LMFDB - Embedded newform 1110.2.o.b.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.6
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.b.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.19936 - 1.88721i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.19936 - 1.88721i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-1.19936 - 1.88721i) q^{10} +0.249077i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.83382 q^{13} +(-1.50593 + 1.50593i) q^{14} +(2.18253 + 0.486383i) q^{15} +1.00000 q^{16} +7.29402i q^{17} -1.00000i q^{18} +(-1.89479 - 1.89479i) q^{19} +(-1.19936 - 1.88721i) q^{20} -2.12971i q^{21} +0.249077i q^{22} -8.28835 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.12309 + 4.52686i) q^{25} -2.83382 q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.50593 + 1.50593i) q^{28} +(2.37266 - 2.37266i) q^{29} +(2.18253 + 0.486383i) q^{30} +(1.83366 + 1.83366i) q^{31} +1.00000 q^{32} +(-0.176124 - 0.176124i) q^{33} +7.29402i q^{34} +(4.64816 + 1.03586i) q^{35} -1.00000i q^{36} +(-5.25654 - 3.06084i) q^{37} +(-1.89479 - 1.89479i) q^{38} +(2.00381 - 2.00381i) q^{39} +(-1.19936 - 1.88721i) q^{40} +10.3232i q^{41} -2.12971i q^{42} -7.61240 q^{43} +0.249077i q^{44} +(-1.88721 + 1.19936i) q^{45} -8.28835 q^{46} +(-2.82753 + 2.82753i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.46433i q^{49} +(-2.12309 + 4.52686i) q^{50} +(-5.15765 - 5.15765i) q^{51} -2.83382 q^{52} +(4.20587 + 4.20587i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.470059 - 0.298732i) q^{55} +(-1.50593 + 1.50593i) q^{56} +2.67964 q^{57} +(2.37266 - 2.37266i) q^{58} +(-6.26117 - 6.26117i) q^{59} +(2.18253 + 0.486383i) q^{60} +(-3.22008 - 3.22008i) q^{61} +(1.83366 + 1.83366i) q^{62} +(1.50593 + 1.50593i) q^{63} +1.00000 q^{64} +(3.39876 + 5.34800i) q^{65} +(-0.176124 - 0.176124i) q^{66} +(-5.68165 - 5.68165i) q^{67} +7.29402i q^{68} +(5.86075 - 5.86075i) q^{69} +(4.64816 + 1.03586i) q^{70} +3.37315 q^{71} -1.00000i q^{72} +(7.48228 - 7.48228i) q^{73} +(-5.25654 - 3.06084i) q^{74} +(-1.69973 - 4.70223i) q^{75} +(-1.89479 - 1.89479i) q^{76} +(-0.375093 - 0.375093i) q^{77} +(2.00381 - 2.00381i) q^{78} +(-5.99818 - 5.99818i) q^{79} +(-1.19936 - 1.88721i) q^{80} -1.00000 q^{81} +10.3232i q^{82} +(5.98449 + 5.98449i) q^{83} -2.12971i q^{84} +(13.7653 - 8.74813i) q^{85} -7.61240 q^{86} +3.35545i q^{87} +0.249077i q^{88} +(-5.37576 + 5.37576i) q^{89} +(-1.88721 + 1.19936i) q^{90} +(4.26754 - 4.26754i) q^{91} -8.28835 q^{92} -2.59319 q^{93} +(-2.82753 + 2.82753i) q^{94} +(-1.30333 + 5.84838i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.94731i q^{97} +2.46433i q^{98} +0.249077 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	$ 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) $ 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.00000			0.500000
$5$	−1.19936	−	1.88721i	−0.536368	−	0.843984i
$5$	−1.19936	−	1.88721i	−0.536368	−	0.843984i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.50593	+	1.50593i	−0.569189	+	0.569189i	−0.931901	−	0.362712i	$-0.881851\pi$
$7$	−1.50593	+	1.50593i	−0.569189	+	0.569189i	0.362712	+	0.931901i	$0.381851\pi$
$8$	1.00000			0.353553
$9$		−	1.00000i		−	0.333333i
$10$	−1.19936	−	1.88721i	−0.379270	−	0.596787i
$11$			0.249077i			0.0750994i	0.999295	+	0.0375497i	$0.0119553\pi$
$11$			0.249077i			0.0750994i	−0.999295	+	0.0375497i	$0.988045\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−2.83382			−0.785959			−0.392980	−	0.919547i	$-0.628556\pi$
$13$	−2.83382			−0.785959			−0.392980	+	0.919547i	$0.628556\pi$
$14$	−1.50593	+	1.50593i	−0.402478	+	0.402478i
$15$	2.18253	+	0.486383i	0.563527	+	0.125583i
$16$	1.00000			0.250000
$17$			7.29402i			1.76906i	0.466484	+	0.884530i	$0.345520\pi$
$17$			7.29402i			1.76906i	−0.466484	+	0.884530i	$0.654480\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.89479	−	1.89479i	−0.434694	−	0.434694i	0.455527	−	0.890222i	$-0.349451\pi$
$19$	−1.89479	−	1.89479i	−0.434694	−	0.434694i	−0.890222	+	0.455527i	$0.849451\pi$
$20$	−1.19936	−	1.88721i	−0.268184	−	0.421992i
$21$		−	2.12971i		−	0.464741i
$22$			0.249077i			0.0531033i
$23$	−8.28835			−1.72824			−0.864120	−	0.503286i	$-0.832124\pi$
$23$	−8.28835			−1.72824			−0.864120	+	0.503286i	$0.832124\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−2.12309	+	4.52686i	−0.424618	+	0.905373i
$26$	−2.83382			−0.555757
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.50593	+	1.50593i	−0.284595	+	0.284595i
$29$	2.37266	−	2.37266i	0.440592	−	0.440592i	−0.451619	−	0.892211i	$-0.649153\pi$
$29$	2.37266	−	2.37266i	0.440592	−	0.440592i	0.892211	+	0.451619i	$0.149153\pi$
$30$	2.18253	+	0.486383i	0.398473	+	0.0888009i
$31$	1.83366	+	1.83366i	0.329335	+	0.329335i	0.852334	−	0.522999i	$-0.175187\pi$
$31$	1.83366	+	1.83366i	0.329335	+	0.329335i	−0.522999	+	0.852334i	$0.675187\pi$
$32$	1.00000			0.176777
$33$	−0.176124	−	0.176124i	−0.0306592	−	0.0306592i
$34$			7.29402i			1.25091i
$35$	4.64816	+	1.03586i	0.785682	+	0.175091i
$36$		−	1.00000i		−	0.166667i
$37$	−5.25654	−	3.06084i	−0.864170	−	0.503200i
$37$	−5.25654	−	3.06084i	−0.864170	−	0.503200i
$38$	−1.89479	−	1.89479i	−0.307375	−	0.307375i
$39$	2.00381	−	2.00381i	0.320867	−	0.320867i
$40$	−1.19936	−	1.88721i	−0.189635	−	0.298393i
$41$			10.3232i			1.61221i	0.591771	+	0.806106i	$0.298429\pi$
$41$			10.3232i			1.61221i	−0.591771	+	0.806106i	$0.701571\pi$
$42$		−	2.12971i		−	0.328622i
$43$	−7.61240			−1.16088			−0.580440	−	0.814303i	$-0.697120\pi$
$43$	−7.61240			−1.16088			−0.580440	+	0.814303i	$0.697120\pi$
$44$			0.249077i			0.0375497i
$45$	−1.88721	+	1.19936i	−0.281328	+	0.178789i
$46$	−8.28835			−1.22205
$47$	−2.82753	+	2.82753i	−0.412437	+	0.412437i	−0.882587	−	0.470150i	$-0.844200\pi$
$47$	−2.82753	+	2.82753i	−0.412437	+	0.412437i	0.470150	+	0.882587i	$0.344200\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			2.46433i			0.352047i
$50$	−2.12309	+	4.52686i	−0.300250	+	0.640195i
$51$	−5.15765	−	5.15765i	−0.722215	−	0.722215i
$52$	−2.83382			−0.392980
$53$	4.20587	+	4.20587i	0.577721	+	0.577721i	0.934275	−	0.356554i	$-0.116048\pi$
$53$	4.20587	+	4.20587i	0.577721	+	0.577721i	−0.356554	+	0.934275i	$0.616048\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	0.470059	−	0.298732i	0.0633827	−	0.0402810i
$56$	−1.50593	+	1.50593i	−0.201239	+	0.201239i
$57$	2.67964			0.354926
$58$	2.37266	−	2.37266i	0.311546	−	0.311546i
$59$	−6.26117	−	6.26117i	−0.815135	−	0.815135i	0.170264	−	0.985398i	$-0.445538\pi$
$59$	−6.26117	−	6.26117i	−0.815135	−	0.815135i	−0.985398	+	0.170264i	$0.945538\pi$
$60$	2.18253	+	0.486383i	0.281763	+	0.0627917i
$61$	−3.22008	−	3.22008i	−0.412290	−	0.412290i	0.470246	−	0.882535i	$-0.344165\pi$
$61$	−3.22008	−	3.22008i	−0.412290	−	0.412290i	−0.882535	+	0.470246i	$0.844165\pi$
$62$	1.83366	+	1.83366i	0.232875	+	0.232875i
$63$	1.50593	+	1.50593i	0.189730	+	0.189730i
$64$	1.00000			0.125000
$65$	3.39876	+	5.34800i	0.421564	+	0.663337i
$66$	−0.176124	−	0.176124i	−0.0216793	−	0.0216793i
$67$	−5.68165	−	5.68165i	−0.694124	−	0.694124i	0.269013	−	0.963137i	$-0.413303\pi$
$67$	−5.68165	−	5.68165i	−0.694124	−	0.694124i	−0.963137	+	0.269013i	$0.913303\pi$
$68$			7.29402i			0.884530i
$69$	5.86075	−	5.86075i	0.705551	−	0.705551i
$70$	4.64816	+	1.03586i	0.555561	+	0.123808i
$71$	3.37315			0.400320			0.200160	−	0.979763i	$-0.435854\pi$
$71$	3.37315			0.400320			0.200160	+	0.979763i	$0.435854\pi$
$72$		−	1.00000i		−	0.117851i
$73$	7.48228	−	7.48228i	0.875735	−	0.875735i	−0.117355	−	0.993090i	$-0.537442\pi$
$73$	7.48228	−	7.48228i	0.875735	−	0.875735i	0.993090	+	0.117355i	$0.0374416\pi$
$74$	−5.25654	−	3.06084i	−0.611061	−	0.355816i
$75$	−1.69973	−	4.70223i	−0.196267	−	0.542966i
$76$	−1.89479	−	1.89479i	−0.217347	−	0.217347i
$77$	−0.375093	−	0.375093i	−0.0427458	−	0.0427458i
$78$	2.00381	−	2.00381i	0.226887	−	0.226887i
$79$	−5.99818	−	5.99818i	−0.674848	−	0.674848i	0.283982	−	0.958830i	$-0.408345\pi$
$79$	−5.99818	−	5.99818i	−0.674848	−	0.674848i	−0.958830	+	0.283982i	$0.908345\pi$
$80$	−1.19936	−	1.88721i	−0.134092	−	0.210996i
$81$	−1.00000			−0.111111
$82$			10.3232i			1.14001i
$83$	5.98449	+	5.98449i	0.656883	+	0.656883i	0.954641	−	0.297759i	$-0.0962390\pi$
$83$	5.98449	+	5.98449i	0.656883	+	0.656883i	−0.297759	+	0.954641i	$0.596239\pi$
$84$		−	2.12971i		−	0.232371i
$85$	13.7653	−	8.74813i	1.49306	−	0.948867i
$86$	−7.61240			−0.820867
$87$			3.35545i			0.359742i
$88$			0.249077i			0.0265517i
$89$	−5.37576	+	5.37576i	−0.569829	+	0.569829i	−0.932081	−	0.362251i	$-0.882008\pi$
$89$	−5.37576	+	5.37576i	−0.569829	+	0.569829i	0.362251	+	0.932081i	$0.382008\pi$
$90$	−1.88721	+	1.19936i	−0.198929	+	0.126423i
$91$	4.26754	−	4.26754i	0.447360	−	0.447360i
$92$	−8.28835			−0.864120
$93$	−2.59319			−0.268901
$94$	−2.82753	+	2.82753i	−0.291637	+	0.291637i
$95$	−1.30333	+	5.84838i	−0.133719	+	0.600031i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			5.94731i			0.603858i	0.953330	+	0.301929i	$0.0976305\pi$
$97$			5.94731i			0.603858i	−0.953330	+	0.301929i	$0.902369\pi$
$98$			2.46433i			0.248935i
$99$	0.249077			0.0250331
$100$	−2.12309	+	4.52686i	−0.212309	+	0.452686i
$101$		−	10.2985i		−	1.02474i	−0.858766	−	0.512368i	$-0.828768\pi$
$101$		−	10.2985i		−	1.02474i	0.858766	−	0.512368i	$-0.171232\pi$
$102$	−5.15765	−	5.15765i	−0.510683	−	0.510683i
$103$		−	8.34427i		−	0.822186i	−0.911594	−	0.411093i	$-0.865147\pi$
$103$		−	8.34427i		−	0.822186i	0.911594	−	0.411093i	$-0.134853\pi$
$104$	−2.83382			−0.277879
$105$	−4.01920	+	2.55428i	−0.392234	+	0.249273i
$106$	4.20587	+	4.20587i	0.408511	+	0.408511i
$107$	−2.10671	+	2.10671i	−0.203663	+	0.203663i	−0.801568	−	0.597904i	$-0.796000\pi$
$107$	−2.10671	+	2.10671i	−0.203663	+	0.203663i	0.597904	+	0.801568i	$0.296000\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$	10.6743	+	10.6743i	1.02242	+	1.02242i	0.999743	+	0.0226738i	$0.00721791\pi$
$109$	10.6743	+	10.6743i	1.02242	+	1.02242i	0.0226738	+	0.999743i	$0.492782\pi$
$110$	0.470059	−	0.298732i	0.0448183	−	0.0284829i
$111$	5.88128	−	1.55259i	0.558226	−	0.147366i
$112$	−1.50593	+	1.50593i	−0.142297	+	0.142297i
$113$			4.25290i			0.400080i	0.979788	+	0.200040i	$0.0641071\pi$
$113$			4.25290i			0.400080i	−0.979788	+	0.200040i	$0.935893\pi$
$114$	2.67964			0.250971
$115$	9.94068	+	15.6418i	0.926973	+	1.45861i
$116$	2.37266	−	2.37266i	0.220296	−	0.220296i
$117$			2.83382i			0.261986i
$118$	−6.26117	−	6.26117i	−0.576387	−	0.576387i
$119$	−10.9843	−	10.9843i	−1.00693	−	1.00693i
$120$	2.18253	+	0.486383i	0.199237	+	0.0444005i
$121$	10.9380			0.994360
$122$	−3.22008	−	3.22008i	−0.291533	−	0.291533i
$123$	−7.29960	−	7.29960i	−0.658183	−	0.658183i
$124$	1.83366	+	1.83366i	0.164668	+	0.164668i
$125$	11.0895	−	1.42262i	0.991872	−	0.127243i
$126$	1.50593	+	1.50593i	0.134159	+	0.134159i
$127$	12.5469	−	12.5469i	1.11336	−	1.11336i	0.120665	−	0.992693i	$-0.461497\pi$
$127$	12.5469	−	12.5469i	1.11336	−	1.11336i	0.992693	−	0.120665i	$-0.0385026\pi$
$128$	1.00000			0.0883883
$129$	5.38278	−	5.38278i	0.473928	−	0.473928i
$130$	3.39876	+	5.34800i	0.298091	+	0.469050i
$131$	3.81040	+	3.81040i	0.332916	+	0.332916i	0.853693	−	0.520777i	$-0.174358\pi$
$131$	3.81040	+	3.81040i	0.332916	+	0.332916i	−0.520777	+	0.853693i	$0.674358\pi$
$132$	−0.176124	−	0.176124i	−0.0153296	−	0.0153296i
$133$	5.70685			0.494847
$134$	−5.68165	−	5.68165i	−0.490820	−	0.490820i
$135$	0.486383	−	2.18253i	0.0418612	−	0.187842i
$136$			7.29402i			0.625457i
$137$	−2.72768	+	2.72768i	−0.233041	+	0.233041i	−0.813961	−	0.580920i	$-0.802693\pi$
$137$	−2.72768	+	2.72768i	−0.233041	+	0.233041i	0.580920	+	0.813961i	$0.302693\pi$
$138$	5.86075	−	5.86075i	0.498900	−	0.498900i
$139$	−2.31516			−0.196369			−0.0981847	−	0.995168i	$-0.531304\pi$
$139$	−2.31516			−0.196369			−0.0981847	+	0.995168i	$0.531304\pi$
$140$	4.64816	+	1.03586i	0.392841	+	0.0875457i
$141$		−	3.99873i		−	0.336753i
$142$	3.37315			0.283069
$143$		−	0.705838i		−	0.0590251i
$144$		−	1.00000i		−	0.0833333i
$145$	−7.32336	−	1.63203i	−0.608172	−	0.135533i
$146$	7.48228	−	7.48228i	0.619238	−	0.619238i
$147$	−1.74254	−	1.74254i	−0.143722	−	0.143722i
$148$	−5.25654	−	3.06084i	−0.432085	−	0.251600i
$149$		−	8.45695i		−	0.692821i	−0.938083	−	0.346410i	$-0.887400\pi$
$149$		−	8.45695i		−	0.692821i	0.938083	−	0.346410i	$-0.112600\pi$
$150$	−1.69973	−	4.70223i	−0.138782	−	0.383935i
$151$		−	12.3871i		−	1.00805i	−0.863690	−	0.504024i	$-0.831852\pi$
$151$		−	12.3871i		−	1.00805i	0.863690	−	0.504024i	$-0.168148\pi$
$152$	−1.89479	−	1.89479i	−0.153688	−	0.153688i
$153$	7.29402			0.589686
$154$	−0.375093	−	0.375093i	−0.0302259	−	0.0302259i
$155$	1.26128	−	5.65970i	0.101309	−	0.454598i
$156$	2.00381	−	2.00381i	0.160433	−	0.160433i
$157$	−10.3496	+	10.3496i	−0.825986	+	0.825986i	−0.986959	−	0.160973i	$-0.948537\pi$
$157$	−10.3496	+	10.3496i	−0.825986	+	0.825986i	0.160973	+	0.986959i	$0.448537\pi$
$158$	−5.99818	−	5.99818i	−0.477190	−	0.477190i
$159$	−5.94800			−0.471707
$160$	−1.19936	−	1.88721i	−0.0948174	−	0.149197i
$161$	12.4817	−	12.4817i	0.983696	−	0.983696i
$162$	−1.00000			−0.0785674
$163$		−	8.69039i		−	0.680684i	−0.940302	−	0.340342i	$-0.889457\pi$
$163$		−	8.69039i		−	0.680684i	0.940302	−	0.340342i	$-0.110543\pi$
$164$			10.3232i			0.806106i
$165$	−0.121147	+	0.543617i	−0.00943125	+	0.0423205i
$166$	5.98449	+	5.98449i	0.464486	+	0.464486i
$167$			18.5233i			1.43337i	0.697395	+	0.716687i	$0.254342\pi$
$167$			18.5233i			1.43337i	−0.697395	+	0.716687i	$0.745658\pi$
$168$		−	2.12971i		−	0.164311i
$169$	−4.96948			−0.382268
$170$	13.7653	−	8.74813i	1.05575	−	0.670951i
$171$	−1.89479	+	1.89479i	−0.144898	+	0.144898i
$172$	−7.61240			−0.580440
$173$	−6.60085	+	6.60085i	−0.501854	+	0.501854i	−0.912014	−	0.410160i	$-0.865473\pi$
$173$	−6.60085	+	6.60085i	−0.501854	+	0.501854i	0.410160	+	0.912014i	$0.365473\pi$
$174$			3.35545i			0.254376i
$175$	−3.61993	−	10.0144i	−0.273641	−	0.757017i
$176$			0.249077i			0.0187749i
$177$	8.85463			0.665555
$178$	−5.37576	+	5.37576i	−0.402930	+	0.402930i
$179$	−11.1031	+	11.1031i	−0.829883	+	0.829883i	−0.987500	−	0.157617i	$-0.949619\pi$
$179$	−11.1031	+	11.1031i	−0.829883	+	0.829883i	0.157617	+	0.987500i	$0.449619\pi$
$180$	−1.88721	+	1.19936i	−0.140664	+	0.0893947i
$181$	19.1102			1.42045			0.710223	−	0.703977i	$-0.248594\pi$
$181$	19.1102			1.42045			0.710223	+	0.703977i	$0.248594\pi$
$182$	4.26754	−	4.26754i	0.316331	−	0.316331i
$183$	4.55389			0.336633
$184$	−8.28835			−0.611025
$185$	0.528025	+	13.5912i	0.0388211	+	0.999246i
$186$	−2.59319			−0.190142
$187$	−1.81677			−0.132855
$188$	−2.82753	+	2.82753i	−0.206219	+	0.206219i
$189$	−2.12971			−0.154914
$190$	−1.30333	+	5.84838i	−0.0945534	+	0.424286i
$191$	−4.13848	+	4.13848i	−0.299450	+	0.299450i	−0.840798	−	0.541349i	$-0.817914\pi$
$191$	−4.13848	+	4.13848i	−0.299450	+	0.299450i	0.541349	+	0.840798i	$0.317914\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	−1.65600			−0.119201			−0.0596007	−	0.998222i	$-0.518983\pi$
$193$	−1.65600			−0.119201			−0.0596007	+	0.998222i	$0.518983\pi$
$194$			5.94731i			0.426992i
$195$	−6.18489	−	1.37832i	−0.442909	−	0.0987035i
$196$			2.46433i			0.176023i
$197$	14.1878	−	14.1878i	1.01084	−	1.01084i	0.0108958	−	0.999941i	$-0.496532\pi$
$197$	14.1878	−	14.1878i	1.01084	−	1.01084i	0.999941	−	0.0108958i	$-0.00346830\pi$
$198$	0.249077			0.0177011
$199$	3.69181	−	3.69181i	0.261705	−	0.261705i	−0.564041	−	0.825747i	$-0.690754\pi$
$199$	3.69181	−	3.69181i	0.261705	−	0.261705i	0.825747	+	0.564041i	$0.190754\pi$
$200$	−2.12309	+	4.52686i	−0.150125	+	0.320098i
$201$	8.03506			0.566750
$202$		−	10.2985i		−	0.724598i
$203$			7.14614i			0.501561i
$204$	−5.15765	−	5.15765i	−0.361108	−	0.361108i
$205$	19.4820	−	12.3812i	1.36068	−	0.864740i
$206$		−	8.34427i		−	0.581373i
$207$			8.28835i			0.576080i
$208$	−2.83382			−0.196490
$209$	0.471948	−	0.471948i	0.0326453	−	0.0326453i
$210$	−4.01920	+	2.55428i	−0.277351	+	0.176262i
$211$	−8.15505			−0.561417			−0.280708	−	0.959793i	$-0.590569\pi$
$211$	−8.15505			−0.561417			−0.280708	+	0.959793i	$0.590569\pi$
$212$	4.20587	+	4.20587i	0.288861	+	0.288861i
$213$	−2.38518	+	2.38518i	−0.163430	+	0.163430i
$214$	−2.10671	+	2.10671i	−0.144012	+	0.144012i
$215$	9.12998	+	14.3662i	0.622660	+	0.979765i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−5.52274			−0.374908
$218$	10.6743	+	10.6743i	0.722958	+	0.722958i
$219$			10.5815i			0.715034i
$220$	0.470059	−	0.298732i	0.0316914	−	0.0201405i
$221$		−	20.6699i		−	1.39041i
$222$	5.88128	−	1.55259i	0.394726	−	0.104203i
$223$	18.0980	+	18.0980i	1.21193	+	1.21193i	0.970390	+	0.241543i	$0.0776536\pi$
$223$	18.0980	+	18.0980i	1.21193	+	1.21193i	0.241543	+	0.970390i	$0.422346\pi$
$224$	−1.50593	+	1.50593i	−0.100619	+	0.100619i
$225$	4.52686	+	2.12309i	0.301791	+	0.141539i
$226$			4.25290i			0.282899i
$227$			15.2040i			1.00913i	0.863375	+	0.504563i	$0.168346\pi$
$227$			15.2040i			1.00913i	−0.863375	+	0.504563i	$0.831654\pi$
$228$	2.67964			0.177463
$229$			22.1160i			1.46147i	0.682662	+	0.730735i	$0.260822\pi$
$229$			22.1160i			1.46147i	−0.682662	+	0.730735i	$0.739178\pi$
$230$	9.94068	+	15.6418i	0.655469	+	1.03139i
$231$	0.530462			0.0349018
$232$	2.37266	−	2.37266i	0.155773	−	0.155773i
$233$	4.77285	−	4.77285i	0.312680	−	0.312680i	−0.533267	−	0.845947i	$-0.679036\pi$
$233$	4.77285	−	4.77285i	0.312680	−	0.312680i	0.845947	+	0.533267i	$0.179036\pi$
$234$			2.83382i			0.185252i
$235$	8.72733	+	1.94491i	0.569308	+	0.126872i
$236$	−6.26117	−	6.26117i	−0.407567	−	0.407567i
$237$	8.48271			0.551011
$238$	−10.9843	−	10.9843i	−0.712007	−	0.712007i
$239$	−19.8498	−	19.8498i	−1.28398	−	1.28398i	−0.938385	−	0.345593i	$-0.887678\pi$
$239$	−19.8498	−	19.8498i	−1.28398	−	1.28398i	−0.345593	−	0.938385i	$-0.612322\pi$
$240$	2.18253	+	0.486383i	0.140882	+	0.0313959i
$241$	21.3229	−	21.3229i	1.37353	−	1.37353i	0.518380	−	0.855150i	$-0.326535\pi$
$241$	21.3229	−	21.3229i	1.37353	−	1.37353i	0.855150	−	0.518380i	$-0.173465\pi$
$242$	10.9380			0.703119
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−3.22008	−	3.22008i	−0.206145	−	0.206145i
$245$	4.65069	−	2.95561i	0.297122	−	0.188827i
$246$	−7.29960	−	7.29960i	−0.465405	−	0.465405i
$247$	5.36948	+	5.36948i	0.341652	+	0.341652i
$248$	1.83366	+	1.83366i	0.116438	+	0.116438i
$249$	−8.46334			−0.536342
$250$	11.0895	−	1.42262i	0.701359	−	0.0899742i
$251$	14.6439	+	14.6439i	0.924315	+	0.924315i	0.997331	−	0.0730156i	$-0.0232623\pi$
$251$	14.6439	+	14.6439i	0.924315	+	0.924315i	−0.0730156	+	0.997331i	$0.523262\pi$
$252$	1.50593	+	1.50593i	0.0948649	+	0.0948649i
$253$		−	2.06443i		−	0.129790i
$254$	12.5469	−	12.5469i	0.787263	−	0.787263i
$255$	−3.54768	+	15.9194i	−0.222165	+	0.996912i
$256$	1.00000			0.0625000
$257$		−	17.8930i		−	1.11614i	−0.829795	−	0.558069i	$-0.811543\pi$
$257$		−	17.8930i		−	1.11614i	0.829795	−	0.558069i	$-0.188457\pi$
$258$	5.38278	−	5.38278i	0.335117	−	0.335117i
$259$	12.5254	−	3.30658i	0.778293	−	0.205461i
$260$	3.39876	+	5.34800i	0.210782	+	0.331669i
$261$	−2.37266	−	2.37266i	−0.146864	−	0.146864i
$262$	3.81040	+	3.81040i	0.235407	+	0.235407i
$263$	−21.7610	+	21.7610i	−1.34184	+	1.34184i	−0.447617	+	0.894225i	$0.647727\pi$
$263$	−21.7610	+	21.7610i	−1.34184	+	1.34184i	−0.894225	+	0.447617i	$0.852273\pi$
$264$	−0.176124	−	0.176124i	−0.0108397	−	0.0108397i
$265$	2.89301	−	12.9817i	0.177716	−	0.797459i
$266$	5.70685			0.349910
$267$		−	7.60247i		−	0.465264i
$268$	−5.68165	−	5.68165i	−0.347062	−	0.347062i
$269$		−	17.8478i		−	1.08820i	−0.839020	−	0.544101i	$-0.816871\pi$
$269$		−	17.8478i		−	1.08820i	0.839020	−	0.544101i	$-0.183129\pi$
$270$	0.486383	−	2.18253i	0.0296003	−	0.132824i
$271$	2.29360			0.139327			0.0696633	−	0.997571i	$-0.477808\pi$
$271$	2.29360			0.139327			0.0696633	+	0.997571i	$0.477808\pi$
$272$			7.29402i			0.442265i
$273$			6.03521i			0.365268i
$274$	−2.72768	+	2.72768i	−0.164785	+	0.164785i
$275$	−1.12754	−	0.528812i	−0.0679930	−	0.0318886i
$276$	5.86075	−	5.86075i	0.352776	−	0.352776i
$277$	1.48608			0.0892897			0.0446448	−	0.999003i	$-0.485784\pi$
$277$	1.48608			0.0892897			0.0446448	+	0.999003i	$0.485784\pi$
$278$	−2.31516			−0.138854
$279$	1.83366	−	1.83366i	0.109778	−	0.109778i
$280$	4.64816	+	1.03586i	0.277781	+	0.0619042i
$281$	−18.5876	+	18.5876i	−1.10884	+	1.10884i	−0.115541	+	0.993303i	$0.536860\pi$
$281$	−18.5876	+	18.5876i	−1.10884	+	1.10884i	−0.993303	+	0.115541i	$0.963140\pi$
$282$		−	3.99873i		−	0.238121i
$283$		−	16.6153i		−	0.987676i	−0.869554	−	0.493838i	$-0.835594\pi$
$283$		−	16.6153i		−	0.987676i	0.869554	−	0.493838i	$-0.164406\pi$
$284$	3.37315			0.200160
$285$	−3.21384	−	5.05702i	−0.190371	−	0.299552i
$286$		−	0.705838i		−	0.0417371i
$287$	−15.5460	−	15.5460i	−0.917654	−	0.917654i
$288$		−	1.00000i		−	0.0589256i
$289$	−36.2027			−2.12957
$290$	−7.32336	−	1.63203i	−0.430043	−	0.0958362i
$291$	−4.20538	−	4.20538i	−0.246524	−	0.246524i
$292$	7.48228	−	7.48228i	0.437867	−	0.437867i
$293$	9.37884	+	9.37884i	0.547918	+	0.547918i	0.925838	−	0.377920i	$-0.123361\pi$
$293$	9.37884	+	9.37884i	0.547918	+	0.547918i	−0.377920	+	0.925838i	$0.623361\pi$
$294$	−1.74254	−	1.74254i	−0.101627	−	0.101627i
$295$	−4.30674	+	19.3255i	−0.250748	+	1.12517i
$296$	−5.25654	−	3.06084i	−0.305530	−	0.177908i
$297$	−0.176124	+	0.176124i	−0.0102197	+	0.0102197i
$298$		−	8.45695i		−	0.489898i
$299$	23.4877			1.35833
$300$	−1.69973	−	4.70223i	−0.0981337	−	0.271483i
$301$	11.4638	−	11.4638i	0.660761	−	0.660761i
$302$		−	12.3871i		−	0.712797i
$303$	7.28212	+	7.28212i	0.418347	+	0.418347i
$304$	−1.89479	−	1.89479i	−0.108674	−	0.108674i
$305$	−2.21493	+	9.93899i	−0.126827	+	0.569105i
$306$	7.29402			0.416971
$307$	−3.36862	−	3.36862i	−0.192258	−	0.192258i	0.604413	−	0.796671i	$-0.293408\pi$
$307$	−3.36862	−	3.36862i	−0.192258	−	0.192258i	−0.796671	+	0.604413i	$0.793408\pi$
$308$	−0.375093	−	0.375093i	−0.0213729	−	0.0213729i
$309$	5.90029	+	5.90029i	0.335656	+	0.335656i
$310$	1.26128	−	5.65970i	0.0716360	−	0.321450i
$311$	22.4334	+	22.4334i	1.27208	+	1.27208i	0.944994	+	0.327087i	$0.106067\pi$
$311$	22.4334	+	22.4334i	1.27208	+	1.27208i	0.327087	+	0.944994i	$0.393933\pi$
$312$	2.00381	−	2.00381i	0.113443	−	0.113443i
$313$	−19.2752			−1.08950			−0.544750	−	0.838599i	$-0.683375\pi$
$313$	−19.2752			−1.08950			−0.544750	+	0.838599i	$0.683375\pi$
$314$	−10.3496	+	10.3496i	−0.584060	+	0.584060i
$315$	1.03586	−	4.64816i	0.0583638	−	0.261894i
$316$	−5.99818	−	5.99818i	−0.337424	−	0.337424i
$317$	3.94817	+	3.94817i	0.221751	+	0.221751i	0.809236	−	0.587484i	$-0.199882\pi$
$317$	3.94817	+	3.94817i	0.221751	+	0.221751i	−0.587484	+	0.809236i	$0.699882\pi$
$318$	−5.94800			−0.333548
$319$	0.590974	+	0.590974i	0.0330882	+	0.0330882i
$320$	−1.19936	−	1.88721i	−0.0670461	−	0.105498i
$321$		−	2.97934i		−	0.166291i
$322$	12.4817	−	12.4817i	0.695578	−	0.695578i
$323$	13.8206	−	13.8206i	0.769000	−	0.769000i
$324$	−1.00000			−0.0555556
$325$	6.01645	−	12.8283i	0.333732	−	0.711586i
$326$		−	8.69039i		−	0.481316i
$327$	−15.0958			−0.834800
$328$			10.3232i			0.570003i
$329$		−	8.51613i		−	0.469510i
$330$	−0.121147	+	0.543617i	−0.00666890	+	0.0299251i
$331$	−2.89997	+	2.89997i	−0.159397	+	0.159397i	−0.782299	−	0.622902i	$-0.785953\pi$
$331$	−2.89997	+	2.89997i	−0.159397	+	0.159397i	0.622902	+	0.782299i	$0.285953\pi$
$332$	5.98449	+	5.98449i	0.328441	+	0.328441i
$333$	−3.06084	+	5.25654i	−0.167733	+	0.288057i
$334$			18.5233i			1.01355i
$335$	−3.90812	+	17.5368i	−0.213523	+	0.958135i
$336$		−	2.12971i		−	0.116185i
$337$	1.55976	+	1.55976i	0.0849654	+	0.0849654i	0.748312	−	0.663347i	$-0.230865\pi$
$337$	1.55976	+	1.55976i	0.0849654	+	0.0849654i	−0.663347	+	0.748312i	$0.730865\pi$
$338$	−4.96948			−0.270304
$339$	−3.00726	−	3.00726i	−0.163332	−	0.163332i
$340$	13.7653	−	8.74813i	0.746529	−	0.474434i
$341$	−0.456722	+	0.456722i	−0.0247329	+	0.0247329i
$342$	−1.89479	+	1.89479i	−0.102458	+	0.102458i
$343$	−14.2526	−	14.2526i	−0.769571	−	0.769571i
$344$	−7.61240			−0.410433
$345$	−18.0896	−	4.03131i	−0.973909	−	0.217038i
$346$	−6.60085	+	6.60085i	−0.354864	+	0.354864i
$347$	−9.43617			−0.506560			−0.253280	−	0.967393i	$-0.581509\pi$
$347$	−9.43617			−0.506560			−0.253280	+	0.967393i	$0.581509\pi$
$348$			3.35545i			0.179871i
$349$		−	7.25908i		−	0.388569i	−0.980945	−	0.194285i	$-0.937761\pi$
$349$		−	7.25908i		−	0.388569i	0.980945	−	0.194285i	$-0.0622386\pi$
$350$	−3.61993	−	10.0144i	−0.193493	−	0.535292i
$351$	−2.00381	−	2.00381i	−0.106956	−	0.106956i
$352$			0.249077i			0.0132758i
$353$		−	6.63465i		−	0.353127i	−0.984289	−	0.176563i	$-0.943502\pi$
$353$		−	6.63465i		−	0.353127i	0.984289	−	0.176563i	$-0.0564981\pi$
$354$	8.85463			0.470618
$355$	−4.04561	−	6.36583i	−0.214719	−	0.337863i
$356$	−5.37576	+	5.37576i	−0.284915	+	0.284915i
$357$	15.5342			0.822155
$358$	−11.1031	+	11.1031i	−0.586816	+	0.586816i
$359$			3.64712i			0.192488i	0.995358	+	0.0962438i	$0.0306828\pi$
$359$			3.64712i			0.192488i	−0.995358	+	0.0962438i	$0.969317\pi$
$360$	−1.88721	+	1.19936i	−0.0994645	+	0.0632116i
$361$		−	11.8196i		−	0.622082i
$362$	19.1102			1.00441
$363$	−7.73431	+	7.73431i	−0.405946	+	0.405946i
$364$	4.26754	−	4.26754i	0.223680	−	0.223680i
$365$	−23.0945	−	5.14668i	−1.20882	−	0.269390i
$366$	4.55389			0.238036
$367$	−2.67398	+	2.67398i	−0.139580	+	0.139580i	−0.773444	−	0.633864i	$-0.781468\pi$
$367$	−2.67398	+	2.67398i	−0.139580	+	0.139580i	0.633864	+	0.773444i	$0.281468\pi$
$368$	−8.28835			−0.432060
$369$	10.3232			0.537404
$370$	0.528025	+	13.5912i	0.0274507	+	0.706574i
$371$	−12.6675			−0.657666
$372$	−2.59319			−0.134450
$373$	−8.22916	+	8.22916i	−0.426090	+	0.426090i	−0.887294	−	0.461204i	$-0.847418\pi$
$373$	−8.22916	+	8.22916i	−0.426090	+	0.426090i	0.461204	+	0.887294i	$0.347418\pi$
$374$	−1.81677			−0.0939429
$375$	−6.83549	+	8.84738i	−0.352983	+	0.456877i
$376$	−2.82753	+	2.82753i	−0.145819	+	0.145819i
$377$	−6.72369	+	6.72369i	−0.346287	+	0.346287i
$378$	−2.12971			−0.109541
$379$		−	23.2988i		−	1.19678i	−0.801206	−	0.598389i	$-0.795808\pi$
$379$		−	23.2988i		−	1.19678i	0.801206	−	0.598389i	$-0.204192\pi$
$380$	−1.30333	+	5.84838i	−0.0668593	+	0.300016i
$381$			17.7440i			0.909053i
$382$	−4.13848	+	4.13848i	−0.211743	+	0.211743i
$383$	1.82589			0.0932984			0.0466492	−	0.998911i	$-0.485146\pi$
$383$	1.82589			0.0932984			0.0466492	+	0.998911i	$0.485146\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−0.258007	+	1.15775i	−0.0131493	+	0.0590043i
$386$	−1.65600			−0.0842881
$387$			7.61240i			0.386960i
$388$			5.94731i			0.301929i
$389$	−1.87840	−	1.87840i	−0.0952388	−	0.0952388i	0.657882	−	0.753121i	$-0.271453\pi$
$389$	−1.87840	−	1.87840i	−0.0952388	−	0.0952388i	−0.753121	+	0.657882i	$0.771453\pi$
$390$	−6.18489	−	1.37832i	−0.313184	−	0.0697939i
$391$		−	60.4554i		−	3.05736i
$392$			2.46433i			0.124467i
$393$	−5.38872			−0.271825
$394$	14.1878	−	14.1878i	0.714769	−	0.714769i
$395$	−4.12584	+	18.5138i	−0.207594	+	0.931528i
$396$	0.249077			0.0125166
$397$	−12.0046	−	12.0046i	−0.602492	−	0.602492i	0.338481	−	0.940973i	$-0.390087\pi$
$397$	−12.0046	−	12.0046i	−0.602492	−	0.602492i	−0.940973	+	0.338481i	$0.890087\pi$
$398$	3.69181	−	3.69181i	0.185054	−	0.185054i
$399$	−4.03535	+	4.03535i	−0.202020	+	0.202020i
$400$	−2.12309	+	4.52686i	−0.106154	+	0.226343i
$401$	−23.2046	−	23.2046i	−1.15878	−	1.15878i	−0.984738	−	0.174043i	$-0.944317\pi$
$401$	−23.2046	−	23.2046i	−1.15878	−	1.15878i	−0.174043	−	0.984738i	$-0.555683\pi$
$402$	8.03506			0.400753
$403$	−5.19626	−	5.19626i	−0.258844	−	0.258844i
$404$		−	10.2985i		−	0.512368i
$405$	1.19936	+	1.88721i	0.0595965	+	0.0937760i
$406$			7.14614i			0.354657i
$407$	0.762385	−	1.30928i	0.0377900	−	0.0648987i
$408$	−5.15765	−	5.15765i	−0.255342	−	0.255342i
$409$	−12.7469	+	12.7469i	−0.630292	+	0.630292i	−0.948141	−	0.317850i	$-0.897039\pi$
$409$	−12.7469	+	12.7469i	−0.630292	+	0.630292i	0.317850	+	0.948141i	$0.397039\pi$
$410$	19.4820	−	12.3812i	0.962147	−	0.611463i
$411$		−	3.85752i		−	0.190278i
$412$		−	8.34427i		−	0.411093i
$413$	18.8578			0.927932
$414$			8.28835i			0.407350i
$415$	4.11642	−	18.4715i	0.202067	−	0.906729i
$416$	−2.83382			−0.138939
$417$	1.63707	−	1.63707i	0.0801675	−	0.0801675i
$418$	0.471948	−	0.471948i	0.0230837	−	0.0230837i
$419$			22.1539i			1.08229i	0.840929	+	0.541145i	$0.182009\pi$
$419$			22.1539i			1.08229i	−0.840929	+	0.541145i	$0.817991\pi$
$420$	−4.01920	+	2.55428i	−0.196117	+	0.124636i
$421$	−18.3106	−	18.3106i	−0.892404	−	0.892404i	0.102345	−	0.994749i	$-0.467365\pi$
$421$	−18.3106	−	18.3106i	−0.892404	−	0.892404i	−0.994749	+	0.102345i	$0.967365\pi$
$422$	−8.15505			−0.396981
$423$	2.82753	+	2.82753i	0.137479	+	0.137479i
$424$	4.20587	+	4.20587i	0.204255	+	0.204255i
$425$	−33.0190	−	15.4858i	−1.60166	−	0.751174i
$426$	−2.38518	+	2.38518i	−0.115562	+	0.115562i
$427$	9.69847			0.469342
$428$	−2.10671	+	2.10671i	−0.101832	+	0.101832i
$429$	0.499103	+	0.499103i	0.0240969	+	0.0240969i
$430$	9.12998	+	14.3662i	0.440287	+	0.692798i
$431$	−8.32782	−	8.32782i	−0.401137	−	0.401137i	0.477497	−	0.878634i	$-0.341544\pi$
$431$	−8.32782	−	8.32782i	−0.401137	−	0.401137i	−0.878634	+	0.477497i	$0.841544\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−6.11268	−	6.11268i	−0.293757	−	0.293757i	0.544806	−	0.838562i	$-0.316603\pi$
$433$	−6.11268	−	6.11268i	−0.293757	−	0.293757i	−0.838562	+	0.544806i	$0.816603\pi$
$434$	−5.52274			−0.265100
$435$	6.33242	−	4.02438i	0.303616	−	0.192954i
$436$	10.6743	+	10.6743i	0.511208	+	0.511208i
$437$	15.7047	+	15.7047i	0.751256	+	0.751256i
$438$			10.5815i			0.505606i
$439$	−16.2052	+	16.2052i	−0.773431	+	0.773431i	−0.978705	−	0.205273i	$-0.934192\pi$
$439$	−16.2052	+	16.2052i	−0.773431	+	0.773431i	0.205273	+	0.978705i	$0.434192\pi$
$440$	0.470059	−	0.298732i	0.0224092	−	0.0142415i
$441$	2.46433			0.117349
$442$		−	20.6699i		−	0.983167i
$443$	6.30399	−	6.30399i	0.299512	−	0.299512i	−0.541311	−	0.840823i	$-0.682072\pi$
$443$	6.30399	−	6.30399i	0.299512	−	0.299512i	0.840823	+	0.541311i	$0.182072\pi$
$444$	5.88128	−	1.55259i	0.279113	−	0.0736828i
$445$	16.5926	+	3.69771i	0.786565	+	0.175288i
$446$	18.0980	+	18.0980i	0.856966	+	0.856966i
$447$	5.97997	+	5.97997i	0.282843	+	0.282843i
$448$	−1.50593	+	1.50593i	−0.0711487	+	0.0711487i
$449$	19.8634	+	19.8634i	0.937412	+	0.937412i	0.998154	−	0.0607412i	$-0.0193464\pi$
$449$	19.8634	+	19.8634i	0.937412	+	0.937412i	−0.0607412	+	0.998154i	$0.519346\pi$
$450$	4.52686	+	2.12309i	0.213398	+	0.100083i
$451$	−2.57127			−0.121076
$452$			4.25290i			0.200040i
$453$	8.75900	+	8.75900i	0.411534	+	0.411534i
$454$			15.2040i			0.713560i
$455$	−13.1720	−	2.93542i	−0.617514	−	0.137615i
$456$	2.67964			0.125485
$457$			40.2606i			1.88331i	0.336575	+	0.941657i	$0.390731\pi$
$457$			40.2606i			1.88331i	−0.336575	+	0.941657i	$0.609269\pi$
$458$			22.1160i			1.03341i
$459$	−5.15765	+	5.15765i	−0.240738	+	0.240738i
$460$	9.94068	+	15.6418i	0.463487	+	0.729303i
$461$	−15.0948	+	15.0948i	−0.703036	+	0.703036i	−0.965061	−	0.262025i	$-0.915610\pi$
$461$	−15.0948	+	15.0948i	−0.703036	+	0.703036i	0.262025	+	0.965061i	$0.415610\pi$
$462$	0.530462			0.0246793
$463$	−25.5478			−1.18730			−0.593652	−	0.804722i	$-0.702315\pi$
$463$	−25.5478			−1.18730			−0.593652	+	0.804722i	$0.702315\pi$
$464$	2.37266	−	2.37266i	0.110148	−	0.110148i
$465$	3.11015	+	4.89388i	0.144230	+	0.226948i
$466$	4.77285	−	4.77285i	0.221098	−	0.221098i
$467$			30.7343i			1.42221i	0.703085	+	0.711106i	$0.251805\pi$
$467$			30.7343i			1.42221i	−0.703085	+	0.711106i	$0.748195\pi$
$468$			2.83382i			0.130993i
$469$	17.1124			0.790176
$470$	8.72733	+	1.94491i	0.402562	+	0.0897121i
$471$		−	14.6365i		−	0.674415i
$472$	−6.26117	−	6.26117i	−0.288194	−	0.288194i
$473$		−	1.89607i		−	0.0871815i
$474$	8.48271			0.389624
$475$	12.6003	−	4.55464i	0.578139	−	0.208981i
$476$	−10.9843	−	10.9843i	−0.503465	−	0.503465i
$477$	4.20587	−	4.20587i	0.192574	−	0.192574i
$478$	−19.8498	−	19.8498i	−0.907909	−	0.907909i
$479$	0.00977229	+	0.00977229i	0.000446507	+	0.000446507i	0.707330	−	0.706883i	$-0.249900\pi$
$479$	0.00977229	+	0.00977229i	0.000446507	+	0.000446507i	−0.706883	+	0.707330i	$0.749900\pi$
$480$	2.18253	+	0.486383i	0.0996184	+	0.0222002i
$481$	14.8961	+	8.67387i	0.679203	+	0.395495i
$482$	21.3229	−	21.3229i	0.971233	−	0.971233i
$483$			17.6518i			0.803184i
$484$	10.9380			0.497180
$485$	11.2238	−	7.13294i	0.509646	−	0.323890i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$			0.0126739i			0.000574311i	1.00000		0.000287155i	$9.14044e-5\pi$
$487$			0.0126739i			0.000574311i	−1.00000		0.000287155i	$0.999909\pi$
$488$	−3.22008	−	3.22008i	−0.145766	−	0.145766i
$489$	6.14503	+	6.14503i	0.277888	+	0.277888i
$490$	4.65069	−	2.95561i	0.210097	−	0.133521i
$491$	24.8512			1.12152			0.560760	−	0.827979i	$-0.310509\pi$
$491$	24.8512			1.12152			0.560760	+	0.827979i	$0.310509\pi$
$492$	−7.29960	−	7.29960i	−0.329091	−	0.329091i
$493$	17.3062	+	17.3062i	0.779433	+	0.779433i
$494$	5.36948	+	5.36948i	0.241584	+	0.241584i
$495$	−0.298732	−	0.470059i	−0.0134270	−	0.0211276i
$496$	1.83366	+	1.83366i	0.0823338	+	0.0823338i
$497$	−5.07975	+	5.07975i	−0.227858	+	0.227858i
$498$	−8.46334			−0.379251
$499$	−30.1549	+	30.1549i	−1.34992	+	1.34992i	−0.464175	+	0.885744i	$0.653649\pi$
$499$	−30.1549	+	30.1549i	−1.34992	+	1.34992i	−0.885744	+	0.464175i	$0.846351\pi$
$500$	11.0895	−	1.42262i	0.495936	−	0.0636214i
$501$	−13.0979	−	13.0979i	−0.585172	−	0.585172i
$502$	14.6439	+	14.6439i	0.653590	+	0.653590i
$503$	−33.2862			−1.48416			−0.742080	−	0.670312i	$-0.766160\pi$
$503$	−33.2862			−1.48416			−0.742080	+	0.670312i	$0.766160\pi$
$504$	1.50593	+	1.50593i	0.0670796	+	0.0670796i
$505$	−19.4353	+	12.3515i	−0.864861	+	0.549636i
$506$		−	2.06443i		−	0.0917753i
$507$	3.51395	−	3.51395i	0.156060	−	0.156060i
$508$	12.5469	−	12.5469i	0.556679	−	0.556679i
$509$	−35.6979			−1.58228			−0.791140	−	0.611635i	$-0.790512\pi$
$509$	−35.6979			−1.58228			−0.791140	+	0.611635i	$0.790512\pi$
$510$	−3.54768	+	15.9194i	−0.157094	+	0.704923i
$511$			22.5356i			0.996918i
$512$	1.00000			0.0441942
$513$		−	2.67964i		−	0.118309i
$514$		−	17.8930i		−	0.789228i
$515$	−15.7474	+	10.0078i	−0.693911	+	0.440994i
$516$	5.38278	−	5.38278i	0.236964	−	0.236964i
$517$	−0.704271	−	0.704271i	−0.0309738	−	0.0309738i
$518$	12.5254	−	3.30658i	0.550336	−	0.145283i
$519$		−	9.33502i		−	0.409762i
$520$	3.39876	+	5.34800i	0.149045	+	0.234525i
$521$			0.701242i			0.0307220i	0.999882	+	0.0153610i	$0.00488975\pi$
$521$			0.701242i			0.0307220i	−0.999882	+	0.0153610i	$0.995110\pi$
$522$	−2.37266	−	2.37266i	−0.103849	−	0.103849i
$523$	−35.1652			−1.53767			−0.768833	−	0.639449i	$-0.779162\pi$
$523$	−35.1652			−1.53767			−0.768833	+	0.639449i	$0.779162\pi$
$524$	3.81040	+	3.81040i	0.166458	+	0.166458i
$525$	9.64092	+	4.52157i	0.420764	+	0.197337i
$526$	−21.7610	+	21.7610i	−0.948826	+	0.948826i
$527$	−13.3747	+	13.3747i	−0.582613	+	0.582613i
$528$	−0.176124	−	0.176124i	−0.00766480	−	0.00766480i
$529$	45.6967			1.98681
$530$	2.89301	−	12.9817i	0.125664	−	0.563889i
$531$	−6.26117	+	6.26117i	−0.271712	+	0.271712i
$532$	5.70685			0.247423
$533$		−	29.2540i		−	1.26713i
$534$		−	7.60247i		−	0.328991i
$535$	6.50250	+	1.44910i	0.281127	+	0.0626500i
$536$	−5.68165	−	5.68165i	−0.245410	−	0.245410i
$537$		−	15.7021i		−	0.677597i
$538$		−	17.8478i		−	0.769475i
$539$	−0.613806			−0.0264385
$540$	0.486383	−	2.18253i	0.0209306	−	0.0939211i
$541$	−5.47295	+	5.47295i	−0.235300	+	0.235300i	−0.814901	−	0.579600i	$-0.803209\pi$
$541$	−5.47295	+	5.47295i	−0.235300	+	0.235300i	0.579600	+	0.814901i	$0.303209\pi$
$542$	2.29360			0.0985188
$543$	−13.5129	+	13.5129i	−0.579895	+	0.579895i
$544$			7.29402i			0.312728i
$545$	7.34234	−	32.9470i	0.314511	−	1.41130i
$546$			6.03521i			0.258283i
$547$	14.4568			0.618127			0.309064	−	0.951041i	$-0.399984\pi$
$547$	14.4568			0.618127			0.309064	+	0.951041i	$0.399984\pi$
$548$	−2.72768	+	2.72768i	−0.116521	+	0.116521i
$549$	−3.22008	+	3.22008i	−0.137430	+	0.137430i
$550$	−1.12754	−	0.528812i	−0.0480783	−	0.0225486i
$551$	−8.99138			−0.383046
$552$	5.86075	−	5.86075i	0.249450	−	0.249450i
$553$	18.0657			0.768233
$554$	1.48608			0.0631373
$555$	−9.98381	−	9.23707i	−0.423789	−	0.392092i
$556$	−2.31516			−0.0981847
$557$	16.2684			0.689316			0.344658	−	0.938728i	$-0.387995\pi$
$557$	16.2684			0.689316			0.344658	+	0.938728i	$0.387995\pi$
$558$	1.83366	−	1.83366i	0.0776250	−	0.0776250i
$559$	21.5722			0.912405
$560$	4.64816	+	1.03586i	0.196421	+	0.0437729i
$561$	1.28465	−	1.28465i	0.0542380	−	0.0542380i
$562$	−18.5876	+	18.5876i	−0.784071	+	0.784071i
$563$	6.03926			0.254525			0.127262	−	0.991869i	$-0.459381\pi$
$563$	6.03926			0.254525			0.127262	+	0.991869i	$0.459381\pi$
$564$		−	3.99873i		−	0.168377i
$565$	8.02610	−	5.10075i	0.337661	−	0.214590i
$566$		−	16.6153i		−	0.698392i
$567$	1.50593	−	1.50593i	0.0632433	−	0.0632433i
$568$	3.37315			0.141534
$569$	13.8974	−	13.8974i	0.582609	−	0.582609i	−0.353010	−	0.935620i	$-0.614842\pi$
$569$	13.8974	−	13.8974i	0.582609	−	0.582609i	0.935620	+	0.353010i	$0.114842\pi$
$570$	−3.21384	−	5.05702i	−0.134613	−	0.211815i
$571$	−28.3787			−1.18761			−0.593805	−	0.804609i	$-0.702375\pi$
$571$	−28.3787			−1.18761			−0.593805	+	0.804609i	$0.702375\pi$
$572$		−	0.705838i		−	0.0295126i
$573$		−	5.85269i		−	0.244500i
$574$	−15.5460	−	15.5460i	−0.648879	−	0.648879i
$575$	17.5969	−	37.5202i	0.733841	−	1.56470i
$576$		−	1.00000i		−	0.0416667i
$577$			35.3160i			1.47023i	0.677945	+	0.735113i	$0.262871\pi$
$577$			35.3160i			1.47023i	−0.677945	+	0.735113i	$0.737129\pi$
$578$	−36.2027			−1.50583
$579$	1.17097	−	1.17097i	0.0486638	−	0.0486638i
$580$	−7.32336	−	1.63203i	−0.304086	−	0.0677665i
$581$	−18.0245			−0.747781
$582$	−4.20538	−	4.20538i	−0.174319	−	0.174319i
$583$	−1.04759	+	1.04759i	−0.0433865	+	0.0433865i
$584$	7.48228	−	7.48228i	0.309619	−	0.309619i
$585$	5.34800	−	3.39876i	0.221112	−	0.140521i
$586$	9.37884	+	9.37884i	0.387436	+	0.387436i
$587$	−33.3247			−1.37546			−0.687729	−	0.725968i	$-0.741392\pi$
$587$	−33.3247			−1.37546			−0.687729	+	0.725968i	$0.741392\pi$
$588$	−1.74254	−	1.74254i	−0.0718612	−	0.0718612i
$589$		−	6.94879i		−	0.286320i
$590$	−4.30674	+	19.3255i	−0.177306	+	0.795617i
$591$			20.0645i			0.825344i
$592$	−5.25654	−	3.06084i	−0.216043	−	0.125800i
$593$	29.5804	+	29.5804i	1.21472	+	1.21472i	0.969456	+	0.245266i	$0.0788753\pi$
$593$	29.5804	+	29.5804i	1.21472	+	1.21472i	0.245266	+	0.969456i	$0.421125\pi$
$594$	−0.176124	+	0.176124i	−0.00722645	+	0.00722645i
$595$	−7.55555	+	33.9037i	−0.309747	+	1.38992i
$596$		−	8.45695i		−	0.346410i
$597$			5.22101i			0.213682i
$598$	23.4877			0.960482
$599$		−	16.4095i		−	0.670473i	−0.942134	−	0.335236i	$-0.891184\pi$
$599$		−	16.4095i		−	0.670473i	0.942134	−	0.335236i	$-0.108816\pi$
$600$	−1.69973	−	4.70223i	−0.0693910	−	0.191968i
$601$	−24.3063			−0.991473			−0.495736	−	0.868473i	$-0.665102\pi$
$601$	−24.3063			−0.991473			−0.495736	+	0.868473i	$0.665102\pi$
$602$	11.4638	−	11.4638i	0.467229	−	0.467229i
$603$	−5.68165	+	5.68165i	−0.231375	+	0.231375i
$604$		−	12.3871i		−	0.504024i
$605$	−13.1185	−	20.6422i	−0.533343	−	0.839224i
$606$	7.28212	+	7.28212i	0.295816	+	0.295816i
$607$	−2.93171			−0.118994			−0.0594972	−	0.998228i	$-0.518950\pi$
$607$	−2.93171			−0.118994			−0.0594972	+	0.998228i	$0.518950\pi$
$608$	−1.89479	−	1.89479i	−0.0768438	−	0.0768438i
$609$	−5.05308	−	5.05308i	−0.204761	−	0.204761i
$610$	−2.21493	+	9.93899i	−0.0896800	+	0.402418i
$611$	8.01269	−	8.01269i	0.324159	−	0.324159i
$612$	7.29402			0.294843
$613$	15.0778	−	15.0778i	0.608986	−	0.608986i	−0.333695	−	0.942681i	$-0.608296\pi$
$613$	15.0778	−	15.0778i	0.608986	−	0.608986i	0.942681	+	0.333695i	$0.108296\pi$
$614$	−3.36862	−	3.36862i	−0.135947	−	0.135947i
$615$	−5.02102	+	22.5307i	−0.202467	+	0.908524i
$616$	−0.375093	−	0.375093i	−0.0151129	−	0.0151129i
$617$	31.1997	+	31.1997i	1.25605	+	1.25605i	0.952962	+	0.303091i	$0.0980185\pi$
$617$	31.1997	+	31.1997i	1.25605	+	1.25605i	0.303091	+	0.952962i	$0.401981\pi$
$618$	5.90029	+	5.90029i	0.237345	+	0.237345i
$619$	11.1366			0.447619			0.223809	−	0.974633i	$-0.428151\pi$
$619$	11.1366			0.447619			0.223809	+	0.974633i	$0.428151\pi$
$620$	1.26128	−	5.65970i	0.0506543	−	0.227299i
$621$	−5.86075	−	5.86075i	−0.235184	−	0.235184i
$622$	22.4334	+	22.4334i	0.899497	+	0.899497i
$623$		−	16.1911i		−	0.648682i
$624$	2.00381	−	2.00381i	0.0802166	−	0.0802166i
$625$	−15.9850	−	19.2219i	−0.639399	−	0.768875i
$626$	−19.2752			−0.770393
$627$			0.667435i			0.0266548i
$628$	−10.3496	+	10.3496i	−0.412993	+	0.412993i
$629$	22.3259	−	38.3413i	0.890190	−	1.52877i
$630$	1.03586	−	4.64816i	0.0412695	−	0.185187i
$631$	19.2236	+	19.2236i	0.765279	+	0.765279i	0.977271	−	0.211992i	$-0.0679951\pi$
$631$	19.2236	+	19.2236i	0.765279	+	0.765279i	−0.211992	+	0.977271i	$0.567995\pi$
$632$	−5.99818	−	5.99818i	−0.238595	−	0.238595i
$633$	5.76649	−	5.76649i	0.229197	−	0.229197i
$634$	3.94817	+	3.94817i	0.156802	+	0.156802i
$635$	−38.7268	−	8.63038i	−1.53683	−	0.342486i
$636$	−5.94800			−0.235854
$637$		−	6.98345i		−	0.276694i
$638$	0.590974	+	0.590974i	0.0233969	+	0.0233969i
$639$		−	3.37315i		−	0.133440i
$640$	−1.19936	−	1.88721i	−0.0474087	−	0.0745983i
$641$	8.52699			0.336796			0.168398	−	0.985719i	$-0.446141\pi$
$641$	8.52699			0.336796			0.168398	+	0.985719i	$0.446141\pi$
$642$		−	2.97934i		−	0.117585i
$643$		−	11.8650i		−	0.467910i	−0.972247	−	0.233955i	$-0.924833\pi$
$643$		−	11.8650i		−	0.467910i	0.972247	−	0.233955i	$-0.0751668\pi$
$644$	12.4817	−	12.4817i	0.491848	−	0.491848i
$645$	−16.6143	−	3.70254i	−0.654187	−	0.145787i
$646$	13.8206	−	13.8206i	0.543765	−	0.543765i
$647$	−1.01194			−0.0397836			−0.0198918	−	0.999802i	$-0.506332\pi$
$647$	−1.01194			−0.0397836			−0.0198918	+	0.999802i	$0.506332\pi$
$648$	−1.00000			−0.0392837
$649$	1.55951	−	1.55951i	0.0612161	−	0.0612161i
$650$	6.01645	−	12.8283i	0.235984	−	0.503167i
$651$	3.90517	−	3.90517i	0.153056	−	0.153056i
$652$		−	8.69039i		−	0.340342i
$653$			14.7798i			0.578377i	0.957272	+	0.289189i	$0.0933855\pi$
$653$			14.7798i			0.578377i	−0.957272	+	0.289189i	$0.906614\pi$
$654$	−15.0958			−0.590293
$655$	2.62098	−	11.7610i	0.102410	−	0.459541i
$656$			10.3232i			0.403053i
$657$	−7.48228	−	7.48228i	−0.291912	−	0.291912i
$658$		−	8.51613i		−	0.331993i
$659$	1.79646			0.0699802			0.0349901	−	0.999388i	$-0.488860\pi$
$659$	1.79646			0.0699802			0.0349901	+	0.999388i	$0.488860\pi$
$660$	−0.121147	+	0.543617i	−0.00471562	+	0.0211603i
$661$	11.0318	+	11.0318i	0.429086	+	0.429086i	0.888317	−	0.459231i	$-0.151875\pi$
$661$	11.0318	+	11.0318i	0.429086	+	0.429086i	−0.459231	+	0.888317i	$0.651875\pi$
$662$	−2.89997	+	2.89997i	−0.112711	+	0.112711i
$663$	14.6158	+	14.6158i	0.567632	+	0.567632i
$664$	5.98449	+	5.98449i	0.232243	+	0.232243i
$665$	−6.84455	−	10.7700i	−0.265420	−	0.417643i
$666$	−3.06084	+	5.25654i	−0.118605	+	0.203687i
$667$	−19.6654	+	19.6654i	−0.761449	+	0.761449i
$668$			18.5233i			0.716687i
$669$	−25.5945			−0.989539
$670$	−3.90812	+	17.5368i	−0.150984	+	0.677504i
$671$	0.802048	−	0.802048i	0.0309627	−	0.0309627i
$672$		−	2.12971i		−	0.0821554i
$673$	12.5759	+	12.5759i	0.484766	+	0.484766i	0.906650	−	0.421884i	$-0.138631\pi$
$673$	12.5759	+	12.5759i	0.484766	+	0.484766i	−0.421884	+	0.906650i	$0.638631\pi$
$674$	1.55976	+	1.55976i	0.0600796	+	0.0600796i
$675$	−4.70223	+	1.69973i	−0.180989	+	0.0654225i
$676$	−4.96948			−0.191134
$677$	18.9213	+	18.9213i	0.727203	+	0.727203i	0.970062	−	0.242859i	$-0.0780851\pi$
$677$	18.9213	+	18.9213i	0.727203	+	0.727203i	−0.242859	+	0.970062i	$0.578085\pi$
$678$	−3.00726	−	3.00726i	−0.115493	−	0.115493i
$679$	−8.95625	−	8.95625i	−0.343710	−	0.343710i
$680$	13.7653	−	8.74813i	0.527876	−	0.335475i
$681$	−10.7509	−	10.7509i	−0.411974	−	0.411974i
$682$	−0.456722	+	0.456722i	−0.0174888	+	0.0174888i
$683$	36.6018			1.40053			0.700265	−	0.713883i	$-0.253065\pi$
$683$	36.6018			1.40053			0.700265	+	0.713883i	$0.253065\pi$
$684$	−1.89479	+	1.89479i	−0.0724490	+	0.0724490i
$685$	8.41915	+	1.87623i	0.321679	+	0.0716871i
$686$	−14.2526	−	14.2526i	−0.544169	−	0.544169i
$687$	−15.6384	−	15.6384i	−0.596642	−	0.596642i
$688$	−7.61240			−0.290220
$689$	−11.9187	−	11.9187i	−0.454066	−	0.454066i
$690$	−18.0896	−	4.03131i	−0.688658	−	0.153469i
$691$			23.7209i			0.902385i	0.892427	+	0.451193i	$0.149001\pi$
$691$			23.7209i			0.902385i	−0.892427	+	0.451193i	$0.850999\pi$
$692$	−6.60085	+	6.60085i	−0.250927	+	0.250927i
$693$	−0.375093	+	0.375093i	−0.0142486	+	0.0142486i
$694$	−9.43617			−0.358192
$695$	2.77670	+	4.36918i	0.105326	+	0.165733i
$696$			3.35545i			0.127188i
$697$	−75.2975			−2.85210
$698$		−	7.25908i		−	0.274760i
$699$			6.74984i			0.255302i
$700$	−3.61993	−	10.0144i	−0.136820	−	0.378508i
$701$	−12.5087	+	12.5087i	−0.472447	+	0.472447i	−0.902706	−	0.430259i	$-0.858422\pi$
$701$	−12.5087	+	12.5087i	−0.472447	+	0.472447i	0.430259	+	0.902706i	$0.358422\pi$
$702$	−2.00381	−	2.00381i	−0.0756290	−	0.0756290i
$703$	4.16038	+	15.7597i	0.156912	+	0.594388i
$704$			0.249077i			0.00938743i
$705$	−7.54642	+	4.79590i	−0.284214	+	0.180624i
$706$		−	6.63465i		−	0.249698i
$707$	15.5088	+	15.5088i	0.583269	+	0.583269i
$708$	8.85463			0.332777
$709$	16.9567	+	16.9567i	0.636822	+	0.636822i	0.949770	−	0.312948i	$-0.101317\pi$
$709$	16.9567	+	16.9567i	0.636822	+	0.636822i	−0.312948	+	0.949770i	$0.601317\pi$
$710$	−4.04561	−	6.36583i	−0.151829	−	0.238906i
$711$	−5.99818	+	5.99818i	−0.224949	+	0.224949i
$712$	−5.37576	+	5.37576i	−0.201465	+	0.201465i
$713$	−15.1980	−	15.1980i	−0.569170	−	0.569170i
$714$	15.5342			0.581351
$715$	−1.33206	+	0.846551i	−0.0498162	+	0.0316592i
$716$	−11.1031	+	11.1031i	−0.414942	+	0.414942i
$717$	28.0719			1.04836
$718$			3.64712i			0.136109i
$719$		−	6.40855i		−	0.238998i	−0.992834	−	0.119499i	$-0.961871\pi$
$719$		−	6.40855i		−	0.238998i	0.992834	−	0.119499i	$-0.0381289\pi$
$720$	−1.88721	+	1.19936i	−0.0703320	+	0.0446974i
$721$	12.5659	+	12.5659i	0.467979	+	0.467979i
$722$		−	11.8196i		−	0.439878i
$723$			30.1552i			1.12148i
$724$	19.1102			0.710223
$725$	5.70334	+	15.7781i	0.211817	+	0.585983i
$726$	−7.73431	+	7.73431i	−0.287047	+	0.287047i
$727$	−6.09536			−0.226064			−0.113032	−	0.993591i	$-0.536056\pi$
$727$	−6.09536			−0.226064			−0.113032	+	0.993591i	$0.536056\pi$
$728$	4.26754	−	4.26754i	0.158166	−	0.158166i
$729$			1.00000i			0.0370370i
$730$	−23.0945	−	5.14668i	−0.854767	−	0.190487i
$731$		−	55.5250i		−	2.05367i
$732$	4.55389			0.168317
$733$	−5.99617	+	5.99617i	−0.221474	+	0.221474i	−0.809119	−	0.587645i	$-0.800055\pi$
$733$	−5.99617	+	5.99617i	−0.221474	+	0.221474i	0.587645	+	0.809119i	$0.300055\pi$
$734$	−2.67398	+	2.67398i	−0.0986982	+	0.0986982i
$735$	−1.19861	+	5.37846i	−0.0442113	+	0.198388i
$736$	−8.28835			−0.305513
$737$	1.41517	−	1.41517i	0.0521283	−	0.0521283i
$738$	10.3232			0.380002
$739$	−31.2325			−1.14891			−0.574453	−	0.818538i	$-0.694785\pi$
$739$	−31.2325			−1.14891			−0.574453	+	0.818538i	$0.694785\pi$
$740$	0.528025	+	13.5912i	0.0194106	+	0.499623i
$741$	−7.59360			−0.278958
$742$	−12.6675			−0.465040
$743$	28.7095	−	28.7095i	1.05325	−	1.05325i	0.0547482	−	0.998500i	$-0.482564\pi$
$743$	28.7095	−	28.7095i	1.05325	−	1.05325i	0.998500	−	0.0547482i	$-0.0174356\pi$
$744$	−2.59319			−0.0950708
$745$	−15.9600	+	10.1429i	−0.584730	+	0.371607i
$746$	−8.22916	+	8.22916i	−0.301291	+	0.301291i
$747$	5.98449	−	5.98449i	0.218961	−	0.218961i
$748$	−1.81677			−0.0664277
$749$		−	6.34514i		−	0.231846i
$750$	−6.83549	+	8.84738i	−0.249597	+	0.323060i
$751$		−	4.99355i		−	0.182217i	−0.995841	−	0.0911086i	$-0.970959\pi$
$751$		−	4.99355i		−	0.182217i	0.995841	−	0.0911086i	$-0.0290410\pi$
$752$	−2.82753	+	2.82753i	−0.103109	+	0.103109i
$753$	−20.7096			−0.754700
$754$	−6.72369	+	6.72369i	−0.244862	+	0.244862i
$755$	−23.3770	+	14.8565i	−0.850776	+	0.540685i
$756$	−2.12971			−0.0774569
$757$		−	20.7849i		−	0.755438i	−0.925920	−	0.377719i	$-0.876708\pi$
$757$		−	20.7849i		−	0.755438i	0.925920	−	0.377719i	$-0.123292\pi$
$758$		−	23.2988i		−	0.846250i
$759$	1.45978	+	1.45978i	0.0529865	+	0.0529865i
$760$	−1.30333	+	5.84838i	−0.0472767	+	0.212143i
$761$			10.4423i			0.378532i	0.981926	+	0.189266i	$0.0606109\pi$
$761$			10.4423i			0.378532i	−0.981926	+	0.189266i	$0.939389\pi$
$762$			17.7440i			0.642798i
$763$	−32.1497			−1.16390
$764$	−4.13848	+	4.13848i	−0.149725	+	0.149725i
$765$	−8.74813	−	13.7653i	−0.316289	−	0.497686i
$766$	1.82589			0.0659719
$767$	17.7430	+	17.7430i	0.640663	+	0.640663i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−36.5206	+	36.5206i	−1.31697	+	1.31697i	−0.400801	+	0.916165i	$0.631268\pi$
$769$	−36.5206	+	36.5206i	−1.31697	+	1.31697i	−0.916165	+	0.400801i	$0.868732\pi$
$770$	−0.258007	+	1.15775i	−0.00929794	+	0.0417223i
$771$	12.6523	+	12.6523i	0.455661	+	0.455661i
$772$	−1.65600			−0.0596007
$773$	36.9436	+	36.9436i	1.32877	+	1.32877i	0.906445	+	0.422323i	$0.138785\pi$
$773$	36.9436	+	36.9436i	1.32877	+	1.32877i	0.422323	+	0.906445i	$0.361215\pi$
$774$			7.61240i			0.273622i
$775$	−12.1938	+	4.40771i	−0.438012	+	0.158329i
$776$			5.94731i			0.213496i
$777$	−6.51872	+	11.1949i	−0.233858	+	0.401616i
$778$	−1.87840	−	1.87840i	−0.0673440	−	0.0673440i
$779$	19.5603	−	19.5603i	0.700819	−	0.700819i
$780$	−6.18489	−	1.37832i	−0.221454	−	0.0493518i
$781$			0.840174i			0.0300638i
$782$		−	60.4554i		−	2.16188i
$783$	3.35545			0.119914
$784$			2.46433i			0.0880117i
$785$	31.9446	+	7.11895i	1.14015	+	0.254086i
$786$	−5.38872			−0.192209
$787$	−5.06401	+	5.06401i	−0.180512	+	0.180512i	−0.791579	−	0.611067i	$-0.790741\pi$
$787$	−5.06401	+	5.06401i	−0.180512	+	0.180512i	0.611067	+	0.791579i	$0.290741\pi$
$788$	14.1878	−	14.1878i	0.505418	−	0.505418i
$789$		−	30.7747i		−	1.09561i
$790$	−4.12584	+	18.5138i	−0.146791	+	0.658690i
$791$	−6.40459	−	6.40459i	−0.227721	−	0.227721i
$792$	0.249077			0.00885055
$793$	9.12513	+	9.12513i	0.324043	+	0.324043i
$794$	−12.0046	−	12.0046i	−0.426026	−	0.426026i
$795$	7.13378	+	11.2251i	0.253009	+	0.398114i
$796$	3.69181	−	3.69181i	0.130853	−	0.130853i
$797$	−21.7157			−0.769210			−0.384605	−	0.923081i	$-0.625662\pi$
$797$	−21.7157			−0.769210			−0.384605	+	0.923081i	$0.625662\pi$
$798$	−4.03535	+	4.03535i	−0.142850	+	0.142850i
$799$	−20.6240	−	20.6240i	−0.729625	−	0.729625i
$800$	−2.12309	+	4.52686i	−0.0750625	+	0.160049i
$801$	5.37576	+	5.37576i	0.189943	+	0.189943i
$802$	−23.2046	−	23.2046i	−0.819382	−	0.819382i
$803$	1.86366	+	1.86366i	0.0657672	+	0.0657672i
$804$	8.03506			0.283375
$805$	−38.5255	−	8.58553i	−1.35785	−	0.302600i
$806$	−5.19626	−	5.19626i	−0.183030	−	0.183030i
$807$	12.6203	+	12.6203i	0.444257	+	0.444257i
$808$		−	10.2985i		−	0.362299i
$809$	23.1152	−	23.1152i	0.812687	−	0.812687i	−0.172349	−	0.985036i	$-0.555136\pi$
$809$	23.1152	−	23.1152i	0.812687	−	0.812687i	0.985036	+	0.172349i	$0.0551358\pi$
$810$	1.19936	+	1.88721i	0.0421411	+	0.0663096i
$811$	45.9301			1.61282			0.806412	−	0.591354i	$-0.201407\pi$
$811$	45.9301			1.61282			0.806412	+	0.591354i	$0.201407\pi$
$812$			7.14614i			0.250780i
$813$	−1.62182	+	1.62182i	−0.0568798	+	0.0568798i
$814$	0.762385	−	1.30928i	0.0267216	−	0.0458903i
$815$	−16.4006	+	10.4229i	−0.574486	+	0.365097i
$816$	−5.15765	−	5.15765i	−0.180554	−	0.180554i
$817$	14.4239	+	14.4239i	0.504628	+	0.504628i
$818$	−12.7469	+	12.7469i	−0.445683	+	0.445683i
$819$	−4.26754	−	4.26754i	−0.149120	−	0.149120i
$820$	19.4820	−	12.3812i	0.680340	−	0.432370i
$821$	−31.8102			−1.11018			−0.555092	−	0.831789i	$-0.687317\pi$
$821$	−31.8102			−1.11018			−0.555092	+	0.831789i	$0.687317\pi$
$822$		−	3.85752i		−	0.134547i
$823$	0.924037	+	0.924037i	0.0322099	+	0.0322099i	0.723028	−	0.690818i	$-0.242750\pi$
$823$	0.924037	+	0.924037i	0.0322099	+	0.0322099i	−0.690818	+	0.723028i	$0.742750\pi$
$824$		−	8.34427i		−	0.290686i
$825$	1.17121	−	0.423362i	0.0407765	−	0.0147396i
$826$	18.8578			0.656147
$827$		−	5.29174i		−	0.184012i	−0.995758	−	0.0920059i	$-0.970672\pi$
$827$		−	5.29174i		−	0.184012i	0.995758	−	0.0920059i	$-0.0293279\pi$
$828$			8.28835i			0.288040i
$829$	14.0039	−	14.0039i	0.486376	−	0.486376i	−0.420784	−	0.907161i	$-0.638245\pi$
$829$	14.0039	−	14.0039i	0.486376	−	0.486376i	0.907161	+	0.420784i	$0.138245\pi$
$830$	4.11642	−	18.4715i	0.142883	−	0.641155i
$831$	−1.05081	+	1.05081i	−0.0364523	+	0.0364523i
$832$	−2.83382			−0.0982449
$833$	−17.9748			−0.622791
$834$	1.63707	−	1.63707i	0.0566870	−	0.0566870i
$835$	34.9572	−	22.2160i	1.20974	−	0.768816i
$836$	0.471948	−	0.471948i	0.0163226	−	0.0163226i
$837$			2.59319i			0.0896336i
$838$			22.1539i			0.765295i
$839$	−5.45096			−0.188188			−0.0940941	−	0.995563i	$-0.529995\pi$
$839$	−5.45096			−0.188188			−0.0940941	+	0.995563i	$0.529995\pi$
$840$	−4.01920	+	2.55428i	−0.138676	+	0.0881312i
$841$			17.7410i			0.611757i
$842$	−18.3106	−	18.3106i	−0.631025	−	0.631025i
$843$		−	26.2868i		−	0.905367i
$844$	−8.15505			−0.280708
$845$	5.96018	+	9.37843i	0.205036	+	0.322628i
$846$	2.82753	+	2.82753i	0.0972123	+	0.0972123i
$847$	−16.4718	+	16.4718i	−0.565979	+	0.565979i
$848$	4.20587	+	4.20587i	0.144430	+	0.144430i
$849$	11.7488	+	11.7488i	0.403217	+	0.403217i
$850$	−33.0190	−	15.4858i	−1.13254	−	0.531160i
$851$	43.5680	+	25.3693i	1.49349	+	0.869650i
$852$	−2.38518	+	2.38518i	−0.0817149	+	0.0817149i
$853$			1.69992i			0.0582041i	0.999576	+	0.0291021i	$0.00926478\pi$
$853$			1.69992i			0.0582041i	−0.999576	+	0.0291021i	$0.990735\pi$
$854$	9.69847			0.331875
$855$	5.84838	+	1.30333i	0.200010	+	0.0445729i
$856$	−2.10671	+	2.10671i	−0.0720059	+	0.0720059i
$857$		−	48.8147i		−	1.66748i	−0.552160	−	0.833738i	$-0.686196\pi$
$857$		−	48.8147i		−	1.66748i	0.552160	−	0.833738i	$-0.313804\pi$
$858$	0.499103	+	0.499103i	0.0170391	+	0.0170391i
$859$	2.09107	+	2.09107i	0.0713463	+	0.0713463i	0.741879	−	0.670533i	$-0.233935\pi$
$859$	2.09107	+	2.09107i	0.0713463	+	0.0713463i	−0.670533	+	0.741879i	$0.733935\pi$
$860$	9.12998	+	14.3662i	0.311330	+	0.489882i
$861$	21.9854			0.749261
$862$	−8.32782	−	8.32782i	−0.283647	−	0.283647i
$863$	−5.37396	−	5.37396i	−0.182932	−	0.182932i	0.609700	−	0.792632i	$-0.291290\pi$
$863$	−5.37396	−	5.37396i	−0.182932	−	0.182932i	−0.792632	+	0.609700i	$0.791290\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	20.3739	+	4.54039i	0.692735	+	0.154378i
$866$	−6.11268	−	6.11268i	−0.207717	−	0.207717i
$867$	25.5992	−	25.5992i	0.869393	−	0.869393i
$868$	−5.52274			−0.187454
$869$	1.49401	−	1.49401i	0.0506807	−	0.0506807i
$870$	6.33242	−	4.02438i	0.214689	−	0.136439i
$871$	16.1008	+	16.1008i	0.545553	+	0.545553i
$872$	10.6743	+	10.6743i	0.361479	+	0.361479i
$873$	5.94731			0.201286
$874$	15.7047	+	15.7047i	0.531218	+	0.531218i
$875$	−14.5576	+	18.8424i	−0.492138	+	0.636988i
$876$			10.5815i			0.357517i
$877$	−6.91171	+	6.91171i	−0.233392	+	0.233392i	−0.814107	−	0.580715i	$-0.802773\pi$
$877$	−6.91171	+	6.91171i	−0.233392	+	0.233392i	0.580715	+	0.814107i	$0.302773\pi$
$878$	−16.2052	+	16.2052i	−0.546899	+	0.546899i
$879$	−13.2637			−0.447373
$880$	0.470059	−	0.298732i	0.0158457	−	0.0100702i
$881$		−	8.64906i		−	0.291394i	−0.989329	−	0.145697i	$-0.953457\pi$
$881$		−	8.64906i		−	0.291394i	0.989329	−	0.145697i	$-0.0465425\pi$
$882$	2.46433			0.0829782
$883$			18.4508i			0.620919i	0.950587	+	0.310460i	$0.100483\pi$
$883$			18.4508i			0.620919i	−0.950587	+	0.310460i	$0.899517\pi$
$884$		−	20.6699i		−	0.695204i
$885$	−10.6199	−	16.7105i	−0.356982	−	0.561717i
$886$	6.30399	−	6.30399i	0.211787	−	0.211787i
$887$	−27.1337	−	27.1337i	−0.911062	−	0.911062i	0.0852937	−	0.996356i	$-0.472817\pi$
$887$	−27.1337	−	27.1337i	−0.911062	−	0.911062i	−0.996356	+	0.0852937i	$0.972817\pi$
$888$	5.88128	−	1.55259i	0.197363	−	0.0521016i
$889$			37.7896i			1.26742i
$890$	16.5926	+	3.69771i	0.556186	+	0.123948i
$891$		−	0.249077i		−	0.00834438i
$892$	18.0980	+	18.0980i	0.605967	+	0.605967i
$893$	10.7151			0.358568
$894$	5.97997	+	5.97997i	0.200000	+	0.200000i
$895$	34.2703	+	7.63724i	1.14553	+	0.255285i
$896$	−1.50593	+	1.50593i	−0.0503097	+	0.0503097i
$897$	−16.6083	+	16.6083i	−0.554534	+	0.554534i
$898$	19.8634	+	19.8634i	0.662851	+	0.662851i
$899$	8.70130			0.290205
$900$	4.52686	+	2.12309i	0.150895	+	0.0707696i
$901$	−30.6777	+	30.6777i	−1.02202	+	1.02202i
$902$	−2.57127			−0.0856138
$903$			16.2122i			0.539509i
$904$			4.25290i			0.141449i
$905$	−22.9199	−	36.0648i	−0.761883	−	1.19883i
$906$	8.75900	+	8.75900i	0.290998	+	0.290998i
$907$		−	20.4243i		−	0.678179i	−0.940754	−	0.339090i	$-0.889881\pi$
$907$		−	20.4243i		−	0.678179i	0.940754	−	0.339090i	$-0.110119\pi$
$908$			15.2040i			0.504563i
$909$	−10.2985			−0.341579
$910$	−13.1720	−	2.93542i	−0.436648	−	0.0973084i
$911$	26.7806	−	26.7806i	0.887279	−	0.887279i	−0.106982	−	0.994261i	$-0.534119\pi$
$911$	26.7806	−	26.7806i	0.887279	−	0.887279i	0.994261	+	0.106982i	$0.0341186\pi$
$912$	2.67964			0.0887316
$913$	−1.49060	+	1.49060i	−0.0493315	+	0.0493315i
$914$			40.2606i			1.33170i
$915$	−5.46173	−	8.59412i	−0.180559	−	0.284113i
$916$			22.1160i			0.730735i
$917$	−11.4764			−0.378985
$918$	−5.15765	+	5.15765i	−0.170228	+	0.170228i
$919$	−31.0865	+	31.0865i	−1.02545	+	1.02545i	−0.0257801	+	0.999668i	$0.508207\pi$
$919$	−31.0865	+	31.0865i	−1.02545	+	1.02545i	−0.999668	+	0.0257801i	$0.991793\pi$
$920$	9.94068	+	15.6418i	0.327735	+	0.515695i
$921$	4.76395			0.156978
$922$	−15.0948	+	15.0948i	−0.497121	+	0.497121i
$923$	−9.55890			−0.314635
$924$	0.530462			0.0174509
$925$	25.0161	−	17.2972i	0.822525	−	0.568729i
$926$	−25.5478			−0.839551
$927$	−8.34427			−0.274062
$928$	2.37266	−	2.37266i	0.0778864	−	0.0778864i
$929$	47.3305			1.55286			0.776431	−	0.630202i	$-0.217028\pi$
$929$	47.3305			1.55286			0.776431	+	0.630202i	$0.217028\pi$
$930$	3.11015	+	4.89388i	0.101986	+	0.160477i
$931$	4.66938	−	4.66938i	0.153033	−	0.153033i
$932$	4.77285	−	4.77285i	0.156340	−	0.156340i
$933$	−31.7256			−1.03865
$934$			30.7343i			1.00566i
$935$	2.17895	+	3.42862i	0.0712594	+	0.112128i
$936$			2.83382i			0.0926262i
$937$	−17.0130	+	17.0130i	−0.555791	+	0.555791i	−0.928106	−	0.372315i	$-0.878564\pi$
$937$	−17.0130	+	17.0130i	−0.555791	+	0.555791i	0.372315	+	0.928106i	$0.378564\pi$
$938$	17.1124			0.558739
$939$	13.6296	−	13.6296i	0.444787	−	0.444787i
$940$	8.72733	+	1.94491i	0.284654	+	0.0634360i
$941$	19.9394			0.650005			0.325002	−	0.945713i	$-0.394635\pi$
$941$	19.9394			0.650005			0.325002	+	0.945713i	$0.394635\pi$
$942$		−	14.6365i		−	0.476883i
$943$		−	85.5622i		−	2.78629i
$944$	−6.26117	−	6.26117i	−0.203784	−	0.203784i
$945$	2.55428	+	4.01920i	0.0830908	+	0.130745i
$946$		−	1.89607i		−	0.0616466i
$947$		−	51.9641i		−	1.68861i	−0.535865	−	0.844304i	$-0.680014\pi$
$947$		−	51.9641i		−	1.68861i	0.535865	−	0.844304i	$-0.319986\pi$
$948$	8.48271			0.275506
$949$	−21.2034	+	21.2034i	−0.688292	+	0.688292i
$950$	12.6003	−	4.55464i	0.408806	−	0.147772i
$951$	−5.58356			−0.181059
$952$	−10.9843	−	10.9843i	−0.356003	−	0.356003i
$953$	−1.57228	+	1.57228i	−0.0509312	+	0.0509312i	−0.732114	−	0.681182i	$-0.761466\pi$
$953$	−1.57228	+	1.57228i	−0.0509312	+	0.0509312i	0.681182	+	0.732114i	$0.261466\pi$
$954$	4.20587	−	4.20587i	0.136170	−	0.136170i
$955$	12.7737	+	2.84665i	0.413346	+	0.0921154i
$956$	−19.8498	−	19.8498i	−0.641989	−	0.641989i
$957$	−0.835764			−0.0270164
$958$	0.00977229	+	0.00977229i	0.000315728	+	0.000315728i
$959$		−	8.21541i		−	0.265289i
$960$	2.18253	+	0.486383i	0.0704408	+	0.0156979i
$961$		−	24.2754i		−	0.783077i
$962$	14.8961	+	8.67387i	0.480269	+	0.279657i
$963$	2.10671	+	2.10671i	0.0678878	+	0.0678878i
$964$	21.3229	−	21.3229i	0.686765	−	0.686765i
$965$	1.98613	+	3.12521i	0.0639358	+	0.100604i
$966$			17.6518i			0.567937i
$967$		−	31.3573i		−	1.00838i	−0.863592	−	0.504192i	$-0.831790\pi$
$967$		−	31.3573i		−	1.00838i	0.863592	−	0.504192i	$-0.168210\pi$
$968$	10.9380			0.351559
$969$			19.5453i			0.627886i
$970$	11.2238	−	7.13294i	0.360374	−	0.229025i
$971$	−32.7570			−1.05122			−0.525611	−	0.850725i	$-0.676163\pi$
$971$	−32.7570			−1.05122			−0.525611	+	0.850725i	$0.676163\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	3.48648	−	3.48648i	0.111771	−	0.111771i
$974$			0.0126739i			0.000406099i
$975$	4.81671	+	13.3252i	0.154258	+	0.426750i
$976$	−3.22008	−	3.22008i	−0.103072	−	0.103072i
$977$	−10.8286			−0.346436			−0.173218	−	0.984883i	$-0.555417\pi$
$977$	−10.8286			−0.346436			−0.173218	+	0.984883i	$0.555417\pi$
$978$	6.14503	+	6.14503i	0.196497	+	0.196497i
$979$	−1.33898	−	1.33898i	−0.0427939	−	0.0427939i
$980$	4.65069	−	2.95561i	0.148561	−	0.0944134i
$981$	10.6743	−	10.6743i	0.340806	−	0.340806i
$982$	24.8512			0.793034
$983$	−32.0672	+	32.0672i	−1.02279	+	1.02279i	−0.0230521	+	0.999734i	$0.507338\pi$
$983$	−32.0672	+	32.0672i	−1.02279	+	1.02279i	−0.999734	+	0.0230521i	$0.992662\pi$
$984$	−7.29960	−	7.29960i	−0.232703	−	0.232703i
$985$	−43.7914	−	9.75904i	−1.39531	−	0.310949i
$986$	17.3062	+	17.3062i	0.551142	+	0.551142i
$987$	6.02182	+	6.02182i	0.191677	+	0.191677i
$988$	5.36948	+	5.36948i	0.170826	+	0.170826i
$989$	63.0943			2.00628
$990$	−0.298732	−	0.470059i	−0.00949431	−	0.0149394i
$991$	10.7854	+	10.7854i	0.342609	+	0.342609i	0.857347	−	0.514738i	$-0.172111\pi$
$991$	10.7854	+	10.7854i	0.342609	+	0.342609i	−0.514738	+	0.857347i	$0.672111\pi$
$992$	1.83366	+	1.83366i	0.0582188	+	0.0582188i
$993$		−	4.10118i		−	0.130147i
$994$	−5.07975	+	5.07975i	−0.161120	+	0.161120i
$995$	−11.3950	−	2.53941i	−0.361246	−	0.0805046i
$996$	−8.46334			−0.268171
$997$		−	27.7799i		−	0.879799i	−0.898047	−	0.439900i	$-0.855014\pi$
$997$		−	27.7799i		−	0.879799i	0.898047	−	0.439900i	$-0.144986\pi$
$998$	−30.1549	+	30.1549i	−0.954536	+	0.954536i
$999$	−1.55259	−	5.88128i	−0.0491219	−	0.186075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.b.253.6	yes	40
5.2	odd	4		1110.2.l.b.697.15	yes	40
37.6	odd	4		1110.2.l.b.43.15	✓	40
185.117	even	4	inner	1110.2.o.b.487.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.15	✓	40	37.6	odd	4
1110.2.l.b.697.15	yes	40	5.2	odd	4
1110.2.o.b.253.6	yes	40	1.1	even	1	trivial
1110.2.o.b.487.6	yes	40	185.117	even	4	inner

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.19936 - 1.88721i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-1.19936 - 1.88721i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.50593 + 1.50593i) q^{7} +1.00000 q^{8} -1.00000i q^{9} +(-1.19936 - 1.88721i) q^{10} +0.249077i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.83382 q^{13} +(-1.50593 + 1.50593i) q^{14} +(2.18253 + 0.486383i) q^{15} +1.00000 q^{16} +7.29402i q^{17} -1.00000i q^{18} +(-1.89479 - 1.89479i) q^{19} +(-1.19936 - 1.88721i) q^{20} -2.12971i q^{21} +0.249077i q^{22} -8.28835 q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.12309 + 4.52686i) q^{25} -2.83382 q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.50593 + 1.50593i) q^{28} +(2.37266 - 2.37266i) q^{29} +(2.18253 + 0.486383i) q^{30} +(1.83366 + 1.83366i) q^{31} +1.00000 q^{32} +(-0.176124 - 0.176124i) q^{33} +7.29402i q^{34} +(4.64816 + 1.03586i) q^{35} -1.00000i q^{36} +(-5.25654 - 3.06084i) q^{37} +(-1.89479 - 1.89479i) q^{38} +(2.00381 - 2.00381i) q^{39} +(-1.19936 - 1.88721i) q^{40} +10.3232i q^{41} -2.12971i q^{42} -7.61240 q^{43} +0.249077i q^{44} +(-1.88721 + 1.19936i) q^{45} -8.28835 q^{46} +(-2.82753 + 2.82753i) q^{47} +(-0.707107 + 0.707107i) q^{48} +2.46433i q^{49} +(-2.12309 + 4.52686i) q^{50} +(-5.15765 - 5.15765i) q^{51} -2.83382 q^{52} +(4.20587 + 4.20587i) q^{53} +(0.707107 + 0.707107i) q^{54} +(0.470059 - 0.298732i) q^{55} +(-1.50593 + 1.50593i) q^{56} +2.67964 q^{57} +(2.37266 - 2.37266i) q^{58} +(-6.26117 - 6.26117i) q^{59} +(2.18253 + 0.486383i) q^{60} +(-3.22008 - 3.22008i) q^{61} +(1.83366 + 1.83366i) q^{62} +(1.50593 + 1.50593i) q^{63} +1.00000 q^{64} +(3.39876 + 5.34800i) q^{65} +(-0.176124 - 0.176124i) q^{66} +(-5.68165 - 5.68165i) q^{67} +7.29402i q^{68} +(5.86075 - 5.86075i) q^{69} +(4.64816 + 1.03586i) q^{70} +3.37315 q^{71} -1.00000i q^{72} +(7.48228 - 7.48228i) q^{73} +(-5.25654 - 3.06084i) q^{74} +(-1.69973 - 4.70223i) q^{75} +(-1.89479 - 1.89479i) q^{76} +(-0.375093 - 0.375093i) q^{77} +(2.00381 - 2.00381i) q^{78} +(-5.99818 - 5.99818i) q^{79} +(-1.19936 - 1.88721i) q^{80} -1.00000 q^{81} +10.3232i q^{82} +(5.98449 + 5.98449i) q^{83} -2.12971i q^{84} +(13.7653 - 8.74813i) q^{85} -7.61240 q^{86} +3.35545i q^{87} +0.249077i q^{88} +(-5.37576 + 5.37576i) q^{89} +(-1.88721 + 1.19936i) q^{90} +(4.26754 - 4.26754i) q^{91} -8.28835 q^{92} -2.59319 q^{93} +(-2.82753 + 2.82753i) q^{94} +(-1.30333 + 5.84838i) q^{95} +(-0.707107 + 0.707107i) q^{96} +5.94731i q^{97} +2.46433i q^{98} +0.249077 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8}+O(q^{10}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8	\( 40 q + 40 q^{2} + 40 q^{4} - 4 q^{7} + 40 q^{8} + 8 q^{13} - 4 q^{14} + 40 q^{16} - 4 q^{19} - 8 q^{25} + 8 q^{26} - 4 q^{28} + 28 q^{31} + 40 q^{32} - 4 q^{33} + 12 q^{35} + 8 q^{37} - 4 q^{38} - 4 q^{39} - 16 q^{47} - 8 q^{50} + 16 q^{51} + 8 q^{52} + 20 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 4 q^{59} - 8 q^{61} + 28 q^{62} + 4 q^{63} + 40 q^{64} + 4 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} + 12 q^{70} + 40 q^{71} - 8 q^{73} + 8 q^{74} + 16 q^{75} - 4 q^{76} + 24 q^{77} - 4 q^{78} + 12 q^{79} - 40 q^{81} - 8 q^{83} + 8 q^{85} - 12 q^{89} - 24 q^{91} - 8 q^{93} - 16 q^{94} + 28 q^{95} - 8 q^{99}+O(q^{100}) \) 40 * q + 40 * q^2 + 40 * q^4 - 4 * q^7 + 40 * q^8 + 8 * q^13 - 4 * q^14 + 40 * q^16 - 4 * q^19 - 8 * q^25 + 8 * q^26 - 4 * q^28 + 28 * q^31 + 40 * q^32 - 4 * q^33 + 12 * q^35 + 8 * q^37 - 4 * q^38 - 4 * q^39 - 16 * q^47 - 8 * q^50 + 16 * q^51 + 8 * q^52 + 20 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 4 * q^59 - 8 * q^61 + 28 * q^62 + 4 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 + 12 * q^70 + 40 * q^71 - 8 * q^73 + 8 * q^74 + 16 * q^75 - 4 * q^76 + 24 * q^77 - 4 * q^78 + 12 * q^79 - 40 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^89 - 24 * q^91 - 8 * q^93 - 16 * q^94 + 28 * q^95 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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