LMFDB - Embedded newform 672.2.bd.a.527.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(431,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([3, 3, 3, 4]))

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

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

chi := DirichletCharacter("672.431");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			527.8
Character	$\chi$	$=$	672.527
Dual form			672.2.bd.a.431.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03943 + 1.38549i) q^{3} +(0.692094 - 1.19874i) q^{5} +(-2.08863 + 1.62408i) q^{7} +(-0.839162 - 2.88024i) q^{9} +(3.82316 - 2.20731i) q^{11} +6.43609i q^{13} +(0.941460 + 2.20490i) q^{15} +(-2.52866 + 1.45992i) q^{17} +(-1.58928 + 2.75271i) q^{19} +(-0.0791630 - 4.58189i) q^{21} +(-1.84696 + 3.19902i) q^{23} +(1.54201 + 2.67084i) q^{25} +(4.86280 + 1.83117i) q^{27} -6.67884 q^{29} +(-2.17580 + 1.25620i) q^{31} +(-0.915722 + 7.59130i) q^{33} +(0.501330 + 3.62774i) q^{35} +(-5.00149 - 2.88761i) q^{37} +(-8.91713 - 6.68987i) q^{39} -0.497427i q^{41} -0.865898 q^{43} +(-4.03345 - 0.987462i) q^{45} +(-1.59001 + 2.75398i) q^{47} +(1.72472 - 6.78420i) q^{49} +(0.605663 - 5.02092i) q^{51} +(4.12906 + 7.15175i) q^{53} -6.11065i q^{55} +(-2.16191 - 5.06319i) q^{57} +(-6.62279 + 3.82367i) q^{59} +(2.99321 + 1.72813i) q^{61} +(6.43045 + 4.65289i) q^{63} +(7.71521 + 4.45438i) q^{65} +(3.36806 + 5.83364i) q^{67} +(-2.51243 - 5.88411i) q^{69} -1.90437 q^{71} +(3.23515 + 5.60345i) q^{73} +(-5.30324 - 0.639719i) q^{75} +(-4.40032 + 10.8194i) q^{77} +(-1.65073 - 0.953048i) q^{79} +(-7.59162 + 4.83398i) q^{81} -7.00064i q^{83} +4.04161i q^{85} +(6.94220 - 9.25347i) q^{87} +(8.22776 + 4.75030i) q^{89} +(-10.4527 - 13.4426i) q^{91} +(0.521147 - 4.32029i) q^{93} +(2.19986 + 3.81027i) q^{95} +1.19214 q^{97} +(-9.56583 - 9.15936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) $ 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Character values

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

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.03943	+	1.38549i	−0.600116	+	0.799913i
$3$	−1.03943	+	1.38549i	−0.600116	+	0.799913i
$4$		0			0
$5$	0.692094	−	1.19874i	0.309514	−	0.536094i	−0.668742	−	0.743494i	$-0.733167\pi$
$5$	0.692094	−	1.19874i	0.309514	−	0.536094i	0.978256	+	0.207401i	$0.0665004\pi$
$6$		0			0
$7$	−2.08863	+	1.62408i	−0.789426	+	0.613845i
$7$	−2.08863	+	1.62408i	−0.789426	+	0.613845i
$8$		0			0
$9$	−0.839162	−	2.88024i	−0.279721	−	0.960081i
$10$		0			0
$11$	3.82316	−	2.20731i	1.15273	−	0.665528i	0.203177	−	0.979142i	$-0.434873\pi$
$11$	3.82316	−	2.20731i	1.15273	−	0.665528i	0.949550	+	0.313614i	$0.101540\pi$
$12$		0			0
$13$			6.43609i			1.78505i	0.450999	+	0.892525i	$0.351068\pi$
$13$			6.43609i			1.78505i	−0.450999	+	0.892525i	$0.648932\pi$
$14$		0			0
$15$	0.941460	+	2.20490i	0.243084	+	0.569303i
$16$		0			0
$17$	−2.52866	+	1.45992i	−0.613289	+	0.354083i	−0.774252	−	0.632878i	$-0.781874\pi$
$17$	−2.52866	+	1.45992i	−0.613289	+	0.354083i	0.160962	+	0.986961i	$0.448540\pi$
$18$		0			0
$19$	−1.58928	+	2.75271i	−0.364606	+	0.631515i	−0.988713	−	0.149823i	$-0.952130\pi$
$19$	−1.58928	+	2.75271i	−0.364606	+	0.631515i	0.624107	+	0.781339i	$0.285463\pi$
$20$		0			0
$21$	−0.0791630	−	4.58189i	−0.0172748	−	0.999851i
$22$		0			0
$23$	−1.84696	+	3.19902i	−0.385117	+	0.667043i	−0.991785	−	0.127912i	$-0.959172\pi$
$23$	−1.84696	+	3.19902i	−0.385117	+	0.667043i	0.606668	+	0.794955i	$0.292506\pi$
$24$		0			0
$25$	1.54201	+	2.67084i	0.308402	+	0.534169i
$26$		0			0
$27$	4.86280	+	1.83117i	0.935846	+	0.352409i
$28$		0			0
$29$	−6.67884			−1.24023			−0.620115	−	0.784511i	$-0.712914\pi$
$29$	−6.67884			−1.24023			−0.620115	+	0.784511i	$0.712914\pi$
$30$		0			0
$31$	−2.17580	+	1.25620i	−0.390786	+	0.225620i	−0.682500	−	0.730885i	$-0.739107\pi$
$31$	−2.17580	+	1.25620i	−0.390786	+	0.225620i	0.291715	+	0.956505i	$0.405774\pi$
$32$		0			0
$33$	−0.915722	+	7.59130i	−0.159407	+	1.32148i
$34$		0			0
$35$	0.501330	+	3.62774i	0.0847402	+	0.613200i
$36$		0			0
$37$	−5.00149	−	2.88761i	−0.822240	−	0.474720i	0.0289485	−	0.999581i	$-0.490784\pi$
$37$	−5.00149	−	2.88761i	−0.822240	−	0.474720i	−0.851188	+	0.524861i	$0.824117\pi$
$38$		0			0
$39$	−8.91713	−	6.68987i	−1.42788	−	1.07124i
$40$		0			0
$41$		−	0.497427i		−	0.0776850i	−0.999245	−	0.0388425i	$-0.987633\pi$
$41$		−	0.497427i		−	0.0776850i	0.999245	−	0.0388425i	$-0.0123671\pi$
$42$		0			0
$43$	−0.865898			−0.132048			−0.0660241	−	0.997818i	$-0.521031\pi$
$43$	−0.865898			−0.132048			−0.0660241	+	0.997818i	$0.521031\pi$
$44$		0			0
$45$	−4.03345	−	0.987462i	−0.601271	−	0.147202i
$46$		0			0
$47$	−1.59001	+	2.75398i	−0.231927	+	0.401710i	−0.958375	−	0.285512i	$-0.907836\pi$
$47$	−1.59001	+	2.75398i	−0.231927	+	0.401710i	0.726448	+	0.687221i	$0.241170\pi$
$48$		0			0
$49$	1.72472	−	6.78420i	0.246388	−	0.969171i
$50$		0			0
$51$	0.605663	−	5.02092i	0.0848097	−	0.703069i
$52$		0			0
$53$	4.12906	+	7.15175i	0.567171	+	0.982368i	0.996844	+	0.0793841i	$0.0252954\pi$
$53$	4.12906	+	7.15175i	0.567171	+	0.982368i	−0.429673	+	0.902984i	$0.641371\pi$
$54$		0			0
$55$		−	6.11065i		−	0.823960i
$56$		0			0
$57$	−2.16191	−	5.06319i	−0.286351	−	0.670635i
$58$		0			0
$59$	−6.62279	+	3.82367i	−0.862214	+	0.497799i	−0.864753	−	0.502197i	$-0.832525\pi$
$59$	−6.62279	+	3.82367i	−0.862214	+	0.497799i	0.00253919	+	0.999997i	$0.499192\pi$
$60$		0			0
$61$	2.99321	+	1.72813i	0.383241	+	0.221265i	0.679228	−	0.733928i	$-0.262315\pi$
$61$	2.99321	+	1.72813i	0.383241	+	0.221265i	−0.295986	+	0.955192i	$0.595648\pi$
$62$		0			0
$63$	6.43045	+	4.65289i	0.810160	+	0.586209i
$64$		0			0
$65$	7.71521	+	4.45438i	0.956954	+	0.552497i
$66$		0			0
$67$	3.36806	+	5.83364i	0.411473	+	0.712693i	0.995051	−	0.0993644i	$-0.0316810\pi$
$67$	3.36806	+	5.83364i	0.411473	+	0.712693i	−0.583578	+	0.812057i	$0.698348\pi$
$68$		0			0
$69$	−2.51243	−	5.88411i	−0.302461	−	0.708363i
$70$		0			0
$71$	−1.90437			−0.226007			−0.113004	−	0.993595i	$-0.536047\pi$
$71$	−1.90437			−0.226007			−0.113004	+	0.993595i	$0.536047\pi$
$72$		0			0
$73$	3.23515	+	5.60345i	0.378646	+	0.655834i	0.990866	−	0.134854i	$-0.0430564\pi$
$73$	3.23515	+	5.60345i	0.378646	+	0.655834i	−0.612219	+	0.790688i	$0.709723\pi$
$74$		0			0
$75$	−5.30324	−	0.639719i	−0.612365	−	0.0738684i
$76$		0			0
$77$	−4.40032	+	10.8194i	−0.501463	+	1.23298i
$78$		0			0
$79$	−1.65073	−	0.953048i	−0.185721	−	0.107226i	0.404257	−	0.914646i	$-0.367530\pi$
$79$	−1.65073	−	0.953048i	−0.185721	−	0.107226i	−0.589978	+	0.807419i	$0.700864\pi$
$80$		0			0
$81$	−7.59162	+	4.83398i	−0.843513	+	0.537109i
$82$		0			0
$83$		−	7.00064i		−	0.768420i	−0.923246	−	0.384210i	$-0.874474\pi$
$83$		−	7.00064i		−	0.768420i	0.923246	−	0.384210i	$-0.125526\pi$
$84$		0			0
$85$			4.04161i			0.438374i
$86$		0			0
$87$	6.94220	−	9.25347i	0.744282	−	0.992076i
$88$		0			0
$89$	8.22776	+	4.75030i	0.872141	+	0.503531i	0.868059	−	0.496461i	$-0.165367\pi$
$89$	8.22776	+	4.75030i	0.872141	+	0.503531i	0.00408165	+	0.999992i	$0.498701\pi$
$90$		0			0
$91$	−10.4527	−	13.4426i	−1.09574	−	1.40916i
$92$		0			0
$93$	0.521147	−	4.32029i	0.0540404	−	0.447993i
$94$		0			0
$95$	2.19986	+	3.81027i	0.225701	+	0.390926i
$96$		0			0
$97$	1.19214			0.121044			0.0605218	−	0.998167i	$-0.480724\pi$
$97$	1.19214			0.121044			0.0605218	+	0.998167i	$0.480724\pi$
$98$		0			0
$99$	−9.56583	−	9.15936i	−0.961402	−	0.920551i
$100$		0			0
$101$	1.03566	+	1.79382i	0.103052	+	0.178491i	0.912941	−	0.408092i	$-0.133806\pi$
$101$	1.03566	+	1.79382i	0.103052	+	0.178491i	−0.809889	+	0.586584i	$0.800473\pi$
$102$		0			0
$103$	4.80043	+	2.77153i	0.473000	+	0.273087i	0.717495	−	0.696564i	$-0.245289\pi$
$103$	4.80043	+	2.77153i	0.473000	+	0.273087i	−0.244495	+	0.969651i	$0.578622\pi$
$104$		0			0
$105$	−5.54729	−	3.07620i	−0.541361	−	0.300207i
$106$		0			0
$107$	5.17522	+	2.98792i	0.500308	+	0.288853i	0.728841	−	0.684683i	$-0.240060\pi$
$107$	5.17522	+	2.98792i	0.500308	+	0.288853i	−0.228533	+	0.973536i	$0.573393\pi$
$108$		0			0
$109$	1.43595	−	0.829048i	0.137539	−	0.0794084i	−0.429651	−	0.902995i	$-0.641364\pi$
$109$	1.43595	−	0.829048i	0.137539	−	0.0794084i	0.567191	+	0.823586i	$0.308030\pi$
$110$		0			0
$111$	9.19946	−	3.92803i	0.873174	−	0.372832i
$112$		0			0
$113$		−	16.4545i		−	1.54791i	−0.633241	−	0.773955i	$-0.718276\pi$
$113$		−	16.4545i		−	1.54791i	0.633241	−	0.773955i	$-0.281724\pi$
$114$		0			0
$115$	2.55654	+	4.42805i	0.238398	+	0.412918i
$116$		0			0
$117$	18.5375	−	5.40092i	1.71379	−	0.499315i
$118$		0			0
$119$	2.91039	−	7.15597i	0.266795	−	0.655987i
$120$		0			0
$121$	4.24439	−	7.35150i	0.385854	−	0.668318i
$122$		0			0
$123$	0.689179	+	0.517041i	0.0621412	+	0.0466200i
$124$		0			0
$125$	11.1898			1.00085
$126$		0			0
$127$			2.31360i			0.205299i	0.994718	+	0.102649i	$0.0327319\pi$
$127$			2.31360i			0.205299i	−0.994718	+	0.102649i	$0.967268\pi$
$128$		0			0
$129$	0.900042	−	1.19969i	0.0792443	−	0.105627i
$130$		0			0
$131$	4.11383	+	2.37512i	0.359427	+	0.207515i	0.668830	−	0.743416i	$-0.266796\pi$
$131$	4.11383	+	2.37512i	0.359427	+	0.207515i	−0.309402	+	0.950931i	$0.600129\pi$
$132$		0			0
$133$	−1.15122	−	8.33050i	−0.0998234	−	0.722346i
$134$		0			0
$135$	5.56061	−	4.56190i	0.478581	−	0.392626i
$136$		0			0
$137$	−0.290760	+	0.167870i	−0.0248413	+	0.0143421i	−0.512369	−	0.858765i	$-0.671232\pi$
$137$	−0.290760	+	0.167870i	−0.0248413	+	0.0143421i	0.487528	+	0.873107i	$0.337899\pi$
$138$		0			0
$139$	9.35410			0.793405			0.396702	−	0.917947i	$-0.370155\pi$
$139$	9.35410			0.793405			0.396702	+	0.917947i	$0.370155\pi$
$140$		0			0
$141$	−2.16290	−	5.06553i	−0.182149	−	0.426594i
$142$		0			0
$143$	14.2064	+	24.6062i	1.18800	+	2.05768i
$144$		0			0
$145$	−4.62239	+	8.00621i	−0.383868	+	0.664880i
$146$		0			0
$147$	7.60671	+	9.44129i	0.627391	+	0.778705i
$148$		0			0
$149$	1.03566	−	1.79382i	0.0848446	−	0.146955i	−0.820480	−	0.571675i	$-0.806294\pi$
$149$	1.03566	−	1.79382i	0.0848446	−	0.146955i	0.905325	+	0.424720i	$0.139627\pi$
$150$		0			0
$151$	20.2661	−	11.7007i	1.64923	−	0.952186i	0.671858	−	0.740680i	$-0.265496\pi$
$151$	20.2661	−	11.7007i	1.64923	−	0.952186i	0.977377	−	0.211506i	$-0.0678369\pi$
$152$		0			0
$153$	6.32688	+	6.05804i	0.511498	+	0.489763i
$154$		0			0
$155$			3.47763i			0.279330i
$156$		0			0
$157$	19.3264	−	11.1581i	1.54241	−	0.890511i	0.543725	−	0.839264i	$-0.317014\pi$
$157$	19.3264	−	11.1581i	1.54241	−	0.890511i	0.998686	−	0.0512477i	$-0.0163198\pi$
$158$		0			0
$159$	−14.2006	−	1.71298i	−1.12618	−	0.135848i
$160$		0			0
$161$	−1.33787	−	9.68118i	−0.105439	−	0.762983i
$162$		0			0
$163$	8.50029	−	14.7229i	0.665794	−	1.15319i	−0.313276	−	0.949662i	$-0.601426\pi$
$163$	8.50029	−	14.7229i	0.665794	−	1.15319i	0.979069	−	0.203526i	$-0.0652403\pi$
$164$		0			0
$165$	8.46624	+	6.35161i	0.659096	+	0.494472i
$166$		0			0
$167$	−23.9142			−1.85054			−0.925269	−	0.379311i	$-0.876161\pi$
$167$	−23.9142			−1.85054			−0.925269	+	0.379311i	$0.876161\pi$
$168$		0			0
$169$	−28.4232			−2.18640
$170$		0			0
$171$	9.26215	+	2.26754i	0.708294	+	0.173403i
$172$		0			0
$173$	−4.38442	+	7.59404i	−0.333341	+	0.577364i	−0.983165	−	0.182721i	$-0.941509\pi$
$173$	−4.38442	+	7.59404i	−0.333341	+	0.577364i	0.649824	+	0.760085i	$0.274843\pi$
$174$		0			0
$175$	−7.55835	−	3.07404i	−0.571358	−	0.232375i
$176$		0			0
$177$	1.58629	−	13.1503i	0.119233	−	0.988433i
$178$		0			0
$179$	5.26665	−	3.04070i	0.393648	−	0.227273i	−0.290092	−	0.956999i	$-0.593686\pi$
$179$	5.26665	−	3.04070i	0.393648	−	0.227273i	0.683740	+	0.729726i	$0.260352\pi$
$180$		0			0
$181$		−	11.5816i		−	0.860857i	−0.902625	−	0.430429i	$-0.858362\pi$
$181$		−	11.5816i		−	0.860857i	0.902625	−	0.430429i	$-0.141638\pi$
$182$		0			0
$183$	−5.50555	+	2.35079i	−0.406982	+	0.173775i
$184$		0			0
$185$	−6.92300	+	3.99700i	−0.508989	+	0.293865i
$186$		0			0
$187$	−6.44498	+	11.1630i	−0.471304	+	0.816322i
$188$		0			0
$189$	−13.1305	+	4.07296i	−0.955106	+	0.296264i
$190$		0			0
$191$	−0.757053	+	1.31125i	−0.0547784	+	0.0948790i	−0.892114	−	0.451810i	$-0.850779\pi$
$191$	−0.757053	+	1.31125i	−0.0547784	+	0.0948790i	0.837336	+	0.546689i	$0.184112\pi$
$192$		0			0
$193$	−7.97806	−	13.8184i	−0.574273	−	0.994670i	−0.996120	−	0.0880034i	$-0.971951\pi$
$193$	−7.97806	−	13.8184i	−0.574273	−	0.994670i	0.421847	−	0.906667i	$-0.361382\pi$
$194$		0			0
$195$	−14.1909	+	6.05931i	−1.01623	+	0.433917i
$196$		0			0
$197$	0.963016			0.0686121			0.0343060	−	0.999411i	$-0.489078\pi$
$197$	0.963016			0.0686121			0.0343060	+	0.999411i	$0.489078\pi$
$198$		0			0
$199$	−1.72593	+	0.996469i	−0.122348	+	0.0706378i	−0.559925	−	0.828543i	$-0.689170\pi$
$199$	−1.72593	+	0.996469i	−0.122348	+	0.0706378i	0.437577	+	0.899181i	$0.355837\pi$
$200$		0			0
$201$	−11.5833	−	1.39727i	−0.817024	−	0.0985559i
$202$		0			0
$203$	13.9496	−	10.8470i	0.979070	−	0.761309i
$204$		0			0
$205$	−0.596286	−	0.344266i	−0.0416464	−	0.0240446i
$206$		0			0
$207$	10.7639	+	2.63519i	0.748141	+	0.183158i
$208$		0			0
$209$			14.0321i			0.970620i
$210$		0			0
$211$	−21.4567			−1.47714			−0.738569	−	0.674178i	$-0.764498\pi$
$211$	−21.4567			−1.47714			−0.738569	+	0.674178i	$0.764498\pi$
$212$		0			0
$213$	1.97947	−	2.63849i	0.135631	−	0.180786i
$214$		0			0
$215$	−0.599283	+	1.03799i	−0.0408707	+	0.0707902i
$216$		0			0
$217$	2.50427	−	6.15741i	0.170001	−	0.417992i
$218$		0			0
$219$	−11.1262	−	1.34214i	−0.751842	−	0.0906931i
$220$		0			0
$221$	−9.39617	−	16.2747i	−0.632055	−	1.09475i
$222$		0			0
$223$			12.1938i			0.816559i	0.912857	+	0.408279i	$0.133871\pi$
$223$			12.1938i			0.816559i	−0.912857	+	0.408279i	$0.866129\pi$
$224$		0			0
$225$	6.39868	−	6.68264i	0.426579	−	0.445509i
$226$		0			0
$227$	−13.5954	+	7.84932i	−0.902360	+	0.520978i	−0.877965	−	0.478724i	$-0.841099\pi$
$227$	−13.5954	+	7.84932i	−0.902360	+	0.520978i	−0.0243951	+	0.999702i	$0.507766\pi$
$228$		0			0
$229$	−10.4894	−	6.05608i	−0.693161	−	0.400197i	0.111634	−	0.993749i	$-0.464392\pi$
$229$	−10.4894	−	6.05608i	−0.693161	−	0.400197i	−0.804795	+	0.593553i	$0.797725\pi$
$230$		0			0
$231$	−10.4163	−	17.3426i	−0.685341	−	1.14106i
$232$		0			0
$233$	5.05877	+	2.92068i	0.331411	+	0.191340i	0.656468	−	0.754354i	$-0.272050\pi$
$233$	5.05877	+	2.92068i	0.331411	+	0.191340i	−0.325056	+	0.945695i	$0.605383\pi$
$234$		0			0
$235$	2.20088	+	3.81203i	0.143569	+	0.248670i
$236$		0			0
$237$	3.03626	−	1.29644i	0.197226	−	0.0842126i
$238$		0			0
$239$	22.6171			1.46298			0.731490	−	0.681852i	$-0.238825\pi$
$239$	22.6171			1.46298			0.731490	+	0.681852i	$0.238825\pi$
$240$		0			0
$241$	12.7459	+	22.0766i	0.821038	+	1.42208i	0.904910	+	0.425604i	$0.139938\pi$
$241$	12.7459	+	22.0766i	0.821038	+	1.42208i	−0.0838714	+	0.996477i	$0.526729\pi$
$242$		0			0
$243$	1.19354	−	15.5427i	0.0765656	−	0.997065i
$244$		0			0
$245$	−6.93884	−	6.76279i	−0.443306	−	0.432059i
$246$		0			0
$247$	−17.7167	−	10.2287i	−1.12729	−	0.650839i
$248$		0			0
$249$	9.69931	+	7.27669i	0.614669	+	0.461141i
$250$		0			0
$251$		−	1.11008i		−	0.0700675i	−0.999386	−	0.0350338i	$-0.988846\pi$
$251$		−	1.11008i		−	0.0700675i	0.999386	−	0.0350338i	$-0.0111539\pi$
$252$		0			0
$253$			16.3072i			1.02522i
$254$		0			0
$255$	−5.59961	−	4.20098i	−0.350661	−	0.263075i
$256$		0			0
$257$	−12.0906	−	6.98049i	−0.754188	−	0.435431i	0.0730169	−	0.997331i	$-0.476737\pi$
$257$	−12.0906	−	6.98049i	−0.754188	−	0.435431i	−0.827205	+	0.561900i	$0.810071\pi$
$258$		0			0
$259$	15.1360	−	2.09169i	0.940503	−	0.129971i
$260$		0			0
$261$	5.60463	+	19.2367i	0.346918	+	1.19072i
$262$		0			0
$263$	−7.08483	−	12.2713i	−0.436870	−	0.756680i	0.560577	−	0.828103i	$-0.310580\pi$
$263$	−7.08483	−	12.2713i	−0.436870	−	0.756680i	−0.997446	+	0.0714223i	$0.977246\pi$
$264$		0			0
$265$	11.4308			0.702189
$266$		0			0
$267$	−15.1337	+	6.46186i	−0.926166	+	0.395459i
$268$		0			0
$269$	9.11023	+	15.7794i	0.555461	+	0.962086i	0.997868	+	0.0652716i	$0.0207914\pi$
$269$	9.11023	+	15.7794i	0.555461	+	0.962086i	−0.442407	+	0.896814i	$0.645875\pi$
$270$		0			0
$271$	21.9278	+	12.6600i	1.33202	+	0.769041i	0.985609	−	0.169042i	$-0.0540673\pi$
$271$	21.9278	+	12.6600i	1.33202	+	0.769041i	0.346410	+	0.938083i	$0.387401\pi$
$272$		0			0
$273$	29.4894	−	0.509500i	1.78478	−	0.0308363i
$274$		0			0
$275$	11.7907	+	6.80738i	0.711008	+	0.410500i
$276$		0			0
$277$	−16.2822	+	9.40051i	−0.978300	+	0.564822i	−0.901756	−	0.432245i	$-0.857722\pi$
$277$	−16.2822	+	9.40051i	−0.978300	+	0.564822i	−0.0765434	+	0.997066i	$0.524388\pi$
$278$		0			0
$279$	5.44401	+	5.21269i	0.325924	+	0.312075i
$280$		0			0
$281$			25.4910i			1.52067i	0.649533	+	0.760333i	$0.274964\pi$
$281$			25.4910i			1.52067i	−0.649533	+	0.760333i	$0.725036\pi$
$282$		0			0
$283$	6.01848	+	10.4243i	0.357761	+	0.619661i	0.987586	−	0.157076i	$-0.0502068\pi$
$283$	6.01848	+	10.4243i	0.357761	+	0.619661i	−0.629825	+	0.776737i	$0.716874\pi$
$284$		0			0
$285$	−7.56570	−	0.912634i	−0.448153	−	0.0540598i
$286$		0			0
$287$	0.807861	+	1.03894i	0.0476865	+	0.0613266i
$288$		0			0
$289$	−4.23726	+	7.33916i	−0.249251	+	0.431715i
$290$		0			0
$291$	−1.23915	+	1.65170i	−0.0726403	+	0.0968244i
$292$		0			0
$293$	−3.90464			−0.228111			−0.114056	−	0.993474i	$-0.536384\pi$
$293$	−3.90464			−0.228111			−0.114056	+	0.993474i	$0.536384\pi$
$294$		0			0
$295$			10.5854i			0.616303i
$296$		0			0
$297$	22.6332	−	3.73282i	1.31331	−	0.216600i
$298$		0			0
$299$	−20.5892	−	11.8872i	−1.19070	−	0.687453i
$300$		0			0
$301$	1.80854	−	1.40629i	0.104242	−	0.0810571i
$302$		0			0
$303$	−3.56181	−	0.429654i	−0.204621	−	0.0246830i
$304$		0			0
$305$	4.14317	−	2.39206i	0.237237	−	0.136969i
$306$		0			0
$307$	11.0339			0.629740			0.314870	−	0.949135i	$-0.398039\pi$
$307$	11.0339			0.629740			0.314870	+	0.949135i	$0.398039\pi$
$308$		0			0
$309$	−8.82964	+	3.77013i	−0.502301	+	0.214475i
$310$		0			0
$311$	−15.6553	−	27.1158i	−0.887732	−	1.53760i	−0.842550	−	0.538618i	$-0.818947\pi$
$311$	−15.6553	−	27.1158i	−0.887732	−	1.53760i	−0.0451815	−	0.998979i	$-0.514387\pi$
$312$		0			0
$313$	6.53063	−	11.3114i	0.369133	−	0.639357i	−0.620297	−	0.784367i	$-0.712988\pi$
$313$	6.53063	−	11.3114i	0.369133	−	0.639357i	0.989430	+	0.145010i	$0.0463213\pi$
$314$		0			0
$315$	10.0281	−	4.48821i	0.565019	−	0.252882i
$316$		0			0
$317$	12.2315	−	21.1856i	0.686990	−	1.18990i	−0.285817	−	0.958284i	$-0.592265\pi$
$317$	12.2315	−	21.1856i	0.686990	−	1.18990i	0.972807	−	0.231618i	$-0.0744018\pi$
$318$		0			0
$319$	−25.5343	+	14.7422i	−1.42965	+	0.825407i
$320$		0			0
$321$	−9.51902	+	4.06448i	−0.531300	+	0.226857i
$322$		0			0
$323$		−	9.28088i		−	0.516402i
$324$		0			0
$325$	−17.1898	+	9.92452i	−0.953517	+	0.550513i
$326$		0			0
$327$	−0.343939	+	2.85124i	−0.0190198	+	0.157674i
$328$		0			0
$329$	−1.15175	−	8.33435i	−0.0634981	−	0.459488i
$330$		0			0
$331$	7.26267	−	12.5793i	0.399192	−	0.691422i	−0.594434	−	0.804144i	$-0.702624\pi$
$331$	7.26267	−	12.5793i	0.399192	−	0.691422i	0.993626	+	0.112723i	$0.0359572\pi$
$332$		0			0
$333$	−4.11997	+	16.8287i	−0.225773	+	0.922206i
$334$		0			0
$335$	9.32404			0.509427
$336$		0			0
$337$	−18.7954			−1.02385			−0.511924	−	0.859030i	$-0.671067\pi$
$337$	−18.7954			−1.02385			−0.511924	+	0.859030i	$0.671067\pi$
$338$		0			0
$339$	22.7975	+	17.1033i	1.23819	+	0.928926i
$340$		0			0
$341$	−5.54563	+	9.60532i	−0.300313	+	0.520157i
$342$		0			0
$343$	7.41581	+	16.9707i	0.400416	+	0.916334i
$344$		0			0
$345$	−8.79236	−	1.06060i	−0.473365	−	0.0571010i
$346$		0			0
$347$	−20.7411	+	11.9749i	−1.11344	+	0.642846i	−0.939719	−	0.341949i	$-0.888913\pi$
$347$	−20.7411	+	11.9749i	−1.11344	+	0.642846i	−0.173723	+	0.984795i	$0.555580\pi$
$348$		0			0
$349$		−	3.59423i		−	0.192395i	−0.995362	−	0.0961974i	$-0.969332\pi$
$349$		−	3.59423i		−	0.192395i	0.995362	−	0.0961974i	$-0.0306680\pi$
$350$		0			0
$351$	−11.7856	+	31.2974i	−0.629067	+	1.67053i
$352$		0			0
$353$	−22.4603	+	12.9675i	−1.19544	+	0.690189i	−0.959536	−	0.281587i	$-0.909139\pi$
$353$	−22.4603	+	12.9675i	−1.19544	+	0.690189i	−0.235907	+	0.971776i	$0.575806\pi$
$354$		0			0
$355$	−1.31800	+	2.28285i	−0.0699524	+	0.121161i
$356$		0			0
$357$	6.88937	+	11.4705i	0.364624	+	0.607081i
$358$		0			0
$359$	14.1756	−	24.5529i	0.748162	−	1.29585i	−0.200541	−	0.979685i	$-0.564270\pi$
$359$	14.1756	−	24.5529i	0.748162	−	1.29585i	0.948703	−	0.316169i	$-0.102397\pi$
$360$		0			0
$361$	4.44838	+	7.70483i	0.234126	+	0.405517i
$362$		0			0
$363$	5.77367	+	13.5219i	0.303039	+	0.709718i
$364$		0			0
$365$	8.95612			0.468785
$366$		0			0
$367$	3.10999	−	1.79556i	0.162340	−	0.0937272i	−0.416629	−	0.909077i	$-0.636789\pi$
$367$	3.10999	−	1.79556i	0.162340	−	0.0937272i	0.578969	+	0.815349i	$0.303455\pi$
$368$		0			0
$369$	−1.43271	+	0.417421i	−0.0745839	+	0.0217301i
$370$		0			0
$371$	−20.2391	−	8.23139i	−1.05076	−	0.427353i
$372$		0			0
$373$	13.4339	+	7.75604i	0.695579	+	0.401593i	0.805699	−	0.592326i	$-0.201790\pi$
$373$	13.4339	+	7.75604i	0.695579	+	0.401593i	−0.110120	+	0.993918i	$0.535123\pi$
$374$		0			0
$375$	−11.6310	+	15.5034i	−0.600625	+	0.800590i
$376$		0			0
$377$		−	42.9856i		−	2.21387i
$378$		0			0
$379$	14.5848			0.749171			0.374586	−	0.927192i	$-0.377785\pi$
$379$	14.5848			0.749171			0.374586	+	0.927192i	$0.377785\pi$
$380$		0			0
$381$	−3.20547	−	2.40483i	−0.164221	−	0.123203i
$382$		0			0
$383$	5.47353	−	9.48043i	0.279684	−	0.484427i	−0.691622	−	0.722260i	$-0.743104\pi$
$383$	5.47353	−	9.48043i	0.279684	−	0.484427i	0.971306	+	0.237832i	$0.0764369\pi$
$384$		0			0
$385$	9.92420	+	12.7629i	0.505784	+	0.650456i
$386$		0			0
$387$	0.726628	+	2.49400i	0.0369366	+	0.126777i
$388$		0			0
$389$	−9.51835	−	16.4863i	−0.482600	−	0.835887i	0.517201	−	0.855864i	$-0.326974\pi$
$389$	−9.51835	−	16.4863i	−0.482600	−	0.835887i	−0.999800	+	0.0199769i	$0.993641\pi$
$390$		0			0
$391$		−	10.7856i		−	0.545453i
$392$		0			0
$393$	−7.56676	+	3.23089i	−0.381692	+	0.162977i
$394$		0			0
$395$	−2.28492	+	1.31920i	−0.114967	+	0.0663760i
$396$		0			0
$397$	−6.49649	−	3.75075i	−0.326050	−	0.188245i	0.328036	−	0.944665i	$-0.393613\pi$
$397$	−6.49649	−	3.75075i	−0.326050	−	0.188245i	−0.654086	+	0.756420i	$0.726947\pi$
$398$		0			0
$399$	12.7384	+	7.06399i	0.637720	+	0.353642i
$400$		0			0
$401$	24.3528	+	14.0601i	1.21612	+	0.702128i	0.964086	−	0.265591i	$-0.0855670\pi$
$401$	24.3528	+	14.0601i	1.21612	+	0.702128i	0.252035	+	0.967718i	$0.418900\pi$
$402$		0			0
$403$	−8.08501	−	14.0036i	−0.402743	−	0.697571i
$404$		0			0
$405$	0.540584	+	12.4460i	0.0268618	+	0.618445i
$406$		0			0
$407$	−25.4954			−1.26376
$408$		0			0
$409$	6.57782	+	11.3931i	0.325252	+	0.563353i	0.981563	−	0.191137i	$-0.0612175\pi$
$409$	6.57782	+	11.3931i	0.325252	+	0.563353i	−0.656311	+	0.754490i	$0.727884\pi$
$410$		0			0
$411$	0.0696427	−	0.577335i	0.00343522	−	0.0284778i
$412$		0			0
$413$	7.62258	−	18.7422i	0.375083	−	0.922242i
$414$		0			0
$415$	−8.39196	−	4.84510i	−0.411945	−	0.237837i
$416$		0			0
$417$	−9.72296	+	12.9600i	−0.476135	+	0.634654i
$418$		0			0
$419$		−	4.42222i		−	0.216040i	−0.994149	−	0.108020i	$-0.965549\pi$
$419$		−	4.42222i		−	0.216040i	0.994149	−	0.108020i	$-0.0344510\pi$
$420$		0			0
$421$			22.2013i			1.08203i	0.841014	+	0.541014i	$0.181959\pi$
$421$			22.2013i			1.08203i	−0.841014	+	0.541014i	$0.818041\pi$
$422$		0			0
$423$	9.26642	+	2.26859i	0.450549	+	0.110303i
$424$		0			0
$425$	−7.79844	−	4.50243i	−0.378280	−	0.218400i
$426$		0			0
$427$	−9.05832	+	1.25180i	−0.438363	+	0.0605788i
$428$		0			0
$429$	−48.8582	−	5.89367i	−2.35890	−	0.284549i
$430$		0			0
$431$	8.76759	+	15.1859i	0.422320	+	0.731479i	0.996166	−	0.0874837i	$-0.0278826\pi$
$431$	8.76759	+	15.1859i	0.422320	+	0.731479i	−0.573846	+	0.818963i	$0.694549\pi$
$432$		0			0
$433$	0.852347			0.0409612			0.0204806	−	0.999790i	$-0.493480\pi$
$433$	0.852347			0.0409612			0.0204806	+	0.999790i	$0.493480\pi$
$434$		0			0
$435$	−6.28786	−	14.7262i	−0.301480	−	0.706066i
$436$		0			0
$437$	−5.87066	−	10.1683i	−0.280832	−	0.486415i
$438$		0			0
$439$	−14.5943	−	8.42604i	−0.696549	−	0.402153i	0.109512	−	0.993986i	$-0.465071\pi$
$439$	−14.5943	−	8.42604i	−0.696549	−	0.402153i	−0.806061	+	0.591833i	$0.798405\pi$
$440$		0			0
$441$	−20.9875	+	0.725433i	−0.999403	+	0.0345444i
$442$		0			0
$443$	24.9578	+	14.4094i	1.18578	+	0.684611i	0.957345	−	0.288948i	$-0.0933055\pi$
$443$	24.9578	+	14.4094i	1.18578	+	0.684611i	0.228436	+	0.973559i	$0.426639\pi$
$444$		0			0
$445$	11.3888	−	6.57531i	0.539879	−	0.311699i
$446$		0			0
$447$	1.40881	+	3.29945i	0.0666347	+	0.156058i
$448$		0			0
$449$			1.27217i			0.0600373i	0.999549	+	0.0300186i	$0.00955666\pi$
$449$			1.27217i			0.0600373i	−0.999549	+	0.0300186i	$0.990443\pi$
$450$		0			0
$451$	−1.09797	−	1.90174i	−0.0517015	−	0.0895496i
$452$		0			0
$453$	−4.85413	+	40.2406i	−0.228067	+	1.89067i
$454$		0			0
$455$	−23.3485	+	3.22660i	−1.09459	+	0.151265i
$456$		0			0
$457$	7.46471	−	12.9293i	0.349185	−	0.604805i	−0.636920	−	0.770930i	$-0.719792\pi$
$457$	7.46471	−	12.9293i	0.349185	−	0.604805i	0.986105	+	0.166124i	$0.0531253\pi$
$458$		0			0
$459$	−14.9697	+	2.46890i	−0.698726	+	0.115239i
$460$		0			0
$461$	−27.1371			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$461$	−27.1371			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$462$		0			0
$463$		−	24.3062i		−	1.12960i	−0.825227	−	0.564801i	$-0.808953\pi$
$463$		−	24.3062i		−	1.12960i	0.825227	−	0.564801i	$-0.191047\pi$
$464$		0			0
$465$	−4.81822	−	3.61476i	−0.223440	−	0.167631i
$466$		0			0
$467$	22.2686	+	12.8568i	1.03047	+	0.594940i	0.917118	−	0.398615i	$-0.130509\pi$
$467$	22.2686	+	12.8568i	1.03047	+	0.594940i	0.113349	+	0.993555i	$0.463842\pi$
$468$		0			0
$469$	−16.5089	−	6.71430i	−0.762311	−	0.310038i
$470$		0			0
$471$	−4.62904	+	38.3745i	−0.213295	+	1.76820i
$472$		0			0
$473$	−3.31047	+	1.91130i	−0.152216	+	0.0878817i
$474$		0			0
$475$	−9.80275			−0.449781
$476$		0			0
$477$	17.1338	−	17.8942i	0.784504	−	0.819319i
$478$		0			0
$479$	−4.48448	−	7.76735i	−0.204901	−	0.354899i	0.745200	−	0.666841i	$-0.232354\pi$
$479$	−4.48448	−	7.76735i	−0.204901	−	0.354899i	−0.950101	+	0.311942i	$0.899021\pi$
$480$		0			0
$481$	18.5849	−	32.1900i	0.847399	−	1.46774i
$482$		0			0
$483$	14.8038	+	8.20932i	0.673596	+	0.373537i
$484$		0			0
$485$	0.825074	−	1.42907i	0.0374647	−	0.0648908i
$486$		0			0
$487$	5.02256	−	2.89978i	0.227594	−	0.131401i	−0.381868	−	0.924217i	$-0.624719\pi$
$487$	5.02256	−	2.89978i	0.227594	−	0.131401i	0.609462	+	0.792816i	$0.291386\pi$
$488$		0			0
$489$	11.5630	+	27.0805i	0.522896	+	1.22462i
$490$		0			0
$491$			13.5893i			0.613275i	0.951826	+	0.306637i	$0.0992039\pi$
$491$			13.5893i			0.613275i	−0.951826	+	0.306637i	$0.900796\pi$
$492$		0			0
$493$	16.8885	−	9.75058i	0.760620	−	0.439144i
$494$		0			0
$495$	−17.6002	+	5.12782i	−0.791069	+	0.230479i
$496$		0			0
$497$	3.97752	−	3.09286i	0.178416	−	0.138734i
$498$		0			0
$499$	−18.6144	+	32.2411i	−0.833294	+	1.44331i	0.0621178	+	0.998069i	$0.480215\pi$
$499$	−18.6144	+	32.2411i	−0.833294	+	1.44331i	−0.895412	+	0.445239i	$0.853119\pi$
$500$		0			0
$501$	24.8572	−	33.1329i	1.11054	−	1.48027i
$502$		0			0
$503$	24.5224			1.09340			0.546699	−	0.837329i	$-0.315884\pi$
$503$	24.5224			1.09340			0.546699	+	0.837329i	$0.315884\pi$
$504$		0			0
$505$	2.86710			0.127584
$506$		0			0
$507$	29.5440	−	39.3800i	1.31209	−	1.74893i
$508$		0			0
$509$	21.4381	−	37.1319i	0.950226	−	1.64584i	0.205294	−	0.978700i	$-0.434185\pi$
$509$	21.4381	−	37.1319i	0.950226	−	1.64584i	0.744932	−	0.667140i	$-0.232482\pi$
$510$		0			0
$511$	−15.8575	−	6.44936i	−0.701494	−	0.285303i
$512$		0			0
$513$	−12.7690	+	10.4756i	−0.563766	+	0.462511i
$514$		0			0
$515$	6.64470	−	3.83632i	0.292800	−	0.169048i
$516$		0			0
$517$			14.0386i			0.617416i
$518$		0			0
$519$	−5.96415	−	13.9681i	−0.261797	−	0.613129i
$520$		0			0
$521$	1.58214	−	0.913450i	0.0693149	−	0.0400190i	−0.464942	−	0.885341i	$-0.653925\pi$
$521$	1.58214	−	0.913450i	0.0693149	−	0.0400190i	0.534257	+	0.845322i	$0.320591\pi$
$522$		0			0
$523$	−12.7145	+	22.0222i	−0.555966	+	0.962962i	0.441861	+	0.897083i	$0.354318\pi$
$523$	−12.7145	+	22.0222i	−0.555966	+	0.962962i	−0.997828	+	0.0658788i	$0.979015\pi$
$524$		0			0
$525$	12.1154	−	7.27676i	0.528761	−	0.317584i
$526$		0			0
$527$	3.66790	−	6.35300i	0.159776	−	0.276741i
$528$		0			0
$529$	4.67750	+	8.10166i	0.203369	+	0.352246i
$530$		0			0
$531$	16.5707	+	15.8666i	0.719107	+	0.688551i
$532$		0			0
$533$	3.20148			0.138671
$534$		0			0
$535$	7.16348	−	4.13584i	0.309704	−	0.178808i
$536$		0			0
$537$	−1.26147	+	10.4575i	−0.0544362	+	0.451274i
$538$		0			0
$539$	−8.38092	−	29.7441i	−0.360992	−	1.28117i
$540$		0			0
$541$	16.3531	+	9.44148i	0.703076	+	0.405921i	0.808492	−	0.588507i	$-0.200284\pi$
$541$	16.3531	+	9.44148i	0.703076	+	0.405921i	−0.105416	+	0.994428i	$0.533618\pi$
$542$		0			0
$543$	16.0463	+	12.0383i	0.688611	+	0.516615i
$544$		0			0
$545$		−	2.29512i		−	0.0983119i
$546$		0			0
$547$	−13.0624			−0.558509			−0.279254	−	0.960217i	$-0.590087\pi$
$547$	−13.0624			−0.558509			−0.279254	+	0.960217i	$0.590087\pi$
$548$		0			0
$549$	2.46565	−	10.0714i	0.105231	−	0.429835i
$550$		0			0
$551$	10.6145	−	18.3849i	0.452195	−	0.783224i
$552$		0			0
$553$	4.99558	−	0.690356i	0.212434	−	0.0293569i
$554$		0			0
$555$	1.65819	−	13.7464i	0.0703864	−	0.583500i
$556$		0			0
$557$	15.9928	+	27.7003i	0.677635	+	1.17370i	0.975691	+	0.219151i	$0.0703286\pi$
$557$	15.9928	+	27.7003i	0.677635	+	1.17370i	−0.298056	+	0.954549i	$0.596338\pi$
$558$		0			0
$559$		−	5.57299i		−	0.235712i
$560$		0			0
$561$	−8.76714	−	20.5327i	−0.370149	−	0.866890i
$562$		0			0
$563$	−31.2546	+	18.0449i	−1.31723	+	0.760501i	−0.983281	−	0.182092i	$-0.941713\pi$
$563$	−31.2546	+	18.0449i	−1.31723	+	0.760501i	−0.333944	+	0.942593i	$0.608380\pi$
$564$		0			0
$565$	−19.7247	−	11.3881i	−0.829825	−	0.479100i
$566$		0			0
$567$	8.00527	−	22.4258i	0.336190	−	0.941794i
$568$		0			0
$569$	−23.5336	−	13.5871i	−0.986579	−	0.569601i	−0.0823288	−	0.996605i	$-0.526236\pi$
$569$	−23.5336	−	13.5871i	−0.986579	−	0.569601i	−0.904250	+	0.427004i	$0.859569\pi$
$570$		0			0
$571$	7.45448	+	12.9115i	0.311960	+	0.540331i	0.978787	−	0.204882i	$-0.0656811\pi$
$571$	7.45448	+	12.9115i	0.311960	+	0.540331i	−0.666826	+	0.745213i	$0.732348\pi$
$572$		0			0
$573$	−1.02982	−	2.41185i	−0.0430215	−	0.100756i
$574$		0			0
$575$	−11.3921			−0.475084
$576$		0			0
$577$	−19.1659	−	33.1963i	−0.797886	−	1.38198i	−0.920990	−	0.389585i	$-0.872618\pi$
$577$	−19.1659	−	33.1963i	−0.797886	−	1.38198i	0.123104	−	0.992394i	$-0.460715\pi$
$578$		0			0
$579$	27.4379	+	3.30978i	1.14028	+	0.137550i
$580$		0			0
$581$	11.3696	+	14.6217i	0.471691	+	0.606611i
$582$		0			0
$583$	31.5722	+	18.2282i	1.30759	+	0.754935i
$584$		0			0
$585$	6.35539	−	25.9596i	0.262763	−	1.07330i
$586$		0			0
$587$		−	0.964880i		−	0.0398249i	−0.999802	−	0.0199124i	$-0.993661\pi$
$587$		−	0.964880i		−	0.0398249i	0.999802	−	0.0199124i	$-0.00633874\pi$
$588$		0			0
$589$		−	7.98581i		−	0.329050i
$590$		0			0
$591$	−1.00099	+	1.33425i	−0.0411752	+	0.0548837i
$592$		0			0
$593$	−14.9519	−	8.63251i	−0.614003	−	0.354495i	0.160528	−	0.987031i	$-0.448680\pi$
$593$	−14.9519	−	8.63251i	−0.614003	−	0.354495i	−0.774530	+	0.632537i	$0.782014\pi$
$594$		0			0
$595$	−6.56390	−	8.44141i	−0.269094	−	0.346064i
$596$		0			0
$597$	0.413395	−	3.42702i	0.0169191	−	0.140259i
$598$		0			0
$599$	6.22127	+	10.7756i	0.254194	+	0.440277i	0.964676	−	0.263438i	$-0.0848565\pi$
$599$	6.22127	+	10.7756i	0.254194	+	0.440277i	−0.710482	+	0.703715i	$0.751523\pi$
$600$		0			0
$601$	−27.7052			−1.13012			−0.565059	−	0.825051i	$-0.691147\pi$
$601$	−27.7052			−1.13012			−0.565059	+	0.825051i	$0.691147\pi$
$602$		0			0
$603$	13.9760	−	14.5962i	0.569146	−	0.594403i
$604$		0			0
$605$	−5.87504	−	10.1759i	−0.238854	−	0.413708i
$606$		0			0
$607$	5.43950	+	3.14050i	0.220783	+	0.127469i	0.606313	−	0.795226i	$-0.292648\pi$
$607$	5.43950	+	3.14050i	0.220783	+	0.127469i	−0.385530	+	0.922695i	$0.625981\pi$
$608$		0			0
$609$	0.528717	+	30.6017i	0.0214247	+	1.24004i
$610$		0			0
$611$	−17.7249	−	10.2335i	−0.717072	−	0.414002i
$612$		0			0
$613$	17.0190	−	9.82590i	0.687389	−	0.396864i	−0.115244	−	0.993337i	$-0.536765\pi$
$613$	17.0190	−	9.82590i	0.687389	−	0.396864i	0.802633	+	0.596473i	$0.203432\pi$
$614$		0			0
$615$	1.09678	−	0.468307i	0.0442263	−	0.0188840i
$616$		0			0
$617$			32.2579i			1.29865i	0.760509	+	0.649327i	$0.224949\pi$
$617$			32.2579i			1.29865i	−0.760509	+	0.649327i	$0.775051\pi$
$618$		0			0
$619$	−13.3846	−	23.1828i	−0.537973	−	0.931797i	−0.999013	−	0.0444173i	$-0.985857\pi$
$619$	−13.3846	−	23.1828i	−0.537973	−	0.931797i	0.461040	−	0.887379i	$-0.347476\pi$
$620$		0			0
$621$	−14.8393	+	12.1741i	−0.595482	+	0.488531i
$622$		0			0
$623$	−24.8996	+	3.44096i	−0.997581	+	0.137859i
$624$		0			0
$625$	0.0343418	−	0.0594818i	0.00137367	−	0.00237927i
$626$		0			0
$627$	−19.4413	−	14.5854i	−0.776411	−	0.582485i
$628$		0			0
$629$	16.8627			0.672361
$630$		0			0
$631$		−	29.4363i		−	1.17184i	−0.810369	−	0.585920i	$-0.800733\pi$
$631$		−	29.4363i		−	1.17184i	0.810369	−	0.585920i	$-0.199267\pi$
$632$		0			0
$633$	22.3027	−	29.7280i	0.886455	−	1.18158i
$634$		0			0
$635$	2.77341	+	1.60123i	0.110059	+	0.0635428i
$636$		0			0
$637$	43.6637	+	11.1004i	1.73002	+	0.439815i
$638$		0			0
$639$	1.59808	+	5.48506i	0.0632189	+	0.216986i
$640$		0			0
$641$	34.2214	−	19.7578i	1.35167	−	0.780384i	0.363183	−	0.931718i	$-0.381690\pi$
$641$	34.2214	−	19.7578i	1.35167	−	0.780384i	0.988483	+	0.151334i	$0.0483568\pi$
$642$		0			0
$643$	−17.3857			−0.685626			−0.342813	−	0.939404i	$-0.611380\pi$
$643$	−17.3857			−0.685626			−0.342813	+	0.939404i	$0.611380\pi$
$644$		0			0
$645$	−0.815208	−	1.90922i	−0.0320988	−	0.0751754i
$646$		0			0
$647$	23.6414	+	40.9480i	0.929438	+	1.60983i	0.784264	+	0.620427i	$0.213041\pi$
$647$	23.6414	+	40.9480i	0.929438	+	1.60983i	0.145174	+	0.989406i	$0.453626\pi$
$648$		0			0
$649$	−16.8800	+	29.2370i	−0.662598	+	1.14765i
$650$		0			0
$651$	5.92802	+	9.86985i	0.232337	+	0.386830i
$652$		0			0
$653$	−14.1939	+	24.5845i	−0.555449	+	0.962067i	0.442419	+	0.896808i	$0.354120\pi$
$653$	−14.1939	+	24.5845i	−0.555449	+	0.962067i	−0.997868	+	0.0652581i	$0.979213\pi$
$654$		0			0
$655$	5.69432	−	3.28762i	0.222495	−	0.128458i
$656$		0			0
$657$	13.4245	−	14.0202i	0.523739	−	0.546981i
$658$		0			0
$659$			3.58703i			0.139731i	0.997556	+	0.0698654i	$0.0222570\pi$
$659$			3.58703i			0.139731i	−0.997556	+	0.0698654i	$0.977743\pi$
$660$		0			0
$661$	1.09189	−	0.630403i	0.0424696	−	0.0245198i	−0.478615	−	0.878025i	$-0.658861\pi$
$661$	1.09189	−	0.630403i	0.0424696	−	0.0245198i	0.521084	+	0.853505i	$0.325528\pi$
$662$		0			0
$663$	32.3150	+	3.89810i	1.25501	+	0.151390i
$664$		0			0
$665$	−10.7829	−	4.38548i	−0.418142	−	0.170062i
$666$		0			0
$667$	12.3355	−	21.3658i	0.477634	−	0.827286i
$668$		0			0
$669$	−16.8944	−	12.6747i	−0.653176	−	0.490030i
$670$		0			0
$671$	15.2581			0.589031
$672$		0			0
$673$	34.9662			1.34785			0.673925	−	0.738800i	$-0.264607\pi$
$673$	34.9662			1.34785			0.673925	+	0.738800i	$0.264607\pi$
$674$		0			0
$675$	2.60773	+	15.8115i	0.100372	+	0.608583i
$676$		0			0
$677$	−2.84885	+	4.93435i	−0.109490	+	0.189642i	−0.915564	−	0.402173i	$-0.868255\pi$
$677$	−2.84885	+	4.93435i	−0.109490	+	0.189642i	0.806074	+	0.591815i	$0.201588\pi$
$678$		0			0
$679$	−2.48994	+	1.93614i	−0.0955551	+	0.0743021i
$680$		0			0
$681$	3.25637	−	26.9952i	0.124784	−	1.03446i
$682$		0			0
$683$	19.9548	−	11.5209i	0.763551	−	0.440836i	−0.0670183	−	0.997752i	$-0.521349\pi$
$683$	19.9548	−	11.5209i	0.763551	−	0.440836i	0.830569	+	0.556915i	$0.188015\pi$
$684$		0			0
$685$			0.464729i			0.0177564i
$686$		0			0
$687$	19.2937	−	8.23812i	0.736100	−	0.314304i
$688$		0			0
$689$	−46.0293	+	26.5750i	−1.75358	+	1.01243i
$690$		0			0
$691$	18.0614	−	31.2833i	0.687090	−	1.19007i	−0.285686	−	0.958323i	$-0.592221\pi$
$691$	18.0614	−	31.2833i	0.687090	−	1.19007i	0.972775	−	0.231751i	$-0.0744454\pi$
$692$		0			0
$693$	34.8550	+	3.59479i	1.32403	+	0.136555i
$694$		0			0
$695$	6.47392	−	11.2132i	0.245570	−	0.425339i
$696$		0			0
$697$	0.726203	+	1.25782i	0.0275069	+	0.0476434i
$698$		0			0
$699$	−9.30483	+	3.97302i	−0.351941	+	0.150274i
$700$		0			0
$701$	29.8672			1.12807			0.564035	−	0.825751i	$-0.309248\pi$
$701$	29.8672			1.12807			0.564035	+	0.825751i	$0.309248\pi$
$702$		0			0
$703$	15.8975	−	9.17844i	0.599586	−	0.346171i
$704$		0			0
$705$	−7.56919	−	0.913056i	−0.285072	−	0.0343877i
$706$		0			0
$707$	−5.07641	−	2.06461i	−0.190918	−	0.0776478i
$708$		0			0
$709$	−42.5302	−	24.5548i	−1.59725	−	0.922175i	−0.992013	−	0.126132i	$-0.959744\pi$
$709$	−42.5302	−	24.5548i	−1.59725	−	0.922175i	−0.605240	−	0.796043i	$-0.706923\pi$
$710$		0			0
$711$	−1.35978	+	5.55426i	−0.0509959	+	0.208301i
$712$		0			0
$713$		−	9.28059i		−	0.347561i
$714$		0			0
$715$	39.3287			1.47081
$716$		0			0
$717$	−23.5090	+	31.3358i	−0.877958	+	1.17026i
$718$		0			0
$719$	8.31324	−	14.3990i	0.310032	−	0.536991i	−0.668337	−	0.743858i	$-0.732994\pi$
$719$	8.31324	−	14.3990i	0.310032	−	0.536991i	0.978369	+	0.206868i	$0.0663270\pi$
$720$		0			0
$721$	−14.5275	+	2.00760i	−0.541032	+	0.0747670i
$722$		0			0
$723$	−43.8355	−	5.28778i	−1.63026	−	0.196655i
$724$		0			0
$725$	−10.2989	−	17.8381i	−0.382490	−	0.662492i
$726$		0			0
$727$		−	6.37182i		−	0.236318i	−0.992995	−	0.118159i	$-0.962301\pi$
$727$		−	6.37182i		−	0.236318i	0.992995	−	0.118159i	$-0.0376992\pi$
$728$		0			0
$729$	20.2936	+	17.8092i	0.751616	+	0.659601i
$730$		0			0
$731$	2.18956	−	1.26414i	0.0809837	−	0.0467560i
$732$		0			0
$733$	33.2648	+	19.2054i	1.22866	+	0.709369i	0.966750	−	0.255723i	$-0.0823135\pi$
$733$	33.2648	+	19.2054i	1.22866	+	0.709369i	0.261912	+	0.965092i	$0.415647\pi$
$734$		0			0
$735$	16.5822	−	2.58422i	0.611645	−	0.0953204i
$736$		0			0
$737$	25.7533	+	14.8687i	0.948634	+	0.547694i
$738$		0			0
$739$	−0.546366	−	0.946333i	−0.0200984	−	0.0348114i	0.855801	−	0.517305i	$-0.173065\pi$
$739$	−0.546366	−	0.946333i	−0.0200984	−	0.0348114i	−0.875900	+	0.482493i	$0.839731\pi$
$740$		0			0
$741$	32.5871	−	13.9142i	1.19712	−	0.511151i
$742$		0			0
$743$	26.5914			0.975545			0.487772	−	0.872971i	$-0.337810\pi$
$743$	26.5914			0.975545			0.487772	+	0.872971i	$0.337810\pi$
$744$		0			0
$745$	−1.43355	−	2.48298i	−0.0525212	−	0.0909693i
$746$		0			0
$747$	−20.1635	+	5.87467i	−0.737746	+	0.214943i
$748$		0			0
$749$	−15.6617	+	2.16435i	−0.572267	+	0.0790835i
$750$		0			0
$751$	24.4781	+	14.1324i	0.893217	+	0.515699i	0.874993	−	0.484135i	$-0.160866\pi$
$751$	24.4781	+	14.1324i	0.893217	+	0.515699i	0.0182235	+	0.999834i	$0.494199\pi$
$752$		0			0
$753$	1.53800	+	1.15385i	0.0560479	+	0.0420487i
$754$		0			0
$755$		−	32.3918i		−	1.17886i
$756$		0			0
$757$		−	26.8780i		−	0.976898i	−0.872592	−	0.488449i	$-0.837563\pi$
$757$		−	26.8780i		−	0.976898i	0.872592	−	0.488449i	$-0.162437\pi$
$758$		0			0
$759$	−22.5934	−	16.9502i	−0.820090	−	0.615254i
$760$		0			0
$761$	46.8523	+	27.0502i	1.69840	+	0.980569i	0.947285	+	0.320393i	$0.103815\pi$
$761$	46.8523	+	27.0502i	1.69840	+	0.980569i	0.751111	+	0.660176i	$0.229518\pi$
$762$		0			0
$763$	−1.65273	+	4.06367i	−0.0598327	+	0.147115i
$764$		0			0
$765$	11.6408	−	3.39156i	0.420875	−	0.122622i
$766$		0			0
$767$	−24.6095	−	42.6248i	−0.888596	−	1.53909i
$768$		0			0
$769$	−9.44304			−0.340525			−0.170262	−	0.985399i	$-0.554462\pi$
$769$	−9.44304			−0.340525			−0.170262	+	0.985399i	$0.554462\pi$
$770$		0			0
$771$	22.2387	−	9.49560i	0.800907	−	0.341976i
$772$		0			0
$773$	18.7073	+	32.4020i	0.672856	+	1.16542i	0.977091	+	0.212823i	$0.0682659\pi$
$773$	18.7073	+	32.4020i	0.672856	+	1.16542i	−0.304235	+	0.952597i	$0.598401\pi$
$774$		0			0
$775$	−6.71022	−	3.87415i	−0.241038	−	0.139164i
$776$		0			0
$777$	−12.8348	+	23.1449i	−0.460445	+	0.830318i
$778$		0			0
$779$	1.36927	+	0.790550i	0.0490593	+	0.0283244i
$780$		0			0
$781$	−7.28073	+	4.20353i	−0.260525	+	0.150414i
$782$		0			0
$783$	−32.4779	−	12.2301i	−1.16066	−	0.437068i
$784$		0			0
$785$		−	30.8897i		−	1.10250i
$786$		0			0
$787$	−6.80641	−	11.7890i	−0.242622	−	0.420234i	0.718838	−	0.695178i	$-0.244674\pi$
$787$	−6.80641	−	11.7890i	−0.242622	−	0.420234i	−0.961460	+	0.274943i	$0.911341\pi$
$788$		0			0
$789$	24.3659	+	2.93921i	0.867451	+	0.104639i
$790$		0			0
$791$	26.7235	+	34.3673i	0.950177	+	1.22196i
$792$		0			0
$793$	−11.1224	+	19.2646i	−0.394968	+	0.684105i
$794$		0			0
$795$	−11.8815	+	15.8373i	−0.421395	+	0.561690i
$796$		0			0
$797$	−45.9884			−1.62899			−0.814496	−	0.580169i	$-0.802987\pi$
$797$	−45.9884			−1.62899			−0.814496	+	0.580169i	$0.802987\pi$
$798$		0			0
$799$		−	9.28517i		−	0.328486i
$800$		0			0
$801$	6.77760	−	27.6842i	0.239475	−	0.978174i
$802$		0			0
$803$	24.7370	+	14.2819i	0.872951	+	0.503999i
$804$		0			0
$805$	−12.5312	−	5.09652i	−0.441666	−	0.179629i
$806$		0			0
$807$	−31.3316	−	3.77947i	−1.10293	−	0.133044i
$808$		0			0
$809$	16.1190	−	9.30630i	0.566713	−	0.327192i	−0.189122	−	0.981954i	$-0.560564\pi$
$809$	16.1190	−	9.30630i	0.566713	−	0.327192i	0.755836	+	0.654762i	$0.227231\pi$
$810$		0			0
$811$	−33.9178			−1.19101			−0.595507	−	0.803350i	$-0.703049\pi$
$811$	−33.9178			−1.19101			−0.595507	+	0.803350i	$0.703049\pi$
$812$		0			0
$813$	−40.3328	+	17.2215i	−1.41453	+	0.603984i
$814$		0			0
$815$	−11.7660	−	20.3793i	−0.412145	−	0.713856i
$816$		0			0
$817$	1.37615	−	2.38357i	0.0481455	−	0.0833904i
$818$		0			0
$819$	−29.9464	+	41.3869i	−1.04641	+	1.44618i
$820$		0			0
$821$	14.0972	−	24.4171i	0.491996	−	0.852162i	−0.507962	−	0.861380i	$-0.669601\pi$
$821$	14.0972	−	24.4171i	0.491996	−	0.852162i	0.999958	+	0.00921774i	$0.00293414\pi$
$822$		0			0
$823$	−16.0158	+	9.24672i	−0.558275	+	0.322320i	−0.752453	−	0.658646i	$-0.771129\pi$
$823$	−16.0158	+	9.24672i	−0.558275	+	0.322320i	0.194178	+	0.980966i	$0.437796\pi$
$824$		0			0
$825$	−21.6872	+	9.26012i	−0.755052	+	0.322396i
$826$		0			0
$827$			14.5655i			0.506491i	0.967402	+	0.253245i	$0.0814980\pi$
$827$			14.5655i			0.506491i	−0.967402	+	0.253245i	$0.918502\pi$
$828$		0			0
$829$	−17.0346	+	9.83492i	−0.591635	+	0.341581i	−0.765744	−	0.643146i	$-0.777629\pi$
$829$	−17.0346	+	9.83492i	−0.591635	+	0.341581i	0.174108	+	0.984726i	$0.444296\pi$
$830$		0			0
$831$	3.89989	−	32.3299i	0.135286	−	1.12151i
$832$		0			0
$833$	5.54317	+	19.6729i	0.192060	+	0.681624i
$834$		0			0
$835$	−16.5509	+	28.6670i	−0.572767	+	0.992062i
$836$		0			0
$837$	−12.8808	+	2.12439i	−0.445226	+	0.0734295i
$838$		0			0
$839$	−26.2321			−0.905631			−0.452816	−	0.891604i	$-0.649580\pi$
$839$	−26.2321			−0.905631			−0.452816	+	0.891604i	$0.649580\pi$
$840$		0			0
$841$	15.6069			0.538171
$842$		0			0
$843$	−35.3175	−	26.4962i	−1.21640	−	0.912577i
$844$		0			0
$845$	−19.6715	+	34.0721i	−0.676721	+	1.17212i
$846$		0			0
$847$	3.07449	+	22.2478i	0.105641	+	0.764443i
$848$		0			0
$849$	−20.6986	−	2.49682i	−0.710373	−	0.0856908i
$850$		0			0
$851$	18.4751	−	10.6666i	0.633317	−	0.365646i
$852$		0			0
$853$		−	21.5548i		−	0.738022i	−0.929425	−	0.369011i	$-0.879696\pi$
$853$		−	21.5548i		−	0.738022i	0.929425	−	0.369011i	$-0.120304\pi$
$854$		0			0
$855$	9.12847	−	9.53357i	0.312187	−	0.326041i
$856$		0			0
$857$	15.7399	−	9.08742i	0.537664	−	0.310420i	−0.206468	−	0.978453i	$-0.566197\pi$
$857$	15.7399	−	9.08742i	0.537664	−	0.310420i	0.744132	+	0.668033i	$0.232864\pi$
$858$		0			0
$859$	−3.84011	+	6.65127i	−0.131023	+	0.226938i	−0.924071	−	0.382220i	$-0.875160\pi$
$859$	−3.84011	+	6.65127i	−0.131023	+	0.226938i	0.793048	+	0.609159i	$0.208493\pi$
$860$		0			0
$861$	−2.27915	+	0.0393778i	−0.0776734	+	0.00134199i
$862$		0			0
$863$	−16.7613	+	29.0314i	−0.570562	+	0.988242i	0.425947	+	0.904748i	$0.359941\pi$
$863$	−16.7613	+	29.0314i	−0.570562	+	0.988242i	−0.996508	+	0.0834933i	$0.973392\pi$
$864$		0			0
$865$	6.06886	+	10.5116i	0.206347	+	0.357404i
$866$		0			0
$867$	−5.76398	−	13.4992i	−0.195755	−	0.458458i
$868$		0			0
$869$	−8.41467			−0.285448
$870$		0			0
$871$	−37.5458	+	21.6771i	−1.27219	+	0.734500i
$872$		0			0
$873$	−1.00040	−	3.43366i	−0.0338584	−	0.116212i
$874$		0			0
$875$	−23.3713	+	18.1732i	−0.790095	+	0.614365i
$876$		0			0
$877$	22.4823	+	12.9802i	0.759174	+	0.438309i	0.828999	−	0.559250i	$-0.188911\pi$
$877$	22.4823	+	12.9802i	0.759174	+	0.438309i	−0.0698251	+	0.997559i	$0.522244\pi$
$878$		0			0
$879$	4.05861	−	5.40983i	0.136893	−	0.182469i
$880$		0			0
$881$			0.0231379i			0.000779536i	1.00000		0.000389768i	$0.000124067\pi$
$881$			0.0231379i			0.000779536i	−1.00000		0.000389768i	$0.999876\pi$
$882$		0			0
$883$	50.1245			1.68682			0.843412	−	0.537268i	$-0.180543\pi$
$883$	50.1245			1.68682			0.843412	+	0.537268i	$0.180543\pi$
$884$		0			0
$885$	−14.6659	−	11.0028i	−0.492989	−	0.369854i
$886$		0			0
$887$	−23.4706	+	40.6522i	−0.788064	+	1.36497i	0.139087	+	0.990280i	$0.455583\pi$
$887$	−23.4706	+	40.6522i	−0.788064	+	1.36497i	−0.927151	+	0.374687i	$0.877750\pi$
$888$		0			0
$889$	−3.75747	−	4.83224i	−0.126022	−	0.162068i
$890$		0			0
$891$	−18.3539	+	35.2381i	−0.614880	+	1.18052i
$892$		0			0
$893$	−5.05395	−	8.75370i	−0.169124	−	0.292931i
$894$		0			0
$895$		−	8.41781i		−	0.281376i
$896$		0			0
$897$	37.8706	−	16.1702i	1.26446	−	0.539907i
$898$		0			0
$899$	14.5318	−	8.38996i	0.484664	−	0.279821i
$900$		0			0
$901$	−20.8820	−	12.0562i	−0.695679	−	0.401651i
$902$		0			0
$903$	0.0685471	+	3.96745i	0.00228110	+	0.132028i
$904$		0			0
$905$	−13.8834	−	8.01559i	−0.461500	−	0.266447i
$906$		0			0
$907$	7.24598	+	12.5504i	0.240599	+	0.416729i	0.960885	−	0.276948i	$-0.0893229\pi$
$907$	7.24598	+	12.5504i	0.240599	+	0.416729i	−0.720286	+	0.693677i	$0.755990\pi$
$908$		0			0
$909$	4.29754	−	4.48826i	0.142541	−	0.148866i
$910$		0			0
$911$	−28.7559			−0.952726			−0.476363	−	0.879249i	$-0.658045\pi$
$911$	−28.7559			−0.952726			−0.476363	+	0.879249i	$0.658045\pi$
$912$		0			0
$913$	−15.4525	−	26.7646i	−0.511404	−	0.885779i
$914$		0			0
$915$	−0.992369	+	8.22670i	−0.0328067	+	0.271966i
$916$		0			0
$917$	−12.4497	+	1.72046i	−0.411124	+	0.0568146i
$918$		0			0
$919$	−14.3049	−	8.25895i	−0.471876	−	0.272438i	0.245149	−	0.969485i	$-0.421163\pi$
$919$	−14.3049	−	8.25895i	−0.471876	−	0.272438i	−0.717025	+	0.697048i	$0.754497\pi$
$920$		0			0
$921$	−11.4690	+	15.2874i	−0.377918	+	0.503737i
$922$		0			0
$923$		−	12.2567i		−	0.403434i
$924$		0			0
$925$		−	17.8109i		−	0.585619i
$926$		0			0
$927$	3.95434	−	16.1522i	0.129878	−	0.530507i
$928$		0			0
$929$	−2.55192	−	1.47335i	−0.0837258	−	0.0483391i	0.457553	−	0.889183i	$-0.348726\pi$
$929$	−2.55192	−	1.47335i	−0.0837258	−	0.0483391i	−0.541278	+	0.840843i	$0.682059\pi$
$930$		0			0
$931$	15.9339	+	15.5296i	0.522212	+	0.508963i
$932$		0			0
$933$	53.8413	+	6.49476i	1.76269	+	0.212629i
$934$		0			0
$935$	8.92106	+	15.4517i	0.291750	+	0.505326i
$936$		0			0
$937$	31.6130			1.03275			0.516375	−	0.856362i	$-0.327281\pi$
$937$	31.6130			1.03275			0.516375	+	0.856362i	$0.327281\pi$
$938$		0			0
$939$	8.88366	+	20.8055i	0.289907	+	0.678963i
$940$		0			0
$941$	16.1958	+	28.0519i	0.527966	+	0.914465i	0.999468	+	0.0325998i	$0.0103787\pi$
$941$	16.1958	+	28.0519i	0.527966	+	0.914465i	−0.471502	+	0.881865i	$0.656288\pi$
$942$		0			0
$943$	1.59128	+	0.918726i	0.0518192	+	0.0299178i
$944$		0			0
$945$	−4.20514	+	18.5590i	−0.136793	+	0.603724i
$946$		0			0
$947$	18.1295	+	10.4671i	0.589129	+	0.340134i	0.764753	−	0.644324i	$-0.222861\pi$
$947$	18.1295	+	10.4671i	0.589129	+	0.340134i	−0.175624	+	0.984457i	$0.556194\pi$
$948$		0			0
$949$	−36.0643	+	20.8217i	−1.17070	+	0.675902i
$950$		0			0
$951$	16.6386	+	38.9676i	0.539543	+	1.26361i
$952$		0			0
$953$			34.4190i			1.11494i	0.830197	+	0.557470i	$0.188228\pi$
$953$			34.4190i			1.11494i	−0.830197	+	0.557470i	$0.811772\pi$
$954$		0			0
$955$	1.04790	+	1.81502i	0.0339094	+	0.0587328i
$956$		0			0
$957$	6.11597	−	50.7011i	0.197701	−	1.63893i
$958$		0			0
$959$	0.334654	−	0.822837i	0.0108065	−	0.0265708i
$960$		0			0
$961$	−12.3439	+	21.3803i	−0.398191	+	0.689687i
$962$		0			0
$963$	4.26308	−	17.4133i	0.137376	−	0.561134i
$964$		0			0
$965$	−22.0863			−0.710982
$966$		0			0
$967$			52.5582i			1.69016i	0.534643	+	0.845078i	$0.320446\pi$
$967$			52.5582i			1.69016i	−0.534643	+	0.845078i	$0.679554\pi$
$968$		0			0
$969$	12.8586	+	9.64685i	0.413077	+	0.309901i
$970$		0			0
$971$	0.310281	+	0.179141i	0.00995738	+	0.00574890i	0.504970	−	0.863137i	$-0.331503\pi$
$971$	0.310281	+	0.179141i	0.00995738	+	0.00574890i	−0.495013	+	0.868886i	$0.664837\pi$
$972$		0			0
$973$	−19.5372	+	15.1918i	−0.626335	+	0.487028i
$974$		0			0
$975$	4.11729	−	34.1321i	0.131859	−	1.09310i
$976$		0			0
$977$	−34.5190	+	19.9296i	−1.10436	+	0.637603i	−0.937363	−	0.348354i	$-0.886741\pi$
$977$	−34.5190	+	19.9296i	−1.10436	+	0.637603i	−0.166998	+	0.985957i	$0.553407\pi$
$978$		0			0
$979$	41.9414			1.34045
$980$		0			0
$981$	−3.59286	−	3.44019i	−0.114711	−	0.109837i
$982$		0			0
$983$	14.8055	+	25.6439i	0.472223	+	0.817914i	0.999495	−	0.0317825i	$-0.0101184\pi$
$983$	14.8055	+	25.6439i	0.472223	+	0.817914i	−0.527272	+	0.849697i	$0.676785\pi$
$984$		0			0
$985$	0.666498	−	1.15441i	0.0212364	−	0.0367825i
$986$		0			0
$987$	12.7443	+	7.06726i	0.405656	+	0.224953i
$988$		0			0
$989$	1.59928	−	2.77003i	0.0508540	−	0.0880818i
$990$		0			0
$991$	19.2020	−	11.0863i	0.609970	−	0.352167i	−0.162983	−	0.986629i	$-0.552112\pi$
$991$	19.2020	−	11.0863i	0.609970	−	0.352167i	0.772954	+	0.634462i	$0.218778\pi$
$992$		0			0
$993$	9.87945	+	23.1377i	0.313515	+	0.734253i
$994$		0			0
$995$			2.75860i			0.0874535i
$996$		0			0
$997$	−19.4291	+	11.2174i	−0.615324	+	0.355258i	−0.775046	−	0.631904i	$-0.782274\pi$
$997$	−19.4291	+	11.2174i	−0.615324	+	0.355258i	0.159722	+	0.987162i	$0.448940\pi$
$998$		0			0
$999$	−19.0335	−	23.2004i	−0.602194	−	0.734030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bd.a.527.8		56
3.2	odd	2	inner	672.2.bd.a.527.27		56
4.3	odd	2		168.2.v.a.107.19	yes	56
7.4	even	3	inner	672.2.bd.a.431.28		56
8.3	odd	2	inner	672.2.bd.a.527.7		56
8.5	even	2		168.2.v.a.107.28	yes	56
12.11	even	2		168.2.v.a.107.10	yes	56
21.11	odd	6	inner	672.2.bd.a.431.7		56
24.5	odd	2		168.2.v.a.107.1	yes	56
24.11	even	2	inner	672.2.bd.a.527.28		56
28.11	odd	6		168.2.v.a.11.1	✓	56
56.11	odd	6	inner	672.2.bd.a.431.27		56
56.53	even	6		168.2.v.a.11.10	yes	56
84.11	even	6		168.2.v.a.11.28	yes	56
168.11	even	6	inner	672.2.bd.a.431.8		56
168.53	odd	6		168.2.v.a.11.19	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.v.a.11.1	✓	56	28.11	odd	6
168.2.v.a.11.10	yes	56	56.53	even	6
168.2.v.a.11.19	yes	56	168.53	odd	6
168.2.v.a.11.28	yes	56	84.11	even	6
168.2.v.a.107.1	yes	56	24.5	odd	2
168.2.v.a.107.10	yes	56	12.11	even	2
168.2.v.a.107.19	yes	56	4.3	odd	2
168.2.v.a.107.28	yes	56	8.5	even	2
672.2.bd.a.431.7		56	21.11	odd	6	inner
672.2.bd.a.431.8		56	168.11	even	6	inner
672.2.bd.a.431.27		56	56.11	odd	6	inner
672.2.bd.a.431.28		56	7.4	even	3	inner
672.2.bd.a.527.7		56	8.3	odd	2	inner
672.2.bd.a.527.8		56	1.1	even	1	trivial
672.2.bd.a.527.27		56	3.2	odd	2	inner
672.2.bd.a.527.28		56	24.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.03943 + 1.38549i) q^{3} +(0.692094 - 1.19874i) q^{5} +(-2.08863 + 1.62408i) q^{7} +(-0.839162 - 2.88024i) q^{9} +(3.82316 - 2.20731i) q^{11} +6.43609i q^{13} +(0.941460 + 2.20490i) q^{15} +(-2.52866 + 1.45992i) q^{17} +(-1.58928 + 2.75271i) q^{19} +(-0.0791630 - 4.58189i) q^{21} +(-1.84696 + 3.19902i) q^{23} +(1.54201 + 2.67084i) q^{25} +(4.86280 + 1.83117i) q^{27} -6.67884 q^{29} +(-2.17580 + 1.25620i) q^{31} +(-0.915722 + 7.59130i) q^{33} +(0.501330 + 3.62774i) q^{35} +(-5.00149 - 2.88761i) q^{37} +(-8.91713 - 6.68987i) q^{39} -0.497427i q^{41} -0.865898 q^{43} +(-4.03345 - 0.987462i) q^{45} +(-1.59001 + 2.75398i) q^{47} +(1.72472 - 6.78420i) q^{49} +(0.605663 - 5.02092i) q^{51} +(4.12906 + 7.15175i) q^{53} -6.11065i q^{55} +(-2.16191 - 5.06319i) q^{57} +(-6.62279 + 3.82367i) q^{59} +(2.99321 + 1.72813i) q^{61} +(6.43045 + 4.65289i) q^{63} +(7.71521 + 4.45438i) q^{65} +(3.36806 + 5.83364i) q^{67} +(-2.51243 - 5.88411i) q^{69} -1.90437 q^{71} +(3.23515 + 5.60345i) q^{73} +(-5.30324 - 0.639719i) q^{75} +(-4.40032 + 10.8194i) q^{77} +(-1.65073 - 0.953048i) q^{79} +(-7.59162 + 4.83398i) q^{81} -7.00064i q^{83} +4.04161i q^{85} +(6.94220 - 9.25347i) q^{87} +(8.22776 + 4.75030i) q^{89} +(-10.4527 - 13.4426i) q^{91} +(0.521147 - 4.32029i) q^{93} +(2.19986 + 3.81027i) q^{95} +1.19214 q^{97} +(-9.56583 - 9.15936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 56 * q + 2 * q^3 - 2 * q^9 + 4 * q^19 - 16 * q^25 + 8 * q^27 - 14 * q^33 + 16 * q^43 - 16 * q^49 + 34 * q^51 + 4 * q^57 + 36 * q^67 + 4 * q^73 - 10 * q^81 - 72 * q^91 - 32 * q^97 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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