LMFDB - Embedded newform 147.4.c.b.146.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.12
Character	$\chi$	$=$	147.146
Dual form			147.4.c.b.146.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.222948i q^{2} +(3.69409 - 3.65427i) q^{3} +7.95029 q^{4} -18.7021 q^{5} +(-0.814713 - 0.823589i) q^{6} -3.55609i q^{8} +(0.292585 - 26.9984i) q^{9} +O(q^{10})$	\(q-0.222948i q^{2} +(3.69409 - 3.65427i) q^{3} +7.95029 q^{4} -18.7021 q^{5} +(-0.814713 - 0.823589i) q^{6} -3.55609i q^{8} +(0.292585 - 26.9984i) q^{9} +4.16960i q^{10} -45.8073i q^{11} +(29.3691 - 29.0525i) q^{12} -59.3740i q^{13} +(-69.0873 + 68.3427i) q^{15} +62.8095 q^{16} -28.9343 q^{17} +(-6.01924 - 0.0652311i) q^{18} +38.9416i q^{19} -148.687 q^{20} -10.2126 q^{22} +1.79304i q^{23} +(-12.9949 - 13.1365i) q^{24} +224.770 q^{25} -13.2373 q^{26} +(-97.5787 - 100.804i) q^{27} +148.759i q^{29} +(15.2369 + 15.4029i) q^{30} -104.052i q^{31} -42.4519i q^{32} +(-167.392 - 169.216i) q^{33} +6.45083i q^{34} +(2.32613 - 214.645i) q^{36} -24.1630 q^{37} +8.68195 q^{38} +(-216.969 - 219.333i) q^{39} +66.5064i q^{40} +254.946 q^{41} -59.6604 q^{43} -364.181i q^{44} +(-5.47195 + 504.928i) q^{45} +0.399755 q^{46} +262.649 q^{47} +(232.024 - 229.523i) q^{48} -50.1119i q^{50} +(-106.886 + 105.734i) q^{51} -472.040i q^{52} +381.628i q^{53} +(-22.4740 + 21.7550i) q^{54} +856.694i q^{55} +(142.303 + 143.854i) q^{57} +33.1654 q^{58} +371.060 q^{59} +(-549.265 + 543.344i) q^{60} +696.288i q^{61} -23.1982 q^{62} +493.012 q^{64} +1110.42i q^{65} +(-37.7264 + 37.3198i) q^{66} +434.164 q^{67} -230.036 q^{68} +(6.55227 + 6.62366i) q^{69} -824.756i q^{71} +(-96.0087 - 1.04046i) q^{72} +0.395276i q^{73} +5.38708i q^{74} +(830.319 - 821.370i) q^{75} +309.597i q^{76} +(-48.8998 + 48.3727i) q^{78} -731.265 q^{79} -1174.67 q^{80} +(-728.829 - 15.7986i) q^{81} -56.8397i q^{82} +586.330 q^{83} +541.132 q^{85} +13.3012i q^{86} +(543.605 + 549.528i) q^{87} -162.895 q^{88} -440.284 q^{89} +(112.573 + 1.21996i) q^{90} +14.2552i q^{92} +(-380.234 - 384.377i) q^{93} -58.5571i q^{94} -728.291i q^{95} +(-155.131 - 156.821i) q^{96} -634.224i q^{97} +(-1236.72 - 13.4025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) $ 24 * q - 96 * q^4 - 64 * q^9	$ 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) $ 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		−	0.222948i		−	0.0788240i	−0.999223	−	0.0394120i	$-0.987452\pi$
$2$		−	0.222948i		−	0.0788240i	0.999223	−	0.0394120i	$-0.0125485\pi$
$3$	3.69409	−	3.65427i	0.710928	−	0.703265i
$3$	3.69409	−	3.65427i	0.710928	−	0.703265i
$4$	7.95029			0.993787
$5$	−18.7021			−1.67277			−0.836385	−	0.548143i	$-0.815335\pi$
$5$	−18.7021			−1.67277			−0.836385	+	0.548143i	$0.815335\pi$
$6$	−0.814713	−	0.823589i	−0.0554342	−	0.0560382i
$7$		0			0
$7$		0			0
$8$		−	3.55609i		−	0.157158i
$9$	0.292585	−	26.9984i	0.0108365	−	0.999941i
$10$			4.16960i			0.131854i
$11$		−	45.8073i		−	1.25558i	−0.778382	−	0.627792i	$-0.783959\pi$
$11$		−	45.8073i		−	1.25558i	0.778382	−	0.627792i	$-0.216041\pi$
$12$	29.3691	−	29.0525i	0.706511	−	0.698896i
$13$		−	59.3740i		−	1.26672i	−0.773857	−	0.633361i	$-0.781675\pi$
$13$		−	59.3740i		−	1.26672i	0.773857	−	0.633361i	$-0.218325\pi$
$14$		0			0
$15$	−69.0873	+	68.3427i	−1.18922	+	1.17640i
$16$	62.8095			0.981399
$17$	−28.9343			−0.412799			−0.206400	−	0.978468i	$-0.566175\pi$
$17$	−28.9343			−0.412799			−0.206400	+	0.978468i	$0.566175\pi$
$18$	−6.01924	−	0.0652311i	−0.0788194	−	0.000854173i
$19$			38.9416i			0.470201i	0.971971	+	0.235100i	$0.0755419\pi$
$19$			38.9416i			0.470201i	−0.971971	+	0.235100i	$0.924458\pi$
$20$	−148.687			−1.66238
$21$		0			0
$22$	−10.2126			−0.0989701
$23$			1.79304i			0.0162554i	0.999967	+	0.00812772i	$0.00258716\pi$
$23$			1.79304i			0.0162554i	−0.999967	+	0.00812772i	$0.997413\pi$
$24$	−12.9949	−	13.1365i	−0.110524	−	0.111728i
$25$	224.770			1.79816
$26$	−13.2373			−0.0998480
$27$	−97.5787	−	100.804i	−0.695520	−	0.718507i
$28$		0			0
$29$			148.759i			0.952545i	0.879298	+	0.476272i	$0.158012\pi$
$29$			148.759i			0.952545i	−0.879298	+	0.476272i	$0.841988\pi$
$30$	15.2369	+	15.4029i	0.0927286	+	0.0937389i
$31$		−	104.052i		−	0.602848i	−0.953490	−	0.301424i	$-0.902538\pi$
$31$		−	104.052i		−	0.602848i	0.953490	−	0.301424i	$-0.0974620\pi$
$32$		−	42.4519i		−	0.234516i
$33$	−167.392	−	169.216i	−0.883008	−	0.892629i
$34$			6.45083i			0.0325385i
$35$		0			0
$36$	2.32613	−	214.645i	0.0107691	−	0.993728i
$37$	−24.1630			−0.107361			−0.0536806	−	0.998558i	$-0.517095\pi$
$37$	−24.1630			−0.107361			−0.0536806	+	0.998558i	$0.517095\pi$
$38$	8.68195			0.0370631
$39$	−216.969	−	219.333i	−0.890841	−	0.900547i
$40$			66.5064i			0.262890i
$41$	254.946			0.971118			0.485559	−	0.874204i	$-0.338616\pi$
$41$	254.946			0.971118			0.485559	+	0.874204i	$0.338616\pi$
$42$		0			0
$43$	−59.6604			−0.211584			−0.105792	−	0.994388i	$-0.533738\pi$
$43$	−59.6604			−0.211584			−0.105792	+	0.994388i	$0.533738\pi$
$44$		−	364.181i		−	1.24778i
$45$	−5.47195	+	504.928i	−0.0181269	+	1.67267i
$46$	0.399755			0.00128132
$47$	262.649			0.815135			0.407567	−	0.913175i	$-0.366377\pi$
$47$	262.649			0.815135			0.407567	+	0.913175i	$0.366377\pi$
$48$	232.024	−	229.523i	0.697704	−	0.690184i
$49$		0			0
$50$		−	50.1119i		−	0.141738i
$51$	−106.886	+	105.734i	−0.293470	+	0.290307i
$52$		−	472.040i		−	1.25885i
$53$			381.628i			0.989069i	0.869158	+	0.494534i	$0.164661\pi$
$53$			381.628i			0.989069i	−0.869158	+	0.494534i	$0.835339\pi$
$54$	−22.4740	+	21.7550i	−0.0566356	+	0.0548237i
$55$			856.694i			2.10030i
$56$		0			0
$57$	142.303	+	143.854i	0.330676	+	0.334279i
$58$	33.1654			0.0750834
$59$	371.060			0.818779			0.409389	−	0.912360i	$-0.365742\pi$
$59$	371.060			0.818779			0.409389	+	0.912360i	$0.365742\pi$
$60$	−549.265	+	543.344i	−1.18183	+	1.16909i
$61$			696.288i			1.46148i	0.682654	+	0.730742i	$0.260826\pi$
$61$			696.288i			1.46148i	−0.682654	+	0.730742i	$0.739174\pi$
$62$	−23.1982			−0.0475189
$63$		0			0
$64$	493.012			0.962913
$65$			1110.42i			2.11893i
$66$	−37.7264	+	37.3198i	−0.0703606	+	0.0696022i
$67$	434.164			0.791665			0.395833	−	0.918323i	$-0.370456\pi$
$67$	434.164			0.791665			0.395833	+	0.918323i	$0.370456\pi$
$68$	−230.036			−0.410235
$69$	6.55227	+	6.62366i	0.0114319	+	0.0115564i
$70$		0			0
$71$		−	824.756i		−	1.37860i	−0.724476	−	0.689300i	$-0.757918\pi$
$71$		−	824.756i		−	1.37860i	0.724476	−	0.689300i	$-0.242082\pi$
$72$	−96.0087	−	1.04046i	−0.157149	−	0.00170304i
$73$			0.395276i			0.000633747i	1.00000		0.000316873i	$0.000100864\pi$
$73$			0.395276i			0.000633747i	−1.00000		0.000316873i	$0.999899\pi$
$74$			5.38708i			0.00846264i
$75$	830.319	−	821.370i	1.27836	−	1.26458i
$76$			309.597i			0.467279i
$77$		0			0
$78$	−48.8998	+	48.3727i	−0.0709847	+	0.0702196i
$79$	−731.265			−1.04144			−0.520720	−	0.853728i	$-0.674336\pi$
$79$	−731.265			−1.04144			−0.520720	+	0.853728i	$0.674336\pi$
$80$	−1174.67			−1.64165
$81$	−728.829	−	15.7986i	−0.999765	−	0.0216717i
$82$		−	56.8397i		−	0.0765474i
$83$	586.330			0.775399			0.387700	−	0.921786i	$-0.373270\pi$
$83$	586.330			0.775399			0.387700	+	0.921786i	$0.373270\pi$
$84$		0			0
$85$	541.132			0.690518
$86$			13.3012i			0.0166779i
$87$	543.605	+	549.528i	0.669891	+	0.677190i
$88$	−162.895			−0.197325
$89$	−440.284			−0.524382			−0.262191	−	0.965016i	$-0.584445\pi$
$89$	−440.284			−0.524382			−0.262191	+	0.965016i	$0.584445\pi$
$90$	112.573	+	1.21996i	0.131847	+	0.00142884i
$91$		0			0
$92$			14.2552i			0.0161544i
$93$	−380.234	−	384.377i	−0.423962	−	0.428581i
$94$		−	58.5571i		−	0.0642522i
$95$		−	728.291i		−	0.786538i
$96$	−155.131	−	156.821i	−0.164927	−	0.166724i
$97$		−	634.224i		−	0.663873i	−0.943302	−	0.331937i	$-0.892298\pi$
$97$		−	634.224i		−	0.663873i	0.943302	−	0.331937i	$-0.107702\pi$
$98$		0			0
$99$	−1236.72	−	13.4025i	−1.25551	−	0.0136061i
$100$	1786.99			1.78699
$101$	1533.91			1.51119			0.755593	−	0.655042i	$-0.227349\pi$
$101$	1533.91			1.51119			0.755593	+	0.655042i	$0.227349\pi$
$102$	23.5731	+	23.8300i	0.0228832	+	0.0231325i
$103$			1214.17i			1.16151i	0.814079	+	0.580754i	$0.197242\pi$
$103$			1214.17i			1.16151i	−0.814079	+	0.580754i	$0.802758\pi$
$104$	−211.139			−0.199076
$105$		0			0
$106$	85.0832			0.0779624
$107$		−	1794.55i		−	1.62136i	−0.585487	−	0.810682i	$-0.699097\pi$
$107$		−	1794.55i		−	1.62136i	0.585487	−	0.810682i	$-0.300903\pi$
$108$	−775.780	−	801.419i	−0.691198	−	0.714043i
$109$	1483.26			1.30340			0.651700	−	0.758477i	$-0.274056\pi$
$109$	1483.26			1.30340			0.651700	+	0.758477i	$0.274056\pi$
$110$	190.998			0.165554
$111$	−89.2601	+	88.2980i	−0.0763261	+	0.0755034i
$112$		0			0
$113$			1665.23i			1.38630i	0.720794	+	0.693150i	$0.243778\pi$
$113$			1665.23i			1.38630i	−0.720794	+	0.693150i	$0.756222\pi$
$114$	32.0719	−	31.7262i	0.0263492	−	0.0260652i
$115$		−	33.5337i		−	0.0271916i
$116$			1182.68i			0.946626i
$117$	−1603.00	−	17.3719i	−1.26665	−	0.0137268i
$118$		−	82.7271i		−	0.0645394i
$119$		0			0
$120$	243.032	+	245.680i	0.184881	+	0.186895i
$121$	−767.307			−0.576489
$122$	155.236			0.115200
$123$	941.793	−	931.642i	0.690395	−	0.682954i
$124$		−	827.244i		−	0.599102i
$125$	−1865.91			−1.33513
$126$		0			0
$127$	−1784.43			−1.24679			−0.623395	−	0.781907i	$-0.714247\pi$
$127$	−1784.43			−1.24679			−0.623395	+	0.781907i	$0.714247\pi$
$128$		−	449.531i		−	0.310417i
$129$	−220.391	+	218.015i	−0.150421	+	0.148800i
$130$	247.566			0.167023
$131$	1103.06			0.735686			0.367843	−	0.929888i	$-0.380096\pi$
$131$	1103.06			0.735686			0.367843	+	0.929888i	$0.380096\pi$
$132$	−1330.82	−	1345.32i	−0.877521	−	0.887083i
$133$		0			0
$134$		−	96.7960i		−	0.0624022i
$135$	1824.93	+	1885.24i	1.16344	+	1.20190i
$136$			102.893i			0.0648748i
$137$		−	2168.96i		−	1.35260i	−0.736625	−	0.676302i	$-0.763582\pi$
$137$		−	2168.96i		−	1.35260i	0.736625	−	0.676302i	$-0.236418\pi$
$138$	1.47673	−	1.46081i	0.000910925	−	0.000901107i
$139$		−	2246.90i		−	1.37107i	−0.728038	−	0.685537i	$-0.759568\pi$
$139$		−	2246.90i		−	1.37107i	0.728038	−	0.685537i	$-0.240432\pi$
$140$		0			0
$141$	970.250	−	959.792i	0.579502	−	0.573256i
$142$	−183.878			−0.108667
$143$	−2719.76			−1.59047
$144$	18.3771	−	1695.76i	0.0106349	−	0.981341i
$145$		−	2782.10i		−	1.59339i
$146$	0.0881259			4.99545e−5
$147$		0			0
$148$	−192.103			−0.106694
$149$			1554.26i			0.854563i	0.904119	+	0.427281i	$0.140529\pi$
$149$			1554.26i			0.854563i	−0.904119	+	0.427281i	$0.859471\pi$
$150$	−183.123	−	185.118i	−0.0996794	−	0.100765i
$151$	−1878.53			−1.01240			−0.506201	−	0.862416i	$-0.668950\pi$
$151$	−1878.53			−1.01240			−0.506201	+	0.862416i	$0.668950\pi$
$152$	138.480			0.0738960
$153$	−8.46572	+	781.179i	−0.00447328	+	0.412775i
$154$		0			0
$155$			1945.99i			1.00843i
$156$	−1724.96	−	1743.76i	−0.885306	−	0.894952i
$157$		−	45.7355i		−	0.0232490i	−0.999932	−	0.0116245i	$-0.996300\pi$
$157$		−	45.7355i		−	0.0232490i	0.999932	−	0.0116245i	$-0.00370028\pi$
$158$			163.034i			0.0820905i
$159$	1394.57	+	1409.77i	0.695578	+	0.703157i
$160$			793.942i			0.392291i
$161$		0			0
$162$	−3.52227	+	162.491i	−0.00170825	+	0.0788055i
$163$	664.899			0.319503			0.159751	−	0.987157i	$-0.448931\pi$
$163$	664.899			0.319503			0.159751	+	0.987157i	$0.448931\pi$
$164$	2026.89			0.965085
$165$	3130.59	+	3164.70i	1.47707	+	1.49316i
$166$		−	130.721i		−	0.0611201i
$167$	88.2591			0.0408964			0.0204482	−	0.999791i	$-0.493491\pi$
$167$	88.2591			0.0408964			0.0204482	+	0.999791i	$0.493491\pi$
$168$		0			0
$169$	−1328.27			−0.604582
$170$		−	120.644i		−	0.0544294i
$171$	1051.36	+	11.3937i	0.470173	+	0.00509531i
$172$	−474.318			−0.210270
$173$	−2730.30			−1.19989			−0.599945	−	0.800041i	$-0.704811\pi$
$173$	−2730.30			−1.19989			−0.599945	+	0.800041i	$0.704811\pi$
$174$	122.516	−	121.196i	0.0533789	−	0.0528035i
$175$		0			0
$176$		−	2877.13i		−	1.23223i
$177$	1370.73	−	1355.96i	0.582092	−	0.575818i
$178$			98.1603i			0.0413339i
$179$			1620.70i			0.676741i	0.941013	+	0.338371i	$0.109876\pi$
$179$			1620.70i			0.676741i	−0.941013	+	0.338371i	$0.890124\pi$
$180$	−43.5036	+	4014.33i	−0.0180143	+	1.66228i
$181$			1433.62i			0.588728i	0.955693	+	0.294364i	$0.0951078\pi$
$181$			1433.62i			0.588728i	−0.955693	+	0.294364i	$0.904892\pi$
$182$		0			0
$183$	2544.43	+	2572.15i	1.02781	+	1.03901i
$184$	6.37621			0.00255468
$185$	451.899			0.179591
$186$	−85.6961	+	84.7725i	−0.0337825	+	0.0334184i
$187$			1325.40i			0.518304i
$188$	2088.14			0.810070
$189$		0			0
$190$	−162.371			−0.0619980
$191$		−	541.389i		−	0.205097i	−0.994728	−	0.102549i	$-0.967300\pi$
$191$		−	541.389i		−	0.205097i	0.994728	−	0.102549i	$-0.0326997\pi$
$192$	1821.23	−	1801.60i	0.684562	−	0.677183i
$193$	−4950.31			−1.84627			−0.923137	−	0.384470i	$-0.874384\pi$
$193$	−4950.31			−1.84627			−0.923137	+	0.384470i	$0.874384\pi$
$194$	−141.399			−0.0523291
$195$	4057.78	+	4101.99i	1.49017	+	1.50641i
$196$		0			0
$197$		−	3674.51i		−	1.32892i	−0.747322	−	0.664462i	$-0.768661\pi$
$197$		−	3674.51i		−	1.32892i	0.747322	−	0.664462i	$-0.231339\pi$
$198$	−2.98806	+	275.725i	−0.00107249	+	0.0989643i
$199$			2322.22i			0.827227i	0.910453	+	0.413613i	$0.135733\pi$
$199$			2322.22i			0.827227i	−0.910453	+	0.413613i	$0.864267\pi$
$200$		−	799.300i		−	0.282595i
$201$	1603.84	−	1586.55i	0.562817	−	0.556750i
$202$		−	341.982i		−	0.119118i
$203$		0			0
$204$	−849.773	+	840.614i	−0.291647	+	0.288504i
$205$	−4768.03			−1.62446
$206$	270.696			0.0915548
$207$	48.4093	+	0.524617i	0.0162545	+	0.000176152i
$208$		−	3729.25i		−	1.24316i
$209$	1783.81			0.590376
$210$		0			0
$211$	4047.51			1.32058			0.660289	−	0.751012i	$-0.270434\pi$
$211$	4047.51			1.32058			0.660289	+	0.751012i	$0.270434\pi$
$212$			3034.06i			0.982924i
$213$	−3013.88	−	3046.72i	−0.969521	−	0.980084i
$214$	−400.092			−0.127802
$215$	1115.78			0.353932
$216$	−358.467	+	346.998i	−0.112919	+	0.109307i
$217$		0			0
$218$		−	330.690i		−	0.102739i
$219$	1.44444	+	1.46018i	0.000445692	+	0.000450548i
$220$			6810.97i			2.08725i
$221$			1717.94i			0.522902i
$222$	19.6859	+	19.9004i	0.00595148	+	0.00601633i
$223$		−	3387.56i		−	1.01725i	−0.860987	−	0.508627i	$-0.830153\pi$
$223$		−	3387.56i		−	1.01725i	0.860987	−	0.508627i	$-0.169847\pi$
$224$		0			0
$225$	65.7641	−	6068.43i	0.0194857	−	1.79805i
$226$	371.260			0.109274
$227$	−2323.62			−0.679402			−0.339701	−	0.940533i	$-0.610326\pi$
$227$	−2323.62			−0.679402			−0.339701	+	0.940533i	$0.610326\pi$
$228$	1131.35	+	1143.68i	0.328621	+	0.332202i
$229$			280.878i			0.0810521i	0.999178	+	0.0405261i	$0.0129034\pi$
$229$			280.878i			0.0810521i	−0.999178	+	0.0405261i	$0.987097\pi$
$230$	−7.47627			−0.00214335
$231$		0			0
$232$	528.999			0.149700
$233$			1559.78i			0.438562i	0.975662	+	0.219281i	$0.0703711\pi$
$233$			1559.78i			0.438562i	−0.975662	+	0.219281i	$0.929629\pi$
$234$	−3.87303	+	357.386i	−0.00108200	+	0.0998422i
$235$	−4912.10			−1.36353
$236$	2950.04			0.813691
$237$	−2701.36	+	2672.24i	−0.740389	+	0.732408i
$238$		0			0
$239$			1346.90i			0.364534i	0.983249	+	0.182267i	$0.0583436\pi$
$239$			1346.90i			0.364534i	−0.983249	+	0.182267i	$0.941656\pi$
$240$	−4339.34	+	4292.57i	−1.16710	+	1.15452i
$241$		−	4034.73i		−	1.07842i	−0.842171	−	0.539211i	$-0.818723\pi$
$241$		−	4034.73i		−	1.07842i	0.842171	−	0.539211i	$-0.181277\pi$
$242$			171.069i			0.0454412i
$243$	−2750.09	+	2604.98i	−0.726002	+	0.687693i
$244$			5535.69i			1.45240i
$245$		0			0
$246$	−207.708	−	209.971i	−0.0538331	−	0.0544197i
$247$	2312.12			0.595613
$248$	−370.018			−0.0947425
$249$	2165.96	−	2142.61i	0.551253	−	0.545311i
$250$			416.000i			0.105241i
$251$	−585.826			−0.147319			−0.0736593	−	0.997283i	$-0.523468\pi$
$251$	−585.826			−0.147319			−0.0736593	+	0.997283i	$0.523468\pi$
$252$		0			0
$253$	82.1344			0.0204101
$254$			397.834i			0.0982770i
$255$	1998.99	−	1977.44i	0.490908	−	0.485617i
$256$	3843.87			0.938445
$257$	1768.90			0.429342			0.214671	−	0.976686i	$-0.431132\pi$
$257$	1768.90			0.429342			0.214671	+	0.976686i	$0.431132\pi$
$258$	48.6061	+	49.1357i	0.0117290	+	0.0118568i
$259$		0			0
$260$			8828.16i			2.10577i
$261$	4016.25	+	43.5245i	0.952489	+	0.0103222i
$262$		−	245.925i		−	0.0579897i
$263$			7837.35i			1.83754i	0.394799	+	0.918768i	$0.370814\pi$
$263$			7837.35i			1.83754i	−0.394799	+	0.918768i	$0.629186\pi$
$264$	−601.747	+	595.261i	−0.140284	+	0.138772i
$265$		−	7137.26i		−	1.65448i
$266$		0			0
$267$	−1626.45	+	1608.92i	−0.372797	+	0.368779i
$268$	3451.73			0.786746
$269$	4786.13			1.08482			0.542408	−	0.840115i	$-0.317513\pi$
$269$	4786.13			1.08482			0.542408	+	0.840115i	$0.317513\pi$
$270$	420.311	−	406.864i	0.0947383	−	0.0917073i
$271$			2088.95i			0.468246i	0.972207	+	0.234123i	$0.0752219\pi$
$271$			2088.95i			0.468246i	−0.972207	+	0.234123i	$0.924778\pi$
$272$	−1817.35			−0.405121
$273$		0			0
$274$	−483.565			−0.106618
$275$		−	10296.1i		−	2.25774i
$276$	52.0925	+	52.6600i	0.0113609	+	0.0114846i
$277$	1577.27			0.342126			0.171063	−	0.985260i	$-0.445280\pi$
$277$	1577.27			0.342126			0.171063	+	0.985260i	$0.445280\pi$
$278$	−500.941			−0.108073
$279$	−2809.24	−	30.4440i	−0.602813	−	0.00653274i
$280$		0			0
$281$		−	4744.03i		−	1.00714i	−0.863956	−	0.503568i	$-0.832020\pi$
$281$		−	4744.03i		−	1.00714i	0.863956	−	0.503568i	$-0.167980\pi$
$282$	−213.984	−	216.315i	−0.0451863	−	0.0456787i
$283$			39.7652i			0.00835264i	0.999991	+	0.00417632i	$0.00132937\pi$
$283$			39.7652i			0.00835264i	−0.999991	+	0.00417632i	$0.998671\pi$
$284$		−	6557.05i		−	1.37003i
$285$	−2661.37	−	2690.37i	−0.553144	−	0.559171i
$286$			606.365i			0.125367i
$287$		0			0
$288$	−1146.14	−	12.4208i	−0.234502	−	0.00254132i
$289$	−4075.81			−0.829597
$290$	−620.264			−0.125597
$291$	−2317.63	−	2342.88i	−0.466879	−	0.471966i
$292$			3.14256i			0.000629809i
$293$	−67.9150			−0.0135414			−0.00677071	−	0.999977i	$-0.502155\pi$
$293$	−67.9150			−0.0135414			−0.00677071	+	0.999977i	$0.502155\pi$
$294$		0			0
$295$	−6939.62			−1.36963
$296$			85.9255i			0.0168727i
$297$	−4617.54	+	4469.82i	−0.902145	+	0.873283i
$298$	346.519			0.0673601
$299$	106.460			0.0205911
$300$	6601.28	−	6530.13i	1.27042	−	1.25672i
$301$		0			0
$302$			418.814i			0.0798015i
$303$	5666.40	−	5605.33i	1.07434	−	1.06276i
$304$			2445.90i			0.461455i
$305$		−	13022.1i		−	2.44473i
$306$	174.162	+	1.88741i	0.0325366	+	0.000352602i
$307$		−	846.145i		−	0.157303i	−0.996902	−	0.0786516i	$-0.974939\pi$
$307$		−	846.145i		−	0.157303i	0.996902	−	0.0786516i	$-0.0250615\pi$
$308$		0			0
$309$	4436.90	+	4485.24i	0.816848	+	0.825749i
$310$	433.855			0.0794881
$311$	−3327.42			−0.606690			−0.303345	−	0.952881i	$-0.598104\pi$
$311$	−3327.42			−0.606690			−0.303345	+	0.952881i	$0.598104\pi$
$312$	−779.966	+	771.559i	−0.141528	+	0.140003i
$313$		−	7816.49i		−	1.41155i	−0.708438	−	0.705773i	$-0.750600\pi$
$313$		−	7816.49i		−	1.41155i	0.708438	−	0.705773i	$-0.249400\pi$
$314$	−10.1966			−0.00183258
$315$		0			0
$316$	−5813.77			−1.03497
$317$			2263.17i			0.400984i	0.979695	+	0.200492i	$0.0642541\pi$
$317$			2263.17i			0.400984i	−0.979695	+	0.200492i	$0.935746\pi$
$318$	314.305	−	310.917i	0.0554256	−	0.0548282i
$319$	6814.23			1.19600
$320$	−9220.37			−1.61073
$321$	−6557.78	−	6629.23i	−1.14025	−	1.15267i
$322$		0			0
$323$		−	1126.75i		−	0.194099i
$324$	−5794.40	−	125.604i	−0.993553	−	0.0215370i
$325$		−	13345.5i		−	2.27776i
$326$		−	148.238i		−	0.0251845i
$327$	5479.29	−	5420.24i	0.926623	−	0.916635i
$328$		−	906.609i		−	0.152619i
$329$		0			0
$330$	705.564	−	697.959i	0.117697	−	0.116428i
$331$	5712.25			0.948562			0.474281	−	0.880374i	$-0.342708\pi$
$331$	5712.25			0.948562			0.474281	+	0.880374i	$0.342708\pi$
$332$	4661.50			0.770581
$333$	−7.06971	+	652.362i	−0.00116342	+	0.107355i
$334$		−	19.6772i		−	0.00322362i
$335$	−8119.79			−1.32427
$336$		0			0
$337$	9067.99			1.46577			0.732886	−	0.680352i	$-0.238173\pi$
$337$	9067.99			1.46577			0.732886	+	0.680352i	$0.238173\pi$
$338$			296.134i			0.0476556i
$339$	6085.21	+	6151.52i	0.974936	+	0.985559i
$340$	4302.16			0.686228
$341$	−4766.34			−0.756926
$342$	2.54020	−	234.399i	0.000401633	−	0.0370609i
$343$		0			0
$344$			212.157i			0.0332522i
$345$	−122.541	−	123.877i	−0.0191229	−	0.0193313i
$346$			608.715i			0.0945801i
$347$			8616.41i			1.33301i	0.745502	+	0.666503i	$0.232210\pi$
$347$			8616.41i			1.33301i	−0.745502	+	0.666503i	$0.767790\pi$
$348$	4321.82	+	4368.91i	0.665729	+	0.672983i
$349$			7966.10i			1.22182i	0.791700	+	0.610911i	$0.209197\pi$
$349$			7966.10i			1.22182i	−0.791700	+	0.610911i	$0.790803\pi$
$350$		0			0
$351$	−5985.12	+	5793.64i	−0.910148	+	0.881030i
$352$	−1944.61			−0.294454
$353$	−12274.8			−1.85077			−0.925385	−	0.379028i	$-0.876259\pi$
$353$	−12274.8			−1.85077			−0.925385	+	0.379028i	$0.876259\pi$
$354$	−302.308	−	305.601i	−0.0453883	−	0.0458829i
$355$			15424.7i			2.30608i
$356$	−3500.38			−0.521124
$357$		0			0
$358$	361.331			0.0533434
$359$			11637.0i			1.71080i	0.517966	+	0.855401i	$0.326689\pi$
$359$			11637.0i			1.71080i	−0.517966	+	0.855401i	$0.673311\pi$
$360$	1795.57	+	19.4587i	0.262874	+	0.00284879i
$361$	5342.55			0.778911
$362$	319.622			0.0464059
$363$	−2834.50	+	2803.95i	−0.409842	+	0.405425i
$364$		0			0
$365$		−	7.39250i		−	0.00106011i
$366$	573.455	−	567.274i	0.0818989	−	0.0810161i
$367$		−	2435.83i		−	0.346455i	−0.984882	−	0.173228i	$-0.944580\pi$
$367$		−	2435.83i		−	0.346455i	0.984882	−	0.173228i	$-0.0554197\pi$
$368$			112.620i			0.0159531i
$369$	74.5932	−	6883.13i	0.0105235	−	0.971061i
$370$		−	100.750i		−	0.0141560i
$371$		0			0
$372$	−3022.97	−	3055.91i	−0.421328	−	0.425918i
$373$	2398.17			0.332902			0.166451	−	0.986050i	$-0.446769\pi$
$373$	2398.17			0.332902			0.166451	+	0.986050i	$0.446769\pi$
$374$	295.495			0.0408548
$375$	−6892.82	+	6818.53i	−0.949183	+	0.938953i
$376$		−	934.003i		−	0.128105i
$377$	8832.39			1.20661
$378$		0			0
$379$	−7291.15			−0.988183			−0.494091	−	0.869410i	$-0.664499\pi$
$379$	−7291.15			−0.988183			−0.494091	+	0.869410i	$0.664499\pi$
$380$		−	5790.13i		−	0.781651i
$381$	−6591.83	+	6520.78i	−0.886377	+	0.876824i
$382$	−120.702			−0.0161666
$383$	9402.66			1.25445			0.627224	−	0.778839i	$-0.284191\pi$
$383$	9402.66			1.25445			0.627224	+	0.778839i	$0.284191\pi$
$384$	−1642.71	−	1660.61i	−0.218305	−	0.220684i
$385$		0			0
$386$			1103.66i			0.145531i
$387$	−17.4557	+	1610.74i	−0.00229283	+	0.211572i
$388$		−	5042.27i		−	0.659748i
$389$			292.651i			0.0381439i	0.999818	+	0.0190720i	$0.00607116\pi$
$389$			292.651i			0.0381439i	−0.999818	+	0.0190720i	$0.993929\pi$
$390$	914.530	−	904.673i	0.118741	−	0.117461i
$391$		−	51.8804i		−	0.00671024i
$392$		0			0
$393$	4074.80	−	4030.88i	0.523019	−	0.517382i
$394$	−819.224			−0.104751
$395$	13676.2			1.74209
$396$	−9832.32	−	106.554i	−1.24771	−	0.0135215i
$397$			6673.62i			0.843676i	0.906671	+	0.421838i	$0.138615\pi$
$397$			6673.62i			0.843676i	−0.906671	+	0.421838i	$0.861385\pi$
$398$	517.735			0.0652053
$399$		0			0
$400$	14117.7			1.76471
$401$		−	2274.67i		−	0.283270i	−0.989919	−	0.141635i	$-0.954764\pi$
$401$		−	2274.67i		−	0.283270i	0.989919	−	0.141635i	$-0.0452360\pi$
$402$	−353.719	−	357.573i	−0.0438853	−	0.0443635i
$403$	−6177.98			−0.763640
$404$	12195.0			1.50180
$405$	13630.7	+	295.468i	1.67238	+	0.0362517i
$406$		0			0
$407$			1106.84i			0.134801i
$408$	375.998	+	380.095i	0.0456242	+	0.0461213i
$409$			14591.8i			1.76411i	0.471151	+	0.882053i	$0.343839\pi$
$409$			14591.8i			1.76411i	−0.471151	+	0.882053i	$0.656161\pi$
$410$			1063.02i			0.128046i
$411$	−7925.97	−	8012.33i	−0.951239	−	0.961603i
$412$			9652.98i			1.15429i
$413$		0			0
$414$	0.116962	−	10.7928i	1.38850e−5	−	0.00128124i
$415$	−10965.6			−1.29706
$416$	−2520.54			−0.297066
$417$	−8210.77	−	8300.23i	−0.964228	−	0.974734i
$418$		−	397.697i		−	0.0465358i
$419$	12090.7			1.40971			0.704855	−	0.709351i	$-0.251012\pi$
$419$	12090.7			1.40971			0.704855	+	0.709351i	$0.251012\pi$
$420$		0			0
$421$	7230.48			0.837036			0.418518	−	0.908209i	$-0.362550\pi$
$421$	7230.48			0.837036			0.418518	+	0.908209i	$0.362550\pi$
$422$		−	902.384i		−	0.104093i
$423$	76.8471	−	7091.11i	0.00883318	−	0.815087i
$424$	1357.10			0.155440
$425$	−6503.54			−0.742278
$426$	−679.261	+	671.939i	−0.0772542	+	0.0764215i
$427$		0			0
$428$		−	14267.2i		−	1.61129i
$429$	−10047.0	+	9938.74i	−1.13071	+	1.11852i
$430$		−	248.760i		−	0.0278983i
$431$			1901.11i			0.212467i	0.994341	+	0.106233i	$0.0338791\pi$
$431$			1901.11i			0.212467i	−0.994341	+	0.106233i	$0.966121\pi$
$432$	−6128.87	−	6331.43i	−0.682582	−	0.705142i
$433$			1867.06i			0.207218i	0.994618	+	0.103609i	$0.0330391\pi$
$433$			1867.06i			0.207218i	−0.994618	+	0.103609i	$0.966961\pi$
$434$		0			0
$435$	−10166.6	−	10277.3i	−1.12057	−	1.13278i
$436$	11792.4			1.29530
$437$	−69.8240			−0.00764333
$438$	0.325545	−	0.322036i	3.55140e−5	−	3.51312e-5i
$439$			7249.39i			0.788142i	0.919080	+	0.394071i	$0.128934\pi$
$439$			7249.39i			0.788142i	−0.919080	+	0.394071i	$0.871066\pi$
$440$	3046.48			0.330080
$441$		0			0
$442$	383.012			0.0412172
$443$		−	10213.3i		−	1.09537i	−0.836684	−	0.547685i	$-0.815509\pi$
$443$		−	10213.3i		−	1.09537i	0.836684	−	0.547685i	$-0.184491\pi$
$444$	−709.644	+	701.995i	−0.0758518	+	0.0750343i
$445$	8234.24			0.877170
$446$	−755.249			−0.0801841
$447$	5679.69	+	5741.57i	0.600984	+	0.607532i
$448$		0			0
$449$			5515.44i			0.579710i	0.957071	+	0.289855i	$0.0936071\pi$
$449$			5515.44i			0.579710i	−0.957071	+	0.289855i	$0.906393\pi$
$450$	−1352.94	−	14.6620i	−0.141730	−	0.00153594i
$451$		−	11678.4i		−	1.21932i
$452$			13239.1i			1.37769i
$453$	−6939.46	+	6864.66i	−0.719744	+	0.711986i
$454$			518.047i			0.0535532i
$455$		0			0
$456$	511.556	−	506.042i	0.0525347	−	0.0519684i
$457$	−7867.61			−0.805320			−0.402660	−	0.915350i	$-0.631914\pi$
$457$	−7867.61			−0.805320			−0.402660	+	0.915350i	$0.631914\pi$
$458$	62.6212			0.00638885
$459$	2823.37	+	2916.68i	0.287110	+	0.296599i
$460$		−	266.603i		−	0.0270227i
$461$	1034.73			0.104538			0.0522691	−	0.998633i	$-0.483355\pi$
$461$	1034.73			0.104538			0.0522691	+	0.998633i	$0.483355\pi$
$462$		0			0
$463$	17777.7			1.78445			0.892226	−	0.451590i	$-0.149143\pi$
$463$	17777.7			1.78445			0.892226	+	0.451590i	$0.149143\pi$
$464$			9343.46i			0.934826i
$465$	7111.19	+	7188.67i	0.709191	+	0.716918i
$466$	347.751			0.0345692
$467$	−1792.39			−0.177606			−0.0888029	−	0.996049i	$-0.528304\pi$
$467$	−1792.39			−0.177606			−0.0888029	+	0.996049i	$0.528304\pi$
$468$	−12744.3	−	138.112i	−1.25878	−	0.0136415i
$469$		0			0
$470$			1095.14i			0.107479i
$471$	−167.130	−	168.951i	−0.0163502	−	0.0165284i
$472$		−	1319.52i		−	0.128678i
$473$			2732.88i			0.265662i
$474$	595.771	+	602.262i	0.0577314	+	0.0583604i
$475$			8752.89i			0.845495i
$476$		0			0
$477$	10303.4	+	111.658i	0.989011	+	0.0107180i
$478$	300.288			0.0287340
$479$	12548.4			1.19697			0.598487	−	0.801133i	$-0.295769\pi$
$479$	12548.4			1.19697			0.598487	+	0.801133i	$0.295769\pi$
$480$	2901.28	+	2932.89i	0.275885	+	0.278891i
$481$			1434.65i			0.135997i
$482$	−899.534			−0.0850055
$483$		0			0
$484$	−6100.31			−0.572907
$485$			11861.3i			1.11051i
$486$	580.774	+	613.127i	0.0542067	+	0.0572264i
$487$	−4480.51			−0.416902			−0.208451	−	0.978033i	$-0.566842\pi$
$487$	−4480.51			−0.416902			−0.208451	+	0.978033i	$0.566842\pi$
$488$	2476.06			0.229684
$489$	2456.20	−	2429.72i	0.227143	−	0.224695i
$490$		0			0
$491$			14924.2i			1.37173i	0.727729	+	0.685865i	$0.240576\pi$
$491$			14924.2i			1.37173i	−0.727729	+	0.685865i	$0.759424\pi$
$492$	7487.53	−	7406.83i	0.686105	−	0.678710i
$493$		−	4304.22i		−	0.393210i
$494$		−	515.482i		−	0.0469486i
$495$	23129.4	+	250.655i	2.10018	+	0.0227598i
$496$		−	6535.46i		−	0.591634i
$497$		0			0
$498$	−477.691	−	482.896i	−0.0429836	−	0.0434519i
$499$	4653.18			0.417445			0.208722	−	0.977975i	$-0.433069\pi$
$499$	4653.18			0.417445			0.208722	+	0.977975i	$0.433069\pi$
$500$	−14834.5			−1.32684
$501$	326.037	−	322.523i	0.0290744	−	0.0287610i
$502$			130.609i			0.0116122i
$503$	−14993.7			−1.32910			−0.664548	−	0.747246i	$-0.731376\pi$
$503$	−14993.7			−1.32910			−0.664548	+	0.747246i	$0.731376\pi$
$504$		0			0
$505$	−28687.4			−2.52787
$506$		−	18.3117i		−	0.00160880i
$507$	−4906.74	+	4853.85i	−0.429814	+	0.425182i
$508$	−14186.7			−1.23904
$509$	2997.18			0.260998			0.130499	−	0.991448i	$-0.458342\pi$
$509$	2997.18			0.260998			0.130499	+	0.991448i	$0.458342\pi$
$510$	−440.867	−	445.671i	−0.0382783	−	0.0386954i
$511$		0			0
$512$		−	4453.23i		−	0.384389i
$513$	3925.46	−	3799.87i	0.337843	−	0.327034i
$514$		−	394.372i		−	0.0338425i
$515$		−	22707.5i		−	1.94294i
$516$	−1752.17	+	1733.29i	−0.149487	+	0.147875i
$517$		−	12031.2i		−	1.02347i
$518$		0			0
$519$	−10086.0	+	9977.27i	−0.853035	+	0.843841i
$520$	3948.75			0.333008
$521$	−15844.1			−1.33233			−0.666164	−	0.745806i	$-0.732065\pi$
$521$	−15844.1			−1.33233			−0.666164	+	0.745806i	$0.732065\pi$
$522$	9.70369	−	895.414i	0.000813638	−	0.0750790i
$523$		−	12833.2i		−	1.07296i	−0.843913	−	0.536480i	$-0.819754\pi$
$523$		−	12833.2i		−	1.07296i	0.843913	−	0.536480i	$-0.180246\pi$
$524$	8769.65			0.731115
$525$		0			0
$526$	1747.32			0.144842
$527$			3010.67i			0.248855i
$528$	−10513.8	−	10628.4i	−0.866583	−	0.876025i
$529$	12163.8			0.999736
$530$	−1591.24			−0.130413
$531$	108.567	−	10018.0i	0.00887267	−	0.818731i
$532$		0			0
$533$		−	15137.1i		−	1.23014i
$534$	358.705	+	362.613i	0.0290687	+	0.0293854i
$535$			33561.9i			2.71217i
$536$		−	1543.92i		−	0.124417i
$537$	5922.47	+	5987.00i	0.475928	+	0.481114i
$538$		−	1067.06i		−	0.0855095i
$539$		0			0
$540$	14508.7	+	14988.2i	1.15622	+	1.19443i
$541$	−8704.63			−0.691759			−0.345879	−	0.938279i	$-0.612419\pi$
$541$	−8704.63			−0.691759			−0.345879	+	0.938279i	$0.612419\pi$
$542$	465.727			0.0369090
$543$	5238.82	+	5295.90i	0.414032	+	0.418543i
$544$			1228.32i			0.0968081i
$545$	−27740.1			−2.18029
$546$		0			0
$547$	−12998.5			−1.01604			−0.508020	−	0.861345i	$-0.669623\pi$
$547$	−12998.5			−1.01604			−0.508020	+	0.861345i	$0.669623\pi$
$548$		−	17243.9i		−	1.34420i
$549$	18798.7	+	203.723i	1.46140	+	0.0158373i
$550$	−2295.49			−0.177964
$551$	−5792.90			−0.447887
$552$	23.5543	−	23.3004i	0.00181619	−	0.00179662i
$553$		0			0
$554$		−	351.649i		−	0.0269678i
$555$	1669.35	−	1651.36i	0.127676	−	0.126300i
$556$		−	17863.5i		−	1.36255i
$557$		−	4992.42i		−	0.379777i	−0.981806	−	0.189888i	$-0.939187\pi$
$557$		−	4992.42i		−	0.379777i	0.981806	−	0.189888i	$-0.0608126\pi$
$558$	−6.78743	+	626.314i	−0.000514937	+	0.0475161i
$559$			3542.27i			0.268018i
$560$		0			0
$561$	4843.37	+	4896.14i	0.364505	+	0.368477i
$562$	−1057.67			−0.0793865
$563$	13270.9			0.993431			0.496715	−	0.867914i	$-0.334539\pi$
$563$	13270.9			0.993431			0.496715	+	0.867914i	$0.334539\pi$
$564$	7713.77	−	7630.63i	0.575901	−	0.569694i
$565$		−	31143.4i		−	2.31896i
$566$	8.86558			0.000658389
$567$		0			0
$568$	−2932.90			−0.216658
$569$			3130.67i			0.230658i	0.993327	+	0.115329i	$0.0367923\pi$
$569$			3130.67i			0.230658i	−0.993327	+	0.115329i	$0.963208\pi$
$570$	−599.813	+	593.348i	−0.0440761	+	0.0436011i
$571$	10740.6			0.787184			0.393592	−	0.919285i	$-0.371232\pi$
$571$	10740.6			0.787184			0.393592	+	0.919285i	$0.371232\pi$
$572$	−21622.9			−1.58059
$573$	−1978.38	−	1999.94i	−0.144238	−	0.145809i
$574$		0			0
$575$			403.022i			0.0292299i
$576$	144.248	−	13310.5i	0.0104346	−	0.962857i
$577$		−	19326.6i		−	1.39441i	−0.716870	−	0.697207i	$-0.754426\pi$
$577$		−	19326.6i		−	1.39441i	0.716870	−	0.697207i	$-0.245574\pi$
$578$			908.693i			0.0653921i
$579$	−18286.9	+	18089.8i	−1.31257	+	1.29842i
$580$		−	22118.5i		−	1.58349i
$581$		0			0
$582$	−522.340	+	516.710i	−0.0372022	+	0.0368013i
$583$	17481.3			1.24186
$584$	1.40563			9.95985e−5
$585$	29979.6	+	324.892i	2.11881	+	0.0229617i
$586$			15.1415i			0.00106739i
$587$	9837.78			0.691736			0.345868	−	0.938283i	$-0.387585\pi$
$587$	9837.78			0.691736			0.345868	+	0.938283i	$0.387585\pi$
$588$		0			0
$589$	4051.95			0.283460
$590$			1547.17i			0.107960i
$591$	−13427.7	−	13574.0i	−0.934585	−	0.944768i
$592$	−1517.66			−0.105364
$593$	−9153.70			−0.633891			−0.316946	−	0.948444i	$-0.602657\pi$
$593$	−9153.70			−0.633891			−0.316946	+	0.948444i	$0.602657\pi$
$594$	996.536	+	1029.47i	0.0688357	+	0.0711107i
$595$		0			0
$596$			12356.8i			0.849253i
$597$	8486.04	+	8578.50i	0.581760	+	0.588098i
$598$		−	23.7351i		−	0.00162307i
$599$		−	19675.1i		−	1.34208i	−0.741422	−	0.671039i	$-0.765848\pi$
$599$		−	19675.1i		−	1.34208i	0.741422	−	0.671039i	$-0.234152\pi$
$600$	−2920.86	−	2952.69i	−0.198739	−	0.200905i
$601$			688.430i			0.0467249i	0.999727	+	0.0233624i	$0.00743717\pi$
$601$			688.430i			0.0467249i	−0.999727	+	0.0233624i	$0.992563\pi$
$602$		0			0
$603$	127.030	−	11721.7i	0.00857885	−	0.791619i
$604$	−14934.9			−1.00611
$605$	14350.3			0.964333
$606$	−1249.70	−	1263.31i	−0.0837713	−	0.0846841i
$607$			12261.9i			0.819926i	0.912102	+	0.409963i	$0.134458\pi$
$607$			12261.9i			0.819926i	−0.912102	+	0.409963i	$0.865542\pi$
$608$	1653.15			0.110270
$609$		0			0
$610$	−2903.24			−0.192703
$611$		−	15594.5i		−	1.03255i
$612$	−67.3049	+	6210.60i	−0.00444549	+	0.410210i
$613$	−24768.2			−1.63194			−0.815969	−	0.578095i	$-0.803796\pi$
$613$	−24768.2			−1.63194			−0.815969	+	0.578095i	$0.803796\pi$
$614$	−188.646			−0.0123993
$615$	−17613.5	+	17423.7i	−1.15487	+	1.14242i
$616$		0			0
$617$			11630.7i			0.758891i	0.925214	+	0.379445i	$0.123885\pi$
$617$			11630.7i			0.758891i	−0.925214	+	0.379445i	$0.876115\pi$
$618$	999.975	−	989.197i	0.0650888	−	0.0643873i
$619$			28222.2i			1.83255i	0.400555	+	0.916273i	$0.368817\pi$
$619$			28222.2i			1.83255i	−0.400555	+	0.916273i	$0.631183\pi$
$620$			15471.2i			1.00216i
$621$	180.745	−	174.963i	0.0116797	−	0.0113060i
$622$			741.842i			0.0478218i
$623$		0			0
$624$	−13627.7	−	13776.2i	−0.874270	−	0.883796i
$625$	6800.20			0.435213
$626$	−1742.67			−0.111264
$627$	6589.55	−	6518.52i	0.419715	−	0.415191i
$628$		−	363.611i		−	0.0231045i
$629$	699.137			0.0443186
$630$		0			0
$631$	5143.24			0.324483			0.162242	−	0.986751i	$-0.448128\pi$
$631$	5143.24			0.324483			0.162242	+	0.986751i	$0.448128\pi$
$632$			2600.44i			0.163671i
$633$	14951.9	−	14790.7i	0.938836	−	0.928716i
$634$	504.568			0.0316072
$635$	33372.6			2.08559
$636$	11087.3	+	11208.1i	0.691256	+	0.698788i
$637$		0			0
$638$		−	1519.22i		−	0.0942734i
$639$	−22267.1	−	241.311i	−1.37852	−	0.0149391i
$640$			8407.20i			0.519256i
$641$			14609.4i			0.900212i	0.892975	+	0.450106i	$0.148614\pi$
$641$			14609.4i			0.900212i	−0.892975	+	0.450106i	$0.851386\pi$
$642$	−1477.97	+	1462.04i	−0.0908582	+	0.0898789i
$643$		−	28909.8i		−	1.77308i	−0.462653	−	0.886539i	$-0.653102\pi$
$643$		−	28909.8i		−	1.77308i	0.462653	−	0.886539i	$-0.346898\pi$
$644$		0			0
$645$	4121.78	−	4077.35i	0.251620	−	0.248908i
$646$	−251.206			−0.0152996
$647$	−27280.4			−1.65765			−0.828827	−	0.559504i	$-0.810992\pi$
$647$	−27280.4			−1.65765			−0.828827	+	0.559504i	$0.810992\pi$
$648$	−56.1813	+	2591.78i	−0.00340588	+	0.157121i
$649$		−	16997.3i		−	1.02804i
$650$	−2975.34			−0.179542
$651$		0			0
$652$	5286.14			0.317517
$653$		−	13193.1i		−	0.790635i	−0.918545	−	0.395317i	$-0.870635\pi$
$653$		−	13193.1i		−	0.790635i	0.918545	−	0.395317i	$-0.129365\pi$
$654$	−1208.43	−	1221.60i	−0.0722529	−	0.0730401i
$655$	−20629.6			−1.23063
$656$	16013.0			0.953055
$657$	10.6718	+	0.115652i	0.000633710	+	6.86757e-6i
$658$		0			0
$659$			17560.9i			1.03805i	0.854759	+	0.519026i	$0.173705\pi$
$659$			17560.9i			1.03805i	−0.854759	+	0.519026i	$0.826295\pi$
$660$	24889.1	+	25160.3i	1.46789	+	1.48388i
$661$			21645.5i			1.27369i	0.770991	+	0.636846i	$0.219761\pi$
$661$			21645.5i			1.27369i	−0.770991	+	0.636846i	$0.780239\pi$
$662$		−	1273.54i		−	0.0747694i
$663$	6277.83	+	6346.23i	0.367738	+	0.371745i
$664$		−	2085.04i		−	0.121860i
$665$		0			0
$666$	145.443	+	1.57618i	0.00846214	+	9.17051e-5i
$667$	−266.731			−0.0154840
$668$	701.686			0.0406423
$669$	−12379.1	−	12513.9i	−0.715400	−	0.723194i
$670$			1810.29i			0.104385i
$671$	31895.0			1.83501
$672$		0			0
$673$	−14429.9			−0.826498			−0.413249	−	0.910618i	$-0.635606\pi$
$673$	−14429.9			−0.826498			−0.413249	+	0.910618i	$0.635606\pi$
$674$		−	2021.69i		−	0.115538i
$675$	−21932.7	−	22657.6i	−1.25065	−	1.29199i
$676$	−10560.1			−0.600826
$677$	16185.5			0.918849			0.459424	−	0.888217i	$-0.348056\pi$
$677$	16185.5			0.918849			0.459424	+	0.888217i	$0.348056\pi$
$678$	1371.47	−	1356.69i	0.0776857	−	0.0768484i
$679$		0			0
$680$		−	1924.31i		−	0.108521i
$681$	−8583.67	+	8491.16i	−0.483006	+	0.477800i
$682$			1062.65i			0.0596639i
$683$			25233.4i			1.41366i	0.707385	+	0.706828i	$0.249875\pi$
$683$			25233.4i			1.41366i	−0.707385	+	0.706828i	$0.750125\pi$
$684$	8358.63	+	90.5834i	0.467252	+	0.00506366i
$685$			40564.2i			2.26259i
$686$		0			0
$687$	1026.40	+	1037.59i	0.0570011	+	0.0576222i
$688$	−3747.24			−0.207649
$689$	22658.8			1.25287
$690$	−27.6180	+	27.3203i	−0.00152377	+	0.00150734i
$691$			2028.23i			0.111661i	0.998440	+	0.0558304i	$0.0177806\pi$
$691$			2028.23i			0.111661i	−0.998440	+	0.0558304i	$0.982219\pi$
$692$	−21706.7			−1.19243
$693$		0			0
$694$	1921.01			0.105073
$695$			42021.7i			2.29349i
$696$	1954.17	−	1933.10i	0.106426	−	0.105279i
$697$	−7376.67			−0.400877
$698$	1776.03			0.0963088
$699$	5699.88	+	5761.98i	0.308425	+	0.311786i
$700$		0			0
$701$		−	33881.6i		−	1.82552i	−0.408497	−	0.912760i	$-0.633947\pi$
$701$		−	33881.6i		−	1.82552i	0.408497	−	0.912760i	$-0.366053\pi$
$702$	1291.68	+	1334.37i	0.0694463	+	0.0717415i
$703$		−	940.944i		−	0.0504813i
$704$		−	22583.5i		−	1.20902i
$705$	−18145.7	+	17950.2i	−0.969373	+	0.958925i
$706$			2736.64i			0.145885i
$707$		0			0
$708$	10897.7	−	10780.2i	0.578476	−	0.572241i
$709$	−17416.8			−0.922570			−0.461285	−	0.887252i	$-0.652611\pi$
$709$	−17416.8			−0.922570			−0.461285	+	0.887252i	$0.652611\pi$
$710$	3438.90			0.181774
$711$	−213.957	+	19743.0i	−0.0112855	+	1.04138i
$712$			1565.69i			0.0824109i
$713$	186.570			0.00979956
$714$		0			0
$715$	50865.3			2.66050
$716$			12885.0i			0.672536i
$717$	4921.94	+	4975.57i	0.256364	+	0.259157i
$718$	2594.45			0.134852
$719$	−31681.3			−1.64327			−0.821637	−	0.570010i	$-0.806939\pi$
$719$	−31681.3			−1.64327			−0.821637	+	0.570010i	$0.806939\pi$
$720$	−343.691	+	31714.3i	−0.0177897	+	1.64156i
$721$		0			0
$722$		−	1191.11i		−	0.0613969i
$723$	−14744.0	−	14904.6i	−0.758416	−	0.766680i
$724$			11397.7i			0.585070i
$725$			33436.4i			1.71283i
$726$	625.134	+	631.946i	0.0319572	+	0.0323054i
$727$		−	19420.1i		−	0.990719i	−0.868688	−	0.495360i	$-0.835036\pi$
$727$		−	19420.1i		−	0.990719i	0.868688	−	0.495360i	$-0.164964\pi$
$728$		0			0
$729$	−639.782	+	19672.6i	−0.0325043	+	0.999472i
$730$	−1.64814			−8.35623e−5
$731$	1726.23			0.0873419
$732$	20228.9	+	20449.3i	1.02142	+	1.03255i
$733$			13762.9i			0.693513i	0.937955	+	0.346756i	$0.112717\pi$
$733$			13762.9i			0.693513i	−0.937955	+	0.346756i	$0.887283\pi$
$734$	−543.063			−0.0273090
$735$		0			0
$736$	76.1181			0.00381216
$737$		−	19887.9i		−	0.994001i
$738$	−1534.58	−	16.6304i	−0.0765429	−	0.000829503i
$739$	14792.1			0.736316			0.368158	−	0.929763i	$-0.379988\pi$
$739$	14792.1			0.736316			0.368158	+	0.929763i	$0.379988\pi$
$740$	3592.73			0.178475
$741$	8541.17	−	8449.11i	0.423438	−	0.418874i
$742$		0			0
$743$		−	24521.7i		−	1.21078i	−0.795928	−	0.605392i	$-0.793016\pi$
$743$		−	24521.7i		−	1.21078i	0.795928	−	0.605392i	$-0.206984\pi$
$744$	−1366.88	+	1352.15i	−0.0673551	+	0.0666291i
$745$		−	29068.0i		−	1.42949i
$746$		−	534.667i		−	0.0262407i
$747$	171.551	−	15830.0i	0.00840258	−	0.775354i
$748$			10537.3i			0.515084i
$749$		0			0
$750$	1520.18	+	1536.74i	0.0740120	+	0.0748184i
$751$	8398.16			0.408060			0.204030	−	0.978965i	$-0.434596\pi$
$751$	8398.16			0.408060			0.204030	+	0.978965i	$0.434596\pi$
$752$	16496.9			0.799972
$753$	−2164.09	+	2140.77i	−0.104733	+	0.103604i
$754$		−	1969.16i		−	0.0951097i
$755$	35132.5			1.69351
$756$		0			0
$757$	−18400.3			−0.883446			−0.441723	−	0.897151i	$-0.645633\pi$
$757$	−18400.3			−0.883446			−0.441723	+	0.897151i	$0.645633\pi$
$758$			1625.55i			0.0778925i
$759$	303.412	−	300.142i	0.0145101	−	0.0143537i
$760$	−2589.86			−0.123611
$761$	−31893.4			−1.51923			−0.759616	−	0.650372i	$-0.774613\pi$
$761$	−31893.4			−1.51923			−0.759616	+	0.650372i	$0.774613\pi$
$762$	1453.80	+	1469.64i	0.0691147	+	0.0698678i
$763$		0			0
$764$		−	4304.20i		−	0.203823i
$765$	158.327	−	14609.7i	0.00748277	−	0.690478i
$766$		−	2096.30i		−	0.0988806i
$767$		−	22031.3i		−	1.03716i
$768$	14199.6	−	14046.6i	0.667167	−	0.659976i
$769$			21058.0i			0.987478i	0.869610	+	0.493739i	$0.164370\pi$
$769$			21058.0i			0.987478i	−0.869610	+	0.493739i	$0.835630\pi$
$770$		0			0
$771$	6534.47	−	6464.04i	0.305231	−	0.301941i
$772$	−39356.4			−1.83480
$773$	−37818.8			−1.75970			−0.879849	−	0.475254i	$-0.842356\pi$
$773$	−37818.8			−1.75970			−0.879849	+	0.475254i	$0.842356\pi$
$774$	359.110	+	3.89171i	0.0166769	+	0.000180730i
$775$		−	23387.7i		−	1.08402i
$776$	−2255.35			−0.104333
$777$		0			0
$778$	65.2459			0.00300666
$779$			9928.00i			0.456621i
$780$	32260.5	+	32612.0i	1.48091	+	1.49705i
$781$	−37779.8			−1.73095
$782$	−11.5666			−0.000528928
$783$	14995.4	−	14515.7i	0.684410	−	0.662514i
$784$		0			0
$785$			855.352i			0.0388902i
$786$	−898.677	−	908.469i	−0.0407821	−	0.0412265i
$787$		−	1973.27i		−	0.0893766i	−0.999001	−	0.0446883i	$-0.985771\pi$
$787$		−	1973.27i		−	0.0893766i	0.999001	−	0.0446883i	$-0.0142295\pi$
$788$		−	29213.4i		−	1.32067i
$789$	28639.8	+	28951.9i	1.29227	+	1.30635i
$790$		−	3049.08i		−	0.137318i
$791$		0			0
$792$	−47.6604	+	4397.90i	−0.00213831	+	0.197314i
$793$	41341.4			1.85129
$794$	1487.87			0.0665019
$795$	−26081.5	−	26365.7i	−1.16354	−	1.17622i
$796$			18462.4i			0.822087i
$797$	7865.72			0.349583			0.174792	−	0.984605i	$-0.444075\pi$
$797$	7865.72			0.349583			0.174792	+	0.984605i	$0.444075\pi$
$798$		0			0
$799$	−7599.56			−0.336487
$800$		−	9541.91i		−	0.421697i
$801$	−128.820	+	11887.0i	−0.00568244	+	0.524351i
$802$	−507.132			−0.0223285
$803$	18.1065			0.000795722
$804$	12751.0	−	12613.6i	0.559320	−	0.553291i
$805$		0			0
$806$			1377.37i			0.0601932i
$807$	17680.4	−	17489.8i	0.771225	−	0.762913i
$808$		−	5454.71i		−	0.237495i
$809$			13314.4i			0.578628i	0.957234	+	0.289314i	$0.0934272\pi$
$809$			13314.4i			0.578628i	−0.957234	+	0.289314i	$0.906573\pi$
$810$	65.8740	−	3038.93i	0.00285750	−	0.131823i
$811$			17376.6i			0.752374i	0.926544	+	0.376187i	$0.122765\pi$
$811$			17376.6i			0.752374i	−0.926544	+	0.376187i	$0.877235\pi$
$812$		0			0
$813$	7633.59	+	7716.77i	0.329301	+	0.332889i
$814$	246.768			0.0106255
$815$	−12435.0			−0.534454
$816$	−6713.44	+	6641.08i	−0.288012	+	0.284907i
$817$		−	2323.27i		−	0.0994871i
$818$	3253.22			0.139054
$819$		0			0
$820$	−37907.2			−1.61436
$821$		−	5793.64i		−	0.246284i	−0.992389	−	0.123142i	$-0.960703\pi$
$821$		−	5793.64i		−	0.246284i	0.992389	−	0.123142i	$-0.0392971\pi$
$822$	−1786.33	+	1767.08i	−0.0757974	+	0.0749804i
$823$	26470.7			1.12115			0.560577	−	0.828103i	$-0.310580\pi$
$823$	26470.7			1.12115			0.560577	+	0.828103i	$0.310580\pi$
$824$	4317.68			0.182541
$825$	−37624.7	−	38034.7i	−1.58779	−	1.60509i
$826$		0			0
$827$			8572.60i			0.360458i	0.983625	+	0.180229i	$0.0576838\pi$
$827$			8572.60i			0.360458i	−0.983625	+	0.180229i	$0.942316\pi$
$828$	384.868	+	4.17086i	0.0161535	+	0.000175057i
$829$			3151.37i			0.132028i	0.997819	+	0.0660141i	$0.0210282\pi$
$829$			3151.37i			0.132028i	−0.997819	+	0.0660141i	$0.978972\pi$
$830$			2444.76i			0.102240i
$831$	5826.58	−	5763.78i	0.243227	−	0.240606i
$832$		−	29272.1i		−	1.21974i
$833$		0			0
$834$	−1850.52	+	1830.57i	−0.0768324	+	0.0760043i
$835$	−1650.63			−0.0684102
$836$	14181.8			0.586708
$837$	−10488.8	+	10153.3i	−0.433150	+	0.419293i
$838$		−	2695.59i		−	0.111119i
$839$	−47134.1			−1.93951			−0.969755	−	0.244082i	$-0.921513\pi$
$839$	−47134.1			−1.93951			−0.969755	+	0.244082i	$0.921513\pi$
$840$		0			0
$841$	2259.85			0.0926587
$842$		−	1612.02i		−	0.0659785i
$843$	−17336.0	−	17524.9i	−0.708283	−	0.716001i
$844$	32178.9			1.31237
$845$	24841.4			1.01133
$846$	−1580.95	−	17.1329i	−0.0642484	−	0.000696266i
$847$		0			0
$848$			23969.9i			0.970671i
$849$	145.313	+	146.896i	0.00587412	+	0.00593813i
$850$			1449.95i			0.0585093i
$851$		−	43.3252i		−	0.00174520i
$852$	−23961.3	−	24222.3i	−0.963497	−	0.973995i
$853$			24635.1i			0.988849i	0.869221	+	0.494424i	$0.164621\pi$
$853$			24635.1i			0.988849i	−0.869221	+	0.494424i	$0.835379\pi$
$854$		0			0
$855$	−19662.7	−	213.087i	−0.786492	−	0.00852329i
$856$	−6381.58			−0.254811
$857$	115.941			0.00462133			0.00231067	−	0.999997i	$-0.499264\pi$
$857$	115.941			0.00462133			0.00231067	+	0.999997i	$0.499264\pi$
$858$	2215.82	+	2239.97i	0.0881666	+	0.0891272i
$859$		−	3735.89i		−	0.148390i	−0.997244	−	0.0741950i	$-0.976361\pi$
$859$		−	3735.89i		−	0.148390i	0.997244	−	0.0741950i	$-0.0236387\pi$
$860$	8870.75			0.351733
$861$		0			0
$862$	423.849			0.0167475
$863$			9534.46i			0.376080i	0.982161	+	0.188040i	$0.0602134\pi$
$863$			9534.46i			0.376080i	−0.982161	+	0.188040i	$0.939787\pi$
$864$	−4279.31	+	4142.41i	−0.168501	+	0.163111i
$865$	51062.5			2.00714
$866$	416.258			0.0163338
$867$	−15056.4	+	14894.1i	−0.589783	+	0.583426i
$868$		0			0
$869$			33497.3i			1.30761i
$870$	−2291.31	+	2266.62i	−0.0892905	+	0.0883281i
$871$		−	25778.0i		−	1.00282i
$872$		−	5274.60i		−	0.204840i
$873$	−17123.0	−	185.564i	−0.663834	−	0.00719404i
$874$			15.5671i			0.000602478i
$875$		0			0
$876$	11.4838	+	11.6089i	0.000442923	+	0.000447749i
$877$	18980.7			0.730825			0.365412	−	0.930846i	$-0.380928\pi$
$877$	18980.7			0.730825			0.365412	+	0.930846i	$0.380928\pi$
$878$	1616.24			0.0621245
$879$	−250.884	+	248.180i	−0.00962697	+	0.00952320i
$880$			53808.5i			2.06123i
$881$	−46006.5			−1.75936			−0.879682	−	0.475563i	$-0.842244\pi$
$881$	−46006.5			−1.75936			−0.879682	+	0.475563i	$0.842244\pi$
$882$		0			0
$883$	17460.6			0.665455			0.332728	−	0.943023i	$-0.392031\pi$
$883$	17460.6			0.665455			0.332728	+	0.943023i	$0.392031\pi$
$884$			13658.1i			0.519653i
$885$	−25635.6	+	25359.3i	−0.973707	+	0.963212i
$886$	−2277.04			−0.0863415
$887$	4844.77			0.183395			0.0916975	−	0.995787i	$-0.470771\pi$
$887$	4844.77			0.183395			0.0916975	+	0.995787i	$0.470771\pi$
$888$	313.995	+	317.417i	0.0118660	+	0.0119953i
$889$		0			0
$890$		−	1835.81i		−	0.0691420i
$891$	−723.692	+	33385.7i	−0.0272106	+	1.25529i
$892$		−	26932.1i		−	1.01093i
$893$			10228.0i			0.383277i
$894$	1280.07	−	1266.27i	0.0478881	−	0.0473720i
$895$		−	30310.5i		−	1.13203i
$896$		0			0
$897$	393.273	−	389.034i	0.0146388	−	0.0144810i
$898$	1229.66			0.0456951
$899$	15478.6			0.574240
$900$	522.844	−	48245.8i	0.0193646	−	1.78688i
$901$		−	11042.1i		−	0.408287i
$902$	−2603.67			−0.0961117
$903$		0			0
$904$	5921.71			0.217868
$905$		−	26811.7i		−	0.984806i
$906$	1530.46	+	1547.14i	0.0561216	+	0.0567331i
$907$	24674.0			0.903294			0.451647	−	0.892197i	$-0.350837\pi$
$907$	24674.0			0.903294			0.451647	+	0.892197i	$0.350837\pi$
$908$	−18473.5			−0.675181
$909$	448.798	−	41413.1i	0.0163759	−	1.51110i
$910$		0			0
$911$		−	27995.1i		−	1.01813i	−0.860727	−	0.509067i	$-0.829990\pi$
$911$		−	27995.1i		−	1.01813i	0.860727	−	0.509067i	$-0.170010\pi$
$912$	8938.00	+	9035.39i	0.324525	+	0.328061i
$913$		−	26858.2i		−	0.973578i
$914$			1754.07i			0.0634786i
$915$	−47586.2	−	48104.7i	−1.71929	−	1.73802i
$916$			2233.06i			0.0805485i
$917$		0			0
$918$	650.268	−	629.464i	0.0233791	−	0.0226312i
$919$	43522.2			1.56220			0.781102	−	0.624403i	$-0.214658\pi$
$919$	43522.2			1.56220			0.781102	+	0.624403i	$0.214658\pi$
$920$	−119.249			−0.00427339
$921$	−3092.05	−	3125.74i	−0.110626	−	0.111831i
$922$		−	230.690i		−	0.00824011i
$923$	−48969.0			−1.74630
$924$		0			0
$925$	−5431.10			−0.193052
$926$		−	3963.51i		−	0.140658i
$927$	32780.6	+	355.246i	1.16144	+	0.0125866i
$928$	6315.09			0.223387
$929$	21771.5			0.768892			0.384446	−	0.923148i	$-0.374393\pi$
$929$	21771.5			0.768892			0.384446	+	0.923148i	$0.374393\pi$
$930$	1602.70	−	1585.43i	0.0565103	−	0.0559012i
$931$		0			0
$932$			12400.7i			0.435837i
$933$	−12291.8	+	12159.3i	−0.431313	+	0.426664i
$934$			399.610i			0.0139996i
$935$		−	24787.8i		−	0.867003i
$936$	−61.7760	+	5700.41i	−0.00215728	+	0.199064i
$937$		−	18715.6i		−	0.652521i	−0.945280	−	0.326260i	$-0.894211\pi$
$937$		−	18715.6i		−	0.652521i	0.945280	−	0.326260i	$-0.105789\pi$
$938$		0			0
$939$	−28563.6	−	28874.8i	−0.992691	−	1.00351i
$940$	−39052.6			−1.35506
$941$	−16024.4			−0.555133			−0.277567	−	0.960706i	$-0.589528\pi$
$941$	−16024.4			−0.555133			−0.277567	+	0.960706i	$0.589528\pi$
$942$	−37.6673	+	37.2613i	−0.00130283	+	0.00128879i
$943$			457.129i			0.0157860i
$944$	23306.1			0.803549
$945$		0			0
$946$	609.290			0.0209405
$947$		−	50339.0i		−	1.72735i	−0.504053	−	0.863673i	$-0.668158\pi$
$947$		−	50339.0i		−	1.72735i	0.504053	−	0.863673i	$-0.331842\pi$
$948$	−21476.6	+	21245.1i	−0.735788	+	0.727858i
$949$	23.4691			0.000802780
$950$	1951.44			0.0666453
$951$	8270.22	+	8360.33i	0.281998	+	0.285071i
$952$		0			0
$953$			46401.8i			1.57723i	0.614887	+	0.788615i	$0.289202\pi$
$953$			46401.8i			1.57723i	−0.614887	+	0.788615i	$0.710798\pi$
$954$	24.8940	−	2297.11i	0.000844836	−	0.0779578i
$955$			10125.1i			0.343080i
$956$			10708.2i			0.362269i
$957$	25172.4	−	24901.1i	0.850269	−	0.841104i
$958$		−	2797.64i		−	0.0943503i
$959$		0			0
$960$	−34060.9	+	33693.7i	−1.14511	+	1.13277i
$961$	18964.2			0.636574
$962$	319.852			0.0107198
$963$	−48450.1	−	525.058i	−1.62127	−	0.0175698i
$964$		−	32077.3i		−	1.07172i
$965$	92581.3			3.08839
$966$		0			0
$967$	27821.0			0.925195			0.462597	−	0.886569i	$-0.346918\pi$
$967$	27821.0			0.925195			0.462597	+	0.886569i	$0.346918\pi$
$968$			2728.61i			0.0906000i
$969$	−4117.44	−	4162.30i	−0.136503	−	0.137990i
$970$	2644.46			0.0875346
$971$	7488.77			0.247504			0.123752	−	0.992313i	$-0.460507\pi$
$971$	7488.77			0.247504			0.123752	+	0.992313i	$0.460507\pi$
$972$	−21864.0	+	20710.3i	−0.721491	+	0.683420i
$973$		0			0
$974$			998.920i			0.0328619i
$975$	−48768.0	−	49299.3i	−1.60187	−	1.61933i
$976$			43733.5i			1.43430i
$977$		−	37379.7i		−	1.22404i	−0.790844	−	0.612018i	$-0.790358\pi$
$977$		−	37379.7i		−	1.22404i	0.790844	−	0.612018i	$-0.209642\pi$
$978$	−541.702	−	547.604i	−0.0177114	−	0.0179043i
$979$			20168.2i			0.658405i
$980$		0			0
$981$	433.979	−	40045.7i	0.0141242	−	1.30332i
$982$	3327.32			0.108125
$983$	−13675.3			−0.443718			−0.221859	−	0.975079i	$-0.571212\pi$
$983$	−13675.3			−0.443718			−0.221859	+	0.975079i	$0.571212\pi$
$984$	−3313.00	−	3349.09i	−0.107332	−	0.108501i
$985$			68721.1i			2.22298i
$986$	−959.618			−0.0309944
$987$		0			0
$988$	18382.0			0.591913
$989$		−	106.974i		−	0.00343940i
$990$	55.8831	−	5156.65i	0.00179402	−	0.165544i
$991$	7130.49			0.228565			0.114282	−	0.993448i	$-0.463543\pi$
$991$	7130.49			0.228565			0.114282	+	0.993448i	$0.463543\pi$
$992$	−4417.21			−0.141378
$993$	21101.6	−	20874.1i	0.674359	−	0.667090i
$994$		0			0
$995$		−	43430.5i		−	1.38376i
$996$	17220.0	−	17034.4i	0.547828	−	0.541923i
$997$			10629.0i			0.337638i	0.985647	+	0.168819i	$0.0539953\pi$
$997$			10629.0i			0.337638i	−0.985647	+	0.168819i	$0.946005\pi$
$998$		−	1037.42i		−	0.0329047i
$999$	2357.79	+	2435.72i	0.0746719	+	0.0771398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.b.146.12	yes	24
3.2	odd	2	inner	147.4.c.b.146.13	yes	24
7.2	even	3		147.4.g.e.80.12		48
7.3	odd	6		147.4.g.e.68.14		48
7.4	even	3		147.4.g.e.68.13		48
7.5	odd	6		147.4.g.e.80.11		48
7.6	odd	2	inner	147.4.c.b.146.11	✓	24
21.2	odd	6		147.4.g.e.80.14		48
21.5	even	6		147.4.g.e.80.13		48
21.11	odd	6		147.4.g.e.68.11		48
21.17	even	6		147.4.g.e.68.12		48
21.20	even	2	inner	147.4.c.b.146.14	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.c.b.146.11	✓	24	7.6	odd	2	inner
147.4.c.b.146.12	yes	24	1.1	even	1	trivial
147.4.c.b.146.13	yes	24	3.2	odd	2	inner
147.4.c.b.146.14	yes	24	21.20	even	2	inner
147.4.g.e.68.11		48	21.11	odd	6
147.4.g.e.68.12		48	21.17	even	6
147.4.g.e.68.13		48	7.4	even	3
147.4.g.e.68.14		48	7.3	odd	6
147.4.g.e.80.11		48	7.5	odd	6
147.4.g.e.80.12		48	7.2	even	3
147.4.g.e.80.13		48	21.5	even	6
147.4.g.e.80.14		48	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.222948i q^{2} +(3.69409 - 3.65427i) q^{3} +7.95029 q^{4} -18.7021 q^{5} +(-0.814713 - 0.823589i) q^{6} -3.55609i q^{8} +(0.292585 - 26.9984i) q^{9} +O(q^{10})\)	\(q-0.222948i q^{2} +(3.69409 - 3.65427i) q^{3} +7.95029 q^{4} -18.7021 q^{5} +(-0.814713 - 0.823589i) q^{6} -3.55609i q^{8} +(0.292585 - 26.9984i) q^{9} +4.16960i q^{10} -45.8073i q^{11} +(29.3691 - 29.0525i) q^{12} -59.3740i q^{13} +(-69.0873 + 68.3427i) q^{15} +62.8095 q^{16} -28.9343 q^{17} +(-6.01924 - 0.0652311i) q^{18} +38.9416i q^{19} -148.687 q^{20} -10.2126 q^{22} +1.79304i q^{23} +(-12.9949 - 13.1365i) q^{24} +224.770 q^{25} -13.2373 q^{26} +(-97.5787 - 100.804i) q^{27} +148.759i q^{29} +(15.2369 + 15.4029i) q^{30} -104.052i q^{31} -42.4519i q^{32} +(-167.392 - 169.216i) q^{33} +6.45083i q^{34} +(2.32613 - 214.645i) q^{36} -24.1630 q^{37} +8.68195 q^{38} +(-216.969 - 219.333i) q^{39} +66.5064i q^{40} +254.946 q^{41} -59.6604 q^{43} -364.181i q^{44} +(-5.47195 + 504.928i) q^{45} +0.399755 q^{46} +262.649 q^{47} +(232.024 - 229.523i) q^{48} -50.1119i q^{50} +(-106.886 + 105.734i) q^{51} -472.040i q^{52} +381.628i q^{53} +(-22.4740 + 21.7550i) q^{54} +856.694i q^{55} +(142.303 + 143.854i) q^{57} +33.1654 q^{58} +371.060 q^{59} +(-549.265 + 543.344i) q^{60} +696.288i q^{61} -23.1982 q^{62} +493.012 q^{64} +1110.42i q^{65} +(-37.7264 + 37.3198i) q^{66} +434.164 q^{67} -230.036 q^{68} +(6.55227 + 6.62366i) q^{69} -824.756i q^{71} +(-96.0087 - 1.04046i) q^{72} +0.395276i q^{73} +5.38708i q^{74} +(830.319 - 821.370i) q^{75} +309.597i q^{76} +(-48.8998 + 48.3727i) q^{78} -731.265 q^{79} -1174.67 q^{80} +(-728.829 - 15.7986i) q^{81} -56.8397i q^{82} +586.330 q^{83} +541.132 q^{85} +13.3012i q^{86} +(543.605 + 549.528i) q^{87} -162.895 q^{88} -440.284 q^{89} +(112.573 + 1.21996i) q^{90} +14.2552i q^{92} +(-380.234 - 384.377i) q^{93} -58.5571i q^{94} -728.291i q^{95} +(-155.131 - 156.821i) q^{96} -634.224i q^{97} +(-1236.72 - 13.4025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 24 * q - 96 * q^4 - 64 * q^9	\( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more