LMFDB - Embedded newform 684.3.bl.a.373.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(373,684)]

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, 5]))

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

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

chi := DirichletCharacter("684.373");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.bl (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			373.16
Character	$\chi$	$=$	684.373
Dual form			684.3.bl.a.673.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11019 - 2.78702i) q^{3} -7.12097 q^{5} +(-5.30926 - 9.19591i) q^{7} +(-6.53494 + 6.18826i) q^{9} +O(q^{10})$	\(q+(-1.11019 - 2.78702i) q^{3} -7.12097 q^{5} +(-5.30926 - 9.19591i) q^{7} +(-6.53494 + 6.18826i) q^{9} +(-9.75715 - 16.8999i) q^{11} +(-0.918228 + 0.530139i) q^{13} +(7.90566 + 19.8463i) q^{15} +(-14.2828 - 24.7386i) q^{17} +(15.2465 + 11.3377i) q^{19} +(-19.7349 + 25.0062i) q^{21} +(15.5525 + 26.9377i) q^{23} +25.7082 q^{25} +(24.5018 + 11.3428i) q^{27} -43.7550i q^{29} +(-22.3220 - 12.8876i) q^{31} +(-36.2679 + 45.9555i) q^{33} +(37.8071 + 65.4838i) q^{35} +33.5831i q^{37} +(2.49692 + 1.97056i) q^{39} -27.1375i q^{41} +(-16.1646 + 27.9978i) q^{43} +(46.5351 - 44.0664i) q^{45} +35.1127 q^{47} +(-31.8765 + 55.2117i) q^{49} +(-53.0901 + 67.2710i) q^{51} +(-2.36455 - 1.36517i) q^{53} +(69.4804 + 120.344i) q^{55} +(14.6717 - 55.0794i) q^{57} -38.2175i q^{59} -35.7272 q^{61} +(91.6024 + 27.2396i) q^{63} +(6.53867 - 3.77511i) q^{65} +(90.8775 - 52.4681i) q^{67} +(57.8096 - 73.2512i) q^{69} +(-75.4263 + 43.5474i) q^{71} +(6.07578 + 10.5236i) q^{73} +(-28.5411 - 71.6493i) q^{75} +(-103.606 + 179.452i) q^{77} +(20.9591 + 12.1008i) q^{79} +(4.41090 - 80.8798i) q^{81} +(-38.3156 - 66.3645i) q^{83} +(101.708 + 176.163i) q^{85} +(-121.946 + 48.5765i) q^{87} +(110.455 + 63.7714i) q^{89} +(9.75022 + 5.62929i) q^{91} +(-11.1363 + 76.5196i) q^{93} +(-108.570 - 80.7353i) q^{95} +(-72.1921 - 41.6801i) q^{97} +(168.343 + 50.0599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9	$ 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) $ 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.11019	−	2.78702i	−0.370064	−	0.929006i
$3$	−1.11019	−	2.78702i	−0.370064	−	0.929006i
$4$		0			0
$5$	−7.12097			−1.42419			−0.712097	−	0.702081i	$-0.752254\pi$
$5$	−7.12097			−1.42419			−0.712097	+	0.702081i	$0.752254\pi$
$6$		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
$9$	−6.53494	+	6.18826i	−0.726105	+	0.687584i
$10$		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
$13$	−0.918228	+	0.530139i	−0.0706329	+	0.0407799i	−0.534901	−	0.844915i	$-0.679651\pi$
$13$	−0.918228	+	0.530139i	−0.0706329	+	0.0407799i	0.464268	+	0.885695i	$0.346318\pi$
$14$		0			0
$15$	7.90566	+	19.8463i	0.527044	+	1.32309i
$16$		0			0
$17$	−14.2828	−	24.7386i	−0.840165	−	1.45521i	−0.889754	−	0.456439i	$-0.849124\pi$
$17$	−14.2828	−	24.7386i	−0.840165	−	1.45521i	0.0495890	−	0.998770i	$-0.484209\pi$
$18$		0			0
$19$	15.2465	+	11.3377i	0.802449	+	0.596720i
$19$	15.2465	+	11.3377i	0.802449	+	0.596720i
$20$		0			0
$21$	−19.7349	+	25.0062i	−0.939755	+	1.19077i
$22$		0			0
$23$	15.5525	+	26.9377i	0.676195	+	1.17120i	0.976118	+	0.217241i	$0.0697059\pi$
$23$	15.5525	+	26.9377i	0.676195	+	1.17120i	−0.299922	+	0.953964i	$0.596961\pi$
$24$		0			0
$25$	25.7082			1.02833
$26$		0			0
$27$	24.5018	+	11.3428i	0.907476	+	0.420105i
$28$		0			0
$29$		−	43.7550i		−	1.50879i	−0.656419	−	0.754396i	$-0.727930\pi$
$29$		−	43.7550i		−	1.50879i	0.656419	−	0.754396i	$-0.272070\pi$
$30$		0			0
$31$	−22.3220	−	12.8876i	−0.720065	−	0.415730i	0.0947114	−	0.995505i	$-0.469807\pi$
$31$	−22.3220	−	12.8876i	−0.720065	−	0.415730i	−0.814777	+	0.579775i	$0.803140\pi$
$32$		0			0
$33$	−36.2679	+	45.9555i	−1.09903	+	1.39259i
$34$		0			0
$35$	37.8071	+	65.4838i	1.08020	+	1.87097i
$36$		0			0
$37$			33.5831i			0.907651i	0.891091	+	0.453826i	$0.149941\pi$
$37$			33.5831i			0.907651i	−0.891091	+	0.453826i	$0.850059\pi$
$38$		0			0
$39$	2.49692	+	1.97056i	0.0640235	+	0.0505272i
$40$		0			0
$41$		−	27.1375i		−	0.661891i	−0.943650	−	0.330945i	$-0.892632\pi$
$41$		−	27.1375i		−	0.661891i	0.943650	−	0.330945i	$-0.107368\pi$
$42$		0			0
$43$	−16.1646	+	27.9978i	−0.375920	+	0.651112i	−0.990464	−	0.137770i	$-0.956007\pi$
$43$	−16.1646	+	27.9978i	−0.375920	+	0.651112i	0.614544	+	0.788882i	$0.289340\pi$
$44$		0			0
$45$	46.5351	−	44.0664i	1.03411	−	0.979254i
$46$		0			0
$47$	35.1127			0.747078			0.373539	−	0.927614i	$-0.378144\pi$
$47$	35.1127			0.747078			0.373539	+	0.927614i	$0.378144\pi$
$48$		0			0
$49$	−31.8765	+	55.2117i	−0.650540	+	1.12677i
$50$		0			0
$51$	−53.0901	+	67.2710i	−1.04098	+	1.31904i
$52$		0			0
$53$	−2.36455	−	1.36517i	−0.0446141	−	0.0257579i	0.477527	−	0.878617i	$-0.341533\pi$
$53$	−2.36455	−	1.36517i	−0.0446141	−	0.0257579i	−0.522141	+	0.852859i	$0.674867\pi$
$54$		0			0
$55$	69.4804	+	120.344i	1.26328	+	2.18806i
$56$		0			0
$57$	14.6717	−	55.0794i	0.257399	−	0.966305i
$58$		0			0
$59$		−	38.2175i		−	0.647753i	−0.946099	−	0.323877i	$-0.895014\pi$
$59$		−	38.2175i		−	0.647753i	0.946099	−	0.323877i	$-0.104986\pi$
$60$		0			0
$61$	−35.7272			−0.585691			−0.292846	−	0.956160i	$-0.594602\pi$
$61$	−35.7272			−0.585691			−0.292846	+	0.956160i	$0.594602\pi$
$62$		0			0
$63$	91.6024	+	27.2396i	1.45401	+	0.432375i
$64$		0			0
$65$	6.53867	−	3.77511i	0.100595	−	0.0580785i
$66$		0			0
$67$	90.8775	−	52.4681i	1.35638	−	0.783106i	0.367246	−	0.930124i	$-0.380301\pi$
$67$	90.8775	−	52.4681i	1.35638	−	0.783106i	0.989134	+	0.147017i	$0.0469673\pi$
$68$		0			0
$69$	57.8096	−	73.2512i	0.837821	−	1.06161i
$70$		0			0
$71$	−75.4263	+	43.5474i	−1.06234	+	0.613344i	−0.926079	−	0.377329i	$-0.876843\pi$
$71$	−75.4263	+	43.5474i	−1.06234	+	0.613344i	−0.136263	+	0.990673i	$0.543509\pi$
$72$		0			0
$73$	6.07578	+	10.5236i	0.0832299	+	0.144158i	0.904636	−	0.426186i	$-0.140143\pi$
$73$	6.07578	+	10.5236i	0.0832299	+	0.144158i	−0.821406	+	0.570344i	$0.806810\pi$
$74$		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
$79$	20.9591	+	12.1008i	0.265305	+	0.153174i	0.626752	−	0.779219i	$-0.284384\pi$
$79$	20.9591	+	12.1008i	0.265305	+	0.153174i	−0.361447	+	0.932393i	$0.617717\pi$
$80$		0			0
$81$	4.41090	−	80.8798i	0.0544556	−	0.998516i
$82$		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
$85$	101.708	+	176.163i	1.19656	+	2.07250i
$86$		0			0
$87$	−121.946	+	48.5765i	−1.40168	+	0.558351i
$88$		0			0
$89$	110.455	+	63.7714i	1.24107	+	0.716533i	0.969312	−	0.245833i	$-0.0790615\pi$
$89$	110.455	+	63.7714i	1.24107	+	0.716533i	0.271759	+	0.962365i	$0.412395\pi$
$90$		0			0
$91$	9.75022	+	5.62929i	0.107145	+	0.0618604i
$92$		0			0
$93$	−11.1363	+	76.5196i	−0.119745	+	0.822792i
$94$		0			0
$95$	−108.570	−	80.7353i	−1.14284	−	0.849846i
$96$		0			0
$97$	−72.1921	−	41.6801i	−0.744249	−	0.429692i	0.0793635	−	0.996846i	$-0.474711\pi$
$97$	−72.1921	−	41.6801i	−0.744249	−	0.429692i	−0.823612	+	0.567154i	$0.808045\pi$
$98$		0			0
$99$	168.343	+	50.0599i	1.70044	+	0.505656i
$100$		0			0
$101$	114.829			1.13692			0.568461	−	0.822710i	$-0.307539\pi$
$101$	114.829			1.13692			0.568461	+	0.822710i	$0.307539\pi$
$102$		0			0
$103$	58.0132	+	33.4940i	0.563235	+	0.325184i	0.754443	−	0.656366i	$-0.227907\pi$
$103$	58.0132	+	33.4940i	0.563235	+	0.325184i	−0.191208	+	0.981550i	$0.561240\pi$
$104$		0			0
$105$	140.531	−	178.069i	1.33839	−	1.69589i
$106$		0			0
$107$		−	48.5633i		−	0.453862i	−0.973911	−	0.226931i	$-0.927131\pi$
$107$		−	48.5633i		−	0.453862i	0.973911	−	0.226931i	$-0.0728692\pi$
$108$		0			0
$109$	160.233	−	92.5106i	1.47003	−	0.848721i	0.470594	−	0.882350i	$-0.344040\pi$
$109$	160.233	−	92.5106i	1.47003	−	0.848721i	0.999434	+	0.0336282i	$0.0107062\pi$
$110$		0			0
$111$	93.5967	−	37.2837i	0.843213	−	0.335889i
$112$		0			0
$113$	−179.963	−	103.902i	−1.59259	−	0.919485i	−0.992860	−	0.119286i	$-0.961940\pi$
$113$	−179.963	−	103.902i	−1.59259	−	0.919485i	−0.599734	−	0.800199i	$-0.704727\pi$
$114$		0			0
$115$	−110.749	−	191.823i	−0.963034	−	1.66802i
$116$		0			0
$117$	2.71993	−	9.14666i	0.0232472	−	0.0781766i
$118$		0			0
$119$	−151.662	+	262.687i	−1.27447	+	2.20745i
$120$		0			0
$121$	−129.904	+	225.000i	−1.07359	+	1.85951i
$122$		0			0
$123$	−75.6328	+	30.1279i	−0.614901	+	0.244942i
$124$		0			0
$125$	−5.04337			−0.0403470
$126$		0			0
$127$	−73.9519	−	42.6961i	−0.582298	−	0.336190i	0.179748	−	0.983713i	$-0.442472\pi$
$127$	−73.9519	−	42.6961i	−0.582298	−	0.336190i	−0.762046	+	0.647523i	$0.775805\pi$
$128$		0			0
$129$	95.9762	+	13.9679i	0.744002	+	0.108278i
$130$		0			0
$131$	−56.2237			−0.429189			−0.214594	−	0.976703i	$-0.568843\pi$
$131$	−56.2237			−0.429189			−0.214594	+	0.976703i	$0.568843\pi$
$132$		0			0
$133$	23.3125	−	200.400i	0.175282	−	1.50677i
$134$		0			0
$135$	−174.477	−	80.7720i	−1.29242	−	0.598311i
$136$		0			0
$137$	−140.862			−1.02819			−0.514096	−	0.857733i	$-0.671873\pi$
$137$	−140.862			−1.02819			−0.514096	+	0.857733i	$0.671873\pi$
$138$		0			0
$139$	58.0682	+	100.577i	0.417757	+	0.723576i	0.995713	−	0.0924915i	$-0.0294831\pi$
$139$	58.0682	+	100.577i	0.417757	+	0.723576i	−0.577957	+	0.816067i	$0.696150\pi$
$140$		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
$147$	189.265	+	27.5447i	1.28752	+	0.187379i
$148$		0			0
$149$	3.78409			0.0253966			0.0126983	−	0.999919i	$-0.495958\pi$
$149$	3.78409			0.0253966			0.0126983	+	0.999919i	$0.495958\pi$
$150$		0			0
$151$	−56.7315	+	32.7540i	−0.375705	+	0.216914i	−0.675948	−	0.736949i	$-0.736266\pi$
$151$	−56.7315	+	32.7540i	−0.375705	+	0.216914i	0.300243	+	0.953863i	$0.402932\pi$
$152$		0			0
$153$	246.426	+	73.2793i	1.61063	+	0.478949i
$154$		0			0
$155$	158.954	+	91.7724i	1.02551	+	0.592080i
$156$		0			0
$157$	−9.90254			−0.0630735			−0.0315368	−	0.999503i	$-0.510040\pi$
$157$	−9.90254			−0.0630735			−0.0315368	+	0.999503i	$0.510040\pi$
$158$		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
$165$	258.263	−	327.248i	1.56523	−	1.98332i
$166$		0			0
$167$	−136.851	+	79.0109i	−0.819467	+	0.473119i	−0.850232	−	0.526407i	$-0.823539\pi$
$167$	−136.851	+	79.0109i	−0.819467	+	0.473119i	0.0307659	+	0.999527i	$0.490205\pi$
$168$		0			0
$169$	−83.9379	+	145.385i	−0.496674	+	0.860265i
$170$		0			0
$171$	−169.796	+	20.2584i	−0.992958	+	0.118470i
$172$		0			0
$173$	−214.733	−	123.976i	−1.24123	−	0.716626i	−0.271887	−	0.962329i	$-0.587648\pi$
$173$	−214.733	−	123.976i	−1.24123	−	0.716626i	−0.969345	+	0.245704i	$0.920981\pi$
$174$		0			0
$175$	−136.492	−	236.411i	−0.779953	−	1.35092i
$176$		0			0
$177$	−106.513	+	42.4288i	−0.601767	+	0.239711i
$178$		0			0
$179$			161.562i			0.902580i	0.892377	+	0.451290i	$0.149036\pi$
$179$			161.562i			0.902580i	−0.892377	+	0.451290i	$0.850964\pi$
$180$		0			0
$181$	−93.7625	−	54.1338i	−0.518025	−	0.299082i	0.218101	−	0.975926i	$-0.430014\pi$
$181$	−93.7625	−	54.1338i	−0.518025	−	0.299082i	−0.736126	+	0.676844i	$0.763347\pi$
$182$		0			0
$183$	39.6641	+	99.5723i	0.216744	+	0.544111i
$184$		0			0
$185$		−	239.144i		−	1.29267i
$186$		0			0
$187$	−278.719	+	482.756i	−1.49048	+	2.58158i
$188$		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
$193$		−	147.088i		−	0.762113i	−0.924552	−	0.381057i	$-0.875560\pi$
$193$		−	147.088i		−	0.762113i	0.924552	−	0.381057i	$-0.124440\pi$
$194$		0			0
$195$	−17.7805	−	14.0323i	−0.0911820	−	0.0719606i
$196$		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	−0.606767	−	0.794879i	$-0.707534\pi$
$199$	76.6154	−	132.702i	0.385002	−	0.666843i	0.991769	+	0.128036i	$0.0408674\pi$
$200$		0			0
$201$	−247.121	−	195.027i	−1.22946	−	0.970286i
$202$		0			0
$203$	−402.367	+	232.307i	−1.98210	+	1.14437i
$204$		0			0
$205$			193.246i			0.942661i
$206$		0			0
$207$	−268.332	−	79.7935i	−1.29629	−	0.385476i
$208$		0			0
$209$	42.8427	−	368.288i	0.204989	−	1.76214i
$210$		0			0
$211$		−	174.863i		−	0.828733i	−0.910110	−	0.414366i	$-0.864003\pi$
$211$		−	174.863i		−	0.828733i	0.910110	−	0.414366i	$-0.135997\pi$
$212$		0			0
$213$	205.105	+	161.868i	0.962935	+	0.759946i
$214$		0			0
$215$	115.107	−	199.372i	0.535383	−	0.927311i
$216$		0			0
$217$			273.695i			1.26127i
$218$		0			0
$219$	22.5841	−	28.6165i	0.103124	−	0.130669i
$220$		0			0
$221$	26.2298	+	15.1438i	0.118687	+	0.0685238i
$222$		0			0
$223$	40.8721	+	23.5975i	0.183283	+	0.105819i	0.588834	−	0.808254i	$-0.299587\pi$
$223$	40.8721	+	23.5975i	0.183283	+	0.105819i	−0.405551	+	0.914072i	$0.632920\pi$
$224$		0			0
$225$	−168.002	+	159.089i	−0.746675	+	0.707063i
$226$		0			0
$227$	38.5978	−	22.2844i	0.170034	−	0.0981693i	−0.412568	−	0.910927i	$-0.635368\pi$
$227$	38.5978	−	22.2844i	0.170034	−	0.0981693i	0.582602	+	0.812758i	$0.302035\pi$
$228$		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
$231$	615.158	+	89.5271i	2.66302	+	0.387563i
$232$		0			0
$233$	−187.563	−	324.868i	−0.804991	−	1.39429i	−0.916297	−	0.400499i	$-0.868837\pi$
$233$	−187.563	−	324.868i	−0.804991	−	1.39429i	0.111306	−	0.993786i	$-0.464496\pi$
$234$		0			0
$235$	−250.036			−1.06398
$236$		0			0
$237$	10.4563	−	71.8477i	0.0441196	−	0.303155i
$238$		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
$241$		−	106.801i		−	0.443157i	−0.975142	−	0.221579i	$-0.928879\pi$
$241$		−	106.801i		−	0.443157i	0.975142	−	0.221579i	$-0.0711210\pi$
$242$		0			0
$243$	−230.310	+	77.4990i	−0.947780	+	0.318926i
$244$		0			0
$245$	226.991	−	393.161i	0.926496	−	1.60474i
$246$		0			0
$247$	−20.0103	−	2.32779i	−0.0810135	−	0.00942426i
$248$		0			0
$249$	−142.421	+	180.464i	−0.571974	+	0.724754i
$250$		0			0
$251$	−56.6823	+	98.1765i	−0.225826	+	0.391142i	−0.956567	−	0.291513i	$-0.905841\pi$
$251$	−56.6823	+	98.1765i	−0.225826	+	0.391142i	0.730741	+	0.682655i	$0.239175\pi$
$252$		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
$257$	44.4428	−	25.6591i	0.172929	−	0.0998407i	−0.411037	−	0.911619i	$-0.634833\pi$
$257$	44.4428	−	25.6591i	0.172929	−	0.0998407i	0.583966	+	0.811778i	$0.301500\pi$
$258$		0			0
$259$	308.827	−	178.301i	1.19238	−	0.688422i
$260$		0			0
$261$	270.767	+	285.936i	1.03742	+	1.09554i
$262$		0			0
$263$	−21.4504	+	37.1532i	−0.0815605	+	0.141267i	−0.903920	−	0.427701i	$-0.859324\pi$
$263$	−21.4504	+	37.1532i	−0.0815605	+	0.141267i	0.822360	+	0.568968i	$0.192657\pi$
$264$		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	−0.278134	−	0.960542i	$-0.589716\pi$
$269$	111.541	−	64.3985i	0.414652	−	0.239400i	0.692787	+	0.721143i	$0.256383\pi$
$270$		0			0
$271$	137.721	+	238.539i	0.508195	+	0.880219i	0.999955	+	0.00948823i	$0.00302024\pi$
$271$	137.721	+	238.539i	0.508195	+	0.880219i	−0.491760	+	0.870731i	$0.663646\pi$
$272$		0			0
$273$	4.86431	−	33.4236i	0.0178180	−	0.122431i
$274$		0			0
$275$	−250.839	−	434.466i	−0.912142	−	1.57988i
$276$		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
$279$	225.625	−	53.9146i	0.808692	−	0.193242i
$280$		0			0
$281$			97.9216i			0.348476i	0.984704	+	0.174238i	$0.0557461\pi$
$281$			97.9216i			0.348476i	−0.984704	+	0.174238i	$0.944254\pi$
$282$		0			0
$283$	348.207			1.23041			0.615207	−	0.788365i	$-0.289072\pi$
$283$	348.207			1.23041			0.615207	+	0.788365i	$0.289072\pi$
$284$		0			0
$285$	−104.477	+	392.219i	−0.366586	+	1.37621i
$286$		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
$291$	−36.0161	+	247.474i	−0.123767	+	0.850425i
$292$		0			0
$293$	186.504	+	107.678i	0.636533	+	0.367503i	0.783278	−	0.621672i	$-0.213546\pi$
$293$	186.504	+	107.678i	0.636533	+	0.367503i	−0.146745	+	0.989174i	$0.546880\pi$
$294$		0			0
$295$			272.145i			0.922527i
$296$		0			0
$297$	−47.3756	−	524.752i	−0.159514	−	1.76684i
$298$		0			0
$299$	−28.5615	−	16.4900i	−0.0955233	−	0.0551504i
$300$		0			0
$301$	343.287			1.14049
$302$		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	−0.0589328	−	0.998262i	$-0.518770\pi$
$307$	238.269	−	137.565i	0.776121	−	0.448094i	0.835054	+	0.550168i	$0.185436\pi$
$308$		0			0
$309$	28.9423	−	198.869i	0.0936646	−	0.643588i
$310$		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
$313$	−66.6598			−0.212971			−0.106485	−	0.994314i	$-0.533960\pi$
$313$	−66.6598			−0.212971			−0.106485	+	0.994314i	$0.533960\pi$
$314$		0			0
$315$	−652.298	−	193.973i	−2.07079	−	0.615786i
$316$		0			0
$317$			493.061i			1.55540i	0.628637	+	0.777699i	$0.283613\pi$
$317$			493.061i			1.55540i	−0.628637	+	0.777699i	$0.716387\pi$
$318$		0			0
$319$	−739.454	+	426.924i	−2.31804	+	1.33832i
$320$		0			0
$321$	−135.347	+	53.9146i	−0.421641	+	0.167958i
$322$		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
$327$	−435.719	−	343.868i	−1.33247	−	1.05158i
$328$		0			0
$329$	−186.422	−	322.893i	−0.566633	−	0.981438i
$330$		0			0
$331$	−127.344	+	73.5220i	−0.384724	+	0.222121i	−0.679872	−	0.733331i	$-0.737965\pi$
$331$	−127.344	+	73.5220i	−0.384724	+	0.222121i	0.295147	+	0.955452i	$0.404631\pi$
$332$		0			0
$333$	−207.821	−	219.463i	−0.624087	−	0.659050i
$334$		0			0
$335$	−647.136	+	373.624i	−1.93175	+	1.11530i
$336$		0			0
$337$			283.245i			0.840491i	0.907410	+	0.420246i	$0.138056\pi$
$337$			283.245i			0.840491i	−0.907410	+	0.420246i	$0.861944\pi$
$338$		0			0
$339$	−89.7822	+	616.912i	−0.264844	+	1.81980i
$340$		0			0
$341$			502.986i			1.47503i
$342$		0			0
$343$	156.654			0.456718
$344$		0			0
$345$	−411.661	+	521.619i	−1.19322	+	1.51194i
$346$		0			0
$347$	−464.588			−1.33887			−0.669435	−	0.742871i	$-0.733464\pi$
$347$	−464.588			−1.33887			−0.669435	+	0.742871i	$0.733464\pi$
$348$		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
$351$	−28.5116	+	2.57408i	−0.0812295	+	0.00733355i
$352$		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
$355$	537.109	−	310.100i	1.51298	−	0.873521i
$356$		0			0
$357$	900.487	+	131.052i	2.52237	+	0.367094i
$358$		0			0
$359$	188.236	+	326.035i	0.524336	+	0.908176i	0.999599	+	0.0283320i	$0.00901957\pi$
$359$	188.236	+	326.035i	0.524336	+	0.908176i	−0.475263	+	0.879844i	$0.657647\pi$
$360$		0			0
$361$	103.914	+	345.721i	0.287850	+	0.957676i
$362$		0			0
$363$	771.298	+	112.251i	2.12479	+	0.309231i
$364$		0			0
$365$	−43.2655	−	74.9380i	−0.118536	−	0.205310i
$366$		0			0
$367$	−366.554			−0.998784			−0.499392	−	0.866376i	$-0.666443\pi$
$367$	−366.554			−0.998784			−0.499392	+	0.866376i	$0.666443\pi$
$368$		0			0
$369$	167.934	+	177.342i	0.455106	+	0.480602i
$370$		0			0
$371$			28.9922i			0.0781461i
$372$		0			0
$373$	123.117	+	71.0814i	0.330072	+	0.190567i	0.655873	−	0.754871i	$-0.272301\pi$
$373$	123.117	+	71.0814i	0.330072	+	0.190567i	−0.325801	+	0.945438i	$0.605634\pi$
$374$		0			0
$375$	5.59912	+	14.0560i	0.0149310	+	0.0374826i
$376$		0			0
$377$	23.1962	+	40.1771i	0.0615285	+	0.106570i
$378$		0			0
$379$			11.1059i			0.0293030i	0.999893	+	0.0146515i	$0.00466389\pi$
$379$			11.1059i			0.0293030i	−0.999893	+	0.0146515i	$0.995336\pi$
$380$		0			0
$381$	−36.8940	+	253.506i	−0.0968347	+	0.665371i
$382$		0			0
$383$			558.662i			1.45865i	0.684169	+	0.729323i	$0.260165\pi$
$383$			558.662i			1.45865i	−0.684169	+	0.729323i	$0.739835\pi$
$384$		0			0
$385$	737.779	−	1277.87i	1.91631	−	3.31914i
$386$		0			0
$387$	−67.6234	−	282.995i	−0.174737	−	0.731252i
$388$		0			0
$389$	−150.105			−0.385873			−0.192937	−	0.981211i	$-0.561801\pi$
$389$	−150.105			−0.385873			−0.192937	+	0.981211i	$0.561801\pi$
$390$		0			0
$391$	444.267	−	769.493i	1.13623	−	1.96801i
$392$		0			0
$393$	62.4192	+	156.696i	0.158827	+	0.398719i
$394$		0			0
$395$	−149.249	−	86.1692i	−0.377847	−	0.218150i
$396$		0			0
$397$	279.859	+	484.729i	0.704933	+	1.22098i	0.966716	+	0.255853i	$0.0823564\pi$
$397$	279.859	+	484.729i	0.704933	+	1.22098i	−0.261782	+	0.965127i	$0.584310\pi$
$398$		0			0
$399$	−584.401	+	157.511i	−1.46466	+	0.394764i
$400$		0			0
$401$			80.8455i			0.201610i	0.994906	+	0.100805i	$0.0321418\pi$
$401$			80.8455i			0.201610i	−0.994906	+	0.100805i	$0.967858\pi$
$402$		0			0
$403$	27.3289			0.0678137
$404$		0			0
$405$	−31.4099	+	575.943i	−0.0775554	+	1.42208i
$406$		0			0
$407$	567.550	−	327.675i	1.39447	−	0.805099i
$408$		0			0
$409$	−561.818	+	324.366i	−1.37364	+	0.793070i	−0.991384	−	0.130987i	$-0.958185\pi$
$409$	−561.818	+	324.366i	−1.37364	+	0.793070i	−0.382254	+	0.924057i	$0.624852\pi$
$410$		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
$421$	566.255	+	326.927i	1.34502	+	0.776549i	0.987540	−	0.157370i	$-0.0503015\pi$
$421$	566.255	+	326.927i	1.34502	+	0.776549i	0.357483	+	0.933919i	$0.383635\pi$
$422$		0			0
$423$	−229.459	+	217.286i	−0.542457	+	0.513679i
$424$		0			0
$425$	−367.186	−	635.985i	−0.863967	−	1.49643i
$426$		0			0
$427$	189.685	+	328.544i	0.444227	+	0.769423i
$428$		0			0
$429$	8.93944	−	61.4247i	0.0208378	−	0.143181i
$430$		0			0
$431$	224.079	+	129.372i	0.519904	+	0.300167i	0.736895	−	0.676007i	$-0.236291\pi$
$431$	224.079	+	129.372i	0.519904	+	0.300167i	−0.216991	+	0.976173i	$0.569624\pi$
$432$		0			0
$433$	−650.365	−	375.488i	−1.50200	−	0.867179i	−0.999997	−	0.00231130i	$-0.999264\pi$
$433$	−650.365	−	375.488i	−1.50200	−	0.867179i	−0.502000	−	0.864867i	$-0.667402\pi$
$434$		0			0
$435$	868.374	−	345.912i	1.99626	−	0.795200i
$436$		0			0
$437$	−68.2896	+	587.036i	−0.156269	+	1.34333i
$438$		0			0
$439$	−47.8953	−	27.6524i	−0.109101	−	0.0629895i	0.444457	−	0.895800i	$-0.353397\pi$
$439$	−47.8953	−	27.6524i	−0.109101	−	0.0629895i	−0.553558	+	0.832811i	$0.686730\pi$
$440$		0			0
$441$	−133.353	−	558.065i	−0.302388	−	1.26545i
$442$		0			0
$443$	340.514			0.768655			0.384328	−	0.923197i	$-0.374433\pi$
$443$	340.514			0.768655			0.384328	+	0.923197i	$0.374433\pi$
$444$		0			0
$445$	−786.549	−	454.114i	−1.76753	−	1.02048i
$446$		0			0
$447$	−4.20107	−	10.5463i	−0.00939836	−	0.0235936i
$448$		0			0
$449$			881.944i			1.96424i	0.188254	+	0.982120i	$0.439717\pi$
$449$			881.944i			1.96424i	−0.188254	+	0.982120i	$0.560283\pi$
$450$		0			0
$451$	−458.621	+	264.785i	−1.01690	+	0.587106i
$452$		0			0
$453$	154.269	+	121.749i	0.340549	+	0.268761i
$454$		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
$459$	−69.3498	−	768.148i	−0.151089	−	1.67352i
$460$		0			0
$461$	157.205	−	272.287i	0.341009	−	0.590645i	−0.643611	−	0.765353i	$-0.722565\pi$
$461$	157.205	−	272.287i	0.341009	−	0.590645i	0.984620	+	0.174707i	$0.0558980\pi$
$462$		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
$465$	79.3012	−	544.894i	0.170540	−	1.17182i
$466$		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
$471$	10.9937	+	27.5986i	0.0233413	+	0.0585957i
$472$		0			0
$473$	630.880			1.33378
$474$		0			0
$475$	391.962	+	291.472i	0.825182	+	0.613625i
$476$		0			0
$477$	23.9002	−	5.71111i	0.0501052	−	0.0119730i
$478$		0			0
$479$	887.013			1.85180			0.925901	−	0.377766i	$-0.123308\pi$
$479$	887.013			1.85180			0.925901	+	0.377766i	$0.123308\pi$
$480$		0			0
$481$	−17.8037	−	30.8369i	−0.0370139	−	0.0641100i
$482$		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	$-0.844135\pi$
$487$		−	458.100i		−	0.940657i	0.882491	−	0.470328i	$-0.155865\pi$
$488$		0			0
$489$	35.1476	+	88.2342i	0.0718765	+	0.180438i
$490$		0			0
$491$	960.396			1.95600			0.978000	−	0.208605i	$-0.0668922\pi$
$491$	960.396			1.95600			0.978000	+	0.208605i	$0.0668922\pi$
$492$		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
$497$	800.916	+	462.409i	1.61150	+	0.930400i
$498$		0			0
$499$	77.9497			0.156212			0.0781059	−	0.996945i	$-0.475113\pi$
$499$	77.9497			0.156212			0.0781059	+	0.996945i	$0.475113\pi$
$500$		0			0
$501$	372.136	+	293.689i	0.742786	+	0.586205i
$502$		0			0
$503$	−169.590	+	293.738i	−0.337156	+	0.583971i	−0.983897	−	0.178739i	$-0.942798\pi$
$503$	−169.590	+	293.738i	−0.337156	+	0.583971i	0.646741	+	0.762710i	$0.276132\pi$
$504$		0			0
$505$	−817.696			−1.61920
$506$		0			0
$507$	498.377	+	72.5313i	0.982992	+	0.143060i
$508$		0			0
$509$	710.709	−	410.328i	1.39628	−	0.806145i	0.402283	−	0.915515i	$-0.368217\pi$
$509$	710.709	−	410.328i	1.39628	−	0.806145i	0.994001	+	0.109371i	$0.0348835\pi$
$510$		0			0
$511$	64.5158	−	111.745i	0.126254	−	0.218678i
$512$		0			0
$513$	244.967	+	450.733i	0.477518	+	0.878622i
$514$		0			0
$515$	−413.111	−	238.510i	−0.802156	−	0.463125i
$516$		0			0
$517$	−342.600	−	593.400i	−0.662669	−	1.14778i
$518$		0			0
$519$	−107.129	+	736.103i	−0.206414	+	1.41831i
$520$		0			0
$521$		−	49.2700i		−	0.0945682i	−0.998881	−	0.0472841i	$-0.984943\pi$
$521$		−	49.2700i		−	0.0945682i	0.998881	−	0.0472841i	$-0.0150566\pi$
$522$		0			0
$523$	−216.127	−	124.781i	−0.413245	−	0.238587i	0.278938	−	0.960309i	$-0.410018\pi$
$523$	−216.127	−	124.781i	−0.413245	−	0.238587i	−0.692183	+	0.721722i	$0.743351\pi$
$524$		0			0
$525$	−507.348	+	642.866i	−0.966378	+	1.22451i
$526$		0			0
$527$			736.286i			1.39713i
$528$		0			0
$529$	−219.260	+	379.770i	−0.414481	+	0.717902i
$530$		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
$535$			345.818i			0.646388i
$536$		0			0
$537$	450.276	−	179.365i	0.838502	−	0.334013i
$538$		0			0
$539$	1244.09			2.30815
$540$		0			0
$541$	−12.3287	+	21.3540i	−0.0227888	+	0.0394713i	−0.877195	−	0.480134i	$-0.840588\pi$
$541$	−12.3287	+	21.3540i	−0.0227888	+	0.0394713i	0.854406	+	0.519606i	$0.173921\pi$
$542$		0			0
$543$	−46.7774	+	321.417i	−0.0861462	+	0.591928i
$544$		0			0
$545$	−1141.02	+	658.766i	−2.09361	+	1.20874i
$546$		0			0
$547$		−	860.453i		−	1.57304i	−0.617564	−	0.786520i	$-0.711880\pi$
$547$		−	860.453i		−	1.57304i	0.617564	−	0.786520i	$-0.288120\pi$
$548$		0			0
$549$	233.475	−	221.089i	0.425273	−	0.402712i
$550$		0			0
$551$	496.080	−	667.112i	0.900327	−	1.21073i
$552$		0			0
$553$		−	256.984i		−	0.464709i
$554$		0			0
$555$	−666.499	+	265.496i	−1.20090	+	0.478372i
$556$		0			0
$557$	−234.760	+	406.616i	−0.421472	+	0.730010i	−0.996084	−	0.0884157i	$-0.971820\pi$
$557$	−234.760	+	406.616i	−0.421472	+	0.730010i	0.574612	+	0.818426i	$0.305153\pi$
$558$		0			0
$559$		−	34.2779i		−	0.0613199i
$560$		0			0
$561$	1654.88	+	240.843i	2.94988	+	0.429310i
$562$		0			0
$563$	−928.134	−	535.858i	−1.64855	−	0.951791i	−0.977649	−	0.210244i	$-0.932574\pi$
$563$	−928.134	−	535.858i	−1.64855	−	0.951791i	−0.670901	−	0.741547i	$-0.734093\pi$
$564$		0			0
$565$	1281.51	+	739.882i	2.26816	+	1.30953i
$566$		0			0
$567$	−767.182	+	388.850i	−1.35305	+	0.685802i
$568$		0			0
$569$	262.240	−	151.404i	0.460879	−	0.266089i	−0.251535	−	0.967848i	$-0.580935\pi$
$569$	262.240	−	151.404i	0.460879	−	0.266089i	0.712414	+	0.701760i	$0.247602\pi$
$570$		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
$573$	241.177	−	305.598i	0.420903	−	0.533330i
$574$		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
$579$	−409.937	+	163.296i	−0.708008	+	0.282031i
$580$		0			0
$581$	−406.855	+	704.693i	−0.700266	+	1.21290i
$582$		0			0
$583$			53.2807i			0.0913906i
$584$		0			0
$585$	−19.3685	+	65.1331i	−0.0331086	+	0.111339i
$586$		0			0
$587$	−510.473	+	884.165i	−0.869630	+	1.50624i	−0.00725492	+	0.999974i	$0.502309\pi$
$587$	−510.473	+	884.165i	−0.869630	+	1.50624i	−0.862375	+	0.506270i	$0.831024\pi$
$588$		0			0
$589$	−194.218	−	449.572i	−0.329741	−	0.763280i
$590$		0			0
$591$	98.9657	+	248.443i	0.167455	+	0.420376i
$592$		0			0
$593$	−62.4534	+	108.173i	−0.105318	+	0.182416i	−0.913868	−	0.406011i	$-0.866919\pi$
$593$	−62.4534	+	108.173i	−0.105318	+	0.182416i	0.808550	+	0.588427i	$0.200253\pi$
$594$		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
$599$	−228.015	+	131.644i	−0.380659	+	0.219774i	−0.678105	−	0.734965i	$-0.737199\pi$
$599$	−228.015	+	131.644i	−0.380659	+	0.219774i	0.297446	+	0.954739i	$0.403865\pi$
$600$		0			0
$601$	242.962	−	140.274i	0.404263	−	0.233402i	−0.284059	−	0.958807i	$-0.591681\pi$
$601$	242.962	−	140.274i	0.404263	−	0.233402i	0.688322	+	0.725405i	$0.258348\pi$
$602$		0			0
$603$	−269.193	+	905.249i	−0.446422	+	1.50124i
$604$		0			0
$605$	925.042	−	1602.22i	1.52900	−	2.64830i
$606$		0			0
$607$	635.619	+	366.975i	1.04715	+	0.604572i	0.921850	−	0.387547i	$-0.126678\pi$
$607$	635.619	+	366.975i	1.04715	+	0.604572i	0.125299	+	0.992119i	$0.460011\pi$
$608$		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	−0.993023	−	0.117917i	$-0.962378\pi$
$613$	−366.961	−	635.595i	−0.598631	−	1.03686i	0.394393	−	0.918942i	$-0.370955\pi$
$614$		0			0
$615$	538.579	−	214.540i	0.875738	−	0.348845i
$616$		0			0
$617$	−248.114	−	429.745i	−0.402129	−	0.696508i	0.591854	−	0.806046i	$-0.298396\pi$
$617$	−248.114	−	429.745i	−0.402129	−	0.696508i	−0.993983	+	0.109537i	$0.965063\pi$
$618$		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
$621$	75.5147	+	836.433i	0.121602	+	1.34691i
$622$		0			0
$623$		−	1354.32i		−	2.17386i
$624$		0			0
$625$	−606.792			−0.970868
$626$		0			0
$627$	−1073.99	+	289.468i	−1.71290	+	0.461671i
$628$		0			0
$629$	830.797	−	479.661i	1.32082	−	0.762577i
$630$		0			0
$631$	−385.601	+	667.881i	−0.611095	+	1.05845i	0.379961	+	0.925003i	$0.375938\pi$
$631$	−385.601	+	667.881i	−0.611095	+	1.05845i	−0.991056	+	0.133446i	$0.957396\pi$
$632$		0			0
$633$	−487.345	+	194.131i	−0.769898	+	0.306684i
$634$		0			0
$635$	526.609	+	304.038i	0.829306	+	0.478800i
$636$		0			0
$637$		−	67.5959i		−	0.106116i
$638$		0			0
$639$	223.424	−	751.337i	0.349646	−	1.17580i
$640$		0			0
$641$	−930.639	−	537.305i	−1.45185	−	0.838229i	−0.453268	−	0.891374i	$-0.649742\pi$
$641$	−930.639	−	537.305i	−1.45185	−	0.838229i	−0.998587	+	0.0531455i	$0.983075\pi$
$642$		0			0
$643$	1192.20			1.85412			0.927060	−	0.374913i	$-0.122327\pi$
$643$	1192.20			1.85412			0.927060	+	0.374913i	$0.122327\pi$
$644$		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
$651$	762.793	−	303.854i	1.17172	−	0.466750i
$652$		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
$655$	400.367			0.611248
$656$		0			0
$657$	−104.827	−	31.1723i	−0.159555	−	0.0474465i
$658$		0			0
$659$			772.963i			1.17293i	0.809973	+	0.586467i	$0.199482\pi$
$659$			772.963i			1.17293i	−0.809973	+	0.586467i	$0.800518\pi$
$660$		0			0
$661$	494.118	−	285.279i	0.747531	−	0.431587i	−0.0772703	−	0.997010i	$-0.524620\pi$
$661$	494.118	−	285.279i	0.747531	−	0.431587i	0.824801	+	0.565423i	$0.191287\pi$
$662$		0			0
$663$	13.0858	−	89.9153i	0.0197373	−	0.135619i
$664$		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
$669$	20.3908	−	140.109i	0.0304795	−	0.209431i
$670$		0			0
$671$	348.595	+	603.785i	0.519516	+	0.899828i
$672$		0			0
$673$	651.912	−	376.382i	0.968666	−	0.559259i	0.0698365	−	0.997558i	$-0.477752\pi$
$673$	651.912	−	376.382i	0.968666	−	0.559259i	0.898829	+	0.438299i	$0.144419\pi$
$674$		0			0
$675$	629.899	+	291.604i	0.933184	+	0.432006i
$676$		0			0
$677$	145.503	−	84.0065i	0.214924	−	0.124086i	−0.388674	−	0.921375i	$-0.627067\pi$
$677$	145.503	−	84.0065i	0.214924	−	0.124086i	0.603598	+	0.797289i	$0.293733\pi$
$678$		0			0
$679$			885.163i			1.30363i
$680$		0			0
$681$	−104.958	−	82.8327i	−0.154124	−	0.121634i
$682$		0			0
$683$			491.889i			0.720189i	0.932916	+	0.360095i	$0.117256\pi$
$683$			491.889i			0.720189i	−0.932916	+	0.360095i	$0.882744\pi$
$684$		0			0
$685$	1003.08			1.46435
$686$		0			0
$687$	−1070.86	−	155.847i	−1.55875	−	0.226852i
$688$		0			0
$689$	2.89492			0.00420163
$690$		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
$693$	−433.431	−	1813.85i	−0.625442	−	2.61739i
$694$		0			0
$695$	−413.502	−	716.206i	−0.594967	−	1.03051i
$696$		0			0
$697$	−671.343	+	387.600i	−0.963189	+	0.556098i
$698$		0			0
$699$	−697.183	+	883.408i	−0.997401	+	1.26382i
$700$		0			0
$701$	−210.851	−	365.204i	−0.300785	−	0.520976i	0.675529	−	0.737334i	$-0.263915\pi$
$701$	−210.851	−	365.204i	−0.300785	−	0.520976i	−0.976314	+	0.216358i	$0.930582\pi$
$702$		0			0
$703$	−380.754	+	512.026i	−0.541614	+	0.728344i
$704$		0			0
$705$	277.589	+	696.856i	0.393743	+	0.988448i
$706$		0			0
$707$	−609.658	−	1055.96i	−0.862317	−	1.49358i
$708$		0			0
$709$	−580.892			−0.819312			−0.409656	−	0.912240i	$-0.634351\pi$
$709$	−580.892			−0.819312			−0.409656	+	0.912240i	$0.634351\pi$
$710$		0			0
$711$	−211.849	+	50.6228i	−0.297960	+	0.0711994i
$712$		0			0
$713$		−	801.739i		−	1.12446i
$714$		0			0
$715$	−127.598	−	73.6685i	−0.178458	−	0.103033i
$716$		0			0
$717$	−725.240	−	105.548i	−1.01149	−	0.147207i
$718$		0			0
$719$	7.29582	+	12.6367i	0.0101472	+	0.0175754i	0.871054	−	0.491187i	$-0.163437\pi$
$719$	7.29582	+	12.6367i	0.0101472	+	0.0175754i	−0.860907	+	0.508762i	$0.830103\pi$
$720$		0			0
$721$		−	711.312i		−	0.986564i
$722$		0			0
$723$	−297.656	+	118.570i	−0.411696	+	0.163997i
$724$		0			0
$725$		−	1124.86i		−	1.55154i
$726$		0			0
$727$	−533.157	+	923.456i	−0.733366	+	1.27023i	0.222070	+	0.975031i	$0.428719\pi$
$727$	−533.157	+	923.456i	−0.733366	+	1.27023i	−0.955436	+	0.295197i	$0.904615\pi$
$728$		0			0
$729$	471.680	+	555.841i	0.647024	+	0.762470i
$730$		0			0
$731$	923.501			1.26334
$732$		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
$735$	−1347.75	−	196.145i	−1.83367	−	0.266864i
$736$		0			0
$737$	−1773.41	−	1023.88i	−2.40626	−	1.38925i
$738$		0			0
$739$	−590.659	−	1023.05i	−0.799268	−	1.38437i	−0.920093	−	0.391699i	$-0.871887\pi$
$739$	−590.659	−	1023.05i	−0.799268	−	1.38437i	0.120825	−	0.992674i	$-0.461446\pi$
$740$		0			0
$741$	15.7278	+	58.3535i	0.0212250	+	0.0787497i
$742$		0			0
$743$			623.721i			0.839463i	0.907648	+	0.419731i	$0.137876\pi$
$743$			623.721i			0.839463i	−0.907648	+	0.419731i	$0.862124\pi$
$744$		0			0
$745$	−26.9464			−0.0361696
$746$		0			0
$747$	661.071	+	196.582i	0.884968	+	0.263161i
$748$		0			0
$749$	−446.583	+	257.835i	−0.596239	+	0.344239i
$750$		0			0
$751$	872.642	−	503.820i	1.16197	−	0.670866i	0.210198	−	0.977659i	$-0.432589\pi$
$751$	872.642	−	503.820i	1.16197	−	0.670866i	0.951776	+	0.306793i	$0.0992560\pi$
$752$		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	0.671467	−	0.741035i	$-0.265665\pi$
$757$	−231.658	−	401.244i	−0.306021	−	0.530045i	−0.977488	+	0.210990i	$0.932331\pi$
$758$		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
$763$	−1701.44	−	982.326i	−2.22993	−	1.28745i
$764$		0			0
$765$	−1754.79	−	521.820i	−2.29385	−	0.682117i
$766$		0			0
$767$	20.2606	+	35.0923i	0.0264153	+	0.0457527i
$768$		0			0
$769$	−476.336	−	825.038i	−0.619422	−	1.07287i	−0.989591	−	0.143907i	$-0.954033\pi$
$769$	−476.336	−	825.038i	−0.619422	−	1.07287i	0.370169	−	0.928965i	$-0.379300\pi$
$770$		0			0
$771$	−120.852	−	95.3763i	−0.156748	−	0.123705i
$772$		0			0
$773$	201.770	+	116.492i	0.261021	+	0.150701i	0.624800	−	0.780784i	$-0.285180\pi$
$773$	201.770	+	116.492i	0.261021	+	0.150701i	−0.363779	+	0.931485i	$0.618514\pi$
$774$		0			0
$775$	−573.860	−	331.318i	−0.740464	−	0.427507i
$776$		0			0
$777$	−839.787	−	662.757i	−1.08081	−	0.852970i
$778$		0			0
$779$	307.677	−	413.753i	0.394964	−	0.531134i
$780$		0			0
$781$	1471.89	+	849.797i	1.88462	+	1.08809i
$782$		0			0
$783$	496.306	−	1072.08i	0.633851	−	1.36919i
$784$		0			0
$785$	70.5157			0.0898289
$786$		0			0
$787$	115.019	+	66.4060i	0.146148	+	0.0843787i	0.571291	−	0.820748i	$-0.306443\pi$
$787$	115.019	+	66.4060i	0.146148	+	0.0843787i	−0.425143	+	0.905126i	$0.639776\pi$
$788$		0			0
$789$	127.361	+	18.5354i	0.161420	+	0.0234923i
$790$		0			0
$791$			2206.57i			2.78959i
$792$		0			0
$793$	32.8057	−	18.9404i	0.0413691	−	0.0238844i
$794$		0			0
$795$	8.40028	−	57.7200i	0.0105664	−	0.0726038i
$796$		0			0
$797$	−373.053	−	215.382i	−0.468071	−	0.270241i	0.247361	−	0.968923i	$-0.420437\pi$
$797$	−373.053	−	215.382i	−0.468071	−	0.270241i	−0.715432	+	0.698682i	$0.753770\pi$
$798$		0			0
$799$	−501.508	−	868.637i	−0.627669	−	1.08716i
$800$		0			0
$801$	−1116.45	+	266.784i	−1.39382	+	0.333063i
$802$		0			0
$803$	118.565	−	205.360i	0.147652	−	0.255741i
$804$		0			0
$805$	−1175.99	+	2036.87i	−1.46086	+	2.53028i
$806$		0			0
$807$	−303.312	−	239.373i	−0.375852	−	0.296621i
$808$		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	0.699470	−	0.714662i	$-0.253419\pi$
$811$	348.965	+	201.475i	0.430289	+	0.248428i	−0.269180	+	0.963090i	$0.586753\pi$
$812$		0			0
$813$	511.917	−	648.655i	0.629664	−	0.797854i
$814$		0			0
$815$	225.443			0.276617
$816$		0			0
$817$	−563.884	+	243.601i	−0.690189	+	0.298166i
$818$		0			0
$819$	−98.5526	+	23.5498i	−0.120333	+	0.0287543i
$820$		0			0
$821$	−480.007			−0.584662			−0.292331	−	0.956317i	$-0.594431\pi$
$821$	−480.007			−0.584662			−0.292331	+	0.956317i	$0.594431\pi$
$822$		0			0
$823$	−778.596	−	1348.57i	−0.946046	−	1.63860i	−0.753642	−	0.657285i	$-0.771705\pi$
$823$	−778.596	−	1348.57i	−0.946046	−	1.63860i	−0.192404	−	0.981316i	$-0.561628\pi$
$824$		0			0
$825$	−932.385	+	1181.43i	−1.13016	+	1.43204i
$826$		0			0
$827$	590.269	+	340.792i	0.713748	+	0.412082i	0.812447	−	0.583035i	$-0.198135\pi$
$827$	590.269	+	340.792i	0.713748	+	0.412082i	−0.0986995	+	0.995117i	$0.531468\pi$
$828$		0			0
$829$		−	377.405i		−	0.455253i	−0.973749	−	0.227626i	$-0.926904\pi$
$829$		−	377.405i		−	0.455253i	0.973749	−	0.227626i	$-0.0730965\pi$
$830$		0			0
$831$	847.337	−	1073.67i	1.01966	−	1.29202i
$832$		0			0
$833$	1821.14			2.18625
$834$		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
$839$	566.197	+	326.894i	0.674847	+	0.389623i	0.797911	−	0.602775i	$-0.205939\pi$
$839$	566.197	+	326.894i	0.674847	+	0.389623i	−0.123063	+	0.992399i	$0.539272\pi$
$840$		0			0
$841$	−1073.50			−1.27646
$842$		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
$849$	−386.578	−	970.460i	−0.455333	−	1.14306i
$850$		0			0
$851$	−904.652	+	522.301i	−1.06305	+	0.613750i
$852$		0			0
$853$	122.580	−	212.315i	0.143705	−	0.248904i	−0.785184	−	0.619262i	$-0.787432\pi$
$853$	122.580	−	212.315i	0.143705	−	0.248904i	0.928889	+	0.370358i	$0.120765\pi$
$854$		0			0
$855$	1209.11	−	144.260i	1.41416	−	0.168725i
$856$		0			0
$857$	−602.944	−	348.110i	−0.703552	−	0.406196i	0.105117	−	0.994460i	$-0.466478\pi$
$857$	−602.944	−	348.110i	−0.703552	−	0.406196i	−0.808669	+	0.588264i	$0.799812\pi$
$858$		0			0
$859$	27.5054	+	47.6408i	0.0320203	+	0.0554608i	0.881591	−	0.472013i	$-0.156473\pi$
$859$	27.5054	+	47.6408i	0.0320203	+	0.0554608i	−0.849571	+	0.527474i	$0.823139\pi$
$860$		0			0
$861$	678.607	+	535.555i	0.788162	+	0.622015i
$862$		0			0
$863$		−	556.252i		−	0.644556i	−0.946645	−	0.322278i	$-0.895551\pi$
$863$		−	556.252i		−	0.644556i	0.946645	−	0.322278i	$-0.104449\pi$
$864$		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
$869$		−	472.276i		−	0.543470i
$870$		0			0
$871$	−55.6308	+	96.3554i	−0.0638701	+	0.110626i
$872$		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
$877$			749.675i			0.854817i	0.904059	+	0.427409i	$0.140573\pi$
$877$			749.675i			0.854817i	−0.904059	+	0.427409i	$0.859427\pi$
$878$		0			0
$879$	93.0455	−	639.334i	0.105854	−	0.727343i
$880$		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	0.170858	+	0.985296i	$0.445346\pi$
$883$	−678.022	+	1174.37i	−0.767862	+	1.32998i	−0.938720	+	0.344680i	$0.887987\pi$
$884$		0			0
$885$	758.474	−	302.134i	0.857033	−	0.341394i
$886$		0			0
$887$	329.929	−	190.485i	0.371961	−	0.214752i	−0.302354	−	0.953196i	$-0.597772\pi$
$887$	329.929	−	190.485i	0.371961	−	0.214752i	0.674315	+	0.738444i	$0.264439\pi$
$888$		0			0
$889$			906.740i			1.01995i
$890$		0			0
$891$	−1409.90	+	714.613i	−1.58238	+	0.802034i
$892$		0			0
$893$	535.347	+	398.097i	0.599493	+	0.445797i
$894$		0			0
$895$		−	1150.48i		−	1.28545i
$896$		0			0
$897$	−14.2491	+	97.9084i	−0.0158853	+	0.109151i
$898$		0			0
$899$	−563.898	+	976.700i	−0.627250	+	1.08643i
$900$		0			0
$901$			77.9939i			0.0865637i
$902$		0			0
$903$	−381.115	−	956.748i	−0.422055	−	1.05952i
$904$		0			0
$905$	667.680	+	385.485i	0.737768	+	0.425951i
$906$		0			0
$907$	−1341.16	−	774.321i	−1.47868	−	0.853716i	−0.478971	−	0.877831i	$-0.658990\pi$
$907$	−1341.16	−	774.321i	−1.47868	−	0.853716i	−0.999709	+	0.0241147i	$0.992323\pi$
$908$		0			0
$909$	−750.402	+	710.593i	−0.825525	+	0.781730i
$910$		0			0
$911$	−1396.43	+	806.230i	−1.53286	+	0.884995i	−0.533628	+	0.845719i	$0.679172\pi$
$911$	−1396.43	+	806.230i	−1.53286	+	0.884995i	−0.999228	+	0.0392755i	$0.987495\pi$
$912$		0			0
$913$	−747.702	+	1295.06i	−0.818950	+	1.41846i
$914$		0			0
$915$	−282.447	−	709.051i	−0.308685	−	0.774919i
$916$		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
$921$	−647.920	−	511.337i	−0.703497	−	0.555198i
$922$		0			0
$923$	46.1724	−	79.9729i	0.0500242	−	0.0866445i
$924$		0			0
$925$			863.362i			0.933365i
$926$		0			0
$927$	−586.382	+	140.120i	−0.632559	+	0.151154i
$928$		0			0
$929$	377.486	−	653.825i	0.406336	−	0.703795i	−0.588140	−	0.808759i	$-0.700140\pi$
$929$	377.486	−	653.825i	0.406336	−	0.703795i	0.994476	+	0.104965i	$0.0334729\pi$
$930$		0			0
$931$	−1111.98	+	480.381i	−1.19439	+	0.515984i
$932$		0			0
$933$	375.907	+	54.7076i	0.402901	+	0.0586363i
$934$		0			0
$935$	1984.75	−	3437.69i	2.12273	−	3.67667i
$936$		0			0
$937$	692.149	−	1198.84i	0.738686	−	1.27944i	−0.214401	−	0.976746i	$-0.568780\pi$
$937$	692.149	−	1198.84i	0.738686	−	1.27944i	0.953087	−	0.302696i	$-0.0978866\pi$
$938$		0			0
$939$	74.0053	+	185.782i	0.0788129	+	0.197851i
$940$		0			0
$941$	−864.894	+	499.347i	−0.919122	+	0.530655i	−0.883355	−	0.468705i	$-0.844721\pi$
$941$	−864.894	+	499.347i	−0.919122	+	0.530655i	−0.0357672	+	0.999360i	$0.511387\pi$
$942$		0			0
$943$	731.023	−	422.056i	0.775210	−	0.447568i
$944$		0			0
$945$	183.571	+	2033.31i	0.194255	+	2.15165i
$946$		0			0
$947$	270.354	−	468.266i	0.285484	−	0.494474i	−0.687242	−	0.726428i	$-0.741179\pi$
$947$	270.354	−	468.266i	0.285484	−	0.494474i	0.972727	+	0.231955i	$0.0745122\pi$
$948$		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	−0.926829	−	0.375484i	$-0.877477\pi$
$953$	−1015.01	+	586.015i	−1.06507	+	0.614916i	−0.138236	+	0.990399i	$0.544143\pi$
$954$		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
$959$	747.875	+	1295.36i	0.779848	+	1.35074i
$960$		0			0
$961$	−148.318	−	256.895i	−0.154337	−	0.267320i
$962$		0			0
$963$	300.522	+	317.358i	0.312069	+	0.329551i
$964$		0			0
$965$			1047.41i			1.08540i
$966$		0			0
$967$	35.2777			0.0364816			0.0182408	−	0.999834i	$-0.494193\pi$
$967$	35.2777			0.0364816			0.0182408	+	0.999834i	$0.494193\pi$
$968$		0			0
$969$	−1572.14	+	423.731i	−1.62243	+	0.437287i
$970$		0			0
$971$	526.816	−	304.158i	0.542550	−	0.313242i	−0.203562	−	0.979062i	$-0.565252\pi$
$971$	526.816	−	304.158i	0.542550	−	0.313242i	0.746112	+	0.665821i	$0.231918\pi$
$972$		0			0
$973$	616.598	−	1067.98i	0.633708	−	1.09761i
$974$		0			0
$975$	64.1914	+	50.6597i	0.0658373	+	0.0519586i
$976$		0			0
$977$	−1028.91	−	594.044i	−1.05314	−	0.608028i	−0.129610	−	0.991565i	$-0.541373\pi$
$977$	−1028.91	−	594.044i	−1.05314	−	0.608028i	−0.923526	+	0.383537i	$0.874706\pi$
$978$		0			0
$979$		−	2488.91i		−	2.54230i
$980$		0			0
$981$	−474.634	+	1596.12i	−0.483827	+	1.62703i
$982$		0			0
$983$	311.075	+	179.599i	0.316455	+	0.182705i	0.649811	−	0.760096i	$-0.274848\pi$
$983$	311.075	+	179.599i	0.316455	+	0.182705i	−0.333356	+	0.942801i	$0.608181\pi$
$984$		0			0
$985$	634.783			0.644450
$986$		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	−0.260752	−	0.965406i	$-0.583971\pi$
$991$	440.933	−	254.573i	0.444938	−	0.256885i	0.705690	+	0.708521i	$0.250637\pi$
$992$		0			0
$993$	346.283	+	273.286i	0.348724	+	0.275212i
$994$		0			0
$995$	−545.576	+	944.966i	−0.548318	+	0.949714i
$996$		0			0
$997$	−1232.09			−1.23579			−0.617897	−	0.786259i	$-0.712015\pi$
$997$	−1232.09			−1.23579			−0.617897	+	0.786259i	$0.712015\pi$
$998$		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.bl.a.373.16	yes	80
3.2	odd	2		2052.3.bl.a.145.35		80
9.2	odd	6		2052.3.s.a.829.6		80
9.7	even	3		684.3.s.a.601.29	yes	80
19.8	odd	6		684.3.s.a.445.29	✓	80
57.8	even	6		2052.3.s.a.901.6		80
171.65	even	6		2052.3.bl.a.1585.35		80
171.160	odd	6	inner	684.3.bl.a.673.16	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.s.a.445.29	✓	80	19.8	odd	6
684.3.s.a.601.29	yes	80	9.7	even	3
684.3.bl.a.373.16	yes	80	1.1	even	1	trivial
684.3.bl.a.673.16	yes	80	171.160	odd	6	inner
2052.3.s.a.829.6		80	9.2	odd	6
2052.3.s.a.901.6		80	57.8	even	6
2052.3.bl.a.145.35		80	3.2	odd	2
2052.3.bl.a.1585.35		80	171.65	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11019 - 2.78702i) q^{3} -7.12097 q^{5} +(-5.30926 - 9.19591i) q^{7} +(-6.53494 + 6.18826i) q^{9} +O(q^{10})\)	\(q+(-1.11019 - 2.78702i) q^{3} -7.12097 q^{5} +(-5.30926 - 9.19591i) q^{7} +(-6.53494 + 6.18826i) q^{9} +(-9.75715 - 16.8999i) q^{11} +(-0.918228 + 0.530139i) q^{13} +(7.90566 + 19.8463i) q^{15} +(-14.2828 - 24.7386i) q^{17} +(15.2465 + 11.3377i) q^{19} +(-19.7349 + 25.0062i) q^{21} +(15.5525 + 26.9377i) q^{23} +25.7082 q^{25} +(24.5018 + 11.3428i) q^{27} -43.7550i q^{29} +(-22.3220 - 12.8876i) q^{31} +(-36.2679 + 45.9555i) q^{33} +(37.8071 + 65.4838i) q^{35} +33.5831i q^{37} +(2.49692 + 1.97056i) q^{39} -27.1375i q^{41} +(-16.1646 + 27.9978i) q^{43} +(46.5351 - 44.0664i) q^{45} +35.1127 q^{47} +(-31.8765 + 55.2117i) q^{49} +(-53.0901 + 67.2710i) q^{51} +(-2.36455 - 1.36517i) q^{53} +(69.4804 + 120.344i) q^{55} +(14.6717 - 55.0794i) q^{57} -38.2175i q^{59} -35.7272 q^{61} +(91.6024 + 27.2396i) q^{63} +(6.53867 - 3.77511i) q^{65} +(90.8775 - 52.4681i) q^{67} +(57.8096 - 73.2512i) q^{69} +(-75.4263 + 43.5474i) q^{71} +(6.07578 + 10.5236i) q^{73} +(-28.5411 - 71.6493i) q^{75} +(-103.606 + 179.452i) q^{77} +(20.9591 + 12.1008i) q^{79} +(4.41090 - 80.8798i) q^{81} +(-38.3156 - 66.3645i) q^{83} +(101.708 + 176.163i) q^{85} +(-121.946 + 48.5765i) q^{87} +(110.455 + 63.7714i) q^{89} +(9.75022 + 5.62929i) q^{91} +(-11.1363 + 76.5196i) q^{93} +(-108.570 - 80.7353i) q^{95} +(-72.1921 - 41.6801i) q^{97} +(168.343 + 50.0599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9}+O(q^{10}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9	\( 80 q - 6 q^{3} - q^{7} - 2 q^{9} - 6 q^{11} - 15 q^{13} + 24 q^{15} - 21 q^{17} - 20 q^{19} + 24 q^{23} + 400 q^{25} + 63 q^{27} + 24 q^{31} + 30 q^{33} - 54 q^{35} - 81 q^{39} + 76 q^{43} + 188 q^{45} + 24 q^{47} - 267 q^{49} - 243 q^{51} - 36 q^{53} + 72 q^{57} + 14 q^{61} + 284 q^{63} + 288 q^{65} - 21 q^{67} - 48 q^{69} - 81 q^{71} + 55 q^{73} - 165 q^{75} + 30 q^{77} - 51 q^{79} - 110 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 204 q^{93} - 432 q^{95} + 90 q^{97} + 260 q^{99}+O(q^{100}) \) 80 * q - 6 * q^3 - q^7 - 2 * q^9 - 6 * q^11 - 15 * q^13 + 24 * q^15 - 21 * q^17 - 20 * q^19 + 24 * q^23 + 400 * q^25 + 63 * q^27 + 24 * q^31 + 30 * q^33 - 54 * q^35 - 81 * q^39 + 76 * q^43 + 188 * q^45 + 24 * q^47 - 267 * q^49 - 243 * q^51 - 36 * q^53 + 72 * q^57 + 14 * q^61 + 284 * q^63 + 288 * q^65 - 21 * q^67 - 48 * q^69 - 81 * q^71 + 55 * q^73 - 165 * q^75 + 30 * q^77 - 51 * q^79 - 110 * q^81 - 93 * q^83 + 306 * q^87 + 216 * q^89 + 96 * q^91 + 204 * q^93 - 432 * q^95 + 90 * q^97 + 260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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