LMFDB - Embedded newform 400.2.bi.d.223.3

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			223.3
Character	$\chi$	$=$	400.223
Dual form			400.2.bi.d.287.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.962089 - 1.88821i) q^{3} +(0.712896 + 2.11938i) q^{5} +(-2.48695 - 2.48695i) q^{7} +(-0.876350 + 1.20619i) q^{9} +O(q^{10})$	\(q+(-0.962089 - 1.88821i) q^{3} +(0.712896 + 2.11938i) q^{5} +(-2.48695 - 2.48695i) q^{7} +(-0.876350 + 1.20619i) q^{9} +(0.636880 + 0.876591i) q^{11} +(-0.803569 - 5.07354i) q^{13} +(3.31596 - 3.38513i) q^{15} +(-5.83245 - 2.97178i) q^{17} +(-1.78319 - 5.48809i) q^{19} +(-2.30321 + 7.08855i) q^{21} +(-1.03666 + 6.54522i) q^{23} +(-3.98356 + 3.02180i) q^{25} +(-3.15861 - 0.500275i) q^{27} +(5.38673 + 1.75025i) q^{29} +(-1.28204 + 0.416562i) q^{31} +(1.04245 - 2.04592i) q^{33} +(3.49787 - 7.04375i) q^{35} +(0.392049 - 0.0620945i) q^{37} +(-8.80678 + 6.39850i) q^{39} +(-5.94040 - 4.31596i) q^{41} +(5.79702 - 5.79702i) q^{43} +(-3.18113 - 0.997430i) q^{45} +(1.36833 - 0.697199i) q^{47} +5.36989i q^{49} +13.8720i q^{51} +(5.76669 - 2.93828i) q^{53} +(-1.40380 + 1.97471i) q^{55} +(-8.64706 + 8.64706i) q^{57} +(-4.21664 - 3.06357i) q^{59} +(8.55062 - 6.21239i) q^{61} +(5.17919 - 0.820303i) q^{63} +(10.1799 - 5.31998i) q^{65} +(-0.158287 + 0.310656i) q^{67} +(13.3561 - 4.33966i) q^{69} +(6.11680 + 1.98747i) q^{71} +(3.41052 + 0.540174i) q^{73} +(9.53831 + 4.61454i) q^{75} +(0.596149 - 3.76393i) q^{77} +(0.562975 - 1.73266i) q^{79} +(3.47642 + 10.6993i) q^{81} +(9.67823 + 4.93131i) q^{83} +(2.14041 - 14.4798i) q^{85} +(-1.87767 - 11.8551i) q^{87} +(-1.98855 - 2.73700i) q^{89} +(-10.6192 + 14.6161i) q^{91} +(2.02000 + 2.02000i) q^{93} +(10.3601 - 7.69170i) q^{95} +(2.35295 + 4.61793i) q^{97} -1.61547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{11}{20}\right)$	$-1$

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
$3$	−0.962089	−	1.88821i	−0.555462	−	1.09016i	−0.982559	−	0.185950i	$-0.940464\pi$
$3$	−0.962089	−	1.88821i	−0.555462	−	1.09016i	0.427097	−	0.904206i	$-0.359536\pi$
$4$		0			0
$5$	0.712896	+	2.11938i	0.318817	+	0.947816i
$5$	0.712896	+	2.11938i	0.318817	+	0.947816i
$6$		0			0
$7$	−2.48695	−	2.48695i	−0.939981	−	0.939981i	0.0583175	−	0.998298i	$-0.481426\pi$
$7$	−2.48695	−	2.48695i	−0.939981	−	0.939981i	−0.998298	+	0.0583175i	$0.981426\pi$
$8$		0			0
$9$	−0.876350	+	1.20619i	−0.292117	+	0.402064i
$10$		0			0
$11$	0.636880	+	0.876591i	0.192027	+	0.264302i	0.894164	−	0.447739i	$-0.147771\pi$
$11$	0.636880	+	0.876591i	0.192027	+	0.264302i	−0.702137	+	0.712041i	$0.747771\pi$
$12$		0			0
$13$	−0.803569	−	5.07354i	−0.222870	−	1.40715i	−0.804626	−	0.593782i	$-0.797634\pi$
$13$	−0.803569	−	5.07354i	−0.222870	−	1.40715i	0.581756	−	0.813364i	$-0.302366\pi$
$14$		0			0
$15$	3.31596	−	3.38513i	0.856177	−	0.874036i
$16$		0			0
$17$	−5.83245	−	2.97178i	−1.41458	−	0.720764i	−0.431187	−	0.902263i	$-0.641905\pi$
$17$	−5.83245	−	2.97178i	−1.41458	−	0.720764i	−0.983391	+	0.181499i	$0.941905\pi$
$18$		0			0
$19$	−1.78319	−	5.48809i	−0.409091	−	1.25905i	−0.917430	−	0.397897i	$-0.869740\pi$
$19$	−1.78319	−	5.48809i	−0.409091	−	1.25905i	0.508339	−	0.861157i	$-0.330260\pi$
$20$		0			0
$21$	−2.30321	+	7.08855i	−0.502602	+	1.54685i
$22$		0			0
$23$	−1.03666	+	6.54522i	−0.216159	+	1.36477i	0.605977	+	0.795482i	$0.292782\pi$
$23$	−1.03666	+	6.54522i	−0.216159	+	1.36477i	−0.822136	+	0.569291i	$0.807218\pi$
$24$		0			0
$25$	−3.98356	+	3.02180i	−0.796712	+	0.604360i
$26$		0			0
$27$	−3.15861	−	0.500275i	−0.607875	−	0.0962780i
$28$		0			0
$29$	5.38673	+	1.75025i	1.00029	+	0.325014i	0.762982	−	0.646420i	$-0.223735\pi$
$29$	5.38673	+	1.75025i	1.00029	+	0.325014i	0.237309	+	0.971434i	$0.423735\pi$
$30$		0			0
$31$	−1.28204	+	0.416562i	−0.230262	+	0.0748167i	−0.421875	−	0.906654i	$-0.638628\pi$
$31$	−1.28204	+	0.416562i	−0.230262	+	0.0748167i	0.191613	+	0.981470i	$0.438628\pi$
$32$		0			0
$33$	1.04245	−	2.04592i	0.181467	−	0.356149i
$34$		0			0
$35$	3.49787	−	7.04375i	0.591247	−	1.19061i
$36$		0			0
$37$	0.392049	−	0.0620945i	0.0644525	−	0.0102083i	−0.124125	−	0.992267i	$-0.539612\pi$
$37$	0.392049	−	0.0620945i	0.0644525	−	0.0102083i	0.188577	+	0.982058i	$0.439612\pi$
$38$		0			0
$39$	−8.80678	+	6.39850i	−1.41021	+	1.02458i
$40$		0			0
$41$	−5.94040	−	4.31596i	−0.927735	−	0.674039i	0.0177019	−	0.999843i	$-0.494365\pi$
$41$	−5.94040	−	4.31596i	−0.927735	−	0.674039i	−0.945437	+	0.325804i	$0.894365\pi$
$42$		0			0
$43$	5.79702	−	5.79702i	0.884037	−	0.884037i	−0.109905	−	0.993942i	$-0.535055\pi$
$43$	5.79702	−	5.79702i	0.884037	−	0.884037i	0.993942	+	0.109905i	$0.0350548\pi$
$44$		0			0
$45$	−3.18113	−	0.997430i	−0.474215	−	0.148688i
$46$		0			0
$47$	1.36833	−	0.697199i	0.199592	−	0.101697i	−0.351338	−	0.936249i	$-0.614273\pi$
$47$	1.36833	−	0.697199i	0.199592	−	0.101697i	0.550930	+	0.834552i	$0.314273\pi$
$48$		0			0
$49$			5.36989i			0.767127i
$50$		0			0
$51$			13.8720i			1.94247i
$52$		0			0
$53$	5.76669	−	2.93828i	0.792116	−	0.403603i	−0.0106158	−	0.999944i	$-0.503379\pi$
$53$	5.76669	−	2.93828i	0.792116	−	0.403603i	0.802732	+	0.596341i	$0.203379\pi$
$54$		0			0
$55$	−1.40380	+	1.97471i	−0.189288	+	0.266270i
$56$		0			0
$57$	−8.64706	+	8.64706i	−1.14533	+	1.14533i
$58$		0			0
$59$	−4.21664	−	3.06357i	−0.548960	−	0.398843i	0.278442	−	0.960453i	$-0.410182\pi$
$59$	−4.21664	−	3.06357i	−0.548960	−	0.398843i	−0.827402	+	0.561610i	$0.810182\pi$
$60$		0			0
$61$	8.55062	−	6.21239i	1.09479	−	0.795415i	0.114592	−	0.993413i	$-0.463444\pi$
$61$	8.55062	−	6.21239i	1.09479	−	0.795415i	0.980202	+	0.197998i	$0.0634439\pi$
$62$		0			0
$63$	5.17919	−	0.820303i	0.652516	−	0.103348i
$64$		0			0
$65$	10.1799	−	5.31998i	1.26266	−	0.659862i
$66$		0			0
$67$	−0.158287	+	0.310656i	−0.0193378	+	0.0379526i	−0.900473	−	0.434911i	$-0.856780\pi$
$67$	−0.158287	+	0.310656i	−0.0193378	+	0.0379526i	0.881136	+	0.472864i	$0.156780\pi$
$68$		0			0
$69$	13.3561	−	4.33966i	1.60788	−	0.522433i
$70$		0			0
$71$	6.11680	+	1.98747i	0.725930	+	0.235869i	0.648593	−	0.761136i	$-0.275358\pi$
$71$	6.11680	+	1.98747i	0.725930	+	0.235869i	0.0773380	+	0.997005i	$0.475358\pi$
$72$		0			0
$73$	3.41052	+	0.540174i	0.399172	+	0.0632226i	0.352793	−	0.935701i	$-0.385232\pi$
$73$	3.41052	+	0.540174i	0.399172	+	0.0632226i	0.0463786	+	0.998924i	$0.485232\pi$
$74$		0			0
$75$	9.53831	+	4.61454i	1.10139	+	0.532841i
$76$		0			0
$77$	0.596149	−	3.76393i	0.0679374	−	0.428940i
$78$		0			0
$79$	0.562975	−	1.73266i	0.0633396	−	0.194939i	−0.914379	−	0.404860i	$-0.867320\pi$
$79$	0.562975	−	1.73266i	0.0633396	−	0.194939i	0.977719	+	0.209920i	$0.0673204\pi$
$80$		0			0
$81$	3.47642	+	10.6993i	0.386268	+	1.18881i
$82$		0			0
$83$	9.67823	+	4.93131i	1.06232	+	0.541281i	0.895663	−	0.444733i	$-0.146701\pi$
$83$	9.67823	+	4.93131i	1.06232	+	0.541281i	0.166661	+	0.986014i	$0.446701\pi$
$84$		0			0
$85$	2.14041	−	14.4798i	0.232160	−	1.57055i
$86$		0			0
$87$	−1.87767	−	11.8551i	−0.201307	−	1.27101i
$88$		0			0
$89$	−1.98855	−	2.73700i	−0.210786	−	0.290122i	0.690513	−	0.723320i	$-0.257385\pi$
$89$	−1.98855	−	2.73700i	−0.210786	−	0.290122i	−0.901299	+	0.433199i	$0.857385\pi$
$90$		0			0
$91$	−10.6192	+	14.6161i	−1.11320	+	1.53218i
$92$		0			0
$93$	2.02000	+	2.02000i	0.209464	+	0.209464i
$94$		0			0
$95$	10.3601	−	7.69170i	1.06293	−	0.789151i
$96$		0			0
$97$	2.35295	+	4.61793i	0.238906	+	0.468880i	0.979064	−	0.203553i	$-0.0652491\pi$
$97$	2.35295	+	4.61793i	0.238906	+	0.468880i	−0.740157	+	0.672434i	$0.765249\pi$
$98$		0			0
$99$	−1.61547			−0.162360
$100$		0			0
$101$	12.8086			1.27451			0.637254	−	0.770654i	$-0.280070\pi$
$101$	12.8086			1.27451			0.637254	+	0.770654i	$0.280070\pi$
$102$		0			0
$103$	5.72678	+	11.2394i	0.564277	+	1.10746i	0.980192	+	0.198052i	$0.0634614\pi$
$103$	5.72678	+	11.2394i	0.564277	+	1.10746i	−0.415915	+	0.909404i	$0.636539\pi$
$104$		0			0
$105$	−16.6653	+	0.172022i	−1.62637	+	0.0167876i
$106$		0			0
$107$	−0.202385	−	0.202385i	−0.0195653	−	0.0195653i	0.697256	−	0.716822i	$-0.254404\pi$
$107$	−0.202385	−	0.202385i	−0.0195653	−	0.0195653i	−0.716822	+	0.697256i	$0.754404\pi$
$108$		0			0
$109$	−11.9659	+	16.4696i	−1.14612	+	1.57750i	−0.393112	+	0.919491i	$0.628602\pi$
$109$	−11.9659	+	16.4696i	−1.14612	+	1.57750i	−0.753009	+	0.658010i	$0.771398\pi$
$110$		0			0
$111$	−0.494433	−	0.680529i	−0.0469295	−	0.0645929i
$112$		0			0
$113$	−1.91924	−	12.1176i	−0.180547	−	1.13993i	−0.896914	−	0.442206i	$-0.854196\pi$
$113$	−1.91924	−	12.1176i	−0.180547	−	1.13993i	0.716366	−	0.697724i	$-0.245804\pi$
$114$		0			0
$115$	−14.6109	+	2.46898i	−1.36247	+	0.230234i
$116$		0			0
$117$	6.82387	+	3.47693i	0.630867	+	0.321443i
$118$		0			0
$119$	7.11436	+	21.8957i	0.652172	+	2.00718i
$120$		0			0
$121$	3.03639	−	9.34505i	0.276036	−	0.849550i
$122$		0			0
$123$	−2.43422	+	15.3690i	−0.219486	+	1.38578i
$124$		0			0
$125$	−9.24421	−	6.28845i	−0.826827	−	0.562456i
$126$		0			0
$127$	−12.4468	−	1.97137i	−1.10447	−	0.174931i	−0.422538	−	0.906345i	$-0.638861\pi$
$127$	−12.4468	−	1.97137i	−1.10447	−	0.174931i	−0.681934	+	0.731414i	$0.738861\pi$
$128$		0			0
$129$	−16.5232	−	5.36871i	−1.45479	−	0.472689i
$130$		0			0
$131$	3.19986	−	1.03970i	0.279573	−	0.0908387i	−0.165875	−	0.986147i	$-0.553045\pi$
$131$	3.19986	−	1.03970i	0.279573	−	0.0908387i	0.445447	+	0.895308i	$0.353045\pi$
$132$		0			0
$133$	−9.21392	+	18.0833i	−0.798948	+	1.56802i
$134$		0			0
$135$	−1.19149	−	7.05095i	−0.102547	−	0.606849i
$136$		0			0
$137$	−1.21798	+	0.192909i	−0.104059	+	0.0164814i	−0.208247	−	0.978076i	$-0.566776\pi$
$137$	−1.21798	+	0.192909i	−0.104059	+	0.0164814i	0.104188	+	0.994558i	$0.466776\pi$
$138$		0			0
$139$	−14.3033	+	10.3919i	−1.21319	+	0.881432i	−0.995516	−	0.0945899i	$-0.969846\pi$
$139$	−14.3033	+	10.3919i	−1.21319	+	0.881432i	−0.217671	+	0.976022i	$0.569846\pi$
$140$		0			0
$141$	−2.63291	−	1.91292i	−0.221731	−	0.161097i
$142$		0			0
$143$	3.93564	−	3.93564i	0.329115	−	0.329115i
$144$		0			0
$145$	0.130723	+	12.6643i	0.0108559	+	1.05171i
$146$		0			0
$147$	10.1395	−	5.16631i	0.836288	−	0.426110i
$148$		0			0
$149$			1.42875i			0.117048i	0.998286	+	0.0585239i	$0.0186394\pi$
$149$			1.42875i			0.117048i	−0.998286	+	0.0585239i	$0.981361\pi$
$150$		0			0
$151$		−	21.1292i		−	1.71947i	−0.510743	−	0.859733i	$-0.670630\pi$
$151$		−	21.1292i		−	1.71947i	0.510743	−	0.859733i	$-0.329370\pi$
$152$		0			0
$153$	8.69581	−	4.43074i	0.703015	−	0.358204i
$154$		0			0
$155$	−1.79682	−	2.42018i	−0.144324	−	0.194393i
$156$		0			0
$157$	7.85643	−	7.85643i	0.627012	−	0.627012i	−0.320303	−	0.947315i	$-0.603785\pi$
$157$	7.85643	−	7.85643i	0.627012	−	0.627012i	0.947315	+	0.320303i	$0.103785\pi$
$158$		0			0
$159$	−11.0961	−	8.06181i	−0.879981	−	0.639343i
$160$		0			0
$161$	18.8558	−	13.6995i	1.48605	−	1.07968i
$162$		0			0
$163$	21.7208	−	3.44023i	1.70130	−	0.269460i	0.771155	−	0.636647i	$-0.219679\pi$
$163$	21.7208	−	3.44023i	1.70130	−	0.269460i	0.930147	+	0.367187i	$0.119679\pi$
$164$		0			0
$165$	5.07924	+	0.750817i	0.395418	+	0.0584510i
$166$		0			0
$167$	5.78847	−	11.3605i	0.447925	−	0.879103i	−0.551078	−	0.834454i	$-0.685783\pi$
$167$	5.78847	−	11.3605i	0.447925	−	0.879103i	0.999003	−	0.0446487i	$-0.0142168\pi$
$168$		0			0
$169$	−12.7313	+	4.13666i	−0.979332	+	0.318204i
$170$		0			0
$171$	8.18239	+	2.65862i	0.625723	+	0.203310i
$172$		0			0
$173$	−14.9452	−	2.36708i	−1.13626	−	0.179966i	−0.440166	−	0.897916i	$-0.645080\pi$
$173$	−14.9452	−	2.36708i	−1.13626	−	0.179966i	−0.696094	+	0.717950i	$0.745080\pi$
$174$		0			0
$175$	17.4220	+	2.39185i	1.31698	+	0.180807i
$176$		0			0
$177$	−1.72786	+	10.9093i	−0.129874	+	0.819994i
$178$		0			0
$179$	2.25869	−	6.95152i	0.168822	−	0.519581i	−0.830475	−	0.557055i	$-0.811931\pi$
$179$	2.25869	−	6.95152i	0.168822	−	0.519581i	0.999298	+	0.0374740i	$0.0119311\pi$
$180$		0			0
$181$	1.30701	+	4.02257i	0.0971494	+	0.298995i	0.987808	−	0.155678i	$-0.0497562\pi$
$181$	1.30701	+	4.02257i	0.0971494	+	0.298995i	−0.890658	+	0.454673i	$0.849756\pi$
$182$		0			0
$183$	−19.9567	−	10.1685i	−1.47524	−	0.751674i
$184$		0			0
$185$	0.411092	+	0.786635i	0.0302241	+	0.0578345i
$186$		0			0
$187$	−1.10954	−	7.00535i	−0.0811374	−	0.512282i
$188$		0			0
$189$	6.61116	+	9.09949i	0.480891	+	0.661890i
$190$		0			0
$191$	−9.92373	+	13.6588i	−0.718056	+	0.988319i	0.281530	+	0.959552i	$0.409158\pi$
$191$	−9.92373	+	13.6588i	−0.718056	+	0.988319i	−0.999586	+	0.0287671i	$0.990842\pi$
$192$		0			0
$193$	6.21959	+	6.21959i	0.447696	+	0.447696i	0.894588	−	0.446892i	$-0.147469\pi$
$193$	6.21959	+	6.21959i	0.447696	+	0.447696i	−0.446892	+	0.894588i	$0.647469\pi$
$194$		0			0
$195$	−19.8392	−	14.1035i	−1.42071	−	1.00997i
$196$		0			0
$197$	−1.51200	−	2.96746i	−0.107725	−	0.211423i	0.830851	−	0.556495i	$-0.187854\pi$
$197$	−1.51200	−	2.96746i	−0.107725	−	0.211423i	−0.938576	+	0.345073i	$0.887854\pi$
$198$		0			0
$199$	−4.51558			−0.320101			−0.160051	−	0.987109i	$-0.551166\pi$
$199$	−4.51558			−0.320101			−0.160051	+	0.987109i	$0.551166\pi$
$200$		0			0
$201$	0.738868			0.0521157
$202$		0			0
$203$	−9.04375	−	17.7494i	−0.634747	−	1.24576i
$204$		0			0
$205$	4.91227	−	15.6668i	0.343088	−	1.09422i
$206$		0			0
$207$	−6.98632	−	6.98632i	−0.485583	−	0.485583i
$208$		0			0
$209$	3.67513	−	5.05838i	0.254214	−	0.349896i
$210$		0			0
$211$	−13.7626	−	18.9426i	−0.947459	−	1.30406i	−0.952647	−	0.304078i	$-0.901651\pi$
$211$	−13.7626	−	18.9426i	−0.947459	−	1.30406i	0.00518831	−	0.999987i	$-0.498349\pi$
$212$		0			0
$213$	−2.13215	−	13.4619i	−0.146093	−	0.922394i
$214$		0			0
$215$	16.4188	+	8.15342i	1.11975	+	0.556058i
$216$		0			0
$217$	4.22436	+	2.15242i	0.286768	+	0.146116i
$218$		0			0
$219$	−2.26127	−	6.95947i	−0.152802	−	0.470277i
$220$		0			0
$221$	−10.3907	+	31.9792i	−0.698952	+	2.15115i
$222$		0			0
$223$	−2.67084	+	16.8630i	−0.178852	+	1.12923i	0.720968	+	0.692969i	$0.243698\pi$
$223$	−2.67084	+	16.8630i	−0.178852	+	1.12923i	−0.899820	+	0.436261i	$0.856302\pi$
$224$		0			0
$225$	−0.153880	−	7.45309i	−0.0102587	−	0.496873i
$226$		0			0
$227$	11.3411	+	1.79625i	0.752735	+	0.119221i	0.520999	−	0.853557i	$-0.325560\pi$
$227$	11.3411	+	1.79625i	0.752735	+	0.119221i	0.231736	+	0.972779i	$0.425560\pi$
$228$		0			0
$229$	4.36702	+	1.41893i	0.288581	+	0.0937656i	0.449730	−	0.893164i	$-0.351520\pi$
$229$	4.36702	+	1.41893i	0.288581	+	0.0937656i	−0.161150	+	0.986930i	$0.551520\pi$
$230$		0			0
$231$	−7.68063	+	2.49559i	−0.505348	+	0.164198i
$232$		0			0
$233$	−11.9215	+	23.3972i	−0.781000	+	1.53280i	0.0639491	+	0.997953i	$0.479630\pi$
$233$	−11.9215	+	23.3972i	−0.781000	+	1.53280i	−0.844949	+	0.534846i	$0.820370\pi$
$234$		0			0
$235$	2.45311	+	2.40298i	0.160023	+	0.156753i
$236$		0			0
$237$	−3.81325	+	0.603959i	−0.247697	+	0.0392314i
$238$		0			0
$239$	19.4046	−	14.0983i	1.25518	−	0.911940i	0.256668	−	0.966500i	$-0.417375\pi$
$239$	19.4046	−	14.0983i	1.25518	−	0.911940i	0.998511	+	0.0545594i	$0.0173754\pi$
$240$		0			0
$241$	−12.8923	−	9.36677i	−0.830463	−	0.603367i	0.0892274	−	0.996011i	$-0.471560\pi$
$241$	−12.8923	−	9.36677i	−0.830463	−	0.603367i	−0.919690	+	0.392645i	$0.871560\pi$
$242$		0			0
$243$	10.0739	−	10.0739i	0.646242	−	0.646242i
$244$		0			0
$245$	−11.3808	+	3.82817i	−0.727095	+	0.244573i
$246$		0			0
$247$	−26.4111	+	13.4571i	−1.68050	+	0.856257i
$248$		0			0
$249$		−	23.0188i		−	1.45876i
$250$		0			0
$251$		−	1.98321i		−	0.125179i	−0.998039	−	0.0625897i	$-0.980064\pi$
$251$		−	1.98321i		−	0.125179i	0.998039	−	0.0625897i	$-0.0199360\pi$
$252$		0			0
$253$	−6.39771	+	3.25980i	−0.402221	+	0.204942i
$254$		0			0
$255$	−29.4000	+	9.88929i	−1.84110	+	0.619292i
$256$		0			0
$257$	−5.62981	+	5.62981i	−0.351178	+	0.351178i	−0.860548	−	0.509370i	$-0.829879\pi$
$257$	−5.62981	+	5.62981i	−0.351178	+	0.351178i	0.509370	+	0.860548i	$0.329879\pi$
$258$		0			0
$259$	−1.12943	−	0.820582i	−0.0701796	−	0.0509885i
$260$		0			0
$261$	−6.83180	+	4.96359i	−0.422878	+	0.307239i
$262$		0			0
$263$	9.71036	−	1.53797i	0.598766	−	0.0948353i	0.150308	−	0.988639i	$-0.451973\pi$
$263$	9.71036	−	1.53797i	0.598766	−	0.0948353i	0.448458	+	0.893804i	$0.351973\pi$
$264$		0			0
$265$	10.3384	+	10.1271i	0.635082	+	0.622105i
$266$		0			0
$267$	−3.25486	+	6.38802i	−0.199194	+	0.390941i
$268$		0			0
$269$	0.0850724	−	0.0276417i	0.00518695	−	0.00168534i	−0.306422	−	0.951896i	$-0.599132\pi$
$269$	0.0850724	−	0.0276417i	0.00518695	−	0.00168534i	0.311609	+	0.950210i	$0.399132\pi$
$270$		0			0
$271$	8.65453	+	2.81203i	0.525725	+	0.170819i	0.559842	−	0.828599i	$-0.310862\pi$
$271$	8.65453	+	2.81203i	0.525725	+	0.170819i	−0.0341167	+	0.999418i	$0.510862\pi$
$272$		0			0
$273$	37.8148	+	5.98928i	2.28866	+	0.362488i
$274$		0			0
$275$	−5.18593	−	1.56742i	−0.312723	−	0.0945193i
$276$		0			0
$277$	−1.22536	+	7.73662i	−0.0736248	+	0.464849i	0.923139	+	0.384466i	$0.125614\pi$
$277$	−1.22536	+	7.73662i	−0.0736248	+	0.464849i	−0.996764	+	0.0803828i	$0.974386\pi$
$278$		0			0
$279$	0.621066	−	1.91145i	0.0371823	−	0.114435i
$280$		0			0
$281$	−7.21730	−	22.2126i	−0.430548	−	1.32509i	−0.897581	−	0.440850i	$-0.854677\pi$
$281$	−7.21730	−	22.2126i	−0.430548	−	1.32509i	0.467033	−	0.884240i	$-0.345323\pi$
$282$		0			0
$283$	−18.3394	−	9.34440i	−1.09017	−	0.555467i	−0.185957	−	0.982558i	$-0.559538\pi$
$283$	−18.3394	−	9.34440i	−1.09017	−	0.555467i	−0.904209	+	0.427091i	$0.859538\pi$
$284$		0			0
$285$	−24.4909	−	12.1620i	−1.45071	−	0.720412i
$286$		0			0
$287$	4.03993	+	25.5071i	0.238469	+	1.50564i
$288$		0			0
$289$	15.1937	+	20.9123i	0.893746	+	1.23014i
$290$		0			0
$291$	6.45586	−	8.88573i	0.378449	−	0.520890i
$292$		0			0
$293$	−7.39422	−	7.39422i	−0.431975	−	0.431975i	0.457325	−	0.889300i	$-0.348808\pi$
$293$	−7.39422	−	7.39422i	−0.431975	−	0.431975i	−0.889300	+	0.457325i	$0.848808\pi$
$294$		0			0
$295$	3.48684	−	11.1207i	0.203012	−	0.647471i
$296$		0			0
$297$	−1.57312	−	3.08742i	−0.0912818	−	0.179151i
$298$		0			0
$299$	34.0405			1.96861
$300$		0			0
$301$	−28.8338			−1.66195
$302$		0			0
$303$	−12.3231	−	24.1854i	−0.707941	−	1.38941i
$304$		0			0
$305$	19.2621	+	13.6932i	1.10295	+	0.784073i
$306$		0			0
$307$	11.5253	+	11.5253i	0.657782	+	0.657782i	0.954855	−	0.297073i	$-0.0960105\pi$
$307$	11.5253	+	11.5253i	0.657782	+	0.657782i	−0.297073	+	0.954855i	$0.596011\pi$
$308$		0			0
$309$	15.7127	−	21.6267i	0.893865	−	1.23030i
$310$		0			0
$311$	10.4903	+	14.4386i	0.594850	+	0.818740i	0.995225	−	0.0976112i	$-0.0311202\pi$
$311$	10.4903	+	14.4386i	0.594850	+	0.818740i	−0.400375	+	0.916351i	$0.631120\pi$
$312$		0			0
$313$	−3.12859	−	19.7531i	−0.176838	−	1.11651i	−0.903206	−	0.429206i	$-0.858793\pi$
$313$	−3.12859	−	19.7531i	−0.176838	−	1.11651i	0.726368	−	0.687306i	$-0.241207\pi$
$314$		0			0
$315$	5.43076	+	10.3919i	0.305989	+	0.585516i
$316$		0			0
$317$	−23.2749	−	11.8592i	−1.30725	−	0.666078i	−0.345092	−	0.938569i	$-0.612152\pi$
$317$	−23.2749	−	11.8592i	−1.30725	−	0.666078i	−0.962158	+	0.272491i	$0.912152\pi$
$318$		0			0
$319$	1.89644	+	5.83666i	0.106181	+	0.326790i
$320$		0			0
$321$	−0.187432	+	0.576857i	−0.0104614	+	0.0321970i
$322$		0			0
$323$	−5.90905	+	37.3083i	−0.328788	+	2.07589i
$324$		0			0
$325$	18.5323	+	17.7825i	1.02799	+	0.986396i
$326$		0			0
$327$	42.6102	+	6.74879i	2.35635	+	0.373209i
$328$		0			0
$329$	−5.13688	−	1.66907i	−0.283205	−	0.0920190i
$330$		0			0
$331$	25.2729	−	8.21167i	1.38912	−	0.451354i	0.483467	−	0.875363i	$-0.339377\pi$
$331$	25.2729	−	8.21167i	1.38912	−	0.451354i	0.905658	+	0.424009i	$0.139377\pi$
$332$		0			0
$333$	−0.268674	+	0.527303i	−0.0147233	+	0.0288960i
$334$		0			0
$335$	−0.771240	−	0.114005i	−0.0421374	−	0.00622877i
$336$		0			0
$337$	−18.7904	+	2.97611i	−1.02358	+	0.162119i	−0.645585	−	0.763688i	$-0.723387\pi$
$337$	−18.7904	+	2.97611i	−1.02358	+	0.162119i	−0.377995	+	0.925807i	$0.623387\pi$
$338$		0			0
$339$	−21.0341	+	15.2822i	−1.14241	+	0.830013i
$340$		0			0
$341$	−1.18166	−	0.858529i	−0.0639907	−	0.0464919i
$342$		0			0
$343$	−4.05401	+	4.05401i	−0.218896	+	0.218896i
$344$		0			0
$345$	18.7189	+	25.2129i	1.00779	+	1.35742i
$346$		0			0
$347$	0.439740	−	0.224059i	0.0236065	−	0.0120281i	−0.442147	−	0.896942i	$-0.645783\pi$
$347$	0.439740	−	0.224059i	0.0236065	−	0.0120281i	0.465754	+	0.884914i	$0.345783\pi$
$348$		0			0
$349$		−	19.5878i		−	1.04851i	−0.851561	−	0.524256i	$-0.824344\pi$
$349$		−	19.5878i		−	1.04851i	0.851561	−	0.524256i	$-0.175656\pi$
$350$		0			0
$351$			16.4273i			0.876826i
$352$		0			0
$353$	7.21547	−	3.67646i	0.384040	−	0.195678i	−0.251302	−	0.967909i	$-0.580859\pi$
$353$	7.21547	−	3.67646i	0.384040	−	0.195678i	0.635343	+	0.772230i	$0.280859\pi$
$354$		0			0
$355$	0.148440	+	14.3807i	0.00787835	+	0.763248i
$356$		0			0
$357$	34.4990	−	34.4990i	1.82588	−	1.82588i
$358$		0			0
$359$	−18.3833	−	13.3563i	−0.970234	−	0.704916i	−0.0147292	−	0.999892i	$-0.504689\pi$
$359$	−18.3833	−	13.3563i	−0.970234	−	0.704916i	−0.955505	+	0.294975i	$0.904689\pi$
$360$		0			0
$361$	−11.5680	+	8.40467i	−0.608844	+	0.442351i
$362$		0			0
$363$	−20.5667	+	3.25744i	−1.07947	+	0.170971i
$364$		0			0
$365$	1.28652	+	7.61329i	0.0673393	+	0.398498i
$366$		0			0
$367$	−5.53713	+	10.8672i	−0.289036	+	0.567265i	−0.989175	−	0.146742i	$-0.953121\pi$
$367$	−5.53713	+	10.8672i	−0.289036	+	0.567265i	0.700139	+	0.714007i	$0.253121\pi$
$368$		0			0
$369$	10.4117	−	3.38298i	0.542014	−	0.176111i
$370$		0			0
$371$	−21.6489	−	7.03414i	−1.12395	−	0.365194i
$372$		0			0
$373$	−0.383855	−	0.0607967i	−0.0198753	−	0.00314793i	0.146489	−	0.989212i	$-0.453203\pi$
$373$	−0.383855	−	0.0607967i	−0.0198753	−	0.00314793i	−0.166364	+	0.986064i	$0.553203\pi$
$374$		0			0
$375$	−2.98013	+	23.5050i	−0.153893	+	1.21379i
$376$		0			0
$377$	4.55137	−	28.7362i	0.234407	−	1.47999i
$378$		0			0
$379$	10.3821	−	31.9529i	0.533294	−	1.64131i	−0.214013	−	0.976831i	$-0.568653\pi$
$379$	10.3821	−	31.9529i	0.533294	−	1.64131i	0.747307	−	0.664479i	$-0.231347\pi$
$380$		0			0
$381$	8.25254	+	25.3987i	0.422790	+	1.30121i
$382$		0			0
$383$	−25.5162	−	13.0011i	−1.30382	−	0.664328i	−0.342433	−	0.939542i	$-0.611251\pi$
$383$	−25.5162	−	13.0011i	−1.30382	−	0.664328i	−0.961383	+	0.275215i	$0.911251\pi$
$384$		0			0
$385$	8.40221	−	1.41983i	0.428216	−	0.0723612i
$386$		0			0
$387$	1.91210	+	12.0725i	0.0971975	+	0.613681i
$388$		0			0
$389$	14.5449	+	20.0193i	0.737455	+	1.01502i	0.998761	+	0.0497636i	$0.0158468\pi$
$389$	14.5449	+	20.0193i	0.737455	+	1.01502i	−0.261306	+	0.965256i	$0.584153\pi$
$390$		0			0
$391$	25.4973	−	35.0940i	1.28945	−	1.77478i
$392$		0			0
$393$	−5.04171	−	5.04171i	−0.254320	−	0.254320i
$394$		0			0
$395$	4.07351	−	0.0420473i	0.204960	−	0.00211563i
$396$		0			0
$397$	−2.70625	−	5.31131i	−0.135823	−	0.266567i	0.813070	−	0.582166i	$-0.197795\pi$
$397$	−2.70625	−	5.31131i	−0.135823	−	0.266567i	−0.948893	+	0.315599i	$0.897795\pi$
$398$		0			0
$399$	43.0097			2.15318
$400$		0			0
$401$	21.3385			1.06559			0.532797	−	0.846243i	$-0.321141\pi$
$401$	21.3385			1.06559			0.532797	+	0.846243i	$0.321141\pi$
$402$		0			0
$403$	3.14365	+	6.16977i	0.156596	+	0.307338i
$404$		0			0
$405$	−20.1976	+	14.9953i	−1.00363	+	0.745125i
$406$		0			0
$407$	0.304120	+	0.304120i	0.0150747	+	0.0150747i
$408$		0			0
$409$	0.0825825	−	0.113665i	0.00408344	−	0.00562038i	−0.806970	−	0.590592i	$-0.798894\pi$
$409$	0.0825825	−	0.113665i	0.00408344	−	0.00562038i	0.811054	+	0.584972i	$0.198894\pi$
$410$		0			0
$411$	1.53606	+	2.11420i	0.0757682	+	0.104286i
$412$		0			0
$413$	2.86764	+	18.1056i	0.141107	+	0.890916i
$414$		0			0
$415$	−3.55174	+	24.0274i	−0.174348	+	1.17946i
$416$		0			0
$417$	33.3831	+	17.0096i	1.63478	+	0.832961i
$418$		0			0
$419$	11.7061	+	36.0277i	0.571881	+	1.76007i	0.646563	+	0.762861i	$0.276206\pi$
$419$	11.7061	+	36.0277i	0.571881	+	1.76007i	−0.0746819	+	0.997207i	$0.523794\pi$
$420$		0			0
$421$	4.51487	−	13.8953i	0.220041	−	0.677217i	−0.778716	−	0.627377i	$-0.784129\pi$
$421$	4.51487	−	13.8953i	0.220041	−	0.677217i	0.998757	−	0.0498407i	$-0.0158714\pi$
$422$		0			0
$423$	−0.358180	+	2.26146i	−0.0174153	+	0.109956i
$424$		0			0
$425$	32.2141	−	5.78623i	1.56261	−	0.280674i
$426$		0			0
$427$	−36.7149	−	5.81507i	−1.77676	−	0.281411i
$428$		0			0
$429$	−11.2177	−	3.64486i	−0.541597	−	0.175975i
$430$		0			0
$431$	−4.56891	+	1.48453i	−0.220077	+	0.0715073i	−0.416980	−	0.908916i	$-0.636912\pi$
$431$	−4.56891	+	1.48453i	−0.220077	+	0.0715073i	0.196903	+	0.980423i	$0.436912\pi$
$432$		0			0
$433$	13.6842	−	26.8568i	0.657622	−	1.29066i	−0.285554	−	0.958363i	$-0.592178\pi$
$433$	13.6842	−	26.8568i	0.657622	−	1.29066i	0.943176	−	0.332293i	$-0.107822\pi$
$434$		0			0
$435$	23.7870	−	12.4310i	1.14050	−	0.596021i
$436$		0			0
$437$	37.7693	−	5.98207i	1.80675	−	0.286161i
$438$		0			0
$439$	18.6354	−	13.5394i	0.889420	−	0.646201i	−0.0463070	−	0.998927i	$-0.514745\pi$
$439$	18.6354	−	13.5394i	0.889420	−	0.646201i	0.935727	+	0.352726i	$0.114745\pi$
$440$		0			0
$441$	−6.47712	−	4.70590i	−0.308434	−	0.224091i
$442$		0			0
$443$	7.49310	−	7.49310i	0.356008	−	0.356008i	−0.506331	−	0.862339i	$-0.668999\pi$
$443$	7.49310	−	7.49310i	0.356008	−	0.356008i	0.862339	+	0.506331i	$0.168999\pi$
$444$		0			0
$445$	4.38312	−	6.16569i	0.207780	−	0.292282i
$446$		0			0
$447$	2.69778	−	1.37459i	0.127600	−	0.0650157i
$448$		0			0
$449$		−	14.7317i		−	0.695230i	−0.937637	−	0.347615i	$-0.886992\pi$
$449$		−	14.7317i		−	0.695230i	0.937637	−	0.347615i	$-0.113008\pi$
$450$		0			0
$451$		−	7.95605i		−	0.374636i
$452$		0			0
$453$	−39.8962	+	20.3281i	−1.87449	+	0.955099i
$454$		0			0
$455$	−38.5475	−	12.0864i	−1.80713	−	0.566620i
$456$		0			0
$457$	−15.8443	+	15.8443i	−0.741163	+	0.741163i	−0.972802	−	0.231639i	$-0.925591\pi$
$457$	−15.8443	+	15.8443i	−0.741163	+	0.741163i	0.231639	+	0.972802i	$0.425591\pi$
$458$		0			0
$459$	16.9357	+	12.3045i	0.790493	+	0.574327i
$460$		0			0
$461$	−9.98246	+	7.25268i	−0.464930	+	0.337791i	−0.795462	−	0.606004i	$-0.792772\pi$
$461$	−9.98246	+	7.25268i	−0.464930	+	0.337791i	0.330532	+	0.943795i	$0.392772\pi$
$462$		0			0
$463$	18.8211	−	2.98097i	0.874690	−	0.138537i	0.297083	−	0.954852i	$-0.403986\pi$
$463$	18.8211	−	2.98097i	0.874690	−	0.138537i	0.577608	+	0.816314i	$0.303986\pi$
$464$		0			0
$465$	−2.84109	+	5.72119i	−0.131753	+	0.265314i
$466$		0			0
$467$	−7.11028	+	13.9547i	−0.329024	+	0.645747i	−0.994961	−	0.100262i	$-0.968032\pi$
$467$	−7.11028	+	13.9547i	−0.329024	+	0.645747i	0.665937	+	0.746008i	$0.268032\pi$
$468$		0			0
$469$	1.16624	−	0.378934i	0.0538519	−	0.0174976i
$470$		0			0
$471$	−22.3931	−	7.27598i	−1.03182	−	0.335259i
$472$		0			0
$473$	8.77361	+	1.38960i	0.403411	+	0.0638941i
$474$		0			0
$475$	23.6873	+	16.4737i	1.08685	+	0.755864i
$476$		0			0
$477$	−1.50951	+	9.53069i	−0.0691159	+	0.436380i
$478$		0			0
$479$	3.39635	−	10.4529i	0.155183	−	0.477605i	−0.842996	−	0.537920i	$-0.819210\pi$
$479$	3.39635	−	10.4529i	0.155183	−	0.477605i	0.998179	+	0.0603144i	$0.0192103\pi$
$480$		0			0
$481$	−0.630077	−	1.93918i	−0.0287290	−	0.0884189i
$482$		0			0
$483$	−44.0085	−	22.4235i	−2.00246	−	1.02030i
$484$		0			0
$485$	−8.10975	+	8.27892i	−0.368245	+	0.375926i
$486$		0			0
$487$	5.39311	+	34.0507i	0.244385	+	1.54299i	0.738899	+	0.673816i	$0.235346\pi$
$487$	5.39311	+	34.0507i	0.244385	+	1.54299i	−0.494514	+	0.869170i	$0.664654\pi$
$488$		0			0
$489$	−27.3932	−	37.7035i	−1.23876	−	1.70501i
$490$		0			0
$491$	7.46855	−	10.2796i	0.337051	−	0.463911i	−0.606526	−	0.795063i	$-0.707437\pi$
$491$	7.46855	−	10.2796i	0.337051	−	0.463911i	0.943577	+	0.331153i	$0.107437\pi$
$492$		0			0
$493$	−26.2165	−	26.2165i	−1.18073	−	1.18073i
$494$		0			0
$495$	−1.15166	−	3.42379i	−0.0517633	−	0.153888i
$496$		0			0
$497$	−10.2695	−	20.1549i	−0.460648	−	0.904073i
$498$		0			0
$499$	0.771267			0.0345266			0.0172633	−	0.999851i	$-0.494505\pi$
$499$	0.771267			0.0345266			0.0172633	+	0.999851i	$0.494505\pi$
$500$		0			0
$501$	−27.0200			−1.20716
$502$		0			0
$503$	−2.87922	−	5.65079i	−0.128378	−	0.251956i	0.817867	−	0.575408i	$-0.195157\pi$
$503$	−2.87922	−	5.65079i	−0.128378	−	0.251956i	−0.946245	+	0.323452i	$0.895157\pi$
$504$		0			0
$505$	9.13124	+	27.1464i	0.406335	+	1.20800i
$506$		0			0
$507$	20.0595	+	20.0595i	0.890874	+	0.890874i
$508$		0			0
$509$	−9.91033	+	13.6404i	−0.439268	+	0.604600i	−0.970049	−	0.242909i	$-0.921898\pi$
$509$	−9.91033	+	13.6404i	−0.439268	+	0.604600i	0.530782	+	0.847509i	$0.321898\pi$
$510$		0			0
$511$	−7.13843	−	9.82521i	−0.315786	−	0.434642i
$512$		0			0
$513$	2.88685	+	18.2268i	0.127457	+	0.804734i
$514$		0			0
$515$	−19.7381	+	20.1498i	−0.869763	+	0.887906i
$516$		0			0
$517$	1.48262	+	0.755433i	0.0652056	+	0.0332239i
$518$		0			0
$519$	9.90905	+	30.4969i	0.434959	+	1.33867i
$520$		0			0
$521$	4.09088	−	12.5904i	0.179225	−	0.551597i	−0.820576	−	0.571537i	$-0.806347\pi$
$521$	4.09088	−	12.5904i	0.179225	−	0.551597i	0.999801	+	0.0199396i	$0.00634740\pi$
$522$		0			0
$523$	0.617847	−	3.90093i	0.0270166	−	0.170576i	−0.970491	−	0.241138i	$-0.922479\pi$
$523$	0.617847	−	3.90093i	0.0270166	−	0.170576i	0.997507	+	0.0705622i	$0.0224793\pi$
$524$		0			0
$525$	−12.2452	−	35.1975i	−0.534425	−	1.53614i
$526$		0			0
$527$	8.71540	+	1.38038i	0.379649	+	0.0601305i
$528$		0			0
$529$	−19.8910	−	6.46297i	−0.864825	−	0.280999i
$530$		0			0
$531$	7.39050	−	2.40132i	0.320721	−	0.104208i
$532$		0			0
$533$	−17.1236	+	33.6070i	−0.741707	+	1.45568i
$534$		0			0
$535$	0.284652	−	0.573211i	0.0123066	−	0.0247821i
$536$		0			0
$537$	−15.2990	+	2.42312i	−0.660199	+	0.104565i
$538$		0			0
$539$	−4.70719	+	3.41998i	−0.202753	+	0.147309i
$540$		0			0
$541$	19.2894	+	14.0146i	0.829316	+	0.602533i	0.919366	−	0.393404i	$-0.128703\pi$
$541$	19.2894	+	14.0146i	0.829316	+	0.602533i	−0.0900497	+	0.995937i	$0.528703\pi$
$542$		0			0
$543$	6.33797	−	6.33797i	0.271988	−	0.271988i
$544$		0			0
$545$	−43.4358	−	13.6191i	−1.86058	−	0.583378i
$546$		0			0
$547$	13.8265	−	7.04496i	0.591179	−	0.301221i	−0.132691	−	0.991158i	$-0.542362\pi$
$547$	13.8265	−	7.04496i	0.591179	−	0.301221i	0.723870	+	0.689937i	$0.242362\pi$
$548$		0			0
$549$			15.7579i			0.672531i
$550$		0			0
$551$		−	32.6839i		−	1.39238i
$552$		0			0
$553$	−5.70914	+	2.90895i	−0.242777	+	0.123701i
$554$		0			0
$555$	1.08982	−	1.53304i	0.0462603	−	0.0650739i
$556$		0			0
$557$	−13.1538	+	13.1538i	−0.557343	+	0.557343i	−0.928550	−	0.371207i	$-0.878944\pi$
$557$	−13.1538	+	13.1538i	−0.557343	+	0.557343i	0.371207	+	0.928550i	$0.378944\pi$
$558$		0			0
$559$	−34.0697	−	24.7531i	−1.44099	−	1.04694i
$560$		0			0
$561$	−12.1601	+	8.83480i	−0.513398	+	0.373006i
$562$		0			0
$563$	−12.3785	+	1.96056i	−0.521691	+	0.0826277i	−0.411726	−	0.911308i	$-0.635074\pi$
$563$	−12.3785	+	1.96056i	−0.521691	+	0.0826277i	−0.109965	+	0.993935i	$0.535074\pi$
$564$		0			0
$565$	24.3136	−	12.7062i	1.02288	−	0.534555i
$566$		0			0
$567$	17.9630	−	35.2544i	0.754375	−	1.48054i
$568$		0			0
$569$	9.54204	−	3.10040i	0.400023	−	0.129975i	−0.102094	−	0.994775i	$-0.532554\pi$
$569$	9.54204	−	3.10040i	0.400023	−	0.129975i	0.502118	+	0.864799i	$0.332554\pi$
$570$		0			0
$571$	−1.54898	−	0.503293i	−0.0648227	−	0.0210622i	0.276426	−	0.961035i	$-0.410850\pi$
$571$	−1.54898	−	0.503293i	−0.0648227	−	0.0210622i	−0.341249	+	0.939973i	$0.610850\pi$
$572$		0			0
$573$	35.3382	+	5.59702i	1.47628	+	0.233819i
$574$		0			0
$575$	−15.6487	−	29.2059i	−0.652598	−	1.21797i
$576$		0			0
$577$	−0.449517	+	2.83814i	−0.0187136	+	0.118153i	−0.995277	−	0.0970778i	$-0.969050\pi$
$577$	−0.449517	+	2.83814i	−0.0187136	+	0.118153i	0.976563	+	0.215231i	$0.0690504\pi$
$578$		0			0
$579$	5.76007	−	17.7277i	0.239380	−	0.736737i
$580$		0			0
$581$	−11.8054	−	36.3333i	−0.489770	−	1.50736i
$582$		0			0
$583$	6.24836	+	3.18370i	0.258780	+	0.131855i
$584$		0			0
$585$	−2.50424	+	16.9411i	−0.103538	+	0.700427i
$586$		0			0
$587$	−6.22563	−	39.3071i	−0.256959	−	1.62238i	−0.691952	−	0.721944i	$-0.743249\pi$
$587$	−6.22563	−	39.3071i	−0.256959	−	1.62238i	0.434992	−	0.900434i	$-0.356751\pi$
$588$		0			0
$589$	4.57225	+	6.29317i	0.188396	+	0.259306i
$590$		0			0
$591$	−4.14850	+	5.70992i	−0.170646	+	0.234875i
$592$		0			0
$593$	24.1631	+	24.1631i	0.992258	+	0.992258i	0.999970	−	0.00771191i	$-0.00245480\pi$
$593$	24.1631	+	24.1631i	0.992258	+	0.992258i	−0.00771191	+	0.999970i	$0.502455\pi$
$594$		0			0
$595$	−41.3336	+	30.6874i	−1.69451	+	1.25806i
$596$		0			0
$597$	4.34439	+	8.52635i	0.177804	+	0.348960i
$598$		0			0
$599$	−34.4806			−1.40884			−0.704420	−	0.709784i	$-0.748793\pi$
$599$	−34.4806			−1.40884			−0.704420	+	0.709784i	$0.748793\pi$
$600$		0			0
$601$	3.13654			0.127942			0.0639710	−	0.997952i	$-0.479623\pi$
$601$	3.13654			0.127942			0.0639710	+	0.997952i	$0.479623\pi$
$602$		0			0
$603$	−0.235996	−	0.463168i	−0.00961049	−	0.0188616i
$604$		0			0
$605$	21.9704	−	0.226781i	0.893223	−	0.00921997i
$606$		0			0
$607$	9.01472	+	9.01472i	0.365896	+	0.365896i	0.865978	−	0.500082i	$-0.166697\pi$
$607$	9.01472	+	9.01472i	0.365896	+	0.365896i	−0.500082	+	0.865978i	$0.666697\pi$
$608$		0			0
$609$	−24.8135	+	34.1529i	−1.00550	+	1.38395i
$610$		0			0
$611$	−4.63681	−	6.38203i	−0.187585	−	0.258189i
$612$		0			0
$613$	0.352820	+	2.22762i	0.0142503	+	0.0899728i	0.993788	−	0.111286i	$-0.0354969\pi$
$613$	0.352820	+	2.22762i	0.0142503	+	0.0899728i	−0.979538	+	0.201258i	$0.935497\pi$
$614$		0			0
$615$	−34.3082	+	5.79750i	−1.38344	+	0.233778i
$616$		0			0
$617$	32.0686	+	16.3398i	1.29103	+	0.657815i	0.958451	−	0.285258i	$-0.0920794\pi$
$617$	32.0686	+	16.3398i	1.29103	+	0.657815i	0.332584	+	0.943074i	$0.392079\pi$
$618$		0			0
$619$	−7.66711	−	23.5969i	−0.308167	−	0.948441i	−0.978476	−	0.206359i	$-0.933839\pi$
$619$	−7.66711	−	23.5969i	−0.308167	−	0.948441i	0.670309	−	0.742082i	$-0.266161\pi$
$620$		0			0
$621$	6.54882	−	20.1552i	0.262795	−	0.808800i
$622$		0			0
$623$	−1.86137	+	11.7522i	−0.0745742	+	0.470843i
$624$		0			0
$625$	6.73746	−	24.0750i	0.269498	−	0.963001i
$626$		0			0
$627$	−13.0871	−	2.07279i	−0.522647	−	0.0827792i
$628$		0			0
$629$	−2.47114	−	0.802922i	−0.0985308	−	0.0320146i
$630$		0			0
$631$	−17.4370	+	5.66562i	−0.694155	+	0.225545i	−0.634782	−	0.772691i	$-0.718910\pi$
$631$	−17.4370	+	5.66562i	−0.694155	+	0.225545i	−0.0593731	+	0.998236i	$0.518910\pi$
$632$		0			0
$633$	−22.5267	+	44.2112i	−0.895357	+	1.75724i
$634$		0			0
$635$	−4.69516	−	27.7848i	−0.186322	−	1.10261i
$636$		0			0
$637$	27.2443	−	4.31508i	1.07946	−	0.170970i
$638$		0			0
$639$	−7.75772	+	5.63632i	−0.306891	+	0.222969i
$640$		0			0
$641$	10.7019	+	7.77539i	0.422700	+	0.307110i	0.778723	−	0.627367i	$-0.215868\pi$
$641$	10.7019	+	7.77539i	0.422700	+	0.307110i	−0.356023	+	0.934477i	$0.615868\pi$
$642$		0			0
$643$	0.271585	−	0.271585i	0.0107103	−	0.0107103i	−0.701731	−	0.712442i	$-0.747589\pi$
$643$	0.271585	−	0.271585i	0.0107103	−	0.0107103i	0.712442	+	0.701731i	$0.247589\pi$
$644$		0			0
$645$	−0.400977	−	38.8463i	−0.0157885	−	1.52957i
$646$		0			0
$647$	38.5106	−	19.6221i	1.51401	−	0.771425i	0.517560	−	0.855647i	$-0.326840\pi$
$647$	38.5106	−	19.6221i	1.51401	−	0.771425i	0.996447	+	0.0842219i	$0.0268404\pi$
$648$		0			0
$649$		−	5.64739i		−	0.221680i
$650$		0			0
$651$		−	10.0473i		−	0.393784i
$652$		0			0
$653$	−17.8566	+	9.09841i	−0.698784	+	0.356048i	−0.767022	−	0.641621i	$-0.778262\pi$
$653$	−17.8566	+	9.09841i	−0.698784	+	0.356048i	0.0682379	+	0.997669i	$0.478262\pi$
$654$		0			0
$655$	4.48468	+	6.04052i	0.175231	+	0.236023i
$656$		0			0
$657$	−3.64037	+	3.64037i	−0.142024	+	0.142024i
$658$		0			0
$659$	27.0464	+	19.6503i	1.05358	+	0.765469i	0.972889	−	0.231271i	$-0.0742883\pi$
$659$	27.0464	+	19.6503i	1.05358	+	0.765469i	0.0806879	+	0.996739i	$0.474288\pi$
$660$		0			0
$661$	−20.3339	+	14.7735i	−0.790899	+	0.574622i	−0.908230	−	0.418471i	$-0.862566\pi$
$661$	−20.3339	+	14.7735i	−0.790899	+	0.574622i	0.117331	+	0.993093i	$0.462566\pi$
$662$		0			0
$663$	70.3801	−	11.1471i	2.73334	−	0.432918i
$664$		0			0
$665$	−44.8941	−	6.63627i	−1.74092	−	0.257343i
$666$		0			0
$667$	−17.0400	+	33.4429i	−0.659792	+	1.29491i
$668$		0			0
$669$	34.4104	−	11.1806i	1.33038	−	0.432267i
$670$		0			0
$671$	10.8914	+	3.53884i	0.420460	+	0.136616i
$672$		0			0
$673$	4.47697	+	0.709083i	0.172575	+	0.0273331i	0.242124	−	0.970245i	$-0.422156\pi$
$673$	4.47697	+	0.709083i	0.172575	+	0.0273331i	−0.0695491	+	0.997579i	$0.522156\pi$
$674$		0			0
$675$	14.0942	−	7.55182i	0.542488	−	0.290670i
$676$		0			0
$677$	−0.610053	+	3.85172i	−0.0234462	+	0.148034i	−0.996634	−	0.0819777i	$-0.973876\pi$
$677$	−0.610053	+	3.85172i	−0.0234462	+	0.148034i	0.973188	+	0.230011i	$0.0738764\pi$
$678$		0			0
$679$	5.63290	−	17.3363i	0.216171	−	0.665306i
$680$		0			0
$681$	−7.51944	−	23.1425i	−0.288146	−	0.886821i
$682$		0			0
$683$	−36.3267	−	18.5094i	−1.39000	−	0.708242i	−0.410915	−	0.911674i	$-0.634791\pi$
$683$	−36.3267	−	18.5094i	−1.39000	−	0.708242i	−0.979089	+	0.203431i	$0.934791\pi$
$684$		0			0
$685$	−1.27714	−	2.44384i	−0.0487972	−	0.0933745i
$686$		0			0
$687$	−1.52223	−	9.61097i	−0.0580766	−	0.366681i
$688$		0			0
$689$	−19.5414	−	26.8964i	−0.744467	−	1.02467i
$690$		0			0
$691$	22.6260	−	31.1420i	0.860733	−	1.18470i	−0.120662	−	0.992694i	$-0.538502\pi$
$691$	22.6260	−	31.1420i	0.860733	−	1.18470i	0.981394	−	0.192003i	$-0.0614983\pi$
$692$		0			0
$693$	4.01759	+	4.01759i	0.152616	+	0.152616i
$694$		0			0
$695$	−32.2212	−	22.9057i	−1.22222	−	0.868863i
$696$		0			0
$697$	21.8211	+	42.8262i	0.826531	+	1.62216i
$698$		0			0
$699$	55.6482			2.10481
$700$		0			0
$701$	18.4118			0.695405			0.347702	−	0.937605i	$-0.386962\pi$
$701$	18.4118			0.695405			0.347702	+	0.937605i	$0.386962\pi$
$702$		0			0
$703$	−1.03988	−	2.04087i	−0.0392197	−	0.0769730i
$704$		0			0
$705$	2.17722	−	6.94386i	0.0819988	−	0.261521i
$706$		0			0
$707$	−31.8545	−	31.8545i	−1.19801	−	1.19801i
$708$		0			0
$709$	7.46847	−	10.2795i	0.280484	−	0.386053i	−0.645410	−	0.763836i	$-0.723313\pi$
$709$	7.46847	−	10.2795i	0.280484	−	0.386053i	0.925894	+	0.377783i	$0.123313\pi$
$710$		0			0
$711$	1.59656	+	2.19747i	0.0598755	+	0.0824116i
$712$		0			0
$713$	−1.39744	−	8.82310i	−0.0523346	−	0.330428i
$714$		0			0
$715$	11.1468	+	5.53542i	0.416867	+	0.207013i
$716$		0			0
$717$	−45.2893	−	23.0761i	−1.69136	−	0.861792i
$718$		0			0
$719$	−0.104956	−	0.323022i	−0.00391420	−	0.0120467i	0.949080	−	0.315034i	$-0.102016\pi$
$719$	−0.104956	−	0.323022i	−0.00391420	−	0.0120467i	−0.952995	+	0.302987i	$0.902016\pi$
$720$		0			0
$721$	13.7097	−	42.1942i	0.510577	−	1.57140i
$722$		0			0
$723$	−5.28289	+	33.3549i	−0.196473	+	1.24048i
$724$		0			0
$725$	−26.7473	+	9.30537i	−0.993368	+	0.345593i
$726$		0			0
$727$	5.35474	+	0.848108i	0.198596	+	0.0314546i	0.254940	−	0.966957i	$-0.417944\pi$
$727$	5.35474	+	0.848108i	0.198596	+	0.0314546i	−0.0563436	+	0.998411i	$0.517944\pi$
$728$		0			0
$729$	3.38428	+	1.09962i	0.125344	+	0.0407266i
$730$		0			0
$731$	−51.0383	+	16.5834i	−1.88772	+	0.613357i
$732$		0			0
$733$	11.2063	−	21.9936i	0.413915	−	0.812354i	−0.586083	−	0.810251i	$-0.699331\pi$
$733$	11.2063	−	21.9936i	0.413915	−	0.812354i	0.999998	−	0.00210249i	$-0.000669243\pi$
$734$		0			0
$735$	18.1778	+	17.8063i	0.670497	+	0.656796i
$736$		0			0
$737$	−0.373128	+	0.0590976i	−0.0137443	+	0.00217689i
$738$		0			0
$739$	−34.0132	+	24.7121i	−1.25120	+	0.909048i	−0.998291	−	0.0584432i	$-0.981386\pi$
$739$	−34.0132	+	24.7121i	−1.25120	+	0.909048i	−0.252906	+	0.967491i	$0.581386\pi$
$740$		0			0
$741$	50.8197	+	36.9226i	1.86691	+	1.35639i
$742$		0			0
$743$	−8.52185	+	8.52185i	−0.312636	+	0.312636i	−0.845930	−	0.533294i	$-0.820954\pi$
$743$	−8.52185	+	8.52185i	−0.312636	+	0.312636i	0.533294	+	0.845930i	$0.320954\pi$
$744$		0			0
$745$	−3.02807	+	1.01855i	−0.110940	+	0.0373168i
$746$		0			0
$747$	−14.4296	+	7.35226i	−0.527952	+	0.269005i
$748$		0			0
$749$			1.00665i			0.0367820i
$750$		0			0
$751$			27.2962i			0.996051i	0.867162	+	0.498026i	$0.165941\pi$
$751$			27.2962i			0.996051i	−0.867162	+	0.498026i	$0.834059\pi$
$752$		0			0
$753$	−3.74472	+	1.90803i	−0.136465	+	0.0695324i
$754$		0			0
$755$	44.7807	−	15.0629i	1.62974	−	0.548195i
$756$		0			0
$757$	16.0964	−	16.0964i	0.585035	−	0.585035i	−0.351248	−	0.936283i	$-0.614242\pi$
$757$	16.0964	−	16.0964i	0.585035	−	0.585035i	0.936283	+	0.351248i	$0.114242\pi$
$758$		0			0
$759$	12.3103	+	8.94398i	0.446837	+	0.324646i
$760$		0			0
$761$	−27.7014	+	20.1263i	−1.00418	+	0.729577i	−0.962980	−	0.269574i	$-0.913117\pi$
$761$	−27.7014	+	20.1263i	−1.00418	+	0.729577i	−0.0411967	+	0.999151i	$0.513117\pi$
$762$		0			0
$763$	70.7177	−	11.2006i	2.56015	−	0.405488i
$764$		0			0
$765$	15.5896	+	15.2711i	0.563645	+	0.552127i
$766$		0			0
$767$	−12.1548	+	23.8551i	−0.438883	+	0.861357i
$768$		0			0
$769$	−23.4610	+	7.62295i	−0.846027	+	0.274891i	−0.699781	−	0.714358i	$-0.746719\pi$
$769$	−23.4610	+	7.62295i	−0.846027	+	0.274891i	−0.146246	+	0.989248i	$0.546719\pi$
$770$		0			0
$771$	16.0466	+	5.21386i	0.577905	+	0.187773i
$772$		0			0
$773$	17.8447	+	2.82632i	0.641830	+	0.101656i	0.468862	−	0.883272i	$-0.344664\pi$
$773$	17.8447	+	2.82632i	0.641830	+	0.101656i	0.172968	+	0.984927i	$0.444664\pi$
$774$		0			0
$775$	3.84833	−	5.53348i	0.138236	−	0.198768i
$776$		0			0
$777$	−0.462811	+	2.92208i	−0.0166033	+	0.104829i
$778$		0			0
$779$	−13.0935	+	40.2976i	−0.469123	+	1.44381i
$780$		0			0
$781$	2.15347	+	6.62771i	0.0770573	+	0.237158i
$782$		0			0
$783$	−16.1390	−	8.22322i	−0.576760	−	0.293874i
$784$		0			0
$785$	22.2516	+	11.0500i	0.794194	+	0.394390i
$786$		0			0
$787$	−2.36811	−	14.9516i	−0.0844138	−	0.532968i	−0.993267	−	0.115851i	$-0.963041\pi$
$787$	−2.36811	−	14.9516i	−0.0844138	−	0.532968i	0.908853	−	0.417117i	$-0.136959\pi$
$788$		0			0
$789$	−12.2462	−	16.8555i	−0.435977	−	0.600071i
$790$		0			0
$791$	−25.3629	+	34.9090i	−0.901801	+	1.24122i
$792$		0			0
$793$	−38.3898	−	38.3898i	−1.36326	−	1.36326i
$794$		0			0
$795$	9.17567	−	29.2642i	0.325427	−	1.03789i
$796$		0			0
$797$	17.9977	+	35.3225i	0.637512	+	1.25119i	0.953204	+	0.302326i	$0.0977632\pi$
$797$	17.9977	+	35.3225i	0.637512	+	1.25119i	−0.315692	+	0.948862i	$0.602237\pi$
$798$		0			0
$799$	−10.0527			−0.355637
$800$		0			0
$801$	5.04401			0.178221
$802$		0			0
$803$	1.69858	+	3.33366i	0.0599418	+	0.117642i
$804$		0			0
$805$	42.4768	+	30.1963i	1.49711	+	1.06428i
$806$		0			0
$807$	−0.134040	−	0.134040i	−0.00471844	−	0.00471844i
$808$		0			0
$809$	−14.4194	+	19.8466i	−0.506960	+	0.697771i	−0.983403	−	0.181435i	$-0.941926\pi$
$809$	−14.4194	+	19.8466i	−0.506960	+	0.697771i	0.476443	+	0.879205i	$0.341926\pi$
$810$		0			0
$811$	17.8717	+	24.5983i	0.627560	+	0.863763i	0.997876	−	0.0651434i	$-0.0207505\pi$
$811$	17.8717	+	24.5983i	0.627560	+	0.863763i	−0.370316	+	0.928906i	$0.620750\pi$
$812$		0			0
$813$	−3.01674	−	19.0470i	−0.105802	−	0.668006i
$814$		0			0
$815$	22.7758	+	43.5821i	0.797802	+	1.52661i
$816$		0			0
$817$	−42.1517	−	21.4774i	−1.47470	−	0.751398i
$818$		0			0
$819$	−8.32367	−	25.6176i	−0.290853	−	0.895152i
$820$		0			0
$821$	−2.99208	+	9.20866i	−0.104424	+	0.321384i	−0.989595	−	0.143882i	$-0.954041\pi$
$821$	−2.99208	+	9.20866i	−0.104424	+	0.321384i	0.885171	+	0.465266i	$0.154041\pi$
$822$		0			0
$823$	−0.404151	+	2.55171i	−0.0140878	+	0.0889469i	−0.993730	−	0.111802i	$-0.964338\pi$
$823$	−0.404151	+	2.55171i	−0.0140878	+	0.0889469i	0.979643	+	0.200749i	$0.0643377\pi$
$824$		0			0
$825$	2.02971	+	11.3001i	0.0706653	+	0.393419i
$826$		0			0
$827$	12.6206	+	1.99890i	0.438861	+	0.0695087i	0.371955	−	0.928251i	$-0.378687\pi$
$827$	12.6206	+	1.99890i	0.438861	+	0.0695087i	0.0669053	+	0.997759i	$0.478687\pi$
$828$		0			0
$829$	−1.82937	−	0.594399i	−0.0635368	−	0.0206443i	0.277076	−	0.960848i	$-0.410635\pi$
$829$	−1.82937	−	0.594399i	−0.0635368	−	0.0206443i	−0.340613	+	0.940204i	$0.610635\pi$
$830$		0			0
$831$	15.7872	−	5.12958i	0.547653	−	0.177943i
$832$		0			0
$833$	15.9581	−	31.3196i	0.552917	−	1.08516i
$834$		0			0
$835$	28.2038	+	4.16911i	0.976034	+	0.144278i
$836$		0			0
$837$	4.25788	−	0.674381i	0.147174	−	0.0233100i
$838$		0			0
$839$	−15.0999	+	10.9707i	−0.521305	+	0.378750i	−0.817095	−	0.576503i	$-0.804417\pi$
$839$	−15.0999	+	10.9707i	−0.521305	+	0.378750i	0.295790	+	0.955253i	$0.404417\pi$
$840$		0			0
$841$	2.49195	+	1.81051i	0.0859294	+	0.0624314i
$842$		0			0
$843$	−34.9982	+	34.9982i	−1.20540	+	1.20540i
$844$		0			0
$845$	−17.8433	−	24.0335i	−0.613827	−	0.826778i
$846$		0			0
$847$	−30.7921	+	15.6894i	−1.05803	+	0.539093i
$848$		0			0
$849$			43.6187i			1.49699i
$850$		0			0
$851$			2.63042i			0.0901696i
$852$		0			0
$853$	13.2729	−	6.76287i	0.454455	−	0.231556i	−0.211752	−	0.977323i	$-0.567917\pi$
$853$	13.2729	−	6.76287i	0.454455	−	0.231556i	0.666207	+	0.745767i	$0.267917\pi$
$854$		0			0
$855$	0.198566	+	19.2369i	0.00679082	+	0.657889i
$856$		0			0
$857$	−17.2553	+	17.2553i	−0.589430	+	0.589430i	−0.937477	−	0.348047i	$-0.886845\pi$
$857$	−17.2553	+	17.2553i	−0.589430	+	0.589430i	0.348047	+	0.937477i	$0.386845\pi$
$858$		0			0
$859$	−26.9260	−	19.5629i	−0.918704	−	0.667477i	0.0244974	−	0.999700i	$-0.492201\pi$
$859$	−26.9260	−	19.5629i	−0.918704	−	0.667477i	−0.943201	+	0.332223i	$0.892201\pi$
$860$		0			0
$861$	44.2759	−	32.1683i	1.50892	−	1.09629i
$862$		0			0
$863$	−34.5831	+	5.47742i	−1.17722	+	0.186454i	−0.714232	−	0.699909i	$-0.753224\pi$
$863$	−34.5831	+	5.47742i	−1.17722	+	0.186454i	−0.462991	+	0.886363i	$0.653224\pi$
$864$		0			0
$865$	−5.63761	−	33.3620i	−0.191684	−	1.13434i
$866$		0			0
$867$	24.8691	−	48.8083i	0.844598	−	1.65762i
$868$		0			0
$869$	1.87738	−	0.609998i	0.0636858	−	0.0206928i
$870$		0			0
$871$	1.70332	+	0.553441i	0.0577147	+	0.0187526i
$872$		0			0
$873$	−7.63213	−	1.20881i	−0.258308	−	0.0409120i
$874$		0			0
$875$	7.35084	+	38.6290i	0.248504	+	1.30590i
$876$		0			0
$877$	6.45449	−	40.7521i	0.217953	−	1.37610i	−0.599625	−	0.800281i	$-0.704684\pi$
$877$	6.45449	−	40.7521i	0.217953	−	1.37610i	0.817578	−	0.575818i	$-0.195316\pi$
$878$		0			0
$879$	−6.84791	+	21.0757i	−0.230974	+	0.710866i
$880$		0			0
$881$	14.7562	+	45.4149i	0.497149	+	1.53007i	0.813581	+	0.581452i	$0.197515\pi$
$881$	14.7562	+	45.4149i	0.497149	+	1.53007i	−0.316432	+	0.948615i	$0.602485\pi$
$882$		0			0
$883$	44.4263	+	22.6364i	1.49507	+	0.761774i	0.994580	−	0.103971i	$-0.0331549\pi$
$883$	44.4263	+	22.6364i	1.49507	+	0.761774i	0.500485	+	0.865745i	$0.333155\pi$
$884$		0			0
$885$	−24.3528	+	4.11520i	−0.818610	+	0.138331i
$886$		0			0
$887$	1.60109	+	10.1089i	0.0537592	+	0.339422i	0.999878	+	0.0156032i	$0.00496685\pi$
$887$	1.60109	+	10.1089i	0.0537592	+	0.339422i	−0.946119	+	0.323819i	$0.895033\pi$
$888$		0			0
$889$	26.0518	+	35.8573i	0.873750	+	1.20261i
$890$		0			0
$891$	−7.16485	+	9.86157i	−0.240032	+	0.330375i
$892$		0			0
$893$	−6.26628	−	6.26628i	−0.209693	−	0.209693i
$894$		0			0
$895$	16.3431	−	0.168696i	0.546291	−	0.00563889i
$896$		0			0
$897$	−32.7499	−	64.2754i	−1.09349	−	2.14609i
$898$		0			0
$899$	−7.63512			−0.254645
$900$		0			0
$901$	−42.3659			−1.41141
$902$		0			0
$903$	27.7407	+	54.4442i	0.923153	+	1.81179i
$904$		0			0
$905$	−7.59359	+	5.63773i	−0.252420	+	0.187404i
$906$		0			0
$907$	6.31185	+	6.31185i	0.209581	+	0.209581i	0.804090	−	0.594508i	$-0.202653\pi$
$907$	6.31185	+	6.31185i	0.209581	+	0.209581i	−0.594508	+	0.804090i	$0.702653\pi$
$908$		0			0
$909$	−11.2249	+	15.4497i	−0.372305	+	0.512434i
$910$		0			0
$911$	14.4677	+	19.9131i	0.479337	+	0.659751i	0.978377	−	0.206828i	$-0.0663140\pi$
$911$	14.4677	+	19.9131i	0.479337	+	0.659751i	−0.499040	+	0.866579i	$0.666314\pi$
$912$		0			0
$913$	1.84114	+	11.6245i	0.0609328	+	0.384715i
$914$		0			0
$915$	7.32377	−	49.5450i	0.242116	−	1.63791i
$916$		0			0
$917$	−10.5436	−	5.37222i	−0.348180	−	0.177406i
$918$		0			0
$919$	2.62738	+	8.08624i	0.0866692	+	0.266740i	0.984993	−	0.172593i	$-0.0552146\pi$
$919$	2.62738	+	8.08624i	0.0866692	+	0.266740i	−0.898324	+	0.439334i	$0.855215\pi$
$920$		0			0
$921$	10.6737	−	32.8504i	0.351712	−	1.08246i
$922$		0			0
$923$	5.16822	−	32.6309i	0.170114	−	1.07406i
$924$		0			0
$925$	−1.37411	+	1.43205i	−0.0451805	+	0.0470855i
$926$		0			0
$927$	−18.5756	−	2.94208i	−0.610103	−	0.0966307i
$928$		0			0
$929$	31.2253	+	10.1457i	1.02447	+	0.332870i	0.772602	−	0.634891i	$-0.218955\pi$
$929$	31.2253	+	10.1457i	1.02447	+	0.332870i	0.251868	+	0.967762i	$0.418955\pi$
$930$		0			0
$931$	29.4704	−	9.57552i	0.965854	−	0.313825i
$932$		0			0
$933$	17.1705	−	33.6991i	0.562138	−	1.10326i
$934$		0			0
$935$	14.0560	−	7.34562i	0.459681	−	0.240227i
$936$		0			0
$937$	26.2424	−	4.15639i	0.857301	−	0.135783i	0.287716	−	0.957716i	$-0.407104\pi$
$937$	26.2424	−	4.15639i	0.857301	−	0.135783i	0.569585	+	0.821932i	$0.307104\pi$
$938$		0			0
$939$	−34.2880	+	24.9117i	−1.11895	+	0.812961i
$940$		0			0
$941$	44.5680	+	32.3806i	1.45288	+	1.05558i	0.985149	+	0.171703i	$0.0549271\pi$
$941$	44.5680	+	32.3806i	1.45288	+	1.05558i	0.467727	+	0.883873i	$0.345073\pi$
$942$		0			0
$943$	34.4071	−	34.4071i	1.12045	−	1.12045i
$944$		0			0
$945$	−14.5722	+	20.4986i	−0.474034	+	0.666818i
$946$		0			0
$947$	11.4151	−	5.81628i	0.370941	−	0.189004i	−0.258576	−	0.965991i	$-0.583253\pi$
$947$	11.4151	−	5.81628i	0.370941	−	0.189004i	0.629516	+	0.776987i	$0.283253\pi$
$948$		0			0
$949$		−	17.7375i		−	0.575783i
$950$		0			0
$951$			55.3574i			1.79509i
$952$		0			0
$953$	−0.373655	+	0.190387i	−0.0121039	+	0.00616723i	−0.460032	−	0.887902i	$-0.652162\pi$
$953$	−0.373655	+	0.190387i	−0.0121039	+	0.00616723i	0.447928	+	0.894070i	$0.352162\pi$
$954$		0			0
$955$	−36.0229	−	11.2948i	−1.16567	−	0.365492i
$956$		0			0
$957$	9.19626	−	9.19626i	0.297273	−	0.297273i
$958$		0			0
$959$	3.50882	+	2.54931i	0.113306	+	0.0823215i
$960$		0			0
$961$	−23.6094	+	17.1532i	−0.761594	+	0.553330i
$962$		0			0
$963$	0.421475	−	0.0667551i	0.0135819	−	0.00215115i
$964$		0			0
$965$	−8.74777	+	17.6156i	−0.281601	+	0.567067i
$966$		0			0
$967$	−2.90835	+	5.70796i	−0.0935262	+	0.183555i	−0.933030	−	0.359798i	$-0.882846\pi$
$967$	−2.90835	+	5.70796i	−0.0935262	+	0.183555i	0.839504	+	0.543353i	$0.182846\pi$
$968$		0			0
$969$	76.1307	−	24.7364i	2.44567	−	0.794647i
$970$		0			0
$971$	−13.3367	−	4.33337i	−0.427996	−	0.139064i	0.0870944	−	0.996200i	$-0.472242\pi$
$971$	−13.3367	−	4.33337i	−0.427996	−	0.139064i	−0.515091	+	0.857136i	$0.672242\pi$
$972$		0			0
$973$	61.4159	+	9.72732i	1.96890	+	0.311843i
$974$		0			0
$975$	15.7473	−	52.1011i	0.504318	−	1.66857i
$976$		0			0
$977$	1.11885	−	7.06411i	0.0357950	−	0.226001i	−0.963305	−	0.268408i	$-0.913503\pi$
$977$	1.11885	−	7.06411i	0.0357950	−	0.226001i	0.999100	+	0.0424068i	$0.0135026\pi$
$978$		0			0
$979$	1.13276	−	3.48628i	0.0362032	−	0.111422i
$980$		0			0
$981$	−9.37921	−	28.8662i	−0.299455	−	0.921628i
$982$		0			0
$983$	−8.71793	−	4.44201i	−0.278059	−	0.141678i	0.309400	−	0.950932i	$-0.399872\pi$
$983$	−8.71793	−	4.44201i	−0.278059	−	0.141678i	−0.587459	+	0.809254i	$0.699872\pi$
$984$		0			0
$985$	5.21128	−	5.31999i	0.166045	−	0.169509i
$986$		0			0
$987$	1.79058	+	11.3053i	0.0569948	+	0.359851i
$988$		0			0
$989$	31.9332	+	43.9523i	1.01542	+	1.39760i
$990$		0			0
$991$	20.3554	−	28.0169i	0.646612	−	0.889985i	−0.352334	−	0.935874i	$-0.614612\pi$
$991$	20.3554	−	28.0169i	0.646612	−	0.889985i	0.998947	+	0.0458890i	$0.0146121\pi$
$992$		0			0
$993$	−39.8201	−	39.8201i	−1.26365	−	1.26365i
$994$		0			0
$995$	−3.21914	−	9.57024i	−0.102054	−	0.303397i
$996$		0			0
$997$	15.2102	+	29.8517i	0.481712	+	0.945414i	0.996132	+	0.0878749i	$0.0280076\pi$
$997$	15.2102	+	29.8517i	0.481712	+	0.945414i	−0.514419	+	0.857539i	$0.671992\pi$
$998$		0			0
$999$	−1.26939			−0.0401619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.223.3	✓	80
4.3	odd	2	inner	400.2.bi.d.223.8	yes	80
25.12	odd	20	inner	400.2.bi.d.287.8	yes	80
100.87	even	20	inner	400.2.bi.d.287.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.223.3	✓	80	1.1	even	1	trivial
400.2.bi.d.223.8	yes	80	4.3	odd	2	inner
400.2.bi.d.287.3	yes	80	100.87	even	20	inner
400.2.bi.d.287.8	yes	80	25.12	odd	20	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)

\(f(q)\)	\(=\)	\(q+(-0.962089 - 1.88821i) q^{3} +(0.712896 + 2.11938i) q^{5} +(-2.48695 - 2.48695i) q^{7} +(-0.876350 + 1.20619i) q^{9} +O(q^{10})\)	\(q+(-0.962089 - 1.88821i) q^{3} +(0.712896 + 2.11938i) q^{5} +(-2.48695 - 2.48695i) q^{7} +(-0.876350 + 1.20619i) q^{9} +(0.636880 + 0.876591i) q^{11} +(-0.803569 - 5.07354i) q^{13} +(3.31596 - 3.38513i) q^{15} +(-5.83245 - 2.97178i) q^{17} +(-1.78319 - 5.48809i) q^{19} +(-2.30321 + 7.08855i) q^{21} +(-1.03666 + 6.54522i) q^{23} +(-3.98356 + 3.02180i) q^{25} +(-3.15861 - 0.500275i) q^{27} +(5.38673 + 1.75025i) q^{29} +(-1.28204 + 0.416562i) q^{31} +(1.04245 - 2.04592i) q^{33} +(3.49787 - 7.04375i) q^{35} +(0.392049 - 0.0620945i) q^{37} +(-8.80678 + 6.39850i) q^{39} +(-5.94040 - 4.31596i) q^{41} +(5.79702 - 5.79702i) q^{43} +(-3.18113 - 0.997430i) q^{45} +(1.36833 - 0.697199i) q^{47} +5.36989i q^{49} +13.8720i q^{51} +(5.76669 - 2.93828i) q^{53} +(-1.40380 + 1.97471i) q^{55} +(-8.64706 + 8.64706i) q^{57} +(-4.21664 - 3.06357i) q^{59} +(8.55062 - 6.21239i) q^{61} +(5.17919 - 0.820303i) q^{63} +(10.1799 - 5.31998i) q^{65} +(-0.158287 + 0.310656i) q^{67} +(13.3561 - 4.33966i) q^{69} +(6.11680 + 1.98747i) q^{71} +(3.41052 + 0.540174i) q^{73} +(9.53831 + 4.61454i) q^{75} +(0.596149 - 3.76393i) q^{77} +(0.562975 - 1.73266i) q^{79} +(3.47642 + 10.6993i) q^{81} +(9.67823 + 4.93131i) q^{83} +(2.14041 - 14.4798i) q^{85} +(-1.87767 - 11.8551i) q^{87} +(-1.98855 - 2.73700i) q^{89} +(-10.6192 + 14.6161i) q^{91} +(2.02000 + 2.02000i) q^{93} +(10.3601 - 7.69170i) q^{95} +(2.35295 + 4.61793i) q^{97} -1.61547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 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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