LMFDB - Embedded newform 702.2.bb.a.449.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			449.10
Character	$\chi$	$=$	702.449
Dual form			702.2.bb.a.197.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.517281 - 1.93052i) q^{5} +(0.686666 + 2.56267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73086 - 0.999310i) q^{10} +(-3.08472 - 3.08472i) q^{11} +(1.90819 - 3.05922i) q^{13} +(2.29763 + 1.32654i) q^{14} -1.00000 q^{16} +(-1.21062 - 2.09686i) q^{17} +(1.64767 - 6.14918i) q^{19} +(-1.93052 + 0.517281i) q^{20} -4.36245 q^{22} +(0.610766 + 1.05788i) q^{23} +(0.870804 - 0.502759i) q^{25} +(-0.813901 - 3.51249i) q^{26} +(2.56267 - 0.686666i) q^{28} -4.47591i q^{29} +(-8.14531 + 2.18253i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.33874 - 0.626664i) q^{34} +(4.59209 - 2.65124i) q^{35} +(2.49571 + 9.31410i) q^{37} +(-3.18305 - 5.51321i) q^{38} +(-0.999310 + 1.73086i) q^{40} +(6.63068 + 1.77669i) q^{41} +(-8.90622 - 5.14201i) q^{43} +(-3.08472 + 3.08472i) q^{44} +(1.17991 + 0.316156i) q^{46} +(-1.40065 + 5.22728i) q^{47} +(-0.0335972 + 0.0193974i) q^{49} +(0.260247 - 0.971255i) q^{50} +(-3.05922 - 1.90819i) q^{52} +0.142416i q^{53} +(-4.35944 + 7.55077i) q^{55} +(1.32654 - 2.29763i) q^{56} +(-3.16495 - 3.16495i) q^{58} +(2.84098 + 2.84098i) q^{59} +(5.02738 - 8.70767i) q^{61} +(-4.21632 + 7.30289i) q^{62} +1.00000i q^{64} +(-6.89295 - 2.10132i) q^{65} +(0.654683 - 2.44331i) q^{67} +(-2.09686 + 1.21062i) q^{68} +(1.37238 - 5.12181i) q^{70} +(7.11876 + 1.90747i) q^{71} +(-4.15800 + 4.15800i) q^{73} +(8.35079 + 4.82133i) q^{74} +(-6.14918 - 1.64767i) q^{76} +(5.78695 - 10.0233i) q^{77} +(-0.161842 - 0.280319i) q^{79} +(0.517281 + 1.93052i) q^{80} +(5.94491 - 3.43230i) q^{82} +(3.79971 + 1.01813i) q^{83} +(-3.42179 + 3.42179i) q^{85} +(-9.93360 + 2.66170i) q^{86} +4.36245i q^{88} +(14.2994 - 3.83151i) q^{89} +(9.15006 + 2.78940i) q^{91} +(1.05788 - 0.610766i) q^{92} +(2.70584 + 4.68665i) q^{94} -12.7234 q^{95} +(8.47838 - 2.27178i) q^{97} +(-0.0100408 + 0.0374729i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.517281	−	1.93052i	−0.231335	−	0.863354i	−0.979767	−	0.200142i	$-0.935860\pi$
$5$	−0.517281	−	1.93052i	−0.231335	−	0.863354i	0.748432	−	0.663212i	$-0.230807\pi$
$6$		0			0
$7$	0.686666	+	2.56267i	0.259535	+	0.968599i	0.965511	+	0.260363i	$0.0838421\pi$
$7$	0.686666	+	2.56267i	0.259535	+	0.968599i	−0.705976	+	0.708236i	$0.749491\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−1.73086	−	0.999310i	−0.547345	−	0.316010i
$11$	−3.08472	−	3.08472i	−0.930078	−	0.930078i	0.0676326	−	0.997710i	$-0.478455\pi$
$11$	−3.08472	−	3.08472i	−0.930078	−	0.930078i	−0.997710	+	0.0676326i	$0.978455\pi$
$12$		0			0
$13$	1.90819	−	3.05922i	0.529236	−	0.848475i
$13$	1.90819	−	3.05922i	0.529236	−	0.848475i
$14$	2.29763	+	1.32654i	0.614067	+	0.354532i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−1.21062	−	2.09686i	−0.293619	−	0.508563i	0.681044	−	0.732243i	$-0.261526\pi$
$17$	−1.21062	−	2.09686i	−0.293619	−	0.508563i	−0.974663	+	0.223680i	$0.928193\pi$
$18$		0			0
$19$	1.64767	−	6.14918i	0.378001	−	1.41072i	−0.470909	−	0.882182i	$-0.656074\pi$
$19$	1.64767	−	6.14918i	0.378001	−	1.41072i	0.848910	−	0.528538i	$-0.177259\pi$
$20$	−1.93052	+	0.517281i	−0.431677	+	0.115668i
$21$		0			0
$22$	−4.36245			−0.930078
$23$	0.610766	+	1.05788i	0.127353	+	0.220583i	0.922650	−	0.385637i	$-0.126018\pi$
$23$	0.610766	+	1.05788i	0.127353	+	0.220583i	−0.795297	+	0.606220i	$0.792685\pi$
$24$		0			0
$25$	0.870804	−	0.502759i	0.174161	−	0.100552i
$26$	−0.813901	−	3.51249i	−0.159619	−	0.688855i
$27$		0			0
$28$	2.56267	−	0.686666i	0.484299	−	0.129768i
$29$		−	4.47591i		−	0.831156i	−0.909557	−	0.415578i	$-0.863579\pi$
$29$		−	4.47591i		−	0.831156i	0.909557	−	0.415578i	$-0.136421\pi$
$30$		0			0
$31$	−8.14531	+	2.18253i	−1.46294	+	0.391994i	−0.900505	−	0.434847i	$-0.856803\pi$
$31$	−8.14531	+	2.18253i	−1.46294	+	0.391994i	−0.562437	+	0.826840i	$0.690136\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−2.33874	−	0.626664i	−0.401091	−	0.107472i
$35$	4.59209	−	2.65124i	0.776204	−	0.448142i
$36$		0			0
$37$	2.49571	+	9.31410i	0.410291	+	1.53123i	0.794083	+	0.607809i	$0.207951\pi$
$37$	2.49571	+	9.31410i	0.410291	+	1.53123i	−0.383792	+	0.923420i	$0.625382\pi$
$38$	−3.18305	−	5.51321i	−0.516359	−	0.894360i
$39$		0			0
$40$	−0.999310	+	1.73086i	−0.158005	+	0.273672i
$41$	6.63068	+	1.77669i	1.03554	+	0.277472i	0.736264	−	0.676695i	$-0.236588\pi$
$41$	6.63068	+	1.77669i	1.03554	+	0.277472i	0.299275	+	0.954167i	$0.403255\pi$
$42$		0			0
$43$	−8.90622	−	5.14201i	−1.35819	−	0.784149i	−0.368807	−	0.929506i	$-0.620234\pi$
$43$	−8.90622	−	5.14201i	−1.35819	−	0.784149i	−0.989379	+	0.145357i	$0.953567\pi$
$44$	−3.08472	+	3.08472i	−0.465039	+	0.465039i
$45$		0			0
$46$	1.17991	+	0.316156i	0.173968	+	0.0466146i
$47$	−1.40065	+	5.22728i	−0.204305	+	0.762477i	0.785355	+	0.619046i	$0.212480\pi$
$47$	−1.40065	+	5.22728i	−0.204305	+	0.762477i	−0.989660	+	0.143432i	$0.954186\pi$
$48$		0			0
$49$	−0.0335972	+	0.0193974i	−0.00479961	+	0.00277105i
$50$	0.260247	−	0.971255i	0.0368045	−	0.137356i
$51$		0			0
$52$	−3.05922	−	1.90819i	−0.424237	−	0.264618i
$53$			0.142416i			0.0195624i	0.999952	+	0.00978119i	$0.00311350\pi$
$53$			0.142416i			0.0195624i	−0.999952	+	0.00978119i	$0.996887\pi$
$54$		0			0
$55$	−4.35944	+	7.55077i	−0.587827	+	1.01815i
$56$	1.32654	−	2.29763i	0.177266	−	0.307034i
$57$		0			0
$58$	−3.16495	−	3.16495i	−0.415578	−	0.415578i
$59$	2.84098	+	2.84098i	0.369865	+	0.369865i	0.867428	−	0.497563i	$-0.165772\pi$
$59$	2.84098	+	2.84098i	0.369865	+	0.369865i	−0.497563	+	0.867428i	$0.665772\pi$
$60$		0			0
$61$	5.02738	−	8.70767i	0.643689	−	1.11490i	−0.340913	−	0.940095i	$-0.610736\pi$
$61$	5.02738	−	8.70767i	0.643689	−	1.11490i	0.984603	−	0.174808i	$-0.0559305\pi$
$62$	−4.21632	+	7.30289i	−0.535474	+	0.927467i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	−6.89295	−	2.10132i	−0.854965	−	0.260636i
$66$		0			0
$67$	0.654683	−	2.44331i	0.0799823	−	0.298498i	−0.914335	−	0.404960i	$-0.867286\pi$
$67$	0.654683	−	2.44331i	0.0799823	−	0.298498i	0.994317	+	0.106462i	$0.0339522\pi$
$68$	−2.09686	+	1.21062i	−0.254281	+	0.146809i
$69$		0			0
$70$	1.37238	−	5.12181i	0.164031	−	0.612173i
$71$	7.11876	+	1.90747i	0.844841	+	0.226375i	0.655178	−	0.755475i	$-0.272594\pi$
$71$	7.11876	+	1.90747i	0.844841	+	0.226375i	0.189663	+	0.981849i	$0.439260\pi$
$72$		0			0
$73$	−4.15800	+	4.15800i	−0.486657	+	0.486657i	−0.907250	−	0.420592i	$-0.861822\pi$
$73$	−4.15800	+	4.15800i	−0.486657	+	0.486657i	0.420592	+	0.907250i	$0.361822\pi$
$74$	8.35079	+	4.82133i	0.970760	+	0.560469i
$75$		0			0
$76$	−6.14918	−	1.64767i	−0.705360	−	0.189001i
$77$	5.78695	−	10.0233i	0.659484	−	1.14226i
$78$		0			0
$79$	−0.161842	−	0.280319i	−0.0182087	−	0.0315383i	0.856777	−	0.515686i	$-0.172463\pi$
$79$	−0.161842	−	0.280319i	−0.0182087	−	0.0315383i	−0.874986	+	0.484148i	$0.839130\pi$
$80$	0.517281	+	1.93052i	0.0578338	+	0.215839i
$81$		0			0
$82$	5.94491	−	3.43230i	0.656505	−	0.379034i
$83$	3.79971	+	1.01813i	0.417072	+	0.111754i	0.461252	−	0.887269i	$-0.347401\pi$
$83$	3.79971	+	1.01813i	0.417072	+	0.111754i	−0.0441792	+	0.999024i	$0.514067\pi$
$84$		0			0
$85$	−3.42179	+	3.42179i	−0.371145	+	0.371145i
$86$	−9.93360	+	2.66170i	−1.07117	+	0.287018i
$87$		0			0
$88$			4.36245i			0.465039i
$89$	14.2994	−	3.83151i	1.51573	−	0.406140i	0.597399	−	0.801944i	$-0.296201\pi$
$89$	14.2994	−	3.83151i	1.51573	−	0.406140i	0.918335	+	0.395805i	$0.129534\pi$
$90$		0			0
$91$	9.15006	+	2.78940i	0.959187	+	0.292408i
$92$	1.05788	−	0.610766i	0.110291	−	0.0636767i
$93$		0			0
$94$	2.70584	+	4.68665i	0.279086	+	0.483391i
$95$	−12.7234			−1.30540
$96$		0			0
$97$	8.47838	−	2.27178i	0.860849	−	0.230664i	0.198723	−	0.980056i	$-0.436321\pi$
$97$	8.47838	−	2.27178i	0.860849	−	0.230664i	0.662127	+	0.749392i	$0.269654\pi$
$98$	−0.0100408	+	0.0374729i	−0.00101428	+	0.00378533i
$99$		0			0
$100$	−0.502759	−	0.870804i	−0.0502759	−	0.0870804i
$101$	3.53374			0.351620			0.175810	−	0.984424i	$-0.443746\pi$
$101$	3.53374			0.351620			0.175810	+	0.984424i	$0.443746\pi$
$102$		0			0
$103$	12.1415	+	7.00991i	1.19634	+	0.690707i	0.959737	−	0.280899i	$-0.0906326\pi$
$103$	12.1415	+	7.00991i	1.19634	+	0.690707i	0.236603	+	0.971606i	$0.423966\pi$
$104$	−3.51249	+	0.813901i	−0.344428	+	0.0798096i
$105$		0			0
$106$	0.100703	+	0.100703i	0.00978119	+	0.00978119i
$107$	8.57787	+	4.95244i	0.829254	+	0.478770i	0.853597	−	0.520933i	$-0.174416\pi$
$107$	8.57787	+	4.95244i	0.829254	+	0.478770i	−0.0243429	+	0.999704i	$0.507749\pi$
$108$		0			0
$109$	5.54653	+	5.54653i	0.531261	+	0.531261i	0.920948	−	0.389687i	$-0.127417\pi$
$109$	5.54653	+	5.54653i	0.531261	+	0.531261i	−0.389687	+	0.920948i	$0.627417\pi$
$110$	2.25661	+	8.42179i	0.215160	+	0.802987i
$111$		0			0
$112$	−0.686666	−	2.56267i	−0.0648838	−	0.242150i
$113$			13.4714i			1.26728i	0.773628	+	0.633640i	$0.218440\pi$
$113$			13.4714i			1.26728i	−0.773628	+	0.633640i	$0.781560\pi$
$114$		0			0
$115$	1.72631	−	1.72631i	0.160980	−	0.160980i
$116$	−4.47591			−0.415578
$117$		0			0
$118$	4.01776			0.369865
$119$	4.54226	−	4.54226i	0.416389	−	0.416389i
$120$		0			0
$121$			8.03098i			0.730089i
$122$	−2.60236	−	9.71214i	−0.235607	−	0.879296i
$123$		0			0
$124$	2.18253	+	8.14531i	0.195997	+	0.731471i
$125$	−8.48722	−	8.48722i	−0.759120	−	0.759120i
$126$		0			0
$127$	−2.38546	−	1.37724i	−0.211675	−	0.122211i	0.390415	−	0.920639i	$-0.372332\pi$
$127$	−2.38546	−	1.37724i	−0.211675	−	0.122211i	−0.602090	+	0.798429i	$0.705665\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−6.35991	+	3.38819i	−0.557801	+	0.297164i
$131$	0.591828	+	0.341692i	0.0517083	+	0.0298538i	0.525631	−	0.850713i	$-0.323829\pi$
$131$	0.591828	+	0.341692i	0.0517083	+	0.0298538i	−0.473923	+	0.880566i	$0.657163\pi$
$132$		0			0
$133$	16.8897			1.46453
$134$	−1.26475	−	2.19061i	−0.109258	−	0.189240i
$135$		0			0
$136$	−0.626664	+	2.33874i	−0.0537360	+	0.200545i
$137$	−21.7576	+	5.82993i	−1.85888	+	0.498085i	−0.999903	−	0.0139339i	$-0.995565\pi$
$137$	−21.7576	+	5.82993i	−1.85888	+	0.498085i	−0.858974	+	0.512019i	$0.828898\pi$
$138$		0			0
$139$	−19.5490			−1.65812			−0.829062	−	0.559157i	$-0.811125\pi$
$139$	−19.5490			−1.65812			−0.829062	+	0.559157i	$0.811125\pi$
$140$	−2.65124	−	4.59209i	−0.224071	−	0.388102i
$141$		0			0
$142$	6.38250	−	3.68494i	0.535608	−	0.309233i
$143$	−15.3231	+	3.55060i	−1.28138	+	0.296916i
$144$		0			0
$145$	−8.64084	+	2.31531i	−0.717582	+	0.192276i
$146$			5.88030i			0.486657i
$147$		0			0
$148$	9.31410	−	2.49571i	0.765614	−	0.205146i
$149$	−3.47487	+	3.47487i	−0.284672	+	0.284672i	−0.834969	−	0.550297i	$-0.814515\pi$
$149$	−3.47487	+	3.47487i	−0.284672	+	0.284672i	0.550297	+	0.834969i	$0.314515\pi$
$150$		0			0
$151$	−3.87030	−	1.03704i	−0.314961	−	0.0843934i	0.0978758	−	0.995199i	$-0.468795\pi$
$151$	−3.87030	−	1.03704i	−0.314961	−	0.0843934i	−0.412836	+	0.910805i	$0.635462\pi$
$152$	−5.51321	+	3.18305i	−0.447180	+	0.258180i
$153$		0			0
$154$	−2.99555	−	11.1795i	−0.241388	−	0.900872i
$155$	8.42683	+	14.5957i	0.676859	+	1.17235i
$156$		0			0
$157$	0.0374157	−	0.0648059i	0.00298610	−	0.00517207i	−0.864528	−	0.502584i	$-0.832383\pi$
$157$	0.0374157	−	0.0648059i	0.00298610	−	0.00517207i	0.867515	+	0.497412i	$0.165716\pi$
$158$	−0.312655	−	0.0837756i	−0.0248735	−	0.00666483i
$159$		0			0
$160$	1.73086	+	0.999310i	0.136836	+	0.0790024i
$161$	−2.29160	+	2.29160i	−0.180603	+	0.180603i
$162$		0			0
$163$	18.0329	+	4.83191i	1.41245	+	0.378464i	0.882798	−	0.469752i	$-0.155657\pi$
$163$	18.0329	+	4.83191i	1.41245	+	0.378464i	0.529649	+	0.848217i	$0.322324\pi$
$164$	1.77669	−	6.63068i	0.138736	−	0.517769i
$165$		0			0
$166$	3.40673	−	1.96687i	0.264413	−	0.152659i
$167$	−4.71072	+	17.5806i	−0.364526	+	1.36043i	0.503535	+	0.863975i	$0.332032\pi$
$167$	−4.71072	+	17.5806i	−0.364526	+	1.36043i	−0.868062	+	0.496456i	$0.834634\pi$
$168$		0			0
$169$	−5.71764	−	11.6751i	−0.439818	−	0.898087i
$170$			4.83914i			0.371145i
$171$		0			0
$172$	−5.14201	+	8.90622i	−0.392075	+	0.679093i
$173$	2.19773	−	3.80657i	0.167090	−	0.289408i	−0.770305	−	0.637675i	$-0.779896\pi$
$173$	2.19773	−	3.80657i	0.167090	−	0.289408i	0.937396	+	0.348267i	$0.113230\pi$
$174$		0			0
$175$	1.88636	+	1.88636i	0.142595	+	0.142595i
$176$	3.08472	+	3.08472i	0.232519	+	0.232519i
$177$		0			0
$178$	7.40192	−	12.8205i	0.554797	−	0.960937i
$179$	5.44340	−	9.42824i	0.406859	−	0.704700i	−0.587677	−	0.809095i	$-0.699958\pi$
$179$	5.44340	−	9.42824i	0.406859	−	0.704700i	0.994536	+	0.104396i	$0.0332909\pi$
$180$		0			0
$181$		−	3.13809i		−	0.233253i	−0.993176	−	0.116626i	$-0.962792\pi$
$181$		−	3.13809i		−	0.233253i	0.993176	−	0.116626i	$-0.0372080\pi$
$182$	8.44247	−	4.49767i	0.625798	−	0.333389i
$183$		0			0
$184$	0.316156	−	1.17991i	0.0233073	−	0.0869840i
$185$	16.6901	−	9.63601i	1.22708	−	0.708454i
$186$		0			0
$187$	−2.73379	+	10.2026i	−0.199914	+	0.746091i
$188$	5.22728	+	1.40065i	0.381239	+	0.102153i
$189$		0			0
$190$	−8.99682	+	8.99682i	−0.652698	+	0.652698i
$191$	14.4072	+	8.31799i	1.04247	+	0.601869i	0.920531	−	0.390669i	$-0.127756\pi$
$191$	14.4072	+	8.31799i	1.04247	+	0.601869i	0.121936	+	0.992538i	$0.461090\pi$
$192$		0			0
$193$	14.7796	+	3.96019i	1.06386	+	0.285060i	0.747968	−	0.663735i	$-0.231030\pi$
$193$	14.7796	+	3.96019i	1.06386	+	0.285060i	0.315892	+	0.948795i	$0.397696\pi$
$194$	4.38873	−	7.60151i	0.315093	−	0.545757i
$195$		0			0
$196$	0.0193974	+	0.0335972i	0.00138553	+	0.00239980i
$197$	−5.36725	−	20.0309i	−0.382401	−	1.42714i	−0.842223	−	0.539129i	$-0.818753\pi$
$197$	−5.36725	−	20.0309i	−0.382401	−	1.42714i	0.459822	−	0.888011i	$-0.347913\pi$
$198$		0			0
$199$	5.37244	−	3.10178i	0.380842	−	0.219879i	−0.297342	−	0.954771i	$-0.596100\pi$
$199$	5.37244	−	3.10178i	0.380842	−	0.219879i	0.678185	+	0.734892i	$0.262767\pi$
$200$	−0.971255	−	0.260247i	−0.0686781	−	0.0184022i
$201$		0			0
$202$	2.49873	−	2.49873i	0.175810	−	0.175810i
$203$	11.4703	−	3.07346i	0.805057	−	0.215714i
$204$		0			0
$205$		−	13.7197i		−	0.958226i
$206$	13.5421	−	3.62860i	0.943524	−	0.252816i
$207$		0			0
$208$	−1.90819	+	3.05922i	−0.132309	+	0.212119i
$209$	−24.0511	+	13.8859i	−1.66365	+	0.960508i
$210$		0			0
$211$	4.22550	+	7.31878i	0.290895	+	0.503845i	0.974022	−	0.226455i	$-0.0727136\pi$
$211$	4.22550	+	7.31878i	0.290895	+	0.503845i	−0.683126	+	0.730300i	$0.739380\pi$
$212$	0.142416			0.00978119
$213$		0			0
$214$	9.56738	−	2.56357i	0.654012	−	0.175242i
$215$	−5.31973	+	19.8535i	−0.362802	+	1.35400i
$216$		0			0
$217$	−11.1862	−	19.3751i	−0.759370	−	1.31527i
$218$	7.84397			0.531261
$219$		0			0
$220$	7.55077	+	4.35944i	0.509073	+	0.293913i
$221$	−8.72484	−	0.297644i	−0.586896	−	0.0200217i
$222$		0			0
$223$	7.78077	+	7.78077i	0.521039	+	0.521039i	0.917885	−	0.396846i	$-0.129895\pi$
$223$	7.78077	+	7.78077i	0.521039	+	0.521039i	−0.396846	+	0.917885i	$0.629895\pi$
$224$	−2.29763	−	1.32654i	−0.153517	−	0.0886329i
$225$		0			0
$226$	9.52570	+	9.52570i	0.633640	+	0.633640i
$227$	2.04965	+	7.64941i	0.136040	+	0.507709i	0.999991	+	0.00413376i	$0.00131582\pi$
$227$	2.04965	+	7.64941i	0.136040	+	0.507709i	−0.863951	+	0.503576i	$0.832018\pi$
$228$		0			0
$229$	0.377414	+	1.40853i	0.0249402	+	0.0930780i	0.977274	−	0.211979i	$-0.0679910\pi$
$229$	0.377414	+	1.40853i	0.0249402	+	0.0930780i	−0.952334	+	0.305057i	$0.901324\pi$
$230$		−	2.44138i		−	0.160980i
$231$		0			0
$232$	−3.16495	+	3.16495i	−0.207789	+	0.207789i
$233$	−4.39305			−0.287799			−0.143899	−	0.989592i	$-0.545964\pi$
$233$	−4.39305			−0.287799			−0.143899	+	0.989592i	$0.545964\pi$
$234$		0			0
$235$	10.8159			0.705551
$236$	2.84098	−	2.84098i	0.184932	−	0.184932i
$237$		0			0
$238$		−	6.42373i		−	0.416389i
$239$	2.40851	+	8.98867i	0.155793	+	0.581429i	0.999036	+	0.0438958i	$0.0139770\pi$
$239$	2.40851	+	8.98867i	0.155793	+	0.581429i	−0.843243	+	0.537533i	$0.819356\pi$
$240$		0			0
$241$	0.431507	+	1.61040i	0.0277958	+	0.103735i	0.978430	−	0.206578i	$-0.0662327\pi$
$241$	0.431507	+	1.61040i	0.0277958	+	0.103735i	−0.950634	+	0.310313i	$0.899566\pi$
$242$	5.67876	+	5.67876i	0.365044	+	0.365044i
$243$		0			0
$244$	−8.70767	−	5.02738i	−0.557451	−	0.321845i
$245$	0.0548262	+	0.0548262i	0.00350272	+	0.00350272i
$246$		0			0
$247$	−15.6676	−	16.7744i	−0.996908	−	1.06733i
$248$	7.30289	+	4.21632i	0.463734	+	0.267737i
$249$		0			0
$250$	−12.0027			−0.759120
$251$	−3.88661	−	6.73180i	−0.245321	−	0.424908i	0.716901	−	0.697175i	$-0.245560\pi$
$251$	−3.88661	−	6.73180i	−0.245321	−	0.424908i	−0.962222	+	0.272267i	$0.912227\pi$
$252$		0			0
$253$	1.37921	−	5.14729i	0.0867104	−	0.323608i
$254$	−2.66063	+	0.712914i	−0.166943	+	0.0447322i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.8935	−	22.3322i	−0.804274	−	1.39304i	−0.916780	−	0.399392i	$-0.869221\pi$
$257$	−12.8935	−	22.3322i	−0.804274	−	1.39304i	0.112507	−	0.993651i	$-0.464112\pi$
$258$		0			0
$259$	−22.1553	+	12.7913i	−1.37666	+	0.794816i
$260$	−2.10132	+	6.89295i	−0.130318	+	0.427483i
$261$		0			0
$262$	0.660098	−	0.176873i	0.0407810	−	0.0109272i
$263$		−	26.7629i		−	1.65027i	−0.564934	−	0.825136i	$-0.691098\pi$
$263$		−	26.7629i		−	1.65027i	0.564934	−	0.825136i	$-0.308902\pi$
$264$		0			0
$265$	0.274937	−	0.0736692i	0.0168893	−	0.00452546i
$266$	11.9428	−	11.9428i	0.732263	−	0.732263i
$267$		0			0
$268$	−2.44331	−	0.654683i	−0.149249	−	0.0399911i
$269$	17.6997	−	10.2189i	1.07917	−	0.623058i	0.148496	−	0.988913i	$-0.452557\pi$
$269$	17.6997	−	10.2189i	1.07917	−	0.623058i	0.930672	+	0.365855i	$0.119223\pi$
$270$		0			0
$271$	−5.01971	−	18.7338i	−0.304926	−	1.13800i	−0.933009	−	0.359853i	$-0.882827\pi$
$271$	−5.01971	−	18.7338i	−0.304926	−	1.13800i	0.628083	−	0.778146i	$-0.283840\pi$
$272$	1.21062	+	2.09686i	0.0734047	+	0.127141i
$273$		0			0
$274$	−11.2626	+	19.5073i	−0.680396	+	1.17848i
$275$	−4.23705	−	1.13531i	−0.255504	−	0.0684621i
$276$		0			0
$277$	−9.25169	−	5.34146i	−0.555880	−	0.320937i	0.195610	−	0.980682i	$-0.437331\pi$
$277$	−9.25169	−	5.34146i	−0.555880	−	0.320937i	−0.751490	+	0.659744i	$0.770665\pi$
$278$	−13.8232	+	13.8232i	−0.829062	+	0.829062i
$279$		0			0
$280$	−5.12181	−	1.37238i	−0.306087	−	0.0820156i
$281$	5.89140	−	21.9870i	0.351451	−	1.31163i	−0.533440	−	0.845838i	$-0.679101\pi$
$281$	5.89140	−	21.9870i	0.351451	−	1.31163i	0.884892	−	0.465797i	$-0.154232\pi$
$282$		0			0
$283$	0.440515	−	0.254332i	0.0261859	−	0.0151184i	−0.486850	−	0.873486i	$-0.661854\pi$
$283$	0.440515	−	0.254332i	0.0261859	−	0.0151184i	0.513036	+	0.858367i	$0.328521\pi$
$284$	1.90747	−	7.11876i	0.113187	−	0.422421i
$285$		0			0
$286$	−8.32438	+	13.3457i	−0.492231	+	0.789147i
$287$			18.2123i			1.07504i
$288$		0			0
$289$	5.56879	−	9.64543i	0.327576	−	0.567378i
$290$	−4.47283	+	7.74716i	−0.262653	+	0.454929i
$291$		0			0
$292$	4.15800	+	4.15800i	0.243329	+	0.243329i
$293$	15.1811	+	15.1811i	0.886888	+	0.886888i	0.994223	−	0.107335i	$-0.0342316\pi$
$293$	15.1811	+	15.1811i	0.886888	+	0.886888i	−0.107335	+	0.994223i	$0.534232\pi$
$294$		0			0
$295$	4.01499	−	6.95416i	0.233762	−	0.404887i
$296$	4.82133	−	8.35079i	0.280234	−	0.485380i
$297$		0			0
$298$			4.91420i			0.284672i
$299$	4.40173	+	0.150163i	0.254559	+	0.00868415i
$300$		0			0
$301$	7.06168	−	26.3546i	0.407029	−	1.51905i
$302$	−3.47002	+	2.00341i	−0.199677	+	0.115284i
$303$		0			0
$304$	−1.64767	+	6.14918i	−0.0945003	+	0.352680i
$305$	−19.4109	−	5.20113i	−1.11146	−	0.297816i
$306$		0			0
$307$	−16.9627	+	16.9627i	−0.968112	+	0.968112i	−0.999507	−	0.0313952i	$-0.990005\pi$
$307$	−16.9627	+	16.9627i	−0.968112	+	0.968112i	0.0313952	+	0.999507i	$0.490005\pi$
$308$	−10.0233	−	5.78695i	−0.571130	−	0.329742i
$309$		0			0
$310$	16.2794	+	4.36205i	0.924607	+	0.247748i
$311$	−16.5307	+	28.6320i	−0.937370	+	1.62357i	−0.167017	+	0.985954i	$0.553413\pi$
$311$	−16.5307	+	28.6320i	−0.937370	+	1.62357i	−0.770353	+	0.637618i	$0.779920\pi$
$312$		0			0
$313$	7.32210	+	12.6823i	0.413870	+	0.716843i	0.995309	−	0.0967464i	$-0.0308436\pi$
$313$	7.32210	+	12.6823i	0.413870	+	0.716843i	−0.581439	+	0.813590i	$0.697510\pi$
$314$	−0.0193678	−	0.0722816i	−0.00109299	−	0.00407908i
$315$		0			0
$316$	−0.280319	+	0.161842i	−0.0157692	+	0.00910433i
$317$	1.34890	+	0.361436i	0.0757616	+	0.0203003i	0.296501	−	0.955033i	$-0.404180\pi$
$317$	1.34890	+	0.361436i	0.0757616	+	0.0203003i	−0.220739	+	0.975333i	$0.570847\pi$
$318$		0			0
$319$	−13.8069	+	13.8069i	−0.773040	+	0.773040i
$320$	1.93052	−	0.517281i	0.107919	−	0.0289169i
$321$		0			0
$322$			3.24081i			0.180603i
$323$	−14.8887	+	3.98941i	−0.828427	+	0.221976i
$324$		0			0
$325$	0.123608	−	3.62334i	0.00685656	−	0.200987i
$326$	16.1679	−	9.33453i	0.895456	−	0.516992i
$327$		0			0
$328$	−3.43230	−	5.94491i	−0.189517	−	0.328253i
$329$	−14.3576			−0.791559
$330$		0			0
$331$	−16.9267	+	4.53549i	−0.930374	+	0.249293i	−0.692014	−	0.721884i	$-0.743276\pi$
$331$	−16.9267	+	4.53549i	−0.930374	+	0.249293i	−0.238360	+	0.971177i	$0.576610\pi$
$332$	1.01813	−	3.79971i	0.0558771	−	0.208536i
$333$		0			0
$334$	9.10041	+	15.7624i	0.497952	+	0.862479i
$335$	−5.05551			−0.276212
$336$		0			0
$337$	−22.3033	−	12.8768i	−1.21494	−	0.701445i	−0.251108	−	0.967959i	$-0.580795\pi$
$337$	−22.3033	−	12.8768i	−1.21494	−	0.701445i	−0.963831	+	0.266514i	$0.914128\pi$
$338$	−12.2985	−	4.21258i	−0.668953	−	0.229134i
$339$		0			0
$340$	3.42179	+	3.42179i	0.185573	+	0.185573i
$341$	31.8585	+	18.3935i	1.72523	+	0.996064i
$342$		0			0
$343$	13.0593	+	13.0593i	0.705134	+	0.705134i
$344$	2.66170	+	9.93360i	0.143509	+	0.535584i
$345$		0			0
$346$	−1.13763	−	4.24568i	−0.0611592	−	0.228249i
$347$		−	22.4935i		−	1.20752i	−0.797168	−	0.603758i	$-0.793669\pi$
$347$		−	22.4935i		−	1.20752i	0.797168	−	0.603758i	$-0.206331\pi$
$348$		0			0
$349$	−11.7660	+	11.7660i	−0.629819	+	0.629819i	−0.948022	−	0.318204i	$-0.896920\pi$
$349$	−11.7660	+	11.7660i	−0.629819	+	0.629819i	0.318204	+	0.948022i	$0.396920\pi$
$350$	2.66771			0.142595
$351$		0			0
$352$	4.36245			0.232519
$353$	−23.7758	+	23.7758i	−1.26546	+	1.26546i	−0.317049	+	0.948409i	$0.602692\pi$
$353$	−23.7758	+	23.7758i	−1.26546	+	1.26546i	−0.948409	+	0.317049i	$0.897308\pi$
$354$		0			0
$355$		−	14.7296i		−	0.781766i
$356$	−3.83151	−	14.2994i	−0.203070	−	0.757867i
$357$		0			0
$358$	−2.81771	−	10.5158i	−0.148921	−	0.555779i
$359$	−18.7010	−	18.7010i	−0.987001	−	0.987001i	0.0129158	−	0.999917i	$-0.495889\pi$
$359$	−18.7010	−	18.7010i	−0.987001	−	0.987001i	−0.999917	+	0.0129158i	$0.995889\pi$
$360$		0			0
$361$	−18.6432	−	10.7636i	−0.981220	−	0.566507i
$362$	−2.21897	−	2.21897i	−0.116626	−	0.116626i
$363$		0			0
$364$	2.78940	−	9.15006i	0.146204	−	0.479593i
$365$	10.1780	+	5.87625i	0.532739	+	0.307577i
$366$		0			0
$367$	35.0360			1.82886			0.914432	−	0.404739i	$-0.132638\pi$
$367$	35.0360			1.82886			0.914432	+	0.404739i	$0.132638\pi$
$368$	−0.610766	−	1.05788i	−0.0318384	−	0.0551457i
$369$		0			0
$370$	4.98797	−	18.6153i	0.259312	−	0.967766i
$371$	−0.364966	+	0.0977923i	−0.0189481	+	0.00507713i
$372$		0			0
$373$	6.34158			0.328355			0.164177	−	0.986431i	$-0.447503\pi$
$373$	6.34158			0.328355			0.164177	+	0.986431i	$0.447503\pi$
$374$	5.28127	+	9.14744i	0.273088	+	0.473003i
$375$		0			0
$376$	4.68665	−	2.70584i	0.241696	−	0.139543i
$377$	−13.6928	−	8.54089i	−0.705215	−	0.439878i
$378$		0			0
$379$	−33.0310	+	8.85063i	−1.69669	+	0.454626i	−0.972102	−	0.234557i	$-0.924636\pi$
$379$	−33.0310	+	8.85063i	−1.69669	+	0.454626i	−0.724587	+	0.689184i	$0.757969\pi$
$380$			12.7234i			0.652698i
$381$		0			0
$382$	16.0691	−	4.30571i	0.822168	−	0.220299i
$383$	11.8444	−	11.8444i	0.605221	−	0.605221i	−0.336473	−	0.941693i	$-0.609234\pi$
$383$	11.8444	−	11.8444i	0.605221	−	0.605221i	0.941693	+	0.336473i	$0.109234\pi$
$384$		0			0
$385$	−22.3436	−	5.98696i	−1.13874	−	0.305124i
$386$	13.2510	−	7.65049i	0.674460	−	0.389400i
$387$		0			0
$388$	−2.27178	−	8.47838i	−0.115332	−	0.430425i
$389$	−5.63377	−	9.75798i	−0.285644	−	0.494749i	0.687121	−	0.726543i	$-0.258874\pi$
$389$	−5.63377	−	9.75798i	−0.285644	−	0.494749i	−0.972765	+	0.231793i	$0.925541\pi$
$390$		0			0
$391$	1.47881	−	2.56138i	0.0747867	−	0.129534i
$392$	0.0374729	+	0.0100408i	0.00189267	+	0.000507138i
$393$		0			0
$394$	−17.9592	−	10.3687i	−0.904771	−	0.522370i
$395$	−0.457443	+	0.457443i	−0.0230164	+	0.0230164i
$396$		0			0
$397$	5.64532	+	1.51266i	0.283331	+	0.0759182i	0.397686	−	0.917522i	$-0.369813\pi$
$397$	5.64532	+	1.51266i	0.283331	+	0.0759182i	−0.114355	+	0.993440i	$0.536480\pi$
$398$	1.60560	−	5.99218i	0.0804814	−	0.300361i
$399$		0			0
$400$	−0.870804	+	0.502759i	−0.0435402	+	0.0251379i
$401$	7.17726	−	26.7859i	0.358415	−	1.33762i	−0.517717	−	0.855552i	$-0.673218\pi$
$401$	7.17726	−	26.7859i	0.358415	−	1.33762i	0.876132	−	0.482071i	$-0.160115\pi$
$402$		0			0
$403$	−8.86595	+	29.0830i	−0.441644	+	1.44873i
$404$		−	3.53374i		−	0.175810i
$405$		0			0
$406$	5.93746	−	10.2840i	0.294671	−	0.510386i
$407$	21.0328	−	36.4299i	1.04256	−	1.80576i
$408$		0			0
$409$	2.88906	+	2.88906i	0.142855	+	0.142855i	0.774917	−	0.632062i	$-0.217791\pi$
$409$	2.88906	+	2.88906i	0.142855	+	0.142855i	−0.632062	+	0.774917i	$0.717791\pi$
$410$	−9.70130	−	9.70130i	−0.479113	−	0.479113i
$411$		0			0
$412$	7.00991	−	12.1415i	0.345354	−	0.598170i
$413$	−5.32970	+	9.23132i	−0.262258	+	0.454243i
$414$		0			0
$415$		−	7.86207i		−	0.385934i
$416$	0.813901	+	3.51249i	0.0399048	+	0.172214i
$417$		0			0
$418$	−7.18788	+	26.8255i	−0.351570	+	1.31208i
$419$	−15.9626	+	9.21604i	−0.779826	+	0.450233i	−0.836369	−	0.548167i	$-0.815326\pi$
$419$	−15.9626	+	9.21604i	−0.779826	+	0.450233i	0.0565426	+	0.998400i	$0.481992\pi$
$420$		0			0
$421$	−8.34557	+	31.1461i	−0.406738	+	1.51797i	0.394090	+	0.919072i	$0.371060\pi$
$421$	−8.34557	+	31.1461i	−0.406738	+	1.51797i	−0.800828	+	0.598895i	$0.795607\pi$
$422$	8.16303	+	2.18728i	0.397370	+	0.106475i
$423$		0			0
$424$	0.100703	−	0.100703i	0.00489059	−	0.00489059i
$425$	−2.10843	−	1.21730i	−0.102274	−	0.0590477i
$426$		0			0
$427$	25.7670	+	6.90425i	1.24695	+	0.334120i
$428$	4.95244	−	8.57787i	0.239385	−	0.414627i
$429$		0			0
$430$	10.2769	+	17.8002i	0.495597	+	0.858400i
$431$	3.39947	+	12.6870i	0.163747	+	0.611112i	0.998197	+	0.0600279i	$0.0191190\pi$
$431$	3.39947	+	12.6870i	0.163747	+	0.611112i	−0.834450	+	0.551084i	$0.814214\pi$
$432$		0			0
$433$	4.72346	−	2.72709i	0.226995	−	0.131056i	−0.382190	−	0.924084i	$-0.624830\pi$
$433$	4.72346	−	2.72709i	0.226995	−	0.131056i	0.609185	+	0.793028i	$0.291497\pi$
$434$	−21.6101	−	5.79041i	−1.03732	−	0.277949i
$435$		0			0
$436$	5.54653	−	5.54653i	0.265630	−	0.265630i
$437$	7.51142	−	2.01268i	0.359320	−	0.0962795i
$438$		0			0
$439$			3.02367i			0.144312i	0.997393	+	0.0721559i	$0.0229879\pi$
$439$			3.02367i			0.144312i	−0.997393	+	0.0721559i	$0.977012\pi$
$440$	8.42179	−	2.25661i	0.401493	−	0.107580i
$441$		0			0
$442$	−6.37986	+	5.95893i	−0.303459	+	0.283437i
$443$	3.45678	−	1.99577i	0.164237	−	0.0948221i	−0.415629	−	0.909534i	$-0.636438\pi$
$443$	3.45678	−	1.99577i	0.164237	−	0.0948221i	0.579865	+	0.814712i	$0.303105\pi$
$444$		0			0
$445$	−14.7936	−	25.6233i	−0.701285	−	1.21466i
$446$	11.0037			0.521039
$447$		0			0
$448$	−2.56267	+	0.686666i	−0.121075	+	0.0324419i
$449$	3.46480	−	12.9308i	0.163514	−	0.610242i	−0.834711	−	0.550688i	$-0.814365\pi$
$449$	3.46480	−	12.9308i	0.163514	−	0.610242i	0.998225	−	0.0595540i	$-0.0189679\pi$
$450$		0			0
$451$	−14.9732	−	25.9344i	−0.705061	−	1.22120i
$452$	13.4714			0.633640
$453$		0			0
$454$	6.85828	+	3.95963i	0.321875	+	0.185835i
$455$	0.651835	−	19.1073i	0.0305585	−	0.895762i
$456$		0			0
$457$	0.947210	+	0.947210i	0.0443086	+	0.0443086i	0.728914	−	0.684605i	$-0.240025\pi$
$457$	0.947210	+	0.947210i	0.0443086	+	0.0443086i	−0.684605	+	0.728914i	$0.740025\pi$
$458$	1.26285	+	0.729107i	0.0590091	+	0.0340689i
$459$		0			0
$460$	−1.72631	−	1.72631i	−0.0804898	−	0.0804898i
$461$	1.31243	+	4.89805i	0.0611260	+	0.228125i	0.989731	−	0.142946i	$-0.0456574\pi$
$461$	1.31243	+	4.89805i	0.0611260	+	0.228125i	−0.928605	+	0.371071i	$0.878991\pi$
$462$		0			0
$463$	−2.00276	−	7.47439i	−0.0930760	−	0.347364i	0.903645	−	0.428283i	$-0.140881\pi$
$463$	−2.00276	−	7.47439i	−0.0930760	−	0.347364i	−0.996721	+	0.0809185i	$0.974215\pi$
$464$			4.47591i			0.207789i
$465$		0			0
$466$	−3.10636	+	3.10636i	−0.143899	+	0.143899i
$467$	−10.4397			−0.483093			−0.241546	−	0.970389i	$-0.577655\pi$
$467$	−10.4397			−0.483093			−0.241546	+	0.970389i	$0.577655\pi$
$468$		0			0
$469$	6.71095			0.309883
$470$	7.64799	−	7.64799i	0.352776	−	0.352776i
$471$		0			0
$472$		−	4.01776i		−	0.184932i
$473$	11.6115	+	43.3348i	0.533899	+	1.99254i
$474$		0			0
$475$	−1.65676	−	6.18311i	−0.0760174	−	0.283701i
$476$	−4.54226	−	4.54226i	−0.208194	−	0.208194i
$477$		0			0
$478$	8.05902	+	4.65288i	0.368611	+	0.212818i
$479$	−4.68529	−	4.68529i	−0.214076	−	0.214076i	0.591920	−	0.805996i	$-0.298370\pi$
$479$	−4.68529	−	4.68529i	−0.214076	−	0.214076i	−0.805996	+	0.591920i	$0.798370\pi$
$480$		0			0
$481$	33.2561	+	10.1381i	1.51635	+	0.462260i
$482$	1.44385	+	0.833607i	0.0657655	+	0.0379697i
$483$		0			0
$484$	8.03098			0.365044
$485$	−8.77141	−	15.1925i	−0.398289	−	0.689857i
$486$		0			0
$487$	−4.31888	+	16.1183i	−0.195707	+	0.730390i	0.796375	+	0.604803i	$0.206748\pi$
$487$	−4.31888	+	16.1183i	−0.195707	+	0.730390i	−0.992083	+	0.125587i	$0.959919\pi$
$488$	−9.71214	+	2.60236i	−0.439648	+	0.117803i
$489$		0			0
$490$	0.0775360			0.00350272
$491$	7.68585	+	13.3123i	0.346858	+	0.600775i	0.985689	−	0.168571i	$-0.0539154\pi$
$491$	7.68585	+	13.3123i	0.346858	+	0.600775i	−0.638832	+	0.769346i	$0.720582\pi$
$492$		0			0
$493$	−9.38535	+	5.41864i	−0.422695	+	0.244043i
$494$	−22.9400	−	0.782586i	−1.03212	−	0.0352102i
$495$		0			0
$496$	8.14531	−	2.18253i	0.365735	−	0.0979985i
$497$			19.5528i			0.877064i
$498$		0			0
$499$	−21.5745	+	5.78088i	−0.965808	+	0.258788i	−0.707057	−	0.707157i	$-0.749978\pi$
$499$	−21.5745	+	5.78088i	−0.965808	+	0.258788i	−0.258751	+	0.965944i	$0.583311\pi$
$500$	−8.48722	+	8.48722i	−0.379560	+	0.379560i
$501$		0			0
$502$	−7.50835	−	2.01186i	−0.335114	−	0.0897936i
$503$	20.4381	−	11.8000i	0.911291	−	0.526134i	0.0304450	−	0.999536i	$-0.490308\pi$
$503$	20.4381	−	11.8000i	0.911291	−	0.526134i	0.880846	+	0.473402i	$0.156974\pi$
$504$		0			0
$505$	−1.82794	−	6.82195i	−0.0813421	−	0.303573i
$506$	−2.66444	−	4.61494i	−0.118449	−	0.205159i
$507$		0			0
$508$	−1.37724	+	2.38546i	−0.0611053	+	0.105838i
$509$	−4.87095	−	1.30517i	−0.215901	−	0.0578506i	0.149247	−	0.988800i	$-0.452315\pi$
$509$	−4.87095	−	1.30517i	−0.215901	−	0.0578506i	−0.365148	+	0.930949i	$0.618982\pi$
$510$		0			0
$511$	−13.5108	−	7.80044i	−0.597680	−	0.345071i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−24.9083	−	6.67416i	−1.09866	−	0.294385i
$515$	7.25219	−	27.0655i	0.319570	−	1.19265i
$516$		0			0
$517$	20.4453	−	11.8041i	0.899183	−	0.519144i
$518$	−6.62129	+	24.7110i	−0.290923	+	1.08574i
$519$		0			0
$520$	3.38819	+	6.35991i	0.148582	+	0.278900i
$521$			42.7218i			1.87168i	0.352428	+	0.935839i	$0.385356\pi$
$521$			42.7218i			1.87168i	−0.352428	+	0.935839i	$0.614644\pi$
$522$		0			0
$523$	5.91448	−	10.2442i	0.258622	−	0.447946i	−0.707251	−	0.706962i	$-0.750065\pi$
$523$	5.91448	−	10.2442i	0.258622	−	0.447946i	0.965873	+	0.259016i	$0.0833983\pi$
$524$	0.341692	−	0.591828i	0.0149269	−	0.0258541i
$525$		0			0
$526$	−18.9242	−	18.9242i	−0.825136	−	0.825136i
$527$	14.4373	+	14.4373i	0.628900	+	0.628900i
$528$		0			0
$529$	10.7539	−	18.6264i	0.467562	−	0.809841i
$530$	0.142318	−	0.246502i	0.00618190	−	0.0107074i
$531$		0			0
$532$		−	16.8897i		−	0.732263i
$533$	18.0879	−	16.8945i	0.783472	−	0.731780i
$534$		0			0
$535$	5.12360	−	19.1216i	0.221513	−	0.826697i
$536$	−2.19061	+	1.26475i	−0.0946201	+	0.0546289i
$537$		0			0
$538$	5.28970	−	19.7414i	0.228055	−	0.851113i
$539$	0.163474	+	0.0438026i	0.00704130	+	0.00188671i
$540$		0			0
$541$	−1.16137	+	1.16137i	−0.0499311	+	0.0499311i	−0.731631	−	0.681700i	$-0.761241\pi$
$541$	−1.16137	+	1.16137i	−0.0499311	+	0.0499311i	0.681700	+	0.731631i	$0.261241\pi$
$542$	−16.7963	−	9.69734i	−0.721463	−	0.416537i
$543$		0			0
$544$	2.33874	+	0.626664i	0.100273	+	0.0268680i
$545$	7.83856	−	13.5768i	0.335767	−	0.581566i
$546$		0			0
$547$	0.539713	+	0.934811i	0.0230765	+	0.0399696i	0.877333	−	0.479882i	$-0.159321\pi$
$547$	0.539713	+	0.934811i	0.0230765	+	0.0399696i	−0.854257	+	0.519852i	$0.825987\pi$
$548$	5.82993	+	21.7576i	0.249042	+	0.929439i
$549$		0			0
$550$	−3.79884	+	2.19326i	−0.161983	+	0.0935209i
$551$	−27.5232	−	7.37483i	−1.17253	−	0.314178i
$552$		0			0
$553$	0.607233	−	0.607233i	0.0258222	−	0.0258222i
$554$	−10.3189	+	2.76495i	−0.438409	+	0.117471i
$555$		0			0
$556$			19.5490i			0.829062i
$557$	22.0126	−	5.89827i	0.932705	−	0.249918i	0.239697	−	0.970848i	$-0.422952\pi$
$557$	22.0126	−	5.89827i	0.932705	−	0.249918i	0.693008	+	0.720930i	$0.256285\pi$
$558$		0			0
$559$	−32.7253	+	17.4342i	−1.38413	+	0.737386i
$560$	−4.59209	+	2.65124i	−0.194051	+	0.112035i
$561$		0			0
$562$	−11.3813	−	19.7130i	−0.480092	−	0.831543i
$563$	12.7743			0.538373			0.269186	−	0.963088i	$-0.413245\pi$
$563$	12.7743			0.538373			0.269186	+	0.963088i	$0.413245\pi$
$564$		0			0
$565$	26.0067	−	6.96849i	1.09411	−	0.293166i
$566$	0.131652	−	0.491331i	0.00553374	−	0.0206522i
$567$		0			0
$568$	−3.68494	−	6.38250i	−0.154617	−	0.267804i
$569$	3.87917			0.162623			0.0813117	−	0.996689i	$-0.474089\pi$
$569$	3.87917			0.162623			0.0813117	+	0.996689i	$0.474089\pi$
$570$		0			0
$571$	−4.28302	−	2.47280i	−0.179239	−	0.103483i	0.407696	−	0.913118i	$-0.366332\pi$
$571$	−4.28302	−	2.47280i	−0.179239	−	0.103483i	−0.586935	+	0.809634i	$0.699666\pi$
$572$	3.55060	+	15.3231i	0.148458	+	0.640689i
$573$		0			0
$574$	12.8780	+	12.8780i	0.537518	+	0.537518i
$575$	1.06371	+	0.614136i	0.0443599	+	0.0256112i
$576$		0			0
$577$	−9.91809	−	9.91809i	−0.412896	−	0.412896i	0.469850	−	0.882746i	$-0.344308\pi$
$577$	−9.91809	−	9.91809i	−0.412896	−	0.412896i	−0.882746	+	0.469850i	$0.844308\pi$
$578$	−2.88262	−	10.7581i	−0.119901	−	0.447477i
$579$		0			0
$580$	2.31531	+	8.64084i	0.0961378	+	0.358791i
$581$			10.4365i			0.432980i
$582$		0			0
$583$	0.439314	−	0.439314i	0.0181945	−	0.0181945i
$584$	5.88030			0.243329
$585$		0			0
$586$	21.4693			0.886888
$587$	−28.9809	+	28.9809i	−1.19617	+	1.19617i	−0.220863	+	0.975305i	$0.570887\pi$
$587$	−28.9809	+	28.9809i	−1.19617	+	1.19617i	−0.975305	+	0.220863i	$0.929113\pi$
$588$		0			0
$589$			53.6831i			2.21197i
$590$	−2.07831	−	7.75636i	−0.0855627	−	0.319324i
$591$		0			0
$592$	−2.49571	−	9.31410i	−0.102573	−	0.382807i
$593$	5.71700	+	5.71700i	0.234769	+	0.234769i	0.814680	−	0.579911i	$-0.196913\pi$
$593$	5.71700	+	5.71700i	0.234769	+	0.234769i	−0.579911	+	0.814680i	$0.696913\pi$
$594$		0			0
$595$	−11.1186	−	6.41930i	−0.455816	−	0.263166i
$596$	3.47487	+	3.47487i	0.142336	+	0.142336i
$597$		0			0
$598$	3.21868	−	3.00631i	0.131621	−	0.122937i
$599$	−33.2498	−	19.1968i	−1.35855	−	0.784359i	−0.369121	−	0.929381i	$-0.620341\pi$
$599$	−33.2498	−	19.1968i	−1.35855	−	0.784359i	−0.989428	+	0.145022i	$0.953675\pi$
$600$		0			0
$601$	20.9115			0.853000			0.426500	−	0.904488i	$-0.359746\pi$
$601$	20.9115			0.853000			0.426500	+	0.904488i	$0.359746\pi$
$602$	−13.6421	−	23.6289i	−0.556011	−	0.963040i
$603$		0			0
$604$	−1.03704	+	3.87030i	−0.0421967	+	0.157480i
$605$	15.5040	−	4.15427i	0.630325	−	0.168895i
$606$		0			0
$607$	35.0835			1.42399			0.711997	−	0.702182i	$-0.247791\pi$
$607$	35.0835			1.42399			0.711997	+	0.702182i	$0.247791\pi$
$608$	3.18305	+	5.51321i	0.129090	+	0.223590i
$609$		0			0
$610$	−17.4033	+	10.0478i	−0.704640	+	0.406824i
$611$	13.3187	+	14.2595i	0.538817	+	0.576878i
$612$		0			0
$613$	37.3103	−	9.99725i	1.50695	−	0.403785i	0.591527	−	0.806285i	$-0.298525\pi$
$613$	37.3103	−	9.99725i	1.50695	−	0.403785i	0.915420	+	0.402500i	$0.131859\pi$
$614$			23.9889i			0.968112i
$615$		0			0
$616$	−11.1795	+	2.99555i	−0.450436	+	0.120694i
$617$	5.51931	−	5.51931i	0.222199	−	0.222199i	−0.587225	−	0.809424i	$-0.699780\pi$
$617$	5.51931	−	5.51931i	0.222199	−	0.222199i	0.809424	+	0.587225i	$0.199780\pi$
$618$		0			0
$619$	27.6086	+	7.39770i	1.10968	+	0.297339i	0.766702	−	0.642003i	$-0.221896\pi$
$619$	27.6086	+	7.39770i	1.10968	+	0.297339i	0.342982	+	0.939342i	$0.388563\pi$
$620$	14.5957	−	8.42683i	0.586177	−	0.338430i
$621$		0			0
$622$	8.55692	+	31.9348i	0.343101	+	1.28047i
$623$	19.6378	+	34.0137i	0.786773	+	1.36273i
$624$		0			0
$625$	−9.48067	+	16.4210i	−0.379227	+	0.656840i
$626$	14.1452	+	3.79020i	0.565356	+	0.151487i
$627$		0			0
$628$	−0.0648059	−	0.0374157i	−0.00258604	−	0.00149305i
$629$	16.5090	−	16.5090i	0.658256	−	0.658256i
$630$		0			0
$631$	−2.02779	−	0.543345i	−0.0807251	−	0.0216302i	0.218230	−	0.975897i	$-0.429972\pi$
$631$	−2.02779	−	0.543345i	−0.0807251	−	0.0216302i	−0.298956	+	0.954267i	$0.596638\pi$
$632$	−0.0837756	+	0.312655i	−0.00333242	+	0.0124367i
$633$		0			0
$634$	1.20939	−	0.698240i	0.0480309	−	0.0277307i
$635$	−1.42484	+	5.31759i	−0.0565432	+	0.211022i
$636$		0			0
$637$	−0.00476905	+	0.139795i	−0.000188956	+	0.00553889i
$638$			19.5260i			0.773040i
$639$		0			0
$640$	0.999310	−	1.73086i	0.0395012	−	0.0684181i
$641$	−9.64616	+	16.7076i	−0.381001	+	0.659912i	−0.991206	−	0.132331i	$-0.957754\pi$
$641$	−9.64616	+	16.7076i	−0.381001	+	0.659912i	0.610205	+	0.792244i	$0.291087\pi$
$642$		0			0
$643$	11.7244	+	11.7244i	0.462364	+	0.462364i	0.899430	−	0.437066i	$-0.143982\pi$
$643$	11.7244	+	11.7244i	0.462364	+	0.462364i	−0.437066	+	0.899430i	$0.643982\pi$
$644$	2.29160	+	2.29160i	0.0903017	+	0.0903017i
$645$		0			0
$646$	−7.70694	+	13.3488i	−0.303225	+	0.525202i
$647$	19.1754	−	33.2127i	0.753861	−	1.30573i	−0.192077	−	0.981380i	$-0.561522\pi$
$647$	19.1754	−	33.2127i	0.753861	−	1.30573i	0.945939	−	0.324346i	$-0.105144\pi$
$648$		0			0
$649$		−	17.5273i		−	0.688006i
$650$	−2.47468	−	2.64949i	−0.0970650	−	0.103922i
$651$		0			0
$652$	4.83191	−	18.0329i	0.189232	−	0.706224i
$653$	−12.7867	+	7.38243i	−0.500384	+	0.288897i	−0.728872	−	0.684650i	$-0.759955\pi$
$653$	−12.7867	+	7.38243i	−0.500384	+	0.288897i	0.228488	+	0.973547i	$0.426622\pi$
$654$		0			0
$655$	0.353502	−	1.31929i	0.0138125	−	0.0515488i
$656$	−6.63068	−	1.77669i	−0.258885	−	0.0693680i
$657$		0			0
$658$	−10.1523	+	10.1523i	−0.395780	+	0.395780i
$659$	−6.91954	−	3.99500i	−0.269547	−	0.155623i	0.359135	−	0.933286i	$-0.383072\pi$
$659$	−6.91954	−	3.99500i	−0.269547	−	0.155623i	−0.628682	+	0.777663i	$0.716405\pi$
$660$		0			0
$661$	23.5969	+	6.32278i	0.917814	+	0.245928i	0.686651	−	0.726987i	$-0.259080\pi$
$661$	23.5969	+	6.32278i	0.917814	+	0.245928i	0.231163	+	0.972915i	$0.425747\pi$
$662$	−8.76189	+	15.1760i	−0.340540	+	0.589833i
$663$		0			0
$664$	−1.96687	−	3.40673i	−0.0763295	−	0.132207i
$665$	−8.73674	−	32.6060i	−0.338796	−	1.26440i
$666$		0			0
$667$	4.73497	−	2.73374i	0.183339	−	0.105851i
$668$	17.5806	+	4.71072i	0.680215	+	0.182263i
$669$		0			0
$670$	−3.57479	+	3.57479i	−0.138106	+	0.138106i
$671$	−42.3687	+	11.3527i	−1.63563	+	0.438265i
$672$		0			0
$673$		−	49.8526i		−	1.92168i	−0.277112	−	0.960838i	$-0.589377\pi$
$673$		−	49.8526i		−	1.92168i	0.277112	−	0.960838i	$-0.410623\pi$
$674$	−24.8761	+	6.66553i	−0.958192	+	0.256747i
$675$		0			0
$676$	−11.6751	+	5.71764i	−0.449043	+	0.219909i
$677$	−7.87586	+	4.54713i	−0.302694	+	0.174760i	−0.643652	−	0.765318i	$-0.722582\pi$
$677$	−7.87586	+	4.54713i	−0.302694	+	0.174760i	0.340959	+	0.940078i	$0.389248\pi$
$678$		0			0
$679$	11.6436	+	20.1674i	0.446841	+	0.773952i
$680$	4.83914			0.185573
$681$		0			0
$682$	35.5335	−	9.52118i	1.36065	−	0.364585i
$683$	7.08606	−	26.4455i	0.271141	−	1.01191i	−0.687243	−	0.726427i	$-0.741179\pi$
$683$	7.08606	−	26.4455i	0.271141	−	1.01191i	0.958384	−	0.285483i	$-0.0921540\pi$
$684$		0			0
$685$	22.5096	+	38.9877i	0.860047	+	1.48965i
$686$	18.4686			0.705134
$687$		0			0
$688$	8.90622	+	5.14201i	0.339546	+	0.196037i
$689$	0.435682	+	0.271757i	0.0165982	+	0.0103531i
$690$		0			0
$691$	−1.38167	−	1.38167i	−0.0525614	−	0.0525614i	0.680338	−	0.732899i	$-0.261833\pi$
$691$	−1.38167	−	1.38167i	−0.0525614	−	0.0525614i	−0.732899	+	0.680338i	$0.761833\pi$
$692$	−3.80657	−	2.19773i	−0.144704	−	0.0835450i
$693$		0			0
$694$	−15.9053	−	15.9053i	−0.603758	−	0.603758i
$695$	10.1123	+	37.7397i	0.383582	+	1.43155i
$696$		0			0
$697$	−4.30179	−	16.0545i	−0.162942	−	0.608107i
$698$			16.6396i			0.629819i
$699$		0			0
$700$	1.88636	−	1.88636i	0.0712976	−	0.0712976i
$701$	−8.14720			−0.307715			−0.153858	−	0.988093i	$-0.549170\pi$
$701$	−8.14720			−0.307715			−0.153858	+	0.988093i	$0.549170\pi$
$702$		0			0
$703$	61.3862			2.31522
$704$	3.08472	−	3.08472i	0.116260	−	0.116260i
$705$		0			0
$706$			33.6241i			1.26546i
$707$	2.42650	+	9.05582i	0.0912579	+	0.340579i
$708$		0			0
$709$	10.7024	+	39.9420i	0.401938	+	1.50005i	0.809634	+	0.586935i	$0.199666\pi$
$709$	10.7024	+	39.9420i	0.401938	+	1.50005i	−0.407696	+	0.913118i	$0.633668\pi$
$710$	−10.4154	−	10.4154i	−0.390883	−	0.390883i
$711$		0			0
$712$	−12.8205	−	7.40192i	−0.480468	−	0.277399i
$713$	−7.28373	−	7.28373i	−0.272778	−	0.272778i
$714$		0			0
$715$	14.7808	+	27.7448i	0.552772	+	1.03760i
$716$	−9.42824	−	5.44340i	−0.352350	−	0.203429i
$717$		0			0
$718$	−26.4472			−0.987001
$719$	24.0105	+	41.5874i	0.895441	+	1.55095i	0.833258	+	0.552885i	$0.186473\pi$
$719$	24.0105	+	41.5874i	0.895441	+	1.55095i	0.0621837	+	0.998065i	$0.480194\pi$
$720$		0			0
$721$	−9.62694	+	35.9282i	−0.358526	+	1.33804i
$722$	−20.7938	+	5.57167i	−0.773864	+	0.207356i
$723$		0			0
$724$	−3.13809			−0.116626
$725$	−2.25030	−	3.89764i	−0.0835742	−	0.144755i
$726$		0			0
$727$	6.36454	−	3.67457i	0.236048	−	0.136282i	−0.377311	−	0.926087i	$-0.623151\pi$
$727$	6.36454	−	3.67457i	0.236048	−	0.136282i	0.613359	+	0.789804i	$0.289818\pi$
$728$	−4.49767	−	8.44247i	−0.166695	−	0.312899i
$729$		0			0
$730$	11.3520	−	3.04177i	0.420158	−	0.112581i
$731$			24.9001i			0.920963i
$732$		0			0
$733$	−7.53620	+	2.01932i	−0.278356	+	0.0745852i	−0.395296	−	0.918554i	$-0.629358\pi$
$733$	−7.53620	+	2.01932i	−0.278356	+	0.0745852i	0.116940	+	0.993139i	$0.462691\pi$
$734$	24.7742	−	24.7742i	0.914432	−	0.914432i
$735$		0			0
$736$	−1.17991	−	0.316156i	−0.0434920	−	0.0116537i
$737$	−9.55644	+	5.51741i	−0.352016	+	0.203237i
$738$		0			0
$739$	−6.40212	−	23.8930i	−0.235506	−	0.878920i	−0.977920	−	0.208979i	$-0.932986\pi$
$739$	−6.40212	−	23.8930i	−0.235506	−	0.878920i	0.742414	−	0.669941i	$-0.233681\pi$
$740$	−9.63601	−	16.6901i	−0.354227	−	0.613539i
$741$		0			0
$742$	−0.188920	+	0.327220i	−0.00693548	+	0.0120126i
$743$	−19.0656	−	5.10861i	−0.699449	−	0.187417i	−0.108465	−	0.994100i	$-0.534594\pi$
$743$	−19.0656	−	5.10861i	−0.699449	−	0.187417i	−0.590984	+	0.806683i	$0.701260\pi$
$744$		0			0
$745$	8.50578	+	4.91081i	0.311628	+	0.179918i
$746$	4.48418	−	4.48418i	0.164177	−	0.164177i
$747$		0			0
$748$	10.2026	+	2.73379i	0.373045	+	0.0999572i
$749$	−6.80134	+	25.3829i	−0.248516	+	0.927473i
$750$		0			0
$751$	9.33335	−	5.38861i	0.340579	−	0.196633i	−0.319949	−	0.947435i	$-0.603666\pi$
$751$	9.33335	−	5.38861i	0.340579	−	0.196633i	0.660528	+	0.750801i	$0.270333\pi$
$752$	1.40065	−	5.22728i	0.0510763	−	0.190619i
$753$		0			0
$754$	−15.7216	+	3.64295i	−0.572547	+	0.132669i
$755$			8.00813i			0.291446i
$756$		0			0
$757$	−25.3500	+	43.9076i	−0.921363	+	1.59585i	−0.124055	+	0.992275i	$0.539590\pi$
$757$	−25.3500	+	43.9076i	−0.921363	+	1.59585i	−0.797308	+	0.603572i	$0.793744\pi$
$758$	−17.0981	+	29.6148i	−0.621031	+	1.07566i
$759$		0			0
$760$	8.99682	+	8.99682i	0.326349	+	0.326349i
$761$	0.501543	+	0.501543i	0.0181809	+	0.0181809i	0.716139	−	0.697958i	$-0.245908\pi$
$761$	0.501543	+	0.501543i	0.0181809	+	0.0181809i	−0.697958	+	0.716139i	$0.745908\pi$
$762$		0			0
$763$	−10.4053	+	18.0225i	−0.376698	+	0.652460i
$764$	8.31799	−	14.4072i	0.300934	−	0.521234i
$765$		0			0
$766$		−	16.7505i		−	0.605221i
$767$	14.1123	−	3.27006i	0.509567	−	0.118075i
$768$		0			0
$769$	−4.82649	+	18.0127i	−0.174048	+	0.649555i	0.822664	+	0.568528i	$0.192487\pi$
$769$	−4.82649	+	18.0127i	−0.174048	+	0.649555i	−0.996712	+	0.0810274i	$0.974180\pi$
$770$	−20.0328	+	11.5659i	−0.721930	+	0.416807i
$771$		0			0
$772$	3.96019	−	14.7796i	0.142530	−	0.531930i
$773$	40.5648	+	10.8693i	1.45902	+	0.390942i	0.899150	−	0.437641i	$-0.144186\pi$
$773$	40.5648	+	10.8693i	1.45902	+	0.390942i	0.559866	+	0.828583i	$0.310853\pi$
$774$		0			0
$775$	−5.99568	+	5.99568i	−0.215371	+	0.215371i
$776$	−7.60151	−	4.38873i	−0.272878	−	0.157546i
$777$		0			0
$778$	−10.8836	−	2.91625i	−0.390196	−	0.104553i
$779$	21.8503	−	37.8459i	0.782870	−	1.35597i
$780$		0			0
$781$	−16.0754	−	27.8434i	−0.575222	−	0.996314i
$782$	−0.765489	−	2.85684i	−0.0273738	−	0.102161i
$783$		0			0
$784$	0.0335972	−	0.0193974i	0.00119990	−	0.000692764i
$785$	−0.144463	−	0.0387088i	−0.00515612	−	0.00138158i
$786$		0			0
$787$	−5.40139	+	5.40139i	−0.192539	+	0.192539i	−0.796792	−	0.604253i	$-0.793471\pi$
$787$	−5.40139	+	5.40139i	−0.192539	+	0.192539i	0.604253	+	0.796792i	$0.293471\pi$
$788$	−20.0309	+	5.36725i	−0.713570	+	0.191201i
$789$		0			0
$790$			0.646922i			0.0230164i
$791$	−34.5227	+	9.25033i	−1.22749	+	0.328904i
$792$		0			0
$793$	−17.0455	−	31.9957i	−0.605303	−	1.13620i
$794$	5.06146	−	2.92223i	0.179624	−	0.103706i
$795$		0			0
$796$	−3.10178	−	5.37244i	−0.109940	−	0.190421i
$797$	−9.14439			−0.323911			−0.161955	−	0.986798i	$-0.551780\pi$
$797$	−9.14439			−0.323911			−0.161955	+	0.986798i	$0.551780\pi$
$798$		0			0
$799$	12.6565	−	3.39130i	0.447755	−	0.119976i
$800$	−0.260247	+	0.971255i	−0.00920112	+	0.0343391i
$801$		0			0
$802$	−13.8654	−	24.0156i	−0.489604	−	0.848019i
$803$	25.6525			0.905258
$804$		0			0
$805$	5.60938	+	3.23858i	0.197705	+	0.114145i
$806$	14.2956	+	26.8339i	0.503541	+	0.945185i
$807$		0			0
$808$	−2.49873	−	2.49873i	−0.0879051	−	0.0879051i
$809$	−22.1408	−	12.7830i	−0.778428	−	0.449425i	0.0574451	−	0.998349i	$-0.481705\pi$
$809$	−22.1408	−	12.7830i	−0.778428	−	0.449425i	−0.835873	+	0.548923i	$0.815038\pi$
$810$		0			0
$811$	31.5345	+	31.5345i	1.10733	+	1.10733i	0.993501	+	0.113826i	$0.0363105\pi$
$811$	31.5345	+	31.5345i	1.10733	+	1.10733i	0.113826	+	0.993501i	$0.463689\pi$
$812$	−3.07346	−	11.4703i	−0.107857	−	0.402529i
$813$		0			0
$814$	−10.8874	−	40.6323i	−0.381603	−	1.42416i
$815$		−	37.3124i		−	1.30699i
$816$		0			0
$817$	−46.2937	+	46.2937i	−1.61961	+	1.61961i
$818$	4.08575			0.142855
$819$		0			0
$820$	−13.7197			−0.479113
$821$	7.50060	−	7.50060i	0.261773	−	0.261773i	−0.564001	−	0.825774i	$-0.690739\pi$
$821$	7.50060	−	7.50060i	0.261773	−	0.261773i	0.825774	+	0.564001i	$0.190739\pi$
$822$		0			0
$823$		−	21.3590i		−	0.744527i	−0.928127	−	0.372263i	$-0.878582\pi$
$823$		−	21.3590i		−	0.744527i	0.928127	−	0.372263i	$-0.121418\pi$
$824$	−3.62860	−	13.5421i	−0.126408	−	0.471762i
$825$		0			0
$826$	2.75886	+	10.2962i	0.0959929	+	0.358250i
$827$	14.6770	+	14.6770i	0.510368	+	0.510368i	0.914639	−	0.404271i	$-0.132475\pi$
$827$	14.6770	+	14.6770i	0.510368	+	0.510368i	−0.404271	+	0.914639i	$0.632475\pi$
$828$		0			0
$829$	3.49885	+	2.02006i	0.121520	+	0.0701596i	0.559528	−	0.828812i	$-0.310982\pi$
$829$	3.49885	+	2.02006i	0.121520	+	0.0701596i	−0.438008	+	0.898971i	$0.644316\pi$
$830$	−5.55932	−	5.55932i	−0.192967	−	0.192967i
$831$		0			0
$832$	3.05922	+	1.90819i	0.106059	+	0.0661545i
$833$	0.0813471	+	0.0469658i	0.00281851	+	0.00162727i
$834$		0			0
$835$	36.3765			1.25886
$836$	13.8859	+	24.0511i	0.480254	+	0.831825i
$837$		0			0
$838$	−4.77057	+	17.8040i	−0.164797	+	0.615029i
$839$	14.2816	−	3.82674i	0.493055	−	0.132114i	−0.00372001	−	0.999993i	$-0.501184\pi$
$839$	14.2816	−	3.82674i	0.493055	−	0.132114i	0.496775	+	0.867879i	$0.334517\pi$
$840$		0			0
$841$	8.96619			0.309179
$842$	16.1224	+	27.9248i	0.555614	+	0.962352i
$843$		0			0
$844$	7.31878	−	4.22550i	0.251923	−	0.145448i
$845$	−19.5814	+	17.0773i	−0.673622	+	0.587478i
$846$		0			0
$847$	−20.5808	+	5.51460i	−0.707163	+	0.189484i
$848$		−	0.142416i		−	0.00489059i
$849$		0			0
$850$	−2.35164	+	0.630121i	−0.0806607	+	0.0216130i
$851$	−8.32888	+	8.32888i	−0.285510	+	0.285510i
$852$		0			0
$853$	−27.2096	−	7.29079i	−0.931639	−	0.249632i	−0.239086	−	0.970999i	$-0.576848\pi$
$853$	−27.2096	−	7.29079i	−0.931639	−	0.249632i	−0.692553	+	0.721367i	$0.743514\pi$
$854$	23.1021	−	13.3380i	0.790537	−	0.456417i
$855$		0			0
$856$	−2.56357	−	9.56738i	−0.0876210	−	0.327006i
$857$	13.1050	+	22.6985i	0.447657	+	0.775365i	0.998233	−	0.0594200i	$-0.0189251\pi$
$857$	13.1050	+	22.6985i	0.447657	+	0.775365i	−0.550576	+	0.834785i	$0.685592\pi$
$858$		0			0
$859$	5.40366	−	9.35941i	0.184370	−	0.319339i	−0.758994	−	0.651098i	$-0.774309\pi$
$859$	5.40366	−	9.35941i	0.184370	−	0.319339i	0.943364	+	0.331759i	$0.107642\pi$
$860$	19.8535	+	5.31973i	0.676998	+	0.181401i
$861$		0			0
$862$	11.3749	+	6.56728i	0.387429	+	0.223682i
$863$	−33.3766	+	33.3766i	−1.13615	+	1.13615i	−0.147018	+	0.989134i	$0.546968\pi$
$863$	−33.3766	+	33.3766i	−1.13615	+	1.13615i	−0.989134	+	0.147018i	$0.953032\pi$
$864$		0			0
$865$	−8.48550	−	2.27368i	−0.288516	−	0.0773076i
$866$	1.41165	−	5.26834i	0.0479697	−	0.179025i
$867$		0			0
$868$	−19.3751	+	11.1862i	−0.657633	+	0.379685i
$869$	−0.365467	+	1.36394i	−0.0123976	+	0.0462685i
$870$		0			0
$871$	−6.22536	−	6.66512i	−0.210938	−	0.225839i
$872$		−	7.84397i		−	0.265630i
$873$		0			0
$874$	3.88820	−	6.73456i	0.131520	−	0.227800i
$875$	15.9221	−	27.5779i	0.538265	−	0.932302i
$876$		0			0
$877$	−27.0793	−	27.0793i	−0.914404	−	0.914404i	0.0822111	−	0.996615i	$-0.473802\pi$
$877$	−27.0793	−	27.0793i	−0.914404	−	0.914404i	−0.996615	+	0.0822111i	$0.973802\pi$
$878$	2.13806	+	2.13806i	0.0721559	+	0.0721559i
$879$		0			0
$880$	4.35944	−	7.55077i	0.146957	−	0.254537i
$881$	−11.0506	+	19.1402i	−0.372304	+	0.644849i	−0.989920	−	0.141631i	$-0.954765\pi$
$881$	−11.0506	+	19.1402i	−0.372304	+	0.644849i	0.617616	+	0.786480i	$0.288099\pi$
$882$		0			0
$883$			13.1593i			0.442846i	0.975178	+	0.221423i	$0.0710702\pi$
$883$			13.1593i			0.442846i	−0.975178	+	0.221423i	$0.928930\pi$
$884$	−0.297644	+	8.72484i	−0.0100108	+	0.293448i
$885$		0			0
$886$	1.03309	−	3.85554i	0.0347073	−	0.129529i
$887$	46.9862	−	27.1275i	1.57764	−	0.910852i	0.582453	−	0.812864i	$-0.302093\pi$
$887$	46.9862	−	27.1275i	1.57764	−	0.910852i	0.995188	−	0.0979875i	$-0.0312405\pi$
$888$		0			0
$889$	1.89141	−	7.05885i	0.0634360	−	0.236746i
$890$	−28.5791	−	7.65774i	−0.957973	−	0.256688i
$891$		0			0
$892$	7.78077	−	7.78077i	0.260519	−	0.260519i
$893$	29.8357	+	17.2257i	0.998414	+	0.576435i
$894$		0			0
$895$	−21.0172	−	5.63153i	−0.702526	−	0.188241i
$896$	−1.32654	+	2.29763i	−0.0443165	+	0.0767584i
$897$		0			0
$898$	−6.69347	−	11.5934i	−0.223364	−	0.386878i
$899$	9.76881	+	36.4577i	0.325808	+	1.21593i
$900$		0			0
$901$	0.298626	−	0.172412i	0.00994869	−	0.00574388i
$902$	−28.9260	−	7.75071i	−0.963132	−	0.258070i
$903$		0			0
$904$	9.52570	−	9.52570i	0.316820	−	0.316820i
$905$	−6.05815	+	1.62328i	−0.201380	+	0.0539595i
$906$		0			0
$907$		−	50.1526i		−	1.66529i	−0.553808	−	0.832644i	$-0.686826\pi$
$907$		−	50.1526i		−	1.66529i	0.553808	−	0.832644i	$-0.313174\pi$
$908$	7.64941	−	2.04965i	0.253855	−	0.0680202i
$909$		0			0
$910$	−13.0500	−	13.9718i	−0.432602	−	0.463160i
$911$	15.3462	−	8.86012i	0.508442	−	0.293549i	−0.223751	−	0.974646i	$-0.571830\pi$
$911$	15.3462	−	8.86012i	0.508442	−	0.293549i	0.732193	+	0.681097i	$0.238497\pi$
$912$		0			0
$913$	−8.58039	−	14.8617i	−0.283970	−	0.491850i
$914$	1.33956			0.0443086
$915$		0			0
$916$	1.40853	−	0.377414i	0.0465390	−	0.0124701i
$917$	−0.469256	+	1.75129i	−0.0154962	+	0.0578327i
$918$		0			0
$919$	−2.14603	−	3.71704i	−0.0707911	−	0.122614i	0.828457	−	0.560052i	$-0.189219\pi$
$919$	−2.14603	−	3.71704i	−0.0707911	−	0.122614i	−0.899248	+	0.437439i	$0.855886\pi$
$920$	−2.44138			−0.0804898
$921$		0			0
$922$	4.39148	+	2.53542i	0.144626	+	0.0834996i
$923$	19.4193	−	18.1380i	0.639194	−	0.597021i
$924$		0			0
$925$	6.85601	+	6.85601i	0.225424	+	0.225424i
$926$	−6.70135	−	3.86903i	−0.220220	−	0.127144i
$927$		0			0
$928$	3.16495	+	3.16495i	0.103895	+	0.103895i
$929$	−13.2874	−	49.5894i	−0.435946	−	1.62697i	−0.738791	−	0.673934i	$-0.764603\pi$
$929$	−13.2874	−	49.5894i	−0.435946	−	1.62697i	0.302845	−	0.953040i	$-0.402064\pi$
$930$		0			0
$931$	0.0639209	+	0.238556i	0.00209492	+	0.00781836i
$932$			4.39305i			0.143899i
$933$		0			0
$934$	−7.38200	+	7.38200i	−0.241546	+	0.241546i
$935$	21.1105			0.690388
$936$		0			0
$937$	13.7998			0.450821			0.225410	−	0.974264i	$-0.427628\pi$
$937$	13.7998			0.450821			0.225410	+	0.974264i	$0.427628\pi$
$938$	4.74536	−	4.74536i	0.154941	−	0.154941i
$939$		0			0
$940$		−	10.8159i		−	0.352776i
$941$	4.97964	+	18.5843i	0.162332	+	0.605830i	0.998365	+	0.0571520i	$0.0182020\pi$
$941$	4.97964	+	18.5843i	0.162332	+	0.605830i	−0.836034	+	0.548678i	$0.815131\pi$
$942$		0			0
$943$	2.17028	+	8.09959i	0.0706740	+	0.263759i
$944$	−2.84098	−	2.84098i	−0.0924662	−	0.0924662i
$945$		0			0
$946$	38.8530	+	22.4318i	1.26322	+	0.729320i
$947$	4.69573	+	4.69573i	0.152591	+	0.152591i	0.779274	−	0.626683i	$-0.215588\pi$
$947$	4.69573	+	4.69573i	0.152591	+	0.152591i	−0.626683	+	0.779274i	$0.715588\pi$
$948$		0			0
$949$	4.78599	+	20.6545i	0.155360	+	0.670473i
$950$	−5.54363	−	3.20061i	−0.179859	−	0.103842i
$951$		0			0
$952$	−6.42373			−0.208194
$953$	10.4833	+	18.1575i	0.339586	+	0.588180i	0.984355	−	0.176197i	$-0.0563797\pi$
$953$	10.4833	+	18.1575i	0.339586	+	0.588180i	−0.644769	+	0.764378i	$0.723046\pi$
$954$		0			0
$955$	8.60548	−	32.1161i	0.278467	−	1.03925i
$956$	8.98867	−	2.40851i	0.290714	−	0.0778967i
$957$		0			0
$958$	−6.62599			−0.214076
$959$	−29.8804	−	51.7544i	−0.964888	−	1.67124i
$960$		0			0
$961$	34.7359	−	20.0548i	1.12051	−	0.646928i
$962$	30.6844	−	16.3469i	0.989305	−	0.527045i
$963$		0			0
$964$	1.61040	−	0.431507i	0.0518676	−	0.0138979i
$965$		−	30.5809i		−	0.984432i
$966$		0			0
$967$	−30.1367	+	8.07510i	−0.969131	+	0.259678i	−0.708461	−	0.705750i	$-0.750610\pi$
$967$	−30.1367	+	8.07510i	−0.969131	+	0.259678i	−0.260670	+	0.965428i	$0.583943\pi$
$968$	5.67876	−	5.67876i	0.182522	−	0.182522i
$969$		0			0
$970$	−16.9451	−	4.54042i	−0.544073	−	0.145784i
$971$	−39.9399	+	23.0593i	−1.28173	+	0.740008i	−0.977165	−	0.212482i	$-0.931845\pi$
$971$	−39.9399	+	23.0593i	−1.28173	+	0.740008i	−0.304567	+	0.952491i	$0.598512\pi$
$972$		0			0
$973$	−13.4236	−	50.0976i	−0.430342	−	1.60606i
$974$	8.34344	+	14.4513i	0.267341	+	0.463048i
$975$		0			0
$976$	−5.02738	+	8.70767i	−0.160922	+	0.278726i
$977$	33.6291	+	9.01089i	1.07589	+	0.288284i	0.752911	−	0.658122i	$-0.228649\pi$
$977$	33.6291	+	9.01089i	1.07589	+	0.288284i	0.322979	+	0.946406i	$0.395316\pi$
$978$		0			0
$979$	−55.9288	−	32.2905i	−1.78749	−	1.03201i
$980$	0.0548262	−	0.0548262i	0.00175136	−	0.00175136i
$981$		0			0
$982$	14.8479	+	3.97849i	0.473816	+	0.126959i
$983$	12.1329	−	45.2806i	0.386979	−	1.44423i	−0.448044	−	0.894011i	$-0.647879\pi$
$983$	12.1329	−	45.2806i	0.386979	−	1.44423i	0.835024	−	0.550214i	$-0.185454\pi$
$984$		0			0
$985$	−35.8936	+	20.7232i	−1.14366	+	0.660295i
$986$	−2.80489	+	10.4680i	−0.0893260	+	0.333369i
$987$		0			0
$988$	−16.7744	+	15.6676i	−0.533664	+	0.498454i
$989$		−	12.5623i		−	0.399456i
$990$		0			0
$991$	−5.58679	+	9.67660i	−0.177470	+	0.307387i	−0.941013	−	0.338369i	$-0.890125\pi$
$991$	−5.58679	+	9.67660i	−0.177470	+	0.307387i	0.763543	+	0.645757i	$0.223458\pi$
$992$	4.21632	−	7.30289i	0.133868	−	0.231867i
$993$		0			0
$994$	13.8259	+	13.8259i	0.438532	+	0.438532i
$995$	−8.76710	−	8.76710i	−0.277936	−	0.277936i
$996$		0			0
$997$	2.80499	−	4.85839i	0.0888350	−	0.153867i	−0.818184	−	0.574957i	$-0.805019\pi$
$997$	2.80499	−	4.85839i	0.0888350	−	0.153867i	0.907019	+	0.421090i	$0.138352\pi$
$998$	−11.1678	+	19.3432i	−0.353510	+	0.612298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.449.10		56
3.2	odd	2		234.2.y.a.59.5	✓	56
9.2	odd	6		702.2.bc.a.683.10		56
9.7	even	3		234.2.z.a.137.5	yes	56
13.2	odd	12		702.2.bc.a.665.10		56
39.2	even	12		234.2.z.a.41.5	yes	56
117.2	even	12	inner	702.2.bb.a.197.10		56
117.106	odd	12		234.2.y.a.119.5	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.59.5	✓	56	3.2	odd	2
234.2.y.a.119.5	yes	56	117.106	odd	12
234.2.z.a.41.5	yes	56	39.2	even	12
234.2.z.a.137.5	yes	56	9.7	even	3
702.2.bb.a.197.10		56	117.2	even	12	inner
702.2.bb.a.449.10		56	1.1	even	1	trivial
702.2.bc.a.665.10		56	13.2	odd	12
702.2.bc.a.683.10		56	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.517281 - 1.93052i) q^{5} +(0.686666 + 2.56267i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.73086 - 0.999310i) q^{10} +(-3.08472 - 3.08472i) q^{11} +(1.90819 - 3.05922i) q^{13} +(2.29763 + 1.32654i) q^{14} -1.00000 q^{16} +(-1.21062 - 2.09686i) q^{17} +(1.64767 - 6.14918i) q^{19} +(-1.93052 + 0.517281i) q^{20} -4.36245 q^{22} +(0.610766 + 1.05788i) q^{23} +(0.870804 - 0.502759i) q^{25} +(-0.813901 - 3.51249i) q^{26} +(2.56267 - 0.686666i) q^{28} -4.47591i q^{29} +(-8.14531 + 2.18253i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.33874 - 0.626664i) q^{34} +(4.59209 - 2.65124i) q^{35} +(2.49571 + 9.31410i) q^{37} +(-3.18305 - 5.51321i) q^{38} +(-0.999310 + 1.73086i) q^{40} +(6.63068 + 1.77669i) q^{41} +(-8.90622 - 5.14201i) q^{43} +(-3.08472 + 3.08472i) q^{44} +(1.17991 + 0.316156i) q^{46} +(-1.40065 + 5.22728i) q^{47} +(-0.0335972 + 0.0193974i) q^{49} +(0.260247 - 0.971255i) q^{50} +(-3.05922 - 1.90819i) q^{52} +0.142416i q^{53} +(-4.35944 + 7.55077i) q^{55} +(1.32654 - 2.29763i) q^{56} +(-3.16495 - 3.16495i) q^{58} +(2.84098 + 2.84098i) q^{59} +(5.02738 - 8.70767i) q^{61} +(-4.21632 + 7.30289i) q^{62} +1.00000i q^{64} +(-6.89295 - 2.10132i) q^{65} +(0.654683 - 2.44331i) q^{67} +(-2.09686 + 1.21062i) q^{68} +(1.37238 - 5.12181i) q^{70} +(7.11876 + 1.90747i) q^{71} +(-4.15800 + 4.15800i) q^{73} +(8.35079 + 4.82133i) q^{74} +(-6.14918 - 1.64767i) q^{76} +(5.78695 - 10.0233i) q^{77} +(-0.161842 - 0.280319i) q^{79} +(0.517281 + 1.93052i) q^{80} +(5.94491 - 3.43230i) q^{82} +(3.79971 + 1.01813i) q^{83} +(-3.42179 + 3.42179i) q^{85} +(-9.93360 + 2.66170i) q^{86} +4.36245i q^{88} +(14.2994 - 3.83151i) q^{89} +(9.15006 + 2.78940i) q^{91} +(1.05788 - 0.610766i) q^{92} +(2.70584 + 4.68665i) q^{94} -12.7234 q^{95} +(8.47838 - 2.27178i) q^{97} +(-0.0100408 + 0.0374729i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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