LMFDB - Embedded newform 476.2.bh.a.457.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [476,2,Mod(9,476)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(476, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 8, 3]))

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

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

chi := DirichletCharacter("476.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 476 = 2^{2} \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	476.bh (of order $24$, degree $8$, 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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			457.5
Character	$\chi$	$=$	476.457
Dual form			476.2.bh.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.940523 + 1.22571i) q^{3} +(0.338941 - 2.57451i) q^{5} +(-1.75980 - 1.97563i) q^{7} +(0.158668 + 0.592157i) q^{9} +O(q^{10})$	\(q+(-0.940523 + 1.22571i) q^{3} +(0.338941 - 2.57451i) q^{5} +(-1.75980 - 1.97563i) q^{7} +(0.158668 + 0.592157i) q^{9} +(-4.68625 + 0.616957i) q^{11} +3.87669i q^{13} +(2.83683 + 2.83683i) q^{15} +(-3.27928 + 2.49926i) q^{17} +(-6.62185 + 1.77432i) q^{19} +(4.07668 - 0.298883i) q^{21} +(-1.66169 - 2.16556i) q^{23} +(-1.68359 - 0.451116i) q^{25} +(-5.15716 - 2.13617i) q^{27} +(0.556997 - 0.230716i) q^{29} +(4.31526 - 5.62375i) q^{31} +(3.65132 - 6.32426i) q^{33} +(-5.68274 + 3.86099i) q^{35} +(-0.582779 - 0.0767242i) q^{37} +(-4.75171 - 3.64611i) q^{39} +(-2.37427 - 0.983455i) q^{41} +(2.76217 - 2.76217i) q^{43} +(1.57829 - 0.207786i) q^{45} +(-6.58180 - 3.80000i) q^{47} +(-0.806224 + 6.95342i) q^{49} +(0.0208658 - 6.37007i) q^{51} +(0.299292 - 1.11697i) q^{53} +12.2739i q^{55} +(4.05320 - 9.78528i) q^{57} +(4.18667 + 1.12181i) q^{59} +(-4.93252 + 3.78485i) q^{61} +(0.890659 - 1.35554i) q^{63} +(9.98058 + 1.31397i) q^{65} +(4.69421 + 8.13062i) q^{67} +4.21721 q^{69} +(2.13143 + 5.14572i) q^{71} +(-11.5155 - 8.83616i) q^{73} +(2.13639 - 1.63931i) q^{75} +(9.46574 + 8.17258i) q^{77} +(8.98710 + 11.7122i) q^{79} +(5.87602 - 3.39252i) q^{81} +(-7.85190 - 7.85190i) q^{83} +(5.32288 + 9.28965i) q^{85} +(-0.241077 + 0.899712i) q^{87} +(1.39374 + 0.804675i) q^{89} +(7.65890 - 6.82219i) q^{91} +(2.83451 + 10.5785i) q^{93} +(2.32359 + 17.6494i) q^{95} +(5.18124 - 2.14614i) q^{97} +(-1.10889 - 2.67711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{5}+O(q^{10}) $ 96 * q + 4 * q^5	$ 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) $ 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$239$	$309$	$409$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{3}\right)$

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
$3$	−0.940523	+	1.22571i	−0.543011	+	0.707666i	−0.981584	−	0.191030i	$-0.938817\pi$
$3$	−0.940523	+	1.22571i	−0.543011	+	0.707666i	0.438573	+	0.898695i	$0.355484\pi$
$4$		0			0
$5$	0.338941	−	2.57451i	0.151579	−	1.15136i	−0.731402	−	0.681947i	$-0.761134\pi$
$5$	0.338941	−	2.57451i	0.151579	−	1.15136i	0.882981	−	0.469409i	$-0.155533\pi$
$6$		0			0
$7$	−1.75980	−	1.97563i	−0.665141	−	0.746718i
$7$	−1.75980	−	1.97563i	−0.665141	−	0.746718i
$8$		0			0
$9$	0.158668	+	0.592157i	0.0528893	+	0.197386i
$10$		0			0
$11$	−4.68625	+	0.616957i	−1.41296	+	0.186020i	−0.798056	−	0.602583i	$-0.794138\pi$
$11$	−4.68625	+	0.616957i	−1.41296	+	0.186020i	−0.614903	+	0.788603i	$0.710805\pi$
$12$		0			0
$13$			3.87669i			1.07520i	0.843200	+	0.537600i	$0.180669\pi$
$13$			3.87669i			1.07520i	−0.843200	+	0.537600i	$0.819331\pi$
$14$		0			0
$15$	2.83683	+	2.83683i	0.732466	+	0.732466i
$16$		0			0
$17$	−3.27928	+	2.49926i	−0.795343	+	0.606159i
$17$	−3.27928	+	2.49926i	−0.795343	+	0.606159i
$18$		0			0
$19$	−6.62185	+	1.77432i	−1.51916	+	0.407057i	−0.919465	−	0.393173i	$-0.871377\pi$
$19$	−6.62185	+	1.77432i	−1.51916	+	0.407057i	−0.599693	+	0.800230i	$0.704711\pi$
$20$		0			0
$21$	4.07668	−	0.298883i	0.889605	−	0.0652215i
$22$		0			0
$23$	−1.66169	−	2.16556i	−0.346487	−	0.451551i	0.587306	−	0.809365i	$-0.300189\pi$
$23$	−1.66169	−	2.16556i	−0.346487	−	0.451551i	−0.933793	+	0.357815i	$0.883522\pi$
$24$		0			0
$25$	−1.68359	−	0.451116i	−0.336718	−	0.0902232i
$26$		0			0
$27$	−5.15716	−	2.13617i	−0.992496	−	0.411105i
$28$		0			0
$29$	0.556997	−	0.230716i	0.103432	−	0.0428428i	−0.330368	−	0.943852i	$-0.607173\pi$
$29$	0.556997	−	0.230716i	0.103432	−	0.0428428i	0.433799	+	0.901010i	$0.357173\pi$
$30$		0			0
$31$	4.31526	−	5.62375i	0.775043	−	1.01006i	−0.224325	−	0.974514i	$-0.572018\pi$
$31$	4.31526	−	5.62375i	0.775043	−	1.01006i	0.999368	−	0.0355417i	$-0.0113157\pi$
$32$		0			0
$33$	3.65132	−	6.32426i	0.635613	−	1.10091i
$34$		0			0
$35$	−5.68274	+	3.86099i	−0.960559	+	0.652627i
$36$		0			0
$37$	−0.582779	−	0.0767242i	−0.0958082	−	0.0126134i	0.0824696	−	0.996594i	$-0.473719\pi$
$37$	−0.582779	−	0.0767242i	−0.0958082	−	0.0126134i	−0.178278	+	0.983980i	$0.557053\pi$
$38$		0			0
$39$	−4.75171	−	3.64611i	−0.760882	−	0.583846i
$40$		0			0
$41$	−2.37427	−	0.983455i	−0.370799	−	0.153590i	0.189499	−	0.981881i	$-0.439313\pi$
$41$	−2.37427	−	0.983455i	−0.370799	−	0.153590i	−0.560298	+	0.828291i	$0.689313\pi$
$42$		0			0
$43$	2.76217	−	2.76217i	0.421228	−	0.421228i	−0.464399	−	0.885626i	$-0.653729\pi$
$43$	2.76217	−	2.76217i	0.421228	−	0.421228i	0.885626	+	0.464399i	$0.153729\pi$
$44$		0			0
$45$	1.57829	−	0.207786i	0.235278	−	0.0309749i
$46$		0			0
$47$	−6.58180	−	3.80000i	−0.960054	−	0.554288i	−0.0638646	−	0.997959i	$-0.520343\pi$
$47$	−6.58180	−	3.80000i	−0.960054	−	0.554288i	−0.896190	+	0.443671i	$0.853676\pi$
$48$		0			0
$49$	−0.806224	+	6.95342i	−0.115175	+	0.993345i
$50$		0			0
$51$	0.0208658	−	6.37007i	0.00292180	−	0.891988i
$52$		0			0
$53$	0.299292	−	1.11697i	0.0411109	−	0.153428i	−0.942319	−	0.334715i	$-0.891360\pi$
$53$	0.299292	−	1.11697i	0.0411109	−	0.153428i	0.983430	+	0.181288i	$0.0580265\pi$
$54$		0			0
$55$			12.2739i			1.65501i
$56$		0			0
$57$	4.05320	−	9.78528i	0.536859	−	1.29609i
$58$		0			0
$59$	4.18667	+	1.12181i	0.545058	+	0.146048i	0.520833	−	0.853659i	$-0.325622\pi$
$59$	4.18667	+	1.12181i	0.545058	+	0.146048i	0.0242250	+	0.999707i	$0.492288\pi$
$60$		0			0
$61$	−4.93252	+	3.78485i	−0.631544	+	0.484601i	−0.874235	−	0.485503i	$-0.838636\pi$
$61$	−4.93252	+	3.78485i	−0.631544	+	0.484601i	0.242691	+	0.970104i	$0.421970\pi$
$62$		0			0
$63$	0.890659	−	1.35554i	0.112212	−	0.170783i
$64$		0			0
$65$	9.98058	+	1.31397i	1.23794	+	0.162978i
$66$		0			0
$67$	4.69421	+	8.13062i	0.573490	+	0.993313i	0.996204	+	0.0870502i	$0.0277440\pi$
$67$	4.69421	+	8.13062i	0.573490	+	0.993313i	−0.422714	+	0.906263i	$0.638923\pi$
$68$		0			0
$69$	4.21721			0.507693
$70$		0			0
$71$	2.13143	+	5.14572i	0.252954	+	0.610685i	0.998440	−	0.0558366i	$-0.0177826\pi$
$71$	2.13143	+	5.14572i	0.252954	+	0.610685i	−0.745486	+	0.666521i	$0.767783\pi$
$72$		0			0
$73$	−11.5155	−	8.83616i	−1.34779	−	1.03419i	−0.995143	−	0.0984377i	$-0.968615\pi$
$73$	−11.5155	−	8.83616i	−1.34779	−	1.03419i	−0.352646	−	0.935757i	$-0.614718\pi$
$74$		0			0
$75$	2.13639	−	1.63931i	0.246689	−	0.189291i
$76$		0			0
$77$	9.46574	+	8.17258i	1.07872	+	0.931352i
$78$		0			0
$79$	8.98710	+	11.7122i	1.01113	+	1.31773i	0.947501	+	0.319754i	$0.103600\pi$
$79$	8.98710	+	11.7122i	1.01113	+	1.31773i	0.0636272	+	0.997974i	$0.479733\pi$
$80$		0			0
$81$	5.87602	−	3.39252i	0.652891	−	0.376947i
$82$		0			0
$83$	−7.85190	−	7.85190i	−0.861858	−	0.861858i	0.129696	−	0.991554i	$-0.458600\pi$
$83$	−7.85190	−	7.85190i	−0.861858	−	0.861858i	−0.991554	+	0.129696i	$0.958600\pi$
$84$		0			0
$85$	5.32288	+	9.28965i	0.577348	+	1.00760i
$86$		0			0
$87$	−0.241077	+	0.899712i	−0.0258462	+	0.0964592i
$88$		0			0
$89$	1.39374	+	0.804675i	0.147736	+	0.0852954i	0.572046	−	0.820222i	$-0.306150\pi$
$89$	1.39374	+	0.804675i	0.147736	+	0.0852954i	−0.424310	+	0.905517i	$0.639483\pi$
$90$		0			0
$91$	7.65890	−	6.82219i	0.802871	−	0.715160i
$92$		0			0
$93$	2.83451	+	10.5785i	0.293925	+	1.09694i
$94$		0			0
$95$	2.32359	+	17.6494i	0.238395	+	1.81079i
$96$		0			0
$97$	5.18124	−	2.14614i	0.526076	−	0.217908i	−0.103808	−	0.994597i	$-0.533103\pi$
$97$	5.18124	−	2.14614i	0.526076	−	0.217908i	0.629883	+	0.776690i	$0.283103\pi$
$98$		0			0
$99$	−1.10889	−	2.67711i	−0.111448	−	0.269059i
$100$		0			0
$101$	−5.24025	−	9.07638i	−0.521424	−	0.903133i	−0.999690	−	0.0249177i	$-0.992068\pi$
$101$	−5.24025	−	9.07638i	−0.521424	−	0.903133i	0.478265	−	0.878215i	$-0.341266\pi$
$102$		0			0
$103$	−1.09915	+	1.90379i	−0.108303	+	0.187586i	−0.915083	−	0.403266i	$-0.867875\pi$
$103$	−1.09915	+	1.90379i	−0.108303	+	0.187586i	0.806780	+	0.590852i	$0.201208\pi$
$104$		0			0
$105$	0.612278	−	10.5968i	0.0597522	−	1.03414i
$106$		0			0
$107$	−2.15266	+	16.3511i	−0.208106	+	1.58072i	0.494523	+	0.869165i	$0.335343\pi$
$107$	−2.15266	+	16.3511i	−0.208106	+	1.58072i	−0.702629	+	0.711557i	$0.747990\pi$
$108$		0			0
$109$	−1.09795	−	8.33974i	−0.105164	−	0.798802i	−0.960019	−	0.279935i	$-0.909687\pi$
$109$	−1.09795	−	8.33974i	−0.105164	−	0.798802i	0.854855	−	0.518867i	$-0.173646\pi$
$110$		0			0
$111$	0.642158	−	0.642158i	0.0609510	−	0.0609510i
$112$		0			0
$113$	4.94194	−	11.9309i	0.464899	−	1.12236i	−0.501463	−	0.865179i	$-0.667205\pi$
$113$	4.94194	−	11.9309i	0.464899	−	1.12236i	0.966362	−	0.257186i	$-0.0827952\pi$
$114$		0			0
$115$	−6.13847	+	3.54405i	−0.572415	+	0.330484i
$116$		0			0
$117$	−2.29561	+	0.615106i	−0.212229	+	0.0568666i
$118$		0			0
$119$	10.7085	+	2.08046i	0.981645	+	0.190715i
$120$		0			0
$121$	10.9552	−	2.93543i	0.995924	−	0.266857i
$122$		0			0
$123$	3.43849	−	1.98521i	0.310038	−	0.179001i
$124$		0			0
$125$	3.23658	−	7.81379i	0.289488	−	0.698887i
$126$		0			0
$127$	8.94738	−	8.94738i	0.793951	−	0.793951i	−0.188183	−	0.982134i	$-0.560260\pi$
$127$	8.94738	−	8.94738i	0.793951	−	0.793951i	0.982134	+	0.188183i	$0.0602597\pi$
$128$		0			0
$129$	0.787745	+	5.98352i	0.0693571	+	0.526820i
$130$		0			0
$131$	1.02803	−	7.80865i	0.0898193	−	0.682245i	−0.886003	−	0.463680i	$-0.846529\pi$
$131$	1.02803	−	7.80865i	0.0898193	−	0.682245i	0.975822	−	0.218566i	$-0.0701378\pi$
$132$		0			0
$133$	15.1585	+	9.95989i	1.31441	+	0.863632i
$134$		0			0
$135$	−7.24755	+	12.5531i	−0.623770	+	1.08040i
$136$		0			0
$137$	−3.87201	−	6.70652i	−0.330808	−	0.572976i	0.651862	−	0.758337i	$-0.273988\pi$
$137$	−3.87201	−	6.70652i	−0.330808	−	0.572976i	−0.982671	+	0.185361i	$0.940655\pi$
$138$		0			0
$139$	5.17646	+	12.4971i	0.439062	+	1.05999i	0.976273	+	0.216542i	$0.0694777\pi$
$139$	5.17646	+	12.4971i	0.439062	+	1.05999i	−0.537211	+	0.843448i	$0.680522\pi$
$140$		0			0
$141$	10.8480	−	4.49341i	0.913570	−	0.378413i
$142$		0			0
$143$	−2.39175	−	18.1672i	−0.200008	−	1.51921i
$144$		0			0
$145$	−0.405191	−	1.51219i	−0.0336493	−	0.125581i
$146$		0			0
$147$	−7.76462	−	7.52804i	−0.640415	−	0.620903i
$148$		0			0
$149$	−20.2765	−	11.7066i	−1.66111	−	0.959044i	−0.972185	−	0.234215i	$-0.924748\pi$
$149$	−20.2765	−	11.7066i	−1.66111	−	0.959044i	−0.688928	−	0.724829i	$-0.741919\pi$
$150$		0			0
$151$	−0.0203649	+	0.0760027i	−0.00165727	+	0.00618501i	−0.966750	−	0.255725i	$-0.917686\pi$
$151$	−0.0203649	+	0.0760027i	−0.00165727	+	0.00618501i	0.965092	+	0.261910i	$0.0843524\pi$
$152$		0			0
$153$	−2.00027	−	1.54530i	−0.161712	−	0.124930i
$154$		0			0
$155$	−13.0158	−	13.0158i	−1.04545	−	1.04545i
$156$		0			0
$157$	−17.0490	+	9.84327i	−1.36066	+	0.785578i	−0.989712	−	0.143075i	$-0.954301\pi$
$157$	−17.0490	+	9.84327i	−1.36066	+	0.785578i	−0.370950	+	0.928653i	$0.620968\pi$
$158$		0			0
$159$	1.08760	+	1.41738i	0.0862520	+	0.112406i
$160$		0			0
$161$	−1.35410	+	7.09384i	−0.106718	+	0.559073i
$162$		0			0
$163$	−19.2654	+	14.7828i	−1.50898	+	1.15788i	−0.566290	+	0.824206i	$0.691622\pi$
$163$	−19.2654	+	14.7828i	−1.50898	+	1.15788i	−0.942688	+	0.333674i	$0.891711\pi$
$164$		0			0
$165$	−15.0443	−	11.5439i	−1.17120	−	0.898691i
$166$		0			0
$167$	−5.68329	−	13.7207i	−0.439786	−	1.06174i	−0.976022	−	0.217670i	$-0.930154\pi$
$167$	−5.68329	−	13.7207i	−0.439786	−	1.06174i	0.536236	−	0.844068i	$-0.319846\pi$
$168$		0			0
$169$	−2.02873			−0.156056
$170$		0			0
$171$	−2.10135	−	3.63965i	−0.160694	−	0.278331i
$172$		0			0
$173$	22.6821	+	2.98616i	1.72449	+	0.227033i	0.926673	−	0.375868i	$-0.122656\pi$
$173$	22.6821	+	2.98616i	1.72449	+	0.227033i	0.797815	+	0.602902i	$0.205989\pi$
$174$		0			0
$175$	2.07154	+	4.12002i	0.156593	+	0.311444i
$176$		0			0
$177$	−5.31268	+	4.07656i	−0.399325	+	0.306413i
$178$		0			0
$179$	19.0358	+	5.10063i	1.42280	+	0.381239i	0.886477	−	0.462772i	$-0.153145\pi$
$179$	19.0358	+	5.10063i	1.42280	+	0.381239i	0.536326	+	0.844011i	$0.319812\pi$
$180$		0			0
$181$	−7.16794	+	17.3049i	−0.532789	+	1.28627i	0.396880	+	0.917870i	$0.370093\pi$
$181$	−7.16794	+	17.3049i	−0.532789	+	1.28627i	−0.929669	+	0.368396i	$0.879907\pi$
$182$		0			0
$183$		−	9.60559i		−	0.710065i
$184$		0			0
$185$	−0.395055	+	1.47436i	−0.0290450	+	0.108397i
$186$		0			0
$187$	13.8256	−	13.7353i	1.01103	−	1.00443i
$188$		0			0
$189$	4.85529	+	13.9479i	0.353170	+	1.01456i
$190$		0			0
$191$	9.30509	+	5.37229i	0.673292	+	0.388726i	0.797323	−	0.603553i	$-0.206249\pi$
$191$	9.30509	+	5.37229i	0.673292	+	0.388726i	−0.124031	+	0.992278i	$0.539582\pi$
$192$		0			0
$193$	1.48285	−	0.195221i	0.106738	−	0.0140523i	−0.0769681	−	0.997034i	$-0.524524\pi$
$193$	1.48285	−	0.195221i	0.106738	−	0.0140523i	0.183706	+	0.982981i	$0.441191\pi$
$194$		0			0
$195$	−10.9975	+	10.9975i	−0.787548	+	0.787548i
$196$		0			0
$197$	−3.41986	−	1.41655i	−0.243655	−	0.100925i	0.257514	−	0.966275i	$-0.417097\pi$
$197$	−3.41986	−	1.41655i	−0.243655	−	0.100925i	−0.501169	+	0.865349i	$0.667097\pi$
$198$		0			0
$199$	1.92885	+	1.48006i	0.136732	+	0.104918i	0.674863	−	0.737943i	$-0.264203\pi$
$199$	1.92885	+	1.48006i	0.136732	+	0.104918i	−0.538131	+	0.842861i	$0.680869\pi$
$200$		0			0
$201$	−14.3808	−	1.89327i	−1.01434	−	0.133541i
$202$		0			0
$203$	−1.43601	−	0.694407i	−0.100788	−	0.0487378i
$204$		0			0
$205$	−3.33665	+	5.77925i	−0.233042	+	0.403640i
$206$		0			0
$207$	1.01869	−	1.32759i	0.0708041	−	0.0922737i
$208$		0			0
$209$	29.9370	−	12.4003i	2.07079	−	0.857748i
$210$		0			0
$211$	15.4780	+	6.41118i	1.06555	+	0.441364i	0.845417	−	0.534107i	$-0.179352\pi$
$211$	15.4780	+	6.41118i	1.06555	+	0.441364i	0.220130	+	0.975471i	$0.429352\pi$
$212$		0			0
$213$	−8.31183	−	2.22715i	−0.569517	−	0.152602i
$214$		0			0
$215$	−6.17503	−	8.04746i	−0.421134	−	0.548832i
$216$		0			0
$217$	−18.7044	+	1.37132i	−1.26974	+	0.0930911i
$218$		0			0
$219$	21.6612	−	5.80410i	1.46373	−	0.392205i
$220$		0			0
$221$	−9.68886	−	12.7128i	−0.651743	−	0.855153i
$222$		0			0
$223$	10.2929	+	10.2929i	0.689262	+	0.689262i	0.962069	−	0.272807i	$-0.0879519\pi$
$223$	10.2929	+	10.2929i	0.689262	+	0.689262i	−0.272807	+	0.962069i	$0.587952\pi$
$224$		0			0
$225$		−	1.06853i		−	0.0712350i
$226$		0			0
$227$	−23.0488	+	3.03443i	−1.52980	+	0.201402i	−0.847945	−	0.530084i	$-0.822160\pi$
$227$	−23.0488	+	3.03443i	−1.52980	+	0.201402i	−0.681856	+	0.731487i	$0.738827\pi$
$228$		0			0
$229$	6.27290	+	23.4108i	0.414525	+	1.54703i	0.785786	+	0.618499i	$0.212259\pi$
$229$	6.27290	+	23.4108i	0.414525	+	1.54703i	−0.371261	+	0.928529i	$0.621074\pi$
$230$		0			0
$231$	−18.9200	+	3.91578i	−1.24484	+	0.257639i
$232$		0			0
$233$	−1.00981	+	7.67024i	−0.0661546	+	0.502494i	0.926004	+	0.377513i	$0.123221\pi$
$233$	−1.00981	+	7.67024i	−0.0661546	+	0.502494i	−0.992159	+	0.124982i	$0.960113\pi$
$234$		0			0
$235$	−12.0140	+	15.6569i	−0.783706	+	1.02135i
$236$		0			0
$237$	−22.8084			−1.48156
$238$		0			0
$239$	−10.4352			−0.675000			−0.337500	−	0.941326i	$-0.609581\pi$
$239$	−10.4352			−0.675000			−0.337500	+	0.941326i	$0.609581\pi$
$240$		0			0
$241$	−4.88820	+	6.37043i	−0.314877	+	0.410355i	−0.923801	−	0.382873i	$-0.874935\pi$
$241$	−4.88820	+	6.37043i	−0.314877	+	0.410355i	0.608924	+	0.793228i	$0.291601\pi$
$242$		0			0
$243$	0.817549	−	6.20990i	0.0524458	−	0.398366i
$244$		0			0
$245$	17.6284	+	4.43243i	1.12624	+	0.283177i
$246$		0			0
$247$	−6.87849	−	25.6709i	−0.437668	−	1.63340i
$248$		0			0
$249$	17.0091	−	2.23929i	1.07791	−	0.141909i
$250$		0			0
$251$			5.23382i			0.330355i	0.986264	+	0.165178i	$0.0528198\pi$
$251$			5.23382i			0.330355i	−0.986264	+	0.165178i	$0.947180\pi$
$252$		0			0
$253$	9.12317	+	9.12317i	0.573569	+	0.573569i
$254$		0			0
$255$	−16.3927	−	2.21279i	−1.02655	−	0.138571i
$256$		0			0
$257$	−5.15111	+	1.38024i	−0.321317	+	0.0860968i	−0.415873	−	0.909423i	$-0.636524\pi$
$257$	−5.15111	+	1.38024i	−0.321317	+	0.0860968i	0.0945552	+	0.995520i	$0.469857\pi$
$258$		0			0
$259$	0.873994	+	1.28637i	0.0543073	+	0.0799314i
$260$		0			0
$261$	0.224997	+	0.293222i	0.0139270	+	0.0181500i
$262$		0			0
$263$	−28.5966	−	7.66244i	−1.76334	−	0.472486i	−0.775953	−	0.630791i	$-0.782731\pi$
$263$	−28.5966	−	7.66244i	−1.76334	−	0.472486i	−0.987390	+	0.158304i	$0.949397\pi$
$264$		0			0
$265$	−2.77421	−	1.14912i	−0.170419	−	0.0705897i
$266$		0			0
$267$	−2.29714	+	0.951507i	−0.140583	+	0.0582313i
$268$		0			0
$269$	−2.18279	+	2.84467i	−0.133087	+	0.173443i	−0.855143	−	0.518392i	$-0.826531\pi$
$269$	−2.18279	+	2.84467i	−0.133087	+	0.173443i	0.722056	+	0.691835i	$0.243197\pi$
$270$		0			0
$271$	5.07286	−	8.78646i	0.308155	−	0.533739i	−0.669804	−	0.742538i	$-0.733622\pi$
$271$	5.07286	−	8.78646i	0.308155	−	0.533739i	0.977959	+	0.208799i	$0.0669553\pi$
$272$		0			0
$273$	1.15868	+	15.8040i	0.0701262	+	0.956504i
$274$		0			0
$275$	8.16804	+	1.07534i	0.492552	+	0.0648456i
$276$		0			0
$277$	−8.61354	−	6.60940i	−0.517537	−	0.397120i	0.316700	−	0.948526i	$-0.397425\pi$
$277$	−8.61354	−	6.60940i	−0.517537	−	0.397120i	−0.834237	+	0.551405i	$0.814092\pi$
$278$		0			0
$279$	4.01484	+	1.66300i	0.240362	+	0.0995612i
$280$		0			0
$281$	1.08360	−	1.08360i	0.0646421	−	0.0646421i	−0.674047	−	0.738689i	$-0.735445\pi$
$281$	1.08360	−	1.08360i	0.0646421	−	0.0646421i	0.738689	+	0.674047i	$0.235445\pi$
$282$		0			0
$283$	−14.3482	+	1.88898i	−0.852914	+	0.112288i	−0.544291	−	0.838896i	$-0.683201\pi$
$283$	−14.3482	+	1.88898i	−0.852914	+	0.112288i	−0.308623	+	0.951185i	$0.599868\pi$
$284$		0			0
$285$	−23.8185	−	13.7516i	−1.41089	−	0.814576i
$286$		0			0
$287$	2.23529	+	6.42136i	0.131945	+	0.379041i
$288$		0			0
$289$	4.50740	−	16.3916i	0.265141	−	0.964210i
$290$		0			0
$291$	−2.24252	+	8.36921i	−0.131459	+	0.490612i
$292$		0			0
$293$		−	7.75901i		−	0.453286i	−0.973978	−	0.226643i	$-0.927225\pi$
$293$		−	7.75901i		−	0.453286i	0.973978	−	0.226643i	$-0.0727751\pi$
$294$		0			0
$295$	4.30715	−	10.3984i	0.250772	−	0.605418i
$296$		0			0
$297$	25.4857	+	6.82887i	1.47883	+	0.396251i
$298$		0			0
$299$	8.39521	−	6.44187i	0.485507	−	0.372543i
$300$		0			0
$301$	−10.3179	−	0.596165i	−0.594714	−	0.0343624i
$302$		0			0
$303$	16.0536	+	2.11350i	0.922255	+	0.121417i
$304$		0			0
$305$	8.07231	+	13.9816i	0.462219	+	0.800587i
$306$		0			0
$307$	−33.9329			−1.93665			−0.968326	−	0.249691i	$-0.919671\pi$
$307$	−33.9329			−1.93665			−0.968326	+	0.249691i	$0.919671\pi$
$308$		0			0
$309$	−1.29972	−	3.13780i	−0.0739384	−	0.178503i
$310$		0			0
$311$	−3.29863	−	2.53113i	−0.187048	−	0.143527i	0.510993	−	0.859585i	$-0.329278\pi$
$311$	−3.29863	−	2.53113i	−0.187048	−	0.143527i	−0.698041	+	0.716058i	$0.745945\pi$
$312$		0			0
$313$	7.77492	−	5.96590i	0.439464	−	0.337213i	−0.365214	−	0.930923i	$-0.619004\pi$
$313$	7.77492	−	5.96590i	0.439464	−	0.337213i	0.804679	+	0.593711i	$0.202338\pi$
$314$		0			0
$315$	−3.18798	−	2.75246i	−0.179622	−	0.155083i
$316$		0			0
$317$	−13.7786	−	17.9567i	−0.773885	−	1.00855i	−0.999411	−	0.0343092i	$-0.989077\pi$
$317$	−13.7786	−	17.9567i	−0.773885	−	1.00855i	0.225526	−	0.974237i	$-0.427590\pi$
$318$		0			0
$319$	−2.46789	+	1.42484i	−0.138175	+	0.0797755i
$320$		0			0
$321$	−18.0171	−	18.0171i	−1.00562	−	1.00562i
$322$		0			0
$323$	17.2805	−	22.3682i	0.961510	−	1.24460i
$324$		0			0
$325$	1.74884	−	6.52675i	0.0970081	−	0.362039i
$326$		0			0
$327$	11.2548	+	6.49794i	0.622390	+	0.359337i
$328$		0			0
$329$	4.07524	+	19.6904i	0.224675	+	1.08557i
$330$		0			0
$331$	−0.358224	−	1.33691i	−0.0196897	−	0.0734831i	0.955382	−	0.295373i	$-0.0954440\pi$
$331$	−0.358224	−	1.33691i	−0.0196897	−	0.0734831i	−0.975072	+	0.221890i	$0.928777\pi$
$332$		0			0
$333$	−0.0470355	−	0.357270i	−0.00257753	−	0.0195783i
$334$		0			0
$335$	22.5234	−	9.32950i	1.23059	−	0.509725i
$336$		0			0
$337$	−6.64750	−	16.0485i	−0.362112	−	0.874216i	−0.994991	−	0.0999653i	$-0.968127\pi$
$337$	−6.64750	−	16.0485i	−0.362112	−	0.874216i	0.632879	−	0.774251i	$-0.281873\pi$
$338$		0			0
$339$	9.97585	+	17.2787i	0.541814	+	0.938449i
$340$		0			0
$341$	−16.7528	+	29.0167i	−0.907214	+	1.57134i
$342$		0			0
$343$	15.1562	−	10.6438i	0.818356	−	0.574712i
$344$		0			0
$345$	1.42939	−	10.8573i	0.0769555	−	0.584535i
$346$		0			0
$347$	−1.48522	−	11.2813i	−0.0797306	−	0.605614i	−0.983937	−	0.178518i	$-0.942870\pi$
$347$	−1.48522	−	11.2813i	−0.0797306	−	0.605614i	0.904206	−	0.427096i	$-0.140463\pi$
$348$		0			0
$349$	−19.4255	+	19.4255i	−1.03982	+	1.03982i	−0.0406475	+	0.999174i	$0.512942\pi$
$349$	−19.4255	+	19.4255i	−1.03982	+	1.03982i	−0.999174	+	0.0406475i	$0.987058\pi$
$350$		0			0
$351$	8.28126	−	19.9927i	0.442021	−	1.06713i
$352$		0			0
$353$	12.7365	−	7.35344i	0.677897	−	0.391384i	−0.121165	−	0.992632i	$-0.538663\pi$
$353$	12.7365	−	7.35344i	0.677897	−	0.391384i	0.799062	+	0.601248i	$0.205330\pi$
$354$		0			0
$355$	13.9701	−	3.74329i	0.741458	−	0.198673i
$356$		0			0
$357$	−12.6216	+	11.1688i	−0.668007	+	0.591116i
$358$		0			0
$359$	9.75560	−	2.61401i	0.514881	−	0.137962i	0.00798322	−	0.999968i	$-0.497459\pi$
$359$	9.75560	−	2.61401i	0.514881	−	0.137962i	0.506898	+	0.862006i	$0.330792\pi$
$360$		0			0
$361$	24.2463	−	13.9986i	1.27612	−	0.736768i
$362$		0			0
$363$	−6.70559	+	16.1887i	−0.351952	+	0.849687i
$364$		0			0
$365$	−26.6519	+	26.6519i	−1.39502	+	1.39502i
$366$		0			0
$367$	0.473498	+	3.59657i	0.0247164	+	0.187740i	0.999349	−	0.0360701i	$-0.0114839\pi$
$367$	0.473498	+	3.59657i	0.0247164	+	0.187740i	−0.974633	+	0.223810i	$0.928151\pi$
$368$		0			0
$369$	0.205639	−	1.56198i	0.0107051	−	0.0813136i
$370$		0			0
$371$	−2.73342	+	1.37436i	−0.141912	+	0.0713530i
$372$		0			0
$373$	−8.53097	+	14.7761i	−0.441717	+	0.765076i	−0.997817	−	0.0660394i	$-0.978964\pi$
$373$	−8.53097	+	14.7761i	−0.441717	+	0.765076i	0.556100	+	0.831115i	$0.312297\pi$
$374$		0			0
$375$	6.53339	+	11.3162i	0.337383	+	0.584364i
$376$		0			0
$377$	0.894414	+	2.15931i	0.0460646	+	0.111210i
$378$		0			0
$379$	−10.0220	+	4.15127i	−0.514798	+	0.213236i	−0.624930	−	0.780681i	$-0.714873\pi$
$379$	−10.0220	+	4.15127i	−0.514798	+	0.213236i	0.110132	+	0.993917i	$0.464873\pi$
$380$		0			0
$381$	2.55171	+	19.3821i	0.130728	+	0.992976i
$382$		0			0
$383$	1.67271	+	6.24262i	0.0854713	+	0.318983i	0.995403	−	0.0957749i	$-0.0305329\pi$
$383$	1.67271	+	6.24262i	0.0854713	+	0.318983i	−0.909932	+	0.414758i	$0.863866\pi$
$384$		0			0
$385$	24.2487	−	21.5996i	1.23583	−	1.10082i
$386$		0			0
$387$	2.07391	+	1.19737i	0.105423	+	0.0608658i
$388$		0			0
$389$	2.53860	−	9.47417i	0.128712	−	0.480359i	−0.871233	−	0.490870i	$-0.836679\pi$
$389$	2.53860	−	9.47417i	0.128712	−	0.480359i	0.999945	+	0.0105106i	$0.00334570\pi$
$390$		0			0
$391$	10.8615	+	2.94848i	0.549288	+	0.149111i
$392$		0			0
$393$	8.60428	+	8.60428i	0.434029	+	0.434029i
$394$		0			0
$395$	33.1993	−	19.1676i	1.67044	−	0.964428i
$396$		0			0
$397$	−16.7267	−	21.7987i	−0.839489	−	1.09404i	−0.994355	−	0.106108i	$-0.966161\pi$
$397$	−16.7267	−	21.7987i	−0.839489	−	1.09404i	0.154865	−	0.987936i	$-0.450506\pi$
$398$		0			0
$399$	−26.4649	+	9.21250i	−1.32490	+	0.461202i
$400$		0			0
$401$	−23.5184	+	18.0463i	−1.17445	+	0.901188i	−0.996561	−	0.0828627i	$-0.973594\pi$
$401$	−23.5184	+	18.0463i	−1.17445	+	0.901188i	−0.177890	+	0.984050i	$0.556927\pi$
$402$		0			0
$403$	21.8016	+	16.7289i	1.08601	+	0.833327i
$404$		0			0
$405$	−6.74245	−	16.2777i	−0.335035	−	0.808846i
$406$		0			0
$407$	2.77838			0.137719
$408$		0			0
$409$	3.86390	+	6.69247i	0.191057	+	0.330921i	0.945601	−	0.325329i	$-0.105475\pi$
$409$	3.86390	+	6.69247i	0.191057	+	0.330921i	−0.754544	+	0.656250i	$0.772142\pi$
$410$		0			0
$411$	11.8620	+	1.56166i	0.585108	+	0.0770309i
$412$		0			0
$413$	−5.15140	−	10.2455i	−0.253484	−	0.504147i
$414$		0			0
$415$	−22.8761	+	17.5535i	−1.12294	+	0.861666i
$416$		0			0
$417$	−20.1864	−	5.40894i	−0.988533	−	0.264877i
$418$		0			0
$419$	−5.17903	+	12.5033i	−0.253012	+	0.610825i	−0.998444	−	0.0557561i	$-0.982243\pi$
$419$	−5.17903	+	12.5033i	−0.253012	+	0.610825i	0.745432	+	0.666581i	$0.232243\pi$
$420$		0			0
$421$		−	2.35377i		−	0.114716i	−0.998354	−	0.0573578i	$-0.981732\pi$
$421$		−	2.35377i		−	0.114716i	0.998354	−	0.0573578i	$-0.0182676\pi$
$422$		0			0
$423$	1.20588	−	4.50040i	0.0586318	−	0.218817i
$424$		0			0
$425$	6.64842	−	2.72839i	0.322496	−	0.132346i
$426$		0			0
$427$	16.1577	+	3.08425i	0.781926	+	0.149257i
$428$		0			0
$429$	24.5172	+	14.1550i	1.18370	+	0.683411i
$430$		0			0
$431$	−33.9277	+	4.46667i	−1.63424	+	0.215152i	−0.891043	−	0.453919i	$-0.850026\pi$
$431$	−33.9277	+	4.46667i	−1.63424	+	0.215152i	−0.743199	+	0.669071i	$0.766692\pi$
$432$		0			0
$433$	12.3068	−	12.3068i	0.591425	−	0.591425i	−0.346591	−	0.938016i	$-0.612661\pi$
$433$	12.3068	−	12.3068i	0.591425	−	0.591425i	0.938016	+	0.346591i	$0.112661\pi$
$434$		0			0
$435$	2.23461	+	0.925604i	0.107141	+	0.0443793i
$436$		0			0
$437$	14.8459	+	11.3916i	0.710175	+	0.544936i
$438$		0			0
$439$	27.7977	+	3.65964i	1.32671	+	0.174665i	0.760362	−	0.649499i	$-0.225022\pi$
$439$	27.7977	+	3.65964i	1.32671	+	0.174665i	0.566351	+	0.824164i	$0.308355\pi$
$440$		0			0
$441$	−4.24543	+	0.625873i	−0.202163	+	0.0298035i
$442$		0			0
$443$	10.7143	−	18.5576i	0.509049	−	0.881699i	−0.490896	−	0.871218i	$-0.663330\pi$
$443$	10.7143	−	18.5576i	0.509049	−	0.881699i	0.999945	−	0.0104810i	$-0.00333628\pi$
$444$		0			0
$445$	2.54404	−	3.31545i	0.120599	−	0.157168i
$446$		0			0
$447$	33.4194	−	13.8428i	1.58069	−	0.654741i
$448$		0			0
$449$	26.5598	+	11.0014i	1.25343	+	0.519189i	0.907888	−	0.419213i	$-0.137694\pi$
$449$	26.5598	+	11.0014i	1.25343	+	0.519189i	0.345546	+	0.938402i	$0.387694\pi$
$450$		0			0
$451$	11.7332	+	3.14390i	0.552494	+	0.148040i
$452$		0			0
$453$	−0.0740039	−	0.0964437i	−0.00347700	−	0.00453132i
$454$		0			0
$455$	−14.9679	−	22.0302i	−0.701705	−	1.03279i
$456$		0			0
$457$	−21.2587	+	5.69625i	−0.994440	+	0.266459i	−0.719114	−	0.694892i	$-0.755452\pi$
$457$	−21.2587	+	5.69625i	−0.994440	+	0.266459i	−0.275326	+	0.961351i	$0.588786\pi$
$458$		0			0
$459$	22.2506	−	5.88399i	1.03857	−	0.274641i
$460$		0			0
$461$	20.8526	+	20.8526i	0.971202	+	0.971202i	0.999597	−	0.0283947i	$-0.00903953\pi$
$461$	20.8526	+	20.8526i	0.971202	+	0.971202i	−0.0283947	+	0.999597i	$0.509040\pi$
$462$		0			0
$463$			38.9687i			1.81103i	0.424314	+	0.905515i	$0.360515\pi$
$463$			38.9687i			1.81103i	−0.424314	+	0.905515i	$0.639485\pi$
$464$		0			0
$465$	28.1953	−	3.71198i	1.30752	−	0.172139i
$466$		0			0
$467$	4.24874	+	15.8565i	0.196608	+	0.733753i	0.991845	+	0.127453i	$0.0406802\pi$
$467$	4.24874	+	15.8565i	0.196608	+	0.733753i	−0.795236	+	0.606300i	$0.792653\pi$
$468$		0			0
$469$	7.80222	−	23.5823i	0.360273	−	1.08893i
$470$		0			0
$471$	3.96999	−	30.1550i	0.182927	−	1.38947i
$472$		0			0
$473$	−11.2401	+	14.6484i	−0.516821	+	0.673534i
$474$		0			0
$475$	11.9489			0.548253
$476$		0			0
$477$	0.708910			0.0324588
$478$		0			0
$479$	1.19794	−	1.56118i	0.0547352	−	0.0713323i	−0.765184	−	0.643812i	$-0.777352\pi$
$479$	1.19794	−	1.56118i	0.0547352	−	0.0713323i	0.819919	+	0.572480i	$0.194019\pi$
$480$		0			0
$481$	0.297436	−	2.25925i	0.0135619	−	0.103013i
$482$		0			0
$483$	−7.42144	−	8.33165i	−0.337687	−	0.379103i
$484$		0			0
$485$	−3.76913	−	14.0666i	−0.171147	−	0.638730i
$486$		0			0
$487$	27.0407	−	3.55997i	1.22533	−	0.161318i	0.510043	−	0.860149i	$-0.329629\pi$
$487$	27.0407	−	3.55997i	1.22533	−	0.161318i	0.715287	+	0.698831i	$0.246296\pi$
$488$		0			0
$489$		−	37.5174i		−	1.69659i
$490$		0			0
$491$	−6.31712	−	6.31712i	−0.285088	−	0.285088i	0.550046	−	0.835134i	$-0.314610\pi$
$491$	−6.31712	−	6.31712i	−0.285088	−	0.285088i	−0.835134	+	0.550046i	$0.814610\pi$
$492$		0			0
$493$	−1.24993	+	2.14866i	−0.0562942	+	0.0967709i
$494$		0			0
$495$	−7.26808	+	1.94748i	−0.326676	+	0.0875326i
$496$		0			0
$497$	6.41516	−	13.2663i	0.287759	−	0.595077i
$498$		0			0
$499$	−23.7853	−	30.9976i	−1.06477	−	1.38764i	−0.917124	−	0.398602i	$-0.869496\pi$
$499$	−23.7853	−	30.9976i	−1.06477	−	1.38764i	−0.147651	−	0.989040i	$-0.547171\pi$
$500$		0			0
$501$	22.1629	+	5.93853i	0.990165	+	0.265314i
$502$		0			0
$503$	−19.3870	−	8.03034i	−0.864422	−	0.358055i	−0.0939866	−	0.995573i	$-0.529961\pi$
$503$	−19.3870	−	8.03034i	−0.864422	−	0.358055i	−0.770435	+	0.637518i	$0.779961\pi$
$504$		0			0
$505$	−25.1433	+	10.4147i	−1.11886	+	0.463449i
$506$		0			0
$507$	1.90807	−	2.48664i	0.0847402	−	0.110436i
$508$		0			0
$509$	−13.0505	+	22.6042i	−0.578454	+	1.00191i	0.417203	+	0.908813i	$0.363010\pi$
$509$	−13.0505	+	22.6042i	−0.578454	+	1.00191i	−0.995657	+	0.0930984i	$0.970323\pi$
$510$		0			0
$511$	2.80799	+	38.3002i	0.124218	+	1.69430i
$512$		0			0
$513$	37.9402	+	4.99493i	1.67510	+	0.220531i
$514$		0			0
$515$	4.52877	+	3.47505i	0.199561	+	0.153129i
$516$		0			0
$517$	33.1884	+	13.7471i	1.45963	+	0.604597i
$518$		0			0
$519$	−24.9932	+	24.9932i	−1.09708	+	1.09708i
$520$		0			0
$521$	−37.0066	+	4.87201i	−1.62129	+	0.213447i	−0.885792	−	0.464082i	$-0.846384\pi$
$521$	−37.0066	+	4.87201i	−1.62129	+	0.213447i	−0.735496	+	0.677529i	$0.763051\pi$
$522$		0			0
$523$	10.0627	+	5.80969i	0.440010	+	0.254040i	0.703602	−	0.710594i	$-0.251574\pi$
$523$	10.0627	+	5.80969i	0.440010	+	0.254040i	−0.263592	+	0.964634i	$0.584907\pi$
$524$		0			0
$525$	−6.99829	−	1.33586i	−0.305430	−	0.0583018i
$526$		0			0
$527$	−0.0957354	+	29.2268i	−0.00417030	+	1.27314i
$528$		0			0
$529$	4.02441	−	15.0193i	0.174974	−	0.653013i
$530$		0			0
$531$			2.65716i			0.115311i
$532$		0			0
$533$	3.81255	−	9.20431i	0.165140	−	0.398683i
$534$		0			0
$535$	41.3665	+	11.0841i	1.78843	+	0.479208i
$536$		0			0
$537$	−24.1555	+	18.5352i	−1.04239	+	0.799852i
$538$		0			0
$539$	−0.511789	−	33.0829i	−0.0220443	−	1.42498i
$540$		0			0
$541$	28.5672	+	3.76095i	1.22820	+	0.161696i	0.716573	−	0.697512i	$-0.245710\pi$
$541$	28.5672	+	3.76095i	1.22820	+	0.161696i	0.511627	+	0.859207i	$0.329043\pi$
$542$		0			0
$543$	−14.4693	−	25.0615i	−0.620936	−	1.07549i
$544$		0			0
$545$	−21.8429			−0.935646
$546$		0			0
$547$	−3.72332	−	8.98888i	−0.159198	−	0.384337i	0.824074	−	0.566482i	$-0.191696\pi$
$547$	−3.72332	−	8.98888i	−0.159198	−	0.384337i	−0.983272	+	0.182145i	$0.941696\pi$
$548$		0			0
$549$	−3.02386	−	2.32029i	−0.129055	−	0.0990274i
$550$		0			0
$551$	−3.27899	+	2.51606i	−0.139690	+	0.107188i
$552$		0			0
$553$	7.32352	−	38.3663i	0.311428	−	1.63150i
$554$		0			0
$555$	−1.43559	−	1.87090i	−0.0609374	−	0.0794151i
$556$		0			0
$557$	4.01428	−	2.31764i	0.170090	−	0.0982017i	−0.412538	−	0.910940i	$-0.635358\pi$
$557$	4.01428	−	2.31764i	0.170090	−	0.0982017i	0.582628	+	0.812739i	$0.302024\pi$
$558$		0			0
$559$	10.7081	+	10.7081i	0.452904	+	0.452904i
$560$		0			0
$561$	3.83228	+	29.8646i	0.161799	+	1.26089i
$562$		0			0
$563$	4.42135	−	16.5007i	0.186337	−	0.695421i	−0.808003	−	0.589179i	$-0.799451\pi$
$563$	4.42135	−	16.5007i	0.186337	−	0.695421i	0.994340	−	0.106242i	$-0.0338819\pi$
$564$		0			0
$565$	−29.0412	−	16.7669i	−1.22177	−	0.705390i
$566$		0			0
$567$	−17.0430	−	5.63868i	−0.715737	−	0.236802i
$568$		0			0
$569$	9.73189	+	36.3199i	0.407982	+	1.52261i	0.798489	+	0.602010i	$0.205633\pi$
$569$	9.73189	+	36.3199i	0.407982	+	1.52261i	−0.390506	+	0.920600i	$0.627700\pi$
$570$		0			0
$571$	−1.58297	−	12.0239i	−0.0662453	−	0.503183i	−0.992114	−	0.125338i	$-0.959998\pi$
$571$	−1.58297	−	12.0239i	−0.0662453	−	0.503183i	0.925869	−	0.377845i	$-0.123335\pi$
$572$		0			0
$573$	−15.3365	+	6.35260i	−0.640693	+	0.265384i
$574$		0			0
$575$	1.82069	+	4.39553i	0.0759279	+	0.183306i
$576$		0			0
$577$	−5.84996	−	10.1324i	−0.243537	−	0.421818i	0.718182	−	0.695855i	$-0.244974\pi$
$577$	−5.84996	−	10.1324i	−0.243537	−	0.421818i	−0.961719	+	0.274037i	$0.911641\pi$
$578$		0			0
$579$	−1.15537	+	2.00116i	−0.0480154	+	0.0831652i
$580$		0			0
$581$	−1.69469	+	29.3302i	−0.0703076	+	1.21682i
$582$		0			0
$583$	−0.713434	+	5.41907i	−0.0295474	+	0.224435i
$584$		0			0
$585$	0.805522	+	6.11855i	0.0333042	+	0.252971i
$586$		0			0
$587$	16.3734	−	16.3734i	0.675803	−	0.675803i	−0.283245	−	0.959048i	$-0.591411\pi$
$587$	16.3734	−	16.3734i	0.675803	−	0.675803i	0.959048	+	0.283245i	$0.0914110\pi$
$588$		0			0
$589$	−18.5967	+	44.8963i	−0.766263	+	1.84992i
$590$		0			0
$591$	4.95275	−	2.85947i	0.203729	−	0.117623i
$592$		0			0
$593$	−27.6428	+	7.40686i	−1.13515	+	0.304163i	−0.777001	−	0.629500i	$-0.783260\pi$
$593$	−27.6428	+	7.40686i	−1.13515	+	0.304163i	−0.358152	+	0.933663i	$0.616593\pi$
$594$		0			0
$595$	8.98570	−	26.8639i	0.368378	−	1.10131i
$596$		0			0
$597$	−3.62825	+	0.972185i	−0.148494	+	0.0397889i
$598$		0			0
$599$	−0.133035	+	0.0768080i	−0.00543567	+	0.00313829i	−0.502715	−	0.864452i	$-0.667666\pi$
$599$	−0.133035	+	0.0768080i	−0.00543567	+	0.00313829i	0.497280	+	0.867590i	$0.334332\pi$
$600$		0			0
$601$	−3.62805	+	8.75889i	−0.147991	+	0.357283i	−0.980440	−	0.196820i	$-0.936939\pi$
$601$	−3.62805	+	8.75889i	−0.147991	+	0.357283i	0.832448	+	0.554103i	$0.186939\pi$
$602$		0			0
$603$	−4.06978	+	4.06978i	−0.165734	+	0.165734i
$604$		0			0
$605$	−3.84414	−	29.1991i	−0.156286	−	1.18711i
$606$		0			0
$607$	−2.24973	+	17.0884i	−0.0913138	+	0.693597i	0.883156	+	0.469079i	$0.155414\pi$
$607$	−2.24973	+	17.0884i	−0.0913138	+	0.693597i	−0.974470	+	0.224518i	$0.927919\pi$
$608$		0			0
$609$	2.20174	−	1.10703i	0.0892192	−	0.0448592i
$610$		0			0
$611$	14.7314	−	25.5156i	0.595970	−	1.03225i
$612$		0			0
$613$	19.1742	+	33.2107i	0.774438	+	1.34137i	0.935110	+	0.354358i	$0.115300\pi$
$613$	19.1742	+	33.2107i	0.774438	+	1.34137i	−0.160672	+	0.987008i	$0.551366\pi$
$614$		0			0
$615$	−3.94550	−	9.52529i	−0.159098	−	0.384097i
$616$		0			0
$617$	5.65774	−	2.34351i	0.227772	−	0.0943463i	−0.265879	−	0.964006i	$-0.585662\pi$
$617$	5.65774	−	2.34351i	0.227772	−	0.0943463i	0.493651	+	0.869660i	$0.335662\pi$
$618$		0			0
$619$	−4.25500	−	32.3199i	−0.171023	−	1.29905i	−0.834565	−	0.550909i	$-0.814281\pi$
$619$	−4.25500	−	32.3199i	−0.171023	−	1.29905i	0.663542	−	0.748139i	$-0.269052\pi$
$620$		0			0
$621$	3.94362	+	14.7178i	0.158252	+	0.590605i
$622$		0			0
$623$	−0.862957	−	4.16957i	−0.0345736	−	0.167050i
$624$		0			0
$625$	−26.5670	−	15.3385i	−1.06268	−	0.613538i
$626$		0			0
$627$	−12.9572	+	48.3570i	−0.517461	+	1.93119i
$628$		0			0
$629$	2.10285	−	1.20491i	0.0838461	−	0.0480431i
$630$		0			0
$631$	−32.6782	−	32.6782i	−1.30090	−	1.30090i	−0.927787	−	0.373111i	$-0.878291\pi$
$631$	−32.6782	−	32.6782i	−1.30090	−	1.30090i	−0.373111	−	0.927787i	$-0.621709\pi$
$632$		0			0
$633$	−22.4156	+	12.9417i	−0.890942	+	0.514385i
$634$		0			0
$635$	−20.0025	−	26.0677i	−0.793774	−	1.03447i
$636$		0			0
$637$	−26.9562	−	3.12548i	−1.06805	−	0.123836i
$638$		0			0
$639$	−2.70888	+	2.07860i	−0.107162	+	0.0822281i
$640$		0			0
$641$	−7.15296	−	5.48866i	−0.282525	−	0.216789i	0.457771	−	0.889070i	$-0.348648\pi$
$641$	−7.15296	−	5.48866i	−0.282525	−	0.216789i	−0.740296	+	0.672281i	$0.765315\pi$
$642$		0			0
$643$	12.0837	+	29.1727i	0.476535	+	1.15046i	0.961223	+	0.275771i	$0.0889330\pi$
$643$	12.0837	+	29.1727i	0.476535	+	1.15046i	−0.484688	+	0.874687i	$0.661067\pi$
$644$		0			0
$645$	15.6716			0.617070
$646$		0			0
$647$	8.37049	+	14.4981i	0.329078	+	0.569979i	0.982329	−	0.187162i	$-0.0599288\pi$
$647$	8.37049	+	14.4981i	0.329078	+	0.569979i	−0.653251	+	0.757141i	$0.726595\pi$
$648$		0			0
$649$	−20.3119	−	2.67411i	−0.797312	−	0.104968i
$650$		0			0
$651$	15.9111	−	24.2160i	0.623605	−	0.949101i
$652$		0			0
$653$	−24.7874	+	19.0200i	−0.970005	+	0.744311i	−0.966760	−	0.255684i	$-0.917699\pi$
$653$	−24.7874	+	19.0200i	−0.970005	+	0.744311i	−0.00324413	+	0.999995i	$0.501033\pi$
$654$		0			0
$655$	−19.7550	−	5.29334i	−0.771892	−	0.206828i
$656$		0			0
$657$	3.40525	−	8.22100i	0.132851	−	0.320732i
$658$		0			0
$659$			44.6423i			1.73902i	0.493918	+	0.869509i	$0.335564\pi$
$659$			44.6423i			1.73902i	−0.493918	+	0.869509i	$0.664436\pi$
$660$		0			0
$661$	10.3835	−	38.7518i	0.403871	−	1.50727i	−0.402256	−	0.915527i	$-0.631774\pi$
$661$	10.3835	−	38.7518i	0.403871	−	1.50727i	0.806128	−	0.591742i	$-0.201559\pi$
$662$		0			0
$663$	24.6948	+	0.0808903i	0.959066	+	0.00314152i
$664$		0			0
$665$	30.7797	−	35.6500i	1.19358	−	1.38245i
$666$		0			0
$667$	−1.42519	−	0.822832i	−0.0551835	−	0.0318602i
$668$		0			0
$669$	−22.2968	+	2.93543i	−0.862044	+	0.113490i
$670$		0			0
$671$	20.7799	−	20.7799i	0.802200	−	0.802200i
$672$		0			0
$673$	−15.1055	−	6.25688i	−0.582272	−	0.241185i	0.0720498	−	0.997401i	$-0.477046\pi$
$673$	−15.1055	−	6.25688i	−0.582272	−	0.241185i	−0.654322	+	0.756216i	$0.727046\pi$
$674$		0			0
$675$	7.71888	+	5.92291i	0.297100	+	0.227973i
$676$		0			0
$677$	−41.0865	−	5.40914i	−1.57908	−	0.207890i	−0.710595	−	0.703601i	$-0.751574\pi$
$677$	−41.0865	−	5.40914i	−1.57908	−	0.207890i	−0.868487	+	0.495711i	$0.834907\pi$
$678$		0			0
$679$	−13.3579	−	6.45944i	−0.512630	−	0.247891i
$680$		0			0
$681$	17.9586	−	31.1051i	0.688173	−	1.19195i
$682$		0			0
$683$	−15.3486	+	20.0026i	−0.587296	+	0.765379i	−0.988600	−	0.150566i	$-0.951890\pi$
$683$	−15.3486	+	20.0026i	−0.587296	+	0.765379i	0.401304	+	0.915945i	$0.368557\pi$
$684$		0			0
$685$	−18.5784	+	7.69541i	−0.709843	+	0.294027i
$686$		0			0
$687$	−34.5947	−	14.3296i	−1.31987	−	0.546708i
$688$		0			0
$689$	4.33016	+	1.16026i	0.164966	+	0.0442024i
$690$		0			0
$691$	11.4923	+	14.9771i	0.437189	+	0.569756i	0.959036	−	0.283283i	$-0.0914235\pi$
$691$	11.4923	+	14.9771i	0.437189	+	0.569756i	−0.521847	+	0.853039i	$0.674757\pi$
$692$		0			0
$693$	−3.33754	+	6.90193i	−0.126783	+	0.262182i
$694$		0			0
$695$	33.9284	−	9.09108i	1.28698	−	0.344844i
$696$		0			0
$697$	10.2438	−	2.70889i	0.388012	−	0.102607i
$698$		0			0
$699$	−8.45177	−	8.45177i	−0.319675	−	0.319675i
$700$		0			0
$701$		−	6.78935i		−	0.256430i	−0.991746	−	0.128215i	$-0.959075\pi$
$701$		−	6.78935i		−	0.256430i	0.991746	−	0.128215i	$-0.0409248\pi$
$702$		0			0
$703$	3.99521	−	0.525979i	0.150682	−	0.0198377i
$704$		0			0
$705$	−7.89148	−	29.4514i	−0.297210	−	1.10920i
$706$		0			0
$707$	−8.70978	+	26.3254i	−0.327565	+	0.990068i
$708$		0			0
$709$	4.91832	−	37.3583i	0.184711	−	1.40302i	−0.608248	−	0.793747i	$-0.708127\pi$
$709$	4.91832	−	37.3583i	0.184711	−	1.40302i	0.792959	−	0.609275i	$-0.208539\pi$
$710$		0			0
$711$	−5.50950	+	7.18012i	−0.206622	+	0.269276i
$712$		0			0
$713$	−19.3492			−0.724634
$714$		0			0
$715$	−47.5822			−1.77947
$716$		0			0
$717$	9.81459	−	12.7906i	0.366532	−	0.477674i
$718$		0			0
$719$	1.08495	−	8.24105i	0.0404620	−	0.307339i	−0.959232	−	0.282618i	$-0.908797\pi$
$719$	1.08495	−	8.24105i	0.0404620	−	0.307339i	0.999694	−	0.0247209i	$-0.00786969\pi$
$720$		0			0
$721$	5.69546	−	1.17876i	0.212110	−	0.0438994i
$722$		0			0
$723$	−3.21085	−	11.9831i	−0.119413	−	0.445655i
$724$		0			0
$725$	−1.04183	+	0.137160i	−0.0386927	+	0.00509399i
$726$		0			0
$727$		−	10.0666i		−	0.373351i	−0.982422	−	0.186675i	$-0.940229\pi$
$727$		−	10.0666i		−	0.373351i	0.982422	−	0.186675i	$-0.0597713\pi$
$728$		0			0
$729$	21.2359	+	21.2359i	0.786514	+	0.786514i
$730$		0			0
$731$	−2.15456	+	15.9613i	−0.0796894	+	0.590352i
$732$		0			0
$733$	2.24023	−	0.600269i	0.0827450	−	0.0221714i	−0.217209	−	0.976125i	$-0.569695\pi$
$733$	2.24023	−	0.600269i	0.0827450	−	0.0221714i	0.299954	+	0.953954i	$0.403029\pi$
$734$		0			0
$735$	−22.0128	+	17.4385i	−0.811953	+	0.643230i
$736$		0			0
$737$	−27.0145	−	35.2060i	−0.995093	−	1.29683i
$738$		0			0
$739$	15.9074	+	4.26238i	0.585164	+	0.156794i	0.539242	−	0.842151i	$-0.318711\pi$
$739$	15.9074	+	4.26238i	0.585164	+	0.156794i	0.0459221	+	0.998945i	$0.485377\pi$
$740$		0			0
$741$	37.9345	+	15.7130i	1.39356	+	0.577231i
$742$		0			0
$743$	−22.5321	+	9.33311i	−0.826623	+	0.342399i	−0.755565	−	0.655074i	$-0.772638\pi$
$743$	−22.5321	+	9.33311i	−0.826623	+	0.342399i	−0.0710582	+	0.997472i	$0.522638\pi$
$744$		0			0
$745$	−37.0113	+	48.2341i	−1.35599	+	1.76716i
$746$		0			0
$747$	3.40371	−	5.89540i	0.124535	−	0.215701i
$748$		0			0
$749$	36.0920	−	24.5218i	1.31877	−	0.896006i
$750$		0			0
$751$	−32.3112	−	4.25385i	−1.17905	−	0.155225i	−0.484581	−	0.874746i	$-0.661028\pi$
$751$	−32.3112	−	4.25385i	−1.17905	−	0.155225i	−0.694470	+	0.719521i	$0.744361\pi$
$752$		0			0
$753$	−6.41515	−	4.92252i	−0.233781	−	0.179387i
$754$		0			0
$755$	0.188767	+	0.0781899i	0.00686994	+	0.00284562i
$756$		0			0
$757$	4.71224	−	4.71224i	0.171269	−	0.171269i	−0.616268	−	0.787537i	$-0.711356\pi$
$757$	4.71224	−	4.71224i	0.171269	−	0.171269i	0.787537	+	0.616268i	$0.211356\pi$
$758$		0			0
$759$	−19.7629	+	2.60184i	−0.717349	+	0.0944408i
$760$		0			0
$761$	44.0230	+	25.4167i	1.59583	+	0.921355i	0.992278	+	0.124034i	$0.0395831\pi$
$761$	44.0230	+	25.4167i	1.59583	+	0.921355i	0.603555	+	0.797321i	$0.293750\pi$
$762$		0			0
$763$	−14.5441	+	16.8454i	−0.526531	+	0.609844i
$764$		0			0
$765$	−4.65635	+	4.62595i	−0.168351	+	0.167252i
$766$		0			0
$767$	−4.34893	+	16.2304i	−0.157031	+	0.586046i
$768$		0			0
$769$		−	28.7301i		−	1.03604i	−0.855370	−	0.518018i	$-0.826670\pi$
$769$		−	28.7301i		−	1.03604i	0.855370	−	0.518018i	$-0.173330\pi$
$770$		0			0
$771$	3.15296	−	7.61193i	0.113551	−	0.274137i
$772$		0			0
$773$	36.7906	+	9.85800i	1.32326	+	0.354568i	0.850200	−	0.526460i	$-0.176481\pi$
$773$	36.7906	+	9.85800i	1.32326	+	0.354568i	0.473064	+	0.881028i	$0.343148\pi$
$774$		0			0
$775$	−9.80209	+	7.52141i	−0.352101	+	0.270177i
$776$		0			0
$777$	−2.39874	−	0.138598i	−0.0860541	−	0.00497218i
$778$		0			0
$779$	17.4670	+	2.29958i	0.625822	+	0.0823910i
$780$		0			0
$781$	−13.1631	−	22.7992i	−0.471013	−	0.815818i
$782$		0			0
$783$	−3.36537			−0.120269
$784$		0			0
$785$	19.5630	+	47.2292i	0.698232	+	1.68568i
$786$		0			0
$787$	−17.6451	−	13.5396i	−0.628981	−	0.482634i	0.244398	−	0.969675i	$-0.421410\pi$
$787$	−17.6451	−	13.5396i	−0.628981	−	0.482634i	−0.873379	+	0.487041i	$0.838076\pi$
$788$		0			0
$789$	36.2877	−	27.8445i	1.29188	−	0.991292i
$790$		0			0
$791$	−32.2678	+	11.2325i	−1.14731	+	0.399383i
$792$		0			0
$793$	−14.6727	−	19.1218i	−0.521043	−	0.679036i
$794$		0			0
$795$	4.01770	−	2.31962i	0.142493	−	0.0822684i
$796$		0			0
$797$	−7.76070	−	7.76070i	−0.274898	−	0.274898i	0.556170	−	0.831068i	$-0.312270\pi$
$797$	−7.76070	−	7.76070i	−0.274898	−	0.274898i	−0.831068	+	0.556170i	$0.812270\pi$
$798$		0			0
$799$	31.0808	−	3.98834i	1.09956	−	0.141097i
$800$		0			0
$801$	−0.255352	+	0.952987i	−0.00902242	+	0.0336721i
$802$		0			0
$803$	59.4162	+	34.3039i	2.09675	+	1.21056i
$804$		0			0
$805$	17.8042	+	5.89054i	0.627515	+	0.207614i
$806$		0			0
$807$	−1.43378	−	5.35096i	−0.0504716	−	0.188363i
$808$		0			0
$809$	−0.360535	−	2.73853i	−0.0126757	−	0.0962817i	0.983938	−	0.178513i	$-0.0571287\pi$
$809$	−0.360535	−	2.73853i	−0.0126757	−	0.0962817i	−0.996613	+	0.0822314i	$0.973795\pi$
$810$		0			0
$811$	−0.158954	+	0.0658408i	−0.00558162	+	0.00231198i	−0.385472	−	0.922719i	$-0.625962\pi$
$811$	−0.158954	+	0.0658408i	−0.00558162	+	0.00231198i	0.379891	+	0.925031i	$0.375962\pi$
$812$		0			0
$813$	5.99853	+	14.4817i	0.210378	+	0.507897i
$814$		0			0
$815$	31.5287	+	54.6093i	1.10440	+	1.91288i
$816$		0			0
$817$	−13.3897	+	23.1917i	−0.468448	+	0.811375i
$818$		0			0
$819$	5.25503	+	3.45281i	0.183626	+	0.120651i
$820$		0			0
$821$	−6.46497	+	49.1063i	−0.225629	+	1.71382i	0.385850	+	0.922561i	$0.373908\pi$
$821$	−6.46497	+	49.1063i	−0.225629	+	1.71382i	−0.611479	+	0.791260i	$0.709425\pi$
$822$		0			0
$823$	3.47201	+	26.3725i	0.121027	+	0.919288i	0.938972	+	0.343993i	$0.111780\pi$
$823$	3.47201	+	26.3725i	0.121027	+	0.919288i	−0.817946	+	0.575295i	$0.804887\pi$
$824$		0			0
$825$	−9.00029	+	9.00029i	−0.313350	+	0.313350i
$826$		0			0
$827$	−10.4038	+	25.1170i	−0.361776	+	0.873405i	0.633265	+	0.773935i	$0.281715\pi$
$827$	−10.4038	+	25.1170i	−0.361776	+	0.873405i	−0.995041	+	0.0994694i	$0.968285\pi$
$828$		0			0
$829$	10.6947	−	6.17459i	0.371442	−	0.214452i	−0.302646	−	0.953103i	$-0.597870\pi$
$829$	10.6947	−	6.17459i	0.371442	−	0.214452i	0.674088	+	0.738651i	$0.264537\pi$
$830$		0			0
$831$	16.2025	−	4.34143i	0.562057	−	0.150603i
$832$		0			0
$833$	−14.7346	−	24.8172i	−0.510522	−	0.859865i
$834$		0			0
$835$	−37.2503	+	9.98119i	−1.28910	+	0.345413i
$836$		0			0
$837$	−34.2678	+	19.7845i	−1.18447	+	0.683853i
$838$		0			0
$839$	−4.68284	+	11.3054i	−0.161670	+	0.390305i	−0.983868	−	0.178896i	$-0.942747\pi$
$839$	−4.68284	+	11.3054i	−0.161670	+	0.390305i	0.822198	+	0.569201i	$0.192747\pi$
$840$		0			0
$841$	−20.2491	+	20.2491i	−0.698244	+	0.698244i
$842$		0			0
$843$	0.309032	+	2.34733i	0.0106436	+	0.0808463i
$844$		0			0
$845$	−0.687619	+	5.22299i	−0.0236548	+	0.179676i
$846$		0			0
$847$	−25.0782	−	16.4776i	−0.861697	−	0.566177i
$848$		0			0
$849$	11.1795	−	19.3634i	0.383679	−	0.664552i
$850$		0			0
$851$	0.802248	+	1.38953i	0.0275007	+	0.0476326i
$852$		0			0
$853$	−0.874162	−	2.11041i	−0.0299307	−	0.0722592i	0.908207	−	0.418520i	$-0.137451\pi$
$853$	−0.874162	−	2.11041i	−0.0299307	−	0.0722592i	−0.938138	+	0.346261i	$0.887451\pi$
$854$		0			0
$855$	−10.0825	+	4.17632i	−0.344816	+	0.142827i
$856$		0			0
$857$	−3.82408	−	29.0468i	−0.130628	−	0.992218i	−0.923707	−	0.383100i	$-0.874857\pi$
$857$	−3.82408	−	29.0468i	−0.130628	−	0.992218i	0.793079	−	0.609119i	$-0.208477\pi$
$858$		0			0
$859$	−2.12627	−	7.93533i	−0.0725472	−	0.270750i	0.920119	−	0.391640i	$-0.128092\pi$
$859$	−2.12627	−	7.93533i	−0.0725472	−	0.270750i	−0.992666	+	0.120890i	$0.961425\pi$
$860$		0			0
$861$	−9.97309	−	3.29961i	−0.339882	−	0.112450i
$862$		0			0
$863$	1.15408	+	0.666309i	0.0392854	+	0.0226814i	0.519514	−	0.854462i	$-0.326113\pi$
$863$	1.15408	+	0.666309i	0.0392854	+	0.0226814i	−0.480229	+	0.877143i	$0.659446\pi$
$864$		0			0
$865$	15.3758	−	57.3832i	0.522792	−	1.95109i
$866$		0			0
$867$	15.8520	+	20.9414i	0.538363	+	0.711208i
$868$		0			0
$869$	−49.3418	−	49.3418i	−1.67381	−	1.67381i
$870$		0			0
$871$	−31.5199	+	18.1980i	−1.06801	+	0.616616i
$872$		0			0
$873$	2.09295	+	2.72758i	0.0708356	+	0.0923147i
$874$		0			0
$875$	−21.1329	+	7.35641i	−0.714422	+	0.248692i
$876$		0			0
$877$	−0.107307	+	0.0823398i	−0.00362351	+	0.00278042i	−0.610572	−	0.791961i	$-0.709060\pi$
$877$	−0.107307	+	0.0823398i	−0.00362351	+	0.00278042i	0.606948	+	0.794741i	$0.292394\pi$
$878$		0			0
$879$	9.51031	+	7.29752i	0.320775	+	0.246139i
$880$		0			0
$881$	−2.10222	−	5.07521i	−0.0708257	−	0.170988i	0.884502	−	0.466536i	$-0.154498\pi$
$881$	−2.10222	−	5.07521i	−0.0708257	−	0.170988i	−0.955328	+	0.295547i	$0.904498\pi$
$882$		0			0
$883$	16.2009			0.545205			0.272602	−	0.962127i	$-0.412116\pi$
$883$	16.2009			0.545205			0.272602	+	0.962127i	$0.412116\pi$
$884$		0			0
$885$	8.69446	+	15.0593i	0.292261	+	0.506211i
$886$		0			0
$887$	−18.7910	−	2.47389i	−0.630941	−	0.0830649i	−0.191728	−	0.981448i	$-0.561409\pi$
$887$	−18.7910	−	2.47389i	−0.630941	−	0.0830649i	−0.439213	+	0.898383i	$0.644743\pi$
$888$		0			0
$889$	−33.4223	−	1.93113i	−1.12095	−	0.0647680i
$890$		0			0
$891$	−25.4435	+	19.5235i	−0.852388	+	0.654061i
$892$		0			0
$893$	50.3262	+	13.4849i	1.68410	+	0.451253i
$894$		0			0
$895$	19.5836	−	47.2791i	0.654609	−	1.58036i
$896$		0			0
$897$			16.3488i			0.545872i
$898$		0			0
$899$	1.10610	−	4.12801i	0.0368904	−	0.137677i
$900$		0			0
$901$	1.81014	+	4.41088i	0.0603045	+	0.146948i
$902$		0			0
$903$	10.4349	−	12.0861i	0.347253	−	0.402199i
$904$		0			0
$905$	42.1222	+	24.3193i	1.40019	+	0.808400i
$906$		0			0
$907$	31.2980	−	4.12045i	1.03923	−	0.136817i	0.408452	−	0.912780i	$-0.366069\pi$
$907$	31.2980	−	4.12045i	1.03923	−	0.136817i	0.630779	+	0.775962i	$0.282735\pi$
$908$		0			0
$909$	4.54318	−	4.54318i	0.150688	−	0.150688i
$910$		0			0
$911$	−22.6155	−	9.36763i	−0.749284	−	0.310363i	−0.0248343	−	0.999692i	$-0.507906\pi$
$911$	−22.6155	−	9.36763i	−0.749284	−	0.310363i	−0.724449	+	0.689328i	$0.757906\pi$
$912$		0			0
$913$	41.6403	+	31.9517i	1.37809	+	1.05745i
$914$		0			0
$915$	−24.7297	−	3.25572i	−0.817538	−	0.107631i
$916$		0			0
$917$	−17.2361	+	11.7106i	−0.569187	+	0.386720i
$918$		0			0
$919$	3.50975	−	6.07906i	0.115776	−	0.200530i	−0.802314	−	0.596903i	$-0.796398\pi$
$919$	3.50975	−	6.07906i	0.115776	−	0.200530i	0.918090	+	0.396373i	$0.129731\pi$
$920$		0			0
$921$	31.9146	−	41.5920i	1.05162	−	1.37050i
$922$		0			0
$923$	−19.9484	+	8.26288i	−0.656608	+	0.271976i
$924$		0			0
$925$	0.946548	+	0.392073i	0.0311223	+	0.0128913i
$926$		0			0
$927$	−1.30174	−	0.348800i	−0.0427548	−	0.0114561i
$928$		0			0
$929$	6.97753	+	9.09330i	0.228925	+	0.298341i	0.893666	−	0.448733i	$-0.148125\pi$
$929$	6.97753	+	9.09330i	0.228925	+	0.298341i	−0.664740	+	0.747074i	$0.731458\pi$
$930$		0			0
$931$	−6.99889	−	47.4750i	−0.229379	−	1.55593i
$932$		0			0
$933$	6.20487	−	1.66259i	0.203138	−	0.0544307i
$934$		0			0
$935$	−30.6757	−	40.2497i	−1.00320	−	1.31630i
$936$		0			0
$937$	11.2251	+	11.2251i	0.366709	+	0.366709i	0.866276	−	0.499566i	$-0.166507\pi$
$937$	11.2251	+	11.2251i	0.366709	+	0.366709i	−0.499566	+	0.866276i	$0.666507\pi$
$938$		0			0
$939$			15.1409i			0.494104i
$940$		0			0
$941$	58.4183	−	7.69092i	1.90438	−	0.250717i	0.915827	−	0.401573i	$-0.131536\pi$
$941$	58.4183	−	7.69092i	1.90438	−	0.250717i	0.988556	+	0.150856i	$0.0482029\pi$
$942$		0			0
$943$	1.81558	+	6.77583i	0.0591233	+	0.220651i
$944$		0			0
$945$	37.5546	−	7.77249i	1.22165	−	0.252839i
$946$		0			0
$947$	7.17016	−	54.4628i	0.232999	−	1.76980i	−0.330617	−	0.943765i	$-0.607257\pi$
$947$	7.17016	−	54.4628i	0.232999	−	1.76980i	0.563616	−	0.826037i	$-0.309410\pi$
$948$		0			0
$949$	34.2551	−	44.6421i	1.11197	−	1.44914i
$950$		0			0
$951$	34.9688			1.13394
$952$		0			0
$953$	57.1733			1.85202			0.926012	−	0.377495i	$-0.123214\pi$
$953$	57.1733			1.85202			0.926012	+	0.377495i	$0.123214\pi$
$954$		0			0
$955$	16.9849	−	22.1351i	0.549618	−	0.716276i
$956$		0			0
$957$	0.574665	−	4.36501i	0.0185763	−	0.141101i
$958$		0			0
$959$	−6.43564	+	19.4518i	−0.207818	+	0.628130i
$960$		0			0
$961$	−4.98177	−	18.5922i	−0.160702	−	0.599749i
$962$		0			0
$963$	−10.0240	+	1.31968i	−0.323018	+	0.0425261i
$964$		0			0
$965$		−	3.88377i		−	0.125023i
$966$		0			0
$967$	−5.68190	−	5.68190i	−0.182718	−	0.182718i	0.609821	−	0.792539i	$-0.291241\pi$
$967$	−5.68190	−	5.68190i	−0.182718	−	0.182718i	−0.792539	+	0.609821i	$0.791241\pi$
$968$		0			0
$969$	11.1644	+	42.2187i	0.358651	+	1.35626i
$970$		0			0
$971$	6.70545	−	1.79672i	0.215188	−	0.0576595i	−0.149614	−	0.988744i	$-0.547803\pi$
$971$	6.70545	−	1.79672i	0.215188	−	0.0576595i	0.364802	+	0.931085i	$0.381137\pi$
$972$		0			0
$973$	15.5801	−	32.2191i	0.499475	−	1.03290i
$974$		0			0
$975$	6.35510	+	8.28213i	0.203526	+	0.265240i
$976$		0			0
$977$	−11.9305	−	3.19677i	−0.381691	−	0.102274i	0.0628717	−	0.998022i	$-0.479974\pi$
$977$	−11.9305	−	3.19677i	−0.381691	−	0.102274i	−0.444562	+	0.895748i	$0.646641\pi$
$978$		0			0
$979$	−7.02786	−	2.91104i	−0.224611	−	0.0930371i
$980$		0			0
$981$	4.76422	−	1.97340i	0.152110	−	0.0630060i
$982$		0			0
$983$	9.66462	−	12.5952i	0.308253	−	0.401724i	−0.613378	−	0.789789i	$-0.710190\pi$
$983$	9.66462	−	12.5952i	0.308253	−	0.401724i	0.921632	+	0.388066i	$0.126857\pi$
$984$		0			0
$985$	−4.80606	+	8.32434i	−0.153134	+	0.265236i
$986$		0			0
$987$	−27.9677	−	13.5242i	−0.890221	−	0.430481i
$988$		0			0
$989$	−10.5715	−	1.39177i	−0.336155	−	0.0442557i
$990$		0			0
$991$	11.7510	+	9.01684i	0.373282	+	0.286429i	0.778317	−	0.627872i	$-0.216074\pi$
$991$	11.7510	+	9.01684i	0.373282	+	0.286429i	−0.405035	+	0.914301i	$0.632741\pi$
$992$		0			0
$993$	1.97558	+	0.818313i	0.0626932	+	0.0259684i
$994$		0			0
$995$	4.46418	−	4.46418i	0.141524	−	0.141524i
$996$		0			0
$997$	7.72156	−	1.01656i	0.244544	−	0.0321949i	−0.00725757	−	0.999974i	$-0.502310\pi$
$997$	7.72156	−	1.01656i	0.244544	−	0.0321949i	0.251802	+	0.967779i	$0.418977\pi$
$998$		0			0
$999$	2.84159	+	1.64059i	0.0899039	+	0.0519060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	476.2.bh.a.457.5	yes	96
7.4	even	3	inner	476.2.bh.a.389.8	yes	96
17.8	even	8	inner	476.2.bh.a.93.8	yes	96
119.25	even	24	inner	476.2.bh.a.25.5	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
476.2.bh.a.25.5	✓	96	119.25	even	24	inner
476.2.bh.a.93.8	yes	96	17.8	even	8	inner
476.2.bh.a.389.8	yes	96	7.4	even	3	inner
476.2.bh.a.457.5	yes	96	1.1	even	1	trivial

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.bh (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.940523 + 1.22571i) q^{3} +(0.338941 - 2.57451i) q^{5} +(-1.75980 - 1.97563i) q^{7} +(0.158668 + 0.592157i) q^{9} +O(q^{10})\)	\(q+(-0.940523 + 1.22571i) q^{3} +(0.338941 - 2.57451i) q^{5} +(-1.75980 - 1.97563i) q^{7} +(0.158668 + 0.592157i) q^{9} +(-4.68625 + 0.616957i) q^{11} +3.87669i q^{13} +(2.83683 + 2.83683i) q^{15} +(-3.27928 + 2.49926i) q^{17} +(-6.62185 + 1.77432i) q^{19} +(4.07668 - 0.298883i) q^{21} +(-1.66169 - 2.16556i) q^{23} +(-1.68359 - 0.451116i) q^{25} +(-5.15716 - 2.13617i) q^{27} +(0.556997 - 0.230716i) q^{29} +(4.31526 - 5.62375i) q^{31} +(3.65132 - 6.32426i) q^{33} +(-5.68274 + 3.86099i) q^{35} +(-0.582779 - 0.0767242i) q^{37} +(-4.75171 - 3.64611i) q^{39} +(-2.37427 - 0.983455i) q^{41} +(2.76217 - 2.76217i) q^{43} +(1.57829 - 0.207786i) q^{45} +(-6.58180 - 3.80000i) q^{47} +(-0.806224 + 6.95342i) q^{49} +(0.0208658 - 6.37007i) q^{51} +(0.299292 - 1.11697i) q^{53} +12.2739i q^{55} +(4.05320 - 9.78528i) q^{57} +(4.18667 + 1.12181i) q^{59} +(-4.93252 + 3.78485i) q^{61} +(0.890659 - 1.35554i) q^{63} +(9.98058 + 1.31397i) q^{65} +(4.69421 + 8.13062i) q^{67} +4.21721 q^{69} +(2.13143 + 5.14572i) q^{71} +(-11.5155 - 8.83616i) q^{73} +(2.13639 - 1.63931i) q^{75} +(9.46574 + 8.17258i) q^{77} +(8.98710 + 11.7122i) q^{79} +(5.87602 - 3.39252i) q^{81} +(-7.85190 - 7.85190i) q^{83} +(5.32288 + 9.28965i) q^{85} +(-0.241077 + 0.899712i) q^{87} +(1.39374 + 0.804675i) q^{89} +(7.65890 - 6.82219i) q^{91} +(2.83451 + 10.5785i) q^{93} +(2.32359 + 17.6494i) q^{95} +(5.18124 - 2.14614i) q^{97} +(-1.10889 - 2.67711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{5}+O(q^{10}) \) 96 * q + 4 * q^5	\( 96 q + 4 q^{5} - 4 q^{11} + 40 q^{15} - 8 q^{17} + 12 q^{23} - 4 q^{25} + 48 q^{27} - 48 q^{33} - 16 q^{35} + 32 q^{37} + 8 q^{39} + 56 q^{41} - 32 q^{43} + 12 q^{45} - 44 q^{49} + 8 q^{51} + 48 q^{53} + 8 q^{59} + 12 q^{61} - 24 q^{63} - 8 q^{65} + 8 q^{67} - 160 q^{69} + 48 q^{71} - 20 q^{73} - 32 q^{75} + 24 q^{77} + 32 q^{79} - 40 q^{83} + 40 q^{85} - 96 q^{87} - 48 q^{91} + 12 q^{93} - 12 q^{95} + 96 q^{97} + 56 q^{99}+O(q^{100}) \) 96 * q + 4 * q^5 - 4 * q^11 + 40 * q^15 - 8 * q^17 + 12 * q^23 - 4 * q^25 + 48 * q^27 - 48 * q^33 - 16 * q^35 + 32 * q^37 + 8 * q^39 + 56 * q^41 - 32 * q^43 + 12 * q^45 - 44 * q^49 + 8 * q^51 + 48 * q^53 + 8 * q^59 + 12 * q^61 - 24 * q^63 - 8 * q^65 + 8 * q^67 - 160 * q^69 + 48 * q^71 - 20 * q^73 - 32 * q^75 + 24 * q^77 + 32 * q^79 - 40 * q^83 + 40 * q^85 - 96 * q^87 - 48 * q^91 + 12 * q^93 - 12 * q^95 + 96 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more