LMFDB - Embedded newform 644.4.i.b.93.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.18
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.73245 + 6.46479i) q^{3} +(5.71334 - 9.89579i) q^{5} +(-6.28887 + 17.4198i) q^{7} +(-14.3624 + 24.8763i) q^{9} +O(q^{10})$	\(q+(3.73245 + 6.46479i) q^{3} +(5.71334 - 9.89579i) q^{5} +(-6.28887 + 17.4198i) q^{7} +(-14.3624 + 24.8763i) q^{9} +(-31.8829 - 55.2228i) q^{11} +90.5765 q^{13} +85.2990 q^{15} +(6.60011 + 11.4317i) q^{17} +(38.4742 - 66.6392i) q^{19} +(-136.088 + 24.3623i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-2.78442 - 4.82275i) q^{25} -12.8749 q^{27} +123.899 q^{29} +(167.605 + 290.300i) q^{31} +(238.002 - 412.232i) q^{33} +(136.452 + 161.759i) q^{35} +(-137.179 + 237.601i) q^{37} +(338.072 + 585.558i) q^{39} +130.587 q^{41} +39.5094 q^{43} +(164.114 + 284.254i) q^{45} +(214.770 - 371.993i) q^{47} +(-263.900 - 219.102i) q^{49} +(-49.2692 + 85.3367i) q^{51} +(195.519 + 338.649i) q^{53} -728.630 q^{55} +574.412 q^{57} +(-317.108 - 549.247i) q^{59} +(11.6176 - 20.1222i) q^{61} +(-343.018 - 406.634i) q^{63} +(517.494 - 896.326i) q^{65} +(-54.0160 - 93.5585i) q^{67} +171.693 q^{69} -992.688 q^{71} +(392.096 + 679.130i) q^{73} +(20.7854 - 36.0014i) q^{75} +(1162.48 - 208.105i) q^{77} +(-184.429 + 319.441i) q^{79} +(339.729 + 588.428i) q^{81} +12.5307 q^{83} +150.835 q^{85} +(462.445 + 800.979i) q^{87} +(497.934 - 862.446i) q^{89} +(-569.624 + 1577.83i) q^{91} +(-1251.15 + 2167.06i) q^{93} +(-439.632 - 761.465i) q^{95} +1661.05 q^{97} +1831.65 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$3$	3.73245	+	6.46479i	0.718310	+	1.24415i	0.961669	+	0.274213i	$0.0884175\pi$
$3$	3.73245	+	6.46479i	0.718310	+	1.24415i	−0.243359	+	0.969936i	$0.578249\pi$
$4$		0			0
$5$	5.71334	−	9.89579i	0.511016	−	0.885106i	−0.488902	−	0.872339i	$-0.662603\pi$
$5$	5.71334	−	9.89579i	0.511016	−	0.885106i	0.999918	−	0.0127676i	$-0.00406416\pi$
$6$		0			0
$7$	−6.28887	+	17.4198i	−0.339567	+	0.940582i
$7$	−6.28887	+	17.4198i	−0.339567	+	0.940582i
$8$		0			0
$9$	−14.3624	+	24.8763i	−0.531939	+	0.921346i
$10$		0			0
$11$	−31.8829	−	55.2228i	−0.873914	−	1.51366i	−0.857915	−	0.513791i	$-0.828241\pi$
$11$	−31.8829	−	55.2228i	−0.873914	−	1.51366i	−0.0159982	−	0.999872i	$-0.505093\pi$
$12$		0			0
$13$	90.5765			1.93241			0.966207	−	0.257766i	$-0.0829863\pi$
$13$	90.5765			1.93241			0.966207	+	0.257766i	$0.0829863\pi$
$14$		0			0
$15$	85.2990			1.46827
$16$		0			0
$17$	6.60011	+	11.4317i	0.0941625	+	0.163094i	0.909259	−	0.416231i	$-0.136649\pi$
$17$	6.60011	+	11.4317i	0.0941625	+	0.163094i	−0.815096	+	0.579326i	$0.803316\pi$
$18$		0			0
$19$	38.4742	−	66.6392i	0.464557	−	0.804636i	−0.534624	−	0.845090i	$-0.679547\pi$
$19$	38.4742	−	66.6392i	0.464557	−	0.804636i	0.999181	+	0.0404534i	$0.0128802\pi$
$20$		0			0
$21$	−136.088	+	24.3623i	−1.41414	+	0.253157i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	−2.78442	−	4.82275i	−0.0222753	−	0.0385820i
$26$		0			0
$27$	−12.8749			−0.0917692
$28$		0			0
$29$	123.899			0.793358			0.396679	−	0.917957i	$-0.370163\pi$
$29$	123.899			0.793358			0.396679	+	0.917957i	$0.370163\pi$
$30$		0			0
$31$	167.605	+	290.300i	0.971056	+	1.68192i	0.692379	+	0.721534i	$0.256563\pi$
$31$	167.605	+	290.300i	0.971056	+	1.68192i	0.278677	+	0.960385i	$0.410104\pi$
$32$		0			0
$33$	238.002	−	412.232i	1.25548	−	2.17456i
$34$		0			0
$35$	136.452	+	161.759i	0.658990	+	0.781206i
$36$		0			0
$37$	−137.179	+	237.601i	−0.609515	+	1.05571i	0.381805	+	0.924243i	$0.375303\pi$
$37$	−137.179	+	237.601i	−0.609515	+	1.05571i	−0.991320	+	0.131468i	$0.958031\pi$
$38$		0			0
$39$	338.072	+	585.558i	1.38807	+	2.40421i
$40$		0			0
$41$	130.587			0.497421			0.248710	−	0.968578i	$-0.419993\pi$
$41$	130.587			0.497421			0.248710	+	0.968578i	$0.419993\pi$
$42$		0			0
$43$	39.5094			0.140119			0.0700595	−	0.997543i	$-0.477681\pi$
$43$	39.5094			0.140119			0.0700595	+	0.997543i	$0.477681\pi$
$44$		0			0
$45$	164.114	+	284.254i	0.543659	+	0.941646i
$46$		0			0
$47$	214.770	−	371.993i	0.666542	−	1.15448i	−0.312323	−	0.949976i	$-0.601107\pi$
$47$	214.770	−	371.993i	0.666542	−	1.15448i	0.978865	−	0.204508i	$-0.0655595\pi$
$48$		0			0
$49$	−263.900	−	219.102i	−0.769388	−	0.638781i
$50$		0			0
$51$	−49.2692	+	85.3367i	−0.135276	+	0.234304i
$52$		0			0
$53$	195.519	+	338.649i	0.506729	+	0.877680i	0.999970	+	0.00778695i	$0.00247869\pi$
$53$	195.519	+	338.649i	0.506729	+	0.877680i	−0.493241	+	0.869893i	$0.664188\pi$
$54$		0			0
$55$	−728.630			−1.78634
$56$		0			0
$57$	574.412			1.33478
$58$		0			0
$59$	−317.108	−	549.247i	−0.699728	−	1.21196i	−0.968561	−	0.248778i	$-0.919971\pi$
$59$	−317.108	−	549.247i	−0.699728	−	1.21196i	0.268833	−	0.963187i	$-0.413362\pi$
$60$		0			0
$61$	11.6176	−	20.1222i	0.0243849	−	0.0422359i	−0.853575	−	0.520969i	$-0.825571\pi$
$61$	11.6176	−	20.1222i	0.0243849	−	0.0422359i	0.877960	+	0.478733i	$0.158904\pi$
$62$		0			0
$63$	−343.018	−	406.634i	−0.685972	−	0.813191i
$64$		0			0
$65$	517.494	−	896.326i	0.987496	−	1.71039i
$66$		0			0
$67$	−54.0160	−	93.5585i	−0.0984941	−	0.170597i	0.812567	−	0.582867i	$-0.198069\pi$
$67$	−54.0160	−	93.5585i	−0.0984941	−	0.170597i	−0.911062	+	0.412270i	$0.864736\pi$
$68$		0			0
$69$	171.693			0.299556
$70$		0			0
$71$	−992.688			−1.65930			−0.829651	−	0.558283i	$-0.811460\pi$
$71$	−992.688			−1.65930			−0.829651	+	0.558283i	$0.811460\pi$
$72$		0			0
$73$	392.096	+	679.130i	0.628649	+	1.08885i	0.987823	+	0.155581i	$0.0497250\pi$
$73$	392.096	+	679.130i	0.628649	+	1.08885i	−0.359174	+	0.933270i	$0.616942\pi$
$74$		0			0
$75$	20.7854	−	36.0014i	0.0320012	−	0.0554277i
$76$		0			0
$77$	1162.48	−	208.105i	1.72048	−	0.307997i
$78$		0			0
$79$	−184.429	+	319.441i	−0.262657	+	0.454936i	−0.966947	−	0.254977i	$-0.917932\pi$
$79$	−184.429	+	319.441i	−0.262657	+	0.454936i	0.704290	+	0.709913i	$0.251266\pi$
$80$		0			0
$81$	339.729	+	588.428i	0.466020	+	0.807171i
$82$		0			0
$83$	12.5307			0.0165713			0.00828566	−	0.999966i	$-0.497363\pi$
$83$	12.5307			0.0165713			0.00828566	+	0.999966i	$0.497363\pi$
$84$		0			0
$85$	150.835			0.192474
$86$		0			0
$87$	462.445	+	800.979i	0.569877	+	0.987057i
$88$		0			0
$89$	497.934	−	862.446i	0.593043	−	1.02718i	−0.400777	−	0.916176i	$-0.631260\pi$
$89$	497.934	−	862.446i	0.593043	−	1.02718i	0.993820	−	0.111005i	$-0.0354070\pi$
$90$		0			0
$91$	−569.624	+	1577.83i	−0.656185	+	1.81759i
$92$		0			0
$93$	−1251.15	+	2167.06i	−1.39504	+	2.41628i
$94$		0			0
$95$	−439.632	−	761.465i	−0.474792	−	0.822365i
$96$		0			0
$97$	1661.05			1.73870			0.869352	−	0.494193i	$-0.164536\pi$
$97$	1661.05			1.73870			0.869352	+	0.494193i	$0.164536\pi$
$98$		0			0
$99$	1831.65			1.85948
$100$		0			0
$101$	274.668	+	475.739i	0.270599	+	0.468691i	0.969015	−	0.247001i	$-0.0794450\pi$
$101$	274.668	+	475.739i	0.270599	+	0.468691i	−0.698417	+	0.715691i	$0.746112\pi$
$102$		0			0
$103$	844.844	−	1463.31i	0.808203	−	1.39985i	−0.105904	−	0.994376i	$-0.533773\pi$
$103$	844.844	−	1463.31i	0.808203	−	1.39985i	0.914107	−	0.405473i	$-0.132893\pi$
$104$		0			0
$105$	−536.434	+	1485.89i	−0.498577	+	1.38103i
$106$		0			0
$107$	−872.241	+	1510.77i	−0.788063	+	1.36496i	0.139090	+	0.990280i	$0.455582\pi$
$107$	−872.241	+	1510.77i	−0.788063	+	1.36496i	−0.927152	+	0.374685i	$0.877751\pi$
$108$		0			0
$109$	−315.901	−	547.156i	−0.277594	−	0.480808i	0.693192	−	0.720753i	$-0.256204\pi$
$109$	−315.901	−	547.156i	−0.277594	−	0.480808i	−0.970786	+	0.239945i	$0.922870\pi$
$110$		0			0
$111$	−2048.05			−1.75128
$112$		0			0
$113$	−925.241			−0.770260			−0.385130	−	0.922862i	$-0.625843\pi$
$113$	−925.241			−0.770260			−0.385130	+	0.922862i	$0.625843\pi$
$114$		0			0
$115$	−131.407	−	227.603i	−0.106554	−	0.184557i
$116$		0			0
$117$	−1300.89	+	2253.21i	−1.02793	+	1.78042i
$118$		0			0
$119$	−240.646	+	43.0801i	−0.185378	+	0.0331861i
$120$		0			0
$121$	−1367.54	+	2368.64i	−1.02745	+	1.77960i
$122$		0			0
$123$	487.409	+	844.218i	0.357303	+	0.618866i
$124$		0			0
$125$	1364.70			0.976500
$126$		0			0
$127$	−1044.72			−0.729953			−0.364976	−	0.931017i	$-0.618923\pi$
$127$	−1044.72			−0.729953			−0.364976	+	0.931017i	$0.618923\pi$
$128$		0			0
$129$	147.467	+	255.420i	0.100649	+	0.174329i
$130$		0			0
$131$	−730.895	+	1265.95i	−0.487470	+	0.844323i	−0.999896	−	0.0144085i	$-0.995413\pi$
$131$	−730.895	+	1265.95i	−0.487470	+	0.844323i	0.512426	+	0.858731i	$0.328747\pi$
$132$		0			0
$133$	918.884	+	1089.30i	0.599078	+	0.710182i
$134$		0			0
$135$	−73.5584	+	127.407i	−0.0468956	+	0.0812255i
$136$		0			0
$137$	−1265.09	−	2191.20i	−0.788934	−	1.36647i	−0.926620	−	0.375999i	$-0.877300\pi$
$137$	−1265.09	−	2191.20i	−0.788934	−	1.36647i	0.137686	−	0.990476i	$-0.456034\pi$
$138$		0			0
$139$	895.303			0.546321			0.273160	−	0.961968i	$-0.411931\pi$
$139$	895.303			0.546321			0.273160	+	0.961968i	$0.411931\pi$
$140$		0			0
$141$	3206.48			1.91514
$142$		0			0
$143$	−2887.84	−	5001.88i	−1.68876	−	2.92502i
$144$		0			0
$145$	707.874	−	1226.07i	0.405419	−	0.702206i
$146$		0			0
$147$	431.455	−	2523.85i	0.242080	−	1.41608i
$148$		0			0
$149$	139.141	−	240.999i	0.0765024	−	0.132506i	−0.825236	−	0.564788i	$-0.808958\pi$
$149$	139.141	−	240.999i	0.0765024	−	0.132506i	0.901739	+	0.432282i	$0.142291\pi$
$150$		0			0
$151$	1230.74	+	2131.71i	0.663287	+	1.14885i	0.979747	+	0.200241i	$0.0641724\pi$
$151$	1230.74	+	2131.71i	0.663287	+	1.14885i	−0.316460	+	0.948606i	$0.602494\pi$
$152$		0			0
$153$	−379.173			−0.200355
$154$		0			0
$155$	3830.33			1.98490
$156$		0			0
$157$	1619.32	+	2804.75i	0.823158	+	1.42575i	0.903319	+	0.428970i	$0.141123\pi$
$157$	1619.32	+	2804.75i	0.823158	+	1.42575i	−0.0801602	+	0.996782i	$0.525543\pi$
$158$		0			0
$159$	−1459.53	+	2527.98i	−0.727977	+	1.26089i
$160$		0			0
$161$	274.656	+	325.593i	0.134447	+	0.159381i
$162$		0			0
$163$	−171.460	+	296.977i	−0.0823911	+	0.142706i	−0.904277	−	0.426947i	$-0.859589\pi$
$163$	−171.460	+	296.977i	−0.0823911	+	0.142706i	0.821885	+	0.569653i	$0.192922\pi$
$164$		0			0
$165$	−2719.58	−	4710.44i	−1.28314	−	2.22247i
$166$		0			0
$167$	−1427.88			−0.661631			−0.330815	−	0.943696i	$-0.607324\pi$
$167$	−1427.88			−0.661631			−0.330815	+	0.943696i	$0.607324\pi$
$168$		0			0
$169$	6007.10			2.73423
$170$		0			0
$171$	1105.16	+	1914.19i	0.494232	+	0.856035i
$172$		0			0
$173$	1364.36	−	2363.14i	0.599598	−	1.03853i	−0.393282	−	0.919418i	$-0.628660\pi$
$173$	1364.36	−	2363.14i	0.599598	−	1.03853i	0.992880	−	0.119116i	$-0.0380062\pi$
$174$		0			0
$175$	101.522	−	18.1744i	0.0438535	−	0.00785059i
$176$		0			0
$177$	2367.18	−	4100.08i	1.00524	−	1.74113i
$178$		0			0
$179$	82.2416	+	142.447i	0.0343409	+	0.0594802i	0.882685	−	0.469965i	$-0.155733\pi$
$179$	82.2416	+	142.447i	0.0343409	+	0.0594802i	−0.848344	+	0.529445i	$0.822400\pi$
$180$		0			0
$181$	1635.06			0.671452			0.335726	−	0.941960i	$-0.391018\pi$
$181$	1635.06			0.671452			0.335726	+	0.941960i	$0.391018\pi$
$182$		0			0
$183$	173.448			0.0700637
$184$		0			0
$185$	1567.50	+	2714.99i	0.622944	+	1.07897i
$186$		0			0
$187$	420.861	−	728.953i	0.164580	−	0.285060i
$188$		0			0
$189$	80.9684	−	224.278i	0.0311618	−	0.0863165i
$190$		0			0
$191$	93.5930	−	162.108i	0.0354563	−	0.0614121i	−0.847753	−	0.530392i	$-0.822045\pi$
$191$	93.5930	−	162.108i	0.0354563	−	0.0614121i	0.883209	+	0.468980i	$0.155378\pi$
$192$		0			0
$193$	−2274.50	−	3939.55i	−0.848302	−	1.46930i	−0.882723	−	0.469894i	$-0.844292\pi$
$193$	−2274.50	−	3939.55i	−0.848302	−	1.46930i	0.0344214	−	0.999407i	$-0.489041\pi$
$194$		0			0
$195$	7726.08			2.83731
$196$		0			0
$197$	−867.036			−0.313573			−0.156786	−	0.987633i	$-0.550113\pi$
$197$	−867.036			−0.313573			−0.156786	+	0.987633i	$0.550113\pi$
$198$		0			0
$199$	−1070.15	−	1853.55i	−0.381210	−	0.660275i	0.610026	−	0.792382i	$-0.291159\pi$
$199$	−1070.15	−	1853.55i	−0.381210	−	0.660275i	−0.991235	+	0.132107i	$0.957826\pi$
$200$		0			0
$201$	403.224	−	698.405i	0.141499	−	0.245083i
$202$		0			0
$203$	−779.182	+	2158.29i	−0.269398	+	0.746218i
$204$		0			0
$205$	746.087	−	1292.26i	0.254190	−	0.440270i
$206$		0			0
$207$	330.334	+	572.156i	0.110917	+	0.192114i
$208$		0			0
$209$	−4906.67			−1.62393
$210$		0			0
$211$	2239.72			0.730753			0.365377	−	0.930860i	$-0.380940\pi$
$211$	2239.72			0.730753			0.365377	+	0.930860i	$0.380940\pi$
$212$		0			0
$213$	−3705.16	−	6417.52i	−1.19189	−	2.06442i
$214$		0			0
$215$	225.730	−	390.976i	0.0716031	−	0.124020i
$216$		0			0
$217$	−6111.03	+	1093.99i	−1.91172	+	0.342233i
$218$		0			0
$219$	−2926.96	+	5069.64i	−0.903130	+	1.56427i
$220$		0			0
$221$	597.815	+	1035.45i	0.181961	+	0.315166i
$222$		0			0
$223$	831.027			0.249550			0.124775	−	0.992185i	$-0.460179\pi$
$223$	831.027			0.249550			0.124775	+	0.992185i	$0.460179\pi$
$224$		0			0
$225$	159.963			0.0473965
$226$		0			0
$227$	−2528.70	−	4379.83i	−0.739364	−	1.28062i	−0.952782	−	0.303655i	$-0.901793\pi$
$227$	−2528.70	−	4379.83i	−0.739364	−	1.28062i	0.213418	−	0.976961i	$-0.431540\pi$
$228$		0			0
$229$	−1030.65	+	1785.14i	−0.297412	+	0.515132i	−0.975543	−	0.219809i	$-0.929457\pi$
$229$	−1030.65	+	1785.14i	−0.297412	+	0.515132i	0.678131	+	0.734941i	$0.262790\pi$
$230$		0			0
$231$	5684.25	+	6738.44i	1.61903	+	1.91929i
$232$		0			0
$233$	−508.441	+	880.646i	−0.142957	+	0.247610i	−0.928609	−	0.371060i	$-0.878995\pi$
$233$	−508.441	+	880.646i	−0.142957	+	0.247610i	0.785652	+	0.618669i	$0.212328\pi$
$234$		0			0
$235$	−2454.11	−	4250.64i	−0.681227	−	1.17992i
$236$		0			0
$237$	−2753.49			−0.754678
$238$		0			0
$239$	−1235.25			−0.334317			−0.167158	−	0.985930i	$-0.553459\pi$
$239$	−1235.25			−0.334317			−0.167158	+	0.985930i	$0.553459\pi$
$240$		0			0
$241$	−827.551	−	1433.36i	−0.221192	−	0.383115i	0.733978	−	0.679173i	$-0.237661\pi$
$241$	−827.551	−	1433.36i	−0.221192	−	0.383115i	−0.955170	+	0.296057i	$0.904328\pi$
$242$		0			0
$243$	−2709.85	+	4693.60i	−0.715379	+	1.23907i
$244$		0			0
$245$	−3675.94	+	1359.70i	−0.958559	+	0.354563i
$246$		0			0
$247$	3484.86	−	6035.95i	0.897717	−	1.55489i
$248$		0			0
$249$	46.7701	+	81.0082i	0.0119034	+	0.0206172i
$250$		0			0
$251$	−1629.96			−0.409888			−0.204944	−	0.978774i	$-0.565701\pi$
$251$	−1629.96			−0.409888			−0.204944	+	0.978774i	$0.565701\pi$
$252$		0			0
$253$	−1466.61			−0.364447
$254$		0			0
$255$	562.983	+	975.114i	0.138256	+	0.239467i
$256$		0			0
$257$	3071.91	−	5320.70i	0.745605	−	1.29143i	−0.204307	−	0.978907i	$-0.565494\pi$
$257$	3071.91	−	5320.70i	0.745605	−	1.29143i	0.949912	−	0.312518i	$-0.101173\pi$
$258$		0			0
$259$	−3276.26	−	3883.87i	−0.786011	−	0.931784i
$260$		0			0
$261$	−1779.48	+	3082.14i	−0.422018	+	0.730957i
$262$		0			0
$263$	−1156.02	−	2002.29i	−0.271039	−	0.469454i	0.698089	−	0.716011i	$-0.254034\pi$
$263$	−1156.02	−	2002.29i	−0.271039	−	0.469454i	−0.969128	+	0.246557i	$0.920701\pi$
$264$		0			0
$265$	4468.27			1.03579
$266$		0			0
$267$	7434.05			1.70396
$268$		0			0
$269$	2493.39	+	4318.68i	0.565148	+	0.978864i	0.997036	+	0.0769372i	$0.0245141\pi$
$269$	2493.39	+	4318.68i	0.565148	+	0.978864i	−0.431888	+	0.901927i	$0.642153\pi$
$270$		0			0
$271$	1186.48	−	2055.05i	0.265954	−	0.460646i	−0.701859	−	0.712316i	$-0.747646\pi$
$271$	1186.48	−	2055.05i	0.265954	−	0.460646i	0.967813	+	0.251670i	$0.0809796\pi$
$272$		0			0
$273$	−12326.4	+	2206.66i	−2.73270	+	0.489205i
$274$		0			0
$275$	−177.550	+	307.526i	−0.0389334	+	0.0674347i
$276$		0			0
$277$	−742.324	−	1285.74i	−0.161018	−	0.278891i	0.774216	−	0.632921i	$-0.218144\pi$
$277$	−742.324	−	1285.74i	−0.161018	−	0.278891i	−0.935234	+	0.354030i	$0.884811\pi$
$278$		0			0
$279$	−9628.81			−2.06617
$280$		0			0
$281$	−3597.63			−0.763760			−0.381880	−	0.924212i	$-0.624723\pi$
$281$	−3597.63			−0.763760			−0.381880	+	0.924212i	$0.624723\pi$
$282$		0			0
$283$	−657.556	−	1138.92i	−0.138119	−	0.239229i	0.788666	−	0.614822i	$-0.210772\pi$
$283$	−657.556	−	1138.92i	−0.138119	−	0.239229i	−0.926785	+	0.375593i	$0.877439\pi$
$284$		0			0
$285$	3281.81	−	5684.26i	0.682097	−	1.18143i
$286$		0			0
$287$	−821.245	+	2274.80i	−0.168908	+	0.467865i
$288$		0			0
$289$	2369.38	−	4103.88i	0.482267	−	0.835311i
$290$		0			0
$291$	6199.80	+	10738.4i	1.24893	+	2.16321i
$292$		0			0
$293$	−3947.26			−0.787036			−0.393518	−	0.919317i	$-0.628742\pi$
$293$	−3947.26			−0.787036			−0.393518	+	0.919317i	$0.628742\pi$
$294$		0			0
$295$	−7246.98			−1.43029
$296$		0			0
$297$	410.488	+	710.986i	0.0801984	+	0.138908i
$298$		0			0
$299$	1041.63	−	1804.16i	0.201468	−	0.348953i
$300$		0			0
$301$	−248.469	+	688.246i	−0.0475798	+	0.131793i
$302$		0			0
$303$	−2050.37	+	3551.34i	−0.388748	+	0.673331i
$304$		0			0
$305$	−132.750	−	229.930i	−0.0249222	−	0.0431664i
$306$		0			0
$307$	−7550.05			−1.40360			−0.701799	−	0.712375i	$-0.747619\pi$
$307$	−7550.05			−1.40360			−0.701799	+	0.712375i	$0.747619\pi$
$308$		0			0
$309$	12613.4			2.32216
$310$		0			0
$311$	2424.16	+	4198.77i	0.441999	+	0.765564i	0.997838	−	0.0657260i	$-0.0209363\pi$
$311$	2424.16	+	4198.77i	0.441999	+	0.765564i	−0.555839	+	0.831290i	$0.687603\pi$
$312$		0			0
$313$	−4438.26	+	7687.28i	−0.801486	+	1.38821i	0.117152	+	0.993114i	$0.462623\pi$
$313$	−4438.26	+	7687.28i	−0.801486	+	1.38821i	−0.918638	+	0.395100i	$0.870710\pi$
$314$		0			0
$315$	−5983.74	+	1071.20i	−1.07030	+	0.191604i
$316$		0			0
$317$	547.363	−	948.060i	0.0969809	−	0.167976i	−0.813453	−	0.581631i	$-0.802415\pi$
$317$	547.363	−	948.060i	0.0969809	−	0.167976i	0.910434	+	0.413655i	$0.135748\pi$
$318$		0			0
$319$	−3950.24	−	6842.02i	−0.693327	−	1.20088i
$320$		0			0
$321$	−13022.4			−2.26429
$322$		0			0
$323$	1015.74			0.174975
$324$		0			0
$325$	−252.203	−	436.828i	−0.0430452	−	0.0745565i
$326$		0			0
$327$	2358.17	−	4084.46i	0.398798	−	0.690738i
$328$		0			0
$329$	5129.39	+	6080.68i	0.859551	+	1.01896i
$330$		0			0
$331$	375.616	−	650.585i	0.0623737	−	0.108034i	−0.833152	−	0.553044i	$-0.813466\pi$
$331$	375.616	−	650.585i	0.0623737	−	0.108034i	0.895526	+	0.445009i	$0.146800\pi$
$332$		0			0
$333$	−3940.42	−	6825.01i	−0.648450	−	1.12315i
$334$		0			0
$335$	−1234.45			−0.201328
$336$		0			0
$337$	−5516.24			−0.891658			−0.445829	−	0.895118i	$-0.647091\pi$
$337$	−5516.24			−0.891658			−0.445829	+	0.895118i	$0.647091\pi$
$338$		0			0
$339$	−3453.41	−	5981.49i	−0.553285	−	0.958318i
$340$		0			0
$341$	10687.5	−	18511.2i	1.69724	−	2.93970i
$342$		0			0
$343$	5476.35	−	3219.19i	0.862085	−	0.506763i
$344$		0			0
$345$	980.938	−	1699.03i	0.153078	−	0.265139i
$346$		0			0
$347$	3330.53	+	5768.65i	0.515252	+	0.892442i	0.999843	+	0.0177016i	$0.00563490\pi$
$347$	3330.53	+	5768.65i	0.515252	+	0.892442i	−0.484592	+	0.874741i	$0.661032\pi$
$348$		0			0
$349$	−10156.8			−1.55782			−0.778910	−	0.627135i	$-0.784227\pi$
$349$	−10156.8			−1.55782			−0.778910	+	0.627135i	$0.784227\pi$
$350$		0			0
$351$	−1166.16			−0.177336
$352$		0			0
$353$	−3641.95	−	6308.04i	−0.549125	−	0.951113i	−0.998335	−	0.0576865i	$-0.981628\pi$
$353$	−3641.95	−	6308.04i	−0.549125	−	0.951113i	0.449209	−	0.893426i	$-0.351706\pi$
$354$		0			0
$355$	−5671.56	+	9823.43i	−0.847930	+	1.46866i
$356$		0			0
$357$	−1176.70	−	1394.93i	−0.174447	−	0.206800i
$358$		0			0
$359$	2228.89	−	3860.56i	0.327678	−	0.567555i	−0.654373	−	0.756172i	$-0.727067\pi$
$359$	2228.89	−	3860.56i	0.327678	−	0.567555i	0.982051	+	0.188617i	$0.0604005\pi$
$360$		0			0
$361$	468.974	+	812.287i	0.0683735	+	0.118426i
$362$		0			0
$363$	−20417.0			−2.95211
$364$		0			0
$365$	8960.70			1.28500
$366$		0			0
$367$	−2782.24	−	4818.98i	−0.395727	−	0.685419i	0.597467	−	0.801894i	$-0.296174\pi$
$367$	−2782.24	−	4818.98i	−0.395727	−	0.685419i	−0.993194	+	0.116474i	$0.962841\pi$
$368$		0			0
$369$	−1875.54	+	3248.53i	−0.264598	+	0.458297i
$370$		0			0
$371$	−7128.80	+	1276.19i	−0.997598	+	0.178588i
$372$		0			0
$373$	3329.96	−	5767.66i	0.462249	−	0.800638i	−0.536824	−	0.843694i	$-0.680376\pi$
$373$	3329.96	−	5767.66i	0.462249	−	0.800638i	0.999073	+	0.0430563i	$0.0137095\pi$
$374$		0			0
$375$	5093.68	+	8822.51i	0.701430	+	1.21491i
$376$		0			0
$377$	11222.3			1.53310
$378$		0			0
$379$	−7581.93			−1.02759			−0.513796	−	0.857912i	$-0.671761\pi$
$379$	−7581.93			−1.02759			−0.513796	+	0.857912i	$0.671761\pi$
$380$		0			0
$381$	−3899.37	−	6753.91i	−0.524333	−	0.908171i
$382$		0			0
$383$	2505.95	−	4340.43i	0.334329	−	0.579075i	−0.649027	−	0.760766i	$-0.724824\pi$
$383$	2505.95	−	4340.43i	0.334329	−	0.579075i	0.983356	+	0.181691i	$0.0581571\pi$
$384$		0			0
$385$	4582.26	−	12692.6i	0.606581	−	1.68020i
$386$		0			0
$387$	−567.448	+	982.848i	−0.0745348	+	0.129098i
$388$		0			0
$389$	−6557.31	−	11357.6i	−0.854675	−	1.48034i	−0.876946	−	0.480589i	$-0.840423\pi$
$389$	−6557.31	−	11357.6i	−0.854675	−	1.48034i	0.0222705	−	0.999752i	$-0.492910\pi$
$390$		0			0
$391$	303.605			0.0392685
$392$		0			0
$393$	−10912.1			−1.40062
$394$		0			0
$395$	2107.41	+	3650.15i	0.268444	+	0.464959i
$396$		0			0
$397$	140.782	−	243.841i	0.0177976	−	0.0308263i	−0.856989	−	0.515334i	$-0.827668\pi$
$397$	140.782	−	243.841i	0.0177976	−	0.0308263i	0.874787	+	0.484508i	$0.161001\pi$
$398$		0			0
$399$	−3612.40	+	10006.2i	−0.453249	+	1.25547i
$400$		0			0
$401$	−3499.69	+	6061.64i	−0.435826	+	0.754873i	−0.997363	−	0.0725790i	$-0.976877\pi$
$401$	−3499.69	+	6061.64i	−0.435826	+	0.754873i	0.561537	+	0.827452i	$0.310210\pi$
$402$		0			0
$403$	15181.1	+	26294.4i	1.87648	+	3.25016i
$404$		0			0
$405$	7763.94			0.952576
$406$		0			0
$407$	17494.6			2.13065
$408$		0			0
$409$	5724.27	+	9914.72i	0.692046	+	1.19866i	0.971166	+	0.238403i	$0.0766238\pi$
$409$	5724.27	+	9914.72i	0.692046	+	1.19866i	−0.279120	+	0.960256i	$0.590043\pi$
$410$		0			0
$411$	9443.78	−	16357.1i	1.13340	−	1.96311i
$412$		0			0
$413$	11562.0	−	2069.82i	1.37756	−	0.246608i
$414$		0			0
$415$	71.5919	−	124.001i	0.00846822	−	0.0146674i
$416$		0			0
$417$	3341.67	+	5787.95i	0.392428	+	0.679705i
$418$		0			0
$419$	−6604.51			−0.770051			−0.385026	−	0.922906i	$-0.625807\pi$
$419$	−6604.51			−0.770051			−0.385026	+	0.922906i	$0.625807\pi$
$420$		0			0
$421$	−4437.86			−0.513748			−0.256874	−	0.966445i	$-0.582693\pi$
$421$	−4437.86			−0.513748			−0.256874	+	0.966445i	$0.582693\pi$
$422$		0			0
$423$	6169.22	+	10685.4i	0.709120	+	1.22823i
$424$		0			0
$425$	36.7549	−	63.6614i	0.00419500	−	0.00726596i
$426$		0			0
$427$	277.464	+	328.922i	0.0314460	+	0.0372779i
$428$		0			0
$429$	21557.4	−	37338.6i	2.42611	−	4.20215i
$430$		0			0
$431$	−2628.73	−	4553.09i	−0.293785	−	0.508851i	0.680917	−	0.732361i	$-0.261582\pi$
$431$	−2628.73	−	4553.09i	−0.293785	−	0.508851i	−0.974702	+	0.223510i	$0.928248\pi$
$432$		0			0
$433$	1287.33			0.142876			0.0714381	−	0.997445i	$-0.477241\pi$
$433$	1287.33			0.142876			0.0714381	+	0.997445i	$0.477241\pi$
$434$		0			0
$435$	10568.4			1.16487
$436$		0			0
$437$	−884.906	−	1532.70i	−0.0968668	−	0.167778i
$438$		0			0
$439$	635.010	−	1099.87i	0.0690373	−	0.119576i	−0.829440	−	0.558595i	$-0.811341\pi$
$439$	635.010	−	1099.87i	0.0690373	−	0.119576i	0.898478	+	0.439019i	$0.144674\pi$
$440$		0			0
$441$	9240.69	−	3418.05i	0.997806	−	0.369080i
$442$		0			0
$443$	−1316.97	+	2281.06i	−0.141244	+	0.244642i	−0.927965	−	0.372667i	$-0.878444\pi$
$443$	−1316.97	+	2281.06i	−0.141244	+	0.244642i	0.786721	+	0.617308i	$0.211777\pi$
$444$		0			0
$445$	−5689.72	−	9854.89i	−0.606110	−	1.04981i
$446$		0			0
$447$	2077.34			0.219810
$448$		0			0
$449$	−5690.79			−0.598140			−0.299070	−	0.954231i	$-0.596676\pi$
$449$	−5690.79			−0.598140			−0.299070	+	0.954231i	$0.596676\pi$
$450$		0			0
$451$	−4163.49	−	7211.37i	−0.434703	−	0.752928i
$452$		0			0
$453$	−9187.36	+	15913.0i	−0.952892	+	1.65046i
$454$		0			0
$455$	12359.4	+	14651.5i	1.27344	+	1.50961i
$456$		0			0
$457$	3351.90	−	5805.66i	0.343097	−	0.594261i	−0.641909	−	0.766781i	$-0.721857\pi$
$457$	3351.90	−	5805.66i	0.343097	−	0.594261i	0.985006	+	0.172519i	$0.0551908\pi$
$458$		0			0
$459$	−84.9756	−	147.182i	−0.00864122	−	0.0149670i
$460$		0			0
$461$	14764.3			1.49163			0.745817	−	0.666151i	$-0.232059\pi$
$461$	14764.3			1.49163			0.745817	+	0.666151i	$0.232059\pi$
$462$		0			0
$463$	−11586.6			−1.16301			−0.581507	−	0.813542i	$-0.697537\pi$
$463$	−11586.6			−1.16301			−0.581507	+	0.813542i	$0.697537\pi$
$464$		0			0
$465$	14296.5	+	24762.3i	1.42578	+	2.46952i
$466$		0			0
$467$	−3980.15	+	6893.83i	−0.394389	+	0.683101i	−0.993023	−	0.117921i	$-0.962377\pi$
$467$	−3980.15	+	6893.83i	−0.394389	+	0.683101i	0.598634	+	0.801022i	$0.295710\pi$
$468$		0			0
$469$	1969.47	−	352.572i	0.193906	−	0.0347127i
$470$		0			0
$471$	−12088.1	+	20937.1i	−1.18257	+	2.04826i
$472$		0			0
$473$	−1259.67	−	2181.82i	−0.122452	−	0.212093i
$474$		0			0
$475$	−428.513			−0.0413927
$476$		0			0
$477$	−11232.5			−1.07820
$478$		0			0
$479$	5770.33	+	9994.51i	0.550424	+	0.953363i	0.998244	+	0.0592390i	$0.0188674\pi$
$479$	5770.33	+	9994.51i	0.550424	+	0.953363i	−0.447819	+	0.894124i	$0.647799\pi$
$480$		0			0
$481$	−12425.2	+	21521.0i	−1.17784	+	2.04007i
$482$		0			0
$483$	−1079.75	+	2990.86i	−0.101719	+	0.281757i
$484$		0			0
$485$	9490.15	−	16437.4i	0.888507	−	1.53894i
$486$		0			0
$487$	−8690.38	−	15052.2i	−0.808622	−	1.40057i	−0.913819	−	0.406123i	$-0.866881\pi$
$487$	−8690.38	−	15052.2i	−0.808622	−	1.40057i	0.105197	−	0.994451i	$-0.466453\pi$
$488$		0			0
$489$	−2559.86			−0.236730
$490$		0			0
$491$	1639.58			0.150699			0.0753493	−	0.997157i	$-0.475993\pi$
$491$	1639.58			0.150699			0.0753493	+	0.997157i	$0.475993\pi$
$492$		0			0
$493$	817.744	+	1416.37i	0.0747046	+	0.129392i
$494$		0			0
$495$	10464.9	−	18125.7i	0.950223	−	1.64583i
$496$		0			0
$497$	6242.89	−	17292.4i	0.563444	−	1.56071i
$498$		0			0
$499$	−1693.44	+	2933.12i	−0.151921	+	0.263135i	−0.931934	−	0.362629i	$-0.881879\pi$
$499$	−1693.44	+	2933.12i	−0.151921	+	0.263135i	0.780013	+	0.625764i	$0.215213\pi$
$500$		0			0
$501$	−5329.47	−	9230.92i	−0.475256	−	0.823168i
$502$		0			0
$503$	12816.5			1.13610			0.568051	−	0.822993i	$-0.307698\pi$
$503$	12816.5			1.13610			0.568051	+	0.822993i	$0.307698\pi$
$504$		0			0
$505$	6277.08			0.553121
$506$		0			0
$507$	22421.2	+	38834.6i	1.96402	+	3.40179i
$508$		0			0
$509$	−7058.77	+	12226.2i	−0.614685	+	1.06467i	0.375755	+	0.926719i	$0.377383\pi$
$509$	−7058.77	+	12226.2i	−0.614685	+	1.06467i	−0.990440	+	0.137946i	$0.955950\pi$
$510$		0			0
$511$	−14296.2	+	2559.28i	−1.23762	+	0.221557i
$512$		0			0
$513$	−495.350	+	857.971i	−0.0426320	+	0.0738409i
$514$		0			0
$515$	−9653.76	−	16720.8i	−0.826010	−	1.43069i
$516$		0			0
$517$	−27390.0			−2.33000
$518$		0			0
$519$	20369.6			1.72279
$520$		0			0
$521$	−3200.43	−	5543.30i	−0.269123	−	0.466135i	0.699512	−	0.714621i	$-0.253401\pi$
$521$	−3200.43	−	5543.30i	−0.269123	−	0.466135i	−0.968636	+	0.248485i	$0.920067\pi$
$522$		0			0
$523$	−801.386	+	1388.04i	−0.0670023	+	0.116051i	−0.897580	−	0.440851i	$-0.854677\pi$
$523$	−801.386	+	1388.04i	−0.0670023	+	0.116051i	0.830578	+	0.556902i	$0.188010\pi$
$524$		0			0
$525$	496.420	+	588.486i	0.0412677	+	0.0489212i
$526$		0			0
$527$	−2212.42	+	3832.03i	−0.182874	+	0.316747i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	18217.7			1.48885
$532$		0			0
$533$	11828.1			0.961224
$534$		0			0
$535$	9966.81	+	17263.0i	0.805426	+	1.39504i
$536$		0			0
$537$	−613.925	+	1063.35i	−0.0493349	+	0.0854505i
$538$		0			0
$539$	−3685.52	+	21558.9i	−0.294521	+	1.72283i
$540$		0			0
$541$	−2994.95	+	5187.41i	−0.238009	+	0.412244i	−0.960143	−	0.279509i	$-0.909828\pi$
$541$	−2994.95	+	5187.41i	−0.238009	+	0.412244i	0.722134	+	0.691754i	$0.243162\pi$
$542$		0			0
$543$	6102.77	+	10570.3i	0.482311	+	0.835387i
$544$		0			0
$545$	−7219.39			−0.567421
$546$		0			0
$547$	−11063.8			−0.864813			−0.432407	−	0.901679i	$-0.642335\pi$
$547$	−11063.8			−0.864813			−0.432407	+	0.901679i	$0.642335\pi$
$548$		0			0
$549$	333.712	+	578.006i	0.0259426	+	0.0449338i
$550$		0			0
$551$	4766.90	−	8256.51i	0.368560	−	0.638365i
$552$		0			0
$553$	−4404.75	−	5221.65i	−0.338715	−	0.401532i
$554$		0			0
$555$	−11701.2	+	20267.1i	−0.894935	+	1.55007i
$556$		0			0
$557$	−3719.68	−	6442.68i	−0.282959	−	0.490099i	0.689153	−	0.724616i	$-0.257983\pi$
$557$	−3719.68	−	6442.68i	−0.282959	−	0.490099i	−0.972112	+	0.234516i	$0.924649\pi$
$558$		0			0
$559$	3578.62			0.270768
$560$		0			0
$561$	6283.37			0.472877
$562$		0			0
$563$	−3039.09	−	5263.86i	−0.227500	−	0.394041i	0.729567	−	0.683910i	$-0.239722\pi$
$563$	−3039.09	−	5263.86i	−0.227500	−	0.394041i	−0.957067	+	0.289868i	$0.906388\pi$
$564$		0			0
$565$	−5286.21	+	9155.99i	−0.393615	+	0.681762i
$566$		0			0
$567$	−12386.8	+	2217.47i	−0.917456	+	0.164242i
$568$		0			0
$569$	−3839.56	+	6650.31i	−0.282887	+	0.489975i	−0.972095	−	0.234589i	$-0.924626\pi$
$569$	−3839.56	+	6650.31i	−0.282887	+	0.489975i	0.689208	+	0.724564i	$0.257959\pi$
$570$		0			0
$571$	8239.77	+	14271.7i	0.603894	+	1.04598i	0.992225	+	0.124455i	$0.0397184\pi$
$571$	8239.77	+	14271.7i	0.603894	+	1.04598i	−0.388331	+	0.921520i	$0.626948\pi$
$572$		0			0
$573$	1397.33			0.101875
$574$		0			0
$575$	−128.083			−0.00928946
$576$		0			0
$577$	−2152.49	−	3728.22i	−0.155302	−	0.268991i	0.777867	−	0.628429i	$-0.216302\pi$
$577$	−2152.49	−	3728.22i	−0.155302	−	0.268991i	−0.933169	+	0.359438i	$0.882968\pi$
$578$		0			0
$579$	16978.9	−	29408.4i	1.21869	−	2.11083i
$580$		0			0
$581$	−78.8038	+	218.282i	−0.00562708	+	0.0155867i
$582$		0			0
$583$	12467.4	−	21594.2i	0.885674	−	1.53403i
$584$		0			0
$585$	14864.9	+	25746.7i	1.05058	+	1.81965i
$586$		0			0
$587$	−19331.1			−1.35925			−0.679626	−	0.733559i	$-0.737858\pi$
$587$	−19331.1			−1.35925			−0.679626	+	0.733559i	$0.737858\pi$
$588$		0			0
$589$	25793.9			1.80444
$590$		0			0
$591$	−3236.17	−	5605.21i	−0.225242	−	0.390131i
$592$		0			0
$593$	−1474.05	+	2553.12i	−0.102077	+	0.176803i	−0.912540	−	0.408987i	$-0.865882\pi$
$593$	−1474.05	+	2553.12i	−0.102077	+	0.176803i	0.810463	+	0.585790i	$0.199216\pi$
$594$		0			0
$595$	−948.580	+	2627.51i	−0.0653579	+	0.181038i
$596$		0			0
$597$	7988.55	−	13836.6i	0.547654	−	0.948565i
$598$		0			0
$599$	−4715.87	−	8168.13i	−0.321678	−	0.557163i	0.659156	−	0.752006i	$-0.270914\pi$
$599$	−4715.87	−	8168.13i	−0.321678	−	0.557163i	−0.980834	+	0.194843i	$0.937580\pi$
$600$		0			0
$601$	16144.8			1.09578			0.547888	−	0.836551i	$-0.315432\pi$
$601$	16144.8			1.09578			0.547888	+	0.836551i	$0.315432\pi$
$602$		0			0
$603$	3103.19			0.209572
$604$		0			0
$605$	15626.4	+	27065.7i	1.05009	+	1.81880i
$606$		0			0
$607$	−4199.19	+	7273.21i	−0.280791	+	0.486343i	−0.971580	−	0.236713i	$-0.923930\pi$
$607$	−4199.19	+	7273.21i	−0.280791	+	0.486343i	0.690789	+	0.723056i	$0.257263\pi$
$608$		0			0
$609$	−16861.2	+	3018.46i	−1.12192	+	0.200844i
$610$		0			0
$611$	19453.1	−	33693.8i	1.28804	−	2.23094i
$612$		0			0
$613$	−13281.9	−	23004.9i	−0.875123	−	1.51576i	−0.856632	−	0.515929i	$-0.827447\pi$
$613$	−13281.9	−	23004.9i	−0.875123	−	1.51576i	−0.0184915	−	0.999829i	$-0.505886\pi$
$614$		0			0
$615$	11138.9			0.730350
$616$		0			0
$617$	−18168.9			−1.18550			−0.592750	−	0.805386i	$-0.701958\pi$
$617$	−18168.9			−1.18550			−0.592750	+	0.805386i	$0.701958\pi$
$618$		0			0
$619$	−5077.10	−	8793.80i	−0.329670	−	0.571006i	0.652776	−	0.757551i	$-0.273604\pi$
$619$	−5077.10	−	8793.80i	−0.329670	−	0.571006i	−0.982446	+	0.186545i	$0.940271\pi$
$620$		0			0
$621$	−148.061	+	256.449i	−0.00956760	+	0.0165716i
$622$		0			0
$623$	11892.2	+	14097.7i	0.764770	+	0.906603i
$624$		0			0
$625$	8145.05	−	14107.6i	0.521283	−	0.902889i
$626$		0			0
$627$	−18313.9	−	31720.6i	−1.16649	−	2.02041i
$628$		0			0
$629$	−3621.58			−0.229574
$630$		0			0
$631$	−3803.68			−0.239971			−0.119986	−	0.992776i	$-0.538285\pi$
$631$	−3803.68			−0.239971			−0.119986	+	0.992776i	$0.538285\pi$
$632$		0			0
$633$	8359.66	+	14479.3i	0.524908	+	0.909167i
$634$		0			0
$635$	−5968.84	+	10338.3i	−0.373018	+	0.646086i
$636$		0			0
$637$	−23903.1	−	19845.5i	−1.48678	−	1.23439i
$638$		0			0
$639$	14257.3	−	24694.4i	0.882648	−	1.52879i
$640$		0			0
$641$	13142.9	+	22764.2i	0.809851	+	1.40270i	0.912967	+	0.408034i	$0.133785\pi$
$641$	13142.9	+	22764.2i	0.809851	+	1.40270i	−0.103116	+	0.994669i	$0.532881\pi$
$642$		0			0
$643$	15340.8			0.940873			0.470436	−	0.882434i	$-0.344096\pi$
$643$	15340.8			0.940873			0.470436	+	0.882434i	$0.344096\pi$
$644$		0			0
$645$	3370.11			0.205733
$646$		0			0
$647$	11062.3	+	19160.4i	0.672185	+	1.16426i	0.977283	+	0.211937i	$0.0679772\pi$
$647$	11062.3	+	19160.4i	0.672185	+	1.16426i	−0.305099	+	0.952321i	$0.598689\pi$
$648$		0			0
$649$	−20220.6	+	35023.2i	−1.22300	+	2.11830i
$650$		0			0
$651$	−29881.5	−	35423.3i	−1.79900	−	2.13264i
$652$		0			0
$653$	−2106.69	+	3648.89i	−0.126250	+	0.218671i	−0.922221	−	0.386664i	$-0.873627\pi$
$653$	−2106.69	+	3648.89i	−0.126250	+	0.218671i	0.795971	+	0.605335i	$0.206961\pi$
$654$		0			0
$655$	8351.69	+	14465.6i	0.498210	+	0.862925i
$656$		0			0
$657$	−22525.7			−1.33761
$658$		0			0
$659$	−22176.6			−1.31089			−0.655445	−	0.755243i	$-0.727519\pi$
$659$	−22176.6			−1.31089			−0.655445	+	0.755243i	$0.727519\pi$
$660$		0			0
$661$	6290.90	+	10896.2i	0.370178	+	0.641167i	0.989593	−	0.143897i	$-0.0459633\pi$
$661$	6290.90	+	10896.2i	0.370178	+	0.641167i	−0.619415	+	0.785064i	$0.712630\pi$
$662$		0			0
$663$	−4462.63	+	7729.50i	−0.261409	+	0.452773i
$664$		0			0
$665$	16029.4	−	2869.55i	0.934725	−	0.167333i
$666$		0			0
$667$	1424.83	−	2467.88i	0.0827133	−	0.143264i
$668$		0			0
$669$	3101.77	+	5372.42i	0.179254	+	0.310478i
$670$		0			0
$671$	−1481.61			−0.0852412
$672$		0			0
$673$	8373.89			0.479628			0.239814	−	0.970819i	$-0.422914\pi$
$673$	8373.89			0.479628			0.239814	+	0.970819i	$0.422914\pi$
$674$		0			0
$675$	35.8490	+	62.0923i	0.00204419	+	0.00354064i
$676$		0			0
$677$	−16859.1	+	29200.8i	−0.957087	+	1.65772i	−0.227569	+	0.973762i	$0.573078\pi$
$677$	−16859.1	+	29200.8i	−0.957087	+	1.65772i	−0.729518	+	0.683962i	$0.760256\pi$
$678$		0			0
$679$	−10446.1	+	28935.2i	−0.590407	+	1.63539i
$680$		0			0
$681$	18876.5	−	32695.0i	1.06219	−	1.83976i
$682$		0			0
$683$	8848.00	+	15325.2i	0.495694	+	0.858568i	0.999988	−	0.00496453i	$-0.00158027\pi$
$683$	8848.00	+	15325.2i	0.495694	+	0.858568i	−0.504293	+	0.863532i	$0.668247\pi$
$684$		0			0
$685$	−28911.6			−1.61263
$686$		0			0
$687$	−15387.4			−0.854535
$688$		0			0
$689$	17709.4	+	30673.6i	0.979210	+	1.69604i
$690$		0			0
$691$	779.810	−	1350.67i	0.0429311	−	0.0743588i	−0.843761	−	0.536718i	$-0.819664\pi$
$691$	779.810	−	1350.67i	0.0429311	−	0.0743588i	0.886692	+	0.462360i	$0.152997\pi$
$692$		0			0
$693$	−11519.0	+	31907.1i	−0.631417	+	1.74899i
$694$		0			0
$695$	5115.17	−	8859.73i	0.279179	−	0.483552i
$696$		0			0
$697$	861.888	+	1492.83i	0.0468384	+	0.0811265i
$698$		0			0
$699$	−7590.93			−0.410751
$700$		0			0
$701$	6568.47			0.353905			0.176953	−	0.984219i	$-0.443376\pi$
$701$	6568.47			0.353905			0.176953	+	0.984219i	$0.443376\pi$
$702$		0			0
$703$	10555.7	+	18283.0i	0.566309	+	0.980876i
$704$		0			0
$705$	18319.7	−	31730.6i	0.978665	−	1.69510i
$706$		0			0
$707$	−10014.6	+	1792.80i	−0.532728	+	0.0953683i
$708$		0			0
$709$	2608.43	−	4517.94i	0.138169	−	0.239316i	−0.788635	−	0.614862i	$-0.789212\pi$
$709$	2608.43	−	4517.94i	0.138169	−	0.239316i	0.926804	+	0.375546i	$0.122545\pi$
$710$		0			0
$711$	−5297.68	−	9175.86i	−0.279436	−	0.483997i
$712$		0			0
$713$	7709.83			0.404958
$714$		0			0
$715$	−65996.8			−3.45194
$716$		0			0
$717$	−4610.51	−	7985.64i	−0.240143	−	0.415940i
$718$		0			0
$719$	−8536.95	+	14786.4i	−0.442802	+	0.766955i	−0.997896	−	0.0648320i	$-0.979349\pi$
$719$	−8536.95	+	14786.4i	−0.442802	+	0.766955i	0.555094	+	0.831787i	$0.312682\pi$
$720$		0			0
$721$	20177.5	+	23919.6i	1.04223	+	1.23552i
$722$		0			0
$723$	6177.58	−	10699.9i	0.317769	−	0.550392i
$724$		0			0
$725$	−344.985	−	597.532i	−0.0176723	−	0.0306094i
$726$		0			0
$727$	−4325.68			−0.220675			−0.110337	−	0.993894i	$-0.535193\pi$
$727$	−4325.68			−0.220675			−0.110337	+	0.993894i	$0.535193\pi$
$728$		0			0
$729$	−22112.2			−1.12342
$730$		0			0
$731$	260.766	+	451.660i	0.0131940	+	0.0228526i
$732$		0			0
$733$	15335.8	−	26562.3i	0.772769	−	1.33848i	−0.163271	−	0.986581i	$-0.552204\pi$
$733$	15335.8	−	26562.3i	0.772769	−	1.33848i	0.936040	−	0.351894i	$-0.114462\pi$
$734$		0			0
$735$	−22510.4	−	18689.2i	−1.12967	−	0.937906i
$736$		0			0
$737$	−3444.37	+	5965.83i	−0.172151	+	0.298174i
$738$		0			0
$739$	6125.26	+	10609.3i	0.304900	+	0.528103i	0.977239	−	0.212141i	$-0.0680435\pi$
$739$	6125.26	+	10609.3i	0.304900	+	0.528103i	−0.672339	+	0.740244i	$0.734710\pi$
$740$		0			0
$741$	52028.2			2.57936
$742$		0			0
$743$	−23181.6			−1.14462			−0.572308	−	0.820039i	$-0.693952\pi$
$743$	−23181.6			−1.14462			−0.572308	+	0.820039i	$0.693952\pi$
$744$		0			0
$745$	−1589.92	−	2753.81i	−0.0781879	−	0.135425i
$746$		0			0
$747$	−179.970	+	311.717i	−0.00881494	+	0.0152679i
$748$		0			0
$749$	−20831.8	−	24695.3i	−1.01626	−	1.20473i
$750$		0			0
$751$	2899.81	−	5022.61i	0.140899	−	0.244045i	−0.786936	−	0.617034i	$-0.788334\pi$
$751$	2899.81	−	5022.61i	0.140899	−	0.244045i	0.927836	+	0.372989i	$0.121667\pi$
$752$		0			0
$753$	−6083.73	−	10537.3i	−0.294427	−	0.509962i
$754$		0			0
$755$	28126.6			1.35580
$756$		0			0
$757$	−16508.6			−0.792623			−0.396311	−	0.918116i	$-0.629710\pi$
$757$	−16508.6			−0.792623			−0.396311	+	0.918116i	$0.629710\pi$
$758$		0			0
$759$	−5474.06	−	9481.35i	−0.261786	−	0.453427i
$760$		0			0
$761$	−17581.4	+	30451.9i	−0.837485	+	1.45057i	0.0545061	+	0.998513i	$0.482642\pi$
$761$	−17581.4	+	30451.9i	−0.837485	+	1.45057i	−0.891991	+	0.452053i	$0.850692\pi$
$762$		0			0
$763$	11518.0	−	2061.94i	0.546501	−	0.0978338i
$764$		0			0
$765$	−2166.34	+	3752.21i	−0.102385	+	0.177335i
$766$		0			0
$767$	−28722.5	−	49748.9i	−1.35216	−	2.34202i
$768$		0			0
$769$	6622.63			0.310557			0.155278	−	0.987871i	$-0.450373\pi$
$769$	6622.63			0.310557			0.155278	+	0.987871i	$0.450373\pi$
$770$		0			0
$771$	45863.0			2.14230
$772$		0			0
$773$	3780.14	+	6547.39i	0.175889	+	0.304649i	0.940469	−	0.339881i	$-0.110387\pi$
$773$	3780.14	+	6547.39i	0.175889	+	0.304649i	−0.764580	+	0.644529i	$0.777053\pi$
$774$		0			0
$775$	933.364	−	1616.63i	0.0432612	−	0.0749306i
$776$		0			0
$777$	12879.9	−	35676.7i	0.594679	−	1.64723i
$778$		0			0
$779$	5024.23	−	8702.22i	0.231080	−	0.400243i
$780$		0			0
$781$	31649.8	+	54819.0i	1.45009	+	2.51162i
$782$		0			0
$783$	−1595.18			−0.0728059
$784$		0			0
$785$	37006.9			1.68259
$786$		0			0
$787$	21497.4	+	37234.6i	0.973697	+	1.68649i	0.684169	+	0.729324i	$0.260165\pi$
$787$	21497.4	+	37234.6i	0.973697	+	1.68649i	0.289529	+	0.957169i	$0.406501\pi$
$788$		0			0
$789$	8629.58	−	14946.9i	0.389380	−	0.674427i
$790$		0			0
$791$	5818.72	−	16117.5i	0.261555	−	0.724492i
$792$		0			0
$793$	1052.28	−	1822.60i	0.0471217	−	0.0816172i
$794$		0			0
$795$	16677.6	+	28886.4i	0.744016	+	1.28867i
$796$		0			0
$797$	−3173.19			−0.141029			−0.0705146	−	0.997511i	$-0.522464\pi$
$797$	−3173.19			−0.141029			−0.0705146	+	0.997511i	$0.522464\pi$
$798$		0			0
$799$	5670.03			0.251053
$800$		0			0
$801$	14303.0	+	24773.5i	0.630926	+	1.09280i
$802$		0			0
$803$	25002.3	−	43305.2i	1.09877	−	1.90312i
$804$		0			0
$805$	4791.21	−	857.714i	0.209774	−	0.0375534i
$806$		0			0
$807$	−18612.9	+	32238.5i	−0.811903	+	1.40626i
$808$		0			0
$809$	−3306.42	−	5726.88i	−0.143693	−	0.248883i	0.785192	−	0.619253i	$-0.212564\pi$
$809$	−3306.42	−	5726.88i	−0.143693	−	0.248883i	−0.928884	+	0.370370i	$0.879231\pi$
$810$		0			0
$811$	−32704.8			−1.41606			−0.708028	−	0.706185i	$-0.750415\pi$
$811$	−32704.8			−1.41606			−0.708028	+	0.706185i	$0.750415\pi$
$812$		0			0
$813$	17713.9			0.764151
$814$		0			0
$815$	1959.21	+	3393.46i	0.0842064	+	0.145850i
$816$		0			0
$817$	1520.09	−	2632.87i	0.0650933	−	0.112745i
$818$		0			0
$819$	−31069.4	−	36831.5i	−1.32558	−	1.57142i
$820$		0			0
$821$	−18683.8	+	32361.4i	−0.794239	+	1.37566i	0.129082	+	0.991634i	$0.458797\pi$
$821$	−18683.8	+	32361.4i	−0.794239	+	1.37566i	−0.923321	+	0.384029i	$0.874536\pi$
$822$		0			0
$823$	11312.8	+	19594.3i	0.479149	+	0.829910i	0.999714	−	0.0239120i	$-0.00761215\pi$
$823$	11312.8	+	19594.3i	0.479149	+	0.829910i	−0.520565	+	0.853822i	$0.674279\pi$
$824$		0			0
$825$	−2650.79			−0.111865
$826$		0			0
$827$	27141.4			1.14123			0.570615	−	0.821218i	$-0.306705\pi$
$827$	27141.4			1.14123			0.570615	+	0.821218i	$0.306705\pi$
$828$		0			0
$829$	−21489.0	−	37220.0i	−0.900293	−	1.55935i	−0.827114	−	0.562034i	$-0.810019\pi$
$829$	−21489.0	−	37220.0i	−0.900293	−	1.55935i	−0.0731786	−	0.997319i	$-0.523314\pi$
$830$		0			0
$831$	5541.38	−	9597.94i	0.231322	−	0.400661i
$832$		0			0
$833$	762.944	−	4462.93i	0.0317340	−	0.185632i
$834$		0			0
$835$	−8157.93	+	14130.0i	−0.338104	+	0.585613i
$836$		0			0
$837$	−2157.89	−	3737.58i	−0.0891131	−	0.154348i
$838$		0			0
$839$	22983.1			0.945727			0.472863	−	0.881136i	$-0.343220\pi$
$839$	22983.1			0.945727			0.472863	+	0.881136i	$0.343220\pi$
$840$		0			0
$841$	−9038.14			−0.370583
$842$		0			0
$843$	−13428.0	−	23257.9i	−0.548616	−	0.950231i
$844$		0			0
$845$	34320.6	−	59445.0i	1.39723	−	2.42008i
$846$		0			0
$847$	−32661.1	−	38718.3i	−1.32497	−	1.57069i
$848$		0			0
$849$	4908.59	−	8501.92i	0.198424	−	0.343681i
$850$		0			0
$851$	3155.11	+	5464.82i	0.127093	+	0.220131i
$852$		0			0
$853$	−4791.26			−0.192321			−0.0961603	−	0.995366i	$-0.530656\pi$
$853$	−4791.26			−0.192321			−0.0961603	+	0.995366i	$0.530656\pi$
$854$		0			0
$855$	25256.6			1.01024
$856$		0			0
$857$	8038.14	+	13922.5i	0.320394	+	0.554939i	0.980569	−	0.196173i	$-0.0628514\pi$
$857$	8038.14	+	13922.5i	0.320394	+	0.554939i	−0.660175	+	0.751112i	$0.729518\pi$
$858$		0			0
$859$	5125.39	−	8877.44i	0.203581	−	0.352613i	−0.746099	−	0.665835i	$-0.768075\pi$
$859$	5125.39	−	8877.44i	0.203581	−	0.352613i	0.949680	+	0.313223i	$0.101409\pi$
$860$		0			0
$861$	−17771.4	+	3181.40i	−0.703422	+	0.125926i
$862$		0			0
$863$	−18619.6	+	32250.1i	−0.734436	+	1.27208i	0.220534	+	0.975379i	$0.429220\pi$
$863$	−18619.6	+	32250.1i	−0.734436	+	1.27208i	−0.954970	+	0.296701i	$0.904113\pi$
$864$		0			0
$865$	−15590.1	−	27002.9i	−0.612809	−	1.06142i
$866$		0			0
$867$	35374.3			1.38567
$868$		0			0
$869$	23520.6			0.918159
$870$		0			0
$871$	−4892.58	−	8474.20i	−0.190332	−	0.329664i
$872$		0			0
$873$	−23856.6	+	41320.9i	−0.924885	+	1.60195i
$874$		0			0
$875$	−8582.43	+	23772.8i	−0.331587	+	0.918478i
$876$		0			0
$877$	−6543.98	+	11334.5i	−0.251966	+	0.436418i	−0.964067	−	0.265659i	$-0.914411\pi$
$877$	−6543.98	+	11334.5i	−0.251966	+	0.436418i	0.712101	+	0.702077i	$0.247744\pi$
$878$		0			0
$879$	−14733.0	−	25518.2i	−0.565336	−	0.979190i
$880$		0			0
$881$	−18252.9			−0.698020			−0.349010	−	0.937119i	$-0.613482\pi$
$881$	−18252.9			−0.698020			−0.349010	+	0.937119i	$0.613482\pi$
$882$		0			0
$883$	1443.42			0.0550112			0.0275056	−	0.999622i	$-0.491244\pi$
$883$	1443.42			0.0550112			0.0275056	+	0.999622i	$0.491244\pi$
$884$		0			0
$885$	−27049.0	−	46850.2i	−1.02739	−	1.77949i
$886$		0			0
$887$	16282.7	−	28202.4i	0.616368	−	1.06758i	−0.373774	−	0.927520i	$-0.621937\pi$
$887$	16282.7	−	28202.4i	0.616368	−	1.06758i	0.990143	−	0.140062i	$-0.0447301\pi$
$888$		0			0
$889$	6570.12	−	18198.9i	0.247868	−	0.686581i
$890$		0			0
$891$	21663.1	−	37521.5i	0.814523	−	1.41080i
$892$		0			0
$893$	−16526.2	−	28624.3i	−0.619293	−	1.07265i
$894$		0			0
$895$	1879.49			0.0701951
$896$		0			0
$897$	15551.3			0.578867
$898$		0			0
$899$	20766.0	+	35967.8i	0.770395	+	1.33436i
$900$		0			0
$901$	−2580.90	+	4470.24i	−0.0954296	+	0.165289i
$902$		0			0
$903$	−5376.77	+	962.541i	−0.198148	+	0.0354721i
$904$		0			0
$905$	9341.63	−	16180.2i	0.343123	−	0.594306i
$906$		0			0
$907$	−2025.31	−	3507.93i	−0.0741447	−	0.128422i	0.826569	−	0.562835i	$-0.190289\pi$
$907$	−2025.31	−	3507.93i	−0.0741447	−	0.128422i	−0.900714	+	0.434413i	$0.856956\pi$
$908$		0			0
$909$	−15779.5			−0.575768
$910$		0			0
$911$	−13068.0			−0.475261			−0.237631	−	0.971356i	$-0.576371\pi$
$911$	−13068.0			−0.475261			−0.237631	+	0.971356i	$0.576371\pi$
$912$		0			0
$913$	−399.514	−	691.978i	−0.0144819	−	0.0250834i
$914$		0			0
$915$	990.967	−	1716.41i	0.0358037	−	0.0620138i
$916$		0			0
$917$	−17456.1	−	20693.4i	−0.628626	−	0.745210i
$918$		0			0
$919$	27450.7	−	47546.0i	0.985326	−	1.70663i	0.344845	−	0.938660i	$-0.387931\pi$
$919$	27450.7	−	47546.0i	0.985326	−	1.70663i	0.640481	−	0.767974i	$-0.278735\pi$
$920$		0			0
$921$	−28180.2	−	48809.5i	−1.00822	−	1.74629i
$922$		0			0
$923$	−89914.2			−3.20646
$924$		0			0
$925$	1527.85			0.0543086
$926$		0			0
$927$	24267.9	+	42033.3i	0.859830	+	1.48927i
$928$		0			0
$929$	−5681.39	+	9840.45i	−0.200646	+	0.347529i	−0.948737	−	0.316067i	$-0.897638\pi$
$929$	−5681.39	+	9840.45i	−0.200646	+	0.347529i	0.748091	+	0.663597i	$0.230971\pi$
$930$		0			0
$931$	−24754.1	+	9156.34i	−0.871411	+	0.322327i
$932$		0			0
$933$	−18096.1	+	31343.4i	−0.634984	+	1.09982i
$934$		0			0
$935$	−4809.04	−	8329.51i	−0.168206	−	0.291341i
$936$		0			0
$937$	−15787.6			−0.550438			−0.275219	−	0.961382i	$-0.588750\pi$
$937$	−15787.6			−0.550438			−0.275219	+	0.961382i	$0.588750\pi$
$938$		0			0
$939$	−66262.3			−2.30286
$940$		0			0
$941$	−1266.59	−	2193.80i	−0.0438786	−	0.0759999i	0.843252	−	0.537518i	$-0.180638\pi$
$941$	−1266.59	−	2193.80i	−0.0438786	−	0.0759999i	−0.887131	+	0.461518i	$0.847305\pi$
$942$		0			0
$943$	1501.75	−	2601.11i	0.0518597	−	0.0898237i
$944$		0			0
$945$	−1756.81	−	2082.62i	−0.0604751	−	0.0716907i
$946$		0			0
$947$	15482.7	−	26816.9i	0.531279	−	0.920203i	−0.468054	−	0.883700i	$-0.655045\pi$
$947$	15482.7	−	26816.9i	0.531279	−	0.920203i	0.999334	−	0.0365031i	$-0.0116219\pi$
$948$		0			0
$949$	35514.7	+	61513.2i	1.21481	+	2.10411i
$950$		0			0
$951$	8172.01			0.278650
$952$		0			0
$953$	−406.494			−0.0138170			−0.00690852	−	0.999976i	$-0.502199\pi$
$953$	−406.494			−0.0138170			−0.00690852	+	0.999976i	$0.502199\pi$
$954$		0			0
$955$	−1069.46	−	1852.35i	−0.0362375	−	0.0627652i
$956$		0			0
$957$	29488.2	−	51075.0i	0.996047	−	1.72520i
$958$		0			0
$959$	46126.3	−	8257.47i	1.55318	−	0.278047i
$960$		0			0
$961$	−41287.4	+	71511.8i	−1.38590	+	2.40045i
$962$		0			0
$963$	−25054.9	−	43396.3i	−0.838403	−	1.45216i
$964$		0			0
$965$	−51980.0			−1.73398
$966$		0			0
$967$	−53777.3			−1.78838			−0.894189	−	0.447689i	$-0.852247\pi$
$967$	−53777.3			−1.78838			−0.894189	+	0.447689i	$0.852247\pi$
$968$		0			0
$969$	3791.18	+	6566.52i	0.125687	+	0.217696i
$970$		0			0
$971$	−18137.4	+	31414.9i	−0.599441	+	1.03826i	0.393462	+	0.919341i	$0.371277\pi$
$971$	−18137.4	+	31414.9i	−0.599441	+	1.03826i	−0.992904	+	0.118922i	$0.962056\pi$
$972$		0			0
$973$	−5630.45	+	15596.0i	−0.185513	+	0.513859i
$974$		0			0
$975$	1882.67	−	3260.88i	0.0618396	−	0.107109i
$976$		0			0
$977$	−4346.11	−	7527.68i	−0.142318	−	0.246501i	0.786051	−	0.618161i	$-0.212122\pi$
$977$	−4346.11	−	7527.68i	−0.142318	−	0.246501i	−0.928369	+	0.371660i	$0.878789\pi$
$978$		0			0
$979$	−63502.2			−2.07307
$980$		0			0
$981$	18148.3			0.590654
$982$		0			0
$983$	5708.01	+	9886.56i	0.185206	+	0.320786i	0.943646	−	0.330957i	$-0.107372\pi$
$983$	5708.01	+	9886.56i	0.185206	+	0.320786i	−0.758440	+	0.651743i	$0.774038\pi$
$984$		0			0
$985$	−4953.67	+	8580.01i	−0.160241	+	0.277545i
$986$		0			0
$987$	−20165.1	+	55856.2i	−0.650317	+	1.80134i
$988$		0			0
$989$	454.358	−	786.970i	0.0146084	−	0.0253025i
$990$		0			0
$991$	−1747.80	−	3027.27i	−0.0560248	−	0.0970378i	0.836653	−	0.547734i	$-0.184509\pi$
$991$	−1747.80	−	3027.27i	−0.0560248	−	0.0970378i	−0.892678	+	0.450696i	$0.851176\pi$
$992$		0			0
$993$	5607.87			0.179215
$994$		0			0
$995$	−24456.5			−0.779218
$996$		0			0
$997$	19320.1	+	33463.4i	0.613715	+	1.06299i	0.990609	+	0.136729i	$0.0436589\pi$
$997$	19320.1	+	33463.4i	0.613715	+	1.06299i	−0.376894	+	0.926257i	$0.623008\pi$
$998$		0			0
$999$	1766.16	−	3059.08i	0.0559347	−	0.0968818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.18	✓	44
7.4	even	3	inner	644.4.i.b.277.18	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.18	✓	44	1.1	even	1	trivial
644.4.i.b.277.18	yes	44	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.73245 + 6.46479i) q^{3} +(5.71334 - 9.89579i) q^{5} +(-6.28887 + 17.4198i) q^{7} +(-14.3624 + 24.8763i) q^{9} +O(q^{10})\)	\(q+(3.73245 + 6.46479i) q^{3} +(5.71334 - 9.89579i) q^{5} +(-6.28887 + 17.4198i) q^{7} +(-14.3624 + 24.8763i) q^{9} +(-31.8829 - 55.2228i) q^{11} +90.5765 q^{13} +85.2990 q^{15} +(6.60011 + 11.4317i) q^{17} +(38.4742 - 66.6392i) q^{19} +(-136.088 + 24.3623i) q^{21} +(11.5000 - 19.9186i) q^{23} +(-2.78442 - 4.82275i) q^{25} -12.8749 q^{27} +123.899 q^{29} +(167.605 + 290.300i) q^{31} +(238.002 - 412.232i) q^{33} +(136.452 + 161.759i) q^{35} +(-137.179 + 237.601i) q^{37} +(338.072 + 585.558i) q^{39} +130.587 q^{41} +39.5094 q^{43} +(164.114 + 284.254i) q^{45} +(214.770 - 371.993i) q^{47} +(-263.900 - 219.102i) q^{49} +(-49.2692 + 85.3367i) q^{51} +(195.519 + 338.649i) q^{53} -728.630 q^{55} +574.412 q^{57} +(-317.108 - 549.247i) q^{59} +(11.6176 - 20.1222i) q^{61} +(-343.018 - 406.634i) q^{63} +(517.494 - 896.326i) q^{65} +(-54.0160 - 93.5585i) q^{67} +171.693 q^{69} -992.688 q^{71} +(392.096 + 679.130i) q^{73} +(20.7854 - 36.0014i) q^{75} +(1162.48 - 208.105i) q^{77} +(-184.429 + 319.441i) q^{79} +(339.729 + 588.428i) q^{81} +12.5307 q^{83} +150.835 q^{85} +(462.445 + 800.979i) q^{87} +(497.934 - 862.446i) q^{89} +(-569.624 + 1577.83i) q^{91} +(-1251.15 + 2167.06i) q^{93} +(-439.632 - 761.465i) q^{95} +1661.05 q^{97} +1831.65 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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