LMFDB - Embedded newform 80.2.s.b.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 3]))

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (of order $4$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.9
Root			$-1.08900 - 0.902261i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41267 - 0.0660953i) q^{2} -0.496487 q^{3} +(1.99126 - 0.186742i) q^{4} +(-2.00635 - 0.987189i) q^{5} +(-0.701372 + 0.0328155i) q^{6} +(1.55426 + 1.55426i) q^{7} +(2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +O(q^{10})$	\(q+(1.41267 - 0.0660953i) q^{2} -0.496487 q^{3} +(1.99126 - 0.186742i) q^{4} +(-2.00635 - 0.987189i) q^{5} +(-0.701372 + 0.0328155i) q^{6} +(1.55426 + 1.55426i) q^{7} +(2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +(-2.89956 - 1.26196i) q^{10} +(-4.19607 + 4.19607i) q^{11} +(-0.988637 + 0.0927148i) q^{12} -5.09530i q^{13} +(2.29838 + 2.09292i) q^{14} +(0.996130 + 0.490127i) q^{15} +(3.93026 - 0.743703i) q^{16} +(0.213542 + 0.213542i) q^{17} +(-3.88978 + 0.181993i) q^{18} +(0.844754 - 0.844754i) q^{19} +(-4.17953 - 1.59108i) q^{20} +(-0.771668 - 0.771668i) q^{21} +(-5.65031 + 6.20499i) q^{22} +(1.70744 - 1.70744i) q^{23} +(-1.39049 + 0.196320i) q^{24} +(3.05092 + 3.96130i) q^{25} +(-0.336775 - 7.19797i) q^{26} +2.85654 q^{27} +(3.38518 + 2.80469i) q^{28} +(2.24750 + 2.24750i) q^{29} +(1.43960 + 0.626547i) q^{30} +0.818209i q^{31} +(5.50299 - 1.31038i) q^{32} +(2.08329 - 2.08329i) q^{33} +(0.315778 + 0.287550i) q^{34} +(-1.58404 - 4.65273i) q^{35} +(-5.48294 + 0.514193i) q^{36} -5.12639i q^{37} +(1.13752 - 1.24919i) q^{38} +2.52975i q^{39} +(-6.00945 - 1.97142i) q^{40} +3.34727i q^{41} +(-1.14111 - 1.03911i) q^{42} +4.49131i q^{43} +(-7.57189 + 9.13905i) q^{44} +(5.52450 + 2.71822i) q^{45} +(2.29920 - 2.52490i) q^{46} +(4.29355 - 4.29355i) q^{47} +(-1.95132 + 0.369239i) q^{48} -2.16858i q^{49} +(4.57176 + 5.39435i) q^{50} +(-0.106021 - 0.106021i) q^{51} +(-0.951504 - 10.1461i) q^{52} -1.00653 q^{53} +(4.03534 - 0.188804i) q^{54} +(12.5611 - 4.27649i) q^{55} +(4.96751 + 3.73835i) q^{56} +(-0.419410 + 0.419410i) q^{57} +(3.32352 + 3.02642i) q^{58} +(-7.65005 - 7.65005i) q^{59} +(2.07508 + 0.789952i) q^{60} +(-1.90291 + 1.90291i) q^{61} +(0.0540798 + 1.15586i) q^{62} +(-4.27964 - 4.27964i) q^{63} +(7.68729 - 2.21485i) q^{64} +(-5.03002 + 10.2230i) q^{65} +(2.80531 - 3.08070i) q^{66} +11.0221i q^{67} +(0.465096 + 0.385341i) q^{68} +(-0.847724 + 0.847724i) q^{69} +(-2.54525 - 6.46807i) q^{70} -10.5331 q^{71} +(-7.71159 + 1.08878i) q^{72} +(2.70854 + 2.70854i) q^{73} +(-0.338831 - 7.24189i) q^{74} +(-1.51474 - 1.96674i) q^{75} +(1.52438 - 1.83988i) q^{76} -13.0435 q^{77} +(0.167205 + 3.57370i) q^{78} -8.32010 q^{79} +(-8.61966 - 2.38777i) q^{80} +6.84226 q^{81} +(0.221239 + 4.72858i) q^{82} -9.17237 q^{83} +(-1.68070 - 1.39249i) q^{84} +(-0.217635 - 0.639248i) q^{85} +(0.296855 + 6.34474i) q^{86} +(-1.11585 - 1.11585i) q^{87} +(-10.0925 + 13.4109i) q^{88} -4.25101 q^{89} +(7.98394 + 3.47481i) q^{90} +(7.91940 - 7.91940i) q^{91} +(3.08112 - 3.71882i) q^{92} -0.406230i q^{93} +(5.78157 - 6.34914i) q^{94} +(-2.52881 + 0.860944i) q^{95} +(-2.73217 + 0.650586i) q^{96} +(-7.16000 - 7.16000i) q^{97} +(-0.143333 - 3.06348i) q^{98} +(11.5539 - 11.5539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.41267	−	0.0660953i	0.998907	−	0.0467365i
$2$	1.41267	−	0.0660953i	0.998907	−	0.0467365i
$3$	−0.496487			−0.286647			−0.143324	−	0.989676i	$-0.545779\pi$
$3$	−0.496487			−0.286647			−0.143324	+	0.989676i	$0.545779\pi$
$4$	1.99126	−	0.186742i	0.995631	−	0.0933708i
$5$	−2.00635	−	0.987189i	−0.897269	−	0.441484i
$5$	−2.00635	−	0.987189i	−0.897269	−	0.441484i
$6$	−0.701372	+	0.0328155i	−0.286334	+	0.0133969i
$7$	1.55426	+	1.55426i	0.587453	+	0.587453i	0.936941	−	0.349488i	$-0.113644\pi$
$7$	1.55426	+	1.55426i	0.587453	+	0.587453i	−0.349488	+	0.936941i	$0.613644\pi$
$8$	2.80065	−	0.395417i	0.990180	−	0.139801i
$9$	−2.75350			−0.917833
$10$	−2.89956	−	1.26196i	−0.916922	−	0.399067i
$11$	−4.19607	+	4.19607i	−1.26516	+	1.26516i	−0.316604	+	0.948558i	$0.602543\pi$
$11$	−4.19607	+	4.19607i	−1.26516	+	1.26516i	−0.948558	+	0.316604i	$0.897457\pi$
$12$	−0.988637	+	0.0927148i	−0.285395	+	0.0267645i
$13$		−	5.09530i		−	1.41318i	−0.707622	−	0.706591i	$-0.750232\pi$
$13$		−	5.09530i		−	1.41318i	0.707622	−	0.706591i	$-0.249768\pi$
$14$	2.29838	+	2.09292i	0.614267	+	0.559356i
$15$	0.996130	+	0.490127i	0.257200	+	0.126550i
$16$	3.93026	−	0.743703i	0.982564	−	0.185926i
$17$	0.213542	+	0.213542i	0.0517916	+	0.0517916i	0.732528	−	0.680737i	$-0.238340\pi$
$17$	0.213542	+	0.213542i	0.0517916	+	0.0517916i	−0.680737	+	0.732528i	$0.738340\pi$
$18$	−3.88978	+	0.181993i	−0.916830	+	0.0428963i
$19$	0.844754	−	0.844754i	0.193800	−	0.193800i	−0.603536	−	0.797336i	$-0.706242\pi$
$19$	0.844754	−	0.844754i	0.193800	−	0.193800i	0.797336	+	0.603536i	$0.206242\pi$
$20$	−4.17953	−	1.59108i	−0.934571	−	0.355777i
$21$	−0.771668	−	0.771668i	−0.168392	−	0.168392i
$22$	−5.65031	+	6.20499i	−1.20465	+	1.32291i
$23$	1.70744	−	1.70744i	0.356027	−	0.356027i	−0.506319	−	0.862346i	$-0.668994\pi$
$23$	1.70744	−	1.70744i	0.356027	−	0.356027i	0.862346	+	0.506319i	$0.168994\pi$
$24$	−1.39049	+	0.196320i	−0.283832	+	0.0400736i
$25$	3.05092	+	3.96130i	0.610183	+	0.792260i
$26$	−0.336775	−	7.19797i	−0.0660471	−	1.41164i
$27$	2.85654			0.549741
$28$	3.38518	+	2.80469i	0.639738	+	0.530036i
$29$	2.24750	+	2.24750i	0.417350	+	0.417350i	0.884289	−	0.466939i	$-0.154643\pi$
$29$	2.24750	+	2.24750i	0.417350	+	0.417350i	−0.466939	+	0.884289i	$0.654643\pi$
$30$	1.43960	+	0.626547i	0.262833	+	0.114391i
$31$			0.818209i			0.146955i	0.997297	+	0.0734773i	$0.0234097\pi$
$31$			0.818209i			0.146955i	−0.997297	+	0.0734773i	$0.976590\pi$
$32$	5.50299	−	1.31038i	0.972801	−	0.231644i
$33$	2.08329	−	2.08329i	0.362655	−	0.362655i
$34$	0.315778	+	0.287550i	0.0541556	+	0.0493144i
$35$	−1.58404	−	4.65273i	−0.267752	−	0.786455i
$36$	−5.48294	+	0.514193i	−0.913824	+	0.0856988i
$37$		−	5.12639i		−	0.842774i	−0.906881	−	0.421387i	$-0.861543\pi$
$37$		−	5.12639i		−	0.842774i	0.906881	−	0.421387i	$-0.138457\pi$
$38$	1.13752	−	1.24919i	0.184531	−	0.202646i
$39$			2.52975i			0.405084i
$40$	−6.00945	−	1.97142i	−0.950177	−	0.311710i
$41$			3.34727i			0.522756i	0.965237	+	0.261378i	$0.0841769\pi$
$41$			3.34727i			0.522756i	−0.965237	+	0.261378i	$0.915823\pi$
$42$	−1.14111	−	1.03911i	−0.176078	−	0.160338i
$43$			4.49131i			0.684919i	0.939533	+	0.342460i	$0.111260\pi$
$43$			4.49131i			0.684919i	−0.939533	+	0.342460i	$0.888740\pi$
$44$	−7.57189	+	9.13905i	−1.14151	+	1.37776i
$45$	5.52450	+	2.71822i	0.823543	+	0.405209i
$46$	2.29920	−	2.52490i	0.338998	−	0.372277i
$47$	4.29355	−	4.29355i	0.626278	−	0.626278i	−0.320851	−	0.947130i	$-0.603969\pi$
$47$	4.29355	−	4.29355i	0.626278	−	0.626278i	0.947130	+	0.320851i	$0.103969\pi$
$48$	−1.95132	+	0.369239i	−0.281649	+	0.0532951i
$49$		−	2.16858i		−	0.309797i
$50$	4.57176	+	5.39435i	0.646544	+	0.762877i
$51$	−0.106021	−	0.106021i	−0.0148459	−	0.0148459i
$52$	−0.951504	−	10.1461i	−0.131950	−	1.40701i
$53$	−1.00653			−0.138258			−0.0691291	−	0.997608i	$-0.522022\pi$
$53$	−1.00653			−0.138258			−0.0691291	+	0.997608i	$0.522022\pi$
$54$	4.03534	−	0.188804i	0.549141	−	0.0256930i
$55$	12.5611	−	4.27649i	1.69374	−	0.576642i
$56$	4.96751	+	3.73835i	0.663811	+	0.499558i
$57$	−0.419410	+	0.419410i	−0.0555521	+	0.0555521i
$58$	3.32352	+	3.02642i	0.436399	+	0.397388i
$59$	−7.65005	−	7.65005i	−0.995952	−	0.995952i	0.00404030	−	0.999992i	$-0.498714\pi$
$59$	−7.65005	−	7.65005i	−0.995952	−	0.995952i	−0.999992	+	0.00404030i	$0.998714\pi$
$60$	2.07508	+	0.789952i	0.267892	+	0.101982i
$61$	−1.90291	+	1.90291i	−0.243643	+	0.243643i	−0.818355	−	0.574712i	$-0.805114\pi$
$61$	−1.90291	+	1.90291i	−0.243643	+	0.243643i	0.574712	+	0.818355i	$0.305114\pi$
$62$	0.0540798	+	1.15586i	0.00686814	+	0.146794i
$63$	−4.27964	−	4.27964i	−0.539184	−	0.539184i
$64$	7.68729	−	2.21485i	0.960911	−	0.276856i
$65$	−5.03002	+	10.2230i	−0.623897	+	1.26800i
$66$	2.80531	−	3.08070i	0.345310	−	0.379208i
$67$			11.0221i			1.34656i	0.739387	+	0.673280i	$0.235115\pi$
$67$			11.0221i			1.34656i	−0.739387	+	0.673280i	$0.764885\pi$
$68$	0.465096	+	0.385341i	0.0564012	+	0.0467295i
$69$	−0.847724	+	0.847724i	−0.102054	+	0.102054i
$70$	−2.54525	−	6.46807i	−0.304216	−	0.773082i
$71$	−10.5331			−1.25005			−0.625027	−	0.780604i	$-0.714912\pi$
$71$	−10.5331			−1.25005			−0.625027	+	0.780604i	$0.714912\pi$
$72$	−7.71159	+	1.08878i	−0.908820	+	0.128314i
$73$	2.70854	+	2.70854i	0.317010	+	0.317010i	0.847618	−	0.530607i	$-0.178036\pi$
$73$	2.70854	+	2.70854i	0.317010	+	0.317010i	−0.530607	+	0.847618i	$0.678036\pi$
$74$	−0.338831	−	7.24189i	−0.0393883	−	0.841853i
$75$	−1.51474	−	1.96674i	−0.174907	−	0.227099i
$76$	1.52438	−	1.83988i	0.174858	−	0.211048i
$77$	−13.0435			−1.48645
$78$	0.167205	+	3.57370i	0.0189322	+	0.404642i
$79$	−8.32010			−0.936085			−0.468042	−	0.883706i	$-0.655041\pi$
$79$	−8.32010			−0.936085			−0.468042	+	0.883706i	$0.655041\pi$
$80$	−8.61966	−	2.38777i	−0.963707	−	0.266961i
$81$	6.84226			0.760252
$82$	0.221239	+	4.72858i	0.0244317	+	0.522185i
$83$	−9.17237			−1.00680			−0.503399	−	0.864054i	$-0.667917\pi$
$83$	−9.17237			−1.00680			−0.503399	+	0.864054i	$0.667917\pi$
$84$	−1.68070	−	1.39249i	−0.183379	−	0.151933i
$85$	−0.217635	−	0.639248i	−0.0236058	−	0.0693362i
$86$	0.296855	+	6.34474i	0.0320107	+	0.684171i
$87$	−1.11585	−	1.11585i	−0.119632	−	0.119632i
$88$	−10.0925	+	13.4109i	−1.07587	+	1.42961i
$89$	−4.25101			−0.450606			−0.225303	−	0.974289i	$-0.572337\pi$
$89$	−4.25101			−0.450606			−0.225303	+	0.974289i	$0.572337\pi$
$90$	7.98394	+	3.47481i	0.841582	+	0.366277i
$91$	7.91940	−	7.91940i	0.830178	−	0.830178i
$92$	3.08112	−	3.71882i	0.321229	−	0.387714i
$93$		−	0.406230i		−	0.0421241i
$94$	5.78157	−	6.34914i	0.596324	−	0.654864i
$95$	−2.52881	+	0.860944i	−0.259450	+	0.0883310i
$96$	−2.73217	+	0.650586i	−0.278850	+	0.0664001i
$97$	−7.16000	−	7.16000i	−0.726987	−	0.726987i	0.243031	−	0.970019i	$-0.421858\pi$
$97$	−7.16000	−	7.16000i	−0.726987	−	0.726987i	−0.970019	+	0.243031i	$0.921858\pi$
$98$	−0.143333	−	3.06348i	−0.0144788	−	0.309458i
$99$	11.5539	−	11.5539i	1.16121	−	1.16121i
$100$	6.81492	+	7.31826i	0.681492	+	0.731826i
$101$	8.38846	+	8.38846i	0.834683	+	0.834683i	0.988153	−	0.153470i	$-0.0490448\pi$
$101$	8.38846	+	8.38846i	0.834683	+	0.834683i	−0.153470	+	0.988153i	$0.549045\pi$
$102$	−0.156780	−	0.142765i	−0.0155235	−	0.0141358i
$103$	−5.16478	+	5.16478i	−0.508901	+	0.508901i	−0.914189	−	0.405288i	$-0.867171\pi$
$103$	−5.16478	+	5.16478i	−0.508901	+	0.508901i	0.405288	+	0.914189i	$0.367171\pi$
$104$	−2.01477	−	14.2702i	−0.197564	−	1.39930i
$105$	0.786458	+	2.31002i	0.0767504	+	0.225435i
$106$	−1.42190	+	0.0665272i	−0.138107	+	0.00646169i
$107$	8.97973			0.868103			0.434052	−	0.900888i	$-0.357084\pi$
$107$	8.97973			0.868103			0.434052	+	0.900888i	$0.357084\pi$
$108$	5.68812	−	0.533435i	0.547340	−	0.0513298i
$109$	10.9081	+	10.9081i	1.04481	+	1.04481i	0.998948	+	0.0458592i	$0.0146025\pi$
$109$	10.9081	+	10.9081i	1.04481	+	1.04481i	0.0458592	+	0.998948i	$0.485397\pi$
$110$	17.4620	−	6.87149i	1.66494	−	0.655171i
$111$			2.54519i			0.241579i
$112$	7.26453	+	4.95272i	0.686433	+	0.467988i
$113$	−4.29684	+	4.29684i	−0.404212	+	0.404212i	−0.879715	−	0.475502i	$-0.842266\pi$
$113$	−4.29684	+	4.29684i	−0.404212	+	0.404212i	0.475502	+	0.879715i	$0.342266\pi$
$114$	−0.564765	+	0.620208i	−0.0528951	+	0.0580878i
$115$	−5.11131	+	1.74017i	−0.476632	+	0.162271i
$116$	4.89506	+	4.05566i	0.454495	+	0.376558i
$117$			14.0299i			1.29707i
$118$	−11.3126	−	10.3013i	−1.04141	−	0.948316i
$119$			0.663798i			0.0608503i
$120$	2.98362	+	0.978787i	0.272366	+	0.0893507i
$121$		−	24.2140i		−	2.20127i
$122$	−2.56241	+	2.81396i	−0.231990	+	0.254764i
$123$		−	1.66188i		−	0.149846i
$124$	0.152794	+	1.62927i	0.0137213	+	0.146313i
$125$	−2.21067	−	10.9596i	−0.197728	−	0.980257i
$126$	−6.32858	−	5.76285i	−0.563795	−	0.513396i
$127$	0.759686	−	0.759686i	0.0674112	−	0.0674112i	−0.672597	−	0.740009i	$-0.734821\pi$
$127$	0.759686	−	0.759686i	0.0674112	−	0.0674112i	0.740009	+	0.672597i	$0.234821\pi$
$128$	10.7132	−	3.63694i	0.946922	−	0.321463i
$129$		−	2.22988i		−	0.196330i
$130$	−6.43006	+	14.7741i	−0.563954	+	1.29578i
$131$	7.59995	+	7.59995i	0.664010	+	0.664010i	0.956323	−	0.292312i	$-0.0944247\pi$
$131$	7.59995	+	7.59995i	0.664010	+	0.664010i	−0.292312	+	0.956323i	$0.594425\pi$
$132$	3.75935	−	4.53742i	0.327209	−	0.394932i
$133$	2.62593			0.227697
$134$	0.728507	+	15.5705i	0.0629335	+	1.34509i
$135$	−5.73123	−	2.81994i	−0.493266	−	0.242702i
$136$	0.682495	+	0.513619i	0.0585235	+	0.0440425i
$137$	12.7789	−	12.7789i	1.09178	−	1.09178i	0.0964376	−	0.995339i	$-0.469255\pi$
$137$	12.7789	−	12.7789i	1.09178	−	1.09178i	0.995339	−	0.0964376i	$-0.0307448\pi$
$138$	−1.14152	+	1.25358i	−0.0971728	+	0.106712i
$139$	7.74227	+	7.74227i	0.656691	+	0.656691i	0.954596	−	0.297905i	$-0.0962877\pi$
$139$	7.74227	+	7.74227i	0.656691	+	0.656691i	−0.297905	+	0.954596i	$0.596288\pi$
$140$	−4.02311	−	8.96900i	−0.340015	−	0.758019i
$141$	−2.13169	+	2.13169i	−0.179521	+	0.179521i
$142$	−14.8798	+	0.696191i	−1.24869	+	0.0584230i
$143$	21.3802	+	21.3802i	1.78790	+	1.78790i
$144$	−10.8220	+	2.04779i	−0.901830	+	0.170649i
$145$	−2.29057	−	6.72798i	−0.190222	−	0.558728i
$146$	4.00529	+	3.64724i	0.331480	+	0.301848i
$147$			1.07667i			0.0888024i
$148$	−0.957310	−	10.2080i	−0.0786904	−	0.839092i
$149$	9.57165	−	9.57165i	0.784140	−	0.784140i	−0.196386	−	0.980527i	$-0.562921\pi$
$149$	9.57165	−	9.57165i	0.784140	−	0.784140i	0.980527	+	0.196386i	$0.0629207\pi$
$150$	−2.26982	−	2.67823i	−0.185330	−	0.218676i
$151$	−9.68791			−0.788391			−0.394195	−	0.919027i	$-0.628977\pi$
$151$	−9.68791			−0.788391			−0.394195	+	0.919027i	$0.628977\pi$
$152$	2.03183	−	2.69989i	0.164803	−	0.218990i
$153$	−0.587989	−	0.587989i	−0.0475361	−	0.0475361i
$154$	−18.4262	+	0.862116i	−1.48482	+	0.0694713i
$155$	0.807726	−	1.64162i	0.0648781	−	0.131858i
$156$	0.472410	+	5.03740i	0.0378230	+	0.403315i
$157$	−9.97637			−0.796201			−0.398101	−	0.917342i	$-0.630331\pi$
$157$	−9.97637			−0.796201			−0.398101	+	0.917342i	$0.630331\pi$
$158$	−11.7535	+	0.549920i	−0.935062	+	0.0437493i
$159$	0.499732			0.0396313
$160$	−12.3345	−	2.80341i	−0.975131	−	0.221629i
$161$	5.30761			0.418298
$162$	9.66585	−	0.452242i	0.759421	−	0.0355315i
$163$	9.48267			0.742740			0.371370	−	0.928485i	$-0.378888\pi$
$163$	9.48267			0.742740			0.371370	+	0.928485i	$0.378888\pi$
$164$	0.625074	+	6.66529i	0.0488101	+	0.520472i
$165$	−6.23643	+	2.12322i	−0.485506	+	0.165293i
$166$	−12.9575	+	0.606250i	−1.00570	+	0.0470542i
$167$	−9.43528	−	9.43528i	−0.730124	−	0.730124i	0.240520	−	0.970644i	$-0.422682\pi$
$167$	−9.43528	−	9.43528i	−0.730124	−	0.730124i	−0.970644	+	0.240520i	$0.922682\pi$
$168$	−2.46630	−	1.85604i	−0.190279	−	0.143197i
$169$	−12.9621			−0.997082
$170$	−0.349697	−	0.888660i	−0.0268206	−	0.0681571i
$171$	−2.32603	+	2.32603i	−0.177876	+	0.177876i
$172$	0.838715	+	8.94339i	0.0639514	+	0.681927i
$173$		−	8.94716i		−	0.680240i	−0.940382	−	0.340120i	$-0.889532\pi$
$173$		−	8.94716i		−	0.680240i	0.940382	−	0.340120i	$-0.110468\pi$
$174$	−1.65008	−	1.50258i	−0.125093	−	0.113910i
$175$	−1.41497	+	10.8988i	−0.106962	+	0.823870i
$176$	−13.3710	+	19.6122i	−1.00788	+	1.47833i
$177$	3.79815	+	3.79815i	0.285487	+	0.285487i
$178$	−6.00526	+	0.280972i	−0.450114	+	0.0210597i
$179$	−3.02430	+	3.02430i	−0.226047	+	0.226047i	−0.811039	−	0.584992i	$-0.801098\pi$
$179$	−3.02430	+	3.02430i	−0.226047	+	0.226047i	0.584992	+	0.811039i	$0.301098\pi$
$180$	11.5083	+	4.38105i	0.857780	+	0.326544i
$181$	−1.54845	−	1.54845i	−0.115095	−	0.115095i	0.647213	−	0.762309i	$-0.275934\pi$
$181$	−1.54845	−	1.54845i	−0.115095	−	0.115095i	−0.762309	+	0.647213i	$0.775934\pi$
$182$	10.6640	−	11.7109i	0.790472	−	0.868071i
$183$	0.944773	−	0.944773i	0.0698396	−	0.0698396i
$184$	4.10680	−	5.45710i	0.302757	−	0.402303i
$185$	−5.06072	+	10.2854i	−0.372071	+	0.756195i
$186$	−0.0268499	−	0.573869i	−0.00196873	−	0.0420781i
$187$	−1.79208			−0.131050
$188$	7.74779	−	9.35136i	0.565066	−	0.682018i
$189$	4.43979	+	4.43979i	0.322947	+	0.322947i
$190$	−3.51546	+	1.38337i	−0.255038	+	0.100360i
$191$		−	20.1005i		−	1.45442i	−0.686415	−	0.727210i	$-0.740817\pi$
$191$		−	20.1005i		−	1.45442i	0.686415	−	0.727210i	$-0.259183\pi$
$192$	−3.81664	+	1.09964i	−0.275442	+	0.0793600i
$193$	3.82483	−	3.82483i	0.275317	−	0.275317i	−0.555919	−	0.831236i	$-0.687634\pi$
$193$	3.82483	−	3.82483i	0.275317	−	0.275317i	0.831236	+	0.555919i	$0.187634\pi$
$194$	−10.5879	−	9.64146i	−0.760170	−	0.692216i
$195$	2.49734	−	5.07558i	0.178838	−	0.363470i
$196$	−0.404964	−	4.31821i	−0.0289260	−	0.308444i
$197$		−	1.11758i		−	0.0796246i	−0.999207	−	0.0398123i	$-0.987324\pi$
$197$		−	1.11758i		−	0.0796246i	0.999207	−	0.0398123i	$-0.0126760\pi$
$198$	15.5581	−	17.0854i	1.10567	−	1.21421i
$199$			25.5830i			1.81353i	0.421635	+	0.906766i	$0.361456\pi$
$199$			25.5830i			1.81353i	−0.421635	+	0.906766i	$0.638544\pi$
$200$	10.1109	+	9.88784i	0.714950	+	0.699176i
$201$		−	5.47232i		−	0.385988i
$202$	12.4046	+	11.2957i	0.872781	+	0.794761i
$203$			6.98637i			0.490347i
$204$	−0.230914	−	0.191317i	−0.0161672	−	0.0133949i
$205$	3.30439	−	6.71581i	0.230788	−	0.469053i
$206$	−6.95475	+	7.63749i	−0.484560	+	0.532129i
$207$	−4.70145	+	4.70145i	−0.326773	+	0.326773i
$208$	−3.78939	−	20.0258i	−0.262747	−	1.38854i
$209$			7.08929i			0.490376i
$210$	1.26369	+	3.21131i	0.0872026	+	0.221602i
$211$	0.411613	+	0.411613i	0.0283366	+	0.0283366i	0.721133	−	0.692797i	$-0.243622\pi$
$211$	0.411613	+	0.411613i	0.0283366	+	0.0283366i	−0.692797	+	0.721133i	$0.743622\pi$
$212$	−2.00427	+	0.187962i	−0.137654	+	0.0129093i
$213$	5.22957			0.358324
$214$	12.6854	−	0.593518i	0.867155	−	0.0405721i
$215$	4.43378	−	9.01117i	0.302381	−	0.614557i
$216$	8.00017	−	1.12952i	0.544343	−	0.0768544i
$217$	−1.27171	+	1.27171i	−0.0863290	+	0.0863290i
$218$	16.1305	+	14.6886i	1.09250	+	0.994835i
$219$	−1.34475	−	1.34475i	−0.0908701	−	0.0908701i
$220$	24.2139	−	10.8613i	1.63250	−	0.732268i
$221$	1.08806	−	1.08806i	0.0731909	−	0.0731909i
$222$	0.168225	+	3.59551i	0.0112905	+	0.241315i
$223$	−16.7466	−	16.7466i	−1.12143	−	1.12143i	−0.991526	−	0.129908i	$-0.958532\pi$
$223$	−16.7466	−	16.7466i	−1.12143	−	1.12143i	−0.129908	−	0.991526i	$-0.541468\pi$
$224$	10.5897	+	6.51639i	0.707555	+	0.435395i
$225$	−8.40070	−	10.9074i	−0.560047	−	0.727163i
$226$	−5.78600	+	6.35401i	−0.384879	+	0.422662i
$227$			13.7807i			0.914659i	0.889297	+	0.457330i	$0.151194\pi$
$227$			13.7807i			0.914659i	−0.889297	+	0.457330i	$0.848806\pi$
$228$	−0.756833	+	0.913476i	−0.0501225	+	0.0604964i
$229$	−7.90971	+	7.90971i	−0.522688	+	0.522688i	−0.918382	−	0.395694i	$-0.870504\pi$
$229$	−7.90971	+	7.90971i	−0.522688	+	0.522688i	0.395694	+	0.918382i	$0.370504\pi$
$230$	−7.10556	+	2.79611i	−0.468527	+	0.184370i
$231$	6.47594			0.426086
$232$	7.18315	+	5.40576i	0.471597	+	0.354905i
$233$	−1.67997	−	1.67997i	−0.110058	−	0.110058i	0.649933	−	0.759991i	$-0.274797\pi$
$233$	−1.67997	−	1.67997i	−0.110058	−	0.110058i	−0.759991	+	0.649933i	$0.774797\pi$
$234$	0.927311	+	19.8196i	0.0606202	+	1.29565i
$235$	−12.8529	+	4.37583i	−0.838432	+	0.285448i
$236$	−16.6618	−	13.8047i	−1.08459	−	0.898608i
$237$	4.13083			0.268326
$238$	0.0438740	+	0.937727i	0.00284393	+	0.0607838i
$239$	11.7685			0.761241			0.380620	−	0.924731i	$-0.375710\pi$
$239$	11.7685			0.761241			0.380620	+	0.924731i	$0.375710\pi$
$240$	4.27955	+	1.18550i	0.276244	+	0.0765236i
$241$	−13.2730			−0.854991			−0.427495	−	0.904018i	$-0.640604\pi$
$241$	−13.2730			−0.854991			−0.427495	+	0.904018i	$0.640604\pi$
$242$	−1.60043	−	34.2063i	−0.102880	−	2.19886i
$243$	−11.9667			−0.767665
$244$	−3.43385	+	4.14455i	−0.219830	+	0.265328i
$245$	−2.14080	+	4.35094i	−0.136770	+	0.277971i
$246$	−0.109842	−	2.34768i	−0.00700329	−	0.149683i
$247$	−4.30427	−	4.30427i	−0.273874	−	0.273874i
$248$	0.323534	+	2.29152i	0.0205444	+	0.145511i
$249$	4.55396			0.288596
$250$	−3.84732	−	15.3362i	−0.243326	−	0.969945i
$251$	10.3795	−	10.3795i	0.655149	−	0.655149i	−0.299079	−	0.954228i	$-0.596679\pi$
$251$	10.3795	−	10.3795i	0.655149	−	0.655149i	0.954228	+	0.299079i	$0.0966795\pi$
$252$	−9.32108	−	7.72271i	−0.587173	−	0.486485i
$253$			14.3291i			0.900863i
$254$	1.02297	−	1.12340i	0.0641870	−	0.0704881i
$255$	0.108053	+	0.317378i	0.00676654	+	0.0198750i
$256$	14.8938	−	5.84588i	0.930863	−	0.365368i
$257$	20.4353	+	20.4353i	1.27472	+	1.27472i	0.943582	+	0.331140i	$0.107433\pi$
$257$	20.4353	+	20.4353i	1.27472	+	1.27472i	0.331140	+	0.943582i	$0.392567\pi$
$258$	−0.147385	−	3.15008i	−0.00917577	−	0.196116i
$259$	7.96772	−	7.96772i	0.495090	−	0.495090i
$260$	−8.10704	+	21.2959i	−0.502777	+	1.32072i
$261$	−6.18848	−	6.18848i	−0.383058	−	0.383058i
$262$	11.2385	+	10.2339i	0.694318	+	0.632251i
$263$	14.0611	−	14.0611i	0.867047	−	0.867047i	−0.125098	−	0.992144i	$-0.539924\pi$
$263$	14.0611	−	14.0611i	0.867047	−	0.867047i	0.992144	+	0.125098i	$0.0399244\pi$
$264$	5.01081	−	6.65835i	0.308394	−	0.409793i
$265$	2.01946	+	0.993639i	0.124055	+	0.0610388i
$266$	3.70956	−	0.173561i	0.227448	−	0.0106417i
$267$	2.11057			0.129165
$268$	2.05828	+	21.9478i	0.125729	+	1.34068i
$269$	−6.61443	−	6.61443i	−0.403289	−	0.403289i	0.476101	−	0.879390i	$-0.342050\pi$
$269$	−6.61443	−	6.61443i	−0.403289	−	0.403289i	−0.879390	+	0.476101i	$0.842050\pi$
$270$	−8.28271	−	3.60484i	−0.504070	−	0.219383i
$271$			10.6219i			0.645237i	0.946529	+	0.322619i	$0.104563\pi$
$271$			10.6219i			0.645237i	−0.946529	+	0.322619i	$0.895437\pi$
$272$	0.998087	+	0.680463i	0.0605179	+	0.0412592i
$273$	−3.93188	+	3.93188i	−0.237968	+	0.237968i
$274$	17.2077	−	18.8970i	1.03956	−	1.14161i
$275$	−29.4237	−	3.82004i	−1.77432	−	0.230357i
$276$	−1.52974	+	1.84635i	−0.0920793	+	0.111137i
$277$		−	8.28511i		−	0.497804i	−0.968529	−	0.248902i	$-0.919930\pi$
$277$		−	8.28511i		−	0.497804i	0.968529	−	0.248902i	$-0.0800697\pi$
$278$	11.4490	+	10.4255i	0.686665	+	0.625282i
$279$		−	2.25294i		−	0.134880i
$280$	−6.27612	−	12.4043i	−0.375070	−	0.741300i
$281$			21.0176i			1.25380i	0.779098	+	0.626902i	$0.215677\pi$
$281$			21.0176i			1.25380i	−0.779098	+	0.626902i	$0.784323\pi$
$282$	−2.87048	+	3.15227i	−0.170934	+	0.187715i
$283$		−	14.4748i		−	0.860436i	−0.902725	−	0.430218i	$-0.858437\pi$
$283$		−	14.4748i		−	0.860436i	0.902725	−	0.430218i	$-0.141563\pi$
$284$	−20.9742	+	1.96697i	−1.24459	+	0.116718i
$285$	1.25552	−	0.427448i	0.0743706	−	0.0253198i
$286$	31.6163	+	28.7900i	1.86951	+	1.70239i
$287$	−5.20251	+	5.20251i	−0.307095	+	0.307095i
$288$	−15.1525	+	3.60812i	−0.892869	+	0.212611i
$289$		−	16.9088i		−	0.994635i
$290$	−3.68051	−	9.35301i	−0.216127	−	0.549228i
$291$	3.55485	+	3.55485i	0.208389	+	0.208389i
$292$	5.89921	+	4.88761i	0.345225	+	0.286026i
$293$	−11.9165			−0.696171			−0.348086	−	0.937463i	$-0.613168\pi$
$293$	−11.9165			−0.696171			−0.348086	+	0.937463i	$0.613168\pi$
$294$	0.0711630	+	1.52098i	0.00415031	+	0.0887054i
$295$	7.79667	+	22.9008i	0.453940	+	1.33333i
$296$	−2.02706	−	14.3572i	−0.117821	−	0.834497i
$297$	−11.9862	+	11.9862i	−0.695512	+	0.695512i
$298$	12.8889	−	14.1542i	0.746635	−	0.819931i
$299$	−8.69993	−	8.69993i	−0.503130	−	0.503130i
$300$	−3.38352	−	3.63342i	−0.195348	−	0.209776i
$301$	−6.98065	+	6.98065i	−0.402358	+	0.402358i
$302$	−13.6858	+	0.640325i	−0.787529	+	0.0368466i
$303$	−4.16477	−	4.16477i	−0.239260	−	0.239260i
$304$	2.69185	−	3.94834i	0.154388	−	0.226453i
$305$	5.69645	−	1.93938i	0.326178	−	0.111049i
$306$	−0.869496	−	0.791769i	−0.0497058	−	0.0452624i
$307$		−	25.4511i		−	1.45257i	−0.687392	−	0.726287i	$-0.741245\pi$
$307$		−	25.4511i		−	1.45257i	0.687392	−	0.726287i	$-0.258755\pi$
$308$	−25.9731	+	2.43577i	−1.47995	+	0.138791i
$309$	2.56425	−	2.56425i	0.145875	−	0.145875i
$310$	1.03255	−	2.37245i	0.0586447	−	0.134746i
$311$	21.4775			1.21788			0.608939	−	0.793217i	$-0.291596\pi$
$311$	21.4775			1.21788			0.608939	+	0.793217i	$0.291596\pi$
$312$	1.00031	+	7.08495i	0.0566312	+	0.401106i
$313$	18.7965	+	18.7965i	1.06244	+	1.06244i	0.997916	+	0.0645277i	$0.0205541\pi$
$313$	18.7965	+	18.7965i	1.06244	+	1.06244i	0.0645277	+	0.997916i	$0.479446\pi$
$314$	−14.0933	+	0.659392i	−0.795331	+	0.0372116i
$315$	4.36167	+	12.8113i	0.245752	+	0.721835i
$316$	−16.5675	+	1.55371i	−0.931995	+	0.0874029i
$317$	16.2531			0.912864			0.456432	−	0.889758i	$-0.349127\pi$
$317$	16.2531			0.912864			0.456432	+	0.889758i	$0.349127\pi$
$318$	0.705955	−	0.0330299i	0.0395880	−	0.00185223i
$319$	−18.8613			−1.05603
$320$	−17.6099	−	3.14503i	−0.984424	−	0.175813i
$321$	−4.45832			−0.248839
$322$	7.49789	−	0.350808i	0.417841	−	0.0195498i
$323$	0.360781			0.0200744
$324$	13.6247	−	1.27773i	0.756930	−	0.0709853i
$325$	20.1840	−	15.5453i	1.11961	−	0.862300i
$326$	13.3959	−	0.626760i	0.741928	−	0.0347130i
$327$	−5.41574	−	5.41574i	−0.299491	−	0.299491i
$328$	1.32357	+	9.37453i	0.0730818	+	0.517622i
$329$	13.3465			0.735818
$330$	−8.66967	+	3.41161i	−0.477250	+	0.187803i
$331$	−8.71558	+	8.71558i	−0.479052	+	0.479052i	−0.904828	−	0.425777i	$-0.860001\pi$
$331$	−8.71558	+	8.71558i	−0.479052	+	0.479052i	0.425777	+	0.904828i	$0.360001\pi$
$332$	−18.2646	+	1.71286i	−1.00240	+	0.0940055i
$333$			14.1155i			0.773526i
$334$	−13.9526	−	12.7053i	−0.763450	−	0.695203i
$335$	10.8809	−	22.1142i	0.594485	−	1.20823i
$336$	−3.60674	−	2.45896i	−0.196764	−	0.134147i
$337$	0.0406874	+	0.0406874i	0.00221638	+	0.00221638i	0.708214	−	0.705998i	$-0.249501\pi$
$337$	0.0406874	+	0.0406874i	0.00221638	+	0.00221638i	−0.705998	+	0.708214i	$0.749501\pi$
$338$	−18.3111	+	0.856732i	−0.995993	+	0.0466001i
$339$	2.13333	−	2.13333i	0.115866	−	0.115866i
$340$	−0.552742	−	1.23227i	−0.0299767	−	0.0668292i
$341$	−3.43326	−	3.43326i	−0.185921	−	0.185921i
$342$	−3.13217	+	3.43965i	−0.169368	+	0.185995i
$343$	14.2503	−	14.2503i	0.769445	−	0.769445i
$344$	1.77594	+	12.5786i	0.0957524	+	0.678193i
$345$	2.53770	−	0.863971i	0.136625	−	0.0465146i
$346$	−0.591366	−	12.6394i	−0.0317920	−	0.679497i
$347$	−35.7094			−1.91698			−0.958491	−	0.285124i	$-0.907965\pi$
$347$	−35.7094			−1.91698			−0.958491	+	0.285124i	$0.907965\pi$
$348$	−2.43033	−	2.01358i	−0.130280	−	0.107939i
$349$	−0.274452	−	0.274452i	−0.0146911	−	0.0146911i	0.699723	−	0.714414i	$-0.253307\pi$
$349$	−0.274452	−	0.274452i	−0.0146911	−	0.0146911i	−0.714414	+	0.699723i	$0.753307\pi$
$350$	−1.27853	+	15.4899i	−0.0683401	+	0.827969i
$351$		−	14.5549i		−	0.776884i
$352$	−17.5925	+	28.5894i	−0.937683	+	1.52382i
$353$	−15.6215	+	15.6215i	−0.831446	+	0.831446i	−0.987715	−	0.156268i	$-0.950054\pi$
$353$	−15.6215	+	15.6215i	−0.831446	+	0.831446i	0.156268	+	0.987715i	$0.450054\pi$
$354$	5.61657	+	5.11449i	0.298517	+	0.271832i
$355$	21.1332	+	10.3982i	1.12163	+	0.551879i
$356$	−8.46487	+	0.793840i	−0.448637	+	0.0420734i
$357$		−	0.329567i		−	0.0174426i
$358$	−4.07244	+	4.47222i	−0.215235	+	0.236364i
$359$		−	0.768787i		−	0.0405750i	−0.999794	−	0.0202875i	$-0.993542\pi$
$359$		−	0.768787i		−	0.0405750i	0.999794	−	0.0202875i	$-0.00645816\pi$
$360$	16.5470	+	5.42832i	0.872105	+	0.286097i
$361$			17.5728i			0.924883i
$362$	−2.28979	−	2.08510i	−0.120349	−	0.109591i
$363$			12.0219i			0.630988i
$364$	14.2907	−	17.2485i	0.749037	−	0.904066i
$365$	−2.76045	−	8.10812i	−0.144488	−	0.424399i
$366$	1.27221	−	1.39710i	0.0664992	−	0.0730273i
$367$	13.7849	−	13.7849i	0.719568	−	0.719568i	−0.248949	−	0.968517i	$-0.580085\pi$
$367$	13.7849	−	13.7849i	0.719568	−	0.719568i	0.968517	+	0.248949i	$0.0800852\pi$
$368$	5.44086	−	7.98052i	0.283624	−	0.416013i
$369$		−	9.21671i		−	0.479803i
$370$	−6.46930	+	14.8643i	−0.336323	+	0.772758i
$371$	−1.56441	−	1.56441i	−0.0812202	−	0.0812202i
$372$	−0.0758601	−	0.808911i	−0.00393316	−	0.0419401i
$373$	−21.4003			−1.10806			−0.554031	−	0.832496i	$-0.686911\pi$
$373$	−21.4003			−1.10806			−0.554031	+	0.832496i	$0.686911\pi$
$374$	−2.53161	+	0.118448i	−0.130906	+	0.00612479i
$375$	1.09757	+	5.44131i	0.0566782	+	0.280988i
$376$	10.3270	−	13.7225i	0.532573	−	0.707682i
$377$	11.4517	−	11.4517i	0.589791	−	0.589791i
$378$	6.56540	+	5.97851i	0.337688	+	0.307501i
$379$	11.3922	+	11.3922i	0.585180	+	0.585180i	0.936322	−	0.351142i	$-0.114207\pi$
$379$	11.3922	+	11.3922i	0.585180	+	0.585180i	−0.351142	+	0.936322i	$0.614207\pi$
$380$	−4.87475	+	2.18660i	−0.250069	+	0.112170i
$381$	−0.377174	+	0.377174i	−0.0193232	+	0.0193232i
$382$	−1.32855	−	28.3953i	−0.0679744	−	1.45283i
$383$	4.42635	+	4.42635i	0.226176	+	0.226176i	0.811093	−	0.584917i	$-0.198873\pi$
$383$	4.42635	+	4.42635i	0.226176	+	0.226176i	−0.584917	+	0.811093i	$0.698873\pi$
$384$	−5.31897	+	1.80570i	−0.271432	+	0.0921465i
$385$	26.1699	+	12.8764i	1.33374	+	0.656243i
$386$	5.15041	−	5.65602i	0.262149	−	0.287884i
$387$		−	12.3668i		−	0.628642i
$388$	−15.5945	−	12.9204i	−0.791691	−	0.655932i
$389$	12.3502	−	12.3502i	0.626180	−	0.626180i	−0.320924	−	0.947105i	$-0.603994\pi$
$389$	12.3502	−	12.3502i	0.626180	−	0.626180i	0.947105	+	0.320924i	$0.103994\pi$
$390$	3.19244	−	7.33517i	0.161656	−	0.371431i
$391$	0.729222			0.0368784
$392$	−0.857493	−	6.07343i	−0.0433099	−	0.306755i
$393$	−3.77328	−	3.77328i	−0.190337	−	0.190337i
$394$	−0.0738671	−	1.57878i	−0.00372137	−	0.0795376i
$395$	16.6931	+	8.21351i	0.839920	+	0.413267i
$396$	20.8492	−	25.1644i	1.04771	−	1.26456i
$397$	17.9832			0.902551			0.451275	−	0.892385i	$-0.350969\pi$
$397$	17.9832			0.902551			0.451275	+	0.892385i	$0.350969\pi$
$398$	1.69092	+	36.1403i	0.0847580	+	1.81155i
$399$	−1.30374			−0.0652686
$400$	14.9369	+	13.2999i	0.746846	+	0.664997i
$401$	9.06570			0.452720			0.226360	−	0.974044i	$-0.427317\pi$
$401$	9.06570			0.452720			0.226360	+	0.974044i	$0.427317\pi$
$402$	−0.361695	−	7.73057i	−0.0180397	−	0.385566i
$403$	4.16902			0.207674
$404$	18.2701	+	15.1372i	0.908972	+	0.753102i
$405$	−13.7280	−	6.75461i	−0.682150	−	0.335639i
$406$	0.461766	+	9.86942i	0.0229171	+	0.489811i
$407$	21.5107	+	21.5107i	1.06625	+	1.06625i
$408$	−0.338850	−	0.255005i	−0.0167756	−	0.0126246i
$409$	−30.0616			−1.48645			−0.743226	−	0.669040i	$-0.766705\pi$
$409$	−30.0616			−1.48645			−0.743226	+	0.669040i	$0.766705\pi$
$410$	4.22412	−	9.70562i	0.208614	−	0.479326i
$411$	−6.34457	+	6.34457i	−0.312955	+	0.312955i
$412$	−9.31995	+	11.2489i	−0.459161	+	0.554194i
$413$		−	23.7803i		−	1.17015i
$414$	−6.33084	+	6.95233i	−0.311144	+	0.341688i
$415$	18.4030	+	9.05486i	0.903369	+	0.444485i
$416$	−6.67676	−	28.0394i	−0.327355	−	1.37474i
$417$	−3.84394	−	3.84394i	−0.188239	−	0.188239i
$418$	0.468569	+	10.0148i	0.0229184	+	0.489840i
$419$	−15.3986	+	15.3986i	−0.752271	+	0.752271i	−0.974903	−	0.222631i	$-0.928535\pi$
$419$	−15.3986	+	15.3986i	−0.752271	+	0.752271i	0.222631	+	0.974903i	$0.428535\pi$
$420$	1.99742	+	4.45300i	0.0974642	+	0.217284i
$421$	−3.86468	−	3.86468i	−0.188353	−	0.188353i	0.606631	−	0.794984i	$-0.292521\pi$
$421$	−3.86468	−	3.86468i	−0.188353	−	0.188353i	−0.794984	+	0.606631i	$0.792521\pi$
$422$	0.608679	+	0.554267i	0.0296300	+	0.0269813i
$423$	−11.8223	+	11.8223i	−0.574819	+	0.574819i
$424$	−2.81895	+	0.398001i	−0.136900	+	0.0193286i
$425$	−0.194406	+	1.49740i	−0.00943006	+	0.0726348i
$426$	7.38764	−	0.345650i	0.357933	−	0.0167468i
$427$	−5.91523			−0.286258
$428$	17.8810	−	1.67689i	0.864311	−	0.0810555i
$429$	−10.6150	−	10.6150i	−0.512497	−	0.512497i
$430$	5.66786	−	13.0228i	0.273328	−	0.628017i
$431$			27.2692i			1.31351i	0.754103	+	0.656756i	$0.228072\pi$
$431$			27.2692i			1.31351i	−0.754103	+	0.656756i	$0.771928\pi$
$432$	11.2269	−	2.12442i	0.540156	−	0.102211i
$433$	19.1435	−	19.1435i	0.919978	−	0.919978i	−0.0770497	−	0.997027i	$-0.524550\pi$
$433$	19.1435	−	19.1435i	0.919978	−	0.919978i	0.997027	+	0.0770497i	$0.0245500\pi$
$434$	−1.71244	+	1.88055i	−0.0821999	+	0.0902694i
$435$	1.13724	+	3.34036i	0.0545265	+	0.160158i
$436$	23.7579	+	19.6839i	1.13780	+	0.942688i
$437$		−	2.88474i		−	0.137996i
$438$	−1.98857	−	1.81081i	−0.0950177	−	0.0865238i
$439$		−	30.1995i		−	1.44134i	−0.693276	−	0.720672i	$-0.743833\pi$
$439$		−	30.1995i		−	1.44134i	0.693276	−	0.720672i	$-0.256167\pi$
$440$	33.4883	−	16.9438i	1.59649	−	0.807765i
$441$			5.97118i			0.284342i
$442$	1.46515	−	1.60899i	0.0696903	−	0.0765316i
$443$		−	27.7051i		−	1.31631i	−0.752884	−	0.658153i	$-0.771338\pi$
$443$		−	27.7051i		−	1.31631i	0.752884	−	0.658153i	$-0.228662\pi$
$444$	0.475292	+	5.06814i	0.0225564	+	0.240523i
$445$	8.52903	+	4.19655i	0.404315	+	0.198935i
$446$	−24.7642	−	22.5505i	−1.17262	−	1.06780i
$447$	−4.75220	+	4.75220i	−0.224772	+	0.224772i
$448$	15.3905	+	8.50557i	0.727131	+	0.401851i
$449$			9.78315i			0.461695i	0.972990	+	0.230848i	$0.0741499\pi$
$449$			9.78315i			0.461695i	−0.972990	+	0.230848i	$0.925850\pi$
$450$	−12.5883	−	14.8534i	−0.593420	−	0.700194i
$451$	−14.0454	−	14.0454i	−0.661371	−	0.661371i
$452$	−7.75373	+	9.35853i	−0.364705	+	0.440188i
$453$	4.80992			0.225990
$454$	0.910842	+	19.4676i	0.0427479	+	0.913660i
$455$	−23.7071	+	8.07118i	−1.11140	+	0.378383i
$456$	−1.00878	+	1.34046i	−0.0472404	+	0.0627729i
$457$	−0.557108	+	0.557108i	−0.0260604	+	0.0260604i	−0.720017	−	0.693957i	$-0.755866\pi$
$457$	−0.557108	+	0.557108i	−0.0260604	+	0.0260604i	0.693957	+	0.720017i	$0.255866\pi$
$458$	−10.6510	+	11.6966i	−0.497689	+	0.546546i
$459$	0.609992	+	0.609992i	0.0284720	+	0.0284720i
$460$	−9.85299	+	4.41962i	−0.459398	+	0.206066i
$461$	−12.5791	+	12.5791i	−0.585865	+	0.585865i	−0.936509	−	0.350644i	$-0.885963\pi$
$461$	−12.5791	+	12.5791i	−0.585865	+	0.585865i	0.350644	+	0.936509i	$0.385963\pi$
$462$	9.14836	−	0.428030i	0.425620	−	0.0199137i
$463$	−3.29549	−	3.29549i	−0.153154	−	0.153154i	0.626371	−	0.779525i	$-0.284540\pi$
$463$	−3.29549	−	3.29549i	−0.153154	−	0.153154i	−0.779525	+	0.626371i	$0.784540\pi$
$464$	10.5047	+	7.16177i	0.487669	+	0.332477i
$465$	−0.401026	+	0.815042i	−0.0185971	+	0.0377967i
$466$	−2.48427	−	2.26220i	−0.115082	−	0.104794i
$467$			10.1995i			0.471979i	0.971756	+	0.235989i	$0.0758331\pi$
$467$			10.1995i			0.471979i	−0.971756	+	0.235989i	$0.924167\pi$
$468$	2.61997	+	27.9372i	0.121108	+	1.29140i
$469$	−17.1311	+	17.1311i	−0.791042	+	0.791042i
$470$	−17.8677	+	7.03112i	−0.824175	+	0.324321i
$471$	4.95314			0.228229
$472$	−24.4501	−	18.4002i	−1.12541	−	0.846936i
$473$	−18.8459	−	18.8459i	−0.866534	−	0.866534i
$474$	5.83549	−	0.273028i	0.268033	−	0.0125406i
$475$	5.92360	+	0.769051i	0.271793	+	0.0352865i
$476$	0.123959	+	1.32180i	0.00568164	+	0.0605845i
$477$	2.77149			0.126898
$478$	16.6250	−	0.777843i	0.760409	−	0.0355777i
$479$	5.65795			0.258518			0.129259	−	0.991611i	$-0.458740\pi$
$479$	5.65795			0.258518			0.129259	+	0.991611i	$0.458740\pi$
$480$	6.12394	+	1.39186i	0.279518	+	0.0635293i
$481$	−26.1205			−1.19099
$482$	−18.7504	+	0.877285i	−0.854057	+	0.0399592i
$483$	−2.63516			−0.119904
$484$	−4.52175	−	48.2164i	−0.205534	−	2.19165i
$485$	7.29722	+	21.4338i	0.331350	+	0.973257i
$486$	−16.9050	+	0.790944i	−0.766826	+	0.0358780i
$487$	−19.7470	−	19.7470i	−0.894823	−	0.894823i	0.100149	−	0.994972i	$-0.468068\pi$
$487$	−19.7470	−	19.7470i	−0.894823	−	0.894823i	−0.994972	+	0.100149i	$0.968068\pi$
$488$	−4.57695	+	6.08184i	−0.207189	+	0.275312i
$489$	−4.70802			−0.212904
$490$	−2.73666	+	6.28793i	−0.123630	+	0.284060i
$491$	−4.21405	+	4.21405i	−0.190177	+	0.190177i	−0.795773	−	0.605595i	$-0.792935\pi$
$491$	−4.21405	+	4.21405i	−0.190177	+	0.190177i	0.605595	+	0.795773i	$0.292935\pi$
$492$	−0.310341	−	3.30923i	−0.0139913	−	0.149192i
$493$			0.959871i			0.0432304i
$494$	−6.36500	−	5.79602i	−0.286375	−	0.260775i
$495$	−34.5870	+	11.7753i	−1.55457	+	0.529261i
$496$	0.608504	+	3.21577i	0.0273226	+	0.144392i
$497$	−16.3712	−	16.3712i	−0.734348	−	0.734348i
$498$	6.43324	−	0.300996i	0.288280	−	0.0134879i
$499$	−16.8862	+	16.8862i	−0.755928	+	0.755928i	−0.975579	−	0.219650i	$-0.929508\pi$
$499$	−16.8862	+	16.8862i	−0.755928	+	0.755928i	0.219650	+	0.975579i	$0.429508\pi$
$500$	−6.44863	−	21.4106i	−0.288392	−	0.957513i
$501$	4.68450	+	4.68450i	0.209288	+	0.209288i
$502$	13.9768	−	15.3488i	0.623814	−	0.685053i
$503$	−20.3714	+	20.3714i	−0.908317	+	0.908317i	−0.996136	−	0.0878190i	$-0.972010\pi$
$503$	−20.3714	+	20.3714i	−0.908317	+	0.908317i	0.0878190	+	0.996136i	$0.472010\pi$
$504$	−13.6780	−	10.2935i	−0.609268	−	0.458511i
$505$	−8.54923	−	25.1112i	−0.380436	−	1.11744i
$506$	0.947086	+	20.2423i	0.0421031	+	0.899878i
$507$	6.43550			0.285811
$508$	1.37087	−	1.65460i	0.0608225	−	0.0734110i
$509$	−20.6309	−	20.6309i	−0.914448	−	0.914448i	0.0821701	−	0.996618i	$-0.473815\pi$
$509$	−20.6309	−	20.6309i	−0.914448	−	0.914448i	−0.996618	+	0.0821701i	$0.973815\pi$
$510$	0.173620	+	0.441209i	0.00768803	+	0.0195370i
$511$			8.41952i			0.372458i
$512$	20.6536	−	9.24271i	0.912770	−	0.408474i
$513$	2.41307	−	2.41307i	0.106540	−	0.106540i
$514$	30.2190	+	27.5177i	1.33290	+	1.21375i
$515$	15.4610	−	5.26376i	0.681293	−	0.231949i
$516$	−0.416411	−	4.44028i	−0.0183315	−	0.195472i
$517$			36.0320i			1.58469i
$518$	10.7291	−	11.7824i	0.471411	−	0.517688i
$519$			4.44215i			0.194989i
$520$	−10.0450	+	30.6199i	−0.440502	+	1.34277i
$521$		−	19.0433i		−	0.834300i	−0.908838	−	0.417150i	$-0.863029\pi$
$521$		−	19.0433i		−	0.834300i	0.908838	−	0.417150i	$-0.136971\pi$
$522$	−9.15131	−	8.33325i	−0.400542	−	0.364736i
$523$			19.1782i			0.838603i	0.907847	+	0.419301i	$0.137725\pi$
$523$			19.1782i			0.838603i	−0.907847	+	0.419301i	$0.862275\pi$
$524$	16.5527	+	13.7143i	0.723109	+	0.599110i
$525$	0.702515	−	5.41111i	0.0306603	−	0.236160i
$526$	18.9343	−	20.7931i	0.825577	−	0.906622i
$527$	−0.174722	+	0.174722i	−0.00761101	+	0.00761101i
$528$	6.63853	−	9.73723i	0.288905	−	0.423759i
$529$			17.1693i			0.746490i
$530$	2.91851	+	1.27021i	0.126772	+	0.0551742i
$531$	21.0644	+	21.0644i	0.914118	+	0.914118i
$532$	5.22891	−	0.490369i	0.226702	−	0.0212602i
$533$	17.0553			0.738749
$534$	2.98154	−	0.139499i	0.129024	−	0.00603671i
$535$	−18.0165	−	8.86469i	−0.778922	−	0.383254i
$536$	4.35831	+	30.8690i	0.188251	+	1.33334i
$537$	1.50153	−	1.50153i	0.0647957	−	0.0647957i
$538$	−9.78118	−	8.90681i	−0.421697	−	0.384000i
$539$	9.09950	+	9.09950i	0.391943	+	0.391943i
$540$	−11.9390	−	4.54499i	−0.513772	−	0.195585i
$541$	14.5231	−	14.5231i	0.624398	−	0.624398i	−0.322255	−	0.946653i	$-0.604441\pi$
$541$	14.5231	−	14.5231i	0.624398	−	0.624398i	0.946653	+	0.322255i	$0.104441\pi$
$542$	0.702061	+	15.0053i	0.0301561	+	0.644532i
$543$	0.768787	+	0.768787i	0.0329918	+	0.0329918i
$544$	1.45494	+	0.895300i	0.0623801	+	0.0383857i
$545$	−11.1172	−	32.6539i	−0.476207	−	1.39874i
$546$	−5.29456	+	5.81432i	−0.226586	+	0.248830i
$547$		−	9.97058i		−	0.426311i	−0.977018	−	0.213156i	$-0.931626\pi$
$547$		−	9.97058i		−	0.426311i	0.977018	−	0.213156i	$-0.0683742\pi$
$548$	23.0598	−	27.8325i	0.985067	−	1.18895i
$549$	5.23967	−	5.23967i	0.223624	−	0.223624i
$550$	−41.8185	−	3.45167i	−1.78315	−	0.147180i
$551$	3.79716			0.161765
$552$	−2.03897	+	2.70938i	−0.0867845	+	0.115319i
$553$	−12.9316	−	12.9316i	−0.549906	−	0.549906i
$554$	−0.547607	−	11.7041i	−0.0232656	−	0.497260i
$555$	2.51258	−	5.10655i	0.106653	−	0.216761i
$556$	16.8627	+	13.9711i	0.715138	+	0.592506i
$557$	11.4424			0.484831			0.242416	−	0.970173i	$-0.422060\pi$
$557$	11.4424			0.484831			0.242416	+	0.970173i	$0.422060\pi$
$558$	−0.148909	−	3.18265i	−0.00630381	−	0.134732i
$559$	22.8846			0.967915
$560$	−9.68595	−	17.1084i	−0.409306	−	0.722960i
$561$	0.889743			0.0375650
$562$	1.38916	+	29.6909i	0.0585984	+	1.25243i
$563$	47.0585			1.98328			0.991640	−	0.129034i	$-0.0411876\pi$
$563$	47.0585			1.98328			0.991640	+	0.129034i	$0.0411876\pi$
$564$	−3.84668	+	4.64283i	−0.161975	+	0.195499i
$565$	12.8628	−	4.37919i	0.541141	−	0.184234i
$566$	−0.956715	−	20.4481i	−0.0402137	−	0.859496i
$567$	10.6346	+	10.6346i	0.446612	+	0.446612i
$568$	−29.4996	+	4.16498i	−1.23778	+	0.174759i
$569$	41.4684			1.73845			0.869224	−	0.494419i	$-0.164619\pi$
$569$	41.4684			1.73845			0.869224	+	0.494419i	$0.164619\pi$
$570$	1.74538	−	0.686826i	0.0731060	−	0.0287680i
$571$	16.1745	−	16.1745i	0.676881	−	0.676881i	−0.282412	−	0.959293i	$-0.591135\pi$
$571$	16.1745	−	16.1745i	0.676881	−	0.676881i	0.959293	+	0.282412i	$0.0911347\pi$
$572$	46.5662	+	38.5811i	1.94703	+	1.61316i
$573$			9.97963i			0.416905i
$574$	−7.00556	+	7.69329i	−0.292407	+	0.321112i
$575$	11.9730	+	1.55443i	0.499307	+	0.0648242i
$576$	−21.1670	+	6.09859i	−0.881957	+	0.254108i
$577$	20.0316	+	20.0316i	0.833926	+	0.833926i	0.988051	−	0.154125i	$-0.0492560\pi$
$577$	20.0316	+	20.0316i	0.833926	+	0.833926i	−0.154125	+	0.988051i	$0.549256\pi$
$578$	−1.11759	−	23.8865i	−0.0464857	−	0.993548i
$579$	−1.89898	+	1.89898i	−0.0789189	+	0.0789189i
$580$	−5.81752	−	12.9694i	−0.241560	−	0.538526i
$581$	−14.2562	−	14.2562i	−0.591447	−	0.591447i
$582$	5.25678	+	4.78686i	0.217900	+	0.198422i
$583$	4.22349	−	4.22349i	0.174919	−	0.174919i
$584$	8.65667	+	6.51467i	0.358215	+	0.269579i
$585$	13.8502	−	28.1490i	0.572634	−	1.16382i
$586$	−16.8341	+	0.787627i	−0.695411	+	0.0325366i
$587$	29.1190			1.20187			0.600935	−	0.799298i	$-0.294795\pi$
$587$	29.1190			1.20187			0.600935	+	0.799298i	$0.294795\pi$
$588$	0.201059	+	2.14394i	0.00829155	+	0.0884145i
$589$	0.691185	+	0.691185i	0.0284798	+	0.0284798i
$590$	12.5277	+	31.8358i	0.515759	+	1.31066i
$591$			0.554866i			0.0228242i
$592$	−3.81251	−	20.1480i	−0.156693	−	0.828079i
$593$	−10.3431	+	10.3431i	−0.424740	+	0.424740i	−0.886832	−	0.462092i	$-0.847099\pi$
$593$	−10.3431	+	10.3431i	−0.424740	+	0.424740i	0.462092	+	0.886832i	$0.347099\pi$
$594$	−16.1403	+	17.7248i	−0.662246	+	0.727258i
$595$	0.655294	−	1.33181i	0.0268644	−	0.0545991i
$596$	17.2722	−	20.8471i	0.707499	−	0.853930i
$597$		−	12.7016i		−	0.519843i
$598$	−12.8651	−	11.7151i	−0.526095	−	0.479066i
$599$		−	2.59479i		−	0.106020i	−0.998594	−	0.0530101i	$-0.983118\pi$
$599$		−	2.59479i		−	0.106020i	0.998594	−	0.0530101i	$-0.0168816\pi$
$600$	−5.01994	−	4.90919i	−0.204938	−	0.200417i
$601$			14.4092i			0.587765i	0.955842	+	0.293882i	$0.0949474\pi$
$601$			14.4092i			0.587765i	−0.955842	+	0.293882i	$0.905053\pi$
$602$	−9.39996	+	10.3227i	−0.383114	+	0.420723i
$603$		−	30.3493i		−	1.23592i
$604$	−19.2912	+	1.80913i	−0.784946	+	0.0736126i
$605$	−23.9038	+	48.5818i	−0.971826	+	1.97513i
$606$	−6.15870	−	5.60816i	−0.250180	−	0.227816i
$607$	−11.8502	+	11.8502i	−0.480985	+	0.480985i	−0.905446	−	0.424461i	$-0.860464\pi$
$607$	−11.8502	+	11.8502i	−0.480985	+	0.480985i	0.424461	+	0.905446i	$0.360464\pi$
$608$	3.54173	−	5.75562i	0.143636	−	0.233421i
$609$		−	3.46864i		−	0.140557i
$610$	7.91902	−	3.11622i	0.320632	−	0.126172i
$611$	−21.8769	−	21.8769i	−0.885045	−	0.885045i
$612$	−1.28064	−	1.06104i	−0.0517669	−	0.0428899i
$613$	16.8256			0.679579			0.339789	−	0.940502i	$-0.389644\pi$
$613$	16.8256			0.679579			0.339789	+	0.940502i	$0.389644\pi$
$614$	−1.68220	−	35.9540i	−0.0678881	−	1.45099i
$615$	−1.64059	+	3.33431i	−0.0661548	+	0.134453i
$616$	−36.5304	+	5.15763i	−1.47185	+	0.207807i
$617$	−22.4849	+	22.4849i	−0.905209	+	0.905209i	−0.995881	−	0.0906720i	$-0.971098\pi$
$617$	−22.4849	+	22.4849i	−0.905209	+	0.905209i	0.0906720	+	0.995881i	$0.471098\pi$
$618$	3.45295	−	3.79191i	0.138898	−	0.152533i
$619$	−14.1269	−	14.1269i	−0.567809	−	0.567809i	0.363705	−	0.931514i	$-0.381512\pi$
$619$	−14.1269	−	14.1269i	−0.567809	−	0.567809i	−0.931514	+	0.363705i	$0.881512\pi$
$620$	1.30184	−	3.41973i	0.0522831	−	0.137340i
$621$	4.87738	−	4.87738i	0.195723	−	0.195723i
$622$	30.3406	−	1.41956i	1.21655	−	0.0569193i
$623$	−6.60715	−	6.60715i	−0.264710	−	0.264710i
$624$	1.88138	+	9.94257i	0.0753156	+	0.398021i
$625$	−6.38382	+	24.1712i	−0.255353	+	0.966848i
$626$	27.7956	+	25.3109i	1.11094	+	1.01163i
$627$		−	3.51974i		−	0.140565i
$628$	−19.8656	+	1.86300i	−0.792723	+	0.0743419i
$629$	1.09470	−	1.09470i	0.0436486	−	0.0436486i
$630$	7.00835	+	17.8098i	0.279219	+	0.709560i
$631$	−33.9235			−1.35047			−0.675236	−	0.737601i	$-0.735958\pi$
$631$	−33.9235			−1.35047			−0.675236	+	0.737601i	$0.735958\pi$
$632$	−23.3017	+	3.28991i	−0.926892	+	0.130866i
$633$	−0.204361	−	0.204361i	−0.00812261	−	0.00812261i
$634$	22.9602	−	1.07425i	0.911867	−	0.0426640i
$635$	−2.27415	+	0.774246i	−0.0902470	+	0.0307250i
$636$	0.995097	−	0.0933206i	0.0394582	−	0.00370040i
$637$	−11.0496			−0.437799
$638$	−26.6448	+	1.24664i	−1.05488	+	0.0493551i
$639$	29.0030			1.14734
$640$	−25.0848	−	3.27896i	−0.991565	−	0.129612i
$641$	18.8495			0.744509			0.372254	−	0.928131i	$-0.378585\pi$
$641$	18.8495			0.744509			0.372254	+	0.928131i	$0.378585\pi$
$642$	−6.29813	+	0.294674i	−0.248567	+	0.0116299i
$643$	−16.4916			−0.650364			−0.325182	−	0.945652i	$-0.605426\pi$
$643$	−16.4916			−0.650364			−0.325182	+	0.945652i	$0.605426\pi$
$644$	10.5688	−	0.991150i	0.416471	−	0.0390568i
$645$	−2.20131	+	4.47393i	−0.0866766	+	0.176161i
$646$	0.509664	−	0.0238459i	0.0200525	−	0.000938206i
$647$	−0.316870	−	0.316870i	−0.0124574	−	0.0124574i	0.700851	−	0.713308i	$-0.252804\pi$
$647$	−0.316870	−	0.316870i	−0.0124574	−	0.0124574i	−0.713308	+	0.700851i	$0.752804\pi$
$648$	19.1628	−	2.70555i	0.752786	−	0.106284i
$649$	64.2002			2.52008
$650$	27.4858	−	23.2945i	1.07808	−	0.913684i
$651$	0.631386	−	0.631386i	0.0247460	−	0.0247460i
$652$	18.8825	−	1.77081i	0.739495	−	0.0693502i
$653$			17.0751i			0.668200i	0.942538	+	0.334100i	$0.108432\pi$
$653$			17.0751i			0.668200i	−0.942538	+	0.334100i	$0.891568\pi$
$654$	−8.00859	−	7.29268i	−0.313161	−	0.285167i
$655$	−7.74560	−	22.7508i	−0.302646	−	0.888946i
$656$	2.48937	+	13.1556i	0.0971937	+	0.513641i
$657$	−7.45796	−	7.45796i	−0.290963	−	0.290963i
$658$	18.8542	−	0.882144i	0.735014	−	0.0343895i
$659$	−7.42245	+	7.42245i	−0.289138	+	0.289138i	−0.836739	−	0.547601i	$-0.815541\pi$
$659$	−7.42245	+	7.42245i	−0.289138	+	0.289138i	0.547601	+	0.836739i	$0.315541\pi$
$660$	−12.0219	+	5.39249i	−0.467951	+	0.209903i
$661$	31.7614	+	31.7614i	1.23538	+	1.23538i	0.961870	+	0.273507i	$0.0881837\pi$
$661$	31.7614	+	31.7614i	1.23538	+	1.23538i	0.273507	+	0.961870i	$0.411816\pi$
$662$	−11.7362	+	12.8883i	−0.456139	+	0.500917i
$663$	−0.540209	+	0.540209i	−0.0209800	+	0.0209800i
$664$	−25.6886	+	3.62691i	−0.996911	+	0.140751i
$665$	−5.26854	−	2.59229i	−0.204305	−	0.100525i
$666$	0.932970	+	19.9406i	0.0361519	+	0.772681i
$667$	7.67495			0.297175
$668$	−20.5501	−	17.0262i	−0.795107	−	0.658762i
$669$	8.31446	+	8.31446i	0.321456	+	0.321456i
$670$	13.9094	−	31.9592i	0.537367	−	1.23469i
$671$		−	15.9695i		−	0.616496i
$672$	−5.25766	−	3.23531i	−0.202819	−	0.124805i
$673$	4.14672	−	4.14672i	0.159844	−	0.159844i	−0.622653	−	0.782498i	$-0.713945\pi$
$673$	4.14672	−	4.14672i	0.159844	−	0.159844i	0.782498	+	0.622653i	$0.213945\pi$
$674$	0.0601670	+	0.0547885i	0.00231755	+	0.00211037i
$675$	8.71507	+	11.3156i	0.335443	+	0.435538i
$676$	−25.8109	+	2.42056i	−0.992727	+	0.0930983i
$677$		−	25.2618i		−	0.970890i	−0.874267	−	0.485445i	$-0.838658\pi$
$677$		−	25.2618i		−	0.970890i	0.874267	−	0.485445i	$-0.161342\pi$
$678$	2.87268	−	3.15468i	0.110325	−	0.121155i
$679$		−	22.2569i		−	0.854143i
$680$	−0.862289	−	1.70425i	−0.0330673	−	0.0653551i
$681$		−	6.84196i		−	0.262184i
$682$	−5.07698	−	4.62313i	−0.194408	−	0.177029i
$683$			8.20306i			0.313881i	0.987608	+	0.156941i	$0.0501631\pi$
$683$			8.20306i			0.313881i	−0.987608	+	0.156941i	$0.949837\pi$
$684$	−4.19737	+	5.06610i	−0.160490	+	0.193707i
$685$	−38.2542	+	13.0238i	−1.46162	+	0.497615i
$686$	19.1891	−	21.0728i	0.732643	−	0.804565i
$687$	3.92707	−	3.92707i	0.149827	−	0.149827i
$688$	3.34020	+	17.6520i	0.127344	+	0.672977i
$689$			5.12859i			0.195384i
$690$	3.52782	−	1.38823i	0.134302	−	0.0528492i
$691$	−7.89158	−	7.89158i	−0.300210	−	0.300210i	0.540886	−	0.841096i	$-0.318089\pi$
$691$	−7.89158	−	7.89158i	−0.300210	−	0.300210i	−0.841096	+	0.540886i	$0.818089\pi$
$692$	−1.67081	−	17.8162i	−0.0635145	−	0.677268i
$693$	35.9153			1.36431
$694$	−50.4455	+	2.36022i	−1.91489	+	0.0895929i
$695$	−7.89066	−	23.1768i	−0.299310	−	0.879147i
$696$	−3.56635	−	2.68389i	−0.135182	−	0.101733i
$697$	−0.714783	+	0.714783i	−0.0270744	+	0.0270744i
$698$	−0.405850	−	0.369570i	−0.0153616	−	0.0139884i
$699$	0.834083	+	0.834083i	0.0315479	+	0.0315479i
$700$	−0.782324	+	21.9666i	−0.0295691	+	0.830258i
$701$	1.50228	−	1.50228i	0.0567405	−	0.0567405i	−0.678167	−	0.734908i	$-0.737225\pi$
$701$	1.50228	−	1.50228i	0.0567405	−	0.0567405i	0.734908	+	0.678167i	$0.237225\pi$
$702$	−0.962012	−	20.5613i	−0.0363088	−	0.776036i
$703$	−4.33054	−	4.33054i	−0.163329	−	0.163329i
$704$	−22.9627	+	41.5501i	−0.865441	+	1.56598i
$705$	6.38131	−	2.17255i	0.240334	−	0.0818228i
$706$	−21.0354	+	23.1004i	−0.791679	+	0.869397i
$707$			26.0756i			0.980675i
$708$	8.27239	+	6.85385i	0.310896	+	0.257583i
$709$	−36.0738	+	36.0738i	−1.35478	+	1.35478i	−0.474551	+	0.880228i	$0.657390\pi$
$709$	−36.0738	+	36.0738i	−1.35478	+	1.35478i	−0.880228	+	0.474551i	$0.842610\pi$
$710$	30.5415	+	13.2924i	1.14620	+	0.498854i
$711$	22.9094			0.859170
$712$	−11.9056	+	1.68092i	−0.446181	+	0.0629952i
$713$	1.39704	+	1.39704i	0.0523197	+	0.0523197i
$714$	−0.0217829	−	0.465570i	−0.000815203	−	0.0174235i
$715$	−21.7900	−	64.0026i	−0.814899	−	2.39356i
$716$	−5.45741	+	6.58694i	−0.203953	+	0.246165i
$717$	−5.84291			−0.218207
$718$	−0.0508132	−	1.08604i	−0.00189633	−	0.0405307i
$719$	−35.0340			−1.30655			−0.653274	−	0.757121i	$-0.726605\pi$
$719$	−35.0340			−1.30655			−0.653274	+	0.757121i	$0.726605\pi$
$720$	23.7342	+	6.57473i	0.884523	+	0.245026i
$721$	−16.0548			−0.597911
$722$	1.16148	+	24.8245i	0.0432258	+	0.923873i
$723$	6.58989			0.245081
$724$	−3.37253	−	2.79421i	−0.125339	−	0.103846i
$725$	−2.04609	+	15.7599i	−0.0759898	+	0.585310i
$726$	0.794593	+	16.9830i	0.0294901	+	0.630298i
$727$	25.4241	+	25.4241i	0.942928	+	0.942928i	0.998457	−	0.0555295i	$-0.0176847\pi$
$727$	25.4241	+	25.4241i	0.942928	+	0.942928i	−0.0555295	+	0.998457i	$0.517685\pi$
$728$	19.0480	−	25.3109i	0.705966	−	0.938085i
$729$	−14.5855			−0.540203
$730$	−4.43551	−	11.2716i	−0.164165	−	0.417182i
$731$	−0.959085	+	0.959085i	−0.0354731	+	0.0354731i
$732$	1.70486	−	2.05772i	0.0630135	−	0.0760555i
$733$			7.37554i			0.272422i	0.990680	+	0.136211i	$0.0434925\pi$
$733$			7.37554i			0.272422i	−0.990680	+	0.136211i	$0.956508\pi$
$734$	18.5624	−	20.3847i	0.685151	−	0.752411i
$735$	1.06288	−	2.16019i	0.0392049	−	0.0796797i
$736$	7.15865	−	11.6334i	0.263871	−	0.428814i
$737$	−46.2494	−	46.2494i	−1.70362	−	1.70362i
$738$	−0.609181	−	13.0202i	−0.0224243	−	0.479278i
$739$	5.55025	−	5.55025i	0.204169	−	0.204169i	−0.597614	−	0.801784i	$-0.703885\pi$
$739$	5.55025	−	5.55025i	0.204169	−	0.204169i	0.801784	+	0.597614i	$0.203885\pi$
$740$	−8.15651	+	21.4259i	−0.299839	+	0.787632i
$741$	2.13702	+	2.13702i	0.0785053	+	0.0785053i
$742$	−2.31339	−	2.10659i	−0.0849274	−	0.0773355i
$743$	−6.78835	+	6.78835i	−0.249040	+	0.249040i	−0.820577	−	0.571536i	$-0.806348\pi$
$743$	−6.78835	+	6.78835i	−0.249040	+	0.249040i	0.571536	+	0.820577i	$0.306348\pi$
$744$	−0.160630	−	1.13771i	−0.00588899	−	0.0417104i
$745$	−28.6532	+	9.75510i	−1.04977	+	0.357399i
$746$	−30.2315	+	1.41446i	−1.10685	+	0.0517869i
$747$	25.2561			0.924073
$748$	−3.56849	+	0.334655i	−0.130477	+	0.0122362i
$749$	13.9568	+	13.9568i	0.509970	+	0.509970i
$750$	1.91015	+	7.61421i	0.0697486	+	0.278032i
$751$			3.93385i			0.143548i	0.997421	+	0.0717742i	$0.0228661\pi$
$751$			3.93385i			0.143548i	−0.997421	+	0.0717742i	$0.977134\pi$
$752$	13.6816	−	20.0679i	0.498917	−	0.731799i
$753$	−5.15330	+	5.15330i	−0.187797	+	0.187797i
$754$	15.4205	−	16.9343i	0.561582	−	0.616711i
$755$	19.4374	+	9.56379i	0.707398	+	0.348062i
$756$	9.66989	+	8.01170i	0.351690	+	0.291383i
$757$		−	21.8327i		−	0.793525i	−0.917921	−	0.396762i	$-0.870134\pi$
$757$		−	21.8327i		−	0.793525i	0.917921	−	0.396762i	$-0.129866\pi$
$758$	16.8464	+	15.3405i	0.611890	+	0.557191i
$759$		−	7.11421i		−	0.258230i
$760$	−6.74187	+	3.41114i	−0.244553	+	0.123735i
$761$		−	4.27291i		−	0.154893i	−0.996997	−	0.0774464i	$-0.975323\pi$
$761$		−	4.27291i		−	0.154893i	0.996997	−	0.0774464i	$-0.0246767\pi$
$762$	−0.507893	+	0.557752i	−0.0183990	+	0.0202052i
$763$			33.9080i			1.22755i
$764$	−3.75359	−	40.0253i	−0.135800	−	1.44807i
$765$	0.599258	+	1.76017i	0.0216662	+	0.0636391i
$766$	6.54552	+	5.96040i	0.236499	+	0.215358i
$767$	−38.9793	+	38.9793i	−1.40746	+	1.40746i
$768$	−7.39459	+	2.90241i	−0.266829	+	0.104732i
$769$			26.1800i			0.944074i	0.881579	+	0.472037i	$0.156481\pi$
$769$			26.1800i			0.944074i	−0.881579	+	0.472037i	$0.843519\pi$
$770$	37.8205	+	16.4604i	1.36296	+	0.593192i
$771$	−10.1459	−	10.1459i	−0.365395	−	0.365395i
$772$	6.90198	−	8.33049i	0.248408	−	0.299821i
$773$	−15.0077			−0.539791			−0.269895	−	0.962890i	$-0.586989\pi$
$773$	−15.0077			−0.539791			−0.269895	+	0.962890i	$0.586989\pi$
$774$	−0.817390	−	17.4702i	−0.0293805	−	0.627955i
$775$	−3.24117	+	2.49629i	−0.116426	+	0.0896693i
$776$	−22.8838	−	17.2215i	−0.821482	−	0.618215i
$777$	−3.95587	+	3.95587i	−0.141916	+	0.141916i
$778$	16.6305	−	18.2630i	0.596231	−	0.654762i
$779$	2.82762	+	2.82762i	0.101310	+	0.101310i
$780$	4.02504	−	10.5732i	0.144120	−	0.378580i
$781$	44.1977	−	44.1977i	1.58152	−	1.58152i
$782$	1.03015	−	0.0481982i	0.0368381	−	0.00172356i
$783$	6.42007	+	6.42007i	0.229434	+	0.229434i
$784$	−1.61278	−	8.52307i	−0.0575992	−	0.304395i
$785$	20.0161	+	9.84856i	0.714407	+	0.351510i
$786$	−5.57978	−	5.08099i	−0.199024	−	0.181233i
$787$		−	42.9223i		−	1.53001i	−0.644022	−	0.765007i	$-0.722736\pi$
$787$		−	42.9223i		−	1.53001i	0.644022	−	0.765007i	$-0.277264\pi$
$788$	−0.208699	−	2.22540i	−0.00743461	−	0.0792767i
$789$	−6.98118	+	6.98118i	−0.248536	+	0.248536i
$790$	24.1247	+	10.4996i	0.858317	+	0.373560i
$791$	−13.3568			−0.474912
$792$	27.7898	−	36.9270i	0.987466	−	1.31214i
$793$	9.69591	+	9.69591i	0.344312	+	0.344312i
$794$	25.4043	−	1.18861i	0.901565	−	0.0421820i
$795$	−1.00264	−	0.493329i	−0.0355599	−	0.0174966i
$796$	4.77741	+	50.9425i	0.169331	+	1.80561i
$797$	0.280831			0.00994753			0.00497377	−	0.999988i	$-0.498417\pi$
$797$	0.280831			0.00994753			0.00497377	+	0.999988i	$0.498417\pi$
$798$	−1.84175	+	0.0861711i	−0.0651973	+	0.00305042i
$799$	1.83371			0.0648719
$800$	21.9800	+	17.8012i	0.777109	+	0.629366i
$801$	11.7052			0.413581
$802$	12.8068	−	0.599200i	0.452225	−	0.0211585i
$803$	−22.7304			−0.802139
$804$	−1.02191	−	10.8968i	−0.0360400	−	0.384301i
$805$	−10.6489	−	5.23961i	−0.375326	−	0.184672i
$806$	5.88944	−	0.275553i	0.207447	−	0.00970593i
$807$	3.28398	+	3.28398i	0.115602	+	0.115602i
$808$	26.8101	+	20.1762i	0.943176	+	0.709797i
$809$	−16.5787			−0.582876			−0.291438	−	0.956590i	$-0.594134\pi$
$809$	−16.5787			−0.582876			−0.291438	+	0.956590i	$0.594134\pi$
$810$	−19.8396	−	8.63466i	−0.697091	−	0.303391i
$811$	7.25384	−	7.25384i	0.254717	−	0.254717i	−0.568184	−	0.822901i	$-0.692354\pi$
$811$	7.25384	−	7.25384i	0.254717	−	0.254717i	0.822901	+	0.568184i	$0.192354\pi$
$812$	1.30465	+	13.9117i	0.0457841	+	0.488205i
$813$		−	5.27366i		−	0.184955i
$814$	31.8092	+	28.9657i	1.11491	+	1.01525i
$815$	−19.0256	−	9.36118i	−0.666437	−	0.327908i
$816$	−0.495538	−	0.337841i	−0.0173473	−	0.0118268i
$817$	3.79405	+	3.79405i	0.132737	+	0.132737i
$818$	−42.4671	+	1.98693i	−1.48483	+	0.0694715i
$819$	−21.8061	+	21.8061i	−0.761965	+	0.761965i
$820$	5.32578	−	13.9900i	0.185984	−	0.488552i
$821$	−15.3525	−	15.3525i	−0.535806	−	0.535806i	0.386489	−	0.922294i	$-0.373688\pi$
$821$	−15.3525	−	15.3525i	−0.535806	−	0.535806i	−0.922294	+	0.386489i	$0.873688\pi$
$822$	−8.54343	+	9.38212i	−0.297986	+	0.327239i
$823$	−26.7794	+	26.7794i	−0.933472	+	0.933472i	−0.997921	−	0.0644492i	$-0.979471\pi$
$823$	−26.7794	+	26.7794i	−0.933472	+	0.933472i	0.0644492	+	0.997921i	$0.479471\pi$
$824$	−12.4225	+	16.5070i	−0.432758	+	0.575048i
$825$	14.6085	+	1.89660i	0.508603	+	0.0660311i
$826$	−1.57176	−	33.5936i	−0.0546887	−	1.16887i
$827$	−39.4186			−1.37072			−0.685359	−	0.728205i	$-0.740355\pi$
$827$	−39.4186			−1.37072			−0.685359	+	0.728205i	$0.740355\pi$
$828$	−8.48386	+	10.2398i	−0.294834	+	0.355857i
$829$	−20.7102	−	20.7102i	−0.719296	−	0.719296i	0.249165	−	0.968461i	$-0.419844\pi$
$829$	−20.7102	−	20.7102i	−0.719296	−	0.719296i	−0.968461	+	0.249165i	$0.919844\pi$
$830$	26.5958	+	11.5752i	0.923155	+	0.401779i
$831$			4.11345i			0.142694i
$832$	−11.2853	−	39.1690i	−0.391248	−	1.35794i
$833$	0.463083	−	0.463083i	0.0160449	−	0.0160449i
$834$	−5.68428	−	5.17615i	−0.196830	−	0.179235i
$835$	9.61612	+	28.2449i	0.332779	+	0.977456i
$836$	1.32386	+	14.1166i	0.0457868	+	0.488234i
$837$			2.33725i			0.0807870i
$838$	−20.7354	+	22.7709i	−0.716291	+	0.786608i
$839$		−	31.8706i		−	1.10029i	−0.835068	−	0.550147i	$-0.814572\pi$
$839$		−	31.8706i		−	1.10029i	0.835068	−	0.550147i	$-0.185428\pi$
$840$	3.11602	+	6.15859i	0.107513	+	0.212491i
$841$		−	18.8975i		−	0.651638i
$842$	−5.71495	−	5.20408i	−0.196950	−	0.179344i
$843$		−	10.4350i		−	0.359399i
$844$	0.896495	+	0.742765i	0.0308586	+	0.0255670i
$845$	26.0065	+	12.7960i	0.894651	+	0.440196i
$846$	−15.9196	+	17.4824i	−0.547326	+	0.601056i
$847$	37.6347	−	37.6347i	1.29314	−	1.29314i
$848$	−3.95594	+	0.748562i	−0.135847	+	0.0257057i
$849$			7.18654i			0.246642i
$850$	−0.175659	+	2.12819i	−0.00602506	+	0.0729961i
$851$	−8.75302	−	8.75302i	−0.300050	−	0.300050i
$852$	10.4134	−	0.976577i	0.356759	−	0.0334570i
$853$	−26.5538			−0.909185			−0.454592	−	0.890700i	$-0.650215\pi$
$853$	−26.5538			−0.909185			−0.454592	+	0.890700i	$0.650215\pi$
$854$	−8.35626	+	0.390969i	−0.285945	+	0.0133787i
$855$	6.96307	−	2.37061i	0.238132	−	0.0810731i
$856$	25.1491	−	3.55074i	0.859578	−	0.121362i
$857$	−20.7249	+	20.7249i	−0.707951	+	0.707951i	−0.966104	−	0.258153i	$-0.916886\pi$
$857$	−20.7249	+	20.7249i	−0.707951	+	0.707951i	0.258153	+	0.966104i	$0.416886\pi$
$858$	−15.6971	−	14.2939i	−0.535890	−	0.487985i
$859$	35.9248	+	35.9248i	1.22574	+	1.22574i	0.965561	+	0.260176i	$0.0837807\pi$
$859$	35.9248	+	35.9248i	1.22574	+	1.22574i	0.260176	+	0.965561i	$0.416219\pi$
$860$	7.14605	−	18.7716i	0.243678	−	0.640105i
$861$	2.58298	−	2.58298i	0.0880278	−	0.0880278i
$862$	1.80237	+	38.5224i	0.0613889	+	1.31208i
$863$	9.19232	+	9.19232i	0.312910	+	0.312910i	0.846036	−	0.533126i	$-0.178983\pi$
$863$	9.19232	+	9.19232i	0.312910	+	0.312910i	−0.533126	+	0.846036i	$0.678983\pi$
$864$	15.7195	−	3.74314i	0.534789	−	0.127344i
$865$	−8.83254	+	17.9512i	−0.300315	+	0.610358i
$866$	25.7781	−	28.3087i	0.875976	−	0.961969i
$867$			8.39500i			0.285109i
$868$	−2.29482	+	2.76978i	−0.0778913	+	0.0940125i
$869$	34.9117	−	34.9117i	1.18430	−	1.18430i
$870$	1.82732	+	4.64365i	0.0619521	+	0.157434i
$871$	56.1608			1.90293
$872$	34.8630	+	26.2365i	1.18061	+	0.888482i
$873$	19.7151	+	19.7151i	0.667253	+	0.667253i
$874$	−0.190668	−	4.07518i	−0.00644943	−	0.137845i
$875$	13.5981	−	20.4700i	0.459699	−	0.692011i
$876$	−2.92888	−	2.42664i	−0.0989577	−	0.0819885i
$877$	−17.9106			−0.604799			−0.302399	−	0.953181i	$-0.597788\pi$
$877$	−17.9106			−0.604799			−0.302399	+	0.953181i	$0.597788\pi$
$878$	−1.99605	−	42.6619i	−0.0673633	−	1.43977i
$879$	5.91641			0.199556
$880$	46.1879	−	26.1494i	1.55699	−	0.881497i
$881$	6.01537			0.202663			0.101332	−	0.994853i	$-0.467690\pi$
$881$	6.01537			0.202663			0.101332	+	0.994853i	$0.467690\pi$
$882$	0.394667	+	8.43530i	0.0132891	+	0.284031i
$883$	19.8374			0.667580			0.333790	−	0.942647i	$-0.391672\pi$
$883$	19.8374			0.667580			0.333790	+	0.942647i	$0.391672\pi$
$884$	1.96343	−	2.36980i	0.0660373	−	0.0797051i
$885$	−3.87095	−	11.3699i	−0.130120	−	0.382196i
$886$	−1.83117	−	39.1381i	−0.0615195	−	1.31487i
$887$	14.3740	+	14.3740i	0.482632	+	0.482632i	0.905971	−	0.423339i	$-0.139142\pi$
$887$	14.3740	+	14.3740i	0.482632	+	0.482632i	−0.423339	+	0.905971i	$0.639142\pi$
$888$	1.00641	+	7.12819i	0.0337729	+	0.239206i
$889$	2.36149			0.0792019
$890$	12.3261	+	5.36460i	0.413171	+	0.179822i
$891$	−28.7106	+	28.7106i	−0.961842	+	0.961842i
$892$	−36.4741	−	30.2196i	−1.22124	−	1.01183i
$893$		−	7.25398i		−	0.242745i
$894$	−6.39919	+	7.02739i	−0.214021	+	0.235031i
$895$	9.05337	−	3.08226i	0.302621	−	0.103029i
$896$	22.3038	+	10.9983i	0.745117	+	0.367428i
$897$	4.31941	+	4.31941i	0.144221	+	0.144221i
$898$	0.646620	+	13.8203i	0.0215780	+	0.461191i
$899$	−1.83892	+	1.83892i	−0.0613315	+	0.0613315i
$900$	−18.7649	−	20.1508i	−0.625496	−	0.671694i
$901$	−0.214938	−	0.214938i	−0.00716061	−	0.00716061i
$902$	−20.7698	−	18.9131i	−0.691558	−	0.629738i
$903$	3.46580	−	3.46580i	0.115335	−	0.115335i
$904$	−10.3349	+	13.7330i	−0.343734	+	0.456752i
$905$	1.57813	+	4.63536i	0.0524588	+	0.154084i
$906$	6.79482	−	0.317913i	0.225743	−	0.0105620i
$907$	−39.0417			−1.29636			−0.648180	−	0.761487i	$-0.724469\pi$
$907$	−39.0417			−1.29636			−0.648180	+	0.761487i	$0.724469\pi$
$908$	2.57343	+	27.4411i	0.0854024	+	0.910663i
$909$	−23.0976	−	23.0976i	−0.766100	−	0.766100i
$910$	−32.9567	+	12.9688i	−1.09251	+	0.429912i
$911$		−	14.0166i		−	0.464392i	−0.972669	−	0.232196i	$-0.925409\pi$
$911$		−	14.0166i		−	0.464392i	0.972669	−	0.232196i	$-0.0745911\pi$
$912$	−1.33647	+	1.96030i	−0.0442550	+	0.0649121i
$913$	38.4879	−	38.4879i	1.27376	−	1.27376i
$914$	−0.750187	+	0.823831i	−0.0248140	+	0.0272499i
$915$	−2.82822	+	0.962880i	−0.0934980	+	0.0318318i
$916$	−14.2732	+	17.2274i	−0.471601	+	0.569209i
$917$			23.6245i			0.780150i
$918$	0.902034	+	0.821399i	0.0297716	+	0.0271102i
$919$		−	8.15149i		−	0.268893i	−0.990921	−	0.134446i	$-0.957074\pi$
$919$		−	8.15149i		−	0.268893i	0.990921	−	0.134446i	$-0.0429256\pi$
$920$	−13.6269	+	6.89470i	−0.449265	+	0.227311i
$921$			12.6362i			0.416376i
$922$	−16.9386	+	18.6015i	−0.557844	+	0.612606i
$923$			53.6695i			1.76655i
$924$	12.8953	−	1.20933i	0.424224	−	0.0397840i
$925$	20.3072	−	15.6402i	0.667696	−	0.514247i
$926$	−4.87325	−	4.43762i	−0.160145	−	0.145829i
$927$	14.2212	−	14.2212i	0.467086	−	0.467086i
$928$	15.3130	+	9.42289i	0.502675	+	0.309322i
$929$		−	13.4779i		−	0.442196i	−0.975252	−	0.221098i	$-0.929036\pi$
$929$		−	13.4779i		−	0.442196i	0.975252	−	0.221098i	$-0.0709641\pi$
$930$	−0.512646	+	1.17789i	−0.0168103	+	0.0386245i
$931$	−1.83192	−	1.83192i	−0.0600386	−	0.0600386i
$932$	−3.65898	−	3.03154i	−0.119854	−	0.0993013i
$933$	−10.6633			−0.349101
$934$	0.674142	+	14.4086i	0.0220586	+	0.471463i
$935$	3.59554	+	1.76912i	0.117587	+	0.0578563i
$936$	5.54766	+	39.2929i	0.181331	+	1.28433i
$937$	−15.8564	+	15.8564i	−0.518005	+	0.518005i	−0.916967	−	0.398963i	$-0.869370\pi$
$937$	−15.8564	+	15.8564i	−0.518005	+	0.518005i	0.398963	+	0.916967i	$0.369370\pi$
$938$	−23.0683	+	25.3329i	−0.753207	+	0.827148i
$939$	−9.33225	−	9.33225i	−0.304546	−	0.304546i
$940$	−24.7764	+	11.1136i	−0.808116	+	0.362486i
$941$	15.7073	−	15.7073i	0.512044	−	0.512044i	−0.403108	−	0.915152i	$-0.632070\pi$
$941$	15.7073	−	15.7073i	0.512044	−	0.512044i	0.915152	+	0.403108i	$0.132070\pi$
$942$	6.99715	−	0.327380i	0.227979	−	0.0106666i
$943$	5.71527	+	5.71527i	0.186115	+	0.186115i
$944$	−35.7560	−	24.3773i	−1.16376	−	0.793413i
$945$	−4.52489	−	13.2907i	−0.147195	−	0.432347i
$946$	−27.8686	−	25.3773i	−0.906085	−	0.825088i
$947$		−	33.6925i		−	1.09486i	−0.836852	−	0.547430i	$-0.815606\pi$
$947$		−	33.6925i		−	1.09486i	0.836852	−	0.547430i	$-0.184394\pi$
$948$	8.22556	−	0.771397i	0.267154	−	0.0250538i
$949$	13.8008	−	13.8008i	0.447993	−	0.447993i
$950$	8.41891	+	0.694892i	0.273145	+	0.0225453i
$951$	−8.06945			−0.261670
$952$	0.262477	+	1.85907i	0.00850693	+	0.0602527i
$953$	−33.5702	−	33.5702i	−1.08745	−	1.08745i	−0.995791	−	0.0916550i	$-0.970784\pi$
$953$	−33.5702	−	33.5702i	−1.08745	−	1.08745i	−0.0916550	−	0.995791i	$-0.529216\pi$
$954$	3.91520	−	0.183183i	0.126759	−	0.00593076i
$955$	−19.8430	+	40.3287i	−0.642103	+	1.30501i
$956$	23.4342	−	2.19767i	0.757915	−	0.0710776i
$957$	9.36440			0.302708
$958$	7.99281	−	0.373964i	0.258236	−	0.0120822i
$959$	39.7234			1.28274
$960$	8.74309	+	1.56147i	0.282182	+	0.0503962i
$961$	30.3305			0.978404
$962$	−36.8996	+	1.72644i	−1.18969	+	0.0556628i
$963$	−24.7257			−0.796774
$964$	−26.4301	+	2.47863i	−0.851256	+	0.0798311i
$965$	−11.4498	+	3.89813i	−0.368582	+	0.125485i
$966$	−3.72261	+	0.174172i	−0.119773	+	0.00560388i
$967$	28.6436	+	28.6436i	0.921115	+	0.921115i	0.997108	−	0.0759933i	$-0.0242128\pi$
$967$	28.6436	+	28.6436i	0.921115	+	0.921115i	−0.0759933	+	0.997108i	$0.524213\pi$
$968$	−9.57461	−	67.8149i	−0.307740	−	2.17965i
$969$	−0.179123			−0.00575427
$970$	11.7252	+	29.7965i	0.376474	+	0.956707i
$971$	−35.7115	+	35.7115i	−1.14604	+	1.14604i	−0.158713	+	0.987325i	$0.550734\pi$
$971$	−35.7115	+	35.7115i	−1.14604	+	1.14604i	−0.987325	+	0.158713i	$0.949266\pi$
$972$	−23.8289	+	2.23468i	−0.764312	+	0.0716775i
$973$			24.0669i			0.771551i
$974$	−29.2012	−	26.5908i	−0.935666	−	0.852024i
$975$	−10.0211	+	7.71806i	−0.320932	+	0.247176i
$976$	−6.06373	+	8.89414i	−0.194095	+	0.284694i
$977$	7.12822	+	7.12822i	0.228052	+	0.228052i	0.811879	−	0.583826i	$-0.198445\pi$
$977$	7.12822	+	7.12822i	0.228052	+	0.228052i	−0.583826	+	0.811879i	$0.698445\pi$
$978$	−6.65088	+	0.311178i	−0.212672	+	0.00995039i
$979$	17.8375	−	17.8375i	0.570090	−	0.570090i
$980$	−3.45039	+	9.06364i	−0.110219	+	0.289527i
$981$	−30.0355	−	30.0355i	−0.958959	−	0.958959i
$982$	−5.67452	+	6.23158i	−0.181081	+	0.198858i
$983$	−23.9941	+	23.9941i	−0.765292	+	0.765292i	−0.977274	−	0.211982i	$-0.932008\pi$
$983$	−23.9941	+	23.9941i	−0.765292	+	0.765292i	0.211982	+	0.977274i	$0.432008\pi$
$984$	−0.657134	−	4.65434i	−0.0209487	−	0.148375i
$985$	−1.10327	+	2.24227i	−0.0351530	+	0.0714447i
$986$	0.0634430	+	1.35598i	0.00202044	+	0.0431832i
$987$	−6.62639			−0.210920
$988$	−9.37472	−	7.76715i	−0.298250	−	0.247106i
$989$	7.66866	+	7.66866i	0.243849	+	0.243849i
$990$	−48.0817	+	18.9206i	−1.52814	+	0.601338i
$991$			40.6040i			1.28983i	0.764255	+	0.644914i	$0.223107\pi$
$991$			40.6040i			1.28983i	−0.764255	+	0.644914i	$0.776893\pi$
$992$	1.07216	+	4.50260i	0.0340412	+	0.142958i
$993$	4.32718	−	4.32718i	0.137319	−	0.137319i
$994$	−24.2091	−	22.0450i	−0.767866	−	0.699225i
$995$	25.2553	−	51.3286i	0.800645	−	1.62723i
$996$	9.06814	−	0.850414i	0.287335	−	0.0269464i
$997$		−	54.9087i		−	1.73898i	−0.493953	−	0.869488i	$-0.664449\pi$
$997$		−	54.9087i		−	1.73898i	0.493953	−	0.869488i	$-0.335551\pi$
$998$	−22.7384	+	24.9706i	−0.719773	+	0.790431i
$999$		−	14.6437i		−	0.463308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.9	yes	18
3.2	odd	2		720.2.z.g.667.1		18
4.3	odd	2		320.2.s.b.207.6		18
5.2	odd	4		400.2.j.d.43.4		18
5.3	odd	4		80.2.j.b.43.6	✓	18
5.4	even	2		400.2.s.d.107.1		18
8.3	odd	2		640.2.s.c.287.4		18
8.5	even	2		640.2.s.d.287.6		18
15.8	even	4		720.2.bd.g.523.4		18
16.3	odd	4		80.2.j.b.67.6	yes	18
16.5	even	4		640.2.j.c.607.6		18
16.11	odd	4		640.2.j.d.607.4		18
16.13	even	4		320.2.j.b.47.4		18
20.3	even	4		320.2.j.b.143.6		18
20.7	even	4		1600.2.j.d.143.4		18
20.19	odd	2		1600.2.s.d.207.4		18
40.3	even	4		640.2.j.c.543.4		18
40.13	odd	4		640.2.j.d.543.6		18
48.35	even	4		720.2.bd.g.307.4		18
80.3	even	4	inner	80.2.s.b.3.9	yes	18
80.13	odd	4		320.2.s.b.303.6		18
80.19	odd	4		400.2.j.d.307.4		18
80.29	even	4		1600.2.j.d.1007.6		18
80.43	even	4		640.2.s.d.223.6		18
80.53	odd	4		640.2.s.c.223.4		18
80.67	even	4		400.2.s.d.243.1		18
80.77	odd	4		1600.2.s.d.943.4		18
240.83	odd	4		720.2.z.g.163.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.6	✓	18	5.3	odd	4
80.2.j.b.67.6	yes	18	16.3	odd	4
80.2.s.b.3.9	yes	18	80.3	even	4	inner
80.2.s.b.27.9	yes	18	1.1	even	1	trivial
320.2.j.b.47.4		18	16.13	even	4
320.2.j.b.143.6		18	20.3	even	4
320.2.s.b.207.6		18	4.3	odd	2
320.2.s.b.303.6		18	80.13	odd	4
400.2.j.d.43.4		18	5.2	odd	4
400.2.j.d.307.4		18	80.19	odd	4
400.2.s.d.107.1		18	5.4	even	2
400.2.s.d.243.1		18	80.67	even	4
640.2.j.c.543.4		18	40.3	even	4
640.2.j.c.607.6		18	16.5	even	4
640.2.j.d.543.6		18	40.13	odd	4
640.2.j.d.607.4		18	16.11	odd	4
640.2.s.c.223.4		18	80.53	odd	4
640.2.s.c.287.4		18	8.3	odd	2
640.2.s.d.223.6		18	80.43	even	4
640.2.s.d.287.6		18	8.5	even	2
720.2.z.g.163.1		18	240.83	odd	4
720.2.z.g.667.1		18	3.2	odd	2
720.2.bd.g.307.4		18	48.35	even	4
720.2.bd.g.523.4		18	15.8	even	4
1600.2.j.d.143.4		18	20.7	even	4
1600.2.j.d.1007.6		18	80.29	even	4
1600.2.s.d.207.4		18	20.19	odd	2
1600.2.s.d.943.4		18	80.77	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41267 - 0.0660953i) q^{2} -0.496487 q^{3} +(1.99126 - 0.186742i) q^{4} +(-2.00635 - 0.987189i) q^{5} +(-0.701372 + 0.0328155i) q^{6} +(1.55426 + 1.55426i) q^{7} +(2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +O(q^{10})\)	\(q+(1.41267 - 0.0660953i) q^{2} -0.496487 q^{3} +(1.99126 - 0.186742i) q^{4} +(-2.00635 - 0.987189i) q^{5} +(-0.701372 + 0.0328155i) q^{6} +(1.55426 + 1.55426i) q^{7} +(2.80065 - 0.395417i) q^{8} -2.75350 q^{9} +(-2.89956 - 1.26196i) q^{10} +(-4.19607 + 4.19607i) q^{11} +(-0.988637 + 0.0927148i) q^{12} -5.09530i q^{13} +(2.29838 + 2.09292i) q^{14} +(0.996130 + 0.490127i) q^{15} +(3.93026 - 0.743703i) q^{16} +(0.213542 + 0.213542i) q^{17} +(-3.88978 + 0.181993i) q^{18} +(0.844754 - 0.844754i) q^{19} +(-4.17953 - 1.59108i) q^{20} +(-0.771668 - 0.771668i) q^{21} +(-5.65031 + 6.20499i) q^{22} +(1.70744 - 1.70744i) q^{23} +(-1.39049 + 0.196320i) q^{24} +(3.05092 + 3.96130i) q^{25} +(-0.336775 - 7.19797i) q^{26} +2.85654 q^{27} +(3.38518 + 2.80469i) q^{28} +(2.24750 + 2.24750i) q^{29} +(1.43960 + 0.626547i) q^{30} +0.818209i q^{31} +(5.50299 - 1.31038i) q^{32} +(2.08329 - 2.08329i) q^{33} +(0.315778 + 0.287550i) q^{34} +(-1.58404 - 4.65273i) q^{35} +(-5.48294 + 0.514193i) q^{36} -5.12639i q^{37} +(1.13752 - 1.24919i) q^{38} +2.52975i q^{39} +(-6.00945 - 1.97142i) q^{40} +3.34727i q^{41} +(-1.14111 - 1.03911i) q^{42} +4.49131i q^{43} +(-7.57189 + 9.13905i) q^{44} +(5.52450 + 2.71822i) q^{45} +(2.29920 - 2.52490i) q^{46} +(4.29355 - 4.29355i) q^{47} +(-1.95132 + 0.369239i) q^{48} -2.16858i q^{49} +(4.57176 + 5.39435i) q^{50} +(-0.106021 - 0.106021i) q^{51} +(-0.951504 - 10.1461i) q^{52} -1.00653 q^{53} +(4.03534 - 0.188804i) q^{54} +(12.5611 - 4.27649i) q^{55} +(4.96751 + 3.73835i) q^{56} +(-0.419410 + 0.419410i) q^{57} +(3.32352 + 3.02642i) q^{58} +(-7.65005 - 7.65005i) q^{59} +(2.07508 + 0.789952i) q^{60} +(-1.90291 + 1.90291i) q^{61} +(0.0540798 + 1.15586i) q^{62} +(-4.27964 - 4.27964i) q^{63} +(7.68729 - 2.21485i) q^{64} +(-5.03002 + 10.2230i) q^{65} +(2.80531 - 3.08070i) q^{66} +11.0221i q^{67} +(0.465096 + 0.385341i) q^{68} +(-0.847724 + 0.847724i) q^{69} +(-2.54525 - 6.46807i) q^{70} -10.5331 q^{71} +(-7.71159 + 1.08878i) q^{72} +(2.70854 + 2.70854i) q^{73} +(-0.338831 - 7.24189i) q^{74} +(-1.51474 - 1.96674i) q^{75} +(1.52438 - 1.83988i) q^{76} -13.0435 q^{77} +(0.167205 + 3.57370i) q^{78} -8.32010 q^{79} +(-8.61966 - 2.38777i) q^{80} +6.84226 q^{81} +(0.221239 + 4.72858i) q^{82} -9.17237 q^{83} +(-1.68070 - 1.39249i) q^{84} +(-0.217635 - 0.639248i) q^{85} +(0.296855 + 6.34474i) q^{86} +(-1.11585 - 1.11585i) q^{87} +(-10.0925 + 13.4109i) q^{88} -4.25101 q^{89} +(7.98394 + 3.47481i) q^{90} +(7.91940 - 7.91940i) q^{91} +(3.08112 - 3.71882i) q^{92} -0.406230i q^{93} +(5.78157 - 6.34914i) q^{94} +(-2.52881 + 0.860944i) q^{95} +(-2.73217 + 0.650586i) q^{96} +(-7.16000 - 7.16000i) q^{97} +(-0.143333 - 3.06348i) q^{98} +(11.5539 - 11.5539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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