LMFDB - Embedded newform 1344.2.s.d.239.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.16
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.d.911.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.861124 - 1.50282i) q^{3} +(1.19856 + 1.19856i) q^{5} -1.00000 q^{7} +(-1.51693 - 2.58823i) q^{9} +O(q^{10})$	\(q+(0.861124 - 1.50282i) q^{3} +(1.19856 + 1.19856i) q^{5} -1.00000 q^{7} +(-1.51693 - 2.58823i) q^{9} +(-1.10347 + 1.10347i) q^{11} +(0.418588 + 0.418588i) q^{13} +(2.83333 - 0.769110i) q^{15} -4.01838i q^{17} +(4.91902 - 4.91902i) q^{19} +(-0.861124 + 1.50282i) q^{21} +3.26657i q^{23} -2.12691i q^{25} +(-5.19590 + 0.0508894i) q^{27} +(4.61925 - 4.61925i) q^{29} -7.31001i q^{31} +(0.708095 + 2.60855i) q^{33} +(-1.19856 - 1.19856i) q^{35} +(2.61222 - 2.61222i) q^{37} +(0.989519 - 0.268606i) q^{39} +8.46457 q^{41} +(-3.91816 - 3.91816i) q^{43} +(1.28401 - 4.92028i) q^{45} +8.08425 q^{47} +1.00000 q^{49} +(-6.03891 - 3.46033i) q^{51} +(1.78619 + 1.78619i) q^{53} -2.64516 q^{55} +(-3.15651 - 11.6283i) q^{57} +(-5.55480 + 5.55480i) q^{59} +(0.325351 + 0.325351i) q^{61} +(1.51693 + 2.58823i) q^{63} +1.00341i q^{65} +(1.41837 - 1.41837i) q^{67} +(4.90907 + 2.81292i) q^{69} +11.7001i q^{71} +2.89479i q^{73} +(-3.19636 - 1.83153i) q^{75} +(1.10347 - 1.10347i) q^{77} +15.6711i q^{79} +(-4.39784 + 7.85233i) q^{81} +(-9.34150 - 9.34150i) q^{83} +(4.81628 - 4.81628i) q^{85} +(-2.96415 - 10.9196i) q^{87} -6.70359 q^{89} +(-0.418588 - 0.418588i) q^{91} +(-10.9856 - 6.29482i) q^{93} +11.7915 q^{95} -3.43505 q^{97} +(4.52994 + 1.18215i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{7}+O(q^{10}) $ 48 * q - 48 * q^7	$ 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) $ 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.861124	−	1.50282i	0.497170	−	0.867653i
$3$	0.861124	−	1.50282i	0.497170	−	0.867653i
$4$		0			0
$5$	1.19856	+	1.19856i	0.536012	+	0.536012i	0.922355	−	0.386343i	$-0.126262\pi$
$5$	1.19856	+	1.19856i	0.536012	+	0.536012i	−0.386343	+	0.922355i	$0.626262\pi$
$6$		0			0
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$		0			0
$9$	−1.51693	−	2.58823i	−0.505644	−	0.862742i
$10$		0			0
$11$	−1.10347	+	1.10347i	−0.332710	+	0.332710i	−0.853615	−	0.520905i	$-0.825595\pi$
$11$	−1.10347	+	1.10347i	−0.332710	+	0.332710i	0.520905	+	0.853615i	$0.325595\pi$
$12$		0			0
$13$	0.418588	+	0.418588i	0.116096	+	0.116096i	0.762768	−	0.646672i	$-0.223840\pi$
$13$	0.418588	+	0.418588i	0.116096	+	0.116096i	−0.646672	+	0.762768i	$0.723840\pi$
$14$		0			0
$15$	2.83333	−	0.769110i	0.731562	−	0.198583i
$16$		0			0
$17$		−	4.01838i		−	0.974601i	−0.873234	−	0.487301i	$-0.837982\pi$
$17$		−	4.01838i		−	0.974601i	0.873234	−	0.487301i	$-0.162018\pi$
$18$		0			0
$19$	4.91902	−	4.91902i	1.12850	−	1.12850i	0.138080	−	0.990421i	$-0.455907\pi$
$19$	4.91902	−	4.91902i	1.12850	−	1.12850i	0.990421	−	0.138080i	$-0.0440930\pi$
$20$		0			0
$21$	−0.861124	+	1.50282i	−0.187913	+	0.327942i
$22$		0			0
$23$			3.26657i			0.681127i	0.940221	+	0.340564i	$0.110618\pi$
$23$			3.26657i			0.681127i	−0.940221	+	0.340564i	$0.889382\pi$
$24$		0			0
$25$		−	2.12691i		−	0.425381i
$26$		0			0
$27$	−5.19590	+	0.0508894i	−0.999952	+	0.00979366i
$28$		0			0
$29$	4.61925	−	4.61925i	0.857772	−	0.857772i	−0.133303	−	0.991075i	$-0.542558\pi$
$29$	4.61925	−	4.61925i	0.857772	−	0.857772i	0.991075	+	0.133303i	$0.0425583\pi$
$30$		0			0
$31$		−	7.31001i		−	1.31292i	−0.754363	−	0.656458i	$-0.772054\pi$
$31$		−	7.31001i		−	1.31292i	0.754363	−	0.656458i	$-0.227946\pi$
$32$		0			0
$33$	0.708095	+	2.60855i	0.123263	+	0.454091i
$34$		0			0
$35$	−1.19856	−	1.19856i	−0.202594	−	0.202594i
$36$		0			0
$37$	2.61222	−	2.61222i	0.429446	−	0.429446i	−0.458994	−	0.888440i	$-0.651790\pi$
$37$	2.61222	−	2.61222i	0.429446	−	0.429446i	0.888440	+	0.458994i	$0.151790\pi$
$38$		0			0
$39$	0.989519	−	0.268606i	0.158450	−	0.0430114i
$40$		0			0
$41$	8.46457			1.32194			0.660972	−	0.750411i	$-0.270144\pi$
$41$	8.46457			1.32194			0.660972	+	0.750411i	$0.270144\pi$
$42$		0			0
$43$	−3.91816	−	3.91816i	−0.597514	−	0.597514i	0.342136	−	0.939650i	$-0.388850\pi$
$43$	−3.91816	−	3.91816i	−0.597514	−	0.597514i	−0.939650	+	0.342136i	$0.888850\pi$
$44$		0			0
$45$	1.28401	−	4.92028i	0.191409	−	0.733472i
$46$		0			0
$47$	8.08425			1.17921			0.589604	−	0.807692i	$-0.299284\pi$
$47$	8.08425			1.17921			0.589604	+	0.807692i	$0.299284\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−6.03891	−	3.46033i	−0.845616	−	0.484543i
$52$		0			0
$53$	1.78619	+	1.78619i	0.245352	+	0.245352i	0.819060	−	0.573708i	$-0.194496\pi$
$53$	1.78619	+	1.78619i	0.245352	+	0.245352i	−0.573708	+	0.819060i	$0.694496\pi$
$54$		0			0
$55$	−2.64516			−0.356674
$56$		0			0
$57$	−3.15651	−	11.6283i	−0.418090	−	1.54020i
$58$		0			0
$59$	−5.55480	+	5.55480i	−0.723173	+	0.723173i	−0.969250	−	0.246077i	$-0.920858\pi$
$59$	−5.55480	+	5.55480i	−0.723173	+	0.723173i	0.246077	+	0.969250i	$0.420858\pi$
$60$		0			0
$61$	0.325351	+	0.325351i	0.0416569	+	0.0416569i	0.727628	−	0.685972i	$-0.240623\pi$
$61$	0.325351	+	0.325351i	0.0416569	+	0.0416569i	−0.685972	+	0.727628i	$0.740623\pi$
$62$		0			0
$63$	1.51693	+	2.58823i	0.191115	+	0.326086i
$64$		0			0
$65$			1.00341i			0.124457i
$66$		0			0
$67$	1.41837	−	1.41837i	0.173282	−	0.173282i	−0.615138	−	0.788420i	$-0.710900\pi$
$67$	1.41837	−	1.41837i	0.173282	−	0.173282i	0.788420	+	0.615138i	$0.210900\pi$
$68$		0			0
$69$	4.90907	+	2.81292i	0.590982	+	0.338636i
$70$		0			0
$71$			11.7001i			1.38855i	0.719712	+	0.694273i	$0.244274\pi$
$71$			11.7001i			1.38855i	−0.719712	+	0.694273i	$0.755726\pi$
$72$		0			0
$73$			2.89479i			0.338809i	0.985547	+	0.169405i	$0.0541844\pi$
$73$			2.89479i			0.338809i	−0.985547	+	0.169405i	$0.945816\pi$
$74$		0			0
$75$	−3.19636	−	1.83153i	−0.369084	−	0.211487i
$76$		0			0
$77$	1.10347	−	1.10347i	0.125753	−	0.125753i
$78$		0			0
$79$			15.6711i			1.76313i	0.472059	+	0.881567i	$0.343511\pi$
$79$			15.6711i			1.76313i	−0.472059	+	0.881567i	$0.656489\pi$
$80$		0			0
$81$	−4.39784	+	7.85233i	−0.488649	+	0.872481i
$82$		0			0
$83$	−9.34150	−	9.34150i	−1.02536	−	1.02536i	−0.999670	−	0.0256926i	$-0.991821\pi$
$83$	−9.34150	−	9.34150i	−1.02536	−	1.02536i	−0.0256926	−	0.999670i	$-0.508179\pi$
$84$		0			0
$85$	4.81628	−	4.81628i	0.522398	−	0.522398i
$86$		0			0
$87$	−2.96415	−	10.9196i	−0.317790	−	1.17071i
$88$		0			0
$89$	−6.70359			−0.710579			−0.355289	−	0.934756i	$-0.615618\pi$
$89$	−6.70359			−0.710579			−0.355289	+	0.934756i	$0.615618\pi$
$90$		0			0
$91$	−0.418588	−	0.418588i	−0.0438800	−	0.0438800i
$92$		0			0
$93$	−10.9856	−	6.29482i	−1.13916	−	0.652742i
$94$		0			0
$95$	11.7915			1.20978
$96$		0			0
$97$	−3.43505			−0.348777			−0.174388	−	0.984677i	$-0.555795\pi$
$97$	−3.43505			−0.348777			−0.174388	+	0.984677i	$0.555795\pi$
$98$		0			0
$99$	4.52994	+	1.18215i	0.455276	+	0.118810i
$100$		0			0
$101$	−9.10445	−	9.10445i	−0.905926	−	0.905926i	0.0900140	−	0.995940i	$-0.471309\pi$
$101$	−9.10445	−	9.10445i	−0.905926	−	0.905926i	−0.995940	+	0.0900140i	$0.971309\pi$
$102$		0			0
$103$	8.02126			0.790358			0.395179	−	0.918604i	$-0.370683\pi$
$103$	8.02126			0.790358			0.395179	+	0.918604i	$0.370683\pi$
$104$		0			0
$105$	−2.83333	+	0.769110i	−0.276504	+	0.0750575i
$106$		0			0
$107$	6.48216	−	6.48216i	0.626654	−	0.626654i	−0.320571	−	0.947225i	$-0.603875\pi$
$107$	6.48216	−	6.48216i	0.626654	−	0.626654i	0.947225	+	0.320571i	$0.103875\pi$
$108$		0			0
$109$	3.96122	+	3.96122i	0.379416	+	0.379416i	0.870891	−	0.491476i	$-0.163542\pi$
$109$	3.96122	+	3.96122i	0.379416	+	0.379416i	−0.491476	+	0.870891i	$0.663542\pi$
$110$		0			0
$111$	−1.67625	−	6.17513i	−0.159102	−	0.586118i
$112$		0			0
$113$			11.3357i			1.06637i	0.845998	+	0.533186i	$0.179005\pi$
$113$			11.3357i			1.06637i	−0.845998	+	0.533186i	$0.820995\pi$
$114$		0			0
$115$	−3.91518	+	3.91518i	−0.365093	+	0.365093i
$116$		0			0
$117$	0.448432	−	1.71837i	0.0414575	−	0.158863i
$118$		0			0
$119$			4.01838i			0.368365i
$120$		0			0
$121$			8.56469i			0.778608i
$122$		0			0
$123$	7.28904	−	12.7207i	0.657231	−	1.14699i
$124$		0			0
$125$	8.54203	−	8.54203i	0.764022	−	0.764022i
$126$		0			0
$127$		−	11.8859i		−	1.05471i	−0.849646	−	0.527353i	$-0.823185\pi$
$127$		−	11.8859i		−	1.05471i	0.849646	−	0.527353i	$-0.176815\pi$
$128$		0			0
$129$	−9.26231	+	2.51427i	−0.815501	+	0.221369i
$130$		0			0
$131$	−2.46217	−	2.46217i	−0.215121	−	0.215121i	0.591318	−	0.806439i	$-0.298608\pi$
$131$	−2.46217	−	2.46217i	−0.215121	−	0.215121i	−0.806439	+	0.591318i	$0.798608\pi$
$132$		0			0
$133$	−4.91902	+	4.91902i	−0.426533	+	0.426533i
$134$		0			0
$135$	−6.28860	−	6.16661i	−0.541236	−	0.530737i
$136$		0			0
$137$	−18.6319			−1.59183			−0.795916	−	0.605407i	$-0.793010\pi$
$137$	−18.6319			−1.59183			−0.795916	+	0.605407i	$0.793010\pi$
$138$		0			0
$139$	15.8218	+	15.8218i	1.34199	+	1.34199i	0.894078	+	0.447912i	$0.147832\pi$
$139$	15.8218	+	15.8218i	1.34199	+	1.34199i	0.447912	+	0.894078i	$0.352168\pi$
$140$		0			0
$141$	6.96154	−	12.1492i	0.586267	−	1.02314i
$142$		0			0
$143$	−0.923803			−0.0772523
$144$		0			0
$145$	11.0729			0.919553
$146$		0			0
$147$	0.861124	−	1.50282i	0.0710243	−	0.123950i
$148$		0			0
$149$	−14.7316	−	14.7316i	−1.20686	−	1.20686i	−0.972039	−	0.234819i	$-0.924550\pi$
$149$	−14.7316	−	14.7316i	−1.20686	−	1.20686i	−0.234819	−	0.972039i	$-0.575450\pi$
$150$		0			0
$151$	−7.80033			−0.634782			−0.317391	−	0.948295i	$-0.602807\pi$
$151$	−7.80033			−0.634782			−0.317391	+	0.948295i	$0.602807\pi$
$152$		0			0
$153$	−10.4005	+	6.09561i	−0.840830	+	0.492801i
$154$		0			0
$155$	8.76148	−	8.76148i	0.703739	−	0.703739i
$156$		0			0
$157$	3.31101	+	3.31101i	0.264248	+	0.264248i	0.826777	−	0.562530i	$-0.190172\pi$
$157$	3.31101	+	3.31101i	0.264248	+	0.264248i	−0.562530	+	0.826777i	$0.690172\pi$
$158$		0			0
$159$	4.22245	−	1.14619i	0.334862	−	0.0908988i
$160$		0			0
$161$		−	3.26657i		−	0.257442i
$162$		0			0
$163$	−6.35075	+	6.35075i	−0.497429	+	0.497429i	−0.910637	−	0.413207i	$-0.864408\pi$
$163$	−6.35075	+	6.35075i	−0.497429	+	0.497429i	0.413207	+	0.910637i	$0.364408\pi$
$164$		0			0
$165$	−2.27781	+	3.97520i	−0.177327	+	0.309469i
$166$		0			0
$167$			23.1146i			1.78866i	0.447407	+	0.894331i	$0.352348\pi$
$167$			23.1146i			1.78866i	−0.447407	+	0.894331i	$0.647652\pi$
$168$		0			0
$169$		−	12.6496i		−	0.973044i
$170$		0			0
$171$	−20.1934	−	5.26973i	−1.54422	−	0.402986i
$172$		0			0
$173$	−11.0546	+	11.0546i	−0.840464	+	0.840464i	−0.988919	−	0.148456i	$-0.952570\pi$
$173$	−11.0546	+	11.0546i	−0.840464	+	0.840464i	0.148456	+	0.988919i	$0.452570\pi$
$174$		0			0
$175$			2.12691i			0.160779i
$176$		0			0
$177$	3.56449	+	13.1312i	0.267923	+	0.987003i
$178$		0			0
$179$	−10.1184	−	10.1184i	−0.756287	−	0.756287i	0.219357	−	0.975645i	$-0.429604\pi$
$179$	−10.1184	−	10.1184i	−0.756287	−	0.756287i	−0.975645	+	0.219357i	$0.929604\pi$
$180$		0			0
$181$	4.85885	−	4.85885i	0.361156	−	0.361156i	−0.503083	−	0.864238i	$-0.667801\pi$
$181$	4.85885	−	4.85885i	0.361156	−	0.361156i	0.864238	+	0.503083i	$0.167801\pi$
$182$		0			0
$183$	0.769110	−	0.208776i	0.0568543	−	0.0154332i
$184$		0			0
$185$	6.26180			0.460377
$186$		0			0
$187$	4.43419	+	4.43419i	0.324260	+	0.324260i
$188$		0			0
$189$	5.19590	−	0.0508894i	0.377946	−	0.00370166i
$190$		0			0
$191$	−2.01613			−0.145882			−0.0729409	−	0.997336i	$-0.523238\pi$
$191$	−2.01613			−0.145882			−0.0729409	+	0.997336i	$0.523238\pi$
$192$		0			0
$193$	−19.8255			−1.42707			−0.713534	−	0.700621i	$-0.752906\pi$
$193$	−19.8255			−1.42707			−0.713534	+	0.700621i	$0.752906\pi$
$194$		0			0
$195$	1.50794	+	0.864057i	0.107986	+	0.0618764i
$196$		0			0
$197$	6.81358	+	6.81358i	0.485448	+	0.485448i	0.906866	−	0.421419i	$-0.138468\pi$
$197$	6.81358	+	6.81358i	0.485448	+	0.485448i	−0.421419	+	0.906866i	$0.638468\pi$
$198$		0			0
$199$	19.4422			1.37822			0.689110	−	0.724656i	$-0.258001\pi$
$199$	19.4422			1.37822			0.689110	+	0.724656i	$0.258001\pi$
$200$		0			0
$201$	−0.910163	−	3.35295i	−0.0641980	−	0.236499i
$202$		0			0
$203$	−4.61925	+	4.61925i	−0.324207	+	0.324207i
$204$		0			0
$205$	10.1453	+	10.1453i	0.708578	+	0.708578i
$206$		0			0
$207$	8.45463	−	4.95517i	0.587638	−	0.344408i
$208$		0			0
$209$			10.8560i			0.750927i
$210$		0			0
$211$	17.4276	−	17.4276i	1.19977	−	1.19977i	0.225530	−	0.974236i	$-0.427589\pi$
$211$	17.4276	−	17.4276i	1.19977	−	1.19977i	0.974236	−	0.225530i	$-0.0724115\pi$
$212$		0			0
$213$	17.5831	+	10.0752i	1.20478	+	0.690344i
$214$		0			0
$215$		−	9.39231i		−	0.640550i
$216$		0			0
$217$			7.31001i			0.496236i
$218$		0			0
$219$	4.35034	+	2.49277i	0.293969	+	0.168446i
$220$		0			0
$221$	1.68205	−	1.68205i	0.113147	−	0.113147i
$222$		0			0
$223$			11.5112i			0.770849i	0.922739	+	0.385425i	$0.125945\pi$
$223$			11.5112i			0.770849i	−0.922739	+	0.385425i	$0.874055\pi$
$224$		0			0
$225$	−5.50492	+	3.22637i	−0.366995	+	0.215091i
$226$		0			0
$227$	4.19702	+	4.19702i	0.278566	+	0.278566i	0.832536	−	0.553970i	$-0.186888\pi$
$227$	4.19702	+	4.19702i	0.278566	+	0.278566i	−0.553970	+	0.832536i	$0.686888\pi$
$228$		0			0
$229$	−5.34847	+	5.34847i	−0.353437	+	0.353437i	−0.861387	−	0.507950i	$-0.830404\pi$
$229$	−5.34847	+	5.34847i	−0.353437	+	0.353437i	0.507950	+	0.861387i	$0.330404\pi$
$230$		0			0
$231$	−0.708095	−	2.60855i	−0.0465892	−	0.171630i
$232$		0			0
$233$	27.0374			1.77128			0.885640	−	0.464372i	$-0.153720\pi$
$233$	27.0374			1.77128			0.885640	+	0.464372i	$0.153720\pi$
$234$		0			0
$235$	9.68946	+	9.68946i	0.632070	+	0.632070i
$236$		0			0
$237$	23.5508	+	13.4947i	1.52979	+	0.876577i
$238$		0			0
$239$	−2.75475			−0.178190			−0.0890950	−	0.996023i	$-0.528397\pi$
$239$	−2.75475			−0.178190			−0.0890950	+	0.996023i	$0.528397\pi$
$240$		0			0
$241$	14.4893			0.933336			0.466668	−	0.884432i	$-0.345454\pi$
$241$	14.4893			0.933336			0.466668	+	0.884432i	$0.345454\pi$
$242$		0			0
$243$	8.01354	+	13.3710i	0.514069	+	0.857749i
$244$		0			0
$245$	1.19856	+	1.19856i	0.0765732	+	0.0765732i
$246$		0			0
$247$	4.11809			0.262028
$248$		0			0
$249$	−22.0828	+	5.99440i	−1.39944	+	0.379879i
$250$		0			0
$251$	1.46929	−	1.46929i	0.0927408	−	0.0927408i	−0.659214	−	0.751955i	$-0.729111\pi$
$251$	1.46929	−	1.46929i	0.0927408	−	0.0927408i	0.751955	+	0.659214i	$0.229111\pi$
$252$		0			0
$253$	−3.60458	−	3.60458i	−0.226618	−	0.226618i
$254$		0			0
$255$	−3.09058	−	11.3854i	−0.193540	−	0.712981i
$256$		0			0
$257$			10.5661i			0.659092i	0.944139	+	0.329546i	$0.106896\pi$
$257$			10.5661i			0.659092i	−0.944139	+	0.329546i	$0.893104\pi$
$258$		0			0
$259$	−2.61222	+	2.61222i	−0.162315	+	0.162315i
$260$		0			0
$261$	−18.9627	−	4.94858i	−1.17376	−	0.306309i
$262$		0			0
$263$		−	3.52053i		−	0.217085i	−0.994092	−	0.108543i	$-0.965382\pi$
$263$		−	3.52053i		−	0.217085i	0.994092	−	0.108543i	$-0.0346184\pi$
$264$		0			0
$265$			4.28171i			0.263024i
$266$		0			0
$267$	−5.77262	+	10.0743i	−0.353279	+	0.616536i
$268$		0			0
$269$	−2.95588	+	2.95588i	−0.180223	+	0.180223i	−0.791453	−	0.611230i	$-0.790675\pi$
$269$	−2.95588	+	2.95588i	−0.180223	+	0.180223i	0.611230	+	0.791453i	$0.290675\pi$
$270$		0			0
$271$			26.4875i			1.60900i	0.593953	+	0.804500i	$0.297566\pi$
$271$			26.4875i			1.60900i	−0.593953	+	0.804500i	$0.702434\pi$
$272$		0			0
$273$	−0.989519	+	0.268606i	−0.0598884	+	0.0162568i
$274$		0			0
$275$	2.34699	+	2.34699i	0.141529	+	0.141529i
$276$		0			0
$277$	−0.907324	+	0.907324i	−0.0545158	+	0.0545158i	−0.733839	−	0.679323i	$-0.762273\pi$
$277$	−0.907324	+	0.907324i	−0.0545158	+	0.0545158i	0.679323	+	0.733839i	$0.262273\pi$
$278$		0			0
$279$	−18.9200	+	11.0888i	−1.13271	+	0.663868i
$280$		0			0
$281$	22.5004			1.34226			0.671130	−	0.741340i	$-0.265809\pi$
$281$	22.5004			1.34226			0.671130	+	0.741340i	$0.265809\pi$
$282$		0			0
$283$	0.463851	+	0.463851i	0.0275731	+	0.0275731i	0.720759	−	0.693186i	$-0.243793\pi$
$283$	0.463851	+	0.463851i	0.0275731	+	0.0275731i	−0.693186	+	0.720759i	$0.743793\pi$
$284$		0			0
$285$	10.1539	−	17.7205i	0.601467	−	1.04967i
$286$		0			0
$287$	−8.46457			−0.499648
$288$		0			0
$289$	0.852586			0.0501521
$290$		0			0
$291$	−2.95801	+	5.16226i	−0.173401	+	0.302617i
$292$		0			0
$293$	−14.0097	−	14.0097i	−0.818455	−	0.818455i	0.167429	−	0.985884i	$-0.446454\pi$
$293$	−14.0097	−	14.0097i	−0.818455	−	0.818455i	−0.985884	+	0.167429i	$0.946454\pi$
$294$		0			0
$295$	−13.3155			−0.775259
$296$		0			0
$297$	5.67739	−	5.78970i	0.329436	−	0.335953i
$298$		0			0
$299$	−1.36735	+	1.36735i	−0.0790758	+	0.0790758i
$300$		0			0
$301$	3.91816	+	3.91816i	0.225839	+	0.225839i
$302$		0			0
$303$	−21.5224	+	5.84228i	−1.23643	+	0.335630i
$304$		0			0
$305$			0.779905i			0.0446572i
$306$		0			0
$307$	−13.0226	+	13.0226i	−0.743236	+	0.743236i	−0.973199	−	0.229963i	$-0.926139\pi$
$307$	−13.0226	+	13.0226i	−0.743236	+	0.743236i	0.229963	+	0.973199i	$0.426139\pi$
$308$		0			0
$309$	6.90730	−	12.0545i	0.392942	−	0.685757i
$310$		0			0
$311$		−	6.02505i		−	0.341649i	−0.985301	−	0.170825i	$-0.945357\pi$
$311$		−	6.02505i		−	0.341649i	0.985301	−	0.170825i	$-0.0546431\pi$
$312$		0			0
$313$			23.2145i			1.31216i	0.754691	+	0.656080i	$0.227787\pi$
$313$			23.2145i			1.31216i	−0.754691	+	0.656080i	$0.772213\pi$
$314$		0			0
$315$	−1.28401	+	4.92028i	−0.0723459	+	0.277226i
$316$		0			0
$317$	−12.0141	+	12.0141i	−0.674781	+	0.674781i	−0.958814	−	0.284034i	$-0.908327\pi$
$317$	−12.0141	+	12.0141i	−0.674781	+	0.674781i	0.284034	+	0.958814i	$0.408327\pi$
$318$		0			0
$319$			10.1944i			0.570779i
$320$		0			0
$321$	−4.15957	−	15.3234i	−0.232165	−	0.855271i
$322$		0			0
$323$	−19.7665	−	19.7665i	−1.09984	−	1.09984i
$324$		0			0
$325$	0.890298	−	0.890298i	0.0493849	−	0.0493849i
$326$		0			0
$327$	9.36409	−	2.54189i	0.517835	−	0.140567i
$328$		0			0
$329$	−8.08425			−0.445699
$330$		0			0
$331$	6.71058	+	6.71058i	0.368847	+	0.368847i	0.867057	−	0.498210i	$-0.166009\pi$
$331$	6.71058	+	6.71058i	0.368847	+	0.368847i	−0.498210	+	0.867057i	$0.666009\pi$
$332$		0			0
$333$	−10.7236	−	2.79846i	−0.587648	−	0.153355i
$334$		0			0
$335$	3.40001			0.185762
$336$		0			0
$337$	12.9404			0.704908			0.352454	−	0.935829i	$-0.385347\pi$
$337$	12.9404			0.704908			0.352454	+	0.935829i	$0.385347\pi$
$338$		0			0
$339$	17.0355	+	9.76143i	0.925241	+	0.530168i
$340$		0			0
$341$	8.06641	+	8.06641i	0.436820	+	0.436820i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$		0			0
$345$	2.51236	+	9.25527i	0.135261	+	0.498287i
$346$		0			0
$347$	5.37894	−	5.37894i	0.288756	−	0.288756i	−0.547832	−	0.836588i	$-0.684547\pi$
$347$	5.37894	−	5.37894i	0.288756	−	0.288756i	0.836588	+	0.547832i	$0.184547\pi$
$348$		0			0
$349$	1.76640	+	1.76640i	0.0945535	+	0.0945535i	0.752801	−	0.658248i	$-0.228702\pi$
$349$	1.76640	+	1.76640i	0.0945535	+	0.0945535i	−0.658248	+	0.752801i	$0.728702\pi$
$350$		0			0
$351$	−2.19625	−	2.15364i	−0.117227	−	0.114953i
$352$		0			0
$353$		−	19.0425i		−	1.01353i	−0.862085	−	0.506764i	$-0.830842\pi$
$353$		−	19.0425i		−	1.01353i	0.862085	−	0.506764i	$-0.169158\pi$
$354$		0			0
$355$	−14.0233	+	14.0233i	−0.744278	+	0.744278i
$356$		0			0
$357$	6.03891	+	3.46033i	0.319613	+	0.183140i
$358$		0			0
$359$			28.4851i			1.50338i	0.659514	+	0.751692i	$0.270762\pi$
$359$			28.4851i			1.50338i	−0.659514	+	0.751692i	$0.729238\pi$
$360$		0			0
$361$		−	29.3935i		−	1.54703i
$362$		0			0
$363$	12.8712	+	7.37526i	0.675562	+	0.387101i
$364$		0			0
$365$	−3.46958	+	3.46958i	−0.181606	+	0.181606i
$366$		0			0
$367$			18.2398i			0.952112i	0.879415	+	0.476056i	$0.157934\pi$
$367$			18.2398i			0.952112i	−0.879415	+	0.476056i	$0.842066\pi$
$368$		0			0
$369$	−12.8402	−	21.9082i	−0.668433	−	1.14050i
$370$		0			0
$371$	−1.78619	−	1.78619i	−0.0927344	−	0.0927344i
$372$		0			0
$373$	−13.6888	+	13.6888i	−0.708779	+	0.708779i	−0.966278	−	0.257499i	$-0.917101\pi$
$373$	−13.6888	+	13.6888i	−0.708779	+	0.708779i	0.257499	+	0.966278i	$0.417101\pi$
$374$		0			0
$375$	−5.48138	−	20.1929i	−0.283057	−	1.04276i
$376$		0			0
$377$	3.86712			0.199167
$378$		0			0
$379$	−21.2201	−	21.2201i	−1.09000	−	1.09000i	−0.995527	−	0.0944749i	$-0.969883\pi$
$379$	−21.2201	−	21.2201i	−1.09000	−	1.09000i	−0.0944749	−	0.995527i	$-0.530117\pi$
$380$		0			0
$381$	−17.8624	−	10.2353i	−0.915118	−	0.524368i
$382$		0			0
$383$	−9.38265			−0.479431			−0.239716	−	0.970843i	$-0.577054\pi$
$383$	−9.38265			−0.479431			−0.239716	+	0.970843i	$0.577054\pi$
$384$		0			0
$385$	2.64516			0.134810
$386$		0			0
$387$	−4.19751	+	16.0847i	−0.213372	+	0.817630i
$388$		0			0
$389$	−1.88977	−	1.88977i	−0.0958149	−	0.0958149i	0.657575	−	0.753389i	$-0.271582\pi$
$389$	−1.88977	−	1.88977i	−0.0958149	−	0.0958149i	−0.753389	+	0.657575i	$0.771582\pi$
$390$		0			0
$391$	13.1263			0.663828
$392$		0			0
$393$	−5.82042	+	1.57996i	−0.293602	+	0.0796985i
$394$		0			0
$395$	−18.7827	+	18.7827i	−0.945061	+	0.945061i
$396$		0			0
$397$	22.5436	+	22.5436i	1.13143	+	1.13143i	0.989939	+	0.141494i	$0.0451905\pi$
$397$	22.5436	+	22.5436i	1.13143	+	1.13143i	0.141494	+	0.989939i	$0.454810\pi$
$398$		0			0
$399$	3.15651	+	11.6283i	0.158023	+	0.582142i
$400$		0			0
$401$		−	3.36660i		−	0.168120i	−0.996461	−	0.0840599i	$-0.973211\pi$
$401$		−	3.36660i		−	0.168120i	0.996461	−	0.0840599i	$-0.0267887\pi$
$402$		0			0
$403$	3.05988	−	3.05988i	0.152424	−	0.152424i
$404$		0			0
$405$	−14.6826	+	4.14041i	−0.729582	+	0.205739i
$406$		0			0
$407$			5.76503i			0.285762i
$408$		0			0
$409$			13.1993i			0.652662i	0.945256	+	0.326331i	$0.105812\pi$
$409$			13.1993i			0.652662i	−0.945256	+	0.326331i	$0.894188\pi$
$410$		0			0
$411$	−16.0444	+	28.0004i	−0.791411	+	1.38116i
$412$		0			0
$413$	5.55480	−	5.55480i	0.273334	−	0.273334i
$414$		0			0
$415$		−	22.3927i		−	1.09921i
$416$		0			0
$417$	37.4019	−	10.1528i	1.83158	−	0.497184i
$418$		0			0
$419$	−4.31964	−	4.31964i	−0.211028	−	0.211028i	0.593676	−	0.804704i	$-0.297676\pi$
$419$	−4.31964	−	4.31964i	−0.211028	−	0.211028i	−0.804704	+	0.593676i	$0.797676\pi$
$420$		0			0
$421$	−3.88545	+	3.88545i	−0.189365	+	0.189365i	−0.795422	−	0.606056i	$-0.792751\pi$
$421$	−3.88545	+	3.88545i	−0.189365	+	0.189365i	0.606056	+	0.795422i	$0.292751\pi$
$422$		0			0
$423$	−12.2632	−	20.9239i	−0.596259	−	1.01735i
$424$		0			0
$425$	−8.54673			−0.414577
$426$		0			0
$427$	−0.325351	−	0.325351i	−0.0157448	−	0.0157448i
$428$		0			0
$429$	−0.795509	+	1.38831i	−0.0384075	+	0.0670282i
$430$		0			0
$431$	7.92801			0.381879			0.190939	−	0.981602i	$-0.438847\pi$
$431$	7.92801			0.381879			0.190939	+	0.981602i	$0.438847\pi$
$432$		0			0
$433$	−7.10644			−0.341514			−0.170757	−	0.985313i	$-0.554621\pi$
$433$	−7.10644			−0.341514			−0.170757	+	0.985313i	$0.554621\pi$
$434$		0			0
$435$	9.53513	−	16.6405i	0.457174	−	0.797853i
$436$		0			0
$437$	16.0683	+	16.0683i	0.768653	+	0.768653i
$438$		0			0
$439$	−5.48850			−0.261952			−0.130976	−	0.991386i	$-0.541811\pi$
$439$	−5.48850			−0.261952			−0.130976	+	0.991386i	$0.541811\pi$
$440$		0			0
$441$	−1.51693	−	2.58823i	−0.0722348	−	0.123249i
$442$		0			0
$443$	19.7138	−	19.7138i	0.936632	−	0.936632i	−0.0614763	−	0.998109i	$-0.519581\pi$
$443$	19.7138	−	19.7138i	0.936632	−	0.936632i	0.998109	+	0.0614763i	$0.0195809\pi$
$444$		0			0
$445$	−8.03465	−	8.03465i	−0.380879	−	0.380879i
$446$		0			0
$447$	−34.8246	+	9.45319i	−1.64715	+	0.447120i
$448$		0			0
$449$		−	29.9224i		−	1.41212i	−0.708150	−	0.706062i	$-0.750470\pi$
$449$		−	29.9224i		−	1.41212i	0.708150	−	0.706062i	$-0.249530\pi$
$450$		0			0
$451$	−9.34044	+	9.34044i	−0.439824	+	0.439824i
$452$		0			0
$453$	−6.71705	+	11.7225i	−0.315594	+	0.550770i
$454$		0			0
$455$		−	1.00341i		−	0.0470404i
$456$		0			0
$457$			35.9554i			1.68192i	0.541097	+	0.840960i	$0.318009\pi$
$457$			35.9554i			1.68192i	−0.541097	+	0.840960i	$0.681991\pi$
$458$		0			0
$459$	0.204493	+	20.8791i	0.00954492	+	0.974555i
$460$		0			0
$461$	−24.1724	+	24.1724i	−1.12582	+	1.12582i	−0.134969	+	0.990850i	$0.543094\pi$
$461$	−24.1724	+	24.1724i	−1.12582	+	1.12582i	−0.990850	+	0.134969i	$0.956906\pi$
$462$		0			0
$463$		−	32.0117i		−	1.48771i	−0.668341	−	0.743855i	$-0.732995\pi$
$463$		−	32.0117i		−	1.48771i	0.668341	−	0.743855i	$-0.267005\pi$
$464$		0			0
$465$	−5.62220	−	20.7116i	−0.260723	−	0.960479i
$466$		0			0
$467$	−5.25892	−	5.25892i	−0.243354	−	0.243354i	0.574882	−	0.818236i	$-0.305048\pi$
$467$	−5.25892	−	5.25892i	−0.243354	−	0.243354i	−0.818236	+	0.574882i	$0.805048\pi$
$468$		0			0
$469$	−1.41837	+	1.41837i	−0.0654944	+	0.0654944i
$470$		0			0
$471$	7.82705	−	2.12466i	0.360651	−	0.0978992i
$472$		0			0
$473$	8.64719			0.397598
$474$		0			0
$475$	−10.4623	−	10.4623i	−0.480043	−	0.480043i
$476$		0			0
$477$	1.91354	−	7.33259i	0.0876149	−	0.335736i
$478$		0			0
$479$	21.8173			0.996860			0.498430	−	0.866930i	$-0.333910\pi$
$479$	21.8173			0.996860			0.498430	+	0.866930i	$0.333910\pi$
$480$		0			0
$481$	2.18689			0.0997135
$482$		0			0
$483$	−4.90907	−	2.81292i	−0.223370	−	0.127992i
$484$		0			0
$485$	−4.11712	−	4.11712i	−0.186949	−	0.186949i
$486$		0			0
$487$	12.5140			0.567064			0.283532	−	0.958963i	$-0.408494\pi$
$487$	12.5140			0.567064			0.283532	+	0.958963i	$0.408494\pi$
$488$		0			0
$489$	4.07525	+	15.0128i	0.184289	+	0.678903i
$490$		0			0
$491$	23.5407	−	23.5407i	1.06238	−	1.06238i	0.0644581	−	0.997920i	$-0.479468\pi$
$491$	23.5407	−	23.5407i	1.06238	−	1.06238i	0.997920	−	0.0644581i	$-0.0205319\pi$
$492$		0			0
$493$	−18.5619	−	18.5619i	−0.835986	−	0.835986i
$494$		0			0
$495$	4.01253	+	6.84628i	0.180350	+	0.307717i
$496$		0			0
$497$		−	11.7001i		−	0.524821i
$498$		0			0
$499$	19.9809	−	19.9809i	0.894466	−	0.894466i	−0.100474	−	0.994940i	$-0.532036\pi$
$499$	19.9809	−	19.9809i	0.894466	−	0.894466i	0.994940	+	0.100474i	$0.0320358\pi$
$500$		0			0
$501$	34.7371	+	19.9045i	1.55194	+	0.889269i
$502$		0			0
$503$		−	22.8810i		−	1.02021i	−0.860111	−	0.510107i	$-0.829606\pi$
$503$		−	22.8810i		−	1.02021i	0.860111	−	0.510107i	$-0.170394\pi$
$504$		0			0
$505$		−	21.8245i		−	0.971176i
$506$		0			0
$507$	−19.0100	−	10.8928i	−0.844264	−	0.483768i
$508$		0			0
$509$	−23.7478	+	23.7478i	−1.05260	+	1.05260i	−0.0540652	+	0.998537i	$0.517218\pi$
$509$	−23.7478	+	23.7478i	−1.05260	+	1.05260i	−0.998537	+	0.0540652i	$0.982782\pi$
$510$		0			0
$511$		−	2.89479i		−	0.128058i
$512$		0			0
$513$	−25.3084	+	25.8091i	−1.11739	+	1.13950i
$514$		0			0
$515$	9.61396	+	9.61396i	0.423642	+	0.423642i
$516$		0			0
$517$	−8.92076	+	8.92076i	−0.392335	+	0.392335i
$518$		0			0
$519$	7.09367	+	26.1324i	0.311377	+	1.14708i
$520$		0			0
$521$	22.7881			0.998365			0.499182	−	0.866497i	$-0.333634\pi$
$521$	22.7881			0.998365			0.499182	+	0.866497i	$0.333634\pi$
$522$		0			0
$523$	1.58537	+	1.58537i	0.0693235	+	0.0693235i	0.740918	−	0.671595i	$-0.234390\pi$
$523$	1.58537	+	1.58537i	0.0693235	+	0.0693235i	−0.671595	+	0.740918i	$0.734390\pi$
$524$		0			0
$525$	3.19636	+	1.83153i	0.139500	+	0.0799345i
$526$		0			0
$527$	−29.3744			−1.27957
$528$		0			0
$529$	12.3295			0.536065
$530$		0			0
$531$	22.8033	+	5.95083i	0.989580	+	0.258244i
$532$		0			0
$533$	3.54317	+	3.54317i	0.153472	+	0.153472i
$534$		0			0
$535$	15.5385			0.671788
$536$		0			0
$537$	−23.9194	+	6.49295i	−1.03220	+	0.280192i
$538$		0			0
$539$	−1.10347	+	1.10347i	−0.0475300	+	0.0475300i
$540$		0			0
$541$	6.57208	+	6.57208i	0.282556	+	0.282556i	0.834128	−	0.551572i	$-0.185972\pi$
$541$	6.57208	+	6.57208i	0.282556	+	0.282556i	−0.551572	+	0.834128i	$0.685972\pi$
$542$		0			0
$543$	−3.11790	−	11.4861i	−0.133802	−	0.492914i
$544$		0			0
$545$			9.49551i			0.406743i
$546$		0			0
$547$	1.65996	−	1.65996i	0.0709749	−	0.0709749i	−0.670728	−	0.741703i	$-0.734018\pi$
$547$	1.65996	−	1.65996i	0.0709749	−	0.0709749i	0.741703	+	0.670728i	$0.234018\pi$
$548$		0			0
$549$	0.348547	−	1.33562i	0.0148756	−	0.0570027i
$550$		0			0
$551$		−	45.4443i		−	1.93599i
$552$		0			0
$553$		−	15.6711i		−	0.666402i
$554$		0			0
$555$	5.39219	−	9.41035i	0.228886	−	0.399447i
$556$		0			0
$557$	−9.02242	+	9.02242i	−0.382292	+	0.382292i	−0.871927	−	0.489635i	$-0.837130\pi$
$557$	−9.02242	+	9.02242i	−0.382292	+	0.382292i	0.489635	+	0.871927i	$0.337130\pi$
$558$		0			0
$559$		−	3.28019i		−	0.138737i
$560$		0			0
$561$	10.4822	−	2.84540i	0.442557	−	0.120133i
$562$		0			0
$563$	20.0512	+	20.0512i	0.845057	+	0.845057i	0.989511	−	0.144454i	$-0.0461427\pi$
$563$	20.0512	+	20.0512i	0.845057	+	0.845057i	−0.144454	+	0.989511i	$0.546143\pi$
$564$		0			0
$565$	−13.5865	+	13.5865i	−0.571589	+	0.571589i
$566$		0			0
$567$	4.39784	−	7.85233i	0.184692	−	0.329767i
$568$		0			0
$569$	33.2100			1.39224			0.696118	−	0.717928i	$-0.254909\pi$
$569$	33.2100			1.39224			0.696118	+	0.717928i	$0.254909\pi$
$570$		0			0
$571$	−32.5442	−	32.5442i	−1.36193	−	1.36193i	−0.871454	−	0.490478i	$-0.836822\pi$
$571$	−32.5442	−	32.5442i	−1.36193	−	1.36193i	−0.490478	−	0.871454i	$-0.663178\pi$
$572$		0			0
$573$	−1.73614	+	3.02988i	−0.0725281	+	0.126575i
$574$		0			0
$575$	6.94770			0.289739
$576$		0			0
$577$	13.4111			0.558311			0.279156	−	0.960246i	$-0.409945\pi$
$577$	13.4111			0.558311			0.279156	+	0.960246i	$0.409945\pi$
$578$		0			0
$579$	−17.0722	+	29.7941i	−0.709495	+	1.23820i
$580$		0			0
$581$	9.34150	+	9.34150i	0.387551	+	0.387551i
$582$		0			0
$583$	−3.94203			−0.163262
$584$		0			0
$585$	2.59704	−	1.52210i	0.107375	−	0.0629310i
$586$		0			0
$587$	9.20109	−	9.20109i	0.379770	−	0.379770i	−0.491249	−	0.871019i	$-0.663460\pi$
$587$	9.20109	−	9.20109i	0.379770	−	0.379770i	0.871019	+	0.491249i	$0.163460\pi$
$588$		0			0
$589$	−35.9581	−	35.9581i	−1.48163	−	1.48163i
$590$		0			0
$591$	16.1069	−	4.37224i	0.662550	−	0.179850i
$592$		0			0
$593$		−	8.75371i		−	0.359472i	−0.983715	−	0.179736i	$-0.942476\pi$
$593$		−	8.75371i		−	0.359472i	0.983715	−	0.179736i	$-0.0575243\pi$
$594$		0			0
$595$	−4.81628	+	4.81628i	−0.197448	+	0.197448i
$596$		0			0
$597$	16.7421	−	29.2181i	0.685210	−	1.19582i
$598$		0			0
$599$			29.7166i			1.21419i	0.794630	+	0.607094i	$0.207665\pi$
$599$			29.7166i			1.21419i	−0.794630	+	0.607094i	$0.792335\pi$
$600$		0			0
$601$			16.8927i			0.689069i	0.938774	+	0.344535i	$0.111963\pi$
$601$			16.8927i			0.689069i	−0.938774	+	0.344535i	$0.888037\pi$
$602$		0			0
$603$	−5.82264	−	1.51950i	−0.237116	−	0.0618787i
$604$		0			0
$605$	−10.2653	+	10.2653i	−0.417343	+	0.417343i
$606$		0			0
$607$		−	2.55183i		−	0.103576i	−0.998658	−	0.0517878i	$-0.983508\pi$
$607$		−	2.55183i		−	0.103576i	0.998658	−	0.0517878i	$-0.0164919\pi$
$608$		0			0
$609$	2.96415	+	10.9196i	0.120113	+	0.442486i
$610$		0			0
$611$	3.38397	+	3.38397i	0.136901	+	0.136901i
$612$		0			0
$613$	10.4070	−	10.4070i	0.420336	−	0.420336i	−0.464983	−	0.885320i	$-0.653940\pi$
$613$	10.4070	−	10.4070i	0.420336	−	0.420336i	0.885320	+	0.464983i	$0.153940\pi$
$614$		0			0
$615$	23.9829	−	6.51019i	0.967084	−	0.262516i
$616$		0			0
$617$	−20.4380			−0.822803			−0.411402	−	0.911454i	$-0.634961\pi$
$617$	−20.4380			−0.822803			−0.411402	+	0.911454i	$0.634961\pi$
$618$		0			0
$619$	8.09052	+	8.09052i	0.325185	+	0.325185i	0.850752	−	0.525567i	$-0.176147\pi$
$619$	8.09052	+	8.09052i	0.325185	+	0.325185i	−0.525567	+	0.850752i	$0.676147\pi$
$620$		0			0
$621$	−0.166234	−	16.9728i	−0.00667073	−	0.681095i
$622$		0			0
$623$	6.70359			0.268574
$624$		0			0
$625$	9.84173			0.393669
$626$		0			0
$627$	16.3147	+	9.34839i	0.651544	+	0.373339i
$628$		0			0
$629$	−10.4969	−	10.4969i	−0.418539	−	0.418539i
$630$		0			0
$631$	−18.0532			−0.718685			−0.359342	−	0.933206i	$-0.616999\pi$
$631$	−18.0532			−0.718685			−0.359342	+	0.933206i	$0.616999\pi$
$632$		0			0
$633$	−11.1832	−	41.1979i	−0.444493	−	1.63747i
$634$		0			0
$635$	14.2460	−	14.2460i	0.565335	−	0.565335i
$636$		0			0
$637$	0.418588	+	0.418588i	0.0165851	+	0.0165851i
$638$		0			0
$639$	30.2825	−	17.7482i	1.19796	−	0.702110i
$640$		0			0
$641$		−	16.0485i		−	0.633879i	−0.948446	−	0.316939i	$-0.897345\pi$
$641$		−	16.0485i		−	0.633879i	0.948446	−	0.316939i	$-0.102655\pi$
$642$		0			0
$643$	−3.36193	+	3.36193i	−0.132582	+	0.132582i	−0.770283	−	0.637702i	$-0.779885\pi$
$643$	−3.36193	+	3.36193i	−0.132582	+	0.132582i	0.637702	+	0.770283i	$0.279885\pi$
$644$		0			0
$645$	−14.1149	−	8.08794i	−0.555775	−	0.318462i
$646$		0			0
$647$		−	33.9767i		−	1.33576i	−0.744267	−	0.667882i	$-0.767201\pi$
$647$		−	33.9767i		−	1.33576i	0.744267	−	0.667882i	$-0.232799\pi$
$648$		0			0
$649$		−	12.2592i		−	0.481214i
$650$		0			0
$651$	10.9856	+	6.29482i	0.430560	+	0.246713i
$652$		0			0
$653$	−12.5270	+	12.5270i	−0.490219	+	0.490219i	−0.908375	−	0.418156i	$-0.862677\pi$
$653$	−12.5270	+	12.5270i	−0.490219	+	0.490219i	0.418156	+	0.908375i	$0.362677\pi$
$654$		0			0
$655$		−	5.90211i		−	0.230615i
$656$		0			0
$657$	7.49236	−	4.39119i	0.292305	−	0.171317i
$658$		0			0
$659$	21.1739	+	21.1739i	0.824816	+	0.824816i	0.986794	−	0.161978i	$-0.0517873\pi$
$659$	21.1739	+	21.1739i	0.824816	+	0.824816i	−0.161978	+	0.986794i	$0.551787\pi$
$660$		0			0
$661$	28.3104	−	28.3104i	1.10115	−	1.10115i	0.106874	−	0.994273i	$-0.465916\pi$
$661$	28.3104	−	28.3104i	1.10115	−	1.10115i	0.994273	−	0.106874i	$-0.0340840\pi$
$662$		0			0
$663$	−1.07936	−	3.97627i	−0.0419190	−	0.154425i
$664$		0			0
$665$	−11.7915			−0.457254
$666$		0			0
$667$	15.0891	+	15.0891i	0.584252	+	0.584252i
$668$		0			0
$669$	17.2993	+	9.91260i	0.668830	+	0.383243i
$670$		0			0
$671$	−0.718033			−0.0277193
$672$		0			0
$673$	−37.1776			−1.43309			−0.716546	−	0.697540i	$-0.754278\pi$
$673$	−37.1776			−1.43309			−0.716546	+	0.697540i	$0.754278\pi$
$674$		0			0
$675$	0.108237	+	11.0512i	0.00416604	+	0.425361i
$676$		0			0
$677$	18.3210	+	18.3210i	0.704133	+	0.704133i	0.965295	−	0.261162i	$-0.0841057\pi$
$677$	18.3210	+	18.3210i	0.704133	+	0.704133i	−0.261162	+	0.965295i	$0.584106\pi$
$678$		0			0
$679$	3.43505			0.131825
$680$		0			0
$681$	9.92152	−	2.69321i	0.380193	−	0.103204i
$682$		0			0
$683$	−22.2865	+	22.2865i	−0.852769	+	0.852769i	−0.990473	−	0.137704i	$-0.956028\pi$
$683$	−22.2865	+	22.2865i	−0.852769	+	0.852769i	0.137704	+	0.990473i	$0.456028\pi$
$684$		0			0
$685$	−22.3315	−	22.3315i	−0.853242	−	0.853242i
$686$		0			0
$687$	3.43209	+	12.6435i	0.130942	+	0.482379i
$688$		0			0
$689$			1.49536i			0.0569686i
$690$		0			0
$691$	−3.15522	+	3.15522i	−0.120030	+	0.120030i	−0.764570	−	0.644540i	$-0.777049\pi$
$691$	−3.15522	+	3.15522i	−0.120030	+	0.120030i	0.644540	+	0.764570i	$0.277049\pi$
$692$		0			0
$693$	−4.52994	−	1.18215i	−0.172078	−	0.0449061i
$694$		0			0
$695$			37.9268i			1.43865i
$696$		0			0
$697$		−	34.0139i		−	1.28837i
$698$		0			0
$699$	23.2826	−	40.6324i	0.880628	−	1.53686i
$700$		0			0
$701$	−28.0109	+	28.0109i	−1.05796	+	1.05796i	−0.0597418	+	0.998214i	$0.519028\pi$
$701$	−28.0109	+	28.0109i	−1.05796	+	1.05796i	−0.998214	+	0.0597418i	$0.980972\pi$
$702$		0			0
$703$		−	25.6991i		−	0.969260i
$704$		0			0
$705$	22.9053	−	6.21768i	0.862664	−	0.234171i
$706$		0			0
$707$	9.10445	+	9.10445i	0.342408	+	0.342408i
$708$		0			0
$709$	30.7888	−	30.7888i	1.15630	−	1.15630i	0.171034	−	0.985265i	$-0.445289\pi$
$709$	30.7888	−	30.7888i	1.15630	−	1.15630i	0.985265	−	0.171034i	$-0.0547107\pi$
$710$		0			0
$711$	40.5603	−	23.7719i	1.52113	−	0.891517i
$712$		0			0
$713$	23.8787			0.894263
$714$		0			0
$715$	−1.10723	−	1.10723i	−0.0414082	−	0.0414082i
$716$		0			0
$717$	−2.37218	+	4.13989i	−0.0885907	+	0.154607i
$718$		0			0
$719$	−22.9619			−0.856333			−0.428166	−	0.903700i	$-0.640840\pi$
$719$	−22.9619			−0.856333			−0.428166	+	0.903700i	$0.640840\pi$
$720$		0			0
$721$	−8.02126			−0.298727
$722$		0			0
$723$	12.4771	−	21.7748i	0.464027	−	0.809812i
$724$		0			0
$725$	−9.82471	−	9.82471i	−0.364880	−	0.364880i
$726$		0			0
$727$	−25.4722			−0.944711			−0.472355	−	0.881408i	$-0.656596\pi$
$727$	−25.4722			−0.944711			−0.472355	+	0.881408i	$0.656596\pi$
$728$		0			0
$729$	26.9948	−	0.528832i	0.999808	−	0.0195864i
$730$		0			0
$731$	−15.7447	+	15.7447i	−0.582338	+	0.582338i
$732$		0			0
$733$	−2.60179	−	2.60179i	−0.0960992	−	0.0960992i	0.657423	−	0.753522i	$-0.271647\pi$
$733$	−2.60179	−	2.60179i	−0.0960992	−	0.0960992i	−0.753522	+	0.657423i	$0.771647\pi$
$734$		0			0
$735$	2.83333	−	0.769110i	0.104509	−	0.0283691i
$736$		0			0
$737$			3.13028i			0.115305i
$738$		0			0
$739$	27.8272	−	27.8272i	1.02364	−	1.02364i	0.0239281	−	0.999714i	$-0.492383\pi$
$739$	27.8272	−	27.8272i	1.02364	−	1.02364i	0.999714	−	0.0239281i	$-0.00761729\pi$
$740$		0			0
$741$	3.54618	−	6.18874i	0.130272	−	0.227349i
$742$		0			0
$743$		−	10.6048i		−	0.389051i	−0.980897	−	0.194525i	$-0.937683\pi$
$743$		−	10.6048i		−	0.389051i	0.980897	−	0.194525i	$-0.0623167\pi$
$744$		0			0
$745$		−	35.3134i		−	1.29378i
$746$		0			0
$747$	−10.0075	+	38.3483i	−0.366156	+	1.40309i
$748$		0			0
$749$	−6.48216	+	6.48216i	−0.236853	+	0.236853i
$750$		0			0
$751$		−	15.4515i		−	0.563833i	−0.959439	−	0.281917i	$-0.909030\pi$
$751$		−	15.4515i		−	0.563833i	0.959439	−	0.281917i	$-0.0909701\pi$
$752$		0			0
$753$	−0.942837	−	3.47332i	−0.0343589	−	0.126575i
$754$		0			0
$755$	−9.34916	−	9.34916i	−0.340251	−	0.340251i
$756$		0			0
$757$	20.2941	−	20.2941i	0.737602	−	0.737602i	−0.234512	−	0.972113i	$-0.575349\pi$
$757$	20.2941	−	20.2941i	0.737602	−	0.737602i	0.972113	+	0.234512i	$0.0753491\pi$
$758$		0			0
$759$	−8.52102	+	2.31304i	−0.309294	+	0.0839581i
$760$		0			0
$761$	0.679283			0.0246240			0.0123120	−	0.999924i	$-0.496081\pi$
$761$	0.679283			0.0246240			0.0123120	+	0.999924i	$0.496081\pi$
$762$		0			0
$763$	−3.96122	−	3.96122i	−0.143406	−	0.143406i
$764$		0			0
$765$	−19.7716	−	5.15966i	−0.714843	−	0.186548i
$766$		0			0
$767$	−4.65035			−0.167914
$768$		0			0
$769$	12.5414			0.452255			0.226128	−	0.974098i	$-0.427393\pi$
$769$	12.5414			0.452255			0.226128	+	0.974098i	$0.427393\pi$
$770$		0			0
$771$	15.8789	+	9.09868i	0.571864	+	0.327681i
$772$		0			0
$773$	23.3063	+	23.3063i	0.838269	+	0.838269i	0.988631	−	0.150362i	$-0.0480439\pi$
$773$	23.3063	+	23.3063i	0.838269	+	0.838269i	−0.150362	+	0.988631i	$0.548044\pi$
$774$		0			0
$775$	−15.5477			−0.558490
$776$		0			0
$777$	1.67625	+	6.17513i	0.0601351	+	0.221532i
$778$		0			0
$779$	41.6374	−	41.6374i	1.49181	−	1.49181i
$780$		0			0
$781$	−12.9108	−	12.9108i	−0.461984	−	0.461984i
$782$		0			0
$783$	−23.7661	+	24.2362i	−0.849331	+	0.866132i
$784$		0			0
$785$			7.93690i			0.283280i
$786$		0			0
$787$	33.1497	−	33.1497i	1.18166	−	1.18166i	0.202345	−	0.979314i	$-0.435144\pi$
$787$	33.1497	−	33.1497i	1.18166	−	1.18166i	0.979314	−	0.202345i	$-0.0648561\pi$
$788$		0			0
$789$	−5.29073	−	3.03162i	−0.188355	−	0.107928i
$790$		0			0
$791$		−	11.3357i		−	0.403051i
$792$		0			0
$793$			0.272376i			0.00967235i
$794$		0			0
$795$	6.43464	+	3.68709i	0.228213	+	0.130767i
$796$		0			0
$797$	21.5577	−	21.5577i	0.763613	−	0.763613i	−0.213360	−	0.976974i	$-0.568441\pi$
$797$	21.5577	−	21.5577i	0.763613	−	0.763613i	0.976974	+	0.213360i	$0.0684408\pi$
$798$		0			0
$799$		−	32.4856i		−	1.14926i
$800$		0			0
$801$	10.1689	+	17.3504i	0.359300	+	0.613047i
$802$		0			0
$803$	−3.19432	−	3.19432i	−0.112725	−	0.112725i
$804$		0			0
$805$	3.91518	−	3.91518i	0.137992	−	0.137992i
$806$		0			0
$807$	1.89677	+	6.98753i	0.0667696	+	0.245973i
$808$		0			0
$809$	36.9991			1.30082			0.650410	−	0.759583i	$-0.274597\pi$
$809$	36.9991			1.30082			0.650410	+	0.759583i	$0.274597\pi$
$810$		0			0
$811$	8.02236	+	8.02236i	0.281703	+	0.281703i	0.833788	−	0.552085i	$-0.186168\pi$
$811$	8.02236	+	8.02236i	0.281703	+	0.281703i	−0.552085	+	0.833788i	$0.686168\pi$
$812$		0			0
$813$	39.8059	+	22.8090i	1.39605	+	0.799946i
$814$		0			0
$815$	−15.2235			−0.533257
$816$		0			0
$817$	−38.5471			−1.34859
$818$		0			0
$819$	−0.448432	+	1.71837i	−0.0156695	+	0.0600448i
$820$		0			0
$821$	−38.2753	−	38.2753i	−1.33582	−	1.33582i	−0.900067	−	0.435752i	$-0.856483\pi$
$821$	−38.2753	−	38.2753i	−1.33582	−	1.33582i	−0.435752	−	0.900067i	$-0.643517\pi$
$822$		0			0
$823$	−38.8930			−1.35573			−0.677863	−	0.735188i	$-0.737094\pi$
$823$	−38.8930			−1.35573			−0.677863	+	0.735188i	$0.737094\pi$
$824$		0			0
$825$	5.54815	−	1.50605i	0.193162	−	0.0524340i
$826$		0			0
$827$	10.0304	−	10.0304i	0.348790	−	0.348790i	−0.510869	−	0.859659i	$-0.670676\pi$
$827$	10.0304	−	10.0304i	0.348790	−	0.348790i	0.859659	+	0.510869i	$0.170676\pi$
$828$		0			0
$829$	14.7744	+	14.7744i	0.513137	+	0.513137i	0.915486	−	0.402350i	$-0.131806\pi$
$829$	14.7744	+	14.7744i	0.513137	+	0.513137i	−0.402350	+	0.915486i	$0.631806\pi$
$830$		0			0
$831$	0.582226	+	2.14486i	0.0201972	+	0.0744044i
$832$		0			0
$833$		−	4.01838i		−	0.139229i
$834$		0			0
$835$	−27.7042	+	27.7042i	−0.958745	+	0.958745i
$836$		0			0
$837$	0.372002	+	37.9821i	0.0128583	+	1.31285i
$838$		0			0
$839$			29.3275i			1.01250i	0.862387	+	0.506249i	$0.168968\pi$
$839$			29.3275i			1.01250i	−0.862387	+	0.506249i	$0.831032\pi$
$840$		0			0
$841$		−	13.6749i		−	0.471547i
$842$		0			0
$843$	19.3756	−	33.8140i	0.667332	−	1.16462i
$844$		0			0
$845$	15.1613	−	15.1613i	0.521563	−	0.521563i
$846$		0			0
$847$		−	8.56469i		−	0.294286i
$848$		0			0
$849$	1.09652	−	0.297651i	0.0376324	−	0.0102154i
$850$		0			0
$851$	8.53300	+	8.53300i	0.292507	+	0.292507i
$852$		0			0
$853$	−32.1800	+	32.1800i	−1.10182	+	1.10182i	−0.107630	+	0.994191i	$0.534326\pi$
$853$	−32.1800	+	32.1800i	−1.10182	+	1.10182i	−0.994191	+	0.107630i	$0.965674\pi$
$854$		0			0
$855$	−17.8869	−	30.5190i	−0.611718	−	1.04373i
$856$		0			0
$857$	−53.4151			−1.82462			−0.912312	−	0.409495i	$-0.865705\pi$
$857$	−53.4151			−1.82462			−0.912312	+	0.409495i	$0.865705\pi$
$858$		0			0
$859$	−3.62080	−	3.62080i	−0.123540	−	0.123540i	0.642634	−	0.766174i	$-0.277842\pi$
$859$	−3.62080	−	3.62080i	−0.123540	−	0.123540i	−0.766174	+	0.642634i	$0.777842\pi$
$860$		0			0
$861$	−7.28904	+	12.7207i	−0.248410	+	0.433521i
$862$		0			0
$863$	−56.4885			−1.92289			−0.961445	−	0.274999i	$-0.911323\pi$
$863$	−56.4885			−1.92289			−0.961445	+	0.274999i	$0.911323\pi$
$864$		0			0
$865$	−26.4991			−0.900998
$866$		0			0
$867$	0.734182	−	1.28128i	0.0249341	−	0.0435147i
$868$		0			0
$869$	−17.2926	−	17.2926i	−0.586612	−	0.586612i
$870$		0			0
$871$	1.18743			0.0402345
$872$		0			0
$873$	5.21074	+	8.89070i	0.176357	+	0.300904i
$874$		0			0
$875$	−8.54203	+	8.54203i	−0.288773	+	0.288773i
$876$		0			0
$877$	7.39009	+	7.39009i	0.249546	+	0.249546i	0.820784	−	0.571239i	$-0.193537\pi$
$877$	7.39009	+	7.39009i	0.249546	+	0.249546i	−0.571239	+	0.820784i	$0.693537\pi$
$878$		0			0
$879$	−33.1181	+	8.98996i	−1.11705	+	0.303224i
$880$		0			0
$881$			55.1865i			1.85928i	0.368470	+	0.929640i	$0.379882\pi$
$881$			55.1865i			1.85928i	−0.368470	+	0.929640i	$0.620118\pi$
$882$		0			0
$883$	−28.4851	+	28.4851i	−0.958600	+	0.958600i	−0.999176	−	0.0405766i	$-0.987081\pi$
$883$	−28.4851	+	28.4851i	−0.958600	+	0.958600i	0.0405766	+	0.999176i	$0.487081\pi$
$884$		0			0
$885$	−11.4663	+	20.0108i	−0.385436	+	0.672656i
$886$		0			0
$887$		−	2.82548i		−	0.0948702i	−0.998874	−	0.0474351i	$-0.984895\pi$
$887$		−	2.82548i		−	0.0948702i	0.998874	−	0.0474351i	$-0.0151047\pi$
$888$		0			0
$889$			11.8859i			0.398641i
$890$		0			0
$891$	−3.81194	−	13.5177i	−0.127705	−	0.452862i
$892$		0			0
$893$	39.7666	−	39.7666i	1.33074	−	1.33074i
$894$		0			0
$895$		−	24.2551i		−	0.810759i
$896$		0			0
$897$	0.877422	+	3.23234i	0.0292963	+	0.107925i
$898$		0			0
$899$	−33.7667	−	33.7667i	−1.12618	−	1.12618i
$900$		0			0
$901$	7.17760	−	7.17760i	0.239121	−	0.239121i
$902$		0			0
$903$	9.26231	−	2.51427i	0.308231	−	0.0836696i
$904$		0			0
$905$	11.6473			0.387168
$906$		0			0
$907$	−19.6410	−	19.6410i	−0.652169	−	0.652169i	0.301346	−	0.953515i	$-0.402564\pi$
$907$	−19.6410	−	19.6410i	−0.652169	−	0.652169i	−0.953515	+	0.301346i	$0.902564\pi$
$908$		0			0
$909$	−9.75356	+	37.3752i	−0.323505	+	1.23966i
$910$		0			0
$911$	−17.7959			−0.589603			−0.294801	−	0.955559i	$-0.595253\pi$
$911$	−17.7959			−0.589603			−0.294801	+	0.955559i	$0.595253\pi$
$912$		0			0
$913$	20.6162			0.682297
$914$		0			0
$915$	1.17206	+	0.671595i	0.0387470	+	0.0222022i
$916$		0			0
$917$	2.46217	+	2.46217i	0.0813079	+	0.0813079i
$918$		0			0
$919$	−17.7656			−0.586032			−0.293016	−	0.956108i	$-0.594659\pi$
$919$	−17.7656			−0.586032			−0.293016	+	0.956108i	$0.594659\pi$
$920$		0			0
$921$	8.35651	+	30.7846i	0.275356	+	1.01439i
$922$		0			0
$923$	−4.89753	+	4.89753i	−0.161204	+	0.161204i
$924$		0			0
$925$	−5.55595	−	5.55595i	−0.182678	−	0.182678i
$926$		0			0
$927$	−12.1677	−	20.7608i	−0.399640	−	0.681875i
$928$		0			0
$929$		−	38.3156i		−	1.25709i	−0.777772	−	0.628547i	$-0.783650\pi$
$929$		−	38.3156i		−	1.25709i	0.777772	−	0.628547i	$-0.216350\pi$
$930$		0			0
$931$	4.91902	−	4.91902i	0.161214	−	0.161214i
$932$		0			0
$933$	−9.05456	−	5.18831i	−0.296433	−	0.169858i
$934$		0			0
$935$			10.6293i			0.347615i
$936$		0			0
$937$		−	14.6294i		−	0.477922i	−0.971029	−	0.238961i	$-0.923193\pi$
$937$		−	14.6294i		−	0.477922i	0.971029	−	0.238961i	$-0.0768067\pi$
$938$		0			0
$939$	34.8872	+	19.9906i	1.13850	+	0.652367i
$940$		0			0
$941$	31.9860	−	31.9860i	1.04271	−	1.04271i	0.0436675	−	0.999046i	$-0.486096\pi$
$941$	31.9860	−	31.9860i	1.04271	−	1.04271i	0.999046	−	0.0436675i	$-0.0139042\pi$
$942$		0			0
$943$			27.6501i			0.900412i
$944$		0			0
$945$	6.28860	+	6.16661i	0.204568	+	0.200600i
$946$		0			0
$947$	7.81766	+	7.81766i	0.254040	+	0.254040i	0.822625	−	0.568585i	$-0.192509\pi$
$947$	7.81766	+	7.81766i	0.254040	+	0.254040i	−0.568585	+	0.822625i	$0.692509\pi$
$948$		0			0
$949$	−1.21172	+	1.21172i	−0.0393342	+	0.0393342i
$950$		0			0
$951$	7.70941	+	28.4007i	0.249995	+	0.920956i
$952$		0			0
$953$	21.9696			0.711667			0.355833	−	0.934549i	$-0.384197\pi$
$953$	21.9696			0.711667			0.355833	+	0.934549i	$0.384197\pi$
$954$		0			0
$955$	−2.41645	−	2.41645i	−0.0781945	−	0.0781945i
$956$		0			0
$957$	15.3204	+	8.77868i	0.495238	+	0.283774i
$958$		0			0
$959$	18.6319			0.601656
$960$		0			0
$961$	−22.4362			−0.723748
$962$		0			0
$963$	−26.6103	−	6.94431i	−0.857504	−	0.223777i
$964$		0			0
$965$	−23.7620	−	23.7620i	−0.764926	−	0.764926i
$966$		0			0
$967$	35.5604			1.14355			0.571773	−	0.820412i	$-0.306256\pi$
$967$	35.5604			1.14355			0.571773	+	0.820412i	$0.306256\pi$
$968$		0			0
$969$	−46.7269	+	12.6841i	−1.50108	+	0.407471i
$970$		0			0
$971$	−25.1898	+	25.1898i	−0.808380	+	0.808380i	−0.984389	−	0.176008i	$-0.943681\pi$
$971$	−25.1898	+	25.1898i	−0.808380	+	0.808380i	0.176008	+	0.984389i	$0.443681\pi$
$972$		0			0
$973$	−15.8218	−	15.8218i	−0.507224	−	0.507224i
$974$		0			0
$975$	−0.571300	−	2.10461i	−0.0182963	−	0.0674016i
$976$		0			0
$977$		−	9.13611i		−	0.292290i	−0.989263	−	0.146145i	$-0.953313\pi$
$977$		−	9.13611i		−	0.292290i	0.989263	−	0.146145i	$-0.0466866\pi$
$978$		0			0
$979$	7.39724	−	7.39724i	0.236417	−	0.236417i
$980$		0			0
$981$	4.24363	−	16.2614i	0.135489	−	0.519187i
$982$		0			0
$983$			4.41394i			0.140783i	0.997519	+	0.0703914i	$0.0224248\pi$
$983$			4.41394i			0.140783i	−0.997519	+	0.0703914i	$0.977575\pi$
$984$		0			0
$985$			16.3330i			0.520412i
$986$		0			0
$987$	−6.96154	+	12.1492i	−0.221588	+	0.386712i
$988$		0			0
$989$	12.7990	−	12.7990i	0.406983	−	0.406983i
$990$		0			0
$991$		−	27.8849i		−	0.885793i	−0.896573	−	0.442896i	$-0.853951\pi$
$991$		−	27.8849i		−	0.885793i	0.896573	−	0.442896i	$-0.146049\pi$
$992$		0			0
$993$	15.8634	−	4.30615i	0.503411	−	0.136651i
$994$		0			0
$995$	23.3026	+	23.3026i	0.738743	+	0.738743i
$996$		0			0
$997$	−39.6685	+	39.6685i	−1.25631	+	1.25631i	−0.303476	+	0.952839i	$0.598147\pi$
$997$	−39.6685	+	39.6685i	−1.25631	+	1.25631i	−0.952839	+	0.303476i	$0.901853\pi$
$998$		0			0
$999$	−13.4399	+	13.7058i	−0.425220	+	0.433631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.d.239.16		48
3.2	odd	2	inner	1344.2.s.d.239.20		48
4.3	odd	2		336.2.s.d.323.19	yes	48
12.11	even	2		336.2.s.d.323.6	yes	48
16.5	even	4		336.2.s.d.155.6	✓	48
16.11	odd	4	inner	1344.2.s.d.911.20		48
48.5	odd	4		336.2.s.d.155.19	yes	48
48.11	even	4	inner	1344.2.s.d.911.16		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.d.155.6	✓	48	16.5	even	4
336.2.s.d.155.19	yes	48	48.5	odd	4
336.2.s.d.323.6	yes	48	12.11	even	2
336.2.s.d.323.19	yes	48	4.3	odd	2
1344.2.s.d.239.16		48	1.1	even	1	trivial
1344.2.s.d.239.20		48	3.2	odd	2	inner
1344.2.s.d.911.16		48	48.11	even	4	inner
1344.2.s.d.911.20		48	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.861124 - 1.50282i) q^{3} +(1.19856 + 1.19856i) q^{5} -1.00000 q^{7} +(-1.51693 - 2.58823i) q^{9} +O(q^{10})\)	\(q+(0.861124 - 1.50282i) q^{3} +(1.19856 + 1.19856i) q^{5} -1.00000 q^{7} +(-1.51693 - 2.58823i) q^{9} +(-1.10347 + 1.10347i) q^{11} +(0.418588 + 0.418588i) q^{13} +(2.83333 - 0.769110i) q^{15} -4.01838i q^{17} +(4.91902 - 4.91902i) q^{19} +(-0.861124 + 1.50282i) q^{21} +3.26657i q^{23} -2.12691i q^{25} +(-5.19590 + 0.0508894i) q^{27} +(4.61925 - 4.61925i) q^{29} -7.31001i q^{31} +(0.708095 + 2.60855i) q^{33} +(-1.19856 - 1.19856i) q^{35} +(2.61222 - 2.61222i) q^{37} +(0.989519 - 0.268606i) q^{39} +8.46457 q^{41} +(-3.91816 - 3.91816i) q^{43} +(1.28401 - 4.92028i) q^{45} +8.08425 q^{47} +1.00000 q^{49} +(-6.03891 - 3.46033i) q^{51} +(1.78619 + 1.78619i) q^{53} -2.64516 q^{55} +(-3.15651 - 11.6283i) q^{57} +(-5.55480 + 5.55480i) q^{59} +(0.325351 + 0.325351i) q^{61} +(1.51693 + 2.58823i) q^{63} +1.00341i q^{65} +(1.41837 - 1.41837i) q^{67} +(4.90907 + 2.81292i) q^{69} +11.7001i q^{71} +2.89479i q^{73} +(-3.19636 - 1.83153i) q^{75} +(1.10347 - 1.10347i) q^{77} +15.6711i q^{79} +(-4.39784 + 7.85233i) q^{81} +(-9.34150 - 9.34150i) q^{83} +(4.81628 - 4.81628i) q^{85} +(-2.96415 - 10.9196i) q^{87} -6.70359 q^{89} +(-0.418588 - 0.418588i) q^{91} +(-10.9856 - 6.29482i) q^{93} +11.7915 q^{95} -3.43505 q^{97} +(4.52994 + 1.18215i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{7}+O(q^{10}) \) 48 * q - 48 * q^7	\( 48 q - 48 q^{7} - 8 q^{19} + 12 q^{27} + 16 q^{37} + 24 q^{39} + 48 q^{43} + 20 q^{45} + 48 q^{49} + 32 q^{55} + 8 q^{61} + 16 q^{67} - 28 q^{69} + 12 q^{75} - 48 q^{85} - 56 q^{87} - 64 q^{93} - 32 q^{99}+O(q^{100}) \) 48 * q - 48 * q^7 - 8 * q^19 + 12 * q^27 + 16 * q^37 + 24 * q^39 + 48 * q^43 + 20 * q^45 + 48 * q^49 + 32 * q^55 + 8 * q^61 + 16 * q^67 - 28 * q^69 + 12 * q^75 - 48 * q^85 - 56 * q^87 - 64 * q^93 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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