LMFDB - Embedded newform 1710.2.t.c.919.8

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			919.8
Root			$2.34324 - 0.627868i$ of defining polynomial
Character	$\chi$	$=$	1710.919
Dual form			1710.2.t.c.1189.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.384547 + 2.20275i) q^{5} -2.51805i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.384547 + 2.20275i) q^{5} -2.51805i q^{7} -1.00000i q^{8} +(0.768349 + 2.09991i) q^{10} -2.88497 q^{11} +(-4.03244 - 2.32813i) q^{13} +(-1.25902 - 2.18069i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.31158 - 3.64399i) q^{17} +(4.11420 - 1.43993i) q^{19} +(1.71537 + 1.43440i) q^{20} +(-2.49846 + 1.44248i) q^{22} +(-1.48237 - 0.855848i) q^{23} +(-4.70425 - 1.69412i) q^{25} -4.65626 q^{26} +(-2.18069 - 1.25902i) q^{28} +(-2.20959 + 3.82712i) q^{29} -9.22060 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.64399 - 6.31158i) q^{34} +(5.54663 + 0.968307i) q^{35} -3.26480i q^{37} +(2.84303 - 3.30411i) q^{38} +(2.20275 + 0.384547i) q^{40} +(-4.48368 - 7.76596i) q^{41} +(5.84894 - 3.37689i) q^{43} +(-1.44248 + 2.49846i) q^{44} -1.71170 q^{46} +(3.98083 + 2.29833i) q^{47} +0.659446 q^{49} +(-4.92106 + 0.884968i) q^{50} +(-4.03244 + 2.32813i) q^{52} +(-9.38113 - 5.41620i) q^{53} +(1.10941 - 6.35487i) q^{55} -2.51805 q^{56} +4.41917i q^{58} +(-4.73274 - 8.19734i) q^{59} +(7.50173 - 12.9934i) q^{61} +(-7.98528 + 4.61030i) q^{62} -1.00000 q^{64} +(6.67896 - 7.98719i) q^{65} +(-9.23107 - 5.32956i) q^{67} -7.28798i q^{68} +(5.28768 - 1.93474i) q^{70} +(5.38040 + 9.31912i) q^{71} +(12.2689 - 7.08348i) q^{73} +(-1.63240 - 2.82740i) q^{74} +(0.810083 - 4.28296i) q^{76} +7.26448i q^{77} +(4.11998 + 7.13601i) q^{79} +(2.09991 - 0.768349i) q^{80} +(-7.76596 - 4.48368i) q^{82} +7.14523i q^{83} +(5.59972 + 15.3041i) q^{85} +(3.37689 - 5.84894i) q^{86} +2.88497i q^{88} +(-2.37111 + 4.10688i) q^{89} +(-5.86233 + 10.1539i) q^{91} +(-1.48237 + 0.855848i) q^{92} +4.59667 q^{94} +(1.58971 + 9.61628i) q^{95} +(1.98898 - 1.14834i) q^{97} +(0.571097 - 0.329723i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.384547	+	2.20275i	−0.171975	+	0.985101i
$5$	−0.384547	+	2.20275i	−0.171975	+	0.985101i
$6$		0			0
$7$		−	2.51805i		−	0.951732i	−0.879518	−	0.475866i	$-0.842135\pi$
$7$		−	2.51805i		−	0.951732i	0.879518	−	0.475866i	$-0.157865\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.768349	+	2.09991i	0.242973	+	0.664051i
$11$	−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	−0.177406	−	0.984138i	$-0.556770\pi$
$13$	−4.03244	−	2.32813i	−1.11840	−	0.645707i	−0.940991	+	0.338431i	$0.890104\pi$
$14$	−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	$-0.321645\pi$
$17$	6.31158	−	3.64399i	1.53078	−	0.883798i	0.999326	−	0.0367122i	$-0.0116885\pi$
$18$		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	0.337426	−	0.941352i	$-0.390444\pi$
$23$	−1.48237	−	0.855848i	−0.309096	−	0.178457i	−0.646522	+	0.762895i	$0.723777\pi$
$24$		0			0
$25$	−4.70425	−	1.69412i	−0.940849	−	0.338825i
$26$	−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
$35$	5.54663	+	0.968307i	0.937552	+	0.163674i
$36$		0			0
$37$		−	3.26480i		−	0.536730i	−0.963317	−	0.268365i	$-0.913517\pi$
$37$		−	3.26480i		−	0.536730i	0.963317	−	0.268365i	$-0.0864834\pi$
$38$	2.84303	−	3.30411i	0.461201	−	0.535998i
$39$		0			0
$40$	2.20275	+	0.384547i	0.348286	+	0.0608022i
$41$	−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	0.0173738	−	0.999849i	$-0.494469\pi$
$43$	5.84894	−	3.37689i	0.891955	−	0.514971i	0.874582	+	0.484878i	$0.161136\pi$
$44$	−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	0.761397	−	0.648286i	$-0.224514\pi$
$47$	3.98083	+	2.29833i	0.580664	+	0.335246i	−0.180733	+	0.983532i	$0.557847\pi$
$48$		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	−0.310193	−	0.950673i	$-0.600394\pi$
$53$	−9.38113	−	5.41620i	−1.28860	−	0.743972i	−0.978404	+	0.206701i	$0.933727\pi$
$54$		0			0
$55$	1.10941	−	6.35487i	0.149592	−	0.856891i
$56$	−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	−0.184386	−	0.982854i	$-0.559030\pi$
$67$	−9.23107	−	5.32956i	−1.12776	−	0.651110i	−0.943369	+	0.331744i	$0.892363\pi$
$68$		−	7.28798i		−	0.883798i
$69$		0			0
$70$	5.28768	−	1.93474i	0.631999	−	0.231246i
$71$	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	0.438405	−	0.898777i	$-0.355543\pi$
$73$	12.2689	−	7.08348i	1.43597	−	0.829059i	0.997567	+	0.0697187i	$0.0222102\pi$
$74$	−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	$0.679915\pi$
$80$	2.09991	−	0.768349i	0.234778	−	0.0859041i
$81$		0			0
$82$	−7.76596	−	4.48368i	−0.857607	−	0.495140i
$83$			7.14523i			0.784291i	0.919903	+	0.392146i	$0.128267\pi$
$83$			7.14523i			0.784291i	−0.919903	+	0.392146i	$0.871733\pi$
$84$		0			0
$85$	5.59972	+	15.3041i	0.607375	+	1.65997i
$86$	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
$95$	1.58971	+	9.61628i	0.163100	+	0.986609i
$96$		0			0
$97$	1.98898	−	1.14834i	0.201950	−	0.116596i	−0.395615	−	0.918417i	$-0.629468\pi$
$97$	1.98898	−	1.14834i	0.201950	−	0.116596i	0.597565	+	0.801821i	$0.296135\pi$
$98$	0.571097	−	0.329723i	0.0576895	−	0.0333070i
$99$		0			0
$100$	−3.81928	+	3.22694i	−0.381928	+	0.322694i
$101$	−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	$0.182070\pi$
$103$			10.9873i			1.08261i	−0.840826	+	0.541305i	$0.817930\pi$
$104$	−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	$-0.948108\pi$
$107$		−	3.35775i		−	0.324605i	0.986741	−	0.162303i	$-0.0518921\pi$
$108$		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	$0.768355\pi$
$110$	−2.21666	−	6.05819i	−0.211351	−	0.577625i
$111$		0			0
$112$	−2.18069	+	1.25902i	−0.206056	+	0.118966i
$113$		−	18.7982i		−	1.76839i	−0.467118	−	0.884195i	$-0.654708\pi$
$113$		−	18.7982i		−	1.76839i	0.467118	−	0.884195i	$-0.345292\pi$
$114$		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	0.962962	−	0.269637i	$-0.0869038\pi$
$127$	13.6465	+	7.87880i	1.21093	+	0.699131i	0.247968	+	0.968768i	$0.420237\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.79055	−	10.2566i	0.157042	−	0.899562i
$131$	−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	−0.140467	−	0.990085i	$-0.544861\pi$
$137$	−12.5023	−	7.21818i	−1.06814	−	0.616691i	−0.927673	+	0.373394i	$0.878194\pi$
$138$		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
$155$	3.54576	−	20.3107i	0.284802	−	1.63140i
$156$		0			0
$157$	−10.6341	+	6.13962i	−0.848696	+	0.489995i	−0.860211	−	0.509939i	$-0.829668\pi$
$157$	−10.6341	+	6.13962i	−0.848696	+	0.489995i	0.0115149	+	0.999934i	$0.496335\pi$
$158$	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	$0.0432403\pi$
$163$			3.45801i			0.270852i	−0.990787	+	0.135426i	$0.956760\pi$
$164$	−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	0.693216	−	0.720730i	$-0.256193\pi$
$167$	5.37144	+	3.10120i	0.415654	+	0.239978i	−0.277562	+	0.960708i	$0.589526\pi$
$168$		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	−0.892512	−	0.451025i	$-0.851059\pi$
$173$	−12.4712	+	7.20026i	−0.948169	+	0.547425i	−0.0556571	+	0.998450i	$0.517725\pi$
$174$		0			0
$175$	−4.26588	+	11.8455i	−0.322471	+	0.895436i
$176$	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
$185$	7.19156	+	1.25547i	0.528734	+	0.0923040i
$186$		0			0
$187$	−18.2087	+	10.5128i	−1.33155	+	0.768772i
$188$	3.98083	−	2.29833i	0.290332	−	0.167623i
$189$		0			0
$190$	6.18487	+	7.53309i	0.448697	+	0.546508i
$191$	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	$-0.308279\pi$
$193$	21.7202	−	12.5401i	1.56345	−	0.902659i	0.996904	−	0.0786292i	$-0.0250543\pi$
$194$	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	$-0.958787\pi$
$197$		−	3.62439i		−	0.258227i	0.991630	−	0.129113i	$-0.0412131\pi$
$198$		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	$0.159931\pi$
$200$	−1.69412	+	4.70425i	−0.119793	+	0.332641i
$201$		0			0
$202$			3.36795i			0.236968i
$203$	9.63686	+	5.56384i	0.676375	+	0.390505i
$204$		0			0
$205$	18.8307	−	6.89006i	1.31519	−	0.481223i
$206$	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
$215$	5.18926	+	14.1824i	0.353905	+	0.967228i
$216$		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	−0.137068	−	0.990562i	$-0.543768\pi$
$223$	9.74016	−	5.62349i	0.652250	−	0.376576i	0.789318	+	0.613985i	$0.210435\pi$
$224$	−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	$0.0946443\pi$
$227$			8.82814i			0.585944i	−0.956121	+	0.292972i	$0.905356\pi$
$228$		0			0
$229$	22.2817			1.47241			0.736207	−	0.676756i	$-0.236615\pi$
$229$	22.2817			1.47241			0.736207	+	0.676756i	$0.236615\pi$
$230$	0.658228	−	3.77045i	0.0434023	−	0.248616i
$231$		0			0
$232$	3.82712	+	2.20959i	0.251263	+	0.145066i
$233$	5.35318	−	3.09066i	0.350699	−	0.202476i	−0.314294	−	0.949326i	$-0.601768\pi$
$233$	5.35318	−	3.09066i	0.350699	−	0.202476i	0.664993	+	0.746850i	$0.268435\pi$
$234$		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
$245$	−0.253588	+	1.45260i	−0.0162011	+	0.0928030i
$246$		0			0
$247$	−19.9426	−	3.77195i	−1.26892	−	0.240004i
$248$			9.22060i			0.585509i
$249$		0			0
$250$	−0.0569884	−	11.1802i	−0.00360426	−	0.707098i
$251$	−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	0.648826	−	0.760937i	$-0.275260\pi$
$257$	5.03779	+	2.90857i	0.314249	+	0.181432i	−0.334577	+	0.942368i	$0.608594\pi$
$258$		0			0
$259$	−8.22092			−0.510823
$260$	−3.57763	−	9.77774i	−0.221875	−	0.606390i
$261$		0			0
$262$	−5.68732	−	3.28357i	−0.351364	−	0.202860i
$263$	−14.9606	+	8.63749i	−0.922508	+	0.532610i	−0.884434	−	0.466665i	$-0.845456\pi$
$263$	−14.9606	+	8.63749i	−0.922508	+	0.532610i	−0.0380737	+	0.999275i	$0.512122\pi$
$264$		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
$275$	13.5716	+	4.88750i	0.818399	+	0.294727i
$276$		0			0
$277$			11.1309i			0.668791i	0.942433	+	0.334396i	$0.108532\pi$
$277$			11.1309i			0.668791i	−0.942433	+	0.334396i	$0.891468\pi$
$278$			6.19455i			0.371525i
$279$		0			0
$280$	0.968307	−	5.54663i	0.0578674	−	0.331475i
$281$	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	−0.673985	−	0.738745i	$-0.735419\pi$
$283$	−6.24466	+	3.60536i	−0.371207	+	0.214316i	0.302779	+	0.953061i	$0.402086\pi$
$284$	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
$290$	−9.73435	−	1.69938i	−0.571621	−	0.0997910i
$291$		0			0
$292$		−	14.1670i		−	0.829059i
$293$			9.26719i			0.541395i	0.962664	+	0.270697i	$0.0872543\pi$
$293$			9.26719i			0.541395i	−0.962664	+	0.270697i	$0.912746\pi$
$294$		0			0
$295$	19.8767	−	7.27279i	1.15727	−	0.423438i
$296$	−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	−0.731897	−	0.681415i	$-0.761365\pi$
$307$	−8.89602	+	5.13612i	−0.507722	+	0.293134i	0.224175	+	0.974549i	$0.428031\pi$
$308$	6.29123	+	3.63224i	0.358476	+	0.206966i
$309$		0			0
$310$	−7.08464	−	19.3625i	−0.402381	−	1.09971i
$311$	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	0.399973	−	0.916527i	$-0.369019\pi$
$313$	−3.42825	−	1.97930i	−0.193776	−	0.111877i	−0.593749	+	0.804650i	$0.702353\pi$
$314$	−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	−0.139958	−	0.990157i	$-0.544697\pi$
$317$	−19.0052	−	10.9727i	−1.06744	−	0.616286i	−0.927480	+	0.373872i	$0.878030\pi$
$318$		0			0
$319$	6.37459	−	11.0411i	0.356908	−	0.618184i
$320$	0.384547	−	2.20275i	0.0214968	−	0.123138i
$321$		0			0
$322$			4.31013i			0.240194i
$323$	20.7200	−	24.0803i	1.15289	−	1.33986i
$324$		0			0
$325$	15.0254	+	17.7835i	0.833461	+	0.986453i
$326$	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	−0.385699	−	0.922625i	$-0.626040\pi$
$337$	4.04725	−	2.33668i	0.220468	−	0.127287i	0.606167	+	0.795338i	$0.292706\pi$
$338$	7.51773	+	4.34036i	0.408911	+	0.236085i
$339$		0			0
$340$	16.0536	+	2.80257i	0.870630	+	0.151991i
$341$	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	−0.783260	−	0.621695i	$-0.786444\pi$
$347$	−11.8564	+	6.84531i	−0.636486	+	0.367475i	0.146774	+	0.989170i	$0.453111\pi$
$348$		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	$-0.974061\pi$
$353$		−	3.05876i		−	0.162802i	0.996681	−	0.0814008i	$-0.0259394\pi$
$354$		0			0
$355$	−22.5967	+	8.26805i	−1.19931	+	0.438823i
$356$	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
$365$	10.8852	+	29.7494i	0.569756	+	1.55715i
$366$		0			0
$367$	4.66821	+	2.69519i	0.243679	+	0.140688i	0.616866	−	0.787068i	$-0.288402\pi$
$367$	4.66821	+	2.69519i	0.243679	+	0.140688i	−0.373188	+	0.927756i	$0.621735\pi$
$368$			1.71170i			0.0892284i
$369$		0			0
$370$	6.85581	−	2.50851i	0.356416	−	0.130411i
$371$	−13.6382	+	23.6221i	−0.708062	+	1.22640i
$372$		0			0
$373$		−	3.85586i		−	0.199649i	−0.995005	−	0.0998244i	$-0.968172\pi$
$373$		−	3.85586i		−	0.199649i	0.995005	−	0.0998244i	$-0.0318281\pi$
$374$	−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	$0.614072\pi$
$380$	9.12280	+	3.43141i	0.467990	+	0.176028i
$381$		0			0
$382$	3.99564	−	2.30688i	0.204435	−	0.118030i
$383$	6.30771	−	3.64176i	0.322309	−	0.186085i	−0.330112	−	0.943942i	$-0.607087\pi$
$383$	6.30771	−	3.64176i	0.322309	−	0.186085i	0.652421	+	0.757857i	$0.273753\pi$
$384$		0			0
$385$	−16.0019	−	2.79354i	−0.815531	−	0.142372i
$386$	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
$395$	−17.3032	+	6.33116i	−0.870618	+	0.318555i
$396$		0			0
$397$	−10.0280	+	5.78964i	−0.503288	+	0.290574i	−0.730071	−	0.683372i	$-0.760513\pi$
$397$	−10.0280	+	5.78964i	−0.503288	+	0.290574i	0.226782	+	0.973946i	$0.427179\pi$
$398$		−	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
$415$	−15.7392	−	2.74768i	−0.772606	−	0.134878i
$416$	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	0.246925	−	0.969035i	$-0.420580\pi$
$433$	−9.75555	−	5.63237i	−0.468822	−	0.270674i	−0.715746	+	0.698360i	$0.753913\pi$
$434$	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	$0.956360\pi$
$440$	−6.35487	−	1.10941i	−0.302957	−	0.0528889i
$441$		0			0
$442$	−29.3883	+	16.9674i	−1.39786	+	0.807055i
$443$	6.09413	+	3.51845i	0.289541	+	0.167167i	0.637735	−	0.770256i	$-0.279872\pi$
$443$	6.09413	+	3.51845i	0.289541	+	0.167167i	−0.348194	+	0.937423i	$0.613205\pi$
$444$		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	$0.0874383\pi$
$457$			11.5975i			0.542508i	−0.962508	+	0.271254i	$0.912562\pi$
$458$	19.2965	−	11.1408i	0.901666	−	0.520577i
$459$		0			0
$460$	−1.31518	−	3.59442i	−0.0613206	−	0.167591i
$461$	−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	$0.0911527\pi$
$463$			12.1559i			0.564934i	−0.959277	+	0.282467i	$0.908847\pi$
$464$	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	$-0.988180\pi$
$467$		−	1.60463i		−	0.0742533i	0.999311	−	0.0371266i	$-0.0118205\pi$
$468$		0			0
$469$	−13.4201	+	23.2443i	−0.619682	+	1.07332i
$470$	−1.76763	+	10.1253i	−0.0815349	+	0.467046i
$471$		0			0
$472$	−8.19734	+	4.73274i	−0.377313	+	0.217842i
$473$	−16.8740	+	9.74222i	−0.775868	+	0.447948i
$474$		0			0
$475$	−21.7936	−	0.196179i	−0.999959	−	0.00900132i
$476$	−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
$485$	1.76465	+	4.82282i	0.0801286	+	0.218993i
$486$		0			0
$487$		−	24.3737i		−	1.10448i	−0.833687	−	0.552238i	$-0.813774\pi$
$487$		−	24.3737i		−	1.10448i	0.833687	−	0.552238i	$-0.186226\pi$
$488$	−12.9934	−	7.50173i	−0.588182	−	0.339587i
$489$		0			0
$490$	0.506685	+	1.38478i	0.0228897	+	0.0625579i
$491$	−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	$0.913224\pi$
$500$	−5.63945	−	9.65384i	−0.252204	−	0.431733i
$501$		0			0
$502$			21.2635i			0.949034i
$503$	−17.0870	−	9.86519i	−0.761872	−	0.439867i	0.0680955	−	0.997679i	$-0.478308\pi$
$503$	−17.0870	−	9.86519i	−0.761872	−	0.439867i	−0.829967	+	0.557812i	$0.811641\pi$
$504$		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
$515$	−24.2023	−	4.22513i	−1.06648	−	0.186181i
$516$		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	0.311753	−	0.950163i	$-0.399084\pi$
$523$	−8.12396	−	4.69037i	−0.355236	−	0.205096i	−0.666989	+	0.745068i	$0.732417\pi$
$524$	−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
$530$	4.16557	−	23.8611i	0.180941	−	1.03646i
$531$		0			0
$532$	−10.7847	−	2.03983i	−0.467576	−	0.0884376i
$533$			41.7543i			1.80858i
$534$		0			0
$535$	7.39629	+	1.29121i	0.319769	+	0.0558239i
$536$	−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
$545$	−8.88879	+	3.25237i	−0.380754	+	0.139316i
$546$		0			0
$547$	5.07734	+	2.93141i	0.217092	+	0.125338i	0.604603	−	0.796527i	$-0.293332\pi$
$547$	5.07734	+	2.93141i	0.217092	+	0.125338i	−0.387511	+	0.921865i	$0.626665\pi$
$548$	−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	0.835653	−	0.549257i	$-0.185089\pi$
$557$	18.3570	+	10.5984i	0.777809	+	0.449068i	−0.0578442	+	0.998326i	$0.518423\pi$
$558$		0			0
$559$	−31.4473			−1.33008
$560$	−1.93474	−	5.28768i	−0.0817576	−	0.223445i
$561$		0			0
$562$		−	5.68717i		−	0.239899i
$563$			26.4882i			1.11634i	0.829725	+	0.558172i	$0.188497\pi$
$563$			26.4882i			1.11634i	−0.829725	+	0.558172i	$0.811503\pi$
$564$		0			0
$565$	41.4079	+	7.22881i	1.74204	+	0.304118i
$566$	−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
$575$	5.52353	+	6.53745i	0.230347	+	0.272630i
$576$		0			0
$577$			27.9608i			1.16402i	0.813180	+	0.582012i	$0.197734\pi$
$577$			27.9608i			1.16402i	−0.813180	+	0.582012i	$0.802266\pi$
$578$		−	36.1147i		−	1.50217i
$579$		0			0
$580$	−9.27989	+	3.39547i	−0.385326	+	0.140989i
$581$	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	−0.301785	−	0.953376i	$-0.597582\pi$
$587$	9.03637	−	5.21715i	0.372971	−	0.215335i	0.674756	+	0.738041i	$0.264249\pi$
$588$		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	0.594859	−	0.803830i	$-0.297208\pi$
$593$	4.77660	+	2.75777i	0.196152	+	0.113248i	−0.398708	+	0.917078i	$0.630541\pi$
$594$		0			0
$595$	38.5365	−	14.1003i	1.57984	−	0.578058i
$596$	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
$605$	1.02942	−	5.89668i	0.0418517	−	0.239734i
$606$		0			0
$607$			6.78955i			0.275579i	0.990462	+	0.137790i	$0.0439998\pi$
$607$			6.78955i			0.275579i	−0.990462	+	0.137790i	$0.956000\pi$
$608$	−4.28296	−	0.810083i	−0.173697	−	0.0328532i
$609$		0			0
$610$	33.0489	+	5.76953i	1.33811	+	0.233602i
$611$	−10.7016	−	18.5358i	−0.432942	−	0.749877i
$612$		0			0
$613$	20.8847	−	12.0578i	0.843524	−	0.487009i	−0.0149366	−	0.999888i	$-0.504755\pi$
$613$	20.8847	−	12.0578i	0.843524	−	0.487009i	0.858460	+	0.512880i	$0.171421\pi$
$614$	−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	−0.364712	−	0.931121i	$-0.618832\pi$
$617$	−33.6188	−	19.4098i	−1.35344	−	0.781410i	−0.988730	+	0.149711i	$0.952166\pi$
$618$		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
$625$	19.2599	+	15.9392i	0.770395	+	0.637567i
$626$	−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
$640$	−0.768349	−	2.09991i	−0.0303717	−	0.0830064i
$641$	−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	−0.995971	−	0.0896801i	$-0.971416\pi$
$643$	−35.9135	+	20.7347i	−1.41629	+	0.817696i	−0.420320	+	0.907376i	$0.638082\pi$
$644$	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	$-0.928315\pi$
$647$		−	11.3601i		−	0.446612i	0.974748	−	0.223306i	$-0.0716848\pi$
$648$		0			0
$649$	13.6538	+	23.6491i	0.535958	+	0.928307i
$650$	21.9042	+	7.88828i	0.859153	+	0.309404i
$651$		0			0
$652$	2.99472	+	1.72900i	0.117282	+	0.0677130i
$653$		−	14.1285i		−	0.552889i	−0.961030	−	0.276444i	$-0.910844\pi$
$653$		−	14.1285i		−	0.552889i	0.961030	−	0.276444i	$-0.0891562\pi$
$654$		0			0
$655$	13.7904	−	5.04586i	0.538837	−	0.197158i
$656$	−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
$665$	24.2142	−	4.00295i	0.938988	−	0.155228i
$666$		0			0
$667$	6.55086	−	3.78214i	0.253650	−	0.146445i
$668$	5.37144	−	3.10120i	0.207827	−	0.119989i
$669$		0			0
$670$	4.09894	−	23.4794i	0.158356	−	0.907089i
$671$	−21.6422	+	37.4855i	−0.835489	+	1.44711i
$672$		0			0
$673$		−	29.7678i		−	1.14747i	−0.819042	−	0.573733i	$-0.805495\pi$
$673$		−	29.7678i		−	1.14747i	0.819042	−	0.573733i	$-0.194505\pi$
$674$	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	$-0.911097\pi$
$677$		−	14.3460i		−	0.551360i	0.961249	−	0.275680i	$-0.0889031\pi$
$678$		0			0
$679$	−2.89157	−	5.00834i	−0.110968	−	0.192202i
$680$	15.3041	−	5.59972i	0.586887	−	0.214739i
$681$		0			0
$682$	23.0373	−	13.3006i	0.882143	−	0.509305i
$683$		−	39.5539i		−	1.51349i	−0.653712	−	0.756744i	$-0.726789\pi$
$683$		−	39.5539i		−	1.51349i	0.653712	−	0.756744i	$-0.273211\pi$
$684$		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
$700$	8.12557	+	9.61712i	0.307118	+	0.363493i
$701$	−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
$725$	16.8781	−	14.2604i	0.626835	−	0.529618i
$726$		0			0
$727$	−15.6863	+	9.05647i	−0.581771	+	0.335886i	−0.761837	−	0.647769i	$-0.775702\pi$
$727$	−15.6863	+	9.05647i	−0.581771	+	0.335886i	0.180066	+	0.983655i	$0.442369\pi$
$728$	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	$-0.950946\pi$
$733$		−	8.31171i		−	0.307000i	0.988149	−	0.153500i	$-0.0490545\pi$
$734$	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	0.137528	−	0.990498i	$-0.456084\pi$
$743$	29.0049	−	16.7460i	1.06409	−	0.614351i	0.926560	+	0.376147i	$0.122751\pi$
$744$		0			0
$745$	−25.1769	+	9.21213i	−0.922412	+	0.337506i
$746$	−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
$755$	2.12091	−	12.1489i	0.0771878	−	0.442145i
$756$		0			0
$757$	−26.9406	+	15.5542i	−0.979174	+	0.565327i	−0.902021	−	0.431693i	$-0.857917\pi$
$757$	−26.9406	+	15.5542i	−0.979174	+	0.565327i	−0.0771537	+	0.997019i	$0.524583\pi$
$758$	−11.8270	+	6.82832i	−0.429576	+	0.248016i
$759$		0			0
$760$	9.61628	−	1.58971i	0.348819	−	0.0576647i
$761$	−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	$0.0324147\pi$
$770$	−15.2548	+	5.58166i	−0.549744	+	0.201149i
$771$		0			0
$772$		−	25.0803i		−	0.902659i
$773$	−11.9910	−	6.92302i	−0.431287	−	0.249004i	0.268608	−	0.963250i	$-0.413437\pi$
$773$	−11.9910	−	6.92302i	−0.431287	−	0.249004i	−0.699895	+	0.714246i	$0.746770\pi$
$774$		0			0
$775$	43.3760	+	15.6209i	1.55811	+	0.561118i
$776$	−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
$785$	−9.43474	−	25.7853i	−0.336740	−	0.920318i
$786$		0			0
$787$		−	0.272719i		−	0.00972137i	−0.999988	−	0.00486069i	$-0.998453\pi$
$787$		−	0.272719i		−	0.00972137i	0.999988	−	0.00486069i	$-0.00154721\pi$
$788$	−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	$-0.987659\pi$
$797$		−	2.18853i		−	0.0775216i	0.999249	−	0.0387608i	$-0.0123410\pi$
$798$		0			0
$799$	33.5004			1.18516
$800$	3.22694	+	3.81928i	0.114089	+	0.135032i
$801$		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
$815$	−7.61714	−	1.32977i	−0.266817	−	0.0465797i
$816$		0			0
$817$	19.2012	−	22.3152i	0.671765	−	0.780711i
$818$		−	0.651522i		−	0.0227799i
$819$		0			0
$820$	3.44837	−	19.7529i	0.120422	−	0.689801i
$821$	−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	−0.0543553	−	0.998522i	$-0.517310\pi$
$823$	−27.1468	−	15.6732i	−0.946278	−	0.546334i	−0.891923	+	0.452188i	$0.850644\pi$
$824$	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	−0.0834244	−	0.996514i	$-0.526586\pi$
$827$	−28.4166	−	16.4063i	−0.988143	−	0.570505i	−0.904719	+	0.426009i	$0.859919\pi$
$828$		0			0
$829$	−51.8181			−1.79972			−0.899858	−	0.436182i	$-0.856330\pi$
$829$	−51.8181			−1.79972			−0.899858	+	0.436182i	$0.856330\pi$
$830$	−15.0044	+	5.49003i	−0.520809	+	0.190562i
$831$		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
$845$	−18.2288	+	6.66983i	−0.627089	+	0.229449i
$846$		0			0
$847$			6.74070i			0.231613i
$848$			10.8324i			0.371986i
$849$		0			0
$850$	−27.8348	+	23.5178i	−0.954727	+	0.806656i
$851$	−2.79418	+	4.83966i	−0.0957831	+	0.165901i
$852$		0			0
$853$	−1.05924	+	0.611551i	−0.0362676	+	0.0209391i	−0.518024	−	0.855366i	$-0.673332\pi$
$853$	−1.05924	+	0.611551i	−0.0362676	+	0.0209391i	0.481757	+	0.876305i	$0.339999\pi$
$854$	−37.7794			−1.29278
$855$		0			0
$856$	−3.35775			−0.114765
$857$	−14.7442	+	8.51258i	−0.503653	+	0.290784i	−0.730221	−	0.683211i	$-0.760583\pi$
$857$	−14.7442	+	8.51258i	−0.503653	+	0.290784i	0.226568	+	0.973995i	$0.427249\pi$
$858$		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	$0.212579\pi$
$860$	14.8769	+	2.59715i	0.507298	+	0.0885619i
$861$		0			0
$862$		−	27.4245i		−	0.934083i
$863$		−	6.06986i		−	0.206620i	−0.994649	−	0.103310i	$-0.967057\pi$
$863$		−	6.06986i		−	0.206620i	0.994649	−	0.103310i	$-0.0329434\pi$
$864$		0			0
$865$	−11.0646	−	30.2398i	−0.376209	−	1.02819i
$866$	−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	0.0881333	−	0.996109i	$-0.471910\pi$
$877$	29.4618	−	17.0098i	0.994855	−	0.574380i	0.906722	+	0.421729i	$0.138577\pi$
$878$	−13.6797	−	7.89796i	−0.461666	−	0.266543i
$879$		0			0
$880$	−6.05819	+	2.21666i	−0.204221	+	0.0747237i
$881$	−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	0.982836	−	0.184480i	$-0.0590602\pi$
$883$	39.0605	+	22.5516i	1.31449	+	0.758921i	0.331653	+	0.943401i	$0.392394\pi$
$884$	−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	0.970022	−	0.243017i	$-0.0781372\pi$
$887$	37.0666	+	21.4004i	1.24457	+	0.718555i	0.274552	+	0.961572i	$0.411471\pi$
$888$		0			0
$889$	19.8392	−	34.3625i	0.665385	−	1.15248i
$890$	−10.4459	−	1.82361i	−0.350149	−	0.0611274i
$891$		0			0
$892$		−	11.2470i		−	0.376576i
$893$	19.6873	+	3.72368i	0.658812	+	0.124608i
$894$		0			0
$895$	−0.746698	+	4.27722i	−0.0249594	+	0.142972i
$896$	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	−0.868065	−	0.496451i	$-0.834636\pi$
$907$	−26.2663	+	15.1648i	−0.872157	+	0.503540i	−0.00409285	+	0.999992i	$0.501303\pi$
$908$	7.64539	+	4.41407i	0.253721	+	0.146486i
$909$		0			0
$910$	−25.8266	−	4.50869i	−0.856142	−	0.149462i
$911$	−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
$925$	−5.53098	+	15.3584i	−0.181858	+	0.504982i
$926$	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
$935$	−16.1550	−	44.1520i	−0.528325	−	1.44392i
$936$		0			0
$937$	22.9312	+	13.2393i	0.749128	+	0.432509i	0.825379	−	0.564579i	$-0.190962\pi$
$937$	22.9312	+	13.2393i	0.749128	+	0.432509i	−0.0762506	+	0.997089i	$0.524295\pi$
$938$			26.8402i			0.876362i
$939$		0			0
$940$	3.53184	+	9.65260i	0.115196	+	0.314833i
$941$	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	0.305257	−	0.952270i	$-0.401258\pi$
$947$	39.4692	−	22.7875i	1.28258	−	0.740495i	0.977318	+	0.211775i	$0.0679243\pi$
$948$		0			0
$949$	−65.9650			−2.14132
$950$	−18.9719	+	10.7269i	−0.615530	+	0.348027i
$951$		0			0
$952$	−15.8928	+	9.17574i	−0.515090	+	0.297387i
$953$	46.7123	−	26.9694i	1.51316	−	0.873623i	0.513278	−	0.858222i	$-0.328431\pi$
$953$	46.7123	−	26.9694i	1.51316	−	0.873623i	0.999881	−	0.0154010i	$-0.00490249\pi$
$954$		0			0
$955$	−1.77421	+	10.1630i	−0.0574121	+	0.328867i
$956$	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
$965$	19.2704	+	52.6664i	0.620336	+	1.69539i
$966$		0			0
$967$	19.5534	−	11.2892i	0.628795	−	0.363035i	−0.151490	−	0.988459i	$-0.548407\pi$
$967$	19.5534	−	11.2892i	0.628795	−	0.363035i	0.780285	+	0.625424i	$0.215074\pi$
$968$			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	$0.00950012\pi$
$977$			1.86548i			0.0596821i	−0.999555	+	0.0298411i	$0.990500\pi$
$978$		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	−0.964052	−	0.265712i	$-0.914393\pi$
$983$	−38.1239	+	22.0109i	−1.21597	+	0.702038i	−0.251913	+	0.967750i	$0.581060\pi$
$984$		0			0
$985$	7.98363	+	1.39375i	0.254380	+	0.0444085i
$986$	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	0.216190	−	0.976351i	$-0.430637\pi$
$997$	−16.4589	−	9.50256i	−0.521259	−	0.300949i	−0.737450	+	0.675402i	$0.763970\pi$
$998$	−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.919.8		20
3.2	odd	2		570.2.q.c.349.3	yes	20
5.4	even	2	inner	1710.2.t.c.919.5		20
15.14	odd	2		570.2.q.c.349.6	yes	20
19.11	even	3	inner	1710.2.t.c.1189.5		20
57.11	odd	6		570.2.q.c.49.6	yes	20
95.49	even	6	inner	1710.2.t.c.1189.8		20
285.239	odd	6		570.2.q.c.49.3	✓	20

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.384547 + 2.20275i) q^{5} -2.51805i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.384547 + 2.20275i) q^{5} -2.51805i q^{7} -1.00000i q^{8} +(0.768349 + 2.09991i) q^{10} -2.88497 q^{11} +(-4.03244 - 2.32813i) q^{13} +(-1.25902 - 2.18069i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.31158 - 3.64399i) q^{17} +(4.11420 - 1.43993i) q^{19} +(1.71537 + 1.43440i) q^{20} +(-2.49846 + 1.44248i) q^{22} +(-1.48237 - 0.855848i) q^{23} +(-4.70425 - 1.69412i) q^{25} -4.65626 q^{26} +(-2.18069 - 1.25902i) q^{28} +(-2.20959 + 3.82712i) q^{29} -9.22060 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.64399 - 6.31158i) q^{34} +(5.54663 + 0.968307i) q^{35} -3.26480i q^{37} +(2.84303 - 3.30411i) q^{38} +(2.20275 + 0.384547i) q^{40} +(-4.48368 - 7.76596i) q^{41} +(5.84894 - 3.37689i) q^{43} +(-1.44248 + 2.49846i) q^{44} -1.71170 q^{46} +(3.98083 + 2.29833i) q^{47} +0.659446 q^{49} +(-4.92106 + 0.884968i) q^{50} +(-4.03244 + 2.32813i) q^{52} +(-9.38113 - 5.41620i) q^{53} +(1.10941 - 6.35487i) q^{55} -2.51805 q^{56} +4.41917i q^{58} +(-4.73274 - 8.19734i) q^{59} +(7.50173 - 12.9934i) q^{61} +(-7.98528 + 4.61030i) q^{62} -1.00000 q^{64} +(6.67896 - 7.98719i) q^{65} +(-9.23107 - 5.32956i) q^{67} -7.28798i q^{68} +(5.28768 - 1.93474i) q^{70} +(5.38040 + 9.31912i) q^{71} +(12.2689 - 7.08348i) q^{73} +(-1.63240 - 2.82740i) q^{74} +(0.810083 - 4.28296i) q^{76} +7.26448i q^{77} +(4.11998 + 7.13601i) q^{79} +(2.09991 - 0.768349i) q^{80} +(-7.76596 - 4.48368i) q^{82} +7.14523i q^{83} +(5.59972 + 15.3041i) q^{85} +(3.37689 - 5.84894i) q^{86} +2.88497i q^{88} +(-2.37111 + 4.10688i) q^{89} +(-5.86233 + 10.1539i) q^{91} +(-1.48237 + 0.855848i) q^{92} +4.59667 q^{94} +(1.58971 + 9.61628i) q^{95} +(1.98898 - 1.14834i) q^{97} +(0.571097 - 0.329723i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4}+O(q^{10}) \) 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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