LMFDB - Embedded newform 104.2.s.c.69.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,2,Mod(69,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("104.69");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$104 = 2^{3} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	104.s (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:	$0.830444181021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.8607891481591137382656.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{16} - 3 x^{15} + 5 x^{14} - 6 x^{13} + 6 x^{12} - 20 x^{10} + 48 x^{9} - 76 x^{8} + 96 x^{7} + \cdots + 256$ x^16 - 3x^15 + 5x^14 - 6x^13 + 6x^12 - 20x^10 + 48x^9 - 76x^8 + 96x^7 - 80x^6 + 96x^4 - 192x^3 + 320x^2 - 384*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$2^{2}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.5
Root			$-0.608487 - 1.27661i$ of defining polynomial
Character	$\chi$	$=$	104.69
Dual form			104.2.s.c.101.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.801337 - 1.16527i) q^{2} +(2.28316 + 1.31818i) q^{3} +(-0.715719 - 1.86755i) q^{4} -3.40672 q^{5} +(3.36562 - 1.60419i) q^{6} +(1.30715 - 0.754684i) q^{7} +(-2.74974 - 0.662529i) q^{8} +(1.97521 + 3.42116i) q^{9} +(-2.72993 + 3.96976i) q^{10} +(-1.69608 + 2.93770i) q^{11} +(0.827672 - 5.20736i) q^{12} +(2.16266 + 2.88494i) q^{13} +(0.168056 - 2.12794i) q^{14} +(-7.77808 - 4.49068i) q^{15} +(-2.97549 + 2.67328i) q^{16} +(-1.32767 - 2.29959i) q^{17} +(5.56938 + 0.439846i) q^{18} +(-3.32953 - 5.76692i) q^{19} +(2.43826 + 6.36223i) q^{20} +3.97924 q^{21} +(2.06409 + 4.33049i) q^{22} +(-0.307150 + 0.532000i) q^{23} +(-5.40475 - 5.13731i) q^{24} +6.60576 q^{25} +(5.09476 - 0.208281i) q^{26} +2.50563i q^{27} +(-2.34496 - 1.90103i) q^{28} +(2.50678 + 1.44729i) q^{29} +(-11.4657 + 5.46504i) q^{30} +0.813985i q^{31} +(0.730733 + 5.60946i) q^{32} +(-7.74485 + 4.47149i) q^{33} +(-3.74357 - 0.295651i) q^{34} +(-4.45310 + 2.57100i) q^{35} +(4.97549 - 6.13739i) q^{36} +(2.53339 - 4.38796i) q^{37} +(-9.38811 - 0.741432i) q^{38} +(1.13482 + 9.43756i) q^{39} +(9.36759 + 2.25705i) q^{40} +(6.98302 + 4.03165i) q^{41} +(3.18871 - 4.63690i) q^{42} +(7.93701 - 4.58243i) q^{43} +(6.70023 + 1.06495i) q^{44} +(-6.72898 - 11.6549i) q^{45} +(0.373794 + 0.784225i) q^{46} -5.88587i q^{47} +(-10.3174 + 2.18129i) q^{48} +(-2.36091 + 4.08921i) q^{49} +(5.29343 - 7.69750i) q^{50} -7.00045i q^{51} +(3.83992 - 6.10369i) q^{52} +0.627889i q^{53} +(2.91974 + 2.00785i) q^{54} +(5.77808 - 10.0079i) q^{55} +(-4.09432 + 1.20916i) q^{56} -17.5557i q^{57} +(3.69527 - 1.76132i) q^{58} +(-1.23678 - 2.14217i) q^{59} +(-2.81965 + 17.7400i) q^{60} +(-5.75913 + 3.32504i) q^{61} +(0.948514 + 0.652276i) q^{62} +(5.16378 + 2.98131i) q^{63} +(7.12211 + 3.64356i) q^{64} +(-7.36759 - 9.82820i) q^{65} +(-0.995727 + 12.6080i) q^{66} +(-0.664263 + 1.15054i) q^{67} +(-3.34437 + 4.12536i) q^{68} +(-1.40255 + 0.809760i) q^{69} +(-0.572519 + 7.24931i) q^{70} +(-5.38030 + 3.10632i) q^{71} +(-3.16468 - 10.7159i) q^{72} +10.2297i q^{73} +(-3.08307 - 6.46832i) q^{74} +(15.0820 + 8.70759i) q^{75} +(-8.38701 + 10.3456i) q^{76} +5.12002i q^{77} +(11.9067 + 6.24029i) q^{78} -1.65534 q^{79} +(10.1367 - 9.10713i) q^{80} +(2.62274 - 4.54272i) q^{81} +(10.2937 - 4.90641i) q^{82} -7.81437 q^{83} +(-2.84802 - 7.43143i) q^{84} +(4.52301 + 7.83408i) q^{85} +(1.02043 - 12.9208i) q^{86} +(3.81559 + 6.60880i) q^{87} +(6.61010 - 6.95420i) q^{88} +(-1.12386 - 0.648863i) q^{89} +(-18.9733 - 1.49843i) q^{90} +(5.00414 + 2.13893i) q^{91} +(1.21337 + 0.192856i) q^{92} +(-1.07298 + 1.85846i) q^{93} +(-6.85865 - 4.71657i) q^{94} +(11.3428 + 19.6463i) q^{95} +(-5.72591 + 13.7705i) q^{96} +(-12.5894 + 7.26849i) q^{97} +(2.87316 + 6.02793i) q^{98} -13.4005 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$16 q + 3 q^{2} - q^{4} + 6 q^{6} + 18 q^{7} + 2 q^{9} - 9 q^{10} - 16 q^{12} - 24 q^{14} - 36 q^{15} - q^{16} + 8 q^{17} - 15 q^{20} + 22 q^{22} - 2 q^{23} - 12 q^{24} - 12 q^{25} + 23 q^{26} - 8 q^{30}+ \cdots - 93 q^{98}+O(q^{100})$ 16 * q + 3 * q^2 - q^4 + 6 * q^6 + 18 * q^7 + 2 * q^9 - 9 * q^10 - 16 * q^12 - 24 * q^14 - 36 * q^15 - q^16 + 8 * q^17 - 15 * q^20 + 22 * q^22 - 2 * q^23 - 12 * q^24 - 12 * q^25 + 23 * q^26 - 8 * q^30 - 27 * q^32 - 30 * q^33 + 33 * q^36 - 14 * q^39 + 26 * q^40 + 24 * q^41 + 14 * q^42 + 42 * q^46 + 6 * q^48 - 14 * q^49 + 6 * q^50 + 28 * q^52 + 6 * q^54 + 4 * q^55 - 8 * q^56 - 33 * q^58 - 4 * q^62 + 50 * q^64 + 6 * q^65 + 40 * q^66 + 5 * q^68 + 6 * q^71 + 39 * q^72 - 29 * q^74 + 24 * q^76 - 20 * q^78 + 32 * q^79 - 33 * q^80 + 12 * q^81 + 9 * q^82 - 24 * q^84 + 34 * q^87 - 8 * q^88 - 30 * q^89 - 62 * q^90 - 4 * q^92 - 24 * q^94 + 28 * q^95 - 30 * q^97 - 93 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$ .

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$ -expansion $a_n$ , the Satake parameters $\alpha_p$ , and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$ .

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.801337	−	1.16527i	0.566631	−	0.823972i
$2$	0.801337	−	1.16527i	0.566631	−	0.823972i
$3$	2.28316	+	1.31818i	1.31818	+	0.761053i	0.983436	−	0.181256i	$-0.0580162\pi$
$3$	2.28316	+	1.31818i	1.31818	+	0.761053i	0.334746	+	0.942308i	$0.391350\pi$
$4$	−0.715719	−	1.86755i	−0.357860	−	0.933775i
$5$	−3.40672			−1.52353			−0.761766	−	0.647852i	$-0.775668\pi$
$5$	−3.40672			−1.52353			−0.761766	+	0.647852i	$0.775668\pi$
$6$	3.36562	−	1.60419i	1.37401	−	0.654909i
$7$	1.30715	−	0.754684i	0.494056	−	0.285244i	−0.232199	−	0.972668i	$-0.574592\pi$
$7$	1.30715	−	0.754684i	0.494056	−	0.285244i	0.726256	+	0.687425i	$0.241259\pi$
$8$	−2.74974	−	0.662529i	−0.972179	−	0.234239i
$9$	1.97521	+	3.42116i	0.658402	+	1.14039i
$10$	−2.72993	+	3.96976i	−0.863280	+	1.25535i
$11$	−1.69608	+	2.93770i	−0.511388	+	0.885751i	0.488525	+	0.872550i	$0.337535\pi$
$11$	−1.69608	+	2.93770i	−0.511388	+	0.885751i	−0.999913	+	0.0132004i	$0.995798\pi$
$12$	0.827672	−	5.20736i	0.238928	−	1.50324i
$13$	2.16266	+	2.88494i	0.599815	+	0.800139i
$13$	2.16266	+	2.88494i	0.599815	+	0.800139i
$14$	0.168056	−	2.12794i	0.0449147	−	0.568716i
$15$	−7.77808	−	4.49068i	−2.00829	−	1.15949i
$16$	−2.97549	+	2.67328i	−0.743873	+	0.668321i
$17$	−1.32767	−	2.29959i	−0.322008	−	0.557734i	0.658894	−	0.752235i	$-0.271024\pi$
$17$	−1.32767	−	2.29959i	−0.322008	−	0.557734i	−0.980902	+	0.194502i	$0.937691\pi$
$18$	5.56938	+	0.439846i	1.31272	+	0.103673i
$19$	−3.32953	−	5.76692i	−0.763847	−	1.32302i	−0.940854	−	0.338813i	$-0.889975\pi$
$19$	−3.32953	−	5.76692i	−0.763847	−	1.32302i	0.177006	−	0.984210i	$-0.443359\pi$
$20$	2.43826	+	6.36223i	0.545211	+	1.42264i
$21$	3.97924			0.868342
$22$	2.06409	+	4.33049i	0.440065	+	0.923263i
$23$	−0.307150	+	0.532000i	−0.0640453	+	0.110930i	−0.896270	−	0.443509i	$-0.853734\pi$
$23$	−0.307150	+	0.532000i	−0.0640453	+	0.110930i	0.832225	+	0.554438i	$0.187067\pi$
$24$	−5.40475	−	5.13731i	−1.10324	−	1.04865i
$25$	6.60576			1.32115
$26$	5.09476	−	0.208281i	0.999165	−	0.0408473i
$27$			2.50563i			0.482209i
$28$	−2.34496	−	1.90103i	−0.443156	−	0.359261i
$29$	2.50678	+	1.44729i	0.465498	+	0.268756i	0.714353	−	0.699785i	$-0.246721\pi$
$29$	2.50678	+	1.44729i	0.465498	+	0.268756i	−0.248855	+	0.968541i	$0.580054\pi$
$30$	−11.4657	+	5.46504i	−2.09335	+	0.997775i
$31$			0.813985i			0.146196i	0.997325	+	0.0730980i	$0.0232886\pi$
$31$			0.813985i			0.146196i	−0.997325	+	0.0730980i	$0.976711\pi$
$32$	0.730733	+	5.60946i	0.129176	+	0.991622i
$33$	−7.74485	+	4.47149i	−1.34821	+	0.778387i
$34$	−3.74357	−	0.295651i	−0.642016	−	0.0507037i
$35$	−4.45310	+	2.57100i	−0.752711	+	0.434578i
$36$	4.97549	−	6.13739i	0.829249	−	1.02290i
$37$	2.53339	−	4.38796i	0.416486	−	0.721376i	−0.579097	−	0.815259i	$-0.696595\pi$
$37$	2.53339	−	4.38796i	0.416486	−	0.721376i	0.995583	+	0.0938831i	$0.0299280\pi$
$38$	−9.38811	−	0.741432i	−1.52295	−	0.120276i
$39$	1.13482	+	9.43756i	0.181717	+	1.51122i
$40$	9.36759	+	2.25705i	1.48115	+	0.356871i
$41$	6.98302	+	4.03165i	1.09056	+	0.629637i	0.933726	−	0.357987i	$-0.116537\pi$
$41$	6.98302	+	4.03165i	1.09056	+	0.629637i	0.156837	+	0.987624i	$0.449870\pi$
$42$	3.18871	−	4.63690i	0.492029	−	0.715489i
$43$	7.93701	−	4.58243i	1.21038	−	0.698815i	0.247540	−	0.968878i	$-0.420378\pi$
$43$	7.93701	−	4.58243i	1.21038	−	0.698815i	0.962843	+	0.270063i	$0.0870446\pi$
$44$	6.70023	+	1.06495i	1.01010	+	0.160548i
$45$	−6.72898	−	11.6549i	−1.00310	−	1.73741i
$46$	0.373794	+	0.784225i	0.0551129	+	0.115628i
$47$		−	5.88587i		−	0.858543i	−0.903176	−	0.429271i	$-0.858770\pi$
$47$		−	5.88587i		−	0.858543i	0.903176	−	0.429271i	$-0.141230\pi$
$48$	−10.3174	+	2.18129i	−1.48919	+	0.314842i
$49$	−2.36091	+	4.08921i	−0.337272	+	0.584173i
$50$	5.29343	−	7.69750i	0.748605	−	1.08859i
$51$		−	7.00045i		−	0.980259i
$52$	3.83992	−	6.10369i	0.532501	−	0.846430i
$53$			0.627889i			0.0862472i	0.999070	+	0.0431236i	$0.0137309\pi$
$53$			0.627889i			0.0862472i	−0.999070	+	0.0431236i	$0.986269\pi$
$54$	2.91974	+	2.00785i	0.397327	+	0.273234i
$55$	5.77808	−	10.0079i	0.779117	−	1.34947i
$56$	−4.09432	+	1.20916i	−0.547127	+	0.161580i
$57$		−	17.5557i		−	2.32531i
$58$	3.69527	−	1.76132i	0.485213	−	0.231272i
$59$	−1.23678	−	2.14217i	−0.161015	−	0.278887i	0.774218	−	0.632919i	$-0.218143\pi$
$59$	−1.23678	−	2.14217i	−0.161015	−	0.278887i	−0.935233	+	0.354033i	$0.884810\pi$
$60$	−2.81965	+	17.7400i	−0.364015	+	2.29023i
$61$	−5.75913	+	3.32504i	−0.737381	+	0.425727i	−0.821116	−	0.570761i	$-0.806648\pi$
$61$	−5.75913	+	3.32504i	−0.737381	+	0.425727i	0.0837352	+	0.996488i	$0.473315\pi$
$62$	0.948514	+	0.652276i	0.120461	+	0.0828391i
$63$	5.16378	+	2.98131i	0.650575	+	0.375610i
$64$	7.12211	+	3.64356i	0.890264	+	0.455445i
$65$	−7.36759	−	9.82820i	−0.913837	−	1.21904i
$66$	−0.995727	+	12.6080i	−0.122566	+	1.55194i
$67$	−0.664263	+	1.15054i	−0.0811526	+	0.140560i	−0.903745	−	0.428071i	$-0.859193\pi$
$67$	−0.664263	+	1.15054i	−0.0811526	+	0.140560i	0.822593	+	0.568631i	$0.192527\pi$
$68$	−3.34437	+	4.12536i	−0.405564	+	0.500273i
$69$	−1.40255	+	0.809760i	−0.168847	+	0.0974837i
$70$	−0.572519	+	7.24931i	−0.0684291	+	0.866458i
$71$	−5.38030	+	3.10632i	−0.638524	+	0.368652i	−0.784046	−	0.620703i	$-0.786847\pi$
$71$	−5.38030	+	3.10632i	−0.638524	+	0.368652i	0.145521	+	0.989355i	$0.453514\pi$
$72$	−3.16468	−	10.7159i	−0.372961	−	1.26288i
$73$			10.2297i			1.19729i	0.801014	+	0.598646i	$0.204294\pi$
$73$			10.2297i			1.19729i	−0.801014	+	0.598646i	$0.795706\pi$
$74$	−3.08307	−	6.46832i	−0.358399	−	0.751927i
$75$	15.0820	+	8.70759i	1.74152	+	1.00547i
$76$	−8.38701	+	10.3456i	−0.962056	+	1.18672i
$77$			5.12002i			0.583481i
$78$	11.9067	+	6.24029i	1.34817	+	0.706573i
$79$	−1.65534			−0.186241			−0.0931203	−	0.995655i	$-0.529684\pi$
$79$	−1.65534			−0.186241			−0.0931203	+	0.995655i	$0.529684\pi$
$80$	10.1367	−	9.10713i	1.13331	−	1.01821i
$81$	2.62274	−	4.54272i	0.291416	−	0.504747i
$82$	10.2937	−	4.90641i	1.13675	−	0.541822i
$83$	−7.81437			−0.857738			−0.428869	−	0.903367i	$-0.641088\pi$
$83$	−7.81437			−0.857738			−0.428869	+	0.903367i	$0.641088\pi$
$84$	−2.84802	−	7.43143i	−0.310744	−	0.810836i
$85$	4.52301	+	7.83408i	0.490589	+	0.849725i
$86$	1.02043	−	12.9208i	0.110036	−	1.39329i
$87$	3.81559	+	6.60880i	0.409074	+	0.708537i
$88$	6.61010	−	6.95420i	0.704639	−	0.741321i
$89$	−1.12386	−	0.648863i	−0.119129	−	0.0687794i	0.439251	−	0.898364i	$-0.355244\pi$
$89$	−1.12386	−	0.648863i	−0.119129	−	0.0687794i	−0.558381	+	0.829585i	$0.688577\pi$
$90$	−18.9733	−	1.49843i	−1.99997	−	0.157949i
$91$	5.00414	+	2.13893i	0.524577	+	0.224220i
$92$	1.21337	+	0.192856i	0.126503	+	0.0201067i
$93$	−1.07298	+	1.85846i	−0.111263	+	0.192713i
$94$	−6.85865	−	4.71657i	−0.707415	−	0.486477i
$95$	11.3428	+	19.6463i	1.16375	+	2.01567i
$96$	−5.72591	+	13.7705i	−0.584398	+	1.40545i
$97$	−12.5894	+	7.26849i	−1.27826	+	0.738004i	−0.976528	−	0.215389i	$-0.930898\pi$
$97$	−12.5894	+	7.26849i	−1.27826	+	0.738004i	−0.301732	+	0.953393i	$0.597565\pi$
$98$	2.87316	+	6.02793i	0.290233	+	0.608913i
$99$	−13.4005			−1.34680
$100$	−4.72787	−	12.3366i	−0.472787	−	1.23366i
$101$	−9.31772	−	5.37959i	−0.927148	−	0.535289i	−0.0412395	−	0.999149i	$-0.513131\pi$
$101$	−9.31772	−	5.37959i	−0.927148	−	0.535289i	−0.885908	+	0.463860i	$0.846464\pi$
$102$	−8.15743	−	5.60972i	−0.807706	−	0.555445i
$103$	−3.40986			−0.335984			−0.167992	−	0.985788i	$-0.553728\pi$
$103$	−3.40986			−0.335984			−0.167992	+	0.985788i	$0.553728\pi$
$104$	−4.03540	−	9.36566i	−0.395703	−	0.918378i
$105$	−13.5562			−1.32295
$106$	0.731662	+	0.503150i	0.0710653	+	0.0488703i
$107$	−0.792036	−	0.457282i	−0.0765690	−	0.0442071i	0.461227	−	0.887282i	$-0.347409\pi$
$107$	−0.792036	−	0.457282i	−0.0765690	−	0.0442071i	−0.537796	+	0.843075i	$0.680743\pi$
$108$	4.67939	−	1.79333i	0.450275	−	0.172563i
$109$	20.3289			1.94716			0.973578	−	0.228355i	$-0.0733348\pi$
$109$	20.3289			1.94716			0.973578	+	0.228355i	$0.0733348\pi$
$110$	−7.03178	−	14.7528i	−0.670454	−	1.40662i
$111$	11.5682	−	6.67893i	1.09801	−	0.633936i
$112$	−1.87193	+	5.73994i	−0.176881	+	0.542373i
$113$	−1.71337	−	2.96765i	−0.161180	−	0.279173i	0.774112	−	0.633049i	$-0.218197\pi$
$113$	−1.71337	−	2.96765i	−0.161180	−	0.279173i	−0.935292	+	0.353876i	$0.884863\pi$
$114$	−20.4572	−	14.0680i	−1.91599	−	1.31759i
$115$	1.04638	−	1.81238i	0.0975751	−	0.169005i
$116$	0.908739	−	5.71740i	0.0843743	−	0.530848i
$117$	−5.59814	+	13.0972i	−0.517548	+	1.21083i
$118$	−3.48729	−	0.275411i	−0.321031	−	0.0253536i
$119$	−3.47093	−	2.00394i	−0.318180	−	0.183701i
$120$	18.4125	+	17.5014i	1.68082	+	1.59765i
$121$	−0.253396	−	0.438894i	−0.0230360	−	0.0398995i
$122$	−0.740430	+	9.37543i	−0.0670354	+	0.848811i
$123$	10.6289	+	18.4098i	0.958374	+	1.65995i
$124$	1.52016	−	0.582584i	0.136514	−	0.0523176i
$125$	−5.47036			−0.489284
$126$	7.61197	−	3.62818i	0.678128	−	0.323224i
$127$	−2.69954	+	4.67573i	−0.239545	+	0.414904i	−0.960584	−	0.277991i	$-0.910332\pi$
$127$	−2.69954	+	4.67573i	−0.239545	+	0.414904i	0.721039	+	0.692895i	$0.243665\pi$
$128$	9.95295	−	5.37948i	0.879725	−	0.475483i
$129$	24.1619			2.12734
$130$	−17.3564	+	0.709556i	−1.52226	+	0.0622322i
$131$		−	13.5230i		−	1.18151i	−0.806850	−	0.590756i	$-0.798829\pi$
$131$		−	13.5230i		−	1.18151i	0.806850	−	0.590756i	$-0.201171\pi$
$132$	13.8939	+	11.2636i	1.20931	+	0.980368i
$133$	−8.70440	−	5.02549i	−0.754767	−	0.435765i
$134$	0.808391	+	1.69601i	0.0698343	+	0.146513i
$135$		−	8.53599i		−	0.734661i
$136$	2.12720	+	7.20290i	0.182406	+	0.617644i
$137$	7.11430	−	4.10744i	0.607816	−	0.350923i	−0.164294	−	0.986411i	$-0.552535\pi$
$137$	7.11430	−	4.10744i	0.607816	−	0.350923i	0.772110	+	0.635489i	$0.219201\pi$
$138$	−0.180320	+	2.28324i	−0.0153499	+	0.194362i
$139$	−16.9128	+	9.76458i	−1.43452	+	0.828221i	−0.997461	−	0.0712113i	$-0.977314\pi$
$139$	−16.9128	+	9.76458i	−1.43452	+	0.828221i	−0.437060	+	0.899432i	$0.643980\pi$
$140$	7.98864	+	6.47628i	0.675163	+	0.547345i
$141$	7.75865	−	13.4384i	0.653396	−	1.13172i
$142$	−0.691726	+	8.75873i	−0.0580484	+	0.735016i
$143$	−12.1432	+	1.46016i	−1.01546	+	0.122104i
$144$	−15.0229	−	4.89934i	−1.25191	−	0.408278i
$145$	−8.53992	−	4.93052i	−0.709202	−	0.409458i
$146$	11.9203	+	8.19741i	0.986535	+	0.678422i
$147$	−10.7806	+	6.22420i	−0.889172	+	0.513364i
$148$	−10.0079	−	1.59069i	−0.822647	−	0.130754i
$149$	6.48603	+	11.2341i	0.531356	+	0.920335i	0.999330	+	0.0365934i	$0.0116506\pi$
$149$	6.48603	+	11.2341i	0.531356	+	0.920335i	−0.467974	+	0.883742i	$0.655016\pi$
$150$	22.2325	−	10.5969i	1.81527	−	0.865234i
$151$		−	16.2580i		−	1.32306i	−0.749920	−	0.661528i	$-0.769908\pi$
$151$		−	16.2580i		−	1.32306i	0.749920	−	0.661528i	$-0.230092\pi$
$152$	5.33459	+	18.0634i	0.432692	+	1.46514i
$153$	5.24485	−	9.08435i	0.424021	−	0.734426i
$154$	5.96622	+	4.10286i	0.480772	+	0.330618i
$155$		−	2.77302i		−	0.222734i
$156$	16.8129	−	8.87398i	1.34611	−	0.710487i
$157$			8.87819i			0.708557i	0.935140	+	0.354278i	$0.115273\pi$
$157$			8.87819i			0.708557i	−0.935140	+	0.354278i	$0.884727\pi$
$158$	−1.32649	+	1.92893i	−0.105530	+	0.153457i
$159$	−0.827672	+	1.43357i	−0.0656386	+	0.113689i
$160$	−2.48940	−	19.1099i	−0.196805	−	1.51077i
$161$			0.927206i			0.0730740i
$162$	−3.19181	−	6.69645i	−0.250772	−	0.526123i
$163$	−2.04217	−	3.53714i	−0.159955	−	0.277050i	0.774897	−	0.632087i	$-0.217802\pi$
$163$	−2.04217	−	3.53714i	−0.159955	−	0.277050i	−0.934852	+	0.355037i	$0.884468\pi$
$164$	2.53143	−	15.9267i	0.197671	−	1.24366i
$165$	26.3846	−	15.2331i	2.05403	−	1.18590i
$166$	−6.26194	+	9.10586i	−0.486021	+	0.706752i
$167$	15.0204	+	8.67204i	1.16231	+	0.671063i	0.951858	−	0.306540i	$-0.0991715\pi$
$167$	15.0204	+	8.67204i	1.16231	+	0.671063i	0.210457	+	0.977603i	$0.432505\pi$
$168$	−10.9419	−	2.63636i	−0.844183	−	0.203400i
$169$	−3.64578	+	12.4783i	−0.280445	+	0.959870i
$170$	12.7533	+	1.00720i	0.978133	+	0.0772487i
$171$	13.1530	−	22.7817i	1.00584	−	1.74216i
$172$	−14.2386	−	11.5430i	−1.08568	−	0.880148i
$173$	−12.2964	+	7.09933i	−0.934878	+	0.539752i	−0.888351	−	0.459165i	$-0.848149\pi$
$173$	−12.2964	+	7.09933i	−0.934878	+	0.539752i	−0.0465270	+	0.998917i	$0.514815\pi$
$174$	10.7586	+	0.849669i	0.815609	+	0.0644132i
$175$	8.63472	−	4.98526i	0.652723	−	0.376850i
$176$	−2.80663	−	13.2752i	−0.211558	−	1.00066i
$177$		−	6.52121i		−	0.490164i
$178$	−1.65670	+	0.789650i	−0.124175	+	0.0591867i
$179$	4.23741	+	2.44647i	0.316719	+	0.182858i	0.649929	−	0.759995i	$-0.274799\pi$
$179$	4.23741	+	2.44647i	0.316719	+	0.182858i	−0.333210	+	0.942853i	$0.608132\pi$
$180$	−16.9501	+	20.9084i	−1.26339	+	1.55842i
$181$		−	21.2024i		−	1.57596i	−0.615702	−	0.787979i	$-0.711127\pi$
$181$		−	21.2024i		−	1.57596i	0.615702	−	0.787979i	$-0.288873\pi$
$182$	6.50244	−	4.11719i	0.481993	−	0.305186i
$183$	−17.5320			−1.29600
$184$	1.19705	−	1.25936i	0.0882476	−	0.0928416i
$185$	−8.63055	+	14.9486i	−0.634531	+	1.09904i
$186$	1.30579	+	2.73956i	0.0957451	+	0.200874i
$187$	9.00737			0.658684
$188$	−10.9922	+	4.21263i	−0.801686	+	0.307238i
$189$	1.89096	+	3.27524i	0.137547	+	0.238238i
$190$	31.9827	+	2.52585i	2.32027	+	0.183245i
$191$	0.733892	+	1.27114i	0.0531026	+	0.0919763i	0.891355	−	0.453306i	$-0.149756\pi$
$191$	0.733892	+	1.27114i	0.0531026	+	0.0919763i	−0.838252	+	0.545283i	$0.816422\pi$
$192$	11.4580	+	17.7071i	0.826912	+	1.27790i
$193$	14.7436	+	8.51223i	1.06127	+	0.612724i	0.925783	−	0.378055i	$-0.123407\pi$
$193$	14.7436	+	8.51223i	1.06127	+	0.612724i	0.135486	+	0.990779i	$0.456740\pi$
$194$	−1.61857	+	20.4946i	−0.116207	+	1.47143i
$195$	−3.86602	−	32.1511i	−0.276852	−	2.30239i
$196$	9.32655	+	1.48239i	0.666182	+	0.105885i
$197$	−8.23055	+	14.2557i	−0.586402	+	1.01568i	0.408297	+	0.912849i	$0.366123\pi$
$197$	−8.23055	+	14.2557i	−0.586402	+	1.01568i	−0.994699	+	0.102829i	$0.967211\pi$
$198$	−10.7383	+	15.6152i	−0.763136	+	1.10972i
$199$	−9.15170	−	15.8512i	−0.648747	−	1.12366i	−0.983422	−	0.181329i	$-0.941960\pi$
$199$	−9.15170	−	15.8512i	−0.648747	−	1.12366i	0.334676	−	0.942333i	$-0.391373\pi$
$200$	−18.1641	−	4.37651i	−1.28440	−	0.309466i
$201$	−3.03323	+	1.75124i	−0.213948	+	0.123523i
$202$	−13.7353	+	6.54682i	−0.966413	+	0.460633i
$203$	4.36899			0.306643
$204$	−13.0737	+	5.01036i	−0.915342	+	0.350795i
$205$	−23.7892	−	13.7347i	−1.66151	−	0.959273i
$206$	−2.73245	+	3.97342i	−0.190379	+	0.276841i
$207$	−2.42674			−0.168670
$208$	−14.1473	−	2.80271i	−0.980936	−	0.194333i
$209$	22.5887			1.56249
$210$	−10.8631	+	15.7966i	−0.749622	+	1.09007i
$211$	3.82356	+	2.20753i	0.263225	+	0.151973i	0.625805	−	0.779980i	$-0.284771\pi$
$211$	3.82356	+	2.20753i	0.263225	+	0.151973i	−0.362580	+	0.931953i	$0.618104\pi$
$212$	1.17261	−	0.449392i	0.0805355	−	0.0308644i
$213$	−16.3788			−1.12226
$214$	−1.16755	+	0.556500i	−0.0798118	+	0.0380416i
$215$	−27.0392	+	15.6111i	−1.84406	+	1.06467i
$216$	1.66005	−	6.88983i	0.112952	−	0.468793i
$217$	0.614301	+	1.06400i	0.0417015	+	0.0722291i
$218$	16.2903	−	23.6887i	1.10332	−	1.60440i
$219$	−13.4846	+	23.3559i	−0.911202	+	1.57825i
$220$	−22.8258	−	3.62799i	−1.53892	−	0.244599i
$221$	3.76289	−	8.80350i	0.253119	−	0.592188i
$222$	1.48729	−	18.8322i	0.0998202	−	1.26394i
$223$	−4.37362	−	2.52511i	−0.292879	−	0.169094i	0.346360	−	0.938102i	$-0.387417\pi$
$223$	−4.37362	−	2.52511i	−0.292879	−	0.169094i	−0.639240	+	0.769008i	$0.720751\pi$
$224$	5.18854	+	6.78093i	0.346674	+	0.453070i
$225$	13.0477	+	22.5993i	0.869849	+	1.50662i
$226$	−4.83110	−	0.381539i	−0.321360	−	0.0253796i
$227$	7.30877	+	12.6592i	0.485100	+	0.840219i	0.999853	−	0.0171199i	$-0.00544971\pi$
$227$	7.30877	+	12.6592i	0.485100	+	0.840219i	−0.514753	+	0.857339i	$0.672116\pi$
$228$	−32.7862	+	12.5650i	−2.17132	+	0.832135i
$229$	12.1681			0.804089			0.402045	−	0.915620i	$-0.368300\pi$
$229$	12.1681			0.804089			0.402045	+	0.915620i	$0.368300\pi$
$230$	−1.27341	−	2.67164i	−0.0839664	−	0.176163i
$231$	−6.74912	+	11.6898i	−0.444060	+	0.769134i
$232$	−5.93413	−	5.64049i	−0.389594	−	0.370317i
$233$	−11.4232			−0.748361			−0.374180	−	0.927356i	$-0.622076\pi$
$233$	−11.4232			−0.748361			−0.374180	+	0.927356i	$0.622076\pi$
$234$	10.7758	+	17.0186i	0.704434	+	1.11254i
$235$			20.0515i			1.30802i
$236$	−3.11542	+	3.84294i	−0.202797	+	0.250154i
$237$	−3.77941	−	2.18204i	−0.245499	−	0.141739i
$238$	−5.11653	+	2.43875i	−0.331655	+	0.158081i
$239$		−	24.6424i		−	1.59398i	−0.603990	−	0.796992i	$-0.706423\pi$
$239$		−	24.6424i		−	1.59398i	0.603990	−	0.796992i	$-0.293577\pi$
$240$	35.1485	−	7.43104i	2.26883	−	0.479672i
$241$	−0.154956	+	0.0894640i	−0.00998161	+	0.00576288i	−0.504982	−	0.863130i	$-0.668501\pi$
$241$	−0.154956	+	0.0894640i	−0.00998161	+	0.00576288i	0.495001	+	0.868892i	$0.335168\pi$
$242$	−0.714487	−	0.0564270i	−0.0459289	−	0.00362727i
$243$	18.4861	−	10.6729i	1.18588	−	0.684670i
$244$	10.3316	+	8.37568i	0.661412	+	0.536198i
$245$	8.04295	−	13.9308i	0.513845	−	0.890006i
$246$	29.9697	+	2.36688i	1.91080	+	0.150907i
$247$	9.43658	−	22.0774i	0.600435	−	1.40475i
$248$	0.539289	−	2.23824i	0.0342449	−	0.142129i
$249$	−17.8414	−	10.3008i	−1.13065	−	0.652784i
$250$	−4.38360	+	6.37446i	−0.277243	+	0.403156i
$251$	17.4835	−	10.0941i	1.10355	−	0.637134i	0.166397	−	0.986059i	$-0.446787\pi$
$251$	17.4835	−	10.0941i	1.10355	−	0.637134i	0.937151	+	0.348925i	$0.113453\pi$
$252$	1.87193	−	11.7774i	0.117921	−	0.741907i
$253$	−1.04191	−	1.80463i	−0.0655040	−	0.113456i
$254$	3.28526	+	6.89253i	0.206136	+	0.432476i
$255$			23.8486i			1.49346i
$256$	1.70711	−	15.9087i	0.106694	−	0.994292i
$257$	−0.0990699	+	0.171594i	−0.00617981	+	0.0107037i	−0.869099	−	0.494639i	$-0.835300\pi$
$257$	−0.0990699	+	0.171594i	−0.00617981	+	0.0107037i	0.862919	+	0.505342i	$0.168634\pi$
$258$	19.3618	−	28.1552i	1.20542	−	1.75287i
$259$		−	7.64763i		−	0.475200i
$260$	−13.0815	+	20.7936i	−0.811282	+	1.28956i
$261$			11.4348i			0.707797i
$262$	−15.7580	−	10.8365i	−0.973533	−	0.669481i
$263$	3.69285	−	6.39620i	0.227711	−	0.394407i	−0.729418	−	0.684068i	$-0.760209\pi$
$263$	3.69285	−	6.39620i	0.227711	−	0.394407i	0.957129	+	0.289661i	$0.0935426\pi$
$264$	24.2588	−	7.16424i	1.49303	−	0.440928i
$265$		−	2.13904i		−	0.131400i
$266$	−12.8312	+	6.11589i	−0.786733	+	0.374989i
$267$	−1.71064	−	2.96291i	−0.104689	−	0.181327i
$268$	2.62411	+	0.417083i	0.160293	+	0.0254774i
$269$	16.0265	−	9.25292i	0.977155	−	0.564161i	0.0757448	−	0.997127i	$-0.475867\pi$
$269$	16.0265	−	9.25292i	0.977155	−	0.564161i	0.901410	+	0.432967i	$0.142533\pi$
$270$	−9.94675	−	6.84020i	−0.605340	−	0.416281i
$271$	−8.18255	−	4.72420i	−0.497055	−	0.286975i	0.230442	−	0.973086i	$-0.425983\pi$
$271$	−8.18255	−	4.72420i	−0.497055	−	0.286975i	−0.727496	+	0.686112i	$0.759316\pi$
$272$	10.0979	+	3.29318i	0.612278	+	0.199679i
$273$	8.60576	+	11.4799i	0.520844	+	0.694794i
$274$	0.914660	−	11.5815i	0.0552566	−	0.699667i
$275$	−11.2039	+	19.4057i	−0.675621	+	1.17021i
$276$	2.51610	+	2.03976i	0.151451	+	0.122779i
$277$	−8.64403	+	4.99063i	−0.519370	+	0.299858i	−0.736677	−	0.676245i	$-0.763606\pi$
$277$	−8.64403	+	4.99063i	−0.519370	+	0.299858i	0.217307	+	0.976103i	$0.430273\pi$
$278$	−2.17441	+	27.5327i	−0.130413	+	1.65130i
$279$	−2.78477	+	1.60779i	−0.166720	+	0.0962557i
$280$	13.9482	−	4.11926i	0.833565	−	0.246173i
$281$		−	11.1204i		−	0.663387i	−0.943387	−	0.331694i	$-0.892380\pi$
$281$		−	11.1204i		−	0.663387i	0.943387	−	0.331694i	$-0.107620\pi$
$282$	−9.44208	−	19.8096i	−0.562268	−	1.17964i
$283$	1.16222	+	0.671005i	0.0690865	+	0.0398871i	0.534145	−	0.845393i	$-0.320633\pi$
$283$	1.16222	+	0.671005i	0.0690865	+	0.0398871i	−0.465059	+	0.885280i	$0.653967\pi$
$284$	9.65199	+	7.82474i	0.572741	+	0.464313i
$285$			59.8075i			3.54269i
$286$	−8.02927	+	15.3202i	−0.474781	+	0.905900i
$287$	12.1705			0.718400
$288$	−17.7475	+	13.5798i	−1.04578	+	0.800197i
$289$	4.97458	−	8.61622i	0.292622	−	0.506836i
$290$	−12.5888	+	6.00032i	−0.739237	+	0.352351i
$291$	−38.3248			−2.24664
$292$	19.1044	−	7.32157i	1.11800	−	0.428462i
$293$	−4.18139	−	7.24239i	−0.244280	−	0.423105i	0.717649	−	0.696405i	$-0.245218\pi$
$293$	−4.18139	−	7.24239i	−0.244280	−	0.423105i	−0.961929	+	0.273300i	$0.911885\pi$
$294$	−1.38603	+	17.5501i	−0.0808348	+	1.02354i
$295$	4.21337	+	7.29777i	0.245312	+	0.424893i
$296$	−9.87330	+	10.3873i	−0.573874	+	0.603749i
$297$	−7.36080	−	4.24976i	−0.427117	−	0.246596i
$298$	18.2883	+	1.44433i	1.05941	+	0.0836678i
$299$	−2.19905	+	0.264426i	−0.127174	+	0.0152921i
$300$	5.46740	−	34.3986i	0.315660	−	1.98600i
$301$	6.91658	−	11.9799i	0.398665	−	0.690508i
$302$	−18.9450	−	13.0281i	−1.09016	−	0.749685i
$303$	−14.1826	−	24.5649i	−0.814766	−	1.41122i
$304$	25.3236	+	8.25864i	1.45241	+	0.473666i
$305$	19.6198	−	11.3275i	1.12342	−	0.648609i
$306$	−6.38285	−	13.3913i	−0.364883	−	0.765530i
$307$	−19.5458			−1.11554			−0.557770	−	0.829996i	$-0.688343\pi$
$307$	−19.5458			−1.11554			−0.557770	+	0.829996i	$0.688343\pi$
$308$	9.56191	−	3.66450i	0.544840	−	0.208804i
$309$	−7.78525	−	4.49482i	−0.442888	−	0.255701i
$310$	−3.23132	−	2.22212i	−0.183527	−	0.126208i
$311$	24.9794			1.41645			0.708226	−	0.705986i	$-0.249496\pi$
$311$	24.9794			1.41645			0.708226	+	0.705986i	$0.249496\pi$
$312$	3.13220	−	26.7027i	0.177326	−	1.51174i
$313$	4.98312			0.281663			0.140831	−	0.990034i	$-0.455022\pi$
$313$	4.98312			0.281663			0.140831	+	0.990034i	$0.455022\pi$
$314$	10.3455	+	7.11442i	0.583831	+	0.401490i
$315$	−17.5916	−	10.1565i	−0.991173	−	0.572254i
$316$	1.18476	+	3.09144i	0.0666480	+	0.173907i
$317$	22.2072			1.24728			0.623639	−	0.781712i	$-0.285653\pi$
$317$	22.2072			1.24728			0.623639	+	0.781712i	$0.285653\pi$
$318$	1.00726	+	2.11323i	0.0564841	+	0.118504i
$319$	−8.50343	+	4.90946i	−0.476101	+	0.274877i
$320$	−24.2630	−	12.4126i	−1.35635	−	0.693886i
$321$	−1.20556	−	2.08809i	−0.0672879	−	0.116546i
$322$	1.08045	+	0.743004i	0.0602110	+	0.0414060i
$323$	−8.84106	+	15.3132i	−0.491930	+	0.852047i
$324$	−10.3609	−	1.64679i	−0.575606	−	0.0914883i
$325$	14.2860	+	19.0572i	0.792446	+	1.05710i
$326$	−5.75819	−	0.454757i	−0.318917	−	0.0251867i
$327$	46.4141	+	26.7972i	2.56671	+	1.48189i
$328$	−16.5304	−	15.7124i	−0.912737	−	0.867573i
$329$	−4.44197	−	7.69372i	−0.244894	−	0.424169i
$330$	3.39217	−	42.9521i	0.186733	−	2.36443i
$331$	6.63759	+	11.4967i	0.364835	+	0.631913i	0.988750	−	0.149579i	$-0.0477920\pi$
$331$	6.63759	+	11.4967i	0.364835	+	0.631913i	−0.623914	+	0.781493i	$0.714459\pi$
$332$	5.59289	+	14.5937i	0.306950	+	0.800935i
$333$	20.0159			1.09686
$334$	22.1417	−	10.5536i	1.21154	−	0.577470i
$335$	2.26296	−	3.91956i	0.123639	−	0.214148i
$336$	−11.8402	+	10.6376i	−0.645936	+	0.580331i
$337$	−16.5718			−0.902723			−0.451361	−	0.892341i	$-0.649061\pi$
$337$	−16.5718			−0.902723			−0.451361	+	0.892341i	$0.649061\pi$
$338$	11.6191	+	14.2477i	0.631998	+	0.774970i
$339$		−	9.03414i		−	0.490667i
$340$	11.3933	−	14.0539i	0.617891	−	0.762182i
$341$	−2.39124	−	1.38059i	−0.129493	−	0.0747629i
$342$	−16.0069	−	33.5827i	−0.865554	−	1.81594i
$343$			17.6925i			0.955306i
$344$	−24.8607	+	7.34199i	−1.34040	+	0.395854i
$345$	4.77808	−	2.75863i	0.257243	−	0.148520i
$346$	−1.58090	+	20.0176i	−0.0849899	+	1.07615i
$347$	8.74418	−	5.04846i	0.469412	−	0.271015i	−0.246581	−	0.969122i	$-0.579307\pi$
$347$	8.74418	−	5.04846i	0.469412	−	0.271015i	0.715994	+	0.698107i	$0.245974\pi$
$348$	9.61137	−	11.8558i	0.515224	−	0.635540i
$349$	−12.5147	+	21.6761i	−0.669897	+	1.16030i	0.308035	+	0.951375i	$0.400328\pi$
$349$	−12.5147	+	21.6761i	−0.669897	+	1.16030i	−0.977933	+	0.208921i	$0.933005\pi$
$350$	1.11013	−	14.0567i	0.0593392	−	0.751360i
$351$	−7.22860	+	5.41884i	−0.385834	+	0.289236i
$352$	−17.7183	−	7.36743i	−0.944389	−	0.392686i
$353$	−3.34290	−	1.93003i	−0.177925	−	0.102725i	0.408393	−	0.912806i	$-0.366089\pi$
$353$	−3.34290	−	1.93003i	−0.177925	−	0.102725i	−0.586317	+	0.810082i	$0.699423\pi$
$354$	−7.59899	−	5.22569i	−0.403882	−	0.277742i
$355$	18.3292	−	10.5824i	0.972813	−	0.561654i
$356$	−0.407414	+	2.56328i	−0.0215929	+	0.135853i
$357$	−5.28313	−	9.15064i	−0.279613	−	0.484303i
$358$	6.24639	−	2.97729i	0.330132	−	0.157355i
$359$			14.0532i			0.741702i	0.928692	+	0.370851i	$0.120934\pi$
$359$			14.0532i			0.741702i	−0.928692	+	0.370851i	$0.879066\pi$
$360$	10.7812	+	36.5061i	0.568219	+	1.92404i
$361$	−12.6716	+	21.9478i	−0.666926	+	1.15515i
$362$	−24.7065	−	16.9902i	−1.29855	−	0.892986i
$363$		−	1.33609i		−	0.0701264i
$364$	0.412993	−	10.8764i	0.0216467	−	0.570076i
$365$		−	34.8496i		−	1.82411i
$366$	−14.0490	+	20.4296i	−0.734355	+	1.06787i
$367$	−10.2165	+	17.6955i	−0.533298	+	0.923699i	0.465946	+	0.884813i	$0.345714\pi$
$367$	−10.2165	+	17.6955i	−0.533298	+	0.923699i	−0.999244	+	0.0388859i	$0.987619\pi$
$368$	−0.508264	−	2.40406i	−0.0264951	−	0.125320i
$369$			31.8533i			1.65822i
$370$	10.5032	+	22.0358i	0.546033	+	1.14558i
$371$	0.473858	+	0.820745i	0.0246015	+	0.0426110i
$372$	4.23871	+	0.673712i	0.219767	+	0.0349303i
$373$	−9.53854	+	5.50708i	−0.493887	+	0.285146i	−0.726186	−	0.687499i	$-0.758709\pi$
$373$	−9.53854	+	5.50708i	−0.493887	+	0.285146i	0.232299	+	0.972645i	$0.425375\pi$
$374$	7.21793	−	10.4960i	0.373230	−	0.542737i
$375$	−12.4897	−	7.21093i	−0.644965	−	0.372371i
$376$	−3.89956	+	16.1846i	−0.201105	+	0.834657i
$377$	1.24597	+	10.3619i	0.0641709	+	0.533667i
$378$	5.33184	+	0.421085i	0.274240	+	0.0216583i
$379$	3.97232	−	6.88027i	0.204045	−	0.353416i	−0.745783	−	0.666189i	$-0.767925\pi$
$379$	3.97232	−	6.88027i	0.204045	−	0.353416i	0.949828	+	0.312773i	$0.101258\pi$
$380$	28.5722	−	35.2445i	1.46572	−	1.80800i
$381$	−12.3269	+	7.11696i	−0.631528	+	0.364613i
$382$	2.06932	+	0.163426i	0.105875	+	0.00836158i
$383$	6.51992	−	3.76428i	0.333152	−	0.192346i	−0.324087	−	0.946027i	$-0.605057\pi$
$383$	6.51992	−	3.76428i	0.333152	−	0.192346i	0.657240	+	0.753681i	$0.271724\pi$
$384$	29.8153	+	0.837603i	1.52150	+	0.0427437i
$385$		−	17.4425i		−	0.888952i
$386$	21.7337	−	10.3592i	1.10621	−	0.527268i
$387$	31.3545	+	18.1025i	1.59384	+	0.920202i
$388$	22.5848	+	18.3091i	1.14657	+	0.929506i
$389$			0.770469i			0.0390643i	0.999809	+	0.0195322i	$0.00621768\pi$
$389$			0.770469i			0.0390643i	−0.999809	+	0.0195322i	$0.993782\pi$
$390$	−40.5628	−	21.2589i	−2.05398	−	1.07649i
$391$	1.63118			0.0824923
$392$	9.20109	−	9.68008i	0.464725	−	0.488918i
$393$	17.8258	−	30.8752i	0.899193	−	1.55745i
$394$	10.0164	+	21.0145i	0.504617	+	1.05869i
$395$	5.63930			0.283744
$396$	9.59096	+	25.0260i	0.481964	+	1.25761i
$397$	−6.90453	−	11.9590i	−0.346528	−	0.600205i	0.639102	−	0.769122i	$-0.279306\pi$
$397$	−6.90453	−	11.9590i	−0.346528	−	0.600205i	−0.985630	+	0.168917i	$0.945973\pi$
$398$	−25.8046	−	2.03793i	−1.29347	−	0.102152i
$399$	−13.2490	−	22.9480i	−0.663280	−	1.14884i
$400$	−19.6554	+	17.6591i	−0.982769	+	0.882953i
$401$	−31.1377	−	17.9773i	−1.55494	−	0.897745i	−0.997728	−	0.0673752i	$-0.978538\pi$
$401$	−31.1377	−	17.9773i	−1.55494	−	0.897745i	−0.557213	−	0.830370i	$-0.688129\pi$
$402$	−0.389972	+	4.93787i	−0.0194500	+	0.246279i
$403$	−2.34830	+	1.76037i	−0.116977	+	0.0876905i
$404$	−3.37778	+	21.2516i	−0.168051	+	1.05731i
$405$	−8.93495	+	15.4758i	−0.443981	+	0.768998i
$406$	3.50103	−	5.09107i	0.173753	−	0.252665i
$407$	8.59367	+	14.8847i	0.425973	+	0.737806i
$408$	−4.63800	+	19.2494i	−0.229615	+	0.952987i
$409$	−3.98302	+	2.29959i	−0.196947	+	0.113708i	−0.595231	−	0.803555i	$-0.702939\pi$
$409$	−3.98302	+	2.29959i	−0.196947	+	0.113708i	0.398283	+	0.917262i	$0.369606\pi$
$410$	−35.0678	+	16.7148i	−1.73188	+	0.825484i
$411$	21.6574			1.06828
$412$	2.44050	+	6.36809i	0.120235	+	0.313733i
$413$	−3.23332	−	1.86676i	−0.159101	−	0.0918571i
$414$	−1.94464	+	2.82781i	−0.0955737	+	0.138980i
$415$	26.6214			1.30679
$416$	−14.6026	+	14.2395i	−0.715953	+	0.698148i
$417$	−51.4860			−2.52128
$418$	18.1011	−	26.3219i	0.885355	−	1.28745i
$419$	33.6915	+	19.4518i	1.64594	+	0.950284i	0.978663	+	0.205474i	$0.0658736\pi$
$419$	33.6915	+	19.4518i	1.64594	+	0.950284i	0.667277	+	0.744810i	$0.267460\pi$
$420$	9.70241	+	25.3168i	0.473429	+	1.23533i
$421$	−25.5891			−1.24714			−0.623568	−	0.781769i	$-0.714317\pi$
$421$	−25.5891			−1.24714			−0.623568	+	0.781769i	$0.714317\pi$
$422$	5.63634	−	2.68651i	0.274373	−	0.130777i
$423$	20.1365	−	11.6258i	0.979070	−	0.565266i
$424$	0.415995	−	1.72653i	0.0202025	−	0.0838477i
$425$	−8.77027	−	15.1906i	−0.425421	−	0.736850i
$426$	−13.1249	+	19.0857i	−0.635904	+	0.924707i
$427$	−5.01870	+	8.69264i	−0.242872	+	0.420666i
$428$	−0.287122	+	1.80645i	−0.0138786	+	0.0873182i
$429$	−29.6495	−	12.6731i	−1.43149	−	0.611864i
$430$	−3.47633	+	44.0177i	−0.167643	+	2.12272i
$431$	−14.9148	−	8.61104i	−0.718419	−	0.414779i	0.0957515	−	0.995405i	$-0.469475\pi$
$431$	−14.9148	−	8.61104i	−0.718419	−	0.414779i	−0.814170	+	0.580626i	$0.802808\pi$
$432$	−6.69826	−	7.45549i	−0.322270	−	0.358702i
$433$	−9.17891	−	15.8983i	−0.441110	−	0.764025i	0.556662	−	0.830739i	$-0.312082\pi$
$433$	−9.17891	−	15.8983i	−0.441110	−	0.764025i	−0.997772	+	0.0667139i	$0.978749\pi$
$434$	1.73211	+	0.136795i	0.0831440	+	0.00656635i
$435$	−12.9987	−	22.5143i	−0.623238	−	1.07948i
$436$	−14.5498	−	37.9653i	−0.696808	−	1.81821i
$437$	4.09067			0.195683
$438$	16.4104	+	34.4292i	0.784117	+	1.64509i
$439$	17.6824	−	30.6269i	0.843937	−	1.46174i	−0.0426041	−	0.999092i	$-0.513565\pi$
$439$	17.6824	−	30.6269i	0.843937	−	1.46174i	0.886541	−	0.462650i	$-0.153101\pi$
$440$	−22.5188	+	23.6910i	−1.07354	+	1.12943i
$441$	−18.6531			−0.888243
$442$	−7.24314	−	11.4394i	−0.344521	−	0.544115i
$443$		−	21.5119i		−	1.02206i	−0.859563	−	0.511030i	$-0.829264\pi$
$443$		−	21.5119i		−	1.02206i	0.859563	−	0.511030i	$-0.170736\pi$
$444$	−20.7529	−	16.8241i	−0.984887	−	0.798434i
$445$	3.82869	+	2.21050i	0.181497	+	0.104788i
$446$	−6.44718	+	3.07299i	−0.305283	+	0.145510i
$447$			34.1990i			1.61756i
$448$	12.0594	−	0.612255i	0.569753	−	0.0289263i
$449$	19.2769	−	11.1295i	0.909731	−	0.525233i	0.0293864	−	0.999568i	$-0.490645\pi$
$449$	19.2769	−	11.1295i	0.909731	−	0.525233i	0.880345	+	0.474335i	$0.157311\pi$
$450$	36.7900	+	2.90551i	1.73430	+	0.136967i
$451$	−23.6875	+	13.6760i	−1.11540	+	0.643978i
$452$	−4.31594	+	5.32381i	−0.203005	+	0.250411i
$453$	21.4310	−	37.1196i	1.00692	−	1.74403i
$454$	20.6082	+	1.62754i	0.967189	+	0.0763844i
$455$	−17.0477	−	7.28673i	−0.799210	−	0.341607i
$456$	−11.6312	+	48.2736i	−0.544680	+	2.26062i
$457$	15.2508	+	8.80505i	0.713402	+	0.411883i	0.812320	−	0.583213i	$-0.198205\pi$
$457$	15.2508	+	8.80505i	0.713402	+	0.411883i	−0.0989172	+	0.995096i	$0.531538\pi$
$458$	9.75073	−	14.1791i	0.455622	−	0.662547i
$459$	5.76194	−	3.32666i	0.268944	−	0.155275i
$460$	−4.13362	−	0.657008i	−0.192731	−	0.0306332i
$461$	−13.2686	−	22.9818i	−0.617979	−	1.07037i	−0.989854	−	0.142088i	$-0.954618\pi$
$461$	−13.2686	−	22.9818i	−0.617979	−	1.07037i	0.371875	−	0.928283i	$-0.378715\pi$
$462$	8.21351	+	17.2321i	0.382127	+	0.801708i
$463$			24.6645i			1.14626i	0.819466	+	0.573128i	$0.194270\pi$
$463$			24.6645i			1.14626i	−0.819466	+	0.573128i	$0.805730\pi$
$464$	−11.3279	+	2.39494i	−0.525887	+	0.111182i
$465$	3.65534	−	6.33124i	0.169512	−	0.293604i
$466$	−9.15386	+	13.3112i	−0.424044	+	0.616628i
$467$		−	16.4718i		−	0.762226i	−0.924528	−	0.381113i	$-0.875541\pi$
$467$		−	16.4718i		−	0.762226i	0.924528	−	0.381113i	$-0.124459\pi$
$468$	28.4663	+	1.08091i	1.31586	+	0.0499652i
$469$			2.00523i			0.0925931i
$470$	23.3655	+	16.0680i	1.07777	+	0.741163i
$471$	−11.7031	+	20.2703i	−0.539249	+	0.934007i
$472$	1.98157	+	6.70980i	0.0912094	+	0.308844i
$473$			31.0888i			1.42946i
$474$	−5.57125	+	2.65549i	−0.255896	+	0.121971i
$475$	−21.9941	−	38.0949i	−1.00916	−	1.74791i
$476$	−1.25825	+	7.91641i	−0.0576720	+	0.362848i
$477$	−2.14811	+	1.24021i	−0.0983551	+	0.0567853i
$478$	−28.7151	−	19.7469i	−1.31340	−	0.903200i
$479$	−28.7794	−	16.6158i	−1.31496	−	0.759194i	−0.332050	−	0.943262i	$-0.607740\pi$
$479$	−28.7794	−	16.6158i	−1.31496	−	0.759194i	−0.982914	+	0.184068i	$0.941073\pi$
$480$	19.5066	−	46.9123i	0.890349	−	2.14124i
$481$	18.1379	−	2.18099i	0.827015	−	0.0994447i
$482$	−0.0199222	+	0.252257i	−0.000907429	+	0.0114900i
$483$	−1.22223	+	2.11696i	−0.0556132	+	0.0963249i
$484$	−0.638297	+	0.787354i	−0.0290135	+	0.0357888i
$485$	42.8886	−	24.7617i	1.94747	−	1.12437i
$486$	2.37669	−	30.0939i	0.107809	−	1.36509i
$487$	−10.7320	+	6.19614i	−0.486315	+	0.280774i	−0.723044	−	0.690802i	$-0.757258\pi$
$487$	−10.7320	+	6.19614i	−0.486315	+	0.280774i	0.236730	+	0.971576i	$0.423924\pi$
$488$	18.0390	−	5.32738i	0.816588	−	0.241159i
$489$		−	10.7678i		−	0.486936i
$490$	−9.78806	−	20.5355i	−0.442179	−	0.927698i
$491$	−9.13776	−	5.27569i	−0.412381	−	0.238089i	0.279431	−	0.960166i	$-0.409854\pi$
$491$	−9.13776	−	5.27569i	−0.412381	−	0.238089i	−0.691812	+	0.722077i	$0.743187\pi$
$492$	26.7739	−	33.0262i	1.20706	−	1.48894i
$493$		−	7.68612i		−	0.346165i
$494$	−18.1643	−	28.6876i	−0.817252	−	1.29072i
$495$	45.6516			2.05189
$496$	−2.17601	−	2.42200i	−0.0977058	−	0.108751i
$497$	−4.68858	+	8.12085i	−0.210311	+	0.364270i
$498$	−26.3002	+	12.5358i	−1.17854	+	0.561740i
$499$	31.2661			1.39966			0.699830	−	0.714309i	$-0.253259\pi$
$499$	31.2661			1.39966			0.699830	+	0.714309i	$0.253259\pi$
$500$	3.91524	+	10.2162i	0.175095	+	0.456881i
$501$	22.8627	+	39.5993i	1.02143	+	1.76917i
$502$	2.24779	−	28.4618i	0.100324	−	1.27031i
$503$	2.06167	+	3.57092i	0.0919253	+	0.159219i	0.908321	−	0.418273i	$-0.137365\pi$
$503$	2.06167	+	3.57092i	0.0919253	+	0.159219i	−0.816396	+	0.577493i	$0.804031\pi$
$504$	−12.2238	−	11.6190i	−0.544493	−	0.517551i
$505$	31.7429	+	18.3268i	1.41254	+	0.815530i
$506$	−2.93781	−	0.232015i	−0.130601	−	0.0103143i
$507$	−24.7726	+	23.6842i	−1.10019	+	1.05185i
$508$	10.6643	+	1.69501i	0.473151	+	0.0752038i
$509$	−11.0588	+	19.1544i	−0.490172	+	0.849002i	−0.999936	−	0.0113120i	$-0.996399\pi$
$509$	−11.0588	+	19.1544i	−0.490172	+	0.849002i	0.509764	+	0.860314i	$0.329733\pi$
$510$	27.7901	+	19.1107i	1.23057	+	0.846238i
$511$	7.72016	+	13.3717i	0.341520	+	0.591530i
$512$	−17.1700	−	14.7374i	−0.758812	−	0.651309i
$513$	14.4498	−	8.34259i	0.637973	−	0.368334i
$514$	0.120566	+	0.252948i	0.00531792	+	0.0111571i
$515$	11.6165			0.511882
$516$	−17.2932	−	45.1236i	−0.761289	−	1.98646i
$517$	17.2909	+	9.98293i	0.760455	+	0.439049i
$518$	−8.91157	−	6.12832i	−0.391552	−	0.269263i
$519$	−37.4328			−1.64312
$520$	13.7475	+	31.9062i	0.602867	+	1.39918i
$521$	36.7823			1.61146			0.805731	−	0.592281i	$-0.201773\pi$
$521$	36.7823			1.61146			0.805731	+	0.592281i	$0.201773\pi$
$522$	13.3247	+	9.16313i	0.583205	+	0.401059i
$523$	−25.6362	−	14.8011i	−1.12099	−	0.647205i	−0.179338	−	0.983788i	$-0.557396\pi$
$523$	−25.6362	−	14.8011i	−1.12099	−	0.647205i	−0.941654	+	0.336582i	$0.890729\pi$
$524$	−25.2549	+	9.67869i	−1.10327	+	0.422816i
$525$	26.2859			1.14721
$526$	−4.49410	−	9.42869i	−0.195952	−	0.411110i
$527$	1.87183	−	1.08070i	0.0815384	−	0.0470762i
$528$	11.0912	−	34.0091i	0.482682	−	1.48005i
$529$	11.3113	+	19.5918i	0.491796	+	0.851816i
$530$	−2.49257	−	1.71409i	−0.108270	−	0.0744555i
$531$	4.88580	−	8.46245i	0.212026	−	0.367239i
$532$	−3.15545	+	19.8528i	−0.136806	+	0.860726i
$533$	3.47084	+	28.8647i	0.150339	+	1.25027i
$534$	−4.82340	−	0.380931i	−0.208729	−	0.0164845i
$535$	2.69825	+	1.55783i	0.116655	+	0.0673510i
$536$	2.58881	−	2.72358i	0.111820	−	0.117641i
$537$	6.44978	+	11.1713i	0.278329	+	0.482079i
$538$	2.06047	−	26.0900i	0.0888333	−	1.12482i
$539$	−8.00858	−	13.8713i	−0.344954	−	0.597478i
$540$	−15.9414	+	6.10937i	−0.686008	+	0.262906i
$541$	22.5906			0.971245			0.485623	−	0.874169i	$-0.338593\pi$
$541$	22.5906			0.971245			0.485623	+	0.874169i	$0.338593\pi$
$542$	−12.0620	+	5.74923i	−0.518105	+	0.246950i
$543$	27.9486	−	48.4083i	1.19939	−	2.07740i
$544$	11.9293	−	9.12791i	0.511465	−	0.391356i
$545$	−69.2549			−2.96655
$546$	20.2733	−	0.828801i	0.867617	−	0.0354694i
$547$		−	22.1421i		−	0.946729i	−0.880867	−	0.473365i	$-0.843039\pi$
$547$		−	22.1421i		−	0.946729i	0.880867	−	0.473365i	$-0.156961\pi$
$548$	−12.7627	−	10.3465i	−0.545196	−	0.441982i
$549$	−22.7509	−	13.1353i	−0.970986	−	0.560599i
$550$	13.6349	+	28.6061i	0.581393	+	1.21977i
$551$		−	19.2752i		−	0.821153i
$552$	4.39312	−	1.29740i	0.186984	−	0.0552210i
$553$	−2.16378	+	1.24926i	−0.0920134	+	0.0531240i
$554$	−1.11133	+	14.0718i	−0.0472160	+	0.597855i
$555$	−39.4098	+	22.7533i	−1.67285	+	0.965822i
$556$	30.3406	+	24.5967i	1.28673	+	1.04313i
$557$	−8.54145	+	14.7942i	−0.361913	+	0.626851i	−0.988276	−	0.152680i	$-0.951209\pi$
$557$	−8.54145	+	14.7942i	−0.361913	+	0.626851i	0.626363	+	0.779532i	$0.284543\pi$
$558$	−0.358028	+	4.53339i	−0.0151565	+	0.191914i
$559$	30.3851	+	12.9876i	1.28515	+	0.549315i
$560$	6.37715	−	19.5544i	0.269484	−	0.826323i
$561$	20.5652	+	11.8733i	0.868265	+	0.501293i
$562$	−12.9583	−	8.91118i	−0.546613	−	0.375896i
$563$	−33.4112	+	19.2900i	−1.40811	+	0.812975i	−0.995206	−	0.0977986i	$-0.968820\pi$
$563$	−33.4112	+	19.2900i	−1.40811	+	0.812975i	−0.412907	+	0.910773i	$0.635487\pi$
$564$	−30.6499	−	4.87157i	−1.29059	−	0.205130i
$565$	5.83698	+	10.1099i	0.245564	+	0.425328i
$566$	1.71323	−	0.816596i	0.0720124	−	0.0343241i
$567$		−	7.91736i		−	0.332498i
$568$	16.8524	−	4.97695i	0.707113	−	0.208828i
$569$	−10.4819	+	18.1552i	−0.439424	+	0.761104i	−0.997645	−	0.0685878i	$-0.978151\pi$
$569$	−10.4819	+	18.1552i	−0.439424	+	0.761104i	0.558221	+	0.829692i	$0.311484\pi$
$570$	69.6920	+	47.9259i	2.91908	+	2.00740i
$571$			35.3147i			1.47787i	0.673774	+	0.738937i	$0.264672\pi$
$571$			35.3147i			1.47787i	−0.673774	+	0.738937i	$0.735328\pi$
$572$	11.4180	+	21.6329i	0.477411	+	0.904517i
$573$			3.86961i			0.161655i
$574$	9.75264	−	14.1819i	0.407067	−	0.591941i
$575$	−2.02896	+	3.51426i	−0.0846135	+	0.146555i
$576$	1.60243	+	31.5626i	0.0667681	+	1.31511i
$577$		−	40.8549i		−	1.70081i	−0.526128	−	0.850405i	$-0.676357\pi$
$577$		−	40.8549i		−	1.70081i	0.526128	−	0.850405i	$-0.323643\pi$
$578$	−6.05393	−	12.7012i	−0.251810	−	0.528301i
$579$	22.4413	+	38.8695i	0.932630	+	1.61536i
$580$	−3.09582	+	19.4776i	−0.128547	+	0.808763i
$581$	−10.2146	+	5.89737i	−0.423771	+	0.244664i
$582$	−30.7111	+	44.6588i	−1.27301	+	1.85117i
$583$	−1.84455	−	1.06495i	−0.0763935	−	0.0441058i
$584$	6.77745	−	28.1289i	0.280453	−	1.16398i
$585$	19.0713	−	44.6184i	0.788501	−	1.84474i
$586$	−11.7901	−	0.931128i	−0.487043	−	0.0384645i
$587$	5.89364	−	10.2081i	0.243256	−	0.421332i	−0.718384	−	0.695647i	$-0.755118\pi$
$587$	5.89364	−	10.2081i	0.243256	−	0.421332i	0.961640	+	0.274315i	$0.0884510\pi$
$588$	19.3399	+	15.6786i	0.797565	+	0.646575i
$589$	4.69419	−	2.71019i	0.193421	−	0.111671i
$590$	11.8802	+	0.938248i	0.489101	+	0.0386271i
$591$	−37.5833	+	21.6987i	−1.54597	+	0.892566i
$592$	4.19218	+	19.8288i	0.172297	+	0.814959i
$593$			37.3071i			1.53202i	0.642830	+	0.766009i	$0.277760\pi$
$593$			37.3071i			1.53202i	−0.642830	+	0.766009i	$0.722240\pi$
$594$	−10.8506	+	5.17185i	−0.445206	+	0.212203i
$595$	11.8245	+	6.82688i	0.484757	+	0.279875i
$596$	16.3381	−	20.1535i	0.669236	−	0.825518i
$597$		−	48.2544i		−	1.97492i
$598$	−1.45405	+	2.77439i	−0.0594607	+	0.113453i
$599$	−20.3759			−0.832536			−0.416268	−	0.909242i	$-0.636662\pi$
$599$	−20.3759			−0.832536			−0.416268	+	0.909242i	$0.636662\pi$
$600$	−35.7025	−	33.9358i	−1.45755	−	1.38542i
$601$	−4.80175	+	8.31688i	−0.195868	+	0.339253i	−0.947185	−	0.320689i	$-0.896086\pi$
$601$	−4.80175	+	8.31688i	−0.195868	+	0.339253i	0.751317	+	0.659942i	$0.229419\pi$
$602$	−8.41729	−	17.6596i	−0.343063	−	0.719751i
$603$	−5.24822			−0.213724
$604$	−30.3626	+	11.6362i	−1.23544	+	0.473469i
$605$	0.863249	+	1.49519i	0.0350961	+	0.0607882i
$606$	−39.9898	−	3.15822i	−1.62447	−	0.128294i
$607$	−13.4951	−	23.3742i	−0.547749	−	0.948729i	−0.998428	−	0.0560433i	$-0.982152\pi$
$607$	−13.4951	−	23.3742i	−0.547749	−	0.948729i	0.450679	−	0.892686i	$-0.351182\pi$
$608$	29.9163	−	22.8910i	1.21327	−	0.928351i
$609$	9.97510	+	5.75913i	0.404211	+	0.233372i
$610$	2.52244	−	31.9395i	0.102131	−	1.29319i
$611$	16.9804	−	12.7292i	0.686954	−	0.514967i
$612$	−20.7193	−	3.29318i	−0.837529	−	0.133119i
$613$	1.49345	−	2.58672i	0.0603197	−	0.104477i	−0.834289	−	0.551328i	$-0.814121\pi$
$613$	1.49345	−	2.58672i	0.0603197	−	0.104477i	0.894608	+	0.446851i	$0.147455\pi$
$614$	−15.6628	+	22.7762i	−0.632099	+	0.919173i
$615$	−36.2097	−	62.7170i	−1.46011	−	2.52899i
$616$	3.39217	−	14.0787i	0.136674	−	0.567248i
$617$	30.9399	−	17.8632i	1.24559	−	0.719144i	0.275366	−	0.961339i	$-0.411201\pi$
$617$	30.9399	−	17.8632i	1.24559	−	0.719144i	0.970227	+	0.242196i	$0.0778676\pi$
$618$	−11.4763	+	5.47008i	−0.461644	+	0.220039i
$619$	−19.9292			−0.801024			−0.400512	−	0.916292i	$-0.631168\pi$
$619$	−19.9292			−0.801024			−0.400512	+	0.916292i	$0.631168\pi$
$620$	−5.17875	+	1.98470i	−0.207984	+	0.0797076i
$621$	−1.33300	−	0.769606i	−0.0534913	−	0.0308832i
$622$	20.0169	−	29.1078i	0.802605	−	1.16712i
$623$	−1.95875			−0.0784755
$624$	−28.6059	−	25.0477i	−1.14515	−	1.00271i
$625$	−14.3928			−0.575711
$626$	3.99316	−	5.80669i	0.159599	−	0.232082i
$627$	51.5735	+	29.7760i	2.05965	+	1.18914i
$628$	16.5805	−	6.35429i	0.661633	−	0.253564i
$629$	−13.4540			−0.536447
$630$	−25.9319	+	12.3602i	−1.03315	+	0.492442i
$631$	−16.1192	+	9.30643i	−0.641695	+	0.370483i	−0.785267	−	0.619157i	$-0.787474\pi$
$631$	−16.1192	+	9.30643i	−0.641695	+	0.370483i	0.143572	+	0.989640i	$0.454141\pi$
$632$	4.55176	+	1.09671i	0.181059	+	0.0436249i
$633$	5.81986	+	10.0803i	0.231319	+	0.400656i
$634$	17.7954	−	25.8774i	0.706746	−	1.02772i
$635$	9.19657	−	15.9289i	0.364955	−	0.632120i
$636$	3.26964	+	0.519686i	0.129650	+	0.0206069i
$637$	−16.9030	+	2.03250i	−0.669720	+	0.0805307i
$638$	−1.09326	+	13.8429i	−0.0432824	+	0.548047i
$639$	−21.2544	−	12.2712i	−0.840812	−	0.485443i
$640$	−33.9069	+	18.3264i	−1.34029	+	0.724414i
$641$	−0.401423	−	0.695285i	−0.0158553	−	0.0274621i	0.857989	−	0.513668i	$-0.171714\pi$
$641$	−0.401423	−	0.695285i	−0.0158553	−	0.0274621i	−0.873844	+	0.486206i	$0.838380\pi$
$642$	−3.39926	−	0.268459i	−0.134158	−	0.0105952i
$643$	10.5732	+	18.3133i	0.416965	+	0.722205i	0.995633	−	0.0933589i	$-0.0297604\pi$
$643$	10.5732	+	18.3133i	0.416965	+	0.722205i	−0.578667	+	0.815564i	$0.696427\pi$
$644$	1.73160	−	0.663619i	0.0682347	−	0.0261502i
$645$	−82.3130			−3.24107
$646$	10.7593	+	22.5732i	0.423320	+	0.888132i
$647$	−19.5120	+	33.7957i	−0.767095	+	1.32865i	0.172037	+	0.985090i	$0.444965\pi$
$647$	−19.5120	+	33.7957i	−0.767095	+	1.32865i	−0.939132	+	0.343557i	$0.888368\pi$
$648$	−10.2215	+	10.7536i	−0.401540	+	0.422443i
$649$	8.39074			0.329365
$650$	33.6548	−	1.37585i	1.32005	−	0.0539655i
$651$			3.23904i			0.126948i
$652$	−5.14417	+	6.34545i	−0.201461	+	0.248507i
$653$	41.6632	+	24.0543i	1.63041	+	0.941316i	0.983967	+	0.178351i	$0.0570762\pi$
$653$	41.6632	+	24.0543i	1.63041	+	0.941316i	0.646440	+	0.762965i	$0.276257\pi$
$654$	68.4193	−	32.6115i	2.67541	−	1.27521i
$655$			46.0692i			1.80007i
$656$	−31.5556	+	6.67145i	−1.23204	+	0.260476i
$657$	−34.9973	+	20.2057i	−1.36537	+	0.788299i
$658$	−12.5248	−	0.989154i	−0.488267	−	0.0385612i
$659$	13.6735	−	7.89443i	0.532646	−	0.307523i	−0.209447	−	0.977820i	$-0.567166\pi$
$659$	13.6735	−	7.89443i	0.532646	−	0.307523i	0.742093	+	0.670297i	$0.233833\pi$
$660$	−47.3326	−	38.3719i	−1.84242	−	1.49362i
$661$	−0.142144	+	0.246200i	−0.00552876	+	0.00957608i	−0.868777	−	0.495204i	$-0.835093\pi$
$661$	−0.142144	+	0.246200i	−0.00552876	+	0.00957608i	0.863248	+	0.504780i	$0.168427\pi$
$662$	18.7157	+	1.47808i	0.727405	+	0.0574473i
$663$	20.1959	−	15.1396i	0.784343	−	0.587974i
$664$	21.4875	+	5.17725i	0.833875	+	0.200916i
$665$	29.6535	+	17.1204i	1.14991	+	0.663902i
$666$	16.0394	−	23.3239i	0.621516	−	0.903784i
$667$	−1.53992	+	0.889073i	−0.0596259	+	0.0344251i
$668$	5.44508	−	34.2581i	0.210676	−	1.32549i
$669$	−6.65711	−	11.5304i	−0.257379	−	0.445793i
$670$	−2.75396	−	5.77785i	−0.106395	−	0.223218i
$671$		−	22.5581i		−	0.870848i
$672$	2.90776	+	22.3214i	0.112169	+	0.861066i
$673$	7.08159	−	12.2657i	0.272975	−	0.472807i	−0.696647	−	0.717414i	$-0.745326\pi$
$673$	7.08159	−	12.2657i	0.272975	−	0.472807i	0.969622	+	0.244607i	$0.0786589\pi$
$674$	−13.2796	+	19.3106i	−0.511510	+	0.743818i
$675$			16.5516i			0.637071i
$676$	25.9132	−	2.12229i	0.996663	−	0.0816264i
$677$			39.2276i			1.50764i	0.657081	+	0.753820i	$0.271791\pi$
$677$			39.2276i			1.50764i	−0.657081	+	0.753820i	$0.728209\pi$
$678$	−10.5272	−	7.23938i	−0.404296	−	0.278027i
$679$	−10.9708	+	19.0020i	−0.421022	+	0.729231i
$680$	−7.24678	−	24.5383i	−0.277901	−	0.941000i
$681$			38.5372i			1.47675i
$682$	−3.52495	+	1.68014i	−0.134977	+	0.0643358i
$683$	3.76785	+	6.52610i	0.144173	+	0.249714i	0.929064	−	0.369919i	$-0.120615\pi$
$683$	3.76785	+	6.52610i	0.144173	+	0.249714i	−0.784891	+	0.619633i	$0.787281\pi$
$684$	−51.9599	−	8.25864i	−1.98674	−	0.315777i
$685$	−24.2364	+	13.9929i	−0.926027	+	0.534642i
$686$	20.6166	+	14.1777i	0.787145	+	0.541306i
$687$	27.7816	+	16.0397i	1.05994	+	0.611954i
$688$	−11.3664	+	34.8529i	−0.433338	+	1.32875i
$689$	−1.81142	+	1.35791i	−0.0690097	+	0.0517323i
$690$	0.614301	−	7.77836i	0.0233860	−	0.296117i
$691$	−1.92252	+	3.32990i	−0.0731360	+	0.126675i	−0.900274	−	0.435323i	$-0.856634\pi$
$691$	−1.92252	+	3.32990i	−0.0731360	+	0.126675i	0.827138	+	0.561999i	$0.189967\pi$
$692$	22.0591	+	17.8830i	0.838562	+	0.679811i
$693$	−17.5164	+	10.1131i	−0.665393	+	0.384165i
$694$	1.12421	−	14.2349i	0.0426743	−	0.540348i
$695$	57.6171	−	33.2652i	2.18554	−	1.26182i
$696$	−6.11335	−	20.7004i	−0.231726	−	0.784646i
$697$		−	21.4108i		−	0.810992i
$698$	15.2301	+	31.9529i	0.576467	+	1.20944i
$699$	−26.0810	−	15.0579i	−0.986476	−	0.569542i
$700$	−15.4903	−	12.5577i	−0.585476	−	0.474638i
$701$			34.5455i			1.30476i	0.757890	+	0.652382i	$0.226230\pi$
$701$			34.5455i			1.30476i	−0.757890	+	0.652382i	$0.773770\pi$
$702$	0.521876	+	12.7656i	0.0196969	+	0.481807i
$703$	−33.7400			−1.27253
$704$	−22.7834	+	14.7429i	−0.858681	+	0.555642i
$705$	−26.4316	+	45.7808i	−0.995470	+	1.72421i
$706$	−4.92780	+	2.34879i	−0.185460	+	0.0883979i
$707$	−16.2396			−0.610751
$708$	−12.1787	+	4.66736i	−0.457703	+	0.175410i
$709$	−13.2970	−	23.0310i	−0.499378	−	0.864948i	0.500622	−	0.865666i	$-0.333105\pi$
$709$	−13.2970	−	23.0310i	−0.499378	−	0.864948i	−1.00000		0.000718230i	$0.999771\pi$
$710$	2.35652	−	29.8385i	0.0884386	−	1.11982i
$711$	−3.26964	−	5.66319i	−0.122621	−	0.212386i
$712$	2.66044	+	2.52880i	0.0997042	+	0.0947706i
$713$	−0.433040	−	0.250016i	−0.0162175	−	0.00936316i
$714$	−14.8966	−	1.17646i	−0.557489	−	0.0440281i
$715$	41.3684	−	4.97435i	1.54709	−	0.186030i
$716$	1.53611	−	9.66456i	0.0574072	−	0.361182i
$717$	32.4831	−	56.2625i	1.21311	−	2.10116i
$718$	16.3759	+	11.2614i	0.611142	+	0.420271i
$719$	19.6503	+	34.0354i	0.732834	+	1.26931i	0.955667	+	0.294449i	$0.0951361\pi$
$719$	19.6503	+	34.0354i	0.732834	+	1.26931i	−0.222833	+	0.974857i	$0.571531\pi$
$720$	51.1790	+	16.6907i	1.90733	+	0.622025i
$721$	−4.45720	+	2.57337i	−0.165995	+	0.0958372i
$722$	15.4210	+	32.3535i	0.573910	+	1.20407i
$723$	−0.471719			−0.0175434
$724$	−39.5965	+	15.1749i	−1.47159	+	0.563972i
$725$	16.5592	+	9.56046i	0.614994	+	0.355067i
$726$	−1.55690	−	1.07066i	−0.0577822	−	0.0397357i
$727$	−28.1259			−1.04313			−0.521566	−	0.853211i	$-0.674652\pi$
$727$	−28.1259			−1.04313			−0.521566	+	0.853211i	$0.674652\pi$
$728$	−12.3430	−	9.19688i	−0.457461	−	0.340859i
$729$	40.5391			1.50145
$730$	−40.6093	−	27.9263i	−1.50302	−	1.03360i
$731$	−21.0755	−	12.1679i	−0.779505	−	0.450047i
$732$	12.5480	+	32.7419i	0.463787	+	1.21018i
$733$	30.6364			1.13158			0.565791	−	0.824549i	$-0.308571\pi$
$733$	30.6364			1.13158			0.565791	+	0.824549i	$0.308571\pi$
$734$	12.4332	+	26.0851i	0.458919	+	0.962819i
$735$	36.7266	−	21.2041i	1.35468	−	0.782126i
$736$	−3.20868	−	1.33420i	−0.118273	−	0.0491792i
$737$	−2.25329	−	3.90281i	−0.0830010	−	0.143762i
$738$	37.1178	+	25.5252i	1.36632	+	0.939597i
$739$	13.8293	−	23.9531i	0.508721	−	0.881130i	−0.491228	−	0.871031i	$-0.663452\pi$
$739$	13.8293	−	23.9531i	0.508721	−	0.881130i	0.999949	−	0.0100991i	$-0.00321468\pi$
$740$	34.0942	+	5.41903i	1.25333	+	0.199207i
$741$	50.6472	−	37.9671i	1.86057	−	1.39476i
$742$	1.33611	+	0.105520i	0.0490502	+	0.00387377i
$743$	−17.1394	−	9.89546i	−0.628785	−	0.363029i	0.151496	−	0.988458i	$-0.451591\pi$
$743$	−17.1394	−	9.89546i	−0.628785	−	0.363029i	−0.780281	+	0.625429i	$0.784924\pi$
$744$	4.18169	−	4.39938i	0.153308	−	0.161289i
$745$	−22.0961	−	38.2715i	−0.809538	−	1.40216i
$746$	−1.22634	+	15.5280i	−0.0448993	+	0.568521i
$747$	−15.4350	−	26.7342i	−0.564736	−	0.978152i
$748$	−6.44674	−	16.8217i	−0.235716	−	0.615063i
$749$	−1.38041			−0.0504392
$750$	−18.4112	+	8.77552i	−0.672280	+	0.320437i
$751$	9.60222	−	16.6315i	0.350390	−	0.606893i	−0.635928	−	0.771749i	$-0.719382\pi$
$751$	9.60222	−	16.6315i	0.350390	−	0.606893i	0.986318	+	0.164855i	$0.0527157\pi$
$752$	15.7346	+	17.5134i	0.573782	+	0.638647i
$753$	53.2234			1.93957
$754$	13.0729	+	6.85150i	0.476088	+	0.249517i
$755$			55.3865i			2.01572i
$756$	4.76328	−	5.87561i	0.173239	−	0.213694i
$757$	8.30082	+	4.79248i	0.301698	+	0.174186i	0.643206	−	0.765694i	$-0.277604\pi$
$757$	8.30082	+	4.79248i	0.301698	+	0.174186i	−0.341507	+	0.939879i	$0.610937\pi$
$758$	−4.83422	−	10.1422i	−0.175587	−	0.368383i
$759$		−	5.49368i		−	0.199408i
$760$	−18.1735	−	61.5371i	−0.659221	−	2.23219i
$761$	−3.55022	+	2.04972i	−0.128695	+	0.0743023i	−0.562966	−	0.826480i	$-0.690340\pi$
$761$	−3.55022	+	2.04972i	−0.128695	+	0.0743023i	0.434270	+	0.900783i	$0.357006\pi$
$762$	−1.58483	+	20.0673i	−0.0574123	+	0.726962i
$763$	26.5729	−	15.3419i	0.962005	−	0.555414i
$764$	1.84865	−	2.28036i	0.0668820	−	0.0825005i
$765$	−17.8677	+	30.9478i	−0.646010	+	1.11892i
$766$	0.838243	−	10.6139i	0.0302869	−	0.383497i
$767$	3.50529	−	8.20083i	0.126569	−	0.296115i
$768$	24.8681	−	34.0717i	0.897351	−	1.22946i
$769$	12.3725	+	7.14328i	0.446165	+	0.257593i	0.706209	−	0.708003i	$-0.250404\pi$
$769$	12.3725	+	7.14328i	0.446165	+	0.257593i	−0.260044	+	0.965597i	$0.583737\pi$
$770$	−20.3253	−	13.9773i	−0.732472	−	0.503708i
$771$	−0.452385	+	0.261184i	−0.0162922	+	0.00940632i
$772$	5.34474	−	33.6268i	0.192361	−	1.21026i
$773$	−9.10369	−	15.7681i	−0.327437	−	0.567138i	0.654565	−	0.756005i	$-0.272852\pi$
$773$	−9.10369	−	15.7681i	−0.327437	−	0.567138i	−0.982003	+	0.188868i	$0.939518\pi$
$774$	46.2198	−	22.0303i	1.66134	−	0.791862i
$775$			5.37698i			0.193147i
$776$	39.4331	−	11.6456i	1.41557	−	0.418053i
$777$	10.0810	−	17.4607i	0.361652	−	0.626400i
$778$	0.897806	+	0.617405i	0.0321879	+	0.0221350i
$779$		−	53.6940i		−	1.92379i
$780$	−57.2769	+	30.2312i	−2.05084	+	1.08245i
$781$		−	21.0743i		−	0.754098i
$782$	1.30712	−	1.90077i	0.0467427	−	0.0679713i
$783$	−3.62638	+	6.28108i	−0.129596	+	0.224467i
$784$	−3.90676	−	18.4788i	−0.139527	−	0.659956i
$785$		−	30.2455i		−	1.07951i
$786$	−21.6936	−	45.5134i	−0.773783	−	1.62341i
$787$	−6.01748	−	10.4226i	−0.214500	−	0.371525i	0.738618	−	0.674125i	$-0.235479\pi$
$787$	−6.01748	−	10.4226i	−0.214500	−	0.371525i	−0.953118	+	0.302599i	$0.902146\pi$
$788$	32.5140	+	5.16787i	1.15826	+	0.184098i
$789$	16.8627	−	9.73569i	0.600329	−	0.346600i
$790$	4.51897	−	6.57131i	0.160778	−	0.233797i
$791$	−4.47927	−	2.58611i	−0.159264	−	0.0919513i
$792$	36.8477	+	8.87819i	1.30933	+	0.315473i
$793$	−22.0476	−	9.42383i	−0.782933	−	0.334650i
$794$	−19.4683	−	1.53752i	−0.690905	−	0.0545647i
$795$	2.81965	−	4.88377i	0.100003	−	0.173210i
$796$	−23.0529	+	28.4363i	−0.817088	+	1.00790i
$797$	−37.8735	+	21.8663i	−1.34155	+	0.774544i	−0.987035	−	0.160507i	$-0.948687\pi$
$797$	−37.8735	+	21.8663i	−1.34155	+	0.774544i	−0.354514	+	0.935051i	$0.615354\pi$
$798$	−37.3576	−	2.95034i	−1.32244	−	0.104441i
$799$	−13.5351	+	7.81451i	−0.478838	+	0.276457i
$800$	4.82704	+	37.0547i	0.170662	+	1.31008i
$801$		−	5.12655i		−	0.181138i
$802$	−45.9002	+	21.8779i	−1.62079	+	0.772537i
$803$	−30.0517	−	17.3504i	−1.06050	−	0.612281i
$804$	5.44147	+	4.41132i	0.191906	+	0.155575i
$805$		−	3.15873i		−	0.111331i
$806$	0.169538	+	4.14706i	0.00597171	+	0.146074i
$807$	48.7881			1.71742
$808$	22.0571	+	20.9657i	0.775968	+	0.737571i
$809$	−6.93343	+	12.0090i	−0.243766	+	0.422216i	−0.961784	−	0.273809i	$-0.911716\pi$
$809$	−6.93343	+	12.0090i	−0.243766	+	0.422216i	0.718018	+	0.696025i	$0.245050\pi$
$810$	10.8736	+	22.8130i	0.382059	+	0.801566i
$811$	−2.29509			−0.0805916			−0.0402958	−	0.999188i	$-0.512830\pi$
$811$	−2.29509			−0.0805916			−0.0402958	+	0.999188i	$0.512830\pi$
$812$	−3.12697	−	8.15932i	−0.109735	−	0.286336i
$813$	−12.4547	−	21.5722i	−0.436805	−	0.756569i
$814$	24.2311	+	1.91367i	0.849301	+	0.0670741i
$815$	6.95710	+	12.0500i	0.243697	+	0.422095i
$816$	18.7142	+	20.8298i	0.655128	+	0.729188i
$817$	−52.8531	−	30.5147i	−1.84910	−	1.06758i
$818$	−0.512082	+	6.48405i	−0.0179045	+	0.226709i
$819$	2.56661	+	21.3448i	0.0896846	+	0.745847i
$820$	−8.62386	+	54.2577i	−0.301158	+	1.89476i
$821$	2.46599	−	4.27121i	0.0860635	−	0.149066i	−0.819780	−	0.572678i	$-0.805905\pi$
$821$	2.46599	−	4.27121i	0.0860635	−	0.149066i	0.905844	+	0.423612i	$0.139238\pi$
$822$	17.3549	−	25.2368i	0.605321	−	0.880235i
$823$	20.3378	+	35.2261i	0.708931	+	1.22790i	0.965254	+	0.261313i	$0.0841555\pi$
$823$	20.3378	+	35.2261i	0.708931	+	1.22790i	−0.256323	+	0.966591i	$0.582511\pi$
$824$	9.37623	+	2.25913i	0.326636	+	0.0787007i
$825$	−51.1606	+	29.5376i	−1.78118	+	1.02837i
$826$	−4.76626	+	2.27180i	−0.165839	+	0.0790459i
$827$	−21.5663			−0.749933			−0.374967	−	0.927038i	$-0.622346\pi$
$827$	−21.5663			−0.749933			−0.374967	+	0.927038i	$0.622346\pi$
$828$	1.73687	+	4.53206i	0.0603602	+	0.157500i
$829$	−26.5594	−	15.3341i	−0.922445	−	0.532574i	−0.0380310	−	0.999277i	$-0.512109\pi$
$829$	−26.5594	−	15.3341i	−0.922445	−	0.532574i	−0.884414	+	0.466702i	$0.845442\pi$
$830$	21.3327	−	31.0211i	0.740468	−	1.07676i
$831$	−26.3143			−0.912831
$832$	4.89125	+	28.4267i	0.169574	+	0.985518i
$833$	12.5380			0.434417
$834$	−41.2576	+	59.9952i	−1.42863	+	2.07746i
$835$	−51.1704	−	29.5432i	−1.77082	−	1.02239i
$836$	−16.1671	−	42.1855i	−0.559152	−	1.45902i
$837$	−2.03955			−0.0704970
$838$	49.6649	−	23.6724i	1.71565	−	0.817748i
$839$	26.4685	−	15.2816i	0.913793	−	0.527579i	0.0321435	−	0.999483i	$-0.489767\pi$
$839$	26.4685	−	15.2816i	0.913793	−	0.527579i	0.881650	+	0.471905i	$0.156433\pi$
$840$	37.2759	+	8.98136i	1.28614	+	0.309886i
$841$	−10.3107	−	17.8586i	−0.355541	−	0.615815i
$842$	−20.5055	+	29.8182i	−0.706665	+	1.02760i
$843$	14.6587	−	25.3896i	0.504873	−	0.874465i
$844$	1.38609	−	8.72067i	0.0477111	−	0.300178i
$845$	12.4202	−	42.5101i	0.427267	−	1.46239i
$846$	2.58888	−	32.7807i	0.0890074	−	1.12702i
$847$	−0.662453	−	0.382467i	−0.0227621	−	0.0131417i
$848$	−1.67853	−	1.86828i	−0.0576408	−	0.0641570i
$849$	1.76901	+	3.06402i	0.0607124	+	0.105157i
$850$	−24.7291	−	1.95300i	−0.848201	−	0.0669872i
$851$	1.55626	+	2.69553i	0.0533480	+	0.0924014i
$852$	11.7226	+	30.5882i	0.401610	+	1.04793i
$853$	36.3580			1.24487			0.622437	−	0.782670i	$-0.286143\pi$
$853$	36.3580			1.24487			0.622437	+	0.782670i	$0.286143\pi$
$854$	6.10763	+	12.8139i	0.208999	+	0.438482i
$855$	−44.8087	+	77.6110i	−1.53243	+	2.65424i
$856$	1.87493	+	1.78215i	0.0640837	+	0.0609127i
$857$	−0.0833458			−0.00284704			−0.00142352	−	0.999999i	$-0.500453\pi$
$857$	−0.0833458			−0.00284704			−0.00142352	+	0.999999i	$0.500453\pi$
$858$	−38.5269	+	24.3943i	−1.31529	+	0.832808i
$859$			55.2828i			1.88622i	0.332476	+	0.943112i	$0.392116\pi$
$859$			55.2828i			1.88622i	−0.332476	+	0.943112i	$0.607884\pi$
$860$	48.5069	+	39.3239i	1.65407	+	1.34093i
$861$	27.7871	+	16.0429i	0.946982	+	0.546740i
$862$	−21.9860	+	10.4794i	−0.748845	+	0.356930i
$863$			14.5282i			0.494546i	0.968946	+	0.247273i	$0.0795345\pi$
$863$			14.5282i			0.494546i	−0.968946	+	0.247273i	$0.920466\pi$
$864$	−14.0552	+	1.83095i	−0.478169	+	0.0622901i
$865$	41.8904	−	24.1854i	1.42432	−	0.822330i
$866$	−25.8813	−	2.04399i	−0.879482	−	0.0694576i
$867$	22.7155	−	13.1148i	0.771458	−	0.445402i
$868$	1.54741	−	1.90876i	0.0525224	−	0.0647877i
$869$	2.80760	−	4.86291i	0.0952413	−	0.164963i
$870$	−36.6516	−	2.89459i	−1.24261	−	0.0981356i
$871$	−4.75581	+	0.571864i	−0.161144	+	0.0193769i
$872$	−55.8991	−	13.4685i	−1.89298	−	0.456101i
$873$	−49.7333	−	28.7135i	−1.68322	−	0.971806i
$874$	3.27800	−	4.76675i	0.110880	−	0.161238i
$875$	−7.15059	+	4.12839i	−0.241734	+	0.139565i
$876$	53.2696	+	8.46681i	1.79981	+	0.286067i
$877$	23.5728	+	40.8294i	0.795998	+	1.37871i	0.922203	+	0.386705i	$0.126387\pi$
$877$	23.5728	+	40.8294i	0.795998	+	1.37871i	−0.126205	+	0.992004i	$0.540280\pi$
$878$	−21.5191	−	45.1473i	−0.726234	−	1.52365i
$879$		−	22.0474i		−	0.743639i
$880$	9.56141	+	45.2250i	0.322315	+	1.52453i
$881$	11.0991	−	19.2242i	0.373937	−	0.647678i	−0.616230	−	0.787566i	$-0.711341\pi$
$881$	11.0991	−	19.2242i	0.373937	−	0.647678i	0.990167	+	0.139888i	$0.0446742\pi$
$882$	−14.9474	+	21.7359i	−0.503305	+	0.731887i
$883$			23.0291i			0.774991i	0.921872	+	0.387496i	$0.126660\pi$
$883$			23.0291i			0.774991i	−0.921872	+	0.387496i	$0.873340\pi$
$884$	−19.1342	−	0.726555i	−0.643552	−	0.0244367i
$885$			22.2160i			0.746781i
$886$	−25.0672	−	17.2383i	−0.842149	−	0.579130i
$887$	27.4780	−	47.5933i	0.922621	−	1.59803i	0.127278	−	0.991867i	$-0.459376\pi$
$887$	27.4780	−	47.5933i	0.922621	−	1.59803i	0.795343	−	0.606160i	$-0.207291\pi$
$888$	−36.2346	+	10.7010i	−1.21595	+	0.359102i
$889$			8.14918i			0.273315i
$890$	5.64390	−	2.69012i	0.189184	−	0.0901729i
$891$	8.89677	+	15.4097i	0.298053	+	0.516243i
$892$	−1.58549	+	9.97522i	−0.0530861	+	0.333995i
$893$	−33.9434	+	19.5972i	−1.13587	+	0.655796i
$894$	39.8512	+	27.4049i	1.33282	+	0.916558i
$895$	−14.4357	−	8.33444i	−0.482531	−	0.278590i
$896$	8.95020	−	14.5431i	0.299005	−	0.485851i
$897$	−5.36934	−	2.29503i	−0.179277	−	0.0766287i
$898$	2.47836	−	31.3813i	0.0827038	−	1.04721i
$899$	−1.17807	+	2.04048i	−0.0392910	+	0.0680540i
$900$	32.8669	−	40.5421i	1.09556	−	1.35140i
$901$	1.44389	−	0.833630i	0.0481030	−	0.0277723i
$902$	−3.04542	+	38.5615i	−0.101401	+	1.28396i
$903$	31.5833	−	18.2346i	1.05103	−	0.606810i
$904$	2.74517	+	9.29540i	0.0913029	+	0.309161i
$905$			72.2305i			2.40102i
$906$	−26.0810	−	54.7182i	−0.866482	−	1.81789i
$907$	−27.9245	−	16.1222i	−0.927217	−	0.535329i	−0.0412866	−	0.999147i	$-0.513146\pi$
$907$	−27.9245	−	16.1222i	−0.927217	−	0.535329i	−0.885930	+	0.463818i	$0.846479\pi$
$908$	18.4106	−	22.7099i	0.610978	−	0.753655i
$909$		−	42.5032i		−	1.40974i
$910$	−22.1520	+	14.0261i	−0.734331	+	0.464961i
$911$	−6.52220			−0.216090			−0.108045	−	0.994146i	$-0.534459\pi$
$911$	−6.52220			−0.216090			−0.108045	+	0.994146i	$0.534459\pi$
$912$	46.9314	+	52.2369i	1.55405	+	1.72974i
$913$	13.2538	−	22.9563i	0.438637	−	0.759742i
$914$	22.4813	−	10.7155i	0.743616	−	0.354438i
$915$	59.7267			1.97450
$916$	−8.70893	−	22.7245i	−0.287751	−	0.750839i
$917$	−10.2056	−	17.6766i	−0.337019	−	0.583734i
$918$	0.740791	−	9.38000i	0.0244498	−	0.309586i
$919$	22.7062	+	39.3283i	0.749009	+	1.29732i	0.948298	+	0.317381i	$0.102803\pi$
$919$	22.7062	+	39.3283i	0.749009	+	1.29732i	−0.199289	+	0.979941i	$0.563863\pi$
$920$	−4.07801	+	4.29031i	−0.134448	+	0.141447i
$921$	−44.6262	−	25.7649i	−1.47048	−	0.848984i
$922$	−37.4127	−	2.95469i	−1.23212	−	0.0973076i
$923$	−20.5973	−	8.80394i	−0.677969	−	0.289785i
$924$	26.6618	+	4.23770i	0.877109	+	0.139410i
$925$	16.7349	−	28.9858i	0.550242	−	0.953046i
$926$	28.7408	+	19.7645i	0.944482	+	0.649503i
$927$	−6.73518	−	11.6657i	−0.221212	−	0.383151i
$928$	−6.28674	+	15.1193i	−0.206372	+	0.496315i
$929$	−14.8259	+	8.55975i	−0.486423	+	0.280836i	−0.723089	−	0.690755i	$-0.757278\pi$
$929$	−14.8259	+	8.55975i	−0.486423	+	0.280836i	0.236667	+	0.971591i	$0.423945\pi$
$930$	−4.44846	−	9.33293i	−0.145871	−	0.306039i
$931$	31.4429			1.03050
$932$	8.17583	+	21.3335i	0.267808	+	0.698801i
$933$	57.0319	+	32.9274i	1.86714	+	1.07799i
$934$	−19.1942	−	13.1995i	−0.628053	−	0.431900i
$935$	−30.6856			−1.00353
$936$	24.0707	−	32.3048i	0.786774	−	1.05592i
$937$	−28.4076			−0.928036			−0.464018	−	0.885826i	$-0.653593\pi$
$937$	−28.4076			−0.928036			−0.464018	+	0.885826i	$0.653593\pi$
$938$	2.33664	+	1.60687i	0.0762941	+	0.0524661i
$939$	11.3773	+	6.56866i	0.371283	+	0.214360i
$940$	37.4473	−	14.3513i	1.22140	−	0.468087i
$941$	−18.6692			−0.608599			−0.304299	−	0.952576i	$-0.598422\pi$
$941$	−18.6692			−0.608599			−0.304299	+	0.952576i	$0.598422\pi$
$942$	14.2423	+	29.8806i	0.464040	+	0.973563i
$943$	−4.28967	+	2.47664i	−0.139691	+	0.0806506i
$944$	9.40666	+	3.06774i	0.306161	+	0.0998464i
$945$	−6.44197	−	11.1578i	−0.209557	−	0.362964i
$946$	36.2269	+	24.9126i	1.17784	+	0.809977i
$947$	−7.05574	+	12.2209i	−0.229281	+	0.397126i	−0.957595	−	0.288117i	$-0.906971\pi$
$947$	−7.05574	+	12.2209i	−0.229281	+	0.397126i	0.728314	+	0.685243i	$0.240304\pi$
$948$	−1.37008	+	8.61997i	−0.0444982	+	0.279964i
$949$	−29.5120	+	22.1233i	−0.958000	+	0.718153i
$950$	−62.0156	−	4.89772i	−2.01205	−	0.158903i
$951$	50.7025	+	29.2731i	1.64414	+	0.949245i
$952$	8.21648	+	7.80992i	0.266298	+	0.253121i
$953$	9.69488	+	16.7920i	0.314048	+	0.543947i	0.979235	−	0.202730i	$-0.0649814\pi$
$953$	9.69488	+	16.7920i	0.314048	+	0.543947i	−0.665187	+	0.746677i	$0.731648\pi$
$954$	−0.276174	+	3.49696i	−0.00894147	+	0.113218i
$955$	−2.50017	−	4.33042i	−0.0809035	−	0.140129i
$956$	−46.0209	+	17.6370i	−1.48842	+	0.570422i
$957$	−25.8862			−0.836783
$958$	−42.4239	+	20.2210i	−1.37065	+	0.653310i
$959$	6.19964	−	10.7381i	0.200197	−	0.346751i
$960$	−39.0343	−	60.3230i	−1.25983	−	1.94692i
$961$	30.3374			0.978627
$962$	11.9931	−	22.8833i	0.386673	−	0.737786i
$963$		−	3.61291i		−	0.116424i
$964$	0.277984	+	0.225357i	0.00895325	+	0.00725827i
$965$	−50.2274	−	28.9988i	−1.61688	−	0.933505i
$966$	1.48742	+	3.12062i	0.0478569	+	0.100404i
$967$		−	4.50833i		−	0.144978i	−0.997369	−	0.0724891i	$-0.976906\pi$
$967$		−	4.50833i		−	0.144978i	0.997369	−	0.0724891i	$-0.0230943\pi$
$968$	0.405991	+	1.37473i	0.0130491	+	0.0441854i
$969$	−40.3710	+	23.3082i	−1.29690	+	0.748768i
$970$	5.51403	−	69.8194i	0.177045	−	2.24177i
$971$	−26.6115	+	15.3641i	−0.854003	+	0.493059i	−0.861999	−	0.506909i	$-0.830788\pi$
$971$	−26.6115	+	15.3641i	−0.854003	+	0.493059i	0.00799665	+	0.999968i	$0.497455\pi$
$972$	−33.1631	−	26.8849i	−1.06371	−	0.862332i
$973$	−14.7383	+	25.5276i	−0.472490	+	0.818376i
$974$	−1.37978	+	17.4709i	−0.0442110	+	0.559805i
$975$	7.49636	+	62.3422i	0.240076	+	1.99655i
$976$	8.24748	−	25.2894i	0.263996	−	0.809494i
$977$	−8.57480	−	4.95066i	−0.274332	−	0.158386i	0.356523	−	0.934287i	$-0.383962\pi$
$977$	−8.57480	−	4.95066i	−0.274332	−	0.158386i	−0.630855	+	0.775901i	$0.717296\pi$
$978$	−12.5474	−	8.62863i	−0.401222	−	0.275913i
$979$	3.81233	−	2.20105i	0.121843	−	0.0703459i
$980$	−31.7730	−	5.05008i	−1.01495	−	0.161319i
$981$	40.1538	+	69.5484i	1.28201	+	2.22051i
$982$	−13.4700	+	6.42038i	−0.429846	+	0.204882i
$983$			9.87697i			0.315026i	0.987517	+	0.157513i	$0.0503477\pi$
$983$			9.87697i			0.315026i	−0.987517	+	0.157513i	$0.949652\pi$
$984$	−17.0296	−	57.6640i	−0.542885	−	1.83826i
$985$	28.0392	−	48.5653i	0.893403	−	1.54742i
$986$	−8.95642	−	6.15917i	−0.285231	−	0.196148i
$987$		−	23.4213i		−	0.745508i
$988$	−47.9846	−	1.82206i	−1.52659	−	0.0579673i
$989$			5.62999i			0.179023i
$990$	36.5823	−	53.1966i	1.16266	−	1.69070i
$991$	20.9826	−	36.3428i	0.666533	−	1.15447i	−0.312335	−	0.949972i	$-0.601111\pi$
$991$	20.9826	−	36.3428i	0.666533	−	1.15447i	0.978867	−	0.204496i	$-0.0655556\pi$
$992$	−4.56601	+	0.594805i	−0.144971	+	0.0188851i
$993$			34.9982i			1.11064i
$994$	5.70588	+	11.9710i	0.180979	+	0.379697i
$995$	31.1773	+	54.0007i	0.988387	+	1.71194i
$996$	−6.46773	+	40.6922i	−0.204938	+	1.28938i
$997$	28.3587	−	16.3729i	0.898128	−	0.518534i	0.0215355	−	0.999768i	$-0.493145\pi$
$997$	28.3587	−	16.3729i	0.898128	−	0.518534i	0.876592	+	0.481234i	$0.159811\pi$
$998$	25.0546	−	36.4335i	0.793091	−	1.15328i
$999$	10.9946	+	6.34774i	0.347854	+	0.200834i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.2.s.c.69.5	yes	16
3.2	odd	2		936.2.dg.d.901.4		16
4.3	odd	2		416.2.ba.c.17.1		16
8.3	odd	2		416.2.ba.c.17.8		16
8.5	even	2	inner	104.2.s.c.69.3	✓	16
13.10	even	6	inner	104.2.s.c.101.3	yes	16
24.5	odd	2		936.2.dg.d.901.6		16
39.23	odd	6		936.2.dg.d.829.6		16
52.23	odd	6		416.2.ba.c.49.8		16
104.75	odd	6		416.2.ba.c.49.1		16
104.101	even	6	inner	104.2.s.c.101.5	yes	16
312.101	odd	6		936.2.dg.d.829.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.s.c.69.3	✓	16	8.5	even	2	inner
104.2.s.c.69.5	yes	16	1.1	even	1	trivial
104.2.s.c.101.3	yes	16	13.10	even	6	inner
104.2.s.c.101.5	yes	16	104.101	even	6	inner
416.2.ba.c.17.1		16	4.3	odd	2
416.2.ba.c.17.8		16	8.3	odd	2
416.2.ba.c.49.1		16	104.75	odd	6
416.2.ba.c.49.8		16	52.23	odd	6
936.2.dg.d.829.4		16	312.101	odd	6
936.2.dg.d.829.6		16	39.23	odd	6
936.2.dg.d.901.4		16	3.2	odd	2
936.2.dg.d.901.6		16	24.5	odd	2

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	104.2.s.c.69.5

Level	$104$
Weight	$2$
Character	104.69
Analytic conductor	$0.830$
Analytic rank	$0$
Dimension	$16$
Inner twists	$4$