LMFDB - Embedded newform 1710.2.t.c.919.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1710.919");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.t (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 49 x^{16} - 8 x^{15} + 72 x^{13} + 2145 x^{12} - 648 x^{11} + 32 x^{10} - 7056 x^{9} + \cdots + 1024 $ x^20 - 49x^16 - 8x^15 + 72x^13 + 2145x^12 - 648x^11 + 32x^10 - 7056x^9 - 11968x^8 + 10368x^7 + 9344x^6 + 18176x^5 + 56320x^4 + 28160x^3 + 8192x^2 + 4096*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.5
Root			$-0.627868 - 2.34324i$ of defining polynomial
Character	$\chi$	$=$	1710.919
Dual form			1710.2.t.c.1189.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.09991 + 0.768349i) q^{5} +2.51805i q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.09991 + 0.768349i) q^{5} +2.51805i q^{7} +1.00000i q^{8} +(-2.20275 + 0.384547i) q^{10} -2.88497 q^{11} +(4.03244 + 2.32813i) q^{13} +(-1.25902 - 2.18069i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.31158 + 3.64399i) q^{17} +(4.11420 - 1.43993i) q^{19} +(1.71537 - 1.43440i) q^{20} +(2.49846 - 1.44248i) q^{22} +(1.48237 + 0.855848i) q^{23} +(3.81928 + 3.22694i) q^{25} -4.65626 q^{26} +(2.18069 + 1.25902i) q^{28} +(-2.20959 + 3.82712i) q^{29} -9.22060 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.64399 - 6.31158i) q^{34} +(-1.93474 + 5.28768i) q^{35} +3.26480i q^{37} +(-2.84303 + 3.30411i) q^{38} +(-0.768349 + 2.09991i) q^{40} +(-4.48368 - 7.76596i) q^{41} +(-5.84894 + 3.37689i) q^{43} +(-1.44248 + 2.49846i) q^{44} -1.71170 q^{46} +(-3.98083 - 2.29833i) q^{47} +0.659446 q^{49} +(-4.92106 - 0.884968i) q^{50} +(4.03244 - 2.32813i) q^{52} +(9.38113 + 5.41620i) q^{53} +(-6.05819 - 2.21666i) q^{55} -2.51805 q^{56} -4.41917i q^{58} +(-4.73274 - 8.19734i) q^{59} +(7.50173 - 12.9934i) q^{61} +(7.98528 - 4.61030i) q^{62} -1.00000 q^{64} +(6.67896 + 7.98719i) q^{65} +(9.23107 + 5.32956i) q^{67} +7.28798i q^{68} +(-0.968307 - 5.54663i) q^{70} +(5.38040 + 9.31912i) q^{71} +(-12.2689 + 7.08348i) q^{73} +(-1.63240 - 2.82740i) q^{74} +(0.810083 - 4.28296i) q^{76} -7.26448i q^{77} +(4.11998 + 7.13601i) q^{79} +(-0.384547 - 2.20275i) q^{80} +(7.76596 + 4.48368i) q^{82} -7.14523i q^{83} +(-16.0536 + 2.80257i) q^{85} +(3.37689 - 5.84894i) q^{86} -2.88497i q^{88} +(-2.37111 + 4.10688i) q^{89} +(-5.86233 + 10.1539i) q^{91} +(1.48237 - 0.855848i) q^{92} +4.59667 q^{94} +(9.74583 + 0.137412i) q^{95} +(-1.98898 + 1.14834i) q^{97} +(-0.571097 + 0.329723i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4}+O(q^{10}) $ 20 * q + 10 * q^4	$ 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.09991	+	0.768349i	0.939110	+	0.343616i
$5$	2.09991	+	0.768349i	0.939110	+	0.343616i
$6$		0			0
$7$			2.51805i			0.951732i	0.879518	+	0.475866i	$0.157865\pi$
$7$			2.51805i			0.951732i	−0.879518	+	0.475866i	$0.842135\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.20275	+	0.384547i	−0.696572	+	0.121604i
$11$	−2.88497			−0.869851			−0.434925	−	0.900467i	$-0.643225\pi$
$11$	−2.88497			−0.869851			−0.434925	+	0.900467i	$0.643225\pi$
$12$		0			0
$13$	4.03244	+	2.32813i	1.11840	+	0.645707i	0.940991	−	0.338431i	$-0.109896\pi$
$13$	4.03244	+	2.32813i	1.11840	+	0.645707i	0.177406	+	0.984138i	$0.443230\pi$
$14$	−1.25902	−	2.18069i	−0.336488	−	0.582814i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−6.31158	+	3.64399i	−1.53078	+	0.883798i	−0.531457	+	0.847085i	$0.678355\pi$
$17$	−6.31158	+	3.64399i	−1.53078	+	0.883798i	−0.999326	+	0.0367122i	$0.988312\pi$
$18$		0			0
$19$	4.11420	−	1.43993i	0.943861	−	0.330342i
$19$	4.11420	−	1.43993i	0.943861	−	0.330342i
$20$	1.71537	−	1.43440i	0.383568	−	0.320743i
$21$		0			0
$22$	2.49846	−	1.44248i	0.532673	−	0.307539i
$23$	1.48237	+	0.855848i	0.309096	+	0.178457i	0.646522	−	0.762895i	$-0.276223\pi$
$23$	1.48237	+	0.855848i	0.309096	+	0.178457i	−0.337426	+	0.941352i	$0.609556\pi$
$24$		0			0
$25$	3.81928	+	3.22694i	0.763856	+	0.645387i
$26$	−4.65626			−0.913167
$27$		0			0
$28$	2.18069	+	1.25902i	0.412112	+	0.237933i
$29$	−2.20959	+	3.82712i	−0.410310	+	0.710678i	−0.994923	−	0.100634i	$-0.967913\pi$
$29$	−2.20959	+	3.82712i	−0.410310	+	0.710678i	0.584613	+	0.811312i	$0.301246\pi$
$30$		0			0
$31$	−9.22060			−1.65607			−0.828035	−	0.560677i	$-0.810541\pi$
$31$	−9.22060			−1.65607			−0.828035	+	0.560677i	$0.810541\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	3.64399	−	6.31158i	0.624939	−	1.08243i
$35$	−1.93474	+	5.28768i	−0.327031	+	0.893781i
$36$		0			0
$37$			3.26480i			0.536730i	0.963317	+	0.268365i	$0.0864834\pi$
$37$			3.26480i			0.536730i	−0.963317	+	0.268365i	$0.913517\pi$
$38$	−2.84303	+	3.30411i	−0.461201	+	0.535998i
$39$		0			0
$40$	−0.768349	+	2.09991i	−0.121487	+	0.332026i
$41$	−4.48368	−	7.76596i	−0.700233	−	1.21284i	−0.968384	−	0.249463i	$-0.919746\pi$
$41$	−4.48368	−	7.76596i	−0.700233	−	1.21284i	0.268151	−	0.963377i	$-0.413587\pi$
$42$		0			0
$43$	−5.84894	+	3.37689i	−0.891955	+	0.514971i	−0.874582	−	0.484878i	$-0.838864\pi$
$43$	−5.84894	+	3.37689i	−0.891955	+	0.514971i	−0.0173738	+	0.999849i	$0.505531\pi$
$44$	−1.44248	+	2.49846i	−0.217463	+	0.376656i
$45$		0			0
$46$	−1.71170			−0.252376
$47$	−3.98083	−	2.29833i	−0.580664	−	0.335246i	0.180733	−	0.983532i	$-0.442153\pi$
$47$	−3.98083	−	2.29833i	−0.580664	−	0.335246i	−0.761397	+	0.648286i	$0.775486\pi$
$48$		0			0
$49$	0.659446			0.0942065
$50$	−4.92106	−	0.884968i	−0.695943	−	0.125153i
$51$		0			0
$52$	4.03244	−	2.32813i	0.559198	−	0.322853i
$53$	9.38113	+	5.41620i	1.28860	+	0.743972i	0.978404	−	0.206701i	$-0.0662729\pi$
$53$	9.38113	+	5.41620i	1.28860	+	0.743972i	0.310193	+	0.950673i	$0.399606\pi$
$54$		0			0
$55$	−6.05819	−	2.21666i	−0.816886	−	0.298895i
$56$	−2.51805			−0.336488
$57$		0			0
$58$		−	4.41917i		−	0.580266i
$59$	−4.73274	−	8.19734i	−0.616150	−	1.06720i	−0.990182	−	0.139787i	$-0.955358\pi$
$59$	−4.73274	−	8.19734i	−0.616150	−	1.06720i	0.374032	−	0.927416i	$-0.377975\pi$
$60$		0			0
$61$	7.50173	−	12.9934i	0.960498	−	1.66363i	0.239244	−	0.970959i	$-0.423100\pi$
$61$	7.50173	−	12.9934i	0.960498	−	1.66363i	0.721254	−	0.692671i	$-0.243566\pi$
$62$	7.98528	−	4.61030i	1.01413	−	0.585509i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	6.67896	+	7.98719i	0.828422	+	0.990689i
$66$		0			0
$67$	9.23107	+	5.32956i	1.12776	+	0.651110i	0.943369	−	0.331744i	$-0.107637\pi$
$67$	9.23107	+	5.32956i	1.12776	+	0.651110i	0.184386	+	0.982854i	$0.440970\pi$
$68$			7.28798i			0.883798i
$69$		0			0
$70$	−0.968307	−	5.54663i	−0.115735	−	0.662950i
$71$	5.38040	+	9.31912i	0.638536	+	1.10598i	0.985754	+	0.168192i	$0.0537929\pi$
$71$	5.38040	+	9.31912i	0.638536	+	1.10598i	−0.347218	+	0.937784i	$0.612874\pi$
$72$		0			0
$73$	−12.2689	+	7.08348i	−1.43597	+	0.829059i	−0.997567	−	0.0697187i	$-0.977790\pi$
$73$	−12.2689	+	7.08348i	−1.43597	+	0.829059i	−0.438405	+	0.898777i	$0.644457\pi$
$74$	−1.63240	−	2.82740i	−0.189763	−	0.328679i
$75$		0			0
$76$	0.810083	−	4.28296i	0.0929229	−	0.491289i
$77$		−	7.26448i		−	0.827865i
$78$		0			0
$79$	4.11998	+	7.13601i	0.463533	+	0.802864i	0.999134	−	0.0416079i	$-0.0132480\pi$
$79$	4.11998	+	7.13601i	0.463533	+	0.802864i	−0.535601	+	0.844471i	$0.679915\pi$
$80$	−0.384547	−	2.20275i	−0.0429937	−	0.246275i
$81$		0			0
$82$	7.76596	+	4.48368i	0.857607	+	0.495140i
$83$		−	7.14523i		−	0.784291i	−0.919903	−	0.392146i	$-0.871733\pi$
$83$		−	7.14523i		−	0.784291i	0.919903	−	0.392146i	$-0.128267\pi$
$84$		0			0
$85$	−16.0536	+	2.80257i	−1.74126	+	0.303982i
$86$	3.37689	−	5.84894i	0.364139	−	0.630708i
$87$		0			0
$88$		−	2.88497i		−	0.307539i
$89$	−2.37111	+	4.10688i	−0.251337	+	0.435328i	−0.963894	−	0.266286i	$-0.914204\pi$
$89$	−2.37111	+	4.10688i	−0.251337	+	0.435328i	0.712557	+	0.701614i	$0.247537\pi$
$90$		0			0
$91$	−5.86233	+	10.1539i	−0.614540	+	1.06441i
$92$	1.48237	−	0.855848i	0.154548	−	0.0892284i
$93$		0			0
$94$	4.59667			0.474110
$95$	9.74583	+	0.137412i	0.999901	+	0.0140982i
$96$		0			0
$97$	−1.98898	+	1.14834i	−0.201950	+	0.116596i	−0.597565	−	0.801821i	$-0.703865\pi$
$97$	−1.98898	+	1.14834i	−0.201950	+	0.116596i	0.395615	+	0.918417i	$0.370532\pi$
$98$	−0.571097	+	0.329723i	−0.0576895	+	0.0333070i
$99$		0			0
$100$	4.70425	−	1.69412i	0.470425	−	0.169412i
$101$	−1.68398	+	2.91673i	−0.167562	+	0.290226i	−0.937562	−	0.347818i	$-0.886923\pi$
$101$	−1.68398	+	2.91673i	−0.167562	+	0.290226i	0.770000	+	0.638044i	$0.220256\pi$
$102$		0			0
$103$		−	10.9873i		−	1.08261i	−0.840826	−	0.541305i	$-0.817930\pi$
$103$		−	10.9873i		−	1.08261i	0.840826	−	0.541305i	$-0.182070\pi$
$104$	−2.32813	+	4.03244i	−0.228292	+	0.395413i
$105$		0			0
$106$	−10.8324			−1.05214
$107$			3.35775i			0.324605i	0.986741	+	0.162303i	$0.0518921\pi$
$107$			3.35775i			0.324605i	−0.986741	+	0.162303i	$0.948108\pi$
$108$		0			0
$109$	2.11647	+	3.66583i	0.202721	+	0.351122i	0.949404	−	0.314057i	$-0.101688\pi$
$109$	2.11647	+	3.66583i	0.202721	+	0.351122i	−0.746683	+	0.665180i	$0.768355\pi$
$110$	6.35487	−	1.10941i	0.605914	−	0.105778i
$111$		0			0
$112$	2.18069	−	1.25902i	0.206056	−	0.118966i
$113$			18.7982i			1.76839i	0.467118	+	0.884195i	$0.345292\pi$
$113$			18.7982i			1.76839i	−0.467118	+	0.884195i	$0.654708\pi$
$114$		0			0
$115$	2.45527	+	2.93619i	0.228955	+	0.273801i
$116$	2.20959	+	3.82712i	0.205155	+	0.355339i
$117$		0			0
$118$	8.19734	+	4.73274i	0.754626	+	0.435684i
$119$	−9.17574	−	15.8928i	−0.841138	−	1.45689i
$120$		0			0
$121$	−2.67696			−0.243360
$122$			15.0035i			1.35835i
$123$		0			0
$124$	−4.61030	+	7.98528i	−0.414017	+	0.717099i
$125$	5.54074	+	9.71083i	0.495579	+	0.868563i
$126$		0			0
$127$	−13.6465	−	7.87880i	−1.21093	−	0.699131i	−0.247968	−	0.968768i	$-0.579763\pi$
$127$	−13.6465	−	7.87880i	−1.21093	−	0.699131i	−0.962962	+	0.269637i	$0.913096\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−9.77774	−	3.57763i	−0.857565	−	0.313779i
$131$	−3.28357	−	5.68732i	−0.286887	−	0.496903i	0.686178	−	0.727434i	$-0.259287\pi$
$131$	−3.28357	−	5.68732i	−0.286887	−	0.496903i	−0.973065	+	0.230531i	$0.925954\pi$
$132$		0			0
$133$	3.62581	+	10.3597i	0.314397	+	0.898303i
$134$	−10.6591			−0.920808
$135$		0			0
$136$	−3.64399	−	6.31158i	−0.312470	−	0.541213i
$137$	12.5023	+	7.21818i	1.06814	+	0.616691i	0.927673	−	0.373394i	$-0.121806\pi$
$137$	12.5023	+	7.21818i	1.06814	+	0.616691i	0.140467	+	0.990085i	$0.455139\pi$
$138$		0			0
$139$	−3.09728	+	5.36464i	−0.262708	+	0.455023i	−0.966960	−	0.254926i	$-0.917949\pi$
$139$	−3.09728	+	5.36464i	−0.262708	+	0.455023i	0.704253	+	0.709949i	$0.251282\pi$
$140$	3.61190	+	4.31937i	0.305261	+	0.365054i
$141$		0			0
$142$	−9.31912	−	5.38040i	−0.782043	−	0.451513i
$143$	−11.6335	−	6.71658i	−0.972838	−	0.561668i
$144$		0			0
$145$	−7.58051	+	6.33888i	−0.629527	+	0.526416i
$146$	7.08348	−	12.2689i	0.586233	−	1.01539i
$147$		0			0
$148$	2.82740	+	1.63240i	0.232411	+	0.134183i
$149$	5.99475	+	10.3832i	0.491109	+	0.850626i	0.999948	−	0.0102357i	$-0.00325819\pi$
$149$	5.99475	+	10.3832i	0.491109	+	0.850626i	−0.508838	+	0.860862i	$0.669925\pi$
$150$		0			0
$151$	−5.51534			−0.448832			−0.224416	−	0.974493i	$-0.572047\pi$
$151$	−5.51534			−0.448832			−0.224416	+	0.974493i	$0.572047\pi$
$152$	1.43993	+	4.11420i	0.116794	+	0.333705i
$153$		0			0
$154$	3.63224	+	6.29123i	0.292694	+	0.506961i
$155$	−19.3625	−	7.08464i	−1.55523	−	0.569052i
$156$		0			0
$157$	10.6341	−	6.13962i	0.848696	−	0.489995i	−0.0115149	−	0.999934i	$-0.503665\pi$
$157$	10.6341	−	6.13962i	0.848696	−	0.489995i	0.860211	+	0.509939i	$0.170332\pi$
$158$	−7.13601	−	4.11998i	−0.567710	−	0.327768i
$159$		0			0
$160$	1.43440	+	1.71537i	0.113400	+	0.135612i
$161$	−2.15507	+	3.73268i	−0.169843	+	0.294177i
$162$		0			0
$163$		−	3.45801i		−	0.270852i	−0.990787	−	0.135426i	$-0.956760\pi$
$163$		−	3.45801i		−	0.270852i	0.990787	−	0.135426i	$-0.0432403\pi$
$164$	−8.96736			−0.700233
$165$		0			0
$166$	3.57262	+	6.18795i	0.277289	+	0.480278i
$167$	−5.37144	−	3.10120i	−0.415654	−	0.239978i	0.277562	−	0.960708i	$-0.410474\pi$
$167$	−5.37144	−	3.10120i	−0.415654	−	0.239978i	−0.693216	+	0.720730i	$0.743807\pi$
$168$		0			0
$169$	4.34036	+	7.51773i	0.333874	+	0.578287i
$170$	12.5016	−	10.4539i	0.958826	−	0.801779i
$171$		0			0
$172$			6.75378i			0.514971i
$173$	12.4712	−	7.20026i	0.948169	−	0.547425i	0.0556571	−	0.998450i	$-0.482275\pi$
$173$	12.4712	−	7.20026i	0.948169	−	0.547425i	0.892512	+	0.451025i	$0.148941\pi$
$174$		0			0
$175$	−8.12557	+	9.61712i	−0.614235	+	0.726986i
$176$	1.44248	+	2.49846i	0.108731	+	0.188328i
$177$		0			0
$178$		−	4.74222i		−	0.355444i
$179$	1.94176			0.145134			0.0725670	−	0.997364i	$-0.476881\pi$
$179$	1.94176			0.145134			0.0725670	+	0.997364i	$0.476881\pi$
$180$		0			0
$181$	−8.81480	+	15.2677i	−0.655199	+	1.13484i	0.326645	+	0.945147i	$0.394082\pi$
$181$	−8.81480	+	15.2677i	−0.655199	+	1.13484i	−0.981844	+	0.189691i	$0.939251\pi$
$182$		−	11.7247i		−	0.869090i
$183$		0			0
$184$	−0.855848	+	1.48237i	−0.0630940	+	0.109282i
$185$	−2.50851	+	6.85581i	−0.184429	+	0.504049i
$186$		0			0
$187$	18.2087	−	10.5128i	1.33155	−	0.768772i
$188$	−3.98083	+	2.29833i	−0.290332	+	0.167623i
$189$		0			0
$190$	−8.50884	+	4.75391i	−0.617296	+	0.344885i
$191$	4.61377			0.333840			0.166920	−	0.985970i	$-0.446618\pi$
$191$	4.61377			0.333840			0.166920	+	0.985970i	$0.446618\pi$
$192$		0			0
$193$	−21.7202	+	12.5401i	−1.56345	+	0.902659i	−0.566547	+	0.824030i	$0.691721\pi$
$193$	−21.7202	+	12.5401i	−1.56345	+	0.902659i	−0.996904	+	0.0786292i	$0.974946\pi$
$194$	1.14834	−	1.98898i	0.0824458	−	0.142800i
$195$		0			0
$196$	0.329723	−	0.571097i	0.0235516	−	0.0407926i
$197$			3.62439i			0.258227i	0.991630	+	0.129113i	$0.0412131\pi$
$197$			3.62439i			0.258227i	−0.991630	+	0.129113i	$0.958787\pi$
$198$		0			0
$199$	0.298493	−	0.517005i	0.0211596	−	0.0366495i	−0.855252	−	0.518213i	$-0.826598\pi$
$199$	0.298493	−	0.517005i	0.0211596	−	0.0366495i	0.876411	+	0.481563i	$0.159931\pi$
$200$	−3.22694	+	3.81928i	−0.228179	+	0.270064i
$201$		0			0
$202$		−	3.36795i		−	0.236968i
$203$	−9.63686	−	5.56384i	−0.676375	−	0.390505i
$204$		0			0
$205$	−3.44837	−	19.7529i	−0.240845	−	1.37960i
$206$	5.49365	+	9.51527i	0.382760	+	0.662961i
$207$		0			0
$208$		−	4.65626i		−	0.322853i
$209$	−11.8693	+	4.15415i	−0.821018	+	0.287349i
$210$		0			0
$211$	11.4644	+	19.8569i	0.789242	+	1.36701i	0.926432	+	0.376462i	$0.122859\pi$
$211$	11.4644	+	19.8569i	0.789242	+	1.36701i	−0.137191	+	0.990545i	$0.543807\pi$
$212$	9.38113	−	5.41620i	0.644299	−	0.371986i
$213$		0			0
$214$	−1.67887	−	2.90789i	−0.114765	−	0.198779i
$215$	−14.8769	+	2.59715i	−1.01460	+	0.177124i
$216$		0			0
$217$		−	23.2179i		−	1.57613i
$218$	−3.66583	−	2.11647i	−0.248281	−	0.143345i
$219$		0			0
$220$	−4.94878	+	4.13821i	−0.333647	+	0.278998i
$221$	−33.9347			−2.28270
$222$		0			0
$223$	−9.74016	+	5.62349i	−0.652250	+	0.376576i	−0.789318	−	0.613985i	$-0.789565\pi$
$223$	−9.74016	+	5.62349i	−0.652250	+	0.376576i	0.137068	+	0.990562i	$0.456232\pi$
$224$	−1.25902	+	2.18069i	−0.0841220	+	0.145704i
$225$		0			0
$226$	−9.39912	−	16.2798i	−0.625220	−	1.08291i
$227$		−	8.82814i		−	0.585944i	−0.956121	−	0.292972i	$-0.905356\pi$
$227$		−	8.82814i		−	0.585944i	0.956121	−	0.292972i	$-0.0946443\pi$
$228$		0			0
$229$	22.2817			1.47241			0.736207	−	0.676756i	$-0.236615\pi$
$229$	22.2817			1.47241			0.736207	+	0.676756i	$0.236615\pi$
$230$	−3.59442	−	1.31518i	−0.237009	−	0.0867205i
$231$		0			0
$232$	−3.82712	−	2.20959i	−0.251263	−	0.145066i
$233$	−5.35318	+	3.09066i	−0.350699	+	0.202476i	−0.664993	−	0.746850i	$-0.731565\pi$
$233$	−5.35318	+	3.09066i	−0.350699	+	0.202476i	0.314294	+	0.949326i	$0.398232\pi$
$234$		0			0
$235$	−6.59348	−	7.88497i	−0.430111	−	0.514359i
$236$	−9.46547			−0.616150
$237$		0			0
$238$	15.8928	+	9.17574i	1.03018	+	0.594775i
$239$	18.1898			1.17660			0.588299	−	0.808644i	$-0.299798\pi$
$239$	18.1898			1.17660			0.588299	+	0.808644i	$0.299798\pi$
$240$		0			0
$241$	−1.24768	+	2.16104i	−0.0803699	+	0.139205i	−0.903409	−	0.428780i	$-0.858943\pi$
$241$	−1.24768	+	2.16104i	−0.0803699	+	0.139205i	0.823039	+	0.567985i	$0.192277\pi$
$242$	2.31831	−	1.33848i	0.149027	−	0.0860407i
$243$		0			0
$244$	−7.50173	−	12.9934i	−0.480249	−	0.831815i
$245$	1.38478	+	0.506685i	0.0884703	+	0.0323709i
$246$		0			0
$247$	19.9426	+	3.77195i	1.26892	+	0.240004i
$248$		−	9.22060i		−	0.585509i
$249$		0			0
$250$	−9.65384	−	5.63945i	−0.610562	−	0.356670i
$251$	−10.6317	+	18.4147i	−0.671069	+	1.16232i	0.306533	+	0.951860i	$0.400831\pi$
$251$	−10.6317	+	18.4147i	−0.671069	+	1.16232i	−0.977601	+	0.210465i	$0.932502\pi$
$252$		0			0
$253$	−4.27660	−	2.46910i	−0.268867	−	0.155231i
$254$	15.7576			0.988720
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.03779	−	2.90857i	−0.314249	−	0.181432i	0.334577	−	0.942368i	$-0.391406\pi$
$257$	−5.03779	−	2.90857i	−0.314249	−	0.181432i	−0.648826	+	0.760937i	$0.724740\pi$
$258$		0			0
$259$	−8.22092			−0.510823
$260$	10.2566	−	1.79055i	0.636087	−	0.111045i
$261$		0			0
$262$	5.68732	+	3.28357i	0.351364	+	0.202860i
$263$	14.9606	−	8.63749i	0.922508	−	0.532610i	0.0380737	−	0.999275i	$-0.487878\pi$
$263$	14.9606	−	8.63749i	0.922508	−	0.532610i	0.884434	+	0.466665i	$0.154544\pi$
$264$		0			0
$265$	15.5380	+	18.5815i	0.954494	+	1.14145i
$266$	−8.31991	−	7.15889i	−0.510126	−	0.438940i
$267$		0			0
$268$	9.23107	−	5.32956i	0.563878	−	0.325555i
$269$	4.82743	+	8.36136i	0.294334	+	0.509801i	0.974830	−	0.222951i	$-0.0715689\pi$
$269$	4.82743	+	8.36136i	0.294334	+	0.509801i	−0.680496	+	0.732752i	$0.738236\pi$
$270$		0			0
$271$	−3.21818	−	5.57406i	−0.195491	−	0.338600i	0.751571	−	0.659653i	$-0.229297\pi$
$271$	−3.21818	−	5.57406i	−0.195491	−	0.338600i	−0.947061	+	0.321053i	$0.895963\pi$
$272$	6.31158	+	3.64399i	0.382696	+	0.220949i
$273$		0			0
$274$	−14.4364			−0.872133
$275$	−11.0185	−	9.30961i	−0.664440	−	0.561390i
$276$		0			0
$277$		−	11.1309i		−	0.668791i	−0.942433	−	0.334396i	$-0.891468\pi$
$277$		−	11.1309i		−	0.668791i	0.942433	−	0.334396i	$-0.108532\pi$
$278$		−	6.19455i		−	0.371525i
$279$		0			0
$280$	−5.28768	−	1.93474i	−0.315999	−	0.115623i
$281$	2.84358	−	4.92523i	0.169634	−	0.293815i	−0.768657	−	0.639661i	$-0.779075\pi$
$281$	2.84358	−	4.92523i	0.169634	−	0.293815i	0.938291	+	0.345846i	$0.112408\pi$
$282$		0			0
$283$	6.24466	−	3.60536i	0.371207	−	0.214316i	−0.302779	−	0.953061i	$-0.597914\pi$
$283$	6.24466	−	3.60536i	0.371207	−	0.214316i	0.673985	+	0.738745i	$0.264581\pi$
$284$	10.7608			0.638536
$285$		0			0
$286$	13.4332			0.794319
$287$	19.5550	−	11.2901i	1.15430	−	0.666434i
$288$		0			0
$289$	18.0573	−	31.2762i	1.06220	−	1.83978i
$290$	3.39547	−	9.27989i	0.199389	−	0.544934i
$291$		0			0
$292$			14.1670i			0.829059i
$293$		−	9.26719i		−	0.541395i	−0.962664	−	0.270697i	$-0.912746\pi$
$293$		−	9.26719i		−	0.541395i	0.962664	−	0.270697i	$-0.0872543\pi$
$294$		0			0
$295$	−3.63992	−	20.8501i	−0.211924	−	1.21394i
$296$	−3.26480			−0.189763
$297$		0			0
$298$	−10.3832	−	5.99475i	−0.601484	−	0.347267i
$299$	3.98505	+	6.90231i	0.230461	+	0.399171i
$300$		0			0
$301$	−8.50316	−	14.7279i	−0.490114	−	0.848902i
$302$	4.77643	−	2.75767i	0.274852	−	0.158686i
$303$		0			0
$304$	−3.30411	−	2.84303i	−0.189504	−	0.163059i
$305$	25.7364	−	21.5210i	1.47366	−	1.23229i
$306$		0			0
$307$	8.89602	−	5.13612i	0.507722	−	0.293134i	−0.224175	−	0.974549i	$-0.571969\pi$
$307$	8.89602	−	5.13612i	0.507722	−	0.293134i	0.731897	+	0.681415i	$0.238635\pi$
$308$	−6.29123	−	3.63224i	−0.358476	−	0.206966i
$309$		0			0
$310$	20.3107	−	3.54576i	1.15357	−	0.201385i
$311$	11.4317			0.648232			0.324116	−	0.946017i	$-0.394933\pi$
$311$	11.4317			0.648232			0.324116	+	0.946017i	$0.394933\pi$
$312$		0			0
$313$	3.42825	+	1.97930i	0.193776	+	0.111877i	0.593749	−	0.804650i	$-0.297647\pi$
$313$	3.42825	+	1.97930i	0.193776	+	0.111877i	−0.399973	+	0.916527i	$0.630981\pi$
$314$	−6.13962	+	10.6341i	−0.346479	+	0.600118i
$315$		0			0
$316$	8.23995			0.463533
$317$	19.0052	+	10.9727i	1.06744	+	0.616286i	0.927480	−	0.373872i	$-0.121970\pi$
$317$	19.0052	+	10.9727i	1.06744	+	0.616286i	0.139958	+	0.990157i	$0.455303\pi$
$318$		0			0
$319$	6.37459	−	11.0411i	0.356908	−	0.618184i
$320$	−2.09991	−	0.768349i	−0.117389	−	0.0429520i
$321$		0			0
$322$		−	4.31013i		−	0.240194i
$323$	−20.7200	+	24.0803i	−1.15289	+	1.33986i
$324$		0			0
$325$	7.88828	+	21.9042i	0.437563	+	1.21503i
$326$	1.72900	+	2.99472i	0.0957606	+	0.165862i
$327$		0			0
$328$	7.76596	−	4.48368i	0.428803	−	0.247570i
$329$	5.78731	−	10.0239i	0.319065	−	0.552636i
$330$		0			0
$331$	7.44789			0.409373			0.204687	−	0.978828i	$-0.434382\pi$
$331$	7.44789			0.409373			0.204687	+	0.978828i	$0.434382\pi$
$332$	−6.18795	−	3.57262i	−0.339608	−	0.196073i
$333$		0			0
$334$	6.20240			0.339380
$335$	15.2895	+	18.2843i	0.835354	+	0.998979i
$336$		0			0
$337$	−4.04725	+	2.33668i	−0.220468	+	0.127287i	−0.606167	−	0.795338i	$-0.707294\pi$
$337$	−4.04725	+	2.33668i	−0.220468	+	0.127287i	0.385699	+	0.922625i	$0.373960\pi$
$338$	−7.51773	−	4.34036i	−0.408911	−	0.236085i
$339$		0			0
$340$	−5.59972	+	15.3041i	−0.303687	+	0.829983i
$341$	26.6011			1.44053
$342$		0			0
$343$			19.2868i			1.04139i
$344$	−3.37689	−	5.84894i	−0.182070	−	0.315354i
$345$		0			0
$346$	−7.20026	+	12.4712i	−0.387088	+	0.670456i
$347$	11.8564	−	6.84531i	0.636486	−	0.367475i	−0.146774	−	0.989170i	$-0.546889\pi$
$347$	11.8564	−	6.84531i	0.636486	−	0.367475i	0.783260	+	0.621695i	$0.213556\pi$
$348$		0			0
$349$	34.7901			1.86227			0.931137	−	0.364671i	$-0.118818\pi$
$349$	34.7901			1.86227			0.931137	+	0.364671i	$0.118818\pi$
$350$	2.22839	−	12.3915i	0.119113	−	0.662351i
$351$		0			0
$352$	−2.49846	−	1.44248i	−0.133168	−	0.0768847i
$353$			3.05876i			0.162802i	0.996681	+	0.0814008i	$0.0259394\pi$
$353$			3.05876i			0.162802i	−0.996681	+	0.0814008i	$0.974061\pi$
$354$		0			0
$355$	4.13803	+	23.7034i	0.219624	+	1.25805i
$356$	2.37111	+	4.10688i	0.125668	+	0.217664i
$357$		0			0
$358$	−1.68161	+	0.970880i	−0.0888760	+	0.0513126i
$359$	−8.49408	−	14.7122i	−0.448300	−	0.776479i	0.549975	−	0.835181i	$-0.314637\pi$
$359$	−8.49408	−	14.7122i	−0.448300	−	0.776479i	−0.998276	+	0.0587020i	$0.981304\pi$
$360$		0			0
$361$	14.8532	−	11.8483i	0.781748	−	0.623595i
$362$		−	17.6296i		−	0.926592i
$363$		0			0
$364$	5.86233	+	10.1539i	0.307270	+	0.532207i
$365$	−31.2063	+	5.44786i	−1.63341	+	0.285154i
$366$		0			0
$367$	−4.66821	−	2.69519i	−0.243679	−	0.140688i	0.373188	−	0.927756i	$-0.378265\pi$
$367$	−4.66821	−	2.69519i	−0.243679	−	0.140688i	−0.616866	+	0.787068i	$0.711598\pi$
$368$		−	1.71170i		−	0.0892284i
$369$		0			0
$370$	−1.25547	−	7.19156i	−0.0652688	−	0.373871i
$371$	−13.6382	+	23.6221i	−0.708062	+	1.22640i
$372$		0			0
$373$			3.85586i			0.199649i	0.995005	+	0.0998244i	$0.0318281\pi$
$373$			3.85586i			0.199649i	−0.995005	+	0.0998244i	$0.968172\pi$
$374$	−10.5128	+	18.2087i	−0.543604	+	0.941550i
$375$		0			0
$376$	2.29833	−	3.98083i	0.118527	−	0.205296i
$377$	−17.8200	+	10.2884i	−0.917779	+	0.529880i
$378$		0			0
$379$	−13.6566			−0.701495			−0.350747	−	0.936470i	$-0.614072\pi$
$379$	−13.6566			−0.701495			−0.350747	+	0.936470i	$0.614072\pi$
$380$	4.99192	−	8.37143i	0.256080	−	0.429445i
$381$		0			0
$382$	−3.99564	+	2.30688i	−0.204435	+	0.118030i
$383$	−6.30771	+	3.64176i	−0.322309	+	0.186085i	−0.652421	−	0.757857i	$-0.726247\pi$
$383$	−6.30771	+	3.64176i	−0.322309	+	0.186085i	0.330112	+	0.943942i	$0.392913\pi$
$384$		0			0
$385$	5.58166	−	15.2548i	0.284468	−	0.777456i
$386$	12.5401	−	21.7202i	0.638276	−	1.10553i
$387$		0			0
$388$			2.29667i			0.116596i
$389$	9.81327	−	16.9971i	0.497553	−	0.861786i	−0.502443	−	0.864610i	$-0.667565\pi$
$389$	9.81327	−	16.9971i	0.497553	−	0.861786i	0.999996	+	0.00282365i	$0.000898797\pi$
$390$		0			0
$391$	−12.4748			−0.630879
$392$			0.659446i			0.0333070i
$393$		0			0
$394$	−1.81219	−	3.13881i	−0.0912969	−	0.158131i
$395$	3.16865	+	18.1506i	0.159432	+	0.913255i
$396$		0			0
$397$	10.0280	−	5.78964i	0.503288	−	0.290574i	−0.226782	−	0.973946i	$-0.572821\pi$
$397$	10.0280	−	5.78964i	0.503288	−	0.290574i	0.730071	+	0.683372i	$0.239487\pi$
$398$			0.596986i			0.0299242i
$399$		0			0
$400$	0.884968	−	4.92106i	0.0442484	−	0.246053i
$401$	−0.738065	−	1.27837i	−0.0368572	−	0.0638386i	0.847008	−	0.531580i	$-0.178401\pi$
$401$	−0.738065	−	1.27837i	−0.0368572	−	0.0638386i	−0.883866	+	0.467741i	$0.845068\pi$
$402$		0			0
$403$	−37.1815	−	21.4667i	−1.85214	−	1.06933i
$404$	1.68398	+	2.91673i	0.0837810	+	0.145113i
$405$		0			0
$406$	11.1277			0.552258
$407$		−	9.41885i		−	0.466875i
$408$		0			0
$409$	0.325761	−	0.564235i	0.0161078	−	0.0278996i	−0.857859	−	0.513885i	$-0.828206\pi$
$409$	0.325761	−	0.564235i	0.0161078	−	0.0278996i	0.873967	+	0.485985i	$0.161539\pi$
$410$	12.8628	+	15.3823i	0.635249	+	0.759678i
$411$		0			0
$412$	−9.51527	−	5.49365i	−0.468784	−	0.270653i
$413$	20.6413	−	11.9172i	1.01569	−	0.586409i
$414$		0			0
$415$	5.49003	−	15.0044i	0.269495	−	0.736536i
$416$	2.32813	+	4.03244i	0.114146	+	0.197706i
$417$		0			0
$418$	8.20206	−	9.53226i	0.401176	−	0.466238i
$419$	25.9557			1.26802			0.634010	−	0.773325i	$-0.281408\pi$
$419$	25.9557			1.26802			0.634010	+	0.773325i	$0.281408\pi$
$420$		0			0
$421$	14.9470	+	25.8890i	0.728473	+	1.26175i	0.957528	+	0.288339i	$0.0931032\pi$
$421$	14.9470	+	25.8890i	0.728473	+	1.26175i	−0.229055	+	0.973414i	$0.573564\pi$
$422$	−19.8569	−	11.4644i	−0.966620	−	0.558078i
$423$		0			0
$424$	−5.41620	+	9.38113i	−0.263034	+	0.455588i
$425$	−35.8646	−	6.44963i	−1.73969	−	0.312853i
$426$		0			0
$427$	32.7179	+	18.8897i	1.58333	+	0.914136i
$428$	2.90789	+	1.67887i	0.140558	+	0.0811514i
$429$		0			0
$430$	11.5852	−	9.68765i	0.558688	−	0.467180i
$431$	13.7123	−	23.7503i	0.660496	−	1.14401i	−0.319989	−	0.947421i	$-0.603679\pi$
$431$	13.7123	−	23.7503i	0.660496	−	1.14401i	0.980485	−	0.196592i	$-0.0629874\pi$
$432$		0			0
$433$	9.75555	+	5.63237i	0.468822	+	0.270674i	0.715746	−	0.698360i	$-0.246087\pi$
$433$	9.75555	+	5.63237i	0.468822	+	0.270674i	−0.246925	+	0.969035i	$0.579420\pi$
$434$	11.6089	+	20.1073i	0.557247	+	0.965181i
$435$		0			0
$436$	4.23293			0.202721
$437$	7.33113	+	1.38662i	0.350696	+	0.0663308i
$438$		0			0
$439$	−7.89796	−	13.6797i	−0.376949	−	0.652895i	0.613668	−	0.789564i	$-0.289693\pi$
$439$	−7.89796	−	13.6797i	−0.376949	−	0.652895i	−0.990617	+	0.136670i	$0.956360\pi$
$440$	2.21666	−	6.05819i	0.105675	−	0.288813i
$441$		0			0
$442$	29.3883	−	16.9674i	1.39786	−	0.807055i
$443$	−6.09413	−	3.51845i	−0.289541	−	0.167167i	0.348194	−	0.937423i	$-0.386795\pi$
$443$	−6.09413	−	3.51845i	−0.289541	−	0.167167i	−0.637735	+	0.770256i	$0.720128\pi$
$444$		0			0
$445$	−8.13464	+	6.80226i	−0.385619	+	0.322458i
$446$	5.62349	−	9.74016i	0.266280	−	0.461210i
$447$		0			0
$448$		−	2.51805i		−	0.118966i
$449$	16.3890			0.773444			0.386722	−	0.922196i	$-0.373607\pi$
$449$	16.3890			0.773444			0.386722	+	0.922196i	$0.373607\pi$
$450$		0			0
$451$	12.9353	+	22.4046i	0.609098	+	1.05499i
$452$	16.2798	+	9.39912i	0.765735	+	0.442097i
$453$		0			0
$454$	4.41407	+	7.64539i	0.207163	+	0.358816i
$455$	−20.1121	+	16.8179i	−0.942870	+	0.788436i
$456$		0			0
$457$		−	11.5975i		−	0.542508i	−0.962508	−	0.271254i	$-0.912562\pi$
$457$		−	11.5975i		−	0.542508i	0.962508	−	0.271254i	$-0.0874383\pi$
$458$	−19.2965	+	11.1408i	−0.901666	+	0.520577i
$459$		0			0
$460$	3.77045	−	0.658228i	0.175798	−	0.0306900i
$461$	−2.39232	−	4.14363i	−0.111422	−	0.192988i	0.804922	−	0.593381i	$-0.202207\pi$
$461$	−2.39232	−	4.14363i	−0.111422	−	0.192988i	−0.916344	+	0.400393i	$0.868874\pi$
$462$		0			0
$463$		−	12.1559i		−	0.564934i	−0.959277	−	0.282467i	$-0.908847\pi$
$463$		−	12.1559i		−	0.564934i	0.959277	−	0.282467i	$-0.0911527\pi$
$464$	4.41917			0.205155
$465$		0			0
$466$	3.09066	−	5.35318i	0.143172	−	0.247981i
$467$			1.60463i			0.0742533i	0.999311	+	0.0371266i	$0.0118205\pi$
$467$			1.60463i			0.0742533i	−0.999311	+	0.0371266i	$0.988180\pi$
$468$		0			0
$469$	−13.4201	+	23.2443i	−0.619682	+	1.07332i
$470$	9.65260	+	3.53184i	0.445241	+	0.162912i
$471$		0			0
$472$	8.19734	−	4.73274i	0.377313	−	0.217842i
$473$	16.8740	−	9.74222i	0.775868	−	0.447948i
$474$		0			0
$475$	20.3598	+	7.77675i	0.934172	+	0.356822i
$476$	−18.3515			−0.841138
$477$		0			0
$478$	−15.7528	+	9.09488i	−0.720516	+	0.415990i
$479$	17.2940	−	29.9541i	0.790184	−	1.36864i	−0.135669	−	0.990754i	$-0.543318\pi$
$479$	17.2940	−	29.9541i	0.790184	−	1.36864i	0.925853	−	0.377884i	$-0.123348\pi$
$480$		0			0
$481$	−7.60088	+	13.1651i	−0.346570	+	0.600277i
$482$		−	2.49535i		−	0.113660i
$483$		0			0
$484$	−1.33848	+	2.31831i	−0.0608399	+	0.105378i
$485$	−5.05901	+	0.883179i	−0.229718	+	0.0401031i
$486$		0			0
$487$			24.3737i			1.10448i	0.833687	+	0.552238i	$0.186226\pi$
$487$			24.3737i			1.10448i	−0.833687	+	0.552238i	$0.813774\pi$
$488$	12.9934	+	7.50173i	0.588182	+	0.339587i
$489$		0			0
$490$	−1.45260	+	0.253588i	−0.0656216	+	0.0114559i
$491$	−5.45453	−	9.44752i	−0.246159	−	0.426360i	0.716298	−	0.697795i	$-0.245835\pi$
$491$	−5.45453	−	9.44752i	−0.246159	−	0.426360i	−0.962457	+	0.271434i	$0.912502\pi$
$492$		0			0
$493$		−	32.2069i		−	1.45052i
$494$	−19.1568	+	6.70468i	−0.861903	+	0.301658i
$495$		0			0
$496$	4.61030	+	7.98528i	0.207009	+	0.358549i
$497$	−23.4660	+	13.5481i	−1.05259	+	0.607715i
$498$		0			0
$499$	−5.54788	−	9.60920i	−0.248357	−	0.430167i	0.714713	−	0.699418i	$-0.246557\pi$
$499$	−5.54788	−	9.60920i	−0.248357	−	0.430167i	−0.963070	+	0.269251i	$0.913224\pi$
$500$	11.1802	+	0.0569884i	0.499994	+	0.00254860i
$501$		0			0
$502$		−	21.2635i		−	0.949034i
$503$	17.0870	+	9.86519i	0.761872	+	0.439867i	0.829967	−	0.557812i	$-0.188359\pi$
$503$	17.0870	+	9.86519i	0.761872	+	0.439867i	−0.0680955	+	0.997679i	$0.521692\pi$
$504$		0			0
$505$	−5.77728	+	4.83101i	−0.257085	+	0.214977i
$506$	4.93819			0.219529
$507$		0			0
$508$	−13.6465	+	7.87880i	−0.605465	+	0.349565i
$509$	16.6873	−	28.9033i	0.739653	−	1.28112i	−0.212999	−	0.977052i	$-0.568323\pi$
$509$	16.6873	−	28.9033i	0.739653	−	1.28112i	0.952652	−	0.304064i	$-0.0983436\pi$
$510$		0			0
$511$	−17.8365	−	30.8938i	−0.789042	−	1.36666i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	5.81714			0.256583
$515$	8.44208	−	23.0724i	0.372002	−	1.01669i
$516$		0			0
$517$	11.4846	+	6.63062i	0.505091	+	0.291614i
$518$	7.11953	−	4.11046i	0.312814	−	0.180603i
$519$		0			0
$520$	−7.98719	+	6.67896i	−0.350261	+	0.292892i
$521$	32.4955			1.42366			0.711828	−	0.702354i	$-0.247868\pi$
$521$	32.4955			1.42366			0.711828	+	0.702354i	$0.247868\pi$
$522$		0			0
$523$	8.12396	+	4.69037i	0.355236	+	0.205096i	0.666989	−	0.745068i	$-0.267583\pi$
$523$	8.12396	+	4.69037i	0.355236	+	0.205096i	−0.311753	+	0.950163i	$0.600916\pi$
$524$	−6.56715			−0.286887
$525$		0			0
$526$	−8.63749	+	14.9606i	−0.376612	+	0.652312i
$527$	58.1966	−	33.5998i	2.53508	−	1.46363i
$528$		0			0
$529$	−10.0350	−	17.3812i	−0.436306	−	0.755705i
$530$	−22.7471	−	8.32306i	−0.988071	−	0.361531i
$531$		0			0
$532$	10.7847	+	2.03983i	0.467576	+	0.0884376i
$533$		−	41.7543i		−	1.80858i
$534$		0			0
$535$	−2.57992	+	7.05098i	−0.111540	+	0.304840i
$536$	−5.32956	+	9.23107i	−0.230202	+	0.398722i
$537$		0			0
$538$	−8.36136	−	4.82743i	−0.360484	−	0.208125i
$539$	−1.90248			−0.0819456
$540$		0			0
$541$	18.8739	−	32.6906i	0.811453	−	1.40548i	−0.100394	−	0.994948i	$-0.532010\pi$
$541$	18.8739	−	32.6906i	0.811453	−	1.40548i	0.911847	−	0.410530i	$-0.134656\pi$
$542$	5.57406	+	3.21818i	0.239426	+	0.138233i
$543$		0			0
$544$	−7.28798			−0.312470
$545$	1.62776	+	9.32410i	0.0697256	+	0.399401i
$546$		0			0
$547$	−5.07734	−	2.93141i	−0.217092	−	0.125338i	0.387511	−	0.921865i	$-0.373335\pi$
$547$	−5.07734	−	2.93141i	−0.217092	−	0.125338i	−0.604603	+	0.796527i	$0.706668\pi$
$548$	12.5023	−	7.21818i	0.534070	−	0.308345i
$549$		0			0
$550$	14.1971	+	2.55311i	0.605366	+	0.108865i
$551$	−3.57990	+	18.9272i	−0.152509	+	0.806324i
$552$		0			0
$553$	−17.9688	+	10.3743i	−0.764111	+	0.441160i
$554$	5.56545	+	9.63965i	0.236453	+	0.409549i
$555$		0			0
$556$	3.09728	+	5.36464i	0.131354	+	0.227511i
$557$	−18.3570	−	10.5984i	−0.777809	−	0.449068i	0.0578442	−	0.998326i	$-0.481577\pi$
$557$	−18.3570	−	10.5984i	−0.777809	−	0.449068i	−0.835653	+	0.549257i	$0.814911\pi$
$558$		0			0
$559$	−31.4473			−1.33008
$560$	5.54663	−	0.968307i	0.234388	−	0.0409184i
$561$		0			0
$562$			5.68717i			0.239899i
$563$		−	26.4882i		−	1.11634i	−0.829725	−	0.558172i	$-0.811503\pi$
$563$		−	26.4882i		−	1.11634i	0.829725	−	0.558172i	$-0.188497\pi$
$564$		0			0
$565$	−14.4436	+	39.4747i	−0.607647	+	1.66071i
$566$	−3.60536	+	6.24466i	−0.151544	+	0.262483i
$567$		0			0
$568$	−9.31912	+	5.38040i	−0.391022	+	0.225757i
$569$	21.8861			0.917514			0.458757	−	0.888562i	$-0.348295\pi$
$569$	21.8861			0.917514			0.458757	+	0.888562i	$0.348295\pi$
$570$		0			0
$571$	−14.0325			−0.587242			−0.293621	−	0.955922i	$-0.594860\pi$
$571$	−14.0325			−0.587242			−0.293621	+	0.955922i	$0.594860\pi$
$572$	−11.6335	+	6.71658i	−0.486419	+	0.280834i
$573$		0			0
$574$	−11.2901	+	19.5550i	−0.471240	+	0.816212i
$575$	2.89983	+	8.05225i	0.120931	+	0.335802i
$576$		0			0
$577$		−	27.9608i		−	1.16402i	−0.813180	−	0.582012i	$-0.802266\pi$
$577$		−	27.9608i		−	1.16402i	0.813180	−	0.582012i	$-0.197734\pi$
$578$			36.1147i			1.50217i
$579$		0			0
$580$	1.69938	+	9.73435i	0.0705629	+	0.404197i
$581$	17.9920			0.746435
$582$		0			0
$583$	−27.0643	−	15.6256i	−1.12089	−	0.647145i
$584$	−7.08348	−	12.2689i	−0.293117	−	0.507693i
$585$		0			0
$586$	4.63359	+	8.02562i	0.191412	+	0.331535i
$587$	−9.03637	+	5.21715i	−0.372971	+	0.215335i	−0.674756	−	0.738041i	$-0.735751\pi$
$587$	−9.03637	+	5.21715i	−0.372971	+	0.215335i	0.301785	+	0.953376i	$0.402418\pi$
$588$		0			0
$589$	−37.9354	+	13.2770i	−1.56310	+	0.547070i
$590$	13.5773	+	16.2368i	0.558969	+	0.668457i
$591$		0			0
$592$	2.82740	−	1.63240i	0.116206	−	0.0670913i
$593$	−4.77660	−	2.75777i	−0.196152	−	0.113248i	0.398708	−	0.917078i	$-0.369459\pi$
$593$	−4.77660	−	2.75777i	−0.196152	−	0.113248i	−0.594859	+	0.803830i	$0.702792\pi$
$594$		0			0
$595$	−7.05700	−	40.4238i	−0.289309	−	1.65721i
$596$	11.9895			0.491109
$597$		0			0
$598$	−6.90231	−	3.98505i	−0.282256	−	0.162961i
$599$	−22.5946	+	39.1349i	−0.923189	+	1.59901i	−0.128741	+	0.991678i	$0.541093\pi$
$599$	−22.5946	+	39.1349i	−0.923189	+	1.59901i	−0.794448	+	0.607332i	$0.792240\pi$
$600$		0			0
$601$	−10.2025			−0.416167			−0.208083	−	0.978111i	$-0.566723\pi$
$601$	−10.2025			−0.416167			−0.208083	+	0.978111i	$0.566723\pi$
$602$	14.7279	+	8.50316i	0.600265	+	0.346563i
$603$		0			0
$604$	−2.75767	+	4.77643i	−0.112208	+	0.194350i
$605$	−5.62138	−	2.05684i	−0.228542	−	0.0836224i
$606$		0			0
$607$		−	6.78955i		−	0.275579i	−0.990462	−	0.137790i	$-0.956000\pi$
$607$		−	6.78955i		−	0.275579i	0.990462	−	0.137790i	$-0.0439998\pi$
$608$	4.28296	+	0.810083i	0.173697	+	0.0328532i
$609$		0			0
$610$	−11.5279	+	31.5060i	−0.466751	+	1.27564i
$611$	−10.7016	−	18.5358i	−0.432942	−	0.749877i
$612$		0			0
$613$	−20.8847	+	12.0578i	−0.843524	+	0.487009i	−0.858460	−	0.512880i	$-0.828579\pi$
$613$	−20.8847	+	12.0578i	−0.843524	+	0.487009i	0.0149366	+	0.999888i	$0.495245\pi$
$614$	−5.13612	+	8.89602i	−0.207277	+	0.359014i
$615$		0			0
$616$	7.26448			0.292694
$617$	33.6188	+	19.4098i	1.35344	+	0.781410i	0.988730	−	0.149711i	$-0.0478343\pi$
$617$	33.6188	+	19.4098i	1.35344	+	0.781410i	0.364712	+	0.931121i	$0.381168\pi$
$618$		0			0
$619$	−43.0532			−1.73046			−0.865228	−	0.501379i	$-0.832826\pi$
$619$	−43.0532			−1.73046			−0.865228	+	0.501379i	$0.832826\pi$
$620$	−15.8167	+	13.2261i	−0.635215	+	0.531172i
$621$		0			0
$622$	−9.90014	+	5.71585i	−0.396959	+	0.229185i
$623$	−10.3413	−	5.97056i	−0.414316	−	0.239205i
$624$		0			0
$625$	4.17378	+	24.6491i	0.166951	+	0.985965i
$626$	−3.95860			−0.158217
$627$		0			0
$628$		−	12.2792i		−	0.489995i
$629$	−11.8969	−	20.6061i	−0.474361	−	0.821617i
$630$		0			0
$631$	20.9642	−	36.3110i	0.834571	−	1.44552i	−0.0598078	−	0.998210i	$-0.519049\pi$
$631$	20.9642	−	36.3110i	0.834571	−	1.44552i	0.894379	−	0.447310i	$-0.147618\pi$
$632$	−7.13601	+	4.11998i	−0.283855	+	0.163884i
$633$		0			0
$634$	−21.9453			−0.871560
$635$	−22.6028	−	27.0301i	−0.896964	−	1.07266i
$636$		0			0
$637$	2.65917	+	1.53527i	0.105360	+	0.0608298i
$638$			12.7492i			0.504745i
$639$		0			0
$640$	2.20275	−	0.384547i	0.0870715	−	0.0152006i
$641$	−0.126170	−	0.218532i	−0.00498340	−	0.00863150i	0.863523	−	0.504310i	$-0.168253\pi$
$641$	−0.126170	−	0.218532i	−0.00498340	−	0.00863150i	−0.868506	+	0.495678i	$0.834920\pi$
$642$		0			0
$643$	35.9135	−	20.7347i	1.41629	−	0.817696i	0.420320	−	0.907376i	$-0.361918\pi$
$643$	35.9135	−	20.7347i	1.41629	−	0.817696i	0.995971	+	0.0896801i	$0.0285845\pi$
$644$	2.15507	+	3.73268i	0.0849215	+	0.147088i
$645$		0			0
$646$	5.90387	−	31.2142i	0.232285	−	1.22810i
$647$			11.3601i			0.446612i	0.974748	+	0.223306i	$0.0716848\pi$
$647$			11.3601i			0.446612i	−0.974748	+	0.223306i	$0.928315\pi$
$648$		0			0
$649$	13.6538	+	23.6491i	0.535958	+	0.928307i
$650$	−17.7835	−	15.0254i	−0.697528	−	0.589346i
$651$		0			0
$652$	−2.99472	−	1.72900i	−0.117282	−	0.0677130i
$653$			14.1285i			0.552889i	0.961030	+	0.276444i	$0.0891562\pi$
$653$			14.1285i			0.552889i	−0.961030	+	0.276444i	$0.910844\pi$
$654$		0			0
$655$	−2.52538	−	14.4658i	−0.0986746	−	0.565226i
$656$	−4.48368	+	7.76596i	−0.175058	+	0.303210i
$657$		0			0
$658$			11.5746i			0.451225i
$659$	14.6536	−	25.3808i	0.570823	−	0.988695i	−0.425658	−	0.904884i	$-0.639957\pi$
$659$	14.6536	−	25.3808i	0.570823	−	0.988695i	0.996482	−	0.0838112i	$-0.0267093\pi$
$660$		0			0
$661$	0.0305882	−	0.0529803i	0.00118974	−	0.00206070i	−0.865430	−	0.501030i	$-0.832955\pi$
$661$	0.0305882	−	0.0529803i	0.00118974	−	0.00206070i	0.866620	+	0.498969i	$0.166288\pi$
$662$	−6.45007	+	3.72395i	−0.250689	+	0.144735i
$663$		0			0
$664$	7.14523			0.277289
$665$	−0.346010	+	24.5404i	−0.0134177	+	0.951637i
$666$		0			0
$667$	−6.55086	+	3.78214i	−0.253650	+	0.146445i
$668$	−5.37144	+	3.10120i	−0.207827	+	0.119989i
$669$		0			0
$670$	−22.3832	−	8.18993i	−0.864740	−	0.316405i
$671$	−21.6422	+	37.4855i	−0.835489	+	1.44711i
$672$		0			0
$673$			29.7678i			1.14747i	0.819042	+	0.573733i	$0.194505\pi$
$673$			29.7678i			1.14747i	−0.819042	+	0.573733i	$0.805495\pi$
$674$	2.33668	−	4.04725i	0.0900055	−	0.155894i
$675$		0			0
$676$	8.68073			0.333874
$677$			14.3460i			0.551360i	0.961249	+	0.275680i	$0.0889031\pi$
$677$			14.3460i			0.551360i	−0.961249	+	0.275680i	$0.911097\pi$
$678$		0			0
$679$	−2.89157	−	5.00834i	−0.110968	−	0.192202i
$680$	−2.80257	−	16.0536i	−0.107474	−	0.615629i
$681$		0			0
$682$	−23.0373	+	13.3006i	−0.882143	+	0.509305i
$683$			39.5539i			1.51349i	0.653712	+	0.756744i	$0.273211\pi$
$683$			39.5539i			1.51349i	−0.653712	+	0.756744i	$0.726789\pi$
$684$		0			0
$685$	20.7076	+	24.7637i	0.791196	+	0.946171i
$686$	−9.64342	−	16.7029i	−0.368187	−	0.637719i
$687$		0			0
$688$	5.84894	+	3.37689i	0.222989	+	0.128743i
$689$	25.2192	+	43.6810i	0.960775	+	1.66411i
$690$		0			0
$691$	−32.4212			−1.23336			−0.616681	−	0.787213i	$-0.711523\pi$
$691$	−32.4212			−1.23336			−0.616681	+	0.787213i	$0.711523\pi$
$692$		−	14.4005i		−	0.547425i
$693$		0			0
$694$	−6.84531	+	11.8564i	−0.259844	+	0.450064i
$695$	−10.6259	+	8.88550i	−0.403065	+	0.337046i
$696$		0			0
$697$	56.5982	+	32.6770i	2.14381	+	1.23773i
$698$	−30.1291	+	17.3951i	−1.14040	+	0.658413i
$699$		0			0
$700$	4.26588	+	11.8455i	0.161235	+	0.447718i
$701$	−10.1662	−	17.6084i	−0.383972	−	0.665059i	0.607654	−	0.794202i	$-0.292111\pi$
$701$	−10.1662	−	17.6084i	−0.383972	−	0.665059i	−0.991626	+	0.129143i	$0.958777\pi$
$702$		0			0
$703$	4.70108	+	13.4320i	0.177305	+	0.506599i
$704$	2.88497			0.108731
$705$		0			0
$706$	−1.52938	−	2.64897i	−0.0575590	−	0.0996952i
$707$	−7.34447	−	4.24033i	−0.276217	−	0.159474i
$708$		0			0
$709$	20.1591	−	34.9165i	0.757089	−	1.31132i	−0.187240	−	0.982314i	$-0.559954\pi$
$709$	20.1591	−	34.9165i	0.757089	−	1.31132i	0.944329	−	0.329003i	$-0.106712\pi$
$710$	−15.4353	−	18.4587i	−0.579278	−	0.692743i
$711$		0			0
$712$	−4.10688	−	2.37111i	−0.153912	−	0.0888610i
$713$	−13.6684	−	7.89144i	−0.511885	−	0.295537i
$714$		0			0
$715$	−19.2686	−	23.0428i	−0.720604	−	0.861752i
$716$	0.970880	−	1.68161i	0.0362835	−	0.0628448i
$717$		0			0
$718$	14.7122	+	8.49408i	0.549054	+	0.316996i
$719$	14.5708	+	25.2374i	0.543401	+	0.941198i	0.998706	+	0.0508623i	$0.0161970\pi$
$719$	14.5708	+	25.2374i	0.543401	+	0.941198i	−0.455305	+	0.890336i	$0.650470\pi$
$720$		0			0
$721$	27.6665			1.03035
$722$	−6.93911	+	17.6875i	−0.258247	+	0.658262i
$723$		0			0
$724$	8.81480	+	15.2677i	0.327600	+	0.567419i
$725$	−20.7889	+	7.48663i	−0.772080	+	0.278047i
$726$		0			0
$727$	15.6863	−	9.05647i	0.581771	−	0.335886i	−0.180066	−	0.983655i	$-0.557631\pi$
$727$	15.6863	−	9.05647i	0.581771	−	0.335886i	0.761837	+	0.647769i	$0.224298\pi$
$728$	−10.1539	−	5.86233i	−0.376327	−	0.217273i
$729$		0			0
$730$	24.3015	−	20.3212i	0.899440	−	0.752120i
$731$	24.6107	−	42.6270i	0.910260	−	1.57662i
$732$		0			0
$733$			8.31171i			0.307000i	0.988149	+	0.153500i	$0.0490545\pi$
$733$			8.31171i			0.307000i	−0.988149	+	0.153500i	$0.950946\pi$
$734$	5.39039			0.198963
$735$		0			0
$736$	0.855848	+	1.48237i	0.0315470	+	0.0546410i
$737$	−26.6314	−	15.3756i	−0.980979	−	0.566368i
$738$		0			0
$739$	7.63311	+	13.2209i	0.280788	+	0.486340i	0.971579	−	0.236715i	$-0.0760708\pi$
$739$	7.63311	+	13.2209i	0.280788	+	0.486340i	−0.690791	+	0.723055i	$0.742737\pi$
$740$	4.68305	+	5.60034i	0.172152	+	0.205872i
$741$		0			0
$742$		−	27.2765i		−	1.00135i
$743$	−29.0049	+	16.7460i	−1.06409	+	0.614351i	−0.926560	−	0.376147i	$-0.877249\pi$
$743$	−29.0049	+	16.7460i	−1.06409	+	0.614351i	−0.137528	+	0.990498i	$0.543916\pi$
$744$		0			0
$745$	4.61053	+	26.4099i	0.168917	+	0.967585i
$746$	−1.92793	−	3.33927i	−0.0705865	−	0.122259i
$747$		0			0
$748$		−	21.0256i		−	0.768772i
$749$	−8.45496			−0.308937
$750$		0			0
$751$	−10.0737	+	17.4481i	−0.367594	+	0.636691i	−0.989189	−	0.146648i	$-0.953152\pi$
$751$	−10.0737	+	17.4481i	−0.367594	+	0.636691i	0.621595	+	0.783339i	$0.286485\pi$
$752$			4.59667i			0.167623i
$753$		0			0
$754$	10.2884	−	17.8200i	0.374682	−	0.648968i
$755$	−11.5817	−	4.23771i	−0.421503	−	0.154226i
$756$		0			0
$757$	26.9406	−	15.5542i	0.979174	−	0.565327i	0.0771537	−	0.997019i	$-0.475417\pi$
$757$	26.9406	−	15.5542i	0.979174	−	0.565327i	0.902021	+	0.431693i	$0.142083\pi$
$758$	11.8270	−	6.82832i	0.429576	−	0.248016i
$759$		0			0
$760$	−0.137412	+	9.74583i	−0.00498446	+	0.353518i
$761$	−2.73496			−0.0991421			−0.0495710	−	0.998771i	$-0.515785\pi$
$761$	−2.73496			−0.0991421			−0.0495710	+	0.998771i	$0.515785\pi$
$762$		0			0
$763$	−9.23072	+	5.32936i	−0.334174	+	0.192936i
$764$	2.30688	−	3.99564i	0.0834601	−	0.144557i
$765$		0			0
$766$	3.64176	−	6.30771i	0.131582	−	0.227907i
$767$		−	44.0737i		−	1.59141i
$768$		0			0
$769$	11.3522	−	19.6626i	0.409371	−	0.709052i	−0.585448	−	0.810710i	$-0.699081\pi$
$769$	11.3522	−	19.6626i	0.409371	−	0.709052i	0.994819	+	0.101658i	$0.0324147\pi$
$770$	2.79354	+	16.0019i	0.100672	+	0.576667i
$771$		0			0
$772$			25.0803i			0.902659i
$773$	11.9910	+	6.92302i	0.431287	+	0.249004i	0.699895	−	0.714246i	$-0.253230\pi$
$773$	11.9910	+	6.92302i	0.431287	+	0.249004i	−0.268608	+	0.963250i	$0.586563\pi$
$774$		0			0
$775$	−35.2161	−	29.7543i	−1.26500	−	1.06881i
$776$	−1.14834	−	1.98898i	−0.0412229	−	0.0714002i
$777$		0			0
$778$			19.6265i			0.703646i
$779$	−29.6292	−	25.4945i	−1.06158	−	0.913435i
$780$		0			0
$781$	−15.5223	−	26.8854i	−0.555431	−	0.962034i
$782$	10.8035	−	6.23741i	0.386333	−	0.223049i
$783$		0			0
$784$	−0.329723	−	0.571097i	−0.0117758	−	0.0203963i
$785$	27.0481	−	4.72194i	0.965389	−	0.168533i
$786$		0			0
$787$			0.272719i			0.00972137i	0.999988	+	0.00486069i	$0.00154721\pi$
$787$			0.272719i			0.00972137i	−0.999988	+	0.00486069i	$0.998453\pi$
$788$	3.13881	+	1.81219i	0.111815	+	0.0645567i
$789$		0			0
$790$	−11.8194	−	14.1345i	−0.420516	−	0.502884i
$791$	−47.3348			−1.68303
$792$		0			0
$793$	60.5005	−	34.9300i	2.14843	−	1.24040i
$794$	−5.78964	+	10.0280i	−0.205467	+	0.355879i
$795$		0			0
$796$	−0.298493	−	0.517005i	−0.0105798	−	0.0183248i
$797$			2.18853i			0.0775216i	0.999249	+	0.0387608i	$0.0123410\pi$
$797$			2.18853i			0.0775216i	−0.999249	+	0.0387608i	$0.987659\pi$
$798$		0			0
$799$	33.5004			1.18516
$800$	1.69412	+	4.70425i	0.0598964	+	0.166320i
$801$		0			0
$802$	1.27837	+	0.738065i	0.0451407	+	0.0260620i
$803$	35.3955	−	20.4356i	1.24908	−	0.721157i
$804$		0			0
$805$	−7.39346	+	6.18247i	−0.260585	+	0.217903i
$806$	42.9335			1.51227
$807$		0			0
$808$	−2.91673	−	1.68398i	−0.102610	−	0.0592421i
$809$	−8.89531			−0.312743			−0.156371	−	0.987698i	$-0.549980\pi$
$809$	−8.89531			−0.312743			−0.156371	+	0.987698i	$0.549980\pi$
$810$		0			0
$811$	6.06868	−	10.5113i	0.213100	−	0.369101i	−0.739583	−	0.673065i	$-0.764977\pi$
$811$	6.06868	−	10.5113i	0.213100	−	0.369101i	0.952683	+	0.303965i	$0.0983106\pi$
$812$	−9.63686	+	5.56384i	−0.338187	+	0.195253i
$813$		0			0
$814$	4.70943	+	8.15697i	0.165065	+	0.285902i
$815$	2.65696	−	7.26152i	0.0930691	−	0.254360i
$816$		0			0
$817$	−19.2012	+	22.3152i	−0.671765	+	0.780711i
$818$			0.651522i			0.0227799i
$819$		0			0
$820$	−18.8307	−	6.89006i	−0.657596	−	0.240611i
$821$	−21.4432	+	37.1408i	−0.748374	+	1.29622i	0.200228	+	0.979749i	$0.435832\pi$
$821$	−21.4432	+	37.1408i	−0.748374	+	1.29622i	−0.948602	+	0.316472i	$0.897502\pi$
$822$		0			0
$823$	27.1468	+	15.6732i	0.946278	+	0.546334i	0.891923	−	0.452188i	$-0.149356\pi$
$823$	27.1468	+	15.6732i	0.946278	+	0.546334i	0.0543553	+	0.998522i	$0.482690\pi$
$824$	10.9873			0.382760
$825$		0			0
$826$	−11.9172	+	20.6413i	−0.414654	+	0.718202i
$827$	28.4166	+	16.4063i	0.988143	+	0.570505i	0.904719	−	0.426009i	$-0.140081\pi$
$827$	28.4166	+	16.4063i	0.988143	+	0.570505i	0.0834244	+	0.996514i	$0.473414\pi$
$828$		0			0
$829$	−51.8181			−1.79972			−0.899858	−	0.436182i	$-0.856330\pi$
$829$	−51.8181			−1.79972			−0.899858	+	0.436182i	$0.856330\pi$
$830$	2.74768	+	15.7392i	0.0953733	+	0.546315i
$831$		0			0
$832$	−4.03244	−	2.32813i	−0.139800	−	0.0807133i
$833$	−4.16214	+	2.40301i	−0.144210	+	0.0832595i
$834$		0			0
$835$	−8.89675	−	10.6394i	−0.307885	−	0.368192i
$836$	−2.33706	+	12.3562i	−0.0808290	+	0.427348i
$837$		0			0
$838$	−22.4783	+	12.9779i	−0.776500	+	0.448313i
$839$	−0.433475	−	0.750801i	−0.0149652	−	0.0259205i	0.858446	−	0.512904i	$-0.171430\pi$
$839$	−0.433475	−	0.750801i	−0.0149652	−	0.0259205i	−0.873411	+	0.486984i	$0.838097\pi$
$840$		0			0
$841$	4.73545	+	8.20204i	0.163291	+	0.282829i
$842$	−25.8890	−	14.9470i	−0.892194	−	0.515109i
$843$		0			0
$844$	22.9288			0.789242
$845$	3.33815	+	19.1215i	0.114836	+	0.657800i
$846$		0			0
$847$		−	6.74070i		−	0.231613i
$848$		−	10.8324i		−	0.371986i
$849$		0			0
$850$	34.2845	−	12.3468i	1.17595	−	0.423490i
$851$	−2.79418	+	4.83966i	−0.0957831	+	0.165901i
$852$		0			0
$853$	1.05924	−	0.611551i	0.0362676	−	0.0209391i	−0.481757	−	0.876305i	$-0.660001\pi$
$853$	1.05924	−	0.611551i	0.0362676	−	0.0209391i	0.518024	+	0.855366i	$0.326668\pi$
$854$	−37.7794			−1.29278
$855$		0			0
$856$	−3.35775			−0.114765
$857$	14.7442	−	8.51258i	0.503653	−	0.290784i	−0.226568	−	0.973995i	$-0.572751\pi$
$857$	14.7442	−	8.51258i	0.503653	−	0.290784i	0.730221	+	0.683211i	$0.239417\pi$
$858$		0			0
$859$	−4.21282	+	7.29683i	−0.143740	+	0.248964i	−0.928902	−	0.370326i	$-0.879246\pi$
$859$	−4.21282	+	7.29683i	−0.143740	+	0.248964i	0.785162	+	0.619290i	$0.212579\pi$
$860$	−5.18926	+	14.1824i	−0.176952	+	0.483614i
$861$		0			0
$862$			27.4245i			0.934083i
$863$			6.06986i			0.206620i	0.994649	+	0.103310i	$0.0329434\pi$
$863$			6.06986i			0.206620i	−0.994649	+	0.103310i	$0.967057\pi$
$864$		0			0
$865$	31.7208	−	5.53768i	1.07854	−	0.188287i
$866$	−11.2647			−0.382791
$867$		0			0
$868$	−20.1073	−	11.6089i	−0.682486	−	0.394033i
$869$	−11.8860	−	20.5872i	−0.403205	−	0.698371i
$870$		0			0
$871$	24.8158	+	42.9822i	0.840852	+	1.45640i
$872$	−3.66583	+	2.11647i	−0.124141	+	0.0716726i
$873$		0			0
$874$	−7.04226	+	2.46472i	−0.238208	+	0.0833705i
$875$	−24.4523	+	13.9518i	−0.826639	+	0.471659i
$876$		0			0
$877$	−29.4618	+	17.0098i	−0.994855	+	0.574380i	−0.906722	−	0.421729i	$-0.861423\pi$
$877$	−29.4618	+	17.0098i	−0.994855	+	0.574380i	−0.0881333	+	0.996109i	$0.528090\pi$
$878$	13.6797	+	7.89796i	0.461666	+	0.266543i
$879$		0			0
$880$	1.10941	+	6.35487i	0.0373981	+	0.214223i
$881$	−37.8182			−1.27413			−0.637064	−	0.770811i	$-0.719851\pi$
$881$	−37.8182			−1.27413			−0.637064	+	0.770811i	$0.719851\pi$
$882$		0			0
$883$	−39.0605	−	22.5516i	−1.31449	−	0.758921i	−0.331653	−	0.943401i	$-0.607606\pi$
$883$	−39.0605	−	22.5516i	−1.31449	−	0.758921i	−0.982836	+	0.184480i	$0.940940\pi$
$884$	−16.9674	+	29.3883i	−0.570674	+	0.988436i
$885$		0			0
$886$	7.03690			0.236409
$887$	−37.0666	−	21.4004i	−1.24457	−	0.718555i	−0.274552	−	0.961572i	$-0.588529\pi$
$887$	−37.0666	−	21.4004i	−1.24457	−	0.718555i	−0.970022	+	0.243017i	$0.921863\pi$
$888$		0			0
$889$	19.8392	−	34.3625i	0.665385	−	1.15248i
$890$	3.64368	−	9.95825i	0.122136	−	0.333801i
$891$		0			0
$892$			11.2470i			0.376576i
$893$	−19.6873	−	3.72368i	−0.658812	−	0.124608i
$894$		0			0
$895$	4.07753	+	1.49195i	0.136297	+	0.0498704i
$896$	1.25902	+	2.18069i	0.0420610	+	0.0728518i
$897$		0			0
$898$	−14.1933	+	8.19449i	−0.473635	+	0.273454i
$899$	20.3737	−	35.2883i	0.679502	−	1.17693i
$900$		0			0
$901$	−78.9463			−2.63008
$902$	−22.4046	−	12.9353i	−0.745990	−	0.430698i
$903$		0			0
$904$	−18.7982			−0.625220
$905$	−30.2412	+	25.2880i	−1.00525	+	0.840601i
$906$		0			0
$907$	26.2663	−	15.1648i	0.872157	−	0.503540i	0.00409285	−	0.999992i	$-0.498697\pi$
$907$	26.2663	−	15.1648i	0.872157	−	0.503540i	0.868065	+	0.496451i	$0.165364\pi$
$908$	−7.64539	−	4.41407i	−0.253721	−	0.146486i
$909$		0			0
$910$	9.00864	−	24.6208i	0.298634	−	0.816171i
$911$	−35.4194			−1.17350			−0.586748	−	0.809770i	$-0.699592\pi$
$911$	−35.4194			−1.17350			−0.586748	+	0.809770i	$0.699592\pi$
$912$		0			0
$913$			20.6138i			0.682216i
$914$	5.79875	+	10.0437i	0.191805	+	0.332217i
$915$		0			0
$916$	11.1408	−	19.2965i	0.368104	−	0.637574i
$917$	14.3209	−	8.26819i	0.472918	−	0.273040i
$918$		0			0
$919$	−17.0531			−0.562531			−0.281265	−	0.959630i	$-0.590754\pi$
$919$	−17.0531			−0.562531			−0.281265	+	0.959630i	$0.590754\pi$
$920$	−2.93619	+	2.45527i	−0.0968033	+	0.0809477i
$921$		0			0
$922$	4.14363	+	2.39232i	0.136463	+	0.0787870i
$923$			50.1050i			1.64923i
$924$		0			0
$925$	−10.5353	+	12.4692i	−0.346399	+	0.409985i
$926$	6.07796	+	10.5273i	0.199734	+	0.345950i
$927$		0			0
$928$	−3.82712	+	2.20959i	−0.125631	+	0.0725332i
$929$	16.0271	+	27.7598i	0.525834	+	0.910771i	0.999547	+	0.0300916i	$0.00957989\pi$
$929$	16.0271	+	27.7598i	0.525834	+	0.910771i	−0.473714	+	0.880679i	$0.657087\pi$
$930$		0			0
$931$	2.71309	−	0.949555i	0.0889179	−	0.0311204i
$932$			6.18132i			0.202476i
$933$		0			0
$934$	−0.802313	−	1.38965i	−0.0262525	−	0.0454706i
$935$	46.3142	−	8.08533i	1.51464	−	0.264419i
$936$		0			0
$937$	−22.9312	−	13.2393i	−0.749128	−	0.432509i	0.0762506	−	0.997089i	$-0.475705\pi$
$937$	−22.9312	−	13.2393i	−0.749128	−	0.432509i	−0.825379	+	0.564579i	$0.809038\pi$
$938$		−	26.8402i		−	0.876362i
$939$		0			0
$940$	−10.1253	+	1.76763i	−0.330252	+	0.0576539i
$941$	7.18502	−	12.4448i	0.234225	−	0.405689i	−0.724822	−	0.688936i	$-0.758078\pi$
$941$	7.18502	−	12.4448i	0.234225	−	0.405689i	0.959047	+	0.283247i	$0.0914115\pi$
$942$		0			0
$943$		−	15.3494i		−	0.499845i
$944$	−4.73274	+	8.19734i	−0.154037	+	0.266801i
$945$		0			0
$946$	−9.74222	+	16.8740i	−0.316747	+	0.548622i
$947$	−39.4692	+	22.7875i	−1.28258	+	0.740495i	−0.977318	−	0.211775i	$-0.932076\pi$
$947$	−39.4692	+	22.7875i	−1.28258	+	0.740495i	−0.305257	+	0.952270i	$0.598742\pi$
$948$		0			0
$949$	−65.9650			−2.14132
$950$	−21.5205	+	3.44504i	−0.698217	+	0.111772i
$951$		0			0
$952$	15.8928	−	9.17574i	0.515090	−	0.297387i
$953$	−46.7123	+	26.9694i	−1.51316	+	0.873623i	−0.513278	+	0.858222i	$0.671569\pi$
$953$	−46.7123	+	26.9694i	−1.51316	+	0.873623i	−0.999881	+	0.0154010i	$0.995098\pi$
$954$		0			0
$955$	9.68851	+	3.54498i	0.313513	+	0.114713i
$956$	9.09488	−	15.7528i	0.294149	−	0.509482i
$957$		0			0
$958$			34.5880i			1.11749i
$959$	−18.1757	+	31.4813i	−0.586924	+	1.01658i
$960$		0			0
$961$	54.0195			1.74257
$962$		−	15.2018i		−	0.490124i
$963$		0			0
$964$	1.24768	+	2.16104i	0.0401849	+	0.0696023i
$965$	−55.2457	+	9.64454i	−1.77842	+	0.310469i
$966$		0			0
$967$	−19.5534	+	11.2892i	−0.628795	+	0.363035i	−0.780285	−	0.625424i	$-0.784926\pi$
$967$	−19.5534	+	11.2892i	−0.628795	+	0.363035i	0.151490	+	0.988459i	$0.451593\pi$
$968$		−	2.67696i		−	0.0860407i
$969$		0			0
$970$	3.93964	−	3.29436i	0.126494	−	0.105776i
$971$	29.4664	+	51.0372i	0.945621	+	1.63786i	0.754504	+	0.656296i	$0.227878\pi$
$971$	29.4664	+	51.0372i	0.945621	+	1.63786i	0.191117	+	0.981567i	$0.438789\pi$
$972$		0			0
$973$	−13.5084	−	7.79909i	−0.433060	−	0.250027i
$974$	−12.1868	−	21.1082i	−0.390491	−	0.676350i
$975$		0			0
$976$	−15.0035			−0.480249
$977$		−	1.86548i		−	0.0596821i	−0.999555	−	0.0298411i	$-0.990500\pi$
$977$		−	1.86548i		−	0.0596821i	0.999555	−	0.0298411i	$-0.00950012\pi$
$978$		0			0
$979$	6.84057	−	11.8482i	0.218626	−	0.378671i
$980$	1.13119	−	0.945912i	0.0361346	−	0.0302160i
$981$		0			0
$982$	9.44752	+	5.45453i	0.301482	+	0.174061i
$983$	38.1239	−	22.0109i	1.21597	−	0.702038i	0.251913	−	0.967750i	$-0.418940\pi$
$983$	38.1239	−	22.0109i	1.21597	−	0.702038i	0.964052	+	0.265712i	$0.0856071\pi$
$984$		0			0
$985$	−2.78479	+	7.61090i	−0.0887309	+	0.242503i
$986$	16.1034	+	27.8920i	0.512838	+	0.888261i
$987$		0			0
$988$	13.2379	−	15.3848i	0.421154	−	0.489456i
$989$	−11.5604			−0.367600
$990$		0			0
$991$	16.2964	+	28.2263i	0.517674	+	0.896637i	0.999789	+	0.0205293i	$0.00653513\pi$
$991$	16.2964	+	28.2263i	0.517674	+	0.896637i	−0.482116	+	0.876108i	$0.660132\pi$
$992$	−7.98528	−	4.61030i	−0.253533	−	0.146377i
$993$		0			0
$994$	13.5481	−	23.4660i	0.429719	−	0.744296i
$995$	1.02405	−	0.856319i	0.0324646	−	0.0271471i
$996$		0			0
$997$	16.4589	+	9.50256i	0.521259	+	0.300949i	0.737450	−	0.675402i	$-0.236030\pi$
$997$	16.4589	+	9.50256i	0.521259	+	0.300949i	−0.216190	+	0.976351i	$0.569363\pi$
$998$	9.60920	+	5.54788i	0.304174	+	0.175615i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.c.919.5		20
3.2	odd	2		570.2.q.c.349.6	yes	20
5.4	even	2	inner	1710.2.t.c.919.8		20
15.14	odd	2		570.2.q.c.349.3	yes	20
19.11	even	3	inner	1710.2.t.c.1189.8		20
57.11	odd	6		570.2.q.c.49.3	✓	20
95.49	even	6	inner	1710.2.t.c.1189.5		20
285.239	odd	6		570.2.q.c.49.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.c.49.3	✓	20	57.11	odd	6
570.2.q.c.49.6	yes	20	285.239	odd	6
570.2.q.c.349.3	yes	20	15.14	odd	2
570.2.q.c.349.6	yes	20	3.2	odd	2
1710.2.t.c.919.5		20	1.1	even	1	trivial
1710.2.t.c.919.8		20	5.4	even	2	inner
1710.2.t.c.1189.5		20	95.49	even	6	inner
1710.2.t.c.1189.8		20	19.11	even	3	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.09991 + 0.768349i) q^{5} +2.51805i q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.09991 + 0.768349i) q^{5} +2.51805i q^{7} +1.00000i q^{8} +(-2.20275 + 0.384547i) q^{10} -2.88497 q^{11} +(4.03244 + 2.32813i) q^{13} +(-1.25902 - 2.18069i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-6.31158 + 3.64399i) q^{17} +(4.11420 - 1.43993i) q^{19} +(1.71537 - 1.43440i) q^{20} +(2.49846 - 1.44248i) q^{22} +(1.48237 + 0.855848i) q^{23} +(3.81928 + 3.22694i) q^{25} -4.65626 q^{26} +(2.18069 + 1.25902i) q^{28} +(-2.20959 + 3.82712i) q^{29} -9.22060 q^{31} +(0.866025 + 0.500000i) q^{32} +(3.64399 - 6.31158i) q^{34} +(-1.93474 + 5.28768i) q^{35} +3.26480i q^{37} +(-2.84303 + 3.30411i) q^{38} +(-0.768349 + 2.09991i) q^{40} +(-4.48368 - 7.76596i) q^{41} +(-5.84894 + 3.37689i) q^{43} +(-1.44248 + 2.49846i) q^{44} -1.71170 q^{46} +(-3.98083 - 2.29833i) q^{47} +0.659446 q^{49} +(-4.92106 - 0.884968i) q^{50} +(4.03244 - 2.32813i) q^{52} +(9.38113 + 5.41620i) q^{53} +(-6.05819 - 2.21666i) q^{55} -2.51805 q^{56} -4.41917i q^{58} +(-4.73274 - 8.19734i) q^{59} +(7.50173 - 12.9934i) q^{61} +(7.98528 - 4.61030i) q^{62} -1.00000 q^{64} +(6.67896 + 7.98719i) q^{65} +(9.23107 + 5.32956i) q^{67} +7.28798i q^{68} +(-0.968307 - 5.54663i) q^{70} +(5.38040 + 9.31912i) q^{71} +(-12.2689 + 7.08348i) q^{73} +(-1.63240 - 2.82740i) q^{74} +(0.810083 - 4.28296i) q^{76} -7.26448i q^{77} +(4.11998 + 7.13601i) q^{79} +(-0.384547 - 2.20275i) q^{80} +(7.76596 + 4.48368i) q^{82} -7.14523i q^{83} +(-16.0536 + 2.80257i) q^{85} +(3.37689 - 5.84894i) q^{86} -2.88497i q^{88} +(-2.37111 + 4.10688i) q^{89} +(-5.86233 + 10.1539i) q^{91} +(1.48237 - 0.855848i) q^{92} +4.59667 q^{94} +(9.74583 + 0.137412i) q^{95} +(-1.98898 + 1.14834i) q^{97} +(-0.571097 + 0.329723i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 20 * q + 10 * q^4	\( 20 q + 10 q^{4} - 2 q^{10} - 12 q^{11} - 10 q^{14} - 10 q^{16} + 6 q^{19} + 14 q^{25} - 8 q^{29} + 40 q^{31} + 12 q^{34} - 2 q^{35} + 2 q^{40} + 14 q^{41} - 6 q^{44} + 44 q^{46} - 8 q^{49} + 8 q^{50} - 20 q^{56} - 8 q^{59} + 16 q^{61} - 20 q^{64} - 40 q^{65} + 8 q^{70} + 4 q^{71} - 26 q^{74} + 8 q^{79} - 16 q^{85} + 20 q^{86} + 2 q^{89} - 44 q^{91} - 32 q^{94} + 80 q^{95}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^10 - 12 * q^11 - 10 * q^14 - 10 * q^16 + 6 * q^19 + 14 * q^25 - 8 * q^29 + 40 * q^31 + 12 * q^34 - 2 * q^35 + 2 * q^40 + 14 * q^41 - 6 * q^44 + 44 * q^46 - 8 * q^49 + 8 * q^50 - 20 * q^56 - 8 * q^59 + 16 * q^61 - 20 * q^64 - 40 * q^65 + 8 * q^70 + 4 * q^71 - 26 * q^74 + 8 * q^79 - 16 * q^85 + 20 * q^86 + 2 * q^89 - 44 * q^91 - 32 * q^94 + 80 * q^95

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