LMFDB - Embedded newform 512.2.i.b.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(33,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15]))

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

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

chi := DirichletCharacter("512.33");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.i (of order $16$, degree $8$, 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:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 64)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	512.161
Dual form			512.2.i.b.353.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23702 + 0.444970i) q^{3} +(2.33237 - 3.49064i) q^{5} +(-1.63661 + 0.677907i) q^{7} +(2.03460 + 0.842759i) q^{9} +O(q^{10})$	\(q+(2.23702 + 0.444970i) q^{3} +(2.33237 - 3.49064i) q^{5} +(-1.63661 + 0.677907i) q^{7} +(2.03460 + 0.842759i) q^{9} +(0.234463 + 1.17872i) q^{11} +(0.154344 + 0.230992i) q^{13} +(6.77078 - 6.77078i) q^{15} +(1.16542 + 1.16542i) q^{17} +(2.64509 - 1.76739i) q^{19} +(-3.96278 + 0.788246i) q^{21} +(-1.18934 + 2.87131i) q^{23} +(-4.83120 - 11.6635i) q^{25} +(-1.51292 - 1.01090i) q^{27} +(0.141213 - 0.709928i) q^{29} +7.01473i q^{31} +2.74115i q^{33} +(-1.45086 + 7.29396i) q^{35} +(-7.22008 - 4.82430i) q^{37} +(0.242485 + 0.585411i) q^{39} +(-0.152591 + 0.368387i) q^{41} +(4.98611 - 0.991798i) q^{43} +(7.68722 - 5.13643i) q^{45} +(2.16092 + 2.16092i) q^{47} +(-2.73080 + 2.73080i) q^{49} +(2.08849 + 3.12564i) q^{51} +(1.84431 + 9.27195i) q^{53} +(4.66135 + 1.93079i) q^{55} +(6.70353 - 2.77669i) q^{57} +(-3.85360 + 5.76732i) q^{59} +(9.69397 + 1.92825i) q^{61} -3.90117 q^{63} +1.16630 q^{65} +(-7.14707 - 1.42164i) q^{67} +(-3.93821 + 5.89395i) q^{69} +(-4.28878 + 1.77647i) q^{71} +(-3.39319 - 1.40550i) q^{73} +(-5.61753 - 28.2413i) q^{75} +(-1.18279 - 1.77017i) q^{77} +(-1.54634 + 1.54634i) q^{79} +(-7.60625 - 7.60625i) q^{81} +(9.93110 - 6.63575i) q^{83} +(6.78626 - 1.34987i) q^{85} +(0.631793 - 1.52528i) q^{87} +(3.81437 + 9.20870i) q^{89} +(-0.409193 - 0.273414i) q^{91} +(-3.12134 + 15.6921i) q^{93} -13.3552i q^{95} +9.29602i q^{97} +(-0.516342 + 2.59583i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	$ 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) $ 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{11}{16}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.23702	+	0.444970i	1.29154	+	0.256904i	0.792605	−	0.609735i	$-0.208724\pi$
$3$	2.23702	+	0.444970i	1.29154	+	0.256904i	0.498936	+	0.866639i	$0.333724\pi$
$4$		0			0
$5$	2.33237	−	3.49064i	1.04307	−	1.56106i	0.234980	−	0.972000i	$-0.424498\pi$
$5$	2.33237	−	3.49064i	1.04307	−	1.56106i	0.808088	−	0.589061i	$-0.200502\pi$
$6$		0			0
$7$	−1.63661	+	0.677907i	−0.618582	+	0.256225i	−0.669893	−	0.742458i	$-0.733660\pi$
$7$	−1.63661	+	0.677907i	−0.618582	+	0.256225i	0.0513111	+	0.998683i	$0.483660\pi$
$8$		0			0
$9$	2.03460	+	0.842759i	0.678200	+	0.280920i
$10$		0			0
$11$	0.234463	+	1.17872i	0.0706931	+	0.355398i	0.999900	−	0.0141624i	$-0.00450818\pi$
$11$	0.234463	+	1.17872i	0.0706931	+	0.355398i	−0.929207	+	0.369561i	$0.879508\pi$
$12$		0			0
$13$	0.154344	+	0.230992i	0.0428073	+	0.0640657i	0.852256	−	0.523125i	$-0.175234\pi$
$13$	0.154344	+	0.230992i	0.0428073	+	0.0640657i	−0.809449	+	0.587191i	$0.800234\pi$
$14$		0			0
$15$	6.77078	−	6.77078i	1.74821	−	1.74821i
$16$		0			0
$17$	1.16542	+	1.16542i	0.282656	+	0.282656i	0.834167	−	0.551511i	$-0.185949\pi$
$17$	1.16542	+	1.16542i	0.282656	+	0.282656i	−0.551511	+	0.834167i	$0.685949\pi$
$18$		0			0
$19$	2.64509	−	1.76739i	0.606824	−	0.405467i	−0.213847	−	0.976867i	$-0.568600\pi$
$19$	2.64509	−	1.76739i	0.606824	−	0.405467i	0.820672	+	0.571400i	$0.193600\pi$
$20$		0			0
$21$	−3.96278	+	0.788246i	−0.864749	+	0.172009i
$22$		0			0
$23$	−1.18934	+	2.87131i	−0.247994	+	0.598710i	−0.998033	−	0.0626831i	$-0.980034\pi$
$23$	−1.18934	+	2.87131i	−0.247994	+	0.598710i	0.750040	+	0.661393i	$0.230034\pi$
$24$		0			0
$25$	−4.83120	−	11.6635i	−0.966239	−	2.33271i
$26$		0			0
$27$	−1.51292	−	1.01090i	−0.291161	−	0.194548i
$28$		0			0
$29$	0.141213	−	0.709928i	0.0262227	−	0.131830i	−0.965456	−	0.260564i	$-0.916091\pi$
$29$	0.141213	−	0.709928i	0.0262227	−	0.131830i	0.991679	+	0.128734i	$0.0410914\pi$
$30$		0			0
$31$			7.01473i			1.25988i	0.776643	+	0.629941i	$0.216921\pi$
$31$			7.01473i			1.25988i	−0.776643	+	0.629941i	$0.783079\pi$
$32$		0			0
$33$			2.74115i			0.477173i
$34$		0			0
$35$	−1.45086	+	7.29396i	−0.245240	+	1.23290i
$36$		0			0
$37$	−7.22008	−	4.82430i	−1.18697	−	0.793111i	−0.204383	−	0.978891i	$-0.565519\pi$
$37$	−7.22008	−	4.82430i	−1.18697	−	0.793111i	−0.982591	+	0.185780i	$0.940519\pi$
$38$		0			0
$39$	0.242485	+	0.585411i	0.0388287	+	0.0937408i
$40$		0			0
$41$	−0.152591	+	0.368387i	−0.0238307	+	0.0575323i	−0.935347	−	0.353732i	$-0.884913\pi$
$41$	−0.152591	+	0.368387i	−0.0238307	+	0.0575323i	0.911516	+	0.411264i	$0.134913\pi$
$42$		0			0
$43$	4.98611	−	0.991798i	0.760374	−	0.151248i	0.200350	−	0.979724i	$-0.435792\pi$
$43$	4.98611	−	0.991798i	0.760374	−	0.151248i	0.560024	+	0.828477i	$0.310792\pi$
$44$		0			0
$45$	7.68722	−	5.13643i	1.14594	−	0.765694i
$46$		0			0
$47$	2.16092	+	2.16092i	0.315203	+	0.315203i	0.846921	−	0.531719i	$-0.178454\pi$
$47$	2.16092	+	2.16092i	0.315203	+	0.315203i	−0.531719	+	0.846921i	$0.678454\pi$
$48$		0			0
$49$	−2.73080	+	2.73080i	−0.390115	+	0.390115i
$50$		0			0
$51$	2.08849	+	3.12564i	0.292447	+	0.437677i
$52$		0			0
$53$	1.84431	+	9.27195i	0.253335	+	1.27360i	0.872607	+	0.488423i	$0.162428\pi$
$53$	1.84431	+	9.27195i	0.253335	+	1.27360i	−0.619272	+	0.785177i	$0.712572\pi$
$54$		0			0
$55$	4.66135	+	1.93079i	0.628536	+	0.260348i
$56$		0			0
$57$	6.70353	−	2.77669i	0.887905	−	0.367782i
$58$		0			0
$59$	−3.85360	+	5.76732i	−0.501696	+	0.750840i	−0.992738	−	0.120295i	$-0.961616\pi$
$59$	−3.85360	+	5.76732i	−0.501696	+	0.750840i	0.491043	+	0.871136i	$0.336616\pi$
$60$		0			0
$61$	9.69397	+	1.92825i	1.24119	+	0.246887i	0.771662	−	0.636033i	$-0.219426\pi$
$61$	9.69397	+	1.92825i	1.24119	+	0.246887i	0.469524	+	0.882920i	$0.344426\pi$
$62$		0			0
$63$	−3.90117			−0.491501
$64$		0			0
$65$	1.16630			0.144661
$66$		0			0
$67$	−7.14707	−	1.42164i	−0.873153	−	0.173681i	−0.261880	−	0.965100i	$-0.584342\pi$
$67$	−7.14707	−	1.42164i	−0.873153	−	0.173681i	−0.611273	+	0.791420i	$0.709342\pi$
$68$		0			0
$69$	−3.93821	+	5.89395i	−0.474105	+	0.709548i
$70$		0			0
$71$	−4.28878	+	1.77647i	−0.508984	+	0.210828i	−0.622370	−	0.782723i	$-0.713830\pi$
$71$	−4.28878	+	1.77647i	−0.508984	+	0.210828i	0.113386	+	0.993551i	$0.463830\pi$
$72$		0			0
$73$	−3.39319	−	1.40550i	−0.397142	−	0.164502i	0.175169	−	0.984538i	$-0.443953\pi$
$73$	−3.39319	−	1.40550i	−0.397142	−	0.164502i	−0.572311	+	0.820037i	$0.693953\pi$
$74$		0			0
$75$	−5.61753	−	28.2413i	−0.648657	−	3.26102i
$76$		0			0
$77$	−1.18279	−	1.77017i	−0.134791	−	0.201730i
$78$		0			0
$79$	−1.54634	+	1.54634i	−0.173977	+	0.173977i	−0.788724	−	0.614747i	$-0.789258\pi$
$79$	−1.54634	+	1.54634i	−0.173977	+	0.173977i	0.614747	+	0.788724i	$0.289258\pi$
$80$		0			0
$81$	−7.60625	−	7.60625i	−0.845139	−	0.845139i
$82$		0			0
$83$	9.93110	−	6.63575i	1.09008	−	0.728368i	0.125483	−	0.992096i	$-0.459952\pi$
$83$	9.93110	−	6.63575i	1.09008	−	0.728368i	0.964597	+	0.263728i	$0.0849520\pi$
$84$		0			0
$85$	6.78626	−	1.34987i	0.736073	−	0.146414i
$86$		0			0
$87$	0.631793	−	1.52528i	0.0677353	−	0.163528i
$88$		0			0
$89$	3.81437	+	9.20870i	0.404322	+	0.976120i	0.986604	+	0.163133i	$0.0521600\pi$
$89$	3.81437	+	9.20870i	0.404322	+	0.976120i	−0.582282	+	0.812987i	$0.697840\pi$
$90$		0			0
$91$	−0.409193	−	0.273414i	−0.0428950	−	0.0286616i
$92$		0			0
$93$	−3.12134	+	15.6921i	−0.323668	+	1.62719i
$94$		0			0
$95$		−	13.3552i		−	1.37022i
$96$		0			0
$97$			9.29602i			0.943868i	0.881634	+	0.471934i	$0.156444\pi$
$97$			9.29602i			0.943868i	−0.881634	+	0.471934i	$0.843556\pi$
$98$		0			0
$99$	−0.516342	+	2.59583i	−0.0518943	+	0.260890i
$100$		0			0
$101$	−6.78178	−	4.53144i	−0.674813	−	0.450895i	0.170365	−	0.985381i	$-0.445505\pi$
$101$	−6.78178	−	4.53144i	−0.674813	−	0.450895i	−0.845177	+	0.534486i	$0.820505\pi$
$102$		0			0
$103$	−2.37519	−	5.73422i	−0.234035	−	0.565009i	0.762610	−	0.646858i	$-0.223917\pi$
$103$	−2.37519	−	5.73422i	−0.234035	−	0.565009i	−0.996645	+	0.0818489i	$0.973917\pi$
$104$		0			0
$105$	−6.49119	+	15.6711i	−0.633475	+	1.52934i
$106$		0			0
$107$	−18.1355	+	3.60738i	−1.75323	+	0.348738i	−0.964110	−	0.265504i	$-0.914461\pi$
$107$	−18.1355	+	3.60738i	−1.75323	+	0.348738i	−0.789117	+	0.614243i	$0.789461\pi$
$108$		0			0
$109$	4.97622	−	3.32500i	0.476636	−	0.318478i	−0.293943	−	0.955823i	$-0.594968\pi$
$109$	4.97622	−	3.32500i	0.476636	−	0.318478i	0.770578	+	0.637345i	$0.219968\pi$
$110$		0			0
$111$	−14.0048	−	14.0048i	−1.32927	−	1.32927i
$112$		0			0
$113$	−2.54136	+	2.54136i	−0.239071	+	0.239071i	−0.816465	−	0.577394i	$-0.804070\pi$
$113$	−2.54136	+	2.54136i	−0.239071	+	0.239071i	0.577394	+	0.816465i	$0.304070\pi$
$114$		0			0
$115$	7.24874	+	10.8485i	0.675948	+	1.01163i
$116$		0			0
$117$	0.119358	+	0.600052i	0.0110346	+	0.0554748i
$118$		0			0
$119$	−2.69739	−	1.11730i	−0.247269	−	0.102422i
$120$		0			0
$121$	8.82826	−	3.65679i	0.802569	−	0.332435i
$122$		0			0
$123$	−0.505269	+	0.756189i	−0.0455586	+	0.0681832i
$124$		0			0
$125$	−31.3939	−	6.24464i	−2.80796	−	0.558537i
$126$		0			0
$127$	6.27367			0.556698			0.278349	−	0.960480i	$-0.410213\pi$
$127$	6.27367			0.556698			0.278349	+	0.960480i	$0.410213\pi$
$128$		0			0
$129$	11.5953			1.02091
$130$		0			0
$131$	−14.9538	−	2.97450i	−1.30652	−	0.259883i	−0.507743	−	0.861509i	$-0.669520\pi$
$131$	−14.9538	−	2.97450i	−1.30652	−	0.259883i	−0.798778	+	0.601625i	$0.794520\pi$
$132$		0			0
$133$	−3.13086	+	4.68566i	−0.271480	+	0.406298i
$134$		0			0
$135$	−7.05737	+	2.92326i	−0.607402	+	0.251594i
$136$		0			0
$137$	3.38200	+	1.40087i	0.288944	+	0.119685i	0.522448	−	0.852671i	$-0.325019\pi$
$137$	3.38200	+	1.40087i	0.288944	+	0.119685i	−0.233504	+	0.972356i	$0.575019\pi$
$138$		0			0
$139$	4.19783	+	21.1039i	0.356055	+	1.79001i	0.579158	+	0.815216i	$0.303382\pi$
$139$	4.19783	+	21.1039i	0.356055	+	1.79001i	−0.223102	+	0.974795i	$0.571618\pi$
$140$		0			0
$141$	3.87247	+	5.79555i	0.326120	+	0.488074i
$142$		0			0
$143$	−0.236088	+	0.236088i	−0.0197426	+	0.0197426i
$144$		0			0
$145$	−2.14874	−	2.14874i	−0.178443	−	0.178443i
$146$		0			0
$147$	−7.32397	+	4.89372i	−0.604071	+	0.403627i
$148$		0			0
$149$	8.61517	−	1.71366i	0.705782	−	0.140389i	0.170867	−	0.985294i	$-0.445343\pi$
$149$	8.61517	−	1.71366i	0.705782	−	0.140389i	0.534916	+	0.844905i	$0.320343\pi$
$150$		0			0
$151$	−3.51806	+	8.49334i	−0.286295	+	0.691178i	−0.999957	−	0.00931286i	$-0.997036\pi$
$151$	−3.51806	+	8.49334i	−0.286295	+	0.691178i	0.713661	+	0.700491i	$0.247036\pi$
$152$		0			0
$153$	1.38900	+	3.35334i	0.112294	+	0.271101i
$154$		0			0
$155$	24.4859	+	16.3610i	1.96675	+	1.31414i
$156$		0			0
$157$	1.02494	−	5.15272i	0.0817990	−	0.411232i	−0.918091	−	0.396371i	$-0.870269\pi$
$157$	1.02494	−	5.15272i	0.0817990	−	0.411232i	0.999890	−	0.0148608i	$-0.00473051\pi$
$158$		0			0
$159$			21.5622i			1.70999i
$160$		0			0
$161$		−	5.50548i		−	0.433893i
$162$		0			0
$163$	3.54698	−	17.8319i	0.277821	−	1.39670i	−0.549745	−	0.835333i	$-0.685275\pi$
$163$	3.54698	−	17.8319i	0.277821	−	1.39670i	0.827566	−	0.561368i	$-0.189725\pi$
$164$		0			0
$165$	9.56837	+	6.39338i	0.744896	+	0.497724i
$166$		0			0
$167$	−7.42288	−	17.9204i	−0.574400	−	1.38672i	−0.897776	−	0.440453i	$-0.854818\pi$
$167$	−7.42288	−	17.9204i	−0.574400	−	1.38672i	0.323376	−	0.946270i	$-0.395182\pi$
$168$		0			0
$169$	4.94535	−	11.9391i	0.380411	−	0.918395i
$170$		0			0
$171$	6.87118	−	1.36676i	0.525452	−	0.104519i
$172$		0			0
$173$	−4.21489	+	2.81630i	−0.320452	+	0.214119i	−0.705383	−	0.708826i	$-0.749225\pi$
$173$	−4.21489	+	2.81630i	−0.320452	+	0.214119i	0.384931	+	0.922945i	$0.374225\pi$
$174$		0			0
$175$	15.8136	+	15.8136i	1.19540	+	1.19540i
$176$		0			0
$177$	−11.1868	+	11.1868i	−0.840854	+	0.840854i
$178$		0			0
$179$	−9.57074	−	14.3236i	−0.715351	−	1.07060i	−0.993912	−	0.110180i	$-0.964857\pi$
$179$	−9.57074	−	14.3236i	−0.715351	−	1.07060i	0.278561	−	0.960419i	$-0.410143\pi$
$180$		0			0
$181$	−2.13516	−	10.7342i	−0.158705	−	0.797865i	−0.975340	−	0.220710i	$-0.929163\pi$
$181$	−2.13516	−	10.7342i	−0.158705	−	0.797865i	0.816634	−	0.577156i	$-0.195837\pi$
$182$		0			0
$183$	20.8276	+	8.62705i	1.53962	+	0.637730i
$184$		0			0
$185$	−33.6798	+	13.9506i	−2.47619	+	1.02567i
$186$		0			0
$187$	−1.10046	+	1.64696i	−0.0804736	+	0.120437i
$188$		0			0
$189$	3.16136	+	0.628833i	0.229955	+	0.0457409i
$190$		0			0
$191$	−20.6704			−1.49566			−0.747830	−	0.663890i	$-0.768904\pi$
$191$	−20.6704			−1.49566			−0.747830	+	0.663890i	$0.768904\pi$
$192$		0			0
$193$	19.6483			1.41432			0.707158	−	0.707056i	$-0.249977\pi$
$193$	19.6483			1.41432			0.707158	+	0.707056i	$0.249977\pi$
$194$		0			0
$195$	2.60903	+	0.518967i	0.186836	+	0.0371640i
$196$		0			0
$197$	11.3923	−	17.0498i	0.811669	−	1.21475i	−0.162001	−	0.986791i	$-0.551795\pi$
$197$	11.3923	−	17.0498i	0.811669	−	1.21475i	0.973671	−	0.227959i	$-0.0732051\pi$
$198$		0			0
$199$	1.25587	−	0.520198i	0.0890262	−	0.0368759i	−0.337726	−	0.941245i	$-0.609658\pi$
$199$	1.25587	−	0.520198i	0.0890262	−	0.0368759i	0.426752	+	0.904369i	$0.359658\pi$
$200$		0			0
$201$	−15.3555	−	6.36046i	−1.08309	−	0.448632i
$202$		0			0
$203$	0.250154	+	1.25761i	0.0175573	+	0.0882667i
$204$		0			0
$205$	0.930007	+	1.39185i	0.0649545	+	0.0972113i
$206$		0			0
$207$	−4.83965	+	4.83965i	−0.336379	+	0.336379i
$208$		0			0
$209$	2.70344	+	2.70344i	0.187001	+	0.187001i
$210$		0			0
$211$	−9.24556	+	6.17768i	−0.636490	+	0.425289i	−0.831510	−	0.555510i	$-0.812523\pi$
$211$	−9.24556	+	6.17768i	−0.636490	+	0.425289i	0.195019	+	0.980799i	$0.437523\pi$
$212$		0			0
$213$	−10.3845	+	2.06561i	−0.711537	+	0.141533i
$214$		0			0
$215$	8.16744	−	19.7179i	0.557015	−	1.34475i
$216$		0			0
$217$	−4.75534	−	11.4804i	−0.322813	−	0.779340i
$218$		0			0
$219$	−6.96520	−	4.65400i	−0.470665	−	0.314488i
$220$		0			0
$221$	−0.0893273	+	0.449078i	−0.00600880	+	0.0302083i
$222$		0			0
$223$			0.398929i			0.0267143i	0.999911	+	0.0133571i	$0.00425183\pi$
$223$			0.398929i			0.0267143i	−0.999911	+	0.0133571i	$0.995748\pi$
$224$		0			0
$225$		−	27.8022i		−	1.85348i
$226$		0			0
$227$	2.31877	−	11.6572i	0.153902	−	0.773718i	−0.824315	−	0.566132i	$-0.808439\pi$
$227$	2.31877	−	11.6572i	0.153902	−	0.773718i	0.978217	−	0.207586i	$-0.0665608\pi$
$228$		0			0
$229$	5.87305	+	3.92425i	0.388102	+	0.259322i	0.734279	−	0.678848i	$-0.237520\pi$
$229$	5.87305	+	3.92425i	0.388102	+	0.259322i	−0.346177	+	0.938169i	$0.612520\pi$
$230$		0			0
$231$	−1.85825	−	4.48620i	−0.122264	−	0.295170i
$232$		0			0
$233$	−2.63067	+	6.35099i	−0.172341	+	0.416067i	−0.986323	−	0.164822i	$-0.947295\pi$
$233$	−2.63067	+	6.35099i	−0.172341	+	0.416067i	0.813983	+	0.580889i	$0.197295\pi$
$234$		0			0
$235$	12.5831	−	2.50293i	0.820828	−	0.163273i
$236$		0			0
$237$	−4.14727	+	2.77111i	−0.269394	+	0.180003i
$238$		0			0
$239$	2.18529	+	2.18529i	0.141355	+	0.141355i	0.774243	−	0.632888i	$-0.218131\pi$
$239$	2.18529	+	2.18529i	0.141355	+	0.141355i	−0.632888	+	0.774243i	$0.718131\pi$
$240$		0			0
$241$	9.11533	−	9.11533i	0.587170	−	0.587170i	−0.349694	−	0.936864i	$-0.613714\pi$
$241$	9.11533	−	9.11533i	0.587170	−	0.587170i	0.936864	+	0.349694i	$0.113714\pi$
$242$		0			0
$243$	−10.5980	−	15.8611i	−0.679865	−	1.01749i
$244$		0			0
$245$	3.16300	+	15.9015i	0.202077	+	1.01591i
$246$		0			0
$247$	0.816506	+	0.338208i	0.0519530	+	0.0215196i
$248$		0			0
$249$	25.1687	−	10.4252i	1.59500	−	0.660672i
$250$		0			0
$251$	10.9216	−	16.3453i	0.689364	−	1.03171i	−0.307420	−	0.951574i	$-0.599466\pi$
$251$	10.9216	−	16.3453i	0.689364	−	1.03171i	0.996784	−	0.0801321i	$-0.0255342\pi$
$252$		0			0
$253$	−3.66333	−	0.728682i	−0.230312	−	0.0458119i
$254$		0			0
$255$	15.7816			0.988283
$256$		0			0
$257$	−16.2065			−1.01093			−0.505466	−	0.862846i	$-0.668680\pi$
$257$	−16.2065			−1.01093			−0.505466	+	0.862846i	$0.668680\pi$
$258$		0			0
$259$	15.0869	+	3.00097i	0.937455	+	0.186471i
$260$		0			0
$261$	0.885611	−	1.32541i	0.0548180	−	0.0820409i
$262$		0			0
$263$	22.6730	−	9.39145i	1.39808	−	0.579102i	0.448824	−	0.893620i	$-0.351843\pi$
$263$	22.6730	−	9.39145i	1.39808	−	0.579102i	0.949251	+	0.314518i	$0.101843\pi$
$264$		0			0
$265$	36.6666	+	15.1878i	2.25241	+	0.932980i
$266$		0			0
$267$	4.43521	+	22.2973i	0.271430	+	1.36457i
$268$		0			0
$269$	−0.381447	−	0.570875i	−0.0232572	−	0.0348069i	0.819659	−	0.572852i	$-0.194163\pi$
$269$	−0.381447	−	0.570875i	−0.0232572	−	0.0348069i	−0.842916	+	0.538045i	$0.819163\pi$
$270$		0			0
$271$	10.0189	−	10.0189i	0.608606	−	0.608606i	−0.333975	−	0.942582i	$-0.608390\pi$
$271$	10.0189	−	10.0189i	0.608606	−	0.608606i	0.942582	+	0.333975i	$0.108390\pi$
$272$		0			0
$273$	−0.793709	−	0.793709i	−0.0480375	−	0.0480375i
$274$		0			0
$275$	12.6153	−	8.42930i	0.760734	−	0.508306i
$276$		0			0
$277$	22.7599	−	4.52722i	1.36751	−	0.272014i	0.543889	−	0.839157i	$-0.316951\pi$
$277$	22.7599	−	4.52722i	1.36751	−	0.272014i	0.823619	+	0.567143i	$0.191951\pi$
$278$		0			0
$279$	−5.91173	+	14.2722i	−0.353926	+	0.854453i
$280$		0			0
$281$	1.29852	+	3.13490i	0.0774631	+	0.187012i	0.957867	−	0.287212i	$-0.0927285\pi$
$281$	1.29852	+	3.13490i	0.0774631	+	0.187012i	−0.880404	+	0.474225i	$0.842728\pi$
$282$		0			0
$283$	−10.2454	−	6.84576i	−0.609026	−	0.406938i	0.212458	−	0.977170i	$-0.431853\pi$
$283$	−10.2454	−	6.84576i	−0.609026	−	0.406938i	−0.821484	+	0.570232i	$0.806853\pi$
$284$		0			0
$285$	5.94269	−	29.8759i	0.352014	−	1.76970i
$286$		0			0
$287$		−	0.706349i		−	0.0416945i
$288$		0			0
$289$		−	14.2836i		−	0.840211i
$290$		0			0
$291$	−4.13645	+	20.7953i	−0.242483	+	1.21904i
$292$		0			0
$293$	11.3488	+	7.58301i	0.663003	+	0.443004i	0.841006	−	0.541026i	$-0.181964\pi$
$293$	11.3488	+	7.58301i	0.663003	+	0.443004i	−0.178004	+	0.984030i	$0.556964\pi$
$294$		0			0
$295$	11.1436	+	26.9030i	0.648806	+	1.56636i
$296$		0			0
$297$	0.836848	−	2.02033i	0.0485588	−	0.117231i
$298$		0			0
$299$	−0.846817	+	0.168442i	−0.0489727	+	0.00974127i
$300$		0			0
$301$	−7.48798	+	5.00331i	−0.431600	+	0.288386i
$302$		0			0
$303$	−13.1546	−	13.1546i	−0.755712	−	0.755712i
$304$		0			0
$305$	29.3408	−	29.3408i	1.68005	−	1.68005i
$306$		0			0
$307$	14.2506	+	21.3276i	0.813326	+	1.21723i	0.973170	+	0.230086i	$0.0739009\pi$
$307$	14.2506	+	21.3276i	0.813326	+	1.21723i	−0.159844	+	0.987142i	$0.551099\pi$
$308$		0			0
$309$	−2.76178	−	13.8844i	−0.157112	−	0.789857i
$310$		0			0
$311$	8.17983	+	3.38820i	0.463835	+	0.192127i	0.602348	−	0.798234i	$-0.294232\pi$
$311$	8.17983	+	3.38820i	0.463835	+	0.192127i	−0.138512	+	0.990361i	$0.544232\pi$
$312$		0			0
$313$	−3.15454	+	1.30665i	−0.178305	+	0.0738564i	−0.470050	−	0.882640i	$-0.655764\pi$
$313$	−3.15454	+	1.30665i	−0.178305	+	0.0738564i	0.291745	+	0.956496i	$0.405764\pi$
$314$		0			0
$315$	−9.09897	+	13.6176i	−0.512669	+	0.767264i
$316$		0			0
$317$	17.1528	+	3.41191i	0.963399	+	0.191632i	0.651639	−	0.758529i	$-0.274082\pi$
$317$	17.1528	+	3.41191i	0.963399	+	0.191632i	0.311760	+	0.950161i	$0.399082\pi$
$318$		0			0
$319$	0.869917			0.0487060
$320$		0			0
$321$	−42.1746			−2.35396
$322$		0			0
$323$	5.14239	+	1.02288i	0.286130	+	0.0569148i
$324$		0			0
$325$	1.94852	−	2.91616i	0.108084	−	0.161760i
$326$		0			0
$327$	12.6114	−	5.22382i	0.697413	−	0.288878i
$328$		0			0
$329$	−5.00149	−	2.07169i	−0.275741	−	0.114216i
$330$		0			0
$331$	−2.90638	−	14.6113i	−0.159749	−	0.803112i	−0.974689	−	0.223566i	$-0.928230\pi$
$331$	−2.90638	−	14.6113i	−0.159749	−	0.803112i	0.814940	−	0.579546i	$-0.196770\pi$
$332$		0			0
$333$	−10.6243	−	15.9003i	−0.582206	−	0.871332i
$334$		0			0
$335$	−21.6320	+	21.6320i	−1.18188	+	1.18188i
$336$		0			0
$337$	−4.78263	−	4.78263i	−0.260527	−	0.260527i	0.564741	−	0.825268i	$-0.308976\pi$
$337$	−4.78263	−	4.78263i	−0.260527	−	0.260527i	−0.825268	+	0.564741i	$0.808976\pi$
$338$		0			0
$339$	−6.81589	+	4.55423i	−0.370188	+	0.247352i
$340$		0			0
$341$	−8.26842	+	1.64469i	−0.447760	+	0.0890650i
$342$		0			0
$343$	7.36339	−	17.7768i	0.397586	−	0.959857i
$344$		0			0
$345$	11.3883	+	27.4937i	0.613124	+	1.48021i
$346$		0			0
$347$	−9.14973	−	6.11366i	−0.491183	−	0.328198i	0.285191	−	0.958471i	$-0.407943\pi$
$347$	−9.14973	−	6.11366i	−0.491183	−	0.328198i	−0.776374	+	0.630273i	$0.782943\pi$
$348$		0			0
$349$	−3.87593	+	19.4856i	−0.207474	+	1.04304i	0.726899	+	0.686744i	$0.240961\pi$
$349$	−3.87593	+	19.4856i	−0.207474	+	1.04304i	−0.934373	+	0.356297i	$0.884039\pi$
$350$		0			0
$351$		−	0.505498i		−	0.0269815i
$352$		0			0
$353$			22.7162i			1.20906i	0.796583	+	0.604529i	$0.206639\pi$
$353$			22.7162i			1.20906i	−0.796583	+	0.604529i	$0.793361\pi$
$354$		0			0
$355$	−3.80200	+	19.1140i	−0.201789	+	1.01446i
$356$		0			0
$357$	−5.53694	−	3.69967i	−0.293046	−	0.195807i
$358$		0			0
$359$	14.0062	+	33.8139i	0.739218	+	1.78463i	0.609039	+	0.793140i	$0.291555\pi$
$359$	14.0062	+	33.8139i	0.739218	+	1.78463i	0.130179	+	0.991490i	$0.458445\pi$
$360$		0			0
$361$	−3.39817	+	8.20392i	−0.178851	+	0.431785i
$362$		0			0
$363$	21.3761	−	4.25197i	1.12196	−	0.223171i
$364$		0			0
$365$	−12.8203	+	8.56624i	−0.671044	+	0.448377i
$366$		0			0
$367$	10.6394	+	10.6394i	0.555373	+	0.555373i	0.927987	−	0.372614i	$-0.121538\pi$
$367$	10.6394	+	10.6394i	0.555373	+	0.555373i	−0.372614	+	0.927987i	$0.621538\pi$
$368$		0			0
$369$	−0.620923	+	0.620923i	−0.0323240	+	0.0323240i
$370$		0			0
$371$	−9.30394	−	13.9243i	−0.483036	−	0.722915i
$372$		0			0
$373$	−0.946981	−	4.76079i	−0.0490328	−	0.246505i	0.948494	−	0.316796i	$-0.102607\pi$
$373$	−0.946981	−	4.76079i	−0.0490328	−	0.246505i	−0.997526	+	0.0702914i	$0.977607\pi$
$374$		0			0
$375$	−67.4500	−	27.9387i	−3.48310	−	1.44275i
$376$		0			0
$377$	0.185783	−	0.0769539i	0.00956831	−	0.00396333i
$378$		0			0
$379$	4.29469	−	6.42746i	0.220603	−	0.330156i	−0.704616	−	0.709589i	$-0.748881\pi$
$379$	4.29469	−	6.42746i	0.220603	−	0.330156i	0.925219	+	0.379432i	$0.123881\pi$
$380$		0			0
$381$	14.0343	+	2.79160i	0.718999	+	0.143018i
$382$		0			0
$383$	−13.2624			−0.677675			−0.338837	−	0.940845i	$-0.610034\pi$
$383$	−13.2624			−0.677675			−0.338837	+	0.940845i	$0.610034\pi$
$384$		0			0
$385$	−8.93773			−0.455509
$386$		0			0
$387$	10.9806	+	2.18417i	0.558174	+	0.111028i
$388$		0			0
$389$	−7.11261	+	10.6448i	−0.360624	+	0.539711i	−0.966772	−	0.255640i	$-0.917714\pi$
$389$	−7.11261	+	10.6448i	−0.360624	+	0.539711i	0.606148	+	0.795352i	$0.292714\pi$
$390$		0			0
$391$	−4.73236	+	1.96021i	−0.239326	+	0.0991320i
$392$		0			0
$393$	−32.1284	−	13.3080i	−1.62066	−	0.671300i
$394$		0			0
$395$	1.79108	+	9.00437i	0.0901190	+	0.453059i
$396$		0			0
$397$	−21.7727	−	32.5851i	−1.09274	−	1.63540i	−0.697064	−	0.717009i	$-0.745511\pi$
$397$	−21.7727	−	32.5851i	−1.09274	−	1.63540i	−0.395675	−	0.918390i	$-0.629489\pi$
$398$		0			0
$399$	−9.08875	+	9.08875i	−0.455007	+	0.455007i
$400$		0			0
$401$	1.79901	+	1.79901i	0.0898380	+	0.0898380i	0.750598	−	0.660760i	$-0.229766\pi$
$401$	1.79901	+	1.79901i	0.0898380	+	0.0898380i	−0.660760	+	0.750598i	$0.729766\pi$
$402$		0			0
$403$	−1.62035	+	1.08268i	−0.0807152	+	0.0539322i
$404$		0			0
$405$	−44.2913	+	8.81008i	−2.20085	+	0.437777i
$406$		0			0
$407$	3.99368	−	9.64159i	0.197959	−	0.477916i
$408$		0			0
$409$	−2.64478	−	6.38506i	−0.130776	−	0.315721i	0.844905	−	0.534916i	$-0.179657\pi$
$409$	−2.64478	−	6.38506i	−0.130776	−	0.315721i	−0.975681	+	0.219195i	$0.929657\pi$
$410$		0			0
$411$	6.94225	+	4.63866i	0.342436	+	0.228808i
$412$		0			0
$413$	2.39714	−	12.0512i	0.117956	−	0.593003i
$414$		0			0
$415$		−	50.1429i		−	2.46142i
$416$		0			0
$417$			49.0777i			2.40334i
$418$		0			0
$419$	1.12208	−	5.64109i	0.0548173	−	0.275585i	−0.943649	−	0.330948i	$-0.892632\pi$
$419$	1.12208	−	5.64109i	0.0548173	−	0.275585i	0.998466	+	0.0553627i	$0.0176315\pi$
$420$		0			0
$421$	−21.9884	−	14.6922i	−1.07165	−	0.716052i	−0.110999	−	0.993821i	$-0.535405\pi$
$421$	−21.9884	−	14.6922i	−1.07165	−	0.716052i	−0.960648	+	0.277769i	$0.910405\pi$
$422$		0			0
$423$	2.57547	+	6.21774i	0.125224	+	0.302317i
$424$		0			0
$425$	7.96255	−	19.2233i	0.386241	−	0.932467i
$426$		0			0
$427$	−17.1725	+	3.41581i	−0.831034	+	0.165303i
$428$		0			0
$429$	−0.633184	+	0.423080i	−0.0305704	+	0.0204265i
$430$		0			0
$431$	−5.66697	−	5.66697i	−0.272968	−	0.272968i	0.557326	−	0.830294i	$-0.311828\pi$
$431$	−5.66697	−	5.66697i	−0.272968	−	0.272968i	−0.830294	+	0.557326i	$0.811828\pi$
$432$		0			0
$433$	−9.43057	+	9.43057i	−0.453204	+	0.453204i	−0.896417	−	0.443212i	$-0.853839\pi$
$433$	−9.43057	+	9.43057i	−0.453204	+	0.453204i	0.443212	+	0.896417i	$0.353839\pi$
$434$		0			0
$435$	−3.85064	−	5.76289i	−0.184624	−	0.276309i
$436$		0			0
$437$	1.92883	+	9.69688i	0.0922684	+	0.463865i
$438$		0			0
$439$	−19.0108	−	7.87451i	−0.907334	−	0.375830i	−0.120299	−	0.992738i	$-0.538385\pi$
$439$	−19.0108	−	7.87451i	−0.907334	−	0.375830i	−0.787036	+	0.616908i	$0.788385\pi$
$440$		0			0
$441$	−7.85750	+	3.25468i	−0.374167	+	0.154985i
$442$		0			0
$443$	−9.86124	+	14.7584i	−0.468522	+	0.701193i	−0.988200	−	0.153170i	$-0.951052\pi$
$443$	−9.86124	+	14.7584i	−0.468522	+	0.701193i	0.519678	+	0.854362i	$0.326052\pi$
$444$		0			0
$445$	41.0408	+	8.16352i	1.94552	+	0.386988i
$446$		0			0
$447$	20.0348			0.947614
$448$		0			0
$449$	12.8596			0.606883			0.303441	−	0.952850i	$-0.401864\pi$
$449$	12.8596			0.606883			0.303441	+	0.952850i	$0.401864\pi$
$450$		0			0
$451$	−0.470003	−	0.0934893i	−0.0221316	−	0.00440224i
$452$		0			0
$453$	−11.6492	+	17.4343i	−0.547328	+	0.819135i
$454$		0			0
$455$	−1.90878	+	0.790642i	−0.0894849	+	0.0370659i
$456$		0			0
$457$	4.61582	+	1.91193i	0.215919	+	0.0894365i	0.488021	−	0.872832i	$-0.337719\pi$
$457$	4.61582	+	1.91193i	0.215919	+	0.0894365i	−0.272102	+	0.962268i	$0.587719\pi$
$458$		0			0
$459$	−0.585063	−	2.94131i	−0.0273084	−	0.137289i
$460$		0			0
$461$	16.4812	+	24.6659i	0.767606	+	1.14880i	0.984972	+	0.172714i	$0.0552535\pi$
$461$	16.4812	+	24.6659i	0.767606	+	1.14880i	−0.217366	+	0.976090i	$0.569746\pi$
$462$		0			0
$463$	14.2150	−	14.2150i	0.660625	−	0.660625i	−0.294903	−	0.955527i	$-0.595287\pi$
$463$	14.2150	−	14.2150i	0.660625	−	0.660625i	0.955527	+	0.294903i	$0.0952872\pi$
$464$		0			0
$465$	47.4952	+	47.4952i	2.20254	+	2.20254i
$466$		0			0
$467$	−9.72658	+	6.49909i	−0.450093	+	0.300742i	−0.759880	−	0.650064i	$-0.774742\pi$
$467$	−9.72658	+	6.49909i	−0.450093	+	0.300742i	0.309787	+	0.950806i	$0.399742\pi$
$468$		0			0
$469$	12.6607	−	2.51837i	0.584618	−	0.116288i
$470$		0			0
$471$	4.58561	−	11.0706i	0.211294	−	0.510108i
$472$		0			0
$473$	2.33811	+	5.64470i	0.107506	+	0.259543i
$474$		0			0
$475$	−33.3929	−	22.3125i	−1.53217	−	1.02377i
$476$		0			0
$477$	−4.06160	+	20.4190i	−0.185968	+	0.934923i
$478$		0			0
$479$			33.3214i			1.52249i	0.648463	+	0.761246i	$0.275412\pi$
$479$			33.3214i			1.52249i	−0.648463	+	0.761246i	$0.724588\pi$
$480$		0			0
$481$		−	2.41238i		−	0.109995i
$482$		0			0
$483$	2.44978	−	12.3159i	0.111469	−	0.560391i
$484$		0			0
$485$	32.4491	+	21.6818i	1.47344	+	0.984519i
$486$		0			0
$487$	−8.84785	−	21.3606i	−0.400934	−	0.967941i	−0.987440	−	0.157996i	$-0.949497\pi$
$487$	−8.84785	−	21.3606i	−0.400934	−	0.967941i	0.586505	−	0.809945i	$-0.300503\pi$
$488$		0			0
$489$	15.8693	−	38.3119i	0.717635	−	1.73252i
$490$		0			0
$491$	16.4921	−	3.28049i	0.744280	−	0.148046i	0.191638	−	0.981466i	$-0.438620\pi$
$491$	16.4921	−	3.28049i	0.744280	−	0.148046i	0.552641	+	0.833419i	$0.313620\pi$
$492$		0			0
$493$	0.991937	−	0.662791i	0.0446746	−	0.0298506i
$494$		0			0
$495$	7.85680	+	7.85680i	0.353137	+	0.353137i
$496$		0			0
$497$	5.81479	−	5.81479i	0.260829	−	0.260829i
$498$		0			0
$499$	8.82586	+	13.2088i	0.395100	+	0.591308i	0.974679	−	0.223607i	$-0.0717833\pi$
$499$	8.82586	+	13.2088i	0.395100	+	0.591308i	−0.579580	+	0.814916i	$0.696783\pi$
$500$		0			0
$501$	−8.63105	−	43.3912i	−0.385607	−	1.93858i
$502$		0			0
$503$	−0.539361	−	0.223411i	−0.0240489	−	0.00996138i	0.370627	−	0.928782i	$-0.379143\pi$
$503$	−0.539361	−	0.223411i	−0.0240489	−	0.00996138i	−0.394675	+	0.918821i	$0.629143\pi$
$504$		0			0
$505$	−31.6353	+	13.1038i	−1.40775	+	0.583109i
$506$		0			0
$507$	16.3754	−	24.5075i	0.727256	−	1.08842i
$508$		0			0
$509$	7.93668	+	1.57870i	0.351787	+	0.0699748i	0.367821	−	0.929897i	$-0.380104\pi$
$509$	7.93668	+	1.57870i	0.351787	+	0.0699748i	−0.0160338	+	0.999871i	$0.505104\pi$
$510$		0			0
$511$	6.50614			0.287814
$512$		0			0
$513$	−5.78845			−0.255566
$514$		0			0
$515$	−25.5559	−	5.08339i	−1.12613	−	0.224001i
$516$		0			0
$517$	−2.04047	+	3.05378i	−0.0897398	+	0.134305i
$518$		0			0
$519$	−10.6819	+	4.42461i	−0.468885	+	0.194219i
$520$		0			0
$521$	0.958515	+	0.397030i	0.0419933	+	0.0173942i	0.403581	−	0.914944i	$-0.367765\pi$
$521$	0.958515	+	0.397030i	0.0419933	+	0.0173942i	−0.361588	+	0.932338i	$0.617765\pi$
$522$		0			0
$523$	0.257581	+	1.29495i	0.0112632	+	0.0566240i	0.986008	−	0.166697i	$-0.0533102\pi$
$523$	0.257581	+	1.29495i	0.0112632	+	0.0566240i	−0.974745	+	0.223321i	$0.928310\pi$
$524$		0			0
$525$	28.3387	+	42.4118i	1.23680	+	1.85100i
$526$		0			0
$527$	−8.17511	+	8.17511i	−0.356113	+	0.356113i
$528$		0			0
$529$	9.43355	+	9.43355i	0.410154	+	0.410154i
$530$		0			0
$531$	−12.7010	+	8.48653i	−0.551176	+	0.368284i
$532$		0			0
$533$	−0.108646	+	0.0216110i	−0.00470598	+	0.000936077i
$534$		0			0
$535$	−29.7067	+	71.7183i	−1.28433	+	3.10065i
$536$		0			0
$537$	−15.0363	−	36.3009i	−0.648865	−	1.56650i
$538$		0			0
$539$	−3.85913	−	2.57859i	−0.166224	−	0.111068i
$540$		0			0
$541$	0.446774	−	2.24608i	0.0192083	−	0.0965667i	−0.969992	−	0.243137i	$-0.921823\pi$
$541$	0.446774	−	2.24608i	0.0192083	−	0.0965667i	0.989200	+	0.146570i	$0.0468235\pi$
$542$		0			0
$543$		−	24.9626i		−	1.07125i
$544$		0			0
$545$		−	25.1253i		−	1.07625i
$546$		0			0
$547$	7.07297	−	35.5582i	0.302418	−	1.52036i	−0.468522	−	0.883452i	$-0.655213\pi$
$547$	7.07297	−	35.5582i	0.302418	−	1.52036i	0.770940	−	0.636907i	$-0.219787\pi$
$548$		0			0
$549$	18.0983	+	12.0929i	0.772417	+	0.516113i
$550$		0			0
$551$	−0.881197	−	2.12740i	−0.0375403	−	0.0906302i
$552$		0			0
$553$	1.48249	−	3.57904i	0.0630418	−	0.152196i
$554$		0			0
$555$	−81.5499	+	16.2213i	−3.46160	+	0.688555i
$556$		0			0
$557$	−19.6484	+	13.1287i	−0.832531	+	0.556280i	−0.897199	−	0.441627i	$-0.854401\pi$
$557$	−19.6484	+	13.1287i	−0.832531	+	0.556280i	0.0646672	+	0.997907i	$0.479401\pi$
$558$		0			0
$559$	0.998673	+	0.998673i	0.0422393	+	0.0422393i
$560$		0			0
$561$	−3.19459	+	3.19459i	−0.134876	+	0.134876i
$562$		0			0
$563$	−10.2079	−	15.2772i	−0.430212	−	0.643858i	0.551512	−	0.834167i	$-0.314051\pi$
$563$	−10.2079	−	15.2772i	−0.430212	−	0.643858i	−0.981724	+	0.190309i	$0.939051\pi$
$564$		0			0
$565$	2.94358	+	14.7984i	0.123837	+	0.622572i
$566$		0			0
$567$	17.6048	+	7.29216i	0.739333	+	0.306242i
$568$		0			0
$569$	32.6965	−	13.5433i	1.37071	−	0.567765i	0.428727	−	0.903434i	$-0.358962\pi$
$569$	32.6965	−	13.5433i	1.37071	−	0.567765i	0.941980	+	0.335669i	$0.108962\pi$
$570$		0			0
$571$	9.13934	−	13.6780i	0.382470	−	0.572406i	−0.589425	−	0.807823i	$-0.700646\pi$
$571$	9.13934	−	13.6780i	0.382470	−	0.572406i	0.971894	+	0.235417i	$0.0756456\pi$
$572$		0			0
$573$	−46.2401	−	9.19773i	−1.93171	−	0.384241i
$574$		0			0
$575$	39.2356			1.63624
$576$		0			0
$577$	−11.7086			−0.487435			−0.243717	−	0.969846i	$-0.578367\pi$
$577$	−11.7086			−0.487435			−0.243717	+	0.969846i	$0.578367\pi$
$578$		0			0
$579$	43.9535	+	8.74290i	1.82665	+	0.363343i
$580$		0			0
$581$	−11.7549	+	17.5925i	−0.487677	+	0.729861i
$582$		0			0
$583$	−10.4966	+	4.34785i	−0.434726	+	0.180070i
$584$		0			0
$585$	2.37295	+	0.982908i	0.0981094	+	0.0406383i
$586$		0			0
$587$	6.29094	+	31.6267i	0.259655	+	1.30537i	0.861906	+	0.507067i	$0.169270\pi$
$587$	6.29094	+	31.6267i	0.259655	+	1.30537i	−0.602252	+	0.798306i	$0.705730\pi$
$588$		0			0
$589$	12.3978	+	18.5546i	0.510841	+	0.764527i
$590$		0			0
$591$	33.0715	−	33.0715i	1.36038	−	1.36038i
$592$		0			0
$593$	−25.2454	−	25.2454i	−1.03670	−	1.03670i	−0.999300	−	0.0374032i	$-0.988091\pi$
$593$	−25.2454	−	25.2454i	−1.03670	−	1.03670i	−0.0374032	−	0.999300i	$-0.511909\pi$
$594$		0			0
$595$	−10.1914	+	6.80967i	−0.417806	+	0.279169i
$596$		0			0
$597$	3.04087	−	0.604867i	0.124455	−	0.0247556i
$598$		0			0
$599$	1.52504	−	3.68178i	0.0623115	−	0.150433i	−0.889657	−	0.456630i	$-0.849056\pi$
$599$	1.52504	−	3.68178i	0.0623115	−	0.150433i	0.951968	+	0.306196i	$0.0990564\pi$
$600$		0			0
$601$	11.5852	+	27.9691i	0.472570	+	1.14088i	0.963024	+	0.269417i	$0.0868310\pi$
$601$	11.5852	+	27.9691i	0.472570	+	1.14088i	−0.490454	+	0.871467i	$0.663169\pi$
$602$		0			0
$603$	−13.3433	−	8.91573i	−0.543382	−	0.363077i
$604$		0			0
$605$	7.82626	−	39.3453i	0.318183	−	1.59961i
$606$		0			0
$607$		−	40.9668i		−	1.66279i	−0.555680	−	0.831396i	$-0.687542\pi$
$607$		−	40.9668i		−	1.66279i	0.555680	−	0.831396i	$-0.312458\pi$
$608$		0			0
$609$			2.92460i			0.118511i
$610$		0			0
$611$	−0.165630	+	0.832680i	−0.00670069	+	0.0336866i
$612$		0			0
$613$	−13.2362	−	8.84413i	−0.534604	−	0.357211i	0.258776	−	0.965937i	$-0.416681\pi$
$613$	−13.2362	−	8.84413i	−0.534604	−	0.357211i	−0.793380	+	0.608726i	$0.791681\pi$
$614$		0			0
$615$	1.46111	+	3.52742i	0.0589175	+	0.142239i
$616$		0			0
$617$	−9.10950	+	21.9923i	−0.366735	+	0.885376i	0.627546	+	0.778579i	$0.284059\pi$
$617$	−9.10950	+	21.9923i	−0.366735	+	0.885376i	−0.994281	+	0.106796i	$0.965941\pi$
$618$		0			0
$619$	44.5733	−	8.86617i	1.79155	−	0.356362i	0.816328	−	0.577589i	$-0.196006\pi$
$619$	44.5733	−	8.86617i	1.79155	−	0.356362i	0.975222	+	0.221227i	$0.0710062\pi$
$620$		0			0
$621$	4.70197	−	3.14176i	0.188684	−	0.126074i
$622$		0			0
$623$	−12.4853	−	12.4853i	−0.500213	−	0.500213i
$624$		0			0
$625$	−50.3856	+	50.3856i	−2.01542	+	2.01542i
$626$		0			0
$627$	4.84468	+	7.25058i	0.193478	+	0.289560i
$628$		0			0
$629$	−2.79209	−	14.0368i	−0.111328	−	0.559683i
$630$		0			0
$631$	−5.81286	−	2.40776i	−0.231406	−	0.0958516i	0.263967	−	0.964532i	$-0.414969\pi$
$631$	−5.81286	−	2.40776i	−0.231406	−	0.0958516i	−0.495374	+	0.868680i	$0.664969\pi$
$632$		0			0
$633$	−23.4313	+	9.70558i	−0.931312	+	0.385762i
$634$		0			0
$635$	14.6325	−	21.8991i	0.580674	−	0.869040i
$636$		0			0
$637$	−1.05228	−	0.209311i	−0.0416927	−	0.00829320i
$638$		0			0
$639$	−10.2231			−0.404419
$640$		0			0
$641$	5.83590			0.230504			0.115252	−	0.993336i	$-0.463232\pi$
$641$	5.83590			0.230504			0.115252	+	0.993336i	$0.463232\pi$
$642$		0			0
$643$	44.3564	+	8.82303i	1.74924	+	0.347946i	0.962903	−	0.269846i	$-0.0869729\pi$
$643$	44.3564	+	8.82303i	1.74924	+	0.347946i	0.786341	+	0.617793i	$0.211973\pi$
$644$		0			0
$645$	27.0446	−	40.4751i	1.06488	−	1.59370i
$646$		0			0
$647$	−39.4132	+	16.3255i	−1.54949	+	0.641820i	−0.983224	−	0.182402i	$-0.941613\pi$
$647$	−39.4132	+	16.3255i	−1.54949	+	0.641820i	−0.566267	+	0.824222i	$0.691613\pi$
$648$		0			0
$649$	−7.70159	−	3.19010i	−0.302314	−	0.125222i
$650$		0			0
$651$	−5.52933	−	27.7978i	−0.216711	−	1.08948i
$652$		0			0
$653$	−9.71620	−	14.5413i	−0.380224	−	0.569046i	0.591161	−	0.806553i	$-0.298670\pi$
$653$	−9.71620	−	14.5413i	−0.380224	−	0.569046i	−0.971386	+	0.237507i	$0.923670\pi$
$654$		0			0
$655$	−45.2608	+	45.2608i	−1.76848	+	1.76848i
$656$		0			0
$657$	−5.71928	−	5.71928i	−0.223130	−	0.223130i
$658$		0			0
$659$	−15.4630	+	10.3321i	−0.602354	+	0.402480i	−0.819019	−	0.573766i	$-0.805482\pi$
$659$	−15.4630	+	10.3321i	−0.602354	+	0.402480i	0.216665	+	0.976246i	$0.430482\pi$
$660$		0			0
$661$	−35.0453	+	6.97094i	−1.36310	+	0.271138i	−0.821842	−	0.569715i	$-0.807053\pi$
$661$	−35.0453	+	6.97094i	−1.36310	+	0.271138i	−0.541262	+	0.840854i	$0.682053\pi$
$662$		0			0
$663$	−0.399653	+	0.964847i	−0.0155212	+	0.0374716i
$664$		0			0
$665$	9.05362	+	21.8574i	0.351084	+	0.847593i
$666$		0			0
$667$	1.87047	+	1.24981i	0.0724250	+	0.0483928i
$668$		0			0
$669$	−0.177511	+	0.892410i	−0.00686299	+	0.0345026i
$670$		0			0
$671$			11.8786i			0.458569i
$672$		0			0
$673$		−	36.6129i		−	1.41132i	−0.708549	−	0.705662i	$-0.750650\pi$
$673$		−	36.6129i		−	1.41132i	0.708549	−	0.705662i	$-0.249350\pi$
$674$		0			0
$675$	−4.48146	+	22.5298i	−0.172492	+	0.867174i
$676$		0			0
$677$	−10.2445	−	6.84516i	−0.393728	−	0.263081i	0.342909	−	0.939368i	$-0.388588\pi$
$677$	−10.2445	−	6.84516i	−0.393728	−	0.263081i	−0.736638	+	0.676288i	$0.763588\pi$
$678$		0			0
$679$	−6.30184	−	15.2140i	−0.241843	−	0.583859i
$680$		0			0
$681$	10.3742	−	25.0456i	0.397542	−	0.959751i
$682$		0			0
$683$	−32.2106	+	6.40709i	−1.23251	+	0.245161i	−0.768023	−	0.640422i	$-0.778759\pi$
$683$	−32.2106	+	6.40709i	−1.23251	+	0.245161i	−0.464482	+	0.885583i	$0.653759\pi$
$684$		0			0
$685$	12.7780	−	8.53800i	0.488223	−	0.326220i
$686$		0			0
$687$	11.3919	+	11.3919i	0.434630	+	0.434630i
$688$		0			0
$689$	−1.85709	+	1.85709i	−0.0707495	+	0.0707495i
$690$		0			0
$691$	12.8884	+	19.2889i	0.490299	+	0.733785i	0.991294	−	0.131666i	$-0.0420325\pi$
$691$	12.8884	+	19.2889i	0.490299	+	0.733785i	−0.500995	+	0.865450i	$0.667033\pi$
$692$		0			0
$693$	−0.914678	−	4.59840i	−0.0347457	−	0.174679i
$694$		0			0
$695$	83.4571	+	34.5690i	3.16571	+	1.31128i
$696$		0			0
$697$	−0.607158	+	0.251493i	−0.0229977	+	0.00952598i
$698$		0			0
$699$	−8.71084	+	13.0367i	−0.329474	+	0.493093i
$700$		0			0
$701$	−7.52527	−	1.49687i	−0.284226	−	0.0565360i	0.0509187	−	0.998703i	$-0.483785\pi$
$701$	−7.52527	−	1.49687i	−0.284226	−	0.0565360i	−0.335144	+	0.942167i	$0.608785\pi$
$702$		0			0
$703$	−27.6242			−1.04186
$704$		0			0
$705$	29.2622			1.10208
$706$		0			0
$707$	14.1711	+	2.81880i	0.532957	+	0.106012i
$708$		0			0
$709$	−10.0146	+	14.9879i	−0.376106	+	0.562883i	−0.970442	−	0.241334i	$-0.922415\pi$
$709$	−10.0146	+	14.9879i	−0.376106	+	0.562883i	0.594336	+	0.804217i	$0.297415\pi$
$710$		0			0
$711$	−4.44938	+	1.84299i	−0.166865	+	0.0691177i
$712$		0			0
$713$	−20.1415	−	8.34287i	−0.754304	−	0.312443i
$714$		0			0
$715$	0.273453	+	1.37474i	0.0102266	+	0.0514124i
$716$		0			0
$717$	3.91614	+	5.86092i	0.146251	+	0.218880i
$718$		0			0
$719$	10.5187	−	10.5187i	0.392280	−	0.392280i	−0.483219	−	0.875499i	$-0.660533\pi$
$719$	10.5187	−	10.5187i	0.392280	−	0.392280i	0.875499	+	0.483219i	$0.160533\pi$
$720$		0			0
$721$	7.77454	+	7.77454i	0.289539	+	0.289539i
$722$		0			0
$723$	24.4472	−	16.3351i	0.909201	−	0.607508i
$724$		0			0
$725$	−8.96250	+	1.78275i	−0.332859	+	0.0662097i
$726$		0			0
$727$	12.9735	−	31.3209i	0.481162	−	1.16163i	−0.477896	−	0.878416i	$-0.658600\pi$
$727$	12.9735	−	31.3209i	0.481162	−	1.16163i	0.959058	−	0.283211i	$-0.0913996\pi$
$728$		0			0
$729$	−4.30086	−	10.3832i	−0.159291	−	0.384563i
$730$		0			0
$731$	6.96677	+	4.65505i	0.257675	+	0.172173i
$732$		0			0
$733$	4.66780	−	23.4666i	0.172409	−	0.866759i	−0.793637	−	0.608391i	$-0.791815\pi$
$733$	4.66780	−	23.4666i	0.172409	−	0.866759i	0.966047	−	0.258368i	$-0.0831848\pi$
$734$		0			0
$735$			36.9793i			1.36400i
$736$		0			0
$737$		−	8.75773i		−	0.322595i
$738$		0			0
$739$	−4.30057	+	21.6204i	−0.158199	+	0.795320i	0.817453	+	0.575996i	$0.195385\pi$
$739$	−4.30057	+	21.6204i	−0.158199	+	0.795320i	−0.975652	+	0.219325i	$0.929615\pi$
$740$		0			0
$741$	1.67604	+	1.11990i	0.0615710	+	0.0411404i
$742$		0			0
$743$	−1.75751	−	4.24301i	−0.0644769	−	0.155661i	0.888357	−	0.459154i	$-0.151847\pi$
$743$	−1.75751	−	4.24301i	−0.0644769	−	0.155661i	−0.952834	+	0.303493i	$0.901847\pi$
$744$		0			0
$745$	14.1120	−	34.0694i	0.517024	−	1.24821i
$746$		0			0
$747$	25.7982	−	5.13158i	0.943906	−	0.187755i
$748$		0			0
$749$	27.2354	−	18.1981i	0.995158	−	0.664944i
$750$		0			0
$751$	25.9585	+	25.9585i	0.947238	+	0.947238i	0.998676	−	0.0514384i	$-0.0163806\pi$
$751$	25.9585	+	25.9585i	0.947238	+	0.947238i	−0.0514384	+	0.998676i	$0.516381\pi$
$752$		0			0
$753$	31.7049	−	31.7049i	1.15539	−	1.15539i
$754$		0			0
$755$	21.4418	+	32.0899i	0.780346	+	1.16787i
$756$		0			0
$757$	1.73528	+	8.72382i	0.0630697	+	0.317073i	0.999422	−	0.0339884i	$-0.0108209\pi$
$757$	1.73528	+	8.72382i	0.0630697	+	0.317073i	−0.936353	+	0.351061i	$0.885821\pi$
$758$		0			0
$759$	−7.87069	−	3.26015i	−0.285688	−	0.118336i
$760$		0			0
$761$	27.8964	−	11.5551i	1.01124	−	0.418871i	0.185336	−	0.982675i	$-0.440663\pi$
$761$	27.8964	−	11.5551i	1.01124	−	0.418871i	0.825909	+	0.563804i	$0.190663\pi$
$762$		0			0
$763$	−5.89011	+	8.81517i	−0.213236	+	0.319130i
$764$		0			0
$765$	14.9449	+	2.97273i	0.540336	+	0.107479i
$766$		0			0
$767$	−1.92698			−0.0695793
$768$		0			0
$769$	17.7614			0.640492			0.320246	−	0.947334i	$-0.396234\pi$
$769$	17.7614			0.640492			0.320246	+	0.947334i	$0.396234\pi$
$770$		0			0
$771$	−36.2542	−	7.21140i	−1.30566	−	0.259712i
$772$		0			0
$773$	−18.1617	+	27.1809i	−0.653230	+	0.977627i	0.345994	+	0.938237i	$0.387542\pi$
$773$	−18.1617	+	27.1809i	−0.653230	+	0.977627i	−0.999224	+	0.0393906i	$0.987458\pi$
$774$		0			0
$775$	81.8166	−	33.8895i	2.93894	−	1.21735i
$776$		0			0
$777$	32.4143	+	13.4264i	1.16286	+	0.481671i
$778$		0			0
$779$	0.247467	+	1.24410i	0.00886643	+	0.0445746i
$780$		0			0
$781$	−3.09952	−	4.63876i	−0.110910	−	0.165988i
$782$		0			0
$783$	−0.931310	+	0.931310i	−0.0332823	+	0.0332823i
$784$		0			0
$785$	−15.5957	−	15.5957i	−0.556636	−	0.556636i
$786$		0			0
$787$	−20.5749	+	13.7477i	−0.733416	+	0.490053i	−0.865326	−	0.501209i	$-0.832889\pi$
$787$	−20.5749	+	13.7477i	−0.733416	+	0.490053i	0.131911	+	0.991262i	$0.457889\pi$
$788$		0			0
$789$	54.8987	−	10.9200i	1.95445	−	0.388763i
$790$		0			0
$791$	2.43642	−	5.88203i	0.0866290	−	0.209141i
$792$		0			0
$793$	1.05080	+	2.53684i	0.0373148	+	0.0900860i
$794$		0			0
$795$	75.2657	+	50.2909i	2.66940	+	1.78364i
$796$		0			0
$797$	−0.0956446	+	0.480838i	−0.00338791	+	0.0170322i	−0.982442	−	0.186567i	$-0.940264\pi$
$797$	−0.0956446	+	0.480838i	−0.00338791	+	0.0170322i	0.979054	+	0.203599i	$0.0652639\pi$
$798$		0			0
$799$			5.03676i			0.178188i
$800$		0			0
$801$			21.9506i			0.775587i
$802$		0			0
$803$	0.861124	−	4.32916i	0.0303884	−	0.152773i
$804$		0			0
$805$	−19.2177	−	12.8408i	−0.677334	−	0.452580i
$806$		0			0
$807$	−0.599279	−	1.44679i	−0.0210956	−	0.0509294i
$808$		0			0
$809$	−20.2707	+	48.9378i	−0.712680	+	1.72056i	−0.0194867	+	0.999810i	$0.506203\pi$
$809$	−20.2707	+	48.9378i	−0.712680	+	1.72056i	−0.693193	+	0.720752i	$0.743797\pi$
$810$		0			0
$811$	1.17029	−	0.232786i	0.0410945	−	0.00817421i	−0.174500	−	0.984657i	$-0.555831\pi$
$811$	1.17029	−	0.232786i	0.0410945	−	0.00817421i	0.215595	+	0.976483i	$0.430831\pi$
$812$		0			0
$813$	26.8706	−	17.9544i	0.942394	−	0.629687i
$814$		0			0
$815$	−53.9718	−	53.9718i	−1.89055	−	1.89055i
$816$		0			0
$817$	11.4358	−	11.4358i	0.400087	−	0.400087i
$818$		0			0
$819$	−0.602122	−	0.901139i	−0.0210398	−	0.0314883i
$820$		0			0
$821$	−5.87139	−	29.5175i	−0.204913	−	1.03017i	−0.937099	−	0.349062i	$-0.886500\pi$
$821$	−5.87139	−	29.5175i	−0.204913	−	1.03017i	0.732187	−	0.681104i	$-0.238500\pi$
$822$		0			0
$823$	−28.7325	−	11.9014i	−1.00155	−	0.414857i	−0.179187	−	0.983815i	$-0.557347\pi$
$823$	−28.7325	−	11.9014i	−1.00155	−	0.414857i	−0.822366	+	0.568958i	$0.807347\pi$
$824$		0			0
$825$	31.9715	−	13.2430i	1.11311	−	0.461063i
$826$		0			0
$827$	2.10263	−	3.14680i	0.0731155	−	0.109425i	−0.793110	−	0.609079i	$-0.791539\pi$
$827$	2.10263	−	3.14680i	0.0731155	−	0.109425i	0.866225	+	0.499654i	$0.166539\pi$
$828$		0			0
$829$	−25.7896	−	5.12986i	−0.895709	−	0.178168i	−0.274291	−	0.961647i	$-0.588443\pi$
$829$	−25.7896	−	5.12986i	−0.895709	−	0.178168i	−0.621418	+	0.783479i	$0.713443\pi$
$830$		0			0
$831$	52.9287			1.83607
$832$		0			0
$833$	−6.36507			−0.220536
$834$		0			0
$835$	−79.8666	−	15.8865i	−2.76390	−	0.549774i
$836$		0			0
$837$	7.09119	−	10.6127i	0.245107	−	0.366829i
$838$		0			0
$839$	21.7694	−	9.01718i	0.751563	−	0.311308i	0.0261841	−	0.999657i	$-0.491664\pi$
$839$	21.7694	−	9.01718i	0.751563	−	0.311308i	0.725379	+	0.688349i	$0.241664\pi$
$840$		0			0
$841$	26.3085	+	10.8973i	0.907188	+	0.375770i
$842$		0			0
$843$	1.50987	+	7.59062i	0.0520026	+	0.261435i
$844$		0			0
$845$	−30.1408	−	45.1089i	−1.03688	−	1.55179i
$846$		0			0
$847$	−11.9695	+	11.9695i	−0.411276	+	0.411276i
$848$		0			0
$849$	−19.8730	−	19.8730i	−0.682038	−	0.682038i
$850$		0			0
$851$	22.4392	−	14.9934i	0.769205	−	0.513966i
$852$		0			0
$853$	13.0606	−	2.59791i	0.447186	−	0.0889509i	0.0336401	−	0.999434i	$-0.489290\pi$
$853$	13.0606	−	2.59791i	0.447186	−	0.0889509i	0.413546	+	0.910483i	$0.364290\pi$
$854$		0			0
$855$	11.2553	−	27.1726i	0.384922	−	0.929284i
$856$		0			0
$857$	−13.3651	−	32.2661i	−0.456542	−	1.10219i	−0.969788	−	0.243948i	$-0.921557\pi$
$857$	−13.3651	−	32.2661i	−0.456542	−	1.10219i	0.513246	−	0.858241i	$-0.328443\pi$
$858$		0			0
$859$	−3.86744	−	2.58414i	−0.131955	−	0.0881697i	0.487841	−	0.872933i	$-0.337785\pi$
$859$	−3.86744	−	2.58414i	−0.131955	−	0.0881697i	−0.619796	+	0.784763i	$0.712785\pi$
$860$		0			0
$861$	0.314304	−	1.58011i	0.0107115	−	0.0538501i
$862$		0			0
$863$			9.50850i			0.323673i	0.986818	+	0.161837i	$0.0517418\pi$
$863$			9.50850i			0.323673i	−0.986818	+	0.161837i	$0.948258\pi$
$864$		0			0
$865$			21.2813i			0.723587i
$866$		0			0
$867$	6.35577	−	31.9526i	0.215853	−	1.08517i
$868$		0			0
$869$	−2.18527	−	1.46015i	−0.0741301	−	0.0495322i
$870$		0			0
$871$	−0.774719	−	1.87034i	−0.0262504	−	0.0633740i
$872$		0			0
$873$	−7.83431	+	18.9137i	−0.265151	+	0.640132i
$874$		0			0
$875$	55.6130	−	11.0621i	1.88006	−	0.373968i
$876$		0			0
$877$	16.1414	−	10.7854i	0.545058	−	0.364196i	−0.252351	−	0.967636i	$-0.581204\pi$
$877$	16.1414	−	10.7854i	0.545058	−	0.364196i	0.797408	+	0.603440i	$0.206204\pi$
$878$		0			0
$879$	22.0132	+	22.0132i	0.742486	+	0.742486i
$880$		0			0
$881$	18.1256	−	18.1256i	0.610667	−	0.610667i	−0.332453	−	0.943120i	$-0.607876\pi$
$881$	18.1256	−	18.1256i	0.610667	−	0.610667i	0.943120	+	0.332453i	$0.107876\pi$
$882$		0			0
$883$	−25.2429	−	37.7787i	−0.849491	−	1.27135i	−0.960709	−	0.277557i	$-0.910475\pi$
$883$	−25.2429	−	37.7787i	−0.849491	−	1.27135i	0.111218	−	0.993796i	$-0.464525\pi$
$884$		0			0
$885$	12.9574	+	65.1411i	0.435557	+	2.18969i
$886$		0			0
$887$	−36.7160	−	15.2083i	−1.23280	−	0.510644i	−0.331345	−	0.943510i	$-0.607502\pi$
$887$	−36.7160	−	15.2083i	−1.23280	−	0.510644i	−0.901458	+	0.432866i	$0.857502\pi$
$888$		0			0
$889$	−10.2676	+	4.25297i	−0.344363	+	0.142640i
$890$		0			0
$891$	7.18228	−	10.7490i	0.240615	−	0.360106i
$892$		0			0
$893$	9.53500	+	1.89663i	0.319077	+	0.0634683i
$894$		0			0
$895$	−72.3211			−2.41743
$896$		0			0
$897$	−1.96929			−0.0657528
$898$		0			0
$899$	4.97995	+	0.990574i	0.166091	+	0.0330375i
$900$		0			0
$901$	−8.65633	+	12.9551i	−0.288384	+	0.431597i
$902$		0			0
$903$	−18.9770	+	7.86055i	−0.631517	+	0.261583i
$904$		0			0
$905$	−42.4491	−	17.5830i	−1.41106	−	0.584479i
$906$		0			0
$907$	−5.87925	−	29.5570i	−0.195217	−	0.981424i	−0.946809	−	0.321796i	$-0.895714\pi$
$907$	−5.87925	−	29.5570i	−0.195217	−	0.981424i	0.751592	−	0.659628i	$-0.229286\pi$
$908$		0			0
$909$	−9.97931	−	14.9351i	−0.330993	−	0.495366i
$910$		0			0
$911$	16.2630	−	16.2630i	0.538818	−	0.538818i	−0.384364	−	0.923182i	$-0.625579\pi$
$911$	16.2630	−	16.2630i	0.538818	−	0.538818i	0.923182	+	0.384364i	$0.125579\pi$
$912$		0			0
$913$	10.1502	+	10.1502i	0.335922	+	0.335922i
$914$		0			0
$915$	78.6915	−	52.5800i	2.60146	−	1.73824i
$916$		0			0
$917$	26.4901	−	5.26920i	0.874779	−	0.174004i
$918$		0			0
$919$	−6.05005	+	14.6061i	−0.199573	+	0.481811i	−0.991704	−	0.128539i	$-0.958971\pi$
$919$	−6.05005	+	14.6061i	−0.199573	+	0.481811i	0.792132	+	0.610350i	$0.208971\pi$
$920$		0			0
$921$	22.3887	+	54.0512i	0.737734	+	1.78105i
$922$		0			0
$923$	−1.07230	−	0.716486i	−0.0352951	−	0.0235834i
$924$		0			0
$925$	−21.3868	+	107.519i	−0.703195	+	3.53520i
$926$		0			0
$927$		−	13.6686i		−	0.448935i
$928$		0			0
$929$			15.1489i			0.497021i	0.968629	+	0.248510i	$0.0799410\pi$
$929$			15.1489i			0.497021i	−0.968629	+	0.248510i	$0.920059\pi$
$930$		0			0
$931$	−2.39681	+	12.0496i	−0.0785524	+	0.394910i
$932$		0			0
$933$	16.7908	+	11.2192i	0.549705	+	0.367301i
$934$		0			0
$935$	3.18225	+	7.68262i	0.104071	+	0.251249i
$936$		0			0
$937$	−16.5832	+	40.0355i	−0.541751	+	1.30790i	0.381736	+	0.924271i	$0.375326\pi$
$937$	−16.5832	+	40.0355i	−0.541751	+	1.30790i	−0.923487	+	0.383630i	$0.874674\pi$
$938$		0			0
$939$	−7.63818	+	1.51933i	−0.249262	+	0.0495814i
$940$		0			0
$941$	−47.9669	+	32.0505i	−1.56368	+	1.04481i	−0.592765	+	0.805376i	$0.701964\pi$
$941$	−47.9669	+	32.0505i	−1.56368	+	1.04481i	−0.970911	+	0.239439i	$0.923036\pi$
$942$		0			0
$943$	−0.876271	−	0.876271i	−0.0285353	−	0.0285353i
$944$		0			0
$945$	9.56849	−	9.56849i	0.311263	−	0.311263i
$946$		0			0
$947$	4.70450	+	7.04078i	0.152876	+	0.228794i	0.900000	−	0.435890i	$-0.143566\pi$
$947$	4.70450	+	7.04078i	0.152876	+	0.228794i	−0.747125	+	0.664684i	$0.768566\pi$
$948$		0			0
$949$	−0.199058	−	1.00073i	−0.00646168	−	0.0324851i
$950$		0			0
$951$	36.8530	+	15.2650i	1.19504	+	0.495001i
$952$		0			0
$953$	−19.9974	+	8.28320i	−0.647780	+	0.268319i	−0.682286	−	0.731085i	$-0.739014\pi$
$953$	−19.9974	+	8.28320i	−0.647780	+	0.268319i	0.0345063	+	0.999404i	$0.489014\pi$
$954$		0			0
$955$	−48.2111	+	72.1531i	−1.56008	+	2.33482i
$956$		0			0
$957$	1.94602	+	0.387087i	0.0629058	+	0.0125127i
$958$		0			0
$959$	−6.48469			−0.209402
$960$		0			0
$961$	−18.2064			−0.587304
$962$		0			0
$963$	−39.9387	−	7.94430i	−1.28701	−	0.256002i
$964$		0			0
$965$	45.8271	−	68.5851i	1.47523	−	2.20783i
$966$		0			0
$967$	−4.47791	+	1.85481i	−0.144000	+	0.0596467i	−0.453519	−	0.891246i	$-0.649832\pi$
$967$	−4.47791	+	1.85481i	−0.144000	+	0.0596467i	0.309520	+	0.950893i	$0.399832\pi$
$968$		0			0
$969$	11.0484	+	4.57642i	0.354927	+	0.147016i
$970$		0			0
$971$	−9.90954	−	49.8186i	−0.318012	−	1.59876i	−0.727280	−	0.686341i	$-0.759216\pi$
$971$	−9.90954	−	49.8186i	−0.318012	−	1.59876i	0.409268	−	0.912414i	$-0.365784\pi$
$972$		0			0
$973$	−21.1767	−	31.6932i	−0.678895	−	1.01604i
$974$		0			0
$975$	5.65647	−	5.65647i	0.181152	−	0.181152i
$976$		0			0
$977$	−26.9502	−	26.9502i	−0.862215	−	0.862215i	0.129380	−	0.991595i	$-0.458701\pi$
$977$	−26.9502	−	26.9502i	−0.862215	−	0.862215i	−0.991595	+	0.129380i	$0.958701\pi$
$978$		0			0
$979$	−9.96018	+	6.65518i	−0.318329	+	0.212700i
$980$		0			0
$981$	12.9268	−	2.57130i	0.412721	−	0.0820953i
$982$		0			0
$983$	5.35576	−	12.9300i	0.170822	−	0.412402i	−0.815163	−	0.579231i	$-0.803353\pi$
$983$	5.35576	−	12.9300i	0.170822	−	0.412402i	0.985986	+	0.166829i	$0.0533529\pi$
$984$		0			0
$985$	−32.9436	−	79.5330i	−1.04967	−	2.53413i
$986$		0			0
$987$	−10.2666	−	6.85991i	−0.326789	−	0.218353i
$988$		0			0
$989$	−3.08239	+	15.4962i	−0.0980144	+	0.492752i
$990$		0			0
$991$			45.6448i			1.44996i	0.688772	+	0.724978i	$0.258150\pi$
$991$			45.6448i			1.44996i	−0.688772	+	0.724978i	$0.741850\pi$
$992$		0			0
$993$		−	33.9790i		−	1.07829i
$994$		0			0
$995$	1.11333	−	5.59708i	0.0352949	−	0.177439i
$996$		0			0
$997$	−25.8151	−	17.2491i	−0.817572	−	0.546284i	0.0750031	−	0.997183i	$-0.476103\pi$
$997$	−25.8151	−	17.2491i	−0.817572	−	0.546284i	−0.892575	+	0.450899i	$0.851103\pi$
$998$		0			0
$999$	6.04651	+	14.5976i	0.191303	+	0.461846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.i.b.161.6		56
4.3	odd	2		512.2.i.a.161.2		56
8.3	odd	2		256.2.i.a.209.6		56
8.5	even	2		64.2.i.a.29.1	✓	56
24.5	odd	2		576.2.bd.a.541.7		56
64.11	odd	16		512.2.i.a.353.2		56
64.21	even	16		64.2.i.a.53.1	yes	56
64.43	odd	16		256.2.i.a.49.6		56
64.53	even	16	inner	512.2.i.b.353.6		56
192.149	odd	16		576.2.bd.a.181.7		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
64.2.i.a.29.1	✓	56	8.5	even	2
64.2.i.a.53.1	yes	56	64.21	even	16
256.2.i.a.49.6		56	64.43	odd	16
256.2.i.a.209.6		56	8.3	odd	2
512.2.i.a.161.2		56	4.3	odd	2
512.2.i.a.353.2		56	64.11	odd	16
512.2.i.b.161.6		56	1.1	even	1	trivial
512.2.i.b.353.6		56	64.53	even	16	inner
576.2.bd.a.181.7		56	192.149	odd	16
576.2.bd.a.541.7		56	24.5	odd	2

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.i (of order \(16\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.23702 + 0.444970i) q^{3} +(2.33237 - 3.49064i) q^{5} +(-1.63661 + 0.677907i) q^{7} +(2.03460 + 0.842759i) q^{9} +O(q^{10})\)	\(q+(2.23702 + 0.444970i) q^{3} +(2.33237 - 3.49064i) q^{5} +(-1.63661 + 0.677907i) q^{7} +(2.03460 + 0.842759i) q^{9} +(0.234463 + 1.17872i) q^{11} +(0.154344 + 0.230992i) q^{13} +(6.77078 - 6.77078i) q^{15} +(1.16542 + 1.16542i) q^{17} +(2.64509 - 1.76739i) q^{19} +(-3.96278 + 0.788246i) q^{21} +(-1.18934 + 2.87131i) q^{23} +(-4.83120 - 11.6635i) q^{25} +(-1.51292 - 1.01090i) q^{27} +(0.141213 - 0.709928i) q^{29} +7.01473i q^{31} +2.74115i q^{33} +(-1.45086 + 7.29396i) q^{35} +(-7.22008 - 4.82430i) q^{37} +(0.242485 + 0.585411i) q^{39} +(-0.152591 + 0.368387i) q^{41} +(4.98611 - 0.991798i) q^{43} +(7.68722 - 5.13643i) q^{45} +(2.16092 + 2.16092i) q^{47} +(-2.73080 + 2.73080i) q^{49} +(2.08849 + 3.12564i) q^{51} +(1.84431 + 9.27195i) q^{53} +(4.66135 + 1.93079i) q^{55} +(6.70353 - 2.77669i) q^{57} +(-3.85360 + 5.76732i) q^{59} +(9.69397 + 1.92825i) q^{61} -3.90117 q^{63} +1.16630 q^{65} +(-7.14707 - 1.42164i) q^{67} +(-3.93821 + 5.89395i) q^{69} +(-4.28878 + 1.77647i) q^{71} +(-3.39319 - 1.40550i) q^{73} +(-5.61753 - 28.2413i) q^{75} +(-1.18279 - 1.77017i) q^{77} +(-1.54634 + 1.54634i) q^{79} +(-7.60625 - 7.60625i) q^{81} +(9.93110 - 6.63575i) q^{83} +(6.78626 - 1.34987i) q^{85} +(0.631793 - 1.52528i) q^{87} +(3.81437 + 9.20870i) q^{89} +(-0.409193 - 0.273414i) q^{91} +(-3.12134 + 15.6921i) q^{93} -13.3552i q^{95} +9.29602i q^{97} +(-0.516342 + 2.59583i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9	\( 56 q + 8 q^{3} + 8 q^{5} - 8 q^{7} - 8 q^{9} + 8 q^{11} + 8 q^{13} - 8 q^{15} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 8 q^{23} - 8 q^{25} + 8 q^{27} + 8 q^{29} + 8 q^{35} + 8 q^{37} - 8 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 8 q^{47} - 8 q^{49} - 24 q^{51} + 8 q^{53} + 56 q^{55} - 8 q^{57} - 56 q^{59} + 8 q^{61} + 64 q^{63} - 16 q^{65} - 72 q^{67} + 8 q^{69} + 56 q^{71} - 8 q^{73} - 56 q^{75} + 8 q^{77} + 24 q^{79} - 8 q^{81} + 8 q^{83} + 8 q^{85} - 8 q^{87} - 8 q^{89} + 8 q^{91} - 16 q^{93} - 16 q^{99}+O(q^{100}) \) 56 * q + 8 * q^3 + 8 * q^5 - 8 * q^7 - 8 * q^9 + 8 * q^11 + 8 * q^13 - 8 * q^15 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 8 * q^23 - 8 * q^25 + 8 * q^27 + 8 * q^29 + 8 * q^35 + 8 * q^37 - 8 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 8 * q^47 - 8 * q^49 - 24 * q^51 + 8 * q^53 + 56 * q^55 - 8 * q^57 - 56 * q^59 + 8 * q^61 + 64 * q^63 - 16 * q^65 - 72 * q^67 + 8 * q^69 + 56 * q^71 - 8 * q^73 - 56 * q^75 + 8 * q^77 + 24 * q^79 - 8 * q^81 + 8 * q^83 + 8 * q^85 - 8 * q^87 - 8 * q^89 + 8 * q^91 - 16 * q^93 - 16 * q^99

Introduction

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Database

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