LMFDB - Embedded newform 672.2.bd.a.527.27

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			527.27
Character	$\chi$	$=$	672.527
Dual form			672.2.bd.a.431.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.71959 - 0.207430i) q^{3} +(-0.692094 + 1.19874i) q^{5} +(-2.08863 + 1.62408i) q^{7} +(2.91395 - 0.713387i) q^{9} +(-3.82316 + 2.20731i) q^{11} +6.43609i q^{13} +(-0.941460 + 2.20490i) q^{15} +(2.52866 - 1.45992i) q^{17} +(-1.58928 + 2.75271i) q^{19} +(-3.25469 + 3.22599i) q^{21} +(1.84696 - 3.19902i) q^{23} +(1.54201 + 2.67084i) q^{25} +(4.86280 - 1.83117i) q^{27} +6.67884 q^{29} +(-2.17580 + 1.25620i) q^{31} +(-6.11640 + 4.58869i) q^{33} +(-0.501330 - 3.62774i) q^{35} +(-5.00149 - 2.88761i) q^{37} +(1.33504 + 11.0674i) q^{39} +0.497427i q^{41} -0.865898 q^{43} +(-1.16156 + 3.98680i) q^{45} +(1.59001 - 2.75398i) q^{47} +(1.72472 - 6.78420i) q^{49} +(4.04541 - 3.03498i) q^{51} +(-4.12906 - 7.15175i) q^{53} -6.11065i q^{55} +(-2.16191 + 5.06319i) q^{57} +(6.62279 - 3.82367i) q^{59} +(2.99321 + 1.72813i) q^{61} +(-4.92754 + 6.22248i) q^{63} +(-7.71521 - 4.45438i) q^{65} +(3.36806 + 5.83364i) q^{67} +(2.51243 - 5.88411i) q^{69} +1.90437 q^{71} +(3.23515 + 5.60345i) q^{73} +(3.20563 + 4.27288i) q^{75} +(4.40032 - 10.8194i) q^{77} +(-1.65073 - 0.953048i) q^{79} +(7.98216 - 4.15754i) q^{81} +7.00064i q^{83} +4.04161i q^{85} +(11.4848 - 1.38539i) q^{87} +(-8.22776 - 4.75030i) q^{89} +(-10.4527 - 13.4426i) q^{91} +(-3.48090 + 2.61147i) q^{93} +(-2.19986 - 3.81027i) q^{95} +1.19214 q^{97} +(-9.56583 + 9.15936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.71959	−	0.207430i	0.992803	−	0.119760i
$3$	1.71959	−	0.207430i	0.992803	−	0.119760i
$4$		0			0
$5$	−0.692094	+	1.19874i	−0.309514	+	0.536094i	−0.978256	−	0.207401i	$-0.933500\pi$
$5$	−0.692094	+	1.19874i	−0.309514	+	0.536094i	0.668742	+	0.743494i	$0.266833\pi$
$6$		0			0
$7$	−2.08863	+	1.62408i	−0.789426	+	0.613845i
$7$	−2.08863	+	1.62408i	−0.789426	+	0.613845i
$8$		0			0
$9$	2.91395	−	0.713387i	0.971315	−	0.237796i
$10$		0			0
$11$	−3.82316	+	2.20731i	−1.15273	+	0.665528i	−0.949550	−	0.313614i	$-0.898460\pi$
$11$	−3.82316	+	2.20731i	−1.15273	+	0.665528i	−0.203177	+	0.979142i	$0.565127\pi$
$12$		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	−0.160962	−	0.986961i	$-0.551460\pi$
$17$	2.52866	−	1.45992i	0.613289	−	0.354083i	0.774252	+	0.632878i	$0.218126\pi$
$18$		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
$21$	−3.25469	+	3.22599i	−0.710231	+	0.703969i
$22$		0			0
$23$	1.84696	−	3.19902i	0.385117	−	0.667043i	−0.606668	−	0.794955i	$-0.707494\pi$
$23$	1.84696	−	3.19902i	0.385117	−	0.667043i	0.991785	+	0.127912i	$0.0408277\pi$
$24$		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	$-0.287086\pi$
$29$	6.67884			1.24023			0.620115	+	0.784511i	$0.287086\pi$
$30$		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
$33$	−6.11640	+	4.58869i	−1.06473	+	0.798788i
$34$		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
$39$	1.33504	+	11.0674i	0.213777	+	1.77220i
$40$		0			0
$41$			0.497427i			0.0776850i	0.999245	+	0.0388425i	$0.0123671\pi$
$41$			0.497427i			0.0776850i	−0.999245	+	0.0388425i	$0.987633\pi$
$42$		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
$45$	−1.16156	+	3.98680i	−0.173155	+	0.594317i
$46$		0			0
$47$	1.59001	−	2.75398i	0.231927	−	0.401710i	−0.726448	−	0.687221i	$-0.758830\pi$
$47$	1.59001	−	2.75398i	0.231927	−	0.401710i	0.958375	+	0.285512i	$0.0921635\pi$
$48$		0			0
$49$	1.72472	−	6.78420i	0.246388	−	0.969171i
$50$		0			0
$51$	4.04541	−	3.03498i	0.566471	−	0.424982i
$52$		0			0
$53$	−4.12906	−	7.15175i	−0.567171	−	0.982368i	−0.996844	−	0.0793841i	$-0.974705\pi$
$53$	−4.12906	−	7.15175i	−0.567171	−	0.982368i	0.429673	−	0.902984i	$-0.358629\pi$
$54$		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	−0.00253919	−	0.999997i	$-0.500808\pi$
$59$	6.62279	−	3.82367i	0.862214	−	0.497799i	0.864753	+	0.502197i	$0.167475\pi$
$60$		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
$63$	−4.92754	+	6.22248i	−0.620812	+	0.783959i
$64$		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	$-0.463953\pi$
$71$	1.90437			0.226007			0.113004	+	0.993595i	$0.463953\pi$
$72$		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
$75$	3.20563	+	4.27288i	0.370155	+	0.493390i
$76$		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
$81$	7.98216	−	4.15754i	0.886906	−	0.461949i
$82$		0			0
$83$			7.00064i			0.768420i	0.923246	+	0.384210i	$0.125526\pi$
$83$			7.00064i			0.768420i	−0.923246	+	0.384210i	$0.874474\pi$
$84$		0			0
$85$			4.04161i			0.438374i
$86$		0			0
$87$	11.4848	−	1.38539i	1.23130	−	0.148530i
$88$		0			0
$89$	−8.22776	−	4.75030i	−0.872141	−	0.503531i	−0.00408165	−	0.999992i	$-0.501299\pi$
$89$	−8.22776	−	4.75030i	−0.872141	−	0.503531i	−0.868059	+	0.496461i	$0.834633\pi$
$90$		0			0
$91$	−10.4527	−	13.4426i	−1.09574	−	1.40916i
$92$		0			0
$93$	−3.48090	+	2.61147i	−0.360953	+	0.270797i
$94$		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	0.809889	−	0.586584i	$-0.199527\pi$
$101$	−1.03566	−	1.79382i	−0.103052	−	0.178491i	−0.912941	+	0.408092i	$0.866194\pi$
$102$		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
$105$	−1.61458	−	6.13422i	−0.157567	−	0.598638i
$106$		0			0
$107$	−5.17522	−	2.98792i	−0.500308	−	0.288853i	0.228533	−	0.973536i	$-0.426607\pi$
$107$	−5.17522	−	2.98792i	−0.500308	−	0.288853i	−0.728841	+	0.684683i	$0.759940\pi$
$108$		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	$0.281724\pi$
$113$			16.4545i			1.54791i	−0.633241	+	0.773955i	$0.718276\pi$
$114$		0			0
$115$	2.55654	+	4.42805i	0.238398	+	0.412918i
$116$		0			0
$117$	4.59142	+	18.7544i	0.424477	+	1.73385i
$118$		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
$123$	0.103181	+	0.855367i	0.00930353	+	0.0771259i
$124$		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
$129$	−1.48898	+	0.179613i	−0.131098	+	0.0158141i
$130$		0			0
$131$	−4.11383	−	2.37512i	−0.359427	−	0.207515i	0.309402	−	0.950931i	$-0.399871\pi$
$131$	−4.11383	−	2.37512i	−0.359427	−	0.207515i	−0.668830	+	0.743416i	$0.733204\pi$
$132$		0			0
$133$	−1.15122	−	8.33050i	−0.0998234	−	0.722346i
$134$		0			0
$135$	−1.17042	+	7.09658i	−0.100733	+	0.610777i
$136$		0			0
$137$	0.290760	−	0.167870i	0.0248413	−	0.0143421i	−0.487528	−	0.873107i	$-0.662101\pi$
$137$	0.290760	−	0.167870i	0.0248413	−	0.0143421i	0.512369	+	0.858765i	$0.328768\pi$
$138$		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
$147$	1.55855	−	12.0238i	0.128547	−	0.991703i
$148$		0			0
$149$	−1.03566	+	1.79382i	−0.0848446	+	0.146955i	−0.905325	−	0.424720i	$-0.860373\pi$
$149$	−1.03566	+	1.79382i	−0.0848446	+	0.146955i	0.820480	+	0.571675i	$0.193706\pi$
$150$		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
$159$	−8.58377	−	11.4416i	−0.680737	−	0.907374i
$160$		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
$165$	−1.26753	−	10.5078i	−0.0986772	−	0.818030i
$166$		0			0
$167$	23.9142			1.85054			0.925269	−	0.379311i	$-0.123839\pi$
$167$	23.9142			1.85054			0.925269	+	0.379311i	$0.123839\pi$
$168$		0			0
$169$	−28.4232			−2.18640
$170$		0			0
$171$	−2.66732	+	9.15502i	−0.203975	+	0.700102i
$172$		0			0
$173$	4.38442	−	7.59404i	0.333341	−	0.577364i	−0.649824	−	0.760085i	$-0.725157\pi$
$173$	4.38442	−	7.59404i	0.333341	−	0.577364i	0.983165	+	0.182721i	$0.0584906\pi$
$174$		0			0
$175$	−7.55835	−	3.07404i	−0.571358	−	0.232375i
$176$		0			0
$177$	10.5953	−	7.94889i	0.796392	−	0.597475i
$178$		0			0
$179$	−5.26665	+	3.04070i	−0.393648	+	0.227273i	−0.683740	−	0.729726i	$-0.739648\pi$
$179$	−5.26665	+	3.04070i	−0.393648	+	0.227273i	0.290092	+	0.956999i	$0.406314\pi$
$180$		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
$189$	−7.18260	+	11.7222i	−0.522457	+	0.852665i
$190$		0			0
$191$	0.757053	−	1.31125i	0.0547784	−	0.0948790i	−0.837336	−	0.546689i	$-0.815888\pi$
$191$	0.757053	−	1.31125i	0.0547784	−	0.0948790i	0.892114	+	0.451810i	$0.149221\pi$
$192$		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	$-0.510922\pi$
$197$	−0.963016			−0.0686121			−0.0343060	+	0.999411i	$0.510922\pi$
$198$		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
$201$	7.00173	+	9.33281i	0.493864	+	0.658286i
$202$		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
$207$	3.09979	−	10.6394i	0.215450	−	0.739488i
$208$		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
$213$	3.27473	−	0.395024i	0.224381	−	0.0270666i
$214$		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
$219$	6.72544	+	8.96454i	0.454463	+	0.605768i
$220$		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	0.0243951	−	0.999702i	$-0.492234\pi$
$227$	13.5954	−	7.84932i	0.902360	−	0.520978i	0.877965	+	0.478724i	$0.158901\pi$
$228$		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
$231$	5.32246	−	19.5176i	0.350192	−	1.28416i
$232$		0			0
$233$	−5.05877	−	2.92068i	−0.331411	−	0.191340i	0.325056	−	0.945695i	$-0.394617\pi$
$233$	−5.05877	−	2.92068i	−0.331411	−	0.191340i	−0.656468	+	0.754354i	$0.727950\pi$
$234$		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	$-0.761175\pi$
$239$	−22.6171			−1.46298			−0.731490	+	0.681852i	$0.761175\pi$
$240$		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
$243$	12.8636	−	8.80499i	0.825200	−	0.564840i
$244$		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
$249$	1.45214	+	12.0382i	0.0920258	+	0.762889i
$250$		0			0
$251$			1.11008i			0.0700675i	0.999386	+	0.0350338i	$0.0111539\pi$
$251$			1.11008i			0.0700675i	−0.999386	+	0.0350338i	$0.988846\pi$
$252$		0			0
$253$			16.3072i			1.02522i
$254$		0			0
$255$	0.838351	+	6.94989i	0.0524996	+	0.435219i
$256$		0			0
$257$	12.0906	+	6.98049i	0.754188	+	0.435431i	0.827205	−	0.561900i	$-0.189929\pi$
$257$	12.0906	+	6.98049i	0.754188	+	0.435431i	−0.0730169	+	0.997331i	$0.523263\pi$
$258$		0			0
$259$	15.1360	−	2.09169i	0.940503	−	0.129971i
$260$		0			0
$261$	19.4618	−	4.76460i	1.20465	−	0.294921i
$262$		0			0
$263$	7.08483	+	12.2713i	0.436870	+	0.756680i	0.997446	−	0.0714223i	$-0.0227538\pi$
$263$	7.08483	+	12.2713i	0.436870	+	0.756680i	−0.560577	+	0.828103i	$0.689420\pi$
$264$		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	$-0.979209\pi$
$269$	−9.11023	−	15.7794i	−0.555461	−	0.962086i	0.442407	−	0.896814i	$-0.354125\pi$
$270$		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
$273$	−20.7628	−	20.9474i	−1.25662	−	1.26780i
$274$		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	$-0.725036\pi$
$281$		−	25.4910i		−	1.52067i	0.649533	−	0.760333i	$-0.274964\pi$
$282$		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
$285$	−4.57321	−	6.09577i	−0.270894	−	0.361082i
$286$		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
$291$	2.04999	−	0.247286i	0.120173	−	0.0144962i
$292$		0			0
$293$	3.90464			0.228111			0.114056	−	0.993474i	$-0.463616\pi$
$293$	3.90464			0.228111			0.114056	+	0.993474i	$0.463616\pi$
$294$		0			0
$295$			10.5854i			0.616303i
$296$		0			0
$297$	−14.5493	+	17.7345i	−0.844238	+	1.02906i
$298$		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
$303$	−2.15300	−	2.86979i	−0.123686	−	0.164865i
$304$		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	$0.181053\pi$
$311$	15.6553	+	27.1158i	0.887732	+	1.53760i	0.0451815	+	0.998979i	$0.485613\pi$
$312$		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
$315$	−4.04883	−	10.2134i	−0.228126	−	0.575460i
$316$		0			0
$317$	−12.2315	+	21.1856i	−0.686990	+	1.18990i	0.285817	+	0.958284i	$0.407735\pi$
$317$	−12.2315	+	21.1856i	−0.686990	+	1.18990i	−0.972807	+	0.231618i	$0.925598\pi$
$318$		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
$327$	2.29727	−	1.72348i	0.127039	−	0.0953085i
$328$		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
$333$	−16.6341	−	4.84634i	−0.911540	−	0.265578i
$334$		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
$339$	3.41316	+	28.2949i	0.185377	+	1.53677i
$340$		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
$345$	5.31469	+	7.08411i	0.286133	+	0.381396i
$346$		0			0
$347$	20.7411	−	11.9749i	1.11344	−	0.642846i	0.173723	−	0.984795i	$-0.444420\pi$
$347$	20.7411	−	11.9749i	1.11344	−	0.642846i	0.939719	+	0.341949i	$0.111087\pi$
$348$		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	0.235907	−	0.971776i	$-0.424194\pi$
$353$	22.4603	−	12.9675i	1.19544	−	0.690189i	0.959536	+	0.281587i	$0.0908607\pi$
$354$		0			0
$355$	−1.31800	+	2.28285i	−0.0699524	+	0.121161i
$356$		0			0
$357$	−3.52030	+	12.9090i	−0.186314	+	0.683217i
$358$		0			0
$359$	−14.1756	+	24.5529i	−0.748162	+	1.29585i	0.200541	+	0.979685i	$0.435730\pi$
$359$	−14.1756	+	24.5529i	−0.748162	+	1.29585i	−0.948703	+	0.316169i	$0.897603\pi$
$360$		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
$369$	0.354858	+	1.44947i	0.0184731	+	0.0754566i
$370$		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
$375$	−19.2418	+	2.32110i	−0.993644	+	0.119861i
$376$		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
$381$	0.479910	+	3.97843i	0.0245865	+	0.203821i
$382$		0			0
$383$	−5.47353	+	9.48043i	−0.279684	+	0.484427i	−0.971306	−	0.237832i	$-0.923563\pi$
$383$	−5.47353	+	9.48043i	−0.279684	+	0.484427i	0.691622	+	0.722260i	$0.256896\pi$
$384$		0			0
$385$	9.92420	+	12.7629i	0.505784	+	0.650456i
$386$		0			0
$387$	−2.52318	+	0.617720i	−0.128260	+	0.0314005i
$388$		0			0
$389$	9.51835	+	16.4863i	0.482600	+	0.835887i	0.999800	−	0.0199769i	$-0.00635927\pi$
$389$	9.51835	+	16.4863i	0.482600	+	0.835887i	−0.517201	+	0.855864i	$0.673026\pi$
$390$		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
$399$	−3.70762	−	14.0862i	−0.185613	−	0.705193i
$400$		0			0
$401$	−24.3528	−	14.0601i	−1.21612	−	0.702128i	−0.252035	−	0.967718i	$-0.581100\pi$
$401$	−24.3528	−	14.0601i	−1.21612	−	0.702128i	−0.964086	+	0.265591i	$0.914433\pi$
$402$		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
$411$	0.465165	−	0.348980i	0.0229449	−	0.0172139i
$412$		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
$417$	16.0852	−	1.94032i	0.787694	−	0.0950179i
$418$		0			0
$419$			4.42222i			0.216040i	0.994149	+	0.108020i	$0.0344510\pi$
$419$			4.42222i			0.216040i	−0.994149	+	0.108020i	$0.965549\pi$
$420$		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
$423$	2.66856	−	9.15925i	0.129750	−	0.445338i
$424$		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
$429$	−29.5332	−	39.3656i	−1.42588	−	1.90059i
$430$		0			0
$431$	−8.76759	−	15.1859i	−0.422320	−	0.731479i	0.573846	−	0.818963i	$-0.305451\pi$
$431$	−8.76759	−	15.1859i	−0.422320	−	0.731479i	−0.996166	+	0.0874837i	$0.972117\pi$
$432$		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
$441$	0.185972	−	20.9992i	0.00885582	−	0.999961i
$442$		0			0
$443$	−24.9578	−	14.4094i	−1.18578	−	0.684611i	−0.228436	−	0.973559i	$-0.573361\pi$
$443$	−24.9578	−	14.4094i	−1.18578	−	0.684611i	−0.957345	+	0.288948i	$0.906695\pi$
$444$		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	$-0.990443\pi$
$449$		−	1.27217i		−	0.0600373i	0.999549	−	0.0300186i	$-0.00955666\pi$
$450$		0			0
$451$	−1.09797	−	1.90174i	−0.0517015	−	0.0895496i
$452$		0			0
$453$	32.4223	−	24.3241i	1.52333	−	1.14285i
$454$		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
$459$	9.62299	−	11.7297i	0.449163	−	0.547495i
$460$		0			0
$461$	27.1371			1.26390			0.631950	−	0.775009i	$-0.282255\pi$
$461$	27.1371			1.26390			0.631950	+	0.775009i	$0.282255\pi$
$462$		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
$465$	−0.721366	−	5.98009i	−0.0334525	−	0.277320i
$466$		0			0
$467$	−22.2686	−	12.8568i	−1.03047	−	0.594940i	−0.113349	−	0.993555i	$-0.536158\pi$
$467$	−22.2686	−	12.8568i	−1.03047	−	0.594940i	−0.917118	+	0.398615i	$0.869491\pi$
$468$		0			0
$469$	−16.5089	−	6.71430i	−0.762311	−	0.310038i
$470$		0			0
$471$	30.9188	−	23.1961i	1.42466	−	1.06882i
$472$		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	0.950101	−	0.311942i	$-0.100979\pi$
$479$	4.48448	+	7.76735i	0.204901	+	0.354899i	−0.745200	+	0.666841i	$0.767646\pi$
$480$		0			0
$481$	18.5849	−	32.1900i	0.847399	−	1.46774i
$482$		0			0
$483$	4.30875	+	16.3701i	0.196055	+	0.744865i
$484$		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	$-0.900796\pi$
$491$		−	13.5893i		−	0.613275i	0.951826	−	0.306637i	$-0.0992039\pi$
$492$		0			0
$493$	16.8885	−	9.75058i	0.760620	−	0.439144i
$494$		0			0
$495$	−4.35926	−	17.8061i	−0.195934	−	0.800325i
$496$		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
$501$	41.1225	−	4.96053i	1.83722	−	0.221620i
$502$		0			0
$503$	−24.5224			−1.09340			−0.546699	−	0.837329i	$-0.684116\pi$
$503$	−24.5224			−1.09340			−0.546699	+	0.837329i	$0.684116\pi$
$504$		0			0
$505$	2.86710			0.127584
$506$		0			0
$507$	−48.8761	+	5.89582i	−2.17066	+	0.261843i
$508$		0			0
$509$	−21.4381	+	37.1319i	−0.950226	+	1.64584i	−0.205294	+	0.978700i	$0.565815\pi$
$509$	−21.4381	+	37.1319i	−0.950226	+	1.64584i	−0.744932	+	0.667140i	$0.767518\pi$
$510$		0			0
$511$	−15.8575	−	6.44936i	−0.701494	−	0.285303i
$512$		0			0
$513$	−2.68766	+	16.2961i	−0.118663	+	0.719492i
$514$		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	−0.534257	−	0.845322i	$-0.679409\pi$
$521$	−1.58214	+	0.913450i	−0.0693149	+	0.0400190i	0.464942	+	0.885341i	$0.346075\pi$
$522$		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
$525$	−13.6349	−	3.71824i	−0.595075	−	0.162277i
$526$		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
$537$	−8.42572	+	6.32121i	−0.363597	+	0.272780i
$538$		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
$543$	−2.40238	−	19.9156i	−0.103096	−	0.854662i
$544$		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
$549$	9.95488	+	2.90036i	0.424864	+	0.123784i
$550$		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
$555$	11.0756	−	8.30921i	0.470133	−	0.352706i
$556$		0			0
$557$	−15.9928	−	27.7003i	−0.677635	−	1.17370i	−0.975691	−	0.219151i	$-0.929671\pi$
$557$	−15.9928	−	27.7003i	−0.677635	−	1.17370i	0.298056	−	0.954549i	$-0.403662\pi$
$558$		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	0.333944	−	0.942593i	$-0.391620\pi$
$563$	31.2546	−	18.0449i	1.31723	−	0.760501i	0.983281	+	0.182092i	$0.0582870\pi$
$564$		0			0
$565$	−19.7247	−	11.3881i	−0.829825	−	0.479100i
$566$		0			0
$567$	−9.91956	+	21.6472i	−0.416582	+	0.909098i
$568$		0			0
$569$	23.5336	+	13.5871i	0.986579	+	0.569601i	0.904250	−	0.427004i	$-0.140431\pi$
$569$	23.5336	+	13.5871i	0.986579	+	0.569601i	0.0823288	+	0.996605i	$0.473764\pi$
$570$		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
$579$	−16.5853	−	22.1070i	−0.689262	−	0.918737i
$580$		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
$585$	−25.6594	−	7.47588i	−1.06089	−	0.309090i
$586$		0			0
$587$			0.964880i			0.0398249i	0.999802	+	0.0199124i	$0.00633874\pi$
$587$			0.964880i			0.0398249i	−0.999802	+	0.0199124i	$0.993661\pi$
$588$		0			0
$589$		−	7.98581i		−	0.329050i
$590$		0			0
$591$	−1.65599	+	0.199758i	−0.0681182	+	0.00821696i
$592$		0			0
$593$	14.9519	+	8.63251i	0.614003	+	0.354495i	0.774530	−	0.632537i	$-0.217986\pi$
$593$	14.9519	+	8.63251i	0.614003	+	0.354495i	−0.160528	+	0.987031i	$0.551320\pi$
$594$		0			0
$595$	−6.56390	−	8.44141i	−0.269094	−	0.346064i
$596$		0			0
$597$	−2.76119	+	2.07152i	−0.113008	+	0.0847818i
$598$		0			0
$599$	−6.22127	−	10.7756i	−0.254194	−	0.440277i	0.710482	−	0.703715i	$-0.248477\pi$
$599$	−6.22127	−	10.7756i	−0.254194	−	0.440277i	−0.964676	+	0.263438i	$0.915144\pi$
$600$		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
$609$	−21.7375	+	21.5459i	−0.880850	+	0.873083i
$610$		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	$-0.775051\pi$
$617$		−	32.2579i		−	1.29865i	0.760509	−	0.649327i	$-0.224949\pi$
$618$		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
$621$	3.12343	−	18.9383i	0.125339	−	0.759968i
$622$		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
$627$	−2.91068	−	24.1294i	−0.116241	−	0.963635i
$628$		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
$633$	−36.8966	+	4.45076i	−1.46651	+	0.176902i
$634$		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
$639$	5.54924	−	1.35855i	0.219524	−	0.0537436i
$640$		0			0
$641$	−34.2214	+	19.7578i	−1.35167	+	0.780384i	−0.988483	−	0.151334i	$-0.951643\pi$
$641$	−34.2214	+	19.7578i	−1.35167	+	0.780384i	−0.363183	+	0.931718i	$0.618310\pi$
$642$		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	$-0.786959\pi$
$647$	−23.6414	−	40.9480i	−0.929438	−	1.60983i	−0.145174	−	0.989406i	$-0.546374\pi$
$648$		0			0
$649$	−16.8800	+	29.2370i	−0.662598	+	1.14765i
$650$		0			0
$651$	3.02907	−	11.1077i	0.118718	−	0.435343i
$652$		0			0
$653$	14.1939	−	24.5845i	0.555449	−	0.962067i	−0.442419	−	0.896808i	$-0.645880\pi$
$653$	14.1939	−	24.5845i	0.555449	−	0.962067i	0.997868	−	0.0652581i	$-0.0207871\pi$
$654$		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	$-0.977743\pi$
$659$		−	3.58703i		−	0.139731i	0.997556	−	0.0698654i	$-0.0222570\pi$
$660$		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
$663$	19.5334	+	26.0366i	0.758613	+	1.01118i
$664$		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
$669$	2.52936	+	20.9683i	0.0977909	+	0.810682i
$670$		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
$675$	12.3893	+	10.1641i	0.476863	+	0.391216i
$676$		0			0
$677$	2.84885	−	4.93435i	0.109490	−	0.189642i	−0.806074	−	0.591815i	$-0.798412\pi$
$677$	2.84885	−	4.93435i	0.109490	−	0.189642i	0.915564	+	0.402173i	$0.131745\pi$
$678$		0			0
$679$	−2.48994	+	1.93614i	−0.0955551	+	0.0743021i
$680$		0			0
$681$	21.7503	−	16.3177i	0.833474	−	0.625295i
$682$		0			0
$683$	−19.9548	+	11.5209i	−0.763551	+	0.440836i	−0.830569	−	0.556915i	$-0.811985\pi$
$683$	−19.9548	+	11.5209i	−0.763551	+	0.440836i	0.0670183	+	0.997752i	$0.478651\pi$
$684$		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
$693$	5.10389	−	34.6662i	0.193881	−	1.31686i
$694$		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	$-0.690752\pi$
$701$	−29.8672			−1.12807			−0.564035	+	0.825751i	$0.690752\pi$
$702$		0			0
$703$	15.8975	−	9.17844i	0.599586	−	0.346171i
$704$		0			0
$705$	4.57533	+	6.09858i	0.172317	+	0.229686i
$706$		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
$711$	−5.49002	−	1.59952i	−0.205892	−	0.0599868i
$712$		0			0
$713$			9.28059i			0.347561i
$714$		0			0
$715$	39.3287			1.47081
$716$		0			0
$717$	−38.8921	+	4.69147i	−1.45245	+	0.175206i
$718$		0			0
$719$	−8.31324	+	14.3990i	−0.310032	+	0.536991i	−0.978369	−	0.206868i	$-0.933673\pi$
$719$	−8.31324	+	14.3990i	−0.310032	+	0.536991i	0.668337	+	0.743858i	$0.267006\pi$
$720$		0			0
$721$	−14.5275	+	2.00760i	−0.541032	+	0.0747670i
$722$		0			0
$723$	26.4971	+	35.3187i	0.985437	+	1.31352i
$724$		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
$735$	13.3347	+	10.1899i	0.491859	+	0.375859i
$736$		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	$-0.662190\pi$
$743$	−26.5914			−0.975545			−0.487772	+	0.872971i	$0.662190\pi$
$744$		0			0
$745$	−1.43355	−	2.48298i	−0.0525212	−	0.0909693i
$746$		0			0
$747$	4.99416	+	20.3995i	0.182727	+	0.746378i
$748$		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
$753$	0.230263	+	1.90887i	0.00839127	+	0.0695632i
$754$		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
$759$	3.38260	+	28.0416i	0.122781	+	1.01785i
$760$		0			0
$761$	−46.8523	−	27.0502i	−1.69840	−	0.980569i	−0.947285	−	0.320393i	$-0.896185\pi$
$761$	−46.8523	−	27.0502i	−1.69840	−	0.980569i	−0.751111	−	0.660176i	$-0.770482\pi$
$762$		0			0
$763$	−1.65273	+	4.06367i	−0.0598327	+	0.147115i
$764$		0			0
$765$	2.88323	+	11.7770i	0.104243	+	0.425799i
$766$		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	$-0.931734\pi$
$773$	−18.7073	−	32.4020i	−0.672856	−	1.16542i	0.304235	−	0.952597i	$-0.401599\pi$
$774$		0			0
$775$	−6.71022	−	3.87415i	−0.241038	−	0.139164i
$776$		0			0
$777$	25.5937	−	6.73649i	0.918168	−	0.241670i
$778$		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
$789$	14.7284	+	19.6319i	0.524345	+	0.698915i
$790$		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
$795$	19.6562	−	2.37109i	0.697135	−	0.0840939i
$796$		0			0
$797$	45.9884			1.62899			0.814496	−	0.580169i	$-0.197013\pi$
$797$	45.9884			1.62899			0.814496	+	0.580169i	$0.197013\pi$
$798$		0			0
$799$		−	9.28517i		−	0.328486i
$800$		0			0
$801$	−27.3640	−	7.97254i	−0.966861	−	0.281696i
$802$		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
$807$	−18.9389	−	25.2443i	−0.666682	−	0.888640i
$808$		0			0
$809$	−16.1190	+	9.30630i	−0.566713	+	0.327192i	−0.755836	−	0.654762i	$-0.772769\pi$
$809$	−16.1190	+	9.30630i	−0.566713	+	0.327192i	0.189122	+	0.981954i	$0.439436\pi$
$810$		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
$819$	−40.0484	−	31.7141i	−1.39941	−	1.10818i
$820$		0			0
$821$	−14.0972	+	24.4171i	−0.491996	+	0.852162i	−0.999958	−	0.00921774i	$-0.997066\pi$
$821$	−14.0972	+	24.4171i	−0.491996	+	0.852162i	0.507962	+	0.861380i	$0.330399\pi$
$822$		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	$-0.918502\pi$
$827$		−	14.5655i		−	0.506491i	0.967402	−	0.253245i	$-0.0814980\pi$
$828$		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
$831$	−26.0486	+	19.5424i	−0.903616	+	0.677918i
$832$		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
$837$	−8.28017	+	10.0929i	−0.286205	+	0.348862i
$838$		0			0
$839$	26.2321			0.905631			0.452816	−	0.891604i	$-0.350420\pi$
$839$	26.2321			0.905631			0.452816	+	0.891604i	$0.350420\pi$
$840$		0			0
$841$	15.6069			0.538171
$842$		0			0
$843$	−5.28760	−	43.8340i	−0.182115	−	1.50972i
$844$		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
$849$	12.5116	+	16.6771i	0.429397	+	0.572355i
$850$		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	−0.744132	−	0.668033i	$-0.767136\pi$
$857$	−15.7399	+	9.08742i	−0.537664	+	0.310420i	0.206468	+	0.978453i	$0.433803\pi$
$858$		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
$861$	−1.60469	−	1.61897i	−0.0546878	−	0.0551743i
$862$		0			0
$863$	16.7613	−	29.0314i	0.570562	−	0.988242i	−0.425947	−	0.904748i	$-0.640059\pi$
$863$	16.7613	−	29.0314i	0.570562	−	0.988242i	0.996508	−	0.0834933i	$-0.0266077\pi$
$864$		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
$873$	3.47384	−	0.850459i	0.117572	−	0.0287837i
$874$		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
$879$	6.71436	−	0.809939i	0.226470	−	0.0273186i
$880$		0			0
$881$		−	0.0231379i		−	0.000779536i	−1.00000		0.000389768i	$-0.999876\pi$
$881$		−	0.0231379i		−	0.000779536i	1.00000		0.000389768i	$-0.000124067\pi$
$882$		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
$885$	2.19572	+	18.2024i	0.0738083	+	0.611868i
$886$		0			0
$887$	23.4706	−	40.6522i	0.788064	−	1.36497i	−0.139087	−	0.990280i	$-0.544417\pi$
$887$	23.4706	−	40.6522i	0.788064	−	1.36497i	0.927151	−	0.374687i	$-0.122250\pi$
$888$		0			0
$889$	−3.75747	−	4.83224i	−0.126022	−	0.162068i
$890$		0			0
$891$	−21.3401	+	33.5140i	−0.714922	+	1.12276i
$892$		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
$903$	2.81823	−	2.79338i	0.0937847	−	0.0929578i
$904$		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	$-0.341955\pi$
$911$	28.7559			0.952726			0.476363	+	0.879249i	$0.341955\pi$
$912$		0			0
$913$	−15.4525	−	26.7646i	−0.511404	−	0.885779i
$914$		0			0
$915$	−6.62834	+	4.97277i	−0.219126	+	0.164395i
$916$		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
$921$	18.9738	−	2.28877i	0.625208	−	0.0754176i
$922$		0			0
$923$			12.2567i			0.403434i
$924$		0			0
$925$		−	17.8109i		−	0.585619i
$926$		0			0
$927$	15.9654	+	4.65152i	0.524371	+	0.152776i
$928$		0			0
$929$	2.55192	+	1.47335i	0.0837258	+	0.0483391i	0.541278	−	0.840843i	$-0.317941\pi$
$929$	2.55192	+	1.47335i	0.0837258	+	0.0483391i	−0.457553	+	0.889183i	$0.651274\pi$
$930$		0			0
$931$	15.9339	+	15.5296i	0.522212	+	0.508963i
$932$		0			0
$933$	32.5453	+	43.3806i	1.06548	+	1.42022i
$934$		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	$-0.989621\pi$
$941$	−16.1958	−	28.0519i	−0.527966	−	0.914465i	0.471502	−	0.881865i	$-0.343712\pi$
$942$		0			0
$943$	1.59128	+	0.918726i	0.0518192	+	0.0299178i
$944$		0			0
$945$	−9.08087	−	16.7230i	−0.295401	−	0.543998i
$946$		0			0
$947$	−18.1295	−	10.4671i	−0.589129	−	0.340134i	0.175624	−	0.984457i	$-0.443806\pi$
$947$	−18.1295	−	10.4671i	−0.589129	−	0.340134i	−0.764753	+	0.644324i	$0.777139\pi$
$948$		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	$-0.811772\pi$
$953$		−	34.4190i		−	1.11494i	0.830197	−	0.557470i	$-0.188228\pi$
$954$		0			0
$955$	1.04790	+	1.81502i	0.0339094	+	0.0587328i
$956$		0			0
$957$	−40.8504	+	30.6471i	−1.32051	+	0.990681i
$958$		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
$963$	−17.2119	−	5.01469i	−0.554645	−	0.161596i
$964$		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
$969$	1.92513	+	15.9593i	0.0618442	+	0.512686i
$970$		0			0
$971$	−0.310281	−	0.179141i	−0.00995738	−	0.00574890i	0.495013	−	0.868886i	$-0.335163\pi$
$971$	−0.310281	−	0.179141i	−0.00995738	−	0.00574890i	−0.504970	+	0.863137i	$0.668497\pi$
$972$		0			0
$973$	−19.5372	+	15.1918i	−0.626335	+	0.487028i
$974$		0			0
$975$	−27.5006	+	20.6317i	−0.880725	+	0.660744i
$976$		0			0
$977$	34.5190	−	19.9296i	1.10436	−	0.637603i	0.166998	−	0.985957i	$-0.446593\pi$
$977$	34.5190	−	19.9296i	1.10436	−	0.637603i	0.937363	+	0.348354i	$0.113259\pi$
$978$		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	0.527272	−	0.849697i	$-0.323215\pi$
$983$	−14.8055	−	25.6439i	−0.472223	−	0.817914i	−0.999495	+	0.0317825i	$0.989882\pi$
$984$		0			0
$985$	0.666498	−	1.15441i	0.0212364	−	0.0367825i
$986$		0			0
$987$	3.70933	+	14.0927i	0.118069	+	0.448576i
$988$		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
$999$	−29.6089	−	4.88330i	−0.936785	−	0.154501i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.71959 - 0.207430i) q^{3} +(-0.692094 + 1.19874i) q^{5} +(-2.08863 + 1.62408i) q^{7} +(2.91395 - 0.713387i) q^{9} +(-3.82316 + 2.20731i) q^{11} +6.43609i q^{13} +(-0.941460 + 2.20490i) q^{15} +(2.52866 - 1.45992i) q^{17} +(-1.58928 + 2.75271i) q^{19} +(-3.25469 + 3.22599i) q^{21} +(1.84696 - 3.19902i) q^{23} +(1.54201 + 2.67084i) q^{25} +(4.86280 - 1.83117i) q^{27} +6.67884 q^{29} +(-2.17580 + 1.25620i) q^{31} +(-6.11640 + 4.58869i) q^{33} +(-0.501330 - 3.62774i) q^{35} +(-5.00149 - 2.88761i) q^{37} +(1.33504 + 11.0674i) q^{39} +0.497427i q^{41} -0.865898 q^{43} +(-1.16156 + 3.98680i) q^{45} +(1.59001 - 2.75398i) q^{47} +(1.72472 - 6.78420i) q^{49} +(4.04541 - 3.03498i) q^{51} +(-4.12906 - 7.15175i) q^{53} -6.11065i q^{55} +(-2.16191 + 5.06319i) q^{57} +(6.62279 - 3.82367i) q^{59} +(2.99321 + 1.72813i) q^{61} +(-4.92754 + 6.22248i) q^{63} +(-7.71521 - 4.45438i) q^{65} +(3.36806 + 5.83364i) q^{67} +(2.51243 - 5.88411i) q^{69} +1.90437 q^{71} +(3.23515 + 5.60345i) q^{73} +(3.20563 + 4.27288i) q^{75} +(4.40032 - 10.8194i) q^{77} +(-1.65073 - 0.953048i) q^{79} +(7.98216 - 4.15754i) q^{81} +7.00064i q^{83} +4.04161i q^{85} +(11.4848 - 1.38539i) q^{87} +(-8.22776 - 4.75030i) q^{89} +(-10.4527 - 13.4426i) q^{91} +(-3.48090 + 2.61147i) q^{93} +(-2.19986 - 3.81027i) q^{95} +1.19214 q^{97} +(-9.56583 + 9.15936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{3} - 2 q^{9} + 4 q^{19} - 16 q^{25} + 8 q^{27} - 14 q^{33} + 16 q^{43} - 16 q^{49} + 34 q^{51} + 4 q^{57} + 36 q^{67} + 4 q^{73} - 10 q^{81} - 72 q^{91} - 32 q^{97} + 44 q^{99}+O(q^{100}) \) 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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