LMFDB - Embedded newform 684.3.s.a.445.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(445,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("684.445");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.s (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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.29
Character	$\chi$	$=$	684.445
Dual form			684.3.s.a.601.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85853 - 2.35496i) q^{3} +(3.56049 + 6.16694i) q^{5} +(-5.30926 - 9.19591i) q^{7} +(-2.09172 - 8.75355i) q^{9} +O(q^{10})$	\(q+(1.85853 - 2.35496i) q^{3} +(3.56049 + 6.16694i) q^{5} +(-5.30926 - 9.19591i) q^{7} +(-2.09172 - 8.75355i) q^{9} +(-9.75715 - 16.8999i) q^{11} +1.06028i q^{13} +(21.1402 + 3.07664i) q^{15} +(-14.2828 + 24.7386i) q^{17} +(15.2465 - 11.3377i) q^{19} +(-31.5235 - 4.58777i) q^{21} -31.1050 q^{23} +(-12.8541 + 22.2640i) q^{25} +(-24.5018 - 11.3428i) q^{27} +(-37.8929 - 21.8775i) q^{29} +(22.3220 + 12.8876i) q^{31} +(-57.9326 - 8.43122i) q^{33} +(37.8071 - 65.4838i) q^{35} -33.5831i q^{37} +(2.49692 + 1.97056i) q^{39} +(23.5018 - 13.5688i) q^{41} +32.3291 q^{43} +(46.5351 - 44.0664i) q^{45} +(-17.5563 + 30.4085i) q^{47} +(-31.8765 + 55.2117i) q^{49} +(31.7134 + 79.6129i) q^{51} +(-2.36455 + 1.36517i) q^{53} +(69.4804 - 120.344i) q^{55} +(1.63633 - 56.9765i) q^{57} +(33.0973 - 19.1087i) q^{59} +(17.8636 - 30.9406i) q^{61} +(-69.3914 + 65.7101i) q^{63} +(-6.53867 + 3.77511i) q^{65} -104.936i q^{67} +(-57.8096 + 73.2512i) q^{69} +(-75.4263 - 43.5474i) q^{71} +(6.07578 - 10.5236i) q^{73} +(28.5411 + 71.6493i) q^{75} +(-103.606 + 179.452i) q^{77} +24.2015i q^{79} +(-72.2494 + 36.6200i) q^{81} +(-38.3156 - 66.3645i) q^{83} -203.415 q^{85} +(-121.946 + 48.5765i) q^{87} +(110.455 - 63.7714i) q^{89} +(9.75022 - 5.62929i) q^{91} +(71.8361 - 28.6155i) q^{93} +(124.204 + 53.6569i) q^{95} -83.3603i q^{97} +(-127.525 + 120.760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q - q^7 + 4 * q^9	$ 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) $ 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	1.85853	−	2.35496i	0.619511	−	0.784988i
$3$	1.85853	−	2.35496i	0.619511	−	0.784988i
$4$		0			0
$5$	3.56049	+	6.16694i	0.712097	+	1.23339i	0.964068	+	0.265654i	$0.0855878\pi$
$5$	3.56049	+	6.16694i	0.712097	+	1.23339i	−0.251971	+	0.967735i	$0.581079\pi$
$6$		0			0
$7$	−5.30926	−	9.19591i	−0.758466	−	1.31370i	−0.943633	−	0.330994i	$-0.892616\pi$
$7$	−5.30926	−	9.19591i	−0.758466	−	1.31370i	0.185167	−	0.982707i	$-0.440717\pi$
$8$		0			0
$9$	−2.09172	−	8.75355i	−0.232413	−	0.972617i
$10$		0			0
$11$	−9.75715	−	16.8999i	−0.887014	−	1.53635i	−0.843388	−	0.537305i	$-0.819443\pi$
$11$	−9.75715	−	16.8999i	−0.887014	−	1.53635i	−0.0436254	−	0.999048i	$-0.513891\pi$
$12$		0			0
$13$			1.06028i			0.0815599i	0.999168	+	0.0407799i	$0.0129843\pi$
$13$			1.06028i			0.0815599i	−0.999168	+	0.0407799i	$0.987016\pi$
$14$		0			0
$15$	21.1402	+	3.07664i	1.40935	+	0.205109i
$16$		0			0
$17$	−14.2828	+	24.7386i	−0.840165	+	1.45521i	0.0495890	+	0.998770i	$0.484209\pi$
$17$	−14.2828	+	24.7386i	−0.840165	+	1.45521i	−0.889754	+	0.456439i	$0.849124\pi$
$18$		0			0
$19$	15.2465	−	11.3377i	0.802449	−	0.596720i
$19$	15.2465	−	11.3377i	0.802449	−	0.596720i
$20$		0			0
$21$	−31.5235	−	4.58777i	−1.50112	−	0.218465i
$22$		0			0
$23$	−31.1050			−1.35239			−0.676195	−	0.736722i	$-0.736373\pi$
$23$	−31.1050			−1.35239			−0.676195	+	0.736722i	$0.736373\pi$
$24$		0			0
$25$	−12.8541	+	22.2640i	−0.514165	+	0.890560i
$26$		0			0
$27$	−24.5018	−	11.3428i	−0.907476	−	0.420105i
$28$		0			0
$29$	−37.8929	−	21.8775i	−1.30665	−	0.754396i	−0.325117	−	0.945674i	$-0.605404\pi$
$29$	−37.8929	−	21.8775i	−1.30665	−	0.754396i	−0.981536	+	0.191277i	$0.938737\pi$
$30$		0			0
$31$	22.3220	+	12.8876i	0.720065	+	0.415730i	0.814777	−	0.579775i	$-0.196860\pi$
$31$	22.3220	+	12.8876i	0.720065	+	0.415730i	−0.0947114	+	0.995505i	$0.530193\pi$
$32$		0			0
$33$	−57.9326	−	8.43122i	−1.75553	−	0.255491i
$34$		0			0
$35$	37.8071	−	65.4838i	1.08020	−	1.87097i
$36$		0			0
$37$		−	33.5831i		−	0.907651i	−0.891091	−	0.453826i	$-0.850059\pi$
$37$		−	33.5831i		−	0.907651i	0.891091	−	0.453826i	$-0.149941\pi$
$38$		0			0
$39$	2.49692	+	1.97056i	0.0640235	+	0.0505272i
$40$		0			0
$41$	23.5018	−	13.5688i	0.573214	−	0.330945i	−0.185218	−	0.982697i	$-0.559299\pi$
$41$	23.5018	−	13.5688i	0.573214	−	0.330945i	0.758432	+	0.651752i	$0.225966\pi$
$42$		0			0
$43$	32.3291			0.751840			0.375920	−	0.926652i	$-0.377327\pi$
$43$	32.3291			0.751840			0.375920	+	0.926652i	$0.377327\pi$
$44$		0			0
$45$	46.5351	−	44.0664i	1.03411	−	0.979254i
$46$		0			0
$47$	−17.5563	+	30.4085i	−0.373539	+	0.646989i	−0.990107	−	0.140313i	$-0.955189\pi$
$47$	−17.5563	+	30.4085i	−0.373539	+	0.646989i	0.616568	+	0.787302i	$0.288523\pi$
$48$		0			0
$49$	−31.8765	+	55.2117i	−0.650540	+	1.12677i
$50$		0			0
$51$	31.7134	+	79.6129i	0.621831	+	1.56104i
$52$		0			0
$53$	−2.36455	+	1.36517i	−0.0446141	+	0.0257579i	−0.522141	−	0.852859i	$-0.674867\pi$
$53$	−2.36455	+	1.36517i	−0.0446141	+	0.0257579i	0.477527	+	0.878617i	$0.341533\pi$
$54$		0			0
$55$	69.4804	−	120.344i	1.26328	−	2.18806i
$56$		0			0
$57$	1.63633	−	56.9765i	0.0287075	−	0.999588i
$58$		0			0
$59$	33.0973	−	19.1087i	0.560971	−	0.323877i	−0.192564	−	0.981284i	$-0.561680\pi$
$59$	33.0973	−	19.1087i	0.560971	−	0.323877i	0.753535	+	0.657408i	$0.228347\pi$
$60$		0			0
$61$	17.8636	−	30.9406i	0.292846	−	0.507223i	−0.681636	−	0.731692i	$-0.738731\pi$
$61$	17.8636	−	30.9406i	0.292846	−	0.507223i	0.974481	+	0.224468i	$0.0720645\pi$
$62$		0			0
$63$	−69.3914	+	65.7101i	−1.10145	+	1.04302i
$64$		0			0
$65$	−6.53867	+	3.77511i	−0.100595	+	0.0580785i
$66$		0			0
$67$		−	104.936i		−	1.56621i	−0.621888	−	0.783106i	$-0.713634\pi$
$67$		−	104.936i		−	1.56621i	0.621888	−	0.783106i	$-0.286366\pi$
$68$		0			0
$69$	−57.8096	+	73.2512i	−0.837821	+	1.06161i
$70$		0			0
$71$	−75.4263	−	43.5474i	−1.06234	−	0.613344i	−0.136263	−	0.990673i	$-0.543509\pi$
$71$	−75.4263	−	43.5474i	−1.06234	−	0.613344i	−0.926079	+	0.377329i	$0.876843\pi$
$72$		0			0
$73$	6.07578	−	10.5236i	0.0832299	−	0.144158i	−0.821406	−	0.570344i	$-0.806810\pi$
$73$	6.07578	−	10.5236i	0.0832299	−	0.144158i	0.904636	+	0.426186i	$0.140143\pi$
$74$		0			0
$75$	28.5411	+	71.6493i	0.380548	+	0.955325i
$76$		0			0
$77$	−103.606	+	179.452i	−1.34554	+	2.33054i
$78$		0			0
$79$			24.2015i			0.306348i	0.988199	+	0.153174i	$0.0489496\pi$
$79$			24.2015i			0.306348i	−0.988199	+	0.153174i	$0.951050\pi$
$80$		0			0
$81$	−72.2494	+	36.6200i	−0.891968	+	0.452098i
$82$		0			0
$83$	−38.3156	−	66.3645i	−0.461633	−	0.799572i	0.537409	−	0.843322i	$-0.319403\pi$
$83$	−38.3156	−	66.3645i	−0.461633	−	0.799572i	−0.999043	+	0.0437492i	$0.986070\pi$
$84$		0			0
$85$	−203.415			−2.39312
$86$		0			0
$87$	−121.946	+	48.5765i	−1.40168	+	0.558351i
$88$		0			0
$89$	110.455	−	63.7714i	1.24107	−	0.716533i	0.271759	−	0.962365i	$-0.412395\pi$
$89$	110.455	−	63.7714i	1.24107	−	0.716533i	0.969312	+	0.245833i	$0.0790615\pi$
$90$		0			0
$91$	9.75022	−	5.62929i	0.107145	−	0.0618604i
$92$		0			0
$93$	71.8361	−	28.6155i	0.772431	−	0.307694i
$94$		0			0
$95$	124.204	+	53.6569i	1.30741	+	0.564809i
$96$		0			0
$97$		−	83.3603i		−	0.859384i	−0.902975	−	0.429692i	$-0.858622\pi$
$97$		−	83.3603i		−	0.859384i	0.902975	−	0.429692i	$-0.141378\pi$
$98$		0			0
$99$	−127.525	+	120.760i	−1.28813	+	1.21979i
$100$		0			0
$101$	−57.4146	+	99.4450i	−0.568461	+	0.984604i	0.428257	+	0.903657i	$0.359128\pi$
$101$	−57.4146	+	99.4450i	−0.568461	+	0.984604i	−0.996718	+	0.0809471i	$0.974206\pi$
$102$		0			0
$103$	−58.0132	−	33.4940i	−0.563235	−	0.325184i	0.191208	−	0.981550i	$-0.438760\pi$
$103$	−58.0132	−	33.4940i	−0.563235	−	0.325184i	−0.754443	+	0.656366i	$0.772093\pi$
$104$		0			0
$105$	−83.9464	−	210.738i	−0.799489	−	2.00703i
$106$		0			0
$107$			48.5633i			0.453862i	0.973911	+	0.226931i	$0.0728692\pi$
$107$			48.5633i			0.453862i	−0.973911	+	0.226931i	$0.927131\pi$
$108$		0			0
$109$	160.233	+	92.5106i	1.47003	+	0.848721i	0.999434	−	0.0336282i	$-0.0107062\pi$
$109$	160.233	+	92.5106i	1.47003	+	0.848721i	0.470594	+	0.882350i	$0.344040\pi$
$110$		0			0
$111$	−79.0870	−	62.4152i	−0.712495	−	0.562299i
$112$		0			0
$113$	179.963	+	103.902i	1.59259	+	0.919485i	0.992860	+	0.119286i	$0.0380604\pi$
$113$	179.963	+	103.902i	1.59259	+	0.919485i	0.599734	+	0.800199i	$0.295273\pi$
$114$		0			0
$115$	−110.749	−	191.823i	−0.963034	−	1.66802i
$116$		0			0
$117$	9.28120	−	2.21780i	0.0793265	−	0.0189556i
$118$		0			0
$119$	303.325			2.54895
$120$		0			0
$121$	−129.904	+	225.000i	−1.07359	+	1.85951i
$122$		0			0
$123$	11.7249	−	80.5638i	0.0953240	−	0.654991i
$124$		0			0
$125$	−5.04337			−0.0403470
$126$		0			0
$127$	−73.9519	+	42.6961i	−0.582298	+	0.336190i	−0.762046	−	0.647523i	$-0.775805\pi$
$127$	−73.9519	+	42.6961i	−0.582298	+	0.336190i	0.179748	+	0.983713i	$0.442472\pi$
$128$		0			0
$129$	60.0847	−	76.1339i	0.465773	−	0.590185i
$130$		0			0
$131$	28.1119	+	48.6912i	0.214594	+	0.371688i	0.953147	−	0.302508i	$-0.0978237\pi$
$131$	28.1119	+	48.6912i	0.214594	+	0.371688i	−0.738553	+	0.674196i	$0.764490\pi$
$132$		0			0
$133$	−185.208	−	80.0110i	−1.39254	−	0.601587i
$134$		0			0
$135$	−17.2878	−	191.487i	−0.128058	−	1.41843i
$136$		0			0
$137$	70.4312	−	121.990i	0.514096	−	0.890440i	−0.485770	−	0.874087i	$-0.661461\pi$
$137$	70.4312	−	121.990i	0.514096	−	0.890440i	0.999866	−	0.0163539i	$-0.00520585\pi$
$138$		0			0
$139$	−116.136			−0.835513			−0.417757	−	0.908559i	$-0.637184\pi$
$139$	−116.136			−0.835513			−0.417757	+	0.908559i	$0.637184\pi$
$140$		0			0
$141$	38.9819	+	97.8597i	0.276467	+	0.694040i
$142$		0			0
$143$	17.9186	−	10.3453i	0.125305	−	0.0723447i
$144$		0			0
$145$		−	311.578i		−	2.14881i
$146$		0			0
$147$	70.7781	+	177.681i	0.481484	+	1.20871i
$148$		0			0
$149$	−1.89204	−	3.27712i	−0.0126983	−	0.0219941i	0.859606	−	0.510957i	$-0.170709\pi$
$149$	−1.89204	−	3.27712i	−0.0126983	−	0.0219941i	−0.872305	+	0.488963i	$0.837375\pi$
$150$		0			0
$151$	56.7315	−	32.7540i	0.375705	−	0.216914i	−0.300243	−	0.953863i	$-0.597068\pi$
$151$	56.7315	−	32.7540i	0.375705	−	0.216914i	0.675948	+	0.736949i	$0.263734\pi$
$152$		0			0
$153$	246.426	+	73.2793i	1.61063	+	0.478949i
$154$		0			0
$155$			183.545i			1.18416i
$156$		0			0
$157$	4.95127	+	8.57585i	0.0315368	+	0.0546233i	0.881363	−	0.472440i	$-0.156627\pi$
$157$	4.95127	+	8.57585i	0.0315368	+	0.0546233i	−0.849826	+	0.527063i	$0.823293\pi$
$158$		0			0
$159$	−1.17965	+	8.10564i	−0.00741920	+	0.0509788i
$160$		0			0
$161$	165.144	+	286.039i	1.02574	+	1.77664i
$162$		0			0
$163$	−31.6590			−0.194227			−0.0971135	−	0.995273i	$-0.530961\pi$
$163$	−31.6590			−0.194227			−0.0971135	+	0.995273i	$0.530961\pi$
$164$		0			0
$165$	−154.273	−	387.286i	−0.934990	−	2.34719i
$166$		0			0
$167$			158.022i			0.946238i	0.880998	+	0.473119i	$0.156872\pi$
$167$			158.022i			0.946238i	−0.880998	+	0.473119i	$0.843128\pi$
$168$		0			0
$169$	167.876			0.993348
$170$		0			0
$171$	−131.137	−	109.746i	−0.766880	−	0.641790i
$172$		0			0
$173$		−	247.952i		−	1.43325i	−0.697458	−	0.716626i	$-0.745686\pi$
$173$		−	247.952i		−	1.43325i	0.697458	−	0.716626i	$-0.254314\pi$
$174$		0			0
$175$	272.983			1.55991
$176$		0			0
$177$	16.5120	−	113.457i	0.0932880	−	0.641001i
$178$		0			0
$179$		−	161.562i		−	0.902580i	−0.892377	−	0.451290i	$-0.850964\pi$
$179$		−	161.562i		−	0.902580i	0.892377	−	0.451290i	$-0.149036\pi$
$180$		0			0
$181$	−93.7625	+	54.1338i	−0.518025	+	0.299082i	−0.736126	−	0.676844i	$-0.763347\pi$
$181$	−93.7625	+	54.1338i	−0.518025	+	0.299082i	0.218101	+	0.975926i	$0.430014\pi$
$182$		0			0
$183$	−39.6641	−	99.5723i	−0.216744	−	0.544111i
$184$		0			0
$185$	207.105	−	119.572i	1.11949	−	0.646336i
$186$		0			0
$187$	557.438			2.98095
$188$		0			0
$189$	25.7790	+	285.539i	0.136397	+	1.51079i
$190$		0			0
$191$	64.8838	+	112.382i	0.339706	+	0.588388i	0.984377	−	0.176072i	$-0.0563391\pi$
$191$	64.8838	+	112.382i	0.339706	+	0.588388i	−0.644671	+	0.764460i	$0.723006\pi$
$192$		0			0
$193$	127.382	−	73.5439i	0.660010	−	0.381057i	−0.132271	−	0.991214i	$-0.542227\pi$
$193$	127.382	−	73.5439i	0.660010	−	0.381057i	0.792281	+	0.610157i	$0.208894\pi$
$194$		0			0
$195$	−3.26209	+	22.4145i	−0.0167287	+	0.114946i
$196$		0			0
$197$	−89.1428			−0.452501			−0.226251	−	0.974069i	$-0.572647\pi$
$197$	−89.1428			−0.452501			−0.226251	+	0.974069i	$0.572647\pi$
$198$		0			0
$199$	76.6154	+	132.702i	0.385002	+	0.666843i	0.991769	−	0.128036i	$-0.0408674\pi$
$199$	76.6154	+	132.702i	0.385002	+	0.666843i	−0.606767	+	0.794879i	$0.707534\pi$
$200$		0			0
$201$	−247.121	−	195.027i	−1.22946	−	0.970286i
$202$		0			0
$203$			464.613i			2.28873i
$204$		0			0
$205$	167.356	+	96.6228i	0.816368	+	0.471331i
$206$		0			0
$207$	65.0629	+	272.279i	0.314314	+	1.31536i
$208$		0			0
$209$	−340.368	−	147.041i	−1.62856	−	0.703546i
$210$		0			0
$211$	151.435	−	87.4313i	0.717703	−	0.414366i	−0.0962034	−	0.995362i	$-0.530670\pi$
$211$	151.435	−	87.4313i	0.717703	−	0.414366i	0.813907	+	0.580995i	$0.197337\pi$
$212$		0			0
$213$	−242.735	+	96.6921i	−1.13960	+	0.453953i
$214$		0			0
$215$	115.107	+	199.372i	0.535383	+	0.927311i
$216$		0			0
$217$		−	273.695i		−	1.26127i
$218$		0			0
$219$	−13.4906	−	33.8666i	−0.0616009	−	0.154642i
$220$		0			0
$221$	−26.2298	−	15.1438i	−0.118687	−	0.0685238i
$222$		0			0
$223$			47.1951i			0.211637i	0.994385	+	0.105819i	$0.0337463\pi$
$223$			47.1951i			0.211637i	−0.994385	+	0.105819i	$0.966254\pi$
$224$		0			0
$225$	221.776	+	65.9492i	0.985672	+	0.293108i
$226$		0			0
$227$	−38.5978	+	22.2844i	−0.170034	+	0.0981693i	−0.582602	−	0.812758i	$-0.697965\pi$
$227$	−38.5978	+	22.2844i	−0.170034	+	0.0981693i	0.412568	+	0.910927i	$0.364632\pi$
$228$		0			0
$229$	180.357	−	312.387i	0.787584	−	1.36414i	−0.139859	−	0.990171i	$-0.544665\pi$
$229$	180.357	−	312.387i	0.787584	−	1.36414i	0.927443	−	0.373964i	$-0.122002\pi$
$230$		0			0
$231$	230.046	+	577.506i	0.995872	+	2.50003i
$232$		0			0
$233$	−187.563	+	324.868i	−0.804991	+	1.39429i	0.111306	+	0.993786i	$0.464496\pi$
$233$	−187.563	+	324.868i	−0.804991	+	1.39429i	−0.916297	+	0.400499i	$0.868837\pi$
$234$		0			0
$235$	−250.036			−1.06398
$236$		0			0
$237$	56.9937	+	44.9793i	0.240480	+	0.189786i
$238$		0			0
$239$	122.147	−	211.564i	0.511074	−	0.885206i	−0.488844	−	0.872371i	$-0.662581\pi$
$239$	122.147	−	211.564i	0.511074	−	0.885206i	0.999918	−	0.0128346i	$-0.00408548\pi$
$240$		0			0
$241$	−92.4923	−	53.4005i	−0.383786	−	0.221579i	0.295678	−	0.955288i	$-0.404454\pi$
$241$	−92.4923	−	53.4005i	−0.383786	−	0.221579i	−0.679464	+	0.733709i	$0.737788\pi$
$242$		0			0
$243$	−48.0392	+	238.204i	−0.197692	+	0.980264i
$244$		0			0
$245$	−453.983			−1.85299
$246$		0			0
$247$	12.0211	+	16.1656i	0.0486684	+	0.0654477i
$248$		0			0
$249$	−227.497	−	33.1087i	−0.913642	−	0.132967i
$250$		0			0
$251$	−56.6823	−	98.1765i	−0.225826	−	0.391142i	0.730741	−	0.682655i	$-0.239175\pi$
$251$	−56.6823	−	98.1765i	−0.225826	−	0.391142i	−0.956567	+	0.291513i	$0.905841\pi$
$252$		0			0
$253$	303.496	+	525.671i	1.19959	+	2.07775i
$254$		0			0
$255$	−378.053	+	479.035i	−1.48256	+	1.87857i
$256$		0			0
$257$		−	51.3181i		−	0.199681i	−0.995003	−	0.0998407i	$-0.968167\pi$
$257$		−	51.3181i		−	0.199681i	0.995003	−	0.0998407i	$-0.0318333\pi$
$258$		0			0
$259$	−308.827	+	178.301i	−1.19238	+	0.688422i
$260$		0			0
$261$	−112.244	+	377.459i	−0.430055	+	1.44620i
$262$		0			0
$263$	42.9008			0.163121			0.0815605	−	0.996668i	$-0.474010\pi$
$263$	42.9008			0.163121			0.0815605	+	0.996668i	$0.474010\pi$
$264$		0			0
$265$	−16.8379	−	9.72134i	−0.0635391	−	0.0366843i
$266$		0			0
$267$	55.1053	−	378.639i	0.206387	−	1.41813i
$268$		0			0
$269$	111.541	+	64.3985i	0.414652	+	0.239400i	0.692787	−	0.721143i	$-0.256383\pi$
$269$	111.541	+	64.3985i	0.414652	+	0.239400i	−0.278134	+	0.960542i	$0.589716\pi$
$270$		0			0
$271$	137.721	−	238.539i	0.508195	−	0.880219i	−0.491760	−	0.870731i	$-0.663646\pi$
$271$	137.721	−	238.539i	0.508195	−	0.880219i	0.999955	−	0.00948823i	$-0.00302024\pi$
$272$		0			0
$273$	4.86431	−	33.4236i	0.0178180	−	0.122431i
$274$		0			0
$275$	501.678			1.82428
$276$		0			0
$277$	227.959	+	394.836i	0.822955	+	1.42540i	0.903472	+	0.428647i	$0.141010\pi$
$277$	227.959	+	394.836i	0.822955	+	1.42540i	−0.0805168	+	0.996753i	$0.525657\pi$
$278$		0			0
$279$	66.1211	−	222.354i	0.236993	−	0.796969i
$280$		0			0
$281$	84.8026	+	48.9608i	0.301789	+	0.174238i	0.643246	−	0.765659i	$-0.277587\pi$
$281$	84.8026	+	48.9608i	0.301789	+	0.174238i	−0.341457	+	0.939897i	$0.610921\pi$
$282$		0			0
$283$	−174.104	−	301.556i	−0.615207	−	1.06557i	−0.990348	−	0.138603i	$-0.955739\pi$
$283$	−174.104	−	301.556i	−0.615207	−	1.06557i	0.375141	−	0.926968i	$-0.377594\pi$
$284$		0			0
$285$	357.197	−	192.773i	1.25332	−	0.676396i
$286$		0			0
$287$	−249.554	−	144.080i	−0.869527	−	0.502021i
$288$		0			0
$289$	−263.497	−	456.391i	−0.911756	−	1.57921i
$290$		0			0
$291$	−196.310	−	154.928i	−0.674607	−	0.532398i
$292$		0			0
$293$	−186.504	−	107.678i	−0.636533	−	0.367503i	0.146745	−	0.989174i	$-0.453120\pi$
$293$	−186.504	−	107.678i	−0.636533	−	0.367503i	−0.783278	+	0.621672i	$0.786454\pi$
$294$		0			0
$295$	235.685	+	136.073i	0.798932	+	0.461263i
$296$		0			0
$297$	47.3756	+	524.752i	0.159514	+	1.76684i
$298$		0			0
$299$		−	32.9799i		−	0.110301i
$300$		0			0
$301$	−171.644	−	297.295i	−0.570245	−	0.987693i
$302$		0			0
$303$	127.483	+	320.031i	0.420735	+	1.05621i
$304$		0			0
$305$	254.412			0.834138
$306$		0			0
$307$	238.269	+	137.565i	0.776121	+	0.448094i	0.835054	−	0.550168i	$-0.185436\pi$
$307$	238.269	+	137.565i	0.776121	+	0.448094i	−0.0589328	+	0.998262i	$0.518770\pi$
$308$		0			0
$309$	−186.697	+	74.3695i	−0.604196	+	0.240678i
$310$		0			0
$311$	−63.3112	+	109.658i	−0.203573	+	0.352599i	−0.949677	−	0.313231i	$-0.898589\pi$
$311$	−63.3112	+	109.658i	−0.203573	+	0.352599i	0.746104	+	0.665829i	$0.231922\pi$
$312$		0			0
$313$	33.3299	−	57.7291i	0.106485	−	0.184438i	−0.807859	−	0.589376i	$-0.799374\pi$
$313$	33.3299	−	57.7291i	0.106485	−	0.184438i	0.914344	+	0.404938i	$0.132707\pi$
$314$		0			0
$315$	−652.298	−	193.973i	−2.07079	−	0.615786i
$316$		0			0
$317$	427.004	+	246.531i	1.34701	+	0.777699i	0.987826	−	0.155566i	$-0.0497200\pi$
$317$	427.004	+	246.531i	1.34701	+	0.777699i	0.359189	+	0.933265i	$0.383053\pi$
$318$		0			0
$319$			853.848i			2.67664i
$320$		0			0
$321$	114.365	+	90.2564i	0.356277	+	0.281172i
$322$		0			0
$323$	62.7145	+	539.111i	0.194163	+	1.66908i
$324$		0			0
$325$	−23.6060	−	13.6289i	−0.0726339	−	0.0419352i
$326$		0			0
$327$	515.658	−	205.409i	1.57693	−	0.628163i
$328$		0			0
$329$	372.845			1.13327
$330$		0			0
$331$	127.344	−	73.5220i	0.384724	−	0.222121i	−0.295147	−	0.955452i	$-0.595369\pi$
$331$	127.344	−	73.5220i	0.384724	−	0.222121i	0.679872	+	0.733331i	$0.262035\pi$
$332$		0			0
$333$	−293.971	+	70.2464i	−0.882797	+	0.210950i
$334$		0			0
$335$	647.136	−	373.624i	1.93175	−	1.11530i
$336$		0			0
$337$	−245.298	+	141.623i	−0.727887	+	0.420246i	−0.817649	−	0.575718i	$-0.804723\pi$
$337$	−245.298	+	141.623i	−0.727887	+	0.420246i	0.0897619	+	0.995963i	$0.471389\pi$
$338$		0			0
$339$	579.152	−	230.702i	1.70841	−	0.680537i
$340$		0			0
$341$		−	502.986i		−	1.47503i
$342$		0			0
$343$	156.654			0.456718
$344$		0			0
$345$	−657.566	−	95.6989i	−1.90599	−	0.277388i
$346$		0			0
$347$	232.294	+	402.345i	0.669435	+	1.15950i	0.978062	+	0.208313i	$0.0667971\pi$
$347$	232.294	+	402.345i	0.669435	+	1.15950i	−0.308627	+	0.951183i	$0.599870\pi$
$348$		0			0
$349$	−127.826	−	221.400i	−0.366263	−	0.634385i	0.622715	−	0.782448i	$-0.286029\pi$
$349$	−127.826	−	221.400i	−0.366263	−	0.634385i	−0.988978	+	0.148063i	$0.952696\pi$
$350$		0			0
$351$	12.0266	−	25.9788i	0.0342637	−	0.0740136i
$352$		0			0
$353$	−206.718	−	358.047i	−0.585604	−	1.01430i	−0.994800	−	0.101850i	$-0.967524\pi$
$353$	−206.718	−	358.047i	−0.585604	−	1.01430i	0.409195	−	0.912447i	$-0.365809\pi$
$354$		0			0
$355$		−	620.200i		−	1.74704i
$356$		0			0
$357$	563.738	−	714.319i	1.57910	−	2.00089i
$358$		0			0
$359$	188.236	−	326.035i	0.524336	−	0.908176i	−0.475263	−	0.879844i	$-0.657647\pi$
$359$	188.236	−	326.035i	0.524336	−	0.908176i	0.999599	−	0.0283320i	$-0.00901957\pi$
$360$		0			0
$361$	103.914	−	345.721i	0.287850	−	0.957676i
$362$		0			0
$363$	288.437	+	724.089i	0.794592	+	1.99474i
$364$		0			0
$365$	86.5309			0.237071
$366$		0			0
$367$	183.277	−	317.445i	0.499392	−	0.864972i	−0.500608	−	0.865674i	$-0.666890\pi$
$367$	183.277	−	317.445i	0.499392	−	0.864972i	1.00000		0.000701836i	$0.000223401\pi$
$368$		0			0
$369$	−167.934	−	177.342i	−0.455106	−	0.480602i
$370$		0			0
$371$	25.1080	+	14.4961i	0.0676765	+	0.0390730i
$372$		0			0
$373$	−123.117	−	71.0814i	−0.330072	−	0.190567i	0.325801	−	0.945438i	$-0.394366\pi$
$373$	−123.117	−	71.0814i	−0.330072	−	0.190567i	−0.655873	+	0.754871i	$0.727699\pi$
$374$		0			0
$375$	−9.37326	+	11.8770i	−0.0249954	+	0.0316719i
$376$		0			0
$377$	23.1962	−	40.1771i	0.0615285	−	0.106570i
$378$		0			0
$379$		−	11.1059i		−	0.0293030i	−0.999893	−	0.0146515i	$-0.995336\pi$
$379$		−	11.1059i		−	0.0293030i	0.999893	−	0.0146515i	$-0.00466389\pi$
$380$		0			0
$381$	−36.8940	+	253.506i	−0.0968347	+	0.665371i
$382$		0			0
$383$	−483.815	+	279.331i	−1.26322	+	0.729323i	−0.973697	−	0.227847i	$-0.926832\pi$
$383$	−483.815	+	279.331i	−1.26322	+	0.729323i	−0.289528	+	0.957170i	$0.593498\pi$
$384$		0			0
$385$	−1475.56			−3.83262
$386$		0			0
$387$	−67.6234	−	282.995i	−0.174737	−	0.731252i
$388$		0			0
$389$	75.0524	−	129.995i	0.192937	−	0.334176i	−0.753285	−	0.657694i	$-0.771532\pi$
$389$	75.0524	−	129.995i	0.192937	−	0.334176i	0.946222	+	0.323517i	$0.104865\pi$
$390$		0			0
$391$	444.267	−	769.493i	1.13623	−	1.96801i
$392$		0			0
$393$	166.913	+	24.2916i	0.424714	+	0.0618108i
$394$		0			0
$395$	−149.249	+	86.1692i	−0.377847	+	0.218150i
$396$		0			0
$397$	279.859	−	484.729i	0.704933	−	1.22098i	−0.261782	−	0.965127i	$-0.584310\pi$
$397$	279.859	−	484.729i	0.704933	−	1.22098i	0.966716	−	0.255853i	$-0.0823564\pi$
$398$		0			0
$399$	−532.638	+	287.456i	−1.33493	+	0.720440i
$400$		0			0
$401$	−70.0143	+	40.4228i	−0.174599	+	0.100805i	−0.584753	−	0.811212i	$-0.698808\pi$
$401$	−70.0143	+	40.4228i	−0.174599	+	0.100805i	0.410154	+	0.912016i	$0.365475\pi$
$402$		0			0
$403$	−13.6645	+	23.6676i	−0.0339069	+	0.0587284i
$404$		0			0
$405$	−483.076	−	315.173i	−1.19278	−	0.778206i
$406$		0			0
$407$	−567.550	+	327.675i	−1.39447	+	0.805099i
$408$		0			0
$409$			648.731i			1.58614i	0.609130	+	0.793070i	$0.291519\pi$
$409$			648.731i			1.58614i	−0.609130	+	0.793070i	$0.708481\pi$
$410$		0			0
$411$	−156.384	−	392.586i	−0.380497	−	0.955197i
$412$		0			0
$413$	−351.444	−	202.906i	−0.850954	−	0.491299i
$414$		0			0
$415$	272.844	−	472.580i	0.657456	−	1.13875i
$416$		0			0
$417$	−215.843	+	273.497i	−0.517609	+	0.655868i
$418$		0			0
$419$	−84.2655	+	145.952i	−0.201111	+	0.348334i	−0.948887	−	0.315617i	$-0.897789\pi$
$419$	−84.2655	+	145.952i	−0.201111	+	0.348334i	0.747776	+	0.663951i	$0.231122\pi$
$420$		0			0
$421$			653.855i			1.55310i	0.630056	+	0.776549i	$0.283032\pi$
$421$			653.855i			1.55310i	−0.630056	+	0.776549i	$0.716968\pi$
$422$		0			0
$423$	302.905	+	90.0744i	0.716088	+	0.212942i
$424$		0			0
$425$	−367.186	−	635.985i	−0.863967	−	1.49643i
$426$		0			0
$427$	−379.370			−0.888453
$428$		0			0
$429$	8.93944	−	61.4247i	0.0208378	−	0.143181i
$430$		0			0
$431$	224.079	−	129.372i	0.519904	−	0.300167i	−0.216991	−	0.976173i	$-0.569624\pi$
$431$	224.079	−	129.372i	0.519904	−	0.300167i	0.736895	+	0.676007i	$0.236291\pi$
$432$		0			0
$433$	−650.365	+	375.488i	−1.50200	+	0.867179i	−0.502000	+	0.864867i	$0.667402\pi$
$433$	−650.365	+	375.488i	−1.50200	+	0.867179i	−0.999997	+	0.00231130i	$0.999264\pi$
$434$		0			0
$435$	−733.755	−	579.078i	−1.68679	−	1.33121i
$436$		0			0
$437$	−474.243	+	352.659i	−1.08523	+	0.806999i
$438$		0			0
$439$		−	55.3048i		−	0.125979i	−0.998014	−	0.0629895i	$-0.979937\pi$
$439$		−	55.3048i		−	0.125979i	0.998014	−	0.0629895i	$-0.0200635\pi$
$440$		0			0
$441$	549.975	+	163.545i	1.24711	+	0.370851i
$442$		0			0
$443$	−170.257	+	294.894i	−0.384328	+	0.665675i	−0.991676	−	0.128761i	$-0.958900\pi$
$443$	−170.257	+	294.894i	−0.384328	+	0.665675i	0.607348	+	0.794436i	$0.292233\pi$
$444$		0			0
$445$	786.549	+	454.114i	1.76753	+	1.02048i
$446$		0			0
$447$	−11.2339	−	1.63493i	−0.0251318	−	0.00365756i
$448$		0			0
$449$		−	881.944i		−	1.96424i	−0.188254	−	0.982120i	$-0.560283\pi$
$449$		−	881.944i		−	1.96424i	0.188254	−	0.982120i	$-0.439717\pi$
$450$		0			0
$451$	−458.621	−	264.785i	−1.01690	−	0.587106i
$452$		0			0
$453$	28.3029	−	194.475i	0.0624788	−	0.429305i
$454$		0			0
$455$	69.4310	+	40.0860i	0.152596	+	0.0881012i
$456$		0			0
$457$	−176.942	−	306.472i	−0.387181	−	0.670618i	0.604888	−	0.796311i	$-0.293218\pi$
$457$	−176.942	−	306.472i	−0.387181	−	0.670618i	−0.992069	+	0.125693i	$0.959885\pi$
$458$		0			0
$459$	630.561	−	444.133i	1.37377	−	0.967609i
$460$		0			0
$461$	−314.410			−0.682018			−0.341009	−	0.940060i	$-0.610769\pi$
$461$	−314.410			−0.682018			−0.341009	+	0.940060i	$0.610769\pi$
$462$		0			0
$463$	−446.192	+	772.827i	−0.963697	+	1.66917i	−0.250622	+	0.968085i	$0.580635\pi$
$463$	−446.192	+	772.827i	−0.963697	+	1.66917i	−0.713075	+	0.701088i	$0.752698\pi$
$464$		0			0
$465$	432.242	+	341.124i	0.929552	+	0.733600i
$466$		0			0
$467$	124.476			0.266545			0.133272	−	0.991079i	$-0.457452\pi$
$467$	124.476			0.266545			0.133272	+	0.991079i	$0.457452\pi$
$468$		0			0
$469$	−964.984	+	557.134i	−2.05754	+	1.18792i
$470$		0			0
$471$	29.3979	+	4.27843i	0.0624160	+	0.00908371i
$472$		0			0
$473$	−315.440	−	546.358i	−0.666892	−	1.15509i
$474$		0			0
$475$	56.4413	+	485.185i	0.118824	+	1.02144i
$476$		0			0
$477$	16.8961	+	17.8426i	0.0354215	+	0.0374059i
$478$		0			0
$479$	−443.507	+	768.176i	−0.925901	+	1.60371i	−0.135795	+	0.990737i	$0.543359\pi$
$479$	−443.507	+	768.176i	−0.925901	+	1.60371i	−0.790106	+	0.612971i	$0.789974\pi$
$480$		0			0
$481$	35.6074			0.0740279
$482$		0			0
$483$	980.537	+	142.702i	2.03010	+	0.295450i
$484$		0			0
$485$	514.078	−	296.803i	1.05995	−	0.611965i
$486$		0			0
$487$			458.100i			0.940657i	0.882491	+	0.470328i	$0.155865\pi$
$487$			458.100i			0.940657i	−0.882491	+	0.470328i	$0.844135\pi$
$488$		0			0
$489$	−58.8393	+	74.5559i	−0.120326	+	0.152466i
$490$		0			0
$491$	−480.198	−	831.727i	−0.978000	−	1.69395i	−0.669657	−	0.742671i	$-0.733559\pi$
$491$	−480.198	−	831.727i	−0.978000	−	1.69395i	−0.308343	−	0.951275i	$-0.599774\pi$
$492$		0			0
$493$	1082.44	−	624.944i	2.19561	−	1.26764i
$494$		0			0
$495$	−1198.77	−	356.475i	−2.42175	−	0.720152i
$496$		0			0
$497$			924.818i			1.86080i
$498$		0			0
$499$	−38.9749	−	67.5064i	−0.0781059	−	0.135283i	0.824327	−	0.566114i	$-0.191554\pi$
$499$	−38.9749	−	67.5064i	−0.0781059	−	0.135283i	−0.902433	+	0.430831i	$0.858221\pi$
$500$		0			0
$501$	372.136	+	293.689i	0.742786	+	0.586205i
$502$		0			0
$503$	−169.590	−	293.738i	−0.337156	−	0.583971i	0.646741	−	0.762710i	$-0.276132\pi$
$503$	−169.590	−	293.738i	−0.337156	−	0.583971i	−0.983897	+	0.178739i	$0.942798\pi$
$504$		0			0
$505$	−817.696			−1.61920
$506$		0			0
$507$	312.003	−	395.342i	0.615390	−	0.779767i
$508$		0			0
$509$		−	820.655i		−	1.61229i	−0.591718	−	0.806145i	$-0.701550\pi$
$509$		−	820.655i		−	1.61229i	0.591718	−	0.806145i	$-0.298450\pi$
$510$		0			0
$511$	−129.032			−0.252508
$512$		0			0
$513$	−502.170	+	104.855i	−0.978888	+	0.204396i
$514$		0			0
$515$		−	477.019i		−	0.926251i
$516$		0			0
$517$	685.199			1.32534
$518$		0			0
$519$	−583.919	−	460.828i	−1.12509	−	0.887914i
$520$		0			0
$521$			49.2700i			0.0945682i	0.998881	+	0.0472841i	$0.0150566\pi$
$521$			49.2700i			0.0945682i	−0.998881	+	0.0472841i	$0.984943\pi$
$522$		0			0
$523$	−216.127	+	124.781i	−0.413245	+	0.238587i	−0.692183	−	0.721722i	$-0.743351\pi$
$523$	−216.127	+	124.781i	−0.413245	+	0.238587i	0.278938	+	0.960309i	$0.410018\pi$
$524$		0			0
$525$	507.348	−	642.866i	0.966378	−	1.22451i
$526$		0			0
$527$	−637.643	+	368.143i	−1.20995	+	0.698564i
$528$		0			0
$529$	438.521			0.828961
$530$		0			0
$531$	−236.499	−	249.749i	−0.445385	−	0.470337i
$532$		0			0
$533$	14.3867	+	24.9184i	0.0269919	+	0.0467513i
$534$		0			0
$535$	−299.487	+	172.909i	−0.559788	+	0.323194i
$536$		0			0
$537$	−380.472	−	300.268i	−0.708514	−	0.559158i
$538$		0			0
$539$	1244.09			2.30815
$540$		0			0
$541$	−12.3287	−	21.3540i	−0.0227888	−	0.0394713i	0.854406	−	0.519606i	$-0.173921\pi$
$541$	−12.3287	−	21.3540i	−0.0227888	−	0.0394713i	−0.877195	+	0.480134i	$0.840588\pi$
$542$		0			0
$543$	−46.7774	+	321.417i	−0.0861462	+	0.591928i
$544$		0			0
$545$			1317.53i			2.41749i
$546$		0			0
$547$	−745.174	−	430.227i	−1.36229	−	0.786520i	−0.372365	−	0.928087i	$-0.621453\pi$
$547$	−745.174	−	430.227i	−1.36229	−	0.786520i	−0.989929	+	0.141566i	$0.954786\pi$
$548$		0			0
$549$	−308.206	−	91.6507i	−0.561395	−	0.166941i
$550$		0			0
$551$	−825.776	+	96.0620i	−1.49869	+	0.174341i
$552$		0			0
$553$	222.555	−	128.492i	0.402450	−	0.232355i
$554$		0			0
$555$	103.323	−	709.954i	0.186168	−	1.27920i
$556$		0			0
$557$	−234.760	−	406.616i	−0.421472	−	0.730010i	0.574612	−	0.818426i	$-0.305153\pi$
$557$	−234.760	−	406.616i	−0.421472	−	0.730010i	−0.996084	+	0.0884157i	$0.971820\pi$
$558$		0			0
$559$			34.2779i			0.0613199i
$560$		0			0
$561$	1036.02	−	1312.75i	1.84673	−	2.34001i
$562$		0			0
$563$	928.134	+	535.858i	1.64855	+	0.951791i	0.977649	+	0.210244i	$0.0674260\pi$
$563$	928.134	+	535.858i	1.64855	+	0.951791i	0.670901	+	0.741547i	$0.265907\pi$
$564$		0			0
$565$			1479.76i			2.61905i
$566$		0			0
$567$	720.345	+	469.974i	1.27045	+	0.828879i
$568$		0			0
$569$	−262.240	+	151.404i	−0.460879	+	0.266089i	−0.712414	−	0.701760i	$-0.752398\pi$
$569$	−262.240	+	151.404i	−0.460879	+	0.266089i	0.251535	+	0.967848i	$0.419065\pi$
$570$		0			0
$571$	137.809	−	238.692i	0.241347	−	0.418024i	−0.719752	−	0.694232i	$-0.755744\pi$
$571$	137.809	−	238.692i	0.241347	−	0.418024i	0.961098	+	0.276207i	$0.0890776\pi$
$572$		0			0
$573$	385.245	+	56.0666i	0.672329	+	0.0978474i
$574$		0			0
$575$	399.827	−	692.521i	0.695352	−	1.20438i
$576$		0			0
$577$	416.774			0.722312			0.361156	−	0.932505i	$-0.382382\pi$
$577$	416.774			0.722312			0.361156	+	0.932505i	$0.382382\pi$
$578$		0			0
$579$	63.5498	−	436.664i	0.109758	−	0.754168i
$580$		0			0
$581$	−406.855	+	704.693i	−0.700266	+	1.21290i
$582$		0			0
$583$	46.1425	+	26.6404i	0.0791466	+	0.0456953i
$584$		0			0
$585$	46.7227	+	49.3402i	0.0798678	+	0.0843422i
$586$		0			0
$587$	1020.95			1.73926			0.869630	−	0.493704i	$-0.164357\pi$
$587$	1020.95			1.73926			0.869630	+	0.493704i	$0.164357\pi$
$588$		0			0
$589$	486.449	−	56.5884i	0.825890	−	0.0960753i
$590$		0			0
$591$	−165.675	+	209.928i	−0.280329	+	0.355208i
$592$		0			0
$593$	−62.4534	−	108.173i	−0.105318	−	0.182416i	0.808550	−	0.588427i	$-0.200253\pi$
$593$	−62.4534	−	108.173i	−0.105318	−	0.182416i	−0.913868	+	0.406011i	$0.866919\pi$
$594$		0			0
$595$	1079.98	+	1870.59i	1.81510	+	3.14384i
$596$		0			0
$597$	454.900	+	66.2039i	0.761977	+	0.110894i
$598$		0			0
$599$			263.289i			0.439548i	0.975551	+	0.219774i	$0.0705319\pi$
$599$			263.289i			0.439548i	−0.975551	+	0.219774i	$0.929468\pi$
$600$		0			0
$601$	−242.962	+	140.274i	−0.404263	+	0.233402i	−0.688322	−	0.725405i	$-0.741652\pi$
$601$	−242.962	+	140.274i	−0.404263	+	0.233402i	0.284059	+	0.958807i	$0.408319\pi$
$602$		0			0
$603$	−918.565	+	219.497i	−1.52333	+	0.364009i
$604$		0			0
$605$	−1850.08			−3.05799
$606$		0			0
$607$	−635.619	−	366.975i	−1.04715	−	0.604572i	−0.125299	−	0.992119i	$-0.539989\pi$
$607$	−635.619	−	366.975i	−1.04715	−	0.604572i	−0.921850	+	0.387547i	$0.873322\pi$
$608$		0			0
$609$	1094.15	+	863.498i	1.79663	+	1.41790i
$610$		0			0
$611$	−32.2414	−	18.6146i	−0.0527683	−	0.0304658i
$612$		0			0
$613$	−366.961	+	635.595i	−0.598631	+	1.03686i	0.394393	+	0.918942i	$0.370955\pi$
$613$	−366.961	+	635.595i	−0.598631	+	1.03686i	−0.993023	+	0.117917i	$0.962378\pi$
$614$		0			0
$615$	538.579	−	214.540i	0.875738	−	0.348845i
$616$		0			0
$617$	496.227			0.804258			0.402129	−	0.915583i	$-0.368270\pi$
$617$	496.227			0.804258			0.402129	+	0.915583i	$0.368270\pi$
$618$		0			0
$619$	72.1763	+	125.013i	0.116601	+	0.201960i	0.918419	−	0.395610i	$-0.129467\pi$
$619$	72.1763	+	125.013i	0.116601	+	0.201960i	−0.801817	+	0.597569i	$0.796133\pi$
$620$		0			0
$621$	762.130	+	352.819i	1.22726	+	0.568146i
$622$		0			0
$623$	−1172.87	−	677.158i	−1.88262	−	1.08693i
$624$		0			0
$625$	303.396	+	525.498i	0.485434	+	0.840796i
$626$		0			0
$627$	−978.862	+	528.275i	−1.56118	+	0.842543i
$628$		0			0
$629$	830.797	+	479.661i	1.32082	+	0.762577i
$630$		0			0
$631$	−385.601	−	667.881i	−0.611095	−	1.05845i	−0.991056	−	0.133446i	$-0.957396\pi$
$631$	−385.601	−	667.881i	−0.611095	−	1.05845i	0.379961	−	0.925003i	$-0.375938\pi$
$632$		0			0
$633$	75.5500	−	519.119i	0.119352	−	0.820093i
$634$		0			0
$635$	−526.609	−	304.038i	−0.829306	−	0.478800i
$636$		0			0
$637$	−58.5397	−	33.7979i	−0.0918991	−	0.0530580i
$638$		0			0
$639$	−223.424	+	751.337i	−0.349646	+	1.17580i
$640$		0			0
$641$		−	1074.61i		−	1.67646i	−0.545319	−	0.838229i	$-0.683591\pi$
$641$		−	1074.61i		−	1.67646i	0.545319	−	0.838229i	$-0.316409\pi$
$642$		0			0
$643$	−596.100	−	1032.47i	−0.927060	−	1.60572i	−0.788214	−	0.615401i	$-0.788994\pi$
$643$	−596.100	−	1032.47i	−0.927060	−	1.60572i	−0.138846	−	0.990314i	$-0.544339\pi$
$644$		0			0
$645$	683.444	+	99.4650i	1.05960	+	0.154209i
$646$		0			0
$647$	685.813			1.05999			0.529994	−	0.848001i	$-0.322194\pi$
$647$	685.813			1.05999			0.529994	+	0.848001i	$0.322194\pi$
$648$		0			0
$649$	−645.870	−	372.893i	−0.995178	−	0.574566i
$650$		0			0
$651$	−644.542	−	508.671i	−0.990080	−	0.781368i
$652$		0			0
$653$	−208.362	+	360.893i	−0.319084	+	0.552669i	−0.980297	−	0.197529i	$-0.936708\pi$
$653$	−208.362	+	360.893i	−0.319084	+	0.552669i	0.661214	+	0.750198i	$0.270042\pi$
$654$		0			0
$655$	−200.184	+	346.728i	−0.305624	+	0.529356i
$656$		0			0
$657$	−104.827	−	31.1723i	−0.159555	−	0.0474465i
$658$		0			0
$659$	669.406	+	386.482i	1.01579	+	0.586467i	0.912882	−	0.408224i	$-0.133852\pi$
$659$	669.406	+	386.482i	1.01579	+	0.586467i	0.102909	+	0.994691i	$0.467185\pi$
$660$		0			0
$661$		−	570.558i		−	0.863174i	−0.902071	−	0.431587i	$-0.857954\pi$
$661$		−	570.558i		−	0.863174i	0.902071	−	0.431587i	$-0.142046\pi$
$662$		0			0
$663$	−84.4118	+	33.6250i	−0.127318	+	0.0507164i
$664$		0			0
$665$	−166.007	−	1427.05i	−0.249635	−	2.14593i
$666$		0			0
$667$	1178.66	+	680.499i	1.76711	+	1.02024i
$668$		0			0
$669$	111.143	+	87.7135i	0.166133	+	0.131111i
$670$		0			0
$671$	−697.191			−1.03903
$672$		0			0
$673$	−651.912	+	376.382i	−0.968666	+	0.559259i	−0.898829	−	0.438299i	$-0.855581\pi$
$673$	−651.912	+	376.382i	−0.968666	+	0.559259i	−0.0698365	+	0.997558i	$0.522248\pi$
$674$		0			0
$675$	567.486	−	399.707i	0.840721	−	0.592158i
$676$		0			0
$677$	−145.503	+	84.0065i	−0.214924	+	0.124086i	−0.603598	−	0.797289i	$-0.706267\pi$
$677$	−145.503	+	84.0065i	−0.214924	+	0.124086i	0.388674	+	0.921375i	$0.372933\pi$
$678$		0			0
$679$	−766.573	+	442.581i	−1.12897	+	0.651813i
$680$		0			0
$681$	−19.2561	+	132.313i	−0.0282763	+	0.194292i
$682$		0			0
$683$		−	491.889i		−	0.720189i	−0.932916	−	0.360095i	$-0.882744\pi$
$683$		−	491.889i		−	0.720189i	0.932916	−	0.360095i	$-0.117256\pi$
$684$		0			0
$685$	1003.08			1.46435
$686$		0			0
$687$	−400.462	−	1005.31i	−0.582914	−	1.46334i
$688$		0			0
$689$	−1.44746	−	2.50708i	−0.00210081	−	0.00363872i
$690$		0			0
$691$	−307.462	−	532.539i	−0.444952	−	0.770679i	0.553097	−	0.833117i	$-0.313446\pi$
$691$	−307.462	−	532.539i	−0.444952	−	0.770679i	−0.998049	+	0.0624380i	$0.980112\pi$
$692$		0			0
$693$	1787.56	+	531.562i	2.57945	+	0.767045i
$694$		0			0
$695$	−413.502	−	716.206i	−0.594967	−	1.03051i
$696$		0			0
$697$			775.200i			1.11220i
$698$		0			0
$699$	416.462	+	1045.48i	0.595797	+	1.49568i
$700$		0			0
$701$	−210.851	+	365.204i	−0.300785	+	0.520976i	−0.976314	−	0.216358i	$-0.930582\pi$
$701$	−210.851	+	365.204i	−0.300785	+	0.520976i	0.675529	+	0.737334i	$0.263915\pi$
$702$		0			0
$703$	−380.754	−	512.026i	−0.541614	−	0.728344i
$704$		0			0
$705$	−464.701	+	588.827i	−0.659150	+	0.835216i
$706$		0			0
$707$	1219.32			1.72463
$708$		0			0
$709$	290.446	−	503.067i	0.409656	−	0.709545i	−0.585195	−	0.810893i	$-0.698982\pi$
$709$	290.446	−	503.067i	0.409656	−	0.709545i	0.994851	+	0.101348i	$0.0323154\pi$
$710$		0			0
$711$	211.849	−	50.6228i	0.297960	−	0.0711994i
$712$		0			0
$713$	−694.326	−	400.870i	−0.973810	−	0.562229i
$714$		0			0
$715$	127.598	+	73.6685i	0.178458	+	0.103033i
$716$		0			0
$717$	−271.213	−	680.850i	−0.378261	−	0.949581i
$718$		0			0
$719$	7.29582	−	12.6367i	0.0101472	−	0.0175754i	−0.860907	−	0.508762i	$-0.830103\pi$
$719$	7.29582	−	12.6367i	0.0101472	−	0.0175754i	0.871054	+	0.491187i	$0.163437\pi$
$720$		0			0
$721$			711.312i			0.986564i
$722$		0			0
$723$	−297.656	+	118.570i	−0.411696	+	0.163997i
$724$		0			0
$725$	974.161	−	562.432i	1.34367	−	0.775768i
$726$		0			0
$727$	1066.31			1.46673			0.733366	−	0.679834i	$-0.237948\pi$
$727$	1066.31			1.46673			0.733366	+	0.679834i	$0.237948\pi$
$728$		0			0
$729$	471.680	+	555.841i	0.647024	+	0.762470i
$730$		0			0
$731$	−461.751	+	799.775i	−0.631670	+	1.09408i
$732$		0			0
$733$	534.160	−	925.193i	0.728732	−	1.26220i	−0.228688	−	0.973500i	$-0.573443\pi$
$733$	534.160	−	925.193i	0.728732	−	1.26220i	0.957419	−	0.288701i	$-0.0932232\pi$
$734$		0			0
$735$	−843.742	+	1069.11i	−1.14795	+	1.45458i
$736$		0			0
$737$	−1773.41	+	1023.88i	−2.40626	+	1.38925i
$738$		0			0
$739$	−590.659	+	1023.05i	−0.799268	+	1.38437i	0.120825	+	0.992674i	$0.461446\pi$
$739$	−590.659	+	1023.05i	−0.799268	+	1.38437i	−0.920093	+	0.391699i	$0.871887\pi$
$740$		0			0
$741$	60.4109	+	1.73496i	0.0815262	+	0.00234138i
$742$		0			0
$743$	−540.158	+	311.860i	−0.726996	+	0.419731i	−0.817322	−	0.576181i	$-0.804542\pi$
$743$	−540.158	+	311.860i	−0.726996	+	0.419731i	0.0903260	+	0.995912i	$0.471209\pi$
$744$		0			0
$745$	13.4732	−	23.3362i	0.0180848	−	0.0313238i
$746$		0			0
$747$	−500.780	+	474.213i	−0.670388	+	0.634824i
$748$		0			0
$749$	446.583	−	257.835i	0.596239	−	0.344239i
$750$		0			0
$751$		−	1007.64i		−	1.34173i	−0.741579	−	0.670866i	$-0.765923\pi$
$751$		−	1007.64i		−	1.34173i	0.741579	−	0.670866i	$-0.234077\pi$
$752$		0			0
$753$	−336.548	−	48.9795i	−0.446943	−	0.0650458i
$754$		0			0
$755$	403.984	+	233.240i	0.535078	+	0.308927i
$756$		0			0
$757$	−231.658	+	401.244i	−0.306021	+	0.530045i	−0.977488	−	0.210990i	$-0.932331\pi$
$757$	−231.658	+	401.244i	−0.306021	+	0.530045i	0.671467	+	0.741035i	$0.265665\pi$
$758$		0			0
$759$	1801.99	+	262.253i	2.37417	+	0.345524i
$760$		0			0
$761$	312.266	−	540.861i	0.410336	−	0.710723i	−0.584590	−	0.811329i	$-0.698745\pi$
$761$	312.266	−	540.861i	0.410336	−	0.710723i	0.994926	+	0.100605i	$0.0320780\pi$
$762$		0			0
$763$		−	1964.65i		−	2.57490i
$764$		0			0
$765$	425.487	+	1780.60i	0.556192	+	2.32759i
$766$		0			0
$767$	20.2606	+	35.0923i	0.0264153	+	0.0457527i
$768$		0			0
$769$	952.672			1.23884			0.619422	−	0.785058i	$-0.287367\pi$
$769$	952.672			1.23884			0.619422	+	0.785058i	$0.287367\pi$
$770$		0			0
$771$	−120.852	−	95.3763i	−0.156748	−	0.123705i
$772$		0			0
$773$	201.770	−	116.492i	0.261021	−	0.150701i	−0.363779	−	0.931485i	$-0.618514\pi$
$773$	201.770	−	116.492i	0.261021	−	0.150701i	0.624800	+	0.780784i	$0.285180\pi$
$774$		0			0
$775$	−573.860	+	331.318i	−0.740464	+	0.427507i
$776$		0			0
$777$	−154.071	+	1058.66i	−0.198290	+	1.36249i
$778$		0			0
$779$	204.482	−	473.332i	0.262494	−	0.607615i
$780$		0			0
$781$			1699.59i			2.17618i
$782$		0			0
$783$	680.294	+	965.852i	0.868830	+	1.23353i
$784$		0			0
$785$	−35.2579	+	61.0684i	−0.0449145	+	0.0777941i
$786$		0			0
$787$	−115.019	−	66.4060i	−0.146148	−	0.0843787i	0.425143	−	0.905126i	$-0.360224\pi$
$787$	−115.019	−	66.4060i	−0.146148	−	0.0843787i	−0.571291	+	0.820748i	$0.693557\pi$
$788$		0			0
$789$	79.7325	−	101.030i	0.101055	−	0.128048i
$790$		0			0
$791$		−	2206.57i		−	2.78959i
$792$		0			0
$793$	32.8057	+	18.9404i	0.0413691	+	0.0238844i
$794$		0			0
$795$	−54.1871	+	21.5851i	−0.0681599	+	0.0271511i
$796$		0			0
$797$	373.053	+	215.382i	0.468071	+	0.270241i	0.715432	−	0.698682i	$-0.246230\pi$
$797$	373.053	+	215.382i	0.468071	+	0.270241i	−0.247361	+	0.968923i	$0.579563\pi$
$798$		0			0
$799$	−501.508	−	868.637i	−0.627669	−	1.08716i
$800$		0			0
$801$	−789.268	−	833.485i	−0.985353	−	1.04056i
$802$		0			0
$803$	−237.129			−0.295304
$804$		0			0
$805$	−1175.99	+	2036.87i	−1.46086	+	2.53028i
$806$		0			0
$807$	358.960	−	142.990i	0.444807	−	0.177187i
$808$		0			0
$809$	−366.486			−0.453011			−0.226505	−	0.974010i	$-0.572730\pi$
$809$	−366.486			−0.453011			−0.226505	+	0.974010i	$0.572730\pi$
$810$		0			0
$811$	348.965	−	201.475i	0.430289	−	0.248428i	−0.269180	−	0.963090i	$-0.586753\pi$
$811$	348.965	−	201.475i	0.430289	−	0.248428i	0.699470	+	0.714662i	$0.253419\pi$
$812$		0			0
$813$	−305.793	−	767.660i	−0.376130	−	0.944232i
$814$		0			0
$815$	−112.721	−	195.239i	−0.138309	−	0.239557i
$816$		0			0
$817$	492.907	−	366.537i	0.603313	−	0.448638i
$818$		0			0
$819$	−69.6710	−	73.5742i	−0.0850684	−	0.0898342i
$820$		0			0
$821$	240.004	−	415.698i	0.292331	−	0.506332i	−0.682030	−	0.731324i	$-0.738903\pi$
$821$	240.004	−	415.698i	0.292331	−	0.506332i	0.974360	+	0.224993i	$0.0722359\pi$
$822$		0			0
$823$	1557.19			1.89209			0.946046	−	0.324031i	$-0.105038\pi$
$823$	1557.19			1.89209			0.946046	+	0.324031i	$0.105038\pi$
$824$		0			0
$825$	932.385	−	1181.43i	1.13016	−	1.43204i
$826$		0			0
$827$	590.269	−	340.792i	0.713748	−	0.412082i	−0.0986995	−	0.995117i	$-0.531468\pi$
$827$	590.269	−	340.792i	0.713748	−	0.412082i	0.812447	+	0.583035i	$0.198135\pi$
$828$		0			0
$829$			377.405i			0.455253i	0.973749	+	0.227626i	$0.0730965\pi$
$829$			377.405i			0.455253i	−0.973749	+	0.227626i	$0.926904\pi$
$830$		0			0
$831$	1353.49	+	196.981i	1.62875	+	0.237040i
$832$		0			0
$833$	−910.571	−	1577.16i	−1.09312	−	1.89334i
$834$		0			0
$835$	−974.512	+	562.635i	−1.16708	+	0.673814i
$836$		0			0
$837$	−400.748	−	568.966i	−0.478791	−	0.679768i
$838$		0			0
$839$			653.788i			0.779247i	0.920974	+	0.389623i	$0.127395\pi$
$839$			653.788i			0.779247i	−0.920974	+	0.389623i	$0.872605\pi$
$840$		0			0
$841$	536.750	+	929.678i	0.638228	+	1.10544i
$842$		0			0
$843$	272.909	−	108.712i	0.323736	−	0.128958i
$844$		0			0
$845$	597.719	+	1035.28i	0.707360	+	1.22518i
$846$		0			0
$847$	2758.77			3.25711
$848$		0			0
$849$	−1033.73	−	150.444i	−1.21759	−	0.177202i
$850$		0			0
$851$			1044.60i			1.22750i
$852$		0			0
$853$	−245.160			−0.287410			−0.143705	−	0.989621i	$-0.545902\pi$
$853$	−245.160			−0.287410			−0.143705	+	0.989621i	$0.545902\pi$
$854$		0			0
$855$	209.889	−	1199.46i	0.245484	−	1.40288i
$856$		0			0
$857$		−	696.220i		−	0.812392i	−0.913786	−	0.406196i	$-0.866855\pi$
$857$		−	696.220i		−	0.812392i	0.913786	−	0.406196i	$-0.133145\pi$
$858$		0			0
$859$	−55.0108			−0.0640406			−0.0320203	−	0.999487i	$-0.510194\pi$
$859$	−55.0108			−0.0640406			−0.0320203	+	0.999487i	$0.510194\pi$
$860$		0			0
$861$	−803.108	+	319.914i	−0.932762	+	0.371561i
$862$		0			0
$863$			556.252i			0.644556i	0.946645	+	0.322278i	$0.104449\pi$
$863$			556.252i			0.644556i	−0.946645	+	0.322278i	$0.895551\pi$
$864$		0			0
$865$	1529.11	−	882.831i	1.76776	−	1.02061i
$866$		0			0
$867$	−1564.50	−	227.690i	−1.80450	−	0.262618i
$868$		0			0
$869$	409.003	−	236.138i	0.470659	−	0.271735i
$870$		0			0
$871$	111.262			0.127740
$872$		0			0
$873$	−729.699	+	174.366i	−0.835852	+	0.199732i
$874$		0			0
$875$	26.7766	+	46.3784i	0.0306018	+	0.0530038i
$876$		0			0
$877$	−649.237	+	374.837i	−0.740293	+	0.427409i	−0.822176	−	0.569233i	$-0.807240\pi$
$877$	−649.237	+	374.837i	−0.740293	+	0.427409i	0.0818825	+	0.996642i	$0.473907\pi$
$878$		0			0
$879$	−600.203	+	239.087i	−0.682824	+	0.271999i
$880$		0			0
$881$	61.3723			0.0696621			0.0348311	−	0.999393i	$-0.488911\pi$
$881$	61.3723			0.0696621			0.0348311	+	0.999393i	$0.488911\pi$
$882$		0			0
$883$	−678.022	−	1174.37i	−0.767862	−	1.32998i	−0.938720	−	0.344680i	$-0.887987\pi$
$883$	−678.022	−	1174.37i	−0.767862	−	1.32998i	0.170858	−	0.985296i	$-0.445346\pi$
$884$		0			0
$885$	758.474	−	302.134i	0.857033	−	0.341394i
$886$		0			0
$887$		−	380.969i		−	0.429503i	−0.976669	−	0.214752i	$-0.931106\pi$
$887$		−	380.969i		−	0.429503i	0.976669	−	0.214752i	$-0.0688942\pi$
$888$		0			0
$889$	785.260	+	453.370i	0.883307	+	0.509977i
$890$		0			0
$891$	1323.82	+	863.700i	1.48577	+	0.969360i
$892$		0			0
$893$	77.0883	+	662.672i	0.0863251	+	0.742074i
$894$		0			0
$895$	996.342	−	575.238i	1.11323	−	0.642724i
$896$		0			0
$897$	−77.6666	−	61.2943i	−0.0865849	−	0.0683325i
$898$		0			0
$899$	−563.898	−	976.700i	−0.627250	−	1.08643i
$900$		0			0
$901$		−	77.9939i		−	0.0865637i
$902$		0			0
$903$	−1019.13	−	148.318i	−1.12860	−	0.164251i
$904$		0			0
$905$	−667.680	−	385.485i	−0.737768	−	0.425951i
$906$		0			0
$907$		−	1548.64i		−	1.70743i	−0.520739	−	0.853716i	$-0.674343\pi$
$907$		−	1548.64i		−	1.70743i	0.520739	−	0.853716i	$-0.325657\pi$
$908$		0			0
$909$	990.593	+	294.571i	1.08976	+	0.324060i
$910$		0			0
$911$	1396.43	−	806.230i	1.53286	−	0.884995i	0.533628	−	0.845719i	$-0.320828\pi$
$911$	1396.43	−	806.230i	1.53286	−	0.884995i	0.999228	−	0.0392755i	$-0.0125050\pi$
$912$		0			0
$913$	−747.702	+	1295.06i	−0.818950	+	1.41846i
$914$		0			0
$915$	472.833	−	599.132i	0.516757	−	0.654789i
$916$		0			0
$917$	298.506	−	517.028i	0.325525	−	0.563825i
$918$		0			0
$919$	−1148.67			−1.24992			−0.624959	−	0.780658i	$-0.714884\pi$
$919$	−1148.67			−1.24992			−0.624959	+	0.780658i	$0.714884\pi$
$920$		0			0
$921$	766.791	−	305.447i	0.832563	−	0.331647i
$922$		0			0
$923$	46.1724	−	79.9729i	0.0500242	−	0.0866445i
$924$		0			0
$925$	747.694	+	431.681i	0.808317	+	0.466682i
$926$		0			0
$927$	−171.844	+	577.882i	−0.185376	+	0.623389i
$928$		0			0
$929$	−754.972			−0.812672			−0.406336	−	0.913724i	$-0.633194\pi$
$929$	−754.972			−0.812672			−0.406336	+	0.913724i	$0.633194\pi$
$930$		0			0
$931$	139.967	+	1203.19i	0.150340	+	1.29237i
$932$		0			0
$933$	140.575	+	352.899i	0.150670	+	0.378241i
$934$		0			0
$935$	1984.75	+	3437.69i	2.12273	+	3.67667i
$936$		0			0
$937$	692.149	+	1198.84i	0.738686	+	1.27944i	0.953087	+	0.302696i	$0.0978866\pi$
$937$	692.149	+	1198.84i	0.738686	+	1.27944i	−0.214401	+	0.976746i	$0.568780\pi$
$938$		0			0
$939$	−74.0053	−	185.782i	−0.0788129	−	0.197851i
$940$		0			0
$941$			998.693i			1.06131i	0.847588	+	0.530655i	$0.178054\pi$
$941$			998.693i			1.06131i	−0.847588	+	0.530655i	$0.821946\pi$
$942$		0			0
$943$	−731.023	+	422.056i	−0.775210	+	0.447568i
$944$		0			0
$945$	−1669.12	+	1175.63i	−1.76626	+	1.24406i
$946$		0			0
$947$	−540.708			−0.570969			−0.285484	−	0.958383i	$-0.592154\pi$
$947$	−540.708			−0.570969			−0.285484	+	0.958383i	$0.592154\pi$
$948$		0			0
$949$	11.1579	+	6.44202i	0.0117575	+	0.00678822i
$950$		0			0
$951$	1374.17	−	547.393i	1.44497	−	0.575598i
$952$		0			0
$953$	−1015.01	−	586.015i	−1.06507	−	0.614916i	−0.138236	−	0.990399i	$-0.544143\pi$
$953$	−1015.01	−	586.015i	−1.06507	−	0.614916i	−0.926829	+	0.375484i	$0.877477\pi$
$954$		0			0
$955$	−462.036	+	800.270i	−0.483807	+	0.837979i
$956$		0			0
$957$	2010.78	+	1586.90i	2.10113	+	1.65821i
$958$		0			0
$959$	−1495.75			−1.55970
$960$		0			0
$961$	−148.318	−	256.895i	−0.154337	−	0.267320i
$962$		0			0
$963$	425.101	−	101.581i	0.441434	−	0.105484i
$964$		0			0
$965$	907.083	+	523.704i	0.939982	+	0.542699i
$966$		0			0
$967$	−17.6388	−	30.5514i	−0.0182408	−	0.0315940i	0.856761	−	0.515714i	$-0.172473\pi$
$967$	−17.6388	−	30.5514i	−0.0182408	−	0.0315940i	−0.875002	+	0.484120i	$0.839140\pi$
$968$		0			0
$969$	1386.15	+	854.265i	1.43049	+	0.881595i
$970$		0			0
$971$	526.816	+	304.158i	0.542550	+	0.313242i	0.746112	−	0.665821i	$-0.231918\pi$
$971$	526.816	+	304.158i	0.542550	+	0.313242i	−0.203562	+	0.979062i	$0.565252\pi$
$972$		0			0
$973$	616.598	+	1067.98i	0.633708	+	1.09761i
$974$		0			0
$975$	−75.9682	+	30.2615i	−0.0779161	+	0.0310375i
$976$		0			0
$977$	1028.91	+	594.044i	1.05314	+	0.608028i	0.923526	−	0.383537i	$-0.125294\pi$
$977$	1028.91	+	594.044i	1.05314	+	0.608028i	0.129610	+	0.991565i	$0.458627\pi$
$978$		0			0
$979$	−2155.46	−	1244.45i	−2.20169	−	1.27115i
$980$		0			0
$981$	474.634	−	1596.12i	0.483827	−	1.62703i
$982$		0			0
$983$			359.199i			0.365411i	0.983168	+	0.182705i	$0.0584854\pi$
$983$			359.199i			0.365411i	−0.983168	+	0.182705i	$0.941515\pi$
$984$		0			0
$985$	−317.392	−	549.738i	−0.322225	−	0.558110i
$986$		0			0
$987$	692.944	−	878.036i	0.702071	−	0.889601i
$988$		0			0
$989$	−1005.60			−1.01678
$990$		0			0
$991$	440.933	+	254.573i	0.444938	+	0.256885i	0.705690	−	0.708521i	$-0.250637\pi$
$991$	440.933	+	254.573i	0.444938	+	0.256885i	−0.260752	+	0.965406i	$0.583971\pi$
$992$		0			0
$993$	63.5308	−	436.533i	0.0639787	−	0.439610i
$994$		0			0
$995$	−545.576	+	944.966i	−0.548318	+	0.949714i
$996$		0			0
$997$	616.043	−	1067.02i	0.617897	−	1.07023i	−0.371972	−	0.928244i	$-0.621318\pi$
$997$	616.043	−	1067.02i	0.617897	−	1.07023i	0.989869	−	0.141985i	$-0.0453483\pi$
$998$		0			0
$999$	−380.927	+	822.847i	−0.381309	+	0.823671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.s.a.445.29	✓	80
3.2	odd	2		2052.3.s.a.901.6		80
9.2	odd	6		2052.3.bl.a.1585.35		80
9.7	even	3		684.3.bl.a.673.16	yes	80
19.12	odd	6		684.3.bl.a.373.16	yes	80
57.50	even	6		2052.3.bl.a.145.35		80
171.88	odd	6	inner	684.3.s.a.601.29	yes	80
171.164	even	6		2052.3.s.a.829.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.29	✓	80	1.1	even	1	trivial
684.3.s.a.601.29	yes	80	171.88	odd	6	inner
684.3.bl.a.373.16	yes	80	19.12	odd	6
684.3.bl.a.673.16	yes	80	9.7	even	3
2052.3.s.a.829.6		80	171.164	even	6
2052.3.s.a.901.6		80	3.2	odd	2
2052.3.bl.a.145.35		80	57.50	even	6
2052.3.bl.a.1585.35		80	9.2	odd	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85853 - 2.35496i) q^{3} +(3.56049 + 6.16694i) q^{5} +(-5.30926 - 9.19591i) q^{7} +(-2.09172 - 8.75355i) q^{9} +O(q^{10})\)	\(q+(1.85853 - 2.35496i) q^{3} +(3.56049 + 6.16694i) q^{5} +(-5.30926 - 9.19591i) q^{7} +(-2.09172 - 8.75355i) q^{9} +(-9.75715 - 16.8999i) q^{11} +1.06028i q^{13} +(21.1402 + 3.07664i) q^{15} +(-14.2828 + 24.7386i) q^{17} +(15.2465 - 11.3377i) q^{19} +(-31.5235 - 4.58777i) q^{21} -31.1050 q^{23} +(-12.8541 + 22.2640i) q^{25} +(-24.5018 - 11.3428i) q^{27} +(-37.8929 - 21.8775i) q^{29} +(22.3220 + 12.8876i) q^{31} +(-57.9326 - 8.43122i) q^{33} +(37.8071 - 65.4838i) q^{35} -33.5831i q^{37} +(2.49692 + 1.97056i) q^{39} +(23.5018 - 13.5688i) q^{41} +32.3291 q^{43} +(46.5351 - 44.0664i) q^{45} +(-17.5563 + 30.4085i) q^{47} +(-31.8765 + 55.2117i) q^{49} +(31.7134 + 79.6129i) q^{51} +(-2.36455 + 1.36517i) q^{53} +(69.4804 - 120.344i) q^{55} +(1.63633 - 56.9765i) q^{57} +(33.0973 - 19.1087i) q^{59} +(17.8636 - 30.9406i) q^{61} +(-69.3914 + 65.7101i) q^{63} +(-6.53867 + 3.77511i) q^{65} -104.936i q^{67} +(-57.8096 + 73.2512i) q^{69} +(-75.4263 - 43.5474i) q^{71} +(6.07578 - 10.5236i) q^{73} +(28.5411 + 71.6493i) q^{75} +(-103.606 + 179.452i) q^{77} +24.2015i q^{79} +(-72.2494 + 36.6200i) q^{81} +(-38.3156 - 66.3645i) q^{83} -203.415 q^{85} +(-121.946 + 48.5765i) q^{87} +(110.455 - 63.7714i) q^{89} +(9.75022 - 5.62929i) q^{91} +(71.8361 - 28.6155i) q^{93} +(124.204 + 53.6569i) q^{95} -83.3603i q^{97} +(-127.525 + 120.760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q - q^7 + 4 * q^9	\( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99}+O(q^{100}) \) 80 * q - q^7 + 4 * q^9 - 6 * q^11 + 33 * q^15 - 21 * q^17 - 20 * q^19 - 48 * q^23 - 200 * q^25 - 63 * q^27 - 27 * q^29 - 24 * q^31 + 27 * q^33 - 54 * q^35 - 81 * q^39 - 18 * q^41 - 152 * q^43 + 188 * q^45 - 12 * q^47 - 267 * q^49 - 126 * q^51 - 36 * q^53 + 126 * q^57 - 135 * q^59 - 7 * q^61 - 190 * q^63 - 288 * q^65 + 48 * q^69 - 81 * q^71 + 55 * q^73 + 165 * q^75 + 30 * q^77 + 28 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 24 * q^93 + 288 * q^95 - 241 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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