LMFDB - Embedded newform 700.2.c.g.699.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,2,Mod(699,700)]

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, 1, 1]))

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

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

chi := DirichletCharacter("700.699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.58952814149$
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			699.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	700.699
Dual form			700.2.c.g.699.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.00000i) q^{2} +2.44949i q^{3} -2.00000i q^{4} +(2.44949 + 2.44949i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(1.00000 - 1.00000i) q^{2} +2.44949i q^{3} -2.00000i q^{4} +(2.44949 + 2.44949i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.00000 - 2.00000i) q^{8} -3.00000 q^{9} -5.00000i q^{11} +4.89898 q^{12} +2.44949 q^{13} +(-1.44949 - 3.44949i) q^{14} -4.00000 q^{16} +4.89898 q^{17} +(-3.00000 + 3.00000i) q^{18} +(6.00000 + 2.44949i) q^{21} +(-5.00000 - 5.00000i) q^{22} +1.00000 q^{23} +(4.89898 - 4.89898i) q^{24} +(2.44949 - 2.44949i) q^{26} +(-4.89898 - 2.00000i) q^{28} +5.00000 q^{29} -7.34847 q^{31} +(-4.00000 + 4.00000i) q^{32} +12.2474 q^{33} +(4.89898 - 4.89898i) q^{34} +6.00000i q^{36} +3.00000i q^{37} +6.00000i q^{39} +12.2474i q^{41} +(8.44949 - 3.55051i) q^{42} +11.0000 q^{43} -10.0000 q^{44} +(1.00000 - 1.00000i) q^{46} -4.89898i q^{47} -9.79796i q^{48} +(-5.00000 - 4.89898i) q^{49} +12.0000i q^{51} -4.89898i q^{52} -4.00000i q^{53} +(-6.89898 + 2.89898i) q^{56} +(5.00000 - 5.00000i) q^{58} -12.2474 q^{59} -12.2474i q^{61} +(-7.34847 + 7.34847i) q^{62} +(-3.00000 + 7.34847i) q^{63} +8.00000i q^{64} +(12.2474 - 12.2474i) q^{66} -3.00000 q^{67} -9.79796i q^{68} +2.44949i q^{69} +5.00000i q^{71} +(6.00000 + 6.00000i) q^{72} +2.44949 q^{73} +(3.00000 + 3.00000i) q^{74} +(-12.2474 - 5.00000i) q^{77} +(6.00000 + 6.00000i) q^{78} -9.00000i q^{79} -9.00000 q^{81} +(12.2474 + 12.2474i) q^{82} +2.44949i q^{83} +(4.89898 - 12.0000i) q^{84} +(11.0000 - 11.0000i) q^{86} +12.2474i q^{87} +(-10.0000 + 10.0000i) q^{88} +2.44949i q^{89} +(2.44949 - 6.00000i) q^{91} -2.00000i q^{92} -18.0000i q^{93} +(-4.89898 - 4.89898i) q^{94} +(-9.79796 - 9.79796i) q^{96} -7.34847 q^{97} +(-9.89898 + 0.101021i) q^{98} +15.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{7} - 8 q^{8} - 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^7 - 8 * q^8 - 12 * q^9	$ 4 q + 4 q^{2} + 4 q^{7} - 8 q^{8} - 12 q^{9} + 4 q^{14} - 16 q^{16} - 12 q^{18} + 24 q^{21} - 20 q^{22} + 4 q^{23} + 20 q^{29} - 16 q^{32} + 24 q^{42} + 44 q^{43} - 40 q^{44} + 4 q^{46} - 20 q^{49} - 8 q^{56} + 20 q^{58} - 12 q^{63} - 12 q^{67} + 24 q^{72} + 12 q^{74} + 24 q^{78} - 36 q^{81} + 44 q^{86} - 40 q^{88} - 20 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^7 - 8 * q^8 - 12 * q^9 + 4 * q^14 - 16 * q^16 - 12 * q^18 + 24 * q^21 - 20 * q^22 + 4 * q^23 + 20 * q^29 - 16 * q^32 + 24 * q^42 + 44 * q^43 - 40 * q^44 + 4 * q^46 - 20 * q^49 - 8 * q^56 + 20 * q^58 - 12 * q^63 - 12 * q^67 + 24 * q^72 + 12 * q^74 + 24 * q^78 - 36 * q^81 + 44 * q^86 - 40 * q^88 - 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
$3$			2.44949i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$3$			2.44949i			1.41421i	−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
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	−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	$-0.728229\pi$
$11$		−	5.00000i		−	1.50756i	0.657129	−	0.753778i	$-0.271771\pi$
$12$	4.89898			1.41421
$13$	2.44949			0.679366			0.339683	−	0.940540i	$-0.389680\pi$
$13$	2.44949			0.679366			0.339683	+	0.940540i	$0.389680\pi$
$14$	−1.44949	−	3.44949i	−0.387392	−	0.921915i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	4.89898			1.18818			0.594089	−	0.804400i	$-0.297513\pi$
$17$	4.89898			1.18818			0.594089	+	0.804400i	$0.297513\pi$
$18$	−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
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$	4.89898	−	4.89898i	1.00000	−	1.00000i
$25$		0			0
$26$	2.44949	−	2.44949i	0.480384	−	0.480384i
$27$		0			0
$28$	−4.89898	−	2.00000i	−0.925820	−	0.377964i
$29$	5.00000			0.928477			0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000			0.928477			0.464238	+	0.885710i	$0.346328\pi$
$30$		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
$33$	12.2474			2.13201
$34$	4.89898	−	4.89898i	0.840168	−	0.840168i
$35$		0			0
$36$			6.00000i			1.00000i
$37$			3.00000i			0.493197i	0.969118	+	0.246598i	$0.0793129\pi$
$37$			3.00000i			0.493197i	−0.969118	+	0.246598i	$0.920687\pi$
$38$		0			0
$39$			6.00000i			0.960769i
$40$		0			0
$41$			12.2474i			1.91273i	0.292174	+	0.956365i	$0.405621\pi$
$41$			12.2474i			1.91273i	−0.292174	+	0.956365i	$0.594379\pi$
$42$	8.44949	−	3.55051i	1.30378	−	0.547856i
$43$	11.0000			1.67748			0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000			1.67748			0.838742	+	0.544529i	$0.183292\pi$
$44$	−10.0000			−1.50756
$45$		0			0
$46$	1.00000	−	1.00000i	0.147442	−	0.147442i
$47$		−	4.89898i		−	0.714590i	−0.933992	−	0.357295i	$-0.883699\pi$
$47$		−	4.89898i		−	0.714590i	0.933992	−	0.357295i	$-0.116301\pi$
$48$		−	9.79796i		−	1.41421i
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$		0			0
$51$			12.0000i			1.68034i
$52$		−	4.89898i		−	0.679366i
$53$		−	4.00000i		−	0.549442i	−0.961524	−	0.274721i	$-0.911414\pi$
$53$		−	4.00000i		−	0.549442i	0.961524	−	0.274721i	$-0.0885855\pi$
$54$		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	$-0.793708\pi$
$59$	−12.2474			−1.59448			−0.797241	+	0.603661i	$0.793708\pi$
$60$		0			0
$61$		−	12.2474i		−	1.56813i	−0.620682	−	0.784063i	$-0.713144\pi$
$61$		−	12.2474i		−	1.56813i	0.620682	−	0.784063i	$-0.286856\pi$
$62$	−7.34847	+	7.34847i	−0.933257	+	0.933257i
$63$	−3.00000	+	7.34847i	−0.377964	+	0.925820i
$64$			8.00000i			1.00000i
$65$		0			0
$66$	12.2474	−	12.2474i	1.50756	−	1.50756i
$67$	−3.00000			−0.366508			−0.183254	−	0.983066i	$-0.558663\pi$
$67$	−3.00000			−0.366508			−0.183254	+	0.983066i	$0.558663\pi$
$68$		−	9.79796i		−	1.18818i
$69$			2.44949i			0.294884i
$70$		0			0
$71$			5.00000i			0.593391i	0.954972	+	0.296695i	$0.0958846\pi$
$71$			5.00000i			0.593391i	−0.954972	+	0.296695i	$0.904115\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$	2.44949			0.286691			0.143346	−	0.989673i	$-0.454214\pi$
$73$	2.44949			0.286691			0.143346	+	0.989673i	$0.454214\pi$
$74$	3.00000	+	3.00000i	0.348743	+	0.348743i
$75$		0			0
$76$		0			0
$77$	−12.2474	−	5.00000i	−1.39573	−	0.569803i
$78$	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
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$	4.89898	−	12.0000i	0.534522	−	1.30931i
$85$		0			0
$86$	11.0000	−	11.0000i	1.18616	−	1.18616i
$87$			12.2474i			1.31306i
$88$	−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
$92$		−	2.00000i		−	0.208514i
$93$		−	18.0000i		−	1.86651i
$94$	−4.89898	−	4.89898i	−0.505291	−	0.505291i
$95$		0			0
$96$	−9.79796	−	9.79796i	−1.00000	−	1.00000i
$97$	−7.34847			−0.746124			−0.373062	−	0.927806i	$-0.621692\pi$
$97$	−7.34847			−0.746124			−0.373062	+	0.927806i	$0.621692\pi$
$98$	−9.89898	+	0.101021i	−0.999948	+	0.0102046i
$99$			15.0000i			1.50756i
$100$		0			0
$101$			12.2474i			1.21867i	0.792914	+	0.609333i	$0.208563\pi$
$101$			12.2474i			1.21867i	−0.792914	+	0.609333i	$0.791437\pi$
$102$	12.0000	+	12.0000i	1.18818	+	1.18818i
$103$			14.6969i			1.44813i	0.689730	+	0.724066i	$0.257729\pi$
$103$			14.6969i			1.44813i	−0.689730	+	0.724066i	$0.742271\pi$
$104$	−4.89898	−	4.89898i	−0.480384	−	0.480384i
$105$		0			0
$106$	−4.00000	−	4.00000i	−0.388514	−	0.388514i
$107$	−8.00000			−0.773389			−0.386695	−	0.922208i	$-0.626383\pi$
$107$	−8.00000			−0.773389			−0.386695	+	0.922208i	$0.626383\pi$
$108$		0			0
$109$	15.0000			1.43674			0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000			1.43674			0.718370	+	0.695662i	$0.244889\pi$
$110$		0			0
$111$	−7.34847			−0.697486
$112$	−4.00000	+	9.79796i	−0.377964	+	0.925820i
$113$			11.0000i			1.03479i	0.855746	+	0.517396i	$0.173099\pi$
$113$			11.0000i			1.03479i	−0.855746	+	0.517396i	$0.826901\pi$
$114$		0			0
$115$		0			0
$116$		−	10.0000i		−	0.928477i
$117$	−7.34847			−0.679366
$118$	−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
$123$	−30.0000			−2.70501
$124$			14.6969i			1.31982i
$125$		0			0
$126$	4.34847	+	10.3485i	0.387392	+	0.921915i
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	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	$0.431347\pi$
$132$		−	24.4949i		−	2.13201i
$133$		0			0
$134$	−3.00000	+	3.00000i	−0.259161	+	0.259161i
$135$		0			0
$136$	−9.79796	−	9.79796i	−0.840168	−	0.840168i
$137$			8.00000i			0.683486i	0.939793	+	0.341743i	$0.111017\pi$
$137$			8.00000i			0.683486i	−0.939793	+	0.341743i	$0.888983\pi$
$138$	2.44949	+	2.44949i	0.208514	+	0.208514i
$139$	−12.2474			−1.03882			−0.519408	−	0.854527i	$-0.673847\pi$
$139$	−12.2474			−1.03882			−0.519408	+	0.854527i	$0.673847\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$	5.00000	+	5.00000i	0.419591	+	0.419591i
$143$		−	12.2474i		−	1.02418i
$144$	12.0000			1.00000
$145$		0			0
$146$	2.44949	−	2.44949i	0.202721	−	0.202721i
$147$	12.0000	−	12.2474i	0.989743	−	1.01015i
$148$	6.00000			0.493197
$149$	5.00000			0.409616			0.204808	−	0.978802i	$-0.434343\pi$
$149$	5.00000			0.409616			0.204808	+	0.978802i	$0.434343\pi$
$150$		0			0
$151$			5.00000i			0.406894i	0.979086	+	0.203447i	$0.0652145\pi$
$151$			5.00000i			0.406894i	−0.979086	+	0.203447i	$0.934786\pi$
$152$		0			0
$153$	−14.6969			−1.18818
$154$	−17.2474	+	7.24745i	−1.38984	+	0.584016i
$155$		0			0
$156$	12.0000			0.960769
$157$	17.1464			1.36843			0.684217	−	0.729279i	$-0.260144\pi$
$157$	17.1464			1.36843			0.684217	+	0.729279i	$0.260144\pi$
$158$	−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
$163$	6.00000			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$163$	6.00000			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$164$	24.4949			1.91273
$165$		0			0
$166$	2.44949	+	2.44949i	0.190117	+	0.190117i
$167$			7.34847i			0.568642i	0.958729	+	0.284321i	$0.0917681\pi$
$167$			7.34847i			0.568642i	−0.958729	+	0.284321i	$0.908232\pi$
$168$	−7.10102	−	16.8990i	−0.547856	−	1.30378i
$169$	−7.00000			−0.538462
$170$		0			0
$171$		0			0
$172$		−	22.0000i		−	1.67748i
$173$	−9.79796			−0.744925			−0.372463	−	0.928047i	$-0.621486\pi$
$173$	−9.79796			−0.744925			−0.372463	+	0.928047i	$0.621486\pi$
$174$	12.2474	+	12.2474i	0.928477	+	0.928477i
$175$		0			0
$176$			20.0000i			1.50756i
$177$		−	30.0000i		−	2.25494i
$178$	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	$-0.849577\pi$
$181$		−	12.2474i		−	0.910346i	0.890403	−	0.455173i	$-0.150423\pi$
$182$	−3.55051	−	8.44949i	−0.263181	−	0.626318i
$183$	30.0000			2.21766
$184$	−2.00000	−	2.00000i	−0.147442	−	0.147442i
$185$		0			0
$186$	−18.0000	−	18.0000i	−1.31982	−	1.31982i
$187$		−	24.4949i		−	1.79124i
$188$	−9.79796			−0.714590
$189$		0			0
$190$		0			0
$191$			10.0000i			0.723575i	0.932261	+	0.361787i	$0.117833\pi$
$191$			10.0000i			0.723575i	−0.932261	+	0.361787i	$0.882167\pi$
$192$	−19.5959			−1.41421
$193$			21.0000i			1.51161i	0.654795	+	0.755807i	$0.272755\pi$
$193$			21.0000i			1.51161i	−0.654795	+	0.755807i	$0.727245\pi$
$194$	−7.34847	+	7.34847i	−0.527589	+	0.527589i
$195$		0			0
$196$	−9.79796	+	10.0000i	−0.699854	+	0.714286i
$197$			23.0000i			1.63868i	0.573306	+	0.819341i	$0.305660\pi$
$197$			23.0000i			1.63868i	−0.573306	+	0.819341i	$0.694340\pi$
$198$	15.0000	+	15.0000i	1.06600	+	1.06600i
$199$	12.2474			0.868199			0.434099	−	0.900865i	$-0.357067\pi$
$199$	12.2474			0.868199			0.434099	+	0.900865i	$0.357067\pi$
$200$		0			0
$201$		−	7.34847i		−	0.518321i
$202$	12.2474	+	12.2474i	0.861727	+	0.861727i
$203$	5.00000	−	12.2474i	0.350931	−	0.859602i
$204$	24.0000			1.68034
$205$		0			0
$206$	14.6969	+	14.6969i	1.02398	+	1.02398i
$207$	−3.00000			−0.208514
$208$	−9.79796			−0.679366
$209$		0			0
$210$		0			0
$211$		−	10.0000i		−	0.688428i	−0.938891	−	0.344214i	$-0.888145\pi$
$211$		−	10.0000i		−	0.688428i	0.938891	−	0.344214i	$-0.111855\pi$
$212$	−8.00000			−0.549442
$213$	−12.2474			−0.839181
$214$	−8.00000	+	8.00000i	−0.546869	+	0.546869i
$215$		0			0
$216$		0			0
$217$	−7.34847	+	18.0000i	−0.498847	+	1.22192i
$218$	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
$223$			2.44949i			0.164030i	0.996631	+	0.0820150i	$0.0261355\pi$
$223$			2.44949i			0.164030i	−0.996631	+	0.0820150i	$0.973864\pi$
$224$	5.79796	+	13.7980i	0.387392	+	0.921915i
$225$		0			0
$226$	11.0000	+	11.0000i	0.731709	+	0.731709i
$227$			19.5959i			1.30063i	0.759666	+	0.650313i	$0.225362\pi$
$227$			19.5959i			1.30063i	−0.759666	+	0.650313i	$0.774638\pi$
$228$		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
$233$			11.0000i			0.720634i	0.932830	+	0.360317i	$0.117331\pi$
$233$			11.0000i			0.720634i	−0.932830	+	0.360317i	$0.882669\pi$
$234$	−7.34847	+	7.34847i	−0.480384	+	0.480384i
$235$		0			0
$236$			24.4949i			1.59448i
$237$	22.0454			1.43200
$238$	−7.10102	−	16.8990i	−0.460291	−	1.09540i
$239$			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
$243$		−	22.0454i		−	1.41421i
$244$	−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	$0.450588\pi$
$252$	14.6969	+	6.00000i	0.925820	+	0.377964i
$253$		−	5.00000i		−	0.314347i
$254$	−3.00000	+	3.00000i	−0.188237	+	0.188237i
$255$		0			0
$256$	16.0000			1.00000
$257$	−7.34847			−0.458385			−0.229192	−	0.973381i	$-0.573609\pi$
$257$	−7.34847			−0.458385			−0.229192	+	0.973381i	$0.573609\pi$
$258$	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
$263$	1.00000			0.0616626			0.0308313	−	0.999525i	$-0.490185\pi$
$263$	1.00000			0.0616626			0.0308313	+	0.999525i	$0.490185\pi$
$264$	−24.4949	−	24.4949i	−1.50756	−	1.50756i
$265$		0			0
$266$		0			0
$267$	−6.00000			−0.367194
$268$			6.00000i			0.366508i
$269$		−	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	$0.325639\pi$
$272$	−19.5959			−1.18818
$273$	14.6969	+	6.00000i	0.889499	+	0.363137i
$274$	8.00000	+	8.00000i	0.483298	+	0.483298i
$275$		0			0
$276$	4.89898			0.294884
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$	−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
$283$		−	9.79796i		−	0.582428i	−0.956658	−	0.291214i	$-0.905941\pi$
$283$		−	9.79796i		−	0.582428i	0.956658	−	0.291214i	$-0.0940592\pi$
$284$	10.0000			0.593391
$285$		0			0
$286$	−12.2474	−	12.2474i	−0.724207	−	0.724207i
$287$	30.0000	+	12.2474i	1.77084	+	0.722944i
$288$	12.0000	−	12.0000i	0.707107	−	0.707107i
$289$	7.00000			0.411765
$290$		0			0
$291$		−	18.0000i		−	1.05518i
$292$		−	4.89898i		−	0.286691i
$293$	2.44949			0.143101			0.0715504	−	0.997437i	$-0.477205\pi$
$293$	2.44949			0.143101			0.0715504	+	0.997437i	$0.477205\pi$
$294$	−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
$303$	−30.0000			−1.72345
$304$		0			0
$305$		0			0
$306$	−14.6969	+	14.6969i	−0.840168	+	0.840168i
$307$		−	4.89898i		−	0.279600i	−0.990180	−	0.139800i	$-0.955354\pi$
$307$		−	4.89898i		−	0.279600i	0.990180	−	0.139800i	$-0.0446459\pi$
$308$	−10.0000	+	24.4949i	−0.569803	+	1.39573i
$309$	−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
$313$	−9.79796			−0.553813			−0.276907	−	0.960897i	$-0.589309\pi$
$313$	−9.79796			−0.553813			−0.276907	+	0.960897i	$0.589309\pi$
$314$	17.1464	−	17.1464i	0.967629	−	0.967629i
$315$		0			0
$316$	−18.0000			−1.01258
$317$		−	17.0000i		−	0.954815i	−0.878682	−	0.477408i	$-0.841577\pi$
$317$		−	17.0000i		−	0.954815i	0.878682	−	0.477408i	$-0.158423\pi$
$318$	9.79796	−	9.79796i	0.549442	−	0.549442i
$319$		−	25.0000i		−	1.39973i
$320$		0			0
$321$		−	19.5959i		−	1.09374i
$322$	−1.44949	−	3.44949i	−0.0807769	−	0.192233i
$323$		0			0
$324$			18.0000i			1.00000i
$325$		0			0
$326$	6.00000	−	6.00000i	0.332309	−	0.332309i
$327$			36.7423i			2.03186i
$328$	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	$0.241100\pi$
$331$			25.0000i			1.37412i	−0.726599	+	0.687062i	$0.758900\pi$
$332$	4.89898			0.268866
$333$		−	9.00000i		−	0.493197i
$334$	7.34847	+	7.34847i	0.402090	+	0.402090i
$335$		0			0
$336$	−24.0000	−	9.79796i	−1.30931	−	0.534522i
$337$		−	12.0000i		−	0.653682i	−0.945079	−	0.326841i	$-0.894016\pi$
$337$		−	12.0000i		−	0.653682i	0.945079	−	0.326841i	$-0.105984\pi$
$338$	−7.00000	+	7.00000i	−0.380750	+	0.380750i
$339$	−26.9444			−1.46342
$340$		0			0
$341$			36.7423i			1.98971i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	−22.0000	−	22.0000i	−1.18616	−	1.18616i
$345$		0			0
$346$	−9.79796	+	9.79796i	−0.526742	+	0.526742i
$347$	17.0000			0.912608			0.456304	−	0.889824i	$-0.349173\pi$
$347$	17.0000			0.912608			0.456304	+	0.889824i	$0.349173\pi$
$348$	24.4949			1.31306
$349$		−	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
$353$	−22.0454			−1.17336			−0.586679	−	0.809819i	$-0.699565\pi$
$353$	−22.0454			−1.17336			−0.586679	+	0.809819i	$0.699565\pi$
$354$	−30.0000	−	30.0000i	−1.59448	−	1.59448i
$355$		0			0
$356$	4.89898			0.259645
$357$	29.3939	+	12.0000i	1.55569	+	0.635107i
$358$	−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
$363$		−	34.2929i		−	1.79991i
$364$	−12.0000	−	4.89898i	−0.628971	−	0.256776i
$365$		0			0
$366$	30.0000	−	30.0000i	1.56813	−	1.56813i
$367$		−	17.1464i		−	0.895036i	−0.894275	−	0.447518i	$-0.852308\pi$
$367$		−	17.1464i		−	0.895036i	0.894275	−	0.447518i	$-0.147692\pi$
$368$	−4.00000			−0.208514
$369$		−	36.7423i		−	1.91273i
$370$		0			0
$371$	−9.79796	−	4.00000i	−0.508685	−	0.207670i
$372$	−36.0000			−1.86651
$373$		−	29.0000i		−	1.50156i	−0.660551	−	0.750782i	$-0.729677\pi$
$373$		−	29.0000i		−	1.50156i	0.660551	−	0.750782i	$-0.270323\pi$
$374$	−24.4949	−	24.4949i	−1.26660	−	1.26660i
$375$		0			0
$376$	−9.79796	+	9.79796i	−0.505291	+	0.505291i
$377$	12.2474			0.630776
$378$		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
$383$			2.44949i			0.125163i	0.998040	+	0.0625815i	$0.0199333\pi$
$383$			2.44949i			0.125163i	−0.998040	+	0.0625815i	$0.980067\pi$
$384$	−19.5959	+	19.5959i	−1.00000	+	1.00000i
$385$		0			0
$386$	21.0000	+	21.0000i	1.06887	+	1.06887i
$387$	−33.0000			−1.67748
$388$			14.6969i			0.746124i
$389$	−5.00000			−0.253510			−0.126755	−	0.991934i	$-0.540456\pi$
$389$	−5.00000			−0.253510			−0.126755	+	0.991934i	$0.540456\pi$
$390$		0			0
$391$	4.89898			0.247752
$392$	0.202041	+	19.7980i	0.0102046	+	0.999948i
$393$			12.0000i			0.605320i
$394$	23.0000	+	23.0000i	1.15872	+	1.15872i
$395$		0			0
$396$	30.0000			1.50756
$397$	−19.5959			−0.983491			−0.491745	−	0.870739i	$-0.663641\pi$
$397$	−19.5959			−0.983491			−0.491745	+	0.870739i	$0.663641\pi$
$398$	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
$403$	−18.0000			−0.896644
$404$	24.4949			1.21867
$405$		0			0
$406$	−7.24745	−	17.2474i	−0.359685	−	0.855977i
$407$	15.0000			0.743522
$408$	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
$412$	29.3939			1.44813
$413$	−12.2474	+	30.0000i	−0.602658	+	1.47620i
$414$	−3.00000	+	3.00000i	−0.147442	+	0.147442i
$415$		0			0
$416$	−9.79796	+	9.79796i	−0.480384	+	0.480384i
$417$		−	30.0000i		−	1.46911i
$418$		0			0
$419$	−12.2474			−0.598327			−0.299164	−	0.954202i	$-0.596708\pi$
$419$	−12.2474			−0.598327			−0.299164	+	0.954202i	$0.596708\pi$
$420$		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
$423$			14.6969i			0.714590i
$424$	−8.00000	+	8.00000i	−0.388514	+	0.388514i
$425$		0			0
$426$	−12.2474	+	12.2474i	−0.593391	+	0.593391i
$427$	−30.0000	−	12.2474i	−1.45180	−	0.592696i
$428$			16.0000i			0.773389i
$429$	30.0000			1.44841
$430$		0			0
$431$			10.0000i			0.481683i	0.970564	+	0.240842i	$0.0774234\pi$
$431$			10.0000i			0.481683i	−0.970564	+	0.240842i	$0.922577\pi$
$432$		0			0
$433$	39.1918			1.88344			0.941720	−	0.336399i	$-0.109209\pi$
$433$	39.1918			1.88344			0.941720	+	0.336399i	$0.109209\pi$
$434$	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	$-0.405590\pi$
$439$	12.2474			0.584539			0.292269	+	0.956336i	$0.405590\pi$
$440$		0			0
$441$	15.0000	+	14.6969i	0.714286	+	0.699854i
$442$	12.0000	−	12.0000i	0.570782	−	0.570782i
$443$	−14.0000			−0.665160			−0.332580	−	0.943075i	$-0.607919\pi$
$443$	−14.0000			−0.665160			−0.332580	+	0.943075i	$0.607919\pi$
$444$			14.6969i			0.697486i
$445$		0			0
$446$	2.44949	+	2.44949i	0.115987	+	0.115987i
$447$			12.2474i			0.579284i
$448$	19.5959	+	8.00000i	0.925820	+	0.377964i
$449$	25.0000			1.17982			0.589911	−	0.807468i	$-0.299163\pi$
$449$	25.0000			1.17982			0.589911	+	0.807468i	$0.299163\pi$
$450$		0			0
$451$	61.2372			2.88355
$452$	22.0000			1.03479
$453$	−12.2474			−0.575435
$454$	19.5959	+	19.5959i	0.919682	+	0.919682i
$455$		0			0
$456$		0			0
$457$			3.00000i			0.140334i	0.997535	+	0.0701670i	$0.0223532\pi$
$457$			3.00000i			0.140334i	−0.997535	+	0.0701670i	$0.977647\pi$
$458$	−9.79796	−	9.79796i	−0.457829	−	0.457829i
$459$		0			0
$460$		0			0
$461$			12.2474i			0.570421i	0.958465	+	0.285210i	$0.0920634\pi$
$461$			12.2474i			0.570421i	−0.958465	+	0.285210i	$0.907937\pi$
$462$	−17.7526	−	42.2474i	−0.825923	−	1.96553i
$463$	36.0000			1.67306			0.836531	−	0.547920i	$-0.184580\pi$
$463$	36.0000			1.67306			0.836531	+	0.547920i	$0.184580\pi$
$464$	−20.0000			−0.928477
$465$		0			0
$466$	11.0000	+	11.0000i	0.509565	+	0.509565i
$467$		−	4.89898i		−	0.226698i	−0.993555	−	0.113349i	$-0.963842\pi$
$467$		−	4.89898i		−	0.226698i	0.993555	−	0.113349i	$-0.0361578\pi$
$468$			14.6969i			0.679366i
$469$	−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
$473$		−	55.0000i		−	2.52890i
$474$	22.0454	−	22.0454i	1.01258	−	1.01258i
$475$		0			0
$476$	−24.0000	−	9.79796i	−1.10004	−	0.449089i
$477$			12.0000i			0.549442i
$478$	26.0000	+	26.0000i	1.18921	+	1.18921i
$479$	36.7423			1.67880			0.839400	−	0.543514i	$-0.182906\pi$
$479$	36.7423			1.67880			0.839400	+	0.543514i	$0.182906\pi$
$480$		0			0
$481$			7.34847i			0.335061i
$482$		0			0
$483$	6.00000	+	2.44949i	0.273009	+	0.111456i
$484$			28.0000i			1.27273i
$485$		0			0
$486$	−22.0454	−	22.0454i	−1.00000	−	1.00000i
$487$	7.00000			0.317200			0.158600	−	0.987343i	$-0.449302\pi$
$487$	7.00000			0.317200			0.158600	+	0.987343i	$0.449302\pi$
$488$	−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	$-0.964011\pi$
$491$		−	5.00000i		−	0.225647i	0.993615	−	0.112823i	$-0.0359894\pi$
$492$			60.0000i			2.70501i
$493$	24.4949			1.10319
$494$		0			0
$495$		0			0
$496$	29.3939			1.31982
$497$	12.2474	+	5.00000i	0.549373	+	0.224281i
$498$	−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
$503$			14.6969i			0.655304i	0.944798	+	0.327652i	$0.106257\pi$
$503$			14.6969i			0.655304i	−0.944798	+	0.327652i	$0.893743\pi$
$504$	20.6969	−	8.69694i	0.921915	−	0.387392i
$505$		0			0
$506$	−5.00000	−	5.00000i	−0.222277	−	0.222277i
$507$		−	17.1464i		−	0.761500i
$508$			6.00000i			0.266207i
$509$			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
$517$	−24.4949			−1.07728
$518$	10.3485	−	4.34847i	0.454686	−	0.191061i
$519$		−	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
$523$		−	9.79796i		−	0.428435i	−0.976786	−	0.214217i	$-0.931280\pi$
$523$		−	9.79796i		−	0.428435i	0.976786	−	0.214217i	$-0.0687201\pi$
$524$		−	9.79796i		−	0.428026i
$525$		0			0
$526$	1.00000	−	1.00000i	0.0436021	−	0.0436021i
$527$	−36.0000			−1.56818
$528$	−48.9898			−2.13201
$529$	−22.0000			−0.956522
$530$		0			0
$531$	36.7423			1.59448
$532$		0			0
$533$			30.0000i			1.29944i
$534$	−6.00000	+	6.00000i	−0.259645	+	0.259645i
$535$		0			0
$536$	6.00000	+	6.00000i	0.259161	+	0.259161i
$537$	34.2929			1.47985
$538$	−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
$543$	30.0000			1.28742
$544$	−19.5959	+	19.5959i	−0.840168	+	0.840168i
$545$		0			0
$546$	20.6969	−	8.69694i	0.885747	−	0.372195i
$547$	27.0000			1.15444			0.577218	−	0.816590i	$-0.304138\pi$
$547$	27.0000			1.15444			0.577218	+	0.816590i	$0.304138\pi$
$548$	16.0000			0.683486
$549$			36.7423i			1.56813i
$550$		0			0
$551$		0			0
$552$	4.89898	−	4.89898i	0.208514	−	0.208514i
$553$	−22.0454	−	9.00000i	−0.937466	−	0.382719i
$554$	−2.00000	−	2.00000i	−0.0849719	−	0.0849719i
$555$		0			0
$556$			24.4949i			1.03882i
$557$		−	37.0000i		−	1.56774i	−0.620925	−	0.783870i	$-0.713243\pi$
$557$		−	37.0000i		−	1.56774i	0.620925	−	0.783870i	$-0.286757\pi$
$558$	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
$563$			14.6969i			0.619402i	0.950834	+	0.309701i	$0.100229\pi$
$563$			14.6969i			0.619402i	−0.950834	+	0.309701i	$0.899771\pi$
$564$		−	24.0000i		−	1.01058i
$565$		0			0
$566$	−9.79796	−	9.79796i	−0.411839	−	0.411839i
$567$	−9.00000	+	22.0454i	−0.377964	+	0.925820i
$568$	10.0000	−	10.0000i	0.419591	−	0.419591i
$569$	−5.00000			−0.209611			−0.104805	−	0.994493i	$-0.533422\pi$
$569$	−5.00000			−0.209611			−0.104805	+	0.994493i	$0.533422\pi$
$570$		0			0
$571$			15.0000i			0.627730i	0.949468	+	0.313865i	$0.101624\pi$
$571$			15.0000i			0.627730i	−0.949468	+	0.313865i	$0.898376\pi$
$572$	−24.4949			−1.02418
$573$	−24.4949			−1.02329
$574$	42.2474	−	17.7526i	1.76337	−	0.740977i
$575$		0			0
$576$		−	24.0000i		−	1.00000i
$577$	−44.0908			−1.83552			−0.917762	−	0.397130i	$-0.870006\pi$
$577$	−44.0908			−1.83552			−0.917762	+	0.397130i	$0.870006\pi$
$578$	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
$583$	−20.0000			−0.828315
$584$	−4.89898	−	4.89898i	−0.202721	−	0.202721i
$585$		0			0
$586$	2.44949	−	2.44949i	0.101187	−	0.101187i
$587$		−	17.1464i		−	0.707709i	−0.935301	−	0.353854i	$-0.884871\pi$
$587$		−	17.1464i		−	0.707709i	0.935301	−	0.353854i	$-0.115129\pi$
$588$	−24.4949	−	24.0000i	−1.01015	−	0.989743i
$589$		0			0
$590$		0			0
$591$	−56.3383			−2.31745
$592$		−	12.0000i		−	0.493197i
$593$	−9.79796			−0.402354			−0.201177	−	0.979555i	$-0.564477\pi$
$593$	−9.79796			−0.402354			−0.201177	+	0.979555i	$0.564477\pi$
$594$		0			0
$595$		0			0
$596$		−	10.0000i		−	0.409616i
$597$			30.0000i			1.22782i
$598$	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			$\pi$
$602$	−15.9444	−	37.9444i	−0.649845	−	1.54650i
$603$	9.00000			0.366508
$604$	10.0000			0.406894
$605$		0			0
$606$	−30.0000	+	30.0000i	−1.21867	+	1.21867i
$607$			7.34847i			0.298265i	0.988817	+	0.149133i	$0.0476481\pi$
$607$			7.34847i			0.298265i	−0.988817	+	0.149133i	$0.952352\pi$
$608$		0			0
$609$	30.0000	+	12.2474i	1.21566	+	0.496292i
$610$		0			0
$611$		−	12.0000i		−	0.485468i
$612$			29.3939i			1.18818i
$613$			11.0000i			0.444286i	0.975014	+	0.222143i	$0.0713052\pi$
$613$			11.0000i			0.444286i	−0.975014	+	0.222143i	$0.928695\pi$
$614$	−4.89898	−	4.89898i	−0.197707	−	0.197707i
$615$		0			0
$616$	14.4949	+	34.4949i	0.584016	+	1.38984i
$617$			13.0000i			0.523360i	0.965155	+	0.261680i	$0.0842766\pi$
$617$			13.0000i			0.523360i	−0.965155	+	0.261680i	$0.915723\pi$
$618$	−36.0000	+	36.0000i	−1.44813	+	1.44813i
$619$	12.2474			0.492267			0.246133	−	0.969236i	$-0.420840\pi$
$619$	12.2474			0.492267			0.246133	+	0.969236i	$0.420840\pi$
$620$		0			0
$621$		0			0
$622$	−19.5959	+	19.5959i	−0.785725	+	0.785725i
$623$	6.00000	+	2.44949i	0.240385	+	0.0981367i
$624$		−	24.0000i		−	0.960769i
$625$		0			0
$626$	−9.79796	+	9.79796i	−0.391605	+	0.391605i
$627$		0			0
$628$		−	34.2929i		−	1.36843i
$629$			14.6969i			0.586005i
$630$		0			0
$631$		−	45.0000i		−	1.79142i	−0.444637	−	0.895711i	$-0.646667\pi$
$631$		−	45.0000i		−	1.79142i	0.444637	−	0.895711i	$-0.353333\pi$
$632$	−18.0000	+	18.0000i	−0.716002	+	0.716002i
$633$	24.4949			0.973585
$634$	−17.0000	−	17.0000i	−0.675156	−	0.675156i
$635$		0			0
$636$		−	19.5959i		−	0.777029i
$637$	−12.2474	−	12.0000i	−0.485262	−	0.475457i
$638$	−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
$643$			39.1918i			1.54558i	0.634665	+	0.772788i	$0.281138\pi$
$643$			39.1918i			1.54558i	−0.634665	+	0.772788i	$0.718862\pi$
$644$	−4.89898	−	2.00000i	−0.193047	−	0.0788110i
$645$		0			0
$646$		0			0
$647$		−	29.3939i		−	1.15559i	−0.816181	−	0.577796i	$-0.803913\pi$
$647$		−	29.3939i		−	1.15559i	0.816181	−	0.577796i	$-0.196087\pi$
$648$	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
$652$		−	12.0000i		−	0.469956i
$653$			16.0000i			0.626128i	0.949732	+	0.313064i	$0.101356\pi$
$653$			16.0000i			0.626128i	−0.949732	+	0.313064i	$0.898644\pi$
$654$	36.7423	+	36.7423i	1.43674	+	1.43674i
$655$		0			0
$656$		−	48.9898i		−	1.91273i
$657$	−7.34847			−0.286691
$658$	−16.8990	+	7.10102i	−0.658791	+	0.276827i
$659$			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	$-0.841952\pi$
$661$		−	24.4949i		−	0.952741i	0.879245	−	0.476371i	$-0.158048\pi$
$662$	25.0000	+	25.0000i	0.971653	+	0.971653i
$663$			29.3939i			1.14156i
$664$	4.89898	−	4.89898i	0.190117	−	0.190117i
$665$		0			0
$666$	−9.00000	−	9.00000i	−0.348743	−	0.348743i
$667$	5.00000			0.193601
$668$	14.6969			0.568642
$669$	−6.00000			−0.231973
$670$		0			0
$671$	−61.2372			−2.36404
$672$	−33.7980	+	14.2020i	−1.30378	+	0.547856i
$673$		−	24.0000i		−	0.925132i	−0.886585	−	0.462566i	$-0.846929\pi$
$673$		−	24.0000i		−	0.925132i	0.886585	−	0.462566i	$-0.153071\pi$
$674$	−12.0000	−	12.0000i	−0.462223	−	0.462223i
$675$		0			0
$676$			14.0000i			0.538462i
$677$	29.3939			1.12970			0.564849	−	0.825194i	$-0.308934\pi$
$677$	29.3939			1.12970			0.564849	+	0.825194i	$0.308934\pi$
$678$	−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
$683$	11.0000			0.420903			0.210452	−	0.977604i	$-0.432507\pi$
$683$	11.0000			0.420903			0.210452	+	0.977604i	$0.432507\pi$
$684$		0			0
$685$		0			0
$686$	−9.65153	+	24.3485i	−0.368497	+	0.929629i
$687$	24.0000			0.915657
$688$	−44.0000			−1.67748
$689$		−	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	$0.707103\pi$
$692$			19.5959i			0.744925i
$693$	36.7423	+	15.0000i	1.39573	+	0.569803i
$694$	17.0000	−	17.0000i	0.645311	−	0.645311i
$695$		0			0
$696$	24.4949	−	24.4949i	0.928477	−	0.928477i
$697$			60.0000i			2.27266i
$698$	−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
$707$	30.0000	+	12.2474i	1.12827	+	0.460613i
$708$	−60.0000			−2.25494
$709$		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
$713$	−7.34847			−0.275202
$714$	41.3939	−	17.3939i	1.54913	−	0.650949i
$715$		0			0
$716$	−28.0000			−1.04641
$717$	−63.6867			−2.37842
$718$	−19.0000	−	19.0000i	−0.709074	−	0.709074i
$719$	−12.2474			−0.456753			−0.228376	−	0.973573i	$-0.573342\pi$
$719$	−12.2474			−0.456753			−0.228376	+	0.973573i	$0.573342\pi$
$720$		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
$727$		−	29.3939i		−	1.09016i	−0.838385	−	0.545079i	$-0.816500\pi$
$727$		−	29.3939i		−	1.09016i	0.838385	−	0.545079i	$-0.183500\pi$
$728$	−16.8990	+	7.10102i	−0.626318	+	0.263181i
$729$	27.0000			1.00000
$730$		0			0
$731$	53.8888			1.99315
$732$		−	60.0000i		−	2.21766i
$733$	39.1918			1.44758			0.723792	−	0.690018i	$-0.242398\pi$
$733$	39.1918			1.44758			0.723792	+	0.690018i	$0.242398\pi$
$734$	−17.1464	−	17.1464i	−0.632886	−	0.632886i
$735$		0			0
$736$	−4.00000	+	4.00000i	−0.147442	+	0.147442i
$737$			15.0000i			0.552532i
$738$	−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
$742$	−13.7980	+	5.79796i	−0.506539	+	0.212850i
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$	−36.0000	+	36.0000i	−1.31982	+	1.31982i
$745$		0			0
$746$	−29.0000	−	29.0000i	−1.06177	−	1.06177i
$747$		−	7.34847i		−	0.268866i
$748$	−48.9898			−1.79124
$749$	−8.00000	+	19.5959i	−0.292314	+	0.716019i
$750$		0			0
$751$		−	20.0000i		−	0.729810i	−0.931045	−	0.364905i	$-0.881101\pi$
$751$		−	20.0000i		−	0.729810i	0.931045	−	0.364905i	$-0.118899\pi$
$752$			19.5959i			0.714590i
$753$			12.0000i			0.437304i
$754$	12.2474	−	12.2474i	0.446026	−	0.446026i
$755$		0			0
$756$		0			0
$757$			3.00000i			0.109037i	0.998513	+	0.0545184i	$0.0173624\pi$
$757$			3.00000i			0.109037i	−0.998513	+	0.0545184i	$0.982638\pi$
$758$	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	$-0.853570\pi$
$761$		−	24.4949i		−	0.887939i	0.896042	−	0.443970i	$-0.146430\pi$
$762$	−7.34847	−	7.34847i	−0.266207	−	0.266207i
$763$	15.0000	−	36.7423i	0.543036	−	1.33016i
$764$	20.0000			0.723575
$765$		0			0
$766$	2.44949	+	2.44949i	0.0885037	+	0.0885037i
$767$	−30.0000			−1.08324
$768$			39.1918i			1.41421i
$769$		−	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
$772$	42.0000			1.51161
$773$	26.9444			0.969122			0.484561	−	0.874757i	$-0.338979\pi$
$773$	26.9444			0.969122			0.484561	+	0.874757i	$0.338979\pi$
$774$	−33.0000	+	33.0000i	−1.18616	+	1.18616i
$775$		0			0
$776$	14.6969	+	14.6969i	0.527589	+	0.527589i
$777$	−7.34847	+	18.0000i	−0.263625	+	0.645746i
$778$	−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
$787$		−	17.1464i		−	0.611204i	−0.952159	−	0.305602i	$-0.901142\pi$
$787$		−	17.1464i		−	0.611204i	0.952159	−	0.305602i	$-0.0988577\pi$
$788$	46.0000			1.63868
$789$			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
$793$		−	30.0000i		−	1.06533i
$794$	−19.5959	+	19.5959i	−0.695433	+	0.695433i
$795$		0			0
$796$		−	24.4949i		−	0.868199i
$797$	−44.0908			−1.56178			−0.780888	−	0.624671i	$-0.785233\pi$
$797$	−44.0908			−1.56178			−0.780888	+	0.624671i	$0.785233\pi$
$798$		0			0
$799$		−	24.0000i		−	0.849059i
$800$		0			0
$801$		−	7.34847i		−	0.259645i
$802$	−23.0000	+	23.0000i	−0.812158	+	0.812158i
$803$		−	12.2474i		−	0.432203i
$804$	−14.6969			−0.518321
$805$		0			0
$806$	−18.0000	+	18.0000i	−0.634023	+	0.634023i
$807$	54.0000			1.90089
$808$	24.4949	−	24.4949i	0.861727	−	0.861727i
$809$	5.00000			0.175791			0.0878953	−	0.996130i	$-0.471986\pi$
$809$	5.00000			0.175791			0.0878953	+	0.996130i	$0.471986\pi$
$810$		0			0
$811$	−19.5959			−0.688106			−0.344053	−	0.938950i	$-0.611800\pi$
$811$	−19.5959			−0.688106			−0.344053	+	0.938950i	$0.611800\pi$
$812$	−24.4949	−	10.0000i	−0.859602	−	0.350931i
$813$			42.0000i			1.47300i
$814$	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
$823$	21.0000			0.732014			0.366007	−	0.930612i	$-0.380725\pi$
$823$	21.0000			0.732014			0.366007	+	0.930612i	$0.380725\pi$
$824$	29.3939	−	29.3939i	1.02398	−	1.02398i
$825$		0			0
$826$	17.7526	+	42.2474i	0.617690	+	1.46998i
$827$	−13.0000			−0.452054			−0.226027	−	0.974121i	$-0.572574\pi$
$827$	−13.0000			−0.452054			−0.226027	+	0.974121i	$0.572574\pi$
$828$			6.00000i			0.208514i
$829$		−	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
$832$			19.5959i			0.679366i
$833$	−24.4949	−	24.0000i	−0.848698	−	0.831551i
$834$	−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	$-0.718688\pi$
$839$	−36.7423			−1.26849			−0.634243	+	0.773133i	$0.718688\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	−23.0000	+	23.0000i	−0.792632	+	0.792632i
$843$			41.6413i			1.43420i
$844$	−20.0000			−0.688428
$845$		0			0
$846$	14.6969	+	14.6969i	0.505291	+	0.505291i
$847$	−14.0000	+	34.2929i	−0.481046	+	1.17832i
$848$			16.0000i			0.549442i
$849$	24.0000			0.823678
$850$		0			0
$851$			3.00000i			0.102839i
$852$			24.4949i			0.839181i
$853$	14.6969			0.503214			0.251607	−	0.967830i	$-0.419041\pi$
$853$	14.6969			0.503214			0.251607	+	0.967830i	$0.419041\pi$
$854$	−42.2474	+	17.7526i	−1.44568	+	0.607480i
$855$		0			0
$856$	16.0000	+	16.0000i	0.546869	+	0.546869i
$857$	41.6413			1.42244			0.711220	−	0.702969i	$-0.248143\pi$
$857$	41.6413			1.42244			0.711220	+	0.702969i	$0.248143\pi$
$858$	30.0000	−	30.0000i	1.02418	−	1.02418i
$859$	24.4949			0.835755			0.417878	−	0.908503i	$-0.362774\pi$
$859$	24.4949			0.835755			0.417878	+	0.908503i	$0.362774\pi$
$860$		0			0
$861$	−30.0000	+	73.4847i	−1.02240	+	2.50435i
$862$	10.0000	+	10.0000i	0.340601	+	0.340601i
$863$	31.0000			1.05525			0.527626	−	0.849477i	$-0.323082\pi$
$863$	31.0000			1.05525			0.527626	+	0.849477i	$0.323082\pi$
$864$		0			0
$865$		0			0
$866$	39.1918	−	39.1918i	1.33179	−	1.33179i
$867$			17.1464i			0.582323i
$868$	36.0000	+	14.6969i	1.22192	+	0.498847i
$869$	−45.0000			−1.52652
$870$		0			0
$871$	−7.34847			−0.248993
$872$	−30.0000	−	30.0000i	−1.01593	−	1.01593i
$873$	22.0454			0.746124
$874$		0			0
$875$		0			0
$876$	12.0000			0.405442
$877$		−	52.0000i		−	1.75592i	−0.478738	−	0.877958i	$-0.658906\pi$
$877$		−	52.0000i		−	1.75592i	0.478738	−	0.877958i	$-0.341094\pi$
$878$	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	$0.0661467\pi$
$881$			12.2474i			0.412627i	−0.978486	+	0.206314i	$0.933853\pi$
$882$	29.6969	−	0.303062i	0.999948	−	0.0102046i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$		−	24.0000i		−	0.807207i
$885$		0			0
$886$	−14.0000	+	14.0000i	−0.470339	+	0.470339i
$887$			56.3383i			1.89165i	0.324671	+	0.945827i	$0.394746\pi$
$887$			56.3383i			1.89165i	−0.324671	+	0.945827i	$0.605254\pi$
$888$	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
$892$	4.89898			0.164030
$893$		0			0
$894$	12.2474	+	12.2474i	0.409616	+	0.409616i
$895$		0			0
$896$	27.5959	−	11.5959i	0.921915	−	0.387392i
$897$			6.00000i			0.200334i
$898$	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
$903$	66.0000	+	26.9444i	2.19634	+	0.896653i
$904$	22.0000	−	22.0000i	0.731709	−	0.731709i
$905$		0			0
$906$	−12.2474	+	12.2474i	−0.406894	+	0.406894i
$907$	−38.0000			−1.26177			−0.630885	−	0.775877i	$-0.717308\pi$
$907$	−38.0000			−1.26177			−0.630885	+	0.775877i	$0.717308\pi$
$908$	39.1918			1.30063
$909$		−	36.7423i		−	1.21867i
$910$		0			0
$911$			35.0000i			1.15960i	0.814758	+	0.579801i	$0.196870\pi$
$911$			35.0000i			1.15960i	−0.814758	+	0.579801i	$0.803130\pi$
$912$		0			0
$913$	12.2474			0.405331
$914$	3.00000	+	3.00000i	0.0992312	+	0.0992312i
$915$		0			0
$916$	−19.5959			−0.647467
$917$	4.89898	−	12.0000i	0.161779	−	0.396275i
$918$		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
$923$			12.2474i			0.403130i
$924$	−60.0000	−	24.4949i	−1.97386	−	0.805823i
$925$		0			0
$926$	36.0000	−	36.0000i	1.18303	−	1.18303i
$927$		−	44.0908i		−	1.44813i
$928$	−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
$932$	22.0000			0.720634
$933$		−	48.0000i		−	1.57145i
$934$	−4.89898	−	4.89898i	−0.160300	−	0.160300i
$935$		0			0
$936$	14.6969	+	14.6969i	0.480384	+	0.480384i
$937$	−7.34847			−0.240064			−0.120032	−	0.992770i	$-0.538300\pi$
$937$	−7.34847			−0.240064			−0.120032	+	0.992770i	$0.538300\pi$
$938$	4.34847	+	10.3485i	0.141983	+	0.337889i
$939$		−	24.0000i		−	0.783210i
$940$		0			0
$941$		−	12.2474i		−	0.399255i	−0.979872	−	0.199628i	$-0.936027\pi$
$941$		−	12.2474i		−	0.399255i	0.979872	−	0.199628i	$-0.0639733\pi$
$942$	42.0000	+	42.0000i	1.36843	+	1.36843i
$943$			12.2474i			0.398832i
$944$	48.9898			1.59448
$945$		0			0
$946$	−55.0000	−	55.0000i	−1.78820	−	1.78820i
$947$	−38.0000			−1.23483			−0.617417	−	0.786636i	$-0.711821\pi$
$947$	−38.0000			−1.23483			−0.617417	+	0.786636i	$0.711821\pi$
$948$		−	44.0908i		−	1.43200i
$949$	6.00000			0.194768
$950$		0			0
$951$	41.6413			1.35031
$952$	−33.7980	+	14.2020i	−1.09540	+	0.460291i
$953$		−	59.0000i		−	1.91120i	−0.294671	−	0.955599i	$-0.595210\pi$
$953$		−	59.0000i		−	1.91120i	0.294671	−	0.955599i	$-0.404790\pi$
$954$	12.0000	+	12.0000i	0.388514	+	0.388514i
$955$		0			0
$956$	52.0000			1.68180
$957$	61.2372			1.97952
$958$	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
$963$	24.0000			0.773389
$964$		0			0
$965$		0			0
$966$	8.44949	−	3.55051i	0.271858	−	0.114236i
$967$	−18.0000			−0.578841			−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000			−0.578841			−0.289420	+	0.957202i	$0.593463\pi$
$968$	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	$0.750164\pi$
$972$	−44.0908			−1.41421
$973$	−12.2474	+	30.0000i	−0.392635	+	0.961756i
$974$	7.00000	−	7.00000i	0.224294	−	0.224294i
$975$		0			0
$976$			48.9898i			1.56813i
$977$		−	17.0000i		−	0.543878i	−0.962314	−	0.271939i	$-0.912335\pi$
$977$		−	17.0000i		−	0.543878i	0.962314	−	0.271939i	$-0.0876649\pi$
$978$	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
$983$		−	22.0454i		−	0.703139i	−0.936162	−	0.351570i	$-0.885648\pi$
$983$		−	22.0454i		−	0.703139i	0.936162	−	0.351570i	$-0.114352\pi$
$984$	60.0000	+	60.0000i	1.91273	+	1.91273i
$985$		0			0
$986$	24.4949	−	24.4949i	0.780076	−	0.780076i
$987$	12.0000	−	29.3939i	0.381964	−	0.935617i
$988$		0			0
$989$	11.0000			0.349780
$990$		0			0
$991$			35.0000i			1.11181i	0.831245	+	0.555906i	$0.187628\pi$
$991$			35.0000i			1.11181i	−0.831245	+	0.555906i	$0.812372\pi$
$992$	29.3939	−	29.3939i	0.933257	−	0.933257i
$993$	−61.2372			−1.94331
$994$	17.2474	−	7.24745i	0.547056	−	0.229875i
$995$		0			0
$996$			12.0000i			0.380235i
$997$	4.89898			0.155152			0.0775761	−	0.996986i	$-0.475282\pi$
$997$	4.89898			0.155152			0.0775761	+	0.996986i	$0.475282\pi$
$998$	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.c.g.699.2		4
4.3	odd	2		700.2.c.a.699.1		4
5.2	odd	4		700.2.g.h.251.4	yes	4
5.3	odd	4		700.2.g.b.251.1	✓	4
5.4	even	2		700.2.c.a.699.3		4
7.6	odd	2	inner	700.2.c.g.699.1		4
20.3	even	4		700.2.g.b.251.4	yes	4
20.7	even	4		700.2.g.h.251.1	yes	4
20.19	odd	2	inner	700.2.c.g.699.4		4
28.27	even	2		700.2.c.a.699.2		4
35.13	even	4		700.2.g.b.251.2	yes	4
35.27	even	4		700.2.g.h.251.3	yes	4
35.34	odd	2		700.2.c.a.699.4		4
140.27	odd	4		700.2.g.h.251.2	yes	4
140.83	odd	4		700.2.g.b.251.3	yes	4
140.139	even	2	inner	700.2.c.g.699.3		4

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.c (of order \(2\), degree \(1\), not minimal)

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

Introduction

L-functions

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