LMFDB - Embedded newform 1344.2.s.c.239.8

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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.8
Character	$\chi$	$=$	1344.239
Dual form			1344.2.s.c.911.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.827739 - 1.52146i) q^{3} +(-1.23935 - 1.23935i) q^{5} +1.00000 q^{7} +(-1.62970 + 2.51875i) q^{9} +O(q^{10})$	\(q+(-0.827739 - 1.52146i) q^{3} +(-1.23935 - 1.23935i) q^{5} +1.00000 q^{7} +(-1.62970 + 2.51875i) q^{9} +(3.57267 - 3.57267i) q^{11} +(1.58965 + 1.58965i) q^{13} +(-0.859765 + 2.91147i) q^{15} +2.20802i q^{17} +(3.76716 - 3.76716i) q^{19} +(-0.827739 - 1.52146i) q^{21} -3.97123i q^{23} -1.92804i q^{25} +(5.18114 + 0.394660i) q^{27} +(4.75337 - 4.75337i) q^{29} -1.24630i q^{31} +(-8.39291 - 2.47844i) q^{33} +(-1.23935 - 1.23935i) q^{35} +(-6.39946 + 6.39946i) q^{37} +(1.10278 - 3.73440i) q^{39} -3.93566 q^{41} +(-1.19053 - 1.19053i) q^{43} +(5.14136 - 1.10184i) q^{45} -8.26073 q^{47} +1.00000 q^{49} +(3.35941 - 1.82766i) q^{51} +(2.18249 + 2.18249i) q^{53} -8.85554 q^{55} +(-8.84982 - 2.61337i) q^{57} +(-5.45245 + 5.45245i) q^{59} +(-5.10830 - 5.10830i) q^{61} +(-1.62970 + 2.51875i) q^{63} -3.94024i q^{65} +(7.23888 - 7.23888i) q^{67} +(-6.04208 + 3.28714i) q^{69} +6.13227i q^{71} -10.2246i q^{73} +(-2.93344 + 1.59591i) q^{75} +(3.57267 - 3.57267i) q^{77} +6.53910i q^{79} +(-3.68817 - 8.20959i) q^{81} +(-12.3619 - 12.3619i) q^{83} +(2.73650 - 2.73650i) q^{85} +(-11.1666 - 3.29753i) q^{87} +9.15394 q^{89} +(1.58965 + 1.58965i) q^{91} +(-1.89620 + 1.03161i) q^{93} -9.33763 q^{95} +7.67756 q^{97} +(3.17628 + 14.8210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) $ 40 * q - 4 * q^3 + 40 * q^7	$ 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) $ 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * 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
$3$	−0.827739	−	1.52146i	−0.477895	−	0.878417i
$3$	−0.827739	−	1.52146i	−0.477895	−	0.878417i
$4$		0			0
$5$	−1.23935	−	1.23935i	−0.554253	−	0.554253i	0.373413	−	0.927665i	$-0.378188\pi$
$5$	−1.23935	−	1.23935i	−0.554253	−	0.554253i	−0.927665	+	0.373413i	$0.878188\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	−1.62970	+	2.51875i	−0.543233	+	0.839582i
$10$		0			0
$11$	3.57267	−	3.57267i	1.07720	−	1.07720i	0.0804398	−	0.996759i	$-0.474368\pi$
$11$	3.57267	−	3.57267i	1.07720	−	1.07720i	0.996759	−	0.0804398i	$-0.0256325\pi$
$12$		0			0
$13$	1.58965	+	1.58965i	0.440888	+	0.440888i	0.892310	−	0.451422i	$-0.149083\pi$
$13$	1.58965	+	1.58965i	0.440888	+	0.440888i	−0.451422	+	0.892310i	$0.649083\pi$
$14$		0			0
$15$	−0.859765	+	2.91147i	−0.221990	+	0.751740i
$16$		0			0
$17$			2.20802i			0.535523i	0.963485	+	0.267761i	$0.0862839\pi$
$17$			2.20802i			0.535523i	−0.963485	+	0.267761i	$0.913716\pi$
$18$		0			0
$19$	3.76716	−	3.76716i	0.864246	−	0.864246i	−0.127582	−	0.991828i	$-0.540722\pi$
$19$	3.76716	−	3.76716i	0.864246	−	0.864246i	0.991828	+	0.127582i	$0.0407216\pi$
$20$		0			0
$21$	−0.827739	−	1.52146i	−0.180627	−	0.332010i
$22$		0			0
$23$		−	3.97123i		−	0.828059i	−0.910264	−	0.414029i	$-0.864121\pi$
$23$		−	3.97123i		−	0.828059i	0.910264	−	0.414029i	$-0.135879\pi$
$24$		0			0
$25$		−	1.92804i		−	0.385608i
$26$		0			0
$27$	5.18114	+	0.394660i	0.997111	+	0.0759524i
$28$		0			0
$29$	4.75337	−	4.75337i	0.882679	−	0.882679i	−0.111128	−	0.993806i	$-0.535446\pi$
$29$	4.75337	−	4.75337i	0.882679	−	0.882679i	0.993806	+	0.111128i	$0.0354462\pi$
$30$		0			0
$31$		−	1.24630i		−	0.223842i	−0.993717	−	0.111921i	$-0.964300\pi$
$31$		−	1.24630i		−	0.223842i	0.993717	−	0.111921i	$-0.0357004\pi$
$32$		0			0
$33$	−8.39291	−	2.47844i	−1.46102	−	0.431442i
$34$		0			0
$35$	−1.23935	−	1.23935i	−0.209488	−	0.209488i
$36$		0			0
$37$	−6.39946	+	6.39946i	−1.05206	+	1.05206i	−0.0534969	+	0.998568i	$0.517037\pi$
$37$	−6.39946	+	6.39946i	−1.05206	+	1.05206i	−0.998568	+	0.0534969i	$0.982963\pi$
$38$		0			0
$39$	1.10278	−	3.73440i	0.176585	−	0.597982i
$40$		0			0
$41$	−3.93566			−0.614646			−0.307323	−	0.951605i	$-0.599433\pi$
$41$	−3.93566			−0.614646			−0.307323	+	0.951605i	$0.599433\pi$
$42$		0			0
$43$	−1.19053	−	1.19053i	−0.181554	−	0.181554i	0.610479	−	0.792033i	$-0.290977\pi$
$43$	−1.19053	−	1.19053i	−0.181554	−	0.181554i	−0.792033	+	0.610479i	$0.790977\pi$
$44$		0			0
$45$	5.14136	−	1.10184i	0.766429	−	0.164253i
$46$		0			0
$47$	−8.26073			−1.20495			−0.602476	−	0.798137i	$-0.705819\pi$
$47$	−8.26073			−1.20495			−0.602476	+	0.798137i	$0.705819\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	3.35941	−	1.82766i	0.470412	−	0.255924i
$52$		0			0
$53$	2.18249	+	2.18249i	0.299788	+	0.299788i	0.840931	−	0.541143i	$-0.182008\pi$
$53$	2.18249	+	2.18249i	0.299788	+	0.299788i	−0.541143	+	0.840931i	$0.682008\pi$
$54$		0			0
$55$	−8.85554			−1.19408
$56$		0			0
$57$	−8.84982	−	2.61337i	−1.17219	−	0.346149i
$58$		0			0
$59$	−5.45245	+	5.45245i	−0.709849	+	0.709849i	−0.966503	−	0.256654i	$-0.917380\pi$
$59$	−5.45245	+	5.45245i	−0.709849	+	0.709849i	0.256654	+	0.966503i	$0.417380\pi$
$60$		0			0
$61$	−5.10830	−	5.10830i	−0.654051	−	0.654051i	0.299915	−	0.953966i	$-0.403042\pi$
$61$	−5.10830	−	5.10830i	−0.654051	−	0.654051i	−0.953966	+	0.299915i	$0.903042\pi$
$62$		0			0
$63$	−1.62970	+	2.51875i	−0.205323	+	0.317332i
$64$		0			0
$65$		−	3.94024i		−	0.488727i
$66$		0			0
$67$	7.23888	−	7.23888i	0.884371	−	0.884371i	−0.109605	−	0.993975i	$-0.534959\pi$
$67$	7.23888	−	7.23888i	0.884371	−	0.884371i	0.993975	+	0.109605i	$0.0349585\pi$
$68$		0			0
$69$	−6.04208	+	3.28714i	−0.727381	+	0.395725i
$70$		0			0
$71$			6.13227i			0.727766i	0.931445	+	0.363883i	$0.118549\pi$
$71$			6.13227i			0.727766i	−0.931445	+	0.363883i	$0.881451\pi$
$72$		0			0
$73$		−	10.2246i		−	1.19670i	−0.801237	−	0.598348i	$-0.795824\pi$
$73$		−	10.2246i		−	1.19670i	0.801237	−	0.598348i	$-0.204176\pi$
$74$		0			0
$75$	−2.93344	+	1.59591i	−0.338725	+	0.184280i
$76$		0			0
$77$	3.57267	−	3.57267i	0.407143	−	0.407143i
$78$		0			0
$79$			6.53910i			0.735706i	0.929884	+	0.367853i	$0.119907\pi$
$79$			6.53910i			0.735706i	−0.929884	+	0.367853i	$0.880093\pi$
$80$		0			0
$81$	−3.68817	−	8.20959i	−0.409797	−	0.912177i
$82$		0			0
$83$	−12.3619	−	12.3619i	−1.35690	−	1.35690i	−0.877715	−	0.479183i	$-0.840933\pi$
$83$	−12.3619	−	12.3619i	−1.35690	−	1.35690i	−0.479183	−	0.877715i	$-0.659067\pi$
$84$		0			0
$85$	2.73650	−	2.73650i	0.296815	−	0.296815i
$86$		0			0
$87$	−11.1666	−	3.29753i	−1.19719	−	0.353532i
$88$		0			0
$89$	9.15394			0.970316			0.485158	−	0.874427i	$-0.338762\pi$
$89$	9.15394			0.970316			0.485158	+	0.874427i	$0.338762\pi$
$90$		0			0
$91$	1.58965	+	1.58965i	0.166640	+	0.166640i
$92$		0			0
$93$	−1.89620	+	1.03161i	−0.196627	+	0.106973i
$94$		0			0
$95$	−9.33763			−0.958021
$96$		0			0
$97$	7.67756			0.779538			0.389769	−	0.920913i	$-0.372555\pi$
$97$	7.67756			0.779538			0.389769	+	0.920913i	$0.372555\pi$
$98$		0			0
$99$	3.17628	+	14.8210i	0.319228	+	1.48957i
$100$		0			0
$101$	−5.10294	−	5.10294i	−0.507761	−	0.507761i	0.406077	−	0.913839i	$-0.366896\pi$
$101$	−5.10294	−	5.10294i	−0.507761	−	0.507761i	−0.913839	+	0.406077i	$0.866896\pi$
$102$		0			0
$103$	−17.2234			−1.69707			−0.848535	−	0.529139i	$-0.822515\pi$
$103$	−17.2234			−1.69707			−0.848535	+	0.529139i	$0.822515\pi$
$104$		0			0
$105$	−0.859765	+	2.91147i	−0.0839044	+	0.284131i
$106$		0			0
$107$	8.98275	−	8.98275i	0.868396	−	0.868396i	−0.123899	−	0.992295i	$-0.539540\pi$
$107$	8.98275	−	8.98275i	0.868396	−	0.868396i	0.992295	+	0.123899i	$0.0395399\pi$
$108$		0			0
$109$	9.91151	+	9.91151i	0.949350	+	0.949350i	0.998778	−	0.0494277i	$-0.0157397\pi$
$109$	9.91151	+	9.91151i	0.949350	+	0.949350i	−0.0494277	+	0.998778i	$0.515740\pi$
$110$		0			0
$111$	15.0336	+	4.43946i	1.42693	+	0.421375i
$112$		0			0
$113$			14.2233i			1.33801i	0.743256	+	0.669007i	$0.233280\pi$
$113$			14.2233i			1.33801i	−0.743256	+	0.669007i	$0.766720\pi$
$114$		0			0
$115$	−4.92173	+	4.92173i	−0.458954	+	0.458954i
$116$		0			0
$117$	−6.59455	+	1.41327i	−0.609667	+	0.130657i
$118$		0			0
$119$			2.20802i			0.202409i
$120$		0			0
$121$		−	14.5279i		−	1.32072i
$122$		0			0
$123$	3.25770	+	5.98796i	0.293737	+	0.539916i
$124$		0			0
$125$	−8.58624	+	8.58624i	−0.767977	+	0.767977i
$126$		0			0
$127$		−	2.23296i		−	0.198143i	−0.995080	−	0.0990717i	$-0.968413\pi$
$127$		−	2.23296i		−	0.198143i	0.995080	−	0.0990717i	$-0.0315873\pi$
$128$		0			0
$129$	−0.825900	+	2.79680i	−0.0727164	+	0.246244i
$130$		0			0
$131$	−4.97791	−	4.97791i	−0.434922	−	0.434922i	0.455377	−	0.890299i	$-0.349505\pi$
$131$	−4.97791	−	4.97791i	−0.434922	−	0.434922i	−0.890299	+	0.455377i	$0.849505\pi$
$132$		0			0
$133$	3.76716	−	3.76716i	0.326654	−	0.326654i
$134$		0			0
$135$	−5.93211	−	6.91035i	−0.510555	−	0.594748i
$136$		0			0
$137$	5.14127			0.439248			0.219624	−	0.975585i	$-0.429517\pi$
$137$	5.14127			0.439248			0.219624	+	0.975585i	$0.429517\pi$
$138$		0			0
$139$	−13.3617	−	13.3617i	−1.13332	−	1.13332i	−0.989621	−	0.143702i	$-0.954099\pi$
$139$	−13.3617	−	13.3617i	−1.13332	−	1.13332i	−0.143702	−	0.989621i	$-0.545901\pi$
$140$		0			0
$141$	6.83772	+	12.5684i	0.575840	+	1.05845i
$142$		0			0
$143$	11.3585			0.949849
$144$		0			0
$145$	−11.7821			−0.978454
$146$		0			0
$147$	−0.827739	−	1.52146i	−0.0682707	−	0.125488i
$148$		0			0
$149$	−14.3514	−	14.3514i	−1.17571	−	1.17571i	−0.980826	−	0.194886i	$-0.937566\pi$
$149$	−14.3514	−	14.3514i	−1.17571	−	1.17571i	−0.194886	−	0.980826i	$-0.562434\pi$
$150$		0			0
$151$	17.5454			1.42782			0.713911	−	0.700236i	$-0.246922\pi$
$151$	17.5454			1.42782			0.713911	+	0.700236i	$0.246922\pi$
$152$		0			0
$153$	−5.56143	−	3.59840i	−0.449615	−	0.290913i
$154$		0			0
$155$	−1.54460	+	1.54460i	−0.124065	+	0.124065i
$156$		0			0
$157$	9.29740	+	9.29740i	0.742014	+	0.742014i	0.972965	−	0.230952i	$-0.0741839\pi$
$157$	9.29740	+	9.29740i	0.742014	+	0.742014i	−0.230952	+	0.972965i	$0.574184\pi$
$158$		0			0
$159$	1.51404	−	5.12710i	0.120071	−	0.406606i
$160$		0			0
$161$		−	3.97123i		−	0.312977i
$162$		0			0
$163$	11.6109	−	11.6109i	0.909434	−	0.909434i	−0.0867928	−	0.996226i	$-0.527662\pi$
$163$	11.6109	−	11.6109i	0.909434	−	0.909434i	0.996226	+	0.0867928i	$0.0276618\pi$
$164$		0			0
$165$	7.33007	+	13.4734i	0.570645	+	1.04890i
$166$		0			0
$167$			4.92377i			0.381013i	0.981686	+	0.190507i	$0.0610130\pi$
$167$			4.92377i			0.381013i	−0.981686	+	0.190507i	$0.938987\pi$
$168$		0			0
$169$		−	7.94606i		−	0.611235i
$170$		0			0
$171$	3.34919	+	15.6279i	0.256119	+	1.19509i
$172$		0			0
$173$	1.92511	−	1.92511i	0.146363	−	0.146363i	−0.630128	−	0.776491i	$-0.716998\pi$
$173$	1.92511	−	1.92511i	0.146363	−	0.146363i	0.776491	+	0.630128i	$0.216998\pi$
$174$		0			0
$175$		−	1.92804i		−	0.145746i
$176$		0			0
$177$	12.8089	+	3.78250i	0.962777	+	0.284310i
$178$		0			0
$179$	−3.30607	−	3.30607i	−0.247107	−	0.247107i	0.572675	−	0.819782i	$-0.305906\pi$
$179$	−3.30607	−	3.30607i	−0.247107	−	0.247107i	−0.819782	+	0.572675i	$0.805906\pi$
$180$		0			0
$181$	14.1503	−	14.1503i	1.05178	−	1.05178i	0.0531972	−	0.998584i	$-0.483059\pi$
$181$	14.1503	−	14.1503i	1.05178	−	1.05178i	0.998584	−	0.0531972i	$-0.0169412\pi$
$182$		0			0
$183$	−3.54375	+	12.0004i	−0.261962	+	0.887097i
$184$		0			0
$185$	15.8623			1.16622
$186$		0			0
$187$	7.88850	+	7.88850i	0.576865	+	0.576865i
$188$		0			0
$189$	5.18114	+	0.394660i	0.376873	+	0.0287073i
$190$		0			0
$191$	8.46813			0.612732			0.306366	−	0.951914i	$-0.400887\pi$
$191$	8.46813			0.612732			0.306366	+	0.951914i	$0.400887\pi$
$192$		0			0
$193$	−17.2773			−1.24365			−0.621823	−	0.783158i	$-0.713608\pi$
$193$	−17.2773			−1.24365			−0.621823	+	0.783158i	$0.713608\pi$
$194$		0			0
$195$	−5.99493	+	3.26149i	−0.429306	+	0.233560i
$196$		0			0
$197$	16.4452	+	16.4452i	1.17167	+	1.17167i	0.981810	+	0.189864i	$0.0608047\pi$
$197$	16.4452	+	16.4452i	1.17167	+	1.17167i	0.189864	+	0.981810i	$0.439195\pi$
$198$		0			0
$199$	−8.20937			−0.581947			−0.290973	−	0.956731i	$-0.593979\pi$
$199$	−8.20937			−0.581947			−0.290973	+	0.956731i	$0.593979\pi$
$200$		0			0
$201$	−17.0056	−	5.02179i	−1.19948	−	0.354210i
$202$		0			0
$203$	4.75337	−	4.75337i	0.333621	−	0.333621i
$204$		0			0
$205$	4.87764	+	4.87764i	0.340669	+	0.340669i
$206$		0			0
$207$	10.0025	+	6.47190i	0.695223	+	0.449828i
$208$		0			0
$209$		−	26.9176i		−	1.86193i
$210$		0			0
$211$	15.5340	−	15.5340i	1.06940	−	1.06940i	0.0719974	−	0.997405i	$-0.477063\pi$
$211$	15.5340	−	15.5340i	1.06940	−	1.06940i	0.997405	−	0.0719974i	$-0.0229373\pi$
$212$		0			0
$213$	9.33002	−	5.07591i	0.639282	−	0.347796i
$214$		0			0
$215$			2.95096i			0.201254i
$216$		0			0
$217$		−	1.24630i		−	0.0846045i
$218$		0			0
$219$	−15.5563	+	8.46327i	−1.05120	+	0.571895i
$220$		0			0
$221$	−3.50996	+	3.50996i	−0.236106	+	0.236106i
$222$		0			0
$223$			4.58037i			0.306724i	0.988170	+	0.153362i	$0.0490101\pi$
$223$			4.58037i			0.306724i	−0.988170	+	0.153362i	$0.950990\pi$
$224$		0			0
$225$	4.85624	+	3.14212i	0.323750	+	0.209475i
$226$		0			0
$227$	15.9988	+	15.9988i	1.06188	+	1.06188i	0.997955	+	0.0639247i	$0.0203617\pi$
$227$	15.9988	+	15.9988i	1.06188	+	1.06188i	0.0639247	+	0.997955i	$0.479638\pi$
$228$		0			0
$229$	−4.16743	+	4.16743i	−0.275392	+	0.275392i	−0.831266	−	0.555875i	$-0.812383\pi$
$229$	−4.16743	+	4.16743i	−0.275392	+	0.275392i	0.555875	+	0.831266i	$0.312383\pi$
$230$		0			0
$231$	−8.39291	−	2.47844i	−0.552213	−	0.163070i
$232$		0			0
$233$	−7.47847			−0.489931			−0.244966	−	0.969532i	$-0.578777\pi$
$233$	−7.47847			−0.489931			−0.244966	+	0.969532i	$0.578777\pi$
$234$		0			0
$235$	10.2379	+	10.2379i	0.667847	+	0.667847i
$236$		0			0
$237$	9.94900	−	5.41267i	0.646257	−	0.351590i
$238$		0			0
$239$	3.99993			0.258734			0.129367	−	0.991597i	$-0.458705\pi$
$239$	3.99993			0.258734			0.129367	+	0.991597i	$0.458705\pi$
$240$		0			0
$241$	3.26993			0.210635			0.105317	−	0.994439i	$-0.466414\pi$
$241$	3.26993			0.210635			0.105317	+	0.994439i	$0.466414\pi$
$242$		0			0
$243$	−9.43775	+	12.4068i	−0.605432	+	0.795897i
$244$		0			0
$245$	−1.23935	−	1.23935i	−0.0791789	−	0.0791789i
$246$		0			0
$247$	11.9769			0.762072
$248$		0			0
$249$	−8.57577	+	29.0407i	−0.543467	+	1.84038i
$250$		0			0
$251$	3.56566	−	3.56566i	0.225062	−	0.225062i	−0.585564	−	0.810626i	$-0.699127\pi$
$251$	3.56566	−	3.56566i	0.225062	−	0.225062i	0.810626	+	0.585564i	$0.199127\pi$
$252$		0			0
$253$	−14.1879	−	14.1879i	−0.891984	−	0.891984i
$254$		0			0
$255$	−6.42858	−	1.89837i	−0.402573	−	0.118881i
$256$		0			0
$257$			17.0440i			1.06318i	0.847002	+	0.531589i	$0.178405\pi$
$257$			17.0440i			1.06318i	−0.847002	+	0.531589i	$0.821595\pi$
$258$		0			0
$259$	−6.39946	+	6.39946i	−0.397643	+	0.397643i
$260$		0			0
$261$	4.22598	+	19.7191i	0.261582	+	1.22058i
$262$		0			0
$263$			26.4446i			1.63064i	0.579009	+	0.815321i	$0.303440\pi$
$263$			26.4446i			1.63064i	−0.579009	+	0.815321i	$0.696560\pi$
$264$		0			0
$265$		−	5.40972i		−	0.332316i
$266$		0			0
$267$	−7.57707	−	13.9274i	−0.463709	−	0.852342i
$268$		0			0
$269$	−11.5967	+	11.5967i	−0.707061	+	0.707061i	−0.965916	−	0.258855i	$-0.916655\pi$
$269$	−11.5967	+	11.5967i	−0.707061	+	0.707061i	0.258855	+	0.965916i	$0.416655\pi$
$270$		0			0
$271$		−	7.02845i		−	0.426948i	−0.976949	−	0.213474i	$-0.931522\pi$
$271$		−	7.02845i		−	0.426948i	0.976949	−	0.213474i	$-0.0684778\pi$
$272$		0			0
$273$	1.10278	−	3.73440i	0.0667430	−	0.226016i
$274$		0			0
$275$	−6.88824	−	6.88824i	−0.415377	−	0.415377i
$276$		0			0
$277$	3.04438	−	3.04438i	0.182919	−	0.182919i	−0.609707	−	0.792627i	$-0.708713\pi$
$277$	3.04438	−	3.04438i	0.182919	−	0.182919i	0.792627	+	0.609707i	$0.208713\pi$
$278$		0			0
$279$	3.13912	+	2.03110i	0.187934	+	0.121599i
$280$		0			0
$281$	9.56982			0.570887			0.285444	−	0.958395i	$-0.407859\pi$
$281$	9.56982			0.570887			0.285444	+	0.958395i	$0.407859\pi$
$282$		0			0
$283$	15.9451	+	15.9451i	0.947839	+	0.947839i	0.998705	−	0.0508666i	$-0.0161983\pi$
$283$	15.9451	+	15.9451i	0.947839	+	0.947839i	−0.0508666	+	0.998705i	$0.516198\pi$
$284$		0			0
$285$	7.72912	+	14.2069i	0.457834	+	0.841542i
$286$		0			0
$287$	−3.93566			−0.232315
$288$		0			0
$289$	12.1247			0.713216
$290$		0			0
$291$	−6.35501	−	11.6811i	−0.372537	−	0.684759i
$292$		0			0
$293$	1.28702	+	1.28702i	0.0751886	+	0.0751886i	0.743701	−	0.668512i	$-0.233069\pi$
$293$	1.28702	+	1.28702i	0.0751886	+	0.0751886i	−0.668512	+	0.743701i	$0.733069\pi$
$294$		0			0
$295$	13.5150			0.786871
$296$		0			0
$297$	19.9205	−	17.1005i	1.15590	−	0.992272i
$298$		0			0
$299$	6.31285	−	6.31285i	0.365081	−	0.365081i
$300$		0			0
$301$	−1.19053	−	1.19053i	−0.0686211	−	0.0686211i
$302$		0			0
$303$	−3.54003	+	11.9878i	−0.203369	+	0.688683i
$304$		0			0
$305$			12.6619i			0.725019i
$306$		0			0
$307$	−6.52035	+	6.52035i	−0.372136	+	0.372136i	−0.868255	−	0.496119i	$-0.834758\pi$
$307$	−6.52035	+	6.52035i	−0.372136	+	0.372136i	0.496119	+	0.868255i	$0.334758\pi$
$308$		0			0
$309$	14.2565	+	26.2047i	0.811022	+	1.49074i
$310$		0			0
$311$			17.8276i			1.01091i	0.862852	+	0.505456i	$0.168676\pi$
$311$			17.8276i			1.01091i	−0.862852	+	0.505456i	$0.831324\pi$
$312$		0			0
$313$			4.87439i			0.275517i	0.990466	+	0.137758i	$0.0439897\pi$
$313$			4.87439i			0.275517i	−0.990466	+	0.137758i	$0.956010\pi$
$314$		0			0
$315$	5.14136	−	1.10184i	0.289683	−	0.0620817i
$316$		0			0
$317$	4.97157	−	4.97157i	0.279231	−	0.279231i	−0.553571	−	0.832802i	$-0.686735\pi$
$317$	4.97157	−	4.97157i	0.279231	−	0.279231i	0.832802	+	0.553571i	$0.186735\pi$
$318$		0			0
$319$		−	33.9644i		−	1.90164i
$320$		0			0
$321$	−21.1023	−	6.23155i	−1.17782	−	0.347811i
$322$		0			0
$323$	8.31795	+	8.31795i	0.462823	+	0.462823i
$324$		0			0
$325$	3.06490	−	3.06490i	0.170010	−	0.170010i
$326$		0			0
$327$	6.87585	−	23.2841i	0.380235	−	1.28761i
$328$		0			0
$329$	−8.26073			−0.455429
$330$		0			0
$331$	−9.97563	−	9.97563i	−0.548310	−	0.548310i	0.377642	−	0.925952i	$-0.376735\pi$
$331$	−9.97563	−	9.97563i	−0.548310	−	0.548310i	−0.925952	+	0.377642i	$0.876735\pi$
$332$		0			0
$333$	−5.68944	−	26.5478i	−0.311779	−	1.45481i
$334$		0			0
$335$	−17.9430			−0.980329
$336$		0			0
$337$	7.16141			0.390107			0.195054	−	0.980793i	$-0.437512\pi$
$337$	7.16141			0.390107			0.195054	+	0.980793i	$0.437512\pi$
$338$		0			0
$339$	21.6402	−	11.7732i	1.17533	−	0.639430i
$340$		0			0
$341$	−4.45262	−	4.45262i	−0.241123	−	0.241123i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	11.5621	+	3.41432i	0.622485	+	0.183821i
$346$		0			0
$347$	7.59346	−	7.59346i	0.407638	−	0.407638i	−0.473276	−	0.880914i	$-0.656929\pi$
$347$	7.59346	−	7.59346i	0.407638	−	0.407638i	0.880914	+	0.473276i	$0.156929\pi$
$348$		0			0
$349$	−7.63248	−	7.63248i	−0.408557	−	0.408557i	0.472678	−	0.881235i	$-0.343287\pi$
$349$	−7.63248	−	7.63248i	−0.408557	−	0.408557i	−0.881235	+	0.472678i	$0.843287\pi$
$350$		0			0
$351$	7.60881	+	8.86355i	0.406128	+	0.473101i
$352$		0			0
$353$			18.8358i			1.00253i	0.865294	+	0.501265i	$0.167132\pi$
$353$			18.8358i			1.00253i	−0.865294	+	0.501265i	$0.832868\pi$
$354$		0			0
$355$	7.60000	−	7.60000i	0.403366	−	0.403366i
$356$		0			0
$357$	3.35941	−	1.82766i	0.177799	−	0.0967300i
$358$		0			0
$359$		−	15.8207i		−	0.834984i	−0.908681	−	0.417492i	$-0.862909\pi$
$359$		−	15.8207i		−	0.834984i	0.908681	−	0.417492i	$-0.137091\pi$
$360$		0			0
$361$		−	9.38299i		−	0.493842i
$362$		0			0
$363$	−22.1036	+	12.0253i	−1.16014	+	0.631164i
$364$		0			0
$365$	−12.6718	+	12.6718i	−0.663271	+	0.663271i
$366$		0			0
$367$		−	25.6082i		−	1.33674i	−0.743831	−	0.668368i	$-0.766993\pi$
$367$		−	25.6082i		−	1.33674i	0.743831	−	0.668368i	$-0.233007\pi$
$368$		0			0
$369$	6.41393	−	9.91292i	0.333896	−	0.516046i
$370$		0			0
$371$	2.18249	+	2.18249i	0.113309	+	0.113309i
$372$		0			0
$373$	−20.8264	+	20.8264i	−1.07835	+	1.07835i	−0.0816898	+	0.996658i	$0.526032\pi$
$373$	−20.8264	+	20.8264i	−1.07835	+	1.07835i	−0.996658	+	0.0816898i	$0.973968\pi$
$374$		0			0
$375$	20.1708	+	5.95648i	1.04162	+	0.307592i
$376$		0			0
$377$	15.1123			0.778325
$378$		0			0
$379$	−7.30890	−	7.30890i	−0.375433	−	0.375433i	0.494018	−	0.869451i	$-0.335528\pi$
$379$	−7.30890	−	7.30890i	−0.375433	−	0.375433i	−0.869451	+	0.494018i	$0.835528\pi$
$380$		0			0
$381$	−3.39737	+	1.84831i	−0.174053	+	0.0946918i
$382$		0			0
$383$	−15.8671			−0.810769			−0.405384	−	0.914146i	$-0.632862\pi$
$383$	−15.8671			−0.810769			−0.405384	+	0.914146i	$0.632862\pi$
$384$		0			0
$385$	−8.85554			−0.451320
$386$		0			0
$387$	4.93885	−	1.05844i	0.251056	−	0.0538036i
$388$		0			0
$389$	−2.42160	−	2.42160i	−0.122780	−	0.122780i	0.643047	−	0.765827i	$-0.277670\pi$
$389$	−2.42160	−	2.42160i	−0.122780	−	0.122780i	−0.765827	+	0.643047i	$0.777670\pi$
$390$		0			0
$391$	8.76854			0.443444
$392$		0			0
$393$	−3.45330	+	11.6941i	−0.174196	+	0.589890i
$394$		0			0
$395$	8.10421	−	8.10421i	0.407767	−	0.407767i
$396$		0			0
$397$	−2.29467	−	2.29467i	−0.115166	−	0.115166i	0.647175	−	0.762341i	$-0.275950\pi$
$397$	−2.29467	−	2.29467i	−0.115166	−	0.115166i	−0.762341	+	0.647175i	$0.775950\pi$
$398$		0			0
$399$	−8.84982	−	2.61337i	−0.443045	−	0.130832i
$400$		0			0
$401$			4.57856i			0.228642i	0.993444	+	0.114321i	$0.0364693\pi$
$401$			4.57856i			0.228642i	−0.993444	+	0.114321i	$0.963531\pi$
$402$		0			0
$403$	1.98118	−	1.98118i	0.0986895	−	0.0986895i
$404$		0			0
$405$	−5.60361	+	14.7455i	−0.278445	+	0.732707i
$406$		0			0
$407$			45.7263i			2.26657i
$408$		0			0
$409$			34.4670i			1.70428i	0.523312	+	0.852141i	$0.324696\pi$
$409$			34.4670i			1.70428i	−0.523312	+	0.852141i	$0.675304\pi$
$410$		0			0
$411$	−4.25563	−	7.82225i	−0.209915	−	0.385843i
$412$		0			0
$413$	−5.45245	+	5.45245i	−0.268298	+	0.268298i
$414$		0			0
$415$			30.6414i			1.50413i
$416$		0			0
$417$	−9.26932	+	31.3893i	−0.453921	+	1.53714i
$418$		0			0
$419$	19.6092	+	19.6092i	0.957971	+	0.957971i	0.999152	−	0.0411805i	$-0.0131119\pi$
$419$	19.6092	+	19.6092i	0.957971	+	0.957971i	−0.0411805	+	0.999152i	$0.513112\pi$
$420$		0			0
$421$	20.9601	−	20.9601i	1.02153	−	1.02153i	0.0217712	−	0.999763i	$-0.493069\pi$
$421$	20.9601	−	20.9601i	1.02153	−	1.02153i	0.999763	−	0.0217712i	$-0.00693054\pi$
$422$		0			0
$423$	13.4625	−	20.8067i	0.654569	−	1.01166i
$424$		0			0
$425$	4.25714			0.206502
$426$		0			0
$427$	−5.10830	−	5.10830i	−0.247208	−	0.247208i
$428$		0			0
$429$	−9.40190	−	17.2816i	−0.453928	−	0.834363i
$430$		0			0
$431$	28.8191			1.38817			0.694083	−	0.719895i	$-0.255810\pi$
$431$	28.8191			1.38817			0.694083	+	0.719895i	$0.255810\pi$
$432$		0			0
$433$	29.7649			1.43041			0.715205	−	0.698915i	$-0.246333\pi$
$433$	29.7649			1.43041			0.715205	+	0.698915i	$0.246333\pi$
$434$		0			0
$435$	9.75254	+	17.9261i	0.467598	+	0.859490i
$436$		0			0
$437$	−14.9603	−	14.9603i	−0.715646	−	0.715646i
$438$		0			0
$439$	10.4581			0.499137			0.249568	−	0.968357i	$-0.419711\pi$
$439$	10.4581			0.499137			0.249568	+	0.968357i	$0.419711\pi$
$440$		0			0
$441$	−1.62970	+	2.51875i	−0.0776046	+	0.119940i
$442$		0			0
$443$	−19.0958	+	19.0958i	−0.907268	+	0.907268i	−0.996051	−	0.0887831i	$-0.971702\pi$
$443$	−19.0958	+	19.0958i	−0.907268	+	0.907268i	0.0887831	+	0.996051i	$0.471702\pi$
$444$		0			0
$445$	−11.3449	−	11.3449i	−0.537800	−	0.537800i
$446$		0			0
$447$	−9.95590	+	33.7143i	−0.470898	+	1.59463i
$448$		0			0
$449$			26.5991i			1.25529i	0.778500	+	0.627645i	$0.215981\pi$
$449$			26.5991i			1.25529i	−0.778500	+	0.627645i	$0.784019\pi$
$450$		0			0
$451$	−14.0608	+	14.0608i	−0.662097	+	0.662097i
$452$		0			0
$453$	−14.5230	−	26.6946i	−0.682349	−	1.25422i
$454$		0			0
$455$		−	3.94024i		−	0.184721i
$456$		0			0
$457$			5.10142i			0.238634i	0.992856	+	0.119317i	$0.0380705\pi$
$457$			5.10142i			0.238634i	−0.992856	+	0.119317i	$0.961929\pi$
$458$		0			0
$459$	−0.871416	+	11.4400i	−0.0406742	+	0.533976i
$460$		0			0
$461$	7.89211	−	7.89211i	0.367572	−	0.367572i	−0.499019	−	0.866591i	$-0.666306\pi$
$461$	7.89211	−	7.89211i	0.367572	−	0.367572i	0.866591	+	0.499019i	$0.166306\pi$
$462$		0			0
$463$			11.5271i			0.535708i	0.963460	+	0.267854i	$0.0863145\pi$
$463$			11.5271i			0.535708i	−0.963460	+	0.267854i	$0.913686\pi$
$464$		0			0
$465$	3.62858	+	1.07153i	0.168271	+	0.0496908i
$466$		0			0
$467$	−17.4574	−	17.4574i	−0.807833	−	0.807833i	0.176472	−	0.984306i	$-0.443531\pi$
$467$	−17.4574	−	17.4574i	−0.807833	−	0.807833i	−0.984306	+	0.176472i	$0.943531\pi$
$468$		0			0
$469$	7.23888	−	7.23888i	0.334261	−	0.334261i
$470$		0			0
$471$	6.44983	−	21.8415i	0.297193	−	1.00640i
$472$		0			0
$473$	−8.50674			−0.391140
$474$		0			0
$475$	−7.26324	−	7.26324i	−0.333260	−	0.333260i
$476$		0			0
$477$	−9.05393	+	1.94034i	−0.414551	+	0.0888420i
$478$		0			0
$479$	2.12141			0.0969295			0.0484648	−	0.998825i	$-0.484567\pi$
$479$	2.12141			0.0969295			0.0484648	+	0.998825i	$0.484567\pi$
$480$		0			0
$481$	−20.3457			−0.927686
$482$		0			0
$483$	−6.04208	+	3.28714i	−0.274924	+	0.149570i
$484$		0			0
$485$	−9.51515	−	9.51515i	−0.432061	−	0.432061i
$486$		0			0
$487$	−34.1205			−1.54615			−0.773073	−	0.634316i	$-0.781282\pi$
$487$	−34.1205			−1.54615			−0.773073	+	0.634316i	$0.781282\pi$
$488$		0			0
$489$	−27.2763	−	8.05474i	−1.23348	−	0.364248i
$490$		0			0
$491$	2.32777	−	2.32777i	0.105051	−	0.105051i	−0.652628	−	0.757679i	$-0.726334\pi$
$491$	2.32777	−	2.32777i	0.105051	−	0.105051i	0.757679	+	0.652628i	$0.226334\pi$
$492$		0			0
$493$	10.4955	+	10.4955i	0.472694	+	0.472694i
$494$		0			0
$495$	14.4319	−	22.3049i	0.648664	−	1.00253i
$496$		0			0
$497$			6.13227i			0.275070i
$498$		0			0
$499$	−16.4946	+	16.4946i	−0.738401	+	0.738401i	−0.972269	−	0.233867i	$-0.924862\pi$
$499$	−16.4946	+	16.4946i	−0.738401	+	0.738401i	0.233867	+	0.972269i	$0.424862\pi$
$500$		0			0
$501$	7.49134	−	4.07560i	0.334688	−	0.182084i
$502$		0			0
$503$		−	21.0199i		−	0.937231i	−0.883402	−	0.468616i	$-0.844753\pi$
$503$		−	21.0199i		−	0.937231i	0.883402	−	0.468616i	$-0.155247\pi$
$504$		0			0
$505$			12.6486i			0.562856i
$506$		0			0
$507$	−12.0896	+	6.57726i	−0.536919	+	0.292106i
$508$		0			0
$509$	15.8208	−	15.8208i	0.701244	−	0.701244i	−0.263433	−	0.964678i	$-0.584855\pi$
$509$	15.8208	−	15.8208i	0.701244	−	0.701244i	0.964678	+	0.263433i	$0.0848549\pi$
$510$		0			0
$511$		−	10.2246i		−	0.452308i
$512$		0			0
$513$	21.0049	−	18.0314i	0.927391	−	0.796108i
$514$		0			0
$515$	21.3457	+	21.3457i	0.940606	+	0.940606i
$516$		0			0
$517$	−29.5128	+	29.5128i	−1.29797	+	1.29797i
$518$		0			0
$519$	−4.52246	−	1.33549i	−0.198514	−	0.0586216i
$520$		0			0
$521$	9.99923			0.438074			0.219037	−	0.975717i	$-0.429708\pi$
$521$	9.99923			0.438074			0.219037	+	0.975717i	$0.429708\pi$
$522$		0			0
$523$	17.9456	+	17.9456i	0.784708	+	0.784708i	0.980621	−	0.195913i	$-0.0627671\pi$
$523$	17.9456	+	17.9456i	0.784708	+	0.784708i	−0.195913	+	0.980621i	$0.562767\pi$
$524$		0			0
$525$	−2.93344	+	1.59591i	−0.128026	+	0.0696514i
$526$		0			0
$527$	2.75186			0.119873
$528$		0			0
$529$	7.22933			0.314319
$530$		0			0
$531$	−4.84750	−	22.6192i	−0.210364	−	0.981590i
$532$		0			0
$533$	−6.25630	−	6.25630i	−0.270990	−	0.270990i
$534$		0			0
$535$	−22.2655			−0.962621
$536$		0			0
$537$	−2.29350	+	7.76662i	−0.0989718	+	0.335154i
$538$		0			0
$539$	3.57267	−	3.57267i	0.153886	−	0.153886i
$540$		0			0
$541$	−19.7562	−	19.7562i	−0.849384	−	0.849384i	0.140672	−	0.990056i	$-0.455074\pi$
$541$	−19.7562	−	19.7562i	−0.849384	−	0.849384i	−0.990056	+	0.140672i	$0.955074\pi$
$542$		0			0
$543$	−33.2418	−	9.81638i	−1.42654	−	0.421261i
$544$		0			0
$545$		−	24.5676i		−	1.05236i
$546$		0			0
$547$	−13.7252	+	13.7252i	−0.586847	+	0.586847i	−0.936776	−	0.349929i	$-0.886206\pi$
$547$	−13.7252	+	13.7252i	−0.586847	+	0.586847i	0.349929	+	0.936776i	$0.386206\pi$
$548$		0			0
$549$	21.1915	−	4.54153i	0.904432	−	0.193828i
$550$		0			0
$551$		−	35.8134i		−	1.52570i
$552$		0			0
$553$			6.53910i			0.278071i
$554$		0			0
$555$	−13.1298	−	24.1339i	−0.557331	−	1.02443i
$556$		0			0
$557$	−6.97099	+	6.97099i	−0.295370	+	0.295370i	−0.839197	−	0.543827i	$-0.816975\pi$
$557$	−6.97099	+	6.97099i	−0.295370	+	0.295370i	0.543827	+	0.839197i	$0.316975\pi$
$558$		0			0
$559$		−	3.78504i		−	0.160090i
$560$		0			0
$561$	5.47245	−	18.5317i	0.231047	−	0.782408i
$562$		0			0
$563$	12.0301	+	12.0301i	0.507009	+	0.507009i	0.913607	−	0.406598i	$-0.133285\pi$
$563$	12.0301	+	12.0301i	0.507009	+	0.507009i	−0.406598	+	0.913607i	$0.633285\pi$
$564$		0			0
$565$	17.6276	−	17.6276i	0.741597	−	0.741597i
$566$		0			0
$567$	−3.68817	−	8.20959i	−0.154889	−	0.344770i
$568$		0			0
$569$	5.33785			0.223774			0.111887	−	0.993721i	$-0.464310\pi$
$569$	5.33785			0.223774			0.111887	+	0.993721i	$0.464310\pi$
$570$		0			0
$571$	−29.1035	−	29.1035i	−1.21795	−	1.21795i	−0.968350	−	0.249595i	$-0.919703\pi$
$571$	−29.1035	−	29.1035i	−1.21795	−	1.21795i	−0.249595	−	0.968350i	$-0.580297\pi$
$572$		0			0
$573$	−7.00940	−	12.8839i	−0.292822	−	0.538235i
$574$		0			0
$575$	−7.65669			−0.319306
$576$		0			0
$577$	−8.17753			−0.340435			−0.170217	−	0.985407i	$-0.554447\pi$
$577$	−8.17753			−0.340435			−0.170217	+	0.985407i	$0.554447\pi$
$578$		0			0
$579$	14.3011	+	26.2867i	0.594332	+	1.09244i
$580$		0			0
$581$	−12.3619	−	12.3619i	−0.512859	−	0.512859i
$582$		0			0
$583$	15.5946			0.645862
$584$		0			0
$585$	9.92447	+	6.42140i	0.410327	+	0.265492i
$586$		0			0
$587$	25.8580	−	25.8580i	1.06727	−	1.06727i	0.0697047	−	0.997568i	$-0.477794\pi$
$587$	25.8580	−	25.8580i	1.06727	−	1.06727i	0.997568	−	0.0697047i	$-0.0222057\pi$
$588$		0			0
$589$	−4.69502	−	4.69502i	−0.193455	−	0.193455i
$590$		0			0
$591$	11.4085	−	38.6332i	0.469281	−	1.58916i
$592$		0			0
$593$		−	18.1350i		−	0.744714i	−0.928090	−	0.372357i	$-0.878550\pi$
$593$		−	18.1350i		−	0.744714i	0.928090	−	0.372357i	$-0.121450\pi$
$594$		0			0
$595$	2.73650	−	2.73650i	0.112185	−	0.112185i
$596$		0			0
$597$	6.79521	+	12.4902i	0.278109	+	0.511192i
$598$		0			0
$599$		−	4.71552i		−	0.192671i	−0.995349	−	0.0963354i	$-0.969288\pi$
$599$		−	4.71552i		−	0.192671i	0.995349	−	0.0963354i	$-0.0307122\pi$
$600$		0			0
$601$			14.1554i			0.577413i	0.957418	+	0.288706i	$0.0932251\pi$
$601$			14.1554i			0.577413i	−0.957418	+	0.288706i	$0.906775\pi$
$602$		0			0
$603$	6.43572	+	30.0301i	0.262083	+	1.22292i
$604$		0			0
$605$	−18.0051	+	18.0051i	−0.732011	+	0.732011i
$606$		0			0
$607$		−	7.96072i		−	0.323116i	−0.986863	−	0.161558i	$-0.948348\pi$
$607$		−	7.96072i		−	0.323116i	0.986863	−	0.161558i	$-0.0516518\pi$
$608$		0			0
$609$	−11.1666	−	3.29753i	−0.452494	−	0.133623i
$610$		0			0
$611$	−13.1316	−	13.1316i	−0.531249	−	0.531249i
$612$		0			0
$613$	17.7697	−	17.7697i	0.717713	−	0.717713i	−0.250423	−	0.968136i	$-0.580570\pi$
$613$	17.7697	−	17.7697i	0.717713	−	0.717713i	0.968136	+	0.250423i	$0.0805697\pi$
$614$		0			0
$615$	3.38374	−	11.4586i	0.136446	−	0.462054i
$616$		0			0
$617$	21.7284			0.874752			0.437376	−	0.899279i	$-0.355908\pi$
$617$	21.7284			0.874752			0.437376	+	0.899279i	$0.355908\pi$
$618$		0			0
$619$	19.6253	+	19.6253i	0.788807	+	0.788807i	0.981299	−	0.192491i	$-0.0616567\pi$
$619$	19.6253	+	19.6253i	0.788807	+	0.788807i	−0.192491	+	0.981299i	$0.561657\pi$
$620$		0			0
$621$	1.56729	−	20.5755i	0.0628930	−	0.825667i
$622$		0			0
$623$	9.15394			0.366745
$624$		0			0
$625$	11.6425			0.465698
$626$		0			0
$627$	−40.9541	+	22.2807i	−1.63555	+	0.889807i
$628$		0			0
$629$	−14.1301	−	14.1301i	−0.563405	−	0.563405i
$630$		0			0
$631$	26.1699			1.04181			0.520904	−	0.853616i	$-0.325595\pi$
$631$	26.1699			1.04181			0.520904	+	0.853616i	$0.325595\pi$
$632$		0			0
$633$	−36.4924	−	10.7763i	−1.45044	−	0.428319i
$634$		0			0
$635$	−2.76742	+	2.76742i	−0.109822	+	0.109822i
$636$		0			0
$637$	1.58965	+	1.58965i	0.0629840	+	0.0629840i
$638$		0			0
$639$	−15.4456	−	9.99374i	−0.611020	−	0.395346i
$640$		0			0
$641$		−	19.6364i		−	0.775592i	−0.921745	−	0.387796i	$-0.873237\pi$
$641$		−	19.6364i		−	0.775592i	0.921745	−	0.387796i	$-0.126763\pi$
$642$		0			0
$643$	−8.37406	+	8.37406i	−0.330241	+	0.330241i	−0.852678	−	0.522437i	$-0.825023\pi$
$643$	−8.37406	+	8.37406i	−0.330241	+	0.330241i	0.522437	+	0.852678i	$0.325023\pi$
$644$		0			0
$645$	4.48978	−	2.44262i	0.176785	−	0.0961782i
$646$		0			0
$647$		−	15.9115i		−	0.625544i	−0.949828	−	0.312772i	$-0.898742\pi$
$647$		−	15.9115i		−	0.625544i	0.949828	−	0.312772i	$-0.101258\pi$
$648$		0			0
$649$			38.9596i			1.52930i
$650$		0			0
$651$	−1.89620	+	1.03161i	−0.0743180	+	0.0404321i
$652$		0			0
$653$	−7.56494	+	7.56494i	−0.296039	+	0.296039i	−0.839460	−	0.543421i	$-0.817129\pi$
$653$	−7.56494	+	7.56494i	−0.296039	+	0.296039i	0.543421	+	0.839460i	$0.317129\pi$
$654$		0			0
$655$			12.3387i			0.482114i
$656$		0			0
$657$	25.7531	+	16.6630i	1.00472	+	0.650084i
$658$		0			0
$659$	−21.0236	−	21.0236i	−0.818963	−	0.818963i	0.166995	−	0.985958i	$-0.446594\pi$
$659$	−21.0236	−	21.0236i	−0.818963	−	0.818963i	−0.985958	+	0.166995i	$0.946594\pi$
$660$		0			0
$661$	18.6305	−	18.6305i	0.724643	−	0.724643i	−0.244904	−	0.969547i	$-0.578756\pi$
$661$	18.6305	−	18.6305i	0.724643	−	0.724643i	0.969547	+	0.244904i	$0.0787565\pi$
$662$		0			0
$663$	8.24561	+	2.43495i	0.320233	+	0.0945655i
$664$		0			0
$665$	−9.33763			−0.362098
$666$		0			0
$667$	−18.8767	−	18.8767i	−0.730910	−	0.730910i
$668$		0			0
$669$	6.96887	−	3.79135i	0.269432	−	0.146582i
$670$		0			0
$671$	−36.5005			−1.40909
$672$		0			0
$673$	48.8310			1.88230			0.941148	−	0.337995i	$-0.109749\pi$
$673$	48.8310			1.88230			0.941148	+	0.337995i	$0.109749\pi$
$674$		0			0
$675$	0.760921	−	9.98945i	0.0292879	−	0.384494i
$676$		0			0
$677$	−17.2859	−	17.2859i	−0.664352	−	0.664352i	0.292051	−	0.956403i	$-0.405662\pi$
$677$	−17.2859	−	17.2859i	−0.664352	−	0.664352i	−0.956403	+	0.292051i	$0.905662\pi$
$678$		0			0
$679$	7.67756			0.294638
$680$		0			0
$681$	11.0988	−	37.5845i	0.425306	−	1.44024i
$682$		0			0
$683$	18.1722	−	18.1722i	0.695338	−	0.695338i	−0.268063	−	0.963401i	$-0.586384\pi$
$683$	18.1722	−	18.1722i	0.695338	−	0.695338i	0.963401	+	0.268063i	$0.0863835\pi$
$684$		0			0
$685$	−6.37181	−	6.37181i	−0.243454	−	0.243454i
$686$		0			0
$687$	9.79014	+	2.89105i	0.373517	+	0.110300i
$688$		0			0
$689$			6.93876i			0.264346i
$690$		0			0
$691$	−28.3836	+	28.3836i	−1.07976	+	1.07976i	−0.0832314	+	0.996530i	$0.526524\pi$
$691$	−28.3836	+	28.3836i	−1.07976	+	1.07976i	−0.996530	+	0.0832314i	$0.973476\pi$
$692$		0			0
$693$	3.17628	+	14.8210i	0.120657	+	0.563003i
$694$		0			0
$695$			33.1195i			1.25629i
$696$		0			0
$697$		−	8.69000i		−	0.329157i
$698$		0			0
$699$	6.19022	+	11.3782i	0.234136	+	0.430364i
$700$		0			0
$701$	8.31473	−	8.31473i	0.314043	−	0.314043i	−0.532431	−	0.846474i	$-0.678721\pi$
$701$	8.31473	−	8.31473i	0.314043	−	0.314043i	0.846474	+	0.532431i	$0.178721\pi$
$702$		0			0
$703$			48.2156i			1.81849i
$704$		0			0
$705$	7.10228	−	24.0509i	0.267487	−	0.905809i
$706$		0			0
$707$	−5.10294	−	5.10294i	−0.191916	−	0.191916i
$708$		0			0
$709$	−34.8067	+	34.8067i	−1.30719	+	1.30719i	−0.383757	+	0.923434i	$0.625370\pi$
$709$	−34.8067	+	34.8067i	−1.30719	+	1.30719i	−0.923434	+	0.383757i	$0.874630\pi$
$710$		0			0
$711$	−16.4703	−	10.6568i	−0.617686	−	0.399660i
$712$		0			0
$713$	−4.94935			−0.185355
$714$		0			0
$715$	−14.0772	−	14.0772i	−0.526456	−	0.526456i
$716$		0			0
$717$	−3.31090	−	6.08575i	−0.123648	−	0.227276i
$718$		0			0
$719$	7.90389			0.294765			0.147383	−	0.989080i	$-0.452915\pi$
$719$	7.90389			0.294765			0.147383	+	0.989080i	$0.452915\pi$
$720$		0			0
$721$	−17.2234			−0.641432
$722$		0			0
$723$	−2.70665	−	4.97507i	−0.100661	−	0.185025i
$724$		0			0
$725$	−9.16469	−	9.16469i	−0.340368	−	0.340368i
$726$		0			0
$727$	28.1472			1.04392			0.521960	−	0.852970i	$-0.325201\pi$
$727$	28.1472			1.04392			0.521960	+	0.852970i	$0.325201\pi$
$728$		0			0
$729$	26.6885	+	4.08958i	0.988462	+	0.151466i
$730$		0			0
$731$	2.62871	−	2.62871i	0.0972264	−	0.0972264i
$732$		0			0
$733$	28.6742	+	28.6742i	1.05911	+	1.05911i	0.998140	+	0.0609673i	$0.0194185\pi$
$733$	28.6742	+	28.6742i	1.05911	+	1.05911i	0.0609673	+	0.998140i	$0.480581\pi$
$734$		0			0
$735$	−0.859765	+	2.91147i	−0.0317129	+	0.107391i
$736$		0			0
$737$		−	51.7242i		−	1.90529i
$738$		0			0
$739$	−1.83024	+	1.83024i	−0.0673263	+	0.0673263i	−0.739968	−	0.672642i	$-0.765159\pi$
$739$	−1.83024	+	1.83024i	−0.0673263	+	0.0673263i	0.672642	+	0.739968i	$0.265159\pi$
$740$		0			0
$741$	−9.91374	−	18.2224i	−0.364190	−	0.669417i
$742$		0			0
$743$			1.62576i			0.0596432i	0.999555	+	0.0298216i	$0.00949392\pi$
$743$			1.62576i			0.0596432i	−0.999555	+	0.0298216i	$0.990506\pi$
$744$		0			0
$745$			35.5727i			1.30328i
$746$		0			0
$747$	51.2828	−	10.9904i	1.87634	−	0.402116i
$748$		0			0
$749$	8.98275	−	8.98275i	0.328223	−	0.328223i
$750$		0			0
$751$			30.5920i			1.11632i	0.829734	+	0.558159i	$0.188492\pi$
$751$			30.5920i			1.11632i	−0.829734	+	0.558159i	$0.811508\pi$
$752$		0			0
$753$	−8.37645	−	2.47358i	−0.305255	−	0.0901424i
$754$		0			0
$755$	−21.7448	−	21.7448i	−0.791374	−	0.791374i
$756$		0			0
$757$	−11.0220	+	11.0220i	−0.400602	+	0.400602i	−0.878445	−	0.477843i	$-0.841419\pi$
$757$	−11.0220	+	11.0220i	−0.400602	+	0.400602i	0.477843	+	0.878445i	$0.341419\pi$
$758$		0			0
$759$	−9.84247	+	33.3302i	−0.357259	+	1.20981i
$760$		0			0
$761$	2.53536			0.0919066			0.0459533	−	0.998944i	$-0.485367\pi$
$761$	2.53536			0.0919066			0.0459533	+	0.998944i	$0.485367\pi$
$762$		0			0
$763$	9.91151	+	9.91151i	0.358821	+	0.358821i
$764$		0			0
$765$	2.43288	+	11.3522i	0.0879610	+	0.410440i
$766$		0			0
$767$	−17.3349			−0.625928
$768$		0			0
$769$	−1.37099			−0.0494393			−0.0247196	−	0.999694i	$-0.507869\pi$
$769$	−1.37099			−0.0494393			−0.0247196	+	0.999694i	$0.507869\pi$
$770$		0			0
$771$	25.9319	−	14.1080i	0.933914	−	0.508088i
$772$		0			0
$773$	3.38228	+	3.38228i	0.121652	+	0.121652i	0.765312	−	0.643660i	$-0.222585\pi$
$773$	3.38228	+	3.38228i	0.121652	+	0.121652i	−0.643660	+	0.765312i	$0.722585\pi$
$774$		0			0
$775$	−2.40292			−0.0863154
$776$		0			0
$777$	15.0336	+	4.43946i	0.539328	+	0.159265i
$778$		0			0
$779$	−14.8263	+	14.8263i	−0.531206	+	0.531206i
$780$		0			0
$781$	21.9085	+	21.9085i	0.783949	+	0.783949i
$782$		0			0
$783$	26.5039	−	22.7519i	0.947170	−	0.813087i
$784$		0			0
$785$		−	23.0454i		−	0.822526i
$786$		0			0
$787$	−37.7087	+	37.7087i	−1.34417	+	1.34417i	−0.452308	+	0.891862i	$0.649399\pi$
$787$	−37.7087	+	37.7087i	−1.34417	+	1.34417i	−0.891862	+	0.452308i	$0.850601\pi$
$788$		0			0
$789$	40.2344	−	21.8892i	1.43238	−	0.779276i
$790$		0			0
$791$			14.2233i			0.505721i
$792$		0			0
$793$		−	16.2408i		−	0.576727i
$794$		0			0
$795$	−8.23068	+	4.47783i	−0.291912	+	0.158812i
$796$		0			0
$797$	11.4184	−	11.4184i	0.404459	−	0.404459i	−0.475342	−	0.879801i	$-0.657676\pi$
$797$	11.4184	−	11.4184i	0.404459	−	0.404459i	0.879801	+	0.475342i	$0.157676\pi$
$798$		0			0
$799$		−	18.2398i		−	0.645278i
$800$		0			0
$801$	−14.9182	+	23.0565i	−0.527107	+	0.814660i
$802$		0			0
$803$	−36.5290	−	36.5290i	−1.28908	−	1.28908i
$804$		0			0
$805$	−4.92173	+	4.92173i	−0.173468	+	0.173468i
$806$		0			0
$807$	27.2429	+	8.04489i	0.958995	+	0.283193i
$808$		0			0
$809$	−10.3878			−0.365216			−0.182608	−	0.983186i	$-0.558454\pi$
$809$	−10.3878			−0.365216			−0.182608	+	0.983186i	$0.558454\pi$
$810$		0			0
$811$	−20.4489	−	20.4489i	−0.718058	−	0.718058i	0.250149	−	0.968207i	$-0.419520\pi$
$811$	−20.4489	−	20.4489i	−0.718058	−	0.718058i	−0.968207	+	0.250149i	$0.919520\pi$
$812$		0			0
$813$	−10.6935	+	5.81772i	−0.375038	+	0.204036i
$814$		0			0
$815$	−28.7798			−1.00811
$816$		0			0
$817$	−8.96984			−0.313815
$818$		0			0
$819$	−6.59455	+	1.41327i	−0.230432	+	0.0493837i
$820$		0			0
$821$	11.8610	+	11.8610i	0.413952	+	0.413952i	0.883113	−	0.469161i	$-0.155444\pi$
$821$	11.8610	+	11.8610i	0.413952	+	0.413952i	−0.469161	+	0.883113i	$0.655444\pi$
$822$		0			0
$823$	−4.69616			−0.163698			−0.0818490	−	0.996645i	$-0.526083\pi$
$823$	−4.69616			−0.163698			−0.0818490	+	0.996645i	$0.526083\pi$
$824$		0			0
$825$	−4.77854	+	16.1819i	−0.166367	+	0.563380i
$826$		0			0
$827$	−13.0079	+	13.0079i	−0.452329	+	0.452329i	−0.896127	−	0.443798i	$-0.853631\pi$
$827$	−13.0079	+	13.0079i	−0.452329	+	0.452329i	0.443798	+	0.896127i	$0.353631\pi$
$828$		0			0
$829$	−20.0165	−	20.0165i	−0.695203	−	0.695203i	0.268169	−	0.963372i	$-0.413582\pi$
$829$	−20.0165	−	20.0165i	−0.695203	−	0.695203i	−0.963372	+	0.268169i	$0.913582\pi$
$830$		0			0
$831$	−7.15187	−	2.11196i	−0.248096	−	0.0732632i
$832$		0			0
$833$			2.20802i			0.0765032i
$834$		0			0
$835$	6.10226	−	6.10226i	0.211177	−	0.211177i
$836$		0			0
$837$	0.491866	−	6.45727i	0.0170014	−	0.223196i
$838$		0			0
$839$		−	35.4357i		−	1.22338i	−0.791099	−	0.611688i	$-0.790491\pi$
$839$		−	35.4357i		−	1.22338i	0.791099	−	0.611688i	$-0.209509\pi$
$840$		0			0
$841$		−	16.1890i		−	0.558243i
$842$		0			0
$843$	−7.92131	−	14.5601i	−0.272824	−	0.501477i
$844$		0			0
$845$	−9.84792	+	9.84792i	−0.338779	+	0.338779i
$846$		0			0
$847$		−	14.5279i		−	0.499184i
$848$		0			0
$849$	11.0615	−	37.4583i	0.379630	−	1.28557i
$850$		0			0
$851$	25.4137	+	25.4137i	0.871172	+	0.871172i
$852$		0			0
$853$	4.77904	−	4.77904i	0.163631	−	0.163631i	−0.620542	−	0.784173i	$-0.713087\pi$
$853$	4.77904	−	4.77904i	0.163631	−	0.163631i	0.784173	+	0.620542i	$0.213087\pi$
$854$		0			0
$855$	15.2175	−	23.5191i	0.520428	−	0.804338i
$856$		0			0
$857$	13.0169			0.444647			0.222324	−	0.974973i	$-0.428636\pi$
$857$	13.0169			0.444647			0.222324	+	0.974973i	$0.428636\pi$
$858$		0			0
$859$	13.5335	+	13.5335i	0.461758	+	0.461758i	0.899231	−	0.437473i	$-0.144127\pi$
$859$	13.5335	+	13.5335i	0.461758	+	0.461758i	−0.437473	+	0.899231i	$0.644127\pi$
$860$		0			0
$861$	3.25770	+	5.98796i	0.111022	+	0.204069i
$862$		0			0
$863$	28.1516			0.958293			0.479146	−	0.877735i	$-0.340946\pi$
$863$	28.1516			0.958293			0.479146	+	0.877735i	$0.340946\pi$
$864$		0			0
$865$	−4.77175			−0.162244
$866$		0			0
$867$	−10.0361	−	18.4472i	−0.340842	−	0.626501i
$868$		0			0
$869$	23.3620	+	23.3620i	0.792502	+	0.792502i
$870$		0			0
$871$	23.0145			0.779817
$872$		0			0
$873$	−12.5121	+	19.3378i	−0.423470	+	0.654486i
$874$		0			0
$875$	−8.58624	+	8.58624i	−0.290268	+	0.290268i
$876$		0			0
$877$	−31.2389	−	31.2389i	−1.05486	−	1.05486i	−0.998405	−	0.0564564i	$-0.982020\pi$
$877$	−31.2389	−	31.2389i	−1.05486	−	1.05486i	−0.0564564	−	0.998405i	$-0.517980\pi$
$878$		0			0
$879$	0.892838	−	3.02347i	0.0301147	−	0.101979i
$880$		0			0
$881$			36.9138i			1.24366i	0.783154	+	0.621828i	$0.213610\pi$
$881$			36.9138i			1.24366i	−0.783154	+	0.621828i	$0.786390\pi$
$882$		0			0
$883$	14.6891	−	14.6891i	0.494329	−	0.494329i	−0.415338	−	0.909667i	$-0.636337\pi$
$883$	14.6891	−	14.6891i	0.494329	−	0.494329i	0.909667	+	0.415338i	$0.136337\pi$
$884$		0			0
$885$	−11.1869	−	20.5625i	−0.376042	−	0.691201i
$886$		0			0
$887$			8.84622i			0.297027i	0.988910	+	0.148514i	$0.0474488\pi$
$887$			8.84622i			0.297027i	−0.988910	+	0.148514i	$0.952551\pi$
$888$		0			0
$889$		−	2.23296i		−	0.0748912i
$890$		0			0
$891$	−42.5067	−	16.1535i	−1.42403	−	0.541163i
$892$		0			0
$893$	−31.1195	+	31.1195i	−1.04137	+	1.04137i
$894$		0			0
$895$			8.19473i			0.273920i
$896$		0			0
$897$	−14.8301	−	4.37937i	−0.495164	−	0.146223i
$898$		0			0
$899$	−5.92413	−	5.92413i	−0.197581	−	0.197581i
$900$		0			0
$901$	−4.81897	+	4.81897i	−0.160543	+	0.160543i
$902$		0			0
$903$	−0.825900	+	2.79680i	−0.0274842	+	0.0930716i
$904$		0			0
$905$	−35.0742			−1.16591
$906$		0			0
$907$	26.6472	+	26.6472i	0.884804	+	0.884804i	0.994018	−	0.109214i	$-0.0348333\pi$
$907$	26.6472	+	26.6472i	0.884804	+	0.884804i	−0.109214	+	0.994018i	$0.534833\pi$
$908$		0			0
$909$	21.1693	−	4.53676i	0.702140	−	0.150475i
$910$		0			0
$911$	48.5784			1.60947			0.804737	−	0.593632i	$-0.202306\pi$
$911$	48.5784			1.60947			0.804737	+	0.593632i	$0.202306\pi$
$912$		0			0
$913$	−88.3301			−2.92330
$914$		0			0
$915$	19.2646	−	10.4808i	0.636869	−	0.346483i
$916$		0			0
$917$	−4.97791	−	4.97791i	−0.164385	−	0.164385i
$918$		0			0
$919$	−31.5660			−1.04126			−0.520632	−	0.853781i	$-0.674304\pi$
$919$	−31.5660			−1.04126			−0.520632	+	0.853781i	$0.674304\pi$
$920$		0			0
$921$	15.3176	+	4.52333i	0.504733	+	0.149049i
$922$		0			0
$923$	−9.74813	+	9.74813i	−0.320864	+	0.320864i
$924$		0			0
$925$	12.3384	+	12.3384i	0.405685	+	0.405685i
$926$		0			0
$927$	28.0689	−	43.3813i	0.921904	−	1.42483i
$928$		0			0
$929$		−	8.25723i		−	0.270911i	−0.990783	−	0.135456i	$-0.956750\pi$
$929$		−	8.25723i		−	0.270911i	0.990783	−	0.135456i	$-0.0432498\pi$
$930$		0			0
$931$	3.76716	−	3.76716i	0.123464	−	0.123464i
$932$		0			0
$933$	27.1241	−	14.7566i	0.888002	−	0.483110i
$934$		0			0
$935$		−	19.5532i		−	0.639457i
$936$		0			0
$937$			11.4367i			0.373620i	0.982396	+	0.186810i	$0.0598149\pi$
$937$			11.4367i			0.373620i	−0.982396	+	0.186810i	$0.940185\pi$
$938$		0			0
$939$	7.41620	−	4.03472i	0.242018	−	0.131668i
$940$		0			0
$941$	38.7594	−	38.7594i	1.26352	−	1.26352i	0.314144	−	0.949375i	$-0.398283\pi$
$941$	38.7594	−	38.7594i	1.26352	−	1.26352i	0.949375	−	0.314144i	$-0.101717\pi$
$942$		0			0
$943$			15.6294i			0.508963i
$944$		0			0
$945$	−5.93211	−	6.91035i	−0.192972	−	0.224794i
$946$		0			0
$947$	−11.9692	−	11.9692i	−0.388948	−	0.388948i	0.485364	−	0.874312i	$-0.338687\pi$
$947$	−11.9692	−	11.9692i	−0.388948	−	0.388948i	−0.874312	+	0.485364i	$0.838687\pi$
$948$		0			0
$949$	16.2534	−	16.2534i	0.527609	−	0.527609i
$950$		0			0
$951$	−11.6792	−	3.44890i	−0.378725	−	0.111838i
$952$		0			0
$953$	−30.7222			−0.995190			−0.497595	−	0.867409i	$-0.665783\pi$
$953$	−30.7222			−0.995190			−0.497595	+	0.867409i	$0.665783\pi$
$954$		0			0
$955$	−10.4950	−	10.4950i	−0.339609	−	0.339609i
$956$		0			0
$957$	−51.6756	+	28.1136i	−1.67043	+	0.908785i
$958$		0			0
$959$	5.14127			0.166020
$960$		0			0
$961$	29.4467			0.949895
$962$		0			0
$963$	7.98611	+	37.2645i	0.257349	+	1.20083i
$964$		0			0
$965$	21.4125	+	21.4125i	0.689294	+	0.689294i
$966$		0			0
$967$	14.1286			0.454346			0.227173	−	0.973854i	$-0.427052\pi$
$967$	14.1286			0.454346			0.227173	+	0.973854i	$0.427052\pi$
$968$		0			0
$969$	5.77036	−	19.5405i	0.185371	−	0.627733i
$970$		0			0
$971$	3.35904	−	3.35904i	0.107797	−	0.107797i	−0.651151	−	0.758948i	$-0.725714\pi$
$971$	3.35904	−	3.35904i	0.107797	−	0.107797i	0.758948	+	0.651151i	$0.225714\pi$
$972$		0			0
$973$	−13.3617	−	13.3617i	−0.428356	−	0.428356i
$974$		0			0
$975$	−7.20007	−	2.12619i	−0.230587	−	0.0680927i
$976$		0			0
$977$		−	15.4506i		−	0.494310i	−0.968976	−	0.247155i	$-0.920504\pi$
$977$		−	15.4506i		−	0.494310i	0.968976	−	0.247155i	$-0.0794957\pi$
$978$		0			0
$979$	32.7040	−	32.7040i	1.04522	−	1.04522i
$980$		0			0
$981$	−41.1173	+	8.81182i	−1.31278	+	0.281340i
$982$		0			0
$983$			24.7893i			0.790655i	0.918540	+	0.395327i	$0.129369\pi$
$983$			24.7893i			0.790655i	−0.918540	+	0.395327i	$0.870631\pi$
$984$		0			0
$985$		−	40.7627i		−	1.29881i
$986$		0			0
$987$	6.83772	+	12.5684i	0.217647	+	0.400056i
$988$		0			0
$989$	−4.72787	+	4.72787i	−0.150338	+	0.150338i
$990$		0			0
$991$			6.86472i			0.218065i	0.994038	+	0.109033i	$0.0347753\pi$
$991$			6.86472i			0.218065i	−0.994038	+	0.109033i	$0.965225\pi$
$992$		0			0
$993$	−6.92033	+	23.4348i	−0.219610	+	0.743680i
$994$		0			0
$995$	10.1743	+	10.1743i	0.322545	+	0.322545i
$996$		0			0
$997$	−42.8927	+	42.8927i	−1.35842	+	1.35842i	−0.482563	+	0.875861i	$0.660294\pi$
$997$	−42.8927	+	42.8927i	−1.35842	+	1.35842i	−0.875861	+	0.482563i	$0.839706\pi$
$998$		0			0
$999$	−35.6821	+	30.6309i	−1.12893	+	0.969119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.c.239.8		40
3.2	odd	2	inner	1344.2.s.c.239.16		40
4.3	odd	2		336.2.s.c.323.1	yes	40
12.11	even	2		336.2.s.c.323.20	yes	40
16.5	even	4		336.2.s.c.155.20	yes	40
16.11	odd	4	inner	1344.2.s.c.911.16		40
48.5	odd	4		336.2.s.c.155.1	✓	40
48.11	even	4	inner	1344.2.s.c.911.8		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.1	✓	40	48.5	odd	4
336.2.s.c.155.20	yes	40	16.5	even	4
336.2.s.c.323.1	yes	40	4.3	odd	2
336.2.s.c.323.20	yes	40	12.11	even	2
1344.2.s.c.239.8		40	1.1	even	1	trivial
1344.2.s.c.239.16		40	3.2	odd	2	inner
1344.2.s.c.911.8		40	48.11	even	4	inner
1344.2.s.c.911.16		40	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)

\(f(q)\)	\(=\)	\(q+(-0.827739 - 1.52146i) q^{3} +(-1.23935 - 1.23935i) q^{5} +1.00000 q^{7} +(-1.62970 + 2.51875i) q^{9} +O(q^{10})\)	\(q+(-0.827739 - 1.52146i) q^{3} +(-1.23935 - 1.23935i) q^{5} +1.00000 q^{7} +(-1.62970 + 2.51875i) q^{9} +(3.57267 - 3.57267i) q^{11} +(1.58965 + 1.58965i) q^{13} +(-0.859765 + 2.91147i) q^{15} +2.20802i q^{17} +(3.76716 - 3.76716i) q^{19} +(-0.827739 - 1.52146i) q^{21} -3.97123i q^{23} -1.92804i q^{25} +(5.18114 + 0.394660i) q^{27} +(4.75337 - 4.75337i) q^{29} -1.24630i q^{31} +(-8.39291 - 2.47844i) q^{33} +(-1.23935 - 1.23935i) q^{35} +(-6.39946 + 6.39946i) q^{37} +(1.10278 - 3.73440i) q^{39} -3.93566 q^{41} +(-1.19053 - 1.19053i) q^{43} +(5.14136 - 1.10184i) q^{45} -8.26073 q^{47} +1.00000 q^{49} +(3.35941 - 1.82766i) q^{51} +(2.18249 + 2.18249i) q^{53} -8.85554 q^{55} +(-8.84982 - 2.61337i) q^{57} +(-5.45245 + 5.45245i) q^{59} +(-5.10830 - 5.10830i) q^{61} +(-1.62970 + 2.51875i) q^{63} -3.94024i q^{65} +(7.23888 - 7.23888i) q^{67} +(-6.04208 + 3.28714i) q^{69} +6.13227i q^{71} -10.2246i q^{73} +(-2.93344 + 1.59591i) q^{75} +(3.57267 - 3.57267i) q^{77} +6.53910i q^{79} +(-3.68817 - 8.20959i) q^{81} +(-12.3619 - 12.3619i) q^{83} +(2.73650 - 2.73650i) q^{85} +(-11.1666 - 3.29753i) q^{87} +9.15394 q^{89} +(1.58965 + 1.58965i) q^{91} +(-1.89620 + 1.03161i) q^{93} -9.33763 q^{95} +7.67756 q^{97} +(3.17628 + 14.8210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 40 q^{7}+O(q^{10}) \) 40 * q - 4 * q^3 + 40 * q^7	\( 40 q - 4 q^{3} + 40 q^{7} + 24 q^{13} - 16 q^{19} - 4 q^{21} + 32 q^{27} + 24 q^{33} - 8 q^{37} + 64 q^{39} - 24 q^{43} - 28 q^{45} + 40 q^{49} + 32 q^{51} - 16 q^{55} - 48 q^{61} - 40 q^{67} + 4 q^{69} - 40 q^{75} + 56 q^{81} - 48 q^{85} - 32 q^{87} + 24 q^{91} + 56 q^{93} + 16 q^{97} - 24 q^{99}+O(q^{100}) \) 40 * q - 4 * q^3 + 40 * q^7 + 24 * q^13 - 16 * q^19 - 4 * q^21 + 32 * q^27 + 24 * q^33 - 8 * q^37 + 64 * q^39 - 24 * q^43 - 28 * q^45 + 40 * q^49 + 32 * q^51 - 16 * q^55 - 48 * q^61 - 40 * q^67 + 4 * q^69 - 40 * q^75 + 56 * q^81 - 48 * q^85 - 32 * q^87 + 24 * q^91 + 56 * q^93 + 16 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more