LMFDB - Embedded newform 234.2.y.a.11.5

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			11.5
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.09699 + 1.34038i) q^{3} -1.00000i q^{4} +(0.994452 + 0.266463i) q^{5} +(-1.72348 - 0.172100i) q^{6} +(0.339163 + 0.0908784i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.593221 + 2.94076i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.09699 + 1.34038i) q^{3} -1.00000i q^{4} +(0.994452 + 0.266463i) q^{5} +(-1.72348 - 0.172100i) q^{6} +(0.339163 + 0.0908784i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.593221 + 2.94076i) q^{9} +(-0.891601 + 0.514766i) q^{10} +(2.56893 + 2.56893i) q^{11} +(1.34038 - 1.09699i) q^{12} +(0.0241746 - 3.60547i) q^{13} +(-0.304085 + 0.175564i) q^{14} +(0.733745 + 1.62525i) q^{15} -1.00000 q^{16} +(-1.67236 + 2.89660i) q^{17} +(-1.65996 - 2.49890i) q^{18} +(-0.969723 + 0.259837i) q^{19} +(0.266463 - 0.994452i) q^{20} +(0.250247 + 0.554299i) q^{21} -3.63301 q^{22} +(0.735260 - 1.27351i) q^{23} +(-0.172100 + 1.72348i) q^{24} +(-3.41219 - 1.97003i) q^{25} +(2.53236 + 2.56655i) q^{26} +(-4.59249 + 2.43085i) q^{27} +(0.0908784 - 0.339163i) q^{28} +5.82075i q^{29} +(-1.66806 - 0.630388i) q^{30} +(1.48558 - 5.54424i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.625241 + 6.26142i) q^{33} +(-0.865675 - 3.23074i) q^{34} +(0.313065 + 0.180748i) q^{35} +(2.94076 + 0.593221i) q^{36} +(4.96682 + 1.33085i) q^{37} +(0.501966 - 0.869430i) q^{38} +(4.85921 - 3.92277i) q^{39} +(0.514766 + 0.891601i) q^{40} +(-2.41936 - 9.02916i) q^{41} +(-0.568900 - 0.214997i) q^{42} +(2.37192 - 1.36943i) q^{43} +(2.56893 - 2.56893i) q^{44} +(-1.37353 + 2.76638i) q^{45} +(0.380599 + 1.42041i) q^{46} +(8.18256 - 2.19251i) q^{47} +(-1.09699 - 1.34038i) q^{48} +(-5.95541 - 3.43835i) q^{49} +(3.80581 - 1.01976i) q^{50} +(-5.71710 + 0.935962i) q^{51} +(-3.60547 - 0.0241746i) q^{52} -2.67501i q^{53} +(1.52851 - 4.96625i) q^{54} +(1.87015 + 3.23920i) q^{55} +(0.175564 + 0.304085i) q^{56} +(-1.41206 - 1.01476i) q^{57} +(-4.11589 - 4.11589i) q^{58} +(-3.42622 - 3.42622i) q^{59} +(1.62525 - 0.733745i) q^{60} +(-2.86325 - 4.95929i) q^{61} +(2.86991 + 4.97083i) q^{62} +(-0.468450 + 0.943486i) q^{63} +1.00000i q^{64} +(0.984764 - 3.57903i) q^{65} +(-3.98538 - 4.86960i) q^{66} +(14.5603 - 3.90143i) q^{67} +(2.89660 + 1.67236i) q^{68} +(2.51355 - 0.411501i) q^{69} +(-0.349179 + 0.0935622i) q^{70} +(-1.53985 - 5.74681i) q^{71} +(-2.49890 + 1.65996i) q^{72} +(2.47165 - 2.47165i) q^{73} +(-4.45313 + 2.57101i) q^{74} +(-1.10256 - 6.73473i) q^{75} +(0.259837 + 0.969723i) q^{76} +(0.637824 + 1.10474i) q^{77} +(-0.662166 + 6.20979i) q^{78} +(-1.76544 + 3.05783i) q^{79} +(-0.994452 - 0.266463i) q^{80} +(-8.29618 - 3.48905i) q^{81} +(8.09532 + 4.67384i) q^{82} +(-2.23652 - 8.34680i) q^{83} +(0.554299 - 0.250247i) q^{84} +(-2.43491 + 2.43491i) q^{85} +(-0.708868 + 2.64553i) q^{86} +(-7.80200 + 6.38531i) q^{87} +3.63301i q^{88} +(-2.68520 + 10.0213i) q^{89} +(-0.984889 - 2.92736i) q^{90} +(0.335858 - 1.22064i) q^{91} +(-1.27351 - 0.735260i) q^{92} +(9.06104 - 4.09075i) q^{93} +(-4.23561 + 7.33629i) q^{94} -1.03358 q^{95} +(1.72348 + 0.172100i) q^{96} +(-3.82280 + 14.2669i) q^{97} +(6.64239 - 1.77982i) q^{98} +(-9.07854 + 6.03066i) 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 $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	1.09699	+	1.34038i	0.633348	+	0.773867i
$3$	1.09699	+	1.34038i	0.633348	+	0.773867i
$4$		−	1.00000i		−	0.500000i
$5$	0.994452	+	0.266463i	0.444732	+	0.119166i	0.474234	−	0.880399i	$-0.342725\pi$
$5$	0.994452	+	0.266463i	0.444732	+	0.119166i	−0.0295011	+	0.999565i	$0.509392\pi$
$6$	−1.72348	−	0.172100i	−0.703608	−	0.0702595i
$7$	0.339163	+	0.0908784i	0.128191	+	0.0343488i	0.322344	−	0.946622i	$-0.395529\pi$
$7$	0.339163	+	0.0908784i	0.128191	+	0.0343488i	−0.194153	+	0.980971i	$0.562196\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.593221	+	2.94076i	−0.197740	+	0.980254i
$10$	−0.891601	+	0.514766i	−0.281949	+	0.162783i
$11$	2.56893	+	2.56893i	0.774560	+	0.774560i	0.978900	−	0.204340i	$-0.0655047\pi$
$11$	2.56893	+	2.56893i	0.774560	+	0.774560i	−0.204340	+	0.978900i	$0.565505\pi$
$12$	1.34038	−	1.09699i	0.386934	−	0.316674i
$13$	0.0241746	−	3.60547i	0.00670484	−	0.999978i
$13$	0.0241746	−	3.60547i	0.00670484	−	0.999978i
$14$	−0.304085	+	0.175564i	−0.0812701	+	0.0469213i
$15$	0.733745	+	1.62525i	0.189452	+	0.419637i
$16$	−1.00000			−0.250000
$17$	−1.67236	+	2.89660i	−0.405606	+	0.702530i	−0.994392	−	0.105759i	$-0.966273\pi$
$17$	−1.67236	+	2.89660i	−0.405606	+	0.702530i	0.588786	+	0.808289i	$0.299606\pi$
$18$	−1.65996	−	2.49890i	−0.391257	−	0.588997i
$19$	−0.969723	+	0.259837i	−0.222470	+	0.0596106i	−0.368332	−	0.929694i	$-0.620071\pi$
$19$	−0.969723	+	0.259837i	−0.222470	+	0.0596106i	0.145862	+	0.989305i	$0.453404\pi$
$20$	0.266463	−	0.994452i	0.0595829	−	0.222366i
$21$	0.250247	+	0.554299i	0.0546084	+	0.120958i
$22$	−3.63301			−0.774560
$23$	0.735260	−	1.27351i	0.153312	−	0.265545i	−0.779131	−	0.626861i	$-0.784339\pi$
$23$	0.735260	−	1.27351i	0.153312	−	0.265545i	0.932443	+	0.361317i	$0.117673\pi$
$24$	−0.172100	+	1.72348i	−0.0351297	+	0.351804i
$25$	−3.41219	−	1.97003i	−0.682439	−	0.394006i
$26$	2.53236	+	2.56655i	0.496636	+	0.503341i
$27$	−4.59249	+	2.43085i	−0.883825	+	0.467817i
$28$	0.0908784	−	0.339163i	0.0171744	−	0.0640957i
$29$			5.82075i			1.08089i	0.841380	+	0.540443i	$0.181743\pi$
$29$			5.82075i			1.08089i	−0.841380	+	0.540443i	$0.818257\pi$
$30$	−1.66806	−	0.630388i	−0.304545	−	0.115093i
$31$	1.48558	−	5.54424i	0.266817	−	0.995775i	−0.694312	−	0.719675i	$-0.744291\pi$
$31$	1.48558	−	5.54424i	0.266817	−	0.995775i	0.961129	−	0.276101i	$-0.0890423\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.625241	+	6.26142i	−0.108840	+	1.08997i
$34$	−0.865675	−	3.23074i	−0.148462	−	0.554068i
$35$	0.313065	+	0.180748i	0.0529177	+	0.0305520i
$36$	2.94076	+	0.593221i	0.490127	+	0.0988702i
$37$	4.96682	+	1.33085i	0.816540	+	0.218791i	0.642833	−	0.766006i	$-0.277759\pi$
$37$	4.96682	+	1.33085i	0.816540	+	0.218791i	0.173707	+	0.984797i	$0.444426\pi$
$38$	0.501966	−	0.869430i	0.0814296	−	0.141040i
$39$	4.85921	−	3.92277i	0.778096	−	0.628145i
$40$	0.514766	+	0.891601i	0.0813917	+	0.140975i
$41$	−2.41936	−	9.02916i	−0.377840	−	1.41012i	−0.849151	−	0.528151i	$-0.822886\pi$
$41$	−2.41936	−	9.02916i	−0.377840	−	1.41012i	0.471311	−	0.881967i	$-0.343781\pi$
$42$	−0.568900	−	0.214997i	−0.0877831	−	0.0331747i
$43$	2.37192	−	1.36943i	0.361714	−	0.208836i	−0.308118	−	0.951348i	$-0.599699\pi$
$43$	2.37192	−	1.36943i	0.361714	−	0.208836i	0.669833	+	0.742512i	$0.266366\pi$
$44$	2.56893	−	2.56893i	0.387280	−	0.387280i
$45$	−1.37353	+	2.76638i	−0.204754	+	0.412387i
$46$	0.380599	+	1.42041i	0.0561162	+	0.209429i
$47$	8.18256	−	2.19251i	1.19355	−	0.319811i	0.393262	−	0.919427i	$-0.371347\pi$
$47$	8.18256	−	2.19251i	1.19355	−	0.319811i	0.800288	+	0.599616i	$0.204680\pi$
$48$	−1.09699	−	1.34038i	−0.158337	−	0.193467i
$49$	−5.95541	−	3.43835i	−0.850772	−	0.491194i
$50$	3.80581	−	1.01976i	0.538223	−	0.144216i
$51$	−5.71710	+	0.935962i	−0.800554	+	0.131061i
$52$	−3.60547	−	0.0241746i	−0.499989	−	0.00335242i
$53$		−	2.67501i		−	0.367442i	−0.982978	−	0.183721i	$-0.941186\pi$
$53$		−	2.67501i		−	0.367442i	0.982978	−	0.183721i	$-0.0588142\pi$
$54$	1.52851	−	4.96625i	0.208004	−	0.675821i
$55$	1.87015	+	3.23920i	0.252171	+	0.436773i
$56$	0.175564	+	0.304085i	0.0234607	+	0.0406351i
$57$	−1.41206	−	1.01476i	−0.187031	−	0.134408i
$58$	−4.11589	−	4.11589i	−0.540443	−	0.540443i
$59$	−3.42622	−	3.42622i	−0.446055	−	0.446055i	0.447985	−	0.894041i	$-0.352142\pi$
$59$	−3.42622	−	3.42622i	−0.446055	−	0.446055i	−0.894041	+	0.447985i	$0.852142\pi$
$60$	1.62525	−	0.733745i	0.209819	−	0.0947260i
$61$	−2.86325	−	4.95929i	−0.366601	−	0.634972i	0.622431	−	0.782675i	$-0.286145\pi$
$61$	−2.86325	−	4.95929i	−0.366601	−	0.634972i	−0.989032	+	0.147703i	$0.952812\pi$
$62$	2.86991	+	4.97083i	0.364479	+	0.631296i
$63$	−0.468450	+	0.943486i	−0.0590192	+	0.118868i
$64$			1.00000i			0.125000i
$65$	0.984764	−	3.57903i	0.122145	−	0.443924i
$66$	−3.98538	−	4.86960i	−0.490566	−	0.599407i
$67$	14.5603	−	3.90143i	1.77883	−	0.476636i	0.788459	−	0.615087i	$-0.210879\pi$
$67$	14.5603	−	3.90143i	1.77883	−	0.476636i	0.990369	+	0.138451i	$0.0442125\pi$
$68$	2.89660	+	1.67236i	0.351265	+	0.202803i
$69$	2.51355	−	0.411501i	0.302596	−	0.0495389i
$70$	−0.349179	+	0.0935622i	−0.0417349	+	0.0111828i
$71$	−1.53985	−	5.74681i	−0.182747	−	0.682021i	−0.995102	−	0.0988571i	$-0.968481\pi$
$71$	−1.53985	−	5.74681i	−0.182747	−	0.682021i	0.812355	−	0.583164i	$-0.198185\pi$
$72$	−2.49890	+	1.65996i	−0.294499	+	0.195628i
$73$	2.47165	−	2.47165i	0.289285	−	0.289285i	−0.547513	−	0.836797i	$-0.684425\pi$
$73$	2.47165	−	2.47165i	0.289285	−	0.289285i	0.836797	+	0.547513i	$0.184425\pi$
$74$	−4.45313	+	2.57101i	−0.517665	+	0.298874i
$75$	−1.10256	−	6.73473i	−0.127313	−	0.777660i
$76$	0.259837	+	0.969723i	0.0298053	+	0.111235i
$77$	0.637824	+	1.10474i	0.0726868	+	0.125897i
$78$	−0.662166	+	6.20979i	−0.0749755	+	0.703121i
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	−0.948084	−	0.318021i	$-0.896982\pi$
$79$	−1.76544	+	3.05783i	−0.198627	+	0.344033i	0.749456	+	0.662054i	$0.230315\pi$
$80$	−0.994452	−	0.266463i	−0.111183	−	0.0297914i
$81$	−8.29618	−	3.48905i	−0.921797	−	0.387672i
$82$	8.09532	+	4.67384i	0.893979	+	0.516139i
$83$	−2.23652	−	8.34680i	−0.245490	−	0.916181i	−0.973137	−	0.230228i	$-0.926053\pi$
$83$	−2.23652	−	8.34680i	−0.245490	−	0.916181i	0.727647	−	0.685952i	$-0.240614\pi$
$84$	0.554299	−	0.250247i	0.0604789	−	0.0273042i
$85$	−2.43491	+	2.43491i	−0.264103	+	0.264103i
$86$	−0.708868	+	2.64553i	−0.0764392	+	0.285275i
$87$	−7.80200	+	6.38531i	−0.836462	+	0.684577i
$88$			3.63301i			0.387280i
$89$	−2.68520	+	10.0213i	−0.284630	+	1.06225i	0.664479	+	0.747307i	$0.268653\pi$
$89$	−2.68520	+	10.0213i	−0.284630	+	1.06225i	−0.949109	+	0.314947i	$0.898013\pi$
$90$	−0.984889	−	2.92736i	−0.103816	−	0.308571i
$91$	0.335858	−	1.22064i	0.0352075	−	0.127958i
$92$	−1.27351	−	0.735260i	−0.132772	−	0.0766562i
$93$	9.06104	−	4.09075i	0.939586	−	0.424191i
$94$	−4.23561	+	7.33629i	−0.436869	+	0.756680i
$95$	−1.03358			−0.106043
$96$	1.72348	+	0.172100i	0.175902	+	0.0175649i
$97$	−3.82280	+	14.2669i	−0.388147	+	1.44858i	0.444999	+	0.895531i	$0.353204\pi$
$97$	−3.82280	+	14.2669i	−0.388147	+	1.44858i	−0.833146	+	0.553053i	$0.813463\pi$
$98$	6.64239	−	1.77982i	0.670983	−	0.179789i
$99$	−9.07854	+	6.03066i	−0.912428	+	0.606104i
$100$	−1.97003	+	3.41219i	−0.197003	+	0.341219i
$101$	−17.3422			−1.72561			−0.862804	−	0.505538i	$-0.831294\pi$
$101$	−17.3422			−1.72561			−0.862804	+	0.505538i	$0.831294\pi$
$102$	3.38078	−	4.70443i	0.334747	−	0.465808i
$103$	9.22402	−	5.32549i	0.908870	−	0.524736i	0.0288023	−	0.999585i	$-0.490831\pi$
$103$	9.22402	−	5.32549i	0.908870	−	0.524736i	0.880067	+	0.474849i	$0.157497\pi$
$104$	2.56655	−	2.53236i	0.251671	−	0.248318i
$105$	0.101159	+	0.617905i	0.00987210	+	0.0603013i
$106$	1.89152	+	1.89152i	0.183721	+	0.183721i
$107$	0.693025	−	0.400118i	0.0669973	−	0.0386809i	−0.466127	−	0.884718i	$-0.654351\pi$
$107$	0.693025	−	0.400118i	0.0669973	−	0.0386809i	0.533124	+	0.846037i	$0.321018\pi$
$108$	2.43085	+	4.59249i	0.233909	+	0.441913i
$109$	5.83921	+	5.83921i	0.559294	+	0.559294i	0.929107	−	0.369812i	$-0.120578\pi$
$109$	5.83921	+	5.83921i	0.559294	+	0.559294i	−0.369812	+	0.929107i	$0.620578\pi$
$110$	−3.61285	−	0.968061i	−0.344472	−	0.0923010i
$111$	3.66471	+	8.11734i	0.347839	+	0.770464i
$112$	−0.339163	−	0.0908784i	−0.0320479	−	0.00858720i
$113$			13.4923i			1.26925i	0.772822	+	0.634623i	$0.218844\pi$
$113$			13.4923i			1.26925i	−0.772822	+	0.634623i	$0.781156\pi$
$114$	1.71602	−	0.280934i	0.160720	−	0.0263119i
$115$	1.07052	−	1.07052i	0.0998268	−	0.0998268i
$116$	5.82075			0.540443
$117$	10.5885	+	2.20993i	0.978907	+	0.204308i
$118$	4.84540			0.446055
$119$	−0.830439	+	0.830439i	−0.0761262	+	0.0761262i
$120$	−0.630388	+	1.66806i	−0.0575463	+	0.152272i
$121$			2.19876i			0.199887i
$122$	5.53137	+	1.48213i	0.500787	+	0.134185i
$123$	9.44847	−	13.1478i	0.851939	−	1.18549i
$124$	−5.54424	−	1.48558i	−0.497888	−	0.133409i
$125$	−6.50827	−	6.50827i	−0.582117	−	0.582117i
$126$	−0.335901	−	0.998390i	−0.0299244	−	0.0889436i
$127$	−16.2637	+	9.38987i	−1.44317	+	0.833216i	−0.998060	−	0.0622590i	$-0.980170\pi$
$127$	−16.2637	+	9.38987i	−1.44317	+	0.833216i	−0.445112	+	0.895475i	$0.646836\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	4.43753	+	1.67702i	0.390702	+	0.147653i
$130$	1.83442	+	3.22709i	0.160889	+	0.283034i
$131$	−2.91497	+	1.68296i	−0.254682	+	0.147041i	−0.621906	−	0.783092i	$-0.713642\pi$
$131$	−2.91497	+	1.68296i	−0.254682	+	0.147041i	0.367224	+	0.930133i	$0.380308\pi$
$132$	6.26142	+	0.625241i	0.544986	+	0.0544202i
$133$	−0.352507			−0.0305663
$134$	−7.53699	+	13.0544i	−0.651096	+	1.12773i
$135$	−5.21474	+	1.19364i	−0.448814	+	0.102732i
$136$	−3.23074	+	0.865675i	−0.277034	+	0.0742310i
$137$	−1.00768	+	3.76073i	−0.0860923	+	0.321301i	−0.995519	−	0.0945638i	$-0.969854\pi$
$137$	−1.00768	+	3.76073i	−0.0860923	+	0.321301i	0.909426	+	0.415865i	$0.136521\pi$
$138$	−1.48638	+	2.06833i	−0.126529	+	0.176068i
$139$	0.552490			0.0468616			0.0234308	−	0.999725i	$-0.492541\pi$
$139$	0.552490			0.0468616			0.0234308	+	0.999725i	$0.492541\pi$
$140$	0.180748	−	0.313065i	0.0152760	−	0.0264588i
$141$	11.9150	+	8.56256i	1.00342	+	0.721097i
$142$	5.15245	+	2.97477i	0.432384	+	0.249637i
$143$	9.32429	−	9.20008i	0.779736	−	0.769350i
$144$	0.593221	−	2.94076i	0.0494351	−	0.245064i
$145$	−1.55101	+	5.78846i	−0.128805	+	0.480705i
$146$			3.49544i			0.289285i
$147$	−1.92433	−	11.7543i	−0.158716	−	0.969481i
$148$	1.33085	−	4.96682i	0.109396	−	0.408270i
$149$	−9.15442	+	9.15442i	−0.749960	+	0.749960i	−0.974471	−	0.224512i	$-0.927921\pi$
$149$	−9.15442	+	9.15442i	−0.749960	+	0.749960i	0.224512	+	0.974471i	$0.427921\pi$
$150$	5.54180	+	3.98255i	0.452486	+	0.325174i
$151$	2.33886	+	8.72875i	0.190334	+	0.710336i	0.993426	+	0.114480i	$0.0365203\pi$
$151$	2.33886	+	8.72875i	0.190334	+	0.710336i	−0.803092	+	0.595856i	$0.796813\pi$
$152$	−0.869430	−	0.501966i	−0.0705201	−	0.0407148i
$153$	−7.52615	−	6.63633i	−0.608453	−	0.536515i
$154$	−1.23218	−	0.330162i	−0.0992920	−	0.0266052i
$155$	2.95467	−	5.11763i	0.237325	−	0.411058i
$156$	−3.92277	−	4.85921i	−0.314073	−	0.389048i
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	0.998188	−	0.0601763i	$-0.0191663\pi$
$157$	5.60064	+	9.70059i	0.446980	+	0.774191i	−0.551208	+	0.834368i	$0.685833\pi$
$158$	−0.913858	−	3.41056i	−0.0727026	−	0.271330i
$159$	3.58553	−	2.93447i	0.284351	−	0.232718i
$160$	0.891601	−	0.514766i	0.0704873	−	0.0406958i
$161$	0.365107	−	0.365107i	0.0287745	−	0.0287745i
$162$	8.33341	−	3.39915i	0.654735	−	0.267063i
$163$	−2.29883	−	8.57937i	−0.180059	−	0.671988i	−0.995635	−	0.0933377i	$-0.970246\pi$
$163$	−2.29883	−	8.57937i	−0.180059	−	0.671988i	0.815576	−	0.578650i	$-0.196420\pi$
$164$	−9.02916	+	2.41936i	−0.705059	+	0.188920i
$165$	−2.29021	+	6.06008i	−0.178292	+	0.471776i
$166$	7.48354	+	4.32062i	0.580835	+	0.335345i
$167$	−8.97462	+	2.40474i	−0.694477	+	0.186084i	−0.588755	−	0.808311i	$-0.700382\pi$
$167$	−8.97462	+	2.40474i	−0.694477	+	0.186084i	−0.105721	+	0.994396i	$0.533715\pi$
$168$	−0.214997	+	0.568900i	−0.0165874	+	0.0438916i
$169$	−12.9988	−	0.174322i	−0.999910	−	0.0134094i
$170$		−	3.44349i		−	0.264103i
$171$	−0.188857	−	3.00587i	−0.0144423	−	0.229864i
$172$	−1.36943	−	2.37192i	−0.104418	−	0.180857i
$173$	5.29421	+	9.16985i	0.402512	+	0.697171i	0.994028	−	0.109122i	$-0.0348040\pi$
$173$	5.29421	+	9.16985i	0.402512	+	0.697171i	−0.591517	+	0.806293i	$0.701471\pi$
$174$	1.00175	−	10.0319i	0.0759425	−	0.760520i
$175$	−0.978256	−	0.978256i	−0.0739492	−	0.0739492i
$176$	−2.56893	−	2.56893i	−0.193640	−	0.193640i
$177$	0.833893	−	8.35095i	0.0626792	−	0.627696i
$178$	−5.18740	−	8.98484i	−0.388812	−	0.673442i
$179$	−12.5097	−	21.6674i	−0.935018	−	1.61950i	−0.774601	−	0.632450i	$-0.782049\pi$
$179$	−12.5097	−	21.6674i	−0.935018	−	1.61950i	−0.160417	−	0.987049i	$-0.551284\pi$
$180$	2.76638	+	1.37353i	0.206194	+	0.102377i
$181$		−	23.3875i		−	1.73838i	−0.494482	−	0.869188i	$-0.664642\pi$
$181$		−	23.3875i		−	1.73838i	0.494482	−	0.869188i	$-0.335358\pi$
$182$	0.625638	+	1.10061i	0.0463754	+	0.0815829i
$183$	3.50636	−	9.27813i	0.259198	−	0.685859i
$184$	1.42041	−	0.380599i	0.104714	−	0.0280581i
$185$	4.58464	+	2.64694i	0.337069	+	0.194607i
$186$	−3.51452	+	9.29972i	−0.257697	+	0.681889i
$187$	−11.7373	+	3.14500i	−0.858318	+	0.229986i
$188$	−2.19251	−	8.18256i	−0.159905	−	0.596775i
$189$	−1.77851	+	0.407096i	−0.129368	+	0.0296119i
$190$	0.730852	−	0.730852i	0.0530215	−	0.0530215i
$191$	10.6625	−	6.15600i	0.771512	−	0.445432i	−0.0619020	−	0.998082i	$-0.519717\pi$
$191$	10.6625	−	6.15600i	0.771512	−	0.445432i	0.833414	+	0.552650i	$0.186383\pi$
$192$	−1.34038	+	1.09699i	−0.0967334	+	0.0791685i
$193$	−3.34912	−	12.4991i	−0.241075	−	0.899704i	−0.975316	−	0.220815i	$-0.929128\pi$
$193$	−3.34912	−	12.4991i	−0.241075	−	0.899704i	0.734241	−	0.678889i	$-0.237538\pi$
$194$	−7.38509	−	12.7913i	−0.530218	−	0.918365i
$195$	5.87752	−	2.60620i	0.420898	−	0.186634i
$196$	−3.43835	+	5.95541i	−0.245597	+	0.425386i
$197$	−20.6372	−	5.52972i	−1.47034	−	0.393976i	−0.567292	−	0.823517i	$-0.692009\pi$
$197$	−20.6372	−	5.52972i	−1.47034	−	0.393976i	−0.903048	+	0.429540i	$0.858676\pi$
$198$	2.15518	−	10.6838i	0.153162	−	0.759266i
$199$	19.2376	+	11.1069i	1.36372	+	0.787344i	0.990117	−	0.140245i	$-0.0447889\pi$
$199$	19.2376	+	11.1069i	1.36372	+	0.787344i	0.373603	+	0.927589i	$0.378122\pi$
$200$	−1.01976	−	3.80581i	−0.0721082	−	0.269111i
$201$	21.2019	+	15.2365i	1.49547	+	1.07470i
$202$	12.2628	−	12.2628i	0.862804	−	0.862804i
$203$	−0.528980	+	1.97418i	−0.0371271	+	0.138560i
$204$	0.935962	+	5.71710i	0.0655305	+	0.400277i
$205$		−	9.62373i		−	0.672151i
$206$	−2.75668	+	10.2881i	−0.192067	+	0.716803i
$207$	3.30891	+	2.91770i	0.229985	+	0.202794i
$208$	−0.0241746	+	3.60547i	−0.00167621	+	0.249994i
$209$	−3.15865	−	1.82365i	−0.218488	−	0.126144i
$210$	−0.508455	−	0.365395i	−0.0350867	−	0.0252146i
$211$	−9.17554	+	15.8925i	−0.631670	+	1.09408i	0.355540	+	0.934661i	$0.384297\pi$
$211$	−9.17554	+	15.8925i	−0.631670	+	1.09408i	−0.987210	+	0.159424i	$0.949036\pi$
$212$	−2.67501			−0.183721
$213$	6.01369	−	8.36818i	0.412051	−	0.573378i
$214$	−0.207116	+	0.772969i	−0.0141582	+	0.0528391i
$215$	2.72366	−	0.729803i	0.185752	−	0.0497722i
$216$	−4.96625	−	1.52851i	−0.337911	−	0.104002i
$217$	1.00770	−	1.74539i	0.0684073	−	0.118485i
$218$	−8.25788			−0.559294
$219$	6.02432	+	0.601565i	0.407086	+	0.0406500i
$220$	3.23920	−	1.87015i	0.218387	−	0.126086i
$221$	10.4032	+	6.09965i	0.699794	+	0.410307i
$222$	−8.33117	−	3.14849i	−0.559151	−	0.211313i
$223$	17.9280	+	17.9280i	1.20055	+	1.20055i	0.974000	+	0.226550i	$0.0727446\pi$
$223$	17.9280	+	17.9280i	1.20055	+	1.20055i	0.226550	+	0.974000i	$0.427255\pi$
$224$	0.304085	−	0.175564i	0.0203175	−	0.0117303i
$225$	7.81758	−	8.86579i	0.521172	−	0.591053i
$226$	−9.54047	−	9.54047i	−0.634623	−	0.634623i
$227$	24.0759	+	6.45111i	1.59797	+	0.428175i	0.944429	−	0.328715i	$-0.106616\pi$
$227$	24.0759	+	6.45111i	1.59797	+	0.428175i	0.653542	+	0.756890i	$0.273282\pi$
$228$	−1.01476	+	1.41206i	−0.0672039	+	0.0935157i
$229$	−1.49912	−	0.401688i	−0.0990647	−	0.0265443i	0.208946	−	0.977927i	$-0.432997\pi$
$229$	−1.49912	−	0.401688i	−0.0990647	−	0.0265443i	−0.308011	+	0.951383i	$0.599663\pi$
$230$			1.51395i			0.0998268i
$231$	−0.781086	+	2.06682i	−0.0513917	+	0.135987i
$232$	−4.11589	+	4.11589i	−0.270222	+	0.270222i
$233$	9.96467			0.652807			0.326403	−	0.945231i	$-0.394163\pi$
$233$	9.96467			0.652807			0.326403	+	0.945231i	$0.394163\pi$
$234$	−9.04985	+	5.92454i	−0.591608	+	0.387299i
$235$	8.72139			0.568921
$236$	−3.42622	+	3.42622i	−0.223028	+	0.223028i
$237$	−6.03531	+	0.988058i	−0.392036	+	0.0641812i
$238$		−	1.17442i		−	0.0761262i
$239$	−0.0697473	−	0.0186887i	−0.00451158	−	0.00120887i	0.256563	−	0.966528i	$-0.417410\pi$
$239$	−0.0697473	−	0.0186887i	−0.00451158	−	0.00120887i	−0.261074	+	0.965319i	$0.584077\pi$
$240$	−0.733745	−	1.62525i	−0.0473630	−	0.104909i
$241$	−18.0719	−	4.84236i	−1.16412	−	0.311924i	−0.375507	−	0.926819i	$-0.622532\pi$
$241$	−18.0719	−	4.84236i	−1.16412	−	0.311924i	−0.788609	+	0.614895i	$0.789198\pi$
$242$	−1.55476	−	1.55476i	−0.0999436	−	0.0999436i
$243$	−4.42419	−	14.9475i	−0.283812	−	0.958880i
$244$	−4.95929	+	2.86325i	−0.317486	+	0.183301i
$245$	−5.00617	−	5.00617i	−0.319833	−	0.319833i
$246$	2.61579	+	15.9779i	0.166777	+	1.01872i
$247$	0.913390	+	3.50259i	0.0581176	+	0.222864i
$248$	4.97083	−	2.86991i	0.315648	−	0.182240i
$249$	8.73442	−	12.1541i	0.553521	−	0.770238i
$250$	9.20409			0.582117
$251$	−10.5789	+	18.3232i	−0.667735	+	1.15655i	0.310802	+	0.950475i	$0.399403\pi$
$251$	−10.5789	+	18.3232i	−0.667735	+	1.15655i	−0.978536	+	0.206075i	$0.933931\pi$
$252$	0.943486	+	0.468450i	0.0594340	+	0.0295096i
$253$	5.16037	−	1.38272i	0.324430	−	0.0869308i
$254$	4.86055	−	18.1398i	0.304978	−	1.13819i
$255$	−5.93478	−	0.592624i	−0.371650	−	0.0371116i
$256$	1.00000			0.0625000
$257$	−7.32194	+	12.6820i	−0.456730	+	0.791079i	−0.998786	−	0.0492631i	$-0.984313\pi$
$257$	−7.32194	+	12.6820i	−0.456730	+	0.791079i	0.542056	+	0.840342i	$0.317646\pi$
$258$	−4.32363	+	1.95197i	−0.269178	+	0.121525i
$259$	1.56361	+	0.902752i	0.0971582	+	0.0560943i
$260$	−3.57903	−	0.984764i	−0.221962	−	0.0610724i
$261$	−17.1175	−	3.45299i	−1.05954	−	0.213735i
$262$	0.871165	−	3.25123i	0.0538207	−	0.200862i
$263$			11.5254i			0.710686i	0.934736	+	0.355343i	$0.115636\pi$
$263$			11.5254i			0.710686i	−0.934736	+	0.355343i	$0.884364\pi$
$264$	−4.86960	+	3.98538i	−0.299703	+	0.245283i
$265$	0.712791	−	2.66017i	0.0437864	−	0.163413i
$266$	0.249260	−	0.249260i	0.0152831	−	0.0152831i
$267$	−16.3779	+	7.39409i	−1.00231	+	0.452511i
$268$	−3.90143	−	14.5603i	−0.238318	−	0.889414i
$269$	17.7279	+	10.2352i	1.08089	+	0.624052i	0.931136	−	0.364671i	$-0.118818\pi$
$269$	17.7279	+	10.2352i	1.08089	+	0.624052i	0.149754	+	0.988723i	$0.452152\pi$
$270$	2.84335	−	4.53141i	0.173041	−	0.275773i
$271$	0.537040	+	0.143899i	0.0326229	+	0.00874127i	0.275094	−	0.961417i	$-0.411291\pi$
$271$	0.537040	+	0.143899i	0.0326229	+	0.00874127i	−0.242471	+	0.970159i	$0.577958\pi$
$272$	1.67236	−	2.89660i	0.101401	−	0.175632i
$273$	2.00456	−	0.888859i	0.121321	−	0.0537962i
$274$	−1.94670	−	3.37178i	−0.117604	−	0.203697i
$275$	−3.70481	−	13.8265i	−0.223408	−	0.833772i
$276$	−0.411501	−	2.51355i	−0.0247694	−	0.151298i
$277$	10.4571	−	6.03744i	0.628309	−	0.362754i	−0.151788	−	0.988413i	$-0.548503\pi$
$277$	10.4571	−	6.03744i	0.628309	−	0.362754i	0.780097	+	0.625659i	$0.215170\pi$
$278$	−0.390670	+	0.390670i	−0.0234308	+	0.0234308i
$279$	15.4230	+	7.65769i	0.923352	+	0.458454i
$280$	0.0935622	+	0.349179i	0.00559141	+	0.0208674i
$281$	14.0707	−	3.77024i	0.839388	−	0.224913i	0.186583	−	0.982439i	$-0.440259\pi$
$281$	14.0707	−	3.77024i	0.839388	−	0.224913i	0.652805	+	0.757526i	$0.273592\pi$
$282$	−14.4798	+	2.37053i	−0.862260	+	0.141163i
$283$	−11.5559	−	6.67178i	−0.686925	−	0.396596i	0.115534	−	0.993304i	$-0.463142\pi$
$283$	−11.5559	−	6.67178i	−0.686925	−	0.396596i	−0.802459	+	0.596707i	$0.796475\pi$
$284$	−5.74681	+	1.53985i	−0.341010	+	0.0913735i
$285$	−1.13383	−	1.38539i	−0.0671622	−	0.0820632i
$286$	−0.0878267	+	13.0987i	−0.00519330	+	0.774543i
$287$		−	3.28222i		−	0.193743i
$288$	1.65996	+	2.49890i	0.0978142	+	0.147249i
$289$	2.90646	+	5.03413i	0.170968	+	0.296125i
$290$	−2.99633	−	5.18979i	−0.175950	−	0.304755i
$291$	−23.3166	+	10.5267i	−1.36684	+	0.617084i
$292$	−2.47165	−	2.47165i	−0.144642	−	0.144642i
$293$	14.9275	+	14.9275i	0.872071	+	0.872071i	0.992698	−	0.120627i	$-0.0384904\pi$
$293$	14.9275	+	14.9275i	0.872071	+	0.872071i	−0.120627	+	0.992698i	$0.538490\pi$
$294$	9.67228	+	6.95086i	0.564099	+	0.405382i
$295$	−2.49425	−	4.32017i	−0.145221	−	0.251530i
$296$	2.57101	+	4.45313i	0.149437	+	0.258833i
$297$	−18.0424	−	5.55309i	−1.04693	−	0.322223i
$298$		−	12.9463i		−	0.749960i
$299$	−4.57382	−	2.68174i	−0.264511	−	0.155089i
$300$	−6.73473	+	1.10256i	−0.388830	+	0.0636564i
$301$	0.928918	−	0.248903i	0.0535419	−	0.0143465i
$302$	−7.82599	−	4.51833i	−0.450335	−	0.260001i
$303$	−19.0242	−	23.2450i	−1.09291	−	1.33539i
$304$	0.969723	−	0.259837i	0.0556174	−	0.0149027i
$305$	−1.52590	−	5.69472i	−0.0873726	−	0.326079i
$306$	10.0144	−	0.629199i	0.572484	−	0.0359689i
$307$	−10.9437	+	10.9437i	−0.624590	+	0.624590i	−0.946702	−	0.322111i	$-0.895607\pi$
$307$	−10.9437	+	10.9437i	−0.624590	+	0.624590i	0.322111	+	0.946702i	$0.395607\pi$
$308$	1.10474	−	0.637824i	0.0629486	−	0.0363434i
$309$	17.2568	+	6.52165i	0.981707	+	0.371004i
$310$	1.52945	+	5.70798i	0.0868668	+	0.324191i
$311$	12.9553	+	22.4392i	0.734626	+	1.27241i	0.954887	+	0.296968i	$0.0959756\pi$
$311$	12.9553	+	22.4392i	0.734626	+	1.27241i	−0.220262	+	0.975441i	$0.570691\pi$
$312$	6.20979	+	0.662166i	0.351560	+	0.0374877i
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.438028	−	0.898961i	$-0.355677\pi$
$313$	17.6482	−	30.5676i	0.997537	−	1.72779i	0.559509	−	0.828824i	$-0.310990\pi$
$314$	−10.8196	−	2.89910i	−0.610586	−	0.163606i
$315$	−0.717255	+	0.813427i	−0.0404127	+	0.0458314i
$316$	3.05783	+	1.76544i	0.172016	+	0.0993137i
$317$	−3.27025	−	12.2048i	−0.183676	−	0.685487i	−0.994910	−	0.100766i	$-0.967871\pi$
$317$	−3.27025	−	12.2048i	−0.183676	−	0.685487i	0.811234	−	0.584721i	$-0.198796\pi$
$318$	−0.460370	+	4.61033i	−0.0258163	+	0.258535i
$319$	−14.9531	+	14.9531i	−0.837212	+	0.837212i
$320$	−0.266463	+	0.994452i	−0.0148957	+	0.0555916i
$321$	1.29655	+	0.489989i	0.0723665	+	0.0273485i
$322$			0.516339i			0.0287745i
$323$	0.869078	−	3.24344i	0.0483568	−	0.180470i
$324$	−3.48905	+	8.29618i	−0.193836	+	0.460899i
$325$	−7.18538	+	12.2549i	−0.398573	+	0.679782i
$326$	7.69205	+	4.44101i	0.426023	+	0.245965i
$327$	−1.42118	+	14.2323i	−0.0785915	+	0.787048i
$328$	4.67384	−	8.09532i	0.258069	−	0.446989i
$329$	2.97447			0.163988
$330$	−2.66570	−	5.90454i	−0.146742	−	0.325034i
$331$	−2.57987	+	9.62819i	−0.141802	+	0.529213i	0.858075	+	0.513525i	$0.171661\pi$
$331$	−2.57987	+	9.62819i	−0.141802	+	0.529213i	−0.999877	+	0.0156883i	$0.995006\pi$
$332$	−8.34680	+	2.23652i	−0.458090	+	0.122745i
$333$	−6.86015	+	13.8167i	−0.375934	+	0.757153i
$334$	4.64560	−	8.04642i	0.254196	−	0.440281i
$335$	15.5191			0.847901
$336$	−0.250247	−	0.554299i	−0.0136521	−	0.0302395i
$337$	−25.2475	+	14.5766i	−1.37532	+	0.794040i	−0.991592	−	0.129406i	$-0.958693\pi$
$337$	−25.2475	+	14.5766i	−1.37532	+	0.794040i	−0.383727	+	0.923447i	$0.625360\pi$
$338$	9.31483	−	9.06830i	0.506660	−	0.493250i
$339$	−18.0847	+	14.8009i	−0.982227	+	0.803874i
$340$	2.43491	+	2.43491i	0.132052	+	0.132052i
$341$	18.0591	−	10.4264i	0.977954	−	0.564622i
$342$	2.25901	+	1.99193i	0.122153	+	0.107711i
$343$	−3.44537	−	3.44537i	−0.186032	−	0.186032i
$344$	2.64553	+	0.708868i	0.142638	+	0.0382196i
$345$	2.60926	+	0.260550i	0.140478	+	0.0140276i
$346$	−10.2276	−	2.74049i	−0.549841	−	0.147329i
$347$		−	14.3451i		−	0.770084i	−0.922899	−	0.385042i	$-0.874187\pi$
$347$		−	14.3451i		−	0.770084i	0.922899	−	0.385042i	$-0.125813\pi$
$348$	6.38531	+	7.80200i	0.342289	+	0.418231i
$349$	18.7095	−	18.7095i	1.00150	−	1.00150i	0.00149761	−	0.999999i	$-0.499523\pi$
$349$	18.7095	−	18.7095i	1.00150	−	1.00150i	0.999999	−	0.00149761i	$-0.000476704\pi$
$350$	1.38346			0.0739492
$351$	8.65334	+	16.6169i	0.461881	+	0.886942i
$352$	3.63301			0.193640
$353$	−8.42845	+	8.42845i	−0.448601	+	0.448601i	−0.894889	−	0.446288i	$-0.852746\pi$
$353$	−8.42845	+	8.42845i	−0.448601	+	0.448601i	0.446288	+	0.894889i	$0.352746\pi$
$354$	5.31536	+	6.49466i	0.282508	+	0.345188i
$355$		−	6.12524i		−	0.325094i
$356$	10.0213	+	2.68520i	0.531127	+	0.142315i
$357$	−2.02409	−	0.202117i	−0.107126	−	0.0106972i
$358$	24.1669	+	6.47549i	1.27726	+	0.342240i
$359$	13.9898	+	13.9898i	0.738351	+	0.738351i	0.972259	−	0.233907i	$-0.0751513\pi$
$359$	13.9898	+	13.9898i	0.738351	+	0.738351i	−0.233907	+	0.972259i	$0.575151\pi$
$360$	−2.92736	+	0.984889i	−0.154285	+	0.0519082i
$361$	−15.5816	+	8.99606i	−0.820086	+	0.473477i
$362$	16.5374	+	16.5374i	0.869188	+	0.869188i
$363$	−2.94717	+	2.41202i	−0.154686	+	0.126598i
$364$	−1.22064	−	0.335858i	−0.0639791	−	0.0176038i
$365$	3.11654	−	1.79934i	0.163127	−	0.0941815i
$366$	4.08125	+	9.04000i	0.213331	+	0.472528i
$367$	16.6794			0.870658			0.435329	−	0.900271i	$-0.356632\pi$
$367$	16.6794			0.870658			0.435329	+	0.900271i	$0.356632\pi$
$368$	−0.735260	+	1.27351i	−0.0383281	+	0.0663862i
$369$	27.9878	−	1.75846i	1.45699	−	0.0915419i
$370$	−5.11350	+	1.37016i	−0.265838	+	0.0712311i
$371$	0.243101	−	0.907265i	0.0126212	−	0.0471029i
$372$	−4.09075	−	9.06104i	−0.212096	−	0.469793i
$373$	−0.533360			−0.0276163			−0.0138082	−	0.999905i	$-0.504395\pi$
$373$	−0.533360			−0.0276163			−0.0138082	+	0.999905i	$0.504395\pi$
$374$	6.07568	−	10.5234i	0.314166	−	0.544152i
$375$	1.58402	−	15.8631i	0.0817986	−	0.819165i
$376$	7.33629	+	4.23561i	0.378340	+	0.218435i
$377$	20.9865	+	0.140715i	1.08086	+	0.00724717i
$378$	0.969738	−	1.54546i	0.0498780	−	0.0794898i
$379$	−8.93403	+	33.3422i	−0.458910	+	1.71268i	0.217421	+	0.976078i	$0.430236\pi$
$379$	−8.93403	+	33.3422i	−0.458910	+	1.71268i	−0.676331	+	0.736598i	$0.736431\pi$
$380$			1.03358i			0.0530215i
$381$	−30.4271	−	11.4989i	−1.55883	−	0.589108i
$382$	−3.18658	+	11.8925i	−0.163040	+	0.608472i
$383$	1.42871	−	1.42871i	0.0730038	−	0.0730038i	−0.669662	−	0.742666i	$-0.733561\pi$
$383$	1.42871	−	1.42871i	0.0730038	−	0.0730038i	0.742666	+	0.669662i	$0.233561\pi$
$384$	0.172100	−	1.72348i	0.00878244	−	0.0879509i
$385$	0.339912	+	1.26857i	0.0173235	+	0.0646523i
$386$	11.2064	+	6.47000i	0.570389	+	0.329314i
$387$	2.62009	+	7.78763i	0.133187	+	0.395867i
$388$	14.2669	+	3.82280i	0.724292	+	0.194073i
$389$	0.968658	−	1.67777i	0.0491129	−	0.0850661i	−0.840424	−	0.541930i	$-0.817694\pi$
$389$	0.968658	−	1.67777i	0.0491129	−	0.0850661i	0.889537	+	0.456864i	$0.151027\pi$
$390$	−2.31317	+	5.99890i	−0.117132	+	0.303766i
$391$	2.45923	+	4.25951i	0.124369	+	0.215413i
$392$	−1.77982	−	6.64239i	−0.0898947	−	0.335491i
$393$	−5.45350	−	2.06097i	−0.275093	−	0.103962i
$394$	18.5028	−	10.6826i	0.932158	−	0.538182i
$395$	−2.57044	+	2.57044i	−0.129333	+	0.129333i
$396$	6.03066	+	9.07854i	0.303052	+	0.456214i
$397$	−8.86089	−	33.0693i	−0.444716	−	1.65970i	−0.716687	−	0.697395i	$-0.754342\pi$
$397$	−8.86089	−	33.0693i	−0.444716	−	1.65970i	0.271971	−	0.962305i	$-0.412324\pi$
$398$	−21.4568	+	5.74933i	−1.07553	+	0.288188i
$399$	−0.386698	−	0.472493i	−0.0193591	−	0.0236542i
$400$	3.41219	+	1.97003i	0.170610	+	0.0985016i
$401$	8.68363	−	2.32677i	0.433640	−	0.116193i	−0.0353944	−	0.999373i	$-0.511269\pi$
$401$	8.68363	−	2.32677i	0.433640	−	0.116193i	0.469034	+	0.883180i	$0.344602\pi$
$402$	−25.7659	+	4.21820i	−1.28509	+	0.210385i
$403$	−19.9537	−	5.49023i	−0.993964	−	0.273488i
$404$			17.3422i			0.862804i
$405$	−7.32045	−	5.68031i	−0.363756	−	0.282257i
$406$	−1.02191	−	1.77000i	−0.0507166	−	0.0878438i
$407$	9.34052	+	16.1783i	0.462992	+	0.801926i
$408$	−4.70443	−	3.38078i	−0.232904	−	0.167373i
$409$	−10.4309	−	10.4309i	−0.515772	−	0.515772i	0.400517	−	0.916289i	$-0.368831\pi$
$409$	−10.4309	−	10.4309i	−0.515772	−	0.515772i	−0.916289	+	0.400517i	$0.868831\pi$
$410$	6.80501	+	6.80501i	0.336075	+	0.336075i
$411$	−6.14622	+	2.77481i	−0.303171	+	0.136871i
$412$	−5.32549	−	9.22402i	−0.262368	−	0.454435i
$413$	−0.850676	−	1.47341i	−0.0418590	−	0.0725019i
$414$	−4.40288	+	0.276631i	−0.216390	+	0.0135957i
$415$		−	8.89644i		−	0.436709i
$416$	−2.53236	−	2.56655i	−0.124159	−	0.125835i
$417$	0.606077	+	0.740545i	0.0296797	+	0.0362647i
$418$	3.52301	−	0.943989i	0.172316	−	0.0461720i
$419$	−30.2692	−	17.4759i	−1.47875	−	0.853755i	−0.479036	−	0.877795i	$-0.659014\pi$
$419$	−30.2692	−	17.4759i	−1.47875	−	0.853755i	−0.999711	+	0.0240402i	$0.992347\pi$
$420$	0.617905	−	0.101159i	0.0301507	−	0.00493605i
$421$	2.55665	−	0.685052i	0.124603	−	0.0333874i	−0.195978	−	0.980608i	$-0.562788\pi$
$421$	2.55665	−	0.685052i	0.124603	−	0.0333874i	0.320582	+	0.947221i	$0.396122\pi$
$422$	−4.74961	−	17.7258i	−0.231207	−	0.862878i
$423$	1.59359	+	25.3636i	0.0774828	+	1.23322i
$424$	1.89152	−	1.89152i	0.0918604	−	0.0918604i
$425$	11.4128	−	6.58918i	0.553602	−	0.319622i
$426$	1.66488	+	10.1695i	0.0806637	+	0.492715i
$427$	−0.520414	−	1.94221i	−0.0251846	−	0.0939903i
$428$	−0.400118	−	0.693025i	−0.0193404	−	0.0334986i
$429$	22.5602	+	2.40565i	1.08922	+	0.116146i
$430$	−1.40987	+	2.44197i	−0.0679900	+	0.117762i
$431$	−14.1857	−	3.80104i	−0.683301	−	0.183090i	−0.0995618	−	0.995031i	$-0.531744\pi$
$431$	−14.1857	−	3.80104i	−0.683301	−	0.183090i	−0.583739	+	0.811942i	$0.698411\pi$
$432$	4.59249	−	2.43085i	0.220956	−	0.116954i
$433$	−13.2828	−	7.66884i	−0.638332	−	0.368541i	0.145640	−	0.989338i	$-0.453476\pi$
$433$	−13.2828	−	7.66884i	−0.638332	−	0.368541i	−0.783972	+	0.620797i	$0.786809\pi$
$434$	0.521626	+	1.94673i	0.0250388	+	0.0934462i
$435$	−9.46017	+	4.27095i	−0.453580	+	0.204776i
$436$	5.83921	−	5.83921i	0.279647	−	0.279647i
$437$	−0.382095	+	1.42600i	−0.0182781	+	0.0682147i
$438$	−4.68521	+	3.83447i	−0.223868	+	0.183218i
$439$		−	10.8523i		−	0.517952i	−0.965884	−	0.258976i	$-0.916615\pi$
$439$		−	10.8523i		−	0.517952i	0.965884	−	0.258976i	$-0.0833851\pi$
$440$	−0.968061	+	3.61285i	−0.0461505	+	0.172236i
$441$	13.6443	−	15.4737i	0.649727	−	0.736844i
$442$	−11.6693	+	3.04306i	−0.555051	+	0.144744i
$443$	28.8694	+	16.6678i	1.37163	+	0.791909i	0.991133	−	0.132874i	$-0.0424205\pi$
$443$	28.8694	+	16.6678i	1.37163	+	0.791909i	0.380494	+	0.924783i	$0.375754\pi$
$444$	8.11734	−	3.66471i	0.385232	−	0.173919i
$445$	−5.34060	+	9.25018i	−0.253169	+	0.438501i
$446$	−25.3541			−1.20055
$447$	−22.3127	−	2.22806i	−1.05535	−	0.105384i
$448$	−0.0908784	+	0.339163i	−0.00429360	+	0.0160239i
$449$	−17.6413	+	4.72697i	−0.832543	+	0.223079i	−0.649823	−	0.760086i	$-0.725157\pi$
$449$	−17.6413	+	4.72697i	−0.832543	+	0.223079i	−0.182720	+	0.983165i	$0.558490\pi$
$450$	0.741196	+	11.7969i	0.0349403	+	0.556112i
$451$	16.9801	−	29.4104i	0.799561	−	1.38488i
$452$	13.4923			0.634623
$453$	−9.13411	+	12.7103i	−0.429158	+	0.597183i
$454$	−21.5858	+	12.4626i	−1.01307	+	0.584898i
$455$	0.659251	−	1.12438i	0.0309062	−	0.0527117i
$456$	−0.280934	−	1.71602i	−0.0131559	−	0.0803598i
$457$	4.51133	+	4.51133i	0.211031	+	0.211031i	0.804705	−	0.593674i	$-0.202323\pi$
$457$	4.51133	+	4.51133i	0.211031	+	0.211031i	−0.593674	+	0.804705i	$0.702323\pi$
$458$	1.34408	−	0.776002i	0.0628045	−	0.0362602i
$459$	0.639063	−	17.3679i	0.0298289	−	0.810663i
$460$	−1.07052	−	1.07052i	−0.0499134	−	0.0499134i
$461$	−34.7844	−	9.32045i	−1.62007	−	0.434097i	−0.669049	−	0.743219i	$-0.733298\pi$
$461$	−34.7844	−	9.32045i	−1.62007	−	0.434097i	−0.951022	+	0.309122i	$0.899965\pi$
$462$	−0.909150	−	2.01377i	−0.0422975	−	0.0936892i
$463$	21.6855	+	5.81062i	1.00781	+	0.270042i	0.724715	−	0.689049i	$-0.241972\pi$
$463$	21.6855	+	5.81062i	1.00781	+	0.270042i	0.283097	+	0.959091i	$0.408638\pi$
$464$		−	5.82075i		−	0.270222i
$465$	10.1008	−	1.65363i	0.468413	−	0.0766852i
$466$	−7.04608	+	7.04608i	−0.326403	+	0.326403i
$467$	14.0000			0.647843			0.323921	−	0.946084i	$-0.394999\pi$
$467$	14.0000			0.647843			0.323921	+	0.946084i	$0.394999\pi$
$468$	2.20993	−	10.5885i	0.102154	−	0.489453i
$469$	5.29288			0.244402
$470$	−6.16695	+	6.16695i	−0.284460	+	0.284460i
$471$	−6.85860	+	18.1484i	−0.316028	+	0.836235i
$472$		−	4.84540i		−	0.223028i
$473$	9.61125	+	2.57533i	0.441926	+	0.118414i
$474$	3.56895	−	4.96627i	0.163927	−	0.228108i
$475$	3.82077	+	1.02377i	0.175309	+	0.0469739i
$476$	0.830439	+	0.830439i	0.0380631	+	0.0380631i
$477$	7.86658	+	1.58688i	0.360186	+	0.0726581i
$478$	0.0625337	−	0.0361039i	0.00286023	−	0.00165135i
$479$	−18.8236	−	18.8236i	−0.860073	−	0.860073i	0.131273	−	0.991346i	$-0.458093\pi$
$479$	−18.8236	−	18.8236i	−0.860073	−	0.860073i	−0.991346	+	0.131273i	$0.958093\pi$
$480$	1.66806	+	0.630388i	0.0761362	+	0.0287731i
$481$	4.91843	−	17.8755i	0.224261	−	0.815054i
$482$	16.2029	−	9.35472i	0.738020	−	0.426096i
$483$	0.889900	+	0.0888619i	0.0404919	+	0.00404336i
$484$	2.19876			0.0999436
$485$	−7.60319	+	13.1691i	−0.345243	+	0.597978i
$486$	13.6978	+	7.44107i	0.621346	+	0.337534i
$487$	−14.7534	+	3.95317i	−0.668542	+	0.179135i	−0.577098	−	0.816675i	$-0.695815\pi$
$487$	−14.7534	+	3.95317i	−0.668542	+	0.179135i	−0.0914441	+	0.995810i	$0.529148\pi$
$488$	1.48213	−	5.53137i	0.0670927	−	0.250393i
$489$	8.97778	−	12.4928i	0.405989	−	0.564944i
$490$	7.07980			0.319833
$491$	−0.935816	+	1.62088i	−0.0422328	+	0.0731493i	−0.886369	−	0.462979i	$-0.846780\pi$
$491$	−0.935816	+	1.62088i	−0.0422328	+	0.0731493i	0.844136	+	0.536129i	$0.180114\pi$
$492$	−13.1478	−	9.44847i	−0.592747	−	0.425970i
$493$	−16.8604	−	9.73437i	−0.759355	−	0.438414i
$494$	−3.12257	−	1.83084i	−0.140491	−	0.0823734i
$495$	−10.6351	+	3.57811i	−0.478013	+	0.160824i
$496$	−1.48558	+	5.54424i	−0.0667043	+	0.248944i
$497$		−	2.08904i		−	0.0937064i
$498$	2.41811	+	14.7704i	0.108358	+	0.661880i
$499$	−2.93283	+	10.9455i	−0.131291	+	0.489986i	−0.999986	−	0.00536247i	$-0.998293\pi$
$499$	−2.93283	+	10.9455i	−0.131291	+	0.489986i	0.868694	+	0.495349i	$0.164960\pi$
$500$	−6.50827	+	6.50827i	−0.291059	+	0.291059i
$501$	−13.0683	−	9.39139i	−0.583850	−	0.419576i
$502$	−5.47604	−	20.4369i	−0.244408	−	0.912142i
$503$	0.311572	+	0.179886i	0.0138923	+	0.00802072i	0.506930	−	0.861987i	$-0.330780\pi$
$503$	0.311572	+	0.179886i	0.0138923	+	0.00802072i	−0.493038	+	0.870008i	$0.664114\pi$
$504$	−0.998390	+	0.335901i	−0.0444718	+	0.0149622i
$505$	−17.2459	−	4.62104i	−0.767434	−	0.205633i
$506$	−2.67121	+	4.62667i	−0.118750	+	0.205680i
$507$	−14.0259	−	17.6146i	−0.622914	−	0.782290i
$508$	9.38987	+	16.2637i	0.416608	+	0.721586i
$509$	−11.1705	−	41.6889i	−0.495124	−	1.84783i	−0.529333	−	0.848414i	$-0.677558\pi$
$509$	−11.1705	−	41.6889i	−0.495124	−	1.84783i	0.0342084	−	0.999415i	$-0.489109\pi$
$510$	4.61557	−	3.77748i	0.204381	−	0.167269i
$511$	1.06291	−	0.613672i	0.0470204	−	0.0271472i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.82182	−	3.55055i	0.168738	−	0.156761i
$514$	−3.79011	−	14.1449i	−0.167175	−	0.623905i
$515$	10.5919	−	2.83809i	0.466734	−	0.125061i
$516$	1.67702	−	4.43753i	0.0738265	−	0.195351i
$517$	26.6528	+	15.3880i	1.17219	+	0.676763i
$518$	−1.74398	+	0.467299i	−0.0766262	+	0.0205319i
$519$	−6.48335	+	17.1555i	−0.284587	+	0.753042i
$520$	3.22709	−	1.83442i	0.141517	−	0.0804447i
$521$			39.0644i			1.71144i	0.517436	+	0.855722i	$0.326887\pi$
$521$			39.0644i			1.71144i	−0.517436	+	0.855722i	$0.673113\pi$
$522$	14.5455	−	9.66223i	0.636639	−	0.422904i
$523$	−22.3670	−	38.7408i	−0.978041	−	1.69402i	−0.669512	−	0.742801i	$-0.733497\pi$
$523$	−22.3670	−	38.7408i	−0.978041	−	1.69402i	−0.308529	−	0.951215i	$-0.599837\pi$
$524$	1.68296	+	2.91497i	0.0735205	+	0.127341i
$525$	0.238094	−	2.38437i	0.0103913	−	0.104062i
$526$	−8.14968	−	8.14968i	−0.355343	−	0.355343i
$527$	13.5751	+	13.5751i	0.591339	+	0.591339i
$528$	0.625241	−	6.26142i	0.0272101	−	0.272493i
$529$	10.4188	+	18.0459i	0.452991	+	0.784603i
$530$	1.37701	+	2.38505i	0.0598134	+	0.103600i
$531$	12.1082	−	8.04319i	0.525451	−	0.349045i
$532$			0.352507i			0.0152831i
$533$	−32.6128	+	8.50464i	−1.41262	+	0.368377i
$534$	6.35254	−	16.8094i	0.274901	−	0.727412i
$535$	0.795797	−	0.213233i	0.0344053	−	0.00921887i
$536$	13.0544	+	7.53699i	0.563866	+	0.325548i
$537$	15.3195	−	40.5367i	0.661085	−	1.74929i
$538$	−19.7729	+	5.29814i	−0.852471	+	0.228419i
$539$	−6.46612	−	24.1319i	−0.278515	−	1.03943i
$540$	1.19364	+	5.21474i	0.0513660	+	0.224407i
$541$	20.3887	−	20.3887i	0.876580	−	0.876580i	−0.116599	−	0.993179i	$-0.537199\pi$
$541$	20.3887	−	20.3887i	0.876580	−	0.876580i	0.993179	+	0.116599i	$0.0371993\pi$
$542$	−0.481497	+	0.277992i	−0.0206821	+	0.0119408i
$543$	31.3480	−	25.6558i	1.34527	−	1.10100i
$544$	0.865675	+	3.23074i	0.0371155	+	0.138517i
$545$	4.25088	+	7.36274i	0.182088	+	0.315385i
$546$	−0.788918	+	2.04595i	−0.0337626	+	0.0875587i
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	−0.589751	−	0.807585i	$-0.700774\pi$
$547$	9.46079	−	16.3866i	0.404514	−	0.700639i	0.994265	+	0.106947i	$0.0341074\pi$
$548$	3.76073	+	1.00768i	0.160650	+	0.0430462i
$549$	16.2826	−	5.47818i	0.694926	−	0.233803i
$550$	12.3965	+	7.15714i	0.528590	+	0.305182i
$551$	−1.51244	−	5.64452i	−0.0644323	−	0.240465i
$552$	2.06833	+	1.48638i	0.0880338	+	0.0632644i
$553$	−0.876661	+	0.876661i	−0.0372794	+	0.0372794i
$554$	−3.12521	+	11.6634i	−0.132777	+	0.495532i
$555$	1.48141	+	9.04882i	0.0628822	+	0.384101i
$556$		−	0.552490i		−	0.0234308i
$557$	0.839623	−	3.13351i	0.0355760	−	0.132771i	−0.945854	−	0.324593i	$-0.894773\pi$
$557$	0.839623	−	3.13351i	0.0355760	−	0.132771i	0.981430	+	0.191821i	$0.0614394\pi$
$558$	−16.3205	+	5.49092i	−0.690903	+	0.232449i
$559$	−4.88009	−	8.58499i	−0.206406	−	0.363106i
$560$	−0.313065	−	0.180748i	−0.0132294	−	0.00763801i
$561$	−17.0912	−	12.2824i	−0.721592	−	0.518563i
$562$	−7.28354	+	12.6155i	−0.307237	+	0.532151i
$563$	2.30675			0.0972180			0.0486090	−	0.998818i	$-0.484521\pi$
$563$	2.30675			0.0972180			0.0486090	+	0.998818i	$0.484521\pi$
$564$	8.56256	−	11.9150i	0.360549	−	0.501712i
$565$	−3.59518	+	13.4174i	−0.151251	+	0.564475i
$566$	12.8889	−	3.45357i	0.541761	−	0.145164i
$567$	−2.49667	−	1.93730i	−0.104850	−	0.0813588i
$568$	2.97477	−	5.15245i	0.124818	−	0.216192i
$569$	9.50229			0.398357			0.199178	−	0.979963i	$-0.436173\pi$
$569$	9.50229			0.398357			0.199178	+	0.979963i	$0.436173\pi$
$570$	1.78135	+	0.177879i	0.0746127	+	0.00745053i
$571$	−22.0695	+	12.7418i	−0.923578	+	0.533228i	−0.884775	−	0.466019i	$-0.845688\pi$
$571$	−22.0695	+	12.7418i	−0.923578	+	0.533228i	−0.0388033	+	0.999247i	$0.512355\pi$
$572$	−9.20008	−	9.32429i	−0.384675	−	0.389868i
$573$	19.9480	+	7.53870i	0.833341	+	0.314934i
$574$	2.32088	+	2.32088i	0.0968717	+	0.0968717i
$575$	−5.01770	+	2.89697i	−0.209253	+	0.120812i
$576$	−2.94076	−	0.593221i	−0.122532	−	0.0247176i
$577$	17.9008	+	17.9008i	0.745221	+	0.745221i	0.973577	−	0.228357i	$-0.0733353\pi$
$577$	17.9008	+	17.9008i	0.745221	+	0.745221i	−0.228357	+	0.973577i	$0.573335\pi$
$578$	−5.61484	−	1.50449i	−0.233547	−	0.0625786i
$579$	13.0795	−	18.2005i	0.543567	−	0.756385i
$580$	5.78846	+	1.55101i	0.240353	+	0.0644023i
$581$		−	3.03417i		−	0.125879i
$582$	9.04385	−	23.9308i	0.374880	−	0.991964i
$583$	6.87191	−	6.87191i	0.284606	−	0.284606i
$584$	3.49544			0.144642
$585$	9.94088	+	5.01911i	0.411005	+	0.207515i
$586$	−21.1106			−0.872071
$587$	−21.8482	+	21.8482i	−0.901773	+	0.901773i	−0.995590	−	0.0938164i	$-0.970093\pi$
$587$	−21.8482	+	21.8482i	−0.901773	+	0.901773i	0.0938164	+	0.995590i	$0.470093\pi$
$588$	−11.7543	+	1.92433i	−0.484741	+	0.0793582i
$589$			5.76239i			0.237435i
$590$	4.81852	+	1.29112i	0.198375	+	0.0531545i
$591$	−15.2269	−	33.7277i	−0.626352	−	1.38737i
$592$	−4.96682	−	1.33085i	−0.204135	−	0.0546978i
$593$	1.91150	+	1.91150i	0.0784959	+	0.0784959i	0.745265	−	0.666769i	$-0.232323\pi$
$593$	1.91150	+	1.91150i	0.0784959	+	0.0784959i	−0.666769	+	0.745265i	$0.732323\pi$
$594$	16.6846	−	8.83130i	0.684576	−	0.362353i
$595$	−1.04711	+	0.604551i	−0.0429274	+	0.0247842i
$596$	9.15442	+	9.15442i	0.374980	+	0.374980i
$597$	6.21614	+	37.9698i	0.254410	+	1.55400i
$598$	5.13046	−	1.33790i	0.209800	−	0.0547108i
$599$	−24.8798	+	14.3643i	−1.01656	+	0.586911i	−0.913105	−	0.407723i	$-0.866323\pi$
$599$	−24.8798	+	14.3643i	−1.01656	+	0.586911i	−0.103454	+	0.994634i	$0.532989\pi$
$600$	3.98255	−	5.54180i	0.162587	−	0.226243i
$601$	30.9870			1.26399			0.631993	−	0.774974i	$-0.282237\pi$
$601$	30.9870			1.26399			0.631993	+	0.774974i	$0.282237\pi$
$602$	−0.480843	+	0.832845i	−0.0195977	+	0.0339442i
$603$	2.83568	+	45.1329i	0.115478	+	1.83795i
$604$	8.72875	−	2.33886i	0.355168	−	0.0951670i
$605$	−0.585887	+	2.18656i	−0.0238197	+	0.0888963i
$606$	29.8888	+	2.98458i	1.21415	+	0.121240i
$607$	10.0680			0.408647			0.204323	−	0.978903i	$-0.434501\pi$
$607$	10.0680			0.408647			0.204323	+	0.978903i	$0.434501\pi$
$608$	−0.501966	+	0.869430i	−0.0203574	+	0.0352600i
$609$	−3.22643	+	1.45663i	−0.130742	+	0.0590255i
$610$	5.10575	+	2.94781i	0.206726	+	0.119353i
$611$	−7.70722	−	29.5550i	−0.311801	−	1.19567i
$612$	−6.63633	+	7.52615i	−0.268258	+	0.304227i
$613$	−5.97413	+	22.2957i	−0.241293	+	0.900516i	0.733918	+	0.679238i	$0.237690\pi$
$613$	−5.97413	+	22.2957i	−0.241293	+	0.900516i	−0.975211	+	0.221278i	$0.928977\pi$
$614$		−	15.4767i		−	0.624590i
$615$	12.8994	−	10.5571i	0.520155	−	0.425705i
$616$	−0.330162	+	1.23218i	−0.0133026	+	0.0496460i
$617$	18.5480	−	18.5480i	0.746714	−	0.746714i	−0.227146	−	0.973861i	$-0.572940\pi$
$617$	18.5480	−	18.5480i	0.746714	−	0.746714i	0.973861	+	0.227146i	$0.0729396\pi$
$618$	−16.8139	+	7.59092i	−0.676355	+	0.305352i
$619$	5.49310	+	20.5005i	0.220786	+	0.823985i	0.984049	+	0.177897i	$0.0569295\pi$
$619$	5.49310	+	20.5005i	0.220786	+	0.823985i	−0.763263	+	0.646088i	$0.776404\pi$
$620$	−5.11763	−	2.95467i	−0.205529	−	0.118662i
$621$	−0.280967	+	7.63588i	−0.0112748	+	0.306417i
$622$	−25.0277	−	6.70614i	−1.00352	−	0.268892i
$623$	−1.82144	+	3.15482i	−0.0729743	+	0.126395i
$624$	−4.85921	+	3.92277i	−0.194524	+	0.157036i
$625$	5.11220	+	8.85460i	0.204488	+	0.354184i
$626$	9.13540	+	34.0938i	0.365124	+	1.36266i
$627$	−1.02063	−	6.23430i	−0.0407602	−	0.248974i
$628$	9.70059	−	5.60064i	0.387096	−	0.223490i
$629$	−12.1612	+	12.1612i	−0.484900	+	0.484900i
$630$	−0.0680039	−	1.08236i	−0.00270934	−	0.0431221i
$631$	2.60255	+	9.71284i	0.103606	+	0.386662i	0.998183	−	0.0602509i	$-0.0191901\pi$
$631$	2.60255	+	9.71284i	0.103606	+	0.386662i	−0.894578	+	0.446913i	$0.852523\pi$
$632$	−3.41056	+	0.913858i	−0.135665	+	0.0363513i
$633$	−31.3674	+	5.13525i	−1.24674	+	0.204108i
$634$	10.9425	+	6.31764i	0.434581	+	0.250906i
$635$	−18.6755	+	5.00410i	−0.741116	+	0.198582i
$636$	−2.93447	−	3.58553i	−0.116359	−	0.142175i
$637$	−12.5409	+	21.3889i	−0.496887	+	0.847460i
$638$		−	21.1468i		−	0.837212i
$639$	17.8135	−	1.11921i	0.704690	−	0.0442754i
$640$	−0.514766	−	0.891601i	−0.0203479	−	0.0352436i
$641$	−3.23854	−	5.60931i	−0.127915	−	0.221555i	0.794954	−	0.606670i	$-0.207495\pi$
$641$	−3.23854	−	5.60931i	−0.127915	−	0.221555i	−0.922868	+	0.385115i	$0.874162\pi$
$642$	−1.26328	+	0.570326i	−0.0498575	+	0.0225090i
$643$	−5.14668	−	5.14668i	−0.202965	−	0.202965i	0.598304	−	0.801269i	$-0.295841\pi$
$643$	−5.14668	−	5.14668i	−0.202965	−	0.202965i	−0.801269	+	0.598304i	$0.795841\pi$
$644$	−0.365107	−	0.365107i	−0.0143872	−	0.0143872i
$645$	3.96604	+	2.85015i	0.156163	+	0.112224i
$646$	1.67893	+	2.90799i	0.0660566	+	0.114413i
$647$	−2.67717	−	4.63699i	−0.105250	−	0.182299i	0.808590	−	0.588372i	$-0.200231\pi$
$647$	−2.67717	−	4.63699i	−0.105250	−	0.182299i	−0.913840	+	0.406073i	$0.866898\pi$
$648$	−3.39915	−	8.33341i	−0.133531	−	0.327367i
$649$		−	17.6034i		−	0.690993i
$650$	−3.58472	−	13.7464i	−0.140604	−	0.539177i
$651$	3.44493	−	0.563978i	0.135017	−	0.0221041i
$652$	−8.57937	+	2.29883i	−0.335994	+	0.0900293i
$653$	−11.7085	−	6.75992i	−0.458190	−	0.264536i	0.253093	−	0.967442i	$-0.418552\pi$
$653$	−11.7085	−	6.75992i	−0.458190	−	0.264536i	−0.711283	+	0.702906i	$0.751886\pi$
$654$	−9.05882	−	11.0687i	−0.354228	−	0.432820i
$655$	−3.34725	+	0.896892i	−0.130788	+	0.0350445i
$656$	2.41936	+	9.02916i	0.0944600	+	0.352529i
$657$	5.80230	+	8.73477i	0.226369	+	0.340776i
$658$	−2.10327	+	2.10327i	−0.0819940	+	0.0819940i
$659$	−22.4923	+	12.9859i	−0.876176	+	0.505861i	−0.869396	−	0.494116i	$-0.835492\pi$
$659$	−22.4923	+	12.9859i	−0.876176	+	0.505861i	−0.00678051	+	0.999977i	$0.502158\pi$
$660$	6.06008	+	2.29021i	0.235888	+	0.0891461i
$661$	3.57302	+	13.3347i	0.138975	+	0.518660i	0.999950	+	0.0100133i	$0.00318737\pi$
$661$	3.57302	+	13.3347i	0.138975	+	0.518660i	−0.860975	+	0.508647i	$0.830146\pi$
$662$	−4.98392	−	8.63240i	−0.193706	−	0.335508i
$663$	3.23638	+	20.6355i	0.125690	+	0.801415i
$664$	4.32062	−	7.48354i	0.167673	−	0.290418i
$665$	−0.350552	−	0.0939301i	−0.0135938	−	0.00364245i
$666$	−4.91905	−	14.6208i	−0.190609	−	0.566543i
$667$	7.41277	+	4.27977i	0.287024	+	0.165713i
$668$	2.40474	+	8.97462i	0.0930422	+	0.347238i
$669$	−4.36343	+	43.6972i	−0.168700	+	1.68943i
$670$	−10.9737	+	10.9737i	−0.423951	+	0.423951i
$671$	5.38458	−	20.0955i	0.207869	−	0.775779i
$672$	0.568900	+	0.214997i	0.0219458	+	0.00829368i
$673$			28.2814i			1.09017i	0.838382	+	0.545083i	$0.183502\pi$
$673$			28.2814i			1.09017i	−0.838382	+	0.545083i	$0.816498\pi$
$674$	7.54543	−	28.1599i	0.290639	−	1.08468i
$675$	20.4593	+	0.752815i	0.787480	+	0.0289759i
$676$	−0.174322	+	12.9988i	−0.00670468	+	0.499955i
$677$	−34.1714	−	19.7289i	−1.31331	−	0.758242i	−0.330671	−	0.943746i	$-0.607275\pi$
$677$	−34.1714	−	19.7289i	−1.31331	−	0.758242i	−0.982644	+	0.185504i	$0.940608\pi$
$678$	2.32202	−	23.2536i	0.0891765	−	0.893051i
$679$	−2.59310	+	4.49139i	−0.0995142	+	0.172364i
$680$	−3.44349			−0.132052
$681$	17.7641	+	39.3475i	0.680721	+	1.50780i
$682$	−5.39711	+	20.1423i	−0.206666	+	0.771288i
$683$	25.3130	−	6.78259i	0.968574	−	0.259529i	0.260348	−	0.965515i	$-0.416163\pi$
$683$	25.3130	−	6.78259i	0.968574	−	0.259529i	0.708226	+	0.705986i	$0.249496\pi$
$684$	−3.00587	+	0.188857i	−0.114932	+	0.00722114i
$685$	−2.00419	+	3.47136i	−0.0765761	+	0.132634i
$686$	4.87249			0.186032
$687$	−1.10611	−	2.45004i	−0.0422007	−	0.0934747i
$688$	−2.37192	+	1.36943i	−0.0904286	+	0.0522090i
$689$	−9.64469	−	0.0646675i	−0.367433	−	0.00246363i
$690$	−2.02926	+	1.66079i	−0.0772527	+	0.0632251i
$691$	8.34355	+	8.34355i	0.317404	+	0.317404i	0.847769	−	0.530366i	$-0.177945\pi$
$691$	8.34355	+	8.34355i	0.317404	+	0.317404i	−0.530366	+	0.847769i	$0.677945\pi$
$692$	9.16985	−	5.29421i	0.348585	−	0.201256i
$693$	−3.62716	+	1.22033i	−0.137784	+	0.0463566i
$694$	10.1435	+	10.1435i	0.385042	+	0.385042i
$695$	0.549425	+	0.147218i	0.0208409	+	0.00558430i
$696$	−10.0319	−	1.00175i	−0.380260	−	0.0379713i
$697$	30.1999	+	8.09204i	1.14390	+	0.306508i
$698$			26.4592i			1.00150i
$699$	10.9311	+	13.3564i	0.413454	+	0.505186i
$700$	−0.978256	+	0.978256i	−0.0369746	+	0.0369746i
$701$	−32.2520			−1.21814			−0.609071	−	0.793115i	$-0.708458\pi$
$701$	−32.2520			−1.21814			−0.609071	+	0.793115i	$0.708458\pi$
$702$	−17.8687	−	5.63105i	−0.674411	−	0.212530i
$703$	−5.16224			−0.194698
$704$	−2.56893	+	2.56893i	−0.0968200	+	0.0968200i
$705$	9.56729	+	11.6900i	0.360325	+	0.440269i
$706$		−	11.9196i		−	0.448601i
$707$	−5.88181	−	1.57603i	−0.221208	−	0.0592726i
$708$	−8.35095	−	0.833893i	−0.313848	−	0.0313396i
$709$	−13.0734	−	3.50300i	−0.490981	−	0.131558i	0.00482996	−	0.999988i	$-0.498463\pi$
$709$	−13.0734	−	3.50300i	−0.490981	−	0.131558i	−0.495811	+	0.868430i	$0.665129\pi$
$710$	4.33120	+	4.33120i	0.162547	+	0.162547i
$711$	−7.94505	−	7.00570i	−0.297963	−	0.262734i
$712$	−8.98484	+	5.18740i	−0.336721	+	0.194406i
$713$	−5.96835	−	5.96835i	−0.223516	−	0.223516i
$714$	1.57416	−	1.28833i	0.0589116	−	0.0482144i
$715$	11.7240	−	6.66447i	0.438454	−	0.249237i
$716$	−21.6674	+	12.5097i	−0.809750	+	0.467509i
$717$	−0.0514622	−	0.113989i	−0.00192189	−	0.00425700i
$718$	−19.7845			−0.738351
$719$	5.20762	−	9.01985i	0.194211	−	0.336384i	−0.752430	−	0.658672i	$-0.771119\pi$
$719$	5.20762	−	9.01985i	0.194211	−	0.336384i	0.946642	+	0.322288i	$0.104452\pi$
$720$	1.37353	−	2.76638i	0.0511886	−	0.103097i
$721$	3.61241	−	0.967944i	0.134533	−	0.0360481i
$722$	4.65670	−	17.3791i	0.173305	−	0.646781i
$723$	−13.3342	−	29.5352i	−0.495903	−	1.09843i
$724$	−23.3875			−0.869188
$725$	11.4671	−	19.8615i	0.425876	−	0.737639i
$726$	0.378406	−	3.78952i	0.0140440	−	0.140642i
$727$	20.0010	+	11.5476i	0.741796	+	0.428276i	0.822722	−	0.568444i	$-0.192454\pi$
$727$	20.0010	+	11.5476i	0.741796	+	0.428276i	−0.0809260	+	0.996720i	$0.525788\pi$
$728$	1.10061	−	0.625638i	0.0407914	−	0.0231877i
$729$	15.1819	−	22.3273i	0.562294	−	0.826938i
$730$	−0.931405	+	3.47605i	−0.0344728	+	0.128654i
$731$			9.16068i			0.338820i
$732$	−9.27813	−	3.50636i	−0.342929	−	0.129599i
$733$	6.58200	−	24.5643i	0.243112	−	0.907305i	−0.731212	−	0.682151i	$-0.761045\pi$
$733$	6.58200	−	24.5643i	0.243112	−	0.907305i	0.974323	−	0.225154i	$-0.0722885\pi$
$734$	−11.7941	+	11.7941i	−0.435329	+	0.435329i
$735$	1.21843	−	12.2019i	0.0449426	−	0.450073i
$736$	−0.380599	−	1.42041i	−0.0140290	−	0.0523571i
$737$	47.4269	+	27.3819i	1.74699	+	1.00863i
$738$	−18.5470	+	21.0338i	−0.682723	+	0.774265i
$739$	23.9997	+	6.43070i	0.882843	+	0.236557i	0.671633	−	0.740884i	$-0.265593\pi$
$739$	23.9997	+	6.43070i	0.882843	+	0.236557i	0.211209	+	0.977441i	$0.432260\pi$
$740$	2.64694	−	4.58464i	0.0973035	−	0.168535i
$741$	−3.69281	+	5.06660i	−0.135659	+	0.186126i
$742$	0.469635	+	0.813432i	0.0172408	+	0.0298620i
$743$	5.53701	+	20.6644i	0.203133	+	0.758104i	0.990010	+	0.140994i	$0.0450299\pi$
$743$	5.53701	+	20.6644i	0.203133	+	0.758104i	−0.786877	+	0.617110i	$0.788303\pi$
$744$	9.29972	+	3.51452i	0.340944	+	0.128849i
$745$	−11.5429	+	6.66432i	−0.422901	+	0.244162i
$746$	0.377142	−	0.377142i	0.0138082	−	0.0138082i
$747$	25.8727	−	1.62557i	0.946633	−	0.0594765i
$748$	3.14500	+	11.7373i	0.114993	+	0.429159i
$749$	0.271410	−	0.0727242i	0.00991712	−	0.00265728i
$750$	10.0968	+	12.3369i	0.368683	+	0.450482i
$751$	36.9669	+	21.3428i	1.34894	+	0.778812i	0.988100	−	0.153816i	$-0.0491562\pi$
$751$	36.9669	+	21.3428i	1.34894	+	0.778812i	0.360842	+	0.932627i	$0.382490\pi$
$752$	−8.18256	+	2.19251i	−0.298387	+	0.0799527i
$753$	−36.1650	+	5.92066i	−1.31792	+	0.215761i
$754$	−14.9392	+	14.7402i	−0.544055	+	0.536808i
$755$			9.30355i			0.338591i
$756$	0.407096	+	1.77851i	0.0148059	+	0.0646839i
$757$	8.17298	+	14.1560i	0.297052	+	0.514509i	0.975460	−	0.220176i	$-0.0706632\pi$
$757$	8.17298	+	14.1560i	0.297052	+	0.514509i	−0.678408	+	0.734685i	$0.737330\pi$
$758$	−17.2592	−	29.8938i	−0.626883	−	1.08579i
$759$	7.51425	+	5.40002i	0.272750	+	0.196008i
$760$	−0.730852	−	0.730852i	−0.0265108	−	0.0265108i
$761$	−4.38948	−	4.38948i	−0.159119	−	0.159119i	0.623057	−	0.782176i	$-0.285890\pi$
$761$	−4.38948	−	4.38948i	−0.159119	−	0.159119i	−0.782176	+	0.623057i	$0.785890\pi$
$762$	29.6462	−	13.3843i	1.07397	−	0.484860i
$763$	1.44978	+	2.51110i	0.0524857	+	0.0909078i
$764$	−6.15600	−	10.6625i	−0.222716	−	0.385756i
$765$	−5.71606	−	8.60495i	−0.206665	−	0.311113i
$766$			2.02050i			0.0730038i
$767$	−12.4359	+	12.2703i	−0.449036	+	0.443055i
$768$	1.09699	+	1.34038i	0.0395843	+	0.0483667i
$769$	−22.4859	+	6.02508i	−0.810863	+

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.09699 + 1.34038i) q^{3} -1.00000i q^{4} +(0.994452 + 0.266463i) q^{5} +(-1.72348 - 0.172100i) q^{6} +(0.339163 + 0.0908784i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.593221 + 2.94076i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.09699 + 1.34038i) q^{3} -1.00000i q^{4} +(0.994452 + 0.266463i) q^{5} +(-1.72348 - 0.172100i) q^{6} +(0.339163 + 0.0908784i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.593221 + 2.94076i) q^{9} +(-0.891601 + 0.514766i) q^{10} +(2.56893 + 2.56893i) q^{11} +(1.34038 - 1.09699i) q^{12} +(0.0241746 - 3.60547i) q^{13} +(-0.304085 + 0.175564i) q^{14} +(0.733745 + 1.62525i) q^{15} -1.00000 q^{16} +(-1.67236 + 2.89660i) q^{17} +(-1.65996 - 2.49890i) q^{18} +(-0.969723 + 0.259837i) q^{19} +(0.266463 - 0.994452i) q^{20} +(0.250247 + 0.554299i) q^{21} -3.63301 q^{22} +(0.735260 - 1.27351i) q^{23} +(-0.172100 + 1.72348i) q^{24} +(-3.41219 - 1.97003i) q^{25} +(2.53236 + 2.56655i) q^{26} +(-4.59249 + 2.43085i) q^{27} +(0.0908784 - 0.339163i) q^{28} +5.82075i q^{29} +(-1.66806 - 0.630388i) q^{30} +(1.48558 - 5.54424i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.625241 + 6.26142i) q^{33} +(-0.865675 - 3.23074i) q^{34} +(0.313065 + 0.180748i) q^{35} +(2.94076 + 0.593221i) q^{36} +(4.96682 + 1.33085i) q^{37} +(0.501966 - 0.869430i) q^{38} +(4.85921 - 3.92277i) q^{39} +(0.514766 + 0.891601i) q^{40} +(-2.41936 - 9.02916i) q^{41} +(-0.568900 - 0.214997i) q^{42} +(2.37192 - 1.36943i) q^{43} +(2.56893 - 2.56893i) q^{44} +(-1.37353 + 2.76638i) q^{45} +(0.380599 + 1.42041i) q^{46} +(8.18256 - 2.19251i) q^{47} +(-1.09699 - 1.34038i) q^{48} +(-5.95541 - 3.43835i) q^{49} +(3.80581 - 1.01976i) q^{50} +(-5.71710 + 0.935962i) q^{51} +(-3.60547 - 0.0241746i) q^{52} -2.67501i q^{53} +(1.52851 - 4.96625i) q^{54} +(1.87015 + 3.23920i) q^{55} +(0.175564 + 0.304085i) q^{56} +(-1.41206 - 1.01476i) q^{57} +(-4.11589 - 4.11589i) q^{58} +(-3.42622 - 3.42622i) q^{59} +(1.62525 - 0.733745i) q^{60} +(-2.86325 - 4.95929i) q^{61} +(2.86991 + 4.97083i) q^{62} +(-0.468450 + 0.943486i) q^{63} +1.00000i q^{64} +(0.984764 - 3.57903i) q^{65} +(-3.98538 - 4.86960i) q^{66} +(14.5603 - 3.90143i) q^{67} +(2.89660 + 1.67236i) q^{68} +(2.51355 - 0.411501i) q^{69} +(-0.349179 + 0.0935622i) q^{70} +(-1.53985 - 5.74681i) q^{71} +(-2.49890 + 1.65996i) q^{72} +(2.47165 - 2.47165i) q^{73} +(-4.45313 + 2.57101i) q^{74} +(-1.10256 - 6.73473i) q^{75} +(0.259837 + 0.969723i) q^{76} +(0.637824 + 1.10474i) q^{77} +(-0.662166 + 6.20979i) q^{78} +(-1.76544 + 3.05783i) q^{79} +(-0.994452 - 0.266463i) q^{80} +(-8.29618 - 3.48905i) q^{81} +(8.09532 + 4.67384i) q^{82} +(-2.23652 - 8.34680i) q^{83} +(0.554299 - 0.250247i) q^{84} +(-2.43491 + 2.43491i) q^{85} +(-0.708868 + 2.64553i) q^{86} +(-7.80200 + 6.38531i) q^{87} +3.63301i q^{88} +(-2.68520 + 10.0213i) q^{89} +(-0.984889 - 2.92736i) q^{90} +(0.335858 - 1.22064i) q^{91} +(-1.27351 - 0.735260i) q^{92} +(9.06104 - 4.09075i) q^{93} +(-4.23561 + 7.33629i) q^{94} -1.03358 q^{95} +(1.72348 + 0.172100i) q^{96} +(-3.82280 + 14.2669i) q^{97} +(6.64239 - 1.77982i) q^{98} +(-9.07854 + 6.03066i) 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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