LMFDB - Embedded newform 650.2.j.f.307.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(307,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,-4,0,-2,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	650.307
Dual form			650.2.j.f.343.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} -1.00000 q^{4} +(1.15831 + 1.15831i) q^{6} -3.00000 q^{7} -1.00000i q^{8} +0.316625i q^{9} +(3.31662 - 3.31662i) q^{11} +(-1.15831 + 1.15831i) q^{12} +(3.00000 - 2.00000i) q^{13} -3.00000i q^{14} +1.00000 q^{16} +(3.15831 - 3.15831i) q^{17} -0.316625 q^{18} +(2.00000 - 2.00000i) q^{19} +(-3.47494 + 3.47494i) q^{21} +(3.31662 + 3.31662i) q^{22} +(3.31662 + 3.31662i) q^{23} +(-1.15831 - 1.15831i) q^{24} +(2.00000 + 3.00000i) q^{26} +(3.84169 + 3.84169i) q^{27} +3.00000 q^{28} -6.31662i q^{29} +(1.00000 + 1.00000i) q^{31} +1.00000i q^{32} -7.68338i q^{33} +(3.15831 + 3.15831i) q^{34} -0.316625i q^{36} -3.00000 q^{37} +(2.00000 + 2.00000i) q^{38} +(1.15831 - 5.79156i) q^{39} +(-6.31662 - 6.31662i) q^{41} +(-3.47494 - 3.47494i) q^{42} +(-2.47494 - 2.47494i) q^{43} +(-3.31662 + 3.31662i) q^{44} +(-3.31662 + 3.31662i) q^{46} +9.31662 q^{47} +(1.15831 - 1.15831i) q^{48} +2.00000 q^{49} -7.31662i q^{51} +(-3.00000 + 2.00000i) q^{52} +(-9.63325 + 9.63325i) q^{53} +(-3.84169 + 3.84169i) q^{54} +3.00000i q^{56} -4.63325i q^{57} +6.31662 q^{58} +(0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} -0.949874i q^{63} -1.00000 q^{64} +7.68338 q^{66} +4.94987i q^{67} +(-3.15831 + 3.15831i) q^{68} +7.68338 q^{69} +(-2.84169 - 2.84169i) q^{71} +0.316625 q^{72} -4.00000i q^{73} -3.00000i q^{74} +(-2.00000 + 2.00000i) q^{76} +(-9.94987 + 9.94987i) q^{77} +(5.79156 + 1.15831i) q^{78} +12.9499i q^{79} +7.94987 q^{81} +(6.31662 - 6.31662i) q^{82} -6.31662 q^{83} +(3.47494 - 3.47494i) q^{84} +(2.47494 - 2.47494i) q^{86} +(-7.31662 - 7.31662i) q^{87} +(-3.31662 - 3.31662i) q^{88} +(0.316625 + 0.316625i) q^{89} +(-9.00000 + 6.00000i) q^{91} +(-3.31662 - 3.31662i) q^{92} +2.31662 q^{93} +9.31662i q^{94} +(1.15831 + 1.15831i) q^{96} -8.94987i q^{97} +2.00000i q^{98} +(1.05013 + 1.05013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{4} - 2 q^{6} - 12 q^{7} + 2 q^{12} + 12 q^{13} + 4 q^{16} + 6 q^{17} + 12 q^{18} + 8 q^{19} + 6 q^{21} + 2 q^{24} + 8 q^{26} + 22 q^{27} + 12 q^{28} + 4 q^{31} + 6 q^{34} - 12 q^{37}+ \cdots + 44 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^4 - 2 * q^6 - 12 * q^7 + 2 * q^12 + 12 * q^13 + 4 * q^16 + 6 * q^17 + 12 * q^18 + 8 * q^19 + 6 * q^21 + 2 * q^24 + 8 * q^26 + 22 * q^27 + 12 * q^28 + 4 * q^31 + 6 * q^34 - 12 * q^37 + 8 * q^38 - 2 * q^39 - 12 * q^41 + 6 * q^42 + 10 * q^43 + 24 * q^47 - 2 * q^48 + 8 * q^49 - 12 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 44 * q^66 - 6 * q^68 + 44 * q^69 - 18 * q^71 - 12 * q^72 - 8 * q^76 - 10 * q^78 - 8 * q^81 + 12 * q^82 - 12 * q^83 - 6 * q^84 - 10 * q^86 - 16 * q^87 - 12 * q^89 - 36 * q^91 - 4 * q^93 - 2 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.15831	−	1.15831i	0.668752	−	0.668752i	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	1.15831	−	1.15831i	0.668752	−	0.668752i	0.957427	+	0.288675i	$0.0932147\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	1.15831	+	1.15831i	0.472879	+	0.472879i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$		−	1.00000i		−	0.353553i
$9$			0.316625i			0.105542i
$10$		0			0
$11$	3.31662	−	3.31662i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$11$	3.31662	−	3.31662i	1.00000	−	1.00000i	1.00000			$0$
$12$	−1.15831	+	1.15831i	−0.334376	+	0.334376i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$13$	3.00000	−	2.00000i	0.832050	−	0.554700i
$14$		−	3.00000i		−	0.801784i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.15831	−	3.15831i	0.766003	−	0.766003i	−0.211397	−	0.977400i	$-0.567801\pi$
$17$	3.15831	−	3.15831i	0.766003	−	0.766003i	0.977400	+	0.211397i	$0.0678013\pi$
$18$	−0.316625			−0.0746292
$19$	2.00000	−	2.00000i	0.458831	−	0.458831i	−0.439440	−	0.898272i	$-0.644823\pi$
$19$	2.00000	−	2.00000i	0.458831	−	0.458831i	0.898272	+	0.439440i	$0.144823\pi$
$20$		0			0
$21$	−3.47494	+	3.47494i	−0.758293	+	0.758293i
$22$	3.31662	+	3.31662i	0.707107	+	0.707107i
$23$	3.31662	+	3.31662i	0.691564	+	0.691564i	0.962576	−	0.271012i	$-0.0873583\pi$
$23$	3.31662	+	3.31662i	0.691564	+	0.691564i	−0.271012	+	0.962576i	$0.587358\pi$
$24$	−1.15831	−	1.15831i	−0.236440	−	0.236440i
$25$		0			0
$26$	2.00000	+	3.00000i	0.392232	+	0.588348i
$27$	3.84169	+	3.84169i	0.739333	+	0.739333i
$28$	3.00000			0.566947
$29$		−	6.31662i		−	1.17297i	−0.809961	−	0.586484i	$-0.800512\pi$
$29$		−	6.31662i		−	1.17297i	0.809961	−	0.586484i	$-0.199488\pi$
$30$		0			0
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$			1.00000i			0.176777i
$33$		−	7.68338i		−	1.33750i
$34$	3.15831	+	3.15831i	0.541646	+	0.541646i
$35$		0			0
$36$		−	0.316625i		−	0.0527708i
$37$	−3.00000			−0.493197			−0.246598	−	0.969118i	$-0.579313\pi$
$37$	−3.00000			−0.493197			−0.246598	+	0.969118i	$0.579313\pi$
$38$	2.00000	+	2.00000i	0.324443	+	0.324443i
$39$	1.15831	−	5.79156i	0.185478	−	0.927392i
$40$		0			0
$41$	−6.31662	−	6.31662i	−0.986491	−	0.986491i	0.0134189	−	0.999910i	$-0.495729\pi$
$41$	−6.31662	−	6.31662i	−0.986491	−	0.986491i	−0.999910	+	0.0134189i	$0.995729\pi$
$42$	−3.47494	−	3.47494i	−0.536194	−	0.536194i
$43$	−2.47494	−	2.47494i	−0.377424	−	0.377424i	0.492748	−	0.870172i	$-0.335993\pi$
$43$	−2.47494	−	2.47494i	−0.377424	−	0.377424i	−0.870172	+	0.492748i	$0.835993\pi$
$44$	−3.31662	+	3.31662i	−0.500000	+	0.500000i
$45$		0			0
$46$	−3.31662	+	3.31662i	−0.489010	+	0.489010i
$47$	9.31662			1.35897			0.679485	−	0.733690i	$-0.262203\pi$
$47$	9.31662			1.35897			0.679485	+	0.733690i	$0.262203\pi$
$48$	1.15831	−	1.15831i	0.167188	−	0.167188i
$49$	2.00000			0.285714
$50$		0			0
$51$		−	7.31662i		−	1.02453i
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	−9.63325	+	9.63325i	−1.32323	+	1.32323i	−0.412082	+	0.911147i	$0.635198\pi$
$53$	−9.63325	+	9.63325i	−1.32323	+	1.32323i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	−3.84169	+	3.84169i	−0.522787	+	0.522787i
$55$		0			0
$56$			3.00000i			0.400892i
$57$		−	4.63325i		−	0.613689i
$58$	6.31662			0.829413
$59$	0.316625	+	0.316625i	0.0412210	+	0.0412210i	0.727417	−	0.686196i	$-0.240721\pi$
$59$	0.316625	+	0.316625i	0.0412210	+	0.0412210i	−0.686196	+	0.727417i	$0.740721\pi$
$60$		0			0
$61$	2.00000			0.256074			0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000			0.256074			0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	+	1.00000i	−0.127000	+	0.127000i
$63$		−	0.949874i		−	0.119673i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	7.68338			0.945758
$67$			4.94987i			0.604723i	0.953193	+	0.302362i	$0.0977750\pi$
$67$			4.94987i			0.604723i	−0.953193	+	0.302362i	$0.902225\pi$
$68$	−3.15831	+	3.15831i	−0.383002	+	0.383002i
$69$	7.68338			0.924970
$70$		0			0
$71$	−2.84169	−	2.84169i	−0.337246	−	0.337246i	0.518084	−	0.855330i	$-0.326646\pi$
$71$	−2.84169	−	2.84169i	−0.337246	−	0.337246i	−0.855330	+	0.518084i	$0.826646\pi$
$72$	0.316625			0.0373146
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$		−	3.00000i		−	0.348743i
$75$		0			0
$76$	−2.00000	+	2.00000i	−0.229416	+	0.229416i
$77$	−9.94987	+	9.94987i	−1.13389	+	1.13389i
$78$	5.79156	+	1.15831i	0.655765	+	0.131153i
$79$			12.9499i			1.45697i	0.685059	+	0.728487i	$0.259776\pi$
$79$			12.9499i			1.45697i	−0.685059	+	0.728487i	$0.740224\pi$
$80$		0			0
$81$	7.94987			0.883319
$82$	6.31662	−	6.31662i	0.697555	−	0.697555i
$83$	−6.31662			−0.693340			−0.346670	−	0.937987i	$-0.612688\pi$
$83$	−6.31662			−0.693340			−0.346670	+	0.937987i	$0.612688\pi$
$84$	3.47494	−	3.47494i	0.379147	−	0.379147i
$85$		0			0
$86$	2.47494	−	2.47494i	0.266879	−	0.266879i
$87$	−7.31662	−	7.31662i	−0.784425	−	0.784425i
$88$	−3.31662	−	3.31662i	−0.353553	−	0.353553i
$89$	0.316625	+	0.316625i	0.0335622	+	0.0335622i	0.723689	−	0.690127i	$-0.242445\pi$
$89$	0.316625	+	0.316625i	0.0335622	+	0.0335622i	−0.690127	+	0.723689i	$0.742445\pi$
$90$		0			0
$91$	−9.00000	+	6.00000i	−0.943456	+	0.628971i
$92$	−3.31662	−	3.31662i	−0.345782	−	0.345782i
$93$	2.31662			0.240223
$94$			9.31662i			0.960936i
$95$		0			0
$96$	1.15831	+	1.15831i	0.118220	+	0.118220i
$97$		−	8.94987i		−	0.908722i	−0.890818	−	0.454361i	$-0.849868\pi$
$97$		−	8.94987i		−	0.908722i	0.890818	−	0.454361i	$-0.150132\pi$
$98$			2.00000i			0.202031i
$99$	1.05013	+	1.05013i	0.105542	+	0.105542i
$100$		0			0
$101$			19.2665i			1.91709i	0.284944	+	0.958544i	$0.408025\pi$
$101$			19.2665i			1.91709i	−0.284944	+	0.958544i	$0.591975\pi$
$102$	7.31662			0.724454
$103$	7.94987	+	7.94987i	0.783324	+	0.783324i	0.980390	−	0.197066i	$-0.0631413\pi$
$103$	7.94987	+	7.94987i	0.783324	+	0.783324i	−0.197066	+	0.980390i	$0.563141\pi$
$104$	−2.00000	−	3.00000i	−0.196116	−	0.294174i
$105$		0			0
$106$	−9.63325	−	9.63325i	−0.935664	−	0.935664i
$107$	9.63325	+	9.63325i	0.931281	+	0.931281i	0.997786	−	0.0665047i	$-0.0211847\pi$
$107$	9.63325	+	9.63325i	0.931281	+	0.931281i	−0.0665047	+	0.997786i	$0.521185\pi$
$108$	−3.84169	−	3.84169i	−0.369667	−	0.369667i
$109$	−1.47494	+	1.47494i	−0.141273	+	0.141273i	−0.774206	−	0.632933i	$-0.781851\pi$
$109$	−1.47494	+	1.47494i	−0.141273	+	0.141273i	0.632933	+	0.774206i	$0.281851\pi$
$110$		0			0
$111$	−3.47494	+	3.47494i	−0.329826	+	0.329826i
$112$	−3.00000			−0.283473
$113$	−2.68338	+	2.68338i	−0.252431	+	0.252431i	−0.821967	−	0.569536i	$-0.807123\pi$
$113$	−2.68338	+	2.68338i	−0.252431	+	0.252431i	0.569536	+	0.821967i	$0.307123\pi$
$114$	4.63325			0.433944
$115$		0			0
$116$			6.31662i			0.586484i
$117$	0.633250	+	0.949874i	0.0585439	+	0.0878159i
$118$	−0.316625	+	0.316625i	−0.0291477	+	0.0291477i
$119$	−9.47494	+	9.47494i	−0.868566	+	0.868566i
$120$		0			0
$121$		−	11.0000i		−	1.00000i
$122$			2.00000i			0.181071i
$123$	−14.6332			−1.31944
$124$	−1.00000	−	1.00000i	−0.0898027	−	0.0898027i
$125$		0			0
$126$	0.949874			0.0846215
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	−0.324676	−	0.945825i	$-0.605255\pi$
$127$	7.00000	−	7.00000i	0.621150	−	0.621150i	0.945825	+	0.324676i	$0.105255\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−5.73350			−0.504807
$130$		0			0
$131$	−3.00000			−0.262111			−0.131056	−	0.991375i	$-0.541837\pi$
$131$	−3.00000			−0.262111			−0.131056	+	0.991375i	$0.541837\pi$
$132$			7.68338i			0.668752i
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−4.94987			−0.427604
$135$		0			0
$136$	−3.15831	−	3.15831i	−0.270823	−	0.270823i
$137$	−5.68338			−0.485564			−0.242782	−	0.970081i	$-0.578060\pi$
$137$	−5.68338			−0.485564			−0.242782	+	0.970081i	$0.578060\pi$
$138$			7.68338i			0.654052i
$139$		−	15.9499i		−	1.35285i	−0.736511	−	0.676425i	$-0.763528\pi$
$139$		−	15.9499i		−	1.35285i	0.736511	−	0.676425i	$-0.236472\pi$
$140$		0			0
$141$	10.7916	−	10.7916i	0.908813	−	0.908813i
$142$	2.84169	−	2.84169i	0.238469	−	0.238469i
$143$	3.31662	−	16.5831i	0.277350	−	1.38675i
$144$			0.316625i			0.0263854i
$145$		0			0
$146$	4.00000			0.331042
$147$	2.31662	−	2.31662i	0.191072	−	0.191072i
$148$	3.00000			0.246598
$149$	−15.3166	+	15.3166i	−1.25479	+	1.25479i	−0.301238	+	0.953549i	$0.597400\pi$
$149$	−15.3166	+	15.3166i	−1.25479	+	1.25479i	−0.953549	+	0.301238i	$0.902600\pi$
$150$		0			0
$151$	4.47494	−	4.47494i	0.364165	−	0.364165i	−0.501179	−	0.865344i	$-0.667100\pi$
$151$	4.47494	−	4.47494i	0.364165	−	0.364165i	0.865344	+	0.501179i	$0.167100\pi$
$152$	−2.00000	−	2.00000i	−0.162221	−	0.162221i
$153$	1.00000	+	1.00000i	0.0808452	+	0.0808452i
$154$	−9.94987	−	9.94987i	−0.801784	−	0.801784i
$155$		0			0
$156$	−1.15831	+	5.79156i	−0.0927392	+	0.463696i
$157$	−10.0000	−	10.0000i	−0.798087	−	0.798087i	0.184707	−	0.982794i	$-0.440866\pi$
$157$	−10.0000	−	10.0000i	−0.798087	−	0.798087i	−0.982794	+	0.184707i	$0.940866\pi$
$158$	−12.9499			−1.03024
$159$			22.3166i			1.76982i
$160$		0			0
$161$	−9.94987	−	9.94987i	−0.784160	−	0.784160i
$162$			7.94987i			0.624601i
$163$			2.94987i			0.231052i	0.993304	+	0.115526i	$0.0368554\pi$
$163$			2.94987i			0.231052i	−0.993304	+	0.115526i	$0.963145\pi$
$164$	6.31662	+	6.31662i	0.493246	+	0.493246i
$165$		0			0
$166$		−	6.31662i		−	0.490265i
$167$	−12.6332			−0.977590			−0.488795	−	0.872399i	$-0.662563\pi$
$167$	−12.6332			−0.977590			−0.488795	+	0.872399i	$0.662563\pi$
$168$	3.47494	+	3.47494i	0.268097	+	0.268097i
$169$	5.00000	−	12.0000i	0.384615	−	0.923077i
$170$		0			0
$171$	0.633250	+	0.633250i	0.0484258	+	0.0484258i
$172$	2.47494	+	2.47494i	0.188712	+	0.188712i
$173$	3.31662	+	3.31662i	0.252158	+	0.252158i	0.821855	−	0.569697i	$-0.192939\pi$
$173$	3.31662	+	3.31662i	0.252158	+	0.252158i	−0.569697	+	0.821855i	$0.692939\pi$
$174$	7.31662	−	7.31662i	0.554672	−	0.554672i
$175$		0			0
$176$	3.31662	−	3.31662i	0.250000	−	0.250000i
$177$	0.733501			0.0551333
$178$	−0.316625	+	0.316625i	−0.0237320	+	0.0237320i
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		0			0
$181$			6.94987i			0.516580i	0.966067	+	0.258290i	$0.0831590\pi$
$181$			6.94987i			0.516580i	−0.966067	+	0.258290i	$0.916841\pi$
$182$	−6.00000	−	9.00000i	−0.444750	−	0.667124i
$183$	2.31662	−	2.31662i	0.171250	−	0.171250i
$184$	3.31662	−	3.31662i	0.244505	−	0.244505i
$185$		0			0
$186$			2.31662i			0.169863i
$187$		−	20.9499i		−	1.53201i
$188$	−9.31662			−0.679485
$189$	−11.5251	−	11.5251i	−0.838325	−	0.838325i
$190$		0			0
$191$	5.05013			0.365414			0.182707	−	0.983167i	$-0.441514\pi$
$191$	5.05013			0.365414			0.182707	+	0.983167i	$0.441514\pi$
$192$	−1.15831	+	1.15831i	−0.0835940	+	0.0835940i
$193$		−	10.9499i		−	0.788189i	−0.919070	−	0.394095i	$-0.871058\pi$
$193$		−	10.9499i		−	0.788189i	0.919070	−	0.394095i	$-0.128942\pi$
$194$	8.94987			0.642564
$195$		0			0
$196$	−2.00000			−0.142857
$197$		−	3.94987i		−	0.281417i	−0.990051	−	0.140708i	$-0.955062\pi$
$197$		−	3.94987i		−	0.281417i	0.990051	−	0.140708i	$-0.0449380\pi$
$198$	−1.05013	+	1.05013i	−0.0746292	+	0.0746292i
$199$	16.9499			1.20154			0.600772	−	0.799420i	$-0.294860\pi$
$199$	16.9499			1.20154			0.600772	+	0.799420i	$0.294860\pi$
$200$		0			0
$201$	5.73350	+	5.73350i	0.404410	+	0.404410i
$202$	−19.2665			−1.35559
$203$			18.9499i			1.33002i
$204$			7.31662i			0.512266i
$205$		0			0
$206$	−7.94987	+	7.94987i	−0.553894	+	0.553894i
$207$	−1.05013	+	1.05013i	−0.0729888	+	0.0729888i
$208$	3.00000	−	2.00000i	0.208013	−	0.138675i
$209$		−	13.2665i		−	0.917663i
$210$		0			0
$211$	−19.9499			−1.37341			−0.686703	−	0.726938i	$-0.740943\pi$
$211$	−19.9499			−1.37341			−0.686703	+	0.726938i	$0.740943\pi$
$212$	9.63325	−	9.63325i	0.661614	−	0.661614i
$213$	−6.58312			−0.451068
$214$	−9.63325	+	9.63325i	−0.658515	+	0.658515i
$215$		0			0
$216$	3.84169	−	3.84169i	0.261394	−	0.261394i
$217$	−3.00000	−	3.00000i	−0.203653	−	0.203653i
$218$	−1.47494	−	1.47494i	−0.0998954	−	0.0998954i
$219$	−4.63325	−	4.63325i	−0.313086	−	0.313086i
$220$		0			0
$221$	3.15831	−	15.7916i	0.212451	−	1.06226i
$222$	−3.47494	−	3.47494i	−0.233223	−	0.233223i
$223$	−15.9499			−1.06808			−0.534041	−	0.845458i	$-0.679327\pi$
$223$	−15.9499			−1.06808			−0.534041	+	0.845458i	$0.679327\pi$
$224$		−	3.00000i		−	0.200446i
$225$		0			0
$226$	−2.68338	−	2.68338i	−0.178495	−	0.178495i
$227$			18.0000i			1.19470i	0.801980	+	0.597351i	$0.203780\pi$
$227$			18.0000i			1.19470i	−0.801980	+	0.597351i	$0.796220\pi$
$228$			4.63325i			0.306844i
$229$	−3.52506	−	3.52506i	−0.232943	−	0.232943i	0.580977	−	0.813920i	$-0.302671\pi$
$229$	−3.52506	−	3.52506i	−0.232943	−	0.232943i	−0.813920	+	0.580977i	$0.802671\pi$
$230$		0			0
$231$			23.0501i			1.51659i
$232$	−6.31662			−0.414707
$233$	6.79156	+	6.79156i	0.444930	+	0.444930i	0.893665	−	0.448735i	$-0.148125\pi$
$233$	6.79156	+	6.79156i	0.444930	+	0.444930i	−0.448735	+	0.893665i	$0.648125\pi$
$234$	−0.949874	+	0.633250i	−0.0620952	+	0.0413968i
$235$		0			0
$236$	−0.316625	−	0.316625i	−0.0206105	−	0.0206105i
$237$	15.0000	+	15.0000i	0.974355	+	0.974355i
$238$	−9.47494	−	9.47494i	−0.614169	−	0.614169i
$239$	−11.8417	+	11.8417i	−0.765975	+	0.765975i	−0.977395	−	0.211420i	$-0.932191\pi$
$239$	−11.8417	+	11.8417i	−0.765975	+	0.765975i	0.211420	+	0.977395i	$0.432191\pi$
$240$		0			0
$241$	16.0000	−	16.0000i	1.03065	−	1.03065i	0.0311354	−	0.999515i	$-0.490088\pi$
$241$	16.0000	−	16.0000i	1.03065	−	1.03065i	0.999515	−	0.0311354i	$-0.00991232\pi$
$242$	11.0000			0.707107
$243$	−2.31662	+	2.31662i	−0.148612	+	0.148612i
$244$	−2.00000			−0.128037
$245$		0			0
$246$		−	14.6332i		−	0.932982i
$247$	2.00000	−	10.0000i	0.127257	−	0.636285i
$248$	1.00000	−	1.00000i	0.0635001	−	0.0635001i
$249$	−7.31662	+	7.31662i	−0.463672	+	0.463672i
$250$		0			0
$251$			19.2665i			1.21609i	0.793902	+	0.608045i	$0.208046\pi$
$251$			19.2665i			1.21609i	−0.793902	+	0.608045i	$0.791954\pi$
$252$			0.949874i			0.0598365i
$253$	22.0000			1.38313
$254$	7.00000	+	7.00000i	0.439219	+	0.439219i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−11.8417	+	11.8417i	−0.738664	+	0.738664i	−0.972319	−	0.233655i	$-0.924931\pi$
$257$	−11.8417	+	11.8417i	−0.738664	+	0.738664i	0.233655	+	0.972319i	$0.424931\pi$
$258$		−	5.73350i		−	0.356952i
$259$	9.00000			0.559233
$260$		0			0
$261$	2.00000			0.123797
$262$		−	3.00000i		−	0.185341i
$263$	12.3166	−	12.3166i	0.759476	−	0.759476i	−0.216751	−	0.976227i	$-0.569546\pi$
$263$	12.3166	−	12.3166i	0.759476	−	0.759476i	0.976227	+	0.216751i	$0.0695461\pi$
$264$	−7.68338			−0.472879
$265$		0			0
$266$	−6.00000	−	6.00000i	−0.367884	−	0.367884i
$267$	0.733501			0.0448895
$268$		−	4.94987i		−	0.302362i
$269$		−	13.2665i		−	0.808873i	−0.914566	−	0.404436i	$-0.867468\pi$
$269$		−	13.2665i		−	0.808873i	0.914566	−	0.404436i	$-0.132532\pi$
$270$		0			0
$271$	−10.5251	+	10.5251i	−0.639352	+	0.639352i	−0.950396	−	0.311044i	$-0.899321\pi$
$271$	−10.5251	+	10.5251i	−0.639352	+	0.639352i	0.311044	+	0.950396i	$0.399321\pi$
$272$	3.15831	−	3.15831i	0.191501	−	0.191501i
$273$	−3.47494	+	17.3747i	−0.210313	+	1.05156i
$274$		−	5.68338i		−	0.343345i
$275$		0			0
$276$	−7.68338			−0.462485
$277$	−21.8997	+	21.8997i	−1.31583	+	1.31583i	−0.398783	+	0.917045i	$0.630567\pi$
$277$	−21.8997	+	21.8997i	−1.31583	+	1.31583i	−0.917045	+	0.398783i	$0.869433\pi$
$278$	15.9499			0.956610
$279$	−0.316625	+	0.316625i	−0.0189558	+	0.0189558i
$280$		0			0
$281$	−11.6834	+	11.6834i	−0.696972	+	0.696972i	−0.963756	−	0.266784i	$-0.914039\pi$
$281$	−11.6834	+	11.6834i	−0.696972	+	0.696972i	0.266784	+	0.963756i	$0.414039\pi$
$282$	10.7916	+	10.7916i	0.642628	+	0.642628i
$283$	7.94987	+	7.94987i	0.472571	+	0.472571i	0.902746	−	0.430175i	$-0.141548\pi$
$283$	7.94987	+	7.94987i	0.472571	+	0.472571i	−0.430175	+	0.902746i	$0.641548\pi$
$284$	2.84169	+	2.84169i	0.168623	+	0.168623i
$285$		0			0
$286$	16.5831	+	3.31662i	0.980581	+	0.196116i
$287$	18.9499	+	18.9499i	1.11858	+	1.11858i
$288$	−0.316625			−0.0186573
$289$		−	2.94987i		−	0.173522i
$290$		0			0
$291$	−10.3668	−	10.3668i	−0.607710	−	0.607710i
$292$			4.00000i			0.234082i
$293$		−	22.8997i		−	1.33782i	−0.743344	−	0.668909i	$-0.766762\pi$
$293$		−	22.8997i		−	1.33782i	0.743344	−	0.668909i	$-0.233238\pi$
$294$	2.31662	+	2.31662i	0.135108	+	0.135108i
$295$		0			0
$296$			3.00000i			0.174371i
$297$	25.4829			1.47867
$298$	−15.3166	−	15.3166i	−0.887268	−	0.887268i
$299$	16.5831	+	3.31662i	0.959027	+	0.191805i
$300$		0			0
$301$	7.42481	+	7.42481i	0.427959	+	0.427959i
$302$	4.47494	+	4.47494i	0.257504	+	0.257504i
$303$	22.3166	+	22.3166i	1.28206	+	1.28206i
$304$	2.00000	−	2.00000i	0.114708	−	0.114708i
$305$		0			0
$306$	−1.00000	+	1.00000i	−0.0571662	+	0.0571662i
$307$	25.8997			1.47818			0.739088	−	0.673608i	$-0.235257\pi$
$307$	25.8997			1.47818			0.739088	+	0.673608i	$0.235257\pi$
$308$	9.94987	−	9.94987i	0.566947	−	0.566947i
$309$	18.4169			1.04770
$310$		0			0
$311$			19.2665i			1.09250i	0.837621	+	0.546251i	$0.183946\pi$
$311$			19.2665i			1.09250i	−0.837621	+	0.546251i	$0.816054\pi$
$312$	−5.79156	−	1.15831i	−0.327883	−	0.0655765i
$313$	15.4248	−	15.4248i	0.871862	−	0.871862i	−0.120813	−	0.992675i	$-0.538550\pi$
$313$	15.4248	−	15.4248i	0.871862	−	0.871862i	0.992675	+	0.120813i	$0.0385503\pi$
$314$	10.0000	−	10.0000i	0.564333	−	0.564333i
$315$		0			0
$316$		−	12.9499i		−	0.728487i
$317$		−	12.0000i		−	0.673987i	−0.941507	−	0.336994i	$-0.890590\pi$
$317$		−	12.0000i		−	0.673987i	0.941507	−	0.336994i	$-0.109410\pi$
$318$	−22.3166			−1.25145
$319$	−20.9499	−	20.9499i	−1.17297	−	1.17297i
$320$		0			0
$321$	22.3166			1.24559
$322$	9.94987	−	9.94987i	0.554485	−	0.554485i
$323$		−	12.6332i		−	0.702933i
$324$	−7.94987			−0.441660
$325$		0			0
$326$	−2.94987			−0.163378
$327$			3.41688i			0.188954i
$328$	−6.31662	+	6.31662i	−0.348777	+	0.348777i
$329$	−27.9499			−1.54093
$330$		0			0
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	0.734055	−	0.679090i	$-0.237625\pi$
$331$	1.00000	+	1.00000i	0.0549650	+	0.0549650i	−0.679090	+	0.734055i	$0.737625\pi$
$332$	6.31662			0.346670
$333$		−	0.949874i		−	0.0520528i
$334$		−	12.6332i		−	0.691261i
$335$		0			0
$336$	−3.47494	+	3.47494i	−0.189573	+	0.189573i
$337$	3.52506	−	3.52506i	0.192022	−	0.192022i	−0.604547	−	0.796569i	$-0.706646\pi$
$337$	3.52506	−	3.52506i	0.192022	−	0.192022i	0.796569	+	0.604547i	$0.206646\pi$
$338$	12.0000	+	5.00000i	0.652714	+	0.271964i
$339$			6.21637i			0.337627i
$340$		0			0
$341$	6.63325			0.359211
$342$	−0.633250	+	0.633250i	−0.0342422	+	0.0342422i
$343$	15.0000			0.809924
$344$	−2.47494	+	2.47494i	−0.133440	+	0.133440i
$345$		0			0
$346$	−3.31662	+	3.31662i	−0.178303	+	0.178303i
$347$	−0.791562	−	0.791562i	−0.0424933	−	0.0424933i	0.685541	−	0.728034i	$-0.259566\pi$
$347$	−0.791562	−	0.791562i	−0.0424933	−	0.0424933i	−0.728034	+	0.685541i	$0.759566\pi$
$348$	7.31662	+	7.31662i	0.392212	+	0.392212i
$349$	18.4248	+	18.4248i	0.986258	+	0.986258i	0.999907	−	0.0136493i	$-0.00434484\pi$
$349$	18.4248	+	18.4248i	0.986258	+	0.986258i	−0.0136493	+	0.999907i	$0.504345\pi$
$350$		0			0
$351$	19.2084	+	3.84169i	1.02527	+	0.205054i
$352$	3.31662	+	3.31662i	0.176777	+	0.176777i
$353$	7.58312			0.403609			0.201804	−	0.979426i	$-0.435319\pi$
$353$	7.58312			0.403609			0.201804	+	0.979426i	$0.435319\pi$
$354$			0.733501i			0.0389851i
$355$		0			0
$356$	−0.316625	−	0.316625i	−0.0167811	−	0.0167811i
$357$			21.9499i			1.16171i
$358$			15.0000i			0.792775i
$359$	22.2665	+	22.2665i	1.17518	+	1.17518i	0.980957	+	0.194224i	$0.0622187\pi$
$359$	22.2665	+	22.2665i	1.17518	+	1.17518i	0.194224	+	0.980957i	$0.437781\pi$
$360$		0			0
$361$			11.0000i			0.578947i
$362$	−6.94987			−0.365277
$363$	−12.7414	−	12.7414i	−0.668752	−	0.668752i
$364$	9.00000	−	6.00000i	0.471728	−	0.314485i
$365$		0			0
$366$	2.31662	+	2.31662i	0.121092	+	0.121092i
$367$	−1.94987	−	1.94987i	−0.101783	−	0.101783i	0.654382	−	0.756164i	$-0.272929\pi$
$367$	−1.94987	−	1.94987i	−0.101783	−	0.101783i	−0.756164	+	0.654382i	$0.772929\pi$
$368$	3.31662	+	3.31662i	0.172891	+	0.172891i
$369$	2.00000	−	2.00000i	0.104116	−	0.104116i
$370$		0			0
$371$	28.8997	−	28.8997i	1.50040	−	1.50040i
$372$	−2.31662			−0.120111
$373$	20.0000	−	20.0000i	1.03556	−	1.03556i	0.0362168	−	0.999344i	$-0.488469\pi$
$373$	20.0000	−	20.0000i	1.03556	−	1.03556i	0.999344	−	0.0362168i	$-0.0115307\pi$
$374$	20.9499			1.08329
$375$		0			0
$376$		−	9.31662i		−	0.480468i
$377$	−12.6332	−	18.9499i	−0.650645	−	0.975968i
$378$	11.5251	−	11.5251i	0.592785	−	0.592785i
$379$	−13.0000	+	13.0000i	−0.667765	+	0.667765i	−0.957198	−	0.289433i	$-0.906533\pi$
$379$	−13.0000	+	13.0000i	−0.667765	+	0.667765i	0.289433	+	0.957198i	$0.406533\pi$
$380$		0			0
$381$		−	16.2164i		−	0.830790i
$382$			5.05013i			0.258387i
$383$	−14.3668			−0.734107			−0.367053	−	0.930200i	$-0.619633\pi$
$383$	−14.3668			−0.734107			−0.367053	+	0.930200i	$0.619633\pi$
$384$	−1.15831	−	1.15831i	−0.0591099	−	0.0591099i
$385$		0			0
$386$	10.9499			0.557334
$387$	0.783626	−	0.783626i	0.0398340	−	0.0398340i
$388$			8.94987i			0.454361i
$389$	−13.8997			−0.704745			−0.352373	−	0.935860i	$-0.614625\pi$
$389$	−13.8997			−0.704745			−0.352373	+	0.935860i	$0.614625\pi$
$390$		0			0
$391$	20.9499			1.05948
$392$		−	2.00000i		−	0.101015i
$393$	−3.47494	+	3.47494i	−0.175287	+	0.175287i
$394$	3.94987			0.198992
$395$		0			0
$396$	−1.05013	−	1.05013i	−0.0527708	−	0.0527708i
$397$	−18.0000			−0.903394			−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000			−0.903394			−0.451697	+	0.892171i	$0.649181\pi$
$398$			16.9499i			0.849620i
$399$			13.8997i			0.695858i
$400$		0			0
$401$	−10.5831	+	10.5831i	−0.528496	+	0.528496i	−0.920124	−	0.391628i	$-0.871912\pi$
$401$	−10.5831	+	10.5831i	−0.528496	+	0.528496i	0.391628	+	0.920124i	$0.371912\pi$
$402$	−5.73350	+	5.73350i	−0.285961	+	0.285961i
$403$	5.00000	+	1.00000i	0.249068	+	0.0498135i
$404$		−	19.2665i		−	0.958544i
$405$		0			0
$406$	−18.9499			−0.940466
$407$	−9.94987	+	9.94987i	−0.493197	+	0.493197i
$408$	−7.31662			−0.362227
$409$	23.9499	−	23.9499i	1.18425	−	1.18425i	0.205611	−	0.978634i	$-0.434082\pi$
$409$	23.9499	−	23.9499i	1.18425	−	1.18425i	0.978634	−	0.205611i	$-0.0659183\pi$
$410$		0			0
$411$	−6.58312	+	6.58312i	−0.324722	+	0.324722i
$412$	−7.94987	−	7.94987i	−0.391662	−	0.391662i
$413$	−0.949874	−	0.949874i	−0.0467403	−	0.0467403i
$414$	−1.05013	−	1.05013i	−0.0516109	−	0.0516109i
$415$		0			0
$416$	2.00000	+	3.00000i	0.0980581	+	0.147087i
$417$	−18.4749	−	18.4749i	−0.904722	−	0.904722i
$418$	13.2665			0.648886
$419$			8.68338i			0.424211i	0.977247	+	0.212105i	$0.0680320\pi$
$419$			8.68338i			0.424211i	−0.977247	+	0.212105i	$0.931968\pi$
$420$		0			0
$421$	−2.47494	−	2.47494i	−0.120621	−	0.120621i	0.644220	−	0.764841i	$-0.277182\pi$
$421$	−2.47494	−	2.47494i	−0.120621	−	0.120621i	−0.764841	+	0.644220i	$0.777182\pi$
$422$		−	19.9499i		−	0.971145i
$423$			2.94987i			0.143428i
$424$	9.63325	+	9.63325i	0.467832	+	0.467832i
$425$		0			0
$426$		−	6.58312i		−	0.318953i
$427$	−6.00000			−0.290360
$428$	−9.63325	−	9.63325i	−0.465641	−	0.465641i
$429$	−15.3668	−	23.0501i	−0.741914	−	1.11287i
$430$		0			0
$431$	12.1583	+	12.1583i	0.585645	+	0.585645i	0.936449	−	0.350804i	$-0.114092\pi$
$431$	12.1583	+	12.1583i	0.585645	+	0.585645i	−0.350804	+	0.936449i	$0.614092\pi$
$432$	3.84169	+	3.84169i	0.184833	+	0.184833i
$433$	12.5251	+	12.5251i	0.601916	+	0.601916i	0.940821	−	0.338905i	$-0.110056\pi$
$433$	12.5251	+	12.5251i	0.601916	+	0.601916i	−0.338905	+	0.940821i	$0.610056\pi$
$434$	3.00000	−	3.00000i	0.144005	−	0.144005i
$435$		0			0
$436$	1.47494	−	1.47494i	0.0706367	−	0.0706367i
$437$	13.2665			0.634623
$438$	4.63325	−	4.63325i	0.221385	−	0.221385i
$439$	−33.8997			−1.61795			−0.808973	−	0.587845i	$-0.799976\pi$
$439$	−33.8997			−1.61795			−0.808973	+	0.587845i	$0.799976\pi$
$440$		0			0
$441$			0.633250i			0.0301547i
$442$	15.7916	+	3.15831i	0.751128	+	0.150226i
$443$	−20.0581	+	20.0581i	−0.952987	+	0.952987i	−0.998943	−	0.0459562i	$-0.985367\pi$
$443$	−20.0581	+	20.0581i	−0.952987	+	0.952987i	0.0459562	+	0.998943i	$0.485367\pi$
$444$	3.47494	−	3.47494i	0.164913	−	0.164913i
$445$		0			0
$446$		−	15.9499i		−	0.755248i
$447$			35.4829i			1.67828i
$448$	3.00000			0.141737
$449$	−21.6332	−	21.6332i	−1.02094	−	1.02094i	−0.999776	−	0.0211601i	$-0.993264\pi$
$449$	−21.6332	−	21.6332i	−1.02094	−	1.02094i	−0.0211601	−	0.999776i	$-0.506736\pi$
$450$		0			0
$451$	−41.8997			−1.97298
$452$	2.68338	−	2.68338i	0.126215	−	0.126215i
$453$		−	10.3668i		−	0.487072i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	−4.63325			−0.216972
$457$		−	2.00000i		−	0.0935561i	−0.998905	−	0.0467780i	$-0.985105\pi$
$457$		−	2.00000i		−	0.0935561i	0.998905	−	0.0467780i	$-0.0148953\pi$
$458$	3.52506	−	3.52506i	0.164715	−	0.164715i
$459$	24.2665			1.13266
$460$		0			0
$461$	4.10819	+	4.10819i	0.191337	+	0.191337i	0.796274	−	0.604936i	$-0.206801\pi$
$461$	4.10819	+	4.10819i	0.191337	+	0.191337i	−0.604936	+	0.796274i	$0.706801\pi$
$462$	−23.0501			−1.07239
$463$			9.89975i			0.460080i	0.973181	+	0.230040i	$0.0738858\pi$
$463$			9.89975i			0.460080i	−0.973181	+	0.230040i	$0.926114\pi$
$464$		−	6.31662i		−	0.293242i
$465$		0			0
$466$	−6.79156	+	6.79156i	−0.314613	+	0.314613i
$467$	−8.36675	+	8.36675i	−0.387167	+	0.387167i	−0.873676	−	0.486509i	$-0.838270\pi$
$467$	−8.36675	+	8.36675i	−0.387167	+	0.387167i	0.486509	+	0.873676i	$0.338270\pi$
$468$	−0.633250	−	0.949874i	−0.0292720	−	0.0439080i
$469$		−	14.8496i		−	0.685692i
$470$		0			0
$471$	−23.1662			−1.06744
$472$	0.316625	−	0.316625i	0.0145738	−	0.0145738i
$473$	−16.4169			−0.754849
$474$	−15.0000	+	15.0000i	−0.688973	+	0.688973i
$475$		0			0
$476$	9.47494	−	9.47494i	0.434283	−	0.434283i
$477$	−3.05013	−	3.05013i	−0.139656	−	0.139656i
$478$	−11.8417	−	11.8417i	−0.541626	−	0.541626i
$479$	−3.15831	−	3.15831i	−0.144307	−	0.144307i	0.631262	−	0.775569i	$-0.282537\pi$
$479$	−3.15831	−	3.15831i	−0.144307	−	0.144307i	−0.775569	+	0.631262i	$0.782537\pi$
$480$		0			0
$481$	−9.00000	+	6.00000i	−0.410365	+	0.273576i
$482$	16.0000	+	16.0000i	0.728780	+	0.728780i
$483$	−23.0501			−1.04882
$484$			11.0000i			0.500000i
$485$		0			0
$486$	−2.31662	−	2.31662i	−0.105084	−	0.105084i
$487$		−	2.00000i		−	0.0906287i	−0.998973	−	0.0453143i	$-0.985571\pi$
$487$		−	2.00000i		−	0.0906287i	0.998973	−	0.0453143i	$-0.0144289\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	3.41688	+	3.41688i	0.154516	+	0.154516i
$490$		0			0
$491$		−	32.6834i		−	1.47498i	−0.675358	−	0.737490i	$-0.736011\pi$
$491$		−	32.6834i		−	1.47498i	0.675358	−	0.737490i	$-0.263989\pi$
$492$	14.6332			0.659718
$493$	−19.9499	−	19.9499i	−0.898497	−	0.898497i
$494$	10.0000	+	2.00000i	0.449921	+	0.0899843i
$495$		0			0
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	8.52506	+	8.52506i	0.382401	+	0.382401i
$498$	−7.31662	−	7.31662i	−0.327866	−	0.327866i
$499$	8.94987	−	8.94987i	0.400651	−	0.400651i	−0.477811	−	0.878463i	$-0.658570\pi$
$499$	8.94987	−	8.94987i	0.400651	−	0.400651i	0.878463	+	0.477811i	$0.158570\pi$
$500$		0			0
$501$	−14.6332	+	14.6332i	−0.653765	+	0.653765i
$502$	−19.2665			−0.859906
$503$	−1.58312	+	1.58312i	−0.0705880	+	0.0705880i	−0.741519	−	0.670931i	$-0.765894\pi$
$503$	−1.58312	+	1.58312i	−0.0705880	+	0.0705880i	0.670931	+	0.741519i	$0.265894\pi$
$504$	−0.949874			−0.0423108
$505$		0			0
$506$			22.0000i			0.978019i
$507$	−8.10819	−	19.6913i	−0.360097	−	0.874522i
$508$	−7.00000	+	7.00000i	−0.310575	+	0.310575i
$509$	−15.3166	+	15.3166i	−0.678897	+	0.678897i	−0.959751	−	0.280853i	$-0.909383\pi$
$509$	−15.3166	+	15.3166i	−0.678897	+	0.678897i	0.280853	+	0.959751i	$0.409383\pi$
$510$		0			0
$511$			12.0000i			0.530849i
$512$			1.00000i			0.0441942i
$513$	15.3668			0.678459
$514$	−11.8417	−	11.8417i	−0.522314	−	0.522314i
$515$		0			0
$516$	5.73350			0.252403
$517$	30.8997	−	30.8997i	1.35897	−	1.35897i
$518$			9.00000i			0.395437i
$519$	7.68338			0.337263
$520$		0			0
$521$	10.8997			0.477527			0.238763	−	0.971078i	$-0.423258\pi$
$521$	10.8997			0.477527			0.238763	+	0.971078i	$0.423258\pi$
$522$			2.00000i			0.0875376i
$523$	5.00000	−	5.00000i	0.218635	−	0.218635i	−0.589288	−	0.807923i	$-0.700592\pi$
$523$	5.00000	−	5.00000i	0.218635	−	0.218635i	0.807923	+	0.589288i	$0.200592\pi$
$524$	3.00000			0.131056
$525$		0			0
$526$	12.3166	+	12.3166i	0.537030	+	0.537030i
$527$	6.31662			0.275156
$528$		−	7.68338i		−	0.334376i
$529$		−	1.00000i		−	0.0434783i
$530$		0			0
$531$	−0.100251	+	0.100251i	−0.00435053	+	0.00435053i
$532$	6.00000	−	6.00000i	0.260133	−	0.260133i
$533$	−31.5831	−	6.31662i	−1.36802	−	0.273603i
$534$			0.733501i			0.0317417i
$535$		0			0
$536$	4.94987			0.213802
$537$	17.3747	−	17.3747i	0.749773	−	0.749773i
$538$	13.2665			0.571959
$539$	6.63325	−	6.63325i	0.285714	−	0.285714i
$540$		0			0
$541$	4.47494	−	4.47494i	0.192393	−	0.192393i	−0.604337	−	0.796729i	$-0.706562\pi$
$541$	4.47494	−	4.47494i	0.192393	−	0.192393i	0.796729	+	0.604337i	$0.206562\pi$
$542$	−10.5251	−	10.5251i	−0.452090	−	0.452090i
$543$	8.05013	+	8.05013i	0.345464	+	0.345464i
$544$	3.15831	+	3.15831i	0.135412	+	0.135412i
$545$		0			0
$546$	−17.3747	−	3.47494i	−0.743568	−	0.148714i
$547$	−21.5251	−	21.5251i	−0.920345	−	0.920345i	0.0767083	−	0.997054i	$-0.475559\pi$
$547$	−21.5251	−	21.5251i	−0.920345	−	0.920345i	−0.997054	+	0.0767083i	$0.975559\pi$
$548$	5.68338			0.242782
$549$			0.633250i			0.0270264i
$550$		0			0
$551$	−12.6332	−	12.6332i	−0.538195	−	0.538195i
$552$		−	7.68338i		−	0.327026i
$553$		−	38.8496i		−	1.65205i
$554$	−21.8997	−	21.8997i	−0.930431	−	0.930431i
$555$		0			0
$556$			15.9499i			0.676425i
$557$	−4.58312			−0.194193			−0.0970966	−	0.995275i	$-0.530956\pi$
$557$	−4.58312			−0.194193			−0.0970966	+	0.995275i	$0.530956\pi$
$558$	−0.316625	−	0.316625i	−0.0134038	−	0.0134038i
$559$	−12.3747	−	2.47494i	−0.523393	−	0.104679i
$560$		0			0
$561$	−24.2665	−	24.2665i	−1.02453	−	1.02453i
$562$	−11.6834	−	11.6834i	−0.492833	−	0.492833i
$563$	6.79156	+	6.79156i	0.286230	+	0.286230i	0.835588	−	0.549357i	$-0.185127\pi$
$563$	6.79156	+	6.79156i	0.286230	+	0.286230i	−0.549357	+	0.835588i	$0.685127\pi$
$564$	−10.7916	+	10.7916i	−0.454407	+	0.454407i
$565$		0			0
$566$	−7.94987	+	7.94987i	−0.334158	+	0.334158i
$567$	−23.8496			−1.00159
$568$	−2.84169	+	2.84169i	−0.119235	+	0.119235i
$569$	42.7995			1.79425			0.897124	−	0.441779i	$-0.145652\pi$
$569$	42.7995			1.79425			0.897124	+	0.441779i	$0.145652\pi$
$570$		0			0
$571$		−	28.8997i		−	1.20942i	−0.796447	−	0.604708i	$-0.793290\pi$
$571$		−	28.8997i		−	1.20942i	0.796447	−	0.604708i	$-0.206710\pi$
$572$	−3.31662	+	16.5831i	−0.138675	+	0.693375i
$573$	5.84962	−	5.84962i	0.244372	−	0.244372i
$574$	−18.9499	+	18.9499i	−0.790952	+	0.790952i
$575$		0			0
$576$		−	0.316625i		−	0.0131927i
$577$			41.8997i			1.74431i	0.489230	+	0.872155i	$0.337278\pi$
$577$			41.8997i			1.74431i	−0.489230	+	0.872155i	$0.662722\pi$
$578$	2.94987			0.122699
$579$	−12.6834	−	12.6834i	−0.527103	−	0.527103i
$580$		0			0
$581$	18.9499			0.786173
$582$	10.3668	−	10.3668i	0.429716	−	0.429716i
$583$			63.8997i			2.64646i
$584$	−4.00000			−0.165521
$585$		0			0
$586$	22.8997			0.945980
$587$			24.9499i			1.02979i	0.857253	+	0.514896i	$0.172169\pi$
$587$			24.9499i			1.02979i	−0.857253	+	0.514896i	$0.827831\pi$
$588$	−2.31662	+	2.31662i	−0.0955360	+	0.0955360i
$589$	4.00000			0.164817
$590$		0			0
$591$	−4.57519	−	4.57519i	−0.188198	−	0.188198i
$592$	−3.00000			−0.123299
$593$			12.9499i			0.531788i	0.964002	+	0.265894i	$0.0856671\pi$
$593$			12.9499i			0.531788i	−0.964002	+	0.265894i	$0.914333\pi$
$594$			25.4829i			1.04557i
$595$		0			0
$596$	15.3166	−	15.3166i	0.627393	−	0.627393i
$597$	19.6332	−	19.6332i	0.803535	−	0.803535i
$598$	−3.31662	+	16.5831i	−0.135627	+	0.678134i
$599$		−	13.2665i		−	0.542054i	−0.962572	−	0.271027i	$-0.912637\pi$
$599$		−	13.2665i		−	0.542054i	0.962572	−	0.271027i	$-0.0873633\pi$
$600$		0			0
$601$	−6.05013			−0.246790			−0.123395	−	0.992358i	$-0.539378\pi$
$601$	−6.05013			−0.246790			−0.123395	+	0.992358i	$0.539378\pi$
$602$	−7.42481	+	7.42481i	−0.302613	+	0.302613i
$603$	−1.56725			−0.0638235
$604$	−4.47494	+	4.47494i	−0.182083	+	0.182083i
$605$		0			0
$606$	−22.3166	+	22.3166i	−0.906551	+	0.906551i
$607$	−3.05013	−	3.05013i	−0.123801	−	0.123801i	0.642492	−	0.766293i	$-0.277901\pi$
$607$	−3.05013	−	3.05013i	−0.123801	−	0.123801i	−0.766293	+	0.642492i	$0.777901\pi$
$608$	2.00000	+	2.00000i	0.0811107	+	0.0811107i
$609$	21.9499	+	21.9499i	0.889454	+	0.889454i
$610$		0			0
$611$	27.9499	−	18.6332i	1.13073	−	0.753821i
$612$	−1.00000	−	1.00000i	−0.0404226	−	0.0404226i
$613$	−24.0000			−0.969351			−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000			−0.969351			−0.484675	+	0.874694i	$0.661062\pi$
$614$			25.8997i			1.04523i
$615$		0			0
$616$	9.94987	+	9.94987i	0.400892	+	0.400892i
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$			18.4169i			0.740835i
$619$	21.8997	+	21.8997i	0.880225	+	0.880225i	0.993557	−	0.113332i	$-0.0361524\pi$
$619$	21.8997	+	21.8997i	0.880225	+	0.880225i	−0.113332	+	0.993557i	$0.536152\pi$
$620$		0			0
$621$			25.4829i			1.02259i
$622$	−19.2665			−0.772516
$623$	−0.949874	−	0.949874i	−0.0380559	−	0.0380559i
$624$	1.15831	−	5.79156i	0.0463696	−	0.231848i
$625$		0			0
$626$	15.4248	+	15.4248i	0.616499	+	0.616499i
$627$	−15.3668	−	15.3668i	−0.613689	−	0.613689i
$628$	10.0000	+	10.0000i	0.399043	+	0.399043i
$629$	−9.47494	+	9.47494i	−0.377790	+	0.377790i
$630$		0			0
$631$	4.47494	−	4.47494i	0.178144	−	0.178144i	−0.612402	−	0.790546i	$-0.709797\pi$
$631$	4.47494	−	4.47494i	0.178144	−	0.178144i	0.790546	+	0.612402i	$0.209797\pi$
$632$	12.9499			0.515118
$633$	−23.1082	+	23.1082i	−0.918468	+	0.918468i
$634$	12.0000			0.476581
$635$		0			0
$636$		−	22.3166i		−	0.884912i
$637$	6.00000	−	4.00000i	0.237729	−	0.158486i
$638$	20.9499	−	20.9499i	0.829413	−	0.829413i
$639$	0.899749	−	0.899749i	0.0355935	−	0.0355935i
$640$		0			0
$641$			5.36675i			0.211974i	0.994368	+	0.105987i	$0.0338002\pi$
$641$			5.36675i			0.211974i	−0.994368	+	0.105987i	$0.966200\pi$
$642$			22.3166i			0.880767i
$643$	12.9499			0.510693			0.255347	−	0.966850i	$-0.417810\pi$
$643$	12.9499			0.510693			0.255347	+	0.966850i	$0.417810\pi$
$644$	9.94987	+	9.94987i	0.392080	+	0.392080i
$645$		0			0
$646$	12.6332			0.497049
$647$	6.63325	−	6.63325i	0.260780	−	0.260780i	−0.564591	−	0.825371i	$-0.690966\pi$
$647$	6.63325	−	6.63325i	0.260780	−	0.260780i	0.825371	+	0.564591i	$0.190966\pi$
$648$		−	7.94987i		−	0.312301i
$649$	2.10025			0.0824421
$650$		0			0
$651$	−6.94987			−0.272387
$652$		−	2.94987i		−	0.115526i
$653$	−31.5831	+	31.5831i	−1.23594	+	1.23594i	−0.274299	+	0.961645i	$0.588446\pi$
$653$	−31.5831	+	31.5831i	−1.23594	+	1.23594i	−0.961645	+	0.274299i	$0.911554\pi$
$654$	−3.41688			−0.133610
$655$		0			0
$656$	−6.31662	−	6.31662i	−0.246623	−	0.246623i
$657$	1.26650			0.0494108
$658$		−	27.9499i		−	1.08960i
$659$			0.633250i			0.0246679i	0.999924	+	0.0123340i	$0.00392612\pi$
$659$			0.633250i			0.0246679i	−0.999924	+	0.0123340i	$0.996074\pi$
$660$		0			0
$661$	−12.8997	+	12.8997i	−0.501742	+	0.501742i	−0.911979	−	0.410237i	$-0.865446\pi$
$661$	−12.8997	+	12.8997i	−0.501742	+	0.501742i	0.410237	+	0.911979i	$0.365446\pi$
$662$	−1.00000	+	1.00000i	−0.0388661	+	0.0388661i
$663$	−14.6332	−	21.9499i	−0.568308	−	0.852462i
$664$			6.31662i			0.245133i
$665$		0			0
$666$	0.949874			0.0368069
$667$	20.9499	−	20.9499i	0.811182	−	0.811182i
$668$	12.6332			0.488795
$669$	−18.4749	+	18.4749i	−0.714282	+	0.714282i
$670$		0			0
$671$	6.63325	−	6.63325i	0.256074	−	0.256074i
$672$	−3.47494	−	3.47494i	−0.134049	−	0.134049i
$673$	11.4248	+	11.4248i	0.440394	+	0.440394i	0.892144	−	0.451750i	$-0.149200\pi$
$673$	11.4248	+	11.4248i	0.440394	+	0.440394i	−0.451750	+	0.892144i	$0.649200\pi$
$674$	3.52506	+	3.52506i	0.135780	+	0.135780i
$675$		0			0
$676$	−5.00000	+	12.0000i	−0.192308	+	0.461538i
$677$	2.68338	+	2.68338i	0.103130	+	0.103130i	0.756789	−	0.653659i	$-0.226767\pi$
$677$	2.68338	+	2.68338i	0.103130	+	0.103130i	−0.653659	+	0.756789i	$0.726767\pi$
$678$	−6.21637			−0.238738
$679$			26.8496i			1.03039i
$680$		0			0
$681$	20.8496	+	20.8496i	0.798959	+	0.798959i
$682$			6.63325i			0.254000i
$683$		−	30.9499i		−	1.18426i	−0.805841	−	0.592132i	$-0.798286\pi$
$683$		−	30.9499i		−	1.18426i	0.805841	−	0.592132i	$-0.201714\pi$
$684$	−0.633250	−	0.633250i	−0.0242129	−	0.0242129i
$685$		0			0
$686$			15.0000i			0.572703i
$687$	−8.16625			−0.311562
$688$	−2.47494	−	2.47494i	−0.0943561	−	0.0943561i
$689$	−9.63325	+	48.1662i	−0.366998	+	1.83499i
$690$		0			0
$691$	−14.0000	−	14.0000i	−0.532585	−	0.532585i	0.388756	−	0.921341i	$-0.372905\pi$
$691$	−14.0000	−	14.0000i	−0.532585	−	0.532585i	−0.921341	+	0.388756i	$0.872905\pi$
$692$	−3.31662	−	3.31662i	−0.126079	−	0.126079i
$693$	−3.15038	−	3.15038i	−0.119673	−	0.119673i
$694$	0.791562	−	0.791562i	0.0300473	−	0.0300473i
$695$		0			0
$696$	−7.31662	+	7.31662i	−0.277336	+	0.277336i
$697$	−39.8997			−1.51131
$698$	−18.4248	+	18.4248i	−0.697389	+	0.697389i
$699$	15.7335			0.595096
$700$		0			0
$701$		−	45.4829i		−	1.71786i	−0.512089	−	0.858932i	$-0.671128\pi$
$701$		−	45.4829i		−	1.71786i	0.512089	−	0.858932i	$-0.328872\pi$
$702$	−3.84169	+	19.2084i	−0.144995	+	0.724976i
$703$	−6.00000	+	6.00000i	−0.226294	+	0.226294i
$704$	−3.31662	+	3.31662i	−0.125000	+	0.125000i
$705$		0			0
$706$			7.58312i			0.285395i
$707$		−	57.7995i		−	2.17377i
$708$	−0.733501			−0.0275666
$709$	29.9499	+	29.9499i	1.12479	+	1.12479i	0.991011	+	0.133780i	$0.0427116\pi$
$709$	29.9499	+	29.9499i	1.12479	+	1.12479i	0.133780	+	0.991011i	$0.457288\pi$
$710$		0			0
$711$	−4.10025			−0.153771
$712$	0.316625	−	0.316625i	0.0118660	−	0.0118660i
$713$			6.63325i			0.248417i
$714$	−21.9499			−0.821453
$715$		0			0
$716$	−15.0000			−0.560576
$717$			27.4327i			1.02449i
$718$	−22.2665	+	22.2665i	−0.830978	+	0.830978i
$719$	−6.94987			−0.259187			−0.129593	−	0.991567i	$-0.541367\pi$
$719$	−6.94987			−0.259187			−0.129593	+	0.991567i	$0.541367\pi$
$720$		0			0
$721$	−23.8496	−	23.8496i	−0.888206	−	0.888206i
$722$	−11.0000			−0.409378
$723$		−	37.0660i		−	1.37850i
$724$		−	6.94987i		−	0.258290i
$725$		0			0
$726$	12.7414	−	12.7414i	0.472879	−	0.472879i
$727$	13.9499	−	13.9499i	0.517372	−	0.517372i	−0.399403	−	0.916775i	$-0.630783\pi$
$727$	13.9499	−	13.9499i	0.517372	−	0.517372i	0.916775	+	0.399403i	$0.130783\pi$
$728$	6.00000	+	9.00000i	0.222375	+	0.333562i
$729$			29.2164i			1.08209i
$730$		0			0
$731$	−15.6332			−0.578217
$732$	−2.31662	+	2.31662i	−0.0856249	+	0.0856249i
$733$	−36.7995			−1.35922			−0.679610	−	0.733573i	$-0.737851\pi$
$733$	−36.7995			−1.35922			−0.679610	+	0.733573i	$0.737851\pi$
$734$	1.94987	−	1.94987i	0.0719712	−	0.0719712i
$735$		0			0
$736$	−3.31662	+	3.31662i	−0.122252	+	0.122252i
$737$	16.4169	+	16.4169i	0.604723	+	0.604723i
$738$	2.00000	+	2.00000i	0.0736210	+	0.0736210i
$739$	−35.8997	−	35.8997i	−1.32059	−	1.32059i	−0.913295	−	0.407299i	$-0.866471\pi$
$739$	−35.8997	−	35.8997i	−1.32059	−	1.32059i	−0.407299	−	0.913295i	$-0.633529\pi$
$740$		0			0
$741$	−9.26650	−	13.8997i	−0.340413	−	0.510620i
$742$	28.8997	+	28.8997i	1.06094	+	1.06094i
$743$	15.6332			0.573528			0.286764	−	0.958001i	$-0.407420\pi$
$743$	15.6332			0.573528			0.286764	+	0.958001i	$0.407420\pi$
$744$		−	2.31662i		−	0.0849316i
$745$		0			0
$746$	20.0000	+	20.0000i	0.732252	+	0.732252i
$747$		−	2.00000i		−	0.0731762i
$748$			20.9499i			0.766003i
$749$	−28.8997	−	28.8997i	−1.05597	−	1.05597i
$750$		0			0
$751$		−	13.8997i		−	0.507209i	−0.967308	−	0.253605i	$-0.918384\pi$
$751$		−	13.8997i		−	0.507209i	0.967308	−	0.253605i	$-0.0816162\pi$
$752$	9.31662			0.339742
$753$	22.3166	+	22.3166i	0.813263	+	0.813263i
$754$	18.9499	−	12.6332i	0.690114	−	0.460076i
$755$		0			0
$756$	11.5251	+	11.5251i	0.419162	+	0.419162i
$757$	5.00000	+	5.00000i	0.181728	+	0.181728i	0.792108	−	0.610380i	$-0.208983\pi$
$757$	5.00000	+	5.00000i	0.181728	+	0.181728i	−0.610380	+	0.792108i	$0.708983\pi$
$758$	−13.0000	−	13.0000i	−0.472181	−	0.472181i
$759$	25.4829	−	25.4829i	0.924970	−	0.924970i
$760$		0			0
$761$	−25.5831	+	25.5831i	−0.927388	+	0.927388i	−0.997537	−	0.0701490i	$-0.977653\pi$
$761$	−25.5831	+	25.5831i	−0.927388	+	0.927388i	0.0701490	+	0.997537i	$0.477653\pi$
$762$	16.2164			0.587457
$763$	4.42481	−	4.42481i	0.160189	−	0.160189i
$764$	−5.05013			−0.182707
$765$		0			0
$766$		−	14.3668i		−	0.519092i
$767$	1.58312	+	0.316625i	0.0571633	+	0.0114327i
$768$	1.15831	−	1.15831i	0.0417970	−	0.0417970i
$769$	−4.94987	+	4.94987i	−0.178497	+	0.178497i	−0.790700	−	0.612203i	$-0.790283\pi$
$769$	−4.94987	+	4.94987i	−0.178497	+	0.178497i	0.612203	+	0.790700i	$0.290283\pi$
$770$		0			0
$771$			27.4327i			0.987966i
$772$			10.9499i			0.394095i
$773$	22.5831			0.812259			0.406129	−	0.913816i	$-0.366878\pi$
$773$	22.5831			0.812259			0.406129	+	0.913816i	$0.366878\pi$
$774$	0.783626	+	0.783626i	0.0281669	+	0.0281669i
$775$		0			0
$776$	−8.94987			−0.321282
$777$	10.4248	−	10.4248i	0.373988	−	0.373988i
$778$		−	13.8997i		−	0.498330i
$779$	−25.2665			−0.905266
$780$		0			0
$781$	−18.8496			−0.674493
$782$			20.9499i			0.749166i
$783$	24.2665	−	24.2665i	0.867214	−	0.867214i
$784$	2.00000			0.0714286
$785$		0			0
$786$	−3.47494	−	3.47494i	−0.123947	−	0.123947i
$787$	25.8997			0.923226			0.461613	−	0.887081i	$-0.347271\pi$
$787$	25.8997			0.923226			0.461613	+	0.887081i	$0.347271\pi$
$788$			3.94987i			0.140708i
$789$		−	28.5330i		−	1.01580i
$790$		0			0
$791$	8.05013	−	8.05013i	0.286230	−	0.286230i
$792$	1.05013	−	1.05013i	0.0373146	−	0.0373146i
$793$	6.00000	−	4.00000i	0.213066	−	0.142044i
$794$		−	18.0000i		−	0.638796i
$795$		0			0
$796$	−16.9499			−0.600772
$797$	−7.26650	+	7.26650i	−0.257393	+	0.257393i	−0.823993	−	0.566600i	$-0.808258\pi$
$797$	−7.26650	+	7.26650i	−0.257393	+	0.257393i	0.566600	+	0.823993i	$0.308258\pi$
$798$	−13.8997			−0.492046
$799$	29.4248	−	29.4248i	1.04098	−	1.04098i
$800$		0			0
$801$	−0.100251	+	0.100251i	−0.00354220	+	0.00354220i
$802$	−10.5831	−	10.5831i	−0.373703	−	0.373703i
$803$	−13.2665	−	13.2665i	−0.468165	−	0.468165i
$804$	−5.73350	−	5.73350i	−0.202205	−	0.202205i
$805$		0			0
$806$	−1.00000	+	5.00000i	−0.0352235	+	0.176117i
$807$	−15.3668	−	15.3668i	−0.540935	−	0.540935i
$808$	19.2665			0.677793
$809$		−	14.3668i		−	0.505108i	−0.967583	−	0.252554i	$-0.918729\pi$
$809$		−	14.3668i		−	0.505108i	0.967583	−	0.252554i	$-0.0812705\pi$
$810$		0			0
$811$	22.9499	+	22.9499i	0.805879	+	0.805879i	0.984007	−	0.178128i	$-0.0570042\pi$
$811$	22.9499	+	22.9499i	0.805879	+	0.805879i	−0.178128	+	0.984007i	$0.557004\pi$
$812$		−	18.9499i		−	0.665010i
$813$			24.3826i			0.855136i
$814$	−9.94987	−	9.94987i	−0.348743	−	0.348743i
$815$		0			0
$816$		−	7.31662i		−	0.256133i
$817$	−9.89975			−0.346348
$818$	23.9499	+	23.9499i	0.837388	+	0.837388i
$819$	−1.89975	−	2.84962i	−0.0663826	−	0.0995739i
$820$		0			0
$821$	−24.7916	−	24.7916i	−0.865231	−	0.865231i	0.126709	−	0.991940i	$-0.459559\pi$
$821$	−24.7916	−	24.7916i	−0.865231	−	0.865231i	−0.991940	+	0.126709i	$0.959559\pi$
$822$	−6.58312	−	6.58312i	−0.229613	−	0.229613i
$823$	−27.8997	−	27.8997i	−0.972524	−	0.972524i	0.0271084	−	0.999632i	$-0.491370\pi$
$823$	−27.8997	−	27.8997i	−0.972524	−	0.972524i	−0.999632	+	0.0271084i	$0.991370\pi$
$824$	7.94987	−	7.94987i	0.276947	−	0.276947i
$825$		0			0
$826$	0.949874	−	0.949874i	0.0330504	−	0.0330504i
$827$	31.2665			1.08724			0.543621	−	0.839331i	$-0.317053\pi$
$827$	31.2665			1.08724			0.543621	+	0.839331i	$0.317053\pi$
$828$	1.05013	−	1.05013i	0.0364944	−	0.0364944i
$829$	30.8496			1.07145			0.535726	−	0.844392i	$-0.320038\pi$
$829$	30.8496			1.07145			0.535726	+	0.844392i	$0.320038\pi$
$830$		0			0
$831$			50.7335i			1.75993i
$832$	−3.00000	+	2.00000i	−0.104006	+	0.0693375i
$833$	6.31662	−	6.31662i	0.218858	−	0.218858i
$834$	18.4749	−	18.4749i	0.639735	−	0.639735i
$835$		0			0
$836$			13.2665i			0.458831i
$837$			7.68338i			0.265576i
$838$	−8.68338			−0.299962
$839$	−21.6332	−	21.6332i	−0.746863	−	0.746863i	0.227026	−	0.973889i	$-0.427100\pi$
$839$	−21.6332	−	21.6332i	−0.746863	−	0.746863i	−0.973889	+	0.227026i	$0.927100\pi$
$840$		0			0
$841$	−10.8997			−0.375853
$842$	2.47494	−	2.47494i	0.0852920	−	0.0852920i
$843$			27.0660i			0.932202i
$844$	19.9499			0.686703
$845$		0			0
$846$	−2.94987			−0.101419
$847$			33.0000i			1.13389i
$848$	−9.63325	+	9.63325i	−0.330807	+	0.330807i
$849$	18.4169			0.632066
$850$		0			0
$851$	−9.94987	−	9.94987i	−0.341077	−	0.341077i
$852$	6.58312			0.225534
$853$			4.05013i			0.138674i	0.997593	+	0.0693368i	$0.0220883\pi$
$853$			4.05013i			0.138674i	−0.997593	+	0.0693368i	$0.977912\pi$
$854$		−	6.00000i		−	0.205316i
$855$		0			0
$856$	9.63325	−	9.63325i	0.329258	−	0.329258i
$857$	−15.3166	+	15.3166i	−0.523206	+	0.523206i	−0.918538	−	0.395332i	$-0.870629\pi$
$857$	−15.3166	+	15.3166i	−0.523206	+	0.523206i	0.395332	+	0.918538i	$0.370629\pi$
$858$	23.0501	−	15.3668i	0.786918	−	0.524612i
$859$			19.8997i			0.678971i	0.940611	+	0.339485i	$0.110253\pi$
$859$			19.8997i			0.678971i	−0.940611	+	0.339485i	$0.889747\pi$
$860$		0			0
$861$	43.8997			1.49610
$862$	−12.1583	+	12.1583i	−0.414114	+	0.414114i
$863$	22.5831			0.768738			0.384369	−	0.923179i	$-0.374419\pi$
$863$	22.5831			0.768738			0.384369	+	0.923179i	$0.374419\pi$
$864$	−3.84169	+	3.84169i	−0.130697	+	0.130697i
$865$		0			0
$866$	−12.5251	+	12.5251i	−0.425619	+	0.425619i
$867$	−3.41688	−	3.41688i	−0.116043	−	0.116043i
$868$	3.00000	+	3.00000i	0.101827	+	0.101827i
$869$	42.9499	+	42.9499i	1.45697	+	1.45697i
$870$		0			0
$871$	9.89975	+	14.8496i	0.335440	+	0.503160i
$872$	1.47494	+	1.47494i	0.0499477	+	0.0499477i
$873$	2.83375			0.0959080
$874$			13.2665i			0.448746i
$875$		0			0
$876$	4.63325	+	4.63325i	0.156543	+	0.156543i
$877$			6.05013i			0.204298i	0.994769	+	0.102149i	$0.0325719\pi$
$877$			6.05013i			0.204298i	−0.994769	+	0.102149i	$0.967428\pi$
$878$		−	33.8997i		−	1.14406i
$879$	−26.5251	−	26.5251i	−0.894668	−	0.894668i
$880$		0			0
$881$		−	16.5831i		−	0.558700i	−0.960189	−	0.279350i	$-0.909881\pi$
$881$		−	16.5831i		−	0.558700i	0.960189	−	0.279350i	$-0.0901189\pi$
$882$	−0.633250			−0.0213226
$883$	−24.4248	−	24.4248i	−0.821960	−	0.821960i	0.164429	−	0.986389i	$-0.447422\pi$
$883$	−24.4248	−	24.4248i	−0.821960	−	0.821960i	−0.986389	+	0.164429i	$0.947422\pi$
$884$	−3.15831	+	15.7916i	−0.106226	+	0.531128i
$885$		0			0
$886$	−20.0581	−	20.0581i	−0.673864	−	0.673864i
$887$	−5.36675	−	5.36675i	−0.180198	−	0.180198i	0.611244	−	0.791442i	$-0.290669\pi$
$887$	−5.36675	−	5.36675i	−0.180198	−	0.180198i	−0.791442	+	0.611244i	$0.790669\pi$
$888$	3.47494	+	3.47494i	0.116611	+	0.116611i
$889$	−21.0000	+	21.0000i	−0.704317	+	0.704317i
$890$		0			0
$891$	26.3668	−	26.3668i	0.883319	−	0.883319i
$892$	15.9499			0.534041
$893$	18.6332	−	18.6332i	0.623538	−	0.623538i
$894$	−35.4829			−1.18672
$895$		0			0
$896$			3.00000i			0.100223i
$897$	23.0501	−	15.3668i	0.769621	−	0.513081i
$898$	21.6332	−	21.6332i	0.721911	−	0.721911i
$899$	6.31662	−	6.31662i	0.210671	−	0.210671i
$900$		0			0
$901$			60.8496i			2.02719i
$902$		−	41.8997i		−	1.39511i
$903$	17.2005			0.572397
$904$	2.68338	+	2.68338i	0.0892477	+	0.0892477i
$905$		0			0
$906$	10.3668			0.344412
$907$	−32.3246	+	32.3246i	−1.07332	+	1.07332i	−0.0762291	+	0.997090i	$0.524288\pi$
$907$	−32.3246	+	32.3246i	−1.07332	+	1.07332i	−0.997090	+	0.0762291i	$0.975712\pi$
$908$		−	18.0000i		−	0.597351i
$909$	−6.10025			−0.202333
$910$		0			0
$911$	−11.0501			−0.366107			−0.183053	−	0.983103i	$-0.558598\pi$
$911$	−11.0501			−0.366107			−0.183053	+	0.983103i	$0.558598\pi$
$912$		−	4.63325i		−	0.153422i
$913$	−20.9499	+	20.9499i	−0.693340	+	0.693340i
$914$	2.00000			0.0661541
$915$		0			0
$916$	3.52506	+	3.52506i	0.116471	+	0.116471i
$917$	9.00000			0.297206
$918$			24.2665i			0.800914i
$919$		−	10.1003i		−	0.333177i	−0.986027	−	0.166588i	$-0.946725\pi$
$919$		−	10.1003i		−	0.333177i	0.986027	−	0.166588i	$-0.0532751\pi$
$920$		0			0
$921$	30.0000	−	30.0000i	0.988534	−	0.988534i
$922$	−4.10819	+	4.10819i	−0.135296	+	0.135296i
$923$	−14.2084	−	2.84169i	−0.467676	−	0.0935353i
$924$		−	23.0501i		−	0.758293i
$925$		0			0
$926$	−9.89975			−0.325326
$927$	−2.51713	+	2.51713i	−0.0826733	+	0.0826733i
$928$	6.31662			0.207353
$929$	13.5831	−	13.5831i	0.445648	−	0.445648i	−0.448257	−	0.893905i	$-0.647955\pi$
$929$	13.5831	−	13.5831i	0.445648	−	0.445648i	0.893905	+	0.448257i	$0.147955\pi$
$930$		0			0
$931$	4.00000	−	4.00000i	0.131095	−	0.131095i
$932$	−6.79156	−	6.79156i	−0.222465	−	0.222465i
$933$	22.3166	+	22.3166i	0.730613	+	0.730613i
$934$	−8.36675	−	8.36675i	−0.273768	−	0.273768i
$935$		0			0
$936$	0.949874	−	0.633250i	0.0310476	−	0.0206984i
$937$	−1.94987	−	1.94987i	−0.0636996	−	0.0636996i	0.674539	−	0.738239i	$-0.264342\pi$
$937$	−1.94987	−	1.94987i	−0.0636996	−	0.0636996i	−0.738239	+	0.674539i	$0.764342\pi$
$938$	14.8496			0.484857
$939$		−	35.7335i		−	1.16612i
$940$		0			0
$941$	−1.74144	−	1.74144i	−0.0567692	−	0.0567692i	0.678152	−	0.734921i	$-0.262781\pi$
$941$	−1.74144	−	1.74144i	−0.0567692	−	0.0567692i	−0.734921	+	0.678152i	$0.762781\pi$
$942$		−	23.1662i		−	0.754797i
$943$		−	41.8997i		−	1.36444i
$944$	0.316625	+	0.316625i	0.0103053	+	0.0103053i
$945$		0			0
$946$		−	16.4169i		−	0.533759i
$947$	−5.68338			−0.184685			−0.0923424	−	0.995727i	$-0.529435\pi$
$947$	−5.68338			−0.184685			−0.0923424	+	0.995727i	$0.529435\pi$
$948$	−15.0000	−	15.0000i	−0.487177	−	0.487177i
$949$	−8.00000	−	12.0000i	−0.259691	−	0.389536i
$950$		0			0
$951$	−13.8997	−	13.8997i	−0.450730	−	0.450730i
$952$	9.47494	+	9.47494i	0.307084	+	0.307084i
$953$	−21.0079	−	21.0079i	−0.680514	−	0.680514i	0.279602	−	0.960116i	$-0.409797\pi$
$953$	−21.0079	−	21.0079i	−0.680514	−	0.680514i	−0.960116	+	0.279602i	$0.909797\pi$
$954$	3.05013	−	3.05013i	0.0987515	−	0.0987515i
$955$		0			0
$956$	11.8417	−	11.8417i	0.382988	−	0.382988i
$957$	−48.5330			−1.56885
$958$	3.15831	−	3.15831i	0.102040	−	0.102040i
$959$	17.0501			0.550577
$960$		0			0
$961$		−	29.0000i		−	0.935484i
$962$	−6.00000	−	9.00000i	−0.193448	−	0.290172i
$963$	−3.05013	+	3.05013i	−0.0982889	+	0.0982889i
$964$	−16.0000	+	16.0000i	−0.515325	+	0.515325i
$965$		0			0
$966$		−	23.0501i		−	0.741626i
$967$			36.0501i			1.15929i	0.814868	+	0.579647i	$0.196810\pi$
$967$			36.0501i			1.15929i	−0.814868	+	0.579647i	$0.803190\pi$
$968$	−11.0000			−0.353553
$969$	−14.6332	−	14.6332i	−0.470088	−	0.470088i
$970$		0			0
$971$	20.0501			0.643439			0.321720	−	0.946835i	$-0.395739\pi$
$971$	20.0501			0.643439			0.321720	+	0.946835i	$0.395739\pi$
$972$	2.31662	−	2.31662i	0.0743058	−	0.0743058i
$973$			47.8496i			1.53399i
$974$	2.00000			0.0640841
$975$		0			0
$976$	2.00000			0.0640184
$977$		−	35.0501i		−	1.12135i	−0.828035	−	0.560676i	$-0.810541\pi$
$977$		−	35.0501i		−	1.12135i	0.828035	−	0.560676i	$-0.189459\pi$
$978$	−3.41688	+	3.41688i	−0.109260	+	0.109260i
$979$	2.10025			0.0671243
$980$		0			0
$981$	−0.467002	−	0.467002i	−0.0149102	−	0.0149102i
$982$	32.6834			1.04297
$983$		−	2.05013i		−	0.0653889i	−0.999465	−	0.0326944i	$-0.989591\pi$
$983$		−	2.05013i		−	0.0653889i	0.999465	−	0.0326944i	$-0.0104088\pi$
$984$			14.6332i			0.466491i
$985$		0			0
$986$	19.9499	−	19.9499i	0.635333	−	0.635333i
$987$	−32.3747	+	32.3747i	−1.03050	+	1.03050i
$988$	−2.00000	+	10.0000i	−0.0636285	+	0.318142i
$989$		−	16.4169i		−	0.522026i
$990$		0			0
$991$	59.7995			1.89959			0.949797	−	0.312867i	$-0.101290\pi$
$991$	59.7995			1.89959			0.949797	+	0.312867i	$0.101290\pi$
$992$	−1.00000	+	1.00000i	−0.0317500	+	0.0317500i
$993$	2.31662			0.0735159
$994$	−8.52506	+	8.52506i	−0.270399	+	0.270399i
$995$		0			0
$996$	7.31662	−	7.31662i	0.231836	−	0.231836i
$997$	−8.89975	−	8.89975i	−0.281858	−	0.281858i	0.551992	−	0.833850i	$-0.313868\pi$
$997$	−8.89975	−	8.89975i	−0.281858	−	0.281858i	−0.833850	+	0.551992i	$0.813868\pi$
$998$	8.94987	+	8.94987i	0.283303	+	0.283303i
$999$	−11.5251	−	11.5251i	−0.364637	−	0.364637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.j.f.307.2		4
5.2	odd	4		130.2.g.d.73.1	yes	4
5.3	odd	4		650.2.g.g.593.2		4
5.4	even	2		130.2.j.d.47.1	yes	4
13.5	odd	4		650.2.g.g.57.2		4
15.2	even	4		1170.2.m.e.73.1		4
15.14	odd	2		1170.2.w.e.307.1		4
20.7	even	4		1040.2.bg.k.593.2		4
20.19	odd	2		1040.2.cd.i.177.2		4
65.18	even	4	inner	650.2.j.f.343.2		4
65.44	odd	4		130.2.g.d.57.1	✓	4
65.57	even	4		130.2.j.d.83.1	yes	4
195.44	even	4		1170.2.m.e.577.2		4
195.122	odd	4		1170.2.w.e.343.1		4
260.187	odd	4		1040.2.cd.i.993.2		4
260.239	even	4		1040.2.bg.k.577.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.g.d.57.1	✓	4	65.44	odd	4
130.2.g.d.73.1	yes	4	5.2	odd	4
130.2.j.d.47.1	yes	4	5.4	even	2
130.2.j.d.83.1	yes	4	65.57	even	4
650.2.g.g.57.2		4	13.5	odd	4
650.2.g.g.593.2		4	5.3	odd	4
650.2.j.f.307.2		4	1.1	even	1	trivial
650.2.j.f.343.2		4	65.18	even	4	inner
1040.2.bg.k.577.2		4	260.239	even	4
1040.2.bg.k.593.2		4	20.7	even	4
1040.2.cd.i.177.2		4	20.19	odd	2
1040.2.cd.i.993.2		4	260.187	odd	4
1170.2.m.e.73.1		4	15.2	even	4
1170.2.m.e.577.2		4	195.44	even	4
1170.2.w.e.307.1		4	15.14	odd	2
1170.2.w.e.343.1		4	195.122	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.15831 - 1.15831i) q^{3} -1.00000 q^{4} +(1.15831 + 1.15831i) q^{6} -3.00000 q^{7} -1.00000i q^{8} +0.316625i q^{9} +(3.31662 - 3.31662i) q^{11} +(-1.15831 + 1.15831i) q^{12} +(3.00000 - 2.00000i) q^{13} -3.00000i q^{14} +1.00000 q^{16} +(3.15831 - 3.15831i) q^{17} -0.316625 q^{18} +(2.00000 - 2.00000i) q^{19} +(-3.47494 + 3.47494i) q^{21} +(3.31662 + 3.31662i) q^{22} +(3.31662 + 3.31662i) q^{23} +(-1.15831 - 1.15831i) q^{24} +(2.00000 + 3.00000i) q^{26} +(3.84169 + 3.84169i) q^{27} +3.00000 q^{28} -6.31662i q^{29} +(1.00000 + 1.00000i) q^{31} +1.00000i q^{32} -7.68338i q^{33} +(3.15831 + 3.15831i) q^{34} -0.316625i q^{36} -3.00000 q^{37} +(2.00000 + 2.00000i) q^{38} +(1.15831 - 5.79156i) q^{39} +(-6.31662 - 6.31662i) q^{41} +(-3.47494 - 3.47494i) q^{42} +(-2.47494 - 2.47494i) q^{43} +(-3.31662 + 3.31662i) q^{44} +(-3.31662 + 3.31662i) q^{46} +9.31662 q^{47} +(1.15831 - 1.15831i) q^{48} +2.00000 q^{49} -7.31662i q^{51} +(-3.00000 + 2.00000i) q^{52} +(-9.63325 + 9.63325i) q^{53} +(-3.84169 + 3.84169i) q^{54} +3.00000i q^{56} -4.63325i q^{57} +6.31662 q^{58} +(0.316625 + 0.316625i) q^{59} +2.00000 q^{61} +(-1.00000 + 1.00000i) q^{62} -0.949874i q^{63} -1.00000 q^{64} +7.68338 q^{66} +4.94987i q^{67} +(-3.15831 + 3.15831i) q^{68} +7.68338 q^{69} +(-2.84169 - 2.84169i) q^{71} +0.316625 q^{72} -4.00000i q^{73} -3.00000i q^{74} +(-2.00000 + 2.00000i) q^{76} +(-9.94987 + 9.94987i) q^{77} +(5.79156 + 1.15831i) q^{78} +12.9499i q^{79} +7.94987 q^{81} +(6.31662 - 6.31662i) q^{82} -6.31662 q^{83} +(3.47494 - 3.47494i) q^{84} +(2.47494 - 2.47494i) q^{86} +(-7.31662 - 7.31662i) q^{87} +(-3.31662 - 3.31662i) q^{88} +(0.316625 + 0.316625i) q^{89} +(-9.00000 + 6.00000i) q^{91} +(-3.31662 - 3.31662i) q^{92} +2.31662 q^{93} +9.31662i q^{94} +(1.15831 + 1.15831i) q^{96} -8.94987i q^{97} +2.00000i q^{98} +(1.05013 + 1.05013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} - 2 q^{6} - 12 q^{7} + 2 q^{12} + 12 q^{13} + 4 q^{16} + 6 q^{17} + 12 q^{18} + 8 q^{19} + 6 q^{21} + 2 q^{24} + 8 q^{26} + 22 q^{27} + 12 q^{28} + 4 q^{31} + 6 q^{34} - 12 q^{37}+ \cdots + 44 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^4 - 2 * q^6 - 12 * q^7 + 2 * q^12 + 12 * q^13 + 4 * q^16 + 6 * q^17 + 12 * q^18 + 8 * q^19 + 6 * q^21 + 2 * q^24 + 8 * q^26 + 22 * q^27 + 12 * q^28 + 4 * q^31 + 6 * q^34 - 12 * q^37 + 8 * q^38 - 2 * q^39 - 12 * q^41 + 6 * q^42 + 10 * q^43 + 24 * q^47 - 2 * q^48 + 8 * q^49 - 12 * q^52 - 12 * q^53 - 22 * q^54 + 12 * q^58 - 12 * q^59 + 8 * q^61 - 4 * q^62 - 4 * q^64 + 44 * q^66 - 6 * q^68 + 44 * q^69 - 18 * q^71 - 12 * q^72 - 8 * q^76 - 10 * q^78 - 8 * q^81 + 12 * q^82 - 12 * q^83 - 6 * q^84 - 10 * q^86 - 16 * q^87 - 12 * q^89 - 36 * q^91 - 4 * q^93 - 2 * q^96 + 44 * q^99

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