LMFDB - Embedded newform 672.2.bi.c.593.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(17,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bi (of order $6$, degree $2$, not 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			593.18
Character	$\chi$	$=$	672.593
Dual form			672.2.bi.c.17.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09218 + 1.34430i) q^{3} +(-2.46958 - 1.42581i) q^{5} +(1.02032 - 2.44110i) q^{7} +(-0.614290 + 2.93643i) q^{9} +O(q^{10})$	\(q+(1.09218 + 1.34430i) q^{3} +(-2.46958 - 1.42581i) q^{5} +(1.02032 - 2.44110i) q^{7} +(-0.614290 + 2.93643i) q^{9} +(-2.42621 - 4.20231i) q^{11} -2.75221 q^{13} +(-0.780502 - 4.87710i) q^{15} +(-1.75366 - 3.03743i) q^{17} +(3.14493 - 5.44717i) q^{19} +(4.39594 - 1.29450i) q^{21} +(3.15865 + 1.82365i) q^{23} +(1.56588 + 2.71219i) q^{25} +(-4.61837 + 2.38132i) q^{27} -3.90427 q^{29} +(0.858051 - 0.495396i) q^{31} +(2.99932 - 7.85123i) q^{33} +(-6.00030 + 4.57370i) q^{35} +(-1.06516 - 0.614970i) q^{37} +(-3.00591 - 3.69980i) q^{39} +2.10659 q^{41} +5.11768i q^{43} +(5.70384 - 6.37590i) q^{45} +(5.61268 - 9.72145i) q^{47} +(-4.91791 - 4.98138i) q^{49} +(2.16791 - 5.67487i) q^{51} +(1.00417 + 1.73927i) q^{53} +13.8373i q^{55} +(10.7575 - 1.72156i) q^{57} +(-0.890996 + 0.514417i) q^{59} +(-1.24347 + 2.15376i) q^{61} +(6.54135 + 4.49563i) q^{63} +(6.79681 + 3.92414i) q^{65} +(5.02777 - 2.90279i) q^{67} +(0.998281 + 6.23793i) q^{69} +9.75277i q^{71} +(0.291019 - 0.168020i) q^{73} +(-1.93577 + 5.06722i) q^{75} +(-12.7338 + 1.63491i) q^{77} +(2.80082 - 4.85116i) q^{79} +(-8.24530 - 3.60764i) q^{81} -0.138115i q^{83} +10.0016i q^{85} +(-4.26417 - 5.24852i) q^{87} +(-0.580993 + 1.00631i) q^{89} +(-2.80813 + 6.71841i) q^{91} +(1.60311 + 0.612418i) q^{93} +(-15.5333 + 8.96815i) q^{95} -11.0953i q^{97} +(13.8302 - 4.54296i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 4 * q^7 - 14 * q^9	$ 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) $ 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	1.09218	+	1.34430i	0.630570	+	0.776132i
$3$	1.09218	+	1.34430i	0.630570	+	0.776132i
$4$		0			0
$5$	−2.46958	−	1.42581i	−1.10443	−	0.637643i	−0.167049	−	0.985949i	$-0.553424\pi$
$5$	−2.46958	−	1.42581i	−1.10443	−	0.637643i	−0.937381	+	0.348306i	$0.886757\pi$
$6$		0			0
$7$	1.02032	−	2.44110i	0.385643	−	0.922648i
$7$	1.02032	−	2.44110i	0.385643	−	0.922648i
$8$		0			0
$9$	−0.614290	+	2.93643i	−0.204763	+	0.978812i
$10$		0			0
$11$	−2.42621	−	4.20231i	−0.731529	−	1.26705i	−0.956230	−	0.292617i	$-0.905474\pi$
$11$	−2.42621	−	4.20231i	−0.731529	−	1.26705i	0.224701	−	0.974428i	$-0.427860\pi$
$12$		0			0
$13$	−2.75221			−0.763326			−0.381663	−	0.924302i	$-0.624649\pi$
$13$	−2.75221			−0.763326			−0.381663	+	0.924302i	$0.624649\pi$
$14$		0			0
$15$	−0.780502	−	4.87710i	−0.201525	−	1.25926i
$16$		0			0
$17$	−1.75366	−	3.03743i	−0.425326	−	0.736686i	0.571125	−	0.820863i	$-0.306507\pi$
$17$	−1.75366	−	3.03743i	−0.425326	−	0.736686i	−0.996451	+	0.0841773i	$0.973174\pi$
$18$		0			0
$19$	3.14493	−	5.44717i	0.721496	−	1.24967i	−0.238905	−	0.971043i	$-0.576788\pi$
$19$	3.14493	−	5.44717i	0.721496	−	1.24967i	0.960400	−	0.278624i	$-0.0898784\pi$
$20$		0			0
$21$	4.39594	−	1.29450i	0.959272	−	0.282484i
$22$		0			0
$23$	3.15865	+	1.82365i	0.658624	+	0.380257i	0.791753	−	0.610842i	$-0.209169\pi$
$23$	3.15865	+	1.82365i	0.658624	+	0.380257i	−0.133128	+	0.991099i	$0.542502\pi$
$24$		0			0
$25$	1.56588	+	2.71219i	0.313177	+	0.542438i
$26$		0			0
$27$	−4.61837	+	2.38132i	−0.888805	+	0.458286i
$28$		0			0
$29$	−3.90427			−0.725005			−0.362503	−	0.931983i	$-0.618078\pi$
$29$	−3.90427			−0.725005			−0.362503	+	0.931983i	$0.618078\pi$
$30$		0			0
$31$	0.858051	−	0.495396i	0.154111	−	0.0889758i	−0.420962	−	0.907078i	$-0.638307\pi$
$31$	0.858051	−	0.495396i	0.154111	−	0.0889758i	0.575072	+	0.818103i	$0.304974\pi$
$32$		0			0
$33$	2.99932	−	7.85123i	0.522115	−	1.36672i
$34$		0			0
$35$	−6.00030	+	4.57370i	−1.01424	+	0.773097i
$36$		0			0
$37$	−1.06516	−	0.614970i	−0.175111	−	0.101100i	0.409883	−	0.912138i	$-0.365570\pi$
$37$	−1.06516	−	0.614970i	−0.175111	−	0.101100i	−0.584994	+	0.811038i	$0.698903\pi$
$38$		0			0
$39$	−3.00591	−	3.69980i	−0.481330	−	0.592442i
$40$		0			0
$41$	2.10659			0.328995			0.164497	−	0.986378i	$-0.447400\pi$
$41$	2.10659			0.328995			0.164497	+	0.986378i	$0.447400\pi$
$42$		0			0
$43$			5.11768i			0.780439i	0.920722	+	0.390220i	$0.127601\pi$
$43$			5.11768i			0.780439i	−0.920722	+	0.390220i	$0.872399\pi$
$44$		0			0
$45$	5.70384	−	6.37590i	0.850279	−	0.950463i
$46$		0			0
$47$	5.61268	−	9.72145i	0.818693	−	1.41802i	−0.0879518	−	0.996125i	$-0.528032\pi$
$47$	5.61268	−	9.72145i	0.818693	−	1.41802i	0.906645	−	0.421894i	$-0.138635\pi$
$48$		0			0
$49$	−4.91791	−	4.98138i	−0.702558	−	0.711626i
$50$		0			0
$51$	2.16791	−	5.67487i	0.303568	−	0.794641i
$52$		0			0
$53$	1.00417	+	1.73927i	0.137933	+	0.238907i	0.926714	−	0.375767i	$-0.122621\pi$
$53$	1.00417	+	1.73927i	0.137933	+	0.238907i	−0.788781	+	0.614674i	$0.789288\pi$
$54$		0			0
$55$			13.8373i			1.86582i
$56$		0			0
$57$	10.7575	−	1.72156i	1.42486	−	0.228026i
$58$		0			0
$59$	−0.890996	+	0.514417i	−0.115998	+	0.0669714i	−0.556876	−	0.830595i	$-0.688000\pi$
$59$	−0.890996	+	0.514417i	−0.115998	+	0.0669714i	0.440879	+	0.897567i	$0.354667\pi$
$60$		0			0
$61$	−1.24347	+	2.15376i	−0.159211	+	0.275761i	−0.934584	−	0.355742i	$-0.884228\pi$
$61$	−1.24347	+	2.15376i	−0.159211	+	0.275761i	0.775374	+	0.631503i	$0.217562\pi$
$62$		0			0
$63$	6.54135	+	4.49563i	0.824133	+	0.566397i
$64$		0			0
$65$	6.79681	+	3.92414i	0.843040	+	0.486729i
$66$		0			0
$67$	5.02777	−	2.90279i	0.614240	−	0.354632i	−0.160383	−	0.987055i	$-0.551273\pi$
$67$	5.02777	−	2.90279i	0.614240	−	0.354632i	0.774623	+	0.632423i	$0.217940\pi$
$68$		0			0
$69$	0.998281	+	6.23793i	0.120179	+	0.750958i
$70$		0			0
$71$			9.75277i			1.15744i	0.815526	+	0.578720i	$0.196448\pi$
$71$			9.75277i			1.15744i	−0.815526	+	0.578720i	$0.803552\pi$
$72$		0			0
$73$	0.291019	−	0.168020i	0.0340612	−	0.0196652i	−0.482873	−	0.875691i	$-0.660407\pi$
$73$	0.291019	−	0.168020i	0.0340612	−	0.0196652i	0.516934	+	0.856025i	$0.327073\pi$
$74$		0			0
$75$	−1.93577	+	5.06722i	−0.223524	+	0.585112i
$76$		0			0
$77$	−12.7338	+	1.63491i	−1.45115	+	0.186316i
$78$		0			0
$79$	2.80082	−	4.85116i	0.315117	−	0.545798i	−0.664346	−	0.747426i	$-0.731290\pi$
$79$	2.80082	−	4.85116i	0.315117	−	0.545798i	0.979462	+	0.201627i	$0.0646230\pi$
$80$		0			0
$81$	−8.24530	−	3.60764i	−0.916144	−	0.400849i
$82$		0			0
$83$		−	0.138115i		−	0.0151600i	−0.999971	−	0.00758002i	$-0.997587\pi$
$83$		−	0.138115i		−	0.0151600i	0.999971	−	0.00758002i	$-0.00241282\pi$
$84$		0			0
$85$			10.0016i			1.08482i
$86$		0			0
$87$	−4.26417	−	5.24852i	−0.457167	−	0.562700i
$88$		0			0
$89$	−0.580993	+	1.00631i	−0.0615852	+	0.106669i	−0.895174	−	0.445717i	$-0.852949\pi$
$89$	−0.580993	+	1.00631i	−0.0615852	+	0.106669i	0.833589	+	0.552385i	$0.186282\pi$
$90$		0			0
$91$	−2.80813	+	6.71841i	−0.294372	+	0.704281i
$92$		0			0
$93$	1.60311	+	0.612418i	0.166234	+	0.0635048i
$94$		0			0
$95$	−15.5333	+	8.96815i	−1.59368	+	0.920113i
$96$		0			0
$97$		−	11.0953i		−	1.12656i	−0.826266	−	0.563280i	$-0.809539\pi$
$97$		−	11.0953i		−	1.12656i	0.826266	−	0.563280i	$-0.190461\pi$
$98$		0			0
$99$	13.8302	−	4.54296i	1.38999	−	0.456585i
$100$		0			0
$101$	6.16256	−	3.55796i	0.613198	−	0.354030i	−0.161018	−	0.986951i	$-0.551478\pi$
$101$	6.16256	−	3.55796i	0.613198	−	0.354030i	0.774216	+	0.632922i	$0.218144\pi$
$102$		0			0
$103$	−1.50519	−	0.869021i	−0.148311	−	0.0856271i	0.424008	−	0.905658i	$-0.360623\pi$
$103$	−1.50519	−	0.869021i	−0.148311	−	0.0856271i	−0.572319	+	0.820031i	$0.693956\pi$
$104$		0			0
$105$	−12.7018	−	3.07091i	−1.23957	−	0.299690i
$106$		0			0
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	−0.839163	−	0.543881i	$-0.816954\pi$
$107$	0.532028	−	0.921500i	0.0514331	−	0.0890847i	0.890596	+	0.454796i	$0.150288\pi$
$108$		0			0
$109$	7.85874	−	4.53725i	0.752731	−	0.434589i	−0.0739489	−	0.997262i	$-0.523560\pi$
$109$	7.85874	−	4.53725i	0.752731	−	0.434589i	0.826680	+	0.562673i	$0.190227\pi$
$110$		0			0
$111$	−0.336640	−	2.10355i	−0.0319524	−	0.199660i
$112$		0			0
$113$			16.8126i			1.58159i	0.612078	+	0.790797i	$0.290334\pi$
$113$			16.8126i			1.58159i	−0.612078	+	0.790797i	$0.709666\pi$
$114$		0			0
$115$	−5.20036	−	9.00729i	−0.484936	−	0.839934i
$116$		0			0
$117$	1.69066	−	8.08169i	0.156301	−	0.747152i
$118$		0			0
$119$	−9.20396	+	1.18172i	−0.843726	+	0.108328i
$120$		0			0
$121$	−6.27296	+	10.8651i	−0.570269	+	0.987735i
$122$		0			0
$123$	2.30078	+	2.83190i	0.207454	+	0.255343i
$124$		0			0
$125$			5.32750i			0.476506i
$126$		0			0
$127$	−15.6371			−1.38756			−0.693782	−	0.720185i	$-0.744057\pi$
$127$	−15.6371			−1.38756			−0.693782	+	0.720185i	$0.744057\pi$
$128$		0			0
$129$	−6.87971	+	5.58943i	−0.605724	+	0.492122i
$130$		0			0
$131$	−8.73260	−	5.04177i	−0.762971	−	0.440502i	0.0673904	−	0.997727i	$-0.478533\pi$
$131$	−8.73260	−	5.04177i	−0.762971	−	0.440502i	−0.830361	+	0.557225i	$0.811866\pi$
$132$		0			0
$133$	−10.0883	−	13.2349i	−0.874763	−	1.14761i
$134$		0			0
$135$	14.8007	+	0.704060i	1.27385	+	0.0605958i
$136$		0			0
$137$	−17.0704	+	9.85557i	−1.45842	+	0.842019i	−0.998934	−	0.0461669i	$-0.985299\pi$
$137$	−17.0704	+	9.85557i	−1.45842	+	0.842019i	−0.459485	+	0.888185i	$0.651966\pi$
$138$		0			0
$139$	−0.111832			−0.00948546			−0.00474273	−	0.999989i	$-0.501510\pi$
$139$	−0.111832			−0.00948546			−0.00474273	+	0.999989i	$0.501510\pi$
$140$		0			0
$141$	19.1986	−	3.07243i	1.61681	−	0.258745i
$142$		0			0
$143$	6.67743	+	11.5657i	0.558395	+	0.967169i
$144$		0			0
$145$	9.64192	+	5.56676i	0.800718	+	0.462295i
$146$		0			0
$147$	1.32524	−	12.0517i	0.109304	−	0.994008i
$148$		0			0
$149$	5.49834	−	9.52340i	0.450441	−	0.780187i	−0.547972	−	0.836497i	$-0.684600\pi$
$149$	5.49834	−	9.52340i	0.450441	−	0.780187i	0.998413	+	0.0563094i	$0.0179333\pi$
$150$		0			0
$151$	−4.16727	−	7.21792i	−0.339127	−	0.587386i	0.645141	−	0.764063i	$-0.276798\pi$
$151$	−4.16727	−	7.21792i	−0.339127	−	0.587386i	−0.984269	+	0.176677i	$0.943465\pi$
$152$		0			0
$153$	9.99648	−	3.28365i	0.808168	−	0.265468i
$154$		0			0
$155$	−2.82537			−0.226939
$156$		0			0
$157$	5.42198	+	9.39114i	0.432721	+	0.749495i	0.997107	−	0.0760165i	$-0.0242202\pi$
$157$	5.42198	+	9.39114i	0.432721	+	0.749495i	−0.564386	+	0.825511i	$0.690887\pi$
$158$		0			0
$159$	−1.24137	+	3.24949i	−0.0984470	+	0.257702i
$160$		0			0
$161$	7.67452	−	5.84987i	0.604837	−	0.461035i
$162$		0			0
$163$	10.0621	+	5.80934i	0.788122	+	0.455022i	0.839301	−	0.543667i	$-0.182965\pi$
$163$	10.0621	+	5.80934i	0.788122	+	0.455022i	−0.0511792	+	0.998689i	$0.516298\pi$
$164$		0			0
$165$	−18.6014	+	15.1128i	−1.44812	+	1.17653i
$166$		0			0
$167$	−7.75061			−0.599761			−0.299880	−	0.953977i	$-0.596947\pi$
$167$	−7.75061			−0.599761			−0.299880	+	0.953977i	$0.596947\pi$
$168$		0			0
$169$	−5.42533			−0.417333
$170$		0			0
$171$	14.0634	+	12.5810i	1.07545	+	0.962094i
$172$		0			0
$173$	0.880487	+	0.508349i	0.0669422	+	0.0386491i	0.533098	−	0.846054i	$-0.321028\pi$
$173$	0.880487	+	0.508349i	0.0669422	+	0.0386491i	−0.466155	+	0.884703i	$0.654361\pi$
$174$		0			0
$175$	8.21842	−	1.05518i	0.621254	−	0.0797642i
$176$		0			0
$177$	−1.66466	−	0.635932i	−0.125123	−	0.0477996i
$178$		0			0
$179$	10.8103	+	18.7240i	0.808002	+	1.39950i	0.914246	+	0.405160i	$0.132784\pi$
$179$	10.8103	+	18.7240i	0.808002	+	1.39950i	−0.106244	+	0.994340i	$0.533883\pi$
$180$		0			0
$181$	9.37049			0.696503			0.348251	−	0.937401i	$-0.386776\pi$
$181$	9.37049			0.696503			0.348251	+	0.937401i	$0.386776\pi$
$182$		0			0
$183$	−4.25340	+	0.680689i	−0.314420	+	0.0503180i
$184$		0			0
$185$	1.75366	+	3.03743i	0.128932	+	0.223317i
$186$		0			0
$187$	−8.50950	+	14.7389i	−0.622276	+	1.07781i
$188$		0			0
$189$	1.10084	+	13.7036i	0.0800744	+	0.996789i
$190$		0			0
$191$	7.70657	+	4.44939i	0.557628	+	0.321947i	0.752193	−	0.658943i	$-0.228996\pi$
$191$	7.70657	+	4.44939i	0.557628	+	0.321947i	−0.194565	+	0.980890i	$0.562329\pi$
$192$		0			0
$193$	7.45779	+	12.9173i	0.536824	+	0.929806i	0.999073	+	0.0430556i	$0.0137093\pi$
$193$	7.45779	+	12.9173i	0.536824	+	0.929806i	−0.462249	+	0.886750i	$0.652957\pi$
$194$		0			0
$195$	2.14811	+	13.4228i	0.153829	+	0.961228i
$196$		0			0
$197$	−2.74394			−0.195497			−0.0977487	−	0.995211i	$-0.531164\pi$
$197$	−2.74394			−0.195497			−0.0977487	+	0.995211i	$0.531164\pi$
$198$		0			0
$199$	20.1826	−	11.6525i	1.43071	−	0.826021i	0.433535	−	0.901137i	$-0.357266\pi$
$199$	20.1826	−	11.6525i	1.43071	−	0.826021i	0.997175	+	0.0751162i	$0.0239328\pi$
$200$		0			0
$201$	9.39344	+	3.58848i	0.662562	+	0.253112i
$202$		0			0
$203$	−3.98360	+	9.53071i	−0.279594	+	0.668925i
$204$		0			0
$205$	−5.20240	−	3.00361i	−0.363352	−	0.209781i
$206$		0			0
$207$	−7.29535	+	8.15492i	−0.507062	+	0.566806i
$208$		0			0
$209$	−30.5210			−2.11118
$210$		0			0
$211$		−	20.3918i		−	1.40383i	−0.712259	−	0.701916i	$-0.752328\pi$
$211$		−	20.3918i		−	1.40383i	0.712259	−	0.701916i	$-0.247672\pi$
$212$		0			0
$213$	−13.1107	+	10.6518i	−0.898328	+	0.729847i
$214$		0			0
$215$	7.29686	−	12.6385i	0.497642	−	0.861941i
$216$		0			0
$217$	−0.333826	−	2.60005i	−0.0226616	−	0.176503i
$218$		0			0
$219$	0.543714	+	0.207709i	0.0367408	+	0.0140357i
$220$		0			0
$221$	4.82645	+	8.35966i	0.324662	+	0.562332i
$222$		0			0
$223$		−	11.4666i		−	0.767860i	−0.923362	−	0.383930i	$-0.874570\pi$
$223$		−	11.4666i		−	0.767860i	0.923362	−	0.383930i	$-0.125430\pi$
$224$		0			0
$225$	−8.92608	+	2.93204i	−0.595072	+	0.195470i
$226$		0			0
$227$	18.3699	−	10.6059i	1.21926	−	0.703938i	0.254497	−	0.967073i	$-0.418090\pi$
$227$	18.3699	−	10.6059i	1.21926	−	0.703938i	0.964759	+	0.263136i	$0.0847567\pi$
$228$		0			0
$229$	−1.13465	+	1.96528i	−0.0749800	+	0.129869i	−0.901078	−	0.433658i	$-0.857223\pi$
$229$	−1.13465	+	1.96528i	−0.0749800	+	0.129869i	0.826098	+	0.563527i	$0.190556\pi$
$230$		0			0
$231$	−16.1054	−	15.3324i	−1.05965	−	1.00880i
$232$		0			0
$233$	22.5624	+	13.0264i	1.47811	+	0.853389i	0.999694	−	0.0247423i	$-0.00787651\pi$
$233$	22.5624	+	13.0264i	1.47811	+	0.853389i	0.478420	+	0.878131i	$0.341210\pi$
$234$		0			0
$235$	−27.7219	+	16.0053i	−1.80838	+	1.04407i
$236$		0			0
$237$	9.58042	−	1.53319i	0.622315	−	0.0995916i
$238$		0			0
$239$			8.32874i			0.538742i	0.963037	+	0.269371i	$0.0868157\pi$
$239$			8.32874i			0.538742i	−0.963037	+	0.269371i	$0.913184\pi$
$240$		0			0
$241$	6.24112	−	3.60331i	0.402026	−	0.232110i	−0.285332	−	0.958429i	$-0.592104\pi$
$241$	6.24112	−	3.60331i	0.402026	−	0.232110i	0.687358	+	0.726319i	$0.258771\pi$
$242$		0			0
$243$	−4.15558	−	15.0244i	−0.266581	−	0.963813i
$244$		0			0
$245$	5.04265	+	19.3139i	0.322163	+	1.23392i
$246$		0			0
$247$	−8.65550	+	14.9918i	−0.550736	+	0.953904i
$248$		0			0
$249$	0.185668	−	0.150846i	0.0117662	−	0.00955947i
$250$		0			0
$251$		−	8.41270i		−	0.531005i	−0.964110	−	0.265502i	$-0.914462\pi$
$251$		−	8.41270i		−	0.531005i	0.964110	−	0.265502i	$-0.0855378\pi$
$252$		0			0
$253$		−	17.6982i		−	1.11268i
$254$		0			0
$255$	−13.4451	+	10.9235i	−0.841967	+	0.684057i
$256$		0			0
$257$	15.1284	−	26.2032i	0.943685	−	1.63451i	0.185321	−	0.982678i	$-0.440668\pi$
$257$	15.1284	−	26.2032i	0.943685	−	1.63451i	0.758364	−	0.651832i	$-0.225999\pi$
$258$		0			0
$259$	−2.58800	+	1.97269i	−0.160810	+	0.122577i
$260$		0			0
$261$	2.39836	−	11.4646i	0.148454	−	0.709644i
$262$		0			0
$263$	20.9078	−	12.0711i	1.28923	−	0.744338i	0.310714	−	0.950504i	$-0.399432\pi$
$263$	20.9078	−	12.0711i	1.28923	−	0.744338i	0.978517	+	0.206166i	$0.0660986\pi$
$264$		0			0
$265$		−	5.72701i		−	0.351808i
$266$		0			0
$267$	−1.98733	+	0.318041i	−0.121623	+	0.0194638i
$268$		0			0
$269$	−17.4083	+	10.0507i	−1.06140	+	0.612800i	−0.925819	−	0.377966i	$-0.876623\pi$
$269$	−17.4083	+	10.0507i	−1.06140	+	0.612800i	−0.135581	+	0.990766i	$0.543290\pi$
$270$		0			0
$271$	1.57903	+	0.911656i	0.0959195	+	0.0553791i	0.547192	−	0.837007i	$-0.315697\pi$
$271$	1.57903	+	0.911656i	0.0959195	+	0.0553791i	−0.451273	+	0.892386i	$0.649030\pi$
$272$		0			0
$273$	−12.0985	+	3.56274i	−0.732237	+	0.215627i
$274$		0			0
$275$	7.59832	−	13.1607i	0.458196	−	0.793618i
$276$		0			0
$277$	11.4072	−	6.58598i	0.685395	−	0.395713i	−0.116490	−	0.993192i	$-0.537164\pi$
$277$	11.4072	−	6.58598i	0.685395	−	0.395713i	0.801885	+	0.597479i	$0.203831\pi$
$278$		0			0
$279$	0.927606	+	2.82393i	0.0555343	+	0.169064i
$280$		0			0
$281$		−	15.3821i		−	0.917618i	−0.888535	−	0.458809i	$-0.848276\pi$
$281$		−	15.3821i		−	0.917618i	0.888535	−	0.458809i	$-0.151724\pi$
$282$		0			0
$283$	−4.64882	−	8.05200i	−0.276344	−	0.478641i	0.694129	−	0.719850i	$-0.255790\pi$
$283$	−4.64882	−	8.05200i	−0.276344	−	0.478641i	−0.970473	+	0.241209i	$0.922456\pi$
$284$		0			0
$285$	−29.0210	−	11.0866i	−1.71906	−	0.656713i
$286$		0			0
$287$	2.14939	−	5.14240i	0.126875	−	0.303546i
$288$		0			0
$289$	2.34933	−	4.06916i	0.138196	−	0.239362i
$290$		0			0
$291$	14.9154	−	12.1181i	0.874359	−	0.710374i
$292$		0			0
$293$		−	17.8462i		−	1.04258i	−0.853378	−	0.521292i	$-0.825450\pi$
$293$		−	17.8462i		−	1.04258i	0.853378	−	0.521292i	$-0.174550\pi$
$294$		0			0
$295$	2.93385			0.170815
$296$		0			0
$297$	21.2122	+	13.6302i	1.23086	+	0.790907i
$298$		0			0
$299$	−8.69327	−	5.01906i	−0.502745	−	0.290260i
$300$		0			0
$301$	12.4928	+	5.22166i	0.720071	+	0.300971i
$302$		0			0
$303$	11.5136	+	4.39841i	0.661438	+	0.252682i
$304$		0			0
$305$	6.14172	−	3.54592i	0.351674	−	0.203039i
$306$		0			0
$307$	17.6654			1.00822			0.504110	−	0.863640i	$-0.331821\pi$
$307$	17.6654			1.00822			0.504110	+	0.863640i	$0.331821\pi$
$308$		0			0
$309$	−0.475709	−	2.97255i	−0.0270622	−	0.169103i
$310$		0			0
$311$	−4.15091	−	7.18958i	−0.235376	−	0.407684i	0.724006	−	0.689794i	$-0.242299\pi$
$311$	−4.15091	−	7.18958i	−0.235376	−	0.407684i	−0.959382	+	0.282110i	$0.908966\pi$
$312$		0			0
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.324101	−	0.946023i	$-0.605062\pi$
$313$	−23.0954	−	13.3342i	−1.30543	−	0.753691i	−0.981330	+	0.192332i	$0.938395\pi$
$314$		0			0
$315$	−9.74446	−	20.4291i	−0.549038	−	1.15105i
$316$		0			0
$317$	14.4097	−	24.9584i	0.809331	−	1.40180i	−0.103996	−	0.994578i	$-0.533163\pi$
$317$	14.4097	−	24.9584i	0.809331	−	1.40180i	0.913328	−	0.407225i	$-0.133504\pi$
$318$		0			0
$319$	9.47258	+	16.4070i	0.530362	+	0.918615i
$320$		0			0
$321$	1.81984	−	0.291237i	0.101574	−	0.0162553i
$322$		0			0
$323$	−22.0606			−1.22748
$324$		0			0
$325$	−4.30964	−	7.46452i	−0.239056	−	0.414057i
$326$		0			0
$327$	14.6826	+	5.60903i	0.811948	+	0.310180i
$328$		0			0
$329$	−18.0043	−	23.6200i	−0.992608	−	1.30222i
$330$		0			0
$331$	2.24514	+	1.29623i	0.123404	+	0.0712472i	0.560431	−	0.828201i	$-0.310635\pi$
$331$	2.24514	+	1.29623i	0.123404	+	0.0712472i	−0.437027	+	0.899448i	$0.643969\pi$
$332$		0			0
$333$	2.46013	−	2.75000i	0.134815	−	0.150699i
$334$		0			0
$335$	−16.5553			−0.904513
$336$		0			0
$337$	11.1713			0.608541			0.304271	−	0.952586i	$-0.401587\pi$
$337$	11.1713			0.608541			0.304271	+	0.952586i	$0.401587\pi$
$338$		0			0
$339$	−22.6012	+	18.3623i	−1.22753	+	0.997306i
$340$		0			0
$341$	−4.16362	−	2.40387i	−0.225473	−	0.130177i
$342$		0			0
$343$	−17.1779	+	6.92250i	−0.927517	+	0.373780i
$344$		0			0
$345$	6.42878	−	16.8284i	0.346114	−	0.906012i
$346$		0			0
$347$	7.23643	+	12.5339i	0.388472	+	0.672853i	0.992244	−	0.124304i	$-0.0396697\pi$
$347$	7.23643	+	12.5339i	0.388472	+	0.672853i	−0.603772	+	0.797157i	$0.706336\pi$
$348$		0			0
$349$	−22.8018			−1.22055			−0.610275	−	0.792189i	$-0.708941\pi$
$349$	−22.8018			−1.22055			−0.610275	+	0.792189i	$0.708941\pi$
$350$		0			0
$351$	12.7107	−	6.55390i	0.678448	−	0.349821i
$352$		0			0
$353$	−2.06060	−	3.56907i	−0.109675	−	0.189962i	0.805964	−	0.591965i	$-0.201648\pi$
$353$	−2.06060	−	3.56907i	−0.109675	−	0.189962i	−0.915639	+	0.402003i	$0.868314\pi$
$354$		0			0
$355$	13.9056	−	24.0852i	0.738034	−	1.27831i
$356$		0			0
$357$	−11.6410	−	11.0822i	−0.616105	−	0.586535i
$358$		0			0
$359$	−9.83790	−	5.67992i	−0.519225	−	0.299775i	0.217393	−	0.976084i	$-0.430245\pi$
$359$	−9.83790	−	5.67992i	−0.519225	−	0.299775i	−0.736617	+	0.676310i	$0.763578\pi$
$360$		0			0
$361$	−10.2811	−	17.8074i	−0.541112	−	0.937234i
$362$		0			0
$363$	−21.4571	+	3.43387i	−1.12621	+	0.180232i
$364$		0			0
$365$	−0.958259			−0.0501576
$366$		0			0
$367$	−24.2527	+	14.0023i	−1.26598	+	0.730914i	−0.974225	−	0.225580i	$-0.927572\pi$
$367$	−24.2527	+	14.0023i	−1.26598	+	0.730914i	−0.291755	+	0.956493i	$0.594239\pi$
$368$		0			0
$369$	−1.29406	+	6.18587i	−0.0673660	+	0.322024i
$370$		0			0
$371$	5.27029	−	0.676664i	0.273620	−	0.0351306i
$372$		0			0
$373$	27.1273	+	15.6619i	1.40460	+	0.810944i	0.994860	−	0.101259i	$-0.0322872\pi$
$373$	27.1273	+	15.6619i	1.40460	+	0.810944i	0.409737	+	0.912204i	$0.365621\pi$
$374$		0			0
$375$	−7.16176	+	5.81858i	−0.369832	+	0.300470i
$376$		0			0
$377$	10.7454			0.553416
$378$		0			0
$379$			28.8128i			1.48001i	0.672600	+	0.740006i	$0.265178\pi$
$379$			28.8128i			1.48001i	−0.672600	+	0.740006i	$0.734822\pi$
$380$		0			0
$381$	−17.0785	−	21.0209i	−0.874956	−	1.07693i
$382$		0			0
$383$	12.6701	−	21.9453i	0.647413	−	1.12135i	−0.336325	−	0.941746i	$-0.609184\pi$
$383$	12.6701	−	21.9453i	0.647413	−	1.12135i	0.983738	−	0.179607i	$-0.0574826\pi$
$384$		0			0
$385$	33.7781	+	14.1184i	1.72149	+	0.719540i
$386$		0			0
$387$	−15.0277	−	3.14374i	−0.763903	−	0.159805i
$388$		0			0
$389$	2.20886	+	3.82586i	0.111994	+	0.193979i	0.916574	−	0.399865i	$-0.130943\pi$
$389$	2.20886	+	3.82586i	0.111994	+	0.193979i	−0.804580	+	0.593844i	$0.797610\pi$
$390$		0			0
$391$		−	12.7923i		−	0.646932i
$392$		0			0
$393$	−2.75991	−	17.2458i	−0.139219	−	0.869934i
$394$		0			0
$395$	−13.8337	+	7.98689i	−0.696049	+	0.401864i
$396$		0			0
$397$	−8.01775	+	13.8871i	−0.402399	+	0.696976i	−0.994015	−	0.109244i	$-0.965157\pi$
$397$	−8.01775	+	13.8871i	−0.402399	+	0.696976i	0.591616	+	0.806220i	$0.298490\pi$
$398$		0			0
$399$	6.77352	−	28.0165i	0.339100	−	1.40258i
$400$		0			0
$401$	−6.53545	−	3.77324i	−0.326365	−	0.188427i	0.327861	−	0.944726i	$-0.393672\pi$
$401$	−6.53545	−	3.77324i	−0.326365	−	0.188427i	−0.654226	+	0.756299i	$0.727006\pi$
$402$		0			0
$403$	−2.36154	+	1.36343i	−0.117637	+	0.0679175i
$404$		0			0
$405$	15.2186	+	20.6656i	0.756218	+	1.02688i
$406$		0			0
$407$			5.96817i			0.295831i
$408$		0			0
$409$	−24.3612	+	14.0650i	−1.20458	+	0.695467i	−0.961571	−	0.274556i	$-0.911469\pi$
$409$	−24.3612	+	14.0650i	−1.20458	+	0.695467i	−0.243013	+	0.970023i	$0.578136\pi$
$410$		0			0
$411$	−31.8927	−	12.1836i	−1.57315	−	0.600975i
$412$		0			0
$413$	0.346643	+	2.69988i	0.0170572	+	0.132852i
$414$		0			0
$415$	−0.196926	+	0.341085i	−0.00966670	+	0.0167432i
$416$		0			0
$417$	−0.122140	−	0.150336i	−0.00598125	−	0.00736197i
$418$		0			0
$419$		−	19.5661i		−	0.955866i	−0.878396	−	0.477933i	$-0.841386\pi$
$419$		−	19.5661i		−	0.955866i	0.878396	−	0.477933i	$-0.158614\pi$
$420$		0			0
$421$			26.0983i			1.27195i	0.771708	+	0.635977i	$0.219403\pi$
$421$			26.0983i			1.27195i	−0.771708	+	0.635977i	$0.780597\pi$
$422$		0			0
$423$	25.0986	+	22.4531i	1.22033	+	1.09170i
$424$		0			0
$425$	5.49207	−	9.51254i	0.266404	−	0.461426i
$426$		0			0
$427$	3.98880	+	5.23296i	0.193032	+	0.253241i
$428$		0			0
$429$	−8.25477	+	21.6082i	−0.398544	+	1.04326i
$430$		0			0
$431$	10.4072	−	6.00858i	0.501296	−	0.289423i	−0.227953	−	0.973672i	$-0.573203\pi$
$431$	10.4072	−	6.00858i	0.501296	−	0.289423i	0.729248	+	0.684249i	$0.239870\pi$
$432$		0			0
$433$			35.6343i			1.71247i	0.516583	+	0.856237i	$0.327204\pi$
$433$			35.6343i			1.71247i	−0.516583	+	0.856237i	$0.672796\pi$
$434$		0			0
$435$	3.04729	+	19.0415i	0.146107	+	0.912972i
$436$		0			0
$437$	19.8674	−	11.4705i	0.950389	−	0.548707i
$438$		0			0
$439$	11.6950	+	6.75210i	0.558171	+	0.322260i	0.752411	−	0.658694i	$-0.228891\pi$
$439$	11.6950	+	6.75210i	0.558171	+	0.322260i	−0.194240	+	0.980954i	$0.562224\pi$
$440$		0			0
$441$	17.6485	−	11.3811i	0.840406	−	0.541957i
$442$		0			0
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	−0.438565	−	0.898700i	$-0.644513\pi$
$443$	11.7659	−	20.3791i	0.559014	−	0.968241i	0.997579	−	0.0695416i	$-0.0221536\pi$
$444$		0			0
$445$	2.86962	−	1.65678i	0.136033	−	0.0785387i
$446$		0			0
$447$	18.8075	−	3.00984i	0.889563	−	0.142360i
$448$		0			0
$449$			30.6292i			1.44548i	0.691120	+	0.722740i	$0.257117\pi$
$449$			30.6292i			1.44548i	−0.691120	+	0.722740i	$0.742883\pi$
$450$		0			0
$451$	−5.11103	−	8.85257i	−0.240669	−	0.416851i
$452$		0			0
$453$	5.15165	−	13.4853i	0.242046	−	0.633596i
$454$		0			0
$455$	16.5141	−	12.5878i	0.774193	−	0.590125i
$456$		0			0
$457$	5.80736	−	10.0587i	0.271657	−	0.470524i	−0.697629	−	0.716459i	$-0.745762\pi$
$457$	5.80736	−	10.0587i	0.271657	−	0.470524i	0.969286	+	0.245935i	$0.0790950\pi$
$458$		0			0
$459$	15.3322	+	9.85194i	0.715644	+	0.459849i
$460$		0			0
$461$		−	30.8362i		−	1.43618i	−0.695948	−	0.718092i	$-0.745015\pi$
$461$		−	30.8362i		−	1.43618i	0.695948	−	0.718092i	$-0.254985\pi$
$462$		0			0
$463$	32.3199			1.50203			0.751016	−	0.660284i	$-0.229564\pi$
$463$	32.3199			1.50203			0.751016	+	0.660284i	$0.229564\pi$
$464$		0			0
$465$	−3.08581	−	3.79815i	−0.143101	−	0.176135i
$466$		0			0
$467$	29.3749	+	16.9596i	1.35931	+	0.784797i	0.989531	−	0.144323i	$-0.0461004\pi$
$467$	29.3749	+	16.9596i	1.35931	+	0.784797i	0.369778	+	0.929120i	$0.379434\pi$
$468$		0			0
$469$	−1.95606	−	15.2350i	−0.0903225	−	0.703489i
$470$		0			0
$471$	−6.70275	+	17.5456i	−0.308846	+	0.808458i
$472$		0			0
$473$	21.5061	−	12.4166i	0.988852	−	0.570914i
$474$		0			0
$475$	19.6984			0.903823
$476$		0			0
$477$	−5.72409	+	1.88025i	−0.262088	+	0.0860910i
$478$		0			0
$479$	−17.6827	−	30.6273i	−0.807943	−	1.39940i	−0.914286	−	0.405068i	$-0.867248\pi$
$479$	−17.6827	−	30.6273i	−0.807943	−	1.39940i	0.106344	−	0.994329i	$-0.466086\pi$
$480$		0			0
$481$	2.93154	+	1.69253i	0.133667	+	0.0771726i
$482$		0			0
$483$	16.2459	+	3.92776i	0.739216	+	0.178719i
$484$		0			0
$485$	−15.8198	+	27.4008i	−0.718342	+	1.24421i
$486$		0			0
$487$	−16.4191	−	28.4386i	−0.744018	−	1.28868i	−0.950652	−	0.310259i	$-0.899584\pi$
$487$	−16.4191	−	28.4386i	−0.744018	−	1.28868i	0.206634	−	0.978418i	$-0.433749\pi$
$488$		0			0
$489$	3.18008	+	19.8713i	0.143808	+	0.898610i
$490$		0			0
$491$	22.5295			1.01674			0.508371	−	0.861138i	$-0.330248\pi$
$491$	22.5295			1.01674			0.508371	+	0.861138i	$0.330248\pi$
$492$		0			0
$493$	6.84678	+	11.8590i	0.308363	+	0.534101i
$494$		0			0
$495$	−40.6322	−	8.50009i	−1.82628	−	0.382051i
$496$		0			0
$497$	23.8075	+	9.95092i	1.06791	+	0.446360i
$498$		0			0
$499$	−11.3117	−	6.53084i	−0.506383	−	0.292361i	0.224962	−	0.974367i	$-0.427774\pi$
$499$	−11.3117	−	6.53084i	−0.506383	−	0.292361i	−0.731346	+	0.682007i	$0.761107\pi$
$500$		0			0
$501$	−8.46506	−	10.4192i	−0.378191	−	0.465494i
$502$		0			0
$503$	−2.77607			−0.123779			−0.0618894	−	0.998083i	$-0.519713\pi$
$503$	−2.77607			−0.123779			−0.0618894	+	0.998083i	$0.519713\pi$
$504$		0			0
$505$	−20.2919			−0.902978
$506$		0			0
$507$	−5.92543	−	7.29328i	−0.263158	−	0.323906i
$508$		0			0
$509$	27.2704	+	15.7446i	1.20874	+	0.697866i	0.962484	−	0.271339i	$-0.0874665\pi$
$509$	27.2704	+	15.7446i	1.20874	+	0.697866i	0.246255	+	0.969205i	$0.420800\pi$
$510$		0			0
$511$	−0.113221	−	0.881838i	−0.00500861	−	0.0390102i
$512$		0			0
$513$	−1.55295	+	32.6461i	−0.0685645	+	1.44136i
$514$		0			0
$515$	2.47812	+	4.29223i	0.109199	+	0.189138i
$516$		0			0
$517$	−54.4701			−2.39559
$518$		0			0
$519$	0.278275	+	1.73885i	0.0122149	+	0.0763270i
$520$		0			0
$521$	−2.92633	−	5.06856i	−0.128205	−	0.222058i	0.794776	−	0.606903i	$-0.207588\pi$
$521$	−2.92633	−	5.06856i	−0.128205	−	0.222058i	−0.922981	+	0.384845i	$0.874255\pi$
$522$		0			0
$523$	9.81038	−	16.9921i	0.428978	−	0.743012i	−0.567805	−	0.823163i	$-0.692207\pi$
$523$	9.81038	−	16.9921i	0.428978	−	0.743012i	0.996783	+	0.0801516i	$0.0255405\pi$
$524$		0			0
$525$	10.3945	+	9.89558i	0.453652	+	0.431879i
$526$		0			0
$527$	−3.00947	−	1.73752i	−0.131094	−	0.0756874i
$528$		0			0
$529$	−4.84862	−	8.39806i	−0.210810	−	0.365133i
$530$		0			0
$531$	−0.963222	−	2.93235i	−0.0418003	−	0.127253i
$532$		0			0
$533$	−5.79779			−0.251130
$534$		0			0
$535$	−2.62777	+	1.51715i	−0.113609	+	0.0655919i
$536$		0			0
$537$	−13.3639	+	34.9823i	−0.576696	+	1.50960i
$538$		0			0
$539$	−9.00148	+	32.7525i	−0.387721	+	1.41075i
$540$		0			0
$541$	−35.5120	−	20.5029i	−1.52678	−	0.881488i	−0.999494	−	0.0318007i	$-0.989876\pi$
$541$	−35.5120	−	20.5029i	−1.52678	−	0.881488i	−0.527287	−	0.849687i	$-0.676791\pi$
$542$		0			0
$543$	10.2343	+	12.5968i	0.439194	+	0.540579i
$544$		0			0
$545$	−25.8771			−1.10845
$546$		0			0
$547$		−	13.0813i		−	0.559315i	−0.960100	−	0.279658i	$-0.909779\pi$
$547$		−	13.0813i		−	0.559315i	0.960100	−	0.279658i	$-0.0902209\pi$
$548$		0			0
$549$	−5.56053	−	4.97442i	−0.237317	−	0.212303i
$550$		0			0
$551$	−12.2787	+	21.2673i	−0.523088	+	0.906016i
$552$		0			0
$553$	−8.98443	−	11.7868i	−0.382057	−	0.501225i
$554$		0			0
$555$	−2.16791	+	5.67487i	−0.0920227	+	0.240885i
$556$		0			0
$557$	19.2814	+	33.3964i	0.816980	+	1.41505i	0.907898	+	0.419192i	$0.137687\pi$
$557$	19.2814	+	33.3964i	0.816980	+	1.41505i	−0.0909180	+	0.995858i	$0.528980\pi$
$558$		0			0
$559$		−	14.0849i		−	0.595730i
$560$		0			0
$561$	−29.1074	+	4.65817i	−1.22891	+	0.196668i
$562$		0			0
$563$	9.75701	−	5.63321i	0.411209	−	0.237411i	−0.280100	−	0.959971i	$-0.590368\pi$
$563$	9.75701	−	5.63321i	0.411209	−	0.237411i	0.691309	+	0.722559i	$0.257034\pi$
$564$		0			0
$565$	23.9716	−	41.5200i	1.00849	−	1.74676i
$566$		0			0
$567$	−17.2194	+	16.4466i	−0.723148	+	0.690693i
$568$		0			0
$569$	−26.7497	−	15.4440i	−1.12141	−	0.647445i	−0.179648	−	0.983731i	$-0.557496\pi$
$569$	−26.7497	−	15.4440i	−1.12141	−	0.647445i	−0.941760	+	0.336286i	$0.890829\pi$
$570$		0			0
$571$	6.49082	−	3.74748i	0.271633	−	0.156827i	−0.357997	−	0.933723i	$-0.616540\pi$
$571$	6.49082	−	3.74748i	0.271633	−	0.156827i	0.629629	+	0.776896i	$0.283207\pi$
$572$		0			0
$573$	2.43564	+	15.2195i	0.101750	+	0.635803i
$574$		0			0
$575$			11.4225i			0.476350i
$576$		0			0
$577$	18.4495	−	10.6518i	0.768064	−	0.443442i	−0.0641196	−	0.997942i	$-0.520424\pi$
$577$	18.4495	−	10.6518i	0.768064	−	0.443442i	0.832184	+	0.554500i	$0.187091\pi$
$578$		0			0
$579$	−9.21946	+	24.1335i	−0.383148	+	1.00295i
$580$		0			0
$581$	−0.337151	−	0.140921i	−0.0139874	−	0.00584637i
$582$		0			0
$583$	4.87263	−	8.43964i	0.201804	−	0.349534i
$584$		0			0
$585$	−15.6982	+	17.5478i	−0.649040	+	0.725513i
$586$		0			0
$587$		−	15.2002i		−	0.627381i	−0.949525	−	0.313691i	$-0.898435\pi$
$587$		−	15.2002i		−	0.627381i	0.949525	−	0.313691i	$-0.101565\pi$
$588$		0			0
$589$		−	6.23194i		−	0.256783i
$590$		0			0
$591$	−2.99687	−	3.68868i	−0.123275	−	0.151732i
$592$		0			0
$593$	4.55071	−	7.88206i	0.186875	−	0.323678i	−0.757332	−	0.653031i	$-0.773497\pi$
$593$	4.55071	−	7.88206i	0.186875	−	0.323678i	0.944207	+	0.329353i	$0.106831\pi$
$594$		0			0
$595$	24.4148	+	10.2048i	1.00091	+	0.418355i
$596$		0			0
$597$	37.7075	+	14.4050i	1.54326	+	0.589557i
$598$		0			0
$599$	−37.6136	+	21.7162i	−1.53685	+	0.887302i	−0.537831	+	0.843053i	$0.680756\pi$
$599$	−37.6136	+	21.7162i	−1.53685	+	0.887302i	−0.999021	+	0.0442488i	$0.985911\pi$
$600$		0			0
$601$			15.5284i			0.633415i	0.948523	+	0.316708i	$0.102577\pi$
$601$			15.5284i			0.633415i	−0.948523	+	0.316708i	$0.897423\pi$
$602$		0			0
$603$	5.43533	+	16.5469i	0.221344	+	0.673841i
$604$		0			0
$605$	30.9831	−	17.8881i	1.25964	−	0.727256i
$606$		0			0
$607$	−1.01612	−	0.586656i	−0.0412430	−	0.0238116i	0.479237	−	0.877686i	$-0.340914\pi$
$607$	−1.01612	−	0.586656i	−0.0412430	−	0.0238116i	−0.520480	+	0.853874i	$0.674247\pi$
$608$		0			0
$609$	−17.1629	+	5.05409i	−0.695478	+	0.204802i
$610$		0			0
$611$	−15.4473	+	26.7555i	−0.624930	+	1.08241i
$612$		0			0
$613$	−35.7276	+	20.6273i	−1.44302	+	0.833131i	−0.998050	−	0.0624126i	$-0.980121\pi$
$613$	−35.7276	+	20.6273i	−1.44302	+	0.833131i	−0.444974	+	0.895543i	$0.646787\pi$
$614$		0			0
$615$	−1.64420	−	10.2741i	−0.0663006	−	0.414291i
$616$		0			0
$617$			15.3232i			0.616887i	0.951243	+	0.308444i	$0.0998081\pi$
$617$			15.3232i			0.616887i	−0.951243	+	0.308444i	$0.900192\pi$
$618$		0			0
$619$	7.95796	+	13.7836i	0.319857	+	0.554009i	0.980458	−	0.196728i	$-0.0630316\pi$
$619$	7.95796	+	13.7836i	0.319857	+	0.554009i	−0.660601	+	0.750738i	$0.729698\pi$
$620$		0			0
$621$	−18.9305	−	0.900509i	−0.759655	−	0.0361362i
$622$		0			0
$623$	1.86370	+	2.44502i	0.0746677	+	0.0979575i
$624$		0			0
$625$	15.4254	−	26.7176i	0.617017	−	1.06871i
$626$		0			0
$627$	−33.3344	−	41.0294i	−1.33125	−	1.63856i
$628$		0			0
$629$			4.31380i			0.172002i
$630$		0			0
$631$	27.9268			1.11175			0.555875	−	0.831266i	$-0.312383\pi$
$631$	27.9268			1.11175			0.555875	+	0.831266i	$0.312383\pi$
$632$		0			0
$633$	27.4128	−	22.2715i	1.08956	−	0.885215i
$634$		0			0
$635$	38.6170	+	22.2955i	1.53247	+	0.884770i
$636$		0			0
$637$	13.5351	+	13.7098i	0.536281	+	0.543203i
$638$		0			0
$639$	−28.6384	−	5.99103i	−1.13292	−	0.237001i
$640$		0			0
$641$	−7.03036	+	4.05898i	−0.277683	+	0.160320i	−0.632374	−	0.774663i	$-0.717919\pi$
$641$	−7.03036	+	4.05898i	−0.277683	+	0.160320i	0.354691	+	0.934984i	$0.384586\pi$
$642$		0			0
$643$	−21.5611			−0.850285			−0.425143	−	0.905126i	$-0.639776\pi$
$643$	−21.5611			−0.850285			−0.425143	+	0.905126i	$0.639776\pi$
$644$		0			0
$645$	24.9595	−	3.99436i	0.982778	−	0.157278i
$646$		0			0
$647$	19.5173	+	33.8049i	0.767304	+	1.32901i	0.939020	+	0.343863i	$0.111736\pi$
$647$	19.5173	+	33.8049i	0.767304	+	1.32901i	−0.171716	+	0.985147i	$0.554931\pi$
$648$		0			0
$649$	4.32348	+	2.49616i	0.169712	+	0.0979830i
$650$		0			0
$651$	3.13065	−	3.28848i	0.122700	−	0.128886i
$652$		0			0
$653$	8.53952	−	14.7909i	0.334177	−	0.578812i	−0.649149	−	0.760661i	$-0.724875\pi$
$653$	8.53952	−	14.7909i	0.334177	−	0.578812i	0.983326	+	0.181849i	$0.0582083\pi$
$654$		0			0
$655$	14.3772	+	24.9021i	0.561765	+	0.973006i
$656$		0			0
$657$	0.314609	+	0.957770i	0.0122741	+	0.0373662i
$658$		0			0
$659$	−6.99022			−0.272300			−0.136150	−	0.990688i	$-0.543473\pi$
$659$	−6.99022			−0.272300			−0.136150	+	0.990688i	$0.543473\pi$
$660$		0			0
$661$	23.0740	+	39.9653i	0.897474	+	1.55447i	0.830712	+	0.556702i	$0.187933\pi$
$661$	23.0740	+	39.9653i	0.897474	+	1.55447i	0.0667617	+	0.997769i	$0.478733\pi$
$662$		0			0
$663$	−5.96655	+	15.6184i	−0.231722	+	0.606570i
$664$		0			0
$665$	6.04325	+	47.0686i	0.234347	+	1.82524i
$666$		0			0
$667$	−12.3322	−	7.12002i	−0.477506	−	0.275688i
$668$		0			0
$669$	15.4145	−	12.5236i	0.595961	−	0.484189i
$670$		0			0
$671$	12.0677			0.465869
$672$		0			0
$673$	8.04494			0.310110			0.155055	−	0.987906i	$-0.450445\pi$
$673$	8.04494			0.310110			0.155055	+	0.987906i	$0.450445\pi$
$674$		0			0
$675$	−13.6904	−	8.79702i	−0.526945	−	0.338597i
$676$		0			0
$677$	8.53140	+	4.92561i	0.327888	+	0.189306i	0.654903	−	0.755713i	$-0.272709\pi$
$677$	8.53140	+	4.92561i	0.327888	+	0.189306i	−0.327015	+	0.945019i	$0.606043\pi$
$678$		0			0
$679$	−27.0847	−	11.3207i	−1.03942	−	0.434450i
$680$		0			0
$681$	34.3208	+	13.1112i	1.31518	+	0.502422i
$682$		0			0
$683$	−20.1018	−	34.8173i	−0.769173	−	1.33225i	−0.938012	−	0.346603i	$-0.887335\pi$
$683$	−20.1018	−	34.8173i	−0.769173	−	1.33225i	0.168839	−	0.985644i	$-0.445998\pi$
$684$		0			0
$685$	56.2088			2.14763
$686$		0			0
$687$	−3.88117	+	0.621119i	−0.148076	+	0.0236972i
$688$		0			0
$689$	−2.76368	−	4.78683i	−0.105288	−	0.182364i
$690$		0			0
$691$	−17.2791	+	29.9282i	−0.657326	+	1.13852i	0.323979	+	0.946064i	$0.394979\pi$
$691$	−17.2791	+	29.9282i	−0.657326	+	1.13852i	−0.981305	+	0.192458i	$0.938354\pi$
$692$		0			0
$693$	3.02139	−	38.3961i	0.114773	−	1.45855i
$694$		0			0
$695$	0.276178	+	0.159451i	0.0104760	+	0.00604834i
$696$		0			0
$697$	−3.69426	−	6.39864i	−0.139930	−	0.242366i
$698$		0			0
$699$	7.13078	+	44.5579i	0.269711	+	1.68533i
$700$		0			0
$701$	−29.6534			−1.11999			−0.559997	−	0.828495i	$-0.689198\pi$
$701$	−29.6534			−1.11999			−0.559997	+	0.828495i	$0.689198\pi$
$702$		0			0
$703$	−6.69969	+	3.86807i	−0.252684	+	0.145887i
$704$		0			0
$705$	−51.7932	−	19.7860i	−1.95064	−	0.745184i
$706$		0			0
$707$	−2.39755	−	18.6736i	−0.0901692	−	0.702295i
$708$		0			0
$709$	−9.81381	−	5.66601i	−0.368565	−	0.212791i	0.304266	−	0.952587i	$-0.401589\pi$
$709$	−9.81381	−	5.66601i	−0.368565	−	0.212791i	−0.672832	+	0.739796i	$0.734922\pi$
$710$		0			0
$711$	12.5246	+	11.2044i	0.469709	+	0.420199i
$712$		0			0
$713$	3.61371			0.135335
$714$		0			0
$715$		−	38.0831i		−	1.42423i
$716$		0			0
$717$	−11.1963	+	9.09648i	−0.418135	+	0.339714i
$718$		0			0
$719$	−8.51080	+	14.7411i	−0.317399	+	0.549752i	−0.979945	−	0.199270i	$-0.936143\pi$
$719$	−8.51080	+	14.7411i	−0.317399	+	0.549752i	0.662545	+	0.749022i	$0.269476\pi$
$720$		0			0
$721$	−3.65713	+	2.78763i	−0.136199	+	0.103817i
$722$		0			0
$723$	11.6604	+	4.45448i	0.433653	+	0.165664i
$724$		0			0
$725$	−6.11364	−	10.5891i	−0.227055	−	0.393271i
$726$		0			0
$727$			42.1153i			1.56197i	0.624550	+	0.780985i	$0.285282\pi$
$727$			42.1153i			1.56197i	−0.624550	+	0.780985i	$0.714718\pi$
$728$		0			0
$729$	15.6586	−	21.9956i	0.579949	−	0.814653i
$730$		0			0
$731$	15.5446	−	8.97469i	0.574939	−	0.331941i
$732$		0			0
$733$	−20.3500	+	35.2472i	−0.751644	+	1.30189i	0.195382	+	0.980727i	$0.437405\pi$
$733$	−20.3500	+	35.2472i	−0.751644	+	1.30189i	−0.947026	+	0.321158i	$0.895928\pi$
$734$		0			0
$735$	−20.4563	+	27.8731i	−0.754541	+	1.02812i
$736$		0			0
$737$	−24.3968	−	14.0855i	−0.898669	−	0.518847i
$738$		0			0
$739$	−7.63741	+	4.40946i	−0.280947	+	0.162205i	−0.633852	−	0.773454i	$-0.718527\pi$
$739$	−7.63741	+	4.40946i	−0.280947	+	0.162205i	0.352905	+	0.935659i	$0.385194\pi$
$740$		0			0
$741$	−29.6068	+	4.73810i	−1.08763	+	0.174058i
$742$		0			0
$743$		−	16.3412i		−	0.599502i	−0.954017	−	0.299751i	$-0.903096\pi$
$743$		−	16.3412i		−	0.599502i	0.954017	−	0.299751i	$-0.0969036\pi$
$744$		0			0
$745$	−27.1572	+	15.6792i	−0.994962	+	0.574441i
$746$		0			0
$747$	0.405564	+	0.0848424i	0.0148388	+	0.00310422i
$748$		0			0
$749$	−1.70663	−	2.23895i	−0.0623590	−	0.0818096i
$750$		0			0
$751$	−6.17492	+	10.6953i	−0.225326	+	0.390276i	−0.956417	−	0.292004i	$-0.905678\pi$
$751$	−6.17492	+	10.6953i	−0.225326	+	0.390276i	0.731091	+	0.682280i	$0.239011\pi$
$752$		0			0
$753$	11.3092	−	9.18817i	0.412130	−	0.334836i
$754$		0			0
$755$			23.7670i			0.864969i
$756$		0			0
$757$		−	29.0246i		−	1.05492i	−0.849581	−	0.527459i	$-0.823145\pi$
$757$		−	29.0246i		−	1.05492i	0.849581	−	0.527459i	$-0.176855\pi$
$758$		0			0
$759$	23.7917	−	19.3296i	0.863583	−	0.701620i
$760$		0			0
$761$	−15.5050	+	26.8554i	−0.562055	+	0.973507i	0.435262	+	0.900304i	$0.356656\pi$
$761$	−15.5050	+	26.8554i	−0.562055	+	0.973507i	−0.997317	+	0.0732037i	$0.976678\pi$
$762$		0			0
$763$	−3.05745	−	23.8134i	−0.110687	−	0.862102i
$764$		0			0
$765$	−29.3690	−	6.14387i	−1.06184	−	0.222132i
$766$		0			0
$767$	2.45221	−	1.41578i	0.0885442	−	0.0511210i
$768$		0			0
$769$		−	42.3916i		−	1.52868i	−0.644813	−	0.764340i	$-0.723065\pi$
$769$		−	42.3916i		−	1.52868i	0.644813	−	0.764340i	$-0.276935\pi$
$770$		0			0
$771$	51.7479	−	8.28143i	1.86366	−	0.298248i
$772$		0			0
$773$	−2.88336	+	1.66471i	−0.103707	+	0.0598754i	−0.550957	−	0.834534i	$-0.685737\pi$
$773$	−2.88336	+	1.66471i	−0.103707	+	0.0598754i	0.447249	+	0.894409i	$0.352404\pi$
$774$		0			0
$775$	2.68722	+	1.55147i	0.0965277	+	0.0557303i
$776$		0			0
$777$	−5.47845	−	1.32452i	−0.196538	−	0.0475168i
$778$		0			0
$779$	6.62508	−	11.4750i	0.237368	−	0.411134i
$780$		0			0
$781$	40.9842	−	23.6622i	1.46653	−	0.846701i
$782$		0			0
$783$	18.0314	−	9.29733i	0.644388	−	0.332260i
$784$		0			0
$785$		−	30.9229i		−	1.10369i
$786$		0			0
$787$	11.2617	+	19.5059i	0.401437	+	0.695309i	0.993900	−	0.110289i	$-0.0351777\pi$
$787$	11.2617	+	19.5059i	0.401437	+	0.695309i	−0.592463	+	0.805598i	$0.701844\pi$
$788$		0			0
$789$	39.0623	+	14.9226i	1.39065	+	0.531257i
$790$		0			0
$791$	41.0411	+	17.1542i	1.45925	+	0.609932i
$792$		0			0
$793$	3.42230	−	5.92761i	0.121530	−	0.210495i
$794$		0			0
$795$	7.69883	−	6.25492i	0.273049	−	0.221839i
$796$		0			0
$797$			20.3781i			0.721831i	0.932599	+	0.360915i	$0.117536\pi$
$797$			20.3781i			0.721831i	−0.932599	+	0.360915i	$0.882464\pi$
$798$		0			0
$799$	−39.3710			−1.39285
$800$		0			0
$801$	−2.59807	−	2.32422i	−0.0917981	−	0.0821221i
$802$		0			0
$803$	−1.41214	−	0.815301i	−0.0498335	−	0.0287714i
$804$		0			0
$805$	−27.2937	+	3.50430i	−0.961976	+	0.123510i
$806$		0			0
$807$	−32.5241	−	12.4248i	−1.14490	−	0.437374i
$808$		0			0
$809$	5.45505	−	3.14948i	0.191789	−	0.110730i	−0.401031	−	0.916065i	$-0.631348\pi$
$809$	5.45505	−	3.14948i	0.191789	−	0.110730i	0.592820	+	0.805335i	$0.298015\pi$
$810$		0			0
$811$	−9.32889			−0.327582			−0.163791	−	0.986495i	$-0.552372\pi$
$811$	−9.32889			−0.327582			−0.163791	+	0.986495i	$0.552372\pi$
$812$		0			0
$813$	0.499048	+	3.11839i	0.0175024	+	0.109367i
$814$		0			0
$815$	−16.5660	−	28.6932i	−0.580283	−	1.00508i
$816$		0			0
$817$	27.8769	+	16.0947i	0.975290	+	0.563084i
$818$		0			0
$819$	−18.0032	−	12.3729i	−0.629082	−	0.432345i
$820$		0			0
$821$	−21.8378	+	37.8241i	−0.762143	+	1.32007i	0.179600	+	0.983740i	$0.442520\pi$
$821$	−21.8378	+	37.8241i	−0.762143	+	1.32007i	−0.941744	+	0.336331i	$0.890814\pi$
$822$		0			0
$823$	−12.0388	−	20.8519i	−0.419647	−	0.726850i	0.576257	−	0.817269i	$-0.304513\pi$
$823$	−12.0388	−	20.8519i	−0.419647	−	0.726850i	−0.995904	+	0.0904188i	$0.971179\pi$
$824$		0			0
$825$	25.9906	−	4.15938i	0.904877	−	0.144811i
$826$		0			0
$827$	−40.9864			−1.42524			−0.712618	−	0.701553i	$-0.752490\pi$
$827$	−40.9864			−1.42524			−0.712618	+	0.701553i	$0.752490\pi$
$828$		0			0
$829$	−8.07095	−	13.9793i	−0.280316	−	0.485521i	0.691147	−	0.722714i	$-0.257106\pi$
$829$	−8.07095	−	13.9793i	−0.280316	−	0.485521i	−0.971462	+	0.237194i	$0.923772\pi$
$830$		0			0
$831$	21.3123	+	8.14170i	0.739315	+	0.282433i
$832$		0			0
$833$	−6.50627	+	23.6735i	−0.225429	+	0.820238i
$834$		0			0
$835$	19.1408	+	11.0509i	0.662393	+	0.382433i
$836$		0			0
$837$	−2.78310	+	4.33122i	−0.0961979	+	0.149709i
$838$		0			0
$839$	−40.8898			−1.41167			−0.705836	−	0.708375i	$-0.749429\pi$
$839$	−40.8898			−1.41167			−0.705836	+	0.708375i	$0.749429\pi$
$840$		0			0
$841$	−13.7566			−0.474367
$842$		0			0
$843$	20.6781	−	16.8000i	0.712193	−	0.578622i
$844$		0			0
$845$	13.3983	+	7.73551i	0.460915	+	0.266110i
$846$		0			0
$847$	20.1223	+	26.3987i	0.691411	+	0.907071i
$848$		0			0
$849$	5.74696	−	15.0436i	0.197235	−	0.516296i
$850$		0			0
$851$	−2.24298	−	3.88495i	−0.0768882	−	0.133174i
$852$		0			0
$853$	23.3041			0.797917			0.398958	−	0.916969i	$-0.369372\pi$
$853$	23.3041			0.797917			0.398958	+	0.916969i	$0.369372\pi$
$854$		0			0
$855$	−16.7924	−	51.1216i	−0.574290	−	1.74832i
$856$		0			0
$857$	−3.23327	−	5.60019i	−0.110447	−	0.191299i	0.805504	−	0.592591i	$-0.201895\pi$
$857$	−3.23327	−	5.60019i	−0.110447	−	0.191299i	−0.915950	+	0.401292i	$0.868561\pi$
$858$		0			0
$859$	−1.10393	+	1.91207i	−0.0376657	+	0.0652390i	−0.884244	−	0.467026i	$-0.845326\pi$
$859$	−1.10393	+	1.91207i	−0.0376657	+	0.0652390i	0.846578	+	0.532265i	$0.178659\pi$
$860$		0			0
$861$	9.26045	−	2.72699i	0.315595	−	0.0929356i
$862$		0			0
$863$	21.2034	+	12.2418i	0.721771	+	0.416715i	0.815404	−	0.578892i	$-0.196515\pi$
$863$	21.2034	+	12.2418i	0.721771	+	0.416715i	−0.0936330	+	0.995607i	$0.529848\pi$
$864$		0			0
$865$	−1.44962	−	2.51082i	−0.0492886	−	0.0853704i
$866$		0			0
$867$	8.03607	−	1.28604i	0.272919	−	0.0436764i
$868$		0			0
$869$	−27.1815			−0.922068
$870$		0			0
$871$	−13.8375	+	7.98908i	−0.468866	+	0.270700i
$872$		0			0
$873$	32.5807	+	6.81574i	1.10269	+	0.230678i
$874$		0			0
$875$	13.0049	+	5.43574i	0.439647	+	0.183761i
$876$		0			0
$877$	−15.3248	−	8.84776i	−0.517481	−	0.298768i	0.218422	−	0.975854i	$-0.429909\pi$
$877$	−15.3248	−	8.84776i	−0.517481	−	0.298768i	−0.735903	+	0.677087i	$0.763242\pi$
$878$		0			0
$879$	23.9906	−	19.4912i	0.809183	−	0.657422i
$880$		0			0
$881$	55.0445			1.85450			0.927249	−	0.374446i	$-0.122167\pi$
$881$	55.0445			1.85450			0.927249	+	0.374446i	$0.122167\pi$
$882$		0			0
$883$			49.3732i			1.66154i	0.556616	+	0.830770i	$0.312100\pi$
$883$			49.3732i			1.66154i	−0.556616	+	0.830770i	$0.687900\pi$
$884$		0			0
$885$	3.20429	+	3.94398i	0.107711	+	0.132575i
$886$		0			0
$887$	12.2514	−	21.2201i	0.411363	−	0.712502i	−0.583676	−	0.811987i	$-0.698386\pi$
$887$	12.2514	−	21.2201i	0.411363	−	0.712502i	0.995039	+	0.0994850i	$0.0317195\pi$
$888$		0			0
$889$	−15.9547	+	38.1716i	−0.535105	+	1.28023i
$890$		0			0
$891$	4.84434	+	43.4022i	0.162292	+	1.45403i
$892$		0			0
$893$	−35.3029	−	61.1465i	−1.18137	−	2.04619i
$894$		0			0
$895$		−	61.6540i		−	2.06087i
$896$		0			0
$897$	−2.74748	−	17.1681i	−0.0917357	−	0.573226i
$898$		0			0
$899$	−3.35007	+	1.93416i	−0.111731	+	0.0645079i
$900$		0			0
$901$	3.52194	−	6.10018i	0.117333	−	0.203226i
$902$		0			0
$903$	6.62485	+	22.4970i	0.220461	+	0.748654i
$904$		0			0
$905$	−23.1412	−	13.3606i	−0.769239	−	0.444120i
$906$		0			0
$907$	6.23747	−	3.60121i	0.207112	−	0.119576i	−0.392857	−	0.919600i	$-0.628513\pi$
$907$	6.23747	−	3.60121i	0.207112	−	0.119576i	0.599968	+	0.800024i	$0.295180\pi$
$908$		0			0
$909$	6.66211	+	20.2816i	0.220968	+	0.672697i
$910$		0			0
$911$			13.3025i			0.440730i	0.975417	+	0.220365i	$0.0707248\pi$
$911$			13.3025i			0.440730i	−0.975417	+	0.220365i	$0.929275\pi$
$912$		0			0
$913$	−0.580401	+	0.335095i	−0.0192085	+	0.0110900i
$914$		0			0
$915$	11.4746	+	4.38354i	0.379340	+	0.144915i
$916$		0			0
$917$	−21.2175	+	16.1729i	−0.700663	+	0.534077i
$918$		0			0
$919$	3.29521	−	5.70747i	0.108699	−	0.188272i	−0.806544	−	0.591173i	$-0.798665\pi$
$919$	3.29521	−	5.70747i	0.108699	−	0.188272i	0.915243	+	0.402901i	$0.131998\pi$
$920$		0			0
$921$	19.2938	+	23.7477i	0.635753	+	0.782512i
$922$		0			0
$923$		−	26.8417i		−	0.883505i
$924$		0			0
$925$		−	3.85188i		−	0.126649i
$926$		0			0
$927$	3.47644	−	3.88606i	0.114181	−	0.127635i
$928$		0			0
$929$	−6.17532	+	10.6960i	−0.202606	+	0.350923i	−0.949367	−	0.314169i	$-0.898274\pi$
$929$	−6.17532	+	10.6960i	−0.202606	+	0.350923i	0.746762	+	0.665092i	$0.231608\pi$
$930$		0			0
$931$	−42.6009	+	11.1226i	−1.39619	+	0.364529i
$932$		0			0
$933$	5.13143	−	13.4324i	0.167995	−	0.439756i
$934$		0			0
$935$	42.0298	−	24.2659i	1.37452	−	0.793580i
$936$		0			0
$937$			11.2161i			0.366413i	0.983074	+	0.183206i	$0.0586476\pi$
$937$			11.2161i			0.366413i	−0.983074	+	0.183206i	$0.941352\pi$
$938$		0			0
$939$	−7.29923	−	45.6105i	−0.238201	−	1.48844i
$940$		0			0
$941$	8.10816	−	4.68125i	0.264318	−	0.152604i	−0.361985	−	0.932184i	$-0.617901\pi$
$941$	8.10816	−	4.68125i	0.264318	−	0.152604i	0.626303	+	0.779580i	$0.284567\pi$
$942$		0			0
$943$	6.65399	+	3.84168i	0.216684	+	0.125102i
$944$		0			0
$945$	16.8201	−	35.4117i	0.547159	−	1.15194i
$946$		0			0
$947$	−19.4899	+	33.7574i	−0.633335	+	1.09697i	0.353530	+	0.935423i	$0.384981\pi$
$947$	−19.4899	+	33.7574i	−0.633335	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$948$		0			0
$949$	−0.800945	+	0.462426i	−0.0259998	+	0.0150110i
$950$		0			0
$951$	49.2896	−	7.88801i	1.59832	−	0.255786i
$952$		0			0
$953$		−	0.425521i		−	0.0137840i	−0.999976	−	0.00689198i	$-0.997806\pi$
$953$		−	0.425521i		−	0.0137840i	0.999976	−	0.00689198i	$-0.00219380\pi$
$954$		0			0
$955$	−12.6880	−	21.9763i	−0.410574	−	0.711135i
$956$		0			0
$957$	−11.7102	+	30.6534i	−0.378536	+	0.990882i
$958$		0			0
$959$	6.64124	+	51.7262i	0.214457	+	1.67033i
$960$		0			0
$961$	−15.0092	+	25.9966i	−0.484167	+	0.838601i
$962$		0			0
$963$	2.37910	+	2.12833i	0.0766656	+	0.0685846i
$964$		0			0
$965$		−	42.5337i		−	1.36921i
$966$		0			0
$967$	25.1685			0.809365			0.404682	−	0.914457i	$-0.367382\pi$
$967$	25.1685			0.809365			0.404682	+	0.914457i	$0.367382\pi$
$968$		0			0
$969$	−24.0941	−	29.6560i	−0.774014	−	0.952689i
$970$		0			0
$971$	11.2476	+	6.49383i	0.360954	+	0.208397i	0.669499	−	0.742813i	$-0.266509\pi$
$971$	11.2476	+	6.49383i	0.360954	+	0.208397i	−0.308545	+	0.951210i	$0.599842\pi$
$972$		0			0
$973$	−0.114104	+	0.272993i	−0.00365801	+	0.00875174i
$974$		0			0
$975$	5.32766	−	13.9461i	0.170622	−	0.446631i
$976$		0			0
$977$	33.4781	−	19.3286i	1.07106	−	0.618377i	0.142589	−	0.989782i	$-0.454457\pi$
$977$	33.4781	−	19.3286i	1.07106	−	0.618377i	0.928471	+	0.371405i	$0.121124\pi$
$978$		0			0
$979$	5.63844			0.180205
$980$		0			0
$981$	8.49578	+	25.8639i	0.271249	+	0.825770i
$982$		0			0
$983$	−24.2049	−	41.9241i	−0.772017	−	1.33717i	−0.936456	−	0.350785i	$-0.885915\pi$
$983$	−24.2049	−	41.9241i	−0.772017	−	1.33717i	0.164439	−	0.986387i	$-0.447419\pi$
$984$		0			0
$985$	6.77637	+	3.91234i	0.215913	+	0.124657i
$986$		0			0
$987$	12.0886	−	50.0005i	0.384783	−	1.59153i
$988$		0			0
$989$	−9.33285	+	16.1650i	−0.296767	+	0.514016i
$990$		0			0
$991$	−8.16959	−	14.1502i	−0.259516	−	0.449494i	0.706597	−	0.707617i	$-0.250230\pi$
$991$	−8.16959	−	14.1502i	−0.259516	−	0.449494i	−0.966112	+	0.258122i	$0.916896\pi$
$992$		0			0
$993$	0.709567	+	4.43385i	0.0225174	+	0.140704i
$994$		0			0
$995$	−66.4569			−2.10682
$996$		0			0
$997$	−4.94566	−	8.56614i	−0.156631	−	0.271292i	0.777021	−	0.629475i	$-0.216730\pi$
$997$	−4.94566	−	8.56614i	−0.156631	−	0.271292i	−0.933652	+	0.358182i	$0.883397\pi$
$998$		0			0
$999$	6.38373	+	0.303669i	0.201972	+	0.00960767i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bi.c.593.18		48
3.2	odd	2	inner	672.2.bi.c.593.17		48
4.3	odd	2		168.2.ba.c.5.4	✓	48
7.3	odd	6	inner	672.2.bi.c.17.8		48
8.3	odd	2		168.2.ba.c.5.11	yes	48
8.5	even	2	inner	672.2.bi.c.593.7		48
12.11	even	2		168.2.ba.c.5.21	yes	48
21.17	even	6	inner	672.2.bi.c.17.7		48
24.5	odd	2	inner	672.2.bi.c.593.8		48
24.11	even	2		168.2.ba.c.5.14	yes	48
28.3	even	6		168.2.ba.c.101.14	yes	48
56.3	even	6		168.2.ba.c.101.21	yes	48
56.45	odd	6	inner	672.2.bi.c.17.17		48
84.59	odd	6		168.2.ba.c.101.11	yes	48
168.59	odd	6		168.2.ba.c.101.4	yes	48
168.101	even	6	inner	672.2.bi.c.17.18		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.4	✓	48	4.3	odd	2
168.2.ba.c.5.11	yes	48	8.3	odd	2
168.2.ba.c.5.14	yes	48	24.11	even	2
168.2.ba.c.5.21	yes	48	12.11	even	2
168.2.ba.c.101.4	yes	48	168.59	odd	6
168.2.ba.c.101.11	yes	48	84.59	odd	6
168.2.ba.c.101.14	yes	48	28.3	even	6
168.2.ba.c.101.21	yes	48	56.3	even	6
672.2.bi.c.17.7		48	21.17	even	6	inner
672.2.bi.c.17.8		48	7.3	odd	6	inner
672.2.bi.c.17.17		48	56.45	odd	6	inner
672.2.bi.c.17.18		48	168.101	even	6	inner
672.2.bi.c.593.7		48	8.5	even	2	inner
672.2.bi.c.593.8		48	24.5	odd	2	inner
672.2.bi.c.593.17		48	3.2	odd	2	inner
672.2.bi.c.593.18		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09218 + 1.34430i) q^{3} +(-2.46958 - 1.42581i) q^{5} +(1.02032 - 2.44110i) q^{7} +(-0.614290 + 2.93643i) q^{9} +O(q^{10})\)	\(q+(1.09218 + 1.34430i) q^{3} +(-2.46958 - 1.42581i) q^{5} +(1.02032 - 2.44110i) q^{7} +(-0.614290 + 2.93643i) q^{9} +(-2.42621 - 4.20231i) q^{11} -2.75221 q^{13} +(-0.780502 - 4.87710i) q^{15} +(-1.75366 - 3.03743i) q^{17} +(3.14493 - 5.44717i) q^{19} +(4.39594 - 1.29450i) q^{21} +(3.15865 + 1.82365i) q^{23} +(1.56588 + 2.71219i) q^{25} +(-4.61837 + 2.38132i) q^{27} -3.90427 q^{29} +(0.858051 - 0.495396i) q^{31} +(2.99932 - 7.85123i) q^{33} +(-6.00030 + 4.57370i) q^{35} +(-1.06516 - 0.614970i) q^{37} +(-3.00591 - 3.69980i) q^{39} +2.10659 q^{41} +5.11768i q^{43} +(5.70384 - 6.37590i) q^{45} +(5.61268 - 9.72145i) q^{47} +(-4.91791 - 4.98138i) q^{49} +(2.16791 - 5.67487i) q^{51} +(1.00417 + 1.73927i) q^{53} +13.8373i q^{55} +(10.7575 - 1.72156i) q^{57} +(-0.890996 + 0.514417i) q^{59} +(-1.24347 + 2.15376i) q^{61} +(6.54135 + 4.49563i) q^{63} +(6.79681 + 3.92414i) q^{65} +(5.02777 - 2.90279i) q^{67} +(0.998281 + 6.23793i) q^{69} +9.75277i q^{71} +(0.291019 - 0.168020i) q^{73} +(-1.93577 + 5.06722i) q^{75} +(-12.7338 + 1.63491i) q^{77} +(2.80082 - 4.85116i) q^{79} +(-8.24530 - 3.60764i) q^{81} -0.138115i q^{83} +10.0016i q^{85} +(-4.26417 - 5.24852i) q^{87} +(-0.580993 + 1.00631i) q^{89} +(-2.80813 + 6.71841i) q^{91} +(1.60311 + 0.612418i) q^{93} +(-15.5333 + 8.96815i) q^{95} -11.0953i q^{97} +(13.8302 - 4.54296i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 4 * q^7 - 14 * q^9	\( 48 q + 4 q^{7} - 14 q^{9} - 4 q^{15} - 8 q^{25} - 48 q^{31} - 42 q^{33} + 8 q^{39} - 36 q^{49} + 4 q^{57} + 6 q^{63} - 36 q^{73} + 56 q^{79} + 42 q^{81} + 132 q^{87}+O(q^{100}) \) 48 * q + 4 * q^7 - 14 * q^9 - 4 * q^15 - 8 * q^25 - 48 * q^31 - 42 * q^33 + 8 * q^39 - 36 * q^49 + 4 * q^57 + 6 * q^63 - 36 * q^73 + 56 * q^79 + 42 * q^81 + 132 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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