LMFDB - Embedded newform 580.2.j.a.17.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [580,2,Mod(17,580)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("580.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(580, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 580 = 2^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	580.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.63132331723$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.9
Character	$\chi$	$=$	580.17
Dual form			580.2.j.a.273.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.357354i q^{3} +(1.56439 + 1.59771i) q^{5} +(-1.34106 - 1.34106i) q^{7} +2.87230 q^{9} +(1.61681 - 1.61681i) q^{11} +(-1.85250 - 1.85250i) q^{13} +(-0.570947 + 0.559042i) q^{15} +6.21240 q^{17} +(3.14262 + 3.14262i) q^{19} +(0.479234 - 0.479234i) q^{21} +(-4.90258 + 4.90258i) q^{23} +(-0.105340 + 4.99889i) q^{25} +2.09849i q^{27} +(3.60969 - 3.99627i) q^{29} +(-2.06229 + 2.06229i) q^{31} +(0.577773 + 0.577773i) q^{33} +(0.0446752 - 4.24058i) q^{35} +0.925135i q^{37} +(0.661999 - 0.661999i) q^{39} +(5.64139 + 5.64139i) q^{41} +0.378555i q^{43} +(4.49341 + 4.58909i) q^{45} -10.2851i q^{47} -3.40309i q^{49} +2.22002i q^{51} +(-1.55716 + 1.55716i) q^{53} +(5.11252 + 0.0538612i) q^{55} +(-1.12303 + 1.12303i) q^{57} +6.98888i q^{59} +(-6.26387 + 6.26387i) q^{61} +(-3.85194 - 3.85194i) q^{63} +(0.0617129 - 5.85781i) q^{65} +(5.40499 - 5.40499i) q^{67} +(-1.75196 - 1.75196i) q^{69} -11.9571i q^{71} -0.668863 q^{73} +(-1.78637 - 0.0376436i) q^{75} -4.33649 q^{77} +(-5.45374 - 5.45374i) q^{79} +7.86699 q^{81} +(-7.98469 + 7.98469i) q^{83} +(9.71865 + 9.92560i) q^{85} +(1.42808 + 1.28993i) q^{87} +(-6.43075 - 6.43075i) q^{89} +4.96865i q^{91} +(-0.736966 - 0.736966i) q^{93} +(-0.104691 + 9.93728i) q^{95} -4.41209i q^{97} +(4.64396 - 4.64396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) $ 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$.

$n$	$117$	$291$	$321$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$			0.357354i			0.206318i	0.994665	+	0.103159i	$0.0328951\pi$
$3$			0.357354i			0.206318i	−0.994665	+	0.103159i	$0.967105\pi$
$4$		0			0
$5$	1.56439	+	1.59771i	0.699618	+	0.714517i
$5$	1.56439	+	1.59771i	0.699618	+	0.714517i
$6$		0			0
$7$	−1.34106	−	1.34106i	−0.506875	−	0.506875i	0.406691	−	0.913566i	$-0.366683\pi$
$7$	−1.34106	−	1.34106i	−0.506875	−	0.506875i	−0.913566	+	0.406691i	$0.866683\pi$
$8$		0			0
$9$	2.87230			0.957433
$10$		0			0
$11$	1.61681	−	1.61681i	0.487487	−	0.487487i	−0.420026	−	0.907512i	$-0.637979\pi$
$11$	1.61681	−	1.61681i	0.487487	−	0.487487i	0.907512	+	0.420026i	$0.137979\pi$
$12$		0			0
$13$	−1.85250	−	1.85250i	−0.513792	−	0.513792i	0.401894	−	0.915686i	$-0.368352\pi$
$13$	−1.85250	−	1.85250i	−0.513792	−	0.513792i	−0.915686	+	0.401894i	$0.868352\pi$
$14$		0			0
$15$	−0.570947	+	0.559042i	−0.147418	+	0.144344i
$16$		0			0
$17$	6.21240			1.50673			0.753364	−	0.657603i	$-0.228430\pi$
$17$	6.21240			1.50673			0.753364	+	0.657603i	$0.228430\pi$
$18$		0			0
$19$	3.14262	+	3.14262i	0.720966	+	0.720966i	0.968802	−	0.247836i	$-0.0797194\pi$
$19$	3.14262	+	3.14262i	0.720966	+	0.720966i	−0.247836	+	0.968802i	$0.579719\pi$
$20$		0			0
$21$	0.479234	−	0.479234i	0.104577	−	0.104577i
$22$		0			0
$23$	−4.90258	+	4.90258i	−1.02226	+	1.02226i	−0.0225124	+	0.999747i	$0.507167\pi$
$23$	−4.90258	+	4.90258i	−1.02226	+	1.02226i	−0.999747	+	0.0225124i	$0.992833\pi$
$24$		0			0
$25$	−0.105340	+	4.99889i	−0.0210680	+	0.999778i
$26$		0			0
$27$			2.09849i			0.403854i
$28$		0			0
$29$	3.60969	−	3.99627i	0.670302	−	0.742089i
$29$	3.60969	−	3.99627i	0.670302	−	0.742089i
$30$		0			0
$31$	−2.06229	+	2.06229i	−0.370398	+	0.370398i	−0.867622	−	0.497224i	$-0.834353\pi$
$31$	−2.06229	+	2.06229i	−0.370398	+	0.370398i	0.497224	+	0.867622i	$0.334353\pi$
$32$		0			0
$33$	0.577773	+	0.577773i	0.100577	+	0.100577i
$34$		0			0
$35$	0.0446752	−	4.24058i	0.00755149	−	0.716789i
$36$		0			0
$37$			0.925135i			0.152091i	0.997104	+	0.0760456i	$0.0242295\pi$
$37$			0.925135i			0.152091i	−0.997104	+	0.0760456i	$0.975771\pi$
$38$		0			0
$39$	0.661999	−	0.661999i	0.106005	−	0.106005i
$40$		0			0
$41$	5.64139	+	5.64139i	0.881037	+	0.881037i	0.993640	−	0.112603i	$-0.0359190\pi$
$41$	5.64139	+	5.64139i	0.881037	+	0.881037i	−0.112603	+	0.993640i	$0.535919\pi$
$42$		0			0
$43$			0.378555i			0.0577292i	0.999583	+	0.0288646i	$0.00918916\pi$
$43$			0.378555i			0.0577292i	−0.999583	+	0.0288646i	$0.990811\pi$
$44$		0			0
$45$	4.49341	+	4.58909i	0.669838	+	0.684102i
$46$		0			0
$47$		−	10.2851i		−	1.50024i	−0.661302	−	0.750120i	$-0.729996\pi$
$47$		−	10.2851i		−	1.50024i	0.661302	−	0.750120i	$-0.270004\pi$
$48$		0			0
$49$		−	3.40309i		−	0.486156i
$50$		0			0
$51$			2.22002i			0.310866i
$52$		0			0
$53$	−1.55716	+	1.55716i	−0.213892	+	0.213892i	−0.805918	−	0.592027i	$-0.798328\pi$
$53$	−1.55716	+	1.55716i	−0.213892	+	0.213892i	0.592027	+	0.805918i	$0.298328\pi$
$54$		0			0
$55$	5.11252	+	0.0538612i	0.689372	+	0.00726264i
$56$		0			0
$57$	−1.12303	+	1.12303i	−0.148748	+	0.148748i
$58$		0			0
$59$			6.98888i			0.909875i	0.890523	+	0.454938i	$0.150338\pi$
$59$			6.98888i			0.909875i	−0.890523	+	0.454938i	$0.849662\pi$
$60$		0			0
$61$	−6.26387	+	6.26387i	−0.802007	+	0.802007i	−0.983409	−	0.181402i	$-0.941936\pi$
$61$	−6.26387	+	6.26387i	−0.802007	+	0.802007i	0.181402	+	0.983409i	$0.441936\pi$
$62$		0			0
$63$	−3.85194	−	3.85194i	−0.485299	−	0.485299i
$64$		0			0
$65$	0.0617129	−	5.85781i	0.00765454	−	0.726571i
$66$		0			0
$67$	5.40499	−	5.40499i	0.660325	−	0.660325i	−0.295132	−	0.955457i	$-0.595364\pi$
$67$	5.40499	−	5.40499i	0.660325	−	0.660325i	0.955457	+	0.295132i	$0.0953636\pi$
$68$		0			0
$69$	−1.75196	−	1.75196i	−0.210911	−	0.210911i
$70$		0			0
$71$		−	11.9571i		−	1.41905i	−0.704682	−	0.709523i	$-0.748910\pi$
$71$		−	11.9571i		−	1.41905i	0.704682	−	0.709523i	$-0.251090\pi$
$72$		0			0
$73$	−0.668863			−0.0782845			−0.0391423	−	0.999234i	$-0.512463\pi$
$73$	−0.668863			−0.0782845			−0.0391423	+	0.999234i	$0.512463\pi$
$74$		0			0
$75$	−1.78637	−	0.0376436i	−0.206272	−	0.00434670i
$76$		0			0
$77$	−4.33649			−0.494189
$78$		0			0
$79$	−5.45374	−	5.45374i	−0.613594	−	0.613594i	0.330287	−	0.943881i	$-0.392855\pi$
$79$	−5.45374	−	5.45374i	−0.613594	−	0.613594i	−0.943881	+	0.330287i	$0.892855\pi$
$80$		0			0
$81$	7.86699			0.874110
$82$		0			0
$83$	−7.98469	+	7.98469i	−0.876433	+	0.876433i	−0.993164	−	0.116730i	$-0.962759\pi$
$83$	−7.98469	+	7.98469i	−0.876433	+	0.876433i	0.116730	+	0.993164i	$0.462759\pi$
$84$		0			0
$85$	9.71865	+	9.92560i	1.05414	+	1.07658i
$86$		0			0
$87$	1.42808	+	1.28993i	0.153106	+	0.138295i
$88$		0			0
$89$	−6.43075	−	6.43075i	−0.681658	−	0.681658i	0.278715	−	0.960374i	$-0.410091\pi$
$89$	−6.43075	−	6.43075i	−0.681658	−	0.681658i	−0.960374	+	0.278715i	$0.910091\pi$
$90$		0			0
$91$			4.96865i			0.520856i
$92$		0			0
$93$	−0.736966	−	0.736966i	−0.0764199	−	0.0764199i
$94$		0			0
$95$	−0.104691	+	9.93728i	−0.0107410	+	1.01954i
$96$		0			0
$97$		−	4.41209i		−	0.447980i	−0.974591	−	0.223990i	$-0.928092\pi$
$97$		−	4.41209i		−	0.447980i	0.974591	−	0.223990i	$-0.0719083\pi$
$98$		0			0
$99$	4.64396	−	4.64396i	0.466736	−	0.466736i
$100$		0			0
$101$	0.178790	−	0.178790i	0.0177903	−	0.0177903i	−0.698156	−	0.715946i	$-0.745996\pi$
$101$	0.178790	−	0.178790i	0.0177903	−	0.0177903i	0.715946	+	0.698156i	$0.245996\pi$
$102$		0			0
$103$	6.79609	−	6.79609i	0.669638	−	0.669638i	−0.287994	−	0.957632i	$-0.592988\pi$
$103$	6.79609	−	6.79609i	0.669638	−	0.669638i	0.957632	+	0.287994i	$0.0929883\pi$
$104$		0			0
$105$	1.51539	+	0.0159648i	0.147887	+	0.00155801i
$106$		0			0
$107$	−4.07318	−	4.07318i	−0.393769	−	0.393769i	0.482259	−	0.876029i	$-0.339816\pi$
$107$	−4.07318	−	4.07318i	−0.393769	−	0.393769i	−0.876029	+	0.482259i	$0.839816\pi$
$108$		0			0
$109$	0.443155			0.0424465			0.0212233	−	0.999775i	$-0.493244\pi$
$109$	0.443155			0.0424465			0.0212233	+	0.999775i	$0.493244\pi$
$110$		0			0
$111$	−0.330600			−0.0313792
$112$		0			0
$113$	−20.4914			−1.92767			−0.963836	−	0.266497i	$-0.914134\pi$
$113$	−20.4914			−1.92767			−0.963836	+	0.266497i	$0.914134\pi$
$114$		0			0
$115$	−15.5025	−	0.163321i	−1.44561	−	0.0152297i
$116$		0			0
$117$	−5.32094	−	5.32094i	−0.491921	−	0.491921i
$118$		0			0
$119$	−8.33123	−	8.33123i	−0.763723	−	0.763723i
$120$		0			0
$121$			5.77185i			0.524713i
$122$		0			0
$123$	−2.01597	+	2.01597i	−0.181774	+	0.181774i
$124$		0			0
$125$	−8.15156	+	7.65193i	−0.729098	+	0.684410i
$126$		0			0
$127$	−5.30072			−0.470363			−0.235181	−	0.971951i	$-0.575568\pi$
$127$	−5.30072			−0.470363			−0.235181	+	0.971951i	$0.575568\pi$
$128$		0			0
$129$	−0.135278			−0.0119106
$130$		0			0
$131$	−13.8224	−	13.8224i	−1.20767	−	1.20767i	−0.971781	−	0.235884i	$-0.924202\pi$
$131$	−13.8224	−	13.8224i	−1.20767	−	1.20767i	−0.235884	−	0.971781i	$-0.575798\pi$
$132$		0			0
$133$		−	8.42891i		−	0.730879i
$134$		0			0
$135$	−3.35277	+	3.28286i	−0.288560	+	0.282544i
$136$		0			0
$137$	−21.3777			−1.82642			−0.913209	−	0.407490i	$-0.866404\pi$
$137$	−21.3777			−1.82642			−0.913209	+	0.407490i	$0.866404\pi$
$138$		0			0
$139$		−	0.385470i		−	0.0326951i	−0.999866	−	0.0163476i	$-0.994796\pi$
$139$		−	0.385470i		−	0.0326951i	0.999866	−	0.0163476i	$-0.00520382\pi$
$140$		0			0
$141$	3.67542			0.309527
$142$		0			0
$143$	−5.99029			−0.500934
$144$		0			0
$145$	12.0318	−	0.484519i	0.999190	−	0.0402371i
$146$		0			0
$147$	1.21611			0.100303
$148$		0			0
$149$	18.1307			1.48533			0.742663	−	0.669665i	$-0.233562\pi$
$149$	18.1307			1.48533			0.742663	+	0.669665i	$0.233562\pi$
$150$		0			0
$151$			13.5604i			1.10353i	0.833999	+	0.551765i	$0.186046\pi$
$151$			13.5604i			1.10353i	−0.833999	+	0.551765i	$0.813954\pi$
$152$		0			0
$153$	17.8439			1.44259
$154$		0			0
$155$	−6.52117	−	0.0687015i	−0.523793	−	0.00551824i
$156$		0			0
$157$			3.37237i			0.269144i	0.990904	+	0.134572i	$0.0429660\pi$
$157$			3.37237i			0.269144i	−0.990904	+	0.134572i	$0.957034\pi$
$158$		0			0
$159$	−0.556455	−	0.556455i	−0.0441298	−	0.0441298i
$160$		0			0
$161$	13.1494			1.03631
$162$		0			0
$163$	−14.2104			−1.11304			−0.556522	−	0.830833i	$-0.687865\pi$
$163$	−14.2104			−1.11304			−0.556522	+	0.830833i	$0.687865\pi$
$164$		0			0
$165$	−0.0192475	+	1.82698i	−0.00149841	+	0.142230i
$166$		0			0
$167$	3.75499	−	3.75499i	0.290570	−	0.290570i	−0.546735	−	0.837305i	$-0.684130\pi$
$167$	3.75499	−	3.75499i	0.290570	−	0.290570i	0.837305	+	0.546735i	$0.184130\pi$
$168$		0			0
$169$		−	6.13646i		−	0.472035i
$170$		0			0
$171$	9.02653	+	9.02653i	0.690276	+	0.690276i
$172$		0			0
$173$	−11.2001	−	11.2001i	−0.851525	−	0.851525i	0.138796	−	0.990321i	$-0.455677\pi$
$173$	−11.2001	−	11.2001i	−0.851525	−	0.851525i	−0.990321	+	0.138796i	$0.955677\pi$
$174$		0			0
$175$	6.84510	−	6.56257i	0.517441	−	0.496083i
$176$		0			0
$177$	−2.49750			−0.187724
$178$		0			0
$179$	8.76990			0.655493			0.327747	−	0.944766i	$-0.393711\pi$
$179$	8.76990			0.655493			0.327747	+	0.944766i	$0.393711\pi$
$180$		0			0
$181$	22.6172			1.68112			0.840561	−	0.541718i	$-0.182226\pi$
$181$	22.6172			1.68112			0.840561	+	0.541718i	$0.182226\pi$
$182$		0			0
$183$	−2.23842	−	2.23842i	−0.165469	−	0.165469i
$184$		0			0
$185$	−1.47810	+	1.44728i	−0.108672	+	0.106406i
$186$		0			0
$187$	10.0443	−	10.0443i	0.734510	−	0.734510i
$188$		0			0
$189$	2.81421	−	2.81421i	0.204703	−	0.204703i
$190$		0			0
$191$	−9.69768	+	9.69768i	−0.701699	+	0.701699i	−0.964775	−	0.263076i	$-0.915263\pi$
$191$	−9.69768	+	9.69768i	−0.701699	+	0.701699i	0.263076	+	0.964775i	$0.415263\pi$
$192$		0			0
$193$			5.80624i			0.417942i	0.977922	+	0.208971i	$0.0670114\pi$
$193$			5.80624i			0.417942i	−0.977922	+	0.208971i	$0.932989\pi$
$194$		0			0
$195$	2.09331	+	0.0220533i	0.149905	+	0.00157927i
$196$		0			0
$197$	−6.15586	−	6.15586i	−0.438587	−	0.438587i	0.452950	−	0.891536i	$-0.350372\pi$
$197$	−6.15586	−	6.15586i	−0.438587	−	0.438587i	−0.891536	+	0.452950i	$0.850372\pi$
$198$		0			0
$199$		−	21.1728i		−	1.50090i	−0.660928	−	0.750449i	$-0.729837\pi$
$199$		−	21.1728i		−	1.50090i	0.660928	−	0.750449i	$-0.270163\pi$
$200$		0			0
$201$	1.93149	+	1.93149i	0.136237	+	0.136237i
$202$		0			0
$203$	−10.2001	+	0.518433i	−0.715905	+	0.0363869i
$204$		0			0
$205$	−0.187933	+	17.8386i	−0.0131258	+	1.24590i
$206$		0			0
$207$	−14.0817	+	14.0817i	−0.978744	+	0.978744i
$208$		0			0
$209$	10.1620			0.702923
$210$		0			0
$211$	−5.09402	−	5.09402i	−0.350687	−	0.350687i	0.509678	−	0.860365i	$-0.329764\pi$
$211$	−5.09402	−	5.09402i	−0.350687	−	0.350687i	−0.860365	+	0.509678i	$0.829764\pi$
$212$		0			0
$213$	4.27291			0.292775
$214$		0			0
$215$	−0.604821	+	0.592210i	−0.0412484	+	0.0403884i
$216$		0			0
$217$	5.53133			0.375491
$218$		0			0
$219$		−	0.239021i		−	0.0161515i
$220$		0			0
$221$	−11.5085	−	11.5085i	−0.774145	−	0.774145i
$222$		0			0
$223$	−8.21203	+	8.21203i	−0.549918	+	0.549918i	−0.926417	−	0.376499i	$-0.877128\pi$
$223$	−8.21203	+	8.21203i	−0.549918	+	0.549918i	0.376499	+	0.926417i	$0.377128\pi$
$224$		0			0
$225$	−0.302567	+	14.3583i	−0.0201712	+	0.957220i
$226$		0			0
$227$	17.0030	+	17.0030i	1.12853	+	1.12853i	0.990417	+	0.138111i	$0.0441030\pi$
$227$	17.0030	+	17.0030i	1.12853	+	1.12853i	0.138111	+	0.990417i	$0.455897\pi$
$228$		0			0
$229$	−11.2929	+	11.2929i	−0.746253	+	0.746253i	−0.973773	−	0.227520i	$-0.926938\pi$
$229$	−11.2929	+	11.2929i	−0.746253	+	0.746253i	0.227520	+	0.973773i	$0.426938\pi$
$230$		0			0
$231$		−	1.54966i		−	0.101960i
$232$		0			0
$233$	−0.270518	+	0.270518i	−0.0177222	+	0.0177222i	−0.715912	−	0.698190i	$-0.753989\pi$
$233$	−0.270518	+	0.270518i	−0.0177222	+	0.0177222i	0.698190	+	0.715912i	$0.253989\pi$
$234$		0			0
$235$	16.4326	−	16.0900i	1.07195	−	1.04959i
$236$		0			0
$237$	1.94891	−	1.94891i	0.126596	−	0.126596i
$238$		0			0
$239$			10.7719i			0.696777i	0.937350	+	0.348388i	$0.113271\pi$
$239$			10.7719i			0.696777i	−0.937350	+	0.348388i	$0.886729\pi$
$240$		0			0
$241$		−	21.0089i		−	1.35330i	−0.736304	−	0.676651i	$-0.763431\pi$
$241$		−	21.0089i		−	1.35330i	0.736304	−	0.676651i	$-0.236569\pi$
$242$		0			0
$243$			9.10676i			0.584199i
$244$		0			0
$245$	5.43715	−	5.32378i	0.347367	−	0.340124i
$246$		0			0
$247$		−	11.6434i		−	0.740853i
$248$		0			0
$249$	−2.85336	−	2.85336i	−0.180824	−	0.180824i
$250$		0			0
$251$	−13.7825	+	13.7825i	−0.869943	+	0.869943i	−0.992466	−	0.122523i	$-0.960902\pi$
$251$	−13.7825	+	13.7825i	−0.869943	+	0.869943i	0.122523	+	0.992466i	$0.460902\pi$
$252$		0			0
$253$			15.8531i			0.996675i
$254$		0			0
$255$	−3.54695	+	3.47299i	−0.222119	+	0.217487i
$256$		0			0
$257$	1.16484	+	1.16484i	0.0726610	+	0.0726610i	0.742503	−	0.669842i	$-0.233638\pi$
$257$	1.16484	+	1.16484i	0.0726610	+	0.0726610i	−0.669842	+	0.742503i	$0.733638\pi$
$258$		0			0
$259$	1.24067	−	1.24067i	0.0770912	−	0.0770912i
$260$		0			0
$261$	10.3681	−	11.4785i	0.641769	−	0.710500i
$262$		0			0
$263$		−	9.90969i		−	0.611058i	−0.952183	−	0.305529i	$-0.901167\pi$
$263$		−	9.90969i		−	0.611058i	0.952183	−	0.305529i	$-0.0988332\pi$
$264$		0			0
$265$	−4.92389	−	0.0518739i	−0.302472	−	0.00318659i
$266$		0			0
$267$	2.29805	−	2.29805i	0.140639	−	0.140639i
$268$		0			0
$269$	−6.93623	+	6.93623i	−0.422909	+	0.422909i	−0.886204	−	0.463295i	$-0.846667\pi$
$269$	−6.93623	+	6.93623i	−0.422909	+	0.422909i	0.463295	+	0.886204i	$0.346667\pi$
$270$		0			0
$271$	7.30835	+	7.30835i	0.443950	+	0.443950i	0.893337	−	0.449387i	$-0.148357\pi$
$271$	7.30835	+	7.30835i	0.443950	+	0.443950i	−0.449387	+	0.893337i	$0.648357\pi$
$272$		0			0
$273$	−1.77557			−0.107462
$274$		0			0
$275$	7.91194	+	8.25257i	0.477108	+	0.497649i
$276$		0			0
$277$	13.6940	+	13.6940i	0.822792	+	0.822792i	0.986508	−	0.163715i	$-0.0523478\pi$
$277$	13.6940	+	13.6940i	0.822792	+	0.822792i	−0.163715	+	0.986508i	$0.552348\pi$
$278$		0			0
$279$	−5.92351	+	5.92351i	−0.354631	+	0.354631i
$280$		0			0
$281$	−19.3400			−1.15373			−0.576863	−	0.816841i	$-0.695723\pi$
$281$	−19.3400			−1.15373			−0.576863	+	0.816841i	$0.695723\pi$
$282$		0			0
$283$	20.5737	+	20.5737i	1.22298	+	1.22298i	0.966568	+	0.256411i	$0.0825400\pi$
$283$	20.5737	+	20.5737i	1.22298	+	1.22298i	0.256411	+	0.966568i	$0.417460\pi$
$284$		0			0
$285$	−3.55112	−	0.0374116i	−0.210350	−	0.00221607i
$286$		0			0
$287$		−	15.1309i		−	0.893150i
$288$		0			0
$289$	21.5939			1.27023
$290$		0			0
$291$	1.57668			0.0924264
$292$		0			0
$293$		−	4.90775i		−	0.286714i	−0.989671	−	0.143357i	$-0.954210\pi$
$293$		−	4.90775i		−	0.286714i	0.989671	−	0.143357i	$-0.0457897\pi$
$294$		0			0
$295$	−11.1662	+	10.9334i	−0.650121	+	0.636565i
$296$		0			0
$297$	3.39286	+	3.39286i	0.196873	+	0.196873i
$298$		0			0
$299$	18.1641			1.05046
$300$		0			0
$301$	0.507667	−	0.507667i	0.0292615	−	0.0292615i
$302$		0			0
$303$	0.0638913	+	0.0638913i	0.00367046	+	0.00367046i
$304$		0			0
$305$	−19.8070	−	0.208670i	−1.13415	−	0.0119484i
$306$		0			0
$307$	28.5853			1.63145			0.815725	−	0.578440i	$-0.196338\pi$
$307$	28.5853			1.63145			0.815725	+	0.578440i	$0.196338\pi$
$308$		0			0
$309$	2.42861	+	2.42861i	0.138159	+	0.138159i
$310$		0			0
$311$	13.2265	−	13.2265i	0.750008	−	0.750008i	−0.224473	−	0.974480i	$-0.572066\pi$
$311$	13.2265	−	13.2265i	0.750008	−	0.750008i	0.974480	+	0.224473i	$0.0720659\pi$
$312$		0			0
$313$	19.8846	−	19.8846i	1.12395	−	1.12395i	0.132804	−	0.991142i	$-0.457602\pi$
$313$	19.8846	−	19.8846i	1.12395	−	1.12395i	0.991142	−	0.132804i	$-0.0423980\pi$
$314$		0			0
$315$	0.128320	−	12.1802i	0.00723004	−	0.686278i
$316$		0			0
$317$		−	21.1780i		−	1.18947i	−0.803920	−	0.594737i	$-0.797256\pi$
$317$		−	21.1780i		−	1.18947i	0.803920	−	0.594737i	$-0.202744\pi$
$318$		0			0
$319$	−0.625032	−	12.2974i	−0.0349951	−	0.688522i
$320$		0			0
$321$	1.45557	−	1.45557i	0.0812418	−	0.0812418i
$322$		0			0
$323$	19.5232	+	19.5232i	1.08630	+	1.08630i
$324$		0			0
$325$	9.45560	−	9.06532i	0.524503	−	0.502853i
$326$		0			0
$327$			0.158363i			0.00875749i
$328$		0			0
$329$	−13.7930	+	13.7930i	−0.760433	+	0.760433i
$330$		0			0
$331$	15.0254	+	15.0254i	0.825873	+	0.825873i	0.986943	−	0.161070i	$-0.0514946\pi$
$331$	15.0254	+	15.0254i	0.825873	+	0.825873i	−0.161070	+	0.986943i	$0.551495\pi$
$332$		0			0
$333$			2.65726i			0.145617i
$334$		0			0
$335$	17.0911	+	0.180058i	0.933788	+	0.00983760i
$336$		0			0
$337$			11.3239i			0.616854i	0.951248	+	0.308427i	$0.0998026\pi$
$337$			11.3239i			0.616854i	−0.951248	+	0.308427i	$0.900197\pi$
$338$		0			0
$339$		−	7.32269i		−	0.397714i
$340$		0			0
$341$			6.66866i			0.361128i
$342$		0			0
$343$	−13.9512	+	13.9512i	−0.753295	+	0.753295i
$344$		0			0
$345$	0.0583633	−	5.53986i	0.00314217	−	0.298256i
$346$		0			0
$347$	4.31859	−	4.31859i	0.231834	−	0.231834i	−0.581624	−	0.813458i	$-0.697582\pi$
$347$	4.31859	−	4.31859i	0.231834	−	0.231834i	0.813458	+	0.581624i	$0.197582\pi$
$348$		0			0
$349$			6.50844i			0.348389i	0.984711	+	0.174195i	$0.0557322\pi$
$349$			6.50844i			0.348389i	−0.984711	+	0.174195i	$0.944268\pi$
$350$		0			0
$351$	3.88745	−	3.88745i	0.207497	−	0.207497i
$352$		0			0
$353$	0.333192	+	0.333192i	0.0177340	+	0.0177340i	0.715918	−	0.698184i	$-0.246008\pi$
$353$	0.333192	+	0.333192i	0.0177340	+	0.0177340i	−0.698184	+	0.715918i	$0.746008\pi$
$354$		0			0
$355$	19.1039	−	18.7056i	1.01393	−	0.992791i
$356$		0			0
$357$	2.97720	−	2.97720i	0.157570	−	0.157570i
$358$		0			0
$359$	2.45103	+	2.45103i	0.129361	+	0.129361i	0.768823	−	0.639462i	$-0.220843\pi$
$359$	2.45103	+	2.45103i	0.129361	+	0.129361i	−0.639462	+	0.768823i	$0.720843\pi$
$360$		0			0
$361$			0.752088i			0.0395836i
$362$		0			0
$363$	−2.06259			−0.108258
$364$		0			0
$365$	−1.04637	−	1.06865i	−0.0547693	−	0.0559356i
$366$		0			0
$367$	−6.40450			−0.334312			−0.167156	−	0.985930i	$-0.553458\pi$
$367$	−6.40450			−0.334312			−0.167156	+	0.985930i	$0.553458\pi$
$368$		0			0
$369$	16.2037	+	16.2037i	0.843533	+	0.843533i
$370$		0			0
$371$	4.17649			0.216833
$372$		0			0
$373$	−12.2474	+	12.2474i	−0.634148	+	0.634148i	−0.949106	−	0.314957i	$-0.898010\pi$
$373$	−12.2474	+	12.2474i	−0.634148	+	0.634148i	0.314957	+	0.949106i	$0.398010\pi$
$374$		0			0
$375$	−2.73445	−	2.91299i	−0.141206	−	0.150426i
$376$		0			0
$377$	−14.0901	+	0.716147i	−0.725675	+	0.0368835i
$378$		0			0
$379$	19.4098	+	19.4098i	0.997014	+	0.997014i	0.999996	−	0.00298123i	$-0.000948955\pi$
$379$	19.4098	+	19.4098i	0.997014	+	0.997014i	−0.00298123	+	0.999996i	$0.500949\pi$
$380$		0			0
$381$		−	1.89423i		−	0.0970444i
$382$		0			0
$383$	−16.3414	−	16.3414i	−0.835008	−	0.835008i	0.153189	−	0.988197i	$-0.451046\pi$
$383$	−16.3414	−	16.3414i	−0.835008	−	0.835008i	−0.988197	+	0.153189i	$0.951046\pi$
$384$		0			0
$385$	−6.78399	−	6.92845i	−0.345744	−	0.353107i
$386$		0			0
$387$			1.08732i			0.0552718i
$388$		0			0
$389$	0.984007	−	0.984007i	0.0498911	−	0.0498911i	−0.681721	−	0.731612i	$-0.738768\pi$
$389$	0.984007	−	0.984007i	0.0498911	−	0.0498911i	0.731612	+	0.681721i	$0.238768\pi$
$390$		0			0
$391$	−30.4568	+	30.4568i	−1.54027	+	1.54027i
$392$		0			0
$393$	4.93947	−	4.93947i	0.249163	−	0.249163i
$394$		0			0
$395$	0.181682	−	17.2453i	0.00914140	−	0.867705i
$396$		0			0
$397$	4.23517	+	4.23517i	0.212557	+	0.212557i	0.805353	−	0.592796i	$-0.201976\pi$
$397$	4.23517	+	4.23517i	0.212557	+	0.212557i	−0.592796	+	0.805353i	$0.701976\pi$
$398$		0			0
$399$	3.01210			0.150794
$400$		0			0
$401$	−11.4927			−0.573920			−0.286960	−	0.957942i	$-0.592645\pi$
$401$	−11.4927			−0.573920			−0.286960	+	0.957942i	$0.592645\pi$
$402$		0			0
$403$	7.64080			0.380615
$404$		0			0
$405$	12.3071	+	12.5692i	0.611544	+	0.624566i
$406$		0			0
$407$	1.49577	+	1.49577i	0.0741425	+	0.0741425i
$408$		0			0
$409$	−1.47196	−	1.47196i	−0.0727836	−	0.0727836i	0.669778	−	0.742561i	$-0.266389\pi$
$409$	−1.47196	−	1.47196i	−0.0727836	−	0.0727836i	−0.742561	+	0.669778i	$0.766389\pi$
$410$		0			0
$411$		−	7.63939i		−	0.376823i
$412$		0			0
$413$	9.37254	−	9.37254i	0.461193	−	0.461193i
$414$		0			0
$415$	−25.2484	−	0.265996i	−1.23940	−	0.0130572i
$416$		0			0
$417$	0.137749			0.00674560
$418$		0			0
$419$	−35.5076			−1.73466			−0.867329	−	0.497736i	$-0.834165\pi$
$419$	−35.5076			−1.73466			−0.867329	+	0.497736i	$0.834165\pi$
$420$		0			0
$421$	−15.7463	−	15.7463i	−0.767425	−	0.767425i	0.210227	−	0.977653i	$-0.432580\pi$
$421$	−15.7463	−	15.7463i	−0.767425	−	0.767425i	−0.977653	+	0.210227i	$0.932580\pi$
$422$		0			0
$423$		−	29.5419i		−	1.43638i
$424$		0			0
$425$	−0.654413	+	31.0551i	−0.0317437	+	1.50639i
$426$		0			0
$427$	16.8005			0.813034
$428$		0			0
$429$		−	2.14065i		−	0.103352i
$430$		0			0
$431$	4.71919			0.227315			0.113658	−	0.993520i	$-0.463743\pi$
$431$	4.71919			0.227315			0.113658	+	0.993520i	$0.463743\pi$
$432$		0			0
$433$	−25.4558			−1.22333			−0.611665	−	0.791117i	$-0.709500\pi$
$433$	−25.4558			−1.22333			−0.611665	+	0.791117i	$0.709500\pi$
$434$		0			0
$435$	0.173144	+	4.29962i	0.00830164	+	0.206151i
$436$		0			0
$437$	−30.8139			−1.47403
$438$		0			0
$439$	−26.3909			−1.25957			−0.629783	−	0.776771i	$-0.716856\pi$
$439$	−26.3909			−1.25957			−0.629783	+	0.776771i	$0.716856\pi$
$440$		0			0
$441$		−	9.77470i		−	0.465462i
$442$		0			0
$443$	33.6225			1.59745			0.798726	−	0.601695i	$-0.205508\pi$
$443$	33.6225			1.59745			0.798726	+	0.601695i	$0.205508\pi$
$444$		0			0
$445$	0.214229	−	20.3347i	0.0101554	−	0.963957i
$446$		0			0
$447$			6.47908i			0.306450i
$448$		0			0
$449$	−0.730045	−	0.730045i	−0.0344530	−	0.0344530i	0.689670	−	0.724123i	$-0.257755\pi$
$449$	−0.730045	−	0.730045i	−0.0344530	−	0.0344530i	−0.724123	+	0.689670i	$0.757755\pi$
$450$		0			0
$451$	18.2421			0.858987
$452$		0			0
$453$	−4.84586			−0.227679
$454$		0			0
$455$	−7.93846	+	7.77293i	−0.372161	+	0.364401i
$456$		0			0
$457$	−23.8236	+	23.8236i	−1.11442	+	1.11442i	−0.121874	+	0.992546i	$0.538890\pi$
$457$	−23.8236	+	23.8236i	−1.11442	+	1.11442i	−0.992546	+	0.121874i	$0.961110\pi$
$458$		0			0
$459$			13.0366i			0.608499i
$460$		0			0
$461$	1.37015	+	1.37015i	0.0638142	+	0.0638142i	0.738294	−	0.674479i	$-0.235632\pi$
$461$	1.37015	+	1.37015i	0.0638142	+	0.0638142i	−0.674479	+	0.738294i	$0.735632\pi$
$462$		0			0
$463$	3.42609	+	3.42609i	0.159224	+	0.159224i	0.782223	−	0.622999i	$-0.214086\pi$
$463$	3.42609	+	3.42609i	0.159224	+	0.159224i	−0.622999	+	0.782223i	$0.714086\pi$
$464$		0			0
$465$	0.0245507	−	2.33036i	0.00113851	−	0.108068i
$466$		0			0
$467$	18.3397			0.848659			0.424330	−	0.905508i	$-0.360510\pi$
$467$	18.3397			0.848659			0.424330	+	0.905508i	$0.360510\pi$
$468$		0			0
$469$	−14.4969			−0.669404
$470$		0			0
$471$	−1.20513			−0.0555294
$472$		0			0
$473$	0.612052	+	0.612052i	0.0281422	+	0.0281422i
$474$		0			0
$475$	−16.0406	+	15.3786i	−0.735995	+	0.705617i
$476$		0			0
$477$	−4.47262	+	4.47262i	−0.204787	+	0.204787i
$478$		0			0
$479$	−1.47739	+	1.47739i	−0.0675037	+	0.0675037i	−0.740053	−	0.672549i	$-0.765199\pi$
$479$	−1.47739	+	1.47739i	−0.0675037	+	0.0675037i	0.672549	+	0.740053i	$0.265199\pi$
$480$		0			0
$481$	1.71382	−	1.71382i	0.0781433	−	0.0781433i
$482$		0			0
$483$			4.69897i			0.213811i
$484$		0			0
$485$	7.04923	−	6.90225i	0.320089	−	0.313415i
$486$		0			0
$487$	3.53906	+	3.53906i	0.160370	+	0.160370i	0.782731	−	0.622361i	$-0.213826\pi$
$487$	3.53906	+	3.53906i	0.160370	+	0.160370i	−0.622361	+	0.782731i	$0.713826\pi$
$488$		0			0
$489$		−	5.07814i		−	0.229641i
$490$		0			0
$491$	−29.0344	−	29.0344i	−1.31030	−	1.31030i	−0.921190	−	0.389114i	$-0.872781\pi$
$491$	−29.0344	−	29.0344i	−1.31030	−	1.31030i	−0.389114	−	0.921190i	$-0.627219\pi$
$492$		0			0
$493$	22.4248	−	24.8264i	1.00996	−	1.11813i
$494$		0			0
$495$	14.6847	+	0.154705i	0.660027	+	0.00695349i
$496$		0			0
$497$	−16.0352	+	16.0352i	−0.719279	+	0.719279i
$498$		0			0
$499$	−32.5899			−1.45892			−0.729462	−	0.684021i	$-0.760230\pi$
$499$	−32.5899			−1.45892			−0.729462	+	0.684021i	$0.760230\pi$
$500$		0			0
$501$	1.34186	+	1.34186i	0.0599499	+	0.0599499i
$502$		0			0
$503$	18.2663			0.814455			0.407228	−	0.913327i	$-0.366496\pi$
$503$	18.2663			0.814455			0.407228	+	0.913327i	$0.366496\pi$
$504$		0			0
$505$	0.565353	+	0.00595608i	0.0251579	+	0.000265042i
$506$		0			0
$507$	2.19289			0.0973895
$508$		0			0
$509$			3.51992i			0.156018i	0.996953	+	0.0780089i	$0.0248562\pi$
$509$			3.51992i			0.156018i	−0.996953	+	0.0780089i	$0.975144\pi$
$510$		0			0
$511$	0.896989	+	0.896989i	0.0396804	+	0.0396804i
$512$		0			0
$513$	−6.59474	+	6.59474i	−0.291165	+	0.291165i
$514$		0			0
$515$	21.4899	+	0.226400i	0.946959	+	0.00997636i
$516$		0			0
$517$	−16.6291	−	16.6291i	−0.731347	−	0.731347i
$518$		0			0
$519$	4.00238	−	4.00238i	0.175685	−	0.175685i
$520$		0			0
$521$		−	40.8909i		−	1.79146i	−0.444597	−	0.895731i	$-0.646653\pi$
$521$		−	40.8909i		−	1.79146i	0.444597	−	0.895731i	$-0.353347\pi$
$522$		0			0
$523$	26.0733	−	26.0733i	1.14010	−	1.14010i	0.151673	−	0.988431i	$-0.451534\pi$
$523$	26.0733	−	26.0733i	1.14010	−	1.14010i	0.988431	−	0.151673i	$-0.0484662\pi$
$524$		0			0
$525$	2.34516	+	2.44612i	0.102351	+	0.106758i
$526$		0			0
$527$	−12.8118	+	12.8118i	−0.558090	+	0.558090i
$528$		0			0
$529$		−	25.0706i		−	1.09003i
$530$		0			0
$531$			20.0742i			0.871144i
$532$		0			0
$533$		−	20.9014i		−	0.905339i
$534$		0			0
$535$	0.135691	−	12.8798i	0.00586643	−	0.556843i
$536$		0			0
$537$			3.13396i			0.135240i
$538$		0			0
$539$	−5.50215	−	5.50215i	−0.236995	−	0.236995i
$540$		0			0
$541$	−32.2573	+	32.2573i	−1.38685	+	1.38685i	−0.555000	+	0.831851i	$0.687282\pi$
$541$	−32.2573	+	32.2573i	−1.38685	+	1.38685i	−0.831851	+	0.555000i	$0.812718\pi$
$542$		0			0
$543$			8.08233i			0.346846i
$544$		0			0
$545$	0.693269	+	0.708032i	0.0296964	+	0.0303287i
$546$		0			0
$547$	−3.15658	−	3.15658i	−0.134966	−	0.134966i	0.636397	−	0.771362i	$-0.280424\pi$
$547$	−3.15658	−	3.15658i	−0.134966	−	0.134966i	−0.771362	+	0.636397i	$0.780424\pi$
$548$		0			0
$549$	−17.9917	+	17.9917i	−0.767868	+	0.767868i
$550$		0			0
$551$	23.9026	−	1.21488i	1.01829	−	0.0517558i
$552$		0			0
$553$			14.6276i			0.622031i
$554$		0			0
$555$	−0.517189	−	0.528203i	−0.0219535	−	0.0224210i
$556$		0			0
$557$	−11.6611	+	11.6611i	−0.494098	+	0.494098i	−0.909595	−	0.415497i	$-0.863608\pi$
$557$	−11.6611	+	11.6611i	−0.494098	+	0.494098i	0.415497	+	0.909595i	$0.363608\pi$
$558$		0			0
$559$	0.701275	−	0.701275i	0.0296608	−	0.0296608i
$560$		0			0
$561$	3.58936	+	3.58936i	0.151543	+	0.151543i
$562$		0			0
$563$	29.6342			1.24893			0.624466	−	0.781052i	$-0.285317\pi$
$563$	29.6342			1.24893			0.624466	+	0.781052i	$0.285317\pi$
$564$		0			0
$565$	−32.0567	−	32.7393i	−1.34863	−	1.37735i
$566$		0			0
$567$	−10.5501	−	10.5501i	−0.443064	−	0.443064i
$568$		0			0
$569$	−4.43267	+	4.43267i	−0.185827	+	0.185827i	−0.793889	−	0.608062i	$-0.791947\pi$
$569$	−4.43267	+	4.43267i	−0.185827	+	0.185827i	0.608062	+	0.793889i	$0.291947\pi$
$570$		0			0
$571$	−2.73583			−0.114491			−0.0572454	−	0.998360i	$-0.518232\pi$
$571$	−2.73583			−0.114491			−0.0572454	+	0.998360i	$0.518232\pi$
$572$		0			0
$573$	−3.46550	−	3.46550i	−0.144773	−	0.144773i
$574$		0			0
$575$	−23.9910	−	25.0239i	−1.00050	−	1.04357i
$576$		0			0
$577$		−	36.6599i		−	1.52617i	−0.646297	−	0.763086i	$-0.723683\pi$
$577$		−	36.6599i		−	1.52617i	0.646297	−	0.763086i	$-0.276317\pi$
$578$		0			0
$579$	−2.07488			−0.0862290
$580$		0			0
$581$	21.4160			0.888484
$582$		0			0
$583$			5.03525i			0.208539i
$584$		0			0
$585$	0.177258	−	16.8254i	0.00732871	−	0.695643i
$586$		0			0
$587$	26.7124	+	26.7124i	1.10254	+	1.10254i	0.994104	+	0.108435i	$0.0345838\pi$
$587$	26.7124	+	26.7124i	1.10254	+	1.10254i	0.108435	+	0.994104i	$0.465416\pi$
$588$		0			0
$589$	−12.9620			−0.534089
$590$		0			0
$591$	2.19982	−	2.19982i	0.0904884	−	0.0904884i
$592$		0			0
$593$	−16.1049	−	16.1049i	−0.661347	−	0.661347i	0.294350	−	0.955698i	$-0.404897\pi$
$593$	−16.1049	−	16.1049i	−0.661347	−	0.661347i	−0.955698	+	0.294350i	$0.904897\pi$
$594$		0			0
$595$	0.277540	−	26.3442i	0.0113780	−	1.08001i
$596$		0			0
$597$	7.56617			0.309663
$598$		0			0
$599$	−7.57553	−	7.57553i	−0.309528	−	0.309528i	0.535199	−	0.844726i	$-0.320237\pi$
$599$	−7.57553	−	7.57553i	−0.309528	−	0.309528i	−0.844726	+	0.535199i	$0.820237\pi$
$600$		0			0
$601$	−12.7325	+	12.7325i	−0.519371	+	0.519371i	−0.917381	−	0.398010i	$-0.869701\pi$
$601$	−12.7325	+	12.7325i	−0.519371	+	0.519371i	0.398010	+	0.917381i	$0.369701\pi$
$602$		0			0
$603$	15.5247	−	15.5247i	0.632216	−	0.632216i
$604$		0			0
$605$	−9.22173	+	9.02945i	−0.374916	+	0.367099i
$606$		0			0
$607$			27.1738i			1.10295i	0.834191	+	0.551475i	$0.185935\pi$
$607$			27.1738i			1.10295i	−0.834191	+	0.551475i	$0.814065\pi$
$608$		0			0
$609$	−0.185264	−	3.64503i	−0.00750728	−	0.147704i
$610$		0			0
$611$	−19.0532	+	19.0532i	−0.770811	+	0.770811i
$612$		0			0
$613$	14.1516	+	14.1516i	0.571576	+	0.571576i	0.932569	−	0.360993i	$-0.117562\pi$
$613$	14.1516	+	14.1516i	0.571576	+	0.571576i	−0.360993	+	0.932569i	$0.617562\pi$
$614$		0			0
$615$	−6.37470	−	0.0671585i	−0.257053	−	0.00270809i
$616$		0			0
$617$			5.81327i			0.234034i	0.993130	+	0.117017i	$0.0373331\pi$
$617$			5.81327i			0.234034i	−0.993130	+	0.117017i	$0.962667\pi$
$618$		0			0
$619$	−9.61724	+	9.61724i	−0.386549	+	0.386549i	−0.873455	−	0.486905i	$-0.838126\pi$
$619$	−9.61724	+	9.61724i	−0.386549	+	0.386549i	0.486905	+	0.873455i	$0.338126\pi$
$620$		0			0
$621$	−10.2880	−	10.2880i	−0.412843	−	0.412843i
$622$		0			0
$623$			17.2481i			0.691031i
$624$		0			0
$625$	−24.9778	−	1.05316i	−0.999112	−	0.0421266i
$626$		0			0
$627$			3.63144i			0.145026i
$628$		0			0
$629$			5.74731i			0.229160i
$630$		0			0
$631$			28.7081i			1.14285i	0.820653	+	0.571427i	$0.193610\pi$
$631$			28.7081i			1.14285i	−0.820653	+	0.571427i	$0.806390\pi$
$632$		0			0
$633$	1.82037	−	1.82037i	0.0723531	−	0.0723531i
$634$		0			0
$635$	−8.29242	−	8.46900i	−0.329075	−	0.336082i
$636$		0			0
$637$	−6.30424	+	6.30424i	−0.249783	+	0.249783i
$638$		0			0
$639$		−	34.3444i		−	1.35864i
$640$		0			0
$641$	25.0121	−	25.0121i	0.987919	−	0.987919i	−0.0120088	−	0.999928i	$-0.503823\pi$
$641$	25.0121	−	25.0121i	0.987919	−	0.987919i	0.999928	+	0.0120088i	$0.00382260\pi$
$642$		0			0
$643$	16.4141	+	16.4141i	0.647308	+	0.647308i	0.952342	−	0.305033i	$-0.0986676\pi$
$643$	16.4141	+	16.4141i	0.647308	+	0.647308i	−0.305033	+	0.952342i	$0.598668\pi$
$644$		0			0
$645$	−0.211628	−	0.216135i	−0.00833286	−	0.00851031i
$646$		0			0
$647$	−13.6894	+	13.6894i	−0.538186	+	0.538186i	−0.922996	−	0.384810i	$-0.874267\pi$
$647$	−13.6894	+	13.6894i	−0.538186	+	0.538186i	0.384810	+	0.922996i	$0.374267\pi$
$648$		0			0
$649$	11.2997	+	11.2997i	0.443552	+	0.443552i
$650$		0			0
$651$			1.97664i			0.0774706i
$652$		0			0
$653$	−20.5346			−0.803583			−0.401791	−	0.915731i	$-0.631612\pi$
$653$	−20.5346			−0.803583			−0.401791	+	0.915731i	$0.631612\pi$
$654$		0			0
$655$	0.460467	−	43.7077i	0.0179919	−	1.70780i
$656$		0			0
$657$	−1.92117			−0.0749522
$658$		0			0
$659$	−3.26927	−	3.26927i	−0.127353	−	0.127353i	0.640558	−	0.767910i	$-0.278703\pi$
$659$	−3.26927	−	3.26927i	−0.127353	−	0.127353i	−0.767910	+	0.640558i	$0.778703\pi$
$660$		0			0
$661$	29.6384			1.15280			0.576401	−	0.817167i	$-0.304457\pi$
$661$	29.6384			1.15280			0.576401	+	0.817167i	$0.304457\pi$
$662$		0			0
$663$	4.11260	−	4.11260i	0.159720	−	0.159720i
$664$		0			0
$665$	13.4669	−	13.1861i	0.522225	−	0.511336i
$666$		0			0
$667$	1.89526	+	37.2888i	0.0733846	+	1.44383i
$668$		0			0
$669$	−2.93460	−	2.93460i	−0.113458	−	0.113458i
$670$		0			0
$671$			20.2550i			0.781935i
$672$		0			0
$673$	14.6571	+	14.6571i	0.564988	+	0.564988i	0.930720	−	0.365732i	$-0.119181\pi$
$673$	14.6571	+	14.6571i	0.564988	+	0.564988i	−0.365732	+	0.930720i	$0.619181\pi$
$674$		0			0
$675$	−10.4901	−	0.221054i	−0.403764	−	0.00850838i
$676$		0			0
$677$		−	20.6938i		−	0.795328i	−0.917531	−	0.397664i	$-0.869821\pi$
$677$		−	20.6938i		−	0.795328i	0.917531	−	0.397664i	$-0.130179\pi$
$678$		0			0
$679$	−5.91690	+	5.91690i	−0.227070	+	0.227070i
$680$		0			0
$681$	−6.07608	+	6.07608i	−0.232836	+	0.232836i
$682$		0			0
$683$	3.48959	−	3.48959i	0.133525	−	0.133525i	−0.637185	−	0.770711i	$-0.719901\pi$
$683$	3.48959	−	3.48959i	0.133525	−	0.133525i	0.770711	+	0.637185i	$0.219901\pi$
$684$		0			0
$685$	−33.4431	−	34.1553i	−1.27780	−	1.30501i
$686$		0			0
$687$	−4.03554	−	4.03554i	−0.153966	−	0.153966i
$688$		0			0
$689$	5.76927			0.219792
$690$		0			0
$691$	−15.5782			−0.592623			−0.296311	−	0.955091i	$-0.595757\pi$
$691$	−15.5782			−0.592623			−0.296311	+	0.955091i	$0.595757\pi$
$692$		0			0
$693$	−12.4557			−0.473153
$694$		0			0
$695$	0.615868	−	0.603027i	0.0233612	−	0.0228741i
$696$		0			0
$697$	35.0466	+	35.0466i	1.32748	+	1.32748i
$698$		0			0
$699$	−0.0966706	−	0.0966706i	−0.00365642	−	0.00365642i
$700$		0			0
$701$		−	24.8088i		−	0.937016i	−0.883459	−	0.468508i	$-0.844792\pi$
$701$		−	24.8088i		−	0.937016i	0.883459	−	0.468508i	$-0.155208\pi$
$702$		0			0
$703$	−2.90735	+	2.90735i	−0.109653	+	0.109653i
$704$		0			0
$705$	5.74981	+	5.87225i	0.216551	+	0.221162i
$706$		0			0
$707$	−0.479538			−0.0180349
$708$		0			0
$709$	23.8053			0.894027			0.447013	−	0.894527i	$-0.352488\pi$
$709$	23.8053			0.894027			0.447013	+	0.894527i	$0.352488\pi$
$710$		0			0
$711$	−15.6648	−	15.6648i	−0.587475	−	0.587475i
$712$		0			0
$713$		−	20.2211i		−	0.757286i
$714$		0			0
$715$	−9.37118	−	9.57074i	−0.350462	−	0.357925i
$716$		0			0
$717$	−3.84938			−0.143758
$718$		0			0
$719$			34.5635i			1.28900i	0.764604	+	0.644500i	$0.222934\pi$
$719$			34.5635i			1.28900i	−0.764604	+	0.644500i	$0.777066\pi$
$720$		0			0
$721$	−18.2280			−0.678846
$722$		0			0
$723$	7.50760			0.279211
$724$		0			0
$725$	19.5967	+	18.4654i	0.727802	+	0.685787i
$726$		0			0
$727$	8.24406			0.305755			0.152878	−	0.988245i	$-0.451146\pi$
$727$	8.24406			0.305755			0.152878	+	0.988245i	$0.451146\pi$
$728$		0			0
$729$	20.3466			0.753580
$730$		0			0
$731$			2.35174i			0.0869822i
$732$		0			0
$733$	−6.27551			−0.231791			−0.115896	−	0.993261i	$-0.536974\pi$
$733$	−6.27551			−0.231791			−0.115896	+	0.993261i	$0.536974\pi$
$734$		0			0
$735$	1.90247	+	1.94298i	0.0701737	+	0.0716680i
$736$		0			0
$737$		−	17.4777i		−	0.643799i
$738$		0			0
$739$	23.5358	+	23.5358i	0.865780	+	0.865780i	0.992002	−	0.126222i	$-0.0402852\pi$
$739$	23.5358	+	23.5358i	0.865780	+	0.865780i	−0.126222	+	0.992002i	$0.540285\pi$
$740$		0			0
$741$	4.16082			0.152851
$742$		0			0
$743$	4.49416			0.164875			0.0824374	−	0.996596i	$-0.473730\pi$
$743$	4.49416			0.164875			0.0824374	+	0.996596i	$0.473730\pi$
$744$		0			0
$745$	28.3636	+	28.9676i	1.03916	+	1.06129i
$746$		0			0
$747$	−22.9344	+	22.9344i	−0.839126	+	0.839126i
$748$		0			0
$749$			10.9248i			0.399183i
$750$		0			0
$751$	−32.0441	−	32.0441i	−1.16931	−	1.16931i	−0.982373	−	0.186933i	$-0.940145\pi$
$751$	−32.0441	−	32.0441i	−1.16931	−	1.16931i	−0.186933	−	0.982373i	$-0.559855\pi$
$752$		0			0
$753$	−4.92522	−	4.92522i	−0.179485	−	0.179485i
$754$		0			0
$755$	−21.6656	+	21.2138i	−0.788491	+	0.772051i
$756$		0			0
$757$	45.7340			1.66223			0.831115	−	0.556101i	$-0.187703\pi$
$757$	45.7340			1.66223			0.831115	+	0.556101i	$0.187703\pi$
$758$		0			0
$759$	−5.66516			−0.205632
$760$		0			0
$761$	24.4564			0.886542			0.443271	−	0.896388i	$-0.353818\pi$
$761$	24.4564			0.886542			0.443271	+	0.896388i	$0.353818\pi$
$762$		0			0
$763$	−0.594299	−	0.594299i	−0.0215151	−	0.0215151i
$764$		0			0
$765$	27.9149	+	28.5093i	1.00926	+	1.03076i
$766$		0			0
$767$	12.9469	−	12.9469i	0.467487	−	0.467487i
$768$		0			0
$769$	−28.8908	+	28.8908i	−1.04183	+	1.04183i	−0.0427412	+	0.999086i	$0.513609\pi$
$769$	−28.8908	+	28.8908i	−1.04183	+	1.04183i	−0.999086	+	0.0427412i	$0.986391\pi$
$770$		0			0
$771$	−0.416261	+	0.416261i	−0.0149913	+	0.0149913i
$772$		0			0
$773$			31.9368i			1.14869i	0.818614	+	0.574344i	$0.194743\pi$
$773$			31.9368i			1.14869i	−0.818614	+	0.574344i	$0.805257\pi$
$774$		0			0
$775$	−10.0919	−	10.5264i	−0.362512	−	0.378119i
$776$		0			0
$777$	0.443356	+	0.443356i	0.0159053	+	0.0159053i
$778$		0			0
$779$			35.4574i			1.27039i
$780$		0			0
$781$	−19.3324	−	19.3324i	−0.691766	−	0.691766i
$782$		0			0
$783$	8.38612	+	7.57488i	0.299695	+	0.270704i
$784$		0			0
$785$	−5.38806	+	5.27572i	−0.192308	+	0.188298i
$786$		0			0
$787$	38.2446	−	38.2446i	1.36327	−	1.36327i	0.493560	−	0.869712i	$-0.335695\pi$
$787$	38.2446	−	38.2446i	1.36327	−	1.36327i	0.869712	−	0.493560i	$-0.164305\pi$
$788$		0			0
$789$	3.54126			0.126072
$790$		0			0
$791$	27.4803	+	27.4803i	0.977088	+	0.977088i
$792$		0			0
$793$	23.2077			0.824129
$794$		0			0
$795$	0.0185373	−	1.75957i	0.000657451	−	0.0624054i
$796$		0			0
$797$	−29.8653			−1.05788			−0.528941	−	0.848658i	$-0.677411\pi$
$797$	−29.8653			−1.05788			−0.528941	+	0.848658i	$0.677411\pi$
$798$		0			0
$799$		−	63.8953i		−	2.26045i
$800$		0			0
$801$	−18.4710	−	18.4710i	−0.652642	−	0.652642i
$802$		0			0
$803$	−1.08143	+	1.08143i	−0.0381627	+	0.0381627i
$804$		0			0
$805$	20.5708	+	21.0088i	0.725025	+	0.740464i
$806$		0			0
$807$	−2.47869	−	2.47869i	−0.0872539	−	0.0872539i
$808$		0			0
$809$	−10.6719	+	10.6719i	−0.375204	+	0.375204i	−0.869369	−	0.494164i	$-0.835474\pi$
$809$	−10.6719	+	10.6719i	−0.375204	+	0.375204i	0.494164	+	0.869369i	$0.335474\pi$
$810$		0			0
$811$		−	32.8193i		−	1.15244i	−0.817294	−	0.576221i	$-0.804527\pi$
$811$		−	32.8193i		−	1.15244i	0.817294	−	0.576221i	$-0.195473\pi$
$812$		0			0
$813$	−2.61166	+	2.61166i	−0.0915951	+	0.0915951i
$814$		0			0
$815$	−22.2307	−	22.7041i	−0.778706	−	0.795289i
$816$		0			0
$817$	−1.18965	+	1.18965i	−0.0416208	+	0.0416208i
$818$		0			0
$819$			14.2715i			0.498685i
$820$		0			0
$821$			35.0977i			1.22492i	0.790503	+	0.612458i	$0.209819\pi$
$821$			35.0977i			1.22492i	−0.790503	+	0.612458i	$0.790181\pi$
$822$		0			0
$823$		−	3.88675i		−	0.135484i	−0.997703	−	0.0677419i	$-0.978421\pi$
$823$		−	3.88675i		−	0.135484i	0.997703	−	0.0677419i	$-0.0215794\pi$
$824$		0			0
$825$	−2.94909	+	2.82736i	−0.102674	+	0.0984361i
$826$		0			0
$827$			4.16368i			0.144785i	0.997376	+	0.0723927i	$0.0230635\pi$
$827$			4.16368i			0.144785i	−0.997376	+	0.0723927i	$0.976937\pi$
$828$		0			0
$829$	13.4182	+	13.4182i	0.466032	+	0.466032i	0.900626	−	0.434594i	$-0.143108\pi$
$829$	13.4182	+	13.4182i	0.466032	+	0.466032i	−0.434594	+	0.900626i	$0.643108\pi$
$830$		0			0
$831$	−4.89360	+	4.89360i	−0.169757	+	0.169757i
$832$		0			0
$833$		−	21.1414i		−	0.732505i
$834$		0			0
$835$	11.8737	+	0.125091i	0.410905	+	0.00432895i
$836$		0			0
$837$	−4.32769	−	4.32769i	−0.149587	−	0.149587i
$838$		0			0
$839$	40.0757	−	40.0757i	1.38357	−	1.38357i	0.545378	−	0.838190i	$-0.316386\pi$
$839$	40.0757	−	40.0757i	1.38357	−	1.38357i	0.838190	−	0.545378i	$-0.183614\pi$
$840$		0			0
$841$	−2.94034	−	28.8506i	−0.101391	−	0.994847i
$842$		0			0
$843$		−	6.91120i		−	0.238035i
$844$		0			0
$845$	9.80427	−	9.59985i	0.337277	−	0.330245i
$846$		0			0
$847$	7.74042	−	7.74042i	0.265964	−	0.265964i
$848$		0			0
$849$	−7.35208	+	7.35208i	−0.252323	+	0.252323i
$850$		0			0
$851$	−4.53555	−	4.53555i	−0.155477	−	0.155477i
$852$		0			0
$853$	30.8663			1.05684			0.528421	−	0.848983i	$-0.322784\pi$
$853$	30.8663			1.05684			0.528421	+	0.848983i	$0.322784\pi$
$854$		0			0
$855$	−0.300703	+	28.5428i	−0.0102838	+	0.976144i
$856$		0			0
$857$	9.45947	+	9.45947i	0.323129	+	0.323129i	0.849966	−	0.526837i	$-0.176622\pi$
$857$	9.45947	+	9.45947i	0.323129	+	0.323129i	−0.526837	+	0.849966i	$0.676622\pi$
$858$		0			0
$859$	−14.1102	+	14.1102i	−0.481432	+	0.481432i	−0.905589	−	0.424157i	$-0.860571\pi$
$859$	−14.1102	+	14.1102i	−0.481432	+	0.481432i	0.424157	+	0.905589i	$0.360571\pi$
$860$		0			0
$861$	5.40709			0.184273
$862$		0			0
$863$	38.7326	+	38.7326i	1.31847	+	1.31847i	0.914985	+	0.403487i	$0.132202\pi$
$863$	38.7326	+	38.7326i	1.31847	+	1.31847i	0.403487	+	0.914985i	$0.367798\pi$
$864$		0			0
$865$	0.373110	−	35.4157i	0.0126861	−	1.20417i
$866$		0			0
$867$			7.71667i			0.262072i
$868$		0			0
$869$	−17.6353			−0.598238
$870$		0			0
$871$	−20.0255			−0.678539
$872$		0			0
$873$		−	12.6728i		−	0.428911i
$874$		0			0
$875$	21.1935	+	0.670029i	0.716471	+	0.0226511i
$876$		0			0
$877$	−1.77620	−	1.77620i	−0.0599781	−	0.0599781i	0.676481	−	0.736460i	$-0.263504\pi$
$877$	−1.77620	−	1.77620i	−0.0599781	−	0.0599781i	−0.736460	+	0.676481i	$0.763504\pi$
$878$		0			0
$879$	1.75380			0.0591543
$880$		0			0
$881$	−11.1999	+	11.1999i	−0.377335	+	0.377335i	−0.870140	−	0.492805i	$-0.835972\pi$
$881$	−11.1999	+	11.1999i	−0.377335	+	0.377335i	0.492805	+	0.870140i	$0.335972\pi$
$882$		0			0
$883$	6.18242	+	6.18242i	0.208055	+	0.208055i	0.803440	−	0.595385i	$-0.203001\pi$
$883$	6.18242	+	6.18242i	0.208055	+	0.208055i	−0.595385	+	0.803440i	$0.703001\pi$
$884$		0			0
$885$	−3.90708	−	3.99028i	−0.131335	−	0.134132i
$886$		0			0
$887$	45.1793			1.51697			0.758487	−	0.651688i	$-0.225939\pi$
$887$	45.1793			1.51697			0.758487	+	0.651688i	$0.225939\pi$
$888$		0			0
$889$	7.10861	+	7.10861i	0.238415	+	0.238415i
$890$		0			0
$891$	12.7194	−	12.7194i	0.426117	−	0.426117i
$892$		0			0
$893$	32.3222	−	32.3222i	1.08162	−	1.08162i
$894$		0			0
$895$	13.7196	+	14.0117i	0.458595	+	0.468361i
$896$		0			0
$897$			6.49101i			0.216728i
$898$		0			0
$899$	0.797247	+	15.6857i	0.0265897	+	0.523147i
$900$		0			0
$901$	−9.67368	+	9.67368i	−0.322277	+	0.322277i
$902$		0			0
$903$	0.181417	+	0.181417i	0.00603717	+	0.00603717i
$904$		0			0
$905$	35.3822	+	36.1356i	1.17614	+	1.20119i
$906$		0			0
$907$		−	19.6727i		−	0.653220i	−0.945159	−	0.326610i	$-0.894094\pi$
$907$		−	19.6727i		−	0.653220i	0.945159	−	0.326610i	$-0.105906\pi$
$908$		0			0
$909$	0.513539	−	0.513539i	0.0170330	−	0.0170330i
$910$		0			0
$911$	33.9555	+	33.9555i	1.12500	+	1.12500i	0.990979	+	0.134016i	$0.0427873\pi$
$911$	33.9555	+	33.9555i	1.12500	+	1.12500i	0.134016	+	0.990979i	$0.457213\pi$
$912$		0			0
$913$			25.8195i			0.854499i
$914$		0			0
$915$	0.0745689	−	7.07811i	0.00246517	−	0.233995i
$916$		0			0
$917$			37.0733i			1.22427i
$918$		0			0
$919$			27.7955i			0.916888i	0.888723	+	0.458444i	$0.151593\pi$
$919$			27.7955i			0.916888i	−0.888723	+	0.458444i	$0.848407\pi$
$920$		0			0
$921$			10.2151i			0.336598i
$922$		0			0
$923$	−22.1506	+	22.1506i	−0.729095	+	0.729095i
$924$		0			0
$925$	−4.62465	−	0.0974536i	−0.152058	−	0.00320425i
$926$		0			0
$927$	19.5204	−	19.5204i	0.641134	−	0.641134i
$928$		0			0
$929$		−	24.2873i		−	0.796840i	−0.917203	−	0.398420i	$-0.869559\pi$
$929$		−	24.2873i		−	0.796840i	0.917203	−	0.398420i	$-0.130441\pi$
$930$		0			0
$931$	10.6946	−	10.6946i	0.350502	−	0.350502i
$932$		0			0
$933$	4.72655	+	4.72655i	0.154740	+	0.154740i
$934$		0			0
$935$	31.7610	+	0.334607i	1.03870	+	0.0109428i
$936$		0			0
$937$	20.3454	−	20.3454i	0.664656	−	0.664656i	−0.291818	−	0.956474i	$-0.594260\pi$
$937$	20.3454	−	20.3454i	0.664656	−	0.664656i	0.956474	+	0.291818i	$0.0942601\pi$
$938$		0			0
$939$	7.10585	+	7.10585i	0.231891	+	0.231891i
$940$		0			0
$941$		−	9.97351i		−	0.325127i	−0.986698	−	0.162564i	$-0.948024\pi$
$941$		−	9.97351i		−	0.325127i	0.986698	−	0.162564i	$-0.0519763\pi$
$942$		0			0
$943$	−55.3147			−1.80130
$944$		0			0
$945$	8.89881	+	0.0937503i	0.289478	+	0.00304970i
$946$		0			0
$947$	−17.2530			−0.560648			−0.280324	−	0.959905i	$-0.590442\pi$
$947$	−17.2530			−0.560648			−0.280324	+	0.959905i	$0.590442\pi$
$948$		0			0
$949$	1.23907	+	1.23907i	0.0402220	+	0.0402220i
$950$		0			0
$951$	7.56803			0.245410
$952$		0			0
$953$	29.7590	−	29.7590i	0.963990	−	0.963990i	−0.0353838	−	0.999374i	$-0.511265\pi$
$953$	29.7590	−	29.7590i	0.963990	−	0.963990i	0.999374	+	0.0353838i	$0.0112654\pi$
$954$		0			0
$955$	−30.6650	−	0.323061i	−0.992298	−	0.0104540i
$956$		0			0
$957$	4.39452	−	0.223357i	0.142055	−	0.00722012i
$958$		0			0
$959$	28.6689	+	28.6689i	0.925766	+	0.925766i
$960$		0			0
$961$			22.4939i			0.725611i
$962$		0			0
$963$	−11.6994	−	11.6994i	−0.377008	−	0.377008i
$964$		0			0
$965$	−9.27667	+	9.08324i	−0.298627	+	0.292400i
$966$		0			0
$967$			0.152020i			0.00488865i	0.999997	+	0.00244432i	$0.000778053\pi$
$967$			0.152020i			0.00488865i	−0.999997	+	0.00244432i	$0.999222\pi$
$968$		0			0
$969$	−6.97669	+	6.97669i	−0.224123	+	0.224123i
$970$		0			0
$971$	26.6877	−	26.6877i	0.856450	−	0.856450i	−0.134468	−	0.990918i	$-0.542932\pi$
$971$	26.6877	−	26.6877i	0.856450	−	0.856450i	0.990918	+	0.134468i	$0.0429325\pi$
$972$		0			0
$973$	−0.516940	+	0.516940i	−0.0165723	+	0.0165723i
$974$		0			0
$975$	3.23952	+	3.37899i	0.103748	+	0.108214i
$976$		0			0
$977$	−37.6042	−	37.6042i	−1.20306	−	1.20306i	−0.973230	−	0.229834i	$-0.926182\pi$
$977$	−37.6042	−	37.6042i	−1.20306	−	1.20306i	−0.229834	−	0.973230i	$-0.573818\pi$
$978$		0			0
$979$	−20.7946			−0.664599
$980$		0			0
$981$	1.27287			0.0406397
$982$		0			0
$983$	−42.9608			−1.37024			−0.685118	−	0.728432i	$-0.740249\pi$
$983$	−42.9608			−1.37024			−0.685118	+	0.728432i	$0.740249\pi$
$984$		0			0
$985$	0.205071	−	19.4654i	0.00653412	−	0.620221i
$986$		0			0
$987$	−4.92898	−	4.92898i	−0.156891	−	0.156891i
$988$		0			0
$989$	−1.85590	−	1.85590i	−0.0590142	−	0.0590142i
$990$		0			0
$991$		−	28.3989i		−	0.902121i	−0.892493	−	0.451061i	$-0.851046\pi$
$991$		−	28.3989i		−	0.902121i	0.892493	−	0.451061i	$-0.148954\pi$
$992$		0			0
$993$	−5.36939	+	5.36939i	−0.170393	+	0.170393i
$994$		0			0
$995$	33.8279	−	33.1226i	1.07242	−	1.05006i
$996$		0			0
$997$	22.8843			0.724752			0.362376	−	0.932032i	$-0.381966\pi$
$997$	22.8843			0.724752			0.362376	+	0.932032i	$0.381966\pi$
$998$		0			0
$999$	−1.94138			−0.0614227

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.17.9	✓	30
5.2	odd	4		2900.2.s.d.1293.9		30
5.3	odd	4		580.2.s.a.133.7	yes	30
5.4	even	2		2900.2.j.d.1757.7		30
29.12	odd	4		580.2.s.a.157.7	yes	30
145.12	even	4		2900.2.j.d.2593.9		30
145.99	odd	4		2900.2.s.d.157.9		30
145.128	even	4	inner	580.2.j.a.273.7	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.9	✓	30	1.1	even	1	trivial
580.2.j.a.273.7	yes	30	145.128	even	4	inner
580.2.s.a.133.7	yes	30	5.3	odd	4
580.2.s.a.157.7	yes	30	29.12	odd	4
2900.2.j.d.1757.7		30	5.4	even	2
2900.2.j.d.2593.9		30	145.12	even	4
2900.2.s.d.157.9		30	145.99	odd	4
2900.2.s.d.1293.9		30	5.2	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.357354i q^{3} +(1.56439 + 1.59771i) q^{5} +(-1.34106 - 1.34106i) q^{7} +2.87230 q^{9} +(1.61681 - 1.61681i) q^{11} +(-1.85250 - 1.85250i) q^{13} +(-0.570947 + 0.559042i) q^{15} +6.21240 q^{17} +(3.14262 + 3.14262i) q^{19} +(0.479234 - 0.479234i) q^{21} +(-4.90258 + 4.90258i) q^{23} +(-0.105340 + 4.99889i) q^{25} +2.09849i q^{27} +(3.60969 - 3.99627i) q^{29} +(-2.06229 + 2.06229i) q^{31} +(0.577773 + 0.577773i) q^{33} +(0.0446752 - 4.24058i) q^{35} +0.925135i q^{37} +(0.661999 - 0.661999i) q^{39} +(5.64139 + 5.64139i) q^{41} +0.378555i q^{43} +(4.49341 + 4.58909i) q^{45} -10.2851i q^{47} -3.40309i q^{49} +2.22002i q^{51} +(-1.55716 + 1.55716i) q^{53} +(5.11252 + 0.0538612i) q^{55} +(-1.12303 + 1.12303i) q^{57} +6.98888i q^{59} +(-6.26387 + 6.26387i) q^{61} +(-3.85194 - 3.85194i) q^{63} +(0.0617129 - 5.85781i) q^{65} +(5.40499 - 5.40499i) q^{67} +(-1.75196 - 1.75196i) q^{69} -11.9571i q^{71} -0.668863 q^{73} +(-1.78637 - 0.0376436i) q^{75} -4.33649 q^{77} +(-5.45374 - 5.45374i) q^{79} +7.86699 q^{81} +(-7.98469 + 7.98469i) q^{83} +(9.71865 + 9.92560i) q^{85} +(1.42808 + 1.28993i) q^{87} +(-6.43075 - 6.43075i) q^{89} +4.96865i q^{91} +(-0.736966 - 0.736966i) q^{93} +(-0.104691 + 9.93728i) q^{95} -4.41209i q^{97} +(4.64396 - 4.64396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more