LMFDB - Embedded newform 234.2.y.a.59.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			59.5
Character	$\chi$	$=$	234.59
Dual form			234.2.y.a.119.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.851088 - 1.50853i) q^{3} -1.00000i q^{4} +(0.517281 + 1.93052i) q^{5} +(0.464878 + 1.66850i) q^{6} +(0.686666 + 2.56267i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.55130 - 2.56778i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.851088 - 1.50853i) q^{3} -1.00000i q^{4} +(0.517281 + 1.93052i) q^{5} +(0.464878 + 1.66850i) q^{6} +(0.686666 + 2.56267i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.55130 - 2.56778i) q^{9} +(-1.73086 - 0.999310i) q^{10} +(3.08472 + 3.08472i) q^{11} +(-1.50853 - 0.851088i) q^{12} +(1.90819 - 3.05922i) q^{13} +(-2.29763 - 1.32654i) q^{14} +(3.35249 + 0.862710i) q^{15} -1.00000 q^{16} +(1.21062 + 2.09686i) q^{17} +(2.91263 + 0.718758i) q^{18} +(1.64767 - 6.14918i) q^{19} +(1.93052 - 0.517281i) q^{20} +(4.45027 + 1.14521i) q^{21} -4.36245 q^{22} +(-0.610766 - 1.05788i) q^{23} +(1.66850 - 0.464878i) q^{24} +(0.870804 - 0.502759i) q^{25} +(0.813901 + 3.51249i) q^{26} +(-5.19385 + 0.154769i) q^{27} +(2.56267 - 0.686666i) q^{28} +4.47591i q^{29} +(-2.98060 + 1.76054i) q^{30} +(-8.14531 + 2.18253i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.27874 - 2.02801i) q^{33} +(-2.33874 - 0.626664i) q^{34} +(-4.59209 + 2.65124i) q^{35} +(-2.56778 + 1.55130i) q^{36} +(2.49571 + 9.31410i) q^{37} +(3.18305 + 5.51321i) q^{38} +(-2.99087 - 5.48221i) q^{39} +(-0.999310 + 1.73086i) q^{40} +(-6.63068 - 1.77669i) q^{41} +(-3.95660 + 2.33703i) q^{42} +(-8.90622 - 5.14201i) q^{43} +(3.08472 - 3.08472i) q^{44} +(4.15468 - 4.32307i) q^{45} +(1.17991 + 0.316156i) q^{46} +(1.40065 - 5.22728i) q^{47} +(-0.851088 + 1.50853i) q^{48} +(-0.0335972 + 0.0193974i) q^{49} +(-0.260247 + 0.971255i) q^{50} +(4.19351 - 0.0416426i) q^{51} +(-3.05922 - 1.90819i) q^{52} -0.142416i q^{53} +(3.56317 - 3.78204i) q^{54} +(-4.35944 + 7.55077i) q^{55} +(-1.32654 + 2.29763i) q^{56} +(-7.87389 - 7.71905i) q^{57} +(-3.16495 - 3.16495i) q^{58} +(-2.84098 - 2.84098i) q^{59} +(0.862710 - 3.35249i) q^{60} +(5.02738 - 8.70767i) q^{61} +(4.21632 - 7.30289i) q^{62} +(5.51514 - 5.73867i) q^{63} +1.00000i q^{64} +(6.89295 + 2.10132i) q^{65} +(-3.71283 + 6.58087i) q^{66} +(0.654683 - 2.44331i) q^{67} +(2.09686 - 1.21062i) q^{68} +(-2.11565 + 0.0210090i) q^{69} +(1.37238 - 5.12181i) q^{70} +(-7.11876 - 1.90747i) q^{71} +(0.718758 - 2.91263i) q^{72} +(-4.15800 + 4.15800i) q^{73} +(-8.35079 - 4.82133i) q^{74} +(-0.0172938 - 1.74152i) q^{75} +(-6.14918 - 1.64767i) q^{76} +(-5.78695 + 10.0233i) q^{77} +(5.99138 + 1.76164i) q^{78} +(-0.161842 - 0.280319i) q^{79} +(-0.517281 - 1.93052i) q^{80} +(-4.18695 + 7.96677i) q^{81} +(5.94491 - 3.43230i) q^{82} +(-3.79971 - 1.01813i) q^{83} +(1.14521 - 4.45027i) q^{84} +(-3.42179 + 3.42179i) q^{85} +(9.93360 - 2.66170i) q^{86} +(6.75203 + 3.80940i) q^{87} +4.36245i q^{88} +(-14.2994 + 3.83151i) q^{89} +(0.119069 + 5.99468i) q^{90} +(9.15006 + 2.78940i) q^{91} +(-1.05788 + 0.610766i) q^{92} +(-3.63998 + 14.1449i) q^{93} +(2.70584 + 4.68665i) q^{94} +12.7234 q^{95} +(-0.464878 - 1.66850i) q^{96} +(8.47838 - 2.27178i) q^{97} +(0.0100408 - 0.0374729i) q^{98} +(3.13555 - 12.7062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	0.851088	−	1.50853i	0.491376	−	0.870948i
$3$	0.851088	−	1.50853i	0.491376	−	0.870948i
$4$		−	1.00000i		−	0.500000i
$5$	0.517281	+	1.93052i	0.231335	+	0.863354i	0.979767	+	0.200142i	$0.0641405\pi$
$5$	0.517281	+	1.93052i	0.231335	+	0.863354i	−0.748432	+	0.663212i	$0.769193\pi$
$6$	0.464878	+	1.66850i	0.189786	+	0.681162i
$7$	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
$9$	−1.55130	−	2.56778i	−0.517099	−	0.855925i
$10$	−1.73086	−	0.999310i	−0.547345	−	0.316010i
$11$	3.08472	+	3.08472i	0.930078	+	0.930078i	0.997710	−	0.0676326i	$-0.0215446\pi$
$11$	3.08472	+	3.08472i	0.930078	+	0.930078i	−0.0676326	+	0.997710i	$0.521545\pi$
$12$	−1.50853	−	0.851088i	−0.435474	−	0.245688i
$13$	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
$15$	3.35249	+	0.862710i	0.865609	+	0.222751i
$16$	−1.00000			−0.250000
$17$	1.21062	+	2.09686i	0.293619	+	0.508563i	0.974663	−	0.223680i	$-0.0718071\pi$
$17$	1.21062	+	2.09686i	0.293619	+	0.508563i	−0.681044	+	0.732243i	$0.738474\pi$
$18$	2.91263	+	0.718758i	0.686512	+	0.169413i
$19$	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
$21$	4.45027	+	1.14521i	0.971128	+	0.249905i
$22$	−4.36245			−0.930078
$23$	−0.610766	−	1.05788i	−0.127353	−	0.220583i	0.795297	−	0.606220i	$-0.207315\pi$
$23$	−0.610766	−	1.05788i	−0.127353	−	0.220583i	−0.922650	+	0.385637i	$0.873982\pi$
$24$	1.66850	−	0.464878i	0.340581	−	0.0948929i
$25$	0.870804	−	0.502759i	0.174161	−	0.100552i
$26$	0.813901	+	3.51249i	0.159619	+	0.688855i
$27$	−5.19385	+	0.154769i	−0.999556	+	0.0297854i
$28$	2.56267	−	0.686666i	0.484299	−	0.129768i
$29$			4.47591i			0.831156i	0.909557	+	0.415578i	$0.136421\pi$
$29$			4.47591i			0.831156i	−0.909557	+	0.415578i	$0.863579\pi$
$30$	−2.98060	+	1.76054i	−0.544180	+	0.321429i
$31$	−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
$33$	7.27874	−	2.02801i	1.26707	−	0.353031i
$34$	−2.33874	−	0.626664i	−0.401091	−	0.107472i
$35$	−4.59209	+	2.65124i	−0.776204	+	0.448142i
$36$	−2.56778	+	1.55130i	−0.427963	+	0.258550i
$37$	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
$39$	−2.99087	−	5.48221i	−0.478923	−	0.877857i
$40$	−0.999310	+	1.73086i	−0.158005	+	0.273672i
$41$	−6.63068	−	1.77669i	−1.03554	−	0.277472i	−0.299275	−	0.954167i	$-0.596745\pi$
$41$	−6.63068	−	1.77669i	−1.03554	−	0.277472i	−0.736264	+	0.676695i	$0.763412\pi$
$42$	−3.95660	+	2.33703i	−0.610516	+	0.360612i
$43$	−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
$45$	4.15468	−	4.32307i	0.619344	−	0.644446i
$46$	1.17991	+	0.316156i	0.173968	+	0.0466146i
$47$	1.40065	−	5.22728i	0.204305	−	0.762477i	−0.785355	−	0.619046i	$-0.787520\pi$
$47$	1.40065	−	5.22728i	0.204305	−	0.762477i	0.989660	−	0.143432i	$-0.0458138\pi$
$48$	−0.851088	+	1.50853i	−0.122844	+	0.217737i
$49$	−0.0335972	+	0.0193974i	−0.00479961	+	0.00277105i
$50$	−0.260247	+	0.971255i	−0.0368045	+	0.137356i
$51$	4.19351	−	0.0416426i	0.587209	−	0.00583113i
$52$	−3.05922	−	1.90819i	−0.424237	−	0.264618i
$53$		−	0.142416i		−	0.0195624i	−0.999952	−	0.00978119i	$-0.996887\pi$
$53$		−	0.142416i		−	0.0195624i	0.999952	−	0.00978119i	$-0.00311350\pi$
$54$	3.56317	−	3.78204i	0.484885	−	0.514671i
$55$	−4.35944	+	7.55077i	−0.587827	+	1.01815i
$56$	−1.32654	+	2.29763i	−0.177266	+	0.307034i
$57$	−7.87389	−	7.71905i	−1.04292	−	1.02241i
$58$	−3.16495	−	3.16495i	−0.415578	−	0.415578i
$59$	−2.84098	−	2.84098i	−0.369865	−	0.369865i	0.497563	−	0.867428i	$-0.334228\pi$
$59$	−2.84098	−	2.84098i	−0.369865	−	0.369865i	−0.867428	+	0.497563i	$0.834228\pi$
$60$	0.862710	−	3.35249i	0.111375	−	0.432804i
$61$	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
$63$	5.51514	−	5.73867i	0.694843	−	0.723005i
$64$			1.00000i			0.125000i
$65$	6.89295	+	2.10132i	0.854965	+	0.260636i
$66$	−3.71283	+	6.58087i	−0.457018	+	0.810049i
$67$	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
$69$	−2.11565	+	0.0210090i	−0.254694	+	0.00252918i
$70$	1.37238	−	5.12181i	0.164031	−	0.612173i
$71$	−7.11876	−	1.90747i	−0.844841	−	0.226375i	−0.189663	−	0.981849i	$-0.560740\pi$
$71$	−7.11876	−	1.90747i	−0.844841	−	0.226375i	−0.655178	+	0.755475i	$0.727406\pi$
$72$	0.718758	−	2.91263i	0.0847065	−	0.343256i
$73$	−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
$75$	−0.0172938	−	1.74152i	−0.00199691	−	0.201094i
$76$	−6.14918	−	1.64767i	−0.705360	−	0.189001i
$77$	−5.78695	+	10.0233i	−0.659484	+	1.14226i
$78$	5.99138	+	1.76164i	0.678390	+	0.199467i
$79$	−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
$81$	−4.18695	+	7.96677i	−0.465216	+	0.885197i
$82$	5.94491	−	3.43230i	0.656505	−	0.379034i
$83$	−3.79971	−	1.01813i	−0.417072	−	0.111754i	0.0441792	−	0.999024i	$-0.485933\pi$
$83$	−3.79971	−	1.01813i	−0.417072	−	0.111754i	−0.461252	+	0.887269i	$0.652599\pi$
$84$	1.14521	−	4.45027i	0.124952	−	0.485564i
$85$	−3.42179	+	3.42179i	−0.371145	+	0.371145i
$86$	9.93360	−	2.66170i	1.07117	−	0.287018i
$87$	6.75203	+	3.80940i	0.723894	+	0.408410i
$88$			4.36245i			0.465039i
$89$	−14.2994	+	3.83151i	−1.51573	+	0.406140i	−0.918335	−	0.395805i	$-0.870466\pi$
$89$	−14.2994	+	3.83151i	−1.51573	+	0.406140i	−0.597399	+	0.801944i	$0.703799\pi$
$90$	0.119069	+	5.99468i	0.0125510	+	0.631895i
$91$	9.15006	+	2.78940i	0.959187	+	0.292408i
$92$	−1.05788	+	0.610766i	−0.110291	+	0.0636767i
$93$	−3.63998	+	14.1449i	−0.377448	+	1.46676i
$94$	2.70584	+	4.68665i	0.279086	+	0.483391i
$95$	12.7234			1.30540
$96$	−0.464878	−	1.66850i	−0.0474465	−	0.170290i
$97$	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
$99$	3.13555	−	12.7062i	0.315134	−	1.27702i
$100$	−0.502759	−	0.870804i	−0.0502759	−	0.0870804i
$101$	−3.53374			−0.351620			−0.175810	−	0.984424i	$-0.556254\pi$
$101$	−3.53374			−0.351620			−0.175810	+	0.984424i	$0.556254\pi$
$102$	−2.93581	+	2.99470i	−0.290689	+	0.296520i
$103$	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
$105$	0.0911967	+	9.18372i	0.00889989	+	0.896239i
$106$	0.100703	+	0.100703i	0.00978119	+	0.00978119i
$107$	−8.57787	−	4.95244i	−0.829254	−	0.478770i	0.0243429	−	0.999704i	$-0.492251\pi$
$107$	−8.57787	−	4.95244i	−0.829254	−	0.478770i	−0.853597	+	0.520933i	$0.825584\pi$
$108$	0.154769	+	5.19385i	0.0148927	+	0.499778i
$109$	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
$111$	16.1746	+	4.16228i	1.53523	+	0.395066i
$112$	−0.686666	−	2.56267i	−0.0648838	−	0.242150i
$113$		−	13.4714i		−	1.26728i	−0.773628	−	0.633640i	$-0.781560\pi$
$113$		−	13.4714i		−	1.26728i	0.773628	−	0.633640i	$-0.218440\pi$
$114$	11.0259	−	0.109490i	1.03267	−	0.0102547i
$115$	1.72631	−	1.72631i	0.160980	−	0.160980i
$116$	4.47591			0.415578
$117$	−10.8156	−	0.154039i	−0.999899	−	0.0142410i
$118$	4.01776			0.369865
$119$	−4.54226	+	4.54226i	−0.416389	+	0.416389i
$120$	1.76054	+	2.98060i	0.160715	+	0.272090i
$121$			8.03098i			0.730089i
$122$	2.60236	+	9.71214i	0.235607	+	0.879296i
$123$	−8.32347	+	8.49044i	−0.750502	+	0.765557i
$124$	2.18253	+	8.14531i	0.195997	+	0.731471i
$125$	8.48722	+	8.48722i	0.759120	+	0.759120i
$126$	0.158059	+	7.95765i	0.0140810	+	0.708924i
$127$	−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
$129$	−15.3368	+	9.05896i	−1.35033	+	0.797597i
$130$	−6.35991	+	3.38819i	−0.557801	+	0.297164i
$131$	−0.591828	−	0.341692i	−0.0517083	−	0.0298538i	0.473923	−	0.880566i	$-0.342837\pi$
$131$	−0.591828	−	0.341692i	−0.0517083	−	0.0298538i	−0.525631	+	0.850713i	$0.676171\pi$
$132$	−2.02801	−	7.27874i	−0.176516	−	0.633533i
$133$	16.8897			1.46453
$134$	1.26475	+	2.19061i	0.109258	+	0.189240i
$135$	−2.98546	−	9.94676i	−0.256948	−	0.856081i
$136$	−0.626664	+	2.33874i	−0.0537360	+	0.200545i
$137$	21.7576	−	5.82993i	1.85888	−	0.498085i	0.858974	−	0.512019i	$-0.171102\pi$
$137$	21.7576	−	5.82993i	1.85888	−	0.498085i	0.999903	+	0.0139339i	$0.00443546\pi$
$138$	1.48114	−	1.51085i	0.126083	−	0.128612i
$139$	−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
$141$	−6.69341	−	6.56179i	−0.563687	−	0.552602i
$142$	6.38250	−	3.68494i	0.535608	−	0.309233i
$143$	15.3231	−	3.55060i	1.28138	−	0.296916i
$144$	1.55130	+	2.56778i	0.129275	+	0.213981i
$145$	−8.64084	+	2.31531i	−0.717582	+	0.192276i
$146$		−	5.88030i		−	0.486657i
$147$	0.000667226		0.0671912i	5.50318e−5		0.00554184i
$148$	9.31410	−	2.49571i	0.765614	−	0.205146i
$149$	3.47487	−	3.47487i	0.284672	−	0.284672i	−0.550297	−	0.834969i	$-0.685485\pi$
$149$	3.47487	−	3.47487i	0.284672	−	0.284672i	0.834969	+	0.550297i	$0.185485\pi$
$150$	1.24367	+	1.21921i	0.101545	+	0.0995483i
$151$	−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
$153$	3.50623	−	6.36145i	0.283462	−	0.514293i
$154$	−2.99555	−	11.1795i	−0.241388	−	0.900872i
$155$	−8.42683	−	14.5957i	−0.676859	−	1.17235i
$156$	−5.48221	+	2.99087i	−0.438928	+	0.239461i
$157$	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
$159$	−0.214838	−	0.121209i	−0.0170378	−	0.00961248i
$160$	1.73086	+	0.999310i	0.136836	+	0.0790024i
$161$	2.29160	−	2.29160i	0.180603	−	0.180603i
$162$	−2.67274	−	8.59398i	−0.209990	−	0.675207i
$163$	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
$165$	7.68027	+	13.0027i	0.597908	+	1.01226i
$166$	3.40673	−	1.96687i	0.264413	−	0.152659i
$167$	4.71072	−	17.5806i	0.364526	−	1.36043i	−0.503535	−	0.863975i	$-0.667968\pi$
$167$	4.71072	−	17.5806i	0.364526	−	1.36043i	0.868062	−	0.496456i	$-0.165366\pi$
$168$	2.33703	+	3.95660i	0.180306	+	0.305258i
$169$	−5.71764	−	11.6751i	−0.439818	−	0.898087i
$170$		−	4.83914i		−	0.371145i
$171$	−18.3458	+	5.30837i	−1.40293	+	0.405942i
$172$	−5.14201	+	8.90622i	−0.392075	+	0.679093i
$173$	−2.19773	+	3.80657i	−0.167090	+	0.289408i	−0.937396	−	0.348267i	$-0.886770\pi$
$173$	−2.19773	+	3.80657i	−0.167090	+	0.289408i	0.770305	+	0.637675i	$0.220104\pi$
$174$	−7.46806	+	2.08076i	−0.566152	+	0.157742i
$175$	1.88636	+	1.88636i	0.142595	+	0.142595i
$176$	−3.08472	−	3.08472i	−0.232519	−	0.232519i
$177$	−6.70363	+	1.86777i	−0.503875	+	0.140390i
$178$	7.40192	−	12.8205i	0.554797	−	0.960937i
$179$	−5.44340	+	9.42824i	−0.406859	+	0.704700i	−0.994536	−	0.104396i	$-0.966709\pi$
$179$	−5.44340	+	9.42824i	−0.406859	+	0.704700i	0.587677	+	0.809095i	$0.300042\pi$
$180$	−4.32307	−	4.15468i	−0.322223	−	0.309672i
$181$		−	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
$183$	−8.85700	−	14.9949i	−0.654728	−	1.10846i
$184$	0.316156	−	1.17991i	0.0233073	−	0.0869840i
$185$	−16.6901	+	9.63601i	−1.22708	+	0.708454i
$186$	−7.42813	−	12.5758i	−0.544657	−	0.922105i
$187$	−2.73379	+	10.2026i	−0.199914	+	0.746091i
$188$	−5.22728	−	1.40065i	−0.381239	−	0.102153i
$189$	−3.96306	−	13.2038i	−0.288270	−	0.960439i
$190$	−8.99682	+	8.99682i	−0.652698	+	0.652698i
$191$	−14.4072	−	8.31799i	−1.04247	−	0.601869i	−0.121936	−	0.992538i	$-0.538910\pi$
$191$	−14.4072	−	8.31799i	−1.04247	−	0.601869i	−0.920531	+	0.390669i	$0.872244\pi$
$192$	1.50853	+	0.851088i	0.108868	+	0.0614220i
$193$	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
$195$	9.03640	−	8.60978i	0.647110	−	0.616559i
$196$	0.0193974	+	0.0335972i	0.00138553	+	0.00239980i
$197$	5.36725	+	20.0309i	0.382401	+	1.42714i	0.842223	+	0.539129i	$0.181247\pi$
$197$	5.36725	+	20.0309i	0.382401	+	1.42714i	−0.459822	+	0.888011i	$0.652087\pi$
$198$	6.76746	+	11.2018i	0.480943	+	0.796077i
$199$	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
$201$	−3.12860	−	3.06708i	−0.220675	−	0.216335i
$202$	2.49873	−	2.49873i	0.175810	−	0.175810i
$203$	−11.4703	+	3.07346i	−0.805057	+	0.215714i
$204$	−0.0416426	−	4.19351i	−0.00291557	−	0.293604i
$205$		−	13.7197i		−	0.958226i
$206$	−13.5421	+	3.62860i	−0.943524	+	0.252816i
$207$	−1.76891	+	3.20939i	−0.122948	+	0.223068i
$208$	−1.90819	+	3.05922i	−0.132309	+	0.212119i
$209$	24.0511	−	13.8859i	1.66365	−	0.960508i
$210$	−6.55836	−	6.42938i	−0.452570	−	0.443670i
$211$	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
$213$	−8.93615	+	9.11541i	−0.612295	+	0.624577i
$214$	9.56738	−	2.56357i	0.654012	−	0.175242i
$215$	5.31973	−	19.8535i	0.362802	−	1.35400i
$216$	−3.78204	−	3.56317i	−0.257335	−	0.242443i
$217$	−11.1862	−	19.3751i	−0.759370	−	1.31527i
$218$	−7.84397			−0.531261
$219$	2.73363	+	9.81128i	0.184721	+	0.662985i
$220$	7.55077	+	4.35944i	0.509073	+	0.293913i
$221$	8.72484	+	0.297644i	0.586896	+	0.0200217i
$222$	−14.3804	+	8.49401i	−0.965147	+	0.570080i
$223$	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
$225$	−2.64185	−	1.45610i	−0.176123	−	0.0970733i
$226$	9.52570	+	9.52570i	0.633640	+	0.633640i
$227$	−2.04965	−	7.64941i	−0.136040	−	0.507709i	−0.999991	−	0.00413376i	$-0.998684\pi$
$227$	−2.04965	−	7.64941i	−0.136040	−	0.507709i	0.863951	−	0.503576i	$-0.167982\pi$
$228$	−7.71905	+	7.87389i	−0.511206	+	0.521461i
$229$	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
$231$	10.1952	+	17.2605i	0.670794	+	1.13566i
$232$	−3.16495	+	3.16495i	−0.207789	+	0.207789i
$233$	4.39305			0.287799			0.143899	−	0.989592i	$-0.454036\pi$
$233$	4.39305			0.287799			0.143899	+	0.989592i	$0.454036\pi$
$234$	7.75668	−	7.53883i	0.507070	−	0.492829i
$235$	10.8159			0.705551
$236$	−2.84098	+	2.84098i	−0.184932	+	0.184932i
$237$	−0.560610	+	0.00556700i	−0.0364155	+	0.000361615i
$238$		−	6.42373i		−	0.416389i
$239$	−2.40851	−	8.98867i	−0.155793	−	0.581429i	−0.999036	−	0.0438958i	$-0.986023\pi$
$239$	−2.40851	−	8.98867i	−0.155793	−	0.581429i	0.843243	−	0.537533i	$-0.180644\pi$
$240$	−3.35249	−	0.862710i	−0.216402	−	0.0556877i
$241$	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
$243$	8.45462	+	13.0965i	0.542364	+	0.840144i
$244$	−8.70767	−	5.02738i	−0.557451	−	0.321845i
$245$	−0.0548262	−	0.0548262i	−0.00350272	−	0.00350272i
$246$	−0.118063	−	11.8892i	−0.00752743	−	0.758030i
$247$	−15.6676	−	16.7744i	−0.996908	−	1.06733i
$248$	−7.30289	−	4.21632i	−0.463734	−	0.267737i
$249$	−4.76976	+	4.86544i	−0.302271	+	0.308335i
$250$	−12.0027			−0.759120
$251$	3.88661	+	6.73180i	0.245321	+	0.424908i	0.962222	−	0.272267i	$-0.0877734\pi$
$251$	3.88661	+	6.73180i	0.245321	+	0.424908i	−0.716901	+	0.697175i	$0.754440\pi$
$252$	−5.73867	−	5.51514i	−0.361502	−	0.347421i
$253$	1.37921	−	5.14729i	0.0867104	−	0.323608i
$254$	2.66063	−	0.712914i	0.166943	−	0.0447322i
$255$	2.24961	+	8.07410i	0.140876	+	0.505620i
$256$	1.00000			0.0625000
$257$	12.8935	+	22.3322i	0.804274	+	1.39304i	0.916780	+	0.399392i	$0.130779\pi$
$257$	12.8935	+	22.3322i	0.804274	+	1.39304i	−0.112507	+	0.993651i	$0.535888\pi$
$258$	4.43913	−	17.2504i	0.276368	−	1.07396i
$259$	−22.1553	+	12.7913i	−1.37666	+	0.794816i
$260$	2.10132	−	6.89295i	0.130318	−	0.427483i
$261$	11.4931	−	6.94348i	0.711408	−	0.429790i
$262$	0.660098	−	0.176873i	0.0407810	−	0.0109272i
$263$			26.7629i			1.65027i	0.564934	+	0.825136i	$0.308902\pi$
$263$			26.7629i			1.65027i	−0.564934	+	0.825136i	$0.691098\pi$
$264$	6.58087	+	3.71283i	0.405024	+	0.228509i
$265$	0.274937	−	0.0736692i	0.0168893	−	0.00452546i
$266$	−11.9428	+	11.9428i	−0.732263	+	0.732263i
$267$	−6.39012	+	24.8320i	−0.391069	+	1.51969i
$268$	−2.44331	−	0.654683i	−0.149249	−	0.0399911i
$269$	−17.6997	+	10.2189i	−1.07917	+	0.623058i	−0.930672	−	0.365855i	$-0.880777\pi$
$269$	−17.6997	+	10.2189i	−1.07917	+	0.623058i	−0.148496	+	0.988913i	$0.547443\pi$
$270$	9.14446	+	4.92238i	0.556514	+	0.299567i
$271$	−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
$273$	11.9954	−	11.4291i	0.725994	−	0.691719i
$274$	−11.2626	+	19.5073i	−0.680396	+	1.17848i
$275$	4.23705	+	1.13531i	0.255504	+	0.0684621i
$276$	0.0210090	+	2.11565i	0.00126459	+	0.127347i
$277$	−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
$279$	18.2401	+	17.5296i	1.09200	+	1.04947i
$280$	−5.12181	−	1.37238i	−0.306087	−	0.0820156i
$281$	−5.89140	+	21.9870i	−0.351451	+	1.31163i	0.533440	+	0.845838i	$0.320899\pi$
$281$	−5.89140	+	21.9870i	−0.351451	+	1.31163i	−0.884892	+	0.465797i	$0.845768\pi$
$282$	9.37284	−	0.0930747i	0.558145	−	0.00554252i
$283$	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
$285$	10.8288	−	19.1936i	0.641440	−	1.13693i
$286$	−8.32438	+	13.3457i	−0.492231	+	0.789147i
$287$		−	18.2123i		−	1.07504i
$288$	−2.91263	−	0.718758i	−0.171628	−	0.0423532i
$289$	5.56879	−	9.64543i	0.327576	−	0.567378i
$290$	4.47283	−	7.74716i	0.262653	−	0.454929i
$291$	3.78882	−	14.7233i	0.222104	−	0.863097i
$292$	4.15800	+	4.15800i	0.243329	+	0.243329i
$293$	−15.1811	−	15.1811i	−0.886888	−	0.886888i	0.107335	−	0.994223i	$-0.465768\pi$
$293$	−15.1811	−	15.1811i	−0.886888	−	0.886888i	−0.994223	+	0.107335i	$0.965768\pi$
$294$	−0.0479831	−	0.0470395i	−0.00279843	−	0.00274340i
$295$	4.01499	−	6.95416i	0.233762	−	0.404887i
$296$	−4.82133	+	8.35079i	−0.280234	+	0.485380i
$297$	−16.4990	−	15.5441i	−0.957368	−	0.901962i
$298$			4.91420i			0.284672i
$299$	−4.40173	−	0.150163i	−0.254559	−	0.00868415i
$300$	−1.74152	+	0.0172938i	−0.100547	+	0.000998455i
$301$	7.06168	−	26.3546i	0.407029	−	1.51905i
$302$	3.47002	−	2.00341i	0.199677	−	0.115284i
$303$	−3.00752	+	5.33074i	−0.172778	+	0.306243i
$304$	−1.64767	+	6.14918i	−0.0945003	+	0.352680i
$305$	19.4109	+	5.20113i	1.11146	+	0.297816i
$306$	2.01895	+	6.97750i	0.115416	+	0.398877i
$307$	−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
$309$	20.9081	−	12.3497i	1.18942	−	0.702553i
$310$	16.2794	+	4.36205i	0.924607	+	0.247748i
$311$	16.5307	−	28.6320i	0.937370	−	1.62357i	0.167017	−	0.985954i	$-0.446587\pi$
$311$	16.5307	−	28.6320i	0.937370	−	1.62357i	0.770353	−	0.637618i	$-0.220080\pi$
$312$	1.76164	−	5.99138i	0.0997335	−	0.339195i
$313$	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
$315$	13.9315	+	7.67858i	0.784951	+	0.432639i
$316$	−0.280319	+	0.161842i	−0.0157692	+	0.00910433i
$317$	−1.34890	−	0.361436i	−0.0757616	−	0.0203003i	0.220739	−	0.975333i	$-0.429153\pi$
$317$	−1.34890	−	0.361436i	−0.0757616	−	0.0203003i	−0.296501	+	0.955033i	$0.595820\pi$
$318$	0.237621	−	0.0662062i	0.0133251	−	0.00371266i
$319$	−13.8069	+	13.8069i	−0.773040	+	0.773040i
$320$	−1.93052	+	0.517281i	−0.107919	+	0.0289169i
$321$	−14.7714	+	8.72498i	−0.824459	+	0.486981i
$322$			3.24081i			0.180603i
$323$	14.8887	−	3.98941i	0.828427	−	0.221976i
$324$	7.96677	+	4.18695i	0.442598	+	0.232608i
$325$	0.123608	−	3.62334i	0.00685656	−	0.200987i
$326$	−16.1679	+	9.33453i	−0.895456	+	0.516992i
$327$	13.0877	−	3.64649i	0.723749	−	0.201652i
$328$	−3.43230	−	5.94491i	−0.189517	−	0.328253i
$329$	14.3576			0.791559
$330$	−14.6251	−	3.76353i	−0.805083	−	0.207176i
$331$	−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
$333$	20.0449	−	20.8574i	1.09846	−	1.14298i
$334$	9.10041	+	15.7624i	0.497952	+	0.862479i
$335$	5.05551			0.276212
$336$	−4.45027	−	1.14521i	−0.242782	−	0.0624761i
$337$	−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
$339$	−20.3219	−	11.4653i	−1.10373	−	0.622711i
$340$	3.42179	+	3.42179i	0.185573	+	0.185573i
$341$	−31.8585	−	18.3935i	−1.72523	−	0.996064i
$342$	9.21882	−	16.7260i	0.498497	−	0.904438i
$343$	13.0593	+	13.0593i	0.705134	+	0.705134i
$344$	−2.66170	−	9.93360i	−0.143509	−	0.535584i
$345$	−1.13494	−	4.07344i	−0.0611033	−	0.219306i
$346$	−1.13763	−	4.24568i	−0.0611592	−	0.228249i
$347$			22.4935i			1.20752i	0.797168	+	0.603758i	$0.206331\pi$
$347$			22.4935i			1.20752i	−0.797168	+	0.603758i	$0.793669\pi$
$348$	3.80940	−	6.75203i	0.204205	−	0.361947i
$349$	−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
$351$	−9.43736	+	16.1844i	−0.503729	+	0.863862i
$352$	4.36245			0.232519
$353$	23.7758	−	23.7758i	1.26546	−	1.26546i	0.317049	−	0.948409i	$-0.397308\pi$
$353$	23.7758	−	23.7758i	1.26546	−	1.26546i	0.948409	−	0.317049i	$-0.102692\pi$
$354$	3.41947	−	6.06089i	0.181743	−	0.322133i
$355$		−	14.7296i		−	0.781766i
$356$	3.83151	+	14.2994i	0.203070	+	0.757867i
$357$	2.98625	+	10.7180i	0.158049	+	0.567256i
$358$	−2.81771	−	10.5158i	−0.148921	−	0.555779i
$359$	18.7010	+	18.7010i	0.987001	+	0.987001i	0.999917	−	0.0129158i	$-0.00411134\pi$
$359$	18.7010	+	18.7010i	0.987001	+	0.987001i	−0.0129158	+	0.999917i	$0.504111\pi$
$360$	5.99468	−	0.119069i	0.315947	−	0.00627549i
$361$	−18.6432	−	10.7636i	−0.981220	−	0.566507i
$362$	2.21897	+	2.21897i	0.116626	+	0.116626i
$363$	12.1149	+	6.83507i	0.635869	+	0.358748i
$364$	2.78940	−	9.15006i	0.146204	−	0.479593i
$365$	−10.1780	−	5.87625i	−0.532739	−	0.307577i
$366$	16.8659	+	4.34016i	0.881592	+	0.226864i
$367$	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
$369$	5.72404	+	19.7823i	0.297981	+	1.02982i
$370$	4.98797	−	18.6153i	0.259312	−	0.967766i
$371$	0.364966	−	0.0977923i	0.0189481	−	0.00507713i
$372$	14.1449	+	3.63998i	0.733381	+	0.188724i
$373$	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
$375$	20.0266	−	5.57982i	1.03417	−	0.288141i
$376$	4.68665	−	2.70584i	0.241696	−	0.139543i
$377$	13.6928	+	8.54089i	0.705215	+	0.439878i
$378$	12.1388	+	6.53422i	0.624354	+	0.336084i
$379$	−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
$381$	−4.10784	+	2.42637i	−0.210451	+	0.124307i
$382$	16.0691	−	4.30571i	0.822168	−	0.220299i
$383$	−11.8444	+	11.8444i	−0.605221	+	0.605221i	−0.941693	−	0.336473i	$-0.890766\pi$
$383$	−11.8444	+	11.8444i	−0.605221	+	0.605221i	0.336473	+	0.941693i	$0.390766\pi$
$384$	−1.66850	+	0.464878i	−0.0851452	+	0.0237232i
$385$	−22.3436	−	5.98696i	−1.13874	−	0.305124i
$386$	−13.2510	+	7.65049i	−0.674460	+	0.389400i
$387$	0.612677	+	30.8460i	0.0311441	+	1.56799i
$388$	−2.27178	−	8.47838i	−0.115332	−	0.430425i
$389$	5.63377	+	9.75798i	0.285644	+	0.494749i	0.972765	−	0.231793i	$-0.0744593\pi$
$389$	5.63377	+	9.75798i	0.285644	+	0.494749i	−0.687121	+	0.726543i	$0.741126\pi$
$390$	−0.301663	+	12.4777i	−0.0152753	+	0.631835i
$391$	1.47881	−	2.56138i	0.0747867	−	0.129534i
$392$	−0.0374729	−	0.0100408i	−0.00189267	−	0.000507138i
$393$	−1.01915	+	0.601978i	−0.0514093	+	0.0303658i
$394$	−17.9592	−	10.3687i	−0.904771	−	0.522370i
$395$	0.457443	−	0.457443i	0.0230164	−	0.0230164i
$396$	−12.7062	−	3.13555i	−0.638510	−	0.157567i
$397$	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
$399$	14.3747	−	25.4786i	0.719633	−	1.27553i
$400$	−0.870804	+	0.502759i	−0.0435402	+	0.0251379i
$401$	−7.17726	+	26.7859i	−0.358415	+	1.33762i	0.517717	+	0.855552i	$0.326782\pi$
$401$	−7.17726	+	26.7859i	−0.358415	+	1.33762i	−0.876132	+	0.482071i	$0.839885\pi$
$402$	4.38101	−	0.0435046i	0.218505	−	0.00216981i
$403$	−8.86595	+	29.0830i	−0.441644	+	1.44873i
$404$			3.53374i			0.175810i
$405$	−17.5458	−	3.96192i	−0.871859	−	0.196869i
$406$	5.93746	−	10.2840i	0.294671	−	0.510386i
$407$	−21.0328	+	36.4299i	−1.04256	+	1.80576i
$408$	2.99470	+	2.93581i	0.148260	+	0.145344i
$409$	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
$411$	9.72303	−	37.7837i	0.479602	−	1.86373i
$412$	7.00991	−	12.1415i	0.345354	−	0.598170i
$413$	5.32970	−	9.23132i	0.262258	−	0.454243i
$414$	−1.01857	−	3.52019i	−0.0500602	−	0.173008i
$415$		−	7.86207i		−	0.385934i
$416$	−0.813901	−	3.51249i	−0.0399048	−	0.172214i
$417$	−16.6379	+	29.4901i	−0.814762	+	1.44414i
$418$	−7.18788	+	26.8255i	−0.351570	+	1.31208i
$419$	15.9626	−	9.21604i	0.779826	−	0.450233i	−0.0565426	−	0.998400i	$-0.518008\pi$
$419$	15.9626	−	9.21604i	0.779826	−	0.450233i	0.836369	+	0.548167i	$0.184674\pi$
$420$	9.18372	−	0.0911967i	0.448120	−	0.00444994i
$421$	−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
$423$	−15.5953	+	4.51253i	−0.758270	+	0.219407i
$424$	0.100703	−	0.100703i	0.00489059	−	0.00489059i
$425$	2.10843	+	1.21730i	0.102274	+	0.0590477i
$426$	−0.126754	−	12.7644i	−0.00614123	−	0.618436i
$427$	25.7670	+	6.90425i	1.24695	+	0.334120i
$428$	−4.95244	+	8.57787i	−0.239385	+	0.414627i
$429$	7.68509	−	26.1371i	0.371040	−	1.26191i
$430$	10.2769	+	17.8002i	0.495597	+	0.858400i
$431$	−3.39947	−	12.6870i	−0.163747	−	0.611112i	−0.998197	−	0.0600279i	$-0.980881\pi$
$431$	−3.39947	−	12.6870i	−0.163747	−	0.611112i	0.834450	−	0.551084i	$-0.185786\pi$
$432$	5.19385	−	0.154769i	0.249889	−	0.00744635i
$433$	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
$435$	−3.86142	+	15.0055i	−0.185141	+	0.719456i
$436$	5.54653	−	5.54653i	0.265630	−	0.265630i
$437$	−7.51142	+	2.01268i	−0.359320	+	0.0962795i
$438$	−8.87059	−	5.00466i	−0.423853	−	0.239132i
$439$			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
$441$	0.101927	+	0.0561791i	0.00485369	+	0.00267519i
$442$	−6.37986	+	5.95893i	−0.303459	+	0.283437i
$443$	−3.45678	+	1.99577i	−0.164237	+	0.0948221i	−0.579865	−	0.814712i	$-0.696895\pi$
$443$	−3.45678	+	1.99577i	−0.164237	+	0.0948221i	0.415629	+	0.909534i	$0.363562\pi$
$444$	4.16228	−	16.1746i	0.197533	−	0.767614i
$445$	−14.7936	−	25.6233i	−0.701285	−	1.21466i
$446$	−11.0037			−0.521039
$447$	−2.28451	−	8.19934i	−0.108054	−	0.387816i
$448$	−2.56267	+	0.686666i	−0.121075	+	0.0324419i
$449$	−3.46480	+	12.9308i	−0.163514	+	0.610242i	0.834711	+	0.550688i	$0.185635\pi$
$449$	−3.46480	+	12.9308i	−0.163514	+	0.610242i	−0.998225	+	0.0595540i	$0.981032\pi$
$450$	2.89769	−	0.838450i	0.136598	−	0.0395249i
$451$	−14.9732	−	25.9344i	−0.705061	−	1.22120i
$452$	−13.4714			−0.633640
$453$	−4.85837	+	4.95583i	−0.228266	+	0.232845i
$454$	6.85828	+	3.95963i	0.321875	+	0.185835i
$455$	−0.651835	+	19.1073i	−0.0305585	+	0.895762i
$456$	−0.109490	−	11.0259i	−0.00512733	−	0.516334i
$457$	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
$459$	−6.61231	−	10.7034i	−0.308636	−	0.499591i
$460$	−1.72631	−	1.72631i	−0.0804898	−	0.0804898i
$461$	−1.31243	−	4.89805i	−0.0611260	−	0.228125i	0.928605	−	0.371071i	$-0.121009\pi$
$461$	−1.31243	−	4.89805i	−0.0611260	−	0.228125i	−0.989731	+	0.142946i	$0.954343\pi$
$462$	−19.4141	−	4.99591i	−0.903225	−	0.232431i
$463$	−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
$465$	−29.1900	+	0.289864i	−1.35365	+	0.0134421i
$466$	−3.10636	+	3.10636i	−0.143899	+	0.143899i
$467$	10.4397			0.483093			0.241546	−	0.970389i	$-0.422345\pi$
$467$	10.4397			0.483093			0.241546	+	0.970389i	$0.422345\pi$
$468$	−0.154039	+	10.8156i	−0.00712048	+	0.499949i
$469$	6.71095			0.309883
$470$	−7.64799	+	7.64799i	−0.352776	+	0.352776i
$471$	−0.0659173	−	0.111598i	−0.00303731	−	0.00514217i
$472$		−	4.01776i		−	0.184932i
$473$	−11.6115	−	43.3348i	−0.533899	−	1.99254i
$474$	0.392474	−	0.400347i	0.0180270	−	0.0183886i
$475$	−1.65676	−	6.18311i	−0.0760174	−	0.283701i
$476$	4.54226	+	4.54226i	0.208194	+	0.208194i
$477$	−0.365693	+	0.220930i	−0.0167439	+	0.0101157i
$478$	8.05902	+	4.65288i	0.368611	+	0.212818i
$479$	4.68529	+	4.68529i	0.214076	+	0.214076i	0.805996	−	0.591920i	$-0.201630\pi$
$479$	4.68529	+	4.68529i	0.214076	+	0.214076i	−0.591920	+	0.805996i	$0.701630\pi$
$480$	2.98060	−	1.76054i	0.136045	−	0.0803573i
$481$	33.2561	+	10.1381i	1.51635	+	0.462260i
$482$	−1.44385	−	0.833607i	−0.0657655	−	0.0379697i
$483$	−1.50658	−	5.40729i	−0.0685519	−	0.246040i
$484$	8.03098			0.365044
$485$	8.77141	+	15.1925i	0.398289	+	0.689857i
$486$	−15.2390	−	3.28234i	−0.691254	−	0.148890i
$487$	−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
$489$	22.6367	−	23.0907i	1.02367	−	1.04420i
$490$	0.0775360			0.00350272
$491$	−7.68585	−	13.3123i	−0.346858	−	0.600775i	0.638832	−	0.769346i	$-0.279418\pi$
$491$	−7.68585	−	13.3123i	−0.346858	−	0.600775i	−0.985689	+	0.168571i	$0.946085\pi$
$492$	8.49044	+	8.32347i	0.382779	+	0.375251i
$493$	−9.38535	+	5.41864i	−0.422695	+	0.244043i
$494$	22.9400	+	0.782586i	1.03212	+	0.0352102i
$495$	26.1515	−	0.519433i	1.17542	−	0.0233468i
$496$	8.14531	−	2.18253i	0.365735	−	0.0979985i
$497$		−	19.5528i		−	0.877064i
$498$	−0.0676560	−	6.81312i	−0.00303174	−	0.305303i
$499$	−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
$501$	−22.5116	−	22.0689i	−1.00574	−	0.985966i
$502$	−7.50835	−	2.01186i	−0.335114	−	0.0897936i
$503$	−20.4381	+	11.8000i	−0.911291	+	0.526134i	−0.880846	−	0.473402i	$-0.843026\pi$
$503$	−20.4381	+	11.8000i	−0.911291	+	0.526134i	−0.0304450	+	0.999536i	$0.509692\pi$
$504$	7.95765	−	0.158059i	0.354462	−	0.00704049i
$505$	−1.82794	−	6.82195i	−0.0813421	−	0.303573i
$506$	2.66444	+	4.61494i	0.118449	+	0.205159i
$507$	−22.4784	−	1.31136i	−0.998303	−	0.0582397i
$508$	−1.37724	+	2.38546i	−0.0611053	+	0.105838i
$509$	4.87095	+	1.30517i	0.215901	+	0.0578506i	0.365148	−	0.930949i	$-0.381018\pi$
$509$	4.87095	+	1.30517i	0.215901	+	0.0578506i	−0.149247	+	0.988800i	$0.547685\pi$
$510$	−7.29997	−	4.11854i	−0.323248	−	0.182372i
$511$	−13.5108	−	7.80044i	−0.597680	−	0.345071i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−7.60604	+	32.1929i	−0.335815	+	1.42135i
$514$	−24.9083	−	6.67416i	−1.09866	−	0.294385i
$515$	−7.25219	+	27.0655i	−0.319570	+	1.19265i
$516$	9.05896	+	15.3368i	0.398798	+	0.675166i
$517$	20.4453	−	11.8041i	0.899183	−	0.519144i
$518$	6.62129	−	24.7110i	0.290923	−	1.08574i
$519$	3.87185	+	6.55505i	0.169956	+	0.287735i
$520$	3.38819	+	6.35991i	0.148582	+	0.278900i
$521$		−	42.7218i		−	1.87168i	−0.352428	−	0.935839i	$-0.614644\pi$
$521$		−	42.7218i		−	1.87168i	0.352428	−	0.935839i	$-0.385356\pi$
$522$	−3.21710	+	13.0367i	−0.140809	+	0.570599i
$523$	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
$525$	4.45107	−	1.24016i	0.194261	−	0.0541251i
$526$	−18.9242	−	18.9242i	−0.825136	−	0.825136i
$527$	−14.4373	−	14.4373i	−0.628900	−	0.628900i
$528$	−7.27874	+	2.02801i	−0.316767	+	0.0882578i
$529$	10.7539	−	18.6264i	0.467562	−	0.809841i
$530$	−0.142318	+	0.246502i	−0.00618190	+	0.0107074i
$531$	−2.88780	+	11.7022i	−0.125320	+	0.507833i
$532$		−	16.8897i		−	0.732263i
$533$	−18.0879	+	16.8945i	−0.783472	+	0.731780i
$534$	−13.0404	−	22.0773i	−0.564312	−	0.955380i
$535$	5.12360	−	19.1216i	0.221513	−	0.826697i
$536$	2.19061	−	1.26475i	0.0946201	−	0.0546289i
$537$	9.58993	+	16.2358i	0.413836	+	0.700625i
$538$	5.28970	−	19.7414i	0.228055	−	0.851113i
$539$	−0.163474	−	0.0438026i	−0.00704130	−	0.00188671i
$540$	−9.94676	+	2.98546i	−0.428040	+	0.128474i
$541$	−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
$543$	−4.73390	−	2.67079i	−0.203151	−	0.114615i
$544$	2.33874	+	0.626664i	0.100273	+	0.0268680i
$545$	−7.83856	+	13.5768i	−0.335767	+	0.581566i
$546$	−0.400443	+	16.5636i	−0.0171374	+	0.708856i
$547$	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
$549$	−30.1583	+	0.599018i	−1.28712	+	0.0255655i
$550$	−3.79884	+	2.19326i	−0.161983	+	0.0935209i
$551$	27.5232	+	7.37483i	1.17253	+	0.314178i
$552$	−1.51085	−	1.48114i	−0.0643059	−	0.0630413i
$553$	0.607233	−	0.607233i	0.0258222	−	0.0258222i
$554$	10.3189	−	2.76495i	0.438409	−	0.117471i
$555$	0.331457	+	33.3785i	0.0140696	+	1.41684i
$556$			19.5490i			0.829062i
$557$	−22.0126	+	5.89827i	−0.932705	+	0.249918i	−0.693008	−	0.720930i	$-0.743715\pi$
$557$	−22.0126	+	5.89827i	−0.932705	+	0.249918i	−0.239697	+	0.970848i	$0.577048\pi$
$558$	−25.2930	+	0.502381i	−1.07074	+	0.0212675i
$559$	−32.7253	+	17.4342i	−1.38413	+	0.737386i
$560$	4.59209	−	2.65124i	0.194051	−	0.112035i
$561$	13.0642	+	12.8073i	0.551573	+	0.540726i
$562$	−11.3813	−	19.7130i	−0.480092	−	0.831543i
$563$	−12.7743			−0.538373			−0.269186	−	0.963088i	$-0.586755\pi$
$563$	−12.7743			−0.538373			−0.269186	+	0.963088i	$0.586755\pi$
$564$	−6.56179	+	6.69341i	−0.276301	+	0.281844i
$565$	26.0067	−	6.96849i	1.09411	−	0.293166i
$566$	−0.131652	+	0.491331i	−0.00553374	+	0.0206522i
$567$	−23.2913	−	5.25926i	−0.978141	−	0.220868i
$568$	−3.68494	−	6.38250i	−0.154617	−	0.267804i
$569$	−3.87917			−0.162623			−0.0813117	−	0.996689i	$-0.525911\pi$
$569$	−3.87917			−0.162623			−0.0813117	+	0.996689i	$0.525911\pi$
$570$	5.91485	+	21.2290i	0.247746	+	0.889186i
$571$	−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
$573$	−24.8097	+	14.6543i	−1.03644	+	0.612191i
$574$	12.8780	+	12.8780i	0.537518	+	0.537518i
$575$	−1.06371	−	0.614136i	−0.0443599	−	0.0256112i
$576$	2.56778	−	1.55130i	0.106991	−	0.0646374i
$577$	−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
$579$	18.5528	−	18.9250i	0.771028	−	0.786494i
$580$	2.31531	+	8.64084i	0.0961378	+	0.358791i
$581$		−	10.4365i		−	0.432980i
$582$	7.73187	+	13.0901i	0.320496	+	0.542601i
$583$	0.439314	−	0.439314i	0.0181945	−	0.0181945i
$584$	−5.88030			−0.243329
$585$	−5.29731	−	20.9593i	−0.219017	−	0.866561i
$586$	21.4693			0.886888
$587$	28.9809	−	28.9809i	1.19617	−	1.19617i	0.220863	−	0.975305i	$-0.429113\pi$
$587$	28.9809	−	28.9809i	1.19617	−	1.19617i	0.975305	−	0.220863i	$-0.0708875\pi$
$588$	0.0671912		0.000667226i	0.00277092		2.75159e-5i
$589$			53.6831i			2.21197i
$590$	2.07831	+	7.75636i	0.0855627	+	0.319324i
$591$	34.7851	+	8.95139i	1.43087	+	0.368211i
$592$	−2.49571	−	9.31410i	−0.102573	−	0.382807i
$593$	−5.71700	−	5.71700i	−0.234769	−	0.234769i	0.579911	−	0.814680i	$-0.303087\pi$
$593$	−5.71700	−	5.71700i	−0.234769	−	0.234769i	−0.814680	+	0.579911i	$0.803087\pi$
$594$	22.6579	−	0.675174i	0.929665	−	0.0277027i
$595$	−11.1186	−	6.41930i	−0.455816	−	0.263166i
$596$	−3.47487	−	3.47487i	−0.142336	−	0.142336i
$597$	−0.106694	−	10.7443i	−0.00436670	−	0.439737i
$598$	3.21868	−	3.00631i	0.131621	−	0.122937i
$599$	33.2498	+	19.1968i	1.35855	+	0.784359i	0.989428	−	0.145022i	$-0.0463254\pi$
$599$	33.2498	+	19.1968i	1.35855	+	0.784359i	0.369121	+	0.929381i	$0.379659\pi$
$600$	1.21921	−	1.24367i	0.0497742	−	0.0507726i
$601$	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
$603$	−7.28949	+	2.10922i	−0.296851	+	0.0858943i
$604$	−1.03704	+	3.87030i	−0.0421967	+	0.157480i
$605$	−15.5040	+	4.15427i	−0.630325	+	0.168895i
$606$	−1.64276	−	5.89604i	−0.0667326	−	0.239510i
$607$	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
$609$	−5.12585	+	19.9190i	−0.207710	+	0.807159i
$610$	−17.4033	+	10.0478i	−0.704640	+	0.406824i
$611$	−13.3187	−	14.2595i	−0.538817	−	0.576878i
$612$	−6.36145	−	3.50623i	−0.257147	−	0.141731i
$613$	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
$615$	−20.6965	−	11.6767i	−0.834565	−	0.470849i
$616$	−11.1795	+	2.99555i	−0.450436	+	0.120694i
$617$	−5.51931	+	5.51931i	−0.222199	+	0.222199i	−0.809424	−	0.587225i	$-0.800220\pi$
$617$	−5.51931	+	5.51931i	−0.222199	+	0.222199i	0.587225	+	0.809424i	$0.300220\pi$
$618$	−6.05170	+	23.5169i	−0.243435	+	0.945988i
$619$	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
$621$	3.33595	+	5.39993i	0.133867	+	0.216692i
$622$	8.55692	+	31.9348i	0.343101	+	1.28047i
$623$	−19.6378	−	34.0137i	−0.786773	−	1.36273i
$624$	2.99087	+	5.48221i	0.119731	+	0.219464i
$625$	−9.48067	+	16.4210i	−0.379227	+	0.656840i
$626$	−14.1452	−	3.79020i	−0.565356	−	0.151487i
$627$	−0.477644	−	48.0998i	−0.0190752	−	1.92092i
$628$	−0.0648059	−	0.0374157i	−0.00258604	−	0.00149305i
$629$	−16.5090	+	16.5090i	−0.658256	+	0.658256i
$630$	−15.2806	+	4.42148i	−0.608795	+	0.176156i
$631$	−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
$633$	14.6368	−	0.145347i	0.581762	−	0.00577704i
$634$	1.20939	−	0.698240i	0.0480309	−	0.0277307i
$635$	1.42484	−	5.31759i	0.0565432	−	0.211022i
$636$	−0.121209	+	0.214838i	−0.00480624	+	0.00851890i
$637$	−0.00476905	+	0.139795i	−0.000188956	+	0.00553889i
$638$		−	19.5260i		−	0.773040i
$639$	6.14537	+	21.2384i	0.243107	+	0.840179i
$640$	0.999310	−	1.73086i	0.0395012	−	0.0684181i
$641$	9.64616	−	16.7076i	0.381001	−	0.659912i	−0.610205	−	0.792244i	$-0.708913\pi$
$641$	9.64616	−	16.7076i	0.381001	−	0.659912i	0.991206	+	0.132331i	$0.0422463\pi$
$642$	4.27547	−	16.6145i	0.168739	−	0.655720i
$643$	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
$645$	−25.4219	−	24.9220i	−1.00099	−	0.981303i
$646$	−7.70694	+	13.3488i	−0.303225	+	0.525202i
$647$	−19.1754	+	33.2127i	−0.753861	+	1.30573i	0.192077	+	0.981380i	$0.438478\pi$
$647$	−19.1754	+	33.2127i	−0.753861	+	1.30573i	−0.945939	+	0.324346i	$0.894856\pi$
$648$	−8.59398	+	2.67274i	−0.337603	+	0.104995i
$649$		−	17.5273i		−	0.688006i
$650$	2.47468	+	2.64949i	0.0970650	+	0.103922i
$651$	−38.7483	+	0.384780i	−1.51866	+	0.0150807i
$652$	4.83191	−	18.0329i	0.189232	−	0.706224i
$653$	12.7867	−	7.38243i	0.500384	−	0.288897i	−0.228488	−	0.973547i	$-0.573378\pi$
$653$	12.7867	−	7.38243i	0.500384	−	0.288897i	0.728872	+	0.684650i	$0.240045\pi$
$654$	−6.67591	+	11.8328i	−0.261049	+	0.462700i
$655$	0.353502	−	1.31929i	0.0138125	−	0.0515488i
$656$	6.63068	+	1.77669i	0.258885	+	0.0693680i
$657$	17.1271	+	4.22652i	0.668193	+	0.164892i
$658$	−10.1523	+	10.1523i	−0.395780	+	0.395780i
$659$	6.91954	+	3.99500i	0.269547	+	0.155623i	0.628682	−	0.777663i	$-0.283595\pi$
$659$	6.91954	+	3.99500i	0.269547	+	0.155623i	−0.359135	+	0.933286i	$0.616928\pi$
$660$	13.0027	−	7.68027i	0.506129	−	0.298954i
$661$	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
$663$	7.87461	−	12.9083i	0.305824	−	0.501318i
$664$	−1.96687	−	3.40673i	−0.0763295	−	0.132207i
$665$	8.73674	+	32.6060i	0.338796	+	1.26440i
$666$	0.574468	+	28.9223i	0.0222602	+	1.12072i
$667$	4.73497	−	2.73374i	0.183339	−	0.105851i
$668$	−17.5806	−	4.71072i	−0.680215	−	0.182263i
$669$	18.3596	−	5.11537i	0.709823	−	0.197772i
$670$	−3.57479	+	3.57479i	−0.138106	+	0.138106i
$671$	42.3687	−	11.3527i	1.63563	−	0.438265i
$672$	3.95660	−	2.33703i	0.152629	−	0.0901530i
$673$		−	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
$675$	−4.44501	+	2.74603i	−0.171088	+	0.105695i
$676$	−11.6751	+	5.71764i	−0.449043	+	0.219909i
$677$	7.87586	−	4.54713i	0.302694	−	0.174760i	−0.340959	−	0.940078i	$-0.610752\pi$
$677$	7.87586	−	4.54713i	0.302694	−	0.174760i	0.643652	+	0.765318i	$0.277418\pi$
$678$	22.4770	−	6.26255i	0.863223	−	0.240512i
$679$	11.6436	+	20.1674i	0.446841	+	0.773952i
$680$	−4.83914			−0.185573
$681$	−13.2838	−	3.41837i	−0.509035	−	0.130992i
$682$	35.5335	−	9.52118i	1.36065	−	0.364585i
$683$	−7.08606	+	26.4455i	−0.271141	+	1.01191i	0.687243	+	0.726427i	$0.258821\pi$
$683$	−7.08606	+	26.4455i	−0.271141	+	1.01191i	−0.958384	+	0.285483i	$0.907846\pi$
$684$	5.30837	+	18.3458i	0.202971	+	0.701467i
$685$	22.5096	+	38.9877i	0.860047	+	1.48965i
$686$	−18.4686			−0.705134
$687$	2.44601	+	0.629442i	0.0933211	+	0.0240147i
$688$	8.90622	+	5.14201i	0.339546	+	0.196037i
$689$	−0.435682	−	0.271757i	−0.0165982	−	0.0103531i
$690$	3.68288	+	2.07783i	0.140205	+	0.0791015i
$691$	−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
$693$	34.7149	−	0.689523i	1.31871	−	0.0261928i
$694$	−15.9053	−	15.9053i	−0.603758	−	0.603758i
$695$	−10.1123	−	37.7397i	−0.383582	−	1.43155i
$696$	2.08076	+	7.46806i	0.0788709	+	0.283076i
$697$	−4.30179	−	16.0545i	−0.162942	−	0.608107i
$698$		−	16.6396i		−	0.629819i
$699$	3.73888	−	6.62703i	0.141417	−	0.250657i
$700$	1.88636	−	1.88636i	0.0712976	−	0.0712976i
$701$	8.14720			0.307715			0.153858	−	0.988093i	$-0.450830\pi$
$701$	8.14720			0.307715			0.153858	+	0.988093i	$0.450830\pi$
$702$	−4.77090	−	18.1174i	−0.180066	−	0.683795i
$703$	61.3862			2.31522
$704$	−3.08472	+	3.08472i	−0.116260	+	0.116260i
$705$	9.20528	−	16.3161i	0.346691	−	0.614498i
$706$			33.6241i			1.26546i
$707$	−2.42650	−	9.05582i	−0.0912579	−	0.340579i
$708$	1.86777	+	6.70363i	0.0701951	+	0.251938i
$709$	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
$711$	−0.468730	+	0.850432i	−0.0175788	+	0.0318937i
$712$	−12.8205	−	7.40192i	−0.480468	−	0.277399i
$713$	7.28373	+	7.28373i	0.272778	+	0.272778i
$714$	−9.69036	−	5.46716i	−0.362653	−	0.204603i
$715$	14.7808	+	27.7448i	0.552772	+	1.03760i
$716$	9.42824	+	5.44340i	0.352350	+	0.203429i
$717$	−15.6095	−	4.01686i	−0.582947	−	0.150012i
$718$	−26.4472			−0.987001
$719$	−24.0105	−	41.5874i	−0.895441	−	1.55095i	−0.833258	−	0.552885i	$-0.813527\pi$
$719$	−24.0105	−	41.5874i	−0.895441	−	1.55095i	−0.0621837	−	0.998065i	$-0.519806\pi$
$720$	−4.15468	+	4.32307i	−0.154836	+	0.161111i
$721$	−9.62694	+	35.9282i	−0.358526	+	1.33804i
$722$	20.7938	−	5.57167i	0.773864	−	0.207356i
$723$	2.79659	+	0.719657i	0.104006	+	0.0267643i
$724$	−3.13809			−0.116626
$725$	2.25030	+	3.89764i	0.0835742	+	0.144755i
$726$	−13.3997	+	3.73343i	−0.497309	+	0.138561i
$727$	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
$729$	26.9521	−	1.60770i	0.998226	−	0.0595443i
$730$	11.3520	−	3.04177i	0.420158	−	0.112581i
$731$		−	24.9001i		−	0.920963i
$732$	−14.9949	+	8.85700i	−0.554228	+	0.327364i
$733$	−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
$735$	−0.129369	+	0.0360448i	−0.00477184	+	0.00132953i
$736$	−1.17991	−	0.316156i	−0.0434920	−	0.0116537i
$737$	9.55644	−	5.51741i	0.352016	−	0.203237i
$738$	−18.0357	−	9.94068i	−0.663903	−	0.365922i
$739$	−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
$741$	−38.6391	+	9.35855i	−1.41944	+	0.343795i
$742$	−0.188920	+	0.327220i	−0.00693548	+	0.0120126i
$743$	19.0656	+	5.10861i	0.699449	+	0.187417i	0.590984	−	0.806683i	$-0.298740\pi$
$743$	19.0656	+	5.10861i	0.699449	+	0.187417i	0.108465	+	0.994100i	$0.465406\pi$
$744$	−12.5758	+	7.42813i	−0.461052	+	0.272328i
$745$	8.50578	+	4.91081i	0.311628	+	0.179918i
$746$	−4.48418	+	4.48418i	−0.164177	+	0.164177i
$747$	3.28016	+	11.3362i	0.120015	+	0.414771i
$748$	10.2026	+	2.73379i	0.373045	+	0.0999572i
$749$	6.80134	−	25.3829i	0.248516	−	0.927473i
$750$	−10.2154	+	18.1065i	−0.373014	+	0.661154i
$751$	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
$753$	13.4629	−	0.133691i	0.490617	−	0.00487195i
$754$	−15.7216	+	3.64295i	−0.572547	+	0.132669i
$755$		−	8.00813i		−	0.291446i
$756$	−13.2038	+	3.96306i	−0.480219	+	0.144135i
$757$	−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
$759$	−6.59099	−	6.46138i	−0.239238	−	0.234533i
$760$	8.99682	+	8.99682i	0.326349	+	0.326349i
$761$	−0.501543	−	0.501543i	−0.0181809	−	0.0181809i	0.697958	−	0.716139i	$-0.254092\pi$
$761$	−0.501543	−	0.501543i	−0.0181809	−	0.0181809i	−0.716139	+	0.697958i	$0.754092\pi$
$762$	1.18898	−	4.62038i	0.0430723	−	0.167379i
$763$	−10.4053	+	18.0225i	−0.376698	+	0.652460i
$764$	−8.31799	+	14.4072i	−0.300934	+	0.521234i
$765$	14.0946	+	3.47817i	0.509592	+	0.125754i
$766$		−	16.7505i		−	0.605221i
$767$	−14.1123	+	3.27006i	−0.509567	+	0.118075i
$768$	0.851088	−	1.50853i	0.0307110	−	0.0544342i
$769$	−4.82649	+	18.0127i	−0.174048

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.851088 - 1.50853i) q^{3} -1.00000i q^{4} +(0.517281 + 1.93052i) q^{5} +(0.464878 + 1.66850i) q^{6} +(0.686666 + 2.56267i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.55130 - 2.56778i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.851088 - 1.50853i) q^{3} -1.00000i q^{4} +(0.517281 + 1.93052i) q^{5} +(0.464878 + 1.66850i) q^{6} +(0.686666 + 2.56267i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-1.55130 - 2.56778i) q^{9} +(-1.73086 - 0.999310i) q^{10} +(3.08472 + 3.08472i) q^{11} +(-1.50853 - 0.851088i) q^{12} +(1.90819 - 3.05922i) q^{13} +(-2.29763 - 1.32654i) q^{14} +(3.35249 + 0.862710i) q^{15} -1.00000 q^{16} +(1.21062 + 2.09686i) q^{17} +(2.91263 + 0.718758i) q^{18} +(1.64767 - 6.14918i) q^{19} +(1.93052 - 0.517281i) q^{20} +(4.45027 + 1.14521i) q^{21} -4.36245 q^{22} +(-0.610766 - 1.05788i) q^{23} +(1.66850 - 0.464878i) q^{24} +(0.870804 - 0.502759i) q^{25} +(0.813901 + 3.51249i) q^{26} +(-5.19385 + 0.154769i) q^{27} +(2.56267 - 0.686666i) q^{28} +4.47591i q^{29} +(-2.98060 + 1.76054i) q^{30} +(-8.14531 + 2.18253i) q^{31} +(0.707107 - 0.707107i) q^{32} +(7.27874 - 2.02801i) q^{33} +(-2.33874 - 0.626664i) q^{34} +(-4.59209 + 2.65124i) q^{35} +(-2.56778 + 1.55130i) q^{36} +(2.49571 + 9.31410i) q^{37} +(3.18305 + 5.51321i) q^{38} +(-2.99087 - 5.48221i) q^{39} +(-0.999310 + 1.73086i) q^{40} +(-6.63068 - 1.77669i) q^{41} +(-3.95660 + 2.33703i) q^{42} +(-8.90622 - 5.14201i) q^{43} +(3.08472 - 3.08472i) q^{44} +(4.15468 - 4.32307i) q^{45} +(1.17991 + 0.316156i) q^{46} +(1.40065 - 5.22728i) q^{47} +(-0.851088 + 1.50853i) q^{48} +(-0.0335972 + 0.0193974i) q^{49} +(-0.260247 + 0.971255i) q^{50} +(4.19351 - 0.0416426i) q^{51} +(-3.05922 - 1.90819i) q^{52} -0.142416i q^{53} +(3.56317 - 3.78204i) q^{54} +(-4.35944 + 7.55077i) q^{55} +(-1.32654 + 2.29763i) q^{56} +(-7.87389 - 7.71905i) q^{57} +(-3.16495 - 3.16495i) q^{58} +(-2.84098 - 2.84098i) q^{59} +(0.862710 - 3.35249i) q^{60} +(5.02738 - 8.70767i) q^{61} +(4.21632 - 7.30289i) q^{62} +(5.51514 - 5.73867i) q^{63} +1.00000i q^{64} +(6.89295 + 2.10132i) q^{65} +(-3.71283 + 6.58087i) q^{66} +(0.654683 - 2.44331i) q^{67} +(2.09686 - 1.21062i) q^{68} +(-2.11565 + 0.0210090i) q^{69} +(1.37238 - 5.12181i) q^{70} +(-7.11876 - 1.90747i) q^{71} +(0.718758 - 2.91263i) q^{72} +(-4.15800 + 4.15800i) q^{73} +(-8.35079 - 4.82133i) q^{74} +(-0.0172938 - 1.74152i) q^{75} +(-6.14918 - 1.64767i) q^{76} +(-5.78695 + 10.0233i) q^{77} +(5.99138 + 1.76164i) q^{78} +(-0.161842 - 0.280319i) q^{79} +(-0.517281 - 1.93052i) q^{80} +(-4.18695 + 7.96677i) q^{81} +(5.94491 - 3.43230i) q^{82} +(-3.79971 - 1.01813i) q^{83} +(1.14521 - 4.45027i) q^{84} +(-3.42179 + 3.42179i) q^{85} +(9.93360 - 2.66170i) q^{86} +(6.75203 + 3.80940i) q^{87} +4.36245i q^{88} +(-14.2994 + 3.83151i) q^{89} +(0.119069 + 5.99468i) q^{90} +(9.15006 + 2.78940i) q^{91} +(-1.05788 + 0.610766i) q^{92} +(-3.63998 + 14.1449i) q^{93} +(2.70584 + 4.68665i) q^{94} +12.7234 q^{95} +(-0.464878 - 1.66850i) q^{96} +(8.47838 - 2.27178i) q^{97} +(0.0100408 - 0.0374729i) q^{98} +(3.13555 - 12.7062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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