LMFDB - Embedded newform 1232.2.q.g.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1232,2,Mod(177,1232)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1232, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("1232.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, 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:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			177.2
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1232.177
Dual form			1232.2.q.g.529.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32288 + 2.29129i) q^{3} +(0.822876 - 1.42526i) q^{5} +(1.32288 - 2.29129i) q^{7} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(1.32288 + 2.29129i) q^{3} +(0.822876 - 1.42526i) q^{5} +(1.32288 - 2.29129i) q^{7} +(-2.00000 + 3.46410i) q^{9} +(0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +4.35425 q^{15} +(-3.00000 - 5.19615i) q^{17} +(-2.82288 + 4.88936i) q^{19} +7.00000 q^{21} +(0.822876 - 1.42526i) q^{23} +(1.14575 + 1.98450i) q^{25} -2.64575 q^{27} +6.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.32288 + 2.29129i) q^{33} +(-2.17712 - 3.77089i) q^{35} +(-1.82288 + 3.15731i) q^{37} +(6.61438 + 11.4564i) q^{39} +10.9373 q^{41} +4.00000 q^{43} +(3.29150 + 5.70105i) q^{45} +(1.35425 - 2.34563i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(7.93725 - 13.7477i) q^{51} +(-0.822876 - 1.42526i) q^{53} +1.64575 q^{55} -14.9373 q^{57} +(2.32288 + 4.02334i) q^{59} +(-7.14575 + 12.3768i) q^{61} +(5.29150 + 9.16515i) q^{63} +(4.11438 - 7.12631i) q^{65} +(-5.96863 - 10.3380i) q^{67} +4.35425 q^{69} -4.35425 q^{71} +(-0.177124 - 0.306788i) q^{73} +(-3.03137 + 5.25049i) q^{75} +2.64575 q^{77} +(-1.32288 + 2.29129i) q^{79} +(2.50000 + 4.33013i) q^{81} -2.70850 q^{83} -9.87451 q^{85} +(8.32288 + 14.4156i) q^{87} +(-3.29150 + 5.70105i) q^{89} +(6.61438 - 11.4564i) q^{91} +(5.29150 - 9.16515i) q^{93} +(4.64575 + 8.04668i) q^{95} -16.2915 q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{5} - 8 q^{9}+O(q^{10}) $ 4 * q - 2 * q^5 - 8 * q^9	$ 4 q - 2 q^{5} - 8 q^{9} + 2 q^{11} + 20 q^{13} + 28 q^{15} - 12 q^{17} - 6 q^{19} + 28 q^{21} - 2 q^{23} - 6 q^{25} + 4 q^{29} - 8 q^{31} - 14 q^{35} - 2 q^{37} + 12 q^{41} + 16 q^{43} - 8 q^{45} + 16 q^{47} - 14 q^{49} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 4 q^{59} - 18 q^{61} - 10 q^{65} - 8 q^{67} + 28 q^{69} - 28 q^{71} - 6 q^{73} - 28 q^{75} + 10 q^{81} - 32 q^{83} + 24 q^{85} + 28 q^{87} + 8 q^{89} + 8 q^{95} - 44 q^{97} - 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^5 - 8 * q^9 + 2 * q^11 + 20 * q^13 + 28 * q^15 - 12 * q^17 - 6 * q^19 + 28 * q^21 - 2 * q^23 - 6 * q^25 + 4 * q^29 - 8 * q^31 - 14 * q^35 - 2 * q^37 + 12 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 14 * q^49 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 4 * q^59 - 18 * q^61 - 10 * q^65 - 8 * q^67 + 28 * q^69 - 28 * q^71 - 6 * q^73 - 28 * q^75 + 10 * q^81 - 32 * q^83 + 24 * q^85 + 28 * q^87 + 8 * q^89 + 8 * q^95 - 44 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	0.940898	+	0.338689i	$0.109984\pi$
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	−0.177136	+	0.984186i	$0.556683\pi$
$4$		0			0
$5$	0.822876	−	1.42526i	0.368001	−	0.637397i	−0.621252	−	0.783611i	$-0.713376\pi$
$5$	0.822876	−	1.42526i	0.368001	−	0.637397i	0.989253	+	0.146214i	$0.0467089\pi$
$6$		0			0
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$7$	1.32288	−	2.29129i	0.500000	−	0.866025i
$8$		0			0
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	5.00000			1.38675			0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000			1.38675			0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$	4.35425			1.12426
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−2.82288	+	4.88936i	−0.647612	+	1.12170i	0.336080	+	0.941834i	$0.390899\pi$
$19$	−2.82288	+	4.88936i	−0.647612	+	1.12170i	−0.983692	+	0.179863i	$0.942434\pi$
$20$		0			0
$21$	7.00000			1.52753
$22$		0			0
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	−0.767391	−	0.641179i	$-0.778446\pi$
$23$	0.822876	−	1.42526i	0.171581	−	0.297188i	0.938973	+	0.343991i	$0.111779\pi$
$24$		0			0
$25$	1.14575	+	1.98450i	0.229150	+	0.396900i
$26$		0			0
$27$	−2.64575			−0.509175
$28$		0			0
$29$	6.29150			1.16830			0.584151	−	0.811645i	$-0.301427\pi$
$29$	6.29150			1.16830			0.584151	+	0.811645i	$0.301427\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	−1.32288	+	2.29129i	−0.230283	+	0.398862i
$34$		0			0
$35$	−2.17712	−	3.77089i	−0.368001	−	0.637397i
$36$		0			0
$37$	−1.82288	+	3.15731i	−0.299679	+	0.519059i	−0.976062	−	0.217491i	$-0.930213\pi$
$37$	−1.82288	+	3.15731i	−0.299679	+	0.519059i	0.676384	+	0.736550i	$0.263546\pi$
$38$		0			0
$39$	6.61438	+	11.4564i	1.05915	+	1.83450i
$40$		0			0
$41$	10.9373			1.70811			0.854056	−	0.520181i	$-0.174136\pi$
$41$	10.9373			1.70811			0.854056	+	0.520181i	$0.174136\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$		0			0
$45$	3.29150	+	5.70105i	0.490668	+	0.849862i
$46$		0			0
$47$	1.35425	−	2.34563i	0.197537	−	0.342145i	−0.750192	−	0.661220i	$-0.770039\pi$
$47$	1.35425	−	2.34563i	0.197537	−	0.342145i	0.947729	+	0.319075i	$0.103372\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$	7.93725	−	13.7477i	1.11144	−	1.92507i
$52$		0			0
$53$	−0.822876	−	1.42526i	−0.113031	−	0.195775i	0.803960	−	0.594683i	$-0.202722\pi$
$53$	−0.822876	−	1.42526i	−0.113031	−	0.195775i	−0.916991	+	0.398908i	$0.869389\pi$
$54$		0			0
$55$	1.64575			0.221913
$56$		0			0
$57$	−14.9373			−1.97849
$58$		0			0
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	0.976682	−	0.214692i	$-0.0688746\pi$
$59$	2.32288	+	4.02334i	0.302413	+	0.523794i	−0.674269	+	0.738486i	$0.735541\pi$
$60$		0			0
$61$	−7.14575	+	12.3768i	−0.914920	+	1.58469i	−0.107901	+	0.994162i	$0.534413\pi$
$61$	−7.14575	+	12.3768i	−0.914920	+	1.58469i	−0.807019	+	0.590526i	$0.798920\pi$
$62$		0			0
$63$	5.29150	+	9.16515i	0.666667	+	1.15470i
$64$		0			0
$65$	4.11438	−	7.12631i	0.510326	−	0.883910i
$66$		0			0
$67$	−5.96863	−	10.3380i	−0.729184	−	1.26298i	−0.957229	−	0.289333i	$-0.906567\pi$
$67$	−5.96863	−	10.3380i	−0.729184	−	1.26298i	0.228045	−	0.973651i	$-0.426767\pi$
$68$		0			0
$69$	4.35425			0.524190
$70$		0			0
$71$	−4.35425			−0.516754			−0.258377	−	0.966044i	$-0.583188\pi$
$71$	−4.35425			−0.516754			−0.258377	+	0.966044i	$0.583188\pi$
$72$		0			0
$73$	−0.177124	−	0.306788i	−0.0207308	−	0.0359069i	0.855474	−	0.517846i	$-0.173266\pi$
$73$	−0.177124	−	0.306788i	−0.0207308	−	0.0359069i	−0.876205	+	0.481939i	$0.839933\pi$
$74$		0			0
$75$	−3.03137	+	5.25049i	−0.350033	+	0.606275i
$76$		0			0
$77$	2.64575			0.301511
$78$		0			0
$79$	−1.32288	+	2.29129i	−0.148835	+	0.257790i	−0.930797	−	0.365536i	$-0.880886\pi$
$79$	−1.32288	+	2.29129i	−0.148835	+	0.257790i	0.781962	+	0.623326i	$0.214219\pi$
$80$		0			0
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$		0			0
$83$	−2.70850			−0.297296			−0.148648	−	0.988890i	$-0.547492\pi$
$83$	−2.70850			−0.297296			−0.148648	+	0.988890i	$0.547492\pi$
$84$		0			0
$85$	−9.87451			−1.07104
$86$		0			0
$87$	8.32288	+	14.4156i	0.892306	+	1.54552i
$88$		0			0
$89$	−3.29150	+	5.70105i	−0.348899	+	0.604310i	−0.986054	−	0.166425i	$-0.946778\pi$
$89$	−3.29150	+	5.70105i	−0.348899	+	0.604310i	0.637156	+	0.770735i	$0.280111\pi$
$90$		0			0
$91$	6.61438	−	11.4564i	0.693375	−	1.20096i
$92$		0			0
$93$	5.29150	−	9.16515i	0.548703	−	0.950382i
$94$		0			0
$95$	4.64575	+	8.04668i	0.476644	+	0.825572i
$96$		0			0
$97$	−16.2915			−1.65415			−0.827076	−	0.562090i	$-0.809997\pi$
$97$	−16.2915			−1.65415			−0.827076	+	0.562090i	$0.809997\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	−1.46863	+	2.54374i	−0.144708	+	0.250642i	−0.929264	−	0.369416i	$-0.879558\pi$
$103$	−1.46863	+	2.54374i	−0.144708	+	0.250642i	0.784556	+	0.620058i	$0.212891\pi$
$104$		0			0
$105$	5.76013	−	9.97684i	0.562131	−	0.973640i
$106$		0			0
$107$	−5.46863	+	9.47194i	−0.528672	+	0.915687i	0.470769	+	0.882257i	$0.343977\pi$
$107$	−5.46863	+	9.47194i	−0.528672	+	0.915687i	−0.999441	+	0.0334304i	$0.989357\pi$
$108$		0			0
$109$	5.29150	+	9.16515i	0.506834	+	0.877862i	0.999969	+	0.00790932i	$0.00251764\pi$
$109$	5.29150	+	9.16515i	0.506834	+	0.877862i	−0.493135	+	0.869953i	$0.664149\pi$
$110$		0			0
$111$	−9.64575			−0.915534
$112$		0			0
$113$	−18.2915			−1.72072			−0.860360	−	0.509687i	$-0.829761\pi$
$113$	−18.2915			−1.72072			−0.860360	+	0.509687i	$0.829761\pi$
$114$		0			0
$115$	−1.35425	−	2.34563i	−0.126284	−	0.218731i
$116$		0			0
$117$	−10.0000	+	17.3205i	−0.924500	+	1.60128i
$118$		0			0
$119$	−15.8745			−1.45521
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$	14.4686	+	25.0604i	1.30459	+	2.25962i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	−15.9373			−1.41420			−0.707101	−	0.707112i	$-0.749998\pi$
$127$	−15.9373			−1.41420			−0.707101	+	0.707112i	$0.749998\pi$
$128$		0			0
$129$	5.29150	+	9.16515i	0.465891	+	0.806947i
$130$		0			0
$131$	5.17712	−	8.96704i	0.452327	−	0.783454i	−0.546203	−	0.837653i	$-0.683927\pi$
$131$	5.17712	−	8.96704i	0.452327	−	0.783454i	0.998530	+	0.0541989i	$0.0172605\pi$
$132$		0			0
$133$	7.46863	+	12.9360i	0.647612	+	1.12170i
$134$		0			0
$135$	−2.17712	+	3.77089i	−0.187377	+	0.324547i
$136$		0			0
$137$	6.43725	+	11.1497i	0.549972	+	0.952579i	0.998276	+	0.0586978i	$0.0186948\pi$
$137$	6.43725	+	11.1497i	0.549972	+	0.952579i	−0.448304	+	0.893881i	$0.647972\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	7.16601			0.603487
$142$		0			0
$143$	2.50000	+	4.33013i	0.209061	+	0.362103i
$144$		0			0
$145$	5.17712	−	8.96704i	0.429937	−	0.744672i
$146$		0			0
$147$	9.26013	−	16.0390i	0.763763	−	1.32288i
$148$		0			0
$149$	7.64575	−	13.2428i	0.626364	−	1.08489i	−0.361911	−	0.932213i	$-0.617876\pi$
$149$	7.64575	−	13.2428i	0.626364	−	1.08489i	0.988275	−	0.152682i	$-0.0487911\pi$
$150$		0			0
$151$	−4.32288	−	7.48744i	−0.351791	−	0.609319i	0.634773	−	0.772699i	$-0.281094\pi$
$151$	−4.32288	−	7.48744i	−0.351791	−	0.609319i	−0.986563	+	0.163380i	$0.947760\pi$
$152$		0			0
$153$	24.0000			1.94029
$154$		0			0
$155$	−6.58301			−0.528760
$156$		0			0
$157$	−10.5830	−	18.3303i	−0.844616	−	1.46292i	−0.885954	−	0.463772i	$-0.846496\pi$
$157$	−10.5830	−	18.3303i	−0.844616	−	1.46292i	0.0413387	−	0.999145i	$-0.486838\pi$
$158$		0			0
$159$	2.17712	−	3.77089i	0.172657	−	0.299051i
$160$		0			0
$161$	−2.17712	−	3.77089i	−0.171581	−	0.297188i
$162$		0			0
$163$	0.322876	−	0.559237i	0.0252896	−	0.0438028i	−0.853104	−	0.521741i	$-0.825283\pi$
$163$	0.322876	−	0.559237i	0.0252896	−	0.0438028i	0.878393	+	0.477939i	$0.158616\pi$
$164$		0			0
$165$	2.17712	+	3.77089i	0.169489	+	0.293563i
$166$		0			0
$167$	11.2288			0.868907			0.434454	−	0.900694i	$-0.356941\pi$
$167$	11.2288			0.868907			0.434454	+	0.900694i	$0.356941\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−11.2915	−	19.5575i	−0.863483	−	1.49560i
$172$		0			0
$173$	0.145751	−	0.252449i	0.0110813	−	0.0191933i	−0.860432	−	0.509566i	$-0.829806\pi$
$173$	0.145751	−	0.252449i	0.0110813	−	0.0191933i	0.871513	+	0.490373i	$0.163139\pi$
$174$		0			0
$175$	6.06275			0.458301
$176$		0			0
$177$	−6.14575	+	10.6448i	−0.461943	+	0.800109i
$178$		0			0
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	−0.950153	−	0.311785i	$-0.899073\pi$
$179$	−9.96863	−	17.2662i	−0.745090	−	1.29053i	0.205062	−	0.978749i	$-0.434260\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$	−37.8118			−2.79513
$184$		0			0
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$		0			0
$189$	−3.50000	+	6.06218i	−0.254588	+	0.440959i
$190$		0			0
$191$	−1.35425	+	2.34563i	−0.0979900	+	0.169724i	−0.910853	−	0.412732i	$-0.864575\pi$
$191$	−1.35425	+	2.34563i	−0.0979900	+	0.169724i	0.812863	+	0.582456i	$0.197908\pi$
$192$		0			0
$193$	−12.7601	−	22.1012i	−0.918494	−	1.59088i	−0.801703	−	0.597722i	$-0.796073\pi$
$193$	−12.7601	−	22.1012i	−0.918494	−	1.59088i	−0.116791	−	0.993157i	$-0.537261\pi$
$194$		0			0
$195$	21.7712			1.55907
$196$		0			0
$197$	−12.8745			−0.917271			−0.458635	−	0.888625i	$-0.651662\pi$
$197$	−12.8745			−0.917271			−0.458635	+	0.888625i	$0.651662\pi$
$198$		0			0
$199$	2.11438	+	3.66221i	0.149884	+	0.259607i	0.931185	−	0.364548i	$-0.118777\pi$
$199$	2.11438	+	3.66221i	0.149884	+	0.259607i	−0.781300	+	0.624155i	$0.785443\pi$
$200$		0			0
$201$	15.7915	−	27.3517i	1.11385	−	1.92924i
$202$		0			0
$203$	8.32288	−	14.4156i	0.584151	−	1.01178i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$		0			0
$207$	3.29150	+	5.70105i	0.228775	+	0.396250i
$208$		0			0
$209$	−5.64575			−0.390525
$210$		0			0
$211$	−0.937254			−0.0645232			−0.0322616	−	0.999479i	$-0.510271\pi$
$211$	−0.937254			−0.0645232			−0.0322616	+	0.999479i	$0.510271\pi$
$212$		0			0
$213$	−5.76013	−	9.97684i	−0.394678	−	0.683602i
$214$		0			0
$215$	3.29150	−	5.70105i	0.224479	−	0.388808i
$216$		0			0
$217$	−10.5830			−0.718421
$218$		0			0
$219$	0.468627	−	0.811686i	0.0316669	−	0.0548486i
$220$		0			0
$221$	−15.0000	−	25.9808i	−1.00901	−	1.74766i
$222$		0			0
$223$	17.6458			1.18165			0.590823	−	0.806801i	$-0.298803\pi$
$223$	17.6458			1.18165			0.590823	+	0.806801i	$0.298803\pi$
$224$		0			0
$225$	−9.16601			−0.611067
$226$		0			0
$227$	−1.35425	−	2.34563i	−0.0898846	−	0.155685i	0.817578	−	0.575818i	$-0.195317\pi$
$227$	−1.35425	−	2.34563i	−0.0898846	−	0.155685i	−0.907462	+	0.420134i	$0.861983\pi$
$228$		0			0
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	−0.470787	−	0.882247i	$-0.656030\pi$
$229$	8.00000	−	13.8564i	0.528655	−	0.915657i	0.999442	−	0.0334101i	$-0.0106368\pi$
$230$		0			0
$231$	3.50000	+	6.06218i	0.230283	+	0.398862i
$232$		0			0
$233$	−0.531373	+	0.920365i	−0.0348114	+	0.0602951i	−0.882906	−	0.469549i	$-0.844416\pi$
$233$	−0.531373	+	0.920365i	−0.0348114	+	0.0602951i	0.848095	+	0.529845i	$0.177750\pi$
$234$		0			0
$235$	−2.22876	−	3.86032i	−0.145388	−	0.251819i
$236$		0			0
$237$	−7.00000			−0.454699
$238$		0			0
$239$	17.2288			1.11444			0.557218	−	0.830366i	$-0.311869\pi$
$239$	17.2288			1.11444			0.557218	+	0.830366i	$0.311869\pi$
$240$		0			0
$241$	12.4059	+	21.4876i	0.799133	+	1.38414i	0.920181	+	0.391492i	$0.128041\pi$
$241$	12.4059	+	21.4876i	0.799133	+	1.38414i	−0.121048	+	0.992647i	$0.538626\pi$
$242$		0			0
$243$	−10.5830	+	18.3303i	−0.678900	+	1.17589i
$244$		0			0
$245$	−11.5203			−0.736002
$246$		0			0
$247$	−14.1144	+	24.4468i	−0.898076	+	1.55551i
$248$		0			0
$249$	−3.58301	−	6.20595i	−0.227064	−	0.393286i
$250$		0			0
$251$	3.29150			0.207758			0.103879	−	0.994590i	$-0.466875\pi$
$251$	3.29150			0.207758			0.103879	+	0.994590i	$0.466875\pi$
$252$		0			0
$253$	1.64575			0.103467
$254$		0			0
$255$	−13.0627	−	22.6253i	−0.818021	−	1.41685i
$256$		0			0
$257$	10.7915	−	18.6914i	0.673155	−	1.16594i	−0.303849	−	0.952720i	$-0.598272\pi$
$257$	10.7915	−	18.6914i	0.673155	−	1.16594i	0.977004	−	0.213219i	$-0.0683948\pi$
$258$		0			0
$259$	4.82288	+	8.35347i	0.299679	+	0.519059i
$260$		0			0
$261$	−12.5830	+	21.7944i	−0.778868	+	1.34904i
$262$		0			0
$263$	9.96863	+	17.2662i	0.614692	+	1.06468i	0.990438	+	0.137955i	$0.0440530\pi$
$263$	9.96863	+	17.2662i	0.614692	+	1.06468i	−0.375747	+	0.926722i	$0.622614\pi$
$264$		0			0
$265$	−2.70850			−0.166382
$266$		0			0
$267$	−17.4170			−1.06590
$268$		0			0
$269$	−2.70850	−	4.69126i	−0.165140	−	0.286031i	0.771565	−	0.636151i	$-0.219474\pi$
$269$	−2.70850	−	4.69126i	−0.165140	−	0.286031i	−0.936705	+	0.350120i	$0.886141\pi$
$270$		0			0
$271$	−1.03137	+	1.78639i	−0.0626514	+	0.108515i	−0.895650	−	0.444760i	$-0.853289\pi$
$271$	−1.03137	+	1.78639i	−0.0626514	+	0.108515i	0.832998	+	0.553275i	$0.186622\pi$
$272$		0			0
$273$	35.0000			2.11830
$274$		0			0
$275$	−1.14575	+	1.98450i	−0.0690914	+	0.119670i
$276$		0			0
$277$	11.1458	+	19.3050i	0.669683	+	1.15993i	0.977993	+	0.208639i	$0.0669035\pi$
$277$	11.1458	+	19.3050i	0.669683	+	1.15993i	−0.308309	+	0.951286i	$0.599763\pi$
$278$		0			0
$279$	16.0000			0.957895
$280$		0			0
$281$	−22.9373			−1.36832			−0.684161	−	0.729331i	$-0.739831\pi$
$281$	−22.9373			−1.36832			−0.684161	+	0.729331i	$0.739831\pi$
$282$		0			0
$283$	−1.17712	−	2.03884i	−0.0699728	−	0.121196i	0.828916	−	0.559373i	$-0.188958\pi$
$283$	−1.17712	−	2.03884i	−0.0699728	−	0.121196i	−0.898889	+	0.438176i	$0.855625\pi$
$284$		0			0
$285$	−12.2915	+	21.2895i	−0.728086	+	1.26108i
$286$		0			0
$287$	14.4686	−	25.0604i	0.854056	−	1.47927i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	−21.5516	−	37.3285i	−1.26338	−	2.18824i
$292$		0			0
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$	7.64575			0.445153
$296$		0			0
$297$	−1.32288	−	2.29129i	−0.0767610	−	0.132954i
$298$		0			0
$299$	4.11438	−	7.12631i	0.237941	−	0.412125i
$300$		0			0
$301$	5.29150	−	9.16515i	0.304997	−	0.528271i
$302$		0			0
$303$	3.96863	−	6.87386i	0.227992	−	0.394893i
$304$		0			0
$305$	11.7601	+	20.3691i	0.673383	+	1.16633i
$306$		0			0
$307$	−22.2288			−1.26866			−0.634331	−	0.773062i	$-0.718724\pi$
$307$	−22.2288			−1.26866			−0.634331	+	0.773062i	$0.718724\pi$
$308$		0			0
$309$	−7.77124			−0.442091
$310$		0			0
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	0.880698	−	0.473678i	$-0.157074\pi$
$311$	0.531373	+	0.920365i	0.0301314	+	0.0521891i	−0.850566	+	0.525868i	$0.823741\pi$
$312$		0			0
$313$	−11.7915	+	20.4235i	−0.666495	+	1.15440i	0.312382	+	0.949956i	$0.398873\pi$
$313$	−11.7915	+	20.4235i	−0.666495	+	1.15440i	−0.978878	+	0.204447i	$0.934460\pi$
$314$		0			0
$315$	17.4170			0.981336
$316$		0			0
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	3.14575	+	5.44860i	0.176128	+	0.305063i
$320$		0			0
$321$	−28.9373			−1.61512
$322$		0			0
$323$	33.8745			1.88483
$324$		0			0
$325$	5.72876	+	9.92250i	0.317774	+	0.550401i
$326$		0			0
$327$	−14.0000	+	24.2487i	−0.774202	+	1.34096i
$328$		0			0
$329$	−3.58301	−	6.20595i	−0.197537	−	0.342145i
$330$		0			0
$331$	−10.3229	+	17.8797i	−0.567397	+	0.982760i	0.429426	+	0.903102i	$0.358716\pi$
$331$	−10.3229	+	17.8797i	−0.567397	+	0.982760i	−0.996822	+	0.0796575i	$0.974617\pi$
$332$		0			0
$333$	−7.29150	−	12.6293i	−0.399572	−	0.692079i
$334$		0			0
$335$	−19.6458			−1.07336
$336$		0			0
$337$	9.06275			0.493679			0.246840	−	0.969056i	$-0.420608\pi$
$337$	9.06275			0.493679			0.246840	+	0.969056i	$0.420608\pi$
$338$		0			0
$339$	−24.1974	−	41.9111i	−1.31422	−	2.27630i
$340$		0			0
$341$	2.00000	−	3.46410i	0.108306	−	0.187592i
$342$		0			0
$343$	−18.5203			−1.00000
$344$		0			0
$345$	3.58301	−	6.20595i	0.192903	−	0.334117i
$346$		0			0
$347$	−10.4059	−	18.0235i	−0.558617	−	0.967553i	−0.997612	−	0.0690636i	$-0.977999\pi$
$347$	−10.4059	−	18.0235i	−0.558617	−	0.967553i	0.438995	−	0.898489i	$-0.355334\pi$
$348$		0			0
$349$	−1.87451			−0.100340			−0.0501701	−	0.998741i	$-0.515976\pi$
$349$	−1.87451			−0.100340			−0.0501701	+	0.998741i	$0.515976\pi$
$350$		0			0
$351$	−13.2288			−0.706099
$352$		0			0
$353$	−3.58301	−	6.20595i	−0.190704	−	0.330309i	0.754780	−	0.655978i	$-0.227744\pi$
$353$	−3.58301	−	6.20595i	−0.190704	−	0.330309i	−0.945484	+	0.325669i	$0.894410\pi$
$354$		0			0
$355$	−3.58301	+	6.20595i	−0.190166	+	0.329377i
$356$		0			0
$357$	−21.0000	−	36.3731i	−1.11144	−	1.92507i
$358$		0			0
$359$	−12.9686	+	22.4623i	−0.684458	+	1.18552i	0.289149	+	0.957284i	$0.406628\pi$
$359$	−12.9686	+	22.4623i	−0.684458	+	1.18552i	−0.973607	+	0.228232i	$0.926706\pi$
$360$		0			0
$361$	−6.43725	−	11.1497i	−0.338803	−	0.586824i
$362$		0			0
$363$	−2.64575			−0.138866
$364$		0			0
$365$	−0.583005			−0.0305159
$366$		0			0
$367$	−18.1144	−	31.3750i	−0.945563	−	1.63776i	−0.754620	−	0.656162i	$-0.772179\pi$
$367$	−18.1144	−	31.3750i	−0.945563	−	1.63776i	−0.190943	−	0.981601i	$-0.561154\pi$
$368$		0			0
$369$	−21.8745	+	37.8878i	−1.13874	+	1.97236i
$370$		0			0
$371$	−4.35425			−0.226061
$372$		0			0
$373$	−10.4373	+	18.0779i	−0.540421	+	0.936036i	0.458459	+	0.888715i	$0.348402\pi$
$373$	−10.4373	+	18.0779i	−0.540421	+	0.936036i	−0.998880	+	0.0473204i	$0.984932\pi$
$374$		0			0
$375$	15.8745	+	27.4955i	0.819756	+	1.41986i
$376$		0			0
$377$	31.4575			1.62014
$378$		0			0
$379$	−6.06275			−0.311422			−0.155711	−	0.987803i	$-0.549767\pi$
$379$	−6.06275			−0.311422			−0.155711	+	0.987803i	$0.549767\pi$
$380$		0			0
$381$	−21.0830	−	36.5168i	−1.08012	−	1.87081i
$382$		0			0
$383$	12.0516	−	20.8740i	0.615810	−	1.06661i	−0.374432	−	0.927254i	$-0.622162\pi$
$383$	12.0516	−	20.8740i	0.615810	−	1.06661i	0.990242	−	0.139359i	$-0.0445043\pi$
$384$		0			0
$385$	2.17712	−	3.77089i	0.110957	−	0.192182i
$386$		0			0
$387$	−8.00000	+	13.8564i	−0.406663	+	0.704361i
$388$		0			0
$389$	−13.4059	−	23.2197i	−0.679705	−	1.17728i	−0.975070	−	0.221899i	$-0.928774\pi$
$389$	−13.4059	−	23.2197i	−0.679705	−	1.17728i	0.295364	−	0.955385i	$-0.404559\pi$
$390$		0			0
$391$	−9.87451			−0.499375
$392$		0			0
$393$	27.3948			1.38188
$394$		0			0
$395$	2.17712	+	3.77089i	0.109543	+	0.189734i
$396$		0			0
$397$	5.58301	−	9.67005i	0.280203	−	0.485326i	−0.691232	−	0.722633i	$-0.742932\pi$
$397$	5.58301	−	9.67005i	0.280203	−	0.485326i	0.971435	+	0.237307i	$0.0762649\pi$
$398$		0			0
$399$	−19.7601	+	34.2255i	−0.989244	+	1.71342i
$400$		0			0
$401$	−10.7915	+	18.6914i	−0.538902	+	0.933406i	0.460062	+	0.887887i	$0.347827\pi$
$401$	−10.7915	+	18.6914i	−0.538902	+	0.933406i	−0.998963	+	0.0455185i	$0.985506\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$		0			0
$405$	8.22876			0.408890
$406$		0			0
$407$	−3.64575			−0.180713
$408$		0			0
$409$	−1.53137	−	2.65242i	−0.0757215	−	0.131154i	0.825678	−	0.564141i	$-0.190793\pi$
$409$	−1.53137	−	2.65242i	−0.0757215	−	0.131154i	−0.901400	+	0.432988i	$0.857459\pi$
$410$		0			0
$411$	−17.0314	+	29.4992i	−0.840096	+	1.45509i
$412$		0			0
$413$	12.2915			0.604825
$414$		0			0
$415$	−2.22876	+	3.86032i	−0.109405	+	0.189496i
$416$		0			0
$417$	5.29150	+	9.16515i	0.259126	+	0.448819i
$418$		0			0
$419$	9.87451			0.482401			0.241201	−	0.970475i	$-0.422459\pi$
$419$	9.87451			0.482401			0.241201	+	0.970475i	$0.422459\pi$
$420$		0			0
$421$	9.16601			0.446724			0.223362	−	0.974736i	$-0.428297\pi$
$421$	9.16601			0.446724			0.223362	+	0.974736i	$0.428297\pi$
$422$		0			0
$423$	5.41699	+	9.38251i	0.263383	+	0.456193i
$424$		0			0
$425$	6.87451	−	11.9070i	0.333463	−	0.577574i
$426$		0			0
$427$	18.9059	+	32.7459i	0.914920	+	1.58469i
$428$		0			0
$429$	−6.61438	+	11.4564i	−0.319345	+	0.553122i
$430$		0			0
$431$	14.6144	+	25.3128i	0.703950	+	1.21928i	0.967069	+	0.254514i	$0.0819154\pi$
$431$	14.6144	+	25.3128i	0.703950	+	1.21928i	−0.263119	+	0.964763i	$0.584751\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	27.3948			1.31348
$436$		0			0
$437$	4.64575	+	8.04668i	0.222236	+	0.384925i
$438$		0			0
$439$	1.96863	−	3.40976i	0.0939574	−	0.162739i	−0.815216	−	0.579158i	$-0.803382\pi$
$439$	1.96863	−	3.40976i	0.0939574	−	0.162739i	0.909173	+	0.416419i	$0.136715\pi$
$440$		0			0
$441$	28.0000			1.33333
$442$		0			0
$443$	17.2288	−	29.8411i	0.818563	−	1.41779i	−0.0881781	−	0.996105i	$-0.528104\pi$
$443$	17.2288	−	29.8411i	0.818563	−	1.41779i	0.906741	−	0.421688i	$-0.138562\pi$
$444$		0			0
$445$	5.41699	+	9.38251i	0.256790	+	0.444774i
$446$		0			0
$447$	40.4575			1.91357
$448$		0			0
$449$	−21.8745			−1.03232			−0.516161	−	0.856492i	$-0.672639\pi$
$449$	−21.8745			−1.03232			−0.516161	+	0.856492i	$0.672639\pi$
$450$		0			0
$451$	5.46863	+	9.47194i	0.257508	+	0.446016i
$452$		0			0
$453$	11.4373	−	19.8099i	0.537369	−	0.930751i
$454$		0			0
$455$	−10.8856	−	18.8544i	−0.510326	−	0.883910i
$456$		0			0
$457$	−1.58301	+	2.74185i	−0.0740499	+	0.128258i	−0.900673	−	0.434498i	$-0.856926\pi$
$457$	−1.58301	+	2.74185i	−0.0740499	+	0.128258i	0.826623	+	0.562756i	$0.190259\pi$
$458$		0			0
$459$	7.93725	+	13.7477i	0.370479	+	0.641689i
$460$		0			0
$461$	10.1660			0.473478			0.236739	−	0.971573i	$-0.423921\pi$
$461$	10.1660			0.473478			0.236739	+	0.971573i	$0.423921\pi$
$462$		0			0
$463$	−30.4575			−1.41548			−0.707740	−	0.706473i	$-0.750285\pi$
$463$	−30.4575			−1.41548			−0.707740	+	0.706473i	$0.750285\pi$
$464$		0			0
$465$	−8.70850	−	15.0836i	−0.403847	−	0.699483i
$466$		0			0
$467$	10.6458	−	18.4390i	0.492627	−	0.853254i	−0.507337	−	0.861748i	$-0.669370\pi$
$467$	10.6458	−	18.4390i	0.492627	−	0.853254i	0.999964	+	0.00849322i	$0.00270351\pi$
$468$		0			0
$469$	−31.5830			−1.45837
$470$		0			0
$471$	28.0000	−	48.4974i	1.29017	−	2.23464i
$472$		0			0
$473$	2.00000	+	3.46410i	0.0919601	+	0.159280i
$474$		0			0
$475$	−12.9373			−0.593602
$476$		0			0
$477$	6.58301			0.301415
$478$		0			0
$479$	−5.03137	−	8.71459i	−0.229889	−	0.398180i	0.727886	−	0.685698i	$-0.240503\pi$
$479$	−5.03137	−	8.71459i	−0.229889	−	0.398180i	−0.957775	+	0.287518i	$0.907170\pi$
$480$		0			0
$481$	−9.11438	+	15.7866i	−0.415580	+	0.719805i
$482$		0			0
$483$	5.76013	−	9.97684i	0.262095	−	0.453962i
$484$		0			0
$485$	−13.4059	+	23.2197i	−0.608730	+	1.05435i
$486$		0			0
$487$	−4.70850	−	8.15536i	−0.213362	−	0.369554i	0.739402	−	0.673264i	$-0.235108\pi$
$487$	−4.70850	−	8.15536i	−0.213362	−	0.369554i	−0.952765	+	0.303709i	$0.901775\pi$
$488$		0			0
$489$	1.70850			0.0772609
$490$		0			0
$491$	−21.2915			−0.960872			−0.480436	−	0.877030i	$-0.659522\pi$
$491$	−21.2915			−0.960872			−0.480436	+	0.877030i	$0.659522\pi$
$492$		0			0
$493$	−18.8745	−	32.6916i	−0.850065	−	1.47236i
$494$		0			0
$495$	−3.29150	+	5.70105i	−0.147942	+	0.256243i
$496$		0			0
$497$	−5.76013	+	9.97684i	−0.258377	+	0.447522i
$498$		0			0
$499$	−6.93725	+	12.0157i	−0.310554	+	0.537896i	−0.978482	−	0.206330i	$-0.933848\pi$
$499$	−6.93725	+	12.0157i	−0.310554	+	0.537896i	0.667928	+	0.744226i	$0.267181\pi$
$500$		0			0
$501$	14.8542	+	25.7283i	0.663639	+	1.14946i
$502$		0			0
$503$	4.06275			0.181149			0.0905744	−	0.995890i	$-0.471130\pi$
$503$	4.06275			0.181149			0.0905744	+	0.995890i	$0.471130\pi$
$504$		0			0
$505$	−4.93725			−0.219705
$506$		0			0
$507$	15.8745	+	27.4955i	0.705012	+	1.22112i
$508$		0			0
$509$	0.291503	−	0.504897i	0.0129206	−	0.0223792i	−0.859493	−	0.511148i	$-0.829220\pi$
$509$	0.291503	−	0.504897i	0.0129206	−	0.0223792i	0.872413	+	0.488769i	$0.162554\pi$
$510$		0			0
$511$	−0.937254			−0.0414617
$512$		0			0
$513$	7.46863	−	12.9360i	0.329748	−	0.571140i
$514$		0			0
$515$	2.41699	+	4.18636i	0.106506	+	0.184473i
$516$		0			0
$517$	2.70850			0.119120
$518$		0			0
$519$	0.771243			0.0338538
$520$		0			0
$521$	16.9373	+	29.3362i	0.742035	+	1.28524i	0.951567	+	0.307440i	$0.0994723\pi$
$521$	16.9373	+	29.3362i	0.742035	+	1.28524i	−0.209533	+	0.977802i	$0.567194\pi$
$522$		0			0
$523$	−10.7601	+	18.6371i	−0.470508	+	0.814943i	−0.999431	−	0.0337264i	$-0.989263\pi$
$523$	−10.7601	+	18.6371i	−0.470508	+	0.814943i	0.528923	+	0.848670i	$0.322596\pi$
$524$		0			0
$525$	8.02026	+	13.8915i	0.350033	+	0.606275i
$526$		0			0
$527$	−12.0000	+	20.7846i	−0.522728	+	0.905392i
$528$		0			0
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$		0			0
$531$	−18.5830			−0.806434
$532$		0			0
$533$	54.6863			2.36873
$534$		0			0
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	26.3745	−	45.6820i	1.13814	−	1.97132i
$538$		0			0
$539$	3.50000	−	6.06218i	0.150756	−	0.261116i
$540$		0			0
$541$	−1.14575	+	1.98450i	−0.0492597	+	0.0853203i	−0.889604	−	0.456733i	$-0.849020\pi$
$541$	−1.14575	+	1.98450i	−0.0492597	+	0.0853203i	0.840344	+	0.542053i	$0.182353\pi$
$542$		0			0
$543$	−13.2288	−	22.9129i	−0.567700	−	0.983286i
$544$		0			0
$545$	17.4170			0.746062
$546$		0			0
$547$	9.52026			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$547$	9.52026			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$548$		0			0
$549$	−28.5830	−	49.5072i	−1.21989	−	2.11292i
$550$		0			0
$551$	−17.7601	+	30.7614i	−0.756607	+	1.31048i
$552$		0			0
$553$	3.50000	+	6.06218i	0.148835	+	0.257790i
$554$		0			0
$555$	−7.93725	+	13.7477i	−0.336918	+	0.583559i
$556$		0			0
$557$	15.8745	+	27.4955i	0.672624	+	1.16502i	0.977157	+	0.212518i	$0.0681664\pi$
$557$	15.8745	+	27.4955i	0.672624	+	1.16502i	−0.304533	+	0.952502i	$0.598500\pi$
$558$		0			0
$559$	20.0000			0.845910
$560$		0			0
$561$	15.8745			0.670222
$562$		0			0
$563$	14.4686	+	25.0604i	0.609780	+	1.05617i	0.991276	+	0.131800i	$0.0420755\pi$
$563$	14.4686	+	25.0604i	0.609780	+	1.05617i	−0.381496	+	0.924370i	$0.624591\pi$
$564$		0			0
$565$	−15.0516	+	26.0702i	−0.633227	+	1.09678i
$566$		0			0
$567$	13.2288			0.555556
$568$		0			0
$569$	−0.583005	+	1.00979i	−0.0244409	+	0.0423328i	−0.877987	−	0.478684i	$-0.841114\pi$
$569$	−0.583005	+	1.00979i	−0.0244409	+	0.0423328i	0.853546	+	0.521017i	$0.174447\pi$
$570$		0			0
$571$	−14.5314	−	25.1691i	−0.608119	−	1.05329i	−0.991550	−	0.129724i	$-0.958591\pi$
$571$	−14.5314	−	25.1691i	−0.608119	−	1.05329i	0.383431	−	0.923569i	$-0.374742\pi$
$572$		0			0
$573$	−7.16601			−0.299364
$574$		0			0
$575$	3.77124			0.157272
$576$		0			0
$577$	−13.7288	−	23.7789i	−0.571536	−	0.989929i	−0.996409	−	0.0846757i	$-0.973015\pi$
$577$	−13.7288	−	23.7789i	−0.571536	−	0.989929i	0.424873	−	0.905253i	$-0.360319\pi$
$578$		0			0
$579$	33.7601	−	58.4743i	1.40302	−	2.43011i
$580$		0			0
$581$	−3.58301	+	6.20595i	−0.148648	+	0.257466i
$582$		0			0
$583$	0.822876	−	1.42526i	0.0340800	−	0.0590283i
$584$		0			0
$585$	16.4575	+	28.5052i	0.680434	+	1.17855i
$586$		0			0
$587$	−7.93725			−0.327606			−0.163803	−	0.986493i	$-0.552376\pi$
$587$	−7.93725			−0.327606			−0.163803	+	0.986493i	$0.552376\pi$
$588$		0			0
$589$	22.5830			0.930517
$590$		0			0
$591$	−17.0314	−	29.4992i	−0.700577	−	1.21344i
$592$		0			0
$593$	−3.53137	+	6.11652i	−0.145016	+	0.251175i	−0.929379	−	0.369127i	$-0.879657\pi$
$593$	−3.53137	+	6.11652i	−0.145016	+	0.251175i	0.784363	+	0.620302i	$0.212990\pi$
$594$		0			0
$595$	−13.0627	+	22.6253i	−0.535520	+	0.927549i
$596$		0			0
$597$	−5.59412	+	9.68930i	−0.228952	+	0.396557i
$598$		0			0
$599$	21.8745	+	37.8878i	0.893768	+	1.54805i	0.835322	+	0.549761i	$0.185281\pi$
$599$	21.8745	+	37.8878i	0.893768	+	1.54805i	0.0584464	+	0.998291i	$0.481385\pi$
$600$		0			0
$601$	−3.41699			−0.139382			−0.0696911	−	0.997569i	$-0.522201\pi$
$601$	−3.41699			−0.139382			−0.0696911	+	0.997569i	$0.522201\pi$
$602$		0			0
$603$	47.7490			1.94449
$604$		0			0
$605$	0.822876	+	1.42526i	0.0334547	+	0.0579452i
$606$		0			0
$607$	5.35425	−	9.27383i	0.217322	−	0.376413i	−0.736666	−	0.676257i	$-0.763601\pi$
$607$	5.35425	−	9.27383i	0.217322	−	0.376413i	0.953988	+	0.299843i	$0.0969344\pi$
$608$		0			0
$609$	44.0405			1.78461
$610$		0			0
$611$	6.77124	−	11.7281i	0.273935	−	0.474470i
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$		0			0
$615$	47.6235			1.92037
$616$		0			0
$617$	−5.70850			−0.229815			−0.114908	−	0.993376i	$-0.536657\pi$
$617$	−5.70850			−0.229815			−0.114908	+	0.993376i	$0.536657\pi$
$618$		0			0
$619$	6.70850	+	11.6195i	0.269637	+	0.467025i	0.968768	−	0.247968i	$-0.0797629\pi$
$619$	6.70850	+	11.6195i	0.269637	+	0.467025i	−0.699131	+	0.714994i	$0.746430\pi$
$620$		0			0
$621$	−2.17712	+	3.77089i	−0.0873650	+	0.151321i
$622$		0			0
$623$	8.70850	+	15.0836i	0.348899	+	0.604310i
$624$		0			0
$625$	4.14575	−	7.18065i	0.165830	−	0.287226i
$626$		0			0
$627$	−7.46863	−	12.9360i	−0.298268	−	0.516616i
$628$		0			0
$629$	21.8745			0.872194
$630$		0			0
$631$	12.8118			0.510028			0.255014	−	0.966937i	$-0.417920\pi$
$631$	12.8118			0.510028			0.255014	+	0.966937i	$0.417920\pi$
$632$		0			0
$633$	−1.23987	−	2.14752i	−0.0492804	−	0.0853562i
$634$		0			0
$635$	−13.1144	+	22.7148i	−0.520428	+	0.901408i
$636$		0			0
$637$	−17.5000	−	30.3109i	−0.693375	−	1.20096i
$638$		0			0
$639$	8.70850	−	15.0836i	0.344503	−	0.596696i
$640$		0			0
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	0.710437	−	0.703761i	$-0.248497\pi$
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	−0.964693	+	0.263376i	$0.915164\pi$
$642$		0			0
$643$	30.5203			1.20360			0.601801	−	0.798646i	$-0.294450\pi$
$643$	30.5203			1.20360			0.601801	+	0.798646i	$0.294450\pi$
$644$		0			0
$645$	17.4170			0.685793
$646$		0			0
$647$	−4.40588	−	7.63121i	−0.173213	−	0.300014i	0.766328	−	0.642449i	$-0.222082\pi$
$647$	−4.40588	−	7.63121i	−0.173213	−	0.300014i	−0.939541	+	0.342435i	$0.888748\pi$
$648$		0			0
$649$	−2.32288	+	4.02334i	−0.0911808	+	0.157930i
$650$		0			0
$651$	−14.0000	−	24.2487i	−0.548703	−	0.950382i
$652$		0			0
$653$	−3.82288	+	6.62141i	−0.149601	+	0.259116i	−0.931080	−	0.364815i	$-0.881132\pi$
$653$	−3.82288	+	6.62141i	−0.149601	+	0.259116i	0.781479	+	0.623931i	$0.214465\pi$
$654$		0			0
$655$	−8.52026	−	14.7575i	−0.332914	−	0.576624i
$656$		0			0
$657$	1.41699			0.0552822
$658$		0			0
$659$	6.58301			0.256437			0.128219	−	0.991746i	$-0.459074\pi$
$659$	6.58301			0.256437			0.128219	+	0.991746i	$0.459074\pi$
$660$		0			0
$661$	−3.70850	−	6.42331i	−0.144244	−	0.249838i	0.784847	−	0.619690i	$-0.212742\pi$
$661$	−3.70850	−	6.42331i	−0.144244	−	0.249838i	−0.929091	+	0.369852i	$0.879408\pi$
$662$		0			0
$663$	39.6863	−	68.7386i	1.54129	−	2.66959i
$664$		0			0
$665$	24.5830			0.953288
$666$		0			0
$667$	5.17712	−	8.96704i	0.200459	−	0.347205i
$668$		0			0
$669$	23.3431	+	40.4315i	0.902498	+	1.56317i
$670$		0			0
$671$	−14.2915			−0.551717
$672$		0			0
$673$	0.937254			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$673$	0.937254			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$674$		0			0
$675$	−3.03137	−	5.25049i	−0.116678	−	0.202092i
$676$		0			0
$677$	16.9373	−	29.3362i	0.650952	−	1.12748i	−0.331941	−	0.943300i	$-0.607703\pi$
$677$	16.9373	−	29.3362i	0.650952	−	1.12748i	0.982892	−	0.184181i	$-0.0589632\pi$
$678$		0			0
$679$	−21.5516	+	37.3285i	−0.827076	+	1.43254i
$680$		0			0
$681$	3.58301	−	6.20595i	0.137301	−	0.237812i
$682$		0			0
$683$	0.968627	+	1.67771i	0.0370635	+	0.0641958i	0.883962	−	0.467559i	$-0.154866\pi$
$683$	0.968627	+	1.67771i	0.0370635	+	0.0641958i	−0.846899	+	0.531754i	$0.821533\pi$
$684$		0			0
$685$	21.1882			0.809561
$686$		0			0
$687$	42.3320			1.61507
$688$		0			0
$689$	−4.11438	−	7.12631i	−0.156745	−	0.271491i
$690$		0			0
$691$	−22.6144	+	39.1693i	−0.860291	+	1.49007i	0.0113561	+	0.999936i	$0.496385\pi$
$691$	−22.6144	+	39.1693i	−0.860291	+	1.49007i	−0.871648	+	0.490133i	$0.836948\pi$
$692$		0			0
$693$	−5.29150	+	9.16515i	−0.201008	+	0.348155i
$694$		0			0
$695$	3.29150	−	5.70105i	0.124854	−	0.216253i
$696$		0			0
$697$	−32.8118	−	56.8316i	−1.24283	−	2.15265i
$698$		0			0
$699$	−2.81176			−0.106351
$700$		0			0
$701$	24.8745			0.939497			0.469749	−	0.882800i	$-0.344345\pi$
$701$	24.8745			0.939497			0.469749	+	0.882800i	$0.344345\pi$
$702$		0			0
$703$	−10.2915	−	17.8254i	−0.388151	−	0.672298i
$704$		0			0
$705$	5.89674	−	10.2134i	0.222084	−	0.384661i
$706$		0			0
$707$	−7.93725			−0.298511
$708$		0			0
$709$	−20.4059	+	35.3440i	−0.766359	+	1.32737i	0.173166	+	0.984893i	$0.444600\pi$
$709$	−20.4059	+	35.3440i	−0.766359	+	1.32737i	−0.939525	+	0.342480i	$0.888733\pi$
$710$		0			0
$711$	−5.29150	−	9.16515i	−0.198447	−	0.343720i
$712$		0			0
$713$	−6.58301			−0.246535
$714$		0			0
$715$	8.22876			0.307738
$716$		0			0
$717$	22.7915	+	39.4760i	0.851164	+	1.47426i
$718$		0			0
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	−0.479964	−	0.877288i	$-0.659350\pi$
$719$	13.9373	−	24.1400i	0.519772	−	0.900271i	0.999736	−	0.0229831i	$-0.00731639\pi$
$720$		0			0
$721$	3.88562	+	6.73009i	0.144708	+	0.250642i
$722$		0			0
$723$	−32.8229	+	56.8509i	−1.22070	+	2.11431i
$724$		0			0
$725$	7.20850	+	12.4855i	0.267717	+	0.463699i
$726$		0			0
$727$	6.70850			0.248804			0.124402	−	0.992232i	$-0.460299\pi$
$727$	6.70850			0.248804			0.124402	+	0.992232i	$0.460299\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	5.72876	−	9.92250i	0.211596	−	0.366496i	−0.740618	−	0.671926i	$-0.765467\pi$
$733$	5.72876	−	9.92250i	0.211596	−	0.366496i	0.952214	+	0.305431i	$0.0988004\pi$
$734$		0			0
$735$	−15.2399	−	26.3962i	−0.562131	−	0.973640i
$736$		0			0
$737$	5.96863	−	10.3380i	0.219857	−	0.380804i
$738$		0			0
$739$	11.9373	+	20.6759i	0.439119	+	0.760576i	0.997622	−	0.0689263i	$-0.0219573\pi$
$739$	11.9373	+	20.6759i	0.439119	+	0.760576i	−0.558503	+	0.829503i	$0.688624\pi$
$740$		0			0
$741$	−74.6863			−2.74367
$742$		0			0
$743$	45.2915			1.66158			0.830792	−	0.556583i	$-0.187888\pi$
$743$	45.2915			1.66158			0.830792	+	0.556583i	$0.187888\pi$
$744$		0			0
$745$	−12.5830	−	21.7944i	−0.461006	−	0.798485i
$746$		0			0
$747$	5.41699	−	9.38251i	0.198197	−	0.343288i
$748$		0			0
$749$	14.4686	+	25.0604i	0.528672	+	0.915687i
$750$		0			0
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	−0.974265	−	0.225407i	$-0.927629\pi$
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	0.682341	+	0.731034i	$0.260962\pi$
$752$		0			0
$753$	4.35425	+	7.54178i	0.158678	+	0.274838i
$754$		0			0
$755$	−14.2288			−0.517837
$756$		0			0
$757$	−23.1660			−0.841983			−0.420991	−	0.907065i	$-0.638318\pi$
$757$	−23.1660			−0.841983			−0.420991	+	0.907065i	$0.638318\pi$
$758$		0			0
$759$	2.17712	+	3.77089i	0.0790246	+	0.136875i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$		0			0
$763$	28.0000			1.01367
$764$		0			0
$765$	19.7490	−	34.2063i	0.714027	−	1.23673i
$766$		0			0
$767$	11.6144	+	20.1167i	0.419371	+	0.726372i
$768$		0			0
$769$	27.1660			0.979631			0.489816	−	0.871826i	$-0.337064\pi$
$769$	27.1660			0.979631			0.489816	+	0.871826i	$0.337064\pi$
$770$		0			0
$771$	57.1033			2.05652
$772$		0			0
$773$	9.29150	+	16.0934i	0.334192	+	0.578838i	0.983329	−	0.181834i	$-0.0582032\pi$
$773$	9.29150	+	16.0934i	0.334192	+	0.578838i	−0.649137	+	0.760671i	$0.724870\pi$
$774$		0			0
$775$	4.58301	−	7.93800i	0.164626	−	0.285141i
$776$		0			0
$777$	−12.7601	+	22.1012i	−0.457767	+	0.792876i
$778$		0			0
$779$	−30.8745	+	53.4762i	−1.10619	+	1.91598i
$780$		0			0
$781$	−2.17712	−	3.77089i	−0.0779036	−	0.134933i
$782$		0			0
$783$	−16.6458			−0.594871
$784$		0			0
$785$	−34.8340			−1.24328
$786$		0			0
$787$	23.4059	+	40.5402i	0.834330	+	1.44510i	0.894575	+	0.446918i	$0.147478\pi$
$787$	23.4059	+	40.5402i	0.834330	+	1.44510i	−0.0602456	+	0.998184i	$0.519188\pi$
$788$		0			0
$789$	−26.3745	+	45.6820i	−0.938957	+	1.62632i
$790$		0			0
$791$	−24.1974	+	41.9111i	−0.860360	+	1.49019i
$792$		0			0
$793$	−35.7288	+	61.8840i	−1.26877	+	2.19757i
$794$		0			0
$795$	−3.58301	−	6.20595i	−0.127076	−	0.220102i
$796$		0			0
$797$	7.16601			0.253833			0.126917	−	0.991913i	$-0.459492\pi$
$797$	7.16601			0.253833			0.126917	+	0.991913i	$0.459492\pi$
$798$		0			0
$799$	−16.2510			−0.574918
$800$		0			0
$801$	−13.1660	−	22.8042i	−0.465198	−	0.805747i
$802$		0			0
$803$	0.177124	−	0.306788i	0.00625058	−	0.0108263i
$804$		0			0
$805$	−7.16601			−0.252569
$806$		0			0
$807$	7.16601	−	12.4119i	0.252256	−	0.436919i
$808$		0			0
$809$	−14.7085	−	25.4759i	−0.517123	−	0.895684i	−0.999802	−	0.0198864i	$-0.993670\pi$
$809$	−14.7085	−	25.4759i	−0.517123	−	0.895684i	0.482679	−	0.875797i	$-0.339664\pi$
$810$		0			0
$811$	35.7490			1.25532			0.627659	−	0.778489i	$-0.284013\pi$
$811$	35.7490			1.25532			0.627659	+	0.778489i	$0.284013\pi$
$812$		0			0
$813$	−5.45751			−0.191403
$814$		0			0
$815$	−0.531373	−	0.920365i	−0.0186132	−	0.0322390i
$816$		0			0
$817$	−11.2915	+	19.5575i	−0.395040	+	0.684229i
$818$		0			0
$819$	26.4575	+	45.8258i	0.924500	+	1.60128i
$820$		0			0
$821$	9.14575	−	15.8409i	0.319189	−	0.552851i	−0.661130	−	0.750271i	$-0.729923\pi$
$821$	9.14575	−	15.8409i	0.319189	−	0.552851i	0.980319	+	0.197420i	$0.0632562\pi$
$822$		0			0
$823$	−6.06275	−	10.5010i	−0.211334	−	0.366041i	0.740798	−	0.671728i	$-0.234447\pi$
$823$	−6.06275	−	10.5010i	−0.211334	−	0.366041i	−0.952132	+	0.305686i	$0.901114\pi$
$824$		0			0
$825$	−6.06275			−0.211078
$826$		0			0
$827$	−33.3948			−1.16125			−0.580625	−	0.814171i	$-0.697192\pi$
$827$	−33.3948			−1.16125			−0.580625	+	0.814171i	$0.697192\pi$
$828$		0			0
$829$	12.6974	+	21.9925i	0.440998	+	0.763832i	0.997764	−	0.0668382i	$-0.0212911\pi$
$829$	12.6974	+	21.9925i	0.440998	+	0.763832i	−0.556765	+	0.830670i	$0.687958\pi$
$830$		0			0
$831$	−29.4889	+	51.0762i	−1.02296	+	1.77182i
$832$		0			0
$833$	−21.0000	+	36.3731i	−0.727607	+	1.26025i
$834$		0			0
$835$	9.23987	−	16.0039i	0.319759	−	0.553839i
$836$		0			0
$837$	5.29150	+	9.16515i	0.182901	+	0.316794i
$838$		0			0
$839$	3.87451			0.133763			0.0668814	−	0.997761i	$-0.478695\pi$
$839$	3.87451			0.133763			0.0668814	+	0.997761i	$0.478695\pi$
$840$		0			0
$841$	10.5830			0.364931
$842$		0			0
$843$	−30.3431	−	52.5559i	−1.04507	−	1.81012i
$844$		0			0
$845$	9.87451	−	17.1031i	0.339693	−	0.588366i
$846$		0			0
$847$	1.32288	+	2.29129i	0.0454545	+	0.0787296i
$848$		0			0
$849$	3.11438	−	5.39426i	0.106885	−	0.185131i
$850$		0			0
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		0			0
$853$	39.1660			1.34102			0.670509	−	0.741901i	$-0.266076\pi$
$853$	39.1660			1.34102			0.670509	+	0.741901i	$0.266076\pi$
$854$		0			0
$855$	−37.1660			−1.27105
$856$		0			0
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	−0.990408	−	0.138177i	$-0.955876\pi$
$857$	−18.0000	−	31.1769i	−0.614868	−	1.06498i	0.375539	−	0.926806i	$-0.377458\pi$
$858$		0			0
$859$	−4.90588	+	8.49723i	−0.167386	+	0.289922i	−0.937500	−	0.347985i	$-0.886866\pi$
$859$	−4.90588	+	8.49723i	−0.167386	+	0.289922i	0.770114	+	0.637907i	$0.220199\pi$
$860$		0			0
$861$	76.5608			2.60918
$862$		0			0
$863$	−6.23987	+	10.8078i	−0.212408	+	0.367901i	−0.952468	−	0.304640i	$-0.901464\pi$
$863$	−6.23987	+	10.8078i	−0.212408	+	0.367901i	0.740060	+	0.672541i	$0.234797\pi$
$864$		0			0
$865$	−0.239870	−	0.415468i	−0.00815584	−	0.0141263i
$866$		0			0
$867$	−50.2693			−1.70723
$868$		0			0
$869$	−2.64575			−0.0897510
$870$		0			0
$871$	−29.8431	−	51.6898i	−1.01120	−	1.75144i
$872$		0			0
$873$	32.5830	−	56.4354i	1.10277	−	1.91005i
$874$		0			0
$875$	15.8745	−	27.4955i	0.536656	−	0.929516i
$876$		0			0
$877$	11.4373	−	19.8099i	0.386209	−	0.668933i	−0.605727	−	0.795672i	$-0.707118\pi$
$877$	11.4373	−	19.8099i	0.386209	−	0.668933i	0.991936	+	0.126739i	$0.0404511\pi$
$878$		0			0
$879$	15.8745	+	27.4955i	0.535434	+	0.927399i
$880$		0			0
$881$	−24.8745			−0.838043			−0.419022	−	0.907976i	$-0.637627\pi$
$881$	−24.8745			−0.838043			−0.419022	+	0.907976i	$0.637627\pi$
$882$		0			0
$883$	−21.9373			−0.738247			−0.369124	−	0.929380i	$-0.620342\pi$
$883$	−21.9373			−0.738247			−0.369124	+	0.929380i	$0.620342\pi$
$884$		0			0
$885$	10.1144	+	17.5186i	0.339991	+	0.588882i
$886$		0			0
$887$	22.5516	−	39.0606i	0.757210	−	1.31153i	−0.187059	−	0.982349i	$-0.559895\pi$
$887$	22.5516	−	39.0606i	0.757210	−	1.31153i	0.944268	−	0.329177i	$-0.106771\pi$
$888$		0			0
$889$	−21.0830	+	36.5168i	−0.707101	+	1.22474i
$890$		0			0
$891$	−2.50000	+	4.33013i	−0.0837532	+	0.145065i
$892$		0			0
$893$	7.64575	+	13.2428i	0.255855	+	0.443154i
$894$		0			0
$895$	−32.8118			−1.09678
$896$		0			0
$897$	21.7712			0.726921
$898$		0			0
$899$	−12.5830	−	21.7944i	−0.419667	−	0.726884i
$900$		0			0
$901$	−4.93725	+	8.55157i	−0.164484	+	0.284894i
$902$		0			0
$903$	28.0000			0.931782
$904$		0			0
$905$	−8.22876	+	14.2526i	−0.273533	+	0.473773i
$906$		0			0
$907$	21.2288	+	36.7693i	0.704889	+	1.22090i	0.966731	+	0.255793i	$0.0823367\pi$
$907$	21.2288	+	36.7693i	0.704889	+	1.22090i	−0.261842	+	0.965111i	$0.584330\pi$
$908$		0			0
$909$	12.0000			0.398015
$910$		0			0
$911$	−9.29150			−0.307841			−0.153921	−	0.988083i	$-0.549190\pi$
$911$	−9.29150			−0.307841			−0.153921	+	0.988083i	$0.549190\pi$
$912$		0			0
$913$	−1.35425	−	2.34563i	−0.0448191	−	0.0776289i
$914$		0			0
$915$	−31.1144	+	53.8917i	−1.02861	+	1.78160i
$916$		0			0
$917$	−13.6974	−	23.7246i	−0.452327	−	0.783454i
$918$		0			0
$919$	−12.3542	+	21.3982i	−0.407529	+	0.705861i	−0.994612	−	0.103666i	$-0.966943\pi$
$919$	−12.3542	+	21.3982i	−0.407529	+	0.705861i	0.587083	+	0.809527i	$0.300276\pi$
$920$		0			0
$921$	−29.4059	−	50.9325i	−0.968957	−	1.67828i
$922$		0			0
$923$	−21.7712			−0.716609
$924$		0			0
$925$	−8.35425			−0.274686
$926$		0			0
$927$	−5.87451	−	10.1749i	−0.192944	−	0.334189i
$928$		0			0
$929$	−7.20850	+	12.4855i	−0.236503	+	0.409635i	−0.959708	−	0.280998i	$-0.909335\pi$
$929$	−7.20850	+	12.4855i	−0.236503	+	0.409635i	0.723205	+	0.690633i	$0.242668\pi$
$930$		0			0
$931$	39.5203			1.29522
$932$		0			0
$933$	−1.40588	+	2.43506i	−0.0460265	+	0.0797202i
$934$		0			0
$935$	−4.93725	−	8.55157i	−0.161465	−	0.279666i
$936$		0			0
$937$	32.6863			1.06781			0.533907	−	0.845543i	$-0.320723\pi$
$937$	32.6863			1.06781			0.533907	+	0.845543i	$0.320723\pi$
$938$		0			0
$939$	−62.3948			−2.03618
$940$		0			0
$941$	−25.3118	−	43.8413i	−0.825140	−	1.42918i	−0.901812	−	0.432128i	$-0.857763\pi$
$941$	−25.3118	−	43.8413i	−0.825140	−	1.42918i	0.0766725	−	0.997056i	$-0.475570\pi$
$942$		0			0
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$		0			0
$945$	5.76013	+	9.97684i	0.187377	+	0.324547i
$946$		0			0
$947$	−1.06275	+	1.84073i	−0.0345346	+	0.0598157i	−0.882776	−	0.469794i	$-0.844328\pi$
$947$	−1.06275	+	1.84073i	−0.0345346	+	0.0598157i	0.848242	+	0.529610i	$0.177662\pi$
$948$		0			0
$949$	−0.885622	−	1.53394i	−0.0287485	−	0.0497939i
$950$		0			0
$951$	−31.7490			−1.02953
$952$		0			0
$953$	11.5203			0.373178			0.186589	−	0.982438i	$-0.440257\pi$
$953$	11.5203			0.373178			0.186589	+	0.982438i	$0.440257\pi$
$954$		0			0
$955$	2.22876	+	3.86032i	0.0721209	+	0.124917i
$956$		0			0
$957$	−8.32288	+	14.4156i	−0.269040	+	0.465992i
$958$		0			0
$959$	34.0627			1.09994
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−21.8745	−	37.8878i	−0.704896	−	1.22092i
$964$		0			0
$965$	−42.0000			−1.35203
$966$		0			0
$967$	−58.3320			−1.87583			−0.937916	−	0.346863i	$-0.887247\pi$
$967$	−58.3320			−1.87583			−0.937916	+	0.346863i	$0.887247\pi$
$968$		0			0
$969$	44.8118	+	77.6162i	1.43956	+	2.49339i
$970$		0			0
$971$	−5.03137	+	8.71459i	−0.161464	+	0.279665i	−0.935394	−	0.353607i	$-0.884955\pi$
$971$	−5.03137	+	8.71459i	−0.161464	+	0.279665i	0.773930	+	0.633272i	$0.218288\pi$
$972$		0			0
$973$	5.29150	−	9.16515i	0.169638	−	0.293821i
$974$		0			0
$975$	−15.1569	+	26.2525i	−0.485408	+	0.840752i
$976$		0			0
$977$	8.22876	+	14.2526i	0.263261	+	0.455982i	0.967107	−	0.254371i	$-0.0818685\pi$
$977$	8.22876	+	14.2526i	0.263261	+	0.455982i	−0.703845	+	0.710353i	$0.748535\pi$
$978$		0			0
$979$	−6.58301			−0.210394
$980$		0			0
$981$	−42.3320			−1.35156
$982$		0			0
$983$	−13.3542	−	23.1302i	−0.425934	−	0.737740i	0.570573	−	0.821247i	$-0.306721\pi$
$983$	−13.3542	−	23.1302i	−0.425934	−	0.737740i	−0.996507	+	0.0835070i	$0.973388\pi$
$984$		0			0
$985$	−10.5941	+	18.3496i	−0.337557	+	0.584665i
$986$		0			0
$987$	9.47974	−	16.4194i	0.301743	−	0.522635i
$988$		0			0
$989$	3.29150	−	5.70105i	0.104664	−	0.181283i
$990$		0			0
$991$	−11.3431	−	19.6469i	−0.360327	−	0.624104i	0.627688	−	0.778465i	$-0.284001\pi$
$991$	−11.3431	−	19.6469i	−0.360327	−	0.624104i	−0.988014	+	0.154361i	$0.950668\pi$
$992$		0			0
$993$	−54.6235			−1.73343
$994$		0			0
$995$	6.95948			0.220630
$996$		0			0
$997$	10.7085	+	18.5477i	0.339142	+	0.587410i	0.984271	−	0.176663i	$-0.0565301\pi$
$997$	10.7085	+	18.5477i	0.339142	+	0.587410i	−0.645130	+	0.764073i	$0.723197\pi$
$998$		0			0
$999$	4.82288	−	8.35347i	0.152589	−	0.264292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.g.177.2		4
4.3	odd	2		154.2.e.f.23.1	✓	4
7.2	even	3		8624.2.a.ca.1.1		2
7.4	even	3	inner	1232.2.q.g.529.2		4
7.5	odd	6		8624.2.a.bk.1.2		2
12.11	even	2		1386.2.k.s.793.1		4
28.3	even	6		1078.2.e.v.67.2		4
28.11	odd	6		154.2.e.f.67.1	yes	4
28.19	even	6		1078.2.a.n.1.1		2
28.23	odd	6		1078.2.a.s.1.2		2
28.27	even	2		1078.2.e.v.177.2		4
84.11	even	6		1386.2.k.s.991.1		4
84.23	even	6		9702.2.a.cz.1.2		2
84.47	odd	6		9702.2.a.dr.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.f.23.1	✓	4	4.3	odd	2
154.2.e.f.67.1	yes	4	28.11	odd	6
1078.2.a.n.1.1		2	28.19	even	6
1078.2.a.s.1.2		2	28.23	odd	6
1078.2.e.v.67.2		4	28.3	even	6
1078.2.e.v.177.2		4	28.27	even	2
1232.2.q.g.177.2		4	1.1	even	1	trivial
1232.2.q.g.529.2		4	7.4	even	3	inner
1386.2.k.s.793.1		4	12.11	even	2
1386.2.k.s.991.1		4	84.11	even	6
8624.2.a.bk.1.2		2	7.5	odd	6
8624.2.a.ca.1.1		2	7.2	even	3
9702.2.a.cz.1.2		2	84.23	even	6
9702.2.a.dr.1.1		2	84.47	odd	6

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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32288 + 2.29129i) q^{3} +(0.822876 - 1.42526i) q^{5} +(1.32288 - 2.29129i) q^{7} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(1.32288 + 2.29129i) q^{3} +(0.822876 - 1.42526i) q^{5} +(1.32288 - 2.29129i) q^{7} +(-2.00000 + 3.46410i) q^{9} +(0.500000 + 0.866025i) q^{11} +5.00000 q^{13} +4.35425 q^{15} +(-3.00000 - 5.19615i) q^{17} +(-2.82288 + 4.88936i) q^{19} +7.00000 q^{21} +(0.822876 - 1.42526i) q^{23} +(1.14575 + 1.98450i) q^{25} -2.64575 q^{27} +6.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(-1.32288 + 2.29129i) q^{33} +(-2.17712 - 3.77089i) q^{35} +(-1.82288 + 3.15731i) q^{37} +(6.61438 + 11.4564i) q^{39} +10.9373 q^{41} +4.00000 q^{43} +(3.29150 + 5.70105i) q^{45} +(1.35425 - 2.34563i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(7.93725 - 13.7477i) q^{51} +(-0.822876 - 1.42526i) q^{53} +1.64575 q^{55} -14.9373 q^{57} +(2.32288 + 4.02334i) q^{59} +(-7.14575 + 12.3768i) q^{61} +(5.29150 + 9.16515i) q^{63} +(4.11438 - 7.12631i) q^{65} +(-5.96863 - 10.3380i) q^{67} +4.35425 q^{69} -4.35425 q^{71} +(-0.177124 - 0.306788i) q^{73} +(-3.03137 + 5.25049i) q^{75} +2.64575 q^{77} +(-1.32288 + 2.29129i) q^{79} +(2.50000 + 4.33013i) q^{81} -2.70850 q^{83} -9.87451 q^{85} +(8.32288 + 14.4156i) q^{87} +(-3.29150 + 5.70105i) q^{89} +(6.61438 - 11.4564i) q^{91} +(5.29150 - 9.16515i) q^{93} +(4.64575 + 8.04668i) q^{95} -16.2915 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{5} - 8 q^{9}+O(q^{10}) \) 4 * q - 2 * q^5 - 8 * q^9	\( 4 q - 2 q^{5} - 8 q^{9} + 2 q^{11} + 20 q^{13} + 28 q^{15} - 12 q^{17} - 6 q^{19} + 28 q^{21} - 2 q^{23} - 6 q^{25} + 4 q^{29} - 8 q^{31} - 14 q^{35} - 2 q^{37} + 12 q^{41} + 16 q^{43} - 8 q^{45} + 16 q^{47} - 14 q^{49} + 2 q^{53} - 4 q^{55} - 28 q^{57} + 4 q^{59} - 18 q^{61} - 10 q^{65} - 8 q^{67} + 28 q^{69} - 28 q^{71} - 6 q^{73} - 28 q^{75} + 10 q^{81} - 32 q^{83} + 24 q^{85} + 28 q^{87} + 8 q^{89} + 8 q^{95} - 44 q^{97} - 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^5 - 8 * q^9 + 2 * q^11 + 20 * q^13 + 28 * q^15 - 12 * q^17 - 6 * q^19 + 28 * q^21 - 2 * q^23 - 6 * q^25 + 4 * q^29 - 8 * q^31 - 14 * q^35 - 2 * q^37 + 12 * q^41 + 16 * q^43 - 8 * q^45 + 16 * q^47 - 14 * q^49 + 2 * q^53 - 4 * q^55 - 28 * q^57 + 4 * q^59 - 18 * q^61 - 10 * q^65 - 8 * q^67 + 28 * q^69 - 28 * q^71 - 6 * q^73 - 28 * q^75 + 10 * q^81 - 32 * q^83 + 24 * q^85 + 28 * q^87 + 8 * q^89 + 8 * q^95 - 44 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more