246$	45.9288	+	15.3548i	0.186702	+	0.0624180i
$247$	−20.8109			−0.0842545
$248$		−	52.1904i		−	0.210445i
$249$	−33.9508	+	101.552i	−0.136349	+	0.407841i
$250$	106.356			0.425425
$251$			70.2069i			0.279709i	0.990172	+	0.139854i	$0.0446634\pi$
$251$			70.2069i			0.279709i	−0.990172	+	0.139854i	$0.955337\pi$
$252$		0			0
$253$	−476.617			−1.88386
$254$			57.4442i			0.226158i
$255$	−107.440	−	35.9191i	−0.421332	−	0.140859i
$256$	16.0000			0.0625000
$257$		−	69.9514i		−	0.272184i	−0.990696	−	0.136092i	$-0.956546\pi$
$257$		−	69.9514i		−	0.272184i	0.990696	−	0.136092i	$-0.0434543\pi$
$258$	−72.8329	+	217.855i	−0.282298	+	0.844399i
$259$		0			0
$260$			16.9706i			0.0652714i
$261$	102.973	−	136.791i	0.394532	−	0.524105i
$262$	91.2604			0.348322
$263$		−	130.964i		−	0.497962i	−0.968508	−	0.248981i	$-0.919904\pi$
$263$		−	130.964i		−	0.497962i	0.968508	−	0.248981i	$-0.0800957\pi$
$264$	−144.833	−	48.4203i	−0.548610	−	0.183410i
$265$	251.712			0.949858
$266$		0			0
$267$	−152.536	+	456.258i	−0.571294	+	1.70883i
$268$	−43.9508			−0.163996
$269$			348.788i			1.29661i	0.761381	+	0.648304i	$0.224522\pi$
$269$			348.788i			1.29661i	−0.761381	+	0.648304i	$0.775478\pi$
$270$	−133.047	−	193.275i	−0.492765	−	0.715832i
$271$	−77.0221			−0.284214			−0.142107	−	0.989851i	$-0.545388\pi$
$271$	−77.0221			−0.284214			−0.142107	+	0.989851i	$0.545388\pi$
$272$		−	24.5802i		−	0.0903684i
$273$		0			0
$274$	84.0221			0.306650
$275$			229.676i			0.835185i
$276$	50.3808	−	150.697i	0.182539	−	0.546004i
$277$	7.28499			0.0262996			0.0131498	−	0.999914i	$-0.495814\pi$
$277$	7.28499			0.0262996			0.0131498	+	0.999914i	$0.495814\pi$
$278$		−	84.3802i		−	0.303526i
$279$	−132.678	−	99.8766i	−0.475549	−	0.357981i
$280$		0			0
$281$		−	167.048i		−	0.594475i	−0.954804	−	0.297238i	$-0.903935\pi$
$281$		−	167.048i		−	0.594475i	0.954804	−	0.297238i	$-0.0960653\pi$
$282$	216.033	+	72.2239i	0.766075	+	0.256113i
$283$	121.450			0.429150			0.214575	−	0.976707i	$-0.431163\pi$
$283$	121.450			0.429150			0.214575	+	0.976707i	$0.431163\pi$
$284$		−	218.866i		−	0.770655i
$285$	88.0946	−	263.505i	0.309104	−	0.924579i
$286$	35.1450			0.122885
$287$		0			0
$288$	30.6192	−	40.6751i	0.106317	−	0.141233i
$289$	251.238			0.869337
$290$		−	165.327i		−	0.570095i
$291$	338.307	+	113.102i	1.16257	+	0.388668i
$292$	−28.4767			−0.0975229
$293$			477.594i			1.63001i	0.579451	+	0.815007i	$0.303267\pi$
$293$			477.594i			1.63001i	−0.579451	+	0.815007i	$0.696733\pi$
$294$		0			0
$295$	335.307			1.13663
$296$		−	2.82843i		−	0.00955550i
$297$	−400.260	+	275.532i	−1.34768	+	0.927716i
$298$	2.07125			0.00695049
$299$			36.5680i			0.122301i
$300$	−72.6192	−	24.2779i	−0.242064	−	0.0809264i
$301$		0			0
$302$		−	243.210i		−	0.805331i
$303$	30.3465	−	90.7712i	0.100153	−	0.299575i
$304$	60.2850			0.198306
$305$			440.979i			1.44583i
$306$	−62.4877	−	47.0391i	−0.204208	−	0.153723i
$307$	123.381			0.401892			0.200946	−	0.979602i	$-0.435598\pi$
$307$	123.381			0.401892			0.200946	+	0.979602i	$0.435598\pi$
$308$		0			0
$309$	533.473	+	178.350i	1.72645	+	0.577184i
$310$	−160.356			−0.517278
$311$			398.386i			1.28098i	0.767965	+	0.640492i	$0.221270\pi$
$311$			398.386i			1.28098i	−0.767965	+	0.640492i	$0.778730\pi$
$312$	−3.71501	+	11.1122i	−0.0119071	+	0.0356160i
$313$	53.0984			0.169643			0.0848217	−	0.996396i	$-0.472968\pi$
$313$	53.0984			0.169643			0.0848217	+	0.996396i	$0.472968\pi$
$314$		−	1.41421i		−	0.00450386i
$315$		0			0
$316$	−185.474			−0.586943
$317$			369.261i			1.16486i	0.812881	+	0.582430i	$0.197898\pi$
$317$			369.261i			1.16486i	−0.812881	+	0.582430i	$0.802102\pi$
$318$	164.819	+	55.1022i	0.518300	+	0.173277i
$319$	−342.383			−1.07330
$320$		−	49.1604i		−	0.153626i
$321$	24.3575	−	72.8572i	0.0758801	−	0.226969i
$322$		0			0
$323$		−	92.6136i		−	0.286729i
$324$	−44.8083	−	155.680i	−0.138297	−	0.480493i
$325$	17.6217			0.0542206
$326$			353.449i			1.08420i
$327$	−135.486	−	45.2956i	−0.414332	−	0.138519i
$328$	32.2850			0.0984298
$329$		0			0
$330$	−148.773	+	445.003i	−0.450826	+	1.34849i
$331$	−136.501			−0.412391			−0.206195	−	0.978511i	$-0.566108\pi$
$331$	−136.501			−0.412391			−0.206195	+	0.978511i	$0.566108\pi$
$332$			71.3848i			0.215014i
$333$	−7.19042	−	5.41276i	−0.0215928	−	0.0162545i
$334$	38.0492			0.113920
$335$			135.040i			0.403104i
$336$		0			0
$337$	157.381			0.467005			0.233503	−	0.972356i	$-0.424981\pi$
$337$	157.381			0.467005			0.233503	+	0.972356i	$0.424981\pi$
$338$			236.306i			0.699129i
$339$	95.4767	−	285.586i	0.281642	−	0.842437i
$340$	−75.5233			−0.222127
$341$			332.088i			0.973866i
$342$	115.367	−	153.256i	0.337331	−	0.448118i
$343$		0			0
$344$			153.138i			0.445169i
$345$	−463.021	−	154.796i	−1.34209	−	0.448685i
$346$	129.118			0.373173
$347$			267.635i			0.771284i	0.922649	+	0.385642i	$0.126020\pi$
$347$			267.635i			0.771284i	−0.922649	+	0.385642i	$0.873980\pi$
$348$	36.1917	−	108.255i	0.103999	−	0.311078i
$349$	190.236			0.545088			0.272544	−	0.962143i	$-0.412135\pi$
$349$	190.236			0.545088			0.272544	+	0.962143i	$0.412135\pi$
$350$		0			0
$351$	21.1400	+	30.7097i	0.0602278	+	0.0874919i
$352$	−101.808			−0.289228
$353$		−	105.613i		−	0.299186i	−0.988748	−	0.149593i	$-0.952204\pi$
$353$		−	105.613i		−	0.299186i	0.988748	−	0.149593i	$-0.0477963\pi$
$354$	219.556	+	73.4018i	0.620216	+	0.207350i
$355$	−672.472			−1.89429
$356$			320.721i			0.900901i
$357$		0			0
$358$	−341.639			−0.954298
$359$		−	389.296i		−	1.08439i	−0.840253	−	0.542195i	$-0.817593\pi$
$359$		−	389.296i		−	1.08439i	0.840253	−	0.542195i	$-0.182407\pi$
$360$	−124.975	−	94.0782i	−0.347154	−	0.261328i
$361$	−133.858			−0.370796
$362$		−	28.1523i		−	0.0777688i
$363$	577.305	+	193.004i	1.59037	+	0.531690i
$364$		0			0
$365$			87.4953i			0.239713i
$366$	−96.5344	+	288.750i	−0.263755	+	0.788934i
$367$	−367.499			−1.00136			−0.500679	−	0.865633i	$-0.666916\pi$
$367$	−367.499			−1.00136			−0.500679	+	0.865633i	$0.666916\pi$
$368$		−	105.930i		−	0.287855i
$369$	61.7837	−	82.0748i	0.167436	−	0.222425i
$370$	−8.69042			−0.0234876
$371$		0			0
$372$	−105.000	−	35.1034i	−0.282258	−	0.0943641i
$373$	229.477			0.615219			0.307609	−	0.951513i	$-0.400471\pi$
$373$	229.477			0.615219			0.307609	+	0.951513i	$0.400471\pi$
$374$			156.404i			0.418193i
$375$	71.5356	−	213.974i	0.190762	−	0.570599i
$376$	151.858			0.403876
$377$			26.2691i			0.0696793i
$378$		0			0
$379$	368.899			0.973348			0.486674	−	0.873584i	$-0.338210\pi$
$379$	368.899			0.973348			0.486674	+	0.873584i	$0.338210\pi$
$380$		−	185.227i		−	0.487440i
$381$	115.570	+	38.6372i	0.303333	+	0.101410i
$382$	140.499			0.367798
$383$		−	612.634i		−	1.59957i	−0.600289	−	0.799783i	$-0.704948\pi$
$383$		−	612.634i		−	1.59957i	0.600289	−	0.799783i	$-0.295052\pi$
$384$	10.7617	−	32.1899i	0.0280252	−	0.0838277i
$385$		0			0
$386$			544.264i			1.41001i
$387$	389.307	+	293.060i	1.00596	+	0.757261i
$388$	237.808			0.612908
$389$			263.059i			0.676245i	0.941102	+	0.338123i	$0.109792\pi$
$389$			263.059i			0.676245i	−0.941102	+	0.338123i	$0.890208\pi$
$390$	34.1425	+	11.4145i	0.0875449	+	0.0292679i
$391$	−162.737			−0.416207
$392$		0			0
$393$	61.3821	−	183.604i	0.156189	−	0.467185i
$394$	−149.381			−0.379139
$395$			569.874i			1.44272i
$396$	−194.830	+	258.817i	−0.491996	+	0.653577i
$397$	603.329			1.51972			0.759860	−	0.650086i	$-0.225267\pi$
$397$	603.329			1.51972			0.759860	+	0.650086i	$0.225267\pi$
$398$			58.2850i			0.146445i
$399$		0			0
$400$	−51.0467			−0.127617
$401$			682.705i			1.70251i	0.524755	+	0.851254i	$0.324157\pi$
$401$			682.705i			1.70251i	−0.524755	+	0.851254i	$0.675843\pi$
$402$	−29.5615	+	88.4231i	−0.0735360	+	0.219958i
$403$	25.4792			0.0632239
$404$		−	63.8063i		−	0.157936i
$405$	−478.330	+	137.675i	−1.18106	+	0.339938i
$406$		0			0
$407$			17.9973i			0.0442195i
$408$	−49.4521	−	16.5327i	−0.121206	−	0.0405214i
$409$	−614.567			−1.50261			−0.751305	−	0.659955i	$-0.770575\pi$
$409$	−614.567			−1.50261			−0.751305	+	0.659955i	$0.770575\pi$
$410$		−	99.1965i		−	0.241943i
$411$	56.5136	−	169.041i	0.137503	−	0.411292i
$412$	374.997			0.910188
$413$		0			0
$414$	−269.296	−	202.719i	−0.650473	−	0.489659i
$415$	219.332			0.528510
$416$			7.81116i			0.0187768i
$417$	−169.762	−	56.7545i	−0.407102	−	0.136102i
$418$	−383.595			−0.917690
$419$		−	775.997i		−	1.85202i	−0.377498	−	0.926010i	$-0.623216\pi$
$419$		−	775.997i		−	1.85202i	0.377498	−	0.926010i	$-0.376784\pi$
$420$		0			0
$421$	−161.194			−0.382884			−0.191442	−	0.981504i	$-0.561316\pi$
$421$	−161.194			−0.382884			−0.191442	+	0.981504i	$0.561316\pi$
$422$		−	353.352i		−	0.837327i
$423$	290.609	−	386.052i	0.687020	−	0.912651i
$424$	115.858			0.273249
$425$			78.4211i			0.184520i
$426$	−440.329	−	147.210i	−1.03364	−	0.345564i
$427$		0			0
$428$		−	51.2140i		−	0.119659i
$429$	23.6387	−	70.7071i	0.0551018	−	0.164818i
$430$	470.521			1.09423
$431$			478.256i			1.10964i	0.831969	+	0.554821i	$0.187213\pi$
$431$			478.256i			1.10964i	−0.831969	+	0.554821i	$0.812787\pi$
$432$	−61.2383	−	88.9599i	−0.141755	−	0.205926i
$433$	97.5674			0.225329			0.112664	−	0.993633i	$-0.464061\pi$
$433$	97.5674			0.225329			0.112664	+	0.993633i	$0.464061\pi$
$434$		0			0
$435$	−332.617	−	111.200i	−0.764636	−	0.255632i
$436$	−95.2383			−0.218437
$437$		−	399.126i		−	0.913332i
$438$	−19.1535	+	57.2912i	−0.0437295	+	0.130802i
$439$	236.113			0.537842			0.268921	−	0.963162i	$-0.413333\pi$
$439$	236.113			0.537842			0.268921	+	0.963162i	$0.413333\pi$
$440$			312.809i			0.710929i
$441$		0			0
$442$	12.0000			0.0271493
$443$		−	461.952i		−	1.04278i	−0.853318	−	0.521391i	$-0.825413\pi$
$443$		−	461.952i		−	1.04278i	0.853318	−	0.521391i	$-0.174587\pi$
$444$	−5.69042	−	1.90241i	−0.0128163	−	0.00428471i
$445$	985.422			2.21443
$446$			241.021i			0.540406i
$447$	1.39313	−	4.16707i	0.00311662	−	0.00932231i
$448$		0			0
$449$			296.954i			0.661367i	0.943742	+	0.330683i	$0.107279\pi$
$449$			296.954i			0.661367i	−0.943742	+	0.330683i	$0.892721\pi$
$450$	−97.6879	+	129.771i	−0.217084	+	0.288379i
$451$	−205.430			−0.455499
$452$		−	200.749i		−	0.444134i
$453$	−489.306	−	163.584i	−1.08015	−	0.361113i
$454$	−485.211			−1.06875
$455$		0			0
$456$	40.5479	−	121.285i	0.0889209	−	0.265977i
$457$	−363.093			−0.794515			−0.397257	−	0.917707i	$-0.630038\pi$
$457$	−363.093			−0.794515			−0.397257	+	0.917707i	$0.630038\pi$
$458$		−	381.563i		−	0.833107i
$459$	−136.666	+	94.0782i	−0.297747	+	0.204963i
$460$	−325.474			−0.707552
$461$		−	616.559i		−	1.33744i	−0.743515	−	0.668719i	$-0.766843\pi$
$461$		−	616.559i		−	1.33744i	0.743515	−	0.668719i	$-0.233157\pi$
$462$		0			0
$463$	352.049			0.760365			0.380183	−	0.924911i	$-0.375861\pi$
$463$	352.049			0.760365			0.380183	+	0.924911i	$0.375861\pi$
$464$		−	76.0964i		−	0.164001i
$465$	−107.856	+	322.615i	−0.231949	+	0.693796i
$466$	−444.022			−0.952837
$467$			519.296i			1.11198i	0.831188	+	0.555991i	$0.187661\pi$
$467$			519.296i			1.11198i	−0.831188	+	0.555991i	$0.812339\pi$
$468$	19.8575	+	14.9482i	0.0424306	+	0.0319406i
$469$		0			0
$470$		−	466.586i		−	0.992736i
$471$	−2.84521	−	0.951206i	−0.00604078	−	0.00201954i
$472$	154.334			0.326979
$473$		−	974.421i		−	2.06009i
$474$	−124.751	+	373.149i	−0.263187	+	0.787234i
$475$	−192.334			−0.404914
$476$		0			0
$477$	221.716	−	294.532i	0.464814	−	0.617468i
$478$	−84.4275			−0.176627
$479$		−	238.281i		−	0.497455i	−0.968573	−	0.248728i	$-0.919988\pi$
$479$		−	238.281i		−	0.497455i	0.968573	−	0.248728i	$-0.0800124\pi$
$480$	−98.9042	−	33.0655i	−0.206050	−	0.0688864i
$481$	1.38083			0.00287075
$482$		−	437.395i		−	0.907459i
$483$		0			0
$484$	405.808			0.838447
$485$		−	730.672i		−	1.50654i
$486$	−343.345	−	14.5626i	−0.706472	−	0.0299641i
$487$	−298.781			−0.613514			−0.306757	−	0.951788i	$-0.599244\pi$
$487$	−298.781			−0.613514			−0.306757	+	0.951788i	$0.599244\pi$
$488$			202.973i			0.415928i
$489$	711.092	+	237.731i	1.45418	+	0.486158i
$490$		0			0
$491$		−	474.060i		−	0.965499i	−0.875758	−	0.482750i	$-0.839638\pi$
$491$		−	474.060i		−	0.965499i	0.875758	−	0.482750i	$-0.160362\pi$
$492$	21.7150	−	64.9531i	0.0441362	−	0.132018i
$493$	−116.904			−0.237128
$494$			29.4310i			0.0595769i
$495$	795.221	+	598.621i	1.60651	+	1.20934i
$496$	−73.8083			−0.148807
$497$		0			0
$498$	143.617	+	48.0137i	0.288387	+	0.0964130i
$499$	478.830			0.959580			0.479790	−	0.877383i	$-0.340713\pi$
$499$	478.830			0.959580			0.479790	+	0.877383i	$0.340713\pi$
$500$		−	150.410i		−	0.300821i
$501$	25.5920	−	76.5499i	0.0510819	−	0.152794i
$502$	99.2875			0.197784
$503$			879.634i			1.74877i	0.485229	+	0.874387i	$0.338736\pi$
$503$			879.634i			1.74877i	−0.485229	+	0.874387i	$0.661264\pi$
$504$		0			0
$505$	−196.047			−0.388211
$506$			674.038i			1.33209i
$507$	475.415	+	158.940i	0.937703	+	0.313491i
$508$	81.2383			0.159918
$509$		−	419.266i		−	0.823705i	−0.911251	−	0.411852i	$-0.864882\pi$
$509$		−	419.266i		−	0.823705i	0.911251	−	0.411852i	$-0.135118\pi$
$510$	−50.7973	+	151.943i	−0.0996025	+	0.297927i
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$	−230.735	−	335.184i	−0.449775	−	0.653381i
$514$	−98.9262			−0.192463
$515$		−	1152.19i		−	2.23726i
$516$	308.093	+	103.001i	0.597080	+	0.199615i
$517$	−966.272			−1.86900
$518$		0			0
$519$	86.8452	−	259.768i	0.167332	−	0.500516i
$520$	24.0000			0.0461538
$521$			33.8943i			0.0650563i	0.999471	+	0.0325282i	$0.0103559\pi$
$521$			33.8943i			0.0650563i	−0.999471	+	0.0325282i	$0.989644\pi$
$522$	−193.452	−	145.626i	−0.370598	−	0.278976i
$523$	501.351			0.958606			0.479303	−	0.877649i	$-0.340889\pi$
$523$	501.351			0.958606			0.479303	+	0.877649i	$0.340889\pi$
$524$		−	129.062i		−	0.246301i
$525$		0			0
$526$	−185.211			−0.352113
$527$			113.389i			0.215159i
$528$	−68.4767	+	204.825i	−0.129691	+	0.387926i
$529$	−172.329			−0.325764
$530$		−	355.975i		−	0.671651i
$531$	295.349	−	392.348i	0.556213	−	0.738885i
$532$		0			0
$533$			15.7615i			0.0295712i
$534$	645.247	+	215.718i	1.20833	+	0.403966i
$535$	−157.356			−0.294124
$536$			62.1558i			0.115962i
$537$	−229.788	+	687.331i	−0.427910	+	1.27995i
$538$	493.260			0.916841
$539$		0			0
$540$	−273.332	+	188.156i	−0.506170	+	0.348438i
$541$	929.516			1.71814			0.859072	−	0.511855i	$-0.171042\pi$
$541$	929.516			1.71814			0.859072	+	0.511855i	$0.171042\pi$
$542$			108.926i			0.200970i
$543$	−56.6387	−	18.9354i	−0.104307	−	0.0348718i
$544$	−34.7617			−0.0639001
$545$			292.622i			0.536922i
$546$		0			0
$547$	−905.754			−1.65586			−0.827929	−	0.560833i	$-0.810481\pi$
$547$	−905.754			−1.65586			−0.827929	+	0.560833i	$0.810481\pi$
$548$		−	118.825i		−	0.216834i
$549$	515.996	+	388.428i	0.939884	+	0.707520i
$550$	324.811			0.590565
$551$		−	286.717i		−	0.520358i
$552$	−213.118	−	71.2493i	−0.386083	−	0.129075i
$553$		0			0
$554$		−	10.3025i		−	0.0185966i
$555$	−5.84521	+	17.4840i	−0.0105319	+	0.0315026i
$556$	−119.332			−0.214625
$557$		−	423.435i		−	0.760207i	−0.924944	−	0.380103i	$-0.875888\pi$
$557$		−	423.435i		−	0.760207i	0.924944	−	0.380103i	$-0.124112\pi$
$558$	−141.247	+	187.635i	−0.253131	+	0.336264i
$559$	−74.7617			−0.133742
$560$		0			0
$561$	314.665	+	105.198i	0.560899	+	0.187519i
$562$	−236.241			−0.420357
$563$		−	647.388i		−	1.14989i	−0.818192	−	0.574945i	$-0.805023\pi$
$563$		−	647.388i		−	1.14989i	0.818192	−	0.574945i	$-0.194977\pi$
$564$	102.140	−	305.517i	0.181099	−	0.541697i
$565$	−616.806			−1.09169
$566$		−	171.756i		−	0.303455i
$567$		0			0
$568$	−309.523			−0.544935
$569$			653.716i			1.14889i	0.818545	+	0.574443i	$0.194781\pi$
$569$			653.716i			1.14889i	−0.818545	+	0.574443i	$0.805219\pi$
$570$	−372.652	−	124.585i	−0.653776	−	0.218569i
$571$	−577.833			−1.01197			−0.505983	−	0.862543i	$-0.668870\pi$
$571$	−577.833			−1.01197			−0.505983	+	0.862543i	$0.668870\pi$
$572$		−	49.7026i		−	0.0868926i
$573$	94.5000	−	282.665i	0.164921	−	0.493306i
$574$		0			0
$575$			337.962i			0.587760i
$576$	−57.5233	−	43.3020i	−0.0998669	−	0.0751772i
$577$	932.518			1.61615			0.808075	−	0.589080i	$-0.200510\pi$
$577$	932.518			1.61615			0.808075	+	0.589080i	$0.200510\pi$
$578$		−	355.305i		−	0.614714i
$579$	1094.99	+	366.074i	1.89117	+	0.632252i
$580$	−233.808			−0.403118
$581$		0			0
$582$	159.951	−	478.438i	0.274830	−	0.822059i
$583$	−737.204			−1.26450
$584$			40.2721i			0.0689591i
$585$	45.9288	−	61.0127i	0.0785107	−	0.104295i
$586$	675.420			1.15259
$587$		−	170.852i		−	0.291060i	−0.989354	−	0.145530i	$-0.953511\pi$
$587$		−	170.852i		−	0.291060i	0.989354	−	0.145530i	$-0.0464888\pi$
$588$		0			0
$589$	−278.096			−0.472149
$590$		−	474.196i		−	0.803722i
$591$	−100.474	+	300.534i	−0.170007	+	0.508518i
$592$	−4.00000			−0.00675676
$593$			153.084i			0.258152i	0.991635	+	0.129076i	$0.0412011\pi$
$593$			153.084i			0.258152i	−0.991635	+	0.129076i	$0.958799\pi$
$594$	389.661	+	566.054i	0.655995	+	0.952952i
$595$		0			0
$596$		−	2.92919i		−	0.00491474i
$597$	117.262	+	39.2027i	0.196418	+	0.0656662i
$598$	51.7150			0.0864800
$599$			720.587i			1.20298i	0.798879	+	0.601491i	$0.205427\pi$
$599$			720.587i			1.20298i	−0.798879	+	0.601491i	$0.794573\pi$
$600$	−34.3342	+	102.699i	−0.0572236	+	0.171165i
$601$	110.422			0.183731			0.0918656	−	0.995771i	$-0.470717\pi$
$601$	110.422			0.183731			0.0918656	+	0.995771i	$0.470717\pi$
$602$		0			0
$603$	158.012	+	118.947i	0.262044	+	0.197260i
$604$	−343.951			−0.569455
$605$		−	1246.86i		−	2.06092i
$606$	−128.370	−	42.9164i	−0.211831	−	0.0708191i
$607$	−358.167			−0.590061			−0.295031	−	0.955488i	$-0.595330\pi$
$607$	−358.167			−0.590061			−0.295031	+	0.955488i	$0.595330\pi$
$608$		−	85.2558i		−	0.140223i
$609$		0			0
$610$	623.639			1.02236
$611$			74.1365i			0.121336i
$612$	−66.5233	+	88.3710i	−0.108698	+	0.144397i
$613$	158.951			0.259300			0.129650	−	0.991560i	$-0.458615\pi$
$613$	158.951			0.259300			0.129650	+	0.991560i	$0.458615\pi$
$614$		−	174.487i		−	0.284181i
$615$	−199.570	−	66.7199i	−0.324504	−	0.108488i
$616$		0			0
$617$			382.473i			0.619892i	0.950754	+	0.309946i	$0.100311\pi$
$617$			382.473i			0.619892i	−0.950754	+	0.309946i	$0.899689\pi$
$618$	252.225	−	754.445i	0.408131	−	1.22078i
$619$	−1024.26			−1.65469			−0.827347	−	0.561691i	$-0.810151\pi$
$619$	−1024.26			−1.65469			−0.827347	+	0.561691i	$0.810151\pi$
$620$			226.778i			0.365771i
$621$	−588.973	+	405.438i	−0.948427	+	0.652879i
$622$	563.403			0.905792
$623$		0			0
$624$	15.7150	+	5.25382i	0.0251843	+	0.00841958i
$625$	−781.182			−1.24989
$626$		−	75.0924i		−	0.119956i
$627$	−258.007	+	771.741i	−0.411495	+	1.23085i
$628$	−2.00000			−0.00318471
$629$			6.14505i			0.00976956i
$630$		0			0
$631$	−75.8524			−0.120210			−0.0601049	−	0.998192i	$-0.519144\pi$
$631$	−75.8524			−0.120210			−0.0601049	+	0.998192i	$0.519144\pi$
$632$			262.300i			0.415032i
$633$	−710.897	−	237.666i	−1.12306	−	0.375459i
$634$	522.214			0.823681
$635$		−	249.607i		−	0.393082i
$636$	77.9262	−	233.090i	0.122525	−	0.366493i
$637$		0			0
$638$			484.203i			0.758939i
$639$	−592.334	+	786.869i	−0.926971	+	1.23141i
$640$	−69.5233			−0.108630
$641$		−	36.7923i		−	0.0573983i	−0.999588	−	0.0286992i	$-0.990864\pi$
$641$		−	36.7923i		−	0.0573983i	0.999588	−	0.0286992i	$-0.00913648\pi$
$642$	−103.036	−	34.4467i	−0.160492	−	0.0536553i
$643$	105.277			0.163728			0.0818642	−	0.996643i	$-0.473913\pi$
$643$	105.277			0.163728			0.0818642	+	0.996643i	$0.473913\pi$
$644$		0			0
$645$	316.474	−	946.625i	0.490658	−	1.46764i
$646$	−130.975			−0.202748
$647$			940.297i			1.45332i	0.686998	+	0.726659i	$0.258928\pi$
$647$			940.297i			1.45332i	−0.686998	+	0.726659i	$0.741072\pi$
$648$	−220.165	+	63.3685i	−0.339760	+	0.0977909i
$649$	−982.031			−1.51315
$650$		−	24.9209i		−	0.0383398i
$651$		0			0
$652$	499.852			0.766645
$653$		−	1140.70i		−	1.74686i	−0.486947	−	0.873432i	$-0.661889\pi$
$653$		−	1140.70i		−	1.74686i	0.486947	−	0.873432i	$-0.338111\pi$
$654$	−64.0577	+	191.607i	−0.0979475	+	0.292977i
$655$	−396.545			−0.605413
$656$		−	45.6579i		−	0.0696004i
$657$	102.380	+	77.0686i	0.155829	+	0.117304i
$658$		0			0
$659$		−	69.5711i		−	0.105571i	−0.998606	−	0.0527854i	$-0.983190\pi$
$659$		−	69.5711i		−	0.105571i	0.998606	−	0.0527854i	$-0.0168099\pi$
$660$	629.329	+	210.396i	0.953529	+	0.318782i
$661$	542.798			0.821177			0.410589	−	0.911821i	$-0.365323\pi$
$661$	542.798			0.821177			0.410589	+	0.911821i	$0.365323\pi$
$662$			193.042i			0.291604i
$663$	8.07125	−	24.1424i	0.0121738	−	0.0364139i
$664$	100.953			0.152038
$665$		0			0
$666$	−7.65479	+	10.1688i	−0.0114937	+	0.0152684i
$667$	−503.808			−0.755335
$668$		−	53.8097i		−	0.0805534i
$669$	484.902	+	162.112i	0.724816	+	0.242319i
$670$	190.975			0.285038
$671$		−	1291.52i		−	1.92477i
$672$		0			0
$673$	−419.858			−0.623860			−0.311930	−	0.950105i	$-0.600975\pi$
$673$	−419.858			−0.623860			−0.311930	+	0.950105i	$0.600975\pi$
$674$		−	222.570i		−	0.330223i
$675$	195.376	+	283.819i	0.289446	+	0.420473i
$676$	334.187			0.494359
$677$		−	768.767i		−	1.13555i	−0.823184	−	0.567775i	$-0.807804\pi$
$677$		−	768.767i		−	1.13555i	0.823184	−	0.567775i	$-0.192196\pi$
$678$	−403.880	−	135.024i	−0.595693	−	0.199151i
$679$		0			0
$680$			106.806i			0.157068i
$681$	−326.355	+	976.180i	−0.479229	+	1.43345i
$682$	469.644			0.688627
$683$			286.931i			0.420103i	0.977690	+	0.210052i	$0.0673632\pi$
$683$			286.931i			0.420103i	−0.977690	+	0.210052i	$0.932637\pi$
$684$	−216.737	−	163.154i	−0.316867	−	0.238529i
$685$	−365.093			−0.532983
$686$		0			0
$687$	−767.654	−	256.641i	−1.11740	−	0.373567i
$688$	216.570			0.314782
$689$			56.5614i			0.0820920i
$690$	−218.915	+	654.810i	−0.317268	+	0.949000i
$691$	−902.929			−1.30670			−0.653349	−	0.757057i	$-0.726637\pi$
$691$	−902.929			−1.30670			−0.653349	+	0.757057i	$0.726637\pi$
$692$		−	182.600i		−	0.263873i
$693$		0			0
$694$	378.494			0.545380
$695$			366.650i			0.527553i
$696$	−153.096	−	51.1828i	−0.219965	−	0.0735385i
$697$	−70.1425			−0.100635
$698$		−	269.034i		−	0.385436i
$699$	−298.651	+	893.313i	−0.427255	+	1.27799i
$700$		0			0
$701$			671.817i			0.958370i	0.877714	+	0.479185i	$0.159068\pi$
$701$			671.817i			0.958370i	−0.877714	+	0.479185i	$0.840932\pi$
$702$	43.4300	−	29.8964i	0.0618661	−	0.0425875i
$703$	−15.0712			−0.0214385
$704$			143.979i			0.204515i
$705$	−938.709	−	313.828i	−1.33150	−	0.445146i
$706$	−149.359			−0.211556
$707$		0			0
$708$	103.806	−	310.500i	0.146618	−	0.438559i
$709$	737.280			1.03989			0.519944	−	0.854201i	$-0.325953\pi$
$709$	737.280			1.03989			0.519944	+	0.854201i	$0.325953\pi$
$710$			951.018i			1.33946i
$711$	666.818	+	501.963i	0.937859	+	0.705996i
$712$	453.567			0.637033
$713$			488.659i			0.685357i
$714$		0			0
$715$	−152.712			−0.213584
$716$			483.150i			0.674791i
$717$	−56.7863	+	169.857i	−0.0791998	+	0.236899i
$718$	−550.548			−0.766780
$719$		−	1152.83i		−	1.60337i	−0.597745	−	0.801686i	$-0.703936\pi$
$719$		−	1152.83i		−	1.60337i	0.597745	−	0.801686i	$-0.296064\pi$
$720$	−133.047	+	176.742i	−0.184787	+	0.245475i
$721$		0			0
$722$			189.303i			0.262193i
$723$	−879.980	−	294.194i	−1.21712	−	0.406907i
$724$	−39.8134			−0.0549909
$725$			242.779i			0.334868i
$726$	272.948	−	816.432i	0.375962	−	1.12456i
$727$	101.386			0.139458			0.0697290	−	0.997566i	$-0.477787\pi$
$727$	101.386			0.139458			0.0697290	+	0.997566i	$0.477787\pi$
$728$		0			0
$729$	−260.233	+	680.970i	−0.356973	+	0.934115i
$730$	123.737			0.169503
$731$		−	332.708i		−	0.455142i
$732$	408.354	+	136.520i	0.557860	+	0.186503i
$733$	1420.33			1.93770			0.968848	−	0.247655i	$-0.0796599\pi$
$733$	1420.33			1.93770			0.968848	+	0.247655i	$0.0796599\pi$
$734$			519.722i			0.708068i
$735$		0			0
$736$	−149.808			−0.203544
$737$		−	395.499i		−	0.536633i
$738$	−116.071	−	87.3754i	−0.157278	−	0.118395i
$739$	−646.118			−0.874314			−0.437157	−	0.899385i	$-0.644015\pi$
$739$	−646.118			−0.874314			−0.437157	+	0.899385i	$0.644015\pi$
$740$			12.2901i			0.0166082i
$741$	59.2112	+	19.7954i	0.0799072	+	0.0267144i
$742$		0			0
$743$			693.562i			0.933462i	0.884399	+	0.466731i	$0.154568\pi$
$743$			693.562i			0.933462i	−0.884399	+	0.466731i	$0.845432\pi$
$744$	−49.6438	+	148.492i	−0.0667255	+	0.199587i
$745$	−9.00000			−0.0120805
$746$		−	324.529i		−	0.435026i
$747$	193.194	−	256.643i	0.258627	−	0.343565i
$748$	221.189			0.295707
$749$		0			0
$750$	−302.606	−	101.167i	−0.403474	−	0.134889i
$751$	1325.30			1.76472			0.882358	−	0.470578i	$-0.155955\pi$
$751$	1325.30			1.76472			0.882358	+	0.470578i	$0.155955\pi$
$752$		−	214.759i		−	0.285584i
$753$	66.7812	−	199.753i	0.0886868	−	0.265276i
$754$	37.1501			0.0492707
$755$			1056.80i			1.39973i
$756$		0			0
$757$	999.091			1.31980			0.659901	−	0.751352i	$-0.270598\pi$
$757$	999.091			1.31980			0.659901	+	0.751352i	$0.270598\pi$
$758$		−	521.702i		−	0.688261i
$759$	1356.07	+	453.360i	1.78666	+	0.597313i
$760$	−261.951			−0.344672
$761$			1332.39i			1.75084i	0.483360	+	0.875422i	$0.339416\pi$
$761$			1332.39i			1.75084i	−0.483360	+	0.875422i	$0.660584\pi$
$762$	54.6412	−	163.441i	0.0717076	−	0.214489i
$763$		0			0
$764$		−	198.695i		−	0.260072i
$765$	271.522	+	204.395i	0.354931	+	0.267183i
$766$	−866.395			−1.13106
$767$			75.3456i			0.0982341i
$768$	−45.5233	−	15.2193i	−0.0592752	−	0.0198168i
$769$	1379.09			1.79336			0.896678	−	0.442683i	$-0.145973\pi$
$769$	1379.09			1.79336			0.896678	+	0.442683i	$0.145973\pi$
$770$		0			0
$771$	−66.5382	+	199.026i	−0.0863011	+	0.258140i
$772$	769.705			0.997027
$773$			1388.94i			1.79682i	0.439155	+	0.898411i	$0.355278\pi$
$773$			1388.94i			1.79682i	−0.439155	+	0.898411i	$0.644722\pi$
$774$	414.450	−	550.563i	0.535465	−	0.711322i
$775$	235.479			0.303844
$776$		−	336.312i		−	0.433391i
$777$		0			0
$778$	372.022			0.478177
$779$		−	172.030i		−	0.220835i
$780$	16.1425	−	48.2848i	0.0206955	−	0.0619036i
$781$	1969.50			2.52177
$782$			230.145i			0.294303i
$783$	−423.096	+	291.251i	−0.540352	+	0.371968i
$784$		0			0
$785$			6.14505i			0.00782809i
$786$	−259.655	−	86.8074i	−0.330350	−	0.110442i
$787$	−46.4470			−0.0590178			−0.0295089	−	0.999565i	$-0.509394\pi$
$787$	−46.4470			−0.0590178			−0.0295089	+	0.999565i	$0.509394\pi$
$788$			211.256i			0.268092i
$789$	−124.574	+	372.620i	−0.157888	+	0.472269i
$790$	805.924			1.02016
$791$		0			0
$792$	366.022	+	275.532i	0.462149	+	0.347894i
$793$	−99.0908			−0.124957
$794$		−	853.236i		−	1.07460i
$795$	−716.174	−	239.430i	−0.900848	−	0.301170i
$796$	82.4275			0.103552
$797$			422.335i			0.529906i	0.964261	+	0.264953i	$0.0853565\pi$
$797$			422.335i			0.529906i	−0.964261	+	0.264953i	$0.914644\pi$
$798$		0			0
$799$	−329.926			−0.412924
$800$			72.1909i			0.0902386i
$801$	867.991	−	1153.06i	1.08363	−	1.43952i
$802$	965.491			1.20385
$803$		−	256.252i		−	0.319119i
$804$	125.049	+	41.8063i	0.155534	+	0.0519978i
$805$		0			0
$806$		−	36.0330i		−	0.0447060i
$807$	331.769	−	992.374i	0.411114	−	1.22971i
$808$	−90.2358			−0.111678
$809$			1243.61i			1.53722i	0.639719	+	0.768609i	$0.279051\pi$
$809$			1243.61i			1.53722i	−0.639719	+	0.768609i	$0.720949\pi$
$810$	194.701	+	676.461i	0.240372	+	0.835137i
$811$	−1110.32			−1.36907			−0.684537	−	0.728978i	$-0.739996\pi$
$811$	−1110.32			−1.36907			−0.684537	+	0.728978i	$0.739996\pi$
$812$		0			0
$813$	219.144	+	73.2638i	0.269550	+	0.0901154i
$814$	25.4521			0.0312679
$815$		−	1535.81i		−	1.88443i
$816$	−23.3808	+	69.9358i	−0.0286530	+	0.0857056i
$817$	815.995			0.998770
$818$			869.130i			1.06251i
$819$		0			0
$820$	−140.285			−0.171079
$821$			1304.70i			1.58915i	0.607163	+	0.794577i	$0.292307\pi$
$821$			1304.70i			1.58915i	−0.607163	+	0.794577i	$0.707693\pi$
$822$	−239.060	−	79.9223i	−0.290828	−	0.0972290i
$823$	−1032.02			−1.25397			−0.626986	−	0.779030i	$-0.715712\pi$
$823$	−1032.02			−1.25397			−0.626986	+	0.779030i	$0.715712\pi$
$824$		−	530.326i		−	0.643600i
$825$	218.469	−	653.476i	0.264811	−	0.792092i
$826$		0			0
$827$			1109.55i			1.34166i	0.741613	+	0.670828i	$0.234061\pi$
$827$			1109.55i			1.34166i	−0.741613	+	0.670828i	$0.765939\pi$
$828$	−286.688	+	380.842i	−0.346241	+	0.459954i
$829$	731.231			0.882064			0.441032	−	0.897491i	$-0.354613\pi$
$829$	731.231			0.882064			0.441032	+	0.897491i	$0.354613\pi$
$830$		−	310.182i		−	0.373713i
$831$	−20.7273	−	6.92952i	−0.0249426	−	0.00833878i
$832$	11.0467			0.0132772
$833$		0			0
$834$	−80.2629	+	240.079i	−0.0962385	+	0.287865i
$835$	−165.332			−0.198002
$836$			542.485i			0.648905i
$837$	282.494	+	410.374i	0.337507	+	0.490291i
$838$	−1097.42			−1.30958
$839$			636.854i			0.759064i	0.925179	+	0.379532i	$0.123915\pi$
$839$			636.854i			0.759064i	−0.925179	+	0.379532i	$0.876085\pi$
$840$		0			0
$841$	479.083			0.569659
$842$			227.963i			0.270740i
$843$	−158.897	+	475.285i	−0.188489	+	0.563802i
$844$	−499.715			−0.592079
$845$		−	1026.80i		−	1.21514i
$846$	−545.959	−	410.984i	−0.645342	−	0.485796i
$847$		0			0
$848$		−	163.847i		−	0.193216i
$849$	−345.549	−	115.523i	−0.407007	−	0.136070i
$850$	110.904			0.130475
$851$			26.4826i			0.0311194i
$852$	−208.187	+	622.719i	−0.244350	+	0.730891i
$853$	−620.427			−0.727348			−0.363674	−	0.931526i	$-0.618478\pi$
$853$	−620.427			−0.727348			−0.363674	+	0.931526i	$0.618478\pi$
$854$		0			0
$855$	−501.295	+	665.930i	−0.586310	+	0.778866i
$856$	−72.4275			−0.0846115
$857$			1234.95i			1.44101i	0.693449	+	0.720506i	$0.256090\pi$
$857$			1234.95i			1.44101i	−0.693449	+	0.720506i	$0.743910\pi$
$858$	−99.9949	−	33.4302i	−0.116544	−	0.0389629i
$859$	178.206			0.207458			0.103729	−	0.994606i	$-0.466923\pi$
$859$	178.206			0.207458			0.103729	+	0.994606i	$0.466923\pi$
$860$		−	665.417i		−	0.773741i
$861$		0			0
$862$	676.356			0.784636
$863$			109.219i			0.126558i	0.997996	+	0.0632790i	$0.0201558\pi$
$863$			109.219i			0.126558i	−0.997996	+	0.0632790i	$0.979844\pi$
$864$	−125.808	+	86.6041i	−0.145611	+	0.100236i
$865$	−561.044			−0.648606
$866$		−	137.981i		−	0.159332i
$867$	−714.825	−	238.979i	−0.824481	−	0.275639i
$868$		0			0
$869$		−	1669.02i		−	1.92062i
$870$	−157.260	+	470.391i	−0.180759	+	0.540679i
$871$	−30.3443			−0.0348385
$872$			134.687i			0.154458i
$873$	−854.970	−	643.599i	−0.979347	−	0.737227i
$874$	−564.450			−0.645823
$875$		0			0
$876$	81.0221	+	27.0872i	0.0924909	+	0.0309214i
$877$	2.18407			0.00249039			0.00124519	−	0.999999i	$-0.499604\pi$
$877$	2.18407			0.00249039			0.00124519	+	0.999999i	$0.499604\pi$
$878$		−	333.914i		−	0.380312i
$879$	454.290	−	1358.85i	0.516826	−	1.54591i
$880$	442.378			0.502703
$881$		−	360.009i		−	0.408637i	−0.978904	−	0.204318i	$-0.934502\pi$
$881$		−	360.009i		−	0.408637i	0.978904	−	0.204318i	$-0.0654978\pi$
$882$		0			0
$883$	108.718			0.123123			0.0615615	−	0.998103i	$-0.480392\pi$
$883$	108.718			0.123123			0.0615615	+	0.998103i	$0.480392\pi$
$884$		−	16.9706i		−	0.0191975i
$885$	−954.018	−	318.946i	−1.07799	−	0.360391i
$886$	−653.299			−0.737358
$887$			1062.93i			1.19834i	0.800622	+	0.599170i	$0.204503\pi$
$887$			1062.93i			1.19834i	−0.800622	+	0.599170i	$0.795497\pi$
$888$	−2.69042	+	8.04746i	−0.00302975	+	0.00906246i
$889$		0			0
$890$		−	1393.60i		−	1.56584i
$891$	1400.91	−	403.215i	1.57229	−	0.452542i
$892$	340.855			0.382124
$893$		−	809.171i		−	0.906127i
$894$	−5.89313	−	1.97018i	−0.00659187	−	0.00220378i
$895$	1484.49			1.65865
$896$		0			0
$897$	34.7837	−	104.044i	0.0387778	−	0.115991i
$898$	419.956			0.467657
$899$			351.034i			0.390472i
$900$	183.523	+	138.152i	0.203915	+	0.153502i
$901$	−251.712			−0.279370
$902$			290.522i			0.322086i
$903$		0			0
$904$	−283.902			−0.314050
$905$			122.328i			0.135169i
$906$	−231.343	+	691.983i	−0.255345	+	0.763778i
$907$	842.457			0.928839			0.464420	−	0.885615i	$-0.346263\pi$
$907$	842.457			0.928839			0.464420	+	0.885615i	$0.346263\pi$
$908$			686.192i			0.755718i
$909$	−172.684	+	229.397i	−0.189971	+	0.252362i
$910$		0			0
$911$		−	579.417i		−	0.636023i	−0.948087	−	0.318012i	$-0.896985\pi$
$911$		−	579.417i		−	0.636023i	0.948087	−	0.318012i	$-0.103015\pi$
$912$	−171.523	−	57.3434i	−0.188074	−	0.0628766i
$913$	−642.368			−0.703580
$914$			513.491i			0.561807i
$915$	419.462	−	1254.68i	0.458428	−	1.37123i
$916$	−539.612			−0.589096
$917$		0			0
$918$	133.047	+	193.275i	0.144931	+	0.210539i
$919$	−1159.73			−1.26195			−0.630974	−	0.775804i	$-0.717344\pi$
$919$	−1159.73			−1.26195			−0.630974	+	0.775804i	$0.717344\pi$
$920$			460.290i			0.500315i
$921$	−351.044	−	117.361i	−0.381155	−	0.127427i
$922$	−871.946			−0.945711
$923$		−	151.109i		−	0.163715i
$924$		0			0
$925$	12.7617			0.0137964
$926$		−	497.873i		−	0.537660i
$927$	−1348.19	−	1014.88i	−1.45436	−	1.09481i
$928$	−107.617			−0.115966
$929$			870.382i			0.936902i	0.883489	+	0.468451i	$0.155188\pi$
$929$			870.382i			0.936902i	−0.883489	+	0.468451i	$0.844812\pi$
$930$	456.247	+	152.532i	0.490588	+	0.164013i
$931$		0			0
$932$			627.942i			0.673758i
$933$	378.947	−	1133.49i	0.406160	−	1.21489i
$934$	734.395			0.786290
$935$		−	679.609i		−	0.726855i
$936$	21.1400	−	28.0828i	0.0225854	−	0.0300029i
$937$	1339.70			1.42978			0.714888	−	0.699239i	$-0.246478\pi$
$937$	1339.70			1.42978			0.714888	+	0.699239i	$0.246478\pi$
$938$		0			0
$939$	−151.076	−	50.5075i	−0.160890	−	0.0537886i
$940$	−659.852			−0.701971
$941$		−	506.203i		−	0.537942i	−0.963148	−	0.268971i	$-0.913316\pi$
$941$		−	506.203i		−	0.537942i	0.963148	−	0.268971i	$-0.0866836\pi$
$942$	−1.34521	+	4.02373i	−0.00142803	+	0.00427148i
$943$	−302.285			−0.320557
$944$		−	218.261i		−	0.231209i
$945$		0			0
$946$	−1378.04			−1.45670
$947$			718.533i			0.758747i	0.925244	+	0.379373i	$0.123860\pi$
$947$			718.533i			0.758747i	−0.925244	+	0.379373i	$0.876140\pi$
$948$	527.712	+	176.424i	0.556659	+	0.186101i
$949$	−19.6607			−0.0207173
$950$			272.002i			0.286317i
$951$	351.243	−	1050.62i	0.369341	−	1.10476i
$952$		0			0
$953$		−	1620.84i		−	1.70078i	−0.526152	−	0.850391i	$-0.676366\pi$
$953$		−	1620.84i		−	1.70078i	0.526152	−	0.850391i	$-0.323634\pi$
$954$	−416.532	−	313.554i	−0.436616	−	0.328673i
$955$	−610.496			−0.639263
$956$			119.398i			0.124894i
$957$	974.152	+	325.677i	1.01792	+	0.340310i
$958$	−336.980			−0.351754
$959$		0			0
$960$	−46.7617	+	139.872i	−0.0487101	+	0.145700i
$961$	−620.521			−0.645703
$962$		−	1.95279i		−	0.00202993i
$963$	−138.604	+	184.125i	−0.143930	+	0.191199i
$964$	−618.570			−0.641670
$965$		−	2364.94i		−	2.45071i
$966$		0			0
$967$	−713.562			−0.737914			−0.368957	−	0.929447i	$-0.620285\pi$
$967$	−713.562			−0.737914			−0.368957	+	0.929447i	$0.620285\pi$
$968$		−	573.900i		−	0.592872i
$969$	−88.0946	+	263.505i	−0.0909129	+	0.271935i
$970$	−1033.33			−1.06529
$971$			915.352i			0.942690i	0.881949	+	0.471345i	$0.156231\pi$
$971$			915.352i			0.942690i	−0.881949	+	0.471345i	$0.843769\pi$
$972$	−20.5946	+	485.563i	−0.0211878	+	0.499551i
$973$		0			0
$974$			422.540i			0.433820i
$975$	−50.1374	−	16.7619i	−0.0514230	−	0.0171917i
$976$	287.047			0.294105
$977$		−	563.307i		−	0.576568i	−0.957545	−	0.288284i	$-0.906915\pi$
$977$		−	563.307i		−	0.576568i	0.957545	−	0.288284i	$-0.0930847\pi$
$978$	336.203	−	1005.64i	0.343766	−	1.02826i
$979$	−2886.06			−2.94797
$980$		0			0
$981$	342.402	+	257.751i	0.349033	+	0.262743i
$982$	−670.422			−0.682711
$983$		−	697.664i		−	0.709730i	−0.934918	−	0.354865i	$-0.884527\pi$
$983$		−	697.664i		−	0.709730i	0.934918	−	0.354865i	$-0.115473\pi$
$984$	−91.8575	−	30.7097i	−0.0933511	−	0.0312090i
$985$	649.091			0.658975
$986$			165.327i			0.167675i
$987$		0			0
$988$	41.6217			0.0421272
$989$		−	1433.84i		−	1.44978i
$990$	846.578	−	1124.61i	0.855130	−	1.13597i
$991$	−84.7863			−0.0855563			−0.0427781	−	0.999085i	$-0.513621\pi$
$991$	−84.7863			−0.0855563			−0.0427781	+	0.999085i	$0.513621\pi$
$992$			104.381i			0.105223i
$993$	388.374	+	129.841i	0.391112	+	0.130756i
$994$		0			0
$995$		−	253.261i		−	0.254533i
$996$	67.9016	−	203.105i	0.0681743	−	0.203920i
$997$	911.290			0.914032			0.457016	−	0.889458i	$-0.348918\pi$
$997$	911.290			0.914032			0.457016	+	0.889458i	$0.348918\pi$
$998$		−	677.168i		−	0.678525i
$999$	15.3096	+	22.2400i	0.0153249	+	0.0222622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.3.b.e.197.1		4
3.2	odd	2	inner	294.3.b.e.197.3		4
7.2	even	3		294.3.h.h.263.2		8
7.3	odd	6		42.3.h.b.23.4	yes	8
7.4	even	3		294.3.h.h.275.3		8
7.5	odd	6		42.3.h.b.11.1	✓	8
7.6	odd	2		294.3.b.i.197.2		4
21.2	odd	6		294.3.h.h.263.3		8
21.5	even	6		42.3.h.b.11.4	yes	8
21.11	odd	6		294.3.h.h.275.2		8
21.17	even	6		42.3.h.b.23.1	yes	8
21.20	even	2		294.3.b.i.197.4		4
28.3	even	6		336.3.bn.g.65.2		8
28.19	even	6		336.3.bn.g.305.4		8
84.47	odd	6		336.3.bn.g.305.2		8
84.59	odd	6		336.3.bn.g.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.3.h.b.11.1	✓	8	7.5	odd	6
42.3.h.b.11.4	yes	8	21.5	even	6
42.3.h.b.23.1	yes	8	21.17	even	6
42.3.h.b.23.4	yes	8	7.3	odd	6
294.3.b.e.197.1		4	1.1	even	1	trivial
294.3.b.e.197.3		4	3.2	odd	2	inner
294.3.b.i.197.2		4	7.6	odd	2
294.3.b.i.197.4		4	21.20	even	2
294.3.h.h.263.2		8	7.2	even	3
294.3.h.h.263.3		8	21.2	odd	6
294.3.h.h.275.2		8	21.11	odd	6
294.3.h.h.275.3		8	7.4	even	3
336.3.bn.g.65.2		8	28.3	even	6
336.3.bn.g.65.4		8	84.59	odd	6
336.3.bn.g.305.2		8	84.47	odd	6
336.3.bn.g.305.4		8	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	294.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +(-2.84521 - 0.951206i) q^{3} -2.00000 q^{4} +6.14505i q^{5} +(-1.34521 + 4.02373i) q^{6} +2.82843i q^{8} +(7.19042 + 5.41276i) q^{9} +O(q^{10})\)	\(q-1.41421i q^{2} +(-2.84521 - 0.951206i) q^{3} -2.00000 q^{4} +6.14505i q^{5} +(-1.34521 + 4.02373i) q^{6} +2.82843i q^{8} +(7.19042 + 5.41276i) q^{9} +8.69042 q^{10} -17.9973i q^{11} +(5.69042 + 1.90241i) q^{12} -1.38083 q^{13} +(5.84521 - 17.4840i) q^{15} +4.00000 q^{16} -6.14505i q^{17} +(7.65479 - 10.1688i) q^{18} +15.0712 q^{19} -12.2901i q^{20} -25.4521 q^{22} -26.4826i q^{23} +(2.69042 - 8.04746i) q^{24} -12.7617 q^{25} +1.95279i q^{26} +(-15.3096 - 22.2400i) q^{27} -19.0241i q^{29} +(-24.7260 - 8.26637i) q^{30} -18.4521 q^{31} -5.65685i q^{32} +(-17.1192 + 51.2062i) q^{33} -8.69042 q^{34} +(-14.3808 - 10.8255i) q^{36} -1.00000 q^{37} -21.3140i q^{38} +(3.92875 + 1.31345i) q^{39} -17.3808 q^{40} -11.4145i q^{41} +54.1425 q^{43} +35.9947i q^{44} +(-33.2617 + 44.1855i) q^{45} -37.4521 q^{46} -53.6897i q^{47} +(-11.3808 - 3.80482i) q^{48} +18.0477i q^{50} +(-5.84521 + 17.4840i) q^{51} +2.76166 q^{52} -40.9618i q^{53} +(-31.4521 + 21.6510i) q^{54} +110.595 q^{55} +(-42.8808 - 14.3359i) q^{57} -26.9042 q^{58} -54.5654i q^{59} +(-11.6904 + 34.9679i) q^{60} +71.7617 q^{61} +26.0952i q^{62} -8.00000 q^{64} -8.48528i q^{65} +(72.4165 + 24.2102i) q^{66} +21.9754 q^{67} +12.2901i q^{68} +(-25.1904 + 75.3486i) q^{69} +109.433i q^{71} +(-15.3096 + 20.3376i) q^{72} +14.2383 q^{73} +1.41421i q^{74} +(36.3096 + 12.1390i) q^{75} -30.1425 q^{76} +(1.85751 - 5.55610i) q^{78} +92.7371 q^{79} +24.5802i q^{80} +(22.4042 + 77.8399i) q^{81} -16.1425 q^{82} -35.6924i q^{83} +37.7617 q^{85} -76.5691i q^{86} +(-18.0958 + 54.1276i) q^{87} +50.9042 q^{88} -160.360i q^{89} +(62.4877 + 47.0391i) q^{90} +52.9652i q^{92} +(52.5000 + 17.5517i) q^{93} -75.9288 q^{94} +92.6136i q^{95} +(-5.38083 + 16.0949i) q^{96} -118.904 q^{97} +(97.4152 - 129.408i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9	\( 4 q - 2 q^{3} - 8 q^{4} + 4 q^{6} + 10 q^{9} + 16 q^{10} + 4 q^{12} + 32 q^{13} + 14 q^{15} + 16 q^{16} + 40 q^{18} + 4 q^{19} - 8 q^{22} - 8 q^{24} + 24 q^{25} - 80 q^{27} - 52 q^{30} + 20 q^{31} - 106 q^{33} - 16 q^{34} - 20 q^{36} - 4 q^{37} + 72 q^{39} - 32 q^{40} + 104 q^{43} - 58 q^{45} - 56 q^{46} - 8 q^{48} - 14 q^{51} - 64 q^{52} - 32 q^{54} + 236 q^{55} - 134 q^{57} + 80 q^{58} - 28 q^{60} + 212 q^{61} - 32 q^{64} + 224 q^{66} - 156 q^{67} - 82 q^{69} - 80 q^{72} + 132 q^{73} + 164 q^{75} - 8 q^{76} + 120 q^{78} + 52 q^{79} - 98 q^{81} + 48 q^{82} + 76 q^{85} - 260 q^{87} + 16 q^{88} + 128 q^{90} + 210 q^{93} - 360 q^{94} + 16 q^{96} - 288 q^{97} - 70 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 8 * q^4 + 4 * q^6 + 10 * q^9 + 16 * q^10 + 4 * q^12 + 32 * q^13 + 14 * q^15 + 16 * q^16 + 40 * q^18 + 4 * q^19 - 8 * q^22 - 8 * q^24 + 24 * q^25 - 80 * q^27 - 52 * q^30 + 20 * q^31 - 106 * q^33 - 16 * q^34 - 20 * q^36 - 4 * q^37 + 72 * q^39 - 32 * q^40 + 104 * q^43 - 58 * q^45 - 56 * q^46 - 8 * q^48 - 14 * q^51 - 64 * q^52 - 32 * q^54 + 236 * q^55 - 134 * q^57 + 80 * q^58 - 28 * q^60 + 212 * q^61 - 32 * q^64 + 224 * q^66 - 156 * q^67 - 82 * q^69 - 80 * q^72 + 132 * q^73 + 164 * q^75 - 8 * q^76 + 120 * q^78 + 52 * q^79 - 98 * q^81 + 48 * q^82 + 76 * q^85 - 260 * q^87 + 16 * q^88 + 128 * q^90 + 210 * q^93 - 360 * q^94 + 16 * q^96 - 288 * q^97 - 70 * q^99

Introduction

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