LMFDB - Embedded newform 400.2.bi.c.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 32 x^{14} - 64 x^{13} + 66 x^{12} - 28 x^{11} + 160 x^{10} - 392 x^{9} + 419 x^{8} + \cdots + 1 $ x^16 - 8x^15 + 32x^14 - 64x^13 + 66x^12 - 28x^11 + 160x^10 - 392x^9 + 419x^8 + 164x^7 + 200x^6 - 576x^5 + 726x^4 + 668x^3 + 288x^2 + 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			63.2
Root			$-0.313766 - 0.313766i$ of defining polynomial
Character	$\chi$	$=$	400.63
Dual form			400.2.bi.c.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.58417 + 1.31670i) q^{3} -2.23607 q^{5} +(1.62753 + 1.62753i) q^{7} +(3.18088 + 4.37811i) q^{9} +(-1.12460 + 1.54787i) q^{11} +(-0.951057 - 0.150633i) q^{13} +(-5.77838 - 2.94423i) q^{15} +(2.48990 + 4.88670i) q^{17} +(1.87751 - 5.77838i) q^{19} +(2.06285 + 6.34879i) q^{21} +(2.55374 - 0.404473i) q^{23} +5.00000 q^{25} +(1.09417 + 6.90832i) q^{27} +(2.65063 - 0.861243i) q^{29} +(-9.86654 - 3.20583i) q^{31} +(-4.94424 + 2.51921i) q^{33} +(-3.63927 - 3.63927i) q^{35} +(1.58628 - 10.0154i) q^{37} +(-2.25935 - 1.64152i) q^{39} +(-8.52488 + 6.19369i) q^{41} +(6.17421 - 6.17421i) q^{43} +(-7.11267 - 9.78975i) q^{45} +(0.494291 - 0.970102i) q^{47} -1.70228i q^{49} +15.9065i q^{51} +(-4.26445 + 8.36946i) q^{53} +(2.51467 - 3.46115i) q^{55} +(12.4602 - 12.4602i) q^{57} +(7.85962 - 5.71035i) q^{59} +(-0.975062 - 0.708424i) q^{61} +(-1.94852 + 12.3025i) q^{63} +(2.12663 + 0.336825i) q^{65} +(-5.77838 + 2.94423i) q^{67} +(7.13188 + 2.31729i) q^{69} +(8.83270 - 2.86992i) q^{71} +(-0.212028 - 1.33869i) q^{73} +(12.9209 + 6.58350i) q^{75} +(-4.34953 + 0.688898i) q^{77} +(2.28496 + 7.03239i) q^{79} +(-1.25180 + 3.85265i) q^{81} +(-6.97154 - 13.6824i) q^{83} +(-5.56758 - 10.9270i) q^{85} +(7.98369 + 1.26449i) q^{87} +(-1.95788 + 2.69479i) q^{89} +(-1.30272 - 1.79303i) q^{91} +(-21.2757 - 21.2757i) q^{93} +(-4.19824 + 12.9209i) q^{95} +(2.23955 + 1.14111i) q^{97} -10.3540 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93}+ \cdots - 80 q^{97}+O(q^{100}) $ 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$-1$

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
$3$	2.58417	+	1.31670i	1.49197	+	0.760198i	0.994244	−	0.107136i	$-0.0341681\pi$
$3$	2.58417	+	1.31670i	1.49197	+	0.760198i	0.497727	+	0.867334i	$0.334168\pi$
$4$		0			0
$5$	−2.23607			−1.00000
$5$	−2.23607			−1.00000
$6$		0			0
$7$	1.62753	+	1.62753i	0.615149	+	0.615149i	0.944283	−	0.329134i	$-0.106757\pi$
$7$	1.62753	+	1.62753i	0.615149	+	0.615149i	−0.329134	+	0.944283i	$0.606757\pi$
$8$		0			0
$9$	3.18088	+	4.37811i	1.06029	+	1.45937i
$10$		0			0
$11$	−1.12460	+	1.54787i	−0.339079	+	0.466702i	−0.944172	−	0.329453i	$-0.893136\pi$
$11$	−1.12460	+	1.54787i	−0.339079	+	0.466702i	0.605093	+	0.796154i	$0.293136\pi$
$12$		0			0
$13$	−0.951057	−	0.150633i	−0.263776	−	0.0417780i	0.0231457	−	0.999732i	$-0.492632\pi$
$13$	−0.951057	−	0.150633i	−0.263776	−	0.0417780i	−0.286921	+	0.957954i	$0.592632\pi$
$14$		0			0
$15$	−5.77838	−	2.94423i	−1.49197	−	0.760198i
$16$		0			0
$17$	2.48990	+	4.88670i	0.603889	+	1.18520i	0.967315	+	0.253576i	$0.0816068\pi$
$17$	2.48990	+	4.88670i	0.603889	+	1.18520i	−0.363426	+	0.931623i	$0.618393\pi$
$18$		0			0
$19$	1.87751	−	5.77838i	0.430730	−	1.32565i	−0.466669	−	0.884432i	$-0.654546\pi$
$19$	1.87751	−	5.77838i	0.430730	−	1.32565i	0.897399	−	0.441219i	$-0.145454\pi$
$20$		0			0
$21$	2.06285	+	6.34879i	0.450150	+	1.38542i
$22$		0			0
$23$	2.55374	−	0.404473i	0.532493	−	0.0843385i	0.115603	−	0.993296i	$-0.463120\pi$
$23$	2.55374	−	0.404473i	0.532493	−	0.0843385i	0.416890	+	0.908957i	$0.363120\pi$
$24$		0			0
$25$	5.00000			1.00000
$26$		0			0
$27$	1.09417	+	6.90832i	0.210573	+	1.32951i
$28$		0			0
$29$	2.65063	−	0.861243i	0.492210	−	0.159929i	−0.0523865	−	0.998627i	$-0.516683\pi$
$29$	2.65063	−	0.861243i	0.492210	−	0.159929i	0.544597	+	0.838698i	$0.316683\pi$
$30$		0			0
$31$	−9.86654	−	3.20583i	−1.77208	−	0.575784i	−0.773749	−	0.633492i	$-0.781621\pi$
$31$	−9.86654	−	3.20583i	−1.77208	−	0.575784i	−0.998334	+	0.0577079i	$0.981621\pi$
$32$		0			0
$33$	−4.94424	+	2.51921i	−0.860681	+	0.438539i
$34$		0			0
$35$	−3.63927	−	3.63927i	−0.615149	−	0.615149i
$36$		0			0
$37$	1.58628	−	10.0154i	0.260782	−	1.64651i	−0.415297	−	0.909686i	$-0.636322\pi$
$37$	1.58628	−	10.0154i	0.260782	−	1.64651i	0.676080	−	0.736829i	$-0.263678\pi$
$38$		0			0
$39$	−2.25935	−	1.64152i	−0.361786	−	0.262853i
$40$		0			0
$41$	−8.52488	+	6.19369i	−1.33136	+	0.967292i	−0.331648	+	0.943403i	$0.607605\pi$
$41$	−8.52488	+	6.19369i	−1.33136	+	0.967292i	−0.999715	+	0.0238886i	$0.992395\pi$
$42$		0			0
$43$	6.17421	−	6.17421i	0.941558	−	0.941558i	−0.0568258	−	0.998384i	$-0.518098\pi$
$43$	6.17421	−	6.17421i	0.941558	−	0.941558i	0.998384	+	0.0568258i	$0.0180979\pi$
$44$		0			0
$45$	−7.11267	−	9.78975i	−1.06029	−	1.45937i
$46$		0			0
$47$	0.494291	−	0.970102i	0.0720998	−	0.141504i	−0.852143	−	0.523309i	$-0.824697\pi$
$47$	0.494291	−	0.970102i	0.0720998	−	0.141504i	0.924243	+	0.381805i	$0.124697\pi$
$48$		0			0
$49$		−	1.70228i		−	0.243183i
$50$		0			0
$51$			15.9065i			2.22736i
$52$		0			0
$53$	−4.26445	+	8.36946i	−0.585768	+	1.14963i	0.387909	+	0.921698i	$0.373198\pi$
$53$	−4.26445	+	8.36946i	−0.585768	+	1.14963i	−0.973676	+	0.227936i	$0.926802\pi$
$54$		0			0
$55$	2.51467	−	3.46115i	0.339079	−	0.466702i
$56$		0			0
$57$	12.4602	−	12.4602i	1.65039	−	1.65039i
$58$		0			0
$59$	7.85962	−	5.71035i	1.02323	−	0.743424i	0.0562914	−	0.998414i	$-0.482072\pi$
$59$	7.85962	−	5.71035i	1.02323	−	0.743424i	0.966944	+	0.254991i	$0.0820724\pi$
$60$		0			0
$61$	−0.975062	−	0.708424i	−0.124844	−	0.0907044i	0.523611	−	0.851957i	$-0.324585\pi$
$61$	−0.975062	−	0.708424i	−0.124844	−	0.0907044i	−0.648455	+	0.761253i	$0.724585\pi$
$62$		0			0
$63$	−1.94852	+	12.3025i	−0.245491	+	1.54997i
$64$		0			0
$65$	2.12663	+	0.336825i	0.263776	+	0.0417780i
$66$		0			0
$67$	−5.77838	+	2.94423i	−0.705942	+	0.359695i	−0.769819	−	0.638263i	$-0.779653\pi$
$67$	−5.77838	+	2.94423i	−0.705942	+	0.359695i	0.0638771	+	0.997958i	$0.479653\pi$
$68$		0			0
$69$	7.13188	+	2.31729i	0.858578	+	0.278969i
$70$		0			0
$71$	8.83270	−	2.86992i	1.04825	−	0.340597i	0.266268	−	0.963899i	$-0.414210\pi$
$71$	8.83270	−	2.86992i	1.04825	−	0.340597i	0.781981	+	0.623303i	$0.214210\pi$
$72$		0			0
$73$	−0.212028	−	1.33869i	−0.0248160	−	0.156682i	0.972169	−	0.234282i	$-0.0752741\pi$
$73$	−0.212028	−	1.33869i	−0.0248160	−	0.156682i	−0.996985	+	0.0776007i	$0.975274\pi$
$74$		0			0
$75$	12.9209	+	6.58350i	1.49197	+	0.760198i
$76$		0			0
$77$	−4.34953	+	0.688898i	−0.495675	+	0.0785072i
$78$		0			0
$79$	2.28496	+	7.03239i	0.257078	+	0.791206i	0.993413	+	0.114588i	$0.0365548\pi$
$79$	2.28496	+	7.03239i	0.257078	+	0.791206i	−0.736335	+	0.676617i	$0.763445\pi$
$80$		0			0
$81$	−1.25180	+	3.85265i	−0.139089	+	0.428072i
$82$		0			0
$83$	−6.97154	−	13.6824i	−0.765225	−	1.50184i	−0.862209	−	0.506554i	$-0.830919\pi$
$83$	−6.97154	−	13.6824i	−0.765225	−	1.50184i	0.0969830	−	0.995286i	$-0.469081\pi$
$84$		0			0
$85$	−5.56758	−	10.9270i	−0.603889	−	1.18520i
$86$		0			0
$87$	7.98369	+	1.26449i	0.855941	+	0.135568i
$88$		0			0
$89$	−1.95788	+	2.69479i	−0.207534	+	0.285647i	−0.900077	−	0.435730i	$-0.856490\pi$
$89$	−1.95788	+	2.69479i	−0.207534	+	0.285647i	0.692543	+	0.721377i	$0.256490\pi$
$90$		0			0
$91$	−1.30272	−	1.79303i	−0.136562	−	0.187961i
$92$		0			0
$93$	−21.2757	−	21.2757i	−2.20619	−	2.20619i
$94$		0			0
$95$	−4.19824	+	12.9209i	−0.430730	+	1.32565i
$96$		0			0
$97$	2.23955	+	1.14111i	0.227392	+	0.115862i	0.563975	−	0.825792i	$-0.309271\pi$
$97$	2.23955	+	1.14111i	0.227392	+	0.115862i	−0.336583	+	0.941654i	$0.609271\pi$
$98$		0			0
$99$	−10.3540			−1.04061
$100$		0			0
$101$	2.89806			0.288367			0.144184	−	0.989551i	$-0.453944\pi$
$101$	2.89806			0.288367			0.144184	+	0.989551i	$0.453944\pi$
$102$		0			0
$103$	7.80741	+	3.97807i	0.769287	+	0.391971i	0.794152	−	0.607720i	$-0.207916\pi$
$103$	7.80741	+	3.97807i	0.769287	+	0.391971i	−0.0248649	+	0.999691i	$0.507916\pi$
$104$		0			0
$105$	−4.61267	−	14.1963i	−0.450150	−	1.38542i
$106$		0			0
$107$	−11.2441	−	11.2441i	−1.08701	−	1.08701i	−0.995835	−	0.0911721i	$-0.970939\pi$
$107$	−11.2441	−	11.2441i	−1.08701	−	1.08701i	−0.0911721	−	0.995835i	$-0.529061\pi$
$108$		0			0
$109$	5.03556	+	6.93085i	0.482319	+	0.663855i	0.978949	−	0.204107i	$-0.0654292\pi$
$109$	5.03556	+	6.93085i	0.482319	+	0.663855i	−0.496629	+	0.867963i	$0.665429\pi$
$110$		0			0
$111$	17.2864	−	23.7927i	1.64076	−	2.25831i
$112$		0			0
$113$	−5.16807	−	0.818542i	−0.486171	−	0.0770020i	−0.0914631	−	0.995808i	$-0.529154\pi$
$113$	−5.16807	−	0.818542i	−0.486171	−	0.0770020i	−0.394708	+	0.918806i	$0.629154\pi$
$114$		0			0
$115$	−5.71035	+	0.904430i	−0.532493	+	0.0843385i
$116$		0			0
$117$	−2.36571	−	4.64297i	−0.218710	−	0.429243i
$118$		0			0
$119$	−3.90087	+	12.0056i	−0.357592	+	1.10056i
$120$		0			0
$121$	2.26799	+	6.98015i	0.206181	+	0.634559i
$122$		0			0
$123$	−30.1850	+	4.78083i	−2.72169	+	0.431073i
$124$		0			0
$125$	−11.1803			−1.00000
$126$		0			0
$127$	−2.77391	−	17.5138i	−0.246145	−	1.55410i	−0.732764	−	0.680483i	$-0.761770\pi$
$127$	−2.77391	−	17.5138i	−0.246145	−	1.55410i	0.486619	−	0.873614i	$-0.338230\pi$
$128$		0			0
$129$	24.0848	−	7.82563i	2.12055	−	0.689008i
$130$		0			0
$131$	−14.5010	−	4.71166i	−1.26696	−	0.411660i	−0.402989	−	0.915205i	$-0.632029\pi$
$131$	−14.5010	−	4.71166i	−1.26696	−	0.411660i	−0.863969	+	0.503545i	$0.832029\pi$
$132$		0			0
$133$	12.4602	−	6.34879i	1.08044	−	0.550510i
$134$		0			0
$135$	−2.44664	−	15.4475i	−0.210573	−	1.32951i
$136$		0			0
$137$	0.153395	−	0.968498i	0.0131054	−	0.0827443i	−0.980269	−	0.197669i	$-0.936663\pi$
$137$	0.153395	−	0.968498i	0.0131054	−	0.0827443i	0.993374	+	0.114925i	$0.0366628\pi$
$138$		0			0
$139$	3.91731	+	2.84609i	0.332262	+	0.241403i	0.741390	−	0.671075i	$-0.234167\pi$
$139$	3.91731	+	2.84609i	0.332262	+	0.241403i	−0.409128	+	0.912477i	$0.634167\pi$
$140$		0			0
$141$	2.55467	−	1.85607i	0.215142	−	0.156310i
$142$		0			0
$143$	1.30272	−	1.30272i	0.108939	−	0.108939i
$144$		0			0
$145$	−5.92699	+	1.92580i	−0.492210	+	0.159929i
$146$		0			0
$147$	2.24140	−	4.39899i	0.184867	−	0.362822i
$148$		0			0
$149$			9.16129i			0.750522i	0.926919	+	0.375261i	$0.122447\pi$
$149$			9.16129i			0.750522i	−0.926919	+	0.375261i	$0.877553\pi$
$150$		0			0
$151$			15.6035i			1.26979i	0.772597	+	0.634897i	$0.218957\pi$
$151$			15.6035i			1.26979i	−0.772597	+	0.634897i	$0.781043\pi$
$152$		0			0
$153$	−13.4744	+	26.4451i	−1.08934	+	2.13796i
$154$		0			0
$155$	22.0622	+	7.16846i	1.77208	+	0.575784i
$156$		0			0
$157$	−5.05644	+	5.05644i	−0.403548	+	0.403548i	−0.879481	−	0.475933i	$-0.842110\pi$
$157$	−5.05644	+	5.05644i	−0.403548	+	0.403548i	0.475933	+	0.879481i	$0.342110\pi$
$158$		0			0
$159$	−22.0401	+	16.0131i	−1.74790	+	1.26992i
$160$		0			0
$161$	4.81459	+	3.49801i	0.379443	+	0.275682i
$162$		0			0
$163$	−0.542005	+	3.42208i	−0.0424531	+	0.268038i	−0.999780	−	0.0209686i	$-0.993325\pi$
$163$	−0.542005	+	3.42208i	−0.0424531	+	0.268038i	0.957327	+	0.289007i	$0.0933250\pi$
$164$		0			0
$165$	11.0557	−	5.63314i	0.860681	−	0.438539i
$166$		0			0
$167$	12.2007	−	6.21658i	0.944121	−	0.481054i	0.0870224	−	0.996206i	$-0.472265\pi$
$167$	12.2007	−	6.21658i	0.944121	−	0.481054i	0.857098	+	0.515153i	$0.172265\pi$
$168$		0			0
$169$	−11.4819	−	3.73070i	−0.883224	−	0.286977i
$170$		0			0
$171$	31.2705	−	10.1604i	2.39132	−	0.776986i
$172$		0			0
$173$	−0.0270578	−	0.170836i	−0.00205716	−	0.0129884i	0.986638	−	0.162925i	$-0.0520930\pi$
$173$	−0.0270578	−	0.170836i	−0.00205716	−	0.0129884i	−0.988696	+	0.149937i	$0.952093\pi$
$174$		0			0
$175$	8.13766	+	8.13766i	0.615149	+	0.615149i
$176$		0			0
$177$	27.8294	−	4.40775i	2.09179	−	0.331306i
$178$		0			0
$179$	3.01577	+	9.28158i	0.225409	+	0.693738i	0.998250	+	0.0591379i	$0.0188352\pi$
$179$	3.01577	+	9.28158i	0.225409	+	0.693738i	−0.772841	+	0.634600i	$0.781165\pi$
$180$		0			0
$181$	−5.57180	+	17.1482i	−0.414148	+	1.27462i	0.498862	+	0.866681i	$0.333751\pi$
$181$	−5.57180	+	17.1482i	−0.414148	+	1.27462i	−0.913010	+	0.407936i	$0.866249\pi$
$182$		0			0
$183$	−1.58694	−	3.11455i	−0.117310	−	0.230234i
$184$		0			0
$185$	−3.54702	+	22.3950i	−0.260782	+	1.64651i
$186$		0			0
$187$	−10.3641	−	1.64152i	−0.757900	−	0.120040i
$188$		0			0
$189$	−9.46271	+	13.0243i	−0.688311	+	0.947379i
$190$		0			0
$191$	−3.50986	−	4.83091i	−0.253965	−	0.349552i	0.662930	−	0.748681i	$-0.269313\pi$
$191$	−3.50986	−	4.83091i	−0.253965	−	0.349552i	−0.916895	+	0.399129i	$0.869313\pi$
$192$		0			0
$193$	5.93294	+	5.93294i	0.427062	+	0.427062i	0.887626	−	0.460564i	$-0.152353\pi$
$193$	5.93294	+	5.93294i	0.427062	+	0.427062i	−0.460564	+	0.887626i	$0.652353\pi$
$194$		0			0
$195$	5.05207	+	3.67054i	0.361786	+	0.262853i
$196$		0			0
$197$	9.22957	+	4.70270i	0.657580	+	0.335054i	0.750740	−	0.660598i	$-0.229697\pi$
$197$	9.22957	+	4.70270i	0.657580	+	0.335054i	−0.0931606	+	0.995651i	$0.529697\pi$
$198$		0			0
$199$	12.1515			0.861397			0.430698	−	0.902496i	$-0.358267\pi$
$199$	12.1515			0.861397			0.430698	+	0.902496i	$0.358267\pi$
$200$		0			0
$201$	−18.8090			−1.32668
$202$		0			0
$203$	5.71569	+	2.91229i	0.401163	+	0.204403i
$204$		0			0
$205$	19.0622	−	13.8495i	1.33136	−	0.967292i
$206$		0			0
$207$	9.89399	+	9.89399i	0.687680	+	0.687680i
$208$		0			0
$209$	6.83277	+	9.40450i	0.472632	+	0.650523i
$210$		0			0
$211$	−0.265481	+	0.365404i	−0.0182765	+	0.0251554i	−0.818057	−	0.575137i	$-0.804949\pi$
$211$	−0.265481	+	0.365404i	−0.0182765	+	0.0251554i	0.799781	+	0.600292i	$0.204949\pi$
$212$		0			0
$213$	26.6040	+	4.21366i	1.82288	+	0.288715i
$214$		0			0
$215$	−13.8060	+	13.8060i	−0.941558	+	0.941558i
$216$		0			0
$217$	−10.8405	−	21.2757i	−0.735902	−	1.44429i
$218$		0			0
$219$	1.21474	−	3.73858i	0.0820844	−	0.252630i
$220$		0			0
$221$	−1.63194	−	5.02259i	−0.109776	−	0.337856i
$222$		0			0
$223$	−8.45289	+	1.33881i	−0.566048	+	0.0896531i	−0.432898	−	0.901443i	$-0.642509\pi$
$223$	−8.45289	+	1.33881i	−0.566048	+	0.0896531i	−0.133149	+	0.991096i	$0.542509\pi$
$224$		0			0
$225$	15.9044	+	21.8905i	1.06029	+	1.45937i
$226$		0			0
$227$	0.623179	+	3.93460i	0.0413619	+	0.261149i	0.999700	−	0.0244872i	$-0.00779528\pi$
$227$	0.623179	+	3.93460i	0.0413619	+	0.261149i	−0.958338	+	0.285636i	$0.907795\pi$
$228$		0			0
$229$	−6.21003	+	2.01776i	−0.410371	+	0.133337i	−0.506925	−	0.861990i	$-0.669218\pi$
$229$	−6.21003	+	2.01776i	−0.410371	+	0.133337i	0.0965543	+	0.995328i	$0.469218\pi$
$230$		0			0
$231$	−12.1470	−	3.94680i	−0.799214	−	0.259680i
$232$		0			0
$233$	−12.7395	+	6.49110i	−0.834592	+	0.425246i	−0.818418	−	0.574623i	$-0.805149\pi$
$233$	−12.7395	+	6.49110i	−0.834592	+	0.425246i	−0.0161739	+	0.999869i	$0.505149\pi$
$234$		0			0
$235$	−1.10527	+	2.16921i	−0.0720998	+	0.141504i
$236$		0			0
$237$	−3.35482	+	21.1815i	−0.217919	+	1.37589i
$238$		0			0
$239$	6.67715	+	4.85123i	0.431909	+	0.313800i	0.782412	−	0.622762i	$-0.213989\pi$
$239$	6.67715	+	4.85123i	0.431909	+	0.313800i	−0.350503	+	0.936562i	$0.613989\pi$
$240$		0			0
$241$	6.93466	−	5.03832i	0.446700	−	0.324547i	−0.341591	−	0.939849i	$-0.610966\pi$
$241$	6.93466	−	5.03832i	0.446700	−	0.324547i	0.788292	+	0.615302i	$0.210966\pi$
$242$		0			0
$243$	6.52978	−	6.52978i	0.418885	−	0.418885i
$244$		0			0
$245$			3.80642i			0.243183i
$246$		0			0
$247$	−2.65603	+	5.21275i	−0.168999	+	0.331680i
$248$		0			0
$249$		−	44.5371i		−	2.82242i
$250$		0			0
$251$			17.5281i			1.10636i	0.833061	+	0.553182i	$0.186586\pi$
$251$			17.5281i			1.10636i	−0.833061	+	0.553182i	$0.813414\pi$
$252$		0			0
$253$	−2.24586	+	4.40775i	−0.141196	+	0.277113i
$254$		0			0
$255$		−	35.5681i		−	2.22736i
$256$		0			0
$257$	−12.1447	+	12.1447i	−0.757568	+	0.757568i	−0.975879	−	0.218311i	$-0.929945\pi$
$257$	−12.1447	+	12.1447i	−0.757568	+	0.757568i	0.218311	+	0.975879i	$0.429945\pi$
$258$		0			0
$259$	18.8820	−	13.7186i	1.17327	−	0.852432i
$260$		0			0
$261$	12.2020	+	8.86524i	0.755282	+	0.548745i
$262$		0			0
$263$	0.382691	−	2.41621i	0.0235977	−	0.148990i	−0.973076	−	0.230484i	$-0.925969\pi$
$263$	0.382691	−	2.41621i	0.0235977	−	0.148990i	0.996674	+	0.0814938i	$0.0259691\pi$
$264$		0			0
$265$	9.53560	−	18.7147i	0.585768	−	1.14963i
$266$		0			0
$267$	−8.60771	+	4.38585i	−0.526783	+	0.268410i
$268$		0			0
$269$	−7.51890	−	2.44304i	−0.458436	−	0.148955i	0.0706899	−	0.997498i	$-0.477480\pi$
$269$	−7.51890	−	2.44304i	−0.458436	−	0.148955i	−0.529126	+	0.848544i	$0.677480\pi$
$270$		0			0
$271$	−10.8617	+	3.52919i	−0.659803	+	0.214383i	−0.619731	−	0.784814i	$-0.712758\pi$
$271$	−10.8617	+	3.52919i	−0.659803	+	0.214383i	−0.0400712	+	0.999197i	$0.512758\pi$
$272$		0			0
$273$	−1.00555	−	6.34879i	−0.0608586	−	0.384246i
$274$		0			0
$275$	−5.62298	+	7.73937i	−0.339079	+	0.466702i
$276$		0			0
$277$	−5.09695	+	0.807278i	−0.306246	+	0.0485047i	−0.307666	−	0.951494i	$-0.599548\pi$
$277$	−5.09695	+	0.807278i	−0.306246	+	0.0485047i	0.00141993	+	0.999999i	$0.499548\pi$
$278$		0			0
$279$	−17.3488	−	53.3941i	−1.03865	−	3.19662i
$280$		0			0
$281$	0.292927	−	0.901537i	0.0174746	−	0.0537812i	−0.941939	−	0.335784i	$-0.890999\pi$
$281$	0.292927	−	0.901537i	0.0174746	−	0.0537812i	0.959414	+	0.282003i	$0.0909988\pi$
$282$		0			0
$283$	−2.13911	−	4.19824i	−0.127157	−	0.249559i	0.818648	−	0.574296i	$-0.194724\pi$
$283$	−2.13911	−	4.19824i	−0.127157	−	0.249559i	−0.945804	+	0.324737i	$0.894724\pi$
$284$		0			0
$285$	−27.8619	+	27.8619i	−1.65039	+	1.65039i
$286$		0			0
$287$	−23.9549	−	3.79409i	−1.41402	−	0.223958i
$288$		0			0
$289$	−7.68790	+	10.5815i	−0.452229	+	0.622440i
$290$		0			0
$291$	4.28488	+	5.89763i	0.251184	+	0.345725i
$292$		0			0
$293$	−17.4021	−	17.4021i	−1.01664	−	1.01664i	−0.999859	−	0.0167798i	$-0.994659\pi$
$293$	−17.4021	−	17.4021i	−1.01664	−	1.01664i	−0.0167798	−	0.999859i	$-0.505341\pi$
$294$		0			0
$295$	−17.5746	+	12.7687i	−1.02323	+	0.743424i
$296$		0			0
$297$	−11.9237	−	6.07543i	−0.691884	−	0.352532i
$298$		0			0
$299$	−2.48968			−0.143982
$300$		0			0
$301$	20.0974			1.15840
$302$		0			0
$303$	7.48907	+	3.81587i	0.430236	+	0.219216i
$304$		0			0
$305$	2.18031	+	1.58408i	0.124844	+	0.0907044i
$306$		0			0
$307$	9.15421	+	9.15421i	0.522458	+	0.522458i	0.918313	−	0.395855i	$-0.129552\pi$
$307$	9.15421	+	9.15421i	0.522458	+	0.522458i	−0.395855	+	0.918313i	$0.629552\pi$
$308$		0			0
$309$	14.9377	+	20.5600i	0.849778	+	1.16962i
$310$		0			0
$311$	−14.5504	+	20.0269i	−0.825079	+	1.13562i	0.163740	+	0.986504i	$0.447644\pi$
$311$	−14.5504	+	20.0269i	−0.825079	+	1.13562i	−0.988819	+	0.149120i	$0.952356\pi$
$312$		0			0
$313$	24.1995	+	3.83282i	1.36784	+	0.216644i	0.796781	−	0.604268i	$-0.206534\pi$
$313$	24.1995	+	3.83282i	1.36784	+	0.216644i	0.571055	+	0.820912i	$0.306534\pi$
$314$		0			0
$315$	4.35703	−	27.5092i	0.245491	−	1.54997i
$316$		0			0
$317$	5.10607	+	10.0212i	0.286785	+	0.562848i	0.988788	−	0.149326i	$-0.0477105\pi$
$317$	5.10607	+	10.0212i	0.286785	+	0.562848i	−0.702003	+	0.712174i	$0.747711\pi$
$318$		0			0
$319$	−1.64780	+	5.07140i	−0.0922589	+	0.283944i
$320$		0			0
$321$	−14.2515	−	43.8618i	−0.795444	−	2.44812i
$322$		0			0
$323$	32.9120	−	5.21275i	1.83127	−	0.290045i
$324$		0			0
$325$	−4.75528	−	0.753163i	−0.263776	−	0.0417780i
$326$		0			0
$327$	3.88689	+	24.5408i	0.214945	+	1.35711i
$328$		0			0
$329$	2.38335	−	0.774396i	0.131398	−	0.0426938i
$330$		0			0
$331$	−20.0332	−	6.50919i	−1.10113	−	0.357777i	−0.298590	−	0.954382i	$-0.596516\pi$
$331$	−20.0332	−	6.50919i	−1.10113	−	0.357777i	−0.802536	+	0.596604i	$0.796516\pi$
$332$		0			0
$333$	48.8941	−	24.9128i	2.67938	−	1.36521i
$334$		0			0
$335$	12.9209	−	6.58350i	0.705942	−	0.359695i
$336$		0			0
$337$	−0.744661	+	4.70160i	−0.0405643	+	0.256113i	−0.999634	−	0.0270577i	$-0.991386\pi$
$337$	−0.744661	+	4.70160i	−0.0405643	+	0.256113i	0.959070	+	0.283170i	$0.0913862\pi$
$338$		0			0
$339$	−12.2774	−	8.92006i	−0.666817	−	0.484471i
$340$		0			0
$341$	16.0581	−	11.6669i	0.869595	−	0.631798i
$342$		0			0
$343$	14.1632	−	14.1632i	0.764743	−	0.764743i
$344$		0			0
$345$	−15.9474	−	5.18162i	−0.858578	−	0.278969i
$346$		0			0
$347$	−2.39689	+	4.70415i	−0.128672	+	0.252532i	−0.946350	−	0.323143i	$-0.895261\pi$
$347$	−2.39689	+	4.70415i	−0.128672	+	0.252532i	0.817679	+	0.575675i	$0.195261\pi$
$348$		0			0
$349$		−	1.87772i		−	0.100512i	−0.998736	−	0.0502560i	$-0.983996\pi$
$349$		−	1.87772i		−	0.100512i	0.998736	−	0.0502560i	$-0.0160037\pi$
$350$		0			0
$351$		−	6.73502i		−	0.359489i
$352$		0			0
$353$	−2.87675	+	5.64593i	−0.153114	+	0.300503i	−0.954804	−	0.297238i	$-0.903935\pi$
$353$	−2.87675	+	5.64593i	−0.153114	+	0.300503i	0.801690	+	0.597740i	$0.203935\pi$
$354$		0			0
$355$	−19.7505	+	6.41733i	−1.04825	+	0.340597i
$356$		0			0
$357$	−25.8884	+	25.8884i	−1.37016	+	1.37016i
$358$		0			0
$359$	9.96018	−	7.23649i	0.525678	−	0.381928i	−0.293060	−	0.956094i	$-0.594674\pi$
$359$	9.96018	−	7.23649i	0.525678	−	0.381928i	0.818739	+	0.574166i	$0.194674\pi$
$360$		0			0
$361$	−14.4933	−	10.5300i	−0.762806	−	0.554211i
$362$		0			0
$363$	−3.32990	+	21.0242i	−0.174774	+	1.10348i
$364$		0			0
$365$	0.474108	+	2.99340i	0.0248160	+	0.156682i
$366$		0			0
$367$	8.31332	−	4.23585i	0.433952	−	0.221109i	−0.223348	−	0.974739i	$-0.571699\pi$
$367$	8.31332	−	4.23585i	0.433952	−	0.221109i	0.657300	+	0.753629i	$0.271699\pi$
$368$		0			0
$369$	−54.2333	−	17.6215i	−2.82327	−	0.917336i
$370$		0			0
$371$	−20.5621	+	6.68103i	−1.06753	+	0.346862i
$372$		0			0
$373$	−0.744661	−	4.70160i	−0.0385571	−	0.243440i	0.960881	−	0.276962i	$-0.0893276\pi$
$373$	−0.744661	−	4.70160i	−0.0385571	−	0.243440i	−0.999438	+	0.0335221i	$0.989328\pi$
$374$		0			0
$375$	−28.8919	−	14.7212i	−1.49197	−	0.760198i
$376$		0			0
$377$	−2.65063	+	0.419819i	−0.136515	+	0.0216218i
$378$		0			0
$379$	8.61253	+	26.5066i	0.442396	+	1.36155i	0.885314	+	0.464993i	$0.153943\pi$
$379$	8.61253	+	26.5066i	0.442396	+	1.36155i	−0.442918	+	0.896562i	$0.646057\pi$
$380$		0			0
$381$	15.8922	−	48.9110i	0.814180	−	2.50579i
$382$		0			0
$383$	5.76109	+	11.3068i	0.294378	+	0.577750i	0.990067	−	0.140593i	$-0.0449009\pi$
$383$	5.76109	+	11.3068i	0.294378	+	0.577750i	−0.695689	+	0.718343i	$0.744901\pi$
$384$		0			0
$385$	9.72585	−	1.54042i	0.495675	−	0.0785072i
$386$		0			0
$387$	46.6708	+	7.39193i	2.37241	+	0.375753i
$388$		0			0
$389$	3.10772	−	4.27741i	0.157568	−	0.216873i	−0.722933	−	0.690918i	$-0.757207\pi$
$389$	3.10772	−	4.27741i	0.157568	−	0.216873i	0.880501	+	0.474045i	$0.157207\pi$
$390$		0			0
$391$	8.33510	+	11.4723i	0.421524	+	0.580178i
$392$		0			0
$393$	−31.2692	−	31.2692i	−1.57732	−	1.57732i
$394$		0			0
$395$	−5.10933	−	15.7249i	−0.257078	−	0.791206i
$396$		0			0
$397$	−24.5503	−	12.5090i	−1.23214	−	0.627808i	−0.288091	−	0.957603i	$-0.593020\pi$
$397$	−24.5503	−	12.5090i	−1.23214	−	0.627808i	−0.944053	+	0.329795i	$0.893020\pi$
$398$		0			0
$399$	40.5588			2.03048
$400$		0			0
$401$	−32.1362			−1.60481			−0.802403	−	0.596783i	$-0.796445\pi$
$401$	−32.1362			−1.60481			−0.802403	+	0.596783i	$0.796445\pi$
$402$		0			0
$403$	8.90073	+	4.53515i	0.443377	+	0.225912i
$404$		0			0
$405$	2.79911	−	8.61479i	0.139089	−	0.428072i
$406$		0			0
$407$	13.7186	+	13.7186i	0.680005	+	0.680005i
$408$		0			0
$409$	−17.8888	−	24.6219i	−0.884546	−	1.21747i	−0.975141	−	0.221585i	$-0.928877\pi$
$409$	−17.8888	−	24.6219i	−0.884546	−	1.21747i	0.0905950	−	0.995888i	$-0.471123\pi$
$410$		0			0
$411$	1.67162	−	2.30079i	0.0824549	−	0.113489i
$412$		0			0
$413$	22.0855	+	3.49801i	1.08676	+	0.172126i
$414$		0			0
$415$	15.5888	+	30.5948i	0.765225	+	1.50184i
$416$		0			0
$417$	6.37555	+	12.5127i	0.312212	+	0.612751i
$418$		0			0
$419$	5.60088	−	17.2377i	0.273621	−	0.842118i	−0.715960	−	0.698141i	$-0.754011\pi$
$419$	5.60088	−	17.2377i	0.273621	−	0.842118i	0.989581	−	0.143977i	$-0.0459892\pi$
$420$		0			0
$421$	8.04143	+	24.7490i	0.391915	+	1.20619i	0.931338	+	0.364156i	$0.118642\pi$
$421$	8.04143	+	24.7490i	0.391915	+	1.20619i	−0.539423	+	0.842035i	$0.681358\pi$
$422$		0			0
$423$	5.81949	−	0.921717i	0.282953	−	0.0448154i
$424$		0			0
$425$	12.4495	+	24.4335i	0.603889	+	1.18520i
$426$		0			0
$427$	−0.433962	−	2.73993i	−0.0210009	−	0.132594i
$428$		0			0
$429$	5.08172	−	1.65115i	0.245348	−	0.0797184i
$430$		0			0
$431$	25.3453	+	8.23518i	1.22084	+	0.396675i	0.847388	−	0.530975i	$-0.178174\pi$
$431$	25.3453	+	8.23518i	1.22084	+	0.396675i	0.373452	+	0.927650i	$0.378174\pi$
$432$		0			0
$433$	27.7248	−	14.1265i	1.33237	−	0.678876i	0.364706	−	0.931123i	$-0.381169\pi$
$433$	27.7248	−	14.1265i	1.33237	−	0.678876i	0.967663	+	0.252246i	$0.0811693\pi$
$434$		0			0
$435$	−17.8521	−	2.82749i	−0.855941	−	0.135568i
$436$		0			0
$437$	2.45748	−	15.5159i	0.117557	−	0.742227i
$438$		0			0
$439$	−7.74387	−	5.62625i	−0.369595	−	0.268526i	0.387448	−	0.921891i	$-0.373357\pi$
$439$	−7.74387	−	5.62625i	−0.369595	−	0.268526i	−0.757043	+	0.653365i	$0.773357\pi$
$440$		0			0
$441$	7.45277	−	5.41476i	0.354894	−	0.257846i
$442$		0			0
$443$	−9.95720	+	9.95720i	−0.473081	+	0.473081i	−0.902910	−	0.429829i	$-0.858574\pi$
$443$	−9.95720	+	9.95720i	−0.473081	+	0.473081i	0.429829	+	0.902910i	$0.358574\pi$
$444$		0			0
$445$	4.37794	−	6.02572i	0.207534	−	0.285647i
$446$		0			0
$447$	−12.0627	+	23.6743i	−0.570545	+	1.11976i
$448$		0			0
$449$		−	24.2916i		−	1.14639i	−0.819419	−	0.573195i	$-0.805704\pi$
$449$		−	24.2916i		−	1.14639i	0.819419	−	0.573195i	$-0.194296\pi$
$450$		0			0
$451$		−	20.1608i		−	0.949337i
$452$		0			0
$453$	−20.5451	+	40.3221i	−0.965294	+	1.89450i
$454$		0			0
$455$	2.91296	+	4.00935i	0.136562	+	0.187961i
$456$		0			0
$457$	19.1711	−	19.1711i	0.896786	−	0.896786i	−0.0983649	−	0.995150i	$-0.531361\pi$
$457$	19.1711	−	19.1711i	0.896786	−	0.896786i	0.995150	+	0.0983649i	$0.0313612\pi$
$458$		0			0
$459$	−31.0345	+	22.5479i	−1.44857	+	1.05245i
$460$		0			0
$461$	−11.1879	−	8.12849i	−0.521073	−	0.378582i	0.295935	−	0.955208i	$-0.404369\pi$
$461$	−11.1879	−	8.12849i	−0.521073	−	0.378582i	−0.817008	+	0.576626i	$0.804369\pi$
$462$		0			0
$463$	4.57144	−	28.8629i	0.212453	−	1.34137i	−0.618830	−	0.785525i	$-0.712393\pi$
$463$	4.57144	−	28.8629i	0.212453	−	1.34137i	0.831283	−	0.555850i	$-0.187607\pi$
$464$		0			0
$465$	47.5739	+	47.5739i	2.20619	+	2.20619i
$466$		0			0
$467$	1.17085	−	0.596577i	0.0541804	−	0.0276063i	−0.426690	−	0.904398i	$-0.640321\pi$
$467$	1.17085	−	0.596577i	0.0541804	−	0.0276063i	0.480871	+	0.876791i	$0.340321\pi$
$468$		0			0
$469$	−14.1963	−	4.61267i	−0.655526	−	0.212993i
$470$		0			0
$471$	−19.7245	+	6.40889i	−0.908858	+	0.295306i
$472$		0			0
$473$	2.61341	+	16.5004i	0.120165	+	0.758689i
$474$		0			0
$475$	9.38755	−	28.8919i	0.430730	−	1.32565i
$476$		0			0
$477$	−50.2071	+	7.95202i	−2.29883	+	0.364098i
$478$		0			0
$479$	−1.74144	−	5.35960i	−0.0795684	−	0.244886i	0.903357	−	0.428888i	$-0.141095\pi$
$479$	−1.74144	−	5.35960i	−0.0795684	−	0.244886i	−0.982926	+	0.184002i	$0.941095\pi$
$480$		0			0
$481$	−3.01728	+	9.28622i	−0.137576	+	0.423415i
$482$		0			0
$483$	7.83590	+	15.3788i	0.356546	+	0.699761i
$484$		0			0
$485$	−5.00778	−	2.55159i	−0.227392	−	0.115862i
$486$		0			0
$487$	−21.6062	−	3.42208i	−0.979070	−	0.155069i	−0.353667	−	0.935371i	$-0.615065\pi$
$487$	−21.6062	−	3.42208i	−0.979070	−	0.155069i	−0.625403	+	0.780302i	$0.715065\pi$
$488$		0			0
$489$	−5.90649	+	8.12959i	−0.267101	+	0.367633i
$490$		0			0
$491$	−24.4969	−	33.7171i	−1.10553	−	1.52163i	−0.827841	−	0.560963i	$-0.810431\pi$
$491$	−24.4969	−	33.7171i	−1.10553	−	1.52163i	−0.277691	−	0.960671i	$-0.589569\pi$
$492$		0			0
$493$	10.8084	+	10.8084i	0.486788	+	0.486788i
$494$		0			0
$495$	23.1522			1.04061
$496$		0			0
$497$	19.0464	+	9.70461i	0.854347	+	0.435311i
$498$		0			0
$499$	−31.4385			−1.40738			−0.703690	−	0.710508i	$-0.748465\pi$
$499$	−31.4385			−1.40738			−0.703690	+	0.710508i	$0.748465\pi$
$500$		0			0
$501$	39.7141			1.77430
$502$		0			0
$503$	−25.4190	−	12.9516i	−1.13338	−	0.577483i	−0.216351	−	0.976316i	$-0.569416\pi$
$503$	−25.4190	−	12.9516i	−1.13338	−	0.577483i	−0.917024	+	0.398832i	$0.869416\pi$
$504$		0			0
$505$	−6.48025			−0.288367
$506$		0			0
$507$	−24.7590	−	24.7590i	−1.09959	−	1.09959i
$508$		0			0
$509$	−11.3987	−	15.6889i	−0.505237	−	0.695400i	0.477870	−	0.878431i	$-0.341409\pi$
$509$	−11.3987	−	15.6889i	−0.505237	−	0.695400i	−0.983107	+	0.183031i	$0.941409\pi$
$510$		0			0
$511$	1.83368	−	2.52384i	0.0811171	−	0.111648i
$512$		0			0
$513$	41.9732	+	6.64791i	1.85316	+	0.293512i
$514$		0			0
$515$	−17.4579	−	8.89524i	−0.769287	−	0.391971i
$516$		0			0
$517$	0.945717	+	1.85607i	0.0415926	+	0.0816300i
$518$		0			0
$519$	0.155018	−	0.477096i	0.00680453	−	0.0209422i
$520$		0			0
$521$	−3.07842	−	9.47439i	−0.134868	−	0.415081i	0.860702	−	0.509110i	$-0.170025\pi$
$521$	−3.07842	−	9.47439i	−0.134868	−	0.415081i	−0.995569	+	0.0940291i	$0.970025\pi$
$522$		0			0
$523$	6.66792	−	1.05610i	0.291568	−	0.0461798i	−0.00893708	−	0.999960i	$-0.502845\pi$
$523$	6.66792	−	1.05610i	0.291568	−	0.0461798i	0.300505	+	0.953780i	$0.402845\pi$
$524$		0			0
$525$	10.3142	+	31.7440i	0.450150	+	1.38542i
$526$		0			0
$527$	−8.90073	−	56.1970i	−0.387722	−	2.44798i
$528$		0			0
$529$	−15.5163	+	5.04155i	−0.674621	+	0.219198i
$530$		0			0
$531$	50.0010	+	16.2463i	2.16986	+	0.705030i
$532$		0			0
$533$	9.04062	−	4.60642i	0.391593	−	0.199526i
$534$		0			0
$535$	25.1426	+	25.1426i	1.08701	+	1.08701i
$536$		0			0
$537$	−4.42780	+	27.9561i	−0.191074	+	1.20639i
$538$		0			0
$539$	2.63492	+	1.91438i	0.113494	+	0.0824582i
$540$		0			0
$541$	−35.9536	+	26.1218i	−1.54577	+	1.12306i	−0.599179	+	0.800615i	$0.704506\pi$
$541$	−35.9536	+	26.1218i	−1.54577	+	1.12306i	−0.946587	+	0.322449i	$0.895494\pi$
$542$		0			0
$543$	−36.9776	+	36.9776i	−1.58686	+	1.58686i
$544$		0			0
$545$	−11.2599	−	15.4979i	−0.482319	−	0.663855i
$546$		0			0
$547$	13.3756	−	26.2510i	0.571897	−	1.12241i	−0.406107	−	0.913826i	$-0.633114\pi$
$547$	13.3756	−	26.2510i	0.571897	−	1.12241i	0.978004	−	0.208586i	$-0.0668861\pi$
$548$		0			0
$549$		−	6.52234i		−	0.278367i
$550$		0			0
$551$		−	16.9334i		−	0.721385i
$552$		0			0
$553$	−7.72659	+	15.1643i	−0.328568	+	0.644851i
$554$		0			0
$555$	−38.6536	+	53.2022i	−1.64076	+	2.25831i
$556$		0			0
$557$	8.25814	−	8.25814i	0.349908	−	0.349908i	−0.510167	−	0.860075i	$-0.670416\pi$
$557$	8.25814	−	8.25814i	0.349908	−	0.349908i	0.860075	+	0.510167i	$0.170416\pi$
$558$		0			0
$559$	−6.80206	+	4.94199i	−0.287697	+	0.209024i
$560$		0			0
$561$	−24.6213	−	17.8884i	−1.03951	−	0.755250i
$562$		0			0
$563$	2.84609	−	17.9695i	0.119949	−	0.757325i	−0.852244	−	0.523144i	$-0.824759\pi$
$563$	2.84609	−	17.9695i	0.119949	−	0.757325i	0.972193	−	0.234181i	$-0.0752410\pi$
$564$		0			0
$565$	11.5562	+	1.83032i	0.486171	+	0.0770020i
$566$		0			0
$567$	−8.30766	+	4.23296i	−0.348889	+	0.177768i
$568$		0			0
$569$	22.1612	+	7.20061i	0.929046	+	0.301865i	0.734172	−	0.678963i	$-0.237570\pi$
$569$	22.1612	+	7.20061i	0.929046	+	0.301865i	0.194873	+	0.980828i	$0.437570\pi$
$570$		0			0
$571$	4.48095	−	1.45595i	0.187522	−	0.0609296i	−0.213751	−	0.976888i	$-0.568568\pi$
$571$	4.48095	−	1.45595i	0.187522	−	0.0609296i	0.401273	+	0.915959i	$0.368568\pi$
$572$		0			0
$573$	−2.70922	−	17.1053i	−0.113179	−	0.714585i
$574$		0			0
$575$	12.7687	−	2.02237i	0.532493	−	0.0843385i
$576$		0			0
$577$	−25.3479	+	4.01471i	−1.05525	+	0.167135i	−0.659867	−	0.751383i	$-0.729387\pi$
$577$	−25.3479	+	4.01471i	−1.05525	+	0.167135i	−0.395380	+	0.918517i	$0.629387\pi$
$578$		0			0
$579$	7.51982	+	23.1436i	0.312513	+	0.961816i
$580$		0			0
$581$	10.9222	−	33.6149i	0.453128	−	1.39458i
$582$		0			0
$583$	−8.15908	−	16.0131i	−0.337915	−	0.663195i
$584$		0			0
$585$	5.28989	+	10.3820i	0.218710	+	0.429243i
$586$		0			0
$587$	3.46115	+	0.548193i	0.142857	+	0.0226263i	0.227453	−	0.973789i	$-0.426960\pi$
$587$	3.46115	+	0.548193i	0.142857	+	0.0226263i	−0.0845963	+	0.996415i	$0.526960\pi$
$588$		0			0
$589$	−37.0490	+	50.9936i	−1.52658	+	2.10116i
$590$		0			0
$591$	17.6587	+	24.3052i	0.726383	+	0.999781i
$592$		0			0
$593$	−9.16670	−	9.16670i	−0.376431	−	0.376431i	0.493382	−	0.869813i	$-0.335761\pi$
$593$	−9.16670	−	9.16670i	−0.376431	−	0.376431i	−0.869813	+	0.493382i	$0.835761\pi$
$594$		0			0
$595$	8.72261	−	26.8454i	0.357592	−	1.10056i
$596$		0			0
$597$	31.4015	+	15.9999i	1.28518	+	0.654832i
$598$		0			0
$599$	−1.02128			−0.0417284			−0.0208642	−	0.999782i	$-0.506642\pi$
$599$	−1.02128			−0.0417284			−0.0208642	+	0.999782i	$0.506642\pi$
$600$		0			0
$601$	24.7175			1.00825			0.504124	−	0.863631i	$-0.331816\pi$
$601$	24.7175			1.00825			0.504124	+	0.863631i	$0.331816\pi$
$602$		0			0
$603$	−31.2705	−	15.9331i	−1.27343	−	0.648847i
$604$		0			0
$605$	−5.07138	−	15.6081i	−0.206181	−	0.634559i
$606$		0			0
$607$	−15.6989	−	15.6989i	−0.637199	−	0.637199i	0.312664	−	0.949864i	$-0.398778\pi$
$607$	−15.6989	−	15.6989i	−0.637199	−	0.637199i	−0.949864	+	0.312664i	$0.898778\pi$
$608$		0			0
$609$	10.9357	+	15.0517i	0.443137	+	0.609926i
$610$		0			0
$611$	−0.616228	+	0.848165i	−0.0249299	+	0.0343131i
$612$		0			0
$613$	24.4360	+	3.87028i	0.986961	+	0.156319i	0.628990	−	0.777413i	$-0.283469\pi$
$613$	24.4360	+	3.87028i	0.986961	+	0.156319i	0.357971	+	0.933733i	$0.383469\pi$
$614$		0			0
$615$	67.4957	−	10.6903i	2.72169	−	0.431073i
$616$		0			0
$617$	20.2483	+	39.7395i	0.815166	+	1.59985i	0.800024	+	0.599968i	$0.204820\pi$
$617$	20.2483	+	39.7395i	0.815166	+	1.59985i	0.0151422	+	0.999885i	$0.495180\pi$
$618$		0			0
$619$	−5.01747	+	15.4422i	−0.201669	+	0.620674i	0.798165	+	0.602439i	$0.205805\pi$
$619$	−5.01747	+	15.4422i	−0.201669	+	0.620674i	−0.999834	+	0.0182344i	$0.994195\pi$
$620$		0			0
$621$	5.58846	+	17.1995i	0.224257	+	0.690193i
$622$		0			0
$623$	−7.57235	+	1.19934i	−0.303380	+	0.0480507i
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$	5.27413	+	33.2995i	0.210628	+	1.32986i
$628$		0			0
$629$	52.8917	−	17.1856i	2.10893	−	0.685233i
$630$		0			0
$631$	33.0642	+	10.7432i	1.31626	+	0.427680i	0.881210	−	0.472725i	$-0.156730\pi$
$631$	33.0642	+	10.7432i	1.31626	+	0.427680i	0.435053	+	0.900405i	$0.356730\pi$
$632$		0			0
$633$	−1.16718	+	0.594706i	−0.0463911	+	0.0236374i
$634$		0			0
$635$	6.20265	+	39.1620i	0.246145	+	1.55410i
$636$		0			0
$637$	−0.256419	+	1.61897i	−0.0101597	+	0.0641458i
$638$		0			0
$639$	40.6606	+	29.5416i	1.60851	+	1.16865i
$640$		0			0
$641$	24.7800	−	18.0037i	0.978751	−	0.711104i	0.0213220	−	0.999773i	$-0.493212\pi$
$641$	24.7800	−	18.0037i	0.978751	−	0.711104i	0.957429	+	0.288668i	$0.0932125\pi$
$642$		0			0
$643$	−14.8959	+	14.8959i	−0.587438	+	0.587438i	−0.936937	−	0.349499i	$-0.886352\pi$
$643$	−14.8959	+	14.8959i	−0.587438	+	0.587438i	0.349499	+	0.936937i	$0.386352\pi$
$644$		0			0
$645$	−53.8553	+	17.4986i	−2.12055	+	0.689008i
$646$		0			0
$647$	−6.63750	+	13.0268i	−0.260947	+	0.512137i	−0.983891	−	0.178769i	$-0.942788\pi$
$647$	−6.63750	+	13.0268i	−0.260947	+	0.512137i	0.722944	+	0.690907i	$0.242788\pi$
$648$		0			0
$649$			18.5875i			0.729625i
$650$		0			0
$651$		−	69.2537i		−	2.71427i
$652$		0			0
$653$	11.8246	−	23.2070i	0.462731	−	0.908161i	−0.535253	−	0.844692i	$-0.679784\pi$
$653$	11.8246	−	23.2070i	0.462731	−	0.908161i	0.997984	−	0.0634688i	$-0.0202163\pi$
$654$		0			0
$655$	32.4252	+	10.5356i	1.26696	+	0.411660i
$656$		0			0
$657$	5.18649	−	5.18649i	0.202344	−	0.202344i
$658$		0			0
$659$	24.4969	−	17.7981i	0.954265	−	0.693314i	0.00245356	−	0.999997i	$-0.499219\pi$
$659$	24.4969	−	17.7981i	0.954265	−	0.693314i	0.951812	+	0.306683i	$0.0992190\pi$
$660$		0			0
$661$	22.1513	+	16.0939i	0.861587	+	0.625980i	0.928316	−	0.371791i	$-0.121256\pi$
$661$	22.1513	+	16.0939i	0.861587	+	0.625980i	−0.0667289	+	0.997771i	$0.521256\pi$
$662$		0			0
$663$	2.39604	−	15.1280i	0.0930545	−	0.587523i
$664$		0			0
$665$	−27.8619	+	14.1963i	−1.08044	+	0.550510i
$666$		0			0
$667$	6.42069	−	3.27150i	0.248610	−	0.126673i
$668$		0			0
$669$	−23.6065	−	7.67022i	−0.912681	−	0.296548i
$670$		0			0
$671$	2.19310	−	0.712582i	0.0846638	−	0.0275089i
$672$		0			0
$673$	2.72840	+	17.2265i	0.105172	+	0.664031i	0.982798	+	0.184684i	$0.0591263\pi$
$673$	2.72840	+	17.2265i	0.105172	+	0.664031i	−0.877626	+	0.479347i	$0.840874\pi$
$674$		0			0
$675$	5.47085	+	34.5416i	0.210573	+	1.32951i
$676$		0			0
$677$	−30.9741	+	4.90581i	−1.19043	+	0.188546i	−0.720052	−	0.693920i	$-0.755882\pi$
$677$	−30.9741	+	4.90581i	−1.19043	+	0.188546i	−0.470377	+	0.882465i	$0.655882\pi$
$678$		0			0
$679$	1.78775	+	5.50212i	0.0686075	+	0.211152i
$680$		0			0
$681$	−3.57029	+	10.9882i	−0.136814	+	0.421069i
$682$		0			0
$683$	12.0790	+	23.7064i	0.462191	+	0.907101i	0.998027	+	0.0627792i	$0.0199964\pi$
$683$	12.0790	+	23.7064i	0.462191	+	0.907101i	−0.535836	+	0.844322i	$0.680004\pi$
$684$		0			0
$685$	−0.343002	+	2.16563i	−0.0131054	+	0.0827443i
$686$		0			0
$687$	−18.7046	−	2.96251i	−0.713624	−	0.113027i
$688$		0			0
$689$	5.31645	−	7.31746i	0.202541	−	0.278773i
$690$		0			0
$691$	12.0424	+	16.5750i	0.458115	+	0.630541i	0.974116	−	0.226047i	$-0.0725802\pi$
$691$	12.0424	+	16.5750i	0.458115	+	0.630541i	−0.516002	+	0.856588i	$0.672580\pi$
$692$		0			0
$693$	−16.8514	−	16.8514i	−0.640132	−	0.640132i
$694$		0			0
$695$	−8.75938	−	6.36406i	−0.332262	−	0.241403i
$696$		0			0
$697$	−51.4928	−	26.2369i	−1.95043	−	0.993793i
$698$		0			0
$699$	−41.4679			−1.56846
$700$		0			0
$701$	0.0556153			0.00210056			0.00105028	−	0.999999i	$-0.499666\pi$
$701$	0.0556153			0.00210056			0.00105028	+	0.999999i	$0.499666\pi$
$702$		0			0
$703$	−54.8943	−	27.9700i	−2.07038	−	1.05491i
$704$		0			0
$705$	−5.71241	+	4.15031i	−0.215142	+	0.156310i
$706$		0			0
$707$	4.71668	+	4.71668i	0.177389	+	0.177389i
$708$		0			0
$709$	26.2864	+	36.1801i	0.987206	+	1.35877i	0.932855	+	0.360251i	$0.117309\pi$
$709$	26.2864	+	36.1801i	0.987206	+	1.35877i	0.0543509	+	0.998522i	$0.482691\pi$
$710$		0			0
$711$	−23.5204	+	32.3730i	−0.882082	+	1.21408i
$712$		0			0
$713$	−26.4933	−	4.19612i	−0.992181	−	0.157146i
$714$		0			0
$715$	−2.91296	+	2.91296i	−0.108939	+	0.108939i
$716$		0			0
$717$	10.8673	+	21.3282i	0.405845	+	0.796517i
$718$		0			0
$719$	−6.24759	+	19.2281i	−0.232996	+	0.717087i	0.764385	+	0.644760i	$0.223043\pi$
$719$	−6.24759	+	19.2281i	−0.232996	+	0.717087i	−0.997381	+	0.0723273i	$0.976957\pi$
$720$		0			0
$721$	6.23236	+	19.1812i	0.232105	+	0.714347i
$722$		0			0
$723$	24.5543	−	3.88902i	0.913184	−	0.144634i
$724$		0			0
$725$	13.2532	−	4.30621i	0.492210	−	0.159929i
$726$		0			0
$727$	−1.18294	−	7.46881i	−0.0438729	−	0.277003i	0.955993	−	0.293390i	$-0.0947835\pi$
$727$	−1.18294	−	7.46881i	−0.0438729	−	0.277003i	−0.999866	+	0.0163874i	$0.994783\pi$
$728$		0			0
$729$	37.0298	−	12.0317i	1.37147	−	0.445619i
$730$		0			0
$731$	45.5447	+	14.7984i	1.68453	+	0.547337i
$732$		0			0
$733$	−4.47992	+	2.28263i	−0.165470	+	0.0843110i	−0.534764	−	0.845002i	$-0.679599\pi$
$733$	−4.47992	+	2.28263i	−0.165470	+	0.0843110i	0.369294	+	0.929313i	$0.379599\pi$
$734$		0			0
$735$	−5.01191	+	9.83643i	−0.184867	+	0.362822i
$736$		0			0
$737$	1.94105	−	12.2553i	0.0714994	−	0.451429i
$738$		0			0
$739$	−25.4921	−	18.5211i	−0.937743	−	0.681310i	0.0101332	−	0.999949i	$-0.496774\pi$
$739$	−25.4921	−	18.5211i	−0.937743	−	0.681310i	−0.947876	+	0.318638i	$0.896774\pi$
$740$		0			0
$741$	−13.7273	+	9.97345i	−0.504284	+	0.366384i
$742$		0			0
$743$	4.53704	−	4.53704i	0.166448	−	0.166448i	−0.618968	−	0.785416i	$-0.712449\pi$
$743$	4.53704	−	4.53704i	0.166448	−	0.166448i	0.785416	+	0.618968i	$0.212449\pi$
$744$		0			0
$745$		−	20.4853i		−	0.750522i
$746$		0			0
$747$	37.7274	−	74.0443i	1.38037	−	2.70914i
$748$		0			0
$749$		−	36.6002i		−	1.33734i
$750$		0			0
$751$		−	45.1400i		−	1.64718i	−0.567184	−	0.823591i	$-0.691967\pi$
$751$		−	45.1400i		−	1.64718i	0.567184	−	0.823591i	$-0.308033\pi$
$752$		0			0
$753$	−23.0793	+	45.2956i	−0.841055	+	1.65066i
$754$		0			0
$755$		−	34.8905i		−	1.26979i
$756$		0			0
$757$	−11.2118	+	11.2118i	−0.407500	+	0.407500i	−0.880866	−	0.473366i	$-0.843039\pi$
$757$	−11.2118	+	11.2118i	−0.407500	+	0.407500i	0.473366	+	0.880866i	$0.343039\pi$
$758$		0			0
$759$	−11.6074	+	8.43324i	−0.421321	+	0.306107i
$760$		0			0
$761$	16.6208	+	12.0757i	0.602503	+	0.437744i	0.846767	−	0.531965i	$-0.178546\pi$
$761$	16.6208	+	12.0757i	0.602503	+	0.437744i	−0.244263	+	0.969709i	$0.578546\pi$
$762$		0			0
$763$	−3.08465	+	19.4757i	−0.111672	+	0.705068i
$764$		0			0
$765$	30.1297	−	59.1329i	1.08934	−	2.13796i
$766$		0			0
$767$	−8.33510	+	4.24695i	−0.300963	+	0.153348i
$768$		0			0
$769$	−22.0022	−	7.14894i	−0.793419	−	0.257797i	−0.115859	−	0.993266i	$-0.536962\pi$
$769$	−22.0022	−	7.14894i	−0.793419	−	0.257797i	−0.677559	+	0.735468i	$0.736962\pi$
$770$		0			0
$771$	−47.3751	+	15.3931i	−1.70617	+	0.554369i
$772$		0			0
$773$	−6.27729	−	39.6333i	−0.225779	−	1.42551i	−0.796635	−	0.604460i	$-0.793389\pi$
$773$	−6.27729	−	39.6333i	−0.225779	−	1.42551i	0.570857	−	0.821050i	$-0.306611\pi$
$774$		0			0
$775$	−49.3327	−	16.0292i	−1.77208	−	0.575784i
$776$		0			0
$777$	66.8577	−	10.5892i	2.39850	−	0.379886i
$778$		0			0
$779$	19.7839	+	60.8887i	0.708833	+	2.18157i
$780$		0			0
$781$	−5.49095	+	16.8994i	−0.196482	+	0.604708i
$782$		0			0
$783$	8.84998	+	17.3691i	0.316273	+	0.620720i
$784$		0			0
$785$	11.3065	−	11.3065i	0.403548	−	0.403548i
$786$		0			0
$787$	14.5622	+	2.30642i	0.519085	+	0.0822150i	0.410479	−	0.911870i	$-0.365361\pi$
$787$	14.5622	+	2.30642i	0.519085	+	0.0822150i	0.108606	+	0.994085i	$0.465361\pi$
$788$		0			0
$789$	4.17037	−	5.74002i	0.148469	−	0.204350i
$790$		0			0
$791$	−7.07900	−	9.74341i	−0.251700	−	0.346436i
$792$		0			0
$793$	0.820627	+	0.820627i	0.0291413	+	0.0291413i
$794$		0			0
$795$	49.2833	−	35.8064i	1.74790	−	1.26992i
$796$		0			0
$797$	17.3154	+	8.82266i	0.613344	+	0.312515i	0.732924	−	0.680310i	$-0.238155\pi$
$797$	17.3154	+	8.82266i	0.613344	+	0.312515i	−0.119580	+	0.992825i	$0.538155\pi$
$798$		0			0
$799$	5.97133			0.211251
$800$		0			0
$801$	−18.0258			−0.636911
$802$		0			0
$803$	2.31057	+	1.17729i	0.0815382	+	0.0415458i
$804$		0			0
$805$	−10.7658	−	7.82178i	−0.379443	−	0.275682i
$806$		0			0
$807$	−16.2134	−	16.2134i	−0.570738	−	0.570738i
$808$		0			0
$809$	12.0110	+	16.5317i	0.422284	+	0.581224i	0.966161	−	0.257941i	$-0.0830441\pi$
$809$	12.0110	+	16.5317i	0.422284	+	0.581224i	−0.543877	+	0.839165i	$0.683044\pi$
$810$		0			0
$811$	−7.49205	+	10.3119i	−0.263081	+	0.362101i	−0.920039	−	0.391827i	$-0.871843\pi$
$811$	−7.49205	+	10.3119i	−0.263081	+	0.362101i	0.656957	+	0.753928i	$0.271843\pi$
$812$		0			0
$813$	−32.7154	−	5.18162i	−1.14738	−	0.181727i
$814$		0			0
$815$	1.21196	−	7.65201i	0.0424531	−	0.268038i
$816$		0			0
$817$	−24.0848	−	47.2691i	−0.842621	−	1.65374i
$818$		0			0
$819$	3.70631	−	11.4069i	0.129509	−	0.398588i
$820$		0			0
$821$	−13.2734	−	40.8514i	−0.463246	−	1.42572i	−0.861175	−	0.508309i	$-0.830271\pi$
$821$	−13.2734	−	40.8514i	−0.463246	−	1.42572i	0.397929	−	0.917416i	$-0.369729\pi$
$822$		0			0
$823$	14.1588	−	2.24253i	0.493545	−	0.0781698i	0.0952992	−	0.995449i	$-0.469619\pi$
$823$	14.1588	−	2.24253i	0.493545	−	0.0781698i	0.398246	+	0.917279i	$0.369619\pi$
$824$		0			0
$825$	−24.7212	+	12.5961i	−0.860681	+	0.438539i
$826$		0			0
$827$	3.59722	+	22.7120i	0.125088	+	0.789773i	0.967858	+	0.251499i	$0.0809234\pi$
$827$	3.59722	+	22.7120i	0.125088	+	0.789773i	−0.842770	+	0.538274i	$0.819077\pi$
$828$		0			0
$829$	−53.7472	+	17.4635i	−1.86672	+	0.606533i	−0.874022	+	0.485886i	$0.838497\pi$
$829$	−53.7472	+	17.4635i	−1.86672	+	0.606533i	−0.992695	+	0.120648i	$0.961503\pi$
$830$		0			0
$831$	−14.2343	−	4.62502i	−0.493784	−	0.160440i
$832$		0			0
$833$	8.31854	−	4.23851i	0.288220	−	0.146856i
$834$		0			0
$835$	−27.2817	+	13.9007i	−0.944121	+	0.481054i
$836$		0			0
$837$	11.3512	−	71.6689i	0.392356	−	2.47724i
$838$		0			0
$839$	−45.5611	−	33.1021i	−1.57294	−	1.14281i	−0.924266	−	0.381748i	$-0.875322\pi$
$839$	−45.5611	−	33.1021i	−1.57294	−	1.14281i	−0.648678	−	0.761063i	$-0.724678\pi$
$840$		0			0
$841$	−17.1774	+	12.4801i	−0.592323	+	0.430348i
$842$		0			0
$843$	1.94403	−	1.94403i	0.0669559	−	0.0669559i
$844$		0			0
$845$	25.6743	+	8.34210i	0.883224	+	0.286977i
$846$		0			0
$847$	−7.66920	+	15.0516i	−0.263517	+	0.517181i
$848$		0			0
$849$		−	13.6655i		−	0.469000i
$850$		0			0
$851$		−	26.2183i		−	0.898751i
$852$		0			0
$853$	2.05888	−	4.04078i	0.0704948	−	0.138354i	−0.853070	−	0.521797i	$-0.825262\pi$
$853$	2.05888	−	4.04078i	0.0704948	−	0.138354i	0.923564	+	0.383443i	$0.125262\pi$
$854$		0			0
$855$	−69.9230	+	22.7194i	−2.39132	+	0.776986i
$856$		0			0
$857$	31.5213	−	31.5213i	1.07675	−	1.07675i	0.0799464	−	0.996799i	$-0.474525\pi$
$857$	31.5213	−	31.5213i	1.07675	−	1.07675i	0.996799	−	0.0799464i	$-0.0254749\pi$
$858$		0			0
$859$	44.9222	−	32.6379i	1.53272	−	1.11359i	0.578025	−	0.816019i	$-0.303824\pi$
$859$	44.9222	−	32.6379i	1.53272	−	1.11359i	0.954700	−	0.297570i	$-0.0961763\pi$
$860$		0			0
$861$	−56.9080	−	41.3461i	−1.93942	−	1.40907i
$862$		0			0
$863$	5.82545	−	36.7804i	0.198301	−	1.25202i	−0.664813	−	0.747010i	$-0.731489\pi$
$863$	5.82545	−	36.7804i	0.198301	−	1.25202i	0.863113	−	0.505010i	$-0.168511\pi$
$864$		0			0
$865$	0.0605030	+	0.382001i	0.00205716	+	0.0129884i
$866$		0			0
$867$	−33.7995	+	17.2217i	−1.14789	+	0.584880i
$868$		0			0
$869$	−13.4549	−	4.37177i	−0.456427	−	0.148302i
$870$		0			0
$871$	5.93906	−	1.92972i	0.201238	−	0.0653860i
$872$		0			0
$873$	2.12785	+	13.4347i	0.0720168	+	0.454696i
$874$		0			0
$875$	−18.1964	−	18.1964i	−0.615149	−	0.615149i
$876$		0			0
$877$	33.6877	−	5.33560i	1.13755	−	0.180170i	0.440884	−	0.897564i	$-0.354665\pi$
$877$	33.6877	−	5.33560i	1.13755	−	0.180170i	0.696668	+	0.717394i	$0.254665\pi$
$878$		0			0
$879$	−22.0566	−	67.8832i	−0.743950	−	2.28964i
$880$		0			0
$881$	−10.0398	+	30.8993i	−0.338250	+	1.04103i	0.626849	+	0.779140i	$0.284344\pi$
$881$	−10.0398	+	30.8993i	−0.338250	+	1.04103i	−0.965099	+	0.261885i	$0.915656\pi$
$882$		0			0
$883$	19.0062	+	37.3018i	0.639611	+	1.25531i	0.952216	+	0.305424i	$0.0987982\pi$
$883$	19.0062	+	37.3018i	0.639611	+	1.25531i	−0.312606	+	0.949883i	$0.601202\pi$
$884$		0			0
$885$	−62.2284	+	9.85602i	−2.09179	+	0.331306i
$886$		0			0
$887$	15.7111	+	2.48840i	0.527528	+	0.0835522i	0.414517	−	0.910042i	$-0.363951\pi$
$887$	15.7111	+	2.48840i	0.527528	+	0.0835522i	0.113011	+	0.993594i	$0.463951\pi$
$888$		0			0
$889$	23.9896	−	33.0189i	0.804586	−	1.10742i
$890$		0			0
$891$	−4.55565	−	6.27031i	−0.152620	−	0.210063i
$892$		0			0
$893$	−4.67758	−	4.67758i	−0.156529	−	0.156529i
$894$		0			0
$895$	−6.74346	−	20.7542i	−0.225409	−	0.693738i
$896$		0			0
$897$	−6.43376	−	3.27817i	−0.214817	−	0.109455i
$898$		0			0
$899$	−28.9136			−0.964321
$900$		0			0
$901$	−51.5171			−1.71628
$902$		0			0
$903$	51.9352	+	26.4623i	1.72830	+	0.880611i
$904$		0			0
$905$	12.4589	−	38.3446i	0.414148	−	1.27462i
$906$		0			0
$907$	26.6340	+	26.6340i	0.884368	+	0.884368i	0.993975	−	0.109607i	$-0.0349593\pi$
$907$	26.6340	+	26.6340i	0.884368	+	0.884368i	−0.109607	+	0.993975i	$0.534959\pi$
$908$		0			0
$909$	9.21837	+	12.6880i	0.305754	+	0.420834i
$910$		0			0
$911$	−10.7990	+	14.8635i	−0.357786	+	0.492450i	−0.949530	−	0.313676i	$-0.898440\pi$
$911$	−10.7990	+	14.8635i	−0.357786	+	0.492450i	0.591744	+	0.806126i	$0.298440\pi$
$912$		0			0
$913$	29.0188	+	4.59613i	0.960383	+	0.152110i
$914$		0			0
$915$	3.54852	+	6.96435i	0.117310	+	0.230234i
$916$		0			0
$917$	−15.9325	−	31.2692i	−0.526136	−	1.03260i
$918$		0			0
$919$	3.79079	−	11.6668i	0.125047	−	0.384854i	−0.868863	−	0.495053i	$-0.835149\pi$
$919$	3.79079	−	11.6668i	0.125047	−	0.384854i	0.993910	+	0.110199i	$0.0351488\pi$
$920$		0			0
$921$	11.6027	+	35.7094i	0.382322	+	1.17666i
$922$		0			0
$923$	−8.83270	+	1.39896i	−0.290732	+	0.0460474i
$924$		0			0
$925$	7.93138	−	50.0768i	0.260782	−	1.64651i
$926$		0			0
$927$	7.41801	+	46.8354i	0.243639	+	1.53828i
$928$		0			0
$929$	−22.8891	+	7.43712i	−0.750967	+	0.244004i	−0.659397	−	0.751795i	$-0.729188\pi$
$929$	−22.8891	+	7.43712i	−0.750967	+	0.244004i	−0.0915697	+	0.995799i	$0.529188\pi$
$930$		0			0
$931$	−9.83643	−	3.19605i	−0.322376	−	0.104746i
$932$		0			0
$933$	−63.9703	+	32.5945i	−2.09429	+	1.06710i
$934$		0			0
$935$	23.1749	+	3.67054i	0.757900	+	0.120040i
$936$		0			0
$937$	−4.35021	+	27.4661i	−0.142115	+	0.897280i	0.808858	+	0.588005i	$0.200086\pi$
$937$	−4.35021	+	27.4661i	−0.142115	+	0.897280i	−0.950973	+	0.309275i	$0.899914\pi$
$938$		0			0
$939$	57.4889	+	41.7682i	1.87608	+	1.36305i
$940$		0			0
$941$	26.2811	−	19.0943i	0.856739	−	0.622458i	−0.0702566	−	0.997529i	$-0.522382\pi$
$941$	26.2811	−	19.0943i	0.856739	−	0.622458i	0.926996	+	0.375071i	$0.122382\pi$
$942$		0			0
$943$	−19.2652	+	19.2652i	−0.627361	+	0.627361i
$944$		0			0
$945$	21.1593	−	29.1232i	0.688311	−	0.947379i
$946$		0			0
$947$	−19.6510	+	38.5672i	−0.638570	+	1.25327i	0.314137	+	0.949378i	$0.398285\pi$
$947$	−19.6510	+	38.5672i	−0.638570	+	1.25327i	−0.952708	+	0.303888i	$0.901715\pi$
$948$		0			0
$949$			1.30511i			0.0423656i
$950$		0			0
$951$			32.6197i			1.05777i
$952$		0			0
$953$	−17.2271	+	33.8100i	−0.558039	+	1.09521i	0.423845	+	0.905735i	$0.360680\pi$
$953$	−17.2271	+	33.8100i	−0.558039	+	1.09521i	−0.981885	+	0.189479i	$0.939320\pi$
$954$		0			0
$955$	7.84829	+	10.8022i	0.253965	+	0.349552i
$956$		0			0
$957$	−10.9357	+	10.9357i	−0.353501	+	0.353501i
$958$		0			0
$959$	1.82592	−	1.32661i	0.0589619	−	0.0428383i
$960$		0			0
$961$	61.9917	+	45.0396i	1.99973	+	1.45289i
$962$		0			0
$963$	13.4617	−	84.9940i	0.433798	−	2.73889i
$964$		0			0
$965$	−13.2665	−	13.2665i	−0.427062	−	0.427062i
$966$		0			0
$967$	34.9580	−	17.8120i	1.12417	−	0.572795i	0.209832	−	0.977738i	$-0.432708\pi$
$967$	34.9580	−	17.8120i	1.12417	−	0.572795i	0.914342	+	0.404942i	$0.132708\pi$
$968$		0			0
$969$	91.9139	+	29.8646i	2.95270	+	0.959391i
$970$		0			0
$971$	−17.7840	+	5.77838i	−0.570717	+	0.185437i	−0.580138	−	0.814519i	$-0.697001\pi$
$971$	−17.7840	+	5.77838i	−0.570717	+	0.185437i	0.00942088	+	0.999956i	$0.497001\pi$
$972$		0			0
$973$	1.74344	+	11.0077i	0.0558922	+	0.352889i
$974$		0			0
$975$	−11.2968	−	8.20758i	−0.361786	−	0.262853i
$976$		0			0
$977$	39.6220	−	6.27550i	1.26762	−	0.200771i	0.513832	−	0.857891i	$-0.328225\pi$
$977$	39.6220	−	6.27550i	1.26762	−	0.200771i	0.753786	+	0.657119i	$0.228225\pi$
$978$		0			0
$979$	−1.96937	−	6.06109i	−0.0629413	−	0.193713i
$980$		0			0
$981$	−14.3265	+	44.0924i	−0.457410	+	1.40776i
$982$		0			0
$983$	14.9499	+	29.3408i	0.476827	+	0.935826i	0.996668	+	0.0815629i	$0.0259912\pi$
$983$	14.9499	+	29.3408i	0.476827	+	0.935826i	−0.519841	+	0.854263i	$0.674009\pi$
$984$		0			0
$985$	−20.6379	−	10.5156i	−0.657580	−	0.335054i
$986$		0			0
$987$	7.17862	+	1.13698i	0.228498	+	0.0361905i
$988$		0			0
$989$	13.2701	−	18.2647i	0.421963	−	0.580782i
$990$		0			0
$991$	5.75905	+	7.92666i	0.182942	+	0.251799i	0.890632	−	0.454725i	$-0.150262\pi$
$991$	5.75905	+	7.92666i	0.182942	+	0.251799i	−0.707690	+	0.706524i	$0.750262\pi$
$992$		0			0
$993$	−43.1986	−	43.1986i	−1.37087	−	1.37087i
$994$		0			0
$995$	−27.1716			−0.861397
$996$		0			0
$997$	19.0371	+	9.69989i	0.602911	+	0.307198i	0.728673	−	0.684862i	$-0.240138\pi$
$997$	19.0371	+	9.69989i	0.602911	+	0.307198i	−0.125762	+	0.992060i	$0.540138\pi$
$998$		0			0
$999$	70.9249			2.24397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.c.63.2	yes	16
4.3	odd	2	inner	400.2.bi.c.63.1	✓	16
25.2	odd	20	inner	400.2.bi.c.127.1	yes	16
100.27	even	20	inner	400.2.bi.c.127.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.c.63.1	✓	16	4.3	odd	2	inner
400.2.bi.c.63.2	yes	16	1.1	even	1	trivial
400.2.bi.c.127.1	yes	16	25.2	odd	20	inner
400.2.bi.c.127.2	yes	16	100.27	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.58417 + 1.31670i) q^{3} -2.23607 q^{5} +(1.62753 + 1.62753i) q^{7} +(3.18088 + 4.37811i) q^{9} +(-1.12460 + 1.54787i) q^{11} +(-0.951057 - 0.150633i) q^{13} +(-5.77838 - 2.94423i) q^{15} +(2.48990 + 4.88670i) q^{17} +(1.87751 - 5.77838i) q^{19} +(2.06285 + 6.34879i) q^{21} +(2.55374 - 0.404473i) q^{23} +5.00000 q^{25} +(1.09417 + 6.90832i) q^{27} +(2.65063 - 0.861243i) q^{29} +(-9.86654 - 3.20583i) q^{31} +(-4.94424 + 2.51921i) q^{33} +(-3.63927 - 3.63927i) q^{35} +(1.58628 - 10.0154i) q^{37} +(-2.25935 - 1.64152i) q^{39} +(-8.52488 + 6.19369i) q^{41} +(6.17421 - 6.17421i) q^{43} +(-7.11267 - 9.78975i) q^{45} +(0.494291 - 0.970102i) q^{47} -1.70228i q^{49} +15.9065i q^{51} +(-4.26445 + 8.36946i) q^{53} +(2.51467 - 3.46115i) q^{55} +(12.4602 - 12.4602i) q^{57} +(7.85962 - 5.71035i) q^{59} +(-0.975062 - 0.708424i) q^{61} +(-1.94852 + 12.3025i) q^{63} +(2.12663 + 0.336825i) q^{65} +(-5.77838 + 2.94423i) q^{67} +(7.13188 + 2.31729i) q^{69} +(8.83270 - 2.86992i) q^{71} +(-0.212028 - 1.33869i) q^{73} +(12.9209 + 6.58350i) q^{75} +(-4.34953 + 0.688898i) q^{77} +(2.28496 + 7.03239i) q^{79} +(-1.25180 + 3.85265i) q^{81} +(-6.97154 - 13.6824i) q^{83} +(-5.56758 - 10.9270i) q^{85} +(7.98369 + 1.26449i) q^{87} +(-1.95788 + 2.69479i) q^{89} +(-1.30272 - 1.79303i) q^{91} +(-21.2757 - 21.2757i) q^{93} +(-4.19824 + 12.9209i) q^{95} +(2.23955 + 1.14111i) q^{97} -10.3540 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{9} + 20 q^{21} + 80 q^{25} + 20 q^{29} - 20 q^{33} - 40 q^{37} - 12 q^{41} + 20 q^{45} - 40 q^{53} + 20 q^{57} - 12 q^{61} - 60 q^{69} - 40 q^{73} - 100 q^{77} - 24 q^{81} - 60 q^{89} - 100 q^{93}+ \cdots - 80 q^{97}+O(q^{100}) \) 16 * q + 20 * q^9 + 20 * q^21 + 80 * q^25 + 20 * q^29 - 20 * q^33 - 40 * q^37 - 12 * q^41 + 20 * q^45 - 40 * q^53 + 20 * q^57 - 12 * q^61 - 60 * q^69 - 40 * q^73 - 100 * q^77 - 24 * q^81 - 60 * q^89 - 100 * q^93 - 80 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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