LMFDB - Embedded newform 512.2.k.a.49.2

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			49.2
Character	$\chi$	$=$	512.49
Dual form			512.2.k.a.209.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.247362 - 2.51150i) q^{3} +(-3.44799 - 1.84299i) q^{5} +(0.702840 - 3.53342i) q^{7} +(-3.30411 + 0.657229i) q^{9} +O(q^{10})$	\(q+(-0.247362 - 2.51150i) q^{3} +(-3.44799 - 1.84299i) q^{5} +(0.702840 - 3.53342i) q^{7} +(-3.30411 + 0.657229i) q^{9} +(0.0383653 + 0.0467482i) q^{11} +(0.520664 + 0.974094i) q^{13} +(-3.77578 + 9.11554i) q^{15} +(2.03571 + 4.91463i) q^{17} +(0.124884 - 0.411689i) q^{19} +(-9.04804 - 0.891155i) q^{21} +(1.99917 + 1.33580i) q^{23} +(5.71419 + 8.55189i) q^{25} +(0.270207 + 0.890754i) q^{27} +(-5.07402 - 4.16414i) q^{29} +(-5.93044 - 5.93044i) q^{31} +(0.107918 - 0.107918i) q^{33} +(-8.93544 + 10.8879i) q^{35} +(5.72870 - 1.73778i) q^{37} +(2.31765 - 1.54860i) q^{39} +(1.72499 - 2.58163i) q^{41} +(0.124433 - 1.26339i) q^{43} +(12.6038 + 3.82333i) q^{45} +(-4.52719 + 1.87522i) q^{47} +(-5.52388 - 2.28807i) q^{49} +(11.8396 - 6.32838i) q^{51} +(-6.40548 + 5.25684i) q^{53} +(-0.0461267 - 0.231894i) q^{55} +(-1.06485 - 0.211812i) q^{57} +(-0.185120 + 0.346334i) q^{59} +(4.85534 - 0.478209i) q^{61} +12.1367i q^{63} -4.31825i q^{65} +(-0.299339 + 0.0294823i) q^{67} +(2.86035 - 5.35134i) q^{69} +(-8.61912 - 1.71445i) q^{71} +(-2.84871 - 14.3214i) q^{73} +(20.0646 - 16.4666i) q^{75} +(0.192146 - 0.102704i) q^{77} +(12.7928 + 5.29893i) q^{79} +(-7.16692 + 2.96864i) q^{81} +(-4.10477 - 1.24517i) q^{83} +(2.03852 - 20.6974i) q^{85} +(-9.20314 + 13.7735i) q^{87} +(8.24669 - 5.51026i) q^{89} +(3.80782 - 1.15509i) q^{91} +(-13.4274 + 16.3613i) q^{93} +(-1.18934 + 1.18934i) q^{95} +(-3.50840 - 3.50840i) q^{97} +(-0.157487 - 0.129247i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

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

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
$3$	−0.247362	−	2.51150i	−0.142814	−	1.45002i	−0.753136	−	0.657865i	$-0.771460\pi$
$3$	−0.247362	−	2.51150i	−0.142814	−	1.45002i	0.610322	−	0.792153i	$-0.291040\pi$
$4$		0			0
$5$	−3.44799	−	1.84299i	−1.54199	−	0.824210i	−0.542119	−	0.840302i	$-0.682378\pi$
$5$	−3.44799	−	1.84299i	−1.54199	−	0.824210i	−0.999871	+	0.0160914i	$0.994878\pi$
$6$		0			0
$7$	0.702840	−	3.53342i	0.265649	−	1.33551i	−0.585539	−	0.810644i	$-0.699117\pi$
$7$	0.702840	−	3.53342i	0.265649	−	1.33551i	0.851188	−	0.524861i	$-0.175883\pi$
$8$		0			0
$9$	−3.30411	+	0.657229i	−1.10137	+	0.219076i
$10$		0			0
$11$	0.0383653	+	0.0467482i	0.0115676	+	0.0140951i	0.778762	−	0.627319i	$-0.215848\pi$
$11$	0.0383653	+	0.0467482i	0.0115676	+	0.0140951i	−0.767195	+	0.641414i	$0.778348\pi$
$12$		0			0
$13$	0.520664	+	0.974094i	0.144406	+	0.270165i	0.943718	−	0.330752i	$-0.107302\pi$
$13$	0.520664	+	0.974094i	0.144406	+	0.270165i	−0.799312	+	0.600917i	$0.794802\pi$
$14$		0			0
$15$	−3.77578	+	9.11554i	−0.974902	+	2.35362i
$16$		0			0
$17$	2.03571	+	4.91463i	0.493731	+	1.19197i	0.952807	+	0.303576i	$0.0981806\pi$
$17$	2.03571	+	4.91463i	0.493731	+	1.19197i	−0.459076	+	0.888397i	$0.651819\pi$
$18$		0			0
$19$	0.124884	−	0.411689i	0.0286505	−	0.0944479i	−0.941449	−	0.337155i	$-0.890535\pi$
$19$	0.124884	−	0.411689i	0.0286505	−	0.0944479i	0.970100	+	0.242707i	$0.0780354\pi$
$20$		0			0
$21$	−9.04804	−	0.891155i	−1.97445	−	0.194466i
$22$		0			0
$23$	1.99917	+	1.33580i	0.416855	+	0.278533i	0.746259	−	0.665655i	$-0.231848\pi$
$23$	1.99917	+	1.33580i	0.416855	+	0.278533i	−0.329404	+	0.944189i	$0.606848\pi$
$24$		0			0
$25$	5.71419	+	8.55189i	1.14284	+	1.71038i
$26$		0			0
$27$	0.270207	+	0.890754i	0.0520014	+	0.171426i
$28$		0			0
$29$	−5.07402	−	4.16414i	−0.942221	−	0.773261i	0.0318522	−	0.999493i	$-0.489859\pi$
$29$	−5.07402	−	4.16414i	−0.942221	−	0.773261i	−0.974074	+	0.226232i	$0.927359\pi$
$30$		0			0
$31$	−5.93044	−	5.93044i	−1.06514	−	1.06514i	−0.997725	−	0.0674141i	$-0.978525\pi$
$31$	−5.93044	−	5.93044i	−1.06514	−	1.06514i	−0.0674141	−	0.997725i	$-0.521475\pi$
$32$		0			0
$33$	0.107918	−	0.107918i	0.0187862	−	0.0187862i
$34$		0			0
$35$	−8.93544	+	10.8879i	−1.51036	+	1.84038i
$36$		0			0
$37$	5.72870	−	1.73778i	0.941792	−	0.285689i	0.218189	−	0.975906i	$-0.429985\pi$
$37$	5.72870	−	1.73778i	0.941792	−	0.285689i	0.723602	+	0.690217i	$0.242485\pi$
$38$		0			0
$39$	2.31765	−	1.54860i	0.371121	−	0.247975i
$40$		0			0
$41$	1.72499	−	2.58163i	0.269398	−	0.403183i	−0.671962	−	0.740586i	$-0.734548\pi$
$41$	1.72499	−	2.58163i	0.269398	−	0.403183i	0.941361	+	0.337402i	$0.109548\pi$
$42$		0			0
$43$	0.124433	−	1.26339i	0.0189758	−	0.192665i	−0.981023	−	0.193889i	$-0.937890\pi$
$43$	0.124433	−	1.26339i	0.0189758	−	0.192665i	0.999999	+	0.00122456i	$0.000389788\pi$
$44$		0			0
$45$	12.6038	+	3.82333i	1.87887	+	0.569948i
$46$		0			0
$47$	−4.52719	+	1.87522i	−0.660359	+	0.273530i	−0.687590	−	0.726100i	$-0.741331\pi$
$47$	−4.52719	+	1.87522i	−0.660359	+	0.273530i	0.0272306	+	0.999629i	$0.491331\pi$
$48$		0			0
$49$	−5.52388	−	2.28807i	−0.789126	−	0.326867i
$50$		0			0
$51$	11.8396	−	6.32838i	1.65787	−	0.886150i
$52$		0			0
$53$	−6.40548	+	5.25684i	−0.879860	+	0.722082i	−0.961566	−	0.274574i	$-0.911463\pi$
$53$	−6.40548	+	5.25684i	−0.879860	+	0.722082i	0.0817061	+	0.996656i	$0.473963\pi$
$54$		0			0
$55$	−0.0461267	−	0.231894i	−0.00621972	−	0.0312686i
$56$		0			0
$57$	−1.06485	−	0.211812i	−0.141043	−	0.0280552i
$58$		0			0
$59$	−0.185120	+	0.346334i	−0.0241005	+	0.0450889i	−0.893683	−	0.448698i	$-0.851888\pi$
$59$	−0.185120	+	0.346334i	−0.0241005	+	0.0450889i	0.869583	+	0.493787i	$0.164388\pi$
$60$		0			0
$61$	4.85534	−	0.478209i	0.621663	−	0.0612284i	0.217718	−	0.976012i	$-0.430139\pi$
$61$	4.85534	−	0.478209i	0.621663	−	0.0612284i	0.403945	+	0.914783i	$0.367639\pi$
$62$		0			0
$63$			12.1367i			1.52908i
$64$		0			0
$65$		−	4.31825i		−	0.535613i
$66$		0			0
$67$	−0.299339	+	0.0294823i	−0.0365701	+	0.00360184i	−0.116286	−	0.993216i	$-0.537099\pi$
$67$	−0.299339	+	0.0294823i	−0.0365701	+	0.00360184i	0.0797156	+	0.996818i	$0.474599\pi$
$68$		0			0
$69$	2.86035	−	5.35134i	0.344346	−	0.644226i
$70$		0			0
$71$	−8.61912	−	1.71445i	−1.02290	−	0.203468i	−0.344986	−	0.938608i	$-0.612116\pi$
$71$	−8.61912	−	1.71445i	−1.02290	−	0.203468i	−0.677915	+	0.735140i	$0.737116\pi$
$72$		0			0
$73$	−2.84871	−	14.3214i	−0.333417	−	1.67620i	−0.676149	−	0.736765i	$-0.736352\pi$
$73$	−2.84871	−	14.3214i	−0.333417	−	1.67620i	0.342732	−	0.939433i	$-0.388648\pi$
$74$		0			0
$75$	20.0646	−	16.4666i	2.31687	−	1.90140i
$76$		0			0
$77$	0.192146	−	0.102704i	0.0218970	−	0.0117042i
$78$		0			0
$79$	12.7928	+	5.29893i	1.43930	+	0.596176i	0.959628	−	0.281273i	$-0.0907566\pi$
$79$	12.7928	+	5.29893i	1.43930	+	0.596176i	0.479669	+	0.877449i	$0.340757\pi$
$80$		0			0
$81$	−7.16692	+	2.96864i	−0.796325	+	0.329849i
$82$		0			0
$83$	−4.10477	−	1.24517i	−0.450557	−	0.136675i	0.0568476	−	0.998383i	$-0.481895\pi$
$83$	−4.10477	−	1.24517i	−0.450557	−	0.136675i	−0.507405	+	0.861708i	$0.669395\pi$
$84$		0			0
$85$	2.03852	−	20.6974i	0.221108	−	2.24495i
$86$		0			0
$87$	−9.20314	+	13.7735i	−0.986680	+	1.47667i
$88$		0			0
$89$	8.24669	−	5.51026i	0.874147	−	0.584086i	−0.0355458	−	0.999368i	$-0.511317\pi$
$89$	8.24669	−	5.51026i	0.874147	−	0.584086i	0.909693	+	0.415282i	$0.136317\pi$
$90$		0			0
$91$	3.80782	−	1.15509i	0.399168	−	0.121086i
$92$		0			0
$93$	−13.4274	+	16.3613i	−1.39235	+	1.69659i
$94$		0			0
$95$	−1.18934	+	1.18934i	−0.122024	+	0.122024i
$96$		0			0
$97$	−3.50840	−	3.50840i	−0.356225	−	0.356225i	0.506195	−	0.862419i	$-0.331052\pi$
$97$	−3.50840	−	3.50840i	−0.356225	−	0.356225i	−0.862419	+	0.506195i	$0.831052\pi$
$98$		0			0
$99$	−0.157487	−	0.129247i	−0.0158281	−	0.0129898i
$100$		0			0
$101$	1.65082	+	5.44201i	0.164262	+	0.541500i	0.999971	−	0.00767350i	$-0.00244258\pi$
$101$	1.65082	+	5.44201i	0.164262	+	0.541500i	−0.835708	+	0.549174i	$0.814943\pi$
$102$		0			0
$103$	−9.26873	−	13.8716i	−0.913275	−	1.36681i	−0.930238	−	0.366957i	$-0.880400\pi$
$103$	−9.26873	−	13.8716i	−0.913275	−	1.36681i	0.0169631	−	0.999856i	$-0.494600\pi$
$104$		0			0
$105$	29.5552	+	19.7482i	2.88429	+	1.92722i
$106$		0			0
$107$	0.959173	+	0.0944703i	0.0927268	+	0.00913279i	0.144274	−	0.989538i	$-0.453915\pi$
$107$	0.959173	+	0.0944703i	0.0927268	+	0.00913279i	−0.0515473	+	0.998671i	$0.516415\pi$
$108$		0			0
$109$	−1.78304	+	5.87790i	−0.170784	+	0.563001i	0.829207	+	0.558941i	$0.188792\pi$
$109$	−1.78304	+	5.87790i	−0.170784	+	0.563001i	−0.999992	+	0.00405957i	$0.998708\pi$
$110$		0			0
$111$	−5.78151	−	13.9578i	−0.548756	−	1.32481i
$112$		0			0
$113$	−4.28538	+	10.3458i	−0.403134	+	0.973253i	0.583766	+	0.811922i	$0.301579\pi$
$113$	−4.28538	+	10.3458i	−0.403134	+	0.973253i	−0.986900	+	0.161331i	$0.948421\pi$
$114$		0			0
$115$	−4.43124	−	8.29027i	−0.413215	−	0.773072i
$116$		0			0
$117$	−2.36053	−	2.87632i	−0.218232	−	0.265916i
$118$		0			0
$119$	18.7962	−	3.73880i	1.72305	−	0.342735i
$120$		0			0
$121$	2.14528	−	10.7851i	0.195025	−	0.980459i
$122$		0			0
$123$	−6.91048	−	3.69373i	−0.623097	−	0.333052i
$124$		0			0
$125$	−2.02538	−	20.5640i	−0.181155	−	1.83930i
$126$		0			0
$127$	4.34032			0.385141			0.192571	−	0.981283i	$-0.438318\pi$
$127$	4.34032			0.385141			0.192571	+	0.981283i	$0.438318\pi$
$128$		0			0
$129$	−3.20378			−0.282077
$130$		0			0
$131$	−1.94098	−	19.7071i	−0.169584	−	1.72181i	−0.584023	−	0.811737i	$-0.698522\pi$
$131$	−1.94098	−	19.7071i	−0.169584	−	1.72181i	0.414439	−	0.910077i	$-0.363978\pi$
$132$		0			0
$133$	−1.36689	−	0.730620i	−0.118525	−	0.0633528i
$134$		0			0
$135$	0.709978	−	3.56930i	0.0611052	−	0.307197i
$136$		0			0
$137$	−4.86249	+	0.967210i	−0.415431	+	0.0826343i	−0.398380	−	0.917220i	$-0.630428\pi$
$137$	−4.86249	+	0.967210i	−0.415431	+	0.0826343i	−0.0170504	+	0.999855i	$0.505428\pi$
$138$		0			0
$139$	6.60756	+	8.05133i	0.560446	+	0.682905i	0.973732	−	0.227696i	$-0.0731192\pi$
$139$	6.60756	+	8.05133i	0.560446	+	0.682905i	−0.413286	+	0.910601i	$0.635619\pi$
$140$		0			0
$141$	5.82949	+	10.9062i	0.490932	+	0.918468i
$142$		0			0
$143$	−0.0255617	+	0.0617115i	−0.00213758	+	0.00516057i
$144$		0			0
$145$	9.82071	+	23.7093i	0.815565	+	1.96895i
$146$		0			0
$147$	−4.38009	+	14.4392i	−0.361264	+	1.19093i
$148$		0			0
$149$	18.1637	+	1.78897i	1.48803	+	0.146558i	0.809110	−	0.587657i	$-0.199949\pi$
$149$	18.1637	+	1.78897i	1.48803	+	0.146558i	0.678917	+	0.734215i	$0.262449\pi$
$150$		0			0
$151$	1.08698	+	0.726294i	0.0884569	+	0.0591050i	0.599012	−	0.800740i	$-0.295560\pi$
$151$	1.08698	+	0.726294i	0.0884569	+	0.0591050i	−0.510555	+	0.859845i	$0.670560\pi$
$152$		0			0
$153$	−9.95624	−	14.9006i	−0.804914	−	1.20464i
$154$		0			0
$155$	9.51838	+	31.3779i	0.764534	+	2.52033i
$156$		0			0
$157$	5.17147	+	4.24411i	0.412728	+	0.338717i	0.817733	−	0.575597i	$-0.195230\pi$
$157$	5.17147	+	4.24411i	0.412728	+	0.338717i	−0.405005	+	0.914314i	$0.632730\pi$
$158$		0			0
$159$	14.7870	+	14.7870i	1.17269	+	1.17269i
$160$		0			0
$161$	6.12503	−	6.12503i	0.482720	−	0.482720i
$162$		0			0
$163$	−1.68301	+	2.05075i	−0.131824	+	0.160628i	−0.834739	−	0.550646i	$-0.814381\pi$
$163$	−1.68301	+	2.05075i	−0.131824	+	0.160628i	0.702915	+	0.711274i	$0.251881\pi$
$164$		0			0
$165$	−0.570994	+	0.173209i	−0.0444518	+	0.0134843i
$166$		0			0
$167$	13.7457	−	9.18457i	1.06367	−	0.710723i	0.104780	−	0.994495i	$-0.466586\pi$
$167$	13.7457	−	9.18457i	1.06367	−	0.710723i	0.958892	+	0.283772i	$0.0915860\pi$
$168$		0			0
$169$	6.54465	−	9.79475i	0.503434	−	0.753443i
$170$		0			0
$171$	−0.142058	+	1.44234i	−0.0108635	+	0.110299i
$172$		0			0
$173$	4.25123	+	1.28960i	0.323215	+	0.0980462i	0.447723	−	0.894172i	$-0.352235\pi$
$173$	4.25123	+	1.28960i	0.323215	+	0.0980462i	−0.124508	+	0.992219i	$0.539735\pi$
$174$		0			0
$175$	34.2335	−	14.1800i	2.58781	−	1.07191i
$176$		0			0
$177$	0.915612	+	0.379259i	0.0688216	+	0.0285068i
$178$		0			0
$179$	−9.85631	+	5.26831i	−0.736695	+	0.393772i	−0.796659	−	0.604429i	$-0.793401\pi$
$179$	−9.85631	+	5.26831i	−0.736695	+	0.393772i	0.0599641	+	0.998201i	$0.480901\pi$
$180$		0			0
$181$	−8.96273	+	7.35553i	−0.666195	+	0.546732i	−0.905571	−	0.424195i	$-0.860557\pi$
$181$	−8.96273	+	7.35553i	−0.666195	+	0.546732i	0.239376	+	0.970927i	$0.423057\pi$
$182$		0			0
$183$	−2.40205	−	12.0759i	−0.177565	−	0.892678i
$184$		0			0
$185$	−22.9552	−	4.56608i	−1.68770	−	0.335705i
$186$		0			0
$187$	−0.151650	+	0.283717i	−0.0110897	+	0.0207474i
$188$		0			0
$189$	3.33731	−	0.328697i	0.242754	−	0.0239092i
$190$		0			0
$191$		−	11.2680i		−	0.815324i	−0.913133	−	0.407662i	$-0.866344\pi$
$191$		−	11.2680i		−	0.815324i	0.913133	−	0.407662i	$-0.133656\pi$
$192$		0			0
$193$			10.7393i			0.773031i	0.922283	+	0.386515i	$0.126321\pi$
$193$			10.7393i			0.773031i	−0.922283	+	0.386515i	$0.873679\pi$
$194$		0			0
$195$	−10.8453	+	1.06817i	−0.776648	+	0.0764932i
$196$		0			0
$197$	0.872985	−	1.63324i	0.0621976	−	0.116364i	−0.848901	−	0.528552i	$-0.822735\pi$
$197$	0.872985	−	1.63324i	0.0621976	−	0.116364i	0.911099	+	0.412188i	$0.135235\pi$
$198$		0			0
$199$	−6.18605	−	1.23048i	−0.438517	−	0.0872265i	−0.0291058	−	0.999576i	$-0.509266\pi$
$199$	−6.18605	−	1.23048i	−0.438517	−	0.0872265i	−0.409412	+	0.912350i	$0.634266\pi$
$200$		0			0
$201$	0.148090	+	0.744498i	0.0104455	+	0.0525129i
$202$		0			0
$203$	−18.2799	+	15.0019i	−1.28299	+	1.05293i
$204$		0			0
$205$	−10.7057	+	5.72231i	−0.747717	+	0.399663i
$206$		0			0
$207$	−7.48339	−	3.09972i	−0.520132	−	0.215446i
$208$		0			0
$209$	0.0240369	−	0.00995643i	0.00166267	−	0.000688700i
$210$		0			0
$211$	3.49110	+	1.05901i	0.240337	+	0.0729054i	0.408155	−	0.912913i	$-0.366172\pi$
$211$	3.49110	+	1.05901i	0.240337	+	0.0729054i	−0.167818	+	0.985818i	$0.553672\pi$
$212$		0			0
$213$	−2.17381	+	22.0711i	−0.148947	+	1.51228i
$214$		0			0
$215$	−2.75745	+	4.12682i	−0.188057	+	0.281447i
$216$		0			0
$217$	−25.1229	+	16.7866i	−1.70545	+	1.13955i
$218$		0			0
$219$	−35.2637	+	10.6971i	−2.38290	+	0.722845i
$220$		0			0
$221$	−3.72739	+	4.54184i	−0.250731	+	0.305517i
$222$		0			0
$223$	−10.9965	+	10.9965i	−0.736377	+	0.736377i	−0.971875	−	0.235498i	$-0.924328\pi$
$223$	−10.9965	+	10.9965i	−0.736377	+	0.736377i	0.235498	+	0.971875i	$0.424328\pi$
$224$		0			0
$225$	−24.5009	−	24.5009i	−1.63339	−	1.63339i
$226$		0			0
$227$	−8.73533	−	7.16890i	−0.579784	−	0.475816i	0.298202	−	0.954503i	$-0.403613\pi$
$227$	−8.73533	−	7.16890i	−0.579784	−	0.475816i	−0.877986	+	0.478686i	$0.841113\pi$
$228$		0			0
$229$	−6.25169	−	20.6091i	−0.413123	−	1.36188i	−0.878910	−	0.476988i	$-0.841729\pi$
$229$	−6.25169	−	20.6091i	−0.413123	−	1.36188i	0.465787	−	0.884897i	$-0.345771\pi$
$230$		0			0
$231$	−0.305471	−	0.457169i	−0.0200985	−	0.0300795i
$232$		0			0
$233$	−15.4486	−	10.3224i	−1.01207	−	0.676246i	−0.0652069	−	0.997872i	$-0.520771\pi$
$233$	−15.4486	−	10.3224i	−1.01207	−	0.676246i	−0.946867	+	0.321626i	$0.895771\pi$
$234$		0			0
$235$	19.0658	+	1.87781i	1.24371	+	0.122495i
$236$		0			0
$237$	10.1439	−	33.4398i	0.658914	−	2.17215i
$238$		0			0
$239$	−1.78163	−	4.30123i	−0.115244	−	0.278224i	0.855724	−	0.517432i	$-0.173112\pi$
$239$	−1.78163	−	4.30123i	−0.115244	−	0.278224i	−0.970968	+	0.239209i	$0.923112\pi$
$240$		0			0
$241$	4.11976	−	9.94598i	0.265377	−	0.640677i	−0.733877	−	0.679282i	$-0.762291\pi$
$241$	4.11976	−	9.94598i	0.265377	−	0.640677i	0.999255	+	0.0386049i	$0.0122914\pi$
$242$		0			0
$243$	10.5449	+	19.7282i	0.676459	+	1.26557i
$244$		0			0
$245$	14.8294	+	18.0697i	0.947417	+	1.15443i
$246$		0			0
$247$	0.466046	−	0.0927024i	0.0296538	−	0.00589851i
$248$		0			0
$249$	−2.11188	+	10.6172i	−0.133835	+	0.672835i
$250$		0			0
$251$	9.43288	+	5.04198i	0.595398	+	0.318247i	0.741427	−	0.671033i	$-0.234149\pi$
$251$	9.43288	+	5.04198i	0.595398	+	0.318247i	−0.146029	+	0.989280i	$0.546649\pi$
$252$		0			0
$253$	0.0142523	+	0.144706i	0.000896033	+	0.00909757i
$254$		0			0
$255$	−52.4859			−3.28679
$256$		0			0
$257$	24.3840			1.52104			0.760518	−	0.649317i	$-0.224945\pi$
$257$	24.3840			1.52104			0.760518	+	0.649317i	$0.224945\pi$
$258$		0			0
$259$	−2.11395	−	21.4632i	−0.131354	−	1.33366i
$260$		0			0
$261$	19.5019	+	10.4240i	1.20714	+	0.645229i
$262$		0			0
$263$	−4.69491	+	23.6029i	−0.289501	+	1.45542i	0.512805	+	0.858505i	$0.328606\pi$
$263$	−4.69491	+	23.6029i	−0.289501	+	1.45542i	−0.802306	+	0.596913i	$0.796394\pi$
$264$		0			0
$265$	31.7743	−	6.32031i	1.95188	−	0.388254i
$266$		0			0
$267$	−15.8790	−	19.3486i	−0.971777	−	1.18411i
$268$		0			0
$269$	−1.87737	−	3.51231i	−0.114465	−	0.214149i	0.818165	−	0.574984i	$-0.194992\pi$
$269$	−1.87737	−	3.51231i	−0.114465	−	0.214149i	−0.932630	+	0.360835i	$0.882492\pi$
$270$		0			0
$271$	−1.81145	+	4.37323i	−0.110038	+	0.265655i	−0.969300	−	0.245880i	$-0.920923\pi$
$271$	−1.81145	+	4.37323i	−0.110038	+	0.265655i	0.859262	+	0.511535i	$0.170923\pi$
$272$		0			0
$273$	−3.84292	−	9.27764i	−0.232584	−	0.561508i
$274$		0			0
$275$	−0.180559	+	0.595224i	−0.0108881	+	0.0358933i
$276$		0			0
$277$	−2.64687	−	0.260694i	−0.159035	−	0.0156636i	0.0181862	−	0.999835i	$-0.494211\pi$
$277$	−2.64687	−	0.260694i	−0.159035	−	0.0156636i	−0.177221	+	0.984171i	$0.556711\pi$
$278$		0			0
$279$	23.4925	+	15.6972i	1.40646	+	0.939766i
$280$		0			0
$281$	−9.65516	−	14.4500i	−0.575979	−	0.862013i	0.423049	−	0.906107i	$-0.360960\pi$
$281$	−9.65516	−	14.4500i	−0.575979	−	0.862013i	−0.999027	+	0.0440938i	$0.985960\pi$
$282$		0			0
$283$	−4.80191	−	15.8298i	−0.285444	−	0.940982i	−0.976012	−	0.217715i	$-0.930140\pi$
$283$	−4.80191	−	15.8298i	−0.285444	−	0.940982i	0.690569	−	0.723267i	$-0.257360\pi$
$284$		0			0
$285$	3.28123	+	2.69283i	0.194363	+	0.159510i
$286$		0			0
$287$	−7.90959	−	7.90959i	−0.466888	−	0.466888i
$288$		0			0
$289$	−7.98867	+	7.98867i	−0.469922	+	0.469922i
$290$		0			0
$291$	−7.94353	+	9.67922i	−0.465658	+	0.567406i
$292$		0			0
$293$	−3.08008	+	0.934333i	−0.179940	+	0.0545843i	−0.378969	−	0.925409i	$-0.623721\pi$
$293$	−3.08008	+	0.934333i	−0.179940	+	0.0545843i	0.199029	+	0.979994i	$0.436221\pi$
$294$		0			0
$295$	1.27658	−	0.852985i	0.0743255	−	0.0496627i
$296$		0			0
$297$	−0.0312746	+	0.0468057i	−0.00181473	+	0.00271594i
$298$		0			0
$299$	−0.260301	+	2.64288i	−0.0150536	+	0.152842i
$300$		0			0
$301$	−4.37661	−	1.32763i	−0.252264	−	0.0765234i
$302$		0			0
$303$	13.2593	−	5.49217i	0.761726	−	0.315517i
$304$		0			0
$305$	−17.6225	−	7.29948i	−1.00906	−	0.417967i
$306$		0			0
$307$	−13.2201	+	7.06631i	−0.754513	+	0.403295i	−0.803347	−	0.595511i	$-0.796949\pi$
$307$	−13.2201	+	7.06631i	−0.754513	+	0.403295i	0.0488341	+	0.998807i	$0.484449\pi$
$308$		0			0
$309$	−32.5459	+	26.7098i	−1.85147	+	1.51947i
$310$		0			0
$311$	−2.59092	−	13.0255i	−0.146918	−	0.738606i	−0.982060	−	0.188571i	$-0.939614\pi$
$311$	−2.59092	−	13.0255i	−0.146918	−	0.738606i	0.835142	−	0.550035i	$-0.185386\pi$
$312$		0			0
$313$	20.9944	+	4.17605i	1.18667	+	0.236044i	0.748679	−	0.662933i	$-0.230689\pi$
$313$	20.9944	+	4.17605i	1.18667	+	0.236044i	0.437996	+	0.898977i	$0.355689\pi$
$314$		0			0
$315$	22.3679	−	41.8474i	1.26029	−	2.35783i
$316$		0			0
$317$	15.9918	−	1.57505i	0.898188	−	0.0884638i	0.361624	−	0.932324i	$-0.382222\pi$
$317$	15.9918	−	1.57505i	0.898188	−	0.0884638i	0.536563	+	0.843860i	$0.319722\pi$
$318$		0			0
$319$		−	0.396960i		−	0.0222255i
$320$		0			0
$321$		−	2.43234i		−	0.135760i
$322$		0			0
$323$	2.27753	−	0.224317i	0.126725	−	0.0124813i
$324$		0			0
$325$	−5.35517	+	10.0188i	−0.297051	+	0.555744i
$326$		0			0
$327$	15.2034	+	3.02415i	0.840751	+	0.167236i
$328$		0			0
$329$	3.44406	+	17.3144i	0.189877	+	0.954576i
$330$		0			0
$331$	−5.51832	+	4.52876i	−0.303314	+	0.248923i	−0.773721	−	0.633526i	$-0.781607\pi$
$331$	−5.51832	+	4.52876i	−0.303314	+	0.248923i	0.470407	+	0.882449i	$0.344107\pi$
$332$		0			0
$333$	−17.7861	+	9.50689i	−0.974674	+	0.520974i
$334$		0			0
$335$	1.08645	+	0.450024i	0.0593593	+	0.0245874i
$336$		0			0
$337$	15.4160	−	6.38550i	0.839761	−	0.347840i	0.0790017	−	0.996874i	$-0.474827\pi$
$337$	15.4160	−	6.38550i	0.839761	−	0.347840i	0.760759	+	0.649034i	$0.224827\pi$
$338$		0			0
$339$	27.0436	+	8.20359i	1.46881	+	0.445558i
$340$		0			0
$341$	0.0497146	−	0.504761i	0.00269220	−	0.0273343i
$342$		0			0
$343$	2.04354	−	3.05837i	0.110341	−	0.165136i
$344$		0			0
$345$	−19.7249	+	13.1798i	−1.06195	+	0.709576i
$346$		0			0
$347$	−7.74084	+	2.34816i	−0.415550	+	0.126056i	−0.491135	−	0.871084i	$-0.663418\pi$
$347$	−7.74084	+	2.34816i	−0.415550	+	0.126056i	0.0755845	+	0.997139i	$0.475918\pi$
$348$		0			0
$349$	13.7641	−	16.7715i	0.736773	−	0.897760i	−0.260940	−	0.965355i	$-0.584032\pi$
$349$	13.7641	−	16.7715i	0.736773	−	0.897760i	0.997713	+	0.0675947i	$0.0215325\pi$
$350$		0			0
$351$	−0.726990	+	0.726990i	−0.0388039	+	0.0388039i
$352$		0			0
$353$	−8.84923	−	8.84923i	−0.470997	−	0.470997i	0.431240	−	0.902237i	$-0.358076\pi$
$353$	−8.84923	−	8.84923i	−0.470997	−	0.470997i	−0.902237	+	0.431240i	$0.858076\pi$
$354$		0			0
$355$	26.5590	+	21.7964i	1.40960	+	1.15683i
$356$		0			0
$357$	−14.0395	−	46.2819i	−0.743047	−	2.44950i
$358$		0			0
$359$	−3.19879	−	4.78732i	−0.168825	−	0.252665i	0.737403	−	0.675453i	$-0.236052\pi$
$359$	−3.19879	−	4.78732i	−0.168825	−	0.252665i	−0.906229	+	0.422787i	$0.861052\pi$
$360$		0			0
$361$	15.6440	+	10.4530i	0.823370	+	0.550158i
$362$		0			0
$363$	−27.6174	−	2.72007i	−1.44954	−	0.142767i
$364$		0			0
$365$	−16.5719	+	54.6304i	−0.867415	+	2.85949i
$366$		0			0
$367$	5.08336	+	12.2723i	0.265349	+	0.640610i	0.999253	−	0.0386438i	$-0.0123038\pi$
$367$	5.08336	+	12.2723i	0.265349	+	0.640610i	−0.733904	+	0.679253i	$0.762304\pi$
$368$		0			0
$369$	−4.00284	+	9.66372i	−0.208380	+	0.503073i
$370$		0			0
$371$	14.0726	+	26.3279i	0.730611	+	1.36688i
$372$		0			0
$373$	−10.2805	−	12.5268i	−0.532304	−	0.648614i	0.435539	−	0.900170i	$-0.356558\pi$
$373$	−10.2805	−	12.5268i	−0.532304	−	0.648614i	−0.967843	+	0.251556i	$0.919058\pi$
$374$		0			0
$375$	−51.1456	+	10.1735i	−2.64115	+	0.525357i
$376$		0			0
$377$	1.41440	−	7.11069i	0.0728455	−	0.366219i
$378$		0			0
$379$	28.2889	+	15.1207i	1.45310	+	0.776699i	0.993758	−	0.111559i	$-0.0355843\pi$
$379$	28.2889	+	15.1207i	1.45310	+	0.776699i	0.459345	+	0.888258i	$0.348084\pi$
$380$		0			0
$381$	−1.07363	−	10.9007i	−0.0550037	−	0.558462i
$382$		0			0
$383$	32.0042			1.63534			0.817670	−	0.575687i	$-0.195265\pi$
$383$	32.0042			1.63534			0.817670	+	0.575687i	$0.195265\pi$
$384$		0			0
$385$	−0.851799			−0.0434117
$386$		0			0
$387$	0.419194	+	4.25615i	0.0213088	+	0.216352i
$388$		0			0
$389$	23.4371	+	12.5274i	1.18831	+	0.635164i	0.942517	−	0.334159i	$-0.108452\pi$
$389$	23.4371	+	12.5274i	1.18831	+	0.635164i	0.245791	+	0.969323i	$0.420952\pi$
$390$		0			0
$391$	−2.49525	+	12.5445i	−0.126190	+	0.634400i
$392$		0			0
$393$	−49.0143	+	9.74954i	−2.47244	+	0.491799i
$394$		0			0
$395$	−34.3434	−	41.8476i	−1.72801	−	2.10558i
$396$		0			0
$397$	14.8060	+	27.7001i	0.743092	+	1.39023i	0.914319	+	0.404995i	$0.132727\pi$
$397$	14.8060	+	27.7001i	0.743092	+	1.39023i	−0.171227	+	0.985232i	$0.554773\pi$
$398$		0			0
$399$	−1.49684	+	3.61369i	−0.0749356	+	0.180911i
$400$		0			0
$401$	−14.3179	−	34.5666i	−0.715004	−	1.72617i	−0.687101	−	0.726562i	$-0.741117\pi$
$401$	−14.3179	−	34.5666i	−0.715004	−	1.72617i	−0.0279034	−	0.999611i	$-0.508883\pi$
$402$		0			0
$403$	2.68904	−	8.86458i	0.133951	−	0.441576i
$404$		0			0
$405$	30.1827	+	2.97273i	1.49979	+	0.147716i
$406$		0			0
$407$	0.301021	+	0.201136i	0.0149211	+	0.00996994i
$408$		0			0
$409$	11.8044	+	17.6665i	0.583688	+	0.873550i	0.999353	−	0.0359673i	$-0.0114512\pi$
$409$	11.8044	+	17.6665i	0.583688	+	0.873550i	−0.415665	+	0.909518i	$0.636451\pi$
$410$		0			0
$411$	3.63195	+	11.9729i	0.179151	+	0.590581i
$412$		0			0
$413$	1.09363	+	0.897522i	0.0538142	+	0.0441642i
$414$		0			0
$415$	11.8584	+	11.8584i	0.582105	+	0.582105i
$416$		0			0
$417$	18.5865	−	18.5865i	0.910185	−	0.910185i
$418$		0			0
$419$	16.4019	−	19.9857i	0.801284	−	0.976367i	−0.198709	−	0.980058i	$-0.563675\pi$
$419$	16.4019	−	19.9857i	0.801284	−	0.976367i	0.999993	+	0.00369123i	$0.00117496\pi$
$420$		0			0
$421$	13.3683	−	4.05522i	0.651529	−	0.197639i	0.0528178	−	0.998604i	$-0.483180\pi$
$421$	13.3683	−	4.05522i	0.651529	−	0.197639i	0.598711	+	0.800965i	$0.295680\pi$
$422$		0			0
$423$	13.7259	−	9.17135i	0.667376	−	0.445927i
$424$		0			0
$425$	−30.3970	+	45.4923i	−1.47447	+	2.20670i
$426$		0			0
$427$	1.72282	−	17.4920i	0.0833729	−	0.846499i
$428$		0			0
$429$	0.161312	+	0.0489334i	0.00778820	+	0.00236252i
$430$		0			0
$431$	−10.5379	+	4.36495i	−0.507594	+	0.210252i	−0.621758	−	0.783210i	$-0.713581\pi$
$431$	−10.5379	+	4.36495i	−0.507594	+	0.210252i	0.114164	+	0.993462i	$0.463581\pi$
$432$		0			0
$433$	12.0164	+	4.97736i	0.577472	+	0.239197i	0.652250	−	0.758004i	$-0.273825\pi$
$433$	12.0164	+	4.97736i	0.577472	+	0.239197i	−0.0747787	+	0.997200i	$0.523825\pi$
$434$		0			0
$435$	57.1167	−	30.5295i	2.73854	−	1.46378i
$436$		0			0
$437$	0.799598	−	0.656213i	0.0382500	−	0.0313909i
$438$		0			0
$439$	3.36331	+	16.9085i	0.160522	+	0.807000i	0.974200	+	0.225684i	$0.0724618\pi$
$439$	3.36331	+	16.9085i	0.160522	+	0.807000i	−0.813678	+	0.581316i	$0.802538\pi$
$440$		0			0
$441$	19.7553	+	3.92958i	0.940729	+	0.187123i
$442$		0			0
$443$	−17.4346	+	32.6178i	−0.828343	+	1.54972i	0.00699026	+	0.999976i	$0.497775\pi$
$443$	−17.4346	+	32.6178i	−0.828343	+	1.54972i	−0.835333	+	0.549744i	$0.814725\pi$
$444$		0			0
$445$	−38.5899	+	3.80077i	−1.82934	+	0.180174i
$446$		0			0
$447$		−	46.0607i		−	2.17860i
$448$		0			0
$449$			39.3683i			1.85791i	0.370197	+	0.928953i	$0.379290\pi$
$449$			39.3683i			1.85791i	−0.370197	+	0.928953i	$0.620710\pi$
$450$		0			0
$451$	0.186866	−	0.0184047i	0.00879920	−	0.000866646i
$452$		0			0
$453$	1.55522	−	2.90960i	0.0730704	−	0.136705i
$454$		0			0
$455$	−15.2582	−	3.03504i	−0.715314	−	0.142285i
$456$		0			0
$457$	−4.66875	−	23.4714i	−0.218395	−	1.09795i	−0.921951	−	0.387306i	$-0.873406\pi$
$457$	−4.66875	−	23.4714i	−0.218395	−	1.09795i	0.703556	−	0.710639i	$-0.251594\pi$
$458$		0			0
$459$	−3.82766	+	3.14128i	−0.178660	+	0.146622i
$460$		0			0
$461$	20.5438	−	10.9809i	0.956820	−	0.511431i	0.0823991	−	0.996599i	$-0.473742\pi$
$461$	20.5438	−	10.9809i	0.956820	−	0.511431i	0.874421	+	0.485169i	$0.161242\pi$
$462$		0			0
$463$	−7.27612	−	3.01387i	−0.338150	−	0.140066i	0.207146	−	0.978310i	$-0.433583\pi$
$463$	−7.27612	−	3.01387i	−0.338150	−	0.140066i	−0.545296	+	0.838244i	$0.683583\pi$
$464$		0			0
$465$	76.4512	−	31.6671i	3.54534	−	1.46853i
$466$		0			0
$467$	−16.8420	−	5.10896i	−0.779353	−	0.236414i	−0.124550	−	0.992213i	$-0.539749\pi$
$467$	−16.8420	−	5.10896i	−0.779353	−	0.236414i	−0.654804	+	0.755799i	$0.727249\pi$
$468$		0			0
$469$	−0.106214	+	1.07841i	−0.00490451	+	0.0497964i
$470$		0			0
$471$	9.37989	−	14.0380i	0.432202	−	0.646837i
$472$		0			0
$473$	0.0638349	−	0.0426531i	0.00293513	−	0.00196119i
$474$		0			0
$475$	4.23433	−	1.28447i	0.194284	−	0.0589355i
$476$		0			0
$477$	17.7095	−	21.5790i	0.810861	−	0.988037i
$478$		0			0
$479$	23.9259	−	23.9259i	1.09320	−	1.09320i	0.0980158	−	0.995185i	$-0.468750\pi$
$479$	23.9259	−	23.9259i	1.09320	−	1.09320i	0.995185	−	0.0980158i	$-0.0312496\pi$
$480$		0			0
$481$	4.67549	+	4.67549i	0.213184	+	0.213184i
$482$		0			0
$483$	−16.8981	−	13.8679i	−0.768892	−	0.631013i
$484$		0			0
$485$	5.63100	+	18.5629i	0.255690	+	0.842898i
$486$		0			0
$487$	13.8712	+	20.7597i	0.628562	+	0.940710i	0.999925	+	0.0122223i	$0.00389056\pi$
$487$	13.8712	+	20.7597i	0.628562	+	0.940710i	−0.371363	+	0.928488i	$0.621109\pi$
$488$		0			0
$489$	5.56679	+	3.71961i	0.251739	+	0.168207i
$490$		0			0
$491$	34.3988	+	3.38798i	1.55239	+	0.152898i	0.837540	−	0.546376i	$-0.183993\pi$
$491$	34.3988	+	3.38798i	1.55239	+	0.152898i	0.714855	+	0.699273i	$0.246493\pi$
$492$		0			0
$493$	10.1360	−	33.4139i	0.456502	−	1.50489i
$494$		0			0
$495$	0.304815	+	0.735889i	0.0137004	+	0.0330758i
$496$		0			0
$497$	−12.1157	+	29.2500i	−0.543465	+	1.31204i
$498$		0			0
$499$	−8.48482	−	15.8740i	−0.379833	−	0.710617i	0.617265	−	0.786756i	$-0.288241\pi$
$499$	−8.48482	−	15.8740i	−0.379833	−	0.710617i	−0.997097	+	0.0761386i	$0.975741\pi$
$500$		0			0
$501$	−26.4672	−	32.2504i	−1.18247	−	1.44084i
$502$		0			0
$503$	1.80143	−	0.358326i	0.0803216	−	0.0159770i	−0.154766	−	0.987951i	$-0.549462\pi$
$503$	1.80143	−	0.358326i	0.0803216	−	0.0159770i	0.235088	+	0.971974i	$0.424462\pi$
$504$		0			0
$505$	4.33757	−	21.8064i	0.193019	−	0.970374i
$506$		0			0
$507$	−26.2185	−	14.0141i	−1.16440	−	0.622386i
$508$		0			0
$509$	−2.27683	−	23.1171i	−0.100919	−	1.02465i	−0.903640	−	0.428292i	$-0.859115\pi$
$509$	−2.27683	−	23.1171i	−0.100919	−	1.02465i	0.802722	−	0.596354i	$-0.203385\pi$
$510$		0			0
$511$	−52.6058			−2.32714
$512$		0			0
$513$	0.400458			0.0176806
$514$		0			0
$515$	6.39322	+	64.9115i	0.281719	+	2.86034i
$516$		0			0
$517$	−0.261350	−	0.139695i	−0.0114942	−	0.00614377i
$518$		0			0
$519$	2.18724	−	10.9960i	0.0960090	−	0.482670i
$520$		0			0
$521$	15.0753	−	2.99867i	0.660461	−	0.131374i	0.146531	−	0.989206i	$-0.453189\pi$
$521$	15.0753	−	2.99867i	0.660461	−	0.131374i	0.513930	+	0.857832i	$0.328189\pi$
$522$		0			0
$523$	−22.3248	−	27.2029i	−0.976197	−	1.18950i	−0.981878	−	0.189516i	$-0.939308\pi$
$523$	−22.3248	−	27.2029i	−0.976197	−	1.18950i	0.00568080	−	0.999984i	$-0.498192\pi$
$524$		0			0
$525$	−44.0812	−	82.4701i	−1.92386	−	3.59929i
$526$		0			0
$527$	17.0733	−	41.2186i	0.743724	−	1.79551i
$528$		0			0
$529$	−6.58942	−	15.9083i	−0.286496	−	0.691663i
$530$		0			0
$531$	0.384035	−	1.26599i	0.0166657	−	0.0549394i
$532$		0			0
$533$	3.41289	+	0.336141i	0.147829	+	0.0145599i
$534$		0			0
$535$	−3.13311	−	2.09348i	−0.135456	−	0.0905090i
$536$		0			0
$537$	15.6694	+	23.4510i	0.676187	+	1.01198i
$538$		0			0
$539$	−0.104962	−	0.346014i	−0.00452104	−	0.0149039i
$540$		0			0
$541$	−18.5752	−	15.2443i	−0.798609	−	0.655402i	0.143896	−	0.989593i	$-0.454037\pi$
$541$	−18.5752	−	15.2443i	−0.798609	−	0.655402i	−0.942505	+	0.334191i	$0.891537\pi$
$542$		0			0
$543$	20.6905	+	20.6905i	0.887913	+	0.887913i
$544$		0			0
$545$	16.9808	−	16.9808i	0.727379	−	0.727379i
$546$		0			0
$547$	5.30428	−	6.46329i	0.226795	−	0.276350i	−0.647164	−	0.762351i	$-0.724045\pi$
$547$	5.30428	−	6.46329i	0.226795	−	0.276350i	0.873958	+	0.486001i	$0.161545\pi$
$548$		0			0
$549$	−15.7283	+	4.77113i	−0.671267	+	0.203627i
$550$		0			0
$551$	−2.34799	+	1.56888i	−0.100028	+	0.0668365i
$552$		0			0
$553$	27.7146	−	41.4778i	1.17854	−	1.76382i
$554$		0			0
$555$	−5.78948	+	58.7816i	−0.245750	+	2.49514i
$556$		0			0
$557$	18.2713	+	5.54253i	0.774178	+	0.234844i	0.652565	−	0.757733i	$-0.273693\pi$
$557$	18.2713	+	5.54253i	0.774178	+	0.234844i	0.121614	+	0.992577i	$0.461193\pi$
$558$		0			0
$559$	1.29544	−	0.536591i	0.0547915	−	0.0226954i
$560$		0			0
$561$	0.750068	+	0.310688i	0.0316679	+	0.0131173i
$562$		0			0
$563$	13.4624	−	7.19582i	0.567374	−	0.303268i	−0.162656	−	0.986683i	$-0.552006\pi$
$563$	13.4624	−	7.19582i	0.567374	−	0.303268i	0.730030	+	0.683415i	$0.239506\pi$
$564$		0			0
$565$	33.8432	−	27.7744i	1.42379	−	1.16848i
$566$		0			0
$567$	5.45223	+	27.4102i	0.228972	+	1.15112i
$568$		0			0
$569$	−13.4120	−	2.66782i	−0.562261	−	0.111841i	−0.0942266	−	0.995551i	$-0.530038\pi$
$569$	−13.4120	−	2.66782i	−0.562261	−	0.111841i	−0.468035	+	0.883710i	$0.655038\pi$
$570$		0			0
$571$	14.7518	−	27.5987i	0.617343	−	1.15497i	−0.357885	−	0.933766i	$-0.616502\pi$
$571$	14.7518	−	27.5987i	0.617343	−	1.15497i	0.975228	−	0.221202i	$-0.0709981\pi$
$572$		0			0
$573$	−28.2996	+	2.78727i	−1.18223	+	0.116440i
$574$		0			0
$575$			24.7297i			1.03130i
$576$		0			0
$577$			15.4878i			0.644765i	0.946609	+	0.322383i	$0.104484\pi$
$577$			15.4878i			0.644765i	−0.946609	+	0.322383i	$0.895516\pi$
$578$		0			0
$579$	26.9718	−	2.65649i	1.12091	−	0.110400i
$580$		0			0
$581$	−7.28470	+	13.6287i	−0.302220	+	0.565414i
$582$		0			0
$583$	−0.491496	−	0.0977646i	−0.0203557	−	0.00404899i
$584$		0			0
$585$	2.83808	+	14.2680i	0.117340	+	0.589908i
$586$		0			0
$587$	4.87628	−	4.00186i	0.201265	−	0.165174i	−0.528362	−	0.849019i	$-0.677194\pi$
$587$	4.87628	−	4.00186i	0.201265	−	0.165174i	0.729627	+	0.683845i	$0.239694\pi$
$588$		0			0
$589$	−3.18212	+	1.70088i	−0.131117	+	0.0700834i
$590$		0			0
$591$	−4.31783	−	1.78851i	−0.177612	−	0.0735693i
$592$		0			0
$593$	3.00281	−	1.24380i	0.123311	−	0.0510769i	−0.320175	−	0.947358i	$-0.603742\pi$
$593$	3.00281	−	1.24380i	0.123311	−	0.0510769i	0.443486	+	0.896282i	$0.353742\pi$
$594$		0			0
$595$	−71.6997	−	21.7499i	−2.93940	−	0.891658i
$596$		0			0
$597$	−1.56017	+	15.8407i	−0.0638535	+	0.648315i
$598$		0			0
$599$	−5.18293	+	7.75680i	−0.211769	+	0.316934i	−0.922113	−	0.386920i	$-0.873539\pi$
$599$	−5.18293	+	7.75680i	−0.211769	+	0.316934i	0.710345	+	0.703854i	$0.248539\pi$
$600$		0			0
$601$	−11.1247	+	7.43329i	−0.453786	+	0.303210i	−0.761378	−	0.648308i	$-0.775477\pi$
$601$	−11.1247	+	7.43329i	−0.453786	+	0.303210i	0.307592	+	0.951518i	$0.400477\pi$
$602$		0			0
$603$	0.969673	−	0.294147i	0.0394881	−	0.0119786i
$604$		0			0
$605$	−27.2737	+	33.2330i	−1.10883	+	1.35112i
$606$		0			0
$607$	−6.24782	+	6.24782i	−0.253591	+	0.253591i	−0.822441	−	0.568850i	$-0.807388\pi$
$607$	−6.24782	+	6.24782i	−0.253591	+	0.253591i	0.568850	+	0.822441i	$0.307388\pi$
$608$		0			0
$609$	42.1990	+	42.1990i	1.70999	+	1.70999i
$610$		0			0
$611$	−4.18379	−	3.43355i	−0.169258	−	0.138907i
$612$		0			0
$613$	7.84358	+	25.8568i	0.316799	+	1.04435i	0.960316	+	0.278915i	$0.0899747\pi$
$613$	7.84358	+	25.8568i	0.316799	+	1.04435i	−0.643517	+	0.765432i	$0.722525\pi$
$614$		0			0
$615$	17.0198	+	25.4719i	0.686304	+	1.02713i
$616$		0			0
$617$	−4.19077	−	2.80018i	−0.168714	−	0.112731i	0.468347	−	0.883545i	$-0.344850\pi$
$617$	−4.19077	−	2.80018i	−0.168714	−	0.112731i	−0.637060	+	0.770814i	$0.719850\pi$
$618$		0			0
$619$	49.0334	+	4.82937i	1.97082	+	0.194109i	0.999114	−	0.0420835i	$-0.0133996\pi$
$619$	49.0334	+	4.82937i	1.97082	+	0.194109i	0.971706	+	0.236192i	$0.0758996\pi$
$620$		0			0
$621$	−0.649680	+	2.14171i	−0.0260707	+	0.0859437i
$622$		0			0
$623$	−13.6739	−	33.0118i	−0.547835	−	1.32259i
$624$		0			0
$625$	−11.2358	+	27.1255i	−0.449430	+	1.08502i
$626$		0			0
$627$	−0.0309514	−	0.0579060i	−0.00123608	−	0.00231254i
$628$		0			0
$629$	20.2025	+	24.6168i	0.805526	+	0.981537i
$630$		0			0
$631$	−24.7678	+	4.92662i	−0.985991	+	0.196126i	−0.661649	−	0.749814i	$-0.730143\pi$
$631$	−24.7678	+	4.92662i	−0.985991	+	0.196126i	−0.324342	+	0.945940i	$0.605143\pi$
$632$		0			0
$633$	1.79615	−	9.02986i	0.0713906	−	0.358905i
$634$		0			0
$635$	−14.9654	−	7.99917i	−0.593884	−	0.317437i
$636$		0			0
$637$	−0.647295	−	6.57209i	−0.0256468	−	0.260396i
$638$		0			0
$639$	29.6053			1.17117
$640$		0			0
$641$	−23.9268			−0.945051			−0.472525	−	0.881317i	$-0.656657\pi$
$641$	−23.9268			−0.945051			−0.472525	+	0.881317i	$0.656657\pi$
$642$		0			0
$643$	−2.81438	−	28.5748i	−0.110988	−	1.12688i	−0.875815	−	0.482646i	$-0.839676\pi$
$643$	−2.81438	−	28.5748i	−0.110988	−	1.12688i	0.764827	−	0.644235i	$-0.222824\pi$
$644$		0			0
$645$	11.0466	+	5.90454i	0.434960	+	0.232491i
$646$		0			0
$647$	−6.46521	+	32.5028i	−0.254174	+	1.27782i	0.617047	+	0.786926i	$0.288329\pi$
$647$	−6.46521	+	32.5028i	−0.254174	+	1.27782i	−0.871221	+	0.490891i	$0.836671\pi$
$648$		0			0
$649$	−0.0232927	+	0.00463320i	−0.000914317	+	0.000181869i
$650$		0			0
$651$	48.3740	+	58.9439i	1.89593	+	2.31019i
$652$		0			0
$653$	−11.6576	−	21.8099i	−0.456199	−	0.853488i	−0.999899	−	0.0142084i	$-0.995477\pi$
$653$	−11.6576	−	21.8099i	−0.456199	−	0.853488i	0.543700	−	0.839279i	$-0.317023\pi$
$654$		0			0
$655$	−29.6275	+	71.5270i	−1.15764	+	2.79479i
$656$		0			0
$657$	18.8249	+	45.4474i	0.734431	+	1.77307i
$658$		0			0
$659$	12.8933	−	42.5035i	0.502252	−	1.65570i	−0.228872	−	0.973457i	$-0.573504\pi$
$659$	12.8933	−	42.5035i	0.502252	−	1.65570i	0.731123	−	0.682245i	$-0.238996\pi$
$660$		0			0
$661$	−43.7995	−	4.31388i	−1.70360	−	0.167790i	−0.801117	−	0.598507i	$-0.795761\pi$
$661$	−43.7995	−	4.31388i	−1.70360	−	0.167790i	−0.902487	+	0.430717i	$0.858261\pi$
$662$		0			0
$663$	12.3289	+	8.23788i	0.478813	+	0.319933i
$664$		0			0
$665$	3.36651	+	5.03834i	0.130548	+	0.195379i
$666$		0			0
$667$	−4.58135	−	15.1027i	−0.177390	−	0.584778i
$668$		0			0
$669$	30.3378	+	24.8976i	1.17293	+	0.962595i
$670$		0			0
$671$	0.208632	+	0.208632i	0.00805414	+	0.00805414i
$672$		0			0
$673$	−3.12592	+	3.12592i	−0.120495	+	0.120495i	−0.764783	−	0.644288i	$-0.777154\pi$
$673$	−3.12592	+	3.12592i	−0.120495	+	0.120495i	0.644288	+	0.764783i	$0.277154\pi$
$674$		0			0
$675$	−6.07361	+	7.40072i	−0.233773	+	0.284854i
$676$		0			0
$677$	−17.2538	+	5.23388i	−0.663117	+	0.201154i	−0.603863	−	0.797088i	$-0.706372\pi$
$677$	−17.2538	+	5.23388i	−0.663117	+	0.201154i	−0.0592549	+	0.998243i	$0.518872\pi$
$678$		0			0
$679$	−14.8625	+	9.93080i	−0.570370	+	0.381109i
$680$		0			0
$681$	−15.8439	+	23.7121i	−0.607141	+	0.908651i
$682$		0			0
$683$	1.22697	−	12.4576i	0.0469487	−	0.476678i	−0.942749	−	0.333504i	$-0.891769\pi$
$683$	1.22697	−	12.4576i	0.0469487	−	0.476678i	0.989697	−	0.143174i	$-0.0457310\pi$
$684$		0			0
$685$	18.5484	+	5.62659i	0.708698	+	0.214981i
$686$		0			0
$687$	−50.2133	+	20.7990i	−1.91576	+	0.793533i
$688$		0			0
$689$	−8.45575	−	3.50249i	−0.322139	−	0.133434i
$690$		0			0
$691$	−6.05262	+	3.23520i	−0.230253	+	0.123073i	−0.582489	−	0.812838i	$-0.697921\pi$
$691$	−6.05262	+	3.23520i	−0.230253	+	0.123073i	0.352237	+	0.935911i	$0.385421\pi$
$692$		0			0
$693$	−0.567370	+	0.465629i	−0.0215526	+	0.0176878i
$694$		0			0
$695$	−7.94428	−	39.9386i	−0.301344	−	1.51496i
$696$		0			0
$697$	16.1993	+	3.22225i	0.613594	+	0.122051i
$698$		0			0
$699$	−22.1035	+	41.3527i	−0.836030	+	1.56410i
$700$		0			0
$701$	−9.92907	+	0.977928i	−0.375016	+	0.0369358i	−0.283770	−	0.958893i	$-0.591585\pi$
$701$	−9.92907	+	0.977928i	−0.375016	+	0.0369358i	−0.0912463	+	0.995828i	$0.529085\pi$
$702$		0			0
$703$		−	2.57546i		−	0.0971354i
$704$		0			0
$705$		−	48.3482i		−	1.82090i
$706$		0			0
$707$	20.3891	−	2.00815i	0.766812	−	0.0755244i
$708$		0			0
$709$	−21.2178	+	39.6958i	−0.796853	+	1.49081i	0.0729109	+	0.997338i	$0.476771\pi$
$709$	−21.2178	+	39.6958i	−0.796853	+	1.49081i	−0.869764	+	0.493468i	$0.835729\pi$
$710$		0			0
$711$	−45.7513	−	9.10050i	−1.71581	−	0.341295i
$712$		0			0
$713$	−3.93405	−	19.7778i	−0.147331	−	0.740685i
$714$		0			0
$715$	0.201870	−	0.165671i	0.00754952	−	0.00619573i
$716$		0			0
$717$	−10.3619	+	5.53853i	−0.386971	+	0.206840i
$718$		0			0
$719$	5.70178	+	2.36176i	0.212641	+	0.0880786i	0.486461	−	0.873702i	$-0.338287\pi$
$719$	5.70178	+	2.36176i	0.212641	+	0.0880786i	−0.273821	+	0.961781i	$0.588287\pi$
$720$		0			0
$721$	−55.5287	+	23.0007i	−2.06800	+	0.856592i
$722$		0			0
$723$	−25.9984	−	7.88654i	−0.966893	−	0.293304i
$724$		0			0
$725$	6.61735	−	67.1871i	0.245762	−	2.49527i
$726$		0			0
$727$	−2.26426	+	3.38870i	−0.0839767	+	0.125680i	−0.871080	−	0.491141i	$-0.836580\pi$
$727$	−2.26426	+	3.38870i	−0.0839767	+	0.125680i	0.787103	+	0.616821i	$0.211580\pi$
$728$		0			0
$729$	27.5889	−	18.4343i	1.02181	−	0.682752i
$730$		0			0
$731$	6.46238	−	1.96034i	0.239020	−	0.0725059i
$732$		0			0
$733$	3.99719	−	4.87059i	0.147639	−	0.179899i	−0.693939	−	0.720033i	$-0.744126\pi$
$733$	3.99719	−	4.87059i	0.147639	−	0.179899i	0.841579	+	0.540134i	$0.181626\pi$
$734$		0			0
$735$	41.7139	−	41.7139i	1.53864	−	1.53864i
$736$		0			0
$737$	−0.0128625	−	0.0128625i	−0.000473795	−	0.000473795i
$738$		0			0
$739$	38.1520	+	31.3106i	1.40344	+	1.15178i	0.967818	+	0.251650i	$0.0809732\pi$
$739$	38.1520	+	31.3106i	1.40344	+	1.15178i	0.435627	+	0.900127i	$0.356527\pi$
$740$		0			0
$741$	−0.348104	−	1.14755i	−0.0127879	−	0.0421562i
$742$		0			0
$743$	13.0820	+	19.5786i	0.479933	+	0.718270i	0.989876	−	0.141938i	$-0.0453335\pi$
$743$	13.0820	+	19.5786i	0.479933	+	0.718270i	−0.509943	+	0.860208i	$0.670333\pi$
$744$		0			0
$745$	−59.3312	−	39.6439i	−2.17373	−	1.45244i
$746$		0			0
$747$	14.3810	+	1.41640i	0.526173	+	0.0518235i
$748$		0			0
$749$	1.00795	−	3.32276i	0.0368296	−	0.121411i
$750$		0			0
$751$	5.27025	+	12.7235i	0.192314	+	0.464287i	0.990396	−	0.138262i	$-0.0441517\pi$
$751$	5.27025	+	12.7235i	0.192314	+	0.464287i	−0.798082	+	0.602549i	$0.794152\pi$
$752$		0			0
$753$	10.3296	−	24.9379i	0.376432	−	0.908788i
$754$		0			0
$755$	−2.40933	−	4.50754i	−0.0876846	−	0.164046i
$756$		0			0
$757$	21.0274	+	25.6220i	0.764254	+	0.931246i	0.999169	−	0.0407698i	$-0.0129810\pi$
$757$	21.0274	+	25.6220i	0.764254	+	0.931246i	−0.234915	+	0.972016i	$0.575481\pi$
$758$		0			0
$759$	0.359904	−	0.0715893i	0.0130637	−	0.00259853i
$760$		0			0
$761$	2.16085	−	10.8633i	0.0783307	−	0.393795i	−0.921653	−	0.388016i	$-0.873160\pi$
$761$	2.16085	−	10.8633i	0.0783307	−	0.393795i	0.999983	−	0.00577907i	$-0.00183954\pi$
$762$		0			0
$763$	19.5159	+	10.4314i	0.706522	+	0.377644i
$764$		0			0
$765$	6.86744	+	69.7263i	0.248293	+	2.52096i
$766$		0			0
$767$	−0.433747			−0.0156617
$768$		0			0
$769$	−34.2408			−1.23475			−0.617377	−	0.786667i	$-0.711805\pi$
$769$	−34.2408			−1.23475			−0.617377	+	0.786667i	$0.711805\pi$
$770$		0			0
$771$	−6.03168	−	61.2407i	−0.217226	−	2.20553i
$772$		0			0
$773$	17.3113	+	9.25306i	0.622642	+	0.332809i	0.752370	−	0.658740i	$-0.228910\pi$
$773$	17.3113	+	9.25306i	0.622642	+	0.332809i	−0.129728	+	0.991550i	$0.541410\pi$
$774$		0			0
$775$	16.8288	−	84.6042i	0.604509	−	3.03907i
$776$		0			0
$777$	−53.3821	+	10.6184i	−1.91507	+	0.380932i
$778$		0			0
$779$	−0.847405	−	1.03257i	−0.0303614	−	0.0369955i
$780$		0			0
$781$	−0.250527	−	0.468704i	−0.00896458	−	0.0167715i
$782$		0			0
$783$	2.33819	−	5.64488i	0.0835599	−	0.201732i
$784$		0			0
$785$	−10.0093	−	24.1646i	−0.357248	−	0.862473i
$786$		0			0
$787$	−15.6610	+	51.6273i	−0.558253	+	1.84031i	−0.0163615	+	0.999866i	$0.505208\pi$
$787$	−15.6610	+	51.6273i	−0.558253	+	1.84031i	−0.541892	+	0.840448i	$0.682292\pi$
$788$		0			0
$789$	60.4402	+	5.95284i	2.15173	+	0.211927i
$790$		0			0
$791$	33.5441	+	22.4135i	1.19269	+	0.796931i
$792$		0			0
$793$	2.99382	+	4.48057i	0.106314	+	0.159110i
$794$		0			0
$795$	−23.7332	−	78.2380i	−0.841731	−	2.77482i
$796$		0			0
$797$	−2.20424	−	1.80897i	−0.0780782	−	0.0640771i	0.594545	−	0.804063i	$-0.297332\pi$
$797$	−2.20424	−	1.80897i	−0.0780782	−	0.0640771i	−0.672623	+	0.739985i	$0.734832\pi$
$798$		0			0
$799$	−18.4321	−	18.4321i	−0.652080	−	0.652080i
$800$		0			0
$801$	−23.6265	+	23.6265i	−0.834801	+	0.834801i
$802$		0			0
$803$	0.560210	−	0.682618i	0.0197694	−	0.0240891i
$804$		0			0
$805$	−32.4074	+	9.83069i	−1.14221	+	0.346486i
$806$		0			0
$807$	−8.35679	+	5.58383i	−0.294173	+	0.196560i
$808$		0			0
$809$	22.2569	−	33.3099i	0.782513	−	1.17111i	−0.199053	−	0.979989i	$-0.563787\pi$
$809$	22.2569	−	33.3099i	0.782513	−	1.17111i	0.981566	−	0.191124i	$-0.0612133\pi$
$810$		0			0
$811$	−2.20806	+	22.4188i	−0.0775355	+	0.787231i	0.875267	+	0.483640i	$0.160686\pi$
$811$	−2.20806	+	22.4188i	−0.0775355	+	0.787231i	−0.952802	+	0.303591i	$0.901814\pi$
$812$		0			0
$813$	11.4315	+	3.46770i	0.400919	+	0.121618i
$814$		0			0
$815$	9.58253	−	3.96921i	0.335661	−	0.139036i
$816$		0			0
$817$	−0.504582	−	0.209005i	−0.0176531	−	0.00731215i
$818$		0			0
$819$	−11.8223	+	6.31916i	−0.413105	+	0.220809i
$820$		0			0
$821$	39.8222	−	32.6812i	1.38980	−	1.14058i	0.417014	−	0.908900i	$-0.363077\pi$
$821$	39.8222	−	32.6812i	1.38980	−	1.14058i	0.972791	−	0.231683i	$-0.0744232\pi$
$822$		0			0
$823$	−1.66310	−	8.36096i	−0.0579720	−	0.291445i	0.940913	−	0.338647i	$-0.109969\pi$
$823$	−1.66310	−	8.36096i	−0.0579720	−	0.291445i	−0.998885	+	0.0472026i	$0.984969\pi$
$824$		0			0
$825$	1.53957	+	0.306240i	0.0536010	+	0.0106619i
$826$		0			0
$827$	15.8193	−	29.5958i	0.550091	−	1.02915i	−0.441194	−	0.897412i	$-0.645445\pi$
$827$	15.8193	−	29.5958i	0.550091	−	1.02915i	0.991285	−	0.131736i	$-0.0420550\pi$
$828$		0			0
$829$	50.6839	−	4.99193i	1.76032	−	0.173377i	0.834418	−	0.551132i	$-0.185804\pi$
$829$	50.6839	−	4.99193i	1.76032	−	0.173377i	0.925906	+	0.377755i	$0.123304\pi$
$830$		0			0
$831$			6.71212i			0.232841i
$832$		0			0
$833$		−	31.8057i		−	1.10200i
$834$		0			0
$835$	−64.3221	+	6.33517i	−2.22596	+	0.219238i
$836$		0			0
$837$	3.68012	−	6.88501i	0.127203	−	0.237981i
$838$		0			0
$839$	−56.6852	−	11.2754i	−1.95699	−	0.389270i	−0.991818	−	0.127658i	$-0.959254\pi$
$839$	−56.6852	−	11.2754i	−1.95699	−	0.389270i	−0.965173	−	0.261612i	$-0.915746\pi$
$840$		0			0
$841$	2.74798	+	13.8150i	0.0947580	+	0.476381i
$842$		0			0
$843$	−33.9029	+	27.8234i	−1.16768	+	0.958287i
$844$		0			0
$845$	−40.6175	+	21.7105i	−1.39729	+	0.746865i
$846$		0			0
$847$	−36.6003	−	15.1603i	−1.25760	−	0.520915i
$848$		0			0
$849$	−38.5687	+	15.9757i	−1.32368	+	0.548284i
$850$		0			0
$851$	13.7739	+	4.17828i	0.472165	+	0.143230i
$852$		0			0
$853$	−1.37092	+	13.9192i	−0.0469395	+	0.476585i	0.942765	+	0.333458i	$0.108216\pi$
$853$	−1.37092	+	13.9192i	−0.0469395	+	0.476585i	−0.989704	+	0.143127i	$0.954284\pi$
$854$		0			0
$855$	3.14804	−	4.71138i	0.107661	−	0.161126i
$856$		0			0
$857$	−26.6402	+	17.8004i	−0.910013	+	0.608051i	−0.920008	−	0.391899i	$-0.871818\pi$
$857$	−26.6402	+	17.8004i	−0.910013	+	0.608051i	0.00999513	+	0.999950i	$0.496818\pi$
$858$		0			0
$859$	−7.72275	+	2.34267i	−0.263497	+	0.0799309i	−0.419269	−	0.907862i	$-0.637714\pi$
$859$	−7.72275	+	2.34267i	−0.263497	+	0.0799309i	0.155772	+	0.987793i	$0.450214\pi$
$860$		0			0
$861$	−17.9084	+	21.8215i	−0.610318	+	0.743674i
$862$		0			0
$863$	13.4156	−	13.4156i	0.456671	−	0.456671i	−0.440890	−	0.897561i	$-0.645337\pi$
$863$	13.4156	−	13.4156i	0.456671	−	0.456671i	0.897561	+	0.440890i	$0.145337\pi$
$864$		0			0
$865$	−12.2815	−	12.2815i	−0.417583	−	0.417583i
$866$		0			0
$867$	22.0397	+	18.0875i	0.748507	+	0.614283i
$868$		0			0
$869$	0.243082	+	0.801333i	0.00824598	+	0.0271834i
$870$		0			0
$871$	−0.184574	−	0.276234i	−0.00625404	−	0.00935983i
$872$		0			0
$873$	13.8980	+	9.28634i	0.470376	+	0.314295i
$874$		0			0
$875$	−74.0846	−	7.29670i	−2.50452	−	0.246674i
$876$		0			0
$877$	−4.31540	+	14.2260i	−0.145721	+	0.480377i	−0.999167	−	0.0408035i	$-0.987008\pi$
$877$	−4.31540	+	14.2260i	−0.145721	+	0.480377i	0.853446	+	0.521181i	$0.174508\pi$
$878$		0			0
$879$	3.10848	+	7.50453i	0.104846	+	0.253121i
$880$		0			0
$881$	3.66699	−	8.85290i	0.123544	−	0.298262i	−0.849992	−	0.526796i	$-0.823393\pi$
$881$	3.66699	−	8.85290i	0.123544	−	0.298262i	0.973536	+	0.228534i	$0.0733932\pi$
$882$		0			0
$883$	3.34251	+	6.25339i	0.112484	+	0.210443i	0.931864	−	0.362808i	$-0.118182\pi$
$883$	3.34251	+	6.25339i	0.112484	+	0.210443i	−0.819380	+	0.573251i	$0.805682\pi$
$884$		0			0
$885$	−2.45805	−	2.99515i	−0.0826265	−	0.100681i
$886$		0			0
$887$	38.7623	−	7.71030i	1.30151	−	0.258886i	0.504794	−	0.863240i	$-0.331569\pi$
$887$	38.7623	−	7.71030i	1.30151	−	0.258886i	0.796716	+	0.604354i	$0.206569\pi$
$888$		0			0
$889$	3.05055	−	15.3362i	0.102312	−	0.514358i
$890$		0			0
$891$	−0.413739	−	0.221148i	−0.0138608	−	0.00740875i
$892$		0			0
$893$	0.206633	+	2.09798i	0.00691471	+	0.0702063i
$894$		0			0
$895$	43.6939			1.46053
$896$		0			0
$897$	6.70199			0.223773
$898$		0			0
$899$	5.39599	+	54.7864i	0.179966	+	1.82723i
$900$		0			0
$901$	−38.8751	−	20.7792i	−1.29512	−	0.692254i
$902$		0			0
$903$	−2.25174	+	11.3203i	−0.0749334	+	0.376716i
$904$		0			0
$905$	44.4596	−	8.84357i	1.47789	−	0.293970i
$906$		0			0
$907$	24.5989	+	29.9738i	0.816792	+	0.995264i	0.999926	+	0.0121762i	$0.00387591\pi$
$907$	24.5989	+	29.9738i	0.816792	+	0.995264i	−0.183134	+	0.983088i	$0.558624\pi$
$908$		0			0
$909$	−9.03112	−	16.8960i	−0.299543	−	0.560406i
$910$		0			0
$911$	6.07312	−	14.6618i	0.201211	−	0.485767i	−0.790776	−	0.612106i	$-0.790323\pi$
$911$	6.07312	−	14.6618i	0.201211	−	0.485767i	0.991987	+	0.126339i	$0.0403226\pi$
$912$		0			0
$913$	−0.0992712	−	0.239662i	−0.00328540	−	0.00793165i
$914$		0			0
$915$	−13.9736	+	46.0646i	−0.461951	+	1.52285i
$916$		0			0
$917$	−70.9974	−	6.99264i	−2.34454	−	0.230917i
$918$		0			0
$919$	−29.6842	−	19.8343i	−0.979190	−	0.654274i	−0.0405521	−	0.999177i	$-0.512912\pi$
$919$	−29.6842	−	19.8343i	−0.979190	−	0.654274i	−0.938638	+	0.344903i	$0.887912\pi$
$920$		0			0
$921$	21.0172	+	31.4545i	0.692541	+	1.03646i
$922$		0			0
$923$	−2.81763	−	9.28849i	−0.0927435	−	0.305734i
$924$		0			0
$925$	47.5962	+	39.0612i	1.56495	+	1.28432i
$926$		0			0
$927$	39.7418	+	39.7418i	1.30529	+	1.30529i
$928$		0			0
$929$	34.6841	−	34.6841i	1.13795	−	1.13795i	0.149132	−	0.988817i	$-0.452352\pi$
$929$	34.6841	−	34.6841i	1.13795	−	1.13795i	0.988817	−	0.149132i	$-0.0476480\pi$
$930$		0			0
$931$	−1.63182	+	1.98838i	−0.0534807	+	0.0651664i
$932$		0			0
$933$	−32.0726	+	9.72911i	−1.05001	+	0.318517i
$934$		0			0
$935$	1.04577	−	0.698764i	0.0342005	−	0.0228520i
$936$		0			0
$937$	−29.2164	+	43.7255i	−0.954459	+	1.42845i	−0.0515241	+	0.998672i	$0.516408\pi$
$937$	−29.2164	+	43.7255i	−0.954459	+	1.42845i	−0.902935	+	0.429777i	$0.858592\pi$
$938$		0			0
$939$	5.29495	−	53.7606i	0.172794	−	1.75441i
$940$		0			0
$941$	4.13746	+	1.25509i	0.134877	+	0.0409146i	0.357002	−	0.934104i	$-0.383799\pi$
$941$	4.13746	+	1.25509i	0.134877	+	0.0409146i	−0.222124	+	0.975018i	$0.571299\pi$
$942$		0			0
$943$	6.89709	−	2.85687i	0.224600	−	0.0930324i
$944$		0			0
$945$	−12.1128	−	5.01730i	−0.394030	−	0.163213i
$946$		0			0
$947$	−21.6468	+	11.5705i	−0.703427	+	0.375990i	−0.784001	−	0.620759i	$-0.786825\pi$
$947$	−21.6468	+	11.5705i	−0.703427	+	0.375990i	0.0805743	+	0.996749i	$0.474325\pi$
$948$		0			0
$949$	12.4672	−	10.2316i	0.404703	−	0.332131i
$950$		0			0
$951$	−7.91150	−	39.7738i	−0.256548	−	1.28975i
$952$		0			0
$953$	50.8198	+	10.1087i	1.64622	+	0.327453i	0.929192	−	0.369597i	$-0.120504\pi$
$953$	50.8198	+	10.1087i	1.64622	+	0.327453i	0.717023	+	0.697049i	$0.245504\pi$
$954$		0			0
$955$	−20.7668	+	38.8520i	−0.671998	+	1.25722i
$956$		0			0
$957$	−0.996966	+	0.0981926i	−0.0322273	+	0.00317411i
$958$		0			0
$959$			17.8610i			0.576762i
$960$		0			0
$961$			39.3403i			1.26904i
$962$		0			0
$963$	−3.23130	+	0.318256i	−0.104127	+	0.0102556i
$964$		0			0
$965$	19.7924	−	37.0290i	0.637140	−	1.19201i
$966$		0			0
$967$	7.76870	+	1.54529i	0.249824	+	0.0496932i	0.318414	−	0.947952i	$-0.396850\pi$
$967$	7.76870	+	1.54529i	0.249824	+	0.0496932i	−0.0685894	+	0.997645i	$0.521850\pi$
$968$		0			0
$969$	−1.12674	−	5.66453i	−0.0361963	−	0.181971i
$970$		0			0
$971$	−20.0170	+	16.4275i	−0.642376	+	0.527184i	−0.898227	−	0.439532i	$-0.855144\pi$
$971$	−20.0170	+	16.4275i	−0.642376	+	0.527184i	0.255851	+	0.966716i	$0.417644\pi$
$972$		0			0
$973$	33.0928	−	17.6885i	1.06091	−	0.567066i
$974$		0			0
$975$	26.4870	+	10.9713i	0.848262	+	0.351362i
$976$		0			0
$977$	−10.4731	+	4.33809i	−0.335063	+	0.138788i	−0.543871	−	0.839169i	$-0.683042\pi$
$977$	−10.4731	+	4.33809i	−0.335063	+	0.138788i	0.208808	+	0.977957i	$0.433042\pi$
$978$		0			0
$979$	0.573981	+	0.174115i	0.0183445	+	0.00556475i
$980$		0			0
$981$	2.02824	−	20.5931i	0.0647568	−	0.657487i
$982$		0			0
$983$	16.8840	−	25.2686i	0.538515	−	0.805945i	−0.458035	−	0.888934i	$-0.651447\pi$
$983$	16.8840	−	25.2686i	0.538515	−	0.805945i	0.996550	+	0.0829892i	$0.0264467\pi$
$984$		0			0
$985$	−6.02009	+	4.02250i	−0.191816	+	0.128167i
$986$		0			0
$987$	42.6334	−	12.9327i	1.35703	−	0.411652i
$988$		0			0
$989$	1.93639	−	2.35950i	0.0615737	−	0.0750278i
$990$		0			0
$991$	−11.0994	+	11.0994i	−0.352584	+	0.352584i	−0.861070	−	0.508486i	$-0.830205\pi$
$991$	−11.0994	+	11.0994i	−0.352584	+	0.352584i	0.508486	+	0.861070i	$0.330205\pi$
$992$		0			0
$993$	12.7390	+	12.7390i	0.404261	+	0.404261i
$994$		0			0
$995$	19.0617	+	15.6435i	0.604296	+	0.495933i
$996$		0			0
$997$	−10.0664	−	33.1843i	−0.318805	−	1.05096i	−0.959156	−	0.282876i	$-0.908711\pi$
$997$	−10.0664	−	33.1843i	−0.318805	−	1.05096i	0.640352	−	0.768082i	$-0.278789\pi$
$998$		0			0
$999$	3.09587	+	4.63330i	0.0979490	+	0.146591i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.k.a.49.2		240
4.3	odd	2		128.2.k.a.53.6	yes	240
128.29	even	32	inner	512.2.k.a.209.2		240
128.99	odd	32		128.2.k.a.29.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.2.k.a.29.6	✓	240	128.99	odd	32
128.2.k.a.53.6	yes	240	4.3	odd	2
512.2.k.a.49.2		240	1.1	even	1	trivial
512.2.k.a.209.2		240	128.29	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)

\(f(q)\)	\(=\)	\(q+(-0.247362 - 2.51150i) q^{3} +(-3.44799 - 1.84299i) q^{5} +(0.702840 - 3.53342i) q^{7} +(-3.30411 + 0.657229i) q^{9} +O(q^{10})\)	\(q+(-0.247362 - 2.51150i) q^{3} +(-3.44799 - 1.84299i) q^{5} +(0.702840 - 3.53342i) q^{7} +(-3.30411 + 0.657229i) q^{9} +(0.0383653 + 0.0467482i) q^{11} +(0.520664 + 0.974094i) q^{13} +(-3.77578 + 9.11554i) q^{15} +(2.03571 + 4.91463i) q^{17} +(0.124884 - 0.411689i) q^{19} +(-9.04804 - 0.891155i) q^{21} +(1.99917 + 1.33580i) q^{23} +(5.71419 + 8.55189i) q^{25} +(0.270207 + 0.890754i) q^{27} +(-5.07402 - 4.16414i) q^{29} +(-5.93044 - 5.93044i) q^{31} +(0.107918 - 0.107918i) q^{33} +(-8.93544 + 10.8879i) q^{35} +(5.72870 - 1.73778i) q^{37} +(2.31765 - 1.54860i) q^{39} +(1.72499 - 2.58163i) q^{41} +(0.124433 - 1.26339i) q^{43} +(12.6038 + 3.82333i) q^{45} +(-4.52719 + 1.87522i) q^{47} +(-5.52388 - 2.28807i) q^{49} +(11.8396 - 6.32838i) q^{51} +(-6.40548 + 5.25684i) q^{53} +(-0.0461267 - 0.231894i) q^{55} +(-1.06485 - 0.211812i) q^{57} +(-0.185120 + 0.346334i) q^{59} +(4.85534 - 0.478209i) q^{61} +12.1367i q^{63} -4.31825i q^{65} +(-0.299339 + 0.0294823i) q^{67} +(2.86035 - 5.35134i) q^{69} +(-8.61912 - 1.71445i) q^{71} +(-2.84871 - 14.3214i) q^{73} +(20.0646 - 16.4666i) q^{75} +(0.192146 - 0.102704i) q^{77} +(12.7928 + 5.29893i) q^{79} +(-7.16692 + 2.96864i) q^{81} +(-4.10477 - 1.24517i) q^{83} +(2.03852 - 20.6974i) q^{85} +(-9.20314 + 13.7735i) q^{87} +(8.24669 - 5.51026i) q^{89} +(3.80782 - 1.15509i) q^{91} +(-13.4274 + 16.3613i) q^{93} +(-1.18934 + 1.18934i) q^{95} +(-3.50840 - 3.50840i) q^{97} +(-0.157487 - 0.129247i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 16 q^{3} - 16 q^{5} + 16 q^{7} - 16 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more