LMFDB - Embedded newform 117.2.t.c.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(25,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("117.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 $ x^20 - 6x^16 + 9x^14 + 54x^12 + 81x^10 + 486x^8 + 729x^6 - 4374*x^4 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.1
Root			$1.66095 + 0.491165i$ of defining polynomial
Character	$\chi$	$=$	117.25
Dual form			117.2.t.c.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14539 - 1.23864i) q^{2} +(-1.72976 + 0.0890572i) q^{3} +(2.06847 + 3.58269i) q^{4} +(-0.771397 + 0.445366i) q^{5} +(3.82132 + 1.95149i) q^{6} +(0.850723 + 0.491165i) q^{7} -5.29379i q^{8} +(2.98414 - 0.308095i) q^{9} +2.20660 q^{10} +(2.49915 + 1.44288i) q^{11} +(-3.89702 - 6.01298i) q^{12} +(0.714352 - 3.53408i) q^{13} +(-1.21676 - 2.10748i) q^{14} +(1.29467 - 0.839075i) q^{15} +(-2.42018 + 4.19187i) q^{16} +5.34353 q^{17} +(-6.78376 - 3.03529i) q^{18} +7.19723i q^{19} +(-3.19122 - 1.84245i) q^{20} +(-1.51529 - 0.773835i) q^{21} +(-3.57443 - 6.19110i) q^{22} +(2.31688 + 4.01296i) q^{23} +(0.471451 + 9.15699i) q^{24} +(-2.10330 + 3.64302i) q^{25} +(-5.91002 + 6.69715i) q^{26} +(-5.13440 + 0.798690i) q^{27} +4.06384i q^{28} +(-0.971133 + 1.68205i) q^{29} +(-3.81688 + 0.196513i) q^{30} +(8.73604 - 5.04375i) q^{31} +(1.21534 - 0.701678i) q^{32} +(-4.45142 - 2.27327i) q^{33} +(-11.4640 - 6.61872i) q^{34} -0.874993 q^{35} +(7.27640 + 10.0540i) q^{36} -4.82809i q^{37} +(8.91479 - 15.4409i) q^{38} +(-0.920923 + 6.17672i) q^{39} +(2.35768 + 4.08361i) q^{40} +(2.39352 - 1.38190i) q^{41} +(2.29238 + 3.53708i) q^{42} +(-2.45501 + 4.25220i) q^{43} +11.9382i q^{44} +(-2.16474 + 1.56670i) q^{45} -11.4791i q^{46} +(-3.82403 - 2.20780i) q^{47} +(3.81301 - 7.46647i) q^{48} +(-3.01751 - 5.22649i) q^{49} +(9.02479 - 5.21047i) q^{50} +(-9.24302 + 0.475880i) q^{51} +(14.1391 - 4.75082i) q^{52} +6.30850 q^{53} +(12.0046 + 4.64619i) q^{54} -2.57044 q^{55} +(2.60013 - 4.50355i) q^{56} +(-0.640965 - 12.4495i) q^{57} +(4.16692 - 2.40577i) q^{58} +(-2.74727 + 1.58614i) q^{59} +(5.68412 + 2.90280i) q^{60} +(2.76034 - 4.78105i) q^{61} -24.9896 q^{62} +(2.69000 + 1.20360i) q^{63} +6.20421 q^{64} +(1.02291 + 3.04432i) q^{65} +(6.73427 + 10.3908i) q^{66} +(-3.15059 + 1.81899i) q^{67} +(11.0529 + 19.1442i) q^{68} +(-4.36503 - 6.73512i) q^{69} +(1.87720 + 1.08380i) q^{70} +6.69715i q^{71} +(-1.63099 - 15.7974i) q^{72} +9.33980i q^{73} +(-5.98027 + 10.3581i) q^{74} +(3.31376 - 6.48886i) q^{75} +(-25.7854 + 14.8872i) q^{76} +(1.41739 + 2.45499i) q^{77} +(9.62649 - 12.1108i) q^{78} +(-2.37380 + 4.11154i) q^{79} -4.31146i q^{80} +(8.81015 - 1.83880i) q^{81} -6.84670 q^{82} +(-4.78313 - 2.76154i) q^{83} +(-0.361914 - 7.02946i) q^{84} +(-4.12198 + 2.37983i) q^{85} +(10.5339 - 6.08176i) q^{86} +(1.53003 - 2.99603i) q^{87} +(7.63833 - 13.2300i) q^{88} -17.5838i q^{89} +(6.58479 - 0.679842i) q^{90} +(2.34353 - 2.65566i) q^{91} +(-9.58479 + 16.6013i) q^{92} +(-14.6621 + 9.50249i) q^{93} +(5.46935 + 9.47320i) q^{94} +(-3.20540 - 5.55192i) q^{95} +(-2.03976 + 1.32197i) q^{96} +(0.213335 + 0.123169i) q^{97} +14.9505i q^{98} +(7.90234 + 3.53579i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) $ 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.14539	−	1.23864i	−1.51702	−	0.875852i	−0.999800	−	0.0199997i	$-0.993633\pi$
$2$	−2.14539	−	1.23864i	−1.51702	−	0.875852i	−0.517220	−	0.855852i	$-0.673033\pi$
$3$	−1.72976	+	0.0890572i	−0.998677	+	0.0514172i
$3$	−1.72976	+	0.0890572i	−0.998677	+	0.0514172i
$4$	2.06847	+	3.58269i	1.03423	+	1.79135i
$5$	−0.771397	+	0.445366i	−0.344979	+	0.199174i	−0.662472	−	0.749087i	$-0.730492\pi$
$5$	−0.771397	+	0.445366i	−0.344979	+	0.199174i	0.317493	+	0.948261i	$0.397159\pi$
$6$	3.82132	+	1.95149i	1.56005	+	0.796693i
$7$	0.850723	+	0.491165i	0.321543	+	0.185643i	0.652080	−	0.758150i	$-0.273897\pi$
$7$	0.850723	+	0.491165i	0.321543	+	0.185643i	−0.330537	+	0.943793i	$0.607230\pi$
$8$		−	5.29379i		−	1.87164i
$9$	2.98414	−	0.308095i	0.994713	−	0.102698i
$10$	2.20660			0.697787
$11$	2.49915	+	1.44288i	0.753521	+	0.435046i	0.826965	−	0.562254i	$-0.190066\pi$
$11$	2.49915	+	1.44288i	0.753521	+	0.435046i	−0.0734436	+	0.997299i	$0.523399\pi$
$12$	−3.89702	−	6.01298i	−1.12497	−	1.73580i
$13$	0.714352	−	3.53408i	0.198126	−	0.980177i
$13$	0.714352	−	3.53408i	0.198126	−	0.980177i
$14$	−1.21676	−	2.10748i	−0.325191	−	0.563248i
$15$	1.29467	−	0.839075i	0.334282	−	0.216648i
$16$	−2.42018	+	4.19187i	−0.605045	+	1.04797i
$17$	5.34353			1.29600			0.647998	−	0.761642i	$-0.275606\pi$
$17$	5.34353			1.29600			0.647998	+	0.761642i	$0.275606\pi$
$18$	−6.78376	−	3.03529i	−1.59895	−	0.715425i
$19$			7.19723i			1.65116i	0.564287	+	0.825579i	$0.309151\pi$
$19$			7.19723i			1.65116i	−0.564287	+	0.825579i	$0.690849\pi$
$20$	−3.19122	−	1.84245i	−0.713578	−	0.411984i
$21$	−1.51529	−	0.773835i	−0.330663	−	0.168865i
$22$	−3.57443	−	6.19110i	−0.762071	−	1.31995i
$23$	2.31688	+	4.01296i	0.483103	+	0.836759i	0.999812	−	0.0194021i	$-0.00617627\pi$
$23$	2.31688	+	4.01296i	0.483103	+	0.836759i	−0.516709	+	0.856161i	$0.672843\pi$
$24$	0.471451	+	9.15699i	0.0962344	+	1.86916i
$25$	−2.10330	+	3.64302i	−0.420660	+	0.728604i
$26$	−5.91002	+	6.69715i	−1.15905	+	1.31342i
$27$	−5.13440	+	0.798690i	−0.988116	+	0.153708i
$28$			4.06384i			0.767993i
$29$	−0.971133	+	1.68205i	−0.180335	+	0.312349i	−0.941995	−	0.335628i	$-0.891051\pi$
$29$	−0.971133	+	1.68205i	−0.180335	+	0.312349i	0.761660	+	0.647977i	$0.224385\pi$
$30$	−3.81688	+	0.196513i	−0.696864	+	0.0358783i
$31$	8.73604	−	5.04375i	1.56904	−	0.905885i	0.572757	−	0.819725i	$-0.305874\pi$
$31$	8.73604	−	5.04375i	1.56904	−	0.905885i	0.996281	−	0.0861597i	$-0.0274595\pi$
$32$	1.21534	−	0.701678i	0.214844	−	0.124040i
$33$	−4.45142	−	2.27327i	−0.774893	−	0.395726i
$34$	−11.4640	−	6.61872i	−1.96605	−	1.13510i
$35$	−0.874993			−0.147901
$36$	7.27640	+	10.0540i	1.21273	+	1.67566i
$37$		−	4.82809i		−	0.793732i	−0.917876	−	0.396866i	$-0.870098\pi$
$37$		−	4.82809i		−	0.793732i	0.917876	−	0.396866i	$-0.129902\pi$
$38$	8.91479	−	15.4409i	1.44617	−	2.50484i
$39$	−0.920923	+	6.17672i	−0.147466	+	0.989067i
$40$	2.35768	+	4.08361i	0.372781	+	0.645676i
$41$	2.39352	−	1.38190i	0.373804	−	0.215816i	−0.301315	−	0.953525i	$-0.597426\pi$
$41$	2.39352	−	1.38190i	0.373804	−	0.215816i	0.675119	+	0.737709i	$0.264092\pi$
$42$	2.29238	+	3.53708i	0.353722	+	0.545783i
$43$	−2.45501	+	4.25220i	−0.374386	+	0.648455i	−0.990235	−	0.139409i	$-0.955480\pi$
$43$	−2.45501	+	4.25220i	−0.374386	+	0.648455i	0.615849	+	0.787864i	$0.288813\pi$
$44$			11.9382i			1.79976i
$45$	−2.16474	+	1.56670i	−0.322700	+	0.233549i
$46$		−	11.4791i		−	1.69251i
$47$	−3.82403	−	2.20780i	−0.557791	−	0.322041i	0.194467	−	0.980909i	$-0.437702\pi$
$47$	−3.82403	−	2.20780i	−0.557791	−	0.322041i	−0.752259	+	0.658868i	$0.771036\pi$
$48$	3.81301	−	7.46647i	0.550361	−	1.07769i
$49$	−3.01751	−	5.22649i	−0.431073	−	0.746641i
$50$	9.02479	−	5.21047i	1.27630	−	0.736871i
$51$	−9.24302	+	0.475880i	−1.29428	+	0.0666365i
$52$	14.1391	−	4.75082i	1.96074	−	0.658820i
$53$	6.30850			0.866540			0.433270	−	0.901264i	$-0.357360\pi$
$53$	6.30850			0.866540			0.433270	+	0.901264i	$0.357360\pi$
$54$	12.0046	+	4.64619i	1.63362	+	0.632266i
$55$	−2.57044			−0.346599
$56$	2.60013	−	4.50355i	0.347456	−	0.601812i
$57$	−0.640965	−	12.4495i	−0.0848979	−	1.64897i
$58$	4.16692	−	2.40577i	0.547143	−	0.315893i
$59$	−2.74727	+	1.58614i	−0.357664	+	0.206498i	−0.668056	−	0.744111i	$-0.732873\pi$
$59$	−2.74727	+	1.58614i	−0.357664	+	0.206498i	0.310391	+	0.950609i	$0.399540\pi$
$60$	5.68412	+	2.90280i	0.733817	+	0.374749i
$61$	2.76034	−	4.78105i	0.353426	−	0.612151i	−0.633422	−	0.773807i	$-0.718350\pi$
$61$	2.76034	−	4.78105i	0.353426	−	0.612151i	0.986847	+	0.161656i	$0.0516834\pi$
$62$	−24.9896			−3.17368
$63$	2.69000	+	1.20360i	0.338908	+	0.151639i
$64$	6.20421			0.775526
$65$	1.02291	+	3.04432i	0.126876	+	0.377602i
$66$	6.73427	+	10.3908i	0.828931	+	1.27902i
$67$	−3.15059	+	1.81899i	−0.384906	+	0.222225i	−0.679950	−	0.733258i	$-0.737999\pi$
$67$	−3.15059	+	1.81899i	−0.384906	+	0.222225i	0.295045	+	0.955483i	$0.404665\pi$
$68$	11.0529	+	19.1442i	1.34036	+	2.32158i
$69$	−4.36503	−	6.73512i	−0.525488	−	0.810813i
$70$	1.87720	+	1.08380i	0.224369	+	0.129539i
$71$			6.69715i			0.794805i	0.917644	+	0.397403i	$0.130088\pi$
$71$			6.69715i			0.794805i	−0.917644	+	0.397403i	$0.869912\pi$
$72$	−1.63099	−	15.7974i	−0.192214	−	1.86174i
$73$			9.33980i			1.09314i	0.837413	+	0.546570i	$0.184067\pi$
$73$			9.33980i			1.09314i	−0.837413	+	0.546570i	$0.815933\pi$
$74$	−5.98027	+	10.3581i	−0.695192	+	1.20411i
$75$	3.31376	−	6.48886i	0.382640	−	0.749269i
$76$	−25.7854	+	14.8872i	−2.95779	+	1.70768i
$77$	1.41739	+	2.45499i	0.161526	+	0.279772i
$78$	9.62649	−	12.1108i	1.08998	−	1.37128i
$79$	−2.37380	+	4.11154i	−0.267073	+	0.462584i	−0.968105	−	0.250546i	$-0.919390\pi$
$79$	−2.37380	+	4.11154i	−0.267073	+	0.462584i	0.701031	+	0.713130i	$0.252723\pi$
$80$		−	4.31146i		−	0.482036i
$81$	8.81015	−	1.83880i	0.978906	−	0.204311i
$82$	−6.84670			−0.756092
$83$	−4.78313	−	2.76154i	−0.525016	−	0.303118i	0.213968	−	0.976841i	$-0.431361\pi$
$83$	−4.78313	−	2.76154i	−0.525016	−	0.303118i	−0.738985	+	0.673722i	$0.764694\pi$
$84$	−0.361914	−	7.02946i	−0.0394880	−	0.766977i
$85$	−4.12198	+	2.37983i	−0.447092	+	0.258129i
$86$	10.5339	−	6.08176i	1.13590	−	0.655813i
$87$	1.53003	−	2.99603i	0.164036	−	0.321208i
$88$	7.63833	−	13.2300i	0.814248	−	1.41032i
$89$		−	17.5838i		−	1.86388i	−0.362615	−	0.931939i	$-0.618116\pi$
$89$		−	17.5838i		−	1.86388i	0.362615	−	0.931939i	$-0.381884\pi$
$90$	6.58479	−	0.679842i	0.694097	−	0.0716616i
$91$	2.34353	−	2.65566i	0.245669	−	0.278388i
$92$	−9.58479	+	16.6013i	−0.999283	+	1.73081i
$93$	−14.6621	+	9.50249i	−1.52039	+	0.985362i
$94$	5.46935	+	9.47320i	0.564121	+	0.977086i
$95$	−3.20540	−	5.55192i	−0.328867	−	0.569615i
$96$	−2.03976	+	1.32197i	−0.208182	+	0.134923i
$97$	0.213335	+	0.123169i	0.0216609	+	0.0125059i	0.510791	−	0.859705i	$-0.329352\pi$
$97$	0.213335	+	0.123169i	0.0216609	+	0.0125059i	−0.489130	+	0.872211i	$0.662686\pi$
$98$			14.9505i			1.51023i
$99$	7.90234	+	3.53579i	0.794215	+	0.355360i
$100$	−17.4024			−1.74024
$101$	2.38713	−	4.13463i	0.237528	−	0.411411i	−0.722476	−	0.691396i	$-0.756996\pi$
$101$	2.38713	−	4.13463i	0.237528	−	0.411411i	0.960004	+	0.279985i	$0.0903294\pi$
$102$	20.4193	+	10.4278i	2.02182	+	1.03251i
$103$	1.71676	+	2.97351i	0.169157	+	0.292988i	0.938124	−	0.346300i	$-0.112562\pi$
$103$	1.71676	+	2.97351i	0.169157	+	0.292988i	−0.768967	+	0.639289i	$0.779229\pi$
$104$	−18.7087	−	3.78163i	−1.83454	−	0.370820i
$105$	1.51353	−	0.0779244i	0.147705	−	0.00760465i
$106$	−13.5342	−	7.81398i	−1.31456	−	0.758960i
$107$	−2.34075			−0.226289			−0.113144	−	0.993579i	$-0.536092\pi$
$107$	−2.34075			−0.226289			−0.113144	+	0.993579i	$0.536092\pi$
$108$	−13.4818	−	16.7429i	−1.29729	−	1.61109i
$109$			10.2127i			0.978195i	0.872229	+	0.489097i	$0.162674\pi$
$109$			10.2127i			0.978195i	−0.872229	+	0.489097i	$0.837326\pi$
$110$	5.51461	+	3.18386i	0.525797	+	0.303569i
$111$	0.429976	+	8.35143i	0.0408115	+	0.792682i
$112$	−4.11780	+	2.37742i	−0.389096	+	0.224645i
$113$	0.605276	+	1.04837i	0.0569396	+	0.0986222i	0.893090	−	0.449878i	$-0.148532\pi$
$113$	0.605276	+	1.04837i	0.0569396	+	0.0986222i	−0.836151	+	0.548500i	$0.815199\pi$
$114$	−14.0453	+	27.5029i	−1.31547	+	2.57588i
$115$	−3.57447	−	2.06372i	−0.333321	−	0.192443i
$116$	−8.03503			−0.746034
$117$	1.04289	−	10.7663i	0.0964155	−	0.995341i
$118$	7.85863			0.723446
$119$	4.54586	+	2.62456i	0.416719	+	0.240593i
$120$	−4.44189	−	6.85370i	−0.405487	−	0.625655i
$121$	−1.33618	−	2.31432i	−0.121471	−	0.210393i
$122$	−11.8440	+	6.83815i	−1.07231	+	0.619097i
$123$	−4.01714	+	2.60351i	−0.362213	+	0.234751i
$124$	36.1404	+	20.8657i	3.24550	+	1.87379i
$125$		−	8.20061i		−	0.733485i
$126$	−4.28027	−	5.91414i	−0.381317	−	0.526873i
$127$	7.58237			0.672827			0.336413	−	0.941714i	$-0.390786\pi$
$127$	7.58237			0.672827			0.336413	+	0.941714i	$0.390786\pi$
$128$	−15.7411	−	9.08815i	−1.39133	−	0.803286i
$129$	3.86789	−	7.57393i	0.340549	−	0.666847i
$130$	1.57629	−	7.79828i	0.138250	−	0.683955i
$131$	−9.40603	−	16.2917i	−0.821809	−	1.42342i	−0.904334	−	0.426826i	$-0.859632\pi$
$131$	−9.40603	−	16.2917i	−0.821809	−	1.42342i	0.0825247	−	0.996589i	$-0.473702\pi$
$132$	−1.06319	−	20.6503i	−0.0925384	−	1.79737i
$133$	−3.53503	+	6.12285i	−0.306526	+	0.530918i
$134$	9.01232			0.778546
$135$	3.60495	−	2.90280i	0.310265	−	0.249833i
$136$		−	28.2875i		−	2.42564i
$137$	15.6417	+	9.03076i	1.33636	+	0.771550i	0.986266	−	0.165163i	$-0.0528150\pi$
$137$	15.6417	+	9.03076i	1.33636	+	0.771550i	0.350098	+	0.936713i	$0.386148\pi$
$138$	1.02230	+	19.8562i	0.0870240	+	1.69027i
$139$	2.42577	+	4.20155i	0.205751	+	0.356371i	0.950372	−	0.311117i	$-0.100703\pi$
$139$	2.42577	+	4.20155i	0.205751	+	0.356371i	−0.744621	+	0.667488i	$0.767370\pi$
$140$	−1.80989	−	3.13483i	−0.152964	−	0.264941i
$141$	6.81127	+	3.47841i	0.573612	+	0.292935i
$142$	8.29537	−	14.3680i	0.696132	−	1.20574i
$143$	6.88453	−	7.80145i	0.575713	−	0.652390i
$144$	−5.93065	+	13.2548i	−0.494221	+	1.10456i
$145$		−	1.73004i		−	0.143672i
$146$	11.5687	−	20.0375i	0.957429	−	1.65832i
$147$	5.68503	+	8.77184i	0.468893	+	0.723489i
$148$	17.2975	−	9.98674i	1.42185	−	0.820905i
$149$	−10.6241	+	6.13383i	−0.870360	+	0.502503i	−0.867468	−	0.497493i	$-0.834254\pi$
$149$	−10.6241	+	6.13383i	−0.870360	+	0.502503i	−0.00289232	+	0.999996i	$0.500921\pi$
$150$	−15.1467	+	9.81658i	−1.23672	+	0.801520i
$151$	−4.82142	−	2.78365i	−0.392362	−	0.226530i	0.290821	−	0.956777i	$-0.406072\pi$
$151$	−4.82142	−	2.78365i	−0.392362	−	0.226530i	−0.683183	+	0.730247i	$0.739405\pi$
$152$	38.1006			3.09037
$153$	15.9458	−	1.64632i	1.28914	−	0.133097i
$154$		−	7.02254i		−	0.565893i
$155$	−4.49263	+	7.78147i	−0.360857	+	0.625023i
$156$	−24.0342	+	9.47697i	−1.92427	+	0.758765i
$157$	2.02526	+	3.50785i	0.161633	+	0.279957i	0.935455	−	0.353447i	$-0.114991\pi$
$157$	2.02526	+	3.50785i	0.161633	+	0.279957i	−0.773821	+	0.633404i	$0.781657\pi$
$158$	10.1855	−	5.88057i	0.810311	−	0.467833i
$159$	−10.9122	+	0.561818i	−0.865393	+	0.0445550i
$160$	−0.625007	+	1.08254i	−0.0494111	+	0.0855826i
$161$			4.55188i			0.358739i
$162$	−21.1788	−	6.96769i	−1.66397	−	0.547433i
$163$		−	10.3387i		−	0.809787i	−0.914364	−	0.404894i	$-0.867309\pi$
$163$		−	10.3387i		−	0.809787i	0.914364	−	0.404894i	$-0.132691\pi$
$164$	9.90182	+	5.71682i	0.773202	+	0.446409i
$165$	4.44625	−	0.228917i	0.346140	−	0.0178211i
$166$	6.84112	+	11.8492i	0.530974	+	0.919673i
$167$	11.4388	−	6.60418i	0.885159	−	0.511047i	0.0128030	−	0.999918i	$-0.495925\pi$
$167$	11.4388	−	6.60418i	0.885159	−	0.511047i	0.872356	+	0.488871i	$0.162591\pi$
$168$	−4.09652	+	8.02162i	−0.316053	+	0.618881i
$169$	−11.9794	−	5.04915i	−0.921492	−	0.388396i
$170$	11.7910			0.904330
$171$	2.21743	+	21.4775i	0.169571	+	1.64243i
$172$	−20.3124			−1.54881
$173$	−5.71416	+	9.89721i	−0.434439	+	0.752471i	−0.997250	−	0.0741150i	$-0.976387\pi$
$173$	−5.71416	+	9.89721i	−0.434439	+	0.752471i	0.562810	+	0.826586i	$0.309720\pi$
$174$	−6.99352	+	4.53250i	−0.530177	+	0.343608i
$175$	−3.57865	+	2.06613i	−0.270520	+	0.156185i
$176$	−12.0968	+	6.98407i	−0.911828	+	0.526444i
$177$	4.61086	−	2.98830i	0.346574	−	0.224615i
$178$	−21.7800	+	37.7241i	−1.63248	+	2.82754i
$179$	0.150491			0.0112482			0.00562411	−	0.999984i	$-0.498210\pi$
$179$	0.150491			0.0112482			0.00562411	+	0.999984i	$0.498210\pi$
$180$	−10.0907	−	4.51493i	−0.752115	−	0.336523i
$181$	−22.0219			−1.63687			−0.818436	−	0.574598i	$-0.805159\pi$
$181$	−22.0219			−1.63687			−0.818436	+	0.574598i	$0.805159\pi$
$182$	−8.31719	+	2.79462i	−0.616511	+	0.207151i
$183$	−4.34894	+	8.51590i	−0.321483	+	0.629513i
$184$	21.2438	−	12.2651i	1.56611	−	0.904195i
$185$	2.15027	+	3.72437i	0.158091	+	0.273821i
$186$	43.2260	−	2.22551i	3.16949	−	0.163182i
$187$	13.3543	+	7.71009i	0.976561	+	0.563818i
$188$		−	18.2671i		−	1.33226i
$189$	−4.76024	−	1.84238i	−0.346257	−	0.134013i
$190$			15.8814i			1.15216i
$191$	9.97868	−	17.2836i	0.722032	−	1.25060i	−0.238152	−	0.971228i	$-0.576542\pi$
$191$	9.97868	−	17.2836i	0.722032	−	1.25060i	0.960184	−	0.279369i	$-0.0901251\pi$
$192$	−10.7318	+	0.552529i	−0.774500	+	0.0398754i
$193$	−8.70542	+	5.02608i	−0.626630	+	0.361785i	−0.779446	−	0.626470i	$-0.784499\pi$
$193$	−8.70542	+	5.02608i	−0.626630	+	0.361785i	0.152816	+	0.988255i	$0.451166\pi$
$194$	−0.305125	−	0.528492i	−0.0219067	−	0.0379435i
$195$	−2.04051	−	5.17485i	−0.146124	−	0.370579i
$196$	12.4833	−	21.6216i	0.891661	−	1.54440i
$197$			3.94715i			0.281223i	0.990065	+	0.140611i	$0.0449068\pi$
$197$			3.94715i			0.281223i	−0.990065	+	0.140611i	$0.955093\pi$
$198$	−12.5740	−	17.3738i	−0.893598	−	1.23470i
$199$	11.4749			0.813433			0.406716	−	0.913554i	$-0.366674\pi$
$199$	11.4749			0.813433			0.406716	+	0.913554i	$0.366674\pi$
$200$	19.2854	+	11.1344i	1.36368	+	0.787323i
$201$	5.28777	−	3.42700i	0.372970	−	0.241722i
$202$	−10.2427	+	5.91360i	−0.720670	+	0.416079i
$203$	−1.65233	+	0.953973i	−0.115971	+	0.0669558i
$204$	−20.8238	−	32.1306i	−1.45796	−	2.24959i
$205$	−1.23090	+	2.13198i	−0.0859698	+	0.148904i
$206$		−	8.50578i		−	0.592626i
$207$	8.15027	+	11.2614i	0.566483	+	0.782721i
$208$	13.0855	+	11.5476i	0.907319	+	0.800680i
$209$	−10.3848	+	17.9869i	−0.718329	+	1.24418i
$210$	−3.34363	−	1.70754i	−0.230732	−	0.117831i
$211$	−5.48306	−	9.49694i	−0.377469	−	0.653796i	0.613224	−	0.789909i	$-0.289872\pi$
$211$	−5.48306	−	9.49694i	−0.377469	−	0.653796i	−0.990693	+	0.136113i	$0.956539\pi$
$212$	13.0489	+	22.6014i	0.896204	+	1.55227i
$213$	−0.596429	−	11.5845i	−0.0408667	−	0.793754i
$214$	5.02182	+	2.89935i	0.343285	+	0.198195i
$215$		−	4.37351i		−	0.298271i
$216$	4.22810	+	27.1805i	0.287686	+	1.84940i
$217$	9.90926			0.672684
$218$	12.6498	−	21.9101i	0.856754	−	1.48394i
$219$	−0.831776	−	16.1556i	−0.0562062	−	1.09169i
$220$	−5.31688	−	9.20911i	−0.358464	−	0.620878i
$221$	3.81716	−	18.8845i	0.256770	−	1.27031i
$222$	9.42196	−	18.4497i	0.632361	−	1.23826i
$223$	−11.1218	−	6.42116i	−0.744770	−	0.429993i	0.0790313	−	0.996872i	$-0.474817\pi$
$223$	−11.1218	−	6.42116i	−0.744770	−	0.429993i	−0.823801	+	0.566879i	$0.808151\pi$
$224$	1.37856			0.0921088
$225$	−5.15413	+	11.5193i	−0.343609	+	0.767952i
$226$		−	2.99888i		−	0.199482i
$227$	−20.4534	−	11.8088i	−1.35754	−	0.783777i	−0.368249	−	0.929727i	$-0.620043\pi$
$227$	−20.4534	−	11.8088i	−1.35754	−	0.783777i	−0.989292	+	0.145950i	$0.953376\pi$
$228$	43.2768	−	28.0477i	2.86608	−	1.85751i
$229$	10.7715	−	6.21892i	0.711800	−	0.410958i	−0.0999271	−	0.994995i	$-0.531861\pi$
$229$	10.7715	−	6.21892i	0.711800	−	0.410958i	0.811727	+	0.584037i	$0.198528\pi$
$230$	5.11242	+	8.85497i	0.337103	+	0.583880i
$231$	−2.67037	−	4.12031i	−0.175698	−	0.271096i
$232$	8.90443	+	5.14098i	0.584605	+	0.337522i
$233$	−18.7821			−1.23046			−0.615230	−	0.788348i	$-0.710937\pi$
$233$	−18.7821			−1.23046			−0.615230	+	0.788348i	$0.710937\pi$
$234$	−15.5730	+	21.8061i	−1.01804	+	1.42551i
$235$	3.93312			0.256568
$236$	−11.3653	−	6.56175i	−0.739817	−	0.427134i
$237$	3.73994	−	7.32338i	0.242935	−	0.475705i
$238$	−6.50177	−	11.2614i	−0.421447	−	0.729968i
$239$	−17.1326	+	9.89154i	−1.10822	+	0.639830i	−0.938367	−	0.345639i	$-0.887662\pi$
$239$	−17.1326	+	9.89154i	−1.10822	+	0.639830i	−0.169851	+	0.985470i	$0.554329\pi$
$240$	0.383967	+	7.45780i	0.0247850	+	0.481399i
$241$	−9.86550	−	5.69585i	−0.635493	−	0.366902i	0.147384	−	0.989079i	$-0.452915\pi$
$241$	−9.86550	−	5.69585i	−0.635493	−	0.366902i	−0.782876	+	0.622178i	$0.786248\pi$
$242$			6.62017i			0.425561i
$243$	−15.0757	+	3.96528i	−0.967106	+	0.254373i
$244$	22.8387			1.46210
$245$	4.65540	+	2.68780i	0.297423	+	0.171717i
$246$	11.8432	−	0.609748i	0.755092	−	0.0388761i
$247$	25.4356	+	5.14136i	1.61843	+	0.327137i
$248$	−26.7006	−	46.2468i	−1.69549	−	2.93667i
$249$	8.51959	+	4.35083i	0.539907	+	0.275723i
$250$	−10.1576	+	17.5935i	−0.642424	+	1.11271i
$251$	−18.6950			−1.18002			−0.590010	−	0.807396i	$-0.700876\pi$
$251$	−18.6950			−1.18002			−0.590010	+	0.807396i	$0.700876\pi$
$252$	1.25205	+	12.1270i	0.0788716	+	0.763932i
$253$			13.3720i			0.840688i
$254$	−16.2672	−	9.39184i	−1.02069	−	0.589297i
$255$	6.91810	−	4.48362i	0.433228	−	0.280775i
$256$	16.3097	+	28.2492i	1.01936	+	1.76558i
$257$	4.37976	+	7.58598i	0.273202	+	0.473200i	0.969680	−	0.244378i	$-0.0785838\pi$
$257$	4.37976	+	7.58598i	0.273202	+	0.473200i	−0.696478	+	0.717578i	$0.745251\pi$
$258$	−17.6795	+	11.4581i	−1.10068	+	0.713350i
$259$	2.37139	−	4.10736i	0.147351	−	0.255219i
$260$	−8.79102	+	9.96185i	−0.545196	+	0.617808i
$261$	−2.37976	+	5.31868i	−0.147304	+	0.329218i
$262$			46.6028i			2.87913i
$263$	−3.86402	+	6.69268i	−0.238266	+	0.412688i	−0.960217	−	0.279256i	$-0.909912\pi$
$263$	−3.86402	+	6.69268i	−0.238266	+	0.412688i	0.721951	+	0.691944i	$0.243246\pi$
$264$	−12.0342	+	23.5649i	−0.740657	+	1.45032i
$265$	−4.86636	+	2.80959i	−0.298938	+	0.172592i
$266$	15.1680	−	8.75727i	0.930012	−	0.536942i
$267$	1.56596	+	30.4157i	0.0958354	+	1.86141i
$268$	−13.0338	−	7.52505i	−0.796165	−	0.459666i
$269$	14.8448			0.905102			0.452551	−	0.891739i	$-0.350514\pi$
$269$	14.8448			0.905102			0.452551	+	0.891739i	$0.350514\pi$
$270$	−11.3296	+	1.76239i	−0.689495	+	0.107255i
$271$		−	19.3486i		−	1.17534i	−0.809100	−	0.587671i	$-0.800045\pi$
$271$		−	19.3486i		−	1.17534i	0.809100	−	0.587671i	$-0.199955\pi$
$272$	−12.9323	+	22.3994i	−0.784136	+	1.35816i
$273$	−3.81724	+	4.80235i	−0.231030	+	0.290652i
$274$	−22.3718	−	38.7490i	−1.35153	−	2.34091i
$275$	−10.5129	+	6.06963i	−0.633952	+	0.366012i
$276$	15.1009	−	29.5699i	0.908968	−	1.77990i
$277$	−0.587762	+	1.01803i	−0.0353152	+	0.0611677i	−0.883143	−	0.469104i	$-0.844577\pi$
$277$	−0.587762	+	1.01803i	−0.0353152	+	0.0611677i	0.847828	+	0.530272i	$0.177910\pi$
$278$		−	12.0186i		−	0.720829i
$279$	24.5156	−	17.7428i	1.46771	−	1.06223i
$280$			4.63203i			0.276817i
$281$	3.96724	+	2.29048i	0.236665	+	0.136639i	0.613643	−	0.789583i	$-0.289703\pi$
$281$	3.96724	+	2.29048i	0.236665	+	0.136639i	−0.376978	+	0.926222i	$0.623037\pi$
$282$	−10.3043	−	15.8993i	−0.613613	−	0.946788i
$283$	−0.0159162	−	0.0275676i	−0.000946118	−	0.00163872i	0.865552	−	0.500819i	$-0.166968\pi$
$283$	−0.0159162	−	0.0275676i	−0.000946118	−	0.00163872i	−0.866498	+	0.499180i	$0.833634\pi$
$284$	−23.9938	+	13.8528i	−1.42377	+	0.822014i
$285$	6.03901	+	9.31802i	0.357720	+	0.551952i
$286$	−24.4332	+	8.20969i	−1.44477	+	0.485449i
$287$	2.71496			0.160259
$288$	3.41056	−	2.46834i	0.200969	−	0.145449i
$289$	11.5533			0.679607
$290$	−2.14290	+	3.71161i	−0.125835	+	0.217953i
$291$	−0.379988	−	0.194054i	−0.0222753	−	0.0113756i
$292$	−33.4616	+	19.3191i	−1.95819	+	1.13056i
$293$	9.44674	−	5.45408i	0.551884	−	0.318631i	−0.197997	−	0.980203i	$-0.563444\pi$
$293$	9.44674	−	5.45408i	0.551884	−	0.318631i	0.749882	+	0.661572i	$0.230110\pi$
$294$	−1.33145	−	25.8607i	−0.0776516	−	1.50823i
$295$	1.41282	−	2.44708i	0.0822578	−	0.142475i
$296$	−25.5589			−1.48558
$297$	−13.9840	−	5.41230i	−0.811437	−	0.314054i
$298$	30.3905			1.76047
$299$	15.8372	−	5.32137i	0.915887	−	0.307743i
$300$	30.1020	−	1.54981i	1.73794	−	0.0894784i
$301$	−4.17707	+	2.41163i	−0.240762	+	0.139004i
$302$	6.89589	+	11.9440i	0.396814	+	0.687302i
$303$	−3.76094	+	7.36451i	−0.216060	+	0.423080i
$304$	−30.1699	−	17.4186i	−1.73036	−	0.999025i
$305$			4.91745i			0.281572i
$306$	−36.2492	−	16.2192i	−2.07223	−	0.927189i
$307$			6.90363i			0.394011i	0.980402	+	0.197005i	$0.0631217\pi$
$307$			6.90363i			0.394011i	−0.980402	+	0.197005i	$0.936878\pi$
$308$	−5.86364	+	10.1561i	−0.334112	+	0.578699i
$309$	−3.23439	−	4.99056i	−0.183998	−	0.283903i
$310$	19.2769	−	11.1295i	1.09485	−	0.632115i
$311$	7.69804	+	13.3334i	0.436516	+	0.756067i	0.997418	−	0.0718148i	$-0.0228791\pi$
$311$	7.69804	+	13.3334i	0.436516	+	0.756067i	−0.560902	+	0.827882i	$0.689546\pi$
$312$	32.6983	+	4.87518i	1.85118	+	0.276002i
$313$	8.67077	−	15.0182i	0.490101	−	0.848879i	−0.509834	−	0.860273i	$-0.670293\pi$
$313$	8.67077	−	15.0182i	0.490101	−	0.848879i	0.999935	+	0.0113932i	$0.00362663\pi$
$314$		−	10.0343i		−	0.566267i
$315$	−2.61110	+	0.269581i	−0.147119	+	0.0151892i
$316$	−19.6405			−1.10486
$317$	−9.21059	−	5.31774i	−0.517318	−	0.298674i	0.218518	−	0.975833i	$-0.429878\pi$
$317$	−9.21059	−	5.31774i	−0.517318	−	0.298674i	−0.735837	+	0.677159i	$0.763211\pi$
$318$	24.1068	+	12.3110i	1.35184	+	0.690366i
$319$	−4.85401	+	2.80246i	−0.271772	+	0.156908i
$320$	−4.78591	+	2.76314i	−0.267540	+	0.154464i
$321$	4.04893	−	0.208461i	0.225989	−	0.0116351i
$322$	5.63815	−	9.76557i	0.314202	−	0.544214i
$323$			38.4586i			2.13989i
$324$	24.8114	+	27.7606i	1.37841	+	1.54225i
$325$	11.3722	+	10.0356i	0.630817	+	0.556676i
$326$	−12.8059	+	22.1805i	−0.709254	+	1.22846i
$327$	−0.909510	−	17.6654i	−0.0502960	−	0.976901i
$328$	−7.31548	−	12.6708i	−0.403930	−	0.699627i
$329$	−2.16879	−	3.75646i	−0.119569	−	0.207100i
$330$	−9.82249	−	5.01620i	−0.540710	−	0.276133i
$331$	27.4350	+	15.8396i	1.50796	+	0.870623i	0.999957	+	0.00926968i	$0.00295067\pi$
$331$	27.4350	+	15.8396i	1.50796	+	0.870623i	0.508006	+	0.861353i	$0.330383\pi$
$332$		−	22.8486i		−	1.25398i
$333$	−1.48751	−	14.4077i	−0.0815150	−	0.789536i
$334$	−32.7208			−1.79041
$335$	1.62024	−	2.80633i	0.0885229	−	0.153326i
$336$	6.91109	−	4.47908i	0.377031	−	0.244354i
$337$	−12.1482	−	21.0414i	−0.661757	−	1.14620i	−0.980154	−	0.198239i	$-0.936478\pi$
$337$	−12.1482	−	21.0414i	−0.661757	−	1.14620i	0.318397	−	0.947958i	$-0.396856\pi$
$338$	19.4464	+	25.6706i	1.05774	+	1.39630i
$339$	−1.14035	−	1.75952i	−0.0619351	−	0.0955641i
$340$	−17.0524	−	9.84519i	−0.924795	−	0.533930i
$341$	29.1102			1.57641
$342$	21.8457	−	48.8243i	1.18128	−	2.64011i
$343$		−	12.8047i		−	0.691389i
$344$	22.5103	+	12.9963i	1.21367	+	0.700714i
$345$	6.36676	+	3.25141i	0.342775	+	0.175050i
$346$	24.5182	−	14.1556i	1.31811	−	0.761009i
$347$	−1.91224	−	3.31209i	−0.102654	−	0.177802i	0.810123	−	0.586260i	$-0.199400\pi$
$347$	−1.91224	−	3.31209i	−0.102654	−	0.177802i	−0.912777	+	0.408457i	$0.866067\pi$
$348$	13.8987	−	0.715577i	0.745047	−	0.0383590i
$349$	20.3799	+	11.7664i	1.09091	+	0.629839i	0.933819	−	0.357745i	$-0.116454\pi$
$349$	20.3799	+	11.7664i	1.09091	+	0.629839i	0.157093	+	0.987584i	$0.449788\pi$
$350$	10.2368			0.547180
$351$	−0.845142	+	18.7159i	−0.0451103	+	0.998982i
$352$	4.04976			0.215853
$353$	20.4327	+	11.7968i	1.08752	+	0.627881i	0.932916	−	0.360095i	$-0.117256\pi$
$353$	20.4327	+	11.7968i	1.08752	+	0.627881i	0.154606	+	0.987976i	$0.450589\pi$
$354$	−13.5935	+	0.699868i	−0.722489	+	0.0371976i
$355$	−2.98268	−	5.16616i	−0.158304	−	0.274191i
$356$	62.9973	−	36.3715i	3.33885	−	1.92769i
$357$	−8.09699	−	4.13501i	−0.428538	−	0.218848i
$358$	−0.322862	−	0.186404i	−0.0170638	−	0.00985177i
$359$			0.220474i			0.0116362i	0.999983	+	0.00581809i	$0.00185196\pi$
$359$			0.220474i			0.0116362i	−0.999983	+	0.00581809i	$0.998148\pi$
$360$	8.29377	+	11.4597i	0.437120	+	0.603978i
$361$	−32.8001			−1.72632
$362$	47.2455	+	27.2772i	2.48317	+	1.43366i
$363$	2.51737	+	3.88423i	0.132128	+	0.203869i
$364$	14.3619	+	2.90301i	0.752768	+	0.152159i
$365$	−4.15963	−	7.20469i	−0.217725	−	0.377111i
$366$	19.8783	−	12.8832i	1.03906	−	0.673413i
$367$	10.2569	−	17.7655i	0.535407	−	0.927353i	−0.463736	−	0.885973i	$-0.653491\pi$
$367$	10.2569	−	17.7655i	0.535407	−	0.927353i	0.999144	−	0.0413794i	$-0.0131752\pi$
$368$	−22.4291			−1.16920
$369$	6.71683	−	4.86120i	0.349664	−	0.253064i
$370$		−	10.6536i		−	0.553856i
$371$	5.36679	+	3.09852i	0.278630	+	0.160867i
$372$	−64.3725	−	32.8740i	−3.33756	−	1.70444i
$373$	−5.42755	−	9.40079i	−0.281028	−	0.486754i	0.690610	−	0.723227i	$-0.257342\pi$
$373$	−5.42755	−	9.40079i	−0.281028	−	0.486754i	−0.971638	+	0.236473i	$0.924009\pi$
$374$	−19.1001	−	33.0823i	−0.987642	−	1.71065i
$375$	0.730324	+	14.1851i	0.0377138	+	0.732515i
$376$	−11.6876	+	20.2436i	−0.602744	+	1.04398i
$377$	5.25077	+	4.63364i	0.270428	+	0.238644i
$378$	7.93054	+	9.84885i	0.407903	+	0.506570i
$379$		−	19.6987i		−	1.01185i	−0.862577	−	0.505927i	$-0.831151\pi$
$379$		−	19.6987i		−	1.01185i	0.862577	−	0.505927i	$-0.168849\pi$
$380$	13.2605	−	22.9679i	0.680251	−	1.17823i
$381$	−13.1157	+	0.675265i	−0.671937	+	0.0345949i
$382$	−42.8164	+	24.7200i	−2.19068	+	1.26479i
$383$	−17.6164	+	10.1708i	−0.900156	+	0.519705i	−0.877251	−	0.480032i	$-0.840625\pi$
$383$	−17.6164	+	10.1708i	−0.900156	+	0.519705i	−0.0229052	+	0.999738i	$0.507292\pi$
$384$	28.0377	+	14.3184i	1.43080	+	0.730685i
$385$	−2.18674	−	1.26251i	−0.111446	−	0.0643436i
$386$	24.9020			1.26748
$387$	−6.01601	+	13.4455i	−0.305811	+	0.683475i
$388$			1.01909i			0.0517362i
$389$	−10.6980	+	18.5295i	−0.542412	+	0.939485i	0.456353	+	0.889799i	$0.349155\pi$
$389$	−10.6980	+	18.5295i	−0.542412	+	0.939485i	−0.998765	+	0.0496861i	$0.984178\pi$
$390$	−2.03210	+	13.6295i	−0.102900	+	0.690158i
$391$	12.3803	+	21.4434i	0.626100	+	1.08444i
$392$	−27.6679	+	15.9741i	−1.39744	+	0.806814i
$393$	17.7211	+	27.3431i	0.893910	+	1.37928i
$394$	4.88911	−	8.46818i	0.246310	−	0.426621i
$395$		−	4.22884i		−	0.212776i
$396$	3.67811	+	35.6253i	0.184832	+	1.79024i
$397$		−	27.7995i		−	1.39522i	−0.716479	−	0.697608i	$-0.754248\pi$
$397$		−	27.7995i		−	1.39522i	0.716479	−	0.697608i	$-0.245752\pi$
$398$	−24.6181	−	14.2133i	−1.23399	−	0.712447i
$399$	5.56946	−	10.9059i	0.278822	−	0.545977i
$400$	−10.1807	−	17.6335i	−0.509036	−	0.881676i
$401$	−13.1515	+	7.59301i	−0.656754	+	0.379177i	−0.791039	−	0.611766i	$-0.790459\pi$
$401$	−13.1515	+	7.59301i	−0.656754	+	0.379177i	0.134285	+	0.990943i	$0.457126\pi$
$402$	−15.5892	+	0.802612i	−0.777516	+	0.0400307i
$403$	−11.5844	−	34.4768i	−0.577060	−	1.71741i
$404$	19.7508			0.982639
$405$	−5.97719	+	5.34219i	−0.297009	+	0.265455i
$406$	4.72652			0.234573
$407$	6.96636	−	12.0661i	0.345310	−	0.598094i
$408$	2.51921	+	48.9307i	0.124720	+	2.42243i
$409$	−2.06606	+	1.19284i	−0.102160	+	0.0589823i	−0.550210	−	0.835027i	$-0.685452\pi$
$409$	−2.06606	+	1.19284i	−0.102160	+	0.0589823i	0.448049	+	0.894009i	$0.352119\pi$
$410$	5.28152	−	3.04929i	0.260836	−	0.150594i
$411$	−27.8607	−	14.2280i	−1.37427	−	0.701818i
$412$	−7.10210	+	12.3012i	−0.349896	+	0.606037i
$413$	−3.11622			−0.153339
$414$	−3.53667	−	34.2553i	−0.173818	−	1.68356i
$415$	4.91958			0.241493
$416$	−1.61160	−	4.79636i	−0.0790153	−	0.235161i
$417$	−4.57017	−	7.05164i	−0.223802	−	0.345320i
$418$	44.5587	−	25.7260i	2.17944	−	1.25830i
$419$	−16.6455	−	28.8308i	−0.813183	−	1.40848i	−0.910625	−	0.413234i	$-0.864399\pi$
$419$	−16.6455	−	28.8308i	−0.813183	−	1.40848i	0.0974415	−	0.995241i	$-0.468934\pi$
$420$	3.40986	+	5.26132i	0.166384	+	0.256726i
$421$	21.0487	+	12.1525i	1.02585	+	0.592275i	0.915793	−	0.401650i	$-0.131563\pi$
$421$	21.0487	+	12.1525i	1.02585	+	0.592275i	0.110057	+	0.993925i	$0.464897\pi$
$422$			27.1662i			1.32243i
$423$	−12.0916	−	5.41022i	−0.587915	−	0.263054i
$424$		−	33.3959i		−	1.62185i
$425$	−11.2390	+	19.4666i	−0.545173	+	0.944268i
$426$	−13.0694	+	25.5920i	−0.633216	+	1.23993i
$427$	4.69657	−	2.71157i	0.227283	−	0.131222i
$428$	−4.84176	−	8.38618i	−0.234035	−	0.405361i
$429$	−11.2138	+	14.1078i	−0.541408	+	0.681129i
$430$	−5.41722	+	9.38289i	−0.261241	+	0.452483i
$431$		−	12.1410i		−	0.584812i	−0.956294	−	0.292406i	$-0.905544\pi$
$431$		−	12.1410i		−	0.584812i	0.956294	−	0.292406i	$-0.0944559\pi$
$432$	9.07817	−	23.4557i	0.436774	−	1.12851i
$433$	−13.2730			−0.637859			−0.318930	−	0.947778i	$-0.603323\pi$
$433$	−13.2730			−0.637859			−0.318930	+	0.947778i	$0.603323\pi$
$434$	−21.2592	−	12.2740i	−1.02048	−	0.589172i
$435$	0.154072	+	2.99255i	0.00738721	+	0.143482i
$436$	−36.5888	+	21.1245i	−1.75228	+	1.01168i
$437$	−28.8822	+	16.6751i	−1.38162	+	0.797680i
$438$	−18.2265	+	35.6904i	−0.870897	+	1.70535i
$439$	6.55074	−	11.3462i	0.312650	−	0.541526i	−0.666285	−	0.745697i	$-0.732117\pi$
$439$	6.55074	−	11.3462i	0.312650	−	0.541526i	0.978935	+	0.204171i	$0.0654500\pi$
$440$			13.6074i			0.648708i
$441$	−10.6149	−	14.6669i	−0.505473	−	0.698423i
$442$	−31.5804	+	35.7864i	−1.50213	+	1.70219i
$443$	17.2195	−	29.8250i	0.818123	−	1.41703i	−0.0889410	−	0.996037i	$-0.528348\pi$
$443$	17.2195	−	29.8250i	0.818123	−	1.41703i	0.907064	−	0.420993i	$-0.138318\pi$
$444$	−29.0312	+	18.8151i	−1.37776	+	0.892926i
$445$	7.83122	+	13.5641i	0.371236	+	0.642999i
$446$	15.9070	+	27.5518i	0.753220	+	1.30462i
$447$	17.8309	−	11.5562i	0.843372	−	0.546590i
$448$	5.27806	+	3.04729i	0.249365	+	0.143971i
$449$		−	5.32385i		−	0.251248i	−0.992078	−	0.125624i	$-0.959907\pi$
$449$		−	5.32385i		−	0.251248i	0.992078	−	0.125624i	$-0.0400933\pi$
$450$	25.3259	−	18.3292i	1.19387	−	0.864049i
$451$	7.97567			0.375559
$452$	−2.50399	+	4.33703i	−0.117778	+	0.203997i
$453$	8.58780	+	4.38566i	0.403490	+	0.206056i
$454$	29.2537	+	50.6689i	1.37294	+	2.37801i
$455$	−0.625053	+	3.09229i	−0.0293029	+	0.144969i
$456$	−65.9050	+	3.39314i	−3.08628	+	0.158898i
$457$	10.7297	+	6.19481i	0.501916	+	0.289781i	0.729504	−	0.683976i	$-0.239751\pi$
$457$	10.7297	+	6.19481i	0.501916	+	0.289781i	−0.227589	+	0.973757i	$0.573084\pi$
$458$	−30.8121			−1.43975
$459$	−27.4358	+	4.26782i	−1.28060	+	0.199205i
$460$		−	17.0750i		−	0.796124i
$461$	11.2633	+	6.50288i	0.524585	+	0.302869i	0.738809	−	0.673915i	$-0.235389\pi$
$461$	11.2633	+	6.50288i	0.524585	+	0.302869i	−0.214223	+	0.976785i	$0.568722\pi$
$462$	0.625408	+	12.1473i	0.0290966	+	0.565144i
$463$	5.56377	−	3.21224i	0.258570	−	0.149286i	−0.365112	−	0.930964i	$-0.618969\pi$
$463$	5.56377	−	3.21224i	0.258570	−	0.149286i	0.623682	+	0.781678i	$0.285636\pi$
$464$	−4.70063	−	8.14173i	−0.218221	−	0.377971i
$465$	7.07818	−	13.8602i	0.328243	−	0.642750i
$466$	40.2950	+	23.2644i	1.86663	+	1.07770i
$467$	13.9598			0.645982			0.322991	−	0.946402i	$-0.395312\pi$
$467$	13.9598			0.645982			0.322991	+	0.946402i	$0.395312\pi$
$468$	40.7294	−	18.5333i	1.88272	−	0.856702i
$469$	−3.57370			−0.165018
$470$	−8.43808	−	4.87173i	−0.389220	−	0.224716i
$471$	−3.81561	−	5.88737i	−0.175814	−	0.271276i
$472$	8.39669	+	14.5435i	0.386489	+	0.669419i
$473$	−12.2709	+	7.08459i	−0.564215	+	0.325750i
$474$	−17.0947	+	11.0791i	−0.785184	+	0.508878i
$475$	−26.2196	−	15.1379i	−1.20304	−	0.694575i
$476$			21.7152i			0.995316i
$477$	18.8254	−	1.94362i	0.861958	−	0.0889922i
$478$	49.0083			2.24159
$479$	−29.9863	−	17.3126i	−1.37011	−	0.791033i	−0.379168	−	0.925328i	$-0.623790\pi$
$479$	−29.9863	−	17.3126i	−1.37011	−	0.791033i	−0.990941	+	0.134295i	$0.957123\pi$
$480$	0.984704	−	1.92820i	0.0449454	−	0.0880100i
$481$	−17.0628	−	3.44895i	−0.777998	−	0.157259i
$482$	14.1102	+	24.4396i	0.642703	+	1.11319i
$483$	−0.405378	−	7.87367i	−0.0184453	−	0.358264i
$484$	5.52767	−	9.57421i	0.251258	−	0.435191i
$485$	−0.219421			−0.00996341
$486$	37.2548	+	10.1663i	1.68991	+	0.461153i
$487$		−	5.78811i		−	0.262284i	−0.991364	−	0.131142i	$-0.958136\pi$
$487$		−	5.78811i		−	0.262284i	0.991364	−	0.131142i	$-0.0418644\pi$
$488$	−25.3099	−	14.6127i	−1.14573	−	0.661485i
$489$	0.920733	+	17.8834i	0.0416370	+	0.808716i
$490$	−6.65843	−	11.5327i	−0.300797	−	0.520996i
$491$	12.4622	+	21.5851i	0.562410	+	0.974123i	0.997285	+	0.0736326i	$0.0234592\pi$
$491$	12.4622	+	21.5851i	0.562410	+	0.974123i	−0.434875	+	0.900491i	$0.643207\pi$
$492$	−17.6369	−	9.00689i	−0.795133	−	0.406062i
$493$	−5.18928	+	8.98810i	−0.233713	+	0.404803i
$494$	−48.2009	−	42.5358i	−2.16866	−	1.91378i
$495$	−7.67056	+	0.791942i	−0.344766	+	0.0355951i
$496$			48.8272i			2.19240i
$497$	−3.28941	+	5.69742i	−0.147550	+	0.255564i
$498$	−12.8887	−	19.8870i	−0.577558	−	0.891156i
$499$	−34.4839	+	19.9093i	−1.54371	+	0.891262i	−0.545112	+	0.838363i	$0.683513\pi$
$499$	−34.4839	+	19.9093i	−1.54371	+	0.891262i	−0.998600	+	0.0528989i	$0.983154\pi$
$500$	29.3803	−	16.9627i	1.31392	−	0.758595i
$501$	−19.1982	+	12.4423i	−0.857711	+	0.555883i
$502$	40.1082	+	23.1565i	1.79011	+	1.03352i
$503$	−12.9120			−0.575720			−0.287860	−	0.957673i	$-0.592944\pi$
$503$	−12.9120			−0.575720			−0.287860	+	0.957673i	$0.592944\pi$
$504$	6.37161	−	14.2403i	0.283814	−	0.634313i
$505$			4.25259i			0.189238i
$506$	16.5631	−	28.6881i	0.736318	−	1.27534i
$507$	21.1712	+	7.66697i	0.940244	+	0.340502i
$508$	15.6839	+	27.1653i	0.695860	+	1.20527i
$509$	32.1750	−	18.5763i	1.42613	−	0.823378i	0.429319	−	0.903153i	$-0.358753\pi$
$509$	32.1750	−	18.5763i	1.42613	−	0.823378i	0.996813	+	0.0797749i	$0.0254202\pi$
$510$	−20.3956	+	1.05008i	−0.903133	+	0.0464981i
$511$	−4.58738	+	7.94558i	−0.202934	+	0.351492i
$512$		−	44.4550i		−	1.96465i
$513$	−5.74835	−	36.9535i	−0.253796	−	1.63154i
$514$		−	21.6998i		−	0.957139i
$515$	−2.64860	−	1.52917i	−0.116711	−	0.0673832i
$516$	35.1356	−	1.80897i	1.54676	−	0.0796354i
$517$	−6.37120	−	11.0352i	−0.280205	−	0.485329i
$518$	−10.1751	+	5.87460i	−0.447068	+	0.258115i
$519$	9.00270	−	17.6287i	0.395175	−	0.773813i
$520$	16.1160	−	5.41507i	0.706734	−	0.237466i
$521$	−24.6907			−1.08172			−0.540859	−	0.841114i	$-0.681901\pi$
$521$	−24.6907			−1.08172			−0.540859	+	0.841114i	$0.681901\pi$
$522$	11.6935	−	8.46296i	0.511809	−	0.370414i
$523$	−33.4434			−1.46238			−0.731189	−	0.682175i	$-0.761034\pi$
$523$	−33.4434			−1.46238			−0.731189	+	0.682175i	$0.761034\pi$
$524$	38.9121	−	67.3978i	1.69989	−	2.94429i
$525$	6.00620	−	3.89262i	0.262132	−	0.169888i
$526$	16.5797	−	9.57227i	0.722908	−	0.417371i
$527$	46.6813	−	26.9515i	2.03347	−	1.17402i
$528$	20.3025	−	13.1581i	0.883554	−	0.572632i
$529$	0.764121	−	1.32350i	0.0332227	−	0.0575433i
$530$	13.9203			0.604660
$531$	−7.70956	+	5.57968i	−0.334566	+	0.242137i
$532$	−29.2484			−1.26808
$533$	−3.17392	−	9.44603i	−0.137478	−	0.409153i
$534$	34.3146	−	67.1933i	1.48494	−	2.90774i
$535$	1.80565	−	1.04249i	0.0780649	−	0.0450708i
$536$	9.62937	+	16.6786i	0.415925	+	0.720404i
$537$	−0.260313	+	0.0134023i	−0.0112333	+	0.000578352i
$538$	−31.8478	−	18.3874i	−1.37306	−	0.792735i
$539$		−	17.4157i		−	0.750146i
$540$	17.8565	+	6.91109i	0.768423	+	0.297406i
$541$			10.9418i			0.470423i	0.971944	+	0.235211i	$0.0755782\pi$
$541$			10.9418i			0.470423i	−0.971944	+	0.235211i	$0.924422\pi$
$542$	−23.9659	+	41.5102i	−1.02943	+	1.78302i
$543$	38.0925	−	1.96121i	1.63471	−	0.0841634i
$544$	6.49422	−	3.74944i	0.278437	−	0.160756i
$545$	−4.54837	−	7.87800i	−0.194831	−	0.337457i
$546$	14.1379	−	5.57473i	0.605045	−	0.238576i
$547$	−5.47407	+	9.48136i	−0.234054	+	0.405394i	−0.958997	−	0.283415i	$-0.908533\pi$
$547$	−5.47407	+	9.48136i	−0.234054	+	0.405394i	0.724943	+	0.688809i	$0.241866\pi$
$548$			74.7194i			3.19185i
$549$	6.76422	−	15.1178i	0.288690	−	0.645210i
$550$	30.0724			1.28229
$551$	−12.1061	−	6.98947i	−0.515738	−	0.297761i
$552$	−35.6543	+	23.1076i	−1.51755	+	0.983524i
$553$	−4.03889	+	2.33185i	−0.171751	+	0.0991605i
$554$	2.52196	−	1.45605i	0.107148	−	0.0618618i
$555$	−4.05112	−	6.25077i	−0.171961	−	0.265330i
$556$	−10.0352	+	17.3815i	−0.425589	+	0.737141i
$557$		−	12.5825i		−	0.533136i	−0.963816	−	0.266568i	$-0.914110\pi$
$557$		−	12.5825i		−	0.533136i	0.963816	−	0.266568i	$-0.0858898\pi$
$558$	−74.5725	+	7.69918i	−3.15690	+	0.325932i
$559$	13.2739	+	11.7138i	0.561425	+	0.495440i
$560$	2.11764	−	3.66786i	0.0894866	−	0.154995i
$561$	−23.7863	−	12.1473i	−1.00426	−	0.512860i
$562$	−5.67418	−	9.82797i	−0.239351	−	0.414568i
$563$	6.07784	+	10.5271i	0.256151	+	0.443666i	0.965207	−	0.261486i	$-0.0842124\pi$
$563$	6.07784	+	10.5271i	0.256151	+	0.443666i	−0.709057	+	0.705151i	$0.750879\pi$
$564$	1.62681	+	31.5976i	0.0685012	+	1.33050i
$565$	−0.933815	−	0.539139i	−0.0392859	−	0.0226817i
$566$			0.0788577i			0.00331464i
$567$	8.39815	+	2.76293i	0.352689	+	0.116032i
$568$	35.4533			1.48759
$569$	−17.6882	+	30.6369i	−0.741529	+	1.28437i	0.210270	+	0.977643i	$0.432566\pi$
$569$	−17.6882	+	30.6369i	−0.741529	+	1.28437i	−0.951799	+	0.306722i	$0.900768\pi$
$570$	−1.41435	−	27.4710i	−0.0592407	−	1.15063i
$571$	6.24561	+	10.8177i	0.261371	+	0.452707i	0.966606	−	0.256266i	$-0.0824922\pi$
$571$	6.24561	+	10.8177i	0.261371	+	0.452707i	−0.705236	+	0.708973i	$0.749159\pi$
$572$	42.1906	+	8.52810i	1.76408	+	0.356578i
$573$	−15.7215	+	30.7851i	−0.656775	+	1.28607i
$574$	−5.82465	−	3.36286i	−0.243116	−	0.140363i
$575$	−19.4924			−0.812888
$576$	18.5142	−	1.91149i	0.771425	−	0.0796453i
$577$			25.1610i			1.04747i	0.851882	+	0.523734i	$0.175461\pi$
$577$			25.1610i			1.04747i	−0.851882	+	0.523734i	$0.824539\pi$
$578$	−24.7864	−	14.3104i	−1.03098	−	0.595235i
$579$	14.6107	−	9.46919i	0.607199	−	0.393526i
$580$	6.19819	−	3.57853i	0.257366	−	0.148590i
$581$	−2.71274	−	4.69861i	−0.112544	−	0.194931i
$582$	0.574859	+	0.886990i	0.0238287	+	0.0367669i
$583$	15.7659	+	9.10243i	0.652956	+	0.376984i
$584$	49.4430			2.04596
$585$	3.99044	+	8.76953i	0.164985	+	0.362575i
$586$	−27.0226			−1.11629
$587$	−3.21529	−	1.85635i	−0.132709	−	0.0766197i	0.432176	−	0.901789i	$-0.357746\pi$
$587$	−3.21529	−	1.85635i	−0.132709	−	0.0766197i	−0.564885	+	0.825170i	$0.691079\pi$
$588$	−19.6675	+	38.5120i	−0.811073	+	1.58821i
$589$	36.3011	+	62.8753i	1.49576	+	2.59073i
$590$	−6.06212	+	3.49997i	−0.249574	+	0.144091i
$591$	−0.351522	−	6.82762i	−0.0144597	−	0.280851i
$592$	20.2387	+	11.6848i	0.831806	+	0.480244i
$593$			31.6710i			1.30057i	0.759689	+	0.650287i	$0.225351\pi$
$593$			31.6710i			1.30057i	−0.759689	+	0.650287i	$0.774649\pi$
$594$	23.2973	+	28.9327i	0.955901	+	1.18712i
$595$	−4.67555			−0.191679
$596$	−43.9512	−	25.3752i	−1.80031	−	1.03941i
$597$	−19.8488	+	1.02192i	−0.812357	+	0.0418244i
$598$	−40.5682	−	8.20015i	−1.65896	−	0.335329i
$599$	14.2298	+	24.6468i	0.581415	+	1.00704i	0.995312	+	0.0967168i	$0.0308341\pi$
$599$	14.2298	+	24.6468i	0.581415	+	1.00704i	−0.413897	+	0.910324i	$0.635833\pi$
$600$	−34.3507	−	17.5424i	−1.40236	−	0.716165i
$601$	−0.635544	+	1.10079i	−0.0259244	+	0.0449023i	−0.878697	−	0.477381i	$-0.841586\pi$
$601$	−0.635544	+	1.10079i	−0.0259244	+	0.0449023i	0.852772	+	0.522283i	$0.174920\pi$
$602$	11.9486			0.486988
$603$	−8.84136	+	6.39880i	−0.360048	+	0.260579i
$604$		−	23.0315i		−	0.937140i
$605$	2.06144	+	1.19017i	0.0838096	+	0.0483875i
$606$	17.1907	−	11.1413i	0.698323	−	0.452584i
$607$	0.373604	+	0.647101i	0.0151641	+	0.0262650i	0.873508	−	0.486810i	$-0.161840\pi$
$607$	0.373604	+	0.647101i	0.0151641	+	0.0262650i	−0.858344	+	0.513075i	$0.828506\pi$
$608$	5.05014	+	8.74709i	0.204810	+	0.354741i
$609$	2.77318	−	1.79730i	0.112375	−	0.0728301i
$610$	6.09096	−	10.5499i	0.246616	−	0.427151i
$611$	−10.5342	+	11.9373i	−0.426170	+	0.482930i
$612$	38.8817	+	53.7236i	1.57170	+	2.17165i
$613$		−	41.1308i		−	1.66126i	−0.556826	−	0.830629i	$-0.687981\pi$
$613$		−	41.1308i		−	1.66126i	0.556826	−	0.830629i	$-0.312019\pi$
$614$	8.55112	−	14.8110i	0.345095	−	0.597723i
$615$	1.93929	−	3.79744i	0.0781999	−	0.153127i
$616$	12.9962	−	7.50336i	0.523632	−	0.302319i
$617$	10.9623	−	6.32908i	0.441325	−	0.254799i	−0.262835	−	0.964841i	$-0.584657\pi$
$617$	10.9623	−	6.32908i	0.441325	−	0.254799i	0.704159	+	0.710042i	$0.251324\pi$
$618$	0.757501	+	14.7130i	0.0304712	+	0.591842i
$619$	7.38692	+	4.26484i	0.296905	+	0.171418i	0.641052	−	0.767498i	$-0.278498\pi$
$619$	7.38692	+	4.26484i	0.296905	+	0.171418i	−0.344147	+	0.938916i	$0.611832\pi$
$620$	−37.1715			−1.49284
$621$	−15.1009	−	18.7537i	−0.605979	−	0.752559i
$622$		−	38.1404i		−	1.52929i
$623$	8.63654	−	14.9589i	0.346016	−	0.599317i
$624$	−23.6632	−	18.8092i	−0.947288	−	0.752969i
$625$	−6.86422	−	11.8892i	−0.274569	−	0.475567i
$626$	−37.2044	+	21.4800i	−1.48699	+	0.858512i
$627$	16.3613	−	32.0379i	0.653406	−	1.27947i
$628$	−8.37836	+	14.5117i	−0.334333	+	0.579082i
$629$		−	25.7990i		−	1.02867i
$630$	5.93574	+	2.65586i	0.236486	+	0.105812i
$631$			2.50848i			0.0998612i	0.998753	+	0.0499306i	$0.0159000\pi$
$631$			2.50848i			0.0998612i	−0.998753	+	0.0499306i	$0.984100\pi$
$632$	21.7656	+	12.5664i	0.865791	+	0.499865i
$633$	10.3301	+	15.9391i	0.410587	+	0.633523i
$634$	13.1735	+	22.8173i	0.523188	+	0.906189i
$635$	−5.84902	+	3.37693i	−0.232111	+	0.134009i
$636$	−24.5843	−	37.9329i	−0.974832	−	1.50414i
$637$	−20.6264	+	6.93057i	−0.817247	+	0.274599i
$638$	13.8850			0.549712
$639$	2.06336	+	19.9852i	0.0816252	+	0.790603i
$640$	16.1902			0.639974
$641$	20.6692	−	35.8000i	0.816383	−	1.41402i	−0.0919475	−	0.995764i	$-0.529309\pi$
$641$	20.6692	−	35.8000i	0.816383	−	1.41402i	0.908331	−	0.418253i	$-0.137357\pi$
$642$	−8.94475	−	4.56795i	−0.353021	−	0.180283i
$643$	17.6848	−	10.2103i	0.697419	−	0.402655i	−0.108966	−	0.994045i	$-0.534754\pi$
$643$	17.6848	−	10.2103i	0.697419	−	0.402655i	0.806385	+	0.591390i	$0.201421\pi$
$644$	−16.3080	+	9.41542i	−0.642625	+	0.371020i
$645$	0.389493	+	7.56513i	0.0153363	+	0.297877i
$646$	47.6365	−	82.5088i	1.87423	−	3.24626i
$647$	15.7134			0.617756			0.308878	−	0.951102i	$-0.400047\pi$
$647$	15.7134			0.617756			0.308878	+	0.951102i	$0.400047\pi$
$648$	−9.73421	−	46.6391i	−0.382396	−	1.83216i
$649$	−9.15445			−0.359344
$650$	−11.9673	−	35.6164i	−0.469396	−	1.39699i
$651$	−17.1406	+	0.882491i	−0.671795	+	0.0345876i
$652$	37.0403	−	21.3852i	1.45061	−	0.837509i
$653$	16.1168	+	27.9151i	0.630700	+	1.09240i	0.987409	+	0.158188i	$0.0505653\pi$
$653$	16.1168	+	27.9151i	0.630700	+	1.09240i	−0.356709	+	0.934215i	$0.616101\pi$
$654$	−19.9299	+	39.0258i	−0.779320	+	1.52603i
$655$	14.5116	+	8.37826i	0.567014	+	0.327366i
$656$			13.3778i			0.522314i
$657$	2.87755	+	27.8712i	0.112264	+	1.08736i
$658$			10.7454i			0.418900i
$659$	2.33379	−	4.04224i	0.0909115	−	0.157463i	−0.816983	−	0.576661i	$-0.804355\pi$
$659$	2.33379	−	4.04224i	0.0909115	−	0.157463i	0.907895	+	0.419198i	$0.137689\pi$
$660$	10.0171	+	15.4560i	0.389914	+	0.601625i
$661$	−19.5539	+	11.2894i	−0.760557	+	0.439108i	−0.829496	−	0.558513i	$-0.811372\pi$
$661$	−19.5539	+	11.2894i	−0.760557	+	0.439108i	0.0689389	+	0.997621i	$0.478039\pi$
$662$	−39.2392	−	67.9642i	−1.52507	−	2.64151i
$663$	−4.92098	+	33.0055i	−0.191115	+	1.28183i
$664$	−14.6190	+	25.3209i	−0.567328	+	0.982641i
$665$		−	6.29753i		−	0.244208i
$666$	−14.6547	+	32.7526i	−0.567856	+	1.26914i
$667$	−9.00000			−0.348481
$668$	47.3215	+	27.3211i	1.83092	+	1.05708i
$669$	19.8099	+	10.1166i	0.765894	+	0.391130i
$670$	−6.95207	+	4.01378i	−0.268582	+	0.155066i
$671$	13.7970	−	7.96570i	0.532627	−	0.307512i
$672$	−2.38458	+	0.122771i	−0.0919870	+	0.00473598i
$673$	1.89964	−	3.29028i	0.0732259	−	0.126831i	−0.827088	−	0.562073i	$-0.810004\pi$
$673$	1.89964	−	3.29028i	0.0732259	−	0.126831i	0.900313	+	0.435242i	$0.143337\pi$
$674$			60.1893i			2.31841i
$675$	7.88954	−	20.3846i	0.303668	−	0.784604i
$676$	−6.68945	−	53.3625i	−0.257287	−	2.05240i
$677$	14.9160	−	25.8352i	0.573267	−	0.992927i	−0.422961	−	0.906148i	$-0.639009\pi$
$677$	14.9160	−	25.8352i	0.573267	−	0.992927i	0.996228	−	0.0867791i	$-0.0276574\pi$
$678$	0.267072	+	5.18734i	0.0102568	+	0.199219i
$679$	0.120993	+	0.209566i	0.00464327	+	0.00804239i
$680$	12.5983	+	21.8209i	0.483123	+	0.836794i
$681$	36.4312	+	18.6048i	1.39605	+	0.712939i
$682$	−62.4527	−	36.0571i	−2.39144	−	1.38070i
$683$			0.0316640i			0.00121159i	1.00000		0.000605795i	$0.000192831\pi$
$683$			0.0316640i			0.00121159i	−1.00000		0.000605795i	$0.999807\pi$
$684$	−72.3606	+	52.3699i	−2.76678	+	2.00241i
$685$	−16.0880			−0.614690
$686$	−15.8604	+	27.4711i	−0.605554	+	1.04885i
$687$	−18.0782	+	11.7165i	−0.689728	+	0.447013i
$688$	−11.8831	−	20.5822i	−0.453040	−	0.784689i
$689$	4.50649	−	22.2947i	0.171684	−	0.849362i
$690$	−9.63186	−	14.8617i	−0.366679	−	0.565774i
$691$	6.85148	+	3.95570i	0.260642	+	0.150482i	0.624628	−	0.780923i	$-0.285251\pi$
$691$	6.85148	+	3.95570i	0.260642	+	0.150482i	−0.363985	+	0.931405i	$0.618584\pi$
$692$	−47.2782			−1.79725
$693$	4.98605	+	6.88933i	0.189404	+	0.261704i
$694$			9.47431i			0.359640i
$695$	−3.74246	−	2.16071i	−0.141959	−	0.0819603i
$696$	−15.8604	−	8.09965i	−0.601186	−	0.307017i
$697$	12.7898	−	7.38421i	0.484449	−	0.279697i
$698$	−29.1486	−	50.4869i	−1.10329	−	1.91096i
$699$	32.4886	−	1.67269i	1.22883	−	0.0632668i
$700$	−14.8046	−	8.54746i	−0.559562	−	0.323064i
$701$	35.2396			1.33098			0.665491	−	0.746406i	$-0.268222\pi$
$701$	35.2396			1.33098			0.665491	+	0.746406i	$0.268222\pi$
$702$	24.9955	−	39.1061i	0.943394	−	1.47597i
$703$	34.7488			1.31058
$704$	15.5052	+	8.95195i	0.584375	+	0.337389i
$705$	−6.80335	+	0.350273i	−0.256229	+	0.0131920i
$706$	−29.2241	−	50.6175i	−1.09986	−	1.90502i
$707$	4.06157	−	2.34495i	0.152751	−	0.0881909i
$708$	20.2436	+	10.3381i	0.760801	+	0.388529i
$709$	19.4230	+	11.2139i	0.729447	+	0.421147i	0.818220	−	0.574905i	$-0.194961\pi$
$709$	19.4230	+	11.2139i	0.729447	+	0.421147i	−0.0887726	+	0.996052i	$0.528294\pi$
$710$			14.7779i			0.554605i
$711$	−5.81700	+	13.0008i	−0.218154	+	0.487566i
$712$	−93.0849			−3.48851
$713$	40.4807	+	23.3716i	1.51601	+	0.875272i
$714$	12.2494	+	18.9005i	0.458423	+	0.707333i
$715$	−1.83620	+	9.08415i	−0.0686701	+	0.339728i
$716$	0.311285	+	0.539162i	0.0116333	+	0.0201494i
$717$	28.7544	−	18.6358i	1.07385	−	0.695965i
$718$	0.273088	−	0.473003i	0.0101916	−	0.0176523i
$719$	−37.6708			−1.40488			−0.702442	−	0.711741i	$-0.747907\pi$
$719$	−37.6708			−1.40488			−0.702442	+	0.711741i	$0.747907\pi$
$720$	−1.32834	−	12.8660i	−0.0495044	−	0.479488i
$721$			3.37284i			0.125611i
$722$	70.3691	+	40.6276i	2.61887	+	1.51200i
$723$	17.5722	+	8.97385i	0.653517	+	0.333741i
$724$	−45.5515	−	78.8975i	−1.69291	−	2.93220i
$725$	−4.08516	−	7.07571i	−0.151719	−	0.262785i
$726$	−0.589574	−	11.4513i	−0.0218812	−	0.424998i
$727$	−22.0067	+	38.1168i	−0.816185	+	1.41367i	0.0922894	+	0.995732i	$0.470582\pi$
$727$	−22.0067	+	38.1168i	−0.816185	+	1.41367i	−0.908474	+	0.417941i	$0.862752\pi$
$728$	−14.0585	−	12.4062i	−0.521042	−	0.459803i
$729$	25.7242	−	8.20159i	0.952748	−	0.303763i
$730$			20.6092i			0.762779i
$731$	−13.1184	+	22.7218i	−0.485202	+	0.840395i
$732$	−39.5055	+	2.03395i	−1.46016	+	0.0751770i
$733$	15.2722	−	8.81743i	0.564093	−	0.325679i	−0.190694	−	0.981650i	$-0.561074\pi$
$733$	15.2722	−	8.81743i	0.564093	−	0.325679i	0.754787	+	0.655970i	$0.227740\pi$
$734$	−44.0102	+	25.4093i	−1.62445	+	0.937875i
$735$	−8.29209	−	4.23465i	−0.305858	−	0.156197i
$736$	5.63161	+	3.25141i	0.207584	+	0.119849i
$737$	−10.4984			−0.386713
$738$	−20.4315	+	2.10944i	−0.752094	+	0.0776494i
$739$			13.4319i			0.494100i	0.969003	+	0.247050i	$0.0794612\pi$
$739$			13.4319i			0.494100i	−0.969003	+	0.247050i	$0.920539\pi$
$740$	−8.89551	+	15.4075i	−0.327005	+	0.566390i
$741$	−44.4553	−	6.62809i	−1.63311	−	0.243489i
$742$	−7.67590	−	13.2951i	−0.281791	−	0.488077i
$743$	28.3946	−	16.3936i	1.04170	−	0.601423i	0.121383	−	0.992606i	$-0.461267\pi$
$743$	28.3946	−	16.3936i	1.04170	−	0.601423i	0.920313	+	0.391182i	$0.127934\pi$
$744$	50.3042	+	77.6179i	1.84424	+	2.84561i
$745$	5.46360	−	9.46323i	0.200171	−	0.346706i
$746$			26.8911i			0.984555i
$747$	−15.1243	−	6.76716i	−0.553370	−	0.247597i
$748$			63.7923i			2.33248i
$749$	−1.99133	−	1.14969i	−0.0727616	−	0.0420089i
$750$	16.0034	−	31.3372i	0.584362	−	1.14427i
$751$	−12.4916	−	21.6360i	−0.455824	−	0.789511i	0.542911	−	0.839790i	$-0.317322\pi$
$751$	−12.4916	−	21.6360i	−0.455824	−	0.789511i	−0.998735	+	0.0502796i	$0.983989\pi$
$752$	18.5097	−	10.6866i	0.674978	−	0.389699i
$753$	32.3379	−	1.66493i	1.17846	−	0.0606733i
$754$	−5.52554	−	16.4448i	−0.201228	−	0.598884i
$755$	4.95897			0.180475
$756$	−3.24574	−	20.8654i	−0.118047	−	0.758866i
$757$	21.6436			0.786652			0.393326	−	0.919399i	$-0.371324\pi$
$757$	21.6436			0.786652			0.393326	+	0.919399i	$0.371324\pi$
$758$	−24.3996	+	42.2614i	−0.886234	+	1.53500i
$759$	−1.19087	−	23.1303i	−0.0432258	−	0.839576i
$760$	−29.3907	+	16.9687i	−1.06611	+	0.615521i
$761$	−17.2650	+	9.96794i	−0.625855	+	0.361338i	−0.779145	−	0.626844i	$-0.784346\pi$
$761$	−17.2650	+	9.96794i	−0.625855	+	0.361338i	0.153290	+	0.988181i	$0.451013\pi$
$762$	28.9747	+	14.7969i	1.04964	+	0.536036i
$763$	−5.01610	+	8.68813i	−0.181595	+	0.314532i
$764$	82.5623			2.98700
$765$	−11.5673	+	8.37170i	−0.418218	+	0.302679i
$766$	50.3921			1.82074
$767$	3.64302	+	10.8421i	0.131542	+	0.391487i
$768$	−30.7277	−	47.4119i	−1.10879	−	1.71083i
$769$	−32.9151	+	19.0035i	−1.18695	+	0.685285i	−0.957612	−	0.288062i	$-0.906989\pi$
$769$	−32.9151	+	19.0035i	−1.18695	+	0.685285i	−0.229337	+	0.973347i	$0.573656\pi$
$770$	3.12760	+	5.41717i	0.112711	+	0.195221i
$771$	−8.25153	−	12.7319i	−0.297171	−	0.458527i
$772$	−36.0138	−	20.7926i	−1.29616	−	0.748341i
$773$		−	36.5619i		−	1.31504i	−0.753437	−	0.657520i	$-0.771605\pi$
$773$		−	36.5619i		−	1.31504i	0.753437	−	0.657520i	$-0.228395\pi$
$774$	29.5609	−	21.3942i	1.06254	−	0.769000i
$775$			42.4341i			1.52428i
$776$	0.652032	−	1.12935i	0.0234066	−	0.0405414i
$777$	−3.73614	+	7.31594i	−0.134033	+	0.262458i
$778$	45.9029	−	26.5021i	1.64570	−	0.950145i
$779$	9.94583	+	17.2267i	0.356346	+	0.617210i
$780$	14.3192	−	18.0145i	0.512709	−	0.645023i
$781$	−9.66320	+	16.7372i	−0.345777	+	0.598903i
$782$		−	61.3392i		−	2.19348i
$783$	3.64275	−	9.41197i	0.130181	−	0.336356i
$784$	29.2117			1.04328
$785$	−3.12456	−	1.80396i	−0.111520	−	0.0643862i
$786$	−4.15032	−	80.6117i	−0.148037	−	2.87532i
$787$	−1.39487	+	0.805329i	−0.0497218	+	0.0287069i	−0.524655	−	0.851315i	$-0.675806\pi$
$787$	−1.39487	+	0.805329i	−0.0497218	+	0.0287069i	0.474933	+	0.880022i	$0.342472\pi$
$788$	−14.1414	+	8.16455i	−0.503767	+	0.290850i
$789$	6.08779	−	11.9208i	0.216731	−	0.424393i
$790$	−5.23802	+	9.07251i	−0.186360	+	0.322785i
$791$			1.18916i			0.0422817i
$792$	18.7177	−	41.8334i	0.665105	−	1.48648i
$793$	−14.9247	−	13.1706i	−0.529993	−	0.467702i
$794$	−34.4336	+	59.6408i	−1.22200	+	2.11657i
$795$	8.16742	−	5.29331i	0.289668	−	0.187734i
$796$	23.7354	+	41.1109i	0.841280	+	1.45714i
$797$	−0.0491630	−	0.0851528i	−0.00174144	−	0.00301627i	0.865153	−	0.501507i	$-0.167221\pi$
$797$	−0.0491630	−	0.0851528i	−0.00174144	−	0.00301627i	−0.866895	+	0.498491i	$0.833888\pi$
$798$	−25.4572	+	16.4988i	−0.901173	+	0.584051i
$799$	−20.4338	−	11.7975i	−0.722896	−	0.417364i
$800$			5.90335i			0.208715i
$801$	−5.41748	−	52.4724i	−0.191417	−	1.85402i
$802$	37.6201			1.32841
$803$	−13.4762	+	23.3415i	−0.475566	+	0.823705i
$804$	23.2155	+	11.8558i	0.818746	+	0.418121i
$805$	−2.02725	−	3.51131i	−0.0714513	−	0.123757i
$806$	−17.8514	+	88.3152i	−0.628788	+	3.11077i
$807$	−25.6779	+	1.32203i	−0.903904	+	0.0465378i
$808$	−21.8879	−	12.6370i	−0.770013	−	0.444567i
$809$	33.5971			1.18121			0.590605	−	0.806961i	$-0.298889\pi$
$809$	33.5971			1.18121			0.590605	+	0.806961i	$0.298889\pi$
$810$	19.4405	−	4.05748i	0.683068	−	0.142565i
$811$			13.9011i			0.488134i	0.969758	+	0.244067i	$0.0784817\pi$
$811$			13.9011i			0.488134i	−0.969758	+	0.244067i	$0.921518\pi$
$812$	−6.83558	−	3.94652i	−0.239882	−	0.138496i
$813$	1.72313	+	33.4684i	0.0604328	+	1.17379i
$814$	−29.8911	+	17.2577i	−1.04768	+	0.604881i
$815$	4.60449	+	7.97521i	0.161288	+	0.279360i
$816$	20.3749	−	39.8973i	0.713266	−	1.39669i
$817$	−30.6041	−	17.6693i	−1.07070	−	0.618170i
$818$	5.91002			0.206639
$819$	6.17522	−	8.64687i	0.215780	−	0.302146i
$820$	−10.1843			−0.355651
$821$	−36.3185	−	20.9685i	−1.26753	−	0.731806i	−0.293007	−	0.956110i	$-0.594656\pi$
$821$	−36.3185	−	20.9685i	−1.26753	−	0.731806i	−0.974519	+	0.224304i	$0.927989\pi$
$822$	42.1487	+	65.0342i	1.47010	+	2.26833i
$823$	−22.4560	−	38.8949i	−0.782766	−	1.35579i	−0.930324	−	0.366737i	$-0.880475\pi$
$823$	−22.4560	−	38.8949i	−0.782766	−	1.35579i	0.147558	−	0.989053i	$-0.452859\pi$
$824$	15.7411	−	9.08815i	0.548368	−	0.316601i
$825$	17.6443	−	11.4352i	0.614294	−	0.398124i
$826$	6.68552	+	3.85988i	0.232619	+	0.134303i
$827$		−	17.5703i		−	0.610980i	−0.952195	−	0.305490i	$-0.901180\pi$
$827$		−	17.5703i		−	0.610980i	0.952195	−	0.305490i	$-0.0988202\pi$
$828$	−23.4875	+	52.4937i	−0.816248	+	1.82428i
$829$	0.797445			0.0276964			0.0138482	−	0.999904i	$-0.495592\pi$
$829$	0.797445			0.0276964			0.0138482	+	0.999904i	$0.495592\pi$
$830$	−10.5544	−	6.09360i	−0.366350	−	0.211512i
$831$	0.926024	−	1.81330i	0.0321234	−	0.0629026i
$832$	4.43199	−	21.9261i	0.153652	−	0.760152i
$833$	−16.1242	−	27.9279i	−0.558670	−	0.967644i
$834$	1.07034	+	20.7893i	0.0370630	+	0.719875i
$835$	−5.88255	+	10.1889i	−0.203574	+	0.352601i
$836$	−85.9222			−2.97168
$837$	−40.8259	+	32.8740i	−1.41115	+	1.13629i
$838$			82.4710i			2.84891i
$839$	−14.4922	−	8.36709i	−0.500327	−	0.288864i	0.228522	−	0.973539i	$-0.426611\pi$
$839$	−14.4922	−	8.36709i	−0.500327	−	0.288864i	−0.728849	+	0.684675i	$0.759944\pi$
$840$	−0.412516	−	8.01230i	−0.0142332	−	0.276451i
$841$	12.6138	+	21.8477i	0.434959	+	0.753371i
$842$	−30.1051	−	52.1436i	−1.03749	−	1.79699i
$843$	−7.06635	−	3.60868i	−0.243378	−	0.124289i
$844$	22.6831	−	39.2882i	0.780783	−	1.35236i
$845$	11.4896	−	1.44032i	0.395254	−	0.0495485i
$846$	19.2399	+	26.5842i	0.661483	+	0.913985i
$847$		−	2.62513i		−	0.0902006i
$848$	−15.2677	+	26.4444i	−0.524295	+	0.908106i
$849$	0.0299862	+	0.0462679i	0.00102912	+	0.00158791i
$850$	48.2243	−	27.8423i	1.65408	−	0.954983i
$851$	19.3749	−	11.1861i	0.664163	−	0.383455i
$852$	40.2698	−	26.0989i	1.37962	−	0.894133i
$853$	−19.7398	−	11.3968i	−0.675876	−	0.390217i	0.122423	−	0.992478i	$-0.460933\pi$
$853$	−19.7398	−	11.3968i	−0.675876	−	0.390217i	−0.798300	+	0.602261i	$0.794267\pi$
$854$	−13.4346			−0.459724
$855$	−11.2759	−	15.5801i	−0.385627	−	0.532829i
$856$			12.3914i			0.423531i
$857$	−21.7623	+	37.6934i	−0.743386	+	1.28758i	0.207559	+	0.978223i	$0.433448\pi$
$857$	−21.7623	+	37.6934i	−0.743386	+	1.28758i	−0.950945	+	0.309360i	$0.899885\pi$
$858$	41.5325	−	16.3767i	1.41789	−	0.559093i
$859$	8.51911	+	14.7555i	0.290668	+	0.503452i	0.973968	−	0.226686i	$-0.0727890\pi$
$859$	8.51911	+	14.7555i	0.290668	+	0.503452i	−0.683300	+	0.730138i	$0.739456\pi$
$860$	15.6689	−	9.04647i	0.534307	−	0.308482i
$861$	−4.69623	+	0.241787i	−0.160047	+	0.00824007i
$862$	−15.0384	+	26.0472i	−0.512209	+	0.887172i
$863$			47.3664i			1.61237i	0.591663	+	0.806186i	$0.298472\pi$
$863$			47.3664i			1.61237i	−0.591663	+	0.806186i	$0.701528\pi$
$864$	−5.67963	+	4.57338i	−0.193225	+	0.155589i
$865$		−	10.1796i		−	0.346116i
$866$	28.4758	+	16.4405i	0.967646	+	0.558671i
$867$	−19.9845	+	1.02891i	−0.678708	+	0.0349435i
$868$	20.4970	+	35.5018i	0.695713	+	1.20501i
$869$	−11.8649	+	6.85023i	−0.402491	+	0.232378i
$870$	3.37615	−	6.61103i	0.114462	−	0.224135i
$871$	4.17783	+	12.4338i	0.141560	+	0.421304i
$872$	54.0637			1.83083
$873$	0.674569	+	0.301826i	0.0228307	+	0.0102153i
$874$	82.6180			2.79460
$875$	4.02785	−	6.97645i	0.136166	−	0.235847i
$876$	56.1600	−	36.3973i	1.89747	−	1.22975i
$877$	40.4664	−	23.3633i	1.36645	−	0.788922i	0.375980	−	0.926628i	$-0.377306\pi$
$877$	40.4664	−	23.3633i	1.36645	−	0.788922i	0.990473	+	0.137706i	$0.0439728\pi$
$878$	−28.1078	+	16.2281i	−0.948593	+	0.547670i
$879$	−15.8549	+	10.2755i	−0.534771	+	0.346586i
$880$	6.22094	−	10.7750i	0.209708	−	0.363225i
$881$	−15.7253			−0.529797			−0.264899	−	0.964276i	$-0.585338\pi$
$881$	−15.7253			−0.529797			−0.264899	+	0.964276i	$0.585338\pi$
$882$	4.60617	+	44.6143i	0.155098	+	1.50224i
$883$	−24.3745			−0.820269			−0.410134	−	0.912025i	$-0.634518\pi$
$883$	−24.3745			−0.820269			−0.410134	+	0.912025i	$0.634518\pi$
$884$	75.5528	−	25.3862i	2.54112	−	0.853829i
$885$	−2.22592	+	4.35869i	−0.0748234	+	0.146516i
$886$	−73.8851	+	42.6576i	−2.48222	+	1.43311i
$887$	1.96001	+	3.39484i	0.0658107	+	0.113987i	0.897053	−	0.441922i	$-0.145703\pi$
$887$	1.96001	+	3.39484i	0.0658107	+	0.113987i	−0.831243	+	0.555910i	$0.812370\pi$
$888$	44.2107	−	2.27620i	1.48362	−	0.0763844i
$889$	6.45050	+	3.72420i	0.216343	+	0.124906i
$890$		−	38.8003i		−	1.30059i
$891$	24.6710	+	8.11660i	0.826511	+	0.271916i
$892$		−	53.1279i		−	1.77885i
$893$	15.8901	−	27.5224i	0.531741	−	0.921002i
$894$	−52.5682	+	2.70649i	−1.75814	+	0.0905186i
$895$	−0.116088	+	0.0670235i	−0.00388040	+	0.00224035i
$896$	−8.92756	−	15.4630i	−0.298249	−	0.516582i
$897$	−26.9206	+	10.6151i	−0.898852	+	0.354428i
$898$	−6.59435	+	11.4217i	−0.220056	+	0.381149i
$899$			19.5926i			0.653450i
$900$	−51.9312	+	5.36160i	−1.73104	+	0.178720i
$901$	33.7097			1.12303
$902$	−17.1109	−	9.87899i	−0.569731	−	0.328934i
$903$	7.01055	−	4.54354i	0.233296	−	0.151200i
$904$	5.54985	−	3.20420i	0.184585	−	0.106570i
$905$	16.9876	−	9.80779i	0.564687	−	0.326022i
$906$	−12.9919	−	20.0462i	−0.431628	−	0.665989i
$907$	−21.7796	+	37.7234i	−0.723181	+	1.25259i	0.236537	+	0.971622i	$0.423987\pi$
$907$	−21.7796	+	37.7234i	−0.723181	+	1.25259i	−0.959718	+	0.280964i	$0.909346\pi$
$908$		−	97.7044i		−	3.24243i
$909$	5.84966	−	13.0738i	0.194021	−	0.433629i
$910$	5.17123	−	5.85996i	0.171424	−	0.194256i
$911$	14.0645	−	24.3604i	0.465976	−	0.807095i	−0.533269	−	0.845946i	$-0.679037\pi$
$911$	14.0645	−	24.3604i	0.465976	−	0.807095i	0.999245	+	0.0388513i	$0.0123699\pi$
$912$	53.7379	+	27.4431i	1.77944	+	0.908733i
$913$	−7.96916	−	13.8030i	−0.263741	−	0.456812i
$914$	−15.3463	−	26.5806i	−0.507611	−	0.879208i
$915$	−0.437934	−	8.50601i	−0.0144777	−	0.281200i
$916$	44.5609	+	25.7273i	1.47234	+	0.850053i
$917$		−	18.4797i		−	0.610252i
$918$	64.1469	+	24.8270i	2.11716	+	0.819414i
$919$	−17.9402			−0.591793			−0.295897	−	0.955220i	$-0.595618\pi$
$919$	−17.9402			−0.591793			−0.295897	+	0.955220i	$0.595618\pi$
$920$	−10.9249	+	18.9225i	−0.360184	+	0.623856i
$921$	−0.614818	−	11.9416i	−0.0202589	−	0.393490i
$922$	−16.1095	−	27.9024i	−0.530538	−	0.918918i
$923$	23.6682	+	4.78412i	0.779050	+	0.157471i
$924$	9.23821	−	18.0899i	0.303915	−	0.595112i
$925$	17.5888	+	10.1549i	0.578316	+	0.333891i
$926$	−15.9153			−0.523008
$927$	6.03916	+	8.34443i	0.198352	+	0.274067i
$928$			2.72569i			0.0894752i
$929$	−37.2632	−	21.5139i	−1.22257	−	0.705849i	−0.257101	−	0.966384i	$-0.582767\pi$
$929$	−37.2632	−	21.5139i	−1.22257	−	0.705849i	−0.965464	+	0.260536i	$0.916101\pi$
$930$	−32.3533	+	20.9682i	−1.06090	+	0.687573i
$931$	37.6162	−	21.7177i	1.23282	−	0.711770i
$932$	−38.8503	−	67.2906i	−1.27258	−	2.20418i
$933$	−14.5032	−	22.3780i	−0.474813	−	0.732623i
$934$	−29.9492	−	17.2912i	−0.979967	−	0.565784i
$935$	−13.7353			−0.449191
$936$	−56.9944	−	5.52086i	−1.86292	−	0.180455i
$937$	20.5616			0.671719			0.335860	−	0.941912i	$-0.390973\pi$
$937$	20.5616			0.671719			0.335860	+	0.941912i	$0.390973\pi$
$938$	7.66699	+	4.42654i	0.250336	+	0.144532i
$939$	−13.6609	+	26.7501i	−0.445805	+	0.872956i
$940$	8.13553	+	14.0912i	0.265352	+	0.459603i
$941$	−31.2579	+	18.0468i	−1.01898	+	0.588308i	−0.913808	−	0.406147i	$-0.866872\pi$
$941$	−31.2579	+	18.0468i	−1.01898	+	0.588308i	−0.105171	+	0.994454i	$0.533539\pi$
$942$	0.893625	+	17.3569i	0.0291159	+	0.565518i
$943$	11.0910	+	6.40338i	0.361172	+	0.208523i
$944$		−	15.3550i		−	0.499761i
$945$	4.49257	−	0.698848i	0.146143	−	0.0227335i
$946$	35.1011			1.14123
$947$	5.32031	+	3.07168i	0.172887	+	0.0998163i	0.583946	−	0.811792i	$-0.301508\pi$
$947$	5.32031	+	3.07168i	0.172887	+	0.0998163i	−0.411059	+	0.911609i	$0.634841\pi$
$948$	33.9733	−	1.74913i	1.10340	−	0.0568090i
$949$	33.0076	+	6.67191i	1.07147	+	0.216579i
$950$	37.5009	+	64.9535i	1.21669	+	2.10737i
$951$	16.4057	+	8.37814i	0.531991	+	0.271680i
$952$	13.8939	−	24.0649i	0.450302	−	0.779947i
$953$	19.7667			0.640305			0.320152	−	0.947366i	$-0.396266\pi$
$953$	19.7667			0.640305			0.320152	+	0.947366i	$0.396266\pi$
$954$	−42.7954	−	19.1482i	−1.38555	−	0.619944i
$955$			17.7767i			0.575240i
$956$	−70.8766	−	40.9206i	−2.29231	−	1.32347i
$957$	8.14669	−	5.27987i	0.263345	−	0.170674i
$958$	42.8882	+	74.2846i	1.38566	+	2.40003i
$959$	8.87119	+	15.3654i	0.286466	+	0.496173i
$960$	8.03239	−	5.20579i	0.259244	−	0.168016i
$961$	35.3789	−	61.2780i	1.14125	−	1.97671i
$962$	32.3344	+	28.5341i	1.04250	+	0.919976i
$963$	−6.98512	+	0.721173i	−0.225092	+	0.0232395i
$964$		−	47.1267i		−	1.51785i
$965$	4.47689	−	7.75420i	0.144116	−	0.249617i
$966$	−8.88296	+	17.3942i	−0.285805	+	0.559650i
$967$	−26.4324	+	15.2608i	−0.850009	+	0.490753i	−0.860654	−	0.509190i	$-0.829945\pi$
$967$	−26.4324	+	15.2608i	−0.850009	+	0.490753i	0.0106449	+	0.999943i	$0.496612\pi$
$968$	−12.2516	+	7.07344i	−0.393780	+	0.227349i
$969$	−3.42502	−	66.5242i	−0.110027	−	2.13706i
$970$	0.470745	+	0.271784i	0.0151147	+	0.00872647i
$971$	−4.05102			−0.130004			−0.0650018	−	0.997885i	$-0.520705\pi$
$971$	−4.05102			−0.130004			−0.0650018	+	0.997885i	$0.520705\pi$
$972$	−45.3900	−	45.8095i	−1.45588	−	1.46934i
$973$			4.76581i			0.152785i
$974$	−7.16940	+	12.4178i	−0.229722	+	0.397891i
$975$	−20.5649	−	16.3464i	−0.658605	−	0.523505i
$976$	13.3610	+	23.1420i	0.427677	+	0.740758i
$977$	−25.1440	+	14.5169i	−0.804426	+	0.464436i	−0.845017	−	0.534740i	$-0.820410\pi$
$977$	−25.1440	+	14.5169i	−0.804426	+	0.464436i	0.0405902	+	0.999176i	$0.487076\pi$
$978$	20.1758	−	39.5074i	0.645151	−	1.26331i
$979$	25.3714	−	43.9445i	0.810872	−	1.40447i
$980$			22.2385i			0.710382i
$981$	3.14647	+	30.4760i	0.100459	+	0.973022i
$982$		−	61.7447i		−	1.97035i
$983$	−5.23002	−	3.01955i	−0.166812	−	0.0963088i	0.414270	−	0.910154i	$-0.364037\pi$
$983$	−5.23002	−	3.01955i	−0.166812	−	0.0963088i	−0.581082	+	0.813845i	$0.697370\pi$
$984$	13.7824	+	21.2659i	0.439368	+	0.677932i
$985$	−1.75793	−	3.04482i	−0.0560122	−	0.0970160i
$986$	22.2661	−	12.8553i	0.709096	−	0.409397i
$987$	4.08603	+	6.30462i	0.130060	+	0.200678i
$988$	34.1927	+	101.762i	1.08782	+	3.23750i
$989$	−22.7519			−0.723467
$990$	17.4373	+	7.80205i	0.554193	+	0.247966i
$991$	−49.4199			−1.56987			−0.784937	−	0.619575i	$-0.787305\pi$
$991$	−49.4199			−1.56987			−0.784937	+	0.619575i	$0.787305\pi$
$992$	7.07818	−	12.2598i	0.224732	−	0.389248i
$993$	−48.8666	−	24.9554i	−1.55073	−	0.791936i
$994$	14.1141	−	8.14879i	0.447673	−	0.258464i
$995$	−8.85169	+	5.11052i	−0.280617	+	0.162014i
$996$	2.03483	+	39.5226i	0.0644762	+	1.25232i
$997$	10.6174	−	18.3899i	0.336257	−	0.582414i	−0.647469	−	0.762092i	$-0.724172\pi$
$997$	10.6174	−	18.3899i	0.336257	−	0.582414i	0.983725	+	0.179678i	$0.0575056\pi$
$998$	98.6419			3.12246
$999$	3.85614	+	24.7893i	0.122003	+	0.784300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.t.c.25.1	✓	20
3.2	odd	2		351.2.t.c.181.10		20
9.2	odd	6		1053.2.b.i.649.1		10
9.4	even	3	inner	117.2.t.c.103.10	yes	20
9.5	odd	6		351.2.t.c.64.1		20
9.7	even	3		1053.2.b.j.649.10		10
13.12	even	2	inner	117.2.t.c.25.10	yes	20
39.38	odd	2		351.2.t.c.181.1		20
117.25	even	6		1053.2.b.j.649.1		10
117.38	odd	6		1053.2.b.i.649.10		10
117.77	odd	6		351.2.t.c.64.10		20
117.103	even	6	inner	117.2.t.c.103.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.1	✓	20	1.1	even	1	trivial
117.2.t.c.25.10	yes	20	13.12	even	2	inner
117.2.t.c.103.1	yes	20	117.103	even	6	inner
117.2.t.c.103.10	yes	20	9.4	even	3	inner
351.2.t.c.64.1		20	9.5	odd	6
351.2.t.c.64.10		20	117.77	odd	6
351.2.t.c.181.1		20	39.38	odd	2
351.2.t.c.181.10		20	3.2	odd	2
1053.2.b.i.649.1		10	9.2	odd	6
1053.2.b.i.649.10		10	117.38	odd	6
1053.2.b.j.649.1		10	117.25	even	6
1053.2.b.j.649.10		10	9.7	even	3

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.14539 - 1.23864i) q^{2} +(-1.72976 + 0.0890572i) q^{3} +(2.06847 + 3.58269i) q^{4} +(-0.771397 + 0.445366i) q^{5} +(3.82132 + 1.95149i) q^{6} +(0.850723 + 0.491165i) q^{7} -5.29379i q^{8} +(2.98414 - 0.308095i) q^{9} +2.20660 q^{10} +(2.49915 + 1.44288i) q^{11} +(-3.89702 - 6.01298i) q^{12} +(0.714352 - 3.53408i) q^{13} +(-1.21676 - 2.10748i) q^{14} +(1.29467 - 0.839075i) q^{15} +(-2.42018 + 4.19187i) q^{16} +5.34353 q^{17} +(-6.78376 - 3.03529i) q^{18} +7.19723i q^{19} +(-3.19122 - 1.84245i) q^{20} +(-1.51529 - 0.773835i) q^{21} +(-3.57443 - 6.19110i) q^{22} +(2.31688 + 4.01296i) q^{23} +(0.471451 + 9.15699i) q^{24} +(-2.10330 + 3.64302i) q^{25} +(-5.91002 + 6.69715i) q^{26} +(-5.13440 + 0.798690i) q^{27} +4.06384i q^{28} +(-0.971133 + 1.68205i) q^{29} +(-3.81688 + 0.196513i) q^{30} +(8.73604 - 5.04375i) q^{31} +(1.21534 - 0.701678i) q^{32} +(-4.45142 - 2.27327i) q^{33} +(-11.4640 - 6.61872i) q^{34} -0.874993 q^{35} +(7.27640 + 10.0540i) q^{36} -4.82809i q^{37} +(8.91479 - 15.4409i) q^{38} +(-0.920923 + 6.17672i) q^{39} +(2.35768 + 4.08361i) q^{40} +(2.39352 - 1.38190i) q^{41} +(2.29238 + 3.53708i) q^{42} +(-2.45501 + 4.25220i) q^{43} +11.9382i q^{44} +(-2.16474 + 1.56670i) q^{45} -11.4791i q^{46} +(-3.82403 - 2.20780i) q^{47} +(3.81301 - 7.46647i) q^{48} +(-3.01751 - 5.22649i) q^{49} +(9.02479 - 5.21047i) q^{50} +(-9.24302 + 0.475880i) q^{51} +(14.1391 - 4.75082i) q^{52} +6.30850 q^{53} +(12.0046 + 4.64619i) q^{54} -2.57044 q^{55} +(2.60013 - 4.50355i) q^{56} +(-0.640965 - 12.4495i) q^{57} +(4.16692 - 2.40577i) q^{58} +(-2.74727 + 1.58614i) q^{59} +(5.68412 + 2.90280i) q^{60} +(2.76034 - 4.78105i) q^{61} -24.9896 q^{62} +(2.69000 + 1.20360i) q^{63} +6.20421 q^{64} +(1.02291 + 3.04432i) q^{65} +(6.73427 + 10.3908i) q^{66} +(-3.15059 + 1.81899i) q^{67} +(11.0529 + 19.1442i) q^{68} +(-4.36503 - 6.73512i) q^{69} +(1.87720 + 1.08380i) q^{70} +6.69715i q^{71} +(-1.63099 - 15.7974i) q^{72} +9.33980i q^{73} +(-5.98027 + 10.3581i) q^{74} +(3.31376 - 6.48886i) q^{75} +(-25.7854 + 14.8872i) q^{76} +(1.41739 + 2.45499i) q^{77} +(9.62649 - 12.1108i) q^{78} +(-2.37380 + 4.11154i) q^{79} -4.31146i q^{80} +(8.81015 - 1.83880i) q^{81} -6.84670 q^{82} +(-4.78313 - 2.76154i) q^{83} +(-0.361914 - 7.02946i) q^{84} +(-4.12198 + 2.37983i) q^{85} +(10.5339 - 6.08176i) q^{86} +(1.53003 - 2.99603i) q^{87} +(7.63833 - 13.2300i) q^{88} -17.5838i q^{89} +(6.58479 - 0.679842i) q^{90} +(2.34353 - 2.65566i) q^{91} +(-9.58479 + 16.6013i) q^{92} +(-14.6621 + 9.50249i) q^{93} +(5.46935 + 9.47320i) q^{94} +(-3.20540 - 5.55192i) q^{95} +(-2.03976 + 1.32197i) q^{96} +(0.213335 + 0.123169i) q^{97} +14.9505i q^{98} +(7.90234 + 3.53579i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 12 q^{4} - 2 q^{9} - 16 q^{10} - 2 q^{12} - 4 q^{13} - 18 q^{14} + 4 q^{16} - 12 q^{17} - 10 q^{22} + 24 q^{23} - 12 q^{25} - 12 q^{26} - 22 q^{27} + 12 q^{29} - 54 q^{30} - 12 q^{35} + 50 q^{36}+ \cdots + 24 q^{95}+O(q^{100}) \) 20 * q + 2 * q^3 + 12 * q^4 - 2 * q^9 - 16 * q^10 - 2 * q^12 - 4 * q^13 - 18 * q^14 + 4 * q^16 - 12 * q^17 - 10 * q^22 + 24 * q^23 - 12 * q^25 - 12 * q^26 - 22 * q^27 + 12 * q^29 - 54 * q^30 - 12 * q^35 + 50 * q^36 + 12 * q^38 - 8 * q^39 - 8 * q^40 + 6 * q^42 + 4 * q^43 + 38 * q^48 - 10 * q^49 - 78 * q^51 + 108 * q^53 + 20 * q^55 + 36 * q^56 - 2 * q^61 - 72 * q^62 + 8 * q^64 - 24 * q^65 + 78 * q^66 + 24 * q^68 + 72 * q^69 - 42 * q^74 - 8 * q^75 - 6 * q^77 + 66 * q^78 - 14 * q^79 + 46 * q^81 - 4 * q^82 - 54 * q^87 + 22 * q^88 + 24 * q^90 - 72 * q^91 - 84 * q^92 + 20 * q^94 + 24 * q^95

Introduction

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