LMFDB - Embedded newform 52.3.k.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,3,Mod(33,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("52.33");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	52.k (of order $12$, degree $4$, 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:	$1.41689737467$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.44991500544.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 38x^{6} + 555x^{4} - 3674x^{2} + 9409 $ x^8 - 38x^6 + 555x^4 - 3674*x^2 + 9409
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			33.2
Root			$2.83160 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	52.33
Dual form			52.3.k.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.84881 - 3.20224i) q^{3} +(-2.68502 - 2.68502i) q^{5} +(3.21484 + 0.861413i) q^{7} +(-2.33621 - 4.04644i) q^{9} +(3.45758 + 12.9039i) q^{11} +(10.7063 - 7.37401i) q^{13} +(-13.5622 + 3.63397i) q^{15} +(-18.0473 + 10.4196i) q^{17} +(-8.17703 + 30.5171i) q^{19} +(8.70208 - 8.70208i) q^{21} +(-20.2227 - 11.6756i) q^{23} -10.5813i q^{25} +16.0018 q^{27} +(16.7306 - 28.9782i) q^{29} +(15.6552 + 15.6552i) q^{31} +(47.7137 + 12.7848i) q^{33} +(-6.31900 - 10.9448i) q^{35} +(-4.36965 - 16.3078i) q^{37} +(-3.81948 - 47.9171i) q^{39} +(-58.8233 + 15.7617i) q^{41} +(43.5891 - 25.1662i) q^{43} +(-4.59199 + 17.1375i) q^{45} +(1.03863 - 1.03863i) q^{47} +(-32.8421 - 18.9614i) q^{49} +77.0557i q^{51} -63.7629 q^{53} +(25.3635 - 43.9309i) q^{55} +(82.6052 + 82.6052i) q^{57} +(-26.8080 - 7.18318i) q^{59} +(46.2192 + 80.0541i) q^{61} +(-4.02488 - 15.0211i) q^{63} +(-48.5459 - 8.94714i) q^{65} +(-40.1854 + 10.7676i) q^{67} +(-74.7758 + 43.1718i) q^{69} +(15.6576 - 58.4350i) q^{71} +(36.8238 - 36.8238i) q^{73} +(-33.8838 - 19.5628i) q^{75} +44.4623i q^{77} -106.238 q^{79} +(50.6101 - 87.6593i) q^{81} +(96.6176 + 96.6176i) q^{83} +(76.4344 + 20.4805i) q^{85} +(-61.8634 - 107.151i) q^{87} +(-6.66127 - 24.8602i) q^{89} +(40.7709 - 14.4837i) q^{91} +(79.0750 - 21.1881i) q^{93} +(103.895 - 59.9836i) q^{95} +(4.20302 - 15.6859i) q^{97} +(44.1371 - 44.1371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9} + 24 q^{11} + 18 q^{13} - 60 q^{15} - 54 q^{17} - 50 q^{19} - 54 q^{21} - 24 q^{23} + 36 q^{27} + 108 q^{29} + 176 q^{31} + 114 q^{33} - 30 q^{35} + 104 q^{37} + 120 q^{39}+ \cdots + 182 q^{97}+O(q^{100}) $ 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9 + 24 * q^11 + 18 * q^13 - 60 * q^15 - 54 * q^17 - 50 * q^19 - 54 * q^21 - 24 * q^23 + 36 * q^27 + 108 * q^29 + 176 * q^31 + 114 * q^33 - 30 * q^35 + 104 * q^37 + 120 * q^39 - 168 * q^41 - 198 * q^43 + 6 * q^45 - 96 * q^47 - 162 * q^49 - 72 * q^53 + 126 * q^55 + 318 * q^57 - 18 * q^61 + 180 * q^63 - 72 * q^65 - 326 * q^67 - 498 * q^69 - 162 * q^71 - 98 * q^73 - 240 * q^75 + 192 * q^79 + 240 * q^81 + 408 * q^83 + 318 * q^85 + 36 * q^87 + 54 * q^89 + 280 * q^91 - 66 * q^93 + 312 * q^95 + 182 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.84881	−	3.20224i	0.616271	−	1.06741i	−0.373890	−	0.927473i	$-0.621976\pi$
$3$	1.84881	−	3.20224i	0.616271	−	1.06741i	0.990160	−	0.139939i	$-0.0446906\pi$
$4$		0			0
$5$	−2.68502	−	2.68502i	−0.537005	−	0.537005i	0.385643	−	0.922648i	$-0.373980\pi$
$5$	−2.68502	−	2.68502i	−0.537005	−	0.537005i	−0.922648	+	0.385643i	$0.873980\pi$
$6$		0			0
$7$	3.21484	+	0.861413i	0.459262	+	0.123059i	0.481030	−	0.876704i	$-0.340263\pi$
$7$	3.21484	+	0.861413i	0.459262	+	0.123059i	−0.0217677	+	0.999763i	$0.506929\pi$
$8$		0			0
$9$	−2.33621	−	4.04644i	−0.259579	−	0.449604i
$10$		0			0
$11$	3.45758	+	12.9039i	0.314326	+	1.17308i	0.924616	+	0.380902i	$0.124386\pi$
$11$	3.45758	+	12.9039i	0.314326	+	1.17308i	−0.610290	+	0.792178i	$0.708947\pi$
$12$		0			0
$13$	10.7063	−	7.37401i	0.823558	−	0.567232i
$13$	10.7063	−	7.37401i	0.823558	−	0.567232i
$14$		0			0
$15$	−13.5622	+	3.63397i	−0.904145	+	0.242265i
$16$		0			0
$17$	−18.0473	+	10.4196i	−1.06161	+	0.612919i	−0.925876	−	0.377827i	$-0.876671\pi$
$17$	−18.0473	+	10.4196i	−1.06161	+	0.612919i	−0.135730	+	0.990746i	$0.543338\pi$
$18$		0			0
$19$	−8.17703	+	30.5171i	−0.430370	+	1.60616i	0.321539	+	0.946896i	$0.395800\pi$
$19$	−8.17703	+	30.5171i	−0.430370	+	1.60616i	−0.751909	+	0.659267i	$0.770867\pi$
$20$		0			0
$21$	8.70208	−	8.70208i	0.414385	−	0.414385i
$22$		0			0
$23$	−20.2227	−	11.6756i	−0.879246	−	0.507633i	−0.00883654	−	0.999961i	$-0.502813\pi$
$23$	−20.2227	−	11.6756i	−0.879246	−	0.507633i	−0.870410	+	0.492328i	$0.836146\pi$
$24$		0			0
$25$		−	10.5813i		−	0.423252i
$26$		0			0
$27$	16.0018			0.592658
$28$		0			0
$29$	16.7306	−	28.9782i	0.576917	−	0.999249i	−0.418914	−	0.908026i	$-0.637589\pi$
$29$	16.7306	−	28.9782i	0.576917	−	0.999249i	0.995831	−	0.0912228i	$-0.0290776\pi$
$30$		0			0
$31$	15.6552	+	15.6552i	0.505005	+	0.505005i	0.912989	−	0.407984i	$-0.133768\pi$
$31$	15.6552	+	15.6552i	0.505005	+	0.505005i	−0.407984	+	0.912989i	$0.633768\pi$
$32$		0			0
$33$	47.7137	+	12.7848i	1.44587	+	0.387420i
$34$		0			0
$35$	−6.31900	−	10.9448i	−0.180543	−	0.312709i
$36$		0			0
$37$	−4.36965	−	16.3078i	−0.118099	−	0.440750i	0.881401	−	0.472368i	$-0.156601\pi$
$37$	−4.36965	−	16.3078i	−0.118099	−	0.440750i	−0.999500	+	0.0316179i	$0.989934\pi$
$38$		0			0
$39$	−3.81948	−	47.9171i	−0.0979354	−	1.22864i
$40$		0			0
$41$	−58.8233	+	15.7617i	−1.43472	+	0.384431i	−0.890680	−	0.454631i	$-0.849771\pi$
$41$	−58.8233	+	15.7617i	−1.43472	+	0.384431i	−0.544036	+	0.839062i	$0.683104\pi$
$42$		0			0
$43$	43.5891	−	25.1662i	1.01370	−	0.585260i	0.101427	−	0.994843i	$-0.467659\pi$
$43$	43.5891	−	25.1662i	1.01370	−	0.585260i	0.912273	+	0.409583i	$0.134326\pi$
$44$		0			0
$45$	−4.59199	+	17.1375i	−0.102044	+	0.380834i
$46$		0			0
$47$	1.03863	−	1.03863i	0.0220986	−	0.0220986i	−0.695971	−	0.718070i	$-0.745026\pi$
$47$	1.03863	−	1.03863i	0.0220986	−	0.0220986i	0.718070	+	0.695971i	$0.245026\pi$
$48$		0			0
$49$	−32.8421	−	18.9614i	−0.670247	−	0.386967i
$50$		0			0
$51$			77.0557i			1.51090i
$52$		0			0
$53$	−63.7629			−1.20307			−0.601537	−	0.798845i	$-0.705445\pi$
$53$	−63.7629			−1.20307			−0.601537	+	0.798845i	$0.705445\pi$
$54$		0			0
$55$	25.3635	−	43.9309i	0.461155	−	0.798744i
$56$		0			0
$57$	82.6052	+	82.6052i	1.44921	+	1.44921i
$58$		0			0
$59$	−26.8080	−	7.18318i	−0.454373	−	0.121749i	0.0243720	−	0.999703i	$-0.492241\pi$
$59$	−26.8080	−	7.18318i	−0.454373	−	0.121749i	−0.478745	+	0.877954i	$0.658908\pi$
$60$		0			0
$61$	46.2192	+	80.0541i	0.757692	+	1.31236i	0.944025	+	0.329875i	$0.107007\pi$
$61$	46.2192	+	80.0541i	0.757692	+	1.31236i	−0.186332	+	0.982487i	$0.559660\pi$
$62$		0			0
$63$	−4.02488	−	15.0211i	−0.0638871	−	0.238430i
$64$		0			0
$65$	−48.5459	−	8.94714i	−0.746861	−	0.137648i
$66$		0			0
$67$	−40.1854	+	10.7676i	−0.599782	+	0.160711i	−0.545920	−	0.837837i	$-0.683820\pi$
$67$	−40.1854	+	10.7676i	−0.599782	+	0.160711i	−0.0538618	+	0.998548i	$0.517153\pi$
$68$		0			0
$69$	−74.7758	+	43.1718i	−1.08371	+	0.625679i
$70$		0			0
$71$	15.6576	−	58.4350i	0.220530	−	0.823028i	−0.763617	−	0.645670i	$-0.776578\pi$
$71$	15.6576	−	58.4350i	0.220530	−	0.823028i	0.984146	−	0.177358i	$-0.0567551\pi$
$72$		0			0
$73$	36.8238	−	36.8238i	0.504436	−	0.504436i	−0.408378	−	0.912813i	$-0.633905\pi$
$73$	36.8238	−	36.8238i	0.504436	−	0.504436i	0.912813	+	0.408378i	$0.133905\pi$
$74$		0			0
$75$	−33.8838	−	19.5628i	−0.451785	−	0.260838i
$76$		0			0
$77$			44.4623i			0.577432i
$78$		0			0
$79$	−106.238			−1.34479			−0.672394	−	0.740193i	$-0.734734\pi$
$79$	−106.238			−1.34479			−0.672394	+	0.740193i	$0.734734\pi$
$80$		0			0
$81$	50.6101	−	87.6593i	0.624816	−	1.08221i
$82$		0			0
$83$	96.6176	+	96.6176i	1.16407	+	1.16407i	0.983577	+	0.180490i	$0.0577685\pi$
$83$	96.6176	+	96.6176i	1.16407	+	1.16407i	0.180490	+	0.983577i	$0.442232\pi$
$84$		0			0
$85$	76.4344	+	20.4805i	0.899228	+	0.240947i
$86$		0			0
$87$	−61.8634	−	107.151i	−0.711073	−	1.23162i
$88$		0			0
$89$	−6.66127	−	24.8602i	−0.0748457	−	0.279328i	0.918353	−	0.395763i	$-0.129520\pi$
$89$	−6.66127	−	24.8602i	−0.0748457	−	0.279328i	−0.993198	+	0.116435i	$0.962853\pi$
$90$		0			0
$91$	40.7709	−	14.4837i	0.448032	−	0.159162i
$92$		0			0
$93$	79.0750	−	21.1881i	0.850268	−	0.227829i
$94$		0			0
$95$	103.895	−	59.9836i	1.09363	−	0.631406i
$96$		0			0
$97$	4.20302	−	15.6859i	0.0433302	−	0.161710i	−0.940871	−	0.338766i	$-0.889991\pi$
$97$	4.20302	−	15.6859i	0.0433302	−	0.161710i	0.984201	+	0.177056i	$0.0566572\pi$
$98$		0			0
$99$	44.1371	−	44.1371i	0.445829	−	0.445829i
$100$		0			0
$101$	−3.92304	−	2.26497i	−0.0388420	−	0.0224254i	0.480453	−	0.877020i	$-0.340472\pi$
$101$	−3.92304	−	2.26497i	−0.0388420	−	0.0224254i	−0.519295	+	0.854595i	$0.673805\pi$
$102$		0			0
$103$			93.5979i			0.908718i	0.890819	+	0.454359i	$0.150132\pi$
$103$			93.5979i			0.908718i	−0.890819	+	0.454359i	$0.849868\pi$
$104$		0			0
$105$	−46.7305			−0.445053
$106$		0			0
$107$	22.5382	−	39.0373i	0.210637	−	0.364834i	−0.741277	−	0.671199i	$-0.765779\pi$
$107$	22.5382	−	39.0373i	0.210637	−	0.364834i	0.951914	+	0.306365i	$0.0991128\pi$
$108$		0			0
$109$	−101.429	−	101.429i	−0.930540	−	0.930540i	0.0671997	−	0.997740i	$-0.478594\pi$
$109$	−101.429	−	101.429i	−0.930540	−	0.930540i	−0.997740	+	0.0671997i	$0.978594\pi$
$110$		0			0
$111$	−60.3000	−	16.1573i	−0.543243	−	0.145561i
$112$		0			0
$113$	44.2717	+	76.6808i	0.391785	+	0.678591i	0.992685	−	0.120733i	$-0.0385244\pi$
$113$	44.2717	+	76.6808i	0.391785	+	0.678591i	−0.600900	+	0.799324i	$0.705191\pi$
$114$		0			0
$115$	22.9492	+	85.6475i	0.199558	+	0.744761i
$116$		0			0
$117$	−54.8505	−	26.0949i	−0.468808	−	0.223034i
$118$		0			0
$119$	−66.9948	+	17.9512i	−0.562981	+	0.150850i
$120$		0			0
$121$	−49.7661	+	28.7325i	−0.411290	+	0.237459i
$122$		0			0
$123$	−58.2807	+	217.507i	−0.473827	+	1.76835i
$124$		0			0
$125$	−95.5366	+	95.5366i	−0.764293	+	0.764293i
$126$		0			0
$127$	−34.4109	−	19.8671i	−0.270952	−	0.156434i	0.358368	−	0.933580i	$-0.383333\pi$
$127$	−34.4109	−	19.8671i	−0.270952	−	0.156434i	−0.629320	+	0.777146i	$0.716667\pi$
$128$		0			0
$129$		−	186.110i		−	1.44271i
$130$		0			0
$131$	152.325			1.16279			0.581393	−	0.813623i	$-0.302508\pi$
$131$	152.325			1.16279			0.581393	+	0.813623i	$0.302508\pi$
$132$		0			0
$133$	−52.5757	+	91.0637i	−0.395306	+	0.684690i
$134$		0			0
$135$	−42.9651	−	42.9651i	−0.318260	−	0.318260i
$136$		0			0
$137$	148.196	+	39.7091i	1.08173	+	0.289847i	0.755302	−	0.655377i	$-0.227490\pi$
$137$	148.196	+	39.7091i	1.08173	+	0.289847i	0.326423	+	0.945224i	$0.394157\pi$
$138$		0			0
$139$	4.30884	+	7.46314i	0.0309989	+	0.0536916i	0.881109	−	0.472914i	$-0.156798\pi$
$139$	4.30884	+	7.46314i	0.0309989	+	0.0536916i	−0.850110	+	0.526606i	$0.823465\pi$
$140$		0			0
$141$	−1.40571	−	5.24619i	−0.00996959	−	0.0372070i
$142$		0			0
$143$	132.171	+	112.656i	0.924274	+	0.787804i
$144$		0			0
$145$	−122.729	+	32.8852i	−0.846408	+	0.226794i
$146$		0			0
$147$	−121.438	+	70.1121i	−0.826107	+	0.476953i
$148$		0			0
$149$	33.7641	−	126.009i	0.226604	−	0.845699i	−0.755151	−	0.655551i	$-0.772436\pi$
$149$	33.7641	−	126.009i	0.226604	−	0.845699i	0.981755	−	0.190148i	$-0.0608969\pi$
$150$		0			0
$151$	23.2789	−	23.2789i	0.154165	−	0.154165i	−0.625810	−	0.779975i	$-0.715232\pi$
$151$	23.2789	−	23.2789i	0.154165	−	0.154165i	0.779975	+	0.625810i	$0.215232\pi$
$152$		0			0
$153$	84.3247	+	48.6849i	0.551142	+	0.318202i
$154$		0			0
$155$		−	84.0689i		−	0.542380i
$156$		0			0
$157$	222.657			1.41820			0.709100	−	0.705108i	$-0.249101\pi$
$157$	222.657			1.41820			0.709100	+	0.705108i	$0.249101\pi$
$158$		0			0
$159$	−117.886	+	204.184i	−0.741419	+	1.28418i
$160$		0			0
$161$	−54.9551	−	54.9551i	−0.341336	−	0.341336i
$162$		0			0
$163$	−241.914	−	64.8207i	−1.48414	−	0.397673i	−0.576383	−	0.817180i	$-0.695536\pi$
$163$	−241.914	−	64.8207i	−1.48414	−	0.397673i	−0.907752	+	0.419507i	$0.862203\pi$
$164$		0			0
$165$	−93.7847	−	162.440i	−0.568392	−	0.984484i
$166$		0			0
$167$	−15.6933	−	58.5680i	−0.0939716	−	0.350707i	0.902890	−	0.429872i	$-0.141441\pi$
$167$	−15.6933	−	58.5680i	−0.0939716	−	0.350707i	−0.996862	+	0.0791650i	$0.974775\pi$
$168$		0			0
$169$	60.2478	−	157.896i	0.356496	−	0.934297i
$170$		0			0
$171$	142.589	−	38.2065i	0.833852	−	0.223430i
$172$		0			0
$173$	101.900	−	58.8317i	0.589015	−	0.340068i	−0.175693	−	0.984445i	$-0.556217\pi$
$173$	101.900	−	58.8317i	0.589015	−	0.340068i	0.764708	+	0.644377i	$0.222883\pi$
$174$		0			0
$175$	9.11488	−	34.0172i	0.0520850	−	0.194384i
$176$		0			0
$177$	−72.5652	+	72.5652i	−0.409973	+	0.409973i
$178$		0			0
$179$	76.9010	+	44.3988i	0.429614	+	0.248038i	0.699182	−	0.714943i	$-0.253548\pi$
$179$	76.9010	+	44.3988i	0.429614	+	0.248038i	−0.269568	+	0.962981i	$0.586881\pi$
$180$		0			0
$181$		−	262.618i		−	1.45093i	−0.688260	−	0.725465i	$-0.741625\pi$
$181$		−	262.618i		−	1.45093i	0.688260	−	0.725465i	$-0.258375\pi$
$182$		0			0
$183$	341.803			1.86777
$184$		0			0
$185$	−32.0541	+	55.5193i	−0.173265	+	0.300104i
$186$		0			0
$187$	−196.854	−	196.854i	−1.05269	−	1.05269i
$188$		0			0
$189$	51.4430	+	13.7841i	0.272185	+	0.0729319i
$190$		0			0
$191$	49.9048	+	86.4376i	0.261282	+	0.452553i	0.966583	−	0.256355i	$-0.0825216\pi$
$191$	49.9048	+	86.4376i	0.261282	+	0.452553i	−0.705301	+	0.708908i	$0.749188\pi$
$192$		0			0
$193$	43.2915	+	161.566i	0.224308	+	0.837130i	0.982680	+	0.185308i	$0.0593283\pi$
$193$	43.2915	+	161.566i	0.224308	+	0.837130i	−0.758372	+	0.651822i	$0.774005\pi$
$194$		0			0
$195$	−118.403	+	138.914i	−0.607196	+	0.712379i
$196$		0			0
$197$	327.442	−	87.7378i	1.66214	−	0.445370i	0.699166	−	0.714959i	$-0.253555\pi$
$197$	327.442	−	87.7378i	1.66214	−	0.445370i	0.962975	+	0.269589i	$0.0868880\pi$
$198$		0			0
$199$	16.3309	−	9.42867i	0.0820650	−	0.0473802i	−0.458406	−	0.888743i	$-0.651579\pi$
$199$	16.3309	−	9.42867i	0.0820650	−	0.0473802i	0.540471	+	0.841363i	$0.318246\pi$
$200$		0			0
$201$	−39.8147	+	148.590i	−0.198083	+	0.739256i
$202$		0			0
$203$	78.7483	−	78.7483i	0.387923	−	0.387923i
$204$		0			0
$205$	200.262	+	115.622i	0.976890	+	0.564008i
$206$		0			0
$207$			109.106i			0.527084i
$208$		0			0
$209$	−422.062			−2.01943
$210$		0			0
$211$	−14.0901	+	24.4047i	−0.0667776	+	0.115662i	−0.897481	−	0.441053i	$-0.854605\pi$
$211$	−14.0901	+	24.4047i	−0.0667776	+	0.115662i	0.830704	+	0.556715i	$0.187938\pi$
$212$		0			0
$213$	−158.175	−	158.175i	−0.742604	−	0.742604i
$214$		0			0
$215$	−184.610	−	49.4660i	−0.858649	−	0.230074i
$216$		0			0
$217$	36.8432	+	63.8143i	0.169784	+	0.294075i
$218$		0			0
$219$	−49.8382	−	185.999i	−0.227572	−	0.849310i
$220$		0			0
$221$	−116.385	+	244.636i	−0.526628	+	1.10695i
$222$		0			0
$223$	−126.883	+	33.9983i	−0.568984	+	0.152459i	−0.531831	−	0.846851i	$-0.678496\pi$
$223$	−126.883	+	33.9983i	−0.568984	+	0.152459i	−0.0371534	+	0.999310i	$0.511829\pi$
$224$		0			0
$225$	−42.8166	+	24.7202i	−0.190296	+	0.109867i
$226$		0			0
$227$	89.8897	−	335.473i	0.395990	−	1.47785i	−0.424098	−	0.905616i	$-0.639409\pi$
$227$	89.8897	−	335.473i	0.395990	−	1.47785i	0.820088	−	0.572237i	$-0.193924\pi$
$228$		0			0
$229$	−309.147	+	309.147i	−1.34999	+	1.34999i	−0.464320	+	0.885668i	$0.653701\pi$
$229$	−309.147	+	309.147i	−1.34999	+	1.34999i	−0.885668	+	0.464320i	$0.846299\pi$
$230$		0			0
$231$	142.379	+	82.2024i	0.616358	+	0.355855i
$232$		0			0
$233$			213.648i			0.916945i	0.888709	+	0.458473i	$0.151603\pi$
$233$			213.648i			0.916945i	−0.888709	+	0.458473i	$0.848397\pi$
$234$		0			0
$235$	−5.57751			−0.0237341
$236$		0			0
$237$	−196.415	+	340.200i	−0.828754	+	1.43544i
$238$		0			0
$239$	5.07685	+	5.07685i	0.0212420	+	0.0212420i	0.717648	−	0.696406i	$-0.245219\pi$
$239$	5.07685	+	5.07685i	0.0212420	+	0.0212420i	−0.696406	+	0.717648i	$0.745219\pi$
$240$		0			0
$241$	−57.9552	−	15.5290i	−0.240478	−	0.0644358i	0.136567	−	0.990631i	$-0.456393\pi$
$241$	−57.9552	−	15.5290i	−0.240478	−	0.0644358i	−0.377045	+	0.926195i	$0.623060\pi$
$242$		0			0
$243$	−115.129	−	199.410i	−0.473783	−	0.820617i
$244$		0			0
$245$	37.2700	+	139.094i	0.152122	+	0.567729i
$246$		0			0
$247$	137.488	+	387.022i	0.556632	+	1.56689i
$248$		0			0
$249$	488.020	−	130.765i	1.95992	−	0.525159i
$250$		0			0
$251$	112.415	−	64.9026i	0.447867	−	0.258576i	−0.259062	−	0.965861i	$-0.583413\pi$
$251$	112.415	−	64.9026i	0.447867	−	0.258576i	0.706929	+	0.707285i	$0.250080\pi$
$252$		0			0
$253$	80.7385	−	301.320i	0.319124	−	1.19099i
$254$		0			0
$255$	206.896	−	206.896i	0.811358	−	0.811358i
$256$		0			0
$257$	−225.400	−	130.135i	−0.877043	−	0.506361i	−0.00736090	−	0.999973i	$-0.502343\pi$
$257$	−225.400	−	130.135i	−0.877043	−	0.506361i	−0.869682	+	0.493612i	$0.835676\pi$
$258$		0			0
$259$		−	56.1909i		−	0.216953i
$260$		0			0
$261$	−156.345			−0.599022
$262$		0			0
$263$	15.3605	−	26.6051i	0.0584048	−	0.101160i	−0.835345	−	0.549727i	$-0.814732\pi$
$263$	15.3605	−	26.6051i	0.0584048	−	0.101160i	0.893749	+	0.448566i	$0.148065\pi$
$264$		0			0
$265$	171.205	+	171.205i	0.646056	+	0.646056i
$266$		0			0
$267$	−91.9236	−	24.6309i	−0.344283	−	0.0922504i
$268$		0			0
$269$	166.534	+	288.445i	0.619085	+	1.07229i	0.989653	+	0.143481i	$0.0458296\pi$
$269$	166.534	+	288.445i	0.619085	+	1.07229i	−0.370568	+	0.928805i	$0.620837\pi$
$270$		0			0
$271$	−66.9949	−	250.028i	−0.247214	−	0.922614i	−0.972258	−	0.233912i	$-0.924847\pi$
$271$	−66.9949	−	250.028i	−0.247214	−	0.922614i	0.725044	−	0.688702i	$-0.241819\pi$
$272$		0			0
$273$	28.9974	−	157.336i	0.106218	−	0.576322i
$274$		0			0
$275$	136.540	−	36.5858i	0.496509	−	0.133039i
$276$		0			0
$277$	152.454	−	88.0191i	0.550374	−	0.317759i	−0.198899	−	0.980020i	$-0.563737\pi$
$277$	152.454	−	88.0191i	0.550374	−	0.317759i	0.749273	+	0.662261i	$0.230403\pi$
$278$		0			0
$279$	26.7738	−	99.9213i	0.0959636	−	0.358141i
$280$		0			0
$281$	−50.8905	+	50.8905i	−0.181105	+	0.181105i	−0.791837	−	0.610732i	$-0.790875\pi$
$281$	−50.8905	+	50.8905i	−0.181105	+	0.181105i	0.610732	+	0.791837i	$0.290875\pi$
$282$		0			0
$283$	90.6574	+	52.3411i	0.320344	+	0.184951i	0.651546	−	0.758609i	$-0.274121\pi$
$283$	90.6574	+	52.3411i	0.320344	+	0.184951i	−0.331202	+	0.943560i	$0.607454\pi$
$284$		0			0
$285$		−	443.594i		−	1.55647i
$286$		0			0
$287$	−202.685			−0.706219
$288$		0			0
$289$	72.6370	−	125.811i	0.251339	−	0.435332i
$290$		0			0
$291$	−42.4594	−	42.4594i	−0.145908	−	0.145908i
$292$		0			0
$293$	−475.220	−	127.335i	−1.62191	−	0.434590i	−0.670349	−	0.742046i	$-0.733856\pi$
$293$	−475.220	−	127.335i	−1.62191	−	0.434590i	−0.951562	+	0.307456i	$0.900522\pi$
$294$		0			0
$295$	52.6931	+	91.2671i	0.178621	+	0.309380i
$296$		0			0
$297$	55.3274	+	206.485i	0.186288	+	0.695235i
$298$		0			0
$299$	−302.605	+	24.1207i	−1.01206	+	0.0806712i
$300$		0			0
$301$	161.810	−	43.3570i	0.537576	−	0.144043i
$302$		0			0
$303$	−14.5059	+	8.37500i	−0.0478743	+	0.0276402i
$304$		0			0
$305$	90.8473	−	339.047i	0.297860	−	1.11163i
$306$		0			0
$307$	121.001	−	121.001i	0.394141	−	0.394141i	−0.482020	−	0.876160i	$-0.660097\pi$
$307$	121.001	−	121.001i	0.394141	−	0.394141i	0.876160	+	0.482020i	$0.160097\pi$
$308$		0			0
$309$	299.723	+	173.045i	0.969976	+	0.560016i
$310$		0			0
$311$			552.796i			1.77748i	0.458413	+	0.888739i	$0.348418\pi$
$311$			552.796i			1.77748i	−0.458413	+	0.888739i	$0.651582\pi$
$312$		0			0
$313$	231.900			0.740893			0.370447	−	0.928854i	$-0.379205\pi$
$313$	231.900			0.740893			0.370447	+	0.928854i	$0.379205\pi$
$314$		0			0
$315$	−29.5250	+	51.1388i	−0.0937302	+	0.162345i
$316$		0			0
$317$	61.8126	+	61.8126i	0.194993	+	0.194993i	0.797849	−	0.602857i	$-0.205971\pi$
$317$	61.8126	+	61.8126i	0.194993	+	0.194993i	−0.602857	+	0.797849i	$0.705971\pi$
$318$		0			0
$319$	431.779	+	115.695i	1.35354	+	0.362680i
$320$		0			0
$321$	−83.3377	−	144.345i	−0.259619	−	0.449673i
$322$		0			0
$323$	−170.403	−	635.953i	−0.527564	−	1.96890i
$324$		0			0
$325$	−78.0267	−	113.286i	−0.240082	−	0.348573i
$326$		0			0
$327$	−512.322	+	137.276i	−1.56673	+	0.419805i
$328$		0			0
$329$	4.23373	−	2.44435i	0.0128685	−	0.00742963i
$330$		0			0
$331$	−162.185	+	605.282i	−0.489984	+	1.82865i	0.0664983	+	0.997787i	$0.478817\pi$
$331$	−162.185	+	605.282i	−0.489984	+	1.82865i	−0.556482	+	0.830859i	$0.687849\pi$
$332$		0			0
$333$	−55.7799	+	55.7799i	−0.167507	+	0.167507i
$334$		0			0
$335$	136.810	+	78.9873i	0.408388	+	0.235783i
$336$		0			0
$337$		−	53.5886i		−	0.159017i	−0.996834	−	0.0795084i	$-0.974665\pi$
$337$		−	53.5886i		−	0.159017i	0.996834	−	0.0795084i	$-0.0253350\pi$
$338$		0			0
$339$	327.400			0.965782
$340$		0			0
$341$	−147.883	+	256.141i	−0.433675	+	0.751147i
$342$		0			0
$343$	−204.566	−	204.566i	−0.596403	−	0.596403i
$344$		0			0
$345$	316.692	+	84.8574i	0.917948	+	0.245963i
$346$		0			0
$347$	8.86795	+	15.3597i	0.0255561	+	0.0442644i	0.878521	−	0.477705i	$-0.158531\pi$
$347$	8.86795	+	15.3597i	0.0255561	+	0.0442644i	−0.852965	+	0.521969i	$0.825198\pi$
$348$		0			0
$349$	98.1957	+	366.471i	0.281363	+	1.05006i	0.951456	+	0.307784i	$0.0995874\pi$
$349$	98.1957	+	366.471i	0.281363	+	1.05006i	−0.670093	+	0.742277i	$0.733746\pi$
$350$		0			0
$351$	171.319	−	117.997i	0.488088	−	0.336174i
$352$		0			0
$353$	−322.022	+	86.2854i	−0.912243	+	0.244435i	−0.684266	−	0.729232i	$-0.739877\pi$
$353$	−322.022	+	86.2854i	−0.912243	+	0.244435i	−0.227976	+	0.973667i	$0.573211\pi$
$354$		0			0
$355$	−198.940	+	114.858i	−0.560395	+	0.323544i
$356$		0			0
$357$	−66.3768	+	247.721i	−0.185929	+	0.693898i
$358$		0			0
$359$	−366.035	+	366.035i	−1.01960	+	1.01960i	−0.0197923	+	0.999804i	$0.506300\pi$
$359$	−366.035	+	366.035i	−1.01960	+	1.01960i	−0.999804	+	0.0197923i	$0.993700\pi$
$360$		0			0
$361$	−551.795	−	318.579i	−1.52852	−	0.882490i
$362$		0			0
$363$			212.484i			0.585355i
$364$		0			0
$365$	−197.745			−0.541768
$366$		0			0
$367$	98.7059	−	170.964i	0.268954	−	0.465841i	−0.699638	−	0.714497i	$-0.746656\pi$
$367$	98.7059	−	170.964i	0.268954	−	0.465841i	0.968592	+	0.248656i	$0.0799889\pi$
$368$		0			0
$369$	201.202	+	201.202i	0.545264	+	0.545264i
$370$		0			0
$371$	−204.987	−	54.9262i	−0.552527	−	0.148049i
$372$		0			0
$373$	−208.142	−	360.513i	−0.558023	−	0.966523i	−0.997661	−	0.0683488i	$-0.978227\pi$
$373$	−208.142	−	360.513i	−0.558023	−	0.966523i	0.439639	−	0.898175i	$-0.355106\pi$
$374$		0			0
$375$	129.302	+	482.560i	0.344804	+	1.28683i
$376$		0			0
$377$	−34.5639	−	433.620i	−0.0916814	−	1.15018i
$378$		0			0
$379$	−13.5864	+	3.64047i	−0.0358481	+	0.00960546i	−0.276699	−	0.960957i	$-0.589240\pi$
$379$	−13.5864	+	3.64047i	−0.0358481	+	0.00960546i	0.240850	+	0.970562i	$0.422574\pi$
$380$		0			0
$381$	−127.238	+	73.4611i	−0.333959	+	0.192811i
$382$		0			0
$383$	−13.2422	+	49.4206i	−0.0345750	+	0.129036i	−0.981056	−	0.193723i	$-0.937944\pi$
$383$	−13.2422	+	49.4206i	−0.0345750	+	0.129036i	0.946481	+	0.322759i	$0.104610\pi$
$384$		0			0
$385$	119.382	−	119.382i	0.310084	−	0.310084i
$386$		0			0
$387$	−203.667	−	117.587i	−0.526271	−	0.303842i
$388$		0			0
$389$		−	451.736i		−	1.16128i	−0.814162	−	0.580638i	$-0.802803\pi$
$389$		−	451.736i		−	1.16128i	0.814162	−	0.580638i	$-0.197197\pi$
$390$		0			0
$391$	486.620			1.24455
$392$		0			0
$393$	281.620	−	487.781i	0.716591	−	1.24117i
$394$		0			0
$395$	285.252	+	285.252i	0.722157	+	0.722157i
$396$		0			0
$397$	373.710	+	100.135i	0.941334	+	0.252230i	0.696681	−	0.717381i	$-0.254659\pi$
$397$	373.710	+	100.135i	0.941334	+	0.252230i	0.244653	+	0.969611i	$0.421326\pi$
$398$		0			0
$399$	194.405	+	336.719i	0.487231	+	0.843908i
$400$		0			0
$401$	−69.1311	−	258.001i	−0.172397	−	0.643393i	−0.996980	−	0.0776533i	$-0.975257\pi$
$401$	−69.1311	−	258.001i	−0.172397	−	0.643393i	0.824584	−	0.565740i	$-0.191409\pi$
$402$		0			0
$403$	283.049	+	52.1668i	0.702356	+	0.129446i
$404$		0			0
$405$	−371.257	+	99.4779i	−0.916683	+	0.245624i
$406$		0			0
$407$	195.325	−	112.771i	0.479914	−	0.277078i
$408$		0			0
$409$	−105.844	+	395.014i	−0.258787	+	0.965805i	0.707158	+	0.707056i	$0.249977\pi$
$409$	−105.844	+	395.014i	−0.258787	+	0.965805i	−0.965945	+	0.258749i	$0.916690\pi$
$410$		0			0
$411$	401.145	−	401.145i	0.976022	−	0.976022i
$412$		0			0
$413$	−79.9957	−	46.1855i	−0.193694	−	0.111829i
$414$		0			0
$415$		−	518.841i		−	1.25022i
$416$		0			0
$417$	31.8650			0.0764148
$418$		0			0
$419$	228.302	−	395.431i	0.544874	−	0.943750i	−0.453741	−	0.891134i	$-0.649911\pi$
$419$	228.302	−	395.431i	0.544874	−	0.943750i	0.998615	−	0.0526160i	$-0.0167559\pi$
$420$		0			0
$421$	−81.6596	−	81.6596i	−0.193966	−	0.193966i	0.603442	−	0.797407i	$-0.293796\pi$
$421$	−81.6596	−	81.6596i	−0.193966	−	0.193966i	−0.797407	+	0.603442i	$0.793796\pi$
$422$		0			0
$423$	−6.62923	−	1.77630i	−0.0156719	−	0.00419929i
$424$		0			0
$425$	110.253	+	190.964i	0.259419	+	0.449327i
$426$		0			0
$427$	79.6277	+	297.175i	0.186482	+	0.695959i
$428$		0			0
$429$	605.111	−	214.964i	1.41051	−	0.501081i
$430$		0			0
$431$	−151.399	+	40.5674i	−0.351275	+	0.0941238i	−0.430142	−	0.902761i	$-0.641536\pi$
$431$	−151.399	+	40.5674i	−0.351275	+	0.0941238i	0.0788669	+	0.996885i	$0.474870\pi$
$432$		0			0
$433$	−251.647	+	145.289i	−0.581171	+	0.335539i	−0.761599	−	0.648049i	$-0.775585\pi$
$433$	−251.647	+	145.289i	−0.581171	+	0.335539i	0.180428	+	0.983588i	$0.442252\pi$
$434$		0			0
$435$	−121.597	+	453.806i	−0.279533	+	1.04323i
$436$		0			0
$437$	521.666	−	521.666i	1.19374	−	1.19374i
$438$		0			0
$439$	−368.628	−	212.827i	−0.839699	−	0.484801i	0.0174626	−	0.999848i	$-0.494441\pi$
$439$	−368.628	−	212.827i	−0.839699	−	0.484801i	−0.857162	+	0.515047i	$0.827775\pi$
$440$		0			0
$441$			177.191i			0.401794i
$442$		0			0
$443$	−593.192			−1.33903			−0.669517	−	0.742797i	$-0.733499\pi$
$443$	−593.192			−1.33903			−0.669517	+	0.742797i	$0.733499\pi$
$444$		0			0
$445$	−48.8645	+	84.6358i	−0.109808	+	0.190193i
$446$		0			0
$447$	−341.088	−	341.088i	−0.763060	−	0.763060i
$448$		0			0
$449$	683.437	+	183.126i	1.52213	+	0.407854i	0.920443	−	0.390877i	$-0.127828\pi$
$449$	683.437	+	183.126i	1.52213	+	0.407854i	0.601689	+	0.798731i	$0.294495\pi$
$450$		0			0
$451$	−406.773	−	704.552i	−0.901936	−	1.56220i
$452$		0			0
$453$	−31.5063	−	117.583i	−0.0695503	−	0.259565i
$454$		0			0
$455$	−148.360	−	70.5817i	−0.326066	−	0.155125i
$456$		0			0
$457$	−382.295	+	102.436i	−0.836532	+	0.224148i	−0.651561	−	0.758596i	$-0.725886\pi$
$457$	−382.295	+	102.436i	−0.836532	+	0.224148i	−0.184971	+	0.982744i	$0.559219\pi$
$458$		0			0
$459$	−288.789	+	166.732i	−0.629169	+	0.363251i
$460$		0			0
$461$	51.8233	−	193.407i	0.112415	−	0.419538i	−0.886666	−	0.462411i	$-0.846984\pi$
$461$	51.8233	−	193.407i	0.112415	−	0.419538i	0.999081	+	0.0428729i	$0.0136511\pi$
$462$		0			0
$463$	−78.9928	+	78.9928i	−0.170611	+	0.170611i	−0.787248	−	0.616637i	$-0.788495\pi$
$463$	−78.9928	+	78.9928i	−0.170611	+	0.170611i	0.616637	+	0.787248i	$0.288495\pi$
$464$		0			0
$465$	−269.208	−	155.428i	−0.578943	−	0.334253i
$466$		0			0
$467$			899.100i			1.92527i	0.270808	+	0.962633i	$0.412709\pi$
$467$			899.100i			1.92527i	−0.270808	+	0.962633i	$0.587291\pi$
$468$		0			0
$469$	−138.465			−0.295234
$470$		0			0
$471$	411.652	−	713.002i	0.873995	−	1.51380i
$472$		0			0
$473$	475.455	+	475.455i	1.00519	+	1.00519i
$474$		0			0
$475$	322.911	+	86.5237i	0.679812	+	0.182155i
$476$		0			0
$477$	148.964	+	258.012i	0.312293	+	0.540907i
$478$		0			0
$479$	83.2815	+	310.811i	0.173865	+	0.648874i	0.996742	+	0.0806543i	$0.0257010\pi$
$479$	83.2815	+	310.811i	0.173865	+	0.648874i	−0.822877	+	0.568220i	$0.807632\pi$
$480$		0			0
$481$	−167.036	−	142.373i	−0.347269	−	0.295994i
$482$		0			0
$483$	−277.581	+	74.3776i	−0.574702	+	0.153991i
$484$		0			0
$485$	−53.4022	+	30.8318i	−0.110108	+	0.0635707i
$486$		0			0
$487$	−11.3837	+	42.4845i	−0.0233751	+	0.0872372i	−0.976628	−	0.214936i	$-0.931046\pi$
$487$	−11.3837	+	42.4845i	−0.0233751	+	0.0872372i	0.953253	+	0.302174i	$0.0977122\pi$
$488$		0			0
$489$	−654.825	+	654.825i	−1.33911	+	1.33911i
$490$		0			0
$491$	314.204	+	181.406i	0.639927	+	0.369462i	0.784586	−	0.620019i	$-0.212875\pi$
$491$	314.204	+	181.406i	0.639927	+	0.369462i	−0.144659	+	0.989482i	$0.546209\pi$
$492$		0			0
$493$			697.305i			1.41441i
$494$		0			0
$495$	−237.018			−0.478824
$496$		0			0
$497$	100.673	−	174.371i	0.202562	−	0.350848i
$498$		0			0
$499$	542.545	+	542.545i	1.08727	+	1.08727i	0.995809	+	0.0914564i	$0.0291522\pi$
$499$	542.545	+	542.545i	1.08727	+	1.08727i	0.0914564	+	0.995809i	$0.470848\pi$
$500$		0			0
$501$	−216.563	−	58.0278i	−0.432261	−	0.115824i
$502$		0			0
$503$	−29.0198	−	50.2638i	−0.0576935	−	0.0999280i	0.835736	−	0.549131i	$-0.185041\pi$
$503$	−29.0198	−	50.2638i	−0.0576935	−	0.0999280i	−0.893430	+	0.449203i	$0.851708\pi$
$504$		0			0
$505$	4.45196	+	16.6149i	0.00881576	+	0.0329009i
$506$		0			0
$507$	−394.234	−	484.848i	−0.777582	−	0.956308i
$508$		0			0
$509$	620.186	−	166.178i	1.21844	−	0.326480i	0.408372	−	0.912816i	$-0.366097\pi$
$509$	620.186	−	166.178i	1.21844	−	0.326480i	0.810068	+	0.586336i	$0.199430\pi$
$510$		0			0
$511$	150.103	−	86.6620i	0.293744	−	0.169593i
$512$		0			0
$513$	−130.847	+	488.327i	−0.255062	+	0.951905i
$514$		0			0
$515$	251.313	−	251.313i	0.487986	−	0.487986i
$516$		0			0
$517$	16.9936	+	9.81124i	0.0328696	+	0.0189773i
$518$		0			0
$519$		−	435.075i		−	0.838295i
$520$		0			0
$521$	−494.531			−0.949196			−0.474598	−	0.880203i	$-0.657406\pi$
$521$	−494.531			−0.949196			−0.474598	+	0.880203i	$0.657406\pi$
$522$		0			0
$523$	−59.9652	+	103.863i	−0.114656	+	0.198590i	−0.917642	−	0.397407i	$-0.869910\pi$
$523$	−59.9652	+	103.863i	−0.114656	+	0.198590i	0.802986	+	0.595998i	$0.203243\pi$
$524$		0			0
$525$	−92.0794	−	92.0794i	−0.175389	−	0.175389i
$526$		0			0
$527$	−445.654	−	119.413i	−0.845644	−	0.226590i
$528$		0			0
$529$	8.13752	+	14.0946i	0.0153828	+	0.0266438i
$530$		0			0
$531$	33.5628	+	125.258i	0.0632069	+	0.235891i
$532$		0			0
$533$	−513.551	+	602.513i	−0.963510	+	1.13042i
$534$		0			0
$535$	−165.331	+	44.3004i	−0.309031	+	0.0828046i
$536$		0			0
$537$	284.351	−	164.170i	0.529517	−	0.305717i
$538$		0			0
$539$	131.121	−	489.351i	0.243268	−	0.907887i
$540$		0			0
$541$	38.1124	−	38.1124i	0.0704480	−	0.0704480i	−0.671005	−	0.741453i	$-0.734137\pi$
$541$	38.1124	−	38.1124i	0.0704480	−	0.0704480i	0.741453	+	0.671005i	$0.234137\pi$
$542$		0			0
$543$	−840.965	−	485.532i	−1.54874	−	0.894165i
$544$		0			0
$545$			544.677i			0.999408i
$546$		0			0
$547$	69.2280			0.126559			0.0632797	−	0.997996i	$-0.479844\pi$
$547$	69.2280			0.126559			0.0632797	+	0.997996i	$0.479844\pi$
$548$		0			0
$549$	215.956	−	374.046i	0.393362	−	0.681323i
$550$		0			0
$551$	747.525	+	747.525i	1.35667	+	1.35667i
$552$		0			0
$553$	−341.539	−	91.5150i	−0.617611	−	0.165488i
$554$		0			0
$555$	118.524	+	205.290i	0.213557	+	0.369891i
$556$		0			0
$557$	−173.421	−	647.216i	−0.311348	−	1.16197i	−0.927341	−	0.374216i	$-0.877912\pi$
$557$	−173.421	−	647.216i	−0.311348	−	1.16197i	0.615993	−	0.787752i	$-0.288755\pi$
$558$		0			0
$559$	281.100	−	590.862i	0.502863	−	1.05700i
$560$		0			0
$561$	−994.317	+	266.427i	−1.77240	+	0.474914i
$562$		0			0
$563$	360.527	−	208.150i	0.640367	−	0.369716i	−0.144389	−	0.989521i	$-0.546122\pi$
$563$	360.527	−	208.150i	0.640367	−	0.369716i	0.784756	+	0.619805i	$0.212788\pi$
$564$		0			0
$565$	87.0192	−	324.760i	0.154016	−	0.574797i
$566$		0			0
$567$	238.214	−	238.214i	0.420131	−	0.420131i
$568$		0			0
$569$	783.324	+	452.252i	1.37667	+	0.794820i	0.991757	−	0.128134i	$-0.0408987\pi$
$569$	783.324	+	452.252i	1.37667	+	0.794820i	0.384911	+	0.922954i	$0.374232\pi$
$570$		0			0
$571$		−	81.7938i		−	0.143247i	−0.997432	−	0.0716233i	$-0.977182\pi$
$571$		−	81.7938i		−	0.143247i	0.997432	−	0.0716233i	$-0.0228179\pi$
$572$		0			0
$573$	369.058			0.644081
$574$		0			0
$575$	−123.543	+	213.982i	−0.214857	+	0.372143i
$576$		0			0
$577$	−86.8716	−	86.8716i	−0.150557	−	0.150557i	0.627810	−	0.778367i	$-0.283952\pi$
$577$	−86.8716	−	86.8716i	−0.150557	−	0.150557i	−0.778367	+	0.627810i	$0.783952\pi$
$578$		0			0
$579$	597.410	+	160.076i	1.03180	+	0.276469i
$580$		0			0
$581$	227.382	+	393.837i	0.391363	+	0.677861i
$582$		0			0
$583$	−220.466	−	822.789i	−0.378157	−	1.41130i
$584$		0			0
$585$	77.2095	+	217.340i	0.131982	+	0.371522i
$586$		0			0
$587$	1004.82	−	269.241i	1.71179	−	0.458672i	0.735926	−	0.677062i	$-0.236747\pi$
$587$	1004.82	−	269.241i	1.71179	−	0.458672i	0.975862	+	0.218389i	$0.0700802\pi$
$588$		0			0
$589$	−605.763	+	349.737i	−1.02846	+	0.593782i
$590$		0			0
$591$	324.421	−	1210.76i	0.548936	−	2.04866i
$592$		0			0
$593$	726.496	−	726.496i	1.22512	−	1.22512i	0.259332	−	0.965788i	$-0.416498\pi$
$593$	726.496	−	726.496i	1.22512	−	1.22512i	0.965788	−	0.259332i	$-0.0835025\pi$
$594$		0			0
$595$	228.082	+	131.683i	0.383331	+	0.221316i
$596$		0			0
$597$		−	69.7273i		−	0.116796i
$598$		0			0
$599$	−1076.91			−1.79785			−0.898923	−	0.438108i	$-0.855649\pi$
$599$	−1076.91			−1.79785			−0.898923	+	0.438108i	$0.855649\pi$
$600$		0			0
$601$	98.1916	−	170.073i	0.163380	−	0.282983i	−0.772699	−	0.634773i	$-0.781094\pi$
$601$	98.1916	−	170.073i	0.163380	−	0.282983i	0.936079	+	0.351790i	$0.114427\pi$
$602$		0			0
$603$	137.452	+	137.452i	0.227947	+	0.227947i
$604$		0			0
$605$	210.771	+	56.4758i	0.348381	+	0.0933485i
$606$		0			0
$607$	306.762	+	531.327i	0.505373	+	0.875332i	0.999981	+	0.00621561i	$0.00197850\pi$
$607$	306.762	+	531.327i	0.505373	+	0.875332i	−0.494607	+	0.869116i	$0.664688\pi$
$608$		0			0
$609$	−106.580	−	397.761i	−0.175008	−	0.653139i
$610$		0			0
$611$	3.46098	−	18.7788i	0.00566445	−	0.0307345i
$612$		0			0
$613$	−62.2311	+	16.6748i	−0.101519	+	0.0272019i	−0.309221	−	0.950990i	$-0.600068\pi$
$613$	−62.2311	+	16.6748i	−0.101519	+	0.0272019i	0.207702	+	0.978192i	$0.433402\pi$
$614$		0			0
$615$	740.495	−	427.525i	1.20406	−	0.695163i
$616$		0			0
$617$	77.8358	−	290.487i	0.126152	−	0.470806i	−0.873726	−	0.486418i	$-0.838303\pi$
$617$	77.8358	−	290.487i	0.126152	−	0.470806i	0.999878	+	0.0156125i	$0.00496982\pi$
$618$		0			0
$619$	−591.538	+	591.538i	−0.955635	+	0.955635i	−0.999057	−	0.0434221i	$-0.986174\pi$
$619$	−591.538	+	591.538i	−0.955635	+	0.955635i	0.0434221	+	0.999057i	$0.486174\pi$
$620$		0			0
$621$	−323.598	−	186.830i	−0.521092	−	0.300853i
$622$		0			0
$623$		−	85.6596i		−	0.137495i
$624$		0			0
$625$	248.503			0.397605
$626$		0			0
$627$	−780.313	+	1351.54i	−1.24452	+	2.15557i
$628$		0			0
$629$	248.781	+	248.781i	0.395519	+	0.395519i
$630$		0			0
$631$	−522.771	−	140.076i	−0.828480	−	0.221991i	−0.180430	−	0.983588i	$-0.557749\pi$
$631$	−522.771	−	140.076i	−0.828480	−	0.221991i	−0.648051	+	0.761597i	$0.724416\pi$
$632$		0			0
$633$	52.0998	+	90.2395i	0.0823061	+	0.142558i
$634$		0			0
$635$	39.0503	+	145.738i	0.0614965	+	0.229508i
$636$		0			0
$637$	−491.438	+	39.1726i	−0.771487	+	0.0614954i
$638$		0			0
$639$	−273.033	+	73.1590i	−0.427282	+	0.114490i
$640$		0			0
$641$	474.405	−	273.898i	0.740101	−	0.427298i	−0.0820047	−	0.996632i	$-0.526132\pi$
$641$	474.405	−	273.898i	0.740101	−	0.427298i	0.822106	+	0.569334i	$0.192799\pi$
$642$		0			0
$643$	−285.002	+	1063.64i	−0.443237	+	1.65418i	0.277311	+	0.960780i	$0.410557\pi$
$643$	−285.002	+	1063.64i	−0.443237	+	1.65418i	−0.720549	+	0.693404i	$0.756110\pi$
$644$		0			0
$645$	−499.710	+	499.710i	−0.774744	+	0.774744i
$646$		0			0
$647$	−689.905	−	398.317i	−1.06631	−	0.615636i	−0.139141	−	0.990273i	$-0.544434\pi$
$647$	−689.905	−	398.317i	−1.06631	−	0.615636i	−0.927172	+	0.374636i	$0.877768\pi$
$648$		0			0
$649$		−	370.764i		−	0.571284i
$650$		0			0
$651$	272.465			0.418533
$652$		0			0
$653$	236.088	−	408.916i	0.361544	−	0.626212i	−0.626671	−	0.779284i	$-0.715583\pi$
$653$	236.088	−	408.916i	0.361544	−	0.626212i	0.988215	+	0.153072i	$0.0489165\pi$
$654$		0			0
$655$	−408.996	−	408.996i	−0.624422	−	0.624422i
$656$		0			0
$657$	−235.033	−	62.9770i	−0.357737	−	0.0958554i
$658$		0			0
$659$	−441.736	−	765.109i	−0.670313	−	1.16102i	−0.977815	−	0.209468i	$-0.932827\pi$
$659$	−441.736	−	765.109i	−0.670313	−	1.16102i	0.307503	−	0.951547i	$-0.400507\pi$
$660$		0			0
$661$	82.0653	+	306.272i	0.124153	+	0.463346i	0.999808	−	0.0195911i	$-0.00623645\pi$
$661$	82.0653	+	306.272i	0.124153	+	0.463346i	−0.875655	+	0.482938i	$0.839570\pi$
$662$		0			0
$663$	568.210	+	824.978i	0.857028	+	1.24431i
$664$		0			0
$665$	385.675	−	103.341i	0.579962	−	0.155400i
$666$		0			0
$667$	−676.674	+	390.678i	−1.01450	+	0.585724i
$668$		0			0
$669$	−125.713	+	469.167i	−0.187912	+	0.701296i
$670$		0			0
$671$	−873.201	+	873.201i	−1.30134	+	1.30134i
$672$		0			0
$673$	754.448	+	435.581i	1.12102	+	0.647223i	0.941662	−	0.336561i	$-0.109264\pi$
$673$	754.448	+	435.581i	1.12102	+	0.647223i	0.179361	+	0.983783i	$0.442597\pi$
$674$		0			0
$675$		−	169.320i		−	0.250844i
$676$		0			0
$677$	461.561			0.681774			0.340887	−	0.940104i	$-0.389273\pi$
$677$	461.561			0.681774			0.340887	+	0.940104i	$0.389273\pi$
$678$		0			0
$679$	27.0241	−	46.8071i	0.0397998	−	0.0689353i
$680$		0			0
$681$	−908.074	−	908.074i	−1.33344	−	1.33344i
$682$		0			0
$683$	−260.947	−	69.9207i	−0.382061	−	0.102373i	0.0626767	−	0.998034i	$-0.480036\pi$
$683$	−260.947	−	69.9207i	−0.382061	−	0.102373i	−0.444737	+	0.895661i	$0.646703\pi$
$684$		0			0
$685$	−291.291	−	504.530i	−0.425242	−	0.736541i
$686$		0			0
$687$	418.407	+	1561.52i	0.609035	+	2.27295i
$688$		0			0
$689$	−682.662	+	470.189i	−0.990801	+	0.682422i
$690$		0			0
$691$	720.453	−	193.045i	1.04262	−	0.279370i	0.303423	−	0.952856i	$-0.401870\pi$
$691$	720.453	−	193.045i	1.04262	−	0.279370i	0.739200	+	0.673486i	$0.235204\pi$
$692$		0			0
$693$	179.914	−	103.873i	0.259616	−	0.149889i
$694$		0			0
$695$	8.46935	−	31.6080i	0.0121861	−	0.0454792i
$696$		0			0
$697$	897.373	−	897.373i	1.28748	−	1.28748i
$698$		0			0
$699$	684.152	+	394.995i	0.978758	+	0.565086i
$700$		0			0
$701$			690.777i			0.985416i	0.870195	+	0.492708i	$0.163993\pi$
$701$			690.777i			0.985416i	−0.870195	+	0.492708i	$0.836007\pi$
$702$		0			0
$703$	533.396			0.758743
$704$		0			0
$705$	−10.3118	+	17.8605i	−0.0146266	+	0.0253341i
$706$		0			0
$707$	−10.6609	−	10.6609i	−0.0150790	−	0.0150790i
$708$		0			0
$709$	−147.552	−	39.5364i	−0.208113	−	0.0557637i	0.153256	−	0.988186i	$-0.451024\pi$
$709$	−147.552	−	39.5364i	−0.208113	−	0.0557637i	−0.361369	+	0.932423i	$0.617691\pi$
$710$		0			0
$711$	248.195	+	429.886i	0.349079	+	0.604622i
$712$		0			0
$713$	−133.806	−	499.372i	−0.187667	−	0.700381i
$714$		0			0
$715$	−52.3988	−	657.366i	−0.0732850	−	0.919394i
$716$		0			0
$717$	25.6434	−	6.87113i	0.0357648	−	0.00958316i
$718$		0			0
$719$	−124.371	+	71.8057i	−0.172978	+	0.0998689i	−0.583989	−	0.811761i	$-0.698509\pi$
$719$	−124.371	+	71.8057i	−0.172978	+	0.0998689i	0.411011	+	0.911630i	$0.365176\pi$
$720$		0			0
$721$	−80.6265	+	300.902i	−0.111826	+	0.417340i
$722$		0			0
$723$	−156.876	+	156.876i	−0.216979	+	0.216979i
$724$		0			0
$725$	−306.627	−	177.031i	−0.422934	−	0.244181i
$726$		0			0
$727$		−	686.820i		−	0.944731i	−0.881403	−	0.472366i	$-0.843400\pi$
$727$		−	686.820i		−	0.944731i	0.881403	−	0.472366i	$-0.156600\pi$
$728$		0			0
$729$	59.5725			0.0817182
$730$		0			0
$731$	−524.444	+	908.364i	−0.717434	+	1.24263i
$732$		0			0
$733$	−872.245	−	872.245i	−1.18997	−	1.18997i	−0.977076	−	0.212890i	$-0.931713\pi$
$733$	−872.245	−	872.245i	−1.18997	−	1.18997i	−0.212890	−	0.977076i	$-0.568287\pi$
$734$		0			0
$735$	514.316	+	137.810i	0.699749	+	0.187497i
$736$		0			0
$737$	−277.889	−	481.317i	−0.377054	−	0.653076i
$738$		0			0
$739$	−6.80119	−	25.3824i	−0.00920324	−	0.0343469i	0.961172	−	0.275952i	$-0.0889930\pi$
$739$	−6.80119	−	25.3824i	−0.00920324	−	0.0343469i	−0.970375	+	0.241605i	$0.922326\pi$
$740$		0			0
$741$	1493.52	+	275.260i	2.01555	+	0.371472i
$742$		0			0
$743$	71.3965	−	19.1306i	0.0960922	−	0.0257478i	−0.210453	−	0.977604i	$-0.567494\pi$
$743$	71.3965	−	19.1306i	0.0960922	−	0.0257478i	0.306545	+	0.951856i	$0.400827\pi$
$744$		0			0
$745$	−428.995	+	247.680i	−0.575832	+	0.332457i
$746$		0			0
$747$	165.238	−	616.676i	0.221202	−	0.825537i
$748$		0			0
$749$	106.084	−	106.084i	0.141634	−	0.141634i
$750$		0			0
$751$	1056.15	+	609.769i	1.40633	+	0.811942i	0.995032	−	0.0995605i	$-0.0317437\pi$
$751$	1056.15	+	609.769i	1.40633	+	0.811942i	0.411294	+	0.911503i	$0.365077\pi$
$752$		0			0
$753$		−	479.971i		−	0.637411i
$754$		0			0
$755$	−125.009			−0.165575
$756$		0			0
$757$	−255.281	+	442.159i	−0.337227	+	0.584094i	−0.983910	−	0.178664i	$-0.942822\pi$
$757$	−255.281	+	442.159i	−0.337227	+	0.584094i	0.646683	+	0.762759i	$0.276156\pi$
$758$		0			0
$759$	−815.628	−	815.628i	−1.07461	−	1.07461i
$760$		0			0
$761$	−200.823	−	53.8104i	−0.263894	−	0.0707101i	0.124446	−	0.992226i	$-0.460285\pi$
$761$	−200.823	−	53.8104i	−0.263894	−	0.0707101i	−0.388340	+	0.921516i	$0.626951\pi$
$762$		0			0
$763$	−238.705	−	413.449i	−0.312851	−	0.541873i
$764$		0			0
$765$	−95.6937	−	357.134i	−0.125090	−	0.466841i
$766$		0			0
$767$	−339.982	+	120.778i	−0.443262	+	0.157467i
$768$		0			0
$769$	674.840	−	180.823i	0.877555	−	0.235140i	0.208203	−	0.978086i	$-0.433238\pi$
$769$	674.840	−	180.823i	0.877555	−	0.235140i	0.669352	+	0.742945i	$0.266572\pi$
$770$		0			0
$771$	−833.445	+	481.190i	−1.08099	+	0.624111i
$772$		0			0
$773$	56.4664	−	210.735i	0.0730483	−	0.272620i	−0.919735	−	0.392539i	$-0.871597\pi$
$773$	56.4664	−	210.735i	0.0730483	−	0.272620i	0.992784	+	0.119919i	$0.0382635\pi$
$774$		0			0
$775$	165.652	−	165.652i	0.213745	−	0.213745i
$776$		0			0
$777$	−179.936	−	103.886i	−0.231578	−	0.133702i
$778$		0			0
$779$		−	1924.00i		−	2.46984i
$780$		0			0
$781$	808.176			1.03480
$782$		0			0
$783$	267.719	−	463.702i	0.341914	−	0.592212i
$784$		0			0
$785$	−597.840	−	597.840i	−0.761580	−	0.761580i
$786$		0			0
$787$	282.834	+	75.7852i	0.359383	+	0.0962963i	0.433993	−	0.900916i	$-0.357104\pi$
$787$	282.834	+	75.7852i	0.359383	+	0.0962963i	−0.0746097	+	0.997213i	$0.523771\pi$
$788$		0			0
$789$	−56.7972	−	98.3757i	−0.0719863	−	0.124684i
$790$		0			0
$791$	76.2724	+	284.653i	0.0964253	+	0.359864i
$792$		0			0
$793$	1085.15	+	516.258i	1.36842	+	0.651019i
$794$		0			0
$795$	864.764	−	231.713i	1.08775	−	0.291463i
$796$		0			0
$797$	−155.324	+	89.6766i	−0.194886	+	0.112518i	−0.594268	−	0.804267i	$-0.702558\pi$
$797$	−155.324	+	89.6766i	−0.194886	+	0.112518i	0.399382	+	0.916785i	$0.369225\pi$
$798$		0			0
$799$	−7.92238	+	29.5667i	−0.00991537	+	0.0370047i
$800$		0			0
$801$	−85.0330	+	85.0330i	−0.106159	+	0.106159i
$802$		0			0
$803$	602.491	+	347.849i	0.750300	+	0.433186i
$804$		0			0
$805$			295.111i			0.366598i
$806$		0			0
$807$	1231.56			1.52610
$808$		0			0
$809$	−430.083	+	744.925i	−0.531622	+	0.920797i	0.467696	+	0.883889i	$0.345084\pi$
$809$	−430.083	+	744.925i	−0.531622	+	0.920797i	−0.999319	+	0.0369079i	$0.988249\pi$
$810$		0			0
$811$	−35.4247	−	35.4247i	−0.0436803	−	0.0436803i	0.684929	−	0.728610i	$-0.259833\pi$
$811$	−35.4247	−	35.4247i	−0.0436803	−	0.0436803i	−0.728610	+	0.684929i	$0.759833\pi$
$812$		0			0
$813$	−924.511	−	247.722i	−1.13716	−	0.304701i
$814$		0			0
$815$	475.500	+	823.590i	0.583435	+	1.01054i
$816$		0			0
$817$	411.570	+	1536.00i	0.503757	+	1.88005i
$818$		0			0
$819$	−153.857	−	131.140i	−0.187860	−	0.160122i
$820$		0			0
$821$	−638.186	+	171.001i	−0.777328	+	0.208284i	−0.625606	−	0.780139i	$-0.715148\pi$
$821$	−638.186	+	171.001i	−0.777328	+	0.208284i	−0.151722	+	0.988423i	$0.548482\pi$
$822$		0			0
$823$	584.548	−	337.489i	0.710264	−	0.410071i	−0.100895	−	0.994897i	$-0.532170\pi$
$823$	584.548	−	337.489i	0.710264	−	0.410071i	0.811159	+	0.584826i	$0.198837\pi$
$824$		0			0
$825$	135.280	−	504.873i	0.163976	−	0.611968i
$826$		0			0
$827$	−181.364	+	181.364i	−0.219304	+	0.219304i	−0.808205	−	0.588901i	$-0.799561\pi$
$827$	−181.364	+	181.364i	−0.219304	+	0.219304i	0.588901	+	0.808205i	$0.299561\pi$
$828$		0			0
$829$	−107.685	−	62.1718i	−0.129897	−	0.0749962i	0.433643	−	0.901085i	$-0.357228\pi$
$829$	−107.685	−	62.1718i	−0.129897	−	0.0749962i	−0.563541	+	0.826088i	$0.690561\pi$
$830$		0			0
$831$		−	650.923i		−	0.783301i
$832$		0			0
$833$	790.282			0.948718
$834$		0			0
$835$	−115.120	+	199.393i	−0.137868	+	0.238794i
$836$		0			0
$837$	250.510	+	250.510i	0.299295	+	0.299295i
$838$		0			0
$839$	−1421.93	−	381.004i	−1.69479	−	0.454117i	−0.723170	−	0.690670i	$-0.757316\pi$
$839$	−1421.93	−	381.004i	−1.69479	−	0.454117i	−0.971618	+	0.236553i	$0.923982\pi$
$840$		0			0
$841$	−139.325	−	241.317i	−0.165665	−	0.286941i
$842$		0			0
$843$	68.8764	+	257.050i	0.0817040	+	0.304923i
$844$		0			0
$845$	−585.722	+	262.188i	−0.693162	+	0.310282i
$846$		0			0
$847$	−184.741	+	49.5011i	−0.218112	+	0.0584429i
$848$		0			0
$849$	335.217	−	193.538i	0.394838	−	0.227960i
$850$		0			0
$851$	−102.036	+	380.805i	−0.119902	+	0.447479i
$852$		0			0
$853$	−99.5753	+	99.5753i	−0.116735	+	0.116735i	−0.763061	−	0.646326i	$-0.776305\pi$
$853$	−99.5753	+	99.5753i	−0.116735	+	0.116735i	0.646326	+	0.763061i	$0.276305\pi$
$854$		0			0
$855$	−485.440	−	280.269i	−0.567766	−	0.327800i
$856$		0			0
$857$			781.188i			0.911537i	0.890098	+	0.455769i	$0.150636\pi$
$857$			781.188i			0.911537i	−0.890098	+	0.455769i	$0.849364\pi$
$858$		0			0
$859$	−988.460			−1.15071			−0.575355	−	0.817904i	$-0.695136\pi$
$859$	−988.460			−1.15071			−0.575355	+	0.817904i	$0.695136\pi$
$860$		0			0
$861$	−374.726	+	649.045i	−0.435222	+	0.753826i
$862$		0			0
$863$	128.890	+	128.890i	0.149351	+	0.149351i	0.777828	−	0.628477i	$-0.216321\pi$
$863$	128.890	+	128.890i	0.149351	+	0.149351i	−0.628477	+	0.777828i	$0.716321\pi$
$864$		0			0
$865$	−431.567	−	115.638i	−0.498921	−	0.133686i
$866$		0			0
$867$	−268.584	−	465.202i	−0.309786	−	0.536565i
$868$		0			0
$869$	−367.328	−	1370.89i	−0.422702	−	1.57754i
$870$		0			0
$871$	−350.834	+	411.609i	−0.402795	+	0.472570i
$872$		0			0
$873$	−73.2911	+	19.6383i	−0.0839532	+	0.0224952i
$874$		0			0
$875$	−389.431	+	224.838i	−0.445064	+	0.256958i
$876$		0			0
$877$	−129.844	+	484.583i	−0.148054	+	0.552546i	0.851546	+	0.524280i	$0.175665\pi$
$877$	−129.844	+	484.583i	−0.148054	+	0.552546i	−0.999600	+	0.0282663i	$0.991001\pi$
$878$		0			0
$879$	−1286.35	+	1286.35i	−1.46342	+	1.46342i
$880$		0			0
$881$	434.781	+	251.021i	0.493508	+	0.284927i	0.726029	−	0.687664i	$-0.241364\pi$
$881$	434.781	+	251.021i	0.493508	+	0.284927i	−0.232520	+	0.972592i	$0.574697\pi$
$882$		0			0
$883$			35.9135i			0.0406722i	0.999793	+	0.0203361i	$0.00647362\pi$
$883$			35.9135i			0.0406722i	−0.999793	+	0.0203361i	$0.993526\pi$
$884$		0			0
$885$	389.678			0.440314
$886$		0			0
$887$	−12.4069	+	21.4894i	−0.0139875	+	0.0242270i	−0.872934	−	0.487838i	$-0.837786\pi$
$887$	−12.4069	+	21.4894i	−0.0139875	+	0.0242270i	0.858947	+	0.512065i	$0.171119\pi$
$888$		0			0
$889$	−93.5115	−	93.5115i	−0.105187	−	0.105187i
$890$		0			0
$891$	1306.13	+	349.978i	1.46592	+	0.392792i
$892$		0			0
$893$	23.2032	+	40.1891i	0.0259834	+	0.0450045i
$894$		0			0
$895$	−87.2691	−	325.693i	−0.0975074	−	0.363902i
$896$		0			0
$897$	−482.219	+	1013.61i	−0.537591	+	1.13000i
$898$		0			0
$899$	715.578	−	191.739i	0.795971	−	0.213280i
$900$		0			0
$901$	1150.75	−	664.385i	1.27719	−	0.737387i
$902$		0			0
$903$	160.318	−	598.314i	0.177539	−	0.662585i
$904$		0			0
$905$	−705.136	+	705.136i	−0.779155	+	0.779155i
$906$		0			0
$907$	−619.873	−	357.884i	−0.683432	−	0.394580i	0.117715	−	0.993047i	$-0.462443\pi$
$907$	−619.873	−	357.884i	−0.683432	−	0.394580i	−0.801147	+	0.598468i	$0.795776\pi$
$908$		0			0
$909$			21.1658i			0.0232847i
$910$		0			0
$911$	−1087.62			−1.19387			−0.596935	−	0.802289i	$-0.703615\pi$
$911$	−1087.62			−1.19387			−0.596935	+	0.802289i	$0.703615\pi$
$912$		0			0
$913$	−912.678	+	1580.80i	−0.999647	+	1.73144i
$914$		0			0
$915$	−917.748	−	917.748i	−1.00300	−	1.00300i
$916$		0			0
$917$	489.700	+	131.215i	0.534024	+	0.143091i
$918$		0			0
$919$	839.377	+	1453.84i	0.913359	+	1.58198i	0.809287	+	0.587414i	$0.199854\pi$
$919$	839.377	+	1453.84i	0.913359	+	1.58198i	0.104072	+	0.994570i	$0.466813\pi$
$920$		0			0
$921$	−163.766	−	611.183i	−0.177813	−	0.663608i
$922$		0			0
$923$	−263.266	−	741.080i	−0.285229	−	0.802903i
$924$		0			0
$925$	−172.557	+	46.2366i	−0.186549	+	0.0499855i
$926$		0			0
$927$	378.738	−	218.665i	0.408563	−	0.235884i
$928$		0			0
$929$	155.112	−	578.885i	0.166966	−	0.623127i	−0.830815	−	0.556549i	$-0.812125\pi$
$929$	155.112	−	578.885i	0.166966	−	0.623127i	0.997781	−	0.0665780i	$-0.0212081\pi$
$930$		0			0
$931$	847.198	−	847.198i	0.909987	−	0.909987i
$932$		0			0
$933$	1770.18	+	1022.02i	1.89730	+	1.09541i
$934$		0			0
$935$			1057.11i			1.13060i
$936$		0			0
$937$	234.285			0.250037			0.125018	−	0.992154i	$-0.460101\pi$
$937$	234.285			0.250037			0.125018	+	0.992154i	$0.460101\pi$
$938$		0			0
$939$	428.739	−	742.597i	0.456591	−	0.790838i
$940$		0			0
$941$	715.410	+	715.410i	0.760265	+	0.760265i	0.976370	−	0.216105i	$-0.0693353\pi$
$941$	715.410	+	715.410i	0.760265	+	0.760265i	−0.216105	+	0.976370i	$0.569335\pi$
$942$		0			0
$943$	1373.59	+	368.053i	1.45662	+	0.390300i
$944$		0			0
$945$	−101.115	−	175.136i	−0.107000	−	0.185330i
$946$		0			0
$947$	−314.762	−	1174.71i	−0.332378	−	1.24045i	−0.906684	−	0.421810i	$-0.861395\pi$
$947$	−314.762	−	1174.71i	−0.332378	−	1.24045i	0.574306	−	0.818640i	$-0.305272\pi$
$948$		0			0
$949$	122.706	−	665.784i	0.129300	−	0.701564i
$950$		0			0
$951$	312.219	−	83.6587i	0.328306	−	0.0879692i
$952$		0			0
$953$	−229.051	+	132.242i	−0.240347	+	0.138764i	−0.615336	−	0.788265i	$-0.710980\pi$
$953$	−229.051	+	132.242i	−0.240347	+	0.138764i	0.374989	+	0.927029i	$0.377646\pi$
$954$		0			0
$955$	98.0915	−	366.082i	0.102714	−	0.383332i
$956$		0			0
$957$	1168.76	−	1168.76i	1.22127	−	1.22127i
$958$		0			0
$959$	442.221	+	255.317i	0.461127	+	0.266232i
$960$		0			0
$961$		−	470.832i		−	0.489940i
$962$		0			0
$963$	−210.616			−0.218708
$964$		0			0
$965$	317.570	−	550.047i	0.329088	−	0.569997i
$966$		0			0
$967$	−309.257	−	309.257i	−0.319810	−	0.319810i	0.528884	−	0.848694i	$-0.322611\pi$
$967$	−309.257	−	309.257i	−0.319810	−	0.319810i	−0.848694	+	0.528884i	$0.822611\pi$
$968$		0			0
$969$	−2351.52	−	630.087i	−2.42675	−	0.650244i
$970$		0			0
$971$	−381.974	−	661.599i	−0.393383	−	0.681359i	0.599511	−	0.800367i	$-0.295362\pi$
$971$	−381.974	−	661.599i	−0.393383	−	0.681359i	−0.992893	+	0.119008i	$0.962029\pi$
$972$		0			0
$973$	7.42339	+	27.7045i	0.00762938	+	0.0284732i
$974$		0			0
$975$	−507.026	+	40.4151i	−0.520026	+	0.0414514i
$976$		0			0
$977$	755.665	−	202.480i	0.773455	−	0.207247i	0.149558	−	0.988753i	$-0.452215\pi$
$977$	755.665	−	202.480i	0.773455	−	0.207247i	0.623897	+	0.781506i	$0.285548\pi$
$978$		0			0
$979$	297.761	−	171.912i	0.304148	−	0.175600i
$980$		0			0
$981$	−173.466	+	647.384i	−0.176826	+	0.659923i
$982$		0			0
$983$	−58.4984	+	58.4984i	−0.0595101	+	0.0595101i	−0.736236	−	0.676725i	$-0.763398\pi$
$983$	−58.4984	+	58.4984i	−0.0595101	+	0.0595101i	0.676725	+	0.736236i	$0.263398\pi$
$984$		0			0
$985$	−1114.77	−	643.611i	−1.13174	−	0.653412i
$986$		0			0
$987$		−	18.0765i		−	0.0183146i
$988$		0			0
$989$	−1175.32			−1.18839
$990$		0			0
$991$	89.6331	−	155.249i	0.0904471	−	0.156659i	−0.817252	−	0.576280i	$-0.804504\pi$
$991$	89.6331	−	155.249i	0.0904471	−	0.156659i	0.907699	+	0.419621i	$0.137837\pi$
$992$		0			0
$993$	1638.41	+	1638.41i	1.64996	+	1.64996i
$994$		0			0
$995$	−69.1651	−	18.5327i	−0.0695127	−	0.0186259i
$996$		0			0
$997$	−43.0656	−	74.5919i	−0.0431952	−	0.0748163i	0.843619	−	0.536941i	$-0.180420\pi$
$997$	−43.0656	−	74.5919i	−0.0431952	−	0.0748163i	−0.886815	+	0.462125i	$0.847087\pi$
$998$		0			0
$999$	−69.9221	−	260.953i	−0.0699921	−	0.261214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.3.k.a.33.2	✓	8
3.2	odd	2		468.3.cd.b.397.2		8
4.3	odd	2		208.3.bd.e.33.1		8
13.2	odd	12	inner	52.3.k.a.41.2	yes	8
13.4	even	6		676.3.g.c.437.1		8
13.6	odd	12		676.3.g.d.577.1		8
13.7	odd	12		676.3.g.c.577.1		8
13.9	even	3		676.3.g.d.437.1		8
39.2	even	12		468.3.cd.b.145.2		8
52.15	even	12		208.3.bd.e.145.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.3.k.a.33.2	✓	8	1.1	even	1	trivial
52.3.k.a.41.2	yes	8	13.2	odd	12	inner
208.3.bd.e.33.1		8	4.3	odd	2
208.3.bd.e.145.1		8	52.15	even	12
468.3.cd.b.145.2		8	39.2	even	12
468.3.cd.b.397.2		8	3.2	odd	2
676.3.g.c.437.1		8	13.4	even	6
676.3.g.c.577.1		8	13.7	odd	12
676.3.g.d.437.1		8	13.9	even	3
676.3.g.d.577.1		8	13.6	odd	12

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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	52.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.84881 - 3.20224i) q^{3} +(-2.68502 - 2.68502i) q^{5} +(3.21484 + 0.861413i) q^{7} +(-2.33621 - 4.04644i) q^{9} +(3.45758 + 12.9039i) q^{11} +(10.7063 - 7.37401i) q^{13} +(-13.5622 + 3.63397i) q^{15} +(-18.0473 + 10.4196i) q^{17} +(-8.17703 + 30.5171i) q^{19} +(8.70208 - 8.70208i) q^{21} +(-20.2227 - 11.6756i) q^{23} -10.5813i q^{25} +16.0018 q^{27} +(16.7306 - 28.9782i) q^{29} +(15.6552 + 15.6552i) q^{31} +(47.7137 + 12.7848i) q^{33} +(-6.31900 - 10.9448i) q^{35} +(-4.36965 - 16.3078i) q^{37} +(-3.81948 - 47.9171i) q^{39} +(-58.8233 + 15.7617i) q^{41} +(43.5891 - 25.1662i) q^{43} +(-4.59199 + 17.1375i) q^{45} +(1.03863 - 1.03863i) q^{47} +(-32.8421 - 18.9614i) q^{49} +77.0557i q^{51} -63.7629 q^{53} +(25.3635 - 43.9309i) q^{55} +(82.6052 + 82.6052i) q^{57} +(-26.8080 - 7.18318i) q^{59} +(46.2192 + 80.0541i) q^{61} +(-4.02488 - 15.0211i) q^{63} +(-48.5459 - 8.94714i) q^{65} +(-40.1854 + 10.7676i) q^{67} +(-74.7758 + 43.1718i) q^{69} +(15.6576 - 58.4350i) q^{71} +(36.8238 - 36.8238i) q^{73} +(-33.8838 - 19.5628i) q^{75} +44.4623i q^{77} -106.238 q^{79} +(50.6101 - 87.6593i) q^{81} +(96.6176 + 96.6176i) q^{83} +(76.4344 + 20.4805i) q^{85} +(-61.8634 - 107.151i) q^{87} +(-6.66127 - 24.8602i) q^{89} +(40.7709 - 14.4837i) q^{91} +(79.0750 - 21.1881i) q^{93} +(103.895 - 59.9836i) q^{95} +(4.20302 - 15.6859i) q^{97} +(44.1371 - 44.1371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{5} + 4 q^{7} - 6 q^{9} + 24 q^{11} + 18 q^{13} - 60 q^{15} - 54 q^{17} - 50 q^{19} - 54 q^{21} - 24 q^{23} + 36 q^{27} + 108 q^{29} + 176 q^{31} + 114 q^{33} - 30 q^{35} + 104 q^{37} + 120 q^{39}+ \cdots + 182 q^{97}+O(q^{100}) \) 8 * q + 6 * q^5 + 4 * q^7 - 6 * q^9 + 24 * q^11 + 18 * q^13 - 60 * q^15 - 54 * q^17 - 50 * q^19 - 54 * q^21 - 24 * q^23 + 36 * q^27 + 108 * q^29 + 176 * q^31 + 114 * q^33 - 30 * q^35 + 104 * q^37 + 120 * q^39 - 168 * q^41 - 198 * q^43 + 6 * q^45 - 96 * q^47 - 162 * q^49 - 72 * q^53 + 126 * q^55 + 318 * q^57 - 18 * q^61 + 180 * q^63 - 72 * q^65 - 326 * q^67 - 498 * q^69 - 162 * q^71 - 98 * q^73 - 240 * q^75 + 192 * q^79 + 240 * q^81 + 408 * q^83 + 318 * q^85 + 36 * q^87 + 54 * q^89 + 280 * q^91 - 66 * q^93 + 312 * q^95 + 182 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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