LMFDB - Embedded newform 117.2.t.c.103.10

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			103.10
Root			$-1.66095 + 0.491165i$ of defining polynomial
Character	$\chi$	$=$	117.103
Dual form			117.2.t.c.25.10

$q$-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} +(-3.41778 + 1.14839i) 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} +(6.01421 - 1.68206i) 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} +(-2.95523 + 14.6202i) 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} +(-3.14792 - 0.636297i) 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} +(10.8193 - 11.0581i) 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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

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

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	0.517220	−	0.855852i	$-0.326967\pi$
$2$	2.14539	−	1.23864i	1.51702	−	0.875852i	0.999800	−	0.0199997i	$-0.00636654\pi$
$3$	−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	$-0.269508\pi$
$5$	0.771397	+	0.445366i	0.344979	+	0.199174i	−0.317493	+	0.948261i	$0.602841\pi$
$6$	−3.82132	+	1.95149i	−1.56005	+	0.796693i
$7$	−0.850723	+	0.491165i	−0.321543	+	0.185643i	−0.652080	−	0.758150i	$-0.726103\pi$
$7$	−0.850723	+	0.491165i	−0.321543	+	0.185643i	0.330537	+	0.943793i	$0.392770\pi$
$8$		−	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	$-0.809934\pi$
$11$	−2.49915	+	1.44288i	−0.753521	+	0.435046i	0.0734436	+	0.997299i	$0.476601\pi$
$12$	−3.89702	+	6.01298i	−1.12497	+	1.73580i
$13$	−3.41778	+	1.14839i	−0.947921	+	0.318506i
$13$	−3.41778	+	1.14839i	−0.947921	+	0.318506i
$14$	−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	−0.516709	−	0.856161i	$-0.672843\pi$
$23$	2.31688	−	4.01296i	0.483103	−	0.836759i	0.999812	+	0.0194021i	$0.00617627\pi$
$24$	−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	0.761660	−	0.647977i	$-0.224385\pi$
$29$	−0.971133	−	1.68205i	−0.180335	−	0.312349i	−0.941995	+	0.335628i	$0.891051\pi$
$30$	−3.81688	−	0.196513i	−0.696864	−	0.0358783i
$31$	−8.73604	−	5.04375i	−1.56904	−	0.905885i	−0.996281	−	0.0861597i	$-0.972540\pi$
$31$	−8.73604	−	5.04375i	−1.56904	−	0.905885i	−0.572757	−	0.819725i	$-0.694126\pi$
$32$	−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
$39$	6.01421	−	1.68206i	0.963044	−	0.269346i
$40$	2.35768	−	4.08361i	0.372781	−	0.645676i
$41$	−2.39352	−	1.38190i	−0.373804	−	0.215816i	0.301315	−	0.953525i	$-0.402574\pi$
$41$	−2.39352	−	1.38190i	−0.373804	−	0.215816i	−0.675119	+	0.737709i	$0.735908\pi$
$42$	2.29238	−	3.53708i	0.353722	−	0.545783i
$43$	−2.45501	−	4.25220i	−0.374386	−	0.648455i	0.615849	−	0.787864i	$-0.288813\pi$
$43$	−2.45501	−	4.25220i	−0.374386	−	0.648455i	−0.990235	+	0.139409i	$0.955480\pi$
$44$			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	$-0.562298\pi$
$47$	3.82403	−	2.20780i	0.557791	−	0.322041i	0.752259	+	0.658868i	$0.228964\pi$
$48$	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
$52$	−2.95523	+	14.6202i	−0.409817	+	2.02746i
$53$	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	$-0.267127\pi$
$59$	2.74727	+	1.58614i	0.357664	+	0.206498i	−0.310391	+	0.950609i	$0.600460\pi$
$60$	−5.68412	+	2.90280i	−0.733817	+	0.374749i
$61$	2.76034	+	4.78105i	0.353426	+	0.612151i	0.986847	−	0.161656i	$-0.0516834\pi$
$61$	2.76034	+	4.78105i	0.353426	+	0.612151i	−0.633422	+	0.773807i	$0.718350\pi$
$62$	−24.9896			−3.17368
$63$	−2.69000	+	1.20360i	−0.338908	+	0.151639i
$64$	6.20421			0.775526
$65$	−3.14792	−	0.636297i	−0.390451	−	0.0789229i
$66$	6.73427	−	10.3908i	0.828931	−	1.27902i
$67$	3.15059	+	1.81899i	0.384906	+	0.222225i	0.679950	−	0.733258i	$-0.262001\pi$
$67$	3.15059	+	1.81899i	0.384906	+	0.222225i	−0.295045	+	0.955483i	$0.595335\pi$
$68$	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
$78$	10.8193	−	11.0581i	1.22505	−	1.25209i
$79$	−2.37380	−	4.11154i	−0.267073	−	0.462584i	0.701031	−	0.713130i	$-0.252723\pi$
$79$	−2.37380	−	4.11154i	−0.267073	−	0.462584i	−0.968105	+	0.250546i	$0.919390\pi$
$80$		−	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	$-0.568639\pi$
$83$	4.78313	−	2.76154i	0.525016	−	0.303118i	0.738985	+	0.673722i	$0.235306\pi$
$84$	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	$-0.670648\pi$
$97$	−0.213335	+	0.123169i	−0.0216609	+	0.0125059i	0.489130	+	0.872211i	$0.337314\pi$
$98$			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	0.960004	−	0.279985i	$-0.0903294\pi$
$101$	2.38713	+	4.13463i	0.237528	+	0.411411i	−0.722476	+	0.691396i	$0.756996\pi$
$102$	−20.4193	+	10.4278i	−2.02182	+	1.03251i
$103$	1.71676	−	2.97351i	0.169157	−	0.292988i	−0.768967	−	0.639289i	$-0.779229\pi$
$103$	1.71676	−	2.97351i	0.169157	−	0.292988i	0.938124	+	0.346300i	$0.112562\pi$
$104$	6.07935	+	18.0930i	0.596129	+	1.77416i
$105$	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	−0.836151	−	0.548500i	$-0.815199\pi$
$113$	0.605276	−	1.04837i	0.0569396	−	0.0986222i	0.893090	+	0.449878i	$0.148532\pi$
$114$	−14.0453	−	27.5029i	−1.31547	−	2.57588i
$115$	3.57447	−	2.06372i	0.333321	−	0.192443i
$116$	−8.03503			−0.746034
$117$	−10.5529	+	2.37396i	−0.975619	+	0.219472i
$118$	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
$130$	−7.54165	+	2.53404i	−0.661447	+	0.222250i
$131$	−9.40603	+	16.2917i	−0.821809	+	1.42342i	0.0825247	+	0.996589i	$0.473702\pi$
$131$	−9.40603	+	16.2917i	−0.821809	+	1.42342i	−0.904334	+	0.426826i	$0.859632\pi$
$132$	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	$-0.947185\pi$
$137$	−15.6417	+	9.03076i	−1.33636	+	0.771550i	−0.350098	+	0.936713i	$0.613852\pi$
$138$	−1.02230	+	19.8562i	−0.0870240	+	1.69027i
$139$	2.42577	−	4.20155i	0.205751	−	0.356371i	−0.744621	−	0.667488i	$-0.767370\pi$
$139$	2.42577	−	4.20155i	0.205751	−	0.356371i	0.950372	+	0.311117i	$0.100703\pi$
$140$	−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	$-0.165746\pi$
$149$	10.6241	+	6.13383i	0.870360	+	0.502503i	0.00289232	+	0.999996i	$0.499079\pi$
$150$	15.1467	+	9.81658i	1.23672	+	0.801520i
$151$	4.82142	−	2.78365i	0.392362	−	0.226530i	−0.290821	−	0.956777i	$-0.593928\pi$
$151$	4.82142	−	2.78365i	0.392362	−	0.226530i	0.683183	+	0.730247i	$0.260595\pi$
$152$	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
$156$	6.41387	−	25.0263i	0.513521	−	2.00371i
$157$	2.02526	−	3.50785i	0.161633	−	0.279957i	−0.773821	−	0.633404i	$-0.781657\pi$
$157$	2.02526	−	3.50785i	0.161633	−	0.279957i	0.935455	+	0.353447i	$0.114991\pi$
$158$	−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	$-0.504075\pi$
$167$	−11.4388	−	6.60418i	−0.885159	−	0.511047i	−0.872356	+	0.488871i	$0.837409\pi$
$168$	−4.09652	−	8.02162i	−0.316053	−	0.618881i
$169$	10.3624	−	7.84989i	0.797107	−	0.603838i
$170$	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	0.562810	−	0.826586i	$-0.309720\pi$
$173$	−5.71416	−	9.89721i	−0.434439	−	0.752471i	−0.997250	+	0.0741150i	$0.976387\pi$
$174$	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	$0.805159\pi$
$182$	1.73838	−	8.60021i	0.128858	−	0.637490i
$183$	−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	0.960184	+	0.279369i	$0.0901251\pi$
$191$	9.97868	+	17.2836i	0.722032	+	1.25060i	−0.238152	+	0.971228i	$0.576542\pi$
$192$	−10.7318	−	0.552529i	−0.774500	−	0.0398754i
$193$	8.70542	+	5.02608i	0.626630	+	0.361785i	0.779446	−	0.626470i	$-0.215501\pi$
$193$	8.70542	+	5.02608i	0.626630	+	0.361785i	−0.152816	+	0.988255i	$0.548834\pi$
$194$	−0.305125	+	0.528492i	−0.0219067	+	0.0379435i
$195$	5.38847	+	1.38098i	0.385876	+	0.0988944i
$196$	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	−0.990693	−	0.136113i	$-0.956539\pi$
$211$	−5.48306	+	9.49694i	−0.377469	+	0.653796i	0.613224	+	0.789909i	$0.289872\pi$
$212$	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
$221$	−18.2630	+	6.13646i	−1.22850	+	0.412783i
$222$	9.42196	+	18.4497i	0.632361	+	1.23826i
$223$	11.1218	−	6.42116i	0.744770	−	0.429993i	−0.0790313	−	0.996872i	$-0.525183\pi$
$223$	11.1218	−	6.42116i	0.744770	−	0.429993i	0.823801	+	0.566879i	$0.191849\pi$
$224$	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	$-0.379957\pi$
$227$	20.4534	−	11.8088i	1.35754	−	0.783777i	0.989292	+	0.145950i	$0.0466240\pi$
$228$	−43.2768	−	28.0477i	−2.86608	−	1.85751i
$229$	−10.7715	−	6.21892i	−0.711800	−	0.410958i	0.0999271	−	0.994995i	$-0.468139\pi$
$229$	−10.7715	−	6.21892i	−0.711800	−	0.410958i	−0.811727	+	0.584037i	$0.801472\pi$
$230$	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	$0.710937\pi$
$234$	−19.6997	+	18.1644i	−1.28781	+	1.18744i
$235$	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	$-0.112338\pi$
$239$	17.1326	+	9.89154i	1.10822	+	0.639830i	0.169851	+	0.985470i	$0.445671\pi$
$240$	−0.383967	+	7.45780i	−0.0247850	+	0.481399i
$241$	9.86550	−	5.69585i	0.635493	−	0.366902i	−0.147384	−	0.989079i	$-0.547085\pi$
$241$	9.86550	−	5.69585i	0.635493	−	0.366902i	0.782876	+	0.622178i	$0.213752\pi$
$242$			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
$247$	−8.26524	−	24.5985i	−0.525904	−	1.56517i
$248$	−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	−0.696478	−	0.717578i	$-0.745251\pi$
$257$	4.37976	−	7.58598i	0.273202	−	0.473200i	0.969680	+	0.244378i	$0.0785838\pi$
$258$	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	0.721951	−	0.691944i	$-0.243246\pi$
$263$	−3.86402	−	6.69268i	−0.238266	−	0.412688i	−0.960217	+	0.279256i	$0.909912\pi$
$264$	−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
$273$	−4.29025	+	4.38494i	−0.259658	+	0.265388i
$274$	−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	0.847828	−	0.530272i	$-0.177910\pi$
$277$	−0.587762	−	1.01803i	−0.0353152	−	0.0611677i	−0.883143	+	0.469104i	$0.844577\pi$
$278$		−	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	$-0.710297\pi$
$281$	−3.96724	+	2.29048i	−0.236665	+	0.136639i	0.376978	+	0.926222i	$0.376963\pi$
$282$	−10.3043	+	15.8993i	−0.613613	+	0.946788i
$283$	−0.0159162	+	0.0275676i	−0.000946118	+	0.00163872i	−0.866498	−	0.499180i	$-0.833634\pi$
$283$	−0.0159162	+	0.0275676i	−0.000946118	+	0.00163872i	0.865552	+	0.500819i	$0.166968\pi$
$284$	23.9938	+	13.8528i	1.42377	+	0.822014i
$285$	6.03901	−	9.31802i	0.357720	−	0.551952i
$286$	5.10681	−	25.2646i	0.301972	−	1.49393i
$287$	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	$-0.436556\pi$
$293$	−9.44674	−	5.45408i	−0.551884	−	0.318631i	−0.749882	+	0.661572i	$0.769890\pi$
$294$	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
$299$	−3.31014	+	16.3761i	−0.191430	+	0.947053i
$300$	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	−0.560902	−	0.827882i	$-0.689546\pi$
$311$	7.69804	−	13.3334i	0.436516	−	0.756067i	0.997418	+	0.0718148i	$0.0228791\pi$
$312$	−8.90450	−	31.8380i	−0.504118	−	1.80247i
$313$	8.67077	+	15.0182i	0.490101	+	0.848879i	0.999935	−	0.0113932i	$-0.00362663\pi$
$313$	8.67077	+	15.0182i	0.490101	+	0.848879i	−0.509834	+	0.860273i	$0.670293\pi$
$314$		−	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	$-0.570122\pi$
$317$	9.21059	−	5.31774i	0.517318	−	0.298674i	0.735837	+	0.677159i	$0.236789\pi$
$318$	−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	−0.508006	+	0.861353i	$0.669617\pi$
$331$	−27.4350	+	15.8396i	−1.50796	+	0.870623i	−0.999957	+	0.00926968i	$0.997049\pi$
$332$		−	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	0.318397	+	0.947958i	$0.396856\pi$
$337$	−12.1482	+	21.0414i	−0.661757	+	1.14620i	−0.980154	+	0.198239i	$0.936478\pi$
$338$	12.5082	−	29.6764i	0.680355	−	1.61418i
$339$	−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	−0.912777	−	0.408457i	$-0.866067\pi$
$347$	−1.91224	+	3.31209i	−0.102654	+	0.177802i	0.810123	+	0.586260i	$0.199400\pi$
$348$	13.8987	+	0.715577i	0.745047	+	0.0383590i
$349$	−20.3799	+	11.7664i	−1.09091	+	0.629839i	−0.933819	−	0.357745i	$-0.883546\pi$
$349$	−20.3799	+	11.7664i	−1.09091	+	0.629839i	−0.157093	+	0.987584i	$0.550212\pi$
$350$	10.2368			0.547180
$351$	18.4655	−	3.16656i	0.985613	−	0.169019i
$352$	4.04976			0.215853
$353$	−20.4327	+	11.7968i	−1.08752	+	0.627881i	−0.932916	−	0.360095i	$-0.882744\pi$
$353$	−20.4327	+	11.7968i	−1.08752	+	0.627881i	−0.154606	+	0.987976i	$0.549411\pi$
$354$	−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
$364$	−4.66687	−	13.8893i	−0.244611	−	0.727996i
$365$	−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	0.999144	+	0.0413794i	$0.0131752\pi$
$367$	10.2569	+	17.7655i	0.535407	+	0.927353i	−0.463736	+	0.885973i	$0.653491\pi$
$368$	−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	−0.971638	−	0.236473i	$-0.924009\pi$
$373$	−5.42755	+	9.40079i	−0.281028	+	0.486754i	0.690610	+	0.723227i	$0.257342\pi$
$374$	−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	$-0.159375\pi$
$383$	17.6164	+	10.1708i	0.900156	+	0.519705i	0.0229052	+	0.999738i	$0.492708\pi$
$384$	−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	−0.998765	−	0.0496861i	$-0.984178\pi$
$389$	−10.6980	−	18.5295i	−0.542412	−	0.939485i	0.456353	−	0.889799i	$-0.349155\pi$
$390$	13.2709	−	3.71163i	0.671999	−	0.187946i
$391$	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	$-0.209541\pi$
$401$	13.1515	+	7.59301i	0.656754	+	0.379177i	−0.134285	+	0.990943i	$0.542874\pi$
$402$	−15.5892	−	0.802612i	−0.777516	−	0.0400307i
$403$	35.6500	+	7.20603i	1.77585	+	0.358958i
$404$	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	$-0.314548\pi$
$409$	2.06606	+	1.19284i	0.102160	+	0.0589823i	−0.448049	+	0.894009i	$0.647881\pi$
$410$	−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
$416$	4.95957	+	1.00249i	0.243163	+	0.0491511i
$417$	−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	0.0974415	+	0.995241i	$0.468934\pi$
$419$	−16.6455	+	28.8308i	−0.813183	+	1.40848i	−0.910625	+	0.413234i	$0.864399\pi$
$420$	3.40986	−	5.26132i	0.166384	−	0.256726i
$421$	−21.0487	+	12.1525i	−1.02585	+	0.592275i	−0.915793	−	0.401650i	$-0.868437\pi$
$421$	−21.0487	+	12.1525i	−1.02585	+	0.592275i	−0.110057	+	0.993925i	$0.535103\pi$
$422$			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
$429$	−12.6034	+	12.8815i	−0.608496	+	0.621926i
$430$	−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	0.978935	−	0.204171i	$-0.0654500\pi$
$439$	6.55074	+	11.3462i	0.312650	+	0.541526i	−0.666285	+	0.745697i	$0.732117\pi$
$440$			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	0.907064	+	0.420993i	$0.138318\pi$
$443$	17.2195	+	29.8250i	0.818123	+	1.41703i	−0.0889410	+	0.996037i	$0.528348\pi$
$444$	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
$455$	2.99053	−	1.00483i	0.140198	−	0.0471074i
$456$	−65.9050	−	3.39314i	−3.08628	−	0.158898i
$457$	−10.7297	+	6.19481i	−0.501916	+	0.289781i	−0.729504	−	0.683976i	$-0.760249\pi$
$457$	−10.7297	+	6.19481i	−0.501916	+	0.289781i	0.227589	+	0.973757i	$0.426916\pi$
$458$	−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	$-0.764611\pi$
$461$	−11.2633	+	6.50288i	−0.524585	+	0.302869i	0.214223	+	0.976785i	$0.431278\pi$
$462$	−0.625408	+	12.1473i	−0.0290966	+	0.565144i
$463$	−5.56377	−	3.21224i	−0.258570	−	0.149286i	0.365112	−	0.930964i	$-0.381031\pi$
$463$	−5.56377	−	3.21224i	−0.258570	−	0.149286i	−0.623682	+	0.781678i	$0.714364\pi$
$464$	−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	$0.395312\pi$
$468$	−13.3232	+	42.7183i	−0.615867	+	1.97466i
$469$	−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	$-0.376210\pi$
$479$	29.9863	−	17.3126i	1.37011	−	0.791033i	0.990941	+	0.134295i	$0.0428769\pi$
$480$	0.984704	+	1.92820i	0.0449454	+	0.0880100i
$481$	5.54453	+	16.5013i	0.252809	+	0.752395i
$482$	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	−0.434875	−	0.900491i	$-0.643207\pi$
$491$	12.4622	−	21.5851i	0.562410	−	0.974123i	0.997285	−	0.0736326i	$-0.0234592\pi$
$492$	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	0.998600	+	0.0528989i	$0.0168461\pi$
$499$	34.4839	+	19.9093i	1.54371	+	0.891262i	0.545112	+	0.838363i	$0.316487\pi$
$500$	−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
$507$	−18.6235	+	12.6556i	−0.827101	+	0.562054i
$508$	15.6839	−	27.1653i	0.695860	−	1.20527i
$509$	−32.1750	−	18.5763i	−1.42613	−	0.823378i	−0.429319	−	0.903153i	$-0.641247\pi$
$509$	−32.1750	−	18.5763i	−1.42613	−	0.823378i	−0.996813	+	0.0797749i	$0.974580\pi$
$510$	−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
$520$	−3.36842	+	16.6644i	−0.147715	+	0.730783i
$521$	−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
$533$	9.76746	+	1.97432i	0.423076	+	0.0855174i
$534$	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
$546$	−3.77290	+	14.7215i	−0.161465	+	0.630021i
$547$	−5.47407	−	9.48136i	−0.234054	−	0.405394i	0.724943	−	0.688809i	$-0.241866\pi$
$547$	−5.47407	−	9.48136i	−0.234054	−	0.405394i	−0.958997	+	0.283415i	$0.908533\pi$
$548$			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	−0.709057	−	0.705151i	$-0.750879\pi$
$563$	6.07784	−	10.5271i	0.256151	−	0.443666i	0.965207	+	0.261486i	$0.0842124\pi$
$564$	−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	−0.951799	−	0.306722i	$-0.900768\pi$
$569$	−17.6882	−	30.6369i	−0.741529	−	1.28437i	0.210270	−	0.977643i	$-0.432566\pi$
$570$	1.41435	−	27.4710i	0.0592407	−	1.15063i
$571$	6.24561	−	10.8177i	0.261371	−	0.452707i	−0.705236	−	0.708973i	$-0.749159\pi$
$571$	6.24561	−	10.8177i	0.261371	−	0.452707i	0.966606	+	0.256266i	$0.0824922\pi$
$572$	−13.7098	−	40.8022i	−0.573234	−	1.70603i
$573$	−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
$585$	−9.19777	−	2.86865i	−0.380281	−	0.118604i
$586$	−27.0226			−1.11629
$587$	3.21529	−	1.85635i	0.132709	−	0.0766197i	−0.432176	−	0.901789i	$-0.642254\pi$
$587$	3.21529	−	1.85635i	0.132709	−	0.0766197i	0.564885	+	0.825170i	$0.308921\pi$
$588$	−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
$598$	13.1826	+	39.2332i	0.539075	+	1.60436i
$599$	14.2298	−	24.6468i	0.581415	−	1.00704i	−0.413897	−	0.910324i	$-0.635833\pi$
$599$	14.2298	−	24.6468i	0.581415	−	1.00704i	0.995312	−	0.0967168i	$-0.0308341\pi$
$600$	34.3507	−	17.5424i	1.40236	−	0.716165i
$601$	−0.635544	−	1.10079i	−0.0259244	−	0.0449023i	0.852772	−	0.522283i	$-0.174920\pi$
$601$	−0.635544	−	1.10079i	−0.0259244	−	0.0449023i	−0.878697	+	0.477381i	$0.841586\pi$
$602$	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	−0.858344	−	0.513075i	$-0.828506\pi$
$607$	0.373604	−	0.647101i	0.0151641	−	0.0262650i	0.873508	+	0.486810i	$0.161840\pi$
$608$	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	$-0.415343\pi$
$617$	−10.9623	−	6.32908i	−0.441325	−	0.254799i	−0.704159	+	0.710042i	$0.748676\pi$
$618$	−0.757501	+	14.7130i	−0.0304712	+	0.591842i
$619$	−7.38692	+	4.26484i	−0.296905	+	0.171418i	−0.641052	−	0.767498i	$-0.721502\pi$
$619$	−7.38692	+	4.26484i	−0.296905	+	0.171418i	0.344147	+	0.938916i	$0.388168\pi$
$620$	−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
$624$	−21.6065	−	21.1399i	−0.864950	−	0.846273i
$625$	−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
$637$	4.31114	−	21.3283i	0.170813	−	0.845056i
$638$	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	0.908331	+	0.418253i	$0.137357\pi$
$641$	20.6692	+	35.8000i	0.816383	+	1.41402i	−0.0919475	+	0.995764i	$0.529309\pi$
$642$	8.94475	−	4.56795i	0.353021	−	0.180283i
$643$	−17.6848	−	10.2103i	−0.697419	−	0.402655i	0.108966	−	0.994045i	$-0.465246\pi$
$643$	−17.6848	−	10.2103i	−0.697419	−	0.402655i	−0.806385	+	0.591390i	$0.798579\pi$
$644$	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
$650$	36.8284	+	7.44422i	1.44453	+	0.291986i
$651$	−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	−0.356709	−	0.934215i	$-0.616101\pi$
$653$	16.1168	−	27.9151i	0.630700	−	1.09240i	0.987409	−	0.158188i	$-0.0505653\pi$
$654$	−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	0.907895	−	0.419198i	$-0.137689\pi$
$659$	2.33379	+	4.04224i	0.0909115	+	0.157463i	−0.816983	+	0.576661i	$0.804355\pi$
$660$	10.0171	−	15.4560i	0.389914	−	0.601625i
$661$	19.5539	+	11.2894i	0.760557	+	0.439108i	0.829496	−	0.558513i	$-0.188628\pi$
$661$	19.5539	+	11.2894i	0.760557	+	0.439108i	−0.0689389	+	0.997621i	$0.521961\pi$
$662$	−39.2392	+	67.9642i	−1.52507	+	2.64151i
$663$	32.1371	−	8.98816i	1.24810	−	0.349071i
$664$	−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	0.900313	−	0.435242i	$-0.143337\pi$
$673$	1.89964	+	3.29028i	0.0732259	+	0.126831i	−0.827088	+	0.562073i	$0.810004\pi$
$674$			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	0.996228	+	0.0867791i	$0.0276574\pi$
$677$	14.9160	+	25.8352i	0.573267	+	0.992927i	−0.422961	+	0.906148i	$0.639009\pi$
$678$	−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
$689$	−21.5611	+	7.24463i	−0.821411	+	0.275998i
$690$	−9.63186	+	14.8617i	−0.366679	+	0.565774i
$691$	−6.85148	+	3.95570i	−0.260642	+	0.150482i	−0.624628	−	0.780923i	$-0.714749\pi$
$691$	−6.85148	+	3.95570i	−0.260642	+	0.150482i	0.363985	+	0.931405i	$0.381416\pi$
$692$	−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	$0.268222\pi$
$702$	35.6934	−	29.6656i	1.34716	−	1.11966i
$703$	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	$-0.805039\pi$
$709$	−19.4230	+	11.2139i	−0.729447	+	0.421147i	0.0887726	+	0.996052i	$0.471706\pi$
$710$			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
$715$	8.78521	−	2.95188i	0.328548	−	0.110394i
$716$	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	−0.908474	−	0.417941i	$-0.862752\pi$
$727$	−22.0067	−	38.1168i	−0.816185	−	1.41367i	0.0922894	−	0.995732i	$-0.470582\pi$
$728$	−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	$-0.438926\pi$
$733$	−15.2722	−	8.81743i	−0.564093	−	0.325679i	−0.754787	+	0.655970i	$0.772260\pi$
$734$	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
$741$	12.1062	+	43.2856i	0.444732	+	1.59014i
$742$	−7.67590	+	13.2951i	−0.281791	+	0.488077i
$743$	−28.3946	−	16.3936i	−1.04170	−	0.601423i	−0.121383	−	0.992606i	$-0.538733\pi$
$743$	−28.3946	−	16.3936i	−1.04170	−	0.601423i	−0.920313	+	0.391182i	$0.872066\pi$
$744$	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	−0.998735	−	0.0502796i	$-0.983989\pi$
$751$	−12.4916	+	21.6360i	−0.455824	+	0.789511i	0.542911	+	0.839790i	$0.317322\pi$
$752$	−18.5097	−	10.6866i	−0.674978	−	0.389699i
$753$	32.3379	+	1.66493i	1.17846	+	0.0606733i
$754$	17.0044	+	3.43714i	0.619263	+	0.125173i
$755$	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	$-0.215654\pi$
$761$	17.2650	+	9.96794i	0.625855	+	0.361338i	−0.153290	+	0.988181i	$0.548987\pi$
$762$	−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
$767$	−11.2111	−	2.26612i	−0.404808	−	0.0818250i
$768$	−30.7277	+	47.4119i	−1.10879	+	1.71083i
$769$	32.9151	+	19.0035i	1.18695	+	0.685285i	0.957612	−	0.288062i	$-0.0930110\pi$
$769$	32.9151	+	19.0035i	1.18695	+	0.685285i	0.229337	+	0.973347i	$0.426344\pi$
$770$	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
$780$	16.0935	−	16.4487i	0.576240	−	0.588958i
$781$	−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	$-0.324194\pi$
$787$	1.39487	+	0.805329i	0.0497218	+	0.0287069i	−0.474933	+	0.880022i	$0.657528\pi$
$788$	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	−0.866895	−	0.498491i	$-0.833888\pi$
$797$	−0.0491630	+	0.0851528i	−0.00174144	+	0.00301627i	0.865153	+	0.501507i	$0.167221\pi$
$798$	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
$806$	85.4089	−	28.6979i	3.00840	−	1.01084i
$807$	−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
$819$	7.81161	−	7.20281i	0.272960	−	0.251687i
$820$	−10.1843			−0.355651
$821$	36.3185	−	20.9685i	1.26753	−	0.731806i	0.293007	−	0.956110i	$-0.405344\pi$
$821$	36.3185	−	20.9685i	1.26753	−	0.731806i	0.974519	+	0.224304i	$0.0720109\pi$
$822$	42.1487	−	65.0342i	1.47010	−	2.26833i
$823$	−22.4560	+	38.8949i	−0.782766	+	1.35579i	0.147558	+	0.989053i	$0.452859\pi$
$823$	−22.4560	+	38.8949i	−0.782766	+	1.35579i	−0.930324	+	0.366737i	$0.880475\pi$
$824$	−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
$832$	−21.2046	+	7.12486i	−0.735137	+	0.247010i
$833$	−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	$-0.573389\pi$
$839$	14.4922	−	8.36709i	0.500327	−	0.288864i	0.728849	+	0.684675i	$0.240056\pi$
$840$	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	$-0.539067\pi$
$853$	19.7398	−	11.3968i	0.675876	−	0.390217i	0.798300	+	0.602261i	$0.205733\pi$
$854$	−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	−0.950945	−	0.309360i	$-0.899885\pi$
$857$	−21.7623	−	37.6934i	−0.743386	−	1.28758i	0.207559	−	0.978223i	$-0.433448\pi$
$858$	−11.0835	+	43.2469i	−0.378386	+	1.47643i
$859$	8.51911	−	14.7555i	0.290668	−	0.503452i	−0.683300	−	0.730138i	$-0.739456\pi$
$859$	8.51911	−	14.7555i	0.290668	−	0.503452i	0.973968	+	0.226686i	$0.0727890\pi$
$860$	−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
$871$	−12.8569	−	2.59880i	−0.435640	−	0.0880571i
$872$	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	$-0.622694\pi$
$877$	−40.4664	−	23.3633i	−1.36645	−	0.788922i	−0.990473	+	0.137706i	$0.956027\pi$
$878$	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	$0.634518\pi$
$884$	−15.7914	+	78.1237i	−0.531121	+	2.62759i
$885$	−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	−0.831243	−	0.555910i	$-0.812370\pi$
$887$	1.96001	−	3.39484i	0.0658107	−	0.113987i	0.897053	+	0.441922i	$0.145703\pi$
$888$	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
$897$	7.18415	−	28.0319i	0.239872	−	0.935957i
$898$	−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	−0.959718	−	0.280964i	$-0.909346\pi$
$907$	−21.7796	−	37.7234i	−0.723181	−	1.25259i	0.236537	−	0.971622i	$-0.423987\pi$
$908$		−	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	0.999245	−	0.0388513i	$-0.0123699\pi$
$911$	14.0645	+	24.3604i	0.465976	+	0.807095i	−0.533269	+	0.845946i	$0.679037\pi$
$912$	−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
$923$	−7.69095	−	22.8894i	−0.253151	−	0.753412i
$924$	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	$-0.417233\pi$
$929$	37.2632	−	21.5139i	1.22257	−	0.705849i	0.965464	+	0.260536i	$0.0838992\pi$
$930$	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
$936$	12.5672	+	55.8650i	0.410773	+	1.82601i
$937$	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	$-0.133128\pi$
$941$	31.2579	+	18.0468i	1.01898	+	0.588308i	0.105171	+	0.994454i	$0.466461\pi$
$942$	−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	$-0.698492\pi$
$947$	−5.32031	+	3.07168i	−0.172887	+	0.0998163i	0.411059	+	0.911609i	$0.365159\pi$
$948$	33.9733	+	1.74913i	1.10340	+	0.0568090i
$949$	−10.7257	−	31.9213i	−0.348172	−	1.03621i
$950$	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	$-0.170055\pi$
$967$	26.4324	+	15.2608i	0.850009	+	0.490753i	−0.0106449	+	0.999943i	$0.503388\pi$
$968$	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
$975$	−18.7775	−	18.3720i	−0.601360	−	0.588374i
$976$	13.3610	−	23.1420i	0.427677	−	0.740758i
$977$	25.1440	+	14.5169i	0.804426	+	0.464436i	0.845017	−	0.534740i	$-0.179590\pi$
$977$	25.1440	+	14.5169i	0.804426	+	0.464436i	−0.0405902	+	0.999176i	$0.512924\pi$
$978$	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	$-0.635963\pi$
$983$	5.23002	−	3.01955i	0.166812	−	0.0963088i	0.581082	+	0.813845i	$0.302630\pi$
$984$	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
$988$	−105.225	−	21.2695i	−3.34766	−	0.676672i
$989$	−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	0.983725	−	0.179678i	$-0.0575056\pi$
$997$	10.6174	+	18.3899i	0.336257	+	0.582414i	−0.647469	+	0.762092i	$0.724172\pi$
$998$	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.103.10	yes	20
3.2	odd	2		351.2.t.c.64.1		20
9.2	odd	6		351.2.t.c.181.10		20
9.4	even	3		1053.2.b.j.649.10		10
9.5	odd	6		1053.2.b.i.649.1		10
9.7	even	3	inner	117.2.t.c.25.1	✓	20
13.12	even	2	inner	117.2.t.c.103.1	yes	20
39.38	odd	2		351.2.t.c.64.10		20
117.25	even	6	inner	117.2.t.c.25.10	yes	20
117.38	odd	6		351.2.t.c.181.1		20
117.77	odd	6		1053.2.b.i.649.10		10
117.103	even	6		1053.2.b.j.649.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.t.c.25.1	✓	20	9.7	even	3	inner
117.2.t.c.25.10	yes	20	117.25	even	6	inner
117.2.t.c.103.1	yes	20	13.12	even	2	inner
117.2.t.c.103.10	yes	20	1.1	even	1	trivial
351.2.t.c.64.1		20	3.2	odd	2
351.2.t.c.64.10		20	39.38	odd	2
351.2.t.c.181.1		20	117.38	odd	6
351.2.t.c.181.10		20	9.2	odd	6
1053.2.b.i.649.1		10	9.5	odd	6
1053.2.b.i.649.10		10	117.77	odd	6
1053.2.b.j.649.1		10	117.103	even	6
1053.2.b.j.649.10		10	9.4	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} +(-3.41778 + 1.14839i) 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} +(6.01421 - 1.68206i) 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} +(-2.95523 + 14.6202i) 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} +(-3.14792 - 0.636297i) 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} +(10.8193 - 11.0581i) 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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