LMFDB - Embedded newform 700.2.g.b.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(251,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("700.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.g (of order $2$, degree $1$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.3
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	700.251
Dual form			700.2.g.b.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} -2.44949 q^{3} -2.00000i q^{4} +(2.44949 - 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} -2.44949 q^{3} -2.00000i q^{4} +(2.44949 - 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +5.00000i q^{11} +4.89898i q^{12} -2.44949i q^{13} +(1.44949 - 3.44949i) q^{14} -4.00000 q^{16} +4.89898i q^{17} +(-3.00000 + 3.00000i) q^{18} +(6.00000 - 2.44949i) q^{21} +(-5.00000 - 5.00000i) q^{22} -1.00000i q^{23} +(-4.89898 - 4.89898i) q^{24} +(2.44949 + 2.44949i) q^{26} +(2.00000 + 4.89898i) q^{28} -5.00000 q^{29} -7.34847 q^{31} +(4.00000 - 4.00000i) q^{32} -12.2474i q^{33} +(-4.89898 - 4.89898i) q^{34} -6.00000i q^{36} +3.00000 q^{37} +6.00000i q^{39} -12.2474i q^{41} +(-3.55051 + 8.44949i) q^{42} -11.0000i q^{43} +10.0000 q^{44} +(1.00000 + 1.00000i) q^{46} -4.89898 q^{47} +9.79796 q^{48} +(5.00000 - 4.89898i) q^{49} -12.0000i q^{51} -4.89898 q^{52} +4.00000 q^{53} +(-6.89898 - 2.89898i) q^{56} +(5.00000 - 5.00000i) q^{58} +12.2474 q^{59} +12.2474i q^{61} +(7.34847 - 7.34847i) q^{62} +(-7.34847 + 3.00000i) q^{63} +8.00000i q^{64} +(12.2474 + 12.2474i) q^{66} -3.00000i q^{67} +9.79796 q^{68} +2.44949i q^{69} -5.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -2.44949i q^{73} +(-3.00000 + 3.00000i) q^{74} +(-5.00000 - 12.2474i) q^{77} +(-6.00000 - 6.00000i) q^{78} -9.00000i q^{79} -9.00000 q^{81} +(12.2474 + 12.2474i) q^{82} -2.44949 q^{83} +(-4.89898 - 12.0000i) q^{84} +(11.0000 + 11.0000i) q^{86} +12.2474 q^{87} +(-10.0000 + 10.0000i) q^{88} +2.44949i q^{89} +(2.44949 + 6.00000i) q^{91} -2.00000 q^{92} +18.0000 q^{93} +(4.89898 - 4.89898i) q^{94} +(-9.79796 + 9.79796i) q^{96} -7.34847i q^{97} +(-0.101021 + 9.89898i) q^{98} +15.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 8 * q^8 + 12 * q^9	$ 4 q - 4 q^{2} + 8 q^{8} + 12 q^{9} - 4 q^{14} - 16 q^{16} - 12 q^{18} + 24 q^{21} - 20 q^{22} + 8 q^{28} - 20 q^{29} + 16 q^{32} + 12 q^{37} - 24 q^{42} + 40 q^{44} + 4 q^{46} + 20 q^{49} + 16 q^{53} - 8 q^{56} + 20 q^{58} + 24 q^{72} - 12 q^{74} - 20 q^{77} - 24 q^{78} - 36 q^{81} + 44 q^{86} - 40 q^{88} - 8 q^{92} + 72 q^{93} - 20 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 + 8 * q^8 + 12 * q^9 - 4 * q^14 - 16 * q^16 - 12 * q^18 + 24 * q^21 - 20 * q^22 + 8 * q^28 - 20 * q^29 + 16 * q^32 + 12 * q^37 - 24 * q^42 + 40 * q^44 + 4 * q^46 + 20 * q^49 + 16 * q^53 - 8 * q^56 + 20 * q^58 + 24 * q^72 - 12 * q^74 - 20 * q^77 - 24 * q^78 - 36 * q^81 + 44 * q^86 - 40 * q^88 - 8 * q^92 + 72 * q^93 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−2.44949			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$3$	−2.44949			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$4$		−	2.00000i		−	1.00000i
$5$		0			0
$5$		0			0
$6$	2.44949	−	2.44949i	1.00000	−	1.00000i
$7$	−2.44949	+	1.00000i	−0.925820	+	0.377964i
$7$	−2.44949	+	1.00000i	−0.925820	+	0.377964i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	3.00000			1.00000
$10$		0			0
$11$			5.00000i			1.50756i	0.657129	+	0.753778i	$0.271771\pi$
$11$			5.00000i			1.50756i	−0.657129	+	0.753778i	$0.728229\pi$
$12$			4.89898i			1.41421i
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	1.44949	−	3.44949i	0.387392	−	0.921915i
$15$		0			0
$16$	−4.00000			−1.00000
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$	−3.00000	+	3.00000i	−0.707107	+	0.707107i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$	6.00000	−	2.44949i	1.30931	−	0.534522i
$22$	−5.00000	−	5.00000i	−1.06600	−	1.06600i
$23$		−	1.00000i		−	0.208514i	−0.994550	−	0.104257i	$-0.966753\pi$
$23$		−	1.00000i		−	0.208514i	0.994550	−	0.104257i	$-0.0332465\pi$
$24$	−4.89898	−	4.89898i	−1.00000	−	1.00000i
$25$		0			0
$26$	2.44949	+	2.44949i	0.480384	+	0.480384i
$27$		0			0
$28$	2.00000	+	4.89898i	0.377964	+	0.925820i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	−7.34847			−1.31982			−0.659912	−	0.751343i	$-0.729406\pi$
$31$	−7.34847			−1.31982			−0.659912	+	0.751343i	$0.729406\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$		−	12.2474i		−	2.13201i
$34$	−4.89898	−	4.89898i	−0.840168	−	0.840168i
$35$		0			0
$36$		−	6.00000i		−	1.00000i
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$		0			0
$39$			6.00000i			0.960769i
$40$		0			0
$41$		−	12.2474i		−	1.91273i	−0.292174	−	0.956365i	$-0.594379\pi$
$41$		−	12.2474i		−	1.91273i	0.292174	−	0.956365i	$-0.405621\pi$
$42$	−3.55051	+	8.44949i	−0.547856	+	1.30378i
$43$		−	11.0000i		−	1.67748i	−0.544529	−	0.838742i	$-0.683292\pi$
$43$		−	11.0000i		−	1.67748i	0.544529	−	0.838742i	$-0.316708\pi$
$44$	10.0000			1.50756
$45$		0			0
$46$	1.00000	+	1.00000i	0.147442	+	0.147442i
$47$	−4.89898			−0.714590			−0.357295	−	0.933992i	$-0.616301\pi$
$47$	−4.89898			−0.714590			−0.357295	+	0.933992i	$0.616301\pi$
$48$	9.79796			1.41421
$49$	5.00000	−	4.89898i	0.714286	−	0.699854i
$50$		0			0
$51$		−	12.0000i		−	1.68034i
$52$	−4.89898			−0.679366
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$		0			0
$55$		0			0
$56$	−6.89898	−	2.89898i	−0.921915	−	0.387392i
$57$		0			0
$58$	5.00000	−	5.00000i	0.656532	−	0.656532i
$59$	12.2474			1.59448			0.797241	−	0.603661i	$-0.206292\pi$
$59$	12.2474			1.59448			0.797241	+	0.603661i	$0.206292\pi$
$60$		0			0
$61$			12.2474i			1.56813i	0.620682	+	0.784063i	$0.286856\pi$
$61$			12.2474i			1.56813i	−0.620682	+	0.784063i	$0.713144\pi$
$62$	7.34847	−	7.34847i	0.933257	−	0.933257i
$63$	−7.34847	+	3.00000i	−0.925820	+	0.377964i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	12.2474	+	12.2474i	1.50756	+	1.50756i
$67$		−	3.00000i		−	0.366508i	−0.983066	−	0.183254i	$-0.941337\pi$
$67$		−	3.00000i		−	0.366508i	0.983066	−	0.183254i	$-0.0586631\pi$
$68$	9.79796			1.18818
$69$			2.44949i			0.294884i
$70$		0			0
$71$		−	5.00000i		−	0.593391i	−0.954972	−	0.296695i	$-0.904115\pi$
$71$		−	5.00000i		−	0.593391i	0.954972	−	0.296695i	$-0.0958846\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$		−	2.44949i		−	0.286691i	−0.989673	−	0.143346i	$-0.954214\pi$
$73$		−	2.44949i		−	0.286691i	0.989673	−	0.143346i	$-0.0457860\pi$
$74$	−3.00000	+	3.00000i	−0.348743	+	0.348743i
$75$		0			0
$76$		0			0
$77$	−5.00000	−	12.2474i	−0.569803	−	1.39573i
$78$	−6.00000	−	6.00000i	−0.679366	−	0.679366i
$79$		−	9.00000i		−	1.01258i	−0.862364	−	0.506290i	$-0.831017\pi$
$79$		−	9.00000i		−	1.01258i	0.862364	−	0.506290i	$-0.168983\pi$
$80$		0			0
$81$	−9.00000			−1.00000
$82$	12.2474	+	12.2474i	1.35250	+	1.35250i
$83$	−2.44949			−0.268866			−0.134433	−	0.990923i	$-0.542921\pi$
$83$	−2.44949			−0.268866			−0.134433	+	0.990923i	$0.542921\pi$
$84$	−4.89898	−	12.0000i	−0.534522	−	1.30931i
$85$		0			0
$86$	11.0000	+	11.0000i	1.18616	+	1.18616i
$87$	12.2474			1.31306
$88$	−10.0000	+	10.0000i	−1.06600	+	1.06600i
$89$			2.44949i			0.259645i	0.991537	+	0.129823i	$0.0414408\pi$
$89$			2.44949i			0.259645i	−0.991537	+	0.129823i	$0.958559\pi$
$90$		0			0
$91$	2.44949	+	6.00000i	0.256776	+	0.628971i
$92$	−2.00000			−0.208514
$93$	18.0000			1.86651
$94$	4.89898	−	4.89898i	0.505291	−	0.505291i
$95$		0			0
$96$	−9.79796	+	9.79796i	−1.00000	+	1.00000i
$97$		−	7.34847i		−	0.746124i	−0.927806	−	0.373062i	$-0.878308\pi$
$97$		−	7.34847i		−	0.746124i	0.927806	−	0.373062i	$-0.121692\pi$
$98$	−0.101021	+	9.89898i	−0.0102046	+	0.999948i
$99$			15.0000i			1.50756i
$100$		0			0
$101$		−	12.2474i		−	1.21867i	−0.792914	−	0.609333i	$-0.791437\pi$
$101$		−	12.2474i		−	1.21867i	0.792914	−	0.609333i	$-0.208563\pi$
$102$	12.0000	+	12.0000i	1.18818	+	1.18818i
$103$	−14.6969			−1.44813			−0.724066	−	0.689730i	$-0.757729\pi$
$103$	−14.6969			−1.44813			−0.724066	+	0.689730i	$0.757729\pi$
$104$	4.89898	−	4.89898i	0.480384	−	0.480384i
$105$		0			0
$106$	−4.00000	+	4.00000i	−0.388514	+	0.388514i
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$		0			0
$109$	−15.0000			−1.43674			−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000			−1.43674			−0.718370	+	0.695662i	$0.755111\pi$
$110$		0			0
$111$	−7.34847			−0.697486
$112$	9.79796	−	4.00000i	0.925820	−	0.377964i
$113$	−11.0000			−1.03479			−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000			−1.03479			−0.517396	+	0.855746i	$0.673099\pi$
$114$		0			0
$115$		0			0
$116$			10.0000i			0.928477i
$117$		−	7.34847i		−	0.679366i
$118$	−12.2474	+	12.2474i	−1.12747	+	1.12747i
$119$	−4.89898	−	12.0000i	−0.449089	−	1.10004i
$120$		0			0
$121$	−14.0000			−1.27273
$122$	−12.2474	−	12.2474i	−1.10883	−	1.10883i
$123$			30.0000i			2.70501i
$124$			14.6969i			1.31982i
$125$		0			0
$126$	4.34847	−	10.3485i	0.387392	−	0.921915i
$127$		−	3.00000i		−	0.266207i	−0.991102	−	0.133103i	$-0.957506\pi$
$127$		−	3.00000i		−	0.266207i	0.991102	−	0.133103i	$-0.0424943\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$			26.9444i			2.37232i
$130$		0			0
$131$	4.89898			0.428026			0.214013	−	0.976831i	$-0.431347\pi$
$131$	4.89898			0.428026			0.214013	+	0.976831i	$0.431347\pi$
$132$	−24.4949			−2.13201
$133$		0			0
$134$	3.00000	+	3.00000i	0.259161	+	0.259161i
$135$		0			0
$136$	−9.79796	+	9.79796i	−0.840168	+	0.840168i
$137$	8.00000			0.683486			0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000			0.683486			0.341743	+	0.939793i	$0.388983\pi$
$138$	−2.44949	−	2.44949i	−0.208514	−	0.208514i
$139$	12.2474			1.03882			0.519408	−	0.854527i	$-0.326153\pi$
$139$	12.2474			1.03882			0.519408	+	0.854527i	$0.326153\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$	5.00000	+	5.00000i	0.419591	+	0.419591i
$143$	12.2474			1.02418
$144$	−12.0000			−1.00000
$145$		0			0
$146$	2.44949	+	2.44949i	0.202721	+	0.202721i
$147$	−12.2474	+	12.0000i	−1.01015	+	0.989743i
$148$		−	6.00000i		−	0.493197i
$149$	−5.00000			−0.409616			−0.204808	−	0.978802i	$-0.565657\pi$
$149$	−5.00000			−0.409616			−0.204808	+	0.978802i	$0.565657\pi$
$150$		0			0
$151$		−	5.00000i		−	0.406894i	−0.979086	−	0.203447i	$-0.934786\pi$
$151$		−	5.00000i		−	0.406894i	0.979086	−	0.203447i	$-0.0652145\pi$
$152$		0			0
$153$			14.6969i			1.18818i
$154$	17.2474	+	7.24745i	1.38984	+	0.584016i
$155$		0			0
$156$	12.0000			0.960769
$157$			17.1464i			1.36843i	0.729279	+	0.684217i	$0.239856\pi$
$157$			17.1464i			1.36843i	−0.729279	+	0.684217i	$0.760144\pi$
$158$	9.00000	+	9.00000i	0.716002	+	0.716002i
$159$	−9.79796			−0.777029
$160$		0			0
$161$	1.00000	+	2.44949i	0.0788110	+	0.193047i
$162$	9.00000	−	9.00000i	0.707107	−	0.707107i
$163$		−	6.00000i		−	0.469956i	−0.972001	−	0.234978i	$-0.924498\pi$
$163$		−	6.00000i		−	0.469956i	0.972001	−	0.234978i	$-0.0755019\pi$
$164$	−24.4949			−1.91273
$165$		0			0
$166$	2.44949	−	2.44949i	0.190117	−	0.190117i
$167$	7.34847			0.568642			0.284321	−	0.958729i	$-0.408232\pi$
$167$	7.34847			0.568642			0.284321	+	0.958729i	$0.408232\pi$
$168$	16.8990	+	7.10102i	1.30378	+	0.547856i
$169$	7.00000			0.538462
$170$		0			0
$171$		0			0
$172$	−22.0000			−1.67748
$173$			9.79796i			0.744925i	0.928047	+	0.372463i	$0.121486\pi$
$173$			9.79796i			0.744925i	−0.928047	+	0.372463i	$0.878514\pi$
$174$	−12.2474	+	12.2474i	−0.928477	+	0.928477i
$175$		0			0
$176$		−	20.0000i		−	1.50756i
$177$	−30.0000			−2.25494
$178$	−2.44949	−	2.44949i	−0.183597	−	0.183597i
$179$		−	14.0000i		−	1.04641i	−0.852207	−	0.523205i	$-0.824736\pi$
$179$		−	14.0000i		−	1.04641i	0.852207	−	0.523205i	$-0.175264\pi$
$180$		0			0
$181$			12.2474i			0.910346i	0.890403	+	0.455173i	$0.150423\pi$
$181$			12.2474i			0.910346i	−0.890403	+	0.455173i	$0.849577\pi$
$182$	−8.44949	−	3.55051i	−0.626318	−	0.263181i
$183$		−	30.0000i		−	2.21766i
$184$	2.00000	−	2.00000i	0.147442	−	0.147442i
$185$		0			0
$186$	−18.0000	+	18.0000i	−1.31982	+	1.31982i
$187$	−24.4949			−1.79124
$188$			9.79796i			0.714590i
$189$		0			0
$190$		0			0
$191$		−	10.0000i		−	0.723575i	−0.932261	−	0.361787i	$-0.882167\pi$
$191$		−	10.0000i		−	0.723575i	0.932261	−	0.361787i	$-0.117833\pi$
$192$		−	19.5959i		−	1.41421i
$193$	−21.0000			−1.51161			−0.755807	−	0.654795i	$-0.772755\pi$
$193$	−21.0000			−1.51161			−0.755807	+	0.654795i	$0.772755\pi$
$194$	7.34847	+	7.34847i	0.527589	+	0.527589i
$195$		0			0
$196$	−9.79796	−	10.0000i	−0.699854	−	0.714286i
$197$	23.0000			1.63868			0.819341	−	0.573306i	$-0.194340\pi$
$197$	23.0000			1.63868			0.819341	+	0.573306i	$0.194340\pi$
$198$	−15.0000	−	15.0000i	−1.06600	−	1.06600i
$199$	−12.2474			−0.868199			−0.434099	−	0.900865i	$-0.642933\pi$
$199$	−12.2474			−0.868199			−0.434099	+	0.900865i	$0.642933\pi$
$200$		0			0
$201$			7.34847i			0.518321i
$202$	12.2474	+	12.2474i	0.861727	+	0.861727i
$203$	12.2474	−	5.00000i	0.859602	−	0.350931i
$204$	−24.0000			−1.68034
$205$		0			0
$206$	14.6969	−	14.6969i	1.02398	−	1.02398i
$207$		−	3.00000i		−	0.208514i
$208$			9.79796i			0.679366i
$209$		0			0
$210$		0			0
$211$			10.0000i			0.688428i	0.938891	+	0.344214i	$0.111855\pi$
$211$			10.0000i			0.688428i	−0.938891	+	0.344214i	$0.888145\pi$
$212$		−	8.00000i		−	0.549442i
$213$			12.2474i			0.839181i
$214$	8.00000	+	8.00000i	0.546869	+	0.546869i
$215$		0			0
$216$		0			0
$217$	18.0000	−	7.34847i	1.22192	−	0.498847i
$218$	15.0000	−	15.0000i	1.01593	−	1.01593i
$219$			6.00000i			0.405442i
$220$		0			0
$221$	12.0000			0.807207
$222$	7.34847	−	7.34847i	0.493197	−	0.493197i
$223$	−2.44949			−0.164030			−0.0820150	−	0.996631i	$-0.526136\pi$
$223$	−2.44949			−0.164030			−0.0820150	+	0.996631i	$0.526136\pi$
$224$	−5.79796	+	13.7980i	−0.387392	+	0.921915i
$225$		0			0
$226$	11.0000	−	11.0000i	0.731709	−	0.731709i
$227$	19.5959			1.30063			0.650313	−	0.759666i	$-0.274638\pi$
$227$	19.5959			1.30063			0.650313	+	0.759666i	$0.274638\pi$
$228$		0			0
$229$		−	9.79796i		−	0.647467i	−0.946148	−	0.323734i	$-0.895062\pi$
$229$		−	9.79796i		−	0.647467i	0.946148	−	0.323734i	$-0.104938\pi$
$230$		0			0
$231$	12.2474	+	30.0000i	0.805823	+	1.97386i
$232$	−10.0000	−	10.0000i	−0.656532	−	0.656532i
$233$	−11.0000			−0.720634			−0.360317	−	0.932830i	$-0.617331\pi$
$233$	−11.0000			−0.720634			−0.360317	+	0.932830i	$0.617331\pi$
$234$	7.34847	+	7.34847i	0.480384	+	0.480384i
$235$		0			0
$236$		−	24.4949i		−	1.59448i
$237$			22.0454i			1.43200i
$238$	16.8990	+	7.10102i	1.09540	+	0.460291i
$239$			26.0000i			1.68180i	0.541190	+	0.840900i	$0.317974\pi$
$239$			26.0000i			1.68180i	−0.541190	+	0.840900i	$0.682026\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	14.0000	−	14.0000i	0.899954	−	0.899954i
$243$	22.0454			1.41421
$244$	24.4949			1.56813
$245$		0			0
$246$	−30.0000	−	30.0000i	−1.91273	−	1.91273i
$247$		0			0
$248$	−14.6969	−	14.6969i	−0.933257	−	0.933257i
$249$	6.00000			0.380235
$250$		0			0
$251$	4.89898			0.309221			0.154610	−	0.987976i	$-0.450588\pi$
$251$	4.89898			0.309221			0.154610	+	0.987976i	$0.450588\pi$
$252$	6.00000	+	14.6969i	0.377964	+	0.925820i
$253$	5.00000			0.314347
$254$	3.00000	+	3.00000i	0.188237	+	0.188237i
$255$		0			0
$256$	16.0000			1.00000
$257$		−	7.34847i		−	0.458385i	−0.973381	−	0.229192i	$-0.926391\pi$
$257$		−	7.34847i		−	0.458385i	0.973381	−	0.229192i	$-0.0736085\pi$
$258$	−26.9444	−	26.9444i	−1.67748	−	1.67748i
$259$	−7.34847	+	3.00000i	−0.456612	+	0.186411i
$260$		0			0
$261$	−15.0000			−0.928477
$262$	−4.89898	+	4.89898i	−0.302660	+	0.302660i
$263$		−	1.00000i		−	0.0616626i	−0.999525	−	0.0308313i	$-0.990185\pi$
$263$		−	1.00000i		−	0.0616626i	0.999525	−	0.0308313i	$-0.00981547\pi$
$264$	24.4949	−	24.4949i	1.50756	−	1.50756i
$265$		0			0
$266$		0			0
$267$		−	6.00000i		−	0.367194i
$268$	−6.00000			−0.366508
$269$		−	22.0454i		−	1.34413i	−0.740491	−	0.672066i	$-0.765407\pi$
$269$		−	22.0454i		−	1.34413i	0.740491	−	0.672066i	$-0.234593\pi$
$270$		0			0
$271$	17.1464			1.04157			0.520786	−	0.853687i	$-0.325639\pi$
$271$	17.1464			1.04157			0.520786	+	0.853687i	$0.325639\pi$
$272$		−	19.5959i		−	1.18818i
$273$	−6.00000	−	14.6969i	−0.363137	−	0.889499i
$274$	−8.00000	+	8.00000i	−0.483298	+	0.483298i
$275$		0			0
$276$	4.89898			0.294884
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	−12.2474	+	12.2474i	−0.734553	+	0.734553i
$279$	−22.0454			−1.31982
$280$		0			0
$281$	17.0000			1.01413			0.507067	−	0.861906i	$-0.330729\pi$
$281$	17.0000			1.01413			0.507067	+	0.861906i	$0.330729\pi$
$282$	−12.0000	+	12.0000i	−0.714590	+	0.714590i
$283$	9.79796			0.582428			0.291214	−	0.956658i	$-0.405941\pi$
$283$	9.79796			0.582428			0.291214	+	0.956658i	$0.405941\pi$
$284$	−10.0000			−0.593391
$285$		0			0
$286$	−12.2474	+	12.2474i	−0.724207	+	0.724207i
$287$	12.2474	+	30.0000i	0.722944	+	1.77084i
$288$	12.0000	−	12.0000i	0.707107	−	0.707107i
$289$	−7.00000			−0.411765
$290$		0			0
$291$			18.0000i			1.05518i
$292$	−4.89898			−0.286691
$293$		−	2.44949i		−	0.143101i	−0.997437	−	0.0715504i	$-0.977205\pi$
$293$		−	2.44949i		−	0.143101i	0.997437	−	0.0715504i	$-0.0227947\pi$
$294$	0.247449	−	24.2474i	0.0144315	−	1.41414i
$295$		0			0
$296$	6.00000	+	6.00000i	0.348743	+	0.348743i
$297$		0			0
$298$	5.00000	−	5.00000i	0.289642	−	0.289642i
$299$	−2.44949			−0.141658
$300$		0			0
$301$	11.0000	+	26.9444i	0.634029	+	1.55305i
$302$	5.00000	+	5.00000i	0.287718	+	0.287718i
$303$			30.0000i			1.72345i
$304$		0			0
$305$		0			0
$306$	−14.6969	−	14.6969i	−0.840168	−	0.840168i
$307$	−4.89898			−0.279600			−0.139800	−	0.990180i	$-0.544646\pi$
$307$	−4.89898			−0.279600			−0.139800	+	0.990180i	$0.544646\pi$
$308$	−24.4949	+	10.0000i	−1.39573	+	0.569803i
$309$	36.0000			2.04797
$310$		0			0
$311$	−19.5959			−1.11118			−0.555591	−	0.831456i	$-0.687508\pi$
$311$	−19.5959			−1.11118			−0.555591	+	0.831456i	$0.687508\pi$
$312$	−12.0000	+	12.0000i	−0.679366	+	0.679366i
$313$			9.79796i			0.553813i	0.960897	+	0.276907i	$0.0893093\pi$
$313$			9.79796i			0.553813i	−0.960897	+	0.276907i	$0.910691\pi$
$314$	−17.1464	−	17.1464i	−0.967629	−	0.967629i
$315$		0			0
$316$	−18.0000			−1.01258
$317$	−17.0000			−0.954815			−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000			−0.954815			−0.477408	+	0.878682i	$0.658423\pi$
$318$	9.79796	−	9.79796i	0.549442	−	0.549442i
$319$		−	25.0000i		−	1.39973i
$320$		0			0
$321$			19.5959i			1.09374i
$322$	−3.44949	−	1.44949i	−0.192233	−	0.0807769i
$323$		0			0
$324$			18.0000i			1.00000i
$325$		0			0
$326$	6.00000	+	6.00000i	0.332309	+	0.332309i
$327$	36.7423			2.03186
$328$	24.4949	−	24.4949i	1.35250	−	1.35250i
$329$	12.0000	−	4.89898i	0.661581	−	0.270089i
$330$		0			0
$331$		−	25.0000i		−	1.37412i	−0.726599	−	0.687062i	$-0.758900\pi$
$331$		−	25.0000i		−	1.37412i	0.726599	−	0.687062i	$-0.241100\pi$
$332$			4.89898i			0.268866i
$333$	9.00000			0.493197
$334$	−7.34847	+	7.34847i	−0.402090	+	0.402090i
$335$		0			0
$336$	−24.0000	+	9.79796i	−1.30931	+	0.534522i
$337$	−12.0000			−0.653682			−0.326841	−	0.945079i	$-0.605984\pi$
$337$	−12.0000			−0.653682			−0.326841	+	0.945079i	$0.605984\pi$
$338$	−7.00000	+	7.00000i	−0.380750	+	0.380750i
$339$	26.9444			1.46342
$340$		0			0
$341$		−	36.7423i		−	1.98971i
$342$		0			0
$343$	−7.34847	+	17.0000i	−0.396780	+	0.917914i
$344$	22.0000	−	22.0000i	1.18616	−	1.18616i
$345$		0			0
$346$	−9.79796	−	9.79796i	−0.526742	−	0.526742i
$347$			17.0000i			0.912608i	0.889824	+	0.456304i	$0.150827\pi$
$347$			17.0000i			0.912608i	−0.889824	+	0.456304i	$0.849173\pi$
$348$		−	24.4949i		−	1.31306i
$349$		−	9.79796i		−	0.524473i	−0.965004	−	0.262236i	$-0.915540\pi$
$349$		−	9.79796i		−	0.524473i	0.965004	−	0.262236i	$-0.0844600\pi$
$350$		0			0
$351$		0			0
$352$	20.0000	+	20.0000i	1.06600	+	1.06600i
$353$			22.0454i			1.17336i	0.809819	+	0.586679i	$0.199565\pi$
$353$			22.0454i			1.17336i	−0.809819	+	0.586679i	$0.800435\pi$
$354$	30.0000	−	30.0000i	1.59448	−	1.59448i
$355$		0			0
$356$	4.89898			0.259645
$357$	12.0000	+	29.3939i	0.635107	+	1.55569i
$358$	14.0000	+	14.0000i	0.739923	+	0.739923i
$359$		−	19.0000i		−	1.00278i	−0.865221	−	0.501391i	$-0.832822\pi$
$359$		−	19.0000i		−	1.00278i	0.865221	−	0.501391i	$-0.167178\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	−12.2474	−	12.2474i	−0.643712	−	0.643712i
$363$	34.2929			1.79991
$364$	12.0000	−	4.89898i	0.628971	−	0.256776i
$365$		0			0
$366$	30.0000	+	30.0000i	1.56813	+	1.56813i
$367$	−17.1464			−0.895036			−0.447518	−	0.894275i	$-0.647692\pi$
$367$	−17.1464			−0.895036			−0.447518	+	0.894275i	$0.647692\pi$
$368$			4.00000i			0.208514i
$369$		−	36.7423i		−	1.91273i
$370$		0			0
$371$	−9.79796	+	4.00000i	−0.508685	+	0.207670i
$372$		−	36.0000i		−	1.86651i
$373$	29.0000			1.50156			0.750782	−	0.660551i	$-0.229677\pi$
$373$	29.0000			1.50156			0.750782	+	0.660551i	$0.229677\pi$
$374$	24.4949	−	24.4949i	1.26660	−	1.26660i
$375$		0			0
$376$	−9.79796	−	9.79796i	−0.505291	−	0.505291i
$377$			12.2474i			0.630776i
$378$		0			0
$379$			1.00000i			0.0513665i	0.999670	+	0.0256833i	$0.00817614\pi$
$379$			1.00000i			0.0513665i	−0.999670	+	0.0256833i	$0.991824\pi$
$380$		0			0
$381$			7.34847i			0.376473i
$382$	10.0000	+	10.0000i	0.511645	+	0.511645i
$383$	−2.44949			−0.125163			−0.0625815	−	0.998040i	$-0.519933\pi$
$383$	−2.44949			−0.125163			−0.0625815	+	0.998040i	$0.519933\pi$
$384$	19.5959	+	19.5959i	1.00000	+	1.00000i
$385$		0			0
$386$	21.0000	−	21.0000i	1.06887	−	1.06887i
$387$		−	33.0000i		−	1.67748i
$388$	−14.6969			−0.746124
$389$	5.00000			0.253510			0.126755	−	0.991934i	$-0.459544\pi$
$389$	5.00000			0.253510			0.126755	+	0.991934i	$0.459544\pi$
$390$		0			0
$391$	4.89898			0.247752
$392$	19.7980	+	0.202041i	0.999948	+	0.0102046i
$393$	−12.0000			−0.605320
$394$	−23.0000	+	23.0000i	−1.15872	+	1.15872i
$395$		0			0
$396$	30.0000			1.50756
$397$		−	19.5959i		−	0.983491i	−0.870739	−	0.491745i	$-0.836359\pi$
$397$		−	19.5959i		−	0.983491i	0.870739	−	0.491745i	$-0.163641\pi$
$398$	12.2474	−	12.2474i	0.613909	−	0.613909i
$399$		0			0
$400$		0			0
$401$	−23.0000			−1.14857			−0.574283	−	0.818657i	$-0.694719\pi$
$401$	−23.0000			−1.14857			−0.574283	+	0.818657i	$0.694719\pi$
$402$	−7.34847	−	7.34847i	−0.366508	−	0.366508i
$403$			18.0000i			0.896644i
$404$	−24.4949			−1.21867
$405$		0			0
$406$	−7.24745	+	17.2474i	−0.359685	+	0.855977i
$407$			15.0000i			0.743522i
$408$	24.0000	−	24.0000i	1.18818	−	1.18818i
$409$		−	34.2929i		−	1.69567i	−0.530258	−	0.847836i	$-0.677905\pi$
$409$		−	34.2929i		−	1.69567i	0.530258	−	0.847836i	$-0.322095\pi$
$410$		0			0
$411$	−19.5959			−0.966595
$412$			29.3939i			1.44813i
$413$	−30.0000	+	12.2474i	−1.47620	+	0.602658i
$414$	3.00000	+	3.00000i	0.147442	+	0.147442i
$415$		0			0
$416$	−9.79796	−	9.79796i	−0.480384	−	0.480384i
$417$	−30.0000			−1.46911
$418$		0			0
$419$	12.2474			0.598327			0.299164	−	0.954202i	$-0.403292\pi$
$419$	12.2474			0.598327			0.299164	+	0.954202i	$0.403292\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$	−10.0000	−	10.0000i	−0.486792	−	0.486792i
$423$	−14.6969			−0.714590
$424$	8.00000	+	8.00000i	0.388514	+	0.388514i
$425$		0			0
$426$	−12.2474	−	12.2474i	−0.593391	−	0.593391i
$427$	−12.2474	−	30.0000i	−0.592696	−	1.45180i
$428$	−16.0000			−0.773389
$429$	−30.0000			−1.44841
$430$		0			0
$431$		−	10.0000i		−	0.481683i	−0.970564	−	0.240842i	$-0.922577\pi$
$431$		−	10.0000i		−	0.481683i	0.970564	−	0.240842i	$-0.0774234\pi$
$432$		0			0
$433$		−	39.1918i		−	1.88344i	−0.336399	−	0.941720i	$-0.609209\pi$
$433$		−	39.1918i		−	1.88344i	0.336399	−	0.941720i	$-0.390791\pi$
$434$	−10.6515	+	25.3485i	−0.511290	+	1.21677i
$435$		0			0
$436$			30.0000i			1.43674i
$437$		0			0
$438$	−6.00000	−	6.00000i	−0.286691	−	0.286691i
$439$	−12.2474			−0.584539			−0.292269	−	0.956336i	$-0.594410\pi$
$439$	−12.2474			−0.584539			−0.292269	+	0.956336i	$0.594410\pi$
$440$		0			0
$441$	15.0000	−	14.6969i	0.714286	−	0.699854i
$442$	−12.0000	+	12.0000i	−0.570782	+	0.570782i
$443$			14.0000i			0.665160i	0.943075	+	0.332580i	$0.107919\pi$
$443$			14.0000i			0.665160i	−0.943075	+	0.332580i	$0.892081\pi$
$444$			14.6969i			0.697486i
$445$		0			0
$446$	2.44949	−	2.44949i	0.115987	−	0.115987i
$447$	12.2474			0.579284
$448$	−8.00000	−	19.5959i	−0.377964	−	0.925820i
$449$	−25.0000			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$449$	−25.0000			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$450$		0			0
$451$	61.2372			2.88355
$452$			22.0000i			1.03479i
$453$			12.2474i			0.575435i
$454$	−19.5959	+	19.5959i	−0.919682	+	0.919682i
$455$		0			0
$456$		0			0
$457$	3.00000			0.140334			0.0701670	−	0.997535i	$-0.477647\pi$
$457$	3.00000			0.140334			0.0701670	+	0.997535i	$0.477647\pi$
$458$	9.79796	+	9.79796i	0.457829	+	0.457829i
$459$		0			0
$460$		0			0
$461$		−	12.2474i		−	0.570421i	−0.958465	−	0.285210i	$-0.907937\pi$
$461$		−	12.2474i		−	0.570421i	0.958465	−	0.285210i	$-0.0920634\pi$
$462$	−42.2474	−	17.7526i	−1.96553	−	0.825923i
$463$		−	36.0000i		−	1.67306i	−0.547920	−	0.836531i	$-0.684580\pi$
$463$		−	36.0000i		−	1.67306i	0.547920	−	0.836531i	$-0.315420\pi$
$464$	20.0000			0.928477
$465$		0			0
$466$	11.0000	−	11.0000i	0.509565	−	0.509565i
$467$	−4.89898			−0.226698			−0.113349	−	0.993555i	$-0.536158\pi$
$467$	−4.89898			−0.226698			−0.113349	+	0.993555i	$0.536158\pi$
$468$	−14.6969			−0.679366
$469$	3.00000	+	7.34847i	0.138527	+	0.339321i
$470$		0			0
$471$		−	42.0000i		−	1.93526i
$472$	24.4949	+	24.4949i	1.12747	+	1.12747i
$473$	55.0000			2.52890
$474$	−22.0454	−	22.0454i	−1.01258	−	1.01258i
$475$		0			0
$476$	−24.0000	+	9.79796i	−1.10004	+	0.449089i
$477$	12.0000			0.549442
$478$	−26.0000	−	26.0000i	−1.18921	−	1.18921i
$479$	−36.7423			−1.67880			−0.839400	−	0.543514i	$-0.817094\pi$
$479$	−36.7423			−1.67880			−0.839400	+	0.543514i	$0.817094\pi$
$480$		0			0
$481$		−	7.34847i		−	0.335061i
$482$		0			0
$483$	−2.44949	−	6.00000i	−0.111456	−	0.273009i
$484$			28.0000i			1.27273i
$485$		0			0
$486$	−22.0454	+	22.0454i	−1.00000	+	1.00000i
$487$			7.00000i			0.317200i	0.987343	+	0.158600i	$0.0506981\pi$
$487$			7.00000i			0.317200i	−0.987343	+	0.158600i	$0.949302\pi$
$488$	−24.4949	+	24.4949i	−1.10883	+	1.10883i
$489$			14.6969i			0.664619i
$490$		0			0
$491$			5.00000i			0.225647i	0.993615	+	0.112823i	$0.0359894\pi$
$491$			5.00000i			0.225647i	−0.993615	+	0.112823i	$0.964011\pi$
$492$	60.0000			2.70501
$493$		−	24.4949i		−	1.10319i
$494$		0			0
$495$		0			0
$496$	29.3939			1.31982
$497$	5.00000	+	12.2474i	0.224281	+	0.549373i
$498$	−6.00000	+	6.00000i	−0.268866	+	0.268866i
$499$			16.0000i			0.716258i	0.933672	+	0.358129i	$0.116585\pi$
$499$			16.0000i			0.716258i	−0.933672	+	0.358129i	$0.883415\pi$
$500$		0			0
$501$	−18.0000			−0.804181
$502$	−4.89898	+	4.89898i	−0.218652	+	0.218652i
$503$	−14.6969			−0.655304			−0.327652	−	0.944798i	$-0.606257\pi$
$503$	−14.6969			−0.655304			−0.327652	+	0.944798i	$0.606257\pi$
$504$	−20.6969	−	8.69694i	−0.921915	−	0.387392i
$505$		0			0
$506$	−5.00000	+	5.00000i	−0.222277	+	0.222277i
$507$	−17.1464			−0.761500
$508$	−6.00000			−0.266207
$509$			26.9444i			1.19429i	0.802134	+	0.597144i	$0.203698\pi$
$509$			26.9444i			1.19429i	−0.802134	+	0.597144i	$0.796302\pi$
$510$		0			0
$511$	2.44949	+	6.00000i	0.108359	+	0.265424i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$		0			0
$514$	7.34847	+	7.34847i	0.324127	+	0.324127i
$515$		0			0
$516$	53.8888			2.37232
$517$		−	24.4949i		−	1.07728i
$518$	4.34847	−	10.3485i	0.191061	−	0.454686i
$519$		−	24.0000i		−	1.05348i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	15.0000	−	15.0000i	0.656532	−	0.656532i
$523$	9.79796			0.428435			0.214217	−	0.976786i	$-0.431280\pi$
$523$	9.79796			0.428435			0.214217	+	0.976786i	$0.431280\pi$
$524$		−	9.79796i		−	0.428026i
$525$		0			0
$526$	1.00000	+	1.00000i	0.0436021	+	0.0436021i
$527$		−	36.0000i		−	1.56818i
$528$			48.9898i			2.13201i
$529$	22.0000			0.956522
$530$		0			0
$531$	36.7423			1.59448
$532$		0			0
$533$	−30.0000			−1.29944
$534$	6.00000	+	6.00000i	0.259645	+	0.259645i
$535$		0			0
$536$	6.00000	−	6.00000i	0.259161	−	0.259161i
$537$			34.2929i			1.47985i
$538$	22.0454	+	22.0454i	0.950445	+	0.950445i
$539$	24.4949	+	25.0000i	1.05507	+	1.07683i
$540$		0			0
$541$	−13.0000			−0.558914			−0.279457	−	0.960158i	$-0.590154\pi$
$541$	−13.0000			−0.558914			−0.279457	+	0.960158i	$0.590154\pi$
$542$	−17.1464	+	17.1464i	−0.736502	+	0.736502i
$543$		−	30.0000i		−	1.28742i
$544$	19.5959	+	19.5959i	0.840168	+	0.840168i
$545$		0			0
$546$	20.6969	+	8.69694i	0.885747	+	0.372195i
$547$			27.0000i			1.15444i	0.816590	+	0.577218i	$0.195862\pi$
$547$			27.0000i			1.15444i	−0.816590	+	0.577218i	$0.804138\pi$
$548$		−	16.0000i		−	0.683486i
$549$			36.7423i			1.56813i
$550$		0			0
$551$		0			0
$552$	−4.89898	+	4.89898i	−0.208514	+	0.208514i
$553$	9.00000	+	22.0454i	0.382719	+	0.937466i
$554$	2.00000	−	2.00000i	0.0849719	−	0.0849719i
$555$		0			0
$556$		−	24.4949i		−	1.03882i
$557$	−37.0000			−1.56774			−0.783870	−	0.620925i	$-0.786757\pi$
$557$	−37.0000			−1.56774			−0.783870	+	0.620925i	$0.786757\pi$
$558$	22.0454	−	22.0454i	0.933257	−	0.933257i
$559$	−26.9444			−1.13963
$560$		0			0
$561$	60.0000			2.53320
$562$	−17.0000	+	17.0000i	−0.717102	+	0.717102i
$563$	−14.6969			−0.619402			−0.309701	−	0.950834i	$-0.600229\pi$
$563$	−14.6969			−0.619402			−0.309701	+	0.950834i	$0.600229\pi$
$564$		−	24.0000i		−	1.01058i
$565$		0			0
$566$	−9.79796	+	9.79796i	−0.411839	+	0.411839i
$567$	22.0454	−	9.00000i	0.925820	−	0.377964i
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$	5.00000			0.209611			0.104805	−	0.994493i	$-0.466578\pi$
$569$	5.00000			0.209611			0.104805	+	0.994493i	$0.466578\pi$
$570$		0			0
$571$		−	15.0000i		−	0.627730i	−0.949468	−	0.313865i	$-0.898376\pi$
$571$		−	15.0000i		−	0.627730i	0.949468	−	0.313865i	$-0.101624\pi$
$572$		−	24.4949i		−	1.02418i
$573$			24.4949i			1.02329i
$574$	−42.2474	−	17.7526i	−1.76337	−	0.740977i
$575$		0			0
$576$			24.0000i			1.00000i
$577$		−	44.0908i		−	1.83552i	−0.397130	−	0.917762i	$-0.629994\pi$
$577$		−	44.0908i		−	1.83552i	0.397130	−	0.917762i	$-0.370006\pi$
$578$	7.00000	−	7.00000i	0.291162	−	0.291162i
$579$	51.4393			2.13774
$580$		0			0
$581$	6.00000	−	2.44949i	0.248922	−	0.101622i
$582$	−18.0000	−	18.0000i	−0.746124	−	0.746124i
$583$			20.0000i			0.828315i
$584$	4.89898	−	4.89898i	0.202721	−	0.202721i
$585$		0			0
$586$	2.44949	+	2.44949i	0.101187	+	0.101187i
$587$	−17.1464			−0.707709			−0.353854	−	0.935301i	$-0.615129\pi$
$587$	−17.1464			−0.707709			−0.353854	+	0.935301i	$0.615129\pi$
$588$	24.0000	+	24.4949i	0.989743	+	1.01015i
$589$		0			0
$590$		0			0
$591$	−56.3383			−2.31745
$592$	−12.0000			−0.493197
$593$			9.79796i			0.402354i	0.979555	+	0.201177i	$0.0644766\pi$
$593$			9.79796i			0.402354i	−0.979555	+	0.201177i	$0.935523\pi$
$594$		0			0
$595$		0			0
$596$			10.0000i			0.409616i
$597$	30.0000			1.22782
$598$	2.44949	−	2.44949i	0.100167	−	0.100167i
$599$			11.0000i			0.449448i	0.974422	+	0.224724i	$0.0721480\pi$
$599$			11.0000i			0.449448i	−0.974422	+	0.224724i	$0.927852\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$	−37.9444	−	15.9444i	−1.54650	−	0.649845i
$603$		−	9.00000i		−	0.366508i
$604$	−10.0000			−0.406894
$605$		0			0
$606$	−30.0000	−	30.0000i	−1.21867	−	1.21867i
$607$	7.34847			0.298265			0.149133	−	0.988817i	$-0.452352\pi$
$607$	7.34847			0.298265			0.149133	+	0.988817i	$0.452352\pi$
$608$		0			0
$609$	−30.0000	+	12.2474i	−1.21566	+	0.496292i
$610$		0			0
$611$			12.0000i			0.485468i
$612$	29.3939			1.18818
$613$	−11.0000			−0.444286			−0.222143	−	0.975014i	$-0.571305\pi$
$613$	−11.0000			−0.444286			−0.222143	+	0.975014i	$0.571305\pi$
$614$	4.89898	−	4.89898i	0.197707	−	0.197707i
$615$		0			0
$616$	14.4949	−	34.4949i	0.584016	−	1.38984i
$617$	13.0000			0.523360			0.261680	−	0.965155i	$-0.415723\pi$
$617$	13.0000			0.523360			0.261680	+	0.965155i	$0.415723\pi$
$618$	−36.0000	+	36.0000i	−1.44813	+	1.44813i
$619$	−12.2474			−0.492267			−0.246133	−	0.969236i	$-0.579160\pi$
$619$	−12.2474			−0.492267			−0.246133	+	0.969236i	$0.579160\pi$
$620$		0			0
$621$		0			0
$622$	19.5959	−	19.5959i	0.785725	−	0.785725i
$623$	−2.44949	−	6.00000i	−0.0981367	−	0.240385i
$624$		−	24.0000i		−	0.960769i
$625$		0			0
$626$	−9.79796	−	9.79796i	−0.391605	−	0.391605i
$627$		0			0
$628$	34.2929			1.36843
$629$			14.6969i			0.586005i
$630$		0			0
$631$			45.0000i			1.79142i	0.444637	+	0.895711i	$0.353333\pi$
$631$			45.0000i			1.79142i	−0.444637	+	0.895711i	$0.646667\pi$
$632$	18.0000	−	18.0000i	0.716002	−	0.716002i
$633$		−	24.4949i		−	0.973585i
$634$	17.0000	−	17.0000i	0.675156	−	0.675156i
$635$		0			0
$636$			19.5959i			0.777029i
$637$	−12.0000	−	12.2474i	−0.475457	−	0.485262i
$638$	25.0000	+	25.0000i	0.989759	+	0.989759i
$639$		−	15.0000i		−	0.593391i
$640$		0			0
$641$	17.0000			0.671460			0.335730	−	0.941958i	$-0.391017\pi$
$641$	17.0000			0.671460			0.335730	+	0.941958i	$0.391017\pi$
$642$	−19.5959	−	19.5959i	−0.773389	−	0.773389i
$643$	−39.1918			−1.54558			−0.772788	−	0.634665i	$-0.781138\pi$
$643$	−39.1918			−1.54558			−0.772788	+	0.634665i	$0.781138\pi$
$644$	4.89898	−	2.00000i	0.193047	−	0.0788110i
$645$		0			0
$646$		0			0
$647$	−29.3939			−1.15559			−0.577796	−	0.816181i	$-0.696087\pi$
$647$	−29.3939			−1.15559			−0.577796	+	0.816181i	$0.696087\pi$
$648$	−18.0000	−	18.0000i	−0.707107	−	0.707107i
$649$			61.2372i			2.40377i
$650$		0			0
$651$	−44.0908	+	18.0000i	−1.72806	+	0.705476i
$652$	−12.0000			−0.469956
$653$	−16.0000			−0.626128			−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000			−0.626128			−0.313064	+	0.949732i	$0.601356\pi$
$654$	−36.7423	+	36.7423i	−1.43674	+	1.43674i
$655$		0			0
$656$			48.9898i			1.91273i
$657$		−	7.34847i		−	0.286691i
$658$	−7.10102	+	16.8990i	−0.276827	+	0.658791i
$659$			16.0000i			0.623272i	0.950202	+	0.311636i	$0.100877\pi$
$659$			16.0000i			0.623272i	−0.950202	+	0.311636i	$0.899123\pi$
$660$		0			0
$661$			24.4949i			0.952741i	0.879245	+	0.476371i	$0.158048\pi$
$661$			24.4949i			0.952741i	−0.879245	+	0.476371i	$0.841952\pi$
$662$	25.0000	+	25.0000i	0.971653	+	0.971653i
$663$	−29.3939			−1.14156
$664$	−4.89898	−	4.89898i	−0.190117	−	0.190117i
$665$		0			0
$666$	−9.00000	+	9.00000i	−0.348743	+	0.348743i
$667$			5.00000i			0.193601i
$668$		−	14.6969i		−	0.568642i
$669$	6.00000			0.231973
$670$		0			0
$671$	−61.2372			−2.36404
$672$	14.2020	−	33.7980i	0.547856	−	1.30378i
$673$	24.0000			0.925132			0.462566	−	0.886585i	$-0.346929\pi$
$673$	24.0000			0.925132			0.462566	+	0.886585i	$0.346929\pi$
$674$	12.0000	−	12.0000i	0.462223	−	0.462223i
$675$		0			0
$676$		−	14.0000i		−	0.538462i
$677$			29.3939i			1.12970i	0.825194	+	0.564849i	$0.191066\pi$
$677$			29.3939i			1.12970i	−0.825194	+	0.564849i	$0.808934\pi$
$678$	−26.9444	+	26.9444i	−1.03479	+	1.03479i
$679$	7.34847	+	18.0000i	0.282008	+	0.690777i
$680$		0			0
$681$	−48.0000			−1.83936
$682$	36.7423	+	36.7423i	1.40694	+	1.40694i
$683$		−	11.0000i		−	0.420903i	−0.977604	−	0.210452i	$-0.932507\pi$
$683$		−	11.0000i		−	0.420903i	0.977604	−	0.210452i	$-0.0674935\pi$
$684$		0			0
$685$		0			0
$686$	−9.65153	−	24.3485i	−0.368497	−	0.929629i
$687$			24.0000i			0.915657i
$688$			44.0000i			1.67748i
$689$		−	9.79796i		−	0.373273i
$690$		0			0
$691$	−31.8434			−1.21138			−0.605689	−	0.795701i	$-0.707103\pi$
$691$	−31.8434			−1.21138			−0.605689	+	0.795701i	$0.707103\pi$
$692$	19.5959			0.744925
$693$	−15.0000	−	36.7423i	−0.569803	−	1.39573i
$694$	−17.0000	−	17.0000i	−0.645311	−	0.645311i
$695$		0			0
$696$	24.4949	+	24.4949i	0.928477	+	0.928477i
$697$	60.0000			2.27266
$698$	9.79796	+	9.79796i	0.370858	+	0.370858i
$699$	26.9444			1.01913
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$		0			0
$704$	−40.0000			−1.50756
$705$		0			0
$706$	−22.0454	−	22.0454i	−0.829690	−	0.829690i
$707$	12.2474	+	30.0000i	0.460613	+	1.12827i
$708$			60.0000i			2.25494i
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$		0			0
$711$		−	27.0000i		−	1.01258i
$712$	−4.89898	+	4.89898i	−0.183597	+	0.183597i
$713$			7.34847i			0.275202i
$714$	−41.3939	−	17.3939i	−1.54913	−	0.650949i
$715$		0			0
$716$	−28.0000			−1.04641
$717$		−	63.6867i		−	2.37842i
$718$	19.0000	+	19.0000i	0.709074	+	0.709074i
$719$	12.2474			0.456753			0.228376	−	0.973573i	$-0.426658\pi$
$719$	12.2474			0.456753			0.228376	+	0.973573i	$0.426658\pi$
$720$		0			0
$721$	36.0000	−	14.6969i	1.34071	−	0.547343i
$722$	19.0000	−	19.0000i	0.707107	−	0.707107i
$723$		0			0
$724$	24.4949			0.910346
$725$		0			0
$726$	−34.2929	+	34.2929i	−1.27273	+	1.27273i
$727$	−29.3939			−1.09016			−0.545079	−	0.838385i	$-0.683500\pi$
$727$	−29.3939			−1.09016			−0.545079	+	0.838385i	$0.683500\pi$
$728$	−7.10102	+	16.8990i	−0.263181	+	0.626318i
$729$	−27.0000			−1.00000
$730$		0			0
$731$	53.8888			1.99315
$732$	−60.0000			−2.21766
$733$		−	39.1918i		−	1.44758i	−0.690018	−	0.723792i	$-0.742398\pi$
$733$		−	39.1918i		−	1.44758i	0.690018	−	0.723792i	$-0.257602\pi$
$734$	17.1464	−	17.1464i	0.632886	−	0.632886i
$735$		0			0
$736$	−4.00000	−	4.00000i	−0.147442	−	0.147442i
$737$	15.0000			0.552532
$738$	36.7423	+	36.7423i	1.35250	+	1.35250i
$739$		−	9.00000i		−	0.331070i	−0.986204	−	0.165535i	$-0.947065\pi$
$739$		−	9.00000i		−	0.331070i	0.986204	−	0.165535i	$-0.0529351\pi$
$740$		0			0
$741$		0			0
$742$	5.79796	−	13.7980i	0.212850	−	0.506539i
$743$			34.0000i			1.24734i	0.781688	+	0.623670i	$0.214359\pi$
$743$			34.0000i			1.24734i	−0.781688	+	0.623670i	$0.785641\pi$
$744$	36.0000	+	36.0000i	1.31982	+	1.31982i
$745$		0			0
$746$	−29.0000	+	29.0000i	−1.06177	+	1.06177i
$747$	−7.34847			−0.268866
$748$			48.9898i			1.79124i
$749$	8.00000	+	19.5959i	0.292314	+	0.716019i
$750$		0			0
$751$			20.0000i			0.729810i	0.931045	+	0.364905i	$0.118899\pi$
$751$			20.0000i			0.729810i	−0.931045	+	0.364905i	$0.881101\pi$
$752$	19.5959			0.714590
$753$	−12.0000			−0.437304
$754$	−12.2474	−	12.2474i	−0.446026	−	0.446026i
$755$		0			0
$756$		0			0
$757$	3.00000			0.109037			0.0545184	−	0.998513i	$-0.482638\pi$
$757$	3.00000			0.109037			0.0545184	+	0.998513i	$0.482638\pi$
$758$	−1.00000	−	1.00000i	−0.0363216	−	0.0363216i
$759$	−12.2474			−0.444554
$760$		0			0
$761$			24.4949i			0.887939i	0.896042	+	0.443970i	$0.146430\pi$
$761$			24.4949i			0.887939i	−0.896042	+	0.443970i	$0.853570\pi$
$762$	−7.34847	−	7.34847i	−0.266207	−	0.266207i
$763$	36.7423	−	15.0000i	1.33016	−	0.543036i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	2.44949	−	2.44949i	0.0885037	−	0.0885037i
$767$		−	30.0000i		−	1.08324i
$768$	−39.1918			−1.41421
$769$		−	22.0454i		−	0.794978i	−0.917607	−	0.397489i	$-0.869882\pi$
$769$		−	22.0454i		−	0.794978i	0.917607	−	0.397489i	$-0.130118\pi$
$770$		0			0
$771$			18.0000i			0.648254i
$772$			42.0000i			1.51161i
$773$		−	26.9444i		−	0.969122i	−0.874757	−	0.484561i	$-0.838979\pi$
$773$		−	26.9444i		−	0.969122i	0.874757	−	0.484561i	$-0.161021\pi$
$774$	33.0000	+	33.0000i	1.18616	+	1.18616i
$775$		0			0
$776$	14.6969	−	14.6969i	0.527589	−	0.527589i
$777$	18.0000	−	7.34847i	0.645746	−	0.263625i
$778$	−5.00000	+	5.00000i	−0.179259	+	0.179259i
$779$		0			0
$780$		0			0
$781$	25.0000			0.894570
$782$	−4.89898	+	4.89898i	−0.175187	+	0.175187i
$783$		0			0
$784$	−20.0000	+	19.5959i	−0.714286	+	0.699854i
$785$		0			0
$786$	12.0000	−	12.0000i	0.428026	−	0.428026i
$787$	−17.1464			−0.611204			−0.305602	−	0.952159i	$-0.598858\pi$
$787$	−17.1464			−0.611204			−0.305602	+	0.952159i	$0.598858\pi$
$788$		−	46.0000i		−	1.63868i
$789$			2.44949i			0.0872041i
$790$		0			0
$791$	26.9444	−	11.0000i	0.958032	−	0.391115i
$792$	−30.0000	+	30.0000i	−1.06600	+	1.06600i
$793$	30.0000			1.06533
$794$	19.5959	+	19.5959i	0.695433	+	0.695433i
$795$		0			0
$796$			24.4949i			0.868199i
$797$		−	44.0908i		−	1.56178i	−0.624671	−	0.780888i	$-0.714767\pi$
$797$		−	44.0908i		−	1.56178i	0.624671	−	0.780888i	$-0.285233\pi$
$798$		0			0
$799$		−	24.0000i		−	0.849059i
$800$		0			0
$801$			7.34847i			0.259645i
$802$	23.0000	−	23.0000i	0.812158	−	0.812158i
$803$	12.2474			0.432203
$804$	14.6969			0.518321
$805$		0			0
$806$	−18.0000	−	18.0000i	−0.634023	−	0.634023i
$807$			54.0000i			1.90089i
$808$	24.4949	−	24.4949i	0.861727	−	0.861727i
$809$	−5.00000			−0.175791			−0.0878953	−	0.996130i	$-0.528014\pi$
$809$	−5.00000			−0.175791			−0.0878953	+	0.996130i	$0.528014\pi$
$810$		0			0
$811$	−19.5959			−0.688106			−0.344053	−	0.938950i	$-0.611800\pi$
$811$	−19.5959			−0.688106			−0.344053	+	0.938950i	$0.611800\pi$
$812$	−10.0000	−	24.4949i	−0.350931	−	0.859602i
$813$	−42.0000			−1.47300
$814$	−15.0000	−	15.0000i	−0.525750	−	0.525750i
$815$		0			0
$816$			48.0000i			1.68034i
$817$		0			0
$818$	34.2929	+	34.2929i	1.19902	+	1.19902i
$819$	7.34847	+	18.0000i	0.256776	+	0.628971i
$820$		0			0
$821$	−8.00000			−0.279202			−0.139601	−	0.990208i	$-0.544582\pi$
$821$	−8.00000			−0.279202			−0.139601	+	0.990208i	$0.544582\pi$
$822$	19.5959	−	19.5959i	0.683486	−	0.683486i
$823$		−	21.0000i		−	0.732014i	−0.930612	−	0.366007i	$-0.880725\pi$
$823$		−	21.0000i		−	0.732014i	0.930612	−	0.366007i	$-0.119275\pi$
$824$	−29.3939	−	29.3939i	−1.02398	−	1.02398i
$825$		0			0
$826$	17.7526	−	42.2474i	0.617690	−	1.46998i
$827$		−	13.0000i		−	0.452054i	−0.974121	−	0.226027i	$-0.927426\pi$
$827$		−	13.0000i		−	0.452054i	0.974121	−	0.226027i	$-0.0725738\pi$
$828$	−6.00000			−0.208514
$829$		−	9.79796i		−	0.340297i	−0.985418	−	0.170149i	$-0.945575\pi$
$829$		−	9.79796i		−	0.340297i	0.985418	−	0.170149i	$-0.0544248\pi$
$830$		0			0
$831$	4.89898			0.169944
$832$	19.5959			0.679366
$833$	24.0000	+	24.4949i	0.831551	+	0.848698i
$834$	30.0000	−	30.0000i	1.03882	−	1.03882i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−12.2474	+	12.2474i	−0.423081	+	0.423081i
$839$	36.7423			1.26849			0.634243	−	0.773133i	$-0.281312\pi$
$839$	36.7423			1.26849			0.634243	+	0.773133i	$0.281312\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	23.0000	−	23.0000i	0.792632	−	0.792632i
$843$	−41.6413			−1.43420
$844$	20.0000			0.688428
$845$		0			0
$846$	14.6969	−	14.6969i	0.505291	−	0.505291i
$847$	34.2929	−	14.0000i	1.17832	−	0.481046i
$848$	−16.0000			−0.549442
$849$	−24.0000			−0.823678
$850$		0			0
$851$		−	3.00000i		−	0.102839i
$852$	24.4949			0.839181
$853$		−	14.6969i		−	0.503214i	−0.967830	−	0.251607i	$-0.919041\pi$
$853$		−	14.6969i		−	0.503214i	0.967830	−	0.251607i	$-0.0809590\pi$
$854$	42.2474	+	17.7526i	1.44568	+	0.607480i
$855$		0			0
$856$	16.0000	−	16.0000i	0.546869	−	0.546869i
$857$			41.6413i			1.42244i	0.702969	+	0.711220i	$0.251857\pi$
$857$			41.6413i			1.42244i	−0.702969	+	0.711220i	$0.748143\pi$
$858$	30.0000	−	30.0000i	1.02418	−	1.02418i
$859$	−24.4949			−0.835755			−0.417878	−	0.908503i	$-0.637226\pi$
$859$	−24.4949			−0.835755			−0.417878	+	0.908503i	$0.637226\pi$
$860$		0			0
$861$	−30.0000	−	73.4847i	−1.02240	−	2.50435i
$862$	10.0000	+	10.0000i	0.340601	+	0.340601i
$863$		−	31.0000i		−	1.05525i	−0.849477	−	0.527626i	$-0.823082\pi$
$863$		−	31.0000i		−	1.05525i	0.849477	−	0.527626i	$-0.176918\pi$
$864$		0			0
$865$		0			0
$866$	39.1918	+	39.1918i	1.33179	+	1.33179i
$867$	17.1464			0.582323
$868$	−14.6969	−	36.0000i	−0.498847	−	1.22192i
$869$	45.0000			1.52652
$870$		0			0
$871$	−7.34847			−0.248993
$872$	−30.0000	−	30.0000i	−1.01593	−	1.01593i
$873$		−	22.0454i		−	0.746124i
$874$		0			0
$875$		0			0
$876$	12.0000			0.405442
$877$	−52.0000			−1.75592			−0.877958	−	0.478738i	$-0.841094\pi$
$877$	−52.0000			−1.75592			−0.877958	+	0.478738i	$0.841094\pi$
$878$	12.2474	−	12.2474i	0.413331	−	0.413331i
$879$			6.00000i			0.202375i
$880$		0			0
$881$		−	12.2474i		−	0.412627i	−0.978486	−	0.206314i	$-0.933853\pi$
$881$		−	12.2474i		−	0.412627i	0.978486	−	0.206314i	$-0.0661467\pi$
$882$	−0.303062	+	29.6969i	−0.0102046	+	0.999948i
$883$			19.0000i			0.639401i	0.947519	+	0.319700i	$0.103582\pi$
$883$			19.0000i			0.639401i	−0.947519	+	0.319700i	$0.896418\pi$
$884$		−	24.0000i		−	0.807207i
$885$		0			0
$886$	−14.0000	−	14.0000i	−0.470339	−	0.470339i
$887$	56.3383			1.89165			0.945827	−	0.324671i	$-0.105254\pi$
$887$	56.3383			1.89165			0.945827	+	0.324671i	$0.105254\pi$
$888$	−14.6969	−	14.6969i	−0.493197	−	0.493197i
$889$	3.00000	+	7.34847i	0.100617	+	0.246460i
$890$		0			0
$891$		−	45.0000i		−	1.50756i
$892$			4.89898i			0.164030i
$893$		0			0
$894$	−12.2474	+	12.2474i	−0.409616	+	0.409616i
$895$		0			0
$896$	27.5959	+	11.5959i	0.921915	+	0.387392i
$897$	6.00000			0.200334
$898$	25.0000	−	25.0000i	0.834261	−	0.834261i
$899$	36.7423			1.22543
$900$		0			0
$901$			19.5959i			0.652835i
$902$	−61.2372	+	61.2372i	−2.03898	+	2.03898i
$903$	−26.9444	−	66.0000i	−0.896653	−	2.19634i
$904$	−22.0000	−	22.0000i	−0.731709	−	0.731709i
$905$		0			0
$906$	−12.2474	−	12.2474i	−0.406894	−	0.406894i
$907$		−	38.0000i		−	1.26177i	−0.775877	−	0.630885i	$-0.782692\pi$
$907$		−	38.0000i		−	1.26177i	0.775877	−	0.630885i	$-0.217308\pi$
$908$		−	39.1918i		−	1.30063i
$909$		−	36.7423i		−	1.21867i
$910$		0			0
$911$		−	35.0000i		−	1.15960i	−0.814758	−	0.579801i	$-0.803130\pi$
$911$		−	35.0000i		−	1.15960i	0.814758	−	0.579801i	$-0.196870\pi$
$912$		0			0
$913$		−	12.2474i		−	0.405331i
$914$	−3.00000	+	3.00000i	−0.0992312	+	0.0992312i
$915$		0			0
$916$	−19.5959			−0.647467
$917$	−12.0000	+	4.89898i	−0.396275	+	0.161779i
$918$		0			0
$919$			41.0000i			1.35247i	0.736688	+	0.676233i	$0.236389\pi$
$919$			41.0000i			1.35247i	−0.736688	+	0.676233i	$0.763611\pi$
$920$		0			0
$921$	12.0000			0.395413
$922$	12.2474	+	12.2474i	0.403348	+	0.403348i
$923$	−12.2474			−0.403130
$924$	60.0000	−	24.4949i	1.97386	−	0.805823i
$925$		0			0
$926$	36.0000	+	36.0000i	1.18303	+	1.18303i
$927$	−44.0908			−1.44813
$928$	−20.0000	+	20.0000i	−0.656532	+	0.656532i
$929$			26.9444i			0.884017i	0.897011	+	0.442008i	$0.145734\pi$
$929$			26.9444i			0.884017i	−0.897011	+	0.442008i	$0.854266\pi$
$930$		0			0
$931$		0			0
$932$			22.0000i			0.720634i
$933$	48.0000			1.57145
$934$	4.89898	−	4.89898i	0.160300	−	0.160300i
$935$		0			0
$936$	14.6969	−	14.6969i	0.480384	−	0.480384i
$937$		−	7.34847i		−	0.240064i	−0.992770	−	0.120032i	$-0.961700\pi$
$937$		−	7.34847i		−	0.240064i	0.992770	−	0.120032i	$-0.0382997\pi$
$938$	−10.3485	−	4.34847i	−0.337889	−	0.141983i
$939$		−	24.0000i		−	0.783210i
$940$		0			0
$941$			12.2474i			0.399255i	0.979872	+	0.199628i	$0.0639733\pi$
$941$			12.2474i			0.399255i	−0.979872	+	0.199628i	$0.936027\pi$
$942$	42.0000	+	42.0000i	1.36843	+	1.36843i
$943$	−12.2474			−0.398832
$944$	−48.9898			−1.59448
$945$		0			0
$946$	−55.0000	+	55.0000i	−1.78820	+	1.78820i
$947$		−	38.0000i		−	1.23483i	−0.786636	−	0.617417i	$-0.788179\pi$
$947$		−	38.0000i		−	1.23483i	0.786636	−	0.617417i	$-0.211821\pi$
$948$	44.0908			1.43200
$949$	−6.00000			−0.194768
$950$		0			0
$951$	41.6413			1.35031
$952$	14.2020	−	33.7980i	0.460291	−	1.09540i
$953$	59.0000			1.91120			0.955599	−	0.294671i	$-0.0952101\pi$
$953$	59.0000			1.91120			0.955599	+	0.294671i	$0.0952101\pi$
$954$	−12.0000	+	12.0000i	−0.388514	+	0.388514i
$955$		0			0
$956$	52.0000			1.68180
$957$			61.2372i			1.97952i
$958$	36.7423	−	36.7423i	1.18709	−	1.18709i
$959$	−19.5959	+	8.00000i	−0.632785	+	0.258333i
$960$		0			0
$961$	23.0000			0.741935
$962$	7.34847	+	7.34847i	0.236924	+	0.236924i
$963$		−	24.0000i		−	0.773389i
$964$		0			0
$965$		0			0
$966$	8.44949	+	3.55051i	0.271858	+	0.114236i
$967$		−	18.0000i		−	0.578841i	−0.957202	−	0.289420i	$-0.906537\pi$
$967$		−	18.0000i		−	0.578841i	0.957202	−	0.289420i	$-0.0934626\pi$
$968$	−28.0000	−	28.0000i	−0.899954	−	0.899954i
$969$		0			0
$970$		0			0
$971$	−44.0908			−1.41494			−0.707471	−	0.706743i	$-0.750164\pi$
$971$	−44.0908			−1.41494			−0.707471	+	0.706743i	$0.750164\pi$
$972$		−	44.0908i		−	1.41421i
$973$	−30.0000	+	12.2474i	−0.961756	+	0.392635i
$974$	−7.00000	−	7.00000i	−0.224294	−	0.224294i
$975$		0			0
$976$		−	48.9898i		−	1.56813i
$977$	−17.0000			−0.543878			−0.271939	−	0.962314i	$-0.587665\pi$
$977$	−17.0000			−0.543878			−0.271939	+	0.962314i	$0.587665\pi$
$978$	−14.6969	−	14.6969i	−0.469956	−	0.469956i
$979$	−12.2474			−0.391430
$980$		0			0
$981$	−45.0000			−1.43674
$982$	−5.00000	−	5.00000i	−0.159556	−	0.159556i
$983$	22.0454			0.703139			0.351570	−	0.936162i	$-0.385648\pi$
$983$	22.0454			0.703139			0.351570	+	0.936162i	$0.385648\pi$
$984$	−60.0000	+	60.0000i	−1.91273	+	1.91273i
$985$		0			0
$986$	24.4949	+	24.4949i	0.780076	+	0.780076i
$987$	−29.3939	+	12.0000i	−0.935617	+	0.381964i
$988$		0			0
$989$	−11.0000			−0.349780
$990$		0			0
$991$		−	35.0000i		−	1.11181i	−0.831245	−	0.555906i	$-0.812372\pi$
$991$		−	35.0000i		−	1.11181i	0.831245	−	0.555906i	$-0.187628\pi$
$992$	−29.3939	+	29.3939i	−0.933257	+	0.933257i
$993$			61.2372i			1.94331i
$994$	−17.2474	−	7.24745i	−0.547056	−	0.229875i
$995$		0			0
$996$		−	12.0000i		−	0.380235i
$997$			4.89898i			0.155152i	0.996986	+	0.0775761i	$0.0247181\pi$
$997$			4.89898i			0.155152i	−0.996986	+	0.0775761i	$0.975282\pi$
$998$	−16.0000	−	16.0000i	−0.506471	−	0.506471i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.g.b.251.3	yes	4
4.3	odd	2	inner	700.2.g.b.251.2	yes	4
5.2	odd	4		700.2.c.a.699.2		4
5.3	odd	4		700.2.c.g.699.3		4
5.4	even	2		700.2.g.h.251.2	yes	4
7.6	odd	2	inner	700.2.g.b.251.4	yes	4
20.3	even	4		700.2.c.a.699.4		4
20.7	even	4		700.2.c.g.699.1		4
20.19	odd	2		700.2.g.h.251.3	yes	4
28.27	even	2	inner	700.2.g.b.251.1	✓	4
35.13	even	4		700.2.c.g.699.4		4
35.27	even	4		700.2.c.a.699.1		4
35.34	odd	2		700.2.g.h.251.1	yes	4
140.27	odd	4		700.2.c.g.699.2		4
140.83	odd	4		700.2.c.a.699.3		4
140.139	even	2		700.2.g.h.251.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.c.a.699.1		4	35.27	even	4
700.2.c.a.699.2		4	5.2	odd	4
700.2.c.a.699.3		4	140.83	odd	4
700.2.c.a.699.4		4	20.3	even	4
700.2.c.g.699.1		4	20.7	even	4
700.2.c.g.699.2		4	140.27	odd	4
700.2.c.g.699.3		4	5.3	odd	4
700.2.c.g.699.4		4	35.13	even	4
700.2.g.b.251.1	✓	4	28.27	even	2	inner
700.2.g.b.251.2	yes	4	4.3	odd	2	inner
700.2.g.b.251.3	yes	4	1.1	even	1	trivial
700.2.g.b.251.4	yes	4	7.6	odd	2	inner
700.2.g.h.251.1	yes	4	35.34	odd	2
700.2.g.h.251.2	yes	4	5.4	even	2
700.2.g.h.251.3	yes	4	20.19	odd	2
700.2.g.h.251.4	yes	4	140.139	even	2

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.44949 q^{3} -2.00000i q^{4} +(2.44949 - 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} -2.44949 q^{3} -2.00000i q^{4} +(2.44949 - 2.44949i) q^{6} +(-2.44949 + 1.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +5.00000i q^{11} +4.89898i q^{12} -2.44949i q^{13} +(1.44949 - 3.44949i) q^{14} -4.00000 q^{16} +4.89898i q^{17} +(-3.00000 + 3.00000i) q^{18} +(6.00000 - 2.44949i) q^{21} +(-5.00000 - 5.00000i) q^{22} -1.00000i q^{23} +(-4.89898 - 4.89898i) q^{24} +(2.44949 + 2.44949i) q^{26} +(2.00000 + 4.89898i) q^{28} -5.00000 q^{29} -7.34847 q^{31} +(4.00000 - 4.00000i) q^{32} -12.2474i q^{33} +(-4.89898 - 4.89898i) q^{34} -6.00000i q^{36} +3.00000 q^{37} +6.00000i q^{39} -12.2474i q^{41} +(-3.55051 + 8.44949i) q^{42} -11.0000i q^{43} +10.0000 q^{44} +(1.00000 + 1.00000i) q^{46} -4.89898 q^{47} +9.79796 q^{48} +(5.00000 - 4.89898i) q^{49} -12.0000i q^{51} -4.89898 q^{52} +4.00000 q^{53} +(-6.89898 - 2.89898i) q^{56} +(5.00000 - 5.00000i) q^{58} +12.2474 q^{59} +12.2474i q^{61} +(7.34847 - 7.34847i) q^{62} +(-7.34847 + 3.00000i) q^{63} +8.00000i q^{64} +(12.2474 + 12.2474i) q^{66} -3.00000i q^{67} +9.79796 q^{68} +2.44949i q^{69} -5.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -2.44949i q^{73} +(-3.00000 + 3.00000i) q^{74} +(-5.00000 - 12.2474i) q^{77} +(-6.00000 - 6.00000i) q^{78} -9.00000i q^{79} -9.00000 q^{81} +(12.2474 + 12.2474i) q^{82} -2.44949 q^{83} +(-4.89898 - 12.0000i) q^{84} +(11.0000 + 11.0000i) q^{86} +12.2474 q^{87} +(-10.0000 + 10.0000i) q^{88} +2.44949i q^{89} +(2.44949 + 6.00000i) q^{91} -2.00000 q^{92} +18.0000 q^{93} +(4.89898 - 4.89898i) q^{94} +(-9.79796 + 9.79796i) q^{96} -7.34847i q^{97} +(-0.101021 + 9.89898i) q^{98} +15.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 8 * q^8 + 12 * q^9	\( 4 q - 4 q^{2} + 8 q^{8} + 12 q^{9} - 4 q^{14} - 16 q^{16} - 12 q^{18} + 24 q^{21} - 20 q^{22} + 8 q^{28} - 20 q^{29} + 16 q^{32} + 12 q^{37} - 24 q^{42} + 40 q^{44} + 4 q^{46} + 20 q^{49} + 16 q^{53} - 8 q^{56} + 20 q^{58} + 24 q^{72} - 12 q^{74} - 20 q^{77} - 24 q^{78} - 36 q^{81} + 44 q^{86} - 40 q^{88} - 8 q^{92} + 72 q^{93} - 20 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 + 8 * q^8 + 12 * q^9 - 4 * q^14 - 16 * q^16 - 12 * q^18 + 24 * q^21 - 20 * q^22 + 8 * q^28 - 20 * q^29 + 16 * q^32 + 12 * q^37 - 24 * q^42 + 40 * q^44 + 4 * q^46 + 20 * q^49 + 16 * q^53 - 8 * q^56 + 20 * q^58 + 24 * q^72 - 12 * q^74 - 20 * q^77 - 24 * q^78 - 36 * q^81 + 44 * q^86 - 40 * q^88 - 8 * q^92 + 72 * q^93 - 20 * q^98

Introduction

L-functions

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