LMFDB - Embedded newform 1344.2.w.a.337.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(337,1344)]

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([0, 3, 0, 0]))

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

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

chi := DirichletCharacter("1344.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.w (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:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 56 x^{15} + 64 x^{14} - 84 x^{13} + 125 x^{12} + \cdots + 1024 $ x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 56x^15 + 64x^14 - 84x^13 + 125x^12 - 120x^11 + 100x^10 - 240x^9 + 500x^8 - 672x^7 + 1024x^6 - 1792x^5 + 2240x^4 - 2048x^3 + 2048x^2 - 2048*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.7
Root			$1.07232 - 0.922026i$ of defining polynomial
Character	$\chi$	$=$	1344.337
Dual form			1344.2.w.a.1009.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-1.17321 + 1.17321i) q^{5} +1.00000i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-1.17321 + 1.17321i) q^{5} +1.00000i q^{7} +1.00000i q^{9} +(0.961187 - 0.961187i) q^{11} +(2.26008 + 2.26008i) q^{13} -1.65917 q^{15} +3.43185 q^{17} +(-0.568789 - 0.568789i) q^{19} +(-0.707107 + 0.707107i) q^{21} -2.04688i q^{23} +2.24717i q^{25} +(-0.707107 + 0.707107i) q^{27} +(6.38455 + 6.38455i) q^{29} -9.65134 q^{31} +1.35932 q^{33} +(-1.17321 - 1.17321i) q^{35} +(-8.01287 + 8.01287i) q^{37} +3.19623i q^{39} -0.877273i q^{41} +(-1.46106 + 1.46106i) q^{43} +(-1.17321 - 1.17321i) q^{45} +0.509593 q^{47} -1.00000 q^{49} +(2.42668 + 2.42668i) q^{51} +(-4.42016 + 4.42016i) q^{53} +2.25534i q^{55} -0.804390i q^{57} +(-1.96461 + 1.96461i) q^{59} +(4.61179 + 4.61179i) q^{61} -1.00000 q^{63} -5.30308 q^{65} +(-0.0452695 - 0.0452695i) q^{67} +(1.44736 - 1.44736i) q^{69} +9.10186i q^{71} -9.52481i q^{73} +(-1.58899 + 1.58899i) q^{75} +(0.961187 + 0.961187i) q^{77} -4.83685 q^{79} -1.00000 q^{81} +(9.73976 + 9.73976i) q^{83} +(-4.02627 + 4.02627i) q^{85} +9.02912i q^{87} -12.5234i q^{89} +(-2.26008 + 2.26008i) q^{91} +(-6.82453 - 6.82453i) q^{93} +1.33462 q^{95} -13.1147 q^{97} +(0.961187 + 0.961187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 12 q^{29} - 24 q^{33} + 12 q^{37} - 4 q^{43} - 20 q^{49} + 8 q^{51} - 36 q^{53} + 8 q^{61} - 20 q^{63} + 16 q^{65} + 12 q^{67} - 16 q^{69} + 16 q^{75} - 12 q^{77} - 24 q^{79} - 20 q^{81} - 40 q^{83} - 16 q^{85} - 72 q^{97} - 12 q^{99}+O(q^{100}) $ 20 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 12 * q^29 - 24 * q^33 + 12 * q^37 - 4 * q^43 - 20 * q^49 + 8 * q^51 - 36 * q^53 + 8 * q^61 - 20 * q^63 + 16 * q^65 + 12 * q^67 - 16 * q^69 + 16 * q^75 - 12 * q^77 - 24 * q^79 - 20 * q^81 - 40 * q^83 - 16 * q^85 - 72 * q^97 - 12 * 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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−1.17321	+	1.17321i	−0.524674	+	0.524674i	−0.918980	−	0.394305i	$-0.870985\pi$
$5$	−1.17321	+	1.17321i	−0.524674	+	0.524674i	0.394305	+	0.918980i	$0.370985\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	0.961187	−	0.961187i	0.289809	−	0.289809i	−0.547196	−	0.837005i	$-0.684305\pi$
$11$	0.961187	−	0.961187i	0.289809	−	0.289809i	0.837005	+	0.547196i	$0.184305\pi$
$12$		0			0
$13$	2.26008	+	2.26008i	0.626832	+	0.626832i	0.947270	−	0.320438i	$-0.103830\pi$
$13$	2.26008	+	2.26008i	0.626832	+	0.626832i	−0.320438	+	0.947270i	$0.603830\pi$
$14$		0			0
$15$	−1.65917			−0.428395
$16$		0			0
$17$	3.43185			0.832345			0.416173	−	0.909286i	$-0.363371\pi$
$17$	3.43185			0.832345			0.416173	+	0.909286i	$0.363371\pi$
$18$		0			0
$19$	−0.568789	−	0.568789i	−0.130489	−	0.130489i	0.638846	−	0.769335i	$-0.279412\pi$
$19$	−0.568789	−	0.568789i	−0.130489	−	0.130489i	−0.769335	+	0.638846i	$0.779412\pi$
$20$		0			0
$21$	−0.707107	+	0.707107i	−0.154303	+	0.154303i
$22$		0			0
$23$		−	2.04688i		−	0.426803i	−0.976965	−	0.213402i	$-0.931546\pi$
$23$		−	2.04688i		−	0.426803i	0.976965	−	0.213402i	$-0.0684543\pi$
$24$		0			0
$25$			2.24717i			0.449434i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	6.38455	+	6.38455i	1.18558	+	1.18558i	0.978276	+	0.207306i	$0.0664694\pi$
$29$	6.38455	+	6.38455i	1.18558	+	1.18558i	0.207306	+	0.978276i	$0.433531\pi$
$30$		0			0
$31$	−9.65134			−1.73343			−0.866716	−	0.498802i	$-0.833774\pi$
$31$	−9.65134			−1.73343			−0.866716	+	0.498802i	$0.833774\pi$
$32$		0			0
$33$	1.35932			0.236628
$34$		0			0
$35$	−1.17321	−	1.17321i	−0.198308	−	0.198308i
$36$		0			0
$37$	−8.01287	+	8.01287i	−1.31731	+	1.31731i	−0.401408	+	0.915899i	$0.631479\pi$
$37$	−8.01287	+	8.01287i	−1.31731	+	1.31731i	−0.915899	+	0.401408i	$0.868521\pi$
$38$		0			0
$39$			3.19623i			0.511806i
$40$		0			0
$41$		−	0.877273i		−	0.137007i	−0.997651	−	0.0685035i	$-0.978178\pi$
$41$		−	0.877273i		−	0.137007i	0.997651	−	0.0685035i	$-0.0218224\pi$
$42$		0			0
$43$	−1.46106	+	1.46106i	−0.222810	+	0.222810i	−0.809681	−	0.586871i	$-0.800360\pi$
$43$	−1.46106	+	1.46106i	−0.222810	+	0.222810i	0.586871	+	0.809681i	$0.300360\pi$
$44$		0			0
$45$	−1.17321	−	1.17321i	−0.174891	−	0.174891i
$46$		0			0
$47$	0.509593			0.0743318			0.0371659	−	0.999309i	$-0.488167\pi$
$47$	0.509593			0.0743318			0.0371659	+	0.999309i	$0.488167\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	2.42668	+	2.42668i	0.339804	+	0.339804i
$52$		0			0
$53$	−4.42016	+	4.42016i	−0.607156	+	0.607156i	−0.942202	−	0.335046i	$-0.891248\pi$
$53$	−4.42016	+	4.42016i	−0.607156	+	0.607156i	0.335046	+	0.942202i	$0.391248\pi$
$54$		0			0
$55$			2.25534i			0.304110i
$56$		0			0
$57$		−	0.804390i		−	0.106544i
$58$		0			0
$59$	−1.96461	+	1.96461i	−0.255771	+	0.255771i	−0.823332	−	0.567561i	$-0.807887\pi$
$59$	−1.96461	+	1.96461i	−0.255771	+	0.255771i	0.567561	+	0.823332i	$0.307887\pi$
$60$		0			0
$61$	4.61179	+	4.61179i	0.590479	+	0.590479i	0.937761	−	0.347281i	$-0.112895\pi$
$61$	4.61179	+	4.61179i	0.590479	+	0.590479i	−0.347281	+	0.937761i	$0.612895\pi$
$62$		0			0
$63$	−1.00000			−0.125988
$64$		0			0
$65$	−5.30308			−0.657766
$66$		0			0
$67$	−0.0452695	−	0.0452695i	−0.00553055	−	0.00553055i	0.704336	−	0.709867i	$-0.251245\pi$
$67$	−0.0452695	−	0.0452695i	−0.00553055	−	0.00553055i	−0.709867	+	0.704336i	$0.751245\pi$
$68$		0			0
$69$	1.44736	−	1.44736i	0.174242	−	0.174242i
$70$		0			0
$71$			9.10186i			1.08019i	0.841603	+	0.540096i	$0.181612\pi$
$71$			9.10186i			1.08019i	−0.841603	+	0.540096i	$0.818388\pi$
$72$		0			0
$73$		−	9.52481i		−	1.11480i	−0.830246	−	0.557398i	$-0.811800\pi$
$73$		−	9.52481i		−	1.11480i	0.830246	−	0.557398i	$-0.188200\pi$
$74$		0			0
$75$	−1.58899	+	1.58899i	−0.183481	+	0.183481i
$76$		0			0
$77$	0.961187	+	0.961187i	0.109537	+	0.109537i
$78$		0			0
$79$	−4.83685			−0.544188			−0.272094	−	0.962271i	$-0.587716\pi$
$79$	−4.83685			−0.544188			−0.272094	+	0.962271i	$0.587716\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	9.73976	+	9.73976i	1.06908	+	1.06908i	0.997430	+	0.0716481i	$0.0228259\pi$
$83$	9.73976	+	9.73976i	1.06908	+	1.06908i	0.0716481	+	0.997430i	$0.477174\pi$
$84$		0			0
$85$	−4.02627	+	4.02627i	−0.436710	+	0.436710i
$86$		0			0
$87$			9.02912i			0.968023i
$88$		0			0
$89$		−	12.5234i		−	1.32748i	−0.747964	−	0.663740i	$-0.768968\pi$
$89$		−	12.5234i		−	1.32748i	0.747964	−	0.663740i	$-0.231032\pi$
$90$		0			0
$91$	−2.26008	+	2.26008i	−0.236920	+	0.236920i
$92$		0			0
$93$	−6.82453	−	6.82453i	−0.707671	−	0.707671i
$94$		0			0
$95$	1.33462			0.136929
$96$		0			0
$97$	−13.1147			−1.33159			−0.665797	−	0.746133i	$-0.731908\pi$
$97$	−13.1147			−1.33159			−0.665797	+	0.746133i	$0.731908\pi$
$98$		0			0
$99$	0.961187	+	0.961187i	0.0966029	+	0.0966029i
$100$		0			0
$101$	1.59669	−	1.59669i	0.158877	−	0.158877i	−0.623192	−	0.782069i	$-0.714165\pi$
$101$	1.59669	−	1.59669i	0.158877	−	0.158877i	0.782069	+	0.623192i	$0.214165\pi$
$102$		0			0
$103$		−	8.93964i		−	0.880849i	−0.897790	−	0.440424i	$-0.854828\pi$
$103$		−	8.93964i		−	0.880849i	0.897790	−	0.440424i	$-0.145172\pi$
$104$		0			0
$105$		−	1.65917i		−	0.161918i
$106$		0			0
$107$	12.0811	−	12.0811i	1.16792	−	1.16792i	0.185226	−	0.982696i	$-0.440698\pi$
$107$	12.0811	−	12.0811i	1.16792	−	1.16792i	0.982696	−	0.185226i	$-0.0593016\pi$
$108$		0			0
$109$	4.37857	+	4.37857i	0.419390	+	0.419390i	0.884994	−	0.465603i	$-0.154163\pi$
$109$	4.37857	+	4.37857i	0.419390	+	0.419390i	−0.465603	+	0.884994i	$0.654163\pi$
$110$		0			0
$111$	−11.3319			−1.07558
$112$		0			0
$113$	16.8217			1.58245			0.791227	−	0.611523i	$-0.209443\pi$
$113$	16.8217			1.58245			0.791227	+	0.611523i	$0.209443\pi$
$114$		0			0
$115$	2.40141	+	2.40141i	0.223933	+	0.223933i
$116$		0			0
$117$	−2.26008	+	2.26008i	−0.208944	+	0.208944i
$118$		0			0
$119$			3.43185i			0.314597i
$120$		0			0
$121$			9.15224i			0.832022i
$122$		0			0
$123$	0.620326	−	0.620326i	0.0559329	−	0.0559329i
$124$		0			0
$125$	−8.50243	−	8.50243i	−0.760481	−	0.760481i
$126$		0			0
$127$	15.0532			1.33576			0.667878	−	0.744271i	$-0.267203\pi$
$127$	15.0532			1.33576			0.667878	+	0.744271i	$0.267203\pi$
$128$		0			0
$129$	−2.06625			−0.181924
$130$		0			0
$131$	−3.27505	−	3.27505i	−0.286143	−	0.286143i	0.549410	−	0.835553i	$-0.314852\pi$
$131$	−3.27505	−	3.27505i	−0.286143	−	0.286143i	−0.835553	+	0.549410i	$0.814852\pi$
$132$		0			0
$133$	0.568789	−	0.568789i	0.0493203	−	0.0493203i
$134$		0			0
$135$		−	1.65917i		−	0.142798i
$136$		0			0
$137$			4.35840i			0.372363i	0.982515	+	0.186182i	$0.0596113\pi$
$137$			4.35840i			0.372363i	−0.982515	+	0.186182i	$0.940389\pi$
$138$		0			0
$139$	−0.600490	+	0.600490i	−0.0509329	+	0.0509329i	−0.732114	−	0.681182i	$-0.761466\pi$
$139$	−0.600490	+	0.600490i	−0.0509329	+	0.0509329i	0.681182	+	0.732114i	$0.261466\pi$
$140$		0			0
$141$	0.360337	+	0.360337i	0.0303458	+	0.0303458i
$142$		0			0
$143$	4.34471			0.363323
$144$		0			0
$145$	−14.9808			−1.24409
$146$		0			0
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$		0			0
$149$	−0.413707	+	0.413707i	−0.0338922	+	0.0338922i	−0.723850	−	0.689958i	$-0.757629\pi$
$149$	−0.413707	+	0.413707i	−0.0338922	+	0.0338922i	0.689958	+	0.723850i	$0.257629\pi$
$150$		0			0
$151$		−	6.98012i		−	0.568034i	−0.958819	−	0.284017i	$-0.908333\pi$
$151$		−	6.98012i		−	0.568034i	0.958819	−	0.284017i	$-0.0916673\pi$
$152$		0			0
$153$			3.43185i			0.277448i
$154$		0			0
$155$	11.3230	−	11.3230i	0.909487	−	0.909487i
$156$		0			0
$157$	15.4731	+	15.4731i	1.23489	+	1.23489i	0.962063	+	0.272828i	$0.0879590\pi$
$157$	15.4731	+	15.4731i	1.23489	+	1.23489i	0.272828	+	0.962063i	$0.412041\pi$
$158$		0			0
$159$	−6.25105			−0.495741
$160$		0			0
$161$	2.04688			0.161316
$162$		0			0
$163$	−0.453951	−	0.453951i	−0.0355562	−	0.0355562i	0.689105	−	0.724661i	$-0.258004\pi$
$163$	−0.453951	−	0.453951i	−0.0355562	−	0.0355562i	−0.724661	+	0.689105i	$0.758004\pi$
$164$		0			0
$165$	−1.59477	+	1.59477i	−0.124153	+	0.124153i
$166$		0			0
$167$		−	0.0340024i		−	0.00263118i	−0.999999	−	0.00131559i	$-0.999581\pi$
$167$		−	0.0340024i		−	0.00263118i	0.999999	−	0.00131559i	$-0.000418766\pi$
$168$		0			0
$169$		−	2.78412i		−	0.214163i
$170$		0			0
$171$	0.568789	−	0.568789i	0.0434964	−	0.0434964i
$172$		0			0
$173$	−1.56144	−	1.56144i	−0.118714	−	0.118714i	0.645254	−	0.763968i	$-0.276751\pi$
$173$	−1.56144	−	1.56144i	−0.118714	−	0.118714i	−0.763968	+	0.645254i	$0.776751\pi$
$174$		0			0
$175$	−2.24717			−0.169870
$176$		0			0
$177$	−2.77838			−0.208836
$178$		0			0
$179$	8.54145	+	8.54145i	0.638418	+	0.638418i	0.950165	−	0.311747i	$-0.100914\pi$
$179$	8.54145	+	8.54145i	0.638418	+	0.638418i	−0.311747	+	0.950165i	$0.600914\pi$
$180$		0			0
$181$	6.50053	−	6.50053i	0.483181	−	0.483181i	−0.422965	−	0.906146i	$-0.639011\pi$
$181$	6.50053	−	6.50053i	0.483181	−	0.483181i	0.906146	+	0.422965i	$0.139011\pi$
$182$		0			0
$183$			6.52206i			0.482124i
$184$		0			0
$185$		−	18.8015i		−	1.38231i
$186$		0			0
$187$	3.29865	−	3.29865i	0.241221	−	0.241221i
$188$		0			0
$189$	−0.707107	−	0.707107i	−0.0514344	−	0.0514344i
$190$		0			0
$191$	−19.9411			−1.44289			−0.721445	−	0.692472i	$-0.756522\pi$
$191$	−19.9411			−1.44289			−0.721445	+	0.692472i	$0.756522\pi$
$192$		0			0
$193$	−10.9429			−0.787691			−0.393845	−	0.919177i	$-0.628855\pi$
$193$	−10.9429			−0.787691			−0.393845	+	0.919177i	$0.628855\pi$
$194$		0			0
$195$	−3.74984	−	3.74984i	−0.268532	−	0.268532i
$196$		0			0
$197$	16.8885	−	16.8885i	1.20326	−	1.20326i	0.230085	−	0.973171i	$-0.426100\pi$
$197$	16.8885	−	16.8885i	1.20326	−	1.20326i	0.973171	−	0.230085i	$-0.0739005\pi$
$198$		0			0
$199$		−	10.2733i		−	0.728254i	−0.931349	−	0.364127i	$-0.881367\pi$
$199$		−	10.2733i		−	0.728254i	0.931349	−	0.364127i	$-0.118633\pi$
$200$		0			0
$201$		−	0.0640207i		−	0.00451567i
$202$		0			0
$203$	−6.38455	+	6.38455i	−0.448108	+	0.448108i
$204$		0			0
$205$	1.02922	+	1.02922i	0.0718841	+	0.0718841i
$206$		0			0
$207$	2.04688			0.142268
$208$		0			0
$209$	−1.09343			−0.0756338
$210$		0			0
$211$	16.6146	+	16.6146i	1.14379	+	1.14379i	0.987750	+	0.156044i	$0.0498741\pi$
$211$	16.6146	+	16.6146i	1.14379	+	1.14379i	0.156044	+	0.987750i	$0.450126\pi$
$212$		0			0
$213$	−6.43599	+	6.43599i	−0.440987	+	0.440987i
$214$		0			0
$215$		−	3.42826i		−	0.233805i
$216$		0			0
$217$		−	9.65134i		−	0.655176i
$218$		0			0
$219$	6.73506	−	6.73506i	0.455113	−	0.455113i
$220$		0			0
$221$	7.75623	+	7.75623i	0.521741	+	0.521741i
$222$		0			0
$223$	−27.8260			−1.86336			−0.931682	−	0.363275i	$-0.881659\pi$
$223$	−27.8260			−1.86336			−0.931682	+	0.363275i	$0.881659\pi$
$224$		0			0
$225$	−2.24717			−0.149811
$226$		0			0
$227$	5.51342	+	5.51342i	0.365939	+	0.365939i	0.865994	−	0.500055i	$-0.166687\pi$
$227$	5.51342	+	5.51342i	0.365939	+	0.365939i	−0.500055	+	0.865994i	$0.666687\pi$
$228$		0			0
$229$	−10.8200	+	10.8200i	−0.715005	+	0.715005i	−0.967578	−	0.252573i	$-0.918723\pi$
$229$	−10.8200	+	10.8200i	−0.715005	+	0.715005i	0.252573	+	0.967578i	$0.418723\pi$
$230$		0			0
$231$			1.35932i			0.0894369i
$232$		0			0
$233$		−	11.7579i		−	0.770283i	−0.922857	−	0.385142i	$-0.874153\pi$
$233$		−	11.7579i		−	0.770283i	0.922857	−	0.385142i	$-0.125847\pi$
$234$		0			0
$235$	−0.597859	+	0.597859i	−0.0390000	+	0.0390000i
$236$		0			0
$237$	−3.42017	−	3.42017i	−0.222164	−	0.222164i
$238$		0			0
$239$	7.00815			0.453319			0.226660	−	0.973974i	$-0.427219\pi$
$239$	7.00815			0.453319			0.226660	+	0.973974i	$0.427219\pi$
$240$		0			0
$241$	25.5849			1.64807			0.824034	−	0.566540i	$-0.191718\pi$
$241$	25.5849			1.64807			0.824034	+	0.566540i	$0.191718\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	1.17321	−	1.17321i	0.0749535	−	0.0749535i
$246$		0			0
$247$		−	2.57101i		−	0.163590i
$248$		0			0
$249$			13.7741i			0.872899i
$250$		0			0
$251$	6.56086	−	6.56086i	0.414118	−	0.414118i	−0.469053	−	0.883170i	$-0.655405\pi$
$251$	6.56086	−	6.56086i	0.414118	−	0.414118i	0.883170	+	0.469053i	$0.155405\pi$
$252$		0			0
$253$	−1.96743	−	1.96743i	−0.123691	−	0.123691i
$254$		0			0
$255$	−5.69400			−0.356572
$256$		0			0
$257$	20.7104			1.29188			0.645938	−	0.763390i	$-0.276466\pi$
$257$	20.7104			1.29188			0.645938	+	0.763390i	$0.276466\pi$
$258$		0			0
$259$	−8.01287	−	8.01287i	−0.497895	−	0.497895i
$260$		0			0
$261$	−6.38455	+	6.38455i	−0.395194	+	0.395194i
$262$		0			0
$263$		−	5.69762i		−	0.351330i	−0.984450	−	0.175665i	$-0.943792\pi$
$263$		−	5.69762i		−	0.351330i	0.984450	−	0.175665i	$-0.0562076\pi$
$264$		0			0
$265$		−	10.3715i		−	0.637118i
$266$		0			0
$267$	8.85539	−	8.85539i	0.541941	−	0.541941i
$268$		0			0
$269$	−7.07864	−	7.07864i	−0.431592	−	0.431592i	0.457578	−	0.889170i	$-0.348717\pi$
$269$	−7.07864	−	7.07864i	−0.431592	−	0.431592i	−0.889170	+	0.457578i	$0.848717\pi$
$270$		0			0
$271$	25.2165			1.53180			0.765898	−	0.642963i	$-0.222295\pi$
$271$	25.2165			1.53180			0.765898	+	0.642963i	$0.222295\pi$
$272$		0			0
$273$	−3.19623			−0.193445
$274$		0			0
$275$	2.15995	+	2.15995i	0.130250	+	0.130250i
$276$		0			0
$277$	0.112949	−	0.112949i	0.00678644	−	0.00678644i	−0.703705	−	0.710492i	$-0.748473\pi$
$277$	0.112949	−	0.112949i	0.00678644	−	0.00678644i	0.710492	+	0.703705i	$0.248473\pi$
$278$		0			0
$279$		−	9.65134i		−	0.577811i
$280$		0			0
$281$			16.1017i			0.960544i	0.877120	+	0.480272i	$0.159462\pi$
$281$			16.1017i			0.960544i	−0.877120	+	0.480272i	$0.840538\pi$
$282$		0			0
$283$	−17.0580	+	17.0580i	−1.01399	+	1.01399i	−0.0140927	+	0.999901i	$0.504486\pi$
$283$	−17.0580	+	17.0580i	−1.01399	+	1.01399i	−0.999901	+	0.0140927i	$0.995514\pi$
$284$		0			0
$285$	0.943716	+	0.943716i	0.0559009	+	0.0559009i
$286$		0			0
$287$	0.877273			0.0517838
$288$		0			0
$289$	−5.22242			−0.307201
$290$		0			0
$291$	−9.27348	−	9.27348i	−0.543621	−	0.543621i
$292$		0			0
$293$	18.4683	−	18.4683i	1.07893	−	1.07893i	0.0823226	−	0.996606i	$-0.473766\pi$
$293$	18.4683	−	18.4683i	1.07893	−	1.07893i	0.996606	−	0.0823226i	$-0.0262338\pi$
$294$		0			0
$295$		−	4.60980i		−	0.268393i
$296$		0			0
$297$			1.35932i			0.0788760i
$298$		0			0
$299$	4.62609	−	4.62609i	0.267534	−	0.267534i
$300$		0			0
$301$	−1.46106	−	1.46106i	−0.0842142	−	0.0842142i
$302$		0			0
$303$	2.25806			0.129722
$304$		0			0
$305$	−10.8212			−0.619619
$306$		0			0
$307$	−2.82642	−	2.82642i	−0.161312	−	0.161312i	0.621836	−	0.783148i	$-0.286387\pi$
$307$	−2.82642	−	2.82642i	−0.161312	−	0.161312i	−0.783148	+	0.621836i	$0.786387\pi$
$308$		0			0
$309$	6.32128	−	6.32128i	0.359605	−	0.359605i
$310$		0			0
$311$		−	12.4925i		−	0.708386i	−0.935172	−	0.354193i	$-0.884756\pi$
$311$		−	12.4925i		−	0.708386i	0.935172	−	0.354193i	$-0.115244\pi$
$312$		0			0
$313$		−	20.5676i		−	1.16255i	−0.813708	−	0.581274i	$-0.802554\pi$
$313$		−	20.5676i		−	1.16255i	0.813708	−	0.581274i	$-0.197446\pi$
$314$		0			0
$315$	1.17321	−	1.17321i	0.0661028	−	0.0661028i
$316$		0			0
$317$	−10.9807	−	10.9807i	−0.616735	−	0.616735i	0.327957	−	0.944693i	$-0.393640\pi$
$317$	−10.9807	−	10.9807i	−0.616735	−	0.616735i	−0.944693	+	0.327957i	$0.893640\pi$
$318$		0			0
$319$	12.2735			0.687184
$320$		0			0
$321$	17.0852			0.953604
$322$		0			0
$323$	−1.95200	−	1.95200i	−0.108612	−	0.108612i
$324$		0			0
$325$	−5.07877	+	5.07877i	−0.281719	+	0.281719i
$326$		0			0
$327$			6.19223i			0.342431i
$328$		0			0
$329$			0.509593i			0.0280948i
$330$		0			0
$331$	−20.7798	+	20.7798i	−1.14216	+	1.14216i	−0.154109	+	0.988054i	$0.549251\pi$
$331$	−20.7798	+	20.7798i	−1.14216	+	1.14216i	−0.988054	+	0.154109i	$0.950749\pi$
$332$		0			0
$333$	−8.01287	−	8.01287i	−0.439102	−	0.439102i
$334$		0			0
$335$	0.106221			0.00580347
$336$		0			0
$337$	−0.807932			−0.0440109			−0.0220054	−	0.999758i	$-0.507005\pi$
$337$	−0.807932			−0.0440109			−0.0220054	+	0.999758i	$0.507005\pi$
$338$		0			0
$339$	11.8947	+	11.8947i	0.646034	+	0.646034i
$340$		0			0
$341$	−9.27674	+	9.27674i	−0.502364	+	0.502364i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			3.39611i			0.182840i
$346$		0			0
$347$	25.0356	−	25.0356i	1.34398	−	1.34398i	0.451923	−	0.892057i	$-0.350738\pi$
$347$	25.0356	−	25.0356i	1.34398	−	1.34398i	0.892057	−	0.451923i	$-0.149262\pi$
$348$		0			0
$349$	5.76864	+	5.76864i	0.308788	+	0.308788i	0.844439	−	0.535651i	$-0.179934\pi$
$349$	5.76864	+	5.76864i	0.308788	+	0.308788i	−0.535651	+	0.844439i	$0.679934\pi$
$350$		0			0
$351$	−3.19623			−0.170602
$352$		0			0
$353$	1.47981			0.0787624			0.0393812	−	0.999224i	$-0.487461\pi$
$353$	1.47981			0.0787624			0.0393812	+	0.999224i	$0.487461\pi$
$354$		0			0
$355$	−10.6784	−	10.6784i	−0.566749	−	0.566749i
$356$		0			0
$357$	−2.42668	+	2.42668i	−0.128434	+	0.128434i
$358$		0			0
$359$		−	10.2630i		−	0.541663i	−0.962627	−	0.270831i	$-0.912701\pi$
$359$		−	10.2630i		−	0.541663i	0.962627	−	0.270831i	$-0.0872986\pi$
$360$		0			0
$361$		−	18.3530i		−	0.965945i
$362$		0			0
$363$	−6.47161	+	6.47161i	−0.339671	+	0.339671i
$364$		0			0
$365$	11.1746	+	11.1746i	0.584904	+	0.584904i
$366$		0			0
$367$	32.5024			1.69661			0.848306	−	0.529507i	$-0.177623\pi$
$367$	32.5024			1.69661			0.848306	+	0.529507i	$0.177623\pi$
$368$		0			0
$369$	0.877273			0.0456690
$370$		0			0
$371$	−4.42016	−	4.42016i	−0.229483	−	0.229483i
$372$		0			0
$373$	20.0920	−	20.0920i	1.04032	−	1.04032i	0.0411724	−	0.999152i	$-0.486891\pi$
$373$	20.0920	−	20.0920i	1.04032	−	1.04032i	0.999152	−	0.0411724i	$-0.0131093\pi$
$374$		0			0
$375$		−	12.0243i		−	0.620930i
$376$		0			0
$377$			28.8591i			1.48632i
$378$		0			0
$379$	0.569455	−	0.569455i	0.0292509	−	0.0292509i	−0.692330	−	0.721581i	$-0.743416\pi$
$379$	0.569455	−	0.569455i	0.0292509	−	0.0292509i	0.721581	+	0.692330i	$0.243416\pi$
$380$		0			0
$381$	10.6442	+	10.6442i	0.545320	+	0.545320i
$382$		0			0
$383$	−31.3107			−1.59990			−0.799950	−	0.600067i	$-0.795141\pi$
$383$	−31.3107			−1.59990			−0.799950	+	0.600067i	$0.795141\pi$
$384$		0			0
$385$	−2.25534			−0.114943
$386$		0			0
$387$	−1.46106	−	1.46106i	−0.0742700	−	0.0742700i
$388$		0			0
$389$	−6.95478	+	6.95478i	−0.352621	+	0.352621i	−0.861084	−	0.508463i	$-0.830214\pi$
$389$	−6.95478	+	6.95478i	−0.352621	+	0.352621i	0.508463	+	0.861084i	$0.330214\pi$
$390$		0			0
$391$		−	7.02457i		−	0.355248i
$392$		0			0
$393$		−	4.63162i		−	0.233634i
$394$		0			0
$395$	5.67463	−	5.67463i	0.285522	−	0.285522i
$396$		0			0
$397$	−22.4270	−	22.4270i	−1.12558	−	1.12558i	−0.990888	−	0.134690i	$-0.956996\pi$
$397$	−22.4270	−	22.4270i	−1.12558	−	1.12558i	−0.134690	−	0.990888i	$-0.543004\pi$
$398$		0			0
$399$	0.804390			0.0402699
$400$		0			0
$401$	14.0464			0.701444			0.350722	−	0.936480i	$-0.385936\pi$
$401$	14.0464			0.701444			0.350722	+	0.936480i	$0.385936\pi$
$402$		0			0
$403$	−21.8128	−	21.8128i	−1.08657	−	1.08657i
$404$		0			0
$405$	1.17321	−	1.17321i	0.0582972	−	0.0582972i
$406$		0			0
$407$			15.4037i			0.763534i
$408$		0			0
$409$		−	14.9137i		−	0.737436i	−0.929541	−	0.368718i	$-0.879797\pi$
$409$		−	14.9137i		−	0.737436i	0.929541	−	0.368718i	$-0.120203\pi$
$410$		0			0
$411$	−3.08186	+	3.08186i	−0.152017	+	0.152017i
$412$		0			0
$413$	−1.96461	−	1.96461i	−0.0966723	−	0.0966723i
$414$		0			0
$415$	−22.8535			−1.12184
$416$		0			0
$417$	−0.849220			−0.0415865
$418$		0			0
$419$	−19.5785	−	19.5785i	−0.956473	−	0.956473i	0.0426187	−	0.999091i	$-0.486430\pi$
$419$	−19.5785	−	19.5785i	−0.956473	−	0.956473i	−0.999091	+	0.0426187i	$0.986430\pi$
$420$		0			0
$421$	12.8137	−	12.8137i	0.624500	−	0.624500i	−0.322179	−	0.946679i	$-0.604415\pi$
$421$	12.8137	−	12.8137i	0.624500	−	0.624500i	0.946679	+	0.322179i	$0.104415\pi$
$422$		0			0
$423$			0.509593i			0.0247773i
$424$		0			0
$425$			7.71194i			0.374084i
$426$		0			0
$427$	−4.61179	+	4.61179i	−0.223180	+	0.223180i
$428$		0			0
$429$	3.07217	+	3.07217i	0.148326	+	0.148326i
$430$		0			0
$431$	38.0130			1.83102			0.915510	−	0.402294i	$-0.131787\pi$
$431$	38.0130			1.83102			0.915510	+	0.402294i	$0.131787\pi$
$432$		0			0
$433$	−17.9303			−0.861677			−0.430839	−	0.902429i	$-0.641782\pi$
$433$	−17.9303			−0.861677			−0.430839	+	0.902429i	$0.641782\pi$
$434$		0			0
$435$	−10.5930	−	10.5930i	−0.507897	−	0.507897i
$436$		0			0
$437$	−1.16424	+	1.16424i	−0.0556932	+	0.0556932i
$438$		0			0
$439$		−	3.65487i		−	0.174437i	−0.996189	−	0.0872187i	$-0.972202\pi$
$439$		−	3.65487i		−	0.174437i	0.996189	−	0.0872187i	$-0.0277979\pi$
$440$		0			0
$441$		−	1.00000i		−	0.0476190i
$442$		0			0
$443$	10.2265	−	10.2265i	0.485878	−	0.485878i	−0.421125	−	0.907003i	$-0.638365\pi$
$443$	10.2265	−	10.2265i	0.485878	−	0.485878i	0.907003	+	0.421125i	$0.138365\pi$
$444$		0			0
$445$	14.6926	+	14.6926i	0.696494	+	0.696494i
$446$		0			0
$447$	−0.585070			−0.0276728
$448$		0			0
$449$	31.2295			1.47381			0.736905	−	0.675996i	$-0.236286\pi$
$449$	31.2295			1.47381			0.736905	+	0.675996i	$0.236286\pi$
$450$		0			0
$451$	−0.843224	−	0.843224i	−0.0397058	−	0.0397058i
$452$		0			0
$453$	4.93569	−	4.93569i	0.231899	−	0.231899i
$454$		0			0
$455$		−	5.30308i		−	0.248612i
$456$		0			0
$457$			25.4927i			1.19250i	0.802799	+	0.596249i	$0.203343\pi$
$457$			25.4927i			1.19250i	−0.802799	+	0.596249i	$0.796657\pi$
$458$		0			0
$459$	−2.42668	+	2.42668i	−0.113268	+	0.113268i
$460$		0			0
$461$	−28.4256	−	28.4256i	−1.32391	−	1.32391i	−0.910579	−	0.413334i	$-0.864364\pi$
$461$	−28.4256	−	28.4256i	−1.32391	−	1.32391i	−0.413334	−	0.910579i	$-0.635636\pi$
$462$		0			0
$463$	22.1165			1.02784			0.513920	−	0.857838i	$-0.328193\pi$
$463$	22.1165			1.02784			0.513920	+	0.857838i	$0.328193\pi$
$464$		0			0
$465$	16.0132			0.742593
$466$		0			0
$467$	−24.8501	−	24.8501i	−1.14992	−	1.14992i	−0.986567	−	0.163358i	$-0.947767\pi$
$467$	−24.8501	−	24.8501i	−1.14992	−	1.14992i	−0.163358	−	0.986567i	$-0.552233\pi$
$468$		0			0
$469$	0.0452695	−	0.0452695i	0.00209035	−	0.00209035i
$470$		0			0
$471$			21.8823i			1.00828i
$472$		0			0
$473$			2.80871i			0.129145i
$474$		0			0
$475$	1.27817	−	1.27817i	0.0586462	−	0.0586462i
$476$		0			0
$477$	−4.42016	−	4.42016i	−0.202385	−	0.202385i
$478$		0			0
$479$	25.0617			1.14510			0.572550	−	0.819870i	$-0.305954\pi$
$479$	25.0617			1.14510			0.572550	+	0.819870i	$0.305954\pi$
$480$		0			0
$481$	−36.2194			−1.65146
$482$		0			0
$483$	1.44736	+	1.44736i	0.0658572	+	0.0658572i
$484$		0			0
$485$	15.3862	−	15.3862i	0.698653	−	0.698653i
$486$		0			0
$487$		−	7.56145i		−	0.342642i	−0.985215	−	0.171321i	$-0.945196\pi$
$487$		−	7.56145i		−	0.342642i	0.985215	−	0.171321i	$-0.0548035\pi$
$488$		0			0
$489$		−	0.641984i		−	0.0290315i
$490$		0			0
$491$	−16.5365	+	16.5365i	−0.746280	+	0.746280i	−0.973778	−	0.227499i	$-0.926945\pi$
$491$	−16.5365	+	16.5365i	−0.746280	+	0.746280i	0.227499	+	0.973778i	$0.426945\pi$
$492$		0			0
$493$	21.9108	+	21.9108i	0.986813	+	0.986813i
$494$		0			0
$495$	−2.25534			−0.101370
$496$		0			0
$497$	−9.10186			−0.408274
$498$		0			0
$499$	18.9348	+	18.9348i	0.847640	+	0.847640i	0.989838	−	0.142198i	$-0.0454171\pi$
$499$	18.9348	+	18.9348i	0.847640	+	0.847640i	−0.142198	+	0.989838i	$0.545417\pi$
$500$		0			0
$501$	0.0240433	−	0.0240433i	0.00107418	−	0.00107418i
$502$		0			0
$503$			14.8446i			0.661889i	0.943650	+	0.330944i	$0.107367\pi$
$503$			14.8446i			0.661889i	−0.943650	+	0.330944i	$0.892633\pi$
$504$		0			0
$505$			3.74650i			0.166717i
$506$		0			0
$507$	1.96867	−	1.96867i	0.0874316	−	0.0874316i
$508$		0			0
$509$	11.3898	+	11.3898i	0.504844	+	0.504844i	0.912939	−	0.408095i	$-0.133807\pi$
$509$	11.3898	+	11.3898i	0.504844	+	0.504844i	−0.408095	+	0.912939i	$0.633807\pi$
$510$		0			0
$511$	9.52481			0.421353
$512$		0			0
$513$	0.804390			0.0355147
$514$		0			0
$515$	10.4881	+	10.4881i	0.462159	+	0.462159i
$516$		0			0
$517$	0.489814	−	0.489814i	0.0215420	−	0.0215420i
$518$		0			0
$519$		−	2.20820i		−	0.0969294i
$520$		0			0
$521$			11.4945i			0.503584i	0.967781	+	0.251792i	$0.0810198\pi$
$521$			11.4945i			0.503584i	−0.967781	+	0.251792i	$0.918980\pi$
$522$		0			0
$523$	−22.2163	+	22.2163i	−0.971453	+	0.971453i	−0.999604	−	0.0281509i	$-0.991038\pi$
$523$	−22.2163	+	22.2163i	−0.971453	+	0.971453i	0.0281509	+	0.999604i	$0.491038\pi$
$524$		0			0
$525$	−1.58899	−	1.58899i	−0.0693491	−	0.0693491i
$526$		0			0
$527$	−33.1219			−1.44281
$528$		0			0
$529$	18.8103			0.817839
$530$		0			0
$531$	−1.96461	−	1.96461i	−0.0852569	−	0.0852569i
$532$		0			0
$533$	1.98270	−	1.98270i	0.0858804	−	0.0858804i
$534$		0			0
$535$			28.3472i			1.22556i
$536$		0			0
$537$			12.0794i			0.521266i
$538$		0			0
$539$	−0.961187	+	0.961187i	−0.0414013	+	0.0414013i
$540$		0			0
$541$	−24.6260	−	24.6260i	−1.05875	−	1.05875i	−0.998163	−	0.0605900i	$-0.980702\pi$
$541$	−24.6260	−	24.6260i	−1.05875	−	1.05875i	−0.0605900	−	0.998163i	$-0.519298\pi$
$542$		0			0
$543$	9.19314			0.394515
$544$		0			0
$545$	−10.2739			−0.440087
$546$		0			0
$547$	4.98919	+	4.98919i	0.213322	+	0.213322i	0.805677	−	0.592355i	$-0.201802\pi$
$547$	4.98919	+	4.98919i	0.213322	+	0.213322i	−0.592355	+	0.805677i	$0.701802\pi$
$548$		0			0
$549$	−4.61179	+	4.61179i	−0.196826	+	0.196826i
$550$		0			0
$551$		−	7.26293i		−	0.309411i
$552$		0			0
$553$		−	4.83685i		−	0.205684i
$554$		0			0
$555$	13.2947	−	13.2947i	0.564328	−	0.564328i
$556$		0			0
$557$	8.30623	+	8.30623i	0.351946	+	0.351946i	0.860833	−	0.508887i	$-0.169943\pi$
$557$	8.30623	+	8.30623i	0.351946	+	0.351946i	−0.508887	+	0.860833i	$0.669943\pi$
$558$		0			0
$559$	−6.60422			−0.279329
$560$		0			0
$561$	4.66499			0.196956
$562$		0			0
$563$	−18.0655	−	18.0655i	−0.761371	−	0.761371i	0.215199	−	0.976570i	$-0.430960\pi$
$563$	−18.0655	−	18.0655i	−0.761371	−	0.761371i	−0.976570	+	0.215199i	$0.930960\pi$
$564$		0			0
$565$	−19.7354	+	19.7354i	−0.830273	+	0.830273i
$566$		0			0
$567$		−	1.00000i		−	0.0419961i
$568$		0			0
$569$			42.9172i			1.79918i	0.436734	+	0.899591i	$0.356135\pi$
$569$			42.9172i			1.79918i	−0.436734	+	0.899591i	$0.643865\pi$
$570$		0			0
$571$	−21.9255	+	21.9255i	−0.917553	+	0.917553i	−0.996851	−	0.0792982i	$-0.974732\pi$
$571$	−21.9255	+	21.9255i	−0.917553	+	0.917553i	0.0792982	+	0.996851i	$0.474732\pi$
$572$		0			0
$573$	−14.1005	−	14.1005i	−0.589057	−	0.589057i
$574$		0			0
$575$	4.59967			0.191820
$576$		0			0
$577$	−19.2611			−0.801849			−0.400924	−	0.916111i	$-0.631311\pi$
$577$	−19.2611			−0.801849			−0.400924	+	0.916111i	$0.631311\pi$
$578$		0			0
$579$	−7.73783	−	7.73783i	−0.321573	−	0.321573i
$580$		0			0
$581$	−9.73976	+	9.73976i	−0.404074	+	0.404074i
$582$		0			0
$583$			8.49720i			0.351918i
$584$		0			0
$585$		−	5.30308i		−	0.219255i
$586$		0			0
$587$	−21.2186	+	21.2186i	−0.875785	+	0.875785i	−0.993095	−	0.117310i	$-0.962573\pi$
$587$	−21.2186	+	21.2186i	−0.875785	+	0.875785i	0.117310	+	0.993095i	$0.462573\pi$
$588$		0			0
$589$	5.48958	+	5.48958i	0.226194	+	0.226194i
$590$		0			0
$591$	23.8839			0.982454
$592$		0			0
$593$	−28.4529			−1.16842			−0.584210	−	0.811603i	$-0.698595\pi$
$593$	−28.4529			−1.16842			−0.584210	+	0.811603i	$0.698595\pi$
$594$		0			0
$595$	−4.02627	−	4.02627i	−0.165061	−	0.165061i
$596$		0			0
$597$	7.26431	−	7.26431i	0.297309	−	0.297309i
$598$		0			0
$599$			34.7302i			1.41904i	0.704686	+	0.709519i	$0.251088\pi$
$599$			34.7302i			1.41904i	−0.704686	+	0.709519i	$0.748912\pi$
$600$		0			0
$601$			1.45838i			0.0594888i	0.999558	+	0.0297444i	$0.00946933\pi$
$601$			1.45838i			0.0594888i	−0.999558	+	0.0297444i	$0.990531\pi$
$602$		0			0
$603$	0.0452695	−	0.0452695i	0.00184352	−	0.00184352i
$604$		0			0
$605$	−10.7375	−	10.7375i	−0.436540	−	0.436540i
$606$		0			0
$607$	45.6052			1.85106			0.925528	−	0.378679i	$-0.123621\pi$
$607$	45.6052			1.85106			0.925528	+	0.378679i	$0.123621\pi$
$608$		0			0
$609$	−9.02912			−0.365878
$610$		0			0
$611$	1.15172	+	1.15172i	0.0465936	+	0.0465936i
$612$		0			0
$613$	17.8426	−	17.8426i	0.720655	−	0.720655i	−0.248084	−	0.968739i	$-0.579801\pi$
$613$	17.8426	−	17.8426i	0.720655	−	0.720655i	0.968739	+	0.248084i	$0.0798008\pi$
$614$		0			0
$615$			1.45554i			0.0586931i
$616$		0			0
$617$			36.6942i			1.47725i	0.674114	+	0.738627i	$0.264526\pi$
$617$			36.6942i			1.47725i	−0.674114	+	0.738627i	$0.735474\pi$
$618$		0			0
$619$	−2.32370	+	2.32370i	−0.0933973	+	0.0933973i	−0.752262	−	0.658864i	$-0.771037\pi$
$619$	−2.32370	+	2.32370i	−0.0933973	+	0.0933973i	0.658864	+	0.752262i	$0.271037\pi$
$620$		0			0
$621$	1.44736	+	1.44736i	0.0580806	+	0.0580806i
$622$		0			0
$623$	12.5234			0.501740
$624$		0			0
$625$	8.71439			0.348576
$626$		0			0
$627$	−0.773169	−	0.773169i	−0.0308774	−	0.0308774i
$628$		0			0
$629$	−27.4989	+	27.4989i	−1.09645	+	1.09645i
$630$		0			0
$631$		−	5.28666i		−	0.210459i	−0.994448	−	0.105229i	$-0.966442\pi$
$631$		−	5.28666i		−	0.210459i	0.994448	−	0.105229i	$-0.0335577\pi$
$632$		0			0
$633$			23.4965i			0.933904i
$634$		0			0
$635$	−17.6605	+	17.6605i	−0.700836	+	0.700836i
$636$		0			0
$637$	−2.26008	−	2.26008i	−0.0895475	−	0.0895475i
$638$		0			0
$639$	−9.10186			−0.360064
$640$		0			0
$641$	4.04137			0.159624			0.0798122	−	0.996810i	$-0.474568\pi$
$641$	4.04137			0.159624			0.0798122	+	0.996810i	$0.474568\pi$
$642$		0			0
$643$	3.16475	+	3.16475i	0.124805	+	0.124805i	0.766751	−	0.641945i	$-0.221872\pi$
$643$	3.16475	+	3.16475i	0.124805	+	0.124805i	−0.641945	+	0.766751i	$0.721872\pi$
$644$		0			0
$645$	2.42415	−	2.42415i	0.0954506	−	0.0954506i
$646$		0			0
$647$		−	4.21349i		−	0.165649i	−0.996564	−	0.0828246i	$-0.973606\pi$
$647$		−	4.21349i		−	0.165649i	0.996564	−	0.0828246i	$-0.0263941\pi$
$648$		0			0
$649$			3.77672i			0.148249i
$650$		0			0
$651$	6.82453	−	6.82453i	0.267474	−	0.267474i
$652$		0			0
$653$	−30.8935	−	30.8935i	−1.20896	−	1.20896i	−0.971365	−	0.237592i	$-0.923642\pi$
$653$	−30.8935	−	30.8935i	−1.20896	−	1.20896i	−0.237592	−	0.971365i	$-0.576358\pi$
$654$		0			0
$655$	7.68463			0.300263
$656$		0			0
$657$	9.52481			0.371598
$658$		0			0
$659$	32.9132	+	32.9132i	1.28212	+	1.28212i	0.939461	+	0.342655i	$0.111326\pi$
$659$	32.9132	+	32.9132i	1.28212	+	1.28212i	0.342655	+	0.939461i	$0.388674\pi$
$660$		0			0
$661$	0.916312	−	0.916312i	0.0356404	−	0.0356404i	−0.689062	−	0.724702i	$-0.741977\pi$
$661$	0.916312	−	0.916312i	0.0356404	−	0.0356404i	0.724702	+	0.689062i	$0.241977\pi$
$662$		0			0
$663$			10.9690i			0.426000i
$664$		0			0
$665$			1.33462i			0.0517542i
$666$		0			0
$667$	13.0684	−	13.0684i	0.506010	−	0.506010i
$668$		0			0
$669$	−19.6759	−	19.6759i	−0.760715	−	0.760715i
$670$		0			0
$671$	8.86559			0.342252
$672$		0			0
$673$	11.7808			0.454117			0.227058	−	0.973881i	$-0.427089\pi$
$673$	11.7808			0.454117			0.227058	+	0.973881i	$0.427089\pi$
$674$		0			0
$675$	−1.58899	−	1.58899i	−0.0611602	−	0.0611602i
$676$		0			0
$677$	−6.20402	+	6.20402i	−0.238440	+	0.238440i	−0.816204	−	0.577764i	$-0.803925\pi$
$677$	−6.20402	+	6.20402i	−0.238440	+	0.238440i	0.577764	+	0.816204i	$0.303925\pi$
$678$		0			0
$679$		−	13.1147i		−	0.503295i
$680$		0			0
$681$			7.79716i			0.298788i
$682$		0			0
$683$	−31.4499	+	31.4499i	−1.20340	+	1.20340i	−0.230271	+	0.973127i	$0.573961\pi$
$683$	−31.4499	+	31.4499i	−1.20340	+	1.20340i	−0.973127	+	0.230271i	$0.926039\pi$
$684$		0			0
$685$	−5.11331	−	5.11331i	−0.195370	−	0.195370i
$686$		0			0
$687$	−15.3018			−0.583799
$688$		0			0
$689$	−19.9798			−0.761169
$690$		0			0
$691$	22.8866	+	22.8866i	0.870647	+	0.870647i	0.992543	−	0.121896i	$-0.0388975\pi$
$691$	22.8866	+	22.8866i	0.870647	+	0.870647i	−0.121896	+	0.992543i	$0.538897\pi$
$692$		0			0
$693$	−0.961187	+	0.961187i	−0.0365125	+	0.0365125i
$694$		0			0
$695$		−	1.40900i		−	0.0534463i
$696$		0			0
$697$		−	3.01067i		−	0.114037i
$698$		0			0
$699$	8.31407	−	8.31407i	0.314467	−	0.314467i
$700$		0			0
$701$	1.29439	+	1.29439i	0.0488884	+	0.0488884i	0.731128	−	0.682240i	$-0.238994\pi$
$701$	1.29439	+	1.29439i	0.0488884	+	0.0488884i	−0.682240	+	0.731128i	$0.738994\pi$
$702$		0			0
$703$	9.11527			0.343789
$704$		0			0
$705$	−0.845500			−0.0318434
$706$		0			0
$707$	1.59669	+	1.59669i	0.0600498	+	0.0600498i
$708$		0			0
$709$	20.6006	−	20.6006i	0.773673	−	0.773673i	−0.205073	−	0.978747i	$-0.565743\pi$
$709$	20.6006	−	20.6006i	0.773673	−	0.773673i	0.978747	+	0.205073i	$0.0657433\pi$
$710$		0			0
$711$		−	4.83685i		−	0.181396i
$712$		0			0
$713$			19.7551i			0.739834i
$714$		0			0
$715$	−5.09725	+	5.09725i	−0.190626	+	0.190626i
$716$		0			0
$717$	4.95551	+	4.95551i	0.185067	+	0.185067i
$718$		0			0
$719$	5.15425			0.192221			0.0961106	−	0.995371i	$-0.469360\pi$
$719$	5.15425			0.192221			0.0961106	+	0.995371i	$0.469360\pi$
$720$		0			0
$721$	8.93964			0.332930
$722$		0			0
$723$	18.0913	+	18.0913i	0.672821	+	0.672821i
$724$		0			0
$725$	−14.3472	+	14.3472i	−0.532840	+	0.532840i
$726$		0			0
$727$			40.1916i			1.49063i	0.666715	+	0.745313i	$0.267700\pi$
$727$			40.1916i			1.49063i	−0.666715	+	0.745313i	$0.732300\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−5.01414	+	5.01414i	−0.185455	+	0.185455i
$732$		0			0
$733$	3.42765	+	3.42765i	0.126603	+	0.126603i	0.767569	−	0.640966i	$-0.221466\pi$
$733$	3.42765	+	3.42765i	0.126603	+	0.126603i	−0.640966	+	0.767569i	$0.721466\pi$
$734$		0			0
$735$	1.65917			0.0611993
$736$		0			0
$737$	−0.0870249			−0.00320560
$738$		0			0
$739$	−14.8361	−	14.8361i	−0.545756	−	0.545756i	0.379455	−	0.925210i	$-0.376112\pi$
$739$	−14.8361	−	14.8361i	−0.545756	−	0.545756i	−0.925210	+	0.379455i	$0.876112\pi$
$740$		0			0
$741$	1.81798	−	1.81798i	0.0667852	−	0.0667852i
$742$		0			0
$743$			7.90350i			0.289951i	0.989435	+	0.144976i	$0.0463104\pi$
$743$			7.90350i			0.289951i	−0.989435	+	0.144976i	$0.953690\pi$
$744$		0			0
$745$		−	0.970728i		−	0.0355647i
$746$		0			0
$747$	−9.73976	+	9.73976i	−0.356359	+	0.356359i
$748$		0			0
$749$	12.0811	+	12.0811i	0.441433	+	0.441433i
$750$		0			0
$751$	−8.71794			−0.318122			−0.159061	−	0.987269i	$-0.550847\pi$
$751$	−8.71794			−0.318122			−0.159061	+	0.987269i	$0.550847\pi$
$752$		0			0
$753$	9.27845			0.338126
$754$		0			0
$755$	8.18913	+	8.18913i	0.298033	+	0.298033i
$756$		0			0
$757$	16.7057	−	16.7057i	0.607179	−	0.607179i	−0.335029	−	0.942208i	$-0.608746\pi$
$757$	16.7057	−	16.7057i	0.607179	−	0.607179i	0.942208	+	0.335029i	$0.108746\pi$
$758$		0			0
$759$		−	2.78237i		−	0.100994i
$760$		0			0
$761$		−	40.2929i		−	1.46061i	−0.683119	−	0.730307i	$-0.739377\pi$
$761$		−	40.2929i		−	1.46061i	0.683119	−	0.730307i	$-0.260623\pi$
$762$		0			0
$763$	−4.37857	+	4.37857i	−0.158515	+	0.158515i
$764$		0			0
$765$	−4.02627	−	4.02627i	−0.145570	−	0.145570i
$766$		0			0
$767$	−8.88035			−0.320651
$768$		0			0
$769$	−14.3244			−0.516550			−0.258275	−	0.966071i	$-0.583154\pi$
$769$	−14.3244			−0.516550			−0.258275	+	0.966071i	$0.583154\pi$
$770$		0			0
$771$	14.6444	+	14.6444i	0.527406	+	0.527406i
$772$		0			0
$773$	−14.5061	+	14.5061i	−0.521747	+	0.521747i	−0.918099	−	0.396352i	$-0.870276\pi$
$773$	−14.5061	+	14.5061i	−0.521747	+	0.521747i	0.396352	+	0.918099i	$0.370276\pi$
$774$		0			0
$775$		−	21.6882i		−	0.779063i
$776$		0			0
$777$		−	11.3319i		−	0.406530i
$778$		0			0
$779$	−0.498984	+	0.498984i	−0.0178779	+	0.0178779i
$780$		0			0
$781$	8.74859	+	8.74859i	0.313049	+	0.313049i
$782$		0			0
$783$	−9.02912			−0.322674
$784$		0			0
$785$	−36.3064			−1.29583
$786$		0			0
$787$	31.0081	+	31.0081i	1.10532	+	1.10532i	0.993758	+	0.111560i	$0.0355847\pi$
$787$	31.0081	+	31.0081i	1.10532	+	1.10532i	0.111560	+	0.993758i	$0.464415\pi$
$788$		0			0
$789$	4.02882	−	4.02882i	0.143430	−	0.143430i
$790$		0			0
$791$			16.8217i			0.598111i
$792$		0			0
$793$			20.8460i			0.740263i
$794$		0			0
$795$	7.33378	−	7.33378i	0.260102	−	0.260102i
$796$		0			0
$797$	3.96132	+	3.96132i	0.140317	+	0.140317i	0.773776	−	0.633459i	$-0.218365\pi$
$797$	3.96132	+	3.96132i	0.140317	+	0.140317i	−0.633459	+	0.773776i	$0.718365\pi$
$798$		0			0
$799$	1.74885			0.0618697
$800$		0			0
$801$	12.5234			0.442493
$802$		0			0
$803$	−9.15513	−	9.15513i	−0.323077	−	0.323077i
$804$		0			0
$805$	−2.40141	+	2.40141i	−0.0846386	+	0.0846386i
$806$		0			0
$807$		−	10.0107i		−	0.352394i
$808$		0			0
$809$		−	19.0324i		−	0.669142i	−0.942370	−	0.334571i	$-0.891409\pi$
$809$		−	19.0324i		−	0.669142i	0.942370	−	0.334571i	$-0.108591\pi$
$810$		0			0
$811$	26.3129	−	26.3129i	0.923972	−	0.923972i	−0.0733352	−	0.997307i	$-0.523364\pi$
$811$	26.3129	−	26.3129i	0.923972	−	0.923972i	0.997307	+	0.0733352i	$0.0233643\pi$
$812$		0			0
$813$	17.8308	+	17.8308i	0.625353	+	0.625353i
$814$		0			0
$815$	1.06516			0.0373109
$816$		0			0
$817$	1.66207			0.0581486
$818$		0			0
$819$	−2.26008	−	2.26008i	−0.0789734	−	0.0789734i
$820$		0			0
$821$	5.68248	−	5.68248i	0.198320	−	0.198320i	−0.600960	−	0.799279i	$-0.705215\pi$
$821$	5.68248	−	5.68248i	0.198320	−	0.198320i	0.799279	+	0.600960i	$0.205215\pi$
$822$		0			0
$823$			31.6238i			1.10234i	0.834394	+	0.551168i	$0.185818\pi$
$823$			31.6238i			1.10234i	−0.834394	+	0.551168i	$0.814182\pi$
$824$		0			0
$825$			3.05463i			0.106349i
$826$		0			0
$827$	2.47748	−	2.47748i	0.0861503	−	0.0861503i	−0.662718	−	0.748869i	$-0.730597\pi$
$827$	2.47748	−	2.47748i	0.0861503	−	0.0861503i	0.748869	+	0.662718i	$0.230597\pi$
$828$		0			0
$829$	16.8198	+	16.8198i	0.584175	+	0.584175i	0.936048	−	0.351873i	$-0.114455\pi$
$829$	16.8198	+	16.8198i	0.584175	+	0.584175i	−0.351873	+	0.936048i	$0.614455\pi$
$830$		0			0
$831$	0.159734			0.00554111
$832$		0			0
$833$	−3.43185			−0.118906
$834$		0			0
$835$	0.0398919	+	0.0398919i	0.00138051	+	0.00138051i
$836$		0			0
$837$	6.82453	−	6.82453i	0.235890	−	0.235890i
$838$		0			0
$839$		−	15.5980i		−	0.538502i	−0.963070	−	0.269251i	$-0.913224\pi$
$839$		−	15.5980i		−	0.538502i	0.963070	−	0.269251i	$-0.0867761\pi$
$840$		0			0
$841$			52.5250i			1.81121i
$842$		0			0
$843$	−11.3856	+	11.3856i	−0.392140	+	0.392140i
$844$		0			0
$845$	3.26635	+	3.26635i	0.112366	+	0.112366i
$846$		0			0
$847$	−9.15224			−0.314475
$848$		0			0
$849$	−24.1237			−0.827922
$850$		0			0
$851$	16.4013	+	16.4013i	0.562231	+	0.562231i
$852$		0			0
$853$	−17.1708	+	17.1708i	−0.587918	+	0.587918i	−0.937067	−	0.349149i	$-0.886471\pi$
$853$	−17.1708	+	17.1708i	−0.587918	+	0.587918i	0.349149	+	0.937067i	$0.386471\pi$
$854$		0			0
$855$			1.33462i			0.0456429i
$856$		0			0
$857$		−	37.6664i		−	1.28666i	−0.765589	−	0.643330i	$-0.777552\pi$
$857$		−	37.6664i		−	1.28666i	0.765589	−	0.643330i	$-0.222448\pi$
$858$		0			0
$859$	−5.66049	+	5.66049i	−0.193133	+	0.193133i	−0.797049	−	0.603915i	$-0.793607\pi$
$859$	−5.66049	+	5.66049i	−0.193133	+	0.193133i	0.603915	+	0.797049i	$0.293607\pi$
$860$		0			0
$861$	0.620326	+	0.620326i	0.0211406	+	0.0211406i
$862$		0			0
$863$	−45.9360			−1.56368			−0.781839	−	0.623480i	$-0.785718\pi$
$863$	−45.9360			−1.56368			−0.781839	+	0.623480i	$0.785718\pi$
$864$		0			0
$865$	3.66378			0.124572
$866$		0			0
$867$	−3.69281	−	3.69281i	−0.125414	−	0.125414i
$868$		0			0
$869$	−4.64912	+	4.64912i	−0.157711	+	0.157711i
$870$		0			0
$871$		−	0.204625i		−	0.00693345i
$872$		0			0
$873$		−	13.1147i		−	0.443865i
$874$		0			0
$875$	8.50243	−	8.50243i	0.287435	−	0.287435i
$876$		0			0
$877$	1.08909	+	1.08909i	0.0367759	+	0.0367759i	0.725256	−	0.688480i	$-0.241722\pi$
$877$	1.08909	+	1.08909i	0.0367759	+	0.0367759i	−0.688480	+	0.725256i	$0.741722\pi$
$878$		0			0
$879$	26.1181			0.880941
$880$		0			0
$881$	23.7198			0.799139			0.399570	−	0.916703i	$-0.369160\pi$
$881$	23.7198			0.799139			0.399570	+	0.916703i	$0.369160\pi$
$882$		0			0
$883$	−24.8700	−	24.8700i	−0.836942	−	0.836942i	0.151513	−	0.988455i	$-0.451585\pi$
$883$	−24.8700	−	24.8700i	−0.836942	−	0.836942i	−0.988455	+	0.151513i	$0.951585\pi$
$884$		0			0
$885$	3.25962	−	3.25962i	0.109571	−	0.109571i
$886$		0			0
$887$			25.7676i			0.865192i	0.901588	+	0.432596i	$0.142402\pi$
$887$			25.7676i			0.865192i	−0.901588	+	0.432596i	$0.857598\pi$
$888$		0			0
$889$			15.0532i			0.504868i
$890$		0			0
$891$	−0.961187	+	0.961187i	−0.0322010	+	0.0322010i
$892$		0			0
$893$	−0.289851	−	0.289851i	−0.00969950	−	0.00969950i
$894$		0			0
$895$	−20.0418			−0.669923
$896$		0			0
$897$	6.54229			0.218441
$898$		0			0
$899$	−61.6195	−	61.6195i	−2.05513	−	2.05513i
$900$		0			0
$901$	−15.1693	+	15.1693i	−0.505363	+	0.505363i
$902$		0			0
$903$		−	2.06625i		−	0.0687606i
$904$		0			0
$905$			15.2529i			0.507025i
$906$		0			0
$907$	0.470598	−	0.470598i	0.0156259	−	0.0156259i	−0.699251	−	0.714877i	$-0.746483\pi$
$907$	0.470598	−	0.470598i	0.0156259	−	0.0156259i	0.714877	+	0.699251i	$0.246483\pi$
$908$		0			0
$909$	1.59669	+	1.59669i	0.0529589	+	0.0529589i
$910$		0			0
$911$	3.08294			0.102142			0.0510712	−	0.998695i	$-0.483736\pi$
$911$	3.08294			0.102142			0.0510712	+	0.998695i	$0.483736\pi$
$912$		0			0
$913$	18.7235			0.619656
$914$		0			0
$915$	−7.65173	−	7.65173i	−0.252958	−	0.252958i
$916$		0			0
$917$	3.27505	−	3.27505i	0.108152	−	0.108152i
$918$		0			0
$919$		−	44.7623i		−	1.47657i	−0.674487	−	0.738287i	$-0.735635\pi$
$919$		−	44.7623i		−	1.47657i	0.674487	−	0.738287i	$-0.264365\pi$
$920$		0			0
$921$		−	3.99716i		−	0.131711i
$922$		0			0
$923$	−20.5709	+	20.5709i	−0.677099	+	0.677099i
$924$		0			0
$925$	−18.0063	−	18.0063i	−0.592042	−	0.592042i
$926$		0			0
$927$	8.93964			0.293616
$928$		0			0
$929$	−27.8328			−0.913165			−0.456582	−	0.889681i	$-0.650927\pi$
$929$	−27.8328			−0.913165			−0.456582	+	0.889681i	$0.650927\pi$
$930$		0			0
$931$	0.568789	+	0.568789i	0.0186413	+	0.0186413i
$932$		0			0
$933$	8.83355	−	8.83355i	0.289197	−	0.289197i
$934$		0			0
$935$			7.73999i			0.253125i
$936$		0			0
$937$		−	29.9177i		−	0.977369i	−0.872461	−	0.488684i	$-0.837477\pi$
$937$		−	29.9177i		−	0.977369i	0.872461	−	0.488684i	$-0.162523\pi$
$938$		0			0
$939$	14.5435	−	14.5435i	0.474608	−	0.474608i
$940$		0			0
$941$	−16.5282	−	16.5282i	−0.538803	−	0.538803i	0.384375	−	0.923177i	$-0.374417\pi$
$941$	−16.5282	−	16.5282i	−0.538803	−	0.538803i	−0.923177	+	0.384375i	$0.874417\pi$
$942$		0			0
$943$	−1.79567			−0.0584750
$944$		0			0
$945$	1.65917			0.0539727
$946$		0			0
$947$	−1.32224	−	1.32224i	−0.0429671	−	0.0429671i	0.685297	−	0.728264i	$-0.259672\pi$
$947$	−1.32224	−	1.32224i	−0.0429671	−	0.0429671i	−0.728264	+	0.685297i	$0.759672\pi$
$948$		0			0
$949$	21.5268	−	21.5268i	0.698789	−	0.698789i
$950$		0			0
$951$		−	15.5290i		−	0.503562i
$952$		0			0
$953$		−	5.57598i		−	0.180624i	−0.995914	−	0.0903119i	$-0.971214\pi$
$953$		−	5.57598i		−	0.180624i	0.995914	−	0.0903119i	$-0.0287864\pi$
$954$		0			0
$955$	23.3951	−	23.3951i	0.757047	−	0.757047i
$956$		0			0
$957$	8.67867	+	8.67867i	0.280542	+	0.280542i
$958$		0			0
$959$	−4.35840			−0.140740
$960$		0			0
$961$	62.1484			2.00479
$962$		0			0
$963$	12.0811	+	12.0811i	0.389307	+	0.389307i
$964$		0			0
$965$	12.8384	−	12.8384i	0.413281	−	0.413281i
$966$		0			0
$967$		−	49.1980i		−	1.58210i	−0.611751	−	0.791051i	$-0.709534\pi$
$967$		−	49.1980i		−	1.58210i	0.611751	−	0.791051i	$-0.290466\pi$
$968$		0			0
$969$		−	2.76054i		−	0.0886814i
$970$		0			0
$971$	−30.6662	+	30.6662i	−0.984126	+	0.984126i	−0.999876	−	0.0157499i	$-0.994986\pi$
$971$	−30.6662	+	30.6662i	−0.984126	+	0.984126i	0.0157499	+	0.999876i	$0.494986\pi$
$972$		0			0
$973$	−0.600490	−	0.600490i	−0.0192508	−	0.0192508i
$974$		0			0
$975$	−7.18246			−0.230023
$976$		0			0
$977$	53.4893			1.71127			0.855636	−	0.517577i	$-0.173166\pi$
$977$	53.4893			1.71127			0.855636	+	0.517577i	$0.173166\pi$
$978$		0			0
$979$	−12.0373	−	12.0373i	−0.384715	−	0.384715i
$980$		0			0
$981$	−4.37857	+	4.37857i	−0.139797	+	0.139797i
$982$		0			0
$983$		−	49.2916i		−	1.57216i	−0.618125	−	0.786080i	$-0.712108\pi$
$983$		−	49.2916i		−	1.57216i	0.618125	−	0.786080i	$-0.287892\pi$
$984$		0			0
$985$			39.6274i			1.26263i
$986$		0			0
$987$	−0.360337	+	0.360337i	−0.0114696	+	0.0114696i
$988$		0			0
$989$	2.99061	+	2.99061i	0.0950960	+	0.0950960i
$990$		0			0
$991$	−36.9072			−1.17240			−0.586198	−	0.810167i	$-0.699376\pi$
$991$	−36.9072			−1.17240			−0.586198	+	0.810167i	$0.699376\pi$
$992$		0			0
$993$	−29.3871			−0.932572
$994$		0			0
$995$	12.0527	+	12.0527i	0.382096	+	0.382096i
$996$		0			0
$997$	−17.6363	+	17.6363i	−0.558547	+	0.558547i	−0.928894	−	0.370347i	$-0.879239\pi$
$997$	−17.6363	+	17.6363i	−0.558547	+	0.558547i	0.370347	+	0.928894i	$0.379239\pi$
$998$		0			0
$999$		−	11.3319i		−	0.358526i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.w.a.337.7		20
4.3	odd	2		336.2.w.a.253.2	yes	20
8.3	odd	2		2688.2.w.a.673.9		20
8.5	even	2		2688.2.w.b.673.4		20
16.3	odd	4		2688.2.w.a.2017.9		20
16.5	even	4	inner	1344.2.w.a.1009.7		20
16.11	odd	4		336.2.w.a.85.2	✓	20
16.13	even	4		2688.2.w.b.2017.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.a.85.2	✓	20	16.11	odd	4
336.2.w.a.253.2	yes	20	4.3	odd	2
1344.2.w.a.337.7		20	1.1	even	1	trivial
1344.2.w.a.1009.7		20	16.5	even	4	inner
2688.2.w.a.673.9		20	8.3	odd	2
2688.2.w.a.2017.9		20	16.3	odd	4
2688.2.w.b.673.4		20	8.5	even	2
2688.2.w.b.2017.4		20	16.13	even	4

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.w (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.17321 + 1.17321i) q^{5} +1.00000i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.17321 + 1.17321i) q^{5} +1.00000i q^{7} +1.00000i q^{9} +(0.961187 - 0.961187i) q^{11} +(2.26008 + 2.26008i) q^{13} -1.65917 q^{15} +3.43185 q^{17} +(-0.568789 - 0.568789i) q^{19} +(-0.707107 + 0.707107i) q^{21} -2.04688i q^{23} +2.24717i q^{25} +(-0.707107 + 0.707107i) q^{27} +(6.38455 + 6.38455i) q^{29} -9.65134 q^{31} +1.35932 q^{33} +(-1.17321 - 1.17321i) q^{35} +(-8.01287 + 8.01287i) q^{37} +3.19623i q^{39} -0.877273i q^{41} +(-1.46106 + 1.46106i) q^{43} +(-1.17321 - 1.17321i) q^{45} +0.509593 q^{47} -1.00000 q^{49} +(2.42668 + 2.42668i) q^{51} +(-4.42016 + 4.42016i) q^{53} +2.25534i q^{55} -0.804390i q^{57} +(-1.96461 + 1.96461i) q^{59} +(4.61179 + 4.61179i) q^{61} -1.00000 q^{63} -5.30308 q^{65} +(-0.0452695 - 0.0452695i) q^{67} +(1.44736 - 1.44736i) q^{69} +9.10186i q^{71} -9.52481i q^{73} +(-1.58899 + 1.58899i) q^{75} +(0.961187 + 0.961187i) q^{77} -4.83685 q^{79} -1.00000 q^{81} +(9.73976 + 9.73976i) q^{83} +(-4.02627 + 4.02627i) q^{85} +9.02912i q^{87} -12.5234i q^{89} +(-2.26008 + 2.26008i) q^{91} +(-6.82453 - 6.82453i) q^{93} +1.33462 q^{95} -13.1147 q^{97} +(0.961187 + 0.961187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 12 q^{29} - 24 q^{33} + 12 q^{37} - 4 q^{43} - 20 q^{49} + 8 q^{51} - 36 q^{53} + 8 q^{61} - 20 q^{63} + 16 q^{65} + 12 q^{67} - 16 q^{69} + 16 q^{75} - 12 q^{77} - 24 q^{79} - 20 q^{81} - 40 q^{83} - 16 q^{85} - 72 q^{97} - 12 q^{99}+O(q^{100}) \) 20 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 12 * q^29 - 24 * q^33 + 12 * q^37 - 4 * q^43 - 20 * q^49 + 8 * q^51 - 36 * q^53 + 8 * q^61 - 20 * q^63 + 16 * q^65 + 12 * q^67 - 16 * q^69 + 16 * q^75 - 12 * q^77 - 24 * q^79 - 20 * q^81 - 40 * q^83 - 16 * q^85 - 72 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more