LMFDB - Embedded newform 825.2.n.p.526.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			526.2
Character	$\chi$	$=$	825.526
Dual form			825.2.n.p.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.650947 + 2.00341i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.97188 - 1.43266i) q^{4} +(-0.650947 - 2.00341i) q^{6} +(-2.68296 - 1.94929i) q^{7} +(0.745386 - 0.541555i) q^{8} +(0.309017 - 0.951057i) q^{9} +(3.31267 - 0.162019i) q^{11} +2.43738 q^{12} +(-0.772198 + 2.37658i) q^{13} +(5.65169 - 4.10619i) q^{14} +(-0.906636 - 2.79034i) q^{16} +(-2.10446 - 6.47687i) q^{17} +(1.70420 + 1.23818i) q^{18} +(0.928503 - 0.674597i) q^{19} +3.31633 q^{21} +(-1.83178 + 6.74209i) q^{22} +5.89026 q^{23} +(-0.284712 + 0.876254i) q^{24} +(-4.25861 - 3.09406i) q^{26} +(0.309017 + 0.951057i) q^{27} +(2.49783 + 7.68753i) q^{28} +(0.908175 + 0.659827i) q^{29} +(-0.338908 + 1.04305i) q^{31} +8.02306 q^{32} +(-2.58477 + 2.07821i) q^{33} +14.3457 q^{34} +(-1.97188 + 1.43266i) q^{36} +(9.33514 + 6.78238i) q^{37} +(0.747087 + 2.29930i) q^{38} +(-0.772198 - 2.37658i) q^{39} +(0.754463 - 0.548149i) q^{41} +(-2.15875 + 6.64396i) q^{42} +0.552188 q^{43} +(-6.76431 - 4.42643i) q^{44} +(-3.83425 + 11.8006i) q^{46} +(1.72666 - 1.25449i) q^{47} +(2.37360 + 1.72452i) q^{48} +(1.23546 + 3.80234i) q^{49} +(5.50956 + 4.00293i) q^{51} +(4.92751 - 3.58005i) q^{52} +(3.59560 - 11.0661i) q^{53} -2.10651 q^{54} -3.05549 q^{56} +(-0.354657 + 1.09152i) q^{57} +(-1.91308 + 1.38993i) q^{58} +(-6.79443 - 4.93644i) q^{59} +(-2.53800 - 7.81115i) q^{61} +(-1.86905 - 1.35794i) q^{62} +(-2.68296 + 1.94929i) q^{63} +(-3.40931 + 10.4928i) q^{64} +(-2.48096 - 6.53116i) q^{66} -4.15419 q^{67} +(-5.12938 + 15.7866i) q^{68} +(-4.76532 + 3.46221i) q^{69} +(3.87323 + 11.9206i) q^{71} +(-0.284712 - 0.876254i) q^{72} +(4.64182 + 3.37248i) q^{73} +(-19.6646 + 14.2871i) q^{74} -2.79736 q^{76} +(-9.20358 - 6.02265i) q^{77} +5.26393 q^{78} +(-1.19514 + 3.67825i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.607052 + 1.86831i) q^{82} +(-1.87899 - 5.78295i) q^{83} +(-6.53941 - 4.75116i) q^{84} +(-0.359446 + 1.10626i) q^{86} -1.12257 q^{87} +(2.38147 - 1.91476i) q^{88} +12.5950 q^{89} +(6.70442 - 4.87105i) q^{91} +(-11.6149 - 8.43872i) q^{92} +(-0.338908 - 1.04305i) q^{93} +(1.38930 + 4.27582i) q^{94} +(-6.49079 + 4.71583i) q^{96} +(-0.886486 + 2.72832i) q^{97} -8.42187 q^{98} +(0.869581 - 3.20060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27}+ \cdots - 120 q^{98}+O(q^{100}) $ 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 22 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 16 * q^21 - 4 * q^22 + 6 * q^24 - 38 * q^26 - 6 * q^27 + 30 * q^28 - 10 * q^31 - 56 * q^32 + 10 * q^33 + 12 * q^34 - 6 * q^36 + 10 * q^37 + 4 * q^38 + 4 * q^39 + 30 * q^41 - 8 * q^42 - 64 * q^43 + 24 * q^44 + 54 * q^46 - 8 * q^47 - 2 * q^48 + 14 * q^49 + 14 * q^51 + 14 * q^52 + 26 * q^53 - 8 * q^54 + 12 * q^56 + 8 * q^57 + 20 * q^58 - 30 * q^59 + 20 * q^61 - 50 * q^62 + 4 * q^63 - 32 * q^64 + 6 * q^66 + 20 * q^67 - 62 * q^68 - 10 * q^69 - 16 * q^71 + 6 * q^72 - 12 * q^73 + 16 * q^74 - 68 * q^76 - 2 * q^77 + 32 * q^78 + 26 * q^79 - 6 * q^81 + 56 * q^82 + 48 * q^83 - 52 * q^86 + 48 * q^88 - 20 * q^89 - 20 * q^91 + 46 * q^92 - 10 * q^93 - 36 * q^94 + 14 * q^96 - 14 * q^97 - 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.650947	+	2.00341i	−0.460289	+	1.41662i	0.404523	+	0.914528i	$0.367438\pi$
$2$	−0.650947	+	2.00341i	−0.460289	+	1.41662i	−0.864812	+	0.502096i	$0.832562\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−1.97188	−	1.43266i	−0.985942	−	0.716328i
$5$		0			0
$5$		0			0
$6$	−0.650947	−	2.00341i	−0.265748	−	0.817888i
$7$	−2.68296	−	1.94929i	−1.01407	−	0.736761i	−0.0490073	−	0.998798i	$-0.515606\pi$
$7$	−2.68296	−	1.94929i	−1.01407	−	0.736761i	−0.965058	+	0.262037i	$0.915606\pi$
$8$	0.745386	−	0.541555i	0.263534	−	0.191469i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	3.31267	−	0.162019i	0.998806	−	0.0488505i
$11$	3.31267	−	0.162019i	0.998806	−	0.0488505i
$12$	2.43738			0.703611
$13$	−0.772198	+	2.37658i	−0.214169	+	0.659145i	0.785042	+	0.619442i	$0.212641\pi$
$13$	−0.772198	+	2.37658i	−0.214169	+	0.659145i	−0.999212	+	0.0397029i	$0.987359\pi$
$14$	5.65169	−	4.10619i	1.51048	−	1.09743i
$15$		0			0
$16$	−0.906636	−	2.79034i	−0.226659	−	0.697584i
$17$	−2.10446	−	6.47687i	−0.510408	−	1.57087i	−0.791486	−	0.611188i	$-0.790692\pi$
$17$	−2.10446	−	6.47687i	−0.510408	−	1.57087i	0.281078	−	0.959685i	$-0.409308\pi$
$18$	1.70420	+	1.23818i	0.401684	+	0.291841i
$19$	0.928503	−	0.674597i	0.213013	−	0.154763i	−0.476163	−	0.879357i	$-0.657973\pi$
$19$	0.928503	−	0.674597i	0.213013	−	0.154763i	0.689176	+	0.724594i	$0.257973\pi$
$20$		0			0
$21$	3.31633			0.723682
$22$	−1.83178	+	6.74209i	−0.390537	+	1.43742i
$23$	5.89026			1.22820			0.614102	−	0.789226i	$-0.289518\pi$
$23$	5.89026			1.22820			0.614102	+	0.789226i	$0.289518\pi$
$24$	−0.284712	+	0.876254i	−0.0581167	+	0.178865i
$25$		0			0
$26$	−4.25861	−	3.09406i	−0.835181	−	0.606795i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	2.49783	+	7.68753i	0.472046	+	1.45281i
$29$	0.908175	+	0.659827i	0.168644	+	0.122527i	0.668906	−	0.743347i	$-0.266763\pi$
$29$	0.908175	+	0.659827i	0.168644	+	0.122527i	−0.500262	+	0.865874i	$0.666763\pi$
$30$		0			0
$31$	−0.338908	+	1.04305i	−0.0608697	+	0.187338i	−0.976867	−	0.213846i	$-0.931401\pi$
$31$	−0.338908	+	1.04305i	−0.0608697	+	0.187338i	0.915998	+	0.401183i	$0.131401\pi$
$32$	8.02306			1.41829
$33$	−2.58477	+	2.07821i	−0.449951	+	0.361770i
$34$	14.3457			2.46027
$35$		0			0
$36$	−1.97188	+	1.43266i	−0.328647	+	0.238776i
$37$	9.33514	+	6.78238i	1.53469	+	1.11502i	0.953560	+	0.301203i	$0.0973883\pi$
$37$	9.33514	+	6.78238i	1.53469	+	1.11502i	0.581128	+	0.813812i	$0.302612\pi$
$38$	0.747087	+	2.29930i	0.121194	+	0.372995i
$39$	−0.772198	−	2.37658i	−0.123651	−	0.380558i
$40$		0			0
$41$	0.754463	−	0.548149i	0.117827	−	0.0856066i	−0.527311	−	0.849672i	$-0.676800\pi$
$41$	0.754463	−	0.548149i	0.117827	−	0.0856066i	0.645138	+	0.764066i	$0.276800\pi$
$42$	−2.15875	+	6.64396i	−0.333103	+	1.02519i
$43$	0.552188			0.0842079			0.0421040	−	0.999113i	$-0.486594\pi$
$43$	0.552188			0.0842079			0.0421040	+	0.999113i	$0.486594\pi$
$44$	−6.76431	−	4.42643i	−1.01976	−	0.667309i
$45$		0			0
$46$	−3.83425	+	11.8006i	−0.565329	+	1.73990i
$47$	1.72666	−	1.25449i	0.251860	−	0.182987i	−0.454691	−	0.890649i	$-0.650250\pi$
$47$	1.72666	−	1.25449i	0.251860	−	0.182987i	0.706551	+	0.707663i	$0.250250\pi$
$48$	2.37360	+	1.72452i	0.342600	+	0.248913i
$49$	1.23546	+	3.80234i	0.176494	+	0.543192i
$50$		0			0
$51$	5.50956	+	4.00293i	0.771493	+	0.560522i
$52$	4.92751	−	3.58005i	0.683323	−	0.496463i
$53$	3.59560	−	11.0661i	0.493893	−	1.52005i	−0.324781	−	0.945789i	$-0.605291\pi$
$53$	3.59560	−	11.0661i	0.493893	−	1.52005i	0.818674	−	0.574258i	$-0.194709\pi$
$54$	−2.10651			−0.286660
$55$		0			0
$56$	−3.05549			−0.408307
$57$	−0.354657	+	1.09152i	−0.0469754	+	0.144575i
$58$	−1.91308	+	1.38993i	−0.251199	+	0.182507i
$59$	−6.79443	−	4.93644i	−0.884559	−	0.642670i	0.0498947	−	0.998754i	$-0.484111\pi$
$59$	−6.79443	−	4.93644i	−0.884559	−	0.642670i	−0.934454	+	0.356085i	$0.884111\pi$
$60$		0			0
$61$	−2.53800	−	7.81115i	−0.324957	−	1.00012i	−0.971460	−	0.237204i	$-0.923769\pi$
$61$	−2.53800	−	7.81115i	−0.324957	−	1.00012i	0.646503	−	0.762912i	$-0.276231\pi$
$62$	−1.86905	−	1.35794i	−0.237369	−	0.172459i
$63$	−2.68296	+	1.94929i	−0.338022	+	0.245587i
$64$	−3.40931	+	10.4928i	−0.426164	+	1.31160i
$65$		0			0
$66$	−2.48096	−	6.53116i	−0.305385	−	0.803930i
$67$	−4.15419			−0.507515			−0.253757	−	0.967268i	$-0.581666\pi$
$67$	−4.15419			−0.507515			−0.253757	+	0.967268i	$0.581666\pi$
$68$	−5.12938	+	15.7866i	−0.622029	+	1.91441i
$69$	−4.76532	+	3.46221i	−0.573677	+	0.416801i
$70$		0			0
$71$	3.87323	+	11.9206i	0.459668	+	1.41471i	0.865566	+	0.500795i	$0.166959\pi$
$71$	3.87323	+	11.9206i	0.459668	+	1.41471i	−0.405897	+	0.913919i	$0.633041\pi$
$72$	−0.284712	−	0.876254i	−0.0335537	−	0.103268i
$73$	4.64182	+	3.37248i	0.543284	+	0.394719i	0.825303	−	0.564690i	$-0.191004\pi$
$73$	4.64182	+	3.37248i	0.543284	+	0.394719i	−0.282019	+	0.959409i	$0.591004\pi$
$74$	−19.6646	+	14.2871i	−2.28596	+	1.66085i
$75$		0			0
$76$	−2.79736			−0.320880
$77$	−9.20358	−	6.02265i	−1.04885	−	0.686344i
$78$	5.26393			0.596022
$79$	−1.19514	+	3.67825i	−0.134463	+	0.413835i	−0.995506	−	0.0946970i	$-0.969812\pi$
$79$	−1.19514	+	3.67825i	−0.134463	+	0.413835i	0.861043	+	0.508532i	$0.169812\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.607052	+	1.86831i	0.0670377	+	0.206321i
$83$	−1.87899	−	5.78295i	−0.206246	−	0.634761i	−0.999660	−	0.0260781i	$-0.991698\pi$
$83$	−1.87899	−	5.78295i	−0.206246	−	0.634761i	0.793414	−	0.608683i	$-0.208302\pi$
$84$	−6.53941	−	4.75116i	−0.713508	−	0.518394i
$85$		0			0
$86$	−0.359446	+	1.10626i	−0.0387600	+	0.119291i
$87$	−1.12257			−0.120352
$88$	2.38147	−	1.91476i	0.253866	−	0.204114i
$89$	12.5950			1.33506			0.667531	−	0.744582i	$-0.267351\pi$
$89$	12.5950			1.33506			0.667531	+	0.744582i	$0.267351\pi$
$90$		0			0
$91$	6.70442	−	4.87105i	0.702814	−	0.510624i
$92$	−11.6149	−	8.43872i	−1.21094	−	0.879798i
$93$	−0.338908	−	1.04305i	−0.0351431	−	0.108159i
$94$	1.38930	+	4.27582i	0.143295	+	0.441017i
$95$		0			0
$96$	−6.49079	+	4.71583i	−0.662463	+	0.481308i
$97$	−0.886486	+	2.72832i	−0.0900090	+	0.277019i	−0.985921	−	0.167213i	$-0.946523\pi$
$97$	−0.886486	+	2.72832i	−0.0900090	+	0.277019i	0.895912	+	0.444232i	$0.146523\pi$
$98$	−8.42187			−0.850737
$99$	0.869581	−	3.20060i	0.0873962	−	0.321672i
$100$		0			0
$101$	3.05000	−	9.38694i	0.303487	−	0.934036i	−0.676751	−	0.736212i	$-0.736613\pi$
$101$	3.05000	−	9.38694i	0.303487	−	0.934036i	0.980238	−	0.197824i	$-0.0633873\pi$
$102$	−11.6059	+	8.43221i	−1.14916	+	0.834913i
$103$	−6.24523	−	4.53743i	−0.615361	−	0.447086i	0.235937	−	0.971768i	$-0.424184\pi$
$103$	−6.24523	−	4.53743i	−0.615361	−	0.447086i	−0.851298	+	0.524682i	$0.824184\pi$
$104$	0.711463	+	2.18966i	0.0697647	+	0.214714i
$105$		0			0
$106$	19.8294	+	14.4069i	1.92600	+	1.39932i
$107$	12.5490	−	9.11737i	1.21316	−	0.881409i	0.217642	−	0.976029i	$-0.430163\pi$
$107$	12.5490	−	9.11737i	1.21316	−	0.881409i	0.995514	+	0.0946194i	$0.0301634\pi$
$108$	0.753192	−	2.31809i	0.0724760	−	0.223058i
$109$	6.79834			0.651163			0.325581	−	0.945514i	$-0.394440\pi$
$109$	6.79834			0.651163			0.325581	+	0.945514i	$0.394440\pi$
$110$		0			0
$111$	−11.5389			−1.09522
$112$	−3.00670	+	9.25367i	−0.284106	+	0.874390i
$113$	0.243910	−	0.177211i	0.0229451	−	0.0166706i	−0.576254	−	0.817271i	$-0.695486\pi$
$113$	0.243910	−	0.177211i	0.0229451	−	0.0166706i	0.599199	+	0.800600i	$0.295486\pi$
$114$	−1.95590	−	1.42104i	−0.183187	−	0.133093i
$115$		0			0
$116$	−0.845508	−	2.60221i	−0.0785034	−	0.241609i
$117$	2.02164	+	1.46881i	0.186901	+	0.135791i
$118$	14.3125	−	10.3987i	1.31757	−	0.957274i
$119$	−6.97909	+	21.4794i	−0.639772	+	1.96902i
$120$		0			0
$121$	10.9475	−	1.07343i	0.995227	−	0.0975844i
$122$	17.3010			1.56636
$123$	−0.288179	+	0.886924i	−0.0259842	+	0.0799713i
$124$	2.16262	−	1.57124i	0.194209	−	0.141101i
$125$		0			0
$126$	−2.15875	−	6.64396i	−0.192317	−	0.591891i
$127$	−2.07208	−	6.37720i	−0.183867	−	0.565885i	0.816060	−	0.577968i	$-0.196154\pi$
$127$	−2.07208	−	6.37720i	−0.183867	−	0.565885i	−0.999927	+	0.0120823i	$0.996154\pi$
$128$	−5.82050	−	4.22884i	−0.514464	−	0.373780i
$129$	−0.446730	+	0.324568i	−0.0393324	+	0.0285766i
$130$		0			0
$131$	−8.07729			−0.705716			−0.352858	−	0.935677i	$-0.614790\pi$
$131$	−8.07729			−0.705716			−0.352858	+	0.935677i	$0.614790\pi$
$132$	8.07423	−	0.394902i	0.702771	−	0.0343718i
$133$	−3.80612			−0.330033
$134$	2.70416	−	8.32254i	0.233604	−	0.718958i
$135$		0			0
$136$	−5.07622	−	3.68809i	−0.435282	−	0.316251i
$137$	−1.98939	−	6.12273i	−0.169965	−	0.523100i	0.829402	−	0.558652i	$-0.188681\pi$
$137$	−1.98939	−	6.12273i	−0.169965	−	0.523100i	−0.999368	+	0.0355519i	$0.988681\pi$
$138$	−3.83425	−	11.8006i	−0.326393	−	1.00453i
$139$	−5.64344	−	4.10020i	−0.478670	−	0.347774i	0.322140	−	0.946692i	$-0.395598\pi$
$139$	−5.64344	−	4.10020i	−0.478670	−	0.347774i	−0.800811	+	0.598918i	$0.795598\pi$
$140$		0			0
$141$	−0.659526	+	2.02981i	−0.0555421	+	0.170941i
$142$	−26.4031			−2.21570
$143$	−2.17298	+	7.99793i	−0.181714	+	0.668820i
$144$	−2.93393			−0.244495
$145$		0			0
$146$	−9.77805	+	7.10417i	−0.809237	+	0.587945i
$147$	−3.23447	−	2.34998i	−0.266774	−	0.193823i
$148$	−8.69099	−	26.7481i	−0.714395	−	2.19868i
$149$	−5.87766	−	18.0896i	−0.481516	−	1.48196i	−0.836963	−	0.547259i	$-0.815671\pi$
$149$	−5.87766	−	18.0896i	−0.481516	−	1.48196i	0.355447	−	0.934696i	$-0.384329\pi$
$150$		0			0
$151$	−3.15582	+	2.29284i	−0.256817	+	0.186589i	−0.708743	−	0.705467i	$-0.750737\pi$
$151$	−3.15582	+	2.29284i	−0.256817	+	0.186589i	0.451925	+	0.892056i	$0.350737\pi$
$152$	0.326762	−	1.00567i	0.0265039	−	0.0815707i
$153$	−6.81019			−0.550571
$154$	18.0569	−	14.5181i	1.45506	−	1.16990i
$155$		0			0
$156$	−1.88214	+	5.79264i	−0.150692	+	0.463782i
$157$	14.8732	−	10.8060i	1.18701	−	0.862413i	0.194065	−	0.980989i	$-0.437833\pi$
$157$	14.8732	−	10.8060i	1.18701	−	0.862413i	0.992945	+	0.118575i	$0.0378327\pi$
$158$	−6.59107	−	4.78869i	−0.524357	−	0.380968i
$159$	3.59560	+	11.0661i	0.285149	+	0.877600i
$160$		0			0
$161$	−15.8034	−	11.4818i	−1.24548	−	0.904894i
$162$	1.70420	−	1.23818i	0.133895	−	0.0972802i
$163$	−5.43005	+	16.7120i	−0.425314	+	1.30898i	0.477379	+	0.878698i	$0.341587\pi$
$163$	−5.43005	+	16.7120i	−0.425314	+	1.30898i	−0.902693	+	0.430285i	$0.858413\pi$
$164$	−2.27302			−0.177493
$165$		0			0
$166$	12.8087			0.994151
$167$	−3.73220	+	11.4865i	−0.288807	+	0.888855i	0.696425	+	0.717629i	$0.254773\pi$
$167$	−3.73220	+	11.4865i	−0.288807	+	0.888855i	−0.985232	+	0.171226i	$0.945227\pi$
$168$	2.47194	−	1.79597i	0.190715	−	0.138562i
$169$	5.46537	+	3.97083i	0.420413	+	0.305448i
$170$		0			0
$171$	−0.354657	−	1.09152i	−0.0271213	−	0.0834707i
$172$	−1.08885	−	0.791097i	−0.0830241	−	0.0603206i
$173$	19.6135	−	14.2500i	1.49119	−	1.08341i	0.517454	−	0.855711i	$-0.326880\pi$
$173$	19.6135	−	14.2500i	1.49119	−	1.08341i	0.973732	−	0.227698i	$-0.0731200\pi$
$174$	0.730731	−	2.24896i	0.0553966	−	0.170493i
$175$		0			0
$176$	−3.45547	−	9.09656i	−0.260466	−	0.685679i
$177$	8.39837			0.631260
$178$	−8.19865	+	25.2329i	−0.614515	+	1.89128i
$179$	16.1310	−	11.7198i	1.20569	−	0.875982i	0.210854	−	0.977517i	$-0.432375\pi$
$179$	16.1310	−	11.7198i	1.20569	−	0.875982i	0.994832	+	0.101535i	$0.0323754\pi$
$180$		0			0
$181$	−1.58615	−	4.88168i	−0.117898	−	0.362852i	0.874643	−	0.484768i	$-0.161096\pi$
$181$	−1.58615	−	4.88168i	−0.117898	−	0.362852i	−0.992540	+	0.121916i	$0.961096\pi$
$182$	5.39448	+	16.6025i	0.399865	+	1.23066i
$183$	6.64456	+	4.82756i	0.491180	+	0.356863i
$184$	4.39052	−	3.18990i	0.323674	−	0.235163i
$185$		0			0
$186$	2.31027			0.169397
$187$	−8.02076	−	21.1148i	−0.586536	−	1.54406i
$188$	−5.20204			−0.379397
$189$	1.02480	−	3.15401i	0.0745433	−	0.229421i
$190$		0			0
$191$	2.27606	+	1.65365i	0.164690	+	0.119654i	0.667078	−	0.744988i	$-0.267545\pi$
$191$	2.27606	+	1.65365i	0.164690	+	0.119654i	−0.502388	+	0.864642i	$0.667545\pi$
$192$	−3.40931	−	10.4928i	−0.246046	−	0.757252i
$193$	−5.96502	−	18.3584i	−0.429371	−	1.32147i	−0.898746	−	0.438470i	$-0.855520\pi$
$193$	−5.96502	−	18.3584i	−0.429371	−	1.32147i	0.469374	−	0.882999i	$-0.344480\pi$
$194$	−4.88889	−	3.55199i	−0.351002	−	0.255018i
$195$		0			0
$196$	3.01128	−	9.26776i	0.215091	−	0.661983i
$197$	3.57956			0.255033			0.127516	−	0.991836i	$-0.459299\pi$
$197$	3.57956			0.255033			0.127516	+	0.991836i	$0.459299\pi$
$198$	5.84606	+	3.82555i	0.415461	+	0.271870i
$199$	12.7087			0.900893			0.450447	−	0.892803i	$-0.351265\pi$
$199$	12.7087			0.900893			0.450447	+	0.892803i	$0.351265\pi$
$200$		0			0
$201$	3.36081	−	2.44177i	0.237053	−	0.172229i
$202$	16.8205	+	12.2208i	1.18349	+	0.859853i
$203$	−1.15041	−	3.54059i	−0.0807427	−	0.248500i
$204$	−5.12938	−	15.7866i	−0.359129	−	1.10528i
$205$		0			0
$206$	13.1556	−	9.55813i	0.916597	−	0.665947i
$207$	1.82019	−	5.60197i	0.126512	−	0.389364i
$208$	7.33157			0.508353
$209$	2.96652	−	2.38515i	0.205199	−	0.164984i
$210$		0			0
$211$	−1.08007	+	3.32412i	−0.0743552	+	0.228842i	−0.981326	−	0.192352i	$-0.938389\pi$
$211$	−1.08007	+	3.32412i	−0.0743552	+	0.228842i	0.906971	+	0.421193i	$0.138389\pi$
$212$	−22.9440	+	16.6698i	−1.57580	+	1.14489i
$213$	−10.1403	−	7.36733i	−0.694799	−	0.504801i
$214$	10.0971	+	31.0757i	0.690223	+	2.12429i
$215$		0			0
$216$	0.745386	+	0.541555i	0.0507171	+	0.0368481i
$217$	2.94249	−	2.13784i	0.199749	−	0.145126i
$218$	−4.42536	+	13.6199i	−0.299723	+	0.922453i
$219$	−5.73761			−0.387712
$220$		0			0
$221$	17.0179			1.14475
$222$	7.51119	−	23.1171i	0.504118	−	1.55152i
$223$	4.21140	−	3.05976i	0.282016	−	0.204897i	−0.437780	−	0.899082i	$-0.644235\pi$
$223$	4.21140	−	3.05976i	0.282016	−	0.204897i	0.719796	+	0.694185i	$0.244235\pi$
$224$	−21.5256	−	15.6392i	−1.43824	−	1.04494i
$225$		0			0
$226$	0.196253	+	0.604005i	0.0130546	+	0.0401778i
$227$	7.84944	+	5.70295i	0.520985	+	0.378518i	0.816975	−	0.576673i	$-0.195649\pi$
$227$	7.84944	+	5.70295i	0.520985	+	0.378518i	−0.295990	+	0.955191i	$0.595649\pi$
$228$	2.26312	−	1.64425i	0.149878	−	0.108893i
$229$	5.71715	−	17.5956i	0.377800	−	1.16275i	−0.563770	−	0.825932i	$-0.690650\pi$
$229$	5.71715	−	17.5956i	0.377800	−	1.16275i	0.941570	−	0.336817i	$-0.109350\pi$
$230$		0			0
$231$	10.9859	−	0.537307i	0.722818	−	0.0353522i
$232$	1.03427			0.0679034
$233$	4.62115	−	14.2224i	0.302741	−	0.931742i	−0.677769	−	0.735275i	$-0.737053\pi$
$233$	4.62115	−	14.2224i	0.302741	−	0.931742i	0.980510	−	0.196467i	$-0.0629469\pi$
$234$	−4.25861	+	3.09406i	−0.278394	+	0.202265i
$235$		0			0
$236$	6.32559	+	19.4682i	0.411761	+	1.26727i
$237$	−1.19514	−	3.67825i	−0.0776324	−	0.238928i
$238$	−38.4891	−	27.9639i	−2.49488	−	1.81263i
$239$	1.21932	−	0.885887i	0.0788712	−	0.0573033i	−0.547651	−	0.836707i	$-0.684478\pi$
$239$	1.21932	−	0.885887i	0.0788712	−	0.0573033i	0.626522	+	0.779404i	$0.284478\pi$
$240$		0			0
$241$	−7.09571			−0.457075			−0.228537	−	0.973535i	$-0.573394\pi$
$241$	−7.09571			−0.457075			−0.228537	+	0.973535i	$0.573394\pi$
$242$	−4.97573	+	22.6311i	−0.319852	+	1.45478i
$243$	1.00000			0.0641500
$244$	−6.18607	+	19.0388i	−0.396022	+	1.21883i
$245$		0			0
$246$	−1.58928	−	1.15468i	−0.101329	−	0.0736198i
$247$	0.886246	+	2.72758i	0.0563905	+	0.173552i
$248$	0.312252	+	0.961014i	0.0198280	+	0.0610244i
$249$	4.91927	+	3.57406i	0.311746	+	0.226497i
$250$		0			0
$251$	−4.22692	+	13.0091i	−0.266801	+	0.821129i	0.724472	+	0.689304i	$0.242084\pi$
$251$	−4.22692	+	13.0091i	−0.266801	+	0.821129i	−0.991273	+	0.131825i	$0.957916\pi$
$252$	8.08315			0.509191
$253$	19.5125	−	0.954333i	1.22674	−	0.0599984i
$254$	14.1250			0.886279
$255$		0			0
$256$	−5.59047	+	4.06172i	−0.349405	+	0.253857i
$257$	−6.71817	−	4.88104i	−0.419068	−	0.304471i	0.358195	−	0.933647i	$-0.383392\pi$
$257$	−6.71817	−	4.88104i	−0.419068	−	0.304471i	−0.777263	+	0.629176i	$0.783392\pi$
$258$	−0.359446	−	1.10626i	−0.0223781	−	0.0688727i
$259$	−11.8250	−	36.3937i	−0.734773	−	2.26140i
$260$		0			0
$261$	0.908175	−	0.659827i	0.0562146	−	0.0408423i
$262$	5.25789	−	16.1821i	0.324834	−	0.999735i
$263$	−11.1345			−0.686582			−0.343291	−	0.939229i	$-0.611542\pi$
$263$	−11.1345			−0.686582			−0.343291	+	0.939229i	$0.611542\pi$
$264$	−0.801187	+	2.94887i	−0.0493096	+	0.181490i
$265$		0			0
$266$	2.47759	−	7.62522i	0.151910	−	0.467532i
$267$	−10.1895	+	7.40313i	−0.623589	+	0.453064i
$268$	8.19157	+	5.95153i	0.500380	+	0.363547i
$269$	7.03209	+	21.6426i	0.428754	+	1.31957i	0.899353	+	0.437223i	$0.144038\pi$
$269$	7.03209	+	21.6426i	0.428754	+	1.31957i	−0.470599	+	0.882347i	$0.655962\pi$
$270$		0			0
$271$	−6.30586	−	4.58148i	−0.383054	−	0.278305i	0.379549	−	0.925172i	$-0.376079\pi$
$271$	−6.30586	−	4.58148i	−0.383054	−	0.278305i	−0.762603	+	0.646867i	$0.776079\pi$
$272$	−16.1647	+	11.7443i	−0.980128	+	0.712105i
$273$	−2.56086	+	7.88152i	−0.154990	+	0.477011i
$274$	13.5613			0.819269
$275$		0			0
$276$	14.3568			0.864179
$277$	−2.92552	+	9.00383i	−0.175778	+	0.540988i	−0.999668	−	0.0257612i	$-0.991799\pi$
$277$	−2.92552	+	9.00383i	−0.175778	+	0.540988i	0.823891	+	0.566749i	$0.191799\pi$
$278$	11.8880	−	8.63711i	0.712992	−	0.518019i
$279$	0.887273	+	0.644641i	0.0531196	+	0.0385937i
$280$		0			0
$281$	9.67271	+	29.7696i	0.577026	+	1.77590i	0.629175	+	0.777263i	$0.283393\pi$
$281$	9.67271	+	29.7696i	0.577026	+	1.77590i	−0.0521495	+	0.998639i	$0.516607\pi$
$282$	−3.63723	−	2.64260i	−0.216594	−	0.157365i
$283$	−19.7500	+	14.3492i	−1.17402	+	0.852972i	−0.991484	−	0.130228i	$-0.958429\pi$
$283$	−19.7500	+	14.3492i	−1.17402	+	0.852972i	−0.182531	+	0.983200i	$0.558429\pi$
$284$	9.44055	−	29.0550i	0.560194	−	1.72410i
$285$		0			0
$286$	−14.6086	−	9.55960i	−0.863826	−	0.565271i
$287$	−3.09270			−0.182556
$288$	2.47926	−	7.63038i	0.146092	−	0.449624i
$289$	−23.7678	+	17.2684i	−1.39811	+	1.01579i
$290$		0			0
$291$	−0.886486	−	2.72832i	−0.0519667	−	0.159937i
$292$	−4.32152	−	13.3003i	−0.252898	−	0.778340i
$293$	9.56230	+	6.94742i	0.558636	+	0.405873i	0.830959	−	0.556333i	$-0.187792\pi$
$293$	9.56230	+	6.94742i	0.558636	+	0.405873i	−0.272324	+	0.962206i	$0.587792\pi$
$294$	6.81343	−	4.95025i	0.397367	−	0.288704i
$295$		0			0
$296$	10.6313			0.617933
$297$	1.17776	+	3.10047i	0.0683405	+	0.179907i
$298$	40.0669			2.32101
$299$	−4.54845	+	13.9987i	−0.263044	+	0.809565i
$300$		0			0
$301$	−1.48150	−	1.07637i	−0.0853923	−	0.0620412i
$302$	−2.53922	−	7.81492i	−0.146116	−	0.449698i
$303$	3.05000	+	9.38694i	0.175218	+	0.539266i
$304$	−2.72417	−	1.97922i	−0.156242	−	0.113516i
$305$		0			0
$306$	4.43307	−	13.6436i	0.253422	−	0.779952i
$307$	−22.3217			−1.27396			−0.636982	−	0.770878i	$-0.719818\pi$
$307$	−22.3217			−1.27396			−0.636982	+	0.770878i	$0.719818\pi$
$308$	9.52000	+	25.0615i	0.542453	+	1.42801i
$309$	7.71953			0.439149
$310$		0			0
$311$	15.7624	−	11.4521i	0.893804	−	0.649386i	−0.0430633	−	0.999072i	$-0.513712\pi$
$311$	15.7624	−	11.4521i	0.893804	−	0.649386i	0.936867	+	0.349686i	$0.113712\pi$
$312$	−1.86264	−	1.35328i	−0.105451	−	0.0766146i
$313$	−5.36228	−	16.5034i	−0.303094	−	0.932827i	−0.980382	−	0.197109i	$-0.936845\pi$
$313$	−5.36228	−	16.5034i	−0.303094	−	0.932827i	0.677288	−	0.735718i	$-0.263155\pi$
$314$	11.9672	+	36.8312i	0.675348	+	2.07851i
$315$		0			0
$316$	7.62634	−	5.54086i	0.429015	−	0.311698i
$317$	−0.256706	+	0.790059i	−0.0144180	+	0.0443741i	−0.958007	−	0.286746i	$-0.907426\pi$
$317$	−0.256706	+	0.790059i	−0.0144180	+	0.0443741i	0.943589	+	0.331120i	$0.107426\pi$
$318$	−24.5105			−1.37448
$319$	3.11538	+	2.03865i	0.174428	+	0.114142i
$320$		0			0
$321$	−4.79328	+	14.7522i	−0.267535	+	0.823388i
$322$	33.2899	−	24.1865i	1.85518	−	1.34786i
$323$	−6.32328	−	4.59413i	−0.351837	−	0.255624i
$324$	0.753192	+	2.31809i	0.0418440	+	0.128783i
$325$		0			0
$326$	−29.9462	−	21.7572i	−1.65857	−	1.20502i
$327$	−5.49997	+	3.99596i	−0.304149	+	0.220977i
$328$	0.265513	−	0.817166i	0.0146605	−	0.0451205i
$329$	−7.07794			−0.390220
$330$		0			0
$331$	−31.5311			−1.73311			−0.866554	−	0.499084i	$-0.833670\pi$
$331$	−31.5311			−1.73311			−0.866554	+	0.499084i	$0.833670\pi$
$332$	−4.57982	+	14.0953i	−0.251351	+	0.773577i
$333$	9.33514	−	6.78238i	0.511563	−	0.371672i
$334$	−20.5828	−	14.9543i	−1.12624	−	0.818261i
$335$		0			0
$336$	−3.00670	−	9.25367i	−0.164029	−	0.504829i
$337$	−13.1335	−	9.54207i	−0.715429	−	0.519790i	0.169491	−	0.985532i	$-0.445788\pi$
$337$	−13.1335	−	9.54207i	−0.715429	−	0.519790i	−0.884921	+	0.465742i	$0.845788\pi$
$338$	−11.5129	+	8.36458i	−0.626217	+	0.454973i
$339$	−0.0931652	+	0.286733i	−0.00506004	+	0.0155732i
$340$		0			0
$341$	−0.953695	+	3.51019i	−0.0516455	+	0.190087i
$342$	2.41763			0.130730
$343$	−3.07643	+	9.46829i	−0.166112	+	0.511239i
$344$	0.411594	−	0.299040i	0.0221916	−	0.0161232i
$345$		0			0
$346$	15.7813	+	48.5698i	0.848408	+	2.61113i
$347$	3.84726	+	11.8406i	0.206532	+	0.635639i	0.999647	+	0.0265674i	$0.00845767\pi$
$347$	3.84726	+	11.8406i	0.206532	+	0.635639i	−0.793115	+	0.609071i	$0.791542\pi$
$348$	2.21357	+	1.60825i	0.118660	+	0.0862113i
$349$	−26.3980	+	19.1793i	−1.41305	+	1.02664i	−0.420182	+	0.907440i	$0.638034\pi$
$349$	−26.3980	+	19.1793i	−1.41305	+	1.02664i	−0.992870	+	0.119203i	$0.961966\pi$
$350$		0			0
$351$	−2.49889			−0.133381
$352$	26.5777	−	1.29989i	1.41660	−	0.0692842i
$353$	15.7921			0.840530			0.420265	−	0.907402i	$-0.361937\pi$
$353$	15.7921			0.840530			0.420265	+	0.907402i	$0.361937\pi$
$354$	−5.46690	+	16.8254i	−0.290562	+	0.894259i
$355$		0			0
$356$	−24.8358	−	18.0443i	−1.31629	−	0.956343i
$357$	−6.97909	−	21.4794i	−0.369373	−	1.13681i
$358$	12.9792	+	39.9460i	0.685974	+	2.11121i
$359$	−14.6935	−	10.6755i	−0.775494	−	0.563429i	0.128129	−	0.991757i	$-0.459103\pi$
$359$	−14.6935	−	10.6755i	−0.775494	−	0.563429i	−0.903623	+	0.428328i	$0.859103\pi$
$360$		0			0
$361$	−5.46429	+	16.8173i	−0.287594	+	0.885123i
$362$	10.8125			0.568292
$363$	−8.22577	+	7.30320i	−0.431741	+	0.383319i
$364$	−20.1989			−1.05871
$365$		0			0
$366$	−13.9968	+	10.1693i	−0.731626	+	0.531558i
$367$	−0.381893	−	0.277462i	−0.0199347	−	0.0144834i	0.577773	−	0.816197i	$-0.303922\pi$
$367$	−0.381893	−	0.277462i	−0.0199347	−	0.0144834i	−0.597708	+	0.801714i	$0.703922\pi$
$368$	−5.34032	−	16.4358i	−0.278383	−	0.856776i
$369$	−0.288179	−	0.886924i	−0.0150020	−	0.0461714i
$370$		0			0
$371$	−31.2179	+	22.6811i	−1.62075	+	1.17755i
$372$	−0.826048	+	2.54231i	−0.0428286	+	0.131813i
$373$	−15.4102			−0.797910			−0.398955	−	0.916970i	$-0.630627\pi$
$373$	−15.4102			−0.797910			−0.398955	+	0.916970i	$0.630627\pi$
$374$	47.5226	−	2.32428i	2.45733	−	0.120186i
$375$		0			0
$376$	0.607653	−	1.87017i	0.0313373	−	0.0964464i
$377$	−2.26942	+	1.64883i	−0.116881	+	0.0849192i
$378$	5.65169	+	4.10619i	0.290692	+	0.211200i
$379$	−5.95617	−	18.3312i	−0.305948	−	0.941611i	−0.979322	−	0.202309i	$-0.935156\pi$
$379$	−5.95617	−	18.3312i	−0.305948	−	0.941611i	0.673374	−	0.739302i	$-0.264844\pi$
$380$		0			0
$381$	5.42477	+	3.94133i	0.277920	+	0.201920i
$382$	−4.79454	+	3.48344i	−0.245310	+	0.178228i
$383$	2.30163	−	7.08369i	0.117608	−	0.361960i	−0.874874	−	0.484350i	$-0.839056\pi$
$383$	2.30163	−	7.08369i	0.117608	−	0.361960i	0.992482	+	0.122390i	$0.0390560\pi$
$384$	7.19453			0.367144
$385$		0			0
$386$	40.6624			2.06966
$387$	0.170636	−	0.525162i	0.00867390	−	0.0266955i
$388$	5.65680	−	4.10990i	0.287180	−	0.208649i
$389$	0.577492	+	0.419572i	0.0292800	+	0.0212732i	0.602329	−	0.798248i	$-0.294240\pi$
$389$	0.577492	+	0.419572i	0.0292800	+	0.0212732i	−0.573049	+	0.819521i	$0.694240\pi$
$390$		0			0
$391$	−12.3958	−	38.1505i	−0.626885	−	1.92935i
$392$	2.98007	+	2.16515i	0.150516	+	0.109356i
$393$	6.53467	−	4.74771i	0.329630	−	0.239490i
$394$	−2.33010	+	7.17132i	−0.117389	+	0.361286i
$395$		0			0
$396$	−6.30007	+	5.06539i	−0.316590	+	0.254546i
$397$	0.764171			0.0383526			0.0191763	−	0.999816i	$-0.493896\pi$
$397$	0.764171			0.0383526			0.0191763	+	0.999816i	$0.493896\pi$
$398$	−8.27267	+	25.4607i	−0.414672	+	1.27623i
$399$	3.07922	−	2.23718i	0.154154	−	0.111999i
$400$		0			0
$401$	−4.86839	−	14.9834i	−0.243116	−	0.748234i	−0.995941	−	0.0900128i	$-0.971309\pi$
$401$	−4.86839	−	14.9834i	−0.243116	−	0.748234i	0.752825	−	0.658221i	$-0.228691\pi$
$402$	2.70416	+	8.32254i	0.134871	+	0.415091i
$403$	−2.21719	−	1.61089i	−0.110446	−	0.0802439i
$404$	−19.4625	+	14.1403i	−0.968296	+	0.703508i
$405$		0			0
$406$	7.84210			0.389197
$407$	32.0231	+	20.9553i	1.58732	+	1.03871i
$408$	6.27456			0.310637
$409$	−0.809935	+	2.49272i	−0.0400487	+	0.123257i	−0.969082	−	0.246739i	$-0.920641\pi$
$409$	−0.809935	+	2.49272i	−0.0400487	+	0.123257i	0.929033	+	0.369996i	$0.120641\pi$
$410$		0			0
$411$	5.20830	+	3.78405i	0.256907	+	0.186654i
$412$	5.81429	+	17.8945i	0.286450	+	0.881601i
$413$	8.60666	+	26.4886i	0.423506	+	1.30342i
$414$	10.0382	+	7.29318i	0.493350	+	0.358440i
$415$		0			0
$416$	−6.19539	+	19.0674i	−0.303754	+	0.934858i
$417$	6.97567			0.341600
$418$	2.84738	+	7.49576i	0.139270	+	0.366630i
$419$	−18.0078			−0.879737			−0.439868	−	0.898062i	$-0.644975\pi$
$419$	−18.0078			−0.879737			−0.439868	+	0.898062i	$0.644975\pi$
$420$		0			0
$421$	−0.947495	+	0.688395i	−0.0461781	+	0.0335503i	−0.610635	−	0.791912i	$-0.709086\pi$
$421$	−0.947495	+	0.688395i	−0.0461781	+	0.0335503i	0.564457	+	0.825463i	$0.309086\pi$
$422$	−5.95650	−	4.32765i	−0.289958	−	0.210667i
$423$	−0.659526	−	2.02981i	−0.0320673	−	0.0986929i
$424$	−3.31280	−	10.1957i	−0.160884	−	0.495149i
$425$		0			0
$426$	21.3606	−	15.5193i	1.03492	−	0.751915i
$427$	−8.41683	+	25.9043i	−0.407319	+	1.25360i
$428$	−37.8072			−1.82748
$429$	−2.94308	−	7.74771i	−0.142093	−	0.374063i
$430$		0			0
$431$	10.8441	−	33.3746i	0.522340	−	1.60760i	−0.247177	−	0.968970i	$-0.579503\pi$
$431$	10.8441	−	33.3746i	0.522340	−	1.60760i	0.769517	−	0.638626i	$-0.220497\pi$
$432$	2.37360	−	1.72452i	0.114200	−	0.0829712i
$433$	14.7452	+	10.7130i	0.708608	+	0.514834i	0.882724	−	0.469891i	$-0.155707\pi$
$433$	14.7452	+	10.7130i	0.708608	+	0.514834i	−0.174116	+	0.984725i	$0.555707\pi$
$434$	2.36757	+	7.28663i	0.113647	+	0.349769i
$435$		0			0
$436$	−13.4055	−	9.73969i	−0.642009	−	0.466446i
$437$	5.46912	−	3.97355i	0.261624	−	0.190081i
$438$	3.73488	−	11.4948i	0.178460	−	0.549242i
$439$	−19.8155			−0.945743			−0.472871	−	0.881131i	$-0.656782\pi$
$439$	−19.8155			−0.945743			−0.472871	+	0.881131i	$0.656782\pi$
$440$		0			0
$441$	3.99802			0.190382
$442$	−11.0777	+	34.0938i	−0.526914	+	1.62168i
$443$	−13.5012	+	9.80922i	−0.641463	+	0.466050i	−0.860352	−	0.509700i	$-0.829757\pi$
$443$	−13.5012	+	9.80922i	−0.641463	+	0.466050i	0.218890	+	0.975750i	$0.429757\pi$
$444$	22.7533	+	16.5312i	1.07982	+	0.784538i
$445$		0			0
$446$	3.38856	+	10.4289i	0.160453	+	0.493823i
$447$	15.3879	+	11.1800i	0.727823	+	0.528794i
$448$	29.6005	−	21.5061i	1.39849	−	1.01607i
$449$	−4.07811	+	12.5511i	−0.192458	+	0.592325i	0.807539	+	0.589815i	$0.200799\pi$
$449$	−4.07811	+	12.5511i	−0.192458	+	0.592325i	−0.999997	+	0.00251063i	$0.999201\pi$
$450$		0			0
$451$	2.41047	−	1.93807i	0.113505	−	0.0912603i
$452$	−0.734843			−0.0345641
$453$	1.20542	−	3.70989i	0.0566354	−	0.174306i
$454$	−16.5349	+	12.0133i	−0.776022	+	0.563813i
$455$		0			0
$456$	0.326762	+	1.00567i	0.0153020	+	0.0470948i
$457$	6.57194	+	20.2264i	0.307423	+	0.946149i	0.978762	+	0.204999i	$0.0657192\pi$
$457$	6.57194	+	20.2264i	0.307423	+	0.946149i	−0.671340	+	0.741150i	$0.734281\pi$
$458$	31.5296	+	22.9076i	1.47328	+	1.07040i
$459$	5.50956	−	4.00293i	0.257164	−	0.186841i
$460$		0			0
$461$	−20.0772			−0.935086			−0.467543	−	0.883970i	$-0.654861\pi$
$461$	−20.0772			−0.935086			−0.467543	+	0.883970i	$0.654861\pi$
$462$	−6.07478	+	22.3590i	−0.282624	+	1.04023i
$463$	−0.962526			−0.0447324			−0.0223662	−	0.999750i	$-0.507120\pi$
$463$	−0.962526			−0.0447324			−0.0223662	+	0.999750i	$0.507120\pi$
$464$	1.01776	−	3.13234i	0.0472482	−	0.145415i
$465$		0			0
$466$	25.4852	+	18.5161i	1.18058	+	0.857742i
$467$	−4.60838	−	14.1831i	−0.213250	−	0.656317i	−0.999273	−	0.0381194i	$-0.987863\pi$
$467$	−4.60838	−	14.1831i	−0.213250	−	0.656317i	0.786023	−	0.618197i	$-0.212137\pi$
$468$	−1.88214	−	5.79264i	−0.0870020	−	0.267765i
$469$	11.1455	+	8.09771i	0.514653	+	0.373917i
$470$		0			0
$471$	−5.68106	+	17.4845i	−0.261769	+	0.805643i
$472$	−7.73783			−0.356162
$473$	1.82922	−	0.0894649i	0.0841074	−	0.00411360i
$474$	8.14701			0.374204
$475$		0			0
$476$	44.5346	−	32.3563i	2.04124	−	1.48305i
$477$	−9.41340	−	6.83923i	−0.431010	−	0.313147i
$478$	0.981082	+	3.01946i	0.0448737	+	0.138107i
$479$	−0.146946	−	0.452253i	−0.00671413	−	0.0206640i	0.947643	−	0.319331i	$-0.103458\pi$
$479$	−0.146946	−	0.452253i	−0.00671413	−	0.0206640i	−0.954357	+	0.298667i	$0.903458\pi$
$480$		0			0
$481$	−23.3274	+	16.9484i	−1.06364	+	0.772780i
$482$	4.61893	−	14.2156i	0.210387	−	0.647503i
$483$	19.5340			0.888829
$484$	−23.1250	−	13.5673i	−1.05114	−	0.616697i
$485$		0			0
$486$	−0.650947	+	2.00341i	−0.0295276	+	0.0908765i
$487$	28.6011	−	20.7799i	1.29604	−	0.941629i	0.296132	−	0.955147i	$-0.404303\pi$
$487$	28.6011	−	20.7799i	1.29604	−	0.941629i	0.999909	+	0.0135183i	$0.00430313\pi$
$488$	−6.12196	−	4.44786i	−0.277128	−	0.201345i
$489$	−5.43005	−	16.7120i	−0.245555	−	0.755741i
$490$		0			0
$491$	24.3779	+	17.7116i	1.10016	+	0.799314i	0.981086	−	0.193572i	$-0.0620072\pi$
$491$	24.3779	+	17.7116i	1.10016	+	0.799314i	0.119075	+	0.992885i	$0.462007\pi$
$492$	1.83891	−	1.33605i	0.0829047	−	0.0602338i
$493$	2.36240	−	7.27072i	0.106397	−	0.327457i
$494$	−6.04137			−0.271814
$495$		0			0
$496$	3.21773			0.144480
$497$	12.8449	−	39.5326i	0.576173	−	1.77328i
$498$	−10.3625	+	7.52879i	−0.464354	+	0.337373i
$499$	29.5127	+	21.4422i	1.32117	+	0.959887i	0.999917	+	0.0128935i	$0.00410424\pi$
$499$	29.5127	+	21.4422i	1.32117	+	0.959887i	0.321254	+	0.946993i	$0.395896\pi$
$500$		0			0
$501$	−3.73220	−	11.4865i	−0.166743	−	0.513181i
$502$	−23.3111	−	16.9365i	−1.04043	−	0.755914i
$503$	−12.4792	+	9.06666i	−0.556420	+	0.404262i	−0.830147	−	0.557545i	$-0.811743\pi$
$503$	−12.4792	+	9.06666i	−0.556420	+	0.404262i	0.273727	+	0.961807i	$0.411743\pi$
$504$	−0.944199	+	2.90595i	−0.0420580	+	0.129441i
$505$		0			0
$506$	−10.7897	+	39.7127i	−0.479659	+	1.76544i
$507$	−6.75557			−0.300025
$508$	−5.05045	+	15.5437i	−0.224077	+	0.689639i
$509$	−10.2238	+	7.42806i	−0.453164	+	0.329243i	−0.790844	−	0.612018i	$-0.790358\pi$
$509$	−10.2238	+	7.42806i	−0.453164	+	0.329243i	0.337680	+	0.941261i	$0.390358\pi$
$510$		0			0
$511$	−5.87991	−	18.0965i	−0.260112	−	0.800542i
$512$	−8.94464	−	27.5288i	−0.395301	−	1.21661i
$513$	0.928503	+	0.674597i	0.0409944	+	0.0297842i
$514$	14.1519	−	10.2819i	0.624213	−	0.453517i
$515$		0			0
$516$	1.34589			0.0592497
$517$	5.51660	−	4.43547i	0.242620	−	0.195072i
$518$	80.6091			3.54176
$519$	−7.49168	+	23.0570i	−0.328848	+	1.01209i
$520$		0			0
$521$	7.43033	+	5.39845i	0.325529	+	0.236510i	0.738531	−	0.674220i	$-0.235520\pi$
$521$	7.43033	+	5.39845i	0.325529	+	0.236510i	−0.413002	+	0.910730i	$0.635520\pi$
$522$	0.730731	+	2.24896i	0.0319832	+	0.0984342i
$523$	10.3781	+	31.9404i	0.453801	+	1.39665i	0.872537	+	0.488547i	$0.162473\pi$
$523$	10.3781	+	31.9404i	0.453801	+	1.39665i	−0.418737	+	0.908108i	$0.637527\pi$
$524$	15.9275	+	11.5720i	0.695795	+	0.505525i
$525$		0			0
$526$	7.24796	−	22.3069i	0.316026	−	0.972629i
$527$	7.46893			0.325352
$528$	8.14236	+	5.32820i	0.354351	+	0.231880i
$529$	11.6952			0.508486
$530$		0			0
$531$	−6.79443	+	4.93644i	−0.294853	+	0.214223i
$532$	7.50523	+	5.45287i	0.325393	+	0.236412i
$533$	0.720127	+	2.21632i	0.0311922	+	0.0959996i
$534$	−8.19865	−	25.2329i	−0.354790	−	1.09193i
$535$		0			0
$536$	−3.09648	+	2.24972i	−0.133747	+	0.0971731i
$537$	−6.16149	+	18.9631i	−0.265888	+	0.818319i
$538$	−47.9364			−2.06669
$539$	4.70870	+	12.3957i	0.202818	+	0.533921i
$540$		0			0
$541$	13.7829	−	42.4194i	0.592573	−	1.82375i	0.0261178	−	0.999659i	$-0.491685\pi$
$541$	13.7829	−	42.4194i	0.592573	−	1.82375i	0.566455	−	0.824093i	$-0.308315\pi$
$542$	13.2834	−	9.65093i	0.570569	−	0.414543i
$543$	4.15260	+	3.01704i	0.178205	+	0.129474i
$544$	−16.8842	−	51.9643i	−0.723906	−	2.22795i
$545$		0			0
$546$	−14.1229	−	10.2609i	−0.604405	−	0.439126i
$547$	−15.5582	+	11.3037i	−0.665219	+	0.483310i	−0.868421	−	0.495827i	$-0.834865\pi$
$547$	−15.5582	+	11.3037i	−0.665219	+	0.483310i	0.203202	+	0.979137i	$0.434865\pi$
$548$	−4.84891	+	14.9234i	−0.207135	+	0.637497i
$549$	−8.21313			−0.350528
$550$		0			0
$551$	1.28836			0.0548860
$552$	−1.67703	+	5.16137i	−0.0713791	+	0.219682i
$553$	10.3765	−	7.53895i	0.441252	−	0.320589i
$554$	−16.1340	−	11.7220i	−0.685468	−	0.498022i
$555$		0			0
$556$	5.25402	+	16.1702i	0.222820	+	0.685770i
$557$	26.9944	+	19.6126i	1.14379	+	0.831011i	0.987643	−	0.156723i	$-0.0500931\pi$
$557$	26.9944	+	19.6126i	1.14379	+	0.831011i	0.156145	+	0.987734i	$0.450093\pi$
$558$	−1.86905	+	1.35794i	−0.0791231	+	0.0574863i
$559$	−0.426399	+	1.31232i	−0.0180348	+	0.0555053i
$560$		0			0
$561$	18.8999	+	12.3677i	0.797953	+	0.522165i
$562$	−65.9370			−2.78139
$563$	−0.646509	+	1.98975i	−0.0272471	+	0.0838580i	−0.963755	−	0.266788i	$-0.914038\pi$
$563$	−0.646509	+	1.98975i	−0.0272471	+	0.0838580i	0.936508	+	0.350646i	$0.114038\pi$
$564$	4.20853	−	3.05768i	0.177211	−	0.128752i
$565$		0			0
$566$	−15.8911	−	48.9079i	−0.667955	−	2.05575i
$567$	1.02480	+	3.15401i	0.0430376	+	0.132456i
$568$	9.34271	+	6.78788i	0.392011	+	0.284813i
$569$	7.53693	−	5.47590i	0.315964	−	0.229562i	−0.418487	−	0.908223i	$-0.637439\pi$
$569$	7.53693	−	5.47590i	0.315964	−	0.229562i	0.734452	+	0.678661i	$0.237439\pi$
$570$		0			0
$571$	2.32989			0.0975029			0.0487514	−	0.998811i	$-0.484476\pi$
$571$	2.32989			0.0975029			0.0487514	+	0.998811i	$0.484476\pi$
$572$	15.7432	−	12.6578i	0.658254	−	0.529251i
$573$	−2.81336			−0.117530
$574$	2.01318	−	6.19594i	0.0840286	−	0.258614i
$575$		0			0
$576$	8.92570	+	6.48490i	0.371904	+	0.270204i
$577$	9.10449	+	28.0207i	0.379025	+	1.16652i	0.940723	+	0.339176i	$0.110148\pi$
$577$	9.10449	+	28.0207i	0.379025	+	1.16652i	−0.561698	+	0.827342i	$0.689852\pi$
$578$	−19.1240	−	58.8575i	−0.795452	−	2.44815i
$579$	15.6166	+	11.3461i	0.649005	+	0.471530i
$580$		0			0
$581$	−6.23136	+	19.1781i	−0.258520	+	0.795643i
$582$	6.04300			0.250491
$583$	10.1181	−	37.2409i	0.419049	−	1.54236i
$584$	5.28634			0.218750
$585$		0			0
$586$	−20.1431	+	14.6348i	−0.832103	+	0.604558i
$587$	−33.5877	−	24.4029i	−1.38631	−	1.00722i	−0.996258	−	0.0864248i	$-0.972456\pi$
$587$	−33.5877	−	24.4029i	−1.38631	−	1.00722i	−0.390056	−	0.920791i	$-0.627544\pi$
$588$	3.01128	+	9.26776i	0.124183	+	0.382196i
$589$	0.388962	+	1.19710i	0.0160269	+	0.0493258i
$590$		0			0
$591$	−2.89592	+	2.10401i	−0.119122	+	0.0865475i
$592$	10.4615	−	32.1973i	0.429967	−	1.32330i
$593$	9.36964			0.384765			0.192383	−	0.981320i	$-0.438379\pi$
$593$	9.36964			0.384765			0.192383	+	0.981320i	$0.438379\pi$
$594$	−6.97816	+	0.341294i	−0.286317	+	0.0140035i
$595$		0			0
$596$	−14.3261	+	44.0912i	−0.586820	+	1.80605i
$597$	−10.2815	+	7.46997i	−0.420795	+	0.305725i
$598$	−25.0843	−	18.2248i	−1.02577	−	0.745268i
$599$	0.406983	+	1.25256i	0.0166289	+	0.0511784i	0.959027	−	0.283316i	$-0.0914345\pi$
$599$	0.406983	+	1.25256i	0.0166289	+	0.0511784i	−0.942398	+	0.334494i	$0.891434\pi$
$600$		0			0
$601$	−12.6422	−	9.18512i	−0.515688	−	0.374669i	0.299289	−	0.954162i	$-0.403250\pi$
$601$	−12.6422	−	9.18512i	−0.515688	−	0.374669i	−0.814977	+	0.579493i	$0.803250\pi$
$602$	3.12080	−	2.26739i	0.127194	−	0.0924120i
$603$	−1.28371	+	3.95087i	−0.0522769	+	0.160892i
$604$	9.50777			0.386866
$605$		0			0
$606$	−20.7913			−0.844588
$607$	−7.48201	+	23.0273i	−0.303685	+	0.934647i	0.676479	+	0.736462i	$0.263505\pi$
$607$	−7.48201	+	23.0273i	−0.303685	+	0.934647i	−0.980165	+	0.198186i	$0.936495\pi$
$608$	7.44943	−	5.41233i	0.302114	−	0.219499i
$609$	3.01180	+	2.18820i	0.122044	+	0.0886705i
$610$		0			0
$611$	1.64808	+	5.07227i	0.0666742	+	0.205202i
$612$	13.4289	+	9.75666i	0.542831	+	0.394390i
$613$	3.30589	−	2.40187i	0.133524	−	0.0970105i	−0.519019	−	0.854763i	$-0.673702\pi$
$613$	3.30589	−	2.40187i	0.133524	−	0.0970105i	0.652542	+	0.757752i	$0.273702\pi$
$614$	14.5302	−	44.7194i	0.586392	−	1.80473i
$615$		0			0
$616$	−10.1218	+	0.495047i	−0.407820	+	0.0199460i
$617$	−16.9835			−0.683731			−0.341866	−	0.939749i	$-0.611059\pi$
$617$	−16.9835			−0.683731			−0.341866	+	0.939749i	$0.611059\pi$
$618$	−5.02501	+	15.4654i	−0.202135	+	0.622109i
$619$	25.9942	−	18.8859i	1.04480	−	0.759089i	0.0735802	−	0.997289i	$-0.476558\pi$
$619$	25.9942	−	18.8859i	1.04480	−	0.759089i	0.971216	+	0.238200i	$0.0765575\pi$
$620$		0			0
$621$	1.82019	+	5.60197i	0.0730417	+	0.224799i
$622$	12.6827	+	39.0332i	0.508528	+	1.56509i
$623$	−33.7918	−	24.5512i	−1.35384	−	0.983623i
$624$	−5.93136	+	4.30939i	−0.237444	+	0.172514i
$625$		0			0
$626$	36.5536			1.46098
$627$	−0.998011	+	3.67330i	−0.0398567	+	0.146698i
$628$	−44.8095			−1.78809
$629$	24.2831	−	74.7358i	0.968232	−	2.97991i
$630$		0			0
$631$	5.10947	+	3.71225i	0.203405	+	0.147782i	0.684825	−	0.728708i	$-0.259879\pi$
$631$	5.10947	+	3.71225i	0.203405	+	0.147782i	−0.481420	+	0.876490i	$0.659879\pi$
$632$	1.10114	+	3.38895i	0.0438008	+	0.134805i
$633$	−1.08007	−	3.32412i	−0.0429290	−	0.132122i
$634$	−1.41571	−	1.02857i	−0.0562250	−	0.0408499i
$635$		0			0
$636$	8.76384	−	26.9723i	0.347509	−	1.06952i
$637$	−9.99059			−0.395842
$638$	−6.11219	+	4.91434i	−0.241984	+	0.194560i
$639$	12.5340			0.495839
$640$		0			0
$641$	−11.8814	+	8.63236i	−0.469288	+	0.340958i	−0.797164	−	0.603763i	$-0.793667\pi$
$641$	−11.8814	+	8.63236i	−0.469288	+	0.340958i	0.327876	+	0.944721i	$0.393667\pi$
$642$	−26.4345	−	19.2058i	−1.04329	−	0.757993i
$643$	4.99093	+	15.3605i	0.196823	+	0.605759i	0.999950	+	0.00995196i	$0.00316786\pi$
$643$	4.99093	+	15.3605i	0.196823	+	0.605759i	−0.803127	+	0.595807i	$0.796832\pi$
$644$	14.7129	+	45.2816i	0.579769	+	1.78434i
$645$		0			0
$646$	13.3200	−	9.67758i	0.524070	−	0.380759i
$647$	−8.58676	+	26.4273i	−0.337581	+	1.03897i	0.627856	+	0.778329i	$0.283933\pi$
$647$	−8.58676	+	26.4273i	−0.337581	+	1.03897i	−0.965437	+	0.260637i	$0.916067\pi$
$648$	−0.921348			−0.0361940
$649$	−23.3075	−	15.2519i	−0.914898	−	0.598691i
$650$		0			0
$651$	−1.12393	+	3.45910i	−0.0440503	+	0.135573i
$652$	34.6499	−	25.1747i	1.35700	−	0.985916i
$653$	−27.5595	−	20.0232i	−1.07849	−	0.783568i	−0.101070	−	0.994879i	$-0.532227\pi$
$653$	−27.5595	−	20.0232i	−1.07849	−	0.783568i	−0.977419	+	0.211312i	$0.932227\pi$
$654$	−4.42536	−	13.6199i	−0.173045	−	0.532579i
$655$		0			0
$656$	−2.21354	−	1.60823i	−0.0864244	−	0.0627910i
$657$	4.64182	−	3.37248i	0.181095	−	0.131573i
$658$	4.60737	−	14.1800i	0.179614	−	0.552795i
$659$	14.4196			0.561709			0.280855	−	0.959750i	$-0.409382\pi$
$659$	14.4196			0.561709			0.280855	+	0.959750i	$0.409382\pi$
$660$		0			0
$661$	26.4275			1.02791			0.513956	−	0.857817i	$-0.328179\pi$
$661$	26.4275			1.02791			0.513956	+	0.857817i	$0.328179\pi$
$662$	20.5251	−	63.1697i	0.797730	−	2.45516i
$663$	−13.7678	+	10.0029i	−0.534695	+	0.388479i
$664$	−4.53236	−	3.29295i	−0.175890	−	0.127791i
$665$		0			0
$666$	7.51119	+	23.1171i	0.291053	+	0.895769i
$667$	5.34939	+	3.88656i	0.207129	+	0.150488i
$668$	23.8157	−	17.3032i	0.921459	−	0.669479i
$669$	−1.60861	+	4.95080i	−0.0621925	+	0.191409i
$670$		0			0
$671$	−9.67309	−	25.4645i	−0.373426	−	0.983047i
$672$	26.6071			1.02639
$673$	−11.2213	+	34.5357i	−0.432550	+	1.33125i	0.463026	+	0.886345i	$0.346764\pi$
$673$	−11.2213	+	34.5357i	−0.432550	+	1.33125i	−0.895576	+	0.444908i	$0.853236\pi$
$674$	27.6659	−	20.1005i	1.06565	−	0.774241i
$675$		0			0
$676$	−5.08824	−	15.6600i	−0.195702	−	0.602308i
$677$	−3.50556	−	10.7890i	−0.134730	−	0.414655i	0.860818	−	0.508913i	$-0.169952\pi$
$677$	−3.50556	−	10.7890i	−0.134730	−	0.414655i	−0.995548	+	0.0942574i	$0.969952\pi$
$678$	−0.513798	−	0.373296i	−0.0197323	−	0.0143363i
$679$	7.69669	−	5.59198i	0.295372	−	0.214600i
$680$		0			0
$681$	−9.70244			−0.371798
$682$	−6.41154	−	4.19559i	−0.245511	−	0.160657i
$683$	−39.4269			−1.50863			−0.754314	−	0.656514i	$-0.772030\pi$
$683$	−39.4269			−1.50863			−0.754314	+	0.656514i	$0.772030\pi$
$684$	−0.864433	+	2.66045i	−0.0330524	+	0.101725i
$685$		0			0
$686$	−16.9663	−	12.3267i	−0.647775	−	0.470636i
$687$	5.71715	+	17.5956i	0.218123	+	0.671313i
$688$	−0.500634	−	1.54079i	−0.0190865	−	0.0587421i
$689$	23.5230	+	17.0905i	0.896155	+	0.651095i
$690$		0			0
$691$	4.56613	−	14.0531i	0.173704	−	0.534606i	−0.825868	−	0.563864i	$-0.809314\pi$
$691$	4.56613	−	14.0531i	0.173704	−	0.534606i	0.999572	+	0.0292578i	$0.00931437\pi$
$692$	−59.0909			−2.24630
$693$	−8.57194	+	6.89203i	−0.325621	+	0.261806i
$694$	−26.2260			−0.995526
$695$		0			0
$696$	−0.836745	+	0.607931i	−0.0317167	+	0.0230436i
$697$	−5.13804	−	3.73300i	−0.194617	−	0.141398i
$698$	−21.2402	−	65.3707i	−0.803954	−	2.47432i
$699$	4.62115	+	14.2224i	0.174788	+	0.537942i
$700$		0			0
$701$	5.76774	−	4.19051i	0.217845	−	0.158273i	−0.473511	−	0.880788i	$-0.657014\pi$
$701$	5.76774	−	4.19051i	0.217845	−	0.158273i	0.691356	+	0.722514i	$0.257014\pi$
$702$	1.62664	−	5.00629i	0.0613937	−	0.188950i
$703$	13.2431			0.499472
$704$	−9.59389	+	35.3115i	−0.361583	+	1.33085i
$705$		0			0
$706$	−10.2798	+	31.6381i	−0.386887	+	1.19071i
$707$	−26.4809	+	19.2395i	−0.995917	+	0.723576i
$708$	−16.5606	−	12.0320i	−0.622386	−	0.452190i
$709$	−1.65473	−	5.09274i	−0.0621447	−	0.191262i	0.915164	−	0.403082i	$-0.132061\pi$
$709$	−1.65473	−	5.09274i	−0.0621447	−	0.191262i	−0.977309	+	0.211820i	$0.932061\pi$
$710$		0			0
$711$	3.12890	+	2.27328i	0.117343	+	0.0852548i
$712$	9.38811	−	6.82086i	0.351834	−	0.255623i
$713$	−1.99626	+	6.14385i	−0.0747604	+	0.230089i
$714$	47.5751			1.78045
$715$		0			0
$716$	−48.5989			−1.81623
$717$	−0.465738	+	1.43340i	−0.0173933	+	0.0535311i
$718$	30.9520	−	22.4880i	1.15512	−	0.839243i
$719$	32.9940	+	23.9716i	1.23047	+	0.893989i	0.996925	−	0.0783569i	$-0.0249674\pi$
$719$	32.9940	+	23.9716i	1.23047	+	0.893989i	0.233545	+	0.972346i	$0.424967\pi$
$720$		0			0
$721$	7.91098	+	24.3475i	0.294620	+	0.906749i
$722$	−30.1351	−	21.8944i	−1.12151	−	0.814825i
$723$	5.74055	−	4.17075i	0.213493	−	0.155112i
$724$	−3.86606	+	11.8985i	−0.143681	+	0.442204i
$725$		0			0
$726$	−9.27676	−	21.2336i	−0.344293	−	0.788052i
$727$	28.6101			1.06109			0.530546	−	0.847656i	$-0.321987\pi$
$727$	28.6101			1.06109			0.530546	+	0.847656i	$0.321987\pi$
$728$	2.35944	−	7.26162i	0.0874468	−	0.269134i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−1.16206	−	3.57646i	−0.0429804	−	0.132280i
$732$	−6.18607	−	19.0388i	−0.228644	−	0.703693i
$733$	3.55653	+	2.58397i	0.131364	+	0.0954412i	0.651527	−	0.758626i	$-0.274129\pi$
$733$	3.55653	+	2.58397i	0.131364	+	0.0954412i	−0.520163	+	0.854067i	$0.674129\pi$
$734$	0.804462	−	0.584476i	0.0296932	−	0.0215734i
$735$		0			0
$736$	47.2579			1.74195
$737$	−13.7614	+	0.673056i	−0.506909	+	0.0247924i
$738$	1.96446			0.0723129
$739$	−3.25000	+	10.0025i	−0.119553	+	0.367947i	−0.992869	−	0.119207i	$-0.961965\pi$
$739$	−3.25000	+	10.0025i	−0.119553	+	0.367947i	0.873316	+	0.487154i	$0.161965\pi$
$740$		0			0
$741$	−2.32022	−	1.68574i	−0.0852355	−	0.0619272i
$742$	−25.1184	−	77.3064i	−0.922125	−	2.83801i
$743$	10.6580	+	32.8020i	0.391005	+	1.20339i	0.932030	+	0.362382i	$0.118036\pi$
$743$	10.6580	+	32.8020i	0.391005	+	1.20339i	−0.541025	+	0.841007i	$0.681964\pi$
$744$	−0.817487	−	0.593939i	−0.0299705	−	0.0217749i
$745$		0			0
$746$	10.0312	−	30.8729i	0.367269	−	1.13034i
$747$	−6.08055			−0.222476
$748$	−14.4342	+	53.1268i	−0.527766	+	1.94251i
$749$	−51.4408			−1.87961
$750$		0			0
$751$	1.92630	−	1.39954i	0.0702918	−	0.0510700i	−0.552084	−	0.833788i	$-0.686167\pi$
$751$	1.92630	−	1.39954i	0.0702918	−	0.0510700i	0.622376	+	0.782718i	$0.286167\pi$
$752$	−5.06591	−	3.68060i	−0.184735	−	0.134218i
$753$	−4.22692	−	13.0091i	−0.154038	−	0.474079i
$754$	−1.82601	−	5.61989i	−0.0664995	−	0.204664i
$755$		0			0
$756$	−6.53941	+	4.75116i	−0.237836	+	0.172798i
$757$	2.59435	−	7.98459i	0.0942932	−	0.290205i	−0.892776	−	0.450502i	$-0.851245\pi$
$757$	2.59435	−	7.98459i	0.0942932	−	0.290205i	0.987069	+	0.160297i	$0.0512452\pi$
$758$	40.6021			1.47473
$759$	−15.2250	+	12.2412i	−0.552631	+	0.444328i
$760$		0			0
$761$	3.23481	−	9.95573i	0.117262	−	0.360895i	−0.875150	−	0.483851i	$-0.839238\pi$
$761$	3.23481	−	9.95573i	0.117262	−	0.360895i	0.992412	+	0.122956i	$0.0392375\pi$
$762$	−11.4273	+	8.30245i	−0.413969	+	0.300766i
$763$	−18.2397	−	13.2519i	−0.660322	−	0.479752i
$764$	−2.11900	−	6.52162i	−0.0766628	−	0.235944i
$765$		0			0
$766$	12.6933	+	9.22222i	0.458627	+	0.333212i
$767$	16.9785	−	12.3356i	0.613058	−	0.445413i
$768$	2.13537	−	6.57200i	0.0770536	−	0.237146i
$769$	−9.70799			−0.350079			−0.175040	−	0.984561i	$-0.556005\pi$
$769$	−9.70799			−0.350079			−0.175040	+	0.984561i	$0.556005\pi$
$770$		0			0
$771$	8.30411			0.299065
$772$	−14.5390	+	44.7465i	−0.523271	+	1.61046i
$773$	25.8560	−	18.7855i	0.929977	−	0.675668i	−0.0160101	−	0.999872i	$-0.505096\pi$
$773$	25.8560	−	18.7855i	0.929977	−	0.675668i	0.945987	+	0.324204i	$0.105096\pi$
$774$	0.941041	+	0.683706i	0.0338250	+	0.0245753i
$775$		0			0
$776$	0.816762	+	2.51374i	0.0293201	+	0.0902378i
$777$	30.9584	+	22.4926i	1.11063	+	0.806917i
$778$	−1.21649	+	0.883833i	−0.0436133	+	0.0316869i
$779$	0.330741	−	1.01792i	0.0118500	−	0.0364706i
$780$		0			0
$781$	14.7621	+	38.8614i	0.528229	+	1.39057i
$782$	84.5001			3.02172
$783$	−0.346892	+	1.06762i	−0.0123969	+	0.0381537i
$784$	9.48971	−	6.89468i	0.338918	−	0.246239i
$785$		0			0
$786$	5.25789	+	16.1821i	0.187543	+	0.577197i
$787$	14.3605	+	44.1971i	0.511896	+	1.57545i	0.788859	+	0.614574i	$0.210672\pi$
$787$	14.3605	+	44.1971i	0.511896	+	1.57545i	−0.276963	+	0.960881i	$0.589328\pi$
$788$	−7.05847	−	5.12828i	−0.251448	−	0.182687i
$789$	9.00799	−	6.54469i	0.320693	−	0.232997i
$790$		0			0
$791$	−0.999835			−0.0355500
$792$	−1.08513	−	2.85661i	−0.0385583	−	0.101505i
$793$	20.5237			0.728817
$794$	−0.497435	+	1.53095i	−0.0176533	+	0.0543313i
$795$		0			0
$796$	−25.0600	−	18.2072i	−0.888228	−	0.645336i
$797$	9.96126	+	30.6576i	0.352846	+	1.08595i	0.957248	+	0.289269i	$0.0934121\pi$
$797$	9.96126	+	30.6576i	0.352846	+	1.08595i	−0.604402	+	0.796680i	$0.706588\pi$
$798$	2.47759	+	7.62522i	0.0877056	+	0.269930i
$799$	−11.7589	−	8.54334i	−0.416000	−	0.302242i
$800$		0			0
$801$	3.89206	−	11.9785i	0.137519	−	0.423240i
$802$	33.1869			1.17187
$803$	15.9232	+	10.4198i	0.561918	+	0.367708i
$804$	−10.1253			−0.357093
$805$		0			0
$806$	4.67054	−	3.39334i	0.164513	−	0.119525i
$807$	−18.4103	−	13.3758i	−0.648072	−	0.470852i
$808$	−2.81011	−	8.64864i	−0.0988595	−	0.304258i
$809$	6.55046	+	20.1603i	0.230302	+	0.708797i	0.997710	+	0.0676376i	$0.0215462\pi$
$809$	6.55046	+	20.1603i	0.230302	+	0.708797i	−0.767408	+	0.641159i	$0.778454\pi$
$810$		0			0
$811$	19.0967	−	13.8746i	0.670578	−	0.487203i	−0.199641	−	0.979869i	$-0.563978\pi$
$811$	19.0967	−	13.8746i	0.670578	−	0.487203i	0.870218	+	0.492666i	$0.163978\pi$
$812$	−2.80398	+	8.62976i	−0.0984004	+	0.302845i
$813$	7.79448			0.273364
$814$	−62.8273	+	50.5145i	−2.20210	+	1.77053i
$815$		0			0
$816$	6.17436	−	19.0027i	0.216146	−	0.665228i
$817$	0.512709	−	0.372505i	0.0179374	−	0.0130323i
$818$	−4.46672	−	3.24526i	−0.156175	−	0.113468i
$819$	−2.56086	−	7.88152i	−0.0894837	−	0.275403i
$820$		0			0
$821$	36.0153	+	26.1667i	1.25694	+	0.913223i	0.998603	−	0.0528314i	$-0.0168246\pi$
$821$	36.0153	+	26.1667i	1.25694	+	0.913223i	0.258340	+	0.966054i	$0.416825\pi$
$822$	−10.9713	+	7.97114i	−0.382669	+	0.278026i
$823$	0.0421588	−	0.129751i	0.00146956	−	0.00452285i	−0.950319	−	0.311278i	$-0.899243\pi$
$823$	0.0421588	−	0.129751i	0.00146956	−	0.00452285i	0.951789	+	0.306755i	$0.0992431\pi$
$824$	−7.11238			−0.247771
$825$		0			0
$826$	−58.6700			−2.04139
$827$	−3.63750	+	11.1951i	−0.126488	+	0.389291i	−0.994169	−	0.107830i	$-0.965610\pi$
$827$	−3.63750	+	11.1951i	−0.126488	+	0.389291i	0.867681	+	0.497121i	$0.165610\pi$
$828$	−11.6149	+	8.43872i	−0.403646	+	0.293266i
$829$	−8.92262	−	6.48266i	−0.309895	−	0.225152i	0.421956	−	0.906616i	$-0.361344\pi$
$829$	−8.92262	−	6.48266i	−0.309895	−	0.225152i	−0.731852	+	0.681464i	$0.761344\pi$
$830$		0			0
$831$	−2.92552	−	9.00383i	−0.101485	−	0.312339i
$832$	−22.3043	−	16.2050i	−0.773263	−	0.561808i
$833$	22.0273	−	16.0038i	0.763202	−	0.554498i
$834$	−4.54080	+	13.9751i	−0.157235	+	0.483919i
$835$		0			0
$836$	−9.26673	+	0.453226i	−0.320497	+	0.0156751i
$837$	−1.09673			−0.0379085
$838$	11.7221	−	36.0769i	0.404933	−	1.24626i
$839$	8.56769	−	6.22479i	0.295790	−	0.214904i	−0.429985	−	0.902836i	$-0.641481\pi$
$839$	8.56769	−	6.22479i	0.295790	−	0.214904i	0.725775	+	0.687932i	$0.241481\pi$
$840$		0			0
$841$	−8.57208	−	26.3822i	−0.295589	−	0.909730i
$842$	−0.762368	−	2.34633i	−0.0262730	−	0.0808598i
$843$	−25.3235	−	18.3986i	−0.872188	−	0.633681i
$844$	6.89209	−	5.00740i	0.237236	−	0.172362i
$845$		0			0
$846$	4.49586			0.154571
$847$	−31.4642	−	18.4599i	−1.08112	−	0.634288i
$848$	−34.1381			−1.17231
$849$	7.54383	−	23.2175i	0.258903	−	0.796823i
$850$		0			0
$851$	54.9864	+	39.9500i	1.88491	+	1.36947i
$852$	9.44055	+	29.0550i	0.323428	+	0.995409i
$853$	−13.7763	−	42.3992i	−0.471693	−	1.45172i	−0.850367	−	0.526190i	$-0.823620\pi$
$853$	−13.7763	−	42.3992i	−0.471693	−	1.45172i	0.378674	−	0.925530i	$-0.376380\pi$
$854$	−46.4181	−	33.7247i	−1.58839	−	1.15404i
$855$		0			0
$856$	4.41628	−	13.5919i	0.150945	−	0.464562i
$857$	−24.3105			−0.830430			−0.415215	−	0.909723i	$-0.636294\pi$
$857$	−24.3105			−0.830430			−0.415215	+	0.909723i	$0.636294\pi$
$858$	17.4376	−	0.852855i	0.595311	−	0.0291160i
$859$	−35.5045			−1.21140			−0.605699	−	0.795694i	$-0.707107\pi$
$859$	−35.5045			−1.21140			−0.605699	+	0.795694i	$0.707107\pi$
$860$		0			0
$861$	2.50205	−	1.81784i	0.0852695	−	0.0619519i
$862$	59.8040	+	43.4502i	2.03693	+	1.47992i
$863$	3.60684	+	11.1007i	0.122778	+	0.377873i	0.993490	−	0.113921i	$-0.0363412\pi$
$863$	3.60684	+	11.1007i	0.122778	+	0.377873i	−0.870711	+	0.491794i	$0.836341\pi$
$864$	2.47926	+	7.63038i	0.0843462	+	0.259591i
$865$		0			0
$866$	−31.0609	+	22.5670i	−1.05549	+	0.766859i
$867$	9.07851	−	27.9408i	0.308322	−	0.948919i
$868$	−8.86503			−0.300899
$869$	−3.36314	+	12.3784i	−0.114087	+	0.419910i
$870$		0			0
$871$	3.20786	−	9.87276i	0.108694	−	0.334526i
$872$	5.06739	−	3.68167i	0.171603	−	0.124677i
$873$	2.32085	+	1.68620i	0.0785489	+	0.0570691i
$874$	4.40054	+	13.5435i	0.148850	+	0.458115i
$875$		0			0
$876$	11.3139	+	8.22003i	0.382261	+	0.277729i
$877$	21.4243	−	15.5657i	0.723447	−	0.525615i	−0.164036	−	0.986454i	$-0.552451\pi$
$877$	21.4243	−	15.5657i	0.723447	−	0.525615i	0.887484	+	0.460839i	$0.152451\pi$
$878$	12.8989	−	39.6986i	0.435315	−	1.33976i
$879$	−11.8197			−0.398667
$880$		0			0
$881$	10.3488			0.348658			0.174329	−	0.984687i	$-0.444224\pi$
$881$	10.3488			0.348658			0.174329	+	0.984687i	$0.444224\pi$
$882$	−2.60250	+	8.00967i	−0.0876307	+	0.269700i
$883$	2.19364	−	1.59377i	0.0738217	−	0.0536346i	−0.550262	−	0.834992i	$-0.685472\pi$
$883$	2.19364	−	1.59377i	0.0738217	−	0.0536346i	0.624084	+	0.781357i	$0.285472\pi$
$884$	−33.5573	−	24.3808i	−1.12865	−	0.820015i
$885$		0			0
$886$	−10.8633	−	33.4338i	−0.364959	−	1.12323i
$887$	−0.0992445	−	0.0721054i	−0.00333230	−	0.00242106i	0.586118	−	0.810226i	$-0.300656\pi$
$887$	−0.0992445	−	0.0721054i	−0.00333230	−	0.00242106i	−0.589450	+	0.807805i	$0.700656\pi$
$888$	−8.60092	+	6.24893i	−0.288628	+	0.209700i
$889$	−6.87169	+	21.1489i	−0.230469	+	0.709311i
$890$		0			0
$891$	−2.77523	−	1.81606i	−0.0929739	−	0.0608403i
$892$	−12.6880			−0.424825
$893$	0.756933	−	2.32960i	0.0253298	−	0.0779571i
$894$	−32.4148	+	23.5507i	−1.08411	+	0.787654i
$895$		0			0
$896$	7.37296	+	22.6916i	0.246313	+	0.758075i
$897$	−4.54845	−	13.9987i	−0.151868	−	0.467403i
$898$	−22.4904	−	16.3403i	−0.750516	−	0.545282i
$899$	−0.996022	+	0.723652i	−0.0332192	+	0.0241352i
$900$		0			0
$901$	−79.2406			−2.63989
$902$	2.31366	+	6.09075i	0.0770365	+	0.202800i
$903$	1.83124			0.0609398
$904$	0.0858376	−	0.264181i	0.00285491	−	0.00878652i
$905$		0			0
$906$	6.64777	+	4.82989i	0.220857	+	0.160462i
$907$	−4.27023	−	13.1424i	−0.141791	−	0.436387i	0.854794	−	0.518968i	$-0.173684\pi$
$907$	−4.27023	−	13.1424i	−0.141791	−	0.436387i	−0.996584	+	0.0825812i	$0.973684\pi$
$908$	−7.30780	−	22.4911i	−0.242518	−	0.746393i
$909$	−7.98501	−	5.80145i	−0.264846	−	0.192422i
$910$		0			0
$911$	7.18645	−	22.1176i	0.238098	−	0.732790i	−0.758598	−	0.651559i	$-0.774115\pi$
$911$	7.18645	−	22.1176i	0.238098	−	0.732790i	0.996695	−	0.0812302i	$-0.0258849\pi$
$912$	3.36725			0.111501
$913$	−7.16142	−	18.8525i	−0.237009	−	0.623928i
$914$	−44.7997			−1.48184
$915$		0			0
$916$	−36.4820	+	26.5057i	−1.20540	+	0.875773i
$917$	21.6711	+	15.7450i	0.715642	+	0.519945i
$918$	4.43307	+	13.6436i	0.146313	+	0.450306i
$919$	8.16663	+	25.1343i	0.269392	+	0.829104i	0.990649	+	0.136436i	$0.0435648\pi$
$919$	8.16663	+	25.1343i	0.269392	+	0.829104i	−0.721257	+	0.692668i	$0.756435\pi$
$920$		0			0
$921$	18.0586	−	13.1203i	0.595051	−	0.432330i
$922$	13.0692	−	40.2228i	0.430410	−	1.32467i
$923$	−31.3212			−1.03095
$924$	−22.4326	−	14.6795i	−0.737980	−	0.482920i
$925$		0			0
$926$	0.626554	−	1.92833i	0.0205898	−	0.0633690i
$927$	−6.24523	+	4.53743i	−0.205120	+	0.149029i
$928$	7.28634	+	5.29383i	0.239186	+	0.173779i
$929$	−2.48284	−	7.64138i	−0.0814592	−	0.250706i	0.902030	−	0.431674i	$-0.142077\pi$
$929$	−2.48284	−	7.64138i	−0.0814592	−	0.250706i	−0.983489	+	0.180968i	$0.942077\pi$
$930$		0			0
$931$	3.71217	+	2.69705i	0.121662	+	0.0883923i
$932$	−29.4882	+	21.4244i	−0.965919	+	0.701781i
$933$	−6.02070	+	18.5298i	−0.197109	+	0.606639i
$934$	31.4144			1.02791
$935$		0			0
$936$	2.30234			0.0752545
$937$	4.16903	−	12.8309i	0.136196	−	0.419169i	−0.859578	−	0.511005i	$-0.829274\pi$
$937$	4.16903	−	12.8309i	0.136196	−	0.419169i	0.995774	+	0.0918359i	$0.0292735\pi$
$938$	−23.4782	+	17.0579i	−0.766590	+	0.556960i
$939$	14.0386	+	10.1997i	0.458133	+	0.332853i
$940$		0			0
$941$	−9.85889	−	30.3425i	−0.321391	−	0.989138i	−0.973044	−	0.230621i	$-0.925924\pi$
$941$	−9.85889	−	30.3425i	−0.321391	−	0.989138i	0.651653	−	0.758517i	$-0.274076\pi$
$942$	−31.3305	−	22.7630i	−1.02080	−	0.741657i
$943$	4.44398	−	3.22874i	0.144716	−	0.105142i
$944$	−7.61426	+	23.4343i	−0.247823	+	0.762721i
$945$		0			0
$946$	−1.01149	+	3.72290i	−0.0328863	+	0.121042i
$947$	−10.2719			−0.333793			−0.166896	−	0.985974i	$-0.553375\pi$
$947$	−10.2719			−0.333793			−0.166896	+	0.985974i	$0.553375\pi$
$948$	−2.91300	+	8.96529i	−0.0946099	+	0.291179i
$949$	−11.5994	+	8.42745i	−0.376532	+	0.273567i
$950$		0			0
$951$	−0.256706	−	0.790059i	−0.00832425	−	0.0256194i
$952$	6.43017	+	19.7900i	0.208403	+	0.641399i
$953$	7.95608	+	5.78043i	0.257723	+	0.187247i	0.709143	−	0.705065i	$-0.249082\pi$
$953$	7.95608	+	5.78043i	0.257723	+	0.187247i	−0.451420	+	0.892312i	$0.649082\pi$
$954$	19.8294	−	14.4069i	0.642001	−	0.466441i
$955$		0			0
$956$	−3.67353			−0.118810
$957$	−3.71868	+	0.181877i	−0.120208	+	0.00587924i
$958$	1.00170			0.0323635
$959$	−6.59748	+	20.3050i	−0.213044	+	0.655681i
$960$		0			0
$961$	24.1064	+	17.5143i	0.777627	+	0.564979i
$962$	−18.7696	−	57.7669i	−0.605157	−	1.86248i
$963$	−4.79328	−	14.7522i	−0.154461	−	0.475383i
$964$	13.9919	+	10.1657i	0.450649	+	0.327416i
$965$		0			0
$966$	−12.7156	+	39.1347i	−0.409118	+	1.25914i
$967$	3.85001			0.123808			0.0619041	−	0.998082i	$-0.480283\pi$
$967$	3.85001			0.123808			0.0619041	+	0.998082i	$0.480283\pi$
$968$	7.57880	−	6.72879i	0.243592	−	0.216272i
$969$	7.81600			0.251086
$970$		0			0
$971$	−17.3065	+	12.5739i	−0.555392	+	0.403516i	−0.829769	−	0.558106i	$-0.811528\pi$
$971$	−17.3065	+	12.5739i	−0.555392	+	0.403516i	0.274378	+	0.961622i	$0.411528\pi$
$972$	−1.97188	−	1.43266i	−0.0632482	−	0.0459525i
$973$	7.14868	+	22.0014i	0.229176	+	0.705332i
$974$	23.0129	+	70.8264i	0.737381	+	2.26942i
$975$		0			0
$976$	−19.4947	+	14.1637i	−0.624011	+	0.453370i
$977$	5.15071	−	15.8523i	0.164786	−	0.507159i	−0.834235	−	0.551410i	$-0.814090\pi$
$977$	5.15071	−	15.8523i	0.164786	−	0.507159i	0.999020	+	0.0442509i	$0.0140901\pi$
$978$	37.0156			1.18363
$979$	41.7229	−	2.04062i	1.33347	−	0.0652185i
$980$		0			0
$981$	2.10080	−	6.46561i	0.0670735	−	0.206431i
$982$	−51.3524	+	37.3097i	−1.63872	+	1.19060i
$983$	41.9532	+	30.4808i	1.33810	+	0.972186i	0.999512	+	0.0312510i	$0.00994913\pi$
$983$	41.9532	+	30.4808i	1.33810	+	0.972186i	0.338588	+	0.940935i	$0.390051\pi$
$984$	0.265513	+	0.817166i	0.00846426	+	0.0260503i
$985$		0			0
$986$	13.0284	+	9.46570i	0.414910	+	0.301449i
$987$	5.72618	−	4.16031i	0.182266	−	0.132424i
$988$	2.16012	−	6.64816i	0.0687226	−	0.211506i
$989$	3.25253			0.103425
$990$		0			0
$991$	19.8195			0.629588			0.314794	−	0.949160i	$-0.398065\pi$
$991$	19.8195			0.629588			0.314794	+	0.949160i	$0.398065\pi$
$992$	−2.71908	+	8.36846i	−0.0863308	+	0.265699i
$993$	25.5092	−	18.5335i	0.809510	−	0.588144i
$994$	70.8386	+	51.4672i	2.24686	+	1.63244i
$995$		0			0
$996$	−4.57982	−	14.0953i	−0.145117	−	0.446625i
$997$	−41.7934	−	30.3647i	−1.32361	−	0.961658i	−0.999880	−	0.0155088i	$-0.995063\pi$
$997$	−41.7934	−	30.3647i	−1.32361	−	0.961658i	−0.323730	−	0.946150i	$-0.604937\pi$
$998$	−62.1688	+	45.1683i	−1.96792	+	1.42978i
$999$	−3.56571	+	10.9741i	−0.112814	+	0.347206i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.p.526.2		24
5.2	odd	4		165.2.s.a.64.3	yes	48
5.3	odd	4		165.2.s.a.64.10	yes	48
5.4	even	2		825.2.n.o.526.5		24
11.4	even	5		9075.2.a.dy.1.3		12
11.5	even	5	inner	825.2.n.p.676.2		24
11.7	odd	10		9075.2.a.ea.1.10		12
15.2	even	4		495.2.ba.c.64.10		48
15.8	even	4		495.2.ba.c.64.3		48
55.4	even	10		9075.2.a.dz.1.10		12
55.7	even	20		1815.2.c.k.364.20		24
55.18	even	20		1815.2.c.k.364.5		24
55.27	odd	20		165.2.s.a.49.10	yes	48
55.29	odd	10		9075.2.a.dx.1.3		12
55.37	odd	20		1815.2.c.j.364.5		24
55.38	odd	20		165.2.s.a.49.3	✓	48
55.48	odd	20		1815.2.c.j.364.20		24
55.49	even	10		825.2.n.o.676.5		24
165.38	even	20		495.2.ba.c.379.10		48
165.137	even	20		495.2.ba.c.379.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.s.a.49.3	✓	48	55.38	odd	20
165.2.s.a.49.10	yes	48	55.27	odd	20
165.2.s.a.64.3	yes	48	5.2	odd	4
165.2.s.a.64.10	yes	48	5.3	odd	4
495.2.ba.c.64.3		48	15.8	even	4
495.2.ba.c.64.10		48	15.2	even	4
495.2.ba.c.379.3		48	165.137	even	20
495.2.ba.c.379.10		48	165.38	even	20
825.2.n.o.526.5		24	5.4	even	2
825.2.n.o.676.5		24	55.49	even	10
825.2.n.p.526.2		24	1.1	even	1	trivial
825.2.n.p.676.2		24	11.5	even	5	inner
1815.2.c.j.364.5		24	55.37	odd	20
1815.2.c.j.364.20		24	55.48	odd	20
1815.2.c.k.364.5		24	55.18	even	20
1815.2.c.k.364.20		24	55.7	even	20
9075.2.a.dx.1.3		12	55.29	odd	10
9075.2.a.dy.1.3		12	11.4	even	5
9075.2.a.dz.1.10		12	55.4	even	10
9075.2.a.ea.1.10		12	11.7	odd	10

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.650947 + 2.00341i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-1.97188 - 1.43266i) q^{4} +(-0.650947 - 2.00341i) q^{6} +(-2.68296 - 1.94929i) q^{7} +(0.745386 - 0.541555i) q^{8} +(0.309017 - 0.951057i) q^{9} +(3.31267 - 0.162019i) q^{11} +2.43738 q^{12} +(-0.772198 + 2.37658i) q^{13} +(5.65169 - 4.10619i) q^{14} +(-0.906636 - 2.79034i) q^{16} +(-2.10446 - 6.47687i) q^{17} +(1.70420 + 1.23818i) q^{18} +(0.928503 - 0.674597i) q^{19} +3.31633 q^{21} +(-1.83178 + 6.74209i) q^{22} +5.89026 q^{23} +(-0.284712 + 0.876254i) q^{24} +(-4.25861 - 3.09406i) q^{26} +(0.309017 + 0.951057i) q^{27} +(2.49783 + 7.68753i) q^{28} +(0.908175 + 0.659827i) q^{29} +(-0.338908 + 1.04305i) q^{31} +8.02306 q^{32} +(-2.58477 + 2.07821i) q^{33} +14.3457 q^{34} +(-1.97188 + 1.43266i) q^{36} +(9.33514 + 6.78238i) q^{37} +(0.747087 + 2.29930i) q^{38} +(-0.772198 - 2.37658i) q^{39} +(0.754463 - 0.548149i) q^{41} +(-2.15875 + 6.64396i) q^{42} +0.552188 q^{43} +(-6.76431 - 4.42643i) q^{44} +(-3.83425 + 11.8006i) q^{46} +(1.72666 - 1.25449i) q^{47} +(2.37360 + 1.72452i) q^{48} +(1.23546 + 3.80234i) q^{49} +(5.50956 + 4.00293i) q^{51} +(4.92751 - 3.58005i) q^{52} +(3.59560 - 11.0661i) q^{53} -2.10651 q^{54} -3.05549 q^{56} +(-0.354657 + 1.09152i) q^{57} +(-1.91308 + 1.38993i) q^{58} +(-6.79443 - 4.93644i) q^{59} +(-2.53800 - 7.81115i) q^{61} +(-1.86905 - 1.35794i) q^{62} +(-2.68296 + 1.94929i) q^{63} +(-3.40931 + 10.4928i) q^{64} +(-2.48096 - 6.53116i) q^{66} -4.15419 q^{67} +(-5.12938 + 15.7866i) q^{68} +(-4.76532 + 3.46221i) q^{69} +(3.87323 + 11.9206i) q^{71} +(-0.284712 - 0.876254i) q^{72} +(4.64182 + 3.37248i) q^{73} +(-19.6646 + 14.2871i) q^{74} -2.79736 q^{76} +(-9.20358 - 6.02265i) q^{77} +5.26393 q^{78} +(-1.19514 + 3.67825i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(0.607052 + 1.86831i) q^{82} +(-1.87899 - 5.78295i) q^{83} +(-6.53941 - 4.75116i) q^{84} +(-0.359446 + 1.10626i) q^{86} -1.12257 q^{87} +(2.38147 - 1.91476i) q^{88} +12.5950 q^{89} +(6.70442 - 4.87105i) q^{91} +(-11.6149 - 8.43872i) q^{92} +(-0.338908 - 1.04305i) q^{93} +(1.38930 + 4.27582i) q^{94} +(-6.49079 + 4.71583i) q^{96} +(-0.886486 + 2.72832i) q^{97} -8.42187 q^{98} +(0.869581 - 3.20060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{2} - 6 q^{3} - 6 q^{4} + 2 q^{6} + 4 q^{7} + 6 q^{8} - 6 q^{9} + 24 q^{12} + 4 q^{13} + 2 q^{14} - 22 q^{16} + 4 q^{17} + 2 q^{18} + 8 q^{19} - 16 q^{21} - 4 q^{22} + 6 q^{24} - 38 q^{26} - 6 q^{27}+ \cdots - 120 q^{98}+O(q^{100}) \) 24 * q + 2 * q^2 - 6 * q^3 - 6 * q^4 + 2 * q^6 + 4 * q^7 + 6 * q^8 - 6 * q^9 + 24 * q^12 + 4 * q^13 + 2 * q^14 - 22 * q^16 + 4 * q^17 + 2 * q^18 + 8 * q^19 - 16 * q^21 - 4 * q^22 + 6 * q^24 - 38 * q^26 - 6 * q^27 + 30 * q^28 - 10 * q^31 - 56 * q^32 + 10 * q^33 + 12 * q^34 - 6 * q^36 + 10 * q^37 + 4 * q^38 + 4 * q^39 + 30 * q^41 - 8 * q^42 - 64 * q^43 + 24 * q^44 + 54 * q^46 - 8 * q^47 - 2 * q^48 + 14 * q^49 + 14 * q^51 + 14 * q^52 + 26 * q^53 - 8 * q^54 + 12 * q^56 + 8 * q^57 + 20 * q^58 - 30 * q^59 + 20 * q^61 - 50 * q^62 + 4 * q^63 - 32 * q^64 + 6 * q^66 + 20 * q^67 - 62 * q^68 - 10 * q^69 - 16 * q^71 + 6 * q^72 - 12 * q^73 + 16 * q^74 - 68 * q^76 - 2 * q^77 + 32 * q^78 + 26 * q^79 - 6 * q^81 + 56 * q^82 + 48 * q^83 - 52 * q^86 + 48 * q^88 - 20 * q^89 - 20 * q^91 + 46 * q^92 - 10 * q^93 - 36 * q^94 + 14 * q^96 - 14 * q^97 - 120 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more