LMFDB - Embedded newform 400.2.bi.d.303.5

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			303.5
Character	$\chi$	$=$	400.303
Dual form			400.2.bi.d.367.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.492336 + 0.0779784i) q^{3} +(1.22885 - 1.86813i) q^{5} +(-2.22378 - 2.22378i) q^{7} +(-2.61686 + 0.850268i) q^{9} +O(q^{10})$	\(q+(-0.492336 + 0.0779784i) q^{3} +(1.22885 - 1.86813i) q^{5} +(-2.22378 - 2.22378i) q^{7} +(-2.61686 + 0.850268i) q^{9} +(-3.66397 - 1.19050i) q^{11} +(0.588152 - 1.15431i) q^{13} +(-0.459334 + 1.01557i) q^{15} +(0.254888 - 1.60930i) q^{17} +(-2.23450 + 1.62346i) q^{19} +(1.26825 + 0.921440i) q^{21} +(1.22347 + 2.40119i) q^{23} +(-1.97985 - 4.59132i) q^{25} +(2.55450 - 1.30158i) q^{27} +(0.145907 - 0.200824i) q^{29} +(-3.50271 - 4.82107i) q^{31} +(1.89674 + 0.300414i) q^{33} +(-6.88701 + 1.42162i) q^{35} +(5.47674 + 2.79054i) q^{37} +(-0.199557 + 0.614173i) q^{39} +(-3.78382 - 11.6454i) q^{41} +(8.17876 - 8.17876i) q^{43} +(-1.62731 + 5.93349i) q^{45} +(-0.962376 - 6.07621i) q^{47} +2.89039i q^{49} +0.812193i q^{51} +(0.973014 + 6.14337i) q^{53} +(-6.72648 + 5.38184i) q^{55} +(0.973529 - 0.973529i) q^{57} +(3.47557 + 10.6967i) q^{59} +(-1.86779 + 5.74847i) q^{61} +(7.71012 + 3.92850i) q^{63} +(-1.43366 - 2.51723i) q^{65} +(10.9816 + 1.73931i) q^{67} +(-0.789599 - 1.08679i) q^{69} +(2.07967 - 2.86241i) q^{71} +(-11.7833 + 6.00388i) q^{73} +(1.33277 + 2.10609i) q^{75} +(5.50046 + 10.7953i) q^{77} +(8.71792 + 6.33394i) q^{79} +(5.52191 - 4.01191i) q^{81} +(-0.233028 + 1.47128i) q^{83} +(-2.69317 - 2.45376i) q^{85} +(-0.0561755 + 0.110251i) q^{87} +(-5.41523 - 1.75951i) q^{89} +(-3.87486 + 1.25902i) q^{91} +(2.10045 + 2.10045i) q^{93} +(0.286970 + 6.16933i) q^{95} +(6.11852 - 0.969078i) q^{97} +10.6003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$-1$

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
$3$	−0.492336	+	0.0779784i	−0.284250	+	0.0450208i	−0.296932	−	0.954899i	$-0.595963\pi$
$3$	−0.492336	+	0.0779784i	−0.284250	+	0.0450208i	0.0126813	+	0.999920i	$0.495963\pi$
$4$		0			0
$5$	1.22885	−	1.86813i	0.549559	−	0.835455i
$5$	1.22885	−	1.86813i	0.549559	−	0.835455i
$6$		0			0
$7$	−2.22378	−	2.22378i	−0.840510	−	0.840510i	0.148415	−	0.988925i	$-0.452583\pi$
$7$	−2.22378	−	2.22378i	−0.840510	−	0.840510i	−0.988925	+	0.148415i	$0.952583\pi$
$8$		0			0
$9$	−2.61686	+	0.850268i	−0.872285	+	0.283423i
$10$		0			0
$11$	−3.66397	−	1.19050i	−1.10473	−	0.358948i	−0.300808	−	0.953685i	$-0.597256\pi$
$11$	−3.66397	−	1.19050i	−1.10473	−	0.358948i	−0.803921	+	0.594737i	$0.797256\pi$
$12$		0			0
$13$	0.588152	−	1.15431i	0.163124	−	0.320149i	−0.794947	−	0.606678i	$-0.792502\pi$
$13$	0.588152	−	1.15431i	0.163124	−	0.320149i	0.958071	+	0.286529i	$0.0925016\pi$
$14$		0			0
$15$	−0.459334	+	1.01557i	−0.118599	+	0.262220i
$16$		0			0
$17$	0.254888	−	1.60930i	0.0618195	−	0.390313i	−0.937306	−	0.348507i	$-0.886689\pi$
$17$	0.254888	−	1.60930i	0.0618195	−	0.390313i	0.999126	−	0.0418061i	$-0.0133112\pi$
$18$		0			0
$19$	−2.23450	+	1.62346i	−0.512629	+	0.372447i	−0.813820	−	0.581117i	$-0.802616\pi$
$19$	−2.23450	+	1.62346i	−0.512629	+	0.372447i	0.301191	+	0.953564i	$0.402616\pi$
$20$		0			0
$21$	1.26825	+	0.921440i	0.276756	+	0.201075i
$22$		0			0
$23$	1.22347	+	2.40119i	0.255111	+	0.500683i	0.982670	−	0.185361i	$-0.0593455\pi$
$23$	1.22347	+	2.40119i	0.255111	+	0.500683i	−0.727560	+	0.686044i	$0.759346\pi$
$24$		0			0
$25$	−1.97985	−	4.59132i	−0.395969	−	0.918264i
$26$		0			0
$27$	2.55450	−	1.30158i	0.491613	−	0.250489i
$28$		0			0
$29$	0.145907	−	0.200824i	0.0270943	−	0.0372921i	−0.795255	−	0.606275i	$-0.792663\pi$
$29$	0.145907	−	0.200824i	0.0270943	−	0.0372921i	0.822349	+	0.568983i	$0.192663\pi$
$30$		0			0
$31$	−3.50271	−	4.82107i	−0.629105	−	0.865889i	0.368871	−	0.929481i	$-0.379744\pi$
$31$	−3.50271	−	4.82107i	−0.629105	−	0.865889i	−0.997976	+	0.0635917i	$0.979744\pi$
$32$		0			0
$33$	1.89674	+	0.300414i	0.330180	+	0.0522953i
$34$		0			0
$35$	−6.88701	+	1.42162i	−1.16412	+	0.240298i
$36$		0			0
$37$	5.47674	+	2.79054i	0.900371	+	0.458762i	0.841966	−	0.539531i	$-0.181398\pi$
$37$	5.47674	+	2.79054i	0.900371	+	0.458762i	0.0584051	+	0.998293i	$0.481398\pi$
$38$		0			0
$39$	−0.199557	+	0.614173i	−0.0319547	+	0.0983464i
$40$		0			0
$41$	−3.78382	−	11.6454i	−0.590933	−	1.81870i	−0.574010	−	0.818848i	$-0.694613\pi$
$41$	−3.78382	−	11.6454i	−0.590933	−	1.81870i	−0.0169227	−	0.999857i	$-0.505387\pi$
$42$		0			0
$43$	8.17876	−	8.17876i	1.24725	−	1.24725i	0.290318	−	0.956930i	$-0.406239\pi$
$43$	8.17876	−	8.17876i	1.24725	−	1.24725i	0.956930	−	0.290318i	$-0.0937612\pi$
$44$		0			0
$45$	−1.62731	+	5.93349i	−0.242585	+	0.884512i
$46$		0			0
$47$	−0.962376	−	6.07621i	−0.140377	−	0.886306i	−0.952880	−	0.303348i	$-0.901895\pi$
$47$	−0.962376	−	6.07621i	−0.140377	−	0.886306i	0.812503	−	0.582957i	$-0.198105\pi$
$48$		0			0
$49$			2.89039i			0.412913i
$50$		0			0
$51$			0.812193i			0.113730i
$52$		0			0
$53$	0.973014	+	6.14337i	0.133654	+	0.843857i	0.959858	+	0.280486i	$0.0904957\pi$
$53$	0.973014	+	6.14337i	0.133654	+	0.843857i	−0.826204	+	0.563371i	$0.809504\pi$
$54$		0			0
$55$	−6.72648	+	5.38184i	−0.906998	+	0.725687i
$56$		0			0
$57$	0.973529	−	0.973529i	0.128947	−	0.128947i
$58$		0			0
$59$	3.47557	+	10.6967i	0.452481	+	1.39259i	0.874067	+	0.485806i	$0.161474\pi$
$59$	3.47557	+	10.6967i	0.452481	+	1.39259i	−0.421586	+	0.906789i	$0.638526\pi$
$60$		0			0
$61$	−1.86779	+	5.74847i	−0.239146	+	0.736016i	0.757398	+	0.652953i	$0.226470\pi$
$61$	−1.86779	+	5.74847i	−0.239146	+	0.736016i	−0.996544	+	0.0830626i	$0.973530\pi$
$62$		0			0
$63$	7.71012	+	3.92850i	0.971384	+	0.494945i
$64$		0			0
$65$	−1.43366	−	2.51723i	−0.177824	−	0.312223i
$66$		0			0
$67$	10.9816	+	1.73931i	1.34162	+	0.212491i	0.785628	−	0.618699i	$-0.212340\pi$
$67$	10.9816	+	1.73931i	1.34162	+	0.212491i	0.555988	+	0.831190i	$0.312340\pi$
$68$		0			0
$69$	−0.789599	−	1.08679i	−0.0950565	−	0.130834i
$70$		0			0
$71$	2.07967	−	2.86241i	0.246811	−	0.339706i	−0.667580	−	0.744538i	$-0.732670\pi$
$71$	2.07967	−	2.86241i	0.246811	−	0.339706i	0.914391	+	0.404832i	$0.132670\pi$
$72$		0			0
$73$	−11.7833	+	6.00388i	−1.37913	+	0.702701i	−0.977071	−	0.212914i	$-0.931705\pi$
$73$	−11.7833	+	6.00388i	−1.37913	+	0.702701i	−0.402057	+	0.915615i	$0.631705\pi$
$74$		0			0
$75$	1.33277	+	2.10609i	0.153895	+	0.243190i
$76$		0			0
$77$	5.50046	+	10.7953i	0.626836	+	1.23023i
$78$		0			0
$79$	8.71792	+	6.33394i	0.980843	+	0.712624i	0.957897	−	0.287113i	$-0.0926954\pi$
$79$	8.71792	+	6.33394i	0.980843	+	0.712624i	0.0229461	+	0.999737i	$0.492695\pi$
$80$		0			0
$81$	5.52191	−	4.01191i	0.613546	−	0.445767i
$82$		0			0
$83$	−0.233028	+	1.47128i	−0.0255781	+	0.161494i	−0.997171	−	0.0751638i	$-0.976052\pi$
$83$	−0.233028	+	1.47128i	−0.0255781	+	0.161494i	0.971593	+	0.236658i	$0.0760520\pi$
$84$		0			0
$85$	−2.69317	−	2.45376i	−0.292115	−	0.266147i
$86$		0			0
$87$	−0.0561755	+	0.110251i	−0.00602265	+	0.0118201i
$88$		0			0
$89$	−5.41523	−	1.75951i	−0.574013	−	0.186508i	0.00760361	−	0.999971i	$-0.497580\pi$
$89$	−5.41523	−	1.75951i	−0.574013	−	0.186508i	−0.581617	+	0.813463i	$0.697580\pi$
$90$		0			0
$91$	−3.87486	+	1.25902i	−0.406196	+	0.131981i
$92$		0			0
$93$	2.10045	+	2.10045i	0.217806	+	0.217806i
$94$		0			0
$95$	0.286970	+	6.16933i	0.0294425	+	0.632960i
$96$		0			0
$97$	6.11852	−	0.969078i	0.621241	−	0.0983949i	0.162124	−	0.986770i	$-0.448166\pi$
$97$	6.11852	−	0.969078i	0.621241	−	0.0983949i	0.459118	+	0.888376i	$0.348166\pi$
$98$		0			0
$99$	10.6003			1.06537
$100$		0			0
$101$	7.86566			0.782662			0.391331	−	0.920250i	$-0.372015\pi$
$101$	7.86566			0.782662			0.391331	+	0.920250i	$0.372015\pi$
$102$		0			0
$103$	10.5728	−	1.67457i	1.04177	−	0.165000i	0.387974	−	0.921670i	$-0.373175\pi$
$103$	10.5728	−	1.67457i	1.04177	−	0.165000i	0.653797	+	0.756670i	$0.273175\pi$
$104$		0			0
$105$	3.27987	−	1.23695i	0.320082	−	0.120714i
$106$		0			0
$107$	−13.3591	−	13.3591i	−1.29147	−	1.29147i	−0.933877	−	0.357593i	$-0.883597\pi$
$107$	−13.3591	−	13.3591i	−1.29147	−	1.29147i	−0.357593	−	0.933877i	$-0.616403\pi$
$108$		0			0
$109$	−8.23666	+	2.67625i	−0.788929	+	0.256339i	−0.675648	−	0.737224i	$-0.736136\pi$
$109$	−8.23666	+	2.67625i	−0.788929	+	0.256339i	−0.113281	+	0.993563i	$0.536136\pi$
$110$		0			0
$111$	−2.91400	−	0.946815i	−0.276584	−	0.0898677i
$112$		0			0
$113$	−1.58696	+	3.11458i	−0.149288	+	0.292995i	−0.953525	−	0.301314i	$-0.902575\pi$
$113$	−1.58696	+	3.11458i	−0.149288	+	0.292995i	0.804236	+	0.594310i	$0.202575\pi$
$114$		0			0
$115$	5.98921	+	0.665106i	0.558497	+	0.0620215i
$116$		0			0
$117$	−0.557633	+	3.52076i	−0.0515532	+	0.325494i
$118$		0			0
$119$	−4.14555	+	3.01192i	−0.380022	+	0.276102i
$120$		0			0
$121$	3.10821	+	2.25824i	0.282564	+	0.205295i
$122$		0			0
$123$	2.77100	+	5.43839i	0.249852	+	0.490363i
$124$		0			0
$125$	−11.0101	−	1.94343i	−0.984776	−	0.173826i
$126$		0			0
$127$	17.4518	−	8.89212i	1.54859	−	0.789048i	0.549668	−	0.835383i	$-0.314754\pi$
$127$	17.4518	−	8.89212i	1.54859	−	0.789048i	0.998926	+	0.0463353i	$0.0147543\pi$
$128$		0			0
$129$	−3.38893	+	4.66446i	−0.298379	+	0.410683i
$130$		0			0
$131$	−10.9922	−	15.1294i	−0.960390	−	1.32186i	−0.946755	−	0.321956i	$-0.895660\pi$
$131$	−10.9922	−	15.1294i	−0.960390	−	1.32186i	−0.0136351	−	0.999907i	$-0.504340\pi$
$132$		0			0
$133$	8.57924	+	1.35882i	0.743915	+	0.117825i
$134$		0			0
$135$	0.707570	−	6.37159i	0.0608979	−	0.548379i
$136$		0			0
$137$	−20.2085	−	10.2967i	−1.72653	−	0.879710i	−0.975669	−	0.219247i	$-0.929640\pi$
$137$	−20.2085	−	10.2967i	−1.72653	−	0.879710i	−0.750858	−	0.660463i	$-0.770360\pi$
$138$		0			0
$139$	−3.31034	+	10.1882i	−0.280779	+	0.864150i	0.706853	+	0.707361i	$0.250114\pi$
$139$	−3.31034	+	10.1882i	−0.280779	+	0.864150i	−0.987632	+	0.156789i	$0.949886\pi$
$140$		0			0
$141$	0.947625	+	2.91649i	0.0798044	+	0.245613i
$142$		0			0
$143$	−3.52918	+	3.52918i	−0.295125	+	0.295125i
$144$		0			0
$145$	−0.195868	−	0.519358i	−0.0162660	−	0.0431303i
$146$		0			0
$147$	−0.225388	−	1.42304i	−0.0185897	−	0.117371i
$148$		0			0
$149$		−	2.31129i		−	0.189348i	−0.995508	−	0.0946740i	$-0.969819\pi$
$149$		−	2.31129i		−	0.189348i	0.995508	−	0.0946740i	$-0.0301809\pi$
$150$		0			0
$151$			9.07081i			0.738172i	0.929395	+	0.369086i	$0.120329\pi$
$151$			9.07081i			0.738172i	−0.929395	+	0.369086i	$0.879671\pi$
$152$		0			0
$153$	0.701331	+	4.42803i	0.0566993	+	0.357985i
$154$		0			0
$155$	−13.3107	+	0.619155i	−1.06914	+	0.0497317i
$156$		0			0
$157$	9.72218	−	9.72218i	0.775914	−	0.775914i	−0.203219	−	0.979133i	$-0.565140\pi$
$157$	9.72218	−	9.72218i	0.775914	−	0.775914i	0.979133	+	0.203219i	$0.0651404\pi$
$158$		0			0
$159$	−0.958100	−	2.94873i	−0.0759822	−	0.233849i
$160$		0			0
$161$	2.61900	−	8.06045i	0.206406	−	0.635252i
$162$		0			0
$163$	1.21454	+	0.618838i	0.0951299	+	0.0484711i	0.500908	−	0.865500i	$-0.332999\pi$
$163$	1.21454	+	0.618838i	0.0951299	+	0.0484711i	−0.405778	+	0.913972i	$0.632999\pi$
$164$		0			0
$165$	2.89202	−	3.17419i	0.225144	−	0.247111i
$166$		0			0
$167$	−0.439489	−	0.0696082i	−0.0340087	−	0.00538645i	0.139407	−	0.990235i	$-0.455480\pi$
$167$	−0.439489	−	0.0696082i	−0.0340087	−	0.00538645i	−0.173416	+	0.984849i	$0.555480\pi$
$168$		0			0
$169$	6.65469	+	9.15940i	0.511899	+	0.704569i
$170$		0			0
$171$	4.46698	−	6.14828i	0.341599	−	0.470170i
$172$		0			0
$173$	14.4008	−	7.33756i	1.09487	−	0.557865i	0.189240	−	0.981931i	$-0.439398\pi$
$173$	14.4008	−	7.33756i	1.09487	−	0.557865i	0.905631	+	0.424066i	$0.139398\pi$
$174$		0			0
$175$	−5.80734	+	14.6128i	−0.438993	+	1.10463i
$176$		0			0
$177$	−2.54526	−	4.99536i	−0.191314	−	0.375474i
$178$		0			0
$179$	−4.78835	−	3.47894i	−0.357898	−	0.260028i	0.394277	−	0.918992i	$-0.370995\pi$
$179$	−4.78835	−	3.47894i	−0.357898	−	0.260028i	−0.752175	+	0.658963i	$0.770995\pi$
$180$		0			0
$181$	−2.22645	+	1.61761i	−0.165491	+	0.120236i	−0.667448	−	0.744656i	$-0.732613\pi$
$181$	−2.22645	+	1.61761i	−0.165491	+	0.120236i	0.501957	+	0.864892i	$0.332613\pi$
$182$		0			0
$183$	0.471324	−	2.97582i	0.0348413	−	0.219979i
$184$		0			0
$185$	11.9432	−	6.80213i	0.878082	−	0.500102i
$186$		0			0
$187$	−2.84977	+	5.59299i	−0.208396	+	0.409000i
$188$		0			0
$189$	−8.57507	−	2.78621i	−0.623745	−	0.202667i
$190$		0			0
$191$	−23.5840	+	7.66291i	−1.70648	+	0.554468i	−0.989741	−	0.142874i	$-0.954365\pi$
$191$	−23.5840	+	7.66291i	−1.70648	+	0.554468i	−0.716738	+	0.697343i	$0.754365\pi$
$192$		0			0
$193$	1.21567	+	1.21567i	0.0875056	+	0.0875056i	0.749505	−	0.661999i	$-0.230292\pi$
$193$	1.21567	+	1.21567i	0.0875056	+	0.0875056i	−0.661999	+	0.749505i	$0.730292\pi$
$194$		0			0
$195$	0.902132	+	1.12753i	0.0646030	+	0.0807438i
$196$		0			0
$197$	9.10163	−	1.44156i	0.648465	−	0.102707i	0.176467	−	0.984307i	$-0.443533\pi$
$197$	9.10163	−	1.44156i	0.648465	−	0.102707i	0.471998	+	0.881600i	$0.343533\pi$
$198$		0			0
$199$	−15.8533			−1.12381			−0.561904	−	0.827202i	$-0.689931\pi$
$199$	−15.8533			−1.12381			−0.561904	+	0.827202i	$0.689931\pi$
$200$		0			0
$201$	−5.54227			−0.390921
$202$		0			0
$203$	−0.771055	+	0.122123i	−0.0541174	+	0.00857136i
$204$		0			0
$205$	−26.4049	−	7.24178i	−1.84420	−	0.505788i
$206$		0			0
$207$	−5.24330	−	5.24330i	−0.364434	−	0.364434i
$208$		0			0
$209$	10.1199	−	3.28814i	0.700005	−	0.227445i
$210$		0			0
$211$	17.4751	+	5.67800i	1.20303	+	0.390889i	0.840876	−	0.541227i	$-0.182040\pi$
$211$	17.4751	+	5.67800i	1.20303	+	0.390889i	0.362158	+	0.932117i	$0.382040\pi$
$212$		0			0
$213$	−0.800688	+	1.57144i	−0.0548622	+	0.107673i
$214$		0			0
$215$	−5.22853	−	25.3295i	−0.356583	−	1.72746i
$216$		0			0
$217$	−2.93173	+	18.5102i	−0.199019	+	1.25656i
$218$		0			0
$219$	5.33316	−	3.87477i	0.360381	−	0.261832i
$220$		0			0
$221$	−1.70772	−	1.24073i	−0.114874	−	0.0834608i
$222$		0			0
$223$	−8.93303	−	17.5321i	−0.598200	−	1.17403i	−0.969401	−	0.245481i	$-0.921054\pi$
$223$	−8.93303	−	17.5321i	−0.598200	−	1.17403i	0.371201	−	0.928552i	$-0.378946\pi$
$224$		0			0
$225$	9.08483	+	10.3314i	0.605655	+	0.688761i
$226$		0			0
$227$	−1.38568	+	0.706041i	−0.0919711	+	0.0468616i	−0.499371	−	0.866388i	$-0.666436\pi$
$227$	−1.38568	+	0.706041i	−0.0919711	+	0.0468616i	0.407400	+	0.913250i	$0.366436\pi$
$228$		0			0
$229$	12.8250	−	17.6521i	0.847499	−	1.16648i	−0.136910	−	0.990584i	$-0.543717\pi$
$229$	12.8250	−	17.6521i	0.847499	−	1.16648i	0.984408	−	0.175898i	$-0.0562829\pi$
$230$		0			0
$231$	−3.54987	−	4.88598i	−0.233564	−	0.321474i
$232$		0			0
$233$	−16.7797	−	2.65765i	−1.09928	−	0.174108i	−0.419664	−	0.907680i	$-0.637852\pi$
$233$	−16.7797	−	2.65765i	−1.09928	−	0.174108i	−0.679612	+	0.733572i	$0.737852\pi$
$234$		0			0
$235$	−12.5338	−	5.66891i	−0.817614	−	0.369799i
$236$		0			0
$237$	−4.78606	−	2.43862i	−0.310888	−	0.158405i
$238$		0			0
$239$	1.98615	−	6.11273i	0.128473	−	0.395400i	−0.866045	−	0.499967i	$-0.833346\pi$
$239$	1.98615	−	6.11273i	0.128473	−	0.395400i	0.994518	+	0.104567i	$0.0333456\pi$
$240$		0			0
$241$	−0.554711	−	1.70722i	−0.0357321	−	0.109972i	0.931600	−	0.363486i	$-0.118414\pi$
$241$	−0.554711	−	1.70722i	−0.0357321	−	0.109972i	−0.967332	+	0.253514i	$0.918414\pi$
$242$		0			0
$243$	−8.48758	+	8.48758i	−0.544478	+	0.544478i
$244$		0			0
$245$	5.39964	+	3.55186i	0.344970	+	0.226920i
$246$		0			0
$247$	0.559754	+	3.53415i	0.0356163	+	0.224873i
$248$		0			0
$249$		−	0.742536i		−	0.0470563i
$250$		0			0
$251$			6.80852i			0.429750i	0.976642	+	0.214875i	$0.0689344\pi$
$251$			6.80852i			0.429750i	−0.976642	+	0.214875i	$0.931066\pi$
$252$		0			0
$253$	−1.62414	−	10.2544i	−0.102109	−	0.644690i
$254$		0			0
$255$	1.51728	+	0.998064i	0.0950160	+	0.0625012i
$256$		0			0
$257$	10.2912	−	10.2912i	0.641948	−	0.641948i	−0.309086	−	0.951034i	$-0.600023\pi$
$257$	10.2912	−	10.2912i	0.641948	−	0.641948i	0.951034	+	0.309086i	$0.100023\pi$
$258$		0			0
$259$	−5.97352	−	18.3846i	−0.371177	−	1.14236i
$260$		0			0
$261$	−0.211064	+	0.649588i	−0.0130645	+	0.0402085i
$262$		0			0
$263$	−7.31713	−	3.72826i	−0.451193	−	0.229895i	0.213601	−	0.976921i	$-0.431481\pi$
$263$	−7.31713	−	3.72826i	−0.451193	−	0.229895i	−0.664794	+	0.747026i	$0.731481\pi$
$264$		0			0
$265$	12.6723	+	5.73157i	0.778455	+	0.352087i
$266$		0			0
$267$	2.80332	+	0.444002i	0.171560	+	0.0271725i
$268$		0			0
$269$	−8.17183	−	11.2476i	−0.498245	−	0.685776i	0.483637	−	0.875269i	$-0.339316\pi$
$269$	−8.17183	−	11.2476i	−0.498245	−	0.685776i	−0.981882	+	0.189493i	$0.939316\pi$
$270$		0			0
$271$	7.67781	−	10.5676i	0.466394	−	0.641936i	−0.509425	−	0.860515i	$-0.670142\pi$
$271$	7.67781	−	10.5676i	0.466394	−	0.641936i	0.975819	+	0.218579i	$0.0701420\pi$
$272$		0			0
$273$	1.80956	−	0.922015i	0.109519	−	0.0558029i
$274$		0			0
$275$	1.78816	+	19.1795i	0.107830	+	1.15656i
$276$		0			0
$277$	10.6609	+	20.9232i	0.640552	+	1.25715i	0.951769	+	0.306816i	$0.0992635\pi$
$277$	10.6609	+	20.9232i	0.640552	+	1.25715i	−0.311217	+	0.950339i	$0.600737\pi$
$278$		0			0
$279$	13.2653	+	9.63779i	0.794172	+	0.576999i
$280$		0			0
$281$	17.6833	−	12.8477i	1.05490	−	0.766427i	0.0817587	−	0.996652i	$-0.473946\pi$
$281$	17.6833	−	12.8477i	1.05490	−	0.766427i	0.973137	+	0.230225i	$0.0739463\pi$
$282$		0			0
$283$	1.01310	−	6.39647i	0.0602226	−	0.380231i	−0.939107	−	0.343625i	$-0.888345\pi$
$283$	1.01310	−	6.39647i	0.0602226	−	0.380231i	0.999330	−	0.0366063i	$-0.0116547\pi$
$284$		0			0
$285$	−0.622360	−	3.01501i	−0.0368654	−	0.178593i
$286$		0			0
$287$	−17.4824	+	34.3112i	−1.03195	+	2.02532i
$288$		0			0
$289$	13.6431	+	4.43291i	0.802534	+	0.260759i
$290$		0			0
$291$	−2.93680	+	0.954224i	−0.172158	+	0.0559376i
$292$		0			0
$293$	−8.48383	−	8.48383i	−0.495630	−	0.495630i	0.414444	−	0.910075i	$-0.363976\pi$
$293$	−8.48383	−	8.48383i	−0.495630	−	0.495630i	−0.910075	+	0.414444i	$0.863976\pi$
$294$		0			0
$295$	24.2539	+	6.65184i	1.41211	+	0.387285i
$296$		0			0
$297$	−10.9091	+	1.72784i	−0.633012	+	0.100259i
$298$		0			0
$299$	3.49131			0.201908
$300$		0			0
$301$	−36.3755			−2.09665
$302$		0			0
$303$	−3.87255	+	0.613351i	−0.222472	+	0.0352361i
$304$		0			0
$305$	8.44367	+	10.5533i	0.483483	+	0.604280i
$306$		0			0
$307$	−13.5971	−	13.5971i	−0.776028	−	0.776028i	0.203124	−	0.979153i	$-0.434890\pi$
$307$	−13.5971	−	13.5971i	−0.776028	−	0.776028i	−0.979153	+	0.203124i	$0.934890\pi$
$308$		0			0
$309$	−5.07480	+	1.64890i	−0.288695	+	0.0938028i
$310$		0			0
$311$	25.4229	+	8.26039i	1.44160	+	0.468404i	0.922396	−	0.386247i	$-0.126229\pi$
$311$	25.4229	+	8.26039i	1.44160	+	0.468404i	0.519204	+	0.854651i	$0.326229\pi$
$312$		0			0
$313$	−8.12137	+	15.9391i	−0.459047	+	0.900930i	0.539225	+	0.842162i	$0.318717\pi$
$313$	−8.12137	+	15.9391i	−0.459047	+	0.900930i	−0.998272	+	0.0587682i	$0.981283\pi$
$314$		0			0
$315$	16.8136	−	9.57599i	0.947337	−	0.539546i
$316$		0			0
$317$	0.747468	−	4.71933i	0.0419820	−	0.265064i	−0.957765	−	0.287552i	$-0.907159\pi$
$317$	0.747468	−	4.71933i	0.0419820	−	0.265064i	0.999747	+	0.0224879i	$0.00715871\pi$
$318$		0			0
$319$	−0.773681	+	0.562112i	−0.0433178	+	0.0314722i
$320$		0			0
$321$	7.61887	+	5.53543i	0.425244	+	0.308958i
$322$		0			0
$323$	2.04308	+	4.00978i	0.113680	+	0.223110i
$324$		0			0
$325$	−6.46427	−	0.415029i	−0.358573	−	0.0230217i
$326$		0			0
$327$	3.84651	−	1.95990i	0.212713	−	0.108383i
$328$		0			0
$329$	−11.3720	+	15.6523i	−0.626960	+	0.862937i
$330$		0			0
$331$	12.4389	+	17.1207i	0.683705	+	0.941039i	0.999971	−	0.00763141i	$-0.00242918\pi$
$331$	12.4389	+	17.1207i	0.683705	+	0.941039i	−0.316266	+	0.948671i	$0.602429\pi$
$332$		0			0
$333$	−16.7045	−	2.64574i	−0.915404	−	0.144986i
$334$		0			0
$335$	16.7440	−	18.3777i	0.914824	−	1.00408i
$336$		0			0
$337$	−20.2626	−	10.3243i	−1.10377	−	0.562400i	−0.195468	−	0.980710i	$-0.562623\pi$
$337$	−20.2626	−	10.3243i	−1.10377	−	0.562400i	−0.908304	+	0.418310i	$0.862623\pi$
$338$		0			0
$339$	0.538447	−	1.65717i	0.0292444	−	0.0900050i
$340$		0			0
$341$	7.09436	+	21.8342i	0.384181	+	1.18239i
$342$		0			0
$343$	−9.13886	+	9.13886i	−0.493452	+	0.493452i
$344$		0			0
$345$	−3.00057	+	0.139573i	−0.161545	+	0.00751436i
$346$		0			0
$347$	4.11605	+	25.9877i	0.220961	+	1.39509i	0.809735	+	0.586796i	$0.199611\pi$
$347$	4.11605	+	25.9877i	0.220961	+	1.39509i	−0.588773	+	0.808298i	$0.700389\pi$
$348$		0			0
$349$		−	12.3219i		−	0.659575i	−0.944055	−	0.329788i	$-0.893023\pi$
$349$		−	12.3219i		−	0.659575i	0.944055	−	0.329788i	$-0.106977\pi$
$350$		0			0
$351$		−	3.71422i		−	0.198250i
$352$		0			0
$353$	−1.72305	−	10.8789i	−0.0917085	−	0.579025i	−0.990159	−	0.139949i	$-0.955306\pi$
$353$	−1.72305	−	10.8789i	−0.0917085	−	0.579025i	0.898450	−	0.439075i	$-0.144694\pi$
$354$		0			0
$355$	−2.79177	−	7.40258i	−0.148172	−	0.392888i
$356$		0			0
$357$	1.80614	−	1.80614i	0.0955909	−	0.0955909i
$358$		0			0
$359$	−0.0740977	−	0.228049i	−0.00391073	−	0.0120360i	0.949082	−	0.315029i	$-0.102014\pi$
$359$	−0.0740977	−	0.228049i	−0.00391073	−	0.0120360i	−0.952993	+	0.302993i	$0.902014\pi$
$360$		0			0
$361$	−3.51396	+	10.8148i	−0.184945	+	0.569203i
$362$		0			0
$363$	−1.70638	−	0.869442i	−0.0895615	−	0.0456339i
$364$		0			0
$365$	−3.26385	+	29.3906i	−0.170838	+	1.53838i
$366$		0			0
$367$	30.7490	+	4.87017i	1.60509	+	0.254221i	0.893728	−	0.448608i	$-0.148080\pi$
$367$	30.7490	+	4.87017i	1.60509	+	0.254221i	0.711359	+	0.702829i	$0.248080\pi$
$368$		0			0
$369$	19.8034	+	27.2571i	1.03092	+	1.41895i
$370$		0			0
$371$	11.4977	−	15.8253i	0.596932	−	0.821607i
$372$		0			0
$373$	28.2074	−	14.3724i	1.46053	−	0.744175i	0.470151	−	0.882586i	$-0.344199\pi$
$373$	28.2074	−	14.3724i	1.46053	−	0.744175i	0.990375	+	0.138411i	$0.0441993\pi$
$374$		0			0
$375$	5.57223	+	0.0982678i	0.287749	+	0.00507453i
$376$		0			0
$377$	−0.145998	−	0.286538i	−0.00751930	−	0.0147575i
$378$		0			0
$379$	−22.0809	−	16.0427i	−1.13422	−	0.824059i	−0.147916	−	0.989000i	$-0.547256\pi$
$379$	−22.0809	−	16.0427i	−1.13422	−	0.824059i	−0.986303	+	0.164941i	$0.947256\pi$
$380$		0			0
$381$	−7.89874	+	5.73877i	−0.404665	+	0.294006i
$382$		0			0
$383$	−1.65545	+	10.4521i	−0.0845893	+	0.534076i	0.908610	+	0.417647i	$0.137145\pi$
$383$	−1.65545	+	10.4521i	−0.0845893	+	0.534076i	−0.993199	+	0.116430i	$0.962855\pi$
$384$		0			0
$385$	26.9262	+	2.99018i	1.37229	+	0.152394i
$386$		0			0
$387$	−14.4485	+	28.3568i	−0.734458	+	1.44145i
$388$		0			0
$389$	4.71750	+	1.53281i	0.239187	+	0.0777165i	0.426158	−	0.904649i	$-0.359867\pi$
$389$	4.71750	+	1.53281i	0.239187	+	0.0777165i	−0.186971	+	0.982366i	$0.559867\pi$
$390$		0			0
$391$	4.17609	−	1.35689i	0.211194	−	0.0686211i
$392$		0			0
$393$	6.59160	+	6.59160i	0.332502	+	0.332502i
$394$		0			0
$395$	22.5457	−	8.50277i	1.13440	−	0.427821i
$396$		0			0
$397$	−16.6205	+	2.63242i	−0.834157	+	0.132117i	−0.558881	−	0.829248i	$-0.688769\pi$
$397$	−16.6205	+	2.63242i	−0.834157	+	0.132117i	−0.275276	+	0.961365i	$0.588769\pi$
$398$		0			0
$399$	−4.32983			−0.216763
$400$		0			0
$401$	−23.3901			−1.16804			−0.584022	−	0.811738i	$-0.698522\pi$
$401$	−23.3901			−1.16804			−0.584022	+	0.811738i	$0.698522\pi$
$402$		0			0
$403$	−7.62515	+	1.20770i	−0.379836	+	0.0601600i
$404$		0			0
$405$	−0.709163	−	15.2457i	−0.0352386	−	0.757566i
$406$		0			0
$407$	−16.7445	−	16.7445i	−0.829993	−	0.829993i
$408$		0			0
$409$	5.07980	−	1.65053i	0.251180	−	0.0816133i	−0.180721	−	0.983534i	$-0.557843\pi$
$409$	5.07980	−	1.65053i	0.251180	−	0.0816133i	0.431901	+	0.901921i	$0.357843\pi$
$410$		0			0
$411$	10.7523	+	3.49363i	0.530371	+	0.172328i
$412$		0			0
$413$	16.0582	−	31.5161i	0.790174	−	1.55080i
$414$		0			0
$415$	2.46219	+	2.24331i	0.120864	+	0.110120i
$416$		0			0
$417$	0.835342	−	5.27414i	0.0409069	−	0.258276i
$418$		0			0
$419$	14.1593	−	10.2873i	0.691726	−	0.502568i	−0.185501	−	0.982644i	$-0.559391\pi$
$419$	14.1593	−	10.2873i	0.691726	−	0.502568i	0.877227	+	0.480076i	$0.159391\pi$
$420$		0			0
$421$	13.3782	+	9.71982i	0.652013	+	0.473715i	0.863956	−	0.503567i	$-0.167979\pi$
$421$	13.3782	+	9.71982i	0.652013	+	0.473715i	−0.211943	+	0.977282i	$0.567979\pi$
$422$		0			0
$423$	7.68480	+	15.0823i	0.373648	+	0.733325i
$424$		0			0
$425$	−7.89345	+	2.01590i	−0.382889	+	0.0977854i
$426$		0			0
$427$	16.9369	−	8.62977i	0.819633	−	0.417624i
$428$		0			0
$429$	1.46234	−	2.01274i	0.0706025	−	0.0971760i
$430$		0			0
$431$	4.61563	+	6.35286i	0.222327	+	0.306007i	0.905581	−	0.424174i	$-0.139436\pi$
$431$	4.61563	+	6.35286i	0.222327	+	0.306007i	−0.683254	+	0.730181i	$0.739436\pi$
$432$		0			0
$433$	31.0274	+	4.91426i	1.49108	+	0.236164i	0.848149	−	0.529758i	$-0.177717\pi$
$433$	31.0274	+	4.91426i	1.49108	+	0.236164i	0.642934	+	0.765922i	$0.277717\pi$
$434$		0			0
$435$	0.136932	+	0.240425i	0.00656537	+	0.0115275i
$436$		0			0
$437$	−6.63207	−	3.37921i	−0.317255	−	0.161650i
$438$		0			0
$439$	8.97881	−	27.6339i	0.428535	−	1.31890i	−0.471033	−	0.882116i	$-0.656119\pi$
$439$	8.97881	−	27.6339i	0.428535	−	1.31890i	0.899568	−	0.436781i	$-0.143881\pi$
$440$		0			0
$441$	−2.45761	−	7.56374i	−0.117029	−	0.360178i
$442$		0			0
$443$	0.0313069	−	0.0313069i	0.00148744	−	0.00148744i	−0.706363	−	0.707850i	$-0.749665\pi$
$443$	0.0313069	−	0.0313069i	0.00148744	−	0.00148744i	0.707850	+	0.706363i	$0.249665\pi$
$444$		0			0
$445$	−9.94152	+	7.95419i	−0.471273	+	0.377065i
$446$		0			0
$447$	0.180230	+	1.13793i	0.00852461	+	0.0538222i
$448$		0			0
$449$			28.1075i			1.32648i	0.748408	+	0.663238i	$0.230818\pi$
$449$			28.1075i			1.32648i	−0.748408	+	0.663238i	$0.769182\pi$
$450$		0			0
$451$			47.1730i			2.22129i
$452$		0			0
$453$	−0.707327	−	4.46589i	−0.0332331	−	0.209826i
$454$		0			0
$455$	−2.40961	+	8.78590i	−0.112964	+	0.411889i
$456$		0			0
$457$	−6.18057	+	6.18057i	−0.289115	+	0.289115i	−0.836730	−	0.547615i	$-0.815536\pi$
$457$	−6.18057	+	6.18057i	−0.289115	+	0.289115i	0.547615	+	0.836730i	$0.315536\pi$
$458$		0			0
$459$	−1.44353	−	4.44271i	−0.0673780	−	0.207368i
$460$		0			0
$461$	−10.8694	+	33.4525i	−0.506238	+	1.55804i	0.292442	+	0.956283i	$0.405532\pi$
$461$	−10.8694	+	33.4525i	−0.506238	+	1.55804i	−0.798679	+	0.601757i	$0.794468\pi$
$462$		0			0
$463$	−19.9154	−	10.1474i	−0.925547	−	0.471590i	−0.0748198	−	0.997197i	$-0.523838\pi$
$463$	−19.9154	−	10.1474i	−0.925547	−	0.471590i	−0.850727	+	0.525607i	$0.823838\pi$
$464$		0			0
$465$	6.50506	−	1.34278i	0.301665	−	0.0622699i
$466$		0			0
$467$	26.3620	+	4.17533i	1.21989	+	0.193211i	0.732985	−	0.680245i	$-0.238127\pi$
$467$	26.3620	+	4.17533i	1.21989	+	0.193211i	0.486903	+	0.873456i	$0.338127\pi$
$468$		0			0
$469$	−20.5528	−	28.2885i	−0.949040	−	1.30624i
$470$		0			0
$471$	−4.02846	+	5.54470i	−0.185622	+	0.255486i
$472$		0			0
$473$	−39.7035	+	20.2299i	−1.82557	+	0.930173i
$474$		0			0
$475$	11.8778	+	7.04509i	0.544990	+	0.323251i
$476$		0			0
$477$	−7.76975	−	15.2490i	−0.355752	−	0.698203i
$478$		0			0
$479$	−16.4384	−	11.9432i	−0.751091	−	0.545699i	0.145074	−	0.989421i	$-0.453658\pi$
$479$	−16.4384	−	11.9432i	−0.751091	−	0.545699i	−0.896165	+	0.443722i	$0.853658\pi$
$480$		0			0
$481$	6.44231	−	4.68061i	0.293744	−	0.213418i
$482$		0			0
$483$	−0.660887	+	4.17267i	−0.0300714	+	0.189863i
$484$		0			0
$485$	5.70838	−	12.6211i	0.259204	−	0.573093i
$486$		0			0
$487$	−17.9225	+	35.1749i	−0.812146	+	1.59393i	−0.00764778	+	0.999971i	$0.502434\pi$
$487$	−17.9225	+	35.1749i	−0.812146	+	1.59393i	−0.804498	+	0.593955i	$0.797566\pi$
$488$		0			0
$489$	−0.646216	−	0.209968i	−0.0292229	−	0.00949510i
$490$		0			0
$491$	−10.4880	+	3.40776i	−0.473318	+	0.153790i	−0.535956	−	0.844246i	$-0.680049\pi$
$491$	−10.4880	+	3.40776i	−0.473318	+	0.153790i	0.0626381	+	0.998036i	$0.480049\pi$
$492$		0			0
$493$	−0.285997	−	0.285997i	−0.0128806	−	0.0128806i
$494$		0			0
$495$	13.0262	−	19.8028i	0.585485	−	0.890070i
$496$		0			0
$497$	−10.9901	+	1.74066i	−0.492973	+	0.0780793i
$498$		0			0
$499$	−16.6777			−0.746597			−0.373299	−	0.927711i	$-0.621773\pi$
$499$	−16.6777			−0.746597			−0.373299	+	0.927711i	$0.621773\pi$
$500$		0			0
$501$	0.221804			0.00990948
$502$		0			0
$503$	−12.4163	+	1.96654i	−0.553614	+	0.0876838i	−0.426972	−	0.904265i	$-0.640420\pi$
$503$	−12.4163	+	1.96654i	−0.553614	+	0.0876838i	−0.126642	+	0.991949i	$0.540420\pi$
$504$		0			0
$505$	9.66573	−	14.6941i	0.430119	−	0.653879i
$506$		0			0
$507$	−3.99058	−	3.99058i	−0.177228	−	0.177228i
$508$		0			0
$509$	25.7482	−	8.36610i	1.14127	−	0.370821i	0.323422	−	0.946255i	$-0.395167\pi$
$509$	25.7482	−	8.36610i	1.14127	−	0.370821i	0.817848	+	0.575434i	$0.195167\pi$
$510$		0			0
$511$	39.5547	+	12.8521i	1.74980	+	0.568544i
$512$		0			0
$513$	−3.59496	+	7.05550i	−0.158721	+	0.311508i
$514$		0			0
$515$	9.86411	−	21.8093i	0.434665	−	0.961031i
$516$		0			0
$517$	−3.70758	+	23.4087i	−0.163059	+	1.02952i
$518$		0			0
$519$	−6.51785	+	4.73549i	−0.286102	+	0.207865i
$520$		0			0
$521$	6.75003	+	4.90419i	0.295724	+	0.214856i	0.725747	−	0.687962i	$-0.241494\pi$
$521$	6.75003	+	4.90419i	0.295724	+	0.214856i	−0.430023	+	0.902818i	$0.641494\pi$
$522$		0			0
$523$	−12.7076	−	24.9401i	−0.555665	−	1.09055i	−0.982507	−	0.186228i	$-0.940374\pi$
$523$	−12.7076	−	24.9401i	−0.555665	−	1.09055i	0.426841	−	0.904327i	$-0.359626\pi$
$524$		0			0
$525$	1.71968	−	7.64727i	0.0750528	−	0.333754i
$526$		0			0
$527$	−8.65135	+	4.40808i	−0.376859	+	0.192019i
$528$		0			0
$529$	9.25021	−	12.7318i	0.402183	−	0.553558i
$530$		0			0
$531$	−18.1902	−	25.0366i	−0.789385	−	1.08650i
$532$		0			0
$533$	−15.6679	−	2.48155i	−0.678652	−	0.107488i
$534$		0			0
$535$	−41.3729	+	8.54022i	−1.78870	+	0.369226i
$536$		0			0
$537$	2.62876	+	1.33942i	0.113439	+	0.0578003i
$538$		0			0
$539$	3.44100	−	10.5903i	0.148214	−	0.456157i
$540$		0			0
$541$	−8.10677	−	24.9501i	−0.348537	−	1.07269i	−0.959663	−	0.281153i	$-0.909283\pi$
$541$	−8.10677	−	24.9501i	−0.348537	−	1.07269i	0.611126	−	0.791533i	$-0.290717\pi$
$542$		0			0
$543$	0.970023	−	0.970023i	0.0416277	−	0.0416277i
$544$		0			0
$545$	−5.12204	+	18.6759i	−0.219404	+	0.799988i
$546$		0			0
$547$	−1.44701	−	9.13608i	−0.0618698	−	0.390630i	−0.999119	−	0.0419699i	$-0.986637\pi$
$547$	−1.44701	−	9.13608i	−0.0618698	−	0.390630i	0.937249	−	0.348660i	$-0.113363\pi$
$548$		0			0
$549$		−	16.6310i		−	0.709795i
$550$		0			0
$551$			0.685616i			0.0292082i
$552$		0			0
$553$	−5.30145	−	33.4720i	−0.225441	−	1.42338i
$554$		0			0
$555$	−5.34965	+	4.28024i	−0.227080	+	0.181686i
$556$		0			0
$557$	6.45409	−	6.45409i	0.273469	−	0.273469i	−0.557026	−	0.830495i	$-0.688058\pi$
$557$	6.45409	−	6.45409i	0.273469	−	0.273469i	0.830495	+	0.557026i	$0.188058\pi$
$558$		0			0
$559$	−4.63049	−	14.2512i	−0.195849	−	0.602761i
$560$		0			0
$561$	0.966912	−	2.97585i	0.0408231	−	0.125640i
$562$		0			0
$563$	−19.5889	−	9.98103i	−0.825572	−	0.420650i	−0.0104545	−	0.999945i	$-0.503328\pi$
$563$	−19.5889	−	9.98103i	−0.825572	−	0.420650i	−0.815118	+	0.579295i	$0.803328\pi$
$564$		0			0
$565$	3.86832	+	6.79201i	0.162741	+	0.285742i
$566$		0			0
$567$	−21.2011	−	3.35793i	−0.890363	−	0.141020i
$568$		0			0
$569$	−3.02986	−	4.17024i	−0.127018	−	0.174826i	0.740772	−	0.671757i	$-0.234460\pi$
$569$	−3.02986	−	4.17024i	−0.127018	−	0.174826i	−0.867790	+	0.496931i	$0.834460\pi$
$570$		0			0
$571$	0.703359	−	0.968091i	0.0294347	−	0.0405134i	−0.794046	−	0.607858i	$-0.792029\pi$
$571$	0.703359	−	0.968091i	0.0294347	−	0.0405134i	0.823481	+	0.567344i	$0.192029\pi$
$572$		0			0
$573$	11.0137	−	5.61177i	0.460104	−	0.234435i
$574$		0			0
$575$	8.60236	−	10.3713i	0.358743	−	0.432514i
$576$		0			0
$577$	−2.75307	−	5.40320i	−0.114612	−	0.224938i	0.826574	−	0.562828i	$-0.190287\pi$
$577$	−2.75307	−	5.40320i	−0.114612	−	0.224938i	−0.941186	+	0.337890i	$0.890287\pi$
$578$		0			0
$579$	−0.693312	−	0.503721i	−0.0288131	−	0.0209339i
$580$		0			0
$581$	3.79001	−	2.75360i	0.157236	−	0.114239i
$582$		0			0
$583$	3.74856	−	23.6675i	0.155250	−	0.980207i
$584$		0			0
$585$	5.89200	+	5.36822i	0.243604	+	0.221949i
$586$		0			0
$587$	−10.2969	+	20.2089i	−0.425000	+	0.834110i	0.574874	+	0.818242i	$0.305051\pi$
$587$	−10.2969	+	20.2089i	−0.425000	+	0.834110i	−0.999874	+	0.0158676i	$0.994949\pi$
$588$		0			0
$589$	15.6536	+	5.08616i	0.644995	+	0.209572i
$590$		0			0
$591$	−4.36865	+	1.41946i	−0.179702	+	0.0583888i
$592$		0			0
$593$	5.48081	+	5.48081i	0.225070	+	0.225070i	0.810629	−	0.585560i	$-0.199125\pi$
$593$	5.48081	+	5.48081i	0.225070	+	0.225070i	−0.585560	+	0.810629i	$0.699125\pi$
$594$		0			0
$595$	0.532400	+	11.4456i	0.0218263	+	0.469225i
$596$		0			0
$597$	7.80514	−	1.23621i	0.319443	−	0.0505948i
$598$		0			0
$599$	27.7629			1.13436			0.567180	−	0.823594i	$-0.308034\pi$
$599$	27.7629			1.13436			0.567180	+	0.823594i	$0.308034\pi$
$600$		0			0
$601$	19.9888			0.815359			0.407680	−	0.913125i	$-0.366338\pi$
$601$	19.9888			0.815359			0.407680	+	0.913125i	$0.366338\pi$
$602$		0			0
$603$	−30.2161	+	4.78577i	−1.23050	+	0.194892i
$604$		0			0
$605$	8.03822	−	3.03150i	0.326800	−	0.123248i
$606$		0			0
$607$	−12.2098	−	12.2098i	−0.495580	−	0.495580i	0.414479	−	0.910059i	$-0.363964\pi$
$607$	−12.2098	−	12.2098i	−0.495580	−	0.495580i	−0.910059	+	0.414479i	$0.863964\pi$
$608$		0			0
$609$	0.370095	−	0.120251i	0.0149970	−	0.00487282i
$610$		0			0
$611$	−7.57987	−	2.46285i	−0.306649	−	0.0996362i
$612$		0			0
$613$	3.84563	−	7.54747i	0.155323	−	0.304839i	−0.800211	−	0.599718i	$-0.795279\pi$
$613$	3.84563	−	7.54747i	0.155323	−	0.304839i	0.955535	+	0.294879i	$0.0952793\pi$
$614$		0			0
$615$	13.5648	+	1.50638i	0.546985	+	0.0607431i
$616$		0			0
$617$	3.08914	−	19.5040i	0.124364	−	0.785203i	−0.844125	−	0.536147i	$-0.819879\pi$
$617$	3.08914	−	19.5040i	0.124364	−	0.785203i	0.968489	−	0.249057i	$-0.0801206\pi$
$618$		0			0
$619$	−17.9346	+	13.0303i	−0.720854	+	0.523731i	−0.886657	−	0.462428i	$-0.846978\pi$
$619$	−17.9346	+	13.0303i	−0.720854	+	0.523731i	0.165803	+	0.986159i	$0.446978\pi$
$620$		0			0
$621$	6.25070	+	4.54140i	0.250832	+	0.182240i
$622$		0			0
$623$	8.12950	+	15.9551i	0.325702	+	0.639226i
$624$		0			0
$625$	−17.1604	+	18.1802i	−0.686416	+	0.727209i
$626$		0			0
$627$	−4.72596	+	2.40800i	−0.188737	+	0.0961662i
$628$		0			0
$629$	5.88677	−	8.10245i	0.234721	−	0.323066i
$630$		0			0
$631$	−0.180540	−	0.248491i	−0.00718716	−	0.00989228i	0.805408	−	0.592720i	$-0.201946\pi$
$631$	−0.180540	−	0.248491i	−0.00718716	−	0.00989228i	−0.812595	+	0.582828i	$0.801946\pi$
$632$		0			0
$633$	−9.04637	−	1.43280i	−0.359561	−	0.0569488i
$634$		0			0
$635$	4.83396	−	43.5293i	0.191830	−	1.72741i
$636$		0			0
$637$	3.33642	+	1.69999i	0.132194	+	0.0673561i
$638$		0			0
$639$	−3.00837	+	9.25880i	−0.119009	+	0.366272i
$640$		0			0
$641$	−10.6721	−	32.8454i	−0.421523	−	1.29731i	−0.906285	−	0.422668i	$-0.861094\pi$
$641$	−10.6721	−	32.8454i	−0.421523	−	1.29731i	0.484762	−	0.874646i	$-0.338906\pi$
$642$		0			0
$643$	3.84603	−	3.84603i	0.151673	−	0.151673i	−0.627192	−	0.778865i	$-0.715796\pi$
$643$	3.84603	−	3.84603i	0.151673	−	0.151673i	0.778865	+	0.627192i	$0.215796\pi$
$644$		0			0
$645$	4.54935	+	12.0629i	0.179130	+	0.474976i
$646$		0			0
$647$	0.923025	+	5.82775i	0.0362879	+	0.229113i	0.999166	−	0.0408224i	$-0.0129978\pi$
$647$	0.923025	+	5.82775i	0.0362879	+	0.229113i	−0.962879	+	0.269935i	$0.912998\pi$
$648$		0			0
$649$		−	43.3301i		−	1.70086i
$650$		0			0
$651$		−	9.34187i		−	0.366137i
$652$		0			0
$653$	7.05423	+	44.5387i	0.276053	+	1.74293i	0.602865	+	0.797843i	$0.294026\pi$
$653$	7.05423	+	44.5387i	0.276053	+	1.74293i	−0.326812	+	0.945089i	$0.605974\pi$
$654$		0			0
$655$	−41.7715	+	1.94303i	−1.63215	+	0.0759203i
$656$		0			0
$657$	25.7302	−	25.7302i	1.00383	−	1.00383i
$658$		0			0
$659$	7.86904	+	24.2184i	0.306534	+	0.943416i	0.979100	+	0.203379i	$0.0651922\pi$
$659$	7.86904	+	24.2184i	0.306534	+	0.943416i	−0.672566	+	0.740037i	$0.734808\pi$
$660$		0			0
$661$	−6.51527	+	20.0519i	−0.253415	+	0.779930i	0.740723	+	0.671810i	$0.234483\pi$
$661$	−6.51527	+	20.0519i	−0.253415	+	0.779930i	−0.994138	+	0.108120i	$0.965517\pi$
$662$		0			0
$663$	0.937525	+	0.477693i	0.0364104	+	0.0185520i
$664$		0			0
$665$	13.0811	−	14.3574i	0.507262	−	0.556756i
$666$		0			0
$667$	0.660731	+	0.104649i	0.0255836	+	0.00405204i
$668$		0			0
$669$	5.76517	+	7.93508i	0.222894	+	0.306788i
$670$		0			0
$671$	13.6871	−	18.8386i	0.528383	−	0.727257i
$672$		0			0
$673$	−13.5805	+	6.91963i	−0.523491	+	0.266732i	−0.695705	−	0.718327i	$-0.744908\pi$
$673$	−13.5805	+	6.91963i	−0.523491	+	0.266732i	0.172214	+	0.985060i	$0.444908\pi$
$674$		0			0
$675$	−11.0335	−	9.15158i	−0.424679	−	0.352244i
$676$		0			0
$677$	14.4552	+	28.3700i	0.555559	+	1.09035i	0.982534	+	0.186083i	$0.0595793\pi$
$677$	14.4552	+	28.3700i	0.555559	+	1.09035i	−0.426975	+	0.904264i	$0.640421\pi$
$678$		0			0
$679$	−15.7612	−	11.4512i	−0.604861	−	0.439457i
$680$		0			0
$681$	0.627166	−	0.455663i	0.0240331	−	0.0174610i
$682$		0			0
$683$	−5.82103	+	36.7525i	−0.222735	+	1.40630i	0.582254	+	0.813007i	$0.302171\pi$
$683$	−5.82103	+	36.7525i	−0.222735	+	1.40630i	−0.804989	+	0.593289i	$0.797829\pi$
$684$		0			0
$685$	−44.0689	+	25.0990i	−1.68379	+	0.958983i
$686$		0			0
$687$	−4.93772	+	9.69082i	−0.188386	+	0.369728i
$688$		0			0
$689$	7.66365	+	2.49007i	0.291962	+	0.0948642i
$690$		0			0
$691$	8.08989	−	2.62856i	0.307754	−	0.0999953i	−0.151069	−	0.988523i	$-0.548271\pi$
$691$	8.08989	−	2.62856i	0.307754	−	0.0999953i	0.458822	+	0.888528i	$0.348271\pi$
$692$		0			0
$693$	−23.5728	−	23.5728i	−0.895456	−	0.895456i
$694$		0			0
$695$	14.9650	+	18.7039i	0.567653	+	0.709480i
$696$		0			0
$697$	−19.7054	+	3.12103i	−0.746395	+	0.118217i
$698$		0			0
$699$	8.46850			0.320308
$700$		0			0
$701$	13.9928			0.528501			0.264250	−	0.964454i	$-0.414875\pi$
$701$	13.9928			0.528501			0.264250	+	0.964454i	$0.414875\pi$
$702$		0			0
$703$	−16.7681	+	2.65580i	−0.632420	+	0.100166i
$704$		0			0
$705$	6.61288	+	1.81364i	0.249056	+	0.0683057i
$706$		0			0
$707$	−17.4915	−	17.4915i	−0.657835	−	0.657835i
$708$		0			0
$709$	−26.5119	+	8.61424i	−0.995676	+	0.323515i	−0.761136	−	0.648592i	$-0.775358\pi$
$709$	−26.5119	+	8.61424i	−0.995676	+	0.323515i	−0.234539	+	0.972107i	$0.575358\pi$
$710$		0			0
$711$	−28.1991	−	9.16244i	−1.05755	−	0.343618i
$712$		0			0
$713$	7.29085	−	14.3091i	0.273045	−	0.535880i
$714$		0			0
$715$	2.25614	+	10.9298i	0.0843748	+	0.408752i
$716$		0			0
$717$	−0.501191	+	3.16439i	−0.0187173	+	0.118176i
$718$		0			0
$719$	12.9929	−	9.43992i	0.484555	−	0.352050i	−0.318532	−	0.947912i	$-0.603190\pi$
$719$	12.9929	−	9.43992i	0.484555	−	0.352050i	0.803086	+	0.595863i	$0.203190\pi$
$720$		0			0
$721$	−27.2355	−	19.7878i	−1.01430	−	0.736935i
$722$		0			0
$723$	0.406231	+	0.797272i	0.0151079	+	0.0296509i
$724$		0			0
$725$	−1.21092	−	0.272306i	−0.0449725	−	0.0101132i
$726$		0			0
$727$	45.9176	−	23.3962i	1.70299	−	0.867717i	0.717801	−	0.696249i	$-0.245149\pi$
$727$	45.9176	−	23.3962i	1.70299	−	0.867717i	0.985190	−	0.171468i	$-0.0548510\pi$
$728$		0			0
$729$	−8.51883	+	11.7252i	−0.315512	+	0.434265i
$730$		0			0
$731$	−11.0774	−	15.2467i	−0.409713	−	0.563921i
$732$		0			0
$733$	38.3664	+	6.07665i	1.41710	+	0.224446i	0.817533	−	0.575881i	$-0.195341\pi$
$733$	38.3664	+	6.07665i	1.41710	+	0.224446i	0.599563	+	0.800327i	$0.295341\pi$
$734$		0			0
$735$	−2.93540	−	1.32765i	−0.108274	−	0.0489713i
$736$		0			0
$737$	−38.1656	−	19.4463i	−1.40585	−	0.716315i
$738$		0			0
$739$	−7.60391	+	23.4024i	−0.279714	+	0.860872i	0.708219	+	0.705993i	$0.249499\pi$
$739$	−7.60391	+	23.4024i	−0.279714	+	0.860872i	−0.987933	+	0.154880i	$0.950501\pi$
$740$		0			0
$741$	−0.551174	−	1.69634i	−0.0202479	−	0.0623166i
$742$		0			0
$743$	21.3267	−	21.3267i	0.782400	−	0.782400i	−0.197835	−	0.980235i	$-0.563391\pi$
$743$	21.3267	−	21.3267i	0.782400	−	0.782400i	0.980235	+	0.197835i	$0.0633911\pi$
$744$		0			0
$745$	−4.31779	−	2.84023i	−0.158192	−	0.104058i
$746$		0			0
$747$	−0.641182	−	4.04827i	−0.0234596	−	0.148118i
$748$		0			0
$749$			59.4153i			2.17099i
$750$		0			0
$751$			33.9430i			1.23860i	0.785156	+	0.619298i	$0.212583\pi$
$751$			33.9430i			1.23860i	−0.785156	+	0.619298i	$0.787417\pi$
$752$		0			0
$753$	−0.530917	−	3.35208i	−0.0193477	−	0.122157i
$754$		0			0
$755$	16.9455	+	11.1467i	0.616709	+	0.405669i
$756$		0			0
$757$	17.7518	−	17.7518i	0.645200	−	0.645200i	−0.306629	−	0.951829i	$-0.599201\pi$
$757$	17.7518	−	17.7518i	0.645200	−	0.645200i	0.951829	+	0.306629i	$0.0992010\pi$
$758$		0			0
$759$	1.59925	+	4.92198i	0.0580490	+	0.178656i
$760$		0			0
$761$	0.965164	−	2.97047i	0.0349872	−	0.107679i	−0.932038	−	0.362361i	$-0.881971\pi$
$761$	0.965164	−	2.97047i	0.0349872	−	0.107679i	0.967025	+	0.254682i	$0.0819707\pi$
$762$		0			0
$763$	24.2679	+	12.3651i	0.878558	+	0.447648i
$764$		0			0
$765$	9.13399	+	4.13121i	0.330240	+	0.149364i
$766$		0			0
$767$	14.3915	+	2.27939i	0.519648	+	0.0823042i
$768$		0			0
$769$	1.87298	+	2.57794i	0.0675414	+	0.0929628i	0.841451	−	0.540333i	$-0.181702\pi$
$769$	1.87298	+	2.57794i	0.0675414	+	0.0929628i	−0.773910	+	0.633296i	$0.781702\pi$
$770$		0			0
$771$	−4.26424	+	5.86923i	−0.153573	+	0.211375i
$772$		0			0
$773$	−3.92778	+	2.00130i	−0.141272	+	0.0719819i	−0.523198	−	0.852211i	$-0.675261\pi$
$773$	−3.92778	+	2.00130i	−0.141272	+	0.0719819i	0.381925	+	0.924193i	$0.375261\pi$
$774$		0			0
$775$	−15.2002	+	25.6270i	−0.546008	+	0.920550i
$776$		0			0
$777$	4.37458	+	8.58560i	0.156937	+	0.308007i
$778$		0			0
$779$	27.3607	+	19.8787i	0.980300	+	0.712230i
$780$		0			0
$781$	−11.0275	+	8.01197i	−0.394596	+	0.286691i
$782$		0			0
$783$	0.111331	−	0.702915i	0.00397864	−	0.0251201i
$784$		0			0
$785$	−6.21521	−	30.1094i	−0.221830	−	1.07465i
$786$		0			0
$787$	7.00238	−	13.7429i	0.249608	−	0.489883i	−0.731874	−	0.681440i	$-0.761354\pi$
$787$	7.00238	−	13.7429i	0.249608	−	0.489883i	0.981481	+	0.191558i	$0.0613539\pi$
$788$		0			0
$789$	3.89321	+	1.26498i	0.138602	+	0.0450345i
$790$		0			0
$791$	10.4552	−	3.39710i	0.371744	−	0.120787i
$792$		0			0
$793$	5.53699	+	5.53699i	0.196624	+	0.196624i
$794$		0			0
$795$	−6.68598	−	1.83369i	−0.237127	−	0.0650343i
$796$		0			0
$797$	26.2508	−	4.15773i	0.929853	−	0.147274i	0.326907	−	0.945056i	$-0.393994\pi$
$797$	26.2508	−	4.15773i	0.929853	−	0.147274i	0.602946	+	0.797782i	$0.293994\pi$
$798$		0			0
$799$	−10.0237			−0.354615
$800$		0			0
$801$	15.6669			0.553564
$802$		0			0
$803$	50.3212	−	7.97009i	1.77580	−	0.281258i
$804$		0			0
$805$	−11.8396	−	14.7977i	−0.417292	−	0.521552i
$806$		0			0
$807$	4.90035	+	4.90035i	0.172501	+	0.172501i
$808$		0			0
$809$	11.6828	−	3.79598i	0.410746	−	0.133459i	−0.0963532	−	0.995347i	$-0.530718\pi$
$809$	11.6828	−	3.79598i	0.410746	−	0.133459i	0.507099	+	0.861888i	$0.330718\pi$
$810$		0			0
$811$	2.75498	+	0.895148i	0.0967405	+	0.0314329i	0.356987	−	0.934109i	$-0.383804\pi$
$811$	2.75498	+	0.895148i	0.0967405	+	0.0314329i	−0.260247	+	0.965542i	$0.583804\pi$
$812$		0			0
$813$	−2.95602	+	5.80151i	−0.103672	+	0.203468i
$814$		0			0
$815$	2.64856	−	1.50846i	0.0927749	−	0.0528390i
$816$		0			0
$817$	−4.99755	+	31.5533i	−0.174842	+	1.10391i
$818$		0			0
$819$	9.06944	−	6.58934i	0.316912	−	0.230250i
$820$		0			0
$821$	25.5237	+	18.5440i	0.890782	+	0.647191i	0.936082	−	0.351783i	$-0.114424\pi$
$821$	25.5237	+	18.5440i	0.890782	+	0.647191i	−0.0453000	+	0.998973i	$0.514424\pi$
$822$		0			0
$823$	2.82627	+	5.54686i	0.0985175	+	0.193351i	0.935005	−	0.354635i	$-0.115395\pi$
$823$	2.82627	+	5.54686i	0.0985175	+	0.193351i	−0.836488	+	0.547986i	$0.815395\pi$
$824$		0			0
$825$	−2.37596	−	9.30330i	−0.0827201	−	0.323899i
$826$		0			0
$827$	28.5274	−	14.5355i	0.991996	−	0.505447i	0.118853	−	0.992912i	$-0.462078\pi$
$827$	28.5274	−	14.5355i	0.991996	−	0.505447i	0.873143	+	0.487465i	$0.162078\pi$
$828$		0			0
$829$	−2.31317	+	3.18381i	−0.0803398	+	0.110578i	−0.847295	−	0.531122i	$-0.821771\pi$
$829$	−2.31317	+	3.18381i	−0.0803398	+	0.110578i	0.766956	+	0.641700i	$0.221771\pi$
$830$		0			0
$831$	−6.88031	−	9.46993i	−0.238675	−	0.328508i
$832$		0			0
$833$	4.65151	+	0.736727i	0.161165	+	0.0255261i
$834$		0			0
$835$	−0.670104	+	0.735486i	−0.0231899	+	0.0254525i
$836$		0			0
$837$	−15.2227	−	7.75634i	−0.526173	−	0.268098i
$838$		0			0
$839$	−3.90313	+	12.0126i	−0.134751	+	0.414721i	−0.995551	−	0.0942219i	$-0.969964\pi$
$839$	−3.90313	+	12.0126i	−0.134751	+	0.414721i	0.860800	+	0.508943i	$0.169964\pi$
$840$		0			0
$841$	8.94245	+	27.5220i	0.308360	+	0.949036i
$842$		0			0
$843$	−7.70428	+	7.70428i	−0.265349	+	0.265349i
$844$		0			0
$845$	25.2886	−	1.17631i	0.869955	−	0.0404664i
$846$		0			0
$847$	−1.89013	−	11.9338i	−0.0649456	−	0.410050i
$848$		0			0
$849$			3.22821i			0.110792i
$850$		0			0
$851$			16.5648i			0.567836i
$852$		0			0
$853$	8.22886	+	51.9550i	0.281751	+	1.77891i	0.570297	+	0.821439i	$0.306828\pi$
$853$	8.22886	+	51.9550i	0.281751	+	1.77891i	−0.288546	+	0.957466i	$0.593172\pi$
$854$		0			0
$855$	−5.99654	−	15.9002i	−0.205077	−	0.543777i
$856$		0			0
$857$	−14.2165	+	14.2165i	−0.485625	+	0.485625i	−0.906922	−	0.421298i	$-0.861575\pi$
$857$	−14.2165	+	14.2165i	−0.485625	+	0.485625i	0.421298	+	0.906922i	$0.361575\pi$
$858$		0			0
$859$	−7.81129	−	24.0407i	−0.266518	−	0.820257i	−0.991340	−	0.131321i	$-0.958078\pi$
$859$	−7.81129	−	24.0407i	−0.266518	−	0.820257i	0.724822	−	0.688936i	$-0.241922\pi$
$860$		0			0
$861$	5.93169	−	18.2559i	0.202152	−	0.622158i
$862$		0			0
$863$	28.1650	+	14.3508i	0.958748	+	0.488506i	0.862059	−	0.506808i	$-0.169175\pi$
$863$	28.1650	+	14.3508i	0.958748	+	0.488506i	0.0966889	+	0.995315i	$0.469175\pi$
$864$		0			0
$865$	3.98887	−	35.9194i	0.135626	−	1.22129i
$866$		0			0
$867$	−7.06265	−	1.11861i	−0.239860	−	0.0379901i
$868$		0			0
$869$	−24.4017	−	33.5860i	−0.827770	−	1.13933i
$870$		0			0
$871$	8.46656	−	11.6532i	0.286879	−	0.394854i
$872$		0			0
$873$	−15.1873	+	7.73831i	−0.514012	+	0.261902i
$874$		0			0
$875$	20.1624	+	28.8059i	0.681612	+	0.973816i
$876$		0			0
$877$	−3.06726	−	6.01983i	−0.103574	−	0.203275i	0.833404	−	0.552665i	$-0.186389\pi$
$877$	−3.06726	−	6.01983i	−0.103574	−	0.203275i	−0.936978	+	0.349389i	$0.886389\pi$
$878$		0			0
$879$	4.83845	+	3.51534i	0.163197	+	0.118569i
$880$		0			0
$881$	−21.9349	+	15.9366i	−0.739004	+	0.536918i	−0.892399	−	0.451247i	$-0.850979\pi$
$881$	−21.9349	+	15.9366i	−0.739004	+	0.536918i	0.153395	+	0.988165i	$0.450979\pi$
$882$		0			0
$883$	4.86869	−	30.7397i	0.163844	−	1.03447i	−0.759502	−	0.650505i	$-0.774557\pi$
$883$	4.86869	−	30.7397i	0.163844	−	1.03447i	0.923346	−	0.383968i	$-0.125443\pi$
$884$		0			0
$885$	−12.4598	−	1.38366i	−0.418830	−	0.0465114i
$886$		0			0
$887$	17.3952	−	34.1400i	0.584073	−	1.14631i	−0.390156	−	0.920749i	$-0.627579\pi$
$887$	17.3952	−	34.1400i	0.584073	−	1.14631i	0.974229	−	0.225560i	$-0.0724210\pi$
$888$		0			0
$889$	−58.5830	−	19.0348i	−1.96481	−	0.638406i
$890$		0			0
$891$	−25.0083	+	8.12568i	−0.837809	+	0.272221i
$892$		0			0
$893$	12.0149	+	12.0149i	0.402063	+	0.402063i
$894$		0			0
$895$	−12.3833	+	4.67018i	−0.413928	+	0.156107i
$896$		0			0
$897$	−1.71890	+	0.272247i	−0.0573924	+	0.00909006i
$898$		0			0
$899$	−1.47926			−0.0493360
$900$		0			0
$901$	10.1345			0.337631
$902$		0			0
$903$	17.9090	−	2.83650i	0.595973	−	0.0943929i
$904$		0			0
$905$	0.285936	+	6.14711i	0.00950485	+	0.204337i
$906$		0			0
$907$	19.0363	+	19.0363i	0.632090	+	0.632090i	0.948592	−	0.316502i	$-0.102508\pi$
$907$	19.0363	+	19.0363i	0.632090	+	0.632090i	−0.316502	+	0.948592i	$0.602508\pi$
$908$		0			0
$909$	−20.5833	+	6.68792i	−0.682705	+	0.221824i
$910$		0			0
$911$	−8.49833	−	2.76127i	−0.281562	−	0.0914851i	0.164832	−	0.986322i	$-0.447292\pi$
$911$	−8.49833	−	2.76127i	−0.281562	−	0.0914851i	−0.446394	+	0.894837i	$0.647292\pi$
$912$		0			0
$913$	2.60536	−	5.11331i	0.0862249	−	0.169226i
$914$		0			0
$915$	−4.98005	−	4.53734i	−0.164635	−	0.150000i
$916$		0			0
$917$	−9.20034	+	58.0886i	−0.303822	+	1.91826i
$918$		0			0
$919$	5.78117	−	4.20027i	0.190703	−	0.138554i	−0.488337	−	0.872655i	$-0.662396\pi$
$919$	5.78117	−	4.20027i	0.190703	−	0.138554i	0.679040	+	0.734101i	$0.262396\pi$
$920$		0			0
$921$	7.75463	+	5.63407i	0.255524	+	0.185649i
$922$		0			0
$923$	−2.08096	−	4.08412i	−0.0684958	−	0.134430i
$924$		0			0
$925$	1.96914	−	30.6703i	0.0647450	−	1.00843i
$926$		0			0
$927$	−26.2437	+	13.3718i	−0.861957	+	0.439189i
$928$		0			0
$929$	−34.6210	+	47.6518i	−1.13588	+	1.56340i	−0.359492	+	0.933148i	$0.617050\pi$
$929$	−34.6210	+	47.6518i	−1.13588	+	1.56340i	−0.776388	+	0.630256i	$0.782950\pi$
$930$		0			0
$931$	−4.69243	−	6.45858i	−0.153788	−	0.211671i
$932$		0			0
$933$	−13.1607	−	2.08445i	−0.430863	−	0.0682420i
$934$		0			0
$935$	6.94650	+	12.1967i	0.227175	+	0.398875i
$936$		0			0
$937$	42.2291	+	21.5168i	1.37956	+	0.702923i	0.977153	−	0.212536i	$-0.0681723\pi$
$937$	42.2291	+	21.5168i	1.37956	+	0.702923i	0.402411	+	0.915459i	$0.368172\pi$
$938$		0			0
$939$	2.75554	−	8.48067i	0.0899236	−	0.276756i
$940$		0			0
$941$	−7.17552	−	22.0840i	−0.233915	−	0.719917i	−0.997263	−	0.0739297i	$-0.976446\pi$
$941$	−7.17552	−	22.0840i	−0.233915	−	0.719917i	0.763348	−	0.645987i	$-0.223554\pi$
$942$		0			0
$943$	23.3334	−	23.3334i	0.759842	−	0.759842i
$944$		0			0
$945$	−15.7425	+	12.5955i	−0.512104	+	0.409733i
$946$		0			0
$947$	−2.64143	−	16.6773i	−0.0858350	−	0.541941i	−0.992709	−	0.120538i	$-0.961538\pi$
$947$	−2.64143	−	16.6773i	−0.0858350	−	0.541941i	0.906874	−	0.421402i	$-0.138462\pi$
$948$		0			0
$949$			17.1328i			0.556154i
$950$		0			0
$951$			2.38178i			0.0772345i
$952$		0			0
$953$	−0.859505	−	5.42670i	−0.0278421	−	0.175788i	0.969849	−	0.243708i	$-0.0783638\pi$
$953$	−0.859505	−	5.42670i	−0.0278421	−	0.175788i	−0.997691	+	0.0679198i	$0.978364\pi$
$954$		0			0
$955$	−14.6659	+	53.4746i	−0.474578	+	1.73040i
$956$		0			0
$957$	0.337078	−	0.337078i	0.0108962	−	0.0108962i
$958$		0			0
$959$	22.0415	+	67.8369i	0.711759	+	2.19057i
$960$		0			0
$961$	−1.39418	+	4.29083i	−0.0449734	+	0.138414i
$962$		0			0
$963$	46.3176	+	23.6000i	1.49256	+	0.760499i
$964$		0			0
$965$	3.76490	−	0.777154i	0.121196	−	0.0250175i
$966$		0			0
$967$	16.9870	+	2.69047i	0.546264	+	0.0865196i	0.423466	−	0.905912i	$-0.360813\pi$
$967$	16.9870	+	2.69047i	0.546264	+	0.0865196i	0.122798	+	0.992432i	$0.460813\pi$
$968$		0			0
$969$	−1.31856	−	1.81484i	−0.0423583	−	0.0583011i
$970$		0			0
$971$	9.02464	−	12.4214i	0.289614	−	0.398620i	−0.639274	−	0.768979i	$-0.720765\pi$
$971$	9.02464	−	12.4214i	0.289614	−	0.398620i	0.928889	+	0.370359i	$0.120765\pi$
$972$		0			0
$973$	30.0177	−	15.2948i	0.962324	−	0.490329i
$974$		0			0
$975$	3.21496	−	0.299740i	0.102961	−	0.00959935i
$976$		0			0
$977$	−6.21704	−	12.2016i	−0.198901	−	0.390364i	0.769915	−	0.638146i	$-0.220298\pi$
$977$	−6.21704	−	12.2016i	−0.198901	−	0.390364i	−0.968816	+	0.247782i	$0.920298\pi$
$978$		0			0
$979$	17.7465	+	12.8936i	0.567182	+	0.412082i
$980$		0			0
$981$	19.2786	−	14.0067i	0.615519	−	0.447201i
$982$		0			0
$983$	−4.74666	+	29.9692i	−0.151395	+	0.955870i	0.788656	+	0.614835i	$0.210777\pi$
$983$	−4.74666	+	29.9692i	−0.151395	+	0.955870i	−0.940051	+	0.341035i	$0.889223\pi$
$984$		0			0
$985$	8.49154	−	18.7745i	0.270563	−	0.598206i
$986$		0			0
$987$	4.37832	−	8.59294i	0.139364	−	0.273516i
$988$		0			0
$989$	29.6452	+	9.63231i	0.942663	+	0.306290i
$990$		0			0
$991$	−51.2411	+	16.6492i	−1.62773	+	0.528880i	−0.973747	−	0.227633i	$-0.926902\pi$
$991$	−51.2411	+	16.6492i	−1.62773	+	0.528880i	−0.653979	+	0.756513i	$0.726902\pi$
$992$		0			0
$993$	−7.45917	−	7.45917i	−0.236710	−	0.236710i
$994$		0			0
$995$	−19.4813	+	29.6160i	−0.617600	+	0.938892i
$996$		0			0
$997$	37.4571	−	5.93263i	1.18628	−	0.187888i	0.468055	−	0.883700i	$-0.344955\pi$
$997$	37.4571	−	5.93263i	1.18628	−	0.187888i	0.718225	+	0.695811i	$0.244955\pi$
$998$		0			0
$999$	17.6224			0.557549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.2.bi.d.303.5	✓	80
4.3	odd	2	inner	400.2.bi.d.303.6	yes	80
25.17	odd	20	inner	400.2.bi.d.367.6	yes	80
100.67	even	20	inner	400.2.bi.d.367.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.bi.d.303.5	✓	80	1.1	even	1	trivial
400.2.bi.d.303.6	yes	80	4.3	odd	2	inner
400.2.bi.d.367.5	yes	80	100.67	even	20	inner
400.2.bi.d.367.6	yes	80	25.17	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)

\(f(q)\)	\(=\)	\(q+(-0.492336 + 0.0779784i) q^{3} +(1.22885 - 1.86813i) q^{5} +(-2.22378 - 2.22378i) q^{7} +(-2.61686 + 0.850268i) q^{9} +O(q^{10})\)	\(q+(-0.492336 + 0.0779784i) q^{3} +(1.22885 - 1.86813i) q^{5} +(-2.22378 - 2.22378i) q^{7} +(-2.61686 + 0.850268i) q^{9} +(-3.66397 - 1.19050i) q^{11} +(0.588152 - 1.15431i) q^{13} +(-0.459334 + 1.01557i) q^{15} +(0.254888 - 1.60930i) q^{17} +(-2.23450 + 1.62346i) q^{19} +(1.26825 + 0.921440i) q^{21} +(1.22347 + 2.40119i) q^{23} +(-1.97985 - 4.59132i) q^{25} +(2.55450 - 1.30158i) q^{27} +(0.145907 - 0.200824i) q^{29} +(-3.50271 - 4.82107i) q^{31} +(1.89674 + 0.300414i) q^{33} +(-6.88701 + 1.42162i) q^{35} +(5.47674 + 2.79054i) q^{37} +(-0.199557 + 0.614173i) q^{39} +(-3.78382 - 11.6454i) q^{41} +(8.17876 - 8.17876i) q^{43} +(-1.62731 + 5.93349i) q^{45} +(-0.962376 - 6.07621i) q^{47} +2.89039i q^{49} +0.812193i q^{51} +(0.973014 + 6.14337i) q^{53} +(-6.72648 + 5.38184i) q^{55} +(0.973529 - 0.973529i) q^{57} +(3.47557 + 10.6967i) q^{59} +(-1.86779 + 5.74847i) q^{61} +(7.71012 + 3.92850i) q^{63} +(-1.43366 - 2.51723i) q^{65} +(10.9816 + 1.73931i) q^{67} +(-0.789599 - 1.08679i) q^{69} +(2.07967 - 2.86241i) q^{71} +(-11.7833 + 6.00388i) q^{73} +(1.33277 + 2.10609i) q^{75} +(5.50046 + 10.7953i) q^{77} +(8.71792 + 6.33394i) q^{79} +(5.52191 - 4.01191i) q^{81} +(-0.233028 + 1.47128i) q^{83} +(-2.69317 - 2.45376i) q^{85} +(-0.0561755 + 0.110251i) q^{87} +(-5.41523 - 1.75951i) q^{89} +(-3.87486 + 1.25902i) q^{91} +(2.10045 + 2.10045i) q^{93} +(0.286970 + 6.16933i) q^{95} +(6.11852 - 0.969078i) q^{97} +10.6003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{5}+O(q^{10}) \) 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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