LMFDB - Embedded newform 256.3.h.b.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,3,Mod(31,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("256.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	256.h (of order $8$, degree $4$, 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:	$6.97549476762$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	256.31
Dual form			256.3.h.b.223.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.70255 - 1.53365i) q^{3} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +O(q^{10})$	\(q+(3.70255 - 1.53365i) q^{3} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +(-6.19818 - 2.56737i) q^{11} +(8.05345 - 3.33585i) q^{13} -31.2354 q^{15} -24.5802i q^{17} +(-4.96459 - 11.9856i) q^{19} +(9.24278 - 22.3140i) q^{21} +(-9.72199 - 9.72199i) q^{23} +(25.2768 + 25.2768i) q^{25} +(-2.97384 + 7.17949i) q^{27} +(5.86371 + 14.1563i) q^{29} +17.5320i q^{31} -26.8865 q^{33} +(-43.3965 + 17.9754i) q^{35} +(36.0346 + 14.9260i) q^{37} +(24.7023 - 24.7023i) q^{39} +(10.9784 - 10.9784i) q^{41} +(22.4024 + 9.27937i) q^{43} +(-50.8439 + 21.0603i) q^{45} +27.0104 q^{47} +12.6792i q^{49} +(-37.6973 - 91.0093i) q^{51} +(34.0172 - 82.1247i) q^{53} +(36.9740 + 36.9740i) q^{55} +(-36.7633 - 36.7633i) q^{57} +(-27.8391 + 67.2095i) q^{59} +(6.37082 + 15.3805i) q^{61} -42.5539i q^{63} -67.9404 q^{65} +(99.2165 - 41.0968i) q^{67} +(-50.9062 - 21.0860i) q^{69} +(-2.55754 + 2.55754i) q^{71} +(30.7498 - 30.7498i) q^{73} +(132.354 + 54.8230i) q^{75} +(-37.3544 + 15.4727i) q^{77} -90.6600 q^{79} +94.6916i q^{81} +(39.3191 + 94.9247i) q^{83} +(-73.3140 + 176.996i) q^{85} +(43.4214 + 43.4214i) q^{87} +(109.290 + 109.290i) q^{89} +(20.1040 - 48.5355i) q^{91} +(26.8879 + 64.9132i) q^{93} +101.113i q^{95} +63.7161 q^{97} +(-43.7650 + 18.1280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} - 8 q^{15} + 4 q^{19} + 4 q^{21} - 68 q^{23} - 4 q^{25} + 100 q^{27} + 4 q^{29} - 8 q^{33} - 92 q^{35} + 4 q^{37} + 188 q^{39} - 4 q^{41} - 92 q^{43} + 40 q^{45} - 8 q^{47} - 224 q^{51} + 164 q^{53} + 252 q^{55} - 4 q^{57} - 124 q^{59} + 68 q^{61} - 8 q^{65} + 164 q^{67} - 188 q^{69} - 260 q^{71} - 4 q^{73} + 488 q^{75} - 220 q^{77} - 520 q^{79} + 484 q^{83} - 96 q^{85} - 452 q^{87} - 4 q^{89} + 196 q^{91} - 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) $ 28 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 - 8 * q^15 + 4 * q^19 + 4 * q^21 - 68 * q^23 - 4 * q^25 + 100 * q^27 + 4 * q^29 - 8 * q^33 - 92 * q^35 + 4 * q^37 + 188 * q^39 - 4 * q^41 - 92 * q^43 + 40 * q^45 - 8 * q^47 - 224 * q^51 + 164 * q^53 + 252 * q^55 - 4 * q^57 - 124 * q^59 + 68 * q^61 - 8 * q^65 + 164 * q^67 - 188 * q^69 - 260 * q^71 - 4 * q^73 + 488 * q^75 - 220 * q^77 - 520 * q^79 + 484 * q^83 - 96 * q^85 - 452 * q^87 - 4 * q^89 + 196 * q^91 - 32 * q^93 - 8 * q^97 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

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
$3$	3.70255	−	1.53365i	1.23418	−	0.511215i	0.332291	−	0.943177i	$-0.392178\pi$
$3$	3.70255	−	1.53365i	1.23418	−	0.511215i	0.901892	+	0.431962i	$0.142178\pi$
$4$		0			0
$5$	−7.20074	−	2.98264i	−1.44015	−	0.596529i	−0.480314	−	0.877097i	$-0.659477\pi$
$5$	−7.20074	−	2.98264i	−1.44015	−	0.596529i	−0.959834	+	0.280568i	$0.909477\pi$
$6$		0			0
$7$	4.26150	−	4.26150i	0.608786	−	0.608786i	−0.333843	−	0.942629i	$-0.608346\pi$
$7$	4.26150	−	4.26150i	0.608786	−	0.608786i	0.942629	+	0.333843i	$0.108346\pi$
$8$		0			0
$9$	4.99283	−	4.99283i	0.554759	−	0.554759i
$10$		0			0
$11$	−6.19818	−	2.56737i	−0.563471	−	0.233397i	0.0827202	−	0.996573i	$-0.473639\pi$
$11$	−6.19818	−	2.56737i	−0.563471	−	0.233397i	−0.646191	+	0.763175i	$0.723639\pi$
$12$		0			0
$13$	8.05345	−	3.33585i	0.619496	−	0.256604i	−0.0507868	−	0.998710i	$-0.516173\pi$
$13$	8.05345	−	3.33585i	0.619496	−	0.256604i	0.670283	+	0.742106i	$0.266173\pi$
$14$		0			0
$15$	−31.2354			−2.08236
$16$		0			0
$17$		−	24.5802i		−	1.44589i	−0.690904	−	0.722947i	$-0.742787\pi$
$17$		−	24.5802i		−	1.44589i	0.690904	−	0.722947i	$-0.257213\pi$
$18$		0			0
$19$	−4.96459	−	11.9856i	−0.261294	−	0.630820i	0.737725	−	0.675101i	$-0.235900\pi$
$19$	−4.96459	−	11.9856i	−0.261294	−	0.630820i	−0.999019	+	0.0442815i	$0.985900\pi$
$20$		0			0
$21$	9.24278	−	22.3140i	0.440132	−	1.06257i
$22$		0			0
$23$	−9.72199	−	9.72199i	−0.422695	−	0.422695i	0.463435	−	0.886131i	$-0.346617\pi$
$23$	−9.72199	−	9.72199i	−0.422695	−	0.422695i	−0.886131	+	0.463435i	$0.846617\pi$
$24$		0			0
$25$	25.2768	+	25.2768i	1.01107	+	1.01107i
$26$		0			0
$27$	−2.97384	+	7.17949i	−0.110142	+	0.265907i
$28$		0			0
$29$	5.86371	+	14.1563i	0.202197	+	0.488147i	0.992155	−	0.125014i	$-0.0398977\pi$
$29$	5.86371	+	14.1563i	0.202197	+	0.488147i	−0.789958	+	0.613161i	$0.789898\pi$
$30$		0			0
$31$			17.5320i			0.565550i	0.959186	+	0.282775i	$0.0912549\pi$
$31$			17.5320i			0.565550i	−0.959186	+	0.282775i	$0.908745\pi$
$32$		0			0
$33$	−26.8865			−0.814743
$34$		0			0
$35$	−43.3965	+	17.9754i	−1.23990	+	0.513583i
$36$		0			0
$37$	36.0346	+	14.9260i	0.973909	+	0.403406i	0.812166	−	0.583427i	$-0.198288\pi$
$37$	36.0346	+	14.9260i	0.973909	+	0.403406i	0.161743	+	0.986833i	$0.448288\pi$
$38$		0			0
$39$	24.7023	−	24.7023i	0.633391	−	0.633391i
$40$		0			0
$41$	10.9784	−	10.9784i	0.267765	−	0.267765i	−0.560434	−	0.828199i	$-0.689366\pi$
$41$	10.9784	−	10.9784i	0.267765	−	0.267765i	0.828199	+	0.560434i	$0.189366\pi$
$42$		0			0
$43$	22.4024	+	9.27937i	0.520985	+	0.215799i	0.627650	−	0.778496i	$-0.284017\pi$
$43$	22.4024	+	9.27937i	0.520985	+	0.215799i	−0.106664	+	0.994295i	$0.534017\pi$
$44$		0			0
$45$	−50.8439	+	21.0603i	−1.12987	+	0.468006i
$46$		0			0
$47$	27.0104			0.574690			0.287345	−	0.957827i	$-0.407227\pi$
$47$	27.0104			0.574690			0.287345	+	0.957827i	$0.407227\pi$
$48$		0			0
$49$			12.6792i			0.258760i
$50$		0			0
$51$	−37.6973	−	91.0093i	−0.739163	−	1.78450i
$52$		0			0
$53$	34.0172	−	82.1247i	0.641833	−	1.54952i	−0.182371	−	0.983230i	$-0.558377\pi$
$53$	34.0172	−	82.1247i	0.641833	−	1.54952i	0.824204	−	0.566293i	$-0.191623\pi$
$54$		0			0
$55$	36.9740	+	36.9740i	0.672254	+	0.672254i
$56$		0			0
$57$	−36.7633	−	36.7633i	−0.644970	−	0.644970i
$58$		0			0
$59$	−27.8391	+	67.2095i	−0.471849	+	1.13914i	0.491497	+	0.870879i	$0.336450\pi$
$59$	−27.8391	+	67.2095i	−0.471849	+	1.13914i	−0.963345	+	0.268264i	$0.913550\pi$
$60$		0			0
$61$	6.37082	+	15.3805i	0.104440	+	0.252140i	0.967457	−	0.253034i	$-0.0814285\pi$
$61$	6.37082	+	15.3805i	0.104440	+	0.252140i	−0.863018	+	0.505174i	$0.831428\pi$
$62$		0			0
$63$		−	42.5539i		−	0.675459i
$64$		0			0
$65$	−67.9404			−1.04524
$66$		0			0
$67$	99.2165	−	41.0968i	1.48084	−	0.613386i	0.511542	−	0.859258i	$-0.329075\pi$
$67$	99.2165	−	41.0968i	1.48084	−	0.613386i	0.969302	+	0.245873i	$0.0790746\pi$
$68$		0			0
$69$	−50.9062	−	21.0860i	−0.737771	−	0.305595i
$70$		0			0
$71$	−2.55754	+	2.55754i	−0.0360217	+	0.0360217i	−0.724888	−	0.688867i	$-0.758109\pi$
$71$	−2.55754	+	2.55754i	−0.0360217	+	0.0360217i	0.688867	+	0.724888i	$0.258109\pi$
$72$		0			0
$73$	30.7498	−	30.7498i	0.421230	−	0.421230i	−0.464397	−	0.885627i	$-0.653729\pi$
$73$	30.7498	−	30.7498i	0.421230	−	0.421230i	0.885627	+	0.464397i	$0.153729\pi$
$74$		0			0
$75$	132.354	+	54.8230i	1.76473	+	0.730973i
$76$		0			0
$77$	−37.3544	+	15.4727i	−0.485122	+	0.200944i
$78$		0			0
$79$	−90.6600			−1.14759			−0.573797	−	0.818997i	$-0.694530\pi$
$79$	−90.6600			−1.14759			−0.573797	+	0.818997i	$0.694530\pi$
$80$		0			0
$81$			94.6916i			1.16903i
$82$		0			0
$83$	39.3191	+	94.9247i	0.473724	+	1.14367i	0.962505	+	0.271264i	$0.0874417\pi$
$83$	39.3191	+	94.9247i	0.473724	+	1.14367i	−0.488781	+	0.872407i	$0.662558\pi$
$84$		0			0
$85$	−73.3140	+	176.996i	−0.862517	+	2.08230i
$86$		0			0
$87$	43.4214	+	43.4214i	0.499096	+	0.499096i
$88$		0			0
$89$	109.290	+	109.290i	1.22798	+	1.22798i	0.964728	+	0.263248i	$0.0847937\pi$
$89$	109.290	+	109.290i	1.22798	+	1.22798i	0.263248	+	0.964728i	$0.415206\pi$
$90$		0			0
$91$	20.1040	−	48.5355i	0.220924	−	0.533357i
$92$		0			0
$93$	26.8879	+	64.9132i	0.289118	+	0.697992i
$94$		0			0
$95$			101.113i			1.06434i
$96$		0			0
$97$	63.7161			0.656867			0.328433	−	0.944527i	$-0.393479\pi$
$97$	63.7161			0.656867			0.328433	+	0.944527i	$0.393479\pi$
$98$		0			0
$99$	−43.7650	+	18.1280i	−0.442070	+	0.183112i
$100$		0			0
$101$	14.4312	+	5.97761i	0.142883	+	0.0591842i	0.452979	−	0.891521i	$-0.350361\pi$
$101$	14.4312	+	5.97761i	0.142883	+	0.0591842i	−0.310096	+	0.950705i	$0.600361\pi$
$102$		0			0
$103$	−9.69681	+	9.69681i	−0.0941438	+	0.0941438i	−0.752610	−	0.658466i	$-0.771205\pi$
$103$	−9.69681	+	9.69681i	−0.0941438	+	0.0941438i	0.658466	+	0.752610i	$0.271205\pi$
$104$		0			0
$105$	−133.110	+	133.110i	−1.26771	+	1.26771i
$106$		0			0
$107$	−138.127	−	57.2140i	−1.29091	−	0.534710i	−0.371650	−	0.928373i	$-0.621208\pi$
$107$	−138.127	−	57.2140i	−1.29091	−	0.534710i	−0.919255	+	0.393662i	$0.871208\pi$
$108$		0			0
$109$	32.0941	−	13.2938i	0.294442	−	0.121962i	−0.230573	−	0.973055i	$-0.574060\pi$
$109$	32.0941	−	13.2938i	0.294442	−	0.121962i	0.525014	+	0.851093i	$0.324060\pi$
$110$		0			0
$111$	156.311			1.40821
$112$		0			0
$113$		−	125.923i		−	1.11436i	−0.830392	−	0.557180i	$-0.811883\pi$
$113$		−	125.923i		−	1.11436i	0.830392	−	0.557180i	$-0.188117\pi$
$114$		0			0
$115$	41.0083	+	99.0028i	0.356594	+	0.860894i
$116$		0			0
$117$	23.5542	−	56.8648i	0.201318	−	0.486024i
$118$		0			0
$119$	−104.748	−	104.748i	−0.880239	−	0.880239i
$120$		0			0
$121$	−53.7338	−	53.7338i	−0.444081	−	0.444081i
$122$		0			0
$123$	23.8110	−	57.4849i	0.193586	−	0.467357i
$124$		0			0
$125$	−32.0540	−	77.3852i	−0.256432	−	0.619081i
$126$		0			0
$127$			79.4160i			0.625322i	0.949865	+	0.312661i	$0.101220\pi$
$127$			79.4160i			0.625322i	−0.949865	+	0.312661i	$0.898780\pi$
$128$		0			0
$129$	97.1771			0.753311
$130$		0			0
$131$	−53.2656	+	22.0633i	−0.406608	+	0.168422i	−0.576607	−	0.817022i	$-0.695624\pi$
$131$	−53.2656	+	22.0633i	−0.406608	+	0.168422i	0.169999	+	0.985444i	$0.445624\pi$
$132$		0			0
$133$	−72.2331	−	29.9199i	−0.543106	−	0.224962i
$134$		0			0
$135$	42.8277	−	42.8277i	0.317242	−	0.317242i
$136$		0			0
$137$	50.7359	−	50.7359i	0.370335	−	0.370335i	−0.497264	−	0.867599i	$-0.665662\pi$
$137$	50.7359	−	50.7359i	0.370335	−	0.370335i	0.867599	+	0.497264i	$0.165662\pi$
$138$		0			0
$139$	−133.213	−	55.1786i	−0.958366	−	0.396968i	−0.151997	−	0.988381i	$-0.548570\pi$
$139$	−133.213	−	55.1786i	−0.958366	−	0.396968i	−0.806369	+	0.591413i	$0.798570\pi$
$140$		0			0
$141$	100.007	−	41.4244i	0.709272	−	0.293790i
$142$		0			0
$143$	−58.4811			−0.408959
$144$		0			0
$145$		−	119.425i		−	0.823620i
$146$		0			0
$147$	19.4455	+	46.9455i	0.132282	+	0.319357i
$148$		0			0
$149$	−5.00779	+	12.0899i	−0.0336093	+	0.0811401i	−0.939793	−	0.341744i	$-0.888982\pi$
$149$	−5.00779	+	12.0899i	−0.0336093	+	0.0811401i	0.906184	+	0.422884i	$0.138982\pi$
$150$		0			0
$151$	−17.6867	−	17.6867i	−0.117130	−	0.117130i	0.646112	−	0.763243i	$-0.276394\pi$
$151$	−17.6867	−	17.6867i	−0.117130	−	0.117130i	−0.763243	+	0.646112i	$0.776394\pi$
$152$		0			0
$153$	−122.725	−	122.725i	−0.802123	−	0.802123i
$154$		0			0
$155$	52.2918	−	126.244i	0.337367	−	0.814475i
$156$		0			0
$157$	−73.8536	−	178.298i	−0.470405	−	1.13566i	−0.963985	−	0.265958i	$-0.914312\pi$
$157$	−73.8536	−	178.298i	−0.470405	−	1.13566i	0.493580	−	0.869701i	$-0.335688\pi$
$158$		0			0
$159$		−	356.241i		−	2.24051i
$160$		0			0
$161$	−82.8605			−0.514662
$162$		0			0
$163$	132.246	−	54.7779i	0.811322	−	0.336061i	0.0618408	−	0.998086i	$-0.480303\pi$
$163$	132.246	−	54.7779i	0.811322	−	0.336061i	0.749481	+	0.662025i	$0.230303\pi$
$164$		0			0
$165$	193.603	+	80.1929i	1.17335	+	0.486018i
$166$		0			0
$167$	−109.750	+	109.750i	−0.657187	+	0.657187i	−0.954714	−	0.297526i	$-0.903838\pi$
$167$	−109.750	+	109.750i	−0.657187	+	0.657187i	0.297526	+	0.954714i	$0.403838\pi$
$168$		0			0
$169$	−65.7709	+	65.7709i	−0.389177	+	0.389177i
$170$		0			0
$171$	−84.6294	−	35.0546i	−0.494909	−	0.204998i
$172$		0			0
$173$	287.188	−	118.957i	1.66005	−	0.687613i	0.661964	−	0.749535i	$-0.269723\pi$
$173$	287.188	−	118.957i	1.66005	−	0.687613i	0.998081	+	0.0619221i	$0.0197230\pi$
$174$		0			0
$175$	215.434			1.23105
$176$		0			0
$177$			291.542i			1.64713i
$178$		0			0
$179$	−48.9443	−	118.162i	−0.273432	−	0.660122i	0.726194	−	0.687490i	$-0.241288\pi$
$179$	−48.9443	−	118.162i	−0.273432	−	0.660122i	−0.999625	+	0.0273677i	$0.991288\pi$
$180$		0			0
$181$	−38.9220	+	93.9660i	−0.215039	+	0.519149i	−0.994184	−	0.107694i	$-0.965653\pi$
$181$	−38.9220	+	93.9660i	−0.215039	+	0.519149i	0.779145	+	0.626843i	$0.215653\pi$
$182$		0			0
$183$	47.1765	+	47.1765i	0.257795	+	0.257795i
$184$		0			0
$185$	−214.957	−	214.957i	−1.16193	−	1.16193i
$186$		0			0
$187$	−63.1065	+	152.353i	−0.337468	+	0.814719i
$188$		0			0
$189$	17.9224	+	43.2684i	0.0948273	+	0.228933i
$190$		0			0
$191$			66.5635i			0.348500i	0.984701	+	0.174250i	$0.0557500\pi$
$191$			66.5635i			0.348500i	−0.984701	+	0.174250i	$0.944250\pi$
$192$		0			0
$193$	275.880			1.42943			0.714714	−	0.699417i	$-0.246557\pi$
$193$	275.880			1.42943			0.714714	+	0.699417i	$0.246557\pi$
$194$		0			0
$195$	−251.553	+	104.197i	−1.29001	+	0.534341i
$196$		0			0
$197$	−167.300	−	69.2980i	−0.849240	−	0.351767i	−0.0847497	−	0.996402i	$-0.527009\pi$
$197$	−167.300	−	69.2980i	−0.849240	−	0.351767i	−0.764490	+	0.644636i	$0.777009\pi$
$198$		0			0
$199$	−233.526	+	233.526i	−1.17350	+	1.17350i	−0.192125	+	0.981370i	$0.561538\pi$
$199$	−233.526	+	233.526i	−1.17350	+	1.17350i	−0.981370	+	0.192125i	$0.938462\pi$
$200$		0			0
$201$	304.326	−	304.326i	1.51406	−	1.51406i
$202$		0			0
$203$	85.3151	+	35.3387i	0.420271	+	0.174082i
$204$		0			0
$205$	−111.797	+	46.3078i	−0.545351	+	0.225892i
$206$		0			0
$207$	−97.0806			−0.468988
$208$		0			0
$209$			87.0348i			0.416434i
$210$		0			0
$211$	−32.7097	−	78.9682i	−0.155022	−	0.374257i	0.827219	−	0.561880i	$-0.189922\pi$
$211$	−32.7097	−	78.9682i	−0.155022	−	0.374257i	−0.982241	+	0.187623i	$0.939922\pi$
$212$		0			0
$213$	−5.54706	+	13.3918i	−0.0260425	+	0.0628722i
$214$		0			0
$215$	−133.637	−	133.637i	−0.621566	−	0.621566i
$216$		0			0
$217$	74.7128	+	74.7128i	0.344298	+	0.344298i
$218$		0			0
$219$	66.6933	−	161.012i	0.304536	−	0.735214i
$220$		0			0
$221$	−81.9957	−	197.955i	−0.371021	−	0.895725i
$222$		0			0
$223$		−	373.446i		−	1.67465i	−0.546708	−	0.837323i	$-0.684119\pi$
$223$		−	373.446i		−	1.67465i	0.546708	−	0.837323i	$-0.315881\pi$
$224$		0			0
$225$	252.406			1.12180
$226$		0			0
$227$	−7.71962	+	3.19757i	−0.0340071	+	0.0140862i	−0.399622	−	0.916680i	$-0.630859\pi$
$227$	−7.71962	+	3.19757i	−0.0340071	+	0.0140862i	0.365615	+	0.930766i	$0.380859\pi$
$228$		0			0
$229$	165.203	+	68.4293i	0.721410	+	0.298818i	0.713017	−	0.701147i	$-0.247328\pi$
$229$	165.203	+	68.4293i	0.721410	+	0.298818i	0.00839310	+	0.999965i	$0.497328\pi$
$230$		0			0
$231$	−114.577	+	114.577i	−0.496004	+	0.496004i
$232$		0			0
$233$	14.0197	−	14.0197i	0.0601703	−	0.0601703i	−0.676381	−	0.736552i	$-0.736453\pi$
$233$	14.0197	−	14.0197i	0.0601703	−	0.0601703i	0.736552	+	0.676381i	$0.236453\pi$
$234$		0			0
$235$	−194.495	−	80.5625i	−0.827638	−	0.342819i
$236$		0			0
$237$	−335.673	+	139.040i	−1.41634	+	0.586668i
$238$		0			0
$239$	−230.951			−0.966321			−0.483161	−	0.875532i	$-0.660511\pi$
$239$	−230.951			−0.966321			−0.483161	+	0.875532i	$0.660511\pi$
$240$		0			0
$241$		−	111.407i		−	0.462269i	−0.972922	−	0.231135i	$-0.925756\pi$
$241$		−	111.407i		−	0.462269i	0.972922	−	0.231135i	$-0.0742438\pi$
$242$		0			0
$243$	118.459	+	285.985i	0.487485	+	1.17689i
$244$		0			0
$245$	37.8177	−	91.3000i	0.154358	−	0.372653i
$246$		0			0
$247$	−79.9641	−	79.9641i	−0.323741	−	0.323741i
$248$		0			0
$249$	291.162	+	291.162i	1.16932	+	1.16932i
$250$		0			0
$251$	−93.4234	+	225.544i	−0.372205	+	0.898581i	0.621172	+	0.783675i	$0.286657\pi$
$251$	−93.4234	+	225.544i	−0.372205	+	0.898581i	−0.993376	+	0.114907i	$0.963343\pi$
$252$		0			0
$253$	35.2987	+	85.2186i	0.139521	+	0.336833i
$254$		0			0
$255$			767.772i			3.01087i
$256$		0			0
$257$	−278.684			−1.08437			−0.542187	−	0.840258i	$-0.682403\pi$
$257$	−278.684			−1.08437			−0.542187	+	0.840258i	$0.682403\pi$
$258$		0			0
$259$	217.169	−	89.9543i	0.838490	−	0.347314i
$260$		0			0
$261$	99.9564	+	41.4033i	0.382975	+	0.158633i
$262$		0			0
$263$	271.210	−	271.210i	1.03122	−	1.03122i	0.0317197	−	0.999497i	$-0.489902\pi$
$263$	271.210	−	271.210i	1.03122	−	1.03122i	0.999497	−	0.0317197i	$-0.0100984\pi$
$264$		0			0
$265$	−489.898	+	489.898i	−1.84867	+	1.84867i
$266$		0			0
$267$	572.263	+	237.039i	2.14331	+	0.887787i
$268$		0			0
$269$	−54.9518	+	22.7618i	−0.204282	+	0.0846163i	−0.482478	−	0.875908i	$-0.660263\pi$
$269$	−54.9518	+	22.7618i	−0.204282	+	0.0846163i	0.278197	+	0.960524i	$0.410263\pi$
$270$		0			0
$271$	443.976			1.63829			0.819143	−	0.573589i	$-0.194449\pi$
$271$	443.976			1.63829			0.819143	+	0.573589i	$0.194449\pi$
$272$		0			0
$273$		−	210.537i		−	0.771199i
$274$		0			0
$275$	−91.7754	−	221.565i	−0.333729	−	0.805693i
$276$		0			0
$277$	−23.1329	+	55.8478i	−0.0835124	+	0.201617i	−0.960119	−	0.279590i	$-0.909801\pi$
$277$	−23.1329	+	55.8478i	−0.0835124	+	0.201617i	0.876607	+	0.481207i	$0.159801\pi$
$278$		0			0
$279$	87.5345	+	87.5345i	0.313744	+	0.313744i
$280$		0			0
$281$	−159.772	−	159.772i	−0.568582	−	0.568582i	0.363149	−	0.931731i	$-0.381702\pi$
$281$	−159.772	−	159.772i	−0.568582	−	0.568582i	−0.931731	+	0.363149i	$0.881702\pi$
$282$		0			0
$283$	185.468	−	447.761i	0.655366	−	1.58219i	−0.149517	−	0.988759i	$-0.547772\pi$
$283$	185.468	−	447.761i	0.655366	−	1.58219i	0.804883	−	0.593434i	$-0.202228\pi$
$284$		0			0
$285$	155.071	+	374.375i	0.544109	+	1.31359i
$286$		0			0
$287$		−	93.5687i		−	0.326023i
$288$		0			0
$289$	−315.186			−1.09061
$290$		0			0
$291$	235.912	−	97.7178i	0.810693	−	0.335800i
$292$		0			0
$293$	−476.574	−	197.403i	−1.62653	−	0.673732i	−0.631696	−	0.775216i	$-0.717641\pi$
$293$	−476.574	−	197.403i	−1.62653	−	0.673732i	−0.994837	+	0.101485i	$0.967641\pi$
$294$		0			0
$295$	400.924	−	400.924i	1.35906	−	1.35906i
$296$		0			0
$297$	36.8648	−	36.8648i	0.124124	−	0.124124i
$298$		0			0
$299$	−110.727	−	45.8645i	−0.370323	−	0.153393i
$300$		0			0
$301$	135.012	−	55.9237i	0.448544	−	0.185793i
$302$		0			0
$303$	62.5998			0.206600
$304$		0			0
$305$		−	129.753i		−	0.425420i
$306$		0			0
$307$	196.212	+	473.698i	0.639127	+	1.54299i	0.827844	+	0.560959i	$0.189567\pi$
$307$	196.212	+	473.698i	0.639127	+	1.54299i	−0.188716	+	0.982032i	$0.560433\pi$
$308$		0			0
$309$	−21.0314	+	50.7744i	−0.0680629	+	0.164318i
$310$		0			0
$311$	386.346	+	386.346i	1.24227	+	1.24227i	0.959057	+	0.283215i	$0.0914008\pi$
$311$	386.346	+	386.346i	1.24227	+	1.24227i	0.283215	+	0.959057i	$0.408599\pi$
$312$		0			0
$313$	127.090	+	127.090i	0.406038	+	0.406038i	0.880354	−	0.474316i	$-0.157305\pi$
$313$	127.090	+	127.090i	0.406038	+	0.406038i	−0.474316	+	0.880354i	$0.657305\pi$
$314$		0			0
$315$	−126.923	+	306.420i	−0.402931	+	0.972761i
$316$		0			0
$317$	24.4377	+	58.9979i	0.0770906	+	0.186113i	0.957726	−	0.287681i	$-0.0928842\pi$
$317$	24.4377	+	58.9979i	0.0770906	+	0.186113i	−0.880636	+	0.473794i	$0.842884\pi$
$318$		0			0
$319$		−	102.797i		−	0.322249i
$320$		0			0
$321$	−599.167			−1.86657
$322$		0			0
$323$	−294.608	+	122.031i	−0.912099	+	0.377804i
$324$		0			0
$325$	287.885	+	119.246i	0.885801	+	0.366911i
$326$		0			0
$327$	98.4421	−	98.4421i	0.301046	−	0.301046i
$328$		0			0
$329$	115.105	−	115.105i	0.349863	−	0.349863i
$330$		0			0
$331$	−53.7512	−	22.2645i	−0.162390	−	0.0672643i	0.300007	−	0.953937i	$-0.403011\pi$
$331$	−53.7512	−	22.2645i	−0.162390	−	0.0672643i	−0.462398	+	0.886673i	$0.653011\pi$
$332$		0			0
$333$	254.438	−	105.392i	0.764078	−	0.316492i
$334$		0			0
$335$	−837.010			−2.49854
$336$		0			0
$337$			368.803i			1.09437i	0.837012	+	0.547185i	$0.184300\pi$
$337$			368.803i			1.09437i	−0.837012	+	0.547185i	$0.815700\pi$
$338$		0			0
$339$	−193.121	−	466.235i	−0.569678	−	1.37532i
$340$		0			0
$341$	45.0113	−	108.667i	0.131998	−	0.318671i
$342$		0			0
$343$	262.846	+	262.846i	0.766315	+	0.766315i
$344$		0			0
$345$	303.670	+	303.670i	0.880204	+	0.880204i
$346$		0			0
$347$	−166.265	+	401.400i	−0.479151	+	1.15677i	0.480857	+	0.876799i	$0.340325\pi$
$347$	−166.265	+	401.400i	−0.479151	+	1.15677i	−0.960008	+	0.279973i	$0.909675\pi$
$348$		0			0
$349$	24.6685	+	59.5550i	0.0706833	+	0.170645i	0.955273	−	0.295726i	$-0.0955614\pi$
$349$	24.6685	+	59.5550i	0.0706833	+	0.170645i	−0.884590	+	0.466370i	$0.845561\pi$
$350$		0			0
$351$			67.7399i			0.192991i
$352$		0			0
$353$	245.534			0.695563			0.347782	−	0.937576i	$-0.386935\pi$
$353$	245.534			0.695563			0.347782	+	0.937576i	$0.386935\pi$
$354$		0			0
$355$	26.0444	−	10.7880i	0.0733646	−	0.0303886i
$356$		0			0
$357$	−548.483	−	227.189i	−1.53637	−	0.636384i
$358$		0			0
$359$	61.7019	−	61.7019i	0.171872	−	0.171872i	−0.615930	−	0.787801i	$-0.711219\pi$
$359$	61.7019	−	61.7019i	0.171872	−	0.171872i	0.787801	+	0.615930i	$0.211219\pi$
$360$		0			0
$361$	136.259	−	136.259i	0.377448	−	0.377448i
$362$		0			0
$363$	−281.361	−	116.543i	−0.775099	−	0.321056i
$364$		0			0
$365$	−313.137	+	129.706i	−0.857910	+	0.355358i
$366$		0			0
$367$	123.349			0.336102			0.168051	−	0.985778i	$-0.446253\pi$
$367$	123.349			0.336102			0.168051	+	0.985778i	$0.446253\pi$
$368$		0			0
$369$		−	109.626i		−	0.297090i
$370$		0			0
$371$	−205.010	−	494.939i	−0.552588	−	1.33407i
$372$		0			0
$373$	11.5942	−	27.9909i	0.0310836	−	0.0750425i	−0.907575	−	0.419889i	$-0.862069\pi$
$373$	11.5942	−	27.9909i	0.0310836	−	0.0750425i	0.938659	+	0.344846i	$0.112069\pi$
$374$		0			0
$375$	−237.363	−	237.363i	−0.632968	−	0.632968i
$376$		0			0
$377$	94.4462	+	94.4462i	0.250520	+	0.250520i
$378$		0			0
$379$	−205.083	+	495.114i	−0.541115	+	1.30637i	0.382821	+	0.923823i	$0.374953\pi$
$379$	−205.083	+	495.114i	−0.541115	+	1.30637i	−0.923937	+	0.382546i	$0.875047\pi$
$380$		0			0
$381$	121.796	+	294.041i	0.319674	+	0.771762i
$382$		0			0
$383$			605.809i			1.58175i	0.611979	+	0.790874i	$0.290374\pi$
$383$			605.809i			1.58175i	−0.611979	+	0.790874i	$0.709626\pi$
$384$		0			0
$385$	315.129			0.818517
$386$		0			0
$387$	158.182	−	65.5210i	0.408738	−	0.169305i
$388$		0			0
$389$	426.567	+	176.690i	1.09657	+	0.454215i	0.856294	−	0.516489i	$-0.172761\pi$
$389$	426.567	+	176.690i	1.09657	+	0.454215i	0.240279	+	0.970704i	$0.422761\pi$
$390$		0			0
$391$	−238.968	+	238.968i	−0.611172	+	0.611172i
$392$		0			0
$393$	−163.381	+	163.381i	−0.415728	+	0.415728i
$394$		0			0
$395$	652.819	+	270.407i	1.65271	+	0.684573i
$396$		0			0
$397$	−294.458	+	121.969i	−0.741708	+	0.307226i	−0.721353	−	0.692567i	$-0.756480\pi$
$397$	−294.458	+	121.969i	−0.741708	+	0.307226i	−0.0203548	+	0.999793i	$0.506480\pi$
$398$		0			0
$399$	−313.333			−0.785296
$400$		0			0
$401$			48.4544i			0.120834i	0.998173	+	0.0604169i	$0.0192430\pi$
$401$			48.4544i			0.120834i	−0.998173	+	0.0604169i	$0.980757\pi$
$402$		0			0
$403$	58.4842	+	141.193i	0.145122	+	0.350356i
$404$		0			0
$405$	282.431	−	681.850i	0.697362	−	1.68358i
$406$		0			0
$407$	−185.029	−	185.029i	−0.454616	−	0.454616i
$408$		0			0
$409$	−242.037	−	242.037i	−0.591778	−	0.591778i	0.346334	−	0.938111i	$-0.387427\pi$
$409$	−242.037	−	242.037i	−0.591778	−	0.591778i	−0.938111	+	0.346334i	$0.887427\pi$
$410$		0			0
$411$	110.041	−	265.663i	0.267740	−	0.646382i
$412$		0			0
$413$	167.777	+	405.049i	0.406239	+	0.980749i
$414$		0			0
$415$		−	800.803i		−	1.92965i
$416$		0			0
$417$	−577.851			−1.38573
$418$		0			0
$419$	−163.261	+	67.6248i	−0.389644	+	0.161396i	−0.568900	−	0.822407i	$-0.692631\pi$
$419$	−163.261	+	67.6248i	−0.389644	+	0.161396i	0.179256	+	0.983802i	$0.442631\pi$
$420$		0			0
$421$	624.400	+	258.635i	1.48314	+	0.614335i	0.969810	−	0.243860i	$-0.0784137\pi$
$421$	624.400	+	258.635i	1.48314	+	0.614335i	0.513325	+	0.858195i	$0.328414\pi$
$422$		0			0
$423$	134.859	−	134.859i	0.318814	−	0.318814i
$424$		0			0
$425$	621.309	−	621.309i	1.46190	−	1.46190i
$426$		0			0
$427$	92.6933	+	38.3948i	0.217080	+	0.0899176i
$428$		0			0
$429$	−216.529	+	89.6893i	−0.504730	+	0.209066i
$430$		0			0
$431$	606.510			1.40722			0.703608	−	0.710588i	$-0.251571\pi$
$431$	606.510			1.40722			0.703608	+	0.710588i	$0.251571\pi$
$432$		0			0
$433$			3.82972i			0.00884462i	0.999990	+	0.00442231i	$0.00140767\pi$
$433$			3.82972i			0.00884462i	−0.999990	+	0.00442231i	$0.998592\pi$
$434$		0			0
$435$	−183.156	−	442.177i	−0.421047	−	1.01650i
$436$		0			0
$437$	−68.2580	+	164.789i	−0.156197	+	0.377092i
$438$		0			0
$439$	−36.3389	−	36.3389i	−0.0827765	−	0.0827765i	0.664506	−	0.747283i	$-0.268642\pi$
$439$	−36.3389	−	36.3389i	−0.0827765	−	0.0827765i	−0.747283	+	0.664506i	$0.768642\pi$
$440$		0			0
$441$	63.3054	+	63.3054i	0.143550	+	0.143550i
$442$		0			0
$443$	208.435	−	503.207i	0.470508	−	1.13591i	−0.493431	−	0.869785i	$-0.664258\pi$
$443$	208.435	−	503.207i	0.470508	−	1.13591i	0.963939	−	0.266122i	$-0.0857425\pi$
$444$		0			0
$445$	−460.995	−	1112.94i	−1.03594	−	2.50099i
$446$		0			0
$447$			52.4435i			0.117323i
$448$		0			0
$449$	431.670			0.961402			0.480701	−	0.876884i	$-0.340382\pi$
$449$	431.670			0.961402			0.480701	+	0.876884i	$0.340382\pi$
$450$		0			0
$451$	−96.2316	+	39.8604i	−0.213374	+	0.0883823i
$452$		0			0
$453$	−92.6110	−	38.3607i	−0.204439	−	0.0846815i
$454$		0			0
$455$	−289.528	+	289.528i	−0.636325	+	0.636325i
$456$		0			0
$457$	−187.054	+	187.054i	−0.409309	+	0.409309i	−0.881497	−	0.472189i	$-0.843464\pi$
$457$	−187.054	+	187.054i	−0.409309	+	0.409309i	0.472189	+	0.881497i	$0.343464\pi$
$458$		0			0
$459$	176.473	+	73.0976i	0.384473	+	0.159254i
$460$		0			0
$461$	−253.784	+	105.121i	−0.550508	+	0.228028i	−0.640558	−	0.767909i	$-0.721297\pi$
$461$	−253.784	+	105.121i	−0.550508	+	0.228028i	0.0900508	+	0.995937i	$0.471297\pi$
$462$		0			0
$463$	−765.246			−1.65280			−0.826400	−	0.563084i	$-0.809615\pi$
$463$	−765.246			−1.65280			−0.826400	+	0.563084i	$0.809615\pi$
$464$		0			0
$465$		−	547.620i		−	1.17768i
$466$		0			0
$467$	110.687	+	267.223i	0.237018	+	0.572211i	0.996972	−	0.0777657i	$-0.0247786\pi$
$467$	110.687	+	267.223i	0.237018	+	0.572211i	−0.759954	+	0.649977i	$0.774779\pi$
$468$		0			0
$469$	247.677	−	597.945i	0.528096	−	1.27494i
$470$		0			0
$471$	−546.893	−	546.893i	−1.16113	−	1.16113i
$472$		0			0
$473$	−115.030	−	115.030i	−0.243193	−	0.243193i
$474$		0			0
$475$	177.468	−	428.447i	0.373618	−	0.901993i
$476$		0			0
$477$	−240.193	−	579.877i	−0.503549	−	1.21568i
$478$		0			0
$479$		−	158.059i		−	0.329977i	−0.986296	−	0.164988i	$-0.947241\pi$
$479$		−	158.059i		−	0.329977i	0.986296	−	0.164988i	$-0.0527586\pi$
$480$		0			0
$481$	339.994			0.706848
$482$		0			0
$483$	−306.795	+	127.079i	−0.635186	+	0.263103i
$484$		0			0
$485$	−458.803	−	190.042i	−0.945985	−	0.391840i
$486$		0			0
$487$	−675.116	+	675.116i	−1.38628	+	1.38628i	−0.553280	+	0.832996i	$0.686624\pi$
$487$	−675.116	+	675.116i	−1.38628	+	1.38628i	−0.832996	+	0.553280i	$0.813376\pi$
$488$		0			0
$489$	405.636	−	405.636i	0.829521	−	0.829521i
$490$		0			0
$491$	−87.1226	−	36.0874i	−0.177439	−	0.0734977i	0.292195	−	0.956359i	$-0.405614\pi$
$491$	−87.1226	−	36.0874i	−0.177439	−	0.0734977i	−0.469634	+	0.882861i	$0.655614\pi$
$492$		0			0
$493$	347.963	−	144.131i	0.705808	−	0.292355i
$494$		0			0
$495$	369.210			0.745878
$496$		0			0
$497$			21.7979i			0.0438590i
$498$		0			0
$499$	−164.812	−	397.892i	−0.330285	−	0.797378i	−0.998569	−	0.0534724i	$-0.982971\pi$
$499$	−164.812	−	397.892i	−0.330285	−	0.797378i	0.668284	−	0.743906i	$-0.267029\pi$
$500$		0			0
$501$	−238.038	+	574.674i	−0.475125	+	1.14705i
$502$		0			0
$503$	−270.905	−	270.905i	−0.538578	−	0.538578i	0.384533	−	0.923111i	$-0.374362\pi$
$503$	−270.905	−	270.905i	−0.538578	−	0.538578i	−0.923111	+	0.384533i	$0.874362\pi$
$504$		0			0
$505$	−86.0864	−	86.0864i	−0.170468	−	0.170468i
$506$		0			0
$507$	−142.651	+	344.389i	−0.281362	+	0.679269i
$508$		0			0
$509$	194.137	+	468.689i	0.381409	+	0.920803i	0.991694	+	0.128621i	$0.0410551\pi$
$509$	194.137	+	468.689i	0.381409	+	0.920803i	−0.610285	+	0.792182i	$0.708945\pi$
$510$		0			0
$511$		−	262.081i		−	0.512878i
$512$		0			0
$513$	100.814			0.196519
$514$		0			0
$515$	98.7463	−	40.9021i	0.191740	−	0.0794215i
$516$		0			0
$517$	−167.416	−	69.3458i	−0.323821	−	0.134131i
$518$		0			0
$519$	880.889	−	880.889i	1.69728	−	1.69728i
$520$		0			0
$521$	−240.434	+	240.434i	−0.461486	+	0.461486i	−0.899142	−	0.437656i	$-0.855809\pi$
$521$	−240.434	+	240.434i	−0.461486	+	0.461486i	0.437656	+	0.899142i	$0.355809\pi$
$522$		0			0
$523$	−846.467	−	350.618i	−1.61848	−	0.670398i	−0.624611	−	0.780936i	$-0.714743\pi$
$523$	−846.467	−	350.618i	−1.61848	−	0.670398i	−0.993872	+	0.110538i	$0.964743\pi$
$524$		0			0
$525$	797.656	−	330.400i	1.51935	−	0.629333i
$526$		0			0
$527$	430.941			0.817725
$528$		0			0
$529$		−	339.966i		−	0.642657i
$530$		0			0
$531$	196.570	+	474.561i	0.370188	+	0.893713i
$532$		0			0
$533$	51.7916	−	125.036i	0.0971699	−	0.234589i
$534$		0			0
$535$	823.967	+	823.967i	1.54012	+	1.54012i
$536$		0			0
$537$	−362.437	−	362.437i	−0.674929	−	0.674929i
$538$		0			0
$539$	32.5523	−	78.5883i	0.0603939	−	0.145804i
$540$		0			0
$541$	6.87337	+	16.5938i	0.0127049	+	0.0306724i	0.930105	−	0.367294i	$-0.119716\pi$
$541$	6.87337	+	16.5938i	0.0127049	+	0.0306724i	−0.917400	+	0.397967i	$0.869716\pi$
$542$		0			0
$543$			407.606i			0.750656i
$544$		0			0
$545$	−270.752			−0.496793
$546$		0			0
$547$	−354.417	+	146.804i	−0.647929	+	0.268381i	−0.682349	−	0.731026i	$-0.739042\pi$
$547$	−354.417	+	146.804i	−0.647929	+	0.268381i	0.0344200	+	0.999407i	$0.489042\pi$
$548$		0			0
$549$	108.601	+	44.9839i	0.197816	+	0.0819379i
$550$		0			0
$551$	140.560	−	140.560i	0.255100	−	0.255100i
$552$		0			0
$553$	−386.348	+	386.348i	−0.698639	+	0.698639i
$554$		0			0
$555$	−1125.56	−	466.221i	−2.02803	−	0.840037i
$556$		0			0
$557$	549.588	−	227.647i	0.986692	−	0.408701i	0.169792	−	0.985480i	$-0.445690\pi$
$557$	549.588	−	227.647i	0.986692	−	0.408701i	0.816900	+	0.576779i	$0.195690\pi$
$558$		0			0
$559$	211.371			0.378123
$560$		0			0
$561$			660.876i			1.17803i
$562$		0			0
$563$	150.445	+	363.205i	0.267219	+	0.645125i	0.999350	−	0.0360391i	$-0.0114741\pi$
$563$	150.445	+	363.205i	0.267219	+	0.645125i	−0.732131	+	0.681164i	$0.761474\pi$
$564$		0			0
$565$	−375.583	+	906.737i	−0.664748	+	1.60484i
$566$		0			0
$567$	403.528	+	403.528i	0.711690	+	0.711690i
$568$		0			0
$569$	510.987	+	510.987i	0.898045	+	0.898045i	0.995263	−	0.0972186i	$-0.0309946\pi$
$569$	510.987	+	510.987i	0.898045	+	0.898045i	−0.0972186	+	0.995263i	$0.530995\pi$
$570$		0			0
$571$	−328.247	+	792.459i	−0.574864	+	1.38784i	0.322507	+	0.946567i	$0.395474\pi$
$571$	−328.247	+	792.459i	−0.574864	+	1.38784i	−0.897371	+	0.441277i	$0.854526\pi$
$572$		0			0
$573$	102.085	+	246.454i	0.178158	+	0.430112i
$574$		0			0
$575$		−	491.482i		−	0.854752i
$576$		0			0
$577$	305.039			0.528663			0.264332	−	0.964432i	$-0.414849\pi$
$577$	305.039			0.528663			0.264332	+	0.964432i	$0.414849\pi$
$578$		0			0
$579$	1021.46	−	423.102i	1.76418	−	0.730746i
$580$		0			0
$581$	572.080	+	236.963i	0.984647	+	0.407854i
$582$		0			0
$583$	−421.689	+	421.689i	−0.723309	+	0.723309i
$584$		0			0
$585$	−339.215	+	339.215i	−0.579855	+	0.579855i
$586$		0			0
$587$	388.900	+	161.088i	0.662521	+	0.274425i	0.688499	−	0.725237i	$-0.258270\pi$
$587$	388.900	+	161.088i	0.662521	+	0.274425i	−0.0259780	+	0.999663i	$0.508270\pi$
$588$		0			0
$589$	210.132	−	87.0394i	0.356760	−	0.147775i
$590$		0			0
$591$	−725.716			−1.22795
$592$		0			0
$593$			1039.64i			1.75319i	0.481228	+	0.876595i	$0.340191\pi$
$593$			1039.64i			1.75319i	−0.481228	+	0.876595i	$0.659809\pi$
$594$		0			0
$595$	441.839	+	1066.69i	0.742587	+	1.79276i
$596$		0			0
$597$	−506.494	+	1222.79i	−0.848399	+	2.04822i
$598$		0			0
$599$	22.4929	+	22.4929i	0.0375507	+	0.0375507i	0.725633	−	0.688082i	$-0.241547\pi$
$599$	22.4929	+	22.4929i	0.0375507	+	0.0375507i	−0.688082	+	0.725633i	$0.741547\pi$
$600$		0			0
$601$	−640.653	−	640.653i	−1.06598	−	1.06598i	−0.997664	−	0.0683147i	$-0.978238\pi$
$601$	−640.653	−	640.653i	−1.06598	−	1.06598i	−0.0683147	−	0.997664i	$-0.521762\pi$
$602$		0			0
$603$	290.182	−	700.561i	0.481230	−	1.16179i
$604$		0			0
$605$	226.654	+	547.192i	0.374636	+	0.904450i
$606$		0			0
$607$			860.149i			1.41705i	0.705686	+	0.708524i	$0.250639\pi$
$607$			860.149i			1.41705i	−0.705686	+	0.708524i	$0.749361\pi$
$608$		0			0
$609$	370.080			0.607685
$610$		0			0
$611$	217.527	−	90.1026i	0.356018	−	0.147467i
$612$		0			0
$613$	−724.830	−	300.235i	−1.18243	−	0.489779i	−0.297148	−	0.954831i	$-0.596035\pi$
$613$	−724.830	−	300.235i	−1.18243	−	0.489779i	−0.885283	+	0.465052i	$0.846035\pi$
$614$		0			0
$615$	−342.914	+	342.914i	−0.557584	+	0.557584i
$616$		0			0
$617$	−704.685	+	704.685i	−1.14212	+	1.14212i	−0.154052	+	0.988063i	$0.549232\pi$
$617$	−704.685	+	704.685i	−1.14212	+	1.14212i	−0.988063	+	0.154052i	$0.950768\pi$
$618$		0			0
$619$	33.0442	+	13.6874i	0.0533832	+	0.0221121i	0.409215	−	0.912438i	$-0.365802\pi$
$619$	33.0442	+	13.6874i	0.0533832	+	0.0221121i	−0.355832	+	0.934550i	$0.615802\pi$
$620$		0			0
$621$	98.7106	−	40.8873i	0.158954	−	0.0658410i
$622$		0			0
$623$	931.477			1.49515
$624$		0			0
$625$		−	240.835i		−	0.385335i
$626$		0			0
$627$	133.481	+	322.250i	0.212888	+	0.513956i
$628$		0			0
$629$	366.885	−	885.738i	0.583282	−	1.40817i
$630$		0			0
$631$	−718.112	−	718.112i	−1.13805	−	1.13805i	−0.988799	−	0.149255i	$-0.952312\pi$
$631$	−718.112	−	718.112i	−1.13805	−	1.13805i	−0.149255	−	0.988799i	$-0.547688\pi$
$632$		0			0
$633$	−242.218	−	242.218i	−0.382651	−	0.382651i
$634$		0			0
$635$	236.870	−	571.854i	0.373023	−	0.900557i
$636$		0			0
$637$	42.2960	+	102.112i	0.0663988	+	0.160301i
$638$		0			0
$639$			25.5388i			0.0399668i
$640$		0			0
$641$	−338.159			−0.527549			−0.263774	−	0.964584i	$-0.584967\pi$
$641$	−338.159			−0.527549			−0.263774	+	0.964584i	$0.584967\pi$
$642$		0			0
$643$	−332.477	+	137.716i	−0.517071	+	0.214178i	−0.625930	−	0.779879i	$-0.715280\pi$
$643$	−332.477	+	137.716i	−0.517071	+	0.214178i	0.108859	+	0.994057i	$0.465280\pi$
$644$		0			0
$645$	−699.747	−	289.845i	−1.08488	−	0.449372i
$646$		0			0
$647$	−31.2745	+	31.2745i	−0.0483377	+	0.0483377i	−0.730862	−	0.682525i	$-0.760882\pi$
$647$	−31.2745	+	31.2745i	−0.0483377	+	0.0483377i	0.682525	+	0.730862i	$0.260882\pi$
$648$		0			0
$649$	345.103	−	345.103i	0.531746	−	0.531746i
$650$		0			0
$651$	391.211	+	162.045i	0.600938	+	0.248917i
$652$		0			0
$653$	−355.409	+	147.215i	−0.544271	+	0.225445i	−0.637841	−	0.770168i	$-0.720172\pi$
$653$	−355.409	+	147.215i	−0.544271	+	0.225445i	0.0935696	+	0.995613i	$0.470172\pi$
$654$		0			0
$655$	449.359			0.686044
$656$		0			0
$657$		−	307.057i		−	0.467363i
$658$		0			0
$659$	116.271	+	280.702i	0.176435	+	0.425952i	0.987214	−	0.159401i	$-0.0509562\pi$
$659$	116.271	+	280.702i	0.176435	+	0.425952i	−0.810779	+	0.585352i	$0.800956\pi$
$660$		0			0
$661$	−179.920	+	434.366i	−0.272194	+	0.657134i	−0.999577	−	0.0290979i	$-0.990737\pi$
$661$	−179.920	+	434.366i	−0.272194	+	0.657134i	0.727383	+	0.686232i	$0.240737\pi$
$662$		0			0
$663$	−607.186	−	607.186i	−0.915817	−	0.915817i
$664$		0			0
$665$	430.892	+	430.892i	0.647957	+	0.647957i
$666$		0			0
$667$	80.6200	−	194.634i	0.120870	−	0.291805i
$668$		0			0
$669$	−572.734	−	1382.70i	−0.856105	−	2.06682i
$670$		0			0
$671$		−	111.688i		−	0.166449i
$672$		0			0
$673$	1168.06			1.73561			0.867803	−	0.496908i	$-0.165531\pi$
$673$	1168.06			1.73561			0.867803	+	0.496908i	$0.165531\pi$
$674$		0			0
$675$	−256.644	+	106.305i	−0.380213	+	0.157490i
$676$		0			0
$677$	604.882	+	250.550i	0.893474	+	0.370089i	0.781707	−	0.623645i	$-0.214349\pi$
$677$	604.882	+	250.550i	0.893474	+	0.370089i	0.111767	+	0.993734i	$0.464349\pi$
$678$		0			0
$679$	271.526	−	271.526i	0.399891	−	0.399891i
$680$		0			0
$681$	−23.6783	+	23.6783i	−0.0347699	+	0.0347699i
$682$		0			0
$683$	369.863	+	153.202i	0.541527	+	0.224308i	0.636644	−	0.771158i	$-0.280322\pi$
$683$	369.863	+	153.202i	0.541527	+	0.224308i	−0.0951163	+	0.995466i	$0.530322\pi$
$684$		0			0
$685$	−516.663	+	214.009i	−0.754253	+	0.312422i
$686$		0			0
$687$	716.618			1.04311
$688$		0			0
$689$		−	774.863i		−	1.12462i
$690$		0			0
$691$	−74.8080	−	180.602i	−0.108260	−	0.261364i	0.860460	−	0.509518i	$-0.170176\pi$
$691$	−74.8080	−	180.602i	−0.108260	−	0.261364i	−0.968721	+	0.248154i	$0.920176\pi$
$692$		0			0
$693$	−109.252	+	263.757i	−0.157650	+	0.380602i
$694$		0			0
$695$	794.653	+	794.653i	1.14339	+	1.14339i
$696$		0			0
$697$	−269.851	−	269.851i	−0.387160	−	0.387160i
$698$		0			0
$699$	30.4073	−	73.4097i	0.0435011	−	0.105021i
$700$		0			0
$701$	−250.206	−	604.050i	−0.356927	−	0.861698i	−0.995729	−	0.0923265i	$-0.970570\pi$
$701$	−250.206	−	604.050i	−0.356927	−	0.861698i	0.638802	−	0.769371i	$-0.279430\pi$
$702$		0			0
$703$		−	505.998i		−	0.719769i
$704$		0			0
$705$	−843.681			−1.19671
$706$		0			0
$707$	86.9722	−	36.0251i	0.123016	−	0.0509548i
$708$		0			0
$709$	771.157	+	319.424i	1.08767	+	0.450527i	0.853193	−	0.521595i	$-0.174663\pi$
$709$	771.157	+	319.424i	1.08767	+	0.450527i	0.234476	+	0.972122i	$0.424663\pi$
$710$		0			0
$711$	−452.650	+	452.650i	−0.636639	+	0.636639i
$712$		0			0
$713$	170.446	−	170.446i	0.239055	−	0.239055i
$714$		0			0
$715$	421.107	+	174.428i	0.588961	+	0.243956i
$716$		0			0
$717$	−855.106	+	354.197i	−1.19262	+	0.493998i
$718$		0			0
$719$	263.077			0.365893			0.182947	−	0.983123i	$-0.441436\pi$
$719$	263.077			0.365893			0.182947	+	0.983123i	$0.441436\pi$
$720$		0			0
$721$			82.6459i			0.114627i
$722$		0			0
$723$	−170.859	−	412.489i	−0.236319	−	0.570525i
$724$		0			0
$725$	−209.609	+	506.041i	−0.289116	+	0.697988i
$726$		0			0
$727$	320.334	+	320.334i	0.440625	+	0.440625i	0.892222	−	0.451597i	$-0.149146\pi$
$727$	320.334	+	320.334i	0.440625	+	0.440625i	−0.451597	+	0.892222i	$0.649146\pi$
$728$		0			0
$729$	274.585	+	274.585i	0.376660	+	0.376660i
$730$		0			0
$731$	228.089	−	550.655i	0.312023	−	0.753289i
$732$		0			0
$733$	−119.193	−	287.758i	−0.162610	−	0.392575i	0.821482	−	0.570234i	$-0.193148\pi$
$733$	−119.193	−	287.758i	−0.162610	−	0.392575i	−0.984092	+	0.177659i	$0.943148\pi$
$734$		0			0
$735$		−	396.041i		−	0.538832i
$736$		0			0
$737$	−720.473			−0.977576
$738$		0			0
$739$	760.509	−	315.013i	1.02911	−	0.426269i	0.196716	−	0.980461i	$-0.436972\pi$
$739$	760.509	−	315.013i	1.02911	−	0.426269i	0.832389	+	0.554191i	$0.186972\pi$
$740$		0			0
$741$	−418.708	−	173.434i	−0.565058	−	0.234054i
$742$		0			0
$743$	89.2306	−	89.2306i	0.120095	−	0.120095i	−0.644505	−	0.764600i	$-0.722937\pi$
$743$	89.2306	−	89.2306i	0.120095	−	0.120095i	0.764600	+	0.644505i	$0.222937\pi$
$744$		0			0
$745$	72.1196	−	72.1196i	0.0968049	−	0.0968049i
$746$		0			0
$747$	670.257	+	277.629i	0.897265	+	0.371659i
$748$		0			0
$749$	−832.445	+	344.810i	−1.11141	+	0.460361i
$750$		0			0
$751$	−418.271			−0.556953			−0.278476	−	0.960443i	$-0.589829\pi$
$751$	−418.271			−0.556953			−0.278476	+	0.960443i	$0.589829\pi$
$752$		0			0
$753$			978.366i			1.29929i
$754$		0			0
$755$	74.6042	+	180.110i	0.0988135	+	0.238557i
$756$		0			0
$757$	212.675	−	513.443i	0.280944	−	0.678260i	−0.718914	−	0.695099i	$-0.755360\pi$
$757$	212.675	−	513.443i	0.280944	−	0.678260i	0.999858	+	0.0168395i	$0.00536042\pi$
$758$		0			0
$759$	261.390	+	261.390i	0.344388	+	0.344388i
$760$		0			0
$761$	60.9342	+	60.9342i	0.0800712	+	0.0800712i	0.746008	−	0.665937i	$-0.231968\pi$
$761$	60.9342	+	60.9342i	0.0800712	+	0.0800712i	−0.665937	+	0.746008i	$0.731968\pi$
$762$		0			0
$763$	80.1175	−	193.421i	0.105003	−	0.253500i
$764$		0			0
$765$	517.665	+	1249.75i	0.676686	+	1.63367i
$766$		0			0
$767$			634.135i			0.826773i
$768$		0			0
$769$	387.688			0.504146			0.252073	−	0.967708i	$-0.418888\pi$
$769$	387.688			0.504146			0.252073	+	0.967708i	$0.418888\pi$
$770$		0			0
$771$	−1031.84	+	427.402i	−1.33831	+	0.554348i
$772$		0			0
$773$	−19.2892	−	7.98984i	−0.0249537	−	0.0103361i	0.370172	−	0.928963i	$-0.379299\pi$
$773$	−19.2892	−	7.98984i	−0.0249537	−	0.0103361i	−0.395125	+	0.918627i	$0.629299\pi$
$774$		0			0
$775$	−443.154	+	443.154i	−0.571812	+	0.571812i
$776$		0			0
$777$	666.120	−	666.120i	0.857297	−	0.857297i
$778$		0			0
$779$	−186.085	−	77.0791i	−0.238877	−	0.0989462i
$780$		0			0
$781$	22.4183	−	9.28595i	0.0287046	−	0.0118898i
$782$		0			0
$783$	−119.072			−0.152072
$784$		0			0
$785$			1504.16i			1.91613i
$786$		0			0
$787$	−521.707	−	1259.51i	−0.662906	−	1.60040i	−0.793228	−	0.608925i	$-0.791601\pi$
$787$	−521.707	−	1259.51i	−0.662906	−	1.60040i	0.130321	−	0.991472i	$-0.458399\pi$
$788$		0			0
$789$	588.228	−	1420.11i	0.745536	−	1.79988i
$790$		0			0
$791$	−536.619	−	536.619i	−0.678406	−	0.678406i
$792$		0			0
$793$	102.614	+	102.614i	0.129400	+	0.129400i
$794$		0			0
$795$	−1062.54	+	2565.20i	−1.33653	+	3.22667i
$796$		0			0
$797$	397.554	+	959.781i	0.498813	+	1.20424i	0.950123	+	0.311875i	$0.100957\pi$
$797$	397.554	+	959.781i	0.498813	+	1.20424i	−0.451310	+	0.892367i	$0.649043\pi$
$798$		0			0
$799$		−	663.921i		−	0.830940i
$800$		0			0
$801$	1091.33			1.36246
$802$		0			0
$803$	−269.539	+	111.647i	−0.335665	+	0.139037i
$804$		0			0
$805$	596.657	+	247.143i	0.741189	+	0.307010i
$806$		0			0
$807$	−168.553	+	168.553i	−0.208864	+	0.208864i
$808$		0			0
$809$	−349.674	+	349.674i	−0.432230	+	0.432230i	−0.889386	−	0.457157i	$-0.848868\pi$
$809$	−349.674	+	349.674i	−0.432230	+	0.432230i	0.457157	+	0.889386i	$0.348868\pi$
$810$		0			0
$811$	−179.312	−	74.2736i	−0.221100	−	0.0915827i	0.269384	−	0.963033i	$-0.413180\pi$
$811$	−179.312	−	74.2736i	−0.221100	−	0.0915827i	−0.490484	+	0.871450i	$0.663180\pi$
$812$		0			0
$813$	1643.84	−	680.901i	2.02194	−	0.837517i
$814$		0			0
$815$	−1115.65			−1.36889
$816$		0			0
$817$		−	314.574i		−	0.385035i
$818$		0			0
$819$	−141.953	−	342.706i	−0.173325	−	0.418444i
$820$		0			0
$821$	41.2552	−	99.5988i	0.0502499	−	0.121314i	−0.896761	−	0.442515i	$-0.854086\pi$
$821$	41.2552	−	99.5988i	0.0502499	−	0.121314i	0.947011	+	0.321201i	$0.104086\pi$
$822$		0			0
$823$	−818.928	−	818.928i	−0.995053	−	0.995053i	0.00493500	−	0.999988i	$-0.498429\pi$
$823$	−818.928	−	818.928i	−0.995053	−	0.995053i	−0.999988	+	0.00493500i	$0.998429\pi$
$824$		0			0
$825$	−679.606	−	679.606i	−0.823765	−	0.823765i
$826$		0			0
$827$	−30.9529	+	74.7270i	−0.0374280	+	0.0903591i	−0.941488	−	0.337046i	$-0.890572\pi$
$827$	−30.9529	+	74.7270i	−0.0374280	+	0.0903591i	0.904060	+	0.427405i	$0.140572\pi$
$828$		0			0
$829$	−87.1070	−	210.295i	−0.105075	−	0.253673i	0.862594	−	0.505896i	$-0.168838\pi$
$829$	−87.1070	−	210.295i	−0.105075	−	0.253673i	−0.967669	+	0.252223i	$0.918838\pi$
$830$		0			0
$831$			242.257i			0.291525i
$832$		0			0
$833$	311.658			0.374140
$834$		0			0
$835$	1117.63	−	462.937i	1.33848	−	0.554416i
$836$		0			0
$837$	−125.871	−	52.1375i	−0.150384	−	0.0622909i
$838$		0			0
$839$	500.637	−	500.637i	0.596707	−	0.596707i	−0.342728	−	0.939435i	$-0.611351\pi$
$839$	500.637	−	500.637i	0.596707	−	0.596707i	0.939435	+	0.342728i	$0.111351\pi$
$840$		0			0
$841$	428.660	−	428.660i	0.509703	−	0.509703i
$842$		0			0
$843$	−836.595	−	346.529i	−0.992402	−	0.411067i
$844$		0			0
$845$	669.771	−	277.428i	0.792628	−	0.328317i
$846$		0			0
$847$	−457.973			−0.540701
$848$		0			0
$849$		−	1942.30i		−	2.28775i
$850$		0			0
$851$	−205.218	−	495.439i	−0.241149	−	0.582184i
$852$		0			0
$853$	−222.935	+	538.212i	−0.261354	+	0.630964i	−0.999023	−	0.0441988i	$-0.985926\pi$
$853$	−222.935	+	538.212i	−0.261354	+	0.630964i	0.737669	+	0.675162i	$0.235926\pi$
$854$		0			0
$855$	504.839	+	504.839i	0.590455	+	0.590455i
$856$		0			0
$857$	−172.645	−	172.645i	−0.201453	−	0.201453i	0.599169	−	0.800622i	$-0.295498\pi$
$857$	−172.645	−	172.645i	−0.201453	−	0.201453i	−0.800622	+	0.599169i	$0.795498\pi$
$858$		0			0
$859$	−66.9122	+	161.540i	−0.0778954	+	0.188056i	−0.958030	−	0.286668i	$-0.907452\pi$
$859$	−66.9122	+	161.540i	−0.0778954	+	0.188056i	0.880135	+	0.474724i	$0.157452\pi$
$860$		0			0
$861$	−143.501	−	346.443i	−0.166668	−	0.402372i
$862$		0			0
$863$		−	325.900i		−	0.377636i	−0.982012	−	0.188818i	$-0.939534\pi$
$863$		−	325.900i		−	0.377636i	0.982012	−	0.188818i	$-0.0604656\pi$
$864$		0			0
$865$	−2422.77			−2.80089
$866$		0			0
$867$	−1166.99	+	483.383i	−1.34601	+	0.557535i
$868$		0			0
$869$	561.927	+	232.758i	0.646637	+	0.267846i
$870$		0			0
$871$	661.942	−	661.942i	0.759980	−	0.759980i
$872$		0			0
$873$	318.124	−	318.124i	0.364403	−	0.364403i
$874$		0			0
$875$	−466.375	−	193.179i	−0.533000	−	0.220776i
$876$		0			0
$877$	−93.3817	+	38.6800i	−0.106479	+	0.0441049i	−0.435287	−	0.900292i	$-0.643353\pi$
$877$	−93.3817	+	38.6800i	−0.106479	+	0.0441049i	0.328808	+	0.944397i	$0.393353\pi$
$878$		0			0
$879$	−2067.29			−2.35186
$880$		0			0
$881$		−	129.296i		−	0.146760i	−0.997304	−	0.0733801i	$-0.976621\pi$
$881$		−	129.296i		−	0.146760i	0.997304	−	0.0733801i	$-0.0233786\pi$
$882$		0			0
$883$	−28.1493	−	67.9584i	−0.0318792	−	0.0769631i	0.907138	−	0.420833i	$-0.138262\pi$
$883$	−28.1493	−	67.9584i	−0.0318792	−	0.0769631i	−0.939017	+	0.343870i	$0.888262\pi$
$884$		0			0
$885$	869.565	−	2099.31i	0.982559	−	2.37211i
$886$		0			0
$887$	338.588	+	338.588i	0.381723	+	0.381723i	0.871723	−	0.490000i	$-0.163003\pi$
$887$	338.588	+	338.588i	0.381723	+	0.381723i	−0.490000	+	0.871723i	$0.663003\pi$
$888$		0			0
$889$	338.431	+	338.431i	0.380687	+	0.380687i
$890$		0			0
$891$	243.109	−	586.916i	0.272849	−	0.658716i
$892$		0			0
$893$	−134.096	−	323.736i	−0.150163	−	0.362526i
$894$		0			0
$895$			996.837i			1.11378i
$896$		0			0
$897$	−480.310			−0.535463
$898$		0			0
$899$	−248.188	+	102.803i	−0.276071	+	0.114352i
$900$		0			0
$901$	−2018.64	−	836.148i	−2.24045	−	0.928023i
$902$		0			0
$903$	414.120	−	414.120i	0.458605	−	0.458605i
$904$		0			0
$905$	560.535	−	560.535i	0.619375	−	0.619375i
$906$		0			0
$907$	−1031.84	−	427.401i	−1.13764	−	0.471225i	−0.267268	−	0.963622i	$-0.586121\pi$
$907$	−1031.84	−	427.401i	−1.13764	−	0.471225i	−0.870371	+	0.492397i	$0.836121\pi$
$908$		0			0
$909$	101.898	−	42.2075i	0.112099	−	0.0464329i
$910$		0			0
$911$	857.136			0.940873			0.470437	−	0.882434i	$-0.344096\pi$
$911$	857.136			0.940873			0.470437	+	0.882434i	$0.344096\pi$
$912$		0			0
$913$		−	689.307i		−	0.754992i
$914$		0			0
$915$	−198.995	−	480.417i	−0.217481	−	0.525046i
$916$		0			0
$917$	−132.968	+	321.014i	−0.145004	+	0.350070i
$918$		0			0
$919$	447.382	+	447.382i	0.486814	+	0.486814i	0.907299	−	0.420486i	$-0.138140\pi$
$919$	447.382	+	447.382i	0.486814	+	0.486814i	−0.420486	+	0.907299i	$0.638140\pi$
$920$		0			0
$921$	1452.97	+	1452.97i	1.57760	+	1.57760i
$922$		0			0
$923$	−12.0655	+	29.1286i	−0.0130720	+	0.0315586i
$924$		0			0
$925$	533.558	+	1288.12i	0.576820	+	1.39257i
$926$		0			0
$927$			96.8291i			0.104454i
$928$		0			0
$929$	−357.338			−0.384648			−0.192324	−	0.981332i	$-0.561602\pi$
$929$	−357.338			−0.384648			−0.192324	+	0.981332i	$0.561602\pi$
$930$		0			0
$931$	151.968	−	62.9473i	0.163231	−	0.0676125i
$932$		0			0
$933$	2022.98	+	837.947i	2.16826	+	0.898122i
$934$		0			0
$935$	908.827	−	908.827i	0.972007	−	0.972007i
$936$		0			0
$937$	−504.116	+	504.116i	−0.538011	+	0.538011i	−0.922944	−	0.384934i	$-0.874224\pi$
$937$	−504.116	+	504.116i	−0.538011	+	0.538011i	0.384934	+	0.922944i	$0.374224\pi$
$938$		0			0
$939$	665.468	+	275.646i	0.708698	+	0.293552i
$940$		0			0
$941$	503.223	−	208.442i	0.534775	−	0.221511i	−0.0989183	−	0.995096i	$-0.531538\pi$
$941$	503.223	−	208.442i	0.534775	−	0.221511i	0.633693	+	0.773585i	$0.281538\pi$
$942$		0			0
$943$	−213.463			−0.226366
$944$		0			0
$945$		−	365.021i		−	0.386265i
$946$		0			0
$947$	137.566	+	332.113i	0.145265	+	0.350700i	0.979719	−	0.200378i	$-0.0642169\pi$
$947$	137.566	+	332.113i	0.145265	+	0.350700i	−0.834454	+	0.551077i	$0.814217\pi$
$948$		0			0
$949$	145.065	−	350.219i	0.152861	−	0.369040i
$950$		0			0
$951$	180.964	+	180.964i	0.190288	+	0.190288i
$952$		0			0
$953$	129.115	+	129.115i	0.135483	+	0.135483i	0.771596	−	0.636113i	$-0.219459\pi$
$953$	129.115	+	129.115i	0.135483	+	0.135483i	−0.636113	+	0.771596i	$0.719459\pi$
$954$		0			0
$955$	198.535	−	479.306i	0.207890	−	0.501891i
$956$		0			0
$957$	−157.655	−	380.612i	−0.164739	−	0.397714i
$958$		0			0
$959$		−	432.422i		−	0.450909i
$960$		0			0
$961$	653.628			0.680154
$962$		0			0
$963$	−975.304	+	403.984i	−1.01278	+	0.419506i
$964$		0			0
$965$	−1986.54	−	822.851i	−2.05859	−	0.852695i
$966$		0			0
$967$	657.007	−	657.007i	0.679428	−	0.679428i	−0.280443	−	0.959871i	$-0.590481\pi$
$967$	657.007	−	657.007i	0.679428	−	0.679428i	0.959871	+	0.280443i	$0.0904813\pi$
$968$		0			0
$969$	−903.648	+	903.648i	−0.932557	+	0.932557i
$970$		0			0
$971$	654.912	+	271.274i	0.674472	+	0.279376i	0.693514	−	0.720443i	$-0.256062\pi$
$971$	654.912	+	271.274i	0.674472	+	0.279376i	−0.0190418	+	0.999819i	$0.506062\pi$
$972$		0			0
$973$	−802.830	+	332.543i	−0.825108	+	0.341771i
$974$		0			0
$975$	1248.79			1.28081
$976$		0			0
$977$		−	1493.20i		−	1.52835i	−0.645010	−	0.764174i	$-0.723147\pi$
$977$		−	1493.20i		−	1.52835i	0.645010	−	0.764174i	$-0.276853\pi$
$978$		0			0
$979$	−396.811	−	957.986i	−0.405323	−	0.978536i
$980$		0			0
$981$	93.8668	−	226.615i	0.0956848	−	0.231004i
$982$		0			0
$983$	−856.189	−	856.189i	−0.870996	−	0.870996i	0.121585	−	0.992581i	$-0.461202\pi$
$983$	−856.189	−	856.189i	−0.870996	−	0.870996i	−0.992581	+	0.121585i	$0.961202\pi$
$984$		0			0
$985$	997.994	+	997.994i	1.01319	+	1.01319i
$986$		0			0
$987$	249.651	−	602.711i	0.252939	−	0.610650i
$988$		0			0
$989$	−127.582	−	308.010i	−0.129001	−	0.311435i
$990$		0			0
$991$			1223.32i			1.23443i	0.786793	+	0.617217i	$0.211740\pi$
$991$			1223.32i			1.23443i	−0.786793	+	0.617217i	$0.788260\pi$
$992$		0			0
$993$	−233.162			−0.234806
$994$		0			0
$995$	2378.08	−	985.034i	2.39003	−	0.989984i
$996$		0			0
$997$	−604.001	−	250.185i	−0.605819	−	0.250938i	0.0586209	−	0.998280i	$-0.481330\pi$
$997$	−604.001	−	250.185i	−0.605819	−	0.250938i	−0.664440	+	0.747342i	$0.731330\pi$
$998$		0			0
$999$	−214.323	+	214.323i	−0.214537	+	0.214537i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.3.h.b.31.6		28
4.3	odd	2		256.3.h.a.31.2		28
8.3	odd	2		128.3.h.a.15.6		28
8.5	even	2		32.3.h.a.27.5	yes	28
24.5	odd	2		288.3.u.a.91.3		28
32.3	odd	8		32.3.h.a.19.5	✓	28
32.13	even	8		256.3.h.a.223.2		28
32.19	odd	8	inner	256.3.h.b.223.6		28
32.29	even	8		128.3.h.a.111.6		28
96.35	even	8		288.3.u.a.19.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.3.h.a.19.5	✓	28	32.3	odd	8
32.3.h.a.27.5	yes	28	8.5	even	2
128.3.h.a.15.6		28	8.3	odd	2
128.3.h.a.111.6		28	32.29	even	8
256.3.h.a.31.2		28	4.3	odd	2
256.3.h.a.223.2		28	32.13	even	8
256.3.h.b.31.6		28	1.1	even	1	trivial
256.3.h.b.223.6		28	32.19	odd	8	inner
288.3.u.a.19.3		28	96.35	even	8
288.3.u.a.91.3		28	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	256.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.70255 - 1.53365i) q^{3} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +O(q^{10})\)	\(q+(3.70255 - 1.53365i) q^{3} +(-7.20074 - 2.98264i) q^{5} +(4.26150 - 4.26150i) q^{7} +(4.99283 - 4.99283i) q^{9} +(-6.19818 - 2.56737i) q^{11} +(8.05345 - 3.33585i) q^{13} -31.2354 q^{15} -24.5802i q^{17} +(-4.96459 - 11.9856i) q^{19} +(9.24278 - 22.3140i) q^{21} +(-9.72199 - 9.72199i) q^{23} +(25.2768 + 25.2768i) q^{25} +(-2.97384 + 7.17949i) q^{27} +(5.86371 + 14.1563i) q^{29} +17.5320i q^{31} -26.8865 q^{33} +(-43.3965 + 17.9754i) q^{35} +(36.0346 + 14.9260i) q^{37} +(24.7023 - 24.7023i) q^{39} +(10.9784 - 10.9784i) q^{41} +(22.4024 + 9.27937i) q^{43} +(-50.8439 + 21.0603i) q^{45} +27.0104 q^{47} +12.6792i q^{49} +(-37.6973 - 91.0093i) q^{51} +(34.0172 - 82.1247i) q^{53} +(36.9740 + 36.9740i) q^{55} +(-36.7633 - 36.7633i) q^{57} +(-27.8391 + 67.2095i) q^{59} +(6.37082 + 15.3805i) q^{61} -42.5539i q^{63} -67.9404 q^{65} +(99.2165 - 41.0968i) q^{67} +(-50.9062 - 21.0860i) q^{69} +(-2.55754 + 2.55754i) q^{71} +(30.7498 - 30.7498i) q^{73} +(132.354 + 54.8230i) q^{75} +(-37.3544 + 15.4727i) q^{77} -90.6600 q^{79} +94.6916i q^{81} +(39.3191 + 94.9247i) q^{83} +(-73.3140 + 176.996i) q^{85} +(43.4214 + 43.4214i) q^{87} +(109.290 + 109.290i) q^{89} +(20.1040 - 48.5355i) q^{91} +(26.8879 + 64.9132i) q^{93} +101.113i q^{95} +63.7161 q^{97} +(-43.7650 + 18.1280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 28 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} - 8 q^{15} + 4 q^{19} + 4 q^{21} - 68 q^{23} - 4 q^{25} + 100 q^{27} + 4 q^{29} - 8 q^{33} - 92 q^{35} + 4 q^{37} + 188 q^{39} - 4 q^{41} - 92 q^{43} + 40 q^{45} - 8 q^{47} - 224 q^{51} + 164 q^{53} + 252 q^{55} - 4 q^{57} - 124 q^{59} + 68 q^{61} - 8 q^{65} + 164 q^{67} - 188 q^{69} - 260 q^{71} - 4 q^{73} + 488 q^{75} - 220 q^{77} - 520 q^{79} + 484 q^{83} - 96 q^{85} - 452 q^{87} - 4 q^{89} + 196 q^{91} - 32 q^{93} - 8 q^{97} - 216 q^{99}+O(q^{100}) \) 28 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 - 8 * q^15 + 4 * q^19 + 4 * q^21 - 68 * q^23 - 4 * q^25 + 100 * q^27 + 4 * q^29 - 8 * q^33 - 92 * q^35 + 4 * q^37 + 188 * q^39 - 4 * q^41 - 92 * q^43 + 40 * q^45 - 8 * q^47 - 224 * q^51 + 164 * q^53 + 252 * q^55 - 4 * q^57 - 124 * q^59 + 68 * q^61 - 8 * q^65 + 164 * q^67 - 188 * q^69 - 260 * q^71 - 4 * q^73 + 488 * q^75 - 220 * q^77 - 520 * q^79 + 484 * q^83 - 96 * q^85 - 452 * q^87 - 4 * q^89 + 196 * q^91 - 32 * q^93 - 8 * q^97 - 216 * q^99

Introduction

L-functions

Modular forms

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Database

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