LMFDB - Embedded newform 256.4.g.b.97.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,4,Mod(33,256)]

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([0, 7]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("256.33");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	256.g (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:	$15.1044889615$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			97.11
Character	$\chi$	$=$	256.97
Dual form			256.4.g.b.161.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.18660 - 3.80522i) q^{3} +(-1.04223 + 2.51617i) q^{5} +(16.1077 + 16.1077i) q^{7} +(50.8221 - 50.8221i) q^{9} +O(q^{10})$	\(q+(9.18660 - 3.80522i) q^{3} +(-1.04223 + 2.51617i) q^{5} +(16.1077 + 16.1077i) q^{7} +(50.8221 - 50.8221i) q^{9} +(-3.72541 - 1.54312i) q^{11} +(-9.23975 - 22.3067i) q^{13} +27.0810i q^{15} +4.95290i q^{17} +(26.0224 + 62.8237i) q^{19} +(209.269 + 86.6820i) q^{21} +(82.8361 - 82.8361i) q^{23} +(83.1435 + 83.1435i) q^{25} +(170.753 - 412.233i) q^{27} +(-150.525 + 62.3496i) q^{29} -141.577 q^{31} -40.0958 q^{33} +(-57.3179 + 23.7419i) q^{35} +(1.05672 - 2.55114i) q^{37} +(-169.764 - 169.764i) q^{39} +(8.70340 - 8.70340i) q^{41} +(-290.048 - 120.142i) q^{43} +(74.9088 + 180.846i) q^{45} -450.158i q^{47} +175.919i q^{49} +(18.8469 + 45.5003i) q^{51} +(114.608 + 47.4724i) q^{53} +(7.76550 - 7.76550i) q^{55} +(478.115 + 478.115i) q^{57} +(-124.292 + 300.067i) q^{59} +(223.938 - 92.7582i) q^{61} +1637.26 q^{63} +65.7576 q^{65} +(-204.137 + 84.5564i) q^{67} +(445.773 - 1076.19i) q^{69} +(-606.304 - 606.304i) q^{71} +(-531.888 + 531.888i) q^{73} +(1080.18 + 447.427i) q^{75} +(-35.1518 - 84.8641i) q^{77} +1123.99i q^{79} -2496.19i q^{81} +(118.647 + 286.439i) q^{83} +(-12.4624 - 5.16208i) q^{85} +(-1145.56 + 1145.56i) q^{87} +(191.511 + 191.511i) q^{89} +(210.480 - 508.143i) q^{91} +(-1300.61 + 538.732i) q^{93} -185.197 q^{95} -38.4790 q^{97} +(-267.758 + 110.909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	$ 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	9.18660	−	3.80522i	1.76796	−	0.732314i	0.772735	−	0.634728i	$-0.218888\pi$
$3$	9.18660	−	3.80522i	1.76796	−	0.732314i	0.995227	−	0.0975856i	$-0.0311120\pi$
$4$		0			0
$5$	−1.04223	+	2.51617i	−0.0932202	+	0.225053i	−0.963611	−	0.267308i	$-0.913866\pi$
$5$	−1.04223	+	2.51617i	−0.0932202	+	0.225053i	0.870391	+	0.492361i	$0.163866\pi$
$6$		0			0
$7$	16.1077	+	16.1077i	0.869736	+	0.869736i	0.992443	−	0.122707i	$-0.0391575\pi$
$7$	16.1077	+	16.1077i	0.869736	+	0.869736i	−0.122707	+	0.992443i	$0.539157\pi$
$8$		0			0
$9$	50.8221	−	50.8221i	1.88230	−	1.88230i
$10$		0			0
$11$	−3.72541	−	1.54312i	−0.102114	−	0.0422970i	0.331042	−	0.943616i	$-0.392600\pi$
$11$	−3.72541	−	1.54312i	−0.102114	−	0.0422970i	−0.433156	+	0.901319i	$0.642600\pi$
$12$		0			0
$13$	−9.23975	−	22.3067i	−0.197127	−	0.475906i	0.794147	−	0.607726i	$-0.207918\pi$
$13$	−9.23975	−	22.3067i	−0.197127	−	0.475906i	−0.991274	+	0.131820i	$0.957918\pi$
$14$		0			0
$15$			27.0810i			0.466153i
$16$		0			0
$17$			4.95290i			0.0706621i	0.999376	+	0.0353310i	$0.0112486\pi$
$17$			4.95290i			0.0706621i	−0.999376	+	0.0353310i	$0.988751\pi$
$18$		0			0
$19$	26.0224	+	62.8237i	0.314208	+	0.758565i	0.999540	+	0.0303344i	$0.00965721\pi$
$19$	26.0224	+	62.8237i	0.314208	+	0.758565i	−0.685332	+	0.728231i	$0.740343\pi$
$20$		0			0
$21$	209.269	+	86.6820i	2.17458	+	0.900741i
$22$		0			0
$23$	82.8361	−	82.8361i	0.750979	−	0.750979i	−0.223683	−	0.974662i	$-0.571808\pi$
$23$	82.8361	−	82.8361i	0.750979	−	0.750979i	0.974662	+	0.223683i	$0.0718079\pi$
$24$		0			0
$25$	83.1435	+	83.1435i	0.665148	+	0.665148i
$26$		0			0
$27$	170.753	−	412.233i	1.21709	−	2.93831i
$28$		0			0
$29$	−150.525	+	62.3496i	−0.963856	+	0.399242i	−0.808422	−	0.588604i	$-0.799678\pi$
$29$	−150.525	+	62.3496i	−0.963856	+	0.399242i	−0.155435	+	0.987846i	$0.549678\pi$
$30$		0			0
$31$	−141.577			−0.820258			−0.410129	−	0.912027i	$-0.634516\pi$
$31$	−141.577			−0.820258			−0.410129	+	0.912027i	$0.634516\pi$
$32$		0			0
$33$	−40.0958			−0.211508
$34$		0			0
$35$	−57.3179	+	23.7419i	−0.276814	+	0.114660i
$36$		0			0
$37$	1.05672	−	2.55114i	0.00469523	−	0.0113353i	−0.921515	−	0.388344i	$-0.873047\pi$
$37$	1.05672	−	2.55114i	0.00469523	−	0.0113353i	0.926210	+	0.377009i	$0.123047\pi$
$38$		0			0
$39$	−169.764	−	169.764i	−0.697025	−	0.697025i
$40$		0			0
$41$	8.70340	−	8.70340i	0.0331523	−	0.0331523i	−0.690336	−	0.723489i	$-0.742537\pi$
$41$	8.70340	−	8.70340i	0.0331523	−	0.0331523i	0.723489	+	0.690336i	$0.242537\pi$
$42$		0			0
$43$	−290.048	−	120.142i	−1.02865	−	0.426081i	−0.196425	−	0.980519i	$-0.562933\pi$
$43$	−290.048	−	120.142i	−1.02865	−	0.426081i	−0.832225	+	0.554438i	$0.812933\pi$
$44$		0			0
$45$	74.9088	+	180.846i	0.248150	+	0.599087i
$46$		0			0
$47$		−	450.158i		−	1.39707i	−0.715576	−	0.698535i	$-0.753836\pi$
$47$		−	450.158i		−	1.39707i	0.715576	−	0.698535i	$-0.246164\pi$
$48$		0			0
$49$			175.919i			0.512882i
$50$		0			0
$51$	18.8469	+	45.5003i	0.0517468	+	0.124928i
$52$		0			0
$53$	114.608	+	47.4724i	0.297032	+	0.123035i	0.526222	−	0.850347i	$-0.323608\pi$
$53$	114.608	+	47.4724i	0.297032	+	0.123035i	−0.229191	+	0.973382i	$0.573608\pi$
$54$		0			0
$55$	7.76550	−	7.76550i	0.0190382	−	0.0190382i
$56$		0			0
$57$	478.115	+	478.115i	1.11102	+	1.11102i
$58$		0			0
$59$	−124.292	+	300.067i	−0.274262	+	0.662126i	−0.999657	−	0.0262068i	$-0.991657\pi$
$59$	−124.292	+	300.067i	−0.274262	+	0.662126i	0.725395	+	0.688333i	$0.241657\pi$
$60$		0			0
$61$	223.938	−	92.7582i	0.470039	−	0.194696i	−0.135075	−	0.990835i	$-0.543128\pi$
$61$	223.938	−	92.7582i	0.470039	−	0.194696i	0.605114	+	0.796139i	$0.293128\pi$
$62$		0			0
$63$	1637.26			3.27421
$64$		0			0
$65$	65.7576			0.125480
$66$		0			0
$67$	−204.137	+	84.5564i	−0.372229	+	0.154182i	−0.560952	−	0.827848i	$-0.689565\pi$
$67$	−204.137	+	84.5564i	−0.372229	+	0.154182i	0.188724	+	0.982030i	$0.439565\pi$
$68$		0			0
$69$	445.773	−	1076.19i	0.777751	−	1.87766i
$70$		0			0
$71$	−606.304	−	606.304i	−1.01345	−	1.01345i	−0.999908	−	0.0135432i	$-0.995689\pi$
$71$	−606.304	−	606.304i	−1.01345	−	1.01345i	−0.0135432	−	0.999908i	$-0.504311\pi$
$72$		0			0
$73$	−531.888	+	531.888i	−0.852779	+	0.852779i	−0.990475	−	0.137696i	$-0.956030\pi$
$73$	−531.888	+	531.888i	−0.852779	+	0.852779i	0.137696	+	0.990475i	$0.456030\pi$
$74$		0			0
$75$	1080.18	+	447.427i	1.66305	+	0.688859i
$76$		0			0
$77$	−35.1518	−	84.8641i	−0.0520250	−	0.125599i
$78$		0			0
$79$			1123.99i			1.60075i	0.599499	+	0.800375i	$0.295366\pi$
$79$			1123.99i			1.60075i	−0.599499	+	0.800375i	$0.704634\pi$
$80$		0			0
$81$		−	2496.19i		−	3.42414i
$82$		0			0
$83$	118.647	+	286.439i	0.156906	+	0.378804i	0.982710	−	0.185153i	$-0.0592782\pi$
$83$	118.647	+	286.439i	0.156906	+	0.378804i	−0.825804	+	0.563957i	$0.809278\pi$
$84$		0			0
$85$	−12.4624	−	5.16208i	−0.0159027	−	0.00658713i
$86$		0			0
$87$	−1145.56	+	1145.56i	−1.41169	+	1.41169i
$88$		0			0
$89$	191.511	+	191.511i	0.228091	+	0.228091i	0.811895	−	0.583804i	$-0.198436\pi$
$89$	191.511	+	191.511i	0.228091	+	0.228091i	−0.583804	+	0.811895i	$0.698436\pi$
$90$		0			0
$91$	210.480	−	508.143i	0.242464	−	0.585361i
$92$		0			0
$93$	−1300.61	+	538.732i	−1.45019	+	0.600687i
$94$		0			0
$95$	−185.197			−0.200008
$96$		0			0
$97$	−38.4790			−0.0402778			−0.0201389	−	0.999797i	$-0.506411\pi$
$97$	−38.4790			−0.0402778			−0.0201389	+	0.999797i	$0.506411\pi$
$98$		0			0
$99$	−267.758	+	110.909i	−0.271825	+	0.112594i
$100$		0			0
$101$	−84.1832	+	203.236i	−0.0829361	+	0.200225i	−0.959907	−	0.280317i	$-0.909560\pi$
$101$	−84.1832	+	203.236i	−0.0829361	+	0.200225i	0.876971	+	0.480543i	$0.159560\pi$
$102$		0			0
$103$	44.6891	+	44.6891i	0.0427509	+	0.0427509i	0.728159	−	0.685408i	$-0.240376\pi$
$103$	44.6891	+	44.6891i	0.0427509	+	0.0427509i	−0.685408	+	0.728159i	$0.740376\pi$
$104$		0			0
$105$	−436.214	+	436.214i	−0.405430	+	0.405430i
$106$		0			0
$107$	−1058.85	−	438.589i	−0.956660	−	0.396261i	−0.150930	−	0.988545i	$-0.548227\pi$
$107$	−1058.85	−	438.589i	−0.956660	−	0.396261i	−0.805730	+	0.592283i	$0.798227\pi$
$108$		0			0
$109$	612.581	+	1478.90i	0.538299	+	1.29957i	0.925909	+	0.377746i	$0.123301\pi$
$109$	612.581	+	1478.90i	0.538299	+	1.29957i	−0.387610	+	0.921824i	$0.626699\pi$
$110$		0			0
$111$		−	27.4574i		−	0.0234787i
$112$		0			0
$113$			1766.08i			1.47025i	0.677931	+	0.735126i	$0.262877\pi$
$113$			1766.08i			1.47025i	−0.677931	+	0.735126i	$0.737123\pi$
$114$		0			0
$115$	122.096	+	294.765i	0.0990041	+	0.239017i
$116$		0			0
$117$	−1603.26	−	664.092i	−1.26685	−	0.524746i
$118$		0			0
$119$	−79.7800	+	79.7800i	−0.0614573	+	0.0614573i
$120$		0			0
$121$	−929.662	−	929.662i	−0.698469	−	0.698469i
$122$		0			0
$123$	46.8364	−	113.073i	0.0343341	−	0.0828898i
$124$		0			0
$125$	−610.380	+	252.828i	−0.436753	+	0.180909i
$126$		0			0
$127$	−2036.13			−1.42265			−0.711327	−	0.702861i	$-0.751906\pi$
$127$	−2036.13			−1.42265			−0.711327	+	0.702861i	$0.751906\pi$
$128$		0			0
$129$	−3121.72			−2.13064
$130$		0			0
$131$	−1199.70	+	496.933i	−0.800141	+	0.331429i	−0.745013	−	0.667050i	$-0.767557\pi$
$131$	−1199.70	+	496.933i	−0.800141	+	0.331429i	−0.0551280	+	0.998479i	$0.517557\pi$
$132$		0			0
$133$	−592.785	+	1431.11i	−0.386474	+	0.933030i
$134$		0			0
$135$	859.287	+	859.287i	0.547820	+	0.547820i
$136$		0			0
$137$	1355.73	−	1355.73i	0.845456	−	0.845456i	−0.144106	−	0.989562i	$-0.546031\pi$
$137$	1355.73	−	1355.73i	0.845456	−	0.845456i	0.989562	+	0.144106i	$0.0460308\pi$
$138$		0			0
$139$	−1922.35	−	796.261i	−1.17303	−	0.485885i	−0.290837	−	0.956773i	$-0.593934\pi$
$139$	−1922.35	−	796.261i	−1.17303	−	0.485885i	−0.882193	+	0.470888i	$0.843934\pi$
$140$		0			0
$141$	−1712.95	−	4135.42i	−1.02309	−	2.46997i
$142$		0			0
$143$			97.3598i			0.0569345i
$144$		0			0
$145$		−	443.731i		−	0.254137i
$146$		0			0
$147$	669.408	+	1616.09i	0.375591	+	0.906756i
$148$		0			0
$149$	2675.49	+	1108.22i	1.47104	+	0.609323i	0.967095	−	0.254415i	$-0.0818828\pi$
$149$	2675.49	+	1108.22i	1.47104	+	0.609323i	0.503941	+	0.863738i	$0.331883\pi$
$150$		0			0
$151$	1002.53	−	1002.53i	0.540298	−	0.540298i	−0.383318	−	0.923616i	$-0.625219\pi$
$151$	1002.53	−	1002.53i	0.540298	−	0.540298i	0.923616	+	0.383318i	$0.125219\pi$
$152$		0			0
$153$	251.717	+	251.717i	0.133007	+	0.133007i
$154$		0			0
$155$	147.556	−	356.233i	0.0764647	−	0.184602i
$156$		0			0
$157$	−2551.29	+	1056.78i	−1.29691	+	0.537199i	−0.921039	−	0.389471i	$-0.872658\pi$
$157$	−2551.29	+	1056.78i	−1.29691	+	0.537199i	−0.375875	+	0.926670i	$0.622658\pi$
$158$		0			0
$159$	1233.51			0.615241
$160$		0			0
$161$	2668.61			1.30631
$162$		0			0
$163$	817.977	−	338.817i	0.393061	−	0.162811i	−0.177395	−	0.984140i	$-0.556767\pi$
$163$	817.977	−	338.817i	0.393061	−	0.162811i	0.570455	+	0.821329i	$0.306767\pi$
$164$		0			0
$165$	41.7891	−	100.888i	0.0197169	−	0.0476007i
$166$		0			0
$167$	−468.145	−	468.145i	−0.216923	−	0.216923i	0.590277	−	0.807200i	$-0.299018\pi$
$167$	−468.145	−	468.145i	−0.216923	−	0.216923i	−0.807200	+	0.590277i	$0.799018\pi$
$168$		0			0
$169$	1141.30	−	1141.30i	0.519479	−	0.519479i
$170$		0			0
$171$	4515.35	+	1870.32i	2.01928	+	0.836414i
$172$		0			0
$173$	173.825	+	419.651i	0.0763913	+	0.184425i	0.957462	−	0.288560i	$-0.0931765\pi$
$173$	173.825	+	419.651i	0.0763913	+	0.184425i	−0.881071	+	0.472985i	$0.843176\pi$
$174$		0			0
$175$			2678.51i			1.15701i
$176$		0			0
$177$			3229.56i			1.37146i
$178$		0			0
$179$	229.250	+	553.458i	0.0957259	+	0.231103i	0.964488	−	0.264127i	$-0.0850839\pi$
$179$	229.250	+	553.458i	0.0957259	+	0.231103i	−0.868762	+	0.495230i	$0.835084\pi$
$180$		0			0
$181$	2681.16	+	1110.57i	1.10105	+	0.456068i	0.857845	−	0.513908i	$-0.171803\pi$
$181$	2681.16	+	1110.57i	1.10105	+	0.456068i	0.243200	+	0.969976i	$0.421803\pi$
$182$		0			0
$183$	1704.27	−	1704.27i	0.688432	−	0.688432i
$184$		0			0
$185$	5.31778	+	5.31778i	0.00211335	+	0.00211335i
$186$		0			0
$187$	7.64290	−	18.4516i	0.00298879	−	0.00721558i
$188$		0			0
$189$	9390.59	−	3889.71i	3.61410	−	1.49701i
$190$		0			0
$191$	−3132.56			−1.18672			−0.593361	−	0.804937i	$-0.702199\pi$
$191$	−3132.56			−1.18672			−0.593361	+	0.804937i	$0.702199\pi$
$192$		0			0
$193$	−1348.21			−0.502830			−0.251415	−	0.967879i	$-0.580896\pi$
$193$	−1348.21			−0.502830			−0.251415	+	0.967879i	$0.580896\pi$
$194$		0			0
$195$	604.089	−	250.222i	0.221845	−	0.0918911i
$196$		0			0
$197$	1199.14	−	2894.97i	0.433680	−	1.04700i	−0.544411	−	0.838819i	$-0.683247\pi$
$197$	1199.14	−	2894.97i	0.433680	−	1.04700i	0.978091	−	0.208178i	$-0.0667532\pi$
$198$		0			0
$199$	2933.43	+	2933.43i	1.04495	+	1.04495i	0.998941	+	0.0460089i	$0.0146503\pi$
$199$	2933.43	+	2933.43i	1.04495	+	1.04495i	0.0460089	+	0.998941i	$0.485350\pi$
$200$		0			0
$201$	−1553.57	+	1553.57i	−0.545176	+	0.545176i
$202$		0			0
$203$	−3428.93	−	1420.31i	−1.18554	−	0.491065i
$204$		0			0
$205$	12.8283	+	30.9703i	0.00437057	+	0.0105515i
$206$		0			0
$207$		−	8419.81i		−	2.82714i
$208$		0			0
$209$		−	274.200i		−	0.0907502i
$210$		0			0
$211$	−1226.47	−	2960.96i	−0.400159	−	0.966069i	−0.987627	−	0.156822i	$-0.949875\pi$
$211$	−1226.47	−	2960.96i	−0.400159	−	0.966069i	0.587468	−	0.809247i	$-0.300125\pi$
$212$		0			0
$213$	−7876.99	−	3262.76i	−2.53391	−	1.04958i
$214$		0			0
$215$	604.596	−	604.596i	0.191782	−	0.191782i
$216$		0			0
$217$	−2280.49	−	2280.49i	−0.713408	−	0.713408i
$218$		0			0
$219$	−2862.30	+	6910.20i	−0.883179	+	2.13218i
$220$		0			0
$221$	110.483	−	45.7636i	0.0336285	−	0.0139294i
$222$		0			0
$223$	1217.92			0.365732			0.182866	−	0.983138i	$-0.441463\pi$
$223$	1217.92			0.365732			0.182866	+	0.983138i	$0.441463\pi$
$224$		0			0
$225$	8451.05			2.50402
$226$		0			0
$227$	5300.89	−	2195.70i	1.54992	−	0.641999i	0.566620	−	0.823979i	$-0.308251\pi$
$227$	5300.89	−	2195.70i	1.54992	−	0.641999i	0.983302	+	0.181980i	$0.0582507\pi$
$228$		0			0
$229$	−1179.47	+	2847.49i	−0.340356	+	0.821693i	0.657323	+	0.753609i	$0.271689\pi$
$229$	−1179.47	+	2847.49i	−0.340356	+	0.821693i	−0.997680	+	0.0680842i	$0.978311\pi$
$230$		0			0
$231$	−645.852	−	645.852i	−0.183956	−	0.183956i
$232$		0			0
$233$	−396.209	+	396.209i	−0.111401	+	0.111401i	−0.760610	−	0.649209i	$-0.775100\pi$
$233$	−396.209	+	396.209i	−0.111401	+	0.111401i	0.649209	+	0.760610i	$0.275100\pi$
$234$		0			0
$235$	1132.68	+	469.169i	0.314415	+	0.130235i
$236$		0			0
$237$	4277.04	+	10325.7i	1.17225	+	2.83007i
$238$		0			0
$239$		−	1399.01i		−	0.378637i	−0.981916	−	0.189318i	$-0.939372\pi$
$239$		−	1399.01i		−	0.378637i	0.981916	−	0.189318i	$-0.0606278\pi$
$240$		0			0
$241$			3174.48i			0.848489i	0.905548	+	0.424245i	$0.139460\pi$
$241$			3174.48i			0.848489i	−0.905548	+	0.424245i	$0.860540\pi$
$242$		0			0
$243$	−4888.24	−	11801.2i	−1.29046	−	3.11543i
$244$		0			0
$245$	−442.642	−	183.348i	−0.115426	−	0.0478110i
$246$		0			0
$247$	1160.95	−	1160.95i	0.299067	−	0.299067i
$248$		0			0
$249$	2179.92	+	2179.92i	0.554807	+	0.554807i
$250$		0			0
$251$	1838.48	−	4438.47i	0.462325	−	1.11615i	−0.505115	−	0.863052i	$-0.668550\pi$
$251$	1838.48	−	4438.47i	0.462325	−	1.11615i	0.967440	−	0.253100i	$-0.0814500\pi$
$252$		0			0
$253$	−436.424	+	180.773i	−0.108450	+	0.0449213i
$254$		0			0
$255$	−134.130			−0.0329393
$256$		0			0
$257$	−1173.76			−0.284891			−0.142446	−	0.989803i	$-0.545497\pi$
$257$	−1173.76			−0.284891			−0.142446	+	0.989803i	$0.545497\pi$
$258$		0			0
$259$	58.1145	−	24.0718i	0.0139423	−	0.00577510i
$260$		0			0
$261$	−4481.27	+	10818.7i	−1.06277	+	2.56576i
$262$		0			0
$263$	−3801.01	−	3801.01i	−0.891181	−	0.891181i	0.103453	−	0.994634i	$-0.467011\pi$
$263$	−3801.01	−	3801.01i	−0.891181	−	0.891181i	−0.994634	+	0.103453i	$0.967011\pi$
$264$		0			0
$265$	−238.898	+	238.898i	−0.0553787	+	0.0553787i
$266$		0			0
$267$	2488.07	+	1030.59i	0.570290	+	0.236222i
$268$		0			0
$269$	−1395.29	−	3368.54i	−0.316255	−	0.763506i	−0.999446	−	0.0332674i	$-0.989409\pi$
$269$	−1395.29	−	3368.54i	−0.316255	−	0.763506i	0.683192	−	0.730239i	$-0.260591\pi$
$270$		0			0
$271$			5189.02i			1.16314i	0.813497	+	0.581569i	$0.197561\pi$
$271$			5189.02i			1.16314i	−0.813497	+	0.581569i	$0.802439\pi$
$272$		0			0
$273$		−	5469.02i		−	1.21246i
$274$		0			0
$275$	−181.444	−	438.044i	−0.0397871	−	0.0960546i
$276$		0			0
$277$	1901.90	+	787.793i	0.412542	+	0.170880i	0.579294	−	0.815118i	$-0.303328\pi$
$277$	1901.90	+	787.793i	0.412542	+	0.170880i	−0.166753	+	0.985999i	$0.553328\pi$
$278$		0			0
$279$	−7195.25	+	7195.25i	−1.54397	+	1.54397i
$280$		0			0
$281$	−150.416	−	150.416i	−0.0319326	−	0.0319326i	0.690960	−	0.722893i	$-0.257188\pi$
$281$	−150.416	−	150.416i	−0.0319326	−	0.0319326i	−0.722893	+	0.690960i	$0.757188\pi$
$282$		0			0
$283$	−861.255	+	2079.25i	−0.180906	+	0.436745i	−0.988154	−	0.153468i	$-0.950956\pi$
$283$	−861.255	+	2079.25i	−0.180906	+	0.436745i	0.807248	+	0.590212i	$0.200956\pi$
$284$		0			0
$285$	−1701.33	+	704.714i	−0.353607	+	0.146469i
$286$		0			0
$287$	280.384			0.0576675
$288$		0			0
$289$	4888.47			0.995007
$290$		0			0
$291$	−353.491	+	146.421i	−0.0712096	+	0.0294960i
$292$		0			0
$293$	3360.08	−	8111.94i	0.669958	−	1.61742i	−0.111720	−	0.993740i	$-0.535636\pi$
$293$	3360.08	−	8111.94i	0.669958	−	1.61742i	0.781678	−	0.623682i	$-0.214364\pi$
$294$		0			0
$295$	−625.480	−	625.480i	−0.123447	−	0.123447i
$296$		0			0
$297$	−1272.25	+	1272.25i	−0.248563	+	0.248563i
$298$		0			0
$299$	−2613.19	−	1082.42i	−0.505433	−	0.209357i
$300$		0			0
$301$	−2736.81	−	6607.24i	−0.524076	−	1.26523i
$302$		0			0
$303$			2187.39i			0.414726i
$304$		0			0
$305$			660.143i			0.123933i
$306$		0			0
$307$	1677.95	+	4050.92i	0.311939	+	0.753088i	0.999633	+	0.0270874i	$0.00862323\pi$
$307$	1677.95	+	4050.92i	0.311939	+	0.753088i	−0.687694	+	0.726001i	$0.741377\pi$
$308$		0			0
$309$	580.593	+	240.489i	0.106889	+	0.0442749i
$310$		0			0
$311$	5768.23	−	5768.23i	1.05172	−	1.05172i	0.0531374	−	0.998587i	$-0.483078\pi$
$311$	5768.23	−	5768.23i	1.05172	−	1.05172i	0.998587	−	0.0531374i	$-0.0169221\pi$
$312$		0			0
$313$	−7050.86	−	7050.86i	−1.27329	−	1.27329i	−0.944354	−	0.328932i	$-0.893311\pi$
$313$	−7050.86	−	7050.86i	−1.27329	−	1.27329i	−0.328932	−	0.944354i	$-0.606689\pi$
$314$		0			0
$315$	−1706.41	+	4119.63i	−0.305223	+	0.736872i
$316$		0			0
$317$	7491.90	−	3103.25i	1.32740	−	0.549828i	0.397490	−	0.917607i	$-0.369881\pi$
$317$	7491.90	−	3103.25i	1.32740	−	0.549828i	0.929914	+	0.367778i	$0.119881\pi$
$318$		0			0
$319$	656.981			0.115310
$320$		0			0
$321$	−11396.1			−1.98153
$322$		0			0
$323$	−311.159	+	128.886i	−0.0536018	+	0.0222026i
$324$		0			0
$325$	1086.43	−	2622.88i	0.185429	−	0.447666i
$326$		0			0
$327$	11255.1	+	11255.1i	1.90339	+	1.90339i
$328$		0			0
$329$	7251.02	−	7251.02i	1.21508	−	1.21508i
$330$		0			0
$331$	7331.81	+	3036.94i	1.21750	+	0.504305i	0.896614	−	0.442812i	$-0.146019\pi$
$331$	7331.81	+	3036.94i	1.21750	+	0.504305i	0.320887	+	0.947118i	$0.396019\pi$
$332$		0			0
$333$	−75.9499	−	183.359i	−0.0124986	−	0.0301742i
$334$		0			0
$335$		−	601.772i		−	0.0981442i
$336$		0			0
$337$			7378.47i			1.19267i	0.802734	+	0.596337i	$0.203378\pi$
$337$			7378.47i			1.19267i	−0.802734	+	0.596337i	$0.796622\pi$
$338$		0			0
$339$	6720.30	+	16224.2i	1.07669	+	2.59935i
$340$		0			0
$341$	527.433	+	218.470i	0.0837598	+	0.0346945i
$342$		0			0
$343$	2691.30	−	2691.30i	0.423664	−	0.423664i
$344$		0			0
$345$	2243.29	+	2243.29i	0.350071	+	0.350071i
$346$		0			0
$347$	3076.51	−	7427.35i	0.475953	−	1.14905i	−0.485538	−	0.874216i	$-0.661376\pi$
$347$	3076.51	−	7427.35i	0.475953	−	1.14905i	0.961491	−	0.274837i	$-0.0886238\pi$
$348$		0			0
$349$	−1966.92	+	814.725i	−0.301682	+	0.124961i	−0.528389	−	0.849002i	$-0.677204\pi$
$349$	−1966.92	+	814.725i	−0.301682	+	0.124961i	0.226708	+	0.973963i	$0.427204\pi$
$350$		0			0
$351$	−10773.3			−1.63828
$352$		0			0
$353$	−1477.00			−0.222699			−0.111349	−	0.993781i	$-0.535517\pi$
$353$	−1477.00			−0.222699			−0.111349	+	0.993781i	$0.535517\pi$
$354$		0			0
$355$	2157.48	−	893.656i	0.322555	−	0.133607i
$356$		0			0
$357$	−429.327	+	1036.49i	−0.0636482	+	0.153660i
$358$		0			0
$359$	420.351	+	420.351i	0.0617975	+	0.0617975i	0.737330	−	0.675533i	$-0.236086\pi$
$359$	420.351	+	420.351i	0.0617975	+	0.0617975i	−0.675533	+	0.737330i	$0.736086\pi$
$360$		0			0
$361$	1580.40	−	1580.40i	0.230412	−	0.230412i
$362$		0			0
$363$	−12078.0	−	5002.87i	−1.74636	−	0.723368i
$364$		0			0
$365$	−783.972	−	1892.68i	−0.112425	−	0.271417i
$366$		0			0
$367$		−	3772.74i		−	0.536609i	−0.963334	−	0.268304i	$-0.913537\pi$
$367$		−	3772.74i		−	0.536609i	0.963334	−	0.268304i	$-0.0864633\pi$
$368$		0			0
$369$		−	884.651i		−	0.124805i
$370$		0			0
$371$	1081.41	+	2610.76i	0.151332	+	0.365347i
$372$		0			0
$373$	−3035.70	−	1257.43i	−0.421401	−	0.174550i	0.161898	−	0.986808i	$-0.448238\pi$
$373$	−3035.70	−	1257.43i	−0.421401	−	0.174550i	−0.583299	+	0.812257i	$0.698238\pi$
$374$		0			0
$375$	−4645.26	+	4645.26i	−0.639680	+	0.639680i
$376$		0			0
$377$	2781.63	+	2781.63i	0.380003	+	0.380003i
$378$		0			0
$379$	−3316.86	+	8007.62i	−0.449540	+	1.08529i	0.522954	+	0.852361i	$0.324830\pi$
$379$	−3316.86	+	8007.62i	−0.449540	+	1.08529i	−0.972495	+	0.232926i	$0.925170\pi$
$380$		0			0
$381$	−18705.1	+	7747.91i	−2.51520	+	1.04183i
$382$		0			0
$383$	1353.16			0.180531			0.0902655	−	0.995918i	$-0.471228\pi$
$383$	1353.16			0.180531			0.0902655	+	0.995918i	$0.471228\pi$
$384$		0			0
$385$	250.169			0.0331164
$386$		0			0
$387$	−20846.7	+	8635.00i	−2.73824	+	1.13422i
$388$		0			0
$389$	2191.72	−	5291.29i	0.285668	−	0.689663i	−0.714280	−	0.699860i	$-0.753246\pi$
$389$	2191.72	−	5291.29i	0.285668	−	0.689663i	0.999948	+	0.0101966i	$0.00324575\pi$
$390$		0			0
$391$	410.279	+	410.279i	0.0530657	+	0.0530657i
$392$		0			0
$393$	−9130.25	+	9130.25i	−1.17191	+	1.17191i
$394$		0			0
$395$	−2828.17	−	1171.47i	−0.360254	−	0.149222i
$396$		0			0
$397$	−3949.31	−	9534.47i	−0.499270	−	1.20534i	−0.949878	−	0.312622i	$-0.898793\pi$
$397$	−3949.31	−	9534.47i	−0.499270	−	1.20534i	0.450608	−	0.892722i	$-0.351207\pi$
$398$		0			0
$399$			15402.7i			1.93258i
$400$		0			0
$401$		−	4554.46i		−	0.567179i	−0.958946	−	0.283589i	$-0.908475\pi$
$401$		−	4554.46i		−	0.567179i	0.958946	−	0.283589i	$-0.0915253\pi$
$402$		0			0
$403$	1308.14	+	3158.12i	0.161695	+	0.390366i
$404$		0			0
$405$	6280.86	+	2601.62i	0.770614	+	0.319199i
$406$		0			0
$407$	−7.87342	+	7.87342i	−0.000958897	+	0.000958897i
$408$		0			0
$409$	33.1152	+	33.1152i	0.00400353	+	0.00400353i	0.709106	−	0.705102i	$-0.249099\pi$
$409$	33.1152	+	33.1152i	0.00400353	+	0.00400353i	−0.705102	+	0.709106i	$0.749099\pi$
$410$		0			0
$411$	7295.68	−	17613.3i	0.875595	−	2.11387i
$412$		0			0
$413$	−6835.47	+	2831.34i	−0.814410	+	0.337340i
$414$		0			0
$415$	−844.387			−0.0998779
$416$		0			0
$417$	−20689.8			−2.42969
$418$		0			0
$419$	−2013.38	+	833.970i	−0.234750	+	0.0972366i	−0.496957	−	0.867775i	$-0.665549\pi$
$419$	−2013.38	+	833.970i	−0.234750	+	0.0972366i	0.262208	+	0.965011i	$0.415549\pi$
$420$		0			0
$421$	−3306.30	+	7982.11i	−0.382753	+	0.924048i	0.608678	+	0.793417i	$0.291700\pi$
$421$	−3306.30	+	7982.11i	−0.382753	+	0.924048i	−0.991431	+	0.130630i	$0.958300\pi$
$422$		0			0
$423$	−22878.0	−	22878.0i	−2.62970	−	2.62970i
$424$		0			0
$425$	−411.801	+	411.801i	−0.0470007	+	0.0470007i
$426$		0			0
$427$	5101.26	+	2113.01i	0.578144	+	0.239475i
$428$		0			0
$429$	370.475	+	894.406i	0.0416939	+	0.100658i
$430$		0			0
$431$		−	9873.54i		−	1.10346i	−0.834023	−	0.551730i	$-0.813968\pi$
$431$		−	9873.54i		−	1.10346i	0.834023	−	0.551730i	$-0.186032\pi$
$432$		0			0
$433$		−	5282.14i		−	0.586244i	−0.956075	−	0.293122i	$-0.905306\pi$
$433$		−	5282.14i		−	0.586244i	0.956075	−	0.293122i	$-0.0946942\pi$
$434$		0			0
$435$	−1688.49	−	4076.38i	−0.186108	−	0.449304i
$436$		0			0
$437$	7359.67	+	3048.47i	0.805631	+	0.333703i
$438$		0			0
$439$	6855.89	−	6855.89i	0.745361	−	0.745361i	−0.228243	−	0.973604i	$-0.573298\pi$
$439$	6855.89	−	6855.89i	0.745361	−	0.745361i	0.973604	+	0.228243i	$0.0732981\pi$
$440$		0			0
$441$	8940.55	+	8940.55i	0.965398	+	0.965398i
$442$		0			0
$443$	−1317.55	+	3180.85i	−0.141306	+	0.341144i	−0.978650	−	0.205533i	$-0.934107\pi$
$443$	−1317.55	+	3180.85i	−0.141306	+	0.341144i	0.837344	+	0.546676i	$0.184107\pi$
$444$		0			0
$445$	−681.473	+	282.275i	−0.0725954	+	0.0300700i
$446$		0			0
$447$	28795.7			3.04695
$448$		0			0
$449$	9878.91			1.03834			0.519170	−	0.854671i	$-0.326241\pi$
$449$	9878.91			1.03834			0.519170	+	0.854671i	$0.326241\pi$
$450$		0			0
$451$	−45.8541	+	18.9934i	−0.00478755	+	0.00198307i
$452$		0			0
$453$	5395.02	−	13024.7i	0.559559	−	1.35090i
$454$		0			0
$455$	1059.21	+	1059.21i	0.109135	+	0.109135i
$456$		0			0
$457$	−8688.50	+	8688.50i	−0.889346	+	0.889346i	−0.994460	−	0.105114i	$-0.966479\pi$
$457$	−8688.50	+	8688.50i	−0.889346	+	0.889346i	0.105114	+	0.994460i	$0.466479\pi$
$458$		0			0
$459$	2041.75	+	845.721i	0.207627	+	0.0860019i
$460$		0			0
$461$	6980.91	+	16853.4i	0.705279	+	1.70269i	0.711474	+	0.702712i	$0.248028\pi$
$461$	6980.91	+	16853.4i	0.705279	+	1.70269i	−0.00619552	+	0.999981i	$0.501972\pi$
$462$		0			0
$463$			2685.83i			0.269592i	0.990873	+	0.134796i	$0.0430379\pi$
$463$			2685.83i			0.269592i	−0.990873	+	0.134796i	$0.956962\pi$
$464$		0			0
$465$		−	3834.05i		−	0.382366i
$466$		0			0
$467$	−2304.77	−	5564.22i	−0.228377	−	0.551352i	0.767603	−	0.640926i	$-0.221449\pi$
$467$	−2304.77	−	5564.22i	−0.228377	−	0.551352i	−0.995980	+	0.0895741i	$0.971449\pi$
$468$		0			0
$469$	−4650.20	−	1926.18i	−0.457838	−	0.189643i
$470$		0			0
$471$	−19416.5	+	19416.5i	−1.89950	+	1.89950i
$472$		0			0
$473$	895.156	+	895.156i	0.0870176	+	0.0870176i
$474$		0			0
$475$	−3059.78	+	7386.97i	−0.295563	+	0.713553i
$476$		0			0
$477$	8237.29	−	3412.00i	0.790691	−	0.327515i
$478$		0			0
$479$	4443.51			0.423860			0.211930	−	0.977285i	$-0.432025\pi$
$479$	4443.51			0.423860			0.211930	+	0.977285i	$0.432025\pi$
$480$		0			0
$481$	−66.6715			−0.00632008
$482$		0			0
$483$	24515.4	−	10154.6i	2.30950	−	0.956628i
$484$		0			0
$485$	40.1041	−	96.8198i	0.00375470	−	0.00906466i
$486$		0			0
$487$	4194.56	+	4194.56i	0.390295	+	0.390295i	0.874793	−	0.484498i	$-0.160998\pi$
$487$	4194.56	+	4194.56i	0.390295	+	0.390295i	−0.484498	+	0.874793i	$0.660998\pi$
$488$		0			0
$489$	6225.15	−	6225.15i	0.575687	−	0.575687i
$490$		0			0
$491$	−1215.45	−	503.456i	−0.111716	−	0.0462742i	0.326125	−	0.945327i	$-0.394257\pi$
$491$	−1215.45	−	503.456i	−0.111716	−	0.0462742i	−0.437841	+	0.899052i	$0.644257\pi$
$492$		0			0
$493$	−308.811	−	745.537i	−0.0282113	−	0.0681081i
$494$		0			0
$495$		−	789.318i		−	0.0716711i
$496$		0			0
$497$		−	19532.4i		−	1.76287i
$498$		0			0
$499$	−6127.16	−	14792.3i	−0.549678	−	1.32704i	−0.917719	−	0.397231i	$-0.869971\pi$
$499$	−6127.16	−	14792.3i	−0.549678	−	1.32704i	0.368040	−	0.929810i	$-0.380029\pi$
$500$		0			0
$501$	−6082.05	−	2519.27i	−0.542368	−	0.224656i
$502$		0			0
$503$	−11805.3	+	11805.3i	−1.04647	+	1.04647i	−0.0475998	+	0.998866i	$0.515157\pi$
$503$	−11805.3	+	11805.3i	−1.04647	+	1.04647i	−0.998866	+	0.0475998i	$0.984843\pi$
$504$		0			0
$505$	−423.639	−	423.639i	−0.0373301	−	0.0373301i
$506$		0			0
$507$	6141.76	−	14827.5i	0.537998	−	1.29884i
$508$		0			0
$509$	3708.64	−	1536.17i	0.322952	−	0.133771i	−0.215317	−	0.976544i	$-0.569079\pi$
$509$	3708.64	−	1536.17i	0.322952	−	0.133771i	0.538269	+	0.842773i	$0.319079\pi$
$510$		0			0
$511$	−17135.0			−1.48338
$512$		0			0
$513$	30341.4			2.61132
$514$		0			0
$515$	−159.022	+	65.8691i	−0.0136065	+	0.00563600i
$516$		0			0
$517$	−694.645	+	1677.02i	−0.0590918	+	0.142660i
$518$		0			0
$519$	3193.73	+	3193.73i	0.270114	+	0.270114i
$520$		0			0
$521$	14817.7	−	14817.7i	1.24602	−	1.24602i	0.288553	−	0.957464i	$-0.406826\pi$
$521$	14817.7	−	14817.7i	1.24602	−	1.24602i	0.957464	−	0.288553i	$-0.0931743\pi$
$522$		0			0
$523$	11999.0	+	4970.15i	1.00321	+	0.415544i	0.822974	−	0.568079i	$-0.192313\pi$
$523$	11999.0	+	4970.15i	1.00321	+	0.415544i	0.180238	+	0.983623i	$0.442313\pi$
$524$		0			0
$525$	10192.3	+	24606.4i	0.847292	+	2.04554i
$526$		0			0
$527$		−	701.218i		−	0.0579611i
$528$		0			0
$529$		−	1556.65i		−	0.127940i
$530$		0			0
$531$	8933.28	+	21566.8i	0.730077	+	1.76256i
$532$		0			0
$533$	−274.562	−	113.727i	−0.0223126	−	0.00924216i
$534$		0			0
$535$	2207.13	−	2207.13i	0.178360	−	0.178360i
$536$		0			0
$537$	4212.05	+	4212.05i	0.338479	+	0.338479i
$538$		0			0
$539$	271.463	−	655.369i	0.0216934	−	0.0523724i
$540$		0			0
$541$	21190.9	−	8777.58i	1.68405	−	0.697556i	0.684542	−	0.728974i	$-0.260002\pi$
$541$	21190.9	−	8777.58i	1.68405	−	0.697556i	0.999506	+	0.0314181i	$0.0100023\pi$
$542$		0			0
$543$	28856.7			2.28059
$544$		0			0
$545$	−4359.63			−0.342653
$546$		0			0
$547$	−1671.23	+	692.246i	−0.130634	+	0.0541103i	−0.447043	−	0.894513i	$-0.647523\pi$
$547$	−1671.23	+	692.246i	−0.130634	+	0.0541103i	0.316409	+	0.948623i	$0.397523\pi$
$548$		0			0
$549$	6666.84	−	16095.2i	0.518277	−	1.25123i
$550$		0			0
$551$	−7834.06	−	7834.06i	−0.605703	−	0.605703i
$552$		0			0
$553$	−18105.0	+	18105.0i	−1.39223	+	1.39223i
$554$		0			0
$555$	69.0876	+	28.6170i	0.00528397	+	0.00218869i
$556$		0			0
$557$	−640.204	−	1545.59i	−0.0487008	−	0.117574i	0.897657	−	0.440695i	$-0.145268\pi$
$557$	−640.204	−	1545.59i	−0.0487008	−	0.117574i	−0.946358	+	0.323121i	$0.895268\pi$
$558$		0			0
$559$			7580.11i			0.573532i
$560$		0			0
$561$		−	198.590i		−	0.0149456i
$562$		0			0
$563$	−4815.18	−	11624.9i	−0.360454	−	0.870212i	−0.995234	−	0.0975194i	$-0.968909\pi$
$563$	−4815.18	−	11624.9i	−0.360454	−	0.870212i	0.634780	−	0.772693i	$-0.281091\pi$
$564$		0			0
$565$	−4443.75	−	1840.66i	−0.330885	−	0.137057i
$566$		0			0
$567$	40208.1	−	40208.1i	2.97809	−	2.97809i
$568$		0			0
$569$	7097.42	+	7097.42i	0.522916	+	0.522916i	0.918451	−	0.395535i	$-0.129441\pi$
$569$	7097.42	+	7097.42i	0.522916	+	0.522916i	−0.395535	+	0.918451i	$0.629441\pi$
$570$		0			0
$571$	5352.89	−	12923.0i	0.392314	−	0.947131i	−0.597120	−	0.802152i	$-0.703689\pi$
$571$	5352.89	−	12923.0i	0.392314	−	0.947131i	0.989435	−	0.144979i	$-0.0463115\pi$
$572$		0			0
$573$	−28777.5	+	11920.0i	−2.09808	+	0.869053i
$574$		0			0
$575$	13774.6			0.999024
$576$		0			0
$577$	21684.6			1.56454			0.782270	−	0.622939i	$-0.214062\pi$
$577$	21684.6			1.56454			0.782270	+	0.622939i	$0.214062\pi$
$578$		0			0
$579$	−12385.5	+	5130.22i	−0.888984	+	0.368229i
$580$		0			0
$581$	−2702.75	+	6525.01i	−0.192993	+	0.465926i
$582$		0			0
$583$	−353.708	−	353.708i	−0.0251271	−	0.0251271i
$584$		0			0
$585$	3341.94	−	3341.94i	0.236192	−	0.236192i
$586$		0			0
$587$	−12411.2	−	5140.88i	−0.872682	−	0.361477i	−0.0990279	−	0.995085i	$-0.531573\pi$
$587$	−12411.2	−	5140.88i	−0.872682	−	0.361477i	−0.773654	+	0.633608i	$0.781573\pi$
$588$		0			0
$589$	−3684.18	−	8894.40i	−0.257732	−	0.622220i
$590$		0			0
$591$		−	31157.9i		−	2.16864i
$592$		0			0
$593$			10264.2i			0.710794i	0.934715	+	0.355397i	$0.115654\pi$
$593$			10264.2i			0.710794i	−0.934715	+	0.355397i	$0.884346\pi$
$594$		0			0
$595$	−117.591	−	283.890i	−0.00810212	−	0.0195603i
$596$		0			0
$597$	38110.5	+	15785.9i	2.61266	+	1.08220i
$598$		0			0
$599$	−10373.9	+	10373.9i	−0.707625	+	0.707625i	−0.966035	−	0.258411i	$-0.916801\pi$
$599$	−10373.9	+	10373.9i	−0.707625	+	0.707625i	0.258411	+	0.966035i	$0.416801\pi$
$600$		0			0
$601$	8644.23	+	8644.23i	0.586698	+	0.586698i	0.936736	−	0.350038i	$-0.113831\pi$
$601$	8644.23	+	8644.23i	0.586698	+	0.586698i	−0.350038	+	0.936736i	$0.613831\pi$
$602$		0			0
$603$	−6077.35	+	14672.0i	−0.410429	+	0.990863i
$604$		0			0
$605$	3308.12	−	1370.27i	0.222304	−	0.0920814i
$606$		0			0
$607$	−17807.3			−1.19073			−0.595367	−	0.803454i	$-0.702993\pi$
$607$	−17807.3			−1.19073			−0.595367	+	0.803454i	$0.702993\pi$
$608$		0			0
$609$	−36904.8			−2.45560
$610$		0			0
$611$	−10041.5	+	4159.35i	−0.664873	+	0.275400i
$612$		0			0
$613$	−6385.20	+	15415.2i	−0.420711	+	1.01569i	0.561428	+	0.827526i	$0.310252\pi$
$613$	−6385.20	+	15415.2i	−0.420711	+	1.01569i	−0.982138	+	0.188160i	$0.939748\pi$
$614$		0			0
$615$	235.697	+	235.697i	0.0154540	+	0.0154540i
$616$		0			0
$617$	−5629.64	+	5629.64i	−0.367327	+	0.367327i	−0.866502	−	0.499174i	$-0.833637\pi$
$617$	−5629.64	+	5629.64i	−0.367327	+	0.367327i	0.499174	+	0.866502i	$0.333637\pi$
$618$		0			0
$619$	5609.95	+	2323.72i	0.364270	+	0.150885i	0.557308	−	0.830306i	$-0.311834\pi$
$619$	5609.95	+	2323.72i	0.364270	+	0.150885i	−0.193039	+	0.981191i	$0.561834\pi$
$620$		0			0
$621$	−20003.3	−	48292.3i	−1.29260	−	3.12062i
$622$		0			0
$623$			6169.61i			0.396758i
$624$		0			0
$625$			12898.5i			0.825504i
$626$		0			0
$627$	−1043.39	−	2518.96i	−0.0664576	−	0.160443i
$628$		0			0
$629$	12.6356	+	5.23382i	0.000800974	+	0.000331774i
$630$		0			0
$631$	−239.580	+	239.580i	−0.0151149	+	0.0151149i	−0.714624	−	0.699509i	$-0.753402\pi$
$631$	−239.580	+	239.580i	−0.0151149	+	0.0151149i	0.699509	+	0.714624i	$0.253402\pi$
$632$		0			0
$633$	−22534.1	−	22534.1i	−1.41493	−	1.41493i
$634$		0			0
$635$	2122.12	−	5123.25i	0.132620	−	0.320173i
$636$		0			0
$637$	3924.17	−	1625.44i	0.244084	−	0.101103i
$638$		0			0
$639$	−61627.3			−3.81524
$640$		0			0
$641$	−26789.7			−1.65075			−0.825373	−	0.564588i	$-0.809035\pi$
$641$	−26789.7			−1.65075			−0.825373	+	0.564588i	$0.809035\pi$
$642$		0			0
$643$	−7545.62	+	3125.50i	−0.462784	+	0.191691i	−0.601878	−	0.798588i	$-0.705581\pi$
$643$	−7545.62	+	3125.50i	−0.462784	+	0.191691i	0.139094	+	0.990279i	$0.455581\pi$
$644$		0			0
$645$	3253.57	−	7854.80i	0.198619	−	0.479508i
$646$		0			0
$647$	−796.707	−	796.707i	−0.0484108	−	0.0484108i	0.682487	−	0.730898i	$-0.260898\pi$
$647$	−796.707	−	796.707i	−0.0484108	−	0.0484108i	−0.730898	+	0.682487i	$0.760898\pi$
$648$		0			0
$649$	926.077	−	926.077i	0.0560119	−	0.0560119i
$650$		0			0
$651$	−29627.7	−	12272.2i	−1.78372	−	0.738840i
$652$		0			0
$653$	10441.9	+	25208.9i	0.625761	+	1.51072i	0.844842	+	0.535015i	$0.179694\pi$
$653$	10441.9	+	25208.9i	0.625761	+	1.51072i	−0.219081	+	0.975707i	$0.570306\pi$
$654$		0			0
$655$		−	3536.58i		−	0.210970i
$656$		0			0
$657$			54063.4i			3.21037i
$658$		0			0
$659$	3151.27	+	7607.83i	0.186276	+	0.449710i	0.989237	−	0.146321i	$-0.0467433\pi$
$659$	3151.27	+	7607.83i	0.186276	+	0.449710i	−0.802961	+	0.596031i	$0.796743\pi$
$660$		0			0
$661$	−21445.8	−	8883.13i	−1.26194	−	0.522714i	−0.351437	−	0.936212i	$-0.614307\pi$
$661$	−21445.8	−	8883.13i	−1.26194	−	0.522714i	−0.910505	+	0.413498i	$0.864307\pi$
$662$		0			0
$663$	840.824	−	840.824i	0.0492532	−	0.0492532i
$664$		0			0
$665$	−2983.10	−	2983.10i	−0.173954	−	0.173954i
$666$		0			0
$667$	−7304.13	+	17633.7i	−0.424013	+	1.02366i
$668$		0			0
$669$	11188.6	−	4634.46i	0.646600	−	0.267830i
$670$		0			0
$671$	−977.399			−0.0562326
$672$		0			0
$673$	6604.78			0.378300			0.189150	−	0.981948i	$-0.439427\pi$
$673$	6604.78			0.378300			0.189150	+	0.981948i	$0.439427\pi$
$674$		0			0
$675$	48471.5	−	20077.5i	2.76395	−	1.14487i
$676$		0			0
$677$	−8312.44	+	20068.0i	−0.471895	+	1.13926i	0.491429	+	0.870918i	$0.336475\pi$
$677$	−8312.44	+	20068.0i	−0.471895	+	1.13926i	−0.963325	+	0.268339i	$0.913525\pi$
$678$		0			0
$679$	−619.809	−	619.809i	−0.0350311	−	0.0350311i
$680$		0			0
$681$	40342.0	−	40342.0i	2.27006	−	2.27006i
$682$		0			0
$683$	15192.4	+	6292.91i	0.851130	+	0.352550i	0.765232	−	0.643754i	$-0.222624\pi$
$683$	15192.4	+	6292.91i	0.851130	+	0.352550i	0.0858980	+	0.996304i	$0.472624\pi$
$684$		0			0
$685$	1998.26	+	4824.22i	0.111459	+	0.269086i
$686$		0			0
$687$			30646.9i			1.70197i
$688$		0			0
$689$		−	2995.17i		−	0.165613i
$690$		0			0
$691$	−4613.08	−	11137.0i	−0.253965	−	0.613125i	0.744552	−	0.667564i	$-0.232663\pi$
$691$	−4613.08	−	11137.0i	−0.253965	−	0.613125i	−0.998517	+	0.0544388i	$0.982663\pi$
$692$		0			0
$693$	−6099.46	−	2526.48i	−0.334343	−	0.138489i
$694$		0			0
$695$	4007.07	−	4007.07i	0.218700	−	0.218700i
$696$		0			0
$697$	43.1071	+	43.1071i	0.00234261	+	0.00234261i
$698$		0			0
$699$	−2132.15	+	5147.48i	−0.115373	+	0.278534i
$700$		0			0
$701$	−9901.90	+	4101.50i	−0.533509	+	0.220987i	−0.633139	−	0.774038i	$-0.718234\pi$
$701$	−9901.90	+	4101.50i	−0.533509	+	0.220987i	0.0996304	+	0.995025i	$0.468234\pi$
$702$		0			0
$703$	187.771			0.0100738
$704$		0			0
$705$	12190.7			0.651247
$706$		0			0
$707$	−4629.68	+	1917.68i	−0.246276	+	0.102011i
$708$		0			0
$709$	−10381.2	+	25062.4i	−0.549893	+	1.32756i	0.367665	+	0.929958i	$0.380157\pi$
$709$	−10381.2	+	25062.4i	−0.549893	+	1.32756i	−0.917558	+	0.397601i	$0.869843\pi$
$710$		0			0
$711$	57123.8	+	57123.8i	3.01309	+	3.01309i
$712$		0			0
$713$	−11727.7	+	11727.7i	−0.615997	+	0.615997i
$714$		0			0
$715$	−244.974	−	101.472i	−0.0128133	−	0.00530745i
$716$		0			0
$717$	−5323.52	−	12852.1i	−0.277281	−	0.669416i
$718$		0			0
$719$		−	33977.2i		−	1.76236i	−0.472782	−	0.881179i	$-0.656750\pi$
$719$		−	33977.2i		−	1.76236i	0.472782	−	0.881179i	$-0.343250\pi$
$720$		0			0
$721$			1439.68i			0.0743641i
$722$		0			0
$723$	12079.6	+	29162.6i	0.621361	+	1.50010i
$724$		0			0
$725$	−17699.1	−	7331.23i	−0.906662	−	0.375552i
$726$		0			0
$727$	5598.51	−	5598.51i	0.285608	−	0.285608i	−0.549732	−	0.835341i	$-0.685270\pi$
$727$	5598.51	−	5598.51i	0.285608	−	0.285608i	0.835341	+	0.549732i	$0.185270\pi$
$728$		0			0
$729$	−42155.5	−	42155.5i	−2.14172	−	2.14172i
$730$		0			0
$731$	595.051	−	1436.58i	0.0301077	−	0.0726865i
$732$		0			0
$733$	27180.8	−	11258.7i	1.36964	−	0.567324i	0.427951	−	0.903802i	$-0.359236\pi$
$733$	27180.8	−	11258.7i	1.36964	−	0.567324i	0.941691	+	0.336478i	$0.109236\pi$
$734$		0			0
$735$	−4764.05			−0.239081
$736$		0			0
$737$	890.975			0.0445312
$738$		0			0
$739$	−17662.9	+	7316.20i	−0.879214	+	0.364182i	−0.776192	−	0.630497i	$-0.782851\pi$
$739$	−17662.9	+	7316.20i	−0.879214	+	0.364182i	−0.103022	+	0.994679i	$0.532851\pi$
$740$		0			0
$741$	6247.52	−	15082.9i	0.309728	−	0.747750i
$742$		0			0
$743$	3418.11	+	3418.11i	0.168773	+	0.168773i	0.786440	−	0.617667i	$-0.211922\pi$
$743$	3418.11	+	3418.11i	0.168773	+	0.168773i	−0.617667	+	0.786440i	$0.711922\pi$
$744$		0			0
$745$	−5576.97	+	5576.97i	−0.274261	+	0.274261i
$746$		0			0
$747$	20587.3	+	8527.54i	1.00837	+	0.417679i
$748$		0			0
$749$	−9990.95	−	24120.3i	−0.487399	−	1.17668i
$750$		0			0
$751$			3348.22i			0.162687i	0.996686	+	0.0813437i	$0.0259211\pi$
$751$			3348.22i			0.162687i	−0.996686	+	0.0813437i	$0.974079\pi$
$752$		0			0
$753$		−	47770.3i		−	2.31188i
$754$		0			0
$755$	1477.68	+	3567.43i	0.0712293	+	0.171963i
$756$		0			0
$757$	15054.7	+	6235.84i	0.722815	+	0.299400i	0.713596	−	0.700558i	$-0.247065\pi$
$757$	15054.7	+	6235.84i	0.722815	+	0.299400i	0.00921923	+	0.999958i	$0.497065\pi$
$758$		0			0
$759$	−3321.38	+	3321.38i	−0.158838	+	0.158838i
$760$		0			0
$761$	9967.70	+	9967.70i	0.474808	+	0.474808i	0.903467	−	0.428658i	$-0.141014\pi$
$761$	9967.70	+	9967.70i	0.474808	+	0.474808i	−0.428658	+	0.903467i	$0.641014\pi$
$762$		0			0
$763$	−13954.5	+	33689.1i	−0.662104	+	1.59846i
$764$		0			0
$765$	−895.711	+	371.016i	−0.0423327	+	0.0175348i
$766$		0			0
$767$	7841.95			0.369174
$768$		0			0
$769$	22151.8			1.03877			0.519386	−	0.854540i	$-0.326161\pi$
$769$	22151.8			1.03877			0.519386	+	0.854540i	$0.326161\pi$
$770$		0			0
$771$	−10782.8	+	4466.40i	−0.503677	+	0.208630i
$772$		0			0
$773$	12270.7	−	29624.1i	0.570953	−	1.37840i	−0.329792	−	0.944053i	$-0.606979\pi$
$773$	12270.7	−	29624.1i	0.570953	−	1.37840i	0.900745	−	0.434348i	$-0.143021\pi$
$774$		0			0
$775$	−11771.2	−	11771.2i	−0.545593	−	0.545593i
$776$		0			0
$777$	442.276	−	442.276i	0.0204203	−	0.0204203i
$778$		0			0
$779$	773.263	+	320.296i	0.0355649	+	0.0147315i
$780$		0			0
$781$	1323.13	+	3194.33i	0.0606216	+	0.146354i
$782$		0			0
$783$			72697.9i			3.31802i
$784$		0			0
$785$		−	7520.92i		−	0.341953i
$786$		0			0
$787$	−9623.88	−	23234.1i	−0.435901	−	1.05236i	−0.977351	−	0.211626i	$-0.932124\pi$
$787$	−9623.88	−	23234.1i	−0.435901	−	1.05236i	0.541449	−	0.840733i	$-0.317876\pi$
$788$		0			0
$789$	−49382.1	−	20454.7i	−2.22820	−	0.922950i
$790$		0			0
$791$	−28447.5	+	28447.5i	−1.27873	+	1.27873i
$792$		0			0
$793$	−4138.27	−	4138.27i	−0.185314	−	0.185314i
$794$		0			0
$795$	−1285.60	+	3103.71i	−0.0573529	+	0.138462i
$796$		0			0
$797$	−7430.32	+	3077.74i	−0.330233	+	0.136787i	−0.541639	−	0.840611i	$-0.682196\pi$
$797$	−7430.32	+	3077.74i	−0.330233	+	0.136787i	0.211406	+	0.977398i	$0.432196\pi$
$798$		0			0
$799$	2229.59			0.0987198
$800$		0			0
$801$	19466.0			0.858671
$802$		0			0
$803$	2802.27	−	1160.74i	0.123151	−	0.0510106i
$804$		0			0
$805$	−2781.31	+	6714.68i	−0.121774	+	0.293989i
$806$		0			0
$807$	−25636.0	−	25636.0i	−1.11825	−	1.11825i
$808$		0			0
$809$	−25547.6	+	25547.6i	−1.11027	+	1.11027i	−0.117151	+	0.993114i	$0.537376\pi$
$809$	−25547.6	+	25547.6i	−1.11027	+	1.11027i	−0.993114	+	0.117151i	$0.962624\pi$
$810$		0			0
$811$	9579.81	+	3968.09i	0.414788	+	0.171811i	0.580311	−	0.814395i	$-0.302931\pi$
$811$	9579.81	+	3968.09i	0.414788	+	0.171811i	−0.165523	+	0.986206i	$0.552931\pi$
$812$		0			0
$813$	19745.3	+	47669.4i	0.851782	+	2.05638i
$814$		0			0
$815$			2411.30i			0.103637i
$816$		0			0
$817$		−	21348.3i		−	0.914176i
$818$		0			0
$819$	−15127.9	−	36521.9i	−0.645434	−	1.55822i
$820$		0			0
$821$	−10011.6	−	4146.96i	−0.425589	−	0.176285i	0.159600	−	0.987182i	$-0.448980\pi$
$821$	−10011.6	−	4146.96i	−0.425589	−	0.176285i	−0.585189	+	0.810897i	$0.698980\pi$
$822$		0			0
$823$	5175.27	−	5175.27i	0.219196	−	0.219196i	−0.588963	−	0.808160i	$-0.700464\pi$
$823$	5175.27	−	5175.27i	0.219196	−	0.219196i	0.808160	+	0.588963i	$0.200464\pi$
$824$		0			0
$825$	−3333.70	−	3333.70i	−0.140684	−	0.140684i
$826$		0			0
$827$	−3761.04	+	9079.96i	−0.158143	+	0.381791i	−0.983014	−	0.183530i	$-0.941248\pi$
$827$	−3761.04	+	9079.96i	−0.158143	+	0.381791i	0.824871	+	0.565321i	$0.191248\pi$
$828$		0			0
$829$	−4411.71	+	1827.39i	−0.184831	+	0.0765596i	−0.473180	−	0.880966i	$-0.656894\pi$
$829$	−4411.71	+	1827.39i	−0.184831	+	0.0765596i	0.288348	+	0.957526i	$0.406894\pi$
$830$		0			0
$831$	20469.7			0.854496
$832$		0			0
$833$	−871.307			−0.0362413
$834$		0			0
$835$	1665.85	−	690.018i	0.0690409	−	0.0285977i
$836$		0			0
$837$	−24174.7	+	58362.8i	−0.998326	+	2.41017i
$838$		0			0
$839$	13781.2	+	13781.2i	0.567078	+	0.567078i	0.931309	−	0.364231i	$-0.118668\pi$
$839$	13781.2	+	13781.2i	0.567078	+	0.567078i	−0.364231	+	0.931309i	$0.618668\pi$
$840$		0			0
$841$	1524.74	−	1524.74i	0.0625176	−	0.0625176i
$842$		0			0
$843$	−1954.18	−	809.447i	−0.0798404	−	0.0330710i
$844$		0			0
$845$	1682.20	+	4061.20i	0.0684847	+	0.165337i
$846$		0			0
$847$		−	29949.5i		−	1.21497i
$848$		0			0
$849$			22378.5i			0.904628i
$850$		0			0
$851$	−123.792	−	298.861i	−0.00498654	−	0.0120386i
$852$		0			0
$853$	18549.2	+	7683.33i	0.744564	+	0.308408i	0.722521	−	0.691349i	$-0.242983\pi$
$853$	18549.2	+	7683.33i	0.744564	+	0.308408i	0.0220423	+	0.999757i	$0.492983\pi$
$854$		0			0
$855$	−9412.09	+	9412.09i	−0.376476	+	0.376476i
$856$		0			0
$857$	26552.5	+	26552.5i	1.05836	+	1.05836i	0.998188	+	0.0601723i	$0.0191650\pi$
$857$	26552.5	+	26552.5i	1.05836	+	1.05836i	0.0601723	+	0.998188i	$0.480835\pi$
$858$		0			0
$859$	1116.56	−	2695.62i	0.0443500	−	0.107070i	−0.900152	−	0.435576i	$-0.856545\pi$
$859$	1116.56	−	2695.62i	0.0443500	−	0.107070i	0.944502	+	0.328505i	$0.106545\pi$
$860$		0			0
$861$	2575.78	−	1066.92i	0.101954	−	0.0422307i
$862$		0			0
$863$	−15473.2			−0.610330			−0.305165	−	0.952300i	$-0.598712\pi$
$863$	−15473.2			−0.610330			−0.305165	+	0.952300i	$0.598712\pi$
$864$		0			0
$865$	−1237.08			−0.0486267
$866$		0			0
$867$	44908.4	−	18601.7i	1.75913	−	0.728657i
$868$		0			0
$869$	1734.45	−	4187.34i	0.0677069	−	0.163459i
$870$		0			0
$871$	3772.35	+	3772.35i	0.146752	+	0.146752i
$872$		0			0
$873$	−1955.58	+	1955.58i	−0.0758149	+	0.0758149i
$874$		0			0
$875$	−13904.3	−	5759.36i	−0.537202	−	0.222517i
$876$		0			0
$877$	−1995.23	−	4816.92i	−0.0768236	−	0.185468i	0.880802	−	0.473485i	$-0.157004\pi$
$877$	−1995.23	−	4816.92i	−0.0768236	−	0.185468i	−0.957625	+	0.288017i	$0.907004\pi$
$878$		0			0
$879$		−	87307.0i		−	3.35016i
$880$		0			0
$881$			31030.7i			1.18667i	0.804957	+	0.593333i	$0.202188\pi$
$881$			31030.7i			1.18667i	−0.804957	+	0.593333i	$0.797812\pi$
$882$		0			0
$883$	−18718.1	−	45189.5i	−0.713380	−	1.72225i	−0.691378	−	0.722494i	$-0.742996\pi$
$883$	−18718.1	−	45189.5i	−0.713380	−	1.72225i	−0.0220023	−	0.999758i	$-0.507004\pi$
$884$		0			0
$885$	−8126.13	−	3365.95i	−0.308652	−	0.127848i
$886$		0			0
$887$	−13792.0	+	13792.0i	−0.522084	+	0.522084i	−0.918200	−	0.396116i	$-0.870358\pi$
$887$	−13792.0	+	13792.0i	−0.522084	+	0.522084i	0.396116	+	0.918200i	$0.370358\pi$
$888$		0			0
$889$	−32797.4	−	32797.4i	−1.23733	−	1.23733i
$890$		0			0
$891$	−3851.92	+	9299.35i	−0.144831	+	0.349652i
$892$		0			0
$893$	28280.6	−	11714.2i	1.05977	−	0.438970i
$894$		0			0
$895$	−1631.53			−0.0609341
$896$		0			0
$897$	−28125.2			−1.04690
$898$		0			0
$899$	21310.9	−	8827.28i	0.790611	−	0.327482i
$900$		0			0
$901$	−235.126	+	567.645i	−0.00869388	+	0.0209889i
$902$		0			0
$903$	−50283.9	−	50283.9i	−1.85309	−	1.85309i
$904$		0			0
$905$	−5588.79	+	5588.79i	−0.205279	+	0.205279i
$906$		0			0
$907$	39259.1	+	16261.7i	1.43724	+	0.595325i	0.959128	−	0.282972i	$-0.0913205\pi$
$907$	39259.1	+	16261.7i	1.43724	+	0.595325i	0.478114	+	0.878298i	$0.341321\pi$
$908$		0			0
$909$	6050.53	+	14607.3i	0.220774	+	0.532995i
$910$		0			0
$911$			39632.6i			1.44137i	0.693263	+	0.720685i	$0.256172\pi$
$911$			39632.6i			1.44137i	−0.693263	+	0.720685i	$0.743828\pi$
$912$		0			0
$913$		−	1250.19i		−	0.0453178i
$914$		0			0
$915$	2511.99	+	6064.47i	0.0907582	+	0.219110i
$916$		0			0
$917$	−27329.0	−	11320.0i	−0.984167	−	0.407656i
$918$		0			0
$919$	1045.92	−	1045.92i	0.0375428	−	0.0375428i	−0.688086	−	0.725629i	$-0.741549\pi$
$919$	1045.92	−	1045.92i	0.0375428	−	0.0375428i	0.725629	+	0.688086i	$0.241549\pi$
$920$		0			0
$921$	30829.2	+	30829.2i	1.10299	+	1.10299i
$922$		0			0
$923$	−7922.57	+	19126.8i	−0.282529	+	0.682086i
$924$		0			0
$925$	299.970	−	124.252i	0.0106627	−	0.00441662i
$926$		0			0
$927$	4542.39			0.160940
$928$		0			0
$929$	−27474.9			−0.970316			−0.485158	−	0.874427i	$-0.661238\pi$
$929$	−27474.9			−0.970316			−0.485158	+	0.874427i	$0.661238\pi$
$930$		0			0
$931$	−11051.9	+	4577.83i	−0.389055	+	0.161152i
$932$		0			0
$933$	31041.1	−	74939.8i	1.08922	−	2.62960i
$934$		0			0
$935$	38.4617	+	38.4617i	0.00134528	+	0.00134528i
$936$		0			0
$937$	4502.22	−	4502.22i	0.156970	−	0.156970i	−0.624252	−	0.781223i	$-0.714596\pi$
$937$	4502.22	−	4502.22i	0.156970	−	0.156970i	0.781223	+	0.624252i	$0.214596\pi$
$938$		0			0
$939$	−91603.5	−	37943.4i	−3.18357	−	1.31868i
$940$		0			0
$941$	2532.80	+	6114.71i	0.0877436	+	0.211832i	0.961660	−	0.274244i	$-0.0884277\pi$
$941$	2532.80	+	6114.71i	0.0877436	+	0.211832i	−0.873916	+	0.486076i	$0.838428\pi$
$942$		0			0
$943$		−	1441.91i		−	0.0497933i
$944$		0			0
$945$			27682.3i			0.952917i
$946$		0			0
$947$	17601.9	+	42494.8i	0.603997	+	1.45818i	0.869433	+	0.494050i	$0.164484\pi$
$947$	17601.9	+	42494.8i	0.603997	+	1.45818i	−0.265436	+	0.964129i	$0.585516\pi$
$948$		0			0
$949$	16779.2	+	6950.18i	0.573948	+	0.237737i
$950$		0			0
$951$	57016.6	−	57016.6i	1.94415	−	1.94415i
$952$		0			0
$953$	3780.28	+	3780.28i	0.128495	+	0.128495i	0.768429	−	0.639935i	$-0.221039\pi$
$953$	3780.28	+	3780.28i	0.128495	+	0.128495i	−0.639935	+	0.768429i	$0.721039\pi$
$954$		0			0
$955$	3264.85	−	7882.06i	0.110626	−	0.267076i
$956$		0			0
$957$	6035.42	−	2499.95i	0.203864	−	0.0844431i
$958$		0			0
$959$	43675.3			1.47065
$960$		0			0
$961$	−9746.91			−0.327176
$962$		0			0
$963$	−76102.8	+	31522.8i	−2.54660	+	1.05484i
$964$		0			0
$965$	1405.15	−	3392.33i	0.0468739	−	0.113164i
$966$		0			0
$967$	26724.8	+	26724.8i	0.888739	+	0.888739i	0.994402	−	0.105663i	$-0.0336965\pi$
$967$	26724.8	+	26724.8i	0.888739	+	0.888739i	−0.105663	+	0.994402i	$0.533697\pi$
$968$		0			0
$969$	−2368.06	+	2368.06i	−0.0785067	+	0.0785067i
$970$		0			0
$971$	45804.4	+	18972.8i	1.51383	+	0.627051i	0.976345	−	0.216219i	$-0.0693726\pi$
$971$	45804.4	+	18972.8i	1.51383	+	0.627051i	0.537490	+	0.843270i	$0.319373\pi$
$972$		0			0
$973$	−18138.7	−	43790.6i	−0.597635	−	1.44282i
$974$		0			0
$975$		−	28229.5i		−	0.927249i
$976$		0			0
$977$		−	14963.7i		−	0.490002i	−0.969523	−	0.245001i	$-0.921212\pi$
$977$		−	14963.7i		−	0.490002i	0.969523	−	0.245001i	$-0.0787883\pi$
$978$		0			0
$979$	−417.933	−	1008.98i	−0.0136437	−	0.0329388i
$980$		0			0
$981$	106294.	+	44028.2i	3.45942	+	1.43294i
$982$		0			0
$983$	15155.2	−	15155.2i	0.491737	−	0.491737i	−0.417116	−	0.908853i	$-0.636959\pi$
$983$	15155.2	−	15155.2i	0.491737	−	0.491737i	0.908853	+	0.417116i	$0.136959\pi$
$984$		0			0
$985$	6034.48	+	6034.48i	0.195202	+	0.195202i
$986$		0			0
$987$	39020.6	−	94204.0i	1.25840	−	3.03804i
$988$		0			0
$989$	−33978.6	+	14074.4i	−1.09247	+	0.452517i
$990$		0			0
$991$	−19029.0			−0.609965			−0.304982	−	0.952358i	$-0.598651\pi$
$991$	−19029.0			−0.609965			−0.304982	+	0.952358i	$0.598651\pi$
$992$		0			0
$993$	78910.6			2.52181
$994$		0			0
$995$	−10438.3	+	4323.70i	−0.332580	+	0.137759i
$996$		0			0
$997$	−8240.12	+	19893.4i	−0.261752	+	0.631926i	−0.999047	−	0.0436451i	$-0.986103\pi$
$997$	−8240.12	+	19893.4i	−0.261752	+	0.631926i	0.737295	+	0.675571i	$0.236103\pi$
$998$		0			0
$999$	−871.229	−	871.229i	−0.0275921	−	0.0275921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.4.g.b.97.11		44
4.3	odd	2		256.4.g.a.97.1		44
8.3	odd	2		128.4.g.a.49.11		44
8.5	even	2		32.4.g.a.21.10	✓	44
32.3	odd	8		256.4.g.a.161.1		44
32.13	even	8		32.4.g.a.29.10	yes	44
32.19	odd	8		128.4.g.a.81.11		44
32.29	even	8	inner	256.4.g.b.161.11		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.4.g.a.21.10	✓	44	8.5	even	2
32.4.g.a.29.10	yes	44	32.13	even	8
128.4.g.a.49.11		44	8.3	odd	2
128.4.g.a.81.11		44	32.19	odd	8
256.4.g.a.97.1		44	4.3	odd	2
256.4.g.a.161.1		44	32.3	odd	8
256.4.g.b.97.11		44	1.1	even	1	trivial
256.4.g.b.161.11		44	32.29	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(9.18660 - 3.80522i) q^{3} +(-1.04223 + 2.51617i) q^{5} +(16.1077 + 16.1077i) q^{7} +(50.8221 - 50.8221i) q^{9} +O(q^{10})\)	\(q+(9.18660 - 3.80522i) q^{3} +(-1.04223 + 2.51617i) q^{5} +(16.1077 + 16.1077i) q^{7} +(50.8221 - 50.8221i) q^{9} +(-3.72541 - 1.54312i) q^{11} +(-9.23975 - 22.3067i) q^{13} +27.0810i q^{15} +4.95290i q^{17} +(26.0224 + 62.8237i) q^{19} +(209.269 + 86.6820i) q^{21} +(82.8361 - 82.8361i) q^{23} +(83.1435 + 83.1435i) q^{25} +(170.753 - 412.233i) q^{27} +(-150.525 + 62.3496i) q^{29} -141.577 q^{31} -40.0958 q^{33} +(-57.3179 + 23.7419i) q^{35} +(1.05672 - 2.55114i) q^{37} +(-169.764 - 169.764i) q^{39} +(8.70340 - 8.70340i) q^{41} +(-290.048 - 120.142i) q^{43} +(74.9088 + 180.846i) q^{45} -450.158i q^{47} +175.919i q^{49} +(18.8469 + 45.5003i) q^{51} +(114.608 + 47.4724i) q^{53} +(7.76550 - 7.76550i) q^{55} +(478.115 + 478.115i) q^{57} +(-124.292 + 300.067i) q^{59} +(223.938 - 92.7582i) q^{61} +1637.26 q^{63} +65.7576 q^{65} +(-204.137 + 84.5564i) q^{67} +(445.773 - 1076.19i) q^{69} +(-606.304 - 606.304i) q^{71} +(-531.888 + 531.888i) q^{73} +(1080.18 + 447.427i) q^{75} +(-35.1518 - 84.8641i) q^{77} +1123.99i q^{79} -2496.19i q^{81} +(118.647 + 286.439i) q^{83} +(-12.4624 - 5.16208i) q^{85} +(-1145.56 + 1145.56i) q^{87} +(191.511 + 191.511i) q^{89} +(210.480 - 508.143i) q^{91} +(-1300.61 + 538.732i) q^{93} -185.197 q^{95} -38.4790 q^{97} +(-267.758 + 110.909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9	\( 44 q + 4 q^{3} + 4 q^{5} - 4 q^{7} - 4 q^{9} + 4 q^{11} + 4 q^{13} + 4 q^{19} + 4 q^{21} + 324 q^{23} - 4 q^{25} + 268 q^{27} + 4 q^{29} - 752 q^{31} - 8 q^{33} + 460 q^{35} + 4 q^{37} + 596 q^{39} - 4 q^{41} - 804 q^{43} - 104 q^{45} + 1384 q^{51} - 748 q^{53} - 292 q^{55} - 4 q^{57} - 1372 q^{59} + 1828 q^{61} + 2512 q^{63} - 8 q^{65} - 2036 q^{67} + 1060 q^{69} + 220 q^{71} - 4 q^{73} + 1712 q^{75} - 1900 q^{77} - 2436 q^{83} - 496 q^{85} - 1292 q^{87} - 4 q^{89} + 3604 q^{91} + 112 q^{93} - 6088 q^{95} - 8 q^{97} + 5424 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 + 4 * q^5 - 4 * q^7 - 4 * q^9 + 4 * q^11 + 4 * q^13 + 4 * q^19 + 4 * q^21 + 324 * q^23 - 4 * q^25 + 268 * q^27 + 4 * q^29 - 752 * q^31 - 8 * q^33 + 460 * q^35 + 4 * q^37 + 596 * q^39 - 4 * q^41 - 804 * q^43 - 104 * q^45 + 1384 * q^51 - 748 * q^53 - 292 * q^55 - 4 * q^57 - 1372 * q^59 + 1828 * q^61 + 2512 * q^63 - 8 * q^65 - 2036 * q^67 + 1060 * q^69 + 220 * q^71 - 4 * q^73 + 1712 * q^75 - 1900 * q^77 - 2436 * q^83 - 496 * q^85 - 1292 * q^87 - 4 * q^89 + 3604 * q^91 + 112 * q^93 - 6088 * q^95 - 8 * q^97 + 5424 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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