LMFDB - Embedded newform 784.2.bp.a.495.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(47,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 5]))

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

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

chi := DirichletCharacter("784.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bp (of order $42$, degree $12$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$9$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			495.1
Character	$\chi$	$=$	784.495
Dual form			784.2.bp.a.255.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56319 - 1.74756i) q^{3} +(-0.669397 - 0.0501644i) q^{5} +(-1.61167 + 2.09822i) q^{7} +(2.41998 + 6.16602i) q^{9} +O(q^{10})$	\(q+(-2.56319 - 1.74756i) q^{3} +(-0.669397 - 0.0501644i) q^{5} +(-1.61167 + 2.09822i) q^{7} +(2.41998 + 6.16602i) q^{9} +(0.286718 + 0.112528i) q^{11} +(2.53908 - 2.02485i) q^{13} +(1.62813 + 1.29839i) q^{15} +(3.22964 + 3.48072i) q^{17} +(1.50563 - 2.60783i) q^{19} +(7.79778 - 2.56164i) q^{21} +(-0.359481 + 0.387429i) q^{23} +(-4.49858 - 0.678052i) q^{25} +(2.50163 - 10.9604i) q^{27} +(-0.589753 - 2.58388i) q^{29} +(-2.57784 - 4.46495i) q^{31} +(-0.538263 - 0.789488i) q^{33} +(1.18411 - 1.32369i) q^{35} +(6.87877 + 2.12182i) q^{37} +(-10.0467 + 0.752894i) q^{39} +(-3.73365 - 7.75301i) q^{41} +(-2.08485 + 4.32925i) q^{43} +(-1.31062 - 4.24891i) q^{45} +(11.4242 - 1.72192i) q^{47} +(-1.80502 - 6.76328i) q^{49} +(-2.19543 - 14.5657i) q^{51} +(-3.18024 + 0.980975i) q^{53} +(-0.186283 - 0.0897092i) q^{55} +(-8.41654 + 4.05319i) q^{57} +(-0.636479 - 8.49322i) q^{59} +(-0.334479 + 1.08435i) q^{61} +(-16.8379 - 4.85996i) q^{63} +(-1.80122 + 1.22805i) q^{65} +(-0.813472 + 0.469658i) q^{67} +(1.59847 - 0.364841i) q^{69} +(10.6445 + 2.42953i) q^{71} +(2.21730 - 14.7108i) q^{73} +(10.3458 + 9.59949i) q^{75} +(-0.698205 + 0.420237i) q^{77} +(10.6030 + 6.12167i) q^{79} +(-10.9990 + 10.2056i) q^{81} +(11.1287 - 13.9550i) q^{83} +(-1.98730 - 2.49200i) q^{85} +(-3.00382 + 7.65360i) q^{87} +(9.49753 - 3.72751i) q^{89} +(0.156400 + 8.59092i) q^{91} +(-1.19525 + 15.9494i) q^{93} +(-1.13868 + 1.67014i) q^{95} +15.1809i q^{97} +2.04023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - q^{3} - 3 q^{5} + 4 q^{7} + 8 q^{9}+O(q^{10}) $ 108 * q - q^3 - 3 * q^5 + 4 * q^7 + 8 * q^9	$ 108 q - q^{3} - 3 q^{5} + 4 q^{7} + 8 q^{9} - 18 q^{11} + 16 q^{17} - 7 q^{19} + 5 q^{21} - 54 q^{23} - 4 q^{25} + 53 q^{27} - 16 q^{29} - 5 q^{31} - 3 q^{33} + 9 q^{35} + 2 q^{37} + 43 q^{39} - 28 q^{41} - 111 q^{45} + 60 q^{47} - 58 q^{49} + 3 q^{51} - 70 q^{53} - 69 q^{55} + 31 q^{57} - 9 q^{59} - 8 q^{61} - 93 q^{63} - 8 q^{65} + 21 q^{67} - 56 q^{69} + 63 q^{71} - 24 q^{73} - 2 q^{75} - 18 q^{77} - 21 q^{79} + 45 q^{81} - 60 q^{83} + 6 q^{85} + 6 q^{87} + 7 q^{89} + 66 q^{93} - 15 q^{95}+O(q^{100}) $ 108 * q - q^3 - 3 * q^5 + 4 * q^7 + 8 * q^9 - 18 * q^11 + 16 * q^17 - 7 * q^19 + 5 * q^21 - 54 * q^23 - 4 * q^25 + 53 * q^27 - 16 * q^29 - 5 * q^31 - 3 * q^33 + 9 * q^35 + 2 * q^37 + 43 * q^39 - 28 * q^41 - 111 * q^45 + 60 * q^47 - 58 * q^49 + 3 * q^51 - 70 * q^53 - 69 * q^55 + 31 * q^57 - 9 * q^59 - 8 * q^61 - 93 * q^63 - 8 * q^65 + 21 * q^67 - 56 * q^69 + 63 * q^71 - 24 * q^73 - 2 * q^75 - 18 * q^77 - 21 * q^79 + 45 * q^81 - 60 * q^83 + 6 * q^85 + 6 * q^87 + 7 * q^89 + 66 * q^93 - 15 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{29}{42}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.56319	−	1.74756i	−1.47986	−	1.00895i	−0.990597	−	0.136815i	$-0.956313\pi$
$3$	−2.56319	−	1.74756i	−1.47986	−	1.00895i	−0.489263	−	0.872136i	$-0.662734\pi$
$4$		0			0
$5$	−0.669397	−	0.0501644i	−0.299363	−	0.0224342i	−0.0757982	−	0.997123i	$-0.524150\pi$
$5$	−0.669397	−	0.0501644i	−0.299363	−	0.0224342i	−0.223565	+	0.974689i	$0.571770\pi$
$6$		0			0
$7$	−1.61167	+	2.09822i	−0.609155	+	0.793051i
$7$	−1.61167	+	2.09822i	−0.609155	+	0.793051i
$8$		0			0
$9$	2.41998	+	6.16602i	0.806662	+	2.05534i
$10$		0			0
$11$	0.286718	+	0.112528i	0.0864487	+	0.0339286i	0.408171	−	0.912905i	$-0.366167\pi$
$11$	0.286718	+	0.112528i	0.0864487	+	0.0339286i	−0.321723	+	0.946834i	$0.604262\pi$
$12$		0			0
$13$	2.53908	−	2.02485i	0.704213	−	0.561591i	−0.204574	−	0.978851i	$-0.565581\pi$
$13$	2.53908	−	2.02485i	0.704213	−	0.561591i	0.908787	+	0.417260i	$0.137010\pi$
$14$		0			0
$15$	1.62813	+	1.29839i	0.420381	+	0.335243i
$16$		0			0
$17$	3.22964	+	3.48072i	0.783302	+	0.844199i	0.990982	−	0.133998i	$-0.0427816\pi$
$17$	3.22964	+	3.48072i	0.783302	+	0.844199i	−0.207679	+	0.978197i	$0.566591\pi$
$18$		0			0
$19$	1.50563	−	2.60783i	0.345415	−	0.598276i	−0.640014	−	0.768363i	$-0.721072\pi$
$19$	1.50563	−	2.60783i	0.345415	−	0.598276i	0.985429	+	0.170087i	$0.0544049\pi$
$20$		0			0
$21$	7.79778	−	2.56164i	1.70161	−	0.558996i
$22$		0			0
$23$	−0.359481	+	0.387429i	−0.0749570	+	0.0807844i	−0.769417	−	0.638747i	$-0.779453\pi$
$23$	−0.359481	+	0.387429i	−0.0749570	+	0.0807844i	0.694460	+	0.719532i	$0.255643\pi$
$24$		0			0
$25$	−4.49858	−	0.678052i	−0.899716	−	0.135610i
$26$		0			0
$27$	2.50163	−	10.9604i	0.481439	−	2.10932i
$28$		0			0
$29$	−0.589753	−	2.58388i	−0.109514	−	0.479814i	−0.999706	−	0.0242285i	$-0.992287\pi$
$29$	−0.589753	−	2.58388i	−0.109514	−	0.479814i	0.890192	−	0.455585i	$-0.150570\pi$
$30$		0			0
$31$	−2.57784	−	4.46495i	−0.462994	−	0.801929i	0.536115	−	0.844145i	$-0.319891\pi$
$31$	−2.57784	−	4.46495i	−0.462994	−	0.801929i	−0.999108	+	0.0422163i	$0.986558\pi$
$32$		0			0
$33$	−0.538263	−	0.789488i	−0.0936996	−	0.137432i
$34$		0			0
$35$	1.18411	−	1.32369i	0.200150	−	0.223744i
$36$		0			0
$37$	6.87877	+	2.12182i	1.13086	+	0.348825i	0.803046	−	0.595917i	$-0.203211\pi$
$37$	6.87877	+	2.12182i	1.13086	+	0.348825i	0.327816	+	0.944741i	$0.393687\pi$
$38$		0			0
$39$	−10.0467	+	0.752894i	−1.60875	+	0.120559i
$40$		0			0
$41$	−3.73365	−	7.75301i	−0.583098	−	1.21082i	−0.958802	−	0.284076i	$-0.908313\pi$
$41$	−3.73365	−	7.75301i	−0.583098	−	1.21082i	0.375703	−	0.926740i	$-0.377401\pi$
$42$		0			0
$43$	−2.08485	+	4.32925i	−0.317937	+	0.660204i	−0.997287	−	0.0736109i	$-0.976548\pi$
$43$	−2.08485	+	4.32925i	−0.317937	+	0.660204i	0.679350	+	0.733815i	$0.262262\pi$
$44$		0			0
$45$	−1.31062	−	4.24891i	−0.195375	−	0.633390i
$46$		0			0
$47$	11.4242	−	1.72192i	1.66639	−	0.251168i	0.752932	−	0.658099i	$-0.228639\pi$
$47$	11.4242	−	1.72192i	1.66639	−	0.251168i	0.913459	+	0.406931i	$0.133401\pi$
$48$		0			0
$49$	−1.80502	−	6.76328i	−0.257859	−	0.966182i
$50$		0			0
$51$	−2.19543	−	14.5657i	−0.307422	−	2.03961i
$52$		0			0
$53$	−3.18024	+	0.980975i	−0.436840	+	0.134747i	−0.505372	−	0.862902i	$-0.668645\pi$
$53$	−3.18024	+	0.980975i	−0.436840	+	0.134747i	0.0685320	+	0.997649i	$0.478168\pi$
$54$		0			0
$55$	−0.186283	−	0.0897092i	−0.0251184	−	0.0120964i
$56$		0			0
$57$	−8.41654	+	4.05319i	−1.11480	+	0.536858i
$58$		0			0
$59$	−0.636479	−	8.49322i	−0.0828625	−	1.10572i	−0.871347	−	0.490668i	$-0.836753\pi$
$59$	−0.636479	−	8.49322i	−0.0828625	−	1.10572i	0.788484	−	0.615055i	$-0.210866\pi$
$60$		0			0
$61$	−0.334479	+	1.08435i	−0.0428256	+	0.138837i	−0.974461	−	0.224558i	$-0.927906\pi$
$61$	−0.334479	+	1.08435i	−0.0428256	+	0.138837i	0.931635	+	0.363395i	$0.118382\pi$
$62$		0			0
$63$	−16.8379	−	4.85996i	−2.12137	−	0.612298i
$64$		0			0
$65$	−1.80122	+	1.22805i	−0.223414	+	0.152321i
$66$		0			0
$67$	−0.813472	+	0.469658i	−0.0993814	+	0.0573779i	−0.548867	−	0.835910i	$-0.684941\pi$
$67$	−0.813472	+	0.469658i	−0.0993814	+	0.0573779i	0.449486	+	0.893288i	$0.351607\pi$
$68$		0			0
$69$	1.59847	−	0.364841i	0.192433	−	0.0439217i
$70$		0			0
$71$	10.6445	+	2.42953i	1.26326	+	0.288332i	0.801137	−	0.598481i	$-0.204229\pi$
$71$	10.6445	+	2.42953i	1.26326	+	0.288332i	0.462128	+	0.886813i	$0.347086\pi$
$72$		0			0
$73$	2.21730	−	14.7108i	0.259515	−	1.72177i	−0.356722	−	0.934211i	$-0.616106\pi$
$73$	2.21730	−	14.7108i	0.259515	−	1.72177i	0.616237	−	0.787561i	$-0.288656\pi$
$74$		0			0
$75$	10.3458	+	9.59949i	1.19463	+	1.10845i
$76$		0			0
$77$	−0.698205	+	0.420237i	−0.0795678	+	0.0478904i
$78$		0			0
$79$	10.6030	+	6.12167i	1.19294	+	0.688742i	0.958971	−	0.283503i	$-0.0914966\pi$
$79$	10.6030	+	6.12167i	1.19294	+	0.688742i	0.233965	+	0.972245i	$0.424830\pi$
$80$		0			0
$81$	−10.9990	+	10.2056i	−1.22211	+	1.13395i
$82$		0			0
$83$	11.1287	−	13.9550i	1.22154	−	1.53176i	0.453643	−	0.891183i	$-0.350124\pi$
$83$	11.1287	−	13.9550i	1.22154	−	1.53176i	0.767894	−	0.640577i	$-0.221305\pi$
$84$		0			0
$85$	−1.98730	−	2.49200i	−0.215553	−	0.270295i
$86$		0			0
$87$	−3.00382	+	7.65360i	−0.322043	+	0.820552i
$88$		0			0
$89$	9.49753	−	3.72751i	1.00674	−	0.395115i	0.196049	−	0.980594i	$-0.437189\pi$
$89$	9.49753	−	3.72751i	1.00674	−	0.395115i	0.810687	+	0.585479i	$0.199094\pi$
$90$		0			0
$91$	0.156400	+	8.59092i	0.0163951	+	0.900573i
$92$		0			0
$93$	−1.19525	+	15.9494i	−0.123941	+	1.65388i
$94$		0			0
$95$	−1.13868	+	1.67014i	−0.116826	+	0.171353i
$96$		0			0
$97$			15.1809i			1.54138i	0.637208	+	0.770691i	$0.280089\pi$
$97$			15.1809i			1.54138i	−0.637208	+	0.770691i	$0.719911\pi$
$98$		0			0
$99$			2.04023i			0.205050i
$100$		0			0
$101$	6.27847	−	9.20883i	0.624732	−	0.916313i	−0.375212	−	0.926939i	$-0.622430\pi$
$101$	6.27847	−	9.20883i	0.624732	−	0.916313i	0.999944	+	0.0106261i	$0.00338246\pi$
$102$		0			0
$103$	−1.09198	+	14.5715i	−0.107596	+	1.43577i	0.638341	+	0.769754i	$0.279621\pi$
$103$	−1.09198	+	14.5715i	−0.107596	+	1.43577i	−0.745937	+	0.666016i	$0.767998\pi$
$104$		0			0
$105$	−5.34831	+	1.32358i	−0.521942	+	0.129169i
$106$		0			0
$107$	6.63414	−	2.60371i	0.641347	−	0.251710i	−0.0223056	−	0.999751i	$-0.507101\pi$
$107$	6.63414	−	2.60371i	0.641347	−	0.251710i	0.663652	+	0.748041i	$0.269005\pi$
$108$		0			0
$109$	5.19846	−	13.2454i	0.497922	−	1.26868i	−0.432315	−	0.901723i	$-0.642303\pi$
$109$	5.19846	−	13.2454i	0.497922	−	1.26868i	0.930236	−	0.366961i	$-0.119602\pi$
$110$		0			0
$111$	−13.9236	−	17.4597i	−1.32157	−	1.65720i
$112$		0			0
$113$	−0.848621	+	1.06414i	−0.0798315	+	0.100106i	−0.820143	−	0.572158i	$-0.806106\pi$
$113$	−0.848621	+	1.06414i	−0.0798315	+	0.100106i	0.740312	+	0.672264i	$0.234678\pi$
$114$		0			0
$115$	0.260071	−	0.241310i	0.0242517	−	0.0225023i
$116$		0			0
$117$	18.6298	+	10.7559i	1.72232	+	0.994383i
$118$		0			0
$119$	−12.5084	+	1.16669i	−1.14665	+	0.106950i
$120$		0			0
$121$	−7.99403	−	7.41737i	−0.726730	−	0.674307i
$122$		0			0
$123$	−3.97874	+	26.3972i	−0.358751	+	2.38016i
$124$		0			0
$125$	6.24954	+	1.42642i	0.558976	+	0.127583i
$126$		0			0
$127$	5.27704	−	1.20445i	0.468262	−	0.106878i	0.0181221	−	0.999836i	$-0.494231\pi$
$127$	5.27704	−	1.20445i	0.468262	−	0.106878i	0.450140	+	0.892958i	$0.351374\pi$
$128$		0			0
$129$	12.9095	−	7.45329i	1.13662	−	0.656226i
$130$		0			0
$131$	−9.54036	+	6.50451i	−0.833545	+	0.568301i	−0.903176	−	0.429271i	$-0.858770\pi$
$131$	−9.54036	+	6.50451i	−0.833545	+	0.568301i	0.0696304	+	0.997573i	$0.477818\pi$
$132$		0			0
$133$	3.04520	+	7.36210i	0.264052	+	0.638375i
$134$		0			0
$135$	−2.22440	+	7.21134i	−0.191446	+	0.620654i
$136$		0			0
$137$	1.11468	+	14.8743i	0.0952333	+	1.27080i	0.816175	+	0.577805i	$0.196091\pi$
$137$	1.11468	+	14.8743i	0.0952333	+	1.27080i	−0.720942	+	0.692996i	$0.756290\pi$
$138$		0			0
$139$	−15.1566	+	7.29902i	−1.28556	+	0.619095i	−0.946814	−	0.321781i	$-0.895718\pi$
$139$	−15.1566	+	7.29902i	−1.28556	+	0.619095i	−0.338750	+	0.940876i	$0.610004\pi$
$140$		0			0
$141$	−32.2916	−	15.5508i	−2.71944	−	1.30961i
$142$		0			0
$143$	0.955851	−	0.294841i	0.0799323	−	0.0246558i
$144$		0			0
$145$	0.265160	+	1.75922i	0.0220204	+	0.146096i
$146$		0			0
$147$	−7.19260	+	20.4899i	−0.593236	+	1.68998i
$148$		0			0
$149$	18.0427	−	2.71950i	1.47811	−	0.222790i	0.640038	−	0.768344i	$-0.278919\pi$
$149$	18.0427	−	2.71950i	1.47811	−	0.222790i	0.838076	+	0.545554i	$0.183681\pi$
$150$		0			0
$151$	−2.47088	−	8.01040i	−0.201077	−	0.651877i	−0.998806	−	0.0488598i	$-0.984441\pi$
$151$	−2.47088	−	8.01040i	−0.201077	−	0.651877i	0.797728	−	0.603017i	$-0.206035\pi$
$152$		0			0
$153$	−13.6465	+	28.3373i	−1.10326	+	2.29093i
$154$		0			0
$155$	1.50162	+	3.11814i	0.120613	+	0.250455i
$156$		0			0
$157$	6.13112	−	0.459464i	0.489317	−	0.0366692i	0.172212	−	0.985060i	$-0.444908\pi$
$157$	6.13112	−	0.459464i	0.489317	−	0.0366692i	0.317104	+	0.948391i	$0.397289\pi$
$158$		0			0
$159$	9.86588	+	3.04322i	0.782415	+	0.241343i
$160$		0			0
$161$	−0.233542	−	1.37868i	−0.0184057	−	0.108655i
$162$		0			0
$163$	−10.1592	−	14.9008i	−0.795729	−	1.16712i	−0.982782	−	0.184770i	$-0.940846\pi$
$163$	−10.1592	−	14.9008i	−0.795729	−	1.16712i	0.187053	−	0.982350i	$-0.440106\pi$
$164$		0			0
$165$	0.320708	+	0.555482i	0.0249671	+	0.0432442i
$166$		0			0
$167$	4.11711	+	18.0382i	0.318592	+	1.39584i	0.840024	+	0.542549i	$0.182541\pi$
$167$	4.11711	+	18.0382i	0.318592	+	1.39584i	−0.521432	+	0.853293i	$0.674602\pi$
$168$		0			0
$169$	−0.545866	+	2.39159i	−0.0419897	+	0.183969i
$170$		0			0
$171$	19.7235	+	2.97284i	1.50829	+	0.227339i
$172$		0			0
$173$	−3.65571	+	3.93992i	−0.277938	+	0.299546i	−0.856558	−	0.516052i	$-0.827401\pi$
$173$	−3.65571	+	3.93992i	−0.277938	+	0.299546i	0.578619	+	0.815598i	$0.303592\pi$
$174$		0			0
$175$	8.67294	−	8.34619i	0.655613	−	0.630913i
$176$		0			0
$177$	−13.2109	+	22.8820i	−0.992996	+	1.71992i
$178$		0			0
$179$	−3.08229	−	3.32192i	−0.230381	−	0.248292i	0.607273	−	0.794494i	$-0.292264\pi$
$179$	−3.08229	−	3.32192i	−0.230381	−	0.248292i	−0.837654	+	0.546202i	$0.816073\pi$
$180$		0			0
$181$	−20.0032	−	15.9521i	−1.48683	−	1.18571i	−0.936455	−	0.350789i	$-0.885913\pi$
$181$	−20.0032	−	15.9521i	−1.48683	−	1.18571i	−0.550375	−	0.834918i	$-0.685515\pi$
$182$		0			0
$183$	2.75230	−	2.19489i	0.203456	−	0.162251i
$184$		0			0
$185$	−4.49819	−	1.76541i	−0.330713	−	0.129795i
$186$		0			0
$187$	0.534315	+	1.36141i	0.0390729	+	0.0995562i
$188$		0			0
$189$	18.9654	+	22.9135i	1.37953	+	1.66671i
$190$		0			0
$191$	21.9411	+	1.64426i	1.58760	+	0.118975i	0.839034	−	0.544080i	$-0.183121\pi$
$191$	21.9411	+	1.64426i	1.58760	+	0.118975i	0.748571	+	0.663054i	$0.230740\pi$
$192$		0			0
$193$	−6.07846	−	4.14422i	−0.437537	−	0.298308i	0.324447	−	0.945904i	$-0.394822\pi$
$193$	−6.07846	−	4.14422i	−0.437537	−	0.298308i	−0.761984	+	0.647596i	$0.775774\pi$
$194$		0			0
$195$	6.76298			0.484307
$196$		0			0
$197$	−2.00980			−0.143193			−0.0715963	−	0.997434i	$-0.522809\pi$
$197$	−2.00980			−0.143193			−0.0715963	+	0.997434i	$0.522809\pi$
$198$		0			0
$199$	4.91413	+	3.35039i	0.348353	+	0.237503i	0.724838	−	0.688920i	$-0.241915\pi$
$199$	4.91413	+	3.35039i	0.348353	+	0.237503i	−0.376484	+	0.926423i	$0.622867\pi$
$200$		0			0
$201$	2.90584	+	0.217763i	0.204962	+	0.0153598i
$202$		0			0
$203$	6.37202	+	2.92694i	0.447228	+	0.205431i
$204$		0			0
$205$	2.11037	+	5.37713i	0.147395	+	0.375555i
$206$		0			0
$207$	−3.25883	−	1.27900i	−0.226504	−	0.0888964i
$208$		0			0
$209$	0.725145	−	0.578284i	0.0501593	−	0.0400007i
$210$		0			0
$211$	12.5526	+	10.0103i	0.864154	+	0.689140i	0.951703	−	0.307020i	$-0.0993319\pi$
$211$	12.5526	+	10.0103i	0.864154	+	0.689140i	−0.0875488	+	0.996160i	$0.527903\pi$
$212$		0			0
$213$	−23.0381	−	24.8291i	−1.57854	−	1.70126i
$214$		0			0
$215$	1.61277	−	2.79340i	0.109990	−	0.190508i
$216$		0			0
$217$	13.5231	+	1.78718i	0.918006	+	0.121322i
$218$		0			0
$219$	−31.3913	+	33.8318i	−2.12123	+	2.28614i
$220$		0			0
$221$	15.2482	+	2.29830i	1.02571	+	0.154600i
$222$		0			0
$223$	−0.0428647	+	0.187802i	−0.00287043	+	0.0125762i	−0.976343	−	0.216228i	$-0.930624\pi$
$223$	−0.0428647	+	0.187802i	−0.00287043	+	0.0125762i	0.973472	+	0.228804i	$0.0734816\pi$
$224$		0			0
$225$	−6.70561	−	29.3792i	−0.447041	−	1.95861i
$226$		0			0
$227$	0.529826	+	0.917686i	0.0351658	+	0.0609090i	0.883073	−	0.469236i	$-0.155471\pi$
$227$	0.529826	+	0.917686i	0.0351658	+	0.0609090i	−0.847907	+	0.530145i	$0.822137\pi$
$228$		0			0
$229$	−6.93517	−	10.1720i	−0.458289	−	0.672186i	0.525648	−	0.850702i	$-0.323823\pi$
$229$	−6.93517	−	10.1720i	−0.458289	−	0.672186i	−0.983937	+	0.178516i	$0.942870\pi$
$230$		0			0
$231$	2.52402	+	0.143004i	0.166068	+	0.00940895i
$232$		0			0
$233$	−11.5203	−	3.55353i	−0.754718	−	0.232800i	−0.106560	−	0.994306i	$-0.533984\pi$
$233$	−11.5203	−	3.55353i	−0.754718	−	0.232800i	−0.648157	+	0.761507i	$0.724460\pi$
$234$		0			0
$235$	−7.73370	+	0.579561i	−0.504491	+	0.0378064i
$236$		0			0
$237$	−16.4797	−	34.2204i	−1.07047	−	2.22286i
$238$		0			0
$239$	11.3340	−	23.5353i	0.733134	−	1.52237i	−0.115453	−	0.993313i	$-0.536832\pi$
$239$	11.3340	−	23.5353i	0.733134	−	1.52237i	0.848587	−	0.529056i	$-0.177454\pi$
$240$		0			0
$241$	−2.05323	−	6.65642i	−0.132260	−	0.428778i	0.865082	−	0.501630i	$-0.167266\pi$
$241$	−2.05323	−	6.65642i	−0.132260	−	0.428778i	−0.997343	+	0.0728522i	$0.976790\pi$
$242$		0			0
$243$	12.6774	−	1.91081i	0.813257	−	0.122579i
$244$		0			0
$245$	0.868996	+	4.61786i	0.0555181	+	0.295025i
$246$		0			0
$247$	−1.45754	−	9.67013i	−0.0927409	−	0.615296i
$248$		0			0
$249$	−52.9122	+	16.3213i	−3.35318	+	1.03432i
$250$		0			0
$251$	−0.918835	−	0.442488i	−0.0579963	−	0.0279296i	0.404661	−	0.914467i	$-0.367390\pi$
$251$	−0.918835	−	0.442488i	−0.0579963	−	0.0279296i	−0.462657	+	0.886537i	$0.653104\pi$
$252$		0			0
$253$	−0.146666	+	0.0706308i	−0.00922084	+	0.00444052i
$254$		0			0
$255$	0.738934	+	9.86039i	0.0462738	+	0.617481i
$256$		0			0
$257$	5.99499	−	19.4353i	0.373957	−	1.21234i	−0.551721	−	0.834029i	$-0.686029\pi$
$257$	5.99499	−	19.4353i	0.373957	−	1.21234i	0.925678	−	0.378311i	$-0.123495\pi$
$258$		0			0
$259$	−15.5384	+	11.0135i	−0.965507	+	0.684343i
$260$		0			0
$261$	14.5050	−	9.88937i	0.897840	−	0.612137i
$262$		0			0
$263$	6.32565	−	3.65212i	0.390056	−	0.225199i	−0.292128	−	0.956379i	$-0.594363\pi$
$263$	6.32565	−	3.65212i	0.390056	−	0.225199i	0.682185	+	0.731180i	$0.261030\pi$
$264$		0			0
$265$	2.17805	−	0.497127i	0.133797	−	0.0305383i
$266$		0			0
$267$	−30.8580	−	7.04314i	−1.88848	−	0.431033i
$268$		0			0
$269$	−3.90842	+	25.9307i	−0.238301	+	1.58102i	0.474886	+	0.880047i	$0.342489\pi$
$269$	−3.90842	+	25.9307i	−0.238301	+	1.58102i	−0.713187	+	0.700974i	$0.752749\pi$
$270$		0			0
$271$	−14.1720	−	13.1497i	−0.860885	−	0.798785i	0.120121	−	0.992759i	$-0.461672\pi$
$271$	−14.1720	−	13.1497i	−0.860885	−	0.798785i	−0.981007	+	0.193974i	$0.937862\pi$
$272$		0			0
$273$	14.6122	−	22.2935i	0.884372	−	1.34926i
$274$		0			0
$275$	−1.21352	−	0.700628i	−0.0731782	−	0.0422494i
$276$		0			0
$277$	0.543674	−	0.504456i	0.0326662	−	0.0303098i	−0.663671	−	0.748025i	$-0.731002\pi$
$277$	0.543674	−	0.504456i	0.0326662	−	0.0303098i	0.696337	+	0.717715i	$0.254812\pi$
$278$		0			0
$279$	21.2926	−	26.7001i	1.27476	−	1.59849i
$280$		0			0
$281$	15.2845	+	19.1662i	0.911798	+	1.14336i	0.989231	+	0.146361i	$0.0467561\pi$
$281$	15.2845	+	19.1662i	0.911798	+	1.14336i	−0.0774331	+	0.996998i	$0.524672\pi$
$282$		0			0
$283$	−0.561663	+	1.43109i	−0.0333874	+	0.0850697i	−0.946595	−	0.322425i	$-0.895502\pi$
$283$	−0.561663	+	1.43109i	−0.0333874	+	0.0850697i	0.913208	+	0.407494i	$0.133597\pi$
$284$		0			0
$285$	5.83733	−	2.29098i	0.345773	−	0.135706i
$286$		0			0
$287$	22.2849	+	4.66131i	1.31544	+	0.275149i
$288$		0			0
$289$	−0.414451	+	5.53047i	−0.0243795	+	0.325322i
$290$		0			0
$291$	26.5294	−	38.9115i	1.55518	−	2.28103i
$292$		0			0
$293$			2.67332i			0.156177i	0.996946	+	0.0780886i	$0.0248817\pi$
$293$			2.67332i			0.156177i	−0.996946	+	0.0780886i	$0.975118\pi$
$294$		0			0
$295$			5.71726i			0.332872i
$296$		0			0
$297$	1.95062	−	2.86103i	0.113186	−	0.166014i
$298$		0			0
$299$	−0.128267	+	1.71160i	−0.00741787	+	0.0989846i
$300$		0			0
$301$	−5.72358	−	11.3518i	−0.329902	−	0.654307i
$302$		0			0
$303$	−32.1859	+	12.6320i	−1.84903	+	0.725691i
$304$		0			0
$305$	0.278295	−	0.709084i	0.0159351	−	0.0406020i
$306$		0			0
$307$	−0.144584	−	0.181303i	−0.00825184	−	0.0103475i	0.777688	−	0.628650i	$-0.216392\pi$
$307$	−0.144584	−	0.181303i	−0.00825184	−	0.0103475i	−0.785940	+	0.618302i	$0.787821\pi$
$308$		0			0
$309$	28.2634	−	35.4412i	1.60785	−	2.01618i
$310$		0			0
$311$	11.9561	−	11.0936i	0.677969	−	0.629063i	−0.264095	−	0.964497i	$-0.585073\pi$
$311$	11.9561	−	11.0936i	0.677969	−	0.629063i	0.942064	+	0.335434i	$0.108883\pi$
$312$		0			0
$313$	−5.40042	−	3.11793i	−0.305250	−	0.176236i	0.339549	−	0.940588i	$-0.389726\pi$
$313$	−5.40042	−	3.11793i	−0.305250	−	0.176236i	−0.644799	+	0.764352i	$0.723059\pi$
$314$		0			0
$315$	11.0274	+	4.09791i	0.621325	+	0.230891i
$316$		0			0
$317$	20.6399	+	19.1511i	1.15925	+	1.07563i	0.996028	+	0.0890423i	$0.0283806\pi$
$317$	20.6399	+	19.1511i	1.15925	+	1.07563i	0.163227	+	0.986589i	$0.447810\pi$
$318$		0			0
$319$	0.121667	−	0.807208i	0.00681204	−	0.0451950i
$320$		0			0
$321$	−21.5547	−	4.91972i	−1.20307	−	0.274592i
$322$		0			0
$323$	13.9397	−	3.18166i	0.775628	−	0.177032i
$324$		0			0
$325$	−12.7952	+	7.38730i	−0.709749	+	0.409774i
$326$		0			0
$327$	−36.4718	+	24.8660i	−2.01689	+	1.37510i
$328$		0			0
$329$	−14.7991	+	26.7456i	−0.815902	+	1.47453i
$330$		0			0
$331$	−2.41026	+	7.81386i	−0.132480	+	0.429489i	−0.997370	−	0.0724715i	$-0.976911\pi$
$331$	−2.41026	+	7.81386i	−0.132480	+	0.429489i	0.864891	+	0.501960i	$0.167388\pi$
$332$		0			0
$333$	3.56333	+	47.5494i	0.195270	+	2.60569i
$334$		0			0
$335$	0.568096	−	0.273580i	0.0310384	−	0.0149473i
$336$		0			0
$337$	13.2447	+	6.37830i	0.721484	+	0.347448i	0.758328	−	0.651873i	$-0.226016\pi$
$337$	13.2447	+	6.37830i	0.721484	+	0.347448i	−0.0368446	+	0.999321i	$0.511731\pi$
$338$		0			0
$339$	4.03482	−	1.24458i	0.219141	−	0.0675961i
$340$		0			0
$341$	−0.236679	−	1.57026i	−0.0128169	−	0.0850344i
$342$		0			0
$343$	17.0999	+	7.11289i	0.923308	+	0.384060i
$344$		0			0
$345$	−1.08831	+	0.164037i	−0.0585929	+	0.00883146i
$346$		0			0
$347$	−10.0620	−	32.6202i	−0.540156	−	1.75114i	−0.652822	−	0.757511i	$-0.726415\pi$
$347$	−10.0620	−	32.6202i	−0.540156	−	1.75114i	0.112666	−	0.993633i	$-0.464061\pi$
$348$		0			0
$349$	−10.3793	+	21.5529i	−0.555594	+	1.15370i	0.414293	+	0.910144i	$0.364029\pi$
$349$	−10.3793	+	21.5529i	−0.555594	+	1.15370i	−0.969886	+	0.243558i	$0.921685\pi$
$350$		0			0
$351$	−15.8412	−	32.8946i	−0.845541	−	1.75578i
$352$		0			0
$353$	12.4498	−	0.932985i	0.662637	−	0.0496578i	0.260834	−	0.965384i	$-0.416003\pi$
$353$	12.4498	−	0.932985i	0.662637	−	0.0496578i	0.401803	+	0.915726i	$0.368384\pi$
$354$		0			0
$355$	−7.00349	−	2.16029i	−0.371707	−	0.114656i
$356$		0			0
$357$	34.1004	+	18.8687i	1.80478	+	0.998638i
$358$		0			0
$359$	−1.86051	−	2.72887i	−0.0981941	−	0.144024i	0.773998	−	0.633189i	$-0.218254\pi$
$359$	−1.86051	−	2.72887i	−0.0981941	−	0.144024i	−0.872192	+	0.489164i	$0.837302\pi$
$360$		0			0
$361$	4.96616	+	8.60165i	0.261377	+	0.452718i
$362$		0			0
$363$	7.52796	+	32.9822i	0.395116	+	1.73111i
$364$		0			0
$365$	−2.22221	+	9.73615i	−0.116316	+	0.509613i
$366$		0			0
$367$	3.42407	+	0.516095i	0.178735	+	0.0269400i	0.237800	−	0.971314i	$-0.423574\pi$
$367$	3.42407	+	0.516095i	0.178735	+	0.0269400i	−0.0590649	+	0.998254i	$0.518812\pi$
$368$		0			0
$369$	38.7698	−	41.7839i	2.01828	−	2.17518i
$370$		0			0
$371$	3.06722	−	8.25385i	0.159242	−	0.428518i
$372$		0			0
$373$	−3.38324	+	5.85994i	−0.175177	+	0.303416i	−0.940223	−	0.340560i	$-0.889383\pi$
$373$	−3.38324	+	5.85994i	−0.175177	+	0.303416i	0.765045	+	0.643976i	$0.222717\pi$
$374$		0			0
$375$	−13.5260	−	14.5776i	−0.698481	−	0.752784i
$376$		0			0
$377$	−6.72938	−	5.36650i	−0.346581	−	0.276389i
$378$		0			0
$379$	3.49529	−	2.78740i	0.179541	−	0.143179i	−0.529596	−	0.848250i	$-0.677656\pi$
$379$	3.49529	−	2.78740i	0.179541	−	0.143179i	0.709137	+	0.705071i	$0.249085\pi$
$380$		0			0
$381$	−15.6309	−	6.13469i	−0.800797	−	0.314290i
$382$		0			0
$383$	−2.24116	−	5.71038i	−0.114518	−	0.291787i	0.862111	−	0.506719i	$-0.169142\pi$
$383$	−2.24116	−	5.71038i	−0.114518	−	0.291787i	−0.976629	+	0.214933i	$0.931047\pi$
$384$		0			0
$385$	0.488457	−	0.246280i	0.0248941	−	0.0125516i
$386$		0			0
$387$	−31.7395	−	2.37855i	−1.61341	−	0.120908i
$388$		0			0
$389$	−16.2621	−	11.0873i	−0.824523	−	0.562150i	0.0759253	−	0.997114i	$-0.475809\pi$
$389$	−16.2621	−	11.0873i	−0.824523	−	0.562150i	−0.900448	+	0.434963i	$0.856761\pi$
$390$		0			0
$391$	−2.50952			−0.126912
$392$		0			0
$393$	35.8208			1.80692
$394$		0			0
$395$	−6.79056	−	4.62972i	−0.341670	−	0.232947i
$396$		0			0
$397$	7.55553	+	0.566209i	0.379201	+	0.0284172i	0.262967	−	0.964805i	$-0.415299\pi$
$397$	7.55553	+	0.566209i	0.379201	+	0.0284172i	0.116234	+	0.993222i	$0.462918\pi$
$398$		0			0
$399$	5.06024	−	24.1921i	0.253329	−	1.21112i
$400$		0			0
$401$	0.976617	+	2.48838i	0.0487699	+	0.124264i	0.953183	−	0.302394i	$-0.0977860\pi$
$401$	0.976617	+	2.48838i	0.0487699	+	0.124264i	−0.904413	+	0.426658i	$0.859691\pi$
$402$		0			0
$403$	−15.5862	−	6.11712i	−0.776402	−	0.304715i
$404$		0			0
$405$	7.87466	−	6.27983i	0.391295	−	0.312047i
$406$		0			0
$407$	1.73350	+	1.38242i	0.0859265	+	0.0685241i
$408$		0			0
$409$	22.5774	+	24.3327i	1.11638	+	1.20317i	0.977069	+	0.212924i	$0.0682988\pi$
$409$	22.5774	+	24.3327i	1.11638	+	1.20317i	0.139313	+	0.990248i	$0.455511\pi$
$410$		0			0
$411$	23.1366	−	40.0738i	1.14124	−	1.97669i
$412$		0			0
$413$	18.8464	+	12.3528i	0.927370	+	0.607843i
$414$		0			0
$415$	−8.14959	+	8.78316i	−0.400047	+	0.431149i
$416$		0			0
$417$	51.6047	+	7.77815i	2.52709	+	0.380898i
$418$		0			0
$419$	−8.09453	+	35.4645i	−0.395444	+	1.73255i	0.249548	+	0.968363i	$0.419718\pi$
$419$	−8.09453	+	35.4645i	−0.395444	+	1.73255i	−0.644991	+	0.764190i	$0.723139\pi$
$420$		0			0
$421$	−1.74101	−	7.62786i	−0.0848516	−	0.371759i	0.914618	−	0.404319i	$-0.132491\pi$
$421$	−1.74101	−	7.62786i	−0.0848516	−	0.371759i	−0.999470	+	0.0325595i	$0.989634\pi$
$422$		0			0
$423$	38.2638	+	66.2748i	1.86045	+	3.22239i
$424$		0			0
$425$	−12.1687	−	17.8482i	−0.590267	−	0.865763i
$426$		0			0
$427$	−1.73614	−	2.44943i	−0.0840175	−	0.118536i
$428$		0			0
$429$	−2.96528	−	0.914668i	−0.143165	−	0.0441606i
$430$		0			0
$431$	−21.9439	+	1.64447i	−1.05700	+	0.0792111i	−0.591871	−	0.806033i	$-0.701611\pi$
$431$	−21.9439	+	1.64447i	−1.05700	+	0.0792111i	−0.465128	+	0.885244i	$0.653992\pi$
$432$		0			0
$433$	−12.1149	−	25.1569i	−0.582206	−	1.20896i	−0.959195	−	0.282746i	$-0.908755\pi$
$433$	−12.1149	−	25.1569i	−0.582206	−	1.20896i	0.376989	−	0.926218i	$-0.376960\pi$
$434$		0			0
$435$	2.39468	−	4.97261i	0.114816	−	0.238419i
$436$		0			0
$437$	0.469101	+	1.52079i	0.0224401	+	0.0727491i
$438$		0			0
$439$	−23.5568	+	3.55061i	−1.12430	+	0.169462i	−0.684766	−	0.728763i	$-0.740096\pi$
$439$	−23.5568	+	3.55061i	−1.12430	+	0.169462i	−0.439538	+	0.898224i	$0.644858\pi$
$440$		0			0
$441$	37.3344	−	27.4968i	1.77783	−	1.30937i
$442$		0			0
$443$	0.359956	+	2.38815i	0.0171020	+	0.113465i	0.995753	−	0.0920644i	$-0.0293466\pi$
$443$	0.359956	+	2.38815i	0.0171020	+	0.113465i	−0.978651	+	0.205529i	$0.934108\pi$
$444$		0			0
$445$	−6.54460	+	2.01874i	−0.310244	+	0.0956976i
$446$		0			0
$447$	−50.9993	−	24.5600i	−2.41218	−	1.16165i
$448$		0			0
$449$	−25.2566	+	12.1630i	−1.19193	+	0.574005i	−0.921366	−	0.388696i	$-0.872926\pi$
$449$	−25.2566	+	12.1630i	−1.19193	+	0.574005i	−0.270568	+	0.962701i	$0.587211\pi$
$450$		0			0
$451$	−0.198071	−	2.64307i	−0.00932678	−	0.124457i
$452$		0			0
$453$	−7.66527	+	24.8502i	−0.360146	+	1.16756i
$454$		0			0
$455$	0.326264	−	5.75858i	0.0152955	−	0.269966i
$456$		0			0
$457$	−8.21834	+	5.60317i	−0.384438	+	0.262105i	−0.740083	−	0.672516i	$-0.765214\pi$
$457$	−8.21834	+	5.60317i	−0.384438	+	0.262105i	0.355645	+	0.934621i	$0.384261\pi$
$458$		0			0
$459$	46.2293	−	26.6905i	2.15780	−	1.24581i
$460$		0			0
$461$	6.62370	−	1.51182i	0.308497	−	0.0704123i	−0.0654699	−	0.997855i	$-0.520855\pi$
$461$	6.62370	−	1.51182i	0.308497	−	0.0704123i	0.373966	+	0.927442i	$0.377997\pi$
$462$		0			0
$463$	−16.6281	−	3.79524i	−0.772771	−	0.176380i	−0.182087	−	0.983283i	$-0.558285\pi$
$463$	−16.6281	−	3.79524i	−0.772771	−	0.176380i	−0.590685	+	0.806903i	$0.701142\pi$
$464$		0			0
$465$	1.60019	−	10.6166i	0.0742069	−	0.492331i
$466$		0			0
$467$	−1.24395	−	1.15422i	−0.0575632	−	0.0534108i	0.650867	−	0.759192i	$-0.274406\pi$
$467$	−1.24395	−	1.15422i	−0.0575632	−	0.0534108i	−0.708430	+	0.705781i	$0.750596\pi$
$468$		0			0
$469$	0.325607	−	2.46378i	0.0150351	−	0.113767i
$470$		0			0
$471$	−16.5182	−	9.53678i	−0.761118	−	0.439432i
$472$		0			0
$473$	−1.08493	+	1.00667i	−0.0498851	+	0.0462866i
$474$		0			0
$475$	−8.54143	+	10.7106i	−0.391908	+	0.491437i
$476$		0			0
$477$	−13.7448	−	17.2355i	−0.629333	−	0.789159i
$478$		0			0
$479$	7.27149	−	18.5275i	0.332243	−	0.846542i	−0.662955	−	0.748659i	$-0.730698\pi$
$479$	7.27149	−	18.5275i	0.332243	−	0.846542i	0.995198	−	0.0978823i	$-0.0312069\pi$
$480$		0			0
$481$	21.7621	−	8.54098i	0.992265	−	0.389435i
$482$		0			0
$483$	−1.81070	+	3.94194i	−0.0823898	+	0.179365i
$484$		0			0
$485$	0.761538	−	10.1620i	0.0345797	−	0.461434i
$486$		0			0
$487$	1.94728	−	2.85614i	0.0882397	−	0.129424i	−0.779581	−	0.626302i	$-0.784568\pi$
$487$	1.94728	−	2.85614i	0.0882397	−	0.129424i	0.867821	+	0.496878i	$0.165520\pi$
$488$		0			0
$489$			55.9473i			2.53003i
$490$		0			0
$491$		−	24.6771i		−	1.11366i	−0.830626	−	0.556831i	$-0.812017\pi$
$491$		−	24.6771i		−	1.11366i	0.830626	−	0.556831i	$-0.187983\pi$
$492$		0			0
$493$	7.08907	−	10.3978i	0.319276	−	0.468291i
$494$		0			0
$495$	0.102347	−	1.36572i	0.00460014	−	0.0613846i
$496$		0			0
$497$	−22.2531	+	18.4188i	−0.998186	+	0.826194i
$498$		0			0
$499$	10.3541	−	4.06369i	0.463513	−	0.181916i	−0.122081	−	0.992520i	$-0.538957\pi$
$499$	10.3541	−	4.06369i	0.463513	−	0.181916i	0.585594	+	0.810605i	$0.300861\pi$
$500$		0			0
$501$	20.9699	−	53.4304i	0.936865	−	2.38709i
$502$		0			0
$503$	6.80093	+	8.52810i	0.303239	+	0.380249i	0.909981	−	0.414649i	$-0.136096\pi$
$503$	6.80093	+	8.52810i	0.303239	+	0.380249i	−0.606743	+	0.794898i	$0.707524\pi$
$504$		0			0
$505$	−4.66475	+	5.84941i	−0.207578	+	0.260295i
$506$		0			0
$507$	5.57860	−	5.17619i	0.247754	−	0.229882i
$508$		0			0
$509$	2.31069	+	1.33408i	0.102419	+	0.0591319i	0.550335	−	0.834944i	$-0.314500\pi$
$509$	2.31069	+	1.33408i	0.102419	+	0.0591319i	−0.447915	+	0.894076i	$0.647833\pi$
$510$		0			0
$511$	27.2929	+	28.3614i	1.20737	+	1.25464i
$512$		0			0
$513$	−24.8162	−	23.0261i	−1.09566	−	1.01663i
$514$		0			0
$515$	1.46194	−	9.69932i	0.0644206	−	0.427403i
$516$		0			0
$517$	3.46929	+	0.791842i	0.152579	+	0.0348252i
$518$		0			0
$519$	16.2555	−	3.71021i	0.713537	−	0.162860i
$520$		0			0
$521$	15.2756	−	8.81939i	0.669237	−	0.386384i	−0.126550	−	0.991960i	$-0.540390\pi$
$521$	15.2756	−	8.81939i	0.669237	−	0.386384i	0.795788	+	0.605576i	$0.207057\pi$
$522$		0			0
$523$	−2.65273	+	1.80860i	−0.115996	+	0.0790847i	−0.619928	−	0.784658i	$-0.712838\pi$
$523$	−2.65273	+	1.80860i	−0.115996	+	0.0790847i	0.503933	+	0.863743i	$0.331886\pi$
$524$		0			0
$525$	−36.8158	+	6.23645i	−1.60677	+	0.272181i
$526$		0			0
$527$	7.21576	−	23.3929i	0.314323	−	1.01901i
$528$		0			0
$529$	1.69792	+	22.6571i	0.0738225	+	0.985093i
$530$		0			0
$531$	50.8291	−	24.4780i	2.20579	−	1.06225i
$532$		0			0
$533$	−25.1787	−	12.1254i	−1.09061	−	0.525209i
$534$		0			0
$535$	−4.57149	+	1.41012i	−0.197643	+	0.0609647i
$536$		0			0
$537$	2.09526	+	13.9012i	0.0904174	+	0.599880i
$538$		0			0
$539$	0.243531	−	2.14227i	0.0104896	−	0.0922740i
$540$		0			0
$541$	−23.9376	+	3.60802i	−1.02916	+	0.155121i	−0.641851	−	0.766830i	$-0.721833\pi$
$541$	−23.9376	+	3.60802i	−1.02916	+	0.155121i	−0.387308	+	0.921950i	$0.626595\pi$
$542$		0			0
$543$	23.3951	+	75.8450i	1.00398	+	3.25482i
$544$		0			0
$545$	−4.14428	+	8.60568i	−0.177521	+	0.368627i
$546$		0			0
$547$	−13.7905	−	28.6363i	−0.589640	−	1.22440i	−0.955847	−	0.293866i	$-0.905058\pi$
$547$	−13.7905	−	28.6363i	−0.589640	−	1.22440i	0.366207	−	0.930533i	$-0.380656\pi$
$548$		0			0
$549$	−7.49558	+	0.561716i	−0.319903	+	0.0239734i
$550$		0			0
$551$	−7.62625	−	2.35239i	−0.324889	−	0.100215i
$552$		0			0
$553$	−29.9332	+	12.3813i	−1.27289	+	0.526508i
$554$		0			0
$555$	8.44457	+	12.3859i	0.358452	+	0.525753i
$556$		0			0
$557$	2.24592	+	3.89005i	0.0951627	+	0.164827i	0.909677	−	0.415318i	$-0.136330\pi$
$557$	2.24592	+	3.89005i	0.0951627	+	0.164827i	−0.814514	+	0.580144i	$0.802996\pi$
$558$		0			0
$559$	3.47245	+	15.2138i	0.146869	+	0.643475i
$560$		0			0
$561$	1.00959	−	4.42330i	0.0426249	−	0.186752i
$562$		0			0
$563$	9.49344	+	1.43091i	0.400101	+	0.0603055i	0.346011	−	0.938231i	$-0.387536\pi$
$563$	9.49344	+	1.43091i	0.400101	+	0.0603055i	0.0540902	+	0.998536i	$0.482774\pi$
$564$		0			0
$565$	0.621446	−	0.669759i	0.0261444	−	0.0281770i
$566$		0			0
$567$	−3.68671	−	39.5264i	−0.154827	−	1.65995i
$568$		0			0
$569$	15.5276	−	26.8946i	0.650951	−	1.12748i	−0.331941	−	0.943300i	$-0.607704\pi$
$569$	15.5276	−	26.8946i	0.650951	−	1.12748i	0.982892	−	0.184180i	$-0.0589631\pi$
$570$		0			0
$571$	−7.35650	−	7.92842i	−0.307860	−	0.331794i	0.560103	−	0.828423i	$-0.310762\pi$
$571$	−7.35650	−	7.92842i	−0.307860	−	0.331794i	−0.867963	+	0.496629i	$0.834571\pi$
$572$		0			0
$573$	−53.3659	−	42.5579i	−2.22939	−	1.77788i
$574$		0			0
$575$	1.87985	−	1.49913i	0.0783952	−	0.0625181i
$576$		0			0
$577$	−2.64765	−	1.03913i	−0.110223	−	0.0432595i	0.309589	−	0.950871i	$-0.399809\pi$
$577$	−2.64765	−	1.03913i	−0.110223	−	0.0432595i	−0.419812	+	0.907611i	$0.637904\pi$
$578$		0			0
$579$	8.33800	+	21.2449i	0.346515	+	0.882907i
$580$		0			0
$581$	11.3447	+	45.8414i	0.470657	+	1.90182i
$582$		0			0
$583$	−1.02222	−	0.0766048i	−0.0423360	−	0.00317265i
$584$		0			0
$585$	−11.9311	−	8.13451i	−0.493292	−	0.336321i
$586$		0			0
$587$	−35.5588			−1.46767			−0.733834	−	0.679328i	$-0.762271\pi$
$587$	−35.5588			−1.46767			−0.733834	+	0.679328i	$0.762271\pi$
$588$		0			0
$589$	−15.5251			−0.639700
$590$		0			0
$591$	5.15151	+	3.51224i	0.211905	+	0.144474i
$592$		0			0
$593$	6.45334	+	0.483611i	0.265007	+	0.0198595i	0.206571	−	0.978432i	$-0.433770\pi$
$593$	6.45334	+	0.483611i	0.265007	+	0.0198595i	0.0584361	+	0.998291i	$0.481389\pi$
$594$		0			0
$595$	8.43163	−	0.153500i	0.345663	−	0.00629288i
$596$		0			0
$597$	−6.74085	−	17.1754i	−0.275885	−	0.702943i
$598$		0			0
$599$	9.04723	+	3.55078i	0.369660	+	0.145081i	0.542897	−	0.839799i	$-0.317327\pi$
$599$	9.04723	+	3.55078i	0.369660	+	0.145081i	−0.173237	+	0.984880i	$0.555423\pi$
$600$		0			0
$601$	−17.8611	+	14.2438i	−0.728570	+	0.581015i	−0.915960	−	0.401271i	$-0.868569\pi$
$601$	−17.8611	+	14.2438i	−0.728570	+	0.581015i	0.187390	+	0.982286i	$0.439997\pi$
$602$		0			0
$603$	−4.86451	−	3.87932i	−0.198098	−	0.157978i
$604$		0			0
$605$	4.97909	+	5.36618i	0.202429	+	0.218166i
$606$		0			0
$607$	−15.6814	+	27.1610i	−0.636488	+	1.10243i	0.349710	+	0.936858i	$0.386280\pi$
$607$	−15.6814	+	27.1610i	−0.636488	+	1.10243i	−0.986198	+	0.165571i	$0.947053\pi$
$608$		0			0
$609$	−11.2177	−	18.6378i	−0.454565	−	0.755240i
$610$		0			0
$611$	25.5203	−	27.5043i	1.03244	−	1.11271i
$612$		0			0
$613$	29.5936	+	4.46051i	1.19527	+	0.180158i	0.716377	−	0.697713i	$-0.245799\pi$
$613$	29.5936	+	4.46051i	1.19527	+	0.180158i	0.478896	+	0.877872i	$0.341037\pi$
$614$		0			0
$615$	3.98755	−	17.4706i	0.160794	−	0.704483i
$616$		0			0
$617$	−10.4040	−	45.5829i	−0.418849	−	1.83510i	−0.538952	−	0.842337i	$-0.681180\pi$
$617$	−10.4040	−	45.5829i	−0.418849	−	1.83510i	0.120103	−	0.992761i	$-0.461678\pi$
$618$		0			0
$619$	−21.4943	−	37.2293i	−0.863930	−	1.49637i	−0.868106	−	0.496379i	$-0.834663\pi$
$619$	−21.4943	−	37.2293i	−0.863930	−	1.49637i	0.00417591	−	0.999991i	$-0.498671\pi$
$620$		0			0
$621$	3.34707	+	4.90925i	0.134313	+	0.197001i
$622$		0			0
$623$	−7.48581	+	25.9354i	−0.299913	+	1.03908i
$624$		0			0
$625$	17.6245	+	5.43644i	0.704980	+	0.217458i
$626$		0			0
$627$	−2.86927	+	0.215022i	−0.114588	+	0.00858716i
$628$		0			0
$629$	14.8305	+	30.7958i	0.591330	+	1.22791i
$630$		0			0
$631$	5.00697	−	10.3971i	0.199324	−	0.413901i	−0.777217	−	0.629233i	$-0.783369\pi$
$631$	5.00697	−	10.3971i	0.199324	−	0.413901i	0.976541	+	0.215332i	$0.0690834\pi$
$632$		0			0
$633$	−14.6810	−	47.5947i	−0.583518	−	1.89172i
$634$		0			0
$635$	−3.59286	+	0.541536i	−0.142578	+	0.0214902i
$636$		0			0
$637$	−18.2777	−	13.5176i	−0.724187	−	0.535587i
$638$		0			0
$639$	10.7789	+	71.5133i	0.426407	+	2.82902i
$640$		0			0
$641$	−6.67007	+	2.05744i	−0.263452	+	0.0812641i	−0.423667	−	0.905818i	$-0.639257\pi$
$641$	−6.67007	+	2.05744i	−0.263452	+	0.0812641i	0.160215	+	0.987082i	$0.448781\pi$
$642$		0			0
$643$	−1.62198	−	0.781106i	−0.0639648	−	0.0308038i	0.401628	−	0.915803i	$-0.368445\pi$
$643$	−1.62198	−	0.781106i	−0.0639648	−	0.0308038i	−0.465593	+	0.884999i	$0.654159\pi$
$644$		0			0
$645$	−9.01546	+	4.34161i	−0.354983	+	0.170951i
$646$		0			0
$647$	0.624417	+	8.33226i	0.0245484	+	0.327575i	0.995935	+	0.0900723i	$0.0287098\pi$
$647$	0.624417	+	8.33226i	0.0245484	+	0.327575i	−0.971387	+	0.237503i	$0.923671\pi$
$648$		0			0
$649$	0.773239	−	2.50678i	0.0303523	−	0.0983997i
$650$		0			0
$651$	−31.5390	−	28.2132i	−1.23611	−	1.10576i
$652$		0			0
$653$	−21.4458	+	14.6215i	−0.839240	+	0.572184i	−0.904884	−	0.425659i	$-0.860042\pi$
$653$	−21.4458	+	14.6215i	−0.839240	+	0.572184i	0.0656440	+	0.997843i	$0.479090\pi$
$654$		0			0
$655$	6.71258	−	3.87551i	0.262282	−	0.151429i
$656$		0			0
$657$	96.0730	−	21.9280i	3.74817	−	0.855495i
$658$		0			0
$659$	6.80639	+	1.55351i	0.265139	+	0.0605163i	0.353024	−	0.935614i	$-0.385153\pi$
$659$	6.80639	+	1.55351i	0.265139	+	0.0605163i	−0.0878844	+	0.996131i	$0.528011\pi$
$660$		0			0
$661$	2.39796	−	15.9094i	0.0932699	−	0.618805i	−0.892544	−	0.450961i	$-0.851081\pi$
$661$	2.39796	−	15.9094i	0.0932699	−	0.618805i	0.985814	−	0.167844i	$-0.0536806\pi$
$662$		0			0
$663$	−35.0677	−	32.5381i	−1.36192	−	1.26367i
$664$		0			0
$665$	−1.66913	−	5.08093i	−0.0647261	−	0.197030i
$666$		0			0
$667$	1.21307	+	0.700368i	0.0469704	+	0.0271184i
$668$		0			0
$669$	0.438065	−	0.406465i	0.0169366	−	0.0157149i
$670$		0			0
$671$	−0.217922	+	0.273265i	−0.00841277	+	0.0105493i
$672$		0			0
$673$	30.8632	+	38.7013i	1.18969	+	1.49182i	0.829101	+	0.559099i	$0.188853\pi$
$673$	30.8632	+	38.7013i	1.18969	+	1.49182i	0.360588	+	0.932725i	$0.382576\pi$
$674$		0			0
$675$	−18.6855	+	47.6098i	−0.719205	+	1.83250i
$676$		0			0
$677$	−28.6881	+	11.2592i	−1.10257	+	0.432728i	−0.845668	−	0.533709i	$-0.820798\pi$
$677$	−28.6881	+	11.2592i	−1.10257	+	0.432728i	−0.256905	+	0.966437i	$0.582703\pi$
$678$		0			0
$679$	−31.8527	−	24.4666i	−1.22240	−	0.938942i
$680$		0			0
$681$	0.245660	−	3.27811i	0.00941372	−	0.125617i
$682$		0			0
$683$	11.0015	−	16.1363i	0.420962	−	0.617438i	−0.555915	−	0.831239i	$-0.687632\pi$
$683$	11.0015	−	16.1363i	0.420962	−	0.617438i	0.976877	+	0.213801i	$0.0685844\pi$
$684$		0			0
$685$		−	10.0128i		−	0.382568i
$686$		0			0
$687$			38.1925i			1.45713i
$688$		0			0
$689$	−6.08855	+	8.93027i	−0.231955	+	0.340216i
$690$		0			0
$691$	−1.26203	+	16.8406i	−0.0480098	+	0.640647i	0.920351	+	0.391093i	$0.127903\pi$
$691$	−1.26203	+	16.8406i	−0.0480098	+	0.640647i	−0.968361	+	0.249554i	$0.919716\pi$
$692$		0			0
$693$	−4.28083	−	3.28818i	−0.162615	−	0.124908i
$694$		0			0
$695$	10.5119	−	4.12562i	0.398740	−	0.156494i
$696$		0			0
$697$	14.9277	−	38.0352i	0.565427	−	1.44069i
$698$		0			0
$699$	23.3187	+	29.2407i	0.881993	+	1.10598i
$700$		0			0
$701$	−5.56077	+	6.97298i	−0.210027	+	0.263366i	−0.875676	−	0.482900i	$-0.839584\pi$
$701$	−5.56077	+	6.97298i	−0.210027	+	0.263366i	0.665648	+	0.746265i	$0.268155\pi$
$702$		0			0
$703$	15.8902	−	14.7440i	0.599311	−	0.556079i
$704$		0			0
$705$	20.8358	+	12.0295i	0.784721	+	0.453059i
$706$		0			0
$707$	9.20326	+	28.0152i	0.346124	+	1.05362i
$708$		0			0
$709$	17.7894	+	16.5061i	0.668093	+	0.619900i	0.939493	−	0.342567i	$-0.111296\pi$
$709$	17.7894	+	16.5061i	0.668093	+	0.619900i	−0.271400	+	0.962467i	$0.587487\pi$
$710$		0			0
$711$	−12.0871	+	80.1930i	−0.453303	+	3.00747i
$712$		0			0
$713$	2.65653	+	0.606337i	0.0994880	+	0.0227075i
$714$		0			0
$715$	−0.654634	+	0.149416i	−0.0244819	+	0.00558784i
$716$		0			0
$717$	−70.1803	+	40.5186i	−2.62093	+	1.51320i
$718$		0			0
$719$	8.74114	−	5.95961i	0.325989	−	0.222256i	−0.389255	−	0.921130i	$-0.627268\pi$
$719$	8.74114	−	5.95961i	0.325989	−	0.222256i	0.715245	+	0.698874i	$0.246315\pi$
$720$		0			0
$721$	−28.8142	−	25.7757i	−1.07310	−	0.959936i
$722$		0			0
$723$	−6.36963	+	20.6498i	−0.236889	+	0.767975i
$724$		0			0
$725$	0.901049	+	12.0237i	0.0334641	+	0.446547i
$726$		0			0
$727$	16.5035	−	7.94766i	0.612081	−	0.294762i	−0.102045	−	0.994780i	$-0.532539\pi$
$727$	16.5035	−	7.94766i	0.612081	−	0.294762i	0.714126	+	0.700017i	$0.246824\pi$
$728$		0			0
$729$	4.72160	+	2.27380i	0.174874	+	0.0842149i
$730$		0			0
$731$	−21.8022	+	6.72510i	−0.806384	+	0.248737i
$732$		0			0
$733$	0.983597	+	6.52574i	0.0363300	+	0.241034i	0.999624	−	0.0274143i	$-0.00872734\pi$
$733$	0.983597	+	6.52574i	0.0363300	+	0.241034i	−0.963294	+	0.268448i	$0.913489\pi$
$734$		0			0
$735$	5.84257	−	13.3551i	0.215506	−	0.492610i
$736$		0			0
$737$	−0.286087	+	0.0431207i	−0.0105381	+	0.00158837i
$738$		0			0
$739$	6.10413	+	19.7891i	0.224544	+	0.727954i	0.995810	+	0.0914414i	$0.0291474\pi$
$739$	6.10413	+	19.7891i	0.224544	+	0.727954i	−0.771266	+	0.636512i	$0.780376\pi$
$740$		0			0
$741$	−13.1631	+	27.3335i	−0.483560	+	1.00412i
$742$		0			0
$743$	16.0047	+	33.2341i	0.587155	+	1.21924i	0.956984	+	0.290140i	$0.0937019\pi$
$743$	16.0047	+	33.2341i	0.587155	+	1.21924i	−0.369829	+	0.929100i	$0.620584\pi$
$744$		0			0
$745$	−12.2141	+	0.915322i	−0.447491	+	0.0335348i
$746$		0			0
$747$	112.978	+	34.8491i	4.13365	+	1.27506i
$748$		0			0
$749$	−5.22893	+	18.1162i	−0.191061	+	0.661951i
$750$		0			0
$751$	−5.35417	−	7.85312i	−0.195376	−	0.286564i	0.716032	−	0.698067i	$-0.245956\pi$
$751$	−5.35417	−	7.85312i	−0.195376	−	0.286564i	−0.911408	+	0.411503i	$0.865004\pi$
$752$		0			0
$753$	1.58188	+	2.73990i	0.0576469	+	0.0998473i
$754$		0			0
$755$	1.25216	+	5.48609i	0.0455709	+	0.199659i
$756$		0			0
$757$	−10.7118	+	46.9313i	−0.389325	+	1.70575i	0.277664	+	0.960678i	$0.410440\pi$
$757$	−10.7118	+	46.9313i	−0.389325	+	1.70575i	−0.666989	+	0.745067i	$0.732417\pi$
$758$		0			0
$759$	0.499366	+	0.0752673i	0.0181258	+	0.00273203i
$760$		0			0
$761$	−18.6421	+	20.0914i	−0.675775	+	0.728312i	−0.974091	−	0.226155i	$-0.927384\pi$
$761$	−18.6421	+	20.0914i	−0.675775	+	0.728312i	0.298316	+	0.954467i	$0.403575\pi$
$762$		0			0
$763$	19.4136	+	32.2548i	0.702819	+	1.16770i
$764$		0			0
$765$	10.5565	−	18.2843i	0.381670	−	0.661071i
$766$		0			0
$767$	−18.8135	−	20.2761i	−0.679317	−	0.732129i
$768$		0			0
$769$	−19.2749	−	15.3713i	−0.695072	−	0.554302i	0.210968	−	0.977493i	$-0.432338\pi$
$769$	−19.2749	−	15.3713i	−0.695072	−	0.554302i	−0.906040	+	0.423191i	$0.860910\pi$
$770$		0			0
$771$	−49.3306	+	39.3398i	−1.77660	+	1.41679i
$772$		0			0
$773$	39.1570	+	15.3680i	1.40838	+	0.552748i	0.943128	−	0.332430i	$-0.107869\pi$
$773$	39.1570	+	15.3680i	1.40838	+	0.552748i	0.465252	+	0.885179i	$0.345964\pi$
$774$		0			0
$775$	8.56915	+	21.8338i	0.307813	+	0.784295i
$776$		0			0
$777$	59.0745	−	1.07546i	2.11928	−	0.0385821i
$778$		0			0
$779$	−25.8400	−	1.93644i	−0.925813	−	0.0693801i
$780$		0			0
$781$	2.77856	+	1.89439i	0.0994249	+	0.0677867i
$782$		0			0
$783$	−29.7956			−1.06481
$784$		0			0
$785$	−4.12720			−0.147306
$786$		0			0
$787$	−15.2149	−	10.3734i	−0.542353	−	0.369770i	0.260939	−	0.965355i	$-0.415968\pi$
$787$	−15.2149	−	10.3734i	−0.542353	−	0.369770i	−0.803292	+	0.595585i	$0.796920\pi$
$788$		0			0
$789$	−22.5961	−	1.69335i	−0.804444	−	0.0602847i
$790$		0			0
$791$	−0.865088	−	3.49563i	−0.0307590	−	0.124290i
$792$		0			0
$793$	1.34638	+	3.43052i	0.0478114	+	0.121821i
$794$		0			0
$795$	−6.45153	−	2.53204i	−0.228812	−	0.0898022i
$796$		0			0
$797$	20.8570	−	16.6329i	0.738793	−	0.589167i	−0.180113	−	0.983646i	$-0.557646\pi$
$797$	20.8570	−	16.6329i	0.738793	−	0.589167i	0.918905	+	0.394479i	$0.129075\pi$
$798$		0			0
$799$	42.8896	+	34.2033i	1.51732	+	1.21002i
$800$		0			0
$801$	45.9678	+	49.5415i	1.62419	+	1.75046i
$802$		0			0
$803$	2.29113	−	3.96835i	0.0808521	−	0.140040i
$804$		0			0
$805$	0.0871719	+	0.934598i	0.00307241	+	0.0329402i
$806$		0			0
$807$	55.3333	−	59.6351i	1.94783	−	2.09926i
$808$		0			0
$809$	−40.3009	−	6.07438i	−1.41690	−	0.213564i	−0.604474	−	0.796625i	$-0.706617\pi$
$809$	−40.3009	−	6.07438i	−1.41690	−	0.213564i	−0.812428	+	0.583061i	$0.801855\pi$
$810$		0			0
$811$	−1.39671	+	6.11937i	−0.0490450	+	0.214880i	−0.993512	−	0.113726i	$-0.963722\pi$
$811$	−1.39671	+	6.11937i	−0.0490450	+	0.214880i	0.944467	+	0.328606i	$0.106579\pi$
$812$		0			0
$813$	13.3457	+	58.4714i	0.468055	+	2.05068i
$814$		0			0
$815$	6.05304	+	10.4842i	0.212029	+	0.367244i
$816$		0			0
$817$	8.15090	+	11.9552i	0.285164	+	0.418259i
$818$		0			0
$819$	−52.5933	+	21.7542i	−1.83776	+	0.760155i
$820$		0			0
$821$	32.9896	+	10.1759i	1.15134	+	0.355143i	0.810936	−	0.585135i	$-0.198958\pi$
$821$	32.9896	+	10.1759i	1.15134	+	0.355143i	0.340408	+	0.940278i	$0.389435\pi$
$822$		0			0
$823$	−47.5025	+	3.55982i	−1.65583	+	0.124087i	−0.869572	−	0.493807i	$-0.835605\pi$
$823$	−47.5025	+	3.55982i	−1.65583	+	0.124087i	−0.786261	+	0.617894i	$0.787986\pi$
$824$		0			0
$825$	1.88611	+	3.91654i	0.0656658	+	0.136356i
$826$		0			0
$827$	−12.9364	+	26.8627i	−0.449842	+	0.934107i	0.545537	+	0.838087i	$0.316326\pi$
$827$	−12.9364	+	26.8627i	−0.449842	+	0.934107i	−0.995379	+	0.0960206i	$0.969389\pi$
$828$		0			0
$829$	6.34728	+	20.5774i	0.220450	+	0.714682i	0.996468	+	0.0839710i	$0.0267603\pi$
$829$	6.34728	+	20.5774i	0.220450	+	0.714682i	−0.776018	+	0.630711i	$0.782764\pi$
$830$		0			0
$831$	−2.27511	+	0.342917i	−0.0789225	+	0.0118957i
$832$		0			0
$833$	17.7115	−	28.1257i	0.613668	−	0.974497i
$834$		0			0
$835$	−1.85111	−	12.2813i	−0.0640601	−	0.425011i
$836$		0			0
$837$	−55.3863	+	17.0844i	−1.91443	+	0.590524i
$838$		0			0
$839$	0.888449	+	0.427855i	0.0306727	+	0.0147712i	0.449157	−	0.893453i	$-0.351724\pi$
$839$	0.888449	+	0.427855i	0.0306727	+	0.0147712i	−0.418485	+	0.908224i	$0.637439\pi$
$840$		0			0
$841$	19.7995	−	9.53493i	0.682741	−	0.328791i
$842$		0			0
$843$	−5.68321	−	75.8372i	−0.195740	−	2.61197i
$844$		0			0
$845$	0.485374	−	1.57354i	0.0166974	−	0.0541315i
$846$		0			0
$847$	28.4470	−	4.81880i	0.977451	−	0.165576i
$848$		0			0
$849$	3.94056	−	2.68663i	0.135240	−	0.0922050i
$850$		0			0
$851$	−3.29484	+	1.90228i	−0.112946	+	0.0652092i
$852$		0			0
$853$	12.4522	−	2.84214i	0.426356	−	0.0973131i	−0.00395793	−	0.999992i	$-0.501260\pi$
$853$	12.4522	−	2.84214i	0.426356	−	0.0973131i	0.430314	+	0.902679i	$0.358403\pi$
$854$		0			0
$855$	−13.0537	−	2.97943i	−0.446428	−	0.101894i
$856$		0			0
$857$	−1.75780	+	11.6622i	−0.0600452	+	0.398374i	0.938539	+	0.345174i	$0.112180\pi$
$857$	−1.75780	+	11.6622i	−0.0600452	+	0.398374i	−0.998584	+	0.0531998i	$0.983058\pi$
$858$		0			0
$859$	−34.9939	−	32.4696i	−1.19398	−	1.10785i	−0.991707	−	0.128518i	$-0.958978\pi$
$859$	−34.9939	−	32.4696i	−1.19398	−	1.10785i	−0.202269	−	0.979330i	$-0.564831\pi$
$860$		0			0
$861$	−48.9746	−	50.8919i	−1.66905	−	1.73439i
$862$		0			0
$863$	17.7045	+	10.2217i	0.602667	+	0.347950i	0.770090	−	0.637935i	$-0.220211\pi$
$863$	17.7045	+	10.2217i	0.602667	+	0.347950i	−0.167423	+	0.985885i	$0.553545\pi$
$864$		0			0
$865$	2.64476	−	2.45398i	0.0899246	−	0.0834379i
$866$		0			0
$867$	10.7271	−	13.4514i	0.364312	−	0.456833i
$868$		0			0
$869$	2.35122	+	2.94834i	0.0797597	+	0.100016i
$870$		0			0
$871$	−1.11448	+	2.83965i	−0.0377628	+	0.0962179i
$872$		0			0
$873$	−93.6055	+	36.7374i	−3.16807	+	1.24337i
$874$		0			0
$875$	−13.0651	+	10.8140i	−0.441683	+	0.365579i
$876$		0			0
$877$	−0.874548	+	11.6700i	−0.0295314	+	0.394069i	0.962779	+	0.270291i	$0.0871200\pi$
$877$	−0.874548	+	11.6700i	−0.0295314	+	0.394069i	−0.992310	+	0.123778i	$0.960499\pi$
$878$		0			0
$879$	4.67178	−	6.85224i	0.157575	−	0.231120i
$880$		0			0
$881$		−	29.3160i		−	0.987682i	−0.869552	−	0.493841i	$-0.835593\pi$
$881$		−	29.3160i		−	0.987682i	0.869552	−	0.493841i	$-0.164407\pi$
$882$		0			0
$883$			59.0936i			1.98866i	0.106347	+	0.994329i	$0.466085\pi$
$883$			59.0936i			1.98866i	−0.106347	+	0.994329i	$0.533915\pi$
$884$		0			0
$885$	9.99123	−	14.6544i	0.335852	−	0.492604i
$886$		0			0
$887$	2.46202	−	32.8534i	0.0826666	−	1.10311i	−0.789451	−	0.613814i	$-0.789635\pi$
$887$	2.46202	−	32.8534i	0.0826666	−	1.10311i	0.872118	−	0.489296i	$-0.162746\pi$
$888$		0			0
$889$	−5.97768	+	13.0136i	−0.200485	+	0.436461i
$890$		0			0
$891$	−4.30203	+	1.68842i	−0.144124	+	0.0565643i
$892$		0			0
$893$	12.7101	−	32.3849i	0.425328	−	1.08372i
$894$		0			0
$895$	1.89663	+	2.37830i	0.0633974	+	0.0794978i
$896$		0			0
$897$	3.31990	−	4.16302i	0.110848	−	0.138999i
$898$		0			0
$899$	−10.0166	+	9.29404i	−0.334072	+	0.309974i
$900$		0			0
$901$	−13.6855	−	7.90135i	−0.455931	−	0.263232i
$902$		0			0
$903$	−5.16726	+	39.0991i	−0.171956	+	1.30114i
$904$		0			0
$905$	12.5899	+	11.6817i	0.418502	+	0.388313i
$906$		0			0
$907$	−4.62561	+	30.6889i	−0.153591	+	1.01901i	0.770667	+	0.637238i	$0.219923\pi$
$907$	−4.62561	+	30.6889i	−0.153591	+	1.01901i	−0.924257	+	0.381770i	$0.875315\pi$
$908$		0			0
$909$	71.9756	+	16.4280i	2.38728	+	0.544881i
$910$		0			0
$911$	30.5190	−	6.96575i	1.01114	−	0.230786i	0.315306	−	0.948990i	$-0.397893\pi$
$911$	30.5190	−	6.96575i	1.01114	−	0.230786i	0.695832	+	0.718204i	$0.255036\pi$
$912$		0			0
$913$	4.76114	−	2.74885i	0.157571	−	0.0909736i
$914$		0			0
$915$	−1.95249	+	1.33118i	−0.0645472	+	0.0440075i
$916$		0			0
$917$	1.72809	−	30.5009i	0.0570666	−	1.00723i
$918$		0			0
$919$	15.3229	−	49.6757i	0.505457	−	1.63865i	−0.239028	−	0.971013i	$-0.576829\pi$
$919$	15.3229	−	49.6757i	0.505457	−	1.63865i	0.744485	−	0.667639i	$-0.232695\pi$
$920$		0			0
$921$	0.0537603	+	0.717382i	0.00177146	+	0.0236385i
$922$		0			0
$923$	31.9465	−	15.3846i	1.05153	−	0.506391i
$924$		0			0
$925$	−29.5060	−	14.2093i	−0.970151	−	0.467200i
$926$		0			0
$927$	−92.4906	+	28.5296i	−3.03779	+	0.937034i
$928$		0			0
$929$	−7.10568	−	47.1431i	−0.233130	−	1.54671i	−0.732767	−	0.680480i	$-0.761772\pi$
$929$	−7.10568	−	47.1431i	−0.233130	−	1.54671i	0.499637	−	0.866235i	$-0.333467\pi$
$930$		0			0
$931$	−20.3551	−	5.47582i	−0.667112	−	0.179463i
$932$		0			0
$933$	−50.0326	+	7.54120i	−1.63799	+	0.246888i
$934$		0			0
$935$	−0.289374	−	0.938128i	−0.00946355	−	0.0306801i
$936$		0			0
$937$	0.259732	−	0.539339i	0.00848508	−	0.0176194i	−0.896683	−	0.442673i	$-0.854030\pi$
$937$	0.259732	−	0.539339i	0.00848508	−	0.0176194i	0.905168	+	0.425053i	$0.139745\pi$
$938$		0			0
$939$	8.39355	+	17.4294i	0.273913	+	0.568787i
$940$		0			0
$941$	43.4263	−	3.25435i	1.41566	−	0.106089i	0.655189	−	0.755465i	$-0.272589\pi$
$941$	43.4263	−	3.25435i	1.41566	−	0.106089i	0.760467	+	0.649376i	$0.224970\pi$
$942$		0			0
$943$	4.34591	+	1.34054i	0.141522	+	0.0436539i
$944$		0			0
$945$	−11.5459	−	16.2896i	−0.375589	−	0.529901i
$946$		0			0
$947$	9.75004	+	14.3007i	0.316834	+	0.464710i	0.951311	−	0.308232i	$-0.0997371\pi$
$947$	9.75004	+	14.3007i	0.316834	+	0.464710i	−0.634478	+	0.772941i	$0.718785\pi$
$948$		0			0
$949$	−24.1572	−	41.8416i	−0.784177	−	1.35823i
$950$		0			0
$951$	−19.4366	−	85.1573i	−0.630275	−	2.76141i
$952$		0			0
$953$	−4.76867	+	20.8929i	−0.154472	+	0.676787i	0.837080	+	0.547080i	$0.184261\pi$
$953$	−4.76867	+	20.8929i	−0.154472	+	0.676787i	−0.991552	+	0.129707i	$0.958596\pi$
$954$		0			0
$955$	−14.6048	−	2.20133i	−0.472602	−	0.0712332i
$956$		0			0
$957$	−1.72250	+	1.85641i	−0.0556804	+	0.0600092i
$958$		0			0
$959$	−33.0061	−	21.6338i	−1.06582	−	0.698590i
$960$		0			0
$961$	2.20948	−	3.82692i	0.0712734	−	0.123449i
$962$		0			0
$963$	32.1090	+	34.6053i	1.03470	+	1.11514i
$964$		0			0
$965$	3.86101	+	3.07905i	0.124290	+	0.0991182i
$966$		0			0
$967$	−5.58578	+	4.45451i	−0.179627	+	0.143248i	−0.709176	−	0.705032i	$-0.750933\pi$
$967$	−5.58578	+	4.45451i	−0.179627	+	0.143248i	0.529549	+	0.848279i	$0.322361\pi$
$968$		0			0
$969$	−41.2904	−	16.2053i	−1.32644	−	0.520589i
$970$		0			0
$971$	13.6555	+	34.7937i	0.438226	+	1.11658i	0.963987	+	0.265950i	$0.0856856\pi$
$971$	13.6555	+	34.7937i	0.438226	+	1.11658i	−0.525761	+	0.850633i	$0.676219\pi$
$972$		0			0
$973$	9.11254	−	43.5654i	0.292135	−	1.39664i
$974$		0			0
$975$	45.7062	+	3.42521i	1.46377	+	0.109694i
$976$		0			0
$977$	−1.44419	−	0.984632i	−0.0462037	−	0.0315012i	0.539998	−	0.841666i	$-0.318425\pi$
$977$	−1.44419	−	0.984632i	−0.0462037	−	0.0315012i	−0.586202	+	0.810165i	$0.699377\pi$
$978$		0			0
$979$	3.14256			0.100437
$980$		0			0
$981$	94.2519			3.00923
$982$		0			0
$983$	−26.6992	−	18.2032i	−0.851571	−	0.580591i	0.0569755	−	0.998376i	$-0.481854\pi$
$983$	−26.6992	−	18.2032i	−0.851571	−	0.580591i	−0.908546	+	0.417785i	$0.862807\pi$
$984$		0			0
$985$	1.34536	+	0.100820i	0.0428666	+	0.00321241i
$986$		0			0
$987$	84.6724	−	42.6919i	2.69515	−	1.35890i
$988$		0			0
$989$	−0.927807	−	2.36401i	−0.0295026	−	0.0751713i
$990$		0			0
$991$	−0.403772	−	0.158469i	−0.0128263	−	0.00503393i	0.358919	−	0.933369i	$-0.383145\pi$
$991$	−0.403772	−	0.158469i	−0.0128263	−	0.00503393i	−0.371745	+	0.928335i	$0.621241\pi$
$992$		0			0
$993$	19.8331	−	15.8164i	0.629384	−	0.501917i
$994$		0			0
$995$	−3.12143	−	2.48926i	−0.0989560	−	0.0789148i
$996$		0			0
$997$	−34.9752	−	37.6943i	−1.10767	−	1.19379i	−0.979374	−	0.202054i	$-0.935238\pi$
$997$	−34.9752	−	37.6943i	−1.10767	−	1.19379i	−0.128301	−	0.991735i	$-0.540952\pi$
$998$		0			0
$999$	40.4641	−	70.0858i	1.28023	−	2.21742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bp.a.495.1	yes	108
4.3	odd	2		784.2.bp.b.495.9	yes	108
49.10	odd	42		784.2.bp.b.255.9	yes	108
196.59	even	42	inner	784.2.bp.a.255.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bp.a.255.1	✓	108	196.59	even	42	inner
784.2.bp.a.495.1	yes	108	1.1	even	1	trivial
784.2.bp.b.255.9	yes	108	49.10	odd	42
784.2.bp.b.495.9	yes	108	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bp (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.56319 - 1.74756i) q^{3} +(-0.669397 - 0.0501644i) q^{5} +(-1.61167 + 2.09822i) q^{7} +(2.41998 + 6.16602i) q^{9} +O(q^{10})\)	\(q+(-2.56319 - 1.74756i) q^{3} +(-0.669397 - 0.0501644i) q^{5} +(-1.61167 + 2.09822i) q^{7} +(2.41998 + 6.16602i) q^{9} +(0.286718 + 0.112528i) q^{11} +(2.53908 - 2.02485i) q^{13} +(1.62813 + 1.29839i) q^{15} +(3.22964 + 3.48072i) q^{17} +(1.50563 - 2.60783i) q^{19} +(7.79778 - 2.56164i) q^{21} +(-0.359481 + 0.387429i) q^{23} +(-4.49858 - 0.678052i) q^{25} +(2.50163 - 10.9604i) q^{27} +(-0.589753 - 2.58388i) q^{29} +(-2.57784 - 4.46495i) q^{31} +(-0.538263 - 0.789488i) q^{33} +(1.18411 - 1.32369i) q^{35} +(6.87877 + 2.12182i) q^{37} +(-10.0467 + 0.752894i) q^{39} +(-3.73365 - 7.75301i) q^{41} +(-2.08485 + 4.32925i) q^{43} +(-1.31062 - 4.24891i) q^{45} +(11.4242 - 1.72192i) q^{47} +(-1.80502 - 6.76328i) q^{49} +(-2.19543 - 14.5657i) q^{51} +(-3.18024 + 0.980975i) q^{53} +(-0.186283 - 0.0897092i) q^{55} +(-8.41654 + 4.05319i) q^{57} +(-0.636479 - 8.49322i) q^{59} +(-0.334479 + 1.08435i) q^{61} +(-16.8379 - 4.85996i) q^{63} +(-1.80122 + 1.22805i) q^{65} +(-0.813472 + 0.469658i) q^{67} +(1.59847 - 0.364841i) q^{69} +(10.6445 + 2.42953i) q^{71} +(2.21730 - 14.7108i) q^{73} +(10.3458 + 9.59949i) q^{75} +(-0.698205 + 0.420237i) q^{77} +(10.6030 + 6.12167i) q^{79} +(-10.9990 + 10.2056i) q^{81} +(11.1287 - 13.9550i) q^{83} +(-1.98730 - 2.49200i) q^{85} +(-3.00382 + 7.65360i) q^{87} +(9.49753 - 3.72751i) q^{89} +(0.156400 + 8.59092i) q^{91} +(-1.19525 + 15.9494i) q^{93} +(-1.13868 + 1.67014i) q^{95} +15.1809i q^{97} +2.04023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - q^{3} - 3 q^{5} + 4 q^{7} + 8 q^{9}+O(q^{10}) \) 108 * q - q^3 - 3 * q^5 + 4 * q^7 + 8 * q^9	\( 108 q - q^{3} - 3 q^{5} + 4 q^{7} + 8 q^{9} - 18 q^{11} + 16 q^{17} - 7 q^{19} + 5 q^{21} - 54 q^{23} - 4 q^{25} + 53 q^{27} - 16 q^{29} - 5 q^{31} - 3 q^{33} + 9 q^{35} + 2 q^{37} + 43 q^{39} - 28 q^{41} - 111 q^{45} + 60 q^{47} - 58 q^{49} + 3 q^{51} - 70 q^{53} - 69 q^{55} + 31 q^{57} - 9 q^{59} - 8 q^{61} - 93 q^{63} - 8 q^{65} + 21 q^{67} - 56 q^{69} + 63 q^{71} - 24 q^{73} - 2 q^{75} - 18 q^{77} - 21 q^{79} + 45 q^{81} - 60 q^{83} + 6 q^{85} + 6 q^{87} + 7 q^{89} + 66 q^{93} - 15 q^{95}+O(q^{100}) \) 108 * q - q^3 - 3 * q^5 + 4 * q^7 + 8 * q^9 - 18 * q^11 + 16 * q^17 - 7 * q^19 + 5 * q^21 - 54 * q^23 - 4 * q^25 + 53 * q^27 - 16 * q^29 - 5 * q^31 - 3 * q^33 + 9 * q^35 + 2 * q^37 + 43 * q^39 - 28 * q^41 - 111 * q^45 + 60 * q^47 - 58 * q^49 + 3 * q^51 - 70 * q^53 - 69 * q^55 + 31 * q^57 - 9 * q^59 - 8 * q^61 - 93 * q^63 - 8 * q^65 + 21 * q^67 - 56 * q^69 + 63 * q^71 - 24 * q^73 - 2 * q^75 - 18 * q^77 - 21 * q^79 + 45 * q^81 - 60 * q^83 + 6 * q^85 + 6 * q^87 + 7 * q^89 + 66 * q^93 - 15 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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