LMFDB - Embedded newform 425.2.e.f.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(251,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("425.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$425 = 5^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	425.e (of order $4$ , degree $2$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.39364208590$
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			251.3
Root			$1.35757i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.f.276.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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

)

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

$2$		−	0.677603i		−	0.479138i	−0.970879	−	0.239569i	$-0.922994\pi$
$2$		−	0.677603i		−	0.479138i	0.970879	−	0.239569i	$-0.0770061\pi$
$3$	1.66705	+	1.66705i	0.962474	+	0.962474i	0.999321	−	0.0368470i	$-0.0117314\pi$
$3$	1.66705	+	1.66705i	0.962474	+	0.962474i	−0.0368470	+	0.999321i	$0.511731\pi$
$4$	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	−0.155339	+	0.987861i	$0.549647\pi$
$7$	−3.02462	+	3.02462i	−1.14320	+	1.14320i	−0.987861	+	0.155339i	$0.950353\pi$
$8$		−	2.39929i		−	0.848279i
$9$			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
$13$	6.21427			1.72353			0.861764	−	0.507309i	$-0.169360\pi$
$13$	6.21427			1.72353			0.861764	+	0.507309i	$0.169360\pi$
$14$	2.04950	+	2.04950i	0.547751	+	0.547751i
$15$		0			0
$16$	1.45594			0.363984
$17$	1.32974	−	3.90279i	0.322509	−	0.946566i
$17$	1.32974	−	3.90279i	0.322509	−	0.946566i
$18$	1.73340			0.408567
$19$			3.38977i			0.777667i	0.921308	+	0.388834i	$0.127122\pi$
$19$			3.38977i			0.777667i	−0.921308	+	0.388834i	$0.872878\pi$
$20$		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	$-0.912033\pi$
$23$	−3.30530	+	3.30530i	−0.689202	+	0.689202i	0.272854	+	0.962056i	$0.412033\pi$
$24$	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	0.425844	−	0.904796i	$-0.359977\pi$
$29$	−2.57924	−	2.57924i	−0.478952	−	0.478952i	−0.904796	+	0.425844i	$0.859977\pi$
$30$		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	$0.836817\pi$
$32$		−	5.78514i		−	1.02268i
$33$	−3.90532			−0.679830
$34$	−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	$-0.394944\pi$
$37$	−3.78314	−	3.78314i	−0.621945	−	0.621945i	−0.946029	+	0.324083i	$0.894944\pi$
$38$	2.29692			0.372610
$39$	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	$0.304662\pi$
$42$			6.83324i			1.05439i
$43$			0.998176i			0.152220i	0.997099	+	0.0761102i	$0.0242501\pi$
$43$			0.998176i			0.152220i	−0.997099	+	0.0761102i	$0.975750\pi$
$44$	−1.80484	+	1.80484i	−0.272090	+	0.272090i
$45$		0			0
$46$	2.23968	+	2.23968i	0.330223	+	0.330223i
$47$	2.00393			0.292303			0.146152	−	0.989262i	$-0.453311\pi$
$47$	2.00393			0.292303			0.146152	+	0.989262i	$0.453311\pi$
$48$	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
$52$	9.57528			1.32785
$53$		−	6.95444i		−	0.955266i	−0.878560	−	0.477633i	$-0.841495\pi$
$53$		−	6.95444i		−	0.955266i	0.878560	−	0.477633i	$-0.158505\pi$
$54$	−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	$-0.865458\pi$
$59$		−	6.30165i		−	0.820405i	0.911995	−	0.410202i	$-0.134542\pi$
$60$		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
$67$	−5.80078			−0.708678			−0.354339	−	0.935117i	$-0.615294\pi$
$67$	−5.80078			−0.708678			−0.354339	+	0.935117i	$0.615294\pi$
$68$	2.04893	−	6.01363i	0.248469	−	0.729260i
$69$	−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	$-0.548486\pi$
$72$	6.13772			0.723337
$73$	7.01789	+	7.01789i	0.821382	+	0.821382i	0.986306	−	0.164924i	$-0.0527380\pi$
$73$	7.01789	+	7.01789i	0.821382	+	0.821382i	−0.164924	+	0.986306i	$0.552738\pi$
$74$	−2.56347	+	2.56347i	−0.297997	+	0.297997i
$75$		0			0
$76$			5.22314i			0.599136i
$77$		−	7.08564i		−	0.807483i
$78$	7.01965	−	7.01965i	0.794818	−	0.794818i
$79$	0.820929	−	0.820929i	0.0923617	−	0.0923617i	−0.659416	−	0.751778i	$-0.729197\pi$
$79$	0.820929	−	0.820929i	0.0923617	−	0.0923617i	0.751778	+	0.659416i	$0.229197\pi$
$80$		0			0
$81$	10.1303			1.12559
$82$	1.04853	+	1.04853i	0.115790	+	0.115790i
$83$			3.65934i			0.401665i	0.979626	+	0.200832i	$0.0643647\pi$
$83$			3.65934i			0.401665i	−0.979626	+	0.200832i	$0.935635\pi$
$84$	−15.5386			−1.69540
$85$		0			0
$86$	0.676367			0.0729346
$87$		−	8.59945i		−	0.921958i
$88$	2.81035	+	2.81035i	0.299585	+	0.299585i
$89$	2.69634			0.285811			0.142906	−	0.989736i	$-0.454355\pi$
$89$	2.69634			0.285811			0.142906	+	0.989736i	$0.454355\pi$
$90$		0			0
$91$	−18.7958	+	18.7958i	−1.97034	+	1.97034i
$92$	−5.09298	+	5.09298i	−0.530980	+	0.530980i
$93$		−	7.07184i		−	0.733315i
$94$		−	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	$-0.428386\pi$
$97$	−7.40348	−	7.40348i	−0.751709	−	0.751709i	−0.974798	+	0.223089i	$0.928386\pi$
$98$	−7.65468			−0.773239
$99$	−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	$0.305088\pi$
$102$	−2.90653	−	5.91067i	−0.287789	−	0.585244i
$103$	−11.3302			−1.11640			−0.558198	−	0.829708i	$-0.688507\pi$
$103$	−11.3302			−1.11640			−0.558198	+	0.829708i	$0.688507\pi$
$104$		−	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	$-0.155196\pi$
$107$	4.29282	+	4.29282i	0.415003	+	0.415003i	−0.468474	+	0.883477i	$0.655196\pi$
$108$	1.13501	−	1.13501i	0.109216	−	0.109216i
$109$	−2.17036	+	2.17036i	−0.207882	+	0.207882i	−0.803367	−	0.595484i	$-0.796960\pi$
$109$	−2.17036	+	2.17036i	−0.207882	+	0.207882i	0.595484	+	0.803367i	$0.296960\pi$
$110$		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	$-0.862910\pi$
$113$	−5.22143	+	5.22143i	−0.491191	+	0.491191i	0.417491	+	0.908681i	$0.362910\pi$
$114$	3.82909	+	3.82909i	0.358627	+	0.358627i
$115$		0			0
$116$	−3.97422	−	3.97422i	−0.368998	−	0.368998i
$117$			15.8969i			1.46967i
$118$	−4.27002			−0.393087
$119$	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
$123$	−5.15921			−0.465191
$124$	−3.26824	−	3.26824i	−0.293497	−	0.293497i
$125$		0			0
$126$	−5.24289	+	5.24289i	−0.467074	+	0.467074i
$127$			14.3835i			1.27633i	0.769900	+	0.638164i	$0.220306\pi$
$127$			14.3835i			1.27633i	−0.769900	+	0.638164i	$0.779694\pi$
$128$		−	10.8871i		−	0.962297i
$129$	−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	$0.815313\pi$
$132$	−6.01753			−0.523759
$133$	−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
$137$	14.5618			1.24410			0.622049	−	0.782978i	$-0.286300\pi$
$137$	14.5618			1.24410			0.622049	+	0.782978i	$0.286300\pi$
$138$			7.46733i			0.635662i
$139$	−3.79682	−	3.79682i	−0.322042	−	0.322042i	0.527508	−	0.849550i	$-0.323127\pi$
$139$	−3.79682	−	3.79682i	−0.322042	−	0.322042i	−0.849550	+	0.527508i	$0.823127\pi$
$140$		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	$-0.673971\pi$
$149$	−12.6885			−1.03948			−0.519741	+	0.854324i	$0.673971\pi$
$150$		0			0
$151$			16.2607i			1.32327i	0.749824	+	0.661637i	$0.230138\pi$
$151$			16.2607i			1.32327i	−0.749824	+	0.661637i	$0.769862\pi$
$152$	8.13306			0.659678
$153$	9.98388	+	3.40165i	0.807149	+	0.275007i
$154$	−4.80125			−0.386896
$155$		0			0
$156$	15.9625	+	15.9625i	1.27802	+	1.27802i
$157$	−10.0238			−0.799985			−0.399993	−	0.916518i	$-0.630987\pi$
$157$	−10.0238			−0.799985			−0.399993	+	0.916518i	$0.630987\pi$
$158$	−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
$162$		−	6.86436i		−	0.539315i
$163$	5.68932	−	5.68932i	0.445622	−	0.445622i	−0.448274	−	0.893896i	$-0.647961\pi$
$163$	5.68932	−	5.68932i	0.445622	−	0.445622i	0.893896	+	0.448274i	$0.147961\pi$
$164$	−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	$-0.416381\pi$
$167$	−9.12361	−	9.12361i	−0.706006	−	0.706006i	−0.965693	+	0.259687i	$0.916381\pi$
$168$			24.1955i			1.86672i
$169$	25.6171			1.97055
$170$		0			0
$171$	−8.67150			−0.663126
$172$			1.53804i			0.117275i
$173$	11.6412	+	11.6412i	0.885065	+	0.885065i	0.994044	−	0.108979i	$-0.0347581\pi$
$173$	11.6412	+	11.6412i	0.885065	+	0.885065i	−0.108979	+	0.994044i	$0.534758\pi$
$174$	−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
$178$		−	1.82705i		−	0.136943i
$179$		−	13.9304i		−	1.04121i	−0.853799	−	0.520603i	$-0.825707\pi$
$179$		−	13.9304i		−	1.04121i	0.853799	−	0.520603i	$-0.174293\pi$
$180$		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
$183$	15.4068			1.13890
$184$	7.93038	+	7.93038i	0.584635	+	0.584635i
$185$		0			0
$186$	−4.79190			−0.351359
$187$	3.01389	+	6.12900i	0.220397	+	0.448197i
$188$	3.08776			0.225198
$189$			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	$-0.582704\pi$
$193$	9.85705	−	9.85705i	0.709526	−	0.709526i	0.966435	+	0.256910i	$0.0827042\pi$
$194$	−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	−0.976545	−	0.215313i	$-0.930923\pi$
$197$	−10.6844	+	10.6844i	−0.761232	+	0.761232i	0.215313	+	0.976545i	$0.430923\pi$
$198$	−2.03038	+	2.03038i	−0.144293	+	0.144293i
$199$	−1.44944	−	1.44944i	−0.102748	−	0.102748i	0.653864	−	0.756612i	$-0.273147\pi$
$199$	−1.44944	−	1.44944i	−0.102748	−	0.102748i	−0.756612	+	0.653864i	$0.773147\pi$
$200$		0			0
$201$	−9.67021	−	9.67021i	−0.682084	−	0.682084i
$202$		−	7.82829i		−	0.550797i
$203$	15.6024			1.09508
$204$	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
$208$	9.04759			0.627337
$209$	−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	$0.254802\pi$
$212$		−	10.7158i		−	0.735962i
$213$		−	32.0312i		−	2.19474i
$214$	2.90883	−	2.90883i	0.198844	−	0.198844i
$215$		0			0
$216$	−1.76734	−	1.76734i	−0.120253	−	0.120253i
$217$	12.8308			0.871012
$218$	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
$222$	−8.54689			−0.573630
$223$			27.2421i			1.82427i	0.409893	+	0.912134i	$0.365566\pi$
$223$			27.2421i			1.82427i	−0.409893	+	0.912134i	$0.634434\pi$
$224$	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	−0.890209	−	0.455551i	$-0.849442\pi$
$227$	−6.54878	+	6.54878i	−0.434658	+	0.434658i	0.455551	+	0.890209i	$0.349442\pi$
$228$	−8.70726	+	8.70726i	−0.576652	+	0.576652i
$229$			11.0731i			0.731728i	0.930668	+	0.365864i	$0.119227\pi$
$229$			11.0731i			0.731728i	−0.930668	+	0.365864i	$0.880773\pi$
$230$		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	0.968060	−	0.250717i	$-0.0806663\pi$
$233$	10.9498	+	10.9498i	0.717344	+	0.717344i	−0.250717	+	0.968060i	$0.580666\pi$
$234$	10.7718			0.704176
$235$		0			0
$236$		−	9.70992i		−	0.632062i
$237$	2.73706			0.177791
$238$	10.7240	−	5.27347i	0.695137	−	0.341828i
$239$	2.34216			0.151501			0.0757507	−	0.997127i	$-0.475865\pi$
$239$	2.34216			0.151501			0.0757507	+	0.997127i	$0.475865\pi$
$240$		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	$0.308007\pi$
$242$	5.59429			0.359615
$243$	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
$247$			21.0650i			1.34033i
$248$	−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
$253$		−	7.74315i		−	0.486808i
$254$	9.74630			0.611537
$255$		0			0
$256$	−9.39347			−0.587092
$257$			3.23036i			0.201504i	0.994912	+	0.100752i	$0.0321249\pi$
$257$			3.23036i			0.201504i	−0.994912	+	0.100752i	$0.967875\pi$
$258$	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
$263$		−	12.4719i		−	0.769051i	−0.923114	−	0.384526i	$-0.874365\pi$
$263$		−	12.4719i		−	0.769051i	0.923114	−	0.384526i	$-0.125635\pi$
$264$			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
$268$	−8.93815			−0.545984
$269$	0.219219	+	0.219219i	0.0133660	+	0.0133660i	0.713758	−	0.700392i	$-0.246992\pi$
$269$	0.219219	+	0.219219i	0.0133660	+	0.0133660i	−0.700392	+	0.713758i	$0.746992\pi$
$270$		0			0
$271$	−18.3441			−1.11433			−0.557164	−	0.830403i	$-0.688110\pi$
$271$	−18.3441			−1.11433			−0.557164	+	0.830403i	$0.688110\pi$
$272$	1.93602	−	5.68222i	0.117388	−	0.344535i
$273$	−62.6673			−3.79280
$274$		−	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	$-0.375168\pi$
$277$	−9.01877	−	9.01877i	−0.541885	−	0.541885i	−0.924081	+	0.382196i	$0.875168\pi$
$278$	−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	0.188836	−	0.982009i	$-0.439528\pi$
$283$	19.6967	−	19.6967i	1.17084	−	1.17084i	0.982009	−	0.188836i	$-0.0604715\pi$
$284$	−14.8032	−	14.8032i	−0.878408	−	0.878408i
$285$		0			0
$286$	4.93223	+	4.93223i	0.291649	+	0.291649i
$287$		−	9.36063i		−	0.552541i
$288$	14.7992			0.872049
$289$	−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
$293$	−31.4302			−1.83617			−0.918086	−	0.396381i	$-0.870266\pi$
$293$	−31.4302			−1.83617			−0.918086	+	0.396381i	$0.870266\pi$
$294$	−12.7608	−	12.7608i	−0.744223	−	0.744223i
$295$		0			0
$296$	−9.07688	+	9.07688i	−0.527583	+	0.527583i
$297$			1.72562i			0.100131i
$298$			8.59776i			0.498055i
$299$	−20.5400	+	20.5400i	−1.18786	+	1.18786i
$300$		0			0
$301$	−3.01911	−	3.01911i	−0.174018	−	0.174018i
$302$	11.0183			0.634031
$303$	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
$307$	4.21985			0.240839			0.120420	−	0.992723i	$-0.461576\pi$
$307$	4.21985			0.240839			0.120420	+	0.992723i	$0.461576\pi$
$308$		−	10.9179i		−	0.622107i
$309$	−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	$-0.849307\pi$
$313$	−7.67977	+	7.67977i	−0.434086	+	0.434086i	0.455930	+	0.890016i	$0.349307\pi$
$314$			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	−0.160167	+	0.987090i	$0.551203\pi$
$317$	−20.4263	+	20.4263i	−1.14726	+	1.14726i	−0.987090	+	0.160167i	$0.948797\pi$
$318$	−7.85574	−	7.85574i	−0.440528	−	0.440528i
$319$	6.04225			0.338301
$320$		0			0
$321$			14.3127i			0.798859i
$322$	−13.5484			−0.755022
$323$	13.2296	+	4.50751i	0.736114	+	0.250804i
$324$	15.6094			0.867188
$325$		0			0
$326$	−3.85510	−	3.85510i	−0.213514	−	0.213514i
$327$	−7.23620			−0.400163
$328$	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	$-0.0642293\pi$
$332$			5.63851i			0.309453i
$333$	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	$-0.131018\pi$
$337$	9.47979	+	9.47979i	0.516397	+	0.516397i	−0.400082	+	0.916479i	$0.631018\pi$
$338$		−	17.3583i		−	0.944165i
$339$	−17.4088			−0.945516
$340$		0			0
$341$	4.96890			0.269081
$342$			5.87584i			0.317729i
$343$	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	0.321543	−	0.946895i	$-0.395798\pi$
$347$	23.6284	−	23.6284i	1.26844	−	1.26844i	0.946895	−	0.321543i	$-0.104202\pi$
$348$		−	13.2505i		−	0.710301i
$349$		−	22.4213i		−	1.20019i	−0.799930	−	0.600093i	$-0.795130\pi$
$349$		−	22.4213i		−	1.20019i	0.799930	−	0.600093i	$-0.204870\pi$
$350$		0			0
$351$	4.57749	−	4.57749i	0.244329	−	0.244329i
$352$	6.77628	+	6.77628i	0.361177	+	0.361177i
$353$	−22.2555			−1.18454			−0.592270	−	0.805739i	$-0.701768\pi$
$353$	−22.2555			−1.18454			−0.592270	+	0.805739i	$0.701768\pi$
$354$	−7.11835	−	7.11835i	−0.378336	−	0.378336i
$355$		0			0
$356$	4.15466			0.220197
$357$	−13.4096	+	39.3574i	−0.709713	+	2.08302i
$358$	−9.43927			−0.498881
$359$			36.6674i			1.93523i	0.252424	+	0.967617i	$0.418772\pi$
$359$			36.6674i			1.93523i	−0.252424	+	0.967617i	$0.581228\pi$
$360$		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	−0.704596	−	0.709608i	$-0.748872\pi$
$367$	0.0960113	−	0.0960113i	0.00501175	−	0.00501175i	0.709608	+	0.704596i	$0.248872\pi$
$368$	−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
$372$		−	10.8967i		−	0.564966i
$373$	0.927465			0.0480223			0.0240111	−	0.999712i	$-0.492356\pi$
$373$	0.927465			0.0480223			0.0240111	+	0.999712i	$0.492356\pi$
$374$	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
$378$	3.01936			0.155299
$379$	5.93013	+	5.93013i	0.304610	+	0.304610i	0.842814	−	0.538204i	$-0.180897\pi$
$379$	5.93013	+	5.93013i	0.304610	+	0.304610i	−0.538204	+	0.842814i	$0.680897\pi$
$380$		0			0
$381$	−23.9780	+	23.9780i	−1.22843	+	1.22843i
$382$		−	3.22243i		−	0.164874i
$383$		−	21.9106i		−	1.11958i	−0.828635	−	0.559789i	$-0.810882\pi$
$383$		−	21.9106i		−	1.11958i	0.828635	−	0.559789i	$-0.189118\pi$
$384$	18.1495	−	18.1495i	0.926186	−	0.926186i
$385$		0			0
$386$	−6.67917	−	6.67917i	−0.339961	−	0.339961i
$387$	−2.55347			−0.129800
$388$	−11.4077	−	11.4077i	−0.579137	−	0.579137i
$389$		−	12.7622i		−	0.647071i	−0.946216	−	0.323536i	$-0.895128\pi$
$389$		−	12.7622i		−	0.647071i	0.946216	−	0.323536i	$-0.104872\pi$
$390$		0			0
$391$	8.50471	+	17.2951i	0.430102	+	0.874649i
$392$	−27.1041			−1.36896
$393$		−	10.9958i		−	0.554663i
$394$	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	−0.101350	−	0.994851i	$-0.532316\pi$
$397$	17.8029	−	17.8029i	0.893501	−	0.893501i	0.994851	+	0.101350i	$0.0323162\pi$
$398$	−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
$407$	8.86259			0.439302
$408$	−10.2916	−	20.9288i	−0.509509	−	1.03613i
$409$	−15.4742			−0.765149			−0.382575	−	0.923925i	$-0.624963\pi$
$409$	−15.4742			−0.765149			−0.382575	+	0.923925i	$0.624963\pi$
$410$		0			0
$411$	24.2753	+	24.2753i	1.19741	+	1.19741i
$412$	−17.4581			−0.860101
$413$	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
$417$		−	12.6590i		−	0.619915i
$418$	−2.69044	+	2.69044i	−0.131594	+	0.131594i
$419$	12.8210	−	12.8210i	0.626348	−	0.626348i	−0.320799	−	0.947147i	$-0.603952\pi$
$419$	12.8210	−	12.8210i	0.626348	−	0.626348i	0.947147	+	0.320799i	$0.103952\pi$
$420$		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
$423$			5.12633i			0.249250i
$424$	−16.6857			−0.810331
$425$		0			0
$426$	−21.7045			−1.05158
$427$			27.9533i			1.35276i
$428$	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
$433$		−	12.8308i		−	0.616610i	−0.951287	−	0.308305i	$-0.900238\pi$
$433$		−	12.8308i		−	0.616610i	0.951287	−	0.308305i	$-0.0997618\pi$
$434$		−	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
$438$	15.8548			0.757573
$439$	−17.1720	−	17.1720i	−0.819573	−	0.819573i	0.166473	−	0.986046i	$-0.446762\pi$
$439$	−17.1720	−	17.1720i	−0.819573	−	0.819573i	−0.986046	+	0.166473i	$0.946762\pi$
$440$		0			0
$441$	28.8985			1.37612
$442$	−16.4339	−	5.59927i	−0.781682	−	0.266330i
$443$	16.1216			0.765962			0.382981	−	0.923756i	$-0.374897\pi$
$443$	16.1216			0.765962			0.382981	+	0.923756i	$0.374897\pi$
$444$		−	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	−0.311867	−	0.950126i	$-0.600954\pi$
$449$	13.5245	−	13.5245i	0.638259	−	0.638259i	0.950126	+	0.311867i	$0.100954\pi$
$450$		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
$457$		−	3.68314i		−	0.172290i	−0.996283	−	0.0861451i	$-0.972545\pi$
$457$		−	3.68314i		−	0.172290i	0.996283	−	0.0861451i	$-0.0274549\pi$
$458$	7.50314			0.350599
$459$	−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
$463$	−23.6496			−1.09909			−0.549545	−	0.835464i	$-0.685199\pi$
$463$	−23.6496			−1.09909			−0.549545	+	0.835464i	$0.685199\pi$
$464$	−3.75521	−	3.75521i	−0.174331	−	0.174331i
$465$		0			0
$466$	7.41961	−	7.41961i	0.343707	−	0.343707i
$467$			5.50118i			0.254564i	0.991867	+	0.127282i	$0.0406254\pi$
$467$			5.50118i			0.254564i	−0.991867	+	0.127282i	$0.959375\pi$
$468$			24.4949i			1.13228i
$469$	17.5452	−	17.5452i	0.810161	−	0.810161i
$470$		0			0
$471$	−16.7102	−	16.7102i	−0.769965	−	0.769965i
$472$	−15.1195			−0.695932
$473$	−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
$477$	17.7904			0.814567
$478$		−	1.58705i		−	0.0725901i
$479$	7.89487	+	7.89487i	0.360726	+	0.360726i	0.864080	−	0.503354i	$-0.167901\pi$
$479$	7.89487	+	7.89487i	0.360726	+	0.360726i	−0.503354	+	0.864080i	$0.667901\pi$
$480$		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	0.146443	−	0.989219i	$-0.453218\pi$
$487$	25.0619	−	25.0619i	1.13566	−	1.13566i	0.989219	−	0.146443i	$-0.0467825\pi$
$488$	−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	$0.906316\pi$
$492$	−7.94959			−0.358395
$493$	−13.4959	+	6.63652i	−0.607826	+	0.298894i
$494$	14.2737			0.642203
$495$		0			0
$496$	−3.08813	−	3.08813i	−0.138661	−	0.138661i
$497$	58.1159			2.60686
$498$	4.13360	+	4.13360i	0.185231	+	0.185231i
$499$	−13.1434	+	13.1434i	−0.588380	+	0.588380i	−0.937192	−	0.348813i	$-0.886585\pi$
$499$	−13.1434	+	13.1434i	−0.588380	+	0.588380i	0.348813	+	0.937192i	$0.386585\pi$
$500$		0			0
$501$		−	30.4191i		−	1.35903i
$502$			6.25429i			0.279143i
$503$	24.0464	−	24.0464i	1.07217	−	1.07217i	0.0749899	−	0.997184i	$-0.476108\pi$
$503$	24.0464	−	24.0464i	1.07217	−	1.07217i	0.997184	−	0.0749899i	$-0.0238925\pi$
$504$	−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
$508$			22.1629i			0.983318i
$509$	−29.8369			−1.32250			−0.661249	−	0.750167i	$-0.729973\pi$
$509$	−29.8369			−1.32250			−0.661249	+	0.750167i	$0.729973\pi$
$510$		0			0
$511$	−42.4530			−1.87801
$512$		−	15.4092i		−	0.680999i
$513$	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
$518$		−	15.5071i		−	0.681342i
$519$			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
$523$	−20.2414			−0.885093			−0.442547	−	0.896745i	$-0.645925\pi$
$523$	−20.2414			−0.885093			−0.442547	+	0.896745i	$0.645925\pi$
$524$	−5.08168	−	5.08168i	−0.221994	−	0.221994i
$525$		0			0
$526$	−8.45101			−0.368482
$527$	−11.0985	+	5.45760i	−0.483458	+	0.237737i
$528$	−5.68591			−0.247447
$529$			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	$0.699801\pi$
$542$			12.4301i			0.533916i
$543$	−30.7656			−1.32028
$544$	−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	0.912442	+	0.409207i	$0.134194\pi$
$547$	30.9108	+	30.9108i	1.32165	+	1.32165i	0.409207	+	0.912442i	$0.365806\pi$
$548$	22.4376			0.958486
$549$	11.8210	+	11.8210i	0.504510	+	0.504510i
$550$		0			0
$551$	8.74302	−	8.74302i	0.372465	−	0.372465i
$552$			26.4407i			1.12539i
$553$			4.96600i			0.211176i
$554$	−6.11115	+	6.11115i	−0.259638	+	0.259638i
$555$		0			0
$556$	−5.85035	−	5.85035i	−0.248110	−	0.248110i
$557$	−29.0497			−1.23088			−0.615438	−	0.788185i	$-0.711021\pi$
$557$	−29.0497			−1.23088			−0.615438	+	0.788185i	$0.711021\pi$
$558$	−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
$562$	21.0921			0.889718
$563$			39.3006i			1.65632i	0.560489	+	0.828162i	$0.310613\pi$
$563$			39.3006i			1.65632i	−0.560489	+	0.828162i	$0.689387\pi$
$564$	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	$-0.903093\pi$
$569$		−	14.3009i		−	0.599525i	0.954014	−	0.299763i	$-0.0969075\pi$
$570$		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
$577$	5.85190			0.243618			0.121809	−	0.992554i	$-0.461131\pi$
$577$	5.85190			0.243618			0.121809	+	0.992554i	$0.461131\pi$
$578$	−7.03310	+	9.12298i	−0.292539	+	0.379466i
$579$	32.8645			1.36580
$580$		0			0
$581$	−11.0681	−	11.0681i	−0.459183	−	0.459183i
$582$	−16.7259			−0.693313
$583$	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
$587$			2.30210i			0.0950176i	0.998871	+	0.0475088i	$0.0151282\pi$
$587$			2.30210i			0.0950176i	−0.998871	+	0.0475088i	$0.984872\pi$
$588$	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
$593$		−	4.89325i		−	0.200942i	−0.994940	−	0.100471i	$-0.967965\pi$
$593$		−	4.89325i		−	0.200942i	0.994940	−	0.100471i	$-0.0320349\pi$
$594$	1.16929			0.0479764
$595$		0			0
$596$	−19.5511			−0.800844
$597$		−	4.83258i		−	0.197784i
$598$	13.9180	+	13.9180i	0.569148	+	0.569148i
$599$	−6.54372			−0.267369			−0.133685	−	0.991024i	$-0.542681\pi$
$599$	−6.54372			−0.267369			−0.133685	+	0.991024i	$0.542681\pi$
$600$		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
$603$		−	14.8392i		−	0.604298i
$604$			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	−0.954801	−	0.297247i	$-0.903932\pi$
$607$	−30.8472	−	30.8472i	−1.25205	−	1.25205i	−0.297247	−	0.954801i	$-0.596068\pi$
$608$	19.6103			0.795302
$609$	26.0101	+	26.0101i	1.05398	+	1.05398i
$610$		0			0
$611$	12.4530			0.503793
$612$	15.3837	+	5.24145i	0.621849	+	0.211873i
$613$	24.9253			1.00672			0.503362	−	0.864076i	$-0.332096\pi$
$613$	24.9253			1.00672			0.503362	+	0.864076i	$0.332096\pi$
$614$		−	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	$-0.133137\pi$
$617$	12.6091	+	12.6091i	0.507625	+	0.507625i	−0.406172	+	0.913797i	$0.633137\pi$
$618$	−12.7986	+	12.7986i	−0.514834	+	0.514834i
$619$	19.5300	−	19.5300i	0.784977	−	0.784977i	−0.195689	−	0.980666i	$-0.562694\pi$
$619$	19.5300	−	19.5300i	0.784977	−	0.784977i	0.980666	+	0.195689i	$0.0626944\pi$
$620$		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
$627$		−	13.2382i		−	0.528681i
$628$	−15.4452			−0.616330
$629$	−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
$633$	−1.03329			−0.0410694
$634$	13.8409	+	13.8409i	0.549694	+	0.549694i
$635$		0			0
$636$	17.8638	−	17.8638i	0.708345	−	0.708345i
$637$		−	70.2007i		−	2.78145i
$638$		−	4.09425i		−	0.162093i
$639$	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	$0.901919\pi$
$642$	9.69836			0.382764
$643$	4.84007	+	4.84007i	0.190874	+	0.190874i	0.796074	−	0.605200i	$-0.206907\pi$
$643$	4.84007	+	4.84007i	0.190874	+	0.190874i	−0.605200	+	0.796074i	$0.706907\pi$
$644$		−	30.8087i		−	1.21403i
$645$		0			0
$646$	3.05430	−	8.96441i	0.120170	−	0.352700i
$647$	−39.1427			−1.53886			−0.769429	−	0.638732i	$-0.779459\pi$
$647$	−39.1427			−1.53886			−0.769429	+	0.638732i	$0.779459\pi$
$648$		−	24.3057i		−	0.954817i
$649$	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	$-0.836761\pi$
$653$	−9.72867	+	9.72867i	−0.380712	+	0.380712i	0.490646	+	0.871359i	$0.336761\pi$
$654$			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	$-0.621178\pi$
$659$	−19.0767			−0.743124			−0.371562	+	0.928408i	$0.621178\pi$
$660$		0			0
$661$			3.89804i			0.151616i	0.997122	+	0.0758082i	$0.0241537\pi$
$661$			3.89804i			0.151616i	−0.997122	+	0.0758082i	$0.975846\pi$
$662$	−4.94142			−0.192054
$663$	54.2065	−	26.6556i	2.10521	−	1.03522i
$664$	8.77984			0.340724
$665$		0			0
$666$	−6.55771	−	6.55771i	−0.254106	−	0.254106i
$667$	17.0503			0.660189
$668$	−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
$672$			58.3398i			2.25050i
$673$	6.34918	−	6.34918i	0.244743	−	0.244743i	−0.574066	−	0.818809i	$-0.694635\pi$
$673$	6.34918	−	6.34918i	0.244743	−	0.244743i	0.818809	+	0.574066i	$0.194635\pi$
$674$	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	$-0.451992\pi$
$677$	−21.8144	−	21.8144i	−0.838397	−	0.838397i	−0.988648	+	0.150251i	$0.951992\pi$
$678$			11.7963i			0.453033i
$679$	44.7855			1.71871
$680$		0			0
$681$	−21.8343			−0.836694
$682$		−	3.36694i		−	0.128927i
$683$	−3.16023	−	3.16023i	−0.120923	−	0.120923i	0.644056	−	0.764979i	$-0.277251\pi$
$683$	−3.16023	−	3.16023i	−0.120923	−	0.120923i	−0.764979	+	0.644056i	$0.777251\pi$
$684$	−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
$688$			1.45328i			0.0554059i
$689$		−	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
$693$	18.1260			0.688551
$694$	−16.0107	−	16.0107i	−0.607757	−	0.607757i
$695$		0			0
$696$	−20.6326			−0.782077
$697$	3.98156	+	8.09684i	0.150812	+	0.306690i
$698$	−15.1928			−0.575054
$699$			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	0.966839	−	0.255387i	$-0.0822028\pi$
$709$	18.9439	+	18.9439i	0.711452	+	0.711452i	−0.255387	+	0.966839i	$0.582203\pi$
$710$		0			0
$711$	2.10005	+	2.10005i	0.0787579	+	0.0787579i
$712$		−	6.46931i		−	0.242448i
$713$	14.0214			0.525107
$714$	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
$718$	24.8460			0.927244
$719$	31.0488	+	31.0488i	1.15792	+	1.15792i	0.984922	+	0.173001i	$0.0553465\pi$
$719$	31.0488	+	31.0488i	1.15792	+	1.15792i	0.173001	+	0.984922i	$0.444653\pi$
$720$		0			0
$721$	34.2695	−	34.2695i	1.27626	−	1.27626i
$722$		−	5.08842i		−	0.189372i
$723$			71.9866i			2.67721i
$724$	−14.2183	+	14.2183i	−0.528419	+	0.528419i
$725$		0			0
$726$	9.32598	+	9.32598i	0.346120	+	0.346120i
$727$	2.37306			0.0880118			0.0440059	−	0.999031i	$-0.485988\pi$
$727$	2.37306			0.0880118			0.0440059	+	0.999031i	$0.485988\pi$
$728$	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
$732$	23.7396			0.877440
$733$		−	27.2035i		−	1.00478i	−0.864640	−	0.502391i	$-0.832454\pi$
$733$		−	27.2035i		−	1.00478i	0.864640	−	0.502391i	$-0.167546\pi$
$734$	−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	$-0.939107\pi$
$739$		−	10.3375i		−	0.380270i	0.981758	−	0.190135i	$-0.0608926\pi$
$740$		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	0.843490	−	0.537146i	$-0.180497\pi$
$743$	8.35033	+	8.35033i	0.306344	+	0.306344i	−0.537146	+	0.843490i	$0.680497\pi$
$744$	−16.9674			−0.622056
$745$		0			0
$746$		−	0.628453i		−	0.0230093i
$747$	−9.36110			−0.342505
$748$	4.64396	+	9.44389i	0.169800	+	0.345303i
$749$	−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	$0.630968\pi$
$752$	2.91760			0.106394
$753$	−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
$757$			4.41769i			0.160564i	0.996772	+	0.0802818i	$0.0255820\pi$
$757$			4.41769i			0.160564i	−0.996772	+	0.0802818i	$0.974418\pi$
$758$	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
$763$		−	13.1290i		−	0.475303i
$764$	7.32773			0.265108
$765$		0			0
$766$	−14.8467			−0.536432
$767$		−	39.1601i		−	1.41399i
$768$	−15.6594	−	15.6594i	−0.565061	−	0.565061i
$769$	−30.7653			−1.10942			−0.554712	−	0.832043i	$-0.687171\pi$
$769$	−30.7653			−1.10942			−0.554712	+	0.832043i	$0.687171\pi$
$770$		0			0
$771$	−5.38518	+	5.38518i	−0.193942	+	0.193942i
$772$	15.1883	−	15.1883i	0.546638	−	0.546638i
$773$			25.2932i			0.909735i	0.890559	+	0.454867i	$0.150313\pi$
$773$			25.2932i			0.909735i	−0.890559	+	0.454867i	$0.849687\pi$
$774$			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
$778$	−8.64773			−0.310036
$779$	−5.24535	−	5.24535i	−0.187934	−	0.187934i
$780$		0			0
$781$	22.5062			0.805334
$782$	11.7192	−	5.76282i	0.419078	−	0.206078i
$783$	−3.79978			−0.135793
$784$		−	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	$-0.363947\pi$
$787$	−13.9008	−	13.9008i	−0.495509	−	0.495509i	−0.910037	+	0.414528i	$0.863947\pi$
$788$	−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
$797$			27.3888i			0.970159i	0.874470	+	0.485080i	$0.161209\pi$
$797$			27.3888i			0.970159i	−0.874470	+	0.485080i	$0.838791\pi$
$798$	−23.1631			−0.819965
$799$	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
$803$	−16.4405			−0.580171
$804$	−14.9004	−	14.9004i	−0.525496	−	0.525496i
$805$		0			0
$806$	−8.93137	+	8.93137i	−0.314594	+	0.314594i
$807$			0.730900i			0.0257289i
$808$		−	27.7188i		−	0.975145i
$809$	−2.66487	+	2.66487i	−0.0936919	+	0.0936919i	−0.752399	−	0.658707i	$-0.771104\pi$
$809$	−2.66487	+	2.66487i	−0.0936919	+	0.0936919i	0.658707	+	0.752399i	$0.271104\pi$
$810$		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	$0.546661\pi$
$812$	24.0411			0.843676
$813$	−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
$817$	−3.38359			−0.118377
$818$			10.4854i			0.366612i
$819$	−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	$-0.739281\pi$
$823$	1.36590	−	1.36590i	0.0476123	−	0.0476123i	0.730512	+	0.682900i	$0.239281\pi$
$824$			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	−0.422361	−	0.906428i	$-0.638799\pi$
$827$	13.9206	−	13.9206i	0.484067	−	0.484067i	0.906428	+	0.422361i	$0.138799\pi$
$828$	−13.0285	−	13.0285i	−0.452773	−	0.452773i
$829$	−21.3907			−0.742930			−0.371465	−	0.928447i	$-0.621145\pi$
$829$	−21.3907			−0.742930			−0.371465	+	0.928447i	$0.621145\pi$
$830$		0			0
$831$		−	30.0696i		−	1.04310i
$832$	−6.26493			−0.217197
$833$	−44.0887	−	15.0216i	−1.52758	−	0.520469i
$834$	−8.57779			−0.297025
$835$		0			0
$836$	−6.11800	−	6.11800i	−0.211595	−	0.211595i
$837$	−3.12479			−0.108008
$838$	−8.68757	−	8.68757i	−0.300107	−	0.300107i
$839$	20.3873	−	20.3873i	0.703846	−	0.703846i	−0.261387	−	0.965234i	$-0.584180\pi$
$839$	20.3873	−	20.3873i	0.703846	−	0.703846i	0.965234	+	0.261387i	$0.0841800\pi$
$840$		0			0
$841$		−	15.6951i		−	0.541210i
$842$		−	6.64822i		−	0.229113i
$843$	−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
$848$		−	10.1252i		−	0.347702i
$849$	65.6708			2.25382
$850$		0			0
$851$	25.0088			0.857292
$852$		−	49.3554i		−	1.69089i
$853$	8.13732	+	8.13732i	0.278617	+	0.278617i	0.832557	−	0.553940i	$-0.186876\pi$
$853$	8.13732	+	8.13732i	0.278617	+	0.278617i	−0.553940	+	0.832557i	$0.686876\pi$
$854$	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	−0.919351	−	0.393438i	$-0.871286\pi$
$857$	−15.3959	+	15.3959i	−0.525913	+	0.525913i	0.393438	+	0.919351i	$0.371286\pi$
$858$			16.4446i			0.561409i
$859$		−	0.00614837i		−	0.000209780i	−1.00000		0.000104890i	$-0.999967\pi$
$859$		−	0.00614837i		−	0.000209780i	1.00000		0.000104890i	$-3.33875e-5\pi$
$860$		0			0
$861$	15.6047	−	15.6047i	0.531806	−	0.531806i
$862$	−8.68472	−	8.68472i	−0.295803	−	0.295803i
$863$	−21.5322			−0.732964			−0.366482	−	0.930425i	$-0.619438\pi$
$863$	−21.5322			−0.732964			−0.366482	+	0.930425i	$0.619438\pi$
$864$	−4.26139	−	4.26139i	−0.144975	−	0.144975i
$865$		0			0
$866$	−8.69421			−0.295441
$867$	−5.14155	−	39.7475i	−0.174616	−	1.34990i
$868$	19.7704			0.671051
$869$			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	−0.693645	−	0.720317i	$-0.743996\pi$
$877$	0.789882	−	0.789882i	0.0266724	−	0.0266724i	0.720317	+	0.693645i	$0.243996\pi$
$878$	−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	$-0.546097\pi$
$882$		−	19.5817i		−	0.659351i
$883$	20.9432			0.704796			0.352398	−	0.935850i	$-0.385366\pi$
$883$	20.9432			0.704796			0.352398	+	0.935850i	$0.385366\pi$
$884$	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	$-0.146621\pi$
$887$	13.4400	+	13.4400i	0.451271	+	0.451271i	−0.444506	+	0.895776i	$0.646621\pi$
$888$	−30.2633			−1.01557
$889$	−43.5046	−	43.5046i	−1.45910	−	1.45910i
$890$		0			0
$891$	−11.8659	+	11.8659i	−0.397524	+	0.397524i
$892$			41.9761i			1.40546i
$893$			6.79286i			0.227315i
$894$	−14.3329	+	14.3329i	−0.479365	+	0.479365i
$895$		0			0
$896$	32.9295	+	32.9295i	1.10010	+	1.10010i
$897$	−68.4826			−2.28657
$898$	−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
$902$	−2.45633			−0.0817869
$903$		−	10.0660i		−	0.334976i
$904$	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	−0.848769	−	0.528764i	$-0.822656\pi$
$907$	−9.63742	+	9.63742i	−0.320005	+	0.320005i	0.528764	+	0.848769i	$0.322656\pi$
$908$	−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
$917$	19.9502			0.658814
$918$	−2.61171	+	1.28429i	−0.0861993	+	0.0423878i
$919$	−31.7339			−1.04681			−0.523403	−	0.852085i	$-0.675338\pi$
$919$	−31.7339			−1.04681			−0.523403	+	0.852085i	$0.675338\pi$
$920$		0			0
$921$	7.03471	+	7.03471i	0.231802	+	0.231802i
$922$	13.3874			0.440889
$923$	−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
$927$		−	28.9841i		−	0.951964i
$928$	−14.9212	+	14.9212i	−0.489813	+	0.489813i
$929$	5.97435	−	5.97435i	0.196012	−	0.196012i	−0.602276	−	0.798288i	$-0.705739\pi$
$929$	5.97435	−	5.97435i	0.196012	−	0.196012i	0.798288	+	0.602276i	$0.205739\pi$
$930$		0			0
$931$	38.2932			1.25501
$932$	16.8720	+	16.8720i	0.552661	+	0.552661i
$933$			36.3300i			1.18939i
$934$	3.72762			0.121971
$935$		0			0
$936$	38.1415			1.24669
$937$			18.0115i			0.588409i	0.955742	+	0.294205i	$0.0950547\pi$
$937$			18.0115i			0.588409i	−0.955742	+	0.294205i	$0.904945\pi$
$938$	−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
$943$		−	10.2293i		−	0.333111i
$944$		−	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	−0.996961	−	0.0778975i	$-0.975179\pi$
$947$	−33.0770	−	33.0770i	−1.07486	−	1.07486i	−0.0778975	−	0.996961i	$-0.524821\pi$
$948$	4.21742			0.136975
$949$	43.6111	+	43.6111i	1.41568	+	1.41568i
$950$		0			0
$951$	−68.1036			−2.20841
$952$	37.9723	−	18.6726i	1.23069	−	0.605181i
$953$	−8.60527			−0.278752			−0.139376	−	0.990240i	$-0.544510\pi$
$953$	−8.60527			−0.278752			−0.139376	+	0.990240i	$0.544510\pi$
$954$		−	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
$967$			29.7257i			0.955913i	0.878383	+	0.477957i	$0.158622\pi$
$967$			29.7257i			0.955913i	−0.878383	+	0.477957i	$0.841378\pi$
$968$	19.8086			0.636671
$969$	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
$973$	22.9679			0.736318
$974$	−16.9820	−	16.9820i	−0.544139	−	0.544139i
$975$		0			0
$976$	6.72783	−	6.72783i	0.215353	−	0.215353i
$977$			51.4273i			1.64530i	0.568545	+	0.822652i	$0.307507\pi$
$977$			51.4273i			1.64530i	−0.568545	+	0.822652i	$0.692493\pi$
$978$		−	12.8533i		−	0.411004i
$979$	−3.15829	+	3.15829i	−0.100939	+	0.100939i
$980$		0			0
$981$	−5.55207	−	5.55207i	−0.177264	−	0.177264i
$982$	8.71114			0.277984
$983$	−9.68389	−	9.68389i	−0.308868	−	0.308868i	0.535602	−	0.844470i	$-0.320085\pi$
$983$	−9.68389	−	9.68389i	−0.308868	−	0.308868i	−0.844470	+	0.535602i	$0.820085\pi$
$984$			12.3785i			0.394611i
$985$		0			0
$986$	4.49693	+	9.14489i	0.143211	+	0.291233i
$987$	−20.2085			−0.643243
$988$			32.4580i			1.03263i
$989$	−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	−0.398642	−	0.917107i	$-0.630518\pi$
$997$	16.3707	−	16.3707i	0.518465	−	0.518465i	0.917107	+	0.398642i	$0.130518\pi$
$998$	8.90601	+	8.90601i	0.281915	+	0.281915i
$999$	−5.57341			−0.176335

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.f.251.3		12
5.2	odd	4		425.2.j.b.149.4		12
5.3	odd	4		425.2.j.c.149.3		12
5.4	even	2		85.2.e.a.81.4	yes	12
15.14	odd	2		765.2.k.b.676.3		12
17.2	even	8		7225.2.a.bb.1.4		6
17.4	even	4	inner	425.2.e.f.276.4		12
17.15	even	8		7225.2.a.z.1.4		6
20.19	odd	2		1360.2.bt.d.81.5		12
85.4	even	4		85.2.e.a.21.3	✓	12
85.9	even	8		1445.2.d.g.866.7		12
85.19	even	8		1445.2.a.n.1.3		6
85.38	odd	4		425.2.j.b.174.4		12
85.49	even	8		1445.2.a.o.1.3		6
85.59	even	8		1445.2.d.g.866.8		12
85.72	odd	4		425.2.j.c.174.3		12
255.89	odd	4		765.2.k.b.361.4		12
340.259	odd	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	85.4	even	4
85.2.e.a.81.4	yes	12	5.4	even	2
425.2.e.f.251.3		12	1.1	even	1	trivial
425.2.e.f.276.4		12	17.4	even	4	inner
425.2.j.b.149.4		12	5.2	odd	4
425.2.j.b.174.4		12	85.38	odd	4
425.2.j.c.149.3		12	5.3	odd	4
425.2.j.c.174.3		12	85.72	odd	4
765.2.k.b.361.4		12	255.89	odd	4
765.2.k.b.676.3		12	15.14	odd	2
1360.2.bt.d.81.5		12	20.19	odd	2
1360.2.bt.d.1041.5		12	340.259	odd	4
1445.2.a.n.1.3		6	85.19	even	8
1445.2.a.o.1.3		6	85.49	even	8
1445.2.d.g.866.7		12	85.9	even	8
1445.2.d.g.866.8		12	85.59	even	8
7225.2.a.z.1.4		6	17.15	even	8
7225.2.a.bb.1.4		6	17.2	even	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	425.2.e.f.251.3

Level	$425$
Weight	$2$
Character	425.251
Analytic conductor	$3.394$
Analytic rank	$0$
Dimension	$12$
Inner twists	$2$