LMFDB - Embedded newform 128.4.g.a.49.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(17,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("128.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.g (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.9
Character	$\chi$	$=$	128.49
Dual form			128.4.g.a.81.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +O(q^{10})$	\(q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +(-3.11257 - 1.28927i) q^{11} +(-28.8862 - 69.7374i) q^{13} -98.9809i q^{15} +66.2302i q^{17} +(12.5299 + 30.2498i) q^{19} +(131.191 + 54.3410i) q^{21} +(63.7309 - 63.7309i) q^{23} +(-102.268 - 102.268i) q^{25} +(-40.7473 + 98.3726i) q^{27} +(190.908 - 79.0767i) q^{29} -123.811 q^{31} -20.3082 q^{33} +(357.370 - 148.028i) q^{35} +(-46.0901 + 111.271i) q^{37} +(-321.739 - 321.739i) q^{39} +(-100.187 + 100.187i) q^{41} +(-27.5836 - 11.4255i) q^{43} +(-58.6652 - 141.630i) q^{45} +394.293i q^{47} +211.932i q^{49} +(152.779 + 368.841i) q^{51} +(135.196 + 56.0002i) q^{53} +(-39.1175 + 39.1175i) q^{55} +(139.560 + 139.560i) q^{57} +(-297.070 + 717.190i) q^{59} +(-548.826 + 227.331i) q^{61} +219.927 q^{63} -1239.46 q^{65} +(-163.352 + 67.6626i) q^{67} +(207.909 - 501.937i) q^{69} +(-194.022 - 194.022i) q^{71} +(547.142 - 547.142i) q^{73} +(-805.449 - 333.628i) q^{75} +(-30.3713 - 73.3227i) q^{77} +715.813i q^{79} +893.911i q^{81} +(-54.6375 - 131.907i) q^{83} +(1004.74 + 416.178i) q^{85} +(880.769 - 880.769i) q^{87} +(220.576 + 220.576i) q^{89} +(680.471 - 1642.80i) q^{91} +(-689.512 + 285.605i) q^{93} +537.638 q^{95} +1364.39 q^{97} +(-29.0587 + 12.0365i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	5.56908	−	2.30679i	1.07177	−	0.443942i	0.224155	−	0.974553i	$-0.428038\pi$
$3$	5.56908	−	2.30679i	1.07177	−	0.443942i	0.847615	+	0.530612i	$0.178038\pi$
$4$		0			0
$5$	6.28381	−	15.1704i	0.562041	−	1.35689i	−0.346091	−	0.938201i	$-0.612491\pi$
$5$	6.28381	−	15.1704i	0.562041	−	1.35689i	0.908131	−	0.418685i	$-0.137509\pi$
$6$		0			0
$7$	16.6573	+	16.6573i	0.899411	+	0.899411i	0.995384	−	0.0959733i	$-0.0305963\pi$
$7$	16.6573	+	16.6573i	0.899411	+	0.899411i	−0.0959733	+	0.995384i	$0.530596\pi$
$8$		0			0
$9$	6.60151	−	6.60151i	0.244500	−	0.244500i
$10$		0			0
$11$	−3.11257	−	1.28927i	−0.0853158	−	0.0353390i	0.339617	−	0.940564i	$-0.389702\pi$
$11$	−3.11257	−	1.28927i	−0.0853158	−	0.0353390i	−0.424933	+	0.905225i	$0.639702\pi$
$12$		0			0
$13$	−28.8862	−	69.7374i	−0.616275	−	1.48782i	−0.855998	−	0.516979i	$-0.827057\pi$
$13$	−28.8862	−	69.7374i	−0.616275	−	1.48782i	0.239723	−	0.970841i	$-0.422943\pi$
$14$		0			0
$15$		−	98.9809i		−	1.70378i
$16$		0			0
$17$			66.2302i			0.944893i	0.881359	+	0.472447i	$0.156629\pi$
$17$			66.2302i			0.944893i	−0.881359	+	0.472447i	$0.843371\pi$
$18$		0			0
$19$	12.5299	+	30.2498i	0.151292	+	0.365251i	0.981296	−	0.192507i	$-0.0616617\pi$
$19$	12.5299	+	30.2498i	0.151292	+	0.365251i	−0.830004	+	0.557758i	$0.811662\pi$
$20$		0			0
$21$	131.191	+	54.3410i	1.36325	+	0.564676i
$22$		0			0
$23$	63.7309	−	63.7309i	0.577775	−	0.577775i	−0.356515	−	0.934290i	$-0.616035\pi$
$23$	63.7309	−	63.7309i	0.577775	−	0.577775i	0.934290	+	0.356515i	$0.116035\pi$
$24$		0			0
$25$	−102.268	−	102.268i	−0.818143	−	0.818143i
$26$		0			0
$27$	−40.7473	+	98.3726i	−0.290438	+	0.701178i
$28$		0			0
$29$	190.908	−	79.0767i	1.22244	−	0.506351i	0.324255	−	0.945970i	$-0.394887\pi$
$29$	190.908	−	79.0767i	1.22244	−	0.506351i	0.898184	+	0.439619i	$0.144887\pi$
$30$		0			0
$31$	−123.811			−0.717325			−0.358662	−	0.933467i	$-0.616767\pi$
$31$	−123.811			−0.717325			−0.358662	+	0.933467i	$0.616767\pi$
$32$		0			0
$33$	−20.3082			−0.107127
$34$		0			0
$35$	357.370	−	148.028i	1.72590	−	0.714892i
$36$		0			0
$37$	−46.0901	+	111.271i	−0.204788	+	0.494403i	−0.992588	−	0.121529i	$-0.961220\pi$
$37$	−46.0901	+	111.271i	−0.204788	+	0.494403i	0.787799	+	0.615932i	$0.211220\pi$
$38$		0			0
$39$	−321.739	−	321.739i	−1.32101	−	1.32101i
$40$		0			0
$41$	−100.187	+	100.187i	−0.381624	+	0.381624i	−0.871687	−	0.490063i	$-0.836974\pi$
$41$	−100.187	+	100.187i	−0.381624	+	0.381624i	0.490063	+	0.871687i	$0.336974\pi$
$42$		0			0
$43$	−27.5836	−	11.4255i	−0.0978246	−	0.0405203i	0.333234	−	0.942844i	$-0.391860\pi$
$43$	−27.5836	−	11.4255i	−0.0978246	−	0.0405203i	−0.431059	+	0.902324i	$0.641860\pi$
$44$		0			0
$45$	−58.6652	−	141.630i	−0.194340	−	0.469178i
$46$		0			0
$47$			394.293i			1.22369i	0.790976	+	0.611847i	$0.209573\pi$
$47$			394.293i			1.22369i	−0.790976	+	0.611847i	$0.790427\pi$
$48$		0			0
$49$			211.932i			0.617879i
$50$		0			0
$51$	152.779	+	368.841i	0.419478	+	1.01271i
$52$		0			0
$53$	135.196	+	56.0002i	0.350390	+	0.145136i	0.550935	−	0.834548i	$-0.314271\pi$
$53$	135.196	+	56.0002i	0.350390	+	0.145136i	−0.200545	+	0.979684i	$0.564271\pi$
$54$		0			0
$55$	−39.1175	+	39.1175i	−0.0959019	+	0.0959019i
$56$		0			0
$57$	139.560	+	139.560i	0.324301	+	0.324301i
$58$		0			0
$59$	−297.070	+	717.190i	−0.655512	+	1.58254i	0.149152	+	0.988814i	$0.452346\pi$
$59$	−297.070	+	717.190i	−0.655512	+	1.58254i	−0.804664	+	0.593731i	$0.797654\pi$
$60$		0			0
$61$	−548.826	+	227.331i	−1.15197	+	0.477160i	−0.875193	−	0.483775i	$-0.839265\pi$
$61$	−548.826	+	227.331i	−1.15197	+	0.477160i	−0.276774	+	0.960935i	$0.589265\pi$
$62$		0			0
$63$	219.927			0.439812
$64$		0			0
$65$	−1239.46			−2.36517
$66$		0			0
$67$	−163.352	+	67.6626i	−0.297860	+	0.123378i	−0.526609	−	0.850108i	$-0.676537\pi$
$67$	−163.352	+	67.6626i	−0.297860	+	0.123378i	0.228749	+	0.973486i	$0.426537\pi$
$68$		0			0
$69$	207.909	−	501.937i	0.362743	−	0.875740i
$70$		0			0
$71$	−194.022	−	194.022i	−0.324312	−	0.324312i	0.526107	−	0.850419i	$-0.323651\pi$
$71$	−194.022	−	194.022i	−0.324312	−	0.324312i	−0.850419	+	0.526107i	$0.823651\pi$
$72$		0			0
$73$	547.142	−	547.142i	0.877235	−	0.877235i	−0.116013	−	0.993248i	$-0.537011\pi$
$73$	547.142	−	547.142i	0.877235	−	0.877235i	0.993248	+	0.116013i	$0.0370113\pi$
$74$		0			0
$75$	−805.449	−	333.628i	−1.24007	−	0.513654i
$76$		0			0
$77$	−30.3713	−	73.3227i	−0.0449497	−	0.108518i
$78$		0			0
$79$			715.813i			1.01943i	0.860342	+	0.509717i	$0.170250\pi$
$79$			715.813i			1.01943i	−0.860342	+	0.509717i	$0.829750\pi$
$80$		0			0
$81$			893.911i			1.22621i
$82$		0			0
$83$	−54.6375	−	131.907i	−0.0722560	−	0.174441i	0.883625	−	0.468195i	$-0.155096\pi$
$83$	−54.6375	−	131.907i	−0.0722560	−	0.174441i	−0.955881	+	0.293754i	$0.905096\pi$
$84$		0			0
$85$	1004.74	+	416.178i	1.28211	+	0.531068i
$86$		0			0
$87$	880.769	−	880.769i	1.08538	−	1.08538i
$88$		0			0
$89$	220.576	+	220.576i	0.262708	+	0.262708i	0.826153	−	0.563445i	$-0.190524\pi$
$89$	220.576	+	220.576i	0.262708	+	0.262708i	−0.563445	+	0.826153i	$0.690524\pi$
$90$		0			0
$91$	680.471	−	1642.80i	0.783877	−	1.89245i
$92$		0			0
$93$	−689.512	+	285.605i	−0.768807	+	0.318450i
$94$		0			0
$95$	537.638			0.580637
$96$		0			0
$97$	1364.39			1.42817			0.714087	−	0.700057i	$-0.246842\pi$
$97$	1364.39			1.42817			0.714087	+	0.700057i	$0.246842\pi$
$98$		0			0
$99$	−29.0587	+	12.0365i	−0.0295001	+	0.0122194i
$100$		0			0
$101$	−349.311	+	843.310i	−0.344136	+	0.830817i	0.653153	+	0.757226i	$0.273446\pi$
$101$	−349.311	+	843.310i	−0.344136	+	0.830817i	−0.997289	+	0.0735909i	$0.976554\pi$
$102$		0			0
$103$	−273.149	−	273.149i	−0.261302	−	0.261302i	0.564281	−	0.825583i	$-0.309154\pi$
$103$	−273.149	−	273.149i	−0.261302	−	0.261302i	−0.825583	+	0.564281i	$0.809154\pi$
$104$		0			0
$105$	1648.76	−	1648.76i	1.53240	−	1.53240i
$106$		0			0
$107$	675.362	+	279.744i	0.610185	+	0.252747i	0.666307	−	0.745677i	$-0.267874\pi$
$107$	675.362	+	279.744i	0.610185	+	0.252747i	−0.0561229	+	0.998424i	$0.517874\pi$
$108$		0			0
$109$	−602.506	−	1454.58i	−0.529446	−	1.27820i	−0.931887	−	0.362749i	$-0.881838\pi$
$109$	−602.506	−	1454.58i	−0.529446	−	1.27820i	0.402441	−	0.915446i	$-0.368162\pi$
$110$		0			0
$111$			726.000i			0.620801i
$112$		0			0
$113$		−	315.691i		−	0.262812i	−0.991329	−	0.131406i	$-0.958051\pi$
$113$		−	315.691i		−	0.262812i	0.991329	−	0.131406i	$-0.0419491\pi$
$114$		0			0
$115$	−566.354	−	1367.30i	−0.459242	−	1.10871i
$116$		0			0
$117$	−651.064	−	269.679i	−0.514452	−	0.213093i
$118$		0			0
$119$	−1103.22	+	1103.22i	−0.849847	+	0.849847i
$120$		0			0
$121$	−933.133	−	933.133i	−0.701077	−	0.701077i
$122$		0			0
$123$	−326.839	+	789.060i	−0.239594	+	0.578432i
$124$		0			0
$125$	−297.776	+	123.343i	−0.213071	+	0.0882569i
$126$		0			0
$127$	−356.698			−0.249227			−0.124613	−	0.992205i	$-0.539769\pi$
$127$	−356.698			−0.249227			−0.124613	+	0.992205i	$0.539769\pi$
$128$		0			0
$129$	−179.971			−0.122834
$130$		0			0
$131$	2481.91	−	1028.04i	1.65531	−	0.685652i	0.657606	−	0.753362i	$-0.271569\pi$
$131$	2481.91	−	1028.04i	1.65531	−	0.685652i	0.997705	+	0.0677095i	$0.0215691\pi$
$132$		0			0
$133$	−295.166	+	712.594i	−0.192437	+	0.464585i
$134$		0			0
$135$	1236.31	+	1236.31i	0.788181	+	0.788181i
$136$		0			0
$137$	−811.069	+	811.069i	−0.505798	+	0.505798i	−0.913234	−	0.407436i	$-0.866423\pi$
$137$	−811.069	+	811.069i	−0.505798	+	0.505798i	0.407436	+	0.913234i	$0.366423\pi$
$138$		0			0
$139$	−2505.86	−	1037.96i	−1.52910	−	0.633373i	−0.549709	−	0.835356i	$-0.685261\pi$
$139$	−2505.86	−	1037.96i	−1.52910	−	0.633373i	−0.979389	+	0.201984i	$0.935261\pi$
$140$		0			0
$141$	909.552	+	2195.85i	0.543249	+	1.31152i
$142$		0			0
$143$			254.304i			0.148713i
$144$		0			0
$145$		−	3393.06i		−	1.94330i
$146$		0			0
$147$	488.883	+	1180.27i	0.274302	+	0.662224i
$148$		0			0
$149$	−610.519	−	252.885i	−0.335676	−	0.139041i	0.208478	−	0.978027i	$-0.433149\pi$
$149$	−610.519	−	252.885i	−0.335676	−	0.139041i	−0.544154	+	0.838986i	$0.683149\pi$
$150$		0			0
$151$	1314.56	−	1314.56i	0.708457	−	0.708457i	−0.257753	−	0.966211i	$-0.582982\pi$
$151$	1314.56	−	1314.56i	0.708457	−	0.708457i	0.966211	+	0.257753i	$0.0829822\pi$
$152$		0			0
$153$	437.219	+	437.219i	0.231027	+	0.231027i
$154$		0			0
$155$	−778.003	+	1878.26i	−0.403166	+	0.973328i
$156$		0			0
$157$	2290.74	−	948.857i	1.16447	−	0.482338i	0.285107	−	0.958496i	$-0.407971\pi$
$157$	2290.74	−	948.857i	1.16447	−	0.482338i	0.879360	+	0.476158i	$0.157971\pi$
$158$		0			0
$159$	882.101			0.439969
$160$		0			0
$161$	2123.17			1.03931
$162$		0			0
$163$	26.3934	−	10.9325i	0.0126828	−	0.00525338i	−0.376333	−	0.926484i	$-0.622815\pi$
$163$	26.3934	−	10.9325i	0.0126828	−	0.00525338i	0.389016	+	0.921231i	$0.372815\pi$
$164$		0			0
$165$	−127.613	+	308.085i	−0.0602100	+	0.145360i
$166$		0			0
$167$	111.233	+	111.233i	0.0515415	+	0.0515415i	0.732408	−	0.680866i	$-0.238397\pi$
$167$	111.233	+	111.233i	0.0515415	+	0.0515415i	−0.680866	+	0.732408i	$0.738397\pi$
$168$		0			0
$169$	−2475.38	+	2475.38i	−1.12671	+	1.12671i
$170$		0			0
$171$	282.410	+	116.978i	0.126295	+	0.0523131i
$172$		0			0
$173$	−835.349	−	2016.71i	−0.367112	−	0.886287i	−0.994221	−	0.107355i	$-0.965762\pi$
$173$	−835.349	−	2016.71i	−0.367112	−	0.886287i	0.627109	−	0.778932i	$-0.284238\pi$
$174$		0			0
$175$		−	3407.02i		−	1.47169i
$176$		0			0
$177$			4679.37i			1.98713i
$178$		0			0
$179$	−539.124	−	1301.56i	−0.225117	−	0.543481i	0.770454	−	0.637496i	$-0.220030\pi$
$179$	−539.124	−	1301.56i	−0.225117	−	0.543481i	−0.995571	+	0.0940151i	$0.970030\pi$
$180$		0			0
$181$	−702.054	−	290.800i	−0.288305	−	0.119420i	0.233844	−	0.972274i	$-0.424870\pi$
$181$	−702.054	−	290.800i	−0.288305	−	0.119420i	−0.522149	+	0.852854i	$0.674870\pi$
$182$		0			0
$183$	−2532.05	+	2532.05i	−1.02281	+	1.02281i
$184$		0			0
$185$	1398.42	+	1398.42i	0.555749	+	0.555749i
$186$		0			0
$187$	85.3885	−	206.146i	0.0333916	−	0.0806144i
$188$		0			0
$189$	−2317.36	+	959.883i	−0.891870	+	0.369425i
$190$		0			0
$191$	−2407.52			−0.912052			−0.456026	−	0.889966i	$-0.650728\pi$
$191$	−2407.52			−0.912052			−0.456026	+	0.889966i	$0.650728\pi$
$192$		0			0
$193$	−1721.96			−0.642224			−0.321112	−	0.947041i	$-0.604057\pi$
$193$	−1721.96			−0.642224			−0.321112	+	0.947041i	$0.604057\pi$
$194$		0			0
$195$	−6902.66	+	2859.18i	−2.53492	+	1.05000i
$196$		0			0
$197$	160.639	−	387.816i	0.0580966	−	0.140258i	−0.892166	−	0.451708i	$-0.850815\pi$
$197$	160.639	−	387.816i	0.0580966	−	0.140258i	0.950262	+	0.311451i	$0.100815\pi$
$198$		0			0
$199$	854.977	+	854.977i	0.304562	+	0.304562i	0.842795	−	0.538234i	$-0.180908\pi$
$199$	854.977	+	854.977i	0.304562	+	0.304562i	−0.538234	+	0.842795i	$0.680908\pi$
$200$		0			0
$201$	−753.637	+	753.637i	−0.264465	+	0.264465i
$202$		0			0
$203$	4497.22	+	1862.81i	1.55489	+	0.644057i
$204$		0			0
$205$	890.326	+	2149.44i	0.303332	+	0.732308i
$206$		0			0
$207$		−	841.441i		−	0.282532i
$208$		0			0
$209$		−	110.309i		−	0.0365082i
$210$		0			0
$211$	819.136	+	1977.57i	0.267259	+	0.645221i	0.999352	−	0.0359838i	$-0.0114565\pi$
$211$	819.136	+	1977.57i	0.267259	+	0.645221i	−0.732093	+	0.681204i	$0.761456\pi$
$212$		0			0
$213$	−1528.09	−	632.956i	−0.491563	−	0.203612i
$214$		0			0
$215$	−346.660	+	346.660i	−0.109963	+	0.109963i
$216$		0			0
$217$	−2062.36	−	2062.36i	−0.645170	−	0.645170i
$218$		0			0
$219$	1784.94	−	4309.22i	0.550753	−	1.32964i
$220$		0			0
$221$	4618.72	−	1913.14i	1.40583	−	0.582314i
$222$		0			0
$223$	−3155.56			−0.947587			−0.473793	−	0.880636i	$-0.657116\pi$
$223$	−3155.56			−0.947587			−0.473793	+	0.880636i	$0.657116\pi$
$224$		0			0
$225$	−1350.24			−0.400073
$226$		0			0
$227$	−329.052	+	136.298i	−0.0962112	+	0.0398520i	−0.430270	−	0.902700i	$-0.641582\pi$
$227$	−329.052	+	136.298i	−0.0962112	+	0.0398520i	0.334059	+	0.942552i	$0.391582\pi$
$228$		0			0
$229$	1834.29	−	4428.38i	0.529317	−	1.27788i	−0.402654	−	0.915352i	$-0.631912\pi$
$229$	1834.29	−	4428.38i	0.529317	−	1.27788i	0.931971	−	0.362532i	$-0.118088\pi$
$230$		0			0
$231$	−338.280	−	338.280i	−0.0963515	−	0.0963515i
$232$		0			0
$233$	−2068.42	+	2068.42i	−0.581573	+	0.581573i	−0.935335	−	0.353762i	$-0.884902\pi$
$233$	−2068.42	+	2068.42i	−0.581573	+	0.581573i	0.353762	+	0.935335i	$0.384902\pi$
$234$		0			0
$235$	5981.61	+	2477.66i	1.66041	+	0.687766i
$236$		0			0
$237$	1651.23	+	3986.42i	0.452569	+	1.09260i
$238$		0			0
$239$		−	1635.41i		−	0.442620i	−0.975204	−	0.221310i	$-0.928967\pi$
$239$		−	1635.41i		−	0.442620i	0.975204	−	0.221310i	$-0.0710332\pi$
$240$		0			0
$241$		−	3798.84i		−	1.01537i	−0.861542	−	0.507686i	$-0.830501\pi$
$241$		−	3798.84i		−	1.01537i	0.861542	−	0.507686i	$-0.169499\pi$
$242$		0			0
$243$	961.887	+	2322.20i	0.253930	+	0.613042i
$244$		0			0
$245$	3215.11	+	1331.74i	0.838391	+	0.347273i
$246$		0			0
$247$	1747.60	−	1747.60i	0.450191	−	0.450191i
$248$		0			0
$249$	−608.562	−	608.562i	−0.154884	−	0.154884i
$250$		0			0
$251$	641.114	−	1547.79i	0.161222	−	0.389224i	−0.822539	−	0.568709i	$-0.807443\pi$
$251$	641.114	−	1547.79i	0.161222	−	0.389224i	0.983761	+	0.179485i	$0.0574430\pi$
$252$		0			0
$253$	−280.533	+	116.201i	−0.0697113	+	0.0288754i
$254$		0			0
$255$	6555.52			1.60989
$256$		0			0
$257$	−576.329			−0.139885			−0.0699424	−	0.997551i	$-0.522282\pi$
$257$	−576.329			−0.139885			−0.0699424	+	0.997551i	$0.522282\pi$
$258$		0			0
$259$	−2621.22	+	1085.75i	−0.628860	+	0.260482i
$260$		0			0
$261$	738.255	−	1782.31i	0.175084	−	0.422690i
$262$		0			0
$263$	−5045.11	−	5045.11i	−1.18287	−	1.18287i	−0.978997	−	0.203873i	$-0.934647\pi$
$263$	−5045.11	−	5045.11i	−1.18287	−	1.18287i	−0.203873	−	0.978997i	$-0.565353\pi$
$264$		0			0
$265$	1699.10	−	1699.10i	0.393867	−	0.393867i
$266$		0			0
$267$	1737.23	+	719.583i	0.398190	+	0.164936i
$268$		0			0
$269$	555.865	+	1341.98i	0.125991	+	0.304170i	0.974271	−	0.225378i	$-0.0723616\pi$
$269$	555.865	+	1341.98i	0.125991	+	0.304170i	−0.848280	+	0.529548i	$0.822362\pi$
$270$		0			0
$271$		−	6517.54i		−	1.46093i	−0.682950	−	0.730465i	$-0.739303\pi$
$271$		−	6517.54i		−	1.46093i	0.682950	−	0.730465i	$-0.260697\pi$
$272$		0			0
$273$		−	10718.6i		−	2.37626i
$274$		0			0
$275$	186.465	+	450.166i	0.0408882	+	0.0987129i
$276$		0			0
$277$	−5983.48	−	2478.44i	−1.29788	−	0.537599i	−0.376555	−	0.926394i	$-0.622891\pi$
$277$	−5983.48	−	2478.44i	−1.29788	−	0.537599i	−0.921324	+	0.388795i	$0.872891\pi$
$278$		0			0
$279$	−817.338	+	817.338i	−0.175386	+	0.175386i
$280$		0			0
$281$	3663.87	+	3663.87i	0.777822	+	0.777822i	0.979460	−	0.201638i	$-0.0646264\pi$
$281$	3663.87	+	3663.87i	0.777822	+	0.777822i	−0.201638	+	0.979460i	$0.564626\pi$
$282$		0			0
$283$	−1065.93	+	2573.38i	−0.223897	+	0.540535i	−0.995413	−	0.0956751i	$-0.969499\pi$
$283$	−1065.93	+	2573.38i	−0.223897	+	0.540535i	0.771516	+	0.636210i	$0.219499\pi$
$284$		0			0
$285$	2994.15	−	1240.22i	0.622309	−	0.257769i
$286$		0			0
$287$	−3337.69			−0.686473
$288$		0			0
$289$	526.558			0.107177
$290$		0			0
$291$	7598.40	−	3147.36i	1.53067	−	0.634026i
$292$		0			0
$293$	1873.89	−	4523.96i	0.373630	−	0.902023i	−0.619499	−	0.784997i	$-0.712664\pi$
$293$	1873.89	−	4523.96i	0.373630	−	0.902023i	0.993129	−	0.117025i	$-0.0373358\pi$
$294$		0			0
$295$	9013.36	+	9013.36i	1.77891	+	1.77891i
$296$		0			0
$297$	253.657	−	253.657i	0.0495578	−	0.0495578i
$298$		0			0
$299$	−6285.37	−	2603.49i	−1.21569	−	0.503557i
$300$		0			0
$301$	−269.151	−	649.787i	−0.0515401	−	0.124429i
$302$		0			0
$303$			5502.25i			1.04322i
$304$		0			0
$305$			9754.44i			1.83127i
$306$		0			0
$307$	−3251.76	−	7850.45i	−0.604521	−	1.45944i	−0.868882	−	0.495019i	$-0.835161\pi$
$307$	−3251.76	−	7850.45i	−0.604521	−	1.45944i	0.264361	−	0.964424i	$-0.414839\pi$
$308$		0			0
$309$	−2151.28	−	891.091i	−0.396059	−	0.164053i
$310$		0			0
$311$	−1620.08	+	1620.08i	−0.295389	+	0.295389i	−0.839205	−	0.543815i	$-0.816979\pi$
$311$	−1620.08	+	1620.08i	−0.295389	+	0.295389i	0.543815	+	0.839205i	$0.316979\pi$
$312$		0			0
$313$	4904.15	+	4904.15i	0.885620	+	0.885620i	0.994099	−	0.108479i	$-0.0345979\pi$
$313$	4904.15	+	4904.15i	0.885620	+	0.885620i	−0.108479	+	0.994099i	$0.534598\pi$
$314$		0			0
$315$	1381.98	−	3336.39i	0.247192	−	0.596775i
$316$		0			0
$317$	−1326.36	+	549.398i	−0.235003	+	0.0973415i	−0.497077	−	0.867706i	$-0.665593\pi$
$317$	−1326.36	+	549.398i	−0.235003	+	0.0973415i	0.262074	+	0.965048i	$0.415593\pi$
$318$		0			0
$319$	−696.165			−0.122187
$320$		0			0
$321$	4406.46			0.766182
$322$		0			0
$323$	−2003.45	+	829.856i	−0.345124	+	0.142955i
$324$		0			0
$325$	−4177.77	+	10086.0i	−0.713049	+	1.72145i
$326$		0			0
$327$	−6710.81	−	6710.81i	−1.13489	−	1.13489i
$328$		0			0
$329$	−6567.87	+	6567.87i	−1.10060	+	1.10060i
$330$		0			0
$331$	−3808.89	−	1577.69i	−0.632494	−	0.261988i	0.0433183	−	0.999061i	$-0.486207\pi$
$331$	−3808.89	−	1577.69i	−0.632494	−	0.261988i	−0.675812	+	0.737074i	$0.736207\pi$
$332$		0			0
$333$	430.295	+	1038.82i	0.0708109	+	0.170953i
$334$		0			0
$335$			2903.30i			0.473505i
$336$		0			0
$337$		−	528.946i		−	0.0855000i	−0.999086	−	0.0427500i	$-0.986388\pi$
$337$		−	528.946i		−	0.0855000i	0.999086	−	0.0427500i	$-0.0136119\pi$
$338$		0			0
$339$	−728.232	−	1758.11i	−0.116673	−	0.281674i
$340$		0			0
$341$	385.369	+	159.625i	0.0611992	+	0.0253495i
$342$		0			0
$343$	2183.23	−	2183.23i	0.343684	−	0.343684i
$344$		0			0
$345$	−6308.14	−	6308.14i	−0.984403	−	0.984403i
$346$		0			0
$347$	−2777.92	+	6706.49i	−0.429759	+	1.03753i	0.549605	+	0.835425i	$0.314778\pi$
$347$	−2777.92	+	6706.49i	−0.429759	+	1.03753i	−0.979364	+	0.202105i	$0.935222\pi$
$348$		0			0
$349$	−2949.74	+	1221.82i	−0.452424	+	0.187400i	−0.597247	−	0.802058i	$-0.703739\pi$
$349$	−2949.74	+	1221.82i	−0.452424	+	0.187400i	0.144823	+	0.989458i	$0.453739\pi$
$350$		0			0
$351$	8037.28			1.22222
$352$		0			0
$353$	9005.55			1.35784			0.678919	−	0.734213i	$-0.262449\pi$
$353$	9005.55			1.35784			0.678919	+	0.734213i	$0.262449\pi$
$354$		0			0
$355$	−4162.59	+	1724.20i	−0.622331	+	0.257778i
$356$		0			0
$357$	−3599.02	+	8688.80i	−0.533558	+	1.28812i
$358$		0			0
$359$	7280.93	+	7280.93i	1.07040	+	1.07040i	0.997327	+	0.0730705i	$0.0232798\pi$
$359$	7280.93	+	7280.93i	1.07040	+	1.07040i	0.0730705	+	0.997327i	$0.476720\pi$
$360$		0			0
$361$	4091.99	−	4091.99i	0.596588	−	0.596588i
$362$		0			0
$363$	−7349.24	−	3044.15i	−1.06263	−	0.440156i
$364$		0			0
$365$	−4862.26	−	11738.5i	−0.697266	−	1.68335i
$366$		0			0
$367$			2730.08i			0.388308i	0.980971	+	0.194154i	$0.0621961\pi$
$367$			2730.08i			0.388308i	−0.980971	+	0.194154i	$0.937804\pi$
$368$		0			0
$369$			1322.77i			0.186614i
$370$		0			0
$371$	1319.20	+	3184.82i	0.184607	+	0.445681i
$372$		0			0
$373$	807.251	+	334.374i	0.112059	+	0.0464162i	0.438008	−	0.898971i	$-0.355684\pi$
$373$	807.251	+	334.374i	0.112059	+	0.0464162i	−0.325950	+	0.945387i	$0.605684\pi$
$374$		0			0
$375$	−1373.81	+	1373.81i	−0.189182	+	0.189182i
$376$		0			0
$377$	−11029.2	−	11029.2i	−1.50672	−	1.50672i
$378$		0			0
$379$	511.994	−	1236.06i	0.0693914	−	0.167526i	−0.885379	−	0.464870i	$-0.846101\pi$
$379$	511.994	−	1236.06i	0.0693914	−	0.167526i	0.954770	+	0.297344i	$0.0961010\pi$
$380$		0			0
$381$	−1986.48	+	822.826i	−0.267114	+	0.110642i
$382$		0			0
$383$	−7830.32			−1.04468			−0.522338	−	0.852739i	$-0.674940\pi$
$383$	−7830.32			−1.04468			−0.522338	+	0.852739i	$0.674940\pi$
$384$		0			0
$385$	−1303.19			−0.172510
$386$		0			0
$387$	−257.519	+	106.668i	−0.0338254	+	0.0140109i
$388$		0			0
$389$	1347.70	−	3253.64i	0.175659	−	0.424077i	−0.811389	−	0.584507i	$-0.801288\pi$
$389$	1347.70	−	3253.64i	0.175659	−	0.424077i	0.987047	+	0.160430i	$0.0512880\pi$
$390$		0			0
$391$	4220.91	+	4220.91i	0.545936	+	0.545936i
$392$		0			0
$393$	11450.5	−	11450.5i	1.46972	−	1.46972i
$394$		0			0
$395$	10859.2	+	4498.03i	1.38326	+	0.572963i
$396$		0			0
$397$	−23.4283	−	56.5609i	−0.00296180	−	0.00715041i	0.922392	−	0.386256i	$-0.126232\pi$
$397$	−23.4283	−	56.5609i	−0.00296180	−	0.00715041i	−0.925354	+	0.379105i	$0.876232\pi$
$398$		0			0
$399$			4649.38i			0.583359i
$400$		0			0
$401$			12034.3i			1.49866i	0.662195	+	0.749332i	$0.269625\pi$
$401$			12034.3i			1.49866i	−0.662195	+	0.749332i	$0.730375\pi$
$402$		0			0
$403$	3576.42	+	8634.24i	0.442070	+	1.06725i
$404$		0			0
$405$	13561.0	+	5617.16i	1.66383	+	0.689183i
$406$		0			0
$407$	286.917	−	286.917i	0.0349434	−	0.0349434i
$408$		0			0
$409$	8440.37	+	8440.37i	1.02041	+	1.02041i	0.999787	+	0.0206265i	$0.00656608\pi$
$409$	8440.37	+	8440.37i	1.02041	+	1.02041i	0.0206265	+	0.999787i	$0.493434\pi$
$410$		0			0
$411$	−2645.94	+	6387.87i	−0.317554	+	0.766644i
$412$		0			0
$413$	−16894.8	+	6998.07i	−2.01293	+	0.833784i
$414$		0			0
$415$	−2344.41			−0.277308
$416$		0			0
$417$	−16349.7			−1.92002
$418$		0			0
$419$	14617.4	−	6054.71i	1.70431	−	0.705947i	0.704315	−	0.709887i	$-0.251254\pi$
$419$	14617.4	−	6054.71i	1.70431	−	0.705947i	0.999992	+	0.00393979i	$0.00125408\pi$
$420$		0			0
$421$	−5214.86	+	12589.8i	−0.603697	+	1.45745i	0.266051	+	0.963959i	$0.414281\pi$
$421$	−5214.86	+	12589.8i	−0.603697	+	1.45745i	−0.869749	+	0.493495i	$0.835719\pi$
$422$		0			0
$423$	2602.93	+	2602.93i	0.299194	+	0.299194i
$424$		0			0
$425$	6773.23	−	6773.23i	0.773058	−	0.773058i
$426$		0			0
$427$	−12928.7	−	5355.24i	−1.46525	−	0.606928i
$428$		0			0
$429$	586.626	+	1416.24i	0.0660200	+	0.159386i
$430$		0			0
$431$		−	3490.31i		−	0.390075i	−0.980796	−	0.195037i	$-0.937517\pi$
$431$		−	3490.31i		−	0.390075i	0.980796	−	0.195037i	$-0.0624828\pi$
$432$		0			0
$433$		−	11691.1i		−	1.29755i	−0.760980	−	0.648775i	$-0.775282\pi$
$433$		−	11691.1i		−	1.29755i	0.760980	−	0.648775i	$-0.224718\pi$
$434$		0			0
$435$	−7827.08	−	18896.2i	−0.862712	−	2.08277i
$436$		0			0
$437$	2726.39	+	1129.31i	0.298446	+	0.123620i
$438$		0			0
$439$	−6721.98	+	6721.98i	−0.730804	+	0.730804i	−0.970779	−	0.239975i	$-0.922861\pi$
$439$	−6721.98	+	6721.98i	−0.730804	+	0.730804i	0.239975	+	0.970779i	$0.422861\pi$
$440$		0			0
$441$	1399.07	+	1399.07i	0.151072	+	0.151072i
$442$		0			0
$443$	3951.12	−	9538.86i	0.423755	−	1.02304i	−0.557475	−	0.830194i	$-0.688230\pi$
$443$	3951.12	−	9538.86i	0.423755	−	1.02304i	0.981230	−	0.192842i	$-0.0617704\pi$
$444$		0			0
$445$	4732.29	−	1960.18i	0.504117	−	0.208812i
$446$		0			0
$447$	−3983.39			−0.421494
$448$		0			0
$449$	−3683.45			−0.387155			−0.193578	−	0.981085i	$-0.562009\pi$
$449$	−3683.45			−0.387155			−0.193578	+	0.981085i	$0.562009\pi$
$450$		0			0
$451$	441.006	−	182.671i	0.0460448	−	0.0190724i
$452$		0			0
$453$	4288.47	−	10353.3i	0.444790	−	1.07382i
$454$		0			0
$455$	−20646.1	−	20646.1i	−2.12726	−	2.12726i
$456$		0			0
$457$	−6693.56	+	6693.56i	−0.685146	+	0.685146i	−0.961155	−	0.276009i	$-0.910988\pi$
$457$	−6693.56	+	6693.56i	−0.685146	+	0.685146i	0.276009	+	0.961155i	$0.410988\pi$
$458$		0			0
$459$	−6515.24	−	2698.70i	−0.662539	−	0.274432i
$460$		0			0
$461$	−2097.99	−	5065.00i	−0.211959	−	0.511715i	0.781765	−	0.623573i	$-0.214320\pi$
$461$	−2097.99	−	5065.00i	−0.211959	−	0.511715i	−0.993724	+	0.111858i	$0.964320\pi$
$462$		0			0
$463$			17006.8i			1.70707i	0.521038	+	0.853534i	$0.325545\pi$
$463$			17006.8i			1.70707i	−0.521038	+	0.853534i	$0.674455\pi$
$464$		0			0
$465$			12254.9i			1.22217i
$466$		0			0
$467$	7003.63	+	16908.3i	0.693981	+	1.67542i	0.736601	+	0.676328i	$0.236430\pi$
$467$	7003.63	+	16908.3i	0.693981	+	1.67542i	−0.0426191	+	0.999091i	$0.513570\pi$
$468$		0			0
$469$	−3848.08	−	1593.93i	−0.378866	−	0.156931i
$470$		0			0
$471$	10568.5	−	10568.5i	1.03391	−	1.03391i
$472$		0			0
$473$	71.1253	+	71.1253i	0.00691404	+	0.00691404i
$474$		0			0
$475$	1812.18	−	4374.99i	0.175049	−	0.422607i
$476$		0			0
$477$	1262.19	−	522.815i	0.121156	−	0.0501846i
$478$		0			0
$479$	12250.2			1.16853			0.584263	−	0.811564i	$-0.301384\pi$
$479$	12250.2			1.16853			0.584263	+	0.811564i	$0.301384\pi$
$480$		0			0
$481$	9091.14			0.861789
$482$		0			0
$483$	11824.1	−	4897.71i	1.11391	−	0.461395i
$484$		0			0
$485$	8573.56	−	20698.4i	0.802691	−	1.93787i
$486$		0			0
$487$	−6781.49	−	6781.49i	−0.631003	−	0.631003i	0.317317	−	0.948320i	$-0.397218\pi$
$487$	−6781.49	−	6781.49i	−0.631003	−	0.631003i	−0.948320	+	0.317317i	$0.897218\pi$
$488$		0			0
$489$	121.768	−	121.768i	0.0112608	−	0.0112608i
$490$		0			0
$491$	2990.34	+	1238.64i	0.274851	+	0.113847i	0.515852	−	0.856678i	$-0.327476\pi$
$491$	2990.34	+	1238.64i	0.274851	+	0.113847i	−0.241000	+	0.970525i	$0.577476\pi$
$492$		0			0
$493$	5237.27	+	12643.9i	0.478447	+	1.15507i
$494$		0			0
$495$			516.469i			0.0468961i
$496$		0			0
$497$		−	6463.76i		−	0.583379i
$498$		0			0
$499$	−672.528	−	1623.63i	−0.0603336	−	0.145658i	0.890838	−	0.454322i	$-0.150118\pi$
$499$	−672.528	−	1623.63i	−0.0603336	−	0.145658i	−0.951171	+	0.308663i	$0.900118\pi$
$500$		0			0
$501$	876.053	+	362.873i	0.0781221	+	0.0323592i
$502$		0			0
$503$	14586.7	−	14586.7i	1.29302	−	1.29302i	0.360107	−	0.932911i	$-0.382740\pi$
$503$	14586.7	−	14586.7i	1.29302	−	1.29302i	0.932911	−	0.360107i	$-0.117260\pi$
$504$		0			0
$505$	10598.4	+	10598.4i	0.933906	+	0.933906i
$506$		0			0
$507$	−8075.40	+	19495.7i	−0.707379	+	1.70776i
$508$		0			0
$509$	10300.8	−	4266.74i	0.897005	−	0.371552i	0.113937	−	0.993488i	$-0.463654\pi$
$509$	10300.8	−	4266.74i	0.897005	−	0.371552i	0.783068	+	0.621936i	$0.213654\pi$
$510$		0			0
$511$	18227.8			1.57799
$512$		0			0
$513$	−3486.31			−0.300047
$514$		0			0
$515$	−5860.20	+	2427.38i	−0.501420	+	0.207695i
$516$		0			0
$517$	508.350	−	1227.26i	0.0432441	−	0.104400i
$518$		0			0
$519$	−9304.25	−	9304.25i	−0.786919	−	0.786919i
$520$		0			0
$521$	10841.1	−	10841.1i	0.911623	−	0.911623i	−0.0847773	−	0.996400i	$-0.527018\pi$
$521$	10841.1	−	10841.1i	0.911623	−	0.911623i	0.996400	+	0.0847773i	$0.0270179\pi$
$522$		0			0
$523$	7489.02	+	3102.05i	0.626142	+	0.259356i	0.673113	−	0.739540i	$-0.264957\pi$
$523$	7489.02	+	3102.05i	0.626142	+	0.259356i	−0.0469711	+	0.998896i	$0.514957\pi$
$524$		0			0
$525$	−7859.27	−	18974.0i	−0.653346	−	1.57732i
$526$		0			0
$527$		−	8200.01i		−	0.677795i
$528$		0			0
$529$			4043.73i			0.332352i
$530$		0			0
$531$	2773.43	+	6695.64i	0.226660	+	0.547205i
$532$		0			0
$533$	9880.79	+	4092.76i	0.802973	+	0.332602i
$534$		0			0
$535$	8487.69	−	8487.69i	0.685897	−	0.685897i
$536$		0			0
$537$	−6004.85	−	6004.85i	−0.482548	−	0.482548i
$538$		0			0
$539$	273.238	−	659.654i	0.0218352	−	0.0527149i
$540$		0			0
$541$	20246.0	−	8386.17i	1.60895	−	0.666451i	0.616308	−	0.787505i	$-0.288628\pi$
$541$	20246.0	−	8386.17i	1.60895	−	0.666451i	0.992646	+	0.121054i	$0.0386276\pi$
$542$		0			0
$543$	−4580.61			−0.362013
$544$		0			0
$545$	−25852.6			−2.03194
$546$		0			0
$547$	−10328.3	+	4278.13i	−0.807325	+	0.334405i	−0.747886	−	0.663827i	$-0.768931\pi$
$547$	−10328.3	+	4278.13i	−0.807325	+	0.334405i	−0.0594388	+	0.998232i	$0.518931\pi$
$548$		0			0
$549$	−2122.35	+	5123.81i	−0.164990	+	0.398322i
$550$		0			0
$551$	4784.11	+	4784.11i	0.369891	+	0.369891i
$552$		0			0
$553$	−11923.5	+	11923.5i	−0.916890	+	0.916890i
$554$		0			0
$555$	11013.7	+	4562.04i	0.842356	+	0.348915i
$556$		0			0
$557$	1262.85	+	3048.78i	0.0960657	+	0.231923i	0.964606	−	0.263696i	$-0.0849414\pi$
$557$	1262.85	+	3048.78i	0.0960657	+	0.231923i	−0.868540	+	0.495619i	$0.834941\pi$
$558$		0			0
$559$			2253.65i			0.170517i
$560$		0			0
$561$		−	1345.02i		−	0.101224i
$562$		0			0
$563$	−3354.10	−	8097.52i	−0.251081	−	0.606163i	0.747211	−	0.664587i	$-0.231393\pi$
$563$	−3354.10	−	8097.52i	−0.251081	−	0.606163i	−0.998292	+	0.0584237i	$0.981393\pi$
$564$		0			0
$565$	−4789.17	−	1983.74i	−0.356605	−	0.147711i
$566$		0			0
$567$	−14890.2	+	14890.2i	−1.10287	+	1.10287i
$568$		0			0
$569$	−8264.07	−	8264.07i	−0.608872	−	0.608872i	0.333780	−	0.942651i	$-0.391676\pi$
$569$	−8264.07	−	8264.07i	−0.608872	−	0.608872i	−0.942651	+	0.333780i	$0.891676\pi$
$570$		0			0
$571$	2298.13	−	5548.17i	0.168430	−	0.406626i	−0.817016	−	0.576615i	$-0.804373\pi$
$571$	2298.13	−	5548.17i	0.168430	−	0.406626i	0.985446	+	0.169989i	$0.0543732\pi$
$572$		0			0
$573$	−13407.7	+	5553.64i	−0.977510	+	0.404898i
$574$		0			0
$575$	−13035.3			−0.945405
$576$		0			0
$577$	−7818.78			−0.564125			−0.282062	−	0.959396i	$-0.591019\pi$
$577$	−7818.78			−0.564125			−0.282062	+	0.959396i	$0.591019\pi$
$578$		0			0
$579$	−9589.72	+	3972.19i	−0.688317	+	0.285110i
$580$		0			0
$581$	1287.10	−	3107.33i	0.0919067	−	0.221882i
$582$		0			0
$583$	−348.609	−	348.609i	−0.0247648	−	0.0247648i
$584$		0			0
$585$	−8182.32	+	8182.32i	−0.578286	+	0.578286i
$586$		0			0
$587$	−12603.6	−	5220.58i	−0.886211	−	0.367081i	−0.107309	−	0.994226i	$-0.534223\pi$
$587$	−12603.6	−	5220.58i	−0.886211	−	0.367081i	−0.778902	+	0.627145i	$0.784223\pi$
$588$		0			0
$589$	−1551.33	−	3745.25i	−0.108526	−	0.262004i
$590$		0			0
$591$		−	2530.34i		−	0.176116i
$592$		0			0
$593$			22972.2i			1.59081i	0.606075	+	0.795407i	$0.292743\pi$
$593$			22972.2i			1.59081i	−0.606075	+	0.795407i	$0.707257\pi$
$594$		0			0
$595$	9803.90	+	23668.7i	0.675497	+	1.63079i
$596$		0			0
$597$	6733.69	+	2789.19i	0.461628	+	0.191212i
$598$		0			0
$599$	−7947.99	+	7947.99i	−0.542147	+	0.542147i	−0.924158	−	0.382011i	$-0.875232\pi$
$599$	−7947.99	+	7947.99i	−0.542147	+	0.542147i	0.382011	+	0.924158i	$0.375232\pi$
$600$		0			0
$601$	−10055.8	−	10055.8i	−0.682506	−	0.682506i	0.278058	−	0.960564i	$-0.410309\pi$
$601$	−10055.8	−	10055.8i	−0.682506	−	0.682506i	−0.960564	+	0.278058i	$0.910309\pi$
$602$		0			0
$603$	−631.694	+	1525.04i	−0.0426610	+	0.102993i
$604$		0			0
$605$	−20019.7	+	8292.42i	−1.34532	+	0.557248i
$606$		0			0
$607$	−24716.9			−1.65277			−0.826383	−	0.563109i	$-0.809605\pi$
$607$	−24716.9			−1.65277			−0.826383	+	0.563109i	$0.809605\pi$
$608$		0			0
$609$	29342.5			1.95241
$610$		0			0
$611$	27497.0	−	11389.6i	1.82064	−	0.754132i
$612$		0			0
$613$	−5388.03	+	13007.9i	−0.355009	+	0.857067i	0.640977	+	0.767560i	$0.278529\pi$
$613$	−5388.03	+	13007.9i	−0.355009	+	0.857067i	−0.995986	+	0.0895074i	$0.971471\pi$
$614$		0			0
$615$	9916.59	+	9916.59i	0.650204	+	0.650204i
$616$		0			0
$617$	−1763.96	+	1763.96i	−0.115096	+	0.115096i	−0.762309	−	0.647213i	$-0.775934\pi$
$617$	−1763.96	+	1763.96i	−0.115096	+	0.115096i	0.647213	+	0.762309i	$0.275934\pi$
$618$		0			0
$619$	21023.8	+	8708.35i	1.36513	+	0.565457i	0.940465	−	0.339891i	$-0.110390\pi$
$619$	21023.8	+	8708.35i	1.36513	+	0.565457i	0.424670	+	0.905348i	$0.360390\pi$
$620$		0			0
$621$	3672.52	+	8866.24i	0.237316	+	0.572931i
$622$		0			0
$623$			7348.41i			0.472565i
$624$		0			0
$625$		−	12786.1i		−	0.818312i
$626$		0			0
$627$	−254.459	−	614.319i	−0.0162075	−	0.0391284i
$628$		0			0
$629$	−7369.53	−	3052.56i	−0.467158	−	0.193503i
$630$		0			0
$631$	−20760.0	+	20760.0i	−1.30973	+	1.30973i	−0.388129	+	0.921605i	$0.626878\pi$
$631$	−20760.0	+	20760.0i	−1.30973	+	1.30973i	−0.921605	+	0.388129i	$0.873122\pi$
$632$		0			0
$633$	9123.67	+	9123.67i	0.572881	+	0.572881i
$634$		0			0
$635$	−2241.42	+	5411.26i	−0.140076	+	0.338172i
$636$		0			0
$637$	14779.6	−	6121.92i	0.919293	−	0.380784i
$638$		0			0
$639$	−2561.67			−0.158589
$640$		0			0
$641$	16062.4			0.989745			0.494872	−	0.868966i	$-0.335215\pi$
$641$	16062.4			0.989745			0.494872	+	0.868966i	$0.335215\pi$
$642$		0			0
$643$	−24877.7	+	10304.7i	−1.52579	+	0.632001i	−0.978741	−	0.205101i	$-0.934248\pi$
$643$	−24877.7	+	10304.7i	−1.52579	+	0.632001i	−0.547046	+	0.837103i	$0.684248\pi$
$644$		0			0
$645$	−1130.91	+	2730.25i	−0.0690378	+	0.166672i
$646$		0			0
$647$	11101.6	+	11101.6i	0.674572	+	0.674572i	0.958767	−	0.284195i	$-0.0917262\pi$
$647$	11101.6	+	11101.6i	0.674572	+	0.674572i	−0.284195	+	0.958767i	$0.591726\pi$
$648$		0			0
$649$	1849.30	−	1849.30i	0.111851	−	0.111851i
$650$		0			0
$651$	−16242.8	−	6728.01i	−0.977891	−	0.405056i
$652$		0			0
$653$	1485.55	+	3586.44i	0.0890262	+	0.214928i	0.962121	−	0.272622i	$-0.0878907\pi$
$653$	1485.55	+	3586.44i	0.0890262	+	0.214928i	−0.873095	+	0.487550i	$0.837891\pi$
$654$		0			0
$655$		−	44111.8i		−	2.63143i
$656$		0			0
$657$		−	7223.93i		−	0.428968i
$658$		0			0
$659$	−10740.4	−	25929.6i	−0.634881	−	1.53274i	−0.833417	−	0.552644i	$-0.813619\pi$
$659$	−10740.4	−	25929.6i	−0.634881	−	1.53274i	0.198537	−	0.980093i	$-0.436381\pi$
$660$		0			0
$661$	−1477.94	−	612.182i	−0.0869670	−	0.0360229i	0.338776	−	0.940867i	$-0.389987\pi$
$661$	−1477.94	−	612.182i	−0.0869670	−	0.0360229i	−0.425743	+	0.904844i	$0.639987\pi$
$662$		0			0
$663$	21308.8	−	21308.8i	1.24821	−	1.24821i
$664$		0			0
$665$	8955.61	+	8955.61i	0.522231	+	0.522231i
$666$		0			0
$667$	7127.12	−	17206.4i	0.413738	−	0.998851i
$668$		0			0
$669$	−17573.6	+	7279.21i	−1.01560	+	0.420673i
$670$		0			0
$671$	2001.35			0.115143
$672$		0			0
$673$	−25713.9			−1.47281			−0.736404	−	0.676543i	$-0.763478\pi$
$673$	−25713.9			−1.47281			−0.736404	+	0.676543i	$0.763478\pi$
$674$		0			0
$675$	14227.5	−	5893.22i	0.811284	−	0.336045i
$676$		0			0
$677$	−4314.50	+	10416.1i	−0.244933	+	0.591321i	−0.997760	−	0.0668981i	$-0.978690\pi$
$677$	−4314.50	+	10416.1i	−0.244933	+	0.591321i	0.752827	+	0.658219i	$0.228690\pi$
$678$		0			0
$679$	22727.1	+	22727.1i	1.28451	+	1.28451i
$680$		0			0
$681$	−1518.11	+	1518.11i	−0.0854244	+	0.0854244i
$682$		0			0
$683$	1854.70	+	768.242i	0.103907	+	0.0430395i	0.434031	−	0.900898i	$-0.357091\pi$
$683$	1854.70	+	768.242i	0.103907	+	0.0430395i	−0.330125	+	0.943937i	$0.607091\pi$
$684$		0			0
$685$	7207.68	+	17400.9i	0.402031	+	0.970589i
$686$		0			0
$687$		−	28893.3i		−	1.60458i
$688$		0			0
$689$		−	11045.9i		−	0.610761i
$690$		0			0
$691$	2881.88	+	6957.49i	0.158657	+	0.383032i	0.983140	−	0.182855i	$-0.0585338\pi$
$691$	2881.88	+	6957.49i	0.158657	+	0.383032i	−0.824483	+	0.565887i	$0.808534\pi$
$692$		0			0
$693$	−684.537	−	283.544i	−0.0375230	−	0.0155425i
$694$		0			0
$695$	−31492.7	+	31492.7i	−1.71883	+	1.71883i
$696$		0			0
$697$	−6635.41	−	6635.41i	−0.360594	−	0.360594i
$698$		0			0
$699$	−6747.78	+	16290.6i	−0.365128	+	0.881497i
$700$		0			0
$701$	26418.3	−	10942.8i	1.42340	−	0.589592i	0.467688	−	0.883893i	$-0.345087\pi$
$701$	26418.3	−	10942.8i	1.42340	−	0.589592i	0.955713	+	0.294302i	$0.0950870\pi$
$702$		0			0
$703$	−3943.44			−0.211564
$704$		0			0
$705$	39027.5			2.08491
$706$		0			0
$707$	−19865.9	+	8228.71i	−1.05676	+	0.437726i
$708$		0			0
$709$	−1886.73	+	4554.97i	−0.0999404	+	0.241277i	−0.965939	−	0.258768i	$-0.916683\pi$
$709$	−1886.73	+	4554.97i	−0.0999404	+	0.241277i	0.865999	+	0.500046i	$0.166683\pi$
$710$		0			0
$711$	4725.45	+	4725.45i	0.249252	+	0.249252i
$712$		0			0
$713$	−7890.58	+	7890.58i	−0.414452	+	0.414452i
$714$		0			0
$715$	3857.91	+	1598.00i	0.201787	+	0.0835828i
$716$		0			0
$717$	−3772.55	−	9107.75i	−0.196497	−	0.474387i
$718$		0			0
$719$			29695.2i			1.54026i	0.637889	+	0.770129i	$0.279808\pi$
$719$			29695.2i			1.54026i	−0.637889	+	0.770129i	$0.720192\pi$
$720$		0			0
$721$		−	9099.85i		−	0.470036i
$722$		0			0
$723$	−8763.12	−	21156.0i	−0.450766	−	1.08825i
$724$		0			0
$725$	−27610.8	−	11436.8i	−1.41440	−	0.585863i
$726$		0			0
$727$	26485.0	−	26485.0i	1.35113	−	1.35113i	0.466739	−	0.884395i	$-0.345429\pi$
$727$	26485.0	−	26485.0i	1.35113	−	1.35113i	0.884395	−	0.466739i	$-0.154571\pi$
$728$		0			0
$729$	−6352.78	−	6352.78i	−0.322755	−	0.322755i
$730$		0			0
$731$	756.713	−	1826.87i	0.0382873	−	0.0924338i
$732$		0			0
$733$	3763.54	−	1558.91i	0.189645	−	0.0785534i	−0.285840	−	0.958277i	$-0.592273\pi$
$733$	3763.54	−	1558.91i	0.189645	−	0.0785534i	0.475485	+	0.879724i	$0.342273\pi$
$734$		0			0
$735$	20977.3			1.05273
$736$		0			0
$737$	595.679			0.0297722
$738$		0			0
$739$	−14266.3	+	5909.30i	−0.710142	+	0.294150i	−0.708363	−	0.705848i	$-0.750566\pi$
$739$	−14266.3	+	5909.30i	−0.710142	+	0.294150i	−0.00177857	+	0.999998i	$0.500566\pi$
$740$		0			0
$741$	5701.18	−	13763.9i	0.282643	−	0.682360i
$742$		0			0
$743$	−17888.3	−	17888.3i	−0.883253	−	0.883253i	0.110611	−	0.993864i	$-0.464719\pi$
$743$	−17888.3	−	17888.3i	−0.883253	−	0.883253i	−0.993864	+	0.110611i	$0.964719\pi$
$744$		0			0
$745$	−7672.77	+	7672.77i	−0.377327	+	0.377327i
$746$		0			0
$747$	−1231.47	−	510.093i	−0.0603176	−	0.0249844i
$748$		0			0
$749$	6589.94	+	15909.5i	0.321483	+	0.776130i
$750$		0			0
$751$			20239.7i			0.983432i	0.870756	+	0.491716i	$0.163630\pi$
$751$			20239.7i			0.983432i	−0.870756	+	0.491716i	$0.836370\pi$
$752$		0			0
$753$		−	10098.7i		−	0.488732i
$754$		0			0
$755$	−11682.0	−	28202.8i	−0.563114	−	1.35948i
$756$		0			0
$757$	−15064.3	−	6239.82i	−0.723275	−	0.299591i	−0.00949004	−	0.999955i	$-0.503021\pi$
$757$	−15064.3	−	6239.82i	−0.723275	−	0.299591i	−0.713785	+	0.700364i	$0.753021\pi$
$758$		0			0
$759$	−1294.26	+	1294.26i	−0.0618955	+	0.0618955i
$760$		0			0
$761$	−3008.89	−	3008.89i	−0.143328	−	0.143328i	0.631802	−	0.775130i	$-0.282316\pi$
$761$	−3008.89	−	3008.89i	−0.143328	−	0.143328i	−0.775130	+	0.631802i	$0.782316\pi$
$762$		0			0
$763$	14193.2	−	34265.5i	0.673433	−	1.62581i
$764$		0			0
$765$	9380.21	−	3885.41i	0.443323	−	0.183631i
$766$		0			0
$767$	58596.1			2.75852
$768$		0			0
$769$	33250.5			1.55923			0.779613	−	0.626261i	$-0.215416\pi$
$769$	33250.5			1.55923			0.779613	+	0.626261i	$0.215416\pi$
$770$		0			0
$771$	−3209.62	+	1329.47i	−0.149924	+	0.0621007i
$772$		0			0
$773$	−6032.84	+	14564.6i	−0.280707	+	0.677686i	−0.999853	−	0.0171732i	$-0.994533\pi$
$773$	−6032.84	+	14564.6i	−0.280707	+	0.677686i	0.719146	+	0.694859i	$0.244533\pi$
$774$		0			0
$775$	12661.9	+	12661.9i	0.586875	+	0.586875i
$776$		0			0
$777$	−12093.2	+	12093.2i	−0.558355	+	0.558355i
$778$		0			0
$779$	−4285.96	−	1775.30i	−0.197125	−	0.0816520i
$780$		0			0
$781$	353.760	+	854.052i	0.0162081	+	0.0391298i
$782$		0			0
$783$			22002.3i			1.00421i
$784$		0			0
$785$		−	40714.0i		−	1.85114i
$786$		0			0
$787$	15236.1	+	36783.2i	0.690100	+	1.66605i	0.744579	+	0.667534i	$0.232650\pi$
$787$	15236.1	+	36783.2i	0.690100	+	1.66605i	−0.0544793	+	0.998515i	$0.517350\pi$
$788$		0			0
$789$	−39734.6	−	16458.6i	−1.79289	−	0.742640i
$790$		0			0
$791$	5258.57	−	5258.57i	0.236376	−	0.236376i
$792$		0			0
$793$	31706.9	+	31706.9i	1.41986	+	1.41986i
$794$		0			0
$795$	5542.95	−	13381.9i	0.247281	−	0.596988i
$796$		0			0
$797$	4162.41	−	1724.12i	0.184994	−	0.0766269i	−0.288264	−	0.957551i	$-0.593078\pi$
$797$	4162.41	−	1724.12i	0.184994	−	0.0766269i	0.473258	+	0.880924i	$0.343078\pi$
$798$		0			0
$799$	−26114.1			−1.15626
$800$		0			0
$801$	2912.27			0.128464
$802$		0			0
$803$	−2408.43	+	997.604i	−0.105843	+	0.0438414i
$804$		0			0
$805$	13341.6	−	32209.5i	0.584136	−	1.41023i
$806$		0			0
$807$	6191.31	+	6191.31i	0.270068	+	0.270068i
$808$		0			0
$809$	24296.9	−	24296.9i	1.05591	−	1.05591i	0.0575706	−	0.998341i	$-0.481665\pi$
$809$	24296.9	−	24296.9i	1.05591	−	1.05591i	0.998341	−	0.0575706i	$-0.0183354\pi$
$810$		0			0
$811$	11241.7	+	4656.46i	0.486744	+	0.201616i	0.612539	−	0.790440i	$-0.290148\pi$
$811$	11241.7	+	4656.46i	0.486744	+	0.201616i	−0.125795	+	0.992056i	$0.540148\pi$
$812$		0			0
$813$	−15034.6	−	36296.7i	−0.648568	−	1.56578i
$814$		0			0
$815$		−	469.098i		−	0.0201617i
$816$		0			0
$817$		−	977.558i		−	0.0418610i
$818$		0			0
$819$	−6352.84	−	15337.1i	−0.271045	−	0.654362i
$820$		0			0
$821$	3924.75	+	1625.68i	0.166839	+	0.0691069i	0.464540	−	0.885552i	$-0.346220\pi$
$821$	3924.75	+	1625.68i	0.166839	+	0.0691069i	−0.297701	+	0.954659i	$0.596220\pi$
$822$		0			0
$823$	−14112.0	+	14112.0i	−0.597708	+	0.597708i	−0.939702	−	0.341994i	$-0.888898\pi$
$823$	−14112.0	+	14112.0i	−0.597708	+	0.597708i	0.341994	+	0.939702i	$0.388898\pi$
$824$		0			0
$825$	2076.88	+	2076.88i	0.0876456	+	0.0876456i
$826$		0			0
$827$	−8156.23	+	19690.9i	−0.342950	+	0.827956i	0.654464	+	0.756093i	$0.272894\pi$
$827$	−8156.23	+	19690.9i	−0.342950	+	0.827956i	−0.997415	+	0.0718625i	$0.977106\pi$
$828$		0			0
$829$	−19708.8	+	8163.65i	−0.825711	+	0.342021i	−0.755203	−	0.655491i	$-0.772462\pi$
$829$	−19708.8	+	8163.65i	−0.825711	+	0.342021i	−0.0705076	+	0.997511i	$0.522462\pi$
$830$		0			0
$831$	−39039.7			−1.62969
$832$		0			0
$833$	−14036.3			−0.583830
$834$		0			0
$835$	2386.41	−	988.484i	0.0989044	−	0.0409675i
$836$		0			0
$837$	5044.95	−	12179.6i	0.208338	−	0.502973i
$838$		0			0
$839$	−18262.0	−	18262.0i	−0.751458	−	0.751458i	0.223293	−	0.974751i	$-0.428319\pi$
$839$	−18262.0	−	18262.0i	−0.751458	−	0.751458i	−0.974751	+	0.223293i	$0.928319\pi$
$840$		0			0
$841$	12947.1	−	12947.1i	0.530859	−	0.530859i
$842$		0			0
$843$	28856.2	+	11952.6i	1.17895	+	0.488339i
$844$		0			0
$845$	21997.8	+	53107.3i	0.895558	+	2.16207i
$846$		0			0
$847$		−	31087.0i		−	1.26111i
$848$		0			0
$849$			16790.2i			0.678727i
$850$		0			0
$851$	4154.07	+	10028.8i	0.167332	+	0.403975i
$852$		0			0
$853$	−2913.29	−	1206.73i	−0.116939	−	0.0484379i	0.323447	−	0.946246i	$-0.395158\pi$
$853$	−2913.29	−	1206.73i	−0.116939	−	0.0484379i	−0.440386	+	0.897809i	$0.645158\pi$
$854$		0			0
$855$	3549.22	−	3549.22i	0.141966	−	0.141966i
$856$		0			0
$857$	7266.15	+	7266.15i	0.289623	+	0.289623i	0.836931	−	0.547308i	$-0.184347\pi$
$857$	7266.15	+	7266.15i	0.289623	+	0.289623i	−0.547308	+	0.836931i	$0.684347\pi$
$858$		0			0
$859$	16409.5	−	39616.1i	0.651787	−	1.57355i	−0.158396	−	0.987376i	$-0.550632\pi$
$859$	16409.5	−	39616.1i	0.651787	−	1.57355i	0.810183	−	0.586177i	$-0.199368\pi$
$860$		0			0
$861$	−18587.9	+	7699.35i	−0.735741	+	0.304754i
$862$		0			0
$863$	29533.5			1.16493			0.582464	−	0.812856i	$-0.302089\pi$
$863$	29533.5			1.16493			0.582464	+	0.812856i	$0.302089\pi$
$864$		0			0
$865$	−35843.6			−1.40892
$866$		0			0
$867$	2932.45	−	1214.66i	0.114869	−	0.0475802i
$868$		0			0
$869$	922.875	−	2228.02i	0.0360258	−	0.0869739i
$870$		0			0
$871$	9437.22	+	9437.22i	0.367128	+	0.367128i
$872$		0			0
$873$	9007.03	−	9007.03i	0.349189	−	0.349189i
$874$		0			0
$875$	−7014.71	−	2905.59i	−0.271018	−	0.112259i
$876$		0			0
$877$	12488.6	+	30150.2i	0.480856	+	1.16089i	0.959203	+	0.282719i	$0.0912363\pi$
$877$	12488.6	+	30150.2i	0.480856	+	1.16089i	−0.478347	+	0.878171i	$0.658764\pi$
$878$		0			0
$879$		−	29517.0i		−	1.13263i
$880$		0			0
$881$			14625.2i			0.559292i	0.960103	+	0.279646i	$0.0902171\pi$
$881$			14625.2i			0.559292i	−0.960103	+	0.279646i	$0.909783\pi$
$882$		0			0
$883$	−18156.7	−	43834.1i	−0.691983	−	1.67059i	−0.740748	−	0.671783i	$-0.765529\pi$
$883$	−18156.7	−	43834.1i	−0.691983	−	1.67059i	0.0487652	−	0.998810i	$-0.484471\pi$
$884$		0			0
$885$	70988.1	+	29404.2i	2.69631	+	1.11685i
$886$		0			0
$887$	3906.55	−	3906.55i	0.147879	−	0.147879i	−0.629291	−	0.777170i	$-0.716654\pi$
$887$	3906.55	−	3906.55i	0.147879	−	0.147879i	0.777170	+	0.629291i	$0.216654\pi$
$888$		0			0
$889$	−5941.62	−	5941.62i	−0.224157	−	0.224157i
$890$		0			0
$891$	1152.49	−	2782.36i	0.0433332	−	0.104616i
$892$		0			0
$893$	−11927.3	+	4940.45i	−0.446956	+	0.185135i
$894$		0			0
$895$	−23133.0			−0.863967
$896$		0			0
$897$	−41009.4			−1.52649
$898$		0			0
$899$	−23636.5	+	9790.55i	−0.876886	+	0.363218i
$900$		0			0
$901$	−3708.91	+	8954.09i	−0.137138	+	0.331081i
$902$		0			0
$903$	−2997.84	−	2997.84i	−0.110478	−	0.110478i
$904$		0			0
$905$	−8823.14	+	8823.14i	−0.324079	+	0.324079i
$906$		0			0
$907$	−15093.4	−	6251.90i	−0.552556	−	0.228876i	0.0888937	−	0.996041i	$-0.471667\pi$
$907$	−15093.4	−	6251.90i	−0.552556	−	0.228876i	−0.641450	+	0.767165i	$0.721667\pi$
$908$		0			0
$909$	3261.14	+	7873.10i	0.118994	+	0.287276i
$910$		0			0
$911$		−	12262.7i		−	0.445971i	−0.974822	−	0.222986i	$-0.928420\pi$
$911$		−	12262.7i		−	0.445971i	0.974822	−	0.222986i	$-0.0715803\pi$
$912$		0			0
$913$			481.011i			0.0174361i
$914$		0			0
$915$	22501.4	+	54323.3i	0.812978	+	1.96270i
$916$		0			0
$917$	58466.4	+	24217.6i	2.10549	+	0.872121i
$918$		0			0
$919$	−26825.0	+	26825.0i	−0.962866	+	0.962866i	−0.999335	−	0.0364685i	$-0.988389\pi$
$919$	−26825.0	+	26825.0i	−0.962866	+	0.962866i	0.0364685	+	0.999335i	$0.488389\pi$
$920$		0			0
$921$	−36218.7	−	36218.7i	−1.29582	−	1.29582i
$922$		0			0
$923$	−7926.02	+	19135.1i	−0.282652	+	0.682383i
$924$		0			0
$925$	16093.0	−	6665.96i	0.572039	−	0.236946i
$926$		0			0
$927$	−3606.39			−0.127777
$928$		0			0
$929$	27282.3			0.963512			0.481756	−	0.876305i	$-0.339999\pi$
$929$	27282.3			0.963512			0.481756	+	0.876305i	$0.339999\pi$
$930$		0			0
$931$	−6410.91	+	2655.49i	−0.225681	+	0.0934802i
$932$		0			0
$933$	−5285.16	+	12759.5i	−0.185454	+	0.447725i
$934$		0			0
$935$	−2590.76	−	2590.76i	−0.0906171	−	0.0906171i
$936$		0			0
$937$	−24857.5	+	24857.5i	−0.866658	+	0.866658i	−0.992101	−	0.125443i	$-0.959965\pi$
$937$	−24857.5	+	24857.5i	−0.866658	+	0.866658i	0.125443	+	0.992101i	$0.459965\pi$
$938$		0			0
$939$	38624.5	+	15998.8i	1.34235	+	0.556018i
$940$		0			0
$941$	−16878.2	−	40747.6i	−0.584712	−	1.41162i	−0.888498	−	0.458880i	$-0.848251\pi$
$941$	−16878.2	−	40747.6i	−0.584712	−	1.41162i	0.303786	−	0.952740i	$-0.401749\pi$
$942$		0			0
$943$			12770.0i			0.440985i
$944$		0			0
$945$			41187.2i			1.41780i
$946$		0			0
$947$	17615.8	+	42528.2i	0.604472	+	1.45933i	0.868934	+	0.494929i	$0.164806\pi$
$947$	17615.8	+	42528.2i	0.604472	+	1.45933i	−0.264461	+	0.964396i	$0.585194\pi$
$948$		0			0
$949$	−53961.1	−	22351.4i	−1.84579	−	0.764550i
$950$		0			0
$951$	−6119.28	+	6119.28i	−0.208655	+	0.208655i
$952$		0			0
$953$	9439.64	+	9439.64i	0.320860	+	0.320860i	0.849097	−	0.528237i	$-0.177147\pi$
$953$	9439.64	+	9439.64i	0.320860	+	0.320860i	−0.528237	+	0.849097i	$0.677147\pi$
$954$		0			0
$955$	−15128.4	+	36523.1i	−0.512610	+	1.23755i
$956$		0			0
$957$	−3877.00	+	1605.91i	−0.130957	+	0.0542440i
$958$		0			0
$959$	−27020.5			−0.909840
$960$		0			0
$961$	−14461.9			−0.485445
$962$		0			0
$963$	6305.14	−	2611.68i	0.210987	−	0.0873936i
$964$		0			0
$965$	−10820.4	+	26122.9i	−0.360956	+	0.871425i
$966$		0			0
$967$	−25745.5	−	25745.5i	−0.856173	−	0.856173i	0.134711	−	0.990885i	$-0.456989\pi$
$967$	−25745.5	−	25745.5i	−0.856173	−	0.856173i	−0.990885	+	0.134711i	$0.956989\pi$
$968$		0			0
$969$	−9243.07	+	9243.07i	−0.306430	+	0.306430i
$970$		0			0
$971$	−18385.2	−	7615.42i	−0.607632	−	0.251689i	0.0575837	−	0.998341i	$-0.481660\pi$
$971$	−18385.2	−	7615.42i	−0.607632	−	0.251689i	−0.665216	+	0.746651i	$0.731660\pi$
$972$		0			0
$973$	−24451.3	−	59030.6i	−0.805624	−	1.94495i
$974$		0			0
$975$			65807.1i			2.16155i
$976$		0			0
$977$			1781.76i			0.0583455i	0.999574	+	0.0291727i	$0.00928729\pi$
$977$			1781.76i			0.0583455i	−0.999574	+	0.0291727i	$0.990713\pi$
$978$		0			0
$979$	−402.176	−	970.939i	−0.0131293	−	0.0316970i
$980$		0			0
$981$	−13579.9	−	5624.96i	−0.441969	−	0.183069i
$982$		0			0
$983$	19228.0	−	19228.0i	0.623883	−	0.623883i	−0.322639	−	0.946522i	$-0.604570\pi$
$983$	19228.0	−	19228.0i	0.623883	−	0.623883i	0.946522	+	0.322639i	$0.104570\pi$
$984$		0			0
$985$	−4873.92	−	4873.92i	−0.157661	−	0.157661i
$986$		0			0
$987$	−21426.3	+	51727.7i	−0.690990	+	1.66820i
$988$		0			0
$989$	−2486.09	+	1029.77i	−0.0799322	+	0.0331090i
$990$		0			0
$991$	−2811.67			−0.0901269			−0.0450634	−	0.998984i	$-0.514349\pi$
$991$	−2811.67			−0.0901269			−0.0450634	+	0.998984i	$0.514349\pi$
$992$		0			0
$993$	−24851.4			−0.794196
$994$		0			0
$995$	18342.9	−	7597.88i	0.584431	−	0.242079i
$996$		0			0
$997$	11942.0	−	28830.7i	0.379347	−	0.915824i	−0.612742	−	0.790283i	$-0.709933\pi$
$997$	11942.0	−	28830.7i	0.379347	−	0.915824i	0.992088	−	0.125541i	$-0.0400665\pi$
$998$		0			0
$999$	−9068.01	−	9068.01i	−0.287186	−	0.287186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.g.a.49.9		44
4.3	odd	2		32.4.g.a.21.2	✓	44
8.3	odd	2		256.4.g.b.97.9		44
8.5	even	2		256.4.g.a.97.3		44
32.3	odd	8		32.4.g.a.29.2	yes	44
32.13	even	8		256.4.g.a.161.3		44
32.19	odd	8		256.4.g.b.161.9		44
32.29	even	8	inner	128.4.g.a.81.9		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.2	✓	44	4.3	odd	2
32.4.g.a.29.2	yes	44	32.3	odd	8
128.4.g.a.49.9		44	1.1	even	1	trivial
128.4.g.a.81.9		44	32.29	even	8	inner
256.4.g.a.97.3		44	8.5	even	2
256.4.g.a.161.3		44	32.13	even	8
256.4.g.b.97.9		44	8.3	odd	2
256.4.g.b.161.9		44	32.19	odd	8

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +O(q^{10})\)	\(q+(5.56908 - 2.30679i) q^{3} +(6.28381 - 15.1704i) q^{5} +(16.6573 + 16.6573i) q^{7} +(6.60151 - 6.60151i) q^{9} +(-3.11257 - 1.28927i) q^{11} +(-28.8862 - 69.7374i) q^{13} -98.9809i q^{15} +66.2302i q^{17} +(12.5299 + 30.2498i) q^{19} +(131.191 + 54.3410i) q^{21} +(63.7309 - 63.7309i) q^{23} +(-102.268 - 102.268i) q^{25} +(-40.7473 + 98.3726i) q^{27} +(190.908 - 79.0767i) q^{29} -123.811 q^{31} -20.3082 q^{33} +(357.370 - 148.028i) q^{35} +(-46.0901 + 111.271i) q^{37} +(-321.739 - 321.739i) q^{39} +(-100.187 + 100.187i) q^{41} +(-27.5836 - 11.4255i) q^{43} +(-58.6652 - 141.630i) q^{45} +394.293i q^{47} +211.932i q^{49} +(152.779 + 368.841i) q^{51} +(135.196 + 56.0002i) q^{53} +(-39.1175 + 39.1175i) q^{55} +(139.560 + 139.560i) q^{57} +(-297.070 + 717.190i) q^{59} +(-548.826 + 227.331i) q^{61} +219.927 q^{63} -1239.46 q^{65} +(-163.352 + 67.6626i) q^{67} +(207.909 - 501.937i) q^{69} +(-194.022 - 194.022i) q^{71} +(547.142 - 547.142i) q^{73} +(-805.449 - 333.628i) q^{75} +(-30.3713 - 73.3227i) q^{77} +715.813i q^{79} +893.911i q^{81} +(-54.6375 - 131.907i) q^{83} +(1004.74 + 416.178i) q^{85} +(880.769 - 880.769i) q^{87} +(220.576 + 220.576i) q^{89} +(680.471 - 1642.80i) q^{91} +(-689.512 + 285.605i) q^{93} +537.638 q^{95} +1364.39 q^{97} +(-29.0587 + 12.0365i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{19} - 4 q^{21} - 324 q^{23} - 4 q^{25} + 268 q^{27} - 4 q^{29} + 752 q^{31} - 8 q^{33} + 460 q^{35} - 4 q^{37} - 596 q^{39} - 4 q^{41} - 804 q^{43} + 104 q^{45} + 1384 q^{51} + 748 q^{53} + 292 q^{55} - 4 q^{57} - 1372 q^{59} - 1828 q^{61} - 2512 q^{63} - 8 q^{65} - 2036 q^{67} - 1060 q^{69} - 220 q^{71} - 4 q^{73} + 1712 q^{75} + 1900 q^{77} - 2436 q^{83} + 496 q^{85} + 1292 q^{87} - 4 q^{89} + 3604 q^{91} - 112 q^{93} + 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^19 - 4 * q^21 - 324 * q^23 - 4 * q^25 + 268 * q^27 - 4 * q^29 + 752 * q^31 - 8 * q^33 + 460 * q^35 - 4 * q^37 - 596 * q^39 - 4 * q^41 - 804 * q^43 + 104 * q^45 + 1384 * q^51 + 748 * q^53 + 292 * q^55 - 4 * q^57 - 1372 * q^59 - 1828 * q^61 - 2512 * q^63 - 8 * q^65 - 2036 * q^67 - 1060 * q^69 - 220 * q^71 - 4 * q^73 + 1712 * q^75 + 1900 * q^77 - 2436 * q^83 + 496 * q^85 + 1292 * q^87 - 4 * q^89 + 3604 * q^91 - 112 * q^93 + 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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