LMFDB - Embedded newform 169.3.f.e.150.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,3,Mod(19,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.19"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$N$	$=$	$169 = 13^{2}$
Weight:	$k$	$=$	$3$
Character orbit:	$[\chi]$	$=$	169.f (of order $12$ , degree $4$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.77720518656.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 121x^{4} + 14641$ x^8 - 121*x^4 + 14641
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			150.1
Root			$-3.20361 + 0.858406i$ of defining polynomial
Character	$\chi$	$=$	169.150
Dual form			169.3.f.e.80.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.20361 + 0.858406i) q^{2} +(1.50000 - 2.59808i) q^{3} +(6.06218 - 3.50000i) q^{4} +(-2.34521 - 2.34521i) q^{5} +(-2.57522 + 9.61084i) q^{6} +(9.61084 + 2.57522i) q^{7} +(-7.03562 + 7.03562i) q^{8} +(9.52628 + 5.50000i) q^{10} +(-1.71681 - 6.40723i) q^{11} -21.0000i q^{12} -33.0000 q^{14} +(-9.61084 + 2.57522i) q^{15} +(2.50000 - 4.33013i) q^{16} +(2.59808 - 1.50000i) q^{17} +(5.15043 - 19.2217i) q^{19} +(-22.4253 - 6.00884i) q^{20} +(21.1069 - 21.1069i) q^{21} +(11.0000 + 19.0526i) q^{22} +(-10.3923 - 6.00000i) q^{23} +(7.72565 + 28.8325i) q^{24} -14.0000i q^{25} +27.0000 q^{27} +(67.2759 - 18.0265i) q^{28} +(21.0000 - 36.3731i) q^{29} +(28.5788 - 16.5000i) q^{30} +(28.1425 + 28.1425i) q^{31} +(6.00884 - 22.4253i) q^{32} +(-19.2217 - 5.15043i) q^{33} +(-7.03562 + 7.03562i) q^{34} +(-16.5000 - 28.5788i) q^{35} +(-12.8761 - 48.0542i) q^{37} +66.0000i q^{38} +33.0000 q^{40} +(-44.8506 + 12.0177i) q^{41} +(-49.5000 + 85.7365i) q^{42} +(-42.4352 + 24.5000i) q^{43} +(-32.8329 - 32.8329i) q^{44} +(38.4434 + 10.3009i) q^{46} +(2.34521 - 2.34521i) q^{47} +(-7.50000 - 12.9904i) q^{48} +(43.3013 + 25.0000i) q^{49} +(12.0177 + 44.8506i) q^{50} -9.00000i q^{51} -24.0000 q^{53} +(-86.4976 + 23.1770i) q^{54} +(-11.0000 + 19.0526i) q^{55} +(-85.7365 + 49.5000i) q^{56} +(-42.2137 - 42.2137i) q^{57} +(-36.0530 + 134.552i) q^{58} +(51.2578 + 13.7345i) q^{59} +(-49.2494 + 49.2494i) q^{60} +(-15.0000 - 25.9808i) q^{61} +(-114.315 - 66.0000i) q^{62} +97.0000i q^{64} +66.0000 q^{66} +(38.4434 - 10.3009i) q^{67} +(10.5000 - 18.1865i) q^{68} +(-31.1769 + 18.0000i) q^{69} +(77.3919 + 77.3919i) q^{70} +(-6.00884 + 22.4253i) q^{71} +(-28.1425 + 28.1425i) q^{73} +(82.5000 + 142.894i) q^{74} +(-36.3731 - 21.0000i) q^{75} +(-36.0530 - 134.552i) q^{76} -66.0000i q^{77} +54.0000 q^{79} +(-16.0181 + 4.29203i) q^{80} +(40.5000 - 70.1481i) q^{81} +(133.368 - 77.0000i) q^{82} +(-32.8329 - 32.8329i) q^{83} +(54.0796 - 201.828i) q^{84} +(-9.61084 - 2.57522i) q^{85} +(114.915 - 114.915i) q^{86} +(-63.0000 - 109.119i) q^{87} +(57.1577 + 33.0000i) q^{88} +(42.9203 + 160.181i) q^{89} -84.0000 q^{92} +(115.330 - 30.9026i) q^{93} +(-5.50000 + 9.52628i) q^{94} +(-57.1577 + 33.0000i) q^{95} +(-49.2494 - 49.2494i) q^{96} +(5.15043 - 19.2217i) q^{97} +(-160.181 - 42.9203i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 12 q^{3} - 264 q^{14} + 20 q^{16} + 88 q^{22} + 216 q^{27} + 168 q^{29} - 132 q^{35} + 264 q^{40} - 396 q^{42} - 60 q^{48} - 192 q^{53} - 88 q^{55} - 120 q^{61} + 528 q^{66} + 84 q^{68} + 660 q^{74}+ \cdots - 44 q^{94}+O(q^{100})$ 8 * q + 12 * q^3 - 264 * q^14 + 20 * q^16 + 88 * q^22 + 216 * q^27 + 168 * q^29 - 132 * q^35 + 264 * q^40 - 396 * q^42 - 60 * q^48 - 192 * q^53 - 88 * q^55 - 120 * q^61 + 528 * q^66 + 84 * q^68 + 660 * q^74 + 432 * q^79 + 324 * q^81 - 504 * q^87 - 672 * q^92 - 44 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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

)

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

$2$	−3.20361	+	0.858406i	−1.60181	+	0.429203i	−0.945588	−	0.325368i	$-0.894512\pi$
$2$	−3.20361	+	0.858406i	−1.60181	+	0.429203i	−0.656219	+	0.754570i	$0.727845\pi$
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i	1.00000			$0$
$4$	6.06218	−	3.50000i	1.51554	−	0.875000i
$5$	−2.34521	−	2.34521i	−0.469042	−	0.469042i	0.432562	−	0.901604i	$-0.357610\pi$
$5$	−2.34521	−	2.34521i	−0.469042	−	0.469042i	−0.901604	+	0.432562i	$0.857610\pi$
$6$	−2.57522	+	9.61084i	−0.429203	+	1.60181i
$7$	9.61084	+	2.57522i	1.37298	+	0.367888i	0.868565	−	0.495575i	$-0.165043\pi$
$7$	9.61084	+	2.57522i	1.37298	+	0.367888i	0.504412	+	0.863463i	$0.331709\pi$
$8$	−7.03562	+	7.03562i	−0.879453	+	0.879453i
$9$		0			0
$10$	9.52628	+	5.50000i	0.952628	+	0.550000i
$11$	−1.71681	−	6.40723i	−0.156074	−	0.582475i	−0.999011	−	0.0444633i	$-0.985842\pi$
$11$	−1.71681	−	6.40723i	−0.156074	−	0.582475i	0.842937	−	0.538012i	$-0.180824\pi$
$12$		−	21.0000i		−	1.75000i
$13$		0			0
$13$		0			0
$14$	−33.0000			−2.35714
$15$	−9.61084	+	2.57522i	−0.640723	+	0.171681i
$16$	2.50000	−	4.33013i	0.156250	−	0.270633i
$17$	2.59808	−	1.50000i	0.152828	−	0.0882353i	−0.421636	−	0.906765i	$-0.638544\pi$
$17$	2.59808	−	1.50000i	0.152828	−	0.0882353i	0.574464	+	0.818530i	$0.305211\pi$
$18$		0			0
$19$	5.15043	−	19.2217i	0.271075	−	1.01167i	−0.687350	−	0.726326i	$-0.741226\pi$
$19$	5.15043	−	19.2217i	0.271075	−	1.01167i	0.958426	−	0.285341i	$-0.0921070\pi$
$20$	−22.4253	−	6.00884i	−1.12126	−	0.300442i
$21$	21.1069	−	21.1069i	1.00509	−	1.00509i
$22$	11.0000	+	19.0526i	0.500000	+	0.866025i
$23$	−10.3923	−	6.00000i	−0.451839	−	0.260870i	0.256767	−	0.966473i	$-0.417343\pi$
$23$	−10.3923	−	6.00000i	−0.451839	−	0.260870i	−0.708607	+	0.705604i	$0.750676\pi$
$24$	7.72565	+	28.8325i	0.321902	+	1.20136i
$25$		−	14.0000i		−	0.560000i
$26$		0			0
$27$	27.0000			1.00000
$28$	67.2759	−	18.0265i	2.40271	−	0.643804i
$29$	21.0000	−	36.3731i	0.724138	−	1.25424i	−0.235190	−	0.971949i	$-0.575571\pi$
$29$	21.0000	−	36.3731i	0.724138	−	1.25424i	0.959328	−	0.282294i	$-0.0910955\pi$
$30$	28.5788	−	16.5000i	0.952628	−	0.550000i
$31$	28.1425	+	28.1425i	0.907822	+	0.907822i	0.996096	−	0.0882738i	$-0.0281351\pi$
$31$	28.1425	+	28.1425i	0.907822	+	0.907822i	−0.0882738	+	0.996096i	$0.528135\pi$
$32$	6.00884	−	22.4253i	0.187776	−	0.700790i
$33$	−19.2217	−	5.15043i	−0.582475	−	0.156074i
$34$	−7.03562	+	7.03562i	−0.206930	+	0.206930i
$35$	−16.5000	−	28.5788i	−0.471429	−	0.816538i
$36$		0			0
$37$	−12.8761	−	48.0542i	−0.348002	−	1.29876i	−0.889065	−	0.457780i	$-0.848645\pi$
$37$	−12.8761	−	48.0542i	−0.348002	−	1.29876i	0.541063	−	0.840982i	$-0.318022\pi$
$38$			66.0000i			1.73684i
$39$		0			0
$40$	33.0000			0.825000
$41$	−44.8506	+	12.0177i	−1.09392	+	0.293114i	−0.760285	−	0.649589i	$-0.774941\pi$
$41$	−44.8506	+	12.0177i	−1.09392	+	0.293114i	−0.333632	+	0.942704i	$0.608274\pi$
$42$	−49.5000	+	85.7365i	−1.17857	+	2.04135i
$43$	−42.4352	+	24.5000i	−0.986866	+	0.569767i	−0.904336	−	0.426821i	$-0.859633\pi$
$43$	−42.4352	+	24.5000i	−0.986866	+	0.569767i	−0.0825301	+	0.996589i	$0.526300\pi$
$44$	−32.8329	−	32.8329i	−0.746203	−	0.746203i
$45$		0			0
$46$	38.4434	+	10.3009i	0.835725	+	0.223932i
$47$	2.34521	−	2.34521i	0.0498980	−	0.0498980i	−0.681717	−	0.731616i	$-0.738767\pi$
$47$	2.34521	−	2.34521i	0.0498980	−	0.0498980i	0.731616	+	0.681717i	$0.238767\pi$
$48$	−7.50000	−	12.9904i	−0.156250	−	0.270633i
$49$	43.3013	+	25.0000i	0.883699	+	0.510204i
$50$	12.0177	+	44.8506i	0.240354	+	0.897012i
$51$		−	9.00000i		−	0.176471i
$52$		0			0
$53$	−24.0000			−0.452830			−0.226415	−	0.974031i	$-0.572701\pi$
$53$	−24.0000			−0.452830			−0.226415	+	0.974031i	$0.572701\pi$
$54$	−86.4976	+	23.1770i	−1.60181	+	0.429203i
$55$	−11.0000	+	19.0526i	−0.200000	+	0.346410i
$56$	−85.7365	+	49.5000i	−1.53101	+	0.883929i
$57$	−42.2137	−	42.2137i	−0.740592	−	0.740592i
$58$	−36.0530	+	134.552i	−0.621604	+	2.31986i
$59$	51.2578	+	13.7345i	0.868777	+	0.232788i	0.665559	−	0.746346i	$-0.268193\pi$
$59$	51.2578	+	13.7345i	0.868777	+	0.232788i	0.203218	+	0.979134i	$0.434860\pi$
$60$	−49.2494	+	49.2494i	−0.820823	+	0.820823i
$61$	−15.0000	−	25.9808i	−0.245902	−	0.425914i	0.716483	−	0.697604i	$-0.245751\pi$
$61$	−15.0000	−	25.9808i	−0.245902	−	0.425914i	−0.962385	+	0.271690i	$0.912417\pi$
$62$	−114.315	−	66.0000i	−1.84380	−	1.06452i
$63$		0			0
$64$			97.0000i			1.51562i
$65$		0			0
$66$	66.0000			1.00000
$67$	38.4434	−	10.3009i	0.573782	−	0.153744i	0.0397512	−	0.999210i	$-0.487343\pi$
$67$	38.4434	−	10.3009i	0.573782	−	0.153744i	0.534030	+	0.845465i	$0.320677\pi$
$68$	10.5000	−	18.1865i	0.154412	−	0.267449i
$69$	−31.1769	+	18.0000i	−0.451839	+	0.260870i
$70$	77.3919	+	77.3919i	1.10560	+	1.10560i
$71$	−6.00884	+	22.4253i	−0.0846315	+	0.315849i	−0.995244	−	0.0974118i	$-0.968944\pi$
$71$	−6.00884	+	22.4253i	−0.0846315	+	0.315849i	0.910613	+	0.413261i	$0.135610\pi$
$72$		0			0
$73$	−28.1425	+	28.1425i	−0.385514	+	0.385514i	−0.873084	−	0.487570i	$-0.837883\pi$
$73$	−28.1425	+	28.1425i	−0.385514	+	0.385514i	0.487570	+	0.873084i	$0.337883\pi$
$74$	82.5000	+	142.894i	1.11486	+	1.93100i
$75$	−36.3731	−	21.0000i	−0.484974	−	0.280000i
$76$	−36.0530	−	134.552i	−0.474382	−	1.77042i
$77$		−	66.0000i		−	0.857143i
$78$		0			0
$79$	54.0000			0.683544			0.341772	−	0.939783i	$-0.388973\pi$
$79$	54.0000			0.683544			0.341772	+	0.939783i	$0.388973\pi$
$80$	−16.0181	+	4.29203i	−0.200226	+	0.0536504i
$81$	40.5000	−	70.1481i	0.500000	−	0.866025i
$82$	133.368	−	77.0000i	1.62644	−	0.939024i
$83$	−32.8329	−	32.8329i	−0.395577	−	0.395577i	0.481093	−	0.876670i	$-0.340240\pi$
$83$	−32.8329	−	32.8329i	−0.395577	−	0.395577i	−0.876670	+	0.481093i	$0.840240\pi$
$84$	54.0796	−	201.828i	0.643804	−	2.40271i
$85$	−9.61084	−	2.57522i	−0.113069	−	0.0302967i
$86$	114.915	−	114.915i	1.33622	−	1.33622i
$87$	−63.0000	−	109.119i	−0.724138	−	1.25424i
$88$	57.1577	+	33.0000i	0.649519	+	0.375000i
$89$	42.9203	+	160.181i	0.482250	+	1.79978i	0.592135	+	0.805839i	$0.298285\pi$
$89$	42.9203	+	160.181i	0.482250	+	1.79978i	−0.109885	+	0.993944i	$0.535048\pi$
$90$		0			0
$91$		0			0
$92$	−84.0000			−0.913043
$93$	115.330	−	30.9026i	1.24011	−	0.332286i
$94$	−5.50000	+	9.52628i	−0.0585106	+	0.101343i
$95$	−57.1577	+	33.0000i	−0.601660	+	0.347368i
$96$	−49.2494	−	49.2494i	−0.513014	−	0.513014i
$97$	5.15043	−	19.2217i	0.0530973	−	0.198162i	−0.934282	−	0.356535i	$-0.883958\pi$
$97$	5.15043	−	19.2217i	0.0530973	−	0.198162i	0.987379	+	0.158373i	$0.0506248\pi$
$98$	−160.181	−	42.9203i	−1.63450	−	0.437962i
$99$		0			0
$100$	−49.0000	−	84.8705i	−0.490000	−	0.848705i
$101$	124.708	+	72.0000i	1.23473	+	0.712871i	0.968012	−	0.250904i	$-0.0807277\pi$
$101$	124.708	+	72.0000i	1.23473	+	0.712871i	0.266717	+	0.963775i	$0.414061\pi$
$102$	7.72565	+	28.8325i	0.0757417	+	0.282672i
$103$		−	26.0000i		−	0.252427i	−0.992003	−	0.126214i	$-0.959718\pi$
$103$		−	26.0000i		−	0.252427i	0.992003	−	0.126214i	$-0.0402825\pi$
$104$		0			0
$105$	−99.0000			−0.942857
$106$	76.8867	−	20.6017i	0.725346	−	0.194356i
$107$	−57.0000	+	98.7269i	−0.532710	+	0.922681i	0.466560	+	0.884489i	$0.345493\pi$
$107$	−57.0000	+	98.7269i	−0.532710	+	0.922681i	−0.999270	+	0.0381918i	$0.987840\pi$
$108$	163.679	−	94.5000i	1.51554	−	0.875000i
$109$	119.606	+	119.606i	1.09730	+	1.09730i	0.994725	+	0.102574i	$0.0327077\pi$
$109$	119.606	+	119.606i	1.09730	+	1.09730i	0.102574	+	0.994725i	$0.467292\pi$
$110$	18.8849	−	70.4795i	0.171681	−	0.640723i
$111$	−144.163	−	38.6283i	−1.29876	−	0.348002i
$112$	35.1781	−	35.1781i	0.314090	−	0.314090i
$113$	63.0000	+	109.119i	0.557522	+	0.965657i	0.997703	+	0.0677473i	$0.0215812\pi$
$113$	63.0000	+	109.119i	0.557522	+	0.965657i	−0.440180	+	0.897909i	$0.645086\pi$
$114$	171.473	+	99.0000i	1.50415	+	0.868421i
$115$	10.3009	+	38.4434i	0.0895728	+	0.334290i
$116$		−	294.000i		−	2.53448i
$117$		0			0
$118$	−176.000			−1.49153
$119$	28.8325	−	7.72565i	0.242290	−	0.0649214i
$120$	49.5000	−	85.7365i	0.412500	−	0.714471i
$121$	66.6840	−	38.5000i	0.551107	−	0.318182i
$122$	70.3562	+	70.3562i	0.576690	+	0.576690i
$123$	−36.0530	+	134.552i	−0.293114	+	1.09392i
$124$	269.104	+	72.1061i	2.17019	+	0.581501i
$125$	−91.4631	+	91.4631i	−0.731705	+	0.731705i
$126$		0			0
$127$	−145.492	−	84.0000i	−1.14561	−	0.661417i	−0.197795	−	0.980243i	$-0.563378\pi$
$127$	−145.492	−	84.0000i	−1.14561	−	0.661417i	−0.947813	+	0.318826i	$0.896711\pi$
$128$	−59.2300	−	221.049i	−0.462734	−	1.72695i
$129$			147.000i			1.13953i
$130$		0			0
$131$	93.0000			0.709924			0.354962	−	0.934881i	$-0.384494\pi$
$131$	93.0000			0.709924			0.354962	+	0.934881i	$0.384494\pi$
$132$	−134.552	+	36.0530i	−1.01933	+	0.273129i
$133$	99.0000	−	171.473i	0.744361	−	1.28927i
$134$	−114.315	+	66.0000i	−0.853100	+	0.492537i
$135$	−63.3206	−	63.3206i	−0.469042	−	0.469042i
$136$	−7.72565	+	28.8325i	−0.0568063	+	0.212004i
$137$	51.2578	+	13.7345i	0.374145	+	0.100252i	0.440991	−	0.897512i	$-0.354627\pi$
$137$	51.2578	+	13.7345i	0.374145	+	0.100252i	−0.0668464	+	0.997763i	$0.521294\pi$
$138$	84.4275	−	84.4275i	0.611793	−	0.611793i
$139$	17.5000	+	30.3109i	0.125899	+	0.218064i	0.922084	−	0.386990i	$-0.126485\pi$
$139$	17.5000	+	30.3109i	0.125899	+	0.218064i	−0.796185	+	0.605053i	$0.793152\pi$
$140$	−200.052	−	115.500i	−1.42894	−	0.825000i
$141$	−2.57522	−	9.61084i	−0.0182640	−	0.0681620i
$142$		−	77.0000i		−	0.542254i
$143$		0			0
$144$		0			0
$145$	−134.552	+	36.0530i	−0.927943	+	0.248642i
$146$	66.0000	−	114.315i	0.452055	−	0.782982i
$147$	129.904	−	75.0000i	0.883699	−	0.510204i
$148$	−246.247	−	246.247i	−1.66383	−	1.66383i
$149$	−17.1681	+	64.0723i	−0.115222	+	0.430015i	−0.999303	−	0.0373181i	$-0.988119\pi$
$149$	−17.1681	+	64.0723i	−0.115222	+	0.430015i	0.884081	+	0.467333i	$0.154785\pi$
$150$	134.552	+	36.0530i	0.897012	+	0.240354i
$151$	−119.606	+	119.606i	−0.792090	+	0.792090i	−0.981834	−	0.189744i	$-0.939234\pi$
$151$	−119.606	+	119.606i	−0.792090	+	0.792090i	0.189744	+	0.981834i	$0.439234\pi$
$152$	99.0000	+	171.473i	0.651316	+	1.12811i
$153$		0			0
$154$	56.6548	+	211.438i	0.367888	+	1.37298i
$155$		−	132.000i		−	0.851613i
$156$		0			0
$157$	80.0000			0.509554			0.254777	−	0.967000i	$-0.417998\pi$
$157$	80.0000			0.509554			0.254777	+	0.967000i	$0.417998\pi$
$158$	−172.995	+	46.3539i	−1.09491	+	0.293379i
$159$	−36.0000	+	62.3538i	−0.226415	+	0.392162i
$160$	−66.6840	+	38.5000i	−0.416775	+	0.240625i
$161$	−84.4275	−	84.4275i	−0.524394	−	0.524394i
$162$	−69.5309	+	259.493i	−0.429203	+	1.60181i
$163$	−115.330	−	30.9026i	−0.707547	−	0.189587i	−0.112938	−	0.993602i	$-0.536026\pi$
$163$	−115.330	−	30.9026i	−0.707547	−	0.189587i	−0.594608	+	0.804015i	$0.702693\pi$
$164$	−229.830	+	229.830i	−1.40140	+	1.40140i
$165$	33.0000	+	57.1577i	0.200000	+	0.346410i
$166$	133.368	+	77.0000i	0.803421	+	0.463855i
$167$	−24.0354	−	89.7012i	−0.143924	−	0.537133i	−0.999801	−	0.0199528i	$-0.993648\pi$
$167$	−24.0354	−	89.7012i	−0.143924	−	0.537133i	0.855877	−	0.517180i	$-0.173018\pi$
$168$			297.000i			1.76786i
$169$		0			0
$170$	33.0000			0.194118
$171$		0			0
$172$	−171.500	+	297.047i	−0.997093	+	1.72702i
$173$	−98.7269	+	57.0000i	−0.570676	+	0.329480i	−0.757419	−	0.652929i	$-0.773540\pi$
$173$	−98.7269	+	57.0000i	−0.570676	+	0.329480i	0.186743	+	0.982409i	$0.440207\pi$
$174$	295.496	+	295.496i	1.69825	+	1.69825i
$175$	36.0530	−	134.552i	0.206017	−	0.768867i
$176$	−32.0361	−	8.58406i	−0.182023	−	0.0487730i
$177$	112.570	−	112.570i	0.635989	−	0.635989i
$178$	−275.000	−	476.314i	−1.54494	−	2.67592i
$179$	−111.717	−	64.5000i	−0.624119	−	0.360335i	0.154352	−	0.988016i	$-0.450671\pi$
$179$	−111.717	−	64.5000i	−0.624119	−	0.360335i	−0.778471	+	0.627681i	$0.784004\pi$
$180$		0			0
$181$			182.000i			1.00552i	0.864425	+	0.502762i	$0.167683\pi$
$181$			182.000i			1.00552i	−0.864425	+	0.502762i	$0.832317\pi$
$182$		0			0
$183$	−90.0000			−0.491803
$184$	115.330	−	30.9026i	0.626794	−	0.167949i
$185$	−82.5000	+	142.894i	−0.445946	+	0.772401i
$186$	−342.946	+	198.000i	−1.84380	+	1.06452i
$187$	−14.0712	−	14.0712i	−0.0752473	−	0.0752473i
$188$	6.00884	−	22.4253i	0.0319619	−	0.119283i
$189$	259.493	+	69.5309i	1.37298	+	0.367888i
$190$	154.784	−	154.784i	0.814651	−	0.814651i
$191$	−15.0000	−	25.9808i	−0.0785340	−	0.136025i	0.824084	−	0.566468i	$-0.191691\pi$
$191$	−15.0000	−	25.9808i	−0.0785340	−	0.136025i	−0.902618	+	0.430443i	$0.858357\pi$
$192$	252.013	+	145.500i	1.31257	+	0.757812i
$193$	−46.3539	−	172.995i	−0.240176	−	0.896348i	−0.975747	−	0.218901i	$-0.929753\pi$
$193$	−46.3539	−	172.995i	−0.240176	−	0.896348i	0.735571	−	0.677447i	$-0.236914\pi$
$194$			66.0000i			0.340206i
$195$		0			0
$196$	350.000			1.78571
$197$	246.678	−	66.0972i	1.25217	−	0.335519i	0.428998	−	0.903305i	$-0.358867\pi$
$197$	246.678	−	66.0972i	1.25217	−	0.335519i	0.823176	+	0.567786i	$0.192200\pi$
$198$		0			0
$199$	239.023	−	138.000i	1.20112	−	0.693467i	0.240316	−	0.970695i	$-0.422749\pi$
$199$	239.023	−	138.000i	1.20112	−	0.693467i	0.960804	+	0.277227i	$0.0894155\pi$
$200$	98.4987	+	98.4987i	0.492494	+	0.492494i
$201$	30.9026	−	115.330i	0.153744	−	0.573782i
$202$	−461.320	−	123.610i	−2.28376	−	0.611933i
$203$	295.496	−	295.496i	1.45565	−	1.45565i
$204$	−31.5000	−	54.5596i	−0.154412	−	0.267449i
$205$	133.368	+	77.0000i	0.650575	+	0.375610i
$206$	22.3185	+	83.2940i	0.108342	+	0.404340i
$207$		0			0
$208$		0			0
$209$	−132.000			−0.631579
$210$	317.158	−	84.9822i	1.51027	−	0.404677i
$211$	−115.500	+	200.052i	−0.547393	+	0.948113i	0.451059	+	0.892494i	$0.351047\pi$
$211$	−115.500	+	200.052i	−0.547393	+	0.948113i	−0.998452	+	0.0556188i	$0.982287\pi$
$212$	−145.492	+	84.0000i	−0.686284	+	0.396226i
$213$	49.2494	+	49.2494i	0.231218	+	0.231218i
$214$	97.8582	−	365.212i	0.457282	−	1.70660i
$215$	156.977	+	42.0619i	0.730126	+	0.195637i
$216$	−189.962	+	189.962i	−0.879453	+	0.879453i
$217$	198.000	+	342.946i	0.912442	+	1.58040i
$218$	−485.840	−	280.500i	−2.22863	−	1.28670i
$219$	30.9026	+	115.330i	0.141108	+	0.526621i
$220$			154.000i			0.700000i
$221$		0			0
$222$	495.000			2.22973
$223$	−336.379	+	90.1326i	−1.50843	+	0.404182i	−0.915913	−	0.401377i	$-0.868532\pi$
$223$	−336.379	+	90.1326i	−1.50843	+	0.404182i	−0.592515	+	0.805559i	$0.701865\pi$
$224$	115.500	−	200.052i	0.515625	−	0.893089i
$225$		0			0
$226$	−295.496	−	295.496i	−1.30751	−	1.30751i
$227$	49.7875	−	185.810i	0.219328	−	0.818544i	−0.765270	−	0.643710i	$-0.777394\pi$
$227$	49.7875	−	185.810i	0.219328	−	0.818544i	0.984598	−	0.174834i	$-0.0559390\pi$
$228$	−403.655	−	108.159i	−1.77042	−	0.474382i
$229$	63.3206	−	63.3206i	0.276509	−	0.276509i	−0.555205	−	0.831714i	$-0.687360\pi$
$229$	63.3206	−	63.3206i	0.276509	−	0.276509i	0.831714	+	0.555205i	$0.187360\pi$
$230$	−66.0000	−	114.315i	−0.286957	−	0.497023i
$231$	−171.473	−	99.0000i	−0.742307	−	0.428571i
$232$	108.159	+	403.655i	0.466203	+	1.73989i
$233$			429.000i			1.84120i	0.390505	+	0.920601i	$0.372300\pi$
$233$			429.000i			1.84120i	−0.390505	+	0.920601i	$0.627700\pi$
$234$		0			0
$235$	−11.0000			−0.0468085
$236$	358.805	−	96.1414i	1.52036	−	0.407379i
$237$	81.0000	−	140.296i	0.341772	−	0.591967i
$238$	−85.7365	+	49.5000i	−0.360237	+	0.207983i
$239$	180.581	+	180.581i	0.755569	+	0.755569i	0.975513	−	0.219944i	$-0.0705873\pi$
$239$	180.581	+	180.581i	0.755569	+	0.755569i	−0.219944	+	0.975513i	$0.570587\pi$
$240$	−12.8761	+	48.0542i	−0.0536504	+	0.200226i
$241$	−365.212	−	97.8582i	−1.51540	−	0.406051i	−0.597177	−	0.802109i	$-0.703711\pi$
$241$	−365.212	−	97.8582i	−1.51540	−	0.406051i	−0.918225	+	0.396059i	$0.870378\pi$
$242$	−180.581	+	180.581i	−0.746203	+	0.746203i
$243$		0			0
$244$	−181.865	−	105.000i	−0.745350	−	0.430328i
$245$	−42.9203	−	160.181i	−0.175185	−	0.653799i
$246$		−	462.000i		−	1.87805i
$247$		0			0
$248$	−396.000			−1.59677
$249$	−134.552	+	36.0530i	−0.540369	+	0.144791i
$250$	214.500	−	371.525i	0.858000	−	1.48610i
$251$	36.3731	−	21.0000i	0.144913	−	0.0836653i	−0.425791	−	0.904822i	$-0.640004\pi$
$251$	36.3731	−	21.0000i	0.144913	−	0.0836653i	0.570703	+	0.821156i	$0.306671\pi$
$252$		0			0
$253$	−20.6017	+	76.8867i	−0.0814298	+	0.303900i
$254$	538.207	+	144.212i	2.11893	+	0.567764i
$255$	−21.1069	+	21.1069i	−0.0827720	+	0.0827720i
$256$	185.500	+	321.295i	0.724609	+	1.25506i
$257$	226.033	+	130.500i	0.879504	+	0.507782i	0.870495	−	0.492177i	$-0.163799\pi$
$257$	226.033	+	130.500i	0.879504	+	0.507782i	0.00900943	+	0.999959i	$0.497132\pi$
$258$	−126.186	−	470.931i	−0.489092	−	1.82531i
$259$		−	495.000i		−	1.91120i
$260$		0			0
$261$		0			0
$262$	−297.936	+	79.8317i	−1.13716	+	0.304701i
$263$	−135.000	+	233.827i	−0.513308	+	0.889076i	0.486573	+	0.873640i	$0.338247\pi$
$263$	−135.000	+	233.827i	−0.513308	+	0.889076i	−0.999881	+	0.0154355i	$0.995087\pi$
$264$	171.473	−	99.0000i	0.649519	−	0.375000i
$265$	56.2850	+	56.2850i	0.212396	+	0.212396i
$266$	−169.964	+	634.315i	−0.638964	+	2.38464i
$267$	480.542	+	128.761i	1.79978	+	0.482250i
$268$	196.997	−	196.997i	0.735065	−	0.735065i
$269$	−93.0000	−	161.081i	−0.345725	−	0.598813i	0.639760	−	0.768575i	$-0.279034\pi$
$269$	−93.0000	−	161.081i	−0.345725	−	0.598813i	−0.985485	+	0.169761i	$0.945700\pi$
$270$	257.210	+	148.500i	0.952628	+	0.550000i
$271$	−12.8761	−	48.0542i	−0.0475132	−	0.177322i	0.938092	−	0.346387i	$-0.112592\pi$
$271$	−12.8761	−	48.0542i	−0.0475132	−	0.177322i	−0.985605	+	0.169066i	$0.945925\pi$
$272$		−	15.0000i		−	0.0551471i
$273$		0			0
$274$	−176.000			−0.642336
$275$	−89.7012	+	24.0354i	−0.326186	+	0.0874013i
$276$	−126.000	+	218.238i	−0.456522	+	0.790719i
$277$	−323.894	+	187.000i	−1.16929	+	0.675090i	−0.953513	−	0.301352i	$-0.902562\pi$
$277$	−323.894	+	187.000i	−1.16929	+	0.675090i	−0.215778	+	0.976443i	$0.569229\pi$
$278$	−82.0823	−	82.0823i	−0.295260	−	0.295260i
$279$		0			0
$280$	317.158	+	84.9822i	1.13271	+	0.303508i
$281$	32.8329	−	32.8329i	0.116843	−	0.116843i	−0.646268	−	0.763111i	$-0.723671\pi$
$281$	32.8329	−	32.8329i	0.116843	−	0.116843i	0.763111	+	0.646268i	$0.223671\pi$
$282$	16.5000	+	28.5788i	0.0585106	+	0.101343i
$283$	57.1577	+	33.0000i	0.201971	+	0.116608i	0.597574	−	0.801814i	$-0.296131\pi$
$283$	57.1577	+	33.0000i	0.201971	+	0.116608i	−0.395604	+	0.918421i	$0.629465\pi$
$284$	42.0619	+	156.977i	0.148105	+	0.552736i
$285$			198.000i			0.694737i
$286$		0			0
$287$	−462.000			−1.60976
$288$		0			0
$289$	−140.000	+	242.487i	−0.484429	+	0.839056i
$290$	400.104	−	231.000i	1.37967	−	0.796552i
$291$	−42.2137	−	42.2137i	−0.145064	−	0.145064i
$292$	−72.1061	+	269.104i	−0.246939	+	0.921587i
$293$	−156.977	−	42.0619i	−0.535758	−	0.143556i	−0.0192121	−	0.999815i	$-0.506116\pi$
$293$	−156.977	−	42.0619i	−0.535758	−	0.143556i	−0.516546	+	0.856260i	$0.672782\pi$
$294$	−351.781	+	351.781i	−1.19653	+	1.19653i
$295$	−88.0000	−	152.420i	−0.298305	−	0.516680i
$296$	428.683	+	247.500i	1.44825	+	0.836149i
$297$	−46.3539	−	172.995i	−0.156074	−	0.582475i
$298$		−	220.000i		−	0.738255i
$299$		0			0
$300$	−294.000			−0.980000
$301$	−470.931	+	126.186i	−1.56456	+	0.419221i
$302$	280.500	−	485.840i	0.928808	−	1.60874i
$303$	374.123	−	216.000i	1.23473	−	0.712871i
$304$	−70.3562	−	70.3562i	−0.231435	−	0.231435i
$305$	−25.7522	+	96.1084i	−0.0844333	+	0.315110i
$306$		0			0
$307$	−393.995	+	393.995i	−1.28337	+	1.28337i	−0.344634	+	0.938737i	$0.611997\pi$
$307$	−393.995	+	393.995i	−1.28337	+	1.28337i	−0.938737	+	0.344634i	$0.888003\pi$
$308$	−231.000	−	400.104i	−0.750000	−	1.29904i
$309$	−67.5500	−	39.0000i	−0.218608	−	0.126214i
$310$	113.310	+	422.877i	0.365515	+	1.36412i
$311$		−	234.000i		−	0.752412i	−0.926536	−	0.376206i	$-0.877229\pi$
$311$		−	234.000i		−	0.752412i	0.926536	−	0.376206i	$-0.122771\pi$
$312$		0			0
$313$	93.0000			0.297125			0.148562	−	0.988903i	$-0.452535\pi$
$313$	93.0000			0.297125			0.148562	+	0.988903i	$0.452535\pi$
$314$	−256.289	+	68.6725i	−0.816207	+	0.218702i
$315$		0			0
$316$	327.358	−	189.000i	1.03594	−	0.598101i
$317$	−215.759	−	215.759i	−0.680628	−	0.680628i	0.279514	−	0.960142i	$-0.409827\pi$
$317$	−215.759	−	215.759i	−0.680628	−	0.680628i	−0.960142	+	0.279514i	$0.909827\pi$
$318$	61.8052	−	230.660i	0.194356	−	0.725346i
$319$	−269.104	−	72.1061i	−0.843585	−	0.226038i
$320$	227.485	−	227.485i	0.710891	−	0.710891i
$321$	171.000	+	296.181i	0.532710	+	0.922681i
$322$	342.946	+	198.000i	1.06505	+	0.614907i
$323$	−15.4513	−	57.6650i	−0.0478368	−	0.178530i
$324$		−	567.000i		−	1.75000i
$325$		0			0
$326$	396.000			1.21472
$327$	490.153	−	131.336i	1.49894	−	0.401639i
$328$	231.000	−	400.104i	0.704268	−	1.21983i
$329$	28.5788	−	16.5000i	0.0868658	−	0.0501520i
$330$	−154.784	−	154.784i	−0.469042	−	0.469042i
$331$	5.15043	−	19.2217i	0.0155602	−	0.0580715i	−0.957709	−	0.287738i	$-0.907097\pi$
$331$	5.15043	−	19.2217i	0.0155602	−	0.0580715i	0.973269	+	0.229666i	$0.0737635\pi$
$332$	−313.954	−	84.1238i	−0.945645	−	0.253385i
$333$		0			0
$334$	154.000	+	266.736i	0.461078	+	0.798610i
$335$	−114.315	−	66.0000i	−0.341240	−	0.197015i
$336$	−38.6283	−	144.163i	−0.114965	−	0.429055i
$337$			429.000i			1.27300i	0.771278	+	0.636499i	$0.219618\pi$
$337$			429.000i			1.27300i	−0.771278	+	0.636499i	$0.780382\pi$
$338$		0			0
$339$	378.000			1.11504
$340$	−67.2759	+	18.0265i	−0.197870	+	0.0530192i
$341$	132.000	−	228.631i	0.387097	−	0.670471i
$342$		0			0
$343$	7.03562	+	7.03562i	0.0205120	+	0.0205120i
$344$	126.186	−	470.931i	0.366819	−	1.36899i
$345$	115.330	+	30.9026i	0.334290	+	0.0895728i
$346$	267.354	−	267.354i	0.772699	−	0.772699i
$347$	82.5000	+	142.894i	0.237752	+	0.411799i	0.960069	−	0.279764i	$-0.0902561\pi$
$347$	82.5000	+	142.894i	0.237752	+	0.411799i	−0.722317	+	0.691562i	$0.756923\pi$
$348$	−763.834	−	441.000i	−2.19493	−	1.26724i
$349$	54.0796	+	201.828i	0.154956	+	0.578303i	0.999109	+	0.0422010i	$0.0134370\pi$
$349$	54.0796	+	201.828i	0.154956	+	0.578303i	−0.844153	+	0.536102i	$0.819896\pi$
$350$			462.000i			1.32000i
$351$		0			0
$352$	−154.000			−0.437500
$353$	621.501	−	166.531i	1.76063	−	0.471758i	0.773785	−	0.633449i	$-0.218361\pi$
$353$	621.501	−	166.531i	1.76063	−	0.471758i	0.986842	+	0.161690i	$0.0516946\pi$
$354$	−264.000	+	457.261i	−0.745763	+	1.29170i
$355$	66.6840	−	38.5000i	0.187842	−	0.108451i
$356$	820.823	+	820.823i	2.30568	+	2.30568i
$357$	23.1770	−	86.4976i	0.0649214	−	0.242290i
$358$	413.266	+	110.734i	1.15437	+	0.309314i
$359$	215.759	−	215.759i	0.601000	−	0.601000i	−0.339578	−	0.940578i	$-0.610284\pi$
$359$	215.759	−	215.759i	0.601000	−	0.601000i	0.940578	+	0.339578i	$0.110284\pi$
$360$		0			0
$361$	−30.3109	−	17.5000i	−0.0839637	−	0.0484765i
$362$	−156.230	−	583.058i	−0.431574	−	1.61066i
$363$		−	231.000i		−	0.636364i
$364$		0			0
$365$	132.000			0.361644
$366$	288.325	−	77.2565i	0.787774	−	0.211083i
$367$	268.000	−	464.190i	0.730245	−	1.26482i	−0.226533	−	0.974003i	$-0.572739\pi$
$367$	268.000	−	464.190i	0.730245	−	1.26482i	0.956778	−	0.290818i	$-0.0939275\pi$
$368$	−51.9615	+	30.0000i	−0.141200	+	0.0815217i
$369$		0			0
$370$	141.637	−	528.596i	0.382803	−	1.42864i
$371$	−230.660	−	61.8052i	−0.621726	−	0.166591i
$372$	590.992	−	590.992i	1.58869	−	1.58869i
$373$	−132.000	−	228.631i	−0.353887	−	0.612951i	0.633039	−	0.774119i	$-0.281807\pi$
$373$	−132.000	−	228.631i	−0.353887	−	0.612951i	−0.986927	+	0.161169i	$0.948474\pi$
$374$	57.1577	+	33.0000i	0.152828	+	0.0882353i
$375$	100.433	+	374.823i	0.267823	+	0.999527i
$376$			33.0000i			0.0877660i
$377$		0			0
$378$	−891.000			−2.35714
$379$	538.207	−	144.212i	1.42007	−	0.380507i	0.534562	−	0.845129i	$-0.320476\pi$
$379$	538.207	−	144.212i	1.42007	−	0.380507i	0.885509	+	0.464622i	$0.153810\pi$
$380$	−231.000	+	400.104i	−0.607895	+	1.05290i
$381$	−436.477	+	252.000i	−1.14561	+	0.661417i
$382$	70.3562	+	70.3562i	0.184179	+	0.184179i
$383$	−72.9645	+	272.307i	−0.190508	+	0.710985i	0.802876	+	0.596146i	$0.203302\pi$
$383$	−72.9645	+	272.307i	−0.190508	+	0.710985i	−0.993384	+	0.114839i	$0.963365\pi$
$384$	−663.148	−	177.690i	−1.72695	−	0.462734i
$385$	−154.784	+	154.784i	−0.402036	+	0.402036i
$386$	297.000	+	514.419i	0.769430	+	1.33269i
$387$		0			0
$388$	−36.0530	−	134.552i	−0.0929202	−	0.346783i
$389$		−	312.000i		−	0.802057i	−0.916066	−	0.401028i	$-0.868653\pi$
$389$		−	312.000i		−	0.802057i	0.916066	−	0.401028i	$-0.131347\pi$
$390$		0			0
$391$	−36.0000			−0.0920716
$392$	−480.542	+	128.761i	−1.22587	+	0.328472i
$393$	139.500	−	241.621i	0.354962	−	0.614812i
$394$	−733.524	+	423.500i	−1.86173	+	1.07487i
$395$	−126.641	−	126.641i	−0.320611	−	0.320611i
$396$		0			0
$397$	−115.330	−	30.9026i	−0.290504	−	0.0778403i	0.110624	−	0.993862i	$-0.464715\pi$
$397$	−115.330	−	30.9026i	−0.290504	−	0.0778403i	−0.401128	+	0.916022i	$0.631382\pi$
$398$	−647.277	+	647.277i	−1.62633	+	1.62633i
$399$	−297.000	−	514.419i	−0.744361	−	1.28927i
$400$	−60.6218	−	35.0000i	−0.151554	−	0.0875000i
$401$	199.150	+	743.238i	0.496634	+	1.85346i	0.520681	+	0.853751i	$0.325678\pi$
$401$	199.150	+	743.238i	0.496634	+	1.85346i	−0.0240472	+	0.999711i	$0.507655\pi$
$402$			396.000i			0.985075i
$403$		0			0
$404$	1008.00			2.49505
$405$	−259.493	+	69.5309i	−0.640723	+	0.171681i
$406$	−693.000	+	1200.31i	−1.70690	+	2.95643i
$407$	−285.788	+	165.000i	−0.702183	+	0.405405i
$408$	63.3206	+	63.3206i	0.155198	+	0.155198i
$409$	−61.8052	+	230.660i	−0.151113	+	0.563961i	0.848294	+	0.529526i	$0.177630\pi$
$409$	−61.8052	+	230.660i	−0.151113	+	0.563961i	−0.999407	+	0.0344357i	$0.989037\pi$
$410$	−493.356	−	132.194i	−1.20331	−	0.322426i
$411$	112.570	−	112.570i	0.273893	−	0.273893i
$412$	−91.0000	−	157.617i	−0.220874	−	0.382565i
$413$	457.261	+	264.000i	1.10717	+	0.639225i
$414$		0			0
$415$			154.000i			0.371084i
$416$		0			0
$417$	105.000			0.251799
$418$	422.877	−	113.310i	1.01167	−	0.271075i
$419$	−193.500	+	335.152i	−0.461814	+	0.799885i	−0.999051	−	0.0435459i	$-0.986135\pi$
$419$	−193.500	+	335.152i	−0.461814	+	0.799885i	0.537238	+	0.843431i	$0.319468\pi$
$420$	−600.156	+	346.500i	−1.42894	+	0.825000i
$421$	−63.3206	−	63.3206i	−0.150405	−	0.150405i	0.627894	−	0.778299i	$-0.283917\pi$
$421$	−63.3206	−	63.3206i	−0.150405	−	0.150405i	−0.778299	+	0.627894i	$0.783917\pi$
$422$	198.292	−	740.035i	0.469886	−	1.75364i
$423$		0			0
$424$	168.855	−	168.855i	0.398243	−	0.398243i
$425$	−21.0000	−	36.3731i	−0.0494118	−	0.0855837i
$426$	−200.052	−	115.500i	−0.469605	−	0.271127i
$427$	−77.2565	−	288.325i	−0.180929	−	0.675235i
$428$			798.000i			1.86449i
$429$		0			0
$430$	−539.000			−1.25349
$431$	−419.673	+	112.451i	−0.973720	+	0.260908i	−0.710398	−	0.703800i	$-0.751485\pi$
$431$	−419.673	+	112.451i	−0.973720	+	0.260908i	−0.263322	+	0.964708i	$0.584818\pi$
$432$	67.5000	−	116.913i	0.156250	−	0.270633i
$433$	272.798	−	157.500i	0.630018	−	0.363741i	−0.150741	−	0.988573i	$-0.548166\pi$
$433$	272.798	−	157.500i	0.630018	−	0.363741i	0.780759	+	0.624832i	$0.214833\pi$
$434$	−928.702	−	928.702i	−2.13987	−	2.13987i
$435$	−108.159	+	403.655i	−0.248642	+	0.927943i
$436$	1143.69	+	306.451i	2.62314	+	0.702869i
$437$	−168.855	+	168.855i	−0.386396	+	0.386396i
$438$	−198.000	−	342.946i	−0.452055	−	0.782982i
$439$	−595.825	−	344.000i	−1.35723	−	0.783599i	−0.367983	−	0.929832i	$-0.619952\pi$
$439$	−595.825	−	344.000i	−1.35723	−	0.783599i	−0.989250	+	0.146233i	$0.953285\pi$
$440$	−56.6548	−	211.438i	−0.128761	−	0.480542i
$441$		0			0
$442$		0			0
$443$	327.000			0.738149			0.369074	−	0.929400i	$-0.379675\pi$
$443$	327.000			0.738149			0.369074	+	0.929400i	$0.379675\pi$
$444$	−1009.14	+	270.398i	−2.27283	+	0.609004i
$445$	275.000	−	476.314i	0.617978	−	1.07037i
$446$	1000.26	−	577.500i	2.24273	−	1.29484i
$447$	140.712	+	140.712i	0.314793	+	0.314793i
$448$	−249.796	+	932.252i	−0.557580	+	2.08092i
$449$	467.728	+	125.327i	1.04171	+	0.279125i	0.738822	−	0.673901i	$-0.235383\pi$
$449$	467.728	+	125.327i	1.04171	+	0.279125i	0.302888	+	0.953026i	$0.402049\pi$
$450$		0			0
$451$	154.000	+	266.736i	0.341463	+	0.591432i
$452$	763.834	+	441.000i	1.68990	+	0.975664i
$453$	131.336	+	490.153i	0.289925	+	1.08202i
$454$			638.000i			1.40529i
$455$		0			0
$456$	594.000			1.30263
$457$	288.325	−	77.2565i	0.630909	−	0.169051i	0.0708266	−	0.997489i	$-0.477436\pi$
$457$	288.325	−	77.2565i	0.630909	−	0.169051i	0.560082	+	0.828437i	$0.310770\pi$
$458$	−148.500	+	257.210i	−0.324236	+	0.561593i
$459$	70.1481	−	40.5000i	0.152828	−	0.0882353i
$460$	196.997	+	196.997i	0.428255	+	0.428255i
$461$	60.9468	−	227.457i	0.132206	−	0.493398i	−0.867788	−	0.496934i	$-0.834459\pi$
$461$	60.9468	−	227.457i	0.132206	−	0.493398i	0.999994	+	0.00353623i	$0.00112562\pi$
$462$	634.315	+	169.964i	1.37298	+	0.367888i
$463$	−393.995	+	393.995i	−0.850961	+	0.850961i	−0.990252	−	0.139291i	$-0.955518\pi$
$463$	−393.995	+	393.995i	−0.850961	+	0.850961i	0.139291	+	0.990252i	$0.455518\pi$
$464$	−105.000	−	181.865i	−0.226293	−	0.391951i
$465$	−342.946	−	198.000i	−0.737518	−	0.425806i
$466$	−368.256	−	1374.35i	−0.790249	−	2.94925i
$467$		−	390.000i		−	0.835118i	−0.908650	−	0.417559i	$-0.862886\pi$
$467$		−	390.000i		−	0.835118i	0.908650	−	0.417559i	$-0.137114\pi$
$468$		0			0
$469$	396.000			0.844350
$470$	35.2397	−	9.44246i	0.0749782	−	0.0200903i
$471$	120.000	−	207.846i	0.254777	−	0.441287i
$472$	−457.261	+	264.000i	−0.968774	+	0.559322i
$473$	229.830	+	229.830i	0.485899	+	0.485899i
$474$	−139.062	+	518.985i	−0.293379	+	1.09491i
$475$	−269.104	−	72.1061i	−0.566534	−	0.151802i
$476$	147.748	−	147.748i	0.310395	−	0.310395i
$477$		0			0
$478$	−733.524	−	423.500i	−1.53457	−	0.885983i
$479$	−124.469	−	464.524i	−0.259851	−	0.969779i	−0.965327	−	0.261044i	$-0.915933\pi$
$479$	−124.469	−	464.524i	−0.259851	−	0.969779i	0.705475	−	0.708734i	$-0.250734\pi$
$480$			231.000i			0.481250i
$481$		0			0
$482$	1254.00			2.60166
$483$	−345.990	+	92.7078i	−0.716336	+	0.191942i
$484$	269.500	−	466.788i	0.556818	−	0.964437i
$485$	−57.1577	+	33.0000i	−0.117851	+	0.0680412i
$486$		0			0
$487$	−61.8052	+	230.660i	−0.126910	+	0.473635i	−0.999901	−	0.0141024i	$-0.995511\pi$
$487$	−61.8052	+	230.660i	−0.126910	+	0.473635i	0.872990	+	0.487737i	$0.162178\pi$
$488$	288.325	+	77.2565i	0.590830	+	0.158313i
$489$	−253.282	+	253.282i	−0.517960	+	0.517960i
$490$	275.000	+	476.314i	0.561224	+	0.972069i
$491$	563.783	+	325.500i	1.14823	+	0.662933i	0.948456	−	0.316909i	$-0.102645\pi$
$491$	563.783	+	325.500i	1.14823	+	0.662933i	0.199777	+	0.979841i	$0.435978\pi$
$492$	252.371	+	941.862i	0.512950	+	1.91435i
$493$		−	126.000i		−	0.255578i
$494$		0			0
$495$		0			0
$496$	192.217	−	51.5043i	0.387534	−	0.103839i
$497$	−115.500	+	200.052i	−0.232394	+	0.402519i
$498$	400.104	−	231.000i	0.803421	−	0.463855i
$499$	211.069	+	211.069i	0.422983	+	0.422983i	0.886230	−	0.463246i	$-0.153315\pi$
$499$	211.069	+	211.069i	0.422983	+	0.422983i	−0.463246	+	0.886230i	$0.653315\pi$
$500$	−234.345	+	874.586i	−0.468689	+	1.74917i
$501$	−269.104	−	72.1061i	−0.537133	−	0.143924i
$502$	−98.4987	+	98.4987i	−0.196213	+	0.196213i
$503$	−405.000	−	701.481i	−0.805169	−	1.39459i	−0.916177	−	0.400774i	$-0.868741\pi$
$503$	−405.000	−	701.481i	−0.805169	−	1.39459i	0.111008	−	0.993820i	$-0.464592\pi$
$504$		0			0
$505$	−123.610	−	461.320i	−0.244773	−	0.913506i
$506$		−	264.000i		−	0.521739i
$507$		0			0
$508$	−1176.00			−2.31496
$509$	−294.732	+	78.9733i	−0.579042	+	0.155154i	−0.536440	−	0.843938i	$-0.680231\pi$
$509$	−294.732	+	78.9733i	−0.579042	+	0.155154i	−0.0426018	+	0.999092i	$0.513565\pi$
$510$	49.5000	−	85.7365i	0.0970588	−	0.168111i
$511$	−342.946	+	198.000i	−0.671127	+	0.387476i
$512$	−222.795	−	222.795i	−0.435146	−	0.435146i
$513$	139.062	−	518.985i	0.271075	−	1.01167i
$514$	−836.143	−	224.044i	−1.62674	−	0.435883i
$515$	−60.9754	+	60.9754i	−0.118399	+	0.118399i
$516$	514.500	+	891.140i	0.997093	+	1.72702i
$517$	−19.0526	−	11.0000i	−0.0368521	−	0.0212766i
$518$	424.911	+	1585.79i	0.820291	+	3.06137i
$519$			342.000i			0.658960i
$520$		0			0
$521$	−843.000			−1.61804			−0.809021	−	0.587780i	$-0.800002\pi$
$521$	−843.000			−1.61804			−0.809021	+	0.587780i	$0.800002\pi$
$522$		0			0
$523$	125.000	−	216.506i	0.239006	−	0.413970i	−0.721424	−	0.692494i	$-0.756512\pi$
$523$	125.000	−	216.506i	0.239006	−	0.413970i	0.960429	+	0.278524i	$0.0898452\pi$
$524$	563.783	−	325.500i	1.07592	−	0.621183i
$525$	−295.496	−	295.496i	−0.562850	−	0.562850i
$526$	231.770	−	864.976i	0.440626	−	1.64444i
$527$	115.330	+	30.9026i	0.218843	+	0.0586387i
$528$	−70.3562	+	70.3562i	−0.133250	+	0.133250i
$529$	−192.500	−	333.420i	−0.363894	−	0.630283i
$530$	−228.631	−	132.000i	−0.431379	−	0.249057i
$531$		0			0
$532$		−	1386.00i		−	2.60526i
$533$		0			0
$534$	−1650.00			−3.08989
$535$	365.212	−	97.8582i	0.682639	−	0.182913i
$536$	−198.000	+	342.946i	−0.369403	+	0.639825i
$537$	−335.152	+	193.500i	−0.624119	+	0.360335i
$538$	436.209	+	436.209i	0.810797	+	0.810797i
$539$	85.8406	−	320.361i	0.159259	−	0.594362i
$540$	−605.483	−	162.239i	−1.12126	−	0.300442i
$541$	429.173	−	429.173i	0.793296	−	0.793296i	−0.188733	−	0.982029i	$-0.560438\pi$
$541$	429.173	−	429.173i	0.793296	−	0.793296i	0.982029	+	0.188733i	$0.0604380\pi$
$542$	82.5000	+	142.894i	0.152214	+	0.263642i
$543$	472.850	+	273.000i	0.870810	+	0.502762i
$544$	−18.0265	−	67.2759i	−0.0331370	−	0.123669i
$545$		−	561.000i		−	1.02936i
$546$		0			0
$547$	301.000			0.550274			0.275137	−	0.961405i	$-0.411277\pi$
$547$	301.000			0.550274			0.275137	+	0.961405i	$0.411277\pi$
$548$	358.805	−	96.1414i	0.654753	−	0.175441i
$549$		0			0
$550$	266.736	−	154.000i	0.484974	−	0.280000i
$551$	−590.992	−	590.992i	−1.07258	−	1.07258i
$552$	92.7078	−	345.990i	0.167949	−	0.626794i
$553$	518.985	+	139.062i	0.938491	+	0.251468i
$554$	877.108	−	877.108i	1.58323	−	1.58323i
$555$	247.500	+	428.683i	0.445946	+	0.772401i
$556$	212.176	+	122.500i	0.381612	+	0.220324i
$557$	−124.469	−	464.524i	−0.223463	−	0.833975i	−0.983015	−	0.183528i	$-0.941248\pi$
$557$	−124.469	−	464.524i	−0.223463	−	0.833975i	0.759552	−	0.650447i	$-0.225418\pi$
$558$		0			0
$559$		0			0
$560$	−165.000			−0.294643
$561$	−57.6650	+	15.4513i	−0.102790	+	0.0275424i
$562$	−77.0000	+	133.368i	−0.137011	+	0.237309i
$563$	−875.552	+	505.500i	−1.55515	+	0.897869i	−0.557445	+	0.830214i	$0.688218\pi$
$563$	−875.552	+	505.500i	−1.55515	+	0.897869i	−0.997709	+	0.0676548i	$0.978448\pi$
$564$	−49.2494	−	49.2494i	−0.0873216	−	0.0873216i
$565$	108.159	−	403.655i	0.191432	−	0.714434i
$566$	−211.438	−	56.6548i	−0.373566	−	0.100097i
$567$	569.886	−	569.886i	1.00509	−	1.00509i
$568$	−115.500	−	200.052i	−0.203345	−	0.352204i
$569$	428.683	+	247.500i	0.753396	+	0.434974i	0.826920	−	0.562320i	$-0.190091\pi$
$569$	428.683	+	247.500i	0.753396	+	0.434974i	−0.0735234	+	0.997293i	$0.523424\pi$
$570$	−169.964	−	634.315i	−0.298183	−	1.11283i
$571$			39.0000i			0.0683012i	0.999417	+	0.0341506i	$0.0108726\pi$
$571$			39.0000i			0.0683012i	−0.999417	+	0.0341506i	$0.989127\pi$
$572$		0			0
$573$	−90.0000			−0.157068
$574$	1480.07	−	396.583i	2.57852	−	0.690912i
$575$	−84.0000	+	145.492i	−0.146087	+	0.253030i
$576$		0			0
$577$	759.847	+	759.847i	1.31689	+	1.31689i	0.916222	+	0.400671i	$0.131223\pi$
$577$	759.847	+	759.847i	1.31689	+	1.31689i	0.400671	+	0.916222i	$0.368777\pi$
$578$	240.354	−	897.012i	0.415837	−	1.55192i
$579$	−518.985	−	139.062i	−0.896348	−	0.240176i
$580$	−689.491	+	689.491i	−1.18878	+	1.18878i
$581$	−231.000	−	400.104i	−0.397590	−	0.688647i
$582$	171.473	+	99.0000i	0.294627	+	0.170103i
$583$	41.2035	+	153.773i	0.0706749	+	0.263762i
$584$		−	396.000i		−	0.678082i
$585$		0			0
$586$	539.000			0.919795
$587$	−294.732	+	78.9733i	−0.502100	+	0.134537i	−0.500974	−	0.865462i	$-0.667025\pi$
$587$	−294.732	+	78.9733i	−0.502100	+	0.134537i	−0.00112532	+	0.999999i	$0.500358\pi$
$588$	525.000	−	909.327i	0.892857	−	1.54647i
$589$	685.892	−	396.000i	1.16450	−	0.672326i
$590$	412.757	+	412.757i	0.699587	+	0.699587i
$591$	198.292	−	740.035i	0.335519	−	1.25217i
$592$	−240.271	−	64.3804i	−0.405863	−	0.108751i
$593$	276.735	−	276.735i	0.466669	−	0.466669i	−0.434165	−	0.900833i	$-0.642956\pi$
$593$	276.735	−	276.735i	0.466669	−	0.466669i	0.900833	+	0.434165i	$0.142956\pi$
$594$	297.000	+	514.419i	0.500000	+	0.866025i
$595$	−85.7365	−	49.5000i	−0.144095	−	0.0831933i
$596$	120.177	+	448.506i	0.201639	+	0.752527i
$597$		−	828.000i		−	1.38693i
$598$		0			0
$599$	−648.000			−1.08180			−0.540902	−	0.841086i	$-0.681917\pi$
$599$	−648.000			−1.08180			−0.540902	+	0.841086i	$0.681917\pi$
$600$	403.655	−	108.159i	0.672759	−	0.180265i
$601$	−37.5000	+	64.9519i	−0.0623960	+	0.108073i	−0.895536	−	0.444989i	$-0.853208\pi$
$601$	−37.5000	+	64.9519i	−0.0623960	+	0.108073i	0.833140	+	0.553062i	$0.186541\pi$
$602$	1400.36	−	808.500i	2.32618	−	1.34302i
$603$		0			0
$604$	−306.451	+	1143.69i	−0.507369	+	1.89353i
$605$	−246.678	−	66.0972i	−0.407733	−	0.109252i
$606$	−1013.13	+	1013.13i	−1.67183	+	1.67183i
$607$	50.0000	+	86.6025i	0.0823723	+	0.142673i	0.904268	−	0.426964i	$-0.140417\pi$
$607$	50.0000	+	86.6025i	0.0823723	+	0.142673i	−0.821896	+	0.569637i	$0.807084\pi$
$608$	−400.104	−	231.000i	−0.658065	−	0.379934i
$609$	−324.477	−	1210.97i	−0.532804	−	1.98845i
$610$		−	330.000i		−	0.540984i
$611$		0			0
$612$		0			0
$613$	38.4434	−	10.3009i	0.0627135	−	0.0168040i	−0.227326	−	0.973819i	$-0.572998\pi$
$613$	38.4434	−	10.3009i	0.0627135	−	0.0168040i	0.290039	+	0.957015i	$0.406332\pi$
$614$	924.000	−	1600.41i	1.50489	−	2.60654i
$615$	400.104	−	231.000i	0.650575	−	0.375610i
$616$	464.351	+	464.351i	0.753817	+	0.753817i
$617$	−240.354	+	897.012i	−0.389552	+	1.45383i	0.441313	+	0.897353i	$0.354513\pi$
$617$	−240.354	+	897.012i	−0.389552	+	1.45383i	−0.830865	+	0.556474i	$0.812154\pi$
$618$	249.882	+	66.9556i	0.404340	+	0.108342i
$619$	520.636	−	520.636i	0.841092	−	0.841092i	−0.147909	−	0.989001i	$-0.547254\pi$
$619$	520.636	−	520.636i	0.841092	−	0.841092i	0.989001	+	0.147909i	$0.0472542\pi$
$620$	−462.000	−	800.207i	−0.745161	−	1.29066i
$621$	−280.592	−	162.000i	−0.451839	−	0.260870i
$622$	200.867	+	749.646i	0.322937	+	1.20522i
$623$			1650.00i			2.64848i
$624$		0			0
$625$	79.0000			0.126400
$626$	−297.936	+	79.8317i	−0.475936	+	0.127527i
$627$	−198.000	+	342.946i	−0.315789	+	0.546963i
$628$	484.974	−	280.000i	0.772252	−	0.445860i
$629$	−105.534	−	105.534i	−0.167781	−	0.167781i
$630$		0			0
$631$	1009.14	+	270.398i	1.59927	+	0.428523i	0.944822	−	0.327585i	$-0.106235\pi$
$631$	1009.14	+	270.398i	1.59927	+	0.428523i	0.654447	+	0.756108i	$0.272902\pi$
$632$	−379.924	+	379.924i	−0.601145	+	0.601145i
$633$	346.500	+	600.156i	0.547393	+	0.948113i
$634$	876.418	+	506.000i	1.38236	+	0.798107i
$635$	144.212	+	538.207i	0.227106	+	0.847570i
$636$			504.000i			0.792453i
$637$		0			0
$638$	924.000			1.44828
$639$		0			0
$640$	−379.500	+	657.313i	−0.592969	+	1.02705i
$641$	711.873	−	411.000i	1.11057	−	0.641186i	0.171590	−	0.985168i	$-0.445110\pi$
$641$	711.873	−	411.000i	1.11057	−	0.641186i	0.938976	+	0.343983i	$0.111776\pi$
$642$	−802.061	−	802.061i	−1.24932	−	1.24932i
$643$	72.1061	−	269.104i	0.112140	−	0.418512i	−0.886917	−	0.461929i	$-0.847158\pi$
$643$	72.1061	−	269.104i	0.112140	−	0.418512i	0.999057	+	0.0434164i	$0.0138242\pi$
$644$	−807.311	−	216.318i	−1.25359	−	0.335898i
$645$	344.746	−	344.746i	0.534489	−	0.534489i
$646$	99.0000	+	171.473i	0.153251	+	0.265438i
$647$	−820.992	−	474.000i	−1.26892	−	0.732612i	−0.294137	−	0.955763i	$-0.595032\pi$
$647$	−820.992	−	474.000i	−1.26892	−	0.732612i	−0.974784	+	0.223151i	$0.928366\pi$
$648$	208.593	+	778.478i	0.321902	+	1.20136i
$649$		−	352.000i		−	0.542373i
$650$		0			0
$651$	1188.00			1.82488
$652$	−807.311	+	216.318i	−1.23821	+	0.331776i
$653$	−174.000	+	301.377i	−0.266462	+	0.461527i	−0.967946	−	0.251159i	$-0.919188\pi$
$653$	−174.000	+	301.377i	−0.266462	+	0.461527i	0.701483	+	0.712686i	$0.252522\pi$
$654$	−1457.52	+	841.500i	−2.22863	+	1.28670i
$655$	−218.104	−	218.104i	−0.332984	−	0.332984i
$656$	−60.0884	+	224.253i	−0.0915982	+	0.341849i
$657$		0			0
$658$	−77.3919	+	77.3919i	−0.117617	+	0.117617i
$659$	63.0000	+	109.119i	0.0955994	+	0.165583i	0.909859	−	0.414918i	$-0.136190\pi$
$659$	63.0000	+	109.119i	0.0955994	+	0.165583i	−0.814259	+	0.580501i	$0.802857\pi$
$660$	400.104	+	231.000i	0.606218	+	0.350000i
$661$	154.513	+	576.650i	0.233756	+	0.872391i	0.978705	+	0.205270i	$0.0658071\pi$
$661$	154.513	+	576.650i	0.233756	+	0.872391i	−0.744949	+	0.667121i	$0.767526\pi$
$662$			66.0000i			0.0996979i
$663$		0			0
$664$	462.000			0.695783
$665$	−634.315	+	169.964i	−0.953858	+	0.255585i
$666$		0			0
$667$	−436.477	+	252.000i	−0.654388	+	0.377811i
$668$	−459.661	−	459.661i	−0.688115	−	0.688115i
$669$	−270.398	+	1009.14i	−0.404182	+	1.50843i
$670$	422.877	+	113.310i	0.631160	+	0.169119i
$671$	−140.712	+	140.712i	−0.209706	+	0.209706i
$672$	−346.500	−	600.156i	−0.515625	−	0.893089i
$673$	−66.6840	−	38.5000i	−0.0990846	−	0.0572065i	0.449639	−	0.893210i	$-0.351553\pi$
$673$	−66.6840	−	38.5000i	−0.0990846	−	0.0572065i	−0.548723	+	0.836004i	$0.684886\pi$
$674$	−368.256	−	1374.35i	−0.546374	−	2.03910i
$675$		−	378.000i		−	0.560000i
$676$		0			0
$677$	−726.000			−1.07238			−0.536189	−	0.844098i	$-0.680137\pi$
$677$	−726.000			−1.07238			−0.536189	+	0.844098i	$0.680137\pi$
$678$	−1210.97	+	324.477i	−1.78609	+	0.478580i
$679$	99.0000	−	171.473i	0.145803	−	0.252538i
$680$	85.7365	−	49.5000i	0.126083	−	0.0727941i
$681$	−408.066	−	408.066i	−0.599216	−	0.599216i
$682$	−226.619	+	845.754i	−0.332286	+	1.24011i
$683$	800.903	+	214.601i	1.17263	+	0.314204i	0.791998	−	0.610524i	$-0.209041\pi$
$683$	800.903	+	214.601i	1.17263	+	0.314204i	0.380628	+	0.924728i	$0.375708\pi$
$684$		0			0
$685$	−88.0000	−	152.420i	−0.128467	−	0.222512i
$686$	−28.5788	−	16.5000i	−0.0416601	−	0.0240525i
$687$	−69.5309	−	259.493i	−0.101209	−	0.377719i
$688$			245.000i			0.356105i
$689$		0			0
$690$	−396.000			−0.573913
$691$	−961.084	+	257.522i	−1.39086	+	0.372680i	−0.875054	−	0.484026i	$-0.839174\pi$
$691$	−961.084	+	257.522i	−1.39086	+	0.372680i	−0.515806	+	0.856705i	$0.672507\pi$
$692$	−399.000	+	691.088i	−0.576590	+	0.998682i
$693$		0			0
$694$	−386.959	−	386.959i	−0.557578	−	0.557578i
$695$	30.0442	−	112.126i	0.0432291	−	0.161333i
$696$	1210.97	+	324.477i	1.73989	+	0.466203i
$697$	−98.4987	+	98.4987i	−0.141318	+	0.141318i
$698$	−346.500	−	600.156i	−0.496418	−	0.859822i
$699$	1114.57	+	643.500i	1.59453	+	0.920601i
$700$	−252.371	−	941.862i	−0.360530	−	1.34552i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−990.000			−1.40825
$704$	621.501	−	166.531i	0.882814	−	0.236549i
$705$	−16.5000	+	28.5788i	−0.0234043	+	0.0405374i
$706$	−1848.10	+	1067.00i	−2.61770	+	1.51133i
$707$	1013.13	+	1013.13i	1.43300	+	1.43300i
$708$	288.424	−	1076.41i	0.407379	−	1.52036i
$709$	−115.330	−	30.9026i	−0.162666	−	0.0435862i	0.176567	−	0.984289i	$-0.443501\pi$
$709$	−115.330	−	30.9026i	−0.162666	−	0.0435862i	−0.339233	+	0.940702i	$0.610167\pi$
$710$	−180.581	+	180.581i	−0.254339	+	0.254339i
$711$		0			0
$712$	−1428.94	−	825.000i	−2.00694	−	1.15871i
$713$	−123.610	−	461.320i	−0.173367	−	0.647013i
$714$			297.000i			0.415966i
$715$		0			0
$716$	−903.000			−1.26117
$717$	740.035	−	198.292i	1.03213	−	0.276557i
$718$	−506.000	+	876.418i	−0.704735	+	1.22064i
$719$	−301.377	+	174.000i	−0.419161	+	0.242003i	−0.694718	−	0.719282i	$-0.744471\pi$
$719$	−301.377	+	174.000i	−0.419161	+	0.242003i	0.275557	+	0.961285i	$0.411138\pi$
$720$		0			0
$721$	66.9556	−	249.882i	0.0928650	−	0.346577i
$722$	112.126	+	30.0442i	0.155300	+	0.0416125i
$723$	−802.061	+	802.061i	−1.10935	+	1.10935i
$724$	637.000	+	1103.32i	0.879834	+	1.52392i
$725$	−509.223	−	294.000i	−0.702376	−	0.405517i
$726$	198.292	+	740.035i	0.273129	+	1.01933i
$727$			702.000i			0.965612i	0.875727	+	0.482806i	$0.160382\pi$
$727$			702.000i			0.965612i	−0.875727	+	0.482806i	$0.839618\pi$
$728$		0			0
$729$	729.000			1.00000
$730$	−422.877	+	113.310i	−0.579284	+	0.155219i
$731$	−73.5000	+	127.306i	−0.100547	+	0.174153i
$732$	−545.596	+	315.000i	−0.745350	+	0.430328i
$733$	−63.3206	−	63.3206i	−0.0863856	−	0.0863856i	0.662594	−	0.748979i	$-0.269456\pi$
$733$	−63.3206	−	63.3206i	−0.0863856	−	0.0863856i	−0.748979	+	0.662594i	$0.769456\pi$
$734$	−460.105	+	1717.14i	−0.626847	+	2.33942i
$735$	−480.542	−	128.761i	−0.653799	−	0.175185i
$736$	−196.997	+	196.997i	−0.267660	+	0.267660i
$737$	−132.000	−	228.631i	−0.179104	−	0.310218i
$738$		0			0
$739$	−46.3539	−	172.995i	−0.0627252	−	0.234094i	0.927445	−	0.373959i	$-0.122000\pi$
$739$	−46.3539	−	172.995i	−0.0627252	−	0.234094i	−0.990171	+	0.139865i	$0.955333\pi$
$740$			1155.00i			1.56081i
$741$		0			0
$742$	792.000			1.06739
$743$	−3.20361	+	0.858406i	−0.00431173	+	0.00115532i	−0.260974	−	0.965346i	$-0.584044\pi$
$743$	−3.20361	+	0.858406i	−0.00431173	+	0.00115532i	0.256663	+	0.966501i	$0.417377\pi$
$744$	−594.000	+	1028.84i	−0.798387	+	1.38285i
$745$	190.526	−	110.000i	0.255739	−	0.147651i
$746$	619.135	+	619.135i	0.829940	+	0.829940i
$747$		0			0
$748$	−134.552	−	36.0530i	−0.179882	−	0.0481992i
$749$	−802.061	+	802.061i	−1.07084	+	1.07084i
$750$	−643.500	−	1114.57i	−0.858000	−	1.48610i
$751$	147.224	+	85.0000i	0.196038	+	0.113182i	0.594806	−	0.803869i	$-0.297229\pi$
$751$	147.224	+	85.0000i	0.196038	+	0.113182i	−0.398768	+	0.917052i	$0.630562\pi$
$752$	−4.29203	−	16.0181i	−0.00570748	−	0.0213006i
$753$		−	126.000i		−	0.167331i
$754$		0			0
$755$	561.000			0.743046
$756$	1816.45	−	486.716i	2.40271	−	0.643804i
$757$	−252.000	+	436.477i	−0.332893	+	0.576588i	−0.983078	−	0.183189i	$-0.941358\pi$
$757$	−252.000	+	436.477i	−0.332893	+	0.576588i	0.650185	+	0.759776i	$0.274691\pi$
$758$	−1600.41	+	924.000i	−2.11137	+	1.21900i
$759$	168.855	+	168.855i	0.222470	+	0.222470i
$760$	169.964	−	634.315i	0.223637	−	0.834626i
$761$	−781.682	−	209.451i	−1.02718	−	0.275231i	−0.294387	−	0.955686i	$-0.595116\pi$
$761$	−781.682	−	209.451i	−1.02718	−	0.275231i	−0.732790	+	0.680455i	$0.761782\pi$
$762$	1181.98	−	1181.98i	1.55116	−	1.55116i
$763$	841.500	+	1457.52i	1.10288	+	1.91025i
$764$	−181.865	−	105.000i	−0.238044	−	0.137435i
$765$		0			0
$766$		−	935.000i		−	1.22063i
$767$		0			0
$768$	1113.00			1.44922
$769$	538.207	−	144.212i	0.699879	−	0.187532i	0.108703	−	0.994074i	$-0.465330\pi$
$769$	538.207	−	144.212i	0.699879	−	0.187532i	0.591176	+	0.806542i	$0.298664\pi$
$770$	363.000	−	628.734i	0.471429	−	0.816538i
$771$	678.098	−	391.500i	0.879504	−	0.507782i
$772$	−886.489	−	886.489i	−1.14830	−	1.14830i
$773$	328.769	−	1226.98i	0.425316	−	1.58730i	−0.337916	−	0.941176i	$-0.609722\pi$
$773$	328.769	−	1226.98i	0.425316	−	1.58730i	0.763232	−	0.646125i	$-0.223612\pi$
$774$		0			0
$775$	393.995	−	393.995i	0.508381	−	0.508381i
$776$	99.0000	+	171.473i	0.127577	+	0.220970i
$777$	−1286.05	−	742.500i	−1.65515	−	0.955598i
$778$	267.823	+	999.527i	0.344245	+	1.28474i
$779$			924.000i			1.18614i
$780$		0			0
$781$	154.000			0.197183
$782$	115.330	−	30.9026i	0.147481	−	0.0395174i
$783$	567.000	−	982.073i	0.724138	−	1.25424i
$784$	216.506	−	125.000i	0.276156	−	0.159439i
$785$	−187.617	−	187.617i	−0.239002	−	0.239002i
$786$	−239.495	+	893.808i	−0.304701	+	1.13716i
$787$	−365.212	−	97.8582i	−0.464056	−	0.124343i	0.0192130	−	0.999815i	$-0.493884\pi$
$787$	−365.212	−	97.8582i	−0.464056	−	0.124343i	−0.483269	+	0.875472i	$0.660551\pi$
$788$	1264.07	−	1264.07i	1.60415	−	1.60415i
$789$	405.000	+	701.481i	0.513308	+	0.889076i
$790$	514.419	+	297.000i	0.651163	+	0.375949i
$791$	324.477	+	1210.97i	0.410212	+	1.53093i
$792$		0			0
$793$		0			0
$794$	396.000			0.498741
$795$	230.660	−	61.8052i	0.290139	−	0.0777424i
$796$	966.000	−	1673.16i	1.21357	−	2.10196i
$797$	982.073	−	567.000i	1.23221	−	0.711418i	0.264721	−	0.964325i	$-0.414720\pi$
$797$	982.073	−	567.000i	1.23221	−	0.711418i	0.967491	+	0.252907i	$0.0813867\pi$
$798$	1393.05	+	1393.05i	1.74568	+	1.74568i
$799$	2.57522	−	9.61084i	0.00322305	−	0.0120286i
$800$	−313.954	−	84.1238i	−0.392443	−	0.105155i
$801$		0			0
$802$	−1276.00	−	2210.10i	−1.59102	−	2.75573i
$803$	228.631	+	132.000i	0.284721	+	0.164384i
$804$	−216.318	−	807.311i	−0.269053	−	1.00412i
$805$			396.000i			0.491925i
$806$		0			0
$807$	−558.000			−0.691450
$808$	−1383.96	+	370.831i	−1.71282	+	0.458950i
$809$	−232.500	+	402.702i	−0.287392	+	0.497777i	−0.973186	−	0.230018i	$-0.926122\pi$
$809$	−232.500	+	402.702i	−0.287392	+	0.497777i	0.685795	+	0.727795i	$0.259455\pi$
$810$	771.629	−	445.500i	0.952628	−	0.550000i
$811$	−1069.41	−	1069.41i	−1.31864	−	1.31864i	−0.914855	−	0.403782i	$-0.867695\pi$
$811$	−1069.41	−	1069.41i	−1.31864	−	1.31864i	−0.403782	−	0.914855i	$-0.632305\pi$
$812$	757.114	−	2825.59i	0.932406	−	3.47979i
$813$	−144.163	−	38.6283i	−0.177322	−	0.0475132i
$814$	773.919	−	773.919i	0.950760	−	0.950760i
$815$	198.000	+	342.946i	0.242945	+	0.420793i
$816$	−38.9711	−	22.5000i	−0.0477588	−	0.0275735i
$817$	252.371	+	941.862i	0.308900	+	1.15283i
$818$		−	792.000i		−	0.968215i
$819$		0			0
$820$	1078.00			1.31463
$821$	496.560	−	133.053i	0.604824	−	0.162062i	0.0566044	−	0.998397i	$-0.481973\pi$
$821$	496.560	−	133.053i	0.604824	−	0.162062i	0.548219	+	0.836335i	$0.315306\pi$
$822$	−264.000	+	457.261i	−0.321168	+	0.556279i
$823$	554.256	−	320.000i	0.673458	−	0.388821i	−0.123927	−	0.992291i	$-0.539549\pi$
$823$	554.256	−	320.000i	0.673458	−	0.388821i	0.797386	+	0.603470i	$0.206216\pi$
$824$	182.926	+	182.926i	0.221998	+	0.221998i
$825$	−72.1061	+	269.104i	−0.0874013	+	0.326186i
$826$	−1691.51	−	453.238i	−2.04783	−	0.548715i
$827$	−820.823	+	820.823i	−0.992531	+	0.992531i	−0.999972	−	0.00744177i	$-0.997631\pi$
$827$	−820.823	+	820.823i	−0.992531	+	0.992531i	0.00744177	+	0.999972i	$0.497631\pi$
$828$		0			0
$829$	−415.692	−	240.000i	−0.501438	−	0.289505i	0.227869	−	0.973692i	$-0.426824\pi$
$829$	−415.692	−	240.000i	−0.501438	−	0.289505i	−0.729307	+	0.684186i	$0.760157\pi$
$830$	−132.194	−	493.356i	−0.159270	−	0.594405i
$831$			1122.00i			1.35018i
$832$		0			0
$833$	150.000			0.180072
$834$	−336.379	+	90.1326i	−0.403333	+	0.108073i
$835$	−154.000	+	266.736i	−0.184431	+	0.319444i
$836$	−800.207	+	462.000i	−0.957186	+	0.552632i
$837$	759.847	+	759.847i	0.907822	+	0.907822i
$838$	332.203	−	1239.80i	0.396424	−	1.47947i
$839$	−448.506	−	120.177i	−0.534572	−	0.143238i	−0.0185733	−	0.999828i	$-0.505912\pi$
$839$	−448.506	−	120.177i	−0.534572	−	0.143238i	−0.515999	+	0.856589i	$0.672579\pi$
$840$	696.527	−	696.527i	0.829199	−	0.829199i
$841$	−461.500	−	799.341i	−0.548751	−	0.950465i
$842$	257.210	+	148.500i	0.305475	+	0.176366i
$843$	−36.0530	−	134.552i	−0.0427675	−	0.159611i
$844$			1617.00i			1.91588i
$845$		0			0
$846$		0			0
$847$	740.035	−	198.292i	0.873713	−	0.234111i
$848$	−60.0000	+	103.923i	−0.0707547	+	0.122551i
$849$	171.473	−	99.0000i	0.201971	−	0.116608i
$850$	98.4987	+	98.4987i	0.115881	+	0.115881i
$851$	−154.513	+	576.650i	−0.181566	+	0.677615i
$852$	470.931	+	126.186i	0.552736	+	0.148105i
$853$	246.247	−	246.247i	0.288683	−	0.288683i	−0.547876	−	0.836559i	$-0.684564\pi$
$853$	246.247	−	246.247i	0.288683	−	0.288683i	0.836559	+	0.547876i	$0.184564\pi$
$854$	495.000	+	857.365i	0.579625	+	1.00394i
$855$		0			0
$856$	−293.575	−	1095.64i	−0.342961	−	1.27995i
$857$		−	1326.00i		−	1.54726i	−0.633639	−	0.773629i	$-0.718439\pi$
$857$		−	1326.00i		−	1.54726i	0.633639	−	0.773629i	$-0.281561\pi$
$858$		0			0
$859$	54.0000			0.0628638			0.0314319	−	0.999506i	$-0.489993\pi$
$859$	54.0000			0.0628638			0.0314319	+	0.999506i	$0.489993\pi$
$860$	1098.84	−	294.433i	1.27772	−	0.342364i
$861$	−693.000	+	1200.31i	−0.804878	+	1.39409i
$862$	1247.94	−	720.500i	1.44773	−	0.835847i
$863$	363.507	+	363.507i	0.421213	+	0.421213i	0.885621	−	0.464408i	$-0.153733\pi$
$863$	363.507	+	363.507i	0.421213	+	0.421213i	−0.464408	+	0.885621i	$0.653733\pi$
$864$	162.239	−	605.483i	0.187776	−	0.700790i
$865$	365.212	+	97.8582i	0.422210	+	0.113131i
$866$	−738.740	+	738.740i	−0.853049	+	0.853049i
$867$	420.000	+	727.461i	0.484429	+	0.839056i
$868$	2400.62	+	1386.00i	2.76569	+	1.59677i
$869$	−92.7078	−	345.990i	−0.106683	−	0.398148i
$870$		−	1386.00i		−	1.59310i
$871$		0			0
$872$	−1683.00			−1.93005
$873$		0			0
$874$	396.000	−	685.892i	0.453089	−	0.784774i
$875$	−1114.57	+	643.500i	−1.27380	+	0.735429i
$876$	590.992	+	590.992i	0.674649	+	0.674649i
$877$	−229.194	+	855.365i	−0.261339	+	0.975330i	0.703114	+	0.711077i	$0.251792\pi$
$877$	−229.194	+	855.365i	−0.261339	+	0.975330i	−0.964453	+	0.264254i	$0.914874\pi$
$878$	2204.09	+	590.583i	2.51035	+	0.672646i
$879$	−344.746	+	344.746i	−0.392202	+	0.392202i
$880$	55.0000	+	95.2628i	0.0625000	+	0.108253i
$881$	563.783	+	325.500i	0.639935	+	0.369467i	0.784589	−	0.620016i	$-0.212874\pi$
$881$	563.783	+	325.500i	0.639935	+	0.369467i	−0.144655	+	0.989482i	$0.546207\pi$
$882$		0			0
$883$		−	819.000i		−	0.927520i	−0.885961	−	0.463760i	$-0.846500\pi$
$883$		−	819.000i		−	0.927520i	0.885961	−	0.463760i	$-0.153500\pi$
$884$		0			0
$885$	−528.000			−0.596610
$886$	−1047.58	+	280.699i	−1.18237	+	0.316816i
$887$	99.0000	−	171.473i	0.111612	−	0.193318i	−0.804808	−	0.593535i	$-0.797732\pi$
$887$	99.0000	−	171.473i	0.111612	−	0.193318i	0.916420	+	0.400217i	$0.131065\pi$
$888$	1286.05	−	742.500i	1.44825	−	0.836149i
$889$	−1181.98	−	1181.98i	−1.32957	−	1.32957i
$890$	−472.123	+	1761.99i	−0.530475	+	1.97976i
$891$	−518.985	−	139.062i	−0.582475	−	0.156074i
$892$	−1723.73	+	1723.73i	−1.93243	+	1.93243i
$893$	−33.0000	−	57.1577i	−0.0369541	−	0.0640064i
$894$	−571.577	−	330.000i	−0.639348	−	0.369128i
$895$	110.734	+	413.266i	0.123726	+	0.461750i
$896$		−	2277.00i		−	2.54129i
$897$		0			0
$898$	−1606.00			−1.78842
$899$	1614.62	−	432.636i	1.79602	−	0.481242i
$900$		0			0
$901$	−62.3538	+	36.0000i	−0.0692051	+	0.0399556i
$902$	−722.324	−	722.324i	−0.800803	−	0.800803i
$903$	−378.557	+	1412.79i	−0.419221	+	1.56456i
$904$	−1210.97	−	324.477i	−1.33956	−	0.358935i
$905$	426.828	−	426.828i	0.471633	−	0.471633i
$906$	−841.500	−	1457.52i	−0.928808	−	1.60874i
$907$	766.432	+	442.500i	0.845019	+	0.487872i	0.858967	−	0.512031i	$-0.171107\pi$
$907$	766.432	+	442.500i	0.845019	+	0.487872i	−0.0139479	+	0.999903i	$0.504440\pi$
$908$	−348.513	−	1300.67i	−0.383825	−	1.43245i
$909$		0			0
$910$		0			0
$911$	−882.000			−0.968167			−0.484083	−	0.875022i	$-0.660847\pi$
$911$	−882.000			−0.968167			−0.484083	+	0.875022i	$0.660847\pi$
$912$	−288.325	+	77.2565i	−0.316146	+	0.0847111i
$913$	−154.000	+	266.736i	−0.168675	+	0.292153i
$914$	−857.365	+	495.000i	−0.938036	+	0.541575i
$915$	211.069	+	211.069i	0.230676	+	0.230676i
$916$	162.239	−	605.483i	0.177116	−	0.661008i
$917$	893.808	+	239.495i	0.974709	+	0.261172i
$918$	−189.962	+	189.962i	−0.206930	+	0.206930i
$919$	−678.000	−	1174.33i	−0.737758	−	1.27784i	−0.953502	−	0.301385i	$-0.902551\pi$
$919$	−678.000	−	1174.33i	−0.737758	−	1.27784i	0.215744	−	0.976450i	$-0.430782\pi$
$920$	−342.946	−	198.000i	−0.372767	−	0.215217i
$921$	432.636	+	1614.62i	0.469746	+	1.75312i
$922$			781.000i			0.847072i
$923$		0			0
$924$	−1386.00			−1.50000
$925$	−672.759	+	180.265i	−0.727307	+	0.194881i
$926$	924.000	−	1600.41i	0.997840	−	1.72831i
$927$		0			0
$928$	−689.491	−	689.491i	−0.742986	−	0.742986i
$929$	−17.1681	+	64.0723i	−0.0184802	+	0.0689691i	−0.974550	−	0.224170i	$-0.928033\pi$
$929$	−17.1681	+	64.0723i	−0.0184802	+	0.0689691i	0.956070	+	0.293139i	$0.0946997\pi$
$930$	1268.63	+	339.929i	1.36412	+	0.365515i
$931$	703.562	−	703.562i	0.755706	−	0.755706i
$932$	1501.50	+	2600.67i	1.61105	+	2.79042i
$933$	−607.950	−	351.000i	−0.651608	−	0.376206i
$934$	334.778	+	1249.41i	0.358435	+	1.33770i
$935$			66.0000i			0.0705882i
$936$		0			0
$937$	210.000			0.224120			0.112060	−	0.993701i	$-0.464255\pi$
$937$	210.000			0.224120			0.112060	+	0.993701i	$0.464255\pi$
$938$	−1268.63	+	339.929i	−1.35249	+	0.362397i
$939$	139.500	−	241.621i	0.148562	−	0.257317i
$940$	−66.6840	+	38.5000i	−0.0709404	+	0.0409574i
$941$	241.556	+	241.556i	0.256702	+	0.256702i	0.823711	−	0.567009i	$-0.191900\pi$
$941$	241.556	+	241.556i	0.256702	+	0.256702i	−0.567009	+	0.823711i	$0.691900\pi$
$942$	−206.017	+	768.867i	−0.218702	+	0.816207i
$943$	538.207	+	144.212i	0.570739	+	0.152929i
$944$	187.617	−	187.617i	0.198746	−	0.198746i
$945$	−445.500	−	771.629i	−0.471429	−	0.816538i
$946$	−933.575	−	539.000i	−0.986866	−	0.569767i
$947$	−269.539	−	1005.93i	−0.284624	−	1.06223i	−0.949113	−	0.314935i	$-0.898017\pi$
$947$	−269.539	−	1005.93i	−0.284624	−	1.06223i	0.664489	−	0.747298i	$-0.268649\pi$
$948$		−	1134.00i		−	1.19620i
$949$		0			0
$950$	924.000			0.972632
$951$	−884.197	+	236.920i	−0.929755	+	0.249127i
$952$	−148.500	+	257.210i	−0.155987	+	0.270178i
$953$	−335.152	+	193.500i	−0.351681	+	0.203043i	−0.665425	−	0.746464i	$-0.731750\pi$
$953$	−335.152	+	193.500i	−0.351681	+	0.203043i	0.313744	+	0.949507i	$0.398416\pi$
$954$		0			0
$955$	−25.7522	+	96.1084i	−0.0269656	+	0.100637i
$956$	1726.75	+	462.681i	1.80622	+	0.483976i
$957$	−590.992	+	590.992i	−0.617547	+	0.617547i
$958$	797.500	+	1381.31i	0.832463	+	1.44187i
$959$	457.261	+	264.000i	0.476811	+	0.275287i
$960$	−249.796	−	932.252i	−0.260204	−	0.971095i
$961$			623.000i			0.648283i
$962$		0			0
$963$		0			0
$964$	−2556.48	+	685.008i	−2.65195	+	0.710589i
$965$	−297.000	+	514.419i	−0.307772	+	0.533077i
$966$	1028.84	−	594.000i	1.06505	−	0.614907i
$967$	−246.247	−	246.247i	−0.254650	−	0.254650i	0.568224	−	0.822874i	$-0.307631\pi$
$967$	−246.247	−	246.247i	−0.254650	−	0.254650i	−0.822874	+	0.568224i	$0.807631\pi$
$968$	−198.292	+	740.035i	−0.204847	+	0.764499i
$969$	−172.995	−	46.3539i	−0.178530	−	0.0478368i
$970$	154.784	−	154.784i	0.159571	−	0.159571i
$971$	823.500	+	1426.34i	0.848095	+	1.46894i	0.882906	+	0.469549i	$0.155584\pi$
$971$	823.500	+	1426.34i	0.848095	+	1.46894i	−0.0348115	+	0.999394i	$0.511083\pi$
$972$		0			0
$973$	90.1326	+	336.379i	0.0926337	+	0.345714i
$974$		−	792.000i		−	0.813142i
$975$		0			0
$976$	−150.000			−0.153689
$977$	−1127.67	+	302.159i	−1.15422	+	0.309272i	−0.784655	−	0.619933i	$-0.787160\pi$
$977$	−1127.67	+	302.159i	−1.15422	+	0.309272i	−0.369564	+	0.929205i	$0.620493\pi$
$978$	594.000	−	1028.84i	0.607362	−	1.05198i
$979$	952.628	−	550.000i	0.973062	−	0.561798i
$980$	−820.823	−	820.823i	−0.837574	−	0.837574i
$981$		0			0
$982$	−2085.55	−	558.822i	−2.12378	−	0.569065i
$983$	185.271	−	185.271i	0.188476	−	0.188476i	−0.606561	−	0.795037i	$-0.707452\pi$
$983$	185.271	−	185.271i	0.188476	−	0.188476i	0.795037	+	0.606561i	$0.207452\pi$
$984$	−693.000	−	1200.31i	−0.704268	−	1.21983i
$985$	−733.524	−	423.500i	−0.744694	−	0.429949i
$986$	108.159	+	403.655i	0.109695	+	0.409387i
$987$		−	99.0000i		−	0.100304i
$988$		0			0
$989$	588.000			0.594540
$990$		0			0
$991$	775.000	−	1342.34i	0.782038	−	1.35453i	−0.148714	−	0.988880i	$-0.547513\pi$
$991$	775.000	−	1342.34i	0.782038	−	1.35453i	0.930752	−	0.365650i	$-0.119153\pi$
$992$	800.207	−	462.000i	0.806661	−	0.465726i
$993$	−42.2137	−	42.2137i	−0.0425113	−	0.0425113i
$994$	198.292	−	740.035i	0.199489	−	0.744502i
$995$	−884.197	−	236.920i	−0.888641	−	0.238111i
$996$	−689.491	+	689.491i	−0.692260	+	0.692260i
$997$	583.000	+	1009.79i	0.584754	+	1.01282i	0.994906	+	0.100807i	$0.0321424\pi$
$997$	583.000	+	1009.79i	0.584754	+	1.01282i	−0.410152	+	0.912017i	$0.634524\pi$
$998$	−857.365	−	495.000i	−0.859083	−	0.495992i
$999$	−347.654	−	1297.46i	−0.348002	−	1.29876i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.e.150.1		8
13.2	odd	12	inner	169.3.f.e.80.1		8
13.3	even	3	inner	169.3.f.e.89.2		8
13.4	even	6		169.3.d.b.99.1	yes	4
13.5	odd	4	inner	169.3.f.e.19.2		8
13.6	odd	12		169.3.d.b.70.2	yes	4
13.7	odd	12		169.3.d.b.70.1	✓	4
13.8	odd	4	inner	169.3.f.e.19.1		8
13.9	even	3		169.3.d.b.99.2	yes	4
13.10	even	6	inner	169.3.f.e.89.1		8
13.11	odd	12	inner	169.3.f.e.80.2		8
13.12	even	2	inner	169.3.f.e.150.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
169.3.d.b.70.1	✓	4	13.7	odd	12
169.3.d.b.70.2	yes	4	13.6	odd	12
169.3.d.b.99.1	yes	4	13.4	even	6
169.3.d.b.99.2	yes	4	13.9	even	3
169.3.f.e.19.1		8	13.8	odd	4	inner
169.3.f.e.19.2		8	13.5	odd	4	inner
169.3.f.e.80.1		8	13.2	odd	12	inner
169.3.f.e.80.2		8	13.11	odd	12	inner
169.3.f.e.89.1		8	13.10	even	6	inner
169.3.f.e.89.2		8	13.3	even	3	inner
169.3.f.e.150.1		8	1.1	even	1	trivial
169.3.f.e.150.2		8	13.12	even	2	inner

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	169.3.f.e.150.1

Level	$169$
Weight	$3$
Character	169.150
Analytic conductor	$4.605$
Analytic rank	$0$
Dimension	$8$
Inner twists	$8$