LMFDB - Embedded newform 672.2.bi.c.17.7

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			17.7
Character	$\chi$	$=$	672.17
Dual form			672.2.bi.c.593.7

$q$-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 $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

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

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	$-0.446576\pi$
$5$	2.46958	−	1.42581i	1.10443	−	0.637643i	0.937381	+	0.348306i	$0.113243\pi$
$6$		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	−0.224701	−	0.974428i	$-0.572140\pi$
$11$	2.42621	−	4.20231i	0.731529	−	1.26705i	0.956230	−	0.292617i	$-0.0945262\pi$
$12$		0			0
$13$	2.75221			0.763326			0.381663	−	0.924302i	$-0.375351\pi$
$13$	2.75221			0.763326			0.381663	+	0.924302i	$0.375351\pi$
$14$		0			0
$15$	−0.780502	+	4.87710i	−0.201525	+	1.25926i
$16$		0			0
$17$	−1.75366	+	3.03743i	−0.425326	+	0.736686i	−0.996451	−	0.0841773i	$-0.973174\pi$
$17$	−1.75366	+	3.03743i	−0.425326	+	0.736686i	0.571125	+	0.820863i	$0.306507\pi$
$18$		0			0
$19$	−3.14493	−	5.44717i	−0.721496	−	1.24967i	−0.960400	−	0.278624i	$-0.910122\pi$
$19$	−3.14493	−	5.44717i	−0.721496	−	1.24967i	0.238905	−	0.971043i	$-0.423212\pi$
$20$		0			0
$21$	−4.39594	−	1.29450i	−0.959272	−	0.282484i
$22$		0			0
$23$	3.15865	−	1.82365i	0.658624	−	0.380257i	−0.133128	−	0.991099i	$-0.542502\pi$
$23$	3.15865	−	1.82365i	0.658624	−	0.380257i	0.791753	+	0.610842i	$0.209169\pi$
$24$		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	$-0.381922\pi$
$29$	3.90427			0.725005			0.362503	+	0.931983i	$0.381922\pi$
$30$		0			0
$31$	0.858051	+	0.495396i	0.154111	+	0.0889758i	0.575072	−	0.818103i	$-0.304974\pi$
$31$	0.858051	+	0.495396i	0.154111	+	0.0889758i	−0.420962	+	0.907078i	$0.638307\pi$
$32$		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	$-0.634430\pi$
$37$	1.06516	−	0.614970i	0.175111	−	0.101100i	0.584994	+	0.811038i	$0.301097\pi$
$38$		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	0.906645	+	0.421894i	$0.138635\pi$
$47$	5.61268	+	9.72145i	0.818693	+	1.41802i	−0.0879518	+	0.996125i	$0.528032\pi$
$48$		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	$-0.877379\pi$
$53$	−1.00417	+	1.73927i	−0.137933	+	0.238907i	0.788781	+	0.614674i	$0.210712\pi$
$54$		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	$-0.312000\pi$
$59$	0.890996	+	0.514417i	0.115998	+	0.0669714i	−0.440879	+	0.897567i	$0.645333\pi$
$60$		0			0
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	0.934584	−	0.355742i	$-0.115772\pi$
$61$	1.24347	+	2.15376i	0.159211	+	0.275761i	−0.775374	+	0.631503i	$0.782438\pi$
$62$		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	$-0.448727\pi$
$67$	−5.02777	−	2.90279i	−0.614240	−	0.354632i	−0.774623	+	0.632423i	$0.782060\pi$
$68$		0			0
$69$	−0.998281	+	6.23793i	−0.120179	+	0.750958i
$70$		0			0
$71$		−	9.75277i		−	1.15744i	−0.815526	−	0.578720i	$-0.803552\pi$
$71$		−	9.75277i		−	1.15744i	0.815526	−	0.578720i	$-0.196448\pi$
$72$		0			0
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	0.516934	−	0.856025i	$-0.327073\pi$
$73$	0.291019	+	0.168020i	0.0340612	+	0.0196652i	−0.482873	+	0.875691i	$0.660407\pi$
$74$		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	0.979462	−	0.201627i	$-0.0646230\pi$
$79$	2.80082	+	4.85116i	0.315117	+	0.545798i	−0.664346	+	0.747426i	$0.731290\pi$
$80$		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	0.833589	−	0.552385i	$-0.186282\pi$
$89$	−0.580993	−	1.00631i	−0.0615852	−	0.106669i	−0.895174	+	0.445717i	$0.852949\pi$
$90$		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	$0.190461\pi$
$97$			11.0953i			1.12656i	−0.826266	+	0.563280i	$0.809539\pi$
$98$		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	$-0.448522\pi$
$101$	−6.16256	−	3.55796i	−0.613198	−	0.354030i	−0.774216	+	0.632922i	$0.781856\pi$
$102$		0			0
$103$	−1.50519	+	0.869021i	−0.148311	+	0.0856271i	−0.572319	−	0.820031i	$-0.693956\pi$
$103$	−1.50519	+	0.869021i	−0.148311	+	0.0856271i	0.424008	+	0.905658i	$0.360623\pi$
$104$		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	$-0.183046\pi$
$107$	−0.532028	−	0.921500i	−0.0514331	−	0.0890847i	−0.890596	+	0.454796i	$0.849712\pi$
$108$		0			0
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	0.0739489	−	0.997262i	$-0.476440\pi$
$109$	−7.85874	−	4.53725i	−0.752731	−	0.434589i	−0.826680	+	0.562673i	$0.809773\pi$
$110$		0			0
$111$	−0.336640	+	2.10355i	−0.0319524	+	0.199660i
$112$		0			0
$113$		−	16.8126i		−	1.58159i	−0.612078	−	0.790797i	$-0.709666\pi$
$113$		−	16.8126i		−	1.58159i	0.612078	−	0.790797i	$-0.290334\pi$
$114$		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	$-0.521467\pi$
$131$	8.73260	−	5.04177i	0.762971	−	0.440502i	0.830361	+	0.557225i	$0.188134\pi$
$132$		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	−0.459485	−	0.888185i	$-0.651966\pi$
$137$	−17.0704	−	9.85557i	−1.45842	−	0.842019i	−0.998934	+	0.0461669i	$0.985299\pi$
$138$		0			0
$139$	0.111832			0.00948546			0.00474273	−	0.999989i	$-0.498490\pi$
$139$	0.111832			0.00948546			0.00474273	+	0.999989i	$0.498490\pi$
$140$		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	$-0.315400\pi$
$149$	−5.49834	−	9.52340i	−0.450441	−	0.780187i	−0.998413	+	0.0563094i	$0.982067\pi$
$150$		0			0
$151$	−4.16727	+	7.21792i	−0.339127	+	0.587386i	−0.984269	−	0.176677i	$-0.943465\pi$
$151$	−4.16727	+	7.21792i	−0.339127	+	0.587386i	0.645141	+	0.764063i	$0.276798\pi$
$152$		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	$-0.975780\pi$
$157$	−5.42198	+	9.39114i	−0.432721	+	0.749495i	0.564386	+	0.825511i	$0.309113\pi$
$158$		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	$-0.817035\pi$
$163$	−10.0621	+	5.80934i	−0.788122	+	0.455022i	0.0511792	+	0.998689i	$0.483702\pi$
$164$		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	$-0.678972\pi$
$173$	−0.880487	+	0.508349i	−0.0669422	+	0.0386491i	0.466155	+	0.884703i	$0.345639\pi$
$174$		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	0.106244	+	0.994340i	$0.466117\pi$
$179$	−10.8103	+	18.7240i	−0.808002	+	1.39950i	−0.914246	+	0.405160i	$0.867216\pi$
$180$		0			0
$181$	−9.37049			−0.696503			−0.348251	−	0.937401i	$-0.613224\pi$
$181$	−9.37049			−0.696503			−0.348251	+	0.937401i	$0.613224\pi$
$182$		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	−0.194565	−	0.980890i	$-0.562329\pi$
$191$	7.70657	−	4.44939i	0.557628	−	0.321947i	0.752193	+	0.658943i	$0.228996\pi$
$192$		0			0
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	−0.462249	−	0.886750i	$-0.652957\pi$
$193$	7.45779	−	12.9173i	0.536824	−	0.929806i	0.999073	−	0.0430556i	$-0.0137093\pi$
$194$		0			0
$195$	−2.14811	+	13.4228i	−0.153829	+	0.961228i
$196$		0			0
$197$	2.74394			0.195497			0.0977487	−	0.995211i	$-0.468836\pi$
$197$	2.74394			0.195497			0.0977487	+	0.995211i	$0.468836\pi$
$198$		0			0
$199$	20.1826	+	11.6525i	1.43071	+	0.826021i	0.997175	−	0.0751162i	$-0.0239328\pi$
$199$	20.1826	+	11.6525i	1.43071	+	0.826021i	0.433535	+	0.901137i	$0.357266\pi$
$200$		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	$0.125430\pi$
$223$			11.4666i			0.767860i	−0.923362	+	0.383930i	$0.874570\pi$
$224$		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	$-0.581910\pi$
$227$	−18.3699	−	10.6059i	−1.21926	−	0.703938i	−0.964759	+	0.263136i	$0.915243\pi$
$228$		0			0
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	0.901078	−	0.433658i	$-0.142777\pi$
$229$	1.13465	+	1.96528i	0.0749800	+	0.129869i	−0.826098	+	0.563527i	$0.809444\pi$
$230$		0			0
$231$	−16.1054	+	15.3324i	−1.05965	+	1.00880i
$232$		0			0
$233$	22.5624	−	13.0264i	1.47811	−	0.853389i	0.478420	−	0.878131i	$-0.341210\pi$
$233$	22.5624	−	13.0264i	1.47811	−	0.853389i	0.999694	+	0.0247423i	$0.00787651\pi$
$234$		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	$-0.913184\pi$
$239$		−	8.32874i		−	0.538742i	0.963037	−	0.269371i	$-0.0868157\pi$
$240$		0			0
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	0.687358	−	0.726319i	$-0.258771\pi$
$241$	6.24112	+	3.60331i	0.402026	+	0.232110i	−0.285332	+	0.958429i	$0.592104\pi$
$242$		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	0.758364	+	0.651832i	$0.225999\pi$
$257$	15.1284	+	26.2032i	0.943685	+	1.63451i	0.185321	+	0.982678i	$0.440668\pi$
$258$		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	0.978517	−	0.206166i	$-0.0660986\pi$
$263$	20.9078	+	12.0711i	1.28923	+	0.744338i	0.310714	+	0.950504i	$0.399432\pi$
$264$		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	$-0.123377\pi$
$269$	17.4083	+	10.0507i	1.06140	+	0.612800i	0.135581	+	0.990766i	$0.456710\pi$
$270$		0			0
$271$	1.57903	−	0.911656i	0.0959195	−	0.0553791i	−0.451273	−	0.892386i	$-0.649030\pi$
$271$	1.57903	−	0.911656i	0.0959195	−	0.0553791i	0.547192	+	0.837007i	$0.315697\pi$
$272$		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	$-0.462836\pi$
$277$	−11.4072	−	6.58598i	−0.685395	−	0.395713i	−0.801885	+	0.597479i	$0.796169\pi$
$278$		0			0
$279$	0.927606	−	2.82393i	0.0555343	−	0.169064i
$280$		0			0
$281$			15.3821i			0.917618i	0.888535	+	0.458809i	$0.151724\pi$
$281$			15.3821i			0.917618i	−0.888535	+	0.458809i	$0.848276\pi$
$282$		0			0
$283$	4.64882	−	8.05200i	0.276344	−	0.478641i	−0.694129	−	0.719850i	$-0.744210\pi$
$283$	4.64882	−	8.05200i	0.276344	−	0.478641i	0.970473	+	0.241209i	$0.0775438\pi$
$284$		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	$-0.668179\pi$
$307$	−17.6654			−1.00822			−0.504110	+	0.863640i	$0.668179\pi$
$308$		0			0
$309$	0.475709	−	2.97255i	0.0270622	−	0.169103i
$310$		0			0
$311$	−4.15091	+	7.18958i	−0.235376	+	0.407684i	−0.959382	−	0.282110i	$-0.908966\pi$
$311$	−4.15091	+	7.18958i	−0.235376	+	0.407684i	0.724006	+	0.689794i	$0.242299\pi$
$312$		0			0
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.981330	−	0.192332i	$-0.938395\pi$
$313$	−23.0954	+	13.3342i	−1.30543	+	0.753691i	−0.324101	+	0.946023i	$0.605062\pi$
$314$		0			0
$315$	9.74446	−	20.4291i	0.549038	−	1.15105i
$316$		0			0
$317$	−14.4097	−	24.9584i	−0.809331	−	1.40180i	−0.913328	−	0.407225i	$-0.866496\pi$
$317$	−14.4097	−	24.9584i	−0.809331	−	1.40180i	0.103996	−	0.994578i	$-0.466837\pi$
$318$		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	$-0.689365\pi$
$331$	−2.24514	+	1.29623i	−0.123404	+	0.0712472i	0.437027	+	0.899448i	$0.356031\pi$
$332$		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	$-0.960330\pi$
$347$	−7.23643	+	12.5339i	−0.388472	+	0.672853i	0.603772	+	0.797157i	$0.293664\pi$
$348$		0			0
$349$	22.8018			1.22055			0.610275	−	0.792189i	$-0.291059\pi$
$349$	22.8018			1.22055			0.610275	+	0.792189i	$0.291059\pi$
$350$		0			0
$351$	12.7107	+	6.55390i	0.678448	+	0.349821i
$352$		0			0
$353$	−2.06060	+	3.56907i	−0.109675	+	0.189962i	−0.915639	−	0.402003i	$-0.868314\pi$
$353$	−2.06060	+	3.56907i	−0.109675	+	0.189962i	0.805964	+	0.591965i	$0.201648\pi$
$354$		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	−0.736617	−	0.676310i	$-0.763578\pi$
$359$	−9.83790	+	5.67992i	−0.519225	+	0.299775i	0.217393	+	0.976084i	$0.430245\pi$
$360$		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	−0.291755	−	0.956493i	$-0.594239\pi$
$367$	−24.2527	−	14.0023i	−1.26598	−	0.730914i	−0.974225	+	0.225580i	$0.927572\pi$
$368$		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	$-0.967713\pi$
$373$	−27.1273	+	15.6619i	−1.40460	+	0.810944i	−0.409737	+	0.912204i	$0.634379\pi$
$374$		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	0.983738	+	0.179607i	$0.0574826\pi$
$383$	12.6701	+	21.9453i	0.647413	+	1.12135i	−0.336325	+	0.941746i	$0.609184\pi$
$384$		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	$-0.869057\pi$
$389$	−2.20886	+	3.82586i	−0.111994	+	0.193979i	0.804580	+	0.593844i	$0.202390\pi$
$390$		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	$-0.0348430\pi$
$397$	8.01775	+	13.8871i	0.402399	+	0.696976i	−0.591616	+	0.806220i	$0.701510\pi$
$398$		0			0
$399$	6.77352	+	28.0165i	0.339100	+	1.40258i
$400$		0			0
$401$	−6.53545	+	3.77324i	−0.326365	+	0.188427i	−0.654226	−	0.756299i	$-0.727006\pi$
$401$	−6.53545	+	3.77324i	−0.326365	+	0.188427i	0.327861	+	0.944726i	$0.393672\pi$
$402$		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	−0.243013	−	0.970023i	$-0.578136\pi$
$409$	−24.3612	−	14.0650i	−1.20458	−	0.695467i	−0.961571	+	0.274556i	$0.911469\pi$
$410$		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	0.729248	−	0.684249i	$-0.239870\pi$
$431$	10.4072	+	6.00858i	0.501296	+	0.289423i	−0.227953	+	0.973672i	$0.573203\pi$
$432$		0			0
$433$		−	35.6343i		−	1.71247i	−0.516583	−	0.856237i	$-0.672796\pi$
$433$		−	35.6343i		−	1.71247i	0.516583	−	0.856237i	$-0.327204\pi$
$434$		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	−0.194240	−	0.980954i	$-0.562224\pi$
$439$	11.6950	−	6.75210i	0.558171	−	0.322260i	0.752411	+	0.658694i	$0.228891\pi$
$440$		0			0
$441$	17.6485	+	11.3811i	0.840406	+	0.541957i
$442$		0			0
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	−0.997579	−	0.0695416i	$-0.977846\pi$
$443$	−11.7659	−	20.3791i	−0.559014	−	0.968241i	0.438565	−	0.898700i	$-0.355487\pi$
$444$		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	$-0.742883\pi$
$449$		−	30.6292i		−	1.44548i	0.691120	−	0.722740i	$-0.257117\pi$
$450$		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	0.969286	−	0.245935i	$-0.0790950\pi$
$457$	5.80736	+	10.0587i	0.271657	+	0.470524i	−0.697629	+	0.716459i	$0.745762\pi$
$458$		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	$-0.953900\pi$
$467$	−29.3749	+	16.9596i	−1.35931	+	0.784797i	−0.369778	+	0.929120i	$0.620566\pi$
$468$		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	0.106344	+	0.994329i	$0.466086\pi$
$479$	−17.6827	+	30.6273i	−0.807943	+	1.39940i	−0.914286	+	0.405068i	$0.867248\pi$
$480$		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	0.206634	+	0.978418i	$0.433749\pi$
$487$	−16.4191	+	28.4386i	−0.744018	+	1.28868i	−0.950652	+	0.310259i	$0.899584\pi$
$488$		0			0
$489$	3.18008	−	19.8713i	0.143808	−	0.898610i
$490$		0			0
$491$	−22.5295			−1.01674			−0.508371	−	0.861138i	$-0.669752\pi$
$491$	−22.5295			−1.01674			−0.508371	+	0.861138i	$0.669752\pi$
$492$		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	$-0.572226\pi$
$499$	11.3117	−	6.53084i	0.506383	−	0.292361i	0.731346	+	0.682007i	$0.238893\pi$
$500$		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	$-0.912534\pi$
$509$	−27.2704	+	15.7446i	−1.20874	+	0.697866i	−0.246255	+	0.969205i	$0.579200\pi$
$510$		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	−0.922981	−	0.384845i	$-0.874255\pi$
$521$	−2.92633	+	5.06856i	−0.128205	+	0.222058i	0.794776	+	0.606903i	$0.207588\pi$
$522$		0			0
$523$	−9.81038	−	16.9921i	−0.428978	−	0.743012i	0.567805	−	0.823163i	$-0.307793\pi$
$523$	−9.81038	−	16.9921i	−0.428978	−	0.743012i	−0.996783	+	0.0801516i	$0.974460\pi$
$524$		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	0.527287	−	0.849687i	$-0.323209\pi$
$541$	35.5120	−	20.5029i	1.52678	−	0.881488i	0.999494	−	0.0318007i	$-0.0101242\pi$
$542$		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	0.0909180	+	0.995858i	$0.471020\pi$
$557$	−19.2814	+	33.3964i	−0.816980	+	1.41505i	−0.907898	+	0.419192i	$0.862313\pi$
$558$		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	$-0.409632\pi$
$563$	−9.75701	−	5.63321i	−0.411209	−	0.237411i	−0.691309	+	0.722559i	$0.742966\pi$
$564$		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	−0.941760	−	0.336286i	$-0.890829\pi$
$569$	−26.7497	+	15.4440i	−1.12141	+	0.647445i	−0.179648	+	0.983731i	$0.557496\pi$
$570$		0			0
$571$	−6.49082	−	3.74748i	−0.271633	−	0.156827i	0.357997	−	0.933723i	$-0.383460\pi$
$571$	−6.49082	−	3.74748i	−0.271633	−	0.156827i	−0.629629	+	0.776896i	$0.716793\pi$
$572$		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	0.832184	−	0.554500i	$-0.187091\pi$
$577$	18.4495	+	10.6518i	0.768064	+	0.443442i	−0.0641196	+	0.997942i	$0.520424\pi$
$578$		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	0.944207	−	0.329353i	$-0.106831\pi$
$593$	4.55071	+	7.88206i	0.186875	+	0.323678i	−0.757332	+	0.653031i	$0.773497\pi$
$594$		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	−0.999021	−	0.0442488i	$-0.985911\pi$
$599$	−37.6136	−	21.7162i	−1.53685	−	0.887302i	−0.537831	−	0.843053i	$-0.680756\pi$
$600$		0			0
$601$		−	15.5284i		−	0.633415i	−0.948523	−	0.316708i	$-0.897423\pi$
$601$		−	15.5284i		−	0.633415i	0.948523	−	0.316708i	$-0.102577\pi$
$602$		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	−0.520480	−	0.853874i	$-0.674247\pi$
$607$	−1.01612	+	0.586656i	−0.0412430	+	0.0238116i	0.479237	+	0.877686i	$0.340914\pi$
$608$		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	$-0.0198795\pi$
$613$	35.7276	+	20.6273i	1.44302	+	0.833131i	0.444974	+	0.895543i	$0.353213\pi$
$614$		0			0
$615$	−1.64420	+	10.2741i	−0.0663006	+	0.414291i
$616$		0			0
$617$		−	15.3232i		−	0.616887i	−0.951243	−	0.308444i	$-0.900192\pi$
$617$		−	15.3232i		−	0.616887i	0.951243	−	0.308444i	$-0.0998081\pi$
$618$		0			0
$619$	−7.95796	+	13.7836i	−0.319857	+	0.554009i	−0.980458	−	0.196728i	$-0.936968\pi$
$619$	−7.95796	+	13.7836i	−0.319857	+	0.554009i	0.660601	+	0.750738i	$0.270302\pi$
$620$		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	0.354691	−	0.934984i	$-0.384586\pi$
$641$	−7.03036	−	4.05898i	−0.277683	−	0.160320i	−0.632374	+	0.774663i	$0.717919\pi$
$642$		0			0
$643$	21.5611			0.850285			0.425143	−	0.905126i	$-0.360224\pi$
$643$	21.5611			0.850285			0.425143	+	0.905126i	$0.360224\pi$
$644$		0			0
$645$	−24.9595	−	3.99436i	−0.982778	−	0.157278i
$646$		0			0
$647$	19.5173	−	33.8049i	0.767304	−	1.32901i	−0.171716	−	0.985147i	$-0.554931\pi$
$647$	19.5173	−	33.8049i	0.767304	−	1.32901i	0.939020	−	0.343863i	$-0.111736\pi$
$648$		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	$-0.275125\pi$
$653$	−8.53952	−	14.7909i	−0.334177	−	0.578812i	−0.983326	+	0.181849i	$0.941792\pi$
$654$		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	$-0.456527\pi$
$659$	6.99022			0.272300			0.136150	+	0.990688i	$0.456527\pi$
$660$		0			0
$661$	−23.0740	+	39.9653i	−0.897474	+	1.55447i	−0.0667617	+	0.997769i	$0.521267\pi$
$661$	−23.0740	+	39.9653i	−0.897474	+	1.55447i	−0.830712	+	0.556702i	$0.812067\pi$
$662$		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	$-0.727291\pi$
$677$	−8.53140	+	4.92561i	−0.327888	+	0.189306i	0.327015	+	0.945019i	$0.393957\pi$
$678$		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	−0.168839	−	0.985644i	$-0.554002\pi$
$683$	20.1018	−	34.8173i	0.769173	−	1.33225i	0.938012	−	0.346603i	$-0.112665\pi$
$684$		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	0.981305	+	0.192458i	$0.0616460\pi$
$691$	17.2791	+	29.9282i	0.657326	+	1.13852i	−0.323979	+	0.946064i	$0.605021\pi$
$692$		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	$-0.310802\pi$
$701$	29.6534			1.11999			0.559997	+	0.828495i	$0.310802\pi$
$702$		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	$-0.598411\pi$
$709$	9.81381	−	5.66601i	0.368565	−	0.212791i	0.672832	+	0.739796i	$0.265078\pi$
$710$		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	0.662545	−	0.749022i	$-0.269476\pi$
$719$	−8.51080	−	14.7411i	−0.317399	−	0.549752i	−0.979945	+	0.199270i	$0.936143\pi$
$720$		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	$-0.714718\pi$
$727$		−	42.1153i		−	1.56197i	0.624550	−	0.780985i	$-0.285282\pi$
$728$		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	0.947026	+	0.321158i	$0.104072\pi$
$733$	20.3500	+	35.2472i	0.751644	+	1.30189i	−0.195382	+	0.980727i	$0.562595\pi$
$734$		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	$-0.281473\pi$
$739$	7.63741	+	4.40946i	0.280947	+	0.162205i	−0.352905	+	0.935659i	$0.614806\pi$
$740$		0			0
$741$	29.6068	+	4.73810i	1.08763	+	0.174058i
$742$		0			0
$743$			16.3412i			0.599502i	0.954017	+	0.299751i	$0.0969036\pi$
$743$			16.3412i			0.599502i	−0.954017	+	0.299751i	$0.903096\pi$
$744$		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	0.731091	−	0.682280i	$-0.239011\pi$
$751$	−6.17492	−	10.6953i	−0.225326	−	0.390276i	−0.956417	+	0.292004i	$0.905678\pi$
$752$		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	−0.997317	−	0.0732037i	$-0.976678\pi$
$761$	−15.5050	−	26.8554i	−0.562055	−	0.973507i	0.435262	−	0.900304i	$-0.356656\pi$
$762$		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	$0.276935\pi$
$769$			42.3916i			1.52868i	−0.644813	+	0.764340i	$0.723065\pi$
$770$		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	$-0.314263\pi$
$773$	2.88336	+	1.66471i	0.103707	+	0.0598754i	−0.447249	+	0.894409i	$0.647596\pi$
$774$		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	$-0.964822\pi$
$787$	−11.2617	+	19.5059i	−0.401437	+	0.695309i	0.592463	+	0.805598i	$0.298156\pi$
$788$		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	0.592820	−	0.805335i	$-0.298015\pi$
$809$	5.45505	+	3.14948i	0.191789	+	0.110730i	−0.401031	+	0.916065i	$0.631348\pi$
$810$		0			0
$811$	9.32889			0.327582			0.163791	−	0.986495i	$-0.447628\pi$
$811$	9.32889			0.327582			0.163791	+	0.986495i	$0.447628\pi$
$812$		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	0.941744	+	0.336331i	$0.109186\pi$
$821$	21.8378	+	37.8241i	0.762143	+	1.32007i	−0.179600	+	0.983740i	$0.557480\pi$
$822$		0			0
$823$	−12.0388	+	20.8519i	−0.419647	+	0.726850i	−0.995904	−	0.0904188i	$-0.971179\pi$
$823$	−12.0388	+	20.8519i	−0.419647	+	0.726850i	0.576257	+	0.817269i	$0.304513\pi$
$824$		0			0
$825$	25.9906	+	4.15938i	0.904877	+	0.144811i
$826$		0			0
$827$	40.9864			1.42524			0.712618	−	0.701553i	$-0.247510\pi$
$827$	40.9864			1.42524			0.712618	+	0.701553i	$0.247510\pi$
$828$		0			0
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	−0.691147	−	0.722714i	$-0.742894\pi$
$829$	8.07095	−	13.9793i	0.280316	−	0.485521i	0.971462	+	0.237194i	$0.0762275\pi$
$830$		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	$-0.630628\pi$
$853$	−23.3041			−0.797917			−0.398958	+	0.916969i	$0.630628\pi$
$854$		0			0
$855$	−16.7924	+	51.1216i	−0.574290	+	1.74832i
$856$		0			0
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	−0.915950	−	0.401292i	$-0.868561\pi$
$857$	−3.23327	+	5.60019i	−0.110447	+	0.191299i	0.805504	+	0.592591i	$0.201895\pi$
$858$		0			0
$859$	1.10393	+	1.91207i	0.0376657	+	0.0652390i	0.884244	−	0.467026i	$-0.154674\pi$
$859$	1.10393	+	1.91207i	0.0376657	+	0.0652390i	−0.846578	+	0.532265i	$0.821341\pi$
$860$		0			0
$861$	−9.26045	−	2.72699i	−0.315595	−	0.0929356i
$862$		0			0
$863$	21.2034	−	12.2418i	0.721771	−	0.416715i	−0.0936330	−	0.995607i	$-0.529848\pi$
$863$	21.2034	−	12.2418i	0.721771	−	0.416715i	0.815404	+	0.578892i	$0.196515\pi$
$864$		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	$-0.570091\pi$
$877$	15.3248	−	8.84776i	0.517481	−	0.298768i	0.735903	+	0.677087i	$0.236758\pi$
$878$		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	0.995039	−	0.0994850i	$-0.0317195\pi$
$887$	12.2514	+	21.2201i	0.411363	+	0.712502i	−0.583676	+	0.811987i	$0.698386\pi$
$888$		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	$-0.371487\pi$
$907$	−6.23747	−	3.60121i	−0.207112	−	0.119576i	−0.599968	+	0.800024i	$0.704820\pi$
$908$		0			0
$909$	−6.66211	+	20.2816i	−0.220968	+	0.672697i
$910$		0			0
$911$		−	13.3025i		−	0.440730i	−0.975417	−	0.220365i	$-0.929275\pi$
$911$		−	13.3025i		−	0.440730i	0.975417	−	0.220365i	$-0.0707248\pi$
$912$		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	0.915243	−	0.402901i	$-0.131998\pi$
$919$	3.29521	+	5.70747i	0.108699	+	0.188272i	−0.806544	+	0.591173i	$0.798665\pi$
$920$		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	0.746762	−	0.665092i	$-0.231608\pi$
$929$	−6.17532	−	10.6960i	−0.202606	−	0.350923i	−0.949367	+	0.314169i	$0.898274\pi$
$930$		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	$-0.941352\pi$
$937$		−	11.2161i		−	0.366413i	0.983074	−	0.183206i	$-0.0586476\pi$
$938$		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	$-0.382099\pi$
$941$	−8.10816	−	4.68125i	−0.264318	−	0.152604i	−0.626303	+	0.779580i	$0.715433\pi$
$942$		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	0.986865	+	0.161546i	$0.0516480\pi$
$947$	19.4899	+	33.7574i	0.633335	+	1.09697i	−0.353530	+	0.935423i	$0.615019\pi$
$948$		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	$0.00219380\pi$
$953$			0.425521i			0.0137840i	−0.999976	+	0.00689198i	$0.997806\pi$
$954$		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	$-0.733491\pi$
$971$	−11.2476	+	6.49383i	−0.360954	+	0.208397i	0.308545	+	0.951210i	$0.400158\pi$
$972$		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	0.928471	−	0.371405i	$-0.121124\pi$
$977$	33.4781	+	19.3286i	1.07106	+	0.618377i	0.142589	+	0.989782i	$0.454457\pi$
$978$		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	0.164439	+	0.986387i	$0.447419\pi$
$983$	−24.2049	+	41.9241i	−0.772017	+	1.33717i	−0.936456	+	0.350785i	$0.885915\pi$
$984$		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	−0.966112	−	0.258122i	$-0.916896\pi$
$991$	−8.16959	+	14.1502i	−0.259516	+	0.449494i	0.706597	+	0.707617i	$0.250230\pi$
$992$		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	$-0.783270\pi$
$997$	4.94566	−	8.56614i	0.156631	−	0.271292i	0.933652	+	0.358182i	$0.116603\pi$
$998$		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.17.7		48
3.2	odd	2	inner	672.2.bi.c.17.8		48
4.3	odd	2		168.2.ba.c.101.11	yes	48
7.5	odd	6	inner	672.2.bi.c.593.17		48
8.3	odd	2		168.2.ba.c.101.4	yes	48
8.5	even	2	inner	672.2.bi.c.17.18		48
12.11	even	2		168.2.ba.c.101.14	yes	48
21.5	even	6	inner	672.2.bi.c.593.18		48
24.5	odd	2	inner	672.2.bi.c.17.17		48
24.11	even	2		168.2.ba.c.101.21	yes	48
28.19	even	6		168.2.ba.c.5.21	yes	48
56.5	odd	6	inner	672.2.bi.c.593.8		48
56.19	even	6		168.2.ba.c.5.14	yes	48
84.47	odd	6		168.2.ba.c.5.4	✓	48
168.5	even	6	inner	672.2.bi.c.593.7		48
168.131	odd	6		168.2.ba.c.5.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.4	✓	48	84.47	odd	6
168.2.ba.c.5.11	yes	48	168.131	odd	6
168.2.ba.c.5.14	yes	48	56.19	even	6
168.2.ba.c.5.21	yes	48	28.19	even	6
168.2.ba.c.101.4	yes	48	8.3	odd	2
168.2.ba.c.101.11	yes	48	4.3	odd	2
168.2.ba.c.101.14	yes	48	12.11	even	2
168.2.ba.c.101.21	yes	48	24.11	even	2
672.2.bi.c.17.7		48	1.1	even	1	trivial
672.2.bi.c.17.8		48	3.2	odd	2	inner
672.2.bi.c.17.17		48	24.5	odd	2	inner
672.2.bi.c.17.18		48	8.5	even	2	inner
672.2.bi.c.593.7		48	168.5	even	6	inner
672.2.bi.c.593.8		48	56.5	odd	6	inner
672.2.bi.c.593.17		48	7.5	odd	6	inner
672.2.bi.c.593.18		48	21.5	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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
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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