LMFDB - Embedded newform 512.2.k.a.17.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(17,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(32))

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

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

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

chi := DirichletCharacter("512.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.k (of order $32$, degree $16$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$15$ over $\Q(\zeta_{32})$
Twist minimal:	no (minimal twist has level 128)
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			17.10
Character	$\chi$	$=$	512.17
Dual form			512.2.k.a.241.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.544320 - 1.01835i) q^{3} +(0.722871 + 0.593245i) q^{5} +(0.369041 + 0.246585i) q^{7} +(0.925956 + 1.38579i) q^{9} +O(q^{10})$	\(q+(0.544320 - 1.01835i) q^{3} +(0.722871 + 0.593245i) q^{5} +(0.369041 + 0.246585i) q^{7} +(0.925956 + 1.38579i) q^{9} +(1.25719 - 4.14439i) q^{11} +(2.13124 + 2.59693i) q^{13} +(0.997605 - 0.413222i) q^{15} +(0.186397 + 0.0772081i) q^{17} +(-0.537097 - 0.0528995i) q^{19} +(0.451987 - 0.241592i) q^{21} +(3.04288 + 0.605267i) q^{23} +(-0.804849 - 4.04625i) q^{25} +(5.36265 - 0.528175i) q^{27} +(6.07798 - 1.84374i) q^{29} +(-5.83359 + 5.83359i) q^{31} +(-3.53614 - 3.53614i) q^{33} +(0.120484 + 0.397181i) q^{35} +(-0.492496 - 5.00040i) q^{37} +(3.80467 - 0.756795i) q^{39} +(-0.219251 + 1.10225i) q^{41} +(-3.08490 - 5.77144i) q^{43} +(-0.152767 + 1.55107i) q^{45} +(-2.50037 + 6.03644i) q^{47} +(-2.60340 - 6.28516i) q^{49} +(0.180085 - 0.147792i) q^{51} +(-3.71182 - 1.12597i) q^{53} +(3.36743 - 2.25004i) q^{55} +(-0.346223 + 0.518160i) q^{57} +(2.62200 - 3.19492i) q^{59} +(10.8521 + 5.80057i) q^{61} +0.739741i q^{63} +3.14160i q^{65} +(2.92853 + 1.56533i) q^{67} +(2.27268 - 2.76926i) q^{69} +(-6.22129 + 9.31081i) q^{71} +(-13.2236 + 8.83574i) q^{73} +(-4.55860 - 1.38284i) q^{75} +(1.48590 - 1.21945i) q^{77} +(-1.92709 - 4.65242i) q^{79} +(0.467701 - 1.12913i) q^{81} +(-0.912400 + 9.26376i) q^{83} +(0.0889376 + 0.166390i) q^{85} +(1.43080 - 7.19310i) q^{87} +(-8.49953 + 1.69066i) q^{89} +(0.146152 + 1.48391i) q^{91} +(2.76530 + 9.11599i) q^{93} +(-0.356870 - 0.356870i) q^{95} +(1.55046 - 1.55046i) q^{97} +(6.90736 - 2.09533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	$ 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) $ 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{7}{32}\right)$	$1$

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
$3$	0.544320	−	1.01835i	0.314263	−	0.587945i	−0.674352	−	0.738410i	$-0.735577\pi$
$3$	0.544320	−	1.01835i	0.314263	−	0.587945i	0.988615	+	0.150465i	$0.0480769\pi$
$4$		0			0
$5$	0.722871	+	0.593245i	0.323278	+	0.265307i	0.782008	−	0.623268i	$-0.214196\pi$
$5$	0.722871	+	0.593245i	0.323278	+	0.265307i	−0.458730	+	0.888576i	$0.651696\pi$
$6$		0			0
$7$	0.369041	+	0.246585i	0.139484	+	0.0932005i	0.623355	−	0.781939i	$-0.285769\pi$
$7$	0.369041	+	0.246585i	0.139484	+	0.0932005i	−0.483870	+	0.875140i	$0.660769\pi$
$8$		0			0
$9$	0.925956	+	1.38579i	0.308652	+	0.461930i
$10$		0			0
$11$	1.25719	−	4.14439i	0.379057	−	1.24958i	−0.535297	−	0.844664i	$-0.679800\pi$
$11$	1.25719	−	4.14439i	0.379057	−	1.24958i	0.914353	−	0.404918i	$-0.132700\pi$
$12$		0			0
$13$	2.13124	+	2.59693i	0.591101	+	0.720259i	0.979548	−	0.201213i	$-0.0644882\pi$
$13$	2.13124	+	2.59693i	0.591101	+	0.720259i	−0.388447	+	0.921471i	$0.626988\pi$
$14$		0			0
$15$	0.997605	−	0.413222i	0.257581	−	0.106693i
$16$		0			0
$17$	0.186397	+	0.0772081i	0.0452079	+	0.0187257i	0.405173	−	0.914240i	$-0.367211\pi$
$17$	0.186397	+	0.0772081i	0.0452079	+	0.0187257i	−0.359965	+	0.932966i	$0.617211\pi$
$18$		0			0
$19$	−0.537097	−	0.0528995i	−0.123219	−	0.0121360i	0.0362198	−	0.999344i	$-0.488468\pi$
$19$	−0.537097	−	0.0528995i	−0.123219	−	0.0121360i	−0.159438	+	0.987208i	$0.550968\pi$
$20$		0			0
$21$	0.451987	−	0.241592i	0.0986317	−	0.0527197i
$22$		0			0
$23$	3.04288	+	0.605267i	0.634485	+	0.126207i	0.501845	−	0.864957i	$-0.332655\pi$
$23$	3.04288	+	0.605267i	0.634485	+	0.126207i	0.132640	+	0.991164i	$0.457655\pi$
$24$		0			0
$25$	−0.804849	−	4.04625i	−0.160970	−	0.809249i
$26$		0			0
$27$	5.36265	−	0.528175i	1.03204	−	0.101647i
$28$		0			0
$29$	6.07798	−	1.84374i	1.12865	−	0.342373i	0.329890	−	0.944019i	$-0.392988\pi$
$29$	6.07798	−	1.84374i	1.12865	−	0.342373i	0.798763	+	0.601646i	$0.205488\pi$
$30$		0			0
$31$	−5.83359	+	5.83359i	−1.04774	+	1.04774i	−0.0489423	+	0.998802i	$0.515585\pi$
$31$	−5.83359	+	5.83359i	−1.04774	+	1.04774i	−0.998802	+	0.0489423i	$0.984415\pi$
$32$		0			0
$33$	−3.53614	−	3.53614i	−0.615562	−	0.615562i
$34$		0			0
$35$	0.120484	+	0.397181i	0.0203655	+	0.0671359i
$36$		0			0
$37$	−0.492496	−	5.00040i	−0.0809658	−	0.822060i	−0.946820	−	0.321764i	$-0.895724\pi$
$37$	−0.492496	−	5.00040i	−0.0809658	−	0.822060i	0.865854	−	0.500296i	$-0.166776\pi$
$38$		0			0
$39$	3.80467	−	0.756795i	0.609234	−	0.121184i
$40$		0			0
$41$	−0.219251	+	1.10225i	−0.0342412	+	0.172142i	−0.994122	−	0.108267i	$-0.965470\pi$
$41$	−0.219251	+	1.10225i	−0.0342412	+	0.172142i	0.959881	+	0.280409i	$0.0904700\pi$
$42$		0			0
$43$	−3.08490	−	5.77144i	−0.470443	−	0.880136i	−0.999502	−	0.0315514i	$-0.989955\pi$
$43$	−3.08490	−	5.77144i	−0.470443	−	0.880136i	0.529060	−	0.848585i	$-0.322545\pi$
$44$		0			0
$45$	−0.152767	+	1.55107i	−0.0227731	+	0.231219i
$46$		0			0
$47$	−2.50037	+	6.03644i	−0.364717	+	0.880505i	0.629880	+	0.776692i	$0.283104\pi$
$47$	−2.50037	+	6.03644i	−0.364717	+	0.880505i	−0.994597	+	0.103812i	$0.966896\pi$
$48$		0			0
$49$	−2.60340	−	6.28516i	−0.371914	−	0.897879i
$50$		0			0
$51$	0.180085	−	0.147792i	0.0252169	−	0.0206950i
$52$		0			0
$53$	−3.71182	−	1.12597i	−0.509857	−	0.154663i	0.0248660	−	0.999691i	$-0.492084\pi$
$53$	−3.71182	−	1.12597i	−0.509857	−	0.154663i	−0.534723	+	0.845027i	$0.679584\pi$
$54$		0			0
$55$	3.36743	−	2.25004i	0.454064	−	0.303396i
$56$		0			0
$57$	−0.346223	+	0.518160i	−0.0458584	+	0.0686319i
$58$		0			0
$59$	2.62200	−	3.19492i	0.341355	−	0.415943i	−0.573831	−	0.818974i	$-0.694543\pi$
$59$	2.62200	−	3.19492i	0.341355	−	0.415943i	0.915186	+	0.403031i	$0.132043\pi$
$60$		0			0
$61$	10.8521	+	5.80057i	1.38947	+	0.742686i	0.985112	−	0.171915i	$-0.0549955\pi$
$61$	10.8521	+	5.80057i	1.38947	+	0.742686i	0.404357	+	0.914601i	$0.367495\pi$
$62$		0			0
$63$			0.739741i			0.0931986i
$64$		0			0
$65$			3.14160i			0.389667i
$66$		0			0
$67$	2.92853	+	1.56533i	0.357777	+	0.191236i	0.640486	−	0.767970i	$-0.278733\pi$
$67$	2.92853	+	1.56533i	0.357777	+	0.191236i	−0.282709	+	0.959206i	$0.591233\pi$
$68$		0			0
$69$	2.27268	−	2.76926i	0.273598	−	0.333380i
$70$		0			0
$71$	−6.22129	+	9.31081i	−0.738331	+	1.10499i	0.252197	+	0.967676i	$0.418847\pi$
$71$	−6.22129	+	9.31081i	−0.738331	+	1.10499i	−0.990528	+	0.137314i	$0.956153\pi$
$72$		0			0
$73$	−13.2236	+	8.83574i	−1.54771	+	1.03415i	−0.570644	+	0.821198i	$0.693306\pi$
$73$	−13.2236	+	8.83574i	−1.54771	+	1.03415i	−0.977064	+	0.212948i	$0.931694\pi$
$74$		0			0
$75$	−4.55860	−	1.38284i	−0.526381	−	0.159676i
$76$		0			0
$77$	1.48590	−	1.21945i	0.169334	−	0.138969i
$78$		0			0
$79$	−1.92709	−	4.65242i	−0.216815	−	0.523438i	0.777627	−	0.628726i	$-0.216423\pi$
$79$	−1.92709	−	4.65242i	−0.216815	−	0.523438i	−0.994442	+	0.105288i	$0.966423\pi$
$80$		0			0
$81$	0.467701	−	1.12913i	0.0519668	−	0.125459i
$82$		0			0
$83$	−0.912400	+	9.26376i	−0.100149	+	1.01683i	0.805441	+	0.592676i	$0.201928\pi$
$83$	−0.912400	+	9.26376i	−0.100149	+	1.01683i	−0.905590	+	0.424154i	$0.860572\pi$
$84$		0			0
$85$	0.0889376	+	0.166390i	0.00964663	+	0.0180476i
$86$		0			0
$87$	1.43080	−	7.19310i	0.153398	−	0.771181i
$88$		0			0
$89$	−8.49953	+	1.69066i	−0.900949	+	0.179210i	−0.623769	−	0.781608i	$-0.714400\pi$
$89$	−8.49953	+	1.69066i	−0.900949	+	0.179210i	−0.277179	+	0.960818i	$0.589400\pi$
$90$		0			0
$91$	0.146152	+	1.48391i	0.0153209	+	0.155556i
$92$		0			0
$93$	2.76530	+	9.11599i	0.286749	+	0.945284i
$94$		0			0
$95$	−0.356870	−	0.356870i	−0.0366141	−	0.0366141i
$96$		0			0
$97$	1.55046	−	1.55046i	0.157425	−	0.157425i	−0.624000	−	0.781425i	$-0.714493\pi$
$97$	1.55046	−	1.55046i	0.157425	−	0.157425i	0.781425	+	0.624000i	$0.214493\pi$
$98$		0			0
$99$	6.90736	−	2.09533i	0.694216	−	0.210588i
$100$		0			0
$101$	−4.76026	+	0.468845i	−0.473664	+	0.0466518i	−0.332033	−	0.943268i	$-0.607735\pi$
$101$	−4.76026	+	0.468845i	−0.473664	+	0.0466518i	−0.141631	+	0.989920i	$0.545235\pi$
$102$		0			0
$103$	0.656616	+	3.30103i	0.0646983	+	0.325261i	0.999557	−	0.0297594i	$-0.00947410\pi$
$103$	0.656616	+	3.30103i	0.0646983	+	0.325261i	−0.934859	+	0.355020i	$0.884474\pi$
$104$		0			0
$105$	0.470052	+	0.0934991i	0.0458724	+	0.00912458i
$106$		0			0
$107$	−13.4775	+	7.20387i	−1.30292	+	0.696425i	−0.969206	−	0.246250i	$-0.920801\pi$
$107$	−13.4775	+	7.20387i	−1.30292	+	0.696425i	−0.333713	+	0.942675i	$0.608301\pi$
$108$		0			0
$109$	−18.2127	−	1.79379i	−1.74446	−	0.171814i	−0.825035	−	0.565082i	$-0.808844\pi$
$109$	−18.2127	−	1.79379i	−1.74446	−	0.171814i	−0.919424	+	0.393268i	$0.871344\pi$
$110$		0			0
$111$	−5.36023	−	2.22028i	−0.508771	−	0.210740i
$112$		0			0
$113$	15.5965	−	6.46026i	1.46719	−	0.607730i	0.500974	−	0.865462i	$-0.332975\pi$
$113$	15.5965	−	6.46026i	1.46719	−	0.607730i	0.966216	+	0.257732i	$0.0829751\pi$
$114$		0			0
$115$	1.84054	+	2.24270i	0.171631	+	0.209133i
$116$		0			0
$117$	−1.62536	+	5.35810i	−0.150265	+	0.495356i
$118$		0			0
$119$	0.0497497	+	0.0744557i	0.00456055	+	0.00682534i
$120$		0			0
$121$	−6.44932	−	4.30929i	−0.586301	−	0.391754i
$122$		0			0
$123$	1.00313	+	0.823249i	0.0904494	+	0.0742299i
$124$		0			0
$125$	4.02272	−	7.52598i	0.359803	−	0.673144i
$126$		0			0
$127$	−18.1137			−1.60733			−0.803667	−	0.595079i	$-0.797121\pi$
$127$	−18.1137			−1.60733			−0.803667	+	0.595079i	$0.797121\pi$
$128$		0			0
$129$	−7.55652			−0.665315
$130$		0			0
$131$	−6.20843	+	11.6151i	−0.542433	+	1.01482i	0.450116	+	0.892970i	$0.351383\pi$
$131$	−6.20843	+	11.6151i	−0.542433	+	1.01482i	−0.992549	+	0.121850i	$0.961117\pi$
$132$		0			0
$133$	−0.185167	−	0.151962i	−0.0160560	−	0.0131768i
$134$		0			0
$135$	4.18984	+	2.79956i	0.360604	+	0.240948i
$136$		0			0
$137$	12.5309	+	18.7538i	1.07059	+	1.60225i	0.757877	+	0.652397i	$0.226237\pi$
$137$	12.5309	+	18.7538i	1.07059	+	1.60225i	0.312710	+	0.949849i	$0.398763\pi$
$138$		0			0
$139$	6.12833	−	20.2024i	0.519799	−	1.71355i	−0.166334	−	0.986069i	$-0.553193\pi$
$139$	6.12833	−	20.2024i	0.519799	−	1.71355i	0.686133	−	0.727477i	$-0.259307\pi$
$140$		0			0
$141$	4.78621	+	5.83201i	0.403071	+	0.491144i
$142$		0			0
$143$	13.4421	−	5.56789i	1.12408	−	0.465610i
$144$		0			0
$145$	5.48738	+	2.27295i	0.455702	+	0.188758i
$146$		0			0
$147$	−7.81758	−	0.769964i	−0.644783	−	0.0635056i
$148$		0			0
$149$	−11.9439	+	6.38413i	−0.978480	+	0.523009i	−0.881452	−	0.472273i	$-0.843434\pi$
$149$	−11.9439	+	6.38413i	−0.978480	+	0.523009i	−0.0970280	+	0.995282i	$0.530934\pi$
$150$		0			0
$151$	−8.49166	−	1.68910i	−0.691042	−	0.137457i	−0.162938	−	0.986636i	$-0.552097\pi$
$151$	−8.49166	−	1.68910i	−0.691042	−	0.137457i	−0.528104	+	0.849180i	$0.677097\pi$
$152$		0			0
$153$	0.0656009	+	0.329798i	0.00530352	+	0.0266626i
$154$		0			0
$155$	−7.67768	+	0.756186i	−0.616686	+	0.0607383i
$156$		0			0
$157$	−11.9132	+	3.61383i	−0.950777	+	0.288415i	−0.727320	−	0.686299i	$-0.759234\pi$
$157$	−11.9132	+	3.61383i	−0.950777	+	0.288415i	−0.223457	+	0.974714i	$0.571734\pi$
$158$		0			0
$159$	−3.16705	+	3.16705i	−0.251163	+	0.251163i
$160$		0			0
$161$	0.973699	+	0.973699i	0.0767382	+	0.0767382i
$162$		0			0
$163$	−3.96369	−	13.0665i	−0.310460	−	1.02345i	−0.963854	−	0.266431i	$-0.914156\pi$
$163$	−3.96369	−	13.0665i	−0.310460	−	1.02345i	0.653394	−	0.757018i	$-0.273344\pi$
$164$		0			0
$165$	−0.458376	−	4.65397i	−0.0356845	−	0.362311i
$166$		0			0
$167$	10.2667	−	2.04218i	0.794465	−	0.158029i	0.218859	−	0.975756i	$-0.429766\pi$
$167$	10.2667	−	2.04218i	0.794465	−	0.158029i	0.575605	+	0.817728i	$0.304766\pi$
$168$		0			0
$169$	0.334337	−	1.68083i	0.0257183	−	0.129294i
$170$		0			0
$171$	−0.424021	−	0.793287i	−0.0324257	−	0.0606642i
$172$		0			0
$173$	1.00559	−	10.2099i	0.0764533	−	0.776244i	−0.878154	−	0.478377i	$-0.841225\pi$
$173$	1.00559	−	10.2099i	0.0764533	−	0.776244i	0.954608	−	0.297866i	$-0.0962749\pi$
$174$		0			0
$175$	0.700723	−	1.69170i	0.0529697	−	0.127880i
$176$		0			0
$177$	−1.82634	−	4.40917i	−0.137276	−	0.331414i
$178$		0			0
$179$	−2.40319	+	1.97224i	−0.179623	+	0.147413i	−0.719908	−	0.694069i	$-0.755816\pi$
$179$	−2.40319	+	1.97224i	−0.179623	+	0.147413i	0.540286	+	0.841482i	$0.318316\pi$
$180$		0			0
$181$	−9.74794	−	2.95700i	−0.724558	−	0.219792i	−0.0936009	−	0.995610i	$-0.529838\pi$
$181$	−9.74794	−	2.95700i	−0.724558	−	0.219792i	−0.630957	+	0.775817i	$0.717338\pi$
$182$		0			0
$183$	11.8140	−	7.89388i	0.873318	−	0.583532i
$184$		0			0
$185$	2.61045	−	3.90681i	0.191924	−	0.287235i
$186$		0			0
$187$	0.554317	−	0.675437i	0.0405356	−	0.0493928i
$188$		0			0
$189$	2.10928	+	1.12743i	0.153427	+	0.0820086i
$190$		0			0
$191$		−	10.0891i		−	0.730024i	−0.931003	−	0.365012i	$-0.881065\pi$
$191$		−	10.0891i		−	0.730024i	0.931003	−	0.365012i	$-0.118935\pi$
$192$		0			0
$193$			8.20239i			0.590421i	0.955432	+	0.295211i	$0.0953898\pi$
$193$			8.20239i			0.590421i	−0.955432	+	0.295211i	$0.904610\pi$
$194$		0			0
$195$	3.19925	+	1.71003i	0.229103	+	0.122458i
$196$		0			0
$197$	12.4235	−	15.1381i	0.885137	−	1.07854i	−0.111265	−	0.993791i	$-0.535490\pi$
$197$	12.4235	−	15.1381i	0.885137	−	1.07854i	0.996402	−	0.0847516i	$-0.0270097\pi$
$198$		0			0
$199$	−3.01565	+	4.51325i	−0.213774	+	0.319936i	−0.922823	−	0.385223i	$-0.874124\pi$
$199$	−3.01565	+	4.51325i	−0.213774	+	0.319936i	0.709049	+	0.705159i	$0.249124\pi$
$200$		0			0
$201$	3.18811	−	2.13023i	0.224872	−	0.150255i
$202$		0			0
$203$	2.69766	+	0.818327i	0.189339	+	0.0574353i
$204$		0			0
$205$	−0.812392	+	0.666713i	−0.0567399	+	0.0465653i
$206$		0			0
$207$	1.97880	+	4.77725i	0.137536	+	0.332042i
$208$		0			0
$209$	−0.894469	+	2.15944i	−0.0618717	+	0.149371i
$210$		0			0
$211$	−1.80947	+	18.3718i	−0.124569	+	1.26477i	0.706144	+	0.708068i	$0.250433\pi$
$211$	−1.80947	+	18.3718i	−0.124569	+	1.26477i	−0.830713	+	0.556701i	$0.812067\pi$
$212$		0			0
$213$	6.09531	+	11.4035i	0.417644	+	0.781356i
$214$		0			0
$215$	1.19389	−	6.00211i	0.0814228	−	0.409340i
$216$		0			0
$217$	−3.59131	+	0.714357i	−0.243794	+	0.0484937i
$218$		0			0
$219$	1.80001	+	18.2758i	0.121633	+	1.23496i
$220$		0			0
$221$	0.196753	+	0.648609i	0.0132351	+	0.0436301i
$222$		0			0
$223$	−4.46837	−	4.46837i	−0.299225	−	0.299225i	0.541486	−	0.840710i	$-0.317862\pi$
$223$	−4.46837	−	4.46837i	−0.299225	−	0.299225i	−0.840710	+	0.541486i	$0.817862\pi$
$224$		0			0
$225$	4.86200	−	4.86200i	0.324133	−	0.324133i
$226$		0			0
$227$	20.5429	−	6.23163i	1.36348	−	0.413608i	0.478032	−	0.878342i	$-0.341350\pi$
$227$	20.5429	−	6.23163i	1.36348	−	0.413608i	0.885450	+	0.464735i	$0.153850\pi$
$228$		0			0
$229$	−19.4392	+	1.91459i	−1.28458	+	0.126520i	−0.717159	−	0.696910i	$-0.754558\pi$
$229$	−19.4392	+	1.91459i	−1.28458	+	0.126520i	−0.567418	+	0.823430i	$0.692058\pi$
$230$		0			0
$231$	−0.433020	−	2.17694i	−0.0284906	−	0.143232i
$232$		0			0
$233$	21.6381	+	4.30409i	1.41756	+	0.281970i	0.843626	−	0.536931i	$-0.180416\pi$
$233$	21.6381	+	4.30409i	1.41756	+	0.281970i	0.573934	+	0.818901i	$0.305416\pi$
$234$		0			0
$235$	−5.38853	+	2.88023i	−0.351509	+	0.187886i
$236$		0			0
$237$	−5.78675	−	0.569945i	−0.375890	−	0.0370219i
$238$		0			0
$239$	14.8712	+	6.15987i	0.961941	+	0.398449i	0.807706	−	0.589585i	$-0.200709\pi$
$239$	14.8712	+	6.15987i	0.961941	+	0.398449i	0.154235	+	0.988034i	$0.450709\pi$
$240$		0			0
$241$	19.7115	−	8.16479i	1.26973	−	0.525940i	0.356849	−	0.934162i	$-0.383851\pi$
$241$	19.7115	−	8.16479i	1.26973	−	0.525940i	0.912883	+	0.408222i	$0.133851\pi$
$242$		0			0
$243$	9.36019	+	11.4054i	0.600457	+	0.731658i
$244$		0			0
$245$	1.84672	−	6.08781i	0.117982	−	0.388936i
$246$		0			0
$247$	−1.00731	−	1.50755i	−0.0640936	−	0.0959228i
$248$		0			0
$249$	8.93712	+	5.97159i	0.566367	+	0.378434i
$250$		0			0
$251$	0.0449481	+	0.0368880i	0.00283710	+	0.00232835i	0.635811	−	0.771845i	$-0.280666\pi$
$251$	0.0449481	+	0.0368880i	0.00283710	+	0.00232835i	−0.632974	+	0.774173i	$0.718166\pi$
$252$		0			0
$253$	6.33394	−	11.8500i	0.398211	−	0.745001i
$254$		0			0
$255$	0.217854			0.0136426
$256$		0			0
$257$	4.21819			0.263124			0.131562	−	0.991308i	$-0.458001\pi$
$257$	4.21819			0.263124			0.131562	+	0.991308i	$0.458001\pi$
$258$		0			0
$259$	1.05127	−	1.96679i	0.0653230	−	0.122211i
$260$		0			0
$261$	8.18297	+	6.71559i	0.506513	+	0.415685i
$262$		0			0
$263$	8.63308	+	5.76844i	0.532339	+	0.355697i	0.792504	−	0.609867i	$-0.208777\pi$
$263$	8.63308	+	5.76844i	0.532339	+	0.355697i	−0.260165	+	0.965564i	$0.583777\pi$
$264$		0			0
$265$	−2.01519	−	3.01595i	−0.123792	−	0.185268i
$266$		0			0
$267$	−2.90478	+	9.57577i	−0.177770	+	0.586028i
$268$		0			0
$269$	−8.78720	−	10.7072i	−0.535765	−	0.652832i	0.432830	−	0.901476i	$-0.357515\pi$
$269$	−8.78720	−	10.7072i	−0.535765	−	0.652832i	−0.968595	+	0.248644i	$0.920015\pi$
$270$		0			0
$271$	22.8523	−	9.46571i	1.38818	−	0.575001i	0.441521	−	0.897251i	$-0.354439\pi$
$271$	22.8523	−	9.46571i	1.38818	−	0.575001i	0.946655	+	0.322250i	$0.104439\pi$
$272$		0			0
$273$	1.59069	+	0.658887i	0.0962731	+	0.0398776i
$274$		0			0
$275$	−17.7811	−	1.75128i	−1.07224	−	0.105606i
$276$		0			0
$277$	1.05780	−	0.565408i	0.0635573	−	0.0339721i	−0.439312	−	0.898335i	$-0.644778\pi$
$277$	1.05780	−	0.565408i	0.0635573	−	0.0339721i	0.502869	+	0.864362i	$0.332278\pi$
$278$		0			0
$279$	−13.4858	−	2.68249i	−0.807373	−	0.160596i
$280$		0			0
$281$	−1.60654	−	8.07662i	−0.0958381	−	0.481811i	−0.998658	−	0.0517916i	$-0.983507\pi$
$281$	−1.60654	−	8.07662i	−0.0958381	−	0.481811i	0.902820	−	0.430019i	$-0.141493\pi$
$282$		0			0
$283$	20.4191	−	2.01111i	1.21379	−	0.119548i	0.529215	−	0.848488i	$-0.322487\pi$
$283$	20.4191	−	2.01111i	1.21379	−	0.119548i	0.684578	+	0.728940i	$0.259987\pi$
$284$		0			0
$285$	−0.557670	+	0.169167i	−0.0330335	+	0.0100206i
$286$		0			0
$287$	−0.352711	+	0.352711i	−0.0208198	+	0.0208198i
$288$		0			0
$289$	−11.9920	−	11.9920i	−0.705414	−	0.705414i
$290$		0			0
$291$	−0.734966	−	2.42286i	−0.0430845	−	0.142030i
$292$		0			0
$293$	−1.28410	−	13.0377i	−0.0750182	−	0.761672i	−0.956942	−	0.290280i	$-0.906252\pi$
$293$	−1.28410	−	13.0377i	−0.0750182	−	0.761672i	0.881924	−	0.471392i	$-0.156248\pi$
$294$		0			0
$295$	3.79074	−	0.754024i	0.220705	−	0.0439010i
$296$		0			0
$297$	4.55289	−	22.8889i	0.264186	−	1.32815i
$298$		0			0
$299$	4.91329	+	9.19212i	0.284143	+	0.531594i
$300$		0			0
$301$	0.284698	−	2.89059i	0.0164097	−	0.166611i
$302$		0			0
$303$	−2.11366	+	5.10282i	−0.121427	+	0.293150i
$304$		0			0
$305$	4.40351	+	10.6310i	0.252144	+	0.608730i
$306$		0			0
$307$	1.53894	−	1.26298i	0.0878321	−	0.0720819i	−0.589453	−	0.807803i	$-0.700657\pi$
$307$	1.53894	−	1.26298i	0.0878321	−	0.0720819i	0.677285	+	0.735721i	$0.263157\pi$
$308$		0			0
$309$	3.71902	+	1.12815i	0.211568	+	0.0641784i
$310$		0			0
$311$	7.58571	−	5.06861i	0.430146	−	0.287415i	−0.321589	−	0.946879i	$-0.604217\pi$
$311$	7.58571	−	5.06861i	0.430146	−	0.287415i	0.751736	+	0.659465i	$0.229217\pi$
$312$		0			0
$313$	4.34582	−	6.50398i	0.245640	−	0.367627i	−0.688077	−	0.725638i	$-0.741545\pi$
$313$	4.34582	−	6.50398i	0.245640	−	0.367627i	0.933717	+	0.358011i	$0.116545\pi$
$314$		0			0
$315$	−0.438848	+	0.534737i	−0.0247263	+	0.0301290i
$316$		0			0
$317$	−1.28140	−	0.684923i	−0.0719706	−	0.0384691i	0.435019	−	0.900421i	$-0.356742\pi$
$317$	−1.28140	−	0.684923i	−0.0719706	−	0.0384691i	−0.506989	+	0.861952i	$0.669242\pi$
$318$		0			0
$319$		−	27.5075i		−	1.54012i
$320$		0			0
$321$			17.6460i			0.984906i
$322$		0			0
$323$	−0.0960290	−	0.0513285i	−0.00534319	−	0.00285600i
$324$		0			0
$325$	8.79249	−	10.7137i	0.487719	−	0.594288i
$326$		0			0
$327$	−11.7402	+	17.5705i	−0.649237	+	0.971652i
$328$		0			0
$329$	−2.41124	+	1.61114i	−0.132936	+	0.0888249i
$330$		0			0
$331$	7.46120	+	2.26333i	0.410105	+	0.124404i	0.488594	−	0.872511i	$-0.337510\pi$
$331$	7.46120	+	2.26333i	0.410105	+	0.124404i	−0.0784897	+	0.996915i	$0.525010\pi$
$332$		0			0
$333$	6.47347	−	5.31264i	0.354744	−	0.291131i
$334$		0			0
$335$	1.18832	+	2.86887i	0.0649250	+	0.156743i
$336$		0			0
$337$	−4.30787	+	10.4001i	−0.234664	+	0.566530i	−0.996715	−	0.0809872i	$-0.974193\pi$
$337$	−4.30787	+	10.4001i	−0.234664	+	0.566530i	0.762051	+	0.647517i	$0.224193\pi$
$338$		0			0
$339$	1.91065	−	19.3991i	0.103772	−	1.05362i
$340$		0			0
$341$	16.8428	+	31.5106i	0.912088	+	1.70640i
$342$		0			0
$343$	1.19519	−	6.00864i	0.0645343	−	0.324436i
$344$		0			0
$345$	3.28570	−	0.653567i	0.176896	−	0.0351869i
$346$		0			0
$347$	1.16504	+	11.8289i	0.0625428	+	0.635008i	0.974449	+	0.224609i	$0.0721105\pi$
$347$	1.16504	+	11.8289i	0.0625428	+	0.635008i	−0.911906	+	0.410399i	$0.865390\pi$
$348$		0			0
$349$	3.54373	+	11.6821i	0.189691	+	0.625329i	0.999266	+	0.0383114i	$0.0121979\pi$
$349$	3.54373	+	11.6821i	0.189691	+	0.625329i	−0.809575	+	0.587017i	$0.800302\pi$
$350$		0			0
$351$	12.8007	+	12.8007i	0.683253	+	0.683253i
$352$		0			0
$353$	−24.9897	+	24.9897i	−1.33007	+	1.33007i	−0.424762	+	0.905305i	$0.639642\pi$
$353$	−24.9897	+	24.9897i	−1.33007	+	1.33007i	−0.905305	+	0.424762i	$0.860358\pi$
$354$		0			0
$355$	−10.0208	+	3.03977i	−0.531848	+	0.161334i
$356$		0			0
$357$	0.102902	−	0.0101349i	0.00544614	−	0.000536398i
$358$		0			0
$359$	−6.55968	−	32.9777i	−0.346207	−	1.74050i	−0.625437	−	0.780274i	$-0.715079\pi$
$359$	−6.55968	−	32.9777i	−0.346207	−	1.74050i	0.279231	−	0.960224i	$-0.409921\pi$
$360$		0			0
$361$	−18.3492	−	3.64989i	−0.965750	−	0.192100i
$362$		0			0
$363$	−7.89887	+	4.22203i	−0.414583	+	0.221599i
$364$		0			0
$365$	−14.8007	−	1.45774i	−0.774706	−	0.0763019i
$366$		0			0
$367$	−22.5337	−	9.33377i	−1.17625	−	0.487219i	−0.292997	−	0.956113i	$-0.594652\pi$
$367$	−22.5337	−	9.33377i	−1.17625	−	0.487219i	−0.883254	+	0.468894i	$0.844652\pi$
$368$		0			0
$369$	−1.73050	+	0.716796i	−0.0900862	+	0.0373149i
$370$		0			0
$371$	−1.09217	−	1.33081i	−0.0567024	−	0.0690921i
$372$		0			0
$373$	2.73990	−	9.03224i	0.141867	−	0.467672i	−0.856997	−	0.515321i	$-0.827673\pi$
$373$	2.73990	−	9.03224i	0.141867	−	0.467672i	0.998864	+	0.0476488i	$0.0151728\pi$
$374$		0			0
$375$	−5.47444	−	8.19308i	−0.282699	−	0.423089i
$376$		0			0
$377$	17.7417	+	11.8546i	0.913745	+	0.610545i
$378$		0			0
$379$	−14.9981	−	12.3086i	−0.770399	−	0.632250i	0.164818	−	0.986324i	$-0.447296\pi$
$379$	−14.9981	−	12.3086i	−0.770399	−	0.632250i	−0.935218	+	0.354074i	$0.884796\pi$
$380$		0			0
$381$	−9.85967	+	18.4462i	−0.505126	+	0.945025i
$382$		0			0
$383$	18.0702			0.923345			0.461672	−	0.887051i	$-0.347250\pi$
$383$	18.0702			0.923345			0.461672	+	0.887051i	$0.347250\pi$
$384$		0			0
$385$	1.79755			0.0916115
$386$		0			0
$387$	5.14153	−	9.61912i	0.261358	−	0.488967i
$388$		0			0
$389$	−1.51958	−	1.24709i	−0.0770459	−	0.0632299i	0.595082	−	0.803665i	$-0.297120\pi$
$389$	−1.51958	−	1.24709i	−0.0770459	−	0.0632299i	−0.672128	+	0.740435i	$0.734620\pi$
$390$		0			0
$391$	0.520452	+	0.347755i	0.0263204	+	0.0175867i
$392$		0			0
$393$	8.44893	+	12.6447i	0.426192	+	0.637842i
$394$		0			0
$395$	1.36698	−	4.50634i	0.0687804	−	0.226738i
$396$		0			0
$397$	15.1834	+	18.5010i	0.762031	+	0.928538i	0.999077	−	0.0429609i	$-0.0136791\pi$
$397$	15.1834	+	18.5010i	0.762031	+	0.928538i	−0.237046	+	0.971499i	$0.576179\pi$
$398$		0			0
$399$	−0.255541	+	0.105849i	−0.0127931	+	0.00529906i
$400$		0			0
$401$	−17.6699	−	7.31912i	−0.882393	−	0.365499i	−0.104969	−	0.994476i	$-0.533474\pi$
$401$	−17.6699	−	7.31912i	−0.882393	−	0.365499i	−0.777425	+	0.628976i	$0.783474\pi$
$402$		0			0
$403$	−27.5822	−	2.71661i	−1.37397	−	0.135324i
$404$		0			0
$405$	1.00794	−	0.538755i	0.0500849	−	0.0267709i
$406$		0			0
$407$	−21.3428	−	4.24534i	−1.05792	−	0.210434i
$408$		0			0
$409$	−4.51798	−	22.7134i	−0.223400	−	1.12311i	−0.915813	−	0.401604i	$-0.868453\pi$
$409$	−4.51798	−	22.7134i	−0.223400	−	1.12311i	0.692414	−	0.721501i	$-0.256547\pi$
$410$		0			0
$411$	25.9188	−	2.55278i	1.27848	−	0.125919i
$412$		0			0
$413$	1.75545	−	0.532509i	0.0863798	−	0.0262030i
$414$		0			0
$415$	−6.15523	+	6.15523i	−0.302148	+	0.302148i
$416$		0			0
$417$	−17.2374	−	17.2374i	−0.844118	−	0.844118i
$418$		0			0
$419$	−10.6550	−	35.1247i	−0.520529	−	1.71596i	−0.684068	−	0.729418i	$-0.739791\pi$
$419$	−10.6550	−	35.1247i	−0.520529	−	1.71596i	0.163538	−	0.986537i	$-0.447709\pi$
$420$		0			0
$421$	0.940660	+	9.55068i	0.0458450	+	0.465472i	0.990511	+	0.137437i	$0.0438864\pi$
$421$	0.940660	+	9.55068i	0.0458450	+	0.465472i	−0.944666	+	0.328035i	$0.893614\pi$
$422$		0			0
$423$	−10.6805	+	2.12448i	−0.519302	+	0.103296i
$424$		0			0
$425$	0.162382	−	0.816348i	0.00787667	−	0.0395987i
$426$		0			0
$427$	2.57454	+	4.81662i	0.124590	+	0.233092i
$428$		0			0
$429$	1.64672	−	16.7195i	0.0795046	−	0.807224i
$430$		0			0
$431$	−4.21146	+	10.1674i	−0.202859	+	0.489745i	−0.992267	−	0.124124i	$-0.960388\pi$
$431$	−4.21146	+	10.1674i	−0.202859	+	0.489745i	0.789408	+	0.613869i	$0.210388\pi$
$432$		0			0
$433$	3.86332	+	9.32687i	0.185659	+	0.448221i	0.989115	−	0.147143i	$-0.0470078\pi$
$433$	3.86332	+	9.32687i	0.185659	+	0.448221i	−0.803456	+	0.595364i	$0.797008\pi$
$434$		0			0
$435$	5.30155	−	4.35087i	0.254190	−	0.208608i
$436$		0			0
$437$	−1.60231	−	0.486054i	−0.0766487	−	0.0232511i
$438$		0			0
$439$	−24.8926	+	16.6327i	−1.18806	+	0.793834i	−0.982764	−	0.184866i	$-0.940815\pi$
$439$	−24.8926	+	16.6327i	−1.18806	+	0.793834i	−0.205294	+	0.978700i	$0.565815\pi$
$440$		0			0
$441$	6.29928	−	9.42754i	0.299966	−	0.448930i
$442$		0			0
$443$	−12.7112	+	15.4887i	−0.603928	+	0.735889i	−0.981789	−	0.189974i	$-0.939160\pi$
$443$	−12.7112	+	15.4887i	−0.603928	+	0.735889i	0.377861	+	0.925862i	$0.376660\pi$
$444$		0			0
$445$	−7.14704	−	3.82017i	−0.338802	−	0.181094i
$446$		0			0
$447$			15.6381i			0.739655i
$448$		0			0
$449$			25.2981i			1.19389i	0.802282	+	0.596945i	$0.203619\pi$
$449$			25.2981i			1.19389i	−0.802282	+	0.596945i	$0.796381\pi$
$450$		0			0
$451$	4.29251	+	2.29439i	0.202126	+	0.108039i
$452$		0			0
$453$	−6.34228	+	7.72809i	−0.297986	+	0.363097i
$454$		0			0
$455$	−0.774672	+	1.15938i	−0.0363172	+	0.0543525i
$456$		0			0
$457$	8.79303	−	5.87532i	0.411321	−	0.274836i	−0.332647	−	0.943051i	$-0.607942\pi$
$457$	8.79303	−	5.87532i	0.411321	−	0.274836i	0.743967	+	0.668216i	$0.232942\pi$
$458$		0			0
$459$	1.04036	+	0.315590i	0.0485598	+	0.0147305i
$460$		0			0
$461$	−16.4326	+	13.4859i	−0.765341	+	0.628099i	−0.933876	−	0.357596i	$-0.883596\pi$
$461$	−16.4326	+	13.4859i	−0.765341	+	0.628099i	0.168535	+	0.985696i	$0.446096\pi$
$462$		0			0
$463$	9.76969	+	23.5861i	0.454036	+	1.09614i	0.970774	+	0.239996i	$0.0771462\pi$
$463$	9.76969	+	23.5861i	0.454036	+	1.09614i	−0.516738	+	0.856144i	$0.672854\pi$
$464$		0			0
$465$	−3.40906	+	8.23019i	−0.158091	+	0.381666i
$466$		0			0
$467$	1.54324	−	15.6688i	0.0714125	−	0.725064i	−0.891096	−	0.453814i	$-0.850063\pi$
$467$	1.54324	−	15.6688i	0.0714125	−	0.725064i	0.962509	−	0.271250i	$-0.0874369\pi$
$468$		0			0
$469$	0.694760	+	1.29980i	0.0320810	+	0.0600194i
$470$		0			0
$471$	−2.80445	+	14.0989i	−0.129222	+	0.649643i
$472$		0			0
$473$	−27.7974	+	5.52925i	−1.27813	+	0.254235i
$474$		0			0
$475$	0.218238	+	2.21580i	0.0100134	+	0.101668i
$476$		0			0
$477$	−1.87662	−	6.18640i	−0.0859246	−	0.283256i
$478$		0			0
$479$	14.7232	+	14.7232i	0.672718	+	0.672718i	0.958342	−	0.285624i	$-0.0922007\pi$
$479$	14.7232	+	14.7232i	0.672718	+	0.672718i	−0.285624	+	0.958342i	$0.592201\pi$
$480$		0			0
$481$	11.9360	−	11.9360i	0.544237	−	0.544237i
$482$		0			0
$483$	1.52157	−	0.461564i	0.0692339	−	0.0210019i
$484$		0			0
$485$	2.04058	−	0.200980i	0.0926581	−	0.00912603i
$486$		0			0
$487$	4.22762	+	21.2537i	0.191572	+	0.963095i	0.950216	+	0.311591i	$0.100862\pi$
$487$	4.22762	+	21.2537i	0.191572	+	0.963095i	−0.758645	+	0.651504i	$0.774138\pi$
$488$		0			0
$489$	−15.4638	−	3.07595i	−0.699298	−	0.139099i
$490$		0			0
$491$	2.28801	−	1.22297i	0.103256	−	0.0551917i	−0.418960	−	0.908005i	$-0.637605\pi$
$491$	2.28801	−	1.22297i	0.103256	−	0.0551917i	0.522216	+	0.852813i	$0.325105\pi$
$492$		0			0
$493$	1.27527	+	0.125603i	0.0574352	+	0.00565687i
$494$		0			0
$495$	6.23617	+	2.58311i	0.280295	+	0.116102i
$496$		0			0
$497$	−4.59182	+	1.90199i	−0.205971	+	0.0853161i
$498$		0			0
$499$	3.52643	+	4.29697i	0.157865	+	0.192359i	0.845936	−	0.533284i	$-0.179042\pi$
$499$	3.52643	+	4.29697i	0.157865	+	0.192359i	−0.688071	+	0.725643i	$0.741542\pi$
$500$		0			0
$501$	3.50874	−	11.5668i	0.156759	−	0.516764i
$502$		0			0
$503$	22.9167	+	34.2973i	1.02181	+	1.52924i	0.837548	+	0.546364i	$0.183989\pi$
$503$	22.9167	+	34.2973i	1.02181	+	1.52924i	0.184259	+	0.982878i	$0.441011\pi$
$504$		0			0
$505$	−3.71920	−	2.48509i	−0.165502	−	0.110585i
$506$		0			0
$507$	−1.52969	−	1.25538i	−0.0679357	−	0.0557534i
$508$		0			0
$509$	17.6193	−	32.9634i	0.780963	−	1.46108i	−0.103581	−	0.994621i	$-0.533030\pi$
$509$	17.6193	−	32.9634i	0.780963	−	1.46108i	0.884544	−	0.466458i	$-0.154470\pi$
$510$		0			0
$511$	−7.05883			−0.312264
$512$		0			0
$513$	−2.90820			−0.128400
$514$		0			0
$515$	−1.48367	+	2.77576i	−0.0653784	+	0.122314i
$516$		0			0
$517$	21.8739	+	17.9515i	0.962014	+	0.789505i
$518$		0			0
$519$	−9.84989	−	6.58149i	−0.432362	−	0.288895i
$520$		0			0
$521$	−6.26644	−	9.37838i	−0.274538	−	0.410874i	0.668422	−	0.743782i	$-0.266970\pi$
$521$	−6.26644	−	9.37838i	−0.274538	−	0.410874i	−0.942959	+	0.332908i	$0.891970\pi$
$522$		0			0
$523$	0.419233	−	1.38202i	0.0183318	−	0.0604317i	−0.947297	−	0.320356i	$-0.896198\pi$
$523$	0.419233	−	1.38202i	0.0183318	−	0.0604317i	0.965629	+	0.259924i	$0.0836975\pi$
$524$		0			0
$525$	−1.34132	−	1.63441i	−0.0585401	−	0.0713314i
$526$		0			0
$527$	−1.53776	+	0.636962i	−0.0669860	+	0.0277465i
$528$		0			0
$529$	−12.3564	−	5.11821i	−0.537237	−	0.222531i
$530$		0			0
$531$	6.85534	+	0.675192i	0.297496	+	0.0293008i
$532$		0			0
$533$	−3.32973	+	1.77978i	−0.144227	+	0.0770908i
$534$		0			0
$535$	−14.0162	−	2.78799i	−0.605971	−	0.120535i
$536$		0			0
$537$	0.700335	+	3.52082i	0.0302217	+	0.151935i
$538$		0			0
$539$	−29.3211	+	2.88788i	−1.26295	+	0.124390i
$540$		0			0
$541$	−28.1469	+	8.53827i	−1.21013	+	0.367089i	−0.829957	−	0.557827i	$-0.811635\pi$
$541$	−28.1469	+	8.53827i	−1.21013	+	0.367089i	−0.380173	+	0.924916i	$0.624135\pi$
$542$		0			0
$543$	−8.31727	+	8.31727i	−0.356928	+	0.356928i
$544$		0			0
$545$	−12.1013	−	12.1013i	−0.518361	−	0.518361i
$546$		0			0
$547$	0.229364	+	0.756110i	0.00980688	+	0.0323289i	0.961707	−	0.274079i	$-0.0883729\pi$
$547$	0.229364	+	0.756110i	0.00980688	+	0.0323289i	−0.951900	+	0.306408i	$0.900873\pi$
$548$		0			0
$549$	2.01019	+	20.4098i	0.0857928	+	0.871069i
$550$		0			0
$551$	−3.36200	+	0.668743i	−0.143226	+	0.0284894i
$552$		0			0
$553$	0.436041	−	2.19213i	0.0185424	−	0.0932187i
$554$		0			0
$555$	−2.55759	−	4.78491i	−0.108564	−	0.203108i
$556$		0			0
$557$	−0.293996	+	2.98499i	−0.0124570	+	0.126478i	−0.999402	−	0.0345799i	$-0.988991\pi$
$557$	−0.293996	+	2.98499i	−0.0124570	+	0.126478i	0.986945	+	0.161058i	$0.0514907\pi$
$558$		0			0
$559$	8.41334	−	20.3116i	0.355847	−	0.859089i
$560$		0			0
$561$	−0.386106	−	0.932143i	−0.0163014	−	0.0393551i
$562$		0			0
$563$	26.3432	−	21.6193i	1.11023	−	0.911146i	0.113633	−	0.993523i	$-0.463751\pi$
$563$	26.3432	−	21.6193i	1.11023	−	0.911146i	0.996601	+	0.0823768i	$0.0262511\pi$
$564$		0			0
$565$	15.1067	+	4.58258i	0.635545	+	0.192791i
$566$		0			0
$567$	0.451028	−	0.301368i	0.0189414	−	0.0126562i
$568$		0			0
$569$	5.43701	−	8.13706i	0.227931	−	0.341123i	−0.699822	−	0.714317i	$-0.746737\pi$
$569$	5.43701	−	8.13706i	0.227931	−	0.341123i	0.927753	+	0.373194i	$0.121737\pi$
$570$		0			0
$571$	4.21942	−	5.14138i	0.176577	−	0.215160i	−0.677199	−	0.735800i	$-0.736807\pi$
$571$	4.21942	−	5.14138i	0.176577	−	0.215160i	0.853776	+	0.520640i	$0.174307\pi$
$572$		0			0
$573$	−10.2743	−	5.49172i	−0.429214	−	0.229420i
$574$		0			0
$575$		−	12.7994i		−	0.533772i
$576$		0			0
$577$		−	29.8145i		−	1.24119i	−0.784130	−	0.620597i	$-0.786890\pi$
$577$		−	29.8145i		−	1.24119i	0.784130	−	0.620597i	$-0.213110\pi$
$578$		0			0
$579$	8.35292	+	4.46473i	0.347135	+	0.185548i
$580$		0			0
$581$	−2.62102	+	3.19372i	−0.108738	+	0.132498i
$582$		0			0
$583$	−9.33290	+	13.9677i	−0.386529	+	0.578482i
$584$		0			0
$585$	−4.35359	+	2.90898i	−0.179999	+	0.120271i
$586$		0			0
$587$	5.76298	+	1.74818i	0.237864	+	0.0721551i	0.406966	−	0.913443i	$-0.366587\pi$
$587$	5.76298	+	1.74818i	0.237864	+	0.0721551i	−0.169102	+	0.985599i	$0.554087\pi$
$588$		0			0
$589$	3.44180	−	2.82461i	0.141817	−	0.116386i
$590$		0			0
$591$	−8.65351	−	20.8914i	−0.355958	−	0.859359i
$592$		0			0
$593$	−8.56069	+	20.6673i	−0.351545	+	0.848705i	0.644885	+	0.764280i	$0.276905\pi$
$593$	−8.56069	+	20.6673i	−0.351545	+	0.848705i	−0.996430	+	0.0844254i	$0.973095\pi$
$594$		0			0
$595$	−0.00820785	+	0.0833357i	−0.000336489	+	0.00341643i
$596$		0			0
$597$	2.95459	+	5.52765i	0.120923	+	0.226232i
$598$		0			0
$599$	−1.81636	+	9.13148i	−0.0742146	+	0.373102i	−0.999988	−	0.00497776i	$-0.998416\pi$
$599$	−1.81636	+	9.13148i	−0.0742146	+	0.373102i	0.925773	+	0.378080i	$0.123416\pi$
$600$		0			0
$601$	−19.5170	+	3.88218i	−0.796116	+	0.158357i	−0.576358	−	0.817197i	$-0.695527\pi$
$601$	−19.5170	+	3.88218i	−0.796116	+	0.158357i	−0.219758	+	0.975554i	$0.570527\pi$
$602$		0			0
$603$	0.542466	+	5.50775i	0.0220909	+	0.224293i
$604$		0			0
$605$	−2.10556	−	6.94109i	−0.0856030	−	0.282195i
$606$		0			0
$607$	13.4628	+	13.4628i	0.546437	+	0.546437i	0.925408	−	0.378972i	$-0.123722\pi$
$607$	13.4628	+	13.4628i	0.546437	+	0.546437i	−0.378972	+	0.925408i	$0.623722\pi$
$608$		0			0
$609$	2.30174	−	2.30174i	0.0932711	−	0.0932711i
$610$		0			0
$611$	−21.0051	+	6.37183i	−0.849775	+	0.257777i
$612$		0			0
$613$	14.5489	−	1.43294i	0.587623	−	0.0578758i	0.200164	−	0.979762i	$-0.435853\pi$
$613$	14.5489	−	1.43294i	0.587623	−	0.0578758i	0.387460	+	0.921887i	$0.373353\pi$
$614$		0			0
$615$	0.236747	+	1.19021i	0.00954655	+	0.0479938i
$616$		0			0
$617$	20.2078	+	4.01959i	0.813537	+	0.161823i	0.584289	−	0.811545i	$-0.301373\pi$
$617$	20.2078	+	4.01959i	0.813537	+	0.161823i	0.229248	+	0.973368i	$0.426373\pi$
$618$		0			0
$619$	7.52172	−	4.02044i	0.302323	−	0.161595i	−0.313259	−	0.949668i	$-0.601421\pi$
$619$	7.52172	−	4.02044i	0.302323	−	0.161595i	0.615582	+	0.788072i	$0.288921\pi$
$620$		0			0
$621$	16.6376	+	1.63866i	0.667643	+	0.0657571i
$622$		0			0
$623$	−3.55357	−	1.47194i	−0.142371	−	0.0589719i
$624$		0			0
$625$	−11.6848	+	4.83998i	−0.467390	+	0.193599i
$626$		0			0
$627$	1.71219	+	2.08631i	0.0683783	+	0.0833192i
$628$		0			0
$629$	0.294271	−	0.970082i	0.0117334	−	0.0386797i
$630$		0			0
$631$	21.3419	+	31.9404i	0.849608	+	1.27153i	0.960664	+	0.277714i	$0.0895768\pi$
$631$	21.3419	+	31.9404i	0.849608	+	1.27153i	−0.111056	+	0.993814i	$0.535423\pi$
$632$		0			0
$633$	17.7240	+	11.8428i	0.704467	+	0.470710i
$634$		0			0
$635$	−13.0939	−	10.7459i	−0.519616	−	0.426438i
$636$		0			0
$637$	10.7736	−	20.1560i	0.426867	−	0.798611i
$638$		0			0
$639$	−18.6635			−0.738315
$640$		0			0
$641$	14.9893			0.592041			0.296021	−	0.955182i	$-0.404340\pi$
$641$	14.9893			0.592041			0.296021	+	0.955182i	$0.404340\pi$
$642$		0			0
$643$	−13.4762	+	25.2122i	−0.531450	+	0.994273i	0.462726	+	0.886501i	$0.346871\pi$
$643$	−13.4762	+	25.2122i	−0.531450	+	0.994273i	−0.994176	+	0.107771i	$0.965629\pi$
$644$		0			0
$645$	−5.46239	−	4.48287i	−0.215082	−	0.176513i
$646$		0			0
$647$	−23.4205	−	15.6491i	−0.920756	−	0.615229i	0.00225749	−	0.999997i	$-0.499281\pi$
$647$	−23.4205	−	15.6491i	−0.920756	−	0.615229i	−0.923013	+	0.384768i	$0.874281\pi$
$648$		0			0
$649$	−9.94464	−	14.8832i	−0.390361	−	0.584217i
$650$		0			0
$651$	−1.22736	+	4.04606i	−0.0481040	+	0.158578i
$652$		0			0
$653$	−9.46728	−	11.5359i	−0.370483	−	0.451435i	0.554080	−	0.832463i	$-0.313070\pi$
$653$	−9.46728	−	11.5359i	−0.370483	−	0.451435i	−0.924563	+	0.381028i	$0.875570\pi$
$654$		0			0
$655$	−11.3785	+	4.71314i	−0.444596	+	0.184158i
$656$		0			0
$657$	−24.4890	−	10.1437i	−0.955406	−	0.395742i
$658$		0			0
$659$	10.8398	+	1.06762i	0.422257	+	0.0415887i	0.306915	−	0.951737i	$-0.400703\pi$
$659$	10.8398	+	1.06762i	0.422257	+	0.0415887i	0.115343	+	0.993326i	$0.463203\pi$
$660$		0			0
$661$	−2.84128	+	1.51870i	−0.110513	+	0.0590705i	−0.525727	−	0.850653i	$-0.676207\pi$
$661$	−2.84128	+	1.51870i	−0.110513	+	0.0590705i	0.415214	+	0.909724i	$0.363707\pi$
$662$		0			0
$663$	0.767608	+	0.152687i	0.0298114	+	0.00592986i
$664$		0			0
$665$	−0.0437008	−	0.219699i	−0.00169464	−	0.00851954i
$666$		0			0
$667$	19.6105	−	1.93147i	0.759323	−	0.0747867i
$668$		0			0
$669$	−6.98260	+	2.11815i	−0.269963	+	0.0818924i
$670$		0			0
$671$	37.6830	−	37.6830i	1.45473	−	1.45473i
$672$		0			0
$673$	34.3807	+	34.3807i	1.32528	+	1.32528i	0.909436	+	0.415843i	$0.136513\pi$
$673$	34.3807	+	34.3807i	1.32528	+	1.32528i	0.415843	+	0.909436i	$0.363487\pi$
$674$		0			0
$675$	−6.45324	−	21.2735i	−0.248385	−	0.818817i
$676$		0			0
$677$	3.91073	+	39.7063i	0.150302	+	1.52604i	0.714052	+	0.700093i	$0.246858\pi$
$677$	3.91073	+	39.7063i	0.150302	+	1.52604i	−0.563750	+	0.825945i	$0.690642\pi$
$678$		0			0
$679$	0.954504	−	0.189863i	0.0366305	−	0.00728626i
$680$		0			0
$681$	4.83594	−	24.3119i	0.185314	−	0.931635i
$682$		0			0
$683$	−1.64273	−	3.07333i	−0.0628572	−	0.117598i	0.848530	−	0.529147i	$-0.177488\pi$
$683$	−1.64273	−	3.07333i	−0.0628572	−	0.117598i	−0.911388	+	0.411549i	$0.864988\pi$
$684$		0			0
$685$	−2.06738	+	20.9905i	−0.0789906	+	0.802005i
$686$		0			0
$687$	−8.63141	+	20.8381i	−0.329309	+	0.795022i
$688$		0			0
$689$	−4.98673	−	12.0390i	−0.189979	−	0.458651i
$690$		0			0
$691$	4.81485	−	3.95144i	0.183165	−	0.150320i	−0.538343	−	0.842726i	$-0.680949\pi$
$691$	4.81485	−	3.95144i	0.183165	−	0.150320i	0.721508	+	0.692406i	$0.243449\pi$
$692$		0			0
$693$	3.06578	+	0.929994i	0.116459	+	0.0353275i
$694$		0			0
$695$	16.4150	−	10.9681i	0.622655	−	0.416045i
$696$		0			0
$697$	−0.125970	+	0.188527i	−0.00477145	+	0.00714098i
$698$		0			0
$699$	16.1611	−	19.6924i	0.611270	−	0.744835i
$700$		0			0
$701$	2.51872	+	1.34629i	0.0951309	+	0.0508485i	0.518276	−	0.855213i	$-0.326574\pi$
$701$	2.51872	+	1.34629i	0.0951309	+	0.0508485i	−0.423145	+	0.906062i	$0.639074\pi$
$702$		0			0
$703$			2.71175i			0.102276i
$704$		0			0
$705$			7.05519i			0.265714i
$706$		0			0
$707$	−1.87234	−	1.00079i	−0.0704167	−	0.0376385i
$708$		0			0
$709$	15.4089	−	18.7758i	0.578692	−	0.705138i	−0.398579	−	0.917134i	$-0.630496\pi$
$709$	15.4089	−	18.7758i	0.578692	−	0.705138i	0.977271	+	0.211996i	$0.0679964\pi$
$710$		0			0
$711$	4.66287	−	6.97848i	0.174871	−	0.261714i
$712$		0			0
$713$	−21.2818	+	14.2200i	−0.797010	+	0.532545i
$714$		0			0
$715$	13.0200	+	3.94958i	0.486921	+	0.147706i
$716$		0			0
$717$	14.3676	−	11.7912i	0.536569	−	0.440351i
$718$		0			0
$719$	−0.0367822	−	0.0888001i	−0.00137174	−	0.00331169i	0.923192	−	0.384339i	$-0.125570\pi$
$719$	−0.0367822	−	0.0888001i	−0.00137174	−	0.00331169i	−0.924564	+	0.381027i	$0.875570\pi$
$720$		0			0
$721$	−0.571668	+	1.38013i	−0.0212900	+	0.0513987i
$722$		0			0
$723$	2.41477	−	24.5175i	0.0898062	−	0.911817i
$724$		0			0
$725$	−12.3521	−	23.1091i	−0.458744	−	0.858250i
$726$		0			0
$727$	4.54666	−	22.8576i	0.168626	−	0.847742i	−0.800149	−	0.599801i	$-0.795246\pi$
$727$	4.54666	−	22.8576i	0.168626	−	0.847742i	0.968775	−	0.247941i	$-0.0797538\pi$
$728$		0			0
$729$	20.3057	−	4.03906i	0.752063	−	0.149595i
$730$		0			0
$731$	−0.129413	−	1.31396i	−0.00478653	−	0.0485984i
$732$		0			0
$733$	7.67566	+	25.3033i	0.283507	+	0.934597i	0.976838	+	0.213978i	$0.0686422\pi$
$733$	7.67566	+	25.3033i	0.283507	+	0.934597i	−0.693331	+	0.720619i	$0.743858\pi$
$734$		0			0
$735$	−5.19432	−	5.19432i	−0.191596	−	0.191596i
$736$		0			0
$737$	10.1691	−	10.1691i	0.374582	−	0.374582i
$738$		0			0
$739$	7.04647	−	2.13752i	0.259209	−	0.0786301i	−0.158006	−	0.987438i	$-0.550506\pi$
$739$	7.04647	−	2.13752i	0.259209	−	0.0786301i	0.417214	+	0.908808i	$0.363006\pi$
$740$		0			0
$741$	−2.08351	+	0.205208i	−0.0765396	+	0.00753850i
$742$		0			0
$743$	−4.78184	−	24.0399i	−0.175429	−	0.881940i	−0.963777	−	0.266710i	$-0.914063\pi$
$743$	−4.78184	−	24.0399i	−0.175429	−	0.881940i	0.788348	−	0.615230i	$-0.210937\pi$
$744$		0			0
$745$	−12.4212	−	2.47074i	−0.455079	−	0.0905208i
$746$		0			0
$747$	−13.6825	+	7.31343i	−0.500615	+	0.267584i
$748$		0			0
$749$	−6.75012	−	0.664829i	−0.246644	−	0.0242923i
$750$		0			0
$751$	−30.2087	−	12.5128i	−1.10233	−	0.456600i	−0.244040	−	0.969765i	$-0.578473\pi$
$751$	−30.2087	−	12.5128i	−1.10233	−	0.456600i	−0.858290	+	0.513165i	$0.828473\pi$
$752$		0			0
$753$	0.0620311	−	0.0256941i	0.00226054	−	0.000936346i
$754$		0			0
$755$	−5.13633	−	6.25864i	−0.186930	−	0.227775i
$756$		0			0
$757$	14.2886	−	47.1032i	0.519328	−	1.71200i	−0.168124	−	0.985766i	$-0.553771\pi$
$757$	14.2886	−	47.1032i	0.519328	−	1.71200i	0.687452	−	0.726230i	$-0.258729\pi$
$758$		0			0
$759$	−8.61974	−	12.9004i	−0.312877	−	0.468253i
$760$		0			0
$761$	10.2369	+	6.84008i	0.371087	+	0.247953i	0.727105	−	0.686527i	$-0.240866\pi$
$761$	10.2369	+	6.84008i	0.371087	+	0.247953i	−0.356017	+	0.934479i	$0.615866\pi$
$762$		0			0
$763$	−6.27891	−	5.15297i	−0.227312	−	0.186550i
$764$		0			0
$765$	−0.148230	+	0.277319i	−0.00535927	+	0.0100265i
$766$		0			0
$767$	13.8851			0.501362
$768$		0			0
$769$	40.7036			1.46781			0.733905	−	0.679252i	$-0.237696\pi$
$769$	40.7036			1.46781			0.733905	+	0.679252i	$0.237696\pi$
$770$		0			0
$771$	2.29605	−	4.29560i	0.0826902	−	0.154702i
$772$		0			0
$773$	−5.32642	−	4.37128i	−0.191578	−	0.157224i	0.533715	−	0.845665i	$-0.320796\pi$
$773$	−5.32642	−	4.37128i	−0.191578	−	0.157224i	−0.725293	+	0.688440i	$0.758296\pi$
$774$		0			0
$775$	28.2993	+	18.9090i	1.01654	+	0.679231i
$776$		0			0
$777$	−1.43066	−	2.14113i	−0.0513246	−	0.0768127i
$778$		0			0
$779$	0.176067	−	0.580416i	0.00630826	−	0.0207955i
$780$		0			0
$781$	30.7663	+	37.4889i	1.10091	+	1.34146i
$782$		0			0
$783$	31.6202	−	13.0975i	1.13002	−	0.468068i
$784$		0			0
$785$	−10.7556	−	4.45511i	−0.383884	−	0.159010i
$786$		0			0
$787$	20.6745	+	2.03626i	0.736966	+	0.0725848i	0.459534	−	0.888160i	$-0.348017\pi$
$787$	20.6745	+	2.03626i	0.736966	+	0.0725848i	0.277432	+	0.960745i	$0.410517\pi$
$788$		0			0
$789$	10.5735	−	5.65163i	0.376425	−	0.201203i
$790$		0			0
$791$	7.34874	+	1.46176i	0.261291	+	0.0519740i
$792$		0			0
$793$	8.06481	+	40.5445i	0.286390	+	1.43978i
$794$		0			0
$795$	−4.16820	+	0.410532i	−0.147831	+	0.0145601i
$796$		0			0
$797$	5.38926	−	1.63481i	0.190897	−	0.0579080i	−0.193388	−	0.981122i	$-0.561948\pi$
$797$	5.38926	−	1.63481i	0.190897	−	0.0579080i	0.384286	+	0.923214i	$0.374448\pi$
$798$		0			0
$799$	−0.932123	+	0.932123i	−0.0329762	+	0.0329762i
$800$		0			0
$801$	−10.2131	−	10.2131i	−0.360862	−	0.360862i
$802$		0			0
$803$	19.9942	+	65.9121i	0.705580	+	2.32599i
$804$		0			0
$805$	0.126217	+	1.28150i	0.00444856	+	0.0451670i
$806$		0			0
$807$	−15.6868	+	3.12029i	−0.552201	+	0.109840i
$808$		0			0
$809$	−1.80961	+	9.09755i	−0.0636227	+	0.319853i	−0.999470	−	0.0325529i	$-0.989636\pi$
$809$	−1.80961	+	9.09755i	−0.0636227	+	0.319853i	0.935847	+	0.352406i	$0.114636\pi$
$810$		0			0
$811$	15.7066	+	29.3851i	0.551535	+	1.03185i	0.991034	+	0.133607i	$0.0426558\pi$
$811$	15.7066	+	29.3851i	0.551535	+	1.03185i	−0.439499	+	0.898243i	$0.644844\pi$
$812$		0			0
$813$	2.79952	−	28.4240i	0.0981834	−	0.996873i
$814$		0			0
$815$	4.88641	−	11.7968i	0.171164	−	0.413225i
$816$		0			0
$817$	1.35158	+	3.26301i	0.0472860	+	0.114158i
$818$		0			0
$819$	−1.92105	+	1.57657i	−0.0671271	+	0.0550898i
$820$		0			0
$821$	12.9090	+	3.91591i	0.450528	+	0.136666i	0.507391	−	0.861716i	$-0.330610\pi$
$821$	12.9090	+	3.91591i	0.450528	+	0.136666i	−0.0568632	+	0.998382i	$0.518110\pi$
$822$		0			0
$823$	9.95219	−	6.64984i	0.346912	−	0.231799i	−0.369891	−	0.929075i	$-0.620605\pi$
$823$	9.95219	−	6.64984i	0.346912	−	0.231799i	0.716802	+	0.697276i	$0.245605\pi$
$824$		0			0
$825$	−11.4620	+	17.1541i	−0.399057	+	0.597230i
$826$		0			0
$827$	−3.89174	+	4.74209i	−0.135329	+	0.164899i	−0.836265	−	0.548325i	$-0.815266\pi$
$827$	−3.89174	+	4.74209i	−0.135329	+	0.164899i	0.700936	+	0.713224i	$0.252766\pi$
$828$		0			0
$829$	0.980402	+	0.524036i	0.0340508	+	0.0182005i	0.488334	−	0.872657i	$-0.337605\pi$
$829$	0.980402	+	0.524036i	0.0340508	+	0.0182005i	−0.454284	+	0.890857i	$0.650105\pi$
$830$		0			0
$831$		−	1.38498i		−	0.0480444i
$832$		0			0
$833$		−	1.37254i		−	0.0475556i
$834$		0			0
$835$	8.63305	+	4.61446i	0.298759	+	0.159690i
$836$		0			0
$837$	−28.2023	+	34.3646i	−0.974815	+	1.18782i
$838$		0			0
$839$	28.1905	−	42.1900i	0.973243	−	1.45656i	0.0854364	−	0.996344i	$-0.472772\pi$
$839$	28.1905	−	42.1900i	0.973243	−	1.45656i	0.887806	−	0.460217i	$-0.152228\pi$
$840$		0			0
$841$	9.42986	−	6.30083i	0.325168	−	0.217270i
$842$		0			0
$843$	−9.09931	−	2.76024i	−0.313397	−	0.0950679i
$844$		0			0
$845$	1.23882	−	1.01668i	0.0426169	−	0.0349748i
$846$		0			0
$847$	−1.31745	−	3.18061i	−0.0452682	−	0.109287i
$848$		0			0
$849$	9.06654	−	21.8886i	0.311163	−	0.751213i
$850$		0			0
$851$	1.52797	−	15.5137i	0.0523780	−	0.531803i
$852$		0			0
$853$	−6.98654	−	13.0709i	−0.239215	−	0.447539i	0.733453	−	0.679740i	$-0.237907\pi$
$853$	−6.98654	−	13.0709i	−0.239215	−	0.447539i	−0.972668	+	0.232201i	$0.925407\pi$
$854$		0			0
$855$	0.164101	−	0.824992i	0.00561214	−	0.0282141i
$856$		0			0
$857$	11.1879	−	2.22542i	0.382172	−	0.0760187i	−0.000265829	−	1.00000i	$-0.500085\pi$
$857$	11.1879	−	2.22542i	0.382172	−	0.0760187i	0.382438	+	0.923981i	$0.375085\pi$
$858$		0			0
$859$	−1.58403	−	16.0829i	−0.0540463	−	0.548742i	−0.983639	−	0.180152i	$-0.942341\pi$
$859$	−1.58403	−	16.0829i	−0.0540463	−	0.548742i	0.929592	−	0.368589i	$-0.120159\pi$
$860$		0			0
$861$	0.167196	+	0.551171i	0.00569802	+	0.0187838i
$862$		0			0
$863$	28.5380	+	28.5380i	0.971445	+	0.971445i	0.999603	−	0.0281588i	$-0.00896439\pi$
$863$	28.5380	+	28.5380i	0.971445	+	0.971445i	−0.0281588	+	0.999603i	$0.508964\pi$
$864$		0			0
$865$	6.78388	−	6.78388i	0.230659	−	0.230659i
$866$		0			0
$867$	−18.7396	+	5.68460i	−0.636430	+	0.193059i
$868$		0			0
$869$	−21.7042	+	2.13767i	−0.736264	+	0.0725156i
$870$		0			0
$871$	2.17636	+	10.9413i	0.0737430	+	0.370731i
$872$		0			0
$873$	3.58427	+	0.712955i	0.121309	+	0.0241299i
$874$		0			0
$875$	3.34035	−	1.78545i	0.112924	−	0.0603593i
$876$		0			0
$877$	26.7332	+	2.63299i	0.902716	+	0.0889098i	0.538714	−	0.842488i	$-0.318910\pi$
$877$	26.7332	+	2.63299i	0.902716	+	0.0889098i	0.364002	+	0.931398i	$0.381410\pi$
$878$		0			0
$879$	−13.9760	−	5.78903i	−0.471397	−	0.195259i
$880$		0			0
$881$	9.97157	−	4.13036i	0.335951	−	0.139155i	−0.208330	−	0.978059i	$-0.566803\pi$
$881$	9.97157	−	4.13036i	0.335951	−	0.139155i	0.544280	+	0.838903i	$0.316803\pi$
$882$		0			0
$883$	1.45617	+	1.77435i	0.0490042	+	0.0597117i	0.796936	−	0.604064i	$-0.206453\pi$
$883$	1.45617	+	1.77435i	0.0490042	+	0.0597117i	−0.747932	+	0.663776i	$0.768953\pi$
$884$		0			0
$885$	1.29551	−	4.27073i	0.0435482	−	0.143559i
$886$		0			0
$887$	−0.00467637	−	0.00699867i	−0.000157017	−	0.000234993i	0.831391	−	0.555688i	$-0.187545\pi$
$887$	−0.00467637	−	0.00699867i	−0.000157017	−	0.000234993i	−0.831548	+	0.555453i	$0.812545\pi$
$888$		0			0
$889$	−6.68472	−	4.46659i	−0.224198	−	0.149804i
$890$		0			0
$891$	−4.09158	−	3.35787i	−0.137073	−	0.112493i
$892$		0			0
$893$	1.66227	−	3.10988i	0.0556257	−	0.104068i
$894$		0			0
$895$	−2.90722			−0.0971776
$896$		0			0
$897$	12.0352			0.401844
$898$		0			0
$899$	−24.7009	+	46.2120i	−0.823820	+	1.54126i
$900$		0			0
$901$	−0.604937	−	0.496459i	−0.0201534	−	0.0165394i
$902$		0			0
$903$	−2.78867	−	1.86333i	−0.0928011	−	0.0620077i
$904$		0			0
$905$	−5.29227	−	7.92045i	−0.175921	−	0.263285i
$906$		0			0
$907$	1.55520	−	5.12680i	0.0516395	−	0.170233i	−0.927328	−	0.374250i	$-0.877900\pi$
$907$	1.55520	−	5.12680i	0.0516395	−	0.170233i	0.978967	+	0.204018i	$0.0654000\pi$
$908$		0			0
$909$	−5.05751	−	6.16260i	−0.167747	−	0.204400i
$910$		0			0
$911$	−48.3431	+	20.0244i	−1.60168	+	0.663437i	−0.991652	−	0.128945i	$-0.958841\pi$
$911$	−48.3431	+	20.0244i	−1.60168	+	0.663437i	−0.610026	+	0.792382i	$0.708841\pi$
$912$		0			0
$913$	37.2456	+	15.4276i	1.23265	+	0.510580i
$914$		0			0
$915$	13.2230	+	1.30235i	0.437140	+	0.0430545i
$916$		0			0
$917$	−5.15529	+	2.75556i	−0.170243	+	0.0909966i
$918$		0			0
$919$	28.4601	+	5.66107i	0.938813	+	0.186742i	0.640702	−	0.767790i	$-0.278643\pi$
$919$	28.4601	+	5.66107i	0.938813	+	0.186742i	0.298111	+	0.954531i	$0.403643\pi$
$920$		0			0
$921$	−0.448477	−	2.25465i	−0.0147778	−	0.0742932i
$922$		0			0
$923$	−37.4386	+	3.68738i	−1.23231	+	0.121372i
$924$		0			0
$925$	−19.8364	+	6.01732i	−0.652218	+	0.197848i
$926$		0			0
$927$	−3.96654	+	3.96654i	−0.130278	+	0.130278i
$928$		0			0
$929$	17.4359	+	17.4359i	0.572053	+	0.572053i	0.932702	−	0.360649i	$-0.117445\pi$
$929$	17.4359	+	17.4359i	0.572053	+	0.572053i	−0.360649	+	0.932702i	$0.617445\pi$
$930$		0			0
$931$	1.06580	+	3.51346i	0.0349301	+	0.115149i
$932$		0			0
$933$	−1.03257	−	10.4839i	−0.0338049	−	0.343226i
$934$		0			0
$935$	0.801399	−	0.159408i	0.0262085	−	0.00521320i
$936$		0			0
$937$	−4.59924	+	23.1219i	−0.150250	+	0.755360i	0.830025	+	0.557726i	$0.188326\pi$
$937$	−4.59924	+	23.1219i	−0.150250	+	0.755360i	−0.980276	+	0.197634i	$0.936674\pi$
$938$		0			0
$939$	−4.25782	−	7.96582i	−0.138949	−	0.259955i
$940$		0			0
$941$	−1.60995	+	16.3461i	−0.0524828	+	0.532866i	0.932615	+	0.360872i	$0.117521\pi$
$941$	−1.60995	+	16.3461i	−0.0524828	+	0.532866i	−0.985098	+	0.171994i	$0.944979\pi$
$942$		0			0
$943$	−1.33431	+	3.22130i	−0.0434510	+	0.104900i
$944$		0			0
$945$	0.855892	+	2.06631i	0.0278422	+	0.0672170i
$946$		0			0
$947$	2.71000	−	2.22404i	0.0880633	−	0.0722717i	−0.589332	−	0.807891i	$-0.700609\pi$
$947$	2.71000	−	2.22404i	0.0880633	−	0.0722717i	0.677395	+	0.735620i	$0.263109\pi$
$948$		0			0
$949$	−51.1286	−	15.5097i	−1.65970	−	0.503465i
$950$		0			0
$951$	−1.39498	+	0.932099i	−0.0452355	+	0.0302254i
$952$		0			0
$953$	−9.89452	+	14.8082i	−0.320515	+	0.479685i	−0.956384	−	0.292112i	$-0.905642\pi$
$953$	−9.89452	+	14.8082i	−0.320515	+	0.479685i	0.635869	+	0.771797i	$0.280642\pi$
$954$		0			0
$955$	5.98533	−	7.29314i	0.193681	−	0.236000i
$956$		0			0
$957$	−28.0123	−	14.9729i	−0.905508	−	0.484004i
$958$		0			0
$959$			10.0109i			0.323268i
$960$		0			0
$961$		−	37.0616i		−	1.19553i
$962$		0			0
$963$	−22.4626	−	12.0065i	−0.723848	−	0.386905i
$964$		0			0
$965$	−4.86603	+	5.92927i	−0.156643	+	0.190870i
$966$		0			0
$967$	19.9966	−	29.9270i	0.643047	−	0.962388i	−0.356557	−	0.934273i	$-0.616050\pi$
$967$	19.9966	−	29.9270i	0.643047	−	0.962388i	0.999605	−	0.0281149i	$-0.00895044\pi$
$968$		0			0
$969$	−0.104541	+	0.0698521i	−0.00335834	+	0.00224397i
$970$		0			0
$971$	34.8180	+	10.5619i	1.11736	+	0.338948i	0.794359	−	0.607449i	$-0.207807\pi$
$971$	34.8180	+	10.5619i	1.11736	+	0.338948i	0.323004	+	0.946398i	$0.395307\pi$
$972$		0			0
$973$	7.24323	−	5.94436i	0.232207	−	0.190568i
$974$		0			0
$975$	−6.12436	−	14.7855i	−0.196136	−	0.473515i
$976$		0			0
$977$	0.212829	−	0.513816i	0.00680902	−	0.0164384i	−0.920438	−	0.390887i	$-0.872168\pi$
$977$	0.212829	−	0.513816i	0.00680902	−	0.0164384i	0.927247	+	0.374449i	$0.122168\pi$
$978$		0			0
$979$	−3.67874	+	37.3509i	−0.117573	+	1.19374i
$980$		0			0
$981$	−14.3783	−	26.8999i	−0.459064	−	0.858849i
$982$		0			0
$983$	−5.76016	+	28.9583i	−0.183721	+	0.923626i	0.773396	+	0.633923i	$0.218556\pi$
$983$	−5.76016	+	28.9583i	−0.183721	+	0.923626i	−0.957117	+	0.289703i	$0.906444\pi$
$984$		0			0
$985$	17.9612	−	3.57270i	0.572290	−	0.113836i
$986$		0			0
$987$	0.328219	+	3.33246i	0.0104473	+	0.106073i
$988$		0			0
$989$	−5.89372	−	19.4290i	−0.187409	−	0.617806i
$990$		0			0
$991$	−25.1855	−	25.1855i	−0.800043	−	0.800043i	0.183059	−	0.983102i	$-0.441400\pi$
$991$	−25.1855	−	25.1855i	−0.800043	−	0.800043i	−0.983102	+	0.183059i	$0.941400\pi$
$992$		0			0
$993$	6.36615	−	6.36615i	0.202024	−	0.202024i
$994$		0			0
$995$	−4.85739	+	1.47347i	−0.153990	+	0.0467122i
$996$		0			0
$997$	−34.4640	+	3.39441i	−1.09149	+	0.107502i	−0.627708	−	0.778449i	$-0.716007\pi$
$997$	−34.4640	+	3.39441i	−1.09149	+	0.107502i	−0.463779	+	0.885951i	$0.653507\pi$
$998$		0			0
$999$	−5.28216	−	26.5552i	−0.167120	−	0.840170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.17.10		240
4.3	odd	2		128.2.k.a.45.1	yes	240
128.37	even	32	inner	512.2.k.a.241.10		240
128.91	odd	32		128.2.k.a.37.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.37.1	✓	240	128.91	odd	32
128.2.k.a.45.1	yes	240	4.3	odd	2
512.2.k.a.17.10		240	1.1	even	1	trivial
512.2.k.a.241.10		240	128.37	even	32	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.k (of order \(32\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.544320 - 1.01835i) q^{3} +(0.722871 + 0.593245i) q^{5} +(0.369041 + 0.246585i) q^{7} +(0.925956 + 1.38579i) q^{9} +O(q^{10})\)	\(q+(0.544320 - 1.01835i) q^{3} +(0.722871 + 0.593245i) q^{5} +(0.369041 + 0.246585i) q^{7} +(0.925956 + 1.38579i) q^{9} +(1.25719 - 4.14439i) q^{11} +(2.13124 + 2.59693i) q^{13} +(0.997605 - 0.413222i) q^{15} +(0.186397 + 0.0772081i) q^{17} +(-0.537097 - 0.0528995i) q^{19} +(0.451987 - 0.241592i) q^{21} +(3.04288 + 0.605267i) q^{23} +(-0.804849 - 4.04625i) q^{25} +(5.36265 - 0.528175i) q^{27} +(6.07798 - 1.84374i) q^{29} +(-5.83359 + 5.83359i) q^{31} +(-3.53614 - 3.53614i) q^{33} +(0.120484 + 0.397181i) q^{35} +(-0.492496 - 5.00040i) q^{37} +(3.80467 - 0.756795i) q^{39} +(-0.219251 + 1.10225i) q^{41} +(-3.08490 - 5.77144i) q^{43} +(-0.152767 + 1.55107i) q^{45} +(-2.50037 + 6.03644i) q^{47} +(-2.60340 - 6.28516i) q^{49} +(0.180085 - 0.147792i) q^{51} +(-3.71182 - 1.12597i) q^{53} +(3.36743 - 2.25004i) q^{55} +(-0.346223 + 0.518160i) q^{57} +(2.62200 - 3.19492i) q^{59} +(10.8521 + 5.80057i) q^{61} +0.739741i q^{63} +3.14160i q^{65} +(2.92853 + 1.56533i) q^{67} +(2.27268 - 2.76926i) q^{69} +(-6.22129 + 9.31081i) q^{71} +(-13.2236 + 8.83574i) q^{73} +(-4.55860 - 1.38284i) q^{75} +(1.48590 - 1.21945i) q^{77} +(-1.92709 - 4.65242i) q^{79} +(0.467701 - 1.12913i) q^{81} +(-0.912400 + 9.26376i) q^{83} +(0.0889376 + 0.166390i) q^{85} +(1.43080 - 7.19310i) q^{87} +(-8.49953 + 1.69066i) q^{89} +(0.146152 + 1.48391i) q^{91} +(2.76530 + 9.11599i) q^{93} +(-0.356870 - 0.356870i) q^{95} +(1.55046 - 1.55046i) q^{97} +(6.90736 - 2.09533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9} + 16 q^{11} - 16 q^{13} + 16 q^{15} - 16 q^{17} + 16 q^{19} - 16 q^{21} + 16 q^{23} - 16 q^{25} + 16 q^{27} - 16 q^{29} + 16 q^{31} - 16 q^{33} + 16 q^{35} - 16 q^{37} + 16 q^{39} - 16 q^{41} + 16 q^{43} - 16 q^{45} + 16 q^{47} - 16 q^{49} + 16 q^{51} - 16 q^{53} + 16 q^{55} - 16 q^{57} + 16 q^{59} - 16 q^{61} + 16 q^{67} - 16 q^{69} + 16 q^{71} - 16 q^{73} + 16 q^{75} - 16 q^{77} + 16 q^{79} - 16 q^{81} + 16 q^{83} - 16 q^{85} + 16 q^{87} - 16 q^{89} + 16 q^{91} - 16 q^{93} + 16 q^{95} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) 240 * q + 16 * q^3 - 16 * q^5 + 16 * q^7 - 16 * q^9 + 16 * q^11 - 16 * q^13 + 16 * q^15 - 16 * q^17 + 16 * q^19 - 16 * q^21 + 16 * q^23 - 16 * q^25 + 16 * q^27 - 16 * q^29 + 16 * q^31 - 16 * q^33 + 16 * q^35 - 16 * q^37 + 16 * q^39 - 16 * q^41 + 16 * q^43 - 16 * q^45 + 16 * q^47 - 16 * q^49 + 16 * q^51 - 16 * q^53 + 16 * q^55 - 16 * q^57 + 16 * q^59 - 16 * q^61 + 16 * q^67 - 16 * q^69 + 16 * q^71 - 16 * q^73 + 16 * q^75 - 16 * q^77 + 16 * q^79 - 16 * q^81 + 16 * q^83 - 16 * q^85 + 16 * q^87 - 16 * q^89 + 16 * q^91 - 16 * q^93 + 16 * q^95 - 16 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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