LMFDB - Embedded newform 245.2.j.g.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(79,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	245.79
Dual form			245.2.j.g.214.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(2.44949 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.67303 - 1.48356i) q^{5} -2.82843 q^{6} +3.00000i q^{8} +(2.50000 - 4.33013i) q^{9} +(-2.19067 + 0.448288i) q^{10} +(-2.44949 - 1.41421i) q^{12} +4.24264i q^{13} +(2.00000 - 6.00000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.67423 + 2.12132i) q^{17} +(-4.33013 + 2.50000i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.12132 - 0.707107i) q^{20} +(3.46410 + 2.00000i) q^{23} +(4.24264 + 7.34847i) q^{24} +(0.598076 - 4.96410i) q^{25} +(2.12132 - 3.67423i) q^{26} -5.65685i q^{27} +(-4.73205 + 4.19615i) q^{30} +(-2.82843 - 4.89898i) q^{31} +(4.33013 - 2.50000i) q^{32} +4.24264 q^{34} -5.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(2.44949 - 1.41421i) q^{38} +(6.00000 + 10.3923i) q^{39} +(4.45069 + 5.01910i) q^{40} +4.24264 q^{41} +(-2.24144 - 10.9534i) q^{45} +(-2.00000 - 3.46410i) q^{46} -2.82843i q^{48} +(-3.00000 + 4.00000i) q^{50} +(-6.00000 + 10.3923i) q^{51} +(3.67423 - 2.12132i) q^{52} +(6.92820 - 4.00000i) q^{53} +(-2.82843 + 4.89898i) q^{54} +8.00000i q^{57} +(4.24264 + 7.34847i) q^{59} +(-6.19615 + 1.26795i) q^{60} +(-4.94975 + 8.57321i) q^{61} +5.65685i q^{62} -7.00000 q^{64} +(6.29423 + 7.09808i) q^{65} +(-10.3923 + 6.00000i) q^{67} +(3.67423 + 2.12132i) q^{68} +11.3137 q^{69} +12.0000 q^{71} +(12.9904 + 7.50000i) q^{72} +(-11.0227 + 6.36396i) q^{73} +(3.00000 + 5.19615i) q^{74} +(-5.55532 - 13.0053i) q^{75} +2.82843 q^{76} -12.0000i q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.448288 - 2.19067i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.67423 - 2.12132i) q^{82} -8.48528i q^{83} +(-3.00000 + 9.00000i) q^{85} +(-2.12132 + 3.67423i) q^{89} +(-3.53553 + 10.6066i) q^{90} -4.00000i q^{92} +(-13.8564 - 8.00000i) q^{93} +(1.26795 + 6.19615i) q^{95} +(7.07107 - 12.2474i) q^{96} +4.24264i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} + 20 q^{9} + 16 q^{15} + 4 q^{16} - 16 q^{25} - 24 q^{30} - 40 q^{36} + 48 q^{39} - 16 q^{46} - 24 q^{50} - 48 q^{51} - 8 q^{60} - 56 q^{64} - 12 q^{65} + 96 q^{71} + 24 q^{74} + 48 q^{79}+ \cdots + 24 q^{95}+O(q^{100}) $ 8 * q - 4 * q^4 + 20 * q^9 + 16 * q^15 + 4 * q^16 - 16 * q^25 - 24 * q^30 - 40 * q^36 + 48 * q^39 - 16 * q^46 - 24 * q^50 - 48 * q^51 - 8 * q^60 - 56 * q^64 - 12 * q^65 + 96 * q^71 + 24 * q^74 + 48 * q^79 - 4 * q^81 - 24 * q^85 + 24 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	2.44949	−	1.41421i	1.41421	−	0.816497i	0.418432	−	0.908248i	$-0.362580\pi$
$3$	2.44949	−	1.41421i	1.41421	−	0.816497i	0.995782	+	0.0917517i	$0.0292466\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.67303	−	1.48356i	0.748203	−	0.663470i
$5$	1.67303	−	1.48356i	0.748203	−	0.663470i
$6$	−2.82843			−1.15470
$7$		0			0
$7$		0			0
$8$			3.00000i			1.06066i
$9$	2.50000	−	4.33013i	0.833333	−	1.44338i
$10$	−2.19067	+	0.448288i	−0.692751	+	0.141761i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−2.44949	−	1.41421i	−0.707107	−	0.408248i
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$		0			0
$15$	2.00000	−	6.00000i	0.516398	−	1.54919i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.67423	+	2.12132i	−0.891133	+	0.514496i	−0.874313	−	0.485363i	$-0.838688\pi$
$17$	−3.67423	+	2.12132i	−0.891133	+	0.514496i	−0.0168199	+	0.999859i	$0.505354\pi$
$18$	−4.33013	+	2.50000i	−1.02062	+	0.589256i
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	−2.12132	−	0.707107i	−0.474342	−	0.158114i
$21$		0			0
$22$		0			0
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$	4.24264	+	7.34847i	0.866025	+	1.50000i
$25$	0.598076	−	4.96410i	0.119615	−	0.992820i
$26$	2.12132	−	3.67423i	0.416025	−	0.720577i
$27$		−	5.65685i		−	1.08866i
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$	−4.73205	+	4.19615i	−0.863950	+	0.766109i
$31$	−2.82843	−	4.89898i	−0.508001	−	0.879883i	−0.999957	−	0.00926296i	$-0.997051\pi$
$31$	−2.82843	−	4.89898i	−0.508001	−	0.879883i	0.491957	−	0.870620i	$-0.336282\pi$
$32$	4.33013	−	2.50000i	0.765466	−	0.441942i
$33$		0			0
$34$	4.24264			0.727607
$35$		0			0
$36$	−5.00000			−0.833333
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	0.00783774	−	0.999969i	$-0.497505\pi$
$37$	−5.19615	−	3.00000i	−0.854242	−	0.493197i	−0.862080	+	0.506772i	$0.830838\pi$
$38$	2.44949	−	1.41421i	0.397360	−	0.229416i
$39$	6.00000	+	10.3923i	0.960769	+	1.66410i
$40$	4.45069	+	5.01910i	0.703716	+	0.793589i
$41$	4.24264			0.662589			0.331295	−	0.943527i	$-0.392515\pi$
$41$	4.24264			0.662589			0.331295	+	0.943527i	$0.392515\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	−2.24144	−	10.9534i	−0.334134	−	1.63283i
$46$	−2.00000	−	3.46410i	−0.294884	−	0.510754i
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$		−	2.82843i		−	0.408248i
$49$		0			0
$50$	−3.00000	+	4.00000i	−0.424264	+	0.565685i
$51$	−6.00000	+	10.3923i	−0.840168	+	1.45521i
$52$	3.67423	−	2.12132i	0.509525	−	0.294174i
$53$	6.92820	−	4.00000i	0.951662	−	0.549442i	0.0580651	−	0.998313i	$-0.481507\pi$
$53$	6.92820	−	4.00000i	0.951662	−	0.549442i	0.893597	+	0.448871i	$0.148174\pi$
$54$	−2.82843	+	4.89898i	−0.384900	+	0.666667i
$55$		0			0
$56$		0			0
$57$			8.00000i			1.05963i
$58$		0			0
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	0.998105	+	0.0615367i	$0.0196001\pi$
$59$	4.24264	+	7.34847i	0.552345	+	0.956689i	−0.445760	+	0.895152i	$0.647067\pi$
$60$	−6.19615	+	1.26795i	−0.799920	+	0.163692i
$61$	−4.94975	+	8.57321i	−0.633750	+	1.09769i	0.353028	+	0.935613i	$0.385152\pi$
$61$	−4.94975	+	8.57321i	−0.633750	+	1.09769i	−0.986778	+	0.162075i	$0.948181\pi$
$62$			5.65685i			0.718421i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	6.29423	+	7.09808i	0.780703	+	0.880408i
$66$		0			0
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.974916	−	0.222571i	$-0.928555\pi$
$67$	−10.3923	+	6.00000i	−1.26962	+	0.733017i	−0.294706	+	0.955588i	$0.595222\pi$
$68$	3.67423	+	2.12132i	0.445566	+	0.257248i
$69$	11.3137			1.36201
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	12.9904	+	7.50000i	1.53093	+	0.883883i
$73$	−11.0227	+	6.36396i	−1.29011	+	0.744845i	−0.978674	−	0.205422i	$-0.934143\pi$
$73$	−11.0227	+	6.36396i	−1.29011	+	0.744845i	−0.311436	+	0.950267i	$0.600810\pi$
$74$	3.00000	+	5.19615i	0.348743	+	0.604040i
$75$	−5.55532	−	13.0053i	−0.641473	−	1.50173i
$76$	2.82843			0.324443
$77$		0			0
$78$		−	12.0000i		−	1.35873i
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$	−0.448288	−	2.19067i	−0.0501201	−	0.244924i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.67423	−	2.12132i	−0.405751	−	0.234261i
$83$		−	8.48528i		−	0.931381i	−0.884948	−	0.465690i	$-0.845806\pi$
$83$		−	8.48528i		−	0.931381i	0.884948	−	0.465690i	$-0.154194\pi$
$84$		0			0
$85$	−3.00000	+	9.00000i	−0.325396	+	0.976187i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.12132	+	3.67423i	−0.224860	+	0.389468i	−0.956277	−	0.292462i	$-0.905526\pi$
$89$	−2.12132	+	3.67423i	−0.224860	+	0.389468i	0.731418	+	0.681930i	$0.238859\pi$
$90$	−3.53553	+	10.6066i	−0.372678	+	1.11803i
$91$		0			0
$92$		−	4.00000i		−	0.417029i
$93$	−13.8564	−	8.00000i	−1.43684	−	0.829561i
$94$		0			0
$95$	1.26795	+	6.19615i	0.130089	+	0.635712i
$96$	7.07107	−	12.2474i	0.721688	−	1.25000i
$97$			4.24264i			0.430775i	0.976529	+	0.215387i	$0.0691014\pi$
$97$			4.24264i			0.430775i	−0.976529	+	0.215387i	$0.930899\pi$
$98$		0			0
$99$		0			0
$100$	−4.59808	+	1.96410i	−0.459808	+	0.196410i
$101$	2.12132	+	3.67423i	0.211079	+	0.365600i	0.952053	−	0.305934i	$-0.0989688\pi$
$101$	2.12132	+	3.67423i	0.211079	+	0.365600i	−0.740973	+	0.671534i	$0.765636\pi$
$102$	10.3923	−	6.00000i	1.02899	−	0.594089i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−12.7279			−1.24808
$105$		0			0
$106$	−8.00000			−0.777029
$107$	−3.46410	−	2.00000i	−0.334887	−	0.193347i	0.323122	−	0.946357i	$-0.395268\pi$
$107$	−3.46410	−	2.00000i	−0.334887	−	0.193347i	−0.658009	+	0.753010i	$0.728601\pi$
$108$	−4.89898	+	2.82843i	−0.471405	+	0.272166i
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	−0.939577	−	0.342337i	$-0.888782\pi$
$109$	−8.00000	−	13.8564i	−0.766261	−	1.32720i	0.173316	−	0.984866i	$-0.444552\pi$
$110$		0			0
$111$	−16.9706			−1.61077
$112$		0			0
$113$		−	8.00000i		−	0.752577i	−0.926503	−	0.376288i	$-0.877200\pi$
$113$		−	8.00000i		−	0.752577i	0.926503	−	0.376288i	$-0.122800\pi$
$114$	4.00000	−	6.92820i	0.374634	−	0.648886i
$115$	8.76268	−	1.79315i	0.817124	−	0.167212i
$116$		0			0
$117$	18.3712	+	10.6066i	1.69842	+	0.980581i
$118$		−	8.48528i		−	0.781133i
$119$		0			0
$120$	18.0000	+	6.00000i	1.64317	+	0.547723i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	8.57321	−	4.94975i	0.776182	−	0.448129i
$123$	10.3923	−	6.00000i	0.937043	−	0.541002i
$124$	−2.82843	+	4.89898i	−0.254000	+	0.439941i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$		0			0
$127$		−	12.0000i		−	1.06483i	−0.846484	−	0.532414i	$-0.821285\pi$
$127$		−	12.0000i		−	1.06483i	0.846484	−	0.532414i	$-0.178715\pi$
$128$	−2.59808	−	1.50000i	−0.229640	−	0.132583i
$129$		0			0
$130$	−1.90192	−	9.29423i	−0.166810	−	0.815158i
$131$	4.24264	−	7.34847i	0.370681	−	0.642039i	−0.618989	−	0.785399i	$-0.712458\pi$
$131$	4.24264	−	7.34847i	0.370681	−	0.642039i	0.989671	+	0.143361i	$0.0457909\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$	−8.39230	−	9.46410i	−0.722295	−	0.814540i
$136$	−6.36396	−	11.0227i	−0.545705	−	0.945189i
$137$	−12.1244	+	7.00000i	−1.03585	+	0.598050i	−0.918656	−	0.395058i	$-0.870724\pi$
$137$	−12.1244	+	7.00000i	−1.03585	+	0.598050i	−0.117198	+	0.993109i	$0.537391\pi$
$138$	−9.79796	−	5.65685i	−0.834058	−	0.481543i
$139$	−2.82843			−0.239904			−0.119952	−	0.992780i	$-0.538274\pi$
$139$	−2.82843			−0.239904			−0.119952	+	0.992780i	$0.538274\pi$
$140$		0			0
$141$		0			0
$142$	−10.3923	−	6.00000i	−0.872103	−	0.503509i
$143$		0			0
$144$	−2.50000	−	4.33013i	−0.208333	−	0.360844i
$145$		0			0
$146$	12.7279			1.05337
$147$		0			0
$148$			6.00000i			0.493197i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	−1.69161	+	14.0406i	−0.138120	+	1.14641i
$151$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$151$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$152$	−7.34847	−	4.24264i	−0.596040	−	0.344124i
$153$			21.2132i			1.71499i
$154$		0			0
$155$	−12.0000	−	4.00000i	−0.963863	−	0.321288i
$156$	6.00000	−	10.3923i	0.480384	−	0.832050i
$157$	3.67423	−	2.12132i	0.293236	−	0.169300i	−0.346164	−	0.938174i	$-0.612516\pi$
$157$	3.67423	−	2.12132i	0.293236	−	0.169300i	0.639400	+	0.768874i	$0.279183\pi$
$158$	−10.3923	+	6.00000i	−0.826767	+	0.477334i
$159$	11.3137	−	19.5959i	0.897235	−	1.55406i
$160$	3.53553	−	10.6066i	0.279508	−	0.838525i
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	20.7846	+	12.0000i	1.62798	+	0.939913i	0.984696	+	0.174282i	$0.0557604\pi$
$163$	20.7846	+	12.0000i	1.62798	+	0.939913i	0.643280	+	0.765631i	$0.277573\pi$
$164$	−2.12132	−	3.67423i	−0.165647	−	0.286910i
$165$		0			0
$166$	−4.24264	+	7.34847i	−0.329293	+	0.570352i
$167$			11.3137i			0.875481i	0.899101	+	0.437741i	$0.144221\pi$
$167$			11.3137i			0.875481i	−0.899101	+	0.437741i	$0.855779\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	7.09808	−	6.29423i	0.544398	−	0.482745i
$171$	7.07107	+	12.2474i	0.540738	+	0.936586i
$172$		0			0
$173$	−3.67423	−	2.12132i	−0.279347	−	0.161281i	0.353781	−	0.935328i	$-0.384896\pi$
$173$	−3.67423	−	2.12132i	−0.279347	−	0.161281i	−0.633128	+	0.774047i	$0.718229\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	20.7846	+	12.0000i	1.56227	+	0.901975i
$178$	3.67423	−	2.12132i	0.275396	−	0.159000i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	−8.36516	+	7.41782i	−0.623502	+	0.552892i
$181$	−18.3848			−1.36653			−0.683265	−	0.730171i	$-0.739441\pi$
$181$	−18.3848			−1.36653			−0.683265	+	0.730171i	$0.739441\pi$
$182$		0			0
$183$			28.0000i			2.06982i
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$	−13.1440	+	2.68973i	−0.966368	+	0.197753i
$186$	8.00000	+	13.8564i	0.586588	+	1.01600i
$187$		0			0
$188$		0			0
$189$		0			0
$190$	2.00000	−	6.00000i	0.145095	−	0.435286i
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	−17.1464	+	9.89949i	−1.23744	+	0.714435i
$193$	−20.7846	+	12.0000i	−1.49611	+	0.863779i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−20.7846	+	12.0000i	−1.49611	+	0.863779i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	2.12132	−	3.67423i	0.152302	−	0.263795i
$195$	25.4558	+	8.48528i	1.82293	+	0.607644i
$196$		0			0
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	−5.65685	−	9.79796i	−0.401004	−	0.694559i	0.592844	−	0.805318i	$-0.298005\pi$
$199$	−5.65685	−	9.79796i	−0.401004	−	0.694559i	−0.993847	+	0.110759i	$0.964672\pi$
$200$	14.8923	+	1.79423i	1.05304	+	0.126871i
$201$	−16.9706	+	29.3939i	−1.19701	+	2.07328i
$202$		−	4.24264i		−	0.298511i
$203$		0			0
$204$	12.0000			0.840168
$205$	7.09808	−	6.29423i	0.495751	−	0.439608i
$206$		0			0
$207$	17.3205	−	10.0000i	1.20386	−	0.695048i
$208$	3.67423	+	2.12132i	0.254762	+	0.147087i
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−6.92820	−	4.00000i	−0.475831	−	0.274721i
$213$	29.3939	−	16.9706i	2.01404	−	1.16280i
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$		0			0
$216$	16.9706			1.15470
$217$		0			0
$218$			16.0000i			1.08366i
$219$	−18.0000	+	31.1769i	−1.21633	+	2.10674i
$220$		0			0
$221$	−9.00000	−	15.5885i	−0.605406	−	1.04859i
$222$	14.6969	+	8.48528i	0.986394	+	0.569495i
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$		0			0
$225$	−20.0000	−	15.0000i	−1.33333	−	1.00000i
$226$	−4.00000	+	6.92820i	−0.266076	+	0.460857i
$227$	2.44949	−	1.41421i	0.162578	−	0.0938647i	−0.416503	−	0.909134i	$-0.636745\pi$
$227$	2.44949	−	1.41421i	0.162578	−	0.0938647i	0.579082	+	0.815270i	$0.303411\pi$
$228$	6.92820	−	4.00000i	0.458831	−	0.264906i
$229$	3.53553	−	6.12372i	0.233635	−	0.404667i	−0.725240	−	0.688496i	$-0.758271\pi$
$229$	3.53553	−	6.12372i	0.233635	−	0.404667i	0.958875	+	0.283829i	$0.0916047\pi$
$230$	−8.48528	−	2.82843i	−0.559503	−	0.186501i
$231$		0			0
$232$		0			0
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	0.0471787	−	0.998886i	$-0.484977\pi$
$233$	−12.1244	−	7.00000i	−0.794293	−	0.458585i	−0.841472	+	0.540301i	$0.818310\pi$
$234$	−10.6066	−	18.3712i	−0.693375	−	1.20096i
$235$		0			0
$236$	4.24264	−	7.34847i	0.276172	−	0.478345i
$237$		−	33.9411i		−	2.20471i
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$	−4.19615	−	4.73205i	−0.270860	−	0.305453i
$241$	4.94975	+	8.57321i	0.318841	+	0.552249i	0.980247	−	0.197779i	$-0.0633730\pi$
$241$	4.94975	+	8.57321i	0.318841	+	0.552249i	−0.661405	+	0.750029i	$0.730040\pi$
$242$	−9.52628	+	5.50000i	−0.612372	+	0.353553i
$243$	12.2474	+	7.07107i	0.785674	+	0.453609i
$244$	9.89949			0.633750
$245$		0			0
$246$	−12.0000			−0.765092
$247$	−10.3923	−	6.00000i	−0.661247	−	0.381771i
$248$	14.6969	−	8.48528i	0.933257	−	0.538816i
$249$	−12.0000	−	20.7846i	−0.760469	−	1.31717i
$250$	0.915158	+	11.1428i	0.0578797	+	0.704734i
$251$	25.4558			1.60676			0.803379	−	0.595468i	$-0.203033\pi$
$251$	25.4558			1.60676			0.803379	+	0.595468i	$0.203033\pi$
$252$		0			0
$253$		0			0
$254$	−6.00000	+	10.3923i	−0.376473	+	0.652071i
$255$	5.37945	+	26.2880i	0.336874	+	1.64622i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−23.2702	−	13.4350i	−1.45155	−	0.838054i	−0.452983	−	0.891519i	$-0.649640\pi$
$257$	−23.2702	−	13.4350i	−1.45155	−	0.838054i	−0.998570	+	0.0534653i	$0.982973\pi$
$258$		0			0
$259$		0			0
$260$	3.00000	−	9.00000i	0.186052	−	0.558156i
$261$		0			0
$262$	−7.34847	+	4.24264i	−0.453990	+	0.262111i
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	−0.00771799	−	0.999970i	$-0.502457\pi$
$263$	13.8564	−	8.00000i	0.854423	−	0.493301i	0.862141	+	0.506669i	$0.169123\pi$
$264$		0			0
$265$	5.65685	−	16.9706i	0.347498	−	1.04249i
$266$		0			0
$267$			12.0000i			0.734388i
$268$	10.3923	+	6.00000i	0.634811	+	0.366508i
$269$	−10.6066	−	18.3712i	−0.646696	−	1.12011i	−0.983907	−	0.178681i	$-0.942817\pi$
$269$	−10.6066	−	18.3712i	−0.646696	−	1.12011i	0.337211	−	0.941429i	$-0.390516\pi$
$270$	2.53590	+	12.3923i	0.154330	+	0.754172i
$271$	2.82843	−	4.89898i	0.171815	−	0.297592i	−0.767240	−	0.641361i	$-0.778370\pi$
$271$	2.82843	−	4.89898i	0.171815	−	0.297592i	0.939054	+	0.343769i	$0.111704\pi$
$272$			4.24264i			0.257248i
$273$		0			0
$274$	14.0000			0.845771
$275$		0			0
$276$	−5.65685	−	9.79796i	−0.340503	−	0.589768i
$277$	20.7846	−	12.0000i	1.24883	−	0.721010i	0.277951	−	0.960595i	$-0.410345\pi$
$277$	20.7846	−	12.0000i	1.24883	−	0.721010i	0.970875	+	0.239585i	$0.0770114\pi$
$278$	2.44949	+	1.41421i	0.146911	+	0.0848189i
$279$	−28.2843			−1.69334
$280$		0			0
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−22.0454	+	12.7279i	−1.31046	+	0.756596i	−0.982173	−	0.187980i	$-0.939806\pi$
$283$	−22.0454	+	12.7279i	−1.31046	+	0.756596i	−0.328291	+	0.944577i	$0.606473\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	11.8685	+	13.3843i	0.703030	+	0.792815i
$286$		0			0
$287$		0			0
$288$		−	25.0000i		−	1.47314i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	6.00000	+	10.3923i	0.351726	+	0.609208i
$292$	11.0227	+	6.36396i	0.645055	+	0.372423i
$293$			1.41421i			0.0826192i	0.999146	+	0.0413096i	$0.0131530\pi$
$293$			1.41421i			0.0826192i	−0.999146	+	0.0413096i	$0.986847\pi$
$294$		0			0
$295$	18.0000	+	6.00000i	1.04800	+	0.349334i
$296$	9.00000	−	15.5885i	0.523114	−	0.906061i
$297$		0			0
$298$	5.19615	−	3.00000i	0.301005	−	0.173785i
$299$	−8.48528	+	14.6969i	−0.490716	+	0.849946i
$300$	−8.48528	+	11.3137i	−0.489898	+	0.653197i
$301$		0			0
$302$		0			0
$303$	10.3923	+	6.00000i	0.597022	+	0.344691i
$304$	1.41421	+	2.44949i	0.0811107	+	0.140488i
$305$	4.43782	+	21.6865i	0.254109	+	1.24177i
$306$	10.6066	−	18.3712i	0.606339	−	1.05021i
$307$			25.4558i			1.45284i	0.687250	+	0.726421i	$0.258818\pi$
$307$			25.4558i			1.45284i	−0.687250	+	0.726421i	$0.741182\pi$
$308$		0			0
$309$		0			0
$310$	8.39230	+	9.46410i	0.476651	+	0.537525i
$311$	16.9706	+	29.3939i	0.962312	+	1.66677i	0.716669	+	0.697414i	$0.245666\pi$
$311$	16.9706	+	29.3939i	0.962312	+	1.66677i	0.245643	+	0.969360i	$0.421001\pi$
$312$	−31.1769	+	18.0000i	−1.76505	+	1.01905i
$313$	−18.3712	−	10.6066i	−1.03840	−	0.599521i	−0.119020	−	0.992892i	$-0.537975\pi$
$313$	−18.3712	−	10.6066i	−1.03840	−	0.599521i	−0.919380	+	0.393371i	$0.871309\pi$
$314$	−4.24264			−0.239426
$315$		0			0
$316$	−12.0000			−0.675053
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	0.292655	−	0.956218i	$-0.405461\pi$
$317$	−6.92820	−	4.00000i	−0.389127	−	0.224662i	−0.681782	+	0.731556i	$0.738795\pi$
$318$	−19.5959	+	11.3137i	−1.09888	+	0.634441i
$319$		0			0
$320$	−11.7112	+	10.3849i	−0.654678	+	0.580536i
$321$	−11.3137			−0.631470
$322$		0			0
$323$		−	12.0000i		−	0.667698i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	21.0609	+	2.53742i	1.16825	+	0.140751i
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	−39.1918	−	22.6274i	−2.16731	−	1.25130i
$328$			12.7279i			0.702782i
$329$		0			0
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$	−7.34847	+	4.24264i	−0.403300	+	0.232845i
$333$	−25.9808	+	15.0000i	−1.42374	+	0.821995i
$334$	5.65685	−	9.79796i	0.309529	−	0.536120i
$335$	−8.48528	+	25.4558i	−0.463600	+	1.39080i
$336$		0			0
$337$			18.0000i			0.980522i	0.871576	+	0.490261i	$0.163099\pi$
$337$			18.0000i			0.980522i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	4.33013	+	2.50000i	0.235528	+	0.135982i
$339$	−11.3137	−	19.5959i	−0.614476	−	1.06430i
$340$	9.29423	−	1.90192i	0.504050	−	0.103146i
$341$		0			0
$342$		−	14.1421i		−	0.764719i
$343$		0			0
$344$		0			0
$345$	18.9282	−	16.7846i	1.01906	−	0.903653i
$346$	2.12132	+	3.67423i	0.114043	+	0.197528i
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	−0.302374	−	0.953189i	$-0.597779\pi$
$347$	6.92820	−	4.00000i	0.371925	−	0.214731i	0.674299	+	0.738458i	$0.264446\pi$
$348$		0			0
$349$	−1.41421			−0.0757011			−0.0378506	−	0.999283i	$-0.512051\pi$
$349$	−1.41421			−0.0757011			−0.0378506	+	0.999283i	$0.512051\pi$
$350$		0			0
$351$	24.0000			1.28103
$352$		0			0
$353$	−13.4722	+	7.77817i	−0.717053	+	0.413990i	−0.813667	−	0.581331i	$-0.802532\pi$
$353$	−13.4722	+	7.77817i	−0.717053	+	0.413990i	0.0966144	+	0.995322i	$0.469199\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$	20.0764	−	17.8028i	1.06554	−	0.944873i
$356$	4.24264			0.224860
$357$		0			0
$358$		−	12.0000i		−	0.634220i
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$	32.8601	−	6.72432i	1.73188	−	0.354403i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	15.9217	+	9.19239i	0.836825	+	0.483141i
$363$		−	31.1127i		−	1.63299i
$364$		0			0
$365$	−9.00000	+	27.0000i	−0.471082	+	1.41324i
$366$	14.0000	−	24.2487i	0.731792	−	1.26750i
$367$	14.6969	−	8.48528i	0.767174	−	0.442928i	−0.0646916	−	0.997905i	$-0.520606\pi$
$367$	14.6969	−	8.48528i	0.767174	−	0.442928i	0.831866	+	0.554977i	$0.187273\pi$
$368$	3.46410	−	2.00000i	0.180579	−	0.104257i
$369$	10.6066	−	18.3712i	0.552158	−	0.956365i
$370$	12.7279	+	4.24264i	0.661693	+	0.220564i
$371$		0			0
$372$			16.0000i			0.829561i
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.146321	−	0.989237i	$-0.546743\pi$
$373$	−20.7846	−	12.0000i	−1.07619	−	0.621336i	−0.929865	+	0.367901i	$0.880077\pi$
$374$		0			0
$375$	−28.5885	−	13.5167i	−1.47630	−	0.697997i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	24.0000			1.23280			0.616399	−	0.787434i	$-0.288591\pi$
$379$	24.0000			1.23280			0.616399	+	0.787434i	$0.288591\pi$
$380$	4.73205	−	4.19615i	0.242749	−	0.215258i
$381$	−16.9706	−	29.3939i	−0.869428	−	1.50589i
$382$	10.3923	−	6.00000i	0.531717	−	0.306987i
$383$	29.3939	+	16.9706i	1.50196	+	0.867155i	0.999997	+	0.00226413i	$0.000720695\pi$
$383$	29.3939	+	16.9706i	1.50196	+	0.867155i	0.501960	+	0.864891i	$0.332613\pi$
$384$	−8.48528			−0.433013
$385$		0			0
$386$	24.0000			1.22157
$387$		0			0
$388$	3.67423	−	2.12132i	0.186531	−	0.107694i
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$	−17.8028	−	20.0764i	−0.901478	−	1.01661i
$391$	−16.9706			−0.858238
$392$		0			0
$393$		−	24.0000i		−	1.21064i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	−5.37945	−	26.2880i	−0.270670	−	1.32270i
$396$		0			0
$397$	−3.67423	−	2.12132i	−0.184405	−	0.106466i	0.404956	−	0.914336i	$-0.367287\pi$
$397$	−3.67423	−	2.12132i	−0.184405	−	0.106466i	−0.589360	+	0.807870i	$0.700620\pi$
$398$			11.3137i			0.567105i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$	29.3939	−	16.9706i	1.46603	−	0.846415i
$403$	20.7846	−	12.0000i	1.03536	−	0.597763i
$404$	2.12132	−	3.67423i	0.105540	−	0.182800i
$405$	−2.12132	−	0.707107i	−0.105409	−	0.0351364i
$406$		0			0
$407$		0			0
$408$	−31.1769	−	18.0000i	−1.54349	−	0.891133i
$409$	9.19239	+	15.9217i	0.454534	+	0.787277i	0.998661	−	0.0517263i	$-0.0164724\pi$
$409$	9.19239	+	15.9217i	0.454534	+	0.787277i	−0.544127	+	0.839003i	$0.683139\pi$
$410$	−9.29423	+	1.90192i	−0.459009	+	0.0939293i
$411$	−19.7990	+	34.2929i	−0.976612	+	1.69154i
$412$		0			0
$413$		0			0
$414$	−20.0000			−0.982946
$415$	−12.5885	−	14.1962i	−0.617943	−	0.696862i
$416$	10.6066	+	18.3712i	0.520031	+	0.900721i
$417$	−6.92820	+	4.00000i	−0.339276	+	0.195881i
$418$		0			0
$419$	−8.48528			−0.414533			−0.207267	−	0.978285i	$-0.566457\pi$
$419$	−8.48528			−0.414533			−0.207267	+	0.978285i	$0.566457\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	−3.46410	−	2.00000i	−0.168630	−	0.0973585i
$423$		0			0
$424$	12.0000	+	20.7846i	0.582772	+	1.00939i
$425$	8.33298	+	19.5080i	0.404209	+	0.946276i
$426$	−33.9411			−1.64445
$427$		0			0
$428$			4.00000i			0.193347i
$429$		0			0
$430$		0			0
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	−0.995706	−	0.0925683i	$-0.970492\pi$
$431$	−12.0000	−	20.7846i	−0.578020	−	1.00116i	0.417687	−	0.908591i	$-0.362841\pi$
$432$	−4.89898	−	2.82843i	−0.235702	−	0.136083i
$433$		−	4.24264i		−	0.203888i	−0.994790	−	0.101944i	$-0.967494\pi$
$433$		−	4.24264i		−	0.203888i	0.994790	−	0.101944i	$-0.0325063\pi$
$434$		0			0
$435$		0			0
$436$	−8.00000	+	13.8564i	−0.383131	+	0.663602i
$437$	−9.79796	+	5.65685i	−0.468700	+	0.270604i
$438$	31.1769	−	18.0000i	1.48969	−	0.860073i
$439$	14.1421	−	24.4949i	0.674967	−	1.16908i	−0.301511	−	0.953463i	$-0.597491\pi$
$439$	14.1421	−	24.4949i	0.674967	−	1.16908i	0.976478	−	0.215615i	$-0.0691756\pi$
$440$		0			0
$441$		0			0
$442$			18.0000i			0.856173i
$443$	−3.46410	−	2.00000i	−0.164584	−	0.0950229i	0.415445	−	0.909618i	$-0.363626\pi$
$443$	−3.46410	−	2.00000i	−0.164584	−	0.0950229i	−0.580030	+	0.814595i	$0.696959\pi$
$444$	8.48528	+	14.6969i	0.402694	+	0.697486i
$445$	1.90192	+	9.29423i	0.0901598	+	0.440589i
$446$		0			0
$447$			16.9706i			0.802680i
$448$		0			0
$449$	18.0000			0.849473			0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000			0.849473			0.424736	+	0.905317i	$0.360367\pi$
$450$	9.82051	+	22.9904i	0.462943	+	1.08378i
$451$		0			0
$452$	−6.92820	+	4.00000i	−0.325875	+	0.188144i
$453$		0			0
$454$	−2.82843			−0.132745
$455$		0			0
$456$	−24.0000			−1.12390
$457$	20.7846	+	12.0000i	0.972263	+	0.561336i	0.899925	−	0.436044i	$-0.143621\pi$
$457$	20.7846	+	12.0000i	0.972263	+	0.561336i	0.0723376	+	0.997380i	$0.476954\pi$
$458$	−6.12372	+	3.53553i	−0.286143	+	0.165205i
$459$	12.0000	+	20.7846i	0.560112	+	0.970143i
$460$	−5.93426	−	6.69213i	−0.276686	−	0.312022i
$461$	21.2132			0.987997			0.493999	−	0.869463i	$-0.335535\pi$
$461$	21.2132			0.987997			0.493999	+	0.869463i	$0.335535\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	−35.0507	+	7.17260i	−1.62544	+	0.332622i
$466$	7.00000	+	12.1244i	0.324269	+	0.561650i
$467$	26.9444	+	15.5563i	1.24684	+	0.719862i	0.970477	−	0.241192i	$-0.0775384\pi$
$467$	26.9444	+	15.5563i	1.24684	+	0.719862i	0.276360	+	0.961054i	$0.410872\pi$
$468$		−	21.2132i		−	0.980581i
$469$		0			0
$470$		0			0
$471$	6.00000	−	10.3923i	0.276465	−	0.478852i
$472$	−22.0454	+	12.7279i	−1.01472	+	0.585850i
$473$		0			0
$474$	−16.9706	+	29.3939i	−0.779484	+	1.35011i
$475$	11.3137	+	8.48528i	0.519109	+	0.389331i
$476$		0			0
$477$		−	40.0000i		−	1.83147i
$478$	20.7846	+	12.0000i	0.950666	+	0.548867i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−6.33975	−	30.9808i	−0.289368	−	1.41407i
$481$	12.7279	−	22.0454i	0.580343	−	1.00518i
$482$		−	9.89949i		−	0.450910i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	6.29423	+	7.09808i	0.285806	+	0.322307i
$486$	−7.07107	−	12.2474i	−0.320750	−	0.555556i
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	−0.716625	−	0.697459i	$-0.754314\pi$
$487$	−10.3923	+	6.00000i	−0.470920	+	0.271886i	0.245705	+	0.969345i	$0.420981\pi$
$488$	−25.7196	−	14.8492i	−1.16427	−	0.672194i
$489$	67.8823			3.06974
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−10.3923	−	6.00000i	−0.468521	−	0.270501i
$493$		0			0
$494$	6.00000	+	10.3923i	0.269953	+	0.467572i
$495$		0			0
$496$	−5.65685			−0.254000
$497$		0			0
$498$			24.0000i			1.07547i
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	−0.968500	−	0.249015i	$-0.919893\pi$
$499$	−6.00000	+	10.3923i	−0.268597	+	0.465223i	0.699903	+	0.714238i	$0.253227\pi$
$500$	−4.77886	+	10.1075i	−0.213717	+	0.452023i
$501$	16.0000	+	27.7128i	0.714827	+	1.23812i
$502$	−22.0454	−	12.7279i	−0.983935	−	0.568075i
$503$		−	16.9706i		−	0.756680i	−0.925667	−	0.378340i	$-0.876495\pi$
$503$		−	16.9706i		−	0.756680i	0.925667	−	0.378340i	$-0.123505\pi$
$504$		0			0
$505$	9.00000	+	3.00000i	0.400495	+	0.133498i
$506$		0			0
$507$	−12.2474	+	7.07107i	−0.543928	+	0.314037i
$508$	−10.3923	+	6.00000i	−0.461084	+	0.266207i
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	−0.971896	−	0.235409i	$-0.924357\pi$
$509$	−6.36396	+	11.0227i	−0.282078	+	0.488573i	0.689819	+	0.723982i	$0.257690\pi$
$510$	8.48528	−	25.4558i	0.375735	−	1.12720i
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$	13.8564	+	8.00000i	0.611775	+	0.353209i
$514$	13.4350	+	23.2702i	0.592594	+	1.02640i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−12.0000			−0.526742
$520$	−21.2942	+	18.8827i	−0.933814	+	0.828061i
$521$	−14.8492	−	25.7196i	−0.650557	−	1.12680i	−0.982988	−	0.183670i	$-0.941202\pi$
$521$	−14.8492	−	25.7196i	−0.650557	−	1.12680i	0.332431	−	0.943128i	$-0.392131\pi$
$522$		0			0
$523$	−7.34847	−	4.24264i	−0.321326	−	0.185518i	0.330657	−	0.943751i	$-0.392730\pi$
$523$	−7.34847	−	4.24264i	−0.321326	−	0.185518i	−0.651984	+	0.758233i	$0.726063\pi$
$524$	−8.48528			−0.370681
$525$		0			0
$526$	−16.0000			−0.697633
$527$	20.7846	+	12.0000i	0.905392	+	0.522728i
$528$		0			0
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$	−13.3843	+	11.8685i	−0.581375	+	0.515535i
$531$	42.4264			1.84115
$532$		0			0
$533$			18.0000i			0.779667i
$534$	6.00000	−	10.3923i	0.259645	−	0.449719i
$535$	−8.76268	+	1.79315i	−0.378844	+	0.0775247i
$536$	−18.0000	−	31.1769i	−0.777482	−	1.34664i
$537$	29.3939	+	16.9706i	1.26844	+	0.732334i
$538$			21.2132i			0.914566i
$539$		0			0
$540$	−4.00000	+	12.0000i	−0.172133	+	0.516398i
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	−0.992036	−	0.125952i	$-0.959801\pi$
$541$	−9.00000	+	15.5885i	−0.386940	+	0.670200i	0.605096	+	0.796152i	$0.293135\pi$
$542$	−4.89898	+	2.82843i	−0.210429	+	0.121491i
$543$	−45.0333	+	26.0000i	−1.93256	+	1.11577i
$544$	−10.6066	+	18.3712i	−0.454754	+	0.787658i
$545$	−33.9411	−	11.3137i	−1.45388	−	0.484626i
$546$		0			0
$547$		−	24.0000i		−	1.02617i	−0.858339	−	0.513083i	$-0.828503\pi$
$547$		−	24.0000i		−	1.02617i	0.858339	−	0.513083i	$-0.171497\pi$
$548$	12.1244	+	7.00000i	0.517927	+	0.299025i
$549$	24.7487	+	42.8661i	1.05625	+	1.82948i
$550$		0			0
$551$		0			0
$552$			33.9411i			1.44463i
$553$		0			0
$554$	−24.0000			−1.01966
$555$	−28.3923	+	25.1769i	−1.20519	+	1.06870i
$556$	1.41421	+	2.44949i	0.0599760	+	0.103882i
$557$	34.6410	−	20.0000i	1.46779	−	0.847427i	0.468438	−	0.883497i	$-0.344817\pi$
$557$	34.6410	−	20.0000i	1.46779	−	0.847427i	0.999349	+	0.0360693i	$0.0114837\pi$
$558$	24.4949	+	14.1421i	1.03695	+	0.598684i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	22.0454	−	12.7279i	0.929103	−	0.536418i	0.0425753	−	0.999093i	$-0.486444\pi$
$563$	22.0454	−	12.7279i	0.929103	−	0.536418i	0.886528	+	0.462675i	$0.153110\pi$
$564$		0			0
$565$	−11.8685	−	13.3843i	−0.499312	−	0.563080i
$566$	25.4558			1.06999
$567$		0			0
$568$			36.0000i			1.51053i
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	−0.496928	−	0.867792i	$-0.665539\pi$
$569$	12.0000	−	20.7846i	0.503066	−	0.871336i	0.999994	−	0.00354413i	$-0.00112814\pi$
$570$	−3.58630	−	17.5254i	−0.150214	−	0.734057i
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$			33.9411i			1.41791i
$574$		0			0
$575$	12.0000	−	16.0000i	0.500435	−	0.667246i
$576$	−17.5000	+	30.3109i	−0.729167	+	1.26295i
$577$	33.0681	−	19.0919i	1.37664	−	0.794805i	0.384890	−	0.922963i	$-0.374240\pi$
$577$	33.0681	−	19.0919i	1.37664	−	0.794805i	0.991754	+	0.128157i	$0.0409062\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$	−33.9411	+	58.7878i	−1.41055	+	2.44314i
$580$		0			0
$581$		0			0
$582$		−	12.0000i		−	0.497416i
$583$		0			0
$584$	−19.0919	−	33.0681i	−0.790028	−	1.36837i
$585$	46.4711	−	9.50962i	1.92135	−	0.393174i
$586$	0.707107	−	1.22474i	0.0292103	−	0.0505937i
$587$		−	42.4264i		−	1.75113i	−0.483105	−	0.875563i	$-0.660491\pi$
$587$		−	42.4264i		−	1.75113i	0.483105	−	0.875563i	$-0.339509\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	−12.5885	−	14.1962i	−0.518259	−	0.584446i
$591$	−11.3137	−	19.5959i	−0.465384	−	0.806068i
$592$	−5.19615	+	3.00000i	−0.213561	+	0.123299i
$593$	−6.12372	−	3.53553i	−0.251471	−	0.145187i	0.368967	−	0.929443i	$-0.379712\pi$
$593$	−6.12372	−	3.53553i	−0.251471	−	0.145187i	−0.620438	+	0.784256i	$0.713045\pi$
$594$		0			0
$595$		0			0
$596$	6.00000			0.245770
$597$	−27.7128	−	16.0000i	−1.13421	−	0.654836i
$598$	14.6969	−	8.48528i	0.601003	−	0.346989i
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$	39.0160	−	16.6660i	1.59282	−	0.680385i
$601$	−41.0122			−1.67292			−0.836461	−	0.548026i	$-0.815379\pi$
$601$	−41.0122			−1.67292			−0.836461	+	0.548026i	$0.815379\pi$
$602$		0			0
$603$			60.0000i			2.44339i
$604$		0			0
$605$	−4.93117	−	24.0974i	−0.200480	−	0.979698i
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	29.3939	+	16.9706i	1.19306	+	0.688814i	0.958999	−	0.283408i	$-0.0914650\pi$
$607$	29.3939	+	16.9706i	1.19306	+	0.688814i	0.234061	+	0.972222i	$0.424798\pi$
$608$			14.1421i			0.573539i
$609$		0			0
$610$	7.00000	−	21.0000i	0.283422	−	0.850265i
$611$		0			0
$612$	18.3712	−	10.6066i	0.742611	−	0.428746i
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	−0.391381	−	0.920229i	$-0.628002\pi$
$613$	5.19615	−	3.00000i	0.209871	−	0.121169i	0.601251	+	0.799060i	$0.294669\pi$
$614$	12.7279	−	22.0454i	0.513657	−	0.889680i
$615$	8.48528	−	25.4558i	0.342160	−	1.02648i
$616$		0			0
$617$			38.0000i			1.52982i	0.644136	+	0.764911i	$0.277217\pi$
$617$			38.0000i			1.52982i	−0.644136	+	0.764911i	$0.722783\pi$
$618$		0			0
$619$	−9.89949	−	17.1464i	−0.397894	−	0.689173i	0.595572	−	0.803302i	$-0.296926\pi$
$619$	−9.89949	−	17.1464i	−0.397894	−	0.689173i	−0.993466	+	0.114129i	$0.963592\pi$
$620$	2.53590	+	12.3923i	0.101844	+	0.497687i
$621$	11.3137	−	19.5959i	0.454003	−	0.786357i
$622$		−	33.9411i		−	1.36092i
$623$		0			0
$624$	12.0000			0.480384
$625$	−24.2846	−	5.93782i	−0.971384	−	0.237513i
$626$	10.6066	+	18.3712i	0.423925	+	0.734260i
$627$		0			0
$628$	−3.67423	−	2.12132i	−0.146618	−	0.0846499i
$629$	25.4558			1.01499
$630$		0			0
$631$	12.0000			0.477712			0.238856	−	0.971055i	$-0.423228\pi$
$631$	12.0000			0.477712			0.238856	+	0.971055i	$0.423228\pi$
$632$	31.1769	+	18.0000i	1.24015	+	0.716002i
$633$	9.79796	−	5.65685i	0.389434	−	0.224840i
$634$	4.00000	+	6.92820i	0.158860	+	0.275154i
$635$	−17.8028	−	20.0764i	−0.706481	−	0.796707i
$636$	−22.6274			−0.897235
$637$		0			0
$638$		0			0
$639$	30.0000	−	51.9615i	1.18678	−	2.05557i
$640$	−6.57201	+	1.34486i	−0.259782	+	0.0531604i
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$	9.79796	+	5.65685i	0.386695	+	0.223258i
$643$		−	8.48528i		−	0.334627i	−0.985904	−	0.167313i	$-0.946491\pi$
$643$		−	8.48528i		−	0.334627i	0.985904	−	0.167313i	$-0.0535092\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−4.89898	+	2.82843i	−0.192599	+	0.111197i	−0.593199	−	0.805056i	$-0.702135\pi$
$647$	−4.89898	+	2.82843i	−0.192599	+	0.111197i	0.400600	+	0.916253i	$0.368802\pi$
$648$	2.59808	−	1.50000i	0.102062	−	0.0589256i
$649$		0			0
$650$	−16.9706	−	12.7279i	−0.665640	−	0.499230i
$651$		0			0
$652$		−	24.0000i		−	0.939913i
$653$	1.73205	+	1.00000i	0.0677804	+	0.0391330i	0.533507	−	0.845796i	$-0.320874\pi$
$653$	1.73205	+	1.00000i	0.0677804	+	0.0391330i	−0.465727	+	0.884929i	$0.654207\pi$
$654$	22.6274	+	39.1918i	0.884802	+	1.53252i
$655$	−3.80385	−	18.5885i	−0.148629	−	0.726311i
$656$	2.12132	−	3.67423i	0.0828236	−	0.143455i
$657$			63.6396i			2.48282i
$658$		0			0
$659$	−48.0000			−1.86981			−0.934907	−	0.354892i	$-0.884518\pi$
$659$	−48.0000			−1.86981			−0.934907	+	0.354892i	$0.884518\pi$
$660$		0			0
$661$	7.77817	+	13.4722i	0.302536	+	0.524008i	0.976710	−	0.214565i	$-0.0688334\pi$
$661$	7.77817	+	13.4722i	0.302536	+	0.524008i	−0.674174	+	0.738573i	$0.735500\pi$
$662$	−6.92820	+	4.00000i	−0.269272	+	0.155464i
$663$	−44.0908	−	25.4558i	−1.71235	−	0.988623i
$664$	25.4558			0.987878
$665$		0			0
$666$	30.0000			1.16248
$667$		0			0
$668$	9.79796	−	5.65685i	0.379094	−	0.218870i
$669$		0			0
$670$	20.0764	−	17.8028i	0.775619	−	0.687781i
$671$		0			0
$672$		0			0
$673$		−	6.00000i		−	0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$673$		−	6.00000i		−	0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$674$	9.00000	−	15.5885i	0.346667	−	0.600445i
$675$	−28.0812	−	3.38323i	−1.08085	−	0.130221i
$676$	2.50000	+	4.33013i	0.0961538	+	0.166543i
$677$	−8.57321	−	4.94975i	−0.329495	−	0.190234i	0.326122	−	0.945328i	$-0.394258\pi$
$677$	−8.57321	−	4.94975i	−0.329495	−	0.190234i	−0.655617	+	0.755094i	$0.727591\pi$
$678$			22.6274i			0.869001i
$679$		0			0
$680$	−27.0000	−	9.00000i	−1.03540	−	0.345134i
$681$	4.00000	−	6.92820i	0.153280	−	0.265489i
$682$		0			0
$683$	−24.2487	+	14.0000i	−0.927851	+	0.535695i	−0.886131	−	0.463434i	$-0.846617\pi$
$683$	−24.2487	+	14.0000i	−0.927851	+	0.535695i	−0.0417198	+	0.999129i	$0.513284\pi$
$684$	7.07107	−	12.2474i	0.270369	−	0.468293i
$685$	−9.89949	+	29.6985i	−0.378240	+	1.13472i
$686$		0			0
$687$		−	20.0000i		−	0.763048i
$688$		0			0
$689$	16.9706	+	29.3939i	0.646527	+	1.11982i
$690$	−24.7846	+	5.07180i	−0.943534	+	0.193080i
$691$	−1.41421	+	2.44949i	−0.0537992	+	0.0931830i	−0.891671	−	0.452684i	$-0.850466\pi$
$691$	−1.41421	+	2.44949i	−0.0537992	+	0.0931830i	0.837872	+	0.545867i	$0.183800\pi$
$692$			4.24264i			0.161281i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	−4.73205	+	4.19615i	−0.179497	+	0.159169i
$696$		0			0
$697$	−15.5885	+	9.00000i	−0.590455	+	0.340899i
$698$	1.22474	+	0.707107i	0.0463573	+	0.0267644i
$699$	−39.5980			−1.49773
$700$		0			0
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$	−20.7846	−	12.0000i	−0.784465	−	0.452911i
$703$	14.6969	−	8.48528i	0.554306	−	0.320028i
$704$		0			0
$705$		0			0
$706$	15.5563			0.585471
$707$		0			0
$708$		−	24.0000i		−	0.901975i
$709$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$709$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$710$	−26.2880	+	5.37945i	−0.986573	+	0.201887i
$711$	−30.0000	−	51.9615i	−1.12509	−	1.94871i
$712$	−11.0227	−	6.36396i	−0.413093	−	0.238500i
$713$		−	22.6274i		−	0.847403i
$714$		0			0
$715$		0			0
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	−58.7878	+	33.9411i	−2.19547	+	1.26755i
$718$	−20.7846	+	12.0000i	−0.775675	+	0.447836i
$719$	−8.48528	+	14.6969i	−0.316448	+	0.548103i	−0.979744	−	0.200253i	$-0.935823\pi$
$719$	−8.48528	+	14.6969i	−0.316448	+	0.548103i	0.663297	+	0.748357i	$0.269157\pi$
$720$	−10.6066	−	3.53553i	−0.395285	−	0.131762i
$721$		0			0
$722$		−	11.0000i		−	0.409378i
$723$	24.2487	+	14.0000i	0.901819	+	0.520666i
$724$	9.19239	+	15.9217i	0.341632	+	0.591725i
$725$		0			0
$726$	−15.5563	+	26.9444i	−0.577350	+	1.00000i
$727$		−	33.9411i		−	1.25881i	−0.777079	−	0.629403i	$-0.783299\pi$
$727$		−	33.9411i		−	1.25881i	0.777079	−	0.629403i	$-0.216701\pi$
$728$		0			0
$729$	43.0000			1.59259
$730$	21.2942	−	18.8827i	0.788135	−	0.698880i
$731$		0			0
$732$	24.2487	−	14.0000i	0.896258	−	0.517455i
$733$	3.67423	+	2.12132i	0.135711	+	0.0783528i	0.566318	−	0.824187i	$-0.308367\pi$
$733$	3.67423	+	2.12132i	0.135711	+	0.0783528i	−0.430607	+	0.902539i	$0.641701\pi$
$734$	−16.9706			−0.626395
$735$		0			0
$736$	20.0000			0.737210
$737$		0			0
$738$	−18.3712	+	10.6066i	−0.676252	+	0.390434i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$	8.90138	+	10.0382i	0.327221	+	0.369011i
$741$	−33.9411			−1.24686
$742$		0			0
$743$		−	28.0000i		−	1.02722i	−0.858024	−	0.513610i	$-0.828308\pi$
$743$		−	28.0000i		−	1.02722i	0.858024	−	0.513610i	$-0.171692\pi$
$744$	24.0000	−	41.5692i	0.879883	−	1.52400i
$745$	2.68973	+	13.1440i	0.0985440	+	0.481560i
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$	−36.7423	−	21.2132i	−1.34433	−	0.776151i
$748$		0			0
$749$		0			0
$750$	18.0000	+	26.0000i	0.657267	+	0.949386i
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$		0			0
$753$	62.3538	−	36.0000i	2.27230	−	1.31191i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	6.00000i		−	0.218074i	−0.994038	−	0.109037i	$-0.965223\pi$
$757$		−	6.00000i		−	0.218074i	0.994038	−	0.109037i	$-0.0347767\pi$
$758$	−20.7846	−	12.0000i	−0.754931	−	0.435860i
$759$		0			0
$760$	−18.5885	+	3.80385i	−0.674274	+	0.137980i
$761$	14.8492	−	25.7196i	0.538285	−	0.932336i	−0.460712	−	0.887550i	$-0.652406\pi$
$761$	14.8492	−	25.7196i	0.538285	−	0.932336i	0.998997	−	0.0447866i	$-0.0142608\pi$
$762$			33.9411i			1.22956i
$763$		0			0
$764$	12.0000			0.434145
$765$	31.4711	+	35.4904i	1.13784	+	1.28316i
$766$	−16.9706	−	29.3939i	−0.613171	−	1.06204i
$767$	−31.1769	+	18.0000i	−1.12573	+	0.649942i
$768$	41.6413	+	24.0416i	1.50260	+	0.867528i
$769$	−24.0416			−0.866963			−0.433482	−	0.901162i	$-0.642715\pi$
$769$	−24.0416			−0.866963			−0.433482	+	0.901162i	$0.642715\pi$
$770$		0			0
$771$	−76.0000			−2.73707
$772$	20.7846	+	12.0000i	0.748054	+	0.431889i
$773$	−18.3712	+	10.6066i	−0.660765	+	0.381493i	−0.792568	−	0.609783i	$-0.791257\pi$
$773$	−18.3712	+	10.6066i	−0.660765	+	0.381493i	0.131803	+	0.991276i	$0.457923\pi$
$774$		0			0
$775$	−26.0106	+	11.1106i	−0.934330	+	0.399106i
$776$	−12.7279			−0.456906
$777$		0			0
$778$		0			0
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$	−5.37945	−	26.2880i	−0.192615	−	0.941263i
$781$		0			0
$782$	14.6969	+	8.48528i	0.525561	+	0.303433i
$783$		0			0
$784$		0			0
$785$	3.00000	−	9.00000i	0.107075	−	0.321224i
$786$	−12.0000	+	20.7846i	−0.428026	+	0.741362i
$787$	−7.34847	+	4.24264i	−0.261945	+	0.151234i	−0.625221	−	0.780447i	$-0.714991\pi$
$787$	−7.34847	+	4.24264i	−0.261945	+	0.151234i	0.363277	+	0.931681i	$0.381658\pi$
$788$	−6.92820	+	4.00000i	−0.246807	+	0.142494i
$789$	22.6274	−	39.1918i	0.805557	−	1.39527i
$790$	−8.48528	+	25.4558i	−0.301893	+	0.905678i
$791$		0			0
$792$		0			0
$793$	−36.3731	−	21.0000i	−1.29165	−	0.745732i
$794$	2.12132	+	3.67423i	0.0752828	+	0.130394i
$795$	−10.1436	−	49.5692i	−0.359756	−	1.75804i
$796$	−5.65685	+	9.79796i	−0.200502	+	0.347279i
$797$			4.24264i			0.150282i	0.997173	+	0.0751410i	$0.0239407\pi$
$797$			4.24264i			0.150282i	−0.997173	+	0.0751410i	$0.976059\pi$
$798$		0			0
$799$		0			0
$800$	−9.82051	−	22.9904i	−0.347207	−	0.812833i
$801$	10.6066	+	18.3712i	0.374766	+	0.649113i
$802$	20.7846	−	12.0000i	0.733930	−	0.423735i
$803$		0			0
$804$	33.9411			1.19701
$805$		0			0
$806$	−24.0000			−0.845364
$807$	−51.9615	−	30.0000i	−1.82913	−	1.05605i
$808$	−11.0227	+	6.36396i	−0.387777	+	0.223883i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$	1.48356	+	1.67303i	0.0521271	+	0.0587844i
$811$	14.1421			0.496598			0.248299	−	0.968683i	$-0.420129\pi$
$811$	14.1421			0.496598			0.248299	+	0.968683i	$0.420129\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$	52.5761	−	10.7589i	1.84166	−	0.376868i
$816$	6.00000	+	10.3923i	0.210042	+	0.363803i
$817$		0			0
$818$		−	18.3848i		−	0.642809i
$819$		0			0
$820$	−9.00000	−	3.00000i	−0.314294	−	0.104765i
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	34.2929	−	19.7990i	1.19610	−	0.690569i
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	−0.0919029	−	0.995768i	$-0.529295\pi$
$823$	20.7846	−	12.0000i	0.724506	−	0.418294i	0.816409	+	0.577474i	$0.195962\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			52.0000i			1.80822i	0.427303	+	0.904109i	$0.359464\pi$
$827$			52.0000i			1.80822i	−0.427303	+	0.904109i	$0.640536\pi$
$828$	−17.3205	−	10.0000i	−0.601929	−	0.347524i
$829$	12.0208	+	20.8207i	0.417500	+	0.723132i	0.995687	−	0.0927727i	$-0.0295730\pi$
$829$	12.0208	+	20.8207i	0.417500	+	0.723132i	−0.578187	+	0.815904i	$0.696240\pi$
$830$	3.80385	+	18.5885i	0.132033	+	0.645215i
$831$	33.9411	−	58.7878i	1.17740	−	2.03932i
$832$		−	29.6985i		−	1.02961i
$833$		0			0
$834$	8.00000			0.277017
$835$	16.7846	+	18.9282i	0.580855	+	0.655037i
$836$		0			0
$837$	−27.7128	+	16.0000i	−0.957895	+	0.553041i
$838$	7.34847	+	4.24264i	0.253849	+	0.146560i
$839$	−16.9706			−0.585889			−0.292944	−	0.956129i	$-0.594635\pi$
$839$	−16.9706			−0.585889			−0.292944	+	0.956129i	$0.594635\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	5.19615	+	3.00000i	0.179071	+	0.103387i
$843$		0			0
$844$	−2.00000	−	3.46410i	−0.0688428	−	0.119239i
$845$	−8.36516	+	7.41782i	−0.287770	+	0.255181i
$846$		0			0
$847$		0			0
$848$		−	8.00000i		−	0.274721i
$849$	−36.0000	+	62.3538i	−1.23552	+	2.13998i
$850$	2.53742	−	21.0609i	0.0870329	−	0.722383i
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−29.3939	−	16.9706i	−1.00702	−	0.581402i
$853$		−	12.7279i		−	0.435796i	−0.975972	−	0.217898i	$-0.930080\pi$
$853$		−	12.7279i		−	0.435796i	0.975972	−	0.217898i	$-0.0699200\pi$
$854$		0			0
$855$	30.0000	+	10.0000i	1.02598	+	0.341993i
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	47.7650	−	27.5772i	1.63162	−	0.942018i	0.648030	−	0.761615i	$-0.275593\pi$
$857$	47.7650	−	27.5772i	1.63162	−	0.942018i	0.983593	−	0.180403i	$-0.0577403\pi$
$858$		0			0
$859$	−15.5563	+	26.9444i	−0.530776	+	0.919331i	0.468579	+	0.883421i	$0.344766\pi$
$859$	−15.5563	+	26.9444i	−0.530776	+	0.919331i	−0.999355	+	0.0359092i	$0.988567\pi$
$860$		0			0
$861$		0			0
$862$			24.0000i			0.817443i
$863$	−13.8564	−	8.00000i	−0.471678	−	0.272323i	0.245264	−	0.969456i	$-0.421125\pi$
$863$	−13.8564	−	8.00000i	−0.471678	−	0.272323i	−0.716942	+	0.697133i	$0.754459\pi$
$864$	−14.1421	−	24.4949i	−0.481125	−	0.833333i
$865$	−9.29423	+	1.90192i	−0.316013	+	0.0646673i
$866$	−2.12132	+	3.67423i	−0.0720854	+	0.124856i
$867$		−	2.82843i		−	0.0960584i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−25.4558	−	44.0908i	−0.862538	−	1.49396i
$872$	41.5692	−	24.0000i	1.40771	−	0.812743i
$873$	18.3712	+	10.6066i	0.621770	+	0.358979i
$874$	11.3137			0.382692
$875$		0			0
$876$	36.0000			1.21633
$877$	25.9808	+	15.0000i	0.877308	+	0.506514i	0.869770	−	0.493458i	$-0.164267\pi$
$877$	25.9808	+	15.0000i	0.877308	+	0.506514i	0.00753813	+	0.999972i	$0.497601\pi$
$878$	−24.4949	+	14.1421i	−0.826663	+	0.477274i
$879$	2.00000	+	3.46410i	0.0674583	+	0.116841i
$880$		0			0
$881$	46.6690			1.57232			0.786160	−	0.618023i	$-0.212066\pi$
$881$	46.6690			1.57232			0.786160	+	0.618023i	$0.212066\pi$
$882$		0			0
$883$		−	36.0000i		−	1.21150i	−0.795656	−	0.605748i	$-0.792874\pi$
$883$		−	36.0000i		−	1.21150i	0.795656	−	0.605748i	$-0.207126\pi$
$884$	−9.00000	+	15.5885i	−0.302703	+	0.524297i
$885$	52.5761	−	10.7589i	1.76733	−	0.361657i
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$	14.6969	+	8.48528i	0.493475	+	0.284908i	0.726015	−	0.687679i	$-0.241370\pi$
$887$	14.6969	+	8.48528i	0.493475	+	0.284908i	−0.232540	+	0.972587i	$0.574704\pi$
$888$		−	50.9117i		−	1.70848i
$889$		0			0
$890$	3.00000	−	9.00000i	0.100560	−	0.301681i
$891$		0			0
$892$		0			0
$893$		0			0
$894$	8.48528	−	14.6969i	0.283790	−	0.491539i
$895$	25.4558	+	8.48528i	0.850895	+	0.283632i
$896$		0			0
$897$			48.0000i			1.60267i
$898$	−15.5885	−	9.00000i	−0.520194	−	0.300334i
$899$		0			0
$900$	−2.99038	+	24.8205i	−0.0996794	+	0.827350i
$901$	−16.9706	+	29.3939i	−0.565371	+	0.979252i
$902$		0			0
$903$		0			0
$904$	24.0000			0.798228
$905$	−30.7583	+	27.2750i	−1.02244	+	0.906651i
$906$		0			0
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	−0.662512	−	0.749051i	$-0.730510\pi$
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	0.317441	+	0.948278i	$0.397176\pi$
$908$	−2.44949	−	1.41421i	−0.0812892	−	0.0469323i
$909$	21.2132			0.703598
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	6.92820	+	4.00000i	0.229416	+	0.132453i
$913$		0			0
$914$	−12.0000	−	20.7846i	−0.396925	−	0.687494i
$915$	41.5398	+	46.8449i	1.37326	+	1.54865i
$916$	−7.07107			−0.233635
$917$		0			0
$918$		−	24.0000i		−	0.792118i
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	−0.652616	−	0.757689i	$-0.726329\pi$
$919$	10.0000	−	17.3205i	0.329870	−	0.571351i	0.982486	+	0.186338i	$0.0596619\pi$
$920$	5.37945	+	26.2880i	0.177355	+	0.866691i
$921$	36.0000	+	62.3538i	1.18624	+	2.05463i
$922$	−18.3712	−	10.6066i	−0.605022	−	0.349310i
$923$			50.9117i			1.67578i
$924$		0			0
$925$	−18.0000	+	24.0000i	−0.591836	+	0.789115i
$926$	−12.0000	+	20.7846i	−0.394344	+	0.683025i
$927$		0			0
$928$		0			0
$929$	−6.36396	+	11.0227i	−0.208795	+	0.361643i	−0.951335	−	0.308158i	$-0.900287\pi$
$929$	−6.36396	+	11.0227i	−0.208795	+	0.361643i	0.742540	+	0.669801i	$0.233621\pi$
$930$	33.9411	+	11.3137i	1.11297	+	0.370991i
$931$		0			0
$932$			14.0000i			0.458585i
$933$	83.1384	+	48.0000i	2.72183	+	1.57145i
$934$	−15.5563	−	26.9444i	−0.509019	−	0.881647i
$935$		0			0
$936$	−31.8198	+	55.1135i	−1.04006	+	1.80144i
$937$		−	12.7279i		−	0.415803i	−0.978150	−	0.207902i	$-0.933337\pi$
$937$		−	12.7279i		−	0.415803i	0.978150	−	0.207902i	$-0.0666634\pi$
$938$		0			0
$939$	−60.0000			−1.95803
$940$		0			0
$941$	10.6066	+	18.3712i	0.345765	+	0.598883i	0.985493	−	0.169719i	$-0.0542860\pi$
$941$	10.6066	+	18.3712i	0.345765	+	0.598883i	−0.639727	+	0.768602i	$0.720953\pi$
$942$	−10.3923	+	6.00000i	−0.338600	+	0.195491i
$943$	14.6969	+	8.48528i	0.478598	+	0.276319i
$944$	8.48528			0.276172
$945$		0			0
$946$		0			0
$947$	6.92820	+	4.00000i	0.225136	+	0.129983i	0.608326	−	0.793687i	$-0.291841\pi$
$947$	6.92820	+	4.00000i	0.225136	+	0.129983i	−0.383190	+	0.923670i	$0.625175\pi$
$948$	−29.3939	+	16.9706i	−0.954669	+	0.551178i
$949$	−27.0000	−	46.7654i	−0.876457	−	1.51807i
$950$	−5.55532	−	13.0053i	−0.180238	−	0.421948i
$951$	−22.6274			−0.733744
$952$		0			0
$953$		−	32.0000i		−	1.03658i	−0.855204	−	0.518291i	$-0.826568\pi$
$953$		−	32.0000i		−	1.03658i	0.855204	−	0.518291i	$-0.173432\pi$
$954$	−20.0000	+	34.6410i	−0.647524	+	1.12154i
$955$	5.37945	+	26.2880i	0.174075	+	0.850661i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−14.0000	+	42.0000i	−0.451848	+	1.35554i
$961$	−0.500000	+	0.866025i	−0.0161290	+	0.0279363i
$962$	−22.0454	+	12.7279i	−0.710772	+	0.410365i
$963$	−17.3205	+	10.0000i	−0.558146	+	0.322245i
$964$	4.94975	−	8.57321i	0.159421	−	0.276125i
$965$	−16.9706	+	50.9117i	−0.546302	+	1.63891i
$966$		0			0
$967$			36.0000i			1.15768i	0.815440	+	0.578841i	$0.196495\pi$
$967$			36.0000i			1.15768i	−0.815440	+	0.578841i	$0.803505\pi$
$968$	28.5788	+	16.5000i	0.918559	+	0.530330i
$969$	−16.9706	−	29.3939i	−0.545173	−	0.944267i
$970$	−1.90192	−	9.29423i	−0.0610671	−	0.298420i
$971$	−4.24264	+	7.34847i	−0.136153	+	0.235824i	−0.926037	−	0.377432i	$-0.876807\pi$
$971$	−4.24264	+	7.34847i	−0.136153	+	0.235824i	0.789884	+	0.613256i	$0.210140\pi$
$972$		−	14.1421i		−	0.453609i
$973$		0			0
$974$	12.0000			0.384505
$975$	55.1769	−	23.5692i	1.76708	−	0.754819i
$976$	4.94975	+	8.57321i	0.158438	+	0.274422i
$977$	−8.66025	+	5.00000i	−0.277066	+	0.159964i	−0.632094	−	0.774891i	$-0.717805\pi$
$977$	−8.66025	+	5.00000i	−0.277066	+	0.159964i	0.355028	+	0.934856i	$0.384471\pi$
$978$	−58.7878	−	33.9411i	−1.87983	−	1.08532i
$979$		0			0
$980$		0			0
$981$	−80.0000			−2.55420
$982$	10.3923	+	6.00000i	0.331632	+	0.191468i
$983$	−24.4949	+	14.1421i	−0.781266	+	0.451064i	−0.836879	−	0.547388i	$-0.815622\pi$
$983$	−24.4949	+	14.1421i	−0.781266	+	0.451064i	0.0556128	+	0.998452i	$0.482289\pi$
$984$	18.0000	+	31.1769i	0.573819	+	0.993884i
$985$	−11.8685	−	13.3843i	−0.378162	−	0.426458i
$986$		0			0
$987$		0			0
$988$			12.0000i			0.381771i
$989$		0			0
$990$		0			0
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	0.662339	−	0.749204i	$-0.269564\pi$
$991$	−10.0000	−	17.3205i	−0.317660	−	0.550204i	−0.979999	+	0.199000i	$0.936231\pi$
$992$	−24.4949	−	14.1421i	−0.777714	−	0.449013i
$993$		−	22.6274i		−	0.718059i
$994$		0			0
$995$	−24.0000	−	8.00000i	−0.760851	−	0.253617i
$996$	−12.0000	+	20.7846i	−0.380235	+	0.658586i
$997$	−47.7650	+	27.5772i	−1.51273	+	0.873378i	−0.512845	+	0.858481i	$0.671409\pi$
$997$	−47.7650	+	27.5772i	−1.51273	+	0.873378i	−0.999889	+	0.0148965i	$0.995258\pi$
$998$	10.3923	−	6.00000i	0.328963	−	0.189927i
$999$	−16.9706	+	29.3939i	−0.536925	+	0.929981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.j.g.79.2		8
5.4	even	2	inner	245.2.j.g.79.3		8
7.2	even	3		245.2.b.f.99.4	yes	4
7.3	odd	6	inner	245.2.j.g.214.4		8
7.4	even	3	inner	245.2.j.g.214.3		8
7.5	odd	6		245.2.b.f.99.3	yes	4
7.6	odd	2	inner	245.2.j.g.79.1		8
21.2	odd	6		2205.2.d.k.1324.2		4
21.5	even	6		2205.2.d.k.1324.1		4
35.2	odd	12		1225.2.a.l.1.2		2
35.4	even	6	inner	245.2.j.g.214.2		8
35.9	even	6		245.2.b.f.99.1	✓	4
35.12	even	12		1225.2.a.l.1.1		2
35.19	odd	6		245.2.b.f.99.2	yes	4
35.23	odd	12		1225.2.a.v.1.1		2
35.24	odd	6	inner	245.2.j.g.214.1		8
35.33	even	12		1225.2.a.v.1.2		2
35.34	odd	2	inner	245.2.j.g.79.4		8
105.44	odd	6		2205.2.d.k.1324.4		4
105.89	even	6		2205.2.d.k.1324.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.b.f.99.1	✓	4	35.9	even	6
245.2.b.f.99.2	yes	4	35.19	odd	6
245.2.b.f.99.3	yes	4	7.5	odd	6
245.2.b.f.99.4	yes	4	7.2	even	3
245.2.j.g.79.1		8	7.6	odd	2	inner
245.2.j.g.79.2		8	1.1	even	1	trivial
245.2.j.g.79.3		8	5.4	even	2	inner
245.2.j.g.79.4		8	35.34	odd	2	inner
245.2.j.g.214.1		8	35.24	odd	6	inner
245.2.j.g.214.2		8	35.4	even	6	inner
245.2.j.g.214.3		8	7.4	even	3	inner
245.2.j.g.214.4		8	7.3	odd	6	inner
1225.2.a.l.1.1		2	35.12	even	12
1225.2.a.l.1.2		2	35.2	odd	12
1225.2.a.v.1.1		2	35.23	odd	12
1225.2.a.v.1.2		2	35.33	even	12
2205.2.d.k.1324.1		4	21.5	even	6
2205.2.d.k.1324.2		4	21.2	odd	6
2205.2.d.k.1324.3		4	105.89	even	6
2205.2.d.k.1324.4		4	105.44	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.44949 - 1.41421i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.67303 - 1.48356i) q^{5} -2.82843 q^{6} +3.00000i q^{8} +(2.50000 - 4.33013i) q^{9} +(-2.19067 + 0.448288i) q^{10} +(-2.44949 - 1.41421i) q^{12} +4.24264i q^{13} +(2.00000 - 6.00000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.67423 + 2.12132i) q^{17} +(-4.33013 + 2.50000i) q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.12132 - 0.707107i) q^{20} +(3.46410 + 2.00000i) q^{23} +(4.24264 + 7.34847i) q^{24} +(0.598076 - 4.96410i) q^{25} +(2.12132 - 3.67423i) q^{26} -5.65685i q^{27} +(-4.73205 + 4.19615i) q^{30} +(-2.82843 - 4.89898i) q^{31} +(4.33013 - 2.50000i) q^{32} +4.24264 q^{34} -5.00000 q^{36} +(-5.19615 - 3.00000i) q^{37} +(2.44949 - 1.41421i) q^{38} +(6.00000 + 10.3923i) q^{39} +(4.45069 + 5.01910i) q^{40} +4.24264 q^{41} +(-2.24144 - 10.9534i) q^{45} +(-2.00000 - 3.46410i) q^{46} -2.82843i q^{48} +(-3.00000 + 4.00000i) q^{50} +(-6.00000 + 10.3923i) q^{51} +(3.67423 - 2.12132i) q^{52} +(6.92820 - 4.00000i) q^{53} +(-2.82843 + 4.89898i) q^{54} +8.00000i q^{57} +(4.24264 + 7.34847i) q^{59} +(-6.19615 + 1.26795i) q^{60} +(-4.94975 + 8.57321i) q^{61} +5.65685i q^{62} -7.00000 q^{64} +(6.29423 + 7.09808i) q^{65} +(-10.3923 + 6.00000i) q^{67} +(3.67423 + 2.12132i) q^{68} +11.3137 q^{69} +12.0000 q^{71} +(12.9904 + 7.50000i) q^{72} +(-11.0227 + 6.36396i) q^{73} +(3.00000 + 5.19615i) q^{74} +(-5.55532 - 13.0053i) q^{75} +2.82843 q^{76} -12.0000i q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.448288 - 2.19067i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.67423 - 2.12132i) q^{82} -8.48528i q^{83} +(-3.00000 + 9.00000i) q^{85} +(-2.12132 + 3.67423i) q^{89} +(-3.53553 + 10.6066i) q^{90} -4.00000i q^{92} +(-13.8564 - 8.00000i) q^{93} +(1.26795 + 6.19615i) q^{95} +(7.07107 - 12.2474i) q^{96} +4.24264i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 20 q^{9} + 16 q^{15} + 4 q^{16} - 16 q^{25} - 24 q^{30} - 40 q^{36} + 48 q^{39} - 16 q^{46} - 24 q^{50} - 48 q^{51} - 8 q^{60} - 56 q^{64} - 12 q^{65} + 96 q^{71} + 24 q^{74} + 48 q^{79}+ \cdots + 24 q^{95}+O(q^{100}) \) 8 * q - 4 * q^4 + 20 * q^9 + 16 * q^15 + 4 * q^16 - 16 * q^25 - 24 * q^30 - 40 * q^36 + 48 * q^39 - 16 * q^46 - 24 * q^50 - 48 * q^51 - 8 * q^60 - 56 * q^64 - 12 * q^65 + 96 * q^71 + 24 * q^74 + 48 * q^79 - 4 * q^81 - 24 * q^85 + 24 * q^95

Introduction

L-functions

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