LMFDB - Embedded newform 644.2.y.a.233.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(9,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 22, 30]))

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

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

chi := DirichletCharacter("644.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.y (of order $33$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			233.5
Character	$\chi$	$=$	644.233
Dual form			644.2.y.a.445.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17050 + 0.111769i) q^{3} +(-1.36749 - 3.95112i) q^{5} +(-0.966088 - 2.46306i) q^{7} +(-1.58820 + 0.306101i) q^{9} +O(q^{10})$	\(q+(-1.17050 + 0.111769i) q^{3} +(-1.36749 - 3.95112i) q^{5} +(-0.966088 - 2.46306i) q^{7} +(-1.58820 + 0.306101i) q^{9} +(0.444864 - 0.178097i) q^{11} +(1.11002 + 0.713363i) q^{13} +(2.04227 + 4.47194i) q^{15} +(0.0590046 + 0.243220i) q^{17} +(-1.97102 + 8.12466i) q^{19} +(1.40610 + 2.77504i) q^{21} +(-0.234517 + 4.79009i) q^{23} +(-9.81101 + 7.71546i) q^{25} +(5.20937 - 1.52961i) q^{27} +(-8.65285 - 2.54071i) q^{29} +(5.37929 - 7.55416i) q^{31} +(-0.500809 + 0.258185i) q^{33} +(-8.41072 + 7.18535i) q^{35} +(3.38969 - 0.653310i) q^{37} +(-1.37901 - 0.710927i) q^{39} +(2.55635 - 2.95018i) q^{41} +(-1.31058 + 2.86978i) q^{43} +(3.38130 + 5.85659i) q^{45} +(1.20447 - 2.08620i) q^{47} +(-5.13335 + 4.75907i) q^{49} +(-0.0962496 - 0.278095i) q^{51} +(-6.28494 - 3.24011i) q^{53} +(-1.31203 - 1.51416i) q^{55} +(1.39900 - 9.73023i) q^{57} +(0.366761 - 7.69926i) q^{59} +(-12.0007 - 1.14593i) q^{61} +(2.28829 + 3.61613i) q^{63} +(1.30064 - 5.36132i) q^{65} +(-9.16689 + 7.20892i) q^{67} +(-0.260883 - 5.63302i) q^{69} +(1.26767 + 8.81683i) q^{71} +(1.36407 + 1.30064i) q^{73} +(10.6214 - 10.1275i) q^{75} +(-0.868442 - 0.923672i) q^{77} +(0.832058 - 0.428956i) q^{79} +(-1.42189 + 0.569241i) q^{81} +(-1.40519 - 1.62167i) q^{83} +(0.880303 - 0.565737i) q^{85} +(10.4121 + 2.00678i) q^{87} +(-2.51475 - 3.53147i) q^{89} +(0.684686 - 3.42321i) q^{91} +(-5.45215 + 9.44339i) q^{93} +(34.7968 - 3.32270i) q^{95} +(-11.2294 + 12.9594i) q^{97} +(-0.652020 + 0.419028i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	$ 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) $ 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{11}\right)$	$1$

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
$3$	−1.17050	+	0.111769i	−0.675789	+	0.0645301i	−0.427307	−	0.904106i	$-0.640538\pi$
$3$	−1.17050	+	0.111769i	−0.675789	+	0.0645301i	−0.248482	+	0.968637i	$0.579932\pi$
$4$		0			0
$5$	−1.36749	−	3.95112i	−0.611562	−	1.76699i	−0.641133	−	0.767430i	$-0.721535\pi$
$5$	−1.36749	−	3.95112i	−0.611562	−	1.76699i	0.0295708	−	0.999563i	$-0.490586\pi$
$6$		0			0
$7$	−0.966088	−	2.46306i	−0.365147	−	0.930950i
$7$	−0.966088	−	2.46306i	−0.365147	−	0.930950i
$8$		0			0
$9$	−1.58820	+	0.306101i	−0.529402	+	0.102034i
$10$		0			0
$11$	0.444864	−	0.178097i	0.134132	−	0.0536982i	−0.303626	−	0.952791i	$-0.598197\pi$
$11$	0.444864	−	0.178097i	0.134132	−	0.0536982i	0.437757	+	0.899093i	$0.355773\pi$
$12$		0			0
$13$	1.11002	+	0.713363i	0.307863	+	0.197851i	0.685445	−	0.728125i	$-0.259608\pi$
$13$	1.11002	+	0.713363i	0.307863	+	0.197851i	−0.377582	+	0.925976i	$0.623244\pi$
$14$		0			0
$15$	2.04227	+	4.47194i	0.527311	+	1.15465i
$16$		0			0
$17$	0.0590046	+	0.243220i	0.0143107	+	0.0589896i	0.978519	−	0.206156i	$-0.0660953\pi$
$17$	0.0590046	+	0.243220i	0.0143107	+	0.0589896i	−0.964209	+	0.265145i	$0.914580\pi$
$18$		0			0
$19$	−1.97102	+	8.12466i	−0.452184	+	1.86393i	0.0493404	+	0.998782i	$0.484288\pi$
$19$	−1.97102	+	8.12466i	−0.452184	+	1.86393i	−0.501524	+	0.865144i	$0.667227\pi$
$20$		0			0
$21$	1.40610	+	2.77504i	0.306837	+	0.605563i
$22$		0			0
$23$	−0.234517	+	4.79009i	−0.0489002	+	0.998804i
$23$	−0.234517	+	4.79009i	−0.0489002	+	0.998804i
$24$		0			0
$25$	−9.81101	+	7.71546i	−1.96220	+	1.54309i
$26$		0			0
$27$	5.20937	−	1.52961i	1.00254	−	0.294374i
$28$		0			0
$29$	−8.65285	−	2.54071i	−1.60679	−	0.471797i	−0.649367	−	0.760475i	$-0.724966\pi$
$29$	−8.65285	−	2.54071i	−1.60679	−	0.471797i	−0.957426	+	0.288678i	$0.906784\pi$
$30$		0			0
$31$	5.37929	−	7.55416i	0.966149	−	1.35677i	0.0321536	−	0.999483i	$-0.489763\pi$
$31$	5.37929	−	7.55416i	0.966149	−	1.35677i	0.933996	−	0.357284i	$-0.116297\pi$
$32$		0			0
$33$	−0.500809	+	0.258185i	−0.0871796	+	0.0449442i
$34$		0			0
$35$	−8.41072	+	7.18535i	−1.42167	+	1.21455i
$36$		0			0
$37$	3.38969	−	0.653310i	0.557262	−	0.107403i	0.0971588	−	0.995269i	$-0.469025\pi$
$37$	3.38969	−	0.653310i	0.557262	−	0.107403i	0.460103	+	0.887865i	$0.347812\pi$
$38$		0			0
$39$	−1.37901	−	0.710927i	−0.220818	−	0.113839i
$40$		0			0
$41$	2.55635	−	2.95018i	0.399235	−	0.460741i	−0.520165	−	0.854066i	$-0.674130\pi$
$41$	2.55635	−	2.95018i	0.399235	−	0.460741i	0.919400	+	0.393324i	$0.128675\pi$
$42$		0			0
$43$	−1.31058	+	2.86978i	−0.199862	+	0.437637i	−0.982852	−	0.184398i	$-0.940967\pi$
$43$	−1.31058	+	2.86978i	−0.199862	+	0.437637i	0.782989	+	0.622035i	$0.213694\pi$
$44$		0			0
$45$	3.38130	+	5.85659i	0.504055	+	0.873049i
$46$		0			0
$47$	1.20447	−	2.08620i	0.175690	−	0.304304i	−0.764710	−	0.644375i	$-0.777118\pi$
$47$	1.20447	−	2.08620i	0.175690	−	0.304304i	0.940400	+	0.340071i	$0.110451\pi$
$48$		0			0
$49$	−5.13335	+	4.75907i	−0.733335	+	0.679867i
$50$		0			0
$51$	−0.0962496	−	0.278095i	−0.0134776	−	0.0389411i
$52$		0			0
$53$	−6.28494	−	3.24011i	−0.863302	−	0.445063i	−0.0310875	−	0.999517i	$-0.509897\pi$
$53$	−6.28494	−	3.24011i	−0.863302	−	0.445063i	−0.832215	+	0.554453i	$0.812927\pi$
$54$		0			0
$55$	−1.31203	−	1.51416i	−0.176914	−	0.204170i
$56$		0			0
$57$	1.39900	−	9.73023i	0.185302	−	1.28880i
$58$		0			0
$59$	0.366761	−	7.69926i	0.0477482	−	1.00236i	−0.840160	−	0.542338i	$-0.817539\pi$
$59$	0.366761	−	7.69926i	0.0477482	−	1.00236i	0.887908	−	0.460020i	$-0.152158\pi$
$60$		0			0
$61$	−12.0007	−	1.14593i	−1.53653	−	0.146721i	−0.707817	−	0.706396i	$-0.750320\pi$
$61$	−12.0007	−	1.14593i	−1.53653	−	0.146721i	−0.828712	+	0.559675i	$0.810926\pi$
$62$		0			0
$63$	2.28829	+	3.61613i	0.288298	+	0.455589i
$64$		0			0
$65$	1.30064	−	5.36132i	0.161325	−	0.664990i
$66$		0			0
$67$	−9.16689	+	7.20892i	−1.11991	+	0.880710i	−0.993786	−	0.111304i	$-0.964497\pi$
$67$	−9.16689	+	7.20892i	−1.11991	+	0.880710i	−0.126128	+	0.992014i	$0.540255\pi$
$68$		0			0
$69$	−0.260883	−	5.63302i	−0.0314067	−	0.678136i
$70$		0			0
$71$	1.26767	+	8.81683i	0.150445	+	1.04637i	0.915476	+	0.402372i	$0.131814\pi$
$71$	1.26767	+	8.81683i	0.150445	+	1.04637i	−0.765031	+	0.643993i	$0.777277\pi$
$72$		0			0
$73$	1.36407	+	1.30064i	0.159652	+	0.152228i	0.765695	−	0.643204i	$-0.222395\pi$
$73$	1.36407	+	1.30064i	0.159652	+	0.152228i	−0.606042	+	0.795432i	$0.707244\pi$
$74$		0			0
$75$	10.6214	−	10.1275i	1.22646	−	1.16943i
$76$		0			0
$77$	−0.868442	−	0.923672i	−0.0989681	−	0.105262i
$78$		0			0
$79$	0.832058	−	0.428956i	0.0936139	−	0.0482613i	−0.410784	−	0.911733i	$-0.634745\pi$
$79$	0.832058	−	0.428956i	0.0936139	−	0.0482613i	0.504398	+	0.863471i	$0.331715\pi$
$80$		0			0
$81$	−1.42189	+	0.569241i	−0.157988	+	0.0632490i
$82$		0			0
$83$	−1.40519	−	1.62167i	−0.154239	−	0.178002i	0.673371	−	0.739305i	$-0.264846\pi$
$83$	−1.40519	−	1.62167i	−0.154239	−	0.178002i	−0.827610	+	0.561303i	$0.810300\pi$
$84$		0			0
$85$	0.880303	−	0.565737i	0.0954823	−	0.0613627i
$86$		0			0
$87$	10.4121	+	2.00678i	1.11630	+	0.215149i
$88$		0			0
$89$	−2.51475	−	3.53147i	−0.266563	−	0.374335i	0.659500	−	0.751705i	$-0.270768\pi$
$89$	−2.51475	−	3.53147i	−0.266563	−	0.374335i	−0.926063	+	0.377370i	$0.876829\pi$
$90$		0			0
$91$	0.684686	−	3.42321i	0.0717746	−	0.358850i
$92$		0			0
$93$	−5.45215	+	9.44339i	−0.565361	+	0.979234i
$94$		0			0
$95$	34.7968	−	3.32270i	3.57008	−	0.340901i
$96$		0			0
$97$	−11.2294	+	12.9594i	−1.14017	+	1.31583i	−0.198192	+	0.980163i	$0.563507\pi$
$97$	−11.2294	+	12.9594i	−1.14017	+	1.31583i	−0.941981	+	0.335666i	$0.891039\pi$
$98$		0			0
$99$	−0.652020	+	0.419028i	−0.0655305	+	0.0421139i
$100$		0			0
$101$	3.13183	−	9.04884i	0.311629	−	0.900393i	−0.675058	−	0.737764i	$-0.735882\pi$
$101$	3.13183	−	9.04884i	0.311629	−	0.900393i	0.986687	−	0.162629i	$-0.0519973\pi$
$102$		0			0
$103$	8.38119	+	6.59104i	0.825823	+	0.649435i	0.938915	−	0.344150i	$-0.111833\pi$
$103$	8.38119	+	6.59104i	0.825823	+	0.649435i	−0.113091	+	0.993585i	$0.536075\pi$
$104$		0			0
$105$	9.04166	−	9.35052i	0.882376	−	0.912518i
$106$		0			0
$107$	−11.1696	−	1.06657i	−1.07981	−	0.103109i	−0.460044	−	0.887896i	$-0.652167\pi$
$107$	−11.1696	−	1.06657i	−1.07981	−	0.103109i	−0.619766	+	0.784786i	$0.712773\pi$
$108$		0			0
$109$	−1.33177	−	5.48963i	−0.127560	−	0.525811i	−0.999354	−	0.0359378i	$-0.988558\pi$
$109$	−1.33177	−	5.48963i	−0.127560	−	0.525811i	0.871794	−	0.489873i	$-0.162957\pi$
$110$		0			0
$111$	−3.89462	+	1.14356i	−0.369661	+	0.108542i
$112$		0			0
$113$	−0.839549	−	5.83919i	−0.0789781	−	0.549305i	−0.990443	−	0.137926i	$-0.955956\pi$
$113$	−0.839549	−	5.83919i	−0.0789781	−	0.549305i	0.911464	−	0.411379i	$-0.134953\pi$
$114$		0			0
$115$	19.2469	−	5.62382i	1.79478	−	0.524424i
$116$		0			0
$117$	−1.98129	−	0.793190i	−0.183171	−	0.0733304i
$118$		0			0
$119$	0.542063	−	0.380304i	0.0496908	−	0.0348624i
$120$		0			0
$121$	−7.79489	+	7.43241i	−0.708626	+	0.675674i
$122$		0			0
$123$	−2.66247	+	3.73892i	−0.240067	+	0.337127i
$124$		0			0
$125$	26.3145	+	16.9113i	2.35364	+	1.51259i
$126$		0			0
$127$	0.545744	−	3.79573i	0.0484269	−	0.336817i	−0.951176	−	0.308648i	$-0.900123\pi$
$127$	0.545744	−	3.79573i	0.0484269	−	0.336817i	0.999603	−	0.0281684i	$-0.00896748\pi$
$128$		0			0
$129$	1.21329	−	3.50556i	0.106824	−	0.308648i
$130$		0			0
$131$	−0.378356	−	7.94266i	−0.0330571	−	0.693954i	−0.953194	−	0.302358i	$-0.902226\pi$
$131$	−0.378356	−	7.94266i	−0.0330571	−	0.693954i	0.920137	−	0.391596i	$-0.128077\pi$
$132$		0			0
$133$	21.9157	−	2.99439i	1.90033	−	0.259647i
$134$		0			0
$135$	−13.1675	−	18.4911i	−1.13327	−	1.59146i
$136$		0			0
$137$	6.88720	+	11.9290i	0.588413	+	1.01916i	0.994440	+	0.105300i	$0.0335804\pi$
$137$	6.88720	+	11.9290i	0.588413	+	1.01916i	−0.406027	+	0.913861i	$0.633086\pi$
$138$		0			0
$139$	10.2810			0.872019			0.436010	−	0.899942i	$-0.356391\pi$
$139$	10.2810			0.872019			0.436010	+	0.899942i	$0.356391\pi$
$140$		0			0
$141$	−1.17666	+	2.57652i	−0.0990926	+	0.216982i
$142$		0			0
$143$	0.620854	+	0.119660i	0.0519184	+	0.0100065i
$144$		0			0
$145$	1.79410	+	37.6628i	0.148992	+	3.12773i
$146$		0			0
$147$	5.47667	−	6.14425i	0.451708	−	0.506769i
$148$		0			0
$149$	−8.74741	−	6.87904i	−0.716616	−	0.563553i	0.191894	−	0.981416i	$-0.438537\pi$
$149$	−8.74741	−	6.87904i	−0.716616	−	0.563553i	−0.908510	+	0.417863i	$0.862779\pi$
$150$		0			0
$151$	0.843411	−	17.7054i	0.0686358	−	1.44084i	−0.657584	−	0.753381i	$-0.728422\pi$
$151$	0.843411	−	17.7054i	0.0686358	−	1.44084i	0.726220	−	0.687462i	$-0.241275\pi$
$152$		0			0
$153$	−0.168162	−	0.368222i	−0.0135951	−	0.0297690i
$154$		0			0
$155$	−37.2035	−	10.9239i	−2.98826	−	0.877432i
$156$		0			0
$157$	−13.9676	−	13.3181i	−1.11474	−	1.06290i	−0.997562	−	0.0697897i	$-0.977767\pi$
$157$	−13.9676	−	13.3181i	−1.11474	−	1.06290i	−0.117177	−	0.993111i	$-0.537384\pi$
$158$		0			0
$159$	7.71867	+	3.09009i	0.612130	+	0.245060i
$160$		0			0
$161$	12.0249	−	4.05002i	0.947692	−	0.319187i
$162$		0			0
$163$	−5.35003	−	2.14183i	−0.419047	−	0.167761i	0.152550	−	0.988296i	$-0.451252\pi$
$163$	−5.35003	−	2.14183i	−0.419047	−	0.167761i	−0.571597	+	0.820535i	$0.693676\pi$
$164$		0			0
$165$	1.70497	+	1.62569i	0.132732	+	0.126560i
$166$		0			0
$167$	2.35897	+	0.692655i	0.182542	+	0.0535993i	0.371726	−	0.928342i	$-0.378766\pi$
$167$	2.35897	+	0.692655i	0.182542	+	0.0535993i	−0.189184	+	0.981942i	$0.560584\pi$
$168$		0			0
$169$	−4.67715	−	10.2415i	−0.359781	−	0.787810i
$170$		0			0
$171$	0.643416	−	13.5070i	0.0492032	−	1.03290i
$172$		0			0
$173$	−13.2545	−	10.4235i	−1.00772	−	0.792483i	−0.0294010	−	0.999568i	$-0.509360\pi$
$173$	−13.2545	−	10.4235i	−1.00772	−	0.792483i	−0.978323	+	0.207085i	$0.933602\pi$
$174$		0			0
$175$	28.4820	+	16.7113i	2.15303	+	1.26326i
$176$		0			0
$177$	0.431247	+	9.05299i	0.0324145	+	0.680464i
$178$		0			0
$179$	3.87946	+	0.747704i	0.289964	+	0.0558860i	0.332159	−	0.943223i	$-0.392223\pi$
$179$	3.87946	+	0.747704i	0.289964	+	0.0558860i	−0.0421948	+	0.999109i	$0.513435\pi$
$180$		0			0
$181$	−0.247994	+	0.543031i	−0.0184332	+	0.0403632i	−0.918625	−	0.395131i	$-0.870699\pi$
$181$	−0.247994	+	0.543031i	−0.0184332	+	0.0403632i	0.900191	+	0.435494i	$0.143426\pi$
$182$		0			0
$183$	14.1749			1.04784
$184$		0			0
$185$	−7.21669	−	12.4997i	−0.530581	−	0.918994i
$186$		0			0
$187$	0.0695659	+	0.0976916i	0.00508716	+	0.00714391i
$188$		0			0
$189$	−8.80024	−	11.3533i	−0.640123	−	0.825829i
$190$		0			0
$191$	−0.242617	−	5.09315i	−0.0175551	−	0.368528i	−0.990502	−	0.137499i	$-0.956094\pi$
$191$	−0.242617	−	5.09315i	−0.0175551	−	0.368528i	0.972947	−	0.231029i	$-0.0742093\pi$
$192$		0			0
$193$	−0.672008	+	1.94164i	−0.0483722	+	0.139762i	−0.966600	−	0.256291i	$-0.917499\pi$
$193$	−0.672008	+	1.94164i	−0.0483722	+	0.139762i	0.918227	+	0.396054i	$0.129621\pi$
$194$		0			0
$195$	−0.923172	+	6.42080i	−0.0661097	+	0.459803i
$196$		0			0
$197$	9.78832	+	6.29057i	0.697389	+	0.448185i	0.840706	−	0.541492i	$-0.182140\pi$
$197$	9.78832	+	6.29057i	0.697389	+	0.448185i	−0.143317	+	0.989677i	$0.545777\pi$
$198$		0			0
$199$	−5.07380	+	7.12516i	−0.359672	+	0.505089i	−0.954275	−	0.298931i	$-0.903370\pi$
$199$	−5.07380	+	7.12516i	−0.359672	+	0.505089i	0.594603	+	0.804020i	$0.297309\pi$
$200$		0			0
$201$	9.92412	−	9.46263i	0.699994	−	0.667443i
$202$		0			0
$203$	2.10150	+	23.7670i	0.147496	+	1.66812i
$204$		0			0
$205$	−15.1523	−	6.06607i	−1.05828	−	0.423673i
$206$		0			0
$207$	−1.09379	−	7.67944i	−0.0760239	−	0.533758i
$208$		0			0
$209$	0.570140	+	3.96541i	0.0394374	+	0.274293i
$210$		0			0
$211$	−4.03576	+	1.18501i	−0.277833	+	0.0815791i	−0.417681	−	0.908594i	$-0.637157\pi$
$211$	−4.03576	+	1.18501i	−0.277833	+	0.0815791i	0.139848	+	0.990173i	$0.455339\pi$
$212$		0			0
$213$	−2.46926	−	10.1784i	−0.169191	−	0.697414i
$214$		0			0
$215$	13.1310	+	1.25386i	0.895530	+	0.0855127i
$216$		0			0
$217$	−23.8032	−	5.95155i	−1.61587	−	0.404017i
$218$		0			0
$219$	−1.74202	−	1.36994i	−0.117715	−	0.0925719i
$220$		0			0
$221$	−0.108008	+	0.312070i	−0.00726544	+	0.0209921i
$222$		0			0
$223$	−20.9312	+	13.4517i	−1.40166	+	0.900792i	−0.999888	−	0.0149486i	$-0.995242\pi$
$223$	−20.9312	+	13.4517i	−1.40166	+	0.900792i	−0.401771	+	0.915740i	$0.631605\pi$
$224$		0			0
$225$	13.2202	−	15.2569i	0.881345	−	1.01713i
$226$		0			0
$227$	4.93758	−	0.471482i	0.327719	−	0.0312934i	0.0701000	−	0.997540i	$-0.477668\pi$
$227$	4.93758	−	0.471482i	0.327719	−	0.0312934i	0.257619	+	0.966247i	$0.417062\pi$
$228$		0			0
$229$	−9.49777	+	16.4506i	−0.627630	+	1.08709i	0.360396	+	0.932800i	$0.382642\pi$
$229$	−9.49777	+	16.4506i	−0.627630	+	1.08709i	−0.988026	+	0.154288i	$0.950692\pi$
$230$		0			0
$231$	1.11975	+	0.984094i	0.0736742	+	0.0647486i
$232$		0			0
$233$	−5.63018	−	7.90648i	−0.368845	−	0.517971i	0.587886	−	0.808944i	$-0.299960\pi$
$233$	−5.63018	−	7.90648i	−0.368845	−	0.517971i	−0.956731	+	0.290973i	$0.906021\pi$
$234$		0			0
$235$	−9.88993	−	1.90613i	−0.645148	−	0.124342i
$236$		0			0
$237$	−0.925981	+	0.595092i	−0.0601489	+	0.0386554i
$238$		0			0
$239$	11.7079	+	13.5117i	0.757324	+	0.873998i	0.995257	−	0.0972836i	$-0.0310154\pi$
$239$	11.7079	+	13.5117i	0.757324	+	0.873998i	−0.237933	+	0.971282i	$0.576470\pi$
$240$		0			0
$241$	−1.68921	+	0.676256i	−0.108811	+	0.0435615i	−0.425429	−	0.904992i	$-0.639877\pi$
$241$	−1.68921	+	0.676256i	−0.108811	+	0.0435615i	0.316618	+	0.948553i	$0.397453\pi$
$242$		0			0
$243$	−12.8766	+	6.63832i	−0.826031	+	0.425849i
$244$		0			0
$245$	25.8235	+	13.7744i	1.64980	+	0.880017i
$246$		0			0
$247$	−7.98370	+	7.61245i	−0.507991	+	0.484368i
$248$		0			0
$249$	1.82603	+	1.74111i	0.115720	+	0.110339i
$250$		0			0
$251$	−1.67120	−	11.6234i	−0.105485	−	0.733664i	−0.972080	−	0.234651i	$-0.924605\pi$
$251$	−1.67120	−	11.6234i	−0.105485	−	0.733664i	0.866595	−	0.499013i	$-0.166304\pi$
$252$		0			0
$253$	0.748773	+	2.17271i	0.0470749	+	0.136597i
$254$		0			0
$255$	−0.967164	+	0.760586i	−0.0605662	+	0.0476298i
$256$		0			0
$257$	4.39485	−	18.1158i	0.274143	−	1.13003i	−0.653608	−	0.756833i	$-0.726746\pi$
$257$	4.39485	−	18.1158i	0.274143	−	1.13003i	0.927751	−	0.373200i	$-0.121739\pi$
$258$		0			0
$259$	−4.88388	−	7.71787i	−0.303470	−	0.479565i
$260$		0			0
$261$	14.5202	+	1.38651i	0.898778	+	0.0858229i
$262$		0			0
$263$	−1.28463	+	26.9678i	−0.0792139	+	1.66291i	0.513947	+	0.857822i	$0.328183\pi$
$263$	−1.28463	+	26.9678i	−0.0792139	+	1.66291i	−0.593161	+	0.805084i	$0.702120\pi$
$264$		0			0
$265$	−4.20743	+	29.2633i	−0.258461	+	1.79763i
$266$		0			0
$267$	3.33823	+	3.85252i	0.204296	+	0.235770i
$268$		0			0
$269$	19.8756	+	10.2466i	1.21184	+	0.624747i	0.941173	−	0.337926i	$-0.109726\pi$
$269$	19.8756	+	10.2466i	1.21184	+	0.624747i	0.270667	+	0.962673i	$0.412756\pi$
$270$		0			0
$271$	−6.58804	−	19.0349i	−0.400195	−	1.15629i	−0.947611	−	0.319427i	$-0.896510\pi$
$271$	−6.58804	−	19.0349i	−0.400195	−	1.15629i	0.547416	−	0.836861i	$-0.315612\pi$
$272$		0			0
$273$	−0.418816	+	4.08340i	−0.0253479	+	0.247138i
$274$		0			0
$275$	−2.99047	+	5.17964i	−0.180332	+	0.312344i
$276$		0			0
$277$	−0.781827	−	1.35416i	−0.0469755	−	0.0813639i	0.841582	−	0.540130i	$-0.181625\pi$
$277$	−0.781827	−	1.35416i	−0.0469755	−	0.0813639i	−0.888557	+	0.458766i	$0.848292\pi$
$278$		0			0
$279$	−6.23108	+	13.6442i	−0.373045	+	0.816854i
$280$		0			0
$281$	20.7365	−	23.9312i	1.23704	−	1.42762i	0.370252	−	0.928931i	$-0.379271\pi$
$281$	20.7365	−	23.9312i	1.23704	−	1.42762i	0.866784	−	0.498684i	$-0.166183\pi$
$282$		0			0
$283$	−9.74486	−	5.02383i	−0.579272	−	0.298636i	0.143580	−	0.989639i	$-0.454139\pi$
$283$	−9.74486	−	5.02383i	−0.579272	−	0.298636i	−0.722852	+	0.691003i	$0.757169\pi$
$284$		0			0
$285$	−40.3584	+	7.77844i	−2.39062	+	0.460755i
$286$		0			0
$287$	−9.73615	−	3.44631i	−0.574707	−	0.203429i
$288$		0			0
$289$	15.0545	−	7.76115i	0.885560	−	0.456538i
$290$		0			0
$291$	11.6956	−	16.4241i	0.685606	−	0.962799i
$292$		0			0
$293$	−20.1593	−	5.91930i	−1.17772	−	0.345809i	−0.366425	−	0.930448i	$-0.619418\pi$
$293$	−20.1593	−	5.91930i	−1.17772	−	0.345809i	−0.811294	+	0.584638i	$0.801236\pi$
$294$		0			0
$295$	−30.9222	+	9.07958i	−1.80036	+	0.528634i
$296$		0			0
$297$	2.04505	−	1.60824i	0.118666	−	0.0933197i
$298$		0			0
$299$	−3.67740	+	5.14978i	−0.212669	+	0.297820i
$300$		0			0
$301$	8.33458	+	0.455591i	0.480397	+	0.0262598i
$302$		0			0
$303$	−2.65443	+	10.9417i	−0.152493	+	0.628586i
$304$		0			0
$305$	11.8832	+	48.9831i	0.680428	+	2.80476i
$306$		0			0
$307$	4.66854	+	10.2227i	0.266447	+	0.583439i	0.994810	−	0.101754i	$-0.0324454\pi$
$307$	4.66854	+	10.2227i	0.266447	+	0.583439i	−0.728362	+	0.685192i	$0.759718\pi$
$308$		0			0
$309$	−10.5469	−	6.77806i	−0.599991	−	0.385591i
$310$		0			0
$311$	−16.2144	+	6.49126i	−0.919434	+	0.368086i	−0.782612	−	0.622510i	$-0.786113\pi$
$311$	−16.2144	+	6.49126i	−0.919434	+	0.368086i	−0.136822	+	0.990596i	$0.543689\pi$
$312$		0			0
$313$	16.5463	−	3.18904i	0.935254	−	0.180255i	0.301215	−	0.953556i	$-0.402608\pi$
$313$	16.5463	−	3.18904i	0.935254	−	0.180255i	0.634039	+	0.773301i	$0.281396\pi$
$314$		0			0
$315$	11.1585	−	13.9863i	0.628710	−	0.788041i
$316$		0			0
$317$	−7.85371	−	22.6918i	−0.441108	−	1.27450i	−0.918365	−	0.395735i	$-0.870490\pi$
$317$	−7.85371	−	22.6918i	−0.441108	−	1.27450i	0.477257	−	0.878764i	$-0.341631\pi$
$318$		0			0
$319$	−4.30184	+	0.410776i	−0.240857	+	0.0229990i
$320$		0			0
$321$	13.1933			0.736378
$322$		0			0
$323$	−2.09238			−0.116423
$324$		0			0
$325$	−16.3943	+	1.56547i	−0.909392	+	0.0868364i
$326$		0			0
$327$	2.17241	+	6.27677i	0.120135	+	0.347106i
$328$		0			0
$329$	−6.30207	−	0.951227i	−0.347444	−	0.0524428i
$330$		0			0
$331$	−19.1180	+	3.68469i	−1.05082	+	0.202529i	−0.685290	−	0.728271i	$-0.740324\pi$
$331$	−19.1180	+	3.68469i	−1.05082	+	0.202529i	−0.365530	+	0.930800i	$0.619112\pi$
$332$		0			0
$333$	−5.18355	+	2.07518i	−0.284057	+	0.113719i
$334$		0			0
$335$	41.0190	+	26.3613i	2.24111	+	1.44027i
$336$		0			0
$337$	6.26208	+	13.7120i	0.341117	+	0.746942i	0.999986	−	0.00531552i	$-0.00169199\pi$
$337$	6.26208	+	13.7120i	0.341117	+	0.746942i	−0.658869	+	0.752258i	$0.728965\pi$
$338$		0			0
$339$	1.63534	+	6.74094i	0.0888192	+	0.366118i
$340$		0			0
$341$	1.04768	−	4.31861i	0.0567353	−	0.233866i
$342$		0			0
$343$	16.6811	+	8.04607i	0.900697	+	0.434447i
$344$		0			0
$345$	−21.9000	+	8.73391i	−1.17905	+	0.470218i
$346$		0			0
$347$	−11.8173	+	9.29325i	−0.634388	+	0.498888i	−0.882789	−	0.469769i	$-0.844337\pi$
$347$	−11.8173	+	9.29325i	−0.634388	+	0.498888i	0.248402	+	0.968657i	$0.420095\pi$
$348$		0			0
$349$	10.9902	−	3.22703i	0.588294	−	0.172739i	0.0259800	−	0.999662i	$-0.491729\pi$
$349$	10.9902	−	3.22703i	0.588294	−	0.172739i	0.562314	+	0.826924i	$0.309911\pi$
$350$		0			0
$351$	6.87365	+	2.01829i	0.366888	+	0.107728i
$352$		0			0
$353$	14.7222	−	20.6744i	0.783584	−	1.10039i	−0.208891	−	0.977939i	$-0.566985\pi$
$353$	14.7222	−	20.6744i	0.783584	−	1.10039i	0.992475	−	0.122450i	$-0.0390752\pi$
$354$		0			0
$355$	33.1028	−	17.0657i	1.75691	−	0.905752i
$356$		0			0
$357$	−0.591979	+	0.505733i	−0.0313309	+	0.0267662i
$358$		0			0
$359$	−4.02630	+	0.776005i	−0.212500	+	0.0409560i	−0.294390	−	0.955685i	$-0.595116\pi$
$359$	−4.02630	+	0.776005i	−0.212500	+	0.0409560i	0.0818902	+	0.996641i	$0.473904\pi$
$360$		0			0
$361$	−45.2374	−	23.3215i	−2.38091	−	1.22745i
$362$		0			0
$363$	8.29321	−	9.57088i	0.435281	−	0.502341i
$364$		0			0
$365$	3.27362	−	7.16822i	0.171349	−	0.375202i
$366$		0			0
$367$	−3.66823	−	6.35356i	−0.191480	−	0.331653i	0.754261	−	0.656575i	$-0.227995\pi$
$367$	−3.66823	−	6.35356i	−0.191480	−	0.331653i	−0.945741	+	0.324922i	$0.894662\pi$
$368$		0			0
$369$	−3.15695	+	5.46800i	−0.164344	+	0.284653i
$370$		0			0
$371$	−1.90879	+	18.6104i	−0.0990994	+	0.966205i
$372$		0			0
$373$	6.03630	+	17.4407i	0.312548	+	0.903047i	0.986426	+	0.164205i	$0.0525058\pi$
$373$	6.03630	+	17.4407i	0.312548	+	0.903047i	−0.673879	+	0.738842i	$0.735373\pi$
$374$		0			0
$375$	−32.6913	−	16.8535i	−1.68817	−	0.870313i
$376$		0			0
$377$	−7.79235	−	8.99285i	−0.401326	−	0.463155i
$378$		0			0
$379$	3.13327	−	21.7923i	0.160945	−	1.11940i	−0.735912	−	0.677077i	$-0.763246\pi$
$379$	3.13327	−	21.7923i	0.160945	−	1.11940i	0.896857	−	0.442320i	$-0.145845\pi$
$380$		0			0
$381$	−0.214547	+	4.50391i	−0.0109916	+	0.230742i
$382$		0			0
$383$	−28.7563	−	2.74589i	−1.46938	−	0.140309i	−0.670548	−	0.741866i	$-0.733941\pi$
$383$	−28.7563	−	2.74589i	−1.46938	−	0.140309i	−0.798830	+	0.601557i	$0.794547\pi$
$384$		0			0
$385$	−2.46194	+	4.69443i	−0.125472	+	0.239250i
$386$		0			0
$387$	1.20303	−	4.95897i	0.0611536	−	0.252079i
$388$		0			0
$389$	6.48989	−	5.10371i	0.329051	−	0.258768i	−0.439942	−	0.898026i	$-0.645001\pi$
$389$	6.48989	−	5.10371i	0.329051	−	0.258768i	0.768992	+	0.639258i	$0.220758\pi$
$390$		0			0
$391$	−1.17889	+	0.225598i	−0.0596188	+	0.0114090i
$392$		0			0
$393$	1.33061	+	9.25461i	0.0671205	+	0.466833i
$394$		0			0
$395$	−2.83269	−	2.70096i	−0.142528	−	0.135900i
$396$		0			0
$397$	14.2979	−	13.6330i	0.717592	−	0.684223i	−0.240511	−	0.970646i	$-0.577315\pi$
$397$	14.2979	−	13.6330i	0.717592	−	0.684223i	0.958103	+	0.286424i	$0.0924665\pi$
$398$		0			0
$399$	−25.3177	+	5.95445i	−1.26747	+	0.298095i
$400$		0			0
$401$	14.9959	−	7.73093i	0.748860	−	0.386064i	−0.0411538	−	0.999153i	$-0.513103\pi$
$401$	14.9959	−	7.73093i	0.748860	−	0.386064i	0.790014	+	0.613088i	$0.210073\pi$
$402$		0			0
$403$	11.3600	−	4.54784i	0.565880	−	0.226544i
$404$		0			0
$405$	4.19357	+	4.83964i	0.208380	+	0.240483i
$406$		0			0
$407$	1.39160	−	0.894328i	0.0689791	−	0.0443302i
$408$		0			0
$409$	−9.66306	−	1.86240i	−0.477808	−	0.0920899i	−0.0553394	−	0.998468i	$-0.517624\pi$
$409$	−9.66306	−	1.86240i	−0.477808	−	0.0920899i	−0.422468	+	0.906378i	$0.638836\pi$
$410$		0			0
$411$	−9.39477	−	13.1931i	−0.463410	−	0.650768i
$412$		0			0
$413$	−19.3181	+	6.53481i	−0.950580	+	0.321557i
$414$		0			0
$415$	−4.48583	+	7.76968i	−0.220201	+	0.381399i
$416$		0			0
$417$	−12.0339	+	1.14910i	−0.589301	+	0.0562714i
$418$		0			0
$419$	5.99929	−	6.92355i	0.293085	−	0.338238i	−0.590042	−	0.807373i	$-0.700889\pi$
$419$	5.99929	−	6.92355i	0.293085	−	0.338238i	0.883126	+	0.469135i	$0.155434\pi$
$420$		0			0
$421$	−1.08324	+	0.696159i	−0.0527941	+	0.0339287i	−0.566772	−	0.823875i	$-0.691808\pi$
$421$	−1.08324	+	0.696159i	−0.0527941	+	0.0339287i	0.513978	+	0.857804i	$0.328171\pi$
$422$		0			0
$423$	−1.27435	+	3.68200i	−0.0619612	+	0.179025i
$424$		0			0
$425$	−2.45545	−	1.93099i	−0.119107	−	0.0936667i
$426$		0			0
$427$	8.77122	+	30.6655i	0.424469	+	1.48401i
$428$		0			0
$429$	−0.740085	−	0.0706696i	−0.0357316	−	0.00341196i
$430$		0			0
$431$	1.44525	+	5.95740i	0.0696153	+	0.286958i	0.995969	−	0.0896962i	$-0.0285896\pi$
$431$	1.44525	+	5.95740i	0.0696153	+	0.286958i	−0.926354	+	0.376654i	$0.877074\pi$
$432$		0			0
$433$	5.52525	−	1.62236i	0.265527	−	0.0779657i	−0.146259	−	0.989246i	$-0.546723\pi$
$433$	5.52525	−	1.62236i	0.265527	−	0.0779657i	0.411786	+	0.911281i	$0.364905\pi$
$434$		0			0
$435$	−6.30954	−	43.8838i	−0.302519	−	2.10407i
$436$		0			0
$437$	−38.4557	−	11.3468i	−1.83958	−	0.542789i
$438$		0			0
$439$	−6.70976	−	2.68618i	−0.320239	−	0.128205i	0.205973	−	0.978558i	$-0.433964\pi$
$439$	−6.70976	−	2.68618i	−0.320239	−	0.128205i	−0.526212	+	0.850353i	$0.676388\pi$
$440$		0			0
$441$	6.69605	−	9.12970i	0.318859	−	0.434748i
$442$		0			0
$443$	−8.25707	+	7.87310i	−0.392305	+	0.374062i	−0.860403	−	0.509614i	$-0.829788\pi$
$443$	−8.25707	+	7.87310i	−0.392305	+	0.374062i	0.468098	+	0.883677i	$0.344940\pi$
$444$		0			0
$445$	−10.5143	+	14.7653i	−0.498428	+	0.699944i
$446$		0			0
$447$	11.0077	+	7.07424i	0.520648	+	0.334600i
$448$		0			0
$449$	−1.94753	+	13.5453i	−0.0919094	+	0.639244i	0.890842	+	0.454313i	$0.150115\pi$
$449$	−1.94753	+	13.5453i	−0.0919094	+	0.639244i	−0.982752	+	0.184931i	$0.940794\pi$
$450$		0			0
$451$	0.611811	−	1.76771i	0.0288090	−	0.0832382i
$452$		0			0
$453$	0.991705	+	20.8184i	0.0465944	+	0.978136i
$454$		0			0
$455$	−14.4618	+	1.97594i	−0.677979	+	0.0926337i
$456$		0			0
$457$	16.5176	+	23.1957i	0.772659	+	1.08505i	0.993949	+	0.109839i	$0.0350336\pi$
$457$	16.5176	+	23.1957i	0.772659	+	1.08505i	−0.221291	+	0.975208i	$0.571027\pi$
$458$		0			0
$459$	0.679409	+	1.17677i	0.0317121	+	0.0549270i
$460$		0			0
$461$	−21.6390			−1.00783			−0.503914	−	0.863754i	$-0.668107\pi$
$461$	−21.6390			−1.00783			−0.503914	+	0.863754i	$0.668107\pi$
$462$		0			0
$463$	−5.02073	+	10.9939i	−0.233333	+	0.510929i	−0.989689	−	0.143232i	$-0.954251\pi$
$463$	−5.02073	+	10.9939i	−0.233333	+	0.510929i	0.756356	+	0.654160i	$0.226978\pi$
$464$		0			0
$465$	44.7677	+	8.62827i	2.07605	+	0.400126i
$466$		0			0
$467$	0.630759	+	13.2413i	0.0291880	+	0.612732i	0.965318	+	0.261077i	$0.0840778\pi$
$467$	0.630759	+	13.2413i	0.0291880	+	0.612732i	−0.936130	+	0.351655i	$0.885619\pi$
$468$		0			0
$469$	26.6120	+	15.6142i	1.22883	+	0.720995i
$470$		0			0
$471$	17.8377	+	14.0277i	0.821917	+	0.646363i
$472$		0			0
$473$	−0.0719337	+	1.51007i	−0.00330751	+	0.0694333i
$474$		0			0
$475$	−43.3478	−	94.9185i	−1.98893	−	4.35516i
$476$		0			0
$477$	10.9736	+	3.22213i	0.502445	+	0.147531i
$478$		0			0
$479$	−7.28389	−	6.94518i	−0.332809	−	0.317333i	0.505186	−	0.863011i	$-0.331424\pi$
$479$	−7.28389	−	6.94518i	−0.332809	−	0.317333i	−0.837995	+	0.545677i	$0.816272\pi$
$480$		0			0
$481$	4.22866	+	1.69290i	0.192810	+	0.0771895i
$482$		0			0
$483$	−13.6225	+	6.08457i	−0.619843	+	0.276857i
$484$		0			0
$485$	66.5603	+	26.6467i	3.02235	+	1.20997i
$486$		0			0
$487$	22.4967	+	21.4505i	1.01942	+	0.972016i	0.999614	−	0.0277877i	$-0.00884622\pi$
$487$	22.4967	+	21.4505i	1.01942	+	0.972016i	0.0198074	+	0.999804i	$0.493695\pi$
$488$		0			0
$489$	6.50161	+	1.90904i	0.294013	+	0.0863300i
$490$		0			0
$491$	1.54913	+	3.39213i	0.0699114	+	0.153085i	0.941362	−	0.337399i	$-0.109547\pi$
$491$	1.54913	+	3.39213i	0.0699114	+	0.153085i	−0.871450	+	0.490484i	$0.836820\pi$
$492$		0			0
$493$	0.107393	−	2.25446i	0.00483675	−	0.101536i
$494$		0			0
$495$	2.54726	+	2.00319i	0.114491	+	0.0900366i
$496$		0			0
$497$	20.4917	−	11.6402i	0.919179	−	0.522134i
$498$		0			0
$499$	0.253306	+	5.31754i	0.0113395	+	0.238046i	0.997420	+	0.0717800i	$0.0228680\pi$
$499$	0.253306	+	5.31754i	0.0113395	+	0.238046i	−0.986081	+	0.166266i	$0.946829\pi$
$500$		0			0
$501$	−2.83859	−	0.547094i	−0.126819	−	0.0244423i
$502$		0			0
$503$	8.82443	−	19.3228i	0.393462	−	0.861562i	−0.604429	−	0.796659i	$-0.706599\pi$
$503$	8.82443	−	19.3228i	0.393462	−	0.861562i	0.997892	−	0.0649032i	$-0.0206739\pi$
$504$		0			0
$505$	−40.0358			−1.78157
$506$		0			0
$507$	6.61930	+	11.4650i	0.293973	+	0.509177i
$508$		0			0
$509$	−9.32465	−	13.0946i	−0.413308	−	0.580410i	0.554474	−	0.832201i	$-0.312920\pi$
$509$	−9.32465	−	13.0946i	−0.413308	−	0.580410i	−0.967781	+	0.251792i	$0.918980\pi$
$510$		0			0
$511$	1.88574	−	4.61632i	0.0834203	−	0.204214i
$512$		0			0
$513$	2.15978	+	45.3393i	0.0953565	+	2.00178i
$514$		0			0
$515$	14.5807	−	42.1283i	0.642504	−	1.85639i
$516$		0			0
$517$	0.164279	−	1.14259i	0.00722500	−	0.0502510i
$518$		0			0
$519$	16.6795	+	10.7193i	0.732148	+	0.470523i
$520$		0			0
$521$	13.4768	−	18.9255i	0.590429	−	0.829142i	−0.405974	−	0.913885i	$-0.633067\pi$
$521$	13.4768	−	18.9255i	0.590429	−	0.829142i	0.996403	+	0.0847429i	$0.0270069\pi$
$522$		0			0
$523$	−22.5126	+	21.4657i	−0.984408	+	0.938631i	−0.998121	−	0.0612753i	$-0.980483\pi$
$523$	−22.5126	+	21.4657i	−0.984408	+	0.938631i	0.0137134	+	0.999906i	$0.495635\pi$
$524$		0			0
$525$	−35.2060	−	16.3772i	−1.53652	−	0.714759i
$526$		0			0
$527$	2.15473	+	0.862623i	0.0938614	+	0.0375765i
$528$		0			0
$529$	−22.8900	−	2.24672i	−0.995218	−	0.0976833i
$530$		0			0
$531$	1.77426	+	12.3403i	0.0769964	+	0.535522i
$532$		0			0
$533$	4.94214	−	1.45114i	0.214068	−	0.0628560i
$534$		0			0
$535$	11.0603	+	45.5911i	0.478178	+	1.97108i
$536$		0			0
$537$	−4.62448	−	0.441585i	−0.199561	−	0.0190558i
$538$		0			0
$539$	−1.43607	+	3.03137i	−0.0618559	+	0.130571i
$540$		0			0
$541$	−12.3398	−	9.70415i	−0.530531	−	0.417214i	0.316631	−	0.948549i	$-0.397448\pi$
$541$	−12.3398	−	9.70415i	−0.530531	−	0.417214i	−0.847162	+	0.531335i	$0.821691\pi$
$542$		0			0
$543$	0.229583	−	0.663337i	0.00985235	−	0.0284665i
$544$		0			0
$545$	−19.8690	+	12.7690i	−0.851093	+	0.546964i
$546$		0			0
$547$	4.06678	−	4.69332i	0.173883	−	0.200672i	−0.662118	−	0.749400i	$-0.730342\pi$
$547$	4.06678	−	4.69332i	0.173883	−	0.200672i	0.836001	+	0.548728i	$0.184888\pi$
$548$		0			0
$549$	19.4103	−	1.85346i	0.828411	−	0.0791037i
$550$		0			0
$551$	37.6973	−	65.2937i	1.60596	−	2.78161i
$552$		0			0
$553$	−1.86039	−	1.63500i	−0.0791117	−	0.0695273i
$554$		0			0
$555$	9.84422	+	13.8243i	0.417864	+	0.586808i
$556$		0			0
$557$	23.0990	+	4.45197i	0.978738	+	0.188636i	0.653442	−	0.756976i	$-0.273324\pi$
$557$	23.0990	+	4.45197i	0.978738	+	0.188636i	0.325295	+	0.945612i	$0.394536\pi$
$558$		0			0
$559$	−3.50196	+	2.25058i	−0.148117	+	0.0951892i
$560$		0			0
$561$	−0.0923459	−	0.106573i	−0.00389885	−	0.00449951i
$562$		0			0
$563$	14.6486	−	5.86442i	0.617366	−	0.247156i	−0.0418332	−	0.999125i	$-0.513320\pi$
$563$	14.6486	−	5.86442i	0.617366	−	0.247156i	0.659199	+	0.751969i	$0.270896\pi$
$564$		0			0
$565$	−21.9232	+	11.3022i	−0.922317	+	0.475488i
$566$		0			0
$567$	2.77575	+	2.95228i	0.116571	+	0.123984i
$568$		0			0
$569$	12.4574	−	11.8781i	0.522242	−	0.497957i	−0.382477	−	0.923965i	$-0.624929\pi$
$569$	12.4574	−	11.8781i	0.522242	−	0.497957i	0.904719	+	0.426008i	$0.140080\pi$
$570$		0			0
$571$	25.3780	+	24.1979i	1.06204	+	1.01265i	0.999894	+	0.0145815i	$0.00464161\pi$
$571$	25.3780	+	24.1979i	1.06204	+	1.01265i	0.0621419	+	0.998067i	$0.480207\pi$
$572$		0			0
$573$	0.853242	+	5.93443i	0.0356447	+	0.247914i
$574$		0			0
$575$	−34.6569	−	48.8051i	−1.44529	−	2.03531i
$576$		0			0
$577$	18.2381	−	14.3426i	0.759262	−	0.597090i	−0.161656	−	0.986847i	$-0.551683\pi$
$577$	18.2381	−	14.3426i	0.759262	−	0.597090i	0.920918	+	0.389757i	$0.127441\pi$
$578$		0			0
$579$	0.569571	−	2.34780i	0.0236706	−	0.0975714i
$580$		0			0
$581$	−2.63674	+	5.02774i	−0.109391	+	0.208586i
$582$		0			0
$583$	−3.37300	−	0.322082i	−0.139695	−	0.0133393i
$584$		0			0
$585$	−0.424578	+	8.91300i	−0.0175542	+	0.368507i
$586$		0			0
$587$	3.76917	−	26.2152i	0.155570	−	1.08202i	−0.751104	−	0.660184i	$-0.770478\pi$
$587$	3.76917	−	26.2152i	0.155570	−	1.08202i	0.906674	−	0.421832i	$-0.138613\pi$
$588$		0			0
$589$	50.7723	+	58.5944i	2.09204	+	2.41434i
$590$		0			0
$591$	−12.1603	−	6.26909i	−0.500210	−	0.257876i
$592$		0			0
$593$	3.60315	+	10.4106i	0.147963	+	0.427512i	0.994490	−	0.104835i	$-0.0334313\pi$
$593$	3.60315	+	10.4106i	0.147963	+	0.427512i	−0.846526	+	0.532347i	$0.821310\pi$
$594$		0			0
$595$	−2.24389	−	1.62169i	−0.0919907	−	0.0664828i
$596$		0			0
$597$	5.14252	−	8.90710i	0.210469	−	0.364543i
$598$		0			0
$599$	−7.35854	−	12.7454i	−0.300662	−	0.520762i	0.675624	−	0.737246i	$-0.263874\pi$
$599$	−7.35854	−	12.7454i	−0.300662	−	0.520762i	−0.976286	+	0.216484i	$0.930541\pi$
$600$		0			0
$601$	9.36587	−	20.5084i	0.382042	−	0.836555i	−0.616738	−	0.787169i	$-0.711546\pi$
$601$	9.36587	−	20.5084i	0.382042	−	0.836555i	0.998780	−	0.0493866i	$-0.0157266\pi$
$602$		0			0
$603$	12.3522	−	14.2552i	0.503022	−	0.580518i
$604$		0			0
$605$	40.0258	+	20.6347i	1.62728	+	0.838921i
$606$		0			0
$607$	24.5486	−	4.73135i	0.996397	−	0.192040i	0.335115	−	0.942177i	$-0.391225\pi$
$607$	24.5486	−	4.73135i	0.996397	−	0.192040i	0.661282	+	0.750138i	$0.270013\pi$
$608$		0			0
$609$	−5.11623	−	27.5845i	−0.207320	−	1.11778i
$610$		0			0
$611$	2.82520	−	1.45649i	0.114295	−	0.0589233i
$612$		0			0
$613$	23.7576	−	33.3629i	0.959562	−	1.34752i	0.0219775	−	0.999758i	$-0.493004\pi$
$613$	23.7576	−	33.3629i	0.959562	−	1.34752i	0.937584	−	0.347758i	$-0.113057\pi$
$614$		0			0
$615$	18.4138	+	5.40678i	0.742516	+	0.218023i
$616$		0			0
$617$	−11.8520	+	3.48005i	−0.477143	+	0.140102i	−0.511456	−	0.859309i	$-0.670894\pi$
$617$	−11.8520	+	3.48005i	−0.477143	+	0.140102i	0.0343134	+	0.999411i	$0.489076\pi$
$618$		0			0
$619$	27.0312	−	21.2576i	1.08648	−	0.854414i	0.0964550	−	0.995337i	$-0.469250\pi$
$619$	27.0312	−	21.2576i	1.08648	−	0.854414i	0.990020	+	0.140924i	$0.0450072\pi$
$620$		0			0
$621$	6.10529	+	25.3121i	0.244997	+	1.01574i
$622$		0			0
$623$	−6.26876	+	9.60569i	−0.251153	+	0.384844i
$624$		0			0
$625$	16.1206	−	66.4500i	0.644824	−	2.65800i
$626$		0			0
$627$	−1.11056	−	4.57779i	−0.0443515	−	0.182819i
$628$		0			0
$629$	0.358906	+	0.785894i	0.0143105	+	0.0313356i
$630$		0			0
$631$	−10.1279	−	6.50882i	−0.403186	−	0.259112i	0.323295	−	0.946298i	$-0.395209\pi$
$631$	−10.1279	−	6.50882i	−0.403186	−	0.259112i	−0.726481	+	0.687186i	$0.758846\pi$
$632$		0			0
$633$	4.59141	−	1.83812i	0.182492	−	0.0730589i
$634$		0			0
$635$	−15.7437	+	3.03434i	−0.624769	+	0.120414i
$636$		0			0
$637$	−9.09304	+	1.62070i	−0.360279	+	0.0642143i
$638$		0			0
$639$	−4.71216	−	13.6149i	−0.186410	−	0.538597i
$640$		0			0
$641$	−33.7790	+	3.22550i	−1.33419	+	0.127400i	−0.737650	−	0.675183i	$-0.764065\pi$
$641$	−33.7790	+	3.22550i	−1.33419	+	0.127400i	−0.596540	+	0.802583i	$0.703458\pi$
$642$		0			0
$643$	−23.3294			−0.920021			−0.460011	−	0.887913i	$-0.652154\pi$
$643$	−23.3294			−0.920021			−0.460011	+	0.887913i	$0.652154\pi$
$644$		0			0
$645$	−15.5101			−0.610708
$646$		0			0
$647$	−27.5736	+	2.63296i	−1.08403	+	0.103512i	−0.621745	−	0.783220i	$-0.713576\pi$
$647$	−27.5736	+	2.63296i	−1.08403	+	0.103512i	−0.462284	+	0.886732i	$0.652970\pi$
$648$		0			0
$649$	−1.20806	−	3.49045i	−0.0474203	−	0.137012i
$650$		0			0
$651$	28.5269	+	4.30582i	1.11806	+	0.168758i
$652$		0			0
$653$	−32.3304	+	6.23118i	−1.26519	+	0.243845i	−0.777338	−	0.629083i	$-0.783430\pi$
$653$	−32.3304	+	6.23118i	−1.26519	+	0.243845i	−0.487849	+	0.872928i	$0.662218\pi$
$654$		0			0
$655$	−30.8650	+	12.3565i	−1.20599	+	0.482807i
$656$		0			0
$657$	−2.56455	−	1.64814i	−0.100053	−	0.0643000i
$658$		0			0
$659$	3.49641	+	7.65608i	0.136201	+	0.298238i	0.965426	−	0.260676i	$-0.0839454\pi$
$659$	3.49641	+	7.65608i	0.136201	+	0.298238i	−0.829225	+	0.558914i	$0.811218\pi$
$660$		0			0
$661$	−6.71837	−	27.6935i	−0.261314	−	1.07715i	−0.939578	−	0.342334i	$-0.888783\pi$
$661$	−6.71837	−	27.6935i	−0.261314	−	1.07715i	0.678264	−	0.734818i	$-0.262733\pi$
$662$		0			0
$663$	0.0915442	−	0.377350i	0.00355528	−	0.0146551i
$664$		0			0
$665$	−41.8008	−	82.4968i	−1.62097	−	3.19909i
$666$		0			0
$667$	14.1995	−	40.8521i	0.549805	−	1.58180i
$668$		0			0
$669$	22.9966	−	18.0847i	0.889098	−	0.699195i
$670$		0			0
$671$	−5.54276	+	1.62750i	−0.213976	+	0.0628290i
$672$		0			0
$673$	24.2961	+	7.13399i	0.936548	+	0.274995i	0.714175	−	0.699967i	$-0.246802\pi$
$673$	24.2961	+	7.13399i	0.936548	+	0.274995i	0.222372	+	0.974962i	$0.428620\pi$
$674$		0			0
$675$	−39.3075	+	55.1997i	−1.51295	+	2.12464i
$676$		0			0
$677$	9.65245	−	4.97618i	0.370974	−	0.191250i	−0.262651	−	0.964891i	$-0.584597\pi$
$677$	9.65245	−	4.97618i	0.370974	−	0.191250i	0.633624	+	0.773641i	$0.281566\pi$
$678$		0			0
$679$	42.7684	+	15.1388i	1.64130	+	0.580973i
$680$		0			0
$681$	−5.72675	+	1.10374i	−0.219450	+	0.0422955i
$682$		0			0
$683$	−16.0138	−	8.25570i	−0.612752	−	0.315896i	0.123768	−	0.992311i	$-0.460502\pi$
$683$	−16.0138	−	8.25570i	−0.612752	−	0.315896i	−0.736520	+	0.676415i	$0.763532\pi$
$684$		0			0
$685$	37.7146	−	43.5249i	1.44100	−	1.66300i
$686$		0			0
$687$	9.27848	−	20.3170i	0.353996	−	0.775143i
$688$		0			0
$689$	−4.66500	−	8.08001i	−0.177722	−	0.307824i
$690$		0			0
$691$	−0.678474	+	1.17515i	−0.0258104	+	0.0447049i	−0.878642	−	0.477481i	$-0.841550\pi$
$691$	−0.678474	+	1.17515i	−0.0258104	+	0.0447049i	0.852832	+	0.522186i	$0.174883\pi$
$692$		0			0
$693$	1.66200	+	1.20115i	0.0631342	+	0.0456278i
$694$		0			0
$695$	−14.0591	−	40.6212i	−0.533294	−	1.54085i
$696$		0			0
$697$	0.868382	+	0.447682i	0.0328923	+	0.0169572i
$698$		0			0
$699$	7.47384	+	8.62527i	0.282687	+	0.326238i
$700$		0			0
$701$	−2.72100	+	18.9250i	−0.102771	+	0.714787i	0.871662	+	0.490108i	$0.163043\pi$
$701$	−2.72100	+	18.9250i	−0.102771	+	0.714787i	−0.974433	+	0.224679i	$0.927867\pi$
$702$		0			0
$703$	−1.37324	+	28.8278i	−0.0517926	+	1.08726i
$704$		0			0
$705$	11.7892	+	1.12573i	0.444008	+	0.0423976i
$706$		0			0
$707$	−25.3135	+	1.02808i	−0.952011	+	0.0386648i
$708$		0			0
$709$	−4.21740	+	17.3843i	−0.158388	+	0.652883i	0.836150	+	0.548501i	$0.184801\pi$
$709$	−4.21740	+	17.3843i	−0.158388	+	0.652883i	−0.994537	+	0.104381i	$0.966714\pi$
$710$		0			0
$711$	−1.19017	+	0.935964i	−0.0446350	+	0.0351014i
$712$		0			0
$713$	34.9236	+	27.5389i	1.30790	+	1.03134i
$714$		0			0
$715$	−0.376225	−	2.61670i	−0.0140700	−	0.0978591i
$716$		0			0
$717$	−15.2144	−	14.5069i	−0.568190	−	0.541768i
$718$		0			0
$719$	17.9180	−	17.0848i	0.668230	−	0.637156i	−0.278027	−	0.960573i	$-0.589680\pi$
$719$	17.9180	−	17.0848i	0.668230	−	0.637156i	0.946256	+	0.323418i	$0.104832\pi$
$720$		0			0
$721$	8.13717	−	27.0109i	0.303044	−	1.00594i
$722$		0			0
$723$	1.90163	−	0.980360i	0.0707225	−	0.0364600i
$724$		0			0
$725$	104.496	−	41.8338i	3.88088	−	1.55367i
$726$		0			0
$727$	17.0729	+	19.7032i	0.633200	+	0.730752i	0.978157	−	0.207866i	$-0.0666519\pi$
$727$	17.0729	+	19.7032i	0.633200	+	0.730752i	−0.344957	+	0.938619i	$0.612106\pi$
$728$		0			0
$729$	18.1955	−	11.6935i	0.673906	−	0.433093i
$730$		0			0
$731$	−0.775319	−	0.149431i	−0.0286762	−	0.00552689i
$732$		0			0
$733$	21.1035	+	29.6358i	0.779477	+	1.09462i	0.993050	+	0.117695i	$0.0375507\pi$
$733$	21.1035	+	29.6358i	0.779477	+	1.09462i	−0.213572	+	0.976927i	$0.568510\pi$
$734$		0			0
$735$	−31.7660	−	13.2367i	−1.17170	−	0.488245i
$736$		0			0
$737$	−2.79414	+	4.83959i	−0.102923	+	0.178269i
$738$		0			0
$739$	−6.60011	+	0.630234i	−0.242789	+	0.0231835i	−0.215741	−	0.976451i	$-0.569217\pi$
$739$	−6.60011	+	0.630234i	−0.242789	+	0.0231835i	−0.0270479	+	0.999634i	$0.508611\pi$
$740$		0			0
$741$	8.49410	−	9.80271i	0.312039	−	0.360112i
$742$		0			0
$743$	6.27045	−	4.02977i	0.230041	−	0.147838i	−0.420543	−	0.907272i	$-0.638161\pi$
$743$	6.27045	−	4.02977i	0.230041	−	0.147838i	0.650584	+	0.759434i	$0.274524\pi$
$744$		0			0
$745$	−15.2178	+	43.9691i	−0.557539	+	1.61090i
$746$		0			0
$747$	2.72812	+	2.14542i	0.0998167	+	0.0784967i
$748$		0			0
$749$	8.16383	+	28.5419i	0.298300	+	1.04290i
$750$		0			0
$751$	18.1930	+	1.73722i	0.663871	+	0.0633920i	0.421552	−	0.906804i	$-0.361486\pi$
$751$	18.1930	+	1.73722i	0.663871	+	0.0633920i	0.242320	+	0.970196i	$0.422092\pi$
$752$		0			0
$753$	3.25528	+	13.4184i	0.118629	+	0.488995i
$754$		0			0
$755$	−71.1094	+	20.8796i	−2.58794	+	0.759886i
$756$		0			0
$757$	0.806408	+	5.60869i	0.0293094	+	0.203851i	0.999214	−	0.0396327i	$-0.0126188\pi$
$757$	0.806408	+	5.60869i	0.0293094	+	0.203851i	−0.969905	+	0.243484i	$0.921710\pi$
$758$		0			0
$759$	−1.11928	−	2.45947i	−0.0406274	−	0.0892731i
$760$		0			0
$761$	31.0916	+	12.4472i	1.12707	+	0.451210i	0.858891	−	0.512159i	$-0.171154\pi$
$761$	31.0916	+	12.4472i	1.12707	+	0.451210i	0.268178	+	0.963369i	$0.413578\pi$
$762$		0			0
$763$	−12.2347	+	8.58370i	−0.442926	+	0.310751i
$764$		0			0
$765$	−1.22493	+	1.16797i	−0.0442874	+	0.0422280i
$766$		0			0
$767$	5.89948	−	8.28466i	0.213018	−	0.299142i
$768$		0			0
$769$	−35.2920	−	22.6808i	−1.27266	−	0.817889i	−0.282697	−	0.959209i	$-0.591229\pi$
$769$	−35.2920	−	22.6808i	−1.27266	−	0.817889i	−0.989964	+	0.141320i	$0.954865\pi$
$770$		0			0
$771$	−3.11938	+	21.6958i	−0.112342	+	0.781355i
$772$		0			0
$773$	−11.0221	+	31.8463i	−0.396438	+	1.14543i	0.553461	+	0.832875i	$0.313307\pi$
$773$	−11.0221	+	31.8463i	−0.396438	+	1.14543i	−0.949899	+	0.312557i	$0.898814\pi$
$774$		0			0
$775$	5.50755	+	115.618i	0.197837	+	4.15311i
$776$		0			0
$777$	6.57921	+	8.48791i	0.236028	+	0.304502i
$778$		0			0
$779$	18.9306	+	26.5844i	0.678261	+	0.952484i
$780$		0			0
$781$	2.13419	+	3.69653i	0.0763674	+	0.132272i
$782$		0			0
$783$	−48.9622			−1.74977
$784$		0			0
$785$	−33.5207	+	73.4002i	−1.19641	+	2.61976i
$786$		0			0
$787$	3.95174	+	0.761634i	0.140864	+	0.0271493i	0.259196	−	0.965825i	$-0.416542\pi$
$787$	3.95174	+	0.761634i	0.140864	+	0.0271493i	−0.118332	+	0.992974i	$0.537755\pi$
$788$		0			0
$789$	−1.51051	−	31.7094i	−0.0537754	−	1.12889i
$790$		0			0
$791$	−13.5712	+	7.70903i	−0.482537	+	0.274102i
$792$		0			0
$793$	−12.5035	−	9.83284i	−0.444011	−	0.349174i
$794$		0			0
$795$	1.65406	−	34.7230i	0.0586636	−	1.23150i
$796$		0			0
$797$	3.43410	+	7.51962i	0.121642	+	0.266359i	0.960651	−	0.277759i	$-0.0895917\pi$
$797$	3.43410	+	7.51962i	0.121642	+	0.266359i	−0.839009	+	0.544118i	$0.816864\pi$
$798$		0			0
$799$	0.578476	+	0.169856i	0.0204650	+	0.00600907i
$800$		0			0
$801$	5.07492	+	4.83893i	0.179314	+	0.170975i
$802$		0			0
$803$	0.838467	+	0.335671i	0.0295888	+	0.0118456i
$804$		0			0
$805$	−32.4460	−	41.9732i	−1.14357	−	1.47936i
$806$		0			0
$807$	−24.4097	−	9.77218i	−0.859263	−	0.343997i
$808$		0			0
$809$	25.6625	+	24.4691i	0.902245	+	0.860289i	0.990738	−	0.135788i	$-0.0433566\pi$
$809$	25.6625	+	24.4691i	0.902245	+	0.860289i	−0.0884929	+	0.996077i	$0.528205\pi$
$810$		0			0
$811$	36.5455	+	10.7307i	1.28329	+	0.376807i	0.851112	−	0.524984i	$-0.175929\pi$
$811$	36.5455	+	10.7307i	1.28329	+	0.376807i	0.432174	+	0.901790i	$0.357747\pi$
$812$		0			0
$813$	9.83883	+	21.5440i	0.345063	+	0.755583i
$814$		0			0
$815$	−1.14648	+	24.0675i	−0.0401594	+	0.843049i
$816$		0			0
$817$	−20.7328	−	16.3045i	−0.725349	−	0.570421i
$818$		0			0
$819$	−0.0395727	+	5.64634i	−0.00138278	+	0.197299i
$820$		0			0
$821$	−1.44989	−	30.4369i	−0.0506014	−	1.06225i	−0.871256	−	0.490829i	$-0.836694\pi$
$821$	−1.44989	−	30.4369i	−0.0506014	−	1.06225i	0.820654	−	0.571425i	$-0.193609\pi$
$822$		0			0
$823$	−9.66983	−	1.86371i	−0.337069	−	0.0649648i	0.0179082	−	0.999840i	$-0.494299\pi$
$823$	−9.66983	−	1.86371i	−0.337069	−	0.0649648i	−0.354977	+	0.934875i	$0.615511\pi$
$824$		0			0
$825$	2.92142	−	6.39702i	0.101711	−	0.222716i
$826$		0			0
$827$	−20.3258			−0.706798			−0.353399	−	0.935473i	$-0.614974\pi$
$827$	−20.3258			−0.706798			−0.353399	+	0.935473i	$0.614974\pi$
$828$		0			0
$829$	−6.17562	−	10.6965i	−0.214488	−	0.371504i	0.738626	−	0.674115i	$-0.235475\pi$
$829$	−6.17562	−	10.6965i	−0.214488	−	0.371504i	−0.953114	+	0.302611i	$0.902142\pi$
$830$		0			0
$831$	1.06648	+	1.49767i	0.0369959	+	0.0519535i
$832$		0			0
$833$	−1.46039	−	0.967728i	−0.0505996	−	0.0335298i
$834$		0			0
$835$	−0.489113	−	10.2678i	−0.0169265	−	0.355330i
$836$		0			0
$837$	16.4678	−	47.5806i	0.569211	−	1.64463i
$838$		0			0
$839$	−4.75231	+	33.0531i	−0.164068	+	1.14112i	0.726797	+	0.686852i	$0.241008\pi$
$839$	−4.75231	+	33.0531i	−0.164068	+	1.14112i	−0.890866	+	0.454267i	$0.849901\pi$
$840$		0			0
$841$	44.0203	+	28.2901i	1.51794	+	0.975521i
$842$		0			0
$843$	−21.5973	+	30.3292i	−0.743851	+	1.04459i
$844$		0			0
$845$	−34.0695	+	32.4852i	−1.17203	+	1.11752i
$846$		0			0
$847$	25.8370	+	12.0189i	0.887771	+	0.412975i
$848$		0			0
$849$	11.9679	+	4.79122i	0.410737	+	0.164434i
$850$		0			0
$851$	2.33447	+	16.3902i	0.0800248	+	0.561847i
$852$		0			0
$853$	−4.45465	−	30.9827i	−0.152524	−	1.06083i	−0.911970	−	0.410258i	$-0.865439\pi$
$853$	−4.45465	−	30.9827i	−0.152524	−	1.06083i	0.759445	−	0.650571i	$-0.225470\pi$
$854$		0			0
$855$	−54.2474	+	15.9285i	−1.85522	+	0.544743i
$856$		0			0
$857$	−9.61030	−	39.6142i	−0.328282	−	1.35320i	−0.861732	−	0.507364i	$-0.830620\pi$
$857$	−9.61030	−	39.6142i	−0.328282	−	1.35320i	0.533450	−	0.845831i	$-0.320895\pi$
$858$		0			0
$859$	−9.67270	−	0.923631i	−0.330028	−	0.0315139i	−0.0712732	−	0.997457i	$-0.522706\pi$
$859$	−9.67270	−	0.923631i	−0.330028	−	0.0315139i	−0.258755	+	0.965943i	$0.583312\pi$
$860$		0			0
$861$	11.7814	+	2.94571i	0.401508	+	0.100389i
$862$		0			0
$863$	20.6874	+	16.2688i	0.704207	+	0.553795i	0.904777	−	0.425885i	$-0.140037\pi$
$863$	20.6874	+	16.2688i	0.704207	+	0.553795i	−0.200570	+	0.979679i	$0.564279\pi$
$864$		0			0
$865$	−23.0589	+	66.6243i	−0.784026	+	2.26529i
$866$		0			0
$867$	−16.7539	+	10.7671i	−0.568992	+	0.365669i
$868$		0			0
$869$	0.293757	−	0.339014i	0.00996504	−	0.0115003i
$870$		0			0
$871$	−15.3180	+	1.46269i	−0.519030	+	0.0495613i
$872$		0			0
$873$	13.8677	−	24.0195i	0.469350	−	0.812938i
$874$		0			0
$875$	16.2314	−	81.1520i	0.548723	−	2.74344i
$876$		0			0
$877$	−12.1654	−	17.0839i	−0.410797	−	0.576883i	0.556399	−	0.830915i	$-0.312183\pi$
$877$	−12.1654	−	17.0839i	−0.410797	−	0.576883i	−0.967196	+	0.254032i	$0.918243\pi$
$878$		0			0
$879$	24.2581	+	4.67536i	0.818205	+	0.157696i
$880$		0			0
$881$	−31.1124	+	19.9947i	−1.04820	+	0.673638i	−0.947002	−	0.321228i	$-0.895905\pi$
$881$	−31.1124	+	19.9947i	−1.04820	+	0.673638i	−0.101200	+	0.994866i	$0.532268\pi$
$882$		0			0
$883$	−12.2654	−	14.1550i	−0.412762	−	0.476353i	0.510856	−	0.859666i	$-0.329328\pi$
$883$	−12.2654	−	14.1550i	−0.412762	−	0.476353i	−0.923618	+	0.383313i	$0.874783\pi$
$884$		0			0
$885$	35.1797	−	14.0838i	1.18255	−	0.473422i
$886$		0			0
$887$	25.2726	−	13.0289i	0.848570	−	0.437468i	0.0216353	−	0.999766i	$-0.493113\pi$
$887$	25.2726	−	13.0289i	0.848570	−	0.437468i	0.826935	+	0.562298i	$0.190082\pi$
$888$		0			0
$889$	−9.87636	+	2.32281i	−0.331242	+	0.0779045i
$890$		0			0
$891$	−0.531170	+	0.506470i	−0.0177949	+	0.0169674i
$892$		0			0
$893$	14.5756	+	13.8979i	0.487755	+	0.465074i
$894$		0			0
$895$	−2.35087	−	16.3507i	−0.0785810	−	0.546543i
$896$		0			0
$897$	3.72881	−	6.43885i	0.124501	−	0.214987i
$898$		0			0
$899$	−65.7391	+	51.6978i	−2.19252	+	1.72422i
$900$		0			0
$901$	0.417220	−	1.71981i	0.0138996	−	0.0572950i
$902$		0			0
$903$	−9.80656	+	0.398281i	−0.326342	+	0.0132540i
$904$		0			0
$905$	2.48471	+	0.237261i	0.0825945	+	0.00788682i
$906$		0			0
$907$	−1.08184	+	22.7107i	−0.0359220	+	0.754096i	0.907010	+	0.421110i	$0.138359\pi$
$907$	−1.08184	+	22.7107i	−0.0359220	+	0.754096i	−0.942932	+	0.332986i	$0.891944\pi$
$908$		0			0
$909$	−2.20413	+	15.3301i	−0.0731064	+	0.508466i
$910$		0			0
$911$	−11.1348	−	12.8503i	−0.368914	−	0.425749i	0.540693	−	0.841220i	$-0.318162\pi$
$911$	−11.1348	−	12.8503i	−0.368914	−	0.425749i	−0.909606	+	0.415471i	$0.863617\pi$
$912$		0			0
$913$	−0.913932	−	0.471165i	−0.0302467	−	0.0155933i
$914$		0			0
$915$	−19.3841	−	56.0066i	−0.640818	−	1.85152i
$916$		0			0
$917$	−19.1977	+	8.60522i	−0.633965	+	0.284170i
$918$		0			0
$919$	−10.2718	+	17.7913i	−0.338836	+	0.586880i	−0.984214	−	0.176983i	$-0.943366\pi$
$919$	−10.2718	+	17.7913i	−0.338836	+	0.586880i	0.645378	+	0.763863i	$0.276700\pi$
$920$		0			0
$921$	−6.60711	−	11.4439i	−0.217712	−	0.377088i
$922$		0			0
$923$	−4.88247	+	10.6911i	−0.160709	+	0.351903i
$924$		0			0
$925$	−28.2157	+	32.5627i	−0.927727	+	1.07065i
$926$		0			0
$927$	−15.3286	−	7.90243i	−0.503456	−	0.259550i
$928$		0			0
$929$	−36.5212	+	7.03888i	−1.19822	+	0.230938i	−0.749054	−	0.662509i	$-0.769491\pi$
$929$	−36.5212	+	7.03888i	−1.19822	+	0.230938i	−0.449167	+	0.893448i	$0.648279\pi$
$930$		0			0
$931$	−28.5479	−	51.0870i	−0.935620	−	1.67431i
$932$		0			0
$933$	18.2534	−	9.41031i	0.597591	−	0.308080i
$934$		0			0
$935$	0.290860	−	0.408455i	0.00951213	−	0.0133579i
$936$		0			0
$937$	−26.2554	−	7.70928i	−0.857726	−	0.251851i	−0.176839	−	0.984240i	$-0.556587\pi$
$937$	−26.2554	−	7.70928i	−0.857726	−	0.251851i	−0.680887	+	0.732389i	$0.738405\pi$
$938$		0			0
$939$	−19.0111	+	5.58215i	−0.620403	+	0.182167i
$940$		0			0
$941$	7.11474	−	5.59509i	0.231934	−	0.182395i	−0.495428	−	0.868649i	$-0.664989\pi$
$941$	7.11474	−	5.59509i	0.231934	−	0.182395i	0.727362	+	0.686254i	$0.240746\pi$
$942$		0			0
$943$	13.5322	+	12.9370i	0.440668	+	0.421287i
$944$		0			0
$945$	−32.8238	+	50.2963i	−1.06776	+	1.63614i
$946$		0			0
$947$	−0.303753	+	1.25209i	−0.00987064	+	0.0406874i	−0.976534	−	0.215364i	$-0.930906\pi$
$947$	−0.303753	+	1.25209i	−0.00987064	+	0.0406874i	0.966663	+	0.256051i	$0.0824215\pi$
$948$		0			0
$949$	0.586311	+	2.41681i	0.0190325	+	0.0784529i
$950$		0			0
$951$	11.7290	+	25.6830i	0.380340	+	0.832828i
$952$		0			0
$953$	6.66673	+	4.28444i	0.215956	+	0.138787i	0.644147	−	0.764902i	$-0.277212\pi$
$953$	6.66673	+	4.28444i	0.215956	+	0.138787i	−0.428191	+	0.903688i	$0.640849\pi$
$954$		0			0
$955$	−19.7919	+	7.92347i	−0.640450	+	0.256397i
$956$		0			0
$957$	4.98939	−	0.961627i	0.161284	−	0.0310850i
$958$		0			0
$959$	22.7282	−	28.4880i	0.733931	−	0.919927i
$960$		0			0
$961$	−17.9894	−	51.9770i	−0.580304	−	1.67668i
$962$		0			0
$963$	18.0662	−	1.72511i	0.582174	−	0.0555909i
$964$		0			0
$965$	8.59062			0.276542
$966$		0			0
$967$	58.3749			1.87721			0.938605	−	0.344994i	$-0.112119\pi$
$967$	58.3749			1.87721			0.938605	+	0.344994i	$0.112119\pi$
$968$		0			0
$969$	2.44914	−	0.233864i	0.0786776	−	0.00751280i
$970$		0			0
$971$	−10.9332	−	31.5894i	−0.350863	−	1.01375i	−0.972992	−	0.230837i	$-0.925854\pi$
$971$	−10.9332	−	31.5894i	−0.350863	−	1.01375i	0.622130	−	0.782914i	$-0.286268\pi$
$972$		0			0
$973$	−9.93231	−	25.3226i	−0.318415	−	0.811806i
$974$		0			0
$975$	19.0146	−	3.66476i	0.608954	−	0.117366i
$976$		0			0
$977$	−4.74434	+	1.89935i	−0.151785	+	0.0607655i	−0.446311	−	0.894878i	$-0.647262\pi$
$977$	−4.74434	+	1.89935i	−0.151785	+	0.0607655i	0.294526	+	0.955643i	$0.404838\pi$
$978$		0			0
$979$	−1.74767	−	1.12316i	−0.0558556	−	0.0358962i
$980$		0			0
$981$	3.79551	+	8.31100i	0.121181	+	0.265350i
$982$		0			0
$983$	5.37536	+	22.1575i	0.171447	+	0.706715i	0.991017	+	0.133736i	$0.0426973\pi$
$983$	5.37536	+	22.1575i	0.171447	+	0.706715i	−0.819570	+	0.572979i	$0.805788\pi$
$984$		0			0
$985$	11.4693	−	47.2771i	0.365442	−	1.50637i
$986$		0			0
$987$	7.48289	+	0.409035i	0.238183	+	0.0130197i
$988$		0			0
$989$	−13.4392	−	6.95083i	−0.427340	−	0.221024i
$990$		0			0
$991$	−10.8467	+	8.52994i	−0.344557	+	0.270962i	−0.775408	−	0.631461i	$-0.782456\pi$
$991$	−10.8467	+	8.52994i	−0.344557	+	0.270962i	0.430851	+	0.902423i	$0.358213\pi$
$992$		0			0
$993$	21.9658	−	6.44974i	0.697064	−	0.204676i
$994$		0			0
$995$	35.0907	+	10.3036i	1.11245	+	0.326645i
$996$		0			0
$997$	−9.10850	+	12.7911i	−0.288469	+	0.405098i	−0.933226	−	0.359289i	$-0.883019\pi$
$997$	−9.10850	+	12.7911i	−0.288469	+	0.405098i	0.644757	+	0.764387i	$0.276958\pi$
$998$		0			0
$999$	16.6589	−	8.58824i	0.527063	−	0.271720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.y.a.233.5	✓	320
7.4	even	3	inner	644.2.y.a.417.12	yes	320
23.8	even	11	inner	644.2.y.a.261.12	yes	320
161.123	even	33	inner	644.2.y.a.445.5	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.y.a.233.5	✓	320	1.1	even	1	trivial
644.2.y.a.261.12	yes	320	23.8	even	11	inner
644.2.y.a.417.12	yes	320	7.4	even	3	inner
644.2.y.a.445.5	yes	320	161.123	even	33	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17050 + 0.111769i) q^{3} +(-1.36749 - 3.95112i) q^{5} +(-0.966088 - 2.46306i) q^{7} +(-1.58820 + 0.306101i) q^{9} +O(q^{10})\)	\(q+(-1.17050 + 0.111769i) q^{3} +(-1.36749 - 3.95112i) q^{5} +(-0.966088 - 2.46306i) q^{7} +(-1.58820 + 0.306101i) q^{9} +(0.444864 - 0.178097i) q^{11} +(1.11002 + 0.713363i) q^{13} +(2.04227 + 4.47194i) q^{15} +(0.0590046 + 0.243220i) q^{17} +(-1.97102 + 8.12466i) q^{19} +(1.40610 + 2.77504i) q^{21} +(-0.234517 + 4.79009i) q^{23} +(-9.81101 + 7.71546i) q^{25} +(5.20937 - 1.52961i) q^{27} +(-8.65285 - 2.54071i) q^{29} +(5.37929 - 7.55416i) q^{31} +(-0.500809 + 0.258185i) q^{33} +(-8.41072 + 7.18535i) q^{35} +(3.38969 - 0.653310i) q^{37} +(-1.37901 - 0.710927i) q^{39} +(2.55635 - 2.95018i) q^{41} +(-1.31058 + 2.86978i) q^{43} +(3.38130 + 5.85659i) q^{45} +(1.20447 - 2.08620i) q^{47} +(-5.13335 + 4.75907i) q^{49} +(-0.0962496 - 0.278095i) q^{51} +(-6.28494 - 3.24011i) q^{53} +(-1.31203 - 1.51416i) q^{55} +(1.39900 - 9.73023i) q^{57} +(0.366761 - 7.69926i) q^{59} +(-12.0007 - 1.14593i) q^{61} +(2.28829 + 3.61613i) q^{63} +(1.30064 - 5.36132i) q^{65} +(-9.16689 + 7.20892i) q^{67} +(-0.260883 - 5.63302i) q^{69} +(1.26767 + 8.81683i) q^{71} +(1.36407 + 1.30064i) q^{73} +(10.6214 - 10.1275i) q^{75} +(-0.868442 - 0.923672i) q^{77} +(0.832058 - 0.428956i) q^{79} +(-1.42189 + 0.569241i) q^{81} +(-1.40519 - 1.62167i) q^{83} +(0.880303 - 0.565737i) q^{85} +(10.4121 + 2.00678i) q^{87} +(-2.51475 - 3.53147i) q^{89} +(0.684686 - 3.42321i) q^{91} +(-5.45215 + 9.44339i) q^{93} +(34.7968 - 3.32270i) q^{95} +(-11.2294 + 12.9594i) q^{97} +(-0.652020 + 0.419028i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9	\( 320 q + 6 q^{5} - 2 q^{7} + 12 q^{9} - 2 q^{11} - 16 q^{15} + 4 q^{17} - 50 q^{21} + 25 q^{23} + 44 q^{25} + 54 q^{27} + 12 q^{29} + 2 q^{31} - 12 q^{33} - 22 q^{35} - 44 q^{37} - 4 q^{39} + 12 q^{41} + 76 q^{43} - 114 q^{45} - 10 q^{47} - 74 q^{49} - 30 q^{51} - 20 q^{53} + 32 q^{55} + 52 q^{57} - 32 q^{59} + 74 q^{61} + 87 q^{63} - 75 q^{65} - 8 q^{67} + 10 q^{69} + 8 q^{73} + 118 q^{75} + 5 q^{77} - 40 q^{79} - 44 q^{81} - 52 q^{83} - 100 q^{85} + 84 q^{87} + 36 q^{89} + 30 q^{91} - 12 q^{93} - 25 q^{95} + 72 q^{97} + 2 q^{99}+O(q^{100}) \) 320 * q + 6 * q^5 - 2 * q^7 + 12 * q^9 - 2 * q^11 - 16 * q^15 + 4 * q^17 - 50 * q^21 + 25 * q^23 + 44 * q^25 + 54 * q^27 + 12 * q^29 + 2 * q^31 - 12 * q^33 - 22 * q^35 - 44 * q^37 - 4 * q^39 + 12 * q^41 + 76 * q^43 - 114 * q^45 - 10 * q^47 - 74 * q^49 - 30 * q^51 - 20 * q^53 + 32 * q^55 + 52 * q^57 - 32 * q^59 + 74 * q^61 + 87 * q^63 - 75 * q^65 - 8 * q^67 + 10 * q^69 + 8 * q^73 + 118 * q^75 + 5 * q^77 - 40 * q^79 - 44 * q^81 - 52 * q^83 - 100 * q^85 + 84 * q^87 + 36 * q^89 + 30 * q^91 - 12 * q^93 - 25 * q^95 + 72 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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