LMFDB - Embedded newform 1050.3.l.b.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(43,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.43");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.l (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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.12745506816.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 23x^{4} + 1 $ x^8 + 23*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.4
Root			$1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	1050.43
Dual form			1050.3.l.b.757.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -14.0884 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.03207 + 6.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(9.54506 - 9.54506i) q^{17} +(-3.00000 - 3.00000i) q^{18} +21.6823i q^{19} +4.58258 q^{21} +(14.0884 - 14.0884i) q^{22} +(-0.423494 - 0.423494i) q^{23} +4.89898i q^{24} -12.0641 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -11.2171i q^{29} -16.4543 q^{31} +(4.00000 - 4.00000i) q^{32} +(-17.2547 - 17.2547i) q^{33} +19.0901i q^{34} +6.00000 q^{36} +(-47.6653 + 47.6653i) q^{37} +(-21.6823 - 21.6823i) q^{38} +14.7755i q^{39} -44.0379 q^{41} +(-4.58258 + 4.58258i) q^{42} +(46.7052 + 46.7052i) q^{43} +28.1767i q^{44} +0.846988 q^{46} +(20.3412 - 20.3412i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +23.3805 q^{51} +(12.0641 - 12.0641i) q^{52} +(18.6273 + 18.6273i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(-26.5553 + 26.5553i) q^{57} +(11.2171 + 11.2171i) q^{58} +13.4774i q^{59} -10.8748 q^{61} +(16.4543 - 16.4543i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +34.5093 q^{66} +(-72.2045 + 72.2045i) q^{67} +(-19.0901 - 19.0901i) q^{68} -1.03734i q^{69} -64.1040 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-51.4407 - 51.4407i) q^{73} -95.3307i q^{74} +43.3646 q^{76} +(-26.3569 + 26.3569i) q^{77} +(-14.7755 - 14.7755i) q^{78} +157.457i q^{79} -9.00000 q^{81} +(44.0379 - 44.0379i) q^{82} +(76.9972 + 76.9972i) q^{83} -9.16515i q^{84} -93.4104 q^{86} +(13.7381 - 13.7381i) q^{87} +(-28.1767 - 28.1767i) q^{88} +37.6912i q^{89} +22.5699 q^{91} +(-0.846988 + 0.846988i) q^{92} +(-20.1523 - 20.1523i) q^{93} +40.6824i q^{94} +9.79796 q^{96} +(-97.2189 + 97.2189i) q^{97} +(7.00000 + 7.00000i) q^{98} -42.2651i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 16 * q^8	$ 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$3$	1.22474	+	1.22474i	0.408248	+	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$		0			0
$5$		0			0
$6$	−2.44949			−0.408248
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$7$	1.87083	−	1.87083i	0.267261	−	0.267261i
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$		0			0
$11$	−14.0884			−1.28076			−0.640380	−	0.768058i	$-0.721223\pi$
$11$	−14.0884			−1.28076			−0.640380	+	0.768058i	$0.721223\pi$
$12$	2.44949	−	2.44949i	0.204124	−	0.204124i
$13$	6.03207	+	6.03207i	0.464005	+	0.464005i	0.899966	−	0.435961i	$-0.143591\pi$
$13$	6.03207	+	6.03207i	0.464005	+	0.464005i	−0.435961	+	0.899966i	$0.643591\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	9.54506	−	9.54506i	0.561474	−	0.561474i	−0.368252	−	0.929726i	$-0.620044\pi$
$17$	9.54506	−	9.54506i	0.561474	−	0.561474i	0.929726	+	0.368252i	$0.120044\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$			21.6823i			1.14117i	0.821237	+	0.570587i	$0.193284\pi$
$19$			21.6823i			1.14117i	−0.821237	+	0.570587i	$0.806716\pi$
$20$		0			0
$21$	4.58258			0.218218
$22$	14.0884	−	14.0884i	0.640380	−	0.640380i
$23$	−0.423494	−	0.423494i	−0.0184128	−	0.0184128i	0.697840	−	0.716253i	$-0.254144\pi$
$23$	−0.423494	−	0.423494i	−0.0184128	−	0.0184128i	−0.716253	+	0.697840i	$0.754144\pi$
$24$			4.89898i			0.204124i
$25$		0			0
$26$	−12.0641			−0.464005
$27$	−3.67423	+	3.67423i	−0.136083	+	0.136083i
$28$	−3.74166	−	3.74166i	−0.133631	−	0.133631i
$29$		−	11.2171i		−	0.386798i	−0.981120	−	0.193399i	$-0.938049\pi$
$29$		−	11.2171i		−	0.386798i	0.981120	−	0.193399i	$-0.0619512\pi$
$30$		0			0
$31$	−16.4543			−0.530782			−0.265391	−	0.964141i	$-0.585501\pi$
$31$	−16.4543			−0.530782			−0.265391	+	0.964141i	$0.585501\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	−17.2547	−	17.2547i	−0.522868	−	0.522868i
$34$			19.0901i			0.561474i
$35$		0			0
$36$	6.00000			0.166667
$37$	−47.6653	+	47.6653i	−1.28825	+	1.28825i	−0.352404	+	0.935848i	$0.614636\pi$
$37$	−47.6653	+	47.6653i	−1.28825	+	1.28825i	−0.935848	+	0.352404i	$0.885364\pi$
$38$	−21.6823	−	21.6823i	−0.570587	−	0.570587i
$39$			14.7755i			0.378859i
$40$		0			0
$41$	−44.0379			−1.07410			−0.537048	−	0.843552i	$-0.680460\pi$
$41$	−44.0379			−1.07410			−0.537048	+	0.843552i	$0.680460\pi$
$42$	−4.58258	+	4.58258i	−0.109109	+	0.109109i
$43$	46.7052	+	46.7052i	1.08617	+	1.08617i	0.995919	+	0.0902487i	$0.0287662\pi$
$43$	46.7052	+	46.7052i	1.08617	+	1.08617i	0.0902487	+	0.995919i	$0.471234\pi$
$44$			28.1767i			0.640380i
$45$		0			0
$46$	0.846988			0.0184128
$47$	20.3412	−	20.3412i	0.432791	−	0.432791i	−0.456785	−	0.889577i	$-0.650999\pi$
$47$	20.3412	−	20.3412i	0.432791	−	0.432791i	0.889577	+	0.456785i	$0.150999\pi$
$48$	−4.89898	−	4.89898i	−0.102062	−	0.102062i
$49$		−	7.00000i		−	0.142857i
$50$		0			0
$51$	23.3805			0.458442
$52$	12.0641	−	12.0641i	0.232003	−	0.232003i
$53$	18.6273	+	18.6273i	0.351458	+	0.351458i	0.860652	−	0.509194i	$-0.170056\pi$
$53$	18.6273	+	18.6273i	0.351458	+	0.351458i	−0.509194	+	0.860652i	$0.670056\pi$
$54$		−	7.34847i		−	0.136083i
$55$		0			0
$56$	7.48331			0.133631
$57$	−26.5553	+	26.5553i	−0.465882	+	0.465882i
$58$	11.2171	+	11.2171i	0.193399	+	0.193399i
$59$			13.4774i			0.228430i	0.993456	+	0.114215i	$0.0364353\pi$
$59$			13.4774i			0.228430i	−0.993456	+	0.114215i	$0.963565\pi$
$60$		0			0
$61$	−10.8748			−0.178275			−0.0891376	−	0.996019i	$-0.528411\pi$
$61$	−10.8748			−0.178275			−0.0891376	+	0.996019i	$0.528411\pi$
$62$	16.4543	−	16.4543i	0.265391	−	0.265391i
$63$	5.61249	+	5.61249i	0.0890871	+	0.0890871i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	34.5093			0.522868
$67$	−72.2045	+	72.2045i	−1.07768	+	1.07768i	−0.0809624	+	0.996717i	$0.525799\pi$
$67$	−72.2045	+	72.2045i	−1.07768	+	1.07768i	−0.996717	+	0.0809624i	$0.974201\pi$
$68$	−19.0901	−	19.0901i	−0.280737	−	0.280737i
$69$		−	1.03734i		−	0.0150340i
$70$		0			0
$71$	−64.1040			−0.902874			−0.451437	−	0.892303i	$-0.649088\pi$
$71$	−64.1040			−0.902874			−0.451437	+	0.892303i	$0.649088\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	−51.4407	−	51.4407i	−0.704667	−	0.704667i	0.260742	−	0.965409i	$-0.416033\pi$
$73$	−51.4407	−	51.4407i	−0.704667	−	0.704667i	−0.965409	+	0.260742i	$0.916033\pi$
$74$		−	95.3307i		−	1.28825i
$75$		0			0
$76$	43.3646			0.570587
$77$	−26.3569	+	26.3569i	−0.342298	+	0.342298i
$78$	−14.7755	−	14.7755i	−0.189429	−	0.189429i
$79$			157.457i			1.99313i	0.0828028	+	0.996566i	$0.473613\pi$
$79$			157.457i			1.99313i	−0.0828028	+	0.996566i	$0.526387\pi$
$80$		0			0
$81$	−9.00000			−0.111111
$82$	44.0379	−	44.0379i	0.537048	−	0.537048i
$83$	76.9972	+	76.9972i	0.927677	+	0.927677i	0.997555	−	0.0698788i	$-0.0222612\pi$
$83$	76.9972	+	76.9972i	0.927677	+	0.927677i	−0.0698788	+	0.997555i	$0.522261\pi$
$84$		−	9.16515i		−	0.109109i
$85$		0			0
$86$	−93.4104			−1.08617
$87$	13.7381	−	13.7381i	0.157910	−	0.157910i
$88$	−28.1767	−	28.1767i	−0.320190	−	0.320190i
$89$			37.6912i			0.423497i	0.977324	+	0.211749i	$0.0679158\pi$
$89$			37.6912i			0.423497i	−0.977324	+	0.211749i	$0.932084\pi$
$90$		0			0
$91$	22.5699			0.248021
$92$	−0.846988	+	0.846988i	−0.00920639	+	0.00920639i
$93$	−20.1523	−	20.1523i	−0.216691	−	0.216691i
$94$			40.6824i			0.432791i
$95$		0			0
$96$	9.79796			0.102062
$97$	−97.2189	+	97.2189i	−1.00226	+	1.00226i	−0.00225910	+	0.999997i	$0.500719\pi$
$97$	−97.2189	+	97.2189i	−1.00226	+	1.00226i	−0.999997	+	0.00225910i	$0.999281\pi$
$98$	7.00000	+	7.00000i	0.0714286	+	0.0714286i
$99$		−	42.2651i		−	0.426920i
$100$		0			0
$101$	26.1142			0.258557			0.129278	−	0.991608i	$-0.458734\pi$
$101$	26.1142			0.258557			0.129278	+	0.991608i	$0.458734\pi$
$102$	−23.3805	+	23.3805i	−0.229221	+	0.229221i
$103$	−52.9553	−	52.9553i	−0.514129	−	0.514129i	0.401660	−	0.915789i	$-0.368433\pi$
$103$	−52.9553	−	52.9553i	−0.514129	−	0.514129i	−0.915789	+	0.401660i	$0.868433\pi$
$104$			24.1283i			0.232003i
$105$		0			0
$106$	−37.2546			−0.351458
$107$	81.7515	−	81.7515i	0.764033	−	0.764033i	−0.213016	−	0.977049i	$-0.568329\pi$
$107$	81.7515	−	81.7515i	0.764033	−	0.764033i	0.977049	+	0.213016i	$0.0683285\pi$
$108$	7.34847	+	7.34847i	0.0680414	+	0.0680414i
$109$			59.2958i			0.543998i	0.962297	+	0.271999i	$0.0876848\pi$
$109$			59.2958i			0.543998i	−0.962297	+	0.271999i	$0.912315\pi$
$110$		0			0
$111$	−116.756			−1.05185
$112$	−7.48331	+	7.48331i	−0.0668153	+	0.0668153i
$113$	−142.193	−	142.193i	−1.25834	−	1.25834i	−0.951884	−	0.306458i	$-0.900856\pi$
$113$	−142.193	−	142.193i	−1.25834	−	1.25834i	−0.306458	−	0.951884i	$-0.599144\pi$
$114$		−	53.1105i		−	0.465882i
$115$		0			0
$116$	−22.4343			−0.193399
$117$	−18.0962	+	18.0962i	−0.154668	+	0.154668i
$118$	−13.4774	−	13.4774i	−0.114215	−	0.114215i
$119$		−	35.7144i		−	0.300121i
$120$		0			0
$121$	77.4821			0.640348
$122$	10.8748	−	10.8748i	0.0891376	−	0.0891376i
$123$	−53.9352	−	53.9352i	−0.438498	−	0.438498i
$124$			32.9085i			0.265391i
$125$		0			0
$126$	−11.2250			−0.0890871
$127$	95.3116	−	95.3116i	0.750485	−	0.750485i	−0.224085	−	0.974570i	$-0.571939\pi$
$127$	95.3116	−	95.3116i	0.750485	−	0.750485i	0.974570	+	0.224085i	$0.0719392\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			114.404i			0.886852i
$130$		0			0
$131$	−191.866			−1.46463			−0.732313	−	0.680968i	$-0.761559\pi$
$131$	−191.866			−1.46463			−0.732313	+	0.680968i	$0.761559\pi$
$132$	−34.5093	+	34.5093i	−0.261434	+	0.261434i
$133$	40.5639	+	40.5639i	0.304991	+	0.304991i
$134$		−	144.409i		−	1.07768i
$135$		0			0
$136$	38.1803			0.280737
$137$	−134.702	+	134.702i	−0.983228	+	0.983228i	−0.999862	−	0.0166339i	$-0.994705\pi$
$137$	−134.702	+	134.702i	−0.983228	+	0.983228i	0.0166339	+	0.999862i	$0.494705\pi$
$138$	1.03734	+	1.03734i	0.00751699	+	0.00751699i
$139$		−	49.6297i		−	0.357048i	−0.983936	−	0.178524i	$-0.942868\pi$
$139$		−	49.6297i		−	0.357048i	0.983936	−	0.178524i	$-0.0571323\pi$
$140$		0			0
$141$	49.8256			0.353373
$142$	64.1040	−	64.1040i	0.451437	−	0.451437i
$143$	−84.9820	−	84.9820i	−0.594279	−	0.594279i
$144$		−	12.0000i		−	0.0833333i
$145$		0			0
$146$	102.881			0.704667
$147$	8.57321	−	8.57321i	0.0583212	−	0.0583212i
$148$	95.3307	+	95.3307i	0.644126	+	0.644126i
$149$			137.142i			0.920415i	0.887811	+	0.460208i	$0.152225\pi$
$149$			137.142i			0.920415i	−0.887811	+	0.460208i	$0.847775\pi$
$150$		0			0
$151$	−197.792			−1.30988			−0.654941	−	0.755680i	$-0.727307\pi$
$151$	−197.792			−1.30988			−0.654941	+	0.755680i	$0.727307\pi$
$152$	−43.3646	+	43.3646i	−0.285293	+	0.285293i
$153$	28.6352	+	28.6352i	0.187158	+	0.187158i
$154$		−	52.7138i		−	0.342298i
$155$		0			0
$156$	29.5510			0.189429
$157$	179.903	−	179.903i	1.14588	−	1.14588i	0.158526	−	0.987355i	$-0.449326\pi$
$157$	179.903	−	179.903i	1.14588	−	1.14588i	0.987355	−	0.158526i	$-0.0506740\pi$
$158$	−157.457	−	157.457i	−0.996566	−	0.996566i
$159$			45.6274i			0.286965i
$160$		0			0
$161$	−1.58457			−0.00984205
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	19.4617	+	19.4617i	0.119397	+	0.119397i	0.764281	−	0.644884i	$-0.223094\pi$
$163$	19.4617	+	19.4617i	0.119397	+	0.119397i	−0.644884	+	0.764281i	$0.723094\pi$
$164$			88.0758i			0.537048i
$165$		0			0
$166$	−153.994			−0.927677
$167$	78.3023	−	78.3023i	0.468876	−	0.468876i	−0.432674	−	0.901550i	$-0.642430\pi$
$167$	78.3023	−	78.3023i	0.468876	−	0.468876i	0.901550	+	0.432674i	$0.142430\pi$
$168$	9.16515	+	9.16515i	0.0545545	+	0.0545545i
$169$		−	96.2284i		−	0.569399i
$170$		0			0
$171$	−65.0469			−0.380391
$172$	93.4104	−	93.4104i	0.543084	−	0.543084i
$173$	−66.9522	−	66.9522i	−0.387007	−	0.387007i	0.486612	−	0.873618i	$-0.338233\pi$
$173$	−66.9522	−	66.9522i	−0.387007	−	0.387007i	−0.873618	+	0.486612i	$0.838233\pi$
$174$			27.4763i			0.157910i
$175$		0			0
$176$	56.3535			0.320190
$177$	−16.5064	+	16.5064i	−0.0932563	+	0.0932563i
$178$	−37.6912	−	37.6912i	−0.211749	−	0.211749i
$179$		−	66.4948i		−	0.371479i	−0.982599	−	0.185740i	$-0.940532\pi$
$179$		−	66.4948i		−	0.371479i	0.982599	−	0.185740i	$-0.0594681\pi$
$180$		0			0
$181$	−33.5180			−0.185183			−0.0925913	−	0.995704i	$-0.529515\pi$
$181$	−33.5180			−0.185183			−0.0925913	+	0.995704i	$0.529515\pi$
$182$	−22.5699	+	22.5699i	−0.124011	+	0.124011i
$183$	−13.3188	−	13.3188i	−0.0727805	−	0.0727805i
$184$		−	1.69398i		−	0.00920639i
$185$		0			0
$186$	40.3045			0.216691
$187$	−134.474	+	134.474i	−0.719114	+	0.719114i
$188$	−40.6824	−	40.6824i	−0.216396	−	0.216396i
$189$			13.7477i			0.0727393i
$190$		0			0
$191$	−209.877			−1.09883			−0.549415	−	0.835549i	$-0.685150\pi$
$191$	−209.877			−1.09883			−0.549415	+	0.835549i	$0.685150\pi$
$192$	−9.79796	+	9.79796i	−0.0510310	+	0.0510310i
$193$	247.934	+	247.934i	1.28463	+	1.28463i	0.938001	+	0.346634i	$0.112675\pi$
$193$	247.934	+	247.934i	1.28463	+	1.28463i	0.346634	+	0.938001i	$0.387325\pi$
$194$		−	194.438i		−	1.00226i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	14.3392	−	14.3392i	0.0727881	−	0.0727881i	−0.669776	−	0.742564i	$-0.733610\pi$
$197$	14.3392	−	14.3392i	0.0727881	−	0.0727881i	0.742564	+	0.669776i	$0.233610\pi$
$198$	42.2651	+	42.2651i	0.213460	+	0.213460i
$199$			282.601i			1.42011i	0.704148	+	0.710053i	$0.251329\pi$
$199$			282.601i			1.42011i	−0.704148	+	0.710053i	$0.748671\pi$
$200$		0			0
$201$	−176.864			−0.879922
$202$	−26.1142	+	26.1142i	−0.129278	+	0.129278i
$203$	−20.9854	−	20.9854i	−0.103376	−	0.103376i
$204$		−	46.7611i		−	0.229221i
$205$		0			0
$206$	105.911			0.514129
$207$	1.27048	−	1.27048i	0.00613759	−	0.00613759i
$208$	−24.1283	−	24.1283i	−0.116001	−	0.116001i
$209$		−	305.468i		−	1.46157i
$210$		0			0
$211$	208.591			0.988584			0.494292	−	0.869296i	$-0.335427\pi$
$211$	208.591			0.988584			0.494292	+	0.869296i	$0.335427\pi$
$212$	37.2546	−	37.2546i	0.175729	−	0.175729i
$213$	−78.5111	−	78.5111i	−0.368597	−	0.368597i
$214$			163.503i			0.764033i
$215$		0			0
$216$	−14.6969			−0.0680414
$217$	−30.7831	+	30.7831i	−0.141858	+	0.141858i
$218$	−59.2958	−	59.2958i	−0.271999	−	0.271999i
$219$		−	126.003i		−	0.575358i
$220$		0			0
$221$	115.153			0.521054
$222$	116.756	−	116.756i	0.525927	−	0.525927i
$223$	205.186	+	205.186i	0.920118	+	0.920118i	0.997037	−	0.0769196i	$-0.0245085\pi$
$223$	205.186	+	205.186i	0.920118	+	0.920118i	−0.0769196	+	0.997037i	$0.524508\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	284.385			1.25834
$227$	−316.050	+	316.050i	−1.39229	+	1.39229i	−0.572120	+	0.820170i	$0.693879\pi$
$227$	−316.050	+	316.050i	−1.39229	+	1.39229i	−0.820170	+	0.572120i	$0.806121\pi$
$228$	53.1105	+	53.1105i	0.232941	+	0.232941i
$229$		−	123.494i		−	0.539274i	−0.962962	−	0.269637i	$-0.913096\pi$
$229$		−	123.494i		−	0.539274i	0.962962	−	0.269637i	$-0.0869036\pi$
$230$		0			0
$231$	−64.5610			−0.279485
$232$	22.4343	−	22.4343i	0.0966995	−	0.0966995i
$233$	−209.367	−	209.367i	−0.898572	−	0.898572i	0.0967375	−	0.995310i	$-0.469159\pi$
$233$	−209.367	−	209.367i	−0.898572	−	0.898572i	−0.995310	+	0.0967375i	$0.969159\pi$
$234$		−	36.1924i		−	0.154668i
$235$		0			0
$236$	26.9548			0.114215
$237$	−192.845	+	192.845i	−0.813693	+	0.813693i
$238$	35.7144	+	35.7144i	0.150060	+	0.150060i
$239$		−	147.491i		−	0.617117i	−0.951205	−	0.308559i	$-0.900153\pi$
$239$		−	147.491i		−	0.617117i	0.951205	−	0.308559i	$-0.0998466\pi$
$240$		0			0
$241$	−180.182			−0.747643			−0.373821	−	0.927501i	$-0.621953\pi$
$241$	−180.182			−0.747643			−0.373821	+	0.927501i	$0.621953\pi$
$242$	−77.4821	+	77.4821i	−0.320174	+	0.320174i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$			21.7496i			0.0891376i
$245$		0			0
$246$	107.870			0.438498
$247$	−130.789	+	130.789i	−0.529510	+	0.529510i
$248$	−32.9085	−	32.9085i	−0.132696	−	0.132696i
$249$			188.604i			0.757445i
$250$		0			0
$251$	25.2366			0.100544			0.0502720	−	0.998736i	$-0.483991\pi$
$251$	25.2366			0.100544			0.0502720	+	0.998736i	$0.483991\pi$
$252$	11.2250	−	11.2250i	0.0445435	−	0.0445435i
$253$	5.96634	+	5.96634i	0.0235824	+	0.0235824i
$254$			190.623i			0.750485i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−228.675	+	228.675i	−0.889784	+	0.889784i	−0.994502	−	0.104718i	$-0.966606\pi$
$257$	−228.675	+	228.675i	−0.889784	+	0.889784i	0.104718	+	0.994502i	$0.466606\pi$
$258$	−114.404	−	114.404i	−0.443426	−	0.443426i
$259$			178.347i			0.688600i
$260$		0			0
$261$	33.6514			0.128933
$262$	191.866	−	191.866i	0.732313	−	0.732313i
$263$	17.1641	+	17.1641i	0.0652629	+	0.0652629i	0.738985	−	0.673722i	$-0.235305\pi$
$263$	17.1641	+	17.1641i	0.0652629	+	0.0652629i	−0.673722	+	0.738985i	$0.735305\pi$
$264$		−	69.0186i		−	0.261434i
$265$		0			0
$266$	−81.1277			−0.304991
$267$	−46.1622	+	46.1622i	−0.172892	+	0.172892i
$268$	144.409	+	144.409i	0.538840	+	0.538840i
$269$		−	503.847i		−	1.87304i	−0.350617	−	0.936519i	$-0.614028\pi$
$269$		−	503.847i		−	1.87304i	0.350617	−	0.936519i	$-0.385972\pi$
$270$		0			0
$271$	147.700			0.545019			0.272510	−	0.962153i	$-0.412146\pi$
$271$	147.700			0.545019			0.272510	+	0.962153i	$0.412146\pi$
$272$	−38.1803	+	38.1803i	−0.140369	+	0.140369i
$273$	27.6424	+	27.6424i	0.101254	+	0.101254i
$274$		−	269.404i		−	0.983228i
$275$		0			0
$276$	−2.07469			−0.00751699
$277$	−2.85013	+	2.85013i	−0.0102893	+	0.0102893i	−0.712233	−	0.701943i	$-0.752316\pi$
$277$	−2.85013	+	2.85013i	−0.0102893	+	0.0102893i	0.701943	+	0.712233i	$0.252316\pi$
$278$	49.6297	+	49.6297i	0.178524	+	0.178524i
$279$		−	49.3628i		−	0.176927i
$280$		0			0
$281$	384.657			1.36889			0.684443	−	0.729066i	$-0.260045\pi$
$281$	384.657			1.36889			0.684443	+	0.729066i	$0.260045\pi$
$282$	−49.8256	+	49.8256i	−0.176686	+	0.176686i
$283$	201.734	+	201.734i	0.712839	+	0.712839i	0.967128	−	0.254289i	$-0.0818414\pi$
$283$	201.734	+	201.734i	0.712839	+	0.712839i	−0.254289	+	0.967128i	$0.581841\pi$
$284$			128.208i			0.451437i
$285$		0			0
$286$	169.964			0.594279
$287$	−82.3874	+	82.3874i	−0.287064	+	0.287064i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$			106.784i			0.369493i
$290$		0			0
$291$	−238.137			−0.818339
$292$	−102.881	+	102.881i	−0.352334	+	0.352334i
$293$	366.878	+	366.878i	1.25214	+	1.25214i	0.954758	+	0.297384i	$0.0961140\pi$
$293$	366.878	+	366.878i	1.25214	+	1.25214i	0.297384	+	0.954758i	$0.403886\pi$
$294$			17.1464i			0.0583212i
$295$		0			0
$296$	−190.661			−0.644126
$297$	51.7640	−	51.7640i	0.174289	−	0.174289i
$298$	−137.142	−	137.142i	−0.460208	−	0.460208i
$299$		−	5.10909i		−	0.0170872i
$300$		0			0
$301$	174.755			0.580581
$302$	197.792	−	197.792i	0.654941	−	0.654941i
$303$	31.9833	+	31.9833i	0.105555	+	0.105555i
$304$		−	86.7292i		−	0.285293i
$305$		0			0
$306$	−57.2704			−0.187158
$307$	412.785	−	412.785i	1.34458	−	1.34458i	0.453136	−	0.891442i	$-0.350305\pi$
$307$	412.785	−	412.785i	1.34458	−	1.34458i	0.891442	−	0.453136i	$-0.149695\pi$
$308$	52.7138	+	52.7138i	0.171149	+	0.171149i
$309$		−	129.713i		−	0.419785i
$310$		0			0
$311$	512.668			1.64845			0.824225	−	0.566263i	$-0.191611\pi$
$311$	512.668			1.64845			0.824225	+	0.566263i	$0.191611\pi$
$312$	−29.5510	+	29.5510i	−0.0947146	+	0.0947146i
$313$	101.469	+	101.469i	0.324182	+	0.324182i	0.850369	−	0.526187i	$-0.176379\pi$
$313$	101.469	+	101.469i	0.324182	+	0.324182i	−0.526187	+	0.850369i	$0.676379\pi$
$314$			359.806i			1.14588i
$315$		0			0
$316$	314.915			0.996566
$317$	202.617	−	202.617i	0.639169	−	0.639169i	−0.311182	−	0.950350i	$-0.600725\pi$
$317$	202.617	−	202.617i	0.639169	−	0.639169i	0.950350	+	0.311182i	$0.100725\pi$
$318$	−45.6274	−	45.6274i	−0.143482	−	0.143482i
$319$			158.031i			0.495396i
$320$		0			0
$321$	200.250			0.623830
$322$	1.58457	−	1.58457i	0.00492102	−	0.00492102i
$323$	206.959	+	206.959i	0.640739	+	0.640739i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−38.9233			−0.119397
$327$	−72.6223	+	72.6223i	−0.222086	+	0.222086i
$328$	−88.0758	−	88.0758i	−0.268524	−	0.268524i
$329$		−	76.1098i		−	0.231337i
$330$		0			0
$331$	65.9564			0.199264			0.0996321	−	0.995024i	$-0.468233\pi$
$331$	65.9564			0.199264			0.0996321	+	0.995024i	$0.468233\pi$
$332$	153.994	−	153.994i	0.463838	−	0.463838i
$333$	−142.996	−	142.996i	−0.429417	−	0.429417i
$334$			156.605i			0.468876i
$335$		0			0
$336$	−18.3303			−0.0545545
$337$	360.772	−	360.772i	1.07054	−	1.07054i	0.0732257	−	0.997315i	$-0.476671\pi$
$337$	360.772	−	360.772i	1.07054	−	1.07054i	0.997315	−	0.0732257i	$-0.0233294\pi$
$338$	96.2284	+	96.2284i	0.284699	+	0.284699i
$339$		−	348.300i		−	1.02743i
$340$		0			0
$341$	231.814			0.679805
$342$	65.0469	−	65.0469i	0.190196	−	0.190196i
$343$	−13.0958	−	13.0958i	−0.0381802	−	0.0381802i
$344$			186.821i			0.543084i
$345$		0			0
$346$	133.904			0.387007
$347$	195.218	−	195.218i	0.562588	−	0.562588i	−0.367454	−	0.930042i	$-0.619770\pi$
$347$	195.218	−	195.218i	0.562588	−	0.562588i	0.930042	+	0.367454i	$0.119770\pi$
$348$	−27.4763	−	27.4763i	−0.0789548	−	0.0789548i
$349$		−	204.957i		−	0.587270i	−0.955918	−	0.293635i	$-0.905135\pi$
$349$		−	204.957i		−	0.587270i	0.955918	−	0.293635i	$-0.0948650\pi$
$350$		0			0
$351$	−44.3264			−0.126286
$352$	−56.3535	+	56.3535i	−0.160095	+	0.160095i
$353$	233.494	+	233.494i	0.661457	+	0.661457i	0.955723	−	0.294267i	$-0.0950754\pi$
$353$	233.494	+	233.494i	0.661457	+	0.661457i	−0.294267	+	0.955723i	$0.595075\pi$
$354$		−	33.0127i		−	0.0932563i
$355$		0			0
$356$	75.3825			0.211749
$357$	43.7410	−	43.7410i	0.122524	−	0.122524i
$358$	66.4948	+	66.4948i	0.185740	+	0.185740i
$359$			263.565i			0.734164i	0.930189	+	0.367082i	$0.119643\pi$
$359$			263.565i			0.734164i	−0.930189	+	0.367082i	$0.880357\pi$
$360$		0			0
$361$	−109.122			−0.302276
$362$	33.5180	−	33.5180i	0.0925913	−	0.0925913i
$363$	94.8958	+	94.8958i	0.261421	+	0.261421i
$364$		−	45.1398i		−	0.124011i
$365$		0			0
$366$	26.6377			0.0727805
$367$	−22.0009	+	22.0009i	−0.0599481	+	0.0599481i	−0.736445	−	0.676497i	$-0.763497\pi$
$367$	−22.0009	+	22.0009i	−0.0599481	+	0.0599481i	0.676497	+	0.736445i	$0.263497\pi$
$368$	1.69398	+	1.69398i	0.00460320	+	0.00460320i
$369$		−	132.114i		−	0.358032i
$370$		0			0
$371$	69.6970			0.187862
$372$	−40.3045	+	40.3045i	−0.108346	+	0.108346i
$373$	170.973	+	170.973i	0.458373	+	0.458373i	0.898121	−	0.439748i	$-0.144932\pi$
$373$	170.973	+	170.973i	0.458373	+	0.458373i	−0.439748	+	0.898121i	$0.644932\pi$
$374$		−	268.949i		−	0.719114i
$375$		0			0
$376$	81.3648			0.216396
$377$	67.6625	−	67.6625i	0.179476	−	0.179476i
$378$	−13.7477	−	13.7477i	−0.0363696	−	0.0363696i
$379$			272.520i			0.719050i	0.933135	+	0.359525i	$0.117061\pi$
$379$			272.520i			0.719050i	−0.933135	+	0.359525i	$0.882939\pi$
$380$		0			0
$381$	233.465			0.612769
$382$	209.877	−	209.877i	0.549415	−	0.549415i
$383$	283.977	+	283.977i	0.741454	+	0.741454i	0.972858	−	0.231403i	$-0.0743317\pi$
$383$	283.977	+	283.977i	0.741454	+	0.741454i	−0.231403	+	0.972858i	$0.574332\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−495.869			−1.28463
$387$	−140.116	+	140.116i	−0.362056	+	0.362056i
$388$	194.438	+	194.438i	0.501128	+	0.501128i
$389$			12.8522i			0.0330392i	0.999864	+	0.0165196i	$0.00525859\pi$
$389$			12.8522i			0.0330392i	−0.999864	+	0.0165196i	$0.994741\pi$
$390$		0			0
$391$	−8.08455			−0.0206766
$392$	14.0000	−	14.0000i	0.0357143	−	0.0357143i
$393$	−234.987	−	234.987i	−0.597931	−	0.597931i
$394$			28.6785i			0.0727881i
$395$		0			0
$396$	−84.5302			−0.213460
$397$	242.868	−	242.868i	0.611757	−	0.611757i	−0.331647	−	0.943404i	$-0.607604\pi$
$397$	242.868	−	242.868i	0.611757	−	0.611757i	0.943404	+	0.331647i	$0.107604\pi$
$398$	−282.601	−	282.601i	−0.710053	−	0.710053i
$399$			99.3607i			0.249024i
$400$		0			0
$401$	−523.505			−1.30550			−0.652749	−	0.757574i	$-0.726385\pi$
$401$	−523.505			−1.30550			−0.652749	+	0.757574i	$0.726385\pi$
$402$	176.864	−	176.864i	0.439961	−	0.439961i
$403$	−99.2531	−	99.2531i	−0.246286	−	0.246286i
$404$		−	52.2284i		−	0.129278i
$405$		0			0
$406$	41.9707			0.103376
$407$	671.527	−	671.527i	1.64994	−	1.64994i
$408$	46.7611	+	46.7611i	0.114610	+	0.114610i
$409$			39.5511i			0.0967019i	0.998830	+	0.0483509i	$0.0153966\pi$
$409$			39.5511i			0.0967019i	−0.998830	+	0.0483509i	$0.984603\pi$
$410$		0			0
$411$	−329.952			−0.802802
$412$	−105.911	+	105.911i	−0.257064	+	0.257064i
$413$	25.2139	+	25.2139i	0.0610506	+	0.0610506i
$414$			2.54096i			0.00613759i
$415$		0			0
$416$	48.2565			0.116001
$417$	60.7838	−	60.7838i	0.145764	−	0.145764i
$418$	305.468	+	305.468i	0.730785	+	0.730785i
$419$			171.715i			0.409822i	0.978781	+	0.204911i	$0.0656905\pi$
$419$			171.715i			0.409822i	−0.978781	+	0.204911i	$0.934310\pi$
$420$		0			0
$421$	361.127			0.857784			0.428892	−	0.903356i	$-0.358904\pi$
$421$	361.127			0.857784			0.428892	+	0.903356i	$0.358904\pi$
$422$	−208.591	+	208.591i	−0.494292	+	0.494292i
$423$	61.0236	+	61.0236i	0.144264	+	0.144264i
$424$			74.5092i			0.175729i
$425$		0			0
$426$	157.022			0.368597
$427$	−20.3449	+	20.3449i	−0.0476460	+	0.0476460i
$428$	−163.503	−	163.503i	−0.382017	−	0.382017i
$429$		−	208.162i		−	0.485227i
$430$		0			0
$431$	323.054			0.749545			0.374772	−	0.927117i	$-0.377721\pi$
$431$	323.054			0.749545			0.374772	+	0.927117i	$0.377721\pi$
$432$	14.6969	−	14.6969i	0.0340207	−	0.0340207i
$433$	−76.7446	−	76.7446i	−0.177239	−	0.177239i	0.612912	−	0.790151i	$-0.289998\pi$
$433$	−76.7446	−	76.7446i	−0.177239	−	0.177239i	−0.790151	+	0.612912i	$0.789998\pi$
$434$		−	61.5662i		−	0.141858i
$435$		0			0
$436$	118.592			0.271999
$437$	9.18232	−	9.18232i	0.0210122	−	0.0210122i
$438$	126.003	+	126.003i	0.287679	+	0.287679i
$439$			864.627i			1.96954i	0.173872	+	0.984768i	$0.444372\pi$
$439$			864.627i			1.96954i	−0.173872	+	0.984768i	$0.555628\pi$
$440$		0			0
$441$	21.0000			0.0476190
$442$	−115.153	+	115.153i	−0.260527	+	0.260527i
$443$	326.831	+	326.831i	0.737768	+	0.737768i	0.972146	−	0.234377i	$-0.0753051\pi$
$443$	326.831	+	326.831i	0.737768	+	0.737768i	−0.234377	+	0.972146i	$0.575305\pi$
$444$			233.511i			0.525927i
$445$		0			0
$446$	−410.372			−0.920118
$447$	−167.964	+	167.964i	−0.375758	+	0.375758i
$448$	14.9666	+	14.9666i	0.0334077	+	0.0334077i
$449$			331.011i			0.737217i	0.929585	+	0.368609i	$0.120166\pi$
$449$			331.011i			0.737217i	−0.929585	+	0.368609i	$0.879834\pi$
$450$		0			0
$451$	620.422			1.37566
$452$	−284.385	+	284.385i	−0.629171	+	0.629171i
$453$	−242.245	−	242.245i	−0.534757	−	0.534757i
$454$		−	632.100i		−	1.39229i
$455$		0			0
$456$	−106.221			−0.232941
$457$	−485.728	+	485.728i	−1.06286	+	1.06286i	−0.0649742	+	0.997887i	$0.520696\pi$
$457$	−485.728	+	485.728i	−1.06286	+	1.06286i	−0.997887	+	0.0649742i	$0.979304\pi$
$458$	123.494	+	123.494i	0.269637	+	0.269637i
$459$			70.1416i			0.152814i
$460$		0			0
$461$	−560.524			−1.21589			−0.607944	−	0.793980i	$-0.708005\pi$
$461$	−560.524			−1.21589			−0.607944	+	0.793980i	$0.708005\pi$
$462$	64.5610	−	64.5610i	0.139742	−	0.139742i
$463$	−279.103	−	279.103i	−0.602814	−	0.602814i	0.338245	−	0.941058i	$-0.390167\pi$
$463$	−279.103	−	279.103i	−0.602814	−	0.602814i	−0.941058	+	0.338245i	$0.890167\pi$
$464$			44.8686i			0.0966995i
$465$		0			0
$466$	418.735			0.898572
$467$	−201.253	+	201.253i	−0.430948	+	0.430948i	−0.888951	−	0.458003i	$-0.848565\pi$
$467$	−201.253	+	201.253i	−0.430948	+	0.430948i	0.458003	+	0.888951i	$0.348565\pi$
$468$	36.1924	+	36.1924i	0.0773342	+	0.0773342i
$469$			270.165i			0.576044i
$470$		0			0
$471$	440.671			0.935607
$472$	−26.9548	+	26.9548i	−0.0571076	+	0.0571076i
$473$	−658.000	−	658.000i	−1.39112	−	1.39112i
$474$		−	385.690i		−	0.813693i
$475$		0			0
$476$	−71.4287			−0.150060
$477$	−55.8819	+	55.8819i	−0.117153	+	0.117153i
$478$	147.491	+	147.491i	0.308559	+	0.308559i
$479$		−	705.419i		−	1.47269i	−0.676606	−	0.736346i	$-0.736550\pi$
$479$		−	705.419i		−	1.47269i	0.676606	−	0.736346i	$-0.263450\pi$
$480$		0			0
$481$	−575.041			−1.19551
$482$	180.182	−	180.182i	0.373821	−	0.373821i
$483$	−1.94069	−	1.94069i	−0.00401800	−	0.00401800i
$484$		−	154.964i		−	0.320174i
$485$		0			0
$486$	22.0454			0.0453609
$487$	457.935	−	457.935i	0.940317	−	0.940317i	−0.0579991	−	0.998317i	$-0.518472\pi$
$487$	457.935	−	457.935i	0.940317	−	0.940317i	0.998317	+	0.0579991i	$0.0184721\pi$
$488$	−21.7496	−	21.7496i	−0.0445688	−	0.0445688i
$489$			47.6711i			0.0974870i
$490$		0			0
$491$	714.606			1.45541			0.727704	−	0.685891i	$-0.240587\pi$
$491$	714.606			1.45541			0.727704	+	0.685891i	$0.240587\pi$
$492$	−107.870	+	107.870i	−0.219249	+	0.219249i
$493$	−107.068	−	107.068i	−0.217177	−	0.217177i
$494$		−	261.578i		−	0.529510i
$495$		0			0
$496$	65.8170			0.132696
$497$	−119.928	+	119.928i	−0.241303	+	0.241303i
$498$	−188.604	−	188.604i	−0.378722	−	0.378722i
$499$		−	746.370i		−	1.49573i	−0.663850	−	0.747866i	$-0.731078\pi$
$499$		−	746.370i		−	1.49573i	0.663850	−	0.747866i	$-0.268922\pi$
$500$		0			0
$501$	191.801			0.382836
$502$	−25.2366	+	25.2366i	−0.0502720	+	0.0502720i
$503$	−10.5315	−	10.5315i	−0.0209375	−	0.0209375i	0.696561	−	0.717498i	$-0.254713\pi$
$503$	−10.5315	−	10.5315i	−0.0209375	−	0.0209375i	−0.717498	+	0.696561i	$0.754713\pi$
$504$			22.4499i			0.0445435i
$505$		0			0
$506$	−11.9327			−0.0235824
$507$	117.855	−	117.855i	0.232456	−	0.232456i
$508$	−190.623	−	190.623i	−0.375243	−	0.375243i
$509$		−	137.581i		−	0.270296i	−0.990825	−	0.135148i	$-0.956849\pi$
$509$		−	137.581i		−	0.270296i	0.990825	−	0.135148i	$-0.0431510\pi$
$510$		0			0
$511$	−192.473			−0.376660
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−79.6658	−	79.6658i	−0.155294	−	0.155294i
$514$		−	457.349i		−	0.889784i
$515$		0			0
$516$	228.808			0.443426
$517$	−286.574	+	286.574i	−0.554302	+	0.554302i
$518$	−178.347	−	178.347i	−0.344300	−	0.344300i
$519$		−	163.999i		−	0.315990i
$520$		0			0
$521$	397.521			0.762995			0.381498	−	0.924370i	$-0.375408\pi$
$521$	397.521			0.762995			0.381498	+	0.924370i	$0.375408\pi$
$522$	−33.6514	+	33.6514i	−0.0644663	+	0.0644663i
$523$	−59.4921	−	59.4921i	−0.113752	−	0.113752i	0.647940	−	0.761692i	$-0.275631\pi$
$523$	−59.4921	−	59.4921i	−0.113752	−	0.113752i	−0.761692	+	0.647940i	$0.775631\pi$
$524$			383.732i			0.732313i
$525$		0			0
$526$	−34.3283			−0.0652629
$527$	−157.057	+	157.057i	−0.298021	+	0.298021i
$528$	69.0186	+	69.0186i	0.130717	+	0.130717i
$529$		−	528.641i		−	0.999322i
$530$		0			0
$531$	−40.4322			−0.0761434
$532$	81.1277	−	81.1277i	0.152496	−	0.152496i
$533$	−265.640	−	265.640i	−0.498386	−	0.498386i
$534$		−	92.3243i		−	0.172892i
$535$		0			0
$536$	−288.818			−0.538840
$537$	81.4392	−	81.4392i	0.151656	−	0.151656i
$538$	503.847	+	503.847i	0.936519	+	0.936519i
$539$			98.6186i			0.182966i
$540$		0			0
$541$	−964.790			−1.78335			−0.891673	−	0.452680i	$-0.850468\pi$
$541$	−964.790			−1.78335			−0.891673	+	0.452680i	$0.850468\pi$
$542$	−147.700	+	147.700i	−0.272510	+	0.272510i
$543$	−41.0510	−	41.0510i	−0.0756004	−	0.0756004i
$544$		−	76.3605i		−	0.140369i
$545$		0			0
$546$	−55.2848			−0.101254
$547$	397.442	−	397.442i	0.726585	−	0.726585i	−0.243353	−	0.969938i	$-0.578247\pi$
$547$	397.442	−	397.442i	0.726585	−	0.726585i	0.969938	+	0.243353i	$0.0782474\pi$
$548$	269.404	+	269.404i	0.491614	+	0.491614i
$549$		−	32.6244i		−	0.0594251i
$550$		0			0
$551$	243.213			0.441404
$552$	2.07469	−	2.07469i	0.00375849	−	0.00375849i
$553$	294.576	+	294.576i	0.532687	+	0.532687i
$554$		−	5.70025i		−	0.0102893i
$555$		0			0
$556$	−99.2595			−0.178524
$557$	−236.896	+	236.896i	−0.425307	+	0.425307i	−0.887026	−	0.461719i	$-0.847233\pi$
$557$	−236.896	+	236.896i	−0.425307	+	0.425307i	0.461719	+	0.887026i	$0.347233\pi$
$558$	49.3628	+	49.3628i	0.0884637	+	0.0884637i
$559$			563.458i			1.00797i
$560$		0			0
$561$	−329.394			−0.587154
$562$	−384.657	+	384.657i	−0.684443	+	0.684443i
$563$	113.926	+	113.926i	0.202355	+	0.202355i	0.801008	−	0.598653i	$-0.204297\pi$
$563$	113.926	+	113.926i	0.202355	+	0.202355i	−0.598653	+	0.801008i	$0.704297\pi$
$564$		−	99.6511i		−	0.176686i
$565$		0			0
$566$	−403.467			−0.712839
$567$	−16.8375	+	16.8375i	−0.0296957	+	0.0296957i
$568$	−128.208	−	128.208i	−0.225718	−	0.225718i
$569$		−	932.914i		−	1.63957i	−0.572673	−	0.819784i	$-0.694093\pi$
$569$		−	932.914i		−	1.63957i	0.572673	−	0.819784i	$-0.305907\pi$
$570$		0			0
$571$	384.804			0.673912			0.336956	−	0.941520i	$-0.390603\pi$
$571$	384.804			0.673912			0.336956	+	0.941520i	$0.390603\pi$
$572$	−169.964	+	169.964i	−0.297140	+	0.297140i
$573$	−257.045	−	257.045i	−0.448596	−	0.448596i
$574$		−	164.775i		−	0.287064i
$575$		0			0
$576$	−24.0000			−0.0416667
$577$	207.248	−	207.248i	0.359182	−	0.359182i	−0.504329	−	0.863512i	$-0.668260\pi$
$577$	207.248	−	207.248i	0.359182	−	0.359182i	0.863512	+	0.504329i	$0.168260\pi$
$578$	−106.784	−	106.784i	−0.184747	−	0.184747i
$579$			607.313i			1.04890i
$580$		0			0
$581$	288.097			0.495864
$582$	238.137	−	238.137i	0.409170	−	0.409170i
$583$	−262.428	−	262.428i	−0.450134	−	0.450134i
$584$		−	205.763i		−	0.352334i
$585$		0			0
$586$	−733.755			−1.25214
$587$	−517.152	+	517.152i	−0.881009	+	0.881009i	−0.993637	−	0.112628i	$-0.964073\pi$
$587$	−517.152	+	517.152i	−0.881009	+	0.881009i	0.112628	+	0.993637i	$0.464073\pi$
$588$	−17.1464	−	17.1464i	−0.0291606	−	0.0291606i
$589$		−	356.766i		−	0.605715i
$590$		0			0
$591$	35.1238			0.0594312
$592$	190.661	−	190.661i	0.322063	−	0.322063i
$593$	455.580	+	455.580i	0.768264	+	0.768264i	0.977801	−	0.209537i	$-0.0671957\pi$
$593$	455.580	+	455.580i	0.768264	+	0.768264i	−0.209537	+	0.977801i	$0.567196\pi$
$594$			103.528i			0.174289i
$595$		0			0
$596$	274.284			0.460208
$597$	−346.114	+	346.114i	−0.579756	+	0.579756i
$598$	5.10909	+	5.10909i	0.00854362	+	0.00854362i
$599$			812.606i			1.35660i	0.734783	+	0.678302i	$0.237284\pi$
$599$			812.606i			1.35660i	−0.734783	+	0.678302i	$0.762716\pi$
$600$		0			0
$601$	−315.588			−0.525105			−0.262552	−	0.964918i	$-0.584564\pi$
$601$	−315.588			−0.525105			−0.262552	+	0.964918i	$0.584564\pi$
$602$	−174.755	+	174.755i	−0.290291	+	0.290291i
$603$	−216.614	−	216.614i	−0.359227	−	0.359227i
$604$			395.584i			0.654941i
$605$		0			0
$606$	−63.9665			−0.105555
$607$	−523.720	+	523.720i	−0.862801	+	0.862801i	−0.991663	−	0.128862i	$-0.958868\pi$
$607$	−523.720	+	523.720i	−0.862801	+	0.862801i	0.128862	+	0.991663i	$0.458868\pi$
$608$	86.7292	+	86.7292i	0.142647	+	0.142647i
$609$		−	51.4034i		−	0.0844063i
$610$		0			0
$611$	245.399			0.401635
$612$	57.2704	−	57.2704i	0.0935791	−	0.0935791i
$613$	239.438	+	239.438i	0.390601	+	0.390601i	0.874901	−	0.484301i	$-0.160926\pi$
$613$	239.438	+	239.438i	0.390601	+	0.390601i	−0.484301	+	0.874901i	$0.660926\pi$
$614$			825.570i			1.34458i
$615$		0			0
$616$	−105.428			−0.171149
$617$	508.117	−	508.117i	0.823529	−	0.823529i	−0.163083	−	0.986612i	$-0.552144\pi$
$617$	508.117	−	508.117i	0.823529	−	0.823529i	0.986612	+	0.163083i	$0.0521439\pi$
$618$	129.713	+	129.713i	0.209892	+	0.209892i
$619$		−	237.357i		−	0.383453i	−0.981448	−	0.191727i	$-0.938591\pi$
$619$		−	237.357i		−	0.383453i	0.981448	−	0.191727i	$-0.0614087\pi$
$620$		0			0
$621$	3.11203			0.00501132
$622$	−512.668	+	512.668i	−0.824225	+	0.824225i
$623$	70.5139	+	70.5139i	0.113184	+	0.113184i
$624$		−	59.1019i		−	0.0947146i
$625$		0			0
$626$	−202.938			−0.324182
$627$	374.120	−	374.120i	0.596683	−	0.596683i
$628$	−359.806	−	359.806i	−0.572940	−	0.572940i
$629$			909.937i			1.44664i
$630$		0			0
$631$	717.680			1.13737			0.568685	−	0.822556i	$-0.307453\pi$
$631$	717.680			1.13737			0.568685	+	0.822556i	$0.307453\pi$
$632$	−314.915	+	314.915i	−0.498283	+	0.498283i
$633$	255.471	+	255.471i	0.403588	+	0.403588i
$634$			405.233i			0.639169i
$635$		0			0
$636$	91.2547			0.143482
$637$	42.2245	−	42.2245i	0.0662864	−	0.0662864i
$638$	−158.031	−	158.031i	−0.247698	−	0.247698i
$639$		−	192.312i		−	0.300958i
$640$		0			0
$641$	−894.582			−1.39560			−0.697802	−	0.716291i	$-0.745838\pi$
$641$	−894.582			−1.39560			−0.697802	+	0.716291i	$0.745838\pi$
$642$	−200.250	+	200.250i	−0.311915	+	0.311915i
$643$	−27.5752	−	27.5752i	−0.0428853	−	0.0428853i	0.685339	−	0.728224i	$-0.259654\pi$
$643$	−27.5752	−	27.5752i	−0.0428853	−	0.0428853i	−0.728224	+	0.685339i	$0.759654\pi$
$644$			3.16914i			0.00492102i
$645$		0			0
$646$	−413.918			−0.640739
$647$	−76.5361	+	76.5361i	−0.118294	+	0.118294i	−0.763776	−	0.645482i	$-0.776657\pi$
$647$	−76.5361	+	76.5361i	−0.118294	+	0.118294i	0.645482	+	0.763776i	$0.276657\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$		−	189.874i		−	0.292565i
$650$		0			0
$651$	−75.4029			−0.115826
$652$	38.9233	−	38.9233i	0.0596983	−	0.0596983i
$653$	−873.233	−	873.233i	−1.33726	−	1.33726i	−0.898700	−	0.438564i	$-0.855487\pi$
$653$	−873.233	−	873.233i	−1.33726	−	1.33726i	−0.438564	−	0.898700i	$-0.644513\pi$
$654$		−	145.245i		−	0.222086i
$655$		0			0
$656$	176.152			0.268524
$657$	154.322	−	154.322i	0.234889	−	0.234889i
$658$	76.1098	+	76.1098i	0.115668	+	0.115668i
$659$		−	62.2133i		−	0.0944055i	−0.998885	−	0.0472028i	$-0.984969\pi$
$659$		−	62.2133i		−	0.0944055i	0.998885	−	0.0472028i	$-0.0150307\pi$
$660$		0			0
$661$	−1086.21			−1.64328			−0.821639	−	0.570008i	$-0.806940\pi$
$661$	−1086.21			−1.64328			−0.821639	+	0.570008i	$0.806940\pi$
$662$	−65.9564	+	65.9564i	−0.0996321	+	0.0996321i
$663$	141.033	+	141.033i	0.212719	+	0.212719i
$664$			307.989i			0.463838i
$665$		0			0
$666$	285.992			0.429417
$667$	−4.75039	+	4.75039i	−0.00712203	+	0.00712203i
$668$	−156.605	−	156.605i	−0.234438	−	0.234438i
$669$			502.602i			0.751273i
$670$		0			0
$671$	153.208			0.228328
$672$	18.3303	−	18.3303i	0.0272772	−	0.0272772i
$673$	−663.103	−	663.103i	−0.985294	−	0.985294i	0.0145998	−	0.999893i	$-0.495353\pi$
$673$	−663.103	−	663.103i	−0.985294	−	0.985294i	−0.999893	+	0.0145998i	$0.995353\pi$
$674$			721.545i			1.07054i
$675$		0			0
$676$	−192.457			−0.284699
$677$	−363.300	+	363.300i	−0.536632	+	0.536632i	−0.922538	−	0.385906i	$-0.873889\pi$
$677$	−363.300	+	363.300i	−0.536632	+	0.536632i	0.385906	+	0.922538i	$0.373889\pi$
$678$	348.300	+	348.300i	0.513716	+	0.513716i
$679$			363.760i			0.535729i
$680$		0			0
$681$	−774.161			−1.13680
$682$	−231.814	+	231.814i	−0.339903	+	0.339903i
$683$	−133.225	−	133.225i	−0.195058	−	0.195058i	0.602819	−	0.797878i	$-0.294044\pi$
$683$	−133.225	−	133.225i	−0.195058	−	0.195058i	−0.797878	+	0.602819i	$0.794044\pi$
$684$			130.094i			0.190196i
$685$		0			0
$686$	26.1916			0.0381802
$687$	151.248	−	151.248i	0.220157	−	0.220157i
$688$	−186.821	−	186.821i	−0.271542	−	0.271542i
$689$			224.722i			0.326157i
$690$		0			0
$691$	−1151.29			−1.66612			−0.833060	−	0.553183i	$-0.813413\pi$
$691$	−1151.29			−1.66612			−0.833060	+	0.553183i	$0.813413\pi$
$692$	−133.904	+	133.904i	−0.193503	+	0.193503i
$693$	−79.0708	−	79.0708i	−0.114099	−	0.114099i
$694$			390.436i			0.562588i
$695$		0			0
$696$	54.9526			0.0789548
$697$	−420.345	+	420.345i	−0.603077	+	0.603077i
$698$	204.957	+	204.957i	0.293635	+	0.293635i
$699$		−	512.843i		−	0.733681i
$700$		0			0
$701$	181.482			0.258890			0.129445	−	0.991587i	$-0.458680\pi$
$701$	181.482			0.258890			0.129445	+	0.991587i	$0.458680\pi$
$702$	44.3264	−	44.3264i	0.0631431	−	0.0631431i
$703$	−1033.49	−	1033.49i	−1.47012	−	1.47012i
$704$		−	112.707i		−	0.160095i
$705$		0			0
$706$	−466.988			−0.661457
$707$	48.8552	−	48.8552i	0.0691022	−	0.0691022i
$708$	33.0127	+	33.0127i	0.0466281	+	0.0466281i
$709$			436.784i			0.616057i	0.951377	+	0.308029i	$0.0996692\pi$
$709$			436.784i			0.616057i	−0.951377	+	0.308029i	$0.900331\pi$
$710$		0			0
$711$	−472.372			−0.664377
$712$	−75.3825	+	75.3825i	−0.105874	+	0.105874i
$713$	6.96828	+	6.96828i	0.00977318	+	0.00977318i
$714$			87.4820i			0.122524i
$715$		0			0
$716$	−132.990			−0.185740
$717$	180.639	−	180.639i	0.251937	−	0.251937i
$718$	−263.565	−	263.565i	−0.367082	−	0.367082i
$719$			553.810i			0.770250i	0.922864	+	0.385125i	$0.125842\pi$
$719$			553.810i			0.770250i	−0.922864	+	0.385125i	$0.874158\pi$
$720$		0			0
$721$	−198.141			−0.274813
$722$	109.122	−	109.122i	0.151138	−	0.151138i
$723$	−220.677	−	220.677i	−0.305224	−	0.305224i
$724$			67.0361i			0.0925913i
$725$		0			0
$726$	−189.792			−0.261421
$727$	377.156	−	377.156i	0.518783	−	0.518783i	−0.398420	−	0.917203i	$-0.630441\pi$
$727$	377.156	−	377.156i	0.518783	−	0.518783i	0.917203	+	0.398420i	$0.130441\pi$
$728$	45.1398	+	45.1398i	0.0620053	+	0.0620053i
$729$		−	27.0000i		−	0.0370370i
$730$		0			0
$731$	891.609			1.21971
$732$	−26.6377	+	26.6377i	−0.0363903	+	0.0363903i
$733$	100.250	+	100.250i	0.136767	+	0.136767i	0.772176	−	0.635409i	$-0.219168\pi$
$733$	100.250	+	100.250i	0.136767	+	0.136767i	−0.635409	+	0.772176i	$0.719168\pi$
$734$		−	44.0019i		−	0.0599481i
$735$		0			0
$736$	−3.38795			−0.00460320
$737$	1017.24	−	1017.24i	1.38025	−	1.38025i
$738$	132.114	+	132.114i	0.179016	+	0.179016i
$739$		−	606.576i		−	0.820806i	−0.911904	−	0.410403i	$-0.865388\pi$
$739$		−	606.576i		−	0.820806i	0.911904	−	0.410403i	$-0.134612\pi$
$740$		0			0
$741$	−320.366			−0.432343
$742$	−69.6970	+	69.6970i	−0.0939312	+	0.0939312i
$743$	345.903	+	345.903i	0.465549	+	0.465549i	0.900469	−	0.434920i	$-0.143223\pi$
$743$	345.903	+	345.903i	0.465549	+	0.465549i	−0.434920	+	0.900469i	$0.643223\pi$
$744$		−	80.6091i		−	0.108346i
$745$		0			0
$746$	−341.946			−0.458373
$747$	−230.992	+	230.992i	−0.309226	+	0.309226i
$748$	268.949	+	268.949i	0.359557	+	0.359557i
$749$		−	305.886i		−	0.408393i
$750$		0			0
$751$	−203.256			−0.270647			−0.135324	−	0.990801i	$-0.543207\pi$
$751$	−203.256			−0.270647			−0.135324	+	0.990801i	$0.543207\pi$
$752$	−81.3648	+	81.3648i	−0.108198	+	0.108198i
$753$	30.9083	+	30.9083i	0.0410469	+	0.0410469i
$754$			135.325i			0.179476i
$755$		0			0
$756$	27.4955			0.0363696
$757$	6.94517	−	6.94517i	0.00917460	−	0.00917460i	−0.702505	−	0.711679i	$-0.747935\pi$
$757$	6.94517	−	6.94517i	0.00917460	−	0.00917460i	0.711679	+	0.702505i	$0.247935\pi$
$758$	−272.520	−	272.520i	−0.359525	−	0.359525i
$759$			14.6145i			0.0192549i
$760$		0			0
$761$	977.803			1.28489			0.642446	−	0.766331i	$-0.277920\pi$
$761$	977.803			1.28489			0.642446	+	0.766331i	$0.277920\pi$
$762$	−233.465	+	233.465i	−0.306384	+	0.306384i
$763$	110.932	+	110.932i	0.145390	+	0.145390i
$764$			419.753i			0.549415i
$765$		0			0
$766$	−567.954			−0.741454
$767$	−81.2965	+	81.2965i	−0.105993	+	0.105993i
$768$	19.5959	+	19.5959i	0.0255155	+	0.0255155i
$769$		−	821.202i		−	1.06788i	−0.845521	−	0.533942i	$-0.820710\pi$
$769$		−	821.202i		−	1.06788i	0.845521	−	0.533942i	$-0.179290\pi$
$770$		0			0
$771$	−560.136			−0.726506
$772$	495.869	−	495.869i	0.642317	−	0.642317i
$773$	−433.236	−	433.236i	−0.560460	−	0.560460i	0.368978	−	0.929438i	$-0.379708\pi$
$773$	−433.236	−	433.236i	−0.560460	−	0.560460i	−0.929438	+	0.368978i	$0.879708\pi$
$774$		−	280.231i		−	0.362056i
$775$		0			0
$776$	−388.876			−0.501128
$777$	−218.430	+	218.430i	−0.281120	+	0.281120i
$778$	−12.8522	−	12.8522i	−0.0165196	−	0.0165196i
$779$		−	954.843i		−	1.22573i
$780$		0			0
$781$	903.121			1.15636
$782$	8.08455	−	8.08455i	0.0103383	−	0.0103383i
$783$	41.2144	+	41.2144i	0.0526365	+	0.0526365i
$784$			28.0000i			0.0357143i
$785$		0			0
$786$	469.974			0.597931
$787$	−427.998	+	427.998i	−0.543835	+	0.543835i	−0.924651	−	0.380816i	$-0.875643\pi$
$787$	−427.998	+	427.998i	−0.543835	+	0.543835i	0.380816	+	0.924651i	$0.375643\pi$
$788$	−28.6785	−	28.6785i	−0.0363940	−	0.0363940i
$789$			42.0434i			0.0532869i
$790$		0			0
$791$	−532.036			−0.672612
$792$	84.5302	−	84.5302i	0.106730	−	0.106730i
$793$	−65.5974	−	65.5974i	−0.0827206	−	0.0827206i
$794$			485.735i			0.611757i
$795$		0			0
$796$	565.202			0.710053
$797$	−156.240	+	156.240i	−0.196035	+	0.196035i	−0.798298	−	0.602263i	$-0.794266\pi$
$797$	−156.240	+	156.240i	−0.196035	+	0.196035i	0.602263	+	0.798298i	$0.294266\pi$
$798$	−99.3607	−	99.3607i	−0.124512	−	0.124512i
$799$		−	388.316i		−	0.486003i
$800$		0			0
$801$	−113.074			−0.141166
$802$	523.505	−	523.505i	0.652749	−	0.652749i
$803$	724.715	+	724.715i	0.902510	+	0.902510i
$804$			353.729i			0.439961i
$805$		0			0
$806$	198.506			0.246286
$807$	617.084	−	617.084i	0.764665	−	0.764665i
$808$	52.2284	+	52.2284i	0.0646392	+	0.0646392i
$809$		−	475.750i		−	0.588072i	−0.955794	−	0.294036i	$-0.905002\pi$
$809$		−	475.750i		−	0.588072i	0.955794	−	0.294036i	$-0.0949985\pi$
$810$		0			0
$811$	321.958			0.396989			0.198494	−	0.980102i	$-0.436395\pi$
$811$	321.958			0.396989			0.198494	+	0.980102i	$0.436395\pi$
$812$	−41.9707	+	41.9707i	−0.0516881	+	0.0516881i
$813$	180.895	+	180.895i	0.222503	+	0.222503i
$814$			1343.05i			1.64994i
$815$		0			0
$816$	−93.5221			−0.114610
$817$	−1012.68	+	1012.68i	−1.23951	+	1.23951i
$818$	−39.5511	−	39.5511i	−0.0483509	−	0.0483509i
$819$			67.7098i			0.0826737i
$820$		0			0
$821$	−372.833			−0.454121			−0.227060	−	0.973881i	$-0.572911\pi$
$821$	−372.833			−0.454121			−0.227060	+	0.973881i	$0.572911\pi$
$822$	329.952	−	329.952i	0.401401	−	0.401401i
$823$	514.145	+	514.145i	0.624721	+	0.624721i	0.946735	−	0.322014i	$-0.104360\pi$
$823$	514.145	+	514.145i	0.624721	+	0.624721i	−0.322014	+	0.946735i	$0.604360\pi$
$824$		−	211.821i		−	0.257064i
$825$		0			0
$826$	−50.4278			−0.0610506
$827$	389.845	−	389.845i	0.471397	−	0.471397i	−0.430970	−	0.902366i	$-0.641828\pi$
$827$	389.845	−	389.845i	0.471397	−	0.471397i	0.902366	+	0.430970i	$0.141828\pi$
$828$	−2.54096	−	2.54096i	−0.00306880	−	0.00306880i
$829$			1442.33i			1.73984i	0.493194	+	0.869919i	$0.335829\pi$
$829$			1442.33i			1.73984i	−0.493194	+	0.869919i	$0.664171\pi$
$830$		0			0
$831$	−6.98135			−0.00840115
$832$	−48.2565	+	48.2565i	−0.0580006	+	0.0580006i
$833$	−66.8154	−	66.8154i	−0.0802106	−	0.0802106i
$834$			121.568i			0.145764i
$835$		0			0
$836$	−610.936			−0.730785
$837$	60.4568	−	60.4568i	0.0722303	−	0.0722303i
$838$	−171.715	−	171.715i	−0.204911	−	0.204911i
$839$			1101.83i			1.31326i	0.754212	+	0.656630i	$0.228019\pi$
$839$			1101.83i			1.31326i	−0.754212	+	0.656630i	$0.771981\pi$
$840$		0			0
$841$	715.176			0.850387
$842$	−361.127	+	361.127i	−0.428892	+	0.428892i
$843$	471.107	+	471.107i	0.558846	+	0.558846i
$844$		−	417.183i		−	0.494292i
$845$		0			0
$846$	−122.047			−0.144264
$847$	144.956	−	144.956i	0.171140	−	0.171140i
$848$	−74.5092	−	74.5092i	−0.0878646	−	0.0878646i
$849$			494.144i			0.582031i
$850$		0			0
$851$	40.3720			0.0474406
$852$	−157.022	+	157.022i	−0.184298	+	0.184298i
$853$	−842.879	−	842.879i	−0.988135	−	0.988135i	0.0117957	−	0.999930i	$-0.496245\pi$
$853$	−842.879	−	842.879i	−0.988135	−	0.988135i	−0.999930	+	0.0117957i	$0.996245\pi$
$854$		−	40.6897i		−	0.0476460i
$855$		0			0
$856$	327.006			0.382017
$857$	655.750	−	655.750i	0.765169	−	0.765169i	−0.212083	−	0.977252i	$-0.568025\pi$
$857$	655.750	−	655.750i	0.765169	−	0.765169i	0.977252	+	0.212083i	$0.0680246\pi$
$858$	208.162	+	208.162i	0.242614	+	0.242614i
$859$		−	800.197i		−	0.931545i	−0.884904	−	0.465773i	$-0.845777\pi$
$859$		−	800.197i		−	0.931545i	0.884904	−	0.465773i	$-0.154223\pi$
$860$		0			0
$861$	−201.807			−0.234387
$862$	−323.054	+	323.054i	−0.374772	+	0.374772i
$863$	112.663	+	112.663i	0.130549	+	0.130549i	0.769362	−	0.638813i	$-0.220574\pi$
$863$	112.663	+	112.663i	0.130549	+	0.130549i	−0.638813	+	0.769362i	$0.720574\pi$
$864$			29.3939i			0.0340207i
$865$		0			0
$866$	153.489			0.177239
$867$	−130.783	+	130.783i	−0.150845	+	0.150845i
$868$	61.5662	+	61.5662i	0.0709288	+	0.0709288i
$869$		−	2218.32i		−	2.55272i
$870$		0			0
$871$	−871.085			−1.00010
$872$	−118.592	+	118.592i	−0.136000	+	0.136000i
$873$	−291.657	−	291.657i	−0.334086	−	0.334086i
$874$			18.3646i			0.0210122i
$875$		0			0
$876$	−252.007			−0.287679
$877$	−9.31315	+	9.31315i	−0.0106193	+	0.0106193i	−0.712397	−	0.701777i	$-0.752390\pi$
$877$	−9.31315	+	9.31315i	−0.0106193	+	0.0106193i	0.701777	+	0.712397i	$0.252390\pi$
$878$	−864.627	−	864.627i	−0.984768	−	0.984768i
$879$			898.663i			1.02237i
$880$		0			0
$881$	−59.1359			−0.0671236			−0.0335618	−	0.999437i	$-0.510685\pi$
$881$	−59.1359			−0.0671236			−0.0335618	+	0.999437i	$0.510685\pi$
$882$	−21.0000	+	21.0000i	−0.0238095	+	0.0238095i
$883$	−77.6453	−	77.6453i	−0.0879335	−	0.0879335i	0.661772	−	0.749705i	$-0.269805\pi$
$883$	−77.6453	−	77.6453i	−0.0879335	−	0.0879335i	−0.749705	+	0.661772i	$0.769805\pi$
$884$		−	230.306i		−	0.260527i
$885$		0			0
$886$	−653.663			−0.737768
$887$	176.382	−	176.382i	0.198852	−	0.198852i	−0.600656	−	0.799508i	$-0.705094\pi$
$887$	176.382	−	176.382i	0.198852	−	0.198852i	0.799508	+	0.600656i	$0.205094\pi$
$888$	−233.511	−	233.511i	−0.262963	−	0.262963i
$889$		−	356.623i		−	0.401151i
$890$		0			0
$891$	126.795			0.142307
$892$	410.372	−	410.372i	0.460059	−	0.460059i
$893$	441.044	+	441.044i	0.493890	+	0.493890i
$894$		−	335.928i		−	0.375758i
$895$		0			0
$896$	−29.9333			−0.0334077
$897$	6.25733	−	6.25733i	0.00697584	−	0.00697584i
$898$	−331.011	−	331.011i	−0.368609	−	0.368609i
$899$			184.570i			0.205306i
$900$		0			0
$901$	355.597			0.394670
$902$	−620.422	+	620.422i	−0.687829	+	0.687829i
$903$	214.030	+	214.030i	0.237021	+	0.237021i
$904$		−	568.771i		−	0.629171i
$905$		0			0
$906$	484.490			0.534757
$907$	626.216	−	626.216i	0.690425	−	0.690425i	−0.271900	−	0.962326i	$-0.587652\pi$
$907$	626.216	−	626.216i	0.690425	−	0.690425i	0.962326	+	0.271900i	$0.0876520\pi$
$908$	632.100	+	632.100i	0.696145	+	0.696145i
$909$			78.3427i			0.0861855i
$910$		0			0
$911$	−969.279			−1.06397			−0.531986	−	0.846753i	$-0.678554\pi$
$911$	−969.279			−1.06397			−0.531986	+	0.846753i	$0.678554\pi$
$912$	106.221	−	106.221i	0.116471	−	0.116471i
$913$	−1084.76	−	1084.76i	−1.18813	−	1.18813i
$914$		−	971.455i		−	1.06286i
$915$		0			0
$916$	−246.987			−0.269637
$917$	−358.948	+	358.948i	−0.391438	+	0.391438i
$918$	−70.1416	−	70.1416i	−0.0764070	−	0.0764070i
$919$		−	581.291i		−	0.632526i	−0.948672	−	0.316263i	$-0.897572\pi$
$919$		−	581.291i		−	0.632526i	0.948672	−	0.316263i	$-0.102428\pi$
$920$		0			0
$921$	1011.11			1.09784
$922$	560.524	−	560.524i	0.607944	−	0.607944i
$923$	−386.680	−	386.680i	−0.418938	−	0.418938i
$924$			129.122i			0.139742i
$925$		0			0
$926$	558.205			0.602814
$927$	158.866	−	158.866i	0.171376	−	0.171376i
$928$	−44.8686	−	44.8686i	−0.0483498	−	0.0483498i
$929$			1578.20i			1.69882i	0.527736	+	0.849409i	$0.323041\pi$
$929$			1578.20i			1.69882i	−0.527736	+	0.849409i	$0.676959\pi$
$930$		0			0
$931$	151.776			0.163025
$932$	−418.735	+	418.735i	−0.449286	+	0.449286i
$933$	627.887	+	627.887i	0.672977	+	0.672977i
$934$		−	402.505i		−	0.430948i
$935$		0			0
$936$	−72.3848			−0.0773342
$937$	−448.839	+	448.839i	−0.479017	+	0.479017i	−0.904817	−	0.425800i	$-0.859993\pi$
$937$	−448.839	+	448.839i	−0.479017	+	0.479017i	0.425800	+	0.904817i	$0.359993\pi$
$938$	−270.165	−	270.165i	−0.288022	−	0.288022i
$939$			248.547i			0.264693i
$940$		0			0
$941$	−10.8693			−0.0115508			−0.00577540	−	0.999983i	$-0.501838\pi$
$941$	−10.8693			−0.0115508			−0.00577540	+	0.999983i	$0.501838\pi$
$942$	−440.671	+	440.671i	−0.467804	+	0.467804i
$943$	18.6498	+	18.6498i	0.0197771	+	0.0197771i
$944$		−	53.9096i		−	0.0571076i
$945$		0			0
$946$	1316.00			1.39112
$947$	223.851	−	223.851i	0.236379	−	0.236379i	−0.578970	−	0.815349i	$-0.696545\pi$
$947$	223.851	−	223.851i	0.236379	−	0.236379i	0.815349	+	0.578970i	$0.196545\pi$
$948$	385.690	+	385.690i	0.406846	+	0.406846i
$949$		−	620.587i		−	0.653938i
$950$		0			0
$951$	496.307			0.521879
$952$	71.4287	−	71.4287i	0.0750302	−	0.0750302i
$953$	−732.839	−	732.839i	−0.768981	−	0.768981i	0.208946	−	0.977927i	$-0.432997\pi$
$953$	−732.839	−	732.839i	−0.768981	−	0.768981i	−0.977927	+	0.208946i	$0.932997\pi$
$954$		−	111.764i		−	0.117153i
$955$		0			0
$956$	−294.982			−0.308559
$957$	−193.548	+	193.548i	−0.202244	+	0.202244i
$958$	705.419	+	705.419i	0.736346	+	0.736346i
$959$			504.009i			0.525557i
$960$		0			0
$961$	−690.258			−0.718270
$962$	575.041	−	575.041i	0.597755	−	0.597755i
$963$	245.255	+	245.255i	0.254678	+	0.254678i
$964$			360.364i			0.373821i
$965$		0			0
$966$	3.88139			0.00401800
$967$	334.532	−	334.532i	0.345948	−	0.345948i	−0.512650	−	0.858598i	$-0.671336\pi$
$967$	334.532	−	334.532i	0.345948	−	0.345948i	0.858598	+	0.512650i	$0.171336\pi$
$968$	154.964	+	154.964i	0.160087	+	0.160087i
$969$			506.944i			0.523162i
$970$		0			0
$971$	922.031			0.949569			0.474784	−	0.880102i	$-0.342526\pi$
$971$	922.031			0.949569			0.474784	+	0.880102i	$0.342526\pi$
$972$	−22.0454	+	22.0454i	−0.0226805	+	0.0226805i
$973$	−92.8487	−	92.8487i	−0.0954252	−	0.0954252i
$974$			915.869i			0.940317i
$975$		0			0
$976$	43.4991			0.0445688
$977$	−0.111963	+	0.111963i	−0.000114599	+	0.000114599i	−0.707164	−	0.707049i	$-0.750026\pi$
$977$	−0.111963	+	0.111963i	−0.000114599	+	0.000114599i	0.707049	+	0.707164i	$0.250026\pi$
$978$	−47.6711	−	47.6711i	−0.0487435	−	0.0487435i
$979$		−	531.008i		−	0.542399i
$980$		0			0
$981$	−177.887			−0.181333
$982$	−714.606	+	714.606i	−0.727704	+	0.727704i
$983$	631.195	+	631.195i	0.642111	+	0.642111i	0.951074	−	0.308963i	$-0.0999820\pi$
$983$	631.195	+	631.195i	0.642111	+	0.642111i	−0.308963	+	0.951074i	$0.599982\pi$
$984$		−	215.741i		−	0.219249i
$985$		0			0
$986$	214.137			0.217177
$987$	93.2151	−	93.2151i	0.0944428	−	0.0944428i
$988$	261.578	+	261.578i	0.264755	+	0.264755i
$989$		−	39.5588i		−	0.0399987i
$990$		0			0
$991$	784.199			0.791321			0.395661	−	0.918397i	$-0.370516\pi$
$991$	784.199			0.791321			0.395661	+	0.918397i	$0.370516\pi$
$992$	−65.8170	+	65.8170i	−0.0663478	+	0.0663478i
$993$	80.7798	+	80.7798i	0.0813492	+	0.0813492i
$994$		−	239.855i		−	0.241303i
$995$		0			0
$996$	377.208			0.378722
$997$	365.331	−	365.331i	0.366430	−	0.366430i	−0.499743	−	0.866174i	$-0.666572\pi$
$997$	365.331	−	365.331i	0.366430	−	0.366430i	0.866174	+	0.499743i	$0.166572\pi$
$998$	746.370	+	746.370i	0.747866	+	0.747866i
$999$		−	350.267i		−	0.350618i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.l.b.43.4		8
5.2	odd	4	inner	1050.3.l.b.757.4		8
5.3	odd	4		210.3.l.a.127.1	yes	8
5.4	even	2		210.3.l.a.43.1	✓	8
15.8	even	4		630.3.o.b.127.4		8
15.14	odd	2		630.3.o.b.253.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.1	✓	8	5.4	even	2
210.3.l.a.127.1	yes	8	5.3	odd	4
630.3.o.b.127.4		8	15.8	even	4
630.3.o.b.253.4		8	15.14	odd	2
1050.3.l.b.43.4		8	1.1	even	1	trivial
1050.3.l.b.757.4		8	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.22474 + 1.22474i) q^{3} -2.00000i q^{4} -2.44949 q^{6} +(1.87083 - 1.87083i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} -14.0884 q^{11} +(2.44949 - 2.44949i) q^{12} +(6.03207 + 6.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(9.54506 - 9.54506i) q^{17} +(-3.00000 - 3.00000i) q^{18} +21.6823i q^{19} +4.58258 q^{21} +(14.0884 - 14.0884i) q^{22} +(-0.423494 - 0.423494i) q^{23} +4.89898i q^{24} -12.0641 q^{26} +(-3.67423 + 3.67423i) q^{27} +(-3.74166 - 3.74166i) q^{28} -11.2171i q^{29} -16.4543 q^{31} +(4.00000 - 4.00000i) q^{32} +(-17.2547 - 17.2547i) q^{33} +19.0901i q^{34} +6.00000 q^{36} +(-47.6653 + 47.6653i) q^{37} +(-21.6823 - 21.6823i) q^{38} +14.7755i q^{39} -44.0379 q^{41} +(-4.58258 + 4.58258i) q^{42} +(46.7052 + 46.7052i) q^{43} +28.1767i q^{44} +0.846988 q^{46} +(20.3412 - 20.3412i) q^{47} +(-4.89898 - 4.89898i) q^{48} -7.00000i q^{49} +23.3805 q^{51} +(12.0641 - 12.0641i) q^{52} +(18.6273 + 18.6273i) q^{53} -7.34847i q^{54} +7.48331 q^{56} +(-26.5553 + 26.5553i) q^{57} +(11.2171 + 11.2171i) q^{58} +13.4774i q^{59} -10.8748 q^{61} +(16.4543 - 16.4543i) q^{62} +(5.61249 + 5.61249i) q^{63} +8.00000i q^{64} +34.5093 q^{66} +(-72.2045 + 72.2045i) q^{67} +(-19.0901 - 19.0901i) q^{68} -1.03734i q^{69} -64.1040 q^{71} +(-6.00000 + 6.00000i) q^{72} +(-51.4407 - 51.4407i) q^{73} -95.3307i q^{74} +43.3646 q^{76} +(-26.3569 + 26.3569i) q^{77} +(-14.7755 - 14.7755i) q^{78} +157.457i q^{79} -9.00000 q^{81} +(44.0379 - 44.0379i) q^{82} +(76.9972 + 76.9972i) q^{83} -9.16515i q^{84} -93.4104 q^{86} +(13.7381 - 13.7381i) q^{87} +(-28.1767 - 28.1767i) q^{88} +37.6912i q^{89} +22.5699 q^{91} +(-0.846988 + 0.846988i) q^{92} +(-20.1523 - 20.1523i) q^{93} +40.6824i q^{94} +9.79796 q^{96} +(-97.2189 + 97.2189i) q^{97} +(7.00000 + 7.00000i) q^{98} -42.2651i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} - 8 q^{11} - 8 q^{13} - 32 q^{16} + 32 q^{17} - 24 q^{18} + 8 q^{22} + 40 q^{23} + 16 q^{26} + 144 q^{31} + 32 q^{32} - 120 q^{33} + 48 q^{36} - 160 q^{37} - 320 q^{41} + 32 q^{43} - 80 q^{46} + 144 q^{47} + 72 q^{51} - 16 q^{52} + 200 q^{53} + 24 q^{57} + 64 q^{58} + 288 q^{61} - 144 q^{62} + 240 q^{66} - 80 q^{67} - 64 q^{68} - 280 q^{71} - 48 q^{72} - 312 q^{73} + 56 q^{77} - 48 q^{78} - 72 q^{81} + 320 q^{82} + 320 q^{83} - 64 q^{86} + 48 q^{87} - 16 q^{88} + 80 q^{92} - 48 q^{93} + 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 - 8 * q^11 - 8 * q^13 - 32 * q^16 + 32 * q^17 - 24 * q^18 + 8 * q^22 + 40 * q^23 + 16 * q^26 + 144 * q^31 + 32 * q^32 - 120 * q^33 + 48 * q^36 - 160 * q^37 - 320 * q^41 + 32 * q^43 - 80 * q^46 + 144 * q^47 + 72 * q^51 - 16 * q^52 + 200 * q^53 + 24 * q^57 + 64 * q^58 + 288 * q^61 - 144 * q^62 + 240 * q^66 - 80 * q^67 - 64 * q^68 - 280 * q^71 - 48 * q^72 - 312 * q^73 + 56 * q^77 - 48 * q^78 - 72 * q^81 + 320 * q^82 + 320 * q^83 - 64 * q^86 + 48 * q^87 - 16 * q^88 + 80 * q^92 - 48 * q^93 + 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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