LMFDB - Embedded newform 552.2.u.a.17.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 11, 7]))

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

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

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.12
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0283990 + 1.73182i) q^{3} +(-2.72873 + 1.75365i) q^{5} +(3.60100 + 0.517745i) q^{7} +(-2.99839 + 0.0983638i) q^{9} +O(q^{10})$	\(q+(0.0283990 + 1.73182i) q^{3} +(-2.72873 + 1.75365i) q^{5} +(3.60100 + 0.517745i) q^{7} +(-2.99839 + 0.0983638i) q^{9} +(0.240426 + 0.526460i) q^{11} +(0.426677 + 2.96760i) q^{13} +(-3.11449 - 4.67586i) q^{15} +(1.22014 - 1.40811i) q^{17} +(-6.16848 + 5.34502i) q^{19} +(-0.794376 + 6.25098i) q^{21} +(-2.09742 - 4.31287i) q^{23} +(2.29361 - 5.02230i) q^{25} +(-0.255499 - 5.18987i) q^{27} +(-0.527834 - 0.457371i) q^{29} +(-9.72048 + 2.85419i) q^{31} +(-0.904905 + 0.431325i) q^{33} +(-10.7341 + 4.90209i) q^{35} +(2.32470 - 3.61730i) q^{37} +(-5.12723 + 0.823204i) q^{39} +(4.41696 + 6.87292i) q^{41} +(0.847780 - 2.88727i) q^{43} +(8.00929 - 5.52652i) q^{45} -4.56555i q^{47} +(5.98268 + 1.75667i) q^{49} +(2.47325 + 2.07307i) q^{51} +(-1.66482 + 11.5790i) q^{53} +(-1.57928 - 1.01494i) q^{55} +(-9.43177 - 10.5309i) q^{57} +(6.58393 - 0.946627i) q^{59} +(-1.16139 - 3.95533i) q^{61} +(-10.8481 - 1.19819i) q^{63} +(-6.36842 - 7.34955i) q^{65} +(8.46328 + 3.86505i) q^{67} +(7.40954 - 3.75483i) q^{69} +(7.41076 + 3.38438i) q^{71} +(9.89429 + 11.4186i) q^{73} +(8.76284 + 3.82948i) q^{75} +(0.593202 + 2.02026i) q^{77} +(-1.09620 + 0.157610i) q^{79} +(8.98065 - 0.589865i) q^{81} +(6.26096 + 4.02367i) q^{83} +(-0.860090 + 5.98206i) q^{85} +(0.777094 - 0.927102i) q^{87} +(4.54197 + 1.33364i) q^{89} +10.9072i q^{91} +(-5.21899 - 16.7531i) q^{93} +(7.45883 - 25.4024i) q^{95} +(4.62308 + 7.19366i) q^{97} +(-0.772676 - 1.55488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

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
$3$	0.0283990	+	1.73182i	0.0163962	+	0.999866i
$3$	0.0283990	+	1.73182i	0.0163962	+	0.999866i
$4$		0			0
$5$	−2.72873	+	1.75365i	−1.22032	+	0.784255i	−0.982356	−	0.187018i	$-0.940118\pi$
$5$	−2.72873	+	1.75365i	−1.22032	+	0.784255i	−0.237968	+	0.971273i	$0.576481\pi$
$6$		0			0
$7$	3.60100	+	0.517745i	1.36105	+	0.195689i	0.783868	−	0.620927i	$-0.213244\pi$
$7$	3.60100	+	0.517745i	1.36105	+	0.195689i	0.577181	+	0.816616i	$0.304153\pi$
$8$		0			0
$9$	−2.99839	+	0.0983638i	−0.999462	+	0.0327879i
$10$		0			0
$11$	0.240426	+	0.526460i	0.0724912	+	0.158734i	0.942409	−	0.334464i	$-0.108555\pi$
$11$	0.240426	+	0.526460i	0.0724912	+	0.158734i	−0.869917	+	0.493198i	$0.835828\pi$
$12$		0			0
$13$	0.426677	+	2.96760i	0.118339	+	0.823065i	0.959385	+	0.282101i	$0.0910314\pi$
$13$	0.426677	+	2.96760i	0.118339	+	0.823065i	−0.841046	+	0.540964i	$0.818059\pi$
$14$		0			0
$15$	−3.11449	−	4.67586i	−0.804158	−	1.20730i
$16$		0			0
$17$	1.22014	−	1.40811i	0.295927	−	0.341518i	−0.588242	−	0.808685i	$-0.700180\pi$
$17$	1.22014	−	1.40811i	0.295927	−	0.341518i	0.884169	+	0.467167i	$0.154725\pi$
$18$		0			0
$19$	−6.16848	+	5.34502i	−1.41515	+	1.22623i	−0.477503	+	0.878630i	$0.658458\pi$
$19$	−6.16848	+	5.34502i	−1.41515	+	1.22623i	−0.937643	+	0.347600i	$0.886997\pi$
$20$		0			0
$21$	−0.794376	+	6.25098i	−0.173347	+	1.36407i
$22$		0			0
$23$	−2.09742	−	4.31287i	−0.437342	−	0.899295i
$23$	−2.09742	−	4.31287i	−0.437342	−	0.899295i
$24$		0			0
$25$	2.29361	−	5.02230i	0.458721	−	1.00446i
$26$		0			0
$27$	−0.255499	−	5.18987i	−0.0491709	−	0.998790i
$28$		0			0
$29$	−0.527834	−	0.457371i	−0.0980164	−	0.0849317i	0.604474	−	0.796625i	$-0.293383\pi$
$29$	−0.527834	−	0.457371i	−0.0980164	−	0.0849317i	−0.702491	+	0.711693i	$0.747929\pi$
$30$		0			0
$31$	−9.72048	+	2.85419i	−1.74585	+	0.512628i	−0.989871	−	0.141968i	$-0.954657\pi$
$31$	−9.72048	+	2.85419i	−1.74585	+	0.512628i	−0.755979	+	0.654596i	$0.772839\pi$
$32$		0			0
$33$	−0.904905	+	0.431325i	−0.157524	+	0.0750841i
$34$		0			0
$35$	−10.7341	+	4.90209i	−1.81439	+	0.828605i
$36$		0			0
$37$	2.32470	−	3.61730i	0.382178	−	0.594680i	−0.595865	−	0.803085i	$-0.703191\pi$
$37$	2.32470	−	3.61730i	0.382178	−	0.594680i	0.978043	+	0.208405i	$0.0668271\pi$
$38$		0			0
$39$	−5.12723	+	0.823204i	−0.821014	+	0.131818i
$40$		0			0
$41$	4.41696	+	6.87292i	0.689813	+	1.07337i	0.992731	+	0.120354i	$0.0384028\pi$
$41$	4.41696	+	6.87292i	0.689813	+	1.07337i	−0.302918	+	0.953017i	$0.597961\pi$
$42$		0			0
$43$	0.847780	−	2.88727i	0.129285	−	0.440305i	−0.869252	−	0.494369i	$-0.835399\pi$
$43$	0.847780	−	2.88727i	0.129285	−	0.440305i	0.998537	+	0.0540637i	$0.0172174\pi$
$44$		0			0
$45$	8.00929	−	5.52652i	1.19395	−	0.823845i
$46$		0			0
$47$		−	4.56555i		−	0.665954i	−0.942935	−	0.332977i	$-0.891947\pi$
$47$		−	4.56555i		−	0.665954i	0.942935	−	0.332977i	$-0.108053\pi$
$48$		0			0
$49$	5.98268	+	1.75667i	0.854668	+	0.250953i
$50$		0			0
$51$	2.47325	+	2.07307i	0.346324	+	0.290288i
$52$		0			0
$53$	−1.66482	+	11.5790i	−0.228680	+	1.59050i	0.474999	+	0.879986i	$0.342448\pi$
$53$	−1.66482	+	11.5790i	−0.228680	+	1.59050i	−0.703679	+	0.710518i	$0.748461\pi$
$54$		0			0
$55$	−1.57928	−	1.01494i	−0.212951	−	0.136855i
$56$		0			0
$57$	−9.43177	−	10.5309i	−1.24927	−	1.39485i
$58$		0			0
$59$	6.58393	−	0.946627i	0.857155	−	0.123240i	0.300295	−	0.953846i	$-0.402915\pi$
$59$	6.58393	−	0.946627i	0.857155	−	0.123240i	0.556860	+	0.830606i	$0.312006\pi$
$60$		0			0
$61$	−1.16139	−	3.95533i	−0.148701	−	0.506428i	0.851128	−	0.524959i	$-0.175919\pi$
$61$	−1.16139	−	3.95533i	−0.148701	−	0.506428i	−0.999828	+	0.0185311i	$0.994101\pi$
$62$		0			0
$63$	−10.8481	−	1.19819i	−1.36673	−	0.150958i
$64$		0			0
$65$	−6.36842	−	7.34955i	−0.789905	−	0.911599i
$66$		0			0
$67$	8.46328	+	3.86505i	1.03395	+	0.472191i	0.858779	−	0.512346i	$-0.171224\pi$
$67$	8.46328	+	3.86505i	1.03395	+	0.472191i	0.175175	+	0.984537i	$0.443951\pi$
$68$		0			0
$69$	7.40954	−	3.75483i	0.892003	−	0.452029i
$70$		0			0
$71$	7.41076	+	3.38438i	0.879495	+	0.401652i	0.803394	−	0.595448i	$-0.203025\pi$
$71$	7.41076	+	3.38438i	0.879495	+	0.401652i	0.0761013	+	0.997100i	$0.475753\pi$
$72$		0			0
$73$	9.89429	+	11.4186i	1.15804	+	1.33645i	0.932055	+	0.362317i	$0.118014\pi$
$73$	9.89429	+	11.4186i	1.15804	+	1.33645i	0.225983	+	0.974131i	$0.427440\pi$
$74$		0			0
$75$	8.76284	+	3.82948i	1.01185	+	0.442190i
$76$		0			0
$77$	0.593202	+	2.02026i	0.0676017	+	0.230230i
$78$		0			0
$79$	−1.09620	+	0.157610i	−0.123333	+	0.0177325i	−0.203705	−	0.979032i	$-0.565298\pi$
$79$	−1.09620	+	0.157610i	−0.123333	+	0.0177325i	0.0803721	+	0.996765i	$0.474389\pi$
$80$		0			0
$81$	8.98065	−	0.589865i	0.997850	−	0.0655406i
$82$		0			0
$83$	6.26096	+	4.02367i	0.687229	+	0.441656i	0.837100	−	0.547050i	$-0.184249\pi$
$83$	6.26096	+	4.02367i	0.687229	+	0.441656i	−0.149870	+	0.988706i	$0.547886\pi$
$84$		0			0
$85$	−0.860090	+	5.98206i	−0.0932898	+	0.648845i
$86$		0			0
$87$	0.777094	−	0.927102i	0.0833132	−	0.0993958i
$88$		0			0
$89$	4.54197	+	1.33364i	0.481447	+	0.141366i	0.513445	−	0.858122i	$-0.328369\pi$
$89$	4.54197	+	1.33364i	0.481447	+	0.141366i	−0.0319981	+	0.999488i	$0.510187\pi$
$90$		0			0
$91$			10.9072i			1.14339i
$92$		0			0
$93$	−5.21899	−	16.7531i	−0.541184	−	1.73721i
$94$		0			0
$95$	7.45883	−	25.4024i	0.765259	−	2.60623i
$96$		0			0
$97$	4.62308	+	7.19366i	0.469403	+	0.730405i	0.992550	−	0.121837i	$-0.0388786\pi$
$97$	4.62308	+	7.19366i	0.469403	+	0.730405i	−0.523147	+	0.852242i	$0.675242\pi$
$98$		0			0
$99$	−0.772676	−	1.55488i	−0.0776568	−	0.156271i
$100$		0			0
$101$	−3.75048	+	5.83586i	−0.373187	+	0.580690i	−0.976155	−	0.217075i	$-0.930348\pi$
$101$	−3.75048	+	5.83586i	−0.373187	+	0.580690i	0.602968	+	0.797765i	$0.293985\pi$
$102$		0			0
$103$	−11.5818	+	5.28922i	−1.14119	+	0.521163i	−0.894116	−	0.447835i	$-0.852195\pi$
$103$	−11.5818	+	5.28922i	−1.14119	+	0.521163i	−0.247071	+	0.968997i	$0.579468\pi$
$104$		0			0
$105$	−8.79437	−	18.4503i	−0.858243	−	1.80056i
$106$		0			0
$107$	−18.6998	+	5.49076i	−1.80778	+	0.530812i	−0.998404	−	0.0564788i	$-0.982013\pi$
$107$	−18.6998	+	5.49076i	−1.80778	+	0.530812i	−0.809376	+	0.587291i	$0.800194\pi$
$108$		0			0
$109$	−0.459038	−	0.397759i	−0.0439679	−	0.0380984i	0.632600	−	0.774479i	$-0.281988\pi$
$109$	−0.459038	−	0.397759i	−0.0439679	−	0.0380984i	−0.676568	+	0.736381i	$0.736533\pi$
$110$		0			0
$111$	6.33052	+	3.92322i	0.600866	+	0.372376i
$112$		0			0
$113$	−0.720497	+	1.57767i	−0.0677786	+	0.148414i	−0.940489	−	0.339823i	$-0.889633\pi$
$113$	−0.720497	+	1.57767i	−0.0677786	+	0.148414i	0.872711	+	0.488238i	$0.162360\pi$
$114$		0			0
$115$	13.2865	+	8.09051i	1.23898	+	0.754444i
$116$		0			0
$117$	−1.57125	−	8.85606i	−0.145262	−	0.818743i
$118$		0			0
$119$	5.12276	−	4.43890i	0.469603	−	0.406913i
$120$		0			0
$121$	6.98411	−	8.06010i	0.634919	−	0.732736i
$122$		0			0
$123$	−11.7772	+	7.84455i	−1.06192	+	0.707320i
$124$		0			0
$125$	0.240614	+	1.67350i	0.0215211	+	0.149683i
$126$		0			0
$127$	−1.56209	−	3.42051i	−0.138613	−	0.303521i	0.827576	−	0.561353i	$-0.189719\pi$
$127$	−1.56209	−	3.42051i	−0.138613	−	0.303521i	−0.966190	+	0.257832i	$0.916992\pi$
$128$		0			0
$129$	5.02431	+	1.38621i	0.442366	+	0.122049i
$130$		0			0
$131$	4.86730	+	0.699812i	0.425258	+	0.0611428i	0.351621	−	0.936142i	$-0.385630\pi$
$131$	4.86730	+	0.699812i	0.425258	+	0.0611428i	0.0736364	+	0.997285i	$0.476540\pi$
$132$		0			0
$133$	−24.9800	+	16.0537i	−2.16604	+	1.39203i
$134$		0			0
$135$	9.79838	+	13.7137i	0.843311	+	1.18029i
$136$		0			0
$137$	19.6979			1.68290			0.841452	−	0.540332i	$-0.181701\pi$
$137$	19.6979			1.68290			0.841452	+	0.540332i	$0.181701\pi$
$138$		0			0
$139$	15.6146			1.32441			0.662207	−	0.749321i	$-0.269620\pi$
$139$	15.6146			1.32441			0.662207	+	0.749321i	$0.269620\pi$
$140$		0			0
$141$	7.90670	−	0.129657i	0.665865	−	0.0109191i
$142$		0			0
$143$	−1.45974	+	0.938118i	−0.122070	+	0.0784494i
$144$		0			0
$145$	2.24238	+	0.322406i	0.186220	+	0.0267744i
$146$		0			0
$147$	−2.87233	+	10.4108i	−0.236906	+	0.858668i
$148$		0			0
$149$	−0.360103	−	0.788515i	−0.0295008	−	0.0645976i	0.894308	−	0.447452i	$-0.147668\pi$
$149$	−0.360103	−	0.788515i	−0.0295008	−	0.0645976i	−0.923809	+	0.382854i	$0.874941\pi$
$150$		0			0
$151$	−1.32695	−	9.22916i	−0.107986	−	0.751058i	−0.969812	−	0.243854i	$-0.921588\pi$
$151$	−1.32695	−	9.22916i	−0.107986	−	0.751058i	0.861826	−	0.507204i	$-0.169321\pi$
$152$		0			0
$153$	−3.51994	+	4.34209i	−0.284570	+	0.351037i
$154$		0			0
$155$	21.5193	−	24.8346i	1.72847	−	1.99476i
$156$		0			0
$157$	7.04357	−	6.10329i	0.562138	−	0.487095i	−0.326819	−	0.945087i	$-0.605977\pi$
$157$	7.04357	−	6.10329i	0.562138	−	0.487095i	0.888956	+	0.457992i	$0.151431\pi$
$158$		0			0
$159$	−20.1001	−	2.55432i	−1.59404	−	0.202571i
$160$		0			0
$161$	−5.31984	−	16.6166i	−0.419262	−	1.30957i
$162$		0			0
$163$	2.33034	−	5.10274i	0.182526	−	0.399677i	−0.796146	−	0.605105i	$-0.793131\pi$
$163$	2.33034	−	5.10274i	0.182526	−	0.399677i	0.978672	+	0.205428i	$0.0658585\pi$
$164$		0			0
$165$	1.71285	−	2.76385i	0.133345	−	0.215166i
$166$		0			0
$167$	−7.85917	−	6.81001i	−0.608161	−	0.526974i	0.295434	−	0.955363i	$-0.404536\pi$
$167$	−7.85917	−	6.81001i	−0.608161	−	0.526974i	−0.903594	+	0.428389i	$0.859081\pi$
$168$		0			0
$169$	3.84879	−	1.13011i	0.296061	−	0.0869312i
$170$		0			0
$171$	17.9697	−	16.6332i	1.37418	−	1.27197i
$172$		0			0
$173$	5.72547	−	2.61474i	0.435300	−	0.198795i	−0.185698	−	0.982607i	$-0.559455\pi$
$173$	5.72547	−	2.61474i	0.435300	−	0.198795i	0.620998	+	0.783812i	$0.286727\pi$
$174$		0			0
$175$	10.8595	−	16.8978i	0.820904	−	1.27735i
$176$		0			0
$177$	1.82636	+	11.3753i	0.137278	+	0.855019i
$178$		0			0
$179$	−8.28990	−	12.8993i	−0.619617	−	0.964142i	−0.999239	−	0.0390007i	$-0.987583\pi$
$179$	−8.28990	−	12.8993i	−0.619617	−	0.964142i	0.379623	−	0.925141i	$-0.376054\pi$
$180$		0			0
$181$	−4.85934	+	16.5494i	−0.361192	+	1.23011i	0.555839	+	0.831290i	$0.312397\pi$
$181$	−4.85934	+	16.5494i	−0.361192	+	1.23011i	−0.917031	+	0.398817i	$0.869421\pi$
$182$		0			0
$183$	6.81692	−	2.12364i	0.503921	−	0.156984i
$184$		0			0
$185$			13.9473i			1.02543i
$186$		0			0
$187$	1.03467	+	0.303806i	0.0756625	+	0.0222165i
$188$		0			0
$189$	1.76698	−	18.8210i	0.128529	−	1.36903i
$190$		0			0
$191$	−1.20248	+	8.36344i	−0.0870084	+	0.605157i	0.898936	+	0.438081i	$0.144342\pi$
$191$	−1.20248	+	8.36344i	−0.0870084	+	0.605157i	−0.985944	+	0.167076i	$0.946567\pi$
$192$		0			0
$193$	7.36402	+	4.73257i	0.530074	+	0.340658i	0.778146	−	0.628084i	$-0.216160\pi$
$193$	7.36402	+	4.73257i	0.530074	+	0.340658i	−0.248072	+	0.968742i	$0.579797\pi$
$194$		0			0
$195$	12.5472	−	11.2377i	0.898525	−	0.804745i
$196$		0			0
$197$	11.8318	−	1.70116i	0.842984	−	0.121203i	0.292725	−	0.956197i	$-0.405438\pi$
$197$	11.8318	−	1.70116i	0.842984	−	0.121203i	0.550259	+	0.834994i	$0.314529\pi$
$198$		0			0
$199$	4.46961	+	15.2221i	0.316842	+	1.07907i	0.951851	+	0.306561i	$0.0991784\pi$
$199$	4.46961	+	15.2221i	0.316842	+	1.07907i	−0.635009	+	0.772505i	$0.719003\pi$
$200$		0			0
$201$	−6.45321	+	14.7666i	−0.455175	+	1.04156i
$202$		0			0
$203$	−1.66393	−	1.92028i	−0.116785	−	0.134777i
$204$		0			0
$205$	−24.1054	−	11.0086i	−1.68359	−	0.768871i
$206$		0			0
$207$	6.71311	+	12.7253i	0.466593	+	0.884472i
$208$		0			0
$209$	−4.29700	−	1.96237i	−0.297230	−	0.135740i
$210$		0			0
$211$	−9.23197	−	10.6543i	−0.635555	−	0.733469i	0.343027	−	0.939325i	$-0.388548\pi$
$211$	−9.23197	−	10.6543i	−0.635555	−	0.733469i	−0.978582	+	0.205856i	$0.934002\pi$
$212$		0			0
$213$	−5.65067	+	12.9302i	−0.387178	+	0.885962i
$214$		0			0
$215$	2.74990	+	9.36530i	0.187542	+	0.638708i
$216$		0			0
$217$	−36.4812	+	5.24520i	−2.47650	+	0.356068i
$218$		0			0
$219$	−19.4940	+	17.4594i	−1.31728	+	1.17980i
$220$		0			0
$221$	4.69933	+	3.02008i	0.316111	+	0.203152i
$222$		0			0
$223$	3.10765	−	21.6142i	0.208104	−	1.44739i	−0.571233	−	0.820788i	$-0.693535\pi$
$223$	3.10765	−	21.6142i	0.208104	−	1.44739i	0.779337	−	0.626605i	$-0.215556\pi$
$224$		0			0
$225$	−6.38310	+	15.2844i	−0.425540	+	1.01896i
$226$		0			0
$227$	−15.2859	−	4.48834i	−1.01456	−	0.297902i	−0.268142	−	0.963379i	$-0.586410\pi$
$227$	−15.2859	−	4.48834i	−1.01456	−	0.297902i	−0.746418	+	0.665478i	$0.768228\pi$
$228$		0			0
$229$		−	13.6713i		−	0.903422i	−0.892164	−	0.451711i	$-0.850814\pi$
$229$		−	13.6713i		−	0.903422i	0.892164	−	0.451711i	$-0.149186\pi$
$230$		0			0
$231$	−3.48188	+	1.08469i	−0.229091	+	0.0713675i
$232$		0			0
$233$	0.0493807	−	0.168175i	0.00323504	−	0.0110175i	−0.957860	−	0.287237i	$-0.907263\pi$
$233$	0.0493807	−	0.168175i	0.00323504	−	0.0110175i	0.961095	+	0.276219i	$0.0890816\pi$
$234$		0			0
$235$	8.00637	+	12.4581i	0.522278	+	0.812680i
$236$		0			0
$237$	−0.304083	−	1.89395i	−0.0197523	−	0.123025i
$238$		0			0
$239$	−10.6296	+	16.5400i	−0.687574	+	1.06989i	0.305477	+	0.952200i	$0.401184\pi$
$239$	−10.6296	+	16.5400i	−0.687574	+	1.06989i	−0.993051	+	0.117687i	$0.962452\pi$
$240$		0			0
$241$	−9.17779	+	4.19136i	−0.591194	+	0.269989i	−0.688466	−	0.725269i	$-0.741716\pi$
$241$	−9.17779	+	4.19136i	−0.591194	+	0.269989i	0.0972722	+	0.995258i	$0.468988\pi$
$242$		0			0
$243$	1.27658	+	15.5361i	0.0818927	+	0.996641i
$244$		0			0
$245$	−19.4057	+	5.69802i	−1.23978	+	0.364033i
$246$		0			0
$247$	−18.4938	−	16.0250i	−1.17673	−	1.01965i
$248$		0			0
$249$	−6.79047	+	10.9571i	−0.430328	+	0.694378i
$250$		0			0
$251$	−8.10282	+	17.7427i	−0.511446	+	1.11991i	0.461132	+	0.887332i	$0.347443\pi$
$251$	−8.10282	+	17.7427i	−0.511446	+	1.11991i	−0.972578	+	0.232578i	$0.925284\pi$
$252$		0			0
$253$	1.76628	−	2.14113i	0.111045	−	0.134612i
$254$		0			0
$255$	−10.3843	−	1.31963i	−0.650287	−	0.0826387i
$256$		0			0
$257$	−4.16250	+	3.60683i	−0.259650	+	0.224988i	−0.774951	−	0.632021i	$-0.782226\pi$
$257$	−4.16250	+	3.60683i	−0.259650	+	0.224988i	0.515301	+	0.857009i	$0.327680\pi$
$258$		0			0
$259$	10.2441	−	11.8223i	0.636535	−	0.734601i
$260$		0			0
$261$	1.62764	+	1.31946i	0.100748	+	0.0816723i
$262$		0			0
$263$	−0.0320729	−	0.223072i	−0.00197770	−	0.0137552i	0.988809	−	0.149189i	$-0.0476663\pi$
$263$	−0.0320729	−	0.223072i	−0.00197770	−	0.0137552i	−0.990786	+	0.135434i	$0.956757\pi$
$264$		0			0
$265$	−15.7627	−	34.5156i	−0.968297	−	2.12027i
$266$		0			0
$267$	−2.18064	+	7.90373i	−0.133453	+	0.483700i
$268$		0			0
$269$	−27.5955	−	3.96763i	−1.68252	−	0.241910i	−0.766273	−	0.642515i	$-0.777891\pi$
$269$	−27.5955	−	3.96763i	−1.68252	−	0.241910i	−0.916251	+	0.400604i	$0.868800\pi$
$270$		0			0
$271$	4.61812	−	2.96788i	0.280531	−	0.180286i	−0.392808	−	0.919621i	$-0.628496\pi$
$271$	4.61812	−	2.96788i	0.280531	−	0.180286i	0.673338	+	0.739335i	$0.264860\pi$
$272$		0			0
$273$	−18.8894	+	0.309755i	−1.14324	+	0.0187472i
$274$		0			0
$275$	3.19548			0.192695
$276$		0			0
$277$	28.1689			1.69250			0.846252	−	0.532783i	$-0.178854\pi$
$277$	28.1689			1.69250			0.846252	+	0.532783i	$0.178854\pi$
$278$		0			0
$279$	28.8650	−	9.51411i	1.72810	−	0.569595i
$280$		0			0
$281$	−6.69365	+	4.30175i	−0.399310	+	0.256621i	−0.724849	−	0.688908i	$-0.758091\pi$
$281$	−6.69365	+	4.30175i	−0.399310	+	0.256621i	0.325539	+	0.945528i	$0.394454\pi$
$282$		0			0
$283$	13.4598	+	1.93523i	0.800103	+	0.115037i	0.530225	−	0.847857i	$-0.322107\pi$
$283$	13.4598	+	1.93523i	0.800103	+	0.115037i	0.269878	+	0.962894i	$0.413017\pi$
$284$		0			0
$285$	44.2042	+	12.1959i	2.61843	+	0.722424i
$286$		0			0
$287$	12.3470	+	27.0362i	0.728823	+	1.59590i
$288$		0			0
$289$	1.92530	+	13.3908i	0.113253	+	0.787693i
$290$		0			0
$291$	−12.3268	+	8.21063i	−0.722610	+	0.481316i
$292$		0			0
$293$	−13.3504	+	15.4071i	−0.779936	+	0.900094i	−0.997105	−	0.0760399i	$-0.975772\pi$
$293$	−13.3504	+	15.4071i	−0.779936	+	0.900094i	0.217169	+	0.976134i	$0.430318\pi$
$294$		0			0
$295$	−16.3057	+	14.1290i	−0.949355	+	0.822621i
$296$		0			0
$297$	2.67083	−	1.38229i	0.154977	−	0.0802086i
$298$		0			0
$299$	11.9040	−	8.06452i	0.688424	−	0.466383i
$300$		0			0
$301$	4.54773	−	9.95813i	0.262127	−	0.573977i
$302$		0			0
$303$	−10.2132	−	6.32942i	−0.586731	−	0.363616i
$304$		0			0
$305$	10.1054	+	8.75635i	0.578631	+	0.501387i
$306$		0			0
$307$	−1.15853	+	0.340174i	−0.0661205	+	0.0194147i	−0.314626	−	0.949216i	$-0.601879\pi$
$307$	−1.15853	+	0.340174i	−0.0661205	+	0.0194147i	0.248505	+	0.968631i	$0.420061\pi$
$308$		0			0
$309$	−9.48888	−	19.9073i	−0.539804	−	1.13249i
$310$		0			0
$311$	15.1031	−	6.89734i	0.856416	−	0.391112i	0.0617009	−	0.998095i	$-0.480348\pi$
$311$	15.1031	−	6.89734i	0.856416	−	0.391112i	0.794715	+	0.606983i	$0.207620\pi$
$312$		0			0
$313$	−10.1188	+	15.7451i	−0.571946	+	0.889965i	−0.999904	−	0.0138333i	$-0.995597\pi$
$313$	−10.1188	+	15.7451i	−0.571946	+	0.889965i	0.427958	+	0.903798i	$0.359233\pi$
$314$		0			0
$315$	31.7028	−	15.7542i	1.78625	−	0.887650i
$316$		0			0
$317$	14.7667	+	22.9774i	0.829378	+	1.29054i	0.954444	+	0.298390i	$0.0964495\pi$
$317$	14.7667	+	22.9774i	0.829378	+	1.29054i	−0.125066	+	0.992148i	$0.539914\pi$
$318$		0			0
$319$	0.113882	−	0.387848i	0.00637619	−	0.0217153i
$320$		0			0
$321$	−10.0401	−	32.2288i	−0.560381	−	1.79883i
$322$		0			0
$323$			15.2076i			0.846172i
$324$		0			0
$325$	15.8828	+	4.66361i	0.881020	+	0.258691i
$326$		0			0
$327$	0.675810	−	0.806267i	0.0373724	−	0.0445866i
$328$		0			0
$329$	2.36379	−	16.4405i	0.130320	−	0.906396i
$330$		0			0
$331$	13.9483	+	8.96400i	0.766665	+	0.492706i	0.864584	−	0.502489i	$-0.167582\pi$
$331$	13.9483	+	8.96400i	0.766665	+	0.492706i	−0.0979186	+	0.995194i	$0.531218\pi$
$332$		0			0
$333$	−6.61453	+	11.0747i	−0.362474	+	0.606891i
$334$		0			0
$335$	−29.8719	+	4.29493i	−1.63208	+	0.234657i
$336$		0			0
$337$	−3.96568	−	13.5059i	−0.216024	−	0.735711i	−0.994189	−	0.107650i	$-0.965667\pi$
$337$	−3.96568	−	13.5059i	−0.216024	−	0.735711i	0.778165	−	0.628060i	$-0.216151\pi$
$338$		0			0
$339$	−2.75269	−	1.20296i	−0.149506	−	0.0653361i
$340$		0			0
$341$	−3.83968	−	4.43122i	−0.207930	−	0.239964i
$342$		0			0
$343$	−2.53077	−	1.15576i	−0.136649	−	0.0624054i
$344$		0			0
$345$	−13.6340	+	23.2396i	−0.734028	+	1.25118i
$346$		0			0
$347$	−1.83124	−	0.836299i	−0.0983061	−	0.0448949i	0.365655	−	0.930750i	$-0.380845\pi$
$347$	−1.83124	−	0.836299i	−0.0983061	−	0.0448949i	−0.463961	+	0.885856i	$0.653572\pi$
$348$		0			0
$349$	10.5824	+	12.2127i	0.566461	+	0.653731i	0.964638	−	0.263578i	$-0.0849025\pi$
$349$	10.5824	+	12.2127i	0.566461	+	0.653731i	−0.398177	+	0.917309i	$0.630357\pi$
$350$		0			0
$351$	15.2925	−	2.97262i	0.816251	−	0.158667i
$352$		0			0
$353$	−0.507595	−	1.72871i	−0.0270166	−	0.0920100i	0.944881	−	0.327414i	$-0.106177\pi$
$353$	−0.507595	−	1.72871i	−0.0270166	−	0.0920100i	−0.971898	+	0.235404i	$0.924359\pi$
$354$		0			0
$355$	−26.1569	+	3.76080i	−1.38827	+	0.199603i
$356$		0			0
$357$	7.83284	+	8.74563i	0.414558	+	0.462868i
$358$		0			0
$359$	−8.88135	−	5.70769i	−0.468740	−	0.301241i	0.284866	−	0.958567i	$-0.408051\pi$
$359$	−8.88135	−	5.70769i	−0.468740	−	0.301241i	−0.753606	+	0.657327i	$0.771687\pi$
$360$		0			0
$361$	6.77693	−	47.1346i	0.356681	−	2.48077i
$362$		0			0
$363$	14.1570	+	11.8663i	0.743048	+	0.622820i
$364$		0			0
$365$	−47.0230	−	13.8072i	−2.46130	−	0.722702i
$366$		0			0
$367$			26.4253i			1.37939i	0.724099	+	0.689696i	$0.242256\pi$
$367$			26.4253i			1.37939i	−0.724099	+	0.689696i	$0.757744\pi$
$368$		0			0
$369$	−13.9198	−	20.1732i	−0.724636	−	1.05018i
$370$		0			0
$371$	−11.9900	+	40.8342i	−0.622489	+	2.12000i
$372$		0			0
$373$	−6.96431	−	10.8367i	−0.360598	−	0.561102i	0.612795	−	0.790242i	$-0.290045\pi$
$373$	−6.96431	−	10.8367i	−0.360598	−	0.561102i	−0.973393	+	0.229140i	$0.926409\pi$
$374$		0			0
$375$	−2.89137	+	0.464225i	−0.149310	+	0.0239725i
$376$		0			0
$377$	1.13208	−	1.76155i	0.0583052	−	0.0907246i
$378$		0			0
$379$	−2.75722	+	1.25918i	−0.141629	+	0.0646798i	−0.484969	−	0.874531i	$-0.661169\pi$
$379$	−2.75722	+	1.25918i	−0.141629	+	0.0646798i	0.343340	+	0.939211i	$0.388442\pi$
$380$		0			0
$381$	5.87933	−	2.80240i	0.301207	−	0.143571i
$382$		0			0
$383$	23.0267	−	6.76125i	1.17661	−	0.345484i	0.365744	−	0.930716i	$-0.380815\pi$
$383$	23.0267	−	6.76125i	1.17661	−	0.345484i	0.810866	+	0.585232i	$0.198997\pi$
$384$		0			0
$385$	−5.16151	−	4.47248i	−0.263055	−	0.227939i
$386$		0			0
$387$	−2.25797	+	8.74056i	−0.114779	+	0.444307i
$388$		0			0
$389$	12.9430	−	28.3413i	0.656239	−	1.43696i	−0.229748	−	0.973250i	$-0.573790\pi$
$389$	12.9430	−	28.3413i	0.656239	−	1.43696i	0.885986	−	0.463712i	$-0.153483\pi$
$390$		0			0
$391$	−8.63216	−	2.30889i	−0.436547	−	0.116765i
$392$		0			0
$393$	−1.07372	+	8.44915i	−0.0541620	+	0.426203i
$394$		0			0
$395$	2.71485	−	2.35243i	0.136599	−	0.118364i
$396$		0			0
$397$	15.9779	−	18.4395i	0.801907	−	0.925450i	−0.196577	−	0.980488i	$-0.562983\pi$
$397$	15.9779	−	18.4395i	0.801907	−	0.925450i	0.998484	+	0.0550381i	$0.0175280\pi$
$398$		0			0
$399$	−28.5115	−	42.8050i	−1.42736	−	2.14293i
$400$		0			0
$401$	1.33896	+	9.31268i	0.0668645	+	0.465053i	0.995554	+	0.0941944i	$0.0300275\pi$
$401$	1.33896	+	9.31268i	0.0668645	+	0.465053i	−0.928689	+	0.370859i	$0.879063\pi$
$402$		0			0
$403$	−12.6176	−	27.6287i	−0.628528	−	1.37629i
$404$		0			0
$405$	−23.4713	+	17.3585i	−1.16630	+	0.862549i
$406$		0			0
$407$	2.46328	+	0.354166i	0.122100	+	0.0175554i
$408$		0			0
$409$	12.5137	−	8.04209i	0.618765	−	0.397656i	−0.193370	−	0.981126i	$-0.561942\pi$
$409$	12.5137	−	8.04209i	0.618765	−	0.397656i	0.812135	+	0.583470i	$0.198305\pi$
$410$		0			0
$411$	0.559400	+	34.1132i	0.0275932	+	1.68268i
$412$		0			0
$413$	24.1988			1.19075
$414$		0			0
$415$	−24.1406			−1.18501
$416$		0			0
$417$	0.443439	+	27.0416i	0.0217153	+	1.32423i
$418$		0			0
$419$	5.62599	−	3.61561i	0.274848	−	0.176634i	−0.395955	−	0.918270i	$-0.629586\pi$
$419$	5.62599	−	3.61561i	0.274848	−	0.176634i	0.670802	+	0.741636i	$0.265950\pi$
$420$		0			0
$421$	−25.1766	−	3.61985i	−1.22703	−	0.176421i	−0.501836	−	0.864963i	$-0.667342\pi$
$421$	−25.1766	−	3.61985i	−1.22703	−	0.176421i	−0.725196	+	0.688542i	$0.758251\pi$
$422$		0			0
$423$	0.449085	+	13.6893i	0.0218352	+	0.665596i
$424$		0			0
$425$	−4.27345	−	9.35755i	−0.207293	−	0.453908i
$426$		0			0
$427$	−2.13431	−	14.8444i	−0.103286	−	0.718372i
$428$		0			0
$429$	−1.66611	−	2.50136i	−0.0804403	−	0.120767i
$430$		0			0
$431$	19.7709	−	22.8168i	0.952330	−	1.09905i	−0.0426617	−	0.999090i	$-0.513584\pi$
$431$	19.7709	−	22.8168i	0.952330	−	1.09905i	0.994992	−	0.0999578i	$-0.0318708\pi$
$432$		0			0
$433$	−10.4220	+	9.03070i	−0.500848	+	0.433988i	−0.868288	−	0.496060i	$-0.834780\pi$
$433$	−10.4220	+	9.03070i	−0.500848	+	0.433988i	0.367440	+	0.930047i	$0.380234\pi$
$434$		0			0
$435$	−0.494667	+	3.89256i	−0.0237175	+	0.186634i
$436$		0			0
$437$	35.9902	+	15.3931i	1.72165	+	0.736351i
$438$		0			0
$439$	13.5516	−	29.6738i	0.646782	−	1.41625i	−0.247561	−	0.968872i	$-0.579629\pi$
$439$	13.5516	−	29.6738i	0.646782	−	1.41625i	0.894343	−	0.447383i	$-0.147644\pi$
$440$		0			0
$441$	−18.1112	−	4.67870i	−0.862437	−	0.222795i
$442$		0			0
$443$	−1.44681	−	1.25367i	−0.0687402	−	0.0595637i	0.619813	−	0.784749i	$-0.287208\pi$
$443$	−1.44681	−	1.25367i	−0.0687402	−	0.0595637i	−0.688553	+	0.725186i	$0.741754\pi$
$444$		0			0
$445$	−14.7325	+	4.32586i	−0.698389	+	0.205065i
$446$		0			0
$447$	1.35534	−	0.646025i	0.0641053	−	0.0305559i
$448$		0			0
$449$	24.0148	−	10.9672i	1.13333	−	0.517573i	0.241703	−	0.970350i	$-0.422294\pi$
$449$	24.0148	−	10.9672i	1.13333	−	0.517573i	0.891624	+	0.452777i	$0.149567\pi$
$450$		0			0
$451$	−2.55637	+	3.97778i	−0.120375	+	0.187307i
$452$		0			0
$453$	15.9455	−	2.56014i	0.749187	−	0.120286i
$454$		0			0
$455$	−19.1275	−	29.7629i	−0.896709	−	1.39531i
$456$		0			0
$457$	−7.04060	+	23.9781i	−0.329345	+	1.12165i	0.613854	+	0.789420i	$0.289618\pi$
$457$	−7.04060	+	23.9781i	−0.329345	+	1.12165i	−0.943199	+	0.332227i	$0.892200\pi$
$458$		0			0
$459$	−7.61967	−	5.97258i	−0.355656	−	0.278776i
$460$		0			0
$461$			4.93471i			0.229832i	0.993375	+	0.114916i	$0.0366600\pi$
$461$			4.93471i			0.229832i	−0.993375	+	0.114916i	$0.963340\pi$
$462$		0			0
$463$	−15.5261	−	4.55887i	−0.721558	−	0.211869i	−0.0997212	−	0.995015i	$-0.531795\pi$
$463$	−15.5261	−	4.55887i	−0.721558	−	0.211869i	−0.621837	+	0.783147i	$0.713613\pi$
$464$		0			0
$465$	43.6202	+	36.5623i	2.02284	+	1.69553i
$466$		0			0
$467$	4.04200	−	28.1127i	0.187041	−	1.30090i	−0.652576	−	0.757723i	$-0.726312\pi$
$467$	4.04200	−	28.1127i	0.187041	−	1.30090i	0.839617	−	0.543178i	$-0.182779\pi$
$468$		0			0
$469$	28.4751	+	18.2999i	1.31486	+	0.845009i
$470$		0			0
$471$	10.7698	+	12.0248i	0.496247	+	0.554076i
$472$		0			0
$473$	1.72386	−	0.247854i	0.0792633	−	0.0113963i
$474$		0			0
$475$	12.6962	+	43.2393i	0.582541	+	1.98395i
$476$		0			0
$477$	3.85280	−	34.8822i	0.176408	−	1.59715i
$478$		0			0
$479$	−18.5793	−	21.4416i	−0.848909	−	0.979693i	0.151052	−	0.988526i	$-0.451734\pi$
$479$	−18.5793	−	21.4416i	−0.848909	−	0.979693i	−0.999961	+	0.00883291i	$0.997188\pi$
$480$		0			0
$481$	11.7266	+	5.35536i	0.534687	+	0.244183i
$482$		0			0
$483$	28.6258	−	9.68489i	1.30252	−	0.440678i
$484$		0			0
$485$	−25.2303	−	11.5223i	−1.14565	−	0.523200i
$486$		0			0
$487$	−19.6912	−	22.7249i	−0.892296	−	1.02976i	−0.999369	−	0.0355129i	$-0.988694\pi$
$487$	−19.6912	−	22.7249i	−0.892296	−	1.02976i	0.107074	−	0.994251i	$-0.465852\pi$
$488$		0			0
$489$	8.90319	+	3.89081i	0.402616	+	0.175949i
$490$		0			0
$491$	−1.17336	−	3.99611i	−0.0529532	−	0.180342i	0.928770	−	0.370657i	$-0.120867\pi$
$491$	−1.17336	−	3.99611i	−0.0529532	−	0.180342i	−0.981723	+	0.190315i	$0.939049\pi$
$492$		0			0
$493$	−1.28806	+	0.185195i	−0.0580114	+	0.00834078i
$494$		0			0
$495$	4.83514	+	2.88785i	0.217323	+	0.129799i
$496$		0			0
$497$	24.9339	+	16.0240i	1.11844	+	0.718776i
$498$		0			0
$499$	3.09324	−	21.5140i	0.138472	−	0.963097i	−0.795551	−	0.605886i	$-0.792819\pi$
$499$	3.09324	−	21.5140i	0.138472	−	0.963097i	0.934024	−	0.357211i	$-0.116272\pi$
$500$		0			0
$501$	11.5705	−	13.8040i	0.516932	−	0.616719i
$502$		0			0
$503$	5.79221	+	1.70075i	0.258262	+	0.0758326i	0.408301	−	0.912848i	$-0.366122\pi$
$503$	5.79221	+	1.70075i	0.258262	+	0.0758326i	−0.150038	+	0.988680i	$0.547940\pi$
$504$		0			0
$505$		−	22.5015i		−	1.00130i
$506$		0			0
$507$	2.06644	+	6.63330i	0.0917738	+	0.294595i
$508$		0			0
$509$	8.04432	−	27.3965i	0.356558	−	1.21433i	−0.564674	−	0.825314i	$-0.690998\pi$
$509$	8.04432	−	27.3965i	0.356558	−	1.21433i	0.921232	−	0.389012i	$-0.127184\pi$
$510$		0			0
$511$	29.7174	+	46.2411i	1.31462	+	2.04559i
$512$		0			0
$513$	29.3160	+	30.6479i	1.29433	+	1.35314i
$514$		0			0
$515$	22.3281	−	34.7432i	0.983894	−	1.53097i
$516$		0			0
$517$	2.40358	−	1.09768i	0.105709	−	0.0482758i
$518$		0			0
$519$	4.69084	+	9.84122i	0.205905	+	0.431982i
$520$		0			0
$521$	31.2558	−	9.17753i	1.36934	−	0.402075i	0.487295	−	0.873238i	$-0.337984\pi$
$521$	31.2558	−	9.17753i	1.36934	−	0.402075i	0.882046	+	0.471163i	$0.156166\pi$
$522$		0			0
$523$	1.09087	+	0.945242i	0.0477003	+	0.0413325i	0.678385	−	0.734707i	$-0.262680\pi$
$523$	1.09087	+	0.945242i	0.0477003	+	0.0413325i	−0.630684	+	0.776039i	$0.717226\pi$
$524$		0			0
$525$	29.5723	+	18.3269i	1.29064	+	0.799850i
$526$		0			0
$527$	−7.84131	+	17.1701i	−0.341573	+	0.747940i
$528$		0			0
$529$	−14.2017	+	18.0918i	−0.617463	+	0.786600i
$530$		0			0
$531$	−19.6481	+	3.48597i	−0.852653	+	0.151278i
$532$		0			0
$533$	−18.5115	+	16.0403i	−0.801822	+	0.694783i
$534$		0			0
$535$	41.3979	−	47.7757i	1.78979	−	2.06552i
$536$		0			0
$537$	22.1039	−	14.7229i	0.953853	−	0.635341i
$538$		0			0
$539$	0.513575	+	3.57199i	0.0221212	+	0.153857i
$540$		0			0
$541$	0.218449	+	0.478336i	0.00939184	+	0.0205653i	0.914270	−	0.405106i	$-0.132765\pi$
$541$	0.218449	+	0.478336i	0.00939184	+	0.0205653i	−0.904878	+	0.425671i	$0.860038\pi$
$542$		0			0
$543$	−28.7985	−	7.94551i	−1.23586	−	0.340974i
$544$		0			0
$545$	1.95012	+	0.280385i	0.0835339	+	0.0120104i
$546$		0			0
$547$	−19.6725	+	12.6428i	−0.841137	+	0.540566i	−0.888799	−	0.458298i	$-0.848459\pi$
$547$	−19.6725	+	12.6428i	−0.841137	+	0.540566i	0.0476617	+	0.998864i	$0.484823\pi$
$548$		0			0
$549$	3.87135	+	11.7454i	0.165225	+	0.501280i
$550$		0			0
$551$	5.70059			0.242853
$552$		0			0
$553$	−4.02903			−0.171332
$554$		0			0
$555$	−24.1542	+	0.396090i	−1.02529	+	0.0168131i
$556$		0			0
$557$	−7.45071	+	4.78828i	−0.315697	+	0.202886i	−0.688887	−	0.724869i	$-0.741900\pi$
$557$	−7.45071	+	4.78828i	−0.315697	+	0.202886i	0.373190	+	0.927755i	$0.378264\pi$
$558$		0			0
$559$	8.93002	+	1.28394i	0.377699	+	0.0543050i
$560$		0			0
$561$	−0.496754	+	1.80049i	−0.0209730	+	0.0760166i
$562$		0			0
$563$	15.2097	+	33.3047i	0.641014	+	1.40363i	0.899203	+	0.437531i	$0.144147\pi$
$563$	15.2097	+	33.3047i	0.641014	+	1.40363i	−0.258189	+	0.966094i	$0.583126\pi$
$564$		0			0
$565$	−0.800633	−	5.56852i	−0.0336829	−	0.234270i
$566$		0			0
$567$	32.6447	+	2.52559i	1.37095	+	0.106065i
$568$		0			0
$569$	−8.59416	+	9.91819i	−0.360286	+	0.415792i	−0.906735	−	0.421700i	$-0.861434\pi$
$569$	−8.59416	+	9.91819i	−0.360286	+	0.415792i	0.546449	+	0.837492i	$0.315979\pi$
$570$		0			0
$571$	−15.4574	+	13.3939i	−0.646873	+	0.560519i	−0.915296	−	0.402782i	$-0.868043\pi$
$571$	−15.4574	+	13.3939i	−0.646873	+	0.560519i	0.268422	+	0.963301i	$0.413498\pi$
$572$		0			0
$573$	−14.5181	−	1.84496i	−0.606502	−	0.0770745i
$574$		0			0
$575$	−26.4711	+	0.641851i	−1.10392	+	0.0267670i
$576$		0			0
$577$	−6.83183	+	14.9596i	−0.284413	+	0.622777i	−0.996880	−	0.0789278i	$-0.974850\pi$
$577$	−6.83183	+	14.9596i	−0.284413	+	0.622777i	0.712467	+	0.701705i	$0.247578\pi$
$578$		0			0
$579$	−7.98682	+	12.8875i	−0.331921	+	0.535588i
$580$		0			0
$581$	20.4625	+	17.7308i	0.848926	+	0.735598i
$582$		0			0
$583$	−6.49617	+	1.90745i	−0.269044	+	0.0789984i
$584$		0			0
$585$	19.8179	+	21.4104i	0.819370	+	0.885209i
$586$		0			0
$587$	−5.71654	+	2.61066i	−0.235947	+	0.107753i	−0.529880	−	0.848073i	$-0.677763\pi$
$587$	−5.71654	+	2.61066i	−0.235947	+	0.107753i	0.293933	+	0.955826i	$0.405036\pi$
$588$		0			0
$589$	44.7049	−	69.5621i	1.84203	−	2.86626i
$590$		0			0
$591$	3.28211	+	20.4423i	0.135008	+	0.840883i
$592$		0			0
$593$	−23.3843	−	36.3867i	−0.960279	−	1.49422i	−0.866833	−	0.498598i	$-0.833848\pi$
$593$	−23.3843	−	36.3867i	−0.960279	−	1.49422i	−0.0934453	−	0.995624i	$-0.529788\pi$
$594$		0			0
$595$	−6.19436	+	21.0961i	−0.253944	+	0.864854i
$596$		0			0
$597$	−26.2350	+	8.17285i	−1.07373	+	0.334492i
$598$		0			0
$599$			3.42973i			0.140135i	0.997542	+	0.0700675i	$0.0223215\pi$
$599$			3.42973i			0.140135i	−0.997542	+	0.0700675i	$0.977679\pi$
$600$		0			0
$601$	39.1627	+	11.4992i	1.59748	+	0.469062i	0.954843	−	0.297111i	$-0.0960230\pi$
$601$	39.1627	+	11.4992i	1.59748	+	0.469062i	0.642635	+	0.766173i	$0.277841\pi$
$602$		0			0
$603$	−25.7564	−	10.7564i	−1.04888	−	0.438036i
$604$		0			0
$605$	−4.92318	+	34.2415i	−0.200156	+	1.39211i
$606$		0			0
$607$	11.9987	+	7.71109i	0.487012	+	0.312983i	0.761003	−	0.648749i	$-0.224707\pi$
$607$	11.9987	+	7.71109i	0.487012	+	0.312983i	−0.273991	+	0.961732i	$0.588344\pi$
$608$		0			0
$609$	3.27832	−	2.93616i	0.132844	−	0.118979i
$610$		0			0
$611$	13.5487	−	1.94802i	0.548124	−	0.0788083i
$612$		0			0
$613$	13.6155	+	46.3701i	0.549925	+	1.87287i	0.484042	+	0.875045i	$0.339168\pi$
$613$	13.6155	+	46.3701i	0.549925	+	1.87287i	0.0658834	+	0.997827i	$0.479013\pi$
$614$		0			0
$615$	18.3802	−	42.0587i	0.741163	−	1.69597i
$616$		0			0
$617$	−10.3528	−	11.9477i	−0.416787	−	0.480998i	0.508068	−	0.861317i	$-0.330360\pi$
$617$	−10.3528	−	11.9477i	−0.416787	−	0.480998i	−0.924855	+	0.380319i	$0.875814\pi$
$618$		0			0
$619$	−22.5688	−	10.3068i	−0.907116	−	0.414266i	−0.0934671	−	0.995622i	$-0.529795\pi$
$619$	−22.5688	−	10.3068i	−0.907116	−	0.414266i	−0.813649	+	0.581356i	$0.802522\pi$
$620$		0			0
$621$	−21.8473	+	11.9873i	−0.876703	+	0.481033i
$622$		0			0
$623$	15.6651	+	7.15402i	0.627610	+	0.286620i
$624$		0			0
$625$	14.4869	+	16.7188i	0.579476	+	0.668751i
$626$		0			0
$627$	3.27644	−	7.49735i	0.130849	−	0.299415i
$628$		0			0
$629$	−2.25712	−	7.68704i	−0.0899972	−	0.306502i
$630$		0			0
$631$	−7.33071	+	1.05400i	−0.291831	+	0.0419589i	−0.286675	−	0.958028i	$-0.592550\pi$
$631$	−7.33071	+	1.05400i	−0.291831	+	0.0419589i	−0.00515546	+	0.999987i	$0.501641\pi$
$632$		0			0
$633$	18.1891	−	16.2907i	0.722950	−	0.647495i
$634$		0			0
$635$	10.2609	+	6.59427i	0.407191	+	0.261686i
$636$		0			0
$637$	−2.66044	+	18.5037i	−0.105410	+	0.733145i
$638$		0			0
$639$	−22.5532	−	9.41873i	−0.892191	−	0.372599i
$640$		0			0
$641$	−9.79626	−	2.87644i	−0.386929	−	0.113613i	0.0824816	−	0.996593i	$-0.473715\pi$
$641$	−9.79626	−	2.87644i	−0.386929	−	0.113613i	−0.469411	+	0.882980i	$0.655534\pi$
$642$		0			0
$643$		−	50.2844i		−	1.98302i	−0.130015	−	0.991512i	$-0.541502\pi$
$643$		−	50.2844i		−	1.98302i	0.130015	−	0.991512i	$-0.458498\pi$
$644$		0			0
$645$	−16.1409	+	5.02829i	−0.635547	+	0.197989i
$646$		0			0
$647$	−5.28823	+	18.0101i	−0.207902	+	0.708049i	0.787841	+	0.615878i	$0.211199\pi$
$647$	−5.28823	+	18.0101i	−0.207902	+	0.708049i	−0.995743	+	0.0921704i	$0.970620\pi$
$648$		0			0
$649$	2.08131	+	3.23858i	0.0816986	+	0.127126i
$650$		0			0
$651$	−10.1198	−	63.0298i	−0.396625	−	2.47033i
$652$		0			0
$653$	−2.82802	+	4.40048i	−0.110669	+	0.172204i	−0.892170	−	0.451700i	$-0.850818\pi$
$653$	−2.82802	+	4.40048i	−0.110669	+	0.172204i	0.781501	+	0.623904i	$0.214454\pi$
$654$		0			0
$655$	−14.5088	+	6.62593i	−0.566904	+	0.258896i
$656$		0			0
$657$	−30.7901	−	33.2642i	−1.20124	−	1.29776i
$658$		0			0
$659$	38.6965	−	11.3623i	1.50740	−	0.442614i	0.579356	−	0.815075i	$-0.303304\pi$
$659$	38.6965	−	11.3623i	1.50740	−	0.442614i	0.928048	+	0.372461i	$0.121486\pi$
$660$		0			0
$661$	−15.5880	−	13.5071i	−0.606302	−	0.525364i	0.296716	−	0.954966i	$-0.404108\pi$
$661$	−15.5880	−	13.5071i	−0.606302	−	0.525364i	−0.903018	+	0.429602i	$0.858654\pi$
$662$		0			0
$663$	−5.09677	+	8.22416i	−0.197942	+	0.319400i
$664$		0			0
$665$	40.0112	−	87.6123i	1.55157	−	3.39746i
$666$		0			0
$667$	−0.865490	+	3.23578i	−0.0335119	+	0.125290i
$668$		0			0
$669$	37.5201	+	4.76806i	1.45061	+	0.184344i
$670$		0			0
$671$	1.80309	−	1.56239i	0.0696076	−	0.0603154i
$672$		0			0
$673$	6.90161	−	7.96488i	0.266038	−	0.307024i	−0.606976	−	0.794721i	$-0.707617\pi$
$673$	6.90161	−	7.96488i	0.266038	−	0.307024i	0.873013	+	0.487697i	$0.162163\pi$
$674$		0			0
$675$	−26.6511	−	10.6203i	−1.02580	−	0.408776i
$676$		0			0
$677$	−4.79872	−	33.3758i	−0.184430	−	1.28274i	−0.846133	−	0.532972i	$-0.821075\pi$
$677$	−4.79872	−	33.3758i	−0.184430	−	1.28274i	0.661703	−	0.749766i	$-0.269834\pi$
$678$		0			0
$679$	12.9232	+	28.2979i	0.495948	+	1.08597i
$680$		0			0
$681$	7.33888	−	26.5998i	0.281227	−	1.01931i
$682$		0			0
$683$	−10.1346	−	1.45713i	−0.387789	−	0.0557557i	−0.0543371	−	0.998523i	$-0.517305\pi$
$683$	−10.1346	−	1.45713i	−0.387789	−	0.0557557i	−0.333452	+	0.942767i	$0.608214\pi$
$684$		0			0
$685$	−53.7502	+	34.5432i	−2.05369	+	1.31983i
$686$		0			0
$687$	23.6761	−	0.388250i	0.903301	−	0.0148127i
$688$		0			0
$689$	−35.0724			−1.33615
$690$		0			0
$691$	0.0747260			0.00284271			0.00142136	−	0.999999i	$-0.499548\pi$
$691$	0.0747260			0.00284271			0.00142136	+	0.999999i	$0.499548\pi$
$692$		0			0
$693$	−1.97737	−	5.99918i	−0.0751141	−	0.227890i
$694$		0			0
$695$	−42.6080	+	27.3825i	−1.61621	+	1.03868i
$696$		0			0
$697$	15.0672	+	2.16633i	0.570710	+	0.0820556i
$698$		0			0
$699$	0.292651	+	0.0807424i	0.0110691	+	0.00305396i
$700$		0			0
$701$	−2.16174	−	4.73355i	−0.0816478	−	0.178784i	0.864405	−	0.502796i	$-0.167695\pi$
$701$	−2.16174	−	4.73355i	−0.0816478	−	0.178784i	−0.946053	+	0.324012i	$0.894968\pi$
$702$		0			0
$703$	4.99468	+	34.7388i	0.188378	+	1.31020i
$704$		0			0
$705$	−21.3479	+	14.2194i	−0.804007	+	0.535532i
$706$		0			0
$707$	−16.5270	+	19.0731i	−0.621561	+	0.717319i
$708$		0			0
$709$	10.1280	−	8.77598i	0.380366	−	0.329589i	−0.443604	−	0.896223i	$-0.646300\pi$
$709$	10.1280	−	8.77598i	0.380366	−	0.329589i	0.823970	+	0.566634i	$0.191755\pi$
$710$		0			0
$711$	3.27134	−	0.580403i	0.122685	−	0.0217668i
$712$		0			0
$713$	32.6977	+	35.9367i	1.22454	+	1.34584i
$714$		0			0
$715$	2.33811	−	5.11974i	0.0874403	−	0.191467i
$716$		0			0
$717$	−28.9462	−	17.9389i	−1.08102	−	0.669940i
$718$		0			0
$719$	32.0510	+	27.7723i	1.19530	+	1.03573i	0.998470	+	0.0552959i	$0.0176102\pi$
$719$	32.0510	+	27.7723i	1.19530	+	1.03573i	0.196830	+	0.980438i	$0.436935\pi$
$720$		0			0
$721$	−44.4445	+	13.0501i	−1.65520	+	0.486010i
$722$		0			0
$723$	−7.51931	−	15.7752i	−0.279646	−	0.586687i
$724$		0			0
$725$	−3.50770	+	1.60191i	−0.130273	+	0.0594935i
$726$		0			0
$727$	−0.832007	+	1.29463i	−0.0308574	+	0.0480151i	−0.856340	−	0.516413i	$-0.827267\pi$
$727$	−0.832007	+	1.29463i	−0.0308574	+	0.0480151i	0.825482	+	0.564428i	$0.190903\pi$
$728$		0			0
$729$	−26.8694	+	2.65201i	−0.995164	+	0.0982228i
$730$		0			0
$731$	−3.03120	−	4.71665i	−0.112113	−	0.174451i
$732$		0			0
$733$	7.75669	−	26.4169i	0.286500	−	0.975729i	−0.682955	−	0.730460i	$-0.739306\pi$
$733$	7.75669	−	26.4169i	0.286500	−	0.975729i	0.969455	−	0.245269i	$-0.0788762\pi$
$734$		0			0
$735$	−10.4190	−	33.4453i	−0.384312	−	1.23365i
$736$		0			0
$737$			5.38484i			0.198353i
$738$		0			0
$739$	−15.7287	−	4.61836i	−0.578590	−	0.169889i	−0.0206731	−	0.999786i	$-0.506581\pi$
$739$	−15.7287	−	4.61836i	−0.578590	−	0.169889i	−0.557917	+	0.829897i	$0.688399\pi$
$740$		0			0
$741$	27.2272	−	32.4831i	1.00022	−	1.19329i
$742$		0			0
$743$	−6.81469	+	47.3972i	−0.250007	+	1.73883i	0.348135	+	0.937444i	$0.386815\pi$
$743$	−6.81469	+	47.3972i	−0.250007	+	1.73883i	−0.598142	+	0.801390i	$0.704094\pi$
$744$		0			0
$745$	2.36540	+	1.52015i	0.0866615	+	0.0556940i
$746$		0			0
$747$	−19.1686	−	11.4487i	−0.701341	−	0.418885i
$748$		0			0
$749$	−70.1808	+	10.0905i	−2.56435	+	0.368698i
$750$		0			0
$751$	−1.24907	−	4.25395i	−0.0455793	−	0.155229i	0.933559	−	0.358424i	$-0.116686\pi$
$751$	−1.24907	−	4.25395i	−0.0455793	−	0.155229i	−0.979138	+	0.203195i	$0.934868\pi$
$752$		0			0
$753$	−30.9573	−	13.5287i	−1.12815	−	0.493015i
$754$		0			0
$755$	19.8056	+	22.8569i	0.720799	+	0.831846i
$756$		0			0
$757$	2.76383	+	1.26220i	0.100453	+	0.0458754i	0.465008	−	0.885307i	$-0.346052\pi$
$757$	2.76383	+	1.26220i	0.100453	+	0.0458754i	−0.364555	+	0.931182i	$0.618779\pi$
$758$		0			0
$759$	3.75822	+	2.99806i	0.136415	+	0.108823i
$760$		0			0
$761$	18.8522	+	8.60951i	0.683391	+	0.312094i	0.726688	−	0.686968i	$-0.241059\pi$
$761$	18.8522	+	8.60951i	0.683391	+	0.312094i	−0.0432964	+	0.999062i	$0.513786\pi$
$762$		0			0
$763$	−1.44706	−	1.66999i	−0.0523870	−	0.0604578i
$764$		0			0
$765$	1.99046	−	18.0211i	0.0719654	−	0.651555i
$766$		0			0
$767$	5.61843	+	19.1346i	0.202870	+	0.690910i
$768$		0			0
$769$	−5.98624	+	0.860692i	−0.215869	+	0.0310373i	−0.249401	−	0.968400i	$-0.580234\pi$
$769$	−5.98624	+	0.860692i	−0.215869	+	0.0310373i	0.0335315	+	0.999438i	$0.489325\pi$
$770$		0			0
$771$	−6.36458	−	7.10627i	−0.229215	−	0.255926i
$772$		0			0
$773$	22.4582	+	14.4330i	0.807766	+	0.519120i	0.878142	−	0.478401i	$-0.158783\pi$
$773$	22.4582	+	14.4330i	0.807766	+	0.519120i	−0.0703755	+	0.997521i	$0.522420\pi$
$774$		0			0
$775$	−7.96036	+	55.3655i	−0.285945	+	1.98879i
$776$		0			0
$777$	20.7650	+	17.4051i	0.744939	+	0.624405i
$778$		0			0
$779$	−63.9818	−	18.7867i	−2.29239	−	0.673105i
$780$		0			0
$781$			4.71516i			0.168722i
$782$		0			0
$783$	−2.23883	+	2.85625i	−0.0800094	+	0.102074i
$784$		0			0
$785$	−8.51697	+	29.0061i	−0.303984	+	1.03527i
$786$		0			0
$787$	−15.8796	−	24.7091i	−0.566046	−	0.880785i	0.433749	−	0.901034i	$-0.357191\pi$
$787$	−15.8796	−	24.7091i	−0.566046	−	0.880785i	−0.999795	+	0.0202486i	$0.993554\pi$
$788$		0			0
$789$	0.385409	−	0.0618794i	0.0137209	−	0.00220296i
$790$		0			0
$791$	−3.41134	+	5.30814i	−0.121293	+	0.188736i
$792$		0			0
$793$	11.2423	−	5.13419i	0.399226	−	0.182320i
$794$		0			0
$795$	59.3270	−	28.2784i	2.10411	−	1.00293i
$796$		0			0
$797$	−10.1200	+	2.97150i	−0.358469	+	0.105256i	−0.456008	−	0.889976i	$-0.650721\pi$
$797$	−10.1200	+	2.97150i	−0.358469	+	0.105256i	0.0975389	+	0.995232i	$0.468903\pi$
$798$		0			0
$799$	−6.42882	−	5.57060i	−0.227435	−	0.197074i
$800$		0			0
$801$	−13.7498	−	3.55201i	−0.485824	−	0.125504i
$802$		0			0
$803$	−3.63260	+	7.95428i	−0.128192	+	0.280700i
$804$		0			0
$805$	43.6560	+	36.0129i	1.53867	+	1.26929i
$806$		0			0
$807$	6.08752	−	47.9030i	0.214291	−	1.68626i
$808$		0			0
$809$	39.4278	−	34.1644i	1.38621	−	1.20116i	0.432049	−	0.901850i	$-0.357791\pi$
$809$	39.4278	−	34.1644i	1.38621	−	1.20116i	0.954157	−	0.299305i	$-0.0967549\pi$
$810$		0			0
$811$	0.595152	−	0.686842i	0.0208986	−	0.0241183i	−0.745204	−	0.666837i	$-0.767648\pi$
$811$	0.595152	−	0.686842i	0.0208986	−	0.0241183i	0.766103	+	0.642718i	$0.222193\pi$
$812$		0			0
$813$	5.27099	+	7.91346i	0.184862	+	0.277537i
$814$		0			0
$815$	2.58953	+	18.0106i	0.0907073	+	0.630883i
$816$		0			0
$817$	10.2030	+	22.3415i	0.356958	+	0.781630i
$818$		0			0
$819$	−1.07288	−	32.7041i	−0.0374894	−	1.14278i
$820$		0			0
$821$	−35.3882	−	5.08806i	−1.23506	−	0.177574i	−0.506306	−	0.862354i	$-0.668989\pi$
$821$	−35.3882	−	5.08806i	−1.23506	−	0.177574i	−0.728750	+	0.684779i	$0.759899\pi$
$822$		0			0
$823$	5.24797	−	3.37267i	0.182933	−	0.117564i	−0.445969	−	0.895048i	$-0.647141\pi$
$823$	5.24797	−	3.37267i	0.182933	−	0.117564i	0.628902	+	0.777484i	$0.283505\pi$
$824$		0			0
$825$	0.0907484	+	5.53399i	0.00315945	+	0.192669i
$826$		0			0
$827$	−13.7692			−0.478801			−0.239400	−	0.970921i	$-0.576951\pi$
$827$	−13.7692			−0.478801			−0.239400	+	0.970921i	$0.576951\pi$
$828$		0			0
$829$	18.3066			0.635815			0.317908	−	0.948122i	$-0.397020\pi$
$829$	18.3066			0.635815			0.317908	+	0.948122i	$0.397020\pi$
$830$		0			0
$831$	0.799968	+	48.7834i	0.0277506	+	1.69228i
$832$		0			0
$833$	9.77329	−	6.28091i	0.338624	−	0.217621i
$834$		0			0
$835$	33.3879	+	4.80045i	1.15544	+	0.166127i
$836$		0			0
$837$	17.2965	+	49.7188i	0.597853	+	1.71853i
$838$		0			0
$839$	−11.3347	−	24.8196i	−0.391319	−	0.856868i	−0.998077	−	0.0619822i	$-0.980258\pi$
$839$	−11.3347	−	24.8196i	−0.391319	−	0.856868i	0.606759	−	0.794886i	$-0.292469\pi$
$840$		0			0
$841$	−4.05771	−	28.2220i	−0.139921	−	0.973172i
$842$		0			0
$843$	−7.63994	−	11.4700i	−0.263133	−	0.395048i
$844$		0			0
$845$	−8.52049	+	9.83317i	−0.293114	+	0.338271i
$846$		0			0
$847$	29.3229	−	25.4084i	1.00755	−	0.873043i
$848$		0			0
$849$	−2.96922	+	23.3649i	−0.101903	+	0.801882i
$850$		0			0
$851$	−20.4768	−	2.43911i	−0.701935	−	0.0836116i
$852$		0			0
$853$	4.57754	−	10.0234i	0.156732	−	0.343195i	−0.814934	−	0.579554i	$-0.803227\pi$
$853$	4.57754	−	10.0234i	0.156732	−	0.343195i	0.971666	+	0.236359i	$0.0759541\pi$
$854$		0			0
$855$	−19.8658	+	76.9000i	−0.679395	+	2.62992i
$856$		0			0
$857$	−35.3268	−	30.6108i	−1.20674	−	1.04565i	−0.997703	−	0.0677378i	$-0.978422\pi$
$857$	−35.3268	−	30.6108i	−1.20674	−	1.04565i	−0.209036	−	0.977908i	$-0.567033\pi$
$858$		0			0
$859$	31.7837	−	9.33255i	1.08445	−	0.318422i	0.309791	−	0.950805i	$-0.399741\pi$
$859$	31.7837	−	9.33255i	1.08445	−	0.318422i	0.774656	+	0.632382i	$0.217923\pi$
$860$		0			0
$861$	−46.4712	+	22.1506i	−1.58373	+	0.754891i
$862$		0			0
$863$	−33.2215	+	15.1717i	−1.13087	+	0.516452i	−0.890842	−	0.454314i	$-0.849885\pi$
$863$	−33.2215	+	15.1717i	−1.13087	+	0.516452i	−0.240030	+	0.970765i	$0.577157\pi$
$864$		0			0
$865$	−11.0379	+	17.1754i	−0.375301	+	0.583980i
$866$		0			0
$867$	−23.1357	+	3.71456i	−0.785730	+	0.126153i
$868$		0			0
$869$	−0.346532	−	0.539214i	−0.0117553	−	0.0182916i
$870$		0			0
$871$	−7.85885	+	26.7648i	−0.266287	+	0.906890i
$872$		0			0
$873$	−14.5694	−	21.1146i	−0.493099	−	0.714622i
$874$		0			0
$875$			6.15086i			0.207937i
$876$		0			0
$877$	−47.5791	−	13.9705i	−1.60663	−	0.471750i	−0.649251	−	0.760574i	$-0.724918\pi$
$877$	−47.5791	−	13.9705i	−1.60663	−	0.471750i	−0.957382	+	0.288824i	$0.906736\pi$
$878$		0			0
$879$	−27.0615	−	22.6828i	−0.912761	−	0.765073i
$880$		0			0
$881$	−5.86873	+	40.8179i	−0.197722	+	1.37519i	0.613150	+	0.789967i	$0.289902\pi$
$881$	−5.86873	+	40.8179i	−0.197722	+	1.37519i	−0.810872	+	0.585223i	$0.801007\pi$
$882$		0			0
$883$	31.3399	+	20.1409i	1.05467	+	0.677796i	0.948572	−	0.316560i	$-0.102528\pi$
$883$	31.3399	+	20.1409i	1.05467	+	0.677796i	0.106098	+	0.994356i	$0.466164\pi$
$884$		0			0
$885$	−24.9319	−	27.8373i	−0.838076	−	0.935740i
$886$		0			0
$887$	29.8888	−	4.29736i	1.00357	−	0.144291i	0.379111	−	0.925351i	$-0.376230\pi$
$887$	29.8888	−	4.29736i	1.00357	−	0.144291i	0.624456	+	0.781060i	$0.285321\pi$
$888$		0			0
$889$	−3.85414	−	13.1260i	−0.129264	−	0.440232i
$890$		0			0
$891$	2.46972	+	4.58613i	0.0827389	+	0.153641i
$892$		0			0
$893$	24.4029	+	28.1625i	0.816613	+	0.942422i
$894$		0			0
$895$	45.2418	+	20.6612i	1.51227	+	0.690629i
$896$		0			0
$897$	14.3043	+	20.3865i	0.477608	+	0.680684i
$898$		0			0
$899$	6.43623	+	2.93933i	0.214660	+	0.0980321i
$900$		0			0
$901$	14.2733	+	16.4723i	0.475513	+	0.548771i
$902$		0			0
$903$	17.3748	+	7.59304i	0.578198	+	0.252680i
$904$		0			0
$905$	−15.7620	−	53.6804i	−0.523946	−	1.78440i
$906$		0			0
$907$	−43.5470	+	6.26112i	−1.44596	+	0.207897i	−0.820180	−	0.572106i	$-0.806127\pi$
$907$	−43.5470	+	6.26112i	−1.44596	+	0.207897i	−0.625776	+	0.780003i	$0.715217\pi$
$908$		0			0
$909$	10.6714	−	17.8671i	0.353947	−	0.592614i
$910$		0			0
$911$	25.5306	+	16.4075i	0.845867	+	0.543606i	0.890283	−	0.455407i	$-0.150506\pi$
$911$	25.5306	+	16.4075i	0.845867	+	0.543606i	−0.0444161	+	0.999013i	$0.514143\pi$
$912$		0			0
$913$	−0.613005	+	4.26354i	−0.0202875	+	0.141103i
$914$		0			0
$915$	−14.8774	+	17.7493i	−0.491832	+	0.586774i
$916$		0			0
$917$	17.1648	+	5.04004i	0.566832	+	0.166437i
$918$		0			0
$919$		−	0.436278i		−	0.0143915i	−0.999974	−	0.00719574i	$-0.997710\pi$
$919$		−	0.436278i		−	0.0143915i	0.999974	−	0.00719574i	$-0.00229049\pi$
$920$		0			0
$921$	−0.622020	−	1.99669i	−0.0204963	−	0.0657933i
$922$		0			0
$923$	−6.88150	+	23.4362i	−0.226507	+	0.771413i
$924$		0			0
$925$	−12.8352	−	19.9720i	−0.422019	−	0.656674i
$926$		0			0
$927$	34.2064	−	16.9984i	1.12349	−	0.558300i
$928$		0			0
$929$	12.7165	−	19.7872i	0.417214	−	0.649198i	−0.567500	−	0.823373i	$-0.692089\pi$
$929$	12.7165	−	19.7872i	0.417214	−	0.649198i	0.984715	+	0.174175i	$0.0557259\pi$
$930$		0			0
$931$	−46.2934	+	21.1415i	−1.51721	+	0.692885i
$932$		0			0
$933$	12.3738	+	25.9599i	0.405101	+	0.849888i
$934$		0			0
$935$	−3.35610	+	0.985440i	−0.109756	+	0.0322273i
$936$		0			0
$937$	−33.4622	−	28.9951i	−1.09316	−	0.947230i	−0.0943295	−	0.995541i	$-0.530071\pi$
$937$	−33.4622	−	28.9951i	−1.09316	−	0.947230i	−0.998832	+	0.0483109i	$0.984616\pi$
$938$		0			0
$939$	−27.5550	−	17.0767i	−0.899223	−	0.557277i
$940$		0			0
$941$	−2.21182	+	4.84322i	−0.0721034	+	0.157884i	−0.942252	−	0.334905i	$-0.891296\pi$
$941$	−2.21182	+	4.84322i	−0.0721034	+	0.157884i	0.870148	+	0.492790i	$0.164023\pi$
$942$		0			0
$943$	20.3778	−	33.4652i	0.663592	−	1.08978i
$944$		0			0
$945$	28.1838	+	54.4560i	0.916818	+	1.77145i
$946$		0			0
$947$	25.0779	−	21.7301i	0.814921	−	0.706133i	−0.144071	−	0.989567i	$-0.546019\pi$
$947$	25.0779	−	21.7301i	0.814921	−	0.706133i	0.958992	+	0.283434i	$0.0914738\pi$
$948$		0			0
$949$	−29.6643	+	34.2344i	−0.962943	+	1.11130i
$950$		0			0
$951$	−39.3733	+	26.2257i	−1.27677	+	0.850427i
$952$		0			0
$953$	1.89508	+	13.1806i	0.0613876	+	0.426960i	0.997220	+	0.0745145i	$0.0237407\pi$
$953$	1.89508	+	13.1806i	0.0613876	+	0.426960i	−0.935832	+	0.352445i	$0.885350\pi$
$954$		0			0
$955$	−11.3853	−	24.9303i	−0.368419	−	0.806725i
$956$		0			0
$957$	0.674916	+	0.186209i	0.0218169	+	0.00601928i
$958$		0			0
$959$	70.9321	+	10.1985i	2.29052	+	0.329326i
$960$		0			0
$961$	60.2625	−	38.7284i	1.94395	−	1.24930i
$962$		0			0
$963$	55.5292	−	18.3028i	1.78940	−	0.589800i
$964$		0			0
$965$	−28.3937			−0.914025
$966$		0			0
$967$	4.46886			0.143709			0.0718545	−	0.997415i	$-0.477108\pi$
$967$	4.46886			0.143709			0.0718545	+	0.997415i	$0.477108\pi$
$968$		0			0
$969$	−26.3368	+	0.431880i	−0.846059	+	0.0138740i
$970$		0			0
$971$	−36.7539	+	23.6203i	−1.17949	+	0.758011i	−0.975292	−	0.220919i	$-0.929094\pi$
$971$	−36.7539	+	23.6203i	−1.17949	+	0.758011i	−0.204196	+	0.978930i	$0.565458\pi$
$972$		0			0
$973$	56.2281	+	8.08439i	1.80259	+	0.259174i
$974$		0			0
$975$	−7.62548	+	27.6386i	−0.244211	+	0.885143i
$976$		0			0
$977$	−20.6061	−	45.1211i	−0.659248	−	1.44355i	−0.883221	−	0.468957i	$-0.844630\pi$
$977$	−20.6061	−	45.1211i	−0.659248	−	1.44355i	0.223973	−	0.974595i	$-0.428097\pi$
$978$		0			0
$979$	0.389899	+	2.71181i	0.0124612	+	0.0866697i
$980$		0			0
$981$	1.41550	+	1.14748i	0.0451934	+	0.0366363i
$982$		0			0
$983$	12.6621	−	14.6129i	0.403859	−	0.466078i	−0.516994	−	0.855989i	$-0.672949\pi$
$983$	12.6621	−	14.6129i	0.403859	−	0.466078i	0.920852	+	0.389911i	$0.127494\pi$
$984$		0			0
$985$	−29.3026	+	25.3909i	−0.933660	+	0.809021i
$986$		0			0
$987$	28.5392	+	3.62676i	0.908411	+	0.115441i
$988$		0			0
$989$	−14.2306	+	2.39947i	−0.452506	+	0.0762986i
$990$		0			0
$991$	−10.6082	+	23.2287i	−0.336981	+	0.737885i	−0.999942	−	0.0107686i	$-0.996572\pi$
$991$	−10.6082	+	23.2287i	−0.336981	+	0.737885i	0.662961	+	0.748654i	$0.269299\pi$
$992$		0			0
$993$	−15.1279	+	24.4104i	−0.480069	+	0.774641i
$994$		0			0
$995$	−38.8906	−	33.6989i	−1.23291	−	1.06833i
$996$		0			0
$997$	−45.2003	+	13.2720i	−1.43151	+	0.420329i	−0.903382	−	0.428837i	$-0.858923\pi$
$997$	−45.2003	+	13.2720i	−1.43151	+	0.420329i	−0.528126	+	0.849166i	$0.677105\pi$
$998$		0			0
$999$	−19.3673	−	11.1406i	−0.612753	−	0.352474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.12	✓	240
3.2	odd	2	inner	552.2.u.a.17.17	yes	240
23.19	odd	22	inner	552.2.u.a.65.17	yes	240
69.65	even	22	inner	552.2.u.a.65.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.12	✓	240	1.1	even	1	trivial
552.2.u.a.17.17	yes	240	3.2	odd	2	inner
552.2.u.a.65.12	yes	240	69.65	even	22	inner
552.2.u.a.65.17	yes	240	23.19	odd	22	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0283990 + 1.73182i) q^{3} +(-2.72873 + 1.75365i) q^{5} +(3.60100 + 0.517745i) q^{7} +(-2.99839 + 0.0983638i) q^{9} +O(q^{10})\)	\(q+(0.0283990 + 1.73182i) q^{3} +(-2.72873 + 1.75365i) q^{5} +(3.60100 + 0.517745i) q^{7} +(-2.99839 + 0.0983638i) q^{9} +(0.240426 + 0.526460i) q^{11} +(0.426677 + 2.96760i) q^{13} +(-3.11449 - 4.67586i) q^{15} +(1.22014 - 1.40811i) q^{17} +(-6.16848 + 5.34502i) q^{19} +(-0.794376 + 6.25098i) q^{21} +(-2.09742 - 4.31287i) q^{23} +(2.29361 - 5.02230i) q^{25} +(-0.255499 - 5.18987i) q^{27} +(-0.527834 - 0.457371i) q^{29} +(-9.72048 + 2.85419i) q^{31} +(-0.904905 + 0.431325i) q^{33} +(-10.7341 + 4.90209i) q^{35} +(2.32470 - 3.61730i) q^{37} +(-5.12723 + 0.823204i) q^{39} +(4.41696 + 6.87292i) q^{41} +(0.847780 - 2.88727i) q^{43} +(8.00929 - 5.52652i) q^{45} -4.56555i q^{47} +(5.98268 + 1.75667i) q^{49} +(2.47325 + 2.07307i) q^{51} +(-1.66482 + 11.5790i) q^{53} +(-1.57928 - 1.01494i) q^{55} +(-9.43177 - 10.5309i) q^{57} +(6.58393 - 0.946627i) q^{59} +(-1.16139 - 3.95533i) q^{61} +(-10.8481 - 1.19819i) q^{63} +(-6.36842 - 7.34955i) q^{65} +(8.46328 + 3.86505i) q^{67} +(7.40954 - 3.75483i) q^{69} +(7.41076 + 3.38438i) q^{71} +(9.89429 + 11.4186i) q^{73} +(8.76284 + 3.82948i) q^{75} +(0.593202 + 2.02026i) q^{77} +(-1.09620 + 0.157610i) q^{79} +(8.98065 - 0.589865i) q^{81} +(6.26096 + 4.02367i) q^{83} +(-0.860090 + 5.98206i) q^{85} +(0.777094 - 0.927102i) q^{87} +(4.54197 + 1.33364i) q^{89} +10.9072i q^{91} +(-5.21899 - 16.7531i) q^{93} +(7.45883 - 25.4024i) q^{95} +(4.62308 + 7.19366i) q^{97} +(-0.772676 - 1.55488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more