LMFDB - Embedded newform 1848.2.bg.f.793.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1848,2,Mod(529,1848)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1848, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1848.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1848.bg (of order $3$, degree $2$, 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:	$14.7563542935$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.33405603984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 9x^{6} + 56x^{4} - 8x^{3} + 112x^{2} + 48x + 144 $ x^8 - x^7 + 9x^6 + 56x^4 - 8x^3 + 112x^2 + 48*x + 144
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.3
Root			$-0.578647 + 1.00225i$ of defining polynomial
Character	$\chi$	$=$	1848.793
Dual form			1848.2.bg.f.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(0.751690 - 1.30196i) q^{5} +(-2.44857 - 1.00225i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(0.751690 - 1.30196i) q^{5} +(-2.44857 - 1.00225i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.15729 q^{13} -1.50338 q^{15} +(0.761920 + 1.31968i) q^{17} +(-2.84395 + 4.92586i) q^{19} +(0.356316 + 2.62165i) q^{21} +(-2.70026 + 4.67699i) q^{23} +(1.36993 + 2.37278i) q^{25} +1.00000 q^{27} -0.972782 q^{29} +(1.57865 + 2.73430i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(-3.14545 + 2.43458i) q^{35} +(3.40898 - 5.90453i) q^{37} +(1.57865 + 2.73430i) q^{39} +10.1326 q^{41} -4.60302 q^{43} +(0.751690 + 1.30196i) q^{45} +(3.58203 - 6.20425i) q^{47} +(4.99101 + 4.90814i) q^{49} +(0.761920 - 1.31968i) q^{51} +(2.40560 + 4.16663i) q^{53} -1.50338 q^{55} +5.68789 q^{57} +(3.35418 + 5.80960i) q^{59} +(-5.64883 + 9.78407i) q^{61} +(2.09226 - 1.61940i) q^{63} +(-2.37330 + 4.11068i) q^{65} +(1.58541 + 2.74600i) q^{67} +5.40052 q^{69} -14.9039 q^{71} +(-3.74270 - 6.48254i) q^{73} +(1.36993 - 2.37278i) q^{75} +(0.356316 + 2.62165i) q^{77} +(2.07527 - 3.59447i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.21279 q^{83} +2.29091 q^{85} +(0.486391 + 0.842453i) q^{87} +(-2.34609 + 4.06354i) q^{89} +(7.73086 + 3.16438i) q^{91} +(1.57865 - 2.73430i) q^{93} +(4.27553 + 7.40543i) q^{95} +16.2662 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^3 + q^7 - 4 * q^9	$ 8 q - 4 q^{3} + q^{7} - 4 q^{9} - 4 q^{11} - 14 q^{13} - q^{17} + 2 q^{19} + q^{21} + 5 q^{23} - 4 q^{25} + 8 q^{27} - 34 q^{29} + 7 q^{31} - 4 q^{33} + 10 q^{35} + 10 q^{37} + 7 q^{39} + 24 q^{41} - 16 q^{43} + 11 q^{47} + 5 q^{49} - q^{51} + 14 q^{53} - 4 q^{57} + q^{59} + 2 q^{61} - 2 q^{63} + 8 q^{65} - 17 q^{67} - 10 q^{69} - 54 q^{71} + 11 q^{73} - 4 q^{75} + q^{77} + 23 q^{79} - 4 q^{81} + 16 q^{83} - 52 q^{85} + 17 q^{87} - 18 q^{89} - 3 q^{91} + 7 q^{93} + 14 q^{95} + 14 q^{97} + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + q^7 - 4 * q^9 - 4 * q^11 - 14 * q^13 - q^17 + 2 * q^19 + q^21 + 5 * q^23 - 4 * q^25 + 8 * q^27 - 34 * q^29 + 7 * q^31 - 4 * q^33 + 10 * q^35 + 10 * q^37 + 7 * q^39 + 24 * q^41 - 16 * q^43 + 11 * q^47 + 5 * q^49 - q^51 + 14 * q^53 - 4 * q^57 + q^59 + 2 * q^61 - 2 * q^63 + 8 * q^65 - 17 * q^67 - 10 * q^69 - 54 * q^71 + 11 * q^73 - 4 * q^75 + q^77 + 23 * q^79 - 4 * q^81 + 16 * q^83 - 52 * q^85 + 17 * q^87 - 18 * q^89 - 3 * q^91 + 7 * q^93 + 14 * q^95 + 14 * q^97 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1848\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$673$	$925$	$1585$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	0.751690	−	1.30196i	0.336166	−	0.582256i	−0.647542	−	0.762030i	$-0.724203\pi$
$5$	0.751690	−	1.30196i	0.336166	−	0.582256i	0.983708	+	0.179773i	$0.0575364\pi$
$6$		0			0
$7$	−2.44857	−	1.00225i	−0.925473	−	0.378813i
$7$	−2.44857	−	1.00225i	−0.925473	−	0.378813i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$	−3.15729			−0.875676			−0.437838	−	0.899054i	$-0.644256\pi$
$13$	−3.15729			−0.875676			−0.437838	+	0.899054i	$0.644256\pi$
$14$		0			0
$15$	−1.50338			−0.388171
$16$		0			0
$17$	0.761920	+	1.31968i	0.184793	+	0.320070i	0.943507	−	0.331354i	$-0.107505\pi$
$17$	0.761920	+	1.31968i	0.184793	+	0.320070i	−0.758714	+	0.651424i	$0.774172\pi$
$18$		0			0
$19$	−2.84395	+	4.92586i	−0.652446	+	1.13007i	0.330082	+	0.943952i	$0.392924\pi$
$19$	−2.84395	+	4.92586i	−0.652446	+	1.13007i	−0.982528	+	0.186117i	$0.940410\pi$
$20$		0			0
$21$	0.356316	+	2.62165i	0.0777545	+	0.572091i
$22$		0			0
$23$	−2.70026	+	4.67699i	−0.563043	+	0.975220i	0.434185	+	0.900824i	$0.357036\pi$
$23$	−2.70026	+	4.67699i	−0.563043	+	0.975220i	−0.997229	+	0.0743963i	$0.976297\pi$
$24$		0			0
$25$	1.36993	+	2.37278i	0.273985	+	0.474556i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−0.972782			−0.180641			−0.0903205	−	0.995913i	$-0.528789\pi$
$29$	−0.972782			−0.180641			−0.0903205	+	0.995913i	$0.528789\pi$
$30$		0			0
$31$	1.57865	+	2.73430i	0.283533	+	0.491094i	0.972252	−	0.233934i	$-0.0751600\pi$
$31$	1.57865	+	2.73430i	0.283533	+	0.491094i	−0.688719	+	0.725028i	$0.741827\pi$
$32$		0			0
$33$	−0.500000	+	0.866025i	−0.0870388	+	0.150756i
$34$		0			0
$35$	−3.14545	+	2.43458i	−0.531679	+	0.411519i
$36$		0			0
$37$	3.40898	−	5.90453i	0.560433	−	0.970699i	−0.437025	−	0.899449i	$-0.643968\pi$
$37$	3.40898	−	5.90453i	0.560433	−	0.970699i	0.997459	−	0.0712497i	$-0.0226987\pi$
$38$		0			0
$39$	1.57865	+	2.73430i	0.252786	+	0.437838i
$40$		0			0
$41$	10.1326			1.58244			0.791219	−	0.611532i	$-0.209447\pi$
$41$	10.1326			1.58244			0.791219	+	0.611532i	$0.209447\pi$
$42$		0			0
$43$	−4.60302			−0.701954			−0.350977	−	0.936384i	$-0.614150\pi$
$43$	−4.60302			−0.701954			−0.350977	+	0.936384i	$0.614150\pi$
$44$		0			0
$45$	0.751690	+	1.30196i	0.112055	+	0.194085i
$46$		0			0
$47$	3.58203	−	6.20425i	0.522492	−	0.904983i	−0.477165	−	0.878814i	$-0.658336\pi$
$47$	3.58203	−	6.20425i	0.522492	−	0.904983i	0.999658	−	0.0261695i	$-0.00833095\pi$
$48$		0			0
$49$	4.99101	+	4.90814i	0.713001	+	0.701163i
$50$		0			0
$51$	0.761920	−	1.31968i	0.106690	−	0.184793i
$52$		0			0
$53$	2.40560	+	4.16663i	0.330435	+	0.572330i	0.982597	−	0.185749i	$-0.0594712\pi$
$53$	2.40560	+	4.16663i	0.330435	+	0.572330i	−0.652162	+	0.758080i	$0.726138\pi$
$54$		0			0
$55$	−1.50338			−0.202716
$56$		0			0
$57$	5.68789			0.753380
$58$		0			0
$59$	3.35418	+	5.80960i	0.436676	+	0.756346i	0.997431	−	0.0716364i	$-0.0228221\pi$
$59$	3.35418	+	5.80960i	0.436676	+	0.756346i	−0.560754	+	0.827982i	$0.689489\pi$
$60$		0			0
$61$	−5.64883	+	9.78407i	−0.723259	+	1.25272i	0.236428	+	0.971649i	$0.424023\pi$
$61$	−5.64883	+	9.78407i	−0.723259	+	1.25272i	−0.959687	+	0.281072i	$0.909310\pi$
$62$		0			0
$63$	2.09226	−	1.61940i	0.263599	−	0.204026i
$64$		0			0
$65$	−2.37330	+	4.11068i	−0.294372	+	0.509868i
$66$		0			0
$67$	1.58541	+	2.74600i	0.193688	+	0.335478i	0.946470	−	0.322793i	$-0.104622\pi$
$67$	1.58541	+	2.74600i	0.193688	+	0.335478i	−0.752782	+	0.658270i	$0.771288\pi$
$68$		0			0
$69$	5.40052			0.650147
$70$		0			0
$71$	−14.9039			−1.76877			−0.884384	−	0.466760i	$-0.845421\pi$
$71$	−14.9039			−1.76877			−0.884384	+	0.466760i	$0.845421\pi$
$72$		0			0
$73$	−3.74270	−	6.48254i	−0.438050	−	0.758724i	0.559489	−	0.828838i	$-0.310997\pi$
$73$	−3.74270	−	6.48254i	−0.438050	−	0.758724i	−0.997539	+	0.0701132i	$0.977664\pi$
$74$		0			0
$75$	1.36993	−	2.37278i	0.158185	−	0.273985i
$76$		0			0
$77$	0.356316	+	2.62165i	0.0406060	+	0.298765i
$78$		0			0
$79$	2.07527	−	3.59447i	0.233486	−	0.404409i	−0.725346	−	0.688385i	$-0.758320\pi$
$79$	2.07527	−	3.59447i	0.233486	−	0.404409i	0.958832	+	0.283975i	$0.0916534\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−6.21279			−0.681943			−0.340971	−	0.940074i	$-0.610756\pi$
$83$	−6.21279			−0.681943			−0.340971	+	0.940074i	$0.610756\pi$
$84$		0			0
$85$	2.29091			0.248484
$86$		0			0
$87$	0.486391	+	0.842453i	0.0521466	+	0.0903205i
$88$		0			0
$89$	−2.34609	+	4.06354i	−0.248685	+	0.430734i	−0.963161	−	0.268925i	$-0.913332\pi$
$89$	−2.34609	+	4.06354i	−0.248685	+	0.430734i	0.714476	+	0.699659i	$0.246665\pi$
$90$		0			0
$91$	7.73086	+	3.16438i	0.810414	+	0.331717i
$92$		0			0
$93$	1.57865	−	2.73430i	0.163698	−	0.283533i
$94$		0			0
$95$	4.27553	+	7.40543i	0.438660	+	0.759781i
$96$		0			0
$97$	16.2662			1.65158			0.825790	−	0.563978i	$-0.190730\pi$
$97$	16.2662			1.65158			0.825790	+	0.563978i	$0.190730\pi$
$98$		0			0
$99$	1.00000			0.100504
$100$		0			0
$101$	5.17428	+	8.96212i	0.514860	+	0.891764i	0.999851	+	0.0172450i	$0.00548953\pi$
$101$	5.17428	+	8.96212i	0.514860	+	0.891764i	−0.484991	+	0.874519i	$0.661177\pi$
$102$		0			0
$103$	3.12108	−	5.40588i	0.307529	−	0.532657i	−0.670292	−	0.742098i	$-0.733831\pi$
$103$	3.12108	−	5.40588i	0.307529	−	0.532657i	0.977821	+	0.209441i	$0.0671644\pi$
$104$		0			0
$105$	3.68113	+	1.50675i	0.359242	+	0.147044i
$106$		0			0
$107$	−5.69973	+	9.87222i	−0.551014	+	0.954384i	0.447188	+	0.894440i	$0.352425\pi$
$107$	−5.69973	+	9.87222i	−0.551014	+	0.954384i	−0.998202	+	0.0599438i	$0.980908\pi$
$108$		0			0
$109$	−4.39661	−	7.61516i	−0.421119	−	0.729400i	0.574930	−	0.818203i	$-0.305029\pi$
$109$	−4.39661	−	7.61516i	−0.421119	−	0.729400i	−0.996049	+	0.0888029i	$0.971696\pi$
$110$		0			0
$111$	−6.81797			−0.647133
$112$		0			0
$113$	−11.9354			−1.12279			−0.561394	−	0.827549i	$-0.689735\pi$
$113$	−11.9354			−1.12279			−0.561394	+	0.827549i	$0.689735\pi$
$114$		0			0
$115$	4.05952	+	7.03129i	0.378552	+	0.655671i
$116$		0			0
$117$	1.57865	−	2.73430i	0.145946	−	0.252786i
$118$		0			0
$119$	−0.542968	−	3.99497i	−0.0497738	−	0.366218i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	−5.06628	−	8.77505i	−0.456811	−	0.791219i
$124$		0			0
$125$	11.6359			1.04075
$126$		0			0
$127$	0.420983			0.0373562			0.0186781	−	0.999826i	$-0.494054\pi$
$127$	0.420983			0.0373562			0.0186781	+	0.999826i	$0.494054\pi$
$128$		0			0
$129$	2.30151	+	3.98633i	0.202637	+	0.350977i
$130$		0			0
$131$	−2.80613	+	4.86035i	−0.245172	+	0.424651i	−0.962180	−	0.272414i	$-0.912178\pi$
$131$	−2.80613	+	4.86035i	−0.245172	+	0.424651i	0.717008	+	0.697065i	$0.245511\pi$
$132$		0			0
$133$	11.9005	−	9.21099i	1.03191	−	0.798694i
$134$		0			0
$135$	0.751690	−	1.30196i	0.0646951	−	0.112055i
$136$		0			0
$137$	9.21173	+	15.9552i	0.787011	+	1.36314i	0.927790	+	0.373102i	$0.121706\pi$
$137$	9.21173	+	15.9552i	0.787011	+	1.36314i	−0.140779	+	0.990041i	$0.544961\pi$
$138$		0			0
$139$	6.44466			0.546629			0.273315	−	0.961925i	$-0.411880\pi$
$139$	6.44466			0.546629			0.273315	+	0.961925i	$0.411880\pi$
$140$		0			0
$141$	−7.16405			−0.603322
$142$		0			0
$143$	1.57865	+	2.73430i	0.132013	+	0.228653i
$144$		0			0
$145$	−0.731230	+	1.26653i	−0.0607253	+	0.105179i
$146$		0			0
$147$	1.75507	−	6.77641i	0.144756	−	0.558909i
$148$		0			0
$149$	−3.37170	+	5.83995i	−0.276220	+	0.478427i	−0.970442	−	0.241334i	$-0.922415\pi$
$149$	−3.37170	+	5.83995i	−0.276220	+	0.478427i	0.694222	+	0.719761i	$0.255749\pi$
$150$		0			0
$151$	5.08326	+	8.80447i	0.413670	+	0.716498i	0.995288	−	0.0969645i	$-0.0309133\pi$
$151$	5.08326	+	8.80447i	0.413670	+	0.716498i	−0.581618	+	0.813462i	$0.697580\pi$
$152$		0			0
$153$	−1.52384			−0.123195
$154$		0			0
$155$	4.74661			0.381257
$156$		0			0
$157$	−3.77838	−	6.54434i	−0.301547	−	0.522295i	0.674939	−	0.737873i	$-0.264170\pi$
$157$	−3.77838	−	6.54434i	−0.301547	−	0.522295i	−0.976487	+	0.215578i	$0.930836\pi$
$158$		0			0
$159$	2.40560	−	4.16663i	0.190777	−	0.330435i
$160$		0			0
$161$	11.2993	−	8.74562i	0.890508	−	0.689252i
$162$		0			0
$163$	−5.14545	+	8.91219i	−0.403023	+	0.698056i	−0.994089	−	0.108567i	$-0.965374\pi$
$163$	−5.14545	+	8.91219i	−0.403023	+	0.698056i	0.591066	+	0.806623i	$0.298707\pi$
$164$		0			0
$165$	0.751690	+	1.30196i	0.0585190	+	0.101358i
$166$		0			0
$167$	−7.93700			−0.614184			−0.307092	−	0.951680i	$-0.599356\pi$
$167$	−7.93700			−0.614184			−0.307092	+	0.951680i	$0.599356\pi$
$168$		0			0
$169$	−3.03150			−0.233192
$170$		0			0
$171$	−2.84395	−	4.92586i	−0.217482	−	0.376690i
$172$		0			0
$173$	−9.28905	+	16.0891i	−0.706233	+	1.22323i	0.260012	+	0.965605i	$0.416274\pi$
$173$	−9.28905	+	16.0891i	−0.706233	+	1.22323i	−0.966245	+	0.257626i	$0.917060\pi$
$174$		0			0
$175$	−0.976253	−	7.18292i	−0.0737978	−	0.542978i
$176$		0			0
$177$	3.35418	−	5.80960i	0.252115	−	0.436676i
$178$		0			0
$179$	−3.31512	−	5.74195i	−0.247784	−	0.429174i	0.715127	−	0.698995i	$-0.246369\pi$
$179$	−3.31512	−	5.74195i	−0.247784	−	0.429174i	−0.962911	+	0.269821i	$0.913036\pi$
$180$		0			0
$181$	−20.0774			−1.49234			−0.746170	−	0.665756i	$-0.768109\pi$
$181$	−20.0774			−1.49234			−0.746170	+	0.665756i	$0.768109\pi$
$182$		0			0
$183$	11.2977			0.835148
$184$		0			0
$185$	−5.12499	−	8.87675i	−0.376797	−	0.652632i
$186$		0			0
$187$	0.761920	−	1.31968i	0.0557171	−	0.0965048i
$188$		0			0
$189$	−2.44857	−	1.00225i	−0.178107	−	0.0729026i
$190$		0			0
$191$	−12.7151	+	22.0232i	−0.920033	+	1.59354i	−0.120672	+	0.992692i	$0.538505\pi$
$191$	−12.7151	+	22.0232i	−0.920033	+	1.59354i	−0.799361	+	0.600852i	$0.794828\pi$
$192$		0			0
$193$	6.99101	+	12.1088i	0.503224	+	0.871609i	0.999993	+	0.00372656i	$0.00118620\pi$
$193$	6.99101	+	12.1088i	0.503224	+	0.871609i	−0.496769	+	0.867883i	$0.665480\pi$
$194$		0			0
$195$	4.74661			0.339912
$196$		0			0
$197$	−13.5783			−0.967412			−0.483706	−	0.875231i	$-0.660710\pi$
$197$	−13.5783			−0.967412			−0.483706	+	0.875231i	$0.660710\pi$
$198$		0			0
$199$	10.2365	+	17.7301i	0.725644	+	1.25685i	0.958708	+	0.284391i	$0.0917915\pi$
$199$	10.2365	+	17.7301i	0.725644	+	1.25685i	−0.233064	+	0.972461i	$0.574875\pi$
$200$		0			0
$201$	1.58541	−	2.74600i	0.111826	−	0.193688i
$202$		0			0
$203$	2.38193	+	0.974966i	0.167178	+	0.0684292i
$204$		0			0
$205$	7.61653	−	13.1922i	0.531962	−	0.921385i
$206$		0			0
$207$	−2.70026	−	4.67699i	−0.187681	−	0.325073i
$208$		0			0
$209$	5.68789			0.393440
$210$		0			0
$211$	−27.3026			−1.87959			−0.939795	−	0.341739i	$-0.888984\pi$
$211$	−27.3026			−1.87959			−0.939795	+	0.341739i	$0.888984\pi$
$212$		0			0
$213$	7.45195	+	12.9072i	0.510599	+	0.884384i
$214$		0			0
$215$	−3.46004	+	5.99297i	−0.235973	+	0.408717i
$216$		0			0
$217$	−1.12499	−	8.27731i	−0.0763696	−	0.561901i
$218$		0			0
$219$	−3.74270	+	6.48254i	−0.252908	+	0.438050i
$220$		0			0
$221$	−2.40560	−	4.16663i	−0.161818	−	0.280278i
$222$		0			0
$223$	14.3318			0.959730			0.479865	−	0.877342i	$-0.340686\pi$
$223$	14.3318			0.959730			0.479865	+	0.877342i	$0.340686\pi$
$224$		0			0
$225$	−2.73985			−0.182657
$226$		0			0
$227$	−4.42098	−	7.65737i	−0.293431	−	0.508237i	0.681188	−	0.732109i	$-0.261464\pi$
$227$	−4.42098	−	7.65737i	−0.293431	−	0.508237i	−0.974619	+	0.223871i	$0.928130\pi$
$228$		0			0
$229$	10.4707	−	18.1358i	0.691924	−	1.19845i	−0.279283	−	0.960209i	$-0.590097\pi$
$229$	10.4707	−	18.1358i	0.691924	−	1.19845i	0.971207	−	0.238239i	$-0.0765700\pi$
$230$		0			0
$231$	2.09226	−	1.61940i	0.137660	−	0.106549i
$232$		0			0
$233$	−0.750081	+	1.29918i	−0.0491394	+	0.0851120i	−0.889549	−	0.456840i	$-0.848981\pi$
$233$	−0.750081	+	1.29918i	−0.0491394	+	0.0851120i	0.840409	+	0.541952i	$0.182315\pi$
$234$		0			0
$235$	−5.38514	−	9.32734i	−0.351288	−	0.608449i
$236$		0			0
$237$	−4.15053			−0.269606
$238$		0			0
$239$	−15.7571			−1.01924			−0.509621	−	0.860399i	$-0.670214\pi$
$239$	−15.7571			−1.01924			−0.509621	+	0.860399i	$0.670214\pi$
$240$		0			0
$241$	10.8519	+	18.7961i	0.699035	+	1.21076i	0.968801	+	0.247838i	$0.0797202\pi$
$241$	10.8519	+	18.7961i	0.699035	+	1.21076i	−0.269766	+	0.962926i	$0.586946\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	10.1419	−	2.80872i	0.647943	−	0.179443i
$246$		0			0
$247$	8.97917	−	15.5524i	0.571331	−	0.989574i
$248$		0			0
$249$	3.10640	+	5.38044i	0.196860	+	0.340971i
$250$		0			0
$251$	−11.4786			−0.724525			−0.362263	−	0.932076i	$-0.617996\pi$
$251$	−11.4786			−0.724525			−0.362263	+	0.932076i	$0.617996\pi$
$252$		0			0
$253$	5.40052			0.339528
$254$		0			0
$255$	−1.14545	−	1.98398i	−0.0717311	−	0.124242i
$256$		0			0
$257$	−4.73309	+	8.19796i	−0.295242	+	0.511374i	−0.975041	−	0.222024i	$-0.928734\pi$
$257$	−4.73309	+	8.19796i	−0.295242	+	0.511374i	0.679799	+	0.733398i	$0.262067\pi$
$258$		0			0
$259$	−14.2649	+	11.0410i	−0.886380	+	0.686056i
$260$		0			0
$261$	0.486391	−	0.842453i	0.0301068	−	0.0521466i
$262$		0			0
$263$	−4.10640	−	7.11249i	−0.253211	−	0.438575i	0.711197	−	0.702993i	$-0.248153\pi$
$263$	−4.10640	−	7.11249i	−0.253211	−	0.438575i	−0.964408	+	0.264418i	$0.914820\pi$
$264$		0			0
$265$	7.23307			0.444324
$266$		0			0
$267$	4.69217			0.287156
$268$		0			0
$269$	9.62409	+	16.6694i	0.586791	+	1.01635i	0.994650	+	0.103307i	$0.0329424\pi$
$269$	9.62409	+	16.6694i	0.586791	+	1.01635i	−0.407858	+	0.913045i	$0.633724\pi$
$270$		0			0
$271$	7.75523	−	13.4325i	0.471097	−	0.815963i	−0.528357	−	0.849022i	$-0.677192\pi$
$271$	7.75523	−	13.4325i	0.471097	−	0.815963i	0.999453	+	0.0330591i	$0.0105250\pi$
$272$		0			0
$273$	−1.12499	−	8.27731i	−0.0680878	−	0.500966i
$274$		0			0
$275$	1.36993	−	2.37278i	0.0826096	−	0.143084i
$276$		0			0
$277$	−3.01147	−	5.21602i	−0.180942	−	0.313400i	0.761260	−	0.648447i	$-0.224581\pi$
$277$	−3.01147	−	5.21602i	−0.180942	−	0.313400i	−0.942201	+	0.335047i	$0.891248\pi$
$278$		0			0
$279$	−3.15729			−0.189022
$280$		0			0
$281$	−5.82331			−0.347390			−0.173695	−	0.984800i	$-0.555571\pi$
$281$	−5.82331			−0.347390			−0.173695	+	0.984800i	$0.555571\pi$
$282$		0			0
$283$	−2.82188	−	4.88763i	−0.167743	−	0.290540i	0.769883	−	0.638185i	$-0.220315\pi$
$283$	−2.82188	−	4.88763i	−0.167743	−	0.290540i	−0.937626	+	0.347646i	$0.886981\pi$
$284$		0			0
$285$	4.27553	−	7.40543i	0.253260	−	0.438660i
$286$		0			0
$287$	−24.8103	−	10.1553i	−1.46450	−	0.599449i
$288$		0			0
$289$	7.33896	−	12.7114i	0.431703	−	0.747732i
$290$		0			0
$291$	−8.13308	−	14.0869i	−0.476770	−	0.825790i
$292$		0			0
$293$	−1.22437			−0.0715284			−0.0357642	−	0.999360i	$-0.511387\pi$
$293$	−1.22437			−0.0715284			−0.0357642	+	0.999360i	$0.511387\pi$
$294$		0			0
$295$	10.0852			0.587183
$296$		0			0
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$		0			0
$299$	8.52552	−	14.7666i	0.493043	−	0.853976i
$300$		0			0
$301$	11.2708	+	4.61335i	0.649639	+	0.265909i
$302$		0			0
$303$	5.17428	−	8.96212i	0.297255	−	0.514860i
$304$		0			0
$305$	8.49234	+	14.7092i	0.486270	+	0.842244i
$306$		0			0
$307$	−4.65051			−0.265419			−0.132709	−	0.991155i	$-0.542368\pi$
$307$	−4.65051			−0.265419			−0.132709	+	0.991155i	$0.542368\pi$
$308$		0			0
$309$	−6.24217			−0.355104
$310$		0			0
$311$	−0.662003	−	1.14662i	−0.0375388	−	0.0650190i	0.846646	−	0.532157i	$-0.178618\pi$
$311$	−0.662003	−	1.14662i	−0.0375388	−	0.0650190i	−0.884184	+	0.467138i	$0.845285\pi$
$312$		0			0
$313$	2.51860	−	4.36234i	0.142360	−	0.246574i	−0.786025	−	0.618194i	$-0.787864\pi$
$313$	2.51860	−	4.36234i	0.142360	−	0.246574i	0.928385	+	0.371621i	$0.121198\pi$
$314$		0			0
$315$	−0.535678	−	3.94133i	−0.0301820	−	0.222069i
$316$		0			0
$317$	−3.80934	+	6.59798i	−0.213954	+	0.370579i	−0.952949	−	0.303132i	$-0.901968\pi$
$317$	−3.80934	+	6.59798i	−0.213954	+	0.370579i	0.738994	+	0.673712i	$0.235301\pi$
$318$		0			0
$319$	0.486391	+	0.842453i	0.0272327	+	0.0471683i
$320$		0			0
$321$	11.3995			0.636256
$322$		0			0
$323$	−8.66743			−0.482269
$324$		0			0
$325$	−4.32526	−	7.49156i	−0.239922	−	0.415557i
$326$		0			0
$327$	−4.39661	+	7.61516i	−0.243133	+	0.421119i
$328$		0			0
$329$	−14.9890	+	11.6015i	−0.826372	+	0.639611i
$330$		0			0
$331$	10.8090	−	18.7217i	0.594115	−	1.02904i	−0.399556	−	0.916709i	$-0.630836\pi$
$331$	10.8090	−	18.7217i	0.594115	−	1.02904i	0.993671	−	0.112329i	$-0.0358309\pi$
$332$		0			0
$333$	3.40898	+	5.90453i	0.186811	+	0.323566i
$334$		0			0
$335$	4.76693			0.260445
$336$		0			0
$337$	−25.9190			−1.41190			−0.705949	−	0.708262i	$-0.749479\pi$
$337$	−25.9190			−1.41190			−0.705949	+	0.708262i	$0.749479\pi$
$338$		0			0
$339$	5.96770	+	10.3364i	0.324121	+	0.561394i
$340$		0			0
$341$	1.57865	−	2.73430i	0.0854885	−	0.148070i
$342$		0			0
$343$	−7.30168	−	17.0201i	−0.394254	−	0.919002i
$344$		0			0
$345$	4.05952	−	7.03129i	0.218557	−	0.378552i
$346$		0			0
$347$	3.39190	+	5.87495i	0.182087	+	0.315384i	0.942591	−	0.333949i	$-0.108381\pi$
$347$	3.39190	+	5.87495i	0.182087	+	0.315384i	−0.760504	+	0.649333i	$0.775048\pi$
$348$		0			0
$349$	−8.87916			−0.475291			−0.237645	−	0.971352i	$-0.576376\pi$
$349$	−8.87916			−0.475291			−0.237645	+	0.971352i	$0.576376\pi$
$350$		0			0
$351$	−3.15729			−0.168524
$352$		0			0
$353$	−8.10025	−	14.0301i	−0.431133	−	0.746744i	0.565838	−	0.824516i	$-0.308553\pi$
$353$	−8.10025	−	14.0301i	−0.431133	−	0.746744i	−0.996971	+	0.0777721i	$0.975219\pi$
$354$		0			0
$355$	−11.2031	+	19.4044i	−0.594599	+	1.02988i
$356$		0			0
$357$	−3.18826	+	2.46771i	−0.168741	+	0.130605i
$358$		0			0
$359$	16.9387	−	29.3387i	0.893989	−	1.54843i	0.0589387	−	0.998262i	$-0.481228\pi$
$359$	16.9387	−	29.3387i	0.893989	−	1.54843i	0.835051	−	0.550173i	$-0.185438\pi$
$360$		0			0
$361$	−6.67605	−	11.5633i	−0.351371	−	0.608593i
$362$		0			0
$363$	1.00000			0.0524864
$364$		0			0
$365$	−11.2534			−0.589029
$366$		0			0
$367$	7.27082	+	12.5934i	0.379534	+	0.657372i	0.990994	−	0.133903i	$-0.0427511\pi$
$367$	7.27082	+	12.5934i	0.379534	+	0.657372i	−0.611461	+	0.791275i	$0.709418\pi$
$368$		0			0
$369$	−5.06628	+	8.77505i	−0.263740	+	0.456811i
$370$		0			0
$371$	−1.71431	−	12.6133i	−0.0890026	−	0.654849i
$372$		0			0
$373$	18.3865	−	31.8463i	0.952014	−	1.64894i	0.210957	−	0.977495i	$-0.432342\pi$
$373$	18.3865	−	31.8463i	0.952014	−	1.64894i	0.741057	−	0.671442i	$-0.234325\pi$
$374$		0			0
$375$	−5.81797	−	10.0770i	−0.300438	−	0.520375i
$376$		0			0
$377$	3.07136			0.158183
$378$		0			0
$379$	−19.6028			−1.00693			−0.503465	−	0.864016i	$-0.667942\pi$
$379$	−19.6028			−1.00693			−0.503465	+	0.864016i	$0.667942\pi$
$380$		0			0
$381$	−0.210491	−	0.364582i	−0.0107838	−	0.0186781i
$382$		0			0
$383$	−3.50471	+	6.07034i	−0.179082	+	0.310180i	−0.941566	−	0.336827i	$-0.890646\pi$
$383$	−3.50471	+	6.07034i	−0.179082	+	0.310180i	0.762484	+	0.647007i	$0.223980\pi$
$384$		0			0
$385$	3.68113	+	1.50675i	0.187608	+	0.0767913i
$386$		0			0
$387$	2.30151	−	3.98633i	0.116992	−	0.202637i
$388$		0			0
$389$	−18.2320	−	31.5788i	−0.924399	−	1.60111i	−0.792524	−	0.609840i	$-0.791234\pi$
$389$	−18.2320	−	31.5788i	−0.924399	−	1.60111i	−0.131875	−	0.991266i	$-0.542100\pi$
$390$		0			0
$391$	−8.22953			−0.416185
$392$		0			0
$393$	5.61225			0.283101
$394$		0			0
$395$	−3.11991	−	5.40385i	−0.156980	−	0.271897i
$396$		0			0
$397$	15.2237	−	26.3683i	0.764057	−	1.32339i	−0.176687	−	0.984267i	$-0.556538\pi$
$397$	15.2237	−	26.3683i	0.764057	−	1.32339i	0.940744	−	0.339119i	$-0.110129\pi$
$398$		0			0
$399$	−13.9272	−	5.70066i	−0.697233	−	0.285390i
$400$		0			0
$401$	−12.5858	+	21.7993i	−0.628507	+	1.08861i	0.359345	+	0.933205i	$0.383000\pi$
$401$	−12.5858	+	21.7993i	−0.628507	+	1.08861i	−0.987852	+	0.155400i	$0.950333\pi$
$402$		0			0
$403$	−4.98425	−	8.63297i	−0.248283	−	0.430039i
$404$		0			0
$405$	−1.50338			−0.0747035
$406$		0			0
$407$	−6.81797			−0.337954
$408$		0			0
$409$	8.36939	+	14.4962i	0.413840	+	0.716792i	0.995306	−	0.0967790i	$-0.0308540\pi$
$409$	8.36939	+	14.4962i	0.413840	+	0.716792i	−0.581466	+	0.813571i	$0.697521\pi$
$410$		0			0
$411$	9.21173	−	15.9552i	0.454381	−	0.787011i
$412$		0			0
$413$	−2.39029	−	17.5869i	−0.117619	−	0.865397i
$414$		0			0
$415$	−4.67009	+	8.08884i	−0.229246	+	0.397065i
$416$		0			0
$417$	−3.22233	−	5.58124i	−0.157798	−	0.273315i
$418$		0			0
$419$	22.3836			1.09351			0.546755	−	0.837292i	$-0.315863\pi$
$419$	22.3836			1.09351			0.546755	+	0.837292i	$0.315863\pi$
$420$		0			0
$421$	−8.26691			−0.402904			−0.201452	−	0.979498i	$-0.564566\pi$
$421$	−8.26691			−0.402904			−0.201452	+	0.979498i	$0.564566\pi$
$422$		0			0
$423$	3.58203	+	6.20425i	0.174164	+	0.301661i
$424$		0			0
$425$	−2.08755	+	3.61574i	−0.101261	+	0.175389i
$426$		0			0
$427$	23.6376	−	18.2955i	1.14390	−	0.885380i
$428$		0			0
$429$	1.57865	−	2.73430i	0.0762178	−	0.132013i
$430$		0			0
$431$	−2.62161	−	4.54077i	−0.126279	−	0.218721i	0.795953	−	0.605358i	$-0.206970\pi$
$431$	−2.62161	−	4.54077i	−0.126279	−	0.218721i	−0.922232	+	0.386637i	$0.873637\pi$
$432$		0			0
$433$	−19.2005			−0.922717			−0.461359	−	0.887214i	$-0.652638\pi$
$433$	−19.2005			−0.922717			−0.461359	+	0.887214i	$0.652638\pi$
$434$		0			0
$435$	1.46246			0.0701196
$436$		0			0
$437$	−15.3588	−	26.6022i	−0.734711	−	1.27256i
$438$		0			0
$439$	−7.56049	+	13.0952i	−0.360842	+	0.624997i	−0.988100	−	0.153815i	$-0.950844\pi$
$439$	−7.56049	+	13.0952i	−0.360842	+	0.624997i	0.627257	+	0.778812i	$0.284177\pi$
$440$		0			0
$441$	−6.74608	+	1.86827i	−0.321242	+	0.0889653i
$442$		0			0
$443$	13.6518	−	23.6457i	0.648619	−	1.12344i	−0.334834	−	0.942277i	$-0.608680\pi$
$443$	13.6518	−	23.6457i	0.648619	−	1.12344i	0.983453	−	0.181163i	$-0.0579863\pi$
$444$		0			0
$445$	3.52706	+	6.10904i	0.167199	+	0.289596i
$446$		0			0
$447$	6.74339			0.318951
$448$		0			0
$449$	−3.60890			−0.170314			−0.0851572	−	0.996368i	$-0.527139\pi$
$449$	−3.60890			−0.170314			−0.0851572	+	0.996368i	$0.527139\pi$
$450$		0			0
$451$	−5.06628	−	8.77505i	−0.238562	−	0.413201i
$452$		0			0
$453$	5.08326	−	8.80447i	0.238833	−	0.413670i
$454$		0			0
$455$	9.93112	−	7.68667i	0.465578	−	0.360357i
$456$		0			0
$457$	−8.19090	+	14.1871i	−0.383154	+	0.663642i	−0.991511	−	0.130021i	$-0.958496\pi$
$457$	−8.19090	+	14.1871i	−0.383154	+	0.663642i	0.608357	+	0.793663i	$0.291829\pi$
$458$		0			0
$459$	0.761920	+	1.31968i	0.0355634	+	0.0615975i
$460$		0			0
$461$	−20.5356			−0.956436			−0.478218	−	0.878241i	$-0.658717\pi$
$461$	−20.5356			−0.956436			−0.478218	+	0.878241i	$0.658717\pi$
$462$		0			0
$463$	19.3713			0.900261			0.450131	−	0.892963i	$-0.351377\pi$
$463$	19.3713			0.900261			0.450131	+	0.892963i	$0.351377\pi$
$464$		0			0
$465$	−2.37330	−	4.11068i	−0.110059	−	0.190628i
$466$		0			0
$467$	−4.98087	+	8.62712i	−0.230487	+	0.399216i	−0.957952	−	0.286930i	$-0.907365\pi$
$467$	−4.98087	+	8.62712i	−0.230487	+	0.399216i	0.727464	+	0.686145i	$0.240699\pi$
$468$		0			0
$469$	−1.12981	−	8.31275i	−0.0521698	−	0.383847i
$470$		0			0
$471$	−3.77838	+	6.54434i	−0.174098	+	0.301547i
$472$		0			0
$473$	2.30151	+	3.98633i	0.105823	+	0.183292i
$474$		0			0
$475$	−15.5840			−0.715042
$476$		0			0
$477$	−4.81121			−0.220290
$478$		0			0
$479$	16.2174	+	28.0894i	0.740993	+	1.28344i	0.952044	+	0.305963i	$0.0989782\pi$
$479$	16.2174	+	28.0894i	0.740993	+	1.28344i	−0.211050	+	0.977475i	$0.567688\pi$
$480$		0			0
$481$	−10.7632	+	18.6423i	−0.490758	+	0.850017i
$482$		0			0
$483$	−13.2236	−	5.41265i	−0.601693	−	0.246284i
$484$		0			0
$485$	12.2271	−	21.1780i	0.555204	−	0.961642i
$486$		0			0
$487$	−17.5496	−	30.3968i	−0.795249	−	1.37741i	−0.922681	−	0.385565i	$-0.874007\pi$
$487$	−17.5496	−	30.3968i	−0.795249	−	1.37741i	0.127431	−	0.991847i	$-0.459327\pi$
$488$		0			0
$489$	10.2909			0.465371
$490$		0			0
$491$	−5.79056			−0.261324			−0.130662	−	0.991427i	$-0.541710\pi$
$491$	−5.79056			−0.261324			−0.130662	+	0.991427i	$0.541710\pi$
$492$		0			0
$493$	−0.741181	−	1.28376i	−0.0333811	−	0.0578178i
$494$		0			0
$495$	0.751690	−	1.30196i	0.0337859	−	0.0585190i
$496$		0			0
$497$	36.4933	+	14.9374i	1.63695	+	0.670032i
$498$		0			0
$499$	−5.22240	+	9.04546i	−0.233787	+	0.404930i	−0.958919	−	0.283679i	$-0.908445\pi$
$499$	−5.22240	+	9.04546i	−0.233787	+	0.404930i	0.725133	+	0.688609i	$0.241778\pi$
$500$		0			0
$501$	3.96850	+	6.87364i	0.177300	+	0.307092i
$502$		0			0
$503$	2.54398			0.113430			0.0567152	−	0.998390i	$-0.481937\pi$
$503$	2.54398			0.113430			0.0567152	+	0.998390i	$0.481937\pi$
$504$		0			0
$505$	15.5578			0.692314
$506$		0			0
$507$	1.51575	+	2.62536i	0.0673168	+	0.116596i
$508$		0			0
$509$	−13.3895	+	23.1913i	−0.593478	+	1.02793i	0.400281	+	0.916392i	$0.368912\pi$
$509$	−13.3895	+	23.1913i	−0.593478	+	1.02793i	−0.993760	+	0.111542i	$0.964421\pi$
$510$		0			0
$511$	2.66717	+	19.6241i	0.117989	+	0.868118i
$512$		0			0
$513$	−2.84395	+	4.92586i	−0.125563	+	0.217482i
$514$		0			0
$515$	−4.69217	−	8.12708i	−0.206762	−	0.358122i
$516$		0			0
$517$	−7.16405			−0.315075
$518$		0			0
$519$	18.5781			0.815488
$520$		0			0
$521$	19.8103	+	34.3124i	0.867904	+	1.50325i	0.864134	+	0.503261i	$0.167867\pi$
$521$	19.8103	+	34.3124i	0.867904	+	1.50325i	0.00376995	+	0.999993i	$0.498800\pi$
$522$		0			0
$523$	3.16442	−	5.48094i	0.138371	−	0.239665i	−0.788509	−	0.615023i	$-0.789147\pi$
$523$	3.16442	−	5.48094i	0.138371	−	0.239665i	0.926880	+	0.375358i	$0.122480\pi$
$524$		0			0
$525$	−5.73247	+	4.43692i	−0.250185	+	0.193643i
$526$		0			0
$527$	−2.40560	+	4.16663i	−0.104790	+	0.181501i
$528$		0			0
$529$	−3.08283	−	5.33961i	−0.134036	−	0.232157i
$530$		0			0
$531$	−6.70835			−0.291118
$532$		0			0
$533$	−31.9914			−1.38570
$534$		0			0
$535$	8.56886	+	14.8417i	0.370464	+	0.641662i
$536$		0			0
$537$	−3.31512	+	5.74195i	−0.143058	+	0.247784i
$538$		0			0
$539$	1.75507	−	6.77641i	0.0755962	−	0.291881i
$540$		0			0
$541$	14.5854	−	25.2627i	0.627076	−	1.08613i	−0.361060	−	0.932543i	$-0.617585\pi$
$541$	14.5854	−	25.2627i	0.627076	−	1.08613i	0.988136	−	0.153584i	$-0.0490816\pi$
$542$		0			0
$543$	10.0387	+	17.3875i	0.430801	+	0.746170i
$544$		0			0
$545$	−13.2196			−0.566263
$546$		0			0
$547$	9.57455			0.409378			0.204689	−	0.978827i	$-0.434382\pi$
$547$	9.57455			0.409378			0.204689	+	0.978827i	$0.434382\pi$
$548$		0			0
$549$	−5.64883	−	9.78407i	−0.241086	−	0.417574i
$550$		0			0
$551$	2.76654	−	4.79178i	0.117858	−	0.204137i
$552$		0			0
$553$	−8.68398	+	6.72139i	−0.369280	+	0.285822i
$554$		0			0
$555$	−5.12499	+	8.87675i	−0.217544	+	0.376797i
$556$		0			0
$557$	−3.29499	−	5.70710i	−0.139613	−	0.241818i	0.787737	−	0.616012i	$-0.211253\pi$
$557$	−3.29499	−	5.70710i	−0.139613	−	0.241818i	−0.927350	+	0.374194i	$0.877919\pi$
$558$		0			0
$559$	14.5331			0.614684
$560$		0			0
$561$	−1.52384			−0.0643365
$562$		0			0
$563$	−6.97340	−	12.0783i	−0.293894	−	0.509039i	0.680833	−	0.732438i	$-0.261618\pi$
$563$	−6.97340	−	12.0783i	−0.293894	−	0.509039i	−0.974727	+	0.223400i	$0.928284\pi$
$564$		0			0
$565$	−8.97172	+	15.5395i	−0.377443	+	0.653751i
$566$		0			0
$567$	0.356316	+	2.62165i	0.0149639	+	0.110099i
$568$		0			0
$569$	19.1094	−	33.0985i	0.801109	−	1.38756i	−0.117778	−	0.993040i	$-0.537577\pi$
$569$	19.1094	−	33.0985i	0.801109	−	1.38756i	0.918887	−	0.394521i	$-0.129089\pi$
$570$		0			0
$571$	18.1101	+	31.3676i	0.757885	+	1.31269i	0.943927	+	0.330153i	$0.107100\pi$
$571$	18.1101	+	31.3676i	0.757885	+	1.31269i	−0.186043	+	0.982542i	$0.559566\pi$
$572$		0			0
$573$	25.4302			1.06236
$574$		0			0
$575$	−14.7966			−0.617062
$576$		0			0
$577$	−17.1645	−	29.7298i	−0.714567	−	1.23767i	−0.963126	−	0.269049i	$-0.913291\pi$
$577$	−17.1645	−	29.7298i	−0.714567	−	1.23767i	0.248560	−	0.968617i	$-0.420043\pi$
$578$		0			0
$579$	6.99101	−	12.1088i	0.290536	−	0.503224i
$580$		0			0
$581$	15.2125	+	6.22674i	0.631120	+	0.258329i
$582$		0			0
$583$	2.40560	−	4.16663i	0.0996299	−	0.172564i
$584$		0			0
$585$	−2.37330	−	4.11068i	−0.0981241	−	0.169956i
$586$		0			0
$587$	32.3352			1.33462			0.667308	−	0.744782i	$-0.267447\pi$
$587$	32.3352			1.33462			0.667308	+	0.744782i	$0.267447\pi$
$588$		0			0
$589$	−17.9583			−0.739960
$590$		0			0
$591$	6.78914	+	11.7591i	0.279268	+	0.483706i
$592$		0			0
$593$	−13.5433	+	23.4577i	−0.556157	+	0.963292i	0.441656	+	0.897185i	$0.354391\pi$
$593$	−13.5433	+	23.4577i	−0.556157	+	0.963292i	−0.997813	+	0.0661073i	$0.978942\pi$
$594$		0			0
$595$	−5.60945	−	2.29605i	−0.229965	−	0.0941290i
$596$		0			0
$597$	10.2365	−	17.7301i	0.418951	−	0.725644i
$598$		0			0
$599$	12.5137	+	21.6743i	0.511295	+	0.885589i	0.999914	+	0.0130919i	$0.00416739\pi$
$599$	12.5137	+	21.6743i	0.511295	+	0.885589i	−0.488619	+	0.872497i	$0.662499\pi$
$600$		0			0
$601$	−29.2969			−1.19505			−0.597523	−	0.801852i	$-0.703848\pi$
$601$	−29.2969			−1.19505			−0.597523	+	0.801852i	$0.703848\pi$
$602$		0			0
$603$	−3.17081			−0.129125
$604$		0			0
$605$	0.751690	+	1.30196i	0.0305605	+	0.0529324i
$606$		0			0
$607$	−0.184882	+	0.320225i	−0.00750413	+	0.0129975i	−0.869753	−	0.493487i	$-0.835722\pi$
$607$	−0.184882	+	0.320225i	−0.00750413	+	0.0129975i	0.862249	+	0.506485i	$0.169055\pi$
$608$		0			0
$609$	−0.346618	−	2.55029i	−0.0140457	−	0.103343i
$610$		0			0
$611$	−11.3095	+	19.5886i	−0.457534	+	0.792472i
$612$		0			0
$613$	−5.70835	−	9.88715i	−0.230558	−	0.399338i	0.727414	−	0.686198i	$-0.240722\pi$
$613$	−5.70835	−	9.88715i	−0.230558	−	0.399338i	−0.957972	+	0.286860i	$0.907389\pi$
$614$		0			0
$615$	−15.2331			−0.614257
$616$		0			0
$617$	33.5240			1.34962			0.674812	−	0.737989i	$-0.264225\pi$
$617$	33.5240			1.34962			0.674812	+	0.737989i	$0.264225\pi$
$618$		0			0
$619$	20.0336	+	34.6992i	0.805219	+	1.39468i	0.916143	+	0.400851i	$0.131285\pi$
$619$	20.0336	+	34.6992i	0.805219	+	1.39468i	−0.110925	+	0.993829i	$0.535381\pi$
$620$		0			0
$621$	−2.70026	+	4.67699i	−0.108358	+	0.187681i
$622$		0			0
$623$	9.81722	−	7.59852i	0.393319	−	0.304428i
$624$		0			0
$625$	1.89698	−	3.28567i	0.0758793	−	0.131427i
$626$		0			0
$627$	−2.84395	−	4.92586i	−0.113576	−	0.196720i
$628$		0			0
$629$	10.3895			0.414256
$630$		0			0
$631$	−0.236471			−0.00941377			−0.00470689	−	0.999989i	$-0.501498\pi$
$631$	−0.236471			−0.00941377			−0.00470689	+	0.999989i	$0.501498\pi$
$632$		0			0
$633$	13.6513	+	23.6448i	0.542591	+	0.939795i
$634$		0			0
$635$	0.316449	−	0.548105i	0.0125579	−	0.0217509i
$636$		0			0
$637$	−15.7581	−	15.4964i	−0.624358	−	0.613991i
$638$		0			0
$639$	7.45195	−	12.9072i	0.294795	−	0.510599i
$640$		0			0
$641$	13.3367	+	23.0999i	0.526769	+	0.912391i	0.999513	+	0.0311910i	$0.00993002\pi$
$641$	13.3367	+	23.0999i	0.526769	+	0.912391i	−0.472744	+	0.881200i	$0.656737\pi$
$642$		0			0
$643$	30.7674			1.21335			0.606674	−	0.794950i	$-0.292503\pi$
$643$	30.7674			1.21335			0.606674	+	0.794950i	$0.292503\pi$
$644$		0			0
$645$	6.92008			0.272478
$646$		0			0
$647$	5.03826	+	8.72652i	0.198074	+	0.343075i	0.947904	−	0.318556i	$-0.103198\pi$
$647$	5.03826	+	8.72652i	0.198074	+	0.343075i	−0.749830	+	0.661631i	$0.769865\pi$
$648$		0			0
$649$	3.35418	−	5.80960i	0.131663	−	0.228047i
$650$		0			0
$651$	−6.60587	+	5.11293i	−0.258904	+	0.200392i
$652$		0			0
$653$	2.79181	−	4.83556i	0.109252	−	0.189230i	−0.806215	−	0.591622i	$-0.798488\pi$
$653$	2.79181	−	4.83556i	0.109252	−	0.189230i	0.915467	+	0.402392i	$0.131821\pi$
$654$		0			0
$655$	4.21867	+	7.30696i	0.164837	+	0.285506i
$656$		0			0
$657$	7.48540			0.292033
$658$		0			0
$659$	−6.72814			−0.262091			−0.131046	−	0.991376i	$-0.541833\pi$
$659$	−6.72814			−0.262091			−0.131046	+	0.991376i	$0.541833\pi$
$660$		0			0
$661$	−10.9302	−	18.9317i	−0.425136	−	0.736358i	0.571297	−	0.820743i	$-0.306440\pi$
$661$	−10.9302	−	18.9317i	−0.425136	−	0.736358i	−0.996433	+	0.0843859i	$0.973107\pi$
$662$		0			0
$663$	−2.40560	+	4.16663i	−0.0934259	+	0.161818i
$664$		0			0
$665$	−3.04688	−	22.4179i	−0.118153	−	0.869327i
$666$		0			0
$667$	2.62676	−	4.54969i	0.101709	−	0.176165i
$668$		0			0
$669$	−7.16591	−	12.4117i	−0.277050	−	0.479865i
$670$		0			0
$671$	11.2977			0.436142
$672$		0			0
$673$	−10.8562			−0.418477			−0.209238	−	0.977865i	$-0.567098\pi$
$673$	−10.8562			−0.418477			−0.209238	+	0.977865i	$0.567098\pi$
$674$		0			0
$675$	1.36993	+	2.37278i	0.0527284	+	0.0913284i
$676$		0			0
$677$	−1.70748	+	2.95745i	−0.0656239	+	0.113664i	−0.896971	−	0.442090i	$-0.854237\pi$
$677$	−1.70748	+	2.95745i	−0.0656239	+	0.113664i	0.831347	+	0.555754i	$0.187570\pi$
$678$		0			0
$679$	−39.8289	−	16.3027i	−1.52849	−	0.625640i
$680$		0			0
$681$	−4.42098	+	7.65737i	−0.169412	+	0.293431i
$682$		0			0
$683$	−0.837894	−	1.45127i	−0.0320611	−	0.0555315i	0.849550	−	0.527509i	$-0.176874\pi$
$683$	−0.837894	−	1.45127i	−0.0320611	−	0.0555315i	−0.881611	+	0.471977i	$0.843540\pi$
$684$		0			0
$685$	27.6974			1.05827
$686$		0			0
$687$	−20.9414			−0.798965
$688$		0			0
$689$	−7.59520	−	13.1553i	−0.289354	−	0.501176i
$690$		0			0
$691$	−25.3442	+	43.8974i	−0.964138	+	1.66994i	−0.252224	+	0.967669i	$0.581162\pi$
$691$	−25.3442	+	43.8974i	−0.964138	+	1.66994i	−0.711914	+	0.702267i	$0.752171\pi$
$692$		0			0
$693$	−2.44857	−	1.00225i	−0.0930136	−	0.0380722i
$694$		0			0
$695$	4.84439	−	8.39072i	0.183758	−	0.318278i
$696$		0			0
$697$	7.72019	+	13.3718i	0.292423	+	0.506492i
$698$		0			0
$699$	1.50016			0.0567413
$700$		0			0
$701$	−10.4018			−0.392869			−0.196435	−	0.980517i	$-0.562936\pi$
$701$	−10.4018			−0.392869			−0.196435	+	0.980517i	$0.562936\pi$
$702$		0			0
$703$	19.3899	+	33.5843i	0.731305	+	1.26666i
$704$		0			0
$705$	−5.38514	+	9.32734i	−0.202816	+	0.351288i
$706$		0			0
$707$	−3.68736	−	27.1303i	−0.138677	−	1.02034i
$708$		0			0
$709$	3.37030	−	5.83752i	0.126574	−	0.219233i	−0.795773	−	0.605595i	$-0.792935\pi$
$709$	3.37030	−	5.83752i	0.126574	−	0.219233i	0.922347	+	0.386362i	$0.126269\pi$
$710$		0			0
$711$	2.07527	+	3.59447i	0.0778286	+	0.134803i
$712$		0			0
$713$	−17.0510			−0.638566
$714$		0			0
$715$	4.74661			0.177513
$716$		0			0
$717$	7.87855	+	13.6460i	0.294230	+	0.509621i
$718$		0			0
$719$	5.49963	−	9.52564i	0.205102	−	0.355246i	−0.745064	−	0.666994i	$-0.767581\pi$
$719$	5.49963	−	9.52564i	0.205102	−	0.355246i	0.950165	+	0.311747i	$0.100914\pi$
$720$		0			0
$721$	−13.0602	+	10.1086i	−0.486388	+	0.376463i
$722$		0			0
$723$	10.8519	−	18.7961i	0.403588	−	0.699035i
$724$		0			0
$725$	−1.33264	−	2.30820i	−0.0494929	−	0.0857243i
$726$		0			0
$727$	30.9823			1.14907			0.574536	−	0.818480i	$-0.305183\pi$
$727$	30.9823			1.14907			0.574536	+	0.818480i	$0.305183\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−3.50713	−	6.07453i	−0.129716	−	0.224674i
$732$		0			0
$733$	21.2980	−	36.8893i	0.786661	−	1.36254i	−0.141341	−	0.989961i	$-0.545141\pi$
$733$	21.2980	−	36.8893i	0.786661	−	1.36254i	0.928002	−	0.372576i	$-0.121525\pi$
$734$		0			0
$735$	−7.50338	−	7.37880i	−0.276766	−	0.272171i
$736$		0			0
$737$	1.58541	−	2.74600i	0.0583992	−	0.101150i
$738$		0			0
$739$	−4.86708	−	8.43003i	−0.179038	−	0.310104i	0.762513	−	0.646973i	$-0.223965\pi$
$739$	−4.86708	−	8.43003i	−0.179038	−	0.310104i	−0.941551	+	0.336869i	$0.890632\pi$
$740$		0			0
$741$	−17.9583			−0.659716
$742$		0			0
$743$	−41.0409			−1.50564			−0.752822	−	0.658224i	$-0.771308\pi$
$743$	−41.0409			−1.50564			−0.752822	+	0.658224i	$0.771308\pi$
$744$		0			0
$745$	5.06894	+	8.77966i	0.185711	+	0.321662i
$746$		0			0
$747$	3.10640	−	5.38044i	0.113657	−	0.196860i
$748$		0			0
$749$	23.8506	−	18.4603i	0.871481	−	0.674525i
$750$		0			0
$751$	15.5930	−	27.0078i	0.568995	−	0.985529i	−0.427670	−	0.903935i	$-0.640666\pi$
$751$	15.5930	−	27.0078i	0.568995	−	0.985529i	0.996666	−	0.0815940i	$-0.0260011\pi$
$752$		0			0
$753$	5.73932	+	9.94079i	0.209152	+	0.362263i
$754$		0			0
$755$	15.2841			0.556247
$756$		0			0
$757$	−45.3766			−1.64924			−0.824620	−	0.565687i	$-0.808611\pi$
$757$	−45.3766			−1.64924			−0.824620	+	0.565687i	$0.808611\pi$
$758$		0			0
$759$	−2.70026	−	4.67699i	−0.0980133	−	0.169764i
$760$		0			0
$761$	−17.3342	+	30.0238i	−0.628366	+	1.08836i	0.359514	+	0.933140i	$0.382943\pi$
$761$	−17.3342	+	30.0238i	−0.628366	+	1.08836i	−0.987880	+	0.155222i	$0.950391\pi$
$762$		0			0
$763$	3.13317	+	23.0527i	0.113428	+	0.834565i
$764$		0			0
$765$	−1.14545	+	1.98398i	−0.0414140	+	0.0717311i
$766$		0			0
$767$	−10.5901	−	18.3426i	−0.382387	−	0.662314i
$768$		0			0
$769$	12.6048			0.454539			0.227270	−	0.973832i	$-0.427020\pi$
$769$	12.6048			0.454539			0.227270	+	0.973832i	$0.427020\pi$
$770$		0			0
$771$	9.46618			0.340916
$772$		0			0
$773$	−13.0172	−	22.5465i	−0.468198	−	0.810942i	0.531142	−	0.847283i	$-0.321763\pi$
$773$	−13.0172	−	22.5465i	−0.468198	−	0.810942i	−0.999339	+	0.0363408i	$0.988430\pi$
$774$		0			0
$775$	−4.32526	+	7.49156i	−0.155368	+	0.269105i
$776$		0			0
$777$	16.6943	+	6.83327i	0.598904	+	0.245142i
$778$		0			0
$779$	−28.8164	+	49.9115i	−1.03246	+	1.78827i
$780$		0			0
$781$	7.45195	+	12.9072i	0.266652	+	0.461854i
$782$		0			0
$783$	−0.972782			−0.0347644
$784$		0			0
$785$	−11.3607			−0.405480
$786$		0			0
$787$	15.7372	+	27.2576i	0.560970	+	0.971628i	0.997412	+	0.0718960i	$0.0229050\pi$
$787$	15.7372	+	27.2576i	0.560970	+	0.971628i	−0.436442	+	0.899732i	$0.643762\pi$
$788$		0			0
$789$	−4.10640	+	7.11249i	−0.146192	+	0.253211i
$790$		0			0
$791$	29.2247	+	11.9622i	1.03911	+	0.425327i
$792$		0			0
$793$	17.8350	−	30.8912i	0.633340	−	1.09698i
$794$		0			0
$795$	−3.61653	−	6.26402i	−0.128265	−	0.222162i
$796$		0			0
$797$	15.0477			0.533016			0.266508	−	0.963833i	$-0.414130\pi$
$797$	15.0477			0.533016			0.266508	+	0.963833i	$0.414130\pi$
$798$		0			0
$799$	10.9169			0.386211
$800$		0			0
$801$	−2.34609	−	4.06354i	−0.0828949	−	0.143578i
$802$		0			0
$803$	−3.74270	+	6.48254i	−0.132077	+	0.228764i
$804$		0			0
$805$	−2.89294	−	21.2853i	−0.101963	−	0.750207i
$806$		0			0
$807$	9.62409	−	16.6694i	0.338784	−	0.586791i
$808$		0			0
$809$	10.4056	+	18.0230i	0.365842	+	0.633656i	0.988911	−	0.148511i	$-0.0474479\pi$
$809$	10.4056	+	18.0230i	0.365842	+	0.633656i	−0.623069	+	0.782167i	$0.714115\pi$
$810$		0			0
$811$	−16.1396			−0.566739			−0.283370	−	0.959011i	$-0.591452\pi$
$811$	−16.1396			−0.566739			−0.283370	+	0.959011i	$0.591452\pi$
$812$		0			0
$813$	−15.5105			−0.543976
$814$		0			0
$815$	7.73557	+	13.3984i	0.270965	+	0.469325i
$816$		0			0
$817$	13.0907	−	22.6738i	0.457987	−	0.793256i
$818$		0			0
$819$	−6.60587	+	5.11293i	−0.230828	+	0.178660i
$820$		0			0
$821$	2.28247	−	3.95336i	0.0796588	−	0.137973i	−0.823444	−	0.567398i	$-0.807950\pi$
$821$	2.28247	−	3.95336i	0.0796588	−	0.137973i	0.903103	+	0.429425i	$0.141284\pi$
$822$		0			0
$823$	15.9465	+	27.6201i	0.555860	+	0.962778i	0.997836	+	0.0657510i	$0.0209443\pi$
$823$	15.9465	+	27.6201i	0.555860	+	0.962778i	−0.441976	+	0.897027i	$0.645722\pi$
$824$		0			0
$825$	−2.73985			−0.0953894
$826$		0			0
$827$	40.0480			1.39261			0.696303	−	0.717748i	$-0.254827\pi$
$827$	40.0480			1.39261			0.696303	+	0.717748i	$0.254827\pi$
$828$		0			0
$829$	−21.0180	−	36.4043i	−0.729986	−	1.26437i	−0.956889	−	0.290455i	$-0.906193\pi$
$829$	−21.0180	−	36.4043i	−0.729986	−	1.26437i	0.226903	−	0.973917i	$-0.427140\pi$
$830$		0			0
$831$	−3.01147	+	5.21602i	−0.104467	+	0.180942i
$832$		0			0
$833$	−2.67444	+	10.3262i	−0.0926640	+	0.357780i
$834$		0			0
$835$	−5.96616	+	10.3337i	−0.206468	+	0.357612i
$836$		0			0
$837$	1.57865	+	2.73430i	0.0545660	+	0.0945111i
$838$		0			0
$839$	21.1737			0.730997			0.365498	−	0.930812i	$-0.380899\pi$
$839$	21.1737			0.730997			0.365498	+	0.930812i	$0.380899\pi$
$840$		0			0
$841$	−28.0537			−0.967369
$842$		0			0
$843$	2.91166	+	5.04313i	0.100283	+	0.173695i
$844$		0			0
$845$	−2.27875	+	3.94691i	−0.0783913	+	0.135778i
$846$		0			0
$847$	2.09226	−	1.61940i	0.0718908	−	0.0556433i
$848$		0			0
$849$	−2.82188	+	4.88763i	−0.0968466	+	0.167743i
$850$		0			0
$851$	18.4103	+	31.8876i	0.631097	+	1.09309i
$852$		0			0
$853$	−32.2443			−1.10402			−0.552012	−	0.833836i	$-0.686140\pi$
$853$	−32.2443			−1.10402			−0.552012	+	0.833836i	$0.686140\pi$
$854$		0			0
$855$	−8.55106			−0.292440
$856$		0			0
$857$	−3.40828	−	5.90331i	−0.116424	−	0.201653i	0.801924	−	0.597426i	$-0.203810\pi$
$857$	−3.40828	−	5.90331i	−0.116424	−	0.201653i	−0.918348	+	0.395773i	$0.870477\pi$
$858$		0			0
$859$	7.99144	−	13.8416i	0.272664	−	0.472268i	−0.696879	−	0.717189i	$-0.745428\pi$
$859$	7.99144	−	13.8416i	0.272664	−	0.472268i	0.969543	+	0.244920i	$0.0787618\pi$
$860$		0			0
$861$	3.61039	+	26.5640i	0.123042	+	0.905298i
$862$		0			0
$863$	−23.9856	+	41.5442i	−0.816478	+	1.41418i	0.0917840	+	0.995779i	$0.470743\pi$
$863$	−23.9856	+	41.5442i	−0.816478	+	1.41418i	−0.908262	+	0.418402i	$0.862590\pi$
$864$		0			0
$865$	13.9650	+	24.1880i	0.474823	+	0.822417i
$866$		0			0
$867$	−14.6779			−0.498488
$868$		0			0
$869$	−4.15053			−0.140797
$870$		0			0
$871$	−5.00559	−	8.66993i	−0.169608	−	0.293770i
$872$		0			0
$873$	−8.13308	+	14.0869i	−0.275263	+	0.476770i
$874$		0			0
$875$	−28.4914	−	11.6621i	−0.963186	−	0.394249i
$876$		0			0
$877$	−19.2600	+	33.3593i	−0.650365	+	1.12646i	0.332670	+	0.943043i	$0.392051\pi$
$877$	−19.2600	+	33.3593i	−0.650365	+	1.12646i	−0.983034	+	0.183421i	$0.941283\pi$
$878$		0			0
$879$	0.612184	+	1.06033i	0.0206485	+	0.0357642i
$880$		0			0
$881$	0.665138			0.0224091			0.0112045	−	0.999937i	$-0.496433\pi$
$881$	0.665138			0.0224091			0.0112045	+	0.999937i	$0.496433\pi$
$882$		0			0
$883$	32.7136			1.10090			0.550451	−	0.834868i	$-0.314456\pi$
$883$	32.7136			1.10090			0.550451	+	0.834868i	$0.314456\pi$
$884$		0			0
$885$	−5.04260	−	8.73404i	−0.169505	−	0.293591i
$886$		0			0
$887$	23.5100	−	40.7205i	0.789389	−	1.36726i	−0.136953	−	0.990578i	$-0.543731\pi$
$887$	23.5100	−	40.7205i	0.789389	−	1.36726i	0.926342	−	0.376684i	$-0.122936\pi$
$888$		0			0
$889$	−1.03081	−	0.421928i	−0.0345722	−	0.0141510i
$890$		0			0
$891$	−0.500000	+	0.866025i	−0.0167506	+	0.0290129i
$892$		0			0
$893$	20.3742	+	35.2891i	0.681796	+	1.18090i
$894$		0			0
$895$	−9.96776			−0.333185
$896$		0			0
$897$	−17.0510			−0.569317
$898$		0			0
$899$	−1.53568	−	2.65987i	−0.0512177	−	0.0887117i
$900$		0			0
$901$	−3.66575	+	6.34927i	−0.122124	+	0.211525i
$902$		0			0
$903$	−1.64013	−	12.0675i	−0.0545801	−	0.401581i
$904$		0			0
$905$	−15.0920	+	26.1400i	−0.501674	+	0.868924i
$906$		0			0
$907$	−4.79218	−	8.30030i	−0.159122	−	0.275607i	0.775430	−	0.631433i	$-0.217533\pi$
$907$	−4.79218	−	8.30030i	−0.159122	−	0.275607i	−0.934552	+	0.355826i	$0.884200\pi$
$908$		0			0
$909$	−10.3486			−0.343240
$910$		0			0
$911$	−11.4534			−0.379467			−0.189733	−	0.981836i	$-0.560762\pi$
$911$	−11.4534			−0.379467			−0.189733	+	0.981836i	$0.560762\pi$
$912$		0			0
$913$	3.10640	+	5.38044i	0.102807	+	0.178066i
$914$		0			0
$915$	8.49234	−	14.7092i	0.280748	−	0.486270i
$916$		0			0
$917$	11.7423	−	9.08850i	0.387764	−	0.300129i
$918$		0			0
$919$	1.13914	−	1.97304i	0.0375766	−	0.0650846i	−0.846625	−	0.532189i	$-0.821370\pi$
$919$	1.13914	−	1.97304i	0.0375766	−	0.0650846i	0.884202	+	0.467105i	$0.154703\pi$
$920$		0			0
$921$	2.32526	+	4.02746i	0.0766198	+	0.132709i
$922$		0			0
$923$	47.0560			1.54887
$924$		0			0
$925$	18.6802			0.614201
$926$		0			0
$927$	3.12108	+	5.40588i	0.102510	+	0.177552i
$928$		0			0
$929$	−6.85026	+	11.8650i	−0.224750	+	0.389278i	−0.956244	−	0.292569i	$-0.905490\pi$
$929$	−6.85026	+	11.8650i	−0.224750	+	0.389278i	0.731494	+	0.681847i	$0.238823\pi$
$930$		0			0
$931$	−38.3710	+	10.6265i	−1.25756	+	0.348270i
$932$		0			0
$933$	−0.662003	+	1.14662i	−0.0216730	+	0.0375388i
$934$		0			0
$935$	−1.14545	−	1.98398i	−0.0374604	−	0.0648832i
$936$		0			0
$937$	−47.8802			−1.56418			−0.782089	−	0.623166i	$-0.785846\pi$
$937$	−47.8802			−1.56418			−0.782089	+	0.623166i	$0.785846\pi$
$938$		0			0
$939$	−5.03720			−0.164383
$940$		0			0
$941$	8.82391	+	15.2835i	0.287651	+	0.498227i	0.973249	−	0.229754i	$-0.0737922\pi$
$941$	8.82391	+	15.2835i	0.287651	+	0.498227i	−0.685597	+	0.727981i	$0.740459\pi$
$942$		0			0
$943$	−27.3605	+	47.3898i	−0.890982	+	1.54323i
$944$		0			0
$945$	−3.14545	+	2.43458i	−0.102322	+	0.0791968i
$946$		0			0
$947$	−6.08293	+	10.5359i	−0.197669	+	0.342372i	−0.947772	−	0.318948i	$-0.896670\pi$
$947$	−6.08293	+	10.5359i	−0.197669	+	0.342372i	0.750103	+	0.661320i	$0.230004\pi$
$948$		0			0
$949$	11.8168	+	20.4673i	0.383589	+	0.664396i
$950$		0			0
$951$	7.61869			0.247053
$952$		0			0
$953$	18.5222			0.599992			0.299996	−	0.953940i	$-0.403015\pi$
$953$	18.5222			0.599992			0.299996	+	0.953940i	$0.403015\pi$
$954$		0			0
$955$	19.1156	+	33.1092i	0.618567	+	1.07139i
$956$		0			0
$957$	0.486391	−	0.842453i	0.0157228	−	0.0272327i
$958$		0			0
$959$	−6.56457	−	48.2998i	−0.211981	−	1.55968i
$960$		0			0
$961$	10.5157	−	18.2138i	0.339218	−	0.587542i
$962$		0			0
$963$	−5.69973	−	9.87222i	−0.183671	−	0.318128i
$964$		0			0
$965$	21.0203			0.676667
$966$		0			0
$967$	−4.90036			−0.157585			−0.0787925	−	0.996891i	$-0.525106\pi$
$967$	−4.90036			−0.157585			−0.0787925	+	0.996891i	$0.525106\pi$
$968$		0			0
$969$	4.33372	+	7.50622i	0.139219	+	0.241134i
$970$		0			0
$971$	24.6147	−	42.6340i	0.789924	−	1.36819i	−0.136088	−	0.990697i	$-0.543453\pi$
$971$	24.6147	−	42.6340i	0.789924	−	1.36819i	0.926013	−	0.377492i	$-0.123214\pi$
$972$		0			0
$973$	−15.7802	−	6.45913i	−0.505890	−	0.207070i
$974$		0			0
$975$	−4.32526	+	7.49156i	−0.138519	+	0.239922i
$976$		0			0
$977$	−14.0688	−	24.3678i	−0.450099	−	0.779595i	0.548292	−	0.836287i	$-0.315278\pi$
$977$	−14.0688	−	24.3678i	−0.450099	−	0.779595i	−0.998392	+	0.0566918i	$0.981945\pi$
$978$		0			0
$979$	4.69217			0.149962
$980$		0			0
$981$	8.79322			0.280746
$982$		0			0
$983$	−7.61680	−	13.1927i	−0.242938	−	0.420781i	0.718612	−	0.695412i	$-0.244778\pi$
$983$	−7.61680	−	13.1927i	−0.242938	−	0.420781i	−0.961550	+	0.274630i	$0.911445\pi$
$984$		0			0
$985$	−10.2066	+	17.6784i	−0.325211	+	0.563282i
$986$		0			0
$987$	17.5417	+	7.18014i	0.558358	+	0.228546i
$988$		0			0
$989$	12.4294	−	21.5283i	0.395230	−	0.684559i
$990$		0			0
$991$	−2.71468	−	4.70197i	−0.0862347	−	0.149363i	0.819682	−	0.572819i	$-0.194150\pi$
$991$	−2.71468	−	4.70197i	−0.0862347	−	0.149363i	−0.905917	+	0.423456i	$0.860817\pi$
$992$		0			0
$993$	−21.6179			−0.686025
$994$		0			0
$995$	30.7786			0.975747
$996$		0			0
$997$	26.7606	+	46.3506i	0.847515	+	1.46794i	0.883419	+	0.468584i	$0.155236\pi$
$997$	26.7606	+	46.3506i	0.847515	+	1.46794i	−0.0359035	+	0.999355i	$0.511431\pi$
$998$		0			0
$999$	3.40898	−	5.90453i	0.107855	−	0.186811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1848.2.bg.f.793.3	yes	8
7.4	even	3	inner	1848.2.bg.f.529.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1848.2.bg.f.529.3	✓	8	7.4	even	3	inner
1848.2.bg.f.793.3	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1848.bg (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.751690 - 1.30196i) q^{5} +(-2.44857 - 1.00225i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(0.751690 - 1.30196i) q^{5} +(-2.44857 - 1.00225i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} -3.15729 q^{13} -1.50338 q^{15} +(0.761920 + 1.31968i) q^{17} +(-2.84395 + 4.92586i) q^{19} +(0.356316 + 2.62165i) q^{21} +(-2.70026 + 4.67699i) q^{23} +(1.36993 + 2.37278i) q^{25} +1.00000 q^{27} -0.972782 q^{29} +(1.57865 + 2.73430i) q^{31} +(-0.500000 + 0.866025i) q^{33} +(-3.14545 + 2.43458i) q^{35} +(3.40898 - 5.90453i) q^{37} +(1.57865 + 2.73430i) q^{39} +10.1326 q^{41} -4.60302 q^{43} +(0.751690 + 1.30196i) q^{45} +(3.58203 - 6.20425i) q^{47} +(4.99101 + 4.90814i) q^{49} +(0.761920 - 1.31968i) q^{51} +(2.40560 + 4.16663i) q^{53} -1.50338 q^{55} +5.68789 q^{57} +(3.35418 + 5.80960i) q^{59} +(-5.64883 + 9.78407i) q^{61} +(2.09226 - 1.61940i) q^{63} +(-2.37330 + 4.11068i) q^{65} +(1.58541 + 2.74600i) q^{67} +5.40052 q^{69} -14.9039 q^{71} +(-3.74270 - 6.48254i) q^{73} +(1.36993 - 2.37278i) q^{75} +(0.356316 + 2.62165i) q^{77} +(2.07527 - 3.59447i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.21279 q^{83} +2.29091 q^{85} +(0.486391 + 0.842453i) q^{87} +(-2.34609 + 4.06354i) q^{89} +(7.73086 + 3.16438i) q^{91} +(1.57865 - 2.73430i) q^{93} +(4.27553 + 7.40543i) q^{95} +16.2662 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^3 + q^7 - 4 * q^9	\( 8 q - 4 q^{3} + q^{7} - 4 q^{9} - 4 q^{11} - 14 q^{13} - q^{17} + 2 q^{19} + q^{21} + 5 q^{23} - 4 q^{25} + 8 q^{27} - 34 q^{29} + 7 q^{31} - 4 q^{33} + 10 q^{35} + 10 q^{37} + 7 q^{39} + 24 q^{41} - 16 q^{43} + 11 q^{47} + 5 q^{49} - q^{51} + 14 q^{53} - 4 q^{57} + q^{59} + 2 q^{61} - 2 q^{63} + 8 q^{65} - 17 q^{67} - 10 q^{69} - 54 q^{71} + 11 q^{73} - 4 q^{75} + q^{77} + 23 q^{79} - 4 q^{81} + 16 q^{83} - 52 q^{85} + 17 q^{87} - 18 q^{89} - 3 q^{91} + 7 q^{93} + 14 q^{95} + 14 q^{97} + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + q^7 - 4 * q^9 - 4 * q^11 - 14 * q^13 - q^17 + 2 * q^19 + q^21 + 5 * q^23 - 4 * q^25 + 8 * q^27 - 34 * q^29 + 7 * q^31 - 4 * q^33 + 10 * q^35 + 10 * q^37 + 7 * q^39 + 24 * q^41 - 16 * q^43 + 11 * q^47 + 5 * q^49 - q^51 + 14 * q^53 - 4 * q^57 + q^59 + 2 * q^61 - 2 * q^63 + 8 * q^65 - 17 * q^67 - 10 * q^69 - 54 * q^71 + 11 * q^73 - 4 * q^75 + q^77 + 23 * q^79 - 4 * q^81 + 16 * q^83 - 52 * q^85 + 17 * q^87 - 18 * q^89 - 3 * q^91 + 7 * q^93 + 14 * q^95 + 14 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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