LMFDB - Embedded newform 104.4.o.a.17.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [104,4,Mod(17,104)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(104, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

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

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

chi := DirichletCharacter("104.17");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 104 = 2^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	104.o (of order $6$, 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:	$6.13619864060$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 340 x^{18} + 48278 x^{16} + 3724852 x^{14} + 170209937 x^{12} + 4703455168 x^{10} + \cdots + 549543481344 $ x^20 + 340x^18 + 48278x^16 + 3724852x^14 + 170209937x^12 + 4703455168x^10 + 76591569568x^8 + 674465272704x^6 + 2596745246976x^4 + 2244726908928*x^2 + 549543481344
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{40} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.9
Root			$7.81696i$ of defining polynomial
Character	$\chi$	$=$	104.17
Dual form			104.4.o.a.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.40848 - 5.90366i) q^{3} -12.7779i q^{5} +(-2.31195 + 1.33481i) q^{7} +(-9.73548 - 16.8623i) q^{9} +O(q^{10})$	\(q+(3.40848 - 5.90366i) q^{3} -12.7779i q^{5} +(-2.31195 + 1.33481i) q^{7} +(-9.73548 - 16.8623i) q^{9} +(-34.8449 - 20.1177i) q^{11} +(25.0545 + 39.6140i) q^{13} +(-75.4364 - 43.5532i) q^{15} +(-16.4208 - 28.4416i) q^{17} +(15.5366 - 8.97007i) q^{19} +18.1987i q^{21} +(68.7952 - 119.157i) q^{23} -38.2746 q^{25} +51.3252 q^{27} +(-51.2989 + 88.8524i) q^{29} -276.308i q^{31} +(-237.536 + 137.142i) q^{33} +(17.0560 + 29.5419i) q^{35} +(350.213 + 202.195i) q^{37} +(319.266 - 12.8900i) q^{39} +(8.94701 + 5.16556i) q^{41} +(102.049 + 176.754i) q^{43} +(-215.465 + 124.399i) q^{45} +160.135i q^{47} +(-167.937 + 290.875i) q^{49} -223.880 q^{51} +547.517 q^{53} +(-257.062 + 445.244i) q^{55} -122.297i q^{57} +(-356.890 + 206.051i) q^{59} +(302.095 + 523.245i) q^{61} +(45.0159 + 25.9900i) q^{63} +(506.184 - 320.144i) q^{65} +(-584.393 - 337.399i) q^{67} +(-468.974 - 812.287i) q^{69} +(624.030 - 360.284i) q^{71} -562.708i q^{73} +(-130.458 + 225.960i) q^{75} +107.413 q^{77} +587.720 q^{79} +(437.799 - 758.290i) q^{81} -583.213i q^{83} +(-363.424 + 209.823i) q^{85} +(349.703 + 605.703i) q^{87} +(-425.924 - 245.907i) q^{89} +(-110.802 - 58.1428i) q^{91} +(-1631.23 - 941.792i) q^{93} +(-114.619 - 198.525i) q^{95} +(-1478.34 + 853.519i) q^{97} +783.422i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 - 54 * q^7 - 72 * q^9	$ 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9} - 42 q^{11} + 24 q^{13} - 70 q^{17} - 102 q^{19} + 90 q^{23} - 628 q^{25} + 708 q^{27} + 170 q^{29} - 678 q^{33} - 544 q^{35} + 582 q^{37} + 1162 q^{39} + 438 q^{41} + 270 q^{43} + 540 q^{45} + 92 q^{49} - 444 q^{51} - 592 q^{53} - 288 q^{55} + 90 q^{59} + 746 q^{61} - 1068 q^{63} - 1412 q^{65} + 846 q^{67} + 682 q^{69} - 1038 q^{71} + 722 q^{75} + 2812 q^{77} - 1008 q^{79} + 694 q^{81} - 180 q^{85} - 338 q^{87} + 2466 q^{89} + 690 q^{91} - 4764 q^{93} - 2592 q^{95} - 846 q^{97}+O(q^{100}) $ 20 * q - 6 * q^3 - 54 * q^7 - 72 * q^9 - 42 * q^11 + 24 * q^13 - 70 * q^17 - 102 * q^19 + 90 * q^23 - 628 * q^25 + 708 * q^27 + 170 * q^29 - 678 * q^33 - 544 * q^35 + 582 * q^37 + 1162 * q^39 + 438 * q^41 + 270 * q^43 + 540 * q^45 + 92 * q^49 - 444 * q^51 - 592 * q^53 - 288 * q^55 + 90 * q^59 + 746 * q^61 - 1068 * q^63 - 1412 * q^65 + 846 * q^67 + 682 * q^69 - 1038 * q^71 + 722 * q^75 + 2812 * q^77 - 1008 * q^79 + 694 * q^81 - 180 * q^85 - 338 * q^87 + 2466 * q^89 + 690 * q^91 - 4764 * q^93 - 2592 * q^95 - 846 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/104\mathbb{Z}\right)^\times$.

$n$	$41$	$53$	$79$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	3.40848	−	5.90366i	0.655962	−	1.13616i	−0.325689	−	0.945477i	$-0.605596\pi$
$3$	3.40848	−	5.90366i	0.655962	−	1.13616i	0.981652	−	0.190683i	$-0.0610703\pi$
$4$		0			0
$5$		−	12.7779i		−	1.14289i	−0.820641	−	0.571445i	$-0.806383\pi$
$5$		−	12.7779i		−	1.14289i	0.820641	−	0.571445i	$-0.193617\pi$
$6$		0			0
$7$	−2.31195	+	1.33481i	−0.124834	+	0.0720728i	−0.561117	−	0.827737i	$-0.689628\pi$
$7$	−2.31195	+	1.33481i	−0.124834	+	0.0720728i	0.436283	+	0.899810i	$0.356295\pi$
$8$		0			0
$9$	−9.73548	−	16.8623i	−0.360573	−	0.624531i
$10$		0			0
$11$	−34.8449	−	20.1177i	−0.955103	−	0.551429i	−0.0604407	−	0.998172i	$-0.519251\pi$
$11$	−34.8449	−	20.1177i	−0.955103	−	0.551429i	−0.894662	+	0.446743i	$0.852584\pi$
$12$		0			0
$13$	25.0545	+	39.6140i	0.534529	+	0.845150i
$13$	25.0545	+	39.6140i	0.534529	+	0.845150i
$14$		0			0
$15$	−75.4364	−	43.5532i	−1.29851	−	0.749693i
$16$		0			0
$17$	−16.4208	−	28.4416i	−0.234272	−	0.405771i	0.724789	−	0.688971i	$-0.241937\pi$
$17$	−16.4208	−	28.4416i	−0.234272	−	0.405771i	−0.959061	+	0.283200i	$0.908604\pi$
$18$		0			0
$19$	15.5366	−	8.97007i	0.187597	−	0.108309i	−0.403260	−	0.915085i	$-0.632123\pi$
$19$	15.5366	−	8.97007i	0.187597	−	0.108309i	0.590857	+	0.806776i	$0.298790\pi$
$20$		0			0
$21$			18.1987i			0.189108i
$22$		0			0
$23$	68.7952	−	119.157i	0.623686	−	1.08026i	−0.365107	−	0.930966i	$-0.618968\pi$
$23$	68.7952	−	119.157i	0.623686	−	1.08026i	0.988793	−	0.149291i	$-0.0476991\pi$
$24$		0			0
$25$	−38.2746			−0.306196
$26$		0			0
$27$	51.3252			0.365835
$28$		0			0
$29$	−51.2989	+	88.8524i	−0.328482	+	0.568947i	−0.982211	−	0.187781i	$-0.939870\pi$
$29$	−51.2989	+	88.8524i	−0.328482	+	0.568947i	0.653729	+	0.756729i	$0.273204\pi$
$30$		0			0
$31$		−	276.308i		−	1.60085i	−0.599431	−	0.800427i	$-0.704606\pi$
$31$		−	276.308i		−	1.60085i	0.599431	−	0.800427i	$-0.295394\pi$
$32$		0			0
$33$	−237.536	+	137.142i	−1.25302	+	0.723433i
$34$		0			0
$35$	17.0560	+	29.5419i	0.0823712	+	0.142671i
$36$		0			0
$37$	350.213	+	202.195i	1.55607	+	0.898398i	0.997627	+	0.0688555i	$0.0219347\pi$
$37$	350.213	+	202.195i	1.55607	+	0.898398i	0.558444	+	0.829542i	$0.311399\pi$
$38$		0			0
$39$	319.266	−	12.8900i	1.31086	−	0.0529243i
$40$		0			0
$41$	8.94701	+	5.16556i	0.0340802	+	0.0196762i	0.516943	−	0.856020i	$-0.327070\pi$
$41$	8.94701	+	5.16556i	0.0340802	+	0.0196762i	−0.482863	+	0.875696i	$0.660403\pi$
$42$		0			0
$43$	102.049	+	176.754i	0.361915	+	0.626855i	0.988276	−	0.152678i	$-0.0487898\pi$
$43$	102.049	+	176.754i	0.361915	+	0.626855i	−0.626361	+	0.779533i	$0.715457\pi$
$44$		0			0
$45$	−215.465	+	124.399i	−0.713770	+	0.412095i
$46$		0			0
$47$			160.135i			0.496982i	0.968634	+	0.248491i	$0.0799346\pi$
$47$			160.135i			0.496982i	−0.968634	+	0.248491i	$0.920065\pi$
$48$		0			0
$49$	−167.937	+	290.875i	−0.489611	+	0.848031i
$50$		0			0
$51$	−223.880			−0.614694
$52$		0			0
$53$	547.517			1.41900			0.709502	−	0.704703i	$-0.248920\pi$
$53$	547.517			1.41900			0.709502	+	0.704703i	$0.248920\pi$
$54$		0			0
$55$	−257.062	+	445.244i	−0.630222	+	1.09158i
$56$		0			0
$57$		−	122.297i		−	0.284187i
$58$		0			0
$59$	−356.890	+	206.051i	−0.787511	+	0.454670i	−0.839085	−	0.544000i	$-0.816909\pi$
$59$	−356.890	+	206.051i	−0.787511	+	0.454670i	0.0515747	+	0.998669i	$0.483576\pi$
$60$		0			0
$61$	302.095	+	523.245i	0.634088	+	1.09827i	0.986708	+	0.162506i	$0.0519575\pi$
$61$	302.095	+	523.245i	0.634088	+	1.09827i	−0.352620	+	0.935767i	$0.614709\pi$
$62$		0			0
$63$	45.0159	+	25.9900i	0.0900234	+	0.0519750i
$64$		0			0
$65$	506.184	−	320.144i	0.965913	−	0.610908i
$66$		0			0
$67$	−584.393	−	337.399i	−1.06560	−	0.615222i	−0.138621	−	0.990345i	$-0.544267\pi$
$67$	−584.393	−	337.399i	−1.06560	−	0.615222i	−0.926975	+	0.375123i	$0.877600\pi$
$68$		0			0
$69$	−468.974	−	812.287i	−0.818230	−	1.41722i
$70$		0			0
$71$	624.030	−	360.284i	1.04308	−	0.602223i	0.122376	−	0.992484i	$-0.460949\pi$
$71$	624.030	−	360.284i	1.04308	−	0.602223i	0.920704	+	0.390261i	$0.127615\pi$
$72$		0			0
$73$		−	562.708i		−	0.902191i	−0.892476	−	0.451096i	$-0.851033\pi$
$73$		−	562.708i		−	0.902191i	0.892476	−	0.451096i	$-0.148967\pi$
$74$		0			0
$75$	−130.458	+	225.960i	−0.200853	+	0.347888i
$76$		0			0
$77$	107.413			0.158972
$78$		0			0
$79$	587.720			0.837008			0.418504	−	0.908215i	$-0.362555\pi$
$79$	587.720			0.837008			0.418504	+	0.908215i	$0.362555\pi$
$80$		0			0
$81$	437.799	−	758.290i	0.600547	−	1.04018i
$82$		0			0
$83$		−	583.213i		−	0.771276i	−0.922650	−	0.385638i	$-0.873981\pi$
$83$		−	583.213i		−	0.771276i	0.922650	−	0.385638i	$-0.126019\pi$
$84$		0			0
$85$	−363.424	+	209.823i	−0.463751	+	0.267747i
$86$		0			0
$87$	349.703	+	605.703i	0.430944	+	0.746416i
$88$		0			0
$89$	−425.924	−	245.907i	−0.507279	−	0.292878i	0.224436	−	0.974489i	$-0.427946\pi$
$89$	−425.924	−	245.907i	−0.507279	−	0.292878i	−0.731714	+	0.681611i	$0.761280\pi$
$90$		0			0
$91$	−110.802	−	58.1428i	−0.127640	−	0.0669782i
$92$		0			0
$93$	−1631.23	−	941.792i	−1.81883	−	1.05010i
$94$		0			0
$95$	−114.619	−	198.525i	−0.123785	−	0.214403i
$96$		0			0
$97$	−1478.34	+	853.519i	−1.54745	+	0.893420i	−0.549113	+	0.835748i	$0.685035\pi$
$97$	−1478.34	+	853.519i	−1.54745	+	0.893420i	−0.998336	+	0.0576723i	$0.981632\pi$
$98$		0			0
$99$			783.422i			0.795322i
$100$		0			0
$101$	607.983	−	1053.06i	0.598976	−	1.03746i	−0.393997	−	0.919112i	$-0.628908\pi$
$101$	607.983	−	1053.06i	0.598976	−	1.03746i	0.992973	−	0.118345i	$-0.0377588\pi$
$102$		0			0
$103$	−778.221			−0.744469			−0.372235	−	0.928139i	$-0.621408\pi$
$103$	−778.221			−0.744469			−0.372235	+	0.928139i	$0.621408\pi$
$104$		0			0
$105$	232.540			0.216130
$106$		0			0
$107$	−982.647	+	1702.00i	−0.887814	+	1.53774i	−0.0453600	+	0.998971i	$0.514443\pi$
$107$	−982.647	+	1702.00i	−0.887814	+	1.53774i	−0.842454	+	0.538768i	$0.818890\pi$
$108$		0			0
$109$			434.187i			0.381537i	0.981635	+	0.190769i	$0.0610980\pi$
$109$			434.187i			0.381537i	−0.981635	+	0.190769i	$0.938902\pi$
$110$		0			0
$111$	2387.39	−	1378.36i	2.04145	−	1.17863i
$112$		0			0
$113$	690.378	+	1195.77i	0.574737	+	0.995473i	0.996070	+	0.0885675i	$0.0282289\pi$
$113$	690.378	+	1195.77i	0.574737	+	0.995473i	−0.421333	+	0.906906i	$0.638438\pi$
$114$		0			0
$115$	−1522.57	−	879.057i	−1.23461	−	0.712805i
$116$		0			0
$117$	424.067	−	808.140i	0.335086	−	0.638569i
$118$		0			0
$119$	75.9281	+	43.8371i	0.0584901	+	0.0337693i
$120$		0			0
$121$	143.945	+	249.320i	0.108148	+	0.187318i
$122$		0			0
$123$	60.9914	−	35.2134i	0.0447106	−	0.0258137i
$124$		0			0
$125$		−	1108.17i		−	0.792941i
$126$		0			0
$127$	−296.754	+	513.993i	−0.207344	+	0.359130i	−0.950877	−	0.309569i	$-0.899815\pi$
$127$	−296.754	+	513.993i	−0.207344	+	0.359130i	0.743533	+	0.668699i	$0.233149\pi$
$128$		0			0
$129$	1391.33			0.949610
$130$		0			0
$131$	134.098			0.0894366			0.0447183	−	0.999000i	$-0.485761\pi$
$131$	134.098			0.0894366			0.0447183	+	0.999000i	$0.485761\pi$
$132$		0			0
$133$	−23.9466	+	41.4768i	−0.0156123	+	0.0270413i
$134$		0			0
$135$		−	655.828i		−	0.418109i
$136$		0			0
$137$	1744.68	−	1007.29i	1.08801	−	0.628166i	0.154968	−	0.987920i	$-0.450473\pi$
$137$	1744.68	−	1007.29i	1.08801	−	0.628166i	0.933047	+	0.359754i	$0.117139\pi$
$138$		0			0
$139$	1321.63	+	2289.13i	0.806471	+	1.39685i	0.915294	+	0.402787i	$0.131958\pi$
$139$	1321.63	+	2289.13i	0.806471	+	1.39685i	−0.108823	+	0.994061i	$0.534708\pi$
$140$		0			0
$141$	945.385	+	545.819i	0.564651	+	0.326002i
$142$		0			0
$143$	−76.0799	−	1884.39i	−0.0444904	−	1.10196i
$144$		0			0
$145$	1135.35	+	655.492i	0.650244	+	0.375419i
$146$		0			0
$147$	1144.82	+	1982.88i	0.642333	+	1.11255i
$148$		0			0
$149$	−2444.08	+	1411.09i	−1.34380	+	0.775844i	−0.987363	−	0.158474i	$-0.949342\pi$
$149$	−2444.08	+	1411.09i	−1.34380	+	0.775844i	−0.356439	+	0.934319i	$0.616009\pi$
$150$		0			0
$151$			3193.28i			1.72096i	0.509483	+	0.860481i	$0.329837\pi$
$151$			3193.28i			1.72096i	−0.509483	+	0.860481i	$0.670163\pi$
$152$		0			0
$153$	−319.728	+	553.785i	−0.168944	+	0.292620i
$154$		0			0
$155$	−3530.64			−1.82960
$156$		0			0
$157$	−2027.72			−1.03076			−0.515381	−	0.856961i	$-0.672350\pi$
$157$	−2027.72			−1.03076			−0.515381	+	0.856961i	$0.672350\pi$
$158$		0			0
$159$	1866.20	−	3232.35i	0.930813	−	1.61222i
$160$		0			0
$161$			367.313i			0.179803i
$162$		0			0
$163$	−517.804	+	298.954i	−0.248819	+	0.143656i	−0.619223	−	0.785215i	$-0.712552\pi$
$163$	−517.804	+	298.954i	−0.248819	+	0.143656i	0.370404	+	0.928871i	$0.379219\pi$
$164$		0			0
$165$	1752.38	+	3035.21i	0.826804	+	1.43207i
$166$		0			0
$167$	−899.026	−	519.053i	−0.416579	−	0.240512i	0.277033	−	0.960860i	$-0.410649\pi$
$167$	−899.026	−	519.053i	−0.416579	−	0.240512i	−0.693613	+	0.720348i	$0.743982\pi$
$168$		0			0
$169$	−941.539	+	1985.02i	−0.428557	+	0.903515i
$170$		0			0
$171$	−302.513	−	174.656i	−0.135285	−	0.0781068i
$172$		0			0
$173$	553.114	+	958.022i	0.243078	+	0.421023i	0.961589	−	0.274492i	$-0.0885096\pi$
$173$	553.114	+	958.022i	0.243078	+	0.421023i	−0.718512	+	0.695515i	$0.755176\pi$
$174$		0			0
$175$	88.4890	−	51.0891i	0.0382236	−	0.0220684i
$176$		0			0
$177$			2809.28i			1.19298i
$178$		0			0
$179$	771.535	−	1336.34i	0.322163	−	0.558003i	−0.658771	−	0.752344i	$-0.728923\pi$
$179$	771.535	−	1336.34i	0.322163	−	0.558003i	0.980934	+	0.194341i	$0.0622567\pi$
$180$		0			0
$181$	−813.346			−0.334009			−0.167004	−	0.985956i	$-0.553409\pi$
$181$	−813.346			−0.334009			−0.167004	+	0.985956i	$0.553409\pi$
$182$		0			0
$183$	4118.74			1.66375
$184$		0			0
$185$	2583.63	−	4474.98i	1.02677	−	1.77842i
$186$		0			0
$187$			1321.39i			0.516737i
$188$		0			0
$189$	−118.661	+	68.5092i	−0.0456685	+	0.0263667i
$190$		0			0
$191$	−1119.72	−	1939.41i	−0.424188	−	0.734715i	0.572157	−	0.820144i	$-0.306107\pi$
$191$	−1119.72	−	1939.41i	−0.424188	−	0.734715i	−0.996344	+	0.0854299i	$0.972774\pi$
$192$		0			0
$193$	−3123.85	−	1803.56i	−1.16508	−	0.672657i	−0.212561	−	0.977148i	$-0.568180\pi$
$193$	−3123.85	−	1803.56i	−1.16508	−	0.672657i	−0.952515	+	0.304491i	$0.901514\pi$
$194$		0			0
$195$	−164.707	−	4079.54i	−0.0604866	−	1.49816i
$196$		0			0
$197$	1838.32	+	1061.35i	0.664847	+	0.383850i	0.794121	−	0.607759i	$-0.207931\pi$
$197$	1838.32	+	1061.35i	0.664847	+	0.383850i	−0.129274	+	0.991609i	$0.541265\pi$
$198$		0			0
$199$	−296.559	−	513.656i	−0.105641	−	0.182975i	0.808359	−	0.588690i	$-0.200356\pi$
$199$	−296.559	−	513.656i	−0.105641	−	0.182975i	−0.914000	+	0.405714i	$0.867023\pi$
$200$		0			0
$201$	−3983.78	+	2300.04i	−1.39798	+	0.807125i
$202$		0			0
$203$		−	273.897i		−	0.0946984i
$204$		0			0
$205$	66.0049	−	114.324i	0.0224877	−	0.0389499i
$206$		0			0
$207$	−2679.02			−0.899538
$208$		0			0
$209$	−721.829			−0.238899
$210$		0			0
$211$	2502.07	−	4333.72i	0.816350	−	1.41396i	−0.0920042	−	0.995759i	$-0.529327\pi$
$211$	2502.07	−	4333.72i	0.816350	−	1.41396i	0.908354	−	0.418201i	$-0.137339\pi$
$212$		0			0
$213$		−	4912.08i		−	1.58014i
$214$		0			0
$215$	2258.54	−	1303.97i	0.716426	−	0.413628i
$216$		0			0
$217$	368.818	+	638.812i	0.115378	+	0.199840i
$218$		0			0
$219$	−3322.04	−	1917.98i	−1.02503	−	0.591804i
$220$		0			0
$221$	715.271	−	1363.08i	0.217712	−	0.414891i
$222$		0			0
$223$	−408.594	−	235.902i	−0.122697	−	0.0708392i	0.437395	−	0.899269i	$-0.355901\pi$
$223$	−408.594	−	235.902i	−0.122697	−	0.0708392i	−0.560092	+	0.828430i	$0.689234\pi$
$224$		0			0
$225$	372.621	+	645.399i	0.110406	+	0.191229i
$226$		0			0
$227$	−2505.80	+	1446.72i	−0.732668	+	0.423006i	−0.819397	−	0.573226i	$-0.805692\pi$
$227$	−2505.80	+	1446.72i	−0.732668	+	0.423006i	0.0867293	+	0.996232i	$0.472358\pi$
$228$		0			0
$229$			2444.04i			0.705269i	0.935761	+	0.352635i	$0.114714\pi$
$229$			2444.04i			0.705269i	−0.935761	+	0.352635i	$0.885286\pi$
$230$		0			0
$231$	366.115	−	634.130i	0.104280	−	0.180618i
$232$		0			0
$233$	−2894.86			−0.813944			−0.406972	−	0.913441i	$-0.633415\pi$
$233$	−2894.86			−0.813944			−0.406972	+	0.913441i	$0.633415\pi$
$234$		0			0
$235$	2046.19			0.567996
$236$		0			0
$237$	2003.23	−	3469.70i	0.549046	−	0.950975i
$238$		0			0
$239$			2819.27i			0.763027i	0.924363	+	0.381513i	$0.124597\pi$
$239$			2819.27i			0.763027i	−0.924363	+	0.381513i	$0.875403\pi$
$240$		0			0
$241$	−39.0443	+	22.5423i	−0.0104360	+	0.00602521i	−0.505209	−	0.862997i	$-0.668585\pi$
$241$	−39.0443	+	22.5423i	−0.0104360	+	0.00602521i	0.494773	+	0.869022i	$0.335251\pi$
$242$		0			0
$243$	−2291.57	−	3969.11i	−0.604955	−	1.04781i
$244$		0			0
$245$	3716.77	+	2145.88i	0.969206	+	0.559571i
$246$		0			0
$247$	744.603	+	390.727i	0.191814	+	0.100653i
$248$		0			0
$249$	−3443.09	−	1987.87i	−0.876293	−	0.505928i
$250$		0			0
$251$	2951.26	+	5111.74i	0.742160	+	1.28546i	0.951510	+	0.307617i	$0.0995317\pi$
$251$	2951.26	+	5111.74i	0.742160	+	1.28546i	−0.209351	+	0.977841i	$0.567135\pi$
$252$		0			0
$253$	−4794.32	+	2768.00i	−1.19137	+	0.687838i
$254$		0			0
$255$			2860.71i			0.702528i
$256$		0			0
$257$	2570.84	−	4452.82i	0.623986	−	1.08078i	−0.364750	−	0.931105i	$-0.618846\pi$
$257$	2570.84	−	4452.82i	0.623986	−	1.08078i	0.988736	−	0.149670i	$-0.0478210\pi$
$258$		0			0
$259$	−1079.57			−0.259000
$260$		0			0
$261$	1997.68			0.473767
$262$		0			0
$263$	−3073.40	+	5323.28i	−0.720585	+	1.24809i	0.240181	+	0.970728i	$0.422793\pi$
$263$	−3073.40	+	5323.28i	−0.720585	+	1.24809i	−0.960766	+	0.277362i	$0.910540\pi$
$264$		0			0
$265$		−	6996.11i		−	1.62177i
$266$		0			0
$267$	−2903.50	+	1676.34i	−0.665512	+	0.384233i
$268$		0			0
$269$	468.880	+	812.125i	0.106276	+	0.184075i	0.914259	−	0.405131i	$-0.132774\pi$
$269$	468.880	+	812.125i	0.106276	+	0.184075i	−0.807983	+	0.589206i	$0.799441\pi$
$270$		0			0
$271$	1526.89	+	881.548i	0.342257	+	0.197602i	0.661270	−	0.750148i	$-0.270018\pi$
$271$	1526.89	+	881.548i	0.342257	+	0.197602i	−0.319012	+	0.947751i	$0.603351\pi$
$272$		0			0
$273$	−720.921	+	455.959i	−0.159825	+	0.101084i
$274$		0			0
$275$	1333.67	+	769.997i	0.292449	+	0.168846i
$276$		0			0
$277$	3298.97	+	5713.98i	0.715581	+	1.23942i	0.962735	+	0.270446i	$0.0871713\pi$
$277$	3298.97	+	5713.98i	0.715581	+	1.23942i	−0.247154	+	0.968976i	$0.579495\pi$
$278$		0			0
$279$	−4659.21	+	2689.99i	−0.999783	+	0.577225i
$280$		0			0
$281$			4163.19i			0.883826i	0.897058	+	0.441913i	$0.145700\pi$
$281$			4163.19i			0.883826i	−0.897058	+	0.441913i	$0.854300\pi$
$282$		0			0
$283$	2958.33	−	5123.98i	0.621394	−	1.07629i	−0.367833	−	0.929892i	$-0.619900\pi$
$283$	2958.33	−	5123.98i	0.621394	−	1.07629i	0.989226	−	0.146393i	$-0.0467665\pi$
$284$		0			0
$285$	−1562.70			−0.324794
$286$		0			0
$287$	−27.5801			−0.00567247
$288$		0			0
$289$	1917.22	−	3320.72i	0.390233	−	0.675904i
$290$		0			0
$291$			11636.8i			2.34420i
$292$		0			0
$293$	5937.45	−	3427.99i	1.18386	−	0.683499i	0.226952	−	0.973906i	$-0.427124\pi$
$293$	5937.45	−	3427.99i	1.18386	−	0.683499i	0.956903	+	0.290406i	$0.0937905\pi$
$294$		0			0
$295$	2632.89	+	4560.30i	0.519637	+	0.900038i
$296$		0			0
$297$	−1788.42	−	1032.55i	−0.349410	−	0.201732i
$298$		0			0
$299$	6443.91	−	260.165i	1.24636	−	0.0503202i
$300$		0			0
$301$	−471.865	−	272.431i	−0.0903583	−	0.0521684i
$302$		0			0
$303$	−4144.60	−	7178.65i	−0.785811	−	1.36106i
$304$		0			0
$305$	6685.96	−	3860.14i	1.25520	−	0.724692i
$306$		0			0
$307$			2846.57i			0.529194i	0.964359	+	0.264597i	$0.0852389\pi$
$307$			2846.57i			0.529194i	−0.964359	+	0.264597i	$0.914761\pi$
$308$		0			0
$309$	−2652.55	+	4594.35i	−0.488344	+	0.845836i
$310$		0			0
$311$	−6018.53			−1.09736			−0.548681	−	0.836032i	$-0.684870\pi$
$311$	−6018.53			−1.09736			−0.548681	+	0.836032i	$0.684870\pi$
$312$		0			0
$313$	−2637.18			−0.476238			−0.238119	−	0.971236i	$-0.576531\pi$
$313$	−2637.18			−0.476238			−0.238119	+	0.971236i	$0.576531\pi$
$314$		0			0
$315$	332.097	−	575.209i	0.0594017	−	0.102887i
$316$		0			0
$317$		−	9016.09i		−	1.59746i	−0.601692	−	0.798728i	$-0.705506\pi$
$317$		−	9016.09i		−	1.59746i	0.601692	−	0.798728i	$-0.294494\pi$
$318$		0			0
$319$	3575.01	−	2064.04i	0.627468	−	0.362269i
$320$		0			0
$321$	6698.67	+	11602.4i	1.16475	+	2.01740i
$322$		0			0
$323$	−510.247	−	294.591i	−0.0878974	−	0.0507476i
$324$		0			0
$325$	−958.952	−	1516.21i	−0.163671	−	0.258782i
$326$		0			0
$327$	2563.29	+	1479.92i	0.433487	+	0.250274i
$328$		0			0
$329$	−213.750	−	370.226i	−0.0358189	−	0.0620401i
$330$		0			0
$331$	4457.08	−	2573.30i	0.740131	−	0.427315i	−0.0819859	−	0.996633i	$-0.526126\pi$
$331$	4457.08	−	2573.30i	0.740131	−	0.427315i	0.822117	+	0.569319i	$0.192793\pi$
$332$		0			0
$333$		−	7873.87i		−	1.29575i
$334$		0			0
$335$	−4311.25	+	7467.31i	−0.703131	+	1.21786i
$336$		0			0
$337$	9709.21			1.56942			0.784710	−	0.619863i	$-0.212812\pi$
$337$	9709.21			1.56942			0.784710	+	0.619863i	$0.212812\pi$
$338$		0			0
$339$	9412.55			1.50802
$340$		0			0
$341$	−5558.69	+	9627.94i	−0.882757	+	1.52898i
$342$		0			0
$343$		−	1812.33i		−	0.285296i
$344$		0			0
$345$	−10379.3	+	5992.50i	−1.61972	+	0.935146i
$346$		0			0
$347$	3406.91	+	5900.94i	0.527068	+	0.912908i	0.999502	+	0.0315424i	$0.0100419\pi$
$347$	3406.91	+	5900.94i	0.527068	+	0.912908i	−0.472435	+	0.881366i	$0.656625\pi$
$348$		0			0
$349$	−2110.42	−	1218.45i	−0.323691	−	0.186883i	0.329345	−	0.944210i	$-0.393172\pi$
$349$	−2110.42	−	1218.45i	−0.323691	−	0.186883i	−0.653037	+	0.757326i	$0.726505\pi$
$350$		0			0
$351$	1285.93	+	2033.20i	0.195549	+	0.309185i
$352$		0			0
$353$	−8711.72	−	5029.71i	−1.31354	−	0.758370i	−0.330856	−	0.943681i	$-0.607337\pi$
$353$	−8711.72	−	5029.71i	−1.31354	−	0.758370i	−0.982680	+	0.185311i	$0.940671\pi$
$354$		0			0
$355$	−4603.67	−	7973.79i	−0.688274	−	1.19213i
$356$		0			0
$357$	517.599	−	298.836i	0.0767346	−	0.0443027i
$358$		0			0
$359$		−	2429.18i		−	0.357123i	−0.983929	−	0.178562i	$-0.942856\pi$
$359$		−	2429.18i		−	0.357123i	0.983929	−	0.178562i	$-0.0571444\pi$
$360$		0			0
$361$	−3268.58	+	5661.34i	−0.476538	+	0.825388i
$362$		0			0
$363$	1962.53			0.283764
$364$		0			0
$365$	−7190.22			−1.03110
$366$		0			0
$367$	−1312.28	+	2272.94i	−0.186650	+	0.323288i	−0.944131	−	0.329569i	$-0.893096\pi$
$367$	−1312.28	+	2272.94i	−0.186650	+	0.323288i	0.757481	+	0.652857i	$0.226430\pi$
$368$		0			0
$369$		−	201.157i		−	0.0283788i
$370$		0			0
$371$	−1265.83	+	730.829i	−0.177140	+	0.102272i
$372$		0			0
$373$	−3787.69	−	6560.46i	−0.525788	−	0.910692i	−0.999549	−	0.0300380i	$-0.990437\pi$
$373$	−3787.69	−	6560.46i	−0.525788	−	0.910692i	0.473761	−	0.880654i	$-0.342896\pi$
$374$		0			0
$375$	−6542.25	−	3777.17i	−0.900908	−	0.520139i
$376$		0			0
$377$	−4805.07	+	193.999i	−0.656429	+	0.0265026i
$378$		0			0
$379$	587.129	+	338.979i	0.0795746	+	0.0459424i	0.539259	−	0.842140i	$-0.318704\pi$
$379$	587.129	+	338.979i	0.0795746	+	0.0459424i	−0.459685	+	0.888082i	$0.652038\pi$
$380$		0			0
$381$	2022.96	+	3503.87i	0.272020	+	0.471152i
$382$		0			0
$383$	−5093.76	+	2940.88i	−0.679579	+	0.392355i	−0.799697	−	0.600404i	$-0.795006\pi$
$383$	−5093.76	+	2940.88i	−0.679579	+	0.392355i	0.120117	+	0.992760i	$0.461673\pi$
$384$		0			0
$385$		−	1372.51i		−	0.181688i
$386$		0			0
$387$	1986.99	−	3441.57i	0.260993	−	0.452054i
$388$		0			0
$389$	6623.27			0.863273			0.431637	−	0.902048i	$-0.357936\pi$
$389$	6623.27			0.863273			0.431637	+	0.902048i	$0.357936\pi$
$390$		0			0
$391$	−4518.68			−0.584449
$392$		0			0
$393$	457.070	−	791.669i	0.0586670	−	0.101614i
$394$		0			0
$395$		−	7509.82i		−	0.956608i
$396$		0			0
$397$	4723.28	−	2726.99i	0.597115	−	0.344744i	−0.170791	−	0.985307i	$-0.554632\pi$
$397$	4723.28	−	2726.99i	0.597115	−	0.344744i	0.767906	+	0.640563i	$0.221299\pi$
$398$		0			0
$399$	163.243	+	282.745i	0.0204822	+	0.0354761i
$400$		0			0
$401$	8578.70	+	4952.92i	1.06833	+	0.616800i	0.927724	−	0.373266i	$-0.121762\pi$
$401$	8578.70	+	4952.92i	1.06833	+	0.616800i	0.140604	+	0.990066i	$0.455095\pi$
$402$		0			0
$403$	10945.7	−	6922.78i	1.35296	−	0.855703i
$404$		0			0
$405$	−9689.35	−	5594.15i	−1.18881	−	0.686359i
$406$		0			0
$407$	−8135.42	−	14091.0i	−0.990805	−	1.71613i
$408$		0			0
$409$	12274.0	−	7086.42i	1.48389	−	0.856726i	0.484061	−	0.875034i	$-0.339161\pi$
$409$	12274.0	−	7086.42i	1.48389	−	0.856726i	0.999832	+	0.0183077i	$0.00582783\pi$
$410$		0			0
$411$		−	13733.3i		−	1.64821i
$412$		0			0
$413$	550.075	−	952.759i	0.0655386	−	0.113516i
$414$		0			0
$415$	−7452.23			−0.881483
$416$		0			0
$417$	18019.0			2.11606
$418$		0			0
$419$	−5639.55	+	9767.99i	−0.657542	+	1.13890i	0.323708	+	0.946157i	$0.395071\pi$
$419$	−5639.55	+	9767.99i	−0.657542	+	1.13890i	−0.981250	+	0.192740i	$0.938263\pi$
$420$		0			0
$421$			2422.46i			0.280436i	0.990121	+	0.140218i	$0.0447803\pi$
$421$			2422.46i			0.280436i	−0.990121	+	0.140218i	$0.955220\pi$
$422$		0			0
$423$	2700.26	−	1559.00i	0.310381	−	0.179198i
$424$		0			0
$425$	628.498	+	1088.59i	0.0717332	+	0.124246i
$426$		0			0
$427$	−1396.86	−	806.478i	−0.158311	−	0.0914009i
$428$		0			0
$429$	−11384.1	−	5973.75i	−1.28119	−	0.672296i
$430$		0			0
$431$	1254.01	+	724.003i	0.140147	+	0.0809141i	0.568434	−	0.822729i	$-0.307549\pi$
$431$	1254.01	+	724.003i	0.140147	+	0.0809141i	−0.428287	+	0.903643i	$0.640883\pi$
$432$		0			0
$433$	−2270.03	−	3931.81i	−0.251942	−	0.436376i	0.712119	−	0.702059i	$-0.247736\pi$
$433$	−2270.03	−	3931.81i	−0.251942	−	0.436376i	−0.964060	+	0.265683i	$0.914402\pi$
$434$		0			0
$435$	7739.61	−	4468.47i	0.853071	−	0.492521i
$436$		0			0
$437$		−	2468.39i		−	0.270204i
$438$		0			0
$439$	5058.37	−	8761.35i	0.549938	−	0.952520i	−0.448340	−	0.893863i	$-0.647985\pi$
$439$	5058.37	−	8761.35i	0.549938	−	0.952520i	0.998278	−	0.0586574i	$-0.0186819\pi$
$440$		0			0
$441$	6539.77			0.706163
$442$		0			0
$443$	−18380.3			−1.97127			−0.985636	−	0.168884i	$-0.945984\pi$
$443$	−18380.3			−1.97127			−0.985636	+	0.168884i	$0.945984\pi$
$444$		0			0
$445$	−3142.17	+	5442.41i	−0.334727	+	0.579764i
$446$		0			0
$447$			19238.7i			2.03570i
$448$		0			0
$449$	−3868.31	+	2233.37i	−0.406586	+	0.234742i	−0.689322	−	0.724455i	$-0.742091\pi$
$449$	−3868.31	+	2233.37i	−0.406586	+	0.234742i	0.282736	+	0.959198i	$0.408758\pi$
$450$		0			0
$451$	−207.838	−	359.987i	−0.0217001	−	0.0375856i
$452$		0			0
$453$	18852.0	+	10884.2i	1.95529	+	1.12889i
$454$		0			0
$455$	−742.942	+	1415.82i	−0.0765487	+	0.145878i
$456$		0			0
$457$	−7125.63	−	4113.98i	−0.729371	−	0.421103i	0.0888207	−	0.996048i	$-0.471690\pi$
$457$	−7125.63	−	4113.98i	−0.729371	−	0.421103i	−0.818192	+	0.574945i	$0.805024\pi$
$458$		0			0
$459$	−842.800	−	1459.77i	−0.0857048	−	0.148445i
$460$		0			0
$461$	−13839.2	+	7990.04i	−1.39816	+	0.807231i	−0.994200	−	0.107544i	$-0.965701\pi$
$461$	−13839.2	+	7990.04i	−1.39816	+	0.807231i	−0.403964	+	0.914775i	$0.632368\pi$
$462$		0			0
$463$		−	8317.95i		−	0.834920i	−0.908695	−	0.417460i	$-0.862920\pi$
$463$		−	8317.95i		−	0.834920i	0.908695	−	0.417460i	$-0.137080\pi$
$464$		0			0
$465$	−12034.1	+	20843.7i	−1.20015	+	2.07872i
$466$		0			0
$467$	7477.40			0.740927			0.370464	−	0.928847i	$-0.379199\pi$
$467$	7477.40			0.740927			0.370464	+	0.928847i	$0.379199\pi$
$468$		0			0
$469$	1801.45			0.177363
$470$		0			0
$471$	−6911.44	+	11971.0i	−0.676141	+	1.17111i
$472$		0			0
$473$		−	8211.97i		−	0.798281i
$474$		0			0
$475$	−594.657	+	343.325i	−0.0574416	+	0.0331639i
$476$		0			0
$477$	−5330.34	−	9232.42i	−0.511655	−	0.886212i
$478$		0			0
$479$	3124.69	+	1804.04i	0.298060	+	0.172085i	0.641571	−	0.767064i	$-0.278283\pi$
$479$	3124.69	+	1804.04i	0.298060	+	0.172085i	−0.343511	+	0.939149i	$0.611616\pi$
$480$		0			0
$481$	764.650	+	18939.2i	0.0724845	+	1.79533i
$482$		0			0
$483$	2168.49	+	1251.98i	0.204285	+	0.117944i
$484$		0			0
$485$	10906.2	+	18890.1i	1.02108	+	1.76856i
$486$		0			0
$487$	6596.81	−	3808.67i	0.613819	−	0.354389i	−0.160640	−	0.987013i	$-0.551356\pi$
$487$	6596.81	−	3808.67i	0.613819	−	0.354389i	0.774459	+	0.632624i	$0.218022\pi$
$488$		0			0
$489$			4075.92i			0.376931i
$490$		0			0
$491$	4797.86	−	8310.14i	0.440987	−	0.763811i	−0.556776	−	0.830663i	$-0.687962\pi$
$491$	4797.86	−	8310.14i	0.440987	−	0.763811i	0.997763	+	0.0668511i	$0.0212953\pi$
$492$		0			0
$493$	3369.47			0.307816
$494$		0			0
$495$	10010.5			0.908965
$496$		0			0
$497$	−961.819	+	1665.92i	−0.0868078	+	0.150355i
$498$		0			0
$499$			5761.93i			0.516913i	0.966023	+	0.258457i	$0.0832139\pi$
$499$			5761.93i			0.516913i	−0.966023	+	0.258457i	$0.916786\pi$
$500$		0			0
$501$	−6128.63	+	3538.36i	−0.546521	+	0.315534i
$502$		0			0
$503$	−3958.66	−	6856.61i	−0.350911	−	0.607795i	0.635499	−	0.772102i	$-0.280795\pi$
$503$	−3958.66	−	6856.61i	−0.350911	−	0.607795i	−0.986409	+	0.164307i	$0.947461\pi$
$504$		0			0
$505$	−13455.9	−	7768.74i	−1.18570	−	0.684563i
$506$		0			0
$507$	8509.68	+	12324.4i	0.745420	+	1.07958i
$508$		0			0
$509$	3408.98	+	1968.18i	0.296858	+	0.171391i	0.641030	−	0.767516i	$-0.278507\pi$
$509$	3408.98	+	1968.18i	0.296858	+	0.171391i	−0.344173	+	0.938906i	$0.611841\pi$
$510$		0			0
$511$	751.106	+	1300.95i	0.0650234	+	0.112624i
$512$		0			0
$513$	797.420	−	460.391i	0.0686295	−	0.0396233i
$514$		0			0
$515$			9944.02i			0.850846i
$516$		0			0
$517$	3221.56	−	5579.90i	0.274050	−	0.474669i
$518$		0			0
$519$	7541.11			0.637800
$520$		0			0
$521$	2588.98			0.217707			0.108853	−	0.994058i	$-0.465282\pi$
$521$	2588.98			0.217707			0.108853	+	0.994058i	$0.465282\pi$
$522$		0			0
$523$	6222.45	−	10777.6i	0.520246	−	0.901093i	−0.479476	−	0.877555i	$-0.659173\pi$
$523$	6222.45	−	10777.6i	0.520246	−	0.901093i	0.999723	−	0.0235385i	$-0.00749324\pi$
$524$		0			0
$525$		−	696.545i		−	0.0579042i
$526$		0			0
$527$	−7858.66	+	4537.20i	−0.649580	+	0.375035i
$528$		0			0
$529$	−3382.05	−	5857.89i	−0.277969	−	0.481457i
$530$		0			0
$531$	6948.99	+	4012.00i	0.567911	+	0.327883i
$532$		0			0
$533$	19.5348	+	483.847i	0.00158751	+	0.0393204i
$534$		0			0
$535$	21747.9	+	12556.2i	1.75747	+	1.01467i
$536$		0			0
$537$	−5259.52	−	9109.76i	−0.422654	−	0.732058i
$538$		0			0
$539$	11703.5	−	6757.00i	0.935258	−	0.539971i
$540$		0			0
$541$			2221.88i			0.176573i	0.996095	+	0.0882866i	$0.0281391\pi$
$541$			2221.88i			0.176573i	−0.996095	+	0.0882866i	$0.971861\pi$
$542$		0			0
$543$	−2772.27	+	4801.72i	−0.219097	+	0.379487i
$544$		0			0
$545$	5547.99			0.436055
$546$		0			0
$547$	−11535.2			−0.901661			−0.450830	−	0.892610i	$-0.648872\pi$
$547$	−11535.2			−0.901661			−0.450830	+	0.892610i	$0.648872\pi$
$548$		0			0
$549$	5882.09	−	10188.1i	0.457270	−	0.792015i
$550$		0			0
$551$			1840.62i			0.142310i
$552$		0			0
$553$	−1358.78	+	784.492i	−0.104487	+	0.0603255i
$554$		0			0
$555$	−17612.5	−	30505.8i	−1.34704	−	2.33315i
$556$		0			0
$557$	11299.7	+	6523.89i	0.859577	+	0.496277i	0.863870	−	0.503714i	$-0.168033\pi$
$557$	11299.7	+	6523.89i	0.859577	+	0.496277i	−0.00429384	+	0.999991i	$0.501367\pi$
$558$		0			0
$559$	−4445.15	+	8471.06i	−0.336332	+	0.640944i
$560$		0			0
$561$	7801.06	+	4503.95i	0.587096	+	0.338960i
$562$		0			0
$563$	4693.55	+	8129.46i	0.351349	+	0.608554i	0.986486	−	0.163845i	$-0.0523897\pi$
$563$	4693.55	+	8129.46i	0.351349	+	0.608554i	−0.635137	+	0.772399i	$0.719056\pi$
$564$		0			0
$565$	15279.4	−	8821.57i	1.13772	−	0.656861i
$566$		0			0
$567$			2337.51i			0.173132i
$568$		0			0
$569$	505.020	−	874.719i	0.0372083	−	0.0644467i	−0.846822	−	0.531877i	$-0.821487\pi$
$569$	505.020	−	874.719i	0.0372083	−	0.0644467i	0.884030	+	0.467430i	$0.154820\pi$
$570$		0			0
$571$	−17206.4			−1.26106			−0.630529	−	0.776166i	$-0.717162\pi$
$571$	−17206.4			−1.26106			−0.630529	+	0.776166i	$0.717162\pi$
$572$		0			0
$573$	−15266.1			−1.11300
$574$		0			0
$575$	−2633.11	+	4560.67i	−0.190971	+	0.330771i
$576$		0			0
$577$		−	5518.55i		−	0.398163i	−0.979983	−	0.199082i	$-0.936204\pi$
$577$		−	5518.55i		−	0.398163i	0.979983	−	0.199082i	$-0.0637958\pi$
$578$		0			0
$579$	−21295.2	+	12294.8i	−1.52849	+	0.882475i
$580$		0			0
$581$	778.476	+	1348.36i	0.0555880	+	0.0962812i
$582$		0			0
$583$	−19078.2	−	11014.8i	−1.35530	−	0.782480i
$584$		0			0
$585$	−10326.3	−	5418.68i	−0.729813	−	0.382966i
$586$		0			0
$587$	13115.4	+	7572.16i	0.922196	+	0.532430i	0.884335	−	0.466853i	$-0.154612\pi$
$587$	13115.4	+	7572.16i	0.922196	+	0.532430i	0.0378611	+	0.999283i	$0.487946\pi$
$588$		0			0
$589$	−2478.51	−	4292.90i	−0.173387	−	0.300315i
$590$		0			0
$591$	12531.8	−	7235.21i	0.872229	−	0.503582i
$592$		0			0
$593$		−	11663.1i		−	0.807667i	−0.914832	−	0.403834i	$-0.867677\pi$
$593$		−	11663.1i		−	0.807667i	0.914832	−	0.403834i	$-0.132323\pi$
$594$		0			0
$595$	560.146	−	970.201i	0.0385945	−	0.0668477i
$596$		0			0
$597$	−4043.27			−0.277186
$598$		0			0
$599$	−13655.9			−0.931492			−0.465746	−	0.884919i	$-0.654214\pi$
$599$	−13655.9			−0.931492			−0.465746	+	0.884919i	$0.654214\pi$
$600$		0			0
$601$	11011.1	−	19071.8i	0.747341	−	1.29443i	−0.201752	−	0.979437i	$-0.564663\pi$
$601$	11011.1	−	19071.8i	0.747341	−	1.29443i	0.949093	−	0.314996i	$-0.102003\pi$
$602$		0			0
$603$			13139.0i			0.887331i
$604$		0			0
$605$	3185.78	−	1839.31i	0.214084	−	0.123601i
$606$		0			0
$607$	2114.49	+	3662.40i	0.141391	+	0.244896i	0.928021	−	0.372529i	$-0.121509\pi$
$607$	2114.49	+	3662.40i	0.141391	+	0.244896i	−0.786630	+	0.617425i	$0.788176\pi$
$608$		0			0
$609$	−1616.99	−	933.572i	−0.107593	−	0.0621186i
$610$		0			0
$611$	−6343.61	+	4012.12i	−0.420024	+	0.265651i
$612$		0			0
$613$	23168.0	+	13376.1i	1.52651	+	0.881329i	0.999505	+	0.0314651i	$0.0100173\pi$
$613$	23168.0	+	13376.1i	1.52651	+	0.881329i	0.527002	+	0.849864i	$0.323316\pi$
$614$		0			0
$615$	−449.953	−	779.341i	−0.0295022	−	0.0510993i
$616$		0			0
$617$	−1182.87	+	682.928i	−0.0771806	+	0.0445602i	−0.538094	−	0.842885i	$-0.680855\pi$
$617$	−1182.87	+	682.928i	−0.0771806	+	0.0445602i	0.460913	+	0.887445i	$0.347522\pi$
$618$		0			0
$619$			21506.1i			1.39645i	0.715879	+	0.698224i	$0.246026\pi$
$619$			21506.1i			1.39645i	−0.715879	+	0.698224i	$0.753974\pi$
$620$		0			0
$621$	3530.93	−	6115.74i	0.228166	−	0.395195i
$622$		0			0
$623$	1312.95			0.0844340
$624$		0			0
$625$	−18944.4			−1.21244
$626$		0			0
$627$	−2460.34	+	4261.43i	−0.156709	+	0.271428i
$628$		0			0
$629$		−	13280.8i		−	0.841878i
$630$		0			0
$631$	16347.6	−	9438.28i	1.03136	−	0.595455i	0.113985	−	0.993483i	$-0.463639\pi$
$631$	16347.6	−	9438.28i	1.03136	−	0.595455i	0.917373	+	0.398028i	$0.130305\pi$
$632$		0			0
$633$	−17056.5	−	29542.8i	−1.07099	−	1.85501i
$634$		0			0
$635$	6567.75	+	3791.89i	0.410446	+	0.236971i
$636$		0			0
$637$	−15730.3	+	635.092i	−0.978425	+	0.0395028i
$638$		0			0
$639$	−12150.5	−	7015.07i	−0.752214	−	0.434291i
$640$		0			0
$641$	−1819.89	−	3152.14i	−0.112139	−	0.194231i	0.804493	−	0.593962i	$-0.202437\pi$
$641$	−1819.89	−	3152.14i	−0.112139	−	0.194231i	−0.916633	+	0.399731i	$0.869104\pi$
$642$		0			0
$643$	−21811.4	+	12592.8i	−1.33773	+	0.772338i	−0.986470	−	0.163941i	$-0.947579\pi$
$643$	−21811.4	+	12592.8i	−1.33773	+	0.772338i	−0.351258	+	0.936279i	$0.614246\pi$
$644$		0			0
$645$		−	17778.2i		−	1.08530i
$646$		0			0
$647$	4778.36	−	8276.36i	0.290350	−	0.502902i	−0.683542	−	0.729911i	$-0.739561\pi$
$647$	4778.36	−	8276.36i	0.290350	−	0.502902i	0.973893	+	0.227009i	$0.0728948\pi$
$648$		0			0
$649$	16581.1			1.00287
$650$		0			0
$651$	5028.44			0.302734
$652$		0			0
$653$	−3020.59	+	5231.82i	−0.181018	+	0.313533i	−0.942228	−	0.334974i	$-0.891273\pi$
$653$	−3020.59	+	5231.82i	−0.181018	+	0.313533i	0.761209	+	0.648506i	$0.224606\pi$
$654$		0			0
$655$		−	1713.49i		−	0.102216i
$656$		0			0
$657$	−9488.57	+	5478.23i	−0.563447	+	0.325306i
$658$		0			0
$659$	−11127.9	−	19274.2i	−0.657789	−	1.13932i	−0.981187	−	0.193061i	$-0.938158\pi$
$659$	−11127.9	−	19274.2i	−0.657789	−	1.13932i	0.323398	−	0.946263i	$-0.395175\pi$
$660$		0			0
$661$	24007.8	+	13860.9i	1.41270	+	0.815622i	0.995642	−	0.0932592i	$-0.0297285\pi$
$661$	24007.8	+	13860.9i	1.41270	+	0.815622i	0.417056	+	0.908881i	$0.363062\pi$
$662$		0			0
$663$	−5609.20	−	8868.77i	−0.328572	−	0.519509i
$664$		0			0
$665$	529.986	+	305.987i	0.0309052	+	0.0178431i
$666$		0			0
$667$	7058.24	+	12225.2i	0.409739	+	0.709689i
$668$		0			0
$669$	−2785.37	+	1608.13i	−0.160969	+	0.0929357i
$670$		0			0
$671$		−	24309.9i		−	1.39862i
$672$		0			0
$673$	1170.57	−	2027.48i	0.0670462	−	0.116127i	−0.830554	−	0.556939i	$-0.811976\pi$
$673$	1170.57	−	2027.48i	0.0670462	−	0.116127i	0.897600	+	0.440811i	$0.145309\pi$
$674$		0			0
$675$	−1964.45			−0.112017
$676$		0			0
$677$	−23282.1			−1.32172			−0.660859	−	0.750510i	$-0.729808\pi$
$677$	−23282.1			−1.32172			−0.660859	+	0.750510i	$0.729808\pi$
$678$		0			0
$679$	2278.57	−	3946.59i	0.128783	−	0.223058i
$680$		0			0
$681$			19724.5i			1.10990i
$682$		0			0
$683$	10508.4	−	6067.02i	0.588715	−	0.339895i	−0.175874	−	0.984413i	$-0.556275\pi$
$683$	10508.4	−	6067.02i	0.588715	−	0.339895i	0.764589	+	0.644518i	$0.222942\pi$
$684$		0			0
$685$	−12871.1	−	22293.3i	−0.717924	−	1.24348i
$686$		0			0
$687$	14428.8	+	8330.46i	0.801299	+	0.462630i
$688$		0			0
$689$	13717.8	+	21689.3i	0.758499	+	1.19927i
$690$		0			0
$691$	7712.28	+	4452.69i	0.424586	+	0.245135i	0.697038	−	0.717035i	$-0.254501\pi$
$691$	7712.28	+	4452.69i	0.424586	+	0.245135i	−0.272451	+	0.962170i	$0.587834\pi$
$692$		0			0
$693$	−1045.72	−	1811.24i	−0.0573211	−	0.0992830i
$694$		0			0
$695$	29250.3	−	16887.7i	1.59644	−	0.921707i
$696$		0			0
$697$		−	339.290i		−	0.0184383i
$698$		0			0
$699$	−9867.09	+	17090.3i	−0.533916	+	0.924770i
$700$		0			0
$701$	−6340.38			−0.341616			−0.170808	−	0.985304i	$-0.554638\pi$
$701$	−6340.38			−0.341616			−0.170808	+	0.985304i	$0.554638\pi$
$702$		0			0
$703$	7254.83			0.389219
$704$		0			0
$705$	6974.41	−	12080.0i	0.372584	−	0.645334i
$706$		0			0
$707$			3246.16i			0.172679i
$708$		0			0
$709$	−1858.25	+	1072.86i	−0.0984316	+	0.0568295i	−0.548408	−	0.836211i	$-0.684766\pi$
$709$	−1858.25	+	1072.86i	−0.0984316	+	0.0568295i	0.449976	+	0.893041i	$0.351432\pi$
$710$		0			0
$711$	−5721.73	−	9910.33i	−0.301803	−	0.522738i
$712$		0			0
$713$	−32924.0	−	19008.7i	−1.72933	−	0.998430i
$714$		0			0
$715$	−24078.5	+	972.141i	−1.25942	+	0.0508476i
$716$		0			0
$717$	16644.0	+	9609.43i	0.866921	+	0.500517i
$718$		0			0
$719$	3993.78	+	6917.43i	0.207153	+	0.358799i	0.950817	−	0.309755i	$-0.100247\pi$
$719$	3993.78	+	6917.43i	0.207153	+	0.358799i	−0.743664	+	0.668554i	$0.766914\pi$
$720$		0			0
$721$	1799.21	−	1038.77i	0.0929349	−	0.0536560i
$722$		0			0
$723$			307.339i			0.0158092i
$724$		0			0
$725$	1963.44	−	3400.79i	0.100580	−	0.174210i
$726$		0			0
$727$	10484.4			0.534863			0.267432	−	0.963577i	$-0.413825\pi$
$727$	10484.4			0.534863			0.267432	+	0.963577i	$0.413825\pi$
$728$		0			0
$729$	−7601.91			−0.386217
$730$		0			0
$731$	3351.45	−	5804.88i	0.169573	−	0.293709i
$732$		0			0
$733$			23183.2i			1.16820i	0.811682	+	0.584100i	$0.198552\pi$
$733$			23183.2i			1.16820i	−0.811682	+	0.584100i	$0.801448\pi$
$734$		0			0
$735$	25337.0	−	14628.4i	1.27153	−	0.734115i
$736$		0			0
$737$	13575.4	+	23513.3i	0.678503	+	1.17520i
$738$		0			0
$739$	−9036.24	−	5217.08i	−0.449802	−	0.259693i	0.257945	−	0.966160i	$-0.416955\pi$
$739$	−9036.24	−	5217.08i	−0.449802	−	0.259693i	−0.707747	+	0.706466i	$0.750288\pi$
$740$		0			0
$741$	4844.68	−	3064.10i	0.240181	−	0.151906i
$742$		0			0
$743$	6004.23	+	3466.54i	0.296465	+	0.171164i	0.640854	−	0.767663i	$-0.278580\pi$
$743$	6004.23	+	3466.54i	0.296465	+	0.171164i	−0.344389	+	0.938827i	$0.611914\pi$
$744$		0			0
$745$	18030.7	+	31230.1i	0.886704	+	1.53582i
$746$		0			0
$747$	−9834.33	+	5677.85i	−0.481686	+	0.278101i
$748$		0			0
$749$		−	5246.58i		−	0.255949i
$750$		0			0
$751$	−5623.54	+	9740.25i	−0.273243	+	0.473271i	−0.969690	−	0.244337i	$-0.921430\pi$
$751$	−5623.54	+	9740.25i	−0.273243	+	0.473271i	0.696447	+	0.717608i	$0.254763\pi$
$752$		0			0
$753$	40237.3			1.94732
$754$		0			0
$755$	40803.4			1.96687
$756$		0			0
$757$	−19825.8	+	34339.3i	−0.951890	+	1.64872i	−0.210559	+	0.977581i	$0.567528\pi$
$757$	−19825.8	+	34339.3i	−0.951890	+	1.64872i	−0.741331	+	0.671140i	$0.765805\pi$
$758$		0			0
$759$			37738.7i			1.80478i
$760$		0			0
$761$	−1430.82	+	826.086i	−0.0681567	+	0.0393503i	−0.533691	−	0.845679i	$-0.679195\pi$
$761$	−1430.82	+	826.086i	−0.0681567	+	0.0393503i	0.465534	+	0.885030i	$0.345862\pi$
$762$		0			0
$763$	−579.555	−	1003.82i	−0.0274984	−	0.0476287i
$764$		0			0
$765$	7076.21	+	4085.45i	0.334433	+	0.193085i
$766$		0			0
$767$	−17104.2	−	8975.34i	−0.805212	−	0.422531i
$768$		0			0
$769$	8646.87	+	4992.27i	0.405480	+	0.234104i	0.688846	−	0.724908i	$-0.258118\pi$
$769$	8646.87	+	4992.27i	0.405480	+	0.234104i	−0.283366	+	0.959012i	$0.591451\pi$
$770$		0			0
$771$	−17525.3	−	30354.7i	−0.818622	−	1.41790i
$772$		0			0
$773$	−4550.65	+	2627.32i	−0.211741	+	0.122248i	−0.602120	−	0.798406i	$-0.705677\pi$
$773$	−4550.65	+	2627.32i	−0.211741	+	0.122248i	0.390379	+	0.920654i	$0.372344\pi$
$774$		0			0
$775$			10575.6i			0.490176i
$776$		0			0
$777$	−3679.68	+	6373.40i	−0.169894	+	0.294266i
$778$		0			0
$779$	185.342			0.00852446
$780$		0			0
$781$	−28992.4			−1.32833
$782$		0			0
$783$	−2632.93	+	4560.37i	−0.120170	+	0.208141i
$784$		0			0
$785$			25910.0i			1.17805i
$786$		0			0
$787$	−11671.4	+	6738.47i	−0.528640	+	0.305210i	−0.740462	−	0.672098i	$-0.765393\pi$
$787$	−11671.4	+	6738.47i	−0.528640	+	0.305210i	0.211823	+	0.977308i	$0.432060\pi$
$788$		0			0
$789$	20951.2	+	36288.6i	0.945353	+	1.63740i
$790$		0			0
$791$	−3192.24	−	1843.04i	−0.143493	−	0.0828458i
$792$		0			0
$793$	−13159.0	+	25076.9i	−0.589266	+	1.12296i
$794$		0			0
$795$	−41302.7	−	23846.1i	−1.84258	−	1.06382i
$796$		0			0
$797$	−16461.3	−	28511.7i	−0.731603	−	1.26717i	−0.956198	−	0.292721i	$-0.905439\pi$
$797$	−16461.3	−	28511.7i	−0.731603	−	1.26717i	0.224595	−	0.974452i	$-0.427894\pi$
$798$		0			0
$799$	4554.51	−	2629.55i	0.201661	−	0.116429i
$800$		0			0
$801$			9576.09i			0.422415i
$802$		0			0
$803$	−11320.4	+	19607.5i	−0.497494	+	0.861686i
$804$		0			0
$805$	4693.49			0.205495
$806$		0			0
$807$	6392.68			0.278851
$808$		0			0
$809$	2675.65	−	4634.36i	0.116280	−	0.201404i	−0.802010	−	0.597310i	$-0.796236\pi$
$809$	2675.65	−	4634.36i	0.116280	−	0.201404i	0.918291	+	0.395906i	$0.129570\pi$
$810$		0			0
$811$		−	26939.7i		−	1.16644i	−0.812315	−	0.583219i	$-0.801793\pi$
$811$		−	26939.7i		−	1.16644i	0.812315	−	0.583219i	$-0.198207\pi$
$812$		0			0
$813$	10408.7	−	6009.48i	0.449016	−	0.259239i
$814$		0			0
$815$	3820.00	+	6616.44i	0.164183	+	0.284373i
$816$		0			0
$817$	3170.99	+	1830.77i	0.135788	+	0.0783974i
$818$		0			0
$819$	98.2872	+	2434.43i	0.00419345	+	0.103865i
$820$		0			0
$821$	−30353.8	−	17524.8i	−1.29032	−	0.744969i	−0.311613	−	0.950209i	$-0.600869\pi$
$821$	−30353.8	−	17524.8i	−1.29032	−	0.744969i	−0.978712	+	0.205240i	$0.934203\pi$
$822$		0			0
$823$	12653.5	+	21916.6i	0.535935	+	0.928267i	0.999117	+	0.0420043i	$0.0133743\pi$
$823$	12653.5	+	21916.6i	0.535935	+	0.928267i	−0.463182	+	0.886263i	$0.653292\pi$
$824$		0			0
$825$	9091.60	−	5249.04i	0.383671	−	0.221513i
$826$		0			0
$827$			1585.60i			0.0666709i	0.999444	+	0.0333355i	$0.0106130\pi$
$827$			1585.60i			0.0666709i	−0.999444	+	0.0333355i	$0.989387\pi$
$828$		0			0
$829$	13274.2	−	22991.5i	0.556129	−	0.963244i	−0.441686	−	0.897170i	$-0.645619\pi$
$829$	13274.2	−	22991.5i	0.556129	−	0.963244i	0.997815	−	0.0660740i	$-0.0210473\pi$
$830$		0			0
$831$	44977.9			1.87758
$832$		0			0
$833$	11030.6			0.458808
$834$		0			0
$835$	−6632.41	+	11487.7i	−0.274879	+	0.476104i
$836$		0			0
$837$		−	14181.6i		−	0.585648i
$838$		0			0
$839$	−8588.06	+	4958.32i	−0.353388	+	0.204029i	−0.666177	−	0.745794i	$-0.732070\pi$
$839$	−8588.06	+	4958.32i	−0.353388	+	0.204029i	0.312788	+	0.949823i	$0.398737\pi$
$840$		0			0
$841$	6931.34	+	12005.4i	0.284199	+	0.492248i
$842$		0			0
$843$	24578.1	+	14190.2i	1.00417	+	0.579757i
$844$		0			0
$845$	25364.4	+	12030.9i	1.03262	+	0.489793i
$846$		0			0
$847$	−665.588	−	384.277i	−0.0270010	−	0.0155891i
$848$		0			0
$849$	−20166.8	−	34929.9i	−0.815222	−	1.41201i
$850$		0			0
$851$	48185.9	−	27820.1i	1.94100	−	1.12064i
$852$		0			0
$853$		−	9649.84i		−	0.387344i	−0.981066	−	0.193672i	$-0.937960\pi$
$853$		−	9649.84i		−	0.387344i	0.981066	−	0.193672i	$-0.0620397\pi$
$854$		0			0
$855$	−2231.73	+	3865.48i	−0.0892674	+	0.154616i
$856$		0			0
$857$	−24910.3			−0.992906			−0.496453	−	0.868063i	$-0.665365\pi$
$857$	−24910.3			−0.992906			−0.496453	+	0.868063i	$0.665365\pi$
$858$		0			0
$859$	−24216.8			−0.961892			−0.480946	−	0.876750i	$-0.659707\pi$
$859$	−24216.8			−0.961892			−0.480946	+	0.876750i	$0.659707\pi$
$860$		0			0
$861$	−94.0061	+	162.823i	−0.00372093	+	0.00644484i
$862$		0			0
$863$		−	35277.7i		−	1.39150i	−0.718282	−	0.695752i	$-0.755071\pi$
$863$		−	35277.7i		−	1.39150i	0.718282	−	0.695752i	$-0.244929\pi$
$864$		0			0
$865$	12241.5	−	7067.63i	0.481183	−	0.277811i
$866$		0			0
$867$	−13069.6	−	22637.2i	−0.511957	−	0.886735i
$868$		0			0
$869$	−20479.0	−	11823.6i	−0.799429	−	0.461551i
$870$		0			0
$871$	−1275.96	−	31603.5i	−0.0496373	−	1.22944i
$872$		0			0
$873$	28784.7	+	16618.8i	1.11594	+	0.644287i
$874$		0			0
$875$	1479.19	+	2562.03i	0.0571495	+	0.0989858i
$876$		0			0
$877$	−21877.6	+	12631.1i	−0.842366	+	0.486340i	−0.858068	−	0.513536i	$-0.828335\pi$
$877$	−21877.6	+	12631.1i	−0.842366	+	0.486340i	0.0157015	+	0.999877i	$0.495002\pi$
$878$		0			0
$879$		−	46737.0i		−	1.79340i
$880$		0			0
$881$	10515.3	−	18213.1i	0.402124	−	0.696499i	−0.591858	−	0.806042i	$-0.701605\pi$
$881$	10515.3	−	18213.1i	0.402124	−	0.696499i	0.993982	+	0.109543i	$0.0349388\pi$
$882$		0			0
$883$	−46166.1			−1.75947			−0.879736	−	0.475463i	$-0.842280\pi$
$883$	−46166.1			−1.75947			−0.879736	+	0.475463i	$0.842280\pi$
$884$		0			0
$885$	35896.7			1.36345
$886$		0			0
$887$	−1720.43	+	2979.87i	−0.0651256	+	0.112801i	−0.896750	−	0.442538i	$-0.854078\pi$
$887$	−1720.43	+	2979.87i	−0.0651256	+	0.112801i	0.831624	+	0.555339i	$0.187411\pi$
$888$		0			0
$889$		−	1584.44i		−	0.0597754i
$890$		0			0
$891$	−30510.1	+	17615.0i	−1.14717	+	0.662318i
$892$		0			0
$893$	1436.43	+	2487.96i	0.0538277	+	0.0932324i
$894$		0			0
$895$	−17075.6	−	9858.59i	−0.637736	−	0.368197i
$896$		0			0
$897$	20428.0	−	38929.4i	0.760392	−	1.44907i
$898$		0			0
$899$	24550.7	+	14174.3i	0.910801	+	0.525851i
$900$		0			0
$901$	−8990.65	−	15572.3i	−0.332433	−	0.575791i
$902$		0			0
$903$	−3216.69	+	1857.15i	−0.118543	+	0.0684410i
$904$		0			0
$905$			10392.9i			0.381735i
$906$		0			0
$907$	−6298.16	+	10908.7i	−0.230570	+	0.399359i	−0.957976	−	0.286849i	$-0.907392\pi$
$907$	−6298.16	+	10908.7i	−0.230570	+	0.399359i	0.727406	+	0.686207i	$0.240726\pi$
$908$		0			0
$909$	−23676.0			−0.863899
$910$		0			0
$911$	−35459.3			−1.28959			−0.644797	−	0.764354i	$-0.723058\pi$
$911$	−35459.3			−1.28959			−0.644797	+	0.764354i	$0.723058\pi$
$912$		0			0
$913$	−11732.9	+	20322.0i	−0.425304	+	0.736648i
$914$		0			0
$915$		−	52628.9i		−	1.90148i
$916$		0			0
$917$	−310.028	+	178.995i	−0.0111647	+	0.00644594i
$918$		0			0
$919$	13026.6	+	22562.8i	0.467584	+	0.809878i	0.999314	−	0.0370353i	$-0.0117914\pi$
$919$	13026.6	+	22562.8i	0.467584	+	0.809878i	−0.531730	+	0.846914i	$0.678458\pi$
$920$		0			0
$921$	16805.2	+	9702.49i	0.601249	+	0.347131i
$922$		0			0
$923$	29907.1	+	15693.6i	1.06653	+	0.559654i
$924$		0			0
$925$	−13404.2	−	7738.94i	−0.476463	−	0.275086i
$926$		0			0
$927$	7576.35	+	13122.6i	0.268436	+	0.464944i
$928$		0			0
$929$	−13504.5	+	7796.81i	−0.476929	+	0.275355i	−0.719136	−	0.694869i	$-0.755462\pi$
$929$	−13504.5	+	7796.81i	−0.476929	+	0.275355i	0.242207	+	0.970225i	$0.422129\pi$
$930$		0			0
$931$			6025.61i			0.212118i
$932$		0			0
$933$	−20514.0	+	35531.4i	−0.719828	+	1.24678i
$934$		0			0
$935$	16884.6			0.590574
$936$		0			0
$937$	−17686.2			−0.616631			−0.308316	−	0.951284i	$-0.599765\pi$
$937$	−17686.2			−0.616631			−0.308316	+	0.951284i	$0.599765\pi$
$938$		0			0
$939$	−8988.79	+	15569.0i	−0.312394	+	0.541082i
$940$		0			0
$941$		−	5601.91i		−	0.194067i	−0.995281	−	0.0970336i	$-0.969065\pi$
$941$		−	5601.91i		−	0.194067i	0.995281	−	0.0970336i	$-0.0309354\pi$
$942$		0			0
$943$	1231.02	−	710.731i	0.0425107	−	0.0245436i
$944$		0			0
$945$	875.404	+	1516.24i	0.0301343	+	0.0521941i
$946$		0			0
$947$	6347.18	+	3664.55i	0.217799	+	0.125746i	0.604931	−	0.796278i	$-0.293201\pi$
$947$	6347.18	+	3664.55i	0.217799	+	0.125746i	−0.387132	+	0.922024i	$0.626534\pi$
$948$		0			0
$949$	22291.1	−	14098.4i	0.762487	−	0.482248i
$950$		0			0
$951$	−53227.9	−	30731.2i	−1.81497	−	1.04787i
$952$		0			0
$953$	−19308.1	−	33442.6i	−0.656296	−	1.13674i	−0.981567	−	0.191117i	$-0.938789\pi$
$953$	−19308.1	−	33442.6i	−0.656296	−	1.13674i	0.325272	−	0.945621i	$-0.394544\pi$
$954$		0			0
$955$	−24781.5	+	14307.6i	−0.839698	+	0.484800i
$956$		0			0
$957$		−	28140.9i		−	0.950539i
$958$		0			0
$959$	−2689.08	+	4657.62i	−0.0905473	+	0.156833i
$960$		0			0
$961$	−46555.3			−1.56273
$962$		0			0
$963$	38266.2			1.28049
$964$		0			0
$965$	−23045.6	+	39916.2i	−0.768773	+	1.33155i
$966$		0			0
$967$			26596.2i			0.884462i	0.896901	+	0.442231i	$0.145813\pi$
$967$			26596.2i			0.884462i	−0.896901	+	0.442231i	$0.854187\pi$
$968$		0			0
$969$	−3478.33	+	2008.22i	−0.115315	+	0.0665770i
$970$		0			0
$971$	15812.8	+	27388.6i	0.522613	+	0.905192i	0.999654	+	0.0263111i	$0.00837605\pi$
$971$	15812.8	+	27388.6i	0.522613	+	0.905192i	−0.477041	+	0.878881i	$0.658291\pi$
$972$		0			0
$973$	−6111.11	−	3528.25i	−0.201349	−	0.116249i
$974$		0			0
$975$	−12219.8	+	493.358i	−0.401380	+	0.0162052i
$976$		0			0
$977$	−28560.6	−	16489.5i	−0.935246	−	0.539964i	−0.0467788	−	0.998905i	$-0.514896\pi$
$977$	−28560.6	−	16489.5i	−0.935246	−	0.539964i	−0.888467	+	0.458941i	$0.848229\pi$
$978$		0			0
$979$	9894.18	+	17137.2i	0.323002	+	0.559457i
$980$		0			0
$981$	7321.40	−	4227.01i	0.238282	−	0.137572i
$982$		0			0
$983$			18103.5i			0.587397i	0.955898	+	0.293699i	$0.0948862\pi$
$983$			18103.5i			0.587397i	−0.955898	+	0.293699i	$0.905114\pi$
$984$		0			0
$985$	13561.9	−	23489.9i	0.438698	−	0.759847i
$986$		0			0
$987$	−2914.25			−0.0939834
$988$		0			0
$989$	28081.9			0.902885
$990$		0			0
$991$	13713.9	−	23753.2i	0.439593	−	0.761398i	−0.558065	−	0.829797i	$-0.688456\pi$
$991$	13713.9	−	23753.2i	0.439593	−	0.761398i	0.997658	+	0.0683995i	$0.0217893\pi$
$992$		0			0
$993$		−	35084.1i		−	1.12121i
$994$		0			0
$995$	−6563.44	+	3789.40i	−0.209121	+	0.120736i
$996$		0			0
$997$	−17249.5	−	29877.0i	−0.547942	−	0.949063i	−0.998415	−	0.0562730i	$-0.982078\pi$
$997$	−17249.5	−	29877.0i	−0.547942	−	0.949063i	0.450474	−	0.892790i	$-0.351255\pi$
$998$		0			0
$999$	17974.7	+	10377.7i	0.569265	+	0.328665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	104.4.o.a.17.9	✓	20
4.3	odd	2		208.4.w.e.17.2		20
13.6	odd	12		1352.4.a.o.1.2		10
13.7	odd	12		1352.4.a.p.1.2		10
13.10	even	6	inner	104.4.o.a.49.9	yes	20
52.23	odd	6		208.4.w.e.49.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.4.o.a.17.9	✓	20	1.1	even	1	trivial
104.4.o.a.49.9	yes	20	13.10	even	6	inner
208.4.w.e.17.2		20	4.3	odd	2
208.4.w.e.49.2		20	52.23	odd	6
1352.4.a.o.1.2		10	13.6	odd	12
1352.4.a.p.1.2		10	13.7	odd	12

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:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	104.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.40848 - 5.90366i) q^{3} -12.7779i q^{5} +(-2.31195 + 1.33481i) q^{7} +(-9.73548 - 16.8623i) q^{9} +O(q^{10})\)	\(q+(3.40848 - 5.90366i) q^{3} -12.7779i q^{5} +(-2.31195 + 1.33481i) q^{7} +(-9.73548 - 16.8623i) q^{9} +(-34.8449 - 20.1177i) q^{11} +(25.0545 + 39.6140i) q^{13} +(-75.4364 - 43.5532i) q^{15} +(-16.4208 - 28.4416i) q^{17} +(15.5366 - 8.97007i) q^{19} +18.1987i q^{21} +(68.7952 - 119.157i) q^{23} -38.2746 q^{25} +51.3252 q^{27} +(-51.2989 + 88.8524i) q^{29} -276.308i q^{31} +(-237.536 + 137.142i) q^{33} +(17.0560 + 29.5419i) q^{35} +(350.213 + 202.195i) q^{37} +(319.266 - 12.8900i) q^{39} +(8.94701 + 5.16556i) q^{41} +(102.049 + 176.754i) q^{43} +(-215.465 + 124.399i) q^{45} +160.135i q^{47} +(-167.937 + 290.875i) q^{49} -223.880 q^{51} +547.517 q^{53} +(-257.062 + 445.244i) q^{55} -122.297i q^{57} +(-356.890 + 206.051i) q^{59} +(302.095 + 523.245i) q^{61} +(45.0159 + 25.9900i) q^{63} +(506.184 - 320.144i) q^{65} +(-584.393 - 337.399i) q^{67} +(-468.974 - 812.287i) q^{69} +(624.030 - 360.284i) q^{71} -562.708i q^{73} +(-130.458 + 225.960i) q^{75} +107.413 q^{77} +587.720 q^{79} +(437.799 - 758.290i) q^{81} -583.213i q^{83} +(-363.424 + 209.823i) q^{85} +(349.703 + 605.703i) q^{87} +(-425.924 - 245.907i) q^{89} +(-110.802 - 58.1428i) q^{91} +(-1631.23 - 941.792i) q^{93} +(-114.619 - 198.525i) q^{95} +(-1478.34 + 853.519i) q^{97} +783.422i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 - 54 * q^7 - 72 * q^9	\( 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9} - 42 q^{11} + 24 q^{13} - 70 q^{17} - 102 q^{19} + 90 q^{23} - 628 q^{25} + 708 q^{27} + 170 q^{29} - 678 q^{33} - 544 q^{35} + 582 q^{37} + 1162 q^{39} + 438 q^{41} + 270 q^{43} + 540 q^{45} + 92 q^{49} - 444 q^{51} - 592 q^{53} - 288 q^{55} + 90 q^{59} + 746 q^{61} - 1068 q^{63} - 1412 q^{65} + 846 q^{67} + 682 q^{69} - 1038 q^{71} + 722 q^{75} + 2812 q^{77} - 1008 q^{79} + 694 q^{81} - 180 q^{85} - 338 q^{87} + 2466 q^{89} + 690 q^{91} - 4764 q^{93} - 2592 q^{95} - 846 q^{97}+O(q^{100}) \) 20 * q - 6 * q^3 - 54 * q^7 - 72 * q^9 - 42 * q^11 + 24 * q^13 - 70 * q^17 - 102 * q^19 + 90 * q^23 - 628 * q^25 + 708 * q^27 + 170 * q^29 - 678 * q^33 - 544 * q^35 + 582 * q^37 + 1162 * q^39 + 438 * q^41 + 270 * q^43 + 540 * q^45 + 92 * q^49 - 444 * q^51 - 592 * q^53 - 288 * q^55 + 90 * q^59 + 746 * q^61 - 1068 * q^63 - 1412 * q^65 + 846 * q^67 + 682 * q^69 - 1038 * q^71 + 722 * q^75 + 2812 * q^77 - 1008 * q^79 + 694 * q^81 - 180 * q^85 - 338 * q^87 + 2466 * q^89 + 690 * q^91 - 4764 * q^93 - 2592 * q^95 - 846 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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