LMFDB - Embedded newform 672.3.bf.b.145.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,3,Mod(145,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 5]))

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

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

chi := DirichletCharacter("672.145");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	672.bf (of order $6$, degree $2$, not 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:	$18.3106737650$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.26
Character	$\chi$	$=$	672.145
Dual form			672.3.bf.b.241.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{3} +(-2.65366 + 4.59628i) q^{5} +(-6.60250 + 2.32529i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{3} +(-2.65366 + 4.59628i) q^{5} +(-6.60250 + 2.32529i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(6.46900 - 3.73488i) q^{11} -10.3115 q^{13} -9.19256 q^{15} +(-19.6827 + 11.3638i) q^{17} +(11.8937 - 20.6004i) q^{19} +(-9.20587 - 7.88999i) q^{21} +(8.19416 - 14.1927i) q^{23} +(-1.58385 - 2.74331i) q^{25} -5.19615 q^{27} -5.55129i q^{29} +(-3.57088 + 2.06165i) q^{31} +(11.2046 + 6.46900i) q^{33} +(6.83314 - 36.5175i) q^{35} +(-35.8054 - 20.6723i) q^{37} +(-8.93006 - 15.4673i) q^{39} +0.0763421i q^{41} -44.6499i q^{43} +(-7.96099 - 13.7888i) q^{45} +(-29.5657 - 17.0697i) q^{47} +(38.1861 - 30.7054i) q^{49} +(-34.0914 - 19.6827i) q^{51} +(49.5422 - 28.6032i) q^{53} +39.6444i q^{55} +41.2009 q^{57} +(-29.0102 - 50.2472i) q^{59} +(-9.19719 + 15.9300i) q^{61} +(3.86248 - 20.6417i) q^{63} +(27.3634 - 47.3947i) q^{65} +(-81.5057 + 47.0573i) q^{67} +28.3854 q^{69} +117.473 q^{71} +(-121.976 + 70.4226i) q^{73} +(2.74331 - 4.75155i) q^{75} +(-34.0269 + 39.7018i) q^{77} +(-66.9499 + 115.961i) q^{79} +(-4.50000 - 7.79423i) q^{81} +78.6508 q^{83} -120.623i q^{85} +(8.32694 - 4.80756i) q^{87} +(-58.9069 - 34.0099i) q^{89} +(68.0820 - 23.9773i) q^{91} +(-6.18495 - 3.57088i) q^{93} +(63.1236 + 109.333i) q^{95} +105.731i q^{97} +22.4093i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 26 q^{7} - 90 q^{9}+O(q^{10}) $ 60 * q - 26 * q^7 - 90 * q^9	$ 60 q - 26 q^{7} - 90 q^{9} - 12 q^{15} - 36 q^{17} + 28 q^{23} - 204 q^{25} - 18 q^{31} - 30 q^{33} + 36 q^{39} - 828 q^{47} - 126 q^{49} - 312 q^{57} + 12 q^{63} + 36 q^{65} - 760 q^{71} - 648 q^{73} - 114 q^{79} - 270 q^{81} + 174 q^{87} - 72 q^{89} + 492 q^{95}+O(q^{100}) $ 60 * q - 26 * q^7 - 90 * q^9 - 12 * q^15 - 36 * q^17 + 28 * q^23 - 204 * q^25 - 18 * q^31 - 30 * q^33 + 36 * q^39 - 828 * q^47 - 126 * q^49 - 312 * q^57 + 12 * q^63 + 36 * q^65 - 760 * q^71 - 648 * q^73 - 114 * q^79 - 270 * q^81 + 174 * q^87 - 72 * q^89 + 492 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$		0			0
$5$	−2.65366	+	4.59628i	−0.530733	+	0.919256i	0.468624	+	0.883398i	$0.344750\pi$
$5$	−2.65366	+	4.59628i	−0.530733	+	0.919256i	−0.999357	+	0.0358582i	$0.988584\pi$
$6$		0			0
$7$	−6.60250	+	2.32529i	−0.943215	+	0.332184i
$7$	−6.60250	+	2.32529i	−0.943215	+	0.332184i
$8$		0			0
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	6.46900	−	3.73488i	0.588091	−	0.339534i	−0.176251	−	0.984345i	$-0.556397\pi$
$11$	6.46900	−	3.73488i	0.588091	−	0.339534i	0.764342	+	0.644811i	$0.223064\pi$
$12$		0			0
$13$	−10.3115			−0.793195			−0.396598	−	0.917993i	$-0.629809\pi$
$13$	−10.3115			−0.793195			−0.396598	+	0.917993i	$0.629809\pi$
$14$		0			0
$15$	−9.19256			−0.612837
$16$		0			0
$17$	−19.6827	+	11.3638i	−1.15780	+	0.668458i	−0.950777	−	0.309877i	$-0.899712\pi$
$17$	−19.6827	+	11.3638i	−1.15780	+	0.668458i	−0.207027	+	0.978335i	$0.566379\pi$
$18$		0			0
$19$	11.8937	−	20.6004i	0.625983	−	1.08423i	−0.362367	−	0.932035i	$-0.618031\pi$
$19$	11.8937	−	20.6004i	0.625983	−	1.08423i	0.988350	−	0.152199i	$-0.0486353\pi$
$20$		0			0
$21$	−9.20587	−	7.88999i	−0.438375	−	0.375714i
$22$		0			0
$23$	8.19416	−	14.1927i	0.356268	−	0.617074i	−0.631066	−	0.775729i	$-0.717382\pi$
$23$	8.19416	−	14.1927i	0.356268	−	0.617074i	0.987334	+	0.158655i	$0.0507158\pi$
$24$		0			0
$25$	−1.58385	−	2.74331i	−0.0633540	−	0.109732i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$		−	5.55129i		−	0.191424i	−0.995409	−	0.0957119i	$-0.969487\pi$
$29$		−	5.55129i		−	0.191424i	0.995409	−	0.0957119i	$-0.0305128\pi$
$30$		0			0
$31$	−3.57088	+	2.06165i	−0.115190	+	0.0665048i	−0.556488	−	0.830856i	$-0.687851\pi$
$31$	−3.57088	+	2.06165i	−0.115190	+	0.0665048i	0.441298	+	0.897361i	$0.354518\pi$
$32$		0			0
$33$	11.2046	+	6.46900i	0.339534	+	0.196030i
$34$		0			0
$35$	6.83314	−	36.5175i	0.195233	−	1.04336i
$36$		0			0
$37$	−35.8054	−	20.6723i	−0.967713	−	0.558709i	−0.0691749	−	0.997605i	$-0.522037\pi$
$37$	−35.8054	−	20.6723i	−0.967713	−	0.558709i	−0.898538	+	0.438895i	$0.855370\pi$
$38$		0			0
$39$	−8.93006	−	15.4673i	−0.228976	−	0.396598i
$40$		0			0
$41$			0.0763421i			0.00186200i	1.00000		0.000931001i	$0.000296347\pi$
$41$			0.0763421i			0.00186200i	−1.00000		0.000931001i	$0.999704\pi$
$42$		0			0
$43$		−	44.6499i		−	1.03837i	−0.854662	−	0.519184i	$-0.826236\pi$
$43$		−	44.6499i		−	1.03837i	0.854662	−	0.519184i	$-0.173764\pi$
$44$		0			0
$45$	−7.96099	−	13.7888i	−0.176911	−	0.306419i
$46$		0			0
$47$	−29.5657	−	17.0697i	−0.629057	−	0.363186i	0.151330	−	0.988483i	$-0.451644\pi$
$47$	−29.5657	−	17.0697i	−0.629057	−	0.363186i	−0.780387	+	0.625297i	$0.784978\pi$
$48$		0			0
$49$	38.1861	−	30.7054i	0.779308	−	0.626642i
$50$		0			0
$51$	−34.0914	−	19.6827i	−0.668458	−	0.385934i
$52$		0			0
$53$	49.5422	−	28.6032i	0.934758	−	0.539683i	0.0464446	−	0.998921i	$-0.485211\pi$
$53$	49.5422	−	28.6032i	0.934758	−	0.539683i	0.888313	+	0.459238i	$0.151878\pi$
$54$		0			0
$55$			39.6444i			0.720808i
$56$		0			0
$57$	41.2009			0.722823
$58$		0			0
$59$	−29.0102	−	50.2472i	−0.491699	−	0.851648i	0.508255	−	0.861206i	$-0.330291\pi$
$59$	−29.0102	−	50.2472i	−0.491699	−	0.851648i	−0.999954	+	0.00955884i	$0.996957\pi$
$60$		0			0
$61$	−9.19719	+	15.9300i	−0.150774	+	0.261148i	−0.931512	−	0.363710i	$-0.881510\pi$
$61$	−9.19719	+	15.9300i	−0.150774	+	0.261148i	0.780738	+	0.624858i	$0.214843\pi$
$62$		0			0
$63$	3.86248	−	20.6417i	0.0613092	−	0.327647i
$64$		0			0
$65$	27.3634	−	47.3947i	0.420975	−	0.729149i
$66$		0			0
$67$	−81.5057	+	47.0573i	−1.21650	+	0.702348i	−0.964168	−	0.265292i	$-0.914532\pi$
$67$	−81.5057	+	47.0573i	−1.21650	+	0.702348i	−0.252334	+	0.967640i	$0.581198\pi$
$68$		0			0
$69$	28.3854			0.411383
$70$		0			0
$71$	117.473			1.65455			0.827277	−	0.561794i	$-0.189889\pi$
$71$	117.473			1.65455			0.827277	+	0.561794i	$0.189889\pi$
$72$		0			0
$73$	−121.976	+	70.4226i	−1.67090	+	0.964693i	−0.703761	+	0.710436i	$0.748498\pi$
$73$	−121.976	+	70.4226i	−1.67090	+	0.964693i	−0.967137	+	0.254257i	$0.918169\pi$
$74$		0			0
$75$	2.74331	−	4.75155i	0.0365775	−	0.0633540i
$76$		0			0
$77$	−34.0269	+	39.7018i	−0.441908	+	0.515608i
$78$		0			0
$79$	−66.9499	+	115.961i	−0.847467	+	1.46786i	0.0359948	+	0.999352i	$0.488540\pi$
$79$	−66.9499	+	115.961i	−0.847467	+	1.46786i	−0.883462	+	0.468504i	$0.844793\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	78.6508			0.947600			0.473800	−	0.880633i	$-0.342882\pi$
$83$	78.6508			0.947600			0.473800	+	0.880633i	$0.342882\pi$
$84$		0			0
$85$		−	120.623i		−	1.41909i
$86$		0			0
$87$	8.32694	−	4.80756i	0.0957119	−	0.0552593i
$88$		0			0
$89$	−58.9069	−	34.0099i	−0.661875	−	0.382134i	0.131116	−	0.991367i	$-0.458144\pi$
$89$	−58.9069	−	34.0099i	−0.661875	−	0.382134i	−0.792991	+	0.609233i	$0.791477\pi$
$90$		0			0
$91$	68.0820	−	23.9773i	0.748154	−	0.263487i
$92$		0			0
$93$	−6.18495	−	3.57088i	−0.0665048	−	0.0383966i
$94$		0			0
$95$	63.1236	+	109.333i	0.664459	+	1.15088i
$96$		0			0
$97$			105.731i			1.09001i	0.838433	+	0.545005i	$0.183472\pi$
$97$			105.731i			1.09001i	−0.838433	+	0.545005i	$0.816528\pi$
$98$		0			0
$99$			22.4093i			0.226356i
$100$		0			0
$101$	−90.0916	−	156.043i	−0.891996	−	1.54498i	−0.837479	−	0.546469i	$-0.815972\pi$
$101$	−90.0916	−	156.043i	−0.891996	−	1.54498i	−0.0545167	−	0.998513i	$-0.517362\pi$
$102$		0			0
$103$	−129.445	−	74.7350i	−1.25675	−	0.725582i	−0.284305	−	0.958734i	$-0.591763\pi$
$103$	−129.445	−	74.7350i	−1.25675	−	0.725582i	−0.972440	+	0.233151i	$0.925096\pi$
$104$		0			0
$105$	60.6939	−	21.3753i	0.578037	−	0.203575i
$106$		0			0
$107$	−141.317	−	81.5892i	−1.32072	−	0.762516i	−0.336873	−	0.941550i	$-0.609369\pi$
$107$	−141.317	−	81.5892i	−1.32072	−	0.762516i	−0.983843	+	0.179034i	$0.942703\pi$
$108$		0			0
$109$	172.315	−	99.4863i	1.58087	−	0.912718i	0.586142	−	0.810208i	$-0.300646\pi$
$109$	172.315	−	99.4863i	1.58087	−	0.912718i	0.994732	−	0.102510i	$-0.0326873\pi$
$110$		0			0
$111$		−	71.6108i		−	0.645142i
$112$		0			0
$113$	−37.0858			−0.328193			−0.164096	−	0.986444i	$-0.552471\pi$
$113$	−37.0858			−0.328193			−0.164096	+	0.986444i	$0.552471\pi$
$114$		0			0
$115$	43.4891	+	75.3253i	0.378166	+	0.655002i
$116$		0			0
$117$	15.4673	−	26.7902i	0.132199	−	0.228976i
$118$		0			0
$119$	103.531	−	120.797i	0.870006	−	1.01510i
$120$		0			0
$121$	−32.6014	+	56.4672i	−0.269433	+	0.466671i
$122$		0			0
$123$	−0.114513	+	0.0661142i	−0.000931001	+	0.000537514i
$124$		0			0
$125$	−115.871			−0.926969
$126$		0			0
$127$	−80.7558			−0.635872			−0.317936	−	0.948112i	$-0.602990\pi$
$127$	−80.7558			−0.635872			−0.317936	+	0.948112i	$0.602990\pi$
$128$		0			0
$129$	66.9748	−	38.6679i	0.519184	−	0.299751i
$130$		0			0
$131$	−111.495	+	193.116i	−0.851110	+	1.47417i	0.0290967	+	0.999577i	$0.490737\pi$
$131$	−111.495	+	193.116i	−0.851110	+	1.47417i	−0.880207	+	0.474590i	$0.842596\pi$
$132$		0			0
$133$	−30.6260	+	163.671i	−0.230271	+	1.23061i
$134$		0			0
$135$	13.7888	−	23.8830i	0.102140	−	0.176911i
$136$		0			0
$137$	−61.0269	−	105.702i	−0.445452	−	0.771546i	0.552631	−	0.833426i	$-0.313624\pi$
$137$	−61.0269	−	105.702i	−0.445452	−	0.771546i	−0.998084	+	0.0618800i	$0.980290\pi$
$138$		0			0
$139$	23.2134			0.167003			0.0835014	−	0.996508i	$-0.473390\pi$
$139$	23.2134			0.167003			0.0835014	+	0.996508i	$0.473390\pi$
$140$		0			0
$141$		−	59.1313i		−	0.419371i
$142$		0			0
$143$	−66.7054	+	38.5124i	−0.466471	+	0.269317i
$144$		0			0
$145$	25.5153	+	14.7313i	0.175967	+	0.101595i
$146$		0			0
$147$	79.1283	+	30.6874i	0.538288	+	0.208758i
$148$		0			0
$149$	154.708	+	89.3205i	1.03831	+	0.599466i	0.919353	−	0.393434i	$-0.128713\pi$
$149$	154.708	+	89.3205i	1.03831	+	0.599466i	0.118953	+	0.992900i	$0.462046\pi$
$150$		0			0
$151$	30.6735	+	53.1281i	0.203136	+	0.351842i	0.949537	−	0.313654i	$-0.101553\pi$
$151$	30.6735	+	53.1281i	0.203136	+	0.351842i	−0.746401	+	0.665496i	$0.768220\pi$
$152$		0			0
$153$		−	68.1827i		−	0.445639i
$154$		0			0
$155$		−	21.8837i		−	0.141185i
$156$		0			0
$157$	98.7757	+	171.084i	0.629144	+	1.08971i	0.987724	+	0.156211i	$0.0499279\pi$
$157$	98.7757	+	171.084i	0.629144	+	1.08971i	−0.358579	+	0.933499i	$0.616739\pi$
$158$		0			0
$159$	85.8095	+	49.5422i	0.539683	+	0.311586i
$160$		0			0
$161$	−21.0998	+	112.761i	−0.131055	+	0.700380i
$162$		0			0
$163$	−60.3806	−	34.8608i	−0.370433	−	0.213870i	0.303214	−	0.952922i	$-0.401940\pi$
$163$	−60.3806	−	34.8608i	−0.370433	−	0.213870i	−0.673648	+	0.739053i	$0.735273\pi$
$164$		0			0
$165$	−59.4667	+	34.3331i	−0.360404	+	0.208079i
$166$		0			0
$167$		−	101.544i		−	0.608047i	−0.952665	−	0.304024i	$-0.901670\pi$
$167$		−	101.544i		−	0.608047i	0.952665	−	0.304024i	$-0.0983302\pi$
$168$		0			0
$169$	−62.6721			−0.370841
$170$		0			0
$171$	35.6810	+	61.8013i	0.208661	+	0.361411i
$172$		0			0
$173$	−84.4792	+	146.322i	−0.488319	+	0.845794i	−0.999910	−	0.0134356i	$-0.995723\pi$
$173$	−84.4792	+	146.322i	−0.488319	+	0.845794i	0.511590	+	0.859229i	$0.329057\pi$
$174$		0			0
$175$	16.8364	+	14.4298i	0.0962078	+	0.0824560i
$176$		0			0
$177$	50.2472	−	87.0307i	0.283883	−	0.491699i
$178$		0			0
$179$	161.140	−	93.0342i	0.900223	−	0.519744i	0.0229503	−	0.999737i	$-0.492694\pi$
$179$	161.140	−	93.0342i	0.900223	−	0.519744i	0.877272	+	0.479993i	$0.159361\pi$
$180$		0			0
$181$	−1.17113			−0.00647030			−0.00323515	−	0.999995i	$-0.501030\pi$
$181$	−1.17113			−0.00647030			−0.00323515	+	0.999995i	$0.501030\pi$
$182$		0			0
$183$	−31.8600			−0.174098
$184$		0			0
$185$	190.031	−	109.714i	1.02719	−	0.593051i
$186$		0			0
$187$	−84.8847	+	147.025i	−0.453929	+	0.786228i
$188$		0			0
$189$	34.3076	−	12.0826i	0.181522	−	0.0639288i
$190$		0			0
$191$	45.8469	−	79.4091i	0.240036	−	0.415754i	−0.720688	−	0.693259i	$-0.756174\pi$
$191$	45.8469	−	79.4091i	0.240036	−	0.415754i	0.960724	+	0.277505i	$0.0895074\pi$
$192$		0			0
$193$	83.3185	+	144.312i	0.431702	+	0.747730i	0.997020	−	0.0771432i	$-0.0245799\pi$
$193$	83.3185	+	144.312i	0.431702	+	0.747730i	−0.565318	+	0.824873i	$0.691247\pi$
$194$		0			0
$195$	94.7894			0.486100
$196$		0			0
$197$			160.858i			0.816538i	0.912862	+	0.408269i	$0.133867\pi$
$197$			160.858i			0.816538i	−0.912862	+	0.408269i	$0.866133\pi$
$198$		0			0
$199$	−125.471	+	72.4408i	−0.630508	+	0.364024i	−0.780949	−	0.624595i	$-0.785264\pi$
$199$	−125.471	+	72.4408i	−0.630508	+	0.364024i	0.150440	+	0.988619i	$0.451931\pi$
$200$		0			0
$201$	−141.172	−	81.5057i	−0.702348	−	0.405501i
$202$		0			0
$203$	12.9084	+	36.6524i	0.0635880	+	0.180554i
$204$		0			0
$205$	−0.350889	−	0.202586i	−0.00171166	−	0.000988225i
$206$		0			0
$207$	24.5825	+	42.5781i	0.118756	+	0.205691i
$208$		0			0
$209$		−	177.686i		−	0.850171i
$210$		0			0
$211$			278.493i			1.31987i	0.751321	+	0.659936i	$0.229417\pi$
$211$			278.493i			1.31987i	−0.751321	+	0.659936i	$0.770583\pi$
$212$		0			0
$213$	101.735	+	176.210i	0.477629	+	0.827277i
$214$		0			0
$215$	205.223	+	118.486i	0.954527	+	0.551096i
$216$		0			0
$217$	18.7828	−	21.9154i	0.0865568	−	0.100992i
$218$		0			0
$219$	−211.268	−	121.976i	−0.964693	−	0.556966i
$220$		0			0
$221$	202.958	−	117.178i	0.918364	−	0.530218i
$222$		0			0
$223$		−	74.5342i		−	0.334234i	−0.985937	−	0.167117i	$-0.946554\pi$
$223$		−	74.5342i		−	0.334234i	0.985937	−	0.167117i	$-0.0534458\pi$
$224$		0			0
$225$	9.50311			0.0422360
$226$		0			0
$227$	48.1208	+	83.3476i	0.211986	+	0.367170i	0.952336	−	0.305051i	$-0.0986736\pi$
$227$	48.1208	+	83.3476i	0.211986	+	0.367170i	−0.740350	+	0.672221i	$0.765340\pi$
$228$		0			0
$229$	−110.626	+	191.610i	−0.483082	+	0.836723i	−0.999811	−	0.0194261i	$-0.993816\pi$
$229$	−110.626	+	191.610i	−0.483082	+	0.836723i	0.516729	+	0.856149i	$0.327149\pi$
$230$		0			0
$231$	−89.0209	−	16.6576i	−0.385372	−	0.0721107i
$232$		0			0
$233$	−9.59369	+	16.6168i	−0.0411747	+	0.0713166i	−0.885878	−	0.463918i	$-0.846443\pi$
$233$	−9.59369	+	16.6168i	−0.0411747	+	0.0713166i	0.844704	+	0.535234i	$0.179777\pi$
$234$		0			0
$235$	156.915	−	90.5947i	0.667722	−	0.385509i
$236$		0			0
$237$	−231.921			−0.978570
$238$		0			0
$239$	−202.445			−0.847052			−0.423526	−	0.905884i	$-0.639208\pi$
$239$	−202.445			−0.847052			−0.423526	+	0.905884i	$0.639208\pi$
$240$		0			0
$241$	−269.467	+	155.577i	−1.11812	+	0.645548i	−0.940921	−	0.338627i	$-0.890038\pi$
$241$	−269.467	+	155.577i	−1.11812	+	0.645548i	−0.177201	+	0.984175i	$0.556704\pi$
$242$		0			0
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$		0			0
$245$	39.7978	+	256.996i	0.162440	+	1.04896i
$246$		0			0
$247$	−122.642	+	212.422i	−0.496527	+	0.860010i
$248$		0			0
$249$	68.1136	+	117.976i	0.273548	+	0.473800i
$250$		0			0
$251$	288.092			1.14778			0.573888	−	0.818934i	$-0.305434\pi$
$251$	288.092			1.14778			0.573888	+	0.818934i	$0.305434\pi$
$252$		0			0
$253$		−	122.417i		−	0.483861i
$254$		0			0
$255$	180.934	−	104.462i	0.709545	−	0.409656i
$256$		0			0
$257$	380.595	+	219.736i	1.48091	+	0.855006i	0.999766	−	0.0216340i	$-0.00688685\pi$
$257$	380.595	+	219.736i	1.48091	+	0.855006i	0.481147	+	0.876640i	$0.340220\pi$
$258$		0			0
$259$	284.474	+	53.2307i	1.09836	+	0.205524i
$260$		0			0
$261$	14.4227	+	8.32694i	0.0552593	+	0.0319040i
$262$		0			0
$263$	−107.217	−	185.705i	−0.407669	−	0.706103i	0.586959	−	0.809617i	$-0.300325\pi$
$263$	−107.217	−	185.705i	−0.407669	−	0.706103i	−0.994628	+	0.103513i	$0.966992\pi$
$264$		0			0
$265$			303.613i			1.14571i
$266$		0			0
$267$		−	117.814i		−	0.441250i
$268$		0			0
$269$	1.72792	+	2.99284i	0.00642349	+	0.0111258i	0.869219	−	0.494427i	$-0.164622\pi$
$269$	1.72792	+	2.99284i	0.00642349	+	0.0111258i	−0.862796	+	0.505553i	$0.831289\pi$
$270$		0			0
$271$	88.2125	+	50.9295i	0.325507	+	0.187932i	0.653845	−	0.756629i	$-0.273155\pi$
$271$	88.2125	+	50.9295i	0.325507	+	0.187932i	−0.328337	+	0.944561i	$0.606488\pi$
$272$		0			0
$273$	94.9267	+	81.3580i	0.347717	+	0.298015i
$274$		0			0
$275$	−20.4919	−	11.8310i	−0.0745159	−	0.0430218i
$276$		0			0
$277$	−120.696	+	69.6841i	−0.435727	+	0.251567i	−0.701783	−	0.712390i	$-0.747613\pi$
$277$	−120.696	+	69.6841i	−0.435727	+	0.251567i	0.266056	+	0.963957i	$0.414279\pi$
$278$		0			0
$279$		−	12.3699i		−	0.0443365i
$280$		0			0
$281$	79.0056			0.281159			0.140579	−	0.990069i	$-0.455104\pi$
$281$	79.0056			0.281159			0.140579	+	0.990069i	$0.455104\pi$
$282$		0			0
$283$	−171.220	−	296.562i	−0.605019	−	1.04792i	−0.992049	−	0.125856i	$-0.959832\pi$
$283$	−171.220	−	296.562i	−0.605019	−	1.04792i	0.387030	−	0.922067i	$-0.373501\pi$
$284$		0			0
$285$	−109.333	+	189.371i	−0.383626	+	0.664459i
$286$		0			0
$287$	−0.177517	−	0.504049i	−0.000618527	−	0.00175627i
$288$		0			0
$289$	113.771	−	197.058i	0.393672	−	0.681860i
$290$		0			0
$291$	−158.597	+	91.5658i	−0.545005	+	0.314659i
$292$		0			0
$293$	46.3334			0.158134			0.0790672	−	0.996869i	$-0.474806\pi$
$293$	46.3334			0.158134			0.0790672	+	0.996869i	$0.474806\pi$
$294$		0			0
$295$	307.934			1.04384
$296$		0			0
$297$	−33.6139	+	19.4070i	−0.113178	+	0.0653434i
$298$		0			0
$299$	−84.4944	+	146.349i	−0.282590	+	0.489460i
$300$		0			0
$301$	103.824	+	294.801i	0.344930	+	0.979405i
$302$		0			0
$303$	156.043	−	270.275i	0.514994	−	0.891996i
$304$		0			0
$305$	−48.8125	−	84.5457i	−0.160041	−	0.277199i
$306$		0			0
$307$	430.216			1.40135			0.700677	−	0.713479i	$-0.252881\pi$
$307$	430.216			1.40135			0.700677	+	0.713479i	$0.252881\pi$
$308$		0			0
$309$		−	258.890i		−	0.837830i
$310$		0			0
$311$	−271.933	+	157.001i	−0.874382	+	0.504825i	−0.868802	−	0.495160i	$-0.835110\pi$
$311$	−271.933	+	157.001i	−0.874382	+	0.504825i	−0.00558015	+	0.999984i	$0.501776\pi$
$312$		0			0
$313$	−182.298	−	105.250i	−0.582423	−	0.336262i	0.179673	−	0.983726i	$-0.442496\pi$
$313$	−182.298	−	105.250i	−0.582423	−	0.336262i	−0.762096	+	0.647464i	$0.775829\pi$
$314$		0			0
$315$	84.6255	+	72.5292i	0.268652	+	0.230252i
$316$		0			0
$317$	−262.686	−	151.662i	−0.828662	−	0.478428i	0.0247322	−	0.999694i	$-0.492127\pi$
$317$	−262.686	−	151.662i	−0.828662	−	0.478428i	−0.853394	+	0.521266i	$0.825460\pi$
$318$		0			0
$319$	−20.7334	−	35.9113i	−0.0649950	−	0.112575i
$320$		0			0
$321$		−	282.633i		−	0.880477i
$322$		0			0
$323$			540.629i			1.67377i
$324$		0			0
$325$	16.3319	+	28.2878i	0.0502521	+	0.0870393i
$326$		0			0
$327$	298.459	+	172.315i	0.912718	+	0.526958i
$328$		0			0
$329$	234.900	+	43.9543i	0.713980	+	0.133600i
$330$		0			0
$331$	−373.913	−	215.879i	−1.12965	−	0.652201i	−0.185800	−	0.982588i	$-0.559488\pi$
$331$	−373.913	−	215.879i	−1.12965	−	0.652201i	−0.943846	+	0.330386i	$0.892821\pi$
$332$		0			0
$333$	107.416	−	62.0168i	0.322571	−	0.186236i
$334$		0			0
$335$		−	499.497i		−	1.49104i
$336$		0			0
$337$	−402.652			−1.19481			−0.597406	−	0.801939i	$-0.703802\pi$
$337$	−402.652			−1.19481			−0.597406	+	0.801939i	$0.703802\pi$
$338$		0			0
$339$	−32.1172	−	55.6286i	−0.0947410	−	0.164096i
$340$		0			0
$341$	−15.4000	+	26.6736i	−0.0451613	+	0.0782217i
$342$		0			0
$343$	−180.725	+	291.526i	−0.526894	+	0.849931i
$344$		0			0
$345$	−75.3253	+	130.467i	−0.218334	+	0.378166i
$346$		0			0
$347$	313.161	−	180.804i	0.902482	−	0.521048i	0.0244775	−	0.999700i	$-0.492208\pi$
$347$	313.161	−	180.804i	0.902482	−	0.521048i	0.878005	+	0.478652i	$0.158874\pi$
$348$		0			0
$349$	142.336			0.407840			0.203920	−	0.978988i	$-0.434632\pi$
$349$	142.336			0.407840			0.203920	+	0.978988i	$0.434632\pi$
$350$		0			0
$351$	53.5803			0.152651
$352$		0			0
$353$	434.109	−	250.633i	1.22977	−	0.710008i	0.262788	−	0.964854i	$-0.415358\pi$
$353$	434.109	−	250.633i	1.22977	−	0.710008i	0.966982	+	0.254846i	$0.0820248\pi$
$354$		0			0
$355$	−311.735	+	539.940i	−0.878126	+	1.52096i
$356$		0			0
$357$	270.856	+	50.6825i	0.758701	+	0.141968i
$358$		0			0
$359$	49.6737	−	86.0374i	0.138367	−	0.239659i	−0.788512	−	0.615020i	$-0.789148\pi$
$359$	49.6737	−	86.0374i	0.138367	−	0.239659i	0.926879	+	0.375361i	$0.122481\pi$
$360$		0			0
$361$	−102.419	−	177.395i	−0.283709	−	0.491398i
$362$		0			0
$363$	−112.934			−0.311114
$364$		0			0
$365$		−	747.512i		−	2.04798i
$366$		0			0
$367$	257.737	−	148.805i	0.702281	−	0.405462i	−0.105915	−	0.994375i	$-0.533777\pi$
$367$	257.737	−	148.805i	0.702281	−	0.405462i	0.808196	+	0.588913i	$0.200444\pi$
$368$		0			0
$369$	−0.198343	−	0.114513i	−0.000537514	−	0.000310334i
$370$		0			0
$371$	−260.592	+	304.052i	−0.702403	+	0.819548i
$372$		0			0
$373$	−484.005	−	279.440i	−1.29760	−	0.749169i	−0.317610	−	0.948221i	$-0.602880\pi$
$373$	−484.005	−	279.440i	−1.29760	−	0.749169i	−0.979989	+	0.199052i	$0.936214\pi$
$374$		0			0
$375$	−100.347	−	173.807i	−0.267593	−	0.463484i
$376$		0			0
$377$			57.2424i			0.151837i
$378$		0			0
$379$		−	456.413i		−	1.20426i	−0.798400	−	0.602128i	$-0.794320\pi$
$379$		−	456.413i		−	1.20426i	0.798400	−	0.602128i	$-0.205680\pi$
$380$		0			0
$381$	−69.9366	−	121.134i	−0.183561	−	0.317936i
$382$		0			0
$383$	−43.9517	−	25.3755i	−0.114756	−	0.0662547i	0.441523	−	0.897250i	$-0.354438\pi$
$383$	−43.9517	−	25.3755i	−0.114756	−	0.0662547i	−0.556280	+	0.830995i	$0.687772\pi$
$384$		0			0
$385$	−92.1847	−	261.752i	−0.239441	−	0.679877i
$386$		0			0
$387$	116.004	+	66.9748i	0.299751	+	0.173061i
$388$		0			0
$389$	388.310	−	224.191i	0.998225	−	0.576326i	0.0905026	−	0.995896i	$-0.471153\pi$
$389$	388.310	−	224.191i	0.998225	−	0.576326i	0.907723	+	0.419571i	$0.137819\pi$
$390$		0			0
$391$			372.467i			0.952600i
$392$		0			0
$393$	−386.232			−0.982778
$394$		0			0
$395$	−355.325	−	615.441i	−0.899556	−	1.55808i
$396$		0			0
$397$	1.01150	−	1.75197i	0.00254786	−	0.00441303i	−0.864749	−	0.502205i	$-0.832522\pi$
$397$	1.01150	−	1.75197i	0.00254786	−	0.00441303i	0.867297	+	0.497792i	$0.165856\pi$
$398$		0			0
$399$	−272.029	+	95.8040i	−0.681777	+	0.240110i
$400$		0			0
$401$	−258.589	+	447.890i	−0.644861	+	1.11693i	0.339473	+	0.940616i	$0.389751\pi$
$401$	−258.589	+	447.890i	−0.644861	+	1.11693i	−0.984334	+	0.176316i	$0.943582\pi$
$402$		0			0
$403$	36.8213	−	21.2588i	0.0913679	−	0.0527513i
$404$		0			0
$405$	47.7659			0.117941
$406$		0			0
$407$	−308.833			−0.758804
$408$		0			0
$409$	−35.6438	+	20.5790i	−0.0871488	+	0.0503154i	−0.542941	−	0.839771i	$-0.682689\pi$
$409$	−35.6438	+	20.5790i	−0.0871488	+	0.0503154i	0.455792	+	0.890086i	$0.349356\pi$
$410$		0			0
$411$	105.702	−	183.081i	0.257182	−	0.445452i
$412$		0			0
$413$	308.379	+	264.300i	0.746681	+	0.639952i
$414$		0			0
$415$	−208.713	+	361.501i	−0.502922	+	0.871086i
$416$		0			0
$417$	20.1034	+	34.8201i	0.0482095	+	0.0835014i
$418$		0			0
$419$	−294.803			−0.703587			−0.351794	−	0.936078i	$-0.614428\pi$
$419$	−294.803			−0.703587			−0.351794	+	0.936078i	$0.614428\pi$
$420$		0			0
$421$		−	256.548i		−	0.609377i	−0.952452	−	0.304689i	$-0.901448\pi$
$421$		−	256.548i		−	0.609377i	0.952452	−	0.304689i	$-0.0985524\pi$
$422$		0			0
$423$	88.6970	−	51.2092i	0.209686	−	0.121062i
$424$		0			0
$425$	62.3488	+	35.9971i	0.146703	+	0.0846990i
$426$		0			0
$427$	23.6826	−	126.564i	0.0554628	−	0.296403i
$428$		0			0
$429$	−115.537	−	66.7054i	−0.269317	−	0.155490i
$430$		0			0
$431$	217.606	+	376.905i	0.504887	+	0.874489i	0.999984	+	0.00565181i	$0.00179904\pi$
$431$	217.606	+	376.905i	0.504887	+	0.874489i	−0.495097	+	0.868837i	$0.664868\pi$
$432$		0			0
$433$		−	486.340i		−	1.12319i	−0.827413	−	0.561594i	$-0.810188\pi$
$433$		−	486.340i		−	1.12319i	0.827413	−	0.561594i	$-0.189812\pi$
$434$		0			0
$435$			51.0306i			0.117312i
$436$		0			0
$437$	−194.917	−	337.607i	−0.446035	−	0.772555i
$438$		0			0
$439$	−208.705	−	120.496i	−0.475410	−	0.274478i	0.243091	−	0.970003i	$-0.421838\pi$
$439$	−208.705	−	120.496i	−0.475410	−	0.274478i	−0.718502	+	0.695525i	$0.755172\pi$
$440$		0			0
$441$	22.4960	+	145.268i	0.0510113	+	0.329407i
$442$		0			0
$443$	−721.115	−	416.336i	−1.62780	−	0.939810i	−0.984748	−	0.173985i	$-0.944335\pi$
$443$	−721.115	−	416.336i	−1.62780	−	0.939810i	−0.643050	−	0.765824i	$-0.722331\pi$
$444$		0			0
$445$	312.638	−	180.502i	0.702557	−	0.405622i
$446$		0			0
$447$			309.415i			0.692204i
$448$		0			0
$449$	−548.100			−1.22071			−0.610356	−	0.792127i	$-0.708974\pi$
$449$	−548.100			−1.22071			−0.610356	+	0.792127i	$0.708974\pi$
$450$		0			0
$451$	0.285128	+	0.493857i	0.000632214	+	0.00109503i
$452$		0			0
$453$	−53.1281	+	92.0206i	−0.117281	+	0.203136i
$454$		0			0
$455$	−70.4602	+	376.551i	−0.154858	+	0.827585i
$456$		0			0
$457$	−101.855	+	176.417i	−0.222877	+	0.386034i	−0.955680	−	0.294406i	$-0.904878\pi$
$457$	−101.855	+	176.417i	−0.222877	+	0.386034i	0.732804	+	0.680440i	$0.238211\pi$
$458$		0			0
$459$	102.274	−	59.0480i	0.222819	−	0.128645i
$460$		0			0
$461$	162.435			0.352354			0.176177	−	0.984358i	$-0.443627\pi$
$461$	162.435			0.352354			0.176177	+	0.984358i	$0.443627\pi$
$462$		0			0
$463$	356.406			0.769776			0.384888	−	0.922963i	$-0.374240\pi$
$463$	356.406			0.769776			0.384888	+	0.922963i	$0.374240\pi$
$464$		0			0
$465$	32.8255	−	18.9518i	0.0705925	−	0.0407566i
$466$		0			0
$467$	−59.4093	+	102.900i	−0.127215	+	0.220343i	−0.922597	−	0.385766i	$-0.873937\pi$
$467$	−59.4093	+	102.900i	−0.127215	+	0.220343i	0.795382	+	0.606109i	$0.207270\pi$
$468$		0			0
$469$	428.719	−	500.220i	0.914114	−	1.06657i
$470$		0			0
$471$	−171.084	+	296.327i	−0.363237	+	0.629144i
$472$		0			0
$473$	−166.762	−	288.840i	−0.352562	−	0.610655i
$474$		0			0
$475$	−75.3512			−0.158634
$476$		0			0
$477$			171.619i			0.359788i
$478$		0			0
$479$	−369.044	+	213.068i	−0.770447	+	0.444818i	−0.833034	−	0.553222i	$-0.813398\pi$
$479$	−369.044	+	213.068i	−0.770447	+	0.444818i	0.0625869	+	0.998040i	$0.480065\pi$
$480$		0			0
$481$	369.209	+	213.163i	0.767586	+	0.443166i
$482$		0			0
$483$	−187.415	+	66.0042i	−0.388022	+	0.136655i
$484$		0			0
$485$	−485.969	−	280.574i	−1.00200	−	0.578504i
$486$		0			0
$487$	−452.779	−	784.237i	−0.929732	−	1.61034i	−0.783769	−	0.621053i	$-0.786705\pi$
$487$	−452.779	−	784.237i	−0.929732	−	1.61034i	−0.145963	−	0.989290i	$-0.546628\pi$
$488$		0			0
$489$		−	120.761i		−	0.246956i
$490$		0			0
$491$		−	202.508i		−	0.412439i	−0.978506	−	0.206220i	$-0.933884\pi$
$491$		−	202.508i		−	0.412439i	0.978506	−	0.206220i	$-0.0661162\pi$
$492$		0			0
$493$	63.0837	+	109.264i	0.127959	+	0.221631i
$494$		0			0
$495$	−102.999	−	59.4667i	−0.208079	−	0.120135i
$496$		0			0
$497$	−775.618	+	273.159i	−1.56060	+	0.549617i
$498$		0			0
$499$	0.242316	+	0.139901i	0.000485604	+	0.000280364i	0.500243	−	0.865885i	$-0.333244\pi$
$499$	0.242316	+	0.139901i	0.000485604	+	0.000280364i	−0.499757	+	0.866166i	$0.666577\pi$
$500$		0			0
$501$	152.316	−	87.9396i	0.304024	−	0.175528i
$502$		0			0
$503$		−	179.728i		−	0.357312i	−0.983912	−	0.178656i	$-0.942825\pi$
$503$		−	179.728i		−	0.357312i	0.983912	−	0.178656i	$-0.0571750\pi$
$504$		0			0
$505$	956.291			1.89364
$506$		0			0
$507$	−54.2756	−	94.0082i	−0.107053	−	0.185420i
$508$		0			0
$509$	−265.487	+	459.837i	−0.521586	+	0.903413i	0.478099	+	0.878306i	$0.341326\pi$
$509$	−265.487	+	459.837i	−0.521586	+	0.903413i	−0.999685	+	0.0251074i	$0.992007\pi$
$510$		0			0
$511$	641.591	−	748.594i	1.25556	−	1.46496i
$512$		0			0
$513$	−61.8013	+	107.043i	−0.120470	+	0.208661i
$514$		0			0
$515$	687.006	−	396.643i	1.33399	−	0.770180i
$516$		0			0
$517$	−255.014			−0.493257
$518$		0			0
$519$	−292.645			−0.563863
$520$		0			0
$521$	320.063	−	184.788i	0.614324	−	0.354680i	−0.160332	−	0.987063i	$-0.551256\pi$
$521$	320.063	−	184.788i	0.614324	−	0.354680i	0.774656	+	0.632383i	$0.217923\pi$
$522$		0			0
$523$	−105.066	+	181.980i	−0.200892	+	0.347954i	−0.948816	−	0.315830i	$-0.897717\pi$
$523$	−105.066	+	181.980i	−0.200892	+	0.347954i	0.747924	+	0.663784i	$0.231051\pi$
$524$		0			0
$525$	−7.06398	+	37.7511i	−0.0134552	+	0.0719069i
$526$		0			0
$527$	46.8563	−	81.1574i	0.0889113	−	0.153999i
$528$		0			0
$529$	130.212	+	225.533i	0.246147	+	0.426338i
$530$		0			0
$531$	174.061			0.327799
$532$		0			0
$533$		−	0.787205i		−	0.00147693i
$534$		0			0
$535$	750.013	−	433.020i	1.40189	−	0.809384i
$536$		0			0
$537$	279.102	+	161.140i	0.519744	+	0.300074i
$538$		0			0
$539$	132.345	−	341.254i	0.245537	−	0.633124i
$540$		0			0
$541$	−640.020	−	369.516i	−1.18303	−	0.683024i	−0.226318	−	0.974053i	$-0.572669\pi$
$541$	−640.020	−	369.516i	−1.18303	−	0.683024i	−0.956714	+	0.291029i	$0.906002\pi$
$542$		0			0
$543$	−1.01422	−	1.75669i	−0.00186782	−	0.00323515i
$544$		0			0
$545$			1056.01i			1.93764i
$546$		0			0
$547$		−	871.318i		−	1.59290i	−0.604702	−	0.796452i	$-0.706708\pi$
$547$		−	871.318i		−	1.59290i	0.604702	−	0.796452i	$-0.293292\pi$
$548$		0			0
$549$	−27.5916	−	47.7900i	−0.0502579	−	0.0870492i
$550$		0			0
$551$	−114.359	−	66.0253i	−0.207548	−	0.119828i
$552$		0			0
$553$	172.395	−	921.308i	0.311745	−	1.66602i
$554$		0			0
$555$	329.143	+	190.031i	0.593051	+	0.342398i
$556$		0			0
$557$	−535.218	+	309.008i	−0.960894	+	0.554772i	−0.896448	−	0.443149i	$-0.853861\pi$
$557$	−535.218	+	309.008i	−0.960894	+	0.554772i	−0.0644457	+	0.997921i	$0.520528\pi$
$558$		0			0
$559$			460.409i			0.823629i
$560$		0			0
$561$	−294.049			−0.524152
$562$		0			0
$563$	337.134	+	583.934i	0.598817	+	1.03718i	0.992996	+	0.118148i	$0.0376958\pi$
$563$	337.134	+	583.934i	0.598817	+	1.03718i	−0.394179	+	0.919034i	$0.628971\pi$
$564$		0			0
$565$	98.4131	−	170.456i	0.174182	−	0.301693i
$566$		0			0
$567$	47.8351	+	40.9976i	0.0843652	+	0.0723062i
$568$		0			0
$569$	75.2685	−	130.369i	0.132282	−	0.229119i	−0.792274	−	0.610166i	$-0.791103\pi$
$569$	75.2685	−	130.369i	0.132282	−	0.229119i	0.924556	+	0.381046i	$0.124436\pi$
$570$		0			0
$571$	318.733	−	184.020i	0.558201	−	0.322277i	−0.194222	−	0.980958i	$-0.562218\pi$
$571$	318.733	−	184.020i	0.558201	−	0.322277i	0.752423	+	0.658680i	$0.228885\pi$
$572$		0			0
$573$	158.818			0.277170
$574$		0			0
$575$	−51.9133			−0.0902840
$576$		0			0
$577$	185.150	−	106.897i	0.320885	−	0.185263i	−0.330902	−	0.943665i	$-0.607353\pi$
$577$	185.150	−	106.897i	0.320885	−	0.185263i	0.651787	+	0.758402i	$0.274020\pi$
$578$		0			0
$579$	−144.312	+	249.955i	−0.249243	+	0.431702i
$580$		0			0
$581$	−519.292	+	182.886i	−0.893790	+	0.314778i
$582$		0			0
$583$	213.659	−	370.068i	0.366482	−	0.634765i
$584$		0			0
$585$	82.0901	+	142.184i	0.140325	+	0.243050i
$586$		0			0
$587$	−230.197			−0.392159			−0.196079	−	0.980588i	$-0.562821\pi$
$587$	−230.197			−0.392159			−0.196079	+	0.980588i	$0.562821\pi$
$588$		0			0
$589$			98.0823i			0.166523i
$590$		0			0
$591$	−241.287	+	139.307i	−0.408269	+	0.235714i
$592$		0			0
$593$	−236.240	−	136.393i	−0.398381	−	0.230005i	0.287404	−	0.957809i	$-0.407208\pi$
$593$	−236.240	−	136.393i	−0.398381	−	0.230005i	−0.685785	+	0.727804i	$0.740541\pi$
$594$		0			0
$595$	280.482	+	796.411i	0.471399	+	1.33851i
$596$		0			0
$597$	−217.322	−	125.471i	−0.364024	−	0.210169i
$598$		0			0
$599$	408.934	+	708.294i	0.682694	+	1.18246i	0.974156	+	0.225878i	$0.0725252\pi$
$599$	408.934	+	708.294i	0.682694	+	1.18246i	−0.291461	+	0.956583i	$0.594142\pi$
$600$		0			0
$601$			1160.52i			1.93099i	0.260422	+	0.965495i	$0.416138\pi$
$601$			1160.52i			1.93099i	−0.260422	+	0.965495i	$0.583862\pi$
$602$		0			0
$603$		−	282.344i		−	0.468232i
$604$		0			0
$605$	−173.026	−	299.690i	−0.285993	−	0.495355i
$606$		0			0
$607$	−399.558	−	230.685i	−0.658250	−	0.380041i	0.133360	−	0.991068i	$-0.457423\pi$
$607$	−399.558	−	230.685i	−0.658250	−	0.380041i	−0.791610	+	0.611027i	$0.790757\pi$
$608$		0			0
$609$	−43.7997	+	51.1045i	−0.0719206	+	0.0839154i
$610$		0			0
$611$	304.868	+	176.015i	0.498965	+	0.288078i
$612$		0			0
$613$	−311.281	+	179.718i	−0.507799	+	0.293178i	−0.731929	−	0.681381i	$-0.761380\pi$
$613$	−311.281	+	179.718i	−0.507799	+	0.293178i	0.224129	+	0.974559i	$0.428046\pi$
$614$		0			0
$615$		−	0.701779i		−	0.00114110i
$616$		0			0
$617$	1076.04			1.74399			0.871997	−	0.489511i	$-0.162825\pi$
$617$	1076.04			1.74399			0.871997	+	0.489511i	$0.162825\pi$
$618$		0			0
$619$	−387.704	−	671.524i	−0.626340	−	1.08485i	−0.988280	−	0.152651i	$-0.951219\pi$
$619$	−387.704	−	671.524i	−0.626340	−	1.08485i	0.361940	−	0.932201i	$-0.382114\pi$
$620$		0			0
$621$	−42.5781	+	73.7474i	−0.0685638	+	0.118756i
$622$		0			0
$623$	468.016	+	87.5750i	0.751229	+	0.140570i
$624$		0			0
$625$	347.079	−	601.159i	0.555327	−	0.961854i
$626$		0			0
$627$	266.529	−	153.880i	0.425085	−	0.245423i
$628$		0			0
$629$	939.660			1.49390
$630$		0			0
$631$	747.318			1.18434			0.592169	−	0.805814i	$-0.298272\pi$
$631$	747.318			1.18434			0.592169	+	0.805814i	$0.298272\pi$
$632$		0			0
$633$	−417.740	+	241.182i	−0.659936	+	0.381014i
$634$		0			0
$635$	214.299	−	371.176i	0.337478	−	0.584529i
$636$		0			0
$637$	−393.757	+	316.620i	−0.618143	+	0.497049i
$638$		0			0
$639$	−176.210	+	305.205i	−0.275759	+	0.477629i
$640$		0			0
$641$	−469.558	−	813.299i	−0.732540	−	1.26880i	−0.955794	−	0.294037i	$-0.905001\pi$
$641$	−469.558	−	813.299i	−0.732540	−	1.26880i	0.223254	−	0.974760i	$-0.428332\pi$
$642$		0			0
$643$	−146.295			−0.227520			−0.113760	−	0.993508i	$-0.536290\pi$
$643$	−146.295			−0.227520			−0.113760	+	0.993508i	$0.536290\pi$
$644$		0			0
$645$			410.446i			0.636351i
$646$		0			0
$647$	148.994	−	86.0218i	0.230285	−	0.132955i	−0.380419	−	0.924814i	$-0.624220\pi$
$647$	148.994	−	86.0218i	0.230285	−	0.132955i	0.610703	+	0.791859i	$0.290887\pi$
$648$		0			0
$649$	−375.334	−	216.699i	−0.578327	−	0.333897i
$650$		0			0
$651$	49.1394	+	9.19496i	0.0754830	+	0.0141244i
$652$		0			0
$653$	7.95187	+	4.59102i	0.0121774	+	0.00703065i	0.506076	−	0.862489i	$-0.331095\pi$
$653$	7.95187	+	4.59102i	0.0121774	+	0.00703065i	−0.493899	+	0.869519i	$0.664429\pi$
$654$		0			0
$655$	−591.743	−	1024.93i	−0.903424	−	1.56478i
$656$		0			0
$657$		−	422.536i		−	0.643129i
$658$		0			0
$659$		−	727.736i		−	1.10430i	−0.833744	−	0.552151i	$-0.813807\pi$
$659$		−	727.736i		−	1.10430i	0.833744	−	0.552151i	$-0.186193\pi$
$660$		0			0
$661$	58.3142	+	101.003i	0.0882211	+	0.152803i	0.906759	−	0.421649i	$-0.138548\pi$
$661$	58.3142	+	101.003i	0.0882211	+	0.152803i	−0.818538	+	0.574452i	$0.805215\pi$
$662$		0			0
$663$	351.534	+	202.958i	0.530218	+	0.306121i
$664$		0			0
$665$	−671.005	−	575.093i	−1.00903	−	0.864801i
$666$		0			0
$667$	−78.7878	−	45.4882i	−0.118123	−	0.0681982i
$668$		0			0
$669$	111.801	−	64.5485i	0.167117	−	0.0964851i
$670$		0			0
$671$			137.402i			0.204771i
$672$		0			0
$673$	893.821			1.32811			0.664057	−	0.747682i	$-0.268833\pi$
$673$	893.821			1.32811			0.664057	+	0.747682i	$0.268833\pi$
$674$		0			0
$675$	8.22993	+	14.2547i	0.0121925	+	0.0211180i
$676$		0			0
$677$	−222.753	+	385.820i	−0.329030	+	0.569896i	−0.982320	−	0.187212i	$-0.940055\pi$
$677$	−222.753	+	385.820i	−0.329030	+	0.569896i	0.653290	+	0.757108i	$0.273388\pi$
$678$		0			0
$679$	−245.855	−	698.089i	−0.362084	−	1.02811i
$680$		0			0
$681$	−83.3476	+	144.362i	−0.122390	+	0.211986i
$682$		0			0
$683$	−116.378	+	67.1911i	−0.170393	+	0.0983764i	−0.582771	−	0.812636i	$-0.698032\pi$
$683$	−116.378	+	67.1911i	−0.170393	+	0.0983764i	0.412378	+	0.911013i	$0.364698\pi$
$684$		0			0
$685$	647.780			0.945664
$686$		0			0
$687$	−383.219			−0.557815
$688$		0			0
$689$	−510.856	+	294.943i	−0.741446	+	0.428074i
$690$		0			0
$691$	−210.723	+	364.983i	−0.304953	+	0.528195i	−0.977251	−	0.212086i	$-0.931974\pi$
$691$	−210.723	+	364.983i	−0.304953	+	0.528195i	0.672297	+	0.740281i	$0.265308\pi$
$692$		0			0
$693$	−52.1080	−	147.957i	−0.0751920	−	0.213503i
$694$		0			0
$695$	−61.6005	+	106.695i	−0.0886338	+	0.153518i
$696$		0			0
$697$	−0.867535	−	1.50261i	−0.00124467	−	0.00215583i
$698$		0			0
$699$	−33.2335			−0.0475444
$700$		0			0
$701$			567.685i			0.809821i	0.914356	+	0.404911i	$0.132697\pi$
$701$			567.685i			0.809821i	−0.914356	+	0.404911i	$0.867303\pi$
$702$		0			0
$703$	−851.715	+	491.738i	−1.21154	+	0.699485i
$704$		0			0
$705$	271.784	+	156.915i	0.385509	+	0.222574i
$706$		0			0
$707$	957.675	+	820.787i	1.35456	+	1.16094i
$708$		0			0
$709$	897.680	+	518.276i	1.26612	+	0.730996i	0.974252	−	0.225463i	$-0.0723893\pi$
$709$	897.680	+	518.276i	1.26612	+	0.730996i	0.291870	+	0.956458i	$0.405723\pi$
$710$		0			0
$711$	−200.850	−	347.882i	−0.282489	−	0.489285i
$712$		0			0
$713$			67.5739i			0.0947741i
$714$		0			0
$715$		−	408.795i		−	0.571742i
$716$		0			0
$717$	−175.323	−	303.668i	−0.244523	−	0.423526i
$718$		0			0
$719$	208.320	+	120.273i	0.289735	+	0.167279i	0.637823	−	0.770183i	$-0.279835\pi$
$719$	208.320	+	120.273i	0.289735	+	0.167279i	−0.348087	+	0.937462i	$0.613169\pi$
$720$		0			0
$721$	1028.44	+	192.441i	1.42641	+	0.266909i
$722$		0			0
$723$	−466.731	−	269.467i	−0.645548	−	0.372707i
$724$		0			0
$725$	−15.2289	+	8.79242i	−0.0210054	+	0.0121275i
$726$		0			0
$727$			577.292i			0.794074i	0.917803	+	0.397037i	$0.129962\pi$
$727$			577.292i			0.794074i	−0.917803	+	0.397037i	$0.870038\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	507.391	+	878.828i	0.694106	+	1.20223i
$732$		0			0
$733$	−432.636	+	749.348i	−0.590227	+	1.02230i	0.403975	+	0.914770i	$0.367628\pi$
$733$	−432.636	+	749.348i	−0.590227	+	1.02230i	−0.994202	+	0.107532i	$0.965705\pi$
$734$		0			0
$735$	−351.028	+	282.262i	−0.477589	+	0.384029i
$736$		0			0
$737$	−351.507	+	608.828i	−0.476943	+	0.826089i
$738$		0			0
$739$	−413.450	+	238.706i	−0.559473	+	0.323012i	−0.752934	−	0.658096i	$-0.771362\pi$
$739$	−413.450	+	238.706i	−0.559473	+	0.323012i	0.193461	+	0.981108i	$0.438029\pi$
$740$		0			0
$741$	−424.845			−0.573340
$742$		0			0
$743$	−699.672			−0.941685			−0.470843	−	0.882217i	$-0.656050\pi$
$743$	−699.672			−0.941685			−0.470843	+	0.882217i	$0.656050\pi$
$744$		0			0
$745$	−821.083	+	474.053i	−1.10213	+	0.636312i
$746$		0			0
$747$	−117.976	+	204.341i	−0.157933	+	0.273548i
$748$		0			0
$749$	1122.76	+	210.091i	1.49901	+	0.280495i
$750$		0			0
$751$	−178.354	+	308.918i	−0.237488	+	0.411342i	−0.959993	−	0.280024i	$-0.909657\pi$
$751$	−178.354	+	308.918i	−0.237488	+	0.411342i	0.722505	+	0.691366i	$0.242991\pi$
$752$		0			0
$753$	249.495	+	432.138i	0.331334	+	0.573888i
$754$		0			0
$755$	−325.589			−0.431244
$756$		0			0
$757$			537.700i			0.710304i	0.934809	+	0.355152i	$0.115571\pi$
$757$			537.700i			0.710304i	−0.934809	+	0.355152i	$0.884429\pi$
$758$		0			0
$759$	183.625	−	106.016i	0.241930	−	0.139679i
$760$		0			0
$761$	80.7169	+	46.6019i	0.106067	+	0.0612378i	0.552095	−	0.833781i	$-0.313829\pi$
$761$	80.7169	+	46.6019i	0.106067	+	0.0612378i	−0.446028	+	0.895019i	$0.647162\pi$
$762$		0			0
$763$	−906.378	+	1057.54i	−1.18791	+	1.38603i
$764$		0			0
$765$	313.387	+	180.934i	0.409656	+	0.236515i
$766$		0			0
$767$	299.140	+	518.126i	0.390013	+	0.675523i
$768$		0			0
$769$		−	985.853i		−	1.28199i	−0.767544	−	0.640997i	$-0.778521\pi$
$769$		−	985.853i		−	1.28199i	0.767544	−	0.640997i	$-0.221479\pi$
$770$		0			0
$771$			761.189i			0.987276i
$772$		0			0
$773$	423.580	+	733.663i	0.547969	+	0.949111i	0.998414	+	0.0563061i	$0.0179323\pi$
$773$	423.580	+	733.663i	0.547969	+	0.949111i	−0.450444	+	0.892805i	$0.648734\pi$
$774$		0			0
$775$	11.3115	+	6.53069i	0.0145955	+	0.00842669i
$776$		0			0
$777$	166.516	+	472.810i	0.214306	+	0.608507i
$778$		0			0
$779$	1.57268	+	0.907988i	0.00201885	+	0.00116558i
$780$		0			0
$781$	759.935	−	438.749i	0.973028	−	0.561778i
$782$		0			0
$783$			28.8454i			0.0368395i
$784$		0			0
$785$	−1048.47			−1.33563
$786$		0			0
$787$	658.742	+	1140.97i	0.837029	+	1.44978i	0.892368	+	0.451309i	$0.149043\pi$
$787$	658.742	+	1140.97i	0.837029	+	1.44978i	−0.0553387	+	0.998468i	$0.517624\pi$
$788$		0			0
$789$	185.705	−	321.651i	0.235368	−	0.407669i
$790$		0			0
$791$	244.859	−	86.2351i	0.309556	−	0.109020i
$792$		0			0
$793$	94.8372	−	164.263i	0.119593	−	0.207141i
$794$		0			0
$795$	−455.419	+	262.936i	−0.572854	+	0.330738i
$796$		0			0
$797$	747.998			0.938518			0.469259	−	0.883061i	$-0.344521\pi$
$797$	747.998			0.938518			0.469259	+	0.883061i	$0.344521\pi$
$798$		0			0
$799$	775.908			0.971099
$800$		0			0
$801$	176.721	−	102.030i	0.220625	−	0.127378i
$802$		0			0
$803$	−526.040	+	911.128i	−0.655093	+	1.13466i
$804$		0			0
$805$	−462.290	−	396.211i	−0.574273	−	0.492187i
$806$		0			0
$807$	−2.99284	+	5.18375i	−0.00370860	+	0.00642349i
$808$		0			0
$809$	−118.652	−	205.511i	−0.146665	−	0.254031i	0.783328	−	0.621609i	$-0.213521\pi$
$809$	−118.652	−	205.511i	−0.146665	−	0.254031i	−0.929993	+	0.367577i	$0.880187\pi$
$810$		0			0
$811$	79.1833			0.0976366			0.0488183	−	0.998808i	$-0.484454\pi$
$811$	79.1833			0.0976366			0.0488183	+	0.998808i	$0.484454\pi$
$812$		0			0
$813$			176.425i			0.217005i
$814$		0			0
$815$	320.460	−	185.017i	0.393202	−	0.227015i
$816$		0			0
$817$	−919.807	−	531.051i	−1.12583	−	0.650001i
$818$		0			0
$819$	−39.8281	+	212.848i	−0.0486301	+	0.259888i
$820$		0			0
$821$	197.328	+	113.927i	0.240351	+	0.138766i	0.615338	−	0.788263i	$-0.289020\pi$
$821$	197.328	+	113.927i	0.240351	+	0.138766i	−0.374987	+	0.927030i	$0.622353\pi$
$822$		0			0
$823$	226.139	+	391.685i	0.274774	+	0.475923i	0.970078	−	0.242793i	$-0.0780635\pi$
$823$	226.139	+	391.685i	0.274774	+	0.475923i	−0.695304	+	0.718716i	$0.744730\pi$
$824$		0			0
$825$		−	40.9837i		−	0.0496773i
$826$		0			0
$827$		−	407.717i		−	0.493007i	−0.969142	−	0.246504i	$-0.920718\pi$
$827$		−	407.717i		−	0.493007i	0.969142	−	0.246504i	$-0.0792818\pi$
$828$		0			0
$829$	−588.577	−	1019.45i	−0.709985	−	1.22973i	−0.964862	−	0.262756i	$-0.915369\pi$
$829$	−588.577	−	1019.45i	−0.709985	−	1.22973i	0.254878	−	0.966973i	$-0.417965\pi$
$830$		0			0
$831$	−209.052	−	120.696i	−0.251567	−	0.145242i
$832$		0			0
$833$	−402.673	+	1038.30i	−0.483401	+	1.24646i
$834$		0			0
$835$	466.724	+	269.463i	0.558951	+	0.322710i
$836$		0			0
$837$	18.5548	−	10.7126i	0.0221683	−	0.0127989i
$838$		0			0
$839$		−	432.537i		−	0.515539i	−0.966206	−	0.257769i	$-0.917013\pi$
$839$		−	432.537i		−	0.515539i	0.966206	−	0.257769i	$-0.0829875\pi$
$840$		0			0
$841$	810.183			0.963357
$842$		0			0
$843$	68.4208	+	118.508i	0.0811635	+	0.140579i
$844$		0			0
$845$	166.311	−	288.059i	0.196817	−	0.340898i
$846$		0			0
$847$	83.9480	−	448.632i	0.0991121	−	0.529672i
$848$		0			0
$849$	296.562	−	513.661i	0.349308	−	0.605019i
$850$		0			0
$851$	−586.790	+	338.783i	−0.689530	+	0.398100i
$852$		0			0
$853$	244.530			0.286670			0.143335	−	0.989674i	$-0.454217\pi$
$853$	244.530			0.286670			0.143335	+	0.989674i	$0.454217\pi$
$854$		0			0
$855$	−378.742			−0.442973
$856$		0			0
$857$	460.515	−	265.879i	0.537357	−	0.310243i	−0.206650	−	0.978415i	$-0.566256\pi$
$857$	460.515	−	265.879i	0.537357	−	0.310243i	0.744007	+	0.668172i	$0.232923\pi$
$858$		0			0
$859$	309.921	−	536.799i	0.360793	−	0.624911i	−0.627299	−	0.778779i	$-0.715840\pi$
$859$	309.921	−	536.799i	0.360793	−	0.624911i	0.988091	+	0.153868i	$0.0491729\pi$
$860$		0			0
$861$	0.602339	−	0.702795i	0.000699580	−	0.000816254i
$862$		0			0
$863$	306.072	−	530.133i	0.354661	−	0.614291i	−0.632399	−	0.774643i	$-0.717930\pi$
$863$	306.072	−	530.133i	0.354661	−	0.614291i	0.987060	+	0.160352i	$0.0512630\pi$
$864$		0			0
$865$	−448.359	−	776.580i	−0.518334	−	0.897781i
$866$		0			0
$867$	394.115			0.454573
$868$		0			0
$869$			1000.20i			1.15098i
$870$		0			0
$871$	840.449	−	485.233i	0.964924	−	0.557099i
$872$		0			0
$873$	−274.697	−	158.597i	−0.314659	−	0.181668i
$874$		0			0
$875$	765.039	−	269.434i	0.874331	−	0.307924i
$876$		0			0
$877$	−870.970	−	502.855i	−0.993125	−	0.573381i	−0.0869178	−	0.996215i	$-0.527702\pi$
$877$	−870.970	−	502.855i	−0.993125	−	0.573381i	−0.906207	+	0.422835i	$0.861035\pi$
$878$		0			0
$879$	40.1259	+	69.5001i	0.0456495	+	0.0790672i
$880$		0			0
$881$		−	1090.05i		−	1.23729i	−0.785672	−	0.618644i	$-0.787682\pi$
$881$		−	1090.05i		−	1.23729i	0.785672	−	0.618644i	$-0.212318\pi$
$882$		0			0
$883$			983.277i			1.11356i	0.830659	+	0.556782i	$0.187964\pi$
$883$			983.277i			1.11356i	−0.830659	+	0.556782i	$0.812036\pi$
$884$		0			0
$885$	266.678	+	461.900i	0.301331	+	0.521921i
$886$		0			0
$887$	853.455	+	492.743i	0.962182	+	0.555516i	0.896844	−	0.442347i	$-0.145854\pi$
$887$	853.455	+	492.743i	0.962182	+	0.555516i	0.0653378	+	0.997863i	$0.479188\pi$
$888$		0			0
$889$	533.190	−	187.780i	0.599764	−	0.211227i
$890$		0			0
$891$	−58.2210	−	33.6139i	−0.0653434	−	0.0377261i
$892$		0			0
$893$	−703.289	+	406.044i	−0.787558	+	0.454697i
$894$		0			0
$895$			987.525i			1.10338i
$896$		0			0
$897$	−292.697			−0.326307
$898$		0			0
$899$	11.4448	+	19.8230i	0.0127306	+	0.0220501i
$900$		0			0
$901$	−650.081	+	1125.97i	−0.721510	+	1.24969i
$902$		0			0
$903$	−352.287	+	411.041i	−0.390130	+	0.455195i
$904$		0			0
$905$	3.10777	−	5.38282i	0.00343400	−	0.00594786i
$906$		0			0
$907$	518.367	−	299.279i	0.571518	−	0.329966i	−0.186237	−	0.982505i	$-0.559629\pi$
$907$	518.367	−	299.279i	0.571518	−	0.329966i	0.757756	+	0.652538i	$0.226296\pi$
$908$		0			0
$909$	540.549			0.594664
$910$		0			0
$911$	−733.733			−0.805415			−0.402708	−	0.915329i	$-0.631931\pi$
$911$	−733.733			−0.805415			−0.402708	+	0.915329i	$0.631931\pi$
$912$		0			0
$913$	508.792	−	293.751i	0.557275	−	0.321743i
$914$		0			0
$915$	84.5457	−	146.438i	0.0923997	−	0.160041i
$916$		0			0
$917$	287.099	−	1534.31i	0.313085	−	1.67318i
$918$		0			0
$919$	582.020	−	1008.09i	0.633319	−	1.09694i	−0.353550	−	0.935416i	$-0.615026\pi$
$919$	582.020	−	1008.09i	0.633319	−	1.09694i	0.986869	−	0.161524i	$-0.0516411\pi$
$920$		0			0
$921$	372.578	+	645.324i	0.404536	+	0.700677i
$922$		0			0
$923$	−1211.33			−1.31239
$924$		0			0
$925$			130.967i			0.141586i
$926$		0			0
$927$	388.334	−	224.205i	0.418915	−	0.241861i
$928$		0			0
$929$	903.173	+	521.447i	0.972199	+	0.561299i	0.899906	−	0.436084i	$-0.143635\pi$
$929$	903.173	+	521.447i	0.972199	+	0.561299i	0.0722932	+	0.997383i	$0.476968\pi$
$930$		0			0
$931$	−178.373	−	1151.85i	−0.191593	−	1.23722i
$932$		0			0
$933$	−471.002	−	271.933i	−0.504825	−	0.291461i
$934$		0			0
$935$	−450.511	−	780.308i	−0.481830	−	0.834554i
$936$		0			0
$937$		−	424.394i		−	0.452928i	−0.974019	−	0.226464i	$-0.927283\pi$
$937$		−	424.394i		−	0.452928i	0.974019	−	0.226464i	$-0.0727166\pi$
$938$		0			0
$939$		−	364.597i		−	0.388282i
$940$		0			0
$941$	37.7006	+	65.2994i	0.0400644	+	0.0693936i	0.885362	−	0.464902i	$-0.153910\pi$
$941$	37.7006	+	65.2994i	0.0400644	+	0.0693936i	−0.845298	+	0.534295i	$0.820577\pi$
$942$		0			0
$943$	1.08350	+	0.625559i	0.00114899	+	0.000663371i
$944$		0			0
$945$	−35.5060	+	189.750i	−0.0375725	+	0.200794i
$946$		0			0
$947$	266.418	+	153.817i	0.281329	+	0.162425i	0.634025	−	0.773313i	$-0.281402\pi$
$947$	266.418	+	153.817i	0.281329	+	0.162425i	−0.352696	+	0.935738i	$0.614735\pi$
$948$		0			0
$949$	1257.76	−	726.166i	1.32535	−	0.765190i
$950$		0			0
$951$		−	525.372i		−	0.552441i
$952$		0			0
$953$	−84.9147			−0.0891025			−0.0445512	−	0.999007i	$-0.514186\pi$
$953$	−84.9147			−0.0891025			−0.0445512	+	0.999007i	$0.514186\pi$
$954$		0			0
$955$	243.324	+	421.450i	0.254790	+	0.441309i
$956$		0			0
$957$	35.9113	−	62.2002i	0.0375249	−	0.0649950i
$958$		0			0
$959$	648.718	+	555.991i	0.676452	+	0.579761i
$960$		0			0
$961$	−471.999	+	817.527i	−0.491154	+	0.850704i
$962$		0			0
$963$	423.950	−	244.768i	0.440239	−	0.254172i
$964$		0			0
$965$	−884.397			−0.916473
$966$		0			0
$967$	327.735			0.338919			0.169460	−	0.985537i	$-0.445798\pi$
$967$	327.735			0.338919			0.169460	+	0.985537i	$0.445798\pi$
$968$		0			0
$969$	−810.943	+	468.198i	−0.836886	+	0.483177i
$970$		0			0
$971$	−2.18332	+	3.78162i	−0.00224853	+	0.00389456i	−0.867147	−	0.498051i	$-0.834049\pi$
$971$	−2.18332	+	3.78162i	−0.00224853	+	0.00389456i	0.864899	+	0.501946i	$0.167382\pi$
$972$		0			0
$973$	−153.266	+	53.9778i	−0.157519	+	0.0554756i
$974$		0			0
$975$	−28.2878	+	48.9958i	−0.0290131	+	0.0502521i
$976$		0			0
$977$	942.113	+	1631.79i	0.964292	+	1.67020i	0.711505	+	0.702681i	$0.248014\pi$
$977$	942.113	+	1631.79i	0.964292	+	1.67020i	0.252787	+	0.967522i	$0.418653\pi$
$978$		0			0
$979$	−508.092			−0.518990
$980$		0			0
$981$			596.918i			0.608479i
$982$		0			0
$983$	−337.812	+	195.036i	−0.343654	+	0.198409i	−0.661887	−	0.749604i	$-0.730244\pi$
$983$	−337.812	+	195.036i	−0.343654	+	0.198409i	0.318233	+	0.948013i	$0.396911\pi$
$984$		0			0
$985$	−739.348	−	426.863i	−0.750607	−	0.433363i
$986$		0			0
$987$	137.497	+	390.415i	0.139308	+	0.395557i
$988$		0			0
$989$	−633.702	−	365.868i	−0.640750	−	0.369937i
$990$		0			0
$991$	482.174	+	835.150i	0.486553	+	0.842735i	0.999881	−	0.0154579i	$-0.00492061\pi$
$991$	482.174	+	835.150i	0.486553	+	0.842735i	−0.513327	+	0.858193i	$0.671587\pi$
$992$		0			0
$993$		−	747.825i		−	0.753097i
$994$		0			0
$995$		−	768.934i		−	0.772798i
$996$		0			0
$997$	−98.6026	−	170.785i	−0.0988993	−	0.171299i	0.812330	−	0.583198i	$-0.198199\pi$
$997$	−98.6026	−	170.785i	−0.0988993	−	0.171299i	−0.911229	+	0.411899i	$0.864866\pi$
$998$		0			0
$999$	186.050	+	107.416i	0.186236	+	0.107524i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.3.bf.b.145.26		60
4.3	odd	2		168.3.x.b.61.8	✓	60
7.3	odd	6	inner	672.3.bf.b.241.5		60
8.3	odd	2		168.3.x.b.61.13	yes	60
8.5	even	2	inner	672.3.bf.b.145.5		60
28.3	even	6		168.3.x.b.157.13	yes	60
56.3	even	6		168.3.x.b.157.8	yes	60
56.45	odd	6	inner	672.3.bf.b.241.26		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.3.x.b.61.8	✓	60	4.3	odd	2
168.3.x.b.61.13	yes	60	8.3	odd	2
168.3.x.b.157.8	yes	60	56.3	even	6
168.3.x.b.157.13	yes	60	28.3	even	6
672.3.bf.b.145.5		60	8.5	even	2	inner
672.3.bf.b.145.26		60	1.1	even	1	trivial
672.3.bf.b.241.5		60	7.3	odd	6	inner
672.3.bf.b.241.26		60	56.45	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{3} +(-2.65366 + 4.59628i) q^{5} +(-6.60250 + 2.32529i) q^{7} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{3} +(-2.65366 + 4.59628i) q^{5} +(-6.60250 + 2.32529i) q^{7} +(-1.50000 + 2.59808i) q^{9} +(6.46900 - 3.73488i) q^{11} -10.3115 q^{13} -9.19256 q^{15} +(-19.6827 + 11.3638i) q^{17} +(11.8937 - 20.6004i) q^{19} +(-9.20587 - 7.88999i) q^{21} +(8.19416 - 14.1927i) q^{23} +(-1.58385 - 2.74331i) q^{25} -5.19615 q^{27} -5.55129i q^{29} +(-3.57088 + 2.06165i) q^{31} +(11.2046 + 6.46900i) q^{33} +(6.83314 - 36.5175i) q^{35} +(-35.8054 - 20.6723i) q^{37} +(-8.93006 - 15.4673i) q^{39} +0.0763421i q^{41} -44.6499i q^{43} +(-7.96099 - 13.7888i) q^{45} +(-29.5657 - 17.0697i) q^{47} +(38.1861 - 30.7054i) q^{49} +(-34.0914 - 19.6827i) q^{51} +(49.5422 - 28.6032i) q^{53} +39.6444i q^{55} +41.2009 q^{57} +(-29.0102 - 50.2472i) q^{59} +(-9.19719 + 15.9300i) q^{61} +(3.86248 - 20.6417i) q^{63} +(27.3634 - 47.3947i) q^{65} +(-81.5057 + 47.0573i) q^{67} +28.3854 q^{69} +117.473 q^{71} +(-121.976 + 70.4226i) q^{73} +(2.74331 - 4.75155i) q^{75} +(-34.0269 + 39.7018i) q^{77} +(-66.9499 + 115.961i) q^{79} +(-4.50000 - 7.79423i) q^{81} +78.6508 q^{83} -120.623i q^{85} +(8.32694 - 4.80756i) q^{87} +(-58.9069 - 34.0099i) q^{89} +(68.0820 - 23.9773i) q^{91} +(-6.18495 - 3.57088i) q^{93} +(63.1236 + 109.333i) q^{95} +105.731i q^{97} +22.4093i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 26 q^{7} - 90 q^{9}+O(q^{10}) \) 60 * q - 26 * q^7 - 90 * q^9	\( 60 q - 26 q^{7} - 90 q^{9} - 12 q^{15} - 36 q^{17} + 28 q^{23} - 204 q^{25} - 18 q^{31} - 30 q^{33} + 36 q^{39} - 828 q^{47} - 126 q^{49} - 312 q^{57} + 12 q^{63} + 36 q^{65} - 760 q^{71} - 648 q^{73} - 114 q^{79} - 270 q^{81} + 174 q^{87} - 72 q^{89} + 492 q^{95}+O(q^{100}) \) 60 * q - 26 * q^7 - 90 * q^9 - 12 * q^15 - 36 * q^17 + 28 * q^23 - 204 * q^25 - 18 * q^31 - 30 * q^33 + 36 * q^39 - 828 * q^47 - 126 * q^49 - 312 * q^57 + 12 * q^63 + 36 * q^65 - 760 * q^71 - 648 * q^73 - 114 * q^79 - 270 * q^81 + 174 * q^87 - 72 * q^89 + 492 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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