LMFDB - Embedded newform 425.2.j.b.149.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(149,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,4] 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.4
Root			$1.35757i$ of defining polynomial
Character	$\chi$	$=$	425.149
Dual form			425.2.j.b.174.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.677603 q^{2} +(1.66705 - 1.66705i) q^{3} -1.54085 q^{4} +(1.12960 - 1.12960i) q^{6} +(-3.02462 - 3.02462i) q^{7} -2.39929 q^{8} -2.55814i q^{9} +(-1.17133 + 1.17133i) q^{11} +(-2.56869 + 2.56869i) q^{12} -6.21427i q^{13} +(-2.04950 - 2.04950i) q^{14} +1.45594 q^{16} +(3.90279 + 1.32974i) q^{17} -1.73340i q^{18} -3.38977i q^{19} -10.0844 q^{21} +(-0.793694 + 0.793694i) q^{22} +(3.30530 + 3.30530i) q^{23} +(-3.99975 + 3.99975i) q^{24} -4.21081i q^{26} +(0.736610 + 0.736610i) q^{27} +(4.66050 + 4.66050i) q^{28} +(2.57924 + 2.57924i) q^{29} +(-2.12106 - 2.12106i) q^{31} +5.78514 q^{32} +3.90532i q^{33} +(2.64455 + 0.901035i) q^{34} +3.94171i q^{36} +(3.78314 - 3.78314i) q^{37} -2.29692i q^{38} +(-10.3595 - 10.3595i) q^{39} +(-1.54740 + 1.54740i) q^{41} -6.83324 q^{42} +0.998176 q^{43} +(1.80484 - 1.80484i) q^{44} +(2.23968 + 2.23968i) q^{46} +2.00393i q^{47} +(2.42713 - 2.42713i) q^{48} +11.2967i q^{49} +(8.72291 - 4.28942i) q^{51} +9.57528i q^{52} -6.95444 q^{53} +(0.499130 + 0.499130i) q^{54} +(7.25696 + 7.25696i) q^{56} +(-5.65093 - 5.65093i) q^{57} +(1.74770 + 1.74770i) q^{58} +6.30165i q^{59} +(4.62096 - 4.62096i) q^{61} +(-1.43724 - 1.43724i) q^{62} +(-7.73740 + 7.73740i) q^{63} +1.00815 q^{64} +2.64626i q^{66} -5.80078i q^{67} +(-6.01363 - 2.04893i) q^{68} +11.0202 q^{69} +(-9.60714 - 9.60714i) q^{71} +6.13772i q^{72} +(7.01789 - 7.01789i) q^{73} +(2.56347 - 2.56347i) q^{74} +5.22314i q^{76} +7.08564 q^{77} +(-7.01965 - 7.01965i) q^{78} +(-0.820929 + 0.820929i) q^{79} +10.1303 q^{81} +(-1.04853 + 1.04853i) q^{82} +3.65934 q^{83} +15.5386 q^{84} +0.676367 q^{86} +8.59945 q^{87} +(2.81035 - 2.81035i) q^{88} -2.69634 q^{89} +(-18.7958 + 18.7958i) q^{91} +(-5.09298 - 5.09298i) q^{92} -7.07184 q^{93} +1.35787i q^{94} +(9.64413 - 9.64413i) q^{96} +(7.40348 - 7.40348i) q^{97} +7.65468i q^{98} +(2.99641 + 2.99641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} + 4 q^{3} + 12 q^{4} - 12 q^{8} - 4 q^{11} - 8 q^{12} + 4 q^{14} + 4 q^{16} - 8 q^{17} - 16 q^{21} + 20 q^{22} + 12 q^{23} - 4 q^{24} + 4 q^{27} + 4 q^{28} + 12 q^{29} + 12 q^{32} + 12 q^{34}+ \cdots + 4 q^{97}+O(q^{100}) $ 12 * q - 4 * q^2 + 4 * q^3 + 12 * q^4 - 12 * q^8 - 4 * q^11 - 8 * q^12 + 4 * q^14 + 4 * q^16 - 8 * q^17 - 16 * q^21 + 20 * q^22 + 12 * q^23 - 4 * q^24 + 4 * q^27 + 4 * q^28 + 12 * q^29 + 12 * q^32 + 12 * q^34 + 12 * q^37 + 20 * q^39 - 24 * q^41 - 16 * q^42 - 16 * q^43 - 8 * q^44 - 24 * q^46 + 20 * q^48 + 32 * q^51 - 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^63 - 28 * q^64 - 60 * q^68 + 28 * q^71 + 48 * q^73 - 28 * q^74 + 48 * q^77 - 92 * q^78 + 8 * q^79 + 28 * q^81 + 40 * q^82 + 40 * q^83 - 96 * q^86 - 48 * q^87 + 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 - 72 * q^93 - 32 * q^96 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.677603			0.479138			0.239569	−	0.970879i	$-0.422994\pi$
$2$	0.677603			0.479138			0.239569	+	0.970879i	$0.422994\pi$
$3$	1.66705	−	1.66705i	0.962474	−	0.962474i	−0.0368470	−	0.999321i	$-0.511731\pi$
$3$	1.66705	−	1.66705i	0.962474	−	0.962474i	0.999321	+	0.0368470i	$0.0117314\pi$
$4$	−1.54085			−0.770427
$5$		0			0
$5$		0			0
$6$	1.12960	−	1.12960i	0.461158	−	0.461158i
$7$	−3.02462	−	3.02462i	−1.14320	−	1.14320i	−0.987861	−	0.155339i	$-0.950353\pi$
$7$	−3.02462	−	3.02462i	−1.14320	−	1.14320i	−0.155339	−	0.987861i	$-0.549647\pi$
$8$	−2.39929			−0.848279
$9$		−	2.55814i		−	0.852712i
$10$		0			0
$11$	−1.17133	+	1.17133i	−0.353168	+	0.353168i	−0.861287	−	0.508119i	$-0.830341\pi$
$11$	−1.17133	+	1.17133i	−0.353168	+	0.353168i	0.508119	+	0.861287i	$0.330341\pi$
$12$	−2.56869	+	2.56869i	−0.741516	+	0.741516i
$13$		−	6.21427i		−	1.72353i	−0.507309	−	0.861764i	$-0.669360\pi$
$13$		−	6.21427i		−	1.72353i	0.507309	−	0.861764i	$-0.330640\pi$
$14$	−2.04950	−	2.04950i	−0.547751	−	0.547751i
$15$		0			0
$16$	1.45594			0.363984
$17$	3.90279	+	1.32974i	0.946566	+	0.322509i
$17$	3.90279	+	1.32974i	0.946566	+	0.322509i
$18$		−	1.73340i		−	0.408567i
$19$		−	3.38977i		−	0.777667i	−0.921308	−	0.388834i	$-0.872878\pi$
$19$		−	3.38977i		−	0.777667i	0.921308	−	0.388834i	$-0.127122\pi$
$20$		0			0
$21$	−10.0844			−2.20060
$22$	−0.793694	+	0.793694i	−0.169216	+	0.169216i
$23$	3.30530	+	3.30530i	0.689202	+	0.689202i	0.962056	−	0.272854i	$-0.0879675\pi$
$23$	3.30530	+	3.30530i	0.689202	+	0.689202i	−0.272854	+	0.962056i	$0.587967\pi$
$24$	−3.99975	+	3.99975i	−0.816446	+	0.816446i
$25$		0			0
$26$		−	4.21081i		−	0.825808i
$27$	0.736610	+	0.736610i	0.141761	+	0.141761i
$28$	4.66050	+	4.66050i	0.880752	+	0.880752i
$29$	2.57924	+	2.57924i	0.478952	+	0.478952i	0.904796	−	0.425844i	$-0.140023\pi$
$29$	2.57924	+	2.57924i	0.478952	+	0.478952i	−0.425844	+	0.904796i	$0.640023\pi$
$30$		0			0
$31$	−2.12106	−	2.12106i	−0.380953	−	0.380953i	0.490492	−	0.871446i	$-0.336817\pi$
$31$	−2.12106	−	2.12106i	−0.380953	−	0.380953i	−0.871446	+	0.490492i	$0.836817\pi$
$32$	5.78514			1.02268
$33$			3.90532i			0.679830i
$34$	2.64455	+	0.901035i	0.453536	+	0.154526i
$35$		0			0
$36$			3.94171i			0.656952i
$37$	3.78314	−	3.78314i	0.621945	−	0.621945i	−0.324083	−	0.946029i	$-0.605056\pi$
$37$	3.78314	−	3.78314i	0.621945	−	0.621945i	0.946029	+	0.324083i	$0.105056\pi$
$38$		−	2.29692i		−	0.372610i
$39$	−10.3595	−	10.3595i	−1.65885	−	1.65885i
$40$		0			0
$41$	−1.54740	+	1.54740i	−0.241664	+	0.241664i	−0.817538	−	0.575874i	$-0.804662\pi$
$41$	−1.54740	+	1.54740i	−0.241664	+	0.241664i	0.575874	+	0.817538i	$0.304662\pi$
$42$	−6.83324			−1.05439
$43$	0.998176			0.152220			0.0761102	−	0.997099i	$-0.475750\pi$
$43$	0.998176			0.152220			0.0761102	+	0.997099i	$0.475750\pi$
$44$	1.80484	−	1.80484i	0.272090	−	0.272090i
$45$		0			0
$46$	2.23968	+	2.23968i	0.330223	+	0.330223i
$47$			2.00393i			0.292303i	0.989262	+	0.146152i	$0.0466887\pi$
$47$			2.00393i			0.292303i	−0.989262	+	0.146152i	$0.953311\pi$
$48$	2.42713	−	2.42713i	0.350326	−	0.350326i
$49$			11.2967i			1.61381i
$50$		0			0
$51$	8.72291	−	4.28942i	1.22145	−	0.600639i
$52$			9.57528i			1.32785i
$53$	−6.95444			−0.955266			−0.477633	−	0.878560i	$-0.658505\pi$
$53$	−6.95444			−0.955266			−0.477633	+	0.878560i	$0.658505\pi$
$54$	0.499130	+	0.499130i	0.0679229	+	0.0679229i
$55$		0			0
$56$	7.25696	+	7.25696i	0.969752	+	0.969752i
$57$	−5.65093	−	5.65093i	−0.748484	−	0.748484i
$58$	1.74770	+	1.74770i	0.229484	+	0.229484i
$59$			6.30165i			0.820405i	0.911995	+	0.410202i	$0.134542\pi$
$59$			6.30165i			0.820405i	−0.911995	+	0.410202i	$0.865458\pi$
$60$		0			0
$61$	4.62096	−	4.62096i	0.591653	−	0.591653i	−0.346425	−	0.938078i	$-0.612604\pi$
$61$	4.62096	−	4.62096i	0.591653	−	0.591653i	0.938078	+	0.346425i	$0.112604\pi$
$62$	−1.43724	−	1.43724i	−0.182529	−	0.182529i
$63$	−7.73740	+	7.73740i	−0.974821	+	0.974821i
$64$	1.00815			0.126019
$65$		0			0
$66$			2.64626i			0.325732i
$67$		−	5.80078i		−	0.708678i	−0.935117	−	0.354339i	$-0.884706\pi$
$67$		−	5.80078i		−	0.708678i	0.935117	−	0.354339i	$-0.115294\pi$
$68$	−6.01363	−	2.04893i	−0.729260	−	0.248469i
$69$	11.0202			1.32668
$70$		0			0
$71$	−9.60714	−	9.60714i	−1.14016	−	1.14016i	−0.988421	−	0.151736i	$-0.951514\pi$
$71$	−9.60714	−	9.60714i	−1.14016	−	1.14016i	−0.151736	−	0.988421i	$-0.548486\pi$
$72$			6.13772i			0.723337i
$73$	7.01789	−	7.01789i	0.821382	−	0.821382i	−0.164924	−	0.986306i	$-0.552738\pi$
$73$	7.01789	−	7.01789i	0.821382	−	0.821382i	0.986306	+	0.164924i	$0.0527380\pi$
$74$	2.56347	−	2.56347i	0.297997	−	0.297997i
$75$		0			0
$76$			5.22314i			0.599136i
$77$	7.08564			0.807483
$78$	−7.01965	−	7.01965i	−0.794818	−	0.794818i
$79$	−0.820929	+	0.820929i	−0.0923617	+	0.0923617i	−0.751778	−	0.659416i	$-0.770803\pi$
$79$	−0.820929	+	0.820929i	−0.0923617	+	0.0923617i	0.659416	+	0.751778i	$0.270803\pi$
$80$		0			0
$81$	10.1303			1.12559
$82$	−1.04853	+	1.04853i	−0.115790	+	0.115790i
$83$	3.65934			0.401665			0.200832	−	0.979626i	$-0.435635\pi$
$83$	3.65934			0.401665			0.200832	+	0.979626i	$0.435635\pi$
$84$	15.5386			1.69540
$85$		0			0
$86$	0.676367			0.0729346
$87$	8.59945			0.921958
$88$	2.81035	−	2.81035i	0.299585	−	0.299585i
$89$	−2.69634			−0.285811			−0.142906	−	0.989736i	$-0.545645\pi$
$89$	−2.69634			−0.285811			−0.142906	+	0.989736i	$0.545645\pi$
$90$		0			0
$91$	−18.7958	+	18.7958i	−1.97034	+	1.97034i
$92$	−5.09298	−	5.09298i	−0.530980	−	0.530980i
$93$	−7.07184			−0.733315
$94$			1.35787i			0.140054i
$95$		0			0
$96$	9.64413	−	9.64413i	0.984300	−	0.984300i
$97$	7.40348	−	7.40348i	0.751709	−	0.751709i	−0.223089	−	0.974798i	$-0.571614\pi$
$97$	7.40348	−	7.40348i	0.751709	−	0.751709i	0.974798	+	0.223089i	$0.0716141\pi$
$98$			7.65468i			0.773239i
$99$	2.99641	+	2.99641i	0.301151	+	0.301151i
$100$		0			0
$101$	11.5529			1.14956			0.574779	−	0.818309i	$-0.305088\pi$
$101$	11.5529			1.14956			0.574779	+	0.818309i	$0.305088\pi$
$102$	5.91067	−	2.90653i	0.585244	−	0.287789i
$103$			11.3302i			1.11640i	0.829708	+	0.558198i	$0.188507\pi$
$103$			11.3302i			1.11640i	−0.829708	+	0.558198i	$0.811493\pi$
$104$			14.9099i			1.46203i
$105$		0			0
$106$	−4.71235			−0.457704
$107$	−4.29282	+	4.29282i	−0.415003	+	0.415003i	−0.883477	−	0.468474i	$-0.844804\pi$
$107$	−4.29282	+	4.29282i	−0.415003	+	0.415003i	0.468474	+	0.883477i	$0.344804\pi$
$108$	−1.13501	−	1.13501i	−0.109216	−	0.109216i
$109$	2.17036	−	2.17036i	0.207882	−	0.207882i	−0.595484	−	0.803367i	$-0.703040\pi$
$109$	2.17036	−	2.17036i	0.207882	−	0.207882i	0.803367	+	0.595484i	$0.203040\pi$
$110$		0			0
$111$		−	12.6134i		−	1.19721i
$112$	−4.40366	−	4.40366i	−0.416107	−	0.416107i
$113$	5.22143	+	5.22143i	0.491191	+	0.491191i	0.908681	−	0.417491i	$-0.137090\pi$
$113$	5.22143	+	5.22143i	0.491191	+	0.491191i	−0.417491	+	0.908681i	$0.637090\pi$
$114$	−3.82909	−	3.82909i	−0.358627	−	0.358627i
$115$		0			0
$116$	−3.97422	−	3.97422i	−0.368998	−	0.368998i
$117$	−15.8969			−1.46967
$118$			4.27002i			0.393087i
$119$	−7.78253	−	15.8264i	−0.713423	−	1.45081i
$120$		0			0
$121$			8.25599i			0.750545i
$122$	3.13118	−	3.13118i	0.283484	−	0.283484i
$123$			5.15921i			0.465191i
$124$	3.26824	+	3.26824i	0.293497	+	0.293497i
$125$		0			0
$126$	−5.24289	+	5.24289i	−0.467074	+	0.467074i
$127$	−14.3835			−1.27633			−0.638164	−	0.769900i	$-0.720306\pi$
$127$	−14.3835			−1.27633			−0.638164	+	0.769900i	$0.720306\pi$
$128$	−10.8871			−0.962297
$129$	1.66401	−	1.66401i	0.146508	−	0.146508i
$130$		0			0
$131$	−3.29797	−	3.29797i	−0.288145	−	0.288145i	0.548202	−	0.836346i	$-0.315313\pi$
$131$	−3.29797	−	3.29797i	−0.288145	−	0.288145i	−0.836346	+	0.548202i	$0.815313\pi$
$132$		−	6.01753i		−	0.523759i
$133$	−10.2528	+	10.2528i	−0.889029	+	0.889029i
$134$		−	3.93063i		−	0.339554i
$135$		0			0
$136$	−9.36395	−	3.19043i	−0.802952	−	0.273577i
$137$			14.5618i			1.24410i	0.782978	+	0.622049i	$0.213700\pi$
$137$			14.5618i			1.24410i	−0.782978	+	0.622049i	$0.786300\pi$
$138$	7.46733			0.635662
$139$	3.79682	+	3.79682i	0.322042	+	0.322042i	0.849550	−	0.527508i	$-0.176873\pi$
$139$	3.79682	+	3.79682i	0.322042	+	0.322042i	−0.527508	+	0.849550i	$0.676873\pi$
$140$		0			0
$141$	3.34066	+	3.34066i	0.281334	+	0.281334i
$142$	−6.50983	−	6.50983i	−0.546293	−	0.546293i
$143$	7.27893	+	7.27893i	0.608695	+	0.608695i
$144$		−	3.72449i		−	0.310374i
$145$		0			0
$146$	4.75535	−	4.75535i	0.393555	−	0.393555i
$147$	18.8322	+	18.8322i	1.55325	+	1.55325i
$148$	−5.82927	+	5.82927i	−0.479163	+	0.479163i
$149$	12.6885			1.03948			0.519741	−	0.854324i	$-0.326029\pi$
$149$	12.6885			1.03948			0.519741	+	0.854324i	$0.326029\pi$
$150$		0			0
$151$			16.2607i			1.32327i	0.749824	+	0.661637i	$0.230138\pi$
$151$			16.2607i			1.32327i	−0.749824	+	0.661637i	$0.769862\pi$
$152$			8.13306i			0.659678i
$153$	3.40165	−	9.98388i	0.275007	−	0.807149i
$154$	4.80125			0.386896
$155$		0			0
$156$	15.9625	+	15.9625i	1.27802	+	1.27802i
$157$		−	10.0238i		−	0.799985i	−0.916518	−	0.399993i	$-0.869013\pi$
$157$		−	10.0238i		−	0.799985i	0.916518	−	0.399993i	$-0.130987\pi$
$158$	−0.556264	+	0.556264i	−0.0442540	+	0.0442540i
$159$	−11.5934	+	11.5934i	−0.919418	+	0.919418i
$160$		0			0
$161$		−	19.9946i		−	1.57579i
$162$	6.86436			0.539315
$163$	−5.68932	−	5.68932i	−0.445622	−	0.445622i	0.448274	−	0.893896i	$-0.352039\pi$
$163$	−5.68932	−	5.68932i	−0.445622	−	0.445622i	−0.893896	+	0.448274i	$0.852039\pi$
$164$	2.38432	−	2.38432i	0.186184	−	0.186184i
$165$		0			0
$166$	2.47958			0.192453
$167$	9.12361	−	9.12361i	0.706006	−	0.706006i	−0.259687	−	0.965693i	$-0.583619\pi$
$167$	9.12361	−	9.12361i	0.706006	−	0.706006i	0.965693	+	0.259687i	$0.0836192\pi$
$168$	24.1955			1.86672
$169$	−25.6171			−1.97055
$170$		0			0
$171$	−8.67150			−0.663126
$172$	−1.53804			−0.117275
$173$	11.6412	−	11.6412i	0.885065	−	0.885065i	−0.108979	−	0.994044i	$-0.534758\pi$
$173$	11.6412	−	11.6412i	0.885065	−	0.885065i	0.994044	+	0.108979i	$0.0347581\pi$
$174$	5.82701			0.441745
$175$		0			0
$176$	−1.70538	+	1.70538i	−0.128548	+	0.128548i
$177$	10.5052	+	10.5052i	0.789618	+	0.789618i
$178$	−1.82705			−0.136943
$179$			13.9304i			1.04121i	0.853799	+	0.520603i	$0.174293\pi$
$179$			13.9304i			1.04121i	−0.853799	+	0.520603i	$0.825707\pi$
$180$		0			0
$181$	−9.22755	+	9.22755i	−0.685878	+	0.685878i	−0.961318	−	0.275440i	$-0.911176\pi$
$181$	−9.22755	+	9.22755i	−0.685878	+	0.685878i	0.275440	+	0.961318i	$0.411176\pi$
$182$	−12.7361	+	12.7361i	−0.944064	+	0.944064i
$183$		−	15.4068i		−	1.13890i
$184$	−7.93038	−	7.93038i	−0.584635	−	0.584635i
$185$		0			0
$186$	−4.79190			−0.351359
$187$	−6.12900	+	3.01389i	−0.448197	+	0.220397i
$188$		−	3.08776i		−	0.225198i
$189$		−	4.45594i		−	0.324122i
$190$		0			0
$191$	4.75563			0.344105			0.172053	−	0.985088i	$-0.444960\pi$
$191$	4.75563			0.344105			0.172053	+	0.985088i	$0.444960\pi$
$192$	1.68064	−	1.68064i	0.121290	−	0.121290i
$193$	−9.85705	−	9.85705i	−0.709526	−	0.709526i	0.256910	−	0.966435i	$-0.417296\pi$
$193$	−9.85705	−	9.85705i	−0.709526	−	0.709526i	−0.966435	+	0.256910i	$0.917296\pi$
$194$	5.01662	−	5.01662i	0.360172	−	0.360172i
$195$		0			0
$196$		−	17.4066i		−	1.24333i
$197$	−10.6844	−	10.6844i	−0.761232	−	0.761232i	0.215313	−	0.976545i	$-0.430923\pi$
$197$	−10.6844	−	10.6844i	−0.761232	−	0.761232i	−0.976545	+	0.215313i	$0.930923\pi$
$198$	2.03038	+	2.03038i	0.144293	+	0.144293i
$199$	1.44944	+	1.44944i	0.102748	+	0.102748i	0.756612	−	0.653864i	$-0.226853\pi$
$199$	1.44944	+	1.44944i	0.102748	+	0.102748i	−0.653864	+	0.756612i	$0.726853\pi$
$200$		0			0
$201$	−9.67021	−	9.67021i	−0.682084	−	0.682084i
$202$	7.82829			0.550797
$203$		−	15.6024i		−	1.09508i
$204$	−13.4407	+	6.60937i	−0.941039	+	0.462749i
$205$		0			0
$206$			7.67737i			0.534907i
$207$	8.45540	−	8.45540i	0.587691	−	0.587691i
$208$		−	9.04759i		−	0.627337i
$209$	3.97053	+	3.97053i	0.274647	+	0.274647i
$210$		0			0
$211$	−0.309914	+	0.309914i	−0.0213353	+	0.0213353i	−0.717694	−	0.696359i	$-0.754802\pi$
$211$	−0.309914	+	0.309914i	−0.0213353	+	0.0213353i	0.696359	+	0.717694i	$0.254802\pi$
$212$	10.7158			0.735962
$213$	−32.0312			−2.19474
$214$	−2.90883	+	2.90883i	−0.198844	+	0.198844i
$215$		0			0
$216$	−1.76734	−	1.76734i	−0.120253	−	0.120253i
$217$			12.8308i			0.871012i
$218$	1.47064	−	1.47064i	0.0996044	−	0.0996044i
$219$		−	23.3984i		−	1.58112i
$220$		0			0
$221$	8.26335	−	24.2530i	0.555853	−	1.63143i
$222$		−	8.54689i		−	0.573630i
$223$	27.2421			1.82427			0.912134	−	0.409893i	$-0.134434\pi$
$223$	27.2421			1.82427			0.912134	+	0.409893i	$0.134434\pi$
$224$	−17.4979	−	17.4979i	−1.16913	−	1.16913i
$225$		0			0
$226$	3.53806	+	3.53806i	0.235348	+	0.235348i
$227$	−6.54878	−	6.54878i	−0.434658	−	0.434658i	0.455551	−	0.890209i	$-0.349442\pi$
$227$	−6.54878	−	6.54878i	−0.434658	−	0.434658i	−0.890209	+	0.455551i	$0.849442\pi$
$228$	8.70726	+	8.70726i	0.576652	+	0.576652i
$229$		−	11.0731i		−	0.731728i	−0.930668	−	0.365864i	$-0.880773\pi$
$229$		−	11.0731i		−	0.731728i	0.930668	−	0.365864i	$-0.119227\pi$
$230$		0			0
$231$	11.8121	−	11.8121i	0.777182	−	0.777182i
$232$	−6.18835	−	6.18835i	−0.406285	−	0.406285i
$233$	10.9498	−	10.9498i	0.717344	−	0.717344i	−0.250717	−	0.968060i	$-0.580666\pi$
$233$	10.9498	−	10.9498i	0.717344	−	0.717344i	0.968060	+	0.250717i	$0.0806663\pi$
$234$	−10.7718			−0.704176
$235$		0			0
$236$		−	9.70992i		−	0.632062i
$237$			2.73706i			0.177791i
$238$	−5.27347	−	10.7240i	−0.341828	−	0.695137i
$239$	−2.34216			−0.151501			−0.0757507	−	0.997127i	$-0.524135\pi$
$239$	−2.34216			−0.151501			−0.0757507	+	0.997127i	$0.524135\pi$
$240$		0			0
$241$	21.5910	+	21.5910i	1.39080	+	1.39080i	0.823545	+	0.567251i	$0.191993\pi$
$241$	21.5910	+	21.5910i	1.39080	+	1.39080i	0.567251	+	0.823545i	$0.308007\pi$
$242$			5.59429i			0.359615i
$243$	14.6780	−	14.6780i	0.941594	−	0.941594i
$244$	−7.12022	+	7.12022i	−0.455826	+	0.455826i
$245$		0			0
$246$			3.49590i			0.222890i
$247$	−21.0650			−1.34033
$248$	5.08904	+	5.08904i	0.323154	+	0.323154i
$249$	6.10032	−	6.10032i	0.386592	−	0.386592i
$250$		0			0
$251$	−9.23001			−0.582593			−0.291297	−	0.956633i	$-0.594087\pi$
$251$	−9.23001			−0.582593			−0.291297	+	0.956633i	$0.594087\pi$
$252$	11.9222	−	11.9222i	0.751028	−	0.751028i
$253$	−7.74315			−0.486808
$254$	−9.74630			−0.611537
$255$		0			0
$256$	−9.39347			−0.587092
$257$	−3.23036			−0.201504			−0.100752	−	0.994912i	$-0.532125\pi$
$257$	−3.23036			−0.201504			−0.100752	+	0.994912i	$0.532125\pi$
$258$	1.12754	−	1.12754i	0.0701976	−	0.0701976i
$259$	−22.8852			−1.42202
$260$		0			0
$261$	6.59804	−	6.59804i	0.408408	−	0.408408i
$262$	−2.23471	−	2.23471i	−0.138061	−	0.138061i
$263$	−12.4719			−0.769051			−0.384526	−	0.923114i	$-0.625635\pi$
$263$	−12.4719			−0.769051			−0.384526	+	0.923114i	$0.625635\pi$
$264$		−	9.37002i		−	0.576685i
$265$		0			0
$266$	−6.94732	+	6.94732i	−0.425968	+	0.425968i
$267$	−4.49494	+	4.49494i	−0.275086	+	0.275086i
$268$			8.93815i			0.545984i
$269$	−0.219219	−	0.219219i	−0.0133660	−	0.0133660i	0.700392	−	0.713758i	$-0.253008\pi$
$269$	−0.219219	−	0.219219i	−0.0133660	−	0.0133660i	−0.713758	+	0.700392i	$0.753008\pi$
$270$		0			0
$271$	−18.3441			−1.11433			−0.557164	−	0.830403i	$-0.688110\pi$
$271$	−18.3441			−1.11433			−0.557164	+	0.830403i	$0.688110\pi$
$272$	5.68222	+	1.93602i	0.344535	+	0.117388i
$273$			62.6673i			3.79280i
$274$			9.86712i			0.596094i
$275$		0			0
$276$	−16.9805			−1.02211
$277$	9.01877	−	9.01877i	0.541885	−	0.541885i	−0.382196	−	0.924081i	$-0.624832\pi$
$277$	9.01877	−	9.01877i	0.541885	−	0.541885i	0.924081	+	0.382196i	$0.124832\pi$
$278$	2.57274	+	2.57274i	0.154303	+	0.154303i
$279$	−5.42596	+	5.42596i	−0.324843	+	0.324843i
$280$		0			0
$281$			31.1275i			1.85691i	0.371441	+	0.928457i	$0.378864\pi$
$281$			31.1275i			1.85691i	−0.371441	+	0.928457i	$0.621136\pi$
$282$	2.26364	+	2.26364i	0.134798	+	0.134798i
$283$	−19.6967	−	19.6967i	−1.17084	−	1.17084i	−0.982009	−	0.188836i	$-0.939528\pi$
$283$	−19.6967	−	19.6967i	−1.17084	−	1.17084i	−0.188836	−	0.982009i	$-0.560472\pi$
$284$	14.8032	+	14.8032i	0.878408	+	0.878408i
$285$		0			0
$286$	4.93223	+	4.93223i	0.291649	+	0.291649i
$287$	9.36063			0.552541
$288$		−	14.7992i		−	0.872049i
$289$	13.4636	+	10.3794i	0.791976	+	0.610552i
$290$		0			0
$291$		−	24.6840i		−	1.44700i
$292$	−10.8135	+	10.8135i	−0.632815	+	0.632815i
$293$			31.4302i			1.83617i	0.396381	+	0.918086i	$0.370266\pi$
$293$			31.4302i			1.83617i	−0.396381	+	0.918086i	$0.629734\pi$
$294$	12.7608	+	12.7608i	0.744223	+	0.744223i
$295$		0			0
$296$	−9.07688	+	9.07688i	−0.527583	+	0.527583i
$297$	−1.72562			−0.100131
$298$	8.59776			0.498055
$299$	20.5400	−	20.5400i	1.18786	−	1.18786i
$300$		0			0
$301$	−3.01911	−	3.01911i	−0.174018	−	0.174018i
$302$			11.0183i			0.634031i
$303$	19.2593	−	19.2593i	1.10642	−	1.10642i
$304$		−	4.93530i		−	0.283059i
$305$		0			0
$306$	2.30497	−	6.76511i	0.131766	−	0.386736i
$307$			4.21985i			0.240839i	0.992723	+	0.120420i	$0.0384240\pi$
$307$			4.21985i			0.240839i	−0.992723	+	0.120420i	$0.961576\pi$
$308$	−10.9179			−0.622107
$309$	18.8880	+	18.8880i	1.07450	+	1.07450i
$310$		0			0
$311$	10.8965	+	10.8965i	0.617882	+	0.617882i	0.944988	−	0.327105i	$-0.106073\pi$
$311$	10.8965	+	10.8965i	0.617882	+	0.617882i	−0.327105	+	0.944988i	$0.606073\pi$
$312$	24.8555	+	24.8555i	1.40717	+	1.40717i
$313$	7.67977	+	7.67977i	0.434086	+	0.434086i	0.890016	−	0.455930i	$-0.150693\pi$
$313$	7.67977	+	7.67977i	0.434086	+	0.434086i	−0.455930	+	0.890016i	$0.650693\pi$
$314$		−	6.79215i		−	0.383303i
$315$		0			0
$316$	1.26493	−	1.26493i	0.0711579	−	0.0711579i
$317$	−20.4263	−	20.4263i	−1.14726	−	1.14726i	−0.987090	−	0.160167i	$-0.948797\pi$
$317$	−20.4263	−	20.4263i	−1.14726	−	1.14726i	−0.160167	−	0.987090i	$-0.551203\pi$
$318$	−7.85574	+	7.85574i	−0.440528	+	0.440528i
$319$	−6.04225			−0.338301
$320$		0			0
$321$			14.3127i			0.798859i
$322$		−	13.5484i		−	0.755022i
$323$	4.50751	−	13.2296i	0.250804	−	0.736114i
$324$	−15.6094			−0.867188
$325$		0			0
$326$	−3.85510	−	3.85510i	−0.213514	−	0.213514i
$327$		−	7.23620i		−	0.400163i
$328$	3.71268	−	3.71268i	0.204998	−	0.204998i
$329$	6.06113	−	6.06113i	0.334161	−	0.334161i
$330$		0			0
$331$		−	7.29249i		−	0.400832i	−0.979711	−	0.200416i	$-0.935771\pi$
$331$		−	7.29249i		−	0.400832i	0.979711	−	0.200416i	$-0.0642293\pi$
$332$	−5.63851			−0.309453
$333$	−9.67780	−	9.67780i	−0.530340	−	0.530340i
$334$	6.18219	−	6.18219i	0.338274	−	0.338274i
$335$		0			0
$336$	−14.6823			−0.800985
$337$	−9.47979	+	9.47979i	−0.516397	+	0.516397i	−0.916479	−	0.400082i	$-0.868982\pi$
$337$	−9.47979	+	9.47979i	−0.516397	+	0.516397i	0.400082	+	0.916479i	$0.368982\pi$
$338$	−17.3583			−0.944165
$339$	17.4088			0.945516
$340$		0			0
$341$	4.96890			0.269081
$342$	−5.87584			−0.317729
$343$	12.9959	−	12.9959i	0.701712	−	0.701712i
$344$	−2.39492			−0.129125
$345$		0			0
$346$	7.88813	−	7.88813i	0.424068	−	0.424068i
$347$	23.6284	+	23.6284i	1.26844	+	1.26844i	0.946895	+	0.321543i	$0.104202\pi$
$347$	23.6284	+	23.6284i	1.26844	+	1.26844i	0.321543	+	0.946895i	$0.395798\pi$
$348$	−13.2505			−0.710301
$349$			22.4213i			1.20019i	0.799930	+	0.600093i	$0.204870\pi$
$349$			22.4213i			1.20019i	−0.799930	+	0.600093i	$0.795130\pi$
$350$		0			0
$351$	4.57749	−	4.57749i	0.244329	−	0.244329i
$352$	−6.77628	+	6.77628i	−0.361177	+	0.361177i
$353$			22.2555i			1.18454i	0.805739	+	0.592270i	$0.201768\pi$
$353$			22.2555i			1.18454i	−0.805739	+	0.592270i	$0.798232\pi$
$354$	7.11835	+	7.11835i	0.378336	+	0.378336i
$355$		0			0
$356$	4.15466			0.220197
$357$	−39.3574	−	13.4096i	−2.08302	−	0.709713i
$358$			9.43927i			0.498881i
$359$		−	36.6674i		−	1.93523i	−0.252424	−	0.967617i	$-0.581228\pi$
$359$		−	36.6674i		−	1.93523i	0.252424	−	0.967617i	$-0.418772\pi$
$360$		0			0
$361$	7.50945			0.395234
$362$	−6.25262	+	6.25262i	−0.328630	+	0.328630i
$363$	13.7632	+	13.7632i	0.722380	+	0.722380i
$364$	28.9616	−	28.9616i	1.51800	−	1.51800i
$365$		0			0
$366$		−	10.4397i		−	0.545691i
$367$	0.0960113	+	0.0960113i	0.00501175	+	0.00501175i	0.709608	−	0.704596i	$-0.248872\pi$
$367$	0.0960113	+	0.0960113i	0.00501175	+	0.00501175i	−0.704596	+	0.709608i	$0.748872\pi$
$368$	4.81231	+	4.81231i	0.250859	+	0.250859i
$369$	3.95847	+	3.95847i	0.206070	+	0.206070i
$370$		0			0
$371$	21.0346	+	21.0346i	1.09206	+	1.09206i
$372$	10.8967			0.564966
$373$		−	0.927465i		−	0.0480223i	−0.999712	−	0.0240111i	$-0.992356\pi$
$373$		−	0.927465i		−	0.0480223i	0.999712	−	0.0240111i	$-0.00764372\pi$
$374$	−4.15303	+	2.04222i	−0.214748	+	0.105601i
$375$		0			0
$376$		−	4.80802i		−	0.247955i
$377$	16.0281	−	16.0281i	0.825487	−	0.825487i
$378$		−	3.01936i		−	0.155299i
$379$	−5.93013	−	5.93013i	−0.304610	−	0.304610i	0.538204	−	0.842814i	$-0.319103\pi$
$379$	−5.93013	−	5.93013i	−0.304610	−	0.304610i	−0.842814	+	0.538204i	$0.819103\pi$
$380$		0			0
$381$	−23.9780	+	23.9780i	−1.22843	+	1.22843i
$382$	3.22243			0.164874
$383$	−21.9106			−1.11958			−0.559789	−	0.828635i	$-0.689118\pi$
$383$	−21.9106			−1.11958			−0.559789	+	0.828635i	$0.689118\pi$
$384$	−18.1495	+	18.1495i	−0.926186	+	0.926186i
$385$		0			0
$386$	−6.67917	−	6.67917i	−0.339961	−	0.339961i
$387$		−	2.55347i		−	0.129800i
$388$	−11.4077	+	11.4077i	−0.579137	+	0.579137i
$389$			12.7622i			0.647071i	0.946216	+	0.323536i	$0.104872\pi$
$389$			12.7622i			0.647071i	−0.946216	+	0.323536i	$0.895128\pi$
$390$		0			0
$391$	8.50471	+	17.2951i	0.430102	+	0.874649i
$392$		−	27.1041i		−	1.36896i
$393$	−10.9958			−0.554663
$394$	−7.23979	−	7.23979i	−0.364735	−	0.364735i
$395$		0			0
$396$	−4.61703	−	4.61703i	−0.232014	−	0.232014i
$397$	17.8029	+	17.8029i	0.893501	+	0.893501i	0.994851	−	0.101350i	$-0.0323162\pi$
$397$	17.8029	+	17.8029i	0.893501	+	0.893501i	−0.101350	+	0.994851i	$0.532316\pi$
$398$	0.982144	+	0.982144i	0.0492304	+	0.0492304i
$399$			34.1839i			1.71133i
$400$		0			0
$401$	4.08634	−	4.08634i	0.204062	−	0.204062i	−0.597676	−	0.801738i	$-0.703909\pi$
$401$	4.08634	−	4.08634i	0.204062	−	0.204062i	0.801738	+	0.597676i	$0.203909\pi$
$402$	−6.55256	−	6.55256i	−0.326812	−	0.326812i
$403$	−13.1808	+	13.1808i	−0.656584	+	0.656584i
$404$	−17.8014			−0.885650
$405$		0			0
$406$		−	10.5723i		−	0.524693i
$407$			8.86259i			0.439302i
$408$	−20.9288	+	10.2916i	−1.03613	+	0.509509i
$409$	15.4742			0.765149			0.382575	−	0.923925i	$-0.375037\pi$
$409$	15.4742			0.765149			0.382575	+	0.923925i	$0.375037\pi$
$410$		0			0
$411$	24.2753	+	24.2753i	1.19741	+	1.19741i
$412$		−	17.4581i		−	0.860101i
$413$	19.0601	−	19.0601i	0.937887	−	0.937887i
$414$	5.72941	−	5.72941i	0.281585	−	0.281585i
$415$		0			0
$416$		−	35.9504i		−	1.76261i
$417$	12.6590			0.619915
$418$	2.69044	+	2.69044i	0.131594	+	0.131594i
$419$	−12.8210	+	12.8210i	−0.626348	+	0.626348i	−0.947147	−	0.320799i	$-0.896048\pi$
$419$	−12.8210	+	12.8210i	−0.626348	+	0.626348i	0.320799	+	0.947147i	$0.396048\pi$
$420$		0			0
$421$	9.81137			0.478177			0.239089	−	0.970998i	$-0.423151\pi$
$421$	9.81137			0.478177			0.239089	+	0.970998i	$0.423151\pi$
$422$	−0.209998	+	0.209998i	−0.0102226	+	0.0102226i
$423$	5.12633			0.249250
$424$	16.6857			0.810331
$425$		0			0
$426$	−21.7045			−1.05158
$427$	−27.9533			−1.35276
$428$	6.61461	−	6.61461i	0.319729	−	0.319729i
$429$	24.2687			1.17171
$430$		0			0
$431$	12.8168	−	12.8168i	0.617364	−	0.617364i	−0.327490	−	0.944855i	$-0.606203\pi$
$431$	12.8168	−	12.8168i	0.617364	−	0.617364i	0.944855	+	0.327490i	$0.106203\pi$
$432$	1.07246	+	1.07246i	0.0515987	+	0.0515987i
$433$	−12.8308			−0.616610			−0.308305	−	0.951287i	$-0.599762\pi$
$433$	−12.8308			−0.616610			−0.308305	+	0.951287i	$0.599762\pi$
$434$			8.69420i			0.417335i
$435$		0			0
$436$	−3.34420	+	3.34420i	−0.160158	+	0.160158i
$437$	11.2042	−	11.2042i	0.535970	−	0.535970i
$438$		−	15.8548i		−	0.757573i
$439$	17.1720	+	17.1720i	0.819573	+	0.819573i	0.986046	−	0.166473i	$-0.0532379\pi$
$439$	17.1720	+	17.1720i	0.819573	+	0.819573i	−0.166473	+	0.986046i	$0.553238\pi$
$440$		0			0
$441$	28.8985			1.37612
$442$	5.59927	−	16.4339i	0.266330	−	0.781682i
$443$		−	16.1216i		−	0.765962i	−0.923756	−	0.382981i	$-0.874897\pi$
$443$		−	16.1216i		−	0.765962i	0.923756	−	0.382981i	$-0.125103\pi$
$444$			19.4354i			0.922364i
$445$		0			0
$446$	18.4594			0.874076
$447$	21.1524	−	21.1524i	1.00047	−	1.00047i
$448$	−3.04928	−	3.04928i	−0.144065	−	0.144065i
$449$	−13.5245	+	13.5245i	−0.638259	+	0.638259i	−0.950126	−	0.311867i	$-0.899046\pi$
$449$	−13.5245	+	13.5245i	−0.638259	+	0.638259i	0.311867	+	0.950126i	$0.399046\pi$
$450$		0			0
$451$		−	3.62503i		−	0.170696i
$452$	−8.04546	−	8.04546i	−0.378426	−	0.378426i
$453$	27.1074	+	27.1074i	1.27362	+	1.27362i
$454$	−4.43748	−	4.43748i	−0.208261	−	0.208261i
$455$		0			0
$456$	13.5582	+	13.5582i	0.634923	+	0.634923i
$457$	3.68314			0.172290			0.0861451	−	0.996283i	$-0.472545\pi$
$457$	3.68314			0.172290			0.0861451	+	0.996283i	$0.472545\pi$
$458$		−	7.50314i		−	0.350599i
$459$	1.89534	+	3.85434i	0.0884669	+	0.179905i
$460$		0			0
$461$			19.7569i			0.920172i	0.887874	+	0.460086i	$0.152181\pi$
$461$			19.7569i			0.920172i	−0.887874	+	0.460086i	$0.847819\pi$
$462$	8.00394	−	8.00394i	0.372377	−	0.372377i
$463$			23.6496i			1.09909i	0.835464	+	0.549545i	$0.185199\pi$
$463$			23.6496i			1.09909i	−0.835464	+	0.549545i	$0.814801\pi$
$464$	3.75521	+	3.75521i	0.174331	+	0.174331i
$465$		0			0
$466$	7.41961	−	7.41961i	0.343707	−	0.343707i
$467$	−5.50118			−0.254564			−0.127282	−	0.991867i	$-0.540625\pi$
$467$	−5.50118			−0.254564			−0.127282	+	0.991867i	$0.540625\pi$
$468$	24.4949			1.13228
$469$	−17.5452	+	17.5452i	−0.810161	+	0.810161i
$470$		0			0
$471$	−16.7102	−	16.7102i	−0.769965	−	0.769965i
$472$		−	15.1195i		−	0.695932i
$473$	−1.16919	+	1.16919i	−0.0537594	+	0.0537594i
$474$			1.85464i			0.0851866i
$475$		0			0
$476$	11.9917	+	24.3862i	0.549640	+	1.11774i
$477$			17.7904i			0.814567i
$478$	−1.58705			−0.0725901
$479$	−7.89487	−	7.89487i	−0.360726	−	0.360726i	0.503354	−	0.864080i	$-0.332099\pi$
$479$	−7.89487	−	7.89487i	−0.360726	−	0.360726i	−0.864080	+	0.503354i	$0.832099\pi$
$480$		0			0
$481$	−23.5095	−	23.5095i	−1.07194	−	1.07194i
$482$	14.6301	+	14.6301i	0.666383	+	0.666383i
$483$	−33.3320	−	33.3320i	−1.51666	−	1.51666i
$484$		−	12.7213i		−	0.578240i
$485$		0			0
$486$	9.94586	−	9.94586i	0.451154	−	0.451154i
$487$	25.0619	+	25.0619i	1.13566	+	1.13566i	0.989219	+	0.146443i	$0.0467825\pi$
$487$	25.0619	+	25.0619i	1.13566	+	1.13566i	0.146443	+	0.989219i	$0.453218\pi$
$488$	−11.0870	+	11.0870i	−0.501887	+	0.501887i
$489$	−18.9688			−0.857799
$490$		0			0
$491$			12.8558i			0.580175i	0.957000	+	0.290087i	$0.0936844\pi$
$491$			12.8558i			0.580175i	−0.957000	+	0.290087i	$0.906316\pi$
$492$		−	7.94959i		−	0.358395i
$493$	6.63652	+	13.4959i	0.298894	+	0.607826i
$494$	−14.2737			−0.642203
$495$		0			0
$496$	−3.08813	−	3.08813i	−0.138661	−	0.138661i
$497$			58.1159i			2.60686i
$498$	4.13360	−	4.13360i	0.185231	−	0.185231i
$499$	13.1434	−	13.1434i	0.588380	−	0.588380i	−0.348813	−	0.937192i	$-0.613415\pi$
$499$	13.1434	−	13.1434i	0.588380	−	0.588380i	0.937192	+	0.348813i	$0.113415\pi$
$500$		0			0
$501$		−	30.4191i		−	1.35903i
$502$	−6.25429			−0.279143
$503$	−24.0464	−	24.0464i	−1.07217	−	1.07217i	−0.997184	−	0.0749899i	$-0.976108\pi$
$503$	−24.0464	−	24.0464i	−1.07217	−	1.07217i	−0.0749899	−	0.997184i	$-0.523892\pi$
$504$	18.5643	−	18.5643i	0.826920	−	0.826920i
$505$		0			0
$506$	−5.24679			−0.233248
$507$	−42.7052	+	42.7052i	−1.89660	+	1.89660i
$508$	22.1629			0.983318
$509$	29.8369			1.32250			0.661249	−	0.750167i	$-0.270027\pi$
$509$	29.8369			1.32250			0.661249	+	0.750167i	$0.270027\pi$
$510$		0			0
$511$	−42.4530			−1.87801
$512$	15.4092			0.680999
$513$	2.49694	−	2.49694i	0.110243	−	0.110243i
$514$	−2.18890			−0.0965483
$515$		0			0
$516$	−2.56400	+	2.56400i	−0.112874	+	0.112874i
$517$	−2.34725	−	2.34725i	−0.103232	−	0.103232i
$518$	−15.5071			−0.681342
$519$		−	38.8131i		−	1.70370i
$520$		0			0
$521$	−27.1655	+	27.1655i	−1.19014	+	1.19014i	−0.213116	+	0.977027i	$0.568361\pi$
$521$	−27.1655	+	27.1655i	−1.19014	+	1.19014i	−0.977027	+	0.213116i	$0.931639\pi$
$522$	4.47085	−	4.47085i	0.195684	−	0.195684i
$523$			20.2414i			0.885093i	0.896745	+	0.442547i	$0.145925\pi$
$523$			20.2414i			0.885093i	−0.896745	+	0.442547i	$0.854075\pi$
$524$	5.08168	+	5.08168i	0.221994	+	0.221994i
$525$		0			0
$526$	−8.45101			−0.368482
$527$	−5.45760	−	11.0985i	−0.237737	−	0.483458i
$528$			5.68591i			0.247447i
$529$		−	1.15003i		−	0.0500014i
$530$		0			0
$531$	16.1205			0.699569
$532$	15.7980	−	15.7980i	0.684932	−	0.684932i
$533$	9.61599	+	9.61599i	0.416515	+	0.416515i
$534$	−3.04579	+	3.04579i	−0.131804	+	0.131804i
$535$		0			0
$536$			13.9178i			0.601156i
$537$	23.2227	+	23.2227i	1.00213	+	1.00213i
$538$	−0.148544	−	0.148544i	−0.00640417	−	0.00640417i
$539$	−13.2321	−	13.2321i	−0.569947	−	0.569947i
$540$		0			0
$541$	5.16605	+	5.16605i	0.222106	+	0.222106i	0.809385	−	0.587279i	$-0.199801\pi$
$541$	5.16605	+	5.16605i	0.222106	+	0.222106i	−0.587279	+	0.809385i	$0.699801\pi$
$542$	−12.4301			−0.533916
$543$			30.7656i			1.32028i
$544$	22.5782	+	7.69271i	0.968032	+	0.329822i
$545$		0			0
$546$			42.4636i			1.81727i
$547$	−30.9108	+	30.9108i	−1.32165	+	1.32165i	−0.409207	+	0.912442i	$0.634194\pi$
$547$	−30.9108	+	30.9108i	−1.32165	+	1.32165i	−0.912442	+	0.409207i	$0.865806\pi$
$548$		−	22.4376i		−	0.958486i
$549$	−11.8210	−	11.8210i	−0.504510	−	0.504510i
$550$		0			0
$551$	8.74302	−	8.74302i	0.372465	−	0.372465i
$552$	−26.4407			−1.12539
$553$	4.96600			0.211176
$554$	6.11115	−	6.11115i	0.259638	−	0.259638i
$555$		0			0
$556$	−5.85035	−	5.85035i	−0.248110	−	0.248110i
$557$		−	29.0497i		−	1.23088i	−0.788185	−	0.615438i	$-0.788979\pi$
$557$		−	29.0497i		−	1.23088i	0.788185	−	0.615438i	$-0.211021\pi$
$558$	−3.67665	+	3.67665i	−0.155645	+	0.155645i
$559$		−	6.20293i		−	0.262356i
$560$		0			0
$561$	−5.19306	+	15.2417i	−0.219251	+	0.643504i
$562$			21.0921i			0.889718i
$563$	39.3006			1.65632			0.828162	−	0.560489i	$-0.189387\pi$
$563$	39.3006			1.65632			0.828162	+	0.560489i	$0.189387\pi$
$564$	−5.14747	−	5.14747i	−0.216747	−	0.216747i
$565$		0			0
$566$	−13.3465	−	13.3465i	−0.560996	−	0.560996i
$567$	−30.6405	−	30.6405i	−1.28678	−	1.28678i
$568$	23.0503	+	23.0503i	0.967171	+	0.967171i
$569$			14.3009i			0.599525i	0.954014	+	0.299763i	$0.0969075\pi$
$569$			14.3009i			0.599525i	−0.954014	+	0.299763i	$0.903093\pi$
$570$		0			0
$571$	16.9121	−	16.9121i	0.707750	−	0.707750i	−0.258311	−	0.966062i	$-0.583166\pi$
$571$	16.9121	−	16.9121i	0.707750	−	0.707750i	0.966062	+	0.258311i	$0.0831660\pi$
$572$	−11.2158	−	11.2158i	−0.468955	−	0.468955i
$573$	7.92789	−	7.92789i	0.331192	−	0.331192i
$574$	6.34280			0.264743
$575$		0			0
$576$		−	2.57899i		−	0.107458i
$577$			5.85190i			0.243618i	0.992554	+	0.121809i	$0.0388695\pi$
$577$			5.85190i			0.243618i	−0.992554	+	0.121809i	$0.961131\pi$
$578$	9.12298	+	7.03310i	0.379466	+	0.292539i
$579$	−32.8645			−1.36580
$580$		0			0
$581$	−11.0681	−	11.0681i	−0.459183	−	0.459183i
$582$		−	16.7259i		−	0.693313i
$583$	8.14591	−	8.14591i	0.337369	−	0.337369i
$584$	−16.8380	+	16.8380i	−0.696761	+	0.696761i
$585$		0			0
$586$			21.2972i			0.879779i
$587$	−2.30210			−0.0950176			−0.0475088	−	0.998871i	$-0.515128\pi$
$587$	−2.30210			−0.0950176			−0.0475088	+	0.998871i	$0.515128\pi$
$588$	−29.0177	−	29.0177i	−1.19667	−	1.19667i
$589$	−7.18990	+	7.18990i	−0.296255	+	0.296255i
$590$		0			0
$591$	−35.6230			−1.46533
$592$	5.50802	−	5.50802i	0.226378	−	0.226378i
$593$	−4.89325			−0.200942			−0.100471	−	0.994940i	$-0.532035\pi$
$593$	−4.89325			−0.200942			−0.100471	+	0.994940i	$0.532035\pi$
$594$	−1.16929			−0.0479764
$595$		0			0
$596$	−19.5511			−0.800844
$597$	4.83258			0.197784
$598$	13.9180	−	13.9180i	0.569148	−	0.569148i
$599$	6.54372			0.267369			0.133685	−	0.991024i	$-0.457319\pi$
$599$	6.54372			0.267369			0.133685	+	0.991024i	$0.457319\pi$
$600$		0			0
$601$	11.3611	−	11.3611i	0.463431	−	0.463431i	−0.436347	−	0.899778i	$-0.643728\pi$
$601$	11.3611	−	11.3611i	0.463431	−	0.463431i	0.899778	+	0.436347i	$0.143728\pi$
$602$	−2.04576	−	2.04576i	−0.0833788	−	0.0833788i
$603$	−14.8392			−0.604298
$604$		−	25.0553i		−	1.01949i
$605$		0			0
$606$	13.0502	−	13.0502i	0.530128	−	0.530128i
$607$	30.8472	−	30.8472i	1.25205	−	1.25205i	0.297247	−	0.954801i	$-0.403932\pi$
$607$	30.8472	−	30.8472i	1.25205	−	1.25205i	0.954801	−	0.297247i	$-0.0960685\pi$
$608$		−	19.6103i		−	0.795302i
$609$	−26.0101	−	26.0101i	−1.05398	−	1.05398i
$610$		0			0
$611$	12.4530			0.503793
$612$	−5.24145	+	15.3837i	−0.211873	+	0.621849i
$613$		−	24.9253i		−	1.00672i	−0.864076	−	0.503362i	$-0.832096\pi$
$613$		−	24.9253i		−	1.00672i	0.864076	−	0.503362i	$-0.167904\pi$
$614$			2.85938i			0.115395i
$615$		0			0
$616$	−17.0005			−0.684971
$617$	−12.6091	+	12.6091i	−0.507625	+	0.507625i	−0.913797	−	0.406172i	$-0.866863\pi$
$617$	−12.6091	+	12.6091i	−0.507625	+	0.507625i	0.406172	+	0.913797i	$0.366863\pi$
$618$	12.7986	+	12.7986i	0.514834	+	0.514834i
$619$	−19.5300	+	19.5300i	−0.784977	+	0.784977i	−0.980666	−	0.195689i	$-0.937306\pi$
$619$	−19.5300	+	19.5300i	−0.784977	+	0.784977i	0.195689	+	0.980666i	$0.437306\pi$
$620$		0			0
$621$			4.86943i			0.195404i
$622$	7.38349	+	7.38349i	0.296051	+	0.296051i
$623$	8.15541	+	8.15541i	0.326740	+	0.326740i
$624$	−15.0828	−	15.0828i	−0.603796	−	0.603796i
$625$		0			0
$626$	5.20384	+	5.20384i	0.207987	+	0.207987i
$627$	13.2382			0.528681
$628$			15.4452i			0.616330i
$629$	19.7954	−	9.73424i	0.789295	−	0.388130i
$630$		0			0
$631$		−	38.2023i		−	1.52081i	−0.649448	−	0.760406i	$-0.725000\pi$
$631$		−	38.2023i		−	1.52081i	0.649448	−	0.760406i	$-0.275000\pi$
$632$	1.96965	−	1.96965i	0.0783484	−	0.0783484i
$633$			1.03329i			0.0410694i
$634$	−13.8409	−	13.8409i	−0.549694	−	0.549694i
$635$		0			0
$636$	17.8638	−	17.8638i	0.708345	−	0.708345i
$637$	70.2007			2.78145
$638$	−4.09425			−0.162093
$639$	−24.5764	+	24.5764i	−0.972226	+	0.972226i
$640$		0			0
$641$	−16.4472	−	16.4472i	−0.649623	−	0.649623i	0.303279	−	0.952902i	$-0.401919\pi$
$641$	−16.4472	−	16.4472i	−0.649623	−	0.649623i	−0.952902	+	0.303279i	$0.901919\pi$
$642$			9.69836i			0.382764i
$643$	4.84007	−	4.84007i	0.190874	−	0.190874i	−0.605200	−	0.796074i	$-0.706907\pi$
$643$	4.84007	−	4.84007i	0.190874	−	0.190874i	0.796074	+	0.605200i	$0.206907\pi$
$644$			30.8087i			1.21403i
$645$		0			0
$646$	3.05430	−	8.96441i	0.120170	−	0.352700i
$647$		−	39.1427i		−	1.53886i	−0.638732	−	0.769429i	$-0.720541\pi$
$647$		−	39.1427i		−	1.53886i	0.638732	−	0.769429i	$-0.279459\pi$
$648$	−24.3057			−0.954817
$649$	−7.38128	−	7.38128i	−0.289741	−	0.289741i
$650$		0			0
$651$	21.3896	+	21.3896i	0.838326	+	0.838326i
$652$	8.76641	+	8.76641i	0.343319	+	0.343319i
$653$	9.72867	+	9.72867i	0.380712	+	0.380712i	0.871359	−	0.490646i	$-0.163239\pi$
$653$	9.72867	+	9.72867i	0.380712	+	0.380712i	−0.490646	+	0.871359i	$0.663239\pi$
$654$		−	4.90327i		−	0.191733i
$655$		0			0
$656$	−2.25292	+	2.25292i	−0.0879619	+	0.0879619i
$657$	−17.9527	−	17.9527i	−0.700402	−	0.700402i
$658$	4.10704	−	4.10704i	0.160109	−	0.160109i
$659$	19.0767			0.743124			0.371562	−	0.928408i	$-0.378822\pi$
$659$	19.0767			0.743124			0.371562	+	0.928408i	$0.378822\pi$
$660$		0			0
$661$			3.89804i			0.151616i	0.997122	+	0.0758082i	$0.0241537\pi$
$661$			3.89804i			0.151616i	−0.997122	+	0.0758082i	$0.975846\pi$
$662$		−	4.94142i		−	0.192054i
$663$	−26.6556	−	54.2065i	−1.03522	−	2.10521i
$664$	−8.77984			−0.340724
$665$		0			0
$666$	−6.55771	−	6.55771i	−0.254106	−	0.254106i
$667$			17.0503i			0.660189i
$668$	−14.0582	+	14.0582i	−0.543926	+	0.543926i
$669$	45.4141	−	45.4141i	1.75581	−	1.75581i
$670$		0			0
$671$			10.8253i			0.417906i
$672$	−58.3398			−2.25050
$673$	−6.34918	−	6.34918i	−0.244743	−	0.244743i	0.574066	−	0.818809i	$-0.305365\pi$
$673$	−6.34918	−	6.34918i	−0.244743	−	0.244743i	−0.818809	+	0.574066i	$0.805365\pi$
$674$	−6.42353	+	6.42353i	−0.247425	+	0.247425i
$675$		0			0
$676$	39.4723			1.51816
$677$	21.8144	−	21.8144i	0.838397	−	0.838397i	−0.150251	−	0.988648i	$-0.548008\pi$
$677$	21.8144	−	21.8144i	0.838397	−	0.838397i	0.988648	+	0.150251i	$0.0480081\pi$
$678$	11.7963			0.453033
$679$	−44.7855			−1.71871
$680$		0			0
$681$	−21.8343			−0.836694
$682$	3.36694			0.128927
$683$	−3.16023	+	3.16023i	−0.120923	+	0.120923i	−0.764979	−	0.644056i	$-0.777251\pi$
$683$	−3.16023	+	3.16023i	−0.120923	+	0.120923i	0.644056	+	0.764979i	$0.277251\pi$
$684$	13.3615			0.510890
$685$		0			0
$686$	8.80606	−	8.80606i	0.336217	−	0.336217i
$687$	−18.4594	−	18.4594i	−0.704270	−	0.704270i
$688$	1.45328			0.0554059
$689$			43.2168i			1.64643i
$690$		0			0
$691$	8.55423	−	8.55423i	0.325418	−	0.325418i	−0.525423	−	0.850841i	$-0.676093\pi$
$691$	8.55423	−	8.55423i	0.325418	−	0.325418i	0.850841	+	0.525423i	$0.176093\pi$
$692$	−17.9374	+	17.9374i	−0.681878	+	0.681878i
$693$		−	18.1260i		−	0.688551i
$694$	16.0107	+	16.0107i	0.607757	+	0.607757i
$695$		0			0
$696$	−20.6326			−0.782077
$697$	−8.09684	+	3.98156i	−0.306690	+	0.150812i
$698$			15.1928i			0.575054i
$699$		−	36.5077i		−	1.38085i
$700$		0			0
$701$	−8.83630			−0.333742			−0.166871	−	0.985979i	$-0.553366\pi$
$701$	−8.83630			−0.333742			−0.166871	+	0.985979i	$0.553366\pi$
$702$	3.10173	−	3.10173i	0.117067	−	0.117067i
$703$	−12.8240	−	12.8240i	−0.483666	−	0.483666i
$704$	−1.18087	+	1.18087i	−0.0445059	+	0.0445059i
$705$		0			0
$706$			15.0804i			0.567558i
$707$	−34.9432	−	34.9432i	−1.31418	−	1.31418i
$708$	−16.1870	−	16.1870i	−0.608343	−	0.608343i
$709$	−18.9439	−	18.9439i	−0.711452	−	0.711452i	0.255387	−	0.966839i	$-0.417797\pi$
$709$	−18.9439	−	18.9439i	−0.711452	−	0.711452i	−0.966839	+	0.255387i	$0.917797\pi$
$710$		0			0
$711$	2.10005	+	2.10005i	0.0787579	+	0.0787579i
$712$	6.46931			0.242448
$713$		−	14.0214i		−	0.525107i
$714$	−26.6687	−	9.08641i	−0.998052	−	0.340050i
$715$		0			0
$716$		−	21.4647i		−	0.802172i
$717$	−3.90450	+	3.90450i	−0.145816	+	0.145816i
$718$		−	24.8460i		−	0.927244i
$719$	−31.0488	−	31.0488i	−1.15792	−	1.15792i	−0.984922	−	0.173001i	$-0.944653\pi$
$719$	−31.0488	−	31.0488i	−1.15792	−	1.15792i	−0.173001	−	0.984922i	$-0.555347\pi$
$720$		0			0
$721$	34.2695	−	34.2695i	1.27626	−	1.27626i
$722$	5.08842			0.189372
$723$	71.9866			2.67721
$724$	14.2183	−	14.2183i	0.528419	−	0.528419i
$725$		0			0
$726$	9.32598	+	9.32598i	0.346120	+	0.346120i
$727$			2.37306i			0.0880118i	0.999031	+	0.0440059i	$0.0140120\pi$
$727$			2.37306i			0.0880118i	−0.999031	+	0.0440059i	$0.985988\pi$
$728$	45.0967	−	45.0967i	1.67140	−	1.67140i
$729$		−	18.5470i		−	0.686926i
$730$		0			0
$731$	3.89567	+	1.32731i	0.144087	+	0.0490924i
$732$			23.7396i			0.877440i
$733$	−27.2035			−1.00478			−0.502391	−	0.864640i	$-0.667546\pi$
$733$	−27.2035			−1.00478			−0.502391	+	0.864640i	$0.667546\pi$
$734$	0.0650576	+	0.0650576i	0.00240132	+	0.00240132i
$735$		0			0
$736$	19.1216	+	19.1216i	0.704831	+	0.704831i
$737$	6.79460	+	6.79460i	0.250282	+	0.250282i
$738$	2.68227	+	2.68227i	0.0987359	+	0.0987359i
$739$			10.3375i			0.380270i	0.981758	+	0.190135i	$0.0608926\pi$
$739$			10.3375i			0.380270i	−0.981758	+	0.190135i	$0.939107\pi$
$740$		0			0
$741$	−35.1164	+	35.1164i	−1.29003	+	1.29003i
$742$	14.2531	+	14.2531i	0.523247	+	0.523247i
$743$	8.35033	−	8.35033i	0.306344	−	0.306344i	−0.537146	−	0.843490i	$-0.680497\pi$
$743$	8.35033	−	8.35033i	0.306344	−	0.306344i	0.843490	+	0.537146i	$0.180497\pi$
$744$	16.9674			0.622056
$745$		0			0
$746$		−	0.628453i		−	0.0230093i
$747$		−	9.36110i		−	0.342505i
$748$	9.44389	−	4.64396i	0.345303	−	0.169800i
$749$	25.9684			0.948863
$750$		0			0
$751$	14.1573	+	14.1573i	0.516607	+	0.516607i	0.916543	−	0.399936i	$-0.130968\pi$
$751$	14.1573	+	14.1573i	0.516607	+	0.516607i	−0.399936	+	0.916543i	$0.630968\pi$
$752$			2.91760i			0.106394i
$753$	−15.3869	+	15.3869i	−0.560731	+	0.560731i
$754$	10.8607	−	10.8607i	0.395522	−	0.395522i
$755$		0			0
$756$			6.86595i			0.249712i
$757$	−4.41769			−0.160564			−0.0802818	−	0.996772i	$-0.525582\pi$
$757$	−4.41769			−0.160564			−0.0802818	+	0.996772i	$0.525582\pi$
$758$	−4.01827	−	4.01827i	−0.145950	−	0.145950i
$759$	−12.9083	+	12.9083i	−0.468540	+	0.468540i
$760$		0			0
$761$	−41.6749			−1.51071			−0.755357	−	0.655314i	$-0.772537\pi$
$761$	−41.6749			−1.51071			−0.755357	+	0.655314i	$0.772537\pi$
$762$	−16.2476	+	16.2476i	−0.588589	+	0.588589i
$763$	−13.1290			−0.475303
$764$	−7.32773			−0.265108
$765$		0			0
$766$	−14.8467			−0.536432
$767$	39.1601			1.41399
$768$	−15.6594	+	15.6594i	−0.565061	+	0.565061i
$769$	30.7653			1.10942			0.554712	−	0.832043i	$-0.312829\pi$
$769$	30.7653			1.10942			0.554712	+	0.832043i	$0.312829\pi$
$770$		0			0
$771$	−5.38518	+	5.38518i	−0.193942	+	0.193942i
$772$	15.1883	+	15.1883i	0.546638	+	0.546638i
$773$	25.2932			0.909735			0.454867	−	0.890559i	$-0.349687\pi$
$773$	25.2932			0.909735			0.454867	+	0.890559i	$0.349687\pi$
$774$		−	1.73024i		−	0.0621922i
$775$		0			0
$776$	−17.7631	+	17.7631i	−0.637659	+	0.637659i
$777$	−38.1508	+	38.1508i	−1.36865	+	1.36865i
$778$			8.64773i			0.310036i
$779$	5.24535	+	5.24535i	0.187934	+	0.187934i
$780$		0			0
$781$	22.5062			0.805334
$782$	5.76282	+	11.7192i	0.206078	+	0.419078i
$783$			3.79978i			0.135793i
$784$			16.4473i			0.587403i
$785$		0			0
$786$	−7.45077			−0.265760
$787$	13.9008	−	13.9008i	0.495509	−	0.495509i	−0.414528	−	0.910037i	$-0.636053\pi$
$787$	13.9008	−	13.9008i	0.495509	−	0.495509i	0.910037	+	0.414528i	$0.136053\pi$
$788$	16.4631	+	16.4631i	0.586474	+	0.586474i
$789$	−20.7913	+	20.7913i	−0.740192	+	0.740192i
$790$		0			0
$791$		−	31.5857i		−	1.12306i
$792$	−7.18927	−	7.18927i	−0.255460	−	0.255460i
$793$	−28.7159	−	28.7159i	−1.01973	−	1.01973i
$794$	12.0633	+	12.0633i	0.428110	+	0.428110i
$795$		0			0
$796$	−2.23337	−	2.23337i	−0.0791598	−	0.0791598i
$797$	−27.3888			−0.970159			−0.485080	−	0.874470i	$-0.661209\pi$
$797$	−27.3888			−0.970159			−0.485080	+	0.874470i	$0.661209\pi$
$798$			23.1631i			0.819965i
$799$	−2.66470	+	7.82092i	−0.0942703	+	0.276684i
$800$		0			0
$801$			6.89760i			0.243715i
$802$	2.76892	−	2.76892i	0.0977739	−	0.0977739i
$803$			16.4405i			0.580171i
$804$	14.9004	+	14.9004i	0.525496	+	0.525496i
$805$		0			0
$806$	−8.93137	+	8.93137i	−0.314594	+	0.314594i
$807$	−0.730900			−0.0257289
$808$	−27.7188			−0.975145
$809$	2.66487	−	2.66487i	0.0936919	−	0.0936919i	−0.658707	−	0.752399i	$-0.728896\pi$
$809$	2.66487	−	2.66487i	0.0936919	−	0.0936919i	0.752399	+	0.658707i	$0.228896\pi$
$810$		0			0
$811$	24.0130	+	24.0130i	0.843209	+	0.843209i	0.989275	−	0.146066i	$-0.0466612\pi$
$811$	24.0130	+	24.0130i	0.843209	+	0.843209i	−0.146066	+	0.989275i	$0.546661\pi$
$812$			24.0411i			0.843676i
$813$	−30.5807	+	30.5807i	−1.07251	+	1.07251i
$814$			6.00532i			0.210486i
$815$		0			0
$816$	12.7000	−	6.24513i	0.444589	−	0.218623i
$817$		−	3.38359i		−	0.118377i
$818$	10.4854			0.366612
$819$	48.0823	+	48.0823i	1.68013	+	1.68013i
$820$		0			0
$821$	19.1918	+	19.1918i	0.669797	+	0.669797i	0.957669	−	0.287872i	$-0.0929477\pi$
$821$	19.1918	+	19.1918i	0.669797	+	0.669797i	−0.287872	+	0.957669i	$0.592948\pi$
$822$	16.4490	+	16.4490i	0.573725	+	0.573725i
$823$	−1.36590	−	1.36590i	−0.0476123	−	0.0476123i	0.682900	−	0.730512i	$-0.260719\pi$
$823$	−1.36590	−	1.36590i	−0.0476123	−	0.0476123i	−0.730512	+	0.682900i	$0.760719\pi$
$824$		−	27.1844i		−	0.947015i
$825$		0			0
$826$	12.9152	−	12.9152i	0.449377	−	0.449377i
$827$	13.9206	+	13.9206i	0.484067	+	0.484067i	0.906428	−	0.422361i	$-0.138799\pi$
$827$	13.9206	+	13.9206i	0.484067	+	0.484067i	−0.422361	+	0.906428i	$0.638799\pi$
$828$	−13.0285	+	13.0285i	−0.452773	+	0.452773i
$829$	21.3907			0.742930			0.371465	−	0.928447i	$-0.378855\pi$
$829$	21.3907			0.742930			0.371465	+	0.928447i	$0.378855\pi$
$830$		0			0
$831$		−	30.0696i		−	1.04310i
$832$		−	6.26493i		−	0.217197i
$833$	−15.0216	+	44.0887i	−0.520469	+	1.52758i
$834$	8.57779			0.297025
$835$		0			0
$836$	−6.11800	−	6.11800i	−0.211595	−	0.211595i
$837$		−	3.12479i		−	0.108008i
$838$	−8.68757	+	8.68757i	−0.300107	+	0.300107i
$839$	−20.3873	+	20.3873i	−0.703846	+	0.703846i	−0.965234	−	0.261387i	$-0.915820\pi$
$839$	−20.3873	+	20.3873i	−0.703846	+	0.703846i	0.261387	+	0.965234i	$0.415820\pi$
$840$		0			0
$841$		−	15.6951i		−	0.541210i
$842$	6.64822			0.229113
$843$	51.8913	+	51.8913i	1.78723	+	1.78723i
$844$	0.477531	−	0.477531i	0.0164373	−	0.0164373i
$845$		0			0
$846$	3.47362			0.119425
$847$	24.9713	−	24.9713i	0.858023	−	0.858023i
$848$	−10.1252			−0.347702
$849$	−65.6708			−2.25382
$850$		0			0
$851$	25.0088			0.857292
$852$	49.3554			1.69089
$853$	8.13732	−	8.13732i	0.278617	−	0.278617i	−0.553940	−	0.832557i	$-0.686876\pi$
$853$	8.13732	−	8.13732i	0.278617	−	0.278617i	0.832557	+	0.553940i	$0.186876\pi$
$854$	−18.9413			−0.648157
$855$		0			0
$856$	10.2997	−	10.2997i	0.352038	−	0.352038i
$857$	−15.3959	−	15.3959i	−0.525913	−	0.525913i	0.393438	−	0.919351i	$-0.371286\pi$
$857$	−15.3959	−	15.3959i	−0.525913	−	0.525913i	−0.919351	+	0.393438i	$0.871286\pi$
$858$	16.4446			0.561409
$859$			0.00614837i			0.000209780i	1.00000		0.000104890i	$3.33875e-5\pi$
$859$			0.00614837i			0.000209780i	−1.00000		0.000104890i	$0.999967\pi$
$860$		0			0
$861$	15.6047	−	15.6047i	0.531806	−	0.531806i
$862$	8.68472	−	8.68472i	0.295803	−	0.295803i
$863$			21.5322i			0.732964i	0.930425	+	0.366482i	$0.119438\pi$
$863$			21.5322i			0.732964i	−0.930425	+	0.366482i	$0.880562\pi$
$864$	4.26139	+	4.26139i	0.144975	+	0.144975i
$865$		0			0
$866$	−8.69421			−0.295441
$867$	39.7475	−	5.14155i	1.34990	−	0.174616i
$868$		−	19.7704i		−	0.671051i
$869$		−	1.92315i		−	0.0652384i
$870$		0			0
$871$	−36.0476			−1.22143
$872$	−5.20732	+	5.20732i	−0.176342	+	0.176342i
$873$	−18.9391	−	18.9391i	−0.640991	−	0.640991i
$874$	7.59200	−	7.59200i	0.256803	−	0.256803i
$875$		0			0
$876$			36.0535i			1.21814i
$877$	0.789882	+	0.789882i	0.0266724	+	0.0266724i	0.720317	−	0.693645i	$-0.243996\pi$
$877$	0.789882	+	0.789882i	0.0266724	+	0.0266724i	−0.693645	+	0.720317i	$0.743996\pi$
$878$	11.6358	+	11.6358i	0.392688	+	0.392688i
$879$	52.3958	+	52.3958i	1.76727	+	1.76727i
$880$		0			0
$881$	−33.6544	−	33.6544i	−1.13385	−	1.13385i	−0.989532	−	0.144313i	$-0.953903\pi$
$881$	−33.6544	−	33.6544i	−1.13385	−	1.13385i	−0.144313	−	0.989532i	$-0.546097\pi$
$882$	19.5817			0.659351
$883$		−	20.9432i		−	0.704796i	−0.935850	−	0.352398i	$-0.885366\pi$
$883$		−	20.9432i		−	0.704796i	0.935850	−	0.352398i	$-0.114634\pi$
$884$	−12.7326	+	37.3703i	−0.428244	+	1.25690i
$885$		0			0
$886$		−	10.9241i		−	0.367001i
$887$	−13.4400	+	13.4400i	−0.451271	+	0.451271i	−0.895776	−	0.444506i	$-0.853379\pi$
$887$	−13.4400	+	13.4400i	−0.451271	+	0.451271i	0.444506	+	0.895776i	$0.353379\pi$
$888$			30.2633i			1.01557i
$889$	43.5046	+	43.5046i	1.45910	+	1.45910i
$890$		0			0
$891$	−11.8659	+	11.8659i	−0.397524	+	0.397524i
$892$	−41.9761			−1.40546
$893$	6.79286			0.227315
$894$	14.3329	−	14.3329i	0.479365	−	0.479365i
$895$		0			0
$896$	32.9295	+	32.9295i	1.10010	+	1.10010i
$897$		−	68.4826i		−	2.28657i
$898$	−9.16422	+	9.16422i	−0.305814	+	0.305814i
$899$		−	10.9414i		−	0.364917i
$900$		0			0
$901$	−27.1417	−	9.24758i	−0.904222	−	0.308082i
$902$		−	2.45633i		−	0.0817869i
$903$	−10.0660			−0.334976
$904$	−12.5277	−	12.5277i	−0.416667	−	0.416667i
$905$		0			0
$906$	18.3681	+	18.3681i	0.610238	+	0.610238i
$907$	−9.63742	−	9.63742i	−0.320005	−	0.320005i	0.528764	−	0.848769i	$-0.322656\pi$
$907$	−9.63742	−	9.63742i	−0.320005	−	0.320005i	−0.848769	+	0.528764i	$0.822656\pi$
$908$	10.0907	+	10.0907i	0.334872	+	0.334872i
$909$		−	29.5539i		−	0.980242i
$910$		0			0
$911$	−23.8810	+	23.8810i	−0.791214	+	0.791214i	−0.981692	−	0.190477i	$-0.938996\pi$
$911$	−23.8810	+	23.8810i	−0.791214	+	0.791214i	0.190477	+	0.981692i	$0.438996\pi$
$912$	−8.22741	−	8.22741i	−0.272437	−	0.272437i
$913$	−4.28628	+	4.28628i	−0.141855	+	0.141855i
$914$	2.49571			0.0825507
$915$		0			0
$916$			17.0620i			0.563743i
$917$			19.9502i			0.658814i
$918$	1.28429	+	2.61171i	0.0423878	+	0.0861993i
$919$	31.7339			1.04681			0.523403	−	0.852085i	$-0.324662\pi$
$919$	31.7339			1.04681			0.523403	+	0.852085i	$0.324662\pi$
$920$		0			0
$921$	7.03471	+	7.03471i	0.231802	+	0.231802i
$922$			13.3874i			0.440889i
$923$	−59.7013	+	59.7013i	−1.96509	+	1.96509i
$924$	−18.2008	+	18.2008i	−0.598762	+	0.598762i
$925$		0			0
$926$			16.0251i			0.526616i
$927$	28.9841			0.951964
$928$	14.9212	+	14.9212i	0.489813	+	0.489813i
$929$	−5.97435	+	5.97435i	−0.196012	+	0.196012i	−0.798288	−	0.602276i	$-0.794261\pi$
$929$	−5.97435	+	5.97435i	−0.196012	+	0.196012i	0.602276	+	0.798288i	$0.294261\pi$
$930$		0			0
$931$	38.2932			1.25501
$932$	−16.8720	+	16.8720i	−0.552661	+	0.552661i
$933$	36.3300			1.18939
$934$	−3.72762			−0.121971
$935$		0			0
$936$	38.1415			1.24669
$937$	−18.0115			−0.588409			−0.294205	−	0.955742i	$-0.595055\pi$
$937$	−18.0115			−0.588409			−0.294205	+	0.955742i	$0.595055\pi$
$938$	−11.8887	+	11.8887i	−0.388179	+	0.388179i
$939$	25.6052			0.835593
$940$		0			0
$941$	−15.1411	+	15.1411i	−0.493586	+	0.493586i	−0.909434	−	0.415848i	$-0.863485\pi$
$941$	−15.1411	+	15.1411i	−0.493586	+	0.493586i	0.415848	+	0.909434i	$0.363485\pi$
$942$	−11.3229	−	11.3229i	−0.368919	−	0.368919i
$943$	−10.2293			−0.333111
$944$			9.17481i			0.298615i
$945$		0			0
$946$	−0.792246	+	0.792246i	−0.0257581	+	0.0257581i
$947$	33.0770	−	33.0770i	1.07486	−	1.07486i	0.0778975	−	0.996961i	$-0.475179\pi$
$947$	33.0770	−	33.0770i	1.07486	−	1.07486i	0.996961	−	0.0778975i	$-0.0248207\pi$
$948$		−	4.21742i		−	0.136975i
$949$	−43.6111	−	43.6111i	−1.41568	−	1.41568i
$950$		0			0
$951$	−68.1036			−2.20841
$952$	18.6726	+	37.9723i	0.605181	+	1.23069i
$953$			8.60527i			0.278752i	0.990240	+	0.139376i	$0.0445097\pi$
$953$			8.60527i			0.278752i	−0.990240	+	0.139376i	$0.955490\pi$
$954$			12.0548i			0.390290i
$955$		0			0
$956$	3.60892			0.116721
$957$	−10.0728	+	10.0728i	−0.325606	+	0.325606i
$958$	−5.34959	−	5.34959i	−0.172837	−	0.172837i
$959$	44.0439	−	44.0439i	1.42225	−	1.42225i
$960$		0			0
$961$		−	22.0022i		−	0.709749i
$962$	−15.9301	−	15.9301i	−0.513607	−	0.513607i
$963$	10.9816	+	10.9816i	0.353878	+	0.353878i
$964$	−33.2685	−	33.2685i	−1.07151	−	1.07151i
$965$		0			0
$966$	−22.5859	−	22.5859i	−0.726689	−	0.726689i
$967$	−29.7257			−0.955913			−0.477957	−	0.878383i	$-0.658622\pi$
$967$	−29.7257			−0.955913			−0.477957	+	0.878383i	$0.658622\pi$
$968$		−	19.8086i		−	0.636671i
$969$	−14.5402	−	29.5687i	−0.467097	−	0.949883i
$970$		0			0
$971$			5.92180i			0.190040i	0.995475	+	0.0950198i	$0.0302915\pi$
$971$			5.92180i			0.190040i	−0.995475	+	0.0950198i	$0.969709\pi$
$972$	−22.6167	+	22.6167i	−0.725430	+	0.725430i
$973$		−	22.9679i		−	0.736318i
$974$	16.9820	+	16.9820i	0.544139	+	0.544139i
$975$		0			0
$976$	6.72783	−	6.72783i	0.215353	−	0.215353i
$977$	−51.4273			−1.64530			−0.822652	−	0.568545i	$-0.807507\pi$
$977$	−51.4273			−1.64530			−0.822652	+	0.568545i	$0.807507\pi$
$978$	−12.8533			−0.411004
$979$	3.15829	−	3.15829i	0.100939	−	0.100939i
$980$		0			0
$981$	−5.55207	−	5.55207i	−0.177264	−	0.177264i
$982$			8.71114i			0.277984i
$983$	−9.68389	+	9.68389i	−0.308868	+	0.308868i	−0.844470	−	0.535602i	$-0.820085\pi$
$983$	−9.68389	+	9.68389i	−0.308868	+	0.308868i	0.535602	+	0.844470i	$0.320085\pi$
$984$		−	12.3785i		−	0.394611i
$985$		0			0
$986$	4.49693	+	9.14489i	0.143211	+	0.291233i
$987$		−	20.2085i		−	0.643243i
$988$	32.4580			1.03263
$989$	3.29927	+	3.29927i	0.104911	+	0.104911i
$990$		0			0
$991$	−37.8301	−	37.8301i	−1.20171	−	1.20171i	−0.973645	−	0.228067i	$-0.926759\pi$
$991$	−37.8301	−	37.8301i	−1.20171	−	1.20171i	−0.228067	−	0.973645i	$-0.573241\pi$
$992$	−12.2706	−	12.2706i	−0.389592	−	0.389592i
$993$	−12.1570	−	12.1570i	−0.385790	−	0.385790i
$994$			39.3796i			1.24904i
$995$		0			0
$996$	−9.39970	+	9.39970i	−0.297841	+	0.297841i
$997$	16.3707	+	16.3707i	0.518465	+	0.518465i	0.917107	−	0.398642i	$-0.130518\pi$
$997$	16.3707	+	16.3707i	0.518465	+	0.518465i	−0.398642	+	0.917107i	$0.630518\pi$
$998$	8.90601	−	8.90601i	0.281915	−	0.281915i
$999$	5.57341			0.176335

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.b.149.4		12
5.2	odd	4		85.2.e.a.81.4	yes	12
5.3	odd	4		425.2.e.f.251.3		12
5.4	even	2		425.2.j.c.149.3		12
15.2	even	4		765.2.k.b.676.3		12
17.4	even	4		425.2.j.c.174.3		12
20.7	even	4		1360.2.bt.d.81.5		12
85.2	odd	8		1445.2.a.n.1.3		6
85.4	even	4	inner	425.2.j.b.174.4		12
85.32	odd	8		1445.2.a.o.1.3		6
85.38	odd	4		425.2.e.f.276.4		12
85.42	odd	8		1445.2.d.g.866.8		12
85.53	odd	8		7225.2.a.bb.1.4		6
85.72	odd	4		85.2.e.a.21.3	✓	12
85.77	odd	8		1445.2.d.g.866.7		12
85.83	odd	8		7225.2.a.z.1.4		6
255.242	even	4		765.2.k.b.361.4		12
340.327	even	4		1360.2.bt.d.1041.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.3	✓	12	85.72	odd	4
85.2.e.a.81.4	yes	12	5.2	odd	4
425.2.e.f.251.3		12	5.3	odd	4
425.2.e.f.276.4		12	85.38	odd	4
425.2.j.b.149.4		12	1.1	even	1	trivial
425.2.j.b.174.4		12	85.4	even	4	inner
425.2.j.c.149.3		12	5.4	even	2
425.2.j.c.174.3		12	17.4	even	4
765.2.k.b.361.4		12	255.242	even	4
765.2.k.b.676.3		12	15.2	even	4
1360.2.bt.d.81.5		12	20.7	even	4
1360.2.bt.d.1041.5		12	340.327	even	4
1445.2.a.n.1.3		6	85.2	odd	8
1445.2.a.o.1.3		6	85.32	odd	8
1445.2.d.g.866.7		12	85.77	odd	8
1445.2.d.g.866.8		12	85.42	odd	8
7225.2.a.z.1.4		6	85.83	odd	8
7225.2.a.bb.1.4		6	85.53	odd	8

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.677603 q^{2} +(1.66705 - 1.66705i) q^{3} -1.54085 q^{4} +(1.12960 - 1.12960i) q^{6} +(-3.02462 - 3.02462i) q^{7} -2.39929 q^{8} -2.55814i q^{9} +(-1.17133 + 1.17133i) q^{11} +(-2.56869 + 2.56869i) q^{12} -6.21427i q^{13} +(-2.04950 - 2.04950i) q^{14} +1.45594 q^{16} +(3.90279 + 1.32974i) q^{17} -1.73340i q^{18} -3.38977i q^{19} -10.0844 q^{21} +(-0.793694 + 0.793694i) q^{22} +(3.30530 + 3.30530i) q^{23} +(-3.99975 + 3.99975i) q^{24} -4.21081i q^{26} +(0.736610 + 0.736610i) q^{27} +(4.66050 + 4.66050i) q^{28} +(2.57924 + 2.57924i) q^{29} +(-2.12106 - 2.12106i) q^{31} +5.78514 q^{32} +3.90532i q^{33} +(2.64455 + 0.901035i) q^{34} +3.94171i q^{36} +(3.78314 - 3.78314i) q^{37} -2.29692i q^{38} +(-10.3595 - 10.3595i) q^{39} +(-1.54740 + 1.54740i) q^{41} -6.83324 q^{42} +0.998176 q^{43} +(1.80484 - 1.80484i) q^{44} +(2.23968 + 2.23968i) q^{46} +2.00393i q^{47} +(2.42713 - 2.42713i) q^{48} +11.2967i q^{49} +(8.72291 - 4.28942i) q^{51} +9.57528i q^{52} -6.95444 q^{53} +(0.499130 + 0.499130i) q^{54} +(7.25696 + 7.25696i) q^{56} +(-5.65093 - 5.65093i) q^{57} +(1.74770 + 1.74770i) q^{58} +6.30165i q^{59} +(4.62096 - 4.62096i) q^{61} +(-1.43724 - 1.43724i) q^{62} +(-7.73740 + 7.73740i) q^{63} +1.00815 q^{64} +2.64626i q^{66} -5.80078i q^{67} +(-6.01363 - 2.04893i) q^{68} +11.0202 q^{69} +(-9.60714 - 9.60714i) q^{71} +6.13772i q^{72} +(7.01789 - 7.01789i) q^{73} +(2.56347 - 2.56347i) q^{74} +5.22314i q^{76} +7.08564 q^{77} +(-7.01965 - 7.01965i) q^{78} +(-0.820929 + 0.820929i) q^{79} +10.1303 q^{81} +(-1.04853 + 1.04853i) q^{82} +3.65934 q^{83} +15.5386 q^{84} +0.676367 q^{86} +8.59945 q^{87} +(2.81035 - 2.81035i) q^{88} -2.69634 q^{89} +(-18.7958 + 18.7958i) q^{91} +(-5.09298 - 5.09298i) q^{92} -7.07184 q^{93} +1.35787i q^{94} +(9.64413 - 9.64413i) q^{96} +(7.40348 - 7.40348i) q^{97} +7.65468i q^{98} +(2.99641 + 2.99641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} + 4 q^{3} + 12 q^{4} - 12 q^{8} - 4 q^{11} - 8 q^{12} + 4 q^{14} + 4 q^{16} - 8 q^{17} - 16 q^{21} + 20 q^{22} + 12 q^{23} - 4 q^{24} + 4 q^{27} + 4 q^{28} + 12 q^{29} + 12 q^{32} + 12 q^{34}+ \cdots + 4 q^{97}+O(q^{100}) \) 12 * q - 4 * q^2 + 4 * q^3 + 12 * q^4 - 12 * q^8 - 4 * q^11 - 8 * q^12 + 4 * q^14 + 4 * q^16 - 8 * q^17 - 16 * q^21 + 20 * q^22 + 12 * q^23 - 4 * q^24 + 4 * q^27 + 4 * q^28 + 12 * q^29 + 12 * q^32 + 12 * q^34 + 12 * q^37 + 20 * q^39 - 24 * q^41 - 16 * q^42 - 16 * q^43 - 8 * q^44 - 24 * q^46 + 20 * q^48 + 32 * q^51 - 28 * q^54 + 40 * q^56 + 36 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^63 - 28 * q^64 - 60 * q^68 + 28 * q^71 + 48 * q^73 - 28 * q^74 + 48 * q^77 - 92 * q^78 + 8 * q^79 + 28 * q^81 + 40 * q^82 + 40 * q^83 - 96 * q^86 - 48 * q^87 + 72 * q^88 - 24 * q^89 - 36 * q^91 + 16 * q^92 - 72 * q^93 - 32 * q^96 + 4 * q^97

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