LMFDB - Embedded newform 476.2.bl.a.129.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(5,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 40, 15]))

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

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

chi := DirichletCharacter("476.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bl (of order $48$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.80087913621$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$12$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			129.1
Character	$\chi$	$=$	476.129
Dual form			476.2.bl.a.369.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29009 - 2.61603i) q^{3} +(-2.77132 + 2.43038i) q^{5} +(-2.19078 - 1.48340i) q^{7} +(-3.35303 + 4.36975i) q^{9} +O(q^{10})$	\(q+(-1.29009 - 2.61603i) q^{3} +(-2.77132 + 2.43038i) q^{5} +(-2.19078 - 1.48340i) q^{7} +(-3.35303 + 4.36975i) q^{9} +(3.07855 - 0.201779i) q^{11} +(2.89190 + 2.89190i) q^{13} +(9.93321 + 4.11447i) q^{15} +(1.63210 + 3.78632i) q^{17} +(-0.417929 - 3.17449i) q^{19} +(-1.05434 + 7.64487i) q^{21} +(3.87692 + 1.91189i) q^{23} +(1.12083 - 8.51352i) q^{25} +(7.17473 + 1.42714i) q^{27} +(-0.411702 - 2.06976i) q^{29} +(-9.89415 + 4.87925i) q^{31} +(-4.49944 - 7.79327i) q^{33} +(9.67659 - 1.21344i) q^{35} +(-0.356568 + 5.44018i) q^{37} +(3.83451 - 11.2961i) q^{39} +(-0.189073 + 0.950533i) q^{41} +(2.99706 + 7.23555i) q^{43} +(-1.32785 - 20.2591i) q^{45} +(-2.06545 + 7.70838i) q^{47} +(2.59903 + 6.49962i) q^{49} +(7.79960 - 9.15431i) q^{51} +(7.82303 + 10.1952i) q^{53} +(-8.04124 + 8.04124i) q^{55} +(-7.76540 + 5.18867i) q^{57} +(2.69499 + 0.354802i) q^{59} +(-2.27291 - 6.69579i) q^{61} +(13.8279 - 4.59926i) q^{63} +(-15.0428 - 0.985958i) q^{65} +(-3.43221 - 1.98159i) q^{67} -12.6087i q^{69} +(-3.51089 - 2.34590i) q^{71} +(2.50005 + 0.848654i) q^{73} +(-23.7176 + 8.05105i) q^{75} +(-7.04373 - 4.12467i) q^{77} +(-4.03454 + 8.18124i) q^{79} +(-1.24587 - 4.64965i) q^{81} +(1.17681 - 2.84107i) q^{83} +(-13.7253 - 6.52649i) q^{85} +(-4.88344 + 3.74720i) q^{87} +(6.34804 + 1.70095i) q^{89} +(-2.04566 - 10.6254i) q^{91} +(25.5286 + 19.5888i) q^{93} +(8.87343 + 7.78179i) q^{95} +(-17.5664 + 3.49418i) q^{97} +(-9.44073 + 14.1290i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) $ 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/476\mathbb{Z}\right)^\times$.

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.29009	−	2.61603i	−0.744831	−	1.51037i	−0.856232	−	0.516592i	$-0.827200\pi$
$3$	−1.29009	−	2.61603i	−0.744831	−	1.51037i	0.111401	−	0.993776i	$-0.464466\pi$
$4$		0			0
$5$	−2.77132	+	2.43038i	−1.23937	+	1.08690i	−0.246325	+	0.969187i	$0.579223\pi$
$5$	−2.77132	+	2.43038i	−1.23937	+	1.08690i	−0.993048	+	0.117713i	$0.962444\pi$
$6$		0			0
$7$	−2.19078	−	1.48340i	−0.828037	−	0.560674i
$7$	−2.19078	−	1.48340i	−0.828037	−	0.560674i
$8$		0			0
$9$	−3.35303	+	4.36975i	−1.11768	+	1.45658i
$10$		0			0
$11$	3.07855	−	0.201779i	0.928216	−	0.0608385i	0.406210	−	0.913780i	$-0.366850\pi$
$11$	3.07855	−	0.201779i	0.928216	−	0.0608385i	0.522007	+	0.852941i	$0.325184\pi$
$12$		0			0
$13$	2.89190	+	2.89190i	0.802069	+	0.802069i	0.983419	−	0.181350i	$-0.0580466\pi$
$13$	2.89190	+	2.89190i	0.802069	+	0.802069i	−0.181350	+	0.983419i	$0.558047\pi$
$14$		0			0
$15$	9.93321	+	4.11447i	2.56474	+	1.06235i
$16$		0			0
$17$	1.63210	+	3.78632i	0.395842	+	0.918318i
$17$	1.63210	+	3.78632i	0.395842	+	0.918318i
$18$		0			0
$19$	−0.417929	−	3.17449i	−0.0958795	−	0.728277i	−0.970093	−	0.242735i	$-0.921956\pi$
$19$	−0.417929	−	3.17449i	−0.0958795	−	0.728277i	0.874213	−	0.485542i	$-0.161378\pi$
$20$		0			0
$21$	−1.05434	+	7.64487i	−0.230077	+	1.66825i
$22$		0			0
$23$	3.87692	+	1.91189i	0.808395	+	0.398656i	0.799023	−	0.601300i	$-0.205350\pi$
$23$	3.87692	+	1.91189i	0.808395	+	0.398656i	0.00937121	+	0.999956i	$0.497017\pi$
$24$		0			0
$25$	1.12083	−	8.51352i	0.224165	−	1.70270i
$26$		0			0
$27$	7.17473	+	1.42714i	1.38078	+	0.274654i
$28$		0			0
$29$	−0.411702	−	2.06976i	−0.0764511	−	0.384346i	−1.00000		0.000864038i	$-0.999725\pi$
$29$	−0.411702	−	2.06976i	−0.0764511	−	0.384346i	0.923549	−	0.383482i	$-0.125275\pi$
$30$		0			0
$31$	−9.89415	+	4.87925i	−1.77704	+	0.876340i	−0.828300	+	0.560285i	$0.810692\pi$
$31$	−9.89415	+	4.87925i	−1.77704	+	0.876340i	−0.948741	+	0.316055i	$0.897642\pi$
$32$		0			0
$33$	−4.49944	−	7.79327i	−0.783253	−	1.35663i
$34$		0			0
$35$	9.67659	−	1.21344i	1.63564	−	0.205110i
$36$		0			0
$37$	−0.356568	+	5.44018i	−0.0586195	+	0.894360i	0.862740	+	0.505648i	$0.168747\pi$
$37$	−0.356568	+	5.44018i	−0.0586195	+	0.894360i	−0.921359	+	0.388712i	$0.872920\pi$
$38$		0			0
$39$	3.83451	−	11.2961i	0.614013	−	1.80882i
$40$		0			0
$41$	−0.189073	+	0.950533i	−0.0295282	+	0.148448i	−0.992737	−	0.120307i	$-0.961612\pi$
$41$	−0.189073	+	0.950533i	−0.0295282	+	0.148448i	0.963209	+	0.268755i	$0.0866122\pi$
$42$		0			0
$43$	2.99706	+	7.23555i	0.457048	+	1.10341i	0.969587	+	0.244747i	$0.0787050\pi$
$43$	2.99706	+	7.23555i	0.457048	+	1.10341i	−0.512539	+	0.858664i	$0.671295\pi$
$44$		0			0
$45$	−1.32785	−	20.2591i	−0.197945	−	3.02005i
$46$		0			0
$47$	−2.06545	+	7.70838i	−0.301278	+	1.12438i	0.634825	+	0.772656i	$0.281072\pi$
$47$	−2.06545	+	7.70838i	−0.301278	+	1.12438i	−0.936103	+	0.351727i	$0.885594\pi$
$48$		0			0
$49$	2.59903	+	6.49962i	0.371289	+	0.928517i
$50$		0			0
$51$	7.79960	−	9.15431i	1.09216	−	1.28186i
$52$		0			0
$53$	7.82303	+	10.1952i	1.07458	+	1.40041i	0.910275	+	0.414004i	$0.135870\pi$
$53$	7.82303	+	10.1952i	1.07458	+	1.40041i	0.164300	+	0.986410i	$0.447463\pi$
$54$		0			0
$55$	−8.04124	+	8.04124i	−1.08428	+	1.08428i
$56$		0			0
$57$	−7.76540	+	5.18867i	−1.02855	+	0.687256i
$58$		0			0
$59$	2.69499	+	0.354802i	0.350858	+	0.0461913i	0.303896	−	0.952705i	$-0.401713\pi$
$59$	2.69499	+	0.354802i	0.350858	+	0.0461913i	0.0469623	+	0.998897i	$0.485046\pi$
$60$		0			0
$61$	−2.27291	−	6.69579i	−0.291017	−	0.857308i	−0.989862	−	0.142035i	$-0.954635\pi$
$61$	−2.27291	−	6.69579i	−0.291017	−	0.857308i	0.698845	−	0.715273i	$-0.253698\pi$
$62$		0			0
$63$	13.8279	−	4.59926i	1.74215	−	0.579453i
$64$		0			0
$65$	−15.0428	−	0.985958i	−1.86583	−	0.122293i
$66$		0			0
$67$	−3.43221	−	1.98159i	−0.419311	−	0.242090i	0.275471	−	0.961309i	$-0.411166\pi$
$67$	−3.43221	−	1.98159i	−0.419311	−	0.242090i	−0.694783	+	0.719220i	$0.744499\pi$
$68$		0			0
$69$		−	12.6087i		−	1.51790i
$70$		0			0
$71$	−3.51089	−	2.34590i	−0.416666	−	0.278407i	0.329515	−	0.944150i	$-0.393115\pi$
$71$	−3.51089	−	2.34590i	−0.416666	−	0.278407i	−0.746181	+	0.665743i	$0.768115\pi$
$72$		0			0
$73$	2.50005	+	0.848654i	0.292609	+	0.0993274i	0.463884	−	0.885896i	$-0.346455\pi$
$73$	2.50005	+	0.848654i	0.292609	+	0.0993274i	−0.171275	+	0.985223i	$0.554789\pi$
$74$		0			0
$75$	−23.7176	+	8.05105i	−2.73868	+	0.929655i
$76$		0			0
$77$	−7.04373	−	4.12467i	−0.802708	−	0.470050i
$78$		0			0
$79$	−4.03454	+	8.18124i	−0.453921	+	0.920462i	0.542824	+	0.839847i	$0.317355\pi$
$79$	−4.03454	+	8.18124i	−0.453921	+	0.920462i	−0.996745	+	0.0806150i	$0.974312\pi$
$80$		0			0
$81$	−1.24587	−	4.64965i	−0.138430	−	0.516628i
$82$		0			0
$83$	1.17681	−	2.84107i	0.129171	−	0.311848i	−0.846041	−	0.533118i	$-0.821020\pi$
$83$	1.17681	−	2.84107i	0.129171	−	0.311848i	0.975213	+	0.221270i	$0.0710203\pi$
$84$		0			0
$85$	−13.7253	−	6.52649i	−1.48872	−	0.707897i
$86$		0			0
$87$	−4.88344	+	3.74720i	−0.523560	+	0.401742i
$88$		0			0
$89$	6.34804	+	1.70095i	0.672890	+	0.180300i	0.579057	−	0.815287i	$-0.303421\pi$
$89$	6.34804	+	1.70095i	0.672890	+	0.180300i	0.0938339	+	0.995588i	$0.470088\pi$
$90$		0			0
$91$	−2.04566	−	10.6254i	−0.214443	−	1.11384i
$92$		0			0
$93$	25.5286	+	19.5888i	2.64719	+	2.03126i
$94$		0			0
$95$	8.87343	+	7.78179i	0.910395	+	0.798395i
$96$		0			0
$97$	−17.5664	+	3.49418i	−1.78360	+	0.354780i	−0.972998	−	0.230815i	$-0.925861\pi$
$97$	−17.5664	+	3.49418i	−1.78360	+	0.354780i	−0.810603	+	0.585596i	$0.800861\pi$
$98$		0			0
$99$	−9.44073	+	14.1290i	−0.948829	+	1.42002i
$100$		0			0
$101$	−2.95795	+	5.12331i	−0.294327	+	0.509789i	−0.974828	−	0.222958i	$-0.928429\pi$
$101$	−2.95795	+	5.12331i	−0.294327	+	0.509789i	0.680501	+	0.732747i	$0.261762\pi$
$102$		0			0
$103$	−7.06599	+	4.07955i	−0.696232	+	0.401970i	−0.805943	−	0.591994i	$-0.798341\pi$
$103$	−7.06599	+	4.07955i	−0.696232	+	0.401970i	0.109710	+	0.993964i	$0.465008\pi$
$104$		0			0
$105$	−15.6580	−	23.7488i	−1.52807	−	2.31765i
$106$		0			0
$107$	4.16349	+	4.74755i	0.402500	+	0.458963i	0.917212	−	0.398400i	$-0.130434\pi$
$107$	4.16349	+	4.74755i	0.402500	+	0.458963i	−0.514712	+	0.857363i	$0.672101\pi$
$108$		0			0
$109$	12.0932	−	13.7897i	1.15832	−	1.32081i	0.219814	−	0.975542i	$-0.429455\pi$
$109$	12.0932	−	13.7897i	1.15832	−	1.32081i	0.938504	−	0.345268i	$-0.112212\pi$
$110$		0			0
$111$	14.6917	−	6.08550i	1.39447	−	0.577610i
$112$		0			0
$113$	−6.74025	−	10.0875i	−0.634070	−	0.948953i	−0.999834	−	0.0182448i	$-0.994192\pi$
$113$	−6.74025	−	10.0875i	−0.634070	−	0.948953i	0.365764	−	0.930708i	$-0.380808\pi$
$114$		0			0
$115$	−15.3908	+	4.12396i	−1.43520	+	0.384561i
$116$		0			0
$117$	−22.3335	+	2.94026i	−2.06473	+	0.271827i
$118$		0			0
$119$	2.04108	−	10.7161i	0.187105	−	0.982340i
$120$		0			0
$121$	−1.46917	+	0.193419i	−0.133561	+	0.0175836i
$122$		0			0
$123$	2.73055	−	0.731648i	0.246205	−	0.0659704i
$124$		0			0
$125$	7.34565	+	10.9935i	0.657015	+	0.983293i
$126$		0			0
$127$	9.17696	−	3.80122i	0.814324	−	0.337304i	0.0636460	−	0.997973i	$-0.479727\pi$
$127$	9.17696	−	3.80122i	0.814324	−	0.337304i	0.750678	+	0.660669i	$0.229727\pi$
$128$		0			0
$129$	15.0620	−	17.1749i	1.32613	−	1.51217i
$130$		0			0
$131$	0.510660	+	0.582296i	0.0446166	+	0.0508754i	0.773718	−	0.633531i	$-0.218395\pi$
$131$	0.510660	+	0.582296i	0.0446166	+	0.0508754i	−0.729101	+	0.684406i	$0.760062\pi$
$132$		0			0
$133$	−3.79345	+	7.57455i	−0.328934	+	0.656797i
$134$		0			0
$135$	−23.3520	+	13.4823i	−2.00982	+	1.16037i
$136$		0			0
$137$	3.94413	−	6.83143i	0.336970	−	0.583649i	−0.646892	−	0.762582i	$-0.723931\pi$
$137$	3.94413	−	6.83143i	0.336970	−	0.583649i	0.983861	+	0.178933i	$0.0572647\pi$
$138$		0			0
$139$	7.68161	−	11.4963i	0.651546	−	0.975107i	−0.347750	−	0.937587i	$-0.613054\pi$
$139$	7.68161	−	11.4963i	0.651546	−	0.975107i	0.999296	−	0.0375197i	$-0.0119457\pi$
$140$		0			0
$141$	22.8300	−	4.54117i	1.92263	−	0.382435i
$142$		0			0
$143$	9.48637	+	8.31932i	0.793290	+	0.695697i
$144$		0			0
$145$	6.17128	+	4.73539i	0.512497	+	0.393253i
$146$		0			0
$147$	13.6503	−	15.1842i	1.12585	−	1.25237i
$148$		0			0
$149$	−8.75337	−	2.34546i	−0.717104	−	0.192148i	−0.118225	−	0.992987i	$-0.537720\pi$
$149$	−8.75337	−	2.34546i	−0.717104	−	0.192148i	−0.598879	+	0.800839i	$0.704387\pi$
$150$		0			0
$151$	−7.20428	+	5.52804i	−0.586276	+	0.449866i	−0.858820	−	0.512278i	$-0.828802\pi$
$151$	−7.20428	+	5.52804i	−0.586276	+	0.449866i	0.272544	+	0.962143i	$0.412135\pi$
$152$		0			0
$153$	−22.0178	−	5.56378i	−1.78003	−	0.449805i
$154$		0			0
$155$	15.5614	−	37.5685i	1.24992	−	3.01758i
$156$		0			0
$157$	3.20232	+	11.9512i	0.255573	+	0.953813i	0.967771	+	0.251833i	$0.0810335\pi$
$157$	3.20232	+	11.9512i	0.255573	+	0.953813i	−0.712197	+	0.701979i	$0.752300\pi$
$158$		0			0
$159$	16.5785	−	33.6179i	1.31476	−	2.66608i
$160$		0			0
$161$	−5.65738	−	9.93957i	−0.445864	−	0.783348i
$162$		0			0
$163$	1.21231	−	0.411523i	0.0949553	−	0.0322330i	−0.273558	−	0.961856i	$-0.588200\pi$
$163$	1.21231	−	0.411523i	0.0949553	−	0.0322330i	0.368513	+	0.929623i	$0.379867\pi$
$164$		0			0
$165$	31.4100	+	10.6623i	2.44527	+	0.830057i
$166$		0			0
$167$	−2.15150	−	1.43758i	−0.166488	−	0.111244i	0.469535	−	0.882914i	$-0.344422\pi$
$167$	−2.15150	−	1.43758i	−0.166488	−	0.111244i	−0.636023	+	0.771670i	$0.719422\pi$
$168$		0			0
$169$			3.72617i			0.286629i
$170$		0			0
$171$	15.2730	+	8.81789i	1.16796	+	0.674321i
$172$		0			0
$173$	21.9832	+	1.44086i	1.67135	+	0.109546i	0.871419	−	0.490540i	$-0.163201\pi$
$173$	21.9832	+	1.44086i	1.67135	+	0.109546i	0.799935	+	0.600087i	$0.204867\pi$
$174$		0			0
$175$	−15.0845	+	16.9886i	−1.14028	+	1.28422i
$176$		0			0
$177$	−2.54859	−	7.50791i	−0.191564	−	0.564329i
$178$		0			0
$179$	−14.0060	−	1.84392i	−1.04686	−	0.137821i	−0.412576	−	0.910923i	$-0.635371\pi$
$179$	−14.0060	−	1.84392i	−1.04686	−	0.137821i	−0.634282	+	0.773102i	$0.718704\pi$
$180$		0			0
$181$	−1.57708	+	1.05377i	−0.117224	+	0.0783263i	−0.612800	−	0.790238i	$-0.709957\pi$
$181$	−1.57708	+	1.05377i	−0.117224	+	0.0783263i	0.495576	+	0.868564i	$0.334957\pi$
$182$		0			0
$183$	−14.5842	+	14.5842i	−1.07809	+	1.07809i
$184$		0			0
$185$	−12.2336	−	15.9431i	−0.899429	−	1.17216i
$186$		0			0
$187$	5.78849	+	11.3270i	0.423296	+	0.828316i
$188$		0			0
$189$	−13.6012	−	13.7696i	−0.989343	−	1.00159i
$190$		0			0
$191$	−3.08272	+	11.5049i	−0.223058	+	0.832464i	0.760115	+	0.649788i	$0.225142\pi$
$191$	−3.08272	+	11.5049i	−0.223058	+	0.832464i	−0.983173	+	0.182676i	$0.941524\pi$
$192$		0			0
$193$	0.753536	+	11.4967i	0.0542407	+	0.827553i	0.935146	+	0.354261i	$0.115268\pi$
$193$	0.753536	+	11.4967i	0.0542407	+	0.827553i	−0.880906	+	0.473292i	$0.843066\pi$
$194$		0			0
$195$	16.8272	+	40.6245i	1.20502	+	2.90918i
$196$		0			0
$197$	−1.91817	+	9.64328i	−0.136664	+	0.687055i	0.850324	+	0.526260i	$0.176406\pi$
$197$	−1.91817	+	9.64328i	−0.136664	+	0.687055i	−0.986988	+	0.160796i	$0.948594\pi$
$198$		0			0
$199$	−5.73101	+	16.8830i	−0.406261	+	1.19681i	0.530757	+	0.847524i	$0.321908\pi$
$199$	−5.73101	+	16.8830i	−0.406261	+	1.19681i	−0.937018	+	0.349282i	$0.886426\pi$
$200$		0			0
$201$	−0.756057	+	11.5352i	−0.0533281	+	0.813630i
$202$		0			0
$203$	−2.16835	+	5.14512i	−0.152188	+	0.361116i
$204$		0			0
$205$	−1.78618	−	3.09375i	−0.124752	−	0.216077i
$206$		0			0
$207$	−21.3539	+	10.5306i	−1.48420	+	0.731926i
$208$		0			0
$209$	−1.92716	−	9.68847i	−0.133304	−	0.670165i
$210$		0			0
$211$	−4.54013	−	0.903089i	−0.312556	−	0.0621712i	0.0363200	−	0.999340i	$-0.488436\pi$
$211$	−4.54013	−	0.903089i	−0.312556	−	0.0621712i	−0.348876	+	0.937169i	$0.613436\pi$
$212$		0			0
$213$	−1.60761	+	12.2110i	−0.110152	+	0.836685i
$214$		0			0
$215$	−25.8910	−	12.7680i	−1.76575	−	0.870772i
$216$		0			0
$217$	28.9138	+	3.98765i	1.96280	+	0.270699i
$218$		0			0
$219$	−1.00517	−	7.63506i	−0.0679234	−	0.515929i
$220$		0			0
$221$	−6.22980	+	15.6695i	−0.419062	+	1.05405i
$222$		0			0
$223$	−8.00038	−	3.31387i	−0.535745	−	0.221913i	0.0983723	−	0.995150i	$-0.468636\pi$
$223$	−8.00038	−	3.31387i	−0.535745	−	0.221913i	−0.634117	+	0.773237i	$0.718636\pi$
$224$		0			0
$225$	33.4438	+	33.4438i	2.22959	+	2.22959i
$226$		0			0
$227$	23.8295	−	1.56187i	1.58162	−	0.103665i	0.750923	−	0.660390i	$-0.229609\pi$
$227$	23.8295	−	1.56187i	1.58162	−	0.103665i	0.830697	+	0.556725i	$0.187942\pi$
$228$		0			0
$229$	6.24233	−	8.13517i	0.412505	−	0.537587i	−0.540179	−	0.841550i	$-0.681643\pi$
$229$	6.24233	−	8.13517i	0.412505	−	0.537587i	0.952684	+	0.303963i	$0.0983101\pi$
$230$		0			0
$231$	−1.70327	+	23.7478i	−0.112067	+	1.56249i
$232$		0			0
$233$	−8.98933	+	7.88343i	−0.588910	+	0.516461i	−0.901130	−	0.433550i	$-0.857261\pi$
$233$	−8.98933	+	7.88343i	−0.588910	+	0.516461i	0.312219	+	0.950010i	$0.398928\pi$
$234$		0			0
$235$	−13.0103	−	26.3823i	−0.848698	−	1.72099i
$236$		0			0
$237$	26.6073			1.72833
$238$		0			0
$239$	−2.36368			−0.152894			−0.0764468	−	0.997074i	$-0.524358\pi$
$239$	−2.36368			−0.152894			−0.0764468	+	0.997074i	$0.524358\pi$
$240$		0			0
$241$	−1.20184	−	2.43709i	−0.0774173	−	0.156987i	0.854723	−	0.519085i	$-0.173727\pi$
$241$	−1.20184	−	2.43709i	−0.0774173	−	0.156987i	−0.932140	+	0.362098i	$0.882061\pi$
$242$		0			0
$243$	5.94342	−	5.21224i	0.381270	−	0.334365i
$244$		0			0
$245$	−22.9993	−	11.6959i	−1.46937	−	0.747224i
$246$		0			0
$247$	7.97169	−	10.3889i	0.507226	−	0.661030i
$248$		0			0
$249$	−8.95051	+	0.586647i	−0.567215	+	0.0371773i
$250$		0			0
$251$	6.48745	+	6.48745i	0.409484	+	0.409484i	0.881559	−	0.472075i	$-0.156495\pi$
$251$	6.48745	+	6.48745i	0.409484	+	0.409484i	−0.472075	+	0.881559i	$0.656495\pi$
$252$		0			0
$253$	12.3211	+	5.10355i	0.774619	+	0.320858i
$254$		0			0
$255$	0.633272	+	44.3256i	0.0396570	+	2.77577i
$256$		0			0
$257$	3.27733	+	24.8938i	0.204434	+	1.55283i	0.718772	+	0.695245i	$0.244704\pi$
$257$	3.27733	+	24.8938i	0.204434	+	1.55283i	−0.514338	+	0.857587i	$0.671962\pi$
$258$		0			0
$259$	8.85115	−	11.3893i	0.549983	−	0.707697i
$260$		0			0
$261$	10.4248	+	5.14094i	0.645279	+	0.318216i
$262$		0			0
$263$	3.19616	−	24.2772i	0.197084	−	1.49700i	−0.551621	−	0.834095i	$-0.685990\pi$
$263$	3.19616	−	24.2772i	0.197084	−	1.49700i	0.748704	−	0.662904i	$-0.230676\pi$
$264$		0			0
$265$	−46.4583	−	9.24113i	−2.85391	−	0.567678i
$266$		0			0
$267$	−3.73976	−	18.8010i	−0.228870	−	1.15061i
$268$		0			0
$269$	1.08175	−	0.533462i	0.0659556	−	0.0325257i	−0.409012	−	0.912529i	$-0.634127\pi$
$269$	1.08175	−	0.533462i	0.0659556	−	0.0325257i	0.474967	+	0.880003i	$0.342460\pi$
$270$		0			0
$271$	−7.73722	−	13.4013i	−0.470002	−	0.814068i	0.529409	−	0.848367i	$-0.322414\pi$
$271$	−7.73722	−	13.4013i	−0.470002	−	0.814068i	−0.999412	+	0.0342986i	$0.989080\pi$
$272$		0			0
$273$	−25.1573	+	19.0591i	−1.52259	+	1.15351i
$274$		0			0
$275$	1.73267	−	26.4354i	0.104484	−	1.59412i
$276$		0			0
$277$	−7.68302	+	22.6335i	−0.461628	+	1.35991i	0.428228	+	0.903671i	$0.359138\pi$
$277$	−7.68302	+	22.6335i	−0.461628	+	1.35991i	−0.889856	+	0.456242i	$0.849195\pi$
$278$		0			0
$279$	11.8542	−	59.5952i	0.709694	−	3.56787i
$280$		0			0
$281$	−4.04622	−	9.76844i	−0.241377	−	0.582736i	0.756043	−	0.654522i	$-0.227130\pi$
$281$	−4.04622	−	9.76844i	−0.241377	−	0.582736i	−0.997420	+	0.0717858i	$0.977130\pi$
$282$		0			0
$283$	−0.469497	−	7.16314i	−0.0279087	−	0.425805i	−0.988836	−	0.149005i	$-0.952393\pi$
$283$	−0.469497	−	7.16314i	−0.0279087	−	0.425805i	0.960928	−	0.276799i	$-0.0892738\pi$
$284$		0			0
$285$	8.90995	−	33.2524i	0.527780	−	1.96970i
$286$		0			0
$287$	1.82424	−	1.80194i	0.107682	−	0.106365i
$288$		0			0
$289$	−11.6725	+	12.3593i	−0.686618	+	0.727019i
$290$		0			0
$291$	31.8031	+	41.4466i	1.86433	+	2.42964i
$292$		0			0
$293$	7.99293	−	7.99293i	0.466952	−	0.466952i	−0.433974	−	0.900925i	$-0.642889\pi$
$293$	7.99293	−	7.99293i	0.466952	−	0.466952i	0.900925	+	0.433974i	$0.142889\pi$
$294$		0			0
$295$	−8.33099	+	5.56659i	−0.485049	+	0.324099i
$296$		0			0
$297$	22.3757	+	2.94582i	1.29837	+	0.170934i
$298$		0			0
$299$	5.68269	+	16.7407i	0.328638	+	0.968138i
$300$		0			0
$301$	4.16734	−	20.2974i	0.240202	−	1.16992i
$302$		0			0
$303$	17.2188	+	1.12858i	0.989192	+	0.0648351i
$304$		0			0
$305$	22.5723	+	13.0321i	1.29249	+	0.746218i
$306$		0			0
$307$		−	23.6696i		−	1.35090i	−0.737407	−	0.675448i	$-0.763950\pi$
$307$		−	23.6696i		−	1.35090i	0.737407	−	0.675448i	$-0.236050\pi$
$308$		0			0
$309$	19.7880	+	13.2219i	1.12570	+	0.752167i
$310$		0			0
$311$	25.6398	+	8.70355i	1.45390	+	0.493533i	0.932935	−	0.360045i	$-0.117239\pi$
$311$	25.6398	+	8.70355i	1.45390	+	0.493533i	0.520966	+	0.853578i	$0.325572\pi$
$312$		0			0
$313$	−4.39490	+	1.49187i	−0.248415	+	0.0843254i	−0.442870	−	0.896586i	$-0.646040\pi$
$313$	−4.39490	+	1.49187i	−0.248415	+	0.0843254i	0.194455	+	0.980911i	$0.437706\pi$
$314$		0			0
$315$	−27.1434	+	46.3530i	−1.52936	+	2.61170i
$316$		0			0
$317$	−12.5925	+	25.5351i	−0.707266	+	1.43419i	0.185025	+	0.982734i	$0.440763\pi$
$317$	−12.5925	+	25.5351i	−0.707266	+	1.43419i	−0.892291	+	0.451460i	$0.850903\pi$
$318$		0			0
$319$	−1.68508	−	6.28879i	−0.0943462	−	0.352105i
$320$		0			0
$321$	7.04850	−	17.0166i	0.393409	−	0.949773i
$322$		0			0
$323$	11.3375	−	6.76349i	0.630837	−	0.376331i
$324$		0			0
$325$	27.8616	−	21.3789i	1.54548	−	1.18589i
$326$		0			0
$327$	−51.6755	−	13.8464i	−2.85766	−	0.765708i
$328$		0			0
$329$	15.9596	−	13.8235i	0.879881	−	0.762112i
$330$		0			0
$331$	1.46073	+	1.12085i	0.0802887	+	0.0616077i	0.648126	−	0.761533i	$-0.275553\pi$
$331$	1.46073	+	1.12085i	0.0802887	+	0.0616077i	−0.567837	+	0.823141i	$0.692220\pi$
$332$		0			0
$333$	−22.5767	−	19.7992i	−1.23719	−	1.08499i
$334$		0			0
$335$	14.3278	−	2.84997i	0.782810	−	0.155711i
$336$		0			0
$337$	−13.4661	+	20.1534i	−0.733545	+	1.09783i	0.257756	+	0.966210i	$0.417017\pi$
$337$	−13.4661	+	20.1534i	−0.733545	+	1.09783i	−0.991301	+	0.131617i	$0.957983\pi$
$338$		0			0
$339$	−17.6937	+	30.6465i	−0.960992	+	1.66449i
$340$		0			0
$341$	−29.4750	+	17.0174i	−1.59616	+	0.921545i
$342$		0			0
$343$	3.94767	−	18.0946i	0.213154	−	0.977019i
$344$		0			0
$345$	30.6439	+	34.9427i	1.64981	+	1.88125i
$346$		0			0
$347$	−4.83311	+	5.51110i	−0.259455	+	0.295852i	−0.866871	−	0.498532i	$-0.833873\pi$
$347$	−4.83311	+	5.51110i	−0.259455	+	0.295852i	0.607416	+	0.794384i	$0.292206\pi$
$348$		0			0
$349$	8.96620	−	3.71392i	0.479950	−	0.198802i	−0.129574	−	0.991570i	$-0.541361\pi$
$349$	8.96620	−	3.71392i	0.479950	−	0.198802i	0.609523	+	0.792768i	$0.291361\pi$
$350$		0			0
$351$	16.6214	+	24.8758i	0.887187	+	1.32777i
$352$		0			0
$353$	−5.42429	+	1.45343i	−0.288706	+	0.0773585i	−0.400265	−	0.916399i	$-0.631082\pi$
$353$	−5.42429	+	1.45343i	−0.288706	+	0.0773585i	0.111560	+	0.993758i	$0.464415\pi$
$354$		0			0
$355$	15.4312	−	2.03156i	0.819005	−	0.107824i
$356$		0			0
$357$	−30.6667	+	8.48510i	−1.62306	+	0.449079i
$358$		0			0
$359$	1.59123	−	0.209490i	0.0839820	−	0.0110564i	−0.0884181	−	0.996083i	$-0.528181\pi$
$359$	1.59123	−	0.209490i	0.0839820	−	0.0110564i	0.172400	+	0.985027i	$0.444848\pi$
$360$		0			0
$361$	8.44990	−	2.26414i	0.444732	−	0.119165i
$362$		0			0
$363$	2.40134	+	3.59386i	0.126038	+	0.188629i
$364$		0			0
$365$	−8.99100	+	3.72420i	−0.470611	+	0.194933i
$366$		0			0
$367$	22.5065	−	25.6638i	1.17483	−	1.33964i	0.245941	−	0.969285i	$-0.420903\pi$
$367$	22.5065	−	25.6638i	1.17483	−	1.33964i	0.928891	−	0.370354i	$-0.120764\pi$
$368$		0			0
$369$	−3.51963	−	4.01336i	−0.183224	−	0.208927i
$370$		0			0
$371$	−2.01497	−	33.9401i	−0.104612	−	1.76208i
$372$		0			0
$373$	−3.68306	+	2.12641i	−0.190701	+	0.110102i	−0.592311	−	0.805710i	$-0.701784\pi$
$373$	−3.68306	+	2.12641i	−0.190701	+	0.110102i	0.401609	+	0.915811i	$0.368451\pi$
$374$		0			0
$375$	19.2830	−	33.3991i	0.995768	−	1.72472i
$376$		0			0
$377$	4.79495	−	7.17615i	0.246953	−	0.369591i
$378$		0			0
$379$	−8.51582	+	1.69390i	−0.437428	+	0.0870099i	−0.408892	−	0.912583i	$-0.634085\pi$
$379$	−8.51582	+	1.69390i	−0.437428	+	0.0870099i	−0.0285365	+	0.999593i	$0.509085\pi$
$380$		0			0
$381$	−21.7832	−	19.1033i	−1.11599	−	0.978694i
$382$		0			0
$383$	24.7414	+	18.9847i	1.26422	+	0.970073i	0.999984	+	0.00561648i	$0.00178779\pi$
$383$	24.7414	+	18.9847i	1.26422	+	0.970073i	0.264240	+	0.964457i	$0.414879\pi$
$384$		0			0
$385$	29.5450	−	5.68817i	1.50575	−	0.289896i
$386$		0			0
$387$	−41.6668	−	11.1646i	−2.11804	−	0.567528i
$388$		0			0
$389$	7.08974	−	5.44015i	0.359464	−	0.275827i	−0.413202	−	0.910640i	$-0.635590\pi$
$389$	7.08974	−	5.44015i	0.359464	−	0.275827i	0.772666	+	0.634813i	$0.218923\pi$
$390$		0			0
$391$	−0.911498	+	17.7997i	−0.0460964	+	0.900169i
$392$		0			0
$393$	0.864511	−	2.08711i	0.0436088	−	0.105281i
$394$		0			0
$395$	−8.70254	−	32.4783i	−0.437872	−	1.63416i
$396$		0			0
$397$	1.92249	−	3.89843i	0.0964872	−	0.195657i	−0.843278	−	0.537478i	$-0.819377\pi$
$397$	1.92249	−	3.89843i	0.0964872	−	0.195657i	0.939765	+	0.341821i	$0.111044\pi$
$398$		0			0
$399$	24.7092	+	0.151986i	1.23701	+	0.00760879i
$400$		0			0
$401$	10.0894	−	3.42488i	0.503839	−	0.171030i	−0.0579358	−	0.998320i	$-0.518452\pi$
$401$	10.0894	−	3.42488i	0.503839	−	0.171030i	0.561775	+	0.827290i	$0.310119\pi$
$402$		0			0
$403$	−42.7232	−	14.5026i	−2.12819	−	0.722424i
$404$		0			0
$405$	14.7531	+	9.85773i	0.733090	+	0.489835i
$406$		0			0
$407$			16.8198i			0.833726i
$408$		0			0
$409$	8.52010	+	4.91908i	0.421292	+	0.243233i	0.695630	−	0.718400i	$-0.255125\pi$
$409$	8.52010	+	4.91908i	0.421292	+	0.243233i	−0.274338	+	0.961633i	$0.588459\pi$
$410$		0			0
$411$	−22.9595	−	1.50485i	−1.13251	−	0.0742286i
$412$		0			0
$413$	−5.37781	−	4.77505i	−0.264625	−	0.234965i
$414$		0			0
$415$	3.64357	+	10.7336i	0.178856	+	0.526892i
$416$		0			0
$417$	−39.9847	−	5.26409i	−1.95806	−	0.257784i
$418$		0			0
$419$	−17.0003	+	11.3592i	−0.830520	+	0.554935i	−0.896581	−	0.442880i	$-0.853957\pi$
$419$	−17.0003	+	11.3592i	−0.830520	+	0.554935i	0.0660613	+	0.997816i	$0.478957\pi$
$420$		0			0
$421$	−2.17057	+	2.17057i	−0.105787	+	0.105787i	−0.758019	−	0.652232i	$-0.773833\pi$
$421$	−2.17057	+	2.17057i	−0.105787	+	0.105787i	0.652232	+	0.758019i	$0.273833\pi$
$422$		0			0
$423$	−26.7582	−	34.8719i	−1.30103	−	1.69553i
$424$		0			0
$425$	34.0643	−	9.65111i	1.65236	−	0.468148i
$426$		0			0
$427$	−4.95311	+	18.0407i	−0.239698	+	0.873048i
$428$		0			0
$429$	9.52540	−	35.5493i	0.459891	−	1.71634i
$430$		0			0
$431$	2.08532	+	31.8159i	0.100447	+	1.53252i	0.689418	+	0.724364i	$0.257866\pi$
$431$	2.08532	+	31.8159i	0.100447	+	1.53252i	−0.588971	+	0.808154i	$0.700467\pi$
$432$		0			0
$433$	−2.29566	−	5.54222i	−0.110323	−	0.266342i	0.859070	−	0.511858i	$-0.171043\pi$
$433$	−2.29566	−	5.54222i	−0.110323	−	0.266342i	−0.969393	+	0.245516i	$0.921043\pi$
$434$		0			0
$435$	4.42646	−	22.2533i	0.212233	−	1.06697i
$436$		0			0
$437$	4.44898	−	13.1063i	0.212824	−	0.626958i
$438$		0			0
$439$	−0.990886	+	15.1180i	−0.0472924	+	0.721543i	0.906712	+	0.421750i	$0.138584\pi$
$439$	−0.990886	+	15.1180i	−0.0472924	+	0.721543i	−0.954004	+	0.299792i	$0.903083\pi$
$440$		0			0
$441$	−37.1163	−	10.4363i	−1.76744	−	0.496967i
$442$		0			0
$443$	−1.00077	−	1.73339i	−0.0475482	−	0.0823559i	0.841272	−	0.540612i	$-0.181807\pi$
$443$	−1.00077	−	1.73339i	−0.0475482	−	0.0823559i	−0.888820	+	0.458257i	$0.848474\pi$
$444$		0			0
$445$	−21.7264	+	10.7143i	−1.02993	+	0.507906i
$446$		0			0
$447$	5.15680	+	25.9250i	0.243908	+	1.22621i
$448$		0			0
$449$	6.88338	+	1.36919i	0.324847	+	0.0646161i	0.354820	−	0.934935i	$-0.384542\pi$
$449$	6.88338	+	1.36919i	0.324847	+	0.0646161i	−0.0299730	+	0.999551i	$0.509542\pi$
$450$		0			0
$451$	−0.390272	+	2.96441i	−0.0183772	+	0.139589i
$452$		0			0
$453$	23.7557	+	11.7150i	1.11614	+	0.550419i
$454$		0			0
$455$	31.4929	+	24.4746i	1.47641	+	1.14739i
$456$		0			0
$457$	−1.81797	−	13.8088i	−0.0850409	−	0.645950i	−0.979884	−	0.199569i	$-0.936046\pi$
$457$	−1.81797	−	13.8088i	−0.0850409	−	0.645950i	0.894843	−	0.446381i	$-0.147287\pi$
$458$		0			0
$459$	6.30625	+	29.4951i	0.294351	+	1.37671i
$460$		0			0
$461$	16.6634	+	6.90221i	0.776092	+	0.321468i	0.735337	−	0.677701i	$-0.237024\pi$
$461$	16.6634	+	6.90221i	0.776092	+	0.321468i	0.0407546	+	0.999169i	$0.487024\pi$
$462$		0			0
$463$	−21.2062	−	21.2062i	−0.985536	−	0.985536i	0.0143609	−	0.999897i	$-0.495429\pi$
$463$	−21.2062	−	21.2062i	−0.985536	−	0.985536i	−0.999897	+	0.0143609i	$0.995429\pi$
$464$		0			0
$465$	−118.356	+	7.75747i	−5.48863	+	0.359744i
$466$		0			0
$467$	−14.7127	+	19.1739i	−0.680822	+	0.887264i	−0.998134	−	0.0610566i	$-0.980553\pi$
$467$	−14.7127	+	19.1739i	−0.680822	+	0.887264i	0.317312	+	0.948321i	$0.397220\pi$
$468$		0			0
$469$	4.57972	+	9.43258i	0.211472	+	0.435556i
$470$		0			0
$471$	27.1336	−	23.7955i	1.25025	−	1.09644i
$472$		0			0
$473$	10.6866	+	21.6702i	0.491369	+	0.996398i
$474$		0			0
$475$	−27.4945			−1.26153
$476$		0			0
$477$	−70.7812			−3.24085
$478$		0			0
$479$	−15.6173	−	31.6688i	−0.713575	−	1.44699i	−0.886824	−	0.462108i	$-0.847093\pi$
$479$	−15.6173	−	31.6688i	−0.713575	−	1.44699i	0.173249	−	0.984878i	$-0.444573\pi$
$480$		0			0
$481$	−16.7636	+	14.7013i	−0.764355	+	0.670321i
$482$		0			0
$483$	−18.7037	+	27.6228i	−0.851049	+	1.25688i
$484$		0			0
$485$	40.1900	−	52.3767i	1.82494	−	2.37830i
$486$		0			0
$487$	35.5775	−	2.33187i	1.61217	−	0.105667i	0.767533	−	0.641009i	$-0.221484\pi$
$487$	35.5775	−	2.33187i	1.61217	−	0.105667i	0.844635	+	0.535342i	$0.179817\pi$
$488$		0			0
$489$	−2.64054	−	2.64054i	−0.119409	−	0.119409i
$490$		0			0
$491$	0.502531	+	0.208155i	0.0226789	+	0.00939390i	0.393994	−	0.919113i	$-0.371093\pi$
$491$	0.502531	+	0.208155i	0.0226789	+	0.00939390i	−0.371315	+	0.928507i	$0.621093\pi$
$492$		0			0
$493$	7.16486	−	4.93690i	0.322689	−	0.222347i
$494$		0			0
$495$	−8.17572	−	62.1007i	−0.367471	−	2.79122i
$496$		0			0
$497$	4.21166	+	10.3474i	0.188919	+	0.464145i
$498$		0			0
$499$	−22.2043	−	10.9499i	−0.994000	−	0.490187i	−0.128831	−	0.991667i	$-0.541122\pi$
$499$	−22.2043	−	10.9499i	−0.994000	−	0.490187i	−0.865169	+	0.501480i	$0.832789\pi$
$500$		0			0
$501$	−0.985155	+	7.48299i	−0.0440135	+	0.334315i
$502$		0			0
$503$	−16.3974	−	3.26165i	−0.731125	−	0.145430i	−0.184530	−	0.982827i	$-0.559076\pi$
$503$	−16.3974	−	3.26165i	−0.731125	−	0.145430i	−0.546595	+	0.837397i	$0.684076\pi$
$504$		0			0
$505$	−4.25420	−	21.3873i	−0.189309	−	0.951722i
$506$		0			0
$507$	9.74779	−	4.80708i	0.432915	−	0.213490i
$508$		0			0
$509$	−7.24625	−	12.5509i	−0.321184	−	0.556308i	0.659548	−	0.751662i	$-0.270748\pi$
$509$	−7.24625	−	12.5509i	−0.321184	−	0.556308i	−0.980733	+	0.195354i	$0.937414\pi$
$510$		0			0
$511$	−4.21817	−	5.56780i	−0.186601	−	0.246305i
$512$		0			0
$513$	1.53192	−	23.3725i	0.0676357	−	1.03192i
$514$		0			0
$515$	9.66725	−	28.4788i	0.425990	−	1.25493i
$516$		0			0
$517$	−4.80321	+	24.1474i	−0.211245	+	1.06200i
$518$		0			0
$519$	−24.5909	−	59.3677i	−1.07942	−	2.60595i
$520$		0			0
$521$	1.31082	+	19.9993i	0.0574281	+	0.876183i	0.925262	+	0.379329i	$0.123845\pi$
$521$	1.31082	+	19.9993i	0.0574281	+	0.876183i	−0.867834	+	0.496855i	$0.834488\pi$
$522$		0			0
$523$	1.44263	−	5.38397i	0.0630818	−	0.235425i	−0.927186	−	0.374602i	$-0.877779\pi$
$523$	1.44263	−	5.38397i	0.0630818	−	0.235425i	0.990267	+	0.139178i	$0.0444459\pi$
$524$		0			0
$525$	63.9030	+	17.5448i	2.78896	+	0.765716i
$526$		0			0
$527$	−34.6227	−	29.4990i	−1.50819	−	1.28500i
$528$		0			0
$529$	−2.62629	−	3.42264i	−0.114186	−	0.148811i
$530$		0			0
$531$	−10.5868	+	10.5868i	−0.459427	+	0.459427i
$532$		0			0
$533$	−3.29563	+	2.20207i	−0.142749	+	0.0953821i
$534$		0			0
$535$	−23.0768	−	3.03811i	−0.997695	−	0.131349i
$536$		0			0
$537$	13.2452	+	39.0190i	0.571571	+	1.68379i
$538$		0			0
$539$	9.31270	+	19.4849i	0.401126	+	0.839276i
$540$		0			0
$541$	−41.5268	−	2.72181i	−1.78538	−	0.117020i	−0.863463	−	0.504412i	$-0.831709\pi$
$541$	−41.5268	−	2.72181i	−1.78538	−	0.117020i	−0.921915	+	0.387393i	$0.873376\pi$
$542$		0			0
$543$	4.79128	+	2.76624i	0.205613	+	0.118711i
$544$		0			0
$545$			67.6067i			2.89595i
$546$		0			0
$547$	7.53997	+	5.03805i	0.322386	+	0.215411i	0.706223	−	0.707989i	$-0.250398\pi$
$547$	7.53997	+	5.03805i	0.322386	+	0.215411i	−0.383837	+	0.923401i	$0.625398\pi$
$548$		0			0
$549$	36.8801	+	12.5191i	1.57400	+	0.534302i
$550$		0			0
$551$	−6.39837	+	2.17196i	−0.272580	+	0.0925284i
$552$		0			0
$553$	20.9749	−	11.9384i	0.891942	−	0.507674i
$554$		0			0
$555$	−25.9253	+	52.5713i	−1.10047	+	2.23153i
$556$		0			0
$557$	−10.9689	−	40.9366i	−0.464768	−	1.73454i	−0.657657	−	0.753317i	$-0.728452\pi$
$557$	−10.9689	−	40.9366i	−0.464768	−	1.73454i	0.192889	−	0.981221i	$-0.438214\pi$
$558$		0			0
$559$	−12.2573	+	29.5917i	−0.518428	+	1.25160i
$560$		0			0
$561$	22.1643	−	29.7557i	0.935777	−	1.25629i
$562$		0			0
$563$	−33.8488	+	25.9731i	−1.42656	+	1.09463i	−0.446755	+	0.894656i	$0.647420\pi$
$563$	−33.8488	+	25.9731i	−1.42656	+	1.09463i	−0.979800	+	0.199978i	$0.935913\pi$
$564$		0			0
$565$	43.1959	+	11.5743i	1.81727	+	0.486935i
$566$		0			0
$567$	−4.16788	+	12.0345i	−0.175035	+	0.505401i
$568$		0			0
$569$	12.9170	+	9.91153i	0.541507	+	0.415513i	0.842967	−	0.537966i	$-0.180807\pi$
$569$	12.9170	+	9.91153i	0.541507	+	0.415513i	−0.301459	+	0.953479i	$0.597474\pi$
$570$		0			0
$571$	−17.0226	−	14.9284i	−0.712373	−	0.624735i	0.224471	−	0.974481i	$-0.427935\pi$
$571$	−17.0226	−	14.9284i	−0.712373	−	0.624735i	−0.936845	+	0.349746i	$0.886268\pi$
$572$		0			0
$573$	34.0741	−	6.77777i	1.42347	−	0.283145i
$574$		0			0
$575$	20.6223	−	30.8634i	0.860008	−	1.28709i
$576$		0			0
$577$	−0.446986	+	0.774202i	−0.0186083	+	0.0322304i	−0.875180	−	0.483798i	$-0.839257\pi$
$577$	−0.446986	+	0.774202i	−0.0186083	+	0.0322304i	0.856571	+	0.516029i	$0.172590\pi$
$578$		0			0
$579$	29.1037	−	16.8030i	1.20951	−	0.698310i
$580$		0			0
$581$	−6.79258	+	4.47847i	−0.281804	+	0.185798i
$582$		0			0
$583$	26.1407	+	29.8078i	1.08264	+	1.23451i
$584$		0			0
$585$	54.7474	−	62.4274i	2.26352	−	2.58106i
$586$		0			0
$587$	−20.7574	+	8.59800i	−0.856750	+	0.354878i	−0.767436	−	0.641126i	$-0.778468\pi$
$587$	−20.7574	+	8.59800i	−0.856750	+	0.354878i	−0.0893145	+	0.996003i	$0.528468\pi$
$588$		0			0
$589$	19.6242	+	29.3696i	0.808600	+	1.21015i
$590$		0			0
$591$	27.7017	−	7.42266i	1.13950	−	0.305327i
$592$		0			0
$593$	25.3155	−	3.33285i	1.03958	−	0.136864i	0.408643	−	0.912694i	$-0.366002\pi$
$593$	25.3155	−	3.33285i	1.03958	−	0.136864i	0.630941	+	0.775830i	$0.282669\pi$
$594$		0			0
$595$	20.3877	+	34.6583i	0.835813	+	1.42085i
$596$		0			0
$597$	51.5600	−	6.78801i	2.11021	−	0.277815i
$598$		0			0
$599$	−42.6659	+	11.4323i	−1.74328	+	0.467111i	−0.983172	−	0.182684i	$-0.941521\pi$
$599$	−42.6659	+	11.4323i	−1.74328	+	0.467111i	−0.760109	+	0.649795i	$0.774855\pi$
$600$		0			0
$601$	−6.25879	−	9.36694i	−0.255301	−	0.382086i	0.681574	−	0.731749i	$-0.261296\pi$
$601$	−6.25879	−	9.36694i	−0.255301	−	0.382086i	−0.936875	+	0.349664i	$0.886296\pi$
$602$		0			0
$603$	20.1673	−	8.35359i	0.821278	−	0.340184i
$604$		0			0
$605$	3.60145	−	4.10667i	0.146420	−	0.166960i
$606$		0			0
$607$	−10.3876	−	11.8448i	−0.421621	−	0.480767i	0.501565	−	0.865120i	$-0.332758\pi$
$607$	−10.3876	−	11.8448i	−0.421621	−	0.480767i	−0.923186	+	0.384353i	$0.874425\pi$
$608$		0			0
$609$	16.2572	−	0.965164i	0.658773	−	0.0391104i
$610$		0			0
$611$	−28.2650	+	16.3188i	−1.14348	+	0.660187i
$612$		0			0
$613$	17.5715	−	30.4347i	0.709704	−	1.22924i	−0.255262	−	0.966872i	$-0.582162\pi$
$613$	17.5715	−	30.4347i	0.709704	−	1.22924i	0.964967	−	0.262372i	$-0.0845048\pi$
$614$		0			0
$615$	−5.78904	+	8.66391i	−0.233436	+	0.349362i
$616$		0			0
$617$	−3.86159	+	0.768118i	−0.155462	+	0.0309233i	−0.272208	−	0.962239i	$-0.587754\pi$
$617$	−3.86159	+	0.768118i	−0.155462	+	0.0309233i	0.116746	+	0.993162i	$0.462754\pi$
$618$		0			0
$619$	26.3901	+	23.1435i	1.06071	+	0.930217i	0.997699	−	0.0677964i	$-0.0215968\pi$
$619$	26.3901	+	23.1435i	1.06071	+	0.930217i	0.0630095	+	0.998013i	$0.479930\pi$
$620$		0			0
$621$	25.0873	+	19.2502i	1.00672	+	0.772484i
$622$		0			0
$623$	−11.3839	−	13.1431i	−0.456088	−	0.526568i
$624$		0			0
$625$	−5.60374	−	1.50152i	−0.224150	−	0.0600607i
$626$		0			0
$627$	−22.8592	+	17.5405i	−0.912907	+	0.700498i
$628$		0			0
$629$	−21.1802	+	7.52883i	−0.844511	+	0.300194i
$630$		0			0
$631$	−1.36302	+	3.29063i	−0.0542610	+	0.130998i	−0.948685	−	0.316222i	$-0.897586\pi$
$631$	−1.36302	+	3.29063i	−0.0542610	+	0.130998i	0.894424	+	0.447219i	$0.147586\pi$
$632$		0			0
$633$	3.49465	+	13.0422i	0.138900	+	0.518381i
$634$		0			0
$635$	−16.1939	+	32.8379i	−0.642635	+	1.30313i
$636$		0			0
$637$	−11.2801	+	26.3124i	−0.446935	+	1.04253i
$638$		0			0
$639$	22.0231	−	7.47584i	0.871221	−	0.295740i
$640$		0			0
$641$	19.6071	+	6.65572i	0.774434	+	0.262885i	0.680554	−	0.732698i	$-0.261739\pi$
$641$	19.6071	+	6.65572i	0.774434	+	0.262885i	0.0938809	+	0.995583i	$0.470073\pi$
$642$		0			0
$643$	20.5321	+	13.7191i	0.809705	+	0.541028i	0.890116	−	0.455734i	$-0.150623\pi$
$643$	20.5321	+	13.7191i	0.809705	+	0.541028i	−0.0804106	+	0.996762i	$0.525623\pi$
$644$		0			0
$645$			84.2036i			3.31551i
$646$		0			0
$647$	−8.89734	−	5.13688i	−0.349790	−	0.201952i	0.314803	−	0.949157i	$-0.398062\pi$
$647$	−8.89734	−	5.13688i	−0.349790	−	0.201952i	−0.664593	+	0.747206i	$0.731395\pi$
$648$		0			0
$649$	8.36824	+	0.548484i	0.328482	+	0.0215299i
$650$		0			0
$651$	−26.8694	−	80.7839i	−1.05310	−	3.16617i
$652$		0			0
$653$	8.42925	+	24.8318i	0.329862	+	0.971742i	0.977708	+	0.209970i	$0.0673368\pi$
$653$	8.42925	+	24.8318i	0.329862	+	0.971742i	−0.647846	+	0.761772i	$0.724330\pi$
$654$		0			0
$655$	−2.83040	−	0.372630i	−0.110593	−	0.0145599i
$656$		0			0
$657$	−12.0912	+	8.07905i	−0.471721	+	0.315194i
$658$		0			0
$659$	2.61709	−	2.61709i	0.101948	−	0.101948i	−0.654293	−	0.756241i	$-0.727034\pi$
$659$	2.61709	−	2.61709i	0.101948	−	0.101948i	0.756241	+	0.654293i	$0.227034\pi$
$660$		0			0
$661$	−12.2173	−	15.9220i	−0.475200	−	0.619292i	0.492831	−	0.870125i	$-0.335962\pi$
$661$	−12.2173	−	15.9220i	−0.475200	−	0.619292i	−0.968030	+	0.250833i	$0.919295\pi$
$662$		0			0
$663$	49.0290	−	3.91767i	1.90413	−	0.152150i
$664$		0			0
$665$	−7.89619	−	30.2111i	−0.306201	−	1.17154i
$666$		0			0
$667$	2.36102	−	8.81145i	0.0914191	−	0.341181i
$668$		0			0
$669$	1.65199	+	25.2044i	0.0638695	+	0.974460i
$670$		0			0
$671$	−8.34834	−	20.1547i	−0.322284	−	0.778063i
$672$		0			0
$673$	7.92406	−	39.8370i	0.305450	−	1.53560i	−0.457538	−	0.889190i	$-0.651269\pi$
$673$	7.92406	−	39.8370i	0.305450	−	1.53560i	0.762989	−	0.646412i	$-0.223731\pi$
$674$		0			0
$675$	20.1916	−	59.4827i	0.777177	−	2.28949i
$676$		0			0
$677$	1.54775	−	23.6141i	0.0594850	−	0.907565i	−0.858967	−	0.512032i	$-0.828893\pi$
$677$	1.54775	−	23.6141i	0.0594850	−	0.907565i	0.918452	−	0.395533i	$-0.129440\pi$
$678$		0			0
$679$	43.6675	+	18.4031i	1.67580	+	0.706248i
$680$		0			0
$681$	−34.8280	−	60.3238i	−1.33461	−	2.31161i
$682$		0			0
$683$	34.3288	−	16.9291i	1.31355	−	0.647773i	0.355585	−	0.934644i	$-0.384282\pi$
$683$	34.3288	−	16.9291i	1.31355	−	0.647773i	0.957969	+	0.286871i	$0.0926150\pi$
$684$		0			0
$685$	5.67255	+	28.5178i	0.216737	+	1.08961i
$686$		0			0
$687$	−29.3350	−	5.83510i	−1.11920	−	0.222623i
$688$		0			0
$689$	−6.85999	+	52.1068i	−0.261345	+	1.98511i
$690$		0			0
$691$	11.9342	+	5.88530i	0.453999	+	0.223888i	0.654887	−	0.755727i	$-0.272716\pi$
$691$	11.9342	+	5.88530i	0.453999	+	0.223888i	−0.200888	+	0.979614i	$0.564383\pi$
$692$		0			0
$693$	41.6416	−	16.9492i	1.58183	−	0.643847i
$694$		0			0
$695$	6.65231	+	50.5293i	0.252337	+	1.91669i
$696$		0			0
$697$	−3.90761	+	0.835474i	−0.148011	+	0.0316458i
$698$		0			0
$699$	32.2203	+	13.3461i	1.21868	+	0.504795i
$700$		0			0
$701$	−4.27375	−	4.27375i	−0.161417	−	0.161417i	0.621777	−	0.783194i	$-0.286411\pi$
$701$	−4.27375	−	4.27375i	−0.161417	−	0.161417i	−0.783194	+	0.621777i	$0.786411\pi$
$702$		0			0
$703$	17.4188	−	1.14169i	0.656962	−	0.0430596i
$704$		0			0
$705$	−52.2325	+	68.0707i	−1.96719	+	2.56369i
$706$		0			0
$707$	14.0802	−	6.83622i	0.529539	−	0.257103i
$708$		0			0
$709$	4.47118	−	3.92112i	0.167919	−	0.147261i	−0.571262	−	0.820767i	$-0.693546\pi$
$709$	4.47118	−	3.92112i	0.167919	−	0.147261i	0.739181	+	0.673507i	$0.235213\pi$
$710$		0			0
$711$	−22.2221	−	45.0619i	−0.833392	−	1.68995i
$712$		0			0
$713$	−47.6874			−1.78591
$714$		0			0
$715$	−46.5089			−1.73934
$716$		0			0
$717$	3.04935	+	6.18346i	0.113880	+	0.230926i
$718$		0			0
$719$	24.2336	−	21.2523i	0.903762	−	0.792578i	−0.0750836	−	0.997177i	$-0.523922\pi$
$719$	24.2336	−	21.2523i	0.903762	−	0.792578i	0.978846	+	0.204599i	$0.0655890\pi$
$720$		0			0
$721$	21.5316	+	1.54432i	0.801880	+	0.0575135i
$722$		0			0
$723$	−4.82504	+	6.28811i	−0.179445	+	0.233857i
$724$		0			0
$725$	−18.0824	+	1.18519i	−0.671565	+	0.0440167i
$726$		0			0
$727$	−1.30805	−	1.30805i	−0.0485130	−	0.0485130i	0.682434	−	0.730947i	$-0.260921\pi$
$727$	−1.30805	−	1.30805i	−0.0485130	−	0.0485130i	−0.730947	+	0.682434i	$0.760921\pi$
$728$		0			0
$729$	−34.6447	−	14.3503i	−1.28314	−	0.531492i
$730$		0			0
$731$	−22.5046	+	23.1570i	−0.832364	+	0.856493i
$732$		0			0
$733$	−5.75940	−	43.7470i	−0.212728	−	1.61583i	−0.681024	−	0.732261i	$-0.738465\pi$
$733$	−5.75940	−	43.7470i	−0.212728	−	1.61583i	0.468296	−	0.883572i	$-0.344868\pi$
$734$		0			0
$735$	−0.925827	+	75.2557i	−0.0341496	+	2.77585i
$736$		0			0
$737$	−10.9661	−	5.40786i	−0.403940	−	0.199201i
$738$		0			0
$739$	2.58769	−	19.6555i	0.0951897	−	0.723038i	−0.875588	−	0.483058i	$-0.839526\pi$
$739$	2.58769	−	19.6555i	0.0951897	−	0.723038i	0.970778	−	0.239980i	$-0.0771407\pi$
$740$		0			0
$741$	−37.4619	−	7.45163i	−1.37620	−	0.273742i
$742$		0			0
$743$	2.90851	+	14.6221i	0.106703	+	0.536431i	0.996750	+	0.0805621i	$0.0256715\pi$
$743$	2.90851	+	14.6221i	0.106703	+	0.536431i	−0.890047	+	0.455869i	$0.849328\pi$
$744$		0			0
$745$	29.9588	−	14.7740i	1.09760	−	0.541279i
$746$		0			0
$747$	8.46888	+	14.6685i	0.309860	+	0.536694i
$748$		0			0
$749$	−2.07875	−	16.5770i	−0.0759560	−	0.605710i
$750$		0			0
$751$	−2.69787	+	41.1616i	−0.0984468	+	1.50201i	0.607827	+	0.794069i	$0.292041\pi$
$751$	−2.69787	+	41.1616i	−0.0984468	+	1.50201i	−0.706274	+	0.707939i	$0.749625\pi$
$752$		0			0
$753$	8.60202	−	25.3407i	0.313475	−	0.923468i
$754$		0			0
$755$	6.53012	−	32.8292i	0.237656	−	1.19478i
$756$		0			0
$757$	9.18142	+	22.1659i	0.333704	+	0.805634i	0.998292	+	0.0584232i	$0.0186073\pi$
$757$	9.18142	+	22.1659i	0.333704	+	0.805634i	−0.664588	+	0.747210i	$0.731393\pi$
$758$		0			0
$759$	−2.54416	−	38.8163i	−0.0923470	−	1.40894i
$760$		0			0
$761$	6.66430	−	24.8715i	0.241581	−	0.901592i	−0.733491	−	0.679700i	$-0.762110\pi$
$761$	6.66430	−	24.8715i	0.241581	−	0.901592i	0.975071	−	0.221892i	$-0.0712232\pi$
$762$		0			0
$763$	−46.9492	+	12.2710i	−1.69967	+	0.444239i
$764$		0			0
$765$	74.5404	−	38.0926i	2.69502	−	1.37724i
$766$		0			0
$767$	6.76759	+	8.81970i	0.244364	+	0.318461i
$768$		0			0
$769$	21.7012	−	21.7012i	0.782566	−	0.782566i	−0.197698	−	0.980263i	$-0.563346\pi$
$769$	21.7012	−	21.7012i	0.782566	−	0.782566i	0.980263	+	0.197698i	$0.0633464\pi$
$770$		0			0
$771$	60.8950	−	40.6887i	2.19308	−	1.46537i
$772$		0			0
$773$	−38.6169	−	5.08401i	−1.38895	−	0.182859i	−0.601323	−	0.799006i	$-0.705359\pi$
$773$	−38.6169	−	5.08401i	−1.38895	−	0.182859i	−0.787631	+	0.616147i	$0.788693\pi$
$774$		0			0
$775$	30.4500	+	89.7028i	1.09380	+	3.22222i
$776$		0			0
$777$	−41.2135	−	8.46173i	−1.47853	−	0.303563i
$778$		0			0
$779$	3.09647	+	0.202953i	0.110943	+	0.00727156i
$780$		0			0
$781$	−11.2818	−	6.51354i	−0.403694	−	0.233073i
$782$		0			0
$783$		−	15.4376i		−	0.551693i
$784$		0			0
$785$	−37.9208	−	25.3378i	−1.35345	−	0.904347i
$786$		0			0
$787$	−23.6067	−	8.01338i	−0.841487	−	0.285646i	−0.132776	−	0.991146i	$-0.542389\pi$
$787$	−23.6067	−	8.01338i	−0.841487	−	0.285646i	−0.708710	+	0.705500i	$0.750723\pi$
$788$		0			0
$789$	−67.6334	+	22.9584i	−2.40781	+	0.817342i
$790$		0			0
$791$	−0.197434	+	32.0980i	−0.00701995	+	1.14127i
$792$		0			0
$793$	12.7905	−	25.9366i	0.454205	−	0.921036i
$794$		0			0
$795$	35.7600	+	133.458i	1.26828	+	4.73328i
$796$		0			0
$797$	−19.6573	+	47.4569i	−0.696297	+	1.68101i	0.0353931	+	0.999373i	$0.488732\pi$
$797$	−19.6573	+	47.4569i	−0.696297	+	1.68101i	−0.731690	+	0.681637i	$0.761268\pi$
$798$		0			0
$799$	−32.5575	+	4.76037i	−1.15180	+	0.168410i
$800$		0			0
$801$	−28.7179	+	22.0360i	−1.01470	+	0.778604i
$802$		0			0
$803$	7.86777	+	2.10816i	0.277647	+	0.0743954i
$804$		0			0
$805$	39.8354	+	13.7961i	1.40401	+	0.486250i
$806$		0			0
$807$	−2.79111	−	2.14169i	−0.0982516	−	0.0753911i
$808$		0			0
$809$	24.7204	+	21.6792i	0.869124	+	0.762201i	0.972613	−	0.232430i	$-0.0746675\pi$
$809$	24.7204	+	21.6792i	0.869124	+	0.762201i	−0.103490	+	0.994631i	$0.533001\pi$
$810$		0			0
$811$	10.8027	−	2.14879i	0.379333	−	0.0754541i	−0.00174105	−	0.999998i	$-0.500554\pi$
$811$	10.8027	−	2.14879i	0.379333	−	0.0754541i	0.381074	+	0.924544i	$0.375554\pi$
$812$		0			0
$813$	−25.0765	+	37.5296i	−0.879470	+	1.31622i
$814$		0			0
$815$	−2.35954	+	4.08684i	−0.0826509	+	0.143156i
$816$		0			0
$817$	21.7166	−	12.5381i	0.759767	−	0.438652i
$818$		0			0
$819$	53.2894	+	26.6881i	1.86208	+	0.932559i
$820$		0			0
$821$	−23.4678	−	26.7599i	−0.819033	−	0.933928i	0.179727	−	0.983717i	$-0.442479\pi$
$821$	−23.4678	−	26.7599i	−0.819033	−	0.933928i	−0.998760	+	0.0497887i	$0.984145\pi$
$822$		0			0
$823$	11.8925	−	13.5608i	0.414545	−	0.472698i	−0.506451	−	0.862268i	$-0.669043\pi$
$823$	11.8925	−	13.5608i	0.414545	−	0.472698i	0.920997	+	0.389570i	$0.127376\pi$
$824$		0			0
$825$	−71.3913	+	29.5712i	−2.48552	+	1.02954i
$826$		0			0
$827$	13.2536	+	19.8354i	0.460872	+	0.689744i	0.987011	−	0.160655i	$-0.0513607\pi$
$827$	13.2536	+	19.8354i	0.460872	+	0.689744i	−0.526139	+	0.850399i	$0.676361\pi$
$828$		0			0
$829$	54.9520	−	14.7243i	1.90856	−	0.511397i	0.914211	−	0.405238i	$-0.132811\pi$
$829$	54.9520	−	14.7243i	1.90856	−	0.511397i	0.994349	−	0.106159i	$-0.0338552\pi$
$830$		0			0
$831$	69.1216	−	9.10004i	2.39780	−	0.315677i
$832$		0			0
$833$	−20.3678	+	20.4488i	−0.705702	+	0.708508i
$834$		0			0
$835$	9.45637	−	1.24495i	0.327251	−	0.0430834i
$836$		0			0
$837$	−77.9512	+	20.8870i	−2.69439	+	0.721959i
$838$		0			0
$839$	−3.23914	−	4.84772i	−0.111828	−	0.167362i	0.771334	−	0.636430i	$-0.219590\pi$
$839$	−3.23914	−	4.84772i	−0.111828	−	0.167362i	−0.883162	+	0.469069i	$0.844590\pi$
$840$		0			0
$841$	22.6781	−	9.39357i	0.782003	−	0.323916i
$842$		0			0
$843$	−20.3346	+	23.1872i	−0.700361	+	0.798609i
$844$		0			0
$845$	−9.05603	−	10.3264i	−0.311537	−	0.355240i
$846$		0			0
$847$	3.50554	+	1.75563i	0.120452	+	0.0603241i
$848$		0			0
$849$	−18.1333	+	10.4693i	−0.622334	+	0.359305i
$850$		0			0
$851$	−11.7834	+	20.4094i	−0.403930	+	0.699627i
$852$		0			0
$853$	31.4435	−	47.0586i	1.07661	−	1.61126i	0.332619	−	0.943061i	$-0.392068\pi$
$853$	31.4435	−	47.0586i	1.07661	−	1.61126i	0.743987	−	0.668194i	$-0.232932\pi$
$854$		0			0
$855$	−63.7574	+	12.6821i	−2.18046	+	0.433720i
$856$		0			0
$857$	41.3785	+	36.2880i	1.41346	+	1.23957i	0.931679	+	0.363284i	$0.118344\pi$
$857$	41.3785	+	36.2880i	1.41346	+	1.23957i	0.481784	+	0.876290i	$0.339989\pi$
$858$		0			0
$859$	39.4774	+	30.2921i	1.34695	+	1.03355i	0.995241	+	0.0974427i	$0.0310663\pi$
$859$	39.4774	+	30.2921i	1.34695	+	1.03355i	0.351710	+	0.936109i	$0.385600\pi$
$860$		0			0
$861$	−7.06735	−	2.44762i	−0.240855	−	0.0834148i
$862$		0			0
$863$	9.14678	+	2.45087i	0.311360	+	0.0834287i	0.411115	−	0.911583i	$-0.365139\pi$
$863$	9.14678	+	2.45087i	0.311360	+	0.0834287i	−0.0997553	+	0.995012i	$0.531806\pi$
$864$		0			0
$865$	−64.4244	+	49.4346i	−2.19050	+	1.68083i
$866$		0			0
$867$	47.3909	+	14.5911i	1.60948	+	0.495539i
$868$		0			0
$869$	−10.7697	+	26.0004i	−0.365338	+	0.882003i
$870$		0			0
$871$	−4.19506	−	15.6562i	−0.142144	−	0.530489i
$872$		0			0
$873$	43.6320	−	88.4770i	1.47672	−	2.99449i
$874$		0			0
$875$	0.215167	−	34.9810i	0.00727399	−	1.18257i
$876$		0			0
$877$	−15.9802	+	5.42456i	−0.539614	+	0.183174i	−0.577922	−	0.816092i	$-0.696136\pi$
$877$	−15.9802	+	5.42456i	−0.539614	+	0.183174i	0.0383084	+	0.999266i	$0.487803\pi$
$878$		0			0
$879$	−31.2213	−	10.5982i	−1.05307	−	0.357469i
$880$		0			0
$881$	−27.9524	−	18.6772i	−0.941740	−	0.629250i	−0.0129734	−	0.999916i	$-0.504130\pi$
$881$	−27.9524	−	18.6772i	−0.941740	−	0.629250i	−0.928766	+	0.370665i	$0.879130\pi$
$882$		0			0
$883$		−	21.8482i		−	0.735251i	−0.929974	−	0.367626i	$-0.880171\pi$
$883$		−	21.8482i		−	0.735251i	0.929974	−	0.367626i	$-0.119829\pi$
$884$		0			0
$885$	25.3101	+	14.6128i	0.850789	+	0.491203i
$886$		0			0
$887$	25.4787	+	1.66996i	0.855491	+	0.0560718i	0.486835	−	0.873494i	$-0.338151\pi$
$887$	25.4787	+	1.66996i	0.855491	+	0.0560718i	0.368656	+	0.929566i	$0.379818\pi$
$888$		0			0
$889$	−25.7434	−	5.28550i	−0.863407	−	0.177270i
$890$		0			0
$891$	−4.77367	−	14.0628i	−0.159924	−	0.471121i
$892$		0			0
$893$	25.3334	+	3.33520i	0.847749	+	0.111608i
$894$		0			0
$895$	43.2966	−	28.9298i	1.44724	−	0.967018i
$896$		0			0
$897$	36.4630	−	36.4630i	1.21746	−	1.21746i
$898$		0			0
$899$	14.1723	+	18.4698i	0.472674	+	0.616001i
$900$		0			0
$901$	−25.8342	+	46.2601i	−0.860664	+	1.54115i
$902$		0			0
$903$	−58.4748	+	15.2834i	−1.94592	+	0.508600i
$904$		0			0
$905$	1.80953	−	6.75326i	0.0601508	−	0.224486i
$906$		0			0
$907$	2.73301	+	41.6977i	0.0907481	+	1.38455i	0.764038	+	0.645171i	$0.223214\pi$
$907$	2.73301	+	41.6977i	0.0907481	+	1.38455i	−0.673290	+	0.739378i	$0.735120\pi$
$908$		0			0
$909$	−12.4695	−	30.1041i	−0.413588	−	0.998490i
$910$		0			0
$911$	5.70360	−	28.6739i	0.188969	−	0.950010i	−0.763601	−	0.645689i	$-0.776570\pi$
$911$	5.70360	−	28.6739i	0.188969	−	0.950010i	0.952569	−	0.304321i	$-0.0984296\pi$
$912$		0			0
$913$	3.04959	−	8.98381i	0.100927	−	0.297321i
$914$		0			0
$915$	4.97229	−	75.8625i	0.164379	−	2.50794i
$916$		0			0
$917$	−0.254963	−	2.03320i	−0.00841961	−	0.0671421i
$918$		0			0
$919$	−2.65163	−	4.59276i	−0.0874692	−	0.151501i	0.818972	−	0.573834i	$-0.194545\pi$
$919$	−2.65163	−	4.59276i	−0.0874692	−	0.151501i	−0.906441	+	0.422333i	$0.861211\pi$
$920$		0			0
$921$	−61.9205	+	30.5358i	−2.04035	+	1.00619i
$922$		0			0
$923$	−3.36903	−	16.9373i	−0.110893	−	0.557496i
$924$		0			0
$925$	45.9155	+	9.13315i	1.50969	+	0.300296i
$926$		0			0
$927$	5.86584	−	44.5554i	0.192659	−	1.46339i
$928$		0			0
$929$	−13.8657	−	6.83779i	−0.454918	−	0.224341i	0.200369	−	0.979720i	$-0.435786\pi$
$929$	−13.8657	−	6.83779i	−0.454918	−	0.224341i	−0.655287	+	0.755380i	$0.727452\pi$
$930$		0			0
$931$	19.5467	−	10.9669i	0.640619	−	0.359427i
$932$		0			0
$933$	−10.3088	−	78.3030i	−0.337494	−	2.56352i
$934$		0			0
$935$	−43.5708	−	17.3226i	−1.42492	−	0.566511i
$936$		0			0
$937$	−8.61282	−	3.56755i	−0.281369	−	0.116547i	0.237536	−	0.971379i	$-0.423660\pi$
$937$	−8.61282	−	3.56755i	−0.281369	−	0.116547i	−0.518905	+	0.854832i	$0.673660\pi$
$938$		0			0
$939$	9.57258	+	9.57258i	0.312389	+	0.312389i
$940$		0			0
$941$	23.0229	−	1.50900i	0.750524	−	0.0491919i	0.314660	−	0.949204i	$-0.398110\pi$
$941$	23.0229	−	1.50900i	0.750524	−	0.0491919i	0.435864	+	0.900013i	$0.356443\pi$
$942$		0			0
$943$	−2.55033	+	3.32366i	−0.0830503	+	0.108233i
$944$		0			0
$945$	71.1587	+	5.10374i	2.31479	+	0.166025i
$946$		0			0
$947$	−9.56491	+	8.38820i	−0.310818	+	0.272580i	−0.800515	−	0.599313i	$-0.795441\pi$
$947$	−9.56491	+	8.38820i	−0.310818	+	0.272580i	0.489697	+	0.871893i	$0.337107\pi$
$948$		0			0
$949$	4.77568	+	9.68413i	0.155025	+	0.314360i
$950$		0			0
$951$	83.0461			2.69295
$952$		0			0
$953$	−9.05809			−0.293420			−0.146710	−	0.989180i	$-0.546868\pi$
$953$	−9.05809			−0.293420			−0.146710	+	0.989180i	$0.546868\pi$
$954$		0			0
$955$	−19.4181	−	39.3759i	−0.628354	−	1.27418i
$956$		0			0
$957$	−14.2778	+	12.5213i	−0.461536	+	0.404756i
$958$		0			0
$959$	−18.7745	+	9.11542i	−0.606260	+	0.294352i
$960$		0			0
$961$	55.2154	−	71.9581i	1.78114	−	2.32123i
$962$		0			0
$963$	−34.7059	+	2.27475i	−1.11838	+	0.0733027i
$964$		0			0
$965$	−30.0298	−	30.0298i	−0.966692	−	0.966692i
$966$		0			0
$967$	29.0106	+	12.0166i	0.932917	+	0.386427i	0.796784	−	0.604264i	$-0.206533\pi$
$967$	29.0106	+	12.0166i	0.932917	+	0.386427i	0.136132	+	0.990691i	$0.456533\pi$
$968$		0			0
$969$	−32.3199	−	20.9339i	−1.03826	−	0.672493i
$970$		0			0
$971$	−2.82323	−	21.4446i	−0.0906018	−	0.688189i	−0.975119	−	0.221682i	$-0.928845\pi$
$971$	−2.82323	−	21.4446i	−0.0906018	−	0.688189i	0.884517	−	0.466507i	$-0.154488\pi$
$972$		0			0
$973$	−33.8824	+	13.7910i	−1.08622	+	0.442120i
$974$		0			0
$975$	−91.8718	−	45.3062i	−2.94225	−	1.45096i
$976$		0			0
$977$	0.720118	−	5.46984i	0.0230386	−	0.174996i	−0.976057	−	0.217515i	$-0.930205\pi$
$977$	0.720118	−	5.46984i	0.0230386	−	0.174996i	0.999096	+	0.0425191i	$0.0135383\pi$
$978$		0			0
$979$	19.8859	+	3.95556i	0.635557	+	0.126420i
$980$		0			0
$981$	19.7085	+	99.0814i	0.629244	+	3.16343i
$982$		0			0
$983$	−45.4990	+	22.4376i	−1.45119	+	0.715648i	−0.985559	−	0.169330i	$-0.945840\pi$
$983$	−45.4990	+	22.4376i	−1.45119	+	0.715648i	−0.465632	+	0.884978i	$0.654173\pi$
$984$		0			0
$985$	−18.1210	−	31.3865i	−0.577383	−	1.00006i
$986$		0			0
$987$	−56.7519	−	23.9174i	−1.80643	−	0.761300i
$988$		0			0
$989$	−2.21417	+	33.7817i	−0.0704066	+	1.07420i
$990$		0			0
$991$	13.2898	−	39.1504i	0.422164	−	1.24365i	−0.503067	−	0.864248i	$-0.667795\pi$
$991$	13.2898	−	39.1504i	0.422164	−	1.24365i	0.925230	−	0.379406i	$-0.123872\pi$
$992$		0			0
$993$	1.04773	−	5.26730i	0.0332488	−	0.167153i
$994$		0			0
$995$	−25.1497	−	60.7168i	−0.797300	−	1.92485i
$996$		0			0
$997$	0.787437	+	12.0140i	0.0249384	+	0.380486i	0.992025	+	0.126040i	$0.0402266\pi$
$997$	0.787437	+	12.0140i	0.0249384	+	0.380486i	−0.967087	+	0.254447i	$0.918107\pi$
$998$		0			0
$999$	−10.3222	+	38.5229i	−0.326580	+	1.21881i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bl.a.129.1	yes	192
7.5	odd	6	inner	476.2.bl.a.61.1	✓	192
17.12	odd	16	inner	476.2.bl.a.437.1	yes	192
119.12	even	48	inner	476.2.bl.a.369.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bl.a.61.1	✓	192	7.5	odd	6	inner
476.2.bl.a.129.1	yes	192	1.1	even	1	trivial
476.2.bl.a.369.1	yes	192	119.12	even	48	inner
476.2.bl.a.437.1	yes	192	17.12	odd	16	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:	\( N \)	\(=\)	\( 476 = 2^{2} \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	476.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29009 - 2.61603i) q^{3} +(-2.77132 + 2.43038i) q^{5} +(-2.19078 - 1.48340i) q^{7} +(-3.35303 + 4.36975i) q^{9} +O(q^{10})\)	\(q+(-1.29009 - 2.61603i) q^{3} +(-2.77132 + 2.43038i) q^{5} +(-2.19078 - 1.48340i) q^{7} +(-3.35303 + 4.36975i) q^{9} +(3.07855 - 0.201779i) q^{11} +(2.89190 + 2.89190i) q^{13} +(9.93321 + 4.11447i) q^{15} +(1.63210 + 3.78632i) q^{17} +(-0.417929 - 3.17449i) q^{19} +(-1.05434 + 7.64487i) q^{21} +(3.87692 + 1.91189i) q^{23} +(1.12083 - 8.51352i) q^{25} +(7.17473 + 1.42714i) q^{27} +(-0.411702 - 2.06976i) q^{29} +(-9.89415 + 4.87925i) q^{31} +(-4.49944 - 7.79327i) q^{33} +(9.67659 - 1.21344i) q^{35} +(-0.356568 + 5.44018i) q^{37} +(3.83451 - 11.2961i) q^{39} +(-0.189073 + 0.950533i) q^{41} +(2.99706 + 7.23555i) q^{43} +(-1.32785 - 20.2591i) q^{45} +(-2.06545 + 7.70838i) q^{47} +(2.59903 + 6.49962i) q^{49} +(7.79960 - 9.15431i) q^{51} +(7.82303 + 10.1952i) q^{53} +(-8.04124 + 8.04124i) q^{55} +(-7.76540 + 5.18867i) q^{57} +(2.69499 + 0.354802i) q^{59} +(-2.27291 - 6.69579i) q^{61} +(13.8279 - 4.59926i) q^{63} +(-15.0428 - 0.985958i) q^{65} +(-3.43221 - 1.98159i) q^{67} -12.6087i q^{69} +(-3.51089 - 2.34590i) q^{71} +(2.50005 + 0.848654i) q^{73} +(-23.7176 + 8.05105i) q^{75} +(-7.04373 - 4.12467i) q^{77} +(-4.03454 + 8.18124i) q^{79} +(-1.24587 - 4.64965i) q^{81} +(1.17681 - 2.84107i) q^{83} +(-13.7253 - 6.52649i) q^{85} +(-4.88344 + 3.74720i) q^{87} +(6.34804 + 1.70095i) q^{89} +(-2.04566 - 10.6254i) q^{91} +(25.5286 + 19.5888i) q^{93} +(8.87343 + 7.78179i) q^{95} +(-17.5664 + 3.49418i) q^{97} +(-9.44073 + 14.1290i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 48 q^{15} - 24 q^{21} + 8 q^{25} - 32 q^{35} - 32 q^{37} - 16 q^{39} + 64 q^{49} + 32 q^{51} - 32 q^{53} - 48 q^{61} + 96 q^{63} + 16 q^{65} - 32 q^{71} + 120 q^{73} - 144 q^{75} + 16 q^{77} + 48 q^{81} - 160 q^{85} + 144 q^{87} - 64 q^{91} + 64 q^{93} + 32 q^{95} - 368 q^{99}+O(q^{100}) \) 192 * q + 8 * q^11 + 48 * q^15 - 24 * q^21 + 8 * q^25 - 32 * q^35 - 32 * q^37 - 16 * q^39 + 64 * q^49 + 32 * q^51 - 32 * q^53 - 48 * q^61 + 96 * q^63 + 16 * q^65 - 32 * q^71 + 120 * q^73 - 144 * q^75 + 16 * q^77 + 48 * q^81 - 160 * q^85 + 144 * q^87 - 64 * q^91 + 64 * q^93 + 32 * q^95 - 368 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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