LMFDB - Embedded newform 805.2.l.a.22.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(22,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0, 2]))

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

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

chi := DirichletCharacter("805.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.l (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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.8
Character	$\chi$	$=$	805.22
Dual form			805.2.l.a.183.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60576 - 1.60576i) q^{2} +(0.871410 - 0.871410i) q^{3} +3.15695i q^{4} +(2.02341 - 0.951750i) q^{5} -2.79856 q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.85780 - 1.85780i) q^{8} +1.48129i q^{9} +O(q^{10})$	\(q+(-1.60576 - 1.60576i) q^{2} +(0.871410 - 0.871410i) q^{3} +3.15695i q^{4} +(2.02341 - 0.951750i) q^{5} -2.79856 q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.85780 - 1.85780i) q^{8} +1.48129i q^{9} +(-4.77740 - 1.72083i) q^{10} +5.11689i q^{11} +(2.75100 + 2.75100i) q^{12} +(-1.17759 + 1.17759i) q^{13} +2.27089 q^{14} +(0.933852 - 2.59258i) q^{15} +0.347548 q^{16} +(5.05771 - 5.05771i) q^{17} +(2.37860 - 2.37860i) q^{18} -0.177493 q^{19} +(3.00463 + 6.38780i) q^{20} +1.23236i q^{21} +(8.21652 - 8.21652i) q^{22} +(-4.48121 + 1.70842i) q^{23} -3.23780i q^{24} +(3.18834 - 3.85155i) q^{25} +3.78186 q^{26} +(3.90504 + 3.90504i) q^{27} +(-2.23230 - 2.23230i) q^{28} +5.33033i q^{29} +(-5.66262 + 2.66353i) q^{30} +7.33641 q^{31} +(-4.27367 - 4.27367i) q^{32} +(4.45891 + 4.45891i) q^{33} -16.2430 q^{34} +(-0.757775 + 2.10375i) q^{35} -4.67636 q^{36} +(0.899035 - 0.899035i) q^{37} +(0.285012 + 0.285012i) q^{38} +2.05232i q^{39} +(1.99092 - 5.52723i) q^{40} +9.00707 q^{41} +(1.97888 - 1.97888i) q^{42} +(-4.95163 - 4.95163i) q^{43} -16.1538 q^{44} +(1.40982 + 2.99725i) q^{45} +(9.93910 + 4.45245i) q^{46} +(8.09939 + 8.09939i) q^{47} +(0.302857 - 0.302857i) q^{48} -1.00000i q^{49} +(-11.3044 + 1.06496i) q^{50} -8.81468i q^{51} +(-3.71759 - 3.71759i) q^{52} +(6.96493 + 6.96493i) q^{53} -12.5411i q^{54} +(4.87000 + 10.3536i) q^{55} +2.62732i q^{56} +(-0.154669 + 0.154669i) q^{57} +(8.55925 - 8.55925i) q^{58} +0.00127673i q^{59} +(8.18466 + 2.94813i) q^{60} -3.67196i q^{61} +(-11.7805 - 11.7805i) q^{62} +(-1.04743 - 1.04743i) q^{63} +13.0299i q^{64} +(-1.26197 + 3.50351i) q^{65} -14.3199i q^{66} +(6.28020 - 6.28020i) q^{67} +(15.9670 + 15.9670i) q^{68} +(-2.41624 + 5.39371i) q^{69} +(4.59494 - 2.16132i) q^{70} -15.2707 q^{71} +(2.75193 + 2.75193i) q^{72} +(2.76584 - 2.76584i) q^{73} -2.88728 q^{74} +(-0.577928 - 6.13464i) q^{75} -0.560338i q^{76} +(-3.61819 - 3.61819i) q^{77} +(3.29555 - 3.29555i) q^{78} -7.06344 q^{79} +(0.703231 - 0.330779i) q^{80} +2.36192 q^{81} +(-14.4632 - 14.4632i) q^{82} +(-7.31116 - 7.31116i) q^{83} -3.89050 q^{84} +(5.42013 - 15.0475i) q^{85} +15.9023i q^{86} +(4.64490 + 4.64490i) q^{87} +(9.50614 + 9.50614i) q^{88} -9.74973 q^{89} +(2.54904 - 7.07671i) q^{90} -1.66536i q^{91} +(-5.39342 - 14.1470i) q^{92} +(6.39302 - 6.39302i) q^{93} -26.0114i q^{94} +(-0.359141 + 0.168929i) q^{95} -7.44824 q^{96} +(3.61536 - 3.61536i) q^{97} +(-1.60576 + 1.60576i) q^{98} -7.57960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{3} - 16 q^{6}+O(q^{10}) $ 144 * q + 8 * q^3 - 16 * q^6	$ 144 q + 8 q^{3} - 16 q^{6} + 32 q^{12} - 16 q^{13} - 192 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} + 8 q^{27} - 40 q^{32} + 208 q^{36} + 32 q^{41} - 80 q^{46} + 16 q^{47} + 24 q^{48} - 56 q^{50} - 64 q^{52} + 56 q^{55} - 24 q^{62} - 16 q^{70} - 96 q^{71} - 48 q^{72} + 32 q^{73} - 32 q^{75} + 40 q^{78} - 160 q^{81} - 96 q^{82} + 16 q^{85} - 16 q^{87} + 112 q^{92} - 8 q^{93} - 120 q^{95} + 272 q^{96}+O(q^{100}) $ 144 * q + 8 * q^3 - 16 * q^6 + 32 * q^12 - 16 * q^13 - 192 * q^16 - 16 * q^18 - 8 * q^23 - 8 * q^25 + 8 * q^27 - 40 * q^32 + 208 * q^36 + 32 * q^41 - 80 * q^46 + 16 * q^47 + 24 * q^48 - 56 * q^50 - 64 * q^52 + 56 * q^55 - 24 * q^62 - 16 * q^70 - 96 * q^71 - 48 * q^72 + 32 * q^73 - 32 * q^75 + 40 * q^78 - 160 * q^81 - 96 * q^82 + 16 * q^85 - 16 * q^87 + 112 * q^92 - 8 * q^93 - 120 * q^95 + 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/805\mathbb{Z}\right)^\times$.

$n$	$162$	$281$	$346$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.60576	−	1.60576i	−1.13545	−	1.13545i	−0.989257	−	0.146190i	$-0.953299\pi$
$2$	−1.60576	−	1.60576i	−1.13545	−	1.13545i	−0.146190	−	0.989257i	$-0.546701\pi$
$3$	0.871410	−	0.871410i	0.503109	−	0.503109i	−0.409294	−	0.912403i	$-0.634225\pi$
$3$	0.871410	−	0.871410i	0.503109	−	0.503109i	0.912403	+	0.409294i	$0.134225\pi$
$4$			3.15695i			1.57848i
$5$	2.02341	−	0.951750i	0.904895	−	0.425636i
$5$	2.02341	−	0.951750i	0.904895	−	0.425636i
$6$	−2.79856			−1.14251
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	1.85780	−	1.85780i	0.656830	−	0.656830i
$9$			1.48129i			0.493763i
$10$	−4.77740	−	1.72083i	−1.51075	−	0.544173i
$11$			5.11689i			1.54280i	0.636350	+	0.771401i	$0.280443\pi$
$11$			5.11689i			1.54280i	−0.636350	+	0.771401i	$0.719557\pi$
$12$	2.75100	+	2.75100i	0.794146	+	0.794146i
$13$	−1.17759	+	1.17759i	−0.326604	+	0.326604i	−0.851294	−	0.524690i	$-0.824181\pi$
$13$	−1.17759	+	1.17759i	−0.326604	+	0.326604i	0.524690	+	0.851294i	$0.324181\pi$
$14$	2.27089			0.606922
$15$	0.933852	−	2.59258i	0.241120	−	0.669402i
$16$	0.347548			0.0868870
$17$	5.05771	−	5.05771i	1.22668	−	1.22668i	0.261461	−	0.965214i	$-0.415796\pi$
$17$	5.05771	−	5.05771i	1.22668	−	1.22668i	0.965214	−	0.261461i	$-0.0842043\pi$
$18$	2.37860	−	2.37860i	0.560641	−	0.560641i
$19$	−0.177493			−0.0407197			−0.0203599	−	0.999793i	$-0.506481\pi$
$19$	−0.177493			−0.0407197			−0.0203599	+	0.999793i	$0.506481\pi$
$20$	3.00463	+	6.38780i	0.671856	+	1.42836i
$21$			1.23236i			0.268923i
$22$	8.21652	−	8.21652i	1.75177	−	1.75177i
$23$	−4.48121	+	1.70842i	−0.934398	+	0.356231i
$23$	−4.48121	+	1.70842i	−0.934398	+	0.356231i
$24$		−	3.23780i		−	0.660914i
$25$	3.18834	−	3.85155i	0.637669	−	0.770311i
$26$	3.78186			0.741683
$27$	3.90504	+	3.90504i	0.751525	+	0.751525i
$28$	−2.23230	−	2.23230i	−0.421866	−	0.421866i
$29$			5.33033i			0.989817i	0.868945	+	0.494908i	$0.164798\pi$
$29$			5.33033i			0.989817i	−0.868945	+	0.494908i	$0.835202\pi$
$30$	−5.66262	+	2.66353i	−1.03385	+	0.486291i
$31$	7.33641			1.31766			0.658829	−	0.752293i	$-0.271052\pi$
$31$	7.33641			1.31766			0.658829	+	0.752293i	$0.271052\pi$
$32$	−4.27367	−	4.27367i	−0.755485	−	0.755485i
$33$	4.45891	+	4.45891i	0.776197	+	0.776197i
$34$	−16.2430			−2.78565
$35$	−0.757775	+	2.10375i	−0.128087	+	0.355599i
$36$	−4.67636			−0.779394
$37$	0.899035	−	0.899035i	0.147800	−	0.147800i	−0.629334	−	0.777135i	$-0.716672\pi$
$37$	0.899035	−	0.899035i	0.147800	−	0.147800i	0.777135	+	0.629334i	$0.216672\pi$
$38$	0.285012	+	0.285012i	0.0462351	+	0.0462351i
$39$			2.05232i			0.328635i
$40$	1.99092	−	5.52723i	0.314792	−	0.873932i
$41$	9.00707			1.40667			0.703334	−	0.710860i	$-0.251694\pi$
$41$	9.00707			1.40667			0.703334	+	0.710860i	$0.251694\pi$
$42$	1.97888	−	1.97888i	0.305348	−	0.305348i
$43$	−4.95163	−	4.95163i	−0.755117	−	0.755117i	0.220313	−	0.975429i	$-0.429292\pi$
$43$	−4.95163	−	4.95163i	−0.755117	−	0.755117i	−0.975429	+	0.220313i	$0.929292\pi$
$44$	−16.1538			−2.43528
$45$	1.40982	+	2.99725i	0.210163	+	0.446804i
$46$	9.93910	+	4.45245i	1.46544	+	0.656477i
$47$	8.09939	+	8.09939i	1.18142	+	1.18142i	0.979377	+	0.202040i	$0.0647571\pi$
$47$	8.09939	+	8.09939i	1.18142	+	1.18142i	0.202040	+	0.979377i	$0.435243\pi$
$48$	0.302857	−	0.302857i	0.0437136	−	0.0437136i
$49$		−	1.00000i		−	0.142857i
$50$	−11.3044	+	1.06496i	−1.59869	+	0.150608i
$51$		−	8.81468i		−	1.23430i
$52$	−3.71759	−	3.71759i	−0.515537	−	0.515537i
$53$	6.96493	+	6.96493i	0.956706	+	0.956706i	0.999101	−	0.0423949i	$-0.0134988\pi$
$53$	6.96493	+	6.96493i	0.956706	+	0.956706i	−0.0423949	+	0.999101i	$0.513499\pi$
$54$		−	12.5411i		−	1.70663i
$55$	4.87000	+	10.3536i	0.656671	+	1.39607i
$56$			2.62732i			0.351090i
$57$	−0.154669	+	0.154669i	−0.0204865	+	0.0204865i
$58$	8.55925	−	8.55925i	1.12388	−	1.12388i
$59$			0.00127673i			0.000166216i	1.00000		8.31079e-5i	$2.64541e-5\pi$
$59$			0.00127673i			0.000166216i	−1.00000		8.31079e-5i	$0.999974\pi$
$60$	8.18466	+	2.94813i	1.05663	+	0.380602i
$61$		−	3.67196i		−	0.470146i	−0.971978	−	0.235073i	$-0.924467\pi$
$61$		−	3.67196i		−	0.470146i	0.971978	−	0.235073i	$-0.0755329\pi$
$62$	−11.7805	−	11.7805i	−1.49613	−	1.49613i
$63$	−1.04743	−	1.04743i	−0.131964	−	0.131964i
$64$			13.0299i			1.62874i
$65$	−1.26197	+	3.50351i	−0.156528	+	0.434557i
$66$		−	14.3199i		−	1.76266i
$67$	6.28020	−	6.28020i	0.767248	−	0.767248i	−0.210373	−	0.977621i	$-0.567468\pi$
$67$	6.28020	−	6.28020i	0.767248	−	0.767248i	0.977621	+	0.210373i	$0.0674678\pi$
$68$	15.9670	+	15.9670i	1.93628	+	1.93628i
$69$	−2.41624	+	5.39371i	−0.290881	+	0.649327i
$70$	4.59494	−	2.16132i	0.549200	−	0.258327i
$71$	−15.2707			−1.81230			−0.906150	−	0.422957i	$-0.860992\pi$
$71$	−15.2707			−1.81230			−0.906150	+	0.422957i	$0.860992\pi$
$72$	2.75193	+	2.75193i	0.324318	+	0.324318i
$73$	2.76584	−	2.76584i	0.323717	−	0.323717i	−0.526474	−	0.850191i	$-0.676486\pi$
$73$	2.76584	−	2.76584i	0.323717	−	0.323717i	0.850191	+	0.526474i	$0.176486\pi$
$74$	−2.88728			−0.335639
$75$	−0.577928	−	6.13464i	−0.0667333	−	0.708367i
$76$		−	0.560338i		−	0.0642752i
$77$	−3.61819	−	3.61819i	−0.412331	−	0.412331i
$78$	3.29555	−	3.29555i	0.373147	−	0.373147i
$79$	−7.06344			−0.794700			−0.397350	−	0.917667i	$-0.630070\pi$
$79$	−7.06344			−0.794700			−0.397350	+	0.917667i	$0.630070\pi$
$80$	0.703231	−	0.330779i	0.0786236	−	0.0369822i
$81$	2.36192			0.262435
$82$	−14.4632	−	14.4632i	−1.59720	−	1.59720i
$83$	−7.31116	−	7.31116i	−0.802504	−	0.802504i	0.180982	−	0.983486i	$-0.442072\pi$
$83$	−7.31116	−	7.31116i	−0.802504	−	0.802504i	−0.983486	+	0.180982i	$0.942072\pi$
$84$	−3.89050			−0.424489
$85$	5.42013	−	15.0475i	0.587895	−	1.63213i
$86$			15.9023i			1.71479i
$87$	4.64490	+	4.64490i	0.497986	+	0.497986i
$88$	9.50614	+	9.50614i	1.01336	+	1.01336i
$89$	−9.74973			−1.03347			−0.516735	−	0.856146i	$-0.672853\pi$
$89$	−9.74973			−1.03347			−0.516735	+	0.856146i	$0.672853\pi$
$90$	2.54904	−	7.07671i	0.268693	−	0.745950i
$91$		−	1.66536i		−	0.174577i
$92$	−5.39342	−	14.1470i	−0.562303	−	1.47493i
$93$	6.39302	−	6.39302i	0.662925	−	0.662925i
$94$		−	26.0114i		−	2.68287i
$95$	−0.359141	+	0.168929i	−0.0368471	+	0.0173318i
$96$	−7.44824			−0.760183
$97$	3.61536	−	3.61536i	0.367084	−	0.367084i	−0.499329	−	0.866413i	$-0.666420\pi$
$97$	3.61536	−	3.61536i	0.367084	−	0.367084i	0.866413	+	0.499329i	$0.166420\pi$
$98$	−1.60576	+	1.60576i	−0.162207	+	0.162207i
$99$	−7.57960			−0.761778
$100$	12.1592	+	10.0655i	1.21592	+	1.00655i
$101$	−6.96295			−0.692840			−0.346420	−	0.938080i	$-0.612603\pi$
$101$	−6.96295			−0.692840			−0.346420	+	0.938080i	$0.612603\pi$
$102$	−14.1543	+	14.1543i	−1.40148	+	1.40148i
$103$	9.94408	+	9.94408i	0.979819	+	0.979819i	0.999800	−	0.0199809i	$-0.00636053\pi$
$103$	9.94408	+	9.94408i	0.979819	+	0.979819i	−0.0199809	+	0.999800i	$0.506361\pi$
$104$			4.37543i			0.429047i
$105$	1.17290	+	2.49356i	0.114463	+	0.243347i
$106$		−	22.3680i		−	2.17258i
$107$	−2.45830	+	2.45830i	−0.237653	+	0.237653i	−0.815878	−	0.578225i	$-0.803746\pi$
$107$	−2.45830	+	2.45830i	−0.237653	+	0.237653i	0.578225	+	0.815878i	$0.303746\pi$
$108$	−12.3280	+	12.3280i	−1.18627	+	1.18627i
$109$	1.65584			0.158600			0.0793002	−	0.996851i	$-0.474731\pi$
$109$	1.65584			0.158600			0.0793002	+	0.996851i	$0.474731\pi$
$110$	8.80528	−	24.4454i	0.839551	−	2.33078i
$111$		−	1.56686i		−	0.148719i
$112$	−0.245754	+	0.245754i	−0.0232215	+	0.0232215i
$113$	−8.11245	−	8.11245i	−0.763155	−	0.763155i	0.213736	−	0.976891i	$-0.431437\pi$
$113$	−8.11245	−	8.11245i	−0.763155	−	0.763155i	−0.976891	+	0.213736i	$0.931437\pi$
$114$	0.496725			0.0465226
$115$	−7.44132	+	7.72183i	−0.693907	+	0.720065i
$116$	−16.8276			−1.56240
$117$	−1.74435	−	1.74435i	−0.161265	−	0.161265i
$118$	0.00205012	−	0.00205012i	0.000188729	−	0.000188729i
$119$			7.15268i			0.655685i
$120$	−3.08158	−	6.55139i	−0.281308	−	0.598057i
$121$	−15.1826			−1.38024
$122$	−5.89629	+	5.89629i	−0.533825	+	0.533825i
$123$	7.84885	−	7.84885i	0.707707	−	0.707707i
$124$			23.1607i			2.07989i
$125$	2.78560	−	10.8278i	0.249151	−	0.968465i
$126$			3.36385i			0.299675i
$127$	9.37869	+	9.37869i	0.832224	+	0.832224i	0.987821	−	0.155597i	$-0.0497301\pi$
$127$	9.37869	+	9.37869i	0.832224	+	0.832224i	−0.155597	+	0.987821i	$0.549730\pi$
$128$	12.3756	−	12.3756i	1.09386	−	1.09386i
$129$	−8.62980			−0.759812
$130$	7.65223	−	3.59938i	0.671145	−	0.315687i
$131$	4.26187			0.372361			0.186180	−	0.982516i	$-0.440389\pi$
$131$	4.26187			0.372361			0.186180	+	0.982516i	$0.440389\pi$
$132$	−14.0766	+	14.0766i	−1.22521	+	1.22521i
$133$	0.125507	−	0.125507i	0.0108828	−	0.0108828i
$134$	−20.1690			−1.74234
$135$	11.6181	+	4.18486i	0.999927	+	0.360175i
$136$		−	18.7924i		−	1.61143i
$137$	−10.7577	+	10.7577i	−0.919090	+	0.919090i	−0.996963	−	0.0778736i	$-0.975187\pi$
$137$	−10.7577	+	10.7577i	−0.919090	+	0.919090i	0.0778736	+	0.996963i	$0.475187\pi$
$138$	12.5409	−	4.78112i	1.06756	−	0.406996i
$139$		−	8.20058i		−	0.695564i	−0.937575	−	0.347782i	$-0.886935\pi$
$139$		−	8.20058i		−	0.695564i	0.937575	−	0.347782i	$-0.113065\pi$
$140$	−6.64145	−	2.39226i	−0.561305	−	0.202183i
$141$	14.1158			1.18876
$142$	24.5212	+	24.5212i	2.05777	+	2.05777i
$143$	−6.02559	−	6.02559i	−0.503885	−	0.503885i
$144$			0.514819i			0.0429016i
$145$	5.07314	+	10.7854i	0.421301	+	0.895680i
$146$	−8.88258			−0.735127
$147$	−0.871410	−	0.871410i	−0.0718727	−	0.0718727i
$148$	2.83821	+	2.83821i	0.233300	+	0.233300i
$149$	20.0963			1.64636			0.823178	−	0.567784i	$-0.192199\pi$
$149$	20.0963			1.64636			0.823178	+	0.567784i	$0.192199\pi$
$150$	−8.92276	+	10.7788i	−0.728541	+	0.880085i
$151$	16.3331			1.32917			0.664585	−	0.747212i	$-0.268608\pi$
$151$	16.3331			1.32917			0.664585	+	0.747212i	$0.268608\pi$
$152$	−0.329746	+	0.329746i	−0.0267459	+	0.0267459i
$153$	7.49193	+	7.49193i	0.605687	+	0.605687i
$154$			11.6199i			0.936359i
$155$	14.8445	−	6.98243i	1.19234	−	0.560842i
$156$	−6.47909			−0.518743
$157$	10.6024	−	10.6024i	0.846166	−	0.846166i	−0.143486	−	0.989652i	$-0.545831\pi$
$157$	10.6024	−	10.6024i	0.846166	−	0.846166i	0.989652	+	0.143486i	$0.0458313\pi$
$158$	11.3422	+	11.3422i	0.902339	+	0.902339i
$159$	12.1386			0.962655
$160$	−12.7148	−	4.57990i	−1.00520	−	0.362073i
$161$	1.96066	−	4.37674i	0.154522	−	0.344935i
$162$	−3.79268	−	3.79268i	−0.297981	−	0.297981i
$163$	−7.21699	+	7.21699i	−0.565278	+	0.565278i	−0.930802	−	0.365524i	$-0.880890\pi$
$163$	−7.21699	+	7.21699i	−0.565278	+	0.565278i	0.365524	+	0.930802i	$0.380890\pi$
$164$			28.4349i			2.22039i
$165$	13.2660	+	4.77842i	1.03275	+	0.371999i
$166$			23.4800i			1.82240i
$167$	−11.5383	−	11.5383i	−0.892862	−	0.892862i	0.101929	−	0.994792i	$-0.467498\pi$
$167$	−11.5383	−	11.5383i	−0.892862	−	0.892862i	−0.994792	+	0.101929i	$0.967498\pi$
$168$	2.28947	+	2.28947i	0.176637	+	0.176637i
$169$			10.2266i			0.786659i
$170$	−32.8661	+	15.4593i	−2.52072	+	1.18567i
$171$		−	0.262919i		−	0.0201059i
$172$	15.6321	−	15.6321i	1.19193	−	1.19193i
$173$	−4.88923	+	4.88923i	−0.371722	+	0.371722i	−0.868104	−	0.496382i	$-0.834661\pi$
$173$	−4.88923	+	4.88923i	−0.371722	+	0.371722i	0.496382	+	0.868104i	$0.334661\pi$
$174$		−	14.9172i		−	1.13087i
$175$	0.468960	+	4.97796i	0.0354500	+	0.376298i
$176$			1.77837i			0.134049i
$177$	0.00111255	+	0.00111255i	8.36246e−5	+	8.36246e-5i
$178$	15.6558	+	15.6558i	1.17345	+	1.17345i
$179$			9.43066i			0.704881i	0.935834	+	0.352440i	$0.114648\pi$
$179$			9.43066i			0.704881i	−0.935834	+	0.352440i	$0.885352\pi$
$180$	−9.46218	+	4.45073i	−0.705269	+	0.331738i
$181$		−	22.3549i		−	1.66163i	−0.556551	−	0.830813i	$-0.687876\pi$
$181$		−	22.3549i		−	1.66163i	0.556551	−	0.830813i	$-0.312124\pi$
$182$	−2.67418	+	2.67418i	−0.198223	+	0.198223i
$183$	−3.19978	−	3.19978i	−0.236534	−	0.236534i
$184$	−5.15128	+	11.4991i	−0.379757	+	0.847724i
$185$	0.963457	−	2.67477i	0.0708347	−	0.196653i
$186$	−20.5314			−1.50543
$187$	25.8798	+	25.8798i	1.89252	+	1.89252i
$188$	−25.5694	+	25.5694i	−1.86484	+	1.86484i
$189$	−5.52256			−0.401707
$190$	0.847956	+	0.305435i	0.0615172	+	0.0221586i
$191$		−	7.38066i		−	0.534046i	−0.963690	−	0.267023i	$-0.913960\pi$
$191$		−	7.38066i		−	0.534046i	0.963690	−	0.267023i	$-0.0860399\pi$
$192$	11.3544	+	11.3544i	0.819433	+	0.819433i
$193$	−9.22954	+	9.22954i	−0.664357	+	0.664357i	−0.956404	−	0.292047i	$-0.905664\pi$
$193$	−9.22954	+	9.22954i	−0.664357	+	0.664357i	0.292047	+	0.956404i	$0.405664\pi$
$194$	−11.6108			−0.833608
$195$	1.95330	+	4.15268i	0.139879	+	0.297380i
$196$	3.15695			0.225497
$197$	−9.00339	−	9.00339i	−0.641465	−	0.641465i	0.309450	−	0.950916i	$-0.399855\pi$
$197$	−9.00339	−	9.00339i	−0.641465	−	0.641465i	−0.950916	+	0.309450i	$0.899855\pi$
$198$	12.1710	+	12.1710i	0.864958	+	0.864958i
$199$	−14.2467			−1.00992			−0.504962	−	0.863142i	$-0.668493\pi$
$199$	−14.2467			−1.00992			−0.504962	+	0.863142i	$0.668493\pi$
$200$	−1.23211	−	13.0787i	−0.0871232	−	0.924803i
$201$		−	10.9453i		−	0.772019i
$202$	11.1809	+	11.1809i	0.786682	+	0.786682i
$203$	−3.76911	−	3.76911i	−0.264540	−	0.264540i
$204$	27.8275			1.94832
$205$	18.2250	−	8.57248i	1.27289	−	0.598728i
$206$		−	31.9357i		−	2.22507i
$207$	−2.53067	−	6.63797i	−0.175894	−	0.461371i
$208$	−0.409268	+	0.409268i	−0.0283777	+	0.0283777i
$209$		−	0.908214i		−	0.0628225i
$210$	2.12068	−	5.88747i	0.146341	−	0.406274i
$211$	−24.0833			−1.65796			−0.828982	−	0.559276i	$-0.811079\pi$
$211$	−24.0833			−1.65796			−0.828982	+	0.559276i	$0.811079\pi$
$212$	−21.9880	+	21.9880i	−1.51014	+	1.51014i
$213$	−13.3070	+	13.3070i	−0.911784	+	0.911784i
$214$	7.89490			0.539684
$215$	−14.7319	−	5.30644i	−1.00471	−	0.361897i
$216$	14.5095			0.987249
$217$	−5.18762	+	5.18762i	−0.352159	+	0.352159i
$218$	−2.65888	−	2.65888i	−0.180082	−	0.180082i
$219$		−	4.82036i		−	0.325730i
$220$	−32.6857	+	15.3744i	−2.20367	+	1.03654i
$221$			11.9118i			0.801274i
$222$	−2.51600	+	2.51600i	−0.168863	+	0.168863i
$223$	−4.29281	+	4.29281i	−0.287468	+	0.287468i	−0.836078	−	0.548610i	$-0.815157\pi$
$223$	−4.29281	+	4.29281i	−0.287468	+	0.287468i	0.548610	+	0.836078i	$0.315157\pi$
$224$	6.04388			0.403824
$225$	5.70526	+	4.72286i	0.380351	+	0.314857i
$226$			26.0534i			1.73304i
$227$	−5.29397	+	5.29397i	−0.351373	+	0.351373i	−0.860620	−	0.509247i	$-0.829924\pi$
$227$	−5.29397	+	5.29397i	−0.351373	+	0.351373i	0.509247	+	0.860620i	$0.329924\pi$
$228$	−0.488284	−	0.488284i	−0.0323374	−	0.0323374i
$229$	2.13155			0.140857			0.0704284	−	0.997517i	$-0.477563\pi$
$229$	2.13155			0.140857			0.0704284	+	0.997517i	$0.477563\pi$
$230$	24.3484	−	0.450430i	1.60549	−	0.0297005i
$231$	−6.30585			−0.414895
$232$	9.90266	+	9.90266i	0.650141	+	0.650141i
$233$	10.5794	−	10.5794i	0.693080	−	0.693080i	−0.269828	−	0.962908i	$-0.586967\pi$
$233$	10.5794	−	10.5794i	0.693080	−	0.693080i	0.962908	+	0.269828i	$0.0869670\pi$
$234$			5.60202i			0.366216i
$235$	24.0969	+	8.67976i	1.57191	+	0.566205i
$236$	−0.00403057			−0.000262368
$237$	−6.15516	+	6.15516i	−0.399820	+	0.399820i
$238$	11.4855	−	11.4855i	0.744496	−	0.744496i
$239$			20.2127i			1.30745i	0.756731	+	0.653726i	$0.226795\pi$
$239$			20.2127i			1.30745i	−0.756731	+	0.653726i	$0.773205\pi$
$240$	0.324558	−	0.901046i	0.0209502	−	0.0581623i
$241$		−	3.93449i		−	0.253443i	−0.991938	−	0.126721i	$-0.959555\pi$
$241$		−	3.93449i		−	0.253443i	0.991938	−	0.126721i	$-0.0404454\pi$
$242$	24.3797	+	24.3797i	1.56718	+	1.56718i
$243$	−9.65692	+	9.65692i	−0.619492	+	0.619492i
$244$	11.5922			0.742114
$245$	−0.951750	−	2.02341i	−0.0608051	−	0.129271i
$246$	−25.2068			−1.60713
$247$	0.209014	−	0.209014i	0.0132992	−	0.0132992i
$248$	13.6295	−	13.6295i	0.865477	−	0.865477i
$249$	−12.7420			−0.807494
$250$	−21.8598	+	12.9138i	−1.38254	+	0.816741i
$251$			13.0565i			0.824118i	0.911157	+	0.412059i	$0.135190\pi$
$251$			13.0565i			0.824118i	−0.911157	+	0.412059i	$0.864810\pi$
$252$	3.30669	−	3.30669i	0.208302	−	0.208302i
$253$	−8.74182	−	22.9299i	−0.549594	−	1.44159i
$254$		−	30.1199i		−	1.88989i
$255$	−8.38937	−	17.8357i	−0.525363	−	1.11691i
$256$	−13.6848			−0.855301
$257$	−0.762361	−	0.762361i	−0.0475547	−	0.0475547i	0.682930	−	0.730484i	$-0.260706\pi$
$257$	−0.762361	−	0.762361i	−0.0475547	−	0.0475547i	−0.730484	+	0.682930i	$0.760706\pi$
$258$	13.8574	+	13.8574i	0.862725	+	0.862725i
$259$			1.27143i			0.0790027i
$260$	−11.0604	−	3.98398i	−0.685938	−	0.247076i
$261$	−7.89575			−0.488735
$262$	−6.84355	−	6.84355i	−0.422796	−	0.422796i
$263$	8.16290	+	8.16290i	0.503346	+	0.503346i	0.912476	−	0.409130i	$-0.134168\pi$
$263$	8.16290	+	8.16290i	0.503346	+	0.503346i	−0.409130	+	0.912476i	$0.634168\pi$
$264$	16.5675			1.01966
$265$	20.7217	+	7.46400i	1.27293	+	0.458510i
$266$	−0.403068			−0.0247137
$267$	−8.49601	+	8.49601i	−0.519948	+	0.519948i
$268$	19.8263	+	19.8263i	1.21108	+	1.21108i
$269$			16.1342i			0.983717i	0.870675	+	0.491859i	$0.163682\pi$
$269$			16.1342i			0.983717i	−0.870675	+	0.491859i	$0.836318\pi$
$270$	−11.9360	−	25.3758i	−0.726404	−	1.54432i
$271$	28.0822			1.70587			0.852937	−	0.522013i	$-0.174819\pi$
$271$	28.0822			1.70587			0.852937	+	0.522013i	$0.174819\pi$
$272$	1.75780	−	1.75780i	0.106582	−	0.106582i
$273$	−1.45121	−	1.45121i	−0.0878314	−	0.0878314i
$274$	34.5485			2.08715
$275$	19.7080	+	16.3144i	1.18844	+	0.983796i
$276$	−17.0277	−	7.62795i	−1.02495	−	0.459149i
$277$	−9.30858	−	9.30858i	−0.559298	−	0.559298i	0.369809	−	0.929108i	$-0.379423\pi$
$277$	−9.30858	−	9.30858i	−0.559298	−	0.559298i	−0.929108	+	0.369809i	$0.879423\pi$
$278$	−13.1682	+	13.1682i	−0.789776	+	0.789776i
$279$			10.8673i			0.650611i
$280$	2.50055	+	5.31613i	0.149437	+	0.317700i
$281$			10.6158i			0.633287i	0.948545	+	0.316644i	$0.102556\pi$
$281$			10.6158i			0.633287i	−0.948545	+	0.316644i	$0.897444\pi$
$282$	−22.6666	−	22.6666i	−1.34978	−	1.34978i
$283$	1.39498	+	1.39498i	0.0829228	+	0.0829228i	0.747352	−	0.664429i	$-0.231325\pi$
$283$	1.39498	+	1.39498i	0.0829228	+	0.0829228i	−0.664429	+	0.747352i	$0.731325\pi$
$284$		−	48.2089i		−	2.86067i
$285$	−0.165752	+	0.460166i	−0.00981833	+	0.0272579i
$286$			19.3514i			1.14427i
$287$	−6.36896	+	6.36896i	−0.375948	+	0.375948i
$288$	6.33054	−	6.33054i	0.373031	−	0.373031i
$289$		−	34.1609i		−	2.00946i
$290$	9.17257	−	25.4651i	0.538632	−	1.49536i
$291$		−	6.30092i		−	0.369366i
$292$	8.73164	+	8.73164i	0.510980	+	0.510980i
$293$	−0.213491	−	0.213491i	−0.0124723	−	0.0124723i	0.700843	−	0.713315i	$-0.252807\pi$
$293$	−0.213491	−	0.213491i	−0.0124723	−	0.0124723i	−0.713315	+	0.700843i	$0.752807\pi$
$294$			2.79856i			0.163215i
$295$	0.00121513	+	0.00258334i	7.07473e−5	+	0.000150408i
$296$		−	3.34045i		−	0.194160i
$297$	−19.9817	+	19.9817i	−1.15945	+	1.15945i
$298$	−32.2700	−	32.2700i	−1.86935	−	1.86935i
$299$	3.26520	−	7.28884i	0.188832	−	0.421525i
$300$	19.3668	−	1.82449i	1.11814	−	0.105337i
$301$	7.00266			0.403627
$302$	−26.2271	−	26.2271i	−1.50920	−	1.50920i
$303$	−6.06759	+	6.06759i	−0.348574	+	0.348574i
$304$	−0.0616874			−0.00353802
$305$	−3.49478	−	7.42986i	−0.200111	−	0.425432i
$306$		−	24.0605i		−	1.37545i
$307$	−21.1411	−	21.1411i	−1.20659	−	1.20659i	−0.972126	−	0.234461i	$-0.924668\pi$
$307$	−21.1411	−	21.1411i	−1.20659	−	1.20659i	−0.234461	−	0.972126i	$-0.575332\pi$
$308$	11.4225	−	11.4225i	0.650855	−	0.650855i
$309$	17.3307			0.985912
$310$	−35.0489	−	12.6247i	−1.99065	−	0.717034i
$311$	22.9906			1.30368			0.651838	−	0.758358i	$-0.273998\pi$
$311$	22.9906			1.30368			0.651838	+	0.758358i	$0.273998\pi$
$312$	3.81280	+	3.81280i	0.215857	+	0.215857i
$313$	−20.7186	−	20.7186i	−1.17109	−	1.17109i	−0.981951	−	0.189136i	$-0.939431\pi$
$313$	−20.7186	−	20.7186i	−1.17109	−	1.17109i	−0.189136	−	0.981951i	$-0.560569\pi$
$314$	−34.0500			−1.92155
$315$	−3.11627	−	1.12248i	−0.175582	−	0.0632448i
$316$		−	22.2990i		−	1.25442i
$317$	12.5484	+	12.5484i	0.704787	+	0.704787i	0.965434	−	0.260647i	$-0.0839360\pi$
$317$	12.5484	+	12.5484i	0.704787	+	0.704787i	−0.260647	+	0.965434i	$0.583936\pi$
$318$	−19.4917	−	19.4917i	−1.09304	−	1.09304i
$319$	−27.2747			−1.52709
$320$	12.4012	+	26.3648i	0.693249	+	1.47384i
$321$			4.28438i			0.239131i
$322$	−10.1764	+	3.87965i	−0.567106	+	0.216204i
$323$	−0.897710	+	0.897710i	−0.0499499	+	0.0499499i
$324$			7.45646i			0.414248i
$325$	0.780988	+	8.29010i	0.0433214	+	0.459852i
$326$	23.1776			1.28369
$327$	1.44291	−	1.44291i	0.0797933	−	0.0797933i
$328$	16.7333	−	16.7333i	0.923941	−	0.923941i
$329$	−11.4543			−0.631494
$330$	−13.6290	−	28.9750i	−0.750251	−	1.59502i
$331$	10.6802			0.587035			0.293517	−	0.955954i	$-0.405174\pi$
$331$	10.6802			0.587035			0.293517	+	0.955954i	$0.405174\pi$
$332$	23.0810	−	23.0810i	1.26673	−	1.26673i
$333$	1.33173	+	1.33173i	0.0729784	+	0.0729784i
$334$			37.0556i			2.02759i
$335$	6.73021	−	18.6846i	0.367711	−	1.02085i
$336$			0.428304i			0.0233659i
$337$	8.15510	−	8.15510i	0.444237	−	0.444237i	−0.449196	−	0.893433i	$-0.648290\pi$
$337$	8.15510	−	8.15510i	0.444237	−	0.444237i	0.893433	+	0.449196i	$0.148290\pi$
$338$	16.4215	−	16.4215i	0.893210	−	0.893210i
$339$	−14.1385			−0.767900
$340$	47.5042	+	17.1111i	2.57628	+	0.927979i
$341$			37.5396i			2.03288i
$342$	−0.422186	+	0.422186i	−0.0228292	+	0.0228292i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−18.3982			−0.991966
$345$	0.244438	+	13.2133i	0.0131601	+	0.711382i
$346$	15.7019			0.844140
$347$	−15.7945	−	15.7945i	−0.847891	−	0.847891i	0.141978	−	0.989870i	$-0.454654\pi$
$347$	−15.7945	−	15.7945i	−0.847891	−	0.847891i	−0.989870	+	0.141978i	$0.954654\pi$
$348$	−14.6637	+	14.6637i	−0.786059	+	0.786059i
$349$		−	14.9580i		−	0.800683i	−0.916366	−	0.400341i	$-0.868892\pi$
$349$		−	14.9580i		−	0.800683i	0.916366	−	0.400341i	$-0.131108\pi$
$350$	7.24039	−	8.74647i	0.387015	−	0.467518i
$351$	−9.19706			−0.490903
$352$	21.8679	−	21.8679i	1.16556	−	1.16556i
$353$	−5.37387	+	5.37387i	−0.286022	+	0.286022i	−0.835505	−	0.549483i	$-0.814825\pi$
$353$	−5.37387	+	5.37387i	−0.286022	+	0.286022i	0.549483	+	0.835505i	$0.314825\pi$
$354$		−	0.00357299i		−	0.000189903i
$355$	−30.8988	+	14.5339i	−1.63994	+	0.771379i
$356$		−	30.7795i		−	1.63131i
$357$	6.23292	+	6.23292i	0.329881	+	0.329881i
$358$	15.1434	−	15.1434i	0.800354	−	0.800354i
$359$	25.9955			1.37199			0.685995	−	0.727606i	$-0.259367\pi$
$359$	25.9955			1.37199			0.685995	+	0.727606i	$0.259367\pi$
$360$	8.18743	+	2.94912i	0.431515	+	0.155432i
$361$	−18.9685			−0.998342
$362$	−35.8967	+	35.8967i	−1.88669	+	1.88669i
$363$	−13.2303	+	13.2303i	−0.694409	+	0.694409i
$364$	5.25747			0.275566
$365$	2.96403	−	8.22881i	0.155144	−	0.430716i
$366$			10.2762i			0.537144i
$367$	6.61291	−	6.61291i	0.345191	−	0.345191i	−0.513123	−	0.858315i	$-0.671512\pi$
$367$	6.61291	−	6.61291i	0.345191	−	0.345191i	0.858315	+	0.513123i	$0.171512\pi$
$368$	−1.55744	+	0.593760i	−0.0811870	+	0.0309519i
$369$			13.3421i			0.694560i
$370$	−5.84213	+	2.74797i	−0.303718	+	0.142860i
$371$	−9.84989			−0.511381
$372$	20.1825	+	20.1825i	1.04641	+	1.04641i
$373$	−9.58468	−	9.58468i	−0.496276	−	0.496276i	0.414001	−	0.910277i	$-0.364131\pi$
$373$	−9.58468	−	9.58468i	−0.496276	−	0.496276i	−0.910277	+	0.414001i	$0.864131\pi$
$374$		−	83.1136i		−	4.29770i
$375$	−7.00802	−	11.8628i	−0.361893	−	0.612593i
$376$	30.0940			1.55198
$377$	−6.27693	−	6.27693i	−0.323278	−	0.323278i
$378$	8.86793	+	8.86793i	0.456117	+	0.456117i
$379$	21.2829			1.09323			0.546614	−	0.837384i	$-0.315916\pi$
$379$	21.2829			1.09323			0.546614	+	0.837384i	$0.315916\pi$
$380$	−0.533302	−	1.13379i	−0.0273578	−	0.0581623i
$381$	16.3454			0.837398
$382$	−11.8516	+	11.8516i	−0.606380	+	0.606380i
$383$	−19.7855	−	19.7855i	−1.01099	−	1.01099i	−0.999939	−	0.0110515i	$-0.996482\pi$
$383$	−19.7855	−	19.7855i	−1.01099	−	1.01099i	−0.0110515	−	0.999939i	$-0.503518\pi$
$384$		−	21.5685i		−	1.10066i
$385$	−10.7647	−	3.87745i	−0.548619	−	0.197613i
$386$	29.6409			1.50868
$387$	7.33480	−	7.33480i	0.372849	−	0.372849i
$388$	11.4135	+	11.4135i	0.579434	+	0.579434i
$389$	−3.47307			−0.176092			−0.0880458	−	0.996116i	$-0.528062\pi$
$389$	−3.47307			−0.176092			−0.0880458	+	0.996116i	$0.528062\pi$
$390$	3.53169	−	9.80477i	0.178834	−	0.496484i
$391$	−14.0240	+	31.3054i	−0.709223	+	1.58318i
$392$	−1.85780	−	1.85780i	−0.0938328	−	0.0938328i
$393$	3.71383	−	3.71383i	0.187338	−	0.187338i
$394$			28.9147i			1.45670i
$395$	−14.2922	+	6.72263i	−0.719119	+	0.338252i
$396$		−	23.9284i		−	1.20245i
$397$	−0.590946	−	0.590946i	−0.0296588	−	0.0296588i	0.692122	−	0.721781i	$-0.256676\pi$
$397$	−0.590946	−	0.590946i	−0.0296588	−	0.0296588i	−0.721781	+	0.692122i	$0.756676\pi$
$398$	22.8769	+	22.8769i	1.14671	+	1.14671i
$399$		−	0.218736i		−	0.0109505i
$400$	1.10810	−	1.33860i	0.0554051	−	0.0669300i
$401$		−	19.3205i		−	0.964818i	−0.875946	−	0.482409i	$-0.839762\pi$
$401$		−	19.3205i		−	0.964818i	0.875946	−	0.482409i	$-0.160238\pi$
$402$	−17.5755	+	17.5755i	−0.876586	+	0.876586i
$403$	−8.63927	+	8.63927i	−0.430352	+	0.430352i
$404$		−	21.9817i		−	1.09363i
$405$	4.77911	−	2.24795i	0.237476	−	0.111702i
$406$			12.1046i			0.600741i
$407$	4.60027	+	4.60027i	0.228027	+	0.228027i
$408$	−16.3759	−	16.3759i	−0.810727	−	0.810727i
$409$		−	31.2804i		−	1.54671i	−0.633971	−	0.773357i	$-0.718576\pi$
$409$		−	31.2804i		−	1.54671i	0.633971	−	0.773357i	$-0.281424\pi$
$410$	−43.0303	−	15.4996i	−2.12512	−	0.765471i
$411$			18.7487i			0.924804i
$412$	−31.3930	+	31.3930i	−1.54662	+	1.54662i
$413$	−0.000902782	0	0.000902782i	−4.44230e−5	0	4.44230e-5i
$414$	−6.59536	+	14.7227i	−0.324144	+	0.723580i
$415$	−21.7518	−	7.83505i	−1.06776	−	0.384607i
$416$	10.0652			0.493489
$417$	−7.14607	−	7.14607i	−0.349944	−	0.349944i
$418$	−1.45838	+	1.45838i	−0.0713316	+	0.0713316i
$419$	−1.14152			−0.0557668			−0.0278834	−	0.999611i	$-0.508877\pi$
$419$	−1.14152			−0.0557668			−0.0278834	+	0.999611i	$0.508877\pi$
$420$	−7.87207	+	3.70279i	−0.384118	+	0.180678i
$421$		−	18.4172i		−	0.897600i	−0.893632	−	0.448800i	$-0.851852\pi$
$421$		−	18.4172i		−	0.897600i	0.893632	−	0.448800i	$-0.148148\pi$
$422$	38.6721	+	38.6721i	1.88253	+	1.88253i
$423$	−11.9975	+	11.9975i	−0.583340	+	0.583340i
$424$	25.8788			1.25679
$425$	−3.35432	−	35.6058i	−0.162709	−	1.72713i
$426$	42.7360			2.07056
$427$	2.59646	+	2.59646i	0.125652	+	0.125652i
$428$	−7.76074	−	7.76074i	−0.375130	−	0.375130i
$429$	−10.5015			−0.507018
$430$	15.1350	+	32.1768i	0.729875	+	1.55170i
$431$		−	1.45198i		−	0.0699396i	−0.999388	−	0.0349698i	$-0.988867\pi$
$431$		−	1.45198i		−	0.0699396i	0.999388	−	0.0349698i	$-0.0111335\pi$
$432$	1.35719	+	1.35719i	0.0652978	+	0.0652978i
$433$	23.8615	+	23.8615i	1.14671	+	1.14671i	0.987196	+	0.159512i	$0.0509922\pi$
$433$	23.8615	+	23.8615i	1.14671	+	1.14671i	0.159512	+	0.987196i	$0.449008\pi$
$434$	16.6602			0.799715
$435$	13.8193	+	4.97774i	0.662585	+	0.238664i
$436$			5.22740i			0.250347i
$437$	0.795385	−	0.303234i	0.0380484	−	0.0145056i
$438$	−7.74037	+	7.74037i	−0.369849	+	0.369849i
$439$		−	8.93212i		−	0.426307i	−0.977019	−	0.213153i	$-0.931627\pi$
$439$		−	8.93212i		−	0.426307i	0.977019	−	0.213153i	$-0.0683734\pi$
$440$	28.2822	+	10.1873i	1.34830	+	0.485661i
$441$	1.48129			0.0705376
$442$	19.1275	−	19.1275i	0.909804	−	0.909804i
$443$	19.6554	−	19.6554i	0.933858	−	0.933858i	−0.0640861	−	0.997944i	$-0.520413\pi$
$443$	19.6554	−	19.6554i	0.933858	−	0.933858i	0.997944	+	0.0640861i	$0.0204132\pi$
$444$	4.94650			0.234750
$445$	−19.7277	+	9.27931i	−0.935181	+	0.439881i
$446$	13.7865			0.652809
$447$	17.5121	−	17.5121i	0.828296	−	0.828296i
$448$	−9.21354	−	9.21354i	−0.435299	−	0.435299i
$449$			2.94394i			0.138933i	0.997584	+	0.0694665i	$0.0221297\pi$
$449$			2.94394i			0.138933i	−0.997584	+	0.0694665i	$0.977870\pi$
$450$	−1.57751	−	16.7451i	−0.0743646	−	0.789372i
$451$			46.0882i			2.17021i
$452$	25.6106	−	25.6106i	1.20462	−	1.20462i
$453$	14.2328	−	14.2328i	0.668718	−	0.668718i
$454$	17.0017			0.797931
$455$	−1.58501	−	3.36970i	−0.0743063	−	0.157974i
$456$			0.574688i			0.0269122i
$457$	8.88589	−	8.88589i	0.415664	−	0.415664i	−0.468042	−	0.883706i	$-0.655040\pi$
$457$	8.88589	−	8.88589i	0.415664	−	0.415664i	0.883706	+	0.468042i	$0.155040\pi$
$458$	−3.42277	−	3.42277i	−0.159935	−	0.159935i
$459$	39.5011			1.84376
$460$	−24.3775	−	23.4919i	−1.13661	−	1.09532i
$461$	13.4101			0.624569			0.312285	−	0.949989i	$-0.398906\pi$
$461$	13.4101			0.624569			0.312285	+	0.949989i	$0.398906\pi$
$462$	10.1257	+	10.1257i	0.471091	+	0.471091i
$463$	9.58408	−	9.58408i	0.445410	−	0.445410i	−0.448415	−	0.893825i	$-0.648011\pi$
$463$	9.58408	−	9.58408i	0.445410	−	0.445410i	0.893825	+	0.448415i	$0.148011\pi$
$464$			1.85254i			0.0860022i
$465$	6.85112	−	19.0202i	0.317713	−	0.882042i
$466$	−33.9761			−1.57391
$467$	−15.8943	+	15.8943i	−0.735499	+	0.735499i	−0.971703	−	0.236204i	$-0.924097\pi$
$467$	−15.8943	+	15.8943i	−0.735499	+	0.735499i	0.236204	+	0.971703i	$0.424097\pi$
$468$	5.50683	−	5.50683i	0.254553	−	0.254553i
$469$			8.88154i			0.410111i
$470$	−24.7564	−	52.6316i	−1.14193	−	2.42772i
$471$		−	18.4781i		−	0.851427i
$472$	0.00237190	+	0.00237190i	0.000109175	+	0.000109175i
$473$	25.3370	−	25.3370i	1.16499	−	1.16499i
$474$	19.7675			0.907949
$475$	−0.565910	+	0.683625i	−0.0259657	+	0.0313669i
$476$	−22.5807			−1.03498
$477$	−10.3171	+	10.3171i	−0.472386	+	0.472386i
$478$	32.4568	−	32.4568i	1.48454	−	1.48454i
$479$	14.2661			0.651833			0.325917	−	0.945398i	$-0.394327\pi$
$479$	14.2661			0.651833			0.325917	+	0.945398i	$0.394327\pi$
$480$	−15.0708	+	7.08886i	−0.687885	+	0.323561i
$481$			2.11739i			0.0965445i
$482$	−6.31786	+	6.31786i	−0.287771	+	0.287771i
$483$	−2.10539	−	5.52247i	−0.0957987	−	0.251281i
$484$		−	47.9307i		−	2.17867i
$485$	3.87442	−	10.7563i	0.175928	−	0.488416i
$486$	31.0135			1.40680
$487$	−3.24711	−	3.24711i	−0.147140	−	0.147140i	0.629699	−	0.776839i	$-0.283178\pi$
$487$	−3.24711	−	3.24711i	−0.147140	−	0.147140i	−0.776839	+	0.629699i	$0.783178\pi$
$488$	−6.82174	−	6.82174i	−0.308806	−	0.308806i
$489$			12.5779i			0.568793i
$490$	−1.72083	+	4.77740i	−0.0777390	+	0.215821i
$491$	−20.4635			−0.923505			−0.461753	−	0.887009i	$-0.652779\pi$
$491$	−20.4635			−0.923505			−0.461753	+	0.887009i	$0.652779\pi$
$492$	24.7785	+	24.7785i	1.11710	+	1.11710i
$493$	26.9593	+	26.9593i	1.21418	+	1.21418i
$494$	−0.671254			−0.0302011
$495$	−15.3366	+	7.21388i	−0.689329	+	0.324240i
$496$	2.54975			0.114487
$497$	10.7980	−	10.7980i	0.484357	−	0.484357i
$498$	20.4607	+	20.4607i	0.916866	+	0.916866i
$499$		−	4.19951i		−	0.187996i	−0.995572	−	0.0939979i	$-0.970035\pi$
$499$		−	4.19951i		−	0.187996i	0.995572	−	0.0939979i	$-0.0299647\pi$
$500$	34.1828	+	8.79401i	1.52870	+	0.393280i
$501$	−20.1092			−0.898414
$502$	20.9656	−	20.9656i	0.935742	−	0.935742i
$503$	−5.36658	−	5.36658i	−0.239284	−	0.239284i	0.577270	−	0.816554i	$-0.304118\pi$
$503$	−5.36658	−	5.36658i	−0.239284	−	0.239284i	−0.816554	+	0.577270i	$0.804118\pi$
$504$	−3.89182			−0.173355
$505$	−14.0889	+	6.62699i	−0.626947	+	0.294897i
$506$	−22.7827	+	50.8573i	−1.01281	+	2.26088i
$507$	8.91154	+	8.91154i	0.395775	+	0.395775i
$508$	−29.6081	+	29.6081i	−1.31365	+	1.31365i
$509$		−	29.0242i		−	1.28648i	−0.765666	−	0.643238i	$-0.777590\pi$
$509$		−	29.0242i		−	1.28648i	0.765666	−	0.643238i	$-0.222410\pi$
$510$	−15.1685	+	42.1112i	−0.671674	+	1.86472i
$511$			3.91149i			0.173034i
$512$	−2.77665	−	2.77665i	−0.122712	−	0.122712i
$513$	−0.693118	−	0.693118i	−0.0306019	−	0.0306019i
$514$			2.44834i			0.107992i
$515$	29.5852	+	10.6566i	1.30368	+	0.469587i
$516$		−	27.2439i		−	1.19935i
$517$	−41.4437	+	41.4437i	−1.82269	+	1.82269i
$518$	2.04161	−	2.04161i	0.0897033	−	0.0897033i
$519$			8.52106i			0.374033i
$520$	4.16432	+	8.85328i	0.182618	+	0.388242i
$521$			14.9875i			0.656613i	0.944571	+	0.328306i	$0.106478\pi$
$521$			14.9875i			0.656613i	−0.944571	+	0.328306i	$0.893522\pi$
$522$	12.6787	+	12.6787i	0.554932	+	0.554932i
$523$	−9.82258	−	9.82258i	−0.429511	−	0.429511i	0.458951	−	0.888462i	$-0.348225\pi$
$523$	−9.82258	−	9.82258i	−0.429511	−	0.429511i	−0.888462	+	0.458951i	$0.848225\pi$
$524$			13.4545i			0.587763i
$525$	4.74650	+	3.92919i	0.207154	+	0.171484i
$526$		−	26.2154i		−	1.14305i
$527$	37.1054	−	37.1054i	1.61634	−	1.61634i
$528$	1.54969	+	1.54969i	0.0674414	+	0.0674414i
$529$	17.1626	−	15.3116i	0.746199	−	0.665723i
$530$	−21.2888	−	45.2596i	−0.924726	−	1.96595i
$531$	−0.00189120			−8.20712e−5
$532$	0.396219	+	0.396219i	0.0171783	+	0.0171783i
$533$	−10.6066	+	10.6066i	−0.459423	+	0.459423i
$534$	27.2852			1.18075
$535$	−2.63445	+	7.31383i	−0.113897	+	0.316204i
$536$		−	23.3346i		−	1.00790i
$537$	8.21797	+	8.21797i	0.354632	+	0.354632i
$538$	25.9077	−	25.9077i	1.11696	−	1.11696i
$539$	5.11689			0.220400
$540$	−13.2114	+	36.6778i	−0.568529	+	1.57836i
$541$	−4.48296			−0.192738			−0.0963688	−	0.995346i	$-0.530723\pi$
$541$	−4.48296			−0.192738			−0.0963688	+	0.995346i	$0.530723\pi$
$542$	−45.0935	−	45.0935i	−1.93693	−	1.93693i
$543$	−19.4803	−	19.4803i	−0.835979	−	0.835979i
$544$	−43.2300			−1.85347
$545$	3.35043	−	1.57594i	0.143517	−	0.0675060i
$546$			4.66061i			0.199456i
$547$	−17.1333	−	17.1333i	−0.732565	−	0.732565i	0.238562	−	0.971127i	$-0.423324\pi$
$547$	−17.1333	−	17.1333i	−0.732565	−	0.732565i	−0.971127	+	0.238562i	$0.923324\pi$
$548$	−33.9615	−	33.9615i	−1.45076	−	1.45076i
$549$	5.43923			0.232141
$550$	−5.44928	−	57.8435i	−0.232358	−	2.46645i
$551$		−	0.946097i		−	0.0403051i
$552$	5.53154	+	14.5093i	0.235438	+	0.617556i
$553$	4.99461	−	4.99461i	0.212392	−	0.212392i
$554$			29.8948i			1.27011i
$555$	−1.49126	−	3.17039i	−0.0633003	−	0.134575i
$556$	25.8889			1.09793
$557$	−20.2285	+	20.2285i	−0.857111	+	0.857111i	−0.990997	−	0.133886i	$-0.957254\pi$
$557$	−20.2285	+	20.2285i	−0.857111	+	0.857111i	0.133886	+	0.990997i	$0.457254\pi$
$558$	17.4504	−	17.4504i	0.738734	−	0.738734i
$559$	11.6620			0.493248
$560$	−0.263363	+	0.731155i	−0.0111291	+	0.0308969i
$561$	45.1038			1.90428
$562$	17.0465	−	17.0465i	0.719064	−	0.719064i
$563$	−15.2919	−	15.2919i	−0.644478	−	0.644478i	0.307175	−	0.951653i	$-0.400616\pi$
$563$	−15.2919	−	15.2919i	−0.644478	−	0.644478i	−0.951653	+	0.307175i	$0.900616\pi$
$564$			44.5629i			1.87644i
$565$	−24.1358	−	8.69375i	−1.01540	−	0.365749i
$566$		−	4.48001i		−	0.188309i
$567$	−1.67013	+	1.67013i	−0.0701387	+	0.0701387i
$568$	−28.3699	+	28.3699i	−1.19037	+	1.19037i
$569$	−41.2764			−1.73039			−0.865197	−	0.501431i	$-0.832807\pi$
$569$	−41.2764			−1.73039			−0.865197	+	0.501431i	$0.832807\pi$
$570$	1.00508	−	0.472758i	0.0420980	−	0.0198017i
$571$			24.3376i			1.01850i	0.860619	+	0.509249i	$0.170077\pi$
$571$			24.3376i			1.01850i	−0.860619	+	0.509249i	$0.829923\pi$
$572$	19.0225	−	19.0225i	0.795371	−	0.795371i
$573$	−6.43158	−	6.43158i	−0.268683	−	0.268683i
$574$	20.4541			0.853737
$575$	−7.70757	+	22.7067i	−0.321428	+	0.946934i
$576$	−19.3011			−0.804211
$577$	2.19429	+	2.19429i	0.0913493	+	0.0913493i	0.751305	−	0.659955i	$-0.229425\pi$
$577$	2.19429	+	2.19429i	0.0913493	+	0.0913493i	−0.659955	+	0.751305i	$0.729425\pi$
$578$	−54.8543	+	54.8543i	−2.28164	+	2.28164i
$579$			16.0854i			0.668487i
$580$	−34.0491	+	16.0157i	−1.41381	+	0.665014i
$581$	10.3395			0.428956
$582$	−10.1178	+	10.1178i	−0.419396	+	0.419396i
$583$	−35.6388	+	35.6388i	−1.47601	+	1.47601i
$584$		−	10.2767i		−	0.425254i
$585$	−5.18971	−	1.86934i	−0.214568	−	0.0772877i
$586$			0.685631i			0.0283232i
$587$	9.71402	+	9.71402i	0.400940	+	0.400940i	0.878564	−	0.477624i	$-0.158502\pi$
$587$	9.71402	+	9.71402i	0.400940	+	0.400940i	−0.477624	+	0.878564i	$0.658502\pi$
$588$	2.75100	−	2.75100i	0.113449	−	0.113449i
$589$	−1.30216			−0.0536547
$590$	0.00219703	−	0.00609943i	9.04501e−5	−	0.000251110i
$591$	−15.6913			−0.645454
$592$	0.312458	−	0.312458i	0.0128419	−	0.0128419i
$593$	16.3366	−	16.3366i	0.670864	−	0.670864i	−0.287051	−	0.957915i	$-0.592675\pi$
$593$	16.3366	−	16.3366i	0.670864	−	0.670864i	0.957915	+	0.287051i	$0.0926750\pi$
$594$	64.1717			2.63300
$595$	6.80757	+	14.4728i	0.279083	+	0.593326i
$596$			63.4432i			2.59873i
$597$	−12.4147	+	12.4147i	−0.508102	+	0.508102i
$598$	−16.9473	+	6.46101i	−0.693027	+	0.264211i
$599$			26.0786i			1.06554i	0.846259	+	0.532771i	$0.178849\pi$
$599$			26.0786i			1.06554i	−0.846259	+	0.532771i	$0.821151\pi$
$600$	−12.4706	−	10.3232i	−0.509109	−	0.421444i
$601$	−9.06689			−0.369846			−0.184923	−	0.982753i	$-0.559204\pi$
$601$	−9.06689			−0.369846			−0.184923	+	0.982753i	$0.559204\pi$
$602$	−11.2446	−	11.2446i	−0.458297	−	0.458297i
$603$	9.30279	+	9.30279i	0.378839	+	0.378839i
$604$			51.5629i			2.09807i
$605$	−30.7205	+	14.4500i	−1.24897	+	0.587477i
$606$	19.4862			0.791574
$607$	−26.0129	−	26.0129i	−1.05583	−	1.05583i	−0.998346	−	0.0574853i	$-0.981692\pi$
$607$	−26.0129	−	26.0129i	−1.05583	−	1.05583i	−0.0574853	−	0.998346i	$-0.518308\pi$
$608$	0.758548	+	0.758548i	0.0307632	+	0.0307632i
$609$	−6.56888			−0.266185
$610$	−6.31880	+	17.5424i	−0.255841	+	0.710271i
$611$	−19.0755			−0.771712
$612$	−23.6517	+	23.6517i	−0.956063	+	0.956063i
$613$	5.84020	+	5.84020i	0.235883	+	0.235883i	0.815143	−	0.579260i	$-0.196658\pi$
$613$	5.84020	+	5.84020i	0.235883	+	0.235883i	−0.579260	+	0.815143i	$0.696658\pi$
$614$			67.8952i			2.74003i
$615$	8.41127	−	23.3516i	0.339175	−	0.941625i
$616$	−13.4437			−0.541663
$617$	6.24759	−	6.24759i	0.251519	−	0.251519i	−0.570074	−	0.821593i	$-0.693086\pi$
$617$	6.24759	−	6.24759i	0.251519	−	0.251519i	0.821593	+	0.570074i	$0.193086\pi$
$618$	−27.8291	−	27.8291i	−1.11945	−	1.11945i
$619$	−36.2172			−1.45569			−0.727846	−	0.685741i	$-0.759478\pi$
$619$	−36.2172			−1.45569			−0.727846	+	0.685741i	$0.759478\pi$
$620$	22.0432	+	46.8635i	0.885276	+	1.88208i
$621$	−24.1708	−	10.8279i	−0.969940	−	0.434507i
$622$	−36.9174	−	36.9174i	−1.48025	−	1.48025i
$623$	6.89410	−	6.89410i	0.276206	−	0.276206i
$624$			0.713281i			0.0285541i
$625$	−4.66893	−	24.5602i	−0.186757	−	0.982406i
$626$			66.5385i			2.65941i
$627$	−0.791427	−	0.791427i	−0.0316065	−	0.0316065i
$628$	33.4714	+	33.4714i	1.33565	+	1.33565i
$629$		−	9.09412i		−	0.362606i
$630$	3.20154	+	6.80643i	0.127553	+	0.271175i
$631$			2.26966i			0.0903538i	0.998979	+	0.0451769i	$0.0143851\pi$
$631$			2.26966i			0.0903538i	−0.998979	+	0.0451769i	$0.985615\pi$
$632$	−13.1224	+	13.1224i	−0.521982	+	0.521982i
$633$	−20.9864	+	20.9864i	−0.834136	+	0.834136i
$634$		−	40.2994i		−	1.60050i
$635$	27.9031	+	10.0507i	1.10730	+	0.398851i
$636$			38.3210i			1.51953i
$637$	1.17759	+	1.17759i	0.0466577	+	0.0466577i
$638$	43.7967	+	43.7967i	1.73393	+	1.73393i
$639$		−	22.6203i		−	0.894847i
$640$	13.2624	−	36.8194i	0.524243	−	1.45541i
$641$			34.5031i			1.36279i	0.731916	+	0.681395i	$0.238626\pi$
$641$			34.5031i			1.36279i	−0.731916	+	0.681395i	$0.761374\pi$
$642$	6.87970	−	6.87970i	0.271520	−	0.271520i
$643$	−2.18441	−	2.18441i	−0.0861445	−	0.0861445i	0.662721	−	0.748866i	$-0.269401\pi$
$643$	−2.18441	−	2.18441i	−0.0861445	−	0.0861445i	−0.748866	+	0.662721i	$0.769401\pi$
$644$	13.8172	+	6.18971i	0.544472	+	0.243909i
$645$	−17.4616	+	8.21341i	−0.687550	+	0.323403i
$646$	2.88302			0.113431
$647$	20.3831	+	20.3831i	0.801343	+	0.801343i	0.983305	−	0.181962i	$-0.0582449\pi$
$647$	20.3831	+	20.3831i	0.801343	+	0.801343i	−0.181962	+	0.983305i	$0.558245\pi$
$648$	4.38796	−	4.38796i	0.172375	−	0.172375i
$649$	−0.00653288			−0.000256438
$650$	12.0579	−	14.5660i	0.472948	−	0.571326i
$651$			9.04110i			0.354348i
$652$	−22.7837	−	22.7837i	−0.892279	−	0.892279i
$653$	−7.89570	+	7.89570i	−0.308983	+	0.308983i	−0.844515	−	0.535532i	$-0.820111\pi$
$653$	−7.89570	+	7.89570i	−0.308983	+	0.308983i	0.535532	+	0.844515i	$0.320111\pi$
$654$	−4.63395			−0.181202
$655$	8.62349	−	4.05623i	0.336947	−	0.158490i
$656$	3.13039			0.122221
$657$	4.09701	+	4.09701i	0.159840	+	0.159840i
$658$	18.3928	+	18.3928i	0.717028	+	0.717028i
$659$	−27.2105			−1.05997			−0.529986	−	0.848007i	$-0.677803\pi$
$659$	−27.2105			−1.05997			−0.529986	+	0.848007i	$0.677803\pi$
$660$	−15.0853	+	41.8800i	−0.587193	+	1.63018i
$661$		−	35.6091i		−	1.38503i	−0.721402	−	0.692517i	$-0.756502\pi$
$661$		−	35.6091i		−	1.38503i	0.721402	−	0.692517i	$-0.243498\pi$
$662$	−17.1498	−	17.1498i	−0.666546	−	0.666546i
$663$	10.3801	+	10.3801i	0.403128	+	0.403128i
$664$	−27.1653			−1.05422
$665$	0.134500	−	0.373402i	0.00521569	−	0.0144799i
$666$		−	4.27689i		−	0.165726i
$667$	−9.10646	−	23.8863i	−0.352604	−	0.924883i
$668$	36.4260	−	36.4260i	1.40936	−	1.40936i
$669$			7.48160i			0.289256i
$670$	−40.8101	+	19.1959i	−1.57663	+	0.741601i
$671$	18.7890			0.725341
$672$	5.26670	−	5.26670i	0.203167	−	0.203167i
$673$	10.1461	−	10.1461i	0.391104	−	0.391104i	−0.483977	−	0.875081i	$-0.660808\pi$
$673$	10.1461	−	10.1461i	0.391104	−	0.391104i	0.875081	+	0.483977i	$0.160808\pi$
$674$	−26.1903			−1.00881
$675$	27.4911	−	2.58986i	1.05813	−	0.0996838i
$676$	−32.2848			−1.24172
$677$	−2.40673	+	2.40673i	−0.0924982	+	0.0924982i	−0.751842	−	0.659344i	$-0.770834\pi$
$677$	−2.40673	+	2.40673i	−0.0924982	+	0.0924982i	0.659344	+	0.751842i	$0.270834\pi$
$678$	22.7032	+	22.7032i	0.871909	+	0.871909i
$679$			5.11289i			0.196215i
$680$	−17.8857	−	38.0246i	−0.685883	−	1.45818i
$681$			9.22645i			0.353558i
$682$	60.2798	−	60.2798i	2.30823	−	2.30823i
$683$	−1.56458	+	1.56458i	−0.0598671	+	0.0598671i	−0.736406	−	0.676539i	$-0.763479\pi$
$683$	−1.56458	+	1.56458i	−0.0598671	+	0.0598671i	0.676539	+	0.736406i	$0.263479\pi$
$684$	0.830023			0.0317367
$685$	−11.5285	+	32.0057i	−0.440482	+	1.22288i
$686$		−	2.27089i		−	0.0867031i
$687$	1.85745	−	1.85745i	0.0708663	−	0.0708663i
$688$	−1.72093	−	1.72093i	−0.0656098	−	0.0656098i
$689$	−16.4036			−0.624928
$690$	20.8250	−	21.6100i	0.792793	−	0.822678i
$691$	−11.4779			−0.436638			−0.218319	−	0.975877i	$-0.570057\pi$
$691$	−11.4779			−0.436638			−0.218319	+	0.975877i	$0.570057\pi$
$692$	−15.4351	−	15.4351i	−0.586754	−	0.586754i
$693$	5.35958	−	5.35958i	0.203594	−	0.203594i
$694$			50.7244i			1.92547i
$695$	−7.80490	−	16.5931i	−0.296057	−	0.629412i
$696$	17.2585			0.654184
$697$	45.5551	−	45.5551i	1.72552	−	1.72552i
$698$	−24.0190	+	24.0190i	−0.909132	+	0.909132i
$699$		−	18.4380i		−	0.697389i
$700$	−15.7152	+	1.48049i	−0.593978	+	0.0559571i
$701$		−	2.19390i		−	0.0828623i	−0.999141	−	0.0414312i	$-0.986808\pi$
$701$		−	2.19390i		−	0.0828623i	0.999141	−	0.0414312i	$-0.0131917\pi$
$702$	14.7683	+	14.7683i	0.557394	+	0.557394i
$703$	−0.159573	+	0.159573i	−0.00601840	+	0.00601840i
$704$	−66.6727			−2.51282
$705$	28.5619	−	13.4347i	1.07571	−	0.505980i
$706$	17.2583			0.649525
$707$	4.92355	−	4.92355i	0.185169	−	0.185169i
$708$	−0.00351228	+	0.00351228i	−0.000132000	+	0.000132000i
$709$	−8.54997			−0.321101			−0.160550	−	0.987028i	$-0.551327\pi$
$709$	−8.54997			−0.321101			−0.160550	+	0.987028i	$0.551327\pi$
$710$	72.9543	+	26.2782i	2.73792	+	0.986205i
$711$		−	10.4630i		−	0.392393i
$712$	−18.1130	+	18.1130i	−0.678813	+	0.678813i
$713$	−32.8760	+	12.5337i	−1.23122	+	0.469391i
$714$		−	20.0172i		−	0.749125i
$715$	−17.9271	−	6.45736i	−0.670435	−	0.241492i
$716$	−29.7722			−1.11264
$717$	17.6136	+	17.6136i	0.657791	+	0.657791i
$718$	−41.7426	−	41.7426i	−1.55782	−	1.55782i
$719$			7.63458i			0.284722i	0.989815	+	0.142361i	$0.0454694\pi$
$719$			7.63458i			0.284722i	−0.989815	+	0.142361i	$0.954531\pi$
$720$	0.489979	+	1.04169i	0.0182604	+	0.0388214i
$721$	−14.0631			−0.523736
$722$	30.4589	+	30.4589i	1.13356	+	1.13356i
$723$	−3.42855	−	3.42855i	−0.127509	−	0.127509i
$724$	70.5734			2.62284
$725$	20.5300	+	16.9949i	0.762467	+	0.631175i
$726$	42.4893			1.57693
$727$	4.95055	−	4.95055i	0.183606	−	0.183606i	−0.609319	−	0.792925i	$-0.708557\pi$
$727$	4.95055	−	4.95055i	0.183606	−	0.183606i	0.792925	+	0.609319i	$0.208557\pi$
$728$	−3.09390	−	3.09390i	−0.114668	−	0.114668i
$729$			23.9160i			0.885779i
$730$	−17.9731	+	8.45399i	−0.665213	+	0.312896i
$731$	−50.0878			−1.85257
$732$	10.1016	−	10.1016i	0.373364	−	0.373364i
$733$	−5.90811	−	5.90811i	−0.218221	−	0.218221i	0.589527	−	0.807748i	$-0.299314\pi$
$733$	−5.90811	−	5.90811i	−0.218221	−	0.218221i	−0.807748	+	0.589527i	$0.799314\pi$
$734$	−21.2376			−0.783893
$735$	−2.59258	−	0.933852i	−0.0956288	−	0.0344456i
$736$	26.4525	+	11.8500i	0.975051	+	0.436797i
$737$	32.1351	+	32.1351i	1.18371	+	1.18371i
$738$	21.4242	−	21.4242i	0.788636	−	0.788636i
$739$		−	28.0166i		−	1.03061i	−0.857008	−	0.515304i	$-0.827679\pi$
$739$		−	28.0166i		−	1.03061i	0.857008	−	0.515304i	$-0.172321\pi$
$740$	8.44413	+	3.04159i	0.310412	+	0.111811i
$741$		−	0.364274i		−	0.0133819i
$742$	15.8166	+	15.8166i	0.580646	+	0.580646i
$743$	−32.1148	−	32.1148i	−1.17818	−	1.17818i	−0.980208	−	0.197971i	$-0.936565\pi$
$743$	−32.1148	−	32.1148i	−1.17818	−	1.17818i	−0.197971	−	0.980208i	$-0.563435\pi$
$744$		−	23.7538i		−	0.870858i
$745$	40.6630	−	19.1267i	1.48978	−	0.700748i
$746$			30.7814i			1.12699i
$747$	10.8299	−	10.8299i	0.396247	−	0.396247i
$748$	−81.7012	+	81.7012i	−2.98729	+	2.98729i
$749$		−	3.47656i		−	0.127031i
$750$	−7.79566	+	30.3021i	−0.284657	+	1.10648i
$751$			17.2167i			0.628247i	0.949382	+	0.314123i	$0.101711\pi$
$751$			17.2167i			0.628247i	−0.949382	+	0.314123i	$0.898289\pi$
$752$	2.81493	+	2.81493i	0.102650	+	0.102650i
$753$	11.3776	+	11.3776i	0.414621	+	0.414621i
$754$			20.1585i			0.734130i
$755$	33.0485	−	15.5451i	1.20276	−	0.565742i
$756$		−	17.4345i		−	0.634086i
$757$	−19.8168	+	19.8168i	−0.720254	+	0.720254i	−0.968657	−	0.248403i	$-0.920094\pi$
$757$	−19.8168	+	19.8168i	−0.720254	+	0.720254i	0.248403	+	0.968657i	$0.420094\pi$
$758$	−34.1753	−	34.1753i	−1.24130	−	1.24130i
$759$	−27.5991	−	12.3636i	−1.00178	−	0.448771i
$760$	−0.353374	+	0.981046i	−0.0128182	+	0.0355863i
$761$	4.09666			0.148504			0.0742520	−	0.997240i	$-0.476343\pi$
$761$	4.09666			0.148504			0.0742520	+	0.997240i	$0.476343\pi$
$762$	−26.2468	−	26.2468i	−0.950821	−	0.950821i
$763$	−1.17085	+	1.17085i	−0.0423877	+	0.0423877i
$764$	23.3004			0.842979
$765$	22.2897	+	8.02877i	0.805885	+	0.290281i
$766$			63.5416i			2.29585i
$767$	−0.00150346	−	0.00150346i	−5.42867e−5	−	5.42867e-5i
$768$	−11.9251	+	11.9251i	−0.430310	+	0.430310i
$769$	−2.46165			−0.0887693			−0.0443847	−	0.999015i	$-0.514133\pi$
$769$	−2.46165			−0.0887693			−0.0443847	+	0.999015i	$0.514133\pi$
$770$	11.0593	+	23.5118i	0.398548	+	0.847307i
$771$	−1.32866			−0.0478504
$772$	−29.1372	−	29.1372i	−1.04867	−	1.04867i
$773$	−25.8564	−	25.8564i	−0.929989	−	0.929989i	0.0677156	−	0.997705i	$-0.478429\pi$
$773$	−25.8564	−	25.8564i	−0.929989	−	0.929989i	−0.997705	+	0.0677156i	$0.978429\pi$
$774$	−23.5559			−0.846699
$775$	23.3910	−	28.2566i	0.840229	−	1.01501i
$776$		−	13.4332i		−	0.482223i
$777$	1.10794	+	1.10794i	0.0397470	+	0.0397470i
$778$	5.57693	+	5.57693i	0.199943	+	0.199943i
$779$	−1.59869			−0.0572792
$780$	−13.1098	+	6.16648i	−0.469407	+	0.220795i
$781$		−	78.1386i		−	2.79602i
$782$	72.7883	−	27.7499i	2.60290	−	0.992334i
$783$	−20.8151	+	20.8151i	−0.743872	+	0.743872i
$784$		−	0.347548i		−	0.0124124i
$785$	11.3622	−	31.5439i	0.405533	−	1.12585i
$786$	−11.9271			−0.425425
$787$	−4.38436	+	4.38436i	−0.156286	+	0.156286i	−0.780919	−	0.624633i	$-0.785249\pi$
$787$	−4.38436	+	4.38436i	−0.156286	+	0.156286i	0.624633	+	0.780919i	$0.285249\pi$
$788$	28.4233	−	28.4233i	1.01254	−	1.01254i
$789$	14.2265			0.506476
$790$	33.7449	+	12.1550i	1.20059	+	0.432454i
$791$	11.4727			0.407924
$792$	−14.0813	+	14.0813i	−0.500359	+	0.500359i
$793$	4.32405	+	4.32405i	0.153552	+	0.153552i
$794$			1.89784i			0.0673518i
$795$	24.5613	−	11.5529i	0.871101	−	0.409740i
$796$		−	44.9763i		−	1.59414i
$797$	−1.04825	+	1.04825i	−0.0371311	+	0.0371311i	−0.725429	−	0.688297i	$-0.758358\pi$
$797$	−1.04825	+	1.04825i	−0.0371311	+	0.0371311i	0.688297	+	0.725429i	$0.258358\pi$
$798$	−0.351238	+	0.351238i	−0.0124337	+	0.0124337i
$799$	81.9287			2.89843
$800$	−30.0862	+	2.83434i	−1.06371	+	0.100209i
$801$		−	14.4422i		−	0.510289i
$802$	−31.0241	+	31.0241i	−1.09550	+	1.09550i
$803$	14.1525	+	14.1525i	0.499431	+	0.499431i
$804$	34.5537			1.21861
$805$	−0.198349	−	10.7220i	−0.00699089	−	0.377900i
$806$	27.7452			0.977284
$807$	14.0595	+	14.0595i	0.494917	+	0.494917i
$808$	−12.9357	+	12.9357i	−0.455078	+	0.455078i
$809$		−	4.06895i		−	0.143057i	−0.997439	−	0.0715283i	$-0.977212\pi$
$809$		−	4.06895i		−	0.143057i	0.997439	−	0.0715283i	$-0.0227876\pi$
$810$	−11.2838	−	4.06445i	−0.396473	−	0.142810i
$811$	18.3262			0.643521			0.321760	−	0.946821i	$-0.395725\pi$
$811$	18.3262			0.643521			0.321760	+	0.946821i	$0.395725\pi$
$812$	11.8989	−	11.8989i	0.417570	−	0.417570i
$813$	24.4712	−	24.4712i	0.858241	−	0.858241i
$814$		−	14.7739i		−	0.517824i
$815$	−7.73413	+	21.4717i	−0.270915	+	0.752120i
$816$		−	3.06353i		−	0.107245i
$817$	0.878881	+	0.878881i	0.0307482	+	0.0307482i
$818$	−50.2289	+	50.2289i	−1.75621	+	1.75621i
$819$	2.46688			0.0861998
$820$	27.0629	+	57.5354i	0.945078	+	2.00922i
$821$	35.7546			1.24784			0.623922	−	0.781487i	$-0.285538\pi$
$821$	35.7546			1.24784			0.623922	+	0.781487i	$0.285538\pi$
$822$	30.1060	−	30.1060i	1.05007	−	1.05007i
$823$	−0.789736	+	0.789736i	−0.0275285	+	0.0275285i	−0.720737	−	0.693209i	$-0.756196\pi$
$823$	−0.789736	+	0.789736i	−0.0275285	+	0.0275285i	0.693209	+	0.720737i	$0.256196\pi$
$824$	36.9481			1.28715
$825$	31.3903	−	2.95719i	1.09287	−	0.102956i
$826$			0.00289931i			0.000100880i
$827$	−29.5585	+	29.5585i	−1.02785	+	1.02785i	−0.0282480	+	0.999601i	$0.508993\pi$
$827$	−29.5585	+	29.5585i	−1.02785	+	1.02785i	−0.999601	+	0.0282480i	$0.991007\pi$
$828$	20.9558	−	7.98921i	0.728264	−	0.277644i
$829$			0.156018i			0.00541874i	0.999996	+	0.00270937i	$0.000862420\pi$
$829$			0.156018i			0.00541874i	−0.999996	+	0.00270937i	$0.999138\pi$
$830$	22.3471	+	47.5096i	0.775678	+	1.64908i
$831$	−16.2232			−0.562776
$832$	−15.3439	−	15.3439i	−0.531953	−	0.531953i
$833$	−5.05771	−	5.05771i	−0.175239	−	0.175239i
$834$			22.9498i			0.794686i
$835$	−34.3283	−	12.3651i	−1.18798	−	0.427912i
$836$	2.86719			0.0991638
$837$	28.6490	+	28.6490i	0.990253	+	0.990253i
$838$	1.83301	+	1.83301i	0.0633202	+	0.0633202i
$839$	−18.1367			−0.626150			−0.313075	−	0.949728i	$-0.601359\pi$
$839$	−18.1367			−0.626150			−0.313075	+	0.949728i	$0.601359\pi$
$840$	6.81154	+	2.45353i	0.235020	+	0.0846547i
$841$	0.587614			0.0202625
$842$	−29.5737	+	29.5737i	−1.01918	+	1.01918i
$843$	9.25074	+	9.25074i	0.318612	+	0.318612i
$844$		−	76.0299i		−	2.61706i
$845$	9.73314	+	20.6925i	0.334830	+	0.711844i
$846$	38.5304			1.32470
$847$	10.7357	−	10.7357i	0.368883	−	0.368883i
$848$	2.42065	+	2.42065i	0.0831253	+	0.0831253i
$849$	2.43120			0.0834384
$850$	−51.7882	+	62.5607i	−1.77632	+	2.14581i
$851$	−2.49284	+	5.56470i	−0.0854533	+	0.190756i
$852$	−42.0097	−	42.0097i	−1.43923	−	1.43923i
$853$	24.4378	−	24.4378i	0.836734	−	0.836734i	−0.151694	−	0.988428i	$-0.548473\pi$
$853$	24.4378	−	24.4378i	0.836734	−	0.836734i	0.988428	+	0.151694i	$0.0484728\pi$
$854$		−	8.33862i		−	0.285342i
$855$	−0.250233	−	0.531992i	−0.00855779	−	0.0181937i
$856$			9.13404i			0.312195i
$857$	−15.8794	−	15.8794i	−0.542431	−	0.542431i	0.381810	−	0.924241i	$-0.375301\pi$
$857$	−15.8794	−	15.8794i	−0.542431	−	0.542431i	−0.924241	+	0.381810i	$0.875301\pi$
$858$	16.8630	+	16.8630i	0.575692	+	0.575692i
$859$			34.7748i			1.18650i	0.805018	+	0.593250i	$0.202156\pi$
$859$			34.7748i			1.18650i	−0.805018	+	0.593250i	$0.797844\pi$
$860$	16.7522	−	46.5079i	0.571245	−	1.58590i
$861$			11.0999i			0.378285i
$862$	−2.33154	+	2.33154i	−0.0794126	+	0.0794126i
$863$	−32.0309	+	32.0309i	−1.09035	+	1.09035i	−0.0948543	+	0.995491i	$0.530239\pi$
$863$	−32.0309	+	32.0309i	−1.09035	+	1.09035i	−0.995491	+	0.0948543i	$0.969761\pi$
$864$		−	33.3777i		−	1.13553i
$865$	−5.23958	+	14.5462i	−0.178151	+	0.494587i
$866$		−	76.6317i		−	2.60405i
$867$	−29.7681	−	29.7681i	−1.01098	−	1.01098i
$868$	−16.3771	−	16.3771i	−0.555875	−	0.555875i
$869$		−	36.1429i		−	1.22606i
$870$	−14.1975	−	30.1836i	−0.481339	−	1.02332i
$871$			14.7910i			0.501173i
$872$	3.07621	−	3.07621i	0.104173	−	0.104173i
$873$	5.35539	+	5.35539i	0.181253	+	0.181253i
$874$	−1.76412	−	0.790279i	−0.0596724	−	0.0267316i
$875$	5.68667	+	9.62610i	0.192245	+	0.325422i
$876$	15.2177			0.514157
$877$	2.28214	+	2.28214i	0.0770623	+	0.0770623i	0.744587	−	0.667525i	$-0.232646\pi$
$877$	2.28214	+	2.28214i	0.0770623	+	0.0770623i	−0.667525	+	0.744587i	$0.732646\pi$
$878$	−14.3429	+	14.3429i	−0.484048	+	0.484048i
$879$	−0.372076			−0.0125498
$880$	1.69256	+	3.59836i	0.0570562	+	0.121301i
$881$		−	43.1349i		−	1.45325i	−0.687034	−	0.726625i	$-0.741088\pi$
$881$		−	43.1349i		−	1.45325i	0.687034	−	0.726625i	$-0.258912\pi$
$882$	−2.37860	−	2.37860i	−0.0800916	−	0.0800916i
$883$	0.0867921	−	0.0867921i	0.00292079	−	0.00292079i	−0.705645	−	0.708566i	$-0.749343\pi$
$883$	0.0867921	−	0.0867921i	0.00292079	−	0.00292079i	0.708566	+	0.705645i	$0.249343\pi$
$884$	−37.6050			−1.26479
$885$	0.00331002	+	0.00119227i	0.000111265	+	4.00779e-5i
$886$	−63.1240			−2.12069
$887$	8.94261	+	8.94261i	0.300264	+	0.300264i	0.841117	−	0.540853i	$-0.181899\pi$
$887$	8.94261	+	8.94261i	0.300264	+	0.300264i	−0.540853	+	0.841117i	$0.681899\pi$
$888$	−2.91090	−	2.91090i	−0.0976834	−	0.0976834i
$889$	−13.2635			−0.444842
$890$	46.5783	+	16.7776i	1.56131	+	0.562386i
$891$			12.0857i			0.404885i
$892$	−13.5522	−	13.5522i	−0.453762	−	0.453762i
$893$	−1.43759	−	1.43759i	−0.0481070	−	0.0481070i
$894$	−56.2407			−1.88097
$895$	8.97563	+	19.0821i	0.300022	+	0.637843i
$896$			17.5018i			0.584693i
$897$	−3.50624	−	9.19690i	−0.117070	−	0.307076i
$898$	4.72727	−	4.72727i	0.157751	−	0.157751i
$899$			39.1055i			1.30424i
$900$	−14.9098	+	18.0113i	−0.496995	+	0.600375i
$901$	70.4532			2.34714
$902$	74.0068	−	74.0068i	2.46416	−	2.46416i
$903$	6.10219	−	6.10219i	0.203068	−	0.203068i
$904$	−30.1425			−1.00253
$905$	−21.2763	−	45.2330i	−0.707247	−	1.50360i
$906$	−45.7092			−1.51859
$907$	−36.4687	+	36.4687i	−1.21092	+	1.21092i	−0.240198	+	0.970724i	$0.577212\pi$
$907$	−36.4687	+	36.4687i	−1.21092	+	1.21092i	−0.970724	+	0.240198i	$0.922788\pi$
$908$	−16.7128	−	16.7128i	−0.554635	−	0.554635i
$909$		−	10.3141i		−	0.342099i
$910$	−2.86580	+	7.95609i	−0.0950002	+	0.263742i
$911$		−	19.8492i		−	0.657632i	−0.944394	−	0.328816i	$-0.893350\pi$
$911$		−	19.8492i		−	0.657632i	0.944394	−	0.328816i	$-0.106650\pi$
$912$	−0.0537551	+	0.0537551i	−0.00178001	+	0.00178001i
$913$	37.4104	−	37.4104i	1.23810	−	1.23810i
$914$	−28.5373			−0.943929
$915$	−9.51984	−	3.42906i	−0.314716	−	0.113361i
$916$			6.72921i			0.222339i
$917$	−3.01359	+	3.01359i	−0.0995177	+	0.0995177i
$918$	−63.4295	−	63.4295i	−2.09349	−	2.09349i
$919$	24.4110			0.805243			0.402621	−	0.915367i	$-0.368099\pi$
$919$	24.4110			0.805243			0.402621	+	0.915367i	$0.368099\pi$
$920$	0.521127	+	28.1700i	0.0171810	+	0.928739i
$921$	−36.8451			−1.21409
$922$	−21.5334	−	21.5334i	−0.709165	−	0.709165i
$923$	17.9826	−	17.9826i	0.591905	−	0.591905i
$924$		−	19.9073i		−	0.654902i
$925$	−0.596249	−	6.32912i	−0.0196045	−	0.208100i
$926$	−30.7795			−1.01148
$927$	−14.7301	+	14.7301i	−0.483799	+	0.483799i
$928$	22.7801	−	22.7801i	0.747792	−	0.747792i
$929$			3.50894i			0.115124i	0.998342	+	0.0575622i	$0.0183328\pi$
$929$			3.50894i			0.115124i	−0.998342	+	0.0575622i	$0.981667\pi$
$930$	−41.5433	+	19.5407i	−1.36226	+	0.640766i
$931$			0.177493i			0.00581711i
$932$	33.3987	+	33.3987i	1.09401	+	1.09401i
$933$	20.0342	−	20.0342i	0.655891	−	0.655891i
$934$	51.0449			1.67024
$935$	76.9963	+	27.7342i	2.51805	+	0.907006i
$936$	−6.48128			−0.211847
$937$	−43.0451	+	43.0451i	−1.40622	+	1.40622i	−0.628040	+	0.778181i	$0.716143\pi$
$937$	−43.0451	+	43.0451i	−1.40622	+	1.40622i	−0.778181	+	0.628040i	$0.783857\pi$
$938$	14.2617	−	14.2617i	0.465660	−	0.465660i
$939$	−36.1089			−1.17837
$940$	−27.4016	+	76.0730i	−0.893742	+	2.48123i
$941$		−	0.196834i		−	0.00641659i	−0.999995	−	0.00320830i	$-0.998979\pi$
$941$		−	0.196834i		−	0.00641659i	0.999995	−	0.00320830i	$-0.00102123\pi$
$942$	−29.6715	+	29.6715i	−0.966750	+	0.966750i
$943$	−40.3626	+	15.3879i	−1.31439	+	0.501099i
$944$		0	0.000443724i		0	1.44420e-5i
$945$	−11.1744	+	5.25610i	−0.363503	+	0.170981i
$946$	−81.3704			−2.64558
$947$	−26.8664	−	26.8664i	−0.873040	−	0.873040i	0.119763	−	0.992803i	$-0.461787\pi$
$947$	−26.8664	−	26.8664i	−0.873040	−	0.873040i	−0.992803	+	0.119763i	$0.961787\pi$
$948$	−19.4315	−	19.4315i	−0.631107	−	0.631107i
$949$			6.51404i			0.211455i
$950$	2.00646	−	0.189023i	0.0650981	−	0.00613271i
$951$	21.8696			0.709169
$952$	13.2882	+	13.2882i	0.430674	+	0.430674i
$953$	3.37953	+	3.37953i	0.109474	+	0.109474i	0.759722	−	0.650248i	$-0.225335\pi$
$953$	3.37953	+	3.37953i	0.109474	+	0.109474i	−0.650248	+	0.759722i	$0.725335\pi$
$954$	33.1335			1.07274
$955$	−7.02454	−	14.9341i	−0.227309	−	0.483255i
$956$	−63.8106			−2.06378
$957$	−23.7675	+	23.7675i	−0.768293	+	0.768293i
$958$	−22.9079	−	22.9079i	−0.740122	−	0.740122i
$959$		−	15.2136i		−	0.491274i
$960$	33.7811	+	12.1680i	1.09028	+	0.392721i
$961$	22.8229			0.736222
$962$	3.40002	−	3.40002i	0.109621	−	0.109621i
$963$	−3.64145	−	3.64145i	−0.117344	−	0.117344i
$964$	12.4210			0.400053
$965$	−9.89089	+	27.4593i	−0.318399	+	0.883947i
$966$	−5.48702	+	12.2485i	−0.176542	+	0.394091i
$967$	−37.8515	−	37.8515i	−1.21722	−	1.21722i	−0.968601	−	0.248622i	$-0.920022\pi$
$967$	−37.8515	−	37.8515i	−1.21722	−	1.21722i	−0.248622	−	0.968601i	$-0.579978\pi$
$968$	−28.2061	+	28.2061i	−0.906580	+	0.906580i
$969$			1.56455i			0.0502605i
$970$	−23.4934	+	11.0506i	−0.754328	+	0.354813i
$971$			30.5794i			0.981339i	0.871346	+	0.490670i	$0.163248\pi$
$971$			30.5794i			0.981339i	−0.871346	+	0.490670i	$0.836752\pi$
$972$	−30.4865	−	30.4865i	−0.977854	−	0.977854i
$973$	5.79869	+	5.79869i	0.185897	+	0.185897i
$974$			10.4282i			0.334140i
$975$	7.90464	+	6.54351i	0.253151	+	0.209560i
$976$		−	1.27618i		−	0.0408496i
$977$	36.2012	−	36.2012i	1.15818	−	1.15818i	0.173313	−	0.984867i	$-0.444553\pi$
$977$	36.2012	−	36.2012i	1.15818	−	1.15818i	0.984867	−	0.173313i	$-0.0554472\pi$
$978$	20.1972	−	20.1972i	0.645834	−	0.645834i
$979$		−	49.8883i		−	1.59444i
$980$	6.38780	−	3.00463i	0.204051	−	0.0959794i
$981$			2.45277i			0.0783110i
$982$	32.8596	+	32.8596i	1.04859	+	1.04859i
$983$	5.47146	+	5.47146i	0.174512	+	0.174512i	0.788959	−	0.614446i	$-0.210621\pi$
$983$	5.47146	+	5.47146i	0.174512	+	0.174512i	−0.614446	+	0.788959i	$0.710621\pi$
$984$		−	29.1631i		−	0.929686i
$985$	−26.7865	−	9.64854i	−0.853489	−	0.307428i
$986$		−	86.5804i		−	2.75728i
$987$	−9.98136	+	9.98136i	−0.317710	+	0.317710i
$988$	0.659847	+	0.659847i	0.0209925	+	0.0209925i
$989$	30.6488	+	13.7298i	0.974575	+	0.436583i
$990$	36.2107	+	13.0432i	1.15085	+	0.414539i
$991$	10.7653			0.341972			0.170986	−	0.985273i	$-0.445305\pi$
$991$	10.7653			0.341972			0.170986	+	0.985273i	$0.445305\pi$
$992$	−31.3534	−	31.3534i	−0.995471	−	0.995471i
$993$	9.30680	−	9.30680i	0.295342	−	0.295342i
$994$	−34.6781			−1.09992
$995$	−28.8269	+	13.5593i	−0.913875	+	0.429860i
$996$		−	40.2260i		−	1.27461i
$997$	17.2471	+	17.2471i	0.546220	+	0.546220i	0.925345	−	0.379125i	$-0.123775\pi$
$997$	17.2471	+	17.2471i	0.546220	+	0.546220i	−0.379125	+	0.925345i	$0.623775\pi$
$998$	−6.74341	+	6.74341i	−0.213459	+	0.213459i
$999$	7.02154			0.222152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.l.a.22.8	yes	144
5.3	odd	4	inner	805.2.l.a.183.7	yes	144
23.22	odd	2	inner	805.2.l.a.22.7	✓	144
115.68	even	4	inner	805.2.l.a.183.8	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.l.a.22.7	✓	144	23.22	odd	2	inner
805.2.l.a.22.8	yes	144	1.1	even	1	trivial
805.2.l.a.183.7	yes	144	5.3	odd	4	inner
805.2.l.a.183.8	yes	144	115.68	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60576 - 1.60576i) q^{2} +(0.871410 - 0.871410i) q^{3} +3.15695i q^{4} +(2.02341 - 0.951750i) q^{5} -2.79856 q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.85780 - 1.85780i) q^{8} +1.48129i q^{9} +O(q^{10})\)	\(q+(-1.60576 - 1.60576i) q^{2} +(0.871410 - 0.871410i) q^{3} +3.15695i q^{4} +(2.02341 - 0.951750i) q^{5} -2.79856 q^{6} +(-0.707107 + 0.707107i) q^{7} +(1.85780 - 1.85780i) q^{8} +1.48129i q^{9} +(-4.77740 - 1.72083i) q^{10} +5.11689i q^{11} +(2.75100 + 2.75100i) q^{12} +(-1.17759 + 1.17759i) q^{13} +2.27089 q^{14} +(0.933852 - 2.59258i) q^{15} +0.347548 q^{16} +(5.05771 - 5.05771i) q^{17} +(2.37860 - 2.37860i) q^{18} -0.177493 q^{19} +(3.00463 + 6.38780i) q^{20} +1.23236i q^{21} +(8.21652 - 8.21652i) q^{22} +(-4.48121 + 1.70842i) q^{23} -3.23780i q^{24} +(3.18834 - 3.85155i) q^{25} +3.78186 q^{26} +(3.90504 + 3.90504i) q^{27} +(-2.23230 - 2.23230i) q^{28} +5.33033i q^{29} +(-5.66262 + 2.66353i) q^{30} +7.33641 q^{31} +(-4.27367 - 4.27367i) q^{32} +(4.45891 + 4.45891i) q^{33} -16.2430 q^{34} +(-0.757775 + 2.10375i) q^{35} -4.67636 q^{36} +(0.899035 - 0.899035i) q^{37} +(0.285012 + 0.285012i) q^{38} +2.05232i q^{39} +(1.99092 - 5.52723i) q^{40} +9.00707 q^{41} +(1.97888 - 1.97888i) q^{42} +(-4.95163 - 4.95163i) q^{43} -16.1538 q^{44} +(1.40982 + 2.99725i) q^{45} +(9.93910 + 4.45245i) q^{46} +(8.09939 + 8.09939i) q^{47} +(0.302857 - 0.302857i) q^{48} -1.00000i q^{49} +(-11.3044 + 1.06496i) q^{50} -8.81468i q^{51} +(-3.71759 - 3.71759i) q^{52} +(6.96493 + 6.96493i) q^{53} -12.5411i q^{54} +(4.87000 + 10.3536i) q^{55} +2.62732i q^{56} +(-0.154669 + 0.154669i) q^{57} +(8.55925 - 8.55925i) q^{58} +0.00127673i q^{59} +(8.18466 + 2.94813i) q^{60} -3.67196i q^{61} +(-11.7805 - 11.7805i) q^{62} +(-1.04743 - 1.04743i) q^{63} +13.0299i q^{64} +(-1.26197 + 3.50351i) q^{65} -14.3199i q^{66} +(6.28020 - 6.28020i) q^{67} +(15.9670 + 15.9670i) q^{68} +(-2.41624 + 5.39371i) q^{69} +(4.59494 - 2.16132i) q^{70} -15.2707 q^{71} +(2.75193 + 2.75193i) q^{72} +(2.76584 - 2.76584i) q^{73} -2.88728 q^{74} +(-0.577928 - 6.13464i) q^{75} -0.560338i q^{76} +(-3.61819 - 3.61819i) q^{77} +(3.29555 - 3.29555i) q^{78} -7.06344 q^{79} +(0.703231 - 0.330779i) q^{80} +2.36192 q^{81} +(-14.4632 - 14.4632i) q^{82} +(-7.31116 - 7.31116i) q^{83} -3.89050 q^{84} +(5.42013 - 15.0475i) q^{85} +15.9023i q^{86} +(4.64490 + 4.64490i) q^{87} +(9.50614 + 9.50614i) q^{88} -9.74973 q^{89} +(2.54904 - 7.07671i) q^{90} -1.66536i q^{91} +(-5.39342 - 14.1470i) q^{92} +(6.39302 - 6.39302i) q^{93} -26.0114i q^{94} +(-0.359141 + 0.168929i) q^{95} -7.44824 q^{96} +(3.61536 - 3.61536i) q^{97} +(-1.60576 + 1.60576i) q^{98} -7.57960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{3} - 16 q^{6}+O(q^{10}) \) 144 * q + 8 * q^3 - 16 * q^6	\( 144 q + 8 q^{3} - 16 q^{6} + 32 q^{12} - 16 q^{13} - 192 q^{16} - 16 q^{18} - 8 q^{23} - 8 q^{25} + 8 q^{27} - 40 q^{32} + 208 q^{36} + 32 q^{41} - 80 q^{46} + 16 q^{47} + 24 q^{48} - 56 q^{50} - 64 q^{52} + 56 q^{55} - 24 q^{62} - 16 q^{70} - 96 q^{71} - 48 q^{72} + 32 q^{73} - 32 q^{75} + 40 q^{78} - 160 q^{81} - 96 q^{82} + 16 q^{85} - 16 q^{87} + 112 q^{92} - 8 q^{93} - 120 q^{95} + 272 q^{96}+O(q^{100}) \) 144 * q + 8 * q^3 - 16 * q^6 + 32 * q^12 - 16 * q^13 - 192 * q^16 - 16 * q^18 - 8 * q^23 - 8 * q^25 + 8 * q^27 - 40 * q^32 + 208 * q^36 + 32 * q^41 - 80 * q^46 + 16 * q^47 + 24 * q^48 - 56 * q^50 - 64 * q^52 + 56 * q^55 - 24 * q^62 - 16 * q^70 - 96 * q^71 - 48 * q^72 + 32 * q^73 - 32 * q^75 + 40 * q^78 - 160 * q^81 - 96 * q^82 + 16 * q^85 - 16 * q^87 + 112 * q^92 - 8 * q^93 - 120 * q^95 + 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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