LMFDB - Embedded newform 392.3.h.a.293.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(293,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("392.293");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.h (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.5
Character	$\chi$	$=$	392.293
Dual form			392.3.h.a.293.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61618 - 1.17812i) q^{2} -2.33563 q^{3} +(1.22408 + 3.80810i) q^{4} +3.10110 q^{5} +(3.77480 + 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} -3.54484 q^{9} +O(q^{10})$	\(q+(-1.61618 - 1.17812i) q^{2} -2.33563 q^{3} +(1.22408 + 3.80810i) q^{4} +3.10110 q^{5} +(3.77480 + 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} -3.54484 q^{9} +(-5.01193 - 3.65346i) q^{10} -4.69506i q^{11} +(-2.85898 - 8.89431i) q^{12} -6.88097 q^{13} -7.24301 q^{15} +(-13.0033 + 9.32281i) q^{16} +16.9953i q^{17} +(5.72910 + 4.17624i) q^{18} +26.2198 q^{19} +(3.79598 + 11.8093i) q^{20} +(-5.53134 + 7.58806i) q^{22} +25.8805 q^{23} +(-5.85792 + 17.7430i) q^{24} -15.3832 q^{25} +(11.1209 + 8.10660i) q^{26} +29.3001 q^{27} -42.2701i q^{29} +(11.7060 + 8.53312i) q^{30} +18.3625i q^{31} +(31.9990 + 0.252068i) q^{32} +10.9659i q^{33} +(20.0225 - 27.4675i) q^{34} +(-4.33915 - 13.4991i) q^{36} -49.8827i q^{37} +(-42.3759 - 30.8900i) q^{38} +16.0714 q^{39} +(7.77776 - 23.5581i) q^{40} -10.7844i q^{41} -24.1791i q^{43} +(17.8793 - 5.74711i) q^{44} -10.9929 q^{45} +(-41.8276 - 30.4903i) q^{46} -13.6809i q^{47} +(30.3708 - 21.7746i) q^{48} +(24.8620 + 18.1232i) q^{50} -39.6947i q^{51} +(-8.42282 - 26.2034i) q^{52} +6.97379i q^{53} +(-47.3542 - 34.5190i) q^{54} -14.5598i q^{55} -61.2396 q^{57} +(-49.7992 + 68.3161i) q^{58} +106.184 q^{59} +(-8.86599 - 27.5821i) q^{60} +93.4609 q^{61} +(21.6332 - 29.6771i) q^{62} +(-51.4192 - 38.1060i) q^{64} -21.3386 q^{65} +(12.9191 - 17.7229i) q^{66} -89.2299i q^{67} +(-64.7199 + 20.8035i) q^{68} -60.4473 q^{69} +81.7898 q^{71} +(-8.89070 + 26.9290i) q^{72} -137.956i q^{73} +(-58.7677 + 80.6194i) q^{74} +35.9294 q^{75} +(32.0950 + 99.8475i) q^{76} +(-25.9743 - 18.9340i) q^{78} -13.1018 q^{79} +(-40.3244 + 28.9109i) q^{80} -36.5306 q^{81} +(-12.7053 + 17.4296i) q^{82} +2.15689 q^{83} +52.7041i q^{85} +(-28.4858 + 39.0777i) q^{86} +98.7272i q^{87} +(-35.6669 - 11.7755i) q^{88} +101.413i q^{89} +(17.7665 + 12.9509i) q^{90} +(31.6797 + 98.5556i) q^{92} -42.8880i q^{93} +(-16.1177 + 22.1108i) q^{94} +81.3101 q^{95} +(-74.7378 - 0.588736i) q^{96} -88.9318i q^{97} +16.6432i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.61618	−	1.17812i	−0.808090	−	0.589059i
$2$	−1.61618	−	1.17812i	−0.808090	−	0.589059i
$3$	−2.33563			−0.778543			−0.389271	−	0.921123i	$-0.627273\pi$
$3$	−2.33563			−0.778543			−0.389271	+	0.921123i	$0.627273\pi$
$4$	1.22408	+	3.80810i	0.306019	+	0.952025i
$5$	3.10110			0.620220			0.310110	−	0.950701i	$-0.399634\pi$
$5$	3.10110			0.620220			0.310110	+	0.950701i	$0.399634\pi$
$6$	3.77480	+	2.75165i	0.629133	+	0.458608i
$7$		0			0
$7$		0			0
$8$	2.50807	−	7.59668i	0.313509	−	0.949585i
$9$	−3.54484			−0.393871
$10$	−5.01193	−	3.65346i	−0.501193	−	0.365346i
$11$		−	4.69506i		−	0.426824i	−0.976962	−	0.213412i	$-0.931542\pi$
$11$		−	4.69506i		−	0.426824i	0.976962	−	0.213412i	$-0.0684576\pi$
$12$	−2.85898	−	8.89431i	−0.238249	−	0.741193i
$13$	−6.88097			−0.529305			−0.264653	−	0.964344i	$-0.585257\pi$
$13$	−6.88097			−0.529305			−0.264653	+	0.964344i	$0.585257\pi$
$14$		0			0
$15$	−7.24301			−0.482868
$16$	−13.0033	+	9.32281i	−0.812705	+	0.582675i
$17$			16.9953i			0.999724i	0.866105	+	0.499862i	$0.166616\pi$
$17$			16.9953i			0.999724i	−0.866105	+	0.499862i	$0.833384\pi$
$18$	5.72910	+	4.17624i	0.318283	+	0.232013i
$19$	26.2198			1.37999			0.689994	−	0.723815i	$-0.257613\pi$
$19$	26.2198			1.37999			0.689994	+	0.723815i	$0.257613\pi$
$20$	3.79598	+	11.8093i	0.189799	+	0.590465i
$21$		0			0
$22$	−5.53134	+	7.58806i	−0.251424	+	0.344912i
$23$	25.8805			1.12524			0.562620	−	0.826716i	$-0.309794\pi$
$23$	25.8805			1.12524			0.562620	+	0.826716i	$0.309794\pi$
$24$	−5.85792	+	17.7430i	−0.244080	+	0.739293i
$25$	−15.3832			−0.615328
$26$	11.1209	+	8.10660i	0.427726	+	0.311792i
$27$	29.3001			1.08519
$28$		0			0
$29$		−	42.2701i		−	1.45759i	−0.684732	−	0.728795i	$-0.740081\pi$
$29$		−	42.2701i		−	1.45759i	0.684732	−	0.728795i	$-0.259919\pi$
$30$	11.7060	+	8.53312i	0.390200	+	0.284437i
$31$			18.3625i			0.592339i	0.955135	+	0.296170i	$0.0957094\pi$
$31$			18.3625i			0.592339i	−0.955135	+	0.296170i	$0.904291\pi$
$32$	31.9990	+	0.252068i	0.999969	+	0.00787711i
$33$			10.9659i			0.332301i
$34$	20.0225	−	27.4675i	0.588896	−	0.807867i
$35$		0			0
$36$	−4.33915	−	13.4991i	−0.120532	−	0.374975i
$37$		−	49.8827i		−	1.34818i	−0.738649	−	0.674090i	$-0.764536\pi$
$37$		−	49.8827i		−	1.34818i	0.738649	−	0.674090i	$-0.235464\pi$
$38$	−42.3759	−	30.8900i	−1.11515	−	0.812894i
$39$	16.0714			0.412087
$40$	7.77776	−	23.5581i	0.194444	−	0.588951i
$41$		−	10.7844i		−	0.263035i	−0.991314	−	0.131517i	$-0.958015\pi$
$41$		−	10.7844i		−	0.263035i	0.991314	−	0.131517i	$-0.0419849\pi$
$42$		0			0
$43$		−	24.1791i		−	0.562304i	−0.959663	−	0.281152i	$-0.909284\pi$
$43$		−	24.1791i		−	0.562304i	0.959663	−	0.281152i	$-0.0907165\pi$
$44$	17.8793	−	5.74711i	0.406347	−	0.130616i
$45$	−10.9929			−0.244287
$46$	−41.8276	−	30.4903i	−0.909295	−	0.662833i
$47$		−	13.6809i		−	0.291083i	−0.989352	−	0.145542i	$-0.953508\pi$
$47$		−	13.6809i		−	0.291083i	0.989352	−	0.145542i	$-0.0464925\pi$
$48$	30.3708	−	21.7746i	0.632726	−	0.453638i
$49$		0			0
$50$	24.8620	+	18.1232i	0.497240	+	0.362464i
$51$		−	39.6947i		−	0.778328i
$52$	−8.42282	−	26.2034i	−0.161977	−	0.503912i
$53$			6.97379i			0.131581i	0.997833	+	0.0657905i	$0.0209569\pi$
$53$			6.97379i			0.131581i	−0.997833	+	0.0657905i	$0.979043\pi$
$54$	−47.3542	−	34.5190i	−0.876930	−	0.639240i
$55$		−	14.5598i		−	0.264724i
$56$		0			0
$57$	−61.2396			−1.07438
$58$	−49.7992	+	68.3161i	−0.858606	+	1.17786i
$59$	106.184			1.79974			0.899868	−	0.436163i	$-0.143663\pi$
$59$	106.184			1.79974			0.899868	+	0.436163i	$0.143663\pi$
$60$	−8.86599	−	27.5821i	−0.147767	−	0.459702i
$61$	93.4609			1.53215			0.766073	−	0.642754i	$-0.222208\pi$
$61$	93.4609			1.53215			0.766073	+	0.642754i	$0.222208\pi$
$62$	21.6332	−	29.6771i	0.348923	−	0.478663i
$63$		0			0
$64$	−51.4192	−	38.1060i	−0.803425	−	0.595406i
$65$	−21.3386			−0.328286
$66$	12.9191	−	17.7229i	0.195745	−	0.268529i
$67$		−	89.2299i		−	1.33179i	−0.746046	−	0.665894i	$-0.768050\pi$
$67$		−	89.2299i		−	1.33179i	0.746046	−	0.665894i	$-0.231950\pi$
$68$	−64.7199	+	20.8035i	−0.951763	+	0.305934i
$69$	−60.4473			−0.876047
$70$		0			0
$71$	81.7898			1.15197			0.575984	−	0.817461i	$-0.304619\pi$
$71$	81.7898			1.15197			0.575984	+	0.817461i	$0.304619\pi$
$72$	−8.89070	+	26.9290i	−0.123482	+	0.374014i
$73$		−	137.956i		−	1.88981i	−0.327347	−	0.944904i	$-0.606155\pi$
$73$		−	137.956i		−	1.88981i	0.327347	−	0.944904i	$-0.393845\pi$
$74$	−58.7677	+	80.6194i	−0.794158	+	1.08945i
$75$	35.9294			0.479059
$76$	32.0950	+	99.8475i	0.422302	+	1.31378i
$77$		0			0
$78$	−25.9743	−	18.9340i	−0.333003	−	0.242744i
$79$	−13.1018			−0.165846			−0.0829228	−	0.996556i	$-0.526426\pi$
$79$	−13.1018			−0.165846			−0.0829228	+	0.996556i	$0.526426\pi$
$80$	−40.3244	+	28.9109i	−0.504056	+	0.361387i
$81$	−36.5306			−0.450995
$82$	−12.7053	+	17.4296i	−0.154943	+	0.212556i
$83$	2.15689			0.0259867			0.0129933	−	0.999916i	$-0.495864\pi$
$83$	2.15689			0.0259867			0.0129933	+	0.999916i	$0.495864\pi$
$84$		0			0
$85$			52.7041i			0.620048i
$86$	−28.4858	+	39.0777i	−0.331230	+	0.454392i
$87$			98.7272i			1.13480i
$88$	−35.6669	−	11.7755i	−0.405306	−	0.133813i
$89$			101.413i			1.13947i	0.821828	+	0.569735i	$0.192954\pi$
$89$			101.413i			1.13947i	−0.821828	+	0.569735i	$0.807046\pi$
$90$	17.7665	+	12.9509i	0.197405	+	0.143899i
$91$		0			0
$92$	31.6797	+	98.5556i	0.344344	+	1.07126i
$93$		−	42.8880i		−	0.461162i
$94$	−16.1177	+	22.1108i	−0.171465	+	0.235222i
$95$	81.3101			0.855895
$96$	−74.7378	−	0.588736i	−0.778519	−	0.00613267i
$97$		−	88.9318i		−	0.916823i	−0.888740	−	0.458412i	$-0.848419\pi$
$97$		−	88.9318i		−	0.916823i	0.888740	−	0.458412i	$-0.151581\pi$
$98$		0			0
$99$			16.6432i			0.168114i
$100$	−18.8302	−	58.5808i	−0.188302	−	0.585808i
$101$	20.8477			0.206413			0.103206	−	0.994660i	$-0.467090\pi$
$101$	20.8477			0.206413			0.103206	+	0.994660i	$0.467090\pi$
$102$	−46.7651	+	64.1538i	−0.458481	+	0.628959i
$103$		−	3.43487i		−	0.0333483i	−0.999861	−	0.0166741i	$-0.994692\pi$
$103$		−	3.43487i		−	0.0333483i	0.999861	−	0.0166741i	$-0.00530779\pi$
$104$	−17.2579	+	52.2725i	−0.165942	+	0.502621i
$105$		0			0
$106$	8.21595	−	11.2709i	0.0775090	−	0.106329i
$107$		−	67.5041i		−	0.630880i	−0.948946	−	0.315440i	$-0.897848\pi$
$107$		−	67.5041i		−	0.630880i	0.948946	−	0.315440i	$-0.102152\pi$
$108$	35.8655	+	111.578i	0.332088	+	1.03313i
$109$			135.055i			1.23903i	0.784984	+	0.619516i	$0.212671\pi$
$109$			135.055i			1.23903i	−0.784984	+	0.619516i	$0.787329\pi$
$110$	−17.1532	+	23.5313i	−0.155938	+	0.213921i
$111$			116.507i			1.04962i
$112$		0			0
$113$	136.328			1.20645			0.603223	−	0.797573i	$-0.293883\pi$
$113$	136.328			1.20645			0.603223	+	0.797573i	$0.293883\pi$
$114$	98.9743	+	72.1475i	0.868195	+	0.632873i
$115$	80.2580			0.697896
$116$	160.969	−	51.7418i	1.38766	−	0.446050i
$117$	24.3919			0.208478
$118$	−171.613	−	125.098i	−1.45435	−	1.06015i
$119$		0			0
$120$	−18.1660	+	55.0229i	−0.151383	+	0.458524i
$121$	98.9564			0.817821
$122$	−151.050	−	110.108i	−1.23811	−	0.902524i
$123$			25.1884i			0.204784i
$124$	−69.9263	+	22.4771i	−0.563922	+	0.181267i
$125$	−125.232			−1.00186
$126$		0			0
$127$	−6.39702			−0.0503702			−0.0251851	−	0.999683i	$-0.508018\pi$
$127$	−6.39702			−0.0503702			−0.0251851	+	0.999683i	$0.508018\pi$
$128$	38.2093	+	122.164i	0.298510	+	0.954406i
$129$			56.4733i			0.437778i
$130$	34.4870	+	25.1393i	0.265284	+	0.193380i
$131$	−173.694			−1.32591			−0.662956	−	0.748659i	$-0.730698\pi$
$131$	−173.694			−1.32591			−0.662956	+	0.748659i	$0.730698\pi$
$132$	−41.7593	+	13.4231i	−0.316359	+	0.101690i
$133$		0			0
$134$	−105.123	+	144.212i	−0.784502	+	1.07621i
$135$	90.8624			0.673055
$136$	129.108	+	42.6254i	0.949323	+	0.313422i
$137$	−76.5851			−0.559016			−0.279508	−	0.960143i	$-0.590171\pi$
$137$	−76.5851			−0.559016			−0.279508	+	0.960143i	$0.590171\pi$
$138$	97.6936	+	71.2140i	0.707925	+	0.516044i
$139$	−72.4724			−0.521384			−0.260692	−	0.965422i	$-0.583951\pi$
$139$	−72.4724			−0.521384			−0.260692	+	0.965422i	$0.583951\pi$
$140$		0			0
$141$			31.9535i			0.226621i
$142$	−132.187	−	96.3580i	−0.930894	−	0.678577i
$143$			32.3066i			0.225920i
$144$	46.0945	−	33.0478i	0.320101	−	0.229499i
$145$		−	131.084i		−	0.904026i
$146$	−162.528	+	222.962i	−1.11321	+	1.52714i
$147$		0			0
$148$	189.958	−	61.0601i	1.28350	−	0.412569i
$149$			244.268i			1.63938i	0.572807	+	0.819690i	$0.305854\pi$
$149$			244.268i			1.63938i	−0.572807	+	0.819690i	$0.694146\pi$
$150$	−58.0684	−	42.3291i	−0.387123	−	0.282194i
$151$	206.218			1.36568			0.682841	−	0.730567i	$-0.260744\pi$
$151$	206.218			1.36568			0.682841	+	0.730567i	$0.260744\pi$
$152$	65.7610	−	199.183i	0.432638	−	1.31042i
$153$		−	60.2456i		−	0.393762i
$154$		0			0
$155$			56.9440i			0.367380i
$156$	19.6726	+	61.2015i	0.126106	+	0.392317i
$157$	−74.5428			−0.474795			−0.237397	−	0.971413i	$-0.576294\pi$
$157$	−74.5428			−0.474795			−0.237397	+	0.971413i	$0.576294\pi$
$158$	21.1749	+	15.4355i	0.134018	+	0.0976929i
$159$		−	16.2882i		−	0.102441i
$160$	99.2321	+	0.781686i	0.620200	+	0.00488554i
$161$		0			0
$162$	59.0400	+	43.0373i	0.364444	+	0.265662i
$163$		−	98.2845i		−	0.602972i	−0.953471	−	0.301486i	$-0.902517\pi$
$163$		−	98.2845i		−	0.602972i	0.953471	−	0.301486i	$-0.0974827\pi$
$164$	41.0682	−	13.2010i	0.250416	−	0.0804936i
$165$			34.0064i			0.206099i
$166$	−3.48593	−	2.54108i	−0.0209996	−	0.0153077i
$167$			252.539i			1.51221i	0.654449	+	0.756106i	$0.272901\pi$
$167$			252.539i			1.51221i	−0.654449	+	0.756106i	$0.727099\pi$
$168$		0			0
$169$	−121.652			−0.719836
$170$	62.0917	−	85.1793i	0.365245	−	0.501055i
$171$	−92.9449			−0.543537
$172$	92.0763	−	29.5970i	0.535327	−	0.172076i
$173$	−150.378			−0.869236			−0.434618	−	0.900615i	$-0.643117\pi$
$173$	−150.378			−0.869236			−0.434618	+	0.900615i	$0.643117\pi$
$174$	116.312	−	159.561i	0.668462	−	0.917017i
$175$		0			0
$176$	43.7711	+	61.0512i	0.248700	+	0.346882i
$177$	−248.007			−1.40117
$178$	119.476	−	163.901i	0.671215	−	0.920794i
$179$		−	103.490i		−	0.578154i	−0.957306	−	0.289077i	$-0.906652\pi$
$179$		−	103.490i		−	0.578154i	0.957306	−	0.289077i	$-0.0933484\pi$
$180$	−13.4561	−	41.8621i	−0.0747563	−	0.232567i
$181$	95.1121			0.525481			0.262741	−	0.964867i	$-0.415374\pi$
$181$	95.1121			0.525481			0.262741	+	0.964867i	$0.415374\pi$
$182$		0			0
$183$	−218.290			−1.19284
$184$	64.9101	−	196.606i	0.352772	−	1.06851i
$185$		−	154.691i		−	0.836168i
$186$	−50.5272	+	69.3148i	−0.271651	+	0.372660i
$187$	79.7940			0.426706
$188$	52.0983	−	16.7465i	0.277119	−	0.0890770i
$189$		0			0
$190$	−131.412	−	95.7929i	−0.691640	−	0.504173i
$191$	3.94503			0.0206546			0.0103273	−	0.999947i	$-0.496713\pi$
$191$	3.94503			0.0206546			0.0103273	+	0.999947i	$0.496713\pi$
$192$	120.096	+	89.0015i	0.625501	+	0.463549i
$193$	−292.182			−1.51390			−0.756949	−	0.653474i	$-0.773311\pi$
$193$	−292.182			−1.51390			−0.756949	+	0.653474i	$0.773311\pi$
$194$	−104.772	+	143.730i	−0.540063	+	0.740876i
$195$	49.8390			0.255584
$196$		0			0
$197$			160.503i			0.814735i	0.913264	+	0.407367i	$0.133553\pi$
$197$			160.503i			0.814735i	−0.913264	+	0.407367i	$0.866447\pi$
$198$	19.6077	−	26.8985i	0.0990288	−	0.135851i
$199$			201.450i			1.01231i	0.862442	+	0.506156i	$0.168934\pi$
$199$			201.450i			1.01231i	−0.862442	+	0.506156i	$0.831066\pi$
$200$	−38.5821	+	116.861i	−0.192910	+	0.584306i
$201$			208.408i			1.03685i
$202$	−33.6936	−	24.5611i	−0.166800	−	0.121589i
$203$		0			0
$204$	151.162	−	48.5893i	0.740988	−	0.238183i
$205$		−	33.4436i		−	0.163139i
$206$	−4.04669	+	5.55138i	−0.0196441	+	0.0269484i
$207$	−91.7422			−0.443199
$208$	89.4752	−	64.1499i	0.430169	−	0.308413i
$209$		−	123.103i		−	0.589012i
$210$		0			0
$211$		−	170.542i		−	0.808256i	−0.914702	−	0.404128i	$-0.867575\pi$
$211$		−	170.542i		−	0.808256i	0.914702	−	0.404128i	$-0.132425\pi$
$212$	−26.5569	+	8.53645i	−0.125268	+	0.0402663i
$213$	−191.030			−0.896857
$214$	−79.5278	+	109.099i	−0.371625	+	0.509808i
$215$		−	74.9816i		−	0.348752i
$216$	73.4866	−	222.583i	0.340216	−	1.03048i
$217$		0			0
$218$	159.110	−	218.273i	0.729864	−	1.00125i
$219$			322.214i			1.47130i
$220$	55.4454	−	17.8223i	0.252024	−	0.0810107i
$221$		−	116.944i		−	0.529159i
$222$	137.259	−	188.297i	0.618286	−	0.848184i
$223$		−	143.446i		−	0.643255i	−0.946866	−	0.321628i	$-0.895770\pi$
$223$		−	143.446i		−	0.643255i	0.946866	−	0.321628i	$-0.104230\pi$
$224$		0			0
$225$	54.5309			0.242360
$226$	−220.331	−	160.611i	−0.974916	−	0.710668i
$227$	23.5193			0.103609			0.0518047	−	0.998657i	$-0.483503\pi$
$227$	23.5193			0.103609			0.0518047	+	0.998657i	$0.483503\pi$
$228$	−74.9619	−	233.207i	−0.328780	−	1.02284i
$229$	61.4080			0.268157			0.134079	−	0.990971i	$-0.457193\pi$
$229$	61.4080			0.268157			0.134079	+	0.990971i	$0.457193\pi$
$230$	−129.711	−	94.5534i	−0.563962	−	0.411102i
$231$		0			0
$232$	−321.113	−	106.016i	−1.38411	−	0.456967i
$233$	104.198			0.447203			0.223601	−	0.974681i	$-0.428219\pi$
$233$	104.198			0.447203			0.223601	+	0.974681i	$0.428219\pi$
$234$	−39.4218	−	28.7366i	−0.168469	−	0.122806i
$235$		−	42.4259i		−	0.180536i
$236$	129.978	+	404.361i	0.550753	+	1.71339i
$237$	30.6010			0.129118
$238$		0			0
$239$	104.695			0.438056			0.219028	−	0.975719i	$-0.429711\pi$
$239$	104.695			0.438056			0.219028	+	0.975719i	$0.429711\pi$
$240$	94.1829	−	67.5252i	0.392429	−	0.281355i
$241$		−	164.718i		−	0.683478i	−0.939795	−	0.341739i	$-0.888984\pi$
$241$		−	164.718i		−	0.683478i	0.939795	−	0.341739i	$-0.111016\pi$
$242$	−159.931	−	116.582i	−0.660873	−	0.481745i
$243$	−178.379			−0.734070
$244$	114.403	+	355.909i	0.468865	+	1.45864i
$245$		0			0
$246$	29.6749	−	40.7090i	0.120630	−	0.165484i
$247$	−180.417			−0.730435
$248$	139.494	+	46.0544i	0.562477	+	0.185703i
$249$	−5.03770			−0.0202317
$250$	202.398	+	147.538i	0.809591	+	0.590153i
$251$	399.066			1.58990			0.794952	−	0.606672i	$-0.207496\pi$
$251$	399.066			1.58990			0.794952	+	0.606672i	$0.207496\pi$
$252$		0			0
$253$		−	121.511i		−	0.480279i
$254$	10.3387	+	7.53644i	0.0407037	+	0.0296710i
$255$		−	123.097i		−	0.482734i
$256$	82.1706	−	242.454i	0.320979	−	0.947086i
$257$		−	2.45191i		−	0.00954049i	−0.999989	−	0.00477025i	$-0.998482\pi$
$257$		−	2.45191i		−	0.00954049i	0.999989	−	0.00477025i	$-0.00151842\pi$
$258$	66.5322	−	91.2710i	0.257877	−	0.353764i
$259$		0			0
$260$	−26.1200	−	81.2594i	−0.100462	−	0.312536i
$261$			149.841i			0.574102i
$262$	280.721	+	204.633i	1.07146	+	0.781040i
$263$	57.5596			0.218858			0.109429	−	0.993995i	$-0.465098\pi$
$263$	57.5596			0.218858			0.109429	+	0.993995i	$0.465098\pi$
$264$	83.3046	+	27.5033i	0.315548	+	0.104179i
$265$			21.6264i			0.0816091i
$266$		0			0
$267$		−	236.863i		−	0.887126i
$268$	339.796	−	109.224i	1.26790	−	0.407552i
$269$	−240.403			−0.893690			−0.446845	−	0.894611i	$-0.647452\pi$
$269$	−240.403			−0.893690			−0.446845	+	0.894611i	$0.647452\pi$
$270$	−146.850	−	107.047i	−0.543889	−	0.396469i
$271$		−	134.531i		−	0.496424i	−0.968706	−	0.248212i	$-0.920157\pi$
$271$		−	134.531i		−	0.496424i	0.968706	−	0.248212i	$-0.0798430\pi$
$272$	−158.444	−	220.995i	−0.582514	−	0.812481i
$273$		0			0
$274$	123.775	+	90.2263i	0.451735	+	0.329293i
$275$			72.2250i			0.262636i
$276$	−73.9920	−	230.189i	−0.268087	−	0.834019i
$277$			110.401i			0.398558i	0.979943	+	0.199279i	$0.0638600\pi$
$277$			110.401i			0.398558i	−0.979943	+	0.199279i	$0.936140\pi$
$278$	117.128	+	85.3811i	0.421325	+	0.307126i
$279$		−	65.0922i		−	0.233305i
$280$		0			0
$281$	−154.087			−0.548351			−0.274175	−	0.961680i	$-0.588405\pi$
$281$	−154.087			−0.548351			−0.274175	+	0.961680i	$0.588405\pi$
$282$	37.6450	−	51.6427i	0.133493	−	0.183130i
$283$	−30.9428			−0.109338			−0.0546692	−	0.998505i	$-0.517410\pi$
$283$	−30.9428			−0.109338			−0.0546692	+	0.998505i	$0.517410\pi$
$284$	100.117	+	311.464i	0.352524	+	1.09670i
$285$	−189.910			−0.666351
$286$	38.0610	−	52.2132i	0.133080	−	0.182564i
$287$		0			0
$288$	−113.431	−	0.893539i	−0.393859	−	0.00310257i
$289$	0.159593			0.000552224
$290$	−154.432	+	211.855i	−0.532524	+	0.730534i
$291$			207.712i			0.713786i
$292$	525.351	−	168.869i	1.79915	−	0.578317i
$293$	511.686			1.74637			0.873184	−	0.487390i	$-0.162051\pi$
$293$	511.686			1.74637			0.873184	+	0.487390i	$0.162051\pi$
$294$		0			0
$295$	329.288			1.11623
$296$	−378.943	−	125.109i	−1.28021	−	0.422666i
$297$		−	137.566i		−	0.463184i
$298$	287.776	−	394.780i	0.965692	−	1.32477i
$299$	−178.083			−0.595595
$300$	43.9803	+	136.823i	0.146601	+	0.456076i
$301$		0			0
$302$	−333.285	−	242.949i	−1.10359	−	0.804468i
$303$	−48.6925			−0.160701
$304$	−340.943	+	244.442i	−1.12152	+	0.804085i
$305$	289.831			0.950267
$306$	−70.9765	+	97.3678i	−0.231949	+	0.318195i
$307$	51.2670			0.166993			0.0834967	−	0.996508i	$-0.473391\pi$
$307$	51.2670			0.166993			0.0834967	+	0.996508i	$0.473391\pi$
$308$		0			0
$309$			8.02259i			0.0259631i
$310$	67.0867	−	92.0317i	0.216409	−	0.296876i
$311$		−	20.5467i		−	0.0660666i	−0.999454	−	0.0330333i	$-0.989483\pi$
$311$		−	20.5467i		−	0.0660666i	0.999454	−	0.0330333i	$-0.0105167\pi$
$312$	40.3081	−	122.089i	0.129193	−	0.391312i
$313$		−	337.127i		−	1.07708i	−0.842599	−	0.538541i	$-0.818976\pi$
$313$		−	337.127i		−	1.07708i	0.842599	−	0.538541i	$-0.181024\pi$
$314$	120.475	+	87.8202i	0.383677	+	0.279682i
$315$		0			0
$316$	−16.0376	−	49.8930i	−0.0507519	−	0.157889i
$317$		−	93.2575i		−	0.294188i	−0.989123	−	0.147094i	$-0.953008\pi$
$317$		−	93.2575i		−	0.294188i	0.989123	−	0.147094i	$-0.0469920\pi$
$318$	−19.1894	+	26.3246i	−0.0603441	+	0.0827819i
$319$	−198.461			−0.622134
$320$	−159.456	−	118.170i	−0.498300	−	0.369283i
$321$			157.665i			0.491167i
$322$		0			0
$323$			445.613i			1.37961i
$324$	−44.7162	−	139.112i	−0.138013	−	0.429358i
$325$	105.851			0.325696
$326$	−115.791	+	158.845i	−0.355186	+	0.487256i
$327$		−	315.437i		−	0.964640i
$328$	−81.9259	−	27.0481i	−0.249774	−	0.0824637i
$329$		0			0
$330$	40.0635	−	54.9604i	0.121405	−	0.166547i
$331$			75.0485i			0.226732i	0.993553	+	0.113366i	$0.0361633\pi$
$331$			75.0485i			0.226732i	−0.993553	+	0.113366i	$0.963837\pi$
$332$	2.64020	+	8.21367i	0.00795241	+	0.0247400i
$333$			176.826i			0.531009i
$334$	297.521	−	408.149i	0.890782	−	1.22200i
$335$		−	276.711i		−	0.826002i
$336$		0			0
$337$	−140.105			−0.415743			−0.207872	−	0.978156i	$-0.566654\pi$
$337$	−140.105			−0.415743			−0.207872	+	0.978156i	$0.566654\pi$
$338$	196.612	+	143.321i	0.581692	+	0.424026i
$339$	−318.412			−0.939269
$340$	−200.703	+	64.5138i	−0.590302	+	0.189746i
$341$	86.2131			0.252824
$342$	150.216	+	109.500i	0.439227	+	0.320176i
$343$		0			0
$344$	−183.681	−	60.6427i	−0.533955	−	0.176287i
$345$	−187.453			−0.543342
$346$	243.038	+	177.163i	0.702421	+	0.512031i
$347$		−	75.0227i		−	0.216204i	−0.994140	−	0.108102i	$-0.965523\pi$
$347$		−	75.0227i		−	0.216204i	0.994140	−	0.108102i	$-0.0344773\pi$
$348$	−375.963	+	120.850i	−1.08035	+	0.347269i
$349$	−603.618			−1.72956			−0.864782	−	0.502148i	$-0.832543\pi$
$349$	−603.618			−1.72956			−0.864782	+	0.502148i	$0.832543\pi$
$350$		0			0
$351$	−201.613			−0.574396
$352$	1.18347	−	150.237i	0.00336214	−	0.426811i
$353$			389.728i			1.10405i	0.833829	+	0.552023i	$0.186144\pi$
$353$			389.728i			1.10405i	−0.833829	+	0.552023i	$0.813856\pi$
$354$	400.824	+	292.182i	1.13227	+	0.825373i
$355$	253.638			0.714473
$356$	−386.190	+	124.137i	−1.08480	+	0.348699i
$357$		0			0
$358$	−121.923	+	167.258i	−0.340567	+	0.467200i
$359$	138.443			0.385635			0.192817	−	0.981235i	$-0.438238\pi$
$359$	138.443			0.385635			0.192817	+	0.981235i	$0.438238\pi$
$360$	−27.5709	+	83.5095i	−0.0765859	+	0.231971i
$361$	326.476			0.904366
$362$	−153.718	−	112.053i	−0.424636	−	0.309539i
$363$	−231.125			−0.636709
$364$		0			0
$365$		−	427.815i		−	1.17210i
$366$	352.796	+	257.171i	0.963923	+	0.702654i
$367$		−	472.069i		−	1.28629i	−0.765744	−	0.643145i	$-0.777629\pi$
$367$		−	472.069i		−	1.28629i	0.765744	−	0.643145i	$-0.222371\pi$
$368$	−336.532	+	241.279i	−0.914488	+	0.655649i
$369$			38.2291i			0.103602i
$370$	−182.244	+	250.009i	−0.492552	+	0.675699i
$371$		0			0
$372$	163.322	−	52.4982i	0.439038	−	0.141124i
$373$			35.2668i			0.0945490i	0.998882	+	0.0472745i	$0.0150536\pi$
$373$			35.2668i			0.0945490i	−0.998882	+	0.0472745i	$0.984946\pi$
$374$	−128.961	−	94.0068i	−0.344817	−	0.251355i
$375$	292.496			0.779989
$376$	−103.930	−	34.3127i	−0.276409	−	0.0912571i
$377$			290.859i			0.771510i
$378$		0			0
$379$			230.447i			0.608039i	0.952666	+	0.304019i	$0.0983287\pi$
$379$			230.447i			0.608039i	−0.952666	+	0.304019i	$0.901671\pi$
$380$	99.5296	+	309.637i	0.261920	+	0.814834i
$381$	14.9411			0.0392154
$382$	−6.37589	−	4.64772i	−0.0166908	−	0.0121668i
$383$			554.279i			1.44720i	0.690217	+	0.723602i	$0.257515\pi$
$383$			554.279i			1.44720i	−0.690217	+	0.723602i	$0.742485\pi$
$384$	−89.2427	−	285.330i	−0.232403	−	0.743046i
$385$		0			0
$386$	472.219	+	344.225i	1.22337	+	0.891776i
$387$			85.7109i			0.221475i
$388$	338.661	−	108.859i	0.872839	−	0.280565i
$389$		−	397.680i		−	1.02231i	−0.859488	−	0.511157i	$-0.829217\pi$
$389$		−	397.680i		−	1.02231i	0.859488	−	0.511157i	$-0.170783\pi$
$390$	−80.5487	−	58.7162i	−0.206535	−	0.150554i
$391$			439.847i			1.12493i
$392$		0			0
$393$	405.686			1.03228
$394$	189.091	−	259.401i	0.479927	−	0.658379i
$395$	−40.6300			−0.102861
$396$	−63.3791	+	20.3726i	−0.160048	+	0.0514459i
$397$	121.909			0.307075			0.153538	−	0.988143i	$-0.450933\pi$
$397$	121.909			0.307075			0.153538	+	0.988143i	$0.450933\pi$
$398$	237.332	−	325.580i	0.596312	−	0.818039i
$399$		0			0
$400$	200.032	−	143.415i	0.500080	−	0.358536i
$401$	248.673			0.620133			0.310067	−	0.950715i	$-0.399649\pi$
$401$	248.673			0.620133			0.310067	+	0.950715i	$0.399649\pi$
$402$	245.529	−	336.825i	0.610769	−	0.837872i
$403$		−	126.352i		−	0.313528i
$404$	25.5192	+	79.3902i	0.0631662	+	0.196510i
$405$	−113.285			−0.279716
$406$		0			0
$407$	−234.202			−0.575435
$408$	−301.548	−	99.5571i	−0.739089	−	0.244012i
$409$			672.869i			1.64516i	0.568653	+	0.822578i	$0.307465\pi$
$409$			672.869i			1.64516i	−0.568653	+	0.822578i	$0.692535\pi$
$410$	−39.4005	+	54.0508i	−0.0960987	+	0.131831i
$411$	178.874			0.435218
$412$	13.0804	−	4.20455i	0.0317484	−	0.0102052i
$413$		0			0
$414$	148.272	+	108.083i	0.358145	+	0.261071i
$415$	6.68874			0.0161174
$416$	−220.184	−	1.73447i	−0.529289	−	0.00416940i
$417$	169.269			0.405920
$418$	−145.030	+	198.957i	−0.346963	+	0.475974i
$419$	−178.795			−0.426718			−0.213359	−	0.976974i	$-0.568440\pi$
$419$	−178.795			−0.426718			−0.213359	+	0.976974i	$0.568440\pi$
$420$		0			0
$421$			212.470i			0.504679i	0.967639	+	0.252340i	$0.0812000\pi$
$421$			212.470i			0.504679i	−0.967639	+	0.252340i	$0.918800\pi$
$422$	−200.919	+	275.627i	−0.476111	+	0.653144i
$423$			48.4967i			0.114649i
$424$	52.9777	+	17.4907i	0.124947	+	0.0412518i
$425$		−	261.442i		−	0.615158i
$426$	308.740	+	225.056i	0.724741	+	0.528302i
$427$		0			0
$428$	257.063	−	82.6301i	0.600614	−	0.193061i
$429$		−	75.4562i		−	0.175888i
$430$	−88.3372	+	121.184i	−0.205435	+	0.281823i
$431$	−691.464			−1.60433			−0.802163	−	0.597105i	$-0.796317\pi$
$431$	−691.464			−1.60433			−0.802163	+	0.597105i	$0.796317\pi$
$432$	−380.997	+	273.159i	−0.881938	+	0.632313i
$433$			99.8389i			0.230575i	0.993332	+	0.115287i	$0.0367789\pi$
$433$			99.8389i			0.230575i	−0.993332	+	0.115287i	$0.963221\pi$
$434$		0			0
$435$			306.163i			0.703823i
$436$	−514.302	+	165.317i	−1.17959	+	0.379167i
$437$	678.581			1.55282
$438$	379.606	−	520.756i	0.866681	−	1.18894i
$439$			692.091i			1.57652i	0.615344	+	0.788259i	$0.289017\pi$
$439$			692.091i			1.57652i	−0.615344	+	0.788259i	$0.710983\pi$
$440$	−110.607	−	36.5171i	−0.251378	−	0.0829934i
$441$		0			0
$442$	−137.774	+	189.003i	−0.311706	+	0.427608i
$443$		−	269.702i		−	0.608809i	−0.952543	−	0.304405i	$-0.901543\pi$
$443$		−	269.702i		−	0.608809i	0.952543	−	0.304405i	$-0.0984575\pi$
$444$	−443.672	+	142.614i	−0.999261	+	0.321202i
$445$			314.491i			0.706722i
$446$	−168.996	+	231.834i	−0.378915	+	0.519808i
$447$		−	570.519i		−	1.27633i
$448$		0			0
$449$	−76.6510			−0.170715			−0.0853575	−	0.996350i	$-0.527203\pi$
$449$	−76.6510			−0.170715			−0.0853575	+	0.996350i	$0.527203\pi$
$450$	−88.1318	−	64.2439i	−0.195848	−	0.142764i
$451$	−50.6336			−0.112270
$452$	166.876	+	519.152i	0.369195	+	1.14857i
$453$	−481.649			−1.06324
$454$	−38.0115	−	27.7086i	−0.0837257	−	0.0610320i
$455$		0			0
$456$	−153.593	+	465.218i	−0.336827	+	1.02022i
$457$	−351.233			−0.768562			−0.384281	−	0.923216i	$-0.625551\pi$
$457$	−351.233			−0.768562			−0.384281	+	0.923216i	$0.625551\pi$
$458$	−99.2464	−	72.3459i	−0.216695	−	0.157960i
$459$			497.964i			1.08489i
$460$	98.2418	+	305.631i	0.213569	+	0.664414i
$461$	296.940			0.644122			0.322061	−	0.946719i	$-0.395624\pi$
$461$	296.940			0.644122			0.322061	+	0.946719i	$0.395624\pi$
$462$		0			0
$463$	25.5350			0.0551513			0.0275756	−	0.999620i	$-0.491221\pi$
$463$	25.5350			0.0551513			0.0275756	+	0.999620i	$0.491221\pi$
$464$	394.076	+	549.650i	0.849302	+	1.18459i
$465$		−	133.000i		−	0.286021i
$466$	−168.403	−	122.758i	−0.361380	−	0.263429i
$467$	−125.520			−0.268780			−0.134390	−	0.990929i	$-0.542907\pi$
$467$	−125.520			−0.268780			−0.134390	+	0.990929i	$0.542907\pi$
$468$	29.8576	+	92.8870i	0.0637982	+	0.198476i
$469$		0			0
$470$	−49.9827	+	68.5678i	−0.106346	+	0.145889i
$471$	174.104			0.369648
$472$	266.318	−	806.649i	0.564232	−	1.70900i
$473$	−113.522			−0.240005
$474$	−49.4567	−	36.0515i	−0.104339	−	0.0760581i
$475$	−403.344			−0.849145
$476$		0			0
$477$		−	24.7210i		−	0.0518259i
$478$	−169.206	−	123.343i	−0.353988	−	0.258041i
$479$		−	173.422i		−	0.362049i	−0.983479	−	0.181025i	$-0.942059\pi$
$479$		−	173.422i		−	0.362049i	0.983479	−	0.181025i	$-0.0579414\pi$
$480$	−231.769	−	1.82573i	−0.482853	−	0.00380360i
$481$			343.241i			0.713599i
$482$	−194.058	+	266.214i	−0.402609	+	0.552312i
$483$		0			0
$484$	121.130	+	376.836i	0.250269	+	0.778587i
$485$		−	275.786i		−	0.568632i
$486$	288.292	+	210.151i	0.593194	+	0.432410i
$487$	−681.511			−1.39941			−0.699704	−	0.714433i	$-0.746685\pi$
$487$	−681.511			−1.39941			−0.699704	+	0.714433i	$0.746685\pi$
$488$	234.406	−	709.993i	0.480341	−	1.45490i
$489$			229.556i			0.469440i
$490$		0			0
$491$		−	278.104i		−	0.566404i	−0.959060	−	0.283202i	$-0.908603\pi$
$491$		−	278.104i		−	0.566404i	0.959060	−	0.283202i	$-0.0913966\pi$
$492$	−95.9201	+	30.8325i	−0.194960	+	0.0626677i
$493$	718.393			1.45719
$494$	291.587	+	212.553i	0.590257	+	0.430269i
$495$			51.6123i			0.104267i
$496$	−171.190	−	238.773i	−0.345142	−	0.481397i
$497$		0			0
$498$	8.14184	+	5.93501i	0.0163491	+	0.0119177i
$499$		−	410.435i		−	0.822515i	−0.911519	−	0.411258i	$-0.865090\pi$
$499$		−	410.435i		−	0.822515i	0.911519	−	0.411258i	$-0.134910\pi$
$500$	−153.294	−	476.897i	−0.306587	−	0.953794i
$501$		−	589.838i		−	1.17732i
$502$	−644.963	−	470.147i	−1.28479	−	0.936548i
$503$		−	554.042i		−	1.10148i	−0.834678	−	0.550738i	$-0.814346\pi$
$503$		−	554.042i		−	1.10148i	0.834678	−	0.550738i	$-0.185654\pi$
$504$		0			0
$505$	64.6508			0.128021
$506$	−143.154	+	196.383i	−0.282913	+	0.388109i
$507$	284.134			0.560423
$508$	−7.83043	−	24.3605i	−0.0154142	−	0.0479537i
$509$	−44.1942			−0.0868255			−0.0434127	−	0.999057i	$-0.513823\pi$
$509$	−44.1942			−0.0868255			−0.0434127	+	0.999057i	$0.513823\pi$
$510$	−145.023	+	198.947i	−0.284359	+	0.390093i
$511$		0			0
$512$	−418.442	+	295.043i	−0.817270	+	0.576256i
$513$	768.241			1.49755
$514$	−2.88864	+	3.96272i	−0.00561992	+	0.00770958i
$515$		−	10.6519i		−	0.0206833i
$516$	−215.056	+	69.1276i	−0.416775	+	0.133968i
$517$	−64.2327			−0.124241
$518$		0			0
$519$	351.227			0.676738
$520$	−53.5186	+	162.102i	−0.102920	+	0.311735i
$521$			420.152i			0.806434i	0.915104	+	0.403217i	$0.132108\pi$
$521$			420.152i			0.806434i	−0.915104	+	0.403217i	$0.867892\pi$
$522$	176.530	−	242.170i	0.338180	−	0.463926i
$523$	274.894			0.525609			0.262805	−	0.964849i	$-0.415353\pi$
$523$	274.894			0.525609			0.262805	+	0.964849i	$0.415353\pi$
$524$	−212.615	−	661.446i	−0.405754	−	1.26230i
$525$		0			0
$526$	−93.0267	−	67.8120i	−0.176857	−	0.128920i
$527$	−312.077			−0.592176
$528$	−102.233	−	142.593i	−0.193623	−	0.270062i
$529$	140.801			0.266164
$530$	25.4785	−	34.9522i	0.0480726	−	0.0659475i
$531$	−376.407			−0.708864
$532$		0			0
$533$			74.2073i			0.139226i
$534$	−279.052	+	382.813i	−0.522570	+	0.716878i
$535$		−	209.337i		−	0.391284i
$536$	−677.851	−	223.795i	−1.26465	−	0.417527i
$537$			241.713i			0.450118i
$538$	388.534	+	283.223i	0.722182	+	0.526436i
$539$		0			0
$540$	111.222	+	346.013i	0.205967	+	0.640766i
$541$		−	560.443i		−	1.03594i	−0.855399	−	0.517969i	$-0.826688\pi$
$541$		−	560.443i		−	1.03594i	0.855399	−	0.517969i	$-0.173312\pi$
$542$	−158.493	+	217.426i	−0.292423	+	0.401156i
$543$	−222.146			−0.409110
$544$	−4.28397	+	543.833i	−0.00787494	+	0.999693i
$545$			418.818i			0.768473i
$546$		0			0
$547$		−	655.564i		−	1.19847i	−0.800573	−	0.599235i	$-0.795471\pi$
$547$		−	655.564i		−	1.19847i	0.800573	−	0.599235i	$-0.204529\pi$
$548$	−93.7460	−	291.644i	−0.171069	−	0.532197i
$549$	−331.304			−0.603468
$550$	85.0896	−	116.729i	0.154708	−	0.212234i
$551$		−	1108.31i		−	2.01146i
$552$	−151.606	+	459.199i	−0.274648	+	0.831882i
$553$		0			0
$554$	130.065	−	178.427i	0.234774	−	0.322071i
$555$			361.301i			0.650993i
$556$	−88.7117	−	275.982i	−0.159553	−	0.496371i
$557$		−	750.754i		−	1.34785i	−0.738798	−	0.673927i	$-0.764606\pi$
$557$		−	750.754i		−	1.34785i	0.738798	−	0.673927i	$-0.235394\pi$
$558$	−76.6863	+	105.201i	−0.137431	+	0.188532i
$559$			166.375i			0.297630i
$560$		0			0
$561$	−186.369			−0.332209
$562$	249.032	+	181.532i	0.443117	+	0.323011i
$563$	634.382			1.12679			0.563394	−	0.826188i	$-0.309495\pi$
$563$	634.382			1.12679			0.563394	+	0.826188i	$0.309495\pi$
$564$	−121.682	+	39.1135i	−0.215749	+	0.0693502i
$565$	422.767			0.748261
$566$	50.0091	+	36.4542i	0.0883553	+	0.0644068i
$567$		0			0
$568$	205.134	−	621.331i	0.361152	−	1.09389i
$569$	392.965			0.690623			0.345312	−	0.938488i	$-0.387773\pi$
$569$	392.965			0.690623			0.345312	+	0.938488i	$0.387773\pi$
$570$	306.929	+	223.737i	0.538472	+	0.392520i
$571$			538.986i			0.943934i	0.881616	+	0.471967i	$0.156456\pi$
$571$			538.986i			0.943934i	−0.881616	+	0.471967i	$0.843544\pi$
$572$	−123.027	+	39.5457i	−0.215082	+	0.0691358i
$573$	−9.21414			−0.0160805
$574$		0			0
$575$	−398.125			−0.692391
$576$	182.273	+	135.080i	0.316446	+	0.234513i
$577$		−	347.973i		−	0.603072i	−0.953455	−	0.301536i	$-0.902501\pi$
$577$		−	347.973i		−	0.603072i	0.953455	−	0.301536i	$-0.0974994\pi$
$578$	−0.257931	−	0.188019i	−0.000446247	−	0.000325293i
$579$	682.430			1.17863
$580$	499.180	−	160.456i	0.860655	−	0.276649i
$581$		0			0
$582$	244.709	−	335.700i	0.420462	−	0.576803i
$583$	32.7424			0.0561619
$584$	−1048.01	−	346.003i	−1.79453	−	0.592471i
$585$	75.6418			0.129302
$586$	−826.977	−	602.827i	−1.41122	−	1.02871i
$587$	−258.936			−0.441118			−0.220559	−	0.975374i	$-0.570788\pi$
$587$	−258.936			−0.441118			−0.220559	+	0.975374i	$0.570788\pi$
$588$		0			0
$589$			481.461i			0.817421i
$590$	−532.189	−	387.940i	−0.902015	−	0.657526i
$591$		−	374.875i		−	0.634306i
$592$	465.047	+	648.638i	0.785552	+	1.09567i
$593$		−	76.9637i		−	0.129787i	−0.997892	−	0.0648935i	$-0.979329\pi$
$593$		−	76.9637i		−	0.129787i	0.997892	−	0.0648935i	$-0.0206708\pi$
$594$	−162.069	+	222.331i	−0.272843	+	0.374294i
$595$		0			0
$596$	−930.196	+	299.002i	−1.56073	+	0.501681i
$597$		−	470.513i		−	0.788128i
$598$	287.814	+	209.803i	0.481295	+	0.350841i
$599$	1158.98			1.93485			0.967426	−	0.253154i	$-0.0814678\pi$
$599$	1158.98			1.93485			0.967426	+	0.253154i	$0.0814678\pi$
$600$	90.1134	−	272.944i	0.150189	−	0.454907i
$601$		−	976.895i		−	1.62545i	−0.582648	−	0.812724i	$-0.697983\pi$
$601$		−	976.895i		−	1.62545i	0.582648	−	0.812724i	$-0.302017\pi$
$602$		0			0
$603$			316.306i			0.524553i
$604$	252.426	+	785.299i	0.417925	+	1.30016i
$605$	306.873			0.507229
$606$	78.6958	+	57.3655i	0.129861	+	0.0946626i
$607$			790.031i			1.30153i	0.759278	+	0.650767i	$0.225552\pi$
$607$			790.031i			1.30153i	−0.759278	+	0.650767i	$0.774448\pi$
$608$	839.007	+	6.60916i	1.37994	+	0.0108703i
$609$		0			0
$610$	−468.420	−	341.456i	−0.767901	−	0.559763i
$611$			94.1380i			0.154072i
$612$	229.421	−	73.7452i	0.374872	−	0.120499i
$613$		−	269.842i		−	0.440198i	−0.975478	−	0.220099i	$-0.929362\pi$
$613$		−	269.842i		−	0.440198i	0.975478	−	0.220099i	$-0.0706381\pi$
$614$	−82.8567	−	60.3986i	−0.134946	−	0.0983690i
$615$			78.1118i			0.127011i
$616$		0			0
$617$	701.515			1.13698			0.568489	−	0.822691i	$-0.307528\pi$
$617$	701.515			1.13698			0.568489	+	0.822691i	$0.307528\pi$
$618$	9.45156	−	12.9660i	0.0152938	−	0.0209805i
$619$	−869.520			−1.40472			−0.702358	−	0.711823i	$-0.747870\pi$
$619$	−869.520			−1.40472			−0.702358	+	0.711823i	$0.747870\pi$
$620$	−216.848	+	69.7037i	−0.349756	+	0.112425i
$621$	758.301			1.22110
$622$	−24.2064	+	33.2072i	−0.0389171	+	0.0533877i
$623$		0			0
$624$	−208.981	+	149.830i	−0.334905	+	0.240113i
$625$	−3.77760			−0.00604415
$626$	−397.175	+	544.857i	−0.634465	+	0.870379i
$627$			287.524i			0.458571i
$628$	−91.2460	−	283.867i	−0.145296	−	0.452017i
$629$	847.771			1.34781
$630$		0			0
$631$	100.362			0.159052			0.0795258	−	0.996833i	$-0.474659\pi$
$631$	100.362			0.159052			0.0795258	+	0.996833i	$0.474659\pi$
$632$	−32.8602	+	99.5303i	−0.0519940	+	0.157485i
$633$			398.323i			0.629262i
$634$	−109.868	+	150.721i	−0.173294	+	0.237730i
$635$	−19.8378			−0.0312406
$636$	62.0271	−	19.9380i	0.0975269	−	0.0313490i
$637$		0			0
$638$	320.748	+	233.810i	0.502740	+	0.366474i
$639$	−289.932			−0.453727
$640$	118.491	+	378.843i	0.185142	+	0.591942i
$641$	1061.14			1.65545			0.827724	−	0.561135i	$-0.189635\pi$
$641$	1061.14			1.65545			0.827724	+	0.561135i	$0.189635\pi$
$642$	185.747	−	254.814i	0.289326	−	0.396907i
$643$	−132.853			−0.206615			−0.103308	−	0.994649i	$-0.532943\pi$
$643$	−132.853			−0.206615			−0.103308	+	0.994649i	$0.532943\pi$
$644$		0			0
$645$			175.129i			0.271518i
$646$	524.985	−	720.191i	0.812670	−	1.11485i
$647$			1152.69i			1.78159i	0.454404	+	0.890796i	$0.349852\pi$
$647$			1152.69i			1.78159i	−0.454404	+	0.890796i	$0.650148\pi$
$648$	−91.6211	+	277.511i	−0.141391	+	0.428258i
$649$		−	498.542i		−	0.768170i
$650$	−171.075	−	124.705i	−0.263192	−	0.191854i
$651$		0			0
$652$	374.277	−	120.308i	0.574045	−	0.184521i
$653$		−	29.0705i		−	0.0445184i	−0.999752	−	0.0222592i	$-0.992914\pi$
$653$		−	29.0705i		−	0.0445184i	0.999752	−	0.0222592i	$-0.00708590\pi$
$654$	−371.622	+	509.804i	−0.568230	+	0.779516i
$655$	−538.643			−0.822356
$656$	100.541	+	140.233i	0.153264	+	0.213770i
$657$			489.032i			0.744341i
$658$		0			0
$659$		−	705.504i		−	1.07057i	−0.844672	−	0.535283i	$-0.820205\pi$
$659$		−	705.504i		−	1.07057i	0.844672	−	0.535283i	$-0.179795\pi$
$660$	−129.500	+	41.6264i	−0.196212	+	0.0630703i
$661$	127.336			0.192641			0.0963204	−	0.995350i	$-0.469293\pi$
$661$	127.336			0.192641			0.0963204	+	0.995350i	$0.469293\pi$
$662$	88.4160	−	121.292i	0.133559	−	0.183220i
$663$			273.138i			0.411973i
$664$	5.40964	−	16.3852i	0.00814705	−	0.0246766i
$665$		0			0
$666$	208.322	−	285.783i	0.312796	−	0.429103i
$667$		−	1093.97i		−	1.64014i
$668$	−961.696	+	309.127i	−1.43966	+	0.462765i
$669$			335.036i			0.500802i
$670$	−325.998	+	447.214i	−0.486564	+	0.667484i
$671$		−	438.805i		−	0.653956i
$672$		0			0
$673$	−463.380			−0.688528			−0.344264	−	0.938873i	$-0.611872\pi$
$673$	−463.380			−0.688528			−0.344264	+	0.938873i	$0.611872\pi$
$674$	226.436	+	165.061i	0.335958	+	0.244897i
$675$	−450.729			−0.667746
$676$	−148.912	−	463.264i	−0.220283	−	0.685302i
$677$	376.275			0.555798			0.277899	−	0.960610i	$-0.410362\pi$
$677$	376.275			0.555798			0.277899	+	0.960610i	$0.410362\pi$
$678$	514.612	+	375.127i	0.759014	+	0.553285i
$679$		0			0
$680$	400.376	+	132.185i	0.588789	+	0.194390i
$681$	−54.9324			−0.0806643
$682$	−139.336	−	101.569i	−0.204305	−	0.148929i
$683$		−	1036.84i		−	1.51807i	−0.651049	−	0.759035i	$-0.725671\pi$
$683$		−	1036.84i		−	1.51807i	0.651049	−	0.759035i	$-0.274329\pi$
$684$	−113.771	−	353.943i	−0.166333	−	0.517461i
$685$	−237.498			−0.346712
$686$		0			0
$687$	−143.426			−0.208772
$688$	225.417	+	314.407i	0.327641	+	0.456987i
$689$		−	47.9865i		−	0.0696465i
$690$	302.958	+	220.842i	0.439069	+	0.320060i
$691$	355.069			0.513849			0.256924	−	0.966432i	$-0.417291\pi$
$691$	355.069			0.513849			0.256924	+	0.966432i	$0.417291\pi$
$692$	−184.074	−	572.654i	−0.266003	−	0.827535i
$693$		0			0
$694$	−88.3856	+	121.250i	−0.127357	+	0.174712i
$695$	−224.744			−0.323373
$696$	750.000	+	247.615i	1.07759	+	0.355768i
$697$	183.285			0.262962
$698$	975.555	+	711.133i	1.39764	+	1.01882i
$699$	−243.368			−0.348167
$700$		0			0
$701$		−	1278.63i		−	1.82400i	−0.410185	−	0.912002i	$-0.634536\pi$
$701$		−	1278.63i		−	1.82400i	0.410185	−	0.912002i	$-0.365464\pi$
$702$	325.843	+	237.524i	0.464164	+	0.338353i
$703$		−	1307.91i		−	1.86047i
$704$	−178.910	+	241.416i	−0.254134	+	0.342921i
$705$			99.0911i			0.140555i
$706$	459.146	−	629.871i	0.650348	−	0.892168i
$707$		0			0
$708$	−303.580	−	944.437i	−0.428785	−	1.33395i
$709$			1200.93i			1.69383i	0.531725	+	0.846917i	$0.321544\pi$
$709$			1200.93i			1.69383i	−0.531725	+	0.846917i	$0.678456\pi$
$710$	−409.925	−	298.816i	−0.577359	−	0.420867i
$711$	46.4438			0.0653218
$712$	770.401	+	254.350i	1.08202	+	0.357234i
$713$			475.231i			0.666524i
$714$		0			0
$715$			100.186i			0.140120i
$716$	394.099	−	126.679i	0.550417	−	0.176926i
$717$	−244.529			−0.341045
$718$	−223.748	−	163.102i	−0.311627	−	0.227162i
$719$			7.38955i			0.0102775i	0.999987	+	0.00513877i	$0.00163573\pi$
$719$			7.38955i			0.0102775i	−0.999987	+	0.00513877i	$0.998364\pi$
$720$	142.944	−	102.485i	0.198533	−	0.142340i
$721$		0			0
$722$	−527.644	−	384.628i	−0.730809	−	0.532725i
$723$			384.721i			0.532117i
$724$	116.424	+	362.196i	0.160807	+	0.500271i
$725$			650.249i			0.896895i
$726$	373.540	+	272.293i	0.514518	+	0.375059i
$727$			1184.67i			1.62953i	0.579788	+	0.814767i	$0.303135\pi$
$727$			1184.67i			1.62953i	−0.579788	+	0.814767i	$0.696865\pi$
$728$		0			0
$729$	745.402			1.02250
$730$	−504.017	+	691.426i	−0.690434	+	0.947159i
$731$	410.930			0.562148
$732$	−267.203	−	831.270i	−0.365032	−	1.13561i
$733$	−939.428			−1.28162			−0.640810	−	0.767699i	$-0.721402\pi$
$733$	−939.428			−1.28162			−0.640810	+	0.767699i	$0.721402\pi$
$734$	−556.153	+	762.948i	−0.757701	+	1.03944i
$735$		0			0
$736$	828.151	+	6.52364i	1.12520	+	0.00886364i
$737$	−418.940			−0.568439
$738$	45.0384	−	61.7851i	0.0610276	−	0.0837196i
$739$			1137.32i			1.53899i	0.638650	+	0.769497i	$0.279493\pi$
$739$			1137.32i			1.53899i	−0.638650	+	0.769497i	$0.720507\pi$
$740$	589.079	−	189.353i	0.796053	−	0.255883i
$741$	421.388			0.568675
$742$		0			0
$743$	−455.212			−0.612667			−0.306333	−	0.951924i	$-0.599102\pi$
$743$	−455.212			−0.612667			−0.306333	+	0.951924i	$0.599102\pi$
$744$	−325.807	−	107.566i	−0.437912	−	0.144578i
$745$			757.498i			1.01678i
$746$	41.5484	−	56.9975i	0.0556950	−	0.0764041i
$747$	−7.64584			−0.0102354
$748$	97.6739	+	303.864i	0.130580	+	0.406235i
$749$		0			0
$750$	−472.726	−	344.595i	−0.630301	−	0.459460i
$751$	188.525			0.251032			0.125516	−	0.992092i	$-0.459941\pi$
$751$	188.525			0.251032			0.125516	+	0.992092i	$0.459941\pi$
$752$	127.545	+	177.897i	0.169607	+	0.236565i
$753$	−932.070			−1.23781
$754$	342.667	−	470.081i	0.454465	−	0.623450i
$755$	639.502			0.847023
$756$		0			0
$757$		−	199.539i		−	0.263591i	−0.991277	−	0.131796i	$-0.957926\pi$
$757$		−	199.539i		−	0.263591i	0.991277	−	0.131796i	$-0.0420743\pi$
$758$	271.493	−	372.443i	0.358171	−	0.491350i
$759$			283.804i			0.373918i
$760$	203.931	−	617.687i	0.268330	−	0.812746i
$761$		−	338.020i		−	0.444179i	−0.975026	−	0.222089i	$-0.928712\pi$
$761$		−	338.020i		−	0.444179i	0.975026	−	0.222089i	$-0.0712877\pi$
$762$	−24.1474	−	17.6023i	−0.0316896	−	0.0231002i
$763$		0			0
$764$	4.82902	+	15.0231i	0.00632071	+	0.0196637i
$765$		−	186.828i		−	0.244219i
$766$	653.006	−	895.815i	0.852489	−	1.16947i
$767$	−730.652			−0.952610
$768$	−191.920	+	566.283i	−0.249896	+	0.737347i
$769$		−	604.446i		−	0.786015i	−0.919535	−	0.393008i	$-0.871435\pi$
$769$		−	604.446i		−	0.786015i	0.919535	−	0.393008i	$-0.128565\pi$
$770$		0			0
$771$			5.72674i			0.00742768i
$772$	−357.653	−	1112.66i	−0.463281	−	1.44127i
$773$	780.427			1.00961			0.504804	−	0.863234i	$-0.331565\pi$
$773$	780.427			1.00961			0.504804	+	0.863234i	$0.331565\pi$
$774$	100.978	−	138.524i	0.130462	−	0.178972i
$775$		−	282.474i		−	0.364483i
$776$	−675.587	−	223.047i	−0.870602	−	0.287432i
$777$		0			0
$778$	−468.514	+	642.722i	−0.602203	+	0.826121i
$779$		−	282.765i		−	0.362985i
$780$	61.0066	+	189.792i	0.0782136	+	0.243323i
$781$		−	384.008i		−	0.491687i
$782$	518.192	−	710.872i	0.662650	−	0.909044i
$783$		−	1238.52i		−	1.58176i
$784$		0			0
$785$	−231.164			−0.294477
$786$	−655.661	−	477.946i	−0.834174	−	0.608073i
$787$	−963.810			−1.22466			−0.612332	−	0.790601i	$-0.709768\pi$
$787$	−963.810			−1.22466			−0.612332	+	0.790601i	$0.709768\pi$
$788$	−611.211	+	196.467i	−0.775648	+	0.249324i
$789$	−134.438			−0.170390
$790$	65.6654	+	47.8669i	0.0831207	+	0.0605911i
$791$		0			0
$792$	126.433	+	41.7424i	0.159638	+	0.0527050i
$793$	−643.101			−0.810973
$794$	−197.027	−	143.623i	−0.248144	−	0.180886i
$795$		−	50.5113i		−	0.0635362i
$796$	−767.143	+	246.590i	−0.963747	+	0.309787i
$797$	677.191			0.849675			0.424837	−	0.905270i	$-0.360331\pi$
$797$	677.191			0.849675			0.424837	+	0.905270i	$0.360331\pi$
$798$		0			0
$799$	232.511			0.291003
$800$	−492.247	−	3.87761i	−0.615309	−	0.00484701i
$801$		−	359.492i		−	0.448804i
$802$	−401.901	−	292.967i	−0.501123	−	0.365295i
$803$	−647.712			−0.806615
$804$	−793.638	+	255.107i	−0.987112	+	0.317297i
$805$		0			0
$806$	−148.858	+	204.207i	−0.184687	+	0.253359i
$807$	561.491			0.695776
$808$	52.2875	−	158.373i	0.0647122	−	0.196007i
$809$	−417.234			−0.515741			−0.257870	−	0.966180i	$-0.583021\pi$
$809$	−417.234			−0.515741			−0.257870	+	0.966180i	$0.583021\pi$
$810$	183.089	+	133.463i	0.226035	+	0.164769i
$811$	1431.94			1.76564			0.882821	−	0.469709i	$-0.155641\pi$
$811$	1431.94			1.76564			0.882821	+	0.469709i	$0.155641\pi$
$812$		0			0
$813$			314.215i			0.386488i
$814$	378.513	+	275.918i	0.465004	+	0.338965i
$815$		−	304.790i		−	0.373975i
$816$	370.066	+	516.162i	0.453512	+	0.632551i
$817$		−	633.969i		−	0.775972i
$818$	792.719	−	1087.48i	0.969094	−	1.32943i
$819$		0			0
$820$	127.357	−	40.9375i	0.155313	−	0.0499237i
$821$			18.3555i			0.0223575i	0.999938	+	0.0111787i	$0.00355838\pi$
$821$			18.3555i			0.0223575i	−0.999938	+	0.0111787i	$0.996442\pi$
$822$	−289.093	−	210.735i	−0.351695	−	0.256369i
$823$	1440.59			1.75041			0.875204	−	0.483753i	$-0.160727\pi$
$823$	1440.59			1.75041			0.875204	+	0.483753i	$0.160727\pi$
$824$	−26.0937	−	8.61490i	−0.0316671	−	0.0104550i
$825$		−	168.691i		−	0.204474i
$826$		0			0
$827$			240.040i			0.290255i	0.989413	+	0.145127i	$0.0463592\pi$
$827$			240.040i			0.290255i	−0.989413	+	0.145127i	$0.953641\pi$
$828$	−112.299	−	349.364i	−0.135627	−	0.421937i
$829$	−1464.13			−1.76614			−0.883070	−	0.469241i	$-0.844527\pi$
$829$	−1464.13			−1.76614			−0.883070	+	0.469241i	$0.844527\pi$
$830$	−10.8102	−	7.88013i	−0.0130243	−	0.00949413i
$831$		−	257.855i		−	0.310294i
$832$	353.814	+	262.206i	0.425257	+	0.315152i
$833$		0			0
$834$	−273.569	−	199.418i	−0.328020	−	0.239111i
$835$			783.149i			0.937903i
$836$	468.790	−	150.688i	0.560754	−	0.180249i
$837$			538.023i			0.642800i
$838$	288.965	+	210.641i	0.344826	+	0.251362i
$839$			896.568i			1.06861i	0.845290	+	0.534307i	$0.179427\pi$
$839$			896.568i			1.06861i	−0.845290	+	0.534307i	$0.820573\pi$
$840$		0			0
$841$	−945.761			−1.12457
$842$	250.315	−	343.390i	0.297286	−	0.407826i
$843$	359.889			0.426914
$844$	649.442	−	208.756i	0.769481	−	0.247342i
$845$	−377.256			−0.446456
$846$	57.1348	−	78.3793i	0.0675352	−	0.0926470i
$847$		0			0
$848$	−65.0153	−	90.6822i	−0.0766690	−	0.106937i
$849$	72.2708			0.0851247
$850$	−308.010	+	422.537i	−0.362364	+	0.497103i
$851$		−	1290.99i		−	1.51703i
$852$	−233.836	−	727.464i	−0.274455	−	0.853830i
$853$	−1376.70			−1.61395			−0.806973	−	0.590588i	$-0.798896\pi$
$853$	−1376.70			−1.61395			−0.806973	+	0.590588i	$0.798896\pi$
$854$		0			0
$855$	−288.231			−0.337112
$856$	−512.807	−	169.305i	−0.599074	−	0.197786i
$857$		−	1210.80i		−	1.41284i	−0.707795	−	0.706418i	$-0.750310\pi$
$857$		−	1210.80i		−	1.41284i	0.707795	−	0.706418i	$-0.249690\pi$
$858$	−88.8963	+	121.951i	−0.103609	+	0.142134i
$859$	−574.651			−0.668977			−0.334488	−	0.942400i	$-0.608564\pi$
$859$	−574.651			−0.668977			−0.334488	+	0.942400i	$0.608564\pi$
$860$	285.538	−	91.7832i	0.332021	−	0.106725i
$861$		0			0
$862$	1117.53	+	814.627i	1.29644	+	0.945043i
$863$	−486.669			−0.563927			−0.281964	−	0.959425i	$-0.590986\pi$
$863$	−486.669			−0.563927			−0.281964	+	0.959425i	$0.590986\pi$
$864$	937.574	+	7.38560i	1.08515	+	0.00854815i
$865$	−466.336			−0.539117
$866$	117.622	−	161.358i	0.135822	−	0.186325i
$867$	−0.372749			−0.000429930
$868$		0			0
$869$			61.5138i			0.0707869i
$870$	360.696	−	494.814i	0.414593	−	0.568752i
$871$			613.988i			0.704923i
$872$	1025.97	+	338.726i	1.17657	+	0.388447i
$873$			315.249i			0.361110i
$874$	−1096.71	−	799.449i	−1.25482	−	0.914701i
$875$		0			0
$876$	−1227.02	+	394.414i	−1.40071	+	0.450244i
$877$			1175.77i			1.34067i	0.742057	+	0.670337i	$0.233850\pi$
$877$			1175.77i			1.34067i	−0.742057	+	0.670337i	$0.766150\pi$
$878$	815.365	−	1118.54i	0.928662	−	1.27397i
$879$	−1195.11			−1.35962
$880$	135.739	+	189.326i	0.154248	+	0.215143i
$881$		−	197.506i		−	0.224183i	−0.993698	−	0.112092i	$-0.964245\pi$
$881$		−	197.506i		−	0.224183i	0.993698	−	0.112092i	$-0.0357550\pi$
$882$		0			0
$883$			739.290i			0.837248i	0.908160	+	0.418624i	$0.137487\pi$
$883$			739.290i			0.837248i	−0.908160	+	0.418624i	$0.862513\pi$
$884$	445.335	−	143.148i	0.503773	−	0.161933i
$885$	−769.095			−0.869034
$886$	−317.741	+	435.888i	−0.358624	+	0.491972i
$887$			438.003i			0.493803i	0.969041	+	0.246902i	$0.0794124\pi$
$887$			438.003i			0.493803i	−0.969041	+	0.246902i	$0.920588\pi$
$888$	885.070	+	292.209i	0.996700	+	0.329064i
$889$		0			0
$890$	370.508	−	508.274i	0.416301	−	0.571095i
$891$			171.513i			0.192495i
$892$	546.257	−	175.589i	0.612395	−	0.196848i
$893$		−	358.710i		−	0.401691i
$894$	−672.138	+	922.061i	−0.751832	+	1.03139i
$895$		−	320.931i		−	0.358582i
$896$		0			0
$897$	415.936			0.463696
$898$	123.882	+	90.3040i	0.137953	+	0.100561i
$899$	776.185			0.863388
$900$	66.7500	+	207.659i	0.0741666	+	0.230733i
$901$	−118.522			−0.131545
$902$	81.8329	+	59.6523i	0.0907239	+	0.0661334i
$903$		0			0
$904$	341.921	−	1035.64i	0.378231	−	1.14562i
$905$	294.952			0.325914
$906$	778.431	+	567.439i	0.859195	+	0.626313i
$907$		−	1319.50i		−	1.45480i	−0.686214	−	0.727400i	$-0.740729\pi$
$907$		−	1319.50i		−	1.45480i	0.686214	−	0.727400i	$-0.259271\pi$
$908$	28.7894	+	89.5640i	0.0317064	+	0.0986388i
$909$	−73.9018			−0.0813001
$910$		0			0
$911$	206.561			0.226741			0.113371	−	0.993553i	$-0.463835\pi$
$911$	206.561			0.226741			0.113371	+	0.993553i	$0.463835\pi$
$912$	796.316	−	570.925i	0.873154	−	0.626015i
$913$		−	10.1268i		−	0.0110917i
$914$	567.656	+	413.794i	0.621067	+	0.452728i
$915$	−676.938			−0.739823
$916$	75.1680	+	233.848i	0.0820611	+	0.255292i
$917$		0			0
$918$	586.660	−	804.799i	0.639064	−	0.876688i
$919$	563.385			0.613042			0.306521	−	0.951864i	$-0.400835\pi$
$919$	563.385			0.613042			0.306521	+	0.951864i	$0.400835\pi$
$920$	201.293	−	609.695i	0.218796	−	0.662711i
$921$	−119.741			−0.130012
$922$	−479.909	−	349.831i	−0.520509	−	0.379426i
$923$	−562.793			−0.609743
$924$		0			0
$925$			767.355i			0.829573i
$926$	−41.2692	−	30.0833i	−0.0445672	−	0.0324874i
$927$			12.1761i			0.0131349i
$928$	10.6549	−	1352.60i	0.0114816	−	1.45754i
$929$			1213.20i			1.30592i	0.757392	+	0.652960i	$0.226473\pi$
$929$			1213.20i			1.30592i	−0.757392	+	0.652960i	$0.773527\pi$
$930$	−156.690	+	214.952i	−0.168484	+	0.231131i
$931$		0			0
$932$	127.547	+	396.798i	0.136853	+	0.425749i
$933$			47.9895i			0.0514357i
$934$	202.863	+	147.878i	0.217198	+	0.158327i
$935$	247.449			0.264651
$936$	61.1766	−	185.298i	0.0653596	−	0.197968i
$937$		−	237.201i		−	0.253149i	−0.991957	−	0.126575i	$-0.959602\pi$
$937$		−	237.201i		−	0.253149i	0.991957	−	0.126575i	$-0.0403983\pi$
$938$		0			0
$939$			787.403i			0.838554i
$940$	161.562	−	51.9325i	0.171874	−	0.0552473i
$941$	−119.204			−0.126678			−0.0633391	−	0.997992i	$-0.520175\pi$
$941$	−119.204			−0.126678			−0.0633391	+	0.997992i	$0.520175\pi$
$942$	−281.384	−	205.115i	−0.298709	−	0.217745i
$943$		−	279.107i		−	0.295977i
$944$	−1380.75	+	989.937i	−1.46265	+	1.04866i
$945$		0			0
$946$	183.472	+	133.743i	0.193945	+	0.141377i
$947$			972.815i			1.02726i	0.858012	+	0.513630i	$0.171699\pi$
$947$			972.815i			1.02726i	−0.858012	+	0.513630i	$0.828301\pi$
$948$	37.4579	+	116.532i	0.0395125	+	0.122924i
$949$			949.271i			1.00029i
$950$	651.876	+	475.187i	0.686185	+	0.500196i
$951$			217.815i			0.229038i
$952$		0			0
$953$	−840.555			−0.882010			−0.441005	−	0.897505i	$-0.645378\pi$
$953$	−840.555			−0.882010			−0.441005	+	0.897505i	$0.645378\pi$
$954$	−29.1242	+	39.9535i	−0.0305285	+	0.0418800i
$955$	12.2339			0.0128104
$956$	128.155	+	398.690i	0.134053	+	0.417040i
$957$	463.530			0.484358
$958$	−204.311	+	280.281i	−0.213268	+	0.292568i
$959$		0			0
$960$	372.430	+	276.002i	0.387948	+	0.287502i
$961$	623.818			0.649134
$962$	404.379	−	554.740i	0.420352	−	0.576652i
$963$			239.291i			0.248485i
$964$	627.264	−	201.628i	0.650689	−	0.209157i
$965$	−906.086			−0.938949
$966$		0			0
$967$	1696.40			1.75429			0.877147	−	0.480222i	$-0.159444\pi$
$967$	1696.40			1.75429			0.877147	+	0.480222i	$0.159444\pi$
$968$	248.189	−	751.740i	0.256394	−	0.776591i
$969$		−	1040.79i		−	1.07408i
$970$	−324.909	+	445.720i	−0.334958	+	0.459506i
$971$	−1288.11			−1.32658			−0.663291	−	0.748361i	$-0.730841\pi$
$971$	−1288.11			−1.32658			−0.663291	+	0.748361i	$0.730841\pi$
$972$	−218.349	−	679.285i	−0.224639	−	0.698853i
$973$		0			0
$974$	1101.44	+	802.901i	1.13085	+	0.824333i
$975$	−247.229			−0.253568
$976$	−1215.30	+	871.318i	−1.24518	+	0.892743i
$977$	−123.909			−0.126826			−0.0634130	−	0.997987i	$-0.520199\pi$
$977$	−123.909			−0.126826			−0.0634130	+	0.997987i	$0.520199\pi$
$978$	270.444	−	371.004i	0.276528	−	0.379350i
$979$	476.139			0.486353
$980$		0			0
$981$		−	478.747i		−	0.488019i
$982$	−327.640	+	449.466i	−0.333645	+	0.457705i
$983$			1645.78i			1.67424i	0.547016	+	0.837122i	$0.315764\pi$
$983$			1645.78i			1.67424i	−0.547016	+	0.837122i	$0.684236\pi$
$984$	191.348	+	63.1743i	0.194460	+	0.0642015i
$985$			497.735i			0.505314i
$986$	−1161.05	−	846.352i	−1.17754	−	0.858369i
$987$		0			0
$988$	−220.844	−	687.048i	−0.223527	−	0.695393i
$989$		−	625.766i		−	0.632726i
$990$	60.8054	−	83.4148i	0.0614196	−	0.0842574i
$991$	453.836			0.457958			0.228979	−	0.973431i	$-0.426461\pi$
$991$	453.836			0.457958			0.228979	+	0.973431i	$0.426461\pi$
$992$	−4.62860	+	587.582i	−0.00466592	+	0.592321i
$993$		−	175.285i		−	0.176521i
$994$		0			0
$995$			624.717i			0.627856i
$996$	−6.16653	−	19.1841i	−0.00619129	−	0.0192611i
$997$	−906.826			−0.909554			−0.454777	−	0.890605i	$-0.650281\pi$
$997$	−906.826			−0.909554			−0.454777	+	0.890605i	$0.650281\pi$
$998$	−483.541	+	663.337i	−0.484510	+	0.664666i
$999$		−	1461.57i		−	1.46303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.h.a.293.5		28
4.3	odd	2		1568.3.h.a.881.19		28
7.2	even	3		392.3.j.e.325.7		28
7.3	odd	6		392.3.j.e.117.13		28
7.4	even	3		56.3.j.a.5.13	yes	28
7.5	odd	6		56.3.j.a.45.7	yes	28
7.6	odd	2	inner	392.3.h.a.293.6		28
8.3	odd	2		1568.3.h.a.881.10		28
8.5	even	2	inner	392.3.h.a.293.8		28
28.11	odd	6		224.3.n.a.145.5		28
28.19	even	6		224.3.n.a.17.10		28
28.27	even	2		1568.3.h.a.881.9		28
56.5	odd	6		56.3.j.a.45.13	yes	28
56.11	odd	6		224.3.n.a.145.10		28
56.13	odd	2	inner	392.3.h.a.293.7		28
56.19	even	6		224.3.n.a.17.5		28
56.27	even	2		1568.3.h.a.881.20		28
56.37	even	6		392.3.j.e.325.13		28
56.45	odd	6		392.3.j.e.117.7		28
56.53	even	6		56.3.j.a.5.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.7	✓	28	56.53	even	6
56.3.j.a.5.13	yes	28	7.4	even	3
56.3.j.a.45.7	yes	28	7.5	odd	6
56.3.j.a.45.13	yes	28	56.5	odd	6
224.3.n.a.17.5		28	56.19	even	6
224.3.n.a.17.10		28	28.19	even	6
224.3.n.a.145.5		28	28.11	odd	6
224.3.n.a.145.10		28	56.11	odd	6
392.3.h.a.293.5		28	1.1	even	1	trivial
392.3.h.a.293.6		28	7.6	odd	2	inner
392.3.h.a.293.7		28	56.13	odd	2	inner
392.3.h.a.293.8		28	8.5	even	2	inner
392.3.j.e.117.7		28	56.45	odd	6
392.3.j.e.117.13		28	7.3	odd	6
392.3.j.e.325.7		28	7.2	even	3
392.3.j.e.325.13		28	56.37	even	6
1568.3.h.a.881.9		28	28.27	even	2
1568.3.h.a.881.10		28	8.3	odd	2
1568.3.h.a.881.19		28	4.3	odd	2
1568.3.h.a.881.20		28	56.27	even	2

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61618 - 1.17812i) q^{2} -2.33563 q^{3} +(1.22408 + 3.80810i) q^{4} +3.10110 q^{5} +(3.77480 + 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} -3.54484 q^{9} +O(q^{10})\)	\(q+(-1.61618 - 1.17812i) q^{2} -2.33563 q^{3} +(1.22408 + 3.80810i) q^{4} +3.10110 q^{5} +(3.77480 + 2.75165i) q^{6} +(2.50807 - 7.59668i) q^{8} -3.54484 q^{9} +(-5.01193 - 3.65346i) q^{10} -4.69506i q^{11} +(-2.85898 - 8.89431i) q^{12} -6.88097 q^{13} -7.24301 q^{15} +(-13.0033 + 9.32281i) q^{16} +16.9953i q^{17} +(5.72910 + 4.17624i) q^{18} +26.2198 q^{19} +(3.79598 + 11.8093i) q^{20} +(-5.53134 + 7.58806i) q^{22} +25.8805 q^{23} +(-5.85792 + 17.7430i) q^{24} -15.3832 q^{25} +(11.1209 + 8.10660i) q^{26} +29.3001 q^{27} -42.2701i q^{29} +(11.7060 + 8.53312i) q^{30} +18.3625i q^{31} +(31.9990 + 0.252068i) q^{32} +10.9659i q^{33} +(20.0225 - 27.4675i) q^{34} +(-4.33915 - 13.4991i) q^{36} -49.8827i q^{37} +(-42.3759 - 30.8900i) q^{38} +16.0714 q^{39} +(7.77776 - 23.5581i) q^{40} -10.7844i q^{41} -24.1791i q^{43} +(17.8793 - 5.74711i) q^{44} -10.9929 q^{45} +(-41.8276 - 30.4903i) q^{46} -13.6809i q^{47} +(30.3708 - 21.7746i) q^{48} +(24.8620 + 18.1232i) q^{50} -39.6947i q^{51} +(-8.42282 - 26.2034i) q^{52} +6.97379i q^{53} +(-47.3542 - 34.5190i) q^{54} -14.5598i q^{55} -61.2396 q^{57} +(-49.7992 + 68.3161i) q^{58} +106.184 q^{59} +(-8.86599 - 27.5821i) q^{60} +93.4609 q^{61} +(21.6332 - 29.6771i) q^{62} +(-51.4192 - 38.1060i) q^{64} -21.3386 q^{65} +(12.9191 - 17.7229i) q^{66} -89.2299i q^{67} +(-64.7199 + 20.8035i) q^{68} -60.4473 q^{69} +81.7898 q^{71} +(-8.89070 + 26.9290i) q^{72} -137.956i q^{73} +(-58.7677 + 80.6194i) q^{74} +35.9294 q^{75} +(32.0950 + 99.8475i) q^{76} +(-25.9743 - 18.9340i) q^{78} -13.1018 q^{79} +(-40.3244 + 28.9109i) q^{80} -36.5306 q^{81} +(-12.7053 + 17.4296i) q^{82} +2.15689 q^{83} +52.7041i q^{85} +(-28.4858 + 39.0777i) q^{86} +98.7272i q^{87} +(-35.6669 - 11.7755i) q^{88} +101.413i q^{89} +(17.7665 + 12.9509i) q^{90} +(31.6797 + 98.5556i) q^{92} -42.8880i q^{93} +(-16.1177 + 22.1108i) q^{94} +81.3101 q^{95} +(-74.7378 - 0.588736i) q^{96} -88.9318i q^{97} +16.6432i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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