LMFDB - Embedded newform 630.3.o.b.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(127,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("630.127");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.o (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:	$17.1662566547$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$-1.54779 - 1.54779i$ of defining polynomial
Character	$\chi$	$=$	630.127
Dual form			630.3.o.b.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.80341 - 6.83723i) q^{10} +14.0884 q^{11} +(-6.03207 + 6.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(9.54506 + 9.54506i) q^{17} -21.6823i q^{19} +(-5.03383 + 8.64064i) q^{20} +(-14.0884 - 14.0884i) q^{22} +(-0.423494 + 0.423494i) q^{23} +(12.3303 + 21.7477i) q^{25} +12.0641 q^{26} +(3.74166 - 3.74166i) q^{28} -11.2171i q^{29} -16.4543 q^{31} +(4.00000 + 4.00000i) q^{32} -19.0901i q^{34} +(-3.37386 - 12.7913i) q^{35} +(47.6653 + 47.6653i) q^{37} +(-21.6823 + 21.6823i) q^{38} +(13.6745 - 3.60681i) q^{40} +44.0379 q^{41} +(-46.7052 + 46.7052i) q^{43} +28.1767i q^{44} +0.846988 q^{46} +(20.3412 + 20.3412i) q^{47} +7.00000i q^{49} +(9.41742 - 34.0780i) q^{50} +(-12.0641 - 12.0641i) q^{52} +(18.6273 - 18.6273i) q^{53} +(60.8662 + 35.4592i) q^{55} -7.48331 q^{56} +(-11.2171 + 11.2171i) q^{58} +13.4774i q^{59} -10.8748 q^{61} +(16.4543 + 16.4543i) q^{62} -8.00000i q^{64} +(-41.2426 + 10.8783i) q^{65} +(72.2045 + 72.2045i) q^{67} +(-19.0901 + 19.0901i) q^{68} +(-9.41742 + 16.1652i) q^{70} +64.1040 q^{71} +(51.4407 - 51.4407i) q^{73} -95.3307i q^{74} +43.3646 q^{76} +(-26.3569 - 26.3569i) q^{77} -157.457i q^{79} +(-17.2813 - 10.0677i) q^{80} +(-44.0379 - 44.0379i) q^{82} +(76.9972 - 76.9972i) q^{83} +(17.2136 + 65.2618i) q^{85} +93.4104 q^{86} +(28.1767 - 28.1767i) q^{88} +37.6912i q^{89} +22.5699 q^{91} +(-0.846988 - 0.846988i) q^{92} -40.6824i q^{94} +(54.5724 - 93.6744i) q^{95} +(97.2189 + 97.2189i) q^{97} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 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 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$			2.00000i			0.500000i
$5$	4.32032	+	2.51691i	0.864064	+	0.503383i
$5$	4.32032	+	2.51691i	0.864064	+	0.503383i
$6$		0			0
$7$	−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
$9$		0			0
$10$	−1.80341	−	6.83723i	−0.180341	−	0.683723i
$11$	14.0884			1.28076			0.640380	−	0.768058i	$-0.278777\pi$
$11$	14.0884			1.28076			0.640380	+	0.768058i	$0.278777\pi$
$12$		0			0
$13$	−6.03207	+	6.03207i	−0.464005	+	0.464005i	−0.899966	−	0.435961i	$-0.856409\pi$
$13$	−6.03207	+	6.03207i	−0.464005	+	0.464005i	0.435961	+	0.899966i	$0.356409\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	−4.00000			−0.250000
$17$	9.54506	+	9.54506i	0.561474	+	0.561474i	0.929726	−	0.368252i	$-0.120044\pi$
$17$	9.54506	+	9.54506i	0.561474	+	0.561474i	−0.368252	+	0.929726i	$0.620044\pi$
$18$		0			0
$19$		−	21.6823i		−	1.14117i	−0.821237	−	0.570587i	$-0.806716\pi$
$19$		−	21.6823i		−	1.14117i	0.821237	−	0.570587i	$-0.193284\pi$
$20$	−5.03383	+	8.64064i	−0.251691	+	0.432032i
$21$		0			0
$22$	−14.0884	−	14.0884i	−0.640380	−	0.640380i
$23$	−0.423494	+	0.423494i	−0.0184128	+	0.0184128i	−0.716253	−	0.697840i	$-0.754144\pi$
$23$	−0.423494	+	0.423494i	−0.0184128	+	0.0184128i	0.697840	+	0.716253i	$0.254144\pi$
$24$		0			0
$25$	12.3303	+	21.7477i	0.493212	+	0.869909i
$26$	12.0641			0.464005
$27$		0			0
$28$	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
$33$		0			0
$34$		−	19.0901i		−	0.561474i
$35$	−3.37386	−	12.7913i	−0.0963961	−	0.365465i
$36$		0			0
$37$	47.6653	+	47.6653i	1.28825	+	1.28825i	0.935848	+	0.352404i	$0.114636\pi$
$37$	47.6653	+	47.6653i	1.28825	+	1.28825i	0.352404	+	0.935848i	$0.385364\pi$
$38$	−21.6823	+	21.6823i	−0.570587	+	0.570587i
$39$		0			0
$40$	13.6745	−	3.60681i	0.341862	−	0.0901703i
$41$	44.0379			1.07410			0.537048	−	0.843552i	$-0.319540\pi$
$41$	44.0379			1.07410			0.537048	+	0.843552i	$0.319540\pi$
$42$		0			0
$43$	−46.7052	+	46.7052i	−1.08617	+	1.08617i	−0.0902487	+	0.995919i	$0.528766\pi$
$43$	−46.7052	+	46.7052i	−1.08617	+	1.08617i	−0.995919	+	0.0902487i	$0.971234\pi$
$44$			28.1767i			0.640380i
$45$		0			0
$46$	0.846988			0.0184128
$47$	20.3412	+	20.3412i	0.432791	+	0.432791i	0.889577	−	0.456785i	$-0.150999\pi$
$47$	20.3412	+	20.3412i	0.432791	+	0.432791i	−0.456785	+	0.889577i	$0.650999\pi$
$48$		0			0
$49$			7.00000i			0.142857i
$50$	9.41742	−	34.0780i	0.188348	−	0.681561i
$51$		0			0
$52$	−12.0641	−	12.0641i	−0.232003	−	0.232003i
$53$	18.6273	−	18.6273i	0.351458	−	0.351458i	−0.509194	−	0.860652i	$-0.670056\pi$
$53$	18.6273	−	18.6273i	0.351458	−	0.351458i	0.860652	+	0.509194i	$0.170056\pi$
$54$		0			0
$55$	60.8662	+	35.4592i	1.10666	+	0.644712i
$56$	−7.48331			−0.133631
$57$		0			0
$58$	−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
$63$		0			0
$64$		−	8.00000i		−	0.125000i
$65$	−41.2426	+	10.8783i	−0.634502	+	0.167358i
$66$		0			0
$67$	72.2045	+	72.2045i	1.07768	+	1.07768i	0.996717	+	0.0809624i	$0.0257994\pi$
$67$	72.2045	+	72.2045i	1.07768	+	1.07768i	0.0809624	+	0.996717i	$0.474201\pi$
$68$	−19.0901	+	19.0901i	−0.280737	+	0.280737i
$69$		0			0
$70$	−9.41742	+	16.1652i	−0.134535	+	0.230931i
$71$	64.1040			0.902874			0.451437	−	0.892303i	$-0.350912\pi$
$71$	64.1040			0.902874			0.451437	+	0.892303i	$0.350912\pi$
$72$		0			0
$73$	51.4407	−	51.4407i	0.704667	−	0.704667i	−0.260742	−	0.965409i	$-0.583967\pi$
$73$	51.4407	−	51.4407i	0.704667	−	0.704667i	0.965409	+	0.260742i	$0.0839671\pi$
$74$		−	95.3307i		−	1.28825i
$75$		0			0
$76$	43.3646			0.570587
$77$	−26.3569	−	26.3569i	−0.342298	−	0.342298i
$78$		0			0
$79$		−	157.457i		−	1.99313i	−0.0828028	−	0.996566i	$-0.526387\pi$
$79$		−	157.457i		−	1.99313i	0.0828028	−	0.996566i	$-0.473613\pi$
$80$	−17.2813	−	10.0677i	−0.216016	−	0.125846i
$81$		0			0
$82$	−44.0379	−	44.0379i	−0.537048	−	0.537048i
$83$	76.9972	−	76.9972i	0.927677	−	0.927677i	−0.0698788	−	0.997555i	$-0.522261\pi$
$83$	76.9972	−	76.9972i	0.927677	−	0.927677i	0.997555	+	0.0698788i	$0.0222612\pi$
$84$		0			0
$85$	17.2136	+	65.2618i	0.202513	+	0.767786i
$86$	93.4104			1.08617
$87$		0			0
$88$	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
$93$		0			0
$94$		−	40.6824i		−	0.432791i
$95$	54.5724	−	93.6744i	0.574447	−	0.986046i
$96$		0			0
$97$	97.2189	+	97.2189i	1.00226	+	1.00226i	0.999997	+	0.00225910i	$0.000719096\pi$
$97$	97.2189	+	97.2189i	1.00226	+	1.00226i	0.00225910	+	0.999997i	$0.499281\pi$
$98$	7.00000	−	7.00000i	0.0714286	−	0.0714286i
$99$		0			0
$100$	−43.4955	+	24.6606i	−0.434955	+	0.246606i
$101$	−26.1142			−0.258557			−0.129278	−	0.991608i	$-0.541266\pi$
$101$	−26.1142			−0.258557			−0.129278	+	0.991608i	$0.541266\pi$
$102$		0			0
$103$	52.9553	−	52.9553i	0.514129	−	0.514129i	−0.401660	−	0.915789i	$-0.631567\pi$
$103$	52.9553	−	52.9553i	0.514129	−	0.514129i	0.915789	+	0.401660i	$0.131567\pi$
$104$			24.1283i			0.232003i
$105$		0			0
$106$	−37.2546			−0.351458
$107$	81.7515	+	81.7515i	0.764033	+	0.764033i	0.977049	−	0.213016i	$-0.0683285\pi$
$107$	81.7515	+	81.7515i	0.764033	+	0.764033i	−0.213016	+	0.977049i	$0.568329\pi$
$108$		0			0
$109$		−	59.2958i		−	0.543998i	−0.962297	−	0.271999i	$-0.912315\pi$
$109$		−	59.2958i		−	0.543998i	0.962297	−	0.271999i	$-0.0876848\pi$
$110$	−25.4070	−	96.3254i	−0.230973	−	0.875686i
$111$		0			0
$112$	7.48331	+	7.48331i	0.0668153	+	0.0668153i
$113$	−142.193	+	142.193i	−1.25834	+	1.25834i	−0.306458	+	0.951884i	$0.599144\pi$
$113$	−142.193	+	142.193i	−1.25834	+	1.25834i	−0.951884	+	0.306458i	$0.900856\pi$
$114$		0			0
$115$	−2.89553	+	0.763732i	−0.0251785	+	0.00664114i
$116$	22.4343			0.193399
$117$		0			0
$118$	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
$123$		0			0
$124$		−	32.9085i		−	0.265391i
$125$	−1.46629	+	124.991i	−0.0117303	+	0.999931i
$126$		0			0
$127$	−95.3116	−	95.3116i	−0.750485	−	0.750485i	0.224085	−	0.974570i	$-0.428061\pi$
$127$	−95.3116	−	95.3116i	−0.750485	−	0.750485i	−0.974570	+	0.224085i	$0.928061\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	52.1209	+	30.3644i	0.400930	+	0.233572i
$131$	191.866			1.46463			0.732313	−	0.680968i	$-0.238441\pi$
$131$	191.866			1.46463			0.732313	+	0.680968i	$0.238441\pi$
$132$		0			0
$133$	−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	0.0166339	−	0.999862i	$-0.494705\pi$
$137$	−134.702	−	134.702i	−0.983228	−	0.983228i	−0.999862	+	0.0166339i	$0.994705\pi$
$138$		0			0
$139$			49.6297i			0.357048i	0.983936	+	0.178524i	$0.0571323\pi$
$139$			49.6297i			0.357048i	−0.983936	+	0.178524i	$0.942868\pi$
$140$	25.5826	−	6.74773i	0.182733	−	0.0481981i
$141$		0			0
$142$	−64.1040	−	64.1040i	−0.451437	−	0.451437i
$143$	−84.9820	+	84.9820i	−0.594279	+	0.594279i
$144$		0			0
$145$	28.2326	−	48.4616i	0.194707	−	0.334218i
$146$	−102.881			−0.704667
$147$		0			0
$148$	−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
$153$		0			0
$154$			52.7138i			0.342298i
$155$	−71.0876	−	41.4139i	−0.458630	−	0.267187i
$156$		0			0
$157$	−179.903	−	179.903i	−1.14588	−	1.14588i	−0.987355	−	0.158526i	$-0.949326\pi$
$157$	−179.903	−	179.903i	−1.14588	−	1.14588i	−0.158526	−	0.987355i	$-0.550674\pi$
$158$	−157.457	+	157.457i	−0.996566	+	0.996566i
$159$		0			0
$160$	7.21362	+	27.3489i	0.0450851	+	0.170931i
$161$	1.58457			0.00984205
$162$		0			0
$163$	−19.4617	+	19.4617i	−0.119397	+	0.119397i	−0.764281	−	0.644884i	$-0.776906\pi$
$163$	−19.4617	+	19.4617i	−0.119397	+	0.119397i	0.644884	+	0.764281i	$0.276906\pi$
$164$			88.0758i			0.537048i
$165$		0			0
$166$	−153.994			−0.927677
$167$	78.3023	+	78.3023i	0.468876	+	0.468876i	0.901550	−	0.432674i	$-0.142430\pi$
$167$	78.3023	+	78.3023i	0.468876	+	0.468876i	−0.432674	+	0.901550i	$0.642430\pi$
$168$		0			0
$169$			96.2284i			0.569399i
$170$	48.0482	−	82.4754i	0.282636	−	0.485150i
$171$		0			0
$172$	−93.4104	−	93.4104i	−0.543084	−	0.543084i
$173$	−66.9522	+	66.9522i	−0.387007	+	0.387007i	−0.873618	−	0.486612i	$-0.838233\pi$
$173$	−66.9522	+	66.9522i	−0.387007	+	0.387007i	0.486612	+	0.873618i	$0.338233\pi$
$174$		0			0
$175$	17.6184	−	63.7542i	0.100677	−	0.364309i
$176$	−56.3535			−0.320190
$177$		0			0
$178$	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
$183$		0			0
$184$			1.69398i			0.00920639i
$185$	85.9599	+	325.899i	0.464648	+	1.76162i
$186$		0			0
$187$	134.474	+	134.474i	0.719114	+	0.719114i
$188$	−40.6824	+	40.6824i	−0.216396	+	0.216396i
$189$		0			0
$190$	−148.247	+	39.1020i	−0.780246	+	0.205800i
$191$	209.877			1.09883			0.549415	−	0.835549i	$-0.314850\pi$
$191$	209.877			1.09883			0.549415	+	0.835549i	$0.314850\pi$
$192$		0			0
$193$	−247.934	+	247.934i	−1.28463	+	1.28463i	−0.346634	+	0.938001i	$0.612675\pi$
$193$	−247.934	+	247.934i	−1.28463	+	1.28463i	−0.938001	+	0.346634i	$0.887325\pi$
$194$		−	194.438i		−	1.00226i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	14.3392	+	14.3392i	0.0727881	+	0.0727881i	0.742564	−	0.669776i	$-0.233610\pi$
$197$	14.3392	+	14.3392i	0.0727881	+	0.0727881i	−0.669776	+	0.742564i	$0.733610\pi$
$198$		0			0
$199$		−	282.601i		−	1.42011i	−0.704148	−	0.710053i	$-0.748671\pi$
$199$		−	282.601i		−	1.42011i	0.704148	−	0.710053i	$-0.251329\pi$
$200$	68.1561	+	18.8348i	0.340780	+	0.0941742i
$201$		0			0
$202$	26.1142	+	26.1142i	0.129278	+	0.129278i
$203$	−20.9854	+	20.9854i	−0.103376	+	0.103376i
$204$		0			0
$205$	190.258	+	110.840i	0.928087	+	0.540681i
$206$	−105.911			−0.514129
$207$		0			0
$208$	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
$213$		0			0
$214$		−	163.503i		−	0.764033i
$215$	−319.334	+	84.2285i	−1.48528	+	0.391760i
$216$		0			0
$217$	30.7831	+	30.7831i	0.141858	+	0.141858i
$218$	−59.2958	+	59.2958i	−0.271999	+	0.271999i
$219$		0			0
$220$	−70.9184	+	121.732i	−0.322356	+	0.553329i
$221$	−115.153			−0.521054
$222$		0			0
$223$	−205.186	+	205.186i	−0.920118	+	0.920118i	−0.997037	−	0.0769196i	$-0.975492\pi$
$223$	−205.186	+	205.186i	−0.920118	+	0.920118i	0.0769196	+	0.997037i	$0.475492\pi$
$224$		−	14.9666i		−	0.0668153i
$225$		0			0
$226$	284.385			1.25834
$227$	−316.050	−	316.050i	−1.39229	−	1.39229i	−0.820170	−	0.572120i	$-0.806121\pi$
$227$	−316.050	−	316.050i	−1.39229	−	1.39229i	−0.572120	−	0.820170i	$-0.693879\pi$
$228$		0			0
$229$			123.494i			0.539274i	0.962962	+	0.269637i	$0.0869036\pi$
$229$			123.494i			0.539274i	−0.962962	+	0.269637i	$0.913096\pi$
$230$	3.65926	+	2.13179i	0.0159098	+	0.00926867i
$231$		0			0
$232$	−22.4343	−	22.4343i	−0.0966995	−	0.0966995i
$233$	−209.367	+	209.367i	−0.898572	+	0.898572i	−0.995310	−	0.0967375i	$-0.969159\pi$
$233$	−209.367	+	209.367i	−0.898572	+	0.898572i	0.0967375	+	0.995310i	$0.469159\pi$
$234$		0			0
$235$	36.6834	+	139.077i	0.156100	+	0.591819i
$236$	−26.9548			−0.114215
$237$		0			0
$238$	−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
$243$		0			0
$244$		−	21.7496i		−	0.0891376i
$245$	−17.6184	+	30.2422i	−0.0719118	+	0.123438i
$246$		0			0
$247$	130.789	+	130.789i	0.529510	+	0.529510i
$248$	−32.9085	+	32.9085i	−0.132696	+	0.132696i
$249$		0			0
$250$	126.458	−	123.525i	0.505831	−	0.494100i
$251$	−25.2366			−0.100544			−0.0502720	−	0.998736i	$-0.516009\pi$
$251$	−25.2366			−0.100544			−0.0502720	+	0.998736i	$0.516009\pi$
$252$		0			0
$253$	−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	0.104718	−	0.994502i	$-0.466606\pi$
$257$	−228.675	−	228.675i	−0.889784	−	0.889784i	−0.994502	+	0.104718i	$0.966606\pi$
$258$		0			0
$259$		−	178.347i		−	0.688600i
$260$	−21.7565	−	82.4852i	−0.0836789	−	0.317251i
$261$		0			0
$262$	−191.866	−	191.866i	−0.732313	−	0.732313i
$263$	17.1641	−	17.1641i	0.0652629	−	0.0652629i	−0.673722	−	0.738985i	$-0.735305\pi$
$263$	17.1641	−	17.1641i	0.0652629	−	0.0652629i	0.738985	+	0.673722i	$0.235305\pi$
$264$		0			0
$265$	127.359	−	33.5926i	0.480600	−	0.126764i
$266$	81.1277			0.304991
$267$		0			0
$268$	−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
$273$		0			0
$274$			269.404i			0.983228i
$275$	173.714	+	306.390i	0.631687	+	1.11415i
$276$		0			0
$277$	2.85013	+	2.85013i	0.0102893	+	0.0102893i	0.712233	−	0.701943i	$-0.247684\pi$
$277$	2.85013	+	2.85013i	0.0102893	+	0.0102893i	−0.701943	+	0.712233i	$0.747684\pi$
$278$	49.6297	−	49.6297i	0.178524	−	0.178524i
$279$		0			0
$280$	−32.3303	−	18.8348i	−0.115465	−	0.0672673i
$281$	−384.657			−1.36889			−0.684443	−	0.729066i	$-0.739955\pi$
$281$	−384.657			−1.36889			−0.684443	+	0.729066i	$0.739955\pi$
$282$		0			0
$283$	−201.734	+	201.734i	−0.712839	+	0.712839i	−0.967128	−	0.254289i	$-0.918159\pi$
$283$	−201.734	+	201.734i	−0.712839	+	0.712839i	0.254289	+	0.967128i	$0.418159\pi$
$284$			128.208i			0.451437i
$285$		0			0
$286$	169.964			0.594279
$287$	−82.3874	−	82.3874i	−0.287064	−	0.287064i
$288$		0			0
$289$		−	106.784i		−	0.369493i
$290$	−76.6942	+	20.2291i	−0.264463	+	0.0697554i
$291$		0			0
$292$	102.881	+	102.881i	0.352334	+	0.352334i
$293$	366.878	−	366.878i	1.25214	−	1.25214i	0.297384	−	0.954758i	$-0.403886\pi$
$293$	366.878	−	366.878i	1.25214	−	1.25214i	0.954758	−	0.297384i	$-0.0961140\pi$
$294$		0			0
$295$	−33.9214	+	58.2266i	−0.114988	+	0.197378i
$296$	190.661			0.644126
$297$		0			0
$298$	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
$303$		0			0
$304$			86.7292i			0.285293i
$305$	−46.9825	−	27.3709i	−0.154041	−	0.0897406i
$306$		0			0
$307$	−412.785	−	412.785i	−1.34458	−	1.34458i	−0.891442	−	0.453136i	$-0.850305\pi$
$307$	−412.785	−	412.785i	−1.34458	−	1.34458i	−0.453136	−	0.891442i	$-0.649695\pi$
$308$	52.7138	−	52.7138i	0.171149	−	0.171149i
$309$		0			0
$310$	29.6737	+	112.502i	0.0957216	+	0.362908i
$311$	−512.668			−1.64845			−0.824225	−	0.566263i	$-0.808389\pi$
$311$	−512.668			−1.64845			−0.824225	+	0.566263i	$0.808389\pi$
$312$		0			0
$313$	−101.469	+	101.469i	−0.324182	+	0.324182i	−0.850369	−	0.526187i	$-0.823621\pi$
$313$	−101.469	+	101.469i	−0.324182	+	0.324182i	0.526187	+	0.850369i	$0.323621\pi$
$314$			359.806i			1.14588i
$315$		0			0
$316$	314.915			0.996566
$317$	202.617	+	202.617i	0.639169	+	0.639169i	0.950350	−	0.311182i	$-0.100725\pi$
$317$	202.617	+	202.617i	0.639169	+	0.639169i	−0.311182	+	0.950350i	$0.600725\pi$
$318$		0			0
$319$		−	158.031i		−	0.495396i
$320$	20.1353	−	34.5625i	0.0629228	−	0.108008i
$321$		0			0
$322$	−1.58457	−	1.58457i	−0.00492102	−	0.00492102i
$323$	206.959	−	206.959i	0.640739	−	0.640739i
$324$		0			0
$325$	−205.561	−	56.8065i	−0.632495	−	0.174789i
$326$	38.9233			0.119397
$327$		0			0
$328$	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
$333$		0			0
$334$		−	156.605i		−	0.468876i
$335$	130.214	+	493.679i	0.388699	+	1.47367i
$336$		0			0
$337$	−360.772	−	360.772i	−1.07054	−	1.07054i	−0.997315	−	0.0732257i	$-0.976671\pi$
$337$	−360.772	−	360.772i	−1.07054	−	1.07054i	−0.0732257	−	0.997315i	$-0.523329\pi$
$338$	96.2284	−	96.2284i	0.284699	−	0.284699i
$339$		0			0
$340$	−130.524	+	34.4272i	−0.383893	+	0.101257i
$341$	−231.814			−0.679805
$342$		0			0
$343$	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	0.930042	−	0.367454i	$-0.119770\pi$
$347$	195.218	+	195.218i	0.562588	+	0.562588i	−0.367454	+	0.930042i	$0.619770\pi$
$348$		0			0
$349$			204.957i			0.587270i	0.955918	+	0.293635i	$0.0948650\pi$
$349$			204.957i			0.587270i	−0.955918	+	0.293635i	$0.905135\pi$
$350$	−81.3725	+	46.1358i	−0.232493	+	0.131816i
$351$		0			0
$352$	56.3535	+	56.3535i	0.160095	+	0.160095i
$353$	233.494	−	233.494i	0.661457	−	0.661457i	−0.294267	−	0.955723i	$-0.595075\pi$
$353$	233.494	−	233.494i	0.661457	−	0.661457i	0.955723	+	0.294267i	$0.0950754\pi$
$354$		0			0
$355$	276.950	+	161.344i	0.780140	+	0.454491i
$356$	−75.3825			−0.211749
$357$		0			0
$358$	−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
$363$		0			0
$364$			45.1398i			0.124011i
$365$	351.712	−	92.7684i	0.963594	−	0.254160i
$366$		0			0
$367$	22.0009	+	22.0009i	0.0599481	+	0.0599481i	0.736445	−	0.676497i	$-0.236503\pi$
$367$	22.0009	+	22.0009i	0.0599481	+	0.0599481i	−0.676497	+	0.736445i	$0.736503\pi$
$368$	1.69398	−	1.69398i	0.00460320	−	0.00460320i
$369$		0			0
$370$	239.939	−	411.859i	0.648484	−	1.11313i
$371$	−69.6970			−0.187862
$372$		0			0
$373$	−170.973	+	170.973i	−0.458373	+	0.458373i	−0.898121	−	0.439748i	$-0.855068\pi$
$373$	−170.973	+	170.973i	−0.458373	+	0.458373i	0.439748	+	0.898121i	$0.355068\pi$
$374$		−	268.949i		−	0.719114i
$375$		0			0
$376$	81.3648			0.216396
$377$	67.6625	+	67.6625i	0.179476	+	0.179476i
$378$		0			0
$379$		−	272.520i		−	0.719050i	−0.933135	−	0.359525i	$-0.882939\pi$
$379$		−	272.520i		−	0.719050i	0.933135	−	0.359525i	$-0.117061\pi$
$380$	187.349	+	109.145i	0.493023	+	0.287223i
$381$		0			0
$382$	−209.877	−	209.877i	−0.549415	−	0.549415i
$383$	283.977	−	283.977i	0.741454	−	0.741454i	−0.231403	−	0.972858i	$-0.574332\pi$
$383$	283.977	−	283.977i	0.741454	−	0.741454i	0.972858	+	0.231403i	$0.0743317\pi$
$384$		0			0
$385$	−47.5322	−	180.208i	−0.123460	−	0.468074i
$386$	495.869			1.28463
$387$		0			0
$388$	−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
$393$		0			0
$394$		−	28.6785i		−	0.0727881i
$395$	396.307	−	680.266i	1.00331	−	1.72219i
$396$		0			0
$397$	−242.868	−	242.868i	−0.611757	−	0.611757i	0.331647	−	0.943404i	$-0.392396\pi$
$397$	−242.868	−	242.868i	−0.611757	−	0.611757i	−0.943404	+	0.331647i	$0.892396\pi$
$398$	−282.601	+	282.601i	−0.710053	+	0.710053i
$399$		0			0
$400$	−49.3212	−	86.9909i	−0.123303	−	0.217477i
$401$	523.505			1.30550			0.652749	−	0.757574i	$-0.273615\pi$
$401$	523.505			1.30550			0.652749	+	0.757574i	$0.273615\pi$
$402$		0			0
$403$	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
$408$		0			0
$409$		−	39.5511i		−	0.0967019i	−0.998830	−	0.0483509i	$-0.984603\pi$
$409$		−	39.5511i		−	0.0967019i	0.998830	−	0.0483509i	$-0.0153966\pi$
$410$	−79.4182	−	301.097i	−0.193703	−	0.734384i
$411$		0			0
$412$	105.911	+	105.911i	0.257064	+	0.257064i
$413$	25.2139	−	25.2139i	0.0610506	−	0.0610506i
$414$		0			0
$415$	526.447	−	138.857i	1.26855	−	0.334596i
$416$	−48.2565			−0.116001
$417$		0			0
$418$	−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
$423$		0			0
$424$		−	74.5092i		−	0.175729i
$425$	−89.8899	+	325.277i	−0.211506	+	0.765358i
$426$		0			0
$427$	20.3449	+	20.3449i	0.0476460	+	0.0476460i
$428$	−163.503	+	163.503i	−0.382017	+	0.382017i
$429$		0			0
$430$	403.563	+	235.106i	0.938518	+	0.546758i
$431$	−323.054			−0.749545			−0.374772	−	0.927117i	$-0.622279\pi$
$431$	−323.054			−0.749545			−0.374772	+	0.927117i	$0.622279\pi$
$432$		0			0
$433$	76.7446	−	76.7446i	0.177239	−	0.177239i	−0.612912	−	0.790151i	$-0.710002\pi$
$433$	76.7446	−	76.7446i	0.177239	−	0.177239i	0.790151	+	0.612912i	$0.210002\pi$
$434$		−	61.5662i		−	0.141858i
$435$		0			0
$436$	118.592			0.271999
$437$	9.18232	+	9.18232i	0.0210122	+	0.0210122i
$438$		0			0
$439$		−	864.627i		−	1.96954i	−0.173872	−	0.984768i	$-0.555628\pi$
$439$		−	864.627i		−	1.96954i	0.173872	−	0.984768i	$-0.444372\pi$
$440$	192.651	−	50.8141i	0.437843	−	0.115487i
$441$		0			0
$442$	115.153	+	115.153i	0.260527	+	0.260527i
$443$	326.831	−	326.831i	0.737768	−	0.737768i	−0.234377	−	0.972146i	$-0.575305\pi$
$443$	326.831	−	326.831i	0.737768	−	0.737768i	0.972146	+	0.234377i	$0.0753051\pi$
$444$		0			0
$445$	−94.8656	+	162.838i	−0.213181	+	0.365929i
$446$	410.372			0.920118
$447$		0			0
$448$	−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
$453$		0			0
$454$			632.100i			1.39229i
$455$	97.5093	+	56.8065i	0.214306	+	0.124849i
$456$		0			0
$457$	485.728	+	485.728i	1.06286	+	1.06286i	0.997887	+	0.0649742i	$0.0206965\pi$
$457$	485.728	+	485.728i	1.06286	+	1.06286i	0.0649742	+	0.997887i	$0.479304\pi$
$458$	123.494	−	123.494i	0.269637	−	0.269637i
$459$		0			0
$460$	−1.52746	−	5.79105i	−0.00332057	−	0.0125892i
$461$	560.524			1.21589			0.607944	−	0.793980i	$-0.291995\pi$
$461$	560.524			1.21589			0.607944	+	0.793980i	$0.291995\pi$
$462$		0			0
$463$	279.103	−	279.103i	0.602814	−	0.602814i	−0.338245	−	0.941058i	$-0.609833\pi$
$463$	279.103	−	279.103i	0.602814	−	0.602814i	0.941058	+	0.338245i	$0.109833\pi$
$464$			44.8686i			0.0966995i
$465$		0			0
$466$	418.735			0.898572
$467$	−201.253	−	201.253i	−0.430948	−	0.430948i	0.458003	−	0.888951i	$-0.348565\pi$
$467$	−201.253	−	201.253i	−0.430948	−	0.430948i	−0.888951	+	0.458003i	$0.848565\pi$
$468$		0			0
$469$		−	270.165i		−	0.576044i
$470$	102.394	−	175.761i	0.217860	−	0.373959i
$471$		0			0
$472$	26.9548	+	26.9548i	0.0571076	+	0.0571076i
$473$	−658.000	+	658.000i	−1.39112	+	1.39112i
$474$		0			0
$475$	471.541	−	267.349i	0.992717	−	0.562840i
$476$	71.4287			0.150060
$477$		0			0
$478$	−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
$483$		0			0
$484$			154.964i			0.320174i
$485$	175.325	+	664.708i	0.361495	+	1.37053i
$486$		0			0
$487$	−457.935	−	457.935i	−0.940317	−	0.940317i	0.0579991	−	0.998317i	$-0.481528\pi$
$487$	−457.935	−	457.935i	−0.940317	−	0.940317i	−0.998317	+	0.0579991i	$0.981528\pi$
$488$	−21.7496	+	21.7496i	−0.0445688	+	0.0445688i
$489$		0			0
$490$	47.8606	−	12.6238i	0.0976747	−	0.0257629i
$491$	−714.606			−1.45541			−0.727704	−	0.685891i	$-0.759413\pi$
$491$	−714.606			−1.45541			−0.727704	+	0.685891i	$0.759413\pi$
$492$		0			0
$493$	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
$498$		0			0
$499$			746.370i			1.49573i	0.663850	+	0.747866i	$0.268922\pi$
$499$			746.370i			1.49573i	−0.663850	+	0.747866i	$0.731078\pi$
$500$	−249.983	−	2.93258i	−0.499966	−	0.00586517i
$501$		0			0
$502$	25.2366	+	25.2366i	0.0502720	+	0.0502720i
$503$	−10.5315	+	10.5315i	−0.0209375	+	0.0209375i	−0.717498	−	0.696561i	$-0.754713\pi$
$503$	−10.5315	+	10.5315i	−0.0209375	+	0.0209375i	0.696561	+	0.717498i	$0.254713\pi$
$504$		0			0
$505$	−112.822	−	65.7272i	−0.223409	−	0.130153i
$506$	11.9327			0.0235824
$507$		0			0
$508$	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
$513$		0			0
$514$			457.349i			0.889784i
$515$	362.067	−	95.4999i	0.703044	−	0.185437i
$516$		0			0
$517$	286.574	+	286.574i	0.554302	+	0.554302i
$518$	−178.347	+	178.347i	−0.344300	+	0.344300i
$519$		0			0
$520$	−60.7287	+	104.242i	−0.116786	+	0.200465i
$521$	−397.521			−0.762995			−0.381498	−	0.924370i	$-0.624592\pi$
$521$	−397.521			−0.762995			−0.381498	+	0.924370i	$0.624592\pi$
$522$		0			0
$523$	59.4921	−	59.4921i	0.113752	−	0.113752i	−0.647940	−	0.761692i	$-0.724369\pi$
$523$	59.4921	−	59.4921i	0.113752	−	0.113752i	0.761692	+	0.647940i	$0.224369\pi$
$524$			383.732i			0.732313i
$525$		0			0
$526$	−34.3283			−0.0652629
$527$	−157.057	−	157.057i	−0.298021	−	0.298021i
$528$		0			0
$529$			528.641i			0.999322i
$530$	−160.952	−	93.7665i	−0.303682	−	0.176918i
$531$		0			0
$532$	−81.1277	−	81.1277i	−0.152496	−	0.152496i
$533$	−265.640	+	265.640i	−0.498386	+	0.498386i
$534$		0			0
$535$	147.431	+	558.954i	0.275572	+	1.04477i
$536$	288.818			0.538840
$537$		0			0
$538$	−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
$543$		0			0
$544$			76.3605i			0.140369i
$545$	149.242	−	256.177i	0.273839	−	0.470049i
$546$		0			0
$547$	−397.442	−	397.442i	−0.726585	−	0.726585i	0.243353	−	0.969938i	$-0.421753\pi$
$547$	−397.442	−	397.442i	−0.726585	−	0.726585i	−0.969938	+	0.243353i	$0.921753\pi$
$548$	269.404	−	269.404i	0.491614	−	0.491614i
$549$		0			0
$550$	132.676	−	480.104i	0.241229	−	0.872916i
$551$	−243.213			−0.441404
$552$		0			0
$553$	−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	0.461719	−	0.887026i	$-0.347233\pi$
$557$	−236.896	−	236.896i	−0.425307	−	0.425307i	−0.887026	+	0.461719i	$0.847233\pi$
$558$		0			0
$559$		−	563.458i		−	1.00797i
$560$	13.4955	+	51.1652i	0.0240990	+	0.0913663i
$561$		0			0
$562$	384.657	+	384.657i	0.684443	+	0.684443i
$563$	113.926	−	113.926i	0.202355	−	0.202355i	−0.598653	−	0.801008i	$-0.704297\pi$
$563$	113.926	−	113.926i	0.202355	−	0.202355i	0.801008	+	0.598653i	$0.204297\pi$
$564$		0			0
$565$	−972.204	+	256.431i	−1.72072	+	0.453860i
$566$	403.467			0.712839
$567$		0			0
$568$	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
$573$		0			0
$574$			164.775i			0.287064i
$575$	−14.4318	−	3.98822i	−0.0250989	−	0.00693604i
$576$		0			0
$577$	−207.248	−	207.248i	−0.359182	−	0.359182i	0.504329	−	0.863512i	$-0.331740\pi$
$577$	−207.248	−	207.248i	−0.359182	−	0.359182i	−0.863512	+	0.504329i	$0.831740\pi$
$578$	−106.784	+	106.784i	−0.184747	+	0.184747i
$579$		0			0
$580$	96.9233	+	56.4651i	0.167109	+	0.0973537i
$581$	−288.097			−0.495864
$582$		0			0
$583$	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	0.112628	−	0.993637i	$-0.464073\pi$
$587$	−517.152	−	517.152i	−0.881009	−	0.881009i	−0.993637	+	0.112628i	$0.964073\pi$
$588$		0			0
$589$			356.766i			0.605715i
$590$	92.1480	−	24.3052i	0.156183	−	0.0411953i
$591$		0			0
$592$	−190.661	−	190.661i	−0.322063	−	0.322063i
$593$	455.580	−	455.580i	0.768264	−	0.768264i	−0.209537	−	0.977801i	$-0.567196\pi$
$593$	455.580	−	455.580i	0.768264	−	0.768264i	0.977801	+	0.209537i	$0.0671957\pi$
$594$		0			0
$595$	89.8899	−	154.297i	0.151075	−	0.259323i
$596$	−274.284			−0.460208
$597$		0			0
$598$	−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
$603$		0			0
$604$		−	395.584i		−	0.654941i
$605$	334.747	+	195.016i	0.553301	+	0.322340i
$606$		0			0
$607$	523.720	+	523.720i	0.862801	+	0.862801i	0.991663	−	0.128862i	$-0.0411324\pi$
$607$	523.720	+	523.720i	0.862801	+	0.862801i	−0.128862	+	0.991663i	$0.541132\pi$
$608$	86.7292	−	86.7292i	0.142647	−	0.142647i
$609$		0			0
$610$	19.6117	+	74.3534i	0.0321503	+	0.121891i
$611$	−245.399			−0.401635
$612$		0			0
$613$	−239.438	+	239.438i	−0.390601	+	0.390601i	−0.874901	−	0.484301i	$-0.839074\pi$
$613$	−239.438	+	239.438i	−0.390601	+	0.390601i	0.484301	+	0.874901i	$0.339074\pi$
$614$			825.570i			1.34458i
$615$		0			0
$616$	−105.428			−0.171149
$617$	508.117	+	508.117i	0.823529	+	0.823529i	0.986612	−	0.163083i	$-0.0521439\pi$
$617$	508.117	+	508.117i	0.823529	+	0.823529i	−0.163083	+	0.986612i	$0.552144\pi$
$618$		0			0
$619$			237.357i			0.383453i	0.981448	+	0.191727i	$0.0614087\pi$
$619$			237.357i			0.383453i	−0.981448	+	0.191727i	$0.938591\pi$
$620$	82.8278	−	142.175i	0.133593	−	0.229315i
$621$		0			0
$622$	512.668	+	512.668i	0.824225	+	0.824225i
$623$	70.5139	−	70.5139i	0.113184	−	0.113184i
$624$		0			0
$625$	−320.927	+	536.312i	−0.513484	+	0.858099i
$626$	202.938			0.324182
$627$		0			0
$628$	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
$633$		0			0
$634$		−	405.233i		−	0.639169i
$635$	−171.886	−	651.667i	−0.270686	−	1.02625i
$636$		0			0
$637$	−42.2245	−	42.2245i	−0.0662864	−	0.0662864i
$638$	−158.031	+	158.031i	−0.247698	+	0.247698i
$639$		0			0
$640$	−54.6978	+	14.4272i	−0.0854654	+	0.0225426i
$641$	894.582			1.39560			0.697802	−	0.716291i	$-0.254162\pi$
$641$	894.582			1.39560			0.697802	+	0.716291i	$0.254162\pi$
$642$		0			0
$643$	27.5752	−	27.5752i	0.0428853	−	0.0428853i	−0.685339	−	0.728224i	$-0.740346\pi$
$643$	27.5752	−	27.5752i	0.0428853	−	0.0428853i	0.728224	+	0.685339i	$0.240346\pi$
$644$			3.16914i			0.00492102i
$645$		0			0
$646$	−413.918			−0.640739
$647$	−76.5361	−	76.5361i	−0.118294	−	0.118294i	0.645482	−	0.763776i	$-0.276657\pi$
$647$	−76.5361	−	76.5361i	−0.118294	−	0.118294i	−0.763776	+	0.645482i	$0.776657\pi$
$648$		0			0
$649$			189.874i			0.292565i
$650$	148.754	+	262.367i	0.228853	+	0.403642i
$651$		0			0
$652$	−38.9233	−	38.9233i	−0.0596983	−	0.0596983i
$653$	−873.233	+	873.233i	−1.33726	+	1.33726i	−0.438564	+	0.898700i	$0.644513\pi$
$653$	−873.233	+	873.233i	−1.33726	+	1.33726i	−0.898700	+	0.438564i	$0.855487\pi$
$654$		0			0
$655$	828.922	+	482.910i	1.26553	+	0.737267i
$656$	−176.152			−0.268524
$657$		0			0
$658$	−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
$663$		0			0
$664$		−	307.989i		−	0.463838i
$665$	−277.344	+	73.1531i	−0.417059	+	0.110005i
$666$		0			0
$667$	4.75039	+	4.75039i	0.00712203	+	0.00712203i
$668$	−156.605	+	156.605i	−0.234438	+	0.234438i
$669$		0			0
$670$	363.465	−	623.893i	0.542485	−	0.931184i
$671$	−153.208			−0.228328
$672$		0			0
$673$	663.103	−	663.103i	0.985294	−	0.985294i	−0.0145998	−	0.999893i	$-0.504647\pi$
$673$	663.103	−	663.103i	0.985294	−	0.985294i	0.999893	+	0.0145998i	$0.00464744\pi$
$674$			721.545i			1.07054i
$675$		0			0
$676$	−192.457			−0.284699
$677$	−363.300	−	363.300i	−0.536632	−	0.536632i	0.385906	−	0.922538i	$-0.373889\pi$
$677$	−363.300	−	363.300i	−0.536632	−	0.536632i	−0.922538	+	0.385906i	$0.873889\pi$
$678$		0			0
$679$		−	363.760i		−	0.535729i
$680$	164.951	+	96.0964i	0.242575	+	0.141318i
$681$		0			0
$682$	231.814	+	231.814i	0.339903	+	0.339903i
$683$	−133.225	+	133.225i	−0.195058	+	0.195058i	−0.797878	−	0.602819i	$-0.794044\pi$
$683$	−133.225	+	133.225i	−0.195058	+	0.195058i	0.602819	+	0.797878i	$0.294044\pi$
$684$		0			0
$685$	−242.923	−	920.990i	−0.354632	−	1.34451i
$686$	−26.1916			−0.0381802
$687$		0			0
$688$	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
$693$		0			0
$694$		−	390.436i		−	0.562588i
$695$	−124.914	+	214.416i	−0.179732	+	0.308513i
$696$		0			0
$697$	420.345	+	420.345i	0.603077	+	0.603077i
$698$	204.957	−	204.957i	0.293635	−	0.293635i
$699$		0			0
$700$	127.508	+	35.2368i	0.182155	+	0.0503383i
$701$	−181.482			−0.258890			−0.129445	−	0.991587i	$-0.541320\pi$
$701$	−181.482			−0.258890			−0.129445	+	0.991587i	$0.541320\pi$
$702$		0			0
$703$	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
$708$		0			0
$709$		−	436.784i		−	0.616057i	−0.951377	−	0.308029i	$-0.900331\pi$
$709$		−	436.784i		−	0.616057i	0.951377	−	0.308029i	$-0.0996692\pi$
$710$	−115.606	−	438.294i	−0.162825	−	0.617316i
$711$		0			0
$712$	75.3825	+	75.3825i	0.105874	+	0.105874i
$713$	6.96828	−	6.96828i	0.00977318	−	0.00977318i
$714$		0			0
$715$	−581.041	+	153.257i	−0.812645	+	0.214345i
$716$	132.990			0.185740
$717$		0			0
$718$	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
$723$		0			0
$724$		−	67.0361i		−	0.0925913i
$725$	243.947	−	138.311i	0.336479	−	0.190773i
$726$		0			0
$727$	−377.156	−	377.156i	−0.518783	−	0.518783i	0.398420	−	0.917203i	$-0.369559\pi$
$727$	−377.156	−	377.156i	−0.518783	−	0.518783i	−0.917203	+	0.398420i	$0.869559\pi$
$728$	45.1398	−	45.1398i	0.0620053	−	0.0620053i
$729$		0			0
$730$	−444.480	−	258.943i	−0.608877	−	0.354717i
$731$	−891.609			−1.21971
$732$		0			0
$733$	−100.250	+	100.250i	−0.136767	+	0.136767i	−0.772176	−	0.635409i	$-0.780832\pi$
$733$	−100.250	+	100.250i	−0.136767	+	0.136767i	0.635409	+	0.772176i	$0.280832\pi$
$734$		−	44.0019i		−	0.0599481i
$735$		0			0
$736$	−3.38795			−0.00460320
$737$	1017.24	+	1017.24i	1.38025	+	1.38025i
$738$		0			0
$739$			606.576i			0.820806i	0.911904	+	0.410403i	$0.134612\pi$
$739$			606.576i			0.820806i	−0.911904	+	0.410403i	$0.865388\pi$
$740$	−651.798	+	171.920i	−0.880808	+	0.232324i
$741$		0			0
$742$	69.6970	+	69.6970i	0.0939312	+	0.0939312i
$743$	345.903	−	345.903i	0.465549	−	0.465549i	−0.434920	−	0.900469i	$-0.643223\pi$
$743$	345.903	−	345.903i	0.465549	−	0.465549i	0.900469	+	0.434920i	$0.143223\pi$
$744$		0			0
$745$	−345.174	+	592.497i	−0.463321	+	0.795298i
$746$	341.946			0.458373
$747$		0			0
$748$	−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
$753$		0			0
$754$		−	135.325i		−	0.179476i
$755$	−854.525	−	497.826i	−1.13182	−	0.659372i
$756$		0			0
$757$	−6.94517	−	6.94517i	−0.00917460	−	0.00917460i	0.702505	−	0.711679i	$-0.252065\pi$
$757$	−6.94517	−	6.94517i	−0.00917460	−	0.00917460i	−0.711679	+	0.702505i	$0.752065\pi$
$758$	−272.520	+	272.520i	−0.359525	+	0.359525i
$759$		0			0
$760$	−78.2039	−	296.494i	−0.102900	−	0.390123i
$761$	−977.803			−1.28489			−0.642446	−	0.766331i	$-0.722080\pi$
$761$	−977.803			−1.28489			−0.642446	+	0.766331i	$0.722080\pi$
$762$		0			0
$763$	−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
$768$		0			0
$769$			821.202i			1.06788i	0.845521	+	0.533942i	$0.179290\pi$
$769$			821.202i			1.06788i	−0.845521	+	0.533942i	$0.820710\pi$
$770$	−132.676	+	227.741i	−0.172307	+	0.295767i
$771$		0			0
$772$	−495.869	−	495.869i	−0.642317	−	0.642317i
$773$	−433.236	+	433.236i	−0.560460	+	0.560460i	−0.929438	−	0.368978i	$-0.879708\pi$
$773$	−433.236	+	433.236i	−0.560460	+	0.560460i	0.368978	+	0.929438i	$0.379708\pi$
$774$		0			0
$775$	−202.886	−	357.843i	−0.261788	−	0.461732i
$776$	388.876			0.501128
$777$		0			0
$778$	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
$783$		0			0
$784$		−	28.0000i		−	0.0357143i
$785$	−324.439	−	1230.04i	−0.413298	−	1.56693i
$786$		0			0
$787$	427.998	+	427.998i	0.543835	+	0.543835i	0.924651	−	0.380816i	$-0.124357\pi$
$787$	427.998	+	427.998i	0.543835	+	0.543835i	−0.380816	+	0.924651i	$0.624357\pi$
$788$	−28.6785	+	28.6785i	−0.0363940	+	0.0363940i
$789$		0			0
$790$	−1076.57	+	283.960i	−1.36275	+	0.359443i
$791$	532.036			0.672612
$792$		0			0
$793$	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	0.602263	−	0.798298i	$-0.294266\pi$
$797$	−156.240	−	156.240i	−0.196035	−	0.196035i	−0.798298	+	0.602263i	$0.794266\pi$
$798$		0			0
$799$			388.316i			0.486003i
$800$	−37.6697	+	136.312i	−0.0470871	+	0.170390i
$801$		0			0
$802$	−523.505	−	523.505i	−0.652749	−	0.652749i
$803$	724.715	−	724.715i	0.902510	−	0.902510i
$804$		0			0
$805$	6.84584	+	3.98822i	0.00850415	+	0.00495431i
$806$	−198.506			−0.246286
$807$		0			0
$808$	−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
$813$		0			0
$814$		−	1343.05i		−	1.64994i
$815$	−133.064	+	35.0973i	−0.163269	+	0.0430641i
$816$		0			0
$817$	1012.68	+	1012.68i	1.23951	+	1.23951i
$818$	−39.5511	+	39.5511i	−0.0483509	+	0.0483509i
$819$		0			0
$820$	−221.679	+	380.516i	−0.270340	+	0.464043i
$821$	372.833			0.454121			0.227060	−	0.973881i	$-0.427089\pi$
$821$	372.833			0.454121			0.227060	+	0.973881i	$0.427089\pi$
$822$		0			0
$823$	−514.145	+	514.145i	−0.624721	+	0.624721i	−0.946735	−	0.322014i	$-0.895640\pi$
$823$	−514.145	+	514.145i	−0.624721	+	0.624721i	0.322014	+	0.946735i	$0.395640\pi$
$824$		−	211.821i		−	0.257064i
$825$		0			0
$826$	−50.4278			−0.0610506
$827$	389.845	+	389.845i	0.471397	+	0.471397i	0.902366	−	0.430970i	$-0.141828\pi$
$827$	389.845	+	389.845i	0.471397	+	0.471397i	−0.430970	+	0.902366i	$0.641828\pi$
$828$		0			0
$829$		−	1442.33i		−	1.73984i	−0.493194	−	0.869919i	$-0.664171\pi$
$829$		−	1442.33i		−	1.73984i	0.493194	−	0.869919i	$-0.335829\pi$
$830$	−665.305	−	387.590i	−0.801572	−	0.466976i
$831$		0			0
$832$	48.2565	+	48.2565i	0.0580006	+	0.0580006i
$833$	−66.8154	+	66.8154i	−0.0802106	+	0.0802106i
$834$		0			0
$835$	141.211	+	535.371i	0.169115	+	0.641163i
$836$	610.936			0.730785
$837$		0			0
$838$	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
$843$		0			0
$844$			417.183i			0.494292i
$845$	−242.198	+	415.737i	−0.286625	+	0.491997i
$846$		0			0
$847$	−144.956	−	144.956i	−0.171140	−	0.171140i
$848$	−74.5092	+	74.5092i	−0.0878646	+	0.0878646i
$849$		0			0
$850$	415.167	−	235.387i	0.488432	−	0.276926i
$851$	−40.3720			−0.0474406
$852$		0			0
$853$	842.879	−	842.879i	0.988135	−	0.988135i	−0.0117957	−	0.999930i	$-0.503755\pi$
$853$	842.879	−	842.879i	0.988135	−	0.988135i	0.999930	+	0.0117957i	$0.00375478\pi$
$854$		−	40.6897i		−	0.0476460i
$855$		0			0
$856$	327.006			0.382017
$857$	655.750	+	655.750i	0.765169	+	0.765169i	0.977252	−	0.212083i	$-0.0680246\pi$
$857$	655.750	+	655.750i	0.765169	+	0.765169i	−0.212083	+	0.977252i	$0.568025\pi$
$858$		0			0
$859$			800.197i			0.931545i	0.884904	+	0.465773i	$0.154223\pi$
$859$			800.197i			0.931545i	−0.884904	+	0.465773i	$0.845777\pi$
$860$	−168.457	−	638.669i	−0.195880	−	0.742638i
$861$		0			0
$862$	323.054	+	323.054i	0.374772	+	0.374772i
$863$	112.663	−	112.663i	0.130549	−	0.130549i	−0.638813	−	0.769362i	$-0.720574\pi$
$863$	112.663	−	112.663i	0.130549	−	0.130549i	0.769362	+	0.638813i	$0.220574\pi$
$864$		0			0
$865$	−457.768	+	120.742i	−0.529211	+	0.139586i
$866$	−153.489			−0.177239
$867$		0			0
$868$	−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
$873$		0			0
$874$		−	18.3646i		−	0.0210122i
$875$	236.581	−	231.094i	0.270378	−	0.264108i
$876$		0			0
$877$	9.31315	+	9.31315i	0.0106193	+	0.0106193i	0.712397	−	0.701777i	$-0.247610\pi$
$877$	9.31315	+	9.31315i	0.0106193	+	0.0106193i	−0.701777	+	0.712397i	$0.747610\pi$
$878$	−864.627	+	864.627i	−0.984768	+	0.984768i
$879$		0			0
$880$	−243.465	−	141.837i	−0.276665	−	0.161178i
$881$	59.1359			0.0671236			0.0335618	−	0.999437i	$-0.489315\pi$
$881$	59.1359			0.0671236			0.0335618	+	0.999437i	$0.489315\pi$
$882$		0			0
$883$	77.6453	−	77.6453i	0.0879335	−	0.0879335i	−0.661772	−	0.749705i	$-0.730195\pi$
$883$	77.6453	−	77.6453i	0.0879335	−	0.0879335i	0.749705	+	0.661772i	$0.230195\pi$
$884$		−	230.306i		−	0.260527i
$885$		0			0
$886$	−653.663			−0.737768
$887$	176.382	+	176.382i	0.198852	+	0.198852i	0.799508	−	0.600656i	$-0.205094\pi$
$887$	176.382	+	176.382i	0.198852	+	0.198852i	−0.600656	+	0.799508i	$0.705094\pi$
$888$		0			0
$889$			356.623i			0.401151i
$890$	257.704	−	67.9726i	0.289555	−	0.0763737i
$891$		0			0
$892$	−410.372	−	410.372i	−0.460059	−	0.460059i
$893$	441.044	−	441.044i	0.493890	−	0.493890i
$894$		0			0
$895$	167.362	−	287.279i	0.186996	−	0.320982i
$896$	29.9333			0.0334077
$897$		0			0
$898$	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
$903$		0			0
$904$			568.771i			0.629171i
$905$	−144.809	−	84.3620i	−0.160009	−	0.0932176i
$906$		0			0
$907$	−626.216	−	626.216i	−0.690425	−	0.690425i	0.271900	−	0.962326i	$-0.412348\pi$
$907$	−626.216	−	626.216i	−0.690425	−	0.690425i	−0.962326	+	0.271900i	$0.912348\pi$
$908$	632.100	−	632.100i	0.696145	−	0.696145i
$909$		0			0
$910$	−40.7027	−	154.316i	−0.0447283	−	0.169578i
$911$	969.279			1.06397			0.531986	−	0.846753i	$-0.321446\pi$
$911$	969.279			1.06397			0.531986	+	0.846753i	$0.321446\pi$
$912$		0			0
$913$	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
$918$		0			0
$919$			581.291i			0.632526i	0.948672	+	0.316263i	$0.102428\pi$
$919$			581.291i			0.632526i	−0.948672	+	0.316263i	$0.897572\pi$
$920$	−4.26359	+	7.31852i	−0.00463434	+	0.00795491i
$921$		0			0
$922$	−560.524	−	560.524i	−0.607944	−	0.607944i
$923$	−386.680	+	386.680i	−0.418938	+	0.418938i
$924$		0			0
$925$	−448.885	+	1624.34i	−0.485281	+	1.75604i
$926$	−558.205			−0.602814
$927$		0			0
$928$	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
$933$		0			0
$934$			402.505i			0.430948i
$935$	242.512	+	919.432i	0.259371	+	0.983350i
$936$		0			0
$937$	448.839	+	448.839i	0.479017	+	0.479017i	0.904817	−	0.425800i	$-0.140007\pi$
$937$	448.839	+	448.839i	0.479017	+	0.479017i	−0.425800	+	0.904817i	$0.640007\pi$
$938$	−270.165	+	270.165i	−0.288022	+	0.288022i
$939$		0			0
$940$	−278.155	+	73.3669i	−0.295909	+	0.0780499i
$941$	10.8693			0.0115508			0.00577540	−	0.999983i	$-0.498162\pi$
$941$	10.8693			0.0115508			0.00577540	+	0.999983i	$0.498162\pi$
$942$		0			0
$943$	−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	0.815349	−	0.578970i	$-0.196545\pi$
$947$	223.851	+	223.851i	0.236379	+	0.236379i	−0.578970	+	0.815349i	$0.696545\pi$
$948$		0			0
$949$			620.587i			0.653938i
$950$	−738.890	−	204.191i	−0.777779	−	0.214938i
$951$		0			0
$952$	−71.4287	−	71.4287i	−0.0750302	−	0.0750302i
$953$	−732.839	+	732.839i	−0.768981	+	0.768981i	−0.977927	−	0.208946i	$-0.932997\pi$
$953$	−732.839	+	732.839i	−0.768981	+	0.768981i	0.208946	+	0.977927i	$0.432997\pi$
$954$		0			0
$955$	906.734	+	528.241i	0.949460	+	0.553132i
$956$	294.982			0.308559
$957$		0			0
$958$	−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
$963$		0			0
$964$		−	360.364i		−	0.373821i
$965$	−1695.18	+	447.126i	−1.75667	+	0.463343i
$966$		0			0
$967$	−334.532	−	334.532i	−0.345948	−	0.345948i	0.512650	−	0.858598i	$-0.328664\pi$
$967$	−334.532	−	334.532i	−0.345948	−	0.345948i	−0.858598	+	0.512650i	$0.828664\pi$
$968$	154.964	−	154.964i	0.160087	−	0.160087i
$969$		0			0
$970$	489.383	−	840.033i	0.504518	−	0.866013i
$971$	−922.031			−0.949569			−0.474784	−	0.880102i	$-0.657474\pi$
$971$	−922.031			−0.949569			−0.474784	+	0.880102i	$0.657474\pi$
$972$		0			0
$973$	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	0.707049	−	0.707164i	$-0.250026\pi$
$977$	−0.111963	−	0.111963i	−0.000114599	−	0.000114599i	−0.707164	+	0.707049i	$0.750026\pi$
$978$		0			0
$979$			531.008i			0.542399i
$980$	−60.4845	−	35.2368i	−0.0617188	−	0.0359559i
$981$		0			0
$982$	714.606	+	714.606i	0.727704	+	0.727704i
$983$	631.195	−	631.195i	0.642111	−	0.642111i	−0.308963	−	0.951074i	$-0.599982\pi$
$983$	631.195	−	631.195i	0.642111	−	0.642111i	0.951074	+	0.308963i	$0.0999820\pi$
$984$		0			0
$985$	25.8595	+	98.0408i	0.0262533	+	0.0995338i
$986$	−214.137			−0.217177
$987$		0			0
$988$	−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
$993$		0			0
$994$			239.855i			0.241303i
$995$	711.283	−	1220.93i	0.714857	−	1.22706i
$996$		0			0
$997$	−365.331	−	365.331i	−0.366430	−	0.366430i	0.499743	−	0.866174i	$-0.333428\pi$
$997$	−365.331	−	365.331i	−0.366430	−	0.366430i	−0.866174	+	0.499743i	$0.833428\pi$
$998$	746.370	−	746.370i	0.747866	−	0.747866i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.l.a.43.1	✓	8	15.8	even	4
210.3.l.a.127.1	yes	8	3.2	odd	2
630.3.o.b.127.4		8	1.1	even	1	trivial
630.3.o.b.253.4		8	5.3	odd	4	inner
1050.3.l.b.43.4		8	15.2	even	4
1050.3.l.b.757.4		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} +(4.32032 + 2.51691i) q^{5} +(-1.87083 - 1.87083i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.80341 - 6.83723i) q^{10} +14.0884 q^{11} +(-6.03207 + 6.03207i) q^{13} +3.74166i q^{14} -4.00000 q^{16} +(9.54506 + 9.54506i) q^{17} -21.6823i q^{19} +(-5.03383 + 8.64064i) q^{20} +(-14.0884 - 14.0884i) q^{22} +(-0.423494 + 0.423494i) q^{23} +(12.3303 + 21.7477i) q^{25} +12.0641 q^{26} +(3.74166 - 3.74166i) q^{28} -11.2171i q^{29} -16.4543 q^{31} +(4.00000 + 4.00000i) q^{32} -19.0901i q^{34} +(-3.37386 - 12.7913i) q^{35} +(47.6653 + 47.6653i) q^{37} +(-21.6823 + 21.6823i) q^{38} +(13.6745 - 3.60681i) q^{40} +44.0379 q^{41} +(-46.7052 + 46.7052i) q^{43} +28.1767i q^{44} +0.846988 q^{46} +(20.3412 + 20.3412i) q^{47} +7.00000i q^{49} +(9.41742 - 34.0780i) q^{50} +(-12.0641 - 12.0641i) q^{52} +(18.6273 - 18.6273i) q^{53} +(60.8662 + 35.4592i) q^{55} -7.48331 q^{56} +(-11.2171 + 11.2171i) q^{58} +13.4774i q^{59} -10.8748 q^{61} +(16.4543 + 16.4543i) q^{62} -8.00000i q^{64} +(-41.2426 + 10.8783i) q^{65} +(72.2045 + 72.2045i) q^{67} +(-19.0901 + 19.0901i) q^{68} +(-9.41742 + 16.1652i) q^{70} +64.1040 q^{71} +(51.4407 - 51.4407i) q^{73} -95.3307i q^{74} +43.3646 q^{76} +(-26.3569 - 26.3569i) q^{77} -157.457i q^{79} +(-17.2813 - 10.0677i) q^{80} +(-44.0379 - 44.0379i) q^{82} +(76.9972 - 76.9972i) q^{83} +(17.2136 + 65.2618i) q^{85} +93.4104 q^{86} +(28.1767 - 28.1767i) q^{88} +37.6912i q^{89} +22.5699 q^{91} +(-0.846988 - 0.846988i) q^{92} -40.6824i q^{94} +(54.5724 - 93.6744i) q^{95} +(97.2189 + 97.2189i) q^{97} +(7.00000 - 7.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 16 * q^8	\( 8 q - 8 q^{2} + 16 q^{8} + 8 q^{11} + 8 q^{13} - 32 q^{16} + 32 q^{17} - 8 q^{22} + 40 q^{23} - 48 q^{25} - 16 q^{26} + 144 q^{31} + 32 q^{32} + 28 q^{35} + 160 q^{37} + 320 q^{41} - 32 q^{43} - 80 q^{46} + 144 q^{47} + 112 q^{50} + 16 q^{52} + 200 q^{53} + 184 q^{55} - 64 q^{58} + 288 q^{61} - 144 q^{62} - 24 q^{65} + 80 q^{67} - 64 q^{68} - 112 q^{70} + 280 q^{71} + 312 q^{73} + 56 q^{77} - 320 q^{82} + 320 q^{83} + 80 q^{85} + 64 q^{86} + 16 q^{88} + 80 q^{92} + 472 q^{95} - 24 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 16 * q^8 + 8 * q^11 + 8 * q^13 - 32 * q^16 + 32 * q^17 - 8 * q^22 + 40 * q^23 - 48 * q^25 - 16 * q^26 + 144 * q^31 + 32 * q^32 + 28 * q^35 + 160 * q^37 + 320 * q^41 - 32 * q^43 - 80 * q^46 + 144 * q^47 + 112 * q^50 + 16 * q^52 + 200 * q^53 + 184 * q^55 - 64 * q^58 + 288 * q^61 - 144 * q^62 - 24 * q^65 + 80 * q^67 - 64 * q^68 - 112 * q^70 + 280 * q^71 + 312 * q^73 + 56 * q^77 - 320 * q^82 + 320 * q^83 + 80 * q^85 + 64 * q^86 + 16 * q^88 + 80 * q^92 + 472 * q^95 - 24 * q^97 + 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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