LMFDB - Embedded newform 1680.2.cz.d.433.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(97,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1680.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.cz (of order $4$, 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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			433.6
Root			$-0.517174 + 1.31626i$ of defining polynomial
Character	$\chi$	$=$	1680.433
Dual form			1680.2.cz.d.97.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(-1.50619 - 1.65269i) q^{5} +(2.20563 + 1.46123i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(-1.50619 - 1.65269i) q^{5} +(2.20563 + 1.46123i) q^{7} -1.00000i q^{9} +1.46279 q^{11} +(0.887844 - 0.887844i) q^{13} +(-2.23367 - 0.103594i) q^{15} +(-2.10614 - 2.10614i) q^{17} +3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(4.13007 + 4.13007i) q^{23} +(-0.462789 + 4.97854i) q^{25} +(-0.707107 - 0.707107i) q^{27} -5.18572i q^{29} -6.10346i q^{31} +(1.03435 - 1.03435i) q^{33} +(-0.907129 - 5.84612i) q^{35} +(2.25560 - 2.25560i) q^{37} -1.25560i q^{39} -0.769968i q^{41} +(5.18572 + 5.18572i) q^{43} +(-1.65269 + 1.50619i) q^{45} +(-8.57041 - 8.57041i) q^{47} +(2.72961 + 6.44587i) q^{49} -2.97854 q^{51} +(-0.544449 - 0.544449i) q^{53} +(-2.20324 - 2.41754i) q^{55} +(2.80005 - 2.80005i) q^{57} +3.19633 q^{59} -1.42064i q^{61} +(1.46123 - 2.20563i) q^{63} +(-2.80460 - 0.130073i) q^{65} +(5.93012 - 5.93012i) q^{67} +5.84081 q^{69} -7.62611 q^{71} +(6.81378 - 6.81378i) q^{73} +(3.19312 + 3.84760i) q^{75} +(3.22637 + 2.13747i) q^{77} +4.52029i q^{79} -1.00000 q^{81} +(6.75794 - 6.75794i) q^{83} +(-0.308559 + 6.65306i) q^{85} +(-3.66686 - 3.66686i) q^{87} +1.19991 q^{89} +(3.25560 - 0.660910i) q^{91} +(-4.31580 - 4.31580i) q^{93} +(-5.96431 - 6.54445i) q^{95} +(-8.68829 - 8.68829i) q^{97} -1.46279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) $ 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	−1.50619	−	1.65269i	−0.673588	−	0.739107i
$5$	−1.50619	−	1.65269i	−0.673588	−	0.739107i
$6$		0			0
$7$	2.20563	+	1.46123i	0.833650	+	0.552293i
$7$	2.20563	+	1.46123i	0.833650	+	0.552293i
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	1.46279			0.441048			0.220524	−	0.975382i	$-0.429223\pi$
$11$	1.46279			0.441048			0.220524	+	0.975382i	$0.429223\pi$
$12$		0			0
$13$	0.887844	−	0.887844i	0.246244	−	0.246244i	−0.573183	−	0.819427i	$-0.694292\pi$
$13$	0.887844	−	0.887844i	0.246244	−	0.246244i	0.819427	+	0.573183i	$0.194292\pi$
$14$		0			0
$15$	−2.23367	−	0.103594i	−0.576730	−	0.0267479i
$16$		0			0
$17$	−2.10614	−	2.10614i	−0.510815	−	0.510815i	0.403961	−	0.914776i	$-0.367633\pi$
$17$	−2.10614	−	2.10614i	−0.510815	−	0.510815i	−0.914776	+	0.403961i	$0.867633\pi$
$18$		0			0
$19$	3.95987			0.908456			0.454228	−	0.890885i	$-0.349915\pi$
$19$	3.95987			0.908456			0.454228	+	0.890885i	$0.349915\pi$
$20$		0			0
$21$	2.59286	−	0.526369i	0.565809	−	0.114863i
$22$		0			0
$23$	4.13007	+	4.13007i	0.861180	+	0.861180i	0.991475	−	0.130295i	$-0.0415926\pi$
$23$	4.13007	+	4.13007i	0.861180	+	0.861180i	−0.130295	+	0.991475i	$0.541593\pi$
$24$		0			0
$25$	−0.462789	+	4.97854i	−0.0925579	+	0.995707i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$		−	5.18572i		−	0.962965i	−0.876456	−	0.481482i	$-0.840099\pi$
$29$		−	5.18572i		−	0.962965i	0.876456	−	0.481482i	$-0.159901\pi$
$30$		0			0
$31$		−	6.10346i		−	1.09621i	−0.836408	−	0.548107i	$-0.815349\pi$
$31$		−	6.10346i		−	1.09621i	0.836408	−	0.548107i	$-0.184651\pi$
$32$		0			0
$33$	1.03435	−	1.03435i	0.180057	−	0.180057i
$34$		0			0
$35$	−0.907129	−	5.84612i	−0.153333	−	0.988175i
$36$		0			0
$37$	2.25560	−	2.25560i	0.370819	−	0.370819i	−0.496957	−	0.867775i	$-0.665549\pi$
$37$	2.25560	−	2.25560i	0.370819	−	0.370819i	0.867775	+	0.496957i	$0.165549\pi$
$38$		0			0
$39$		−	1.25560i		−	0.201057i
$40$		0			0
$41$		−	0.769968i		−	0.120249i	−0.998191	−	0.0601244i	$-0.980850\pi$
$41$		−	0.769968i		−	0.120249i	0.998191	−	0.0601244i	$-0.0191497\pi$
$42$		0			0
$43$	5.18572	+	5.18572i	0.790816	+	0.790816i	0.981627	−	0.190811i	$-0.0611118\pi$
$43$	5.18572	+	5.18572i	0.790816	+	0.790816i	−0.190811	+	0.981627i	$0.561112\pi$
$44$		0			0
$45$	−1.65269	+	1.50619i	−0.246369	+	0.224529i
$46$		0			0
$47$	−8.57041	−	8.57041i	−1.25012	−	1.25012i	−0.955664	−	0.294459i	$-0.904861\pi$
$47$	−8.57041	−	8.57041i	−1.25012	−	1.25012i	−0.294459	−	0.955664i	$-0.595139\pi$
$48$		0			0
$49$	2.72961	+	6.44587i	0.389944	+	0.920839i
$50$		0			0
$51$	−2.97854			−0.417079
$52$		0			0
$53$	−0.544449	−	0.544449i	−0.0747859	−	0.0747859i	0.668724	−	0.743510i	$-0.266841\pi$
$53$	−0.544449	−	0.544449i	−0.0747859	−	0.0747859i	−0.743510	+	0.668724i	$0.766841\pi$
$54$		0			0
$55$	−2.20324	−	2.41754i	−0.297084	−	0.325981i
$56$		0			0
$57$	2.80005	−	2.80005i	0.370876	−	0.370876i
$58$		0			0
$59$	3.19633			0.416127			0.208063	−	0.978115i	$-0.433284\pi$
$59$	3.19633			0.416127			0.208063	+	0.978115i	$0.433284\pi$
$60$		0			0
$61$		−	1.42064i		−	0.181894i	−0.995856	−	0.0909472i	$-0.971011\pi$
$61$		−	1.42064i		−	0.181894i	0.995856	−	0.0909472i	$-0.0289894\pi$
$62$		0			0
$63$	1.46123	−	2.20563i	0.184098	−	0.277883i
$64$		0			0
$65$	−2.80460	−	0.130073i	−0.347867	−	0.0161336i
$66$		0			0
$67$	5.93012	−	5.93012i	0.724480	−	0.724480i	−0.245034	−	0.969514i	$-0.578799\pi$
$67$	5.93012	−	5.93012i	0.724480	−	0.724480i	0.969514	+	0.245034i	$0.0787993\pi$
$68$		0			0
$69$	5.84081			0.703150
$70$		0			0
$71$	−7.62611			−0.905053			−0.452526	−	0.891751i	$-0.649477\pi$
$71$	−7.62611			−0.905053			−0.452526	+	0.891751i	$0.649477\pi$
$72$		0			0
$73$	6.81378	−	6.81378i	0.797493	−	0.797493i	−0.185207	−	0.982700i	$-0.559296\pi$
$73$	6.81378	−	6.81378i	0.797493	−	0.797493i	0.982700	+	0.185207i	$0.0592955\pi$
$74$		0			0
$75$	3.19312	+	3.84760i	0.368709	+	0.444282i
$76$		0			0
$77$	3.22637	+	2.13747i	0.367679	+	0.243588i
$78$		0			0
$79$			4.52029i			0.508573i	0.967129	+	0.254286i	$0.0818405\pi$
$79$			4.52029i			0.508573i	−0.967129	+	0.254286i	$0.918159\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	6.75794	−	6.75794i	0.741781	−	0.741781i	−0.231140	−	0.972921i	$-0.574246\pi$
$83$	6.75794	−	6.75794i	0.741781	−	0.741781i	0.972921	+	0.231140i	$0.0742455\pi$
$84$		0			0
$85$	−0.308559	+	6.65306i	−0.0334679	+	0.721626i
$86$		0			0
$87$	−3.66686	−	3.66686i	−0.393129	−	0.393129i
$88$		0			0
$89$	1.19991			0.127190			0.0635950	−	0.997976i	$-0.479743\pi$
$89$	1.19991			0.127190			0.0635950	+	0.997976i	$0.479743\pi$
$90$		0			0
$91$	3.25560	−	0.660910i	0.341280	−	0.0692822i
$92$		0			0
$93$	−4.31580	−	4.31580i	−0.447527	−	0.447527i
$94$		0			0
$95$	−5.96431	−	6.54445i	−0.611925	−	0.671446i
$96$		0			0
$97$	−8.68829	−	8.68829i	−0.882162	−	0.882162i	0.111592	−	0.993754i	$-0.464405\pi$
$97$	−8.68829	−	8.68829i	−0.882162	−	0.882162i	−0.993754	+	0.111592i	$0.964405\pi$
$98$		0			0
$99$		−	1.46279i		−	0.147016i
$100$		0			0
$101$		−	15.3420i		−	1.52659i	−0.646050	−	0.763295i	$-0.723580\pi$
$101$		−	15.3420i		−	1.52659i	0.646050	−	0.763295i	$-0.276420\pi$
$102$		0			0
$103$	−8.30776	+	8.30776i	−0.818588	+	0.818588i	−0.985903	−	0.167316i	$-0.946490\pi$
$103$	−8.30776	+	8.30776i	−0.818588	+	0.818588i	0.167316	+	0.985903i	$0.446490\pi$
$104$		0			0
$105$	−4.77527	−	3.49239i	−0.466018	−	0.340823i
$106$		0			0
$107$	−4.39022	+	4.39022i	−0.424418	+	0.424418i	−0.886722	−	0.462303i	$-0.847023\pi$
$107$	−4.39022	+	4.39022i	−0.424418	+	0.424418i	0.462303	+	0.886722i	$0.347023\pi$
$108$		0			0
$109$		−	7.44587i		−	0.713185i	−0.934260	−	0.356593i	$-0.883938\pi$
$109$		−	7.44587i		−	0.713185i	0.934260	−	0.356593i	$-0.116062\pi$
$110$		0			0
$111$		−	3.18990i		−	0.302772i
$112$		0			0
$113$	2.54445	+	2.54445i	0.239362	+	0.239362i	0.816586	−	0.577224i	$-0.195864\pi$
$113$	2.54445	+	2.54445i	0.239362	+	0.239362i	−0.577224	+	0.816586i	$0.695864\pi$
$114$		0			0
$115$	0.605073	−	13.0464i	0.0564233	−	1.21658i
$116$		0			0
$117$	−0.887844	−	0.887844i	−0.0820812	−	0.0820812i
$118$		0			0
$119$	−1.56781	−	7.72294i	−0.143721	−	0.707960i
$120$		0			0
$121$	−8.86025			−0.805477
$122$		0			0
$123$	−0.544449	−	0.544449i	−0.0490913	−	0.0490913i
$124$		0			0
$125$	8.92504	−	6.73377i	0.798280	−	0.602287i
$126$		0			0
$127$	−7.86025	+	7.86025i	−0.697484	+	0.697484i	−0.963867	−	0.266383i	$-0.914171\pi$
$127$	−7.86025	+	7.86025i	−0.697484	+	0.697484i	0.266383	+	0.963867i	$0.414171\pi$
$128$		0			0
$129$	7.33372			0.645698
$130$		0			0
$131$			6.18216i			0.540138i	0.962841	+	0.270069i	$0.0870465\pi$
$131$			6.18216i			0.540138i	−0.962841	+	0.270069i	$0.912953\pi$
$132$		0			0
$133$	8.73401	+	5.78628i	0.757334	+	0.501735i
$134$		0			0
$135$	−0.103594	+	2.23367i	−0.00891596	+	0.192243i
$136$		0			0
$137$	9.05565	−	9.05565i	0.773677	−	0.773677i	−0.205071	−	0.978747i	$-0.565742\pi$
$137$	9.05565	−	9.05565i	0.773677	−	0.773677i	0.978747	+	0.205071i	$0.0657424\pi$
$138$		0			0
$139$	11.9913			1.01709			0.508544	−	0.861036i	$-0.330184\pi$
$139$	11.9913			1.01709			0.508544	+	0.861036i	$0.330184\pi$
$140$		0			0
$141$	−12.1204			−1.02072
$142$		0			0
$143$	1.29873	−	1.29873i	0.108605	−	0.108605i
$144$		0			0
$145$	−8.57041	+	7.81068i	−0.711734	+	0.648642i
$146$		0			0
$147$	6.48804	+	2.62780i	0.535125	+	0.216737i
$148$		0			0
$149$			0.0968261i			0.00793230i	0.999992	+	0.00396615i	$0.00126247\pi$
$149$			0.0968261i			0.00793230i	−0.999992	+	0.00396615i	$0.998738\pi$
$150$		0			0
$151$	13.4550			1.09495			0.547475	−	0.836822i	$-0.315589\pi$
$151$	13.4550			1.09495			0.547475	+	0.836822i	$0.315589\pi$
$152$		0			0
$153$	−2.10614	+	2.10614i	−0.170272	+	0.170272i
$154$		0			0
$155$	−10.0871	+	9.19296i	−0.810219	+	0.738397i
$156$		0			0
$157$	1.64757	+	1.64757i	0.131491	+	0.131491i	0.769789	−	0.638298i	$-0.220361\pi$
$157$	1.64757	+	1.64757i	0.131491	+	0.131491i	−0.638298	+	0.769789i	$0.720361\pi$
$158$		0			0
$159$	−0.769968			−0.0610624
$160$		0			0
$161$	3.07442	+	15.1444i	0.242298	+	1.19355i
$162$		0			0
$163$	10.2746	+	10.2746i	0.804771	+	0.804771i	0.983837	−	0.179066i	$-0.0573077\pi$
$163$	10.2746	+	10.2746i	0.804771	+	0.804771i	−0.179066	+	0.983837i	$0.557308\pi$
$164$		0			0
$165$	−3.26738	−	0.151536i	−0.254366	−	0.0117971i
$166$		0			0
$167$	−0.293008	−	0.293008i	−0.0226737	−	0.0226737i	0.695679	−	0.718353i	$-0.255104\pi$
$167$	−0.293008	−	0.293008i	−0.0226737	−	0.0226737i	−0.718353	+	0.695679i	$0.755104\pi$
$168$		0			0
$169$			11.4235i			0.878728i
$170$		0			0
$171$		−	3.95987i		−	0.302819i
$172$		0			0
$173$	−3.45189	+	3.45189i	−0.262442	+	0.262442i	−0.826046	−	0.563603i	$-0.809415\pi$
$173$	−3.45189	+	3.45189i	−0.262442	+	0.262442i	0.563603	+	0.826046i	$0.309415\pi$
$174$		0			0
$175$	−8.29554	+	10.3046i	−0.627084	+	0.778952i
$176$		0			0
$177$	2.26015	−	2.26015i	0.169883	−	0.169883i
$178$		0			0
$179$		−	1.99756i		−	0.149305i	−0.997210	−	0.0746523i	$-0.976215\pi$
$179$		−	1.99756i		−	0.149305i	0.997210	−	0.0746523i	$-0.0237847\pi$
$180$		0			0
$181$			8.48528i			0.630706i	0.948974	+	0.315353i	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		0			0
$183$	−1.00454	−	1.00454i	−0.0742581	−	0.0742581i
$184$		0			0
$185$	−7.12518	−	0.330455i	−0.523854	−	0.0242955i
$186$		0			0
$187$	−3.08084	−	3.08084i	−0.225294	−	0.225294i
$188$		0			0
$189$	−0.526369	−	2.59286i	−0.0382877	−	0.188603i
$190$		0			0
$191$	7.83424			0.566866			0.283433	−	0.958992i	$-0.408527\pi$
$191$	7.83424			0.566866			0.283433	+	0.958992i	$0.408527\pi$
$192$		0			0
$193$	13.5617	+	13.5617i	0.976194	+	0.976194i	0.999723	−	0.0235293i	$-0.00749029\pi$
$193$	13.5617	+	13.5617i	0.976194	+	0.976194i	−0.0235293	+	0.999723i	$0.507490\pi$
$194$		0			0
$195$	−2.07512	+	1.89117i	−0.148603	+	0.135430i
$196$		0			0
$197$	−11.4791	+	11.4791i	−0.817853	+	0.817853i	−0.985797	−	0.167943i	$-0.946287\pi$
$197$	−11.4791	+	11.4791i	−0.817853	+	0.817853i	0.167943	+	0.985797i	$0.446287\pi$
$198$		0			0
$199$	−20.1468			−1.42817			−0.714084	−	0.700061i	$-0.753156\pi$
$199$	−20.1468			−1.42817			−0.714084	+	0.700061i	$0.753156\pi$
$200$		0			0
$201$		−	8.38646i		−	0.591535i
$202$		0			0
$203$	7.57754	−	11.4378i	0.531839	−	0.802775i
$204$		0			0
$205$	−1.27252	+	1.15972i	−0.0888767	+	0.0809981i
$206$		0			0
$207$	4.13007	−	4.13007i	0.287060	−	0.287060i
$208$		0			0
$209$	5.79246			0.400673
$210$		0			0
$211$	−11.9662			−0.823785			−0.411892	−	0.911233i	$-0.635132\pi$
$211$	−11.9662			−0.823785			−0.411892	+	0.911233i	$0.635132\pi$
$212$		0			0
$213$	−5.39247	+	5.39247i	−0.369486	+	0.369486i
$214$		0			0
$215$	0.759730	−	16.3811i	0.0518132	−	1.11718i
$216$		0			0
$217$	8.91857	−	13.4620i	0.605432	−	0.913858i
$218$		0			0
$219$		−	9.63614i		−	0.651150i
$220$		0			0
$221$	−3.73985			−0.251570
$222$		0			0
$223$	0.660910	−	0.660910i	0.0442578	−	0.0442578i	−0.684632	−	0.728889i	$-0.740037\pi$
$223$	0.660910	−	0.660910i	0.0442578	−	0.0442578i	0.728889	+	0.684632i	$0.240037\pi$
$224$		0			0
$225$	4.97854	+	0.462789i	0.331902	+	0.0308526i
$226$		0			0
$227$	17.3487	+	17.3487i	1.15147	+	1.15147i	0.986257	+	0.165216i	$0.0528323\pi$
$227$	17.3487	+	17.3487i	1.15147	+	1.15147i	0.165216	+	0.986257i	$0.447168\pi$
$228$		0			0
$229$	−25.0782			−1.65721			−0.828607	−	0.559831i	$-0.810866\pi$
$229$	−25.0782			−1.65721			−0.828607	+	0.559831i	$0.810866\pi$
$230$		0			0
$231$	3.79281	−	0.769968i	0.249549	−	0.0506601i
$232$		0			0
$233$	2.24138	+	2.24138i	0.146837	+	0.146837i	0.776704	−	0.629866i	$-0.216890\pi$
$233$	2.24138	+	2.24138i	0.146837	+	0.146837i	−0.629866	+	0.776704i	$0.716890\pi$
$234$		0			0
$235$	−1.25560	+	27.0729i	−0.0819064	+	1.76604i
$236$		0			0
$237$	3.19633	+	3.19633i	0.207624	+	0.207624i
$238$		0			0
$239$		−	21.3769i		−	1.38276i	−0.722492	−	0.691380i	$-0.757003\pi$
$239$		−	21.3769i		−	1.38276i	0.722492	−	0.691380i	$-0.242997\pi$
$240$		0			0
$241$			0.624129i			0.0402037i	0.999798	+	0.0201018i	$0.00639905\pi$
$241$			0.624129i			0.0402037i	−0.999798	+	0.0201018i	$0.993601\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	6.54174	−	14.2199i	0.417937	−	0.908476i
$246$		0			0
$247$	3.51575	−	3.51575i	0.223702	−	0.223702i
$248$		0			0
$249$		−	9.55717i		−	0.605661i
$250$		0			0
$251$			16.3443i			1.03164i	0.856696	+	0.515822i	$0.172513\pi$
$251$			16.3443i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$252$		0			0
$253$	6.04143	+	6.04143i	0.379821	+	0.379821i
$254$		0			0
$255$	4.48624	+	4.92261i	0.280939	+	0.308266i
$256$		0			0
$257$	21.3054	+	21.3054i	1.32900	+	1.32900i	0.906247	+	0.422749i	$0.138935\pi$
$257$	21.3054	+	21.3054i	1.32900	+	1.32900i	0.422749	+	0.906247i	$0.361065\pi$
$258$		0			0
$259$	8.27098	−	1.67907i	0.513933	−	0.104332i
$260$		0			0
$261$	−5.18572			−0.320988
$262$		0			0
$263$	16.3449	+	16.3449i	1.00787	+	1.00787i	0.999969	+	0.00789784i	$0.00251399\pi$
$263$	16.3449	+	16.3449i	1.00787	+	1.00787i	0.00789784	+	0.999969i	$0.497486\pi$
$264$		0			0
$265$	−0.0797641	+	1.71985i	−0.00489987	+	0.105650i
$266$		0			0
$267$	0.848464	−	0.848464i	0.0519251	−	0.0519251i
$268$		0			0
$269$	−16.5903			−1.01153			−0.505764	−	0.862672i	$-0.668789\pi$
$269$	−16.5903			−1.01153			−0.505764	+	0.862672i	$0.668789\pi$
$270$		0			0
$271$			7.78033i			0.472621i	0.971678	+	0.236311i	$0.0759383\pi$
$271$			7.78033i			0.472621i	−0.971678	+	0.236311i	$0.924062\pi$
$272$		0			0
$273$	1.83472	−	2.76939i	0.111043	−	0.167611i
$274$		0			0
$275$	−0.676964	+	7.28255i	−0.0408224	+	0.439154i
$276$		0			0
$277$	21.3107	−	21.3107i	1.28043	−	1.28043i	0.340013	−	0.940421i	$-0.389569\pi$
$277$	21.3107	−	21.3107i	1.28043	−	1.28043i	0.940421	−	0.340013i	$-0.110431\pi$
$278$		0			0
$279$	−6.10346			−0.365405
$280$		0			0
$281$	−21.1519			−1.26182			−0.630908	−	0.775858i	$-0.717317\pi$
$281$	−21.1519			−1.26182			−0.630908	+	0.775858i	$0.717317\pi$
$282$		0			0
$283$	−2.65471	+	2.65471i	−0.157806	+	0.157806i	−0.781594	−	0.623788i	$-0.785593\pi$
$283$	−2.65471	+	2.65471i	−0.157806	+	0.157806i	0.623788	+	0.781594i	$0.285593\pi$
$284$		0			0
$285$	−8.84503	−	0.410219i	−0.523934	−	0.0242993i
$286$		0			0
$287$	1.12510	−	1.69826i	0.0664126	−	0.100245i
$288$		0			0
$289$		−	8.12832i		−	0.478136i
$290$		0			0
$291$	−12.2871			−0.720282
$292$		0			0
$293$	−1.56714	+	1.56714i	−0.0915536	+	0.0915536i	−0.751400	−	0.659847i	$-0.770621\pi$
$293$	−1.56714	+	1.56714i	−0.0915536	+	0.0915536i	0.659847	+	0.751400i	$0.270621\pi$
$294$		0			0
$295$	−4.81428	−	5.28255i	−0.280298	−	0.307562i
$296$		0			0
$297$	−1.03435	−	1.03435i	−0.0600190	−	0.0600190i
$298$		0			0
$299$	7.33372			0.424120
$300$		0			0
$301$	3.86025	+	19.0153i	0.222501	+	1.09603i
$302$		0			0
$303$	−10.8485	−	10.8485i	−0.623228	−	0.623228i
$304$		0			0
$305$	−2.34788	+	2.13975i	−0.134439	+	0.122522i
$306$		0			0
$307$	17.3551	+	17.3551i	0.990510	+	0.990510i	0.999955	−	0.00944588i	$-0.00300676\pi$
$307$	17.3551	+	17.3551i	0.990510	+	0.990510i	−0.00944588	+	0.999955i	$0.503007\pi$
$308$		0			0
$309$			11.7489i			0.668374i
$310$		0			0
$311$			31.0648i			1.76153i	0.473558	+	0.880763i	$0.342970\pi$
$311$			31.0648i			1.76153i	−0.473558	+	0.880763i	$0.657030\pi$
$312$		0			0
$313$	5.72426	−	5.72426i	0.323554	−	0.323554i	−0.526575	−	0.850129i	$-0.676524\pi$
$313$	5.72426	−	5.72426i	0.323554	−	0.323554i	0.850129	+	0.526575i	$0.176524\pi$
$314$		0			0
$315$	−5.84612	+	0.907129i	−0.329392	+	0.0511109i
$316$		0			0
$317$	0.752579	−	0.752579i	0.0422691	−	0.0422691i	−0.685656	−	0.727925i	$-0.740485\pi$
$317$	0.752579	−	0.752579i	0.0422691	−	0.0422691i	0.727925	+	0.685656i	$0.240485\pi$
$318$		0			0
$319$		−	7.58562i		−	0.424713i
$320$		0			0
$321$			6.20871i			0.346536i
$322$		0			0
$323$	−8.34005	−	8.34005i	−0.464053	−	0.464053i
$324$		0			0
$325$	4.00928	+	4.83105i	0.222395	+	0.267978i
$326$		0			0
$327$	−5.26503	−	5.26503i	−0.291157	−	0.291157i
$328$		0			0
$329$	−6.37980	−	31.4265i	−0.351730	−	1.73260i
$330$		0			0
$331$	−15.8082			−0.868899			−0.434449	−	0.900696i	$-0.643057\pi$
$331$	−15.8082			−0.868899			−0.434449	+	0.900696i	$0.643057\pi$
$332$		0			0
$333$	−2.25560	−	2.25560i	−0.123606	−	0.123606i
$334$		0			0
$335$	−18.7326	−	0.868788i	−1.02347	−	0.0474670i
$336$		0			0
$337$	−20.0460	+	20.0460i	−1.09197	+	1.09197i	−0.0966558	+	0.995318i	$0.530815\pi$
$337$	−20.0460	+	20.0460i	−1.09197	+	1.09197i	−0.995318	+	0.0966558i	$0.969185\pi$
$338$		0			0
$339$	3.59839			0.195438
$340$		0			0
$341$		−	8.92808i		−	0.483482i
$342$		0			0
$343$	−3.39840	+	18.2058i	−0.183497	+	0.983020i
$344$		0			0
$345$	−8.79736	−	9.65306i	−0.473634	−	0.519703i
$346$		0			0
$347$	20.0847	−	20.0847i	1.07820	−	1.07820i	0.0815328	−	0.996671i	$-0.474018\pi$
$347$	20.0847	−	20.0847i	1.07820	−	1.07820i	0.996671	−	0.0815328i	$-0.0259815\pi$
$348$		0			0
$349$	14.7663			0.790420			0.395210	−	0.918591i	$-0.370672\pi$
$349$	14.7663			0.790420			0.395210	+	0.918591i	$0.370672\pi$
$350$		0			0
$351$	−1.25560			−0.0670190
$352$		0			0
$353$	−12.4890	+	12.4890i	−0.664724	+	0.664724i	−0.956490	−	0.291766i	$-0.905757\pi$
$353$	−12.4890	+	12.4890i	−0.664724	+	0.664724i	0.291766	+	0.956490i	$0.405757\pi$
$354$		0			0
$355$	11.4864	+	12.6036i	0.609633	+	0.668931i
$356$		0			0
$357$	−6.56955	−	4.35233i	−0.347697	−	0.230350i
$358$		0			0
$359$		−	10.5372i		−	0.556133i	−0.960562	−	0.278066i	$-0.910306\pi$
$359$		−	10.5372i		−	0.556133i	0.960562	−	0.278066i	$-0.0896935\pi$
$360$		0			0
$361$	−3.31943			−0.174707
$362$		0			0
$363$	−6.26514	+	6.26514i	−0.328835	+	0.328835i
$364$		0			0
$365$	−21.5239	−	0.998247i	−1.12661	−	0.0522507i
$366$		0			0
$367$	−11.1910	−	11.1910i	−0.584163	−	0.584163i	0.351881	−	0.936045i	$-0.385542\pi$
$367$	−11.1910	−	11.1910i	−0.584163	−	0.584163i	−0.936045	+	0.351881i	$0.885542\pi$
$368$		0			0
$369$	−0.769968			−0.0400829
$370$		0			0
$371$	−0.405287	−	1.99642i	−0.0210415	−	0.103649i
$372$		0			0
$373$	17.2746	+	17.2746i	0.894446	+	0.894446i	0.994938	−	0.100492i	$-0.0320416\pi$
$373$	17.2746	+	17.2746i	0.894446	+	0.894446i	−0.100492	+	0.994938i	$0.532042\pi$
$374$		0			0
$375$	1.54946	−	11.0725i	0.0800140	−	0.571779i
$376$		0			0
$377$	−4.60412	−	4.60412i	−0.237124	−	0.237124i
$378$		0			0
$379$			17.6237i			0.905267i	0.891697	+	0.452634i	$0.149515\pi$
$379$			17.6237i			0.905267i	−0.891697	+	0.452634i	$0.850485\pi$
$380$		0			0
$381$			11.1161i			0.569493i
$382$		0			0
$383$	−16.1249	+	16.1249i	−0.823942	+	0.823942i	−0.986671	−	0.162729i	$-0.947970\pi$
$383$	−16.1249	+	16.1249i	−0.823942	+	0.823942i	0.162729	+	0.986671i	$0.447970\pi$
$384$		0			0
$385$	−1.32694	−	8.55164i	−0.0676270	−	0.435832i
$386$		0			0
$387$	5.18572	−	5.18572i	0.263605	−	0.263605i
$388$		0			0
$389$		−	15.4011i		−	0.780865i	−0.920632	−	0.390432i	$-0.872326\pi$
$389$		−	15.4011i		−	0.780865i	0.920632	−	0.390432i	$-0.127674\pi$
$390$		0			0
$391$		−	17.3971i		−	0.879807i
$392$		0			0
$393$	4.37145	+	4.37145i	0.220510	+	0.220510i
$394$		0			0
$395$	7.47066	−	6.80841i	0.375889	−	0.342568i
$396$		0			0
$397$	16.1781	+	16.1781i	0.811955	+	0.811955i	0.984927	−	0.172972i	$-0.0553370\pi$
$397$	16.1781	+	16.1781i	0.811955	+	0.811955i	−0.172972	+	0.984927i	$0.555337\pi$
$398$		0			0
$399$	10.2674	−	2.08435i	0.514013	−	0.104348i
$400$		0			0
$401$	−0.977595			−0.0488188			−0.0244094	−	0.999702i	$-0.507771\pi$
$401$	−0.977595			−0.0488188			−0.0244094	+	0.999702i	$0.507771\pi$
$402$		0			0
$403$	−5.41892	−	5.41892i	−0.269936	−	0.269936i
$404$		0			0
$405$	1.50619	+	1.65269i	0.0748431	+	0.0821230i
$406$		0			0
$407$	3.29947	−	3.29947i	0.163549	−	0.163549i
$408$		0			0
$409$	24.3171			1.20241			0.601203	−	0.799097i	$-0.294688\pi$
$409$	24.3171			1.20241			0.601203	+	0.799097i	$0.294688\pi$
$410$		0			0
$411$		−	12.8066i		−	0.631704i
$412$		0			0
$413$	7.04992	+	4.67058i	0.346904	+	0.229824i
$414$		0			0
$415$	−21.3475	−	0.990067i	−1.04791	−	0.0486005i
$416$		0			0
$417$	8.47912	−	8.47912i	0.415224	−	0.415224i
$418$		0			0
$419$	−15.9893			−0.781127			−0.390563	−	0.920576i	$-0.627720\pi$
$419$	−15.9893			−0.781127			−0.390563	+	0.920576i	$0.627720\pi$
$420$		0			0
$421$	14.7000			0.716433			0.358216	−	0.933639i	$-0.383385\pi$
$421$	14.7000			0.716433			0.358216	+	0.933639i	$0.383385\pi$
$422$		0			0
$423$	−8.57041	+	8.57041i	−0.416708	+	0.416708i
$424$		0			0
$425$	11.4602	−	9.51081i	0.555902	−	0.461342i
$426$		0			0
$427$	2.07588	−	3.13341i	0.100459	−	0.151636i
$428$		0			0
$429$		−	1.83668i		−	0.0886758i
$430$		0			0
$431$	−22.2722			−1.07281			−0.536407	−	0.843960i	$-0.680219\pi$
$431$	−22.2722			−1.07281			−0.536407	+	0.843960i	$0.680219\pi$
$432$		0			0
$433$	−28.0171	+	28.0171i	−1.34642	+	1.34642i	−0.456896	+	0.889520i	$0.651039\pi$
$433$	−28.0171	+	28.0171i	−1.34642	+	1.34642i	−0.889520	+	0.456896i	$0.848961\pi$
$434$		0			0
$435$	−0.537211	+	11.5832i	−0.0257573	+	0.555371i
$436$		0			0
$437$	16.3545	+	16.3545i	0.782344	+	0.782344i
$438$		0			0
$439$	2.35656			0.112473			0.0562363	−	0.998417i	$-0.482090\pi$
$439$	2.35656			0.112473			0.0562363	+	0.998417i	$0.482090\pi$
$440$		0			0
$441$	6.44587	−	2.72961i	0.306946	−	0.129981i
$442$		0			0
$443$	5.47247	+	5.47247i	0.260005	+	0.260005i	0.825056	−	0.565051i	$-0.191144\pi$
$443$	5.47247	+	5.47247i	0.260005	+	0.260005i	−0.565051	+	0.825056i	$0.691144\pi$
$444$		0			0
$445$	−1.80729	−	1.98308i	−0.0856737	−	0.0940071i
$446$		0			0
$447$	0.0684664	+	0.0684664i	0.00323835	+	0.00323835i
$448$		0			0
$449$			1.20020i			0.0566410i	0.999599	+	0.0283205i	$0.00901591\pi$
$449$			1.20020i			0.0566410i	−0.999599	+	0.0283205i	$0.990984\pi$
$450$		0			0
$451$		−	1.12630i		−	0.0530354i
$452$		0			0
$453$	9.51409	−	9.51409i	0.447011	−	0.447011i
$454$		0			0
$455$	−5.99583	−	4.38505i	−0.281089	−	0.205575i
$456$		0			0
$457$	−21.0775	+	21.0775i	−0.985962	+	0.985962i	−0.999903	−	0.0139406i	$-0.995562\pi$
$457$	−21.0775	+	21.0775i	−0.985962	+	0.985962i	0.0139406	+	0.999903i	$0.495562\pi$
$458$		0			0
$459$			2.97854i			0.139026i
$460$		0			0
$461$			21.9670i			1.02311i	0.859252	+	0.511553i	$0.170929\pi$
$461$			21.9670i			1.02311i	−0.859252	+	0.511553i	$0.829071\pi$
$462$		0			0
$463$	21.6776	+	21.6776i	1.00744	+	1.00744i	0.999972	+	0.00746987i	$0.00237776\pi$
$463$	21.6776	+	21.6776i	1.00744	+	1.00744i	0.00746987	+	0.999972i	$0.497622\pi$
$464$		0			0
$465$	−0.632282	+	13.6331i	−0.0293214	+	0.632220i
$466$		0			0
$467$	−7.11299	−	7.11299i	−0.329150	−	0.329150i	0.523113	−	0.852263i	$-0.324770\pi$
$467$	−7.11299	−	7.11299i	−0.329150	−	0.329150i	−0.852263	+	0.523113i	$0.824770\pi$
$468$		0			0
$469$	21.7449	−	4.41438i	1.00409	−	0.203837i
$470$		0			0
$471$	2.33002			0.107362
$472$		0			0
$473$	7.58562	+	7.58562i	0.348787	+	0.348787i
$474$		0			0
$475$	−1.83259	+	19.7144i	−0.0840848	+	0.904557i
$476$		0			0
$477$	−0.544449	+	0.544449i	−0.0249286	+	0.0249286i
$478$		0			0
$479$	−31.7749			−1.45183			−0.725917	−	0.687782i	$-0.758584\pi$
$479$	−31.7749			−1.45183			−0.725917	+	0.687782i	$0.758584\pi$
$480$		0			0
$481$		−	4.00524i		−	0.182623i
$482$		0			0
$483$	12.8827	+	8.53477i	0.586181	+	0.388345i
$484$		0			0
$485$	−1.27287	+	27.4453i	−0.0577981	+	1.24623i
$486$		0			0
$487$	4.81428	−	4.81428i	0.218156	−	0.218156i	−0.589565	−	0.807721i	$-0.700701\pi$
$487$	4.81428	−	4.81428i	0.218156	−	0.218156i	0.807721	+	0.589565i	$0.200701\pi$
$488$		0			0
$489$	14.5305			0.657092
$490$		0			0
$491$	−28.3401			−1.27897			−0.639484	−	0.768804i	$-0.720852\pi$
$491$	−28.3401			−1.27897			−0.639484	+	0.768804i	$0.720852\pi$
$492$		0			0
$493$	−10.9219	+	10.9219i	−0.491897	+	0.491897i
$494$		0			0
$495$	−2.41754	+	2.20324i	−0.108660	+	0.0990282i
$496$		0			0
$497$	−16.8204	−	11.1435i	−0.754497	−	0.499855i
$498$		0			0
$499$			3.39197i			0.151845i	0.997114	+	0.0759227i	$0.0241902\pi$
$499$			3.39197i			0.151845i	−0.997114	+	0.0759227i	$0.975810\pi$
$500$		0			0
$501$	−0.414376			−0.0185130
$502$		0			0
$503$	8.32921	−	8.32921i	0.371381	−	0.371381i	−0.496599	−	0.867980i	$-0.665418\pi$
$503$	8.32921	−	8.32921i	0.371381	−	0.371381i	0.867980	+	0.496599i	$0.165418\pi$
$504$		0			0
$505$	−25.3557	+	23.1080i	−1.12831	+	1.02829i
$506$		0			0
$507$	8.07761	+	8.07761i	0.358739	+	0.358739i
$508$		0			0
$509$	−38.9452			−1.72622			−0.863108	−	0.505020i	$-0.831485\pi$
$509$	−38.9452			−1.72622			−0.863108	+	0.505020i	$0.831485\pi$
$510$		0			0
$511$	24.9852	−	5.07217i	1.10528	−	0.224380i
$512$		0			0
$513$	−2.80005	−	2.80005i	−0.123625	−	0.123625i
$514$		0			0
$515$	26.2432	+	1.21712i	1.15641	+	0.0536328i
$516$		0			0
$517$	−12.5367	−	12.5367i	−0.551364	−	0.551364i
$518$		0			0
$519$			4.88171i			0.214283i
$520$		0			0
$521$			7.06726i			0.309622i	0.987944	+	0.154811i	$0.0494769\pi$
$521$			7.06726i			0.309622i	−0.987944	+	0.154811i	$0.950523\pi$
$522$		0			0
$523$	−14.5887	+	14.5887i	−0.637921	+	0.637921i	−0.950042	−	0.312121i	$-0.898960\pi$
$523$	−14.5887	+	14.5887i	−0.637921	+	0.637921i	0.312121	+	0.950042i	$0.398960\pi$
$524$		0			0
$525$	1.42060	+	13.1523i	0.0620001	+	0.574012i
$526$		0			0
$527$	−12.8548	+	12.8548i	−0.559962	+	0.559962i
$528$		0			0
$529$			11.1150i			0.483261i
$530$		0			0
$531$		−	3.19633i		−	0.138709i
$532$		0			0
$533$	−0.683611	−	0.683611i	−0.0296105	−	0.0296105i
$534$		0			0
$535$	13.8682	+	0.643185i	0.599574	+	0.0278073i
$536$		0			0
$537$	−1.41249	−	1.41249i	−0.0609533	−	0.0609533i
$538$		0			0
$539$	3.99284	+	9.42895i	0.171984	+	0.406134i
$540$		0			0
$541$	18.6013			0.799731			0.399865	−	0.916574i	$-0.369057\pi$
$541$	18.6013			0.799731			0.399865	+	0.916574i	$0.369057\pi$
$542$		0			0
$543$	6.00000	+	6.00000i	0.257485	+	0.257485i
$544$		0			0
$545$	−12.3057	+	11.2149i	−0.527120	+	0.480393i
$546$		0			0
$547$	7.22715	−	7.22715i	0.309011	−	0.309011i	−0.535515	−	0.844526i	$-0.679882\pi$
$547$	7.22715	−	7.22715i	0.309011	−	0.309011i	0.844526	+	0.535515i	$0.179882\pi$
$548$		0			0
$549$	−1.42064			−0.0606315
$550$		0			0
$551$		−	20.5348i		−	0.874812i
$552$		0			0
$553$	−6.60519	+	9.97009i	−0.280881	+	0.423971i
$554$		0			0
$555$	−5.27193	+	4.80460i	−0.223781	+	0.203944i
$556$		0			0
$557$	−0.558927	+	0.558927i	−0.0236825	+	0.0236825i	−0.718849	−	0.695166i	$-0.755331\pi$
$557$	−0.558927	+	0.558927i	−0.0236825	+	0.0236825i	0.695166	+	0.718849i	$0.255331\pi$
$558$		0			0
$559$	9.20823			0.389467
$560$		0			0
$561$	−4.35697			−0.183951
$562$		0			0
$563$	−0.702475	+	0.702475i	−0.0296058	+	0.0296058i	−0.721755	−	0.692149i	$-0.756664\pi$
$563$	−0.702475	+	0.702475i	−0.0296058	+	0.0296058i	0.692149	+	0.721755i	$0.256664\pi$
$564$		0			0
$565$	0.372772	−	8.03762i	0.0156827	−	0.338145i
$566$		0			0
$567$	−2.20563	−	1.46123i	−0.0926278	−	0.0613659i
$568$		0			0
$569$		−	9.72049i		−	0.407504i	−0.979023	−	0.203752i	$-0.934686\pi$
$569$		−	9.72049i		−	0.407504i	0.979023	−	0.203752i	$-0.0653137\pi$
$570$		0			0
$571$	0.986684			0.0412914			0.0206457	−	0.999787i	$-0.493428\pi$
$571$	0.986684			0.0412914			0.0206457	+	0.999787i	$0.493428\pi$
$572$		0			0
$573$	5.53964	−	5.53964i	0.231422	−	0.231422i
$574$		0			0
$575$	−22.4731	+	18.6504i	−0.937192	+	0.777774i
$576$		0			0
$577$	−10.3510	−	10.3510i	−0.430917	−	0.430917i	0.458024	−	0.888940i	$-0.348558\pi$
$577$	−10.3510	−	10.3510i	−0.430917	−	0.430917i	−0.888940	+	0.458024i	$0.848558\pi$
$578$		0			0
$579$	19.1792			0.797059
$580$		0			0
$581$	24.7804	−	5.03060i	1.02807	−	0.208705i
$582$		0			0
$583$	−0.796415	−	0.796415i	−0.0329841	−	0.0329841i
$584$		0			0
$585$	−0.130073	+	2.80460i	−0.00537785	+	0.115956i
$586$		0			0
$587$	21.1413	+	21.1413i	0.872594	+	0.872594i	0.992755	−	0.120160i	$-0.0383409\pi$
$587$	21.1413	+	21.1413i	0.872594	+	0.872594i	−0.120160	+	0.992755i	$0.538341\pi$
$588$		0			0
$589$		−	24.1689i		−	0.995862i
$590$		0			0
$591$			16.2339i			0.667774i
$592$		0			0
$593$	7.07816	−	7.07816i	0.290665	−	0.290665i	−0.546678	−	0.837343i	$-0.684108\pi$
$593$	7.07816	−	7.07816i	0.290665	−	0.290665i	0.837343	+	0.546678i	$0.184108\pi$
$594$		0			0
$595$	−10.4022	+	14.2233i	−0.426450	+	0.583099i
$596$		0			0
$597$	−14.2459	+	14.2459i	−0.583047	+	0.583047i
$598$		0			0
$599$		−	7.13847i		−	0.291670i	−0.989309	−	0.145835i	$-0.953413\pi$
$599$		−	7.13847i		−	0.291670i	0.989309	−	0.145835i	$-0.0465869\pi$
$600$		0			0
$601$		−	35.0829i		−	1.43106i	−0.698580	−	0.715532i	$-0.746185\pi$
$601$		−	35.0829i		−	1.43106i	0.698580	−	0.715532i	$-0.253815\pi$
$602$		0			0
$603$	−5.93012	−	5.93012i	−0.241493	−	0.241493i
$604$		0			0
$605$	13.3452	+	14.6433i	0.542560	+	0.595334i
$606$		0			0
$607$	5.36385	+	5.36385i	0.217712	+	0.217712i	0.807533	−	0.589822i	$-0.200802\pi$
$607$	5.36385	+	5.36385i	0.217712	+	0.217712i	−0.589822	+	0.807533i	$0.700802\pi$
$608$		0			0
$609$	−2.72961	−	13.4459i	−0.110609	−	0.544854i
$610$		0			0
$611$	−15.2184			−0.615670
$612$		0			0
$613$	−10.4888	−	10.4888i	−0.423639	−	0.423639i	0.462816	−	0.886454i	$-0.346839\pi$
$613$	−10.4888	−	10.4888i	−0.423639	−	0.423639i	−0.886454	+	0.462816i	$0.846839\pi$
$614$		0			0
$615$	−0.0797641	+	1.71985i	−0.00321640	+	0.0693511i
$616$		0			0
$617$	19.7986	−	19.7986i	0.797060	−	0.797060i	−0.185571	−	0.982631i	$-0.559414\pi$
$617$	19.7986	−	19.7986i	0.797060	−	0.797060i	0.982631	+	0.185571i	$0.0594135\pi$
$618$		0			0
$619$	12.0675			0.485034			0.242517	−	0.970147i	$-0.422027\pi$
$619$	12.0675			0.485034			0.242517	+	0.970147i	$0.422027\pi$
$620$		0			0
$621$		−	5.84081i		−	0.234383i
$622$		0			0
$623$	2.64655	+	1.75334i	0.106032	+	0.0702462i
$624$		0			0
$625$	−24.5717	−	4.60803i	−0.982866	−	0.184321i
$626$		0			0
$627$	4.09588	−	4.09588i	0.163574	−	0.163574i
$628$		0			0
$629$	−9.50124			−0.378839
$630$		0			0
$631$	−30.4435			−1.21194			−0.605969	−	0.795488i	$-0.707214\pi$
$631$	−30.4435			−1.21194			−0.605969	+	0.795488i	$0.707214\pi$
$632$		0			0
$633$	−8.46135	+	8.46135i	−0.336309	+	0.336309i
$634$		0			0
$635$	24.8296	+	1.15156i	0.985332	+	0.0456982i
$636$		0			0
$637$	8.14639	+	3.29946i	0.322772	+	0.130729i
$638$		0			0
$639$			7.62611i			0.301684i
$640$		0			0
$641$	36.5929			1.44533			0.722666	−	0.691198i	$-0.242917\pi$
$641$	36.5929			1.44533			0.722666	+	0.691198i	$0.242917\pi$
$642$		0			0
$643$	12.1140	−	12.1140i	0.477731	−	0.477731i	−0.426675	−	0.904405i	$-0.640315\pi$
$643$	12.1140	−	12.1140i	0.477731	−	0.477731i	0.904405	+	0.426675i	$0.140315\pi$
$644$		0			0
$645$	−11.0460	−	12.1204i	−0.434935	−	0.477240i
$646$		0			0
$647$	19.0978	+	19.0978i	0.750814	+	0.750814i	0.974631	−	0.223817i	$-0.0718519\pi$
$647$	19.0978	+	19.0978i	0.750814	+	0.750814i	−0.223817	+	0.974631i	$0.571852\pi$
$648$		0			0
$649$	4.67556			0.183532
$650$		0			0
$651$	−3.21267	−	15.8254i	−0.125915	−	0.620248i
$652$		0			0
$653$	20.3709	+	20.3709i	0.797173	+	0.797173i	0.982649	−	0.185476i	$-0.0593826\pi$
$653$	20.3709	+	20.3709i	0.797173	+	0.797173i	−0.185476	+	0.982649i	$0.559383\pi$
$654$		0			0
$655$	10.2172	−	9.31151i	0.399220	−	0.363831i
$656$		0			0
$657$	−6.81378	−	6.81378i	−0.265831	−	0.265831i
$658$		0			0
$659$			31.4882i			1.22661i	0.789847	+	0.613304i	$0.210160\pi$
$659$			31.4882i			1.22661i	−0.789847	+	0.613304i	$0.789840\pi$
$660$		0			0
$661$		−	48.1880i		−	1.87430i	−0.348931	−	0.937149i	$-0.613455\pi$
$661$		−	48.1880i		−	1.87430i	0.348931	−	0.937149i	$-0.386545\pi$
$662$		0			0
$663$	−2.64448	+	2.64448i	−0.102703	+	0.102703i
$664$		0			0
$665$	−3.59211	−	23.1499i	−0.139296	−	0.897714i
$666$		0			0
$667$	21.4174	−	21.4174i	0.829286	−	0.829286i
$668$		0			0
$669$		−	0.934668i		−	0.0361364i
$670$		0			0
$671$		−	2.07810i		−	0.0802241i
$672$		0			0
$673$	−30.6900	−	30.6900i	−1.18301	−	1.18301i	−0.978960	−	0.204055i	$-0.934588\pi$
$673$	−30.6900	−	30.6900i	−1.18301	−	1.18301i	−0.204055	−	0.978960i	$-0.565412\pi$
$674$		0			0
$675$	3.84760	−	3.19312i	0.148094	−	0.122903i
$676$		0			0
$677$	−1.54060	−	1.54060i	−0.0592101	−	0.0592101i	0.676882	−	0.736092i	$-0.263331\pi$
$677$	−1.54060	−	1.54060i	−0.0592101	−	0.0592101i	−0.736092	+	0.676882i	$0.763331\pi$
$678$		0			0
$679$	−6.46755	−	31.8587i	−0.248202	−	1.22263i
$680$		0			0
$681$	24.5348			0.940174
$682$		0			0
$683$	−14.2154	−	14.2154i	−0.543936	−	0.543936i	0.380744	−	0.924680i	$-0.375668\pi$
$683$	−14.2154	−	14.2154i	−0.543936	−	0.543936i	−0.924680	+	0.380744i	$0.875668\pi$
$684$		0			0
$685$	−28.6057	−	1.32669i	−1.09297	−	0.0506903i
$686$		0			0
$687$	−17.7330	+	17.7330i	−0.676555	+	0.676555i
$688$		0			0
$689$	−0.966772			−0.0368311
$690$		0			0
$691$		−	10.2887i		−	0.391401i	−0.980664	−	0.195700i	$-0.937302\pi$
$691$		−	10.2887i		−	0.391401i	0.980664	−	0.195700i	$-0.0626980\pi$
$692$		0			0
$693$	2.13747	−	3.22637i	0.0811959	−	0.122560i
$694$		0			0
$695$	−18.0611	−	19.8179i	−0.685098	−	0.751736i
$696$		0			0
$697$	−1.62166	+	1.62166i	−0.0614248	+	0.0614248i
$698$		0			0
$699$	3.16979			0.119892
$700$		0			0
$701$	−44.3183			−1.67388			−0.836939	−	0.547297i	$-0.815657\pi$
$701$	−44.3183			−1.67388			−0.836939	+	0.547297i	$0.815657\pi$
$702$		0			0
$703$	8.93189	−	8.93189i	0.336872	−	0.336872i
$704$		0			0
$705$	18.2556	+	20.0313i	0.687546	+	0.754422i
$706$		0			0
$707$	22.4183	−	33.8389i	0.843126	−	1.27264i
$708$		0			0
$709$			0.817976i			0.0307197i	0.999882	+	0.0153599i	$0.00488939\pi$
$709$			0.817976i			0.0307197i	−0.999882	+	0.0153599i	$0.995111\pi$
$710$		0			0
$711$	4.52029			0.169524
$712$		0			0
$713$	25.2077	−	25.2077i	0.944037	−	0.944037i
$714$		0			0
$715$	−4.10253	−	0.190269i	−0.153426	−	0.00711567i
$716$		0			0
$717$	−15.1158	−	15.1158i	−0.564509	−	0.564509i
$718$		0			0
$719$	−0.00762056			−0.000284199			−0.000142099	−	1.00000i	$-0.500045\pi$
$719$	−0.00762056			−0.000284199			−0.000142099		1.00000i	$0.500045\pi$
$720$		0			0
$721$	−30.4634	+	6.18428i	−1.13452	+	0.230315i
$722$		0			0
$723$	0.441326	+	0.441326i	0.0164131	+	0.0164131i
$724$		0			0
$725$	25.8173	+	2.39990i	0.958831	+	0.0891300i
$726$		0			0
$727$	−28.5738	−	28.5738i	−1.05974	−	1.05974i	−0.998098	−	0.0616465i	$-0.980365\pi$
$727$	−28.5738	−	28.5738i	−1.05974	−	1.05974i	−0.0616465	−	0.998098i	$-0.519635\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$		−	21.8438i		−	0.807921i
$732$		0			0
$733$	−24.1522	+	24.1522i	−0.892083	+	0.892083i	−0.994719	−	0.102636i	$-0.967272\pi$
$733$	−24.1522	+	24.1522i	−0.892083	+	0.892083i	0.102636	+	0.994719i	$0.467272\pi$
$734$		0			0
$735$	−5.42928	−	14.6807i	−0.200262	−	0.541506i
$736$		0			0
$737$	8.67452	−	8.67452i	0.319530	−	0.319530i
$738$		0			0
$739$		−	37.9522i		−	1.39609i	−0.716052	−	0.698047i	$-0.754053\pi$
$739$		−	37.9522i		−	1.39609i	0.716052	−	0.698047i	$-0.245947\pi$
$740$		0			0
$741$		−	4.97202i		−	0.182652i
$742$		0			0
$743$	18.8022	+	18.8022i	0.689784	+	0.689784i	0.962184	−	0.272400i	$-0.0878174\pi$
$743$	18.8022	+	18.8022i	0.689784	+	0.689784i	−0.272400	+	0.962184i	$0.587817\pi$
$744$		0			0
$745$	0.160024	−	0.145838i	0.00586282	−	0.00534311i
$746$		0			0
$747$	−6.75794	−	6.75794i	−0.247260	−	0.247260i
$748$		0			0
$749$	−16.0983	+	3.26807i	−0.588220	+	0.119413i
$750$		0			0
$751$	−0.105915			−0.00386490			−0.00193245	−	0.999998i	$-0.500615\pi$
$751$	−0.105915			−0.00386490			−0.00193245	+	0.999998i	$0.500615\pi$
$752$		0			0
$753$	11.5572	+	11.5572i	0.421167	+	0.421167i
$754$		0			0
$755$	−20.2657	−	22.2369i	−0.737545	−	0.809284i
$756$		0			0
$757$	3.14514	−	3.14514i	0.114312	−	0.114312i	−0.647637	−	0.761949i	$-0.724243\pi$
$757$	3.14514	−	3.14514i	0.114312	−	0.114312i	0.761949	+	0.647637i	$0.224243\pi$
$758$		0			0
$759$	8.54387			0.310123
$760$		0			0
$761$		−	35.1123i		−	1.27282i	−0.771351	−	0.636410i	$-0.780419\pi$
$761$		−	35.1123i		−	1.27282i	0.771351	−	0.636410i	$-0.219581\pi$
$762$		0			0
$763$	10.8801	−	16.4228i	0.393887	−	0.594547i
$764$		0			0
$765$	6.65306	+	0.308559i	0.240542	+	0.0111560i
$766$		0			0
$767$	2.83784	−	2.83784i	0.102469	−	0.102469i
$768$		0			0
$769$	8.16835			0.294558			0.147279	−	0.989095i	$-0.452948\pi$
$769$	8.16835			0.294558			0.147279	+	0.989095i	$0.452948\pi$
$770$		0			0
$771$	30.1304			1.08512
$772$		0			0
$773$	−2.51166	+	2.51166i	−0.0903382	+	0.0903382i	−0.750832	−	0.660494i	$-0.770347\pi$
$773$	−2.51166	+	2.51166i	−0.0903382	+	0.0903382i	0.660494	+	0.750832i	$0.270347\pi$
$774$		0			0
$775$	30.3863	+	2.82462i	1.09151	+	0.101463i
$776$		0			0
$777$	4.66118	−	7.03574i	0.167219	−	0.252406i
$778$		0			0
$779$		−	3.04897i		−	0.109241i
$780$		0			0
$781$	−11.1554			−0.399171
$782$		0			0
$783$	−3.66686	+	3.66686i	−0.131043	+	0.131043i
$784$		0			0
$785$	0.241377	−	5.20449i	0.00861510	−	0.185756i
$786$		0			0
$787$	−12.7347	−	12.7347i	−0.453943	−	0.453943i	0.442718	−	0.896661i	$-0.354014\pi$
$787$	−12.7347	−	12.7347i	−0.453943	−	0.453943i	−0.896661	+	0.442718i	$0.854014\pi$
$788$		0			0
$789$	23.1151			0.822920
$790$		0			0
$791$	1.89408	+	9.33014i	0.0673459	+	0.331742i
$792$		0			0
$793$	−1.26131	−	1.26131i	−0.0447903	−	0.0447903i
$794$		0			0
$795$	1.15972	+	1.27252i	0.0411309	+	0.0451316i
$796$		0			0
$797$	23.3462	+	23.3462i	0.826967	+	0.826967i	0.987096	−	0.160129i	$-0.0511912\pi$
$797$	23.3462	+	23.3462i	0.826967	+	0.826967i	−0.160129	+	0.987096i	$0.551191\pi$
$798$		0			0
$799$			36.1010i			1.27716i
$800$		0			0
$801$		−	1.19991i		−	0.0423967i
$802$		0			0
$803$	9.96713	−	9.96713i	0.351732	−	0.351732i
$804$		0			0
$805$	20.3984	−	27.8914i	0.718949	−	0.983043i
$806$		0			0
$807$	−11.7311	+	11.7311i	−0.412955	+	0.412955i
$808$		0			0
$809$			27.8210i			0.978135i	0.872246	+	0.489067i	$0.162663\pi$
$809$			27.8210i			0.978135i	−0.872246	+	0.489067i	$0.837337\pi$
$810$		0			0
$811$		−	5.12216i		−	0.179863i	−0.995948	−	0.0899317i	$-0.971335\pi$
$811$		−	5.12216i		−	0.179863i	0.995948	−	0.0899317i	$-0.0286649\pi$
$812$		0			0
$813$	5.50152	+	5.50152i	0.192947	+	0.192947i
$814$		0			0
$815$	1.50528	−	32.4563i	0.0527275	−	1.13690i
$816$		0			0
$817$	20.5348	+	20.5348i	0.718421	+	0.718421i
$818$		0			0
$819$	−0.660910	−	3.25560i	−0.0230941	−	0.113760i
$820$		0			0
$821$	−26.1405			−0.912308			−0.456154	−	0.889901i	$-0.650773\pi$
$821$	−26.1405			−0.912308			−0.456154	+	0.889901i	$0.650773\pi$
$822$		0			0
$823$	−13.7296	−	13.7296i	−0.478583	−	0.478583i	0.426095	−	0.904678i	$-0.359889\pi$
$823$	−13.7296	−	13.7296i	−0.478583	−	0.478583i	−0.904678	+	0.426095i	$0.859889\pi$
$824$		0			0
$825$	4.67086	+	5.62823i	0.162618	+	0.195950i
$826$		0			0
$827$	−15.7484	+	15.7484i	−0.547624	+	0.547624i	−0.925753	−	0.378129i	$-0.876568\pi$
$827$	−15.7484	+	15.7484i	−0.547624	+	0.547624i	0.378129	+	0.925753i	$0.376568\pi$
$828$		0			0
$829$	47.2996			1.64278			0.821392	−	0.570365i	$-0.193198\pi$
$829$	47.2996			1.64278			0.821392	+	0.570365i	$0.193198\pi$
$830$		0			0
$831$		−	30.1378i		−	1.04547i
$832$		0			0
$833$	7.82698	−	19.3249i	0.271189	−	0.669567i
$834$		0			0
$835$	−0.0429270	+	0.925579i	−0.00148555	+	0.0320310i
$836$		0			0
$837$	−4.31580	+	4.31580i	−0.149176	+	0.149176i
$838$		0			0
$839$	−10.8244			−0.373699			−0.186850	−	0.982389i	$-0.559828\pi$
$839$	−10.8244			−0.373699			−0.186850	+	0.982389i	$0.559828\pi$
$840$		0			0
$841$	2.10826			0.0726986
$842$		0			0
$843$	−14.9566	+	14.9566i	−0.515134	+	0.515134i
$844$		0			0
$845$	18.8795	−	17.2059i	0.649474	−	0.591901i
$846$		0			0
$847$	−19.5424	−	12.9469i	−0.671486	−	0.444860i
$848$		0			0
$849$			3.75433i			0.128848i
$850$		0			0
$851$	18.6316			0.638683
$852$		0			0
$853$	33.5751	−	33.5751i	1.14959	−	1.14959i	0.162958	−	0.986633i	$-0.447897\pi$
$853$	33.5751	−	33.5751i	1.14959	−	1.14959i	0.986633	−	0.162958i	$-0.0521034\pi$
$854$		0			0
$855$	−6.54445	+	5.96431i	−0.223815	+	0.203975i
$856$		0			0
$857$	8.92479	+	8.92479i	0.304865	+	0.304865i	0.842914	−	0.538049i	$-0.180838\pi$
$857$	8.92479	+	8.92479i	0.304865	+	0.304865i	−0.538049	+	0.842914i	$0.680838\pi$
$858$		0			0
$859$	−20.3701			−0.695020			−0.347510	−	0.937676i	$-0.612973\pi$
$859$	−20.3701			−0.695020			−0.347510	+	0.937676i	$0.612973\pi$
$860$		0			0
$861$	−0.405287	−	1.99642i	−0.0138122	−	0.0680378i
$862$		0			0
$863$	14.9014	+	14.9014i	0.507250	+	0.507250i	0.913681	−	0.406431i	$-0.133227\pi$
$863$	14.9014	+	14.9014i	0.507250	+	0.507250i	−0.406431	+	0.913681i	$0.633227\pi$
$864$		0			0
$865$	10.9041	+	0.505716i	0.370751	+	0.0171949i
$866$		0			0
$867$	−5.74759	−	5.74759i	−0.195198	−	0.195198i
$868$		0			0
$869$			6.61223i			0.224305i
$870$		0			0
$871$		−	10.5301i		−	0.356797i
$872$		0			0
$873$	−8.68829	+	8.68829i	−0.294054	+	0.294054i
$874$		0			0
$875$	29.5249	−	1.81065i	0.998125	−	0.0612112i
$876$		0			0
$877$	23.4634	−	23.4634i	0.792302	−	0.792302i	−0.189566	−	0.981868i	$-0.560708\pi$
$877$	23.4634	−	23.4634i	0.792302	−	0.792302i	0.981868	+	0.189566i	$0.0607080\pi$
$878$		0			0
$879$			2.21628i			0.0747532i
$880$		0			0
$881$			34.9639i			1.17796i	0.808147	+	0.588981i	$0.200471\pi$
$881$			34.9639i			1.17796i	−0.808147	+	0.588981i	$0.799529\pi$
$882$		0			0
$883$	−19.3814	−	19.3814i	−0.652235	−	0.652235i	0.301295	−	0.953531i	$-0.402581\pi$
$883$	−19.3814	−	19.3814i	−0.652235	−	0.652235i	−0.953531	+	0.301295i	$0.902581\pi$
$884$		0			0
$885$	−7.13953	−	0.331121i	−0.239993	−	0.0111305i
$886$		0			0
$887$	19.2450	+	19.2450i	0.646184	+	0.646184i	0.952069	−	0.305884i	$-0.0989521\pi$
$887$	19.2450	+	19.2450i	0.646184	+	0.646184i	−0.305884	+	0.952069i	$0.598952\pi$
$888$		0			0
$889$	−28.8224	+	5.85116i	−0.966673	+	0.196242i
$890$		0			0
$891$	−1.46279			−0.0490053
$892$		0			0
$893$	−33.9377	−	33.9377i	−1.13568	−	1.13568i
$894$		0			0
$895$	−3.30135	+	3.00870i	−0.110352	+	0.100570i
$896$		0			0
$897$	5.18572	−	5.18572i	0.173146	−	0.173146i
$898$		0			0
$899$	−31.6509			−1.05562
$900$		0			0
$901$			2.29338i			0.0764035i
$902$		0			0
$903$	16.1755	+	10.7163i	0.538286	+	0.356615i
$904$		0			0
$905$	14.0236	−	12.7804i	0.466159	−	0.424836i
$906$		0			0
$907$	14.8842	−	14.8842i	0.494220	−	0.494220i	−0.415413	−	0.909633i	$-0.636363\pi$
$907$	14.8842	−	14.8842i	0.494220	−	0.494220i	0.909633	+	0.415413i	$0.136363\pi$
$908$		0			0
$909$	−15.3420			−0.508863
$910$		0			0
$911$	23.7484			0.786819			0.393410	−	0.919363i	$-0.371295\pi$
$911$	23.7484			0.786819			0.393410	+	0.919363i	$0.371295\pi$
$912$		0			0
$913$	9.88545	−	9.88545i	0.327161	−	0.327161i
$914$		0			0
$915$	−0.147170	+	3.17324i	−0.00486529	+	0.104904i
$916$		0			0
$917$	−9.03357	+	13.6356i	−0.298315	+	0.450286i
$918$		0			0
$919$		−	35.7695i		−	1.17993i	−0.807430	−	0.589964i	$-0.799142\pi$
$919$		−	35.7695i		−	1.17993i	0.807430	−	0.589964i	$-0.200858\pi$
$920$		0			0
$921$	24.5439			0.808748
$922$		0			0
$923$	−6.77080	+	6.77080i	−0.222863	+	0.222863i
$924$		0			0
$925$	10.1857	+	12.2735i	0.334905	+	0.403549i
$926$		0			0
$927$	8.30776	+	8.30776i	0.272863	+	0.272863i
$928$		0			0
$929$	−5.58936			−0.183381			−0.0916905	−	0.995788i	$-0.529227\pi$
$929$	−5.58936			−0.183381			−0.0916905	+	0.995788i	$0.529227\pi$
$930$		0			0
$931$	10.8089	+	25.5248i	0.354247	+	0.836542i
$932$		0			0
$933$	21.9662	+	21.9662i	0.719140	+	0.719140i
$934$		0			0
$935$	−0.451357	+	9.73202i	−0.0147609	+	0.318271i
$936$		0			0
$937$	−20.4143	−	20.4143i	−0.666906	−	0.666906i	0.290092	−	0.956999i	$-0.406314\pi$
$937$	−20.4143	−	20.4143i	−0.666906	−	0.666906i	−0.956999	+	0.290092i	$0.906314\pi$
$938$		0			0
$939$		−	8.09533i		−	0.264181i
$940$		0			0
$941$			17.1143i			0.557910i	0.960304	+	0.278955i	$0.0899880\pi$
$941$			17.1143i			0.557910i	−0.960304	+	0.278955i	$0.910012\pi$
$942$		0			0
$943$	3.18002	−	3.18002i	0.103556	−	0.103556i
$944$		0			0
$945$	−3.49239	+	4.77527i	−0.113608	+	0.155339i
$946$		0			0
$947$	−6.82151	+	6.82151i	−0.221669	+	0.221669i	−0.809201	−	0.587532i	$-0.800100\pi$
$947$	−6.82151	+	6.82151i	−0.221669	+	0.221669i	0.587532	+	0.809201i	$0.300100\pi$
$948$		0			0
$949$		−	12.0991i		−	0.392755i
$950$		0			0
$951$		−	1.06431i		−	0.0345125i
$952$		0			0
$953$	30.7169	+	30.7169i	0.995017	+	0.995017i	0.999988	−	0.00497101i	$-0.00158233\pi$
$953$	30.7169	+	30.7169i	0.995017	+	0.995017i	−0.00497101	+	0.999988i	$0.501582\pi$
$954$		0			0
$955$	−11.7998	−	12.9476i	−0.381834	−	0.418974i
$956$		0			0
$957$	−5.36385	−	5.36385i	−0.173389	−	0.173389i
$958$		0			0
$959$	33.2058	−	6.74102i	1.07227	−	0.217679i
$960$		0			0
$961$	−6.25222			−0.201684
$962$		0			0
$963$	4.39022	+	4.39022i	0.141473	+	0.141473i
$964$		0			0
$965$	1.98685	−	42.8399i	0.0639589	−	1.37906i
$966$		0			0
$967$	−24.6730	+	24.6730i	−0.793431	+	0.793431i	−0.982050	−	0.188619i	$-0.939599\pi$
$967$	−24.6730	+	24.6730i	−0.793431	+	0.793431i	0.188619	+	0.982050i	$0.439599\pi$
$968$		0			0
$969$	−11.7946			−0.378898
$970$		0			0
$971$		−	21.2020i		−	0.680404i	−0.940352	−	0.340202i	$-0.889504\pi$
$971$		−	21.2020i		−	0.680404i	0.940352	−	0.340202i	$-0.110496\pi$
$972$		0			0
$973$	26.4483	+	17.5220i	0.847895	+	0.561731i
$974$		0			0
$975$	6.25106	+	0.581079i	0.200194	+	0.0186094i
$976$		0			0
$977$	8.19657	−	8.19657i	0.262231	−	0.262231i	−0.563729	−	0.825960i	$-0.690634\pi$
$977$	8.19657	−	8.19657i	0.262231	−	0.262231i	0.825960	+	0.563729i	$0.190634\pi$
$978$		0			0
$979$	1.75521			0.0560969
$980$		0			0
$981$	−7.44587			−0.237728
$982$		0			0
$983$	1.74914	−	1.74914i	0.0557891	−	0.0557891i	−0.678662	−	0.734451i	$-0.737440\pi$
$983$	1.74914	−	1.74914i	0.0557891	−	0.0557891i	0.734451	+	0.678662i	$0.237440\pi$
$984$		0			0
$985$	36.2612	+	1.68174i	1.15538	+	0.0535847i
$986$		0			0
$987$	−26.7331	−	17.7107i	−0.850924	−	0.563738i
$988$		0			0
$989$			42.8348i			1.36207i
$990$		0			0
$991$	37.1253			1.17932			0.589662	−	0.807650i	$-0.299261\pi$
$991$	37.1253			1.17932			0.589662	+	0.807650i	$0.299261\pi$
$992$		0			0
$993$	−11.1781	+	11.1781i	−0.354727	+	0.354727i
$994$		0			0
$995$	30.3449	+	33.2964i	0.961996	+	1.05557i
$996$		0			0
$997$	−40.5538	−	40.5538i	−1.28435	−	1.28435i	−0.938166	−	0.346186i	$-0.887476\pi$
$997$	−40.5538	−	40.5538i	−1.28435	−	1.28435i	−0.346186	−	0.938166i	$-0.612524\pi$
$998$		0			0
$999$	−3.18990			−0.100924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.cz.d.433.6		16
4.3	odd	2		105.2.m.a.13.1	✓	16
5.2	odd	4	inner	1680.2.cz.d.97.3		16
7.6	odd	2	inner	1680.2.cz.d.433.3		16
12.11	even	2		315.2.p.e.118.8		16
20.3	even	4		525.2.m.b.307.7		16
20.7	even	4		105.2.m.a.97.2	yes	16
20.19	odd	2		525.2.m.b.118.8		16
28.3	even	6		735.2.v.a.313.1		32
28.11	odd	6		735.2.v.a.313.2		32
28.19	even	6		735.2.v.a.178.8		32
28.23	odd	6		735.2.v.a.178.7		32
28.27	even	2		105.2.m.a.13.2	yes	16
35.27	even	4	inner	1680.2.cz.d.97.6		16
60.47	odd	4		315.2.p.e.307.7		16
84.83	odd	2		315.2.p.e.118.7		16
140.27	odd	4		105.2.m.a.97.1	yes	16
140.47	odd	12		735.2.v.a.472.2		32
140.67	even	12		735.2.v.a.607.8		32
140.83	odd	4		525.2.m.b.307.8		16
140.87	odd	12		735.2.v.a.607.7		32
140.107	even	12		735.2.v.a.472.1		32
140.139	even	2		525.2.m.b.118.7		16
420.167	even	4		315.2.p.e.307.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.1	✓	16	4.3	odd	2
105.2.m.a.13.2	yes	16	28.27	even	2
105.2.m.a.97.1	yes	16	140.27	odd	4
105.2.m.a.97.2	yes	16	20.7	even	4
315.2.p.e.118.7		16	84.83	odd	2
315.2.p.e.118.8		16	12.11	even	2
315.2.p.e.307.7		16	60.47	odd	4
315.2.p.e.307.8		16	420.167	even	4
525.2.m.b.118.7		16	140.139	even	2
525.2.m.b.118.8		16	20.19	odd	2
525.2.m.b.307.7		16	20.3	even	4
525.2.m.b.307.8		16	140.83	odd	4
735.2.v.a.178.7		32	28.23	odd	6
735.2.v.a.178.8		32	28.19	even	6
735.2.v.a.313.1		32	28.3	even	6
735.2.v.a.313.2		32	28.11	odd	6
735.2.v.a.472.1		32	140.107	even	12
735.2.v.a.472.2		32	140.47	odd	12
735.2.v.a.607.7		32	140.87	odd	12
735.2.v.a.607.8		32	140.67	even	12
1680.2.cz.d.97.3		16	5.2	odd	4	inner
1680.2.cz.d.97.6		16	35.27	even	4	inner
1680.2.cz.d.433.3		16	7.6	odd	2	inner
1680.2.cz.d.433.6		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.cz (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.50619 - 1.65269i) q^{5} +(2.20563 + 1.46123i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(-1.50619 - 1.65269i) q^{5} +(2.20563 + 1.46123i) q^{7} -1.00000i q^{9} +1.46279 q^{11} +(0.887844 - 0.887844i) q^{13} +(-2.23367 - 0.103594i) q^{15} +(-2.10614 - 2.10614i) q^{17} +3.95987 q^{19} +(2.59286 - 0.526369i) q^{21} +(4.13007 + 4.13007i) q^{23} +(-0.462789 + 4.97854i) q^{25} +(-0.707107 - 0.707107i) q^{27} -5.18572i q^{29} -6.10346i q^{31} +(1.03435 - 1.03435i) q^{33} +(-0.907129 - 5.84612i) q^{35} +(2.25560 - 2.25560i) q^{37} -1.25560i q^{39} -0.769968i q^{41} +(5.18572 + 5.18572i) q^{43} +(-1.65269 + 1.50619i) q^{45} +(-8.57041 - 8.57041i) q^{47} +(2.72961 + 6.44587i) q^{49} -2.97854 q^{51} +(-0.544449 - 0.544449i) q^{53} +(-2.20324 - 2.41754i) q^{55} +(2.80005 - 2.80005i) q^{57} +3.19633 q^{59} -1.42064i q^{61} +(1.46123 - 2.20563i) q^{63} +(-2.80460 - 0.130073i) q^{65} +(5.93012 - 5.93012i) q^{67} +5.84081 q^{69} -7.62611 q^{71} +(6.81378 - 6.81378i) q^{73} +(3.19312 + 3.84760i) q^{75} +(3.22637 + 2.13747i) q^{77} +4.52029i q^{79} -1.00000 q^{81} +(6.75794 - 6.75794i) q^{83} +(-0.308559 + 6.65306i) q^{85} +(-3.66686 - 3.66686i) q^{87} +1.19991 q^{89} +(3.25560 - 0.660910i) q^{91} +(-4.31580 - 4.31580i) q^{93} +(-5.96431 - 6.54445i) q^{95} +(-8.68829 - 8.68829i) q^{97} -1.46279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 16 q^{11} - 8 q^{15} + 8 q^{21} + 40 q^{23} + 8 q^{35} + 32 q^{37} + 16 q^{43} + 16 q^{51} + 24 q^{53} + 8 q^{57} - 8 q^{63} + 40 q^{65} + 32 q^{67} - 64 q^{71} - 24 q^{77} - 16 q^{81} + 48 q^{85} + 48 q^{91} + 24 q^{93} + 72 q^{95}+O(q^{100}) \) 16 * q + 8 * q^7 + 16 * q^11 - 8 * q^15 + 8 * q^21 + 40 * q^23 + 8 * q^35 + 32 * q^37 + 16 * q^43 + 16 * q^51 + 24 * q^53 + 8 * q^57 - 8 * q^63 + 40 * q^65 + 32 * q^67 - 64 * q^71 - 24 * q^77 - 16 * q^81 + 48 * q^85 + 48 * q^91 + 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

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Representations

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Database

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