LMFDB - Embedded newform 245.2.j.g.214.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(79,245)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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			214.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	245.214
Dual form			245.2.j.g.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(2.44949 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.448288 - 2.19067i) q^{5} +2.82843 q^{6} +3.00000i q^{8} +(2.50000 + 4.33013i) q^{9} +(-1.48356 - 1.67303i) q^{10} +(-2.44949 + 1.41421i) q^{12} -4.24264i q^{13} +(2.00000 - 6.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.67423 - 2.12132i) q^{17} +(4.33013 + 2.50000i) q^{18} +(1.41421 + 2.44949i) q^{19} +(2.12132 + 0.707107i) q^{20} +(-3.46410 + 2.00000i) q^{23} +(-4.24264 + 7.34847i) q^{24} +(-4.59808 + 1.96410i) q^{25} +(-2.12132 - 3.67423i) q^{26} +5.65685i q^{27} +(-1.26795 - 6.19615i) q^{30} +(2.82843 - 4.89898i) q^{31} +(-4.33013 - 2.50000i) q^{32} -4.24264 q^{34} -5.00000 q^{36} +(5.19615 - 3.00000i) q^{37} +(2.44949 + 1.41421i) q^{38} +(6.00000 - 10.3923i) q^{39} +(6.57201 - 1.34486i) q^{40} -4.24264 q^{41} +(8.36516 - 7.41782i) q^{45} +(-2.00000 + 3.46410i) q^{46} +2.82843i q^{48} +(-3.00000 + 4.00000i) q^{50} +(-6.00000 - 10.3923i) q^{51} +(3.67423 + 2.12132i) q^{52} +(-6.92820 - 4.00000i) q^{53} +(2.82843 + 4.89898i) q^{54} +8.00000i q^{57} +(-4.24264 + 7.34847i) q^{59} +(4.19615 + 4.73205i) q^{60} +(4.94975 + 8.57321i) q^{61} -5.65685i q^{62} -7.00000 q^{64} +(-9.29423 + 1.90192i) q^{65} +(10.3923 + 6.00000i) q^{67} +(3.67423 - 2.12132i) q^{68} -11.3137 q^{69} +12.0000 q^{71} +(-12.9904 + 7.50000i) q^{72} +(-11.0227 - 6.36396i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-14.0406 - 1.69161i) q^{75} -2.82843 q^{76} -12.0000i q^{78} +(6.00000 + 10.3923i) q^{79} +(1.67303 - 1.48356i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.67423 + 2.12132i) q^{82} +8.48528i q^{83} +(-3.00000 + 9.00000i) q^{85} +(2.12132 + 3.67423i) q^{89} +(3.53553 - 10.6066i) q^{90} -4.00000i q^{92} +(13.8564 - 8.00000i) q^{93} +(4.73205 - 4.19615i) q^{95} +(-7.07107 - 12.2474i) q^{96} -4.24264i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	2.44949	+	1.41421i	1.41421	+	0.816497i	0.995782	−	0.0917517i	$-0.0292466\pi$
$3$	2.44949	+	1.41421i	1.41421	+	0.816497i	0.418432	+	0.908248i	$0.362580\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$5$	−0.448288	−	2.19067i	−0.200480	−	0.979698i
$6$	2.82843			1.15470
$7$		0			0
$7$		0			0
$8$			3.00000i			1.06066i
$9$	2.50000	+	4.33013i	0.833333	+	1.44338i
$10$	−1.48356	−	1.67303i	−0.469144	−	0.529059i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−2.44949	+	1.41421i	−0.707107	+	0.408248i
$13$		−	4.24264i		−	1.17670i	−0.808608	−	0.588348i	$-0.799778\pi$
$13$		−	4.24264i		−	1.17670i	0.808608	−	0.588348i	$-0.200222\pi$
$14$		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	−0.0168199	−	0.999859i	$-0.505354\pi$
$17$	−3.67423	−	2.12132i	−0.891133	−	0.514496i	−0.874313	+	0.485363i	$0.838688\pi$
$18$	4.33013	+	2.50000i	1.02062	+	0.589256i
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$	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	$-0.803595\pi$
$23$	−3.46410	+	2.00000i	−0.722315	+	0.417029i	0.0932891	+	0.995639i	$0.470262\pi$
$24$	−4.24264	+	7.34847i	−0.866025	+	1.50000i
$25$	−4.59808	+	1.96410i	−0.919615	+	0.392820i
$26$	−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	$0.5\pi$
$30$	−1.26795	−	6.19615i	−0.231495	−	1.13126i
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	−0.491957	−	0.870620i	$-0.663718\pi$
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	0.999957	−	0.00926296i	$-0.00294853\pi$
$32$	−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	$-0.502495\pi$
$37$	5.19615	−	3.00000i	0.854242	−	0.493197i	0.862080	+	0.506772i	$0.169162\pi$
$38$	2.44949	+	1.41421i	0.397360	+	0.229416i
$39$	6.00000	−	10.3923i	0.960769	−	1.66410i
$40$	6.57201	−	1.34486i	1.03913	−	0.212642i
$41$	−4.24264			−0.662589			−0.331295	−	0.943527i	$-0.607485\pi$
$41$	−4.24264			−0.662589			−0.331295	+	0.943527i	$0.607485\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	8.36516	−	7.41782i	1.24700	−	1.10578i
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$			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	$-0.518493\pi$
$53$	−6.92820	−	4.00000i	−0.951662	−	0.549442i	−0.893597	+	0.448871i	$0.851826\pi$
$54$	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	0.445760	+	0.895152i	$0.352933\pi$
$59$	−4.24264	+	7.34847i	−0.552345	+	0.956689i	−0.998105	+	0.0615367i	$0.980400\pi$
$60$	4.19615	+	4.73205i	0.541721	+	0.610905i
$61$	4.94975	+	8.57321i	0.633750	+	1.09769i	0.986778	+	0.162075i	$0.0518186\pi$
$61$	4.94975	+	8.57321i	0.633750	+	1.09769i	−0.353028	+	0.935613i	$0.614848\pi$
$62$		−	5.65685i		−	0.718421i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−9.29423	+	1.90192i	−1.15281	+	0.235905i
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$	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	−0.311436	−	0.950267i	$-0.600810\pi$
$73$	−11.0227	−	6.36396i	−1.29011	−	0.744845i	−0.978674	+	0.205422i	$0.934143\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−14.0406	−	1.69161i	−1.62127	−	0.195331i
$76$	−2.82843			−0.324443
$77$		0			0
$78$		−	12.0000i		−	1.35873i
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	0.976453	+	0.215728i	$0.0692125\pi$
$79$	6.00000	+	10.3923i	0.675053	+	1.16923i	−0.301401	+	0.953498i	$0.597454\pi$
$80$	1.67303	−	1.48356i	0.187051	−	0.165867i
$81$	−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	$0.154194\pi$
$83$			8.48528i			0.931381i	−0.884948	+	0.465690i	$0.845806\pi$
$84$		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	$-0.0944744\pi$
$89$	2.12132	+	3.67423i	0.224860	+	0.389468i	−0.731418	+	0.681930i	$0.761141\pi$
$90$	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
$95$	4.73205	−	4.19615i	0.485498	−	0.430516i
$96$	−7.07107	−	12.2474i	−0.721688	−	1.25000i
$97$		−	4.24264i		−	0.430775i	−0.976529	−	0.215387i	$-0.930899\pi$
$97$		−	4.24264i		−	0.430775i	0.976529	−	0.215387i	$-0.0691014\pi$
$98$		0			0
$99$		0			0
$100$	0.598076	−	4.96410i	0.0598076	−	0.496410i
$101$	−2.12132	+	3.67423i	−0.211079	+	0.365600i	−0.952053	−	0.305934i	$-0.901031\pi$
$101$	−2.12132	+	3.67423i	−0.211079	+	0.365600i	0.740973	+	0.671534i	$0.234364\pi$
$102$	−10.3923	−	6.00000i	−1.02899	−	0.594089i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	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	$-0.604732\pi$
$107$	3.46410	−	2.00000i	0.334887	−	0.193347i	0.658009	+	0.753010i	$0.271399\pi$
$108$	−4.89898	−	2.82843i	−0.471405	−	0.272166i
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	0.173316	+	0.984866i	$0.444552\pi$
$109$	−8.00000	+	13.8564i	−0.766261	+	1.32720i	−0.939577	+	0.342337i	$0.888782\pi$
$110$		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
$115$	5.93426	+	6.69213i	0.553372	+	0.624044i
$116$		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
$130$	−7.09808	+	6.29423i	−0.622542	+	0.552040i
$131$	−4.24264	−	7.34847i	−0.370681	−	0.642039i	0.618989	−	0.785399i	$-0.287542\pi$
$131$	−4.24264	−	7.34847i	−0.370681	−	0.642039i	−0.989671	+	0.143361i	$0.954209\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$	12.3923	−	2.53590i	1.06656	−	0.218255i
$136$	6.36396	−	11.0227i	0.545705	−	0.945189i
$137$	12.1244	+	7.00000i	1.03585	+	0.598050i	0.918656	−	0.395058i	$-0.129276\pi$
$137$	12.1244	+	7.00000i	1.03585	+	0.598050i	0.117198	+	0.993109i	$0.462609\pi$
$138$	−9.79796	+	5.65685i	−0.834058	+	0.481543i
$139$	2.82843			0.239904			0.119952	−	0.992780i	$-0.461726\pi$
$139$	2.82843			0.239904			0.119952	+	0.992780i	$0.461726\pi$
$140$		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	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−13.0053	+	5.55532i	−1.06188	+	0.453590i
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	−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	0.639400	−	0.768874i	$-0.279183\pi$
$157$	3.67423	+	2.12132i	0.293236	+	0.169300i	−0.346164	+	0.938174i	$0.612516\pi$
$158$	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	−0.643280	+	0.765631i	$0.722427\pi$
$163$	−20.7846	+	12.0000i	−1.62798	+	0.939913i	−0.984696	+	0.174282i	$0.944240\pi$
$164$	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	$-0.855779\pi$
$167$		−	11.3137i		−	0.875481i	0.899101	−	0.437741i	$-0.144221\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	1.90192	+	9.29423i	0.145871	+	0.712835i
$171$	−7.07107	+	12.2474i	−0.540738	+	0.936586i
$172$		0			0
$173$	−3.67423	+	2.12132i	−0.279347	+	0.161281i	−0.633128	−	0.774047i	$-0.718229\pi$
$173$	−3.67423	+	2.12132i	−0.279347	+	0.161281i	0.353781	+	0.935328i	$0.384896\pi$
$174$		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	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$	2.24144	+	10.9534i	0.167067	+	0.816415i
$181$	18.3848			1.36653			0.683265	−	0.730171i	$-0.260559\pi$
$181$	18.3848			1.36653			0.683265	+	0.730171i	$0.260559\pi$
$182$		0			0
$183$			28.0000i			2.06982i
$184$	−6.00000	−	10.3923i	−0.442326	−	0.766131i
$185$	−8.90138	−	10.0382i	−0.654443	−	0.738023i
$186$	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	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$	−17.1464	−	9.89949i	−1.23744	−	0.714435i
$193$	20.7846	+	12.0000i	1.49611	+	0.863779i	0.999990	−	0.00447566i	$-0.00142465\pi$
$193$	20.7846	+	12.0000i	1.49611	+	0.863779i	0.496119	+	0.868255i	$0.334758\pi$
$194$	−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	$-0.701995\pi$
$199$	5.65685	−	9.79796i	0.401004	−	0.694559i	0.993847	+	0.110759i	$0.0353281\pi$
$200$	−5.89230	−	13.7942i	−0.416649	−	0.975399i
$201$	16.9706	+	29.3939i	1.19701	+	2.07328i
$202$			4.24264i			0.298511i
$203$		0			0
$204$	12.0000			0.840168
$205$	1.90192	+	9.29423i	0.132836	+	0.649137i
$206$		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	0.579082	−	0.815270i	$-0.303411\pi$
$227$	2.44949	+	1.41421i	0.162578	+	0.0938647i	−0.416503	+	0.909134i	$0.636745\pi$
$228$	−6.92820	−	4.00000i	−0.458831	−	0.264906i
$229$	−3.53553	−	6.12372i	−0.233635	−	0.404667i	0.725240	−	0.688496i	$-0.241729\pi$
$229$	−3.53553	−	6.12372i	−0.233635	−	0.404667i	−0.958875	+	0.283829i	$0.908395\pi$
$230$	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	$-0.515023\pi$
$233$	12.1244	−	7.00000i	0.794293	−	0.458585i	0.841472	+	0.540301i	$0.181690\pi$
$234$	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	$0.782863\pi$
$240$	6.19615	−	1.26795i	0.399960	−	0.0818458i
$241$	−4.94975	+	8.57321i	−0.318841	+	0.552249i	−0.980247	−	0.197779i	$-0.936627\pi$
$241$	−4.94975	+	8.57321i	−0.318841	+	0.552249i	0.661405	+	0.750029i	$0.269960\pi$
$242$	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
$250$	10.1075	+	4.77886i	0.639257	+	0.302242i
$251$	−25.4558			−1.60676			−0.803379	−	0.595468i	$-0.796967\pi$
$251$	−25.4558			−1.60676			−0.803379	+	0.595468i	$0.796967\pi$
$252$		0			0
$253$		0			0
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	−20.0764	+	17.8028i	−1.25723	+	1.11485i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−23.2702	+	13.4350i	−1.45155	+	0.838054i	−0.998570	−	0.0534653i	$-0.982973\pi$
$257$	−23.2702	+	13.4350i	−1.45155	+	0.838054i	−0.452983	+	0.891519i	$0.649640\pi$
$258$		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	$-0.497543\pi$
$263$	−13.8564	−	8.00000i	−0.854423	−	0.493301i	−0.862141	+	0.506669i	$0.830877\pi$
$264$		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	−0.337211	−	0.941429i	$-0.609484\pi$
$269$	10.6066	−	18.3712i	0.646696	−	1.12011i	0.983907	−	0.178681i	$-0.0571831\pi$
$270$	9.46410	−	8.39230i	0.575967	−	0.510739i
$271$	−2.82843	−	4.89898i	−0.171815	−	0.297592i	0.767240	−	0.641361i	$-0.221630\pi$
$271$	−2.82843	−	4.89898i	−0.171815	−	0.297592i	−0.939054	+	0.343769i	$0.888296\pi$
$272$		−	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	$-0.589655\pi$
$277$	−20.7846	−	12.0000i	−1.24883	−	0.721010i	−0.970875	+	0.239585i	$0.922989\pi$
$278$	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	−0.328291	−	0.944577i	$-0.606473\pi$
$283$	−22.0454	−	12.7279i	−1.31046	−	0.756596i	−0.982173	+	0.187980i	$0.939806\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	17.5254	−	3.58630i	1.03811	−	0.212434i
$286$		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	$-0.986847\pi$
$293$		−	1.41421i		−	0.0826192i	0.999146	−	0.0413096i	$-0.0131530\pi$
$294$		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
$305$	16.5622	−	14.6865i	0.948348	−	0.840948i
$306$	−10.6066	−	18.3712i	−0.606339	−	1.05021i
$307$		−	25.4558i		−	1.45284i	−0.687250	−	0.726421i	$-0.741182\pi$
$307$		−	25.4558i		−	1.45284i	0.687250	−	0.726421i	$-0.258818\pi$
$308$		0			0
$309$		0			0
$310$	−12.3923	+	2.53590i	−0.703836	+	0.144029i
$311$	−16.9706	+	29.3939i	−0.962312	+	1.66677i	−0.245643	+	0.969360i	$0.578999\pi$
$311$	−16.9706	+	29.3939i	−0.962312	+	1.66677i	−0.716669	+	0.697414i	$0.754334\pi$
$312$	31.1769	+	18.0000i	1.76505	+	1.01905i
$313$	−18.3712	+	10.6066i	−1.03840	+	0.599521i	−0.919380	−	0.393371i	$-0.871309\pi$
$313$	−18.3712	+	10.6066i	−1.03840	+	0.599521i	−0.119020	+	0.992892i	$0.537975\pi$
$314$	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	$-0.594539\pi$
$317$	6.92820	−	4.00000i	0.389127	−	0.224662i	0.681782	+	0.731556i	$0.261205\pi$
$318$	−19.5959	−	11.3137i	−1.09888	−	0.634441i
$319$		0			0
$320$	3.13801	+	15.3347i	0.175420	+	0.857236i
$321$	11.3137			0.631470
$322$		0			0
$323$		−	12.0000i		−	0.667698i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	8.33298	+	19.5080i	0.462230	+	1.08211i
$326$	−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	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	−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
$340$	−6.29423	−	7.09808i	−0.341352	−	0.384947i
$341$		0			0
$342$			14.1421i			0.764719i
$343$		0			0
$344$		0			0
$345$	5.07180	+	24.7846i	0.273056	+	1.33436i
$346$	−2.12132	+	3.67423i	−0.114043	+	0.197528i
$347$	−6.92820	−	4.00000i	−0.371925	−	0.214731i	0.302374	−	0.953189i	$-0.402221\pi$
$347$	−6.92820	−	4.00000i	−0.371925	−	0.214731i	−0.674299	+	0.738458i	$0.735554\pi$
$348$		0			0
$349$	1.41421			0.0757011			0.0378506	−	0.999283i	$-0.487949\pi$
$349$	1.41421			0.0757011			0.0378506	+	0.999283i	$0.487949\pi$
$350$		0			0
$351$	24.0000			1.28103
$352$		0			0
$353$	−13.4722	−	7.77817i	−0.717053	−	0.413990i	0.0966144	−	0.995322i	$-0.469199\pi$
$353$	−13.4722	−	7.77817i	−0.717053	−	0.413990i	−0.813667	+	0.581331i	$0.802532\pi$
$354$	−12.0000	+	20.7846i	−0.637793	+	1.10469i
$355$	−5.37945	−	26.2880i	−0.285512	−	1.39522i
$356$	−4.24264			−0.224860
$357$		0			0
$358$		−	12.0000i		−	0.634220i
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$	22.2535	+	25.0955i	1.17286	+	1.32265i
$361$	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	0.831866	−	0.554977i	$-0.187273\pi$
$367$	14.6969	+	8.48528i	0.767174	+	0.442928i	−0.0646916	+	0.997905i	$0.520606\pi$
$368$	−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	$-0.453257\pi$
$373$	20.7846	−	12.0000i	1.07619	−	0.621336i	0.929865	+	0.367901i	$0.119923\pi$
$374$		0			0
$375$	2.58846	+	31.5167i	0.133667	+	1.62751i
$376$		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	$0.288591\pi$
$380$	1.26795	+	6.19615i	0.0650444	+	0.317856i
$381$	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	0.501960	−	0.864891i	$-0.332613\pi$
$383$	29.3939	−	16.9706i	1.50196	−	0.867155i	0.999997	−	0.00226413i	$-0.000720695\pi$
$384$	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	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	−26.2880	+	5.37945i	−1.33115	+	0.272399i
$391$	16.9706			0.858238
$392$		0			0
$393$		−	24.0000i		−	1.21064i
$394$	−4.00000	−	6.92820i	−0.201517	−	0.349038i
$395$	20.0764	−	17.8028i	1.01015	−	0.895754i
$396$		0			0
$397$	−3.67423	+	2.12132i	−0.184405	+	0.106466i	−0.589360	−	0.807870i	$-0.700620\pi$
$397$	−3.67423	+	2.12132i	−0.184405	+	0.106466i	0.404956	+	0.914336i	$0.367287\pi$
$398$		−	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	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$	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	$-0.983528\pi$
$409$	−9.19239	+	15.9217i	−0.454534	+	0.787277i	0.544127	+	0.839003i	$0.316861\pi$
$410$	6.29423	+	7.09808i	0.310850	+	0.350549i
$411$	19.7990	+	34.2929i	0.976612	+	1.69154i
$412$		0			0
$413$		0			0
$414$	−20.0000			−0.982946
$415$	18.5885	−	3.80385i	0.912471	−	0.186724i
$416$	−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	$-0.433543\pi$
$419$	8.48528			0.414533			0.207267	+	0.978285i	$0.433543\pi$
$420$		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
$425$	21.0609	+	2.53742i	1.02160	+	0.123083i
$426$	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	0.417687	+	0.908591i	$0.362841\pi$
$431$	−12.0000	+	20.7846i	−0.578020	+	1.00116i	−0.995706	+	0.0925683i	$0.970492\pi$
$432$	−4.89898	+	2.82843i	−0.235702	+	0.136083i
$433$			4.24264i			0.203888i	0.994790	+	0.101944i	$0.0325063\pi$
$433$			4.24264i			0.203888i	−0.994790	+	0.101944i	$0.967494\pi$
$434$		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	−0.976478	−	0.215615i	$-0.930824\pi$
$439$	−14.1421	−	24.4949i	−0.674967	−	1.16908i	0.301511	−	0.953463i	$-0.402509\pi$
$440$		0			0
$441$		0			0
$442$			18.0000i			0.856173i
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	−0.415445	−	0.909618i	$-0.636374\pi$
$443$	3.46410	−	2.00000i	0.164584	−	0.0950229i	0.580030	+	0.814595i	$0.303041\pi$
$444$	−8.48528	+	14.6969i	−0.402694	+	0.697486i
$445$	7.09808	−	6.29423i	0.336481	−	0.298375i
$446$		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	$0.360367\pi$
$450$	−24.8205	−	2.99038i	−1.17005	−	0.140968i
$451$		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	$-0.856379\pi$
$457$	−20.7846	+	12.0000i	−0.972263	+	0.561336i	−0.0723376	+	0.997380i	$0.523046\pi$
$458$	−6.12372	−	3.53553i	−0.286143	−	0.165205i
$459$	12.0000	−	20.7846i	0.560112	−	0.970143i
$460$	−8.76268	+	1.79315i	−0.408562	+	0.0836061i
$461$	−21.2132			−0.987997			−0.493999	−	0.869463i	$-0.664465\pi$
$461$	−21.2132			−0.987997			−0.493999	+	0.869463i	$0.664465\pi$
$462$		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
$465$	−23.7370	−	26.7685i	−1.10078	−	1.24136i
$466$	7.00000	−	12.1244i	0.324269	−	0.561650i
$467$	26.9444	−	15.5563i	1.24684	−	0.719862i	0.276360	−	0.961054i	$-0.410872\pi$
$467$	26.9444	−	15.5563i	1.24684	−	0.719862i	0.970477	+	0.241192i	$0.0775384\pi$
$468$			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	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−23.6603	+	20.9808i	−1.07994	+	0.957636i
$481$	−12.7279	−	22.0454i	−0.580343	−	1.00518i
$482$			9.89949i			0.450910i
$483$		0			0
$484$	−11.0000			−0.500000
$485$	−9.29423	+	1.90192i	−0.422029	+	0.0863619i
$486$	7.07107	−	12.2474i	0.320750	−	0.555556i
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	0.716625	−	0.697459i	$-0.245686\pi$
$487$	10.3923	+	6.00000i	0.470920	+	0.271886i	−0.245705	+	0.969345i	$0.579019\pi$
$488$	−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	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	−11.1428	+	0.915158i	−0.498322	+	0.0409271i
$501$	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	$0.123505\pi$
$503$			16.9706i			0.756680i	−0.925667	+	0.378340i	$0.876495\pi$
$504$		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	$-0.0756431\pi$
$509$	6.36396	+	11.0227i	0.282078	+	0.488573i	−0.689819	+	0.723982i	$0.742310\pi$
$510$	−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
$520$	−5.70577	−	27.8827i	−0.250215	−	1.22274i
$521$	14.8492	−	25.7196i	0.650557	−	1.12680i	−0.332431	−	0.943128i	$-0.607869\pi$
$521$	14.8492	−	25.7196i	0.650557	−	1.12680i	0.982988	−	0.183670i	$-0.0587979\pi$
$522$		0			0
$523$	−7.34847	+	4.24264i	−0.321326	+	0.185518i	−0.651984	−	0.758233i	$-0.726063\pi$
$523$	−7.34847	+	4.24264i	−0.321326	+	0.185518i	0.330657	+	0.943751i	$0.392730\pi$
$524$	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
$530$	3.58630	+	17.5254i	0.155779	+	0.761253i
$531$	−42.4264			−1.84115
$532$		0			0
$533$			18.0000i			0.779667i
$534$	6.00000	+	10.3923i	0.259645	+	0.449719i
$535$	−5.93426	−	6.69213i	−0.256560	−	0.289326i
$536$	−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	0.605096	−	0.796152i	$-0.293135\pi$
$541$	−9.00000	−	15.5885i	−0.386940	−	0.670200i	−0.992036	+	0.125952i	$0.959801\pi$
$542$	−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
$555$	−7.60770	−	37.1769i	−0.322929	−	1.57807i
$556$	−1.41421	+	2.44949i	−0.0599760	+	0.103882i
$557$	−34.6410	−	20.0000i	−1.46779	−	0.847427i	−0.468438	−	0.883497i	$-0.655183\pi$
$557$	−34.6410	−	20.0000i	−1.46779	−	0.847427i	−0.999349	+	0.0360693i	$0.988516\pi$
$558$	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	0.886528	−	0.462675i	$-0.153110\pi$
$563$	22.0454	+	12.7279i	0.929103	+	0.536418i	0.0425753	+	0.999093i	$0.486444\pi$
$564$		0			0
$565$	−17.5254	+	3.58630i	−0.737298	+	0.150877i
$566$	−25.4558			−1.06999
$567$		0			0
$568$			36.0000i			1.51053i
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$	13.3843	−	11.8685i	0.560605	−	0.497117i
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		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	0.991754	−	0.128157i	$-0.0409062\pi$
$577$	33.0681	+	19.0919i	1.37664	+	0.794805i	0.384890	+	0.922963i	$0.374240\pi$
$578$	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
$585$	−31.4711	−	35.4904i	−1.30117	−	1.46735i
$586$	−0.707107	−	1.22474i	−0.0292103	−	0.0505937i
$587$			42.4264i			1.75113i	0.483105	+	0.875563i	$0.339509\pi$
$587$			42.4264i			1.75113i	−0.483105	+	0.875563i	$0.660491\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	18.5885	−	3.80385i	0.765275	−	0.156602i
$591$	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	−0.620438	−	0.784256i	$-0.713045\pi$
$593$	−6.12372	+	3.53553i	−0.251471	+	0.145187i	0.368967	+	0.929443i	$0.379712\pi$
$594$		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	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$	5.07484	−	42.1218i	0.207180	−	1.71962i
$601$	41.0122			1.67292			0.836461	−	0.548026i	$-0.184621\pi$
$601$	41.0122			1.67292			0.836461	+	0.548026i	$0.184621\pi$
$602$		0			0
$603$			60.0000i			2.44339i
$604$		0			0
$605$	18.4034	−	16.3192i	0.748203	−	0.663470i
$606$	−6.00000	+	10.3923i	−0.243733	+	0.422159i
$607$	29.3939	−	16.9706i	1.19306	−	0.688814i	0.234061	−	0.972222i	$-0.424798\pi$
$607$	29.3939	−	16.9706i	1.19306	−	0.688814i	0.958999	+	0.283408i	$0.0914650\pi$
$608$		−	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	$-0.371998\pi$
$613$	−5.19615	−	3.00000i	−0.209871	−	0.121169i	−0.601251	+	0.799060i	$0.705331\pi$
$614$	−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	$-0.703074\pi$
$619$	9.89949	−	17.1464i	0.397894	−	0.689173i	0.993466	+	0.114129i	$0.0364077\pi$
$620$	9.46410	−	8.39230i	0.380087	−	0.337043i
$621$	−11.3137	−	19.5959i	−0.454003	−	0.786357i
$622$			33.9411i			1.36092i
$623$		0			0
$624$	12.0000			0.480384
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$	−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
$635$	−26.2880	+	5.37945i	−1.04321	+	0.213477i
$636$	22.6274			0.897235
$637$		0			0
$638$		0			0
$639$	30.0000	+	51.9615i	1.18678	+	2.05557i
$640$	−4.45069	−	5.01910i	−0.175929	−	0.198397i
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	−0.999556	−	0.0297987i	$-0.990513\pi$
$641$	−12.0000	+	20.7846i	−0.473972	+	0.820943i	0.525584	+	0.850741i	$0.323847\pi$
$642$	9.79796	−	5.65685i	0.386695	−	0.223258i
$643$			8.48528i			0.334627i	0.985904	+	0.167313i	$0.0535092\pi$
$643$			8.48528i			0.334627i	−0.985904	+	0.167313i	$0.946491\pi$
$644$		0			0
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−4.89898	−	2.82843i	−0.192599	−	0.111197i	0.400600	−	0.916253i	$-0.368802\pi$
$647$	−4.89898	−	2.82843i	−0.192599	−	0.111197i	−0.593199	+	0.805056i	$0.702135\pi$
$648$	−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	$-0.679126\pi$
$653$	−1.73205	+	1.00000i	−0.0677804	+	0.0391330i	0.465727	+	0.884929i	$0.345793\pi$
$654$	−22.6274	+	39.1918i	−0.884802	+	1.53252i
$655$	−14.1962	+	12.5885i	−0.554690	+	0.491872i
$656$	−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	$-0.931167\pi$
$661$	−7.77817	+	13.4722i	−0.302536	+	0.524008i	0.674174	+	0.738573i	$0.264500\pi$
$662$	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
$670$	−5.37945	−	26.2880i	−0.207826	−	1.01560i
$671$		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
$675$	−11.1106	−	26.0106i	−0.427649	−	1.00115i
$676$	2.50000	−	4.33013i	0.0961538	−	0.166543i
$677$	−8.57321	+	4.94975i	−0.329495	+	0.190234i	−0.655617	−	0.755094i	$-0.727591\pi$
$677$	−8.57321	+	4.94975i	−0.329495	+	0.190234i	0.326122	+	0.945328i	$0.394258\pi$
$678$		−	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	$-0.153383\pi$
$683$	24.2487	+	14.0000i	0.927851	+	0.535695i	0.0417198	+	0.999129i	$0.486716\pi$
$684$	−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
$690$	16.7846	+	18.9282i	0.638979	+	0.720584i
$691$	1.41421	+	2.44949i	0.0537992	+	0.0931830i	0.891671	−	0.452684i	$-0.149534\pi$
$691$	1.41421	+	2.44949i	0.0537992	+	0.0931830i	−0.837872	+	0.545867i	$0.816200\pi$
$692$		−	4.24264i		−	0.161281i
$693$		0			0
$694$	−8.00000			−0.303676
$695$	−1.26795	−	6.19615i	−0.0480961	−	0.235033i
$696$		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	$-0.166667\pi$
$709$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$710$	−17.8028	−	20.0764i	−0.668126	−	0.753454i
$711$	−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	$-0.0641765\pi$
$719$	8.48528	+	14.6969i	0.316448	+	0.548103i	−0.663297	+	0.748357i	$0.730843\pi$
$720$	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	$0.216701\pi$
$727$			33.9411i			1.25881i	−0.777079	+	0.629403i	$0.783299\pi$
$728$		0			0
$729$	43.0000			1.59259
$730$	5.70577	+	27.8827i	0.211180	+	1.03198i
$731$		0			0
$732$	−24.2487	−	14.0000i	−0.896258	−	0.517455i
$733$	3.67423	−	2.12132i	0.135711	−	0.0783528i	−0.430607	−	0.902539i	$-0.641701\pi$
$733$	3.67423	−	2.12132i	0.135711	−	0.0783528i	0.566318	+	0.824187i	$0.308367\pi$
$734$	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	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$	13.1440	−	2.68973i	0.483184	−	0.0988763i
$741$	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
$745$	−10.0382	+	8.90138i	−0.367771	+	0.326121i
$746$	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	0.956963	+	0.290209i	$0.0937250\pi$
$751$	20.0000	+	34.6410i	0.729810	+	1.26407i	−0.227153	+	0.973859i	$0.572942\pi$
$752$		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
$760$	12.5885	+	14.1962i	0.456631	+	0.514949i
$761$	−14.8492	−	25.7196i	−0.538285	−	0.932336i	−0.998997	−	0.0447866i	$-0.985739\pi$
$761$	−14.8492	−	25.7196i	−0.538285	−	0.932336i	0.460712	−	0.887550i	$-0.347594\pi$
$762$		−	33.9411i		−	1.22956i
$763$		0			0
$764$	12.0000			0.434145
$765$	−46.4711	+	9.50962i	−1.68017	+	0.343821i
$766$	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	$-0.357285\pi$
$769$	24.0416			0.866963			0.433482	+	0.901162i	$0.357285\pi$
$770$		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	0.131803	−	0.991276i	$-0.457923\pi$
$773$	−18.3712	−	10.6066i	−0.660765	−	0.381493i	−0.792568	+	0.609783i	$0.791257\pi$
$774$		0			0
$775$	−3.38323	+	28.0812i	−0.121529	+	1.00871i
$776$	12.7279			0.456906
$777$		0			0
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$	20.0764	−	17.8028i	0.718850	−	0.637441i
$781$		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	0.363277	−	0.931681i	$-0.381658\pi$
$787$	−7.34847	−	4.24264i	−0.261945	−	0.151234i	−0.625221	+	0.780447i	$0.714991\pi$
$788$	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
$795$	−37.8564	+	33.5692i	−1.34263	+	1.19058i
$796$	5.65685	+	9.79796i	0.200502	+	0.347279i
$797$		−	4.24264i		−	0.150282i	−0.997173	−	0.0751410i	$-0.976059\pi$
$797$		−	4.24264i		−	0.150282i	0.997173	−	0.0751410i	$-0.0239407\pi$
$798$		0			0
$799$		0			0
$800$	24.8205	+	2.99038i	0.877537	+	0.105726i
$801$	−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	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$	2.19067	−	0.448288i	0.0769723	−	0.0157512i
$811$	−14.1421			−0.496598			−0.248299	−	0.968683i	$-0.579871\pi$
$811$	−14.1421			−0.496598			−0.248299	+	0.968683i	$0.579871\pi$
$812$		0			0
$813$		−	16.0000i		−	0.561144i
$814$		0			0
$815$	35.6055	+	40.1528i	1.24721	+	1.40649i
$816$	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	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$	34.2929	+	19.7990i	1.19610	+	0.690569i
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	0.0919029	−	0.995768i	$-0.470705\pi$
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	−0.816409	+	0.577474i	$0.804038\pi$
$824$		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	$-0.970427\pi$
$829$	−12.0208	+	20.8207i	−0.417500	+	0.723132i	0.578187	+	0.815904i	$0.303760\pi$
$830$	14.1962	−	12.5885i	0.492756	−	0.436952i
$831$	−33.9411	−	58.7878i	−1.17740	−	2.03932i
$832$			29.6985i			1.02961i
$833$		0			0
$834$	8.00000			0.277017
$835$	−24.7846	+	5.07180i	−0.857707	+	0.175517i
$836$		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	$-0.405365\pi$
$839$	16.9706			0.585889			0.292944	+	0.956129i	$0.405365\pi$
$840$		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
$845$	2.24144	+	10.9534i	0.0771078	+	0.376807i
$846$		0			0
$847$		0			0
$848$		−	8.00000i		−	0.274721i
$849$	−36.0000	−	62.3538i	−1.23552	−	2.13998i
$850$	19.5080	−	8.33298i	0.669118	−	0.285819i
$851$	−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	$0.0699200\pi$
$853$			12.7279i			0.435796i	−0.975972	+	0.217898i	$0.930080\pi$
$854$		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	0.983593	+	0.180403i	$0.0577403\pi$
$857$	47.7650	+	27.5772i	1.63162	+	0.942018i	0.648030	+	0.761615i	$0.275593\pi$
$858$		0			0
$859$	15.5563	+	26.9444i	0.530776	+	0.919331i	0.999355	+	0.0359092i	$0.0114327\pi$
$859$	15.5563	+	26.9444i	0.530776	+	0.919331i	−0.468579	+	0.883421i	$0.655234\pi$
$860$		0			0
$861$		0			0
$862$			24.0000i			0.817443i
$863$	13.8564	−	8.00000i	0.471678	−	0.272323i	−0.245264	−	0.969456i	$-0.578875\pi$
$863$	13.8564	−	8.00000i	0.471678	−	0.272323i	0.716942	+	0.697133i	$0.245541\pi$
$864$	14.1421	−	24.4949i	0.481125	−	0.833333i
$865$	6.29423	+	7.09808i	0.214010	+	0.241342i
$866$	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	$-0.835733\pi$
$877$	−25.9808	+	15.0000i	−0.877308	+	0.506514i	−0.00753813	+	0.999972i	$0.502399\pi$
$878$	−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	$-0.787934\pi$
$881$	−46.6690			−1.57232			−0.786160	+	0.618023i	$0.787934\pi$
$882$		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
$885$	35.6055	+	40.1528i	1.19687	+	1.34972i
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$	14.6969	−	8.48528i	0.493475	−	0.284908i	−0.232540	−	0.972587i	$-0.574704\pi$
$887$	14.6969	−	8.48528i	0.493475	−	0.284908i	0.726015	+	0.687679i	$0.241370\pi$
$888$			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
$900$	22.9904	−	9.82051i	0.766346	−	0.327350i
$901$	16.9706	+	29.3939i	0.565371	+	0.979252i
$902$		0			0
$903$		0			0
$904$	24.0000			0.798228
$905$	−8.24167	−	40.2750i	−0.273962	−	1.33879i
$906$		0			0
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	0.662512	−	0.749051i	$-0.269490\pi$
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	−0.317441	+	0.948278i	$0.602824\pi$
$908$	−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
$915$	61.3388	−	12.5521i	2.02780	−	0.414958i
$916$	7.07107			0.233635
$917$		0			0
$918$		−	24.0000i		−	0.792118i
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	0.982486	−	0.186338i	$-0.0596619\pi$
$919$	10.0000	+	17.3205i	0.329870	+	0.571351i	−0.652616	+	0.757689i	$0.726329\pi$
$920$	−20.0764	+	17.8028i	−0.661899	+	0.586940i
$921$	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	$-0.0997126\pi$
$929$	6.36396	+	11.0227i	0.208795	+	0.361643i	−0.742540	+	0.669801i	$0.766379\pi$
$930$	−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	$0.0666634\pi$
$937$			12.7279i			0.415803i	−0.978150	+	0.207902i	$0.933337\pi$
$938$		0			0
$939$	−60.0000			−1.95803
$940$		0			0
$941$	−10.6066	+	18.3712i	−0.345765	+	0.598883i	−0.985493	−	0.169719i	$-0.945714\pi$
$941$	−10.6066	+	18.3712i	−0.345765	+	0.598883i	0.639727	+	0.768602i	$0.279047\pi$
$942$	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	$-0.708159\pi$
$947$	−6.92820	+	4.00000i	−0.225136	+	0.129983i	0.383190	+	0.923670i	$0.374825\pi$
$948$	−29.3939	−	16.9706i	−0.954669	−	0.551178i
$949$	−27.0000	+	46.7654i	−0.876457	+	1.51807i
$950$	−14.0406	−	1.69161i	−0.455537	−	0.0548832i
$951$	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
$955$	−20.0764	+	17.8028i	−0.649657	+	0.576084i
$956$	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
$970$	−7.09808	+	6.29423i	−0.227905	+	0.202096i
$971$	4.24264	+	7.34847i	0.136153	+	0.235824i	0.926037	−	0.377432i	$-0.123193\pi$
$971$	4.24264	+	7.34847i	0.136153	+	0.235824i	−0.789884	+	0.613256i	$0.789860\pi$
$972$			14.1421i			0.453609i
$973$		0			0
$974$	12.0000			0.384505
$975$	−7.17691	+	59.5692i	−0.229845	+	1.90774i
$976$	−4.94975	+	8.57321i	−0.158438	+	0.274422i
$977$	8.66025	+	5.00000i	0.277066	+	0.159964i	0.632094	−	0.774891i	$-0.282195\pi$
$977$	8.66025	+	5.00000i	0.277066	+	0.159964i	−0.355028	+	0.934856i	$0.615529\pi$
$978$	−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	0.0556128	−	0.998452i	$-0.482289\pi$
$983$	−24.4949	−	14.1421i	−0.781266	−	0.451064i	−0.836879	+	0.547388i	$0.815622\pi$
$984$	18.0000	−	31.1769i	0.573819	−	0.993884i
$985$	−17.5254	+	3.58630i	−0.558405	+	0.114269i
$986$		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	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$	−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	−0.999889	−	0.0148965i	$-0.995258\pi$
$997$	−47.7650	−	27.5772i	−1.51273	−	0.873378i	−0.512845	−	0.858481i	$-0.671409\pi$
$998$	−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.214.4		8
5.4	even	2	inner	245.2.j.g.214.1		8
7.2	even	3	inner	245.2.j.g.79.1		8
7.3	odd	6		245.2.b.f.99.4	yes	4
7.4	even	3		245.2.b.f.99.3	yes	4
7.5	odd	6	inner	245.2.j.g.79.2		8
7.6	odd	2	inner	245.2.j.g.214.3		8
21.11	odd	6		2205.2.d.k.1324.1		4
21.17	even	6		2205.2.d.k.1324.2		4
35.3	even	12		1225.2.a.v.1.1		2
35.4	even	6		245.2.b.f.99.2	yes	4
35.9	even	6	inner	245.2.j.g.79.4		8
35.17	even	12		1225.2.a.l.1.2		2
35.18	odd	12		1225.2.a.v.1.2		2
35.19	odd	6	inner	245.2.j.g.79.3		8
35.24	odd	6		245.2.b.f.99.1	✓	4
35.32	odd	12		1225.2.a.l.1.1		2
35.34	odd	2	inner	245.2.j.g.214.2		8
105.59	even	6		2205.2.d.k.1324.4		4
105.74	odd	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	35.24	odd	6
245.2.b.f.99.2	yes	4	35.4	even	6
245.2.b.f.99.3	yes	4	7.4	even	3
245.2.b.f.99.4	yes	4	7.3	odd	6
245.2.j.g.79.1		8	7.2	even	3	inner
245.2.j.g.79.2		8	7.5	odd	6	inner
245.2.j.g.79.3		8	35.19	odd	6	inner
245.2.j.g.79.4		8	35.9	even	6	inner
245.2.j.g.214.1		8	5.4	even	2	inner
245.2.j.g.214.2		8	35.34	odd	2	inner
245.2.j.g.214.3		8	7.6	odd	2	inner
245.2.j.g.214.4		8	1.1	even	1	trivial
1225.2.a.l.1.1		2	35.32	odd	12
1225.2.a.l.1.2		2	35.17	even	12
1225.2.a.v.1.1		2	35.3	even	12
1225.2.a.v.1.2		2	35.18	odd	12
2205.2.d.k.1324.1		4	21.11	odd	6
2205.2.d.k.1324.2		4	21.17	even	6
2205.2.d.k.1324.3		4	105.74	odd	6
2205.2.d.k.1324.4		4	105.59	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(2.44949 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.448288 - 2.19067i) q^{5} +2.82843 q^{6} +3.00000i q^{8} +(2.50000 + 4.33013i) q^{9} +(-1.48356 - 1.67303i) q^{10} +(-2.44949 + 1.41421i) q^{12} -4.24264i q^{13} +(2.00000 - 6.00000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.67423 - 2.12132i) q^{17} +(4.33013 + 2.50000i) q^{18} +(1.41421 + 2.44949i) q^{19} +(2.12132 + 0.707107i) q^{20} +(-3.46410 + 2.00000i) q^{23} +(-4.24264 + 7.34847i) q^{24} +(-4.59808 + 1.96410i) q^{25} +(-2.12132 - 3.67423i) q^{26} +5.65685i q^{27} +(-1.26795 - 6.19615i) q^{30} +(2.82843 - 4.89898i) q^{31} +(-4.33013 - 2.50000i) q^{32} -4.24264 q^{34} -5.00000 q^{36} +(5.19615 - 3.00000i) q^{37} +(2.44949 + 1.41421i) q^{38} +(6.00000 - 10.3923i) q^{39} +(6.57201 - 1.34486i) q^{40} -4.24264 q^{41} +(8.36516 - 7.41782i) q^{45} +(-2.00000 + 3.46410i) q^{46} +2.82843i q^{48} +(-3.00000 + 4.00000i) q^{50} +(-6.00000 - 10.3923i) q^{51} +(3.67423 + 2.12132i) q^{52} +(-6.92820 - 4.00000i) q^{53} +(2.82843 + 4.89898i) q^{54} +8.00000i q^{57} +(-4.24264 + 7.34847i) q^{59} +(4.19615 + 4.73205i) q^{60} +(4.94975 + 8.57321i) q^{61} -5.65685i q^{62} -7.00000 q^{64} +(-9.29423 + 1.90192i) q^{65} +(10.3923 + 6.00000i) q^{67} +(3.67423 - 2.12132i) q^{68} -11.3137 q^{69} +12.0000 q^{71} +(-12.9904 + 7.50000i) q^{72} +(-11.0227 - 6.36396i) q^{73} +(3.00000 - 5.19615i) q^{74} +(-14.0406 - 1.69161i) q^{75} -2.82843 q^{76} -12.0000i q^{78} +(6.00000 + 10.3923i) q^{79} +(1.67303 - 1.48356i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.67423 + 2.12132i) q^{82} +8.48528i q^{83} +(-3.00000 + 9.00000i) q^{85} +(2.12132 + 3.67423i) q^{89} +(3.53553 - 10.6066i) q^{90} -4.00000i q^{92} +(13.8564 - 8.00000i) q^{93} +(4.73205 - 4.19615i) q^{95} +(-7.07107 - 12.2474i) q^{96} -4.24264i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} + 20 q^{9} + 16 q^{15} + 4 q^{16} - 16 q^{25} - 24 q^{30} - 40 q^{36} + 48 q^{39} - 16 q^{46} - 24 q^{50} - 48 q^{51} - 8 q^{60} - 56 q^{64} - 12 q^{65} + 96 q^{71} + 24 q^{74} + 48 q^{79}+ \cdots + 24 q^{95}+O(q^{100}) \) 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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