LMFDB - Embedded newform 1120.2.bq.b.719.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(719,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("1120.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.11
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.833565 - 1.44378i) q^{3} +(0.660510 + 2.13629i) q^{5} +(2.56833 - 0.635367i) q^{7} +(0.110340 - 0.191114i) q^{9} +O(q^{10})$	\(q+(-0.833565 - 1.44378i) q^{3} +(0.660510 + 2.13629i) q^{5} +(2.56833 - 0.635367i) q^{7} +(0.110340 - 0.191114i) q^{9} +(0.395322 + 0.684718i) q^{11} +6.84388i q^{13} +(2.53375 - 2.73436i) q^{15} +(1.46309 + 2.53414i) q^{17} +(-1.96683 - 1.13555i) q^{19} +(-3.05820 - 3.17847i) q^{21} +(-0.946588 + 1.63954i) q^{23} +(-4.12745 + 2.82208i) q^{25} -5.36929 q^{27} -2.46658i q^{29} +(2.87365 + 4.97731i) q^{31} +(0.659054 - 1.14151i) q^{33} +(3.05373 + 5.06702i) q^{35} +(2.59082 - 4.48744i) q^{37} +(9.88103 - 5.70482i) q^{39} +3.71071i q^{41} +9.52516i q^{43} +(0.481155 + 0.109485i) q^{45} +(-0.185107 - 0.106871i) q^{47} +(6.19262 - 3.26366i) q^{49} +(2.43916 - 4.22474i) q^{51} +(3.21770 + 5.57322i) q^{53} +(-1.20164 + 1.29679i) q^{55} +3.78622i q^{57} +(-0.430991 + 0.248833i) q^{59} +(5.87951 - 10.1836i) q^{61} +(0.161961 - 0.560949i) q^{63} +(-14.6205 + 4.52045i) q^{65} +(2.83429 - 1.63638i) q^{67} +3.15617 q^{69} -4.40847i q^{71} +(3.18360 + 5.51416i) q^{73} +(7.51495 + 3.60674i) q^{75} +(1.45036 + 1.50741i) q^{77} +(-5.25074 - 3.03152i) q^{79} +(4.14463 + 7.17871i) q^{81} +13.5430 q^{83} +(-4.44727 + 4.79940i) q^{85} +(-3.56120 + 2.05606i) q^{87} +(-9.86730 - 5.69689i) q^{89} +(4.34837 + 17.5773i) q^{91} +(4.79075 - 8.29782i) q^{93} +(1.12675 - 4.95176i) q^{95} +13.0656 q^{97} +0.174479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{9}+O(q^{10}) $ 80 * q - 52 * q^9	$ 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) $ 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.833565	−	1.44378i	−0.481259	−	0.833565i	0.518510	−	0.855072i	$-0.326487\pi$
$3$	−0.833565	−	1.44378i	−0.481259	−	0.833565i	−0.999769	+	0.0215069i	$0.993154\pi$
$4$		0			0
$5$	0.660510	+	2.13629i	0.295389	+	0.955377i
$5$	0.660510	+	2.13629i	0.295389	+	0.955377i
$6$		0			0
$7$	2.56833	−	0.635367i	0.970737	−	0.240146i
$7$	2.56833	−	0.635367i	0.970737	−	0.240146i
$8$		0			0
$9$	0.110340	−	0.191114i	0.0367799	−	0.0637046i
$10$		0			0
$11$	0.395322	+	0.684718i	0.119194	+	0.206450i	0.919449	−	0.393210i	$-0.128636\pi$
$11$	0.395322	+	0.684718i	0.119194	+	0.206450i	−0.800254	+	0.599661i	$0.795302\pi$
$12$		0			0
$13$			6.84388i			1.89815i	0.315049	+	0.949076i	$0.397979\pi$
$13$			6.84388i			1.89815i	−0.315049	+	0.949076i	$0.602021\pi$
$14$		0			0
$15$	2.53375	−	2.73436i	0.654210	−	0.706009i
$16$		0			0
$17$	1.46309	+	2.53414i	0.354851	+	0.614620i	0.987092	−	0.160152i	$-0.0511983\pi$
$17$	1.46309	+	2.53414i	0.354851	+	0.614620i	−0.632242	+	0.774771i	$0.717865\pi$
$18$		0			0
$19$	−1.96683	−	1.13555i	−0.451222	−	0.260513i	0.257124	−	0.966378i	$-0.417225\pi$
$19$	−1.96683	−	1.13555i	−0.451222	−	0.260513i	−0.708346	+	0.705865i	$0.750558\pi$
$20$		0			0
$21$	−3.05820	−	3.17847i	−0.667353	−	0.693600i
$22$		0			0
$23$	−0.946588	+	1.63954i	−0.197377	+	0.341867i	−0.947677	−	0.319230i	$-0.896576\pi$
$23$	−0.946588	+	1.63954i	−0.197377	+	0.341867i	0.750300	+	0.661098i	$0.229909\pi$
$24$		0			0
$25$	−4.12745	+	2.82208i	−0.825491	+	0.564416i
$26$		0			0
$27$	−5.36929			−1.03332
$28$		0			0
$29$		−	2.46658i		−	0.458033i	−0.973423	−	0.229017i	$-0.926449\pi$
$29$		−	2.46658i		−	0.458033i	0.973423	−	0.229017i	$-0.0735510\pi$
$30$		0			0
$31$	2.87365	+	4.97731i	0.516123	+	0.893951i	0.999825	+	0.0187183i	$0.00595857\pi$
$31$	2.87365	+	4.97731i	0.516123	+	0.893951i	−0.483702	+	0.875233i	$0.660708\pi$
$32$		0			0
$33$	0.659054	−	1.14151i	0.114727	−	0.198712i
$34$		0			0
$35$	3.05373	+	5.06702i	0.516175	+	0.856483i
$36$		0			0
$37$	2.59082	−	4.48744i	0.425929	−	0.737730i	−0.570578	−	0.821243i	$-0.693281\pi$
$37$	2.59082	−	4.48744i	0.425929	−	0.737730i	0.996507	+	0.0835133i	$0.0266141\pi$
$38$		0			0
$39$	9.88103	−	5.70482i	1.58223	−	0.913502i
$40$		0			0
$41$			3.71071i			0.579516i	0.957100	+	0.289758i	$0.0935748\pi$
$41$			3.71071i			0.579516i	−0.957100	+	0.289758i	$0.906425\pi$
$42$		0			0
$43$			9.52516i			1.45257i	0.687392	+	0.726286i	$0.258755\pi$
$43$			9.52516i			1.45257i	−0.687392	+	0.726286i	$0.741245\pi$
$44$		0			0
$45$	0.481155	+	0.109485i	0.0717263	+	0.0163210i
$46$		0			0
$47$	−0.185107	−	0.106871i	−0.0270006	−	0.0155888i	0.486439	−	0.873715i	$-0.338296\pi$
$47$	−0.185107	−	0.106871i	−0.0270006	−	0.0155888i	−0.513440	+	0.858126i	$0.671629\pi$
$48$		0			0
$49$	6.19262	−	3.26366i	0.884660	−	0.466237i
$50$		0			0
$51$	2.43916	−	4.22474i	0.341550	−	0.591582i
$52$		0			0
$53$	3.21770	+	5.57322i	0.441985	+	0.765540i	0.997837	−	0.0657412i	$-0.0209412\pi$
$53$	3.21770	+	5.57322i	0.441985	+	0.765540i	−0.555852	+	0.831281i	$0.687608\pi$
$54$		0			0
$55$	−1.20164	+	1.29679i	−0.162029	+	0.174859i
$56$		0			0
$57$			3.78622i			0.501497i
$58$		0			0
$59$	−0.430991	+	0.248833i	−0.0561102	+	0.0323953i	−0.527793	−	0.849373i	$-0.676980\pi$
$59$	−0.430991	+	0.248833i	−0.0561102	+	0.0323953i	0.471682	+	0.881768i	$0.343647\pi$
$60$		0			0
$61$	5.87951	−	10.1836i	0.752794	−	1.30388i	−0.193670	−	0.981067i	$-0.562039\pi$
$61$	5.87951	−	10.1836i	0.752794	−	1.30388i	0.946464	−	0.322810i	$-0.104628\pi$
$62$		0			0
$63$	0.161961	−	0.560949i	0.0204052	−	0.0706730i
$64$		0			0
$65$	−14.6205	+	4.52045i	−1.81345	+	0.560693i
$66$		0			0
$67$	2.83429	−	1.63638i	0.346264	−	0.199916i	−0.316774	−	0.948501i	$-0.602600\pi$
$67$	2.83429	−	1.63638i	0.346264	−	0.199916i	0.663039	+	0.748585i	$0.269266\pi$
$68$		0			0
$69$	3.15617			0.379958
$70$		0			0
$71$		−	4.40847i		−	0.523189i	−0.965178	−	0.261594i	$-0.915752\pi$
$71$		−	4.40847i		−	0.523189i	0.965178	−	0.261594i	$-0.0842483\pi$
$72$		0			0
$73$	3.18360	+	5.51416i	0.372612	+	0.645384i	0.989967	−	0.141302i	$-0.0451288\pi$
$73$	3.18360	+	5.51416i	0.372612	+	0.645384i	−0.617354	+	0.786685i	$0.711795\pi$
$74$		0			0
$75$	7.51495	+	3.60674i	0.867752	+	0.416470i
$76$		0			0
$77$	1.45036	+	1.50741i	0.165284	+	0.171785i
$78$		0			0
$79$	−5.25074	−	3.03152i	−0.590755	−	0.341072i	0.174641	−	0.984632i	$-0.444123\pi$
$79$	−5.25074	−	3.03152i	−0.590755	−	0.341072i	−0.765396	+	0.643560i	$0.777457\pi$
$80$		0			0
$81$	4.14463	+	7.17871i	0.460515	+	0.797635i
$82$		0			0
$83$	13.5430			1.48654			0.743271	−	0.668990i	$-0.233273\pi$
$83$	13.5430			1.48654			0.743271	+	0.668990i	$0.233273\pi$
$84$		0			0
$85$	−4.44727	+	4.79940i	−0.482375	+	0.520568i
$86$		0			0
$87$	−3.56120	+	2.05606i	−0.381800	+	0.220432i
$88$		0			0
$89$	−9.86730	−	5.69689i	−1.04593	−	0.603869i	−0.124424	−	0.992229i	$-0.539708\pi$
$89$	−9.86730	−	5.69689i	−1.04593	−	0.603869i	−0.921508	+	0.388360i	$0.873042\pi$
$90$		0			0
$91$	4.34837	+	17.5773i	0.455833	+	1.84261i
$92$		0			0
$93$	4.79075	−	8.29782i	0.496777	−	0.860444i
$94$		0			0
$95$	1.12675	−	4.95176i	0.115602	−	0.508040i
$96$		0			0
$97$	13.0656			1.32661			0.663303	−	0.748351i	$-0.269154\pi$
$97$	13.0656			1.32661			0.663303	+	0.748351i	$0.269154\pi$
$98$		0			0
$99$	0.174479			0.0175358
$100$		0			0
$101$	5.16640	+	8.94847i	0.514076	+	0.890406i	0.999867	+	0.0163310i	$0.00519856\pi$
$101$	5.16640	+	8.94847i	0.514076	+	0.890406i	−0.485790	+	0.874075i	$0.661468\pi$
$102$		0			0
$103$	17.1988	+	9.92971i	1.69464	+	0.978403i	0.950675	+	0.310189i	$0.100392\pi$
$103$	17.1988	+	9.92971i	1.69464	+	0.978403i	0.743969	+	0.668214i	$0.232941\pi$
$104$		0			0
$105$	4.77017	−	8.63260i	0.465521	−	0.842455i
$106$		0			0
$107$	−13.9595	−	8.05950i	−1.34951	−	0.779142i	−0.361333	−	0.932437i	$-0.617678\pi$
$107$	−13.9595	−	8.05950i	−1.34951	−	0.779142i	−0.988180	+	0.153295i	$0.951011\pi$
$108$		0			0
$109$	12.8463	−	7.41679i	1.23045	−	0.710400i	0.263326	−	0.964707i	$-0.415181\pi$
$109$	12.8463	−	7.41679i	1.23045	−	0.710400i	0.967124	+	0.254307i	$0.0818473\pi$
$110$		0			0
$111$	−8.63847			−0.819928
$112$		0			0
$113$		−	4.32459i		−	0.406823i	−0.979093	−	0.203411i	$-0.934797\pi$
$113$		−	4.32459i		−	0.406823i	0.979093	−	0.203411i	$-0.0652029\pi$
$114$		0			0
$115$	−4.12776	−	0.939254i	−0.384915	−	0.0875859i
$116$		0			0
$117$	1.30796	+	0.755151i	0.120921	+	0.0698138i
$118$		0			0
$119$	5.36780	+	5.57891i	0.492065	+	0.511418i
$120$		0			0
$121$	5.18744	−	8.98491i	0.471585	−	0.816810i
$122$		0			0
$123$	5.35744	−	3.09312i	0.483064	−	0.278897i
$124$		0			0
$125$	−8.75499	−	6.95342i	−0.783071	−	0.621933i
$126$		0			0
$127$	−4.67057			−0.414446			−0.207223	−	0.978294i	$-0.566443\pi$
$127$	−4.67057			−0.414446			−0.207223	+	0.978294i	$0.566443\pi$
$128$		0			0
$129$	13.7522	−	7.93983i	1.21081	−	0.699063i
$130$		0			0
$131$	−13.4161	−	7.74576i	−1.17217	−	0.676750i	−0.217977	−	0.975954i	$-0.569946\pi$
$131$	−13.4161	−	7.74576i	−1.17217	−	0.676750i	−0.954189	+	0.299204i	$0.903279\pi$
$132$		0			0
$133$	−5.77295	−	1.66681i	−0.500579	−	0.144530i
$134$		0			0
$135$	−3.54647	−	11.4703i	−0.305231	−	0.987210i
$136$		0			0
$137$	−12.5411	+	7.24059i	−1.07146	+	0.618606i	−0.928579	−	0.371135i	$-0.878969\pi$
$137$	−12.5411	+	7.24059i	−1.07146	+	0.618606i	−0.142877	+	0.989740i	$0.545635\pi$
$138$		0			0
$139$		−	10.9687i		−	0.930349i	−0.885219	−	0.465175i	$-0.845992\pi$
$139$		−	10.9687i		−	0.930349i	0.885219	−	0.465175i	$-0.154008\pi$
$140$		0			0
$141$			0.356337i			0.0300090i
$142$		0			0
$143$	−4.68613	+	2.70554i	−0.391874	+	0.226249i
$144$		0			0
$145$	5.26933	−	1.62920i	0.437594	−	0.135298i
$146$		0			0
$147$	−9.87394	−	6.22029i	−0.814389	−	0.513041i
$148$		0			0
$149$	12.7792	+	7.37808i	1.04691	+	0.604436i	0.921784	−	0.387704i	$-0.126732\pi$
$149$	12.7792	+	7.37808i	1.04691	+	0.604436i	0.125130	+	0.992140i	$0.460065\pi$
$150$		0			0
$151$	−13.6780	+	7.89697i	−1.11310	+	0.642647i	−0.939630	−	0.342193i	$-0.888830\pi$
$151$	−13.6780	+	7.89697i	−1.11310	+	0.642647i	−0.173467	+	0.984840i	$0.555497\pi$
$152$		0			0
$153$	0.645746			0.0522055
$154$		0			0
$155$	−8.73489	+	9.42651i	−0.701603	+	0.757155i
$156$		0			0
$157$	8.15924	−	4.71074i	0.651178	−	0.375958i	−0.137729	−	0.990470i	$-0.543980\pi$
$157$	8.15924	−	4.71074i	0.651178	−	0.375958i	0.788907	+	0.614512i	$0.210647\pi$
$158$		0			0
$159$	5.36432	−	9.29127i	0.425418	−	0.736846i
$160$		0			0
$161$	−1.38944	+	4.81230i	−0.109503	+	0.379263i
$162$		0			0
$163$	4.19953	+	2.42460i	0.328932	+	0.189909i	0.655367	−	0.755311i	$-0.272514\pi$
$163$	4.19953	+	2.42460i	0.328932	+	0.189909i	−0.326435	+	0.945220i	$0.605847\pi$
$164$		0			0
$165$	2.87391	+	0.653947i	0.223734	+	0.0509097i
$166$		0			0
$167$			10.5301i			0.814840i	0.913241	+	0.407420i	$0.133572\pi$
$167$			10.5301i			0.814840i	−0.913241	+	0.407420i	$0.866428\pi$
$168$		0			0
$169$	−33.8387			−2.60298
$170$		0			0
$171$	−0.434039	+	0.250592i	−0.0331918	+	0.0191633i
$172$		0			0
$173$	−10.0480	−	5.80119i	−0.763933	−	0.441057i	0.0667734	−	0.997768i	$-0.478730\pi$
$173$	−10.0480	−	5.80119i	−0.763933	−	0.441057i	−0.830706	+	0.556712i	$0.812063\pi$
$174$		0			0
$175$	−8.80760	+	9.87047i	−0.665792	+	0.746137i
$176$		0			0
$177$	0.718518	+	0.414836i	0.0540071	+	0.0311810i
$178$		0			0
$179$	−9.70530	−	16.8101i	−0.725408	−	1.25644i	−0.958806	−	0.284062i	$-0.908318\pi$
$179$	−9.70530	−	16.8101i	−0.725408	−	1.25644i	0.233398	−	0.972381i	$-0.425016\pi$
$180$		0			0
$181$	−16.8009			−1.24880			−0.624401	−	0.781104i	$-0.714657\pi$
$181$	−16.8009			−1.24880			−0.624401	+	0.781104i	$0.714657\pi$
$182$		0			0
$183$	−19.6038			−1.44915
$184$		0			0
$185$	11.2977	+	2.57075i	0.830625	+	0.189005i
$186$		0			0
$187$	−1.15678	+	2.00361i	−0.0845923	+	0.146518i
$188$		0			0
$189$	−13.7901	+	3.41147i	−1.00308	+	0.248148i
$190$		0			0
$191$	9.58750	+	5.53535i	0.693727	+	0.400524i	0.805007	−	0.593266i	$-0.202162\pi$
$191$	9.58750	+	5.53535i	0.693727	+	0.400524i	−0.111280	+	0.993789i	$0.535495\pi$
$192$		0			0
$193$	−2.30035	+	1.32811i	−0.165583	+	0.0955994i	−0.580501	−	0.814259i	$-0.697143\pi$
$193$	−2.30035	+	1.32811i	−0.165583	+	0.0955994i	0.414918	+	0.909859i	$0.363810\pi$
$194$		0			0
$195$	18.7137	+	17.3406i	1.34011	+	1.24179i
$196$		0			0
$197$	−9.96943			−0.710292			−0.355146	−	0.934811i	$-0.615569\pi$
$197$	−9.96943			−0.710292			−0.355146	+	0.934811i	$0.615569\pi$
$198$		0			0
$199$	−0.373969	−	0.647733i	−0.0265099	−	0.0459166i	0.852466	−	0.522783i	$-0.175106\pi$
$199$	−0.373969	−	0.647733i	−0.0265099	−	0.0459166i	−0.878976	+	0.476866i	$0.841773\pi$
$200$		0			0
$201$	−4.72514	−	2.72806i	−0.333285	−	0.192422i
$202$		0			0
$203$	−1.56718	−	6.33500i	−0.109995	−	0.444630i
$204$		0			0
$205$	−7.92715	+	2.45096i	−0.553656	+	0.171183i
$206$		0			0
$207$	0.208892	+	0.361812i	0.0145190	+	0.0251477i
$208$		0			0
$209$		−	1.79563i		−	0.124207i
$210$		0			0
$211$	13.0773			0.900281			0.450140	−	0.892958i	$-0.351374\pi$
$211$	13.0773			0.900281			0.450140	+	0.892958i	$0.351374\pi$
$212$		0			0
$213$	−6.36484	+	3.67474i	−0.436112	+	0.251789i
$214$		0			0
$215$	−20.3485	+	6.29146i	−1.38775	+	0.429074i
$216$		0			0
$217$	10.5429	+	10.9575i	0.715698	+	0.743846i
$218$		0			0
$219$	5.30748	−	9.19282i	0.358646	−	0.621193i
$220$		0			0
$221$	−17.3434	+	10.0132i	−1.16664	+	0.673560i
$222$		0			0
$223$			4.09586i			0.274279i	0.990552	+	0.137140i	$0.0437909\pi$
$223$			4.09586i			0.274279i	−0.990552	+	0.137140i	$0.956209\pi$
$224$		0			0
$225$	0.0839164	+	1.10020i	0.00559443	+	0.0733467i
$226$		0			0
$227$	−4.93818	−	8.55319i	−0.327759	−	0.567695i	0.654308	−	0.756228i	$-0.272960\pi$
$227$	−4.93818	−	8.55319i	−0.327759	−	0.567695i	−0.982067	+	0.188533i	$0.939627\pi$
$228$		0			0
$229$	−1.67919	+	2.90845i	−0.110964	+	0.192196i	−0.916159	−	0.400814i	$-0.868727\pi$
$229$	−1.67919	+	2.90845i	−0.110964	+	0.192196i	0.805195	+	0.593010i	$0.202061\pi$
$230$		0			0
$231$	0.967386	−	3.35052i	0.0636493	−	0.220448i
$232$		0			0
$233$	−17.2096	−	9.93598i	−1.12744	−	0.650927i	−0.184150	−	0.982898i	$-0.558953\pi$
$233$	−17.2096	−	9.93598i	−1.12744	−	0.650927i	−0.943290	+	0.331971i	$0.892286\pi$
$234$		0			0
$235$	0.106043	−	0.466031i	0.00691750	−	0.0304005i
$236$		0			0
$237$			10.1079i			0.656576i
$238$		0			0
$239$			6.74480i			0.436285i	0.975917	+	0.218142i	$0.0699997\pi$
$239$			6.74480i			0.436285i	−0.975917	+	0.218142i	$0.930000\pi$
$240$		0			0
$241$	−1.18354	+	0.683317i	−0.0762385	+	0.0440163i	−0.537635	−	0.843178i	$-0.680682\pi$
$241$	−1.18354	+	0.683317i	−0.0762385	+	0.0440163i	0.461396	+	0.887194i	$0.347349\pi$
$242$		0			0
$243$	−1.14430	+	1.98198i	−0.0734067	+	0.127144i
$244$		0			0
$245$	11.0624	+	11.0735i	0.706751	+	0.707462i
$246$		0			0
$247$	7.77157	−	13.4607i	0.494493	−	0.856487i
$248$		0			0
$249$	−11.2890	−	19.5531i	−0.715412	−	1.23913i
$250$		0			0
$251$			15.4536i			0.975423i	0.873005	+	0.487712i	$0.162168\pi$
$251$			15.4536i			0.975423i	−0.873005	+	0.487712i	$0.837832\pi$
$252$		0			0
$253$	−1.49683			−0.0941049
$254$		0			0
$255$	10.6364	+	2.42026i	0.666074	+	0.151562i
$256$		0			0
$257$	12.5171	−	21.6802i	0.780792	−	1.35237i	−0.150688	−	0.988581i	$-0.548149\pi$
$257$	12.5171	−	21.6802i	0.780792	−	1.35237i	0.931481	−	0.363791i	$-0.118518\pi$
$258$		0			0
$259$	3.80292	−	13.1713i	0.236302	−	0.818427i
$260$		0			0
$261$	−0.471398	−	0.272162i	−0.0291788	−	0.0168464i
$262$		0			0
$263$	−14.1558	−	24.5185i	−0.872883	−	1.51188i	−0.859001	−	0.511974i	$-0.828914\pi$
$263$	−14.1558	−	24.5185i	−0.872883	−	1.51188i	−0.0138820	−	0.999904i	$-0.504419\pi$
$264$		0			0
$265$	−9.78068	+	10.5551i	−0.600822	+	0.648394i
$266$		0			0
$267$			18.9949i			1.16247i
$268$		0			0
$269$	1.84643	+	3.19810i	0.112579	+	0.194992i	0.916809	−	0.399325i	$-0.130756\pi$
$269$	1.84643	+	3.19810i	0.112579	+	0.194992i	−0.804231	+	0.594317i	$0.797422\pi$
$270$		0			0
$271$	0.382982	−	0.663345i	0.0232645	−	0.0402953i	−0.854159	−	0.520012i	$-0.825927\pi$
$271$	0.382982	−	0.663345i	0.0232645	−	0.0402953i	0.877423	+	0.479717i	$0.159261\pi$
$272$		0			0
$273$	21.7531	−	20.9299i	1.31656	−	1.26674i
$274$		0			0
$275$	−3.56400	−	1.71051i	−0.214918	−	0.103148i
$276$		0			0
$277$	−9.73148	−	16.8554i	−0.584708	−	1.01274i	−0.994912	−	0.100750i	$-0.967876\pi$
$277$	−9.73148	−	16.8554i	−0.584708	−	1.01274i	0.410204	−	0.911994i	$-0.365458\pi$
$278$		0			0
$279$	1.26831			0.0759318
$280$		0			0
$281$	−7.20046			−0.429544			−0.214772	−	0.976664i	$-0.568901\pi$
$281$	−7.20046			−0.429544			−0.214772	+	0.976664i	$0.568901\pi$
$282$		0			0
$283$	−5.91380	−	10.2430i	−0.351539	−	0.608883i	0.634980	−	0.772528i	$-0.281008\pi$
$283$	−5.91380	−	10.2430i	−0.351539	−	0.608883i	−0.986519	+	0.163645i	$0.947675\pi$
$284$		0			0
$285$	−8.08845	+	2.50083i	−0.479118	+	0.148137i
$286$		0			0
$287$	2.35766	+	9.53033i	0.139168	+	0.562558i
$288$		0			0
$289$	4.21875	−	7.30709i	0.248162	−	0.429829i
$290$		0			0
$291$	−10.8910	−	18.8637i	−0.638441	−	1.10581i
$292$		0			0
$293$			11.8864i			0.694410i	0.937789	+	0.347205i	$0.112869\pi$
$293$			11.8864i			0.694410i	−0.937789	+	0.347205i	$0.887131\pi$
$294$		0			0
$295$	−0.816252	−	0.756364i	−0.0475240	−	0.0440372i
$296$		0			0
$297$	−2.12260	−	3.67645i	−0.123166	−	0.213329i
$298$		0			0
$299$	−11.2208	−	6.47834i	−0.648916	−	0.374652i
$300$		0			0
$301$	6.05197	+	24.4637i	0.348829	+	1.41007i
$302$		0			0
$303$	8.61306	−	14.9183i	0.494808	−	0.857032i
$304$		0			0
$305$	25.6386	+	5.83395i	1.46806	+	0.334051i
$306$		0			0
$307$	18.3489			1.04723			0.523615	−	0.851955i	$-0.324583\pi$
$307$	18.3489			1.04723			0.523615	+	0.851955i	$0.324583\pi$
$308$		0			0
$309$		−	33.1082i		−	1.88346i
$310$		0			0
$311$	3.85642	+	6.67951i	0.218677	+	0.378760i	0.954404	−	0.298518i	$-0.0964924\pi$
$311$	3.85642	+	6.67951i	0.218677	+	0.378760i	−0.735726	+	0.677279i	$0.763159\pi$
$312$		0			0
$313$	−8.58738	+	14.8738i	−0.485387	+	0.840716i	−0.999859	−	0.0167918i	$-0.994655\pi$
$313$	−8.58738	+	14.8738i	−0.485387	+	0.840716i	0.514472	+	0.857507i	$0.327988\pi$
$314$		0			0
$315$	1.30533	−	0.0245169i	0.0735468	−	0.00138137i
$316$		0			0
$317$	−9.77351	+	16.9282i	−0.548935	+	0.950784i	0.449413	+	0.893324i	$0.351633\pi$
$317$	−9.77351	+	16.9282i	−0.548935	+	0.950784i	−0.998348	+	0.0574593i	$0.981700\pi$
$318$		0			0
$319$	1.68892	−	0.975096i	0.0945611	−	0.0545949i
$320$		0			0
$321$			26.8725i			1.49988i
$322$		0			0
$323$		−	6.64563i		−	0.369773i
$324$		0			0
$325$	−19.3140	−	28.2478i	−1.07135	−	1.56691i
$326$		0			0
$327$	−21.4164	−	12.3648i	−1.18433	−	0.683773i
$328$		0			0
$329$	−0.543317	−	0.156870i	−0.0299540	−	0.00864853i
$330$		0			0
$331$	1.08473	−	1.87881i	0.0596222	−	0.103269i	−0.834674	−	0.550745i	$-0.814344\pi$
$331$	1.08473	−	1.87881i	0.0596222	−	0.103269i	0.894296	+	0.447476i	$0.147677\pi$
$332$		0			0
$333$	−0.571741	−	0.990284i	−0.0313312	−	0.0542672i
$334$		0			0
$335$	5.36786	+	4.97403i	0.293278	+	0.271760i
$336$		0			0
$337$			0.664494i			0.0361973i	0.999836	+	0.0180986i	$0.00576129\pi$
$337$			0.664494i			0.0361973i	−0.999836	+	0.0180986i	$0.994239\pi$
$338$		0			0
$339$	−6.24374	+	3.60482i	−0.339113	+	0.195787i
$340$		0			0
$341$	−2.27204	+	3.93528i	−0.123038	+	0.213108i
$342$		0			0
$343$	13.8311	−	12.3167i	0.746807	−	0.665041i
$344$		0			0
$345$	2.08468	+	6.74249i	0.112235	+	0.363003i
$346$		0			0
$347$	23.4079	−	13.5146i	1.25660	−	0.725500i	0.284190	−	0.958768i	$-0.408275\pi$
$347$	23.4079	−	13.5146i	1.25660	−	0.725500i	0.972412	+	0.233268i	$0.0749421\pi$
$348$		0			0
$349$	22.2420			1.19059			0.595295	−	0.803508i	$-0.297035\pi$
$349$	22.2420			1.19059			0.595295	+	0.803508i	$0.297035\pi$
$350$		0			0
$351$		−	36.7468i		−	1.96140i
$352$		0			0
$353$	−6.08471	−	10.5390i	−0.323856	−	0.560936i	0.657424	−	0.753521i	$-0.271646\pi$
$353$	−6.08471	−	10.5390i	−0.323856	−	0.560936i	−0.981280	+	0.192585i	$0.938313\pi$
$354$		0			0
$355$	9.41776	−	2.91183i	0.499843	−	0.154544i
$356$		0			0
$357$	3.58029	−	12.4003i	0.189489	−	0.656293i
$358$		0			0
$359$	28.3997	+	16.3965i	1.49888	+	0.865377i	0.999999	−	0.00129574i	$-0.000412446\pi$
$359$	28.3997	+	16.3965i	1.49888	+	0.865377i	0.498877	+	0.866673i	$0.333746\pi$
$360$		0			0
$361$	−6.92105	−	11.9876i	−0.364266	−	0.630927i
$362$		0			0
$363$	−17.2963			−0.907819
$364$		0			0
$365$	−9.67703	+	10.4432i	−0.506519	+	0.546625i
$366$		0			0
$367$	0.00646496	−	0.00373255i	0.000337468	−	0.000194837i	−0.499831	−	0.866123i	$-0.666605\pi$
$367$	0.00646496	−	0.00373255i	0.000337468	−	0.000194837i	0.500169	+	0.865928i	$0.333271\pi$
$368$		0			0
$369$	0.709169	+	0.409439i	0.0369178	+	0.0213145i
$370$		0			0
$371$	11.8051	+	12.2694i	0.612892	+	0.636997i
$372$		0			0
$373$	17.5825	−	30.4538i	0.910388	−	1.57684i	0.0968723	−	0.995297i	$-0.469116\pi$
$373$	17.5825	−	30.4538i	0.910388	−	1.57684i	0.813516	−	0.581542i	$-0.197551\pi$
$374$		0			0
$375$	−2.74133	+	18.4364i	−0.141562	+	0.952051i
$376$		0			0
$377$	16.8810			0.869416
$378$		0			0
$379$	−17.3297			−0.890165			−0.445082	−	0.895490i	$-0.646826\pi$
$379$	−17.3297			−0.890165			−0.445082	+	0.895490i	$0.646826\pi$
$380$		0			0
$381$	3.89322	+	6.74326i	0.199456	+	0.345468i
$382$		0			0
$383$	−5.87162	−	3.38998i	−0.300026	−	0.173220i	0.342429	−	0.939544i	$-0.388751\pi$
$383$	−5.87162	−	3.38998i	−0.300026	−	0.173220i	−0.642455	+	0.766324i	$0.722084\pi$
$384$		0			0
$385$	−2.26228	+	4.09405i	−0.115296	+	0.208652i
$386$		0			0
$387$	1.82039	+	1.05100i	0.0925356	+	0.0534254i
$388$		0			0
$389$	−4.97969	+	2.87502i	−0.252480	+	0.145770i	−0.620899	−	0.783890i	$-0.713232\pi$
$389$	−4.97969	+	2.87502i	−0.252480	+	0.145770i	0.368419	+	0.929660i	$0.379899\pi$
$390$		0			0
$391$	−5.53977			−0.280158
$392$		0			0
$393$			25.8264i			1.30277i
$394$		0			0
$395$	3.00803	−	13.2194i	0.151350	−	0.665142i
$396$		0			0
$397$	4.00016	+	2.30949i	0.200762	+	0.115910i	0.597011	−	0.802233i	$-0.296355\pi$
$397$	4.00016	+	2.30949i	0.200762	+	0.115910i	−0.396249	+	0.918143i	$0.629688\pi$
$398$		0			0
$399$	2.40564	+	9.72425i	0.120432	+	0.486821i
$400$		0			0
$401$	8.29423	−	14.3660i	0.414194	−	0.717406i	−0.581149	−	0.813797i	$-0.697397\pi$
$401$	8.29423	−	14.3660i	0.414194	−	0.717406i	0.995344	+	0.0963914i	$0.0307301\pi$
$402$		0			0
$403$	−34.0641	+	19.6669i	−1.69685	+	0.979679i
$404$		0			0
$405$	−12.5982	+	13.5957i	−0.626011	+	0.675578i
$406$		0			0
$407$	4.09684			0.203073
$408$		0			0
$409$	14.1437	−	8.16589i	0.699363	−	0.403777i	−0.107747	−	0.994178i	$-0.534364\pi$
$409$	14.1437	−	8.16589i	0.699363	−	0.403777i	0.807110	+	0.590401i	$0.201030\pi$
$410$		0			0
$411$	20.9076	+	12.0710i	1.03130	+	0.595419i
$412$		0			0
$413$	−0.948826	+	0.912921i	−0.0466887	+	0.0449219i
$414$		0			0
$415$	8.94531	+	28.9319i	0.439108	+	1.42021i
$416$		0			0
$417$	−15.8363	+	9.14308i	−0.775506	+	0.447739i
$418$		0			0
$419$			25.5119i			1.24634i	0.782087	+	0.623170i	$0.214155\pi$
$419$			25.5119i			1.24634i	−0.782087	+	0.623170i	$0.785845\pi$
$420$		0			0
$421$		−	5.65879i		−	0.275793i	−0.990447	−	0.137896i	$-0.955966\pi$
$421$		−	5.65879i		−	0.275793i	0.990447	−	0.137896i	$-0.0440341\pi$
$422$		0			0
$423$	−0.0408492	+	0.0235843i	−0.00198616	+	0.00114671i
$424$		0			0
$425$	−13.1904	−	6.33061i	−0.639827	−	0.307080i
$426$		0			0
$427$	8.63018	−	29.8905i	0.417644	−	1.44650i
$428$		0			0
$429$	7.81239	+	4.51048i	0.377186	+	0.217768i
$430$		0			0
$431$	−8.15466	+	4.70809i	−0.392796	+	0.226781i	−0.683371	−	0.730071i	$-0.739487\pi$
$431$	−8.15466	+	4.70809i	−0.392796	+	0.226781i	0.290575	+	0.956852i	$0.406153\pi$
$432$		0			0
$433$	2.39361			0.115030			0.0575148	−	0.998345i	$-0.481682\pi$
$433$	2.39361			0.115030			0.0575148	+	0.998345i	$0.481682\pi$
$434$		0			0
$435$	−6.74453	−	6.24969i	−0.323376	−	0.299650i
$436$		0			0
$437$	3.72356	−	2.14980i	0.178122	−	0.102839i
$438$		0			0
$439$	17.7739	−	30.7852i	0.848300	−	1.46930i	−0.0344242	−	0.999407i	$-0.510960\pi$
$439$	17.7739	−	30.7852i	0.848300	−	1.46930i	0.882724	−	0.469891i	$-0.155707\pi$
$440$		0			0
$441$	0.0595608	−	1.54361i	0.00283623	−	0.0735051i
$442$		0			0
$443$	10.5455	+	6.08847i	0.501033	+	0.289272i	0.729140	−	0.684364i	$-0.239920\pi$
$443$	10.5455	+	6.08847i	0.501033	+	0.289272i	−0.228107	+	0.973636i	$0.573254\pi$
$444$		0			0
$445$	5.65275	−	24.8423i	0.267966	−	1.17764i
$446$		0			0
$447$		−	24.6004i		−	1.16356i
$448$		0			0
$449$	5.65182			0.266726			0.133363	−	0.991067i	$-0.457422\pi$
$449$	5.65182			0.266726			0.133363	+	0.991067i	$0.457422\pi$
$450$		0			0
$451$	−2.54079	+	1.46693i	−0.119641	+	0.0690749i
$452$		0			0
$453$	22.8029	+	13.1653i	1.07138	+	0.618559i
$454$		0			0
$455$	−34.6781	+	20.8994i	−1.62573	+	0.979778i
$456$		0			0
$457$	−17.8188	−	10.2877i	−0.833529	−	0.481238i	0.0215305	−	0.999768i	$-0.493146\pi$
$457$	−17.8188	−	10.2877i	−0.833529	−	0.481238i	−0.855059	+	0.518530i	$0.826479\pi$
$458$		0			0
$459$	−7.85574	−	13.6065i	−0.366675	−	0.635099i
$460$		0			0
$461$	−1.04586			−0.0487106			−0.0243553	−	0.999703i	$-0.507753\pi$
$461$	−1.04586			−0.0487106			−0.0243553	+	0.999703i	$0.507753\pi$
$462$		0			0
$463$	15.3524			0.713488			0.356744	−	0.934202i	$-0.383887\pi$
$463$	15.3524			0.713488			0.356744	+	0.934202i	$0.383887\pi$
$464$		0			0
$465$	20.8909	+	4.75363i	0.968791	+	0.220444i
$466$		0			0
$467$	−8.02282	+	13.8959i	−0.371252	+	0.643027i	−0.989758	−	0.142753i	$-0.954405\pi$
$467$	−8.02282	+	13.8959i	−0.371252	+	0.643027i	0.618507	+	0.785780i	$0.287738\pi$
$468$		0			0
$469$	6.23970	−	6.00358i	0.288122	−	0.277220i
$470$		0			0
$471$	−13.6025	−	7.85341i	−0.626770	−	0.361866i
$472$		0			0
$473$	−6.52205	+	3.76551i	−0.299884	+	0.173138i
$474$		0			0
$475$	11.3226	−	0.863618i	0.519517	−	0.0396255i
$476$		0			0
$477$	1.42016			0.0650246
$478$		0			0
$479$	−10.5683	−	18.3049i	−0.482879	−	0.836371i	0.516928	−	0.856029i	$-0.327076\pi$
$479$	−10.5683	−	18.3049i	−0.482879	−	0.836371i	−0.999807	+	0.0196582i	$0.993742\pi$
$480$		0			0
$481$	30.7115	+	17.7313i	1.40032	+	0.808477i
$482$		0			0
$483$	8.10608	−	2.00532i	0.368839	−	0.0912454i
$484$		0			0
$485$	8.62993	+	27.9118i	0.391865	+	1.26741i
$486$		0			0
$487$	8.49641	+	14.7162i	0.385009	+	0.666855i	0.991770	−	0.128029i	$-0.0408650\pi$
$487$	8.49641	+	14.7162i	0.385009	+	0.666855i	−0.606761	+	0.794884i	$0.707532\pi$
$488$		0			0
$489$		−	8.08424i		−	0.365582i
$490$		0			0
$491$	−13.6290			−0.615070			−0.307535	−	0.951537i	$-0.599504\pi$
$491$	−13.6290			−0.615070			−0.307535	+	0.951537i	$0.599504\pi$
$492$		0			0
$493$	6.25067	−	3.60883i	0.281516	−	0.162533i
$494$		0			0
$495$	0.115245	+	0.372737i	0.00517988	+	0.0167533i
$496$		0			0
$497$	−2.80099	−	11.3224i	−0.125642	−	0.507879i
$498$		0			0
$499$	7.46818	−	12.9353i	0.334322	−	0.579062i	−0.649033	−	0.760760i	$-0.724826\pi$
$499$	7.46818	−	12.9353i	0.334322	−	0.579062i	0.983354	+	0.181699i	$0.0581595\pi$
$500$		0			0
$501$	15.2030	−	8.77748i	0.679222	−	0.392149i
$502$		0			0
$503$			24.2100i			1.07947i	0.841834	+	0.539736i	$0.181476\pi$
$503$			24.2100i			1.07947i	−0.841834	+	0.539736i	$0.818524\pi$
$504$		0			0
$505$	−15.7041	+	16.9475i	−0.698821	+	0.754153i
$506$		0			0
$507$	28.2068	+	48.8555i	1.25271	+	2.16975i
$508$		0			0
$509$	−4.43051	+	7.67386i	−0.196379	+	0.340138i	−0.947352	−	0.320195i	$-0.896252\pi$
$509$	−4.43051	+	7.67386i	−0.196379	+	0.340138i	0.750973	+	0.660333i	$0.229585\pi$
$510$		0			0
$511$	11.6800	+	12.1394i	0.516695	+	0.537016i
$512$		0			0
$513$	10.5605	+	6.09710i	0.466257	+	0.269193i
$514$		0			0
$515$	−9.85277	+	43.3002i	−0.434165	+	1.90803i
$516$		0			0
$517$		−	0.168995i		−	0.00743237i
$518$		0			0
$519$			19.3427i			0.849050i
$520$		0			0
$521$	−26.5478	+	15.3274i	−1.16308	+	0.671505i	−0.952041	−	0.305972i	$-0.901019\pi$
$521$	−26.5478	+	15.3274i	−1.16308	+	0.671505i	−0.211041	+	0.977477i	$0.567685\pi$
$522$		0			0
$523$	−9.06880	+	15.7076i	−0.396551	+	0.686846i	−0.993298	−	0.115583i	$-0.963126\pi$
$523$	−9.06880	+	15.7076i	−0.396551	+	0.686846i	0.596747	+	0.802430i	$0.296460\pi$
$524$		0			0
$525$	21.5925	+	4.48853i	0.942372	+	0.195896i
$526$		0			0
$527$	−8.40880	+	14.5645i	−0.366293	+	0.634439i
$528$		0			0
$529$	9.70794	+	16.8146i	0.422084	+	0.731072i
$530$		0			0
$531$			0.109824i			0.00476598i
$532$		0			0
$533$	−25.3957			−1.10001
$534$		0			0
$535$	7.99706	−	35.1448i	0.345743	−	1.51944i
$536$		0			0
$537$	−16.1800	+	28.0246i	−0.698218	+	1.20935i
$538$		0			0
$539$	4.68277	+	2.95000i	0.201701	+	0.127066i
$540$		0			0
$541$	−23.5104	−	13.5737i	−1.01079	−	0.583580i	−0.0993669	−	0.995051i	$-0.531682\pi$
$541$	−23.5104	−	13.5737i	−1.01079	−	0.583580i	−0.911423	+	0.411471i	$0.865015\pi$
$542$		0			0
$543$	14.0046	+	24.2567i	0.600997	+	1.04096i
$544$		0			0
$545$	24.3295	+	22.5445i	1.04216	+	0.965699i
$546$		0			0
$547$			23.0006i			0.983436i	0.870754	+	0.491718i	$0.163631\pi$
$547$			23.0006i			0.983436i	−0.870754	+	0.491718i	$0.836369\pi$
$548$		0			0
$549$	−1.29749	−	2.24731i	−0.0553753	−	0.0959129i
$550$		0			0
$551$	−2.80093	+	4.85135i	−0.119324	+	0.206674i
$552$		0			0
$553$	−15.4118	−	4.44978i	−0.655374	−	0.189224i
$554$		0			0
$555$	−5.70580	−	18.4543i	−0.242198	−	0.783340i
$556$		0			0
$557$	5.52574	+	9.57086i	0.234133	+	0.405530i	0.959020	−	0.283337i	$-0.0914415\pi$
$557$	5.52574	+	9.57086i	0.234133	+	0.405530i	−0.724887	+	0.688867i	$0.758108\pi$
$558$		0			0
$559$	−65.1890			−2.75720
$560$		0			0
$561$	3.85701			0.162843
$562$		0			0
$563$	−19.8308	−	34.3480i	−0.835770	−	1.44760i	−0.893402	−	0.449259i	$-0.851688\pi$
$563$	−19.8308	−	34.3480i	−0.835770	−	1.44760i	0.0576315	−	0.998338i	$-0.481645\pi$
$564$		0			0
$565$	9.23856	−	2.85643i	0.388669	−	0.120171i
$566$		0			0
$567$	15.2059	+	15.8039i	0.638587	+	0.663703i
$568$		0			0
$569$	14.0325	−	24.3050i	0.588272	−	1.01892i	−0.406187	−	0.913790i	$-0.633142\pi$
$569$	14.0325	−	24.3050i	0.588272	−	1.01892i	0.994459	−	0.105127i	$-0.0335248\pi$
$570$		0			0
$571$	−1.96859	−	3.40970i	−0.0823829	−	0.142691i	0.821890	−	0.569646i	$-0.192920\pi$
$571$	−1.96859	−	3.40970i	−0.0823829	−	0.142691i	−0.904273	+	0.426955i	$0.859586\pi$
$572$		0			0
$573$		−	18.4563i		−	0.771022i
$574$		0			0
$575$	−0.719907	−	9.43847i	−0.0300222	−	0.393611i
$576$		0			0
$577$	−20.6956	−	35.8459i	−0.861571	−	1.49228i	−0.870412	−	0.492324i	$-0.836148\pi$
$577$	−20.6956	−	35.8459i	−0.861571	−	1.49228i	0.00884126	−	0.999961i	$-0.497186\pi$
$578$		0			0
$579$	3.83499	+	2.21413i	0.159377	+	0.0920161i
$580$		0			0
$581$	34.7830	−	8.60480i	1.44304	−	0.356987i
$582$		0			0
$583$	−2.54406	+	4.40643i	−0.105364	+	0.182496i
$584$		0			0
$585$	−0.749300	+	3.29297i	−0.0309798	+	0.136147i
$586$		0			0
$587$	−15.3447			−0.633342			−0.316671	−	0.948535i	$-0.602565\pi$
$587$	−15.3447			−0.633342			−0.316671	+	0.948535i	$0.602565\pi$
$588$		0			0
$589$		−	13.0527i		−	0.537827i
$590$		0			0
$591$	8.31016	+	14.3936i	0.341834	+	0.592075i
$592$		0			0
$593$	−20.8596	+	36.1298i	−0.856600	+	1.48367i	0.0185530	+	0.999828i	$0.494094\pi$
$593$	−20.8596	+	36.1298i	−0.856600	+	1.48367i	−0.875153	+	0.483847i	$0.839239\pi$
$594$		0			0
$595$	−8.37268	+	15.1521i	−0.343246	+	0.621175i
$596$		0			0
$597$	−0.623454	+	1.07985i	−0.0255163	+	0.0441955i
$598$		0			0
$599$	19.4999	−	11.2583i	0.796746	−	0.460001i	−0.0455861	−	0.998960i	$-0.514516\pi$
$599$	19.4999	−	11.2583i	0.796746	−	0.460001i	0.842332	+	0.538959i	$0.181182\pi$
$600$		0			0
$601$		−	8.10668i		−	0.330679i	−0.986237	−	0.165339i	$-0.947128\pi$
$601$		−	8.10668i		−	0.330679i	0.986237	−	0.165339i	$-0.0528719\pi$
$602$		0			0
$603$		−	0.722231i		−	0.0294115i
$604$		0			0
$605$	22.6207	+	5.14725i	0.919663	+	0.209265i
$606$		0			0
$607$	10.6003	+	6.12010i	0.430254	+	0.248407i	0.699455	−	0.714677i	$-0.253426\pi$
$607$	10.6003	+	6.12010i	0.430254	+	0.248407i	−0.269201	+	0.963084i	$0.586760\pi$
$608$		0			0
$609$	−7.83997	+	7.54329i	−0.317692	+	0.305670i
$610$		0			0
$611$	0.731415	−	1.26685i	0.0295899	−	0.0512512i
$612$		0			0
$613$	6.93580	+	12.0132i	0.280134	+	0.485207i	0.971418	−	0.237377i	$-0.0762876\pi$
$613$	6.93580	+	12.0132i	0.280134	+	0.485207i	−0.691283	+	0.722584i	$0.742954\pi$
$614$		0			0
$615$	10.1464	+	9.40200i	0.409144	+	0.379125i
$616$		0			0
$617$		−	1.91696i		−	0.0771739i	−0.999255	−	0.0385870i	$-0.987714\pi$
$617$		−	1.91696i		−	0.0771739i	0.999255	−	0.0385870i	$-0.0122857\pi$
$618$		0			0
$619$	19.2245	−	11.0993i	0.772699	−	0.446118i	−0.0611375	−	0.998129i	$-0.519473\pi$
$619$	19.2245	−	11.0993i	0.772699	−	0.446118i	0.833837	+	0.552011i	$0.186139\pi$
$620$		0			0
$621$	5.08251	−	8.80316i	0.203954	−	0.353259i
$622$		0			0
$623$	−28.9621	−	8.36213i	−1.16034	−	0.335022i
$624$		0			0
$625$	9.07175	−	23.2960i	0.362870	−	0.931840i
$626$		0			0
$627$	−2.59249	+	1.49678i	−0.103534	+	0.0597755i
$628$		0			0
$629$	15.1624			0.604565
$630$		0			0
$631$		−	4.47405i		−	0.178109i	−0.996027	−	0.0890545i	$-0.971615\pi$
$631$		−	4.47405i		−	0.178109i	0.996027	−	0.0890545i	$-0.0283845\pi$
$632$		0			0
$633$	−10.9008	−	18.8807i	−0.433268	−	0.750442i
$634$		0			0
$635$	−3.08496	−	9.97769i	−0.122423	−	0.395952i
$636$		0			0
$637$	22.3361	+	42.3815i	0.884988	+	1.67922i
$638$		0			0
$639$	−0.842519	−	0.486429i	−0.0333295	−	0.0192428i
$640$		0			0
$641$	−16.7611	−	29.0311i	−0.662025	−	1.14666i	−0.980083	−	0.198590i	$-0.936364\pi$
$641$	−16.7611	−	29.0311i	−0.662025	−	1.14666i	0.318058	−	0.948071i	$-0.396969\pi$
$642$		0			0
$643$	1.67625			0.0661048			0.0330524	−	0.999454i	$-0.489477\pi$
$643$	1.67625			0.0661048			0.0330524	+	0.999454i	$0.489477\pi$
$644$		0			0
$645$	26.0452	+	24.1343i	1.02553	+	0.950288i
$646$		0			0
$647$	18.8153	−	10.8630i	0.739707	−	0.427070i	−0.0822561	−	0.996611i	$-0.526213\pi$
$647$	18.8153	−	10.8630i	0.739707	−	0.427070i	0.821963	+	0.569541i	$0.192879\pi$
$648$		0			0
$649$	−0.340761	−	0.196738i	−0.0133760	−	0.00772265i
$650$		0			0
$651$	7.03206	−	24.3554i	0.275608	−	0.954563i
$652$		0			0
$653$	4.45603	−	7.71807i	0.174378	−	0.302031i	−0.765568	−	0.643355i	$-0.777542\pi$
$653$	4.45603	−	7.71807i	0.174378	−	0.302031i	0.939946	+	0.341324i	$0.110875\pi$
$654$		0			0
$655$	7.68575	−	33.7767i	0.300307	−	1.31977i
$656$		0			0
$657$	1.40511			0.0548186
$658$		0			0
$659$	−11.6434			−0.453562			−0.226781	−	0.973946i	$-0.572820\pi$
$659$	−11.6434			−0.453562			−0.226781	+	0.973946i	$0.572820\pi$
$660$		0			0
$661$	−3.07763	−	5.33061i	−0.119706	−	0.207337i	0.799945	−	0.600073i	$-0.204862\pi$
$661$	−3.07763	−	5.33061i	−0.119706	−	0.207337i	−0.919651	+	0.392736i	$0.871528\pi$
$662$		0			0
$663$	28.9136	+	16.6933i	1.12291	+	0.648314i
$664$		0			0
$665$	−0.252313	−	13.4336i	−0.00978430	−	0.520934i
$666$		0			0
$667$	4.04406	+	2.33484i	0.156587	+	0.0904053i
$668$		0			0
$669$	5.91351	−	3.41417i	0.228630	−	0.131999i
$670$		0			0
$671$	9.29720			0.358914
$672$		0			0
$673$		−	29.9527i		−	1.15459i	−0.816535	−	0.577296i	$-0.804108\pi$
$673$		−	29.9527i		−	1.15459i	0.816535	−	0.577296i	$-0.195892\pi$
$674$		0			0
$675$	22.1615	−	15.1526i	0.852996	−	0.583222i
$676$		0			0
$677$	−19.0794	−	11.0155i	−0.733281	−	0.423360i	0.0863404	−	0.996266i	$-0.472483\pi$
$677$	−19.0794	−	11.0155i	−0.733281	−	0.423360i	−0.819621	+	0.572906i	$0.805816\pi$
$678$		0			0
$679$	33.5566	−	8.30142i	1.28779	−	0.318579i
$680$		0			0
$681$	−8.23259	+	14.2593i	−0.315474	+	0.546416i
$682$		0			0
$683$	1.35827	−	0.784199i	0.0519728	−	0.0300065i	−0.473788	−	0.880639i	$-0.657114\pi$
$683$	1.35827	−	0.784199i	0.0519728	−	0.0300065i	0.525761	+	0.850632i	$0.323781\pi$
$684$		0			0
$685$	−23.7515	−	22.0089i	−0.907498	−	0.840916i
$686$		0			0
$687$	5.59887			0.213610
$688$		0			0
$689$	−38.1424	+	22.0215i	−1.45311	+	0.838954i
$690$		0			0
$691$	36.1431	+	20.8673i	1.37495	+	0.793828i	0.991546	−	0.129753i	$-0.0414185\pi$
$691$	36.1431	+	20.8673i	1.37495	+	0.793828i	0.383404	+	0.923581i	$0.374752\pi$
$692$		0			0
$693$	0.448119	−	0.110858i	0.0170226	−	0.00421115i
$694$		0			0
$695$	23.4322	−	7.24490i	0.888834	−	0.274815i
$696$		0			0
$697$	−9.40347	+	5.42910i	−0.356182	+	0.205642i
$698$		0			0
$699$			33.1291i			1.25306i
$700$		0			0
$701$		−	39.2592i		−	1.48280i	−0.671065	−	0.741399i	$-0.734163\pi$
$701$		−	39.2592i		−	1.48280i	0.671065	−	0.741399i	$-0.265837\pi$
$702$		0			0
$703$	−10.1914	+	5.88402i	−0.384377	+	0.221920i
$704$		0			0
$705$	−0.761238	+	0.235364i	−0.0286699	+	0.00886432i
$706$		0			0
$707$	18.9546	+	19.7001i	0.712860	+	0.740897i
$708$		0			0
$709$	7.57554	+	4.37374i	0.284505	+	0.164259i	0.635461	−	0.772133i	$-0.280810\pi$
$709$	7.57554	+	4.37374i	0.284505	+	0.164259i	−0.350956	+	0.936392i	$0.614143\pi$
$710$		0			0
$711$	−1.15873	+	0.668993i	−0.0434558	+	0.0250892i
$712$		0			0
$713$	−10.8807			−0.407484
$714$		0			0
$715$	−8.87505	−	8.22389i	−0.331908	−	0.307556i
$716$		0			0
$717$	9.73798	−	5.62223i	0.363672	−	0.209966i
$718$		0			0
$719$	−1.13078	+	1.95857i	−0.0421709	+	0.0730422i	−0.886340	−	0.463034i	$-0.846761\pi$
$719$	−1.13078	+	1.95857i	−0.0421709	+	0.0730422i	0.844170	+	0.536076i	$0.180094\pi$
$720$		0			0
$721$	50.4811	+	14.5752i	1.88001	+	0.542810i
$722$		0			0
$723$	1.97312	+	1.13918i	0.0733809	+	0.0423665i
$724$		0			0
$725$	6.96089	+	10.1807i	0.258521	+	0.378102i
$726$		0			0
$727$			14.0073i			0.519502i	0.965676	+	0.259751i	$0.0836406\pi$
$727$			14.0073i			0.519502i	−0.965676	+	0.259751i	$0.916359\pi$
$728$		0			0
$729$	28.6832			1.06234
$730$		0			0
$731$	−24.1381	+	13.9361i	−0.892780	+	0.515447i
$732$		0			0
$733$	−0.730569	−	0.421794i	−0.0269842	−	0.0155793i	0.486447	−	0.873710i	$-0.338293\pi$
$733$	−0.730569	−	0.421794i	−0.0269842	−	0.0155793i	−0.513431	+	0.858131i	$0.671626\pi$
$734$		0			0
$735$	6.76649	−	25.2021i	0.249586	−	0.929595i
$736$		0			0
$737$	2.24092	+	1.29380i	0.0825454	+	0.0476576i
$738$		0			0
$739$	24.2171	+	41.9452i	0.890840	+	1.54298i	0.838870	+	0.544331i	$0.183216\pi$
$739$	24.2171	+	41.9452i	0.890840	+	1.54298i	0.0519693	+	0.998649i	$0.483450\pi$
$740$		0			0
$741$	−25.9124			−0.951916
$742$		0			0
$743$	−23.9932			−0.880226			−0.440113	−	0.897942i	$-0.645062\pi$
$743$	−23.9932			−0.880226			−0.440113	+	0.897942i	$0.645062\pi$
$744$		0			0
$745$	−7.32092	+	32.1734i	−0.268218	+	1.17874i
$746$		0			0
$747$	1.49434	−	2.58826i	0.0546749	−	0.0946996i
$748$		0			0
$749$	−40.9732	−	11.8301i	−1.49713	−	0.432261i
$750$		0			0
$751$	15.5172	+	8.95889i	0.566232	+	0.326914i	0.755643	−	0.654983i	$-0.227324\pi$
$751$	15.5172	+	8.95889i	0.566232	+	0.326914i	−0.189411	+	0.981898i	$0.560658\pi$
$752$		0			0
$753$	22.3116	−	12.8816i	0.813078	−	0.469431i
$754$		0			0
$755$	−25.9046	−	24.0040i	−0.942766	−	0.873596i
$756$		0			0
$757$	9.11215			0.331187			0.165593	−	0.986194i	$-0.447046\pi$
$757$	9.11215			0.331187			0.165593	+	0.986194i	$0.447046\pi$
$758$		0			0
$759$	1.24770	+	2.16109i	0.0452888	+	0.0784425i
$760$		0			0
$761$	−0.873293	−	0.504196i	−0.0316568	−	0.0182771i	0.484088	−	0.875019i	$-0.339151\pi$
$761$	−0.873293	−	0.504196i	−0.0316568	−	0.0182771i	−0.515745	+	0.856742i	$0.672485\pi$
$762$		0			0
$763$	28.2810	−	27.2108i	1.02384	−	0.985099i
$764$		0			0
$765$	0.426522	+	1.37950i	0.0154209	+	0.0498759i
$766$		0			0
$767$	−1.70298	−	2.94965i	−0.0614911	−	0.106506i
$768$		0			0
$769$			11.3063i			0.407716i	0.979000	+	0.203858i	$0.0653481\pi$
$769$			11.3063i			0.407716i	−0.979000	+	0.203858i	$0.934652\pi$
$770$		0			0
$771$	−41.7351			−1.50305
$772$		0			0
$773$	−17.9809	+	10.3813i	−0.646729	+	0.373389i	−0.787202	−	0.616695i	$-0.788471\pi$
$773$	−17.9809	+	10.3813i	−0.646729	+	0.373389i	0.140473	+	0.990085i	$0.455138\pi$
$774$		0			0
$775$	−25.9072	−	12.4339i	−0.930615	−	0.446641i
$776$		0			0
$777$	−22.1864	+	5.48860i	−0.795934	+	0.196902i
$778$		0			0
$779$	4.21370	−	7.29834i	0.150971	−	0.261490i
$780$		0			0
$781$	3.01856	−	1.74277i	0.108013	−	0.0623611i
$782$		0			0
$783$			13.2438i			0.473295i
$784$		0			0
$785$	15.4527	+	14.3190i	0.551532	+	0.511067i
$786$		0			0
$787$	1.98158	+	3.43220i	0.0706357	+	0.122345i	0.899180	−	0.437579i	$-0.144164\pi$
$787$	1.98158	+	3.43220i	0.0706357	+	0.122345i	−0.828544	+	0.559923i	$0.810831\pi$
$788$		0			0
$789$	−23.5995	+	40.8756i	−0.840165	+	1.45521i
$790$		0			0
$791$	−2.74770	−	11.1070i	−0.0976969	−	0.394918i
$792$		0			0
$793$	69.6954	+	40.2386i	2.47496	+	1.42892i
$794$		0			0
$795$	23.3920	+	5.32276i	0.829630	+	0.188779i
$796$		0			0
$797$			21.7688i			0.771090i	0.922689	+	0.385545i	$0.125987\pi$
$797$			21.7688i			0.771090i	−0.922689	+	0.385545i	$0.874013\pi$
$798$		0			0
$799$		−	0.625448i		−	0.0221268i
$800$		0			0
$801$	−2.17751	+	1.25719i	−0.0769385	+	0.0444205i
$802$		0			0
$803$	−2.51710	+	4.35974i	−0.0888265	+	0.153852i
$804$		0			0
$805$	−11.1982	+	0.210327i	−0.394685	+	0.00741306i
$806$		0			0
$807$	3.07823	−	5.33165i	0.108359	−	0.187683i
$808$		0			0
$809$	13.0987	+	22.6876i	0.460525	+	0.797652i	0.998987	−	0.0449975i	$-0.0143280\pi$
$809$	13.0987	+	22.6876i	0.460525	+	0.797652i	−0.538462	+	0.842649i	$0.680995\pi$
$810$		0			0
$811$		−	35.2550i		−	1.23797i	−0.785403	−	0.618985i	$-0.787544\pi$
$811$		−	35.2550i		−	1.23797i	0.785403	−	0.618985i	$-0.212456\pi$
$812$		0			0
$813$	−1.27696			−0.0447850
$814$		0			0
$815$	−2.40581	+	10.5729i	−0.0842719	+	0.370351i
$816$		0			0
$817$	10.8163	−	18.7344i	0.378414	−	0.655432i
$818$		0			0
$819$	3.83907	+	1.10844i	0.134148	+	0.0387321i
$820$		0			0
$821$	15.6779	+	9.05167i	0.547164	+	0.315905i	0.747977	−	0.663724i	$-0.231025\pi$
$821$	15.6779	+	9.05167i	0.547164	+	0.315905i	−0.200813	+	0.979630i	$0.564358\pi$
$822$		0			0
$823$	−5.91819	−	10.2506i	−0.206295	−	0.357314i	0.744249	−	0.667902i	$-0.232807\pi$
$823$	−5.91819	−	10.2506i	−0.206295	−	0.357314i	−0.950545	+	0.310588i	$0.899474\pi$
$824$		0			0
$825$	0.501229	+	6.57145i	0.0174506	+	0.228788i
$826$		0			0
$827$		−	36.3034i		−	1.26239i	−0.775623	−	0.631196i	$-0.782564\pi$
$827$		−	36.3034i		−	1.26239i	0.775623	−	0.631196i	$-0.217436\pi$
$828$		0			0
$829$	12.1073	+	20.9704i	0.420502	+	0.728331i	0.995989	−	0.0894800i	$-0.0285205\pi$
$829$	12.1073	+	20.9704i	0.420502	+	0.728331i	−0.575486	+	0.817811i	$0.695187\pi$
$830$		0			0
$831$	−16.2236	+	28.1002i	−0.562792	+	0.974784i
$832$		0			0
$833$	17.3309	+	10.9180i	0.600481	+	0.378285i
$834$		0			0
$835$	−22.4952	+	6.95520i	−0.778480	+	0.240695i
$836$		0			0
$837$	−15.4295	−	26.7246i	−0.533320	−	0.923738i
$838$		0			0
$839$	9.71534			0.335411			0.167705	−	0.985837i	$-0.446364\pi$
$839$	9.71534			0.335411			0.167705	+	0.985837i	$0.446364\pi$
$840$		0			0
$841$	22.9160			0.790206
$842$		0			0
$843$	6.00205	+	10.3959i	0.206722	+	0.358052i
$844$		0			0
$845$	−22.3508	−	72.2892i	−0.768891	−	2.48682i
$846$		0			0
$847$	7.61434	−	26.3721i	0.261632	−	0.906157i
$848$		0			0
$849$	−9.85907	+	17.0764i	−0.338362	+	0.586061i
$850$		0			0
$851$	4.90488	+	8.49551i	0.168137	+	0.291222i
$852$		0			0
$853$			30.1601i			1.03266i	0.856389	+	0.516331i	$0.172703\pi$
$853$			30.1601i			1.03266i	−0.856389	+	0.516331i	$0.827297\pi$
$854$		0			0
$855$	−0.822024	−	0.761713i	−0.0281126	−	0.0260500i
$856$		0			0
$857$	−13.3793	−	23.1737i	−0.457029	−	0.791597i	0.541774	−	0.840524i	$-0.317753\pi$
$857$	−13.3793	−	23.1737i	−0.457029	−	0.791597i	−0.998802	+	0.0489275i	$0.984420\pi$
$858$		0			0
$859$	−24.3388	−	14.0520i	−0.830428	−	0.479448i	0.0235714	−	0.999722i	$-0.492496\pi$
$859$	−24.3388	−	14.0520i	−0.830428	−	0.479448i	−0.853999	+	0.520274i	$0.825830\pi$
$860$		0			0
$861$	11.7944	−	11.3481i	0.401952	−	0.386742i
$862$		0			0
$863$	21.9016	−	37.9347i	0.745539	−	1.29131i	−0.204404	−	0.978887i	$-0.565526\pi$
$863$	21.9016	−	37.9347i	0.745539	−	1.29131i	0.949943	−	0.312424i	$-0.101141\pi$
$864$		0			0
$865$	5.75625	−	25.2971i	0.195718	−	0.860127i
$866$		0			0
$867$	−14.0664			−0.477720
$868$		0			0
$869$		−	4.79371i		−	0.162615i
$870$		0			0
$871$	11.1992	+	19.3976i	0.379470	+	0.657262i
$872$		0			0
$873$	1.44165	−	2.49701i	0.0487924	−	0.0845110i
$874$		0			0
$875$	−26.9037	−	12.2960i	−0.909510	−	0.415682i
$876$		0			0
$877$	−17.7221	+	30.6955i	−0.598431	+	1.03651i	0.394622	+	0.918844i	$0.370876\pi$
$877$	−17.7221	+	30.6955i	−0.598431	+	1.03651i	−0.993053	+	0.117670i	$0.962458\pi$
$878$		0			0
$879$	17.1613	−	9.90808i	0.578836	−	0.334191i
$880$		0			0
$881$		−	11.0583i		−	0.372564i	−0.982496	−	0.186282i	$-0.940356\pi$
$881$		−	11.0583i		−	0.372564i	0.982496	−	0.186282i	$-0.0596438\pi$
$882$		0			0
$883$			18.2084i			0.612760i	0.951909	+	0.306380i	$0.0991178\pi$
$883$			18.2084i			0.612760i	−0.951909	+	0.306380i	$0.900882\pi$
$884$		0			0
$885$	−0.411622	+	1.80896i	−0.0138365	+	0.0608077i
$886$		0			0
$887$	−24.4553	−	14.1193i	−0.821128	−	0.474078i	0.0296774	−	0.999560i	$-0.490552\pi$
$887$	−24.4553	−	14.1193i	−0.821128	−	0.474078i	−0.850805	+	0.525481i	$0.823885\pi$
$888$		0			0
$889$	−11.9956	+	2.96752i	−0.402318	+	0.0995276i
$890$		0			0
$891$	−3.27693	+	5.67581i	−0.109781	+	0.190147i
$892$		0			0
$893$	0.242715	+	0.420395i	0.00812216	+	0.0140680i
$894$		0			0
$895$	29.5007	−	31.8365i	0.986100	−	1.06418i
$896$		0			0
$897$			21.6005i			0.721218i
$898$		0			0
$899$	12.2769	−	7.08810i	0.409459	−	0.236401i
$900$		0			0
$901$	−9.41555	+	16.3082i	−0.313677	+	0.543305i
$902$		0			0
$903$	30.2754	−	29.1298i	1.00750	−	0.969379i
$904$		0			0
$905$	−11.0972	−	35.8916i	−0.368882	−	1.19308i
$906$		0			0
$907$	−28.3649	+	16.3765i	−0.941840	+	0.543771i	−0.890536	−	0.454912i	$-0.849671\pi$
$907$	−28.3649	+	16.3765i	−0.941840	+	0.543771i	−0.0513031	+	0.998683i	$0.516337\pi$
$908$		0			0
$909$	2.28024			0.0756307
$910$		0			0
$911$		−	6.20517i		−	0.205587i	−0.994703	−	0.102793i	$-0.967222\pi$
$911$		−	6.20517i		−	0.205587i	0.994703	−	0.102793i	$-0.0327780\pi$
$912$		0			0
$913$	5.35387	+	9.27318i	0.177187	+	0.306897i
$914$		0			0
$915$	−12.9485	−	41.8794i	−0.428064	−	1.38449i
$916$		0			0
$917$	−39.3782	−	11.3695i	−1.30038	−	0.375456i
$918$		0			0
$919$	−42.5171	−	24.5473i	−1.40251	−	0.809740i	−0.407861	−	0.913044i	$-0.633725\pi$
$919$	−42.5171	−	24.5473i	−1.40251	−	0.809740i	−0.994650	+	0.103304i	$0.967058\pi$
$920$		0			0
$921$	−15.2950	−	26.4918i	−0.503988	−	0.872934i
$922$		0			0
$923$	30.1710			0.993091
$924$		0			0
$925$	1.97039	+	25.8332i	0.0647862	+	0.849390i
$926$		0			0
$927$	3.79541	−	2.19128i	0.124658	−	0.0719711i
$928$		0			0
$929$	16.5181	+	9.53671i	0.541940	+	0.312889i	0.745865	−	0.666097i	$-0.232036\pi$
$929$	16.5181	+	9.53671i	0.541940	+	0.312889i	−0.203925	+	0.978987i	$0.565370\pi$
$930$		0			0
$931$	−15.8859	−	0.612964i	−0.520639	−	0.0200891i
$932$		0			0
$933$	6.42915	−	11.1356i	0.210481	−	0.364564i
$934$		0			0
$935$	−5.04435	−	1.14782i	−0.164968	−	0.0375377i
$936$		0			0
$937$	−4.46637			−0.145910			−0.0729549	−	0.997335i	$-0.523243\pi$
$937$	−4.46637			−0.145910			−0.0729549	+	0.997335i	$0.523243\pi$
$938$		0			0
$939$	28.6325			0.934388
$940$		0			0
$941$	12.8629	+	22.2793i	0.419320	+	0.726283i	0.995871	−	0.0907779i	$-0.0289353\pi$
$941$	12.8629	+	22.2793i	0.419320	+	0.726283i	−0.576552	+	0.817061i	$0.695602\pi$
$942$		0			0
$943$	−6.08386	−	3.51252i	−0.198118	−	0.114383i
$944$		0			0
$945$	−16.3964	−	27.2063i	−0.533374	−	0.885021i
$946$		0			0
$947$	−14.4410	−	8.33751i	−0.469269	−	0.270933i	0.246665	−	0.969101i	$-0.420665\pi$
$947$	−14.4410	−	8.33751i	−0.469269	−	0.270933i	−0.715934	+	0.698168i	$0.753999\pi$
$948$		0			0
$949$	−37.7383	+	21.7882i	−1.22504	+	0.707275i
$950$		0			0
$951$	32.5874			1.05672
$952$		0			0
$953$			13.1368i			0.425544i	0.977102	+	0.212772i	$0.0682492\pi$
$953$			13.1368i			0.425544i	−0.977102	+	0.212772i	$0.931751\pi$
$954$		0			0
$955$	−5.49246	+	24.1378i	−0.177732	+	0.781081i
$956$		0			0
$957$	−2.81564	−	1.62561i	−0.0910167	−	0.0525485i
$958$		0			0
$959$	−27.6092	+	26.5644i	−0.891547	+	0.857809i
$960$		0			0
$961$	−1.01574	+	1.75931i	−0.0327657	+	0.0567519i
$962$		0			0
$963$	−3.08057	+	1.77857i	−0.0992699	+	0.0573135i
$964$		0			0
$965$	−4.35663	−	4.03699i	−0.140245	−	0.129955i
$966$		0			0
$967$	−34.0366			−1.09454			−0.547272	−	0.836955i	$-0.684334\pi$
$967$	−34.0366			−1.09454			−0.547272	+	0.836955i	$0.684334\pi$
$968$		0			0
$969$	−9.59481	+	5.53957i	−0.308230	+	0.177957i
$970$		0			0
$971$	−31.6711	−	18.2853i	−1.01637	−	0.586804i	−0.103323	−	0.994648i	$-0.532948\pi$
$971$	−31.6711	−	18.2853i	−1.01637	−	0.586804i	−0.913052	+	0.407844i	$0.866281\pi$
$972$		0			0
$973$	−6.96912	−	28.1711i	−0.223420	−	0.903124i
$974$		0			0
$975$	−24.6841	+	51.4314i	−0.790523	+	1.64712i
$976$		0			0
$977$	21.9380	−	12.6659i	0.701859	−	0.405218i	−0.106180	−	0.994347i	$-0.533862\pi$
$977$	21.9380	−	12.6659i	0.701859	−	0.405218i	0.808039	+	0.589128i	$0.200529\pi$
$978$		0			0
$979$		−	9.00843i		−	0.287911i
$980$		0			0
$981$		−	3.27347i		−	0.104514i
$982$		0			0
$983$	−39.3227	+	22.7030i	−1.25420	+	0.724113i	−0.971941	−	0.235225i	$-0.924417\pi$
$983$	−39.3227	+	22.7030i	−1.25420	+	0.724113i	−0.282259	+	0.959338i	$0.591084\pi$
$984$		0			0
$985$	−6.58490	−	21.2976i	−0.209812	−	0.678597i
$986$		0			0
$987$	0.226404	+	0.915190i	0.00720653	+	0.0291308i
$988$		0			0
$989$	−15.6169	−	9.01640i	−0.496587	−	0.286705i
$990$		0			0
$991$	13.6639	−	7.88884i	0.434047	−	0.250597i	−0.267022	−	0.963690i	$-0.586040\pi$
$991$	13.6639	−	7.88884i	0.434047	−	0.250597i	0.701069	+	0.713093i	$0.252706\pi$
$992$		0			0
$993$	−3.61677			−0.114775
$994$		0			0
$995$	1.13673	−	1.22674i	0.0360369	−	0.0388902i
$996$		0			0
$997$	−1.31350	+	0.758348i	−0.0415989	+	0.0240171i	−0.520655	−	0.853767i	$-0.674312\pi$
$997$	−1.31350	+	0.758348i	−0.0415989	+	0.0240171i	0.479056	+	0.877784i	$0.340979\pi$
$998$		0			0
$999$	−13.9109	+	24.0943i	−0.440121	+	0.762311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.719.11		80
4.3	odd	2		280.2.ba.b.19.19	yes	80
5.4	even	2	inner	1120.2.bq.b.719.29		80
7.3	odd	6	inner	1120.2.bq.b.1039.30		80
8.3	odd	2	inner	1120.2.bq.b.719.12		80
8.5	even	2		280.2.ba.b.19.6	✓	80
20.19	odd	2		280.2.ba.b.19.22	yes	80
28.3	even	6		280.2.ba.b.59.35	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.12		80
40.19	odd	2	inner	1120.2.bq.b.719.30		80
40.29	even	2		280.2.ba.b.19.35	yes	80
56.3	even	6	inner	1120.2.bq.b.1039.29		80
56.45	odd	6		280.2.ba.b.59.22	yes	80
140.59	even	6		280.2.ba.b.59.6	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.11		80
280.269	odd	6		280.2.ba.b.59.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.6	✓	80	8.5	even	2
280.2.ba.b.19.19	yes	80	4.3	odd	2
280.2.ba.b.19.22	yes	80	20.19	odd	2
280.2.ba.b.19.35	yes	80	40.29	even	2
280.2.ba.b.59.6	yes	80	140.59	even	6
280.2.ba.b.59.19	yes	80	280.269	odd	6
280.2.ba.b.59.22	yes	80	56.45	odd	6
280.2.ba.b.59.35	yes	80	28.3	even	6
1120.2.bq.b.719.11		80	1.1	even	1	trivial
1120.2.bq.b.719.12		80	8.3	odd	2	inner
1120.2.bq.b.719.29		80	5.4	even	2	inner
1120.2.bq.b.719.30		80	40.19	odd	2	inner
1120.2.bq.b.1039.11		80	280.59	even	6	inner
1120.2.bq.b.1039.12		80	35.24	odd	6	inner
1120.2.bq.b.1039.29		80	56.3	even	6	inner
1120.2.bq.b.1039.30		80	7.3	odd	6	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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.833565 - 1.44378i) q^{3} +(0.660510 + 2.13629i) q^{5} +(2.56833 - 0.635367i) q^{7} +(0.110340 - 0.191114i) q^{9} +O(q^{10})\)	\(q+(-0.833565 - 1.44378i) q^{3} +(0.660510 + 2.13629i) q^{5} +(2.56833 - 0.635367i) q^{7} +(0.110340 - 0.191114i) q^{9} +(0.395322 + 0.684718i) q^{11} +6.84388i q^{13} +(2.53375 - 2.73436i) q^{15} +(1.46309 + 2.53414i) q^{17} +(-1.96683 - 1.13555i) q^{19} +(-3.05820 - 3.17847i) q^{21} +(-0.946588 + 1.63954i) q^{23} +(-4.12745 + 2.82208i) q^{25} -5.36929 q^{27} -2.46658i q^{29} +(2.87365 + 4.97731i) q^{31} +(0.659054 - 1.14151i) q^{33} +(3.05373 + 5.06702i) q^{35} +(2.59082 - 4.48744i) q^{37} +(9.88103 - 5.70482i) q^{39} +3.71071i q^{41} +9.52516i q^{43} +(0.481155 + 0.109485i) q^{45} +(-0.185107 - 0.106871i) q^{47} +(6.19262 - 3.26366i) q^{49} +(2.43916 - 4.22474i) q^{51} +(3.21770 + 5.57322i) q^{53} +(-1.20164 + 1.29679i) q^{55} +3.78622i q^{57} +(-0.430991 + 0.248833i) q^{59} +(5.87951 - 10.1836i) q^{61} +(0.161961 - 0.560949i) q^{63} +(-14.6205 + 4.52045i) q^{65} +(2.83429 - 1.63638i) q^{67} +3.15617 q^{69} -4.40847i q^{71} +(3.18360 + 5.51416i) q^{73} +(7.51495 + 3.60674i) q^{75} +(1.45036 + 1.50741i) q^{77} +(-5.25074 - 3.03152i) q^{79} +(4.14463 + 7.17871i) q^{81} +13.5430 q^{83} +(-4.44727 + 4.79940i) q^{85} +(-3.56120 + 2.05606i) q^{87} +(-9.86730 - 5.69689i) q^{89} +(4.34837 + 17.5773i) q^{91} +(4.79075 - 8.29782i) q^{93} +(1.12675 - 4.95176i) q^{95} +13.0656 q^{97} +0.174479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 80 * q - 52 * q^9	\( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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