LMFDB - Embedded newform 400.3.bg.f.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			97.3
Character	$\chi$	$=$	400.97
Dual form			400.3.bg.f.33.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33419 + 0.211315i) q^{3} +(-4.90670 - 0.961386i) q^{5} +(5.78356 + 5.78356i) q^{7} +(-6.82409 + 2.21728i) q^{9} +O(q^{10})$	\(q+(-1.33419 + 0.211315i) q^{3} +(-4.90670 - 0.961386i) q^{5} +(5.78356 + 5.78356i) q^{7} +(-6.82409 + 2.21728i) q^{9} +(5.64771 - 17.3819i) q^{11} +(-8.75031 - 4.45850i) q^{13} +(6.74965 + 0.245813i) q^{15} +(13.2695 + 2.10169i) q^{17} +(13.9237 + 19.1644i) q^{19} +(-8.93854 - 6.49423i) q^{21} +(2.96303 + 5.81527i) q^{23} +(23.1515 + 9.43447i) q^{25} +(19.4684 - 9.91967i) q^{27} +(17.0950 - 23.5293i) q^{29} +(25.1552 - 18.2763i) q^{31} +(-3.86208 + 24.3842i) q^{33} +(-22.8180 - 33.9384i) q^{35} +(9.97352 - 19.5741i) q^{37} +(12.6168 + 4.09943i) q^{39} +(-18.3883 - 56.5935i) q^{41} +(51.6910 - 51.6910i) q^{43} +(35.6155 - 4.31896i) q^{45} +(5.40431 + 34.1215i) q^{47} +17.8991i q^{49} -18.1482 q^{51} +(87.5908 - 13.8730i) q^{53} +(-44.4223 + 79.8581i) q^{55} +(-22.6267 - 22.6267i) q^{57} +(20.7741 - 6.74992i) q^{59} +(-36.8620 + 113.449i) q^{61} +(-52.2913 - 26.6438i) q^{63} +(38.6488 + 30.2890i) q^{65} +(-47.9275 - 7.59097i) q^{67} +(-5.18210 - 7.13255i) q^{69} +(7.81903 + 5.68086i) q^{71} +(16.0773 + 31.5535i) q^{73} +(-32.8822 - 7.69514i) q^{75} +(133.193 - 67.8652i) q^{77} +(-51.6285 + 71.0605i) q^{79} +(28.3658 - 20.6089i) q^{81} +(8.66416 - 54.7034i) q^{83} +(-63.0891 - 23.0695i) q^{85} +(-17.8359 + 35.0050i) q^{87} +(-70.5667 - 22.9285i) q^{89} +(-24.8219 - 76.3939i) q^{91} +(-29.6998 + 29.6998i) q^{93} +(-49.8953 - 107.420i) q^{95} +(-8.90175 - 56.2034i) q^{97} +131.138i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	$ 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) $ 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$	$1$

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
$3$	−1.33419	+	0.211315i	−0.444731	+	0.0704385i	−0.374784	−	0.927112i	$-0.622283\pi$
$3$	−1.33419	+	0.211315i	−0.444731	+	0.0704385i	−0.0699472	+	0.997551i	$0.522283\pi$
$4$		0			0
$5$	−4.90670	−	0.961386i	−0.981341	−	0.192277i
$5$	−4.90670	−	0.961386i	−0.981341	−	0.192277i
$6$		0			0
$7$	5.78356	+	5.78356i	0.826223	+	0.826223i	0.986992	−	0.160769i	$-0.0513975\pi$
$7$	5.78356	+	5.78356i	0.826223	+	0.826223i	−0.160769	+	0.986992i	$0.551398\pi$
$8$		0			0
$9$	−6.82409	+	2.21728i	−0.758232	+	0.246365i
$10$		0			0
$11$	5.64771	−	17.3819i	0.513428	−	1.58017i	−0.272695	−	0.962101i	$-0.587915\pi$
$11$	5.64771	−	17.3819i	0.513428	−	1.58017i	0.786123	−	0.618070i	$-0.212085\pi$
$12$		0			0
$13$	−8.75031	−	4.45850i	−0.673101	−	0.342962i	0.0838087	−	0.996482i	$-0.473292\pi$
$13$	−8.75031	−	4.45850i	−0.673101	−	0.342962i	−0.756909	+	0.653520i	$0.773292\pi$
$14$		0			0
$15$	6.74965	+	0.245813i	0.449976	+	0.0163875i
$16$		0			0
$17$	13.2695	+	2.10169i	0.780561	+	0.123629i	0.533984	−	0.845495i	$-0.320694\pi$
$17$	13.2695	+	2.10169i	0.780561	+	0.123629i	0.246577	+	0.969123i	$0.420694\pi$
$18$		0			0
$19$	13.9237	+	19.1644i	0.732829	+	1.00865i	0.998999	+	0.0447261i	$0.0142415\pi$
$19$	13.9237	+	19.1644i	0.732829	+	1.00865i	−0.266171	+	0.963926i	$0.585758\pi$
$20$		0			0
$21$	−8.93854	−	6.49423i	−0.425645	−	0.309249i
$22$		0			0
$23$	2.96303	+	5.81527i	0.128827	+	0.252838i	0.946406	−	0.322979i	$-0.104684\pi$
$23$	2.96303	+	5.81527i	0.128827	+	0.252838i	−0.817579	+	0.575816i	$0.804684\pi$
$24$		0			0
$25$	23.1515	+	9.43447i	0.926059	+	0.377379i
$26$		0			0
$27$	19.4684	−	9.91967i	0.721054	−	0.367395i
$28$		0			0
$29$	17.0950	−	23.5293i	0.589483	−	0.811354i	−0.405212	−	0.914223i	$-0.632802\pi$
$29$	17.0950	−	23.5293i	0.589483	−	0.811354i	0.994695	+	0.102869i	$0.0328023\pi$
$30$		0			0
$31$	25.1552	−	18.2763i	0.811456	−	0.589558i	−0.102796	−	0.994702i	$-0.532779\pi$
$31$	25.1552	−	18.2763i	0.811456	−	0.589558i	0.914253	+	0.405145i	$0.132779\pi$
$32$		0			0
$33$	−3.86208	+	24.3842i	−0.117033	+	0.738916i
$34$		0			0
$35$	−22.8180	−	33.9384i	−0.651942	−	0.969670i
$36$		0			0
$37$	9.97352	−	19.5741i	0.269555	−	0.529031i	−0.716060	−	0.698039i	$-0.754056\pi$
$37$	9.97352	−	19.5741i	0.269555	−	0.529031i	0.985615	+	0.169008i	$0.0540564\pi$
$38$		0			0
$39$	12.6168	+	4.09943i	0.323506	+	0.105114i
$40$		0			0
$41$	−18.3883	−	56.5935i	−0.448496	−	1.38033i	−0.878604	−	0.477551i	$-0.841525\pi$
$41$	−18.3883	−	56.5935i	−0.448496	−	1.38033i	0.430108	−	0.902777i	$-0.358475\pi$
$42$		0			0
$43$	51.6910	−	51.6910i	1.20212	−	1.20212i	0.228594	−	0.973522i	$-0.426587\pi$
$43$	51.6910	−	51.6910i	1.20212	−	1.20212i	0.973522	−	0.228594i	$-0.0734128\pi$
$44$		0			0
$45$	35.6155	−	4.31896i	0.791455	−	0.0959768i
$46$		0			0
$47$	5.40431	+	34.1215i	0.114985	+	0.725989i	0.976059	+	0.217508i	$0.0697928\pi$
$47$	5.40431	+	34.1215i	0.114985	+	0.725989i	−0.861073	+	0.508481i	$0.830207\pi$
$48$		0			0
$49$			17.8991i			0.365288i
$50$		0			0
$51$	−18.1482			−0.355848
$52$		0			0
$53$	87.5908	−	13.8730i	1.65266	−	0.261755i	0.740638	−	0.671904i	$-0.234523\pi$
$53$	87.5908	−	13.8730i	1.65266	−	0.261755i	0.912018	+	0.410149i	$0.134523\pi$
$54$		0			0
$55$	−44.4223	+	79.8581i	−0.807679	+	1.45196i
$56$		0			0
$57$	−22.6267	−	22.6267i	−0.396960	−	0.396960i
$58$		0			0
$59$	20.7741	−	6.74992i	0.352104	−	0.114405i	−0.127625	−	0.991823i	$-0.540735\pi$
$59$	20.7741	−	6.74992i	0.352104	−	0.114405i	0.479728	+	0.877417i	$0.340735\pi$
$60$		0			0
$61$	−36.8620	+	113.449i	−0.604294	+	1.85983i	−0.102724	+	0.994710i	$0.532756\pi$
$61$	−36.8620	+	113.449i	−0.604294	+	1.85983i	−0.501570	+	0.865117i	$0.667244\pi$
$62$		0			0
$63$	−52.2913	−	26.6438i	−0.830021	−	0.422917i
$64$		0			0
$65$	38.6488	+	30.2890i	0.594597	+	0.465984i
$66$		0			0
$67$	−47.9275	−	7.59097i	−0.715335	−	0.113298i	−0.211851	−	0.977302i	$-0.567949\pi$
$67$	−47.9275	−	7.59097i	−0.715335	−	0.113298i	−0.503485	+	0.864004i	$0.667949\pi$
$68$		0			0
$69$	−5.18210	−	7.13255i	−0.0751030	−	0.103370i
$70$		0			0
$71$	7.81903	+	5.68086i	0.110127	+	0.0800121i	0.641486	−	0.767135i	$-0.278318\pi$
$71$	7.81903	+	5.68086i	0.110127	+	0.0800121i	−0.531359	+	0.847147i	$0.678318\pi$
$72$		0			0
$73$	16.0773	+	31.5535i	0.220237	+	0.432240i	0.974517	−	0.224313i	$-0.0720138\pi$
$73$	16.0773	+	31.5535i	0.220237	+	0.432240i	−0.754280	+	0.656553i	$0.772014\pi$
$74$		0			0
$75$	−32.8822	−	7.69514i	−0.438429	−	0.102602i
$76$		0			0
$77$	133.193	−	67.8652i	1.72978	−	0.881366i
$78$		0			0
$79$	−51.6285	+	71.0605i	−0.653525	+	0.899500i	−0.999246	−	0.0388373i	$-0.987635\pi$
$79$	−51.6285	+	71.0605i	−0.653525	+	0.899500i	0.345720	+	0.938338i	$0.387635\pi$
$80$		0			0
$81$	28.3658	−	20.6089i	0.350195	−	0.254431i
$82$		0			0
$83$	8.66416	−	54.7034i	0.104388	−	0.659077i	−0.878898	−	0.477009i	$-0.841721\pi$
$83$	8.66416	−	54.7034i	0.104388	−	0.659077i	0.983286	−	0.182068i	$-0.0582791\pi$
$84$		0			0
$85$	−63.0891	−	23.0695i	−0.742225	−	0.271406i
$86$		0			0
$87$	−17.8359	+	35.0050i	−0.205011	+	0.402356i
$88$		0			0
$89$	−70.5667	−	22.9285i	−0.792885	−	0.257624i	−0.115553	−	0.993301i	$-0.536864\pi$
$89$	−70.5667	−	22.9285i	−0.792885	−	0.257624i	−0.677332	+	0.735678i	$0.736864\pi$
$90$		0			0
$91$	−24.8219	−	76.3939i	−0.272768	−	0.839494i
$92$		0			0
$93$	−29.6998	+	29.6998i	−0.319352	+	0.319352i
$94$		0			0
$95$	−49.8953	−	107.420i	−0.525214	−	1.13074i
$96$		0			0
$97$	−8.90175	−	56.2034i	−0.0917706	−	0.579417i	−0.990130	−	0.140155i	$-0.955240\pi$
$97$	−8.90175	−	56.2034i	−0.0917706	−	0.579417i	0.898359	−	0.439262i	$-0.144760\pi$
$98$		0			0
$99$			131.138i			1.32463i
$100$		0			0
$101$	−124.014			−1.22786			−0.613932	−	0.789359i	$-0.710413\pi$
$101$	−124.014			−1.22786			−0.613932	+	0.789359i	$0.710413\pi$
$102$		0			0
$103$	134.684	−	21.3318i	1.30761	−	0.207105i	0.536551	−	0.843868i	$-0.319727\pi$
$103$	134.684	−	21.3318i	1.30761	−	0.207105i	0.771060	+	0.636762i	$0.219727\pi$
$104$		0			0
$105$	37.6153	+	40.4586i	0.358241	+	0.385320i
$106$		0			0
$107$	−11.8267	−	11.8267i	−0.110530	−	0.110530i	0.649679	−	0.760209i	$-0.274903\pi$
$107$	−11.8267	−	11.8267i	−0.110530	−	0.110530i	−0.760209	+	0.649679i	$0.774903\pi$
$108$		0			0
$109$	−153.623	+	49.9153i	−1.40939	+	0.457938i	−0.912215	−	0.409712i	$-0.865629\pi$
$109$	−153.623	+	49.9153i	−1.40939	+	0.457938i	−0.497175	+	0.867650i	$0.665629\pi$
$110$		0			0
$111$	−9.17028	+	28.2232i	−0.0826152	+	0.254263i
$112$		0			0
$113$	134.444	+	68.5025i	1.18977	+	0.606217i	0.932867	−	0.360221i	$-0.117299\pi$
$113$	134.444	+	68.5025i	1.18977	+	0.606217i	0.256900	+	0.966438i	$0.417299\pi$
$114$		0			0
$115$	−8.94797	−	31.3824i	−0.0778085	−	0.272890i
$116$		0			0
$117$	69.5987	+	11.0233i	0.594860	+	0.0942166i
$118$		0			0
$119$	64.5899	+	88.9003i	0.542772	+	0.747062i
$120$		0			0
$121$	−172.342	−	125.214i	−1.42431	−	1.03482i
$122$		0			0
$123$	36.4927	+	71.6209i	0.296688	+	0.582283i
$124$		0			0
$125$	−104.527	−	68.5497i	−0.836218	−	0.548397i
$126$		0			0
$127$	−15.0489	+	7.66782i	−0.118496	+	0.0603766i	−0.512234	−	0.858846i	$-0.671182\pi$
$127$	−15.0489	+	7.66782i	−0.118496	+	0.0603766i	0.393738	+	0.919223i	$0.371182\pi$
$128$		0			0
$129$	−58.0426	+	79.8889i	−0.449943	+	0.619293i
$130$		0			0
$131$	102.714	−	74.6258i	0.784073	−	0.569663i	−0.122126	−	0.992515i	$-0.538971\pi$
$131$	102.714	−	74.6258i	0.784073	−	0.569663i	0.906199	+	0.422852i	$0.138971\pi$
$132$		0			0
$133$	−30.3096	+	191.367i	−0.227892	+	1.43885i
$134$		0			0
$135$	−105.063	+	29.9562i	−0.778241	+	0.221898i
$136$		0			0
$137$	10.0960	−	19.8145i	0.0736933	−	0.144631i	−0.851220	−	0.524808i	$-0.824137\pi$
$137$	10.0960	−	19.8145i	0.0736933	−	0.144631i	0.924914	+	0.380177i	$0.124137\pi$
$138$		0			0
$139$	41.0054	+	13.3235i	0.295003	+	0.0958522i	0.452779	−	0.891623i	$-0.350433\pi$
$139$	41.0054	+	13.3235i	0.295003	+	0.0958522i	−0.157777	+	0.987475i	$0.550433\pi$
$140$		0			0
$141$	−14.4208	−	44.3826i	−0.102275	−	0.314770i
$142$		0			0
$143$	−126.916	+	126.916i	−0.887527	+	0.887527i
$144$		0			0
$145$	−106.501	+	99.0162i	−0.734488	+	0.682870i
$146$		0			0
$147$	−3.78236	−	23.8809i	−0.0257303	−	0.162455i
$148$		0			0
$149$			138.783i			0.931429i	0.884935	+	0.465714i	$0.154203\pi$
$149$			138.783i			0.931429i	−0.884935	+	0.465714i	$0.845797\pi$
$150$		0			0
$151$	18.6672			0.123624			0.0618120	−	0.998088i	$-0.480312\pi$
$151$	18.6672			0.123624			0.0618120	+	0.998088i	$0.480312\pi$
$152$		0			0
$153$	−95.2125	+	15.0802i	−0.622304	+	0.0985633i
$154$		0			0
$155$	−140.999	+	65.4925i	−0.909674	+	0.422532i
$156$		0			0
$157$	−147.515	−	147.515i	−0.939584	−	0.939584i	0.0586924	−	0.998276i	$-0.481307\pi$
$157$	−147.515	−	147.515i	−0.939584	−	0.939584i	−0.998276	+	0.0586924i	$0.981307\pi$
$158$		0			0
$159$	−113.931	+	37.0186i	−0.716550	+	0.232821i
$160$		0			0
$161$	−16.4961	+	50.7698i	−0.102460	+	0.315340i
$162$		0			0
$163$	−9.94532	−	5.06740i	−0.0610143	−	0.0310883i	0.423217	−	0.906028i	$-0.360901\pi$
$163$	−9.94532	−	5.06740i	−0.0610143	−	0.0310883i	−0.484231	+	0.874940i	$0.660901\pi$
$164$		0			0
$165$	42.3927	−	115.933i	0.256926	−	0.702625i
$166$		0			0
$167$	183.910	+	29.1285i	1.10126	+	0.174422i	0.680498	−	0.732750i	$-0.261763\pi$
$167$	183.910	+	29.1285i	1.10126	+	0.174422i	0.420760	+	0.907172i	$0.361763\pi$
$168$		0			0
$169$	−42.6461	−	58.6973i	−0.252344	−	0.347321i
$170$		0			0
$171$	−137.510	−	99.9067i	−0.804151	−	0.584250i
$172$		0			0
$173$	17.7535	+	34.8433i	0.102622	+	0.201406i	0.936608	−	0.350379i	$-0.113947\pi$
$173$	17.7535	+	34.8433i	0.102622	+	0.201406i	−0.833987	+	0.551785i	$0.813947\pi$
$174$		0			0
$175$	79.3331	+	188.463i	0.453332	+	1.07693i
$176$		0			0
$177$	−26.2903	+	13.3956i	−0.148533	+	0.0756813i
$178$		0			0
$179$	115.567	−	159.064i	0.645624	−	0.888625i	−0.353276	−	0.935519i	$-0.614932\pi$
$179$	115.567	−	159.064i	0.645624	−	0.888625i	0.998900	+	0.0468941i	$0.0149323\pi$
$180$		0			0
$181$	169.766	−	123.342i	0.937931	−	0.681447i	−0.00999068	−	0.999950i	$-0.503180\pi$
$181$	169.766	−	123.342i	0.937931	−	0.681447i	0.947922	+	0.318503i	$0.103180\pi$
$182$		0			0
$183$	25.2074	−	159.153i	0.137745	−	0.869688i
$184$		0			0
$185$	−67.7554	+	86.4560i	−0.366245	+	0.467330i
$186$		0			0
$187$	111.474	−	218.780i	0.596116	−	1.16994i
$188$		0			0
$189$	169.968	+	55.2259i	0.899301	+	0.292201i
$190$		0			0
$191$	17.5106	+	53.8920i	0.0916783	+	0.282157i	0.986374	−	0.164520i	$-0.0526074\pi$
$191$	17.5106	+	53.8920i	0.0916783	+	0.282157i	−0.894695	+	0.446677i	$0.852607\pi$
$192$		0			0
$193$	81.1090	−	81.1090i	0.420254	−	0.420254i	−0.465037	−	0.885291i	$-0.653959\pi$
$193$	81.1090	−	81.1090i	0.420254	−	0.420254i	0.885291	+	0.465037i	$0.153959\pi$
$194$		0			0
$195$	−57.9655	−	32.2443i	−0.297259	−	0.165355i
$196$		0			0
$197$	−15.4375	−	97.4683i	−0.0783627	−	0.494763i	−0.995388	−	0.0959331i	$-0.969417\pi$
$197$	−15.4375	−	97.4683i	−0.0783627	−	0.494763i	0.917025	−	0.398830i	$-0.130583\pi$
$198$		0			0
$199$			200.052i			1.00529i	0.864494	+	0.502643i	$0.167639\pi$
$199$			200.052i			1.00529i	−0.864494	+	0.502643i	$0.832361\pi$
$200$		0			0
$201$	65.5486			0.326112
$202$		0			0
$203$	234.953	−	37.2129i	1.15740	−	0.183315i
$204$		0			0
$205$	35.8179	+	295.366i	0.174722	+	1.44081i
$206$		0			0
$207$	−33.1140	−	33.1140i	−0.159971	−	0.159971i
$208$		0			0
$209$	411.750	−	133.786i	1.97010	−	0.640123i
$210$		0			0
$211$	101.795	−	313.292i	0.482440	−	1.48480i	−0.353215	−	0.935542i	$-0.614911\pi$
$211$	101.795	−	313.292i	0.482440	−	1.48480i	0.835655	−	0.549255i	$-0.185089\pi$
$212$		0			0
$213$	−11.6325	−	5.92708i	−0.0546129	−	0.0278267i
$214$		0			0
$215$	−303.327	+	203.937i	−1.41082	+	0.948546i
$216$		0			0
$217$	251.188	+	39.7843i	1.15755	+	0.183338i
$218$		0			0
$219$	−28.1180	−	38.7011i	−0.128393	−	0.176717i
$220$		0			0
$221$	−106.742	−	77.5527i	−0.482996	−	0.350917i
$222$		0			0
$223$	79.9619	+	156.934i	0.358574	+	0.703740i	0.997871	−	0.0652194i	$-0.0207747\pi$
$223$	79.9619	+	156.934i	0.358574	+	0.703740i	−0.639297	+	0.768960i	$0.720775\pi$
$224$		0			0
$225$	−178.907	−	13.0484i	−0.795141	−	0.0579927i
$226$		0			0
$227$	−138.596	+	70.6184i	−0.610557	+	0.311094i	−0.731790	−	0.681530i	$-0.761315\pi$
$227$	−138.596	+	70.6184i	−0.610557	+	0.311094i	0.121233	+	0.992624i	$0.461315\pi$
$228$		0			0
$229$	−0.744748	+	1.02506i	−0.00325218	+	0.00447624i	−0.810640	−	0.585545i	$-0.800881\pi$
$229$	−0.744748	+	1.02506i	−0.00325218	+	0.00447624i	0.807388	+	0.590021i	$0.200881\pi$
$230$		0			0
$231$	−163.364	+	118.691i	−0.707204	+	0.513814i
$232$		0			0
$233$	47.8495	−	302.110i	0.205363	−	1.29661i	−0.642456	−	0.766323i	$-0.722084\pi$
$233$	47.8495	−	302.110i	0.205363	−	1.29661i	0.847819	−	0.530286i	$-0.177916\pi$
$234$		0			0
$235$	6.28656	−	172.620i	0.0267513	−	0.734552i
$236$		0			0
$237$	53.8662	−	105.718i	0.227283	−	0.446069i
$238$		0			0
$239$	−31.6776	−	10.2927i	−0.132542	−	0.0430656i	0.241995	−	0.970278i	$-0.422198\pi$
$239$	−31.6776	−	10.2927i	−0.132542	−	0.0430656i	−0.374537	+	0.927212i	$0.622198\pi$
$240$		0			0
$241$	−17.9549	−	55.2595i	−0.0745017	−	0.229293i	0.906870	−	0.421410i	$-0.138465\pi$
$241$	−17.9549	−	55.2595i	−0.0745017	−	0.229293i	−0.981372	+	0.192117i	$0.938465\pi$
$242$		0			0
$243$	−172.543	+	172.543i	−0.710052	+	0.710052i
$244$		0			0
$245$	17.2079	−	87.8256i	0.0702365	−	0.358472i
$246$		0			0
$247$	−36.3925	−	229.773i	−0.147338	−	0.930257i
$248$		0			0
$249$			74.8157i			0.300465i
$250$		0			0
$251$	−496.835			−1.97942			−0.989710	−	0.143085i	$-0.954298\pi$
$251$	−496.835			−1.97942			−0.989710	+	0.143085i	$0.954298\pi$
$252$		0			0
$253$	117.815	−	18.6600i	0.465670	−	0.0737549i
$254$		0			0
$255$	89.0480	+	17.4475i	0.349208	+	0.0684214i
$256$		0			0
$257$	318.776	+	318.776i	1.24037	+	1.24037i	0.959846	+	0.280527i	$0.0905091\pi$
$257$	318.776	+	318.776i	1.24037	+	1.24037i	0.280527	+	0.959846i	$0.409491\pi$
$258$		0			0
$259$	170.891	−	55.5257i	0.659809	−	0.214385i
$260$		0			0
$261$	−64.4869	+	198.470i	−0.247076	+	0.760422i
$262$		0			0
$263$	101.968	+	51.9553i	0.387711	+	0.197549i	0.636971	−	0.770888i	$-0.280187\pi$
$263$	101.968	+	51.9553i	0.387711	+	0.197549i	−0.249260	+	0.968437i	$0.580187\pi$
$264$		0			0
$265$	−443.119	−	16.1378i	−1.67215	−	0.0608973i
$266$		0			0
$267$	98.9948	+	15.6792i	0.370767	+	0.0587237i
$268$		0			0
$269$	153.320	+	211.027i	0.569963	+	0.784486i	0.992550	−	0.121836i	$-0.0388781\pi$
$269$	153.320	+	211.027i	0.569963	+	0.784486i	−0.422588	+	0.906322i	$0.638878\pi$
$270$		0			0
$271$	194.293	+	141.162i	0.716949	+	0.520894i	0.885408	−	0.464815i	$-0.153879\pi$
$271$	194.293	+	141.162i	0.716949	+	0.520894i	−0.168459	+	0.985709i	$0.553879\pi$
$272$		0			0
$273$	49.2604	+	96.6790i	0.180441	+	0.354136i
$274$		0			0
$275$	294.742	−	349.133i	1.07179	−	1.26957i
$276$		0			0
$277$	−406.553	+	207.149i	−1.46770	+	0.747830i	−0.991328	−	0.131414i	$-0.958048\pi$
$277$	−406.553	+	207.149i	−1.46770	+	0.747830i	−0.476372	+	0.879244i	$0.658048\pi$
$278$		0			0
$279$	−131.137	+	180.495i	−0.470026	+	0.646936i
$280$		0			0
$281$	155.214	−	112.770i	0.552364	−	0.401316i	−0.276292	−	0.961074i	$-0.589106\pi$
$281$	155.214	−	112.770i	0.552364	−	0.401316i	0.828656	+	0.559758i	$0.189106\pi$
$282$		0			0
$283$	−41.4223	+	261.530i	−0.146368	+	0.924134i	0.799755	+	0.600327i	$0.204963\pi$
$283$	−41.4223	+	261.530i	−0.146368	+	0.924134i	−0.946123	+	0.323807i	$0.895037\pi$
$284$		0			0
$285$	89.2695	+	132.775i	0.313226	+	0.465879i
$286$		0			0
$287$	220.962	−	433.662i	0.769901	−	1.51102i
$288$		0			0
$289$	−103.192	−	33.5291i	−0.357066	−	0.116018i
$290$		0			0
$291$	23.7533	+	73.1051i	0.0816265	+	0.251220i
$292$		0			0
$293$	356.013	−	356.013i	1.21506	−	1.21506i	0.245719	−	0.969341i	$-0.420976\pi$
$293$	356.013	−	356.013i	1.21506	−	1.21506i	0.969341	−	0.245719i	$-0.0790239\pi$
$294$		0			0
$295$	−108.422	+	13.1479i	−0.367531	+	0.0445692i
$296$		0			0
$297$	−62.4702	−	394.421i	−0.210337	−	1.32802i
$298$		0			0
$299$		−	64.0960i		−	0.214368i
$300$		0			0
$301$	597.916			1.98643
$302$		0			0
$303$	165.459	−	26.2061i	0.546069	−	0.0864889i
$304$		0			0
$305$	289.939	−	521.224i	0.950621	−	1.70893i
$306$		0			0
$307$	260.606	+	260.606i	0.848878	+	0.848878i	0.989993	−	0.141115i	$-0.0450688\pi$
$307$	260.606	+	260.606i	0.848878	+	0.848878i	−0.141115	+	0.989993i	$0.545069\pi$
$308$		0			0
$309$	−175.187	+	56.9216i	−0.566947	+	0.184212i
$310$		0			0
$311$	109.059	−	335.650i	0.350673	−	1.07926i	−0.607803	−	0.794088i	$-0.707949\pi$
$311$	109.059	−	335.650i	0.350673	−	1.07926i	0.958476	−	0.285173i	$-0.0920510\pi$
$312$		0			0
$313$	192.874	+	98.2741i	0.616210	+	0.313975i	0.734089	−	0.679053i	$-0.237609\pi$
$313$	192.874	+	98.2741i	0.616210	+	0.313975i	−0.117879	+	0.993028i	$0.537609\pi$
$314$		0			0
$315$	230.963	+	181.005i	0.733216	+	0.574620i
$316$		0			0
$317$	144.325	+	22.8588i	0.455283	+	0.0721098i	0.379864	−	0.925042i	$-0.375971\pi$
$317$	144.325	+	22.8588i	0.455283	+	0.0721098i	0.0754188	+	0.997152i	$0.475971\pi$
$318$		0			0
$319$	−312.435	−	430.030i	−0.979420	−	1.34806i
$320$		0			0
$321$	18.2782	+	13.2799i	0.0569416	+	0.0413705i
$322$		0			0
$323$	144.484	+	283.566i	0.447319	+	0.877913i
$324$		0			0
$325$	−160.519	−	185.775i	−0.493904	−	0.571617i
$326$		0			0
$327$	194.415	−	99.0596i	0.594543	−	0.302935i
$328$		0			0
$329$	−166.087	+	228.600i	−0.504825	+	0.694832i
$330$		0			0
$331$	−189.171	+	137.441i	−0.571513	+	0.415229i	−0.835655	−	0.549255i	$-0.814911\pi$
$331$	−189.171	+	137.441i	−0.571513	+	0.415229i	0.264141	+	0.964484i	$0.414911\pi$
$332$		0			0
$333$	−24.6588	+	155.690i	−0.0740506	+	0.467537i
$334$		0			0
$335$	227.868	+	83.3234i	0.680203	+	0.248727i
$336$		0			0
$337$	−65.4319	+	128.417i	−0.194160	+	0.381060i	−0.967477	−	0.252959i	$-0.918596\pi$
$337$	−65.4319	+	128.417i	−0.194160	+	0.381060i	0.773317	+	0.634020i	$0.218596\pi$
$338$		0			0
$339$	−193.849	−	62.9855i	−0.571827	−	0.185798i
$340$		0			0
$341$	−175.607	−	540.463i	−0.514977	−	1.58493i
$342$		0			0
$343$	179.874	−	179.874i	0.524414	−	0.524414i
$344$		0			0
$345$	18.5699	+	39.9793i	0.0538258	+	0.115882i
$346$		0			0
$347$	−90.5612	−	571.781i	−0.260983	−	1.64778i	−0.675221	−	0.737616i	$-0.735952\pi$
$347$	−90.5612	−	571.781i	−0.260983	−	1.64778i	0.414238	−	0.910169i	$-0.364048\pi$
$348$		0			0
$349$			78.3236i			0.224423i	0.993684	+	0.112212i	$0.0357934\pi$
$349$			78.3236i			0.224423i	−0.993684	+	0.112212i	$0.964207\pi$
$350$		0			0
$351$	−214.582			−0.611344
$352$		0			0
$353$	−524.312	+	83.0429i	−1.48530	+	0.235249i	−0.845784	−	0.533526i	$-0.820867\pi$
$353$	−524.312	+	83.0429i	−1.48530	+	0.235249i	−0.639519	+	0.768775i	$0.720867\pi$
$354$		0			0
$355$	−32.9042	−	35.3914i	−0.0926878	−	0.0996940i
$356$		0			0
$357$	−104.961	−	104.961i	−0.294009	−	0.294009i
$358$		0			0
$359$	45.1383	−	14.6663i	0.125733	−	0.0408532i	−0.245474	−	0.969403i	$-0.578944\pi$
$359$	45.1383	−	14.6663i	0.125733	−	0.0408532i	0.371208	+	0.928550i	$0.378944\pi$
$360$		0			0
$361$	−61.8480	+	190.349i	−0.171324	+	0.527282i
$362$		0			0
$363$	256.397	+	130.641i	0.706327	+	0.359892i
$364$		0			0
$365$	−48.5515	−	170.280i	−0.133018	−	0.466521i
$366$		0			0
$367$	518.283	+	82.0880i	1.41222	+	0.223673i	0.815490	−	0.578772i	$-0.196468\pi$
$367$	518.283	+	82.0880i	1.41222	+	0.223673i	0.596727	+	0.802445i	$0.296468\pi$
$368$		0			0
$369$	250.967	+	345.427i	0.680128	+	0.936116i
$370$		0			0
$371$	586.822	+	426.351i	1.58173	+	1.14919i
$372$		0			0
$373$	−171.249	−	336.095i	−0.459113	−	0.901060i	−0.998267	−	0.0588526i	$-0.981256\pi$
$373$	−171.249	−	336.095i	−0.459113	−	0.901060i	0.539154	−	0.842207i	$-0.318744\pi$
$374$		0			0
$375$	153.945	+	69.3703i	0.410520	+	0.184987i
$376$		0			0
$377$	−254.492	+	129.670i	−0.675045	+	0.343952i
$378$		0			0
$379$	−131.960	+	181.627i	−0.348179	+	0.479228i	−0.946808	−	0.321799i	$-0.895712\pi$
$379$	−131.960	+	181.627i	−0.348179	+	0.479228i	0.598629	+	0.801027i	$0.295712\pi$
$380$		0			0
$381$	18.4579	−	13.4104i	0.0484459	−	0.0351980i
$382$		0			0
$383$	21.5520	−	136.074i	0.0562717	−	0.355285i	−0.943446	−	0.331526i	$-0.892436\pi$
$383$	21.5520	−	136.074i	0.0562717	−	0.355285i	0.999718	−	0.0237592i	$-0.00756350\pi$
$384$		0			0
$385$	−718.783	+	204.945i	−1.86697	+	0.532323i
$386$		0			0
$387$	−238.131	+	467.357i	−0.615324	+	1.20764i
$388$		0			0
$389$	−301.065	−	97.8218i	−0.773945	−	0.251470i	−0.104692	−	0.994505i	$-0.533386\pi$
$389$	−301.065	−	97.8218i	−0.773945	−	0.251470i	−0.669253	+	0.743035i	$0.733386\pi$
$390$		0			0
$391$	27.0961	+	83.3932i	0.0692995	+	0.213282i
$392$		0			0
$393$	−121.270	+	121.270i	−0.308576	+	0.308576i
$394$		0			0
$395$	321.642	−	299.038i	0.814284	−	0.757058i
$396$		0			0
$397$	42.2230	+	266.585i	0.106355	+	0.671500i	0.982048	+	0.188631i	$0.0604051\pi$
$397$	42.2230	+	266.585i	0.106355	+	0.671500i	−0.875693	+	0.482868i	$0.839595\pi$
$398$		0			0
$399$		−	261.726i		−	0.655954i
$400$		0			0
$401$	211.424			0.527243			0.263621	−	0.964626i	$-0.415083\pi$
$401$	211.424			0.527243			0.263621	+	0.964626i	$0.415083\pi$
$402$		0			0
$403$	−301.600	+	47.7688i	−0.748388	+	0.118533i
$404$		0			0
$405$	−158.996	+	73.8515i	−0.392582	+	0.182349i
$406$		0			0
$407$	−283.907	−	283.907i	−0.697561	−	0.697561i
$408$		0			0
$409$	396.895	−	128.959i	0.970404	−	0.315303i	0.219425	−	0.975629i	$-0.429582\pi$
$409$	396.895	−	128.959i	0.970404	−	0.315303i	0.750979	+	0.660326i	$0.229582\pi$
$410$		0			0
$411$	−9.28289	+	28.5698i	−0.0225861	+	0.0695129i
$412$		0			0
$413$	159.187	+	81.1098i	0.385440	+	0.196392i
$414$		0			0
$415$	−95.1035	+	260.084i	−0.229165	+	0.626708i
$416$		0			0
$417$	−57.5246	−	9.11099i	−0.137949	−	0.0218489i
$418$		0			0
$419$	354.505	+	487.934i	0.846074	+	1.16452i	0.984714	+	0.174178i	$0.0557269\pi$
$419$	354.505	+	487.934i	0.846074	+	1.16452i	−0.138640	+	0.990343i	$0.544273\pi$
$420$		0			0
$421$	−138.860	−	100.888i	−0.329833	−	0.239638i	0.410527	−	0.911849i	$-0.365345\pi$
$421$	−138.860	−	100.888i	−0.329833	−	0.239638i	−0.740360	+	0.672211i	$0.765345\pi$
$422$		0			0
$423$	−112.536	−	220.865i	−0.266044	−	0.522140i
$424$		0			0
$425$	287.381	+	173.848i	0.676190	+	0.409054i
$426$		0			0
$427$	−869.335	+	442.948i	−2.03591	+	1.03735i
$428$		0			0
$429$	142.512	−	196.150i	0.332195	−	0.457227i
$430$		0			0
$431$	−137.927	+	100.210i	−0.320017	+	0.232506i	−0.736183	−	0.676783i	$-0.763374\pi$
$431$	−137.927	+	100.210i	−0.320017	+	0.232506i	0.416166	+	0.909289i	$0.363374\pi$
$432$		0			0
$433$	−34.0037	+	214.691i	−0.0785304	+	0.495822i	0.916804	+	0.399337i	$0.130760\pi$
$433$	−34.0037	+	214.691i	−0.0785304	+	0.495822i	−0.995335	+	0.0964843i	$0.969240\pi$
$434$		0			0
$435$	121.169	−	154.612i	0.278549	−	0.355430i
$436$		0			0
$437$	−70.1896	+	137.755i	−0.160617	+	0.315229i
$438$		0			0
$439$	−501.614	−	162.984i	−1.14263	−	0.371263i	−0.324267	−	0.945966i	$-0.605118\pi$
$439$	−501.614	−	162.984i	−1.14263	−	0.371263i	−0.818362	+	0.574703i	$0.805118\pi$
$440$		0			0
$441$	−39.6874	−	122.145i	−0.0899940	−	0.276973i
$442$		0			0
$443$	−212.287	+	212.287i	−0.479203	+	0.479203i	−0.904877	−	0.425674i	$-0.860037\pi$
$443$	−212.287	+	212.287i	−0.479203	+	0.479203i	0.425674	+	0.904877i	$0.360037\pi$
$444$		0			0
$445$	324.207	+	180.345i	0.728555	+	0.405270i
$446$		0			0
$447$	−29.3270	−	185.163i	−0.0656084	−	0.414235i
$448$		0			0
$449$			459.070i			1.02243i	0.859453	+	0.511214i	$0.170804\pi$
$449$			459.070i			1.02243i	−0.859453	+	0.511214i	$0.829196\pi$
$450$		0			0
$451$	−1087.55			−2.41142
$452$		0			0
$453$	−24.9057	+	3.94467i	−0.0549795	+	0.00870789i
$454$		0			0
$455$	48.3496	+	398.706i	0.106263	+	0.876277i
$456$		0			0
$457$	−49.0327	−	49.0327i	−0.107292	−	0.107292i	0.651423	−	0.758715i	$-0.274173\pi$
$457$	−49.0327	−	49.0327i	−0.107292	−	0.107292i	−0.758715	+	0.651423i	$0.774173\pi$
$458$		0			0
$459$	279.185	−	90.7128i	0.608247	−	0.197631i
$460$		0			0
$461$	−112.803	+	347.171i	−0.244692	+	0.753084i	0.750995	+	0.660308i	$0.229574\pi$
$461$	−112.803	+	347.171i	−0.244692	+	0.753084i	−0.995687	+	0.0927760i	$0.970426\pi$
$462$		0			0
$463$	−778.894	−	396.866i	−1.68228	−	0.857163i	−0.990889	−	0.134679i	$-0.957000\pi$
$463$	−778.894	−	396.866i	−1.68228	−	0.857163i	−0.691388	−	0.722484i	$-0.743000\pi$
$464$		0			0
$465$	174.281	−	117.175i	0.374798	−	0.251989i
$466$		0			0
$467$	−87.7553	−	13.8991i	−0.187913	−	0.0297625i	0.0617686	−	0.998090i	$-0.480326\pi$
$467$	−87.7553	−	13.8991i	−0.187913	−	0.0297625i	−0.249681	+	0.968328i	$0.580326\pi$
$468$		0			0
$469$	−233.289	−	321.094i	−0.497417	−	0.684636i
$470$		0			0
$471$	227.985	+	165.641i	0.484045	+	0.351679i
$472$		0			0
$473$	−606.550	−	1190.42i	−1.28235	−	2.51675i
$474$		0			0
$475$	141.549	+	575.047i	0.297998	+	1.21063i
$476$		0			0
$477$	−566.967	+	288.884i	−1.18861	+	0.605627i
$478$		0			0
$479$	253.215	−	348.521i	0.528634	−	0.727602i	−0.458288	−	0.888804i	$-0.651537\pi$
$479$	253.215	−	348.521i	0.528634	−	0.727602i	0.986921	+	0.161202i	$0.0515371\pi$
$480$		0			0
$481$	−174.543	+	126.813i	−0.362875	+	0.263644i
$482$		0			0
$483$	11.2805	−	71.2226i	0.0233552	−	0.147459i
$484$		0			0
$485$	−10.3550	+	284.332i	−0.0213504	+	0.586251i
$486$		0			0
$487$	−260.995	+	512.232i	−0.535924	+	1.05181i	0.451285	+	0.892380i	$0.350966\pi$
$487$	−260.995	+	512.232i	−0.535924	+	1.05181i	−0.987209	+	0.159430i	$0.949034\pi$
$488$		0			0
$489$	14.3398	+	4.65928i	0.0293247	+	0.00952819i
$490$		0			0
$491$	−248.979	−	766.279i	−0.507086	−	1.56065i	−0.797236	−	0.603668i	$-0.793705\pi$
$491$	−248.979	−	766.279i	−0.507086	−	1.56065i	0.290151	−	0.956981i	$-0.406295\pi$
$492$		0			0
$493$	276.294	−	276.294i	0.560434	−	0.560434i
$494$		0			0
$495$	126.074	−	643.456i	0.254696	−	1.29991i
$496$		0			0
$497$	12.3662	+	78.0774i	0.0248818	+	0.157097i
$498$		0			0
$499$		−	193.481i		−	0.387738i	−0.981027	−	0.193869i	$-0.937896\pi$
$499$		−	193.481i		−	0.387738i	0.981027	−	0.193869i	$-0.0621037\pi$
$500$		0			0
$501$	−251.527			−0.502050
$502$		0			0
$503$	−497.104	+	78.7336i	−0.988279	+	0.156528i	−0.629589	−	0.776929i	$-0.716777\pi$
$503$	−497.104	+	78.7336i	−0.988279	+	0.156528i	−0.358690	+	0.933457i	$0.616777\pi$
$504$		0			0
$505$	608.501	+	119.226i	1.20495	+	0.236090i
$506$		0			0
$507$	69.3018	+	69.3018i	0.136690	+	0.136690i
$508$		0			0
$509$	−478.829	+	155.581i	−0.940725	+	0.305660i	−0.738941	−	0.673770i	$-0.764674\pi$
$509$	−478.829	+	155.581i	−0.940725	+	0.305660i	−0.201784	+	0.979430i	$0.564674\pi$
$510$		0			0
$511$	−89.5075	+	275.476i	−0.175161	+	0.539091i
$512$		0			0
$513$	461.178	+	234.982i	0.898983	+	0.458054i
$514$		0			0
$515$	−681.362	−	24.8143i	−1.32303	−	0.0481830i
$516$		0			0
$517$	623.617	+	98.7713i	1.20622	+	0.191047i
$518$		0			0
$519$	−31.0495	−	42.7360i	−0.0598257	−	0.0823430i
$520$		0			0
$521$	203.613	+	147.934i	0.390813	+	0.283942i	0.765788	−	0.643093i	$-0.222349\pi$
$521$	203.613	+	147.934i	0.390813	+	0.283942i	−0.374976	+	0.927035i	$0.622349\pi$
$522$		0			0
$523$	278.793	+	547.163i	0.533065	+	1.04620i	0.987823	+	0.155584i	$0.0497261\pi$
$523$	278.793	+	547.163i	0.533065	+	1.04620i	−0.454757	+	0.890615i	$0.650274\pi$
$524$		0			0
$525$	−145.671	−	234.681i	−0.277468	−	0.447012i
$526$		0			0
$527$	372.208	−	189.649i	0.706277	−	0.359866i
$528$		0			0
$529$	285.901	−	393.508i	0.540455	−	0.743872i
$530$		0			0
$531$	−126.798	+	92.1242i	−0.238791	+	0.173492i
$532$		0			0
$533$	−91.4187	+	577.195i	−0.171517	+	1.08292i
$534$		0			0
$535$	46.6600	+	69.4001i	0.0872150	+	0.129720i
$536$		0			0
$537$	−120.576	+	236.643i	−0.224536	+	0.440676i
$538$		0			0
$539$	311.120	+	101.089i	0.577217	+	0.187549i
$540$		0			0
$541$	228.152	+	702.181i	0.421724	+	1.29793i	0.906097	+	0.423070i	$0.139048\pi$
$541$	228.152	+	702.181i	0.421724	+	1.29793i	−0.484373	+	0.874861i	$0.660952\pi$
$542$		0			0
$543$	−200.436	+	200.436i	−0.369127	+	0.369127i
$544$		0			0
$545$	801.773	−	97.2281i	1.47114	−	0.178400i
$546$		0			0
$547$	78.8624	+	497.917i	0.144172	+	0.910269i	0.948660	+	0.316299i	$0.102440\pi$
$547$	78.8624	+	497.917i	0.144172	+	0.910269i	−0.804487	+	0.593970i	$0.797560\pi$
$548$		0			0
$549$		−	855.923i		−	1.55906i
$550$		0			0
$551$	688.950			1.25036
$552$		0			0
$553$	−709.579	+	112.386i	−1.28314	+	0.203230i
$554$		0			0
$555$	72.1293	−	129.667i	0.129963	−	0.233634i
$556$		0			0
$557$	501.701	+	501.701i	0.900720	+	0.900720i	0.995498	−	0.0947780i	$-0.0302141\pi$
$557$	501.701	+	501.701i	0.900720	+	0.900720i	−0.0947780	+	0.995498i	$0.530214\pi$
$558$		0			0
$559$	−682.776	+	221.848i	−1.22142	+	0.396865i
$560$		0			0
$561$	−102.496	+	315.450i	−0.182702	+	0.562300i
$562$		0			0
$563$	−290.427	−	147.980i	−0.515856	−	0.262842i	0.176624	−	0.984278i	$-0.443482\pi$
$563$	−290.427	−	147.980i	−0.515856	−	0.262842i	−0.692481	+	0.721436i	$0.743482\pi$
$564$		0			0
$565$	−593.818	−	465.374i	−1.05101	−	0.823670i
$566$		0			0
$567$	283.248	+	44.8621i	0.499556	+	0.0791219i
$568$		0			0
$569$	−404.326	−	556.506i	−0.710590	−	0.978043i	−0.999784	−	0.0207724i	$-0.993387\pi$
$569$	−404.326	−	556.506i	−0.710590	−	0.978043i	0.289195	−	0.957270i	$-0.406613\pi$
$570$		0			0
$571$	619.955	+	450.424i	1.08574	+	0.788833i	0.978674	−	0.205419i	$-0.0658557\pi$
$571$	619.955	+	450.424i	1.08574	+	0.788833i	0.107062	+	0.994252i	$0.465856\pi$
$572$		0			0
$573$	−34.7507	−	68.2020i	−0.0606469	−	0.119026i
$574$		0			0
$575$	13.7345	+	162.587i	0.0238860	+	0.282759i
$576$		0			0
$577$	531.007	−	270.562i	0.920290	−	0.468911i	0.0713801	−	0.997449i	$-0.477260\pi$
$577$	531.007	−	270.562i	0.920290	−	0.468911i	0.848910	+	0.528538i	$0.177260\pi$
$578$		0			0
$579$	−91.0755	+	125.355i	−0.157298	+	0.216502i
$580$		0			0
$581$	366.490	−	266.271i	0.630792	−	0.458297i
$582$		0			0
$583$	253.549	−	1600.84i	0.434903	−	2.74587i
$584$		0			0
$585$	−330.902	−	120.999i	−0.565645	−	0.206837i
$586$		0			0
$587$	−334.421	+	656.338i	−0.569712	+	1.11812i	0.408933	+	0.912564i	$0.365901\pi$
$587$	−334.421	+	656.338i	−0.569712	+	1.11812i	−0.978645	+	0.205558i	$0.934099\pi$
$588$		0			0
$589$	700.508	+	227.609i	1.18932	+	0.386433i
$590$		0			0
$591$	41.1931	+	126.779i	0.0697007	+	0.214517i
$592$		0			0
$593$	3.94039	−	3.94039i	0.00664483	−	0.00664483i	−0.703777	−	0.710421i	$-0.748504\pi$
$593$	3.94039	−	3.94039i	0.00664483	−	0.00664483i	0.710421	+	0.703777i	$0.248504\pi$
$594$		0			0
$595$	−231.456	−	498.303i	−0.389001	−	0.837485i
$596$		0			0
$597$	−42.2740	−	266.908i	−0.0708107	−	0.447081i
$598$		0			0
$599$		−	75.4416i		−	0.125946i	−0.998015	−	0.0629729i	$-0.979942\pi$
$599$		−	75.4416i		−	0.125946i	0.998015	−	0.0629729i	$-0.0200582\pi$
$600$		0			0
$601$	−323.728			−0.538649			−0.269324	−	0.963050i	$-0.586800\pi$
$601$	−323.728			−0.538649			−0.269324	+	0.963050i	$0.586800\pi$
$602$		0			0
$603$	343.893	−	54.4673i	0.570303	−	0.0903271i
$604$		0			0
$605$	725.251	+	780.073i	1.19876	+	1.28938i
$606$		0			0
$607$	358.246	+	358.246i	0.590191	+	0.590191i	0.937683	−	0.347492i	$-0.112967\pi$
$607$	358.246	+	358.246i	0.590191	+	0.590191i	−0.347492	+	0.937683i	$0.612967\pi$
$608$		0			0
$609$	−305.609	+	99.2983i	−0.501821	+	0.163051i
$610$		0			0
$611$	104.841	−	322.669i	0.171590	−	0.528099i
$612$		0			0
$613$	−450.731	−	229.659i	−0.735287	−	0.374648i	0.0458986	−	0.998946i	$-0.485385\pi$
$613$	−450.731	−	229.659i	−0.735287	−	0.374648i	−0.781186	+	0.624299i	$0.785385\pi$
$614$		0			0
$615$	−110.203	−	386.506i	−0.179192	−	0.628465i
$616$		0			0
$617$	−919.191	−	145.586i	−1.48977	−	0.235957i	−0.642161	−	0.766570i	$-0.721962\pi$
$617$	−919.191	−	145.586i	−1.48977	−	0.235957i	−0.847614	+	0.530613i	$0.821962\pi$
$618$		0			0
$619$	−69.1504	−	95.1774i	−0.111713	−	0.153760i	0.749499	−	0.662005i	$-0.230294\pi$
$619$	−69.1504	−	95.1774i	−0.111713	−	0.153760i	−0.861212	+	0.508245i	$0.830294\pi$
$620$		0			0
$621$	115.371	+	83.8220i	0.185783	+	0.134979i
$622$		0			0
$623$	−275.518	−	540.735i	−0.442245	−	0.867954i
$624$		0			0
$625$	446.981	+	436.844i	0.715170	+	0.698950i
$626$		0			0
$627$	−521.083	+	265.505i	−0.831074	+	0.423453i
$628$		0			0
$629$	173.483	−	238.778i	0.275807	−	0.379616i
$630$		0			0
$631$	708.214	−	514.547i	1.12237	−	0.815448i	0.137801	−	0.990460i	$-0.455997\pi$
$631$	708.214	−	514.547i	1.12237	−	0.815448i	0.984566	+	0.175012i	$0.0559965\pi$
$632$		0			0
$633$	−69.6105	+	439.503i	−0.109969	+	0.694318i
$634$		0			0
$635$	81.2125	−	23.1559i	0.127894	−	0.0364660i
$636$		0			0
$637$	79.8032	−	156.623i	0.125280	−	0.245875i
$638$		0			0
$639$	−65.9538	−	21.4297i	−0.103214	−	0.0335363i
$640$		0			0
$641$	−272.899	−	839.896i	−0.425739	−	1.31029i	−0.902285	−	0.431140i	$-0.858111\pi$
$641$	−272.899	−	839.896i	−0.425739	−	1.31029i	0.476546	−	0.879149i	$-0.341889\pi$
$642$		0			0
$643$	261.164	−	261.164i	0.406164	−	0.406164i	−0.474234	−	0.880399i	$-0.657275\pi$
$643$	261.164	−	261.164i	0.406164	−	0.406164i	0.880399	+	0.474234i	$0.157275\pi$
$644$		0			0
$645$	361.602	−	336.189i	0.560623	−	0.521224i
$646$		0			0
$647$	2.03385	+	12.8412i	0.00314350	+	0.0198473i	0.989210	−	0.146503i	$-0.0468018\pi$
$647$	2.03385	+	12.8412i	0.00314350	+	0.0198473i	−0.986067	+	0.166350i	$0.946802\pi$
$648$		0			0
$649$		−	399.215i		−	0.615123i
$650$		0			0
$651$	−343.541			−0.527712
$652$		0			0
$653$	−202.735	+	32.1101i	−0.310467	+	0.0491731i	−0.309724	−	0.950827i	$-0.600237\pi$
$653$	−202.735	+	32.1101i	−0.310467	+	0.0491731i	−0.000743195		1.00000i	$0.500237\pi$
$654$		0			0
$655$	−575.729	+	267.419i	−0.878976	+	0.408274i
$656$		0			0
$657$	−179.676	−	179.676i	−0.273480	−	0.273480i
$658$		0			0
$659$	789.857	−	256.640i	1.19857	−	0.389438i	0.359334	−	0.933209i	$-0.383004\pi$
$659$	789.857	−	256.640i	1.19857	−	0.389438i	0.839234	+	0.543770i	$0.183004\pi$
$660$		0			0
$661$	−277.673	+	854.588i	−0.420080	+	1.29287i	0.487548	+	0.873096i	$0.337891\pi$
$661$	−277.673	+	854.588i	−0.420080	+	1.29287i	−0.907628	+	0.419776i	$0.862109\pi$
$662$		0			0
$663$	158.803	+	80.9140i	0.239521	+	0.122042i
$664$		0			0
$665$	332.698	−	909.843i	0.500297	−	1.36818i
$666$		0			0
$667$	187.482	+	29.6942i	0.281082	+	0.0445191i
$668$		0			0
$669$	−139.847	−	192.483i	−0.209039	−	0.287718i
$670$		0			0
$671$	1763.78	+	1281.46i	2.62858	+	1.90978i
$672$		0			0
$673$	444.366	+	872.118i	0.660277	+	1.29587i	0.941755	+	0.336299i	$0.109175\pi$
$673$	444.366	+	872.118i	0.660277	+	1.29587i	−0.281478	+	0.959568i	$0.590825\pi$
$674$		0			0
$675$	544.310	−	45.9804i	0.806385	−	0.0681192i
$676$		0			0
$677$	−148.782	+	75.8081i	−0.219766	+	0.111977i	−0.560408	−	0.828217i	$-0.689356\pi$
$677$	−148.782	+	75.8081i	−0.219766	+	0.111977i	0.340642	+	0.940193i	$0.389356\pi$
$678$		0			0
$679$	273.572	−	376.540i	0.402904	−	0.554550i
$680$		0			0
$681$	169.992	−	123.506i	0.249621	−	0.181360i
$682$		0			0
$683$	−189.128	+	1194.11i	−0.276907	+	1.74832i	0.321295	+	0.946979i	$0.395882\pi$
$683$	−189.128	+	1194.11i	−0.276907	+	1.74832i	−0.598203	+	0.801345i	$0.704118\pi$
$684$		0			0
$685$	−68.5874	+	87.5177i	−0.100128	+	0.127763i
$686$		0			0
$687$	0.777027	−	1.52500i	0.00113104	−	0.00221980i
$688$		0			0
$689$	−828.299	−	269.131i	−1.20218	−	0.390611i
$690$		0			0
$691$	32.5249	+	100.101i	0.0470693	+	0.144864i	0.971829	−	0.235687i	$-0.0757341\pi$
$691$	32.5249	+	100.101i	0.0470693	+	0.144864i	−0.924760	+	0.380552i	$0.875734\pi$
$692$		0			0
$693$	−758.445	+	758.445i	−1.09444	+	1.09444i
$694$		0			0
$695$	−188.392	−	104.796i	−0.271068	−	0.150786i
$696$		0			0
$697$	−125.063	−	789.615i	−0.179430	−	1.13288i
$698$		0			0
$699$			413.184i			0.591108i
$700$		0			0
$701$	−446.063			−0.636324			−0.318162	−	0.948036i	$-0.603066\pi$
$701$	−446.063			−0.636324			−0.318162	+	0.948036i	$0.603066\pi$
$702$		0			0
$703$	513.995	−	81.4088i	0.731145	−	0.115802i
$704$		0			0
$705$	28.0897	+	231.636i	0.0398435	+	0.328562i
$706$		0			0
$707$	−717.244	−	717.244i	−1.01449	−	1.01449i
$708$		0			0
$709$	94.2141	−	30.6120i	0.132883	−	0.0431763i	−0.241820	−	0.970321i	$-0.577744\pi$
$709$	94.2141	−	30.6120i	0.132883	−	0.0431763i	0.374704	+	0.927145i	$0.377744\pi$
$710$		0			0
$711$	194.756	−	599.398i	0.273919	−	0.843036i
$712$		0			0
$713$	180.817	+	92.1308i	0.253600	+	0.129216i
$714$		0			0
$715$	744.757	−	500.725i	1.04162	−	0.700315i
$716$		0			0
$717$	44.4390	+	7.03845i	0.0619791	+	0.00981653i
$718$		0			0
$719$	−155.847	−	214.505i	−0.216755	−	0.298338i	0.686768	−	0.726876i	$-0.259029\pi$
$719$	−155.847	−	214.505i	−0.216755	−	0.298338i	−0.903524	+	0.428539i	$0.859029\pi$
$720$		0			0
$721$	902.327	+	655.579i	1.25149	+	0.909263i
$722$		0			0
$723$	35.6325	+	69.9327i	0.0492842	+	0.0967257i
$724$		0			0
$725$	617.761	−	383.455i	0.852084	−	0.528903i
$726$		0			0
$727$	−44.0149	+	22.4267i	−0.0605432	+	0.0308483i	−0.484000	−	0.875068i	$-0.660817\pi$
$727$	−44.0149	+	22.4267i	−0.0605432	+	0.0308483i	0.423457	+	0.905916i	$0.360817\pi$
$728$		0			0
$729$	8.26376	−	11.3741i	0.0113357	−	0.0156023i
$730$		0			0
$731$	794.553	−	577.277i	1.08694	−	0.789708i
$732$		0			0
$733$	104.896	−	662.290i	0.143106	−	0.903533i	−0.806761	−	0.590878i	$-0.798782\pi$
$733$	104.896	−	662.290i	0.143106	−	0.903533i	0.949867	−	0.312655i	$-0.101218\pi$
$734$		0			0
$735$	−4.39982	+	120.813i	−0.00598616	+	0.164371i
$736$		0			0
$737$	−402.626	+	790.198i	−0.546304	+	1.07218i
$738$		0			0
$739$	1324.89	+	430.484i	1.79282	+	0.582522i	0.999649	−	0.0264775i	$-0.00842904\pi$
$739$	1324.89	+	430.484i	1.79282	+	0.582522i	0.793170	+	0.609000i	$0.208429\pi$
$740$		0			0
$741$	97.1093	+	298.872i	0.131052	+	0.403336i
$742$		0			0
$743$	−336.073	+	336.073i	−0.452319	+	0.452319i	−0.896124	−	0.443805i	$-0.853628\pi$
$743$	−336.073	+	336.073i	−0.452319	+	0.452319i	0.443805	+	0.896124i	$0.353628\pi$
$744$		0			0
$745$	133.424	−	680.966i	0.179093	−	0.914049i
$746$		0			0
$747$	62.1678	+	392.512i	0.0832232	+	0.525451i
$748$		0			0
$749$		−	136.801i		−	0.182644i
$750$		0			0
$751$	−886.583			−1.18054			−0.590269	−	0.807207i	$-0.700978\pi$
$751$	−886.583			−1.18054			−0.590269	+	0.807207i	$0.700978\pi$
$752$		0			0
$753$	662.873	−	104.989i	0.880310	−	0.139427i
$754$		0			0
$755$	−91.5946	−	17.9464i	−0.121317	−	0.0237701i
$756$		0			0
$757$	−442.028	−	442.028i	−0.583921	−	0.583921i	0.352058	−	0.935978i	$-0.385482\pi$
$757$	−442.028	−	442.028i	−0.583921	−	0.583921i	−0.935978	+	0.352058i	$0.885482\pi$
$758$		0			0
$759$	−153.244	+	49.7921i	−0.201903	+	0.0656022i
$760$		0			0
$761$	−397.737	+	1224.11i	−0.522650	+	1.60855i	0.246266	+	0.969202i	$0.420796\pi$
$761$	−397.737	+	1224.11i	−0.522650	+	1.60855i	−0.768916	+	0.639349i	$0.779204\pi$
$762$		0			0
$763$	−1177.18	−	599.802i	−1.54283	−	0.786111i
$764$		0			0
$765$	481.677	+	17.5420i	0.629644	+	0.0229307i
$766$		0			0
$767$	−211.874	−	33.5576i	−0.276238	−	0.0437518i
$768$		0			0
$769$	−616.021	−	847.881i	−0.801068	−	1.10258i	−0.992641	−	0.121097i	$-0.961359\pi$
$769$	−616.021	−	847.881i	−0.801068	−	1.10258i	0.191572	−	0.981478i	$-0.438641\pi$
$770$		0			0
$771$	−492.671	−	357.946i	−0.639002	−	0.464262i
$772$		0			0
$773$	8.35330	+	16.3943i	0.0108063	+	0.0212086i	0.896347	−	0.443354i	$-0.146212\pi$
$773$	8.35330	+	16.3943i	0.0108063	+	0.0212086i	−0.885540	+	0.464563i	$0.846212\pi$
$774$		0			0
$775$	754.806	−	185.797i	0.973943	−	0.239739i
$776$		0			0
$777$	−216.268	+	110.194i	−0.278337	+	0.141820i
$778$		0			0
$779$	828.545	−	1140.39i	1.06360	−	1.46392i
$780$		0			0
$781$	142.904	−	103.826i	0.182975	−	0.132939i
$782$		0			0
$783$	99.4108	−	627.655i	0.126961	−	0.801603i
$784$		0			0
$785$	581.992	+	865.629i	0.741391	+	1.10271i
$786$		0			0
$787$	−258.299	+	506.940i	−0.328207	+	0.644142i	−0.994864	−	0.101223i	$-0.967725\pi$
$787$	−258.299	+	506.940i	−0.328207	+	0.644142i	0.666657	+	0.745365i	$0.267725\pi$
$788$		0			0
$789$	−147.024	−	47.7710i	−0.186342	−	0.0605462i
$790$		0			0
$791$	381.375	+	1173.75i	0.482143	+	1.48388i
$792$		0			0
$793$	828.368	−	828.368i	1.04460	−	1.04460i
$794$		0			0
$795$	594.617	−	72.1070i	0.747946	−	0.0907007i
$796$		0			0
$797$	−186.252	−	1175.95i	−0.233692	−	1.47547i	−0.773561	−	0.633722i	$-0.781526\pi$
$797$	−186.252	−	1175.95i	−0.233692	−	1.47547i	0.539870	−	0.841749i	$-0.318474\pi$
$798$		0			0
$799$			464.134i			0.580894i
$800$		0			0
$801$	532.393			0.664660
$802$		0			0
$803$	639.259	−	101.249i	0.796089	−	0.126088i
$804$		0			0
$805$	129.751	−	233.253i	0.161181	−	0.289755i
$806$		0			0
$807$	−249.152	−	249.152i	−0.308738	−	0.308738i
$808$		0			0
$809$	607.670	−	197.444i	0.751137	−	0.244059i	0.0916667	−	0.995790i	$-0.470781\pi$
$809$	607.670	−	197.444i	0.751137	−	0.244059i	0.659470	+	0.751730i	$0.270781\pi$
$810$		0			0
$811$	−345.599	+	1063.64i	−0.426139	+	1.31152i	0.475761	+	0.879575i	$0.342173\pi$
$811$	−345.599	+	1063.64i	−0.426139	+	1.31152i	−0.901899	+	0.431946i	$0.857827\pi$
$812$		0			0
$813$	−289.055	−	147.281i	−0.355541	−	0.181157i
$814$		0			0
$815$	43.9270	+	34.4255i	0.0538982	+	0.0422399i
$816$		0			0
$817$	1710.36	+	270.894i	2.09346	+	0.331572i
$818$		0			0
$819$	338.774	+	466.282i	0.413643	+	0.569331i
$820$		0			0
$821$	−815.275	−	592.332i	−0.993026	−	0.721476i	−0.0324446	−	0.999474i	$-0.510329\pi$
$821$	−815.275	−	592.332i	−0.993026	−	0.721476i	−0.960582	+	0.277998i	$0.910329\pi$
$822$		0			0
$823$	−632.714	−	1241.77i	−0.768790	−	1.50884i	−0.858469	−	0.512865i	$-0.828584\pi$
$823$	−632.714	−	1241.77i	−0.768790	−	1.50884i	0.0896791	−	0.995971i	$-0.471416\pi$
$824$		0			0
$825$	−319.465	+	528.094i	−0.387230	+	0.640114i
$826$		0			0
$827$	−1332.47	+	678.926i	−1.61121	+	0.820951i	−0.611652	+	0.791127i	$0.709495\pi$
$827$	−1332.47	+	678.926i	−1.61121	+	0.820951i	−0.999555	+	0.0298236i	$0.990505\pi$
$828$		0			0
$829$	95.3372	−	131.220i	0.115003	−	0.158288i	−0.747635	−	0.664110i	$-0.768811\pi$
$829$	95.3372	−	131.220i	0.115003	−	0.158288i	0.862638	+	0.505822i	$0.168811\pi$
$830$		0			0
$831$	498.646	−	362.288i	0.600056	−	0.435966i
$832$		0			0
$833$	−37.6183	+	237.513i	−0.0451600	+	0.285129i
$834$		0			0
$835$	−874.389	−	319.734i	−1.04717	−	0.382914i
$836$		0			0
$837$	308.437	−	605.342i	0.368503	−	0.723228i
$838$		0			0
$839$	−512.901	−	166.652i	−0.611324	−	0.198631i	−0.0130396	−	0.999915i	$-0.504151\pi$
$839$	−512.901	−	166.652i	−0.611324	−	0.198631i	−0.598285	+	0.801284i	$0.704151\pi$
$840$		0			0
$841$	−1.50344	−	4.62711i	−0.00178768	−	0.00550191i
$842$		0			0
$843$	−183.256	+	183.256i	−0.217385	+	0.217385i
$844$		0			0
$845$	152.821	+	329.010i	0.180853	+	0.389360i
$846$		0			0
$847$	−272.568	−	1720.93i	−0.321804	−	2.03179i
$848$		0			0
$849$		−	357.685i		−	0.421301i
$850$		0			0
$851$	143.381			0.168485
$852$		0			0
$853$	−773.434	+	122.500i	−0.906722	+	0.143611i	−0.592342	−	0.805687i	$-0.701797\pi$
$853$	−773.434	+	122.500i	−0.906722	+	0.143611i	−0.314380	+	0.949297i	$0.601797\pi$
$854$		0			0
$855$	578.671	+	622.412i	0.676808	+	0.727968i
$856$		0			0
$857$	385.958	+	385.958i	0.450359	+	0.450359i	0.895474	−	0.445115i	$-0.146837\pi$
$857$	385.958	+	385.958i	0.450359	+	0.450359i	−0.445115	+	0.895474i	$0.646837\pi$
$858$		0			0
$859$	−370.355	+	120.335i	−0.431146	+	0.140088i	−0.516547	−	0.856259i	$-0.672783\pi$
$859$	−370.355	+	120.335i	−0.431146	+	0.140088i	0.0854009	+	0.996347i	$0.472783\pi$
$860$		0			0
$861$	−203.166	+	625.281i	−0.235965	+	0.726226i
$862$		0			0
$863$	104.393	+	53.1910i	0.120965	+	0.0616350i	0.513426	−	0.858134i	$-0.328376\pi$
$863$	104.393	+	53.1910i	0.120965	+	0.0616350i	−0.392461	+	0.919769i	$0.628376\pi$
$864$		0			0
$865$	−53.6135	−	188.034i	−0.0619809	−	0.217380i
$866$		0			0
$867$	144.763	+	22.9283i	0.166970	+	0.0264455i
$868$		0			0
$869$	943.582	+	1298.73i	1.08583	+	1.49451i
$870$		0			0
$871$	385.536	+	280.108i	0.442636	+	0.321594i
$872$		0			0
$873$	185.365	+	363.800i	0.212331	+	0.416724i
$874$		0			0
$875$	−208.078	−	1001.00i	−0.237804	−	1.14400i
$876$		0			0
$877$	−670.358	+	341.564i	−0.764376	+	0.389469i	−0.792293	−	0.610141i	$-0.791113\pi$
$877$	−670.358	+	341.564i	−0.764376	+	0.389469i	0.0279165	+	0.999610i	$0.491113\pi$
$878$		0			0
$879$	−399.759	+	550.220i	−0.454788	+	0.625962i
$880$		0			0
$881$	296.996	−	215.780i	0.337112	−	0.244926i	−0.406330	−	0.913726i	$-0.633192\pi$
$881$	296.996	−	215.780i	0.337112	−	0.244926i	0.743442	+	0.668800i	$0.233192\pi$
$882$		0			0
$883$	−24.1364	+	152.391i	−0.0273345	+	0.172583i	−0.997579	−	0.0695446i	$-0.977845\pi$
$883$	−24.1364	+	152.391i	−0.0273345	+	0.172583i	0.970244	+	0.242128i	$0.0778454\pi$
$884$		0			0
$885$	141.877	−	40.4530i	0.160313	−	0.0457096i
$886$		0			0
$887$	−393.810	+	772.896i	−0.443980	+	0.871360i	0.555233	+	0.831695i	$0.312629\pi$
$887$	−393.810	+	772.896i	−0.443980	+	0.871360i	−0.999213	+	0.0396652i	$0.987371\pi$
$888$		0			0
$889$	−131.384	−	42.6892i	−0.147788	−	0.0480193i
$890$		0			0
$891$	−198.020	−	609.444i	−0.222245	−	0.684000i
$892$		0			0
$893$	−578.669	+	578.669i	−0.648006	+	0.648006i
$894$		0			0
$895$	−719.973	+	669.375i	−0.804439	+	0.747905i
$896$		0			0
$897$	13.5445	+	85.5165i	0.0150998	+	0.0953361i
$898$		0			0
$899$		−	904.315i		−	1.00591i
$900$		0			0
$901$	1191.45			1.32236
$902$		0			0
$903$	−797.735	+	126.349i	−0.883427	+	0.139921i
$904$		0			0
$905$	−951.568	+	441.992i	−1.05146	+	0.488389i
$906$		0			0
$907$	1218.21	+	1218.21i	1.34311	+	1.34311i	0.892941	+	0.450174i	$0.148638\pi$
$907$	1218.21	+	1218.21i	1.34311	+	1.34311i	0.450174	+	0.892941i	$0.351362\pi$
$908$		0			0
$909$	846.285	−	274.975i	0.931006	−	0.302502i
$910$		0			0
$911$	−191.599	+	589.681i	−0.210317	+	0.647290i	0.789136	+	0.614219i	$0.210529\pi$
$911$	−191.599	+	589.681i	−0.210317	+	0.647290i	−0.999453	+	0.0330713i	$0.989471\pi$
$912$		0			0
$913$	−901.914	−	459.548i	−0.987858	−	0.503339i
$914$		0			0
$915$	−276.692	+	756.682i	−0.302396	+	0.826975i
$916$		0			0
$917$	1025.65	+	162.447i	1.11849	+	0.177151i
$918$		0			0
$919$	−633.477	−	871.906i	−0.689311	−	0.948755i	0.310688	−	0.950512i	$-0.399441\pi$
$919$	−633.477	−	871.906i	−0.689311	−	0.948755i	−0.999998	+	0.00175711i	$0.999441\pi$
$920$		0			0
$921$	−402.768	−	292.628i	−0.437316	−	0.317729i
$922$		0			0
$923$	−43.0908	−	84.5704i	−0.0466856	−	0.0916256i
$924$		0			0
$925$	415.573	−	359.075i	0.449268	−	0.388189i
$926$		0			0
$927$	−871.797	+	444.203i	−0.940450	+	0.479183i
$928$		0			0
$929$	−470.973	+	648.238i	−0.506967	+	0.697780i	−0.983404	−	0.181428i	$-0.941928\pi$
$929$	−470.973	+	648.238i	−0.506967	+	0.697780i	0.476437	+	0.879209i	$0.341928\pi$
$930$		0			0
$931$	−343.025	+	249.223i	−0.368448	+	0.267693i
$932$		0			0
$933$	−74.5781	+	470.868i	−0.0799337	+	0.504681i
$934$		0			0
$935$	−757.300	+	966.317i	−0.809947	+	1.03349i
$936$		0			0
$937$	14.7605	−	28.9690i	0.0157529	−	0.0309168i	−0.882996	−	0.469381i	$-0.844477\pi$
$937$	14.7605	−	28.9690i	0.0157529	−	0.0309168i	0.898749	+	0.438464i	$0.144477\pi$
$938$		0			0
$939$	−278.098	−	90.3594i	−0.296164	−	0.0962294i
$940$		0			0
$941$	−392.278	−	1207.31i	−0.416873	−	1.28300i	−0.910564	−	0.413367i	$-0.864353\pi$
$941$	−392.278	−	1207.31i	−0.416873	−	1.28300i	0.493691	−	0.869637i	$-0.335647\pi$
$942$		0			0
$943$	274.621	−	274.621i	0.291221	−	0.291221i
$944$		0			0
$945$	−780.889	−	434.382i	−0.826337	−	0.459663i
$946$		0			0
$947$	−194.720	−	1229.41i	−0.205618	−	1.29822i	−0.847245	−	0.531202i	$-0.821741\pi$
$947$	−194.720	−	1229.41i	−0.205618	−	1.29822i	0.641628	−	0.767016i	$-0.278259\pi$
$948$		0			0
$949$		−	347.784i		−	0.366474i
$950$		0			0
$951$	−197.388			−0.207558
$952$		0			0
$953$	898.962	−	142.382i	0.943297	−	0.149404i	0.334203	−	0.942501i	$-0.391533\pi$
$953$	898.962	−	142.382i	0.943297	−	0.149404i	0.609094	+	0.793098i	$0.291533\pi$
$954$		0			0
$955$	−34.1081	−	281.266i	−0.0357153	−	0.294520i
$956$		0			0
$957$	507.720	+	507.720i	0.530533	+	0.530533i
$958$		0			0
$959$	172.989	−	56.2075i	0.180385	−	0.0586106i
$960$		0			0
$961$	1.79361	−	5.52015i	0.00186640	−	0.00574418i
$962$		0			0
$963$	106.930	+	54.4833i	0.111038	+	0.0565766i
$964$		0			0
$965$	−475.955	+	320.001i	−0.493217	+	0.331607i
$966$		0			0
$967$	1779.93	+	281.913i	1.84067	+	0.291534i	0.977115	−	0.212714i	$-0.0682303\pi$
$967$	1779.93	+	281.913i	1.84067	+	0.291534i	0.863559	+	0.504248i	$0.168230\pi$
$968$		0			0
$969$	−252.691	−	347.800i	−0.260775	−	0.358927i
$970$		0			0
$971$	−1321.07	−	959.814i	−1.36053	−	0.988480i	−0.998411	−	0.0563459i	$-0.982055\pi$
$971$	−1321.07	−	959.814i	−1.36053	−	0.988480i	−0.362114	−	0.932134i	$-0.617945\pi$
$972$		0			0
$973$	160.100	+	314.214i	0.164543	+	0.322933i
$974$		0			0
$975$	253.420	+	213.940i	0.259918	+	0.219426i
$976$		0			0
$977$	−1410.23	+	718.546i	−1.44342	+	0.735461i	−0.987948	−	0.154787i	$-0.950531\pi$
$977$	−1410.23	+	718.546i	−1.44342	+	0.735461i	−0.455476	+	0.890248i	$0.650531\pi$
$978$		0			0
$979$	−797.081	+	1097.09i	−0.814179	+	1.12062i
$980$		0			0
$981$	937.664	−	681.253i	0.955825	−	0.694448i
$982$		0			0
$983$	−216.622	+	1367.70i	−0.220368	+	1.39135i	0.590933	+	0.806721i	$0.298760\pi$
$983$	−216.622	+	1367.70i	−0.220368	+	1.39135i	−0.811301	+	0.584628i	$0.801240\pi$
$984$		0			0
$985$	−17.9576	+	493.089i	−0.0182311	+	0.500598i
$986$		0			0
$987$	173.286	−	340.093i	0.175568	−	0.344573i
$988$		0			0
$989$	453.759	+	147.435i	0.458805	+	0.149075i
$990$		0			0
$991$	−208.328	−	641.167i	−0.210220	−	0.646990i	−0.999459	−	0.0329033i	$-0.989525\pi$
$991$	−208.328	−	641.167i	−0.210220	−	0.646990i	0.789239	−	0.614086i	$-0.210475\pi$
$992$		0			0
$993$	223.347	−	223.347i	0.224922	−	0.224922i
$994$		0			0
$995$	192.327	−	981.594i	0.193293	−	0.986527i
$996$		0			0
$997$	47.4107	+	299.339i	0.0475533	+	0.300240i	0.999990	−	0.00449705i	$-0.00143146\pi$
$997$	47.4107	+	299.339i	0.0475533	+	0.300240i	−0.952437	+	0.304737i	$0.901431\pi$
$998$		0			0
$999$		−	480.012i		−	0.480492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.f.97.3		64
4.3	odd	2		200.3.u.b.97.6	yes	64
25.8	odd	20	inner	400.3.bg.f.33.3		64
100.83	even	20		200.3.u.b.33.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.3.u.b.33.6	✓	64	100.83	even	20
200.3.u.b.97.6	yes	64	4.3	odd	2
400.3.bg.f.33.3		64	25.8	odd	20	inner
400.3.bg.f.97.3		64	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.33419 + 0.211315i) q^{3} +(-4.90670 - 0.961386i) q^{5} +(5.78356 + 5.78356i) q^{7} +(-6.82409 + 2.21728i) q^{9} +O(q^{10})\)	\(q+(-1.33419 + 0.211315i) q^{3} +(-4.90670 - 0.961386i) q^{5} +(5.78356 + 5.78356i) q^{7} +(-6.82409 + 2.21728i) q^{9} +(5.64771 - 17.3819i) q^{11} +(-8.75031 - 4.45850i) q^{13} +(6.74965 + 0.245813i) q^{15} +(13.2695 + 2.10169i) q^{17} +(13.9237 + 19.1644i) q^{19} +(-8.93854 - 6.49423i) q^{21} +(2.96303 + 5.81527i) q^{23} +(23.1515 + 9.43447i) q^{25} +(19.4684 - 9.91967i) q^{27} +(17.0950 - 23.5293i) q^{29} +(25.1552 - 18.2763i) q^{31} +(-3.86208 + 24.3842i) q^{33} +(-22.8180 - 33.9384i) q^{35} +(9.97352 - 19.5741i) q^{37} +(12.6168 + 4.09943i) q^{39} +(-18.3883 - 56.5935i) q^{41} +(51.6910 - 51.6910i) q^{43} +(35.6155 - 4.31896i) q^{45} +(5.40431 + 34.1215i) q^{47} +17.8991i q^{49} -18.1482 q^{51} +(87.5908 - 13.8730i) q^{53} +(-44.4223 + 79.8581i) q^{55} +(-22.6267 - 22.6267i) q^{57} +(20.7741 - 6.74992i) q^{59} +(-36.8620 + 113.449i) q^{61} +(-52.2913 - 26.6438i) q^{63} +(38.6488 + 30.2890i) q^{65} +(-47.9275 - 7.59097i) q^{67} +(-5.18210 - 7.13255i) q^{69} +(7.81903 + 5.68086i) q^{71} +(16.0773 + 31.5535i) q^{73} +(-32.8822 - 7.69514i) q^{75} +(133.193 - 67.8652i) q^{77} +(-51.6285 + 71.0605i) q^{79} +(28.3658 - 20.6089i) q^{81} +(8.66416 - 54.7034i) q^{83} +(-63.0891 - 23.0695i) q^{85} +(-17.8359 + 35.0050i) q^{87} +(-70.5667 - 22.9285i) q^{89} +(-24.8219 - 76.3939i) q^{91} +(-29.6998 + 29.6998i) q^{93} +(-49.8953 - 107.420i) q^{95} +(-8.90175 - 56.2034i) q^{97} +131.138i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9}+O(q^{10}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9	\( 64 q + 6 q^{5} + 4 q^{7} - 40 q^{9} - 16 q^{11} + 24 q^{13} - 82 q^{15} - 8 q^{17} + 50 q^{19} - 100 q^{21} + 48 q^{23} - 200 q^{25} - 90 q^{27} - 108 q^{31} + 260 q^{33} - 2 q^{35} - 94 q^{37} - 320 q^{39} - 184 q^{41} - 96 q^{43} + 146 q^{45} - 104 q^{47} - 200 q^{51} - 202 q^{53} + 12 q^{55} - 280 q^{57} + 600 q^{59} + 12 q^{61} + 34 q^{63} + 296 q^{65} - 58 q^{67} - 40 q^{69} + 470 q^{71} - 228 q^{73} + 614 q^{75} + 324 q^{77} - 560 q^{79} + 856 q^{81} + 308 q^{83} - 902 q^{85} + 840 q^{87} - 380 q^{89} - 62 q^{91} - 540 q^{93} + 16 q^{95} - 544 q^{97}+O(q^{100}) \) 64 * q + 6 * q^5 + 4 * q^7 - 40 * q^9 - 16 * q^11 + 24 * q^13 - 82 * q^15 - 8 * q^17 + 50 * q^19 - 100 * q^21 + 48 * q^23 - 200 * q^25 - 90 * q^27 - 108 * q^31 + 260 * q^33 - 2 * q^35 - 94 * q^37 - 320 * q^39 - 184 * q^41 - 96 * q^43 + 146 * q^45 - 104 * q^47 - 200 * q^51 - 202 * q^53 + 12 * q^55 - 280 * q^57 + 600 * q^59 + 12 * q^61 + 34 * q^63 + 296 * q^65 - 58 * q^67 - 40 * q^69 + 470 * q^71 - 228 * q^73 + 614 * q^75 + 324 * q^77 - 560 * q^79 + 856 * q^81 + 308 * q^83 - 902 * q^85 + 840 * q^87 - 380 * q^89 - 62 * q^91 - 540 * q^93 + 16 * q^95 - 544 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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