LMFDB - Embedded newform 228.2.i.b.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [228,2,Mod(49,228)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("228.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82058916609$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	228.49
Dual form			228.2.i.b.121.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{3} +(-1.82288 + 3.15731i) q^{5} +4.64575 q^{7} +(-0.500000 - 0.866025i) q^{9} +0.354249 q^{11} +(2.14575 + 3.71655i) q^{13} +(1.82288 + 3.15731i) q^{15} +(1.64575 - 2.85052i) q^{17} +(-2.64575 - 3.46410i) q^{19} +(2.32288 - 4.02334i) q^{21} +(2.82288 + 4.88936i) q^{23} +(-4.14575 - 7.18065i) q^{25} -1.00000 q^{27} +(-3.64575 - 6.31463i) q^{29} -0.645751 q^{31} +(0.177124 - 0.306788i) q^{33} +(-8.46863 + 14.6681i) q^{35} -5.00000 q^{37} +4.29150 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-2.67712 + 4.63692i) q^{43} +3.64575 q^{45} +(-2.64575 - 4.58258i) q^{47} +14.5830 q^{49} +(-1.64575 - 2.85052i) q^{51} +(-3.46863 - 6.00784i) q^{53} +(-0.645751 + 1.11847i) q^{55} +(-4.32288 + 0.559237i) q^{57} +(-3.82288 + 6.62141i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.32288 - 4.02334i) q^{63} -15.6458 q^{65} +(-6.96863 - 12.0700i) q^{67} +5.64575 q^{69} +(5.00000 - 8.66025i) q^{71} +(3.14575 - 5.44860i) q^{73} -8.29150 q^{75} +1.64575 q^{77} +(-1.67712 + 2.90486i) q^{79} +(-0.500000 + 0.866025i) q^{81} +15.2915 q^{83} +(6.00000 + 10.3923i) q^{85} -7.29150 q^{87} +(-6.82288 - 11.8176i) q^{89} +(9.96863 + 17.2662i) q^{91} +(-0.322876 + 0.559237i) q^{93} +(15.7601 - 2.03884i) q^{95} +(-5.29150 + 9.16515i) q^{97} +(-0.177124 - 0.306788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{5} + 8 q^{7} - 2 q^{9} + 12 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 4 q^{21} + 6 q^{23} - 6 q^{25} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 6 q^{33} - 18 q^{35} - 20 q^{37} - 4 q^{39} - 8 q^{41}+ \cdots - 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^5 + 8 * q^7 - 2 * q^9 + 12 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 4 * q^21 + 6 * q^23 - 6 * q^25 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 6 * q^33 - 18 * q^35 - 20 * q^37 - 4 * q^39 - 8 * q^41 - 16 * q^43 + 4 * q^45 + 16 * q^49 + 4 * q^51 + 2 * q^53 + 8 * q^55 - 12 * q^57 - 10 * q^59 - 10 * q^61 - 4 * q^63 - 52 * q^65 - 12 * q^67 + 12 * q^69 + 20 * q^71 + 2 * q^73 - 12 * q^75 - 4 * q^77 - 12 * q^79 - 2 * q^81 + 40 * q^83 + 24 * q^85 - 8 * q^87 - 22 * q^89 + 24 * q^91 + 4 * q^93 + 26 * q^95 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	0.0939588	+	0.995576i	$0.470048\pi$
$5$	−1.82288	+	3.15731i	−0.815215	+	1.41199i	−0.909174	+	0.416417i	$0.863286\pi$
$6$		0			0
$7$	4.64575			1.75593			0.877964	−	0.478726i	$-0.158901\pi$
$7$	4.64575			1.75593			0.877964	+	0.478726i	$0.158901\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.354249			0.106810			0.0534050	−	0.998573i	$-0.482993\pi$
$11$	0.354249			0.106810			0.0534050	+	0.998573i	$0.482993\pi$
$12$		0			0
$13$	2.14575	+	3.71655i	0.595124	+	1.03079i	0.993529	+	0.113576i	$0.0362305\pi$
$13$	2.14575	+	3.71655i	0.595124	+	1.03079i	−0.398405	+	0.917210i	$0.630436\pi$
$14$		0			0
$15$	1.82288	+	3.15731i	0.470664	+	0.815215i
$16$		0			0
$17$	1.64575	−	2.85052i	0.399153	−	0.691354i	−0.594468	−	0.804119i	$-0.702637\pi$
$17$	1.64575	−	2.85052i	0.399153	−	0.691354i	0.993622	+	0.112765i	$0.0359708\pi$
$18$		0			0
$19$	−2.64575	−	3.46410i	−0.606977	−	0.794719i
$19$	−2.64575	−	3.46410i	−0.606977	−	0.794719i
$20$		0			0
$21$	2.32288	−	4.02334i	0.506893	−	0.877964i
$22$		0			0
$23$	2.82288	+	4.88936i	0.588610	+	1.01950i	0.994415	+	0.105543i	$0.0336581\pi$
$23$	2.82288	+	4.88936i	0.588610	+	1.01950i	−0.405804	+	0.913960i	$0.633009\pi$
$24$		0			0
$25$	−4.14575	−	7.18065i	−0.829150	−	1.43613i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.64575	−	6.31463i	−0.676999	−	1.17260i	−0.975880	−	0.218306i	$-0.929947\pi$
$29$	−3.64575	−	6.31463i	−0.676999	−	1.17260i	0.298881	−	0.954290i	$-0.403387\pi$
$30$		0			0
$31$	−0.645751			−0.115980			−0.0579902	−	0.998317i	$-0.518469\pi$
$31$	−0.645751			−0.115980			−0.0579902	+	0.998317i	$0.518469\pi$
$32$		0			0
$33$	0.177124	−	0.306788i	0.0308334	−	0.0534050i
$34$		0			0
$35$	−8.46863	+	14.6681i	−1.43146	+	2.47936i
$36$		0			0
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$		0			0
$39$	4.29150			0.687190
$40$		0			0
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	−0.978870	−	0.204483i	$-0.934449\pi$
$41$	−2.00000	+	3.46410i	−0.312348	+	0.541002i	0.666523	+	0.745485i	$0.267782\pi$
$42$		0			0
$43$	−2.67712	+	4.63692i	−0.408258	+	0.707123i	−0.994695	−	0.102872i	$-0.967197\pi$
$43$	−2.67712	+	4.63692i	−0.408258	+	0.707123i	0.586437	+	0.809995i	$0.300530\pi$
$44$		0			0
$45$	3.64575			0.543477
$46$		0			0
$47$	−2.64575	−	4.58258i	−0.385922	−	0.668437i	0.605974	−	0.795484i	$-0.292783\pi$
$47$	−2.64575	−	4.58258i	−0.385922	−	0.668437i	−0.991897	+	0.127047i	$0.959450\pi$
$48$		0			0
$49$	14.5830			2.08329
$50$		0			0
$51$	−1.64575	−	2.85052i	−0.230451	−	0.399153i
$52$		0			0
$53$	−3.46863	−	6.00784i	−0.476453	−	0.825240i	0.523183	−	0.852220i	$-0.324744\pi$
$53$	−3.46863	−	6.00784i	−0.476453	−	0.825240i	−0.999636	+	0.0269801i	$0.991411\pi$
$54$		0			0
$55$	−0.645751	+	1.11847i	−0.0870731	+	0.150815i
$56$		0			0
$57$	−4.32288	+	0.559237i	−0.572579	+	0.0740728i
$58$		0			0
$59$	−3.82288	+	6.62141i	−0.497696	+	0.862035i	−0.999996	−	0.00265837i	$-0.999154\pi$
$59$	−3.82288	+	6.62141i	−0.497696	+	0.862035i	0.502300	+	0.864693i	$0.332487\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	−2.32288	−	4.02334i	−0.292655	−	0.506893i
$64$		0			0
$65$	−15.6458			−1.94062
$66$		0			0
$67$	−6.96863	−	12.0700i	−0.851353	−	1.47459i	−0.879987	−	0.474997i	$-0.842449\pi$
$67$	−6.96863	−	12.0700i	−0.851353	−	1.47459i	0.0286340	−	0.999590i	$-0.490884\pi$
$68$		0			0
$69$	5.64575			0.679669
$70$		0			0
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	−0.400381	−	0.916349i	$-0.631122\pi$
$71$	5.00000	−	8.66025i	0.593391	−	1.02778i	0.993772	−	0.111434i	$-0.0355445\pi$
$72$		0			0
$73$	3.14575	−	5.44860i	0.368182	−	0.637711i	−0.621099	−	0.783732i	$-0.713314\pi$
$73$	3.14575	−	5.44860i	0.368182	−	0.637711i	0.989281	+	0.146022i	$0.0466469\pi$
$74$		0			0
$75$	−8.29150			−0.957420
$76$		0			0
$77$	1.64575			0.187551
$78$		0			0
$79$	−1.67712	+	2.90486i	−0.188691	+	0.326823i	−0.944814	−	0.327607i	$-0.893758\pi$
$79$	−1.67712	+	2.90486i	−0.188691	+	0.326823i	0.756123	+	0.654430i	$0.227091\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	15.2915			1.67846			0.839230	−	0.543776i	$-0.183006\pi$
$83$	15.2915			1.67846			0.839230	+	0.543776i	$0.183006\pi$
$84$		0			0
$85$	6.00000	+	10.3923i	0.650791	+	1.12720i
$86$		0			0
$87$	−7.29150			−0.781731
$88$		0			0
$89$	−6.82288	−	11.8176i	−0.723223	−	1.25266i	−0.959701	−	0.281023i	$-0.909326\pi$
$89$	−6.82288	−	11.8176i	−0.723223	−	1.25266i	0.236478	−	0.971637i	$-0.424007\pi$
$90$		0			0
$91$	9.96863	+	17.2662i	1.04500	+	1.80999i
$92$		0			0
$93$	−0.322876	+	0.559237i	−0.0334806	+	0.0579902i
$94$		0			0
$95$	15.7601	−	2.03884i	1.61696	−	0.209180i
$96$		0			0
$97$	−5.29150	+	9.16515i	−0.537271	+	0.930580i	0.461779	+	0.886995i	$0.347211\pi$
$97$	−5.29150	+	9.16515i	−0.537271	+	0.930580i	−0.999050	+	0.0435851i	$0.986122\pi$
$98$		0			0
$99$	−0.177124	−	0.306788i	−0.0178017	−	0.0308334i
$100$		0			0
$101$	9.93725	+	17.2118i	0.988794	+	1.71264i	0.623684	+	0.781676i	$0.285635\pi$
$101$	9.93725	+	17.2118i	0.988794	+	1.71264i	0.365109	+	0.930965i	$0.381032\pi$
$102$		0			0
$103$	7.93725			0.782081			0.391040	−	0.920373i	$-0.372115\pi$
$103$	7.93725			0.782081			0.391040	+	0.920373i	$0.372115\pi$
$104$		0			0
$105$	8.46863	+	14.6681i	0.826453	+	1.43146i
$106$		0			0
$107$	14.0000			1.35343			0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000			1.35343			0.676716	+	0.736245i	$0.263403\pi$
$108$		0			0
$109$	4.35425	−	7.54178i	0.417061	−	0.722372i	−0.578581	−	0.815625i	$-0.696393\pi$
$109$	4.35425	−	7.54178i	0.417061	−	0.722372i	0.995642	+	0.0932534i	$0.0297267\pi$
$110$		0			0
$111$	−2.50000	+	4.33013i	−0.237289	+	0.410997i
$112$		0			0
$113$	−5.64575			−0.531108			−0.265554	−	0.964096i	$-0.585555\pi$
$113$	−5.64575			−0.531108			−0.265554	+	0.964096i	$0.585555\pi$
$114$		0			0
$115$	−20.5830			−1.91938
$116$		0			0
$117$	2.14575	−	3.71655i	0.198375	−	0.343595i
$118$		0			0
$119$	7.64575	−	13.2428i	0.700885	−	1.21397i
$120$		0			0
$121$	−10.8745			−0.988592
$122$		0			0
$123$	2.00000	+	3.46410i	0.180334	+	0.312348i
$124$		0			0
$125$	12.0000			1.07331
$126$		0			0
$127$	1.64575	+	2.85052i	0.146037	+	0.252943i	0.929759	−	0.368168i	$-0.120015\pi$
$127$	1.64575	+	2.85052i	0.146037	+	0.252943i	−0.783722	+	0.621111i	$0.786682\pi$
$128$		0			0
$129$	2.67712	+	4.63692i	0.235708	+	0.408258i
$130$		0			0
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	−0.966803	−	0.255524i	$-0.917752\pi$
$131$	−3.00000	+	5.19615i	−0.262111	+	0.453990i	0.704692	+	0.709514i	$0.251085\pi$
$132$		0			0
$133$	−12.2915	−	16.0934i	−1.06581	−	1.39547i
$134$		0			0
$135$	1.82288	−	3.15731i	0.156888	−	0.271738i
$136$		0			0
$137$	−6.64575	−	11.5108i	−0.567785	−	0.983432i	−0.996785	−	0.0801276i	$-0.974467\pi$
$137$	−6.64575	−	11.5108i	−0.567785	−	0.983432i	0.429000	−	0.903305i	$-0.358866\pi$
$138$		0			0
$139$	2.32288	+	4.02334i	0.197024	+	0.341255i	0.947562	−	0.319572i	$-0.103539\pi$
$139$	2.32288	+	4.02334i	0.197024	+	0.341255i	−0.750538	+	0.660827i	$0.770206\pi$
$140$		0			0
$141$	−5.29150			−0.445625
$142$		0			0
$143$	0.760130	+	1.31658i	0.0635652	+	0.110098i
$144$		0			0
$145$	26.5830			2.20760
$146$		0			0
$147$	7.29150	−	12.6293i	0.601393	−	1.04164i
$148$		0			0
$149$	0.822876	−	1.42526i	0.0674126	−	0.116762i	−0.830349	−	0.557244i	$-0.811859\pi$
$149$	0.822876	−	1.42526i	0.0674126	−	0.116762i	0.897762	+	0.440482i	$0.145192\pi$
$150$		0			0
$151$	−0.708497			−0.0576567			−0.0288283	−	0.999584i	$-0.509178\pi$
$151$	−0.708497			−0.0576567			−0.0288283	+	0.999584i	$0.509178\pi$
$152$		0			0
$153$	−3.29150			−0.266102
$154$		0			0
$155$	1.17712	−	2.03884i	0.0945489	−	0.163764i
$156$		0			0
$157$	−5.14575	+	8.91270i	−0.410676	+	0.711311i	−0.994964	−	0.100235i	$-0.968040\pi$
$157$	−5.14575	+	8.91270i	−0.410676	+	0.711311i	0.584288	+	0.811546i	$0.301374\pi$
$158$		0			0
$159$	−6.93725			−0.550160
$160$		0			0
$161$	13.1144	+	22.7148i	1.03356	+	1.79017i
$162$		0			0
$163$	0.0627461			0.00491465			0.00245733	−	0.999997i	$-0.499218\pi$
$163$	0.0627461			0.00491465			0.00245733	+	0.999997i	$0.499218\pi$
$164$		0			0
$165$	0.645751	+	1.11847i	0.0502717	+	0.0870731i
$166$		0			0
$167$	−0.531373	−	0.920365i	−0.0411189	−	0.0712200i	0.844734	−	0.535187i	$-0.179759\pi$
$167$	−0.531373	−	0.920365i	−0.0411189	−	0.0712200i	−0.885852	+	0.463967i	$0.846426\pi$
$168$		0			0
$169$	−2.70850	+	4.69126i	−0.208346	+	0.360866i
$170$		0			0
$171$	−1.67712	+	4.02334i	−0.128253	+	0.307672i
$172$		0			0
$173$	4.93725	−	8.55157i	0.375372	−	0.650164i	−0.615010	−	0.788519i	$-0.710848\pi$
$173$	4.93725	−	8.55157i	0.375372	−	0.650164i	0.990383	+	0.138355i	$0.0441815\pi$
$174$		0			0
$175$	−19.2601	−	33.3595i	−1.45593	−	2.52174i
$176$		0			0
$177$	3.82288	+	6.62141i	0.287345	+	0.497696i
$178$		0			0
$179$	−10.3542			−0.773913			−0.386956	−	0.922098i	$-0.626474\pi$
$179$	−10.3542			−0.773913			−0.386956	+	0.922098i	$0.626474\pi$
$180$		0			0
$181$	13.2915	+	23.0216i	0.987950	+	1.71118i	0.628015	+	0.778202i	$0.283868\pi$
$181$	13.2915	+	23.0216i	0.987950	+	1.71118i	0.359935	+	0.932977i	$0.382799\pi$
$182$		0			0
$183$	−5.00000			−0.369611
$184$		0			0
$185$	9.11438	−	15.7866i	0.670102	−	1.16065i
$186$		0			0
$187$	0.583005	−	1.00979i	0.0426336	−	0.0738435i
$188$		0			0
$189$	−4.64575			−0.337929
$190$		0			0
$191$	−0.937254			−0.0678173			−0.0339087	−	0.999425i	$-0.510796\pi$
$191$	−0.937254			−0.0678173			−0.0339087	+	0.999425i	$0.510796\pi$
$192$		0			0
$193$	−11.0830	+	19.1963i	−0.797772	+	1.38178i	0.123292	+	0.992370i	$0.460655\pi$
$193$	−11.0830	+	19.1963i	−0.797772	+	1.38178i	−0.921064	+	0.389411i	$0.872678\pi$
$194$		0			0
$195$	−7.82288	+	13.5496i	−0.560208	+	0.970308i
$196$		0			0
$197$	−17.6458			−1.25721			−0.628604	−	0.777726i	$-0.716373\pi$
$197$	−17.6458			−1.25721			−0.628604	+	0.777726i	$0.716373\pi$
$198$		0			0
$199$	5.96863	+	10.3380i	0.423105	+	0.732839i	0.996241	−	0.0866209i	$-0.0276069\pi$
$199$	5.96863	+	10.3380i	0.423105	+	0.732839i	−0.573137	+	0.819460i	$0.694274\pi$
$200$		0			0
$201$	−13.9373			−0.983058
$202$		0			0
$203$	−16.9373	−	29.3362i	−1.18876	−	2.05900i
$204$		0			0
$205$	−7.29150	−	12.6293i	−0.509261	−	0.882065i
$206$		0			0
$207$	2.82288	−	4.88936i	0.196203	−	0.339834i
$208$		0			0
$209$	−0.937254	−	1.22715i	−0.0648312	−	0.0848840i
$210$		0			0
$211$	−5.32288	+	9.21949i	−0.366442	+	0.634696i	−0.989006	−	0.147873i	$-0.952757\pi$
$211$	−5.32288	+	9.21949i	−0.366442	+	0.634696i	0.622565	+	0.782568i	$0.286091\pi$
$212$		0			0
$213$	−5.00000	−	8.66025i	−0.342594	−	0.593391i
$214$		0			0
$215$	−9.76013	−	16.9050i	−0.665635	−	1.15291i
$216$		0			0
$217$	−3.00000			−0.203653
$218$		0			0
$219$	−3.14575	−	5.44860i	−0.212570	−	0.368182i
$220$		0			0
$221$	14.1255			0.950183
$222$		0			0
$223$	2.67712	−	4.63692i	0.179274	−	0.310511i	−0.762358	−	0.647155i	$-0.775959\pi$
$223$	2.67712	−	4.63692i	0.179274	−	0.310511i	0.941632	+	0.336644i	$0.109292\pi$
$224$		0			0
$225$	−4.14575	+	7.18065i	−0.276383	+	0.478710i
$226$		0			0
$227$	15.5203			1.03012			0.515058	−	0.857155i	$-0.327770\pi$
$227$	15.5203			1.03012			0.515058	+	0.857155i	$0.327770\pi$
$228$		0			0
$229$	−9.70850			−0.641556			−0.320778	−	0.947154i	$-0.603944\pi$
$229$	−9.70850			−0.641556			−0.320778	+	0.947154i	$0.603944\pi$
$230$		0			0
$231$	0.822876	−	1.42526i	0.0541412	−	0.0937754i
$232$		0			0
$233$	1.93725	−	3.35542i	0.126914	−	0.219821i	−0.795566	−	0.605867i	$-0.792826\pi$
$233$	1.93725	−	3.35542i	0.126914	−	0.219821i	0.922479	+	0.386046i	$0.126160\pi$
$234$		0			0
$235$	19.2915			1.25844
$236$		0			0
$237$	1.67712	+	2.90486i	0.108941	+	0.188691i
$238$		0			0
$239$	4.93725			0.319364			0.159682	−	0.987168i	$-0.448953\pi$
$239$	4.93725			0.319364			0.159682	+	0.987168i	$0.448953\pi$
$240$		0			0
$241$	−5.43725	−	9.41760i	−0.350244	−	0.606641i	0.636048	−	0.771650i	$-0.280568\pi$
$241$	−5.43725	−	9.41760i	−0.350244	−	0.606641i	−0.986292	+	0.165009i	$0.947235\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$	−26.5830	+	46.0431i	−1.69833	+	2.94159i
$246$		0			0
$247$	7.19738	−	17.2662i	0.457959	−	1.09862i
$248$		0			0
$249$	7.64575	−	13.2428i	0.484530	−	0.839230i
$250$		0			0
$251$	6.64575	+	11.5108i	0.419476	+	0.726554i	0.995887	−	0.0906062i	$-0.0288805\pi$
$251$	6.64575	+	11.5108i	0.419476	+	0.726554i	−0.576411	+	0.817160i	$0.695547\pi$
$252$		0			0
$253$	1.00000	+	1.73205i	0.0628695	+	0.108893i
$254$		0			0
$255$	12.0000			0.751469
$256$		0			0
$257$	−7.82288	−	13.5496i	−0.487978	−	0.845202i	0.511927	−	0.859029i	$-0.328932\pi$
$257$	−7.82288	−	13.5496i	−0.487978	−	0.845202i	−0.999904	+	0.0138271i	$0.995599\pi$
$258$		0			0
$259$	−23.2288			−1.44336
$260$		0			0
$261$	−3.64575	+	6.31463i	−0.225666	+	0.390866i
$262$		0			0
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	25.2915			1.55364
$266$		0			0
$267$	−13.6458			−0.835106
$268$		0			0
$269$	6.82288	−	11.8176i	0.415998	−	0.720530i	−0.579535	−	0.814948i	$-0.696766\pi$
$269$	6.82288	−	11.8176i	0.415998	−	0.720530i	0.995533	+	0.0944179i	$0.0300990\pi$
$270$		0			0
$271$	−5.29150	+	9.16515i	−0.321436	+	0.556743i	−0.980785	−	0.195094i	$-0.937499\pi$
$271$	−5.29150	+	9.16515i	−0.321436	+	0.556743i	0.659349	+	0.751837i	$0.270832\pi$
$272$		0			0
$273$	19.9373			1.20666
$274$		0			0
$275$	−1.46863	−	2.54374i	−0.0885615	−	0.153393i
$276$		0			0
$277$	−8.00000			−0.480673			−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000			−0.480673			−0.240337	+	0.970690i	$0.577258\pi$
$278$		0			0
$279$	0.322876	+	0.559237i	0.0193301	+	0.0334806i
$280$		0			0
$281$	3.46863	+	6.00784i	0.206921	+	0.358398i	0.950743	−	0.309980i	$-0.100322\pi$
$281$	3.46863	+	6.00784i	0.206921	+	0.358398i	−0.743822	+	0.668378i	$0.766989\pi$
$282$		0			0
$283$	2.70850	−	4.69126i	0.161003	−	0.278866i	−0.774225	−	0.632910i	$-0.781860\pi$
$283$	2.70850	−	4.69126i	0.161003	−	0.278866i	0.935229	+	0.354044i	$0.115194\pi$
$284$		0			0
$285$	6.11438	−	14.6681i	0.362185	−	0.868863i
$286$		0			0
$287$	−9.29150	+	16.0934i	−0.548460	+	0.949961i
$288$		0			0
$289$	3.08301	+	5.33992i	0.181353	+	0.314113i
$290$		0			0
$291$	5.29150	+	9.16515i	0.310193	+	0.537271i
$292$		0			0
$293$	−24.5830			−1.43615			−0.718077	−	0.695963i	$-0.754978\pi$
$293$	−24.5830			−1.43615			−0.718077	+	0.695963i	$0.754978\pi$
$294$		0			0
$295$	−13.9373	−	24.1400i	−0.811458	−	1.40549i
$296$		0			0
$297$	−0.354249			−0.0205556
$298$		0			0
$299$	−12.1144	+	20.9827i	−0.700593	+	1.21346i
$300$		0			0
$301$	−12.4373	+	21.5420i	−0.716871	+	1.24166i
$302$		0			0
$303$	19.8745			1.14176
$304$		0			0
$305$	18.2288			1.04378
$306$		0			0
$307$	13.9373	−	24.1400i	0.795441	−	1.37774i	−0.127118	−	0.991888i	$-0.540573\pi$
$307$	13.9373	−	24.1400i	0.795441	−	1.37774i	0.922559	−	0.385857i	$-0.126094\pi$
$308$		0			0
$309$	3.96863	−	6.87386i	0.225767	−	0.391040i
$310$		0			0
$311$	17.0627			0.967540			0.483770	−	0.875195i	$-0.339267\pi$
$311$	17.0627			0.967540			0.483770	+	0.875195i	$0.339267\pi$
$312$		0			0
$313$	9.64575	+	16.7069i	0.545210	+	0.944332i	0.998594	+	0.0530161i	$0.0168835\pi$
$313$	9.64575	+	16.7069i	0.545210	+	0.944332i	−0.453384	+	0.891316i	$0.649783\pi$
$314$		0			0
$315$	16.9373			0.954306
$316$		0			0
$317$	5.46863	+	9.47194i	0.307149	+	0.531997i	0.977737	−	0.209832i	$-0.0672918\pi$
$317$	5.46863	+	9.47194i	0.307149	+	0.531997i	−0.670589	+	0.741829i	$0.733958\pi$
$318$		0			0
$319$	−1.29150	−	2.23695i	−0.0723103	−	0.125245i
$320$		0			0
$321$	7.00000	−	12.1244i	0.390702	−	0.676716i
$322$		0			0
$323$	−14.2288	+	1.84073i	−0.791709	+	0.102421i
$324$		0			0
$325$	17.7915	−	30.8158i	0.986895	−	1.70935i
$326$		0			0
$327$	−4.35425	−	7.54178i	−0.240791	−	0.417061i
$328$		0			0
$329$	−12.2915	−	21.2895i	−0.677652	−	1.17373i
$330$		0			0
$331$	−21.2288			−1.16684			−0.583419	−	0.812171i	$-0.698285\pi$
$331$	−21.2288			−1.16684			−0.583419	+	0.812171i	$0.698285\pi$
$332$		0			0
$333$	2.50000	+	4.33013i	0.136999	+	0.237289i
$334$		0			0
$335$	50.8118			2.77614
$336$		0			0
$337$	10.1458	−	17.5730i	0.552674	−	0.957260i	−0.445406	−	0.895329i	$-0.646941\pi$
$337$	10.1458	−	17.5730i	0.552674	−	0.957260i	0.998080	−	0.0619313i	$-0.0197260\pi$
$338$		0			0
$339$	−2.82288	+	4.88936i	−0.153318	+	0.265554i
$340$		0			0
$341$	−0.228757			−0.0123879
$342$		0			0
$343$	35.2288			1.90217
$344$		0			0
$345$	−10.2915	+	17.8254i	−0.554076	+	0.959688i
$346$		0			0
$347$	−9.40588	+	16.2915i	−0.504934	+	0.874572i	0.495050	+	0.868865i	$0.335150\pi$
$347$	−9.40588	+	16.2915i	−0.504934	+	0.874572i	−0.999984	+	0.00570686i	$0.998183\pi$
$348$		0			0
$349$	10.8745			0.582099			0.291050	−	0.956708i	$-0.405996\pi$
$349$	10.8745			0.582099			0.291050	+	0.956708i	$0.405996\pi$
$350$		0			0
$351$	−2.14575	−	3.71655i	−0.114532	−	0.198375i
$352$		0			0
$353$	−10.9373			−0.582131			−0.291066	−	0.956703i	$-0.594010\pi$
$353$	−10.9373			−0.582131			−0.291066	+	0.956703i	$0.594010\pi$
$354$		0			0
$355$	18.2288	+	31.5731i	0.967482	+	1.67573i
$356$		0			0
$357$	−7.64575	−	13.2428i	−0.404656	−	0.700885i
$358$		0			0
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	−5.00000	+	18.3303i	−0.263158	+	0.964753i
$362$		0			0
$363$	−5.43725	+	9.41760i	−0.285382	+	0.494296i
$364$		0			0
$365$	11.4686	+	19.8642i	0.600295	+	1.03974i
$366$		0			0
$367$	6.61438	+	11.4564i	0.345268	+	0.598021i	0.985402	−	0.170241i	$-0.0544548\pi$
$367$	6.61438	+	11.4564i	0.345268	+	0.598021i	−0.640135	+	0.768263i	$0.721121\pi$
$368$		0			0
$369$	4.00000			0.208232
$370$		0			0
$371$	−16.1144	−	27.9109i	−0.836617	−	1.44906i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$		0			0
$377$	15.6458	−	27.0992i	0.805797	−	1.39568i
$378$		0			0
$379$	−8.52026			−0.437656			−0.218828	−	0.975763i	$-0.570223\pi$
$379$	−8.52026			−0.437656			−0.218828	+	0.975763i	$0.570223\pi$
$380$		0			0
$381$	3.29150			0.168629
$382$		0			0
$383$	−5.82288	+	10.0855i	−0.297535	+	0.515346i	−0.975571	−	0.219683i	$-0.929498\pi$
$383$	−5.82288	+	10.0855i	−0.297535	+	0.515346i	0.678036	+	0.735028i	$0.262831\pi$
$384$		0			0
$385$	−3.00000	+	5.19615i	−0.152894	+	0.264820i
$386$		0			0
$387$	5.35425			0.272172
$388$		0			0
$389$	4.88562	+	8.46215i	0.247711	+	0.429048i	0.962890	−	0.269893i	$-0.0869884\pi$
$389$	4.88562	+	8.46215i	0.247711	+	0.429048i	−0.715179	+	0.698941i	$0.753655\pi$
$390$		0			0
$391$	18.5830			0.939783
$392$		0			0
$393$	3.00000	+	5.19615i	0.151330	+	0.262111i
$394$		0			0
$395$	−6.11438	−	10.5904i	−0.307648	−	0.532862i
$396$		0			0
$397$	11.1458	−	19.3050i	0.559389	−	0.968891i	−0.438158	−	0.898898i	$-0.644369\pi$
$397$	11.1458	−	19.3050i	0.559389	−	0.968891i	0.997548	−	0.0699927i	$-0.0222976\pi$
$398$		0			0
$399$	−20.0830	+	2.59808i	−1.00541	+	0.130066i
$400$		0			0
$401$	−7.17712	+	12.4311i	−0.358408	+	0.620782i	−0.987695	−	0.156392i	$-0.950014\pi$
$401$	−7.17712	+	12.4311i	−0.358408	+	0.620782i	0.629287	+	0.777173i	$0.283347\pi$
$402$		0			0
$403$	−1.38562	−	2.39997i	−0.0690227	−	0.119551i
$404$		0			0
$405$	−1.82288	−	3.15731i	−0.0905794	−	0.156888i
$406$		0			0
$407$	−1.77124			−0.0877973
$408$		0			0
$409$	2.35425	+	4.07768i	0.116410	+	0.201628i	0.918343	−	0.395787i	$-0.129528\pi$
$409$	2.35425	+	4.07768i	0.116410	+	0.201628i	−0.801932	+	0.597415i	$0.796195\pi$
$410$		0			0
$411$	−13.2915			−0.655621
$412$		0			0
$413$	−17.7601	+	30.7614i	−0.873919	+	1.51367i
$414$		0			0
$415$	−27.8745	+	48.2801i	−1.36831	+	2.36998i
$416$		0			0
$417$	4.64575			0.227503
$418$		0			0
$419$	22.9373			1.12056			0.560279	−	0.828304i	$-0.310694\pi$
$419$	22.9373			1.12056			0.560279	+	0.828304i	$0.310694\pi$
$420$		0			0
$421$	10.2288	−	17.7167i	0.498519	−	0.863460i	−0.501479	−	0.865170i	$-0.667211\pi$
$421$	10.2288	−	17.7167i	0.498519	−	0.863460i	0.999999	+	0.00170916i	$0.000544044\pi$
$422$		0			0
$423$	−2.64575	+	4.58258i	−0.128641	+	0.222812i
$424$		0			0
$425$	−27.2915			−1.32383
$426$		0			0
$427$	−11.6144	−	20.1167i	−0.562059	−	0.973515i
$428$		0			0
$429$	1.52026			0.0733988
$430$		0			0
$431$	17.2288	+	29.8411i	0.829880	+	1.43739i	0.898132	+	0.439726i	$0.144925\pi$
$431$	17.2288	+	29.8411i	0.829880	+	1.43739i	−0.0682519	+	0.997668i	$0.521742\pi$
$432$		0			0
$433$	5.14575	+	8.91270i	0.247289	+	0.428317i	0.962773	−	0.270312i	$-0.0871270\pi$
$433$	5.14575	+	8.91270i	0.247289	+	0.428317i	−0.715484	+	0.698629i	$0.753794\pi$
$434$		0			0
$435$	13.2915	−	23.0216i	0.637279	−	1.10380i
$436$		0			0
$437$	9.46863	−	22.7148i	0.452946	−	1.08659i
$438$		0			0
$439$	9.26013	−	16.0390i	0.441962	−	0.765500i	−0.555873	−	0.831267i	$-0.687616\pi$
$439$	9.26013	−	16.0390i	0.441962	−	0.765500i	0.997835	+	0.0657667i	$0.0209493\pi$
$440$		0			0
$441$	−7.29150	−	12.6293i	−0.347214	−	0.601393i
$442$		0			0
$443$	−9.64575	−	16.7069i	−0.458283	−	0.793770i	0.540587	−	0.841288i	$-0.318202\pi$
$443$	−9.64575	−	16.7069i	−0.458283	−	0.793770i	−0.998870	+	0.0475179i	$0.984869\pi$
$444$		0			0
$445$	49.7490			2.35833
$446$		0			0
$447$	−0.822876	−	1.42526i	−0.0389207	−	0.0674126i
$448$		0			0
$449$	7.29150			0.344107			0.172054	−	0.985088i	$-0.444960\pi$
$449$	7.29150			0.344107			0.172054	+	0.985088i	$0.444960\pi$
$450$		0			0
$451$	−0.708497	+	1.22715i	−0.0333618	+	0.0577844i
$452$		0			0
$453$	−0.354249	+	0.613577i	−0.0166441	+	0.0288283i
$454$		0			0
$455$	−72.6863			−3.40758
$456$		0			0
$457$	−34.8745			−1.63136			−0.815680	−	0.578503i	$-0.803637\pi$
$457$	−34.8745			−1.63136			−0.815680	+	0.578503i	$0.803637\pi$
$458$		0			0
$459$	−1.64575	+	2.85052i	−0.0768171	+	0.133051i
$460$		0			0
$461$	2.23987	−	3.87957i	0.104321	−	0.180690i	−0.809139	−	0.587617i	$-0.800066\pi$
$461$	2.23987	−	3.87957i	0.104321	−	0.180690i	0.913461	+	0.406927i	$0.133400\pi$
$462$		0			0
$463$	33.2288			1.54427			0.772136	−	0.635458i	$-0.219189\pi$
$463$	33.2288			1.54427			0.772136	+	0.635458i	$0.219189\pi$
$464$		0			0
$465$	−1.17712	−	2.03884i	−0.0545878	−	0.0945489i
$466$		0			0
$467$	−9.16601			−0.424152			−0.212076	−	0.977253i	$-0.568023\pi$
$467$	−9.16601			−0.424152			−0.212076	+	0.977253i	$0.568023\pi$
$468$		0			0
$469$	−32.3745	−	56.0743i	−1.49492	−	2.58927i
$470$		0			0
$471$	5.14575	+	8.91270i	0.237104	+	0.410676i
$472$		0			0
$473$	−0.948368	+	1.64262i	−0.0436060	+	0.0755278i
$474$		0			0
$475$	−13.9059	+	33.3595i	−0.638046	+	1.53064i
$476$		0			0
$477$	−3.46863	+	6.00784i	−0.158818	+	0.275080i
$478$		0			0
$479$	0.416995	+	0.722256i	0.0190530	+	0.0330007i	0.875395	−	0.483409i	$-0.160602\pi$
$479$	0.416995	+	0.722256i	0.0190530	+	0.0330007i	−0.856342	+	0.516410i	$0.827268\pi$
$480$		0			0
$481$	−10.7288	−	18.5828i	−0.489189	−	0.847301i
$482$		0			0
$483$	26.2288			1.19345
$484$		0			0
$485$	−19.2915	−	33.4139i	−0.875982	−	1.51725i
$486$		0			0
$487$	0.708497			0.0321051			0.0160525	−	0.999871i	$-0.494890\pi$
$487$	0.708497			0.0321051			0.0160525	+	0.999871i	$0.494890\pi$
$488$		0			0
$489$	0.0313730	−	0.0543397i	0.00141874	−	0.00245733i
$490$		0			0
$491$	11.5830	−	20.0624i	0.522734	−	0.905401i	−0.476916	−	0.878949i	$-0.658246\pi$
$491$	11.5830	−	20.0624i	0.522734	−	0.905401i	0.999650	−	0.0264527i	$-0.00842113\pi$
$492$		0			0
$493$	−24.0000			−1.08091
$494$		0			0
$495$	1.29150			0.0580487
$496$		0			0
$497$	23.2288	−	40.2334i	1.04195	−	1.80471i
$498$		0			0
$499$	11.5516	−	20.0080i	0.517122	−	0.895682i	−0.482680	−	0.875797i	$-0.660337\pi$
$499$	11.5516	−	20.0080i	0.517122	−	0.895682i	0.999802	−	0.0198850i	$-0.00633002\pi$
$500$		0			0
$501$	−1.06275			−0.0474800
$502$		0			0
$503$	−10.3542	−	17.9341i	−0.461673	−	0.799641i	0.537371	−	0.843346i	$-0.319417\pi$
$503$	−10.3542	−	17.9341i	−0.461673	−	0.799641i	−0.999045	+	0.0437044i	$0.986084\pi$
$504$		0			0
$505$	−72.4575			−3.22432
$506$		0			0
$507$	2.70850	+	4.69126i	0.120289	+	0.208346i
$508$		0			0
$509$	22.1660	+	38.3927i	0.982491	+	1.70172i	0.652594	+	0.757708i	$0.273681\pi$
$509$	22.1660	+	38.3927i	0.982491	+	1.70172i	0.329897	+	0.944017i	$0.392986\pi$
$510$		0			0
$511$	14.6144	−	25.3128i	0.646502	−	1.11977i
$512$		0			0
$513$	2.64575	+	3.46410i	0.116813	+	0.152944i
$514$		0			0
$515$	−14.4686	+	25.0604i	−0.637564	+	1.10429i
$516$		0			0
$517$	−0.937254	−	1.62337i	−0.0412204	−	0.0713958i
$518$		0			0
$519$	−4.93725	−	8.55157i	−0.216721	−	0.375372i
$520$		0			0
$521$	−17.6458			−0.773074			−0.386537	−	0.922274i	$-0.626329\pi$
$521$	−17.6458			−0.773074			−0.386537	+	0.922274i	$0.626329\pi$
$522$		0			0
$523$	17.1974	+	29.7867i	0.751989	+	1.30248i	0.946857	+	0.321654i	$0.104239\pi$
$523$	17.1974	+	29.7867i	0.751989	+	1.30248i	−0.194868	+	0.980829i	$0.562428\pi$
$524$		0			0
$525$	−38.5203			−1.68116
$526$		0			0
$527$	−1.06275	+	1.84073i	−0.0462939	+	0.0801835i
$528$		0			0
$529$	−4.43725	+	7.68555i	−0.192924	+	0.334154i
$530$		0			0
$531$	7.64575			0.331797
$532$		0			0
$533$	−17.1660			−0.743542
$534$		0			0
$535$	−25.5203	+	44.2024i	−1.10334	+	1.91104i
$536$		0			0
$537$	−5.17712	+	8.96704i	−0.223409	+	0.386956i
$538$		0			0
$539$	5.16601			0.222516
$540$		0			0
$541$	−13.4373	−	23.2740i	−0.577713	−	1.00063i	−0.995741	−	0.0921937i	$-0.970612\pi$
$541$	−13.4373	−	23.2740i	−0.577713	−	1.00063i	0.418028	−	0.908434i	$-0.362721\pi$
$542$		0			0
$543$	26.5830			1.14079
$544$		0			0
$545$	15.8745	+	27.4955i	0.679989	+	1.17778i
$546$		0			0
$547$	0.614378	+	1.06413i	0.0262689	+	0.0454991i	0.878861	−	0.477078i	$-0.158304\pi$
$547$	0.614378	+	1.06413i	0.0262689	+	0.0454991i	−0.852592	+	0.522577i	$0.824971\pi$
$548$		0			0
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	−12.2288	+	29.3362i	−0.520963	+	1.24976i
$552$		0			0
$553$	−7.79150	+	13.4953i	−0.331328	+	0.573878i
$554$		0			0
$555$	−9.11438	−	15.7866i	−0.386884	−	0.670102i
$556$		0			0
$557$	17.9373	+	31.0682i	0.760026	+	1.31640i	0.942837	+	0.333255i	$0.108147\pi$
$557$	17.9373	+	31.0682i	0.760026	+	1.31640i	−0.182811	+	0.983148i	$0.558520\pi$
$558$		0			0
$559$	−22.9778			−0.971856
$560$		0			0
$561$	−0.583005	−	1.00979i	−0.0246145	−	0.0426336i
$562$		0			0
$563$	6.00000			0.252870			0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000			0.252870			0.126435	+	0.991975i	$0.459647\pi$
$564$		0			0
$565$	10.2915	−	17.8254i	0.432967	−	0.749920i
$566$		0			0
$567$	−2.32288	+	4.02334i	−0.0975516	+	0.168964i
$568$		0			0
$569$	41.1660			1.72577			0.862884	−	0.505401i	$-0.168656\pi$
$569$	41.1660			1.72577			0.862884	+	0.505401i	$0.168656\pi$
$570$		0			0
$571$	3.93725			0.164769			0.0823845	−	0.996601i	$-0.473746\pi$
$571$	3.93725			0.164769			0.0823845	+	0.996601i	$0.473746\pi$
$572$		0			0
$573$	−0.468627	+	0.811686i	−0.0195772	+	0.0339087i
$574$		0			0
$575$	23.4059	−	40.5402i	0.976093	−	1.69064i
$576$		0			0
$577$	−0.708497			−0.0294951			−0.0147476	−	0.999891i	$-0.504694\pi$
$577$	−0.708497			−0.0294951			−0.0147476	+	0.999891i	$0.504694\pi$
$578$		0			0
$579$	11.0830	+	19.1963i	0.460594	+	0.797772i
$580$		0			0
$581$	71.0405			2.94726
$582$		0			0
$583$	−1.22876	−	2.12827i	−0.0508899	−	0.0881439i
$584$		0			0
$585$	7.82288	+	13.5496i	0.323436	+	0.560208i
$586$		0			0
$587$	13.1144	−	22.7148i	0.541288	−	0.937539i	−0.457542	−	0.889188i	$-0.651270\pi$
$587$	13.1144	−	22.7148i	0.541288	−	0.937539i	0.998830	−	0.0483509i	$-0.0153966\pi$
$588$		0			0
$589$	1.70850	+	2.23695i	0.0703974	+	0.0921718i
$590$		0			0
$591$	−8.82288	+	15.2817i	−0.362925	+	0.628604i
$592$		0			0
$593$	−4.46863	−	7.73989i	−0.183505	−	0.317839i	0.759567	−	0.650429i	$-0.225411\pi$
$593$	−4.46863	−	7.73989i	−0.183505	−	0.317839i	−0.943072	+	0.332590i	$0.892078\pi$
$594$		0			0
$595$	27.8745	+	48.2801i	1.14274	+	1.97929i
$596$		0			0
$597$	11.9373			0.488559
$598$		0			0
$599$	3.82288	+	6.62141i	0.156198	+	0.270544i	0.933495	−	0.358591i	$-0.116743\pi$
$599$	3.82288	+	6.62141i	0.156198	+	0.270544i	−0.777296	+	0.629135i	$0.783409\pi$
$600$		0			0
$601$	−19.7085			−0.803926			−0.401963	−	0.915656i	$-0.631672\pi$
$601$	−19.7085			−0.803926			−0.401963	+	0.915656i	$0.631672\pi$
$602$		0			0
$603$	−6.96863	+	12.0700i	−0.283784	+	0.491529i
$604$		0			0
$605$	19.8229	−	34.3342i	0.805914	−	1.39588i
$606$		0			0
$607$	−35.9373			−1.45865			−0.729324	−	0.684168i	$-0.760165\pi$
$607$	−35.9373			−1.45865			−0.729324	+	0.684168i	$0.760165\pi$
$608$		0			0
$609$	−33.8745			−1.37266
$610$		0			0
$611$	11.3542	−	19.6661i	0.459344	−	0.795607i
$612$		0			0
$613$	4.58301	−	7.93800i	0.185106	−	0.320613i	−0.758506	−	0.651666i	$-0.774071\pi$
$613$	4.58301	−	7.93800i	0.185106	−	0.320613i	0.943612	+	0.331053i	$0.107404\pi$
$614$		0			0
$615$	−14.5830			−0.588044
$616$		0			0
$617$	−9.53137	−	16.5088i	−0.383719	−	0.664620i	0.607872	−	0.794035i	$-0.292023\pi$
$617$	−9.53137	−	16.5088i	−0.383719	−	0.664620i	−0.991591	+	0.129415i	$0.958690\pi$
$618$		0			0
$619$	23.9373			0.962119			0.481060	−	0.876688i	$-0.340252\pi$
$619$	23.9373			0.962119			0.481060	+	0.876688i	$0.340252\pi$
$620$		0			0
$621$	−2.82288	−	4.88936i	−0.113278	−	0.196203i
$622$		0			0
$623$	−31.6974	−	54.9015i	−1.26993	−	2.19958i
$624$		0			0
$625$	−1.14575	+	1.98450i	−0.0458301	+	0.0793800i
$626$		0			0
$627$	−1.53137	+	0.198109i	−0.0611571	+	0.00791171i
$628$		0			0
$629$	−8.22876	+	14.2526i	−0.328102	+	0.568289i
$630$		0			0
$631$	8.96863	+	15.5341i	0.357035	+	0.618403i	0.987464	−	0.157844i	$-0.0504542\pi$
$631$	8.96863	+	15.5341i	0.357035	+	0.618403i	−0.630429	+	0.776247i	$0.717121\pi$
$632$		0			0
$633$	5.32288	+	9.21949i	0.211565	+	0.366442i
$634$		0			0
$635$	−12.0000			−0.476205
$636$		0			0
$637$	31.2915	+	54.1985i	1.23981	+	2.14742i
$638$		0			0
$639$	−10.0000			−0.395594
$640$		0			0
$641$	−0.291503	+	0.504897i	−0.0115137	+	0.0199422i	−0.871725	−	0.489996i	$-0.836998\pi$
$641$	−0.291503	+	0.504897i	−0.0115137	+	0.0199422i	0.860211	+	0.509938i	$0.170332\pi$
$642$		0			0
$643$	22.9686	−	39.7828i	0.905794	−	1.56888i	0.0859467	−	0.996300i	$-0.472609\pi$
$643$	22.9686	−	39.7828i	0.905794	−	1.56888i	0.819848	−	0.572582i	$-0.194058\pi$
$644$		0			0
$645$	−19.5203			−0.768609
$646$		0			0
$647$	16.7085			0.656879			0.328439	−	0.944525i	$-0.393477\pi$
$647$	16.7085			0.656879			0.328439	+	0.944525i	$0.393477\pi$
$648$		0			0
$649$	−1.35425	+	2.34563i	−0.0531589	+	0.0920739i
$650$		0			0
$651$	−1.50000	+	2.59808i	−0.0587896	+	0.101827i
$652$		0			0
$653$	−39.8745			−1.56041			−0.780205	−	0.625524i	$-0.784885\pi$
$653$	−39.8745			−1.56041			−0.780205	+	0.625524i	$0.784885\pi$
$654$		0			0
$655$	−10.9373	−	18.9439i	−0.427354	−	0.740199i
$656$		0			0
$657$	−6.29150			−0.245455
$658$		0			0
$659$	−17.1144	−	29.6430i	−0.666682	−	1.15473i	−0.978826	−	0.204692i	$-0.934381\pi$
$659$	−17.1144	−	29.6430i	−0.666682	−	1.15473i	0.312145	−	0.950034i	$-0.398953\pi$
$660$		0			0
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$		0			0
$663$	7.06275	−	12.2330i	0.274294	−	0.475092i
$664$		0			0
$665$	73.2176	−	9.47194i	2.83926	−	0.367306i
$666$		0			0
$667$	20.5830	−	35.6508i	0.796977	−	1.38040i
$668$		0			0
$669$	−2.67712	−	4.63692i	−0.103504	−	0.179274i
$670$		0			0
$671$	−0.885622	−	1.53394i	−0.0341890	−	0.0592172i
$672$		0			0
$673$	7.12549			0.274668			0.137334	−	0.990525i	$-0.456147\pi$
$673$	7.12549			0.274668			0.137334	+	0.990525i	$0.456147\pi$
$674$		0			0
$675$	4.14575	+	7.18065i	0.159570	+	0.276383i
$676$		0			0
$677$	23.1660			0.890342			0.445171	−	0.895446i	$-0.353143\pi$
$677$	23.1660			0.890342			0.445171	+	0.895446i	$0.353143\pi$
$678$		0			0
$679$	−24.5830	+	42.5790i	−0.943409	+	1.63403i
$680$		0			0
$681$	7.76013	−	13.4409i	0.297369	−	0.515058i
$682$		0			0
$683$	0.228757			0.00875313			0.00437656	−	0.999990i	$-0.498607\pi$
$683$	0.228757			0.00875313			0.00437656	+	0.999990i	$0.498607\pi$
$684$		0			0
$685$	48.4575			1.85147
$686$		0			0
$687$	−4.85425	+	8.40781i	−0.185201	+	0.320778i
$688$		0			0
$689$	14.8856	−	25.7827i	0.567097	−	0.982241i
$690$		0			0
$691$	−13.1660			−0.500859			−0.250429	−	0.968135i	$-0.580572\pi$
$691$	−13.1660			−0.500859			−0.250429	+	0.968135i	$0.580572\pi$
$692$		0			0
$693$	−0.822876	−	1.42526i	−0.0312585	−	0.0541412i
$694$		0			0
$695$	−16.9373			−0.642467
$696$		0			0
$697$	6.58301	+	11.4021i	0.249349	+	0.431885i
$698$		0			0
$699$	−1.93725	−	3.35542i	−0.0732737	−	0.126914i
$700$		0			0
$701$	−22.0516	+	38.1945i	−0.832879	+	1.44259i	0.0628673	+	0.998022i	$0.479976\pi$
$701$	−22.0516	+	38.1945i	−0.832879	+	1.44259i	−0.895746	+	0.444566i	$0.853358\pi$
$702$		0			0
$703$	13.2288	+	17.3205i	0.498932	+	0.653255i
$704$		0			0
$705$	9.64575	−	16.7069i	0.363280	−	0.629219i
$706$		0			0
$707$	46.1660	+	79.9619i	1.73625	+	3.00728i
$708$		0			0
$709$	1.79150	+	3.10297i	0.0672813	+	0.116535i	0.897704	−	0.440600i	$-0.145234\pi$
$709$	1.79150	+	3.10297i	0.0672813	+	0.116535i	−0.830422	+	0.557134i	$0.811901\pi$
$710$		0			0
$711$	3.35425			0.125794
$712$		0			0
$713$	−1.82288	−	3.15731i	−0.0682672	−	0.118242i
$714$		0			0
$715$	−5.54249			−0.207277
$716$		0			0
$717$	2.46863	−	4.27579i	0.0921926	−	0.159682i
$718$		0			0
$719$	0.468627	−	0.811686i	0.0174768	−	0.0302708i	−0.857155	−	0.515059i	$-0.827770\pi$
$719$	0.468627	−	0.811686i	0.0174768	−	0.0302708i	0.874632	+	0.484788i	$0.161103\pi$
$720$		0			0
$721$	36.8745			1.37328
$722$		0			0
$723$	−10.8745			−0.404427
$724$		0			0
$725$	−30.2288	+	52.3577i	−1.12267	+	1.94452i
$726$		0			0
$727$	−12.2601	+	21.2352i	−0.454703	+	0.787569i	−0.998671	−	0.0515372i	$-0.983588\pi$
$727$	−12.2601	+	21.2352i	−0.454703	+	0.787569i	0.543968	+	0.839106i	$0.316921\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	8.81176	+	15.2624i	0.325915	+	0.564501i
$732$		0			0
$733$	−13.1660			−0.486298			−0.243149	−	0.969989i	$-0.578180\pi$
$733$	−13.1660			−0.486298			−0.243149	+	0.969989i	$0.578180\pi$
$734$		0			0
$735$	26.5830	+	46.0431i	0.980529	+	1.69833i
$736$		0			0
$737$	−2.46863	−	4.27579i	−0.0909330	−	0.157501i
$738$		0			0
$739$	16.3229	−	28.2720i	0.600447	−	1.04000i	−0.392307	−	0.919834i	$-0.628323\pi$
$739$	16.3229	−	28.2720i	0.600447	−	1.04000i	0.992753	−	0.120170i	$-0.0383439\pi$
$740$		0			0
$741$	−11.3542	−	14.8662i	−0.417109	−	0.546124i
$742$		0			0
$743$	3.11438	−	5.39426i	0.114255	−	0.197896i	−0.803226	−	0.595674i	$-0.796885\pi$
$743$	3.11438	−	5.39426i	0.114255	−	0.197896i	0.917482	+	0.397778i	$0.130218\pi$
$744$		0			0
$745$	3.00000	+	5.19615i	0.109911	+	0.190372i
$746$		0			0
$747$	−7.64575	−	13.2428i	−0.279743	−	0.484530i
$748$		0			0
$749$	65.0405			2.37653
$750$		0			0
$751$	1.32288	+	2.29129i	0.0482724	+	0.0836103i	0.889152	−	0.457612i	$-0.151295\pi$
$751$	1.32288	+	2.29129i	0.0482724	+	0.0836103i	−0.840880	+	0.541222i	$0.817962\pi$
$752$		0			0
$753$	13.2915			0.484369
$754$		0			0
$755$	1.29150	−	2.23695i	0.0470026	−	0.0814109i
$756$		0			0
$757$	−6.79150	+	11.7632i	−0.246841	+	0.427542i	−0.962648	−	0.270757i	$-0.912726\pi$
$757$	−6.79150	+	11.7632i	−0.246841	+	0.427542i	0.715806	+	0.698299i	$0.246059\pi$
$758$		0			0
$759$	2.00000			0.0725954
$760$		0			0
$761$	−35.5203			−1.28761			−0.643804	−	0.765190i	$-0.722645\pi$
$761$	−35.5203			−1.28761			−0.643804	+	0.765190i	$0.722645\pi$
$762$		0			0
$763$	20.2288	−	35.0372i	0.732330	−	1.26843i
$764$		0			0
$765$	6.00000	−	10.3923i	0.216930	−	0.375735i
$766$		0			0
$767$	−32.8118			−1.18476
$768$		0			0
$769$	5.79150	+	10.0312i	0.208847	+	0.361733i	0.951352	−	0.308107i	$-0.0996956\pi$
$769$	5.79150	+	10.0312i	0.208847	+	0.361733i	−0.742505	+	0.669841i	$0.766362\pi$
$770$		0			0
$771$	−15.6458			−0.563468
$772$		0			0
$773$	−18.8745	−	32.6916i	−0.678869	−	1.17584i	−0.975322	−	0.220788i	$-0.929137\pi$
$773$	−18.8745	−	32.6916i	−0.678869	−	1.17584i	0.296453	−	0.955047i	$-0.404196\pi$
$774$		0			0
$775$	2.67712	+	4.63692i	0.0961651	+	0.166563i
$776$		0			0
$777$	−11.6144	+	20.1167i	−0.416663	+	0.721682i
$778$		0			0
$779$	17.2915	−	2.23695i	0.619532	−	0.0801470i
$780$		0			0
$781$	1.77124	−	3.06788i	0.0633801	−	0.109778i
$782$		0			0
$783$	3.64575	+	6.31463i	0.130289	+	0.225666i
$784$		0			0
$785$	−18.7601	−	32.4935i	−0.669578	−	1.15974i
$786$		0			0
$787$	−19.8118			−0.706213			−0.353107	−	0.935583i	$-0.614875\pi$
$787$	−19.8118			−0.706213			−0.353107	+	0.935583i	$0.614875\pi$
$788$		0			0
$789$	9.00000	+	15.5885i	0.320408	+	0.554964i
$790$		0			0
$791$	−26.2288			−0.932587
$792$		0			0
$793$	10.7288	−	18.5828i	0.380989	−	0.659893i
$794$		0			0
$795$	12.6458	−	21.9031i	0.448499	−	0.776822i
$796$		0			0
$797$	45.2915			1.60431			0.802154	−	0.597118i	$-0.203687\pi$
$797$	45.2915			1.60431			0.802154	+	0.597118i	$0.203687\pi$
$798$		0			0
$799$	−17.4170			−0.616169
$800$		0			0
$801$	−6.82288	+	11.8176i	−0.241074	+	0.417553i
$802$		0			0
$803$	1.11438	−	1.93016i	0.0393256	−	0.0681139i
$804$		0			0
$805$	−95.6235			−3.37029
$806$		0			0
$807$	−6.82288	−	11.8176i	−0.240177	−	0.415998i
$808$		0			0
$809$	−10.9373			−0.384533			−0.192267	−	0.981343i	$-0.561584\pi$
$809$	−10.9373			−0.384533			−0.192267	+	0.981343i	$0.561584\pi$
$810$		0			0
$811$	−2.22876	−	3.86032i	−0.0782622	−	0.135554i	0.824238	−	0.566243i	$-0.191604\pi$
$811$	−2.22876	−	3.86032i	−0.0782622	−	0.135554i	−0.902500	+	0.430689i	$0.858270\pi$
$812$		0			0
$813$	5.29150	+	9.16515i	0.185581	+	0.321436i
$814$		0			0
$815$	−0.114378	+	0.198109i	−0.00400650	+	0.00693946i
$816$		0			0
$817$	23.1458	−	2.99429i	0.809767	−	0.104757i
$818$		0			0
$819$	9.96863	−	17.2662i	0.348332	−	0.603329i
$820$		0			0
$821$	7.06275	+	12.2330i	0.246492	+	0.426936i	0.962550	−	0.271105i	$-0.0873889\pi$
$821$	7.06275	+	12.2330i	0.246492	+	0.426936i	−0.716058	+	0.698040i	$0.754056\pi$
$822$		0			0
$823$	−17.6458	−	30.5633i	−0.615092	−	1.06537i	−0.990368	−	0.138458i	$-0.955785\pi$
$823$	−17.6458	−	30.5633i	−0.615092	−	1.06537i	0.375276	−	0.926913i	$-0.377548\pi$
$824$		0			0
$825$	−2.93725			−0.102262
$826$		0			0
$827$	−8.35425	−	14.4700i	−0.290506	−	0.503171i	0.683424	−	0.730022i	$-0.260490\pi$
$827$	−8.35425	−	14.4700i	−0.290506	−	0.503171i	−0.973929	+	0.226851i	$0.927157\pi$
$828$		0			0
$829$	−51.5830			−1.79155			−0.895776	−	0.444506i	$-0.853379\pi$
$829$	−51.5830			−1.79155			−0.895776	+	0.444506i	$0.853379\pi$
$830$		0			0
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$		0			0
$833$	24.0000	−	41.5692i	0.831551	−	1.44029i
$834$		0			0
$835$	3.87451			0.134083
$836$		0			0
$837$	0.645751			0.0223204
$838$		0			0
$839$	−4.82288	+	8.35347i	−0.166504	+	0.288394i	−0.937188	−	0.348824i	$-0.886581\pi$
$839$	−4.82288	+	8.35347i	−0.166504	+	0.288394i	0.770684	+	0.637217i	$0.219915\pi$
$840$		0			0
$841$	−12.0830	+	20.9284i	−0.416655	+	0.721668i
$842$		0			0
$843$	6.93725			0.238932
$844$		0			0
$845$	−9.87451	−	17.1031i	−0.339693	−	0.588366i
$846$		0			0
$847$	−50.5203			−1.73590
$848$		0			0
$849$	−2.70850	−	4.69126i	−0.0929554	−	0.161003i
$850$		0			0
$851$	−14.1144	−	24.4468i	−0.483835	−	0.838026i
$852$		0			0
$853$	−17.3745	+	30.0935i	−0.594892	+	1.03038i	0.398670	+	0.917094i	$0.369472\pi$
$853$	−17.3745	+	30.0935i	−0.594892	+	1.03038i	−0.993562	+	0.113289i	$0.963862\pi$
$854$		0			0
$855$	−9.64575	−	12.6293i	−0.329878	−	0.431911i
$856$		0			0
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	3.03137	+	5.25049i	0.103429	+	0.179144i	0.913095	−	0.407746i	$-0.133685\pi$
$859$	3.03137	+	5.25049i	0.103429	+	0.179144i	−0.809666	+	0.586891i	$0.800352\pi$
$860$		0			0
$861$	9.29150	+	16.0934i	0.316654	+	0.548460i
$862$		0			0
$863$	−26.7085			−0.909168			−0.454584	−	0.890704i	$-0.650212\pi$
$863$	−26.7085			−0.909168			−0.454584	+	0.890704i	$0.650212\pi$
$864$		0			0
$865$	18.0000	+	31.1769i	0.612018	+	1.06005i
$866$		0			0
$867$	6.16601			0.209409
$868$		0			0
$869$	−0.594119	+	1.02904i	−0.0201541	+	0.0349079i
$870$		0			0
$871$	29.9059	−	51.7985i	1.01332	−	1.75513i
$872$		0			0
$873$	10.5830			0.358180
$874$		0			0
$875$	55.7490			1.88466
$876$		0			0
$877$	9.08301	−	15.7322i	0.306711	−	0.531240i	−0.670930	−	0.741521i	$-0.734105\pi$
$877$	9.08301	−	15.7322i	0.306711	−	0.531240i	0.977641	+	0.210282i	$0.0674381\pi$
$878$		0			0
$879$	−12.2915	+	21.2895i	−0.414582	+	0.718077i
$880$		0			0
$881$	30.6863			1.03385			0.516923	−	0.856032i	$-0.327077\pi$
$881$	30.6863			1.03385			0.516923	+	0.856032i	$0.327077\pi$
$882$		0			0
$883$	−8.67712	−	15.0292i	−0.292008	−	0.505774i	0.682276	−	0.731095i	$-0.260990\pi$
$883$	−8.67712	−	15.0292i	−0.292008	−	0.505774i	−0.974285	+	0.225321i	$0.927657\pi$
$884$		0			0
$885$	−27.8745			−0.936991
$886$		0			0
$887$	−8.05163	−	13.9458i	−0.270347	−	0.468255i	0.698603	−	0.715509i	$-0.253805\pi$
$887$	−8.05163	−	13.9458i	−0.270347	−	0.468255i	−0.968951	+	0.247254i	$0.920472\pi$
$888$		0			0
$889$	7.64575	+	13.2428i	0.256430	+	0.444150i
$890$		0			0
$891$	−0.177124	+	0.306788i	−0.00593389	+	0.0102778i
$892$		0			0
$893$	−8.87451	+	21.2895i	−0.296974	+	0.712426i
$894$		0			0
$895$	18.8745	−	32.6916i	0.630905	−	1.09276i
$896$		0			0
$897$	12.1144	+	20.9827i	0.404487	+	0.700593i
$898$		0			0
$899$	2.35425	+	4.07768i	0.0785186	+	0.135998i
$900$		0			0
$901$	−22.8340			−0.760710
$902$		0			0
$903$	12.4373	+	21.5420i	0.413886	+	0.716871i
$904$		0			0
$905$	−96.9150			−3.22156
$906$		0			0
$907$	1.41699	−	2.45431i	0.0470505	−	0.0814939i	−0.841541	−	0.540193i	$-0.818351\pi$
$907$	1.41699	−	2.45431i	0.0470505	−	0.0814939i	0.888592	+	0.458699i	$0.151684\pi$
$908$		0			0
$909$	9.93725	−	17.2118i	0.329598	−	0.570880i
$910$		0			0
$911$	43.7490			1.44947			0.724735	−	0.689028i	$-0.241962\pi$
$911$	43.7490			1.44947			0.724735	+	0.689028i	$0.241962\pi$
$912$		0			0
$913$	5.41699			0.179276
$914$		0			0
$915$	9.11438	−	15.7866i	0.301312	−	0.521888i
$916$		0			0
$917$	−13.9373	+	24.1400i	−0.460249	+	0.797174i
$918$		0			0
$919$	1.22876			0.0405329			0.0202665	−	0.999795i	$-0.493549\pi$
$919$	1.22876			0.0405329			0.0202665	+	0.999795i	$0.493549\pi$
$920$		0			0
$921$	−13.9373	−	24.1400i	−0.459248	−	0.795441i
$922$		0			0
$923$	42.9150			1.41257
$924$		0			0
$925$	20.7288	+	35.9033i	0.681557	+	1.18049i
$926$		0			0
$927$	−3.96863	−	6.87386i	−0.130347	−	0.225767i
$928$		0			0
$929$	−18.7601	+	32.4935i	−0.615500	+	1.06608i	0.374797	+	0.927107i	$0.377713\pi$
$929$	−18.7601	+	32.4935i	−0.615500	+	1.06608i	−0.990297	+	0.138970i	$0.955621\pi$
$930$		0			0
$931$	−38.5830	−	50.5170i	−1.26451	−	1.65563i
$932$		0			0
$933$	8.53137	−	14.7768i	0.279305	−	0.483770i
$934$		0			0
$935$	2.12549	+	3.68146i	0.0695110	+	0.120397i
$936$		0			0
$937$	3.50000	+	6.06218i	0.114340	+	0.198043i	0.917516	−	0.397699i	$-0.130191\pi$
$937$	3.50000	+	6.06218i	0.114340	+	0.198043i	−0.803176	+	0.595742i	$0.796858\pi$
$938$		0			0
$939$	19.2915			0.629554
$940$		0			0
$941$	19.8745	+	34.4237i	0.647890	+	1.12218i	0.983626	+	0.180223i	$0.0576819\pi$
$941$	19.8745	+	34.4237i	0.647890	+	1.12218i	−0.335735	+	0.941956i	$0.608985\pi$
$942$		0			0
$943$	−22.5830			−0.735404
$944$		0			0
$945$	8.46863	−	14.6681i	0.275484	−	0.477153i
$946$		0			0
$947$	−28.1660	+	48.7850i	−0.915272	+	1.58530i	−0.108770	+	0.994067i	$0.534691\pi$
$947$	−28.1660	+	48.7850i	−0.915272	+	1.58530i	−0.806502	+	0.591231i	$0.798642\pi$
$948$		0			0
$949$	27.0000			0.876457
$950$		0			0
$951$	10.9373			0.354665
$952$		0			0
$953$	−21.7601	+	37.6897i	−0.704880	+	1.22089i	0.261855	+	0.965107i	$0.415666\pi$
$953$	−21.7601	+	37.6897i	−0.704880	+	1.22089i	−0.966735	+	0.255780i	$0.917668\pi$
$954$		0			0
$955$	1.70850	−	2.95920i	0.0552857	−	0.0957576i
$956$		0			0
$957$	−2.58301			−0.0834967
$958$		0			0
$959$	−30.8745	−	53.4762i	−0.996990	−	1.72684i
$960$		0			0
$961$	−30.5830			−0.986549
$962$		0			0
$963$	−7.00000	−	12.1244i	−0.225572	−	0.390702i
$964$		0			0
$965$	−40.4059	−	69.9850i	−1.30071	−	2.25290i
$966$		0			0
$967$	6.96863	−	12.0700i	0.224096	−	0.388146i	−0.731952	−	0.681356i	$-0.761390\pi$
$967$	6.96863	−	12.0700i	0.224096	−	0.388146i	0.956048	+	0.293211i	$0.0947238\pi$
$968$		0			0
$969$	−5.52026	+	13.2428i	−0.177336	+	0.425421i
$970$		0			0
$971$	22.5203	−	39.0062i	0.722710	−	1.25177i	−0.237200	−	0.971461i	$-0.576230\pi$
$971$	22.5203	−	39.0062i	0.722710	−	1.25177i	0.959910	−	0.280309i	$-0.0904369\pi$
$972$		0			0
$973$	10.7915	+	18.6914i	0.345960	+	0.599220i
$974$		0			0
$975$	−17.7915	−	30.8158i	−0.569784	−	0.986895i
$976$		0			0
$977$	−54.9150			−1.75689			−0.878444	−	0.477846i	$-0.841418\pi$
$977$	−54.9150			−1.75689			−0.878444	+	0.477846i	$0.841418\pi$
$978$		0			0
$979$	−2.41699	−	4.18636i	−0.0772475	−	0.133797i
$980$		0			0
$981$	−8.70850			−0.278041
$982$		0			0
$983$	−29.4686	+	51.0412i	−0.939903	+	1.62796i	−0.174255	+	0.984701i	$0.555752\pi$
$983$	−29.4686	+	51.0412i	−0.939903	+	1.62796i	−0.765648	+	0.643260i	$0.777582\pi$
$984$		0			0
$985$	32.1660	−	55.7132i	1.02489	−	1.77517i
$986$		0			0
$987$	−24.5830			−0.782486
$988$		0			0
$989$	−30.2288			−0.961219
$990$		0			0
$991$	−5.96863	+	10.3380i	−0.189600	+	0.328396i	−0.945117	−	0.326733i	$-0.894052\pi$
$991$	−5.96863	+	10.3380i	−0.189600	+	0.328396i	0.755517	+	0.655129i	$0.227386\pi$
$992$		0			0
$993$	−10.6144	+	18.3846i	−0.336837	+	0.583419i
$994$		0			0
$995$	−43.5203			−1.37968
$996$		0			0
$997$	14.0203	+	24.2838i	0.444026	+	0.769076i	0.997984	−	0.0634691i	$-0.0202164\pi$
$997$	14.0203	+	24.2838i	0.444026	+	0.769076i	−0.553958	+	0.832545i	$0.686883\pi$
$998$		0			0
$999$	5.00000			0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.i.b.49.1	✓	4
3.2	odd	2		684.2.k.g.505.2		4
4.3	odd	2		912.2.q.g.49.1		4
12.11	even	2		2736.2.s.u.1873.2		4
19.7	even	3	inner	228.2.i.b.121.1	yes	4
19.8	odd	6		4332.2.a.m.1.2		2
19.11	even	3		4332.2.a.h.1.2		2
57.26	odd	6		684.2.k.g.577.2		4
76.7	odd	6		912.2.q.g.577.1		4
228.83	even	6		2736.2.s.u.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.i.b.49.1	✓	4	1.1	even	1	trivial
228.2.i.b.121.1	yes	4	19.7	even	3	inner
684.2.k.g.505.2		4	3.2	odd	2
684.2.k.g.577.2		4	57.26	odd	6
912.2.q.g.49.1		4	4.3	odd	2
912.2.q.g.577.1		4	76.7	odd	6
2736.2.s.u.577.2		4	228.83	even	6
2736.2.s.u.1873.2		4	12.11	even	2
4332.2.a.h.1.2		2	19.11	even	3
4332.2.a.m.1.2		2	19.8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.82288 + 3.15731i) q^{5} +4.64575 q^{7} +(-0.500000 - 0.866025i) q^{9} +0.354249 q^{11} +(2.14575 + 3.71655i) q^{13} +(1.82288 + 3.15731i) q^{15} +(1.64575 - 2.85052i) q^{17} +(-2.64575 - 3.46410i) q^{19} +(2.32288 - 4.02334i) q^{21} +(2.82288 + 4.88936i) q^{23} +(-4.14575 - 7.18065i) q^{25} -1.00000 q^{27} +(-3.64575 - 6.31463i) q^{29} -0.645751 q^{31} +(0.177124 - 0.306788i) q^{33} +(-8.46863 + 14.6681i) q^{35} -5.00000 q^{37} +4.29150 q^{39} +(-2.00000 + 3.46410i) q^{41} +(-2.67712 + 4.63692i) q^{43} +3.64575 q^{45} +(-2.64575 - 4.58258i) q^{47} +14.5830 q^{49} +(-1.64575 - 2.85052i) q^{51} +(-3.46863 - 6.00784i) q^{53} +(-0.645751 + 1.11847i) q^{55} +(-4.32288 + 0.559237i) q^{57} +(-3.82288 + 6.62141i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.32288 - 4.02334i) q^{63} -15.6458 q^{65} +(-6.96863 - 12.0700i) q^{67} +5.64575 q^{69} +(5.00000 - 8.66025i) q^{71} +(3.14575 - 5.44860i) q^{73} -8.29150 q^{75} +1.64575 q^{77} +(-1.67712 + 2.90486i) q^{79} +(-0.500000 + 0.866025i) q^{81} +15.2915 q^{83} +(6.00000 + 10.3923i) q^{85} -7.29150 q^{87} +(-6.82288 - 11.8176i) q^{89} +(9.96863 + 17.2662i) q^{91} +(-0.322876 + 0.559237i) q^{93} +(15.7601 - 2.03884i) q^{95} +(-5.29150 + 9.16515i) q^{97} +(-0.177124 - 0.306788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{5} + 8 q^{7} - 2 q^{9} + 12 q^{11} - 2 q^{13} + 2 q^{15} - 4 q^{17} + 4 q^{21} + 6 q^{23} - 6 q^{25} - 4 q^{27} - 4 q^{29} + 8 q^{31} + 6 q^{33} - 18 q^{35} - 20 q^{37} - 4 q^{39} - 8 q^{41}+ \cdots - 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^5 + 8 * q^7 - 2 * q^9 + 12 * q^11 - 2 * q^13 + 2 * q^15 - 4 * q^17 + 4 * q^21 + 6 * q^23 - 6 * q^25 - 4 * q^27 - 4 * q^29 + 8 * q^31 + 6 * q^33 - 18 * q^35 - 20 * q^37 - 4 * q^39 - 8 * q^41 - 16 * q^43 + 4 * q^45 + 16 * q^49 + 4 * q^51 + 2 * q^53 + 8 * q^55 - 12 * q^57 - 10 * q^59 - 10 * q^61 - 4 * q^63 - 52 * q^65 - 12 * q^67 + 12 * q^69 + 20 * q^71 + 2 * q^73 - 12 * q^75 - 4 * q^77 - 12 * q^79 - 2 * q^81 + 40 * q^83 + 24 * q^85 - 8 * q^87 - 22 * q^89 + 24 * q^91 + 4 * q^93 + 26 * q^95 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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