LMFDB - Embedded newform 169.3.f.e.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [169,3,Mod(19,169)]

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

lf = mfeigenbasis(mf)

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")

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

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			19.1
Root			$-0.858406 - 3.20361i$ of defining polynomial
Character	$\chi$	$=$	169.19
Dual form			169.3.f.e.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.858406 - 3.20361i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-6.06218 + 3.50000i) q^{4} +(2.34521 - 2.34521i) q^{5} +(-9.61084 - 2.57522i) q^{6} +(2.57522 - 9.61084i) q^{7} +(7.03562 + 7.03562i) q^{8} +(-9.52628 - 5.50000i) q^{10} +(-6.40723 + 1.71681i) q^{11} +21.0000i q^{12} -33.0000 q^{14} +(-2.57522 - 9.61084i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-2.59808 + 1.50000i) q^{17} +(19.2217 + 5.15043i) q^{19} +(-6.00884 + 22.4253i) q^{20} +(-21.1069 - 21.1069i) q^{21} +(11.0000 + 19.0526i) q^{22} +(10.3923 + 6.00000i) q^{23} +(28.8325 - 7.72565i) q^{24} +14.0000i q^{25} +27.0000 q^{27} +(18.0265 + 67.2759i) q^{28} +(21.0000 - 36.3731i) q^{29} +(-28.5788 + 16.5000i) q^{30} +(-28.1425 + 28.1425i) q^{31} +(22.4253 + 6.00884i) q^{32} +(-5.15043 + 19.2217i) q^{33} +(7.03562 + 7.03562i) q^{34} +(-16.5000 - 28.5788i) q^{35} +(-48.0542 + 12.8761i) q^{37} -66.0000i q^{38} +33.0000 q^{40} +(-12.0177 - 44.8506i) q^{41} +(-49.5000 + 85.7365i) q^{42} +(42.4352 - 24.5000i) q^{43} +(32.8329 - 32.8329i) q^{44} +(10.3009 - 38.4434i) q^{46} +(-2.34521 - 2.34521i) q^{47} +(-7.50000 - 12.9904i) q^{48} +(-43.3013 - 25.0000i) q^{49} +(44.8506 - 12.0177i) q^{50} +9.00000i q^{51} -24.0000 q^{53} +(-23.1770 - 86.4976i) q^{54} +(-11.0000 + 19.0526i) q^{55} +(85.7365 - 49.5000i) q^{56} +(42.2137 - 42.2137i) q^{57} +(-134.552 - 36.0530i) q^{58} +(13.7345 - 51.2578i) 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} +(10.3009 + 38.4434i) q^{67} +(10.5000 - 18.1865i) q^{68} +(31.1769 - 18.0000i) q^{69} +(-77.3919 + 77.3919i) q^{70} +(-22.4253 - 6.00884i) q^{71} +(28.1425 + 28.1425i) q^{73} +(82.5000 + 142.894i) q^{74} +(36.3731 + 21.0000i) q^{75} +(-134.552 + 36.0530i) q^{76} +66.0000i q^{77} +54.0000 q^{79} +(-4.29203 - 16.0181i) q^{80} +(40.5000 - 70.1481i) q^{81} +(-133.368 + 77.0000i) q^{82} +(32.8329 - 32.8329i) q^{83} +(201.828 + 54.0796i) q^{84} +(-2.57522 + 9.61084i) q^{85} +(-114.915 - 114.915i) q^{86} +(-63.0000 - 109.119i) q^{87} +(-57.1577 - 33.0000i) q^{88} +(160.181 - 42.9203i) q^{89} -84.0000 q^{92} +(30.9026 + 115.330i) q^{93} +(-5.50000 + 9.52628i) q^{94} +(57.1577 - 33.0000i) q^{95} +(49.2494 - 49.2494i) q^{96} +(19.2217 + 5.15043i) q^{97} +(-42.9203 + 160.181i) 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 $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.858406	−	3.20361i	−0.429203	−	1.60181i	−0.754570	−	0.656219i	$-0.772155\pi$
$2$	−0.858406	−	3.20361i	−0.429203	−	1.60181i	0.325368	−	0.945588i	$-0.394512\pi$
$3$	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	$-0.642390\pi$
$5$	2.34521	−	2.34521i	0.469042	−	0.469042i	0.901604	+	0.432562i	$0.142390\pi$
$6$	−9.61084	−	2.57522i	−1.60181	−	0.429203i
$7$	2.57522	−	9.61084i	0.367888	−	1.37298i	−0.495575	−	0.868565i	$-0.665043\pi$
$7$	2.57522	−	9.61084i	0.367888	−	1.37298i	0.863463	−	0.504412i	$-0.168291\pi$
$8$	7.03562	+	7.03562i	0.879453	+	0.879453i
$9$		0			0
$10$	−9.52628	−	5.50000i	−0.952628	−	0.550000i
$11$	−6.40723	+	1.71681i	−0.582475	+	0.156074i	−0.538012	−	0.842937i	$-0.680824\pi$
$11$	−6.40723	+	1.71681i	−0.582475	+	0.156074i	−0.0444633	+	0.999011i	$0.514158\pi$
$12$			21.0000i			1.75000i
$13$		0			0
$13$		0			0
$14$	−33.0000			−2.35714
$15$	−2.57522	−	9.61084i	−0.171681	−	0.640723i
$16$	2.50000	−	4.33013i	0.156250	−	0.270633i
$17$	−2.59808	+	1.50000i	−0.152828	+	0.0882353i	−0.574464	−	0.818530i	$-0.694789\pi$
$17$	−2.59808	+	1.50000i	−0.152828	+	0.0882353i	0.421636	+	0.906765i	$0.361456\pi$
$18$		0			0
$19$	19.2217	+	5.15043i	1.01167	+	0.271075i	0.726326	−	0.687350i	$-0.241226\pi$
$19$	19.2217	+	5.15043i	1.01167	+	0.271075i	0.285341	+	0.958426i	$0.407893\pi$
$20$	−6.00884	+	22.4253i	−0.300442	+	1.12126i
$21$	−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	0.708607	−	0.705604i	$-0.249324\pi$
$23$	10.3923	+	6.00000i	0.451839	+	0.260870i	−0.256767	+	0.966473i	$0.582657\pi$
$24$	28.8325	−	7.72565i	1.20136	−	0.321902i
$25$			14.0000i			0.560000i
$26$		0			0
$27$	27.0000			1.00000
$28$	18.0265	+	67.2759i	0.643804	+	2.40271i
$29$	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	$-0.971865\pi$
$31$	−28.1425	+	28.1425i	−0.907822	+	0.907822i	0.0882738	+	0.996096i	$0.471865\pi$
$32$	22.4253	+	6.00884i	0.700790	+	0.187776i
$33$	−5.15043	+	19.2217i	−0.156074	+	0.582475i
$34$	7.03562	+	7.03562i	0.206930	+	0.206930i
$35$	−16.5000	−	28.5788i	−0.471429	−	0.816538i
$36$		0			0
$37$	−48.0542	+	12.8761i	−1.29876	+	0.348002i	−0.840982	−	0.541063i	$-0.818022\pi$
$37$	−48.0542	+	12.8761i	−1.29876	+	0.348002i	−0.457780	+	0.889065i	$0.651355\pi$
$38$		−	66.0000i		−	1.73684i
$39$		0			0
$40$	33.0000			0.825000
$41$	−12.0177	−	44.8506i	−0.293114	−	1.09392i	−0.942704	−	0.333632i	$-0.891726\pi$
$41$	−12.0177	−	44.8506i	−0.293114	−	1.09392i	0.649589	−	0.760285i	$-0.274941\pi$
$42$	−49.5000	+	85.7365i	−1.17857	+	2.04135i
$43$	42.4352	−	24.5000i	0.986866	−	0.569767i	0.0825301	−	0.996589i	$-0.473700\pi$
$43$	42.4352	−	24.5000i	0.986866	−	0.569767i	0.904336	+	0.426821i	$0.140367\pi$
$44$	32.8329	−	32.8329i	0.746203	−	0.746203i
$45$		0			0
$46$	10.3009	−	38.4434i	0.223932	−	0.835725i
$47$	−2.34521	−	2.34521i	−0.0498980	−	0.0498980i	0.681717	−	0.731616i	$-0.261233\pi$
$47$	−2.34521	−	2.34521i	−0.0498980	−	0.0498980i	−0.731616	+	0.681717i	$0.761233\pi$
$48$	−7.50000	−	12.9904i	−0.156250	−	0.270633i
$49$	−43.3013	−	25.0000i	−0.883699	−	0.510204i
$50$	44.8506	−	12.0177i	0.897012	−	0.240354i
$51$			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	$0.572701\pi$
$54$	−23.1770	−	86.4976i	−0.429203	−	1.60181i
$55$	−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
$58$	−134.552	−	36.0530i	−2.31986	−	0.621604i
$59$	13.7345	−	51.2578i	0.232788	−	0.868777i	−0.746346	−	0.665559i	$-0.768193\pi$
$59$	13.7345	−	51.2578i	0.232788	−	0.868777i	0.979134	−	0.203218i	$-0.0651400\pi$
$60$	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
$67$	10.3009	+	38.4434i	0.153744	+	0.573782i	0.999210	+	0.0397512i	$0.0126565\pi$
$67$	10.3009	+	38.4434i	0.153744	+	0.573782i	−0.845465	+	0.534030i	$0.820677\pi$
$68$	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
$71$	−22.4253	−	6.00884i	−0.315849	−	0.0846315i	0.0974118	−	0.995244i	$-0.468944\pi$
$71$	−22.4253	−	6.00884i	−0.315849	−	0.0846315i	−0.413261	+	0.910613i	$0.635610\pi$
$72$		0			0
$73$	28.1425	+	28.1425i	0.385514	+	0.385514i	0.873084	−	0.487570i	$-0.162117\pi$
$73$	28.1425	+	28.1425i	0.385514	+	0.385514i	−0.487570	+	0.873084i	$0.662117\pi$
$74$	82.5000	+	142.894i	1.11486	+	1.93100i
$75$	36.3731	+	21.0000i	0.484974	+	0.280000i
$76$	−134.552	+	36.0530i	−1.77042	+	0.474382i
$77$			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	$0.388973\pi$
$80$	−4.29203	−	16.0181i	−0.0536504	−	0.200226i
$81$	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	$-0.659760\pi$
$83$	32.8329	−	32.8329i	0.395577	−	0.395577i	0.876670	+	0.481093i	$0.159760\pi$
$84$	201.828	+	54.0796i	2.40271	+	0.643804i
$85$	−2.57522	+	9.61084i	−0.0302967	+	0.113069i
$86$	−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
$89$	160.181	−	42.9203i	1.79978	−	0.482250i	0.805839	−	0.592135i	$-0.201715\pi$
$89$	160.181	−	42.9203i	1.79978	−	0.482250i	0.993944	+	0.109885i	$0.0350482\pi$
$90$		0			0
$91$		0			0
$92$	−84.0000			−0.913043
$93$	30.9026	+	115.330i	0.332286	+	1.24011i
$94$	−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
$97$	19.2217	+	5.15043i	0.198162	+	0.0530973i	0.356535	−	0.934282i	$-0.383958\pi$
$97$	19.2217	+	5.15043i	0.198162	+	0.0530973i	−0.158373	+	0.987379i	$0.550625\pi$
$98$	−42.9203	+	160.181i	−0.437962	+	1.63450i
$99$		0			0
$100$	−49.0000	−	84.8705i	−0.490000	−	0.848705i
$101$	−124.708	−	72.0000i	−1.23473	−	0.712871i	−0.266717	−	0.963775i	$-0.585939\pi$
$101$	−124.708	−	72.0000i	−1.23473	−	0.712871i	−0.968012	+	0.250904i	$0.919272\pi$
$102$	28.8325	−	7.72565i	0.282672	−	0.0757417i
$103$			26.0000i			0.252427i	0.992003	+	0.126214i	$0.0402825\pi$
$103$			26.0000i			0.252427i	−0.992003	+	0.126214i	$0.959718\pi$
$104$		0			0
$105$	−99.0000			−0.942857
$106$	20.6017	+	76.8867i	0.194356	+	0.725346i
$107$	−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	−0.102574	+	0.994725i	$0.532708\pi$
$109$	−119.606	+	119.606i	−1.09730	+	1.09730i	−0.994725	+	0.102574i	$0.967292\pi$
$110$	70.4795	+	18.8849i	0.640723	+	0.171681i
$111$	−38.6283	+	144.163i	−0.348002	+	1.29876i
$112$	−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
$115$	38.4434	−	10.3009i	0.334290	−	0.0895728i
$116$			294.000i			2.53448i
$117$		0			0
$118$	−176.000			−1.49153
$119$	7.72565	+	28.8325i	0.0649214	+	0.242290i
$120$	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
$123$	−134.552	−	36.0530i	−1.09392	−	0.293114i
$124$	72.1061	−	269.104i	0.581501	−	2.17019i
$125$	91.4631	+	91.4631i	0.731705	+	0.731705i
$126$		0			0
$127$	145.492	+	84.0000i	1.14561	+	0.661417i	0.947813	−	0.318826i	$-0.103289\pi$
$127$	145.492	+	84.0000i	1.14561	+	0.661417i	0.197795	+	0.980243i	$0.436622\pi$
$128$	−221.049	+	59.2300i	−1.72695	+	0.462734i
$129$		−	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	$0.384494\pi$
$132$	−36.0530	−	134.552i	−0.273129	−	1.01933i
$133$	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
$136$	−28.8325	−	7.72565i	−0.212004	−	0.0568063i
$137$	13.7345	−	51.2578i	0.100252	−	0.374145i	−0.897512	−	0.440991i	$-0.854627\pi$
$137$	13.7345	−	51.2578i	0.100252	−	0.374145i	0.997763	+	0.0668464i	$0.0212937\pi$
$138$	−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
$141$	−9.61084	+	2.57522i	−0.0681620	+	0.0182640i
$142$			77.0000i			0.542254i
$143$		0			0
$144$		0			0
$145$	−36.0530	−	134.552i	−0.248642	−	0.927943i
$146$	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
$149$	−64.0723	−	17.1681i	−0.430015	−	0.115222i	0.0373181	−	0.999303i	$-0.488119\pi$
$149$	−64.0723	−	17.1681i	−0.430015	−	0.115222i	−0.467333	+	0.884081i	$0.654785\pi$
$150$	36.0530	−	134.552i	0.240354	−	0.897012i
$151$	119.606	+	119.606i	0.792090	+	0.792090i	0.981834	−	0.189744i	$-0.0607657\pi$
$151$	119.606	+	119.606i	0.792090	+	0.792090i	−0.189744	+	0.981834i	$0.560766\pi$
$152$	99.0000	+	171.473i	0.651316	+	1.12811i
$153$		0			0
$154$	211.438	−	56.6548i	1.37298	−	0.367888i
$155$			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	$0.417998\pi$
$158$	−46.3539	−	172.995i	−0.293379	−	1.09491i
$159$	−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
$162$	−259.493	−	69.5309i	−1.60181	−	0.429203i
$163$	−30.9026	+	115.330i	−0.189587	+	0.707547i	0.804015	+	0.594608i	$0.202693\pi$
$163$	−30.9026	+	115.330i	−0.189587	+	0.707547i	−0.993602	+	0.112938i	$0.963974\pi$
$164$	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
$167$	−89.7012	+	24.0354i	−0.537133	+	0.143924i	−0.517180	−	0.855877i	$-0.673018\pi$
$167$	−89.7012	+	24.0354i	−0.537133	+	0.143924i	−0.0199528	+	0.999801i	$0.506352\pi$
$168$		−	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	−0.186743	−	0.982409i	$-0.559793\pi$
$173$	98.7269	−	57.0000i	0.570676	−	0.329480i	0.757419	+	0.652929i	$0.226460\pi$
$174$	−295.496	+	295.496i	−1.69825	+	1.69825i
$175$	134.552	+	36.0530i	0.768867	+	0.206017i
$176$	−8.58406	+	32.0361i	−0.0487730	+	0.182023i
$177$	−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	0.778471	−	0.627681i	$-0.215996\pi$
$179$	111.717	+	64.5000i	0.624119	+	0.360335i	−0.154352	+	0.988016i	$0.549329\pi$
$180$		0			0
$181$		−	182.000i		−	1.00552i	−0.864425	−	0.502762i	$-0.832317\pi$
$181$		−	182.000i		−	1.00552i	0.864425	−	0.502762i	$-0.167683\pi$
$182$		0			0
$183$	−90.0000			−0.491803
$184$	30.9026	+	115.330i	0.167949	+	0.626794i
$185$	−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
$188$	22.4253	+	6.00884i	0.119283	+	0.0319619i
$189$	69.5309	−	259.493i	0.367888	−	1.37298i
$190$	−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
$193$	−172.995	+	46.3539i	−0.896348	+	0.240176i	−0.677447	−	0.735571i	$-0.736914\pi$
$193$	−172.995	+	46.3539i	−0.896348	+	0.240176i	−0.218901	+	0.975747i	$0.570247\pi$
$194$		−	66.0000i		−	0.340206i
$195$		0			0
$196$	350.000			1.78571
$197$	66.0972	+	246.678i	0.335519	+	1.25217i	0.903305	+	0.428998i	$0.141133\pi$
$197$	66.0972	+	246.678i	0.335519	+	1.25217i	−0.567786	+	0.823176i	$0.692200\pi$
$198$		0			0
$199$	−239.023	+	138.000i	−1.20112	+	0.693467i	−0.960804	−	0.277227i	$-0.910584\pi$
$199$	−239.023	+	138.000i	−1.20112	+	0.693467i	−0.240316	+	0.970695i	$0.577251\pi$
$200$	−98.4987	+	98.4987i	−0.492494	+	0.492494i
$201$	115.330	+	30.9026i	0.573782	+	0.153744i
$202$	−123.610	+	461.320i	−0.611933	+	2.28376i
$203$	−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
$206$	83.2940	−	22.3185i	0.404340	−	0.108342i
$207$		0			0
$208$		0			0
$209$	−132.000			−0.631579
$210$	84.9822	+	317.158i	0.404677	+	1.51027i
$211$	−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
$214$	365.212	+	97.8582i	1.70660	+	0.457282i
$215$	42.0619	−	156.977i	0.195637	−	0.730126i
$216$	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
$219$	115.330	−	30.9026i	0.526621	−	0.141108i
$220$		−	154.000i		−	0.700000i
$221$		0			0
$222$	495.000			2.22973
$223$	−90.1326	−	336.379i	−0.404182	−	1.50843i	−0.805559	−	0.592515i	$-0.798135\pi$
$223$	−90.1326	−	336.379i	−0.404182	−	1.50843i	0.401377	−	0.915913i	$-0.368532\pi$
$224$	115.500	−	200.052i	0.515625	−	0.893089i
$225$		0			0
$226$	295.496	−	295.496i	1.30751	−	1.30751i
$227$	185.810	+	49.7875i	0.818544	+	0.219328i	0.643710	−	0.765270i	$-0.277394\pi$
$227$	185.810	+	49.7875i	0.818544	+	0.219328i	0.174834	+	0.984598i	$0.444061\pi$
$228$	−108.159	+	403.655i	−0.474382	+	1.77042i
$229$	−63.3206	−	63.3206i	−0.276509	−	0.276509i	0.555205	−	0.831714i	$-0.312640\pi$
$229$	−63.3206	−	63.3206i	−0.276509	−	0.276509i	−0.831714	+	0.555205i	$0.812640\pi$
$230$	−66.0000	−	114.315i	−0.286957	−	0.497023i
$231$	171.473	+	99.0000i	0.742307	+	0.428571i
$232$	403.655	−	108.159i	1.73989	−	0.466203i
$233$		−	429.000i		−	1.84120i	−0.390505	−	0.920601i	$-0.627700\pi$
$233$		−	429.000i		−	1.84120i	0.390505	−	0.920601i	$-0.372300\pi$
$234$		0			0
$235$	−11.0000			−0.0468085
$236$	96.1414	+	358.805i	0.407379	+	1.52036i
$237$	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	$-0.929413\pi$
$239$	−180.581	+	180.581i	−0.755569	+	0.755569i	0.219944	+	0.975513i	$0.429413\pi$
$240$	−48.0542	−	12.8761i	−0.200226	−	0.0536504i
$241$	−97.8582	+	365.212i	−0.406051	+	1.51540i	0.396059	+	0.918225i	$0.370378\pi$
$241$	−97.8582	+	365.212i	−0.406051	+	1.51540i	−0.802109	+	0.597177i	$0.796289\pi$
$242$	180.581	+	180.581i	0.746203	+	0.746203i
$243$		0			0
$244$	181.865	+	105.000i	0.745350	+	0.430328i
$245$	−160.181	+	42.9203i	−0.653799	+	0.175185i
$246$			462.000i			1.87805i
$247$		0			0
$248$	−396.000			−1.59677
$249$	−36.0530	−	134.552i	−0.144791	−	0.540369i
$250$	214.500	−	371.525i	0.858000	−	1.48610i
$251$	−36.3731	+	21.0000i	−0.144913	+	0.0836653i	−0.570703	−	0.821156i	$-0.693329\pi$
$251$	−36.3731	+	21.0000i	−0.144913	+	0.0836653i	0.425791	+	0.904822i	$0.359996\pi$
$252$		0			0
$253$	−76.8867	−	20.6017i	−0.303900	−	0.0814298i
$254$	144.212	−	538.207i	0.567764	−	2.11893i
$255$	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	−0.00900943	−	0.999959i	$-0.502868\pi$
$257$	−226.033	−	130.500i	−0.879504	−	0.507782i	−0.870495	+	0.492177i	$0.836201\pi$
$258$	−470.931	+	126.186i	−1.82531	+	0.489092i
$259$			495.000i			1.91120i
$260$		0			0
$261$		0			0
$262$	−79.8317	−	297.936i	−0.304701	−	1.13716i
$263$	−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
$266$	−634.315	−	169.964i	−2.38464	−	0.638964i
$267$	128.761	−	480.542i	0.482250	−	1.79978i
$268$	−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
$271$	−48.0542	+	12.8761i	−0.177322	+	0.0475132i	−0.346387	−	0.938092i	$-0.612592\pi$
$271$	−48.0542	+	12.8761i	−0.177322	+	0.0475132i	0.169066	+	0.985605i	$0.445925\pi$
$272$			15.0000i			0.0551471i
$273$		0			0
$274$	−176.000			−0.642336
$275$	−24.0354	−	89.7012i	−0.0874013	−	0.326186i
$276$	−126.000	+	218.238i	−0.456522	+	0.790719i
$277$	323.894	−	187.000i	1.16929	−	0.675090i	0.215778	−	0.976443i	$-0.430771\pi$
$277$	323.894	−	187.000i	1.16929	−	0.675090i	0.953513	+	0.301352i	$0.0974380\pi$
$278$	82.0823	−	82.0823i	0.295260	−	0.295260i
$279$		0			0
$280$	84.9822	−	317.158i	0.303508	−	1.13271i
$281$	−32.8329	−	32.8329i	−0.116843	−	0.116843i	0.646268	−	0.763111i	$-0.276329\pi$
$281$	−32.8329	−	32.8329i	−0.116843	−	0.116843i	−0.763111	+	0.646268i	$0.776329\pi$
$282$	16.5000	+	28.5788i	0.0585106	+	0.101343i
$283$	−57.1577	−	33.0000i	−0.201971	−	0.116608i	0.395604	−	0.918421i	$-0.370535\pi$
$283$	−57.1577	−	33.0000i	−0.201971	−	0.116608i	−0.597574	+	0.801814i	$0.703869\pi$
$284$	156.977	−	42.0619i	0.552736	−	0.148105i
$285$		−	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
$292$	−269.104	−	72.1061i	−0.921587	−	0.246939i
$293$	−42.0619	+	156.977i	−0.143556	+	0.535758i	0.856260	+	0.516546i	$0.172782\pi$
$293$	−42.0619	+	156.977i	−0.143556	+	0.535758i	−0.999815	+	0.0192121i	$0.993884\pi$
$294$	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
$297$	−172.995	+	46.3539i	−0.582475	+	0.156074i
$298$			220.000i			0.738255i
$299$		0			0
$300$	−294.000			−0.980000
$301$	−126.186	−	470.931i	−0.419221	−	1.56456i
$302$	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
$305$	−96.1084	−	25.7522i	−0.315110	−	0.0844333i
$306$		0			0
$307$	393.995	+	393.995i	1.28337	+	1.28337i	0.938737	+	0.344634i	$0.111997\pi$
$307$	393.995	+	393.995i	1.28337	+	1.28337i	0.344634	+	0.938737i	$0.388003\pi$
$308$	−231.000	−	400.104i	−0.750000	−	1.29904i
$309$	67.5500	+	39.0000i	0.218608	+	0.126214i
$310$	422.877	−	113.310i	1.36412	−	0.365515i
$311$			234.000i			0.752412i	0.926536	+	0.376206i	$0.122771\pi$
$311$			234.000i			0.752412i	−0.926536	+	0.376206i	$0.877229\pi$
$312$		0			0
$313$	93.0000			0.297125			0.148562	−	0.988903i	$-0.452535\pi$
$313$	93.0000			0.297125			0.148562	+	0.988903i	$0.452535\pi$
$314$	−68.6725	−	256.289i	−0.218702	−	0.816207i
$315$		0			0
$316$	−327.358	+	189.000i	−1.03594	+	0.598101i
$317$	215.759	−	215.759i	0.680628	−	0.680628i	−0.279514	−	0.960142i	$-0.590173\pi$
$317$	215.759	−	215.759i	0.680628	−	0.680628i	0.960142	+	0.279514i	$0.0901732\pi$
$318$	230.660	+	61.8052i	0.725346	+	0.194356i
$319$	−72.1061	+	269.104i	−0.226038	+	0.843585i
$320$	−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
$323$	−57.6650	+	15.4513i	−0.178530	+	0.0478368i
$324$			567.000i			1.75000i
$325$		0			0
$326$	396.000			1.21472
$327$	131.336	+	490.153i	0.401639	+	1.49894i
$328$	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
$331$	19.2217	+	5.15043i	0.0580715	+	0.0155602i	0.287738	−	0.957709i	$-0.407097\pi$
$331$	19.2217	+	5.15043i	0.0580715	+	0.0155602i	−0.229666	+	0.973269i	$0.573763\pi$
$332$	−84.1238	+	313.954i	−0.253385	+	0.945645i
$333$		0			0
$334$	154.000	+	266.736i	0.461078	+	0.798610i
$335$	114.315	+	66.0000i	0.341240	+	0.197015i
$336$	−144.163	+	38.6283i	−0.429055	+	0.114965i
$337$		−	429.000i		−	1.27300i	−0.771278	−	0.636499i	$-0.780382\pi$
$337$		−	429.000i		−	1.27300i	0.771278	−	0.636499i	$-0.219618\pi$
$338$		0			0
$339$	378.000			1.11504
$340$	−18.0265	−	67.2759i	−0.0530192	−	0.197870i
$341$	132.000	−	228.631i	0.387097	−	0.670471i
$342$		0			0
$343$	−7.03562	+	7.03562i	−0.0205120	+	0.0205120i
$344$	470.931	+	126.186i	1.36899	+	0.366819i
$345$	30.9026	−	115.330i	0.0895728	−	0.334290i
$346$	−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
$349$	201.828	−	54.0796i	0.578303	−	0.154956i	0.0422010	−	0.999109i	$-0.486563\pi$
$349$	201.828	−	54.0796i	0.578303	−	0.154956i	0.536102	+	0.844153i	$0.319896\pi$
$350$		−	462.000i		−	1.32000i
$351$		0			0
$352$	−154.000			−0.437500
$353$	166.531	+	621.501i	0.471758	+	1.76063i	0.633449	+	0.773785i	$0.281639\pi$
$353$	166.531	+	621.501i	0.471758	+	1.76063i	−0.161690	+	0.986842i	$0.551695\pi$
$354$	−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
$357$	86.4976	+	23.1770i	0.242290	+	0.0649214i
$358$	110.734	−	413.266i	0.309314	−	1.15437i
$359$	−215.759	−	215.759i	−0.601000	−	0.601000i	0.339578	−	0.940578i	$-0.389716\pi$
$359$	−215.759	−	215.759i	−0.601000	−	0.601000i	−0.940578	+	0.339578i	$0.889716\pi$
$360$		0			0
$361$	30.3109	+	17.5000i	0.0839637	+	0.0484765i
$362$	−583.058	+	156.230i	−1.61066	+	0.431574i
$363$			231.000i			0.636364i
$364$		0			0
$365$	132.000			0.361644
$366$	77.2565	+	288.325i	0.211083	+	0.787774i
$367$	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
$370$	528.596	+	141.637i	1.42864	+	0.382803i
$371$	−61.8052	+	230.660i	−0.166591	+	0.621726i
$372$	−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
$375$	374.823	−	100.433i	0.999527	−	0.267823i
$376$		−	33.0000i		−	0.0877660i
$377$		0			0
$378$	−891.000			−2.35714
$379$	144.212	+	538.207i	0.380507	+	1.42007i	0.845129	+	0.534562i	$0.179524\pi$
$379$	144.212	+	538.207i	0.380507	+	1.42007i	−0.464622	+	0.885509i	$0.653810\pi$
$380$	−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
$383$	−272.307	−	72.9645i	−0.710985	−	0.190508i	−0.114839	−	0.993384i	$-0.536635\pi$
$383$	−272.307	−	72.9645i	−0.710985	−	0.190508i	−0.596146	+	0.802876i	$0.703302\pi$
$384$	−177.690	+	663.148i	−0.462734	+	1.72695i
$385$	154.784	+	154.784i	0.402036	+	0.402036i
$386$	297.000	+	514.419i	0.769430	+	1.33269i
$387$		0			0
$388$	−134.552	+	36.0530i	−0.346783	+	0.0929202i
$389$			312.000i			0.802057i	0.916066	+	0.401028i	$0.131347\pi$
$389$			312.000i			0.802057i	−0.916066	+	0.401028i	$0.868653\pi$
$390$		0			0
$391$	−36.0000			−0.0920716
$392$	−128.761	−	480.542i	−0.328472	−	1.22587i
$393$	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
$397$	−30.9026	+	115.330i	−0.0778403	+	0.290504i	−0.993862	−	0.110624i	$-0.964715\pi$
$397$	−30.9026	+	115.330i	−0.0778403	+	0.290504i	0.916022	+	0.401128i	$0.131382\pi$
$398$	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
$401$	743.238	−	199.150i	1.85346	−	0.496634i	0.853751	−	0.520681i	$-0.174322\pi$
$401$	743.238	−	199.150i	1.85346	−	0.496634i	0.999711	+	0.0240472i	$0.00765520\pi$
$402$		−	396.000i		−	0.985075i
$403$		0			0
$404$	1008.00			2.49505
$405$	−69.5309	−	259.493i	−0.171681	−	0.640723i
$406$	−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
$409$	−230.660	−	61.8052i	−0.563961	−	0.151113i	−0.0344357	−	0.999407i	$-0.510963\pi$
$409$	−230.660	−	61.8052i	−0.563961	−	0.151113i	−0.529526	+	0.848294i	$0.677630\pi$
$410$	−132.194	+	493.356i	−0.322426	+	1.20331i
$411$	−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
$418$	113.310	+	422.877i	0.271075	+	1.01167i
$419$	−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	$-0.716083\pi$
$421$	63.3206	−	63.3206i	0.150405	−	0.150405i	0.778299	+	0.627894i	$0.216083\pi$
$422$	740.035	+	198.292i	1.75364	+	0.469886i
$423$		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
$427$	−288.325	+	77.2565i	−0.675235	+	0.180929i
$428$		−	798.000i		−	1.86449i
$429$		0			0
$430$	−539.000			−1.25349
$431$	−112.451	−	419.673i	−0.260908	−	0.973720i	−0.964708	−	0.263322i	$-0.915182\pi$
$431$	−112.451	−	419.673i	−0.260908	−	0.973720i	0.703800	−	0.710398i	$-0.251485\pi$
$432$	67.5000	−	116.913i	0.156250	−	0.270633i
$433$	−272.798	+	157.500i	−0.630018	+	0.363741i	−0.780759	−	0.624832i	$-0.785167\pi$
$433$	−272.798	+	157.500i	−0.630018	+	0.363741i	0.150741	+	0.988573i	$0.451834\pi$
$434$	928.702	−	928.702i	2.13987	−	2.13987i
$435$	−403.655	−	108.159i	−0.927943	−	0.248642i
$436$	306.451	−	1143.69i	0.702869	−	2.62314i
$437$	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	0.989250	−	0.146233i	$-0.0467150\pi$
$439$	595.825	+	344.000i	1.35723	+	0.783599i	0.367983	+	0.929832i	$0.380048\pi$
$440$	−211.438	+	56.6548i	−0.480542	+	0.128761i
$441$		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	$0.379675\pi$
$444$	−270.398	−	1009.14i	−0.609004	−	2.27283i
$445$	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
$448$	−932.252	−	249.796i	−2.08092	−	0.557580i
$449$	125.327	−	467.728i	0.279125	−	1.04171i	−0.673901	−	0.738822i	$-0.735383\pi$
$449$	125.327	−	467.728i	0.279125	−	1.04171i	0.953026	−	0.302888i	$-0.0979508\pi$
$450$		0			0
$451$	154.000	+	266.736i	0.341463	+	0.591432i
$452$	−763.834	−	441.000i	−1.68990	−	0.975664i
$453$	490.153	−	131.336i	1.08202	−	0.289925i
$454$		−	638.000i		−	1.40529i
$455$		0			0
$456$	594.000			1.30263
$457$	77.2565	+	288.325i	0.169051	+	0.630909i	0.997489	+	0.0708266i	$0.0225637\pi$
$457$	77.2565	+	288.325i	0.169051	+	0.630909i	−0.828437	+	0.560082i	$0.810770\pi$
$458$	−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
$461$	227.457	+	60.9468i	0.493398	+	0.132206i	0.496934	−	0.867788i	$-0.334459\pi$
$461$	227.457	+	60.9468i	0.493398	+	0.132206i	−0.00353623	+	0.999994i	$0.501126\pi$
$462$	169.964	−	634.315i	0.367888	−	1.37298i
$463$	393.995	+	393.995i	0.850961	+	0.850961i	0.990252	−	0.139291i	$-0.0444822\pi$
$463$	393.995	+	393.995i	0.850961	+	0.850961i	−0.139291	+	0.990252i	$0.544482\pi$
$464$	−105.000	−	181.865i	−0.226293	−	0.391951i
$465$	342.946	+	198.000i	0.737518	+	0.425806i
$466$	−1374.35	+	368.256i	−2.94925	+	0.790249i
$467$			390.000i			0.835118i	0.908650	+	0.417559i	$0.137114\pi$
$467$			390.000i			0.835118i	−0.908650	+	0.417559i	$0.862886\pi$
$468$		0			0
$469$	396.000			0.844350
$470$	9.44246	+	35.2397i	0.0200903	+	0.0749782i
$471$	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
$474$	−518.985	−	139.062i	−1.09491	−	0.293379i
$475$	−72.1061	+	269.104i	−0.151802	+	0.566534i
$476$	−147.748	−	147.748i	−0.310395	−	0.310395i
$477$		0			0
$478$	733.524	+	423.500i	1.53457	+	0.885983i
$479$	−464.524	+	124.469i	−0.969779	+	0.259851i	−0.708734	−	0.705475i	$-0.750734\pi$
$479$	−464.524	+	124.469i	−0.969779	+	0.259851i	−0.261044	+	0.965327i	$0.584067\pi$
$480$		−	231.000i		−	0.481250i
$481$		0			0
$482$	1254.00			2.60166
$483$	−92.7078	−	345.990i	−0.191942	−	0.716336i
$484$	269.500	−	466.788i	0.556818	−	0.964437i
$485$	57.1577	−	33.0000i	0.117851	−	0.0680412i
$486$		0			0
$487$	−230.660	−	61.8052i	−0.473635	−	0.126910i	0.0141024	−	0.999901i	$-0.495511\pi$
$487$	−230.660	−	61.8052i	−0.473635	−	0.126910i	−0.487737	+	0.872990i	$0.662178\pi$
$488$	77.2565	−	288.325i	0.158313	−	0.590830i
$489$	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	−0.199777	−	0.979841i	$-0.564022\pi$
$491$	−563.783	−	325.500i	−1.14823	−	0.662933i	−0.948456	+	0.316909i	$0.897355\pi$
$492$	941.862	−	252.371i	1.91435	−	0.512950i
$493$			126.000i			0.255578i
$494$		0			0
$495$		0			0
$496$	51.5043	+	192.217i	0.103839	+	0.387534i
$497$	−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	$-0.846685\pi$
$499$	−211.069	+	211.069i	−0.422983	+	0.422983i	0.463246	+	0.886230i	$0.346685\pi$
$500$	−874.586	−	234.345i	−1.74917	−	0.468689i
$501$	−72.1061	+	269.104i	−0.143924	+	0.537133i
$502$	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
$505$	−461.320	+	123.610i	−0.913506	+	0.244773i
$506$			264.000i			0.521739i
$507$		0			0
$508$	−1176.00			−2.31496
$509$	−78.9733	−	294.732i	−0.155154	−	0.579042i	−0.999092	−	0.0426018i	$-0.986435\pi$
$509$	−78.9733	−	294.732i	−0.155154	−	0.579042i	0.843938	−	0.536440i	$-0.180231\pi$
$510$	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
$513$	518.985	+	139.062i	1.01167	+	0.271075i
$514$	−224.044	+	836.143i	−0.435883	+	1.62674i
$515$	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
$518$	1585.79	−	424.911i	3.06137	−	0.820291i
$519$		−	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
$526$	864.976	+	231.770i	1.64444	+	0.440626i
$527$	30.9026	−	115.330i	0.0586387	−	0.218843i
$528$	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
$535$	97.8582	+	365.212i	0.182913	+	0.682639i
$536$	−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
$539$	320.361	+	85.8406i	0.594362	+	0.159259i
$540$	−162.239	+	605.483i	−0.300442	+	1.12126i
$541$	−429.173	−	429.173i	−0.793296	−	0.793296i	0.188733	−	0.982029i	$-0.439562\pi$
$541$	−429.173	−	429.173i	−0.793296	−	0.793296i	−0.982029	+	0.188733i	$0.939562\pi$
$542$	82.5000	+	142.894i	0.152214	+	0.263642i
$543$	−472.850	−	273.000i	−0.870810	−	0.502762i
$544$	−67.2759	+	18.0265i	−0.123669	+	0.0331370i
$545$			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	$0.411277\pi$
$548$	96.1414	+	358.805i	0.175441	+	0.654753i
$549$		0			0
$550$	−266.736	+	154.000i	−0.484974	+	0.280000i
$551$	590.992	−	590.992i	1.07258	−	1.07258i
$552$	345.990	+	92.7078i	0.626794	+	0.167949i
$553$	139.062	−	518.985i	0.251468	−	0.938491i
$554$	−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
$557$	−464.524	+	124.469i	−0.833975	+	0.223463i	−0.650447	−	0.759552i	$-0.725418\pi$
$557$	−464.524	+	124.469i	−0.833975	+	0.223463i	−0.183528	+	0.983015i	$0.558752\pi$
$558$		0			0
$559$		0			0
$560$	−165.000			−0.294643
$561$	−15.4513	−	57.6650i	−0.0275424	−	0.102790i
$562$	−77.0000	+	133.368i	−0.137011	+	0.237309i
$563$	875.552	−	505.500i	1.55515	−	0.897869i	0.557445	−	0.830214i	$-0.311782\pi$
$563$	875.552	−	505.500i	1.55515	−	0.897869i	0.997709	−	0.0676548i	$-0.0215517\pi$
$564$	49.2494	−	49.2494i	0.0873216	−	0.0873216i
$565$	403.655	+	108.159i	0.714434	+	0.191432i
$566$	−56.6548	+	211.438i	−0.100097	+	0.373566i
$567$	−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	0.0735234	−	0.997293i	$-0.476576\pi$
$569$	−428.683	−	247.500i	−0.753396	−	0.434974i	−0.826920	+	0.562320i	$0.809909\pi$
$570$	−634.315	+	169.964i	−1.11283	+	0.298183i
$571$		−	39.0000i		−	0.0683012i	−0.999417	−	0.0341506i	$-0.989127\pi$
$571$		−	39.0000i		−	0.0683012i	0.999417	−	0.0341506i	$-0.0108726\pi$
$572$		0			0
$573$	−90.0000			−0.157068
$574$	396.583	+	1480.07i	0.690912	+	2.57852i
$575$	−84.0000	+	145.492i	−0.146087	+	0.253030i
$576$		0			0
$577$	−759.847	+	759.847i	−1.31689	+	1.31689i	−0.400671	+	0.916222i	$0.631223\pi$
$577$	−759.847	+	759.847i	−1.31689	+	1.31689i	−0.916222	+	0.400671i	$0.868777\pi$
$578$	897.012	+	240.354i	1.55192	+	0.415837i
$579$	−139.062	+	518.985i	−0.240176	+	0.896348i
$580$	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
$583$	153.773	−	41.2035i	0.263762	−	0.0706749i
$584$			396.000i			0.678082i
$585$		0			0
$586$	539.000			0.919795
$587$	−78.9733	−	294.732i	−0.134537	−	0.502100i	−0.999999	−	0.00112532i	$-0.999642\pi$
$587$	−78.9733	−	294.732i	−0.134537	−	0.502100i	0.865462	−	0.500974i	$-0.167025\pi$
$588$	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
$591$	740.035	+	198.292i	1.25217	+	0.335519i
$592$	−64.3804	+	240.271i	−0.108751	+	0.405863i
$593$	−276.735	−	276.735i	−0.466669	−	0.466669i	0.434165	−	0.900833i	$-0.357044\pi$
$593$	−276.735	−	276.735i	−0.466669	−	0.466669i	−0.900833	+	0.434165i	$0.857044\pi$
$594$	297.000	+	514.419i	0.500000	+	0.866025i
$595$	85.7365	+	49.5000i	0.144095	+	0.0831933i
$596$	448.506	−	120.177i	0.752527	−	0.201639i
$597$			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	$0.681917\pi$
$600$	108.159	+	403.655i	0.180265	+	0.672759i
$601$	−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
$604$	−1143.69	−	306.451i	−1.89353	−	0.507369i
$605$	−66.0972	+	246.678i	−0.109252	+	0.407733i
$606$	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
$609$	−1210.97	+	324.477i	−1.98845	+	0.532804i
$610$			330.000i			0.540984i
$611$		0			0
$612$		0			0
$613$	10.3009	+	38.4434i	0.0168040	+	0.0627135i	0.973819	−	0.227326i	$-0.0729983\pi$
$613$	10.3009	+	38.4434i	0.0168040	+	0.0627135i	−0.957015	+	0.290039i	$0.906332\pi$
$614$	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
$617$	−897.012	−	240.354i	−1.45383	−	0.389552i	−0.556474	−	0.830865i	$-0.687846\pi$
$617$	−897.012	−	240.354i	−1.45383	−	0.389552i	−0.897353	+	0.441313i	$0.854513\pi$
$618$	66.9556	−	249.882i	0.108342	−	0.404340i
$619$	−520.636	−	520.636i	−0.841092	−	0.841092i	0.147909	−	0.989001i	$-0.452746\pi$
$619$	−520.636	−	520.636i	−0.841092	−	0.841092i	−0.989001	+	0.147909i	$0.952746\pi$
$620$	−462.000	−	800.207i	−0.745161	−	1.29066i
$621$	280.592	+	162.000i	0.451839	+	0.260870i
$622$	749.646	−	200.867i	1.20522	−	0.322937i
$623$		−	1650.00i		−	2.64848i
$624$		0			0
$625$	79.0000			0.126400
$626$	−79.8317	−	297.936i	−0.127527	−	0.475936i
$627$	−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
$631$	270.398	−	1009.14i	0.428523	−	1.59927i	−0.327585	−	0.944822i	$-0.606235\pi$
$631$	270.398	−	1009.14i	0.428523	−	1.59927i	0.756108	−	0.654447i	$-0.227098\pi$
$632$	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
$635$	538.207	−	144.212i	0.847570	−	0.227106i
$636$		−	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	−0.938976	−	0.343983i	$-0.888224\pi$
$641$	−711.873	+	411.000i	−1.11057	+	0.641186i	−0.171590	+	0.985168i	$0.554890\pi$
$642$	802.061	−	802.061i	1.24932	−	1.24932i
$643$	269.104	+	72.1061i	0.418512	+	0.112140i	0.461929	−	0.886917i	$-0.347158\pi$
$643$	269.104	+	72.1061i	0.418512	+	0.112140i	−0.0434164	+	0.999057i	$0.513824\pi$
$644$	−216.318	+	807.311i	−0.335898	+	1.25359i
$645$	−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	0.974784	−	0.223151i	$-0.0716343\pi$
$647$	820.992	+	474.000i	1.26892	+	0.732612i	0.294137	+	0.955763i	$0.404968\pi$
$648$	778.478	−	208.593i	1.20136	−	0.321902i
$649$			352.000i			0.542373i
$650$		0			0
$651$	1188.00			1.82488
$652$	−216.318	−	807.311i	−0.331776	−	1.23821i
$653$	−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
$656$	−224.253	−	60.0884i	−0.341849	−	0.0915982i
$657$		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
$661$	576.650	−	154.513i	0.872391	−	0.233756i	0.205270	−	0.978705i	$-0.434193\pi$
$661$	576.650	−	154.513i	0.872391	−	0.233756i	0.667121	+	0.744949i	$0.267526\pi$
$662$		−	66.0000i		−	0.0996979i
$663$		0			0
$664$	462.000			0.695783
$665$	−169.964	−	634.315i	−0.255585	−	0.953858i
$666$		0			0
$667$	436.477	−	252.000i	0.654388	−	0.377811i
$668$	459.661	−	459.661i	0.688115	−	0.688115i
$669$	−1009.14	−	270.398i	−1.50843	−	0.404182i
$670$	113.310	−	422.877i	0.169119	−	0.631160i
$671$	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	0.548723	−	0.836004i	$-0.315114\pi$
$673$	66.6840	+	38.5000i	0.0990846	+	0.0572065i	−0.449639	+	0.893210i	$0.648447\pi$
$674$	−1374.35	+	368.256i	−2.03910	+	0.546374i
$675$			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	$0.680137\pi$
$678$	−324.477	−	1210.97i	−0.478580	−	1.78609i
$679$	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
$682$	−845.754	−	226.619i	−1.24011	−	0.332286i
$683$	214.601	−	800.903i	0.314204	−	1.17263i	−0.610524	−	0.791998i	$-0.709041\pi$
$683$	214.601	−	800.903i	0.314204	−	1.17263i	0.924728	−	0.380628i	$-0.124292\pi$
$684$		0			0
$685$	−88.0000	−	152.420i	−0.128467	−	0.222512i
$686$	28.5788	+	16.5000i	0.0416601	+	0.0240525i
$687$	−259.493	+	69.5309i	−0.377719	+	0.101209i
$688$		−	245.000i		−	0.356105i
$689$		0			0
$690$	−396.000			−0.573913
$691$	−257.522	−	961.084i	−0.372680	−	1.39086i	−0.856705	−	0.515806i	$-0.827493\pi$
$691$	−257.522	−	961.084i	−0.372680	−	1.39086i	0.484026	−	0.875054i	$-0.339174\pi$
$692$	−399.000	+	691.088i	−0.576590	+	0.998682i
$693$		0			0
$694$	386.959	−	386.959i	0.557578	−	0.557578i
$695$	112.126	+	30.0442i	0.161333	+	0.0432291i
$696$	324.477	−	1210.97i	0.466203	−	1.73989i
$697$	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
$700$	−941.862	+	252.371i	−1.34552	+	0.360530i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	−990.000			−1.40825
$704$	166.531	+	621.501i	0.236549	+	0.882814i
$705$	−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
$708$	1076.41	+	288.424i	1.52036	+	0.407379i
$709$	−30.9026	+	115.330i	−0.0435862	+	0.162666i	−0.984289	−	0.176567i	$-0.943501\pi$
$709$	−30.9026	+	115.330i	−0.0435862	+	0.162666i	0.940702	+	0.339233i	$0.110167\pi$
$710$	180.581	+	180.581i	0.254339	+	0.254339i
$711$		0			0
$712$	1428.94	+	825.000i	2.00694	+	1.15871i
$713$	−461.320	+	123.610i	−0.647013	+	0.173367i
$714$		−	297.000i		−	0.415966i
$715$		0			0
$716$	−903.000			−1.26117
$717$	198.292	+	740.035i	0.276557	+	1.03213i
$718$	−506.000	+	876.418i	−0.704735	+	1.22064i
$719$	301.377	−	174.000i	0.419161	−	0.242003i	−0.275557	−	0.961285i	$-0.588862\pi$
$719$	301.377	−	174.000i	0.419161	−	0.242003i	0.694718	+	0.719282i	$0.255529\pi$
$720$		0			0
$721$	249.882	+	66.9556i	0.346577	+	0.0928650i
$722$	30.0442	−	112.126i	0.0416125	−	0.155300i
$723$	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
$726$	740.035	−	198.292i	1.01933	−	0.273129i
$727$		−	702.000i		−	0.965612i	−0.875727	−	0.482806i	$-0.839618\pi$
$727$		−	702.000i		−	0.965612i	0.875727	−	0.482806i	$-0.160382\pi$
$728$		0			0
$729$	729.000			1.00000
$730$	−113.310	−	422.877i	−0.155219	−	0.579284i
$731$	−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	$-0.730544\pi$
$733$	63.3206	−	63.3206i	0.0863856	−	0.0863856i	0.748979	+	0.662594i	$0.230544\pi$
$734$	−1717.14	−	460.105i	−2.33942	−	0.626847i
$735$	−128.761	+	480.542i	−0.175185	+	0.653799i
$736$	196.997	+	196.997i	0.267660	+	0.267660i
$737$	−132.000	−	228.631i	−0.179104	−	0.310218i
$738$		0			0
$739$	−172.995	+	46.3539i	−0.234094	+	0.0627252i	−0.373959	−	0.927445i	$-0.622000\pi$
$739$	−172.995	+	46.3539i	−0.234094	+	0.0627252i	0.139865	+	0.990171i	$0.455333\pi$
$740$		−	1155.00i		−	1.56081i
$741$		0			0
$742$	792.000			1.06739
$743$	−0.858406	−	3.20361i	−0.00115532	−	0.00431173i	0.965346	−	0.260974i	$-0.0840438\pi$
$743$	−0.858406	−	3.20361i	−0.00115532	−	0.00431173i	−0.966501	+	0.256663i	$0.917377\pi$
$744$	−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
$748$	−36.0530	+	134.552i	−0.0481992	+	0.179882i
$749$	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	0.398768	−	0.917052i	$-0.369438\pi$
$751$	−147.224	−	85.0000i	−0.196038	−	0.113182i	−0.594806	+	0.803869i	$0.702771\pi$
$752$	−16.0181	+	4.29203i	−0.0213006	+	0.00570748i
$753$			126.000i			0.167331i
$754$		0			0
$755$	561.000			0.743046
$756$	486.716	+	1816.45i	0.643804	+	2.40271i
$757$	−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
$760$	634.315	+	169.964i	0.834626	+	0.223637i
$761$	−209.451	+	781.682i	−0.275231	+	1.02718i	0.680455	+	0.732790i	$0.261782\pi$
$761$	−209.451	+	781.682i	−0.275231	+	1.02718i	−0.955686	+	0.294387i	$0.904884\pi$
$762$	−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
$769$	144.212	+	538.207i	0.187532	+	0.699879i	0.994074	+	0.108703i	$0.0346697\pi$
$769$	144.212	+	538.207i	0.187532	+	0.699879i	−0.806542	+	0.591176i	$0.798664\pi$
$770$	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
$773$	1226.98	+	328.769i	1.58730	+	0.425316i	0.941176	−	0.337916i	$-0.109722\pi$
$773$	1226.98	+	328.769i	1.58730	+	0.425316i	0.646125	+	0.763232i	$0.276388\pi$
$774$		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
$778$	999.527	−	267.823i	1.28474	−	0.344245i
$779$		−	924.000i		−	1.18614i
$780$		0			0
$781$	154.000			0.197183
$782$	30.9026	+	115.330i	0.0395174	+	0.147481i
$783$	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
$786$	−893.808	−	239.495i	−1.13716	−	0.304701i
$787$	−97.8582	+	365.212i	−0.124343	+	0.464056i	−0.999815	−	0.0192130i	$-0.993884\pi$
$787$	−97.8582	+	365.212i	−0.124343	+	0.464056i	0.875472	+	0.483269i	$0.160551\pi$
$788$	−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
$791$	1210.97	−	324.477i	1.53093	−	0.410212i
$792$		0			0
$793$		0			0
$794$	396.000			0.498741
$795$	61.8052	+	230.660i	0.0777424	+	0.290139i
$796$	966.000	−	1673.16i	1.21357	−	2.10196i
$797$	−982.073	+	567.000i	−1.23221	+	0.711418i	−0.967491	−	0.252907i	$-0.918613\pi$
$797$	−982.073	+	567.000i	−1.23221	+	0.711418i	−0.264721	+	0.964325i	$0.585280\pi$
$798$	−1393.05	+	1393.05i	−1.74568	+	1.74568i
$799$	9.61084	+	2.57522i	0.0120286	+	0.00322305i
$800$	−84.1238	+	313.954i	−0.105155	+	0.392443i
$801$		0			0
$802$	−1276.00	−	2210.10i	−1.59102	−	2.75573i
$803$	−228.631	−	132.000i	−0.284721	−	0.164384i
$804$	−807.311	+	216.318i	−1.00412	+	0.269053i
$805$		−	396.000i		−	0.491925i
$806$		0			0
$807$	−558.000			−0.691450
$808$	−370.831	−	1383.96i	−0.458950	−	1.71282i
$809$	−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	0.403782	−	0.914855i	$-0.367695\pi$
$811$	1069.41	−	1069.41i	1.31864	−	1.31864i	0.914855	−	0.403782i	$-0.132305\pi$
$812$	2825.59	+	757.114i	3.47979	+	0.932406i
$813$	−38.6283	+	144.163i	−0.0475132	+	0.177322i
$814$	−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
$817$	941.862	−	252.371i	1.15283	−	0.308900i
$818$			792.000i			0.968215i
$819$		0			0
$820$	1078.00			1.31463
$821$	133.053	+	496.560i	0.162062	+	0.604824i	0.998397	+	0.0566044i	$0.0180274\pi$
$821$	133.053	+	496.560i	0.162062	+	0.604824i	−0.836335	+	0.548219i	$0.815306\pi$
$822$	−264.000	+	457.261i	−0.321168	+	0.556279i
$823$	−554.256	+	320.000i	−0.673458	+	0.388821i	−0.797386	−	0.603470i	$-0.793784\pi$
$823$	−554.256	+	320.000i	−0.673458	+	0.388821i	0.123927	+	0.992291i	$0.460451\pi$
$824$	−182.926	+	182.926i	−0.221998	+	0.221998i
$825$	−269.104	−	72.1061i	−0.326186	−	0.0874013i
$826$	−453.238	+	1691.51i	−0.548715	+	2.04783i
$827$	820.823	+	820.823i	0.992531	+	0.992531i	0.999972	−	0.00744177i	$-0.00236881\pi$
$827$	820.823	+	820.823i	0.992531	+	0.992531i	−0.00744177	+	0.999972i	$0.502369\pi$
$828$		0			0
$829$	415.692	+	240.000i	0.501438	+	0.289505i	0.729307	−	0.684186i	$-0.239843\pi$
$829$	415.692	+	240.000i	0.501438	+	0.289505i	−0.227869	+	0.973692i	$0.573176\pi$
$830$	−493.356	+	132.194i	−0.594405	+	0.159270i
$831$		−	1122.00i		−	1.35018i
$832$		0			0
$833$	150.000			0.180072
$834$	−90.1326	−	336.379i	−0.108073	−	0.403333i
$835$	−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
$838$	1239.80	+	332.203i	1.47947	+	0.396424i
$839$	−120.177	+	448.506i	−0.143238	+	0.534572i	0.856589	+	0.515999i	$0.172579\pi$
$839$	−120.177	+	448.506i	−0.143238	+	0.534572i	−0.999828	+	0.0185733i	$0.994088\pi$
$840$	−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
$843$	−134.552	+	36.0530i	−0.159611	+	0.0427675i
$844$		−	1617.00i		−	1.91588i
$845$		0			0
$846$		0			0
$847$	198.292	+	740.035i	0.234111	+	0.873713i
$848$	−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
$851$	−576.650	−	154.513i	−0.677615	−	0.181566i
$852$	126.186	−	470.931i	0.148105	−	0.552736i
$853$	−246.247	−	246.247i	−0.288683	−	0.288683i	0.547876	−	0.836559i	$-0.315436\pi$
$853$	−246.247	−	246.247i	−0.288683	−	0.288683i	−0.836559	+	0.547876i	$0.815436\pi$
$854$	495.000	+	857.365i	0.579625	+	1.00394i
$855$		0			0
$856$	−1095.64	+	293.575i	−1.27995	+	0.342961i
$857$			1326.00i			1.54726i	0.633639	+	0.773629i	$0.281561\pi$
$857$			1326.00i			1.54726i	−0.633639	+	0.773629i	$0.718439\pi$
$858$		0			0
$859$	54.0000			0.0628638			0.0314319	−	0.999506i	$-0.489993\pi$
$859$	54.0000			0.0628638			0.0314319	+	0.999506i	$0.489993\pi$
$860$	294.433	+	1098.84i	0.342364	+	1.27772i
$861$	−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	$-0.846267\pi$
$863$	−363.507	+	363.507i	−0.421213	+	0.421213i	0.464408	+	0.885621i	$0.346267\pi$
$864$	605.483	+	162.239i	0.700790	+	0.187776i
$865$	97.8582	−	365.212i	0.113131	−	0.422210i
$866$	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
$869$	−345.990	+	92.7078i	−0.398148	+	0.106683i
$870$			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
$877$	−855.365	−	229.194i	−0.975330	−	0.261339i	−0.264254	−	0.964453i	$-0.585126\pi$
$877$	−855.365	−	229.194i	−0.975330	−	0.261339i	−0.711077	+	0.703114i	$0.751792\pi$
$878$	590.583	−	2204.09i	0.672646	−	2.51035i
$879$	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	0.144655	−	0.989482i	$-0.453793\pi$
$881$	−563.783	−	325.500i	−0.639935	−	0.369467i	−0.784589	+	0.620016i	$0.787126\pi$
$882$		0			0
$883$			819.000i			0.927520i	0.885961	+	0.463760i	$0.153500\pi$
$883$			819.000i			0.927520i	−0.885961	+	0.463760i	$0.846500\pi$
$884$		0			0
$885$	−528.000			−0.596610
$886$	−280.699	−	1047.58i	−0.316816	−	1.18237i
$887$	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
$890$	−1761.99	−	472.123i	−1.97976	−	0.530475i
$891$	−139.062	+	518.985i	−0.156074	+	0.582475i
$892$	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
$895$	413.266	−	110.734i	0.461750	−	0.123726i
$896$			2277.00i			2.54129i
$897$		0			0
$898$	−1606.00			−1.78842
$899$	432.636	+	1614.62i	0.481242	+	1.79602i
$900$		0			0
$901$	62.3538	−	36.0000i	0.0692051	−	0.0399556i
$902$	722.324	−	722.324i	0.800803	−	0.800803i
$903$	−1412.79	−	378.557i	−1.56456	−	0.419221i
$904$	−324.477	+	1210.97i	−0.358935	+	1.33956i
$905$	−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	0.0139479	−	0.999903i	$-0.495560\pi$
$907$	−766.432	−	442.500i	−0.845019	−	0.487872i	−0.858967	+	0.512031i	$0.828893\pi$
$908$	−1300.67	+	348.513i	−1.43245	+	0.383825i
$909$		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	$0.660847\pi$
$912$	−77.2565	−	288.325i	−0.0847111	−	0.316146i
$913$	−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
$916$	605.483	+	162.239i	0.661008	+	0.177116i
$917$	239.495	−	893.808i	0.261172	−	0.974709i
$918$	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
$921$	1614.62	−	432.636i	1.75312	−	0.469746i
$922$		−	781.000i		−	0.847072i
$923$		0			0
$924$	−1386.00			−1.50000
$925$	−180.265	−	672.759i	−0.194881	−	0.727307i
$926$	924.000	−	1600.41i	0.997840	−	1.72831i
$927$		0			0
$928$	689.491	−	689.491i	0.742986	−	0.742986i
$929$	−64.0723	−	17.1681i	−0.0689691	−	0.0184802i	0.224170	−	0.974550i	$-0.428033\pi$
$929$	−64.0723	−	17.1681i	−0.0689691	−	0.0184802i	−0.293139	+	0.956070i	$0.594700\pi$
$930$	339.929	−	1268.63i	0.365515	−	1.36412i
$931$	−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
$934$	1249.41	−	334.778i	1.33770	−	0.358435i
$935$		−	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	$0.464255\pi$
$938$	−339.929	−	1268.63i	−0.362397	−	1.35249i
$939$	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	$-0.808100\pi$
$941$	−241.556	+	241.556i	−0.256702	+	0.256702i	0.567009	+	0.823711i	$0.308100\pi$
$942$	−768.867	−	206.017i	−0.816207	−	0.218702i
$943$	144.212	−	538.207i	0.152929	−	0.570739i
$944$	−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
$947$	−1005.93	+	269.539i	−1.06223	+	0.284624i	−0.747298	−	0.664489i	$-0.768649\pi$
$947$	−1005.93	+	269.539i	−1.06223	+	0.284624i	−0.314935	+	0.949113i	$0.601983\pi$
$948$			1134.00i			1.19620i
$949$		0			0
$950$	924.000			0.972632
$951$	−236.920	−	884.197i	−0.249127	−	0.929755i
$952$	−148.500	+	257.210i	−0.155987	+	0.270178i
$953$	335.152	−	193.500i	0.351681	−	0.203043i	−0.313744	−	0.949507i	$-0.601584\pi$
$953$	335.152	−	193.500i	0.351681	−	0.203043i	0.665425	+	0.746464i	$0.268250\pi$
$954$		0			0
$955$	−96.1084	−	25.7522i	−0.100637	−	0.0269656i
$956$	462.681	−	1726.75i	0.483976	−	1.80622i
$957$	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
$960$	−932.252	+	249.796i	−0.971095	+	0.260204i
$961$		−	623.000i		−	0.648283i
$962$		0			0
$963$		0			0
$964$	−685.008	−	2556.48i	−0.710589	−	2.65195i
$965$	−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	$-0.692369\pi$
$967$	246.247	−	246.247i	0.254650	−	0.254650i	0.822874	+	0.568224i	$0.192369\pi$
$968$	−740.035	−	198.292i	−0.764499	−	0.204847i
$969$	−46.3539	+	172.995i	−0.0478368	+	0.178530i
$970$	−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
$973$	336.379	−	90.1326i	0.345714	−	0.0926337i
$974$			792.000i			0.813142i
$975$		0			0
$976$	−150.000			−0.153689
$977$	−302.159	−	1127.67i	−0.309272	−	1.15422i	−0.929205	−	0.369564i	$-0.879507\pi$
$977$	−302.159	−	1127.67i	−0.309272	−	1.15422i	0.619933	−	0.784655i	$-0.287160\pi$
$978$	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
$982$	−558.822	+	2085.55i	−0.569065	+	2.12378i
$983$	−185.271	−	185.271i	−0.188476	−	0.188476i	0.606561	−	0.795037i	$-0.292548\pi$
$983$	−185.271	−	185.271i	−0.188476	−	0.188476i	−0.795037	+	0.606561i	$0.792548\pi$
$984$	−693.000	−	1200.31i	−0.704268	−	1.21983i
$985$	733.524	+	423.500i	0.744694	+	0.429949i
$986$	403.655	−	108.159i	0.409387	−	0.109695i
$987$			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
$994$	740.035	+	198.292i	0.744502	+	0.199489i
$995$	−236.920	+	884.197i	−0.238111	+	0.888641i
$996$	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
$999$	−1297.46	+	347.654i	−1.29876	+	0.348002i

Twists

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

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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