LMFDB - Embedded newform 1170.2.w.h.307.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(307,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.w (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,-14,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2 x^{12} + 4 x^{11} + 112 x^{10} - 208 x^{9} + 200 x^{8} + 392 x^{7} + 1708 x^{6} + \cdots + 8 $ x^14 - 2x^13 + 2x^12 + 4x^11 + 112x^10 - 208x^9 + 200x^8 + 392x^7 + 1708x^6 - 1744x^5 + 872x^4 - 80x^3 + 4x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$-0.202596 - 0.202596i$ of defining polynomial
Character	$\chi$	$=$	1170.307
Dual form			1170.2.w.h.343.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.202596 - 2.22687i) q^{5} -0.902312 q^{7} +1.00000i q^{8} +(-2.22687 + 0.202596i) q^{10} +(2.50645 - 2.50645i) q^{11} +(3.59129 - 0.320354i) q^{13} +0.902312i q^{14} +1.00000 q^{16} +(2.87250 - 2.87250i) q^{17} +(-0.280927 + 0.280927i) q^{19} +(0.202596 + 2.22687i) q^{20} +(-2.50645 - 2.50645i) q^{22} +(0.298938 + 0.298938i) q^{23} +(-4.91791 + 0.902312i) q^{25} +(-0.320354 - 3.59129i) q^{26} +0.902312 q^{28} -2.15343i q^{29} +(-2.62842 - 2.62842i) q^{31} -1.00000i q^{32} +(-2.87250 - 2.87250i) q^{34} +(0.182805 + 2.00933i) q^{35} -7.91467 q^{37} +(0.280927 + 0.280927i) q^{38} +(2.22687 - 0.202596i) q^{40} +(1.01801 + 1.01801i) q^{41} +(-5.17770 - 5.17770i) q^{43} +(-2.50645 + 2.50645i) q^{44} +(0.298938 - 0.298938i) q^{46} -10.2383 q^{47} -6.18583 q^{49} +(0.902312 + 4.91791i) q^{50} +(-3.59129 + 0.320354i) q^{52} +(7.95152 - 7.95152i) q^{53} +(-6.08935 - 5.07375i) q^{55} -0.902312i q^{56} -2.15343 q^{58} +(-1.49031 - 1.49031i) q^{59} +7.45681 q^{61} +(-2.62842 + 2.62842i) q^{62} -1.00000 q^{64} +(-1.44097 - 7.93244i) q^{65} +3.72577i q^{67} +(-2.87250 + 2.87250i) q^{68} +(2.00933 - 0.182805i) q^{70} +(8.48521 + 8.48521i) q^{71} +3.28746i q^{73} +7.91467i q^{74} +(0.280927 - 0.280927i) q^{76} +(-2.26160 + 2.26160i) q^{77} -4.97419i q^{79} +(-0.202596 - 2.22687i) q^{80} +(1.01801 - 1.01801i) q^{82} -1.83873 q^{83} +(-6.97864 - 5.81472i) q^{85} +(-5.17770 + 5.17770i) q^{86} +(2.50645 + 2.50645i) q^{88} +(3.05788 + 3.05788i) q^{89} +(-3.24047 + 0.289060i) q^{91} +(-0.298938 - 0.298938i) q^{92} +10.2383i q^{94} +(0.682504 + 0.568674i) q^{95} +2.01625i q^{97} +6.18583i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{4} + 2 q^{5} + 4 q^{13} + 14 q^{16} - 14 q^{17} - 12 q^{19} - 2 q^{20} - 10 q^{25} - 6 q^{26} + 12 q^{31} + 14 q^{34} - 12 q^{35} + 20 q^{37} + 12 q^{38} + 2 q^{41} + 8 q^{47} + 14 q^{49} - 4 q^{52}+ \cdots - 24 q^{95}+O(q^{100}) $ 14 * q - 14 * q^4 + 2 * q^5 + 4 * q^13 + 14 * q^16 - 14 * q^17 - 12 * q^19 - 2 * q^20 - 10 * q^25 - 6 * q^26 + 12 * q^31 + 14 * q^34 - 12 * q^35 + 20 * q^37 + 12 * q^38 + 2 * q^41 + 8 * q^47 + 14 * q^49 - 4 * q^52 - 6 * q^53 + 32 * q^55 + 16 * q^58 + 16 * q^59 + 24 * q^61 + 12 * q^62 - 14 * q^64 + 4 * q^65 + 14 * q^68 - 4 * q^70 + 24 * q^71 + 12 * q^76 - 16 * q^77 + 2 * q^80 + 2 * q^82 - 8 * q^83 + 2 * q^85 - 42 * q^89 - 8 * q^91 - 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.202596	−	2.22687i	−0.0906039	−	0.995887i
$5$	−0.202596	−	2.22687i	−0.0906039	−	0.995887i
$6$		0			0
$7$	−0.902312			−0.341042			−0.170521	−	0.985354i	$-0.554545\pi$
$7$	−0.902312			−0.341042			−0.170521	+	0.985354i	$0.554545\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.22687	+	0.202596i	−0.704198	+	0.0640666i
$11$	2.50645	−	2.50645i	0.755724	−	0.755724i	−0.219817	−	0.975541i	$-0.570546\pi$
$11$	2.50645	−	2.50645i	0.755724	−	0.755724i	0.975541	+	0.219817i	$0.0705461\pi$
$12$		0			0
$13$	3.59129	−	0.320354i	0.996045	−	0.0888503i
$13$	3.59129	−	0.320354i	0.996045	−	0.0888503i
$14$			0.902312i			0.241153i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.87250	−	2.87250i	0.696683	−	0.696683i	−0.267011	−	0.963694i	$-0.586036\pi$
$17$	2.87250	−	2.87250i	0.696683	−	0.696683i	0.963694	+	0.267011i	$0.0860359\pi$
$18$		0			0
$19$	−0.280927	+	0.280927i	−0.0644492	+	0.0644492i	−0.738597	−	0.674148i	$-0.764511\pi$
$19$	−0.280927	+	0.280927i	−0.0644492	+	0.0644492i	0.674148	+	0.738597i	$0.264511\pi$
$20$	0.202596	+	2.22687i	0.0453019	+	0.497944i
$21$		0			0
$22$	−2.50645	−	2.50645i	−0.534378	−	0.534378i
$23$	0.298938	+	0.298938i	0.0623330	+	0.0623330i	0.737586	−	0.675253i	$-0.235966\pi$
$23$	0.298938	+	0.298938i	0.0623330	+	0.0623330i	−0.675253	+	0.737586i	$0.735966\pi$
$24$		0			0
$25$	−4.91791	+	0.902312i	−0.983582	+	0.180462i
$26$	−0.320354	−	3.59129i	−0.0628267	−	0.704310i
$27$		0			0
$28$	0.902312			0.170521
$29$		−	2.15343i		−	0.399881i	−0.979808	−	0.199941i	$-0.935925\pi$
$29$		−	2.15343i		−	0.399881i	0.979808	−	0.199941i	$-0.0640749\pi$
$30$		0			0
$31$	−2.62842	−	2.62842i	−0.472077	−	0.472077i	0.430509	−	0.902586i	$-0.358334\pi$
$31$	−2.62842	−	2.62842i	−0.472077	−	0.472077i	−0.902586	+	0.430509i	$0.858334\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−2.87250	−	2.87250i	−0.492629	−	0.492629i
$35$	0.182805	+	2.00933i	0.0308997	+	0.339639i
$36$		0			0
$37$	−7.91467			−1.30116			−0.650582	−	0.759436i	$-0.725475\pi$
$37$	−7.91467			−1.30116			−0.650582	+	0.759436i	$0.725475\pi$
$38$	0.280927	+	0.280927i	0.0455724	+	0.0455724i
$39$		0			0
$40$	2.22687	−	0.202596i	0.352099	−	0.0320333i
$41$	1.01801	+	1.01801i	0.158987	+	0.158987i	0.782118	−	0.623131i	$-0.214140\pi$
$41$	1.01801	+	1.01801i	0.158987	+	0.158987i	−0.623131	+	0.782118i	$0.714140\pi$
$42$		0			0
$43$	−5.17770	−	5.17770i	−0.789592	−	0.789592i	0.191835	−	0.981427i	$-0.438556\pi$
$43$	−5.17770	−	5.17770i	−0.789592	−	0.789592i	−0.981427	+	0.191835i	$0.938556\pi$
$44$	−2.50645	+	2.50645i	−0.377862	+	0.377862i
$45$		0			0
$46$	0.298938	−	0.298938i	0.0440761	−	0.0440761i
$47$	−10.2383			−1.49341			−0.746706	−	0.665154i	$-0.768366\pi$
$47$	−10.2383			−1.49341			−0.746706	+	0.665154i	$0.768366\pi$
$48$		0			0
$49$	−6.18583			−0.883690
$50$	0.902312	+	4.91791i	0.127606	+	0.695497i
$51$		0			0
$52$	−3.59129	+	0.320354i	−0.498022	+	0.0444252i
$53$	7.95152	−	7.95152i	1.09222	−	1.09222i	0.0969341	−	0.995291i	$-0.469096\pi$
$53$	7.95152	−	7.95152i	1.09222	−	1.09222i	0.995291	−	0.0969341i	$-0.0309036\pi$
$54$		0			0
$55$	−6.08935	−	5.07375i	−0.821087	−	0.684144i
$56$		−	0.902312i		−	0.120577i
$57$		0			0
$58$	−2.15343			−0.282759
$59$	−1.49031	−	1.49031i	−0.194022	−	0.194022i	0.603410	−	0.797431i	$-0.293808\pi$
$59$	−1.49031	−	1.49031i	−0.194022	−	0.194022i	−0.797431	+	0.603410i	$0.793808\pi$
$60$		0			0
$61$	7.45681			0.954747			0.477373	−	0.878701i	$-0.341589\pi$
$61$	7.45681			0.954747			0.477373	+	0.878701i	$0.341589\pi$
$62$	−2.62842	+	2.62842i	−0.333809	+	0.333809i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.44097	−	7.93244i	−0.178730	−	0.983898i
$66$		0			0
$67$			3.72577i			0.455175i	0.973758	+	0.227588i	$0.0730838\pi$
$67$			3.72577i			0.455175i	−0.973758	+	0.227588i	$0.926916\pi$
$68$	−2.87250	+	2.87250i	−0.348342	+	0.348342i
$69$		0			0
$70$	2.00933	−	0.182805i	0.240161	−	0.0218494i
$71$	8.48521	+	8.48521i	1.00701	+	1.00701i	0.999975	+	0.00703333i	$0.00223880\pi$
$71$	8.48521	+	8.48521i	1.00701	+	1.00701i	0.00703333	+	0.999975i	$0.497761\pi$
$72$		0			0
$73$			3.28746i			0.384768i	0.981320	+	0.192384i	$0.0616219\pi$
$73$			3.28746i			0.384768i	−0.981320	+	0.192384i	$0.938378\pi$
$74$			7.91467i			0.920062i
$75$		0			0
$76$	0.280927	−	0.280927i	0.0322246	−	0.0322246i
$77$	−2.26160	+	2.26160i	−0.257734	+	0.257734i
$78$		0			0
$79$		−	4.97419i		−	0.559640i	−0.960052	−	0.279820i	$-0.909725\pi$
$79$		−	4.97419i		−	0.559640i	0.960052	−	0.279820i	$-0.0902748\pi$
$80$	−0.202596	−	2.22687i	−0.0226510	−	0.248972i
$81$		0			0
$82$	1.01801	−	1.01801i	0.112421	−	0.112421i
$83$	−1.83873			−0.201827			−0.100913	−	0.994895i	$-0.532177\pi$
$83$	−1.83873			−0.201827			−0.100913	+	0.994895i	$0.532177\pi$
$84$		0			0
$85$	−6.97864	−	5.81472i	−0.756940	−	0.630695i
$86$	−5.17770	+	5.17770i	−0.558326	+	0.558326i
$87$		0			0
$88$	2.50645	+	2.50645i	0.267189	+	0.267189i
$89$	3.05788	+	3.05788i	0.324135	+	0.324135i	0.850351	−	0.526216i	$-0.176390\pi$
$89$	3.05788	+	3.05788i	0.324135	+	0.324135i	−0.526216	+	0.850351i	$0.676390\pi$
$90$		0			0
$91$	−3.24047	+	0.289060i	−0.339693	+	0.0303017i
$92$	−0.298938	−	0.298938i	−0.0311665	−	0.0311665i
$93$		0			0
$94$			10.2383i			1.05600i
$95$	0.682504	+	0.568674i	0.0700234	+	0.0583447i
$96$		0			0
$97$			2.01625i			0.204719i	0.994747	+	0.102360i	$0.0326393\pi$
$97$			2.01625i			0.204719i	−0.994747	+	0.102360i	$0.967361\pi$
$98$			6.18583i			0.624863i
$99$		0			0
$100$	4.91791	−	0.902312i	0.491791	−	0.0902312i
$101$		−	12.9392i		−	1.28750i	−0.765236	−	0.643750i	$-0.777377\pi$
$101$		−	12.9392i		−	1.28750i	0.765236	−	0.643750i	$-0.222623\pi$
$102$		0			0
$103$	−4.17144	−	4.17144i	−0.411024	−	0.411024i	0.471071	−	0.882095i	$-0.343867\pi$
$103$	−4.17144	−	4.17144i	−0.411024	−	0.411024i	−0.882095	+	0.471071i	$0.843867\pi$
$104$	0.320354	+	3.59129i	0.0314133	+	0.352155i
$105$		0			0
$106$	−7.95152	−	7.95152i	−0.772320	−	0.772320i
$107$	−3.66987	−	3.66987i	−0.354779	−	0.354779i	0.507105	−	0.861884i	$-0.330716\pi$
$107$	−3.66987	−	3.66987i	−0.354779	−	0.354779i	−0.861884	+	0.507105i	$0.830716\pi$
$108$		0			0
$109$	6.82467	−	6.82467i	0.653685	−	0.653685i	−0.300194	−	0.953878i	$-0.597051\pi$
$109$	6.82467	−	6.82467i	0.653685	−	0.653685i	0.953878	+	0.300194i	$0.0970513\pi$
$110$	−5.07375	+	6.08935i	−0.483763	+	0.580596i
$111$		0			0
$112$	−0.902312			−0.0852605
$113$	11.0880	−	11.0880i	1.04307	−	1.04307i	0.0440448	−	0.999030i	$-0.485976\pi$
$113$	11.0880	−	11.0880i	1.04307	−	1.04307i	0.999030	−	0.0440448i	$-0.0140244\pi$
$114$		0			0
$115$	0.605133	−	0.726261i	0.0564290	−	0.0677242i
$116$			2.15343i			0.199941i
$117$		0			0
$118$	−1.49031	+	1.49031i	−0.137194	+	0.137194i
$119$	−2.59189	+	2.59189i	−0.237598	+	0.237598i
$120$		0			0
$121$		−	1.56461i		−	0.142237i
$122$		−	7.45681i		−	0.675108i
$123$		0			0
$124$	2.62842	+	2.62842i	0.236039	+	0.236039i
$125$	3.00568	+	10.7687i	0.268837	+	0.963186i
$126$		0			0
$127$	−12.1766	+	12.1766i	−1.08050	+	1.08050i	−0.0840366	+	0.996463i	$0.526781\pi$
$127$	−12.1766	+	12.1766i	−1.08050	+	1.08050i	−0.996463	+	0.0840366i	$0.973219\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−7.93244	+	1.44097i	−0.695721	+	0.126382i
$131$	12.8593			1.12352			0.561759	−	0.827301i	$-0.310125\pi$
$131$	12.8593			1.12352			0.561759	+	0.827301i	$0.310125\pi$
$132$		0			0
$133$	0.253484	−	0.253484i	0.0219799	−	0.0219799i
$134$	3.72577			0.321858
$135$		0			0
$136$	2.87250	+	2.87250i	0.246315	+	0.246315i
$137$	−16.8216			−1.43717			−0.718583	−	0.695441i	$-0.755209\pi$
$137$	−16.8216			−1.43717			−0.718583	+	0.695441i	$0.755209\pi$
$138$		0			0
$139$		−	2.71858i		−	0.230587i	−0.993331	−	0.115294i	$-0.963219\pi$
$139$		−	2.71858i		−	0.230587i	0.993331	−	0.115294i	$-0.0367809\pi$
$140$	−0.182805	−	2.00933i	−0.0154499	−	0.169820i
$141$		0			0
$142$	8.48521	−	8.48521i	0.712063	−	0.712063i
$143$	8.19845	−	9.80436i	0.685589	−	0.819881i
$144$		0			0
$145$	−4.79540	+	0.436276i	−0.398236	+	0.0362308i
$146$	3.28746			0.272072
$147$		0			0
$148$	7.91467			0.650582
$149$	0.219650	−	0.219650i	0.0179944	−	0.0179944i	−0.698052	−	0.716047i	$-0.745950\pi$
$149$	0.219650	−	0.219650i	0.0179944	−	0.0179944i	0.716047	+	0.698052i	$0.245950\pi$
$150$		0			0
$151$	14.8047	−	14.8047i	1.20479	−	1.20479i	0.232096	−	0.972693i	$-0.425442\pi$
$151$	14.8047	−	14.8047i	1.20479	−	1.20479i	0.972693	−	0.232096i	$-0.0745583\pi$
$152$	−0.280927	−	0.280927i	−0.0227862	−	0.0227862i
$153$		0			0
$154$	2.26160	+	2.26160i	0.182245	+	0.182245i
$155$	−5.32063	+	6.38565i	−0.427364	+	0.512908i
$156$		0			0
$157$	12.3405	+	12.3405i	0.984881	+	0.984881i	0.999887	−	0.0150064i	$-0.00477685\pi$
$157$	12.3405	+	12.3405i	0.984881	+	0.984881i	−0.0150064	+	0.999887i	$0.504777\pi$
$158$	−4.97419			−0.395725
$159$		0			0
$160$	−2.22687	+	0.202596i	−0.176050	+	0.0160167i
$161$	−0.269736	−	0.269736i	−0.0212582	−	0.0212582i
$162$		0			0
$163$			22.5682i			1.76768i	0.467788	+	0.883841i	$0.345051\pi$
$163$			22.5682i			1.76768i	−0.467788	+	0.883841i	$0.654949\pi$
$164$	−1.01801	−	1.01801i	−0.0794933	−	0.0794933i
$165$		0			0
$166$			1.83873i			0.142713i
$167$	−16.0230			−1.23989			−0.619947	−	0.784644i	$-0.712846\pi$
$167$	−16.0230			−1.23989			−0.619947	+	0.784644i	$0.712846\pi$
$168$		0			0
$169$	12.7947	−	2.30097i	0.984211	−	0.176998i
$170$	−5.81472	+	6.97864i	−0.445969	+	0.535237i
$171$		0			0
$172$	5.17770	+	5.17770i	0.394796	+	0.394796i
$173$	−1.71083	−	1.71083i	−0.130072	−	0.130072i	0.639074	−	0.769146i	$-0.279318\pi$
$173$	−1.71083	−	1.71083i	−0.130072	−	0.130072i	−0.769146	+	0.639074i	$0.779318\pi$
$174$		0			0
$175$	4.43749	−	0.814168i	0.335443	−	0.0615453i
$176$	2.50645	−	2.50645i	0.188931	−	0.188931i
$177$		0			0
$178$	3.05788	−	3.05788i	0.229198	−	0.229198i
$179$	−2.08774			−0.156045			−0.0780226	−	0.996952i	$-0.524861\pi$
$179$	−2.08774			−0.156045			−0.0780226	+	0.996952i	$0.524861\pi$
$180$		0			0
$181$			5.08144i			0.377700i	0.982006	+	0.188850i	$0.0604760\pi$
$181$			5.08144i			0.377700i	−0.982006	+	0.188850i	$0.939524\pi$
$182$	0.289060	+	3.24047i	0.0214265	+	0.240199i
$183$		0			0
$184$	−0.298938	+	0.298938i	−0.0220380	+	0.0220380i
$185$	1.60348	+	17.6250i	0.117891	+	1.29581i
$186$		0			0
$187$		−	14.3996i		−	1.05300i
$188$	10.2383			0.746706
$189$		0			0
$190$	0.568674	−	0.682504i	0.0412560	−	0.0495140i
$191$	12.0401			0.871190			0.435595	−	0.900143i	$-0.356538\pi$
$191$	12.0401			0.871190			0.435595	+	0.900143i	$0.356538\pi$
$192$		0			0
$193$			15.7987i			1.13722i	0.822608	+	0.568608i	$0.192518\pi$
$193$			15.7987i			1.13722i	−0.822608	+	0.568608i	$0.807482\pi$
$194$	2.01625			0.144758
$195$		0			0
$196$	6.18583			0.441845
$197$		−	12.7102i		−	0.905566i	−0.891621	−	0.452783i	$-0.850431\pi$
$197$		−	12.7102i		−	0.905566i	0.891621	−	0.452783i	$-0.149569\pi$
$198$		0			0
$199$	15.5881			1.10501			0.552506	−	0.833509i	$-0.313672\pi$
$199$	15.5881			1.10501			0.552506	+	0.833509i	$0.313672\pi$
$200$	−0.902312	−	4.91791i	−0.0638031	−	0.347749i
$201$		0			0
$202$	−12.9392			−0.910401
$203$			1.94306i			0.136376i
$204$		0			0
$205$	2.06073	−	2.47322i	0.143928	−	0.172738i
$206$	−4.17144	+	4.17144i	−0.290638	+	0.290638i
$207$		0			0
$208$	3.59129	−	0.320354i	0.249011	−	0.0222126i
$209$			1.40826i			0.0974116i
$210$		0			0
$211$	4.32936			0.298046			0.149023	−	0.988834i	$-0.452387\pi$
$211$	4.32936			0.298046			0.149023	+	0.988834i	$0.452387\pi$
$212$	−7.95152	+	7.95152i	−0.546112	+	0.546112i
$213$		0			0
$214$	−3.66987	+	3.66987i	−0.250867	+	0.250867i
$215$	−10.4811	+	12.5791i	−0.714804	+	0.857884i
$216$		0			0
$217$	2.37165	+	2.37165i	0.160998	+	0.160998i
$218$	−6.82467	−	6.82467i	−0.462225	−	0.462225i
$219$		0			0
$220$	6.08935	+	5.07375i	0.410544	+	0.342072i
$221$	9.39576	−	11.2362i	0.632027	−	0.755828i
$222$		0			0
$223$	−8.55297			−0.572749			−0.286375	−	0.958118i	$-0.592450\pi$
$223$	−8.55297			−0.572749			−0.286375	+	0.958118i	$0.592450\pi$
$224$			0.902312i			0.0602883i
$225$		0			0
$226$	−11.0880	−	11.0880i	−0.737565	−	0.737565i
$227$		−	1.30008i		−	0.0862896i	−0.999069	−	0.0431448i	$-0.986262\pi$
$227$		−	1.30008i		−	0.0862896i	0.999069	−	0.0431448i	$-0.0137377\pi$
$228$		0			0
$229$	19.3801	+	19.3801i	1.28067	+	1.28067i	0.940287	+	0.340383i	$0.110557\pi$
$229$	19.3801	+	19.3801i	1.28067	+	1.28067i	0.340383	+	0.940287i	$0.389443\pi$
$230$	−0.726261	−	0.605133i	−0.0478882	−	0.0399013i
$231$		0			0
$232$	2.15343			0.141379
$233$	−3.75807	−	3.75807i	−0.246199	−	0.246199i	0.573210	−	0.819409i	$-0.305698\pi$
$233$	−3.75807	−	3.75807i	−0.246199	−	0.246199i	−0.819409	+	0.573210i	$0.805698\pi$
$234$		0			0
$235$	2.07425	+	22.7994i	0.135309	+	1.48727i
$236$	1.49031	+	1.49031i	0.0970110	+	0.0970110i
$237$		0			0
$238$	2.59189	+	2.59189i	0.168007	+	0.168007i
$239$	−9.12433	+	9.12433i	−0.590204	+	0.590204i	−0.937686	−	0.347482i	$-0.887037\pi$
$239$	−9.12433	+	9.12433i	−0.590204	+	0.590204i	0.347482	+	0.937686i	$0.387037\pi$
$240$		0			0
$241$	17.5200	−	17.5200i	1.12856	−	1.12856i	0.138153	−	0.990411i	$-0.455884\pi$
$241$	17.5200	−	17.5200i	1.12856	−	1.12856i	0.990411	−	0.138153i	$-0.0441164\pi$
$242$	−1.56461			−0.100577
$243$		0			0
$244$	−7.45681			−0.477373
$245$	1.25323	+	13.7751i	0.0800658	+	0.880056i
$246$		0			0
$247$	−0.918896	+	1.09889i	−0.0584679	+	0.0699206i
$248$	2.62842	−	2.62842i	0.166905	−	0.166905i
$249$		0			0
$250$	10.7687	−	3.00568i	0.681075	−	0.190096i
$251$			15.7805i			0.996055i	0.867161	+	0.498027i	$0.165942\pi$
$251$			15.7805i			0.996055i	−0.867161	+	0.498027i	$0.834058\pi$
$252$		0			0
$253$	1.49855			0.0942130
$254$	12.1766	+	12.1766i	0.764028	+	0.764028i
$255$		0			0
$256$	1.00000			0.0625000
$257$	16.8660	−	16.8660i	1.05207	−	1.05207i	0.0535062	−	0.998568i	$-0.482960\pi$
$257$	16.8660	−	16.8660i	1.05207	−	1.05207i	0.998568	−	0.0535062i	$-0.0170397\pi$
$258$		0			0
$259$	7.14151			0.443752
$260$	1.44097	+	7.93244i	0.0893652	+	0.491949i
$261$		0			0
$262$		−	12.8593i		−	0.794448i
$263$	9.75987	−	9.75987i	0.601819	−	0.601819i	−0.338976	−	0.940795i	$-0.610080\pi$
$263$	9.75987	−	9.75987i	0.601819	−	0.601819i	0.940795	+	0.338976i	$0.110080\pi$
$264$		0			0
$265$	−19.3180	−	16.0961i	−1.18669	−	0.988773i
$266$	−0.253484	−	0.253484i	−0.0155421	−	0.0155421i
$267$		0			0
$268$		−	3.72577i		−	0.227588i
$269$		−	5.96510i		−	0.363699i	−0.983326	−	0.181849i	$-0.941792\pi$
$269$		−	5.96510i		−	0.363699i	0.983326	−	0.181849i	$-0.0582083\pi$
$270$		0			0
$271$	−17.0001	+	17.0001i	−1.03268	+	1.03268i	−0.0332329	+	0.999448i	$0.510580\pi$
$271$	−17.0001	+	17.0001i	−1.03268	+	1.03268i	−0.999448	+	0.0332329i	$0.989420\pi$
$272$	2.87250	−	2.87250i	0.174171	−	0.174171i
$273$		0			0
$274$			16.8216i			1.01623i
$275$	−10.0649	+	14.5881i	−0.606937	+	0.879696i
$276$		0			0
$277$	21.0124	−	21.0124i	1.26251	−	1.26251i	0.312644	−	0.949870i	$-0.398785\pi$
$277$	21.0124	−	21.0124i	1.26251	−	1.26251i	0.949870	−	0.312644i	$-0.101215\pi$
$278$	−2.71858			−0.163050
$279$		0			0
$280$	−2.00933	+	0.182805i	−0.120081	+	0.0109247i
$281$	5.01648	−	5.01648i	0.299258	−	0.299258i	−0.541465	−	0.840723i	$-0.682130\pi$
$281$	5.01648	−	5.01648i	0.299258	−	0.299258i	0.840723	+	0.541465i	$0.182130\pi$
$282$		0			0
$283$	5.59976	+	5.59976i	0.332871	+	0.332871i	0.853676	−	0.520805i	$-0.174368\pi$
$283$	5.59976	+	5.59976i	0.332871	+	0.332871i	−0.520805	+	0.853676i	$0.674368\pi$
$284$	−8.48521	−	8.48521i	−0.503504	−	0.503504i
$285$		0			0
$286$	−9.80436	−	8.19845i	−0.579744	−	0.484784i
$287$	−0.918564	−	0.918564i	−0.0542211	−	0.0542211i
$288$		0			0
$289$			0.497511i			0.0292654i
$290$	0.436276	+	4.79540i	0.0256190	+	0.281596i
$291$		0			0
$292$		−	3.28746i		−	0.192384i
$293$		−	4.94053i		−	0.288629i	−0.989532	−	0.144314i	$-0.953902\pi$
$293$		−	4.94053i		−	0.288629i	0.989532	−	0.144314i	$-0.0460977\pi$
$294$		0			0
$295$	−3.01680	+	3.62066i	−0.175645	+	0.210803i
$296$		−	7.91467i		−	0.460031i
$297$		0			0
$298$	−0.219650	−	0.219650i	−0.0127240	−	0.0127240i
$299$	1.16934	+	0.977809i	0.0676247	+	0.0565481i
$300$		0			0
$301$	4.67190	+	4.67190i	0.269284	+	0.269284i
$302$	−14.8047	−	14.8047i	−0.851914	−	0.851914i
$303$		0			0
$304$	−0.280927	+	0.280927i	−0.0161123	+	0.0161123i
$305$	−1.51072	−	16.6054i	−0.0865038	−	0.950820i
$306$		0			0
$307$	20.6482			1.17846			0.589228	−	0.807967i	$-0.299432\pi$
$307$	20.6482			1.17846			0.589228	+	0.807967i	$0.299432\pi$
$308$	2.26160	−	2.26160i	0.128867	−	0.128867i
$309$		0			0
$310$	6.38565	+	5.32063i	0.362680	+	0.302192i
$311$		−	27.3897i		−	1.55313i	−0.630038	−	0.776565i	$-0.716961\pi$
$311$		−	27.3897i		−	1.55313i	0.630038	−	0.776565i	$-0.283039\pi$
$312$		0			0
$313$	−1.07203	+	1.07203i	−0.0605949	+	0.0605949i	−0.736755	−	0.676160i	$-0.763643\pi$
$313$	−1.07203	+	1.07203i	−0.0605949	+	0.0605949i	0.676160	+	0.736755i	$0.263643\pi$
$314$	12.3405	−	12.3405i	0.696416	−	0.696416i
$315$		0			0
$316$			4.97419i			0.279820i
$317$		−	27.2403i		−	1.52997i	−0.644049	−	0.764984i	$-0.722747\pi$
$317$		−	27.2403i		−	1.52997i	0.644049	−	0.764984i	$-0.277253\pi$
$318$		0			0
$319$	−5.39746	−	5.39746i	−0.302200	−	0.302200i
$320$	0.202596	+	2.22687i	0.0113255	+	0.124486i
$321$		0			0
$322$	−0.269736	+	0.269736i	−0.0150318	+	0.0150318i
$323$			1.61393i			0.0898013i
$324$		0			0
$325$	−17.3726	+	4.81594i	−0.963658	+	0.267140i
$326$	22.5682			1.24994
$327$		0			0
$328$	−1.01801	+	1.01801i	−0.0562103	+	0.0562103i
$329$	9.23816			0.509316
$330$		0			0
$331$	19.6653	+	19.6653i	1.08090	+	1.08090i	0.996426	+	0.0844757i	$0.0269215\pi$
$331$	19.6653	+	19.6653i	1.08090	+	1.08090i	0.0844757	+	0.996426i	$0.473078\pi$
$332$	1.83873			0.100913
$333$		0			0
$334$			16.0230i			0.876738i
$335$	8.29681	−	0.754828i	0.453303	−	0.0412407i
$336$		0			0
$337$	−2.03426	+	2.03426i	−0.110813	+	0.110813i	−0.760339	−	0.649526i	$-0.774967\pi$
$337$	−2.03426	+	2.03426i	−0.110813	+	0.110813i	0.649526	+	0.760339i	$0.274967\pi$
$338$	−2.30097	−	12.7947i	−0.125156	−	0.695942i
$339$		0			0
$340$	6.97864	+	5.81472i	0.378470	+	0.315348i
$341$	−13.1760			−0.713520
$342$		0			0
$343$	11.8977			0.642418
$344$	5.17770	−	5.17770i	0.279163	−	0.279163i
$345$		0			0
$346$	−1.71083	+	1.71083i	−0.0919748	+	0.0919748i
$347$	−7.08390	−	7.08390i	−0.380284	−	0.380284i	0.490921	−	0.871204i	$-0.336661\pi$
$347$	−7.08390	−	7.08390i	−0.380284	−	0.380284i	−0.871204	+	0.490921i	$0.836661\pi$
$348$		0			0
$349$	−8.93472	−	8.93472i	−0.478264	−	0.478264i	0.426312	−	0.904576i	$-0.359813\pi$
$349$	−8.93472	−	8.93472i	−0.478264	−	0.478264i	−0.904576	+	0.426312i	$0.859813\pi$
$350$	−0.814168	−	4.43749i	−0.0435191	−	0.237194i
$351$		0			0
$352$	−2.50645	−	2.50645i	−0.133594	−	0.133594i
$353$	3.69337			0.196578			0.0982892	−	0.995158i	$-0.468663\pi$
$353$	3.69337			0.196578			0.0982892	+	0.995158i	$0.468663\pi$
$354$		0			0
$355$	17.1764	−	20.6145i	0.911628	−	1.09411i
$356$	−3.05788	−	3.05788i	−0.162067	−	0.162067i
$357$		0			0
$358$			2.08774i			0.110341i
$359$	15.6735	+	15.6735i	0.827216	+	0.827216i	0.987131	−	0.159915i	$-0.0511220\pi$
$359$	15.6735	+	15.6735i	0.827216	+	0.827216i	−0.159915	+	0.987131i	$0.551122\pi$
$360$		0			0
$361$			18.8422i			0.991693i
$362$	5.08144			0.267074
$363$		0			0
$364$	3.24047	−	0.289060i	0.169847	−	0.0151509i
$365$	7.32075	−	0.666028i	0.383185	−	0.0348615i
$366$		0			0
$367$	9.00704	+	9.00704i	0.470164	+	0.470164i	0.901968	−	0.431804i	$-0.142123\pi$
$367$	9.00704	+	9.00704i	0.470164	+	0.470164i	−0.431804	+	0.901968i	$0.642123\pi$
$368$	0.298938	+	0.298938i	0.0155832	+	0.0155832i
$369$		0			0
$370$	17.6250	−	1.60348i	0.916278	−	0.0833612i
$371$	−7.17475	+	7.17475i	−0.372495	+	0.372495i
$372$		0			0
$373$	−1.94492	+	1.94492i	−0.100704	+	0.100704i	−0.755664	−	0.654960i	$-0.772686\pi$
$373$	−1.94492	+	1.94492i	−0.100704	+	0.100704i	0.654960	+	0.755664i	$0.272686\pi$
$374$	−14.3996			−0.744584
$375$		0			0
$376$		−	10.2383i		−	0.528001i
$377$	−0.689859	−	7.73358i	−0.0355296	−	0.398300i
$378$		0			0
$379$	11.2556	−	11.2556i	0.578162	−	0.578162i	−0.356235	−	0.934396i	$-0.615940\pi$
$379$	11.2556	−	11.2556i	0.578162	−	0.578162i	0.934396	+	0.356235i	$0.115940\pi$
$380$	−0.682504	−	0.568674i	−0.0350117	−	0.0291724i
$381$		0			0
$382$		−	12.0401i		−	0.616025i
$383$	−16.4651			−0.841328			−0.420664	−	0.907217i	$-0.638203\pi$
$383$	−16.4651			−0.841328			−0.420664	+	0.907217i	$0.638203\pi$
$384$		0			0
$385$	5.49449	+	4.57811i	0.280025	+	0.233322i
$386$	15.7987			0.804134
$387$		0			0
$388$		−	2.01625i		−	0.102360i
$389$	26.7942			1.35852			0.679261	−	0.733897i	$-0.262300\pi$
$389$	26.7942			1.35852			0.679261	+	0.733897i	$0.262300\pi$
$390$		0			0
$391$	1.71740			0.0868526
$392$		−	6.18583i		−	0.312432i
$393$		0			0
$394$	−12.7102			−0.640332
$395$	−11.0769	+	1.00775i	−0.557339	+	0.0507056i
$396$		0			0
$397$	−17.9325			−0.900005			−0.450002	−	0.893027i	$-0.648577\pi$
$397$	−17.9325			−0.900005			−0.450002	+	0.893027i	$0.648577\pi$
$398$		−	15.5881i		−	0.781361i
$399$		0			0
$400$	−4.91791	+	0.902312i	−0.245895	+	0.0451156i
$401$	1.68244	−	1.68244i	0.0840170	−	0.0840170i	−0.663849	−	0.747866i	$-0.731078\pi$
$401$	1.68244	−	1.68244i	0.0840170	−	0.0840170i	0.747866	+	0.663849i	$0.231078\pi$
$402$		0			0
$403$	−10.2814	−	8.59738i	−0.512154	−	0.428266i
$404$			12.9392i			0.643750i
$405$		0			0
$406$	1.94306			0.0964326
$407$	−19.8378	+	19.8378i	−0.983321	+	0.983321i
$408$		0			0
$409$	−2.71561	+	2.71561i	−0.134278	+	0.134278i	−0.771051	−	0.636773i	$-0.780269\pi$
$409$	−2.71561	+	2.71561i	−0.134278	+	0.134278i	0.636773	+	0.771051i	$0.280269\pi$
$410$	−2.47322	−	2.06073i	−0.122144	−	0.101772i
$411$		0			0
$412$	4.17144	+	4.17144i	0.205512	+	0.205512i
$413$	1.34473	+	1.34473i	0.0661696	+	0.0661696i
$414$		0			0
$415$	0.372520	+	4.09462i	0.0182863	+	0.200997i
$416$	−0.320354	−	3.59129i	−0.0157067	−	0.176078i
$417$		0			0
$418$	1.40826			0.0688804
$419$			36.7263i			1.79420i	0.441831	+	0.897098i	$0.354329\pi$
$419$			36.7263i			1.79420i	−0.441831	+	0.897098i	$0.645671\pi$
$420$		0			0
$421$	−19.6978	−	19.6978i	−0.960012	−	0.960012i	0.0392186	−	0.999231i	$-0.487513\pi$
$421$	−19.6978	−	19.6978i	−0.960012	−	0.960012i	−0.999231	+	0.0392186i	$0.987513\pi$
$422$		−	4.32936i		−	0.210750i
$423$		0			0
$424$	7.95152	+	7.95152i	0.386160	+	0.386160i
$425$	−11.5348	+	16.7186i	−0.559520	+	0.810970i
$426$		0			0
$427$	−6.72837			−0.325609
$428$	3.66987	+	3.66987i	0.177390	+	0.177390i
$429$		0			0
$430$	12.5791	+	10.4811i	0.606616	+	0.505443i
$431$	27.9045	+	27.9045i	1.34411	+	1.34411i	0.891919	+	0.452194i	$0.149359\pi$
$431$	27.9045	+	27.9045i	1.34411	+	1.34411i	0.452194	+	0.891919i	$0.350641\pi$
$432$		0			0
$433$	−6.60618	−	6.60618i	−0.317473	−	0.317473i	0.530323	−	0.847796i	$-0.322071\pi$
$433$	−6.60618	−	6.60618i	−0.317473	−	0.317473i	−0.847796	+	0.530323i	$0.822071\pi$
$434$	2.37165	−	2.37165i	0.113843	−	0.113843i
$435$		0			0
$436$	−6.82467	+	6.82467i	−0.326842	+	0.326842i
$437$	−0.167960			−0.00803462
$438$		0			0
$439$	−32.3810			−1.54546			−0.772730	−	0.634735i	$-0.781109\pi$
$439$	−32.3810			−1.54546			−0.772730	+	0.634735i	$0.781109\pi$
$440$	5.07375	−	6.08935i	0.241881	−	0.290298i
$441$		0			0
$442$	−11.2362	−	9.39576i	−0.534451	−	0.446911i
$443$	−25.0288	+	25.0288i	−1.18915	+	1.18915i	−0.211852	+	0.977302i	$0.567950\pi$
$443$	−25.0288	+	25.0288i	−1.18915	+	1.18915i	−0.977302	+	0.211852i	$0.932050\pi$
$444$		0			0
$445$	6.18999	−	7.42903i	0.293434	−	0.352170i
$446$			8.55297i			0.404995i
$447$		0			0
$448$	0.902312			0.0426303
$449$	5.77218	+	5.77218i	0.272406	+	0.272406i	0.830068	−	0.557662i	$-0.188302\pi$
$449$	5.77218	+	5.77218i	0.272406	+	0.272406i	−0.557662	+	0.830068i	$0.688302\pi$
$450$		0			0
$451$	5.10319			0.240300
$452$	−11.0880	+	11.0880i	−0.521537	+	0.521537i
$453$		0			0
$454$	−1.30008			−0.0610160
$455$	1.30021	+	7.15754i	0.0609546	+	0.335551i
$456$		0			0
$457$			21.2810i			0.995483i	0.867326	+	0.497741i	$0.165837\pi$
$457$			21.2810i			0.995483i	−0.867326	+	0.497741i	$0.834163\pi$
$458$	19.3801	−	19.3801i	0.905570	−	0.905570i
$459$		0			0
$460$	−0.605133	+	0.726261i	−0.0282145	+	0.0338621i
$461$	−0.427100	−	0.427100i	−0.0198920	−	0.0198920i	0.697091	−	0.716983i	$-0.254477\pi$
$461$	−0.427100	−	0.427100i	−0.0198920	−	0.0198920i	−0.716983	+	0.697091i	$0.754477\pi$
$462$		0			0
$463$		−	37.4058i		−	1.73839i	−0.494467	−	0.869197i	$-0.664637\pi$
$463$		−	37.4058i		−	1.73839i	0.494467	−	0.869197i	$-0.335363\pi$
$464$		−	2.15343i		−	0.0999703i
$465$		0			0
$466$	−3.75807	+	3.75807i	−0.174089	+	0.174089i
$467$	−15.1590	+	15.1590i	−0.701476	+	0.701476i	−0.964727	−	0.263251i	$-0.915205\pi$
$467$	−15.1590	+	15.1590i	−0.701476	+	0.701476i	0.263251	+	0.964727i	$0.415205\pi$
$468$		0			0
$469$		−	3.36181i		−	0.155234i
$470$	22.7994	−	2.07425i	1.05166	−	0.0956779i
$471$		0			0
$472$	1.49031	−	1.49031i	0.0685971	−	0.0685971i
$473$	−25.9553			−1.19343
$474$		0			0
$475$	1.12809	−	1.63506i	0.0517604	−	0.0750217i
$476$	2.59189	−	2.59189i	0.118799	−	0.118799i
$477$		0			0
$478$	9.12433	+	9.12433i	0.417337	+	0.417337i
$479$	−21.9120	−	21.9120i	−1.00118	−	1.00118i	−0.999999	−	0.00118469i	$-0.999623\pi$
$479$	−21.9120	−	21.9120i	−1.00118	−	1.00118i	−0.00118469	−	0.999999i	$-0.500377\pi$
$480$		0			0
$481$	−28.4239	+	2.53550i	−1.29602	+	0.115609i
$482$	−17.5200	−	17.5200i	−0.798015	−	0.798015i
$483$		0			0
$484$			1.56461i			0.0711187i
$485$	4.48993	−	0.408485i	0.203877	−	0.0185484i
$486$		0			0
$487$			25.8968i			1.17349i	0.809770	+	0.586747i	$0.199592\pi$
$487$			25.8968i			1.17349i	−0.809770	+	0.586747i	$0.800408\pi$
$488$			7.45681i			0.337554i
$489$		0			0
$490$	13.7751	−	1.25323i	0.622293	−	0.0566151i
$491$			24.8773i			1.12270i	0.827580	+	0.561348i	$0.189717\pi$
$491$			24.8773i			1.12270i	−0.827580	+	0.561348i	$0.810283\pi$
$492$		0			0
$493$	−6.18571	−	6.18571i	−0.278590	−	0.278590i
$494$	1.09889	+	0.918896i	0.0494413	+	0.0413431i
$495$		0			0
$496$	−2.62842	−	2.62842i	−0.118019	−	0.118019i
$497$	−7.65631	−	7.65631i	−0.343432	−	0.343432i
$498$		0			0
$499$	24.5043	−	24.5043i	1.09696	−	1.09696i	0.102200	−	0.994764i	$-0.467412\pi$
$499$	24.5043	−	24.5043i	1.09696	−	1.09696i	0.994764	−	0.102200i	$-0.0325881\pi$
$500$	−3.00568	−	10.7687i	−0.134418	−	0.481593i
$501$		0			0
$502$	15.7805			0.704317
$503$	28.3021	−	28.3021i	1.26193	−	1.26193i	0.311774	−	0.950156i	$-0.399077\pi$
$503$	28.3021	−	28.3021i	1.26193	−	1.26193i	0.950156	−	0.311774i	$-0.100923\pi$
$504$		0			0
$505$	−28.8140	+	2.62144i	−1.28221	+	0.116653i
$506$		−	1.49855i		−	0.0666187i
$507$		0			0
$508$	12.1766	−	12.1766i	0.540250	−	0.540250i
$509$	−16.9258	+	16.9258i	−0.750224	+	0.750224i	−0.974521	−	0.224297i	$-0.927992\pi$
$509$	−16.9258	+	16.9258i	−0.750224	+	0.750224i	0.224297	+	0.974521i	$0.427992\pi$
$510$		0			0
$511$		−	2.96631i		−	0.131222i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−16.8660	−	16.8660i	−0.743928	−	0.743928i
$515$	−8.44413	+	10.1344i	−0.372093	+	0.446574i
$516$		0			0
$517$	−25.6619	+	25.6619i	−1.12861	+	1.12861i
$518$		−	7.14151i		−	0.313780i
$519$		0			0
$520$	7.93244	−	1.44097i	0.347861	−	0.0631908i
$521$	−1.65021			−0.0722972			−0.0361486	−	0.999346i	$-0.511509\pi$
$521$	−1.65021			−0.0722972			−0.0361486	+	0.999346i	$0.511509\pi$
$522$		0			0
$523$	−13.7318	+	13.7318i	−0.600451	+	0.600451i	−0.940432	−	0.339981i	$-0.889579\pi$
$523$	−13.7318	+	13.7318i	−0.600451	+	0.600451i	0.339981	+	0.940432i	$0.389579\pi$
$524$	−12.8593			−0.561759
$525$		0			0
$526$	−9.75987	−	9.75987i	−0.425551	−	0.425551i
$527$	−15.1002			−0.657776
$528$		0			0
$529$		−	22.8213i		−	0.992229i
$530$	−16.0961	+	19.3180i	−0.699168	+	0.839118i
$531$		0			0
$532$	−0.253484	+	0.253484i	−0.0109899	+	0.0109899i
$533$	3.98210	+	3.32985i	0.172484	+	0.144232i
$534$		0			0
$535$	−7.42882	+	8.91582i	−0.321176	+	0.385465i
$536$	−3.72577			−0.160929
$537$		0			0
$538$	−5.96510			−0.257174
$539$	−15.5045	+	15.5045i	−0.667826	+	0.667826i
$540$		0			0
$541$	9.44639	−	9.44639i	0.406132	−	0.406132i	−0.474255	−	0.880387i	$-0.657283\pi$
$541$	9.44639	−	9.44639i	0.406132	−	0.406132i	0.880387	+	0.474255i	$0.157283\pi$
$542$	17.0001	+	17.0001i	0.730215	+	0.730215i
$543$		0			0
$544$	−2.87250	−	2.87250i	−0.123157	−	0.123157i
$545$	−16.5803	−	13.8150i	−0.710223	−	0.591770i
$546$		0			0
$547$	25.0273	+	25.0273i	1.07009	+	1.07009i	0.997351	+	0.0727389i	$0.0231740\pi$
$547$	25.0273	+	25.0273i	1.07009	+	1.07009i	0.0727389	+	0.997351i	$0.476826\pi$
$548$	16.8216			0.718583
$549$		0			0
$550$	14.5881	+	10.0649i	0.622039	+	0.429169i
$551$	0.604956	+	0.604956i	0.0257720	+	0.0257720i
$552$		0			0
$553$			4.48828i			0.190861i
$554$	−21.0124	−	21.0124i	−0.892732	−	0.892732i
$555$		0			0
$556$			2.71858i			0.115294i
$557$	19.2964			0.817615			0.408808	−	0.912621i	$-0.365945\pi$
$557$	19.2964			0.817615			0.408808	+	0.912621i	$0.365945\pi$
$558$		0			0
$559$	−20.2533	−	16.9359i	−0.856625	−	0.716313i
$560$	0.182805	+	2.00933i	0.00772493	+	0.0849098i
$561$		0			0
$562$	−5.01648	−	5.01648i	−0.211607	−	0.211607i
$563$	16.9672	+	16.9672i	0.715081	+	0.715081i	0.967594	−	0.252512i	$-0.0812568\pi$
$563$	16.9672	+	16.9672i	0.715081	+	0.715081i	−0.252512	+	0.967594i	$0.581257\pi$
$564$		0			0
$565$	−26.9380	−	22.4452i	−1.13329	−	0.944278i
$566$	5.59976	−	5.59976i	0.235375	−	0.235375i
$567$		0			0
$568$	−8.48521	+	8.48521i	−0.356031	+	0.356031i
$569$	23.3312			0.978094			0.489047	−	0.872257i	$-0.337345\pi$
$569$	23.3312			0.978094			0.489047	+	0.872257i	$0.337345\pi$
$570$		0			0
$571$			36.0154i			1.50720i	0.657335	+	0.753598i	$0.271684\pi$
$571$			36.0154i			1.50720i	−0.657335	+	0.753598i	$0.728316\pi$
$572$	−8.19845	+	9.80436i	−0.342794	+	0.409941i
$573$		0			0
$574$	−0.918564	+	0.918564i	−0.0383401	+	0.0383401i
$575$	−1.73989	−	1.20042i	−0.0725583	−	0.0500608i
$576$		0			0
$577$		−	26.8550i		−	1.11799i	−0.829171	−	0.558994i	$-0.811187\pi$
$577$		−	26.8550i		−	1.11799i	0.829171	−	0.558994i	$-0.188813\pi$
$578$	0.497511			0.0206937
$579$		0			0
$580$	4.79540	−	0.436276i	0.199118	−	0.0181154i
$581$	1.65911			0.0688315
$582$		0			0
$583$		−	39.8602i		−	1.65084i
$584$	−3.28746			−0.136036
$585$		0			0
$586$	−4.94053			−0.204091
$587$			30.6103i			1.26342i	0.775204	+	0.631711i	$0.217647\pi$
$587$			30.6103i			1.26342i	−0.775204	+	0.631711i	$0.782353\pi$
$588$		0			0
$589$	1.47679			0.0608500
$590$	3.62066	+	3.01680i	0.149060	+	0.124200i
$591$		0			0
$592$	−7.91467			−0.325291
$593$			9.97399i			0.409583i	0.978806	+	0.204791i	$0.0656516\pi$
$593$			9.97399i			0.409583i	−0.978806	+	0.204791i	$0.934348\pi$
$594$		0			0
$595$	6.29691	+	5.24670i	0.258148	+	0.215094i
$596$	−0.219650	+	0.219650i	−0.00899721	+	0.00899721i
$597$		0			0
$598$	0.977809	−	1.16934i	0.0399856	−	0.0478179i
$599$		−	23.1025i		−	0.943944i	−0.881614	−	0.471972i	$-0.843542\pi$
$599$		−	23.1025i		−	0.943944i	0.881614	−	0.471972i	$-0.156458\pi$
$600$		0			0
$601$	33.4887			1.36603			0.683017	−	0.730402i	$-0.260667\pi$
$601$	33.4887			1.36603			0.683017	+	0.730402i	$0.260667\pi$
$602$	4.67190	−	4.67190i	0.190413	−	0.190413i
$603$		0			0
$604$	−14.8047	+	14.8047i	−0.602394	+	0.602394i
$605$	−3.48419	+	0.316985i	−0.141652	+	0.0128873i
$606$		0			0
$607$	−11.5600	−	11.5600i	−0.469206	−	0.469206i	0.432451	−	0.901657i	$-0.357649\pi$
$607$	−11.5600	−	11.5600i	−0.469206	−	0.469206i	−0.901657	+	0.432451i	$0.857649\pi$
$608$	0.280927	+	0.280927i	0.0113931	+	0.0113931i
$609$		0			0
$610$	−16.6054	+	1.51072i	−0.672331	+	0.0611674i
$611$	−36.7688	+	3.27989i	−1.48751	+	0.132690i
$612$		0			0
$613$	−4.05711			−0.163865			−0.0819326	−	0.996638i	$-0.526109\pi$
$613$	−4.05711			−0.163865			−0.0819326	+	0.996638i	$0.526109\pi$
$614$		−	20.6482i		−	0.833294i
$615$		0			0
$616$	−2.26160	−	2.26160i	−0.0911226	−	0.0911226i
$617$			23.0322i			0.927243i	0.886033	+	0.463622i	$0.153450\pi$
$617$			23.0322i			0.927243i	−0.886033	+	0.463622i	$0.846550\pi$
$618$		0			0
$619$	−11.2579	−	11.2579i	−0.452494	−	0.452494i	0.443687	−	0.896182i	$-0.353670\pi$
$619$	−11.2579	−	11.2579i	−0.452494	−	0.452494i	−0.896182	+	0.443687i	$0.853670\pi$
$620$	5.32063	−	6.38565i	0.213682	−	0.256454i
$621$		0			0
$622$	−27.3897			−1.09823
$623$	−2.75917	−	2.75917i	−0.110544	−	0.110544i
$624$		0			0
$625$	23.3717	−	8.87498i	0.934867	−	0.354999i
$626$	1.07203	+	1.07203i	0.0428471	+	0.0428471i
$627$		0			0
$628$	−12.3405	−	12.3405i	−0.492441	−	0.492441i
$629$	−22.7349	+	22.7349i	−0.906499	+	0.906499i
$630$		0			0
$631$	−30.7473	+	30.7473i	−1.22403	+	1.22403i	−0.257845	+	0.966186i	$0.583013\pi$
$631$	−30.7473	+	30.7473i	−1.22403	+	1.22403i	−0.966186	+	0.257845i	$0.916987\pi$
$632$	4.97419			0.197863
$633$		0			0
$634$	−27.2403			−1.08185
$635$	29.5827	+	24.6488i	1.17395	+	0.978158i
$636$		0			0
$637$	−22.2151	+	1.98166i	−0.880195	+	0.0785162i
$638$	−5.39746	+	5.39746i	−0.213687	+	0.213687i
$639$		0			0
$640$	2.22687	−	0.202596i	0.0880248	−	0.00800833i
$641$			7.90192i			0.312107i	0.987749	+	0.156054i	$0.0498772\pi$
$641$			7.90192i			0.312107i	−0.987749	+	0.156054i	$0.950123\pi$
$642$		0			0
$643$	0.752273			0.0296668			0.0148334	−	0.999890i	$-0.495278\pi$
$643$	0.752273			0.0296668			0.0148334	+	0.999890i	$0.495278\pi$
$644$	0.269736	+	0.269736i	0.0106291	+	0.0106291i
$645$		0			0
$646$	1.61393			0.0634991
$647$	13.6310	−	13.6310i	0.535888	−	0.535888i	−0.386431	−	0.922319i	$-0.626292\pi$
$647$	13.6310	−	13.6310i	0.535888	−	0.535888i	0.922319	+	0.386431i	$0.126292\pi$
$648$		0			0
$649$	−7.47079			−0.293254
$650$	4.81594	+	17.3726i	0.188897	+	0.681409i
$651$		0			0
$652$		−	22.5682i		−	0.883841i
$653$	−13.4609	+	13.4609i	−0.526767	+	0.526767i	−0.919607	−	0.392840i	$-0.871493\pi$
$653$	−13.4609	+	13.4609i	−0.526767	+	0.526767i	0.392840	+	0.919607i	$0.371493\pi$
$654$		0			0
$655$	−2.60524	−	28.6359i	−0.101795	−	1.11890i
$656$	1.01801	+	1.01801i	0.0397467	+	0.0397467i
$657$		0			0
$658$		−	9.23816i		−	0.360141i
$659$			4.05064i			0.157790i	0.996883	+	0.0788952i	$0.0251393\pi$
$659$			4.05064i			0.157790i	−0.996883	+	0.0788952i	$0.974861\pi$
$660$		0			0
$661$	−8.95910	+	8.95910i	−0.348469	+	0.348469i	−0.859539	−	0.511070i	$-0.829249\pi$
$661$	−8.95910	+	8.95910i	−0.348469	+	0.348469i	0.511070	+	0.859539i	$0.329249\pi$
$662$	19.6653	−	19.6653i	0.764313	−	0.764313i
$663$		0			0
$664$		−	1.83873i		−	0.0713566i
$665$	−0.615832	−	0.513122i	−0.0238809	−	0.0198980i
$666$		0			0
$667$	0.643742	−	0.643742i	0.0249258	−	0.0249258i
$668$	16.0230			0.619947
$669$		0			0
$670$	−0.754828	−	8.29681i	−0.0291615	−	0.320534i
$671$	18.6901	−	18.6901i	0.721525	−	0.721525i
$672$		0			0
$673$	−9.48767	−	9.48767i	−0.365723	−	0.365723i	0.500192	−	0.865915i	$-0.333263\pi$
$673$	−9.48767	−	9.48767i	−0.365723	−	0.365723i	−0.865915	+	0.500192i	$0.833263\pi$
$674$	2.03426	+	2.03426i	0.0783569	+	0.0783569i
$675$		0			0
$676$	−12.7947	+	2.30097i	−0.492106	+	0.0884989i
$677$	−14.8157	−	14.8157i	−0.569413	−	0.569413i	0.362551	−	0.931964i	$-0.381906\pi$
$677$	−14.8157	−	14.8157i	−0.569413	−	0.569413i	−0.931964	+	0.362551i	$0.881906\pi$
$678$		0			0
$679$		−	1.81929i		−	0.0698179i
$680$	5.81472	−	6.97864i	0.222985	−	0.267619i
$681$		0			0
$682$			13.1760i			0.504535i
$683$			7.51375i			0.287506i	0.989614	+	0.143753i	$0.0459171\pi$
$683$			7.51375i			0.287506i	−0.989614	+	0.143753i	$0.954083\pi$
$684$		0			0
$685$	3.40800	+	37.4595i	0.130213	+	1.43126i
$686$		−	11.8977i		−	0.454258i
$687$		0			0
$688$	−5.17770	−	5.17770i	−0.197398	−	0.197398i
$689$	26.0089	−	31.1035i	0.990861	−	1.18495i
$690$		0			0
$691$	−13.6012	−	13.6012i	−0.517416	−	0.517416i	0.399373	−	0.916789i	$-0.369228\pi$
$691$	−13.6012	−	13.6012i	−0.517416	−	0.517416i	−0.916789	+	0.399373i	$0.869228\pi$
$692$	1.71083	+	1.71083i	0.0650360	+	0.0650360i
$693$		0			0
$694$	−7.08390	+	7.08390i	−0.268901	+	0.268901i
$695$	−6.05393	+	0.550775i	−0.229639	+	0.0208921i
$696$		0			0
$697$	5.84847			0.221527
$698$	−8.93472	+	8.93472i	−0.338184	+	0.338184i
$699$		0			0
$700$	−4.43749	+	0.814168i	−0.167721	+	0.0307726i
$701$		−	36.5503i		−	1.38049i	−0.723577	−	0.690243i	$-0.757503\pi$
$701$		−	36.5503i		−	1.38049i	0.723577	−	0.690243i	$-0.242497\pi$
$702$		0			0
$703$	2.22345	−	2.22345i	0.0838590	−	0.0838590i
$704$	−2.50645	+	2.50645i	−0.0944655	+	0.0944655i
$705$		0			0
$706$		−	3.69337i		−	0.139002i
$707$			11.6752i			0.439092i
$708$		0			0
$709$	−8.48180	−	8.48180i	−0.318541	−	0.318541i	0.529666	−	0.848206i	$-0.322317\pi$
$709$	−8.48180	−	8.48180i	−0.318541	−	0.318541i	−0.848206	+	0.529666i	$0.822317\pi$
$710$	−20.6145	−	17.1764i	−0.773650	−	0.644618i
$711$		0			0
$712$	−3.05788	+	3.05788i	−0.114599	+	0.114599i
$713$		−	1.57147i		−	0.0588520i
$714$		0			0
$715$	−23.4940	−	16.2706i	−0.878626	−	0.608484i
$716$	2.08774			0.0780226
$717$		0			0
$718$	15.6735	−	15.6735i	0.584930	−	0.584930i
$719$	11.8158			0.440656			0.220328	−	0.975426i	$-0.429287\pi$
$719$	11.8158			0.440656			0.220328	+	0.975426i	$0.429287\pi$
$720$		0			0
$721$	3.76394	+	3.76394i	0.140176	+	0.140176i
$722$	18.8422			0.701233
$723$		0			0
$724$		−	5.08144i		−	0.188850i
$725$	1.94306	+	10.5904i	0.0721635	+	0.393316i
$726$		0			0
$727$	31.9067	−	31.9067i	1.18335	−	1.18335i	0.204485	−	0.978870i	$-0.434448\pi$
$727$	31.9067	−	31.9067i	1.18335	−	1.18335i	0.978870	−	0.204485i	$-0.0655519\pi$
$728$	−0.289060	−	3.24047i	−0.0107133	−	0.120100i
$729$		0			0
$730$	−0.666028	−	7.32075i	−0.0246508	−	0.270953i
$731$	−29.7459			−1.10019
$732$		0			0
$733$	−27.4594			−1.01424			−0.507118	−	0.861877i	$-0.669289\pi$
$733$	−27.4594			−1.01424			−0.507118	+	0.861877i	$0.669289\pi$
$734$	9.00704	−	9.00704i	0.332456	−	0.332456i
$735$		0			0
$736$	0.298938	−	0.298938i	0.0110190	−	0.0110190i
$737$	9.33847	+	9.33847i	0.343987	+	0.343987i
$738$		0			0
$739$	−24.9129	−	24.9129i	−0.916435	−	0.916435i	0.0803334	−	0.996768i	$-0.474402\pi$
$739$	−24.9129	−	24.9129i	−0.916435	−	0.916435i	−0.996768	+	0.0803334i	$0.974402\pi$
$740$	−1.60348	−	17.6250i	−0.0589453	−	0.647906i
$741$		0			0
$742$	7.17475	+	7.17475i	0.263393	+	0.263393i
$743$	−1.45152			−0.0532510			−0.0266255	−	0.999645i	$-0.508476\pi$
$743$	−1.45152			−0.0532510			−0.0266255	+	0.999645i	$0.508476\pi$
$744$		0			0
$745$	−0.533632	−	0.444632i	−0.0195508	−	0.0162900i
$746$	1.94492	+	1.94492i	0.0712085	+	0.0712085i
$747$		0			0
$748$			14.3996i			0.526500i
$749$	3.31137	+	3.31137i	0.120995	+	0.120995i
$750$		0			0
$751$			46.1389i			1.68363i	0.539765	+	0.841815i	$0.318513\pi$
$751$			46.1389i			1.68363i	−0.539765	+	0.841815i	$0.681487\pi$
$752$	−10.2383			−0.373353
$753$		0			0
$754$	−7.73358	+	0.689859i	−0.281640	+	0.0251232i
$755$	−35.9675	−	29.9688i	−1.30899	−	1.09067i
$756$		0			0
$757$	4.45999	+	4.45999i	0.162101	+	0.162101i	0.783497	−	0.621396i	$-0.213434\pi$
$757$	4.45999	+	4.45999i	0.162101	+	0.162101i	−0.621396	+	0.783497i	$0.713434\pi$
$758$	−11.2556	−	11.2556i	−0.408822	−	0.408822i
$759$		0			0
$760$	−0.568674	+	0.682504i	−0.0206280	+	0.0247570i
$761$	14.2992	−	14.2992i	0.518346	−	0.518346i	−0.398725	−	0.917071i	$-0.630547\pi$
$761$	14.2992	−	14.2992i	0.518346	−	0.518346i	0.917071	+	0.398725i	$0.130547\pi$
$762$		0			0
$763$	−6.15798	+	6.15798i	−0.222934	+	0.222934i
$764$	−12.0401			−0.435595
$765$		0			0
$766$			16.4651i			0.594909i
$767$	−5.82957	−	4.87471i	−0.210493	−	0.176016i
$768$		0			0
$769$	23.6603	−	23.6603i	0.853213	−	0.853213i	−0.137314	−	0.990528i	$-0.543847\pi$
$769$	23.6603	−	23.6603i	0.853213	−	0.853213i	0.990528	+	0.137314i	$0.0438470\pi$
$770$	4.57811	−	5.49449i	0.164984	−	0.198008i
$771$		0			0
$772$		−	15.7987i		−	0.568608i
$773$	5.59189			0.201126			0.100563	−	0.994931i	$-0.467936\pi$
$773$	5.59189			0.201126			0.100563	+	0.994931i	$0.467936\pi$
$774$		0			0
$775$	15.2980	+	10.5547i	0.549519	+	0.379134i
$776$	−2.01625			−0.0723792
$777$		0			0
$778$		−	26.7942i		−	0.960620i
$779$	−0.571974			−0.0204931
$780$		0			0
$781$	42.5355			1.52204
$782$		−	1.71740i		−	0.0614141i
$783$		0			0
$784$	−6.18583			−0.220923
$785$	24.9806	−	29.9809i	0.891596	−	1.07006i
$786$		0			0
$787$	−19.0891			−0.680454			−0.340227	−	0.940343i	$-0.610504\pi$
$787$	−19.0891			−0.680454			−0.340227	+	0.940343i	$0.610504\pi$
$788$			12.7102i			0.452783i
$789$		0			0
$790$	1.00775	+	11.0769i	0.0358543	+	0.394098i
$791$	−10.0049	+	10.0049i	−0.355732	+	0.355732i
$792$		0			0
$793$	26.7796	−	2.38882i	0.950971	−	0.0848296i
$794$			17.9325i			0.636400i
$795$		0			0
$796$	−15.5881			−0.552506
$797$	25.7517	−	25.7517i	0.912171	−	0.912171i	−0.0842721	−	0.996443i	$-0.526857\pi$
$797$	25.7517	−	25.7517i	0.912171	−	0.912171i	0.996443	+	0.0842721i	$0.0268565\pi$
$798$		0			0
$799$	−29.4096	+	29.4096i	−1.04044	+	1.04044i
$800$	0.902312	+	4.91791i	0.0319016	+	0.173874i
$801$		0			0
$802$	−1.68244	−	1.68244i	−0.0594090	−	0.0594090i
$803$	8.23986	+	8.23986i	0.290778	+	0.290778i
$804$		0			0
$805$	−0.546019	+	0.655314i	−0.0192447	+	0.0230968i
$806$	−8.59738	+	10.2814i	−0.302830	+	0.362148i
$807$		0			0
$808$	12.9392			0.455200
$809$			15.6385i			0.549819i	0.961470	+	0.274909i	$0.0886479\pi$
$809$			15.6385i			0.549819i	−0.961470	+	0.274909i	$0.911352\pi$
$810$		0			0
$811$	1.09361	+	1.09361i	0.0384018	+	0.0384018i	0.726047	−	0.687645i	$-0.241355\pi$
$811$	1.09361	+	1.09361i	0.0384018	+	0.0384018i	−0.687645	+	0.726047i	$0.741355\pi$
$812$		−	1.94306i		−	0.0681881i
$813$		0			0
$814$	19.8378	+	19.8378i	0.695313	+	0.695313i
$815$	50.2566	−	4.57225i	1.76041	−	0.160159i
$816$		0			0
$817$	2.90912			0.101777
$818$	2.71561	+	2.71561i	0.0949491	+	0.0949491i
$819$		0			0
$820$	−2.06073	+	2.47322i	−0.0719639	+	0.0863688i
$821$	−2.32596	−	2.32596i	−0.0811766	−	0.0811766i	0.665353	−	0.746529i	$-0.268281\pi$
$821$	−2.32596	−	2.32596i	−0.0811766	−	0.0811766i	−0.746529	+	0.665353i	$0.768281\pi$
$822$		0			0
$823$	4.63869	+	4.63869i	0.161694	+	0.161694i	0.783317	−	0.621623i	$-0.213526\pi$
$823$	4.63869	+	4.63869i	0.161694	+	0.161694i	−0.621623	+	0.783317i	$0.713526\pi$
$824$	4.17144	−	4.17144i	0.145319	−	0.145319i
$825$		0			0
$826$	1.34473	−	1.34473i	0.0467890	−	0.0467890i
$827$	27.3159			0.949865			0.474933	−	0.880022i	$-0.342472\pi$
$827$	27.3159			0.949865			0.474933	+	0.880022i	$0.342472\pi$
$828$		0			0
$829$	29.4941			1.02437			0.512186	−	0.858875i	$-0.328836\pi$
$829$	29.4941			1.02437			0.512186	+	0.858875i	$0.328836\pi$
$830$	4.09462	−	0.372520i	0.142126	−	0.0129304i
$831$		0			0
$832$	−3.59129	+	0.320354i	−0.124506	+	0.0111063i
$833$	−17.7688	+	17.7688i	−0.615652	+	0.615652i
$834$		0			0
$835$	3.24620	+	35.6811i	0.112339	+	1.23479i
$836$		−	1.40826i		−	0.0487058i
$837$		0			0
$838$	36.7263			1.26869
$839$	−38.3083	−	38.3083i	−1.32255	−	1.32255i	−0.911707	−	0.410841i	$-0.865235\pi$
$839$	−38.3083	−	38.3083i	−1.32255	−	1.32255i	−0.410841	−	0.911707i	$-0.634765\pi$
$840$		0			0
$841$	24.3628			0.840095
$842$	−19.6978	+	19.6978i	−0.678831	+	0.678831i
$843$		0			0
$844$	−4.32936			−0.149023
$845$	−7.71614	−	28.0261i	−0.265443	−	0.964126i
$846$		0			0
$847$			1.41177i			0.0485089i
$848$	7.95152	−	7.95152i	0.273056	−	0.273056i
$849$		0			0
$850$	16.7186	+	11.5348i	0.573442	+	0.395640i
$851$	−2.36600	−	2.36600i	−0.0811054	−	0.0811054i
$852$		0			0
$853$			27.4148i			0.938664i	0.883022	+	0.469332i	$0.155505\pi$
$853$			27.4148i			0.938664i	−0.883022	+	0.469332i	$0.844495\pi$
$854$			6.72837i			0.230240i
$855$		0			0
$856$	3.66987	−	3.66987i	0.125433	−	0.125433i
$857$	−18.6021	+	18.6021i	−0.635436	+	0.635436i	−0.949426	−	0.313990i	$-0.898334\pi$
$857$	−18.6021	+	18.6021i	−0.635436	+	0.635436i	0.313990	+	0.949426i	$0.398334\pi$
$858$		0			0
$859$		−	9.27736i		−	0.316540i	−0.987396	−	0.158270i	$-0.949408\pi$
$859$		−	9.27736i		−	0.316540i	0.987396	−	0.158270i	$-0.0505916\pi$
$860$	10.4811	−	12.5791i	0.357402	−	0.428942i
$861$		0			0
$862$	27.9045	−	27.9045i	0.950432	−	0.950432i
$863$	3.48175			0.118520			0.0592601	−	0.998243i	$-0.481126\pi$
$863$	3.48175			0.118520			0.0592601	+	0.998243i	$0.481126\pi$
$864$		0			0
$865$	−3.46319	+	4.15640i	−0.117752	+	0.141322i
$866$	−6.60618	+	6.60618i	−0.224487	+	0.224487i
$867$		0			0
$868$	−2.37165	−	2.37165i	−0.0804991	−	0.0804991i
$869$	−12.4676	−	12.4676i	−0.422934	−	0.422934i
$870$		0			0
$871$	1.19357	+	13.3803i	0.0404425	+	0.453375i
$872$	6.82467	+	6.82467i	0.231112	+	0.231112i
$873$		0			0
$874$			0.167960i			0.00568133i
$875$	−2.71207	−	9.71677i	−0.0916846	−	0.328487i
$876$		0			0
$877$			49.5564i			1.67340i	0.547662	+	0.836700i	$0.315518\pi$
$877$			49.5564i			1.67340i	−0.547662	+	0.836700i	$0.684482\pi$
$878$			32.3810i			1.09281i
$879$		0			0
$880$	−6.08935	−	5.07375i	−0.205272	−	0.171036i
$881$		−	14.6069i		−	0.492119i	−0.969255	−	0.246060i	$-0.920864\pi$
$881$		−	14.6069i		−	0.492119i	0.969255	−	0.246060i	$-0.0791359\pi$
$882$		0			0
$883$	−25.1501	−	25.1501i	−0.846367	−	0.846367i	0.143310	−	0.989678i	$-0.454225\pi$
$883$	−25.1501	−	25.1501i	−0.846367	−	0.846367i	−0.989678	+	0.143310i	$0.954225\pi$
$884$	−9.39576	+	11.2362i	−0.316014	+	0.377914i
$885$		0			0
$886$	25.0288	+	25.0288i	0.840859	+	0.840859i
$887$	29.0929	+	29.0929i	0.976846	+	0.976846i	0.999738	−	0.0228924i	$-0.00728750\pi$
$887$	29.0929	+	29.0929i	0.976846	+	0.976846i	−0.0228924	+	0.999738i	$0.507288\pi$
$888$		0			0
$889$	10.9871	−	10.9871i	0.368496	−	0.368496i
$890$	−7.42903	−	6.18999i	−0.249022	−	0.207489i
$891$		0			0
$892$	8.55297			0.286375
$893$	2.87622	−	2.87622i	0.0962492	−	0.0962492i
$894$		0			0
$895$	0.422969	+	4.64913i	0.0141383	+	0.155403i
$896$		−	0.902312i		−	0.0301441i
$897$		0			0
$898$	5.77218	−	5.77218i	0.192620	−	0.192620i
$899$	−5.66010	+	5.66010i	−0.188775	+	0.188775i
$900$		0			0
$901$		−	45.6814i		−	1.52187i
$902$		−	5.10319i		−	0.169918i
$903$		0			0
$904$	11.0880	+	11.0880i	0.368782	+	0.368782i
$905$	11.3157	−	1.02948i	0.376147	−	0.0342211i
$906$		0			0
$907$	−14.7775	+	14.7775i	−0.490679	+	0.490679i	−0.908520	−	0.417841i	$-0.862787\pi$
$907$	−14.7775	+	14.7775i	−0.490679	+	0.490679i	0.417841	+	0.908520i	$0.362787\pi$
$908$			1.30008i			0.0431448i
$909$		0			0
$910$	7.15754	−	1.30021i	0.237270	−	0.0431014i
$911$	−19.4565			−0.644623			−0.322311	−	0.946634i	$-0.604460\pi$
$911$	−19.4565			−0.644623			−0.322311	+	0.946634i	$0.604460\pi$
$912$		0			0
$913$	−4.60869	+	4.60869i	−0.152525	+	0.152525i
$914$	21.2810			0.703912
$915$		0			0
$916$	−19.3801	−	19.3801i	−0.640335	−	0.640335i
$917$	−11.6031			−0.383167
$918$		0			0
$919$			10.6444i			0.351126i	0.984468	+	0.175563i	$0.0561745\pi$
$919$			10.6444i			0.351126i	−0.984468	+	0.175563i	$0.943825\pi$
$920$	0.726261	+	0.605133i	0.0239441	+	0.0199507i
$921$		0			0
$922$	−0.427100	+	0.427100i	−0.0140658	+	0.0140658i
$923$	33.1911	+	27.7546i	1.09250	+	0.913553i
$924$		0			0
$925$	38.9236	−	7.14151i	1.27980	−	0.234811i
$926$	−37.4058			−1.22923
$927$		0			0
$928$	−2.15343			−0.0706897
$929$	8.73291	−	8.73291i	0.286517	−	0.286517i	−0.549184	−	0.835701i	$-0.685061\pi$
$929$	8.73291	−	8.73291i	0.286517	−	0.286517i	0.835701	+	0.549184i	$0.185061\pi$
$930$		0			0
$931$	1.73777	−	1.73777i	0.0569531	−	0.0569531i
$932$	3.75807	+	3.75807i	0.123100	+	0.123100i
$933$		0			0
$934$	15.1590	+	15.1590i	0.496019	+	0.496019i
$935$	−32.0660	+	2.91730i	−1.04867	+	0.0954059i
$936$		0			0
$937$	13.3508	+	13.3508i	0.436152	+	0.436152i	0.890715	−	0.454563i	$-0.150205\pi$
$937$	13.3508	+	13.3508i	0.436152	+	0.436152i	−0.454563	+	0.890715i	$0.650205\pi$
$938$	−3.36181			−0.109767
$939$		0			0
$940$	−2.07425	−	22.7994i	−0.0676545	−	0.743635i
$941$	9.62151	+	9.62151i	0.313652	+	0.313652i	0.846323	−	0.532670i	$-0.178811\pi$
$941$	9.62151	+	9.62151i	0.313652	+	0.313652i	−0.532670	+	0.846323i	$0.678811\pi$
$942$		0			0
$943$			0.608645i			0.0198202i
$944$	−1.49031	−	1.49031i	−0.0485055	−	0.0485055i
$945$		0			0
$946$			25.9553i			0.843880i
$947$	43.6546			1.41858			0.709292	−	0.704915i	$-0.249015\pi$
$947$	43.6546			1.41858			0.709292	+	0.704915i	$0.249015\pi$
$948$		0			0
$949$	1.05315	+	11.8062i	0.0341868	+	0.383246i
$950$	−1.63506	−	1.12809i	−0.0530483	−	0.0366001i
$951$		0			0
$952$	−2.59189	−	2.59189i	−0.0840037	−	0.0840037i
$953$	−24.1126	−	24.1126i	−0.781084	−	0.781084i	0.198930	−	0.980014i	$-0.436253\pi$
$953$	−24.1126	−	24.1126i	−0.781084	−	0.781084i	−0.980014	+	0.198930i	$0.936253\pi$
$954$		0			0
$955$	−2.43928	−	26.8117i	−0.0789332	−	0.867607i
$956$	9.12433	−	9.12433i	0.295102	−	0.295102i
$957$		0			0
$958$	−21.9120	+	21.9120i	−0.707944	+	0.707944i
$959$	15.1783			0.490134
$960$		0			0
$961$		−	17.1829i		−	0.554286i
$962$	2.53550	+	28.4239i	0.0817478	+	0.916423i
$963$		0			0
$964$	−17.5200	+	17.5200i	−0.564282	+	0.564282i
$965$	35.1817	−	3.20076i	1.13254	−	0.103036i
$966$		0			0
$967$		−	52.7379i		−	1.69594i	−0.530046	−	0.847969i	$-0.677825\pi$
$967$		−	52.7379i		−	1.69594i	0.530046	−	0.847969i	$-0.322175\pi$
$968$	1.56461			0.0502885
$969$		0			0
$970$	−0.408485	−	4.48993i	−0.0131157	−	0.144163i
$971$	−48.4650			−1.55532			−0.777658	−	0.628687i	$-0.783593\pi$
$971$	−48.4650			−1.55532			−0.777658	+	0.628687i	$0.783593\pi$
$972$		0			0
$973$			2.45301i			0.0786399i
$974$	25.8968			0.829786
$975$		0			0
$976$	7.45681			0.238687
$977$		−	4.05447i		−	0.129714i	−0.997895	−	0.0648569i	$-0.979341\pi$
$977$		−	4.05447i		−	0.129714i	0.997895	−	0.0648569i	$-0.0206591\pi$
$978$		0			0
$979$	15.3289			0.489913
$980$	−1.25323	−	13.7751i	−0.0400329	−	0.440028i
$981$		0			0
$982$	24.8773			0.793866
$983$		−	31.1178i		−	0.992504i	−0.868178	−	0.496252i	$-0.834709\pi$
$983$		−	31.1178i		−	0.992504i	0.868178	−	0.496252i	$-0.165291\pi$
$984$		0			0
$985$	−28.3040	+	2.57505i	−0.901841	+	0.0820478i
$986$	−6.18571	+	6.18571i	−0.196993	+	0.196993i
$987$		0			0
$988$	0.918896	−	1.09889i	0.0292340	−	0.0349603i
$989$		−	3.09563i		−	0.0984352i
$990$		0			0
$991$	−24.6125			−0.781843			−0.390922	−	0.920424i	$-0.627844\pi$
$991$	−24.6125			−0.781843			−0.390922	+	0.920424i	$0.627844\pi$
$992$	−2.62842	+	2.62842i	−0.0834523	+	0.0834523i
$993$		0			0
$994$	−7.65631	+	7.65631i	−0.242843	+	0.242843i
$995$	−3.15810	−	34.7127i	−0.100118	−	1.10047i
$996$		0			0
$997$	7.41636	+	7.41636i	0.234878	+	0.234878i	0.814725	−	0.579847i	$-0.196888\pi$
$997$	7.41636	+	7.41636i	0.234878	+	0.234878i	−0.579847	+	0.814725i	$0.696888\pi$
$998$	−24.5043	−	24.5043i	−0.775671	−	0.775671i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.w.h.307.3	yes	14
3.2	odd	2		1170.2.w.g.307.5	yes	14
5.3	odd	4		1170.2.m.g.73.1	✓	14
13.5	odd	4		1170.2.m.g.577.1	yes	14
15.8	even	4		1170.2.m.h.73.7	yes	14
39.5	even	4		1170.2.m.h.577.7	yes	14
65.18	even	4	inner	1170.2.w.h.343.3	yes	14
195.83	odd	4		1170.2.w.g.343.5	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.m.g.73.1	✓	14	5.3	odd	4
1170.2.m.g.577.1	yes	14	13.5	odd	4
1170.2.m.h.73.7	yes	14	15.8	even	4
1170.2.m.h.577.7	yes	14	39.5	even	4
1170.2.w.g.307.5	yes	14	3.2	odd	2
1170.2.w.g.343.5	yes	14	195.83	odd	4
1170.2.w.h.307.3	yes	14	1.1	even	1	trivial
1170.2.w.h.343.3	yes	14	65.18	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(-0.202596 - 2.22687i) q^{5} -0.902312 q^{7} +1.00000i q^{8} +(-2.22687 + 0.202596i) q^{10} +(2.50645 - 2.50645i) q^{11} +(3.59129 - 0.320354i) q^{13} +0.902312i q^{14} +1.00000 q^{16} +(2.87250 - 2.87250i) q^{17} +(-0.280927 + 0.280927i) q^{19} +(0.202596 + 2.22687i) q^{20} +(-2.50645 - 2.50645i) q^{22} +(0.298938 + 0.298938i) q^{23} +(-4.91791 + 0.902312i) q^{25} +(-0.320354 - 3.59129i) q^{26} +0.902312 q^{28} -2.15343i q^{29} +(-2.62842 - 2.62842i) q^{31} -1.00000i q^{32} +(-2.87250 - 2.87250i) q^{34} +(0.182805 + 2.00933i) q^{35} -7.91467 q^{37} +(0.280927 + 0.280927i) q^{38} +(2.22687 - 0.202596i) q^{40} +(1.01801 + 1.01801i) q^{41} +(-5.17770 - 5.17770i) q^{43} +(-2.50645 + 2.50645i) q^{44} +(0.298938 - 0.298938i) q^{46} -10.2383 q^{47} -6.18583 q^{49} +(0.902312 + 4.91791i) q^{50} +(-3.59129 + 0.320354i) q^{52} +(7.95152 - 7.95152i) q^{53} +(-6.08935 - 5.07375i) q^{55} -0.902312i q^{56} -2.15343 q^{58} +(-1.49031 - 1.49031i) q^{59} +7.45681 q^{61} +(-2.62842 + 2.62842i) q^{62} -1.00000 q^{64} +(-1.44097 - 7.93244i) q^{65} +3.72577i q^{67} +(-2.87250 + 2.87250i) q^{68} +(2.00933 - 0.182805i) q^{70} +(8.48521 + 8.48521i) q^{71} +3.28746i q^{73} +7.91467i q^{74} +(0.280927 - 0.280927i) q^{76} +(-2.26160 + 2.26160i) q^{77} -4.97419i q^{79} +(-0.202596 - 2.22687i) q^{80} +(1.01801 - 1.01801i) q^{82} -1.83873 q^{83} +(-6.97864 - 5.81472i) q^{85} +(-5.17770 + 5.17770i) q^{86} +(2.50645 + 2.50645i) q^{88} +(3.05788 + 3.05788i) q^{89} +(-3.24047 + 0.289060i) q^{91} +(-0.298938 - 0.298938i) q^{92} +10.2383i q^{94} +(0.682504 + 0.568674i) q^{95} +2.01625i q^{97} +6.18583i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{4} + 2 q^{5} + 4 q^{13} + 14 q^{16} - 14 q^{17} - 12 q^{19} - 2 q^{20} - 10 q^{25} - 6 q^{26} + 12 q^{31} + 14 q^{34} - 12 q^{35} + 20 q^{37} + 12 q^{38} + 2 q^{41} + 8 q^{47} + 14 q^{49} - 4 q^{52}+ \cdots - 24 q^{95}+O(q^{100}) \) 14 * q - 14 * q^4 + 2 * q^5 + 4 * q^13 + 14 * q^16 - 14 * q^17 - 12 * q^19 - 2 * q^20 - 10 * q^25 - 6 * q^26 + 12 * q^31 + 14 * q^34 - 12 * q^35 + 20 * q^37 + 12 * q^38 + 2 * q^41 + 8 * q^47 + 14 * q^49 - 4 * q^52 - 6 * q^53 + 32 * q^55 + 16 * q^58 + 16 * q^59 + 24 * q^61 + 12 * q^62 - 14 * q^64 + 4 * q^65 + 14 * q^68 - 4 * q^70 + 24 * q^71 + 12 * q^76 - 16 * q^77 + 2 * q^80 + 2 * q^82 - 8 * q^83 + 2 * q^85 - 42 * q^89 - 8 * q^91 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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