LMFDB - Embedded newform 400.2.bi.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,2,Mod(47,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 17]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("400.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	400.bi (of order $20$, degree $8$, 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:	$3.19401608085$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	400.127
Dual form			400.2.bi.d.63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.97847 + 1.51761i) q^{3} +(1.69605 + 1.45720i) q^{5} +(1.80351 - 1.80351i) q^{7} +(4.80482 - 6.61326i) q^{9} +O(q^{10})$	\(q+(-2.97847 + 1.51761i) q^{3} +(1.69605 + 1.45720i) q^{5} +(1.80351 - 1.80351i) q^{7} +(4.80482 - 6.61326i) q^{9} +(2.46693 + 3.39544i) q^{11} +(0.731069 - 0.115790i) q^{13} +(-7.26309 - 1.76629i) q^{15} +(-3.09835 + 6.08086i) q^{17} +(0.285040 + 0.877263i) q^{19} +(-2.63469 + 8.10874i) q^{21} +(-3.66187 - 0.579984i) q^{23} +(0.753156 + 4.94295i) q^{25} +(-2.70588 + 17.0843i) q^{27} +(-2.48868 - 0.808620i) q^{29} +(5.85729 - 1.90315i) q^{31} +(-12.5006 - 6.36939i) q^{33} +(5.68691 - 0.430771i) q^{35} +(-0.443143 - 2.79789i) q^{37} +(-2.00175 + 1.45435i) q^{39} +(2.09726 + 1.52375i) q^{41} +(1.85076 + 1.85076i) q^{43} +(17.7860 - 4.21485i) q^{45} +(3.13797 + 6.15862i) q^{47} +0.494689i q^{49} -22.8138i q^{51} +(0.786001 + 1.54261i) q^{53} +(-0.763789 + 9.35362i) q^{55} +(-2.18033 - 2.18033i) q^{57} +(1.10583 + 0.803429i) q^{59} +(-6.13174 + 4.45497i) q^{61} +(-3.26155 - 20.5926i) q^{63} +(1.40866 + 0.868926i) q^{65} +(-8.25963 - 4.20849i) q^{67} +(11.7870 - 3.82982i) q^{69} +(5.26538 + 1.71082i) q^{71} +(0.380123 - 2.40000i) q^{73} +(-9.74472 - 13.5795i) q^{75} +(10.5728 + 1.67457i) q^{77} +(1.89136 - 5.82101i) q^{79} +(-10.2897 - 31.6685i) q^{81} +(-1.10190 + 2.16260i) q^{83} +(-14.1160 + 5.79851i) q^{85} +(8.63962 - 1.36838i) q^{87} +(-5.88076 - 8.09417i) q^{89} +(1.10966 - 1.52732i) q^{91} +(-14.5576 + 14.5576i) q^{93} +(-0.794903 + 1.90324i) q^{95} +(7.27061 - 3.70456i) q^{97} +34.3080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{5}+O(q^{10}) $ 80 * q + 4 * q^5	$ 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) $ 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{1}{20}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.97847	+	1.51761i	−1.71962	+	0.876192i	−0.740734	+	0.671799i	$0.765522\pi$
$3$	−2.97847	+	1.51761i	−1.71962	+	0.876192i	−0.978889	+	0.204393i	$0.934478\pi$
$4$		0			0
$5$	1.69605	+	1.45720i	0.758496	+	0.651678i
$5$	1.69605	+	1.45720i	0.758496	+	0.651678i
$6$		0			0
$7$	1.80351	−	1.80351i	0.681663	−	0.681663i	−0.278711	−	0.960375i	$-0.589907\pi$
$7$	1.80351	−	1.80351i	0.681663	−	0.681663i	0.960375	+	0.278711i	$0.0899073\pi$
$8$		0			0
$9$	4.80482	−	6.61326i	1.60161	−	2.20442i
$10$		0			0
$11$	2.46693	+	3.39544i	0.743807	+	1.02376i	0.998391	+	0.0567116i	$0.0180616\pi$
$11$	2.46693	+	3.39544i	0.743807	+	1.02376i	−0.254584	+	0.967051i	$0.581938\pi$
$12$		0			0
$13$	0.731069	−	0.115790i	0.202762	−	0.0321143i	−0.0542272	−	0.998529i	$-0.517270\pi$
$13$	0.731069	−	0.115790i	0.202762	−	0.0321143i	0.256989	+	0.966414i	$0.417270\pi$
$14$		0			0
$15$	−7.26309	−	1.76629i	−1.87532	−	0.456053i
$16$		0			0
$17$	−3.09835	+	6.08086i	−0.751460	+	1.47482i	0.124386	+	0.992234i	$0.460304\pi$
$17$	−3.09835	+	6.08086i	−0.751460	+	1.47482i	−0.875846	+	0.482590i	$0.839696\pi$
$18$		0			0
$19$	0.285040	+	0.877263i	0.0653926	+	0.201258i	0.978414	−	0.206653i	$-0.0662573\pi$
$19$	0.285040	+	0.877263i	0.0653926	+	0.201258i	−0.913022	+	0.407911i	$0.866257\pi$
$20$		0			0
$21$	−2.63469	+	8.10874i	−0.574936	+	1.76947i
$22$		0			0
$23$	−3.66187	−	0.579984i	−0.763553	−	0.120935i	−0.237501	−	0.971387i	$-0.576328\pi$
$23$	−3.66187	−	0.579984i	−0.763553	−	0.120935i	−0.526052	+	0.850452i	$0.676328\pi$
$24$		0			0
$25$	0.753156	+	4.94295i	0.150631	+	0.988590i
$26$		0			0
$27$	−2.70588	+	17.0843i	−0.520747	+	3.28787i
$28$		0			0
$29$	−2.48868	−	0.808620i	−0.462135	−	0.150157i	0.0686901	−	0.997638i	$-0.478118\pi$
$29$	−2.48868	−	0.808620i	−0.462135	−	0.150157i	−0.530825	+	0.847481i	$0.678118\pi$
$30$		0			0
$31$	5.85729	−	1.90315i	1.05200	−	0.341816i	0.268547	−	0.963266i	$-0.413456\pi$
$31$	5.85729	−	1.90315i	1.05200	−	0.341816i	0.783453	+	0.621451i	$0.213456\pi$
$32$		0			0
$33$	−12.5006	−	6.36939i	−2.17608	−	1.10877i
$34$		0			0
$35$	5.68691	−	0.430771i	0.961264	−	0.0728136i
$36$		0			0
$37$	−0.443143	−	2.79789i	−0.0728523	−	0.459971i	−0.996965	−	0.0778511i	$-0.975194\pi$
$37$	−0.443143	−	2.79789i	−0.0728523	−	0.459971i	0.924113	−	0.382120i	$-0.124806\pi$
$38$		0			0
$39$	−2.00175	+	1.45435i	−0.320536	+	0.232883i
$40$		0			0
$41$	2.09726	+	1.52375i	0.327537	+	0.237970i	0.739385	−	0.673283i	$-0.235116\pi$
$41$	2.09726	+	1.52375i	0.327537	+	0.237970i	−0.411848	+	0.911253i	$0.635116\pi$
$42$		0			0
$43$	1.85076	+	1.85076i	0.282238	+	0.282238i	0.834001	−	0.551763i	$-0.186045\pi$
$43$	1.85076	+	1.85076i	0.282238	+	0.282238i	−0.551763	+	0.834001i	$0.686045\pi$
$44$		0			0
$45$	17.7860	−	4.21485i	2.65138	−	0.628312i
$46$		0			0
$47$	3.13797	+	6.15862i	0.457720	+	0.898327i	0.998370	+	0.0570785i	$0.0181785\pi$
$47$	3.13797	+	6.15862i	0.457720	+	0.898327i	−0.540649	+	0.841248i	$0.681821\pi$
$48$		0			0
$49$			0.494689i			0.0706698i
$50$		0			0
$51$		−	22.8138i		−	3.19456i
$52$		0			0
$53$	0.786001	+	1.54261i	0.107966	+	0.211894i	0.938668	−	0.344822i	$-0.112061\pi$
$53$	0.786001	+	1.54261i	0.107966	+	0.211894i	−0.830702	+	0.556717i	$0.812061\pi$
$54$		0			0
$55$	−0.763789	+	9.35362i	−0.102989	+	1.26124i
$56$		0			0
$57$	−2.18033	−	2.18033i	−0.288791	−	0.288791i
$58$		0			0
$59$	1.10583	+	0.803429i	0.143966	+	0.104598i	0.657437	−	0.753509i	$-0.271641\pi$
$59$	1.10583	+	0.803429i	0.143966	+	0.104598i	−0.513471	+	0.858107i	$0.671641\pi$
$60$		0			0
$61$	−6.13174	+	4.45497i	−0.785088	+	0.570400i	−0.906502	−	0.422202i	$-0.861257\pi$
$61$	−6.13174	+	4.45497i	−0.785088	+	0.570400i	0.121414	+	0.992602i	$0.461257\pi$
$62$		0			0
$63$	−3.26155	−	20.5926i	−0.410917	−	2.59443i
$64$		0			0
$65$	1.40866	+	0.868926i	0.174722	+	0.107777i
$66$		0			0
$67$	−8.25963	−	4.20849i	−1.00907	−	0.514149i	−0.130344	−	0.991469i	$-0.541608\pi$
$67$	−8.25963	−	4.20849i	−1.00907	−	0.514149i	−0.878730	+	0.477320i	$0.841608\pi$
$68$		0			0
$69$	11.7870	−	3.82982i	1.41899	−	0.461057i
$70$		0			0
$71$	5.26538	+	1.71082i	0.624885	+	0.203038i	0.604308	−	0.796751i	$-0.293450\pi$
$71$	5.26538	+	1.71082i	0.624885	+	0.203038i	0.0205772	+	0.999788i	$0.493450\pi$
$72$		0			0
$73$	0.380123	−	2.40000i	0.0444900	−	0.280899i	−0.955406	−	0.295294i	$-0.904582\pi$
$73$	0.380123	−	2.40000i	0.0444900	−	0.280899i	0.999896	+	0.0143953i	$0.00458233\pi$
$74$		0			0
$75$	−9.74472	−	13.5795i	−1.12522	−	1.56802i
$76$		0			0
$77$	10.5728	+	1.67457i	1.20489	+	0.190835i
$78$		0			0
$79$	1.89136	−	5.82101i	0.212795	−	0.654915i	−0.786508	−	0.617580i	$-0.788113\pi$
$79$	1.89136	−	5.82101i	0.212795	−	0.654915i	0.999303	−	0.0373351i	$-0.0118869\pi$
$80$		0			0
$81$	−10.2897	−	31.6685i	−1.14330	−	3.51872i
$82$		0			0
$83$	−1.10190	+	2.16260i	−0.120949	+	0.237377i	−0.943541	−	0.331256i	$-0.892528\pi$
$83$	−1.10190	+	2.16260i	−0.120949	+	0.237377i	0.822591	+	0.568633i	$0.192528\pi$
$84$		0			0
$85$	−14.1160	+	5.79851i	−1.53109	+	0.628937i
$86$		0			0
$87$	8.63962	−	1.36838i	0.926265	−	0.146706i
$88$		0			0
$89$	−5.88076	−	8.09417i	−0.623360	−	0.857981i	0.374233	−	0.927335i	$-0.377906\pi$
$89$	−5.88076	−	8.09417i	−0.623360	−	0.857981i	−0.997592	+	0.0693541i	$0.977906\pi$
$90$		0			0
$91$	1.10966	−	1.52732i	0.116324	−	0.160107i
$92$		0			0
$93$	−14.5576	+	14.5576i	−1.50955	+	1.50955i
$94$		0			0
$95$	−0.794903	+	1.90324i	−0.0815553	+	0.195268i
$96$		0			0
$97$	7.27061	−	3.70456i	0.738218	−	0.376141i	−0.0440939	−	0.999027i	$-0.514040\pi$
$97$	7.27061	−	3.70456i	0.738218	−	0.376141i	0.782312	+	0.622886i	$0.214040\pi$
$98$		0			0
$99$	34.3080			3.44809
$100$		0			0
$101$	16.2083			1.61279			0.806395	−	0.591377i	$-0.201416\pi$
$101$	16.2083			1.61279			0.806395	+	0.591377i	$0.201416\pi$
$102$		0			0
$103$	2.58489	−	1.31707i	0.254696	−	0.129774i	−0.321981	−	0.946746i	$-0.604349\pi$
$103$	2.58489	−	1.31707i	0.254696	−	0.129774i	0.576678	+	0.816972i	$0.304349\pi$
$104$		0			0
$105$	−16.2846	+	9.91355i	−1.58921	+	0.967463i
$106$		0			0
$107$	0.138210	−	0.138210i	0.0133613	−	0.0133613i	−0.700395	−	0.713756i	$-0.746993\pi$
$107$	0.138210	−	0.138210i	0.0133613	−	0.0133613i	0.713756	+	0.700395i	$0.246993\pi$
$108$		0			0
$109$	−7.69962	+	10.5976i	−0.737490	+	1.01507i	0.261270	+	0.965266i	$0.415859\pi$
$109$	−7.69962	+	10.5976i	−0.737490	+	1.01507i	−0.998759	+	0.0498014i	$0.984141\pi$
$110$		0			0
$111$	5.56600	+	7.66094i	0.528301	+	0.727144i
$112$		0			0
$113$	10.0342	−	1.58926i	0.943935	−	0.149505i	0.334549	−	0.942378i	$-0.391416\pi$
$113$	10.0342	−	1.58926i	0.943935	−	0.149505i	0.609386	+	0.792874i	$0.291416\pi$
$114$		0			0
$115$	−5.36556	−	6.31975i	−0.500341	−	0.589320i
$116$		0			0
$117$	2.74690	−	5.39110i	0.253951	−	0.498407i
$118$		0			0
$119$	5.37898	+	16.5548i	0.493091	+	1.51758i
$120$		0			0
$121$	−2.04406	+	6.29097i	−0.185824	+	0.571907i
$122$		0			0
$123$	−8.55910	−	1.35563i	−0.771748	−	0.122233i
$124$		0			0
$125$	−5.92546	+	9.48098i	−0.529989	+	0.848004i
$126$		0			0
$127$	1.67958	−	10.6044i	0.149038	−	0.940990i	−0.793906	−	0.608040i	$-0.791956\pi$
$127$	1.67958	−	10.6044i	0.149038	−	0.940990i	0.942944	−	0.332950i	$-0.108044\pi$
$128$		0			0
$129$	−8.32116	−	2.70371i	−0.732637	−	0.238048i
$130$		0			0
$131$	−14.0985	+	4.58087i	−1.23179	+	0.400232i	−0.851362	−	0.524579i	$-0.824223\pi$
$131$	−14.0985	+	4.58087i	−1.23179	+	0.400232i	−0.380426	+	0.924811i	$0.624223\pi$
$132$		0			0
$133$	2.09623	+	1.06808i	0.181766	+	0.0926144i
$134$		0			0
$135$	−29.4844	+	25.0327i	−2.53762	+	2.15447i
$136$		0			0
$137$	−1.01149	−	6.38631i	−0.0864176	−	0.545619i	−0.992473	−	0.122461i	$-0.960921\pi$
$137$	−1.01149	−	6.38631i	−0.0864176	−	0.545619i	0.906056	−	0.423158i	$-0.139079\pi$
$138$		0			0
$139$	6.90200	−	5.01460i	0.585420	−	0.425333i	−0.255254	−	0.966874i	$-0.582159\pi$
$139$	6.90200	−	5.01460i	0.585420	−	0.425333i	0.840674	+	0.541541i	$0.182159\pi$
$140$		0			0
$141$	−18.6927	−	13.5811i	−1.57421	−	1.14373i
$142$		0			0
$143$	2.19665	+	2.19665i	0.183693	+	0.183693i
$144$		0			0
$145$	−3.04259	−	4.99795i	−0.252674	−	0.415057i
$146$		0			0
$147$	−0.750744	−	1.47342i	−0.0619203	−	0.121525i
$148$		0			0
$149$		−	7.76247i		−	0.635926i	−0.948103	−	0.317963i	$-0.897001\pi$
$149$		−	7.76247i		−	0.635926i	0.948103	−	0.317963i	$-0.102999\pi$
$150$		0			0
$151$		−	0.842328i		−	0.0685477i	−0.999412	−	0.0342739i	$-0.989088\pi$
$151$		−	0.842328i		−	0.0685477i	0.999412	−	0.0342739i	$-0.0109118\pi$
$152$		0			0
$153$	25.3273	+	49.7076i	2.04759	+	4.01862i
$154$		0			0
$155$	12.7075	+	5.30739i	1.02069	+	0.426300i
$156$		0			0
$157$	16.8217	+	16.8217i	1.34252	+	1.34252i	0.893546	+	0.448972i	$0.148210\pi$
$157$	16.8217	+	16.8217i	1.34252	+	1.34252i	0.448972	+	0.893546i	$0.351790\pi$
$158$		0			0
$159$	−4.68217	−	3.40179i	−0.371320	−	0.269780i
$160$		0			0
$161$	−7.65024	+	5.55823i	−0.602923	+	0.438050i
$162$		0			0
$163$	−2.29285	−	14.4765i	−0.179590	−	1.13389i	−0.898562	−	0.438847i	$-0.855387\pi$
$163$	−2.29285	−	14.4765i	−0.179590	−	1.13389i	0.718972	−	0.695040i	$-0.244613\pi$
$164$		0			0
$165$	−11.9202	−	29.0187i	−0.927987	−	2.25910i
$166$		0			0
$167$	13.3623	+	6.80846i	1.03401	+	0.526854i	0.886753	−	0.462244i	$-0.152956\pi$
$167$	13.3623	+	6.80846i	1.03401	+	0.526854i	0.147257	+	0.989098i	$0.452956\pi$
$168$		0			0
$169$	−11.8427	+	3.84792i	−0.910975	+	0.295994i
$170$		0			0
$171$	7.17113	+	2.33004i	0.548390	+	0.178183i
$172$		0			0
$173$	3.76181	−	23.7511i	0.286005	−	1.80576i	−0.257413	−	0.966302i	$-0.582870\pi$
$173$	3.76181	−	23.7511i	0.286005	−	1.80576i	0.543418	−	0.839463i	$-0.317130\pi$
$174$		0			0
$175$	10.2730	+	7.55634i	0.776565	+	0.571206i
$176$		0			0
$177$	−4.51296	−	0.714783i	−0.339215	−	0.0537264i
$178$		0			0
$179$	−5.16249	+	15.8885i	−0.385863	+	1.18756i	0.549990	+	0.835171i	$0.314632\pi$
$179$	−5.16249	+	15.8885i	−0.385863	+	1.18756i	−0.935852	+	0.352392i	$0.885368\pi$
$180$		0			0
$181$	−4.86064	−	14.9595i	−0.361289	−	1.11193i	−0.952273	−	0.305249i	$-0.901260\pi$
$181$	−4.86064	−	14.9595i	−0.361289	−	1.11193i	0.590984	−	0.806683i	$-0.298740\pi$
$182$		0			0
$183$	11.5023	−	22.5746i	0.850276	−	1.66876i
$184$		0			0
$185$	3.32549	−	5.39111i	0.244495	−	0.396362i
$186$		0			0
$187$	−28.2906	+	4.48078i	−2.06881	+	0.327667i
$188$		0			0
$189$	25.9316	+	35.6918i	1.88625	+	2.59620i
$190$		0			0
$191$	10.1295	−	13.9420i	0.732944	−	1.00881i	−0.266050	−	0.963959i	$-0.585719\pi$
$191$	10.1295	−	13.9420i	0.732944	−	1.00881i	0.998994	−	0.0448515i	$-0.0142815\pi$
$192$		0			0
$193$	14.6833	−	14.6833i	1.05693	−	1.05693i	0.0586484	−	0.998279i	$-0.481321\pi$
$193$	14.6833	−	14.6833i	1.05693	−	1.05693i	0.998279	−	0.0586484i	$-0.0186791\pi$
$194$		0			0
$195$	−5.51433	−	0.450284i	−0.394890	−	0.0322455i
$196$		0			0
$197$	22.5852	−	11.5077i	1.60913	−	0.819893i	0.609498	−	0.792787i	$-0.291371\pi$
$197$	22.5852	−	11.5077i	1.60913	−	0.819893i	0.999633	−	0.0271059i	$-0.00862912\pi$
$198$		0			0
$199$	−21.5239			−1.52579			−0.762893	−	0.646525i	$-0.776222\pi$
$199$	−21.5239			−1.52579			−0.762893	+	0.646525i	$0.776222\pi$
$200$		0			0
$201$	30.9879			2.18572
$202$		0			0
$203$	−5.94671	+	3.03000i	−0.417377	+	0.212664i
$204$		0			0
$205$	1.33665	+	5.64048i	0.0933559	+	0.393948i
$206$		0			0
$207$	−21.4302	+	21.4302i	−1.48950	+	1.48950i
$208$		0			0
$209$	−2.27552	+	3.13198i	−0.157401	+	0.216644i
$210$		0			0
$211$	−14.8416	−	20.4277i	−1.02174	−	1.40630i	−0.910979	−	0.412453i	$-0.864672\pi$
$211$	−14.8416	−	20.4277i	−1.02174	−	1.40630i	−0.110758	−	0.993847i	$-0.535328\pi$
$212$		0			0
$213$	−18.2791	+	2.89513i	−1.25247	+	0.198371i
$214$		0			0
$215$	0.442056	+	5.83589i	0.0301479	+	0.398005i
$216$		0			0
$217$	7.13134	−	13.9960i	0.484107	−	0.950114i
$218$		0			0
$219$	2.51008	+	7.72522i	0.169615	+	0.522022i
$220$		0			0
$221$	−1.56101	+	4.80428i	−0.105005	+	0.323171i
$222$		0			0
$223$	−8.46261	−	1.34035i	−0.566698	−	0.0897562i	−0.133490	−	0.991050i	$-0.542619\pi$
$223$	−8.46261	−	1.34035i	−0.566698	−	0.0897562i	−0.433208	+	0.901294i	$0.642619\pi$
$224$		0			0
$225$	36.3078	+	18.7692i	2.42052	+	1.25128i
$226$		0			0
$227$	1.52326	−	9.61748i	0.101102	−	0.638335i	−0.884147	−	0.467209i	$-0.845260\pi$
$227$	1.52326	−	9.61748i	0.101102	−	0.638335i	0.985249	−	0.171126i	$-0.0547405\pi$
$228$		0			0
$229$	−3.78201	−	1.22885i	−0.249922	−	0.0812046i	0.181377	−	0.983414i	$-0.441945\pi$
$229$	−3.78201	−	1.22885i	−0.249922	−	0.0812046i	−0.431299	+	0.902209i	$0.641945\pi$
$230$		0			0
$231$	−34.0323	+	11.0578i	−2.23916	+	0.727547i
$232$		0			0
$233$	−14.7597	−	7.52047i	−0.966943	−	0.492682i	−0.102127	−	0.994771i	$-0.532565\pi$
$233$	−14.7597	−	7.52047i	−0.966943	−	0.492682i	−0.864816	+	0.502089i	$0.832565\pi$
$234$		0			0
$235$	−3.65217	+	15.0179i	−0.238241	+	0.979663i
$236$		0			0
$237$	3.20065	+	20.2081i	0.207904	+	1.31266i
$238$		0			0
$239$	−13.0625	+	9.49048i	−0.844944	+	0.613888i	−0.923747	−	0.383002i	$-0.874890\pi$
$239$	−13.0625	+	9.49048i	−0.844944	+	0.613888i	0.0788030	+	0.996890i	$0.474890\pi$
$240$		0			0
$241$	2.66386	+	1.93541i	0.171594	+	0.124671i	0.670268	−	0.742119i	$-0.266179\pi$
$241$	2.66386	+	1.93541i	0.171594	+	0.124671i	−0.498673	+	0.866790i	$0.666179\pi$
$242$		0			0
$243$	42.0150	+	42.0150i	2.69526	+	2.69526i
$244$		0			0
$245$	−0.720859	+	0.839016i	−0.0460540	+	0.0536028i
$246$		0			0
$247$	0.309962	+	0.608335i	0.0197224	+	0.0387074i
$248$		0			0
$249$		−	8.11351i		−	0.514173i
$250$		0			0
$251$			5.77915i			0.364777i	0.983227	+	0.182388i	$0.0583828\pi$
$251$			5.77915i			0.364777i	−0.983227	+	0.182388i	$0.941617\pi$
$252$		0			0
$253$	−7.06428	−	13.8644i	−0.444128	−	0.871650i
$254$		0			0
$255$	33.2441	−	38.6932i	2.08183	−	2.42306i
$256$		0			0
$257$	−3.35083	−	3.35083i	−0.209019	−	0.209019i	0.594831	−	0.803850i	$-0.297219\pi$
$257$	−3.35083	−	3.35083i	−0.209019	−	0.209019i	−0.803850	+	0.594831i	$0.797219\pi$
$258$		0			0
$259$	−5.84525	−	4.24682i	−0.363206	−	0.263885i
$260$		0			0
$261$	−17.3052	+	12.5730i	−1.07117	+	0.778249i
$262$		0			0
$263$	0.138849	+	0.876661i	0.00856182	+	0.0540572i	0.991599	−	0.129347i	$-0.0412882\pi$
$263$	0.138849	+	0.876661i	0.00856182	+	0.0540572i	−0.983038	+	0.183404i	$0.941288\pi$
$264$		0			0
$265$	−0.914796	+	3.76170i	−0.0561955	+	0.231080i
$266$		0			0
$267$	29.7995	+	15.1836i	1.82370	+	0.929221i
$268$		0			0
$269$	13.2872	−	4.31729i	0.810138	−	0.263230i	0.125482	−	0.992096i	$-0.459952\pi$
$269$	13.2872	−	4.31729i	0.810138	−	0.263230i	0.684656	+	0.728866i	$0.259952\pi$
$270$		0			0
$271$	27.7103	+	9.00363i	1.68328	+	0.546931i	0.985544	−	0.169422i	$-0.0541900\pi$
$271$	27.7103	+	9.00363i	1.68328	+	0.546931i	0.697738	+	0.716353i	$0.254190\pi$
$272$		0			0
$273$	−0.987229	+	6.23312i	−0.0597498	+	0.377245i
$274$		0			0
$275$	−14.9255	+	14.7512i	−0.900041	+	0.889531i
$276$		0			0
$277$	−23.0833	−	3.65604i	−1.38694	−	0.219670i	−0.582081	−	0.813131i	$-0.697761\pi$
$277$	−23.0833	−	3.65604i	−1.38694	−	0.219670i	−0.804863	+	0.593461i	$0.797761\pi$
$278$		0			0
$279$	15.5572	−	47.8801i	0.931384	−	2.86651i
$280$		0			0
$281$	5.37238	+	16.5345i	0.320489	+	0.986365i	0.973436	+	0.228960i	$0.0735327\pi$
$281$	5.37238	+	16.5345i	0.320489	+	0.986365i	−0.652946	+	0.757404i	$0.726467\pi$
$282$		0			0
$283$	−5.68766	+	11.1627i	−0.338096	+	0.663552i	−0.995981	−	0.0895673i	$-0.971452\pi$
$283$	−5.68766	+	11.1627i	−0.338096	+	0.663552i	0.657884	+	0.753119i	$0.271452\pi$
$284$		0			0
$285$	−0.520773	−	6.87510i	−0.0308479	−	0.407246i
$286$		0			0
$287$	6.53054	−	1.03434i	0.385486	−	0.0610549i
$288$		0			0
$289$	−17.3847	−	23.9280i	−1.02263	−	1.40753i
$290$		0			0
$291$	−16.0332	+	22.0679i	−0.939886	+	1.29364i
$292$		0			0
$293$	−6.60873	+	6.60873i	−0.386086	+	0.386086i	−0.873289	−	0.487203i	$-0.838017\pi$
$293$	−6.60873	+	6.60873i	−0.386086	+	0.386086i	0.487203	+	0.873289i	$0.338017\pi$
$294$		0			0
$295$	0.704779	+	2.97406i	0.0410338	+	0.173156i
$296$		0			0
$297$	−64.6838	+	32.9580i	−3.75333	+	1.91242i
$298$		0			0
$299$	−2.74424			−0.158703
$300$		0			0
$301$	6.67573			0.384783
$302$		0			0
$303$	−48.2761	+	24.5979i	−2.77339	+	1.41311i
$304$		0			0
$305$	−16.8915	−	1.37931i	−0.967203	−	0.0789790i
$306$		0			0
$307$	7.96734	−	7.96734i	0.454720	−	0.454720i	−0.442198	−	0.896918i	$-0.645801\pi$
$307$	7.96734	−	7.96734i	0.454720	−	0.454720i	0.896918	+	0.442198i	$0.145801\pi$
$308$		0			0
$309$	−5.70023	+	7.84569i	−0.324275	+	0.446326i
$310$		0			0
$311$	7.89698	+	10.8693i	0.447796	+	0.616339i	0.971922	−	0.235302i	$-0.0756079\pi$
$311$	7.89698	+	10.8693i	0.447796	+	0.616339i	−0.524126	+	0.851641i	$0.675608\pi$
$312$		0			0
$313$	3.13783	−	0.496984i	0.177361	−	0.0280912i	−0.0671222	−	0.997745i	$-0.521382\pi$
$313$	3.13783	−	0.496984i	0.177361	−	0.0280912i	0.244483	+	0.969654i	$0.421382\pi$
$314$		0			0
$315$	24.4758	−	39.6788i	1.37905	−	2.23565i
$316$		0			0
$317$	6.86183	−	13.4671i	0.385399	−	0.756387i	−0.614061	−	0.789259i	$-0.710465\pi$
$317$	6.86183	−	13.4671i	0.385399	−	0.756387i	0.999460	+	0.0328713i	$0.0104651\pi$
$318$		0			0
$319$	−3.39377	−	10.4449i	−0.190015	−	0.584805i
$320$		0			0
$321$	−0.201906	+	0.621404i	−0.0112693	+	0.0346834i
$322$		0			0
$323$	−6.21766	−	0.984781i	−0.345960	−	0.0547947i
$324$		0			0
$325$	1.12295	+	3.52643i	0.0622902	+	0.195611i
$326$		0			0
$327$	6.85008	−	43.2497i	0.378810	−	2.39171i
$328$		0			0
$329$	16.7665	+	5.44777i	0.924368	+	0.300345i
$330$		0			0
$331$	21.4867	−	6.98144i	1.18101	−	0.383735i	0.348270	−	0.937394i	$-0.386769\pi$
$331$	21.4867	−	6.98144i	1.18101	−	0.383735i	0.832743	+	0.553660i	$0.186769\pi$
$332$		0			0
$333$	−20.6324	−	10.5128i	−1.13065	−	0.576095i
$334$		0			0
$335$	−7.87612	−	19.1737i	−0.430319	−	1.04757i
$336$		0			0
$337$	2.51064	+	15.8515i	0.136763	+	0.863488i	0.956709	+	0.291047i	$0.0940035\pi$
$337$	2.51064	+	15.8515i	0.136763	+	0.863488i	−0.819946	+	0.572441i	$0.805996\pi$
$338$		0			0
$339$	−27.4746	+	19.9615i	−1.49222	+	1.08416i
$340$		0			0
$341$	20.9115	+	15.1931i	1.13242	+	0.822754i
$342$		0			0
$343$	13.5168	+	13.5168i	0.729837	+	0.729837i
$344$		0			0
$345$	25.5721	+	10.6804i	1.37676	+	0.575013i
$346$		0			0
$347$	−10.2001	−	20.0188i	−0.547570	−	1.07467i	−0.984535	−	0.175188i	$-0.943947\pi$
$347$	−10.2001	−	20.0188i	−0.547570	−	1.07467i	0.436965	−	0.899479i	$-0.356053\pi$
$348$		0			0
$349$		−	24.8539i		−	1.33040i	−0.746667	−	0.665198i	$-0.768347\pi$
$349$		−	24.8539i		−	1.33040i	0.746667	−	0.665198i	$-0.231653\pi$
$350$		0			0
$351$			12.8031i			0.683378i
$352$		0			0
$353$	−0.378021	−	0.741908i	−0.0201200	−	0.0394878i	0.880728	−	0.473623i	$-0.157054\pi$
$353$	−0.378021	−	0.741908i	−0.0201200	−	0.0394878i	−0.900848	+	0.434135i	$0.857054\pi$
$354$		0			0
$355$	6.43732	+	10.5743i	0.341658	+	0.561227i
$356$		0			0
$357$	−41.1449	−	41.1449i	−2.17762	−	2.17762i
$358$		0			0
$359$	14.5026	+	10.5367i	0.765416	+	0.556107i	0.900567	−	0.434718i	$-0.143152\pi$
$359$	14.5026	+	10.5367i	0.765416	+	0.556107i	−0.135151	+	0.990825i	$0.543152\pi$
$360$		0			0
$361$	14.6830	−	10.6678i	0.772788	−	0.561464i
$362$		0			0
$363$	−3.45905	−	21.8396i	−0.181553	−	1.14628i
$364$		0			0
$365$	4.14198	−	3.51660i	0.216801	−	0.184067i
$366$		0			0
$367$	−18.4572	−	9.40440i	−0.963457	−	0.490906i	−0.0998117	−	0.995006i	$-0.531824\pi$
$367$	−18.4572	−	9.40440i	−0.963457	−	0.490906i	−0.863645	+	0.504101i	$0.831824\pi$
$368$		0			0
$369$	20.1539	−	6.54841i	1.04917	−	0.340896i
$370$		0			0
$371$	4.19968	+	1.36456i	0.218037	+	0.0708444i
$372$		0			0
$373$	3.80037	−	23.9946i	0.196776	−	1.24239i	−0.669494	−	0.742818i	$-0.733489\pi$
$373$	3.80037	−	23.9946i	0.196776	−	1.24239i	0.866270	−	0.499577i	$-0.166511\pi$
$374$		0			0
$375$	3.26043	−	37.2314i	0.168368	−	1.92262i
$376$		0			0
$377$	−1.91302	−	0.302993i	−0.0985257	−	0.0156049i
$378$		0			0
$379$	5.49888	−	16.9238i	0.282458	−	0.869318i	−0.704691	−	0.709515i	$-0.748914\pi$
$379$	5.49888	−	16.9238i	0.282458	−	0.869318i	0.987149	−	0.159803i	$-0.0510858\pi$
$380$		0			0
$381$	11.0908	+	34.1339i	0.568198	+	1.74873i
$382$		0			0
$383$	−4.08575	+	8.01874i	−0.208772	+	0.409738i	−0.971520	−	0.236958i	$-0.923850\pi$
$383$	−4.08575	+	8.01874i	−0.208772	+	0.409738i	0.762748	+	0.646696i	$0.223850\pi$
$384$		0			0
$385$	15.4919	+	18.2469i	0.789539	+	0.929947i
$386$		0			0
$387$	21.1321	−	3.34700i	1.07421	−	0.170137i
$388$		0			0
$389$	−6.42558	−	8.84406i	−0.325790	−	0.448411i	0.614434	−	0.788968i	$-0.289384\pi$
$389$	−6.42558	−	8.84406i	−0.325790	−	0.448411i	−0.940224	+	0.340557i	$0.889384\pi$
$390$		0			0
$391$	14.8726	−	20.4703i	0.752138	−	1.03523i
$392$		0			0
$393$	35.0399	−	35.0399i	1.76753	−	1.76753i
$394$		0			0
$395$	11.6902	−	7.11663i	0.588198	−	0.358077i
$396$		0			0
$397$	−2.25859	+	1.15081i	−0.113355	+	0.0577575i	−0.509749	−	0.860323i	$-0.670262\pi$
$397$	−2.25859	+	1.15081i	−0.113355	+	0.0577575i	0.396393	+	0.918081i	$0.370262\pi$
$398$		0			0
$399$	−7.86449			−0.393717
$400$		0			0
$401$	−4.93727			−0.246555			−0.123278	−	0.992372i	$-0.539341\pi$
$401$	−4.93727			−0.246555			−0.123278	+	0.992372i	$0.539341\pi$
$402$		0			0
$403$	4.06172	−	2.06955i	0.202329	−	0.103092i
$404$		0			0
$405$	28.6953	−	68.7053i	1.42588	−	3.41400i
$406$		0			0
$407$	8.40687	−	8.40687i	0.416713	−	0.416713i
$408$		0			0
$409$	−6.23639	+	8.58366i	−0.308370	+	0.424435i	−0.934872	−	0.354985i	$-0.884486\pi$
$409$	−6.23639	+	8.58366i	−0.308370	+	0.424435i	0.626502	+	0.779420i	$0.284486\pi$
$410$		0			0
$411$	12.7046	+	17.4864i	0.626672	+	0.862541i
$412$		0			0
$413$	3.44336	−	0.545375i	0.169437	−	0.0268362i
$414$		0			0
$415$	−5.02022	+	2.06219i	−0.246433	+	0.101229i
$416$		0			0
$417$	−12.9472	+	25.4104i	−0.634029	+	1.24435i
$418$		0			0
$419$	−4.36269	−	13.4270i	−0.213131	−	0.655951i	−0.999281	−	0.0379148i	$-0.987928\pi$
$419$	−4.36269	−	13.4270i	−0.213131	−	0.655951i	0.786150	−	0.618036i	$-0.212072\pi$
$420$		0			0
$421$	−7.99080	+	24.5932i	−0.389448	+	1.19860i	0.543754	+	0.839245i	$0.317002\pi$
$421$	−7.99080	+	24.5932i	−0.389448	+	1.19860i	−0.933202	+	0.359353i	$0.882998\pi$
$422$		0			0
$423$	55.8059	+	8.83879i	2.71338	+	0.429757i
$424$		0			0
$425$	−32.3909	−	10.7352i	−1.57119	−	0.520732i
$426$		0			0
$427$	−3.02407	+	19.0932i	−0.146345	+	0.923987i
$428$		0			0
$429$	−9.87633	−	3.20901i	−0.476833	−	0.154933i
$430$		0			0
$431$	−7.87355	+	2.55827i	−0.379256	+	0.123228i	−0.492440	−	0.870346i	$-0.663895\pi$
$431$	−7.87355	+	2.55827i	−0.379256	+	0.123228i	0.113184	+	0.993574i	$0.463895\pi$
$432$		0			0
$433$	4.50495	+	2.29539i	0.216494	+	0.110309i	0.558875	−	0.829252i	$-0.311233\pi$
$433$	4.50495	+	2.29539i	0.216494	+	0.110309i	−0.342381	+	0.939561i	$0.611233\pi$
$434$		0			0
$435$	16.6472	+	10.2688i	0.798173	+	0.492351i
$436$		0			0
$437$	−0.534982	−	3.37774i	−0.0255917	−	0.161579i
$438$		0			0
$439$	−23.6456	+	17.1795i	−1.12854	+	0.819935i	−0.985482	−	0.169779i	$-0.945695\pi$
$439$	−23.6456	+	17.1795i	−1.12854	+	0.819935i	−0.143061	+	0.989714i	$0.545695\pi$
$440$		0			0
$441$	3.27151	+	2.37689i	0.155786	+	0.113185i
$442$		0			0
$443$	−15.6903	−	15.6903i	−0.745469	−	0.745469i	0.228156	−	0.973625i	$-0.426730\pi$
$443$	−15.6903	−	15.6903i	−0.745469	−	0.745469i	−0.973625	+	0.228156i	$0.926730\pi$
$444$		0			0
$445$	1.82075	−	22.2975i	0.0863119	−	1.05700i
$446$		0			0
$447$	11.7804	+	23.1203i	0.557193	+	1.09355i
$448$		0			0
$449$		−	12.2469i		−	0.577968i	−0.957334	−	0.288984i	$-0.906683\pi$
$449$		−	12.2469i		−	0.577968i	0.957334	−	0.288984i	$-0.0933174\pi$
$450$		0			0
$451$			10.8801i			0.512324i
$452$		0			0
$453$	1.27832	+	2.50885i	0.0600609	+	0.117876i
$454$		0			0
$455$	4.10765	−	0.973410i	0.192569	−	0.0456342i
$456$		0			0
$457$	23.5526	+	23.5526i	1.10174	+	1.10174i	0.994201	+	0.107542i	$0.0342980\pi$
$457$	23.5526	+	23.5526i	1.10174	+	1.10174i	0.107542	+	0.994201i	$0.465702\pi$
$458$		0			0
$459$	−95.5032	−	69.3871i	−4.45771	−	3.23871i
$460$		0			0
$461$	−19.5673	+	14.2165i	−0.911341	+	0.662128i	−0.941354	−	0.337421i	$-0.890445\pi$
$461$	−19.5673	+	14.2165i	−0.911341	+	0.662128i	0.0300123	+	0.999550i	$0.490445\pi$
$462$		0			0
$463$	5.15925	+	32.5742i	0.239771	+	1.51385i	0.754386	+	0.656431i	$0.227935\pi$
$463$	5.15925	+	32.5742i	0.239771	+	1.51385i	−0.514616	+	0.857421i	$0.672065\pi$
$464$		0			0
$465$	−45.9035	+	3.47709i	−2.12873	+	0.161246i
$466$		0			0
$467$	−14.8934	−	7.58857i	−0.689184	−	0.351157i	0.0740718	−	0.997253i	$-0.476401\pi$
$467$	−14.8934	−	7.58857i	−0.689184	−	0.351157i	−0.763256	+	0.646096i	$0.776401\pi$
$468$		0			0
$469$	−22.4864	+	7.30627i	−1.03833	+	0.337372i
$470$		0			0
$471$	−75.6317	−	24.5742i	−3.48493	−	1.13232i
$472$		0			0
$473$	−1.71844	+	10.8498i	−0.0790141	+	0.498875i
$474$		0			0
$475$	−4.12159	+	2.06965i	−0.189111	+	0.0949622i
$476$		0			0
$477$	13.9783	+	2.21395i	0.640022	+	0.101370i
$478$		0			0
$479$	7.91361	−	24.3556i	0.361582	−	1.11283i	−0.590512	−	0.807029i	$-0.701074\pi$
$479$	7.91361	−	24.3556i	0.361582	−	1.11283i	0.952094	−	0.305806i	$-0.0989258\pi$
$480$		0			0
$481$	−0.647936	−	1.99414i	−0.0295433	−	0.0909250i
$482$		0			0
$483$	14.3508	−	28.1651i	0.652986	−	1.28156i
$484$		0			0
$485$	17.7296	+	4.31160i	0.805058	+	0.195779i
$486$		0			0
$487$	1.91921	−	0.303972i	0.0869675	−	0.0137743i	−0.112799	−	0.993618i	$-0.535982\pi$
$487$	1.91921	−	0.303972i	0.0869675	−	0.0137743i	0.199767	+	0.979844i	$0.435982\pi$
$488$		0			0
$489$	28.7989	+	39.6382i	1.30233	+	1.79250i
$490$		0			0
$491$	−9.17103	+	12.6228i	−0.413883	+	0.569661i	−0.964160	−	0.265321i	$-0.914522\pi$
$491$	−9.17103	+	12.6228i	−0.413883	+	0.569661i	0.550277	+	0.834982i	$0.314522\pi$
$492$		0			0
$493$	12.6279	−	12.6279i	0.568731	−	0.568731i
$494$		0			0
$495$	58.1881	+	49.9936i	2.61536	+	2.24704i
$496$		0			0
$497$	12.5817	−	6.41068i	0.564365	−	0.287558i
$498$		0			0
$499$	23.5658			1.05495			0.527474	−	0.849571i	$-0.323139\pi$
$499$	23.5658			1.05495			0.527474	+	0.849571i	$0.323139\pi$
$500$		0			0
$501$	−50.1320			−2.23973
$502$		0			0
$503$	−8.01432	+	4.08350i	−0.357341	+	0.182074i	−0.623440	−	0.781872i	$-0.714265\pi$
$503$	−8.01432	+	4.08350i	−0.357341	+	0.182074i	0.266099	+	0.963946i	$0.414265\pi$
$504$		0			0
$505$	27.4901	+	23.6187i	1.22329	+	1.05102i
$506$		0			0
$507$	29.4335	−	29.4335i	1.30719	−	1.30719i
$508$		0			0
$509$	−9.88788	+	13.6095i	−0.438272	+	0.603230i	−0.969827	−	0.243794i	$-0.921608\pi$
$509$	−9.88788	+	13.6095i	−0.438272	+	0.603230i	0.531555	+	0.847024i	$0.321608\pi$
$510$		0			0
$511$	−3.64288	−	5.01399i	−0.161151	−	0.221806i
$512$		0			0
$513$	−15.7587	+	2.49593i	−0.695763	+	0.110198i
$514$		0			0
$515$	6.30331	+	1.53288i	0.277757	+	0.0675468i
$516$		0			0
$517$	−13.1700	+	25.8476i	−0.579217	+	1.13678i
$518$		0			0
$519$	24.8404	+	76.4510i	1.09037	+	3.35583i
$520$		0			0
$521$	8.48875	−	26.1257i	0.371899	−	1.14459i	−0.573648	−	0.819102i	$-0.694472\pi$
$521$	8.48875	−	26.1257i	0.371899	−	1.14459i	0.945547	−	0.325485i	$-0.105528\pi$
$522$		0			0
$523$	33.1069	+	5.24362i	1.44767	+	0.229288i	0.830268	−	0.557364i	$-0.188187\pi$
$523$	33.1069	+	5.24362i	1.44767	+	0.229288i	0.617397	+	0.786652i	$0.288187\pi$
$524$		0			0
$525$	−42.0654	−	6.91599i	−1.83589	−	0.301839i
$526$		0			0
$527$	−6.57517	+	41.5140i	−0.286419	+	1.80838i
$528$		0			0
$529$	−8.80136	−	2.85974i	−0.382668	−	0.124336i
$530$		0			0
$531$	10.6266	−	3.45278i	0.461154	−	0.149838i
$532$		0			0
$533$	1.70968	+	0.871124i	0.0740544	+	0.0377326i
$534$		0			0
$535$	0.435810	−	0.0330116i	0.0188417	−	0.00142722i
$536$		0			0
$537$	−8.73620	−	55.1582i	−0.376995	−	2.38025i
$538$		0			0
$539$	−1.67968	+	1.22036i	−0.0723491	+	0.0525647i
$540$		0			0
$541$	5.52929	+	4.01726i	0.237723	+	0.172716i	0.700268	−	0.713880i	$-0.253064\pi$
$541$	5.52929	+	4.01726i	0.237723	+	0.172716i	−0.462545	+	0.886596i	$0.653064\pi$
$542$		0			0
$543$	37.1800	+	37.1800i	1.59555	+	1.59555i
$544$		0			0
$545$	−28.5017	+	6.75420i	−1.22088	+	0.289318i
$546$		0			0
$547$	−12.6576	−	24.8420i	−0.541202	−	1.06217i	−0.986032	−	0.166553i	$-0.946736\pi$
$547$	−12.6576	−	24.8420i	−0.541202	−	1.06217i	0.444831	−	0.895615i	$-0.353264\pi$
$548$		0			0
$549$			61.9561i			2.64422i
$550$		0			0
$551$		−	2.41371i		−	0.102828i
$552$		0			0
$553$	−7.08718	−	13.9094i	−0.301377	−	0.591486i
$554$		0			0
$555$	−1.72330	+	21.1041i	−0.0731498	+	0.895818i
$556$		0			0
$557$	5.60560	+	5.60560i	0.237517	+	0.237517i	0.815821	−	0.578304i	$-0.196285\pi$
$557$	5.60560	+	5.60560i	0.237517	+	0.237517i	−0.578304	+	0.815821i	$0.696285\pi$
$558$		0			0
$559$	1.56733	+	1.13873i	0.0662910	+	0.0481632i
$560$		0			0
$561$	77.4626	−	56.2799i	3.27047	−	2.37614i
$562$		0			0
$563$	−3.73669	−	23.5925i	−0.157483	−	0.994307i	−0.932185	−	0.361981i	$-0.882100\pi$
$563$	−3.73669	−	23.5925i	−0.157483	−	0.994307i	0.774703	−	0.632326i	$-0.217900\pi$
$564$		0			0
$565$	19.3343	+	11.9263i	0.813400	+	0.501743i
$566$		0			0
$567$	−75.6721	−	38.5568i	−3.17793	−	1.61923i
$568$		0			0
$569$	−33.6049	+	10.9189i	−1.40879	+	0.457743i	−0.912022	−	0.410141i	$-0.865480\pi$
$569$	−33.6049	+	10.9189i	−1.40879	+	0.457743i	−0.496767	+	0.867884i	$0.665480\pi$
$570$		0			0
$571$	−2.24668	−	0.729991i	−0.0940207	−	0.0305492i	0.261629	−	0.965169i	$-0.415740\pi$
$571$	−2.24668	−	0.729991i	−0.0940207	−	0.0305492i	−0.355650	+	0.934619i	$0.615740\pi$
$572$		0			0
$573$	−9.01185	+	56.8986i	−0.376476	+	2.37697i
$574$		0			0
$575$	0.108869	−	18.5373i	0.00454015	−	0.773058i
$576$		0			0
$577$	9.18885	+	1.45537i	0.382537	+	0.0605879i	0.344742	−	0.938698i	$-0.387967\pi$
$577$	9.18885	+	1.45537i	0.382537	+	0.0605879i	0.0377951	+	0.999286i	$0.487967\pi$
$578$		0			0
$579$	−21.4503	+	66.0173i	−0.891445	+	2.74359i
$580$		0			0
$581$	1.91299	+	5.88757i	0.0793642	+	0.244258i
$582$		0			0
$583$	−3.29884	+	6.47433i	−0.136624	+	0.268139i
$584$		0			0
$585$	12.5148	−	5.14078i	0.517422	−	0.212545i
$586$		0			0
$587$	17.0624	−	2.70242i	0.704240	−	0.111541i	0.205965	−	0.978559i	$-0.433967\pi$
$587$	17.0624	−	2.70242i	0.704240	−	0.111541i	0.498275	+	0.867019i	$0.333967\pi$
$588$		0			0
$589$	3.33912	+	4.59591i	0.137586	+	0.189371i
$590$		0			0
$591$	−49.8053	+	68.5511i	−2.04871	+	2.81981i
$592$		0			0
$593$	−0.658449	+	0.658449i	−0.0270393	+	0.0270393i	−0.720497	−	0.693458i	$-0.756086\pi$
$593$	−0.658449	+	0.658449i	−0.0270393	+	0.0270393i	0.693458	+	0.720497i	$0.256086\pi$
$594$		0			0
$595$	−15.0006	+	35.9160i	−0.614965	+	1.47241i
$596$		0			0
$597$	64.1082	−	32.6648i	2.62378	−	1.33688i
$598$		0			0
$599$	14.3000			0.584282			0.292141	−	0.956375i	$-0.405632\pi$
$599$	14.3000			0.584282			0.292141	+	0.956375i	$0.405632\pi$
$600$		0			0
$601$	−43.2779			−1.76534			−0.882670	−	0.469993i	$-0.844257\pi$
$601$	−43.2779			−1.76534			−0.882670	+	0.469993i	$0.844257\pi$
$602$		0			0
$603$	−67.5178	+	34.4021i	−2.74954	+	1.40096i
$604$		0			0
$605$	−12.6340	+	7.69119i	−0.513645	+	0.312691i
$606$		0			0
$607$	−2.10383	+	2.10383i	−0.0853919	+	0.0853919i	−0.748513	−	0.663121i	$-0.769232\pi$
$607$	−2.10383	+	2.10383i	−0.0853919	+	0.0853919i	0.663121	+	0.748513i	$0.269232\pi$
$608$		0			0
$609$	13.1138	−	18.0496i	0.531397	−	0.731405i
$610$		0			0
$611$	3.00718	+	4.13903i	0.121657	+	0.167447i
$612$		0			0
$613$	2.36233	−	0.374156i	0.0954136	−	0.0151120i	−0.108545	−	0.994092i	$-0.534619\pi$
$613$	2.36233	−	0.374156i	0.0954136	−	0.0151120i	0.203959	+	0.978979i	$0.434619\pi$
$614$		0			0
$615$	−12.5412	−	14.7715i	−0.505711	−	0.595644i
$616$		0			0
$617$	−11.8828	+	23.3213i	−0.478383	+	0.938880i	0.518118	+	0.855309i	$0.326633\pi$
$617$	−11.8828	+	23.3213i	−0.478383	+	0.938880i	−0.996502	+	0.0835714i	$0.973367\pi$
$618$		0			0
$619$	−8.73974	−	26.8982i	−0.351280	−	1.08113i	−0.958135	−	0.286316i	$-0.907569\pi$
$619$	−8.73974	−	26.8982i	−0.351280	−	1.08113i	0.606855	−	0.794812i	$-0.292431\pi$
$620$		0			0
$621$	19.8172	−	60.9911i	0.795237	−	2.44749i
$622$		0			0
$623$	−25.2040	−	3.99192i	−1.00978	−	0.159933i
$624$		0			0
$625$	−23.8655	+	7.44562i	−0.954620	+	0.297825i
$626$		0			0
$627$	2.02445	−	12.7819i	0.0808487	−	0.510458i
$628$		0			0
$629$	18.3866	+	5.97417i	0.733122	+	0.238206i
$630$		0			0
$631$	47.3830	−	15.3957i	1.88629	−	0.612892i	0.903363	−	0.428878i	$-0.141091\pi$
$631$	47.3830	−	15.3957i	1.88629	−	0.612892i	0.982924	−	0.184014i	$-0.0589091\pi$
$632$		0			0
$633$	75.2065	+	38.3196i	2.98919	+	1.52307i
$634$		0			0
$635$	18.3014	−	15.5381i	0.726267	−	0.616612i
$636$		0			0
$637$	0.0572800	+	0.361652i	0.00226952	+	0.0143292i
$638$		0			0
$639$	36.6133	−	26.6011i	1.44840	−	1.05232i
$640$		0			0
$641$	8.74508	+	6.35368i	0.345410	+	0.250955i	0.746941	−	0.664890i	$-0.231522\pi$
$641$	8.74508	+	6.35368i	0.345410	+	0.250955i	−0.401531	+	0.915845i	$0.631522\pi$
$642$		0			0
$643$	14.9171	+	14.9171i	0.588275	+	0.588275i	0.937164	−	0.348889i	$-0.113441\pi$
$643$	14.9171	+	14.9171i	0.588275	+	0.588275i	−0.348889	+	0.937164i	$0.613441\pi$
$644$		0			0
$645$	−10.1733	−	16.7112i	−0.400571	−	0.658002i
$646$		0			0
$647$	−9.72454	−	19.0855i	−0.382311	−	0.750328i	0.617018	−	0.786949i	$-0.288341\pi$
$647$	−9.72454	−	19.0855i	−0.382311	−	0.750328i	−0.999329	+	0.0366212i	$0.988341\pi$
$648$		0			0
$649$			5.73676i			0.225188i
$650$		0			0
$651$			52.5095i			2.05801i
$652$		0			0
$653$	17.2466	+	33.8484i	0.674912	+	1.32459i	0.933492	+	0.358599i	$0.116746\pi$
$653$	17.2466	+	33.8484i	0.674912	+	1.32459i	−0.258580	+	0.965990i	$0.583254\pi$
$654$		0			0
$655$	−30.5869	−	12.7749i	−1.19513	−	0.499155i
$656$		0			0
$657$	−14.0454	−	14.0454i	−0.547964	−	0.547964i
$658$		0			0
$659$	19.0175	+	13.8170i	0.740817	+	0.538235i	0.892967	−	0.450123i	$-0.148620\pi$
$659$	19.0175	+	13.8170i	0.740817	+	0.538235i	−0.152150	+	0.988357i	$0.548620\pi$
$660$		0			0
$661$	29.7636	−	21.6246i	1.15767	−	0.841098i	0.168190	−	0.985755i	$-0.446208\pi$
$661$	29.7636	−	21.6246i	1.15767	−	0.841098i	0.989482	+	0.144657i	$0.0462078\pi$
$662$		0			0
$663$	−2.64160	−	16.6784i	−0.102591	−	0.647736i
$664$		0			0
$665$	1.99890	+	4.86613i	0.0775139	+	0.188700i
$666$		0			0
$667$	8.64423	+	4.40445i	0.334706	+	0.170541i
$668$		0			0
$669$	27.2398	−	8.85075i	1.05315	−	0.342190i
$670$		0			0
$671$	−30.2531	−	9.82983i	−1.16791	−	0.379476i
$672$		0			0
$673$	−5.27848	+	33.3270i	−0.203471	+	1.28466i	0.648557	+	0.761166i	$0.275373\pi$
$673$	−5.27848	+	33.3270i	−0.203471	+	1.28466i	−0.852028	+	0.523497i	$0.824627\pi$
$674$		0			0
$675$	−86.4847	−	0.507923i	−3.32880	−	0.0195499i
$676$		0			0
$677$	8.26684	+	1.30934i	0.317721	+	0.0503220i	0.313258	−	0.949668i	$-0.398580\pi$
$677$	8.26684	+	1.30934i	0.317721	+	0.0503220i	0.00446258	+	0.999990i	$0.498580\pi$
$678$		0			0
$679$	6.43141	−	19.7938i	0.246815	−	0.759618i
$680$		0			0
$681$	10.0586	+	30.9571i	0.385446	+	1.18628i
$682$		0			0
$683$	19.1698	−	37.6228i	0.733511	−	1.43960i	−0.158395	−	0.987376i	$-0.550632\pi$
$683$	19.1698	−	37.6228i	0.733511	−	1.43960i	0.891906	−	0.452221i	$-0.149368\pi$
$684$		0			0
$685$	7.59057	−	12.3054i	0.290021	−	0.470166i
$686$		0			0
$687$	13.1295	−	2.07951i	0.500923	−	0.0793384i
$688$		0			0
$689$	0.753240	+	1.03675i	0.0286961	+	0.0394969i
$690$		0			0
$691$	−2.78424	+	3.83218i	−0.105918	+	0.145783i	−0.858685	−	0.512503i	$-0.828718\pi$
$691$	−2.78424	+	3.83218i	−0.105918	+	0.145783i	0.752768	+	0.658286i	$0.228718\pi$
$692$		0			0
$693$	61.8750	−	61.8750i	2.35044	−	2.35044i
$694$		0			0
$695$	19.0134	+	1.55258i	0.721219	+	0.0588926i
$696$		0			0
$697$	−15.7638	+	8.03204i	−0.597095	+	0.304235i
$698$		0			0
$699$	55.3746			2.09446
$700$		0			0
$701$	2.87468			0.108575			0.0542876	−	0.998525i	$-0.482711\pi$
$701$	2.87468			0.108575			0.0542876	+	0.998525i	$0.482711\pi$
$702$		0			0
$703$	2.32818	−	1.18626i	0.0878088	−	0.0447408i
$704$		0			0
$705$	−11.9135	−	50.2731i	−0.448688	−	1.89340i
$706$		0			0
$707$	29.2319	−	29.2319i	1.09938	−	1.09938i
$708$		0			0
$709$	−25.3395	+	34.8769i	−0.951646	+	1.30983i	−0.000853438		1.00000i	$0.500272\pi$
$709$	−25.3395	+	34.8769i	−0.951646	+	1.30983i	−0.950792	+	0.309829i	$0.899728\pi$
$710$		0			0
$711$	−29.4083	−	40.4770i	−1.10290	−	1.51801i
$712$		0			0
$713$	−22.5525	+	3.57196i	−0.844596	+	0.133771i
$714$		0			0
$715$	0.524673	+	6.92658i	0.0196216	+	0.259039i
$716$		0			0
$717$	24.5036	−	48.0909i	0.915102	−	1.79599i
$718$		0			0
$719$	−0.734029	−	2.25911i	−0.0273747	−	0.0842505i	0.936436	−	0.350839i	$-0.114104\pi$
$719$	−0.734029	−	2.25911i	−0.0273747	−	0.0842505i	−0.963810	+	0.266588i	$0.914104\pi$
$720$		0			0
$721$	2.28653	−	7.03722i	0.0851548	−	0.262080i
$722$		0			0
$723$	−10.8714	−	1.72187i	−0.404313	−	0.0640369i
$724$		0			0
$725$	2.12261	−	12.9104i	0.0788316	−	0.479481i
$726$		0			0
$727$	−0.773476	+	4.88353i	−0.0286866	+	0.181120i	−0.997871	−	0.0652154i	$-0.979227\pi$
$727$	−0.773476	+	4.88353i	−0.0286866	+	0.181120i	0.969185	+	0.246336i	$0.0792266\pi$
$728$		0			0
$729$	−93.8974	−	30.5091i	−3.47768	−	1.12997i
$730$		0			0
$731$	−16.9885	+	5.51989i	−0.628342	+	0.204161i
$732$		0			0
$733$	−8.23468	−	4.19578i	−0.304155	−	0.154975i	0.295252	−	0.955420i	$-0.404597\pi$
$733$	−8.23468	−	4.19578i	−0.304155	−	0.154975i	−0.599406	+	0.800445i	$0.704597\pi$
$734$		0			0
$735$	0.873762	−	3.59297i	0.0322292	−	0.132529i
$736$		0			0
$737$	−6.08625	−	38.4271i	−0.224190	−	1.41548i
$738$		0			0
$739$	−10.5086	+	7.63492i	−0.386564	+	0.280855i	−0.764046	−	0.645162i	$-0.776790\pi$
$739$	−10.5086	+	7.63492i	−0.386564	+	0.280855i	0.377482	+	0.926017i	$0.376790\pi$
$740$		0			0
$741$	−1.84643	−	1.34151i	−0.0678302	−	0.0492815i
$742$		0			0
$743$	1.02561	+	1.02561i	0.0376262	+	0.0376262i	0.725670	−	0.688043i	$-0.241530\pi$
$743$	1.02561	+	1.02561i	0.0376262	+	0.0376262i	−0.688043	+	0.725670i	$0.741530\pi$
$744$		0			0
$745$	11.3114	−	13.1655i	0.414419	−	0.482347i
$746$		0			0
$747$	9.00743	+	17.6781i	0.329565	+	0.646807i
$748$		0			0
$749$		−	0.498527i		−	0.0182158i
$750$		0			0
$751$		−	36.6492i		−	1.33735i	−0.743556	−	0.668674i	$-0.766862\pi$
$751$		−	36.6492i		−	1.33735i	0.743556	−	0.668674i	$-0.233138\pi$
$752$		0			0
$753$	−8.77049	−	17.2130i	−0.319614	−	0.627278i
$754$		0			0
$755$	1.22744	−	1.42863i	0.0446711	−	0.0519931i
$756$		0			0
$757$	4.07081	+	4.07081i	0.147956	+	0.147956i	0.777204	−	0.629248i	$-0.216637\pi$
$757$	4.07081	+	4.07081i	0.147956	+	0.147956i	−0.629248	+	0.777204i	$0.716637\pi$
$758$		0			0
$759$	42.0816	+	30.5740i	1.52746	+	1.10977i
$760$		0			0
$761$	−24.6849	+	17.9346i	−0.894826	+	0.650129i	−0.937132	−	0.348975i	$-0.886530\pi$
$761$	−24.6849	+	17.9346i	−0.894826	+	0.650129i	0.0423055	+	0.999105i	$0.486530\pi$
$762$		0			0
$763$	5.22657	+	32.9993i	0.189215	+	1.19465i
$764$		0			0
$765$	−29.4775	+	121.213i	−1.06576	+	4.38248i
$766$		0			0
$767$	0.901464	+	0.459319i	0.0325500	+	0.0165850i
$768$		0			0
$769$	40.3790	−	13.1199i	1.45610	−	0.473116i	0.529226	−	0.848481i	$-0.322483\pi$
$769$	40.3790	−	13.1199i	1.45610	−	0.473116i	0.926877	+	0.375365i	$0.122483\pi$
$770$		0			0
$771$	15.0656	+	4.89511i	0.542575	+	0.176293i
$772$		0			0
$773$	−2.40054	+	15.1564i	−0.0863416	+	0.545139i	0.906163	+	0.422929i	$0.138998\pi$
$773$	−2.40054	+	15.1564i	−0.0863416	+	0.545139i	−0.992504	+	0.122210i	$0.961002\pi$
$774$		0			0
$775$	13.8186	+	27.5189i	0.496380	+	0.988509i
$776$		0			0
$777$	23.8549	+	3.77825i	0.855791	+	0.135544i
$778$		0			0
$779$	−0.738926	+	2.27418i	−0.0264748	+	0.0814809i
$780$		0			0
$781$	7.18031	+	22.0987i	0.256932	+	0.790755i
$782$		0			0
$783$	20.5487	−	40.3292i	0.734352	−	1.44125i
$784$		0			0
$785$	4.01788	+	53.0429i	0.143404	+	1.89318i
$786$		0			0
$787$	−50.8951	+	8.06099i	−1.81421	+	0.287343i	−0.968996	−	0.247078i	$-0.920530\pi$
$787$	−50.8951	+	8.06099i	−1.81421	+	0.287343i	−0.845219	+	0.534421i	$0.820530\pi$
$788$		0			0
$789$	−1.74399	−	2.40039i	−0.0620876	−	0.0854562i
$790$		0			0
$791$	15.2305	−	20.9630i	0.541534	−	0.745358i
$792$		0			0
$793$	−3.96688	+	3.96688i	−0.140868	+	0.140868i
$794$		0			0
$795$	−2.98410	−	12.5924i	−0.105835	−	0.446608i
$796$		0			0
$797$	−27.0432	+	13.7792i	−0.957921	+	0.488085i	−0.861780	−	0.507283i	$-0.830650\pi$
$797$	−27.0432	+	13.7792i	−0.957921	+	0.488085i	−0.0961411	+	0.995368i	$0.530650\pi$
$798$		0			0
$799$	−47.1722			−1.66883
$800$		0			0
$801$	−81.7849			−2.88973
$802$		0			0
$803$	9.08679	−	4.62995i	0.320666	−	0.163387i
$804$		0			0
$805$	−21.0746	−	1.72089i	−0.742782	−	0.0606534i
$806$		0			0
$807$	−33.0238	+	33.0238i	−1.16249	+	1.16249i
$808$		0			0
$809$	−26.1764	+	36.0287i	−0.920312	+	1.26670i	0.0432091	+	0.999066i	$0.486242\pi$
$809$	−26.1764	+	36.0287i	−0.920312	+	1.26670i	−0.963521	+	0.267634i	$0.913758\pi$
$810$		0			0
$811$	22.6018	+	31.1087i	0.793657	+	1.09238i	0.993643	+	0.112577i	$0.0359104\pi$
$811$	22.6018	+	31.1087i	0.793657	+	1.09238i	−0.199986	+	0.979799i	$0.564090\pi$
$812$		0			0
$813$	−96.1984	+	15.2363i	−3.37383	+	0.534362i
$814$		0			0
$815$	17.2063	−	27.8940i	0.602711	−	0.977083i
$816$		0			0
$817$	−1.09606	+	2.15114i	−0.0383463	+	0.0752589i
$818$		0			0
$819$	−4.76884	−	14.6770i	−0.166637	−	0.512855i
$820$		0			0
$821$	6.58746	−	20.2741i	0.229904	−	0.707572i	−0.767853	−	0.640627i	$-0.778675\pi$
$821$	6.58746	−	20.2741i	0.229904	−	0.707572i	0.997757	−	0.0669454i	$-0.0213253\pi$
$822$		0			0
$823$	24.8097	+	3.92948i	0.864813	+	0.136973i	0.573053	−	0.819518i	$-0.305759\pi$
$823$	24.8097	+	3.92948i	0.864813	+	0.136973i	0.291761	+	0.956491i	$0.405759\pi$
$824$		0			0
$825$	22.0686	−	66.5871i	0.768331	−	2.31827i
$826$		0			0
$827$	−5.25535	+	33.1810i	−0.182746	+	1.15382i	0.710316	+	0.703883i	$0.248552\pi$
$827$	−5.25535	+	33.1810i	−0.182746	+	1.15382i	−0.893062	+	0.449933i	$0.851448\pi$
$828$		0			0
$829$	35.6481	+	11.5828i	1.23811	+	0.402287i	0.853646	−	0.520853i	$-0.174386\pi$
$829$	35.6481	+	11.5828i	1.23811	+	0.402287i	0.384464	+	0.923140i	$0.374386\pi$
$830$		0			0
$831$	74.3016	−	24.1421i	2.57749	−	0.837478i
$832$		0			0
$833$	−3.00813	−	1.53272i	−0.104226	−	0.0531056i
$834$		0			0
$835$	12.7419	+	31.0190i	0.440952	+	1.07346i
$836$		0			0
$837$	16.6648	+	105.217i	0.576019	+	3.63684i
$838$		0			0
$839$	−34.3401	+	24.9495i	−1.18555	+	0.861354i	−0.992787	−	0.119892i	$-0.961745\pi$
$839$	−34.3401	+	24.9495i	−1.18555	+	0.861354i	−0.192764	+	0.981245i	$0.561745\pi$
$840$		0			0
$841$	−17.9219	−	13.0210i	−0.617995	−	0.449000i
$842$		0			0
$843$	−41.0944	−	41.0944i	−1.41536	−	1.41536i
$844$		0			0
$845$	−25.6929	−	10.7309i	−0.883864	−	0.369153i
$846$		0			0
$847$	7.65936	+	15.0323i	0.263179	+	0.516517i
$848$		0			0
$849$		−	41.8794i		−	1.43730i
$850$		0			0
$851$			10.5026i			0.360023i
$852$		0			0
$853$	1.37933	+	2.70708i	0.0472273	+	0.0926888i	0.913414	−	0.407032i	$-0.133436\pi$
$853$	1.37933	+	2.70708i	0.0472273	+	0.0926888i	−0.866187	+	0.499720i	$0.833436\pi$
$854$		0			0
$855$	8.76726	+	14.4016i	0.299834	+	0.492525i
$856$		0			0
$857$	5.73479	+	5.73479i	0.195897	+	0.195897i	0.798238	−	0.602342i	$-0.205765\pi$
$857$	5.73479	+	5.73479i	0.195897	+	0.195897i	−0.602342	+	0.798238i	$0.705765\pi$
$858$		0			0
$859$	−0.501660	−	0.364478i	−0.0171164	−	0.0124358i	0.579194	−	0.815190i	$-0.303367\pi$
$859$	−0.501660	−	0.364478i	−0.0171164	−	0.0124358i	−0.596311	+	0.802754i	$0.703367\pi$
$860$		0			0
$861$	−17.8813	+	12.9915i	−0.609394	+	0.442751i
$862$		0			0
$863$	−5.80473	−	36.6496i	−0.197595	−	1.24757i	−0.864580	−	0.502495i	$-0.832415\pi$
$863$	−5.80473	−	36.6496i	−0.197595	−	1.24757i	0.666985	−	0.745071i	$-0.267585\pi$
$864$		0			0
$865$	40.9903	−	34.8013i	1.39371	−	1.18328i
$866$		0			0
$867$	88.0931	+	44.8857i	2.99180	+	1.52440i
$868$		0			0
$869$	24.4307	−	7.93803i	0.828756	−	0.269279i
$870$		0			0
$871$	−6.52565	−	2.12031i	−0.221113	−	0.0718441i
$872$		0			0
$873$	10.4347	−	65.8822i	0.353162	−	2.22977i
$874$		0			0
$875$	6.41241	+	27.7857i	0.216779	+	0.939328i
$876$		0			0
$877$	−16.2319	−	2.57088i	−0.548113	−	0.0868125i	−0.123765	−	0.992312i	$-0.539497\pi$
$877$	−16.2319	−	2.57088i	−0.548113	−	0.0868125i	−0.424348	+	0.905499i	$0.639497\pi$
$878$		0			0
$879$	9.65447	−	29.7134i	0.325637	−	1.00221i
$880$		0			0
$881$	−2.25514	−	6.94062i	−0.0759778	−	0.233835i	0.905854	−	0.423591i	$-0.139231\pi$
$881$	−2.25514	−	6.94062i	−0.0759778	−	0.233835i	−0.981831	+	0.189755i	$0.939231\pi$
$882$		0			0
$883$	19.7484	−	38.7584i	0.664586	−	1.30432i	−0.274813	−	0.961498i	$-0.588616\pi$
$883$	19.7484	−	38.7584i	0.664586	−	1.30432i	0.939399	−	0.342825i	$-0.111384\pi$
$884$		0			0
$885$	−6.61262	−	7.78858i	−0.222281	−	0.261810i
$886$		0			0
$887$	36.8656	−	5.83894i	1.23783	−	0.196052i	0.497001	−	0.867750i	$-0.334435\pi$
$887$	36.8656	−	5.83894i	1.23783	−	0.196052i	0.740825	+	0.671698i	$0.234435\pi$
$888$		0			0
$889$	−16.0961	−	22.1543i	−0.539845	−	0.743032i
$890$		0			0
$891$	82.1442	−	113.062i	2.75194	−	3.78771i
$892$		0			0
$893$	−4.50828	+	4.50828i	−0.150864	+	0.150864i
$894$		0			0
$895$	−31.9085	+	19.4249i	−1.06658	+	0.649303i
$896$		0			0
$897$	8.17364	−	4.16468i	0.272910	−	0.139055i
$898$		0			0
$899$	−16.1158			−0.537493
$900$		0			0
$901$	−11.8157			−0.393639
$902$		0			0
$903$	−19.8835	+	10.1311i	−0.661681	+	0.337143i
$904$		0			0
$905$	13.5551	−	32.4550i	0.450586	−	1.07884i
$906$		0			0
$907$	−27.8992	+	27.8992i	−0.926378	+	0.926378i	−0.997470	−	0.0710915i	$-0.977352\pi$
$907$	−27.8992	+	27.8992i	−0.926378	+	0.926378i	0.0710915	+	0.997470i	$0.477352\pi$
$908$		0			0
$909$	77.8781	−	107.190i	2.58305	−	3.55527i
$910$		0			0
$911$	−27.1356	−	37.3490i	−0.899043	−	1.23743i	−0.970772	−	0.240002i	$-0.922852\pi$
$911$	−27.1356	−	37.3490i	−0.899043	−	1.23743i	0.0717299	−	0.997424i	$-0.477148\pi$
$912$		0			0
$913$	−10.0613	+	1.59355i	−0.332980	+	0.0527389i
$914$		0			0
$915$	52.4041	−	21.5264i	1.73243	−	0.711641i
$916$		0			0
$917$	−17.1651	+	33.6884i	−0.566841	+	1.11249i
$918$		0			0
$919$	−8.42038	−	25.9153i	−0.277763	−	0.854865i	−0.988475	−	0.151383i	$-0.951627\pi$
$919$	−8.42038	−	25.9153i	−0.277763	−	0.854865i	0.710713	−	0.703482i	$-0.248373\pi$
$920$		0			0
$921$	−11.6392	+	35.8218i	−0.383525	+	1.18037i
$922$		0			0
$923$	4.04745	+	0.641053i	0.133223	+	0.0211005i
$924$		0			0
$925$	13.4961	−	4.29768i	0.443749	−	0.141307i
$926$		0			0
$927$	3.70981	−	23.4228i	0.121846	−	0.769305i
$928$		0			0
$929$	17.5344	+	5.69727i	0.575284	+	0.186921i	0.582187	−	0.813055i	$-0.302197\pi$
$929$	17.5344	+	5.69727i	0.575284	+	0.186921i	−0.00690260	+	0.999976i	$0.502197\pi$
$930$		0			0
$931$	−0.433972	+	0.141006i	−0.0142229	+	0.00462129i
$932$		0			0
$933$	−40.0162	−	20.3893i	−1.31007	−	0.667515i
$934$		0			0
$935$	−54.5115	−	33.6253i	−1.78272	−	1.09966i
$936$		0			0
$937$	−1.11761	−	7.05631i	−0.0365107	−	0.230519i	0.962685	−	0.270625i	$-0.0872305\pi$
$937$	−1.11761	−	7.05631i	−0.0365107	−	0.230519i	−0.999195	+	0.0401059i	$0.987230\pi$
$938$		0			0
$939$	−8.59173	+	6.24226i	−0.280380	+	0.203708i
$940$		0			0
$941$	−39.6679	−	28.8204i	−1.29314	−	0.939519i	−0.293274	−	0.956028i	$-0.594745\pi$
$941$	−39.6679	−	28.8204i	−1.29314	−	0.939519i	−0.999864	+	0.0165090i	$0.994745\pi$
$942$		0			0
$943$	−6.79616	−	6.79616i	−0.221313	−	0.221313i
$944$		0			0
$945$	−8.02872	+	98.3224i	−0.261174	+	3.19843i
$946$		0			0
$947$	−10.3671	−	20.3465i	−0.336884	−	0.661173i	0.658967	−	0.752172i	$-0.270994\pi$
$947$	−10.3671	−	20.3465i	−0.336884	−	0.661173i	−0.995851	+	0.0909994i	$0.970994\pi$
$948$		0			0
$949$		−	1.79858i		−	0.0583844i
$950$		0			0
$951$			50.5249i			1.63838i
$952$		0			0
$953$	−20.9271	−	41.0717i	−0.677894	−	1.33044i	−0.931715	−	0.363191i	$-0.881687\pi$
$953$	−20.9271	−	41.0717i	−0.677894	−	1.33044i	0.253821	−	0.967251i	$-0.418313\pi$
$954$		0			0
$955$	37.4964	−	8.88572i	1.21335	−	0.287535i
$956$		0			0
$957$	25.9596	+	25.9596i	0.839154	+	0.839154i
$958$		0			0
$959$	−13.3420	−	9.69354i	−0.430836	−	0.313021i
$960$		0			0
$961$	5.60636	−	4.07326i	0.180850	−	0.131395i
$962$		0			0
$963$	−0.249945	−	1.57809i	−0.00805438	−	0.0508533i
$964$		0			0
$965$	46.3000	−	3.50712i	1.49045	−	0.112898i
$966$		0			0
$967$	30.2031	+	15.3893i	0.971268	+	0.494886i	0.866264	−	0.499586i	$-0.166515\pi$
$967$	30.2031	+	15.3893i	0.971268	+	0.494886i	0.105003	+	0.994472i	$0.466515\pi$
$968$		0			0
$969$	20.0137	−	6.50283i	0.642931	−	0.208901i
$970$		0			0
$971$	−21.5602	−	7.00532i	−0.691898	−	0.224811i	−0.0581012	−	0.998311i	$-0.518505\pi$
$971$	−21.5602	−	7.00532i	−0.691898	−	0.224811i	−0.633797	+	0.773499i	$0.718505\pi$
$972$		0			0
$973$	3.40396	−	21.4917i	0.109126	−	0.688993i
$974$		0			0
$975$	−8.69642	−	8.79917i	−0.278508	−	0.281799i
$976$		0			0
$977$	−37.1340	−	5.88145i	−1.18802	−	0.188164i	−0.469030	−	0.883182i	$-0.655396\pi$
$977$	−37.1340	−	5.88145i	−1.18802	−	0.188164i	−0.718992	+	0.695018i	$0.755396\pi$
$978$		0			0
$979$	12.9758	−	39.9355i	0.414709	−	1.27634i
$980$		0			0
$981$	33.0896	+	101.839i	1.05647	+	3.25147i
$982$		0			0
$983$	−14.4545	+	28.3685i	−0.461026	+	0.904814i	0.537094	+	0.843522i	$0.319522\pi$
$983$	−14.4545	+	28.3685i	−0.461026	+	0.904814i	−0.998120	+	0.0612916i	$0.980478\pi$
$984$		0			0
$985$	55.0747	+	13.3934i	1.75483	+	0.426750i
$986$		0			0
$987$	−58.2062	+	9.21895i	−1.85272	+	0.293443i
$988$		0			0
$989$	−5.70383	−	7.85065i	−0.181371	−	0.249636i
$990$		0			0
$991$	12.0951	−	16.6475i	0.384214	−	0.528826i	−0.572481	−	0.819918i	$-0.694019\pi$
$991$	12.0951	−	16.6475i	0.384214	−	0.528826i	0.956695	+	0.291093i	$0.0940188\pi$
$992$		0			0
$993$	−53.4024	+	53.4024i	−1.69467	+	1.69467i
$994$		0			0
$995$	−36.5055	−	31.3645i	−1.15730	−	0.994321i
$996$		0			0
$997$	1.43815	−	0.732773i	0.0455466	−	0.0232072i	−0.431069	−	0.902319i	$-0.641863\pi$
$997$	1.43815	−	0.732773i	0.0455466	−	0.0232072i	0.476616	+	0.879112i	$0.341863\pi$
$998$		0			0
$999$	48.9991			1.55026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.127.1	yes	80
4.3	odd	2	inner	400.2.bi.d.127.10	yes	80
25.13	odd	20	inner	400.2.bi.d.63.10	yes	80
100.63	even	20	inner	400.2.bi.d.63.1	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.63.1	✓	80	100.63	even	20	inner
400.2.bi.d.63.10	yes	80	25.13	odd	20	inner
400.2.bi.d.127.1	yes	80	1.1	even	1	trivial
400.2.bi.d.127.10	yes	80	4.3	odd	2	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	400.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.97847 + 1.51761i) q^{3} +(1.69605 + 1.45720i) q^{5} +(1.80351 - 1.80351i) q^{7} +(4.80482 - 6.61326i) q^{9} +O(q^{10})\)	\(q+(-2.97847 + 1.51761i) q^{3} +(1.69605 + 1.45720i) q^{5} +(1.80351 - 1.80351i) q^{7} +(4.80482 - 6.61326i) q^{9} +(2.46693 + 3.39544i) q^{11} +(0.731069 - 0.115790i) q^{13} +(-7.26309 - 1.76629i) q^{15} +(-3.09835 + 6.08086i) q^{17} +(0.285040 + 0.877263i) q^{19} +(-2.63469 + 8.10874i) q^{21} +(-3.66187 - 0.579984i) q^{23} +(0.753156 + 4.94295i) q^{25} +(-2.70588 + 17.0843i) q^{27} +(-2.48868 - 0.808620i) q^{29} +(5.85729 - 1.90315i) q^{31} +(-12.5006 - 6.36939i) q^{33} +(5.68691 - 0.430771i) q^{35} +(-0.443143 - 2.79789i) q^{37} +(-2.00175 + 1.45435i) q^{39} +(2.09726 + 1.52375i) q^{41} +(1.85076 + 1.85076i) q^{43} +(17.7860 - 4.21485i) q^{45} +(3.13797 + 6.15862i) q^{47} +0.494689i q^{49} -22.8138i q^{51} +(0.786001 + 1.54261i) q^{53} +(-0.763789 + 9.35362i) q^{55} +(-2.18033 - 2.18033i) q^{57} +(1.10583 + 0.803429i) q^{59} +(-6.13174 + 4.45497i) q^{61} +(-3.26155 - 20.5926i) q^{63} +(1.40866 + 0.868926i) q^{65} +(-8.25963 - 4.20849i) q^{67} +(11.7870 - 3.82982i) q^{69} +(5.26538 + 1.71082i) q^{71} +(0.380123 - 2.40000i) q^{73} +(-9.74472 - 13.5795i) q^{75} +(10.5728 + 1.67457i) q^{77} +(1.89136 - 5.82101i) q^{79} +(-10.2897 - 31.6685i) q^{81} +(-1.10190 + 2.16260i) q^{83} +(-14.1160 + 5.79851i) q^{85} +(8.63962 - 1.36838i) q^{87} +(-5.88076 - 8.09417i) q^{89} +(1.10966 - 1.52732i) q^{91} +(-14.5576 + 14.5576i) q^{93} +(-0.794903 + 1.90324i) q^{95} +(7.27061 - 3.70456i) q^{97} +34.3080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 80 * q + 4 * q^5	\( 80 q + 4 q^{5} - 4 q^{13} - 24 q^{17} - 48 q^{25} - 40 q^{29} - 64 q^{33} - 20 q^{37} - 24 q^{45} + 28 q^{53} + 48 q^{57} + 112 q^{65} + 140 q^{69} + 108 q^{73} + 136 q^{77} - 20 q^{81} - 24 q^{85} + 80 q^{89} - 116 q^{93} - 52 q^{97}+O(q^{100}) \) 80 * q + 4 * q^5 - 4 * q^13 - 24 * q^17 - 48 * q^25 - 40 * q^29 - 64 * q^33 - 20 * q^37 - 24 * q^45 + 28 * q^53 + 48 * q^57 + 112 * q^65 + 140 * q^69 + 108 * q^73 + 136 * q^77 - 20 * q^81 - 24 * q^85 + 80 * q^89 - 116 * q^93 - 52 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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