LMFDB - Embedded newform 630.3.v.b.451.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(271,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("630.271");

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.v (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.3
Root			$-1.72286 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.b.271.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(5.79240 - 10.0327i) q^{11} -7.86371i q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-23.9080 - 13.8033i) q^{17} +(27.2149 - 15.7125i) q^{19} -4.47214i q^{20} +16.3834 q^{22} +(9.07959 + 15.7263i) q^{23} +(2.50000 - 4.33013i) q^{25} +(9.63104 - 5.56049i) q^{26} +(-2.08911 + 13.8433i) q^{28} +2.30331 q^{29} +(-4.55860 - 2.63191i) q^{31} +(2.82843 - 4.89898i) q^{32} -39.0416i q^{34} +(-9.76139 + 12.2358i) q^{35} +(-0.993142 - 1.72017i) q^{37} +(38.4876 + 22.2208i) q^{38} +(5.47723 - 3.16228i) q^{40} +22.1905i q^{41} +49.8368 q^{43} +(11.5848 + 20.0655i) q^{44} +(-12.8405 + 22.2404i) q^{46} +(66.3956 - 38.3335i) q^{47} +(35.9317 - 33.3154i) q^{49} +7.07107 q^{50} +(13.6204 + 7.86371i) q^{52} +(28.5477 - 49.4461i) q^{53} +25.9044i q^{55} +(-18.4317 + 7.23003i) q^{56} +(1.62869 + 2.82097i) q^{58} +(60.9245 + 35.1748i) q^{59} +(-58.5590 + 33.8091i) q^{61} -7.44416i q^{62} +8.00000 q^{64} +(8.79190 + 15.2280i) q^{65} +(-49.0823 + 85.0131i) q^{67} +(47.8160 - 27.6066i) q^{68} +(-21.8881 - 3.30318i) q^{70} +34.2597 q^{71} +(16.8801 + 9.74573i) q^{73} +(1.40452 - 2.43269i) q^{74} +62.8501i q^{76} +(12.1010 - 80.1856i) q^{77} +(-45.2142 - 78.3134i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-27.1777 + 15.6911i) q^{82} -133.803i q^{83} +61.7302 q^{85} +(35.2400 + 61.0374i) q^{86} +(-16.3834 + 28.3768i) q^{88} +(9.58232 - 5.53235i) q^{89} +(-20.1012 - 51.2445i) q^{91} -36.3184 q^{92} +(93.8975 + 54.2118i) q^{94} +(-35.1342 + 60.8543i) q^{95} -72.3112i q^{97} +(66.2104 + 20.4496i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$5$	−1.93649	+	1.11803i	−0.387298	+	0.223607i
$6$		0			0
$7$	6.51658	−	2.55620i	0.930940	−	0.365172i
$7$	6.51658	−	2.55620i	0.930940	−	0.365172i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	−2.73861	−	1.58114i	−0.273861	−	0.158114i
$11$	5.79240	−	10.0327i	0.526582	−	0.912066i	−0.472939	−	0.881095i	$-0.656807\pi$
$11$	5.79240	−	10.0327i	0.526582	−	0.912066i	0.999520	−	0.0309707i	$-0.00985985\pi$
$12$		0			0
$13$		−	7.86371i		−	0.604901i	−0.953165	−	0.302451i	$-0.902195\pi$
$13$		−	7.86371i		−	0.604901i	0.953165	−	0.302451i	$-0.0978047\pi$
$14$	7.73861	+	6.17364i	0.552758	+	0.440975i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−23.9080	−	13.8033i	−1.40635	−	0.811959i	−0.411320	−	0.911491i	$-0.634932\pi$
$17$	−23.9080	−	13.8033i	−1.40635	−	0.811959i	−0.995034	+	0.0995321i	$0.968265\pi$
$18$		0			0
$19$	27.2149	−	15.7125i	1.43236	−	0.826974i	0.435061	−	0.900401i	$-0.356727\pi$
$19$	27.2149	−	15.7125i	1.43236	−	0.826974i	0.997301	+	0.0734266i	$0.0233935\pi$
$20$		−	4.47214i		−	0.223607i
$21$		0			0
$22$	16.3834			0.744699
$23$	9.07959	+	15.7263i	0.394765	+	0.683753i	0.993071	−	0.117515i	$-0.0374927\pi$
$23$	9.07959	+	15.7263i	0.394765	+	0.683753i	−0.598306	+	0.801268i	$0.704159\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	9.63104	−	5.56049i	0.370425	−	0.213865i
$27$		0			0
$28$	−2.08911	+	13.8433i	−0.0746112	+	0.494402i
$29$	2.30331			0.0794244			0.0397122	−	0.999211i	$-0.487356\pi$
$29$	2.30331			0.0794244			0.0397122	+	0.999211i	$0.487356\pi$
$30$		0			0
$31$	−4.55860	−	2.63191i	−0.147052	−	0.0849003i	0.424669	−	0.905349i	$-0.360391\pi$
$31$	−4.55860	−	2.63191i	−0.147052	−	0.0849003i	−0.571721	+	0.820448i	$0.693724\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	39.0416i		−	1.14828i
$35$	−9.76139	+	12.2358i	−0.278897	+	0.349595i
$36$		0			0
$37$	−0.993142	−	1.72017i	−0.0268417	−	0.0464912i	0.852293	−	0.523065i	$-0.175212\pi$
$37$	−0.993142	−	1.72017i	−0.0268417	−	0.0464912i	−0.879134	+	0.476574i	$0.841878\pi$
$38$	38.4876	+	22.2208i	1.01283	+	0.584759i
$39$		0			0
$40$	5.47723	−	3.16228i	0.136931	−	0.0790569i
$41$			22.1905i			0.541233i	0.962687	+	0.270616i	$0.0872275\pi$
$41$			22.1905i			0.541233i	−0.962687	+	0.270616i	$0.912773\pi$
$42$		0			0
$43$	49.8368			1.15900			0.579498	−	0.814974i	$-0.303249\pi$
$43$	49.8368			1.15900			0.579498	+	0.814974i	$0.303249\pi$
$44$	11.5848	+	20.0655i	0.263291	+	0.456033i
$45$		0			0
$46$	−12.8405	+	22.2404i	−0.279141	+	0.483486i
$47$	66.3956	−	38.3335i	1.41267	−	0.815606i	0.417032	−	0.908892i	$-0.363070\pi$
$47$	66.3956	−	38.3335i	1.41267	−	0.815606i	0.995639	+	0.0932854i	$0.0297369\pi$
$48$		0			0
$49$	35.9317	−	33.3154i	0.733300	−	0.679906i
$50$	7.07107			0.141421
$51$		0			0
$52$	13.6204	+	7.86371i	0.261930	+	0.151225i
$53$	28.5477	−	49.4461i	0.538636	−	0.932945i	−0.460342	−	0.887742i	$-0.652273\pi$
$53$	28.5477	−	49.4461i	0.538636	−	0.932945i	0.998978	−	0.0452033i	$-0.0143935\pi$
$54$		0			0
$55$			25.9044i			0.470989i
$56$	−18.4317	+	7.23003i	−0.329137	+	0.129108i
$57$		0			0
$58$	1.62869	+	2.82097i	0.0280808	+	0.0486373i
$59$	60.9245	+	35.1748i	1.03262	+	0.596182i	0.917734	−	0.397196i	$-0.130017\pi$
$59$	60.9245	+	35.1748i	1.03262	+	0.596182i	0.114885	+	0.993379i	$0.463350\pi$
$60$		0			0
$61$	−58.5590	+	33.8091i	−0.959984	+	0.554247i	−0.896168	−	0.443715i	$-0.853660\pi$
$61$	−58.5590	+	33.8091i	−0.959984	+	0.554247i	−0.0638160	+	0.997962i	$0.520327\pi$
$62$		−	7.44416i		−	0.120067i
$63$		0			0
$64$	8.00000			0.125000
$65$	8.79190	+	15.2280i	0.135260	+	0.234277i
$66$		0			0
$67$	−49.0823	+	85.0131i	−0.732572	+	1.26885i	0.223208	+	0.974771i	$0.428347\pi$
$67$	−49.0823	+	85.0131i	−0.732572	+	1.26885i	−0.955780	+	0.294081i	$0.904986\pi$
$68$	47.8160	−	27.6066i	0.703177	−	0.405979i
$69$		0			0
$70$	−21.8881	−	3.30318i	−0.312687	−	0.0471882i
$71$	34.2597			0.482531			0.241266	−	0.970459i	$-0.422437\pi$
$71$	34.2597			0.482531			0.241266	+	0.970459i	$0.422437\pi$
$72$		0			0
$73$	16.8801	+	9.74573i	0.231234	+	0.133503i	0.611141	−	0.791521i	$-0.290711\pi$
$73$	16.8801	+	9.74573i	0.231234	+	0.133503i	−0.379907	+	0.925025i	$0.624044\pi$
$74$	1.40452	−	2.43269i	0.0189799	−	0.0328742i
$75$		0			0
$76$			62.8501i			0.826974i
$77$	12.1010	−	80.1856i	0.157155	−	1.04137i
$78$		0			0
$79$	−45.2142	−	78.3134i	−0.572332	−	0.991308i	−0.996326	−	0.0856432i	$-0.972705\pi$
$79$	−45.2142	−	78.3134i	−0.572332	−	0.991308i	0.423994	−	0.905665i	$-0.360628\pi$
$80$	7.74597	+	4.47214i	0.0968246	+	0.0559017i
$81$		0			0
$82$	−27.1777	+	15.6911i	−0.331436	+	0.191355i
$83$		−	133.803i		−	1.61209i	−0.591854	−	0.806045i	$-0.701604\pi$
$83$		−	133.803i		−	1.61209i	0.591854	−	0.806045i	$-0.298396\pi$
$84$		0			0
$85$	61.7302			0.726238
$86$	35.2400	+	61.0374i	0.409767	+	0.709737i
$87$		0			0
$88$	−16.3834	+	28.3768i	−0.186175	+	0.322464i
$89$	9.58232	−	5.53235i	0.107666	−	0.0621613i	−0.445200	−	0.895431i	$-0.646867\pi$
$89$	9.58232	−	5.53235i	0.107666	−	0.0621613i	0.552866	+	0.833270i	$0.313534\pi$
$90$		0			0
$91$	−20.1012	−	51.2445i	−0.220893	−	0.563127i
$92$	−36.3184			−0.394765
$93$		0			0
$94$	93.8975	+	54.2118i	0.998910	+	0.576721i
$95$	−35.1342	+	60.8543i	−0.369834	+	0.640572i
$96$		0			0
$97$		−	72.3112i		−	0.745476i	−0.927937	−	0.372738i	$-0.878419\pi$
$97$		−	72.3112i		−	0.745476i	0.927937	−	0.372738i	$-0.121581\pi$
$98$	66.2104	+	20.4496i	0.675616	+	0.208669i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−43.8670	−	25.3266i	−0.434327	−	0.250759i	0.266861	−	0.963735i	$-0.414013\pi$
$101$	−43.8670	−	25.3266i	−0.434327	−	0.250759i	−0.701188	+	0.712976i	$0.747347\pi$
$102$		0			0
$103$	−171.442	+	98.9823i	−1.66449	+	0.960993i	−0.693958	+	0.720015i	$0.744135\pi$
$103$	−171.442	+	98.9823i	−1.66449	+	0.960993i	−0.970531	+	0.240978i	$0.922532\pi$
$104$			22.2419i			0.213865i
$105$		0			0
$106$	80.7451			0.761746
$107$	73.9679	+	128.116i	0.691289	+	1.19735i	0.971416	+	0.237384i	$0.0762900\pi$
$107$	73.9679	+	128.116i	0.691289	+	1.19735i	−0.280127	+	0.959963i	$0.590377\pi$
$108$		0			0
$109$	27.1610	−	47.0442i	0.249183	−	0.431598i	−0.714116	−	0.700027i	$-0.753171\pi$
$109$	27.1610	−	47.0442i	0.249183	−	0.431598i	0.963299	+	0.268429i	$0.0865046\pi$
$110$	−31.7263	+	18.3172i	−0.288421	+	0.166520i
$111$		0			0
$112$	−21.8881	−	17.4617i	−0.195429	−	0.155908i
$113$	−47.7883			−0.422906			−0.211453	−	0.977388i	$-0.567819\pi$
$113$	−47.7883			−0.422906			−0.211453	+	0.977388i	$0.567819\pi$
$114$		0			0
$115$	−35.1651	−	20.3026i	−0.305784	−	0.176544i
$116$	−2.30331	+	3.98945i	−0.0198561	+	0.0343918i
$117$		0			0
$118$			99.4892i			0.843129i
$119$	−191.083	−	28.8367i	−1.60574	−	0.242325i
$120$		0			0
$121$	−6.60372	−	11.4380i	−0.0545762	−	0.0945288i
$122$	−82.8150	−	47.8132i	−0.678811	−	0.391912i
$123$		0			0
$124$	9.11720	−	5.26382i	0.0735258	−	0.0424501i
$125$			11.1803i			0.0894427i
$126$		0			0
$127$	−101.973			−0.802940			−0.401470	−	0.915872i	$-0.631501\pi$
$127$	−101.973			−0.802940			−0.401470	+	0.915872i	$0.631501\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−12.4336	+	21.5357i	−0.0956433	+	0.165659i
$131$	64.6037	−	37.2990i	0.493158	−	0.284725i	−0.232726	−	0.972542i	$-0.574764\pi$
$131$	64.6037	−	37.2990i	0.493158	−	0.284725i	0.725884	+	0.687817i	$0.241431\pi$
$132$		0			0
$133$	137.184	−	171.959i	1.03146	−	1.29292i
$134$	−138.826			−1.03601
$135$		0			0
$136$	67.6221	+	39.0416i	0.497221	+	0.287071i
$137$	−123.449	+	213.821i	−0.901091	+	1.56074i	−0.0750109	+	0.997183i	$0.523899\pi$
$137$	−123.449	+	213.821i	−0.901091	+	1.56074i	−0.826080	+	0.563553i	$0.809434\pi$
$138$		0			0
$139$		−	155.917i		−	1.12170i	−0.827916	−	0.560852i	$-0.810474\pi$
$139$		−	155.917i		−	1.12170i	0.827916	−	0.560852i	$-0.189526\pi$
$140$	−11.4317	−	29.1430i	−0.0816548	−	0.208165i
$141$		0			0
$142$	24.2253	+	41.9594i	0.170601	+	0.295489i
$143$	−78.8945	−	45.5498i	−0.551710	−	0.318530i
$144$		0			0
$145$	−4.46034	+	2.57518i	−0.0307609	+	0.0177598i
$146$			27.5651i			0.188802i
$147$		0			0
$148$	3.97257			0.0268417
$149$	81.5452	+	141.240i	0.547283	+	0.947922i	0.998459	+	0.0554872i	$0.0176712\pi$
$149$	81.5452	+	141.240i	0.547283	+	0.947922i	−0.451176	+	0.892435i	$0.648995\pi$
$150$		0			0
$151$	37.5149	−	64.9778i	0.248443	−	0.430316i	−0.714651	−	0.699481i	$-0.753414\pi$
$151$	37.5149	−	64.9778i	0.248443	−	0.430316i	0.963094	+	0.269165i	$0.0867477\pi$
$152$	−76.9753	+	44.4417i	−0.506416	+	0.292380i
$153$		0			0
$154$	106.764	−	41.8792i	0.693270	−	0.271943i
$155$	11.7703			0.0759371
$156$		0			0
$157$	−194.622	−	112.365i	−1.23963	−	0.715702i	−0.270614	−	0.962688i	$-0.587227\pi$
$157$	−194.622	−	112.365i	−1.23963	−	0.715702i	−0.969019	+	0.246986i	$0.920560\pi$
$158$	63.9426	−	110.752i	0.404700	−	0.700961i
$159$		0			0
$160$			12.6491i			0.0790569i
$161$	99.3675	+	79.2726i	0.617190	+	0.492376i
$162$		0			0
$163$	115.059	+	199.288i	0.705882	+	1.22262i	0.966372	+	0.257147i	$0.0827823\pi$
$163$	115.059	+	199.288i	0.705882	+	1.22262i	−0.260491	+	0.965476i	$0.583884\pi$
$164$	−38.4351	−	22.1905i	−0.234361	−	0.135308i
$165$		0			0
$166$	163.875	−	94.6133i	0.987199	−	0.569960i
$167$		−	277.788i		−	1.66340i	−0.555223	−	0.831702i	$-0.687367\pi$
$167$		−	277.788i		−	1.66340i	0.555223	−	0.831702i	$-0.312633\pi$
$168$		0			0
$169$	107.162			0.634095
$170$	43.6499	+	75.6038i	0.256764	+	0.444728i
$171$		0			0
$172$	−49.8368	+	86.3199i	−0.289749	+	0.501860i
$173$	−109.176	+	63.0327i	−0.631074	+	0.364351i	−0.781168	−	0.624321i	$-0.785376\pi$
$173$	−109.176	+	63.0327i	−0.631074	+	0.364351i	0.150094	+	0.988672i	$0.452042\pi$
$174$		0			0
$175$	5.22278	−	34.6081i	0.0298445	−	0.197761i
$176$	−46.3392			−0.263291
$177$		0			0
$178$	13.5514	+	7.82393i	0.0761317	+	0.0439547i
$179$	38.5535	−	66.7766i	0.215382	−	0.373053i	−0.738008	−	0.674792i	$-0.764234\pi$
$179$	38.5535	−	66.7766i	0.215382	−	0.373053i	0.953391	+	0.301738i	$0.0975668\pi$
$180$		0			0
$181$			212.012i			1.17134i	0.810551	+	0.585668i	$0.199168\pi$
$181$			212.012i			1.17134i	−0.810551	+	0.585668i	$0.800832\pi$
$182$	48.5478	−	60.8542i	0.266746	−	0.334364i
$183$		0			0
$184$	−25.6810	−	44.4807i	−0.139570	−	0.241743i
$185$	3.84642	+	2.22073i	0.0207915	+	0.0120040i
$186$		0			0
$187$	−276.969	+	159.908i	−1.48112	+	0.855125i
$188$			153.334i			0.815606i
$189$		0			0
$190$	−99.3747			−0.523025
$191$	82.8480	+	143.497i	0.433759	+	0.751293i	0.997193	−	0.0748682i	$-0.0238536\pi$
$191$	82.8480	+	143.497i	0.433759	+	0.751293i	−0.563434	+	0.826161i	$0.690520\pi$
$192$		0			0
$193$	52.6497	−	91.1920i	0.272796	−	0.472497i	−0.696780	−	0.717285i	$-0.745385\pi$
$193$	52.6497	−	91.1920i	0.272796	−	0.472497i	0.969577	+	0.244787i	$0.0787181\pi$
$194$	88.5627	−	51.1317i	0.456509	−	0.263566i
$195$		0			0
$196$	21.7723	+	95.5509i	0.111083	+	0.487504i
$197$	−244.736			−1.24231			−0.621156	−	0.783687i	$-0.713337\pi$
$197$	−244.736			−1.24231			−0.621156	+	0.783687i	$0.713337\pi$
$198$		0			0
$199$	84.8416	+	48.9833i	0.426340	+	0.246147i	0.697786	−	0.716306i	$-0.254169\pi$
$199$	84.8416	+	48.9833i	0.426340	+	0.246147i	−0.271446	+	0.962454i	$0.587502\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$		0			0
$202$		−	71.6346i		−	0.354627i
$203$	15.0097	−	5.88772i	0.0739394	−	0.0290035i
$204$		0			0
$205$	−24.8098	−	42.9718i	−0.121023	−	0.209619i
$206$	−242.456	−	139.982i	−1.17697	−	0.679525i
$207$		0			0
$208$	−27.2407	+	15.7274i	−0.130965	+	0.0756126i
$209$		−	364.052i		−	1.74188i
$210$		0			0
$211$	−388.914			−1.84319			−0.921597	−	0.388149i	$-0.873114\pi$
$211$	−388.914			−1.84319			−0.921597	+	0.388149i	$0.873114\pi$
$212$	57.0954	+	98.8922i	0.269318	+	0.466473i
$213$		0			0
$214$	−104.606	+	181.184i	−0.488815	+	0.846652i
$215$	−96.5086	+	55.7193i	−0.448877	+	0.259159i
$216$		0			0
$217$	−36.4342	−	5.49835i	−0.167899	−	0.0253380i
$218$	76.8228			0.352398
$219$		0			0
$220$	−44.8677	−	25.9044i	−0.203944	−	0.117747i
$221$	−108.545	+	188.006i	−0.491155	+	0.850705i
$222$		0			0
$223$		−	251.913i		−	1.12965i	−0.825210	−	0.564827i	$-0.808943\pi$
$223$		−	251.913i		−	1.12965i	0.825210	−	0.564827i	$-0.191057\pi$
$224$	5.90890	−	39.1546i	0.0263790	−	0.174797i
$225$		0			0
$226$	−33.7915	−	58.5285i	−0.149520	−	0.258976i
$227$	−231.941	−	133.911i	−1.02176	−	0.589916i	−0.107150	−	0.994243i	$-0.534173\pi$
$227$	−231.941	−	133.911i	−1.02176	−	0.589916i	−0.914615	+	0.404327i	$0.867506\pi$
$228$		0			0
$229$	299.237	−	172.765i	1.30671	−	0.754431i	0.325167	−	0.945657i	$-0.394580\pi$
$229$	299.237	−	172.765i	1.30671	−	0.754431i	0.981546	+	0.191226i	$0.0612463\pi$
$230$		−	57.4244i		−	0.249671i
$231$		0			0
$232$	−6.51474			−0.0280808
$233$	−144.032	−	249.471i	−0.618164	−	1.07069i	−0.989821	−	0.142321i	$-0.954543\pi$
$233$	−144.032	−	249.471i	−0.618164	−	1.07069i	0.371656	−	0.928370i	$-0.378790\pi$
$234$		0			0
$235$	−85.7163	+	148.465i	−0.364750	+	0.631766i
$236$	−121.849	+	70.3495i	−0.516309	+	0.298091i
$237$		0			0
$238$	−99.7983	−	254.418i	−0.419320	−	1.06898i
$239$	188.810			0.789999			0.395000	−	0.918681i	$-0.370745\pi$
$239$	188.810			0.789999			0.395000	+	0.918681i	$0.370745\pi$
$240$		0			0
$241$	84.7389	+	48.9240i	0.351614	+	0.203004i	0.665396	−	0.746491i	$-0.268263\pi$
$241$	84.7389	+	48.9240i	0.351614	+	0.203004i	−0.313782	+	0.949495i	$0.601596\pi$
$242$	9.33908	−	16.1758i	0.0385912	−	0.0668420i
$243$		0			0
$244$		−	135.236i		−	0.554247i
$245$	−32.3337	+	104.688i	−0.131974	+	0.427297i
$246$		0			0
$247$	−123.559	−	214.010i	−0.500238	−	0.866437i
$248$	12.8937	+	7.44416i	0.0519906	+	0.0300168i
$249$		0			0
$250$	−13.6931	+	7.90569i	−0.0547723	+	0.0316228i
$251$		−	241.345i		−	0.961533i	−0.876849	−	0.480767i	$-0.840358\pi$
$251$		−	241.345i		−	0.961533i	0.876849	−	0.480767i	$-0.159642\pi$
$252$		0			0
$253$	210.370			0.831504
$254$	−72.1061	−	124.891i	−0.283882	−	0.491698i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	10.8807	−	6.28197i	0.0423373	−	0.0244435i	−0.478682	−	0.877988i	$-0.658885\pi$
$257$	10.8807	−	6.28197i	0.0423373	−	0.0244435i	0.521019	+	0.853545i	$0.325552\pi$
$258$		0			0
$259$	−10.8690	−	8.67098i	−0.0419653	−	0.0334787i
$260$	−35.1676			−0.135260
$261$		0			0
$262$	91.3635	+	52.7487i	0.348716	+	0.201331i
$263$	−106.240	+	184.014i	−0.403956	+	0.699672i	−0.994199	−	0.107554i	$-0.965698\pi$
$263$	−106.240	+	184.014i	−0.403956	+	0.699672i	0.590244	+	0.807225i	$0.299032\pi$
$264$		0			0
$265$			127.669i			0.481771i
$266$	307.609	+	46.4219i	1.15642	+	0.174518i
$267$		0			0
$268$	−98.1647	−	170.026i	−0.366286	−	0.634426i
$269$	289.769	+	167.298i	1.07721	+	0.621927i	0.930142	−	0.367200i	$-0.119683\pi$
$269$	289.769	+	167.298i	1.07721	+	0.621927i	0.147067	+	0.989127i	$0.453017\pi$
$270$		0			0
$271$	−157.920	+	91.1752i	−0.582731	+	0.336440i	−0.762218	−	0.647321i	$-0.775889\pi$
$271$	−157.920	+	91.1752i	−0.582731	+	0.336440i	0.179487	+	0.983760i	$0.442556\pi$
$272$			110.426i			0.405979i
$273$		0			0
$274$	−349.168			−1.27434
$275$	−28.9620	−	50.1636i	−0.105316	−	0.182413i
$276$		0			0
$277$	−83.3807	+	144.420i	−0.301013	+	0.521370i	−0.976366	−	0.216125i	$-0.930658\pi$
$277$	−83.3807	+	144.420i	−0.301013	+	0.521370i	0.675353	+	0.737495i	$0.263991\pi$
$278$	190.958	−	110.250i	0.686900	−	0.396582i
$279$		0			0
$280$	27.6094	−	34.6081i	0.0986049	−	0.123600i
$281$	−38.3085			−0.136329			−0.0681647	−	0.997674i	$-0.521714\pi$
$281$	−38.3085			−0.136329			−0.0681647	+	0.997674i	$0.521714\pi$
$282$		0			0
$283$	−333.849	−	192.748i	−1.17968	−	0.681088i	−0.223739	−	0.974649i	$-0.571826\pi$
$283$	−333.849	−	192.748i	−1.17968	−	0.681088i	−0.955940	+	0.293561i	$0.905160\pi$
$284$	−34.2597	+	59.3396i	−0.120633	+	0.208942i
$285$		0			0
$286$		−	128.834i		−	0.450469i
$287$	56.7235	+	144.606i	0.197643	+	0.503855i
$288$		0			0
$289$	236.562	+	409.738i	0.818555	+	1.41778i
$290$	−6.30787	−	3.64185i	−0.0217513	−	0.0125581i
$291$		0			0
$292$	−33.7602	+	19.4915i	−0.115617	+	0.0667516i
$293$			90.9844i			0.310527i	0.987873	+	0.155264i	$0.0496227\pi$
$293$			90.9844i			0.310527i	−0.987873	+	0.155264i	$0.950377\pi$
$294$		0			0
$295$	−157.306			−0.533242
$296$	2.80903	+	4.86538i	0.00948997	+	0.0164371i
$297$		0			0
$298$	−115.322	+	199.744i	−0.386988	+	0.670282i
$299$	123.667	−	71.3993i	0.413603	−	0.238794i
$300$		0			0
$301$	324.766	−	127.393i	1.07896	−	0.423232i
$302$	106.108			0.351352
$303$		0			0
$304$	−108.859	−	62.8501i	−0.358090	−	0.206744i
$305$	75.5994	−	130.942i	0.247867	−	0.429318i
$306$		0			0
$307$			508.077i			1.65497i	0.561485	+	0.827487i	$0.310230\pi$
$307$			508.077i			1.65497i	−0.561485	+	0.827487i	$0.689770\pi$
$308$	126.785	+	101.145i	0.411638	+	0.328393i
$309$		0			0
$310$	8.32283	+	14.4156i	0.0268478	+	0.0465018i
$311$	−90.3447	−	52.1605i	−0.290497	−	0.167719i	0.347669	−	0.937617i	$-0.386973\pi$
$311$	−90.3447	−	52.1605i	−0.290497	−	0.167719i	−0.638166	+	0.769899i	$0.720307\pi$
$312$		0			0
$313$	230.249	−	132.934i	0.735619	−	0.424710i	−0.0848550	−	0.996393i	$-0.527043\pi$
$313$	230.249	−	132.934i	0.735619	−	0.424710i	0.820474	+	0.571683i	$0.193709\pi$
$314$		−	317.817i		−	1.01216i
$315$		0			0
$316$	180.857			0.572332
$317$	−5.36113	−	9.28575i	−0.0169121	−	0.0292926i	0.857446	−	0.514575i	$-0.172050\pi$
$317$	−5.36113	−	9.28575i	−0.0169121	−	0.0292926i	−0.874358	+	0.485282i	$0.838717\pi$
$318$		0			0
$319$	13.3417	−	23.1085i	0.0418234	−	0.0724403i
$320$	−15.4919	+	8.94427i	−0.0484123	+	0.0279508i
$321$		0			0
$322$	−26.8252	+	177.754i	−0.0833081	+	0.552031i
$323$	−867.538			−2.68588
$324$		0			0
$325$	−34.0509	−	19.6593i	−0.104772	−	0.0604901i
$326$	−162.718	+	281.835i	−0.499134	+	0.864525i
$327$		0			0
$328$		−	62.7643i		−	0.191355i
$329$	334.684	−	419.524i	1.01728	−	1.27515i
$330$		0			0
$331$	176.460	+	305.638i	0.533113	+	0.923379i	0.999252	+	0.0386675i	$0.0123113\pi$
$331$	176.460	+	305.638i	0.533113	+	0.923379i	−0.466139	+	0.884711i	$0.654355\pi$
$332$	231.754	+	133.803i	0.698055	+	0.403022i
$333$		0			0
$334$	340.220	−	196.426i	1.01862	−	0.588102i
$335$		−	219.503i		−	0.655233i
$336$		0			0
$337$	220.634			0.654699			0.327349	−	0.944903i	$-0.393845\pi$
$337$	220.634			0.654699			0.327349	+	0.944903i	$0.393845\pi$
$338$	75.7750	+	131.246i	0.224186	+	0.388302i
$339$		0			0
$340$	−61.7302	+	106.920i	−0.181560	+	0.314470i
$341$	−52.8104	+	30.4901i	−0.154869	+	0.0894138i
$342$		0			0
$343$	148.991	−	308.951i	0.434376	−	0.900732i
$344$	−140.960			−0.409767
$345$		0			0
$346$	−154.398	−	89.1417i	−0.446237	−	0.257635i
$347$	−128.004	+	221.710i	−0.368888	+	0.638933i	−0.989392	−	0.145270i	$-0.953595\pi$
$347$	−128.004	+	221.710i	−0.368888	+	0.638933i	0.620504	+	0.784204i	$0.286928\pi$
$348$		0			0
$349$			407.250i			1.16691i	0.812147	+	0.583453i	$0.198299\pi$
$349$			407.250i			1.16691i	−0.812147	+	0.583453i	$0.801701\pi$
$350$	46.0792	−	18.0751i	0.131655	−	0.0516431i
$351$		0			0
$352$	−32.7667	−	56.7537i	−0.0930873	−	0.161232i
$353$	505.099	+	291.619i	1.43087	+	0.826116i	0.997187	−	0.0749482i	$-0.0238791\pi$
$353$	505.099	+	291.619i	1.43087	+	0.826116i	0.433687	+	0.901064i	$0.357212\pi$
$354$		0			0
$355$	−66.3437	+	38.3035i	−0.186884	+	0.107897i
$356$			22.1294i			0.0621613i
$357$		0			0
$358$	109.046			0.304597
$359$	345.764	+	598.881i	0.963131	+	1.66819i	0.714554	+	0.699580i	$0.246630\pi$
$359$	345.764	+	598.881i	0.963131	+	1.66819i	0.248577	+	0.968612i	$0.420037\pi$
$360$		0			0
$361$	313.266	−	542.593i	0.867773	−	1.50303i
$362$	−259.660	+	149.915i	−0.717294	+	0.414130i
$363$		0			0
$364$	108.859	+	16.4282i	0.299064	+	0.0451324i
$365$	−43.5842			−0.119409
$366$		0			0
$367$	198.949	+	114.863i	0.542096	+	0.312980i	0.745928	−	0.666026i	$-0.232006\pi$
$367$	198.949	+	114.863i	0.542096	+	0.312980i	−0.203832	+	0.979006i	$0.565340\pi$
$368$	36.3184	−	62.9053i	0.0986912	−	0.170938i
$369$		0			0
$370$			6.28118i			0.0169762i
$371$	59.6394	−	395.193i	0.160753	−	1.06521i
$372$		0			0
$373$	202.304	+	350.401i	0.542371	+	0.939414i	0.998767	+	0.0496372i	$0.0158065\pi$
$373$	202.304	+	350.401i	0.542371	+	0.939414i	−0.456397	+	0.889776i	$0.650860\pi$
$374$	−391.694	−	226.145i	−1.04731	−	0.604665i
$375$		0			0
$376$	−187.795	+	108.424i	−0.499455	+	0.288360i
$377$		−	18.1126i		−	0.0480439i
$378$		0			0
$379$	265.866			0.701493			0.350746	−	0.936471i	$-0.385928\pi$
$379$	265.866			0.701493			0.350746	+	0.936471i	$0.385928\pi$
$380$	−70.2685	−	121.709i	−0.184917	−	0.320286i
$381$		0			0
$382$	−117.165	+	202.935i	−0.306714	+	0.531244i
$383$	−265.353	+	153.202i	−0.692829	+	0.400005i	−0.804671	−	0.593721i	$-0.797658\pi$
$383$	−265.353	+	153.202i	−0.692829	+	0.400005i	0.111842	+	0.993726i	$0.464325\pi$
$384$		0			0
$385$	66.2168	+	168.808i	0.171992	+	0.438462i
$386$	148.916			0.385792
$387$		0			0
$388$	125.247	+	72.3112i	0.322801	+	0.186369i
$389$	53.1772	−	92.1056i	0.136702	−	0.236775i	−0.789544	−	0.613694i	$-0.789683\pi$
$389$	53.1772	−	92.1056i	0.136702	−	0.236775i	0.926246	+	0.376918i	$0.123016\pi$
$390$		0			0
$391$		−	501.314i		−	1.28213i
$392$	−101.630	+	94.2301i	−0.259261	+	0.240383i
$393$		0			0
$394$	−173.054	−	299.739i	−0.439224	−	0.760758i
$395$	175.114	+	101.102i	0.443327	+	0.255955i
$396$		0			0
$397$	−188.643	+	108.913i	−0.475172	+	0.274341i	−0.718402	−	0.695628i	$-0.755126\pi$
$397$	−188.643	+	108.913i	−0.475172	+	0.274341i	0.243230	+	0.969969i	$0.421793\pi$
$398$			138.546i			0.348105i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	30.9907	+	53.6775i	0.0772836	+	0.133859i	0.902077	−	0.431575i	$-0.142042\pi$
$401$	30.9907	+	53.6775i	0.0772836	+	0.133859i	−0.824793	+	0.565434i	$0.808709\pi$
$402$		0			0
$403$	−20.6966	+	35.8475i	−0.0513563	+	0.0889517i
$404$	87.7341	−	50.6533i	0.217164	−	0.125379i
$405$		0			0
$406$	17.8244	+	14.2198i	0.0439025	+	0.0350242i
$407$	−23.0107			−0.0565373
$408$		0			0
$409$	−376.167	−	217.180i	−0.919724	−	0.531003i	−0.0361772	−	0.999345i	$-0.511518\pi$
$409$	−376.167	−	217.180i	−0.919724	−	0.531003i	−0.883547	+	0.468342i	$0.844851\pi$
$410$	35.0863	−	60.7713i	0.0855764	−	0.148223i
$411$		0			0
$412$		−	395.929i		−	0.960993i
$413$	486.933	+	73.4840i	1.17901	+	0.177927i
$414$		0			0
$415$	149.597	+	259.109i	0.360474	+	0.624360i
$416$	−38.5242	−	22.2419i	−0.0926062	−	0.0534662i
$417$		0			0
$418$	445.871	−	257.424i	1.06668	−	0.615847i
$419$			457.221i			1.09122i	0.838040	+	0.545609i	$0.183702\pi$
$419$			457.221i			1.09122i	−0.838040	+	0.545609i	$0.816298\pi$
$420$		0			0
$421$	−653.149			−1.55142			−0.775712	−	0.631088i	$-0.782609\pi$
$421$	−653.149			−1.55142			−0.775712	+	0.631088i	$0.782609\pi$
$422$	−275.004	−	476.320i	−0.651667	−	1.12872i
$423$		0			0
$424$	−80.7451	+	139.855i	−0.190437	+	0.329846i
$425$	−119.540	+	69.0165i	−0.281271	+	0.162392i
$426$		0			0
$427$	−295.182	+	370.008i	−0.691293	+	0.866530i
$428$	−295.872			−0.691289
$429$		0			0
$430$	−136.484	−	78.7989i	−0.317404	−	0.183253i
$431$	−235.128	+	407.253i	−0.545540	+	0.944904i	0.453032	+	0.891494i	$0.350342\pi$
$431$	−235.128	+	407.253i	−0.545540	+	0.944904i	−0.998573	+	0.0534095i	$0.982991\pi$
$432$		0			0
$433$		−	32.0299i		−	0.0739719i	−0.999316	−	0.0369860i	$-0.988224\pi$
$433$		−	32.0299i		−	0.0739719i	0.999316	−	0.0369860i	$-0.0117757\pi$
$434$	−19.0288	−	48.5105i	−0.0438451	−	0.111775i
$435$		0			0
$436$	54.3219	+	94.0883i	0.124592	+	0.215799i
$437$	494.200	+	285.326i	1.13089	+	0.652921i
$438$		0			0
$439$	331.028	−	191.119i	0.754051	−	0.435352i	−0.0731046	−	0.997324i	$-0.523291\pi$
$439$	331.028	−	191.119i	0.754051	−	0.435352i	0.827156	+	0.561973i	$0.189957\pi$
$440$		−	73.2687i		−	0.166520i
$441$		0			0
$442$	−307.012			−0.694598
$443$	61.8708	+	107.163i	0.139663	+	0.241904i	0.927369	−	0.374148i	$-0.122065\pi$
$443$	61.8708	+	107.163i	0.139663	+	0.241904i	−0.787706	+	0.616051i	$0.788731\pi$
$444$		0			0
$445$	−12.3707	+	21.4267i	−0.0277994	+	0.0481499i
$446$	308.529	−	178.129i	0.691769	−	0.399393i
$447$		0			0
$448$	52.1327	−	20.4496i	0.116368	−	0.0456464i
$449$	266.985			0.594622			0.297311	−	0.954781i	$-0.403910\pi$
$449$	266.985			0.594622			0.297311	+	0.954781i	$0.403910\pi$
$450$		0			0
$451$	222.632	+	128.536i	0.493640	+	0.285003i
$452$	47.7883	−	82.7718i	0.105726	−	0.183124i
$453$		0			0
$454$		−	378.757i		−	0.834267i
$455$	96.2190	+	76.7608i	0.211470	+	0.168705i
$456$		0			0
$457$	224.670	+	389.140i	0.491619	+	0.851509i	0.999953	−	0.00965069i	$-0.00307196\pi$
$457$	224.670	+	389.140i	0.491619	+	0.851509i	−0.508334	+	0.861160i	$0.669739\pi$
$458$	423.185	+	244.326i	0.923985	+	0.533463i
$459$		0			0
$460$	70.3302	−	40.6052i	0.152892	−	0.0882721i
$461$		−	105.528i		−	0.228912i	−0.993428	−	0.114456i	$-0.963487\pi$
$461$		−	105.528i		−	0.228912i	0.993428	−	0.114456i	$-0.0365125\pi$
$462$		0			0
$463$	588.555			1.27118			0.635588	−	0.772028i	$-0.280758\pi$
$463$	588.555			1.27118			0.635588	+	0.772028i	$0.280758\pi$
$464$	−4.60662	−	7.97889i	−0.00992805	−	0.0171959i
$465$		0			0
$466$	203.692	−	352.805i	0.437108	−	0.757093i
$467$	−316.668	+	182.829i	−0.678091	+	0.391496i	−0.799135	−	0.601151i	$-0.794709\pi$
$467$	−316.668	+	182.829i	−0.678091	+	0.391496i	0.121044	+	0.992647i	$0.461376\pi$
$468$		0			0
$469$	−102.539	+	679.459i	−0.218632	+	1.44874i
$470$	−242.442			−0.515835
$471$		0			0
$472$	−172.320	−	99.4892i	−0.365086	−	0.210782i
$473$	288.675	−	499.999i	0.610306	−	1.05708i
$474$		0			0
$475$		−	157.125i		−	0.330790i
$476$	241.029	−	302.128i	0.506364	−	0.634723i
$477$		0			0
$478$	133.509	+	231.244i	0.279307	+	0.483774i
$479$	421.907	+	243.588i	0.880808	+	0.508535i	0.870925	−	0.491416i	$-0.163521\pi$
$479$	421.907	+	243.588i	0.880808	+	0.508535i	0.00988318	+	0.999951i	$0.496854\pi$
$480$		0			0
$481$	−13.5270	+	7.80979i	−0.0281226	+	0.0162366i
$482$			138.378i			0.287091i
$483$		0			0
$484$	26.4149			0.0545762
$485$	80.8463	+	140.030i	0.166693	+	0.288722i
$486$		0			0
$487$	97.8870	−	169.545i	0.201000	−	0.348142i	−0.747851	−	0.663867i	$-0.768914\pi$
$487$	97.8870	−	169.545i	0.201000	−	0.348142i	0.948851	+	0.315725i	$0.102248\pi$
$488$	165.630	−	95.6265i	0.339406	−	0.195956i
$489$		0			0
$490$	−151.079	+	34.4250i	−0.308325	+	0.0702550i
$491$	349.221			0.711244			0.355622	−	0.934630i	$-0.384269\pi$
$491$	349.221			0.711244			0.355622	+	0.934630i	$0.384269\pi$
$492$		0			0
$493$	−55.0675	−	31.7933i	−0.111699	−	0.0644894i
$494$	174.738	−	302.656i	0.353722	−	0.612664i
$495$		0			0
$496$			21.0553i			0.0424501i
$497$	223.256	−	87.5747i	0.449208	−	0.176207i
$498$		0			0
$499$	167.719	+	290.498i	0.336111	+	0.582161i	0.983698	−	0.179831i	$-0.0575550\pi$
$499$	167.719	+	290.498i	0.336111	+	0.582161i	−0.647587	+	0.761992i	$0.724222\pi$
$500$	−19.3649	−	11.1803i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	295.586	−	170.657i	0.588817	−	0.339953i
$503$		−	523.663i		−	1.04108i	−0.853837	−	0.520540i	$-0.825731\pi$
$503$		−	523.663i		−	1.04108i	0.853837	−	0.520540i	$-0.174269\pi$
$504$		0			0
$505$	113.264			0.224286
$506$	148.754	+	257.650i	0.293981	+	0.509190i
$507$		0			0
$508$	101.973	−	176.623i	0.200735	−	0.347683i
$509$	417.731	−	241.177i	0.820690	−	0.473825i	−0.0299645	−	0.999551i	$-0.509539\pi$
$509$	417.731	−	241.177i	0.820690	−	0.473825i	0.850654	+	0.525726i	$0.176206\pi$
$510$		0			0
$511$	134.913	+	20.3599i	0.264017	+	0.0398433i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	15.3876	+	8.88405i	0.0299370	+	0.0172841i
$515$	221.331	−	383.357i	0.429769	−	0.744382i
$516$		0			0
$517$		−	888.171i		−	1.71793i
$518$	2.93419	−	19.4431i	0.00566446	−	0.0375349i
$519$		0			0
$520$	−24.8673	−	43.0713i	−0.0478216	−	0.0828295i
$521$	61.7509	+	35.6519i	0.118524	+	0.0684298i	0.558090	−	0.829780i	$-0.311534\pi$
$521$	61.7509	+	35.6519i	0.118524	+	0.0684298i	−0.439566	+	0.898210i	$0.644868\pi$
$522$		0			0
$523$	−521.458	+	301.064i	−0.997052	+	0.575648i	−0.907375	−	0.420323i	$-0.861917\pi$
$523$	−521.458	+	301.064i	−0.997052	+	0.575648i	−0.0896773	+	0.995971i	$0.528584\pi$
$524$			149.196i			0.284725i
$525$		0			0
$526$	−300.493			−0.571279
$527$	72.6581	+	125.847i	0.137871	+	0.238800i
$528$		0			0
$529$	99.6220	−	172.550i	0.188321	−	0.326182i
$530$	−156.362	+	90.2758i	−0.295023	+	0.170332i
$531$		0			0
$532$	160.657	+	409.568i	0.301987	+	0.769864i
$533$	174.500			0.327392
$534$		0			0
$535$	−286.476	−	165.397i	−0.535470	−	0.309154i
$536$	138.826	−	240.453i	0.259003	−	0.448607i
$537$		0			0
$538$			473.191i			0.879537i
$539$	−126.114	−	553.469i	−0.233977	−	1.02684i
$540$		0			0
$541$	301.657	+	522.485i	0.557591	+	0.965776i	0.997697	+	0.0678303i	$0.0216077\pi$
$541$	301.657	+	522.485i	0.557591	+	0.965776i	−0.440106	+	0.897946i	$0.645059\pi$
$542$	−223.333	−	128.941i	−0.412053	−	0.237899i
$543$		0			0
$544$	−135.244	+	78.0833i	−0.248611	+	0.143535i
$545$			121.468i			0.222876i
$546$		0			0
$547$	−879.935			−1.60866			−0.804328	−	0.594185i	$-0.797475\pi$
$547$	−879.935			−1.60866			−0.804328	+	0.594185i	$0.797475\pi$
$548$	−246.899	−	427.642i	−0.450546	−	0.780368i
$549$		0			0
$550$	40.9584	−	70.9421i	0.0744699	−	0.128986i
$551$	62.6842	−	36.1908i	0.113765	−	0.0656820i
$552$		0			0
$553$	−494.827	−	394.759i	−0.894805	−	0.713849i
$554$	−235.836			−0.425697
$555$		0			0
$556$	270.056	+	155.917i	0.485712	+	0.280426i
$557$	−441.404	+	764.533i	−0.792466	+	1.37259i	0.131970	+	0.991254i	$0.457870\pi$
$557$	−441.404	+	764.533i	−0.792466	+	1.37259i	−0.924436	+	0.381338i	$0.875464\pi$
$558$		0			0
$559$		−	391.903i		−	0.701078i
$560$	61.9089	+	9.34279i	0.110552	+	0.0166836i
$561$		0			0
$562$	−27.0882	−	46.9182i	−0.0481997	−	0.0834843i
$563$	451.334	+	260.578i	0.801659	+	0.462838i	0.844051	−	0.536263i	$-0.180165\pi$
$563$	451.334	+	260.578i	0.801659	+	0.462838i	−0.0423920	+	0.999101i	$0.513498\pi$
$564$		0			0
$565$	92.5417	−	53.4290i	0.163791	−	0.0945646i
$566$		−	545.174i		−	0.963204i
$567$		0			0
$568$	−96.9011			−0.170601
$569$	122.400	+	212.004i	0.215115	+	0.372590i	0.953308	−	0.301999i	$-0.0976541\pi$
$569$	122.400	+	212.004i	0.215115	+	0.372590i	−0.738193	+	0.674589i	$0.764321\pi$
$570$		0			0
$571$	208.126	−	360.486i	0.364495	−	0.631323i	−0.624200	−	0.781264i	$-0.714575\pi$
$571$	208.126	−	360.486i	0.364495	−	0.631323i	0.988695	+	0.149941i	$0.0479084\pi$
$572$	157.789	−	91.0995i	0.275855	−	0.159265i
$573$		0			0
$574$	−136.996	+	171.724i	−0.238670	+	0.299171i
$575$	90.7959			0.157906
$576$		0			0
$577$	669.929	+	386.784i	1.16106	+	0.670336i	0.951557	−	0.307473i	$-0.0994833\pi$
$577$	669.929	+	386.784i	1.16106	+	0.670336i	0.209499	+	0.977809i	$0.432817\pi$
$578$	−334.550	+	579.457i	−0.578806	+	1.00252i
$579$		0			0
$580$		−	10.3007i		−	0.0177598i
$581$	−342.028	−	871.941i	−0.588689	−	1.50076i
$582$		0			0
$583$	−330.719	−	572.823i	−0.567272	−	0.982543i
$584$	−47.7441	−	27.5651i	−0.0817537	−	0.0472005i
$585$		0			0
$586$	−111.433	+	64.3357i	−0.190158	+	0.109788i
$587$		−	633.860i		−	1.07983i	−0.841720	−	0.539915i	$-0.818456\pi$
$587$		−	633.860i		−	1.07983i	0.841720	−	0.539915i	$-0.181544\pi$
$588$		0			0
$589$	−165.416			−0.280841
$590$	−111.232	−	192.660i	−0.188529	−	0.326543i
$591$		0			0
$592$	−3.97257	+	6.88069i	−0.00671042	+	0.0116228i
$593$	−80.4028	+	46.4206i	−0.135587	+	0.0782809i	−0.566259	−	0.824227i	$-0.691610\pi$
$593$	−80.4028	+	46.4206i	−0.135587	+	0.0782809i	0.430672	+	0.902508i	$0.358276\pi$
$594$		0			0
$595$	402.270	−	157.795i	0.676084	−	0.265201i
$596$	−326.181			−0.547283
$597$		0			0
$598$	174.892	+	100.974i	0.292461	+	0.168853i
$599$	−307.680	+	532.918i	−0.513657	+	0.889679i	0.486218	+	0.873838i	$0.338376\pi$
$599$	−307.680	+	532.918i	−0.513657	+	0.889679i	−0.999875	+	0.0158418i	$0.994957\pi$
$600$		0			0
$601$		−	821.399i		−	1.36672i	−0.730081	−	0.683360i	$-0.760518\pi$
$601$		−	821.399i		−	1.36672i	0.730081	−	0.683360i	$-0.239482\pi$
$602$	385.668	+	307.675i	0.640644	+	0.511088i
$603$		0			0
$604$	75.0299	+	129.956i	0.124222	+	0.215158i
$605$	25.5761	+	14.7664i	0.0422746	+	0.0244072i
$606$		0			0
$607$	−869.979	+	502.282i	−1.43324	+	0.827483i	−0.997367	−	0.0725231i	$-0.976895\pi$
$607$	−869.979	+	502.282i	−1.43324	+	0.827483i	−0.435876	+	0.900006i	$0.643562\pi$
$608$		−	177.767i		−	0.292380i
$609$		0			0
$610$	213.827			0.350537
$611$	−301.444	−	522.116i	−0.493361	−	0.854527i
$612$		0			0
$613$	−556.873	+	964.532i	−0.908438	+	1.57346i	−0.0922038	+	0.995740i	$0.529391\pi$
$613$	−556.873	+	964.532i	−0.908438	+	1.57346i	−0.816234	+	0.577721i	$0.803942\pi$
$614$	−622.264	+	359.265i	−1.01346	+	0.585121i
$615$		0			0
$616$	−34.2267	+	226.799i	−0.0555628	+	0.368180i
$617$	463.256			0.750820			0.375410	−	0.926859i	$-0.377502\pi$
$617$	463.256			0.750820			0.375410	+	0.926859i	$0.377502\pi$
$618$		0			0
$619$	486.109	+	280.655i	0.785314	+	0.453401i	0.838310	−	0.545193i	$-0.183544\pi$
$619$	486.109	+	280.655i	0.785314	+	0.453401i	−0.0529963	+	0.998595i	$0.516877\pi$
$620$	−11.7703	+	20.3867i	−0.0189843	+	0.0328817i
$621$		0			0
$622$		−	147.532i		−	0.237190i
$623$	48.3021	−	60.5464i	0.0775315	−	0.0971852i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	325.621	+	187.997i	0.520161	+	0.300315i
$627$		0			0
$628$	389.245	−	224.731i	0.619816	−	0.357851i
$629$			54.8346i			0.0871774i
$630$		0			0
$631$	244.533			0.387533			0.193767	−	0.981048i	$-0.437930\pi$
$631$	244.533			0.387533			0.193767	+	0.981048i	$0.437930\pi$
$632$	127.885	+	221.504i	0.202350	+	0.350480i
$633$		0			0
$634$	7.58178	−	13.1320i	0.0119587	−	0.0207130i
$635$	197.471	−	114.010i	0.310977	−	0.179543i
$636$		0			0
$637$	−261.983	−	282.556i	−0.411276	−	0.443574i
$638$	37.7360			0.0591473
$639$		0			0
$640$	−21.9089	−	12.6491i	−0.0342327	−	0.0197642i
$641$	325.885	−	564.449i	0.508400	−	0.880575i	−0.491553	−	0.870848i	$-0.663570\pi$
$641$	325.885	−	564.449i	0.508400	−	0.880575i	0.999953	−	0.00972698i	$-0.00309624\pi$
$642$		0			0
$643$			76.4894i			0.118957i	0.998230	+	0.0594786i	$0.0189438\pi$
$643$			76.4894i			0.118957i	−0.998230	+	0.0594786i	$0.981056\pi$
$644$	−236.672	+	92.8371i	−0.367503	+	0.144157i
$645$		0			0
$646$	−613.442	−	1062.51i	−0.949601	−	1.64476i
$647$	−141.933	−	81.9453i	−0.219372	−	0.126654i	0.386288	−	0.922378i	$-0.373757\pi$
$647$	−141.933	−	81.9453i	−0.219372	−	0.126654i	−0.605659	+	0.795724i	$0.707091\pi$
$648$		0			0
$649$	705.797	−	407.492i	1.08752	−	0.627877i
$650$		−	55.6049i		−	0.0855459i
$651$		0			0
$652$	−460.235			−0.705882
$653$	−557.431	−	965.499i	−0.853647	−	1.47856i	−0.877895	−	0.478854i	$-0.841052\pi$
$653$	−557.431	−	965.499i	−0.853647	−	1.47856i	0.0242480	−	0.999706i	$-0.492281\pi$
$654$		0			0
$655$	−83.4031	+	144.458i	−0.127333	+	0.220547i
$656$	76.8703	−	44.3811i	0.117180	−	0.0676541i
$657$		0			0
$658$	750.467	+	113.254i	1.14053	+	0.172119i
$659$	−1164.66			−1.76732			−0.883660	−	0.468130i	$-0.844928\pi$
$659$	−1164.66			−1.76732			−0.883660	+	0.468130i	$0.844928\pi$
$660$		0			0
$661$	542.087	+	312.974i	0.820101	+	0.473485i	0.850451	−	0.526054i	$-0.176329\pi$
$661$	542.087	+	312.974i	0.820101	+	0.473485i	−0.0303505	+	0.999539i	$0.509662\pi$
$662$	−249.553	+	432.238i	−0.376968	+	0.652928i
$663$		0			0
$664$			378.453i			0.569960i
$665$	−73.3994	+	486.372i	−0.110375	+	0.731387i
$666$		0			0
$667$	20.9131	+	36.2226i	0.0313540	+	0.0543067i
$668$	481.144	+	277.788i	0.720275	+	0.415851i
$669$		0			0
$670$	268.835	−	155.212i	0.401246	−	0.231660i
$671$			783.342i			1.16743i
$672$		0			0
$673$	−38.0207			−0.0564943			−0.0282471	−	0.999601i	$-0.508993\pi$
$673$	−38.0207			−0.0564943			−0.0282471	+	0.999601i	$0.508993\pi$
$674$	156.011	+	270.220i	0.231471	+	0.400920i
$675$		0			0
$676$	−107.162	+	185.610i	−0.158524	+	0.274571i
$677$	−676.984	+	390.857i	−0.999976	+	0.577336i	−0.908241	−	0.418447i	$-0.862574\pi$
$677$	−676.984	+	390.857i	−0.999976	+	0.577336i	−0.0917347	+	0.995783i	$0.529241\pi$
$678$		0			0
$679$	−184.842	−	471.222i	−0.272227	−	0.693994i
$680$	−174.599			−0.256764
$681$		0			0
$682$	−74.6852	−	43.1195i	−0.109509	−	0.0632251i
$683$	−67.2190	+	116.427i	−0.0984172	+	0.170464i	−0.911030	−	0.412341i	$-0.864711\pi$
$683$	−67.2190	+	116.427i	−0.0984172	+	0.170464i	0.812612	+	0.582804i	$0.198045\pi$
$684$		0			0
$685$		−	552.083i		−	0.805960i
$686$	483.739	−	35.9855i	0.705158	−	0.0524570i
$687$		0			0
$688$	−99.6736	−	172.640i	−0.144874	−	0.250930i
$689$	−388.830	−	224.491i	−0.564340	−	0.325822i
$690$		0			0
$691$	−393.253	+	227.045i	−0.569107	+	0.328574i	−0.756792	−	0.653655i	$-0.773235\pi$
$691$	−393.253	+	227.045i	−0.569107	+	0.328574i	0.187686	+	0.982229i	$0.439901\pi$
$692$		−	252.131i		−	0.364351i
$693$		0			0
$694$	−362.051			−0.521687
$695$	174.320	+	301.932i	0.250821	+	0.434434i
$696$		0			0
$697$	306.303	−	530.532i	0.439459	−	0.761165i
$698$	−498.778	+	287.969i	−0.714581	+	0.412564i
$699$		0			0
$700$	54.7203	+	43.6543i	0.0781718	+	0.0623632i
$701$	−982.015			−1.40088			−0.700439	−	0.713713i	$-0.747012\pi$
$701$	−982.015			−1.40088			−0.700439	+	0.713713i	$0.747012\pi$
$702$		0			0
$703$	−54.0565	−	31.2095i	−0.0768940	−	0.0443948i
$704$	46.3392	−	80.2618i	0.0658227	−	0.114008i
$705$		0			0
$706$			824.822i			1.16830i
$707$	−350.603	−	52.9102i	−0.495903	−	0.0748376i
$708$		0			0
$709$	166.536	+	288.449i	0.234889	+	0.406839i	0.959240	−	0.282591i	$-0.0911940\pi$
$709$	166.536	+	288.449i	0.234889	+	0.406839i	−0.724352	+	0.689431i	$0.757861\pi$
$710$	−93.8241	−	54.1694i	−0.132147	−	0.0762949i
$711$		0			0
$712$	−27.1029	+	15.6479i	−0.0380658	+	0.0219773i
$713$		−	95.5866i		−	0.134063i
$714$		0			0
$715$	203.705			0.284902
$716$	77.1069	+	133.553i	0.107691	+	0.186527i
$717$		0			0
$718$	−488.984	+	846.946i	−0.681037	+	1.17959i
$719$	−1055.73	+	609.523i	−1.46832	+	0.847737i	−0.999370	−	0.0354852i	$-0.988702\pi$
$719$	−1055.73	+	609.523i	−1.46832	+	0.847737i	−0.468954	+	0.883223i	$0.655369\pi$
$720$		0			0
$721$	−864.200	+	1083.27i	−1.19861	+	1.50245i
$722$	886.051			1.22722
$723$		0			0
$724$	−367.215	−	212.012i	−0.507203	−	0.292834i
$725$	5.75827	−	9.97362i	0.00794244	−	0.0137567i
$726$		0			0
$727$		−	215.108i		−	0.295885i	−0.988996	−	0.147942i	$-0.952735\pi$
$727$		−	215.108i		−	0.295885i	0.988996	−	0.147942i	$-0.0472650\pi$
$728$	56.8549	+	144.941i	0.0780974	+	0.199095i
$729$		0			0
$730$	−30.8187	−	53.3796i	−0.0422174	−	0.0731227i
$731$	−1191.50	−	687.913i	−1.62996	−	0.941057i
$732$		0			0
$733$	−649.047	+	374.728i	−0.885467	+	0.511225i	−0.872457	−	0.488691i	$-0.837475\pi$
$733$	−649.047	+	374.728i	−0.885467	+	0.511225i	−0.0130099	+	0.999915i	$0.504141\pi$
$734$			324.883i			0.442620i
$735$		0			0
$736$	102.724			0.139570
$737$	568.609	+	984.859i	0.771518	+	1.33631i
$738$		0			0
$739$	467.102	−	809.045i	0.632073	−	1.09478i	−0.355054	−	0.934846i	$-0.615538\pi$
$739$	467.102	−	809.045i	0.632073	−	1.09478i	0.987127	−	0.159937i	$-0.0511291\pi$
$740$	−7.69285	+	4.44147i	−0.0103957	+	0.00600198i
$741$		0			0
$742$	526.182	−	206.401i	0.709140	−	0.278168i
$743$	−1232.47			−1.65878			−0.829389	−	0.558671i	$-0.811311\pi$
$743$	−1232.47			−1.65878			−0.829389	+	0.558671i	$0.811311\pi$
$744$		0			0
$745$	−315.823	−	182.341i	−0.423924	−	0.244752i
$746$	−286.101	+	495.542i	−0.383514	+	0.664266i
$747$		0			0
$748$		−	639.634i		−	0.855125i
$749$	809.508	+	645.803i	1.08079	+	0.862220i
$750$		0			0
$751$	−393.353	−	681.307i	−0.523772	−	0.907200i	−0.999617	−	0.0276709i	$-0.991191\pi$
$751$	−393.353	−	681.307i	−0.523772	−	0.907200i	0.475845	−	0.879529i	$-0.342142\pi$
$752$	−265.582	−	153.334i	−0.353168	−	0.203902i
$753$		0			0
$754$	22.1833	−	12.8075i	0.0294208	−	0.0169861i
$755$			167.772i			0.222214i
$756$		0			0
$757$	1303.18			1.72151			0.860753	−	0.509023i	$-0.169993\pi$
$757$	1303.18			1.72151			0.860753	+	0.509023i	$0.169993\pi$
$758$	187.995	+	325.618i	0.248015	+	0.429575i
$759$		0			0
$760$	99.3747	−	172.122i	0.130756	−	0.226476i
$761$	−601.784	+	347.440i	−0.790780	+	0.456557i	−0.840237	−	0.542219i	$-0.817584\pi$
$761$	−601.784	+	347.440i	−0.790780	+	0.456557i	0.0494571	+	0.998776i	$0.484251\pi$
$762$		0			0
$763$	56.7423	−	375.996i	0.0743674	−	0.492786i
$764$	−331.392			−0.433759
$765$		0			0
$766$	−375.266	−	216.660i	−0.489904	−	0.282846i
$767$	276.604	−	479.093i	0.360631	−	0.624632i
$768$		0			0
$769$		−	263.988i		−	0.343287i	−0.985159	−	0.171644i	$-0.945092\pi$
$769$		−	263.988i		−	0.343287i	0.985159	−	0.171644i	$-0.0549077\pi$
$770$	−159.924	+	200.464i	−0.207694	+	0.260343i
$771$		0			0
$772$	105.299	+	182.384i	0.136398	+	0.236249i
$773$	136.278	+	78.6802i	0.176298	+	0.101786i	0.585552	−	0.810635i	$-0.300878\pi$
$773$	136.278	+	78.6802i	0.176298	+	0.101786i	−0.409254	+	0.912420i	$0.634211\pi$
$774$		0			0
$775$	−22.7930	+	13.1595i	−0.0294103	+	0.0169801i
$776$			204.527i			0.263566i
$777$		0			0
$778$	150.408			0.193326
$779$	348.669	+	603.913i	0.447586	+	0.775241i
$780$		0			0
$781$	198.446	−	343.718i	0.254092	−	0.440100i
$782$	613.981	−	354.482i	0.785142	−	0.453302i
$783$		0			0
$784$	−187.271	−	57.8402i	−0.238866	−	0.0737758i
$785$	502.513			0.640144
$786$		0			0
$787$	850.660	+	491.129i	1.08089	+	0.624052i	0.931136	−	0.364671i	$-0.118819\pi$
$787$	850.660	+	491.129i	1.08089	+	0.624052i	0.149754	+	0.988723i	$0.452152\pi$
$788$	244.736	−	423.894i	0.310578	−	0.537937i
$789$		0			0
$790$			285.960i			0.361975i
$791$	−311.417	+	122.157i	−0.393700	+	0.154433i
$792$		0			0
$793$	265.865	+	460.492i	0.335265	+	0.580695i
$794$	−266.782	−	154.027i	−0.335998	−	0.193988i
$795$		0			0
$796$	−169.683	+	97.9667i	−0.213170	+	0.123074i
$797$		−	946.927i		−	1.18811i	−0.804423	−	0.594057i	$-0.797525\pi$
$797$		−	946.927i		−	1.18811i	0.804423	−	0.594057i	$-0.202475\pi$
$798$		0			0
$799$	−2116.52			−2.64896
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−43.8275	+	75.9114i	−0.0546477	+	0.0946526i
$803$	195.553	−	112.902i	0.243527	−	0.140601i
$804$		0			0
$805$	−281.054	−	42.4144i	−0.349135	−	0.0526887i
$806$	−58.5388			−0.0726287
$807$		0			0
$808$	124.075	+	71.6346i	0.153558	+	0.0886567i
$809$	214.568	−	371.642i	0.265226	−	0.459385i	−0.702397	−	0.711786i	$-0.747887\pi$
$809$	214.568	−	371.642i	0.265226	−	0.459385i	0.967623	+	0.252401i	$0.0812201\pi$
$810$		0			0
$811$			948.404i			1.16943i	0.811241	+	0.584713i	$0.198793\pi$
$811$			948.404i			1.16943i	−0.811241	+	0.584713i	$0.801207\pi$
$812$	−4.81187	+	31.8853i	−0.00592595	+	0.0392676i
$813$		0			0
$814$	−16.2710	−	28.1822i	−0.0199890	−	0.0346219i
$815$	−445.620	−	257.279i	−0.546774	−	0.315680i
$816$		0			0
$817$	1356.30	−	783.062i	1.66010	−	0.958460i
$818$		−	614.278i		−	0.750952i
$819$		0			0
$820$	99.2391			0.121023
$821$	−201.884	−	349.673i	−0.245900	−	0.425911i	0.716484	−	0.697603i	$-0.245750\pi$
$821$	−201.884	−	349.673i	−0.245900	−	0.425911i	−0.962384	+	0.271692i	$0.912417\pi$
$822$		0			0
$823$	−433.014	+	750.003i	−0.526141	+	0.911303i	0.473395	+	0.880850i	$0.343028\pi$
$823$	−433.014	+	750.003i	−0.526141	+	0.911303i	−0.999536	+	0.0304530i	$0.990305\pi$
$824$	484.912	−	279.964i	0.588486	−	0.339762i
$825$		0			0
$826$	254.314	+	648.330i	0.307887	+	0.784903i
$827$	363.528			0.439574			0.219787	−	0.975548i	$-0.429464\pi$
$827$	363.528			0.439574			0.219787	+	0.975548i	$0.429464\pi$
$828$		0			0
$829$	208.617	+	120.445i	0.251649	+	0.145290i	0.620519	−	0.784191i	$-0.286922\pi$
$829$	208.617	+	120.445i	0.251649	+	0.145290i	−0.368870	+	0.929481i	$0.620255\pi$
$830$	−211.562	+	366.436i	−0.254894	+	0.441489i
$831$		0			0
$832$		−	62.9097i		−	0.0756126i
$833$	−1318.92	+	300.529i	−1.58333	+	0.360779i
$834$		0			0
$835$	310.577	+	537.935i	0.371948	+	0.644233i
$836$	630.557	+	364.052i	0.754255	+	0.435469i
$837$		0			0
$838$	−559.979	+	323.304i	−0.668232	+	0.385804i
$839$		−	214.638i		−	0.255826i	−0.991785	−	0.127913i	$-0.959172\pi$
$839$		−	214.638i		−	0.255826i	0.991785	−	0.127913i	$-0.0408278\pi$
$840$		0			0
$841$	−835.695			−0.993692
$842$	−461.846	−	799.941i	−0.548511	−	0.950049i
$843$		0			0
$844$	388.914	−	673.618i	0.460798	−	0.798126i
$845$	−207.518	+	119.811i	−0.245584	+	0.141788i
$846$		0			0
$847$	−72.2715	−	57.6561i	−0.0853264	−	0.0680710i
$848$	−228.382			−0.269318
$849$		0			0
$850$	−169.055	−	97.6041i	−0.198889	−	0.114828i
$851$	18.0347	−	31.2369i	0.0211923	−	0.0367062i
$852$		0			0
$853$			1388.39i			1.62765i	0.581110	+	0.813825i	$0.302618\pi$
$853$			1388.39i			1.62765i	−0.581110	+	0.813825i	$0.697382\pi$
$854$	−661.891	−	99.8873i	−0.775048	−	0.116964i
$855$		0			0
$856$	−209.213	−	362.367i	−0.244407	−	0.423326i
$857$	−950.012	−	548.489i	−1.10853	−	0.640011i	−0.170083	−	0.985430i	$-0.554404\pi$
$857$	−950.012	−	548.489i	−1.10853	−	0.640011i	−0.938449	+	0.345419i	$0.887737\pi$
$858$		0			0
$859$	−234.305	+	135.276i	−0.272764	+	0.157481i	−0.630143	−	0.776479i	$-0.717004\pi$
$859$	−234.305	+	135.276i	−0.272764	+	0.157481i	0.357379	+	0.933959i	$0.383670\pi$
$860$		−	222.877i		−	0.259159i
$861$		0			0
$862$	−665.042			−0.771511
$863$	134.107	+	232.280i	0.155396	+	0.269154i	0.933203	−	0.359349i	$-0.117001\pi$
$863$	134.107	+	232.280i	0.155396	+	0.269154i	−0.777807	+	0.628503i	$0.783668\pi$
$864$		0			0
$865$	140.945	−	244.125i	0.162943	−	0.282225i
$866$	39.2284	−	22.6485i	0.0452984	−	0.0261530i
$867$		0			0
$868$	45.9576	−	57.6075i	0.0529465	−	0.0663681i
$869$	−1047.60			−1.20552
$870$		0			0
$871$	668.519	+	385.970i	0.767530	+	0.443134i
$872$	−76.8228	+	133.061i	−0.0880995	+	0.152593i
$873$		0			0
$874$			807.025i			0.923370i
$875$	28.5792	+	72.8576i	0.0326619	+	0.0832658i
$876$		0			0
$877$	−253.705	−	439.430i	−0.289288	−	0.501061i	0.684352	−	0.729152i	$-0.260085\pi$
$877$	−253.705	−	439.430i	−0.289288	−	0.501061i	−0.973640	+	0.228091i	$0.926752\pi$
$878$	468.145	+	270.284i	0.533195	+	0.307840i
$879$		0			0
$880$	89.7354	−	51.8088i	0.101972	−	0.0588736i
$881$			833.545i			0.946135i	0.881026	+	0.473067i	$0.156853\pi$
$881$			833.545i			0.946135i	−0.881026	+	0.473067i	$0.843147\pi$
$882$		0			0
$883$	−1350.99			−1.53000			−0.765002	−	0.644028i	$-0.777262\pi$
$883$	−1350.99			−1.53000			−0.765002	+	0.644028i	$0.777262\pi$
$884$	−217.090	−	376.012i	−0.245577	−	0.425353i
$885$		0			0
$886$	−87.4985	+	151.552i	−0.0987568	+	0.171052i
$887$	−324.005	+	187.065i	−0.365282	+	0.210896i	−0.671395	−	0.741099i	$-0.734305\pi$
$887$	−324.005	+	187.065i	−0.365282	+	0.210896i	0.306113	+	0.951995i	$0.400971\pi$
$888$		0			0
$889$	−664.518	+	260.664i	−0.747489	+	0.293211i
$890$	−34.9897			−0.0393142
$891$		0			0
$892$	436.326	+	251.913i	0.489154	+	0.282413i
$893$	1204.63	−	2086.48i	1.34897	−	2.33649i
$894$		0			0
$895$			172.416i			0.192644i
$896$	61.9089	+	49.3891i	0.0690948	+	0.0551218i
$897$		0			0
$898$	188.787	+	326.989i	0.210230	+	0.364130i
$899$	−10.4999	−	6.06210i	−0.0116795	−	0.00674316i
$900$		0			0
$901$	−1365.04	+	788.105i	−1.51503	+	0.874701i
$902$			363.556i			0.403055i
$903$		0			0
$904$	135.166			0.149520
$905$	−237.036	−	410.559i	−0.261919	−	0.453657i
$906$		0			0
$907$	178.758	−	309.618i	0.197087	−	0.341365i	−0.750496	−	0.660875i	$-0.770185\pi$
$907$	178.758	−	309.618i	0.197087	−	0.341365i	0.947583	+	0.319510i	$0.103518\pi$
$908$	463.881	−	267.822i	0.510882	−	0.294958i
$909$		0			0
$910$	−25.9752	+	172.122i	−0.0285442	+	0.189145i
$911$	1503.55			1.65044			0.825219	−	0.564813i	$-0.191052\pi$
$911$	1503.55			1.65044			0.825219	+	0.564813i	$0.191052\pi$
$912$		0			0
$913$	−1342.41	−	775.043i	−1.47033	−	0.848897i
$914$	−317.731	+	550.327i	−0.347627	+	0.602108i
$915$		0			0
$916$			691.059i			0.754431i
$917$	325.652	−	408.202i	0.355127	−	0.445149i
$918$		0			0
$919$	312.499	+	541.265i	0.340043	+	0.588971i	0.984440	−	0.175719i	$-0.0562251\pi$
$919$	312.499	+	541.265i	0.340043	+	0.588971i	−0.644398	+	0.764691i	$0.722892\pi$
$920$	99.4620	+	57.4244i	0.108111	+	0.0624178i
$921$		0			0
$922$	129.245	−	74.6199i	0.140179	−	0.0809327i
$923$		−	269.409i		−	0.291884i
$924$		0			0
$925$	−9.93142			−0.0107367
$926$	416.171	+	720.829i	0.449429	+	0.778433i
$927$		0			0
$928$	6.51474	−	11.2839i	0.00702019	−	0.0121593i
$929$	942.883	−	544.374i	1.01494	−	0.585978i	0.102309	−	0.994753i	$-0.467377\pi$
$929$	942.883	−	544.374i	1.01494	−	0.585978i	0.912636	+	0.408774i	$0.134044\pi$
$930$		0			0
$931$	454.408	−	1471.25i	0.488086	−	1.58029i
$932$	576.129			0.618164
$933$		0			0
$934$	−447.837	−	258.559i	−0.479483	−	0.276829i
$935$	357.566	−	619.323i	0.382424	−	0.662377i
$936$		0			0
$937$		−	252.836i		−	0.269835i	−0.990857	−	0.134918i	$-0.956923\pi$
$937$		−	252.836i		−	0.269835i	0.990857	−	0.134918i	$-0.0430770\pi$
$938$	−904.670	+	354.867i	−0.964467	+	0.378323i
$939$		0			0
$940$	−171.433	−	296.930i	−0.182375	−	0.315883i
$941$	332.262	+	191.832i	0.353095	+	0.203859i	0.666048	−	0.745909i	$-0.267985\pi$
$941$	332.262	+	191.832i	0.353095	+	0.203859i	−0.312953	+	0.949769i	$0.601318\pi$
$942$		0			0
$943$	−348.975	+	201.481i	−0.370069	+	0.213660i
$944$		−	281.398i		−	0.298091i
$945$		0			0
$946$	816.495			0.863103
$947$	−140.892	−	244.032i	−0.148777	−	0.257690i	0.781999	−	0.623280i	$-0.214200\pi$
$947$	−140.892	−	244.032i	−0.148777	−	0.257690i	−0.930776	+	0.365591i	$0.880867\pi$
$948$		0			0
$949$	76.6377	−	132.740i	0.0807562	−	0.139874i
$950$	192.438	−	111.104i	0.202567	−	0.116952i
$951$		0			0
$952$	540.463	+	81.5624i	0.567713	+	0.0856748i
$953$	332.322			0.348711			0.174356	−	0.984683i	$-0.444216\pi$
$953$	332.322			0.348711			0.174356	+	0.984683i	$0.444216\pi$
$954$		0			0
$955$	−320.869	−	185.254i	−0.335988	−	0.193983i
$956$	−188.810	+	327.028i	−0.197500	+	0.342080i
$957$		0			0
$958$			688.971i			0.719177i
$959$	−257.900	+	1708.94i	−0.268926	+	1.78200i
$960$		0			0
$961$	−466.646	−	808.255i	−0.485584	−	0.841056i
$962$	−19.1300	−	11.0447i	−0.0198857	−	0.0114810i
$963$		0			0
$964$	−169.478	+	97.8480i	−0.175807	+	0.101502i
$965$			235.457i			0.243997i
$966$		0			0
$967$	1155.53			1.19496			0.597482	−	0.801882i	$-0.296168\pi$
$967$	1155.53			1.19496			0.597482	+	0.801882i	$0.296168\pi$
$968$	18.6782	+	32.3515i	0.0192956	+	0.0334210i
$969$		0			0
$970$	−114.334	+	198.032i	−0.117870	+	0.204157i
$971$	1307.94	−	755.140i	1.34700	−	0.777693i	0.359179	−	0.933269i	$-0.383057\pi$
$971$	1307.94	−	755.140i	1.34700	−	0.777693i	0.987824	+	0.155576i	$0.0497233\pi$
$972$		0			0
$973$	−398.555	−	1016.04i	−0.409614	−	1.04424i
$974$	276.866			0.284257
$975$		0			0
$976$	234.236	+	135.236i	0.239996	+	0.138562i
$977$	400.808	−	694.220i	0.410244	−	0.710563i	−0.584672	−	0.811269i	$-0.698777\pi$
$977$	400.808	−	694.220i	0.410244	−	0.710563i	0.994916	+	0.100706i	$0.0321103\pi$
$978$		0			0
$979$		−	128.182i		−	0.130932i
$980$	−148.991	−	160.691i	−0.152032	−	0.163971i
$981$		0			0
$982$	246.937	+	427.707i	0.251463	+	0.435547i
$983$	948.116	+	547.395i	0.964513	+	0.556862i	0.897559	−	0.440894i	$-0.145339\pi$
$983$	948.116	+	547.395i	0.964513	+	0.556862i	0.0669540	+	0.997756i	$0.478672\pi$
$984$		0			0
$985$	473.928	−	273.623i	0.481146	−	0.277790i
$986$		−	89.9249i		−	0.0912018i
$987$		0			0
$988$	494.235			0.500238
$989$	452.498	+	783.750i	0.457531	+	0.792467i
$990$		0			0
$991$	−21.9962	+	38.0986i	−0.0221960	+	0.0384446i	−0.876910	−	0.480655i	$-0.840399\pi$
$991$	−21.9962	+	38.0986i	−0.0221960	+	0.0384446i	0.854714	+	0.519099i	$0.173732\pi$
$992$	−25.7873	+	14.8883i	−0.0259953	+	0.0150084i
$993$		0			0
$994$	265.123	+	211.507i	0.266723	+	0.212784i
$995$	−219.060			−0.220161
$996$		0			0
$997$	10.6141	+	6.12803i	0.0106460	+	0.00614647i	0.505314	−	0.862936i	$-0.331377\pi$
$997$	10.6141	+	6.12803i	0.0106460	+	0.00614647i	−0.494668	+	0.869082i	$0.664710\pi$
$998$	−237.191	+	410.827i	−0.237666	+	0.411650i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.b.451.3		8
3.2	odd	2		210.3.o.a.31.2	✓	8
7.5	odd	6	inner	630.3.v.b.271.3		8
15.2	even	4		1050.3.q.c.199.7		16
15.8	even	4		1050.3.q.c.199.2		16
15.14	odd	2		1050.3.p.b.451.3		8
21.5	even	6		210.3.o.a.61.2	yes	8
21.11	odd	6		1470.3.f.a.391.6		8
21.17	even	6		1470.3.f.a.391.7		8
105.47	odd	12		1050.3.q.c.649.2		16
105.68	odd	12		1050.3.q.c.649.7		16
105.89	even	6		1050.3.p.b.901.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.2	✓	8	3.2	odd	2
210.3.o.a.61.2	yes	8	21.5	even	6
630.3.v.b.271.3		8	7.5	odd	6	inner
630.3.v.b.451.3		8	1.1	even	1	trivial
1050.3.p.b.451.3		8	15.14	odd	2
1050.3.p.b.901.3		8	105.89	even	6
1050.3.q.c.199.2		16	15.8	even	4
1050.3.q.c.199.7		16	15.2	even	4
1050.3.q.c.649.2		16	105.47	odd	12
1050.3.q.c.649.7		16	105.68	odd	12
1470.3.f.a.391.6		8	21.11	odd	6
1470.3.f.a.391.7		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +(6.51658 - 2.55620i) q^{7} -2.82843 q^{8} +(-2.73861 - 1.58114i) q^{10} +(5.79240 - 10.0327i) q^{11} -7.86371i q^{13} +(7.73861 + 6.17364i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-23.9080 - 13.8033i) q^{17} +(27.2149 - 15.7125i) q^{19} -4.47214i q^{20} +16.3834 q^{22} +(9.07959 + 15.7263i) q^{23} +(2.50000 - 4.33013i) q^{25} +(9.63104 - 5.56049i) q^{26} +(-2.08911 + 13.8433i) q^{28} +2.30331 q^{29} +(-4.55860 - 2.63191i) q^{31} +(2.82843 - 4.89898i) q^{32} -39.0416i q^{34} +(-9.76139 + 12.2358i) q^{35} +(-0.993142 - 1.72017i) q^{37} +(38.4876 + 22.2208i) q^{38} +(5.47723 - 3.16228i) q^{40} +22.1905i q^{41} +49.8368 q^{43} +(11.5848 + 20.0655i) q^{44} +(-12.8405 + 22.2404i) q^{46} +(66.3956 - 38.3335i) q^{47} +(35.9317 - 33.3154i) q^{49} +7.07107 q^{50} +(13.6204 + 7.86371i) q^{52} +(28.5477 - 49.4461i) q^{53} +25.9044i q^{55} +(-18.4317 + 7.23003i) q^{56} +(1.62869 + 2.82097i) q^{58} +(60.9245 + 35.1748i) q^{59} +(-58.5590 + 33.8091i) q^{61} -7.44416i q^{62} +8.00000 q^{64} +(8.79190 + 15.2280i) q^{65} +(-49.0823 + 85.0131i) q^{67} +(47.8160 - 27.6066i) q^{68} +(-21.8881 - 3.30318i) q^{70} +34.2597 q^{71} +(16.8801 + 9.74573i) q^{73} +(1.40452 - 2.43269i) q^{74} +62.8501i q^{76} +(12.1010 - 80.1856i) q^{77} +(-45.2142 - 78.3134i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-27.1777 + 15.6911i) q^{82} -133.803i q^{83} +61.7302 q^{85} +(35.2400 + 61.0374i) q^{86} +(-16.3834 + 28.3768i) q^{88} +(9.58232 - 5.53235i) q^{89} +(-20.1012 - 51.2445i) q^{91} -36.3184 q^{92} +(93.8975 + 54.2118i) q^{94} +(-35.1342 + 60.8543i) q^{95} -72.3112i q^{97} +(66.2104 + 20.4496i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more