LMFDB - Embedded newform 722.2.i.a.501.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(7,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(114))

chi = DirichletCharacter(H, H._module([50]))

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

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

chi := DirichletCharacter("722.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.i (of order $57$, degree $36$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$16$ over $\Q(\zeta_{57})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{57}]$

Embedding invariants

Embedding label			501.5
Character	$\chi$	$=$	722.501
Dual form			722.2.i.a.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.926494 + 0.376309i) q^{2} +(-1.05860 - 0.237238i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0324042 - 1.17556i) q^{5} +(-0.891514 - 0.618162i) q^{6} +(0.291339 + 1.15047i) q^{7} +(0.401695 + 0.915773i) q^{8} +(-1.64871 - 0.778047i) q^{9} +O(q^{10})$	\(q+(0.926494 + 0.376309i) q^{2} +(-1.05860 - 0.237238i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0324042 - 1.17556i) q^{5} +(-0.891514 - 0.618162i) q^{6} +(0.291339 + 1.15047i) q^{7} +(0.401695 + 0.915773i) q^{8} +(-1.64871 - 0.778047i) q^{9} +(0.412353 - 1.10135i) q^{10} +(0.486562 - 5.87194i) q^{11} +(-0.593362 - 0.908208i) q^{12} +(-1.00783 - 3.22221i) q^{13} +(-0.163010 + 1.17554i) q^{14} +(-0.244585 + 1.25214i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-1.66654 + 1.62123i) q^{17} +(-1.23474 - 1.34128i) q^{18} +(3.23228 - 2.92445i) q^{19} +(0.796489 - 0.865218i) q^{20} +(-0.0354762 - 1.28701i) q^{21} +(2.66046 - 5.25722i) q^{22} +(-2.51638 + 0.563934i) q^{23} +(-0.207979 - 1.06474i) q^{24} +(3.61151 - 0.199253i) q^{25} +(0.278800 - 3.36462i) q^{26} +(4.12907 + 3.21379i) q^{27} +(-0.593394 + 1.02779i) q^{28} +(1.83880 + 0.519964i) q^{29} +(-0.697799 + 1.06806i) q^{30} +(-4.06328 - 3.16258i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(-1.90812 + 6.10061i) q^{33} +(-2.15412 + 0.874929i) q^{34} +(1.34301 - 0.379768i) q^{35} +(-0.639240 - 1.70733i) q^{36} +(0.868779 - 10.4846i) q^{37} +(4.09518 - 1.49315i) q^{38} +(0.302459 + 3.65014i) q^{39} +(1.06353 - 0.501893i) q^{40} +(3.72583 + 3.24483i) q^{41} +(0.451446 - 1.20576i) q^{42} +(-1.38746 - 3.70575i) q^{43} +(4.44324 - 3.86962i) q^{44} +(-0.861218 + 1.96338i) q^{45} +(-2.54363 - 0.424456i) q^{46} +(-2.99098 - 2.07390i) q^{47} +(0.207979 - 1.06474i) q^{48} +(4.91761 - 2.66128i) q^{49} +(3.42102 + 1.17444i) q^{50} +(2.14882 - 1.32087i) q^{51} +(1.52444 - 3.01238i) q^{52} +(-0.780829 - 0.541415i) q^{53} +(2.61618 + 4.53136i) q^{54} +(-6.91859 - 0.381709i) q^{55} +(-0.936543 + 0.728941i) q^{56} +(-4.11549 + 2.32901i) q^{57} +(1.50797 + 1.17370i) q^{58} +(2.16679 + 1.88706i) q^{59} +(-1.04843 + 0.726964i) q^{60} +(-1.03972 - 1.41459i) q^{61} +(-2.57450 - 4.45916i) q^{62} +(0.414787 - 2.12348i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-3.75526 + 1.28918i) q^{65} +(-4.06358 + 4.93414i) q^{66} +(-11.5377 - 1.27699i) q^{67} -2.32503 q^{68} +2.79763 q^{69} +(1.38720 + 0.153536i) q^{70} +(-2.24812 + 3.05867i) q^{71} +(0.0502337 - 1.82239i) q^{72} +(-4.84945 + 4.71762i) q^{73} +(4.75037 - 9.38699i) q^{74} +(-3.87042 - 0.645860i) q^{75} +(4.35605 + 0.157663i) q^{76} +(6.89726 - 1.15095i) q^{77} +(-1.09336 + 3.49565i) q^{78} +(2.89289 + 7.72657i) q^{79} +(1.17422 - 0.0647837i) q^{80} +(-0.131688 - 0.159900i) q^{81} +(2.23090 + 4.40838i) q^{82} +(-4.00258 + 2.16609i) q^{83} +(0.872000 - 0.947244i) q^{84} +(1.95986 + 1.90659i) q^{85} +(0.109032 - 3.95547i) q^{86} +(-1.82321 - 0.986670i) q^{87} +(5.57281 - 1.91315i) q^{88} +(11.2122 + 10.9074i) q^{89} +(-1.53675 + 1.49497i) q^{90} +(3.41345 - 2.09824i) q^{91} +(-2.19693 - 1.35045i) q^{92} +(3.55111 + 4.31188i) q^{93} +(-1.99070 - 3.04699i) q^{94} +(-3.54261 - 3.70498i) q^{95} +(0.593362 - 0.908208i) q^{96} +(11.8335 - 1.30973i) q^{97} +(5.55760 - 0.615115i) q^{98} +(-5.37084 + 9.30258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) $ 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{57}\right)$

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 $

$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$2$	0.926494	+	0.376309i	0.655130	+	0.266091i
$3$	−1.05860	−	0.237238i	−0.611184	−	0.136970i	−0.0979116	−	0.995195i	$-0.531216\pi$
$3$	−1.05860	−	0.237238i	−0.611184	−	0.136970i	−0.513273	+	0.858225i	$0.671567\pi$
$4$	0.716783	+	0.697297i	0.358391	+	0.348648i
$5$	−0.0324042	−	1.17556i	−0.0144916	−	0.525728i	−0.971685	−	0.236279i	$-0.924072\pi$
$5$	−0.0324042	−	1.17556i	−0.0144916	−	0.525728i	0.957194	−	0.289448i	$-0.0934718\pi$
$6$	−0.891514	−	0.618162i	−0.363959	−	0.252364i
$7$	0.291339	+	1.15047i	0.110116	+	0.434838i	0.999762	−	0.0218125i	$-0.00694370\pi$
$7$	0.291339	+	1.15047i	0.110116	+	0.434838i	−0.889646	+	0.456651i	$0.849049\pi$
$8$	0.401695	+	0.915773i	0.142021	+	0.323775i
$9$	−1.64871	−	0.778047i	−0.549571	−	0.259349i
$10$	0.412353	−	1.10135i	0.130397	−	0.348276i
$11$	0.486562	−	5.87194i	0.146704	−	1.77046i	−0.384417	−	0.923159i	$-0.625598\pi$
$11$	0.486562	−	5.87194i	0.146704	−	1.77046i	0.531121	−	0.847296i	$-0.321771\pi$
$12$	−0.593362	−	0.908208i	−0.171289	−	0.262177i
$13$	−1.00783	−	3.22221i	−0.279522	−	0.893681i	−0.983101	−	0.183064i	$-0.941398\pi$
$13$	−1.00783	−	3.22221i	−0.279522	−	0.893681i	0.703579	−	0.710617i	$-0.251584\pi$
$14$	−0.163010	+	1.17554i	−0.0435662	+	0.314176i
$15$	−0.244585	+	1.25214i	−0.0631517	+	0.323301i
$16$	0.0275543	+	0.999620i	0.00688859	+	0.249905i
$17$	−1.66654	+	1.62123i	−0.404195	+	0.393207i	−0.871104	−	0.491098i	$-0.836596\pi$
$17$	−1.66654	+	1.62123i	−0.404195	+	0.393207i	0.466909	+	0.884305i	$0.345367\pi$
$18$	−1.23474	−	1.34128i	−0.291030	−	0.316143i
$19$	3.23228	−	2.92445i	0.741535	−	0.670914i
$19$	3.23228	−	2.92445i	0.741535	−	0.670914i
$20$	0.796489	−	0.865218i	0.178100	−	0.193469i
$21$	−0.0354762	−	1.28701i	−0.00774154	−	0.280849i
$22$	2.66046	−	5.25722i	0.567212	−	1.12084i
$23$	−2.51638	+	0.563934i	−0.524702	+	0.117588i	−0.472980	−	0.881073i	$-0.656822\pi$
$23$	−2.51638	+	0.563934i	−0.524702	+	0.117588i	−0.0517217	+	0.998662i	$0.516471\pi$
$24$	−0.207979	−	1.06474i	−0.0424536	−	0.217339i
$25$	3.61151	−	0.199253i	0.722302	−	0.0398505i
$26$	0.278800	−	3.36462i	0.0546772	−	0.659856i
$27$	4.12907	+	3.21379i	0.794640	+	0.618493i
$28$	−0.593394	+	1.02779i	−0.112141	+	0.194234i
$29$	1.83880	+	0.519964i	0.341457	+	0.0965549i	0.438515	−	0.898724i	$-0.355505\pi$
$29$	1.83880	+	0.519964i	0.341457	+	0.0965549i	−0.0970578	+	0.995279i	$0.530943\pi$
$30$	−0.697799	+	1.06806i	−0.127400	+	0.195000i
$31$	−4.06328	−	3.16258i	−0.729786	−	0.568015i	0.179714	−	0.983719i	$-0.442483\pi$
$31$	−4.06328	−	3.16258i	−0.729786	−	0.568015i	−0.909500	+	0.415704i	$0.863535\pi$
$32$	−0.350638	+	0.936511i	−0.0619845	+	0.165553i
$33$	−1.90812	+	6.10061i	−0.332162	+	1.06198i
$34$	−2.15412	+	0.874929i	−0.369429	+	0.150049i
$35$	1.34301	−	0.379768i	0.227011	−	0.0641925i
$36$	−0.639240	−	1.70733i	−0.106540	−	0.284556i
$37$	0.868779	−	10.4846i	0.142826	−	1.72366i	−0.429018	−	0.903296i	$-0.641140\pi$
$37$	0.868779	−	10.4846i	0.142826	−	1.72366i	0.571844	−	0.820362i	$-0.306228\pi$
$38$	4.09518	−	1.49315i	0.664326	−	0.242220i
$39$	0.302459	+	3.65014i	0.0484322	+	0.584490i
$40$	1.06353	−	0.501893i	0.168159	−	0.0793562i
$41$	3.72583	+	3.24483i	0.581877	+	0.506757i	0.896845	−	0.442345i	$-0.145853\pi$
$41$	3.72583	+	3.24483i	0.581877	+	0.506757i	−0.314968	+	0.949102i	$0.601994\pi$
$42$	0.451446	−	1.20576i	0.0696596	−	0.186052i
$43$	−1.38746	−	3.70575i	−0.211586	−	0.565122i	0.787075	−	0.616858i	$-0.211595\pi$
$43$	−1.38746	−	3.70575i	−0.211586	−	0.565122i	−0.998661	+	0.0517363i	$0.983524\pi$
$44$	4.44324	−	3.86962i	0.669844	−	0.583368i
$45$	−0.861218	+	1.96338i	−0.128383	+	0.292683i
$46$	−2.54363	−	0.424456i	−0.375037	−	0.0625826i
$47$	−2.99098	−	2.07390i	−0.436280	−	0.302510i	0.331226	−	0.943551i	$-0.392538\pi$
$47$	−2.99098	−	2.07390i	−0.436280	−	0.302510i	−0.767506	+	0.641042i	$0.778503\pi$
$48$	0.207979	−	1.06474i	0.0300192	−	0.153682i
$49$	4.91761	−	2.66128i	0.702515	−	0.380182i
$50$	3.42102	+	1.17444i	0.483806	+	0.166091i
$51$	2.14882	−	1.32087i	0.300895	−	0.184959i
$52$	1.52444	−	3.01238i	0.211402	−	0.417743i
$53$	−0.780829	−	0.541415i	−0.107255	−	0.0743691i	0.514966	−	0.857211i	$-0.327805\pi$
$53$	−0.780829	−	0.541415i	−0.107255	−	0.0743691i	−0.622221	+	0.782842i	$0.713769\pi$
$54$	2.61618	+	4.53136i	0.356017	+	0.616640i
$55$	−6.91859	−	0.381709i	−0.932903	−	0.0514697i
$56$	−0.936543	+	0.728941i	−0.125151	+	0.0974088i
$57$	−4.11549	+	2.32901i	−0.545109	+	0.308485i
$58$	1.50797	+	1.17370i	0.198007	+	0.154115i
$59$	2.16679	+	1.88706i	0.282092	+	0.245674i	0.786208	−	0.617962i	$-0.212041\pi$
$59$	2.16679	+	1.88706i	0.282092	+	0.245674i	−0.504116	+	0.863636i	$0.668182\pi$
$60$	−1.04843	+	0.726964i	−0.135352	+	0.0938507i
$61$	−1.03972	−	1.41459i	−0.133122	−	0.181119i	0.734099	−	0.679043i	$-0.237605\pi$
$61$	−1.03972	−	1.41459i	−0.133122	−	0.181119i	−0.867221	+	0.497923i	$0.834096\pi$
$62$	−2.57450	−	4.45916i	−0.326961	−	0.566314i
$63$	0.414787	−	2.12348i	0.0522582	−	0.267533i
$64$	−0.677282	+	0.735724i	−0.0846602	+	0.0919655i
$65$	−3.75526	+	1.28918i	−0.465782	+	0.159903i
$66$	−4.06358	+	4.93414i	−0.500193	+	0.607350i
$67$	−11.5377	−	1.27699i	−1.40955	−	0.156009i	−0.627207	−	0.778853i	$-0.715802\pi$
$67$	−11.5377	−	1.27699i	−1.40955	−	0.156009i	−0.782347	+	0.622843i	$0.785977\pi$
$68$	−2.32503			−0.281951
$69$	2.79763			0.336796
$70$	1.38720	+	0.153536i	0.165803	+	0.0183510i
$71$	−2.24812	+	3.05867i	−0.266802	+	0.362998i	−0.918459	−	0.395517i	$-0.870566\pi$
$71$	−2.24812	+	3.05867i	−0.266802	+	0.362998i	0.651657	+	0.758514i	$0.274074\pi$
$72$	0.0502337	−	1.82239i	0.00592010	−	0.214770i
$73$	−4.84945	+	4.71762i	−0.567585	+	0.552156i	−0.924108	−	0.382131i	$-0.875190\pi$
$73$	−4.84945	+	4.71762i	−0.567585	+	0.552156i	0.356523	+	0.934287i	$0.383962\pi$
$74$	4.75037	−	9.38699i	0.552220	−	1.09122i
$75$	−3.87042	−	0.645860i	−0.446918	−	0.0745774i
$76$	4.35605	+	0.157663i	0.499673	+	0.0180852i
$77$	6.89726	−	1.15095i	0.786016	−	0.131163i
$78$	−1.09336	+	3.49565i	−0.123798	+	0.395805i
$79$	2.89289	+	7.72657i	0.325476	+	0.869308i	0.992274	+	0.124069i	$0.0395943\pi$
$79$	2.89289	+	7.72657i	0.325476	+	0.869308i	−0.666798	+	0.745239i	$0.732335\pi$
$80$	1.17422	−	0.0647837i	0.131282	−	0.00724304i
$81$	−0.131688	−	0.159900i	−0.0146320	−	0.0177667i
$82$	2.23090	+	4.40838i	0.246362	+	0.486824i
$83$	−4.00258	+	2.16609i	−0.439340	+	0.237759i	−0.680532	−	0.732718i	$-0.738251\pi$
$83$	−4.00258	+	2.16609i	−0.439340	+	0.237759i	0.241192	+	0.970478i	$0.422462\pi$
$84$	0.872000	−	0.947244i	0.0951430	−	0.103353i
$85$	1.95986	+	1.90659i	0.212577	+	0.206798i
$86$	0.109032	−	3.95547i	0.0117572	−	0.426529i
$87$	−1.82321	−	0.986670i	−0.195468	−	0.105782i
$88$	5.57281	−	1.91315i	0.594064	−	0.203942i
$89$	11.2122	+	10.9074i	1.18849	+	1.15618i	0.984162	+	0.177274i	$0.0567279\pi$
$89$	11.2122	+	10.9074i	1.18849	+	1.15618i	0.204325	+	0.978903i	$0.434500\pi$
$90$	−1.53675	+	1.49497i	−0.161988	+	0.157584i
$91$	3.41345	−	2.09824i	0.357827	−	0.219955i
$92$	−2.19693	−	1.35045i	−0.229046	−	0.140794i
$93$	3.55111	+	4.31188i	0.368233	+	0.447121i
$94$	−1.99070	−	3.04699i	−0.205325	−	0.314273i
$95$	−3.54261	−	3.70498i	−0.363464	−	0.380123i
$96$	0.593362	−	0.908208i	0.0605598	−	0.0926936i
$97$	11.8335	−	1.30973i	1.20151	−	0.132983i	0.513114	−	0.858320i	$-0.328492\pi$
$97$	11.8335	−	1.30973i	1.20151	−	0.132983i	0.688393	+	0.725338i	$0.258316\pi$
$98$	5.55760	−	0.615115i	0.561402	−	0.0621360i
$99$	−5.37084	+	9.30258i	−0.539790	+	0.934944i
$100$	2.72761	+	2.37547i	0.272761	+	0.237547i
$101$	11.3978	+	5.37877i	1.13413	+	0.535208i	0.899519	−	0.436882i	$-0.143917\pi$
$101$	11.3978	+	5.37877i	1.13413	+	0.535208i	0.234609	+	0.972090i	$0.424619\pi$
$102$	2.48793	−	0.415162i	0.246341	−	0.0411071i
$103$	−0.921244	+	3.63791i	−0.0907729	+	0.358454i	−0.998075	−	0.0620264i	$-0.980244\pi$
$103$	−0.921244	+	3.63791i	−0.0907729	+	0.358454i	0.907302	+	0.420480i	$0.138138\pi$
$104$	2.54598	−	2.21729i	0.249654	−	0.217423i
$105$	−1.51181	+	0.0834090i	−0.147538	+	0.00813988i
$106$	−0.519694	−	0.795451i	−0.0504772	−	0.0772611i
$107$	−5.27489	+	4.10561i	−0.509943	+	0.396904i	−0.836241	−	0.548363i	$-0.815251\pi$
$107$	−5.27489	+	4.10561i	−0.509943	+	0.396904i	0.326298	+	0.945267i	$0.394199\pi$
$108$	0.718684	+	5.18277i	0.0691554	+	0.498713i
$109$	7.96593	−	5.52345i	0.762998	−	0.529051i	−0.123187	−	0.992384i	$-0.539311\pi$
$109$	7.96593	−	5.52345i	0.762998	−	0.529051i	0.886184	+	0.463333i	$0.153347\pi$
$110$	−6.26640	−	2.95718i	−0.597477	−	0.281956i
$111$	−3.40704	+	10.8929i	−0.323382	+	1.03391i
$112$	−1.14201	+	0.322929i	−0.107910	+	0.0305140i
$113$	−3.18700	+	12.5852i	−0.299808	+	1.18391i	0.617770	+	0.786359i	$0.288036\pi$
$113$	−3.18700	+	12.5852i	−0.299808	+	1.18391i	−0.917578	+	0.397555i	$0.869859\pi$
$114$	−4.68940	+	0.609115i	−0.439203	+	0.0570489i
$115$	0.744481	+	2.93989i	0.0694232	+	0.274146i
$116$	0.955453	+	1.65489i	0.0887116	+	0.153653i
$117$	−0.845409	+	6.09665i	−0.0781581	+	0.563636i
$118$	1.29740	+	2.56373i	0.119435	+	0.236011i
$119$	−2.35071	−	1.44498i	−0.215490	−	0.132461i
$120$	−1.24493	+	0.278994i	−0.113646	+	0.0254686i
$121$	−23.3929	−	3.90359i	−2.12663	−	0.354871i
$122$	−0.430969	−	1.70186i	−0.0390181	−	0.154079i
$123$	−3.17437	−	4.31889i	−0.286224	−	0.389421i
$124$	−0.707232	−	5.10019i	−0.0635113	−	0.458011i
$125$	−0.836832	−	10.0991i	−0.0748485	−	0.903288i
$126$	1.18338	−	1.81130i	0.105424	−	0.161364i
$127$	−2.62386	+	4.54465i	−0.232830	+	0.403273i	−0.958640	−	0.284623i	$-0.908132\pi$
$127$	−2.62386	+	4.54465i	−0.232830	+	0.403273i	0.725810	+	0.687895i	$0.241465\pi$
$128$	−0.904357	+	0.426776i	−0.0799346	+	0.0377221i
$129$	0.589626	+	4.25208i	0.0519137	+	0.374374i
$130$	−3.96435	−	0.218719i	−0.347697	−	0.0191830i
$131$	−0.401659	+	2.89656i	−0.0350931	+	0.253073i	−0.999953	−	0.00969150i	$-0.996915\pi$
$131$	−0.401659	+	2.89656i	−0.0350931	+	0.253073i	0.964860	+	0.262765i	$0.0846343\pi$
$132$	−5.62165	+	3.04228i	−0.489302	+	0.264797i
$133$	4.30619	+	2.86664i	0.373394	+	0.248569i
$134$	−10.2091	−	5.52487i	−0.881929	−	0.477276i
$135$	3.64421	−	4.95812i	0.313643	−	0.426727i
$136$	−2.15412	−	0.874929i	−0.184715	−	0.0750246i
$137$	−13.2907	−	1.47101i	−1.13550	−	0.125677i	−0.477455	−	0.878656i	$-0.658441\pi$
$137$	−13.2907	−	1.47101i	−1.13550	−	0.125677i	−0.658044	+	0.752979i	$0.728616\pi$
$138$	2.59199	+	1.05278i	0.220645	+	0.0896182i
$139$	3.85491	−	4.68076i	0.326969	−	0.397017i	−0.582471	−	0.812851i	$-0.697914\pi$
$139$	3.85491	−	4.68076i	0.326969	−	0.397017i	0.909440	+	0.415835i	$0.136511\pi$
$140$	1.22746	+	0.664268i	0.103739	+	0.0561409i
$141$	2.67425	+	2.90501i	0.225213	+	0.244646i
$142$	−3.23387	+	1.98785i	−0.271381	+	0.166817i
$143$	−19.4110	+	4.35011i	−1.62323	+	0.363774i
$144$	0.732322	−	1.66953i	0.0610269	−	0.139127i
$145$	0.551665	−	2.17848i	0.0458133	−	0.180913i
$146$	−6.26827	+	2.54595i	−0.518766	+	0.210705i
$147$	−5.83715	+	1.65059i	−0.481440	+	0.136138i
$148$	7.93361	−	6.90938i	0.652138	−	0.567948i
$149$	2.56506	+	13.1317i	0.210138	+	1.07579i	0.925994	+	0.377539i	$0.123230\pi$
$149$	2.56506	+	13.1317i	0.210138	+	1.07579i	−0.715856	+	0.698248i	$0.753963\pi$
$150$	−3.34288	−	2.05486i	−0.272945	−	0.167779i
$151$	−1.90506	−	0.654007i	−0.155031	−	0.0532223i	0.246091	−	0.969247i	$-0.420854\pi$
$151$	−1.90506	−	0.654007i	−0.155031	−	0.0532223i	−0.401123	+	0.916024i	$0.631380\pi$
$152$	3.97652	+	1.78530i	0.322538	+	0.144807i
$153$	4.00904	−	1.37631i	0.324112	−	0.111268i
$154$	6.82338	+	1.52916i	0.549844	+	0.123223i
$155$	−3.58614	+	4.87912i	−0.288046	+	0.391900i
$156$	−2.32843	+	2.82726i	−0.186424	+	0.226362i
$157$	−1.90187	−	0.426218i	−0.151785	−	0.0340159i	0.142126	−	0.989849i	$-0.454606\pi$
$157$	−1.90187	−	0.426218i	−0.151785	−	0.0340159i	−0.293911	+	0.955833i	$0.594957\pi$
$158$	−0.227334	+	8.24725i	−0.0180857	+	0.656116i
$159$	0.698144	+	0.758386i	0.0553664	+	0.0601439i
$160$	1.11229	+	0.381850i	0.0879342	+	0.0301879i
$161$	−1.38191	−	2.73073i	−0.108910	−	0.215212i
$162$	−0.0618364	−	0.197702i	−0.00485833	−	0.0155329i
$163$	−6.08317	+	4.73472i	−0.476471	+	0.370852i	−0.823790	−	0.566895i	$-0.808145\pi$
$163$	−6.08317	+	4.73472i	−0.476471	+	0.370852i	0.347319	+	0.937747i	$0.387092\pi$
$164$	0.408001	+	4.92384i	0.0318596	+	0.384488i
$165$	7.23348	+	2.04543i	0.563126	+	0.159237i
$166$	−4.52349	+	0.500660i	−0.351091	+	0.0388587i
$167$	10.6445	+	3.00998i	0.823697	+	0.232919i	0.657770	−	0.753219i	$-0.271500\pi$
$167$	10.6445	+	3.00998i	0.823697	+	0.232919i	0.165927	+	0.986138i	$0.446938\pi$
$168$	1.16436	−	0.549475i	0.0898323	−	0.0423929i
$169$	1.31617	−	0.912611i	0.101244	−	0.0702009i
$170$	1.09834	+	2.50395i	0.0842386	+	0.192045i
$171$	−7.60446	+	2.30672i	−0.581527	+	0.176399i
$172$	1.58950	−	3.62369i	0.121198	−	0.276304i
$173$	−0.968989	−	4.96068i	−0.0736709	−	0.377154i	−1.00000		0.000438388i	$-0.999860\pi$
$173$	−0.968989	−	4.96068i	−0.0736709	−	0.377154i	0.926329	−	0.376715i	$-0.122947\pi$
$174$	−1.31790	−	1.60023i	−0.0999095	−	0.121313i
$175$	1.28141	+	4.09690i	0.0968655	+	0.309696i
$176$	5.88311	+	0.324580i	0.443456	+	0.0244662i
$177$	−1.84609	−	2.51169i	−0.138760	−	0.188790i
$178$	6.28346	+	14.3248i	0.470965	+	1.07369i
$179$	−3.80892	+	0.635596i	−0.284692	+	0.0475067i	−0.305218	−	0.952283i	$-0.598729\pi$
$179$	−3.80892	+	0.635596i	−0.284692	+	0.0475067i	0.0205256	+	0.999789i	$0.493466\pi$
$180$	−1.98636	+	0.806791i	−0.148055	+	0.0601347i
$181$	20.7715	−	8.43666i	1.54394	−	0.627092i	0.563887	−	0.825852i	$-0.309305\pi$
$181$	20.7715	−	8.43666i	1.54394	−	0.627092i	0.980048	+	0.198760i	$0.0636913\pi$
$182$	3.95213	−	0.659494i	0.292951	−	0.0488849i
$183$	0.765052	+	1.74414i	0.0565543	+	0.128931i
$184$	−1.52725	−	2.07791i	−0.112591	−	0.153185i
$185$	−12.3535	−	0.681559i	−0.908244	−	0.0501092i
$186$	1.66748	+	5.33124i	0.122266	+	0.390906i
$187$	8.70890	+	10.5746i	0.636858	+	0.773294i
$188$	−0.697760	−	3.57214i	−0.0508893	−	0.260525i
$189$	−2.49441	+	5.68669i	−0.181442	+	0.413646i
$190$	−1.88799	−	4.76576i	−0.136969	−	0.345744i
$191$	−10.5191	−	23.9810i	−0.761132	−	1.73521i	−0.673663	−	0.739038i	$-0.735280\pi$
$191$	−10.5191	−	23.9810i	−0.761132	−	1.73521i	−0.0874684	−	0.996167i	$-0.527878\pi$
$192$	0.891514	−	0.618162i	0.0643395	−	0.0446120i
$193$	21.5564	−	10.1727i	1.55166	−	0.732247i	0.556533	−	0.830826i	$-0.312131\pi$
$193$	21.5564	−	10.1727i	1.55166	−	0.732247i	0.995129	+	0.0985785i	$0.0314295\pi$
$194$	11.4565	+	3.23959i	0.822529	+	0.232589i
$195$	4.28117	−	0.473839i	0.306581	−	0.0339323i
$196$	5.38055	+	1.52148i	0.384325	+	0.108677i
$197$	−0.0929982	−	1.12232i	−0.00662585	−	0.0799621i	0.992469	−	0.122494i	$-0.0390892\pi$
$197$	−0.0929982	−	1.12232i	−0.00662585	−	0.0799621i	−0.999095	+	0.0425318i	$0.986458\pi$
$198$	−8.47670	+	6.59768i	−0.602413	+	0.468877i
$199$	−1.37105	−	4.38348i	−0.0971909	−	0.310737i	0.893078	−	0.449901i	$-0.148541\pi$
$199$	−1.37105	−	4.38348i	−0.0971909	−	0.310737i	−0.990269	+	0.139165i	$0.955558\pi$
$200$	1.63320	+	3.22729i	0.115484	+	0.228204i
$201$	11.9109	+	4.08901i	0.840129	+	0.288417i
$202$	8.53595	+	9.27251i	0.600587	+	0.652412i
$203$	−0.0624889	+	2.26698i	−0.00438586	+	0.159111i
$204$	2.46128	+	0.551585i	0.172324	+	0.0386187i
$205$	3.69376	−	4.48509i	0.257984	−	0.313252i
$206$	−2.22251	+	3.02383i	−0.154849	+	0.210680i
$207$	4.58756	+	1.02810i	0.318858	+	0.0714577i
$208$	3.19322	−	1.09623i	0.221410	−	0.0760102i
$209$	−15.5995	−	20.4026i	−1.07904	−	1.41128i
$210$	−1.43207	−	0.491631i	−0.0988224	−	0.0339258i
$211$	−3.81745	−	2.34657i	−0.262804	−	0.161545i	0.386004	−	0.922497i	$-0.373855\pi$
$211$	−3.81745	−	2.34657i	−0.262804	−	0.161545i	−0.648808	+	0.760952i	$0.724732\pi$
$212$	−0.182158	−	0.932547i	−0.0125107	−	0.0640476i
$213$	3.10549	−	2.70458i	0.212785	−	0.185315i
$214$	−6.43213	+	1.81883i	−0.439692	+	0.124333i
$215$	−4.31138	+	1.75113i	−0.294034	+	0.119426i
$216$	−1.28447	+	5.07226i	−0.0873971	+	0.345123i
$217$	2.45467	−	5.59608i	0.166634	−	0.379886i
$218$	9.45891	−	2.11979i	0.640638	−	0.143570i
$219$	6.25284	−	3.84361i	0.422528	−	0.259727i
$220$	−4.69296	−	5.09792i	−0.316399	−	0.343701i
$221$	6.90355	+	3.73601i	0.464383	+	0.251312i
$222$	−7.25571	+	8.81012i	−0.486971	+	0.591297i
$223$	7.30657	+	2.96767i	0.489284	+	0.198730i	0.607596	−	0.794246i	$-0.292134\pi$
$223$	7.30657	+	2.96767i	0.489284	+	0.198730i	−0.118311	+	0.992977i	$0.537748\pi$
$224$	−1.17959	−	0.130557i	−0.0788144	−	0.00872317i
$225$	−6.10938	−	2.48141i	−0.407292	−	0.165428i
$226$	−7.68866	+	10.4608i	−0.511442	+	0.695842i
$227$	8.15140	+	4.41132i	0.541027	+	0.292789i	0.723387	−	0.690443i	$-0.242584\pi$
$227$	8.15140	+	4.41132i	0.541027	+	0.292789i	−0.182360	+	0.983232i	$0.558374\pi$
$228$	−4.57392	−	1.20032i	−0.302915	−	0.0794934i
$229$	1.72551	−	0.933800i	0.114025	−	0.0617073i	−0.417934	−	0.908477i	$-0.637246\pi$
$229$	1.72551	−	0.933800i	0.114025	−	0.0617073i	0.531959	+	0.846770i	$0.321456\pi$
$230$	−0.416551	+	3.00395i	−0.0274665	+	0.198074i
$231$	−7.57451	−	0.417897i	−0.498366	−	0.0274956i
$232$	0.262470	+	1.89279i	0.0172320	+	0.124268i
$233$	−21.2289	+	10.0181i	−1.39075	+	0.656310i	−0.968234	−	0.250045i	$-0.919554\pi$
$233$	−21.2289	+	10.0181i	−1.39075	+	0.656310i	−0.422515	+	0.906356i	$0.638853\pi$
$234$	−3.07749	+	5.33038i	−0.201182	+	0.348458i
$235$	−2.34108	+	3.58329i	−0.152715	+	0.233748i
$236$	0.237277	+	2.86351i	0.0154454	+	0.186399i
$237$	−1.22938	−	8.86568i	−0.0798571	−	0.575888i
$238$	−1.63416	−	2.22336i	−0.105927	−	0.144119i
$239$	−0.254187	−	1.00376i	−0.0164420	−	0.0649278i	0.960636	−	0.277812i	$-0.0896091\pi$
$239$	−0.254187	−	1.00376i	−0.0164420	−	0.0649278i	−0.977078	+	0.212884i	$0.931714\pi$
$240$	−1.25840	−	0.209991i	−0.0812297	−	0.0135548i
$241$	−4.16919	+	0.934337i	−0.268561	+	0.0601859i	−0.350881	−	0.936420i	$-0.614118\pi$
$241$	−4.16919	+	0.934337i	−0.268561	+	0.0601859i	0.0823201	+	0.996606i	$0.473767\pi$
$242$	−20.2044	−	12.4196i	−1.29879	−	0.798363i
$243$	−6.98629	−	13.8053i	−0.448171	−	0.885610i
$244$	0.241135	−	1.73894i	0.0154371	−	0.111324i
$245$	−3.28785	−	5.69472i	−0.210053	−	0.363822i
$246$	−1.31580	−	5.19597i	−0.0838923	−	0.331283i
$247$	−12.6808	−	7.46774i	−0.806859	−	0.475161i
$248$	1.26400	−	4.99143i	0.0802642	−	0.316956i
$249$	4.75102	−	1.34346i	0.301084	−	0.0851384i
$250$	3.02505	−	9.67163i	0.191321	−	0.611687i
$251$	19.1651	+	9.04423i	1.20969	+	0.570867i	0.922124	−	0.386894i	$-0.126452\pi$
$251$	19.1651	+	9.04423i	1.20969	+	0.570867i	0.287567	+	0.957761i	$0.407154\pi$
$252$	1.77801	−	1.23284i	0.112004	−	0.0776618i
$253$	2.08701	+	15.0504i	0.131209	+	0.946212i
$254$	−4.14118	+	3.22321i	−0.259841	+	0.202242i
$255$	−1.62240	−	2.48327i	−0.101599	−	0.155508i
$256$	−0.998482	+	0.0550878i	−0.0624051	+	0.00344299i
$257$	21.5971	−	18.8089i	1.34719	−	1.17327i	0.378327	−	0.925672i	$-0.376499\pi$
$257$	21.5971	−	18.8089i	1.34719	−	1.17327i	0.968863	−	0.247597i	$-0.0796409\pi$
$258$	−1.05381	+	4.16140i	−0.0656074	+	0.259078i
$259$	12.3154	−	2.05507i	0.765240	−	0.127696i
$260$	−3.59064	−	1.69447i	−0.222682	−	0.105086i
$261$	−2.62711	−	2.28795i	−0.162614	−	0.141620i
$262$	−1.46214	+	2.53249i	−0.0903311	+	0.156458i
$263$	12.5357	−	1.38745i	0.772983	−	0.0855537i	0.285141	−	0.958486i	$-0.407960\pi$
$263$	12.5357	−	1.38745i	0.772983	−	0.0855537i	0.487842	+	0.872932i	$0.337784\pi$
$264$	−6.35326	+	0.703179i	−0.391016	+	0.0432777i
$265$	−0.611165	+	0.935458i	−0.0375436	+	0.0574647i
$266$	2.91091	+	4.27638i	0.178480	+	0.262202i
$267$	−9.28157	−	14.2065i	−0.568023	−	0.869424i
$268$	−7.37958	−	8.96052i	−0.450779	−	0.547351i
$269$	8.28411	+	5.09222i	0.505091	+	0.310478i	0.752680	−	0.658387i	$-0.228761\pi$
$269$	8.28411	+	5.09222i	0.505091	+	0.310478i	−0.247588	+	0.968865i	$0.579638\pi$
$270$	5.24212	−	3.22232i	0.319025	−	0.196104i
$271$	1.26275	−	1.22843i	0.0767069	−	0.0746216i	−0.657944	−	0.753066i	$-0.728574\pi$
$271$	1.26275	−	1.22843i	0.0767069	−	0.0746216i	0.734651	+	0.678445i	$0.237346\pi$
$272$	−1.66654	−	1.62123i	−0.101049	−	0.0983017i
$273$	−4.11127	+	1.41140i	−0.248825	+	0.0854219i
$274$	−11.7602	−	6.36429i	−0.710459	−	0.384481i
$275$	0.587227	−	21.3035i	0.0354111	−	1.28465i
$276$	2.00530	+	1.95078i	0.120705	+	0.117423i
$277$	18.2553	−	19.8306i	1.09686	−	1.19150i	0.116724	−	0.993164i	$-0.462761\pi$
$277$	18.2553	−	19.8306i	1.09686	−	1.19150i	0.980133	−	0.198340i	$-0.0635550\pi$
$278$	5.33296	−	2.88605i	0.319850	−	0.173094i
$279$	4.23855	+	8.37561i	0.253755	+	0.501434i
$280$	0.887263	+	1.07734i	0.0530241	+	0.0643836i
$281$	12.2459	−	0.675625i	0.730529	−	0.0403044i	0.313995	−	0.949425i	$-0.398332\pi$
$281$	12.2459	−	0.675625i	0.730529	−	0.0403044i	0.416534	+	0.909120i	$0.363245\pi$
$282$	1.38450	+	3.69782i	0.0824455	+	0.220202i
$283$	−6.02064	+	19.2491i	−0.357890	+	1.14424i	0.584972	+	0.811054i	$0.301106\pi$
$283$	−6.02064	+	19.2491i	−0.357890	+	1.14424i	−0.942862	+	0.333185i	$0.891877\pi$
$284$	−3.74421	+	0.624798i	−0.222178	+	0.0370750i
$285$	2.87125	+	4.76254i	0.170078	+	0.282109i
$286$	−19.6212	−	3.27419i	−1.16022	−	0.193607i
$287$	−2.64761	+	5.23181i	−0.156283	+	0.308824i
$288$	1.30675	−	1.27123i	0.0770010	−	0.0749078i
$289$	−0.319472	+	11.5899i	−0.0187925	+	0.681756i
$290$	1.33090	−	1.81075i	0.0781529	−	0.106331i
$291$	−12.8377	−	1.42087i	−0.752557	−	0.0832930i
$292$	−6.76558			−0.395926
$293$	−32.9104			−1.92265			−0.961324	−	0.275420i	$-0.911183\pi$
$293$	−32.9104			−1.92265			−0.961324	+	0.275420i	$0.911183\pi$
$294$	−6.02921	−	0.667313i	−0.351631	−	0.0389185i
$295$	2.14814	−	2.60835i	0.125070	−	0.151864i
$296$	9.95051	−	3.41601i	0.578361	−	0.198552i
$297$	20.8802	−	22.6819i	1.21159	−	1.31614i
$298$	−2.56506	+	13.1317i	−0.148590	+	0.760697i
$299$	4.35320	+	7.53997i	0.251752	+	0.436048i
$300$	−2.32390	−	3.16178i	−0.134170	−	0.182545i
$301$	3.85914	−	2.67587i	0.222437	−	0.154235i
$302$	−1.51891	−	1.32282i	−0.0874037	−	0.0761200i
$303$	−10.7897	−	8.39798i	−0.619854	−	0.482452i
$304$	3.01240	+	3.15047i	0.172773	+	0.180692i
$305$	−1.62924	+	1.26809i	−0.0932901	+	0.0726106i
$306$	4.23227	+	0.233501i	0.241943	+	0.0133484i
$307$	15.4247	+	26.7164i	0.880337	+	1.52479i	0.850967	+	0.525219i	$0.176017\pi$
$307$	15.4247	+	26.7164i	0.880337	+	1.52479i	0.0293699	+	0.999569i	$0.490650\pi$
$308$	5.74639	+	3.98446i	0.327431	+	0.227036i
$309$	1.83828	−	3.63255i	0.104576	−	0.206648i
$310$	−5.15859	+	3.17098i	−0.292988	+	0.180099i
$311$	−6.33614	−	2.17520i	−0.359289	−	0.123344i	0.139144	−	0.990272i	$-0.455565\pi$
$311$	−6.33614	−	2.17520i	−0.359289	−	0.123344i	−0.498433	+	0.866928i	$0.666091\pi$
$312$	−3.22120	+	1.74323i	−0.182365	+	0.0986909i
$313$	0.189649	−	0.970897i	0.0107196	−	0.0548784i	−0.975708	−	0.219075i	$-0.929696\pi$
$313$	0.189649	−	0.970897i	0.0107196	−	0.0548784i	0.986428	+	0.164197i	$0.0525031\pi$
$314$	−1.60168	−	1.11058i	−0.0903879	−	0.0626736i
$315$	−2.50972	−	0.418798i	−0.141407	−	0.0235966i
$316$	−3.31414	+	7.55548i	−0.186435	+	0.425029i
$317$	23.8234	−	20.7478i	1.33806	−	1.16531i	0.365986	−	0.930620i	$-0.380732\pi$
$317$	23.8234	−	20.7478i	1.33806	−	1.16531i	0.972069	−	0.234693i	$-0.0754086\pi$
$318$	0.361438	+	0.965358i	0.0202684	+	0.0541346i
$319$	3.94789	−	10.5443i	0.221039	−	0.590370i
$320$	0.886836	+	0.772346i	0.0495757	+	0.0431755i
$321$	6.55802	−	3.09480i	0.366033	−	0.172735i
$322$	−0.252733	−	3.05003i	−0.0140843	−	0.169972i
$323$	−0.645500	+	10.1140i	−0.0359166	+	0.562757i
$324$	0.0171061	−	0.206439i	0.000950337	−	0.0114689i
$325$	−4.28183	−	11.4362i	−0.237513	−	0.634369i
$326$	−7.41775	+	2.09754i	−0.410831	+	0.116172i
$327$	−9.74313	+	3.95732i	−0.538796	+	0.218840i
$328$	−1.47488	+	4.71545i	−0.0814365	+	0.260367i
$329$	1.51458	−	4.04526i	0.0835014	−	0.223022i
$330$	5.93206	+	4.61711i	0.326549	+	0.254164i
$331$	18.3988	−	28.1615i	1.01129	−	1.54789i	0.186499	−	0.982455i	$-0.440286\pi$
$331$	18.3988	−	28.1615i	1.01129	−	1.54789i	0.824791	−	0.565438i	$-0.191293\pi$
$332$	−4.37939	−	1.23837i	−0.240350	−	0.0679645i
$333$	−9.58988	+	16.6102i	−0.525522	+	0.910232i
$334$	8.72939	+	6.79436i	0.477651	+	0.371771i
$335$	−1.12731	+	13.6047i	−0.0615918	+	0.743302i
$336$	1.28554	−	0.0709255i	0.0701322	−	0.00386930i
$337$	−0.683469	−	3.49898i	−0.0372309	−	0.190602i	0.958198	−	0.286105i	$-0.0923608\pi$
$337$	−0.683469	−	3.49898i	−0.0372309	−	0.190602i	−0.995429	+	0.0955039i	$0.969554\pi$
$338$	1.56285	−	0.350242i	0.0850077	−	0.0190507i
$339$	6.35945	−	12.5666i	0.345398	−	0.682525i
$340$	0.0753405	+	2.73321i	0.00408591	+	0.148229i
$341$	−20.5475	+	22.3205i	−1.11271	+	1.20872i
$342$	−7.91352	−	0.724471i	−0.427914	−	0.0391749i
$343$	10.1210	+	10.9943i	0.546480	+	0.593635i
$344$	2.83629	−	2.75918i	0.152922	−	0.148765i
$345$	−0.0906550	−	3.28879i	−0.00488070	−	0.177063i
$346$	0.968989	−	4.96068i	0.0520932	−	0.266688i
$347$	−1.03129	+	7.43709i	−0.0553623	+	0.399244i	0.942517	+	0.334157i	$0.108452\pi$
$347$	−1.03129	+	7.43709i	−0.0553623	+	0.399244i	−0.997880	+	0.0650866i	$0.979268\pi$
$348$	−0.618841	−	1.97854i	−0.0331733	−	0.106061i
$349$	10.2464	+	15.6833i	0.548477	+	0.839507i	0.998569	−	0.0534755i	$-0.0170299\pi$
$349$	10.2464	+	15.6833i	0.548477	+	0.839507i	−0.450092	+	0.892982i	$0.648609\pi$
$350$	−0.354482	+	4.27796i	−0.0189478	+	0.228666i
$351$	6.19410	−	16.5437i	0.330617	−	0.883038i
$352$	5.32853	+	2.51459i	0.284011	+	0.134028i
$353$	7.40154	+	16.8738i	0.393944	+	0.898103i	0.995091	+	0.0989639i	$0.0315528\pi$
$353$	7.40154	+	16.8738i	0.393944	+	0.898103i	−0.601147	+	0.799139i	$0.705289\pi$
$354$	−0.765216	−	3.02177i	−0.0406708	−	0.160605i
$355$	3.66851	+	2.54369i	0.194704	+	0.135005i
$356$	0.431014	+	15.6364i	0.0228437	+	0.828728i
$357$	2.14567	+	2.08734i	0.113561	+	0.110474i
$358$	−3.76812	−	0.844456i	−0.199151	−	0.0446309i
$359$	−26.4579	−	10.7463i	−1.39639	−	0.567166i	−0.450831	−	0.892609i	$-0.648872\pi$
$359$	−26.4579	−	10.7463i	−1.39639	−	0.567166i	−0.945561	+	0.325444i	$0.894486\pi$
$360$	−2.14396			−0.112996
$361$	1.89522	−	18.9052i	0.0997483	−	0.995013i
$362$	22.4195			1.17834
$363$	23.8377	+	9.68204i	1.25116	+	0.508175i
$364$	3.90980	+	0.876206i	0.204929	+	0.0459257i
$365$	5.70300	+	5.54796i	0.298509	+	0.290394i
$366$	0.0524789	+	1.90384i	0.00274311	+	0.0995151i
$367$	−5.18515	−	3.59530i	−0.270663	−	0.187673i	0.426697	−	0.904395i	$-0.359677\pi$
$367$	−5.18515	−	3.59530i	−0.270663	−	0.187673i	−0.697360	+	0.716721i	$0.745642\pi$
$368$	−0.633057	−	2.49989i	−0.0330004	−	0.130316i
$369$	−3.61820	−	8.24866i	−0.188356	−	0.429408i
$370$	−11.1889	−	5.28018i	−0.581685	−	0.274504i
$371$	0.395397	−	1.05606i	0.0205280	−	0.0548279i
$372$	−0.461283	+	5.56686i	−0.0239164	+	0.288628i
$373$	−6.18164	−	9.46170i	−0.320073	−	0.489908i	0.640492	−	0.767965i	$-0.278731\pi$
$373$	−6.18164	−	9.46170i	−0.320073	−	0.489908i	−0.960565	+	0.278057i	$0.910310\pi$
$374$	4.08941	+	13.0746i	0.211458	+	0.676070i
$375$	−1.51001	+	10.8894i	−0.0779767	+	0.562327i
$376$	0.697760	−	3.57214i	0.0359842	−	0.184219i
$377$	−0.177767	−	6.44905i	−0.00915546	−	0.332143i
$378$	−4.45101	+	4.33001i	−0.228935	+	0.222712i
$379$	−15.8224	−	17.1877i	−0.812740	−	0.882871i	0.182209	−	0.983260i	$-0.441675\pi$
$379$	−15.8224	−	17.1877i	−0.812740	−	0.882871i	−0.994948	+	0.100389i	$0.967991\pi$
$380$	0.0441889	−	5.12591i	0.00226684	−	0.262954i
$381$	3.85579	−	4.18850i	0.197538	−	0.214583i
$382$	−0.721555	−	26.1767i	−0.0369180	−	1.33932i
$383$	5.90907	−	11.6766i	0.301939	−	0.596648i	−0.689935	−	0.723872i	$-0.742361\pi$
$383$	5.90907	−	11.6766i	0.301939	−	0.596648i	0.991874	+	0.127223i	$0.0406064\pi$
$384$	1.05860	−	0.237238i	0.0540216	−	0.0121065i
$385$	−1.57651	−	8.07087i	−0.0803465	−	0.411329i
$386$	23.7999	−	1.31308i	1.21139	−	0.0668340i
$387$	−0.595717	+	7.18924i	−0.0302820	+	0.365449i
$388$	9.39530	+	7.31265i	0.476974	+	0.371244i
$389$	−14.3324	+	24.8245i	−0.726683	+	1.25865i	0.231595	+	0.972812i	$0.425606\pi$
$389$	−14.3324	+	24.8245i	−0.726683	+	1.25865i	−0.958278	+	0.285839i	$0.907728\pi$
$390$	4.14479	+	1.17203i	0.209879	+	0.0593482i
$391$	3.27938	−	5.01946i	0.165845	−	0.253845i
$392$	4.41250	+	3.43439i	0.222865	+	0.173463i
$393$	1.11237	−	2.97101i	0.0561117	−	0.149868i
$394$	0.336178	−	1.07482i	0.0169364	−	0.0541486i
$395$	8.98933	−	3.65115i	0.452302	−	0.183709i
$396$	−10.3364	+	2.92285i	−0.519423	+	0.146879i
$397$	8.30950	+	22.1937i	0.417042	+	1.11387i	0.961433	+	0.275038i	$0.0886903\pi$
$397$	8.30950	+	22.1937i	0.417042	+	1.11387i	−0.544392	+	0.838831i	$0.683240\pi$
$398$	0.379278	−	4.57720i	0.0190115	−	0.229435i
$399$	−3.87846	−	4.05623i	−0.194166	−	0.203065i
$400$	0.298690	+	3.60465i	0.0149345	+	0.180232i
$401$	18.8767	−	8.90811i	0.942656	−	0.444850i	0.107095	−	0.994249i	$-0.465845\pi$
$401$	18.8767	−	8.90811i	0.942656	−	0.444850i	0.835560	+	0.549399i	$0.185143\pi$
$402$	9.49663	+	8.27062i	0.473649	+	0.412501i
$403$	−6.09540	+	16.2801i	−0.303634	+	0.810969i
$404$	4.41917	+	11.8031i	0.219862	+	0.587225i
$405$	−0.183705	+	0.159989i	−0.00912840	+	0.00794993i
$406$	−0.910982	+	2.07683i	−0.0452113	+	0.103071i
$407$	−61.1422	−	10.2028i	−3.03071	−	0.505735i
$408$	2.07279	+	1.43724i	0.102619	+	0.0711541i
$409$	2.01985	−	10.3405i	0.0998753	−	0.511306i	−0.897632	−	0.440745i	$-0.854714\pi$
$409$	2.01985	−	10.3405i	0.0998753	−	0.511306i	0.997508	−	0.0705604i	$-0.0224788\pi$
$410$	5.11003	−	2.76541i	0.252367	−	0.136574i
$411$	13.7206	+	4.71028i	0.676786	+	0.232341i
$412$	−3.19704	+	1.96521i	−0.157507	+	0.0968190i
$413$	−1.53974	+	3.04261i	−0.0757657	+	0.149717i
$414$	3.86347	+	2.67887i	0.189879	+	0.131659i
$415$	2.67607	+	4.63510i	0.131363	+	0.227528i
$416$	3.37102	+	0.185985i	0.165278	+	0.00911864i
$417$	−5.19127	+	4.04053i	−0.254218	+	0.197865i
$418$	−6.77510	−	24.7732i	−0.331381	−	1.21169i
$419$	−12.8312	−	9.98691i	−0.626844	−	0.487892i	0.250269	−	0.968176i	$-0.419481\pi$
$419$	−12.8312	−	9.98691i	−0.626844	−	0.487892i	−0.877113	+	0.480284i	$0.840534\pi$
$420$	−1.14180	−	0.994396i	−0.0557142	−	0.0485215i
$421$	−6.81521	+	4.72556i	−0.332153	+	0.230310i	−0.724127	−	0.689666i	$-0.757757\pi$
$421$	−6.81521	+	4.72556i	−0.332153	+	0.230310i	0.391974	+	0.919976i	$0.371792\pi$
$422$	−2.65380	−	3.61063i	−0.129185	−	0.175763i
$423$	3.31768	+	5.74640i	0.161311	+	0.279399i
$424$	0.182158	−	0.932547i	0.00884637	−	0.0452885i
$425$	−5.69568	+	6.18716i	−0.276281	+	0.300121i
$426$	3.89498	−	1.33715i	0.188712	−	0.0647851i
$427$	1.32453	−	1.60829i	0.0640986	−	0.0778306i
$428$	−6.64378	−	0.735333i	−0.321139	−	0.0355437i
$429$	21.5806			1.04192
$430$	−4.65344			−0.224409
$431$	21.8997	+	2.42385i	1.05487	+	0.116753i	0.620676	−	0.784067i	$-0.286858\pi$
$431$	21.8997	+	2.42385i	1.05487	+	0.116753i	0.434193	+	0.900820i	$0.357034\pi$
$432$	−3.09879	+	4.21606i	−0.149091	+	0.202845i
$433$	−0.673919	+	24.4485i	−0.0323865	+	1.17492i	0.792591	+	0.609754i	$0.208732\pi$
$433$	−0.673919	+	24.4485i	−0.0323865	+	1.17492i	−0.824977	+	0.565166i	$0.808812\pi$
$434$	4.38009	−	4.26102i	0.210251	−	0.204535i
$435$	−1.10081	+	2.17527i	−0.0527799	+	0.104296i
$436$	9.56132	+	1.59550i	0.457904	+	0.0764107i
$437$	−6.48444	+	9.18182i	−0.310193	+	0.439226i
$438$	7.23961	−	1.20808i	0.345922	−	0.0577241i
$439$	2.11403	−	6.75892i	0.100897	−	0.322586i	−0.890229	−	0.455514i	$-0.849456\pi$
$439$	2.11403	−	6.75892i	0.100897	−	0.322586i	0.991126	+	0.132928i	$0.0424380\pi$
$440$	−2.42961	−	6.48919i	−0.115827	−	0.309360i
$441$	−10.1783	+	0.561554i	−0.484682	+	0.0267407i
$442$	4.99020	+	6.05927i	0.237360	+	0.288210i
$443$	15.1608	+	29.9586i	0.720313	+	1.42338i	0.898317	+	0.439348i	$0.144791\pi$
$443$	15.1608	+	29.9586i	0.720313	+	1.42338i	−0.178003	+	0.984030i	$0.556964\pi$
$444$	−10.0377	+	5.43213i	−0.476368	+	0.257798i
$445$	12.4590	−	13.5340i	0.590611	−	0.641575i
$446$	5.65273	+	5.49906i	0.267665	+	0.260388i
$447$	0.399958	−	14.5097i	0.0189174	−	0.686287i
$448$	−1.04375	−	0.564849i	−0.0493125	−	0.0266866i
$449$	19.7249	−	6.77158i	0.930878	−	0.319571i	0.182776	−	0.983155i	$-0.441492\pi$
$449$	19.7249	−	6.77158i	0.930878	−	0.319571i	0.748102	+	0.663584i	$0.230965\pi$
$450$	−4.72652	−	4.59803i	−0.222810	−	0.216753i
$451$	20.8663	−	20.2990i	0.982554	−	0.955843i
$452$	−11.0600	+	6.79855i	−0.520218	+	0.319777i
$453$	1.86154	+	1.14429i	0.0874629	+	0.0537632i
$454$	5.89220	+	7.15450i	0.276535	+	0.335778i
$455$	−2.57722	−	3.94473i	−0.120822	−	0.184932i
$456$	−3.78601	−	2.83330i	−0.177296	−	0.132681i
$457$	16.6556	−	25.4934i	0.779118	−	1.19253i	−0.198077	−	0.980186i	$-0.563470\pi$
$457$	16.6556	−	25.4934i	0.779118	−	1.19253i	0.977195	−	0.212343i	$-0.0681094\pi$
$458$	1.95007	−	0.215834i	0.0911210	−	0.0100853i
$459$	−12.0916	+	1.33829i	−0.564385	+	0.0624661i
$460$	−1.51634	+	2.62639i	−0.0706999	+	0.122456i
$461$	−10.5029	−	9.14698i	−0.489169	−	0.426017i	0.376665	−	0.926350i	$-0.377071\pi$
$461$	−10.5029	−	9.14698i	−0.489169	−	0.426017i	−0.865834	+	0.500332i	$0.833211\pi$
$462$	−6.86048	−	3.23754i	−0.319178	−	0.150624i
$463$	39.0609	−	6.51811i	1.81531	−	0.302922i	0.843229	−	0.537555i	$-0.180652\pi$
$463$	39.0609	−	6.51811i	1.81531	−	0.302922i	0.972084	+	0.234633i	$0.0753889\pi$
$464$	−0.469100	+	1.85243i	−0.0217774	+	0.0859970i
$465$	4.95381	−	4.31428i	0.229727	−	0.200070i
$466$	−23.4383	+	1.29313i	−1.08576	+	0.0599031i
$467$	−13.0295	−	19.9431i	−0.602932	−	0.922856i	−0.999987	−	0.00506116i	$-0.998389\pi$
$467$	−13.0295	−	19.9431i	−0.602932	−	0.922856i	0.397055	−	0.917795i	$-0.370032\pi$
$468$	−4.85715	+	3.78047i	−0.224522	+	0.174752i
$469$	−1.89224	−	13.6458i	−0.0873755	−	0.630107i
$470$	−3.51742	+	2.43893i	−0.162247	+	0.112499i
$471$	1.91220	+	0.902391i	0.0881097	+	0.0415800i
$472$	−0.857729	+	2.74231i	−0.0394802	+	0.126225i
$473$	−22.4350	+	6.34402i	−1.03156	+	0.291698i
$474$	2.19722	−	8.67662i	0.100922	−	0.398531i
$475$	11.0907	−	11.2057i	0.508876	−	0.514153i
$476$	−0.677372	−	2.67488i	−0.0310473	−	0.122603i
$477$	0.866118	+	1.50016i	0.0396568	+	0.0686877i
$478$	0.142222	−	1.02563i	0.00650508	−	0.0469112i
$479$	−15.6830	−	30.9904i	−0.716573	−	1.41599i	−0.901299	−	0.433197i	$-0.857385\pi$
$479$	−15.6830	−	30.9904i	−0.716573	−	1.41599i	0.184726	−	0.982790i	$-0.440860\pi$
$480$	−1.08688	−	0.668105i	−0.0496092	−	0.0304947i
$481$	−34.6592	+	7.76731i	−1.58032	+	0.354159i
$482$	−4.21433	−	0.703247i	−0.191957	−	0.0320320i
$483$	0.815061	+	3.21860i	0.0370866	+	0.146452i
$484$	−14.0457	−	19.1098i	−0.638440	−	0.868628i
$485$	−1.92312	−	13.8685i	−0.0873245	−	0.629738i
$486$	−1.27770	−	15.4195i	−0.0579576	−	0.699444i
$487$	16.9780	−	25.9867i	0.769345	−	1.17757i	−0.210457	−	0.977603i	$-0.567495\pi$
$487$	16.9780	−	25.9867i	0.769345	−	1.17757i	0.979802	−	0.199968i	$-0.0640838\pi$
$488$	0.877790	−	1.52038i	0.0397357	−	0.0688242i
$489$	7.56292	−	3.56903i	0.342007	−	0.161397i
$490$	−0.903195	−	6.51337i	−0.0408022	−	0.294244i
$491$	−0.544761	−	0.0300553i	−0.0245847	−	0.00135638i	0.0427912	−	0.999084i	$-0.486375\pi$
$491$	−0.544761	−	0.0300553i	−0.0245847	−	0.00135638i	−0.0673760	+	0.997728i	$0.521463\pi$
$492$	0.736213	−	5.30919i	0.0331911	−	0.239357i
$493$	−3.90742	+	2.11459i	−0.175981	+	0.0952363i
$494$	−8.93849	−	11.6907i	−0.402162	−	0.525990i
$495$	11.1098	+	6.01232i	0.499348	+	0.270234i
$496$	3.04941	−	4.14888i	0.136923	−	0.186290i
$497$	−4.17388	−	1.69529i	−0.187224	−	0.0760439i
$498$	4.90735	+	0.543146i	0.219904	+	0.0243389i
$499$	0.649403	+	0.263765i	0.0290713	+	0.0118077i	0.390799	−	0.920476i	$-0.372199\pi$
$499$	0.649403	+	0.263765i	0.0290713	+	0.0118077i	−0.361727	+	0.932284i	$0.617813\pi$
$500$	6.44222	−	7.82235i	0.288105	−	0.349826i
$501$	−10.5542	−	5.71166i	−0.471528	−	0.255178i
$502$	14.3529	+	15.5914i	0.640603	+	0.695880i
$503$	−14.5973	+	8.97292i	−0.650861	+	0.400083i	−0.809390	−	0.587271i	$-0.800202\pi$
$503$	−14.5973	+	8.97292i	−0.650861	+	0.400083i	0.158529	+	0.987354i	$0.449325\pi$
$504$	2.11124	−	0.473141i	0.0940422	−	0.0210754i
$505$	5.95374	−	13.5732i	0.264938	−	0.603998i
$506$	−3.73001	+	14.7295i	−0.165819	+	0.654805i
$507$	−1.60981	+	0.653847i	−0.0714940	+	0.0290383i
$508$	−5.04970	+	1.42792i	−0.224044	+	0.0633537i
$509$	−22.7848	+	19.8433i	−1.00992	+	0.879540i	−0.992736	−	0.120312i	$-0.961610\pi$
$509$	−22.7848	+	19.8433i	−1.00992	+	0.879540i	−0.0171839	+	0.999852i	$0.505470\pi$
$510$	−0.568667	−	2.91126i	−0.0251810	−	0.128913i
$511$	−6.84033	−	4.20474i	−0.302598	−	0.186007i
$512$	−0.945817	−	0.324699i	−0.0417996	−	0.0143498i
$513$	22.7448	−	1.68741i	1.00421	−	0.0745010i
$514$	27.0876	−	9.29917i	1.19478	−	0.410169i
$515$	4.30644	+	0.965097i	0.189765	+	0.0425272i
$516$	−2.54232	+	3.45896i	−0.111920	+	0.152272i
$517$	−13.6331	+	16.5538i	−0.599584	+	0.728034i
$518$	12.1835	+	2.73038i	0.535310	+	0.119966i
$519$	−0.151090	+	5.48127i	−0.00663213	+	0.240601i
$520$	−2.68907	−	2.92111i	−0.117923	−	0.128099i
$521$	25.3812	+	8.71339i	1.11197	+	0.381741i	0.818661	−	0.574277i	$-0.194717\pi$
$521$	25.3812	+	8.71339i	1.11197	+	0.381741i	0.293311	+	0.956017i	$0.405243\pi$
$522$	−1.57302	−	3.10837i	−0.0688493	−	0.136050i
$523$	−4.00136	−	12.7931i	−0.174967	−	0.559402i	0.825016	−	0.565109i	$-0.191166\pi$
$523$	−4.00136	−	12.7931i	−0.174967	−	0.559402i	−0.999984	+	0.00570705i	$0.998183\pi$
$524$	−2.30766	+	1.79613i	−0.100811	+	0.0784641i
$525$	−0.384563	−	4.64098i	−0.0167837	−	0.202549i
$526$	12.1363	+	3.43183i	0.529169	+	0.149635i
$527$	11.8989	−	1.31697i	0.518323	−	0.0573680i
$528$	−6.15087	−	1.73930i	−0.267682	−	0.0756934i
$529$	−14.7861	+	6.97771i	−0.642872	+	0.303379i
$530$	−0.918263	+	0.636709i	−0.0398868	+	0.0276569i
$531$	−2.10420	−	4.79709i	−0.0913144	−	0.208176i
$532$	1.08770	+	5.05745i	0.0471578	+	0.219268i
$533$	6.70052	−	15.2757i	0.290232	−	0.661662i
$534$	−3.25328	−	16.6550i	−0.140783	−	0.720732i
$535$	4.99733	+	6.06792i	0.216053	+	0.262339i
$536$	−3.46520	−	11.0789i	−0.149674	−	0.478535i
$537$	4.18292	+	0.230778i	0.180506	+	0.00995881i
$538$	5.75893	+	7.83531i	0.248285	+	0.337804i
$539$	−13.2341	−	30.1707i	−0.570034	−	1.29955i
$540$	6.06939	−	1.01280i	0.261185	−	0.0435840i
$541$	−6.72794	+	2.73265i	−0.289257	+	0.117486i	−0.516324	−	0.856393i	$-0.672700\pi$
$541$	−6.72794	+	2.73265i	−0.289257	+	0.117486i	0.227068	+	0.973879i	$0.427086\pi$
$542$	1.63220	−	0.662944i	0.0701091	−	0.0284759i
$543$	−23.9903	+	4.00327i	−1.02952	+	0.171797i
$544$	−0.933952	−	2.12920i	−0.0400429	−	0.0912886i
$545$	−6.75129	−	9.18546i	−0.289194	−	0.393462i
$546$	−4.34019	−	0.239455i	−0.185743	−	0.0102477i
$547$	4.28957	+	13.7145i	0.183409	+	0.586391i	0.999958	+	0.00911545i	$0.00290158\pi$
$547$	4.28957	+	13.7145i	0.183409	+	0.586391i	−0.816550	+	0.577275i	$0.804116\pi$
$548$	−8.50080	−	10.3219i	−0.363136	−	0.440932i
$549$	0.613582	+	3.14120i	0.0261870	+	0.134063i
$550$	8.56077	−	19.5166i	0.365032	−	0.832190i
$551$	7.46413	−	3.69682i	0.317983	−	0.157490i
$552$	1.12380	+	2.56200i	0.0478320	+	0.109046i
$553$	−8.04640	+	5.57925i	−0.342168	+	0.237254i
$554$	24.3759	−	11.5033i	1.03563	−	0.488727i
$555$	12.9157	+	3.65221i	0.548241	+	0.155028i
$556$	6.02701	−	0.667069i	0.255602	−	0.0282900i
$557$	−13.6735	−	3.86649i	−0.579363	−	0.163828i	−0.0302005	−	0.999544i	$-0.509615\pi$
$557$	−13.6735	−	3.86649i	−0.579363	−	0.163828i	−0.549162	+	0.835716i	$0.685053\pi$
$558$	0.775174	+	9.35496i	0.0328157	+	0.396027i
$559$	−10.5424	+	8.20547i	−0.445896	+	0.347055i
$560$	0.416629	+	1.33204i	0.0176058	+	0.0562889i
$561$	−6.71056	−	13.2604i	−0.283320	−	0.559855i
$562$	11.6000	+	3.98228i	0.489316	+	0.167982i
$563$	18.8391	+	20.4648i	0.793975	+	0.862487i	0.993074	−	0.117492i	$-0.0374855\pi$
$563$	18.8391	+	20.4648i	0.793975	+	0.862487i	−0.199098	+	0.979980i	$0.563801\pi$
$564$	−0.108799	+	3.94701i	−0.00458125	+	0.166199i
$565$	14.8979	+	3.33871i	0.626761	+	0.140460i
$566$	−12.8217	+	15.5685i	−0.538936	+	0.654394i
$567$	0.145595	−	0.198089i	0.00611441	−	0.00831896i
$568$	−3.70411	−	0.830110i	−0.155421	−	0.0348306i
$569$	4.90763	−	1.68479i	0.205739	−	0.0706302i	−0.219904	−	0.975522i	$-0.570574\pi$
$569$	4.90763	−	1.68479i	0.205739	−	0.0706302i	0.425643	+	0.904891i	$0.360048\pi$
$570$	0.868009	+	5.49295i	0.0363569	+	0.230074i
$571$	−27.8760	−	9.56986i	−1.16658	−	0.400486i	−0.327686	−	0.944787i	$-0.606269\pi$
$571$	−27.8760	−	9.56986i	−1.16658	−	0.400486i	−0.838890	+	0.544301i	$0.816795\pi$
$572$	−16.9468	−	10.4172i	−0.708581	−	0.435563i
$573$	5.44627	+	27.8819i	0.227521	+	1.16478i
$574$	−4.42177	+	3.85092i	−0.184561	+	0.160734i
$575$	−8.97557	+	2.53805i	−0.374307	+	0.105844i
$576$	1.68907	−	0.686042i	0.0703780	−	0.0285851i
$577$	−6.88467	+	27.1870i	−0.286613	+	1.13181i	0.643770	+	0.765219i	$0.277369\pi$
$577$	−6.88467	+	27.1870i	−0.286613	+	1.13181i	−0.930383	+	0.366589i	$0.880525\pi$
$578$	−4.65736	+	10.6177i	−0.193721	+	0.441638i
$579$	−25.2330	+	5.65485i	−1.04865	+	0.235007i
$580$	1.91447	−	1.17682i	0.0794940	−	0.0488648i
$581$	−3.65814	−	3.97380i	−0.151765	−	0.164861i
$582$	−11.3593	−	6.14736i	−0.470859	−	0.254816i
$583$	−3.55908	+	4.32155i	−0.147402	+	0.178980i
$584$	−6.26827	−	2.54595i	−0.259383	−	0.105352i
$585$	7.19439	+	0.796275i	0.297451	+	0.0329219i
$586$	−30.4913	−	12.3845i	−1.25958	−	0.511599i
$587$	−17.9036	+	24.3587i	−0.738959	+	1.00539i	0.260247	+	0.965542i	$0.416196\pi$
$587$	−17.9036	+	24.3587i	−0.738959	+	1.00539i	−0.999206	+	0.0398477i	$0.987313\pi$
$588$	−5.33491	−	2.88711i	−0.220008	−	0.119062i
$589$	−22.3824	+	1.66052i	−0.922252	+	0.0684206i
$590$	2.97179	−	1.60825i	0.122347	−	0.0662107i
$591$	−0.167810	+	1.21015i	−0.00690276	+	0.0497791i
$592$	10.5046	+	0.579553i	0.431735	+	0.0238195i
$593$	2.12999	+	15.3604i	0.0874681	+	0.630775i	0.982704	+	0.185182i	$0.0592876\pi$
$593$	2.12999	+	15.3604i	0.0874681	+	0.630775i	−0.895236	+	0.445592i	$0.852993\pi$
$594$	27.8808	−	13.1573i	1.14396	−	0.539849i
$595$	−1.62249	+	2.81023i	−0.0665156	+	0.115208i
$596$	−7.31808	+	11.2011i	−0.299760	+	0.458817i
$597$	0.411464	+	4.96563i	0.0168401	+	0.203230i
$598$	1.19586	+	8.62389i	0.0489022	+	0.352657i
$599$	−26.3626	−	35.8675i	−1.07714	−	1.46551i	−0.873727	−	0.486416i	$-0.838304\pi$
$599$	−26.3626	−	35.8675i	−1.07714	−	1.46551i	−0.203417	−	0.979092i	$-0.565205\pi$
$600$	−0.963271	−	3.80387i	−0.0393254	−	0.155292i
$601$	16.2339	+	2.70897i	0.662196	+	0.110501i	0.486143	−	0.873880i	$-0.338404\pi$
$601$	16.2339	+	2.70897i	0.662196	+	0.110501i	0.176054	+	0.984381i	$0.443667\pi$
$602$	4.58243	−	1.02695i	0.186766	−	0.0418552i
$603$	18.0288	+	11.0823i	0.734190	+	0.451305i
$604$	−0.909475	−	1.79717i	−0.0370060	−	0.0731258i
$605$	−3.83088	+	27.6263i	−0.155748	+	1.12317i
$606$	−6.83638	−	11.8410i	−0.277709	−	0.481006i
$607$	−1.88533	−	7.44501i	−0.0765233	−	0.302184i	0.919292	−	0.393577i	$-0.128763\pi$
$607$	−1.88533	−	7.44501i	−0.0765233	−	0.302184i	−0.995815	+	0.0913936i	$0.970868\pi$
$608$	1.60542	+	4.05248i	0.0651084	+	0.164350i
$609$	0.603966	−	2.38501i	0.0244739	−	0.0966453i
$610$	−1.98668	+	0.561779i	−0.0804382	+	0.0227458i
$611$	−3.66815	+	11.7277i	−0.148398	+	0.474453i
$612$	3.83330	+	1.80898i	0.154952	+	0.0731237i
$613$	6.40669	−	4.44230i	0.258764	−	0.179423i	−0.433320	−	0.901240i	$-0.642658\pi$
$613$	6.40669	−	4.44230i	0.258764	−	0.179423i	0.692084	+	0.721817i	$0.256693\pi$
$614$	4.23729	+	30.5571i	0.171003	+	1.23318i
$615$	−4.97426	+	3.87162i	−0.200582	+	0.156119i
$616$	3.82461	+	5.85400i	0.154098	+	0.235864i
$617$	−14.0620	+	0.775820i	−0.566113	+	0.0312333i	−0.335884	−	0.941903i	$-0.609035\pi$
$617$	−14.0620	+	0.775820i	−0.566113	+	0.0312333i	−0.230229	+	0.973137i	$0.573947\pi$
$618$	3.07012	−	2.67377i	0.123498	−	0.107555i
$619$	8.73598	−	34.4976i	0.351129	−	1.38658i	−0.501997	−	0.864869i	$-0.667401\pi$
$619$	8.73598	−	34.4976i	0.351129	−	1.38658i	0.853125	−	0.521706i	$-0.174704\pi$
$620$	−5.97267	+	0.996663i	−0.239868	+	0.0400270i
$621$	−12.2027	−	5.75858i	−0.489677	−	0.231084i
$622$	−5.05185	−	4.39966i	−0.202561	−	0.176410i
$623$	−9.28208	+	16.0770i	−0.371879	+	0.644113i
$624$	−3.64042	+	0.402922i	−0.145733	+	0.0161298i
$625$	6.13029	−	0.678500i	0.245212	−	0.0271400i
$626$	0.541067	−	0.828164i	0.0216254	−	0.0331001i
$627$	11.6733	+	25.2991i	0.466188	+	1.01035i
$628$	−1.06602	−	1.63167i	−0.0425390	−	0.0651107i
$629$	15.5501	+	18.8815i	0.620025	+	0.752854i
$630$	−2.16764	−	1.33245i	−0.0863610	−	0.0530859i
$631$	−5.83709	+	3.58805i	−0.232371	+	0.142838i	−0.634965	−	0.772541i	$-0.718986\pi$
$631$	−5.83709	+	3.58805i	−0.232371	+	0.142838i	0.402594	+	0.915378i	$0.368108\pi$
$632$	−5.91373	+	5.75296i	−0.235236	+	0.228841i
$633$	3.48446	+	3.38973i	0.138495	+	0.134730i
$634$	29.8798	−	10.2578i	1.18668	−	0.407388i
$635$	5.42754	+	2.93724i	0.215386	+	0.116561i
$636$	−0.0284031	+	1.03041i	−0.00112626	+	0.0408585i
$637$	−13.5313	−	13.1635i	−0.536130	−	0.521555i
$638$	7.62563	−	8.28364i	0.301902	−	0.327953i
$639$	6.08629	−	3.29374i	0.240770	−	0.130298i
$640$	0.531007	+	1.04930i	0.0209899	+	0.0414772i
$641$	15.7259	+	19.0949i	0.621134	+	0.754202i	0.984103	−	0.177600i	$-0.0568333\pi$
$641$	15.7259	+	19.0949i	0.621134	+	0.754202i	−0.362969	+	0.931801i	$0.618237\pi$
$642$	7.24057	−	0.399473i	0.285763	−	0.0157660i
$643$	14.0431	+	37.5075i	0.553806	+	1.47915i	0.851430	+	0.524468i	$0.175736\pi$
$643$	14.0431	+	37.5075i	0.553806	+	1.47915i	−0.297624	+	0.954683i	$0.596194\pi$
$644$	0.913601	−	2.92095i	0.0360009	−	0.115101i
$645$	4.97947	−	0.830927i	0.196067	−	0.0327177i
$646$	−4.40404	+	9.12763i	−0.173274	+	0.359122i
$647$	9.95127	+	1.66057i	0.391225	+	0.0652839i	0.356938	−	0.934128i	$-0.383821\pi$
$647$	9.95127	+	1.66057i	0.391225	+	0.0652839i	0.0342871	+	0.999412i	$0.489084\pi$
$648$	0.0935338	−	0.184828i	0.00367435	−	0.00726072i
$649$	12.1350	−	11.8051i	0.476340	−	0.463390i
$650$	0.336481	−	12.2069i	0.0131979	−	0.478794i
$651$	−3.92612	+	5.34168i	−0.153877	+	0.209357i
$652$	−7.66182	−	0.848010i	−0.300060	−	0.0332106i
$653$	25.8584			1.01192			0.505958	−	0.862558i	$-0.331139\pi$
$653$	25.8584			1.01192			0.505958	+	0.862558i	$0.331139\pi$
$654$	−10.5161			−0.411213
$655$	3.41810	+	0.378315i	0.133556	+	0.0147820i
$656$	−3.14093	+	3.81382i	−0.122633	+	0.148905i
$657$	11.6659	−	4.00491i	0.455130	−	0.156246i
$658$	2.92551	−	3.17796i	0.114048	−	0.123890i
$659$	−6.93742	+	35.5157i	−0.270244	+	1.38350i	0.561105	+	0.827745i	$0.310377\pi$
$659$	−6.93742	+	35.5157i	−0.270244	+	1.38350i	−0.831348	+	0.555752i	$0.812431\pi$
$660$	3.75856	+	6.51002i	0.146302	+	0.253402i
$661$	11.7265	+	15.9545i	0.456108	+	0.620558i	0.971683	−	0.236287i	$-0.0759304\pi$
$661$	11.7265	+	15.9545i	0.456108	+	0.620558i	−0.515575	+	0.856844i	$0.672422\pi$
$662$	27.6438	−	19.1678i	1.07441	−	0.744977i
$663$	−6.42179	−	5.59274i	−0.249402	−	0.217204i
$664$	−3.59147	−	2.79535i	−0.139376	−	0.108481i
$665$	3.23038	−	5.15508i	0.125269	−	0.199906i
$666$	−15.1355	+	11.7805i	−0.586490	+	0.456483i
$667$	−4.92036	−	0.271464i	−0.190517	−	0.0105111i
$668$	5.53095	+	9.57988i	0.213999	+	0.370657i
$669$	−7.03071	−	4.87499i	−0.271823	−	0.188478i
$670$	−6.16401	+	12.1804i	−0.238137	+	0.470571i
$671$	−8.81224	+	5.41686i	−0.340193	+	0.209116i
$672$	1.21774	+	0.418050i	0.0469753	+	0.0161266i
$673$	−41.8804	+	22.6645i	−1.61437	+	0.873654i	−0.618220	+	0.786005i	$0.712146\pi$
$673$	−41.8804	+	22.6645i	−1.61437	+	0.873654i	−0.996151	+	0.0876488i	$0.972065\pi$
$674$	0.683469	−	3.49898i	0.0263262	−	0.134776i
$675$	15.5525	+	10.7839i	0.598618	+	0.415072i
$676$	1.57977	+	0.263617i	0.0607603	+	0.0101391i
$677$	3.85300	−	8.78395i	0.148083	−	0.337595i	−0.826041	−	0.563610i	$-0.809412\pi$
$677$	3.85300	−	8.78395i	0.148083	−	0.337595i	0.974124	+	0.226015i	$0.0725700\pi$
$678$	10.6209	−	9.24978i	0.407894	−	0.355236i
$679$	4.95437	+	13.2325i	0.190131	+	0.507818i
$680$	−0.958731	+	2.56066i	−0.0367657	+	0.0981967i
$681$	−7.58256	−	6.60365i	−0.290564	−	0.253053i
$682$	−27.4365	+	12.9476i	−1.05060	+	0.495790i
$683$	0.0230556	+	0.278240i	0.000882198	+	0.0106465i	0.997011	−	0.0772549i	$-0.0246155\pi$
$683$	0.0230556	+	0.278240i	0.000882198	+	0.0106465i	−0.996129	+	0.0879014i	$0.971984\pi$
$684$	−7.05921	−	3.64915i	−0.269916	−	0.139529i
$685$	−1.29859	+	15.6717i	−0.0496167	+	0.598785i
$686$	5.23975	+	13.9947i	0.200055	+	0.534322i
$687$	−2.04816	+	0.579166i	−0.0781423	+	0.0220965i
$688$	3.66611	−	1.48905i	0.139769	−	0.0567693i
$689$	−0.957612	+	3.06165i	−0.0364821	+	0.116640i
$690$	1.15361	−	3.08116i	0.0439173	−	0.117298i
$691$	−12.3235	−	9.59179i	−0.468809	−	0.364889i	0.352086	−	0.935968i	$-0.385472\pi$
$691$	−12.3235	−	9.59179i	−0.468809	−	0.364889i	−0.820895	+	0.571079i	$0.806525\pi$
$692$	2.76452	−	4.23141i	0.105091	−	0.160854i
$693$	−12.2671	−	3.46881i	−0.465989	−	0.131769i
$694$	−3.75413	+	6.50234i	−0.142505	+	0.246825i
$695$	−5.62744	−	4.38001i	−0.213461	−	0.166143i
$696$	0.171192	−	2.06598i	0.00648903	−	0.0783109i
$697$	−11.4699	+	0.632810i	−0.434452	+	0.0239694i
$698$	3.59146	+	18.3863i	0.135939	+	0.695931i
$699$	24.8496	−	5.56893i	0.939899	−	0.210636i
$700$	−1.93826	+	3.83011i	−0.0732594	+	0.144764i
$701$	0.960827	+	34.8570i	0.0362899	+	1.31653i	0.770426	+	0.637529i	$0.220044\pi$
$701$	0.960827	+	34.8570i	0.0362899	+	1.31653i	−0.734136	+	0.679002i	$0.762413\pi$
$702$	11.9643	−	12.9967i	0.451565	−	0.490531i
$703$	−27.8535	−	36.4298i	−1.05052	−	1.37398i
$704$	3.99058	+	4.33493i	0.150401	+	0.163379i
$705$	3.32837	−	3.23789i	0.125354	−	0.121946i
$706$	0.507710	+	18.4188i	0.0191079	+	0.693199i
$707$	−2.86749	+	14.6800i	−0.107843	+	0.552097i
$708$	0.428152	−	3.08761i	0.0160909	−	0.116039i
$709$	−13.7829	−	44.0662i	−0.517626	−	1.65494i	−0.734397	−	0.678720i	$-0.762535\pi$
$709$	−13.7829	−	44.0662i	−0.517626	−	1.65494i	0.216771	−	0.976222i	$-0.430447\pi$
$710$	2.44164	+	3.73720i	0.0916330	+	0.140255i
$711$	1.24208	−	14.9897i	0.0465818	−	0.562159i
$712$	−5.48479	+	14.6492i	−0.205551	+	0.549003i
$713$	12.0082	+	5.66683i	0.449712	+	0.212224i
$714$	1.20246	+	2.74134i	0.0450011	+	0.102592i
$715$	5.74282	+	22.6779i	0.214769	+	0.848105i
$716$	−3.17337	−	2.20036i	−0.118594	−	0.0822314i
$717$	0.0309521	+	1.12289i	0.00115593	+	0.0419349i
$718$	−20.4691	−	19.9127i	−0.763901	−	0.743135i
$719$	−15.4317	−	3.45832i	−0.575504	−	0.128973i	−0.0787952	−	0.996891i	$-0.525107\pi$
$719$	−15.4317	−	3.45832i	−0.575504	−	0.128973i	−0.496709	+	0.867917i	$0.665458\pi$
$720$	−1.98636	−	0.806791i	−0.0740274	−	0.0300673i
$721$	−4.45371			−0.165865
$722$	8.87013	−	16.8024i	0.330112	−	0.625321i
$723$	4.63517			0.172384
$724$	20.7715	+	8.43666i	0.771968	+	0.313546i
$725$	6.74446	+	1.51147i	0.250483	+	0.0561346i
$726$	18.4421	+	17.9407i	0.684449	+	0.665842i
$727$	0.462193	+	16.7675i	0.0171418	+	0.621872i	0.958602	+	0.284748i	$0.0919101\pi$
$727$	0.462193	+	16.7675i	0.0171418	+	0.621872i	−0.941461	+	0.337123i	$0.890546\pi$
$728$	3.29268	+	2.28309i	0.122035	+	0.0846171i
$729$	4.27312	+	16.8742i	0.158264	+	0.624969i
$730$	3.19604	+	7.28625i	0.118291	+	0.269676i
$731$	8.32015	+	3.92637i	0.307732	+	0.145222i
$732$	−0.667810	+	1.78364i	−0.0246830	+	0.0659252i
$733$	−2.14176	+	25.8472i	−0.0791078	+	0.954689i	0.835273	+	0.549835i	$0.185309\pi$
$733$	−2.14176	+	25.8472i	−0.0791078	+	0.954689i	−0.914381	+	0.404854i	$0.867322\pi$
$734$	−3.45106	−	5.28225i	−0.127381	−	0.194971i
$735$	2.12952	+	6.80844i	0.0785484	+	0.251133i
$736$	0.354207	−	2.55436i	0.0130562	−	0.0941548i
$737$	−13.1122	+	67.1273i	−0.482995	+	2.47266i
$738$	−0.248191	−	9.00390i	−0.00913603	−	0.331438i
$739$	2.13922	−	2.08106i	0.0786923	−	0.0765531i	−0.656899	−	0.753978i	$-0.728132\pi$
$739$	2.13922	−	2.08106i	0.0786923	−	0.0765531i	0.735592	+	0.677425i	$0.236904\pi$
$740$	−8.37949	−	9.10256i	−0.308036	−	0.334617i
$741$	11.6523	+	10.9137i	0.428057	+	0.400926i
$742$	0.763738	−	0.829641i	0.0280377	−	0.0304571i
$743$	0.842203	+	30.5536i	0.0308974	+	1.12090i	0.843178	+	0.537635i	$0.180682\pi$
$743$	0.842203	+	30.5536i	0.0308974	+	1.12090i	−0.812280	+	0.583267i	$0.801774\pi$
$744$	−2.52224	+	4.98407i	−0.0924696	+	0.182725i
$745$	15.3540	−	3.44090i	0.562526	−	0.126065i
$746$	−2.16672	−	11.0924i	−0.0793294	−	0.406122i
$747$	8.28443	−	0.457065i	0.303112	−	0.0167231i
$748$	−1.13127	+	13.6524i	−0.0413633	+	0.499181i
$749$	−6.26018	−	4.87249i	−0.228742	−	0.178037i
$750$	−5.49681	+	9.52075i	−0.200715	+	0.347649i
$751$	−0.0990846	−	0.0280185i	−0.00361565	−	0.00102241i	0.270295	−	0.962778i	$-0.412879\pi$
$751$	−0.0990846	−	0.0280185i	−0.00361565	−	0.00102241i	−0.273911	+	0.961755i	$0.588317\pi$
$752$	1.99070	−	3.04699i	0.0725933	−	0.111112i
$753$	−18.1426	−	14.1209i	−0.661153	−	0.514596i
$754$	2.26214	−	6.04191i	0.0823823	−	0.220033i
$755$	−0.707094	+	2.26071i	−0.0257338	+	0.0822755i
$756$	−5.75326	+	2.33677i	−0.209244	+	0.0849876i
$757$	10.0479	−	2.84127i	0.365197	−	0.103268i	−0.0845611	−	0.996418i	$-0.526949\pi$
$757$	10.0479	−	2.84127i	0.365197	−	0.103268i	0.449758	+	0.893150i	$0.351510\pi$
$758$	−8.19144	−	21.8784i	−0.297526	−	0.794658i
$759$	1.36122	−	16.4275i	0.0494093	−	0.596281i
$760$	1.96987	−	4.73250i	0.0714547	−	0.171666i
$761$	2.39672	+	28.9241i	0.0868809	+	1.04850i	0.890992	+	0.454018i	$0.150010\pi$
$761$	2.39672	+	28.9241i	0.0868809	+	1.04850i	−0.804112	+	0.594478i	$0.797359\pi$
$762$	5.14853	−	2.42965i	0.186512	−	0.0880170i
$763$	8.67537	+	7.55539i	0.314070	+	0.273523i
$764$	9.18202	−	24.5241i	0.332194	−	0.887250i
$765$	−1.74784	−	4.66828i	−0.0631934	−	0.168782i
$766$	9.86875	−	8.59470i	0.356572	−	0.310539i
$767$	3.89675	−	8.88371i	0.140704	−	0.320772i
$768$	1.07006	+	0.178562i	0.0386126	+	0.00644330i
$769$	16.1955	+	11.2297i	0.584023	+	0.404953i	0.824632	−	0.565669i	$-0.191382\pi$
$769$	16.1955	+	11.2297i	0.584023	+	0.404953i	−0.240609	+	0.970622i	$0.577347\pi$
$770$	1.57651	−	8.07087i	0.0568136	−	0.290854i
$771$	−27.3249	+	14.7875i	−0.984084	+	0.532560i
$772$	22.5446	+	7.73958i	0.811399	+	0.278554i
$773$	−6.85801	+	4.21560i	−0.246665	+	0.151625i	−0.641489	−	0.767132i	$-0.721683\pi$
$773$	−6.85801	+	4.21560i	−0.246665	+	0.151625i	0.394823	+	0.918757i	$0.370806\pi$
$774$	−3.25730	+	6.43661i	−0.117081	+	0.231359i
$775$	−15.3047	−	10.6121i	−0.549762	−	0.381196i
$776$	5.95287	+	10.3107i	0.213695	+	0.370131i
$777$	−13.5246	−	0.746174i	−0.485193	−	0.0267688i
$778$	−22.6206	+	17.6063i	−0.810988	+	0.631217i
$779$	21.5322	−	0.407812i	0.771472	−	0.0146114i
$780$	3.39907	+	2.64560i	0.121706	+	0.0947278i
$781$	16.8665	+	14.6890i	0.603530	+	0.525615i
$782$	4.92719	−	3.41644i	0.176196	−	0.122172i
$783$	5.92150	+	8.05649i	0.211617	+	0.287915i
$784$	2.79577	+	4.84241i	0.0998488	+	0.172943i
$785$	−0.439418	+	2.24957i	−0.0156835	+	0.0802907i
$786$	2.14863	−	2.33403i	0.0766390	−	0.0832521i
$787$	−2.21009	+	0.758724i	−0.0787812	+	0.0270456i	−0.363808	−	0.931474i	$-0.618524\pi$
$787$	−2.21009	+	0.758724i	−0.0787812	+	0.0270456i	0.285027	+	0.958519i	$0.407997\pi$
$788$	0.715931	−	0.869307i	0.0255040	−	0.0309678i
$789$	−13.5994	−	1.50519i	−0.484153	−	0.0535861i
$790$	9.70252			0.345200
$791$	−15.4074			−0.547824
$792$	−10.6765	−	1.18167i	−0.379373	−	0.0419890i
$793$	−3.51024	+	4.77585i	−0.124652	+	0.169595i
$794$	−0.652990	+	23.6892i	−0.0231737	+	0.840700i
$795$	0.868907	−	0.845286i	0.0308170	−	0.0299792i
$796$	2.07384	−	4.09803i	0.0735054	−	0.145251i
$797$	−24.4470	−	4.07948i	−0.865957	−	0.144503i	−0.285089	−	0.958501i	$-0.592023\pi$
$797$	−24.4470	−	4.07948i	−0.865957	−	0.144503i	−0.580867	+	0.813998i	$0.697286\pi$
$798$	−2.06698	−	5.21757i	−0.0731702	−	0.184700i
$799$	8.34687	−	1.39285i	0.295291	−	0.0492753i
$800$	−1.07973	+	3.45209i	−0.0381742	+	0.122050i
$801$	−9.99921	−	26.7067i	−0.353305	−	0.943635i
$802$	20.8413	−	1.14985i	0.735933	−	0.0406025i
$803$	25.3420	+	30.7711i	0.894300	+	1.08589i
$804$	5.68626	+	11.2364i	0.200539	+	0.396276i
$805$	−3.16537	+	1.71301i	−0.111565	+	0.0603757i
$806$	−11.7737	+	12.7897i	−0.414711	+	0.450496i
$807$	−7.56151	−	7.35595i	−0.266178	−	0.258942i
$808$	−0.347274	+	12.5985i	−0.0122171	+	0.443212i
$809$	−11.1642	−	6.04176i	−0.392512	−	0.212417i	0.267690	−	0.963505i	$-0.413740\pi$
$809$	−11.1642	−	6.04176i	−0.392512	−	0.212417i	−0.660202	+	0.751088i	$0.729529\pi$
$810$	−0.230407	+	0.0790990i	−0.00809569	+	0.00277925i
$811$	24.1626	+	23.5057i	0.848462	+	0.825397i	0.986283	−	0.165060i	$-0.0527819\pi$
$811$	24.1626	+	23.5057i	0.848462	+	0.825397i	−0.137821	+	0.990457i	$0.544010\pi$
$812$	−1.62555	+	1.58136i	−0.0570456	+	0.0554948i
$813$	−1.62819	+	1.00084i	−0.0571029	+	0.0351011i
$814$	−52.8085	−	32.4612i	−1.85094	−	1.13777i
$815$	5.76309	+	6.99773i	0.201872	+	0.245120i
$816$	1.37958	+	2.11161i	0.0482951	+	0.0739211i
$817$	−15.3219	−	7.92044i	−0.536047	−	0.277101i
$818$	5.76261	−	8.82034i	0.201485	−	0.308396i
$819$	−7.26034	+	0.803574i	−0.253697	+	0.0280791i
$820$	5.77507	−	0.639184i	0.201674	−	0.0223213i
$821$	4.56431	−	7.90562i	0.159295	−	0.275908i	−0.775319	−	0.631569i	$-0.782411\pi$
$821$	4.56431	−	7.90562i	0.159295	−	0.275908i	0.934615	+	0.355662i	$0.115744\pi$
$822$	10.9395	+	9.52722i	0.381559	+	0.332300i
$823$	−39.0810	−	18.4428i	−1.36228	−	0.642875i	−0.400397	−	0.916342i	$-0.631128\pi$
$823$	−39.0810	−	18.4428i	−1.36228	−	0.642875i	−0.961881	+	0.273467i	$0.911830\pi$
$824$	−3.70156	+	0.617681i	−0.128950	+	0.0215179i
$825$	−5.67565	+	22.4126i	−0.197601	+	0.780308i
$826$	−2.57152	+	2.23954i	−0.0894748	+	0.0779236i
$827$	−32.7994	+	1.80959i	−1.14055	+	0.0629257i	−0.615492	−	0.788143i	$-0.711043\pi$
$827$	−32.7994	+	1.80959i	−1.14055	+	0.0629257i	−0.525055	+	0.851069i	$0.675955\pi$
$828$	2.57140	+	3.93581i	0.0893622	+	0.136779i
$829$	2.55810	−	1.99105i	0.0888467	−	0.0691521i	−0.568815	−	0.822465i	$-0.692598\pi$
$829$	2.55810	−	1.99105i	0.0888467	−	0.0691521i	0.657662	+	0.753313i	$0.271545\pi$
$830$	0.735136	+	5.30142i	0.0255170	+	0.184015i
$831$	−24.0297	+	16.6618i	−0.833582	+	0.577993i
$832$	3.05325	+	1.44086i	0.105852	+	0.0499529i
$833$	−3.88083	+	12.4077i	−0.134463	+	0.429901i
$834$	−6.33017	+	1.79000i	−0.219196	+	0.0619827i
$835$	3.19349	−	12.6108i	0.110515	−	0.436415i
$836$	3.04528	−	25.5017i	0.105323	−	0.881995i
$837$	−6.61372	−	26.1170i	−0.228604	−	0.902736i
$838$	−8.12985	−	14.0813i	−0.280841	−	0.486431i
$839$	−3.49079	+	25.1737i	−0.120515	+	0.869094i	0.829856	+	0.557977i	$0.188422\pi$
$839$	−3.49079	+	25.1737i	−0.120515	+	0.869094i	−0.950372	+	0.311117i	$0.899297\pi$
$840$	−0.683672	−	1.35097i	−0.0235889	−	0.0466130i
$841$	−21.5948	−	13.2743i	−0.744649	−	0.457734i
$842$	−8.09253	+	1.81358i	−0.278887	+	0.0625000i
$843$	−13.1238	−	2.18998i	−0.452008	−	0.0754268i
$844$	−1.10002	−	4.34388i	−0.0378642	−	0.149522i
$845$	−1.11548	−	1.51767i	−0.0383737	−	0.0522093i
$846$	0.911391	+	6.57248i	0.0313343	+	0.225966i
$847$	−2.32430	−	28.0502i	−0.0798641	−	0.963816i
$848$	0.519694	−	0.795451i	0.0178464	−	0.0273159i
$849$	10.9401	−	18.9488i	0.375463	−	0.650321i
$850$	−7.60531	+	3.58903i	−0.260860	+	0.123103i
$851$	3.72645	+	26.8732i	0.127741	+	0.921201i
$852$	4.11186	+	0.226858i	0.140870	+	0.00777201i
$853$	6.55329	−	47.2589i	0.224381	−	1.61812i	−0.459264	−	0.888300i	$-0.651887\pi$
$853$	6.55329	−	47.2589i	0.224381	−	1.61812i	0.683644	−	0.729815i	$-0.260394\pi$
$854$	1.83239	−	0.991638i	0.0627030	−	0.0339331i
$855$	2.95810	+	8.86477i	0.101165	+	0.303169i
$856$	−5.87871	−	3.18140i	−0.200930	−	0.108738i
$857$	11.1825	−	15.2143i	0.381986	−	0.519711i	−0.571721	−	0.820448i	$-0.693724\pi$
$857$	11.1825	−	15.2143i	0.381986	−	0.519711i	0.953707	+	0.300737i	$0.0972327\pi$
$858$	19.9943	+	8.12096i	0.682593	+	0.277245i
$859$	47.0627	+	5.20890i	1.60576	+	0.177725i	0.867727	−	0.497041i	$-0.165580\pi$
$859$	47.0627	+	5.20890i	1.60576	+	0.177725i	0.738031	+	0.674767i	$0.235756\pi$
$860$	−4.31138	−	1.75113i	−0.147017	−	0.0597131i
$861$	4.04395	−	4.91030i	0.137817	−	0.167342i
$862$	19.3778	+	10.4867i	0.660010	+	0.357180i
$863$	−27.5620	−	29.9403i	−0.938221	−	1.01918i	−0.999778	−	0.0210762i	$-0.993291\pi$
$863$	−27.5620	−	29.9403i	−0.938221	−	1.01918i	0.0615568	−	0.998104i	$-0.480393\pi$
$864$	−4.45755	+	2.74005i	−0.151649	+	0.0932183i
$865$	−5.80020	+	1.29985i	−0.197213	+	0.0441964i
$866$	−9.82459	+	22.3978i	−0.333853	+	0.761108i
$867$	3.08775	−	12.1933i	0.104866	−	0.414105i
$868$	5.66159	−	2.29954i	0.192167	−	0.0780514i
$869$	46.7775	−	13.2274i	1.58682	−	0.448710i
$870$	−1.83847	+	1.60112i	−0.0623299	+	0.0542832i
$871$	7.51330	+	38.4639i	0.254579	+	1.30330i
$872$	8.25811	+	5.07624i	0.279655	+	0.171903i
$873$	−20.5291	−	7.04763i	−0.694803	−	0.238526i
$874$	−9.46300	+	6.06674i	−0.320091	+	0.205211i
$875$	11.3749	−	3.90501i	0.384542	−	0.132013i
$876$	7.16206	+	1.60506i	0.241984	+	0.0542298i
$877$	2.37754	−	3.23476i	0.0802839	−	0.109230i	−0.763770	−	0.645488i	$-0.776654\pi$
$877$	2.37754	−	3.23476i	0.0802839	−	0.109230i	0.844054	+	0.536258i	$0.180163\pi$
$878$	4.50208	−	5.46657i	0.151938	−	0.184488i
$879$	34.8391	+	7.80762i	1.17509	+	0.263344i
$880$	0.190927	−	6.92648i	0.00643616	−	0.233492i
$881$	−21.8937	−	23.7830i	−0.737619	−	0.801268i	0.248266	−	0.968692i	$-0.420139\pi$
$881$	−21.8937	−	23.7830i	−0.737619	−	0.801268i	−0.985885	+	0.167424i	$0.946455\pi$
$882$	−9.64148	−	3.30992i	−0.324645	−	0.111451i
$883$	−2.24886	−	4.44387i	−0.0756802	−	0.149548i	0.851275	−	0.524719i	$-0.175830\pi$
$883$	−2.24886	−	4.44387i	−0.0756802	−	0.149548i	−0.926956	+	0.375171i	$0.877584\pi$
$884$	2.34323	+	7.49173i	0.0788115	+	0.251974i
$885$	−2.89283	+	2.25158i	−0.0972415	+	0.0756861i
$886$	2.77271	+	33.4617i	0.0931511	+	1.12417i
$887$	52.2373	+	14.7713i	1.75396	+	0.495972i	0.988976	−	0.148079i	$-0.0473090\pi$
$887$	52.2373	+	14.7713i	1.75396	+	0.495972i	0.764982	+	0.644051i	$0.222748\pi$
$888$	−11.3440	+	1.25556i	−0.380681	+	0.0421338i
$889$	−5.99293	−	1.69464i	−0.200996	−	0.0568364i
$890$	16.6361	−	7.85078i	0.557644	−	0.263159i
$891$	−1.00300	+	0.695463i	−0.0336017	+	0.0232989i
$892$	3.16787	+	7.22203i	0.106068	+	0.241811i
$893$	−15.7327	+	2.04355i	−0.526475	+	0.0683848i
$894$	5.83071	−	13.2927i	0.195008	−	0.444574i
$895$	0.870608	+	4.45703i	0.0291012	+	0.148982i
$896$	−0.754470	−	0.916102i	−0.0252051	−	0.0306048i
$897$	−2.81954	−	9.01458i	−0.0941418	−	0.300988i
$898$	20.8233	+	1.14885i	0.694881	+	0.0383377i
$899$	−5.82714	−	7.92811i	−0.194346	−	0.264417i
$900$	−2.64881	−	6.03868i	−0.0882937	−	0.201289i
$901$	2.17904	−	0.363618i	0.0725944	−	0.0121139i
$902$	26.9712	−	10.9547i	0.898042	−	0.364753i
$903$	−4.72012	+	1.91715i	−0.157076	+	0.0637986i
$904$	−12.8054	+	2.13684i	−0.425900	+	0.0710702i
$905$	−10.5909	−	24.1448i	−0.352054	−	0.802602i
$906$	1.29410	+	1.76069i	0.0429937	+	0.0584950i
$907$	21.0197	+	1.15969i	0.697947	+	0.0385068i	0.400587	−	0.916259i	$-0.368806\pi$
$907$	21.0197	+	1.15969i	0.697947	+	0.0385068i	0.297360	+	0.954765i	$0.403894\pi$
$908$	2.76678	+	8.84590i	0.0918189	+	0.293561i
$909$	−14.6068	−	17.7361i	−0.484478	−	0.588270i
$910$	−0.903342	−	4.62461i	−0.0299455	−	0.153304i
$911$	−21.4514	+	48.9042i	−0.710715	+	1.62027i	0.0716361	+	0.997431i	$0.477178\pi$
$911$	−21.4514	+	48.9042i	−0.710715	+	1.62027i	−0.782351	+	0.622837i	$0.785980\pi$
$912$	−2.44152	−	4.04975i	−0.0808469	−	0.134101i
$913$	10.7716	+	24.5568i	0.356489	+	0.812713i
$914$	25.0248	−	17.3518i	0.827745	−	0.573946i
$915$	2.02556	−	0.955884i	0.0669629	−	0.0316006i
$916$	1.88795	+	0.533862i	0.0623797	+	0.0176393i
$917$	−3.44943	+	0.381783i	−0.113910	+	0.0126076i
$918$	−11.7064	−	3.31024i	−0.386368	−	0.109254i
$919$	1.78556	+	21.5486i	0.0589003	+	0.710821i	0.960505	+	0.278261i	$0.0897581\pi$
$919$	1.78556	+	21.5486i	0.0589003	+	0.710821i	−0.901605	+	0.432560i	$0.857610\pi$
$920$	−2.39322	+	1.86272i	−0.0789021	+	0.0614119i
$921$	−9.99051	−	31.9414i	−0.329198	−	1.05251i
$922$	−6.28878	−	12.4270i	−0.207110	−	0.409260i
$923$	12.1214	+	4.16129i	0.398981	+	0.136970i
$924$	−5.13788	−	5.58122i	−0.169024	−	0.183609i
$925$	1.04852	−	38.0384i	0.0344751	−	1.25069i
$926$	38.6425	+	8.65998i	1.26987	+	0.284585i
$927$	4.34933	−	5.28110i	0.142851	−	0.173454i
$928$	−1.13171	+	1.53974i	−0.0371501	+	0.0505445i
$929$	25.4762	+	5.70934i	0.835846	+	0.187317i	0.615532	−	0.788112i	$-0.288941\pi$
$929$	25.4762	+	5.70934i	0.835846	+	0.187317i	0.220314	+	0.975429i	$0.429292\pi$
$930$	6.21318	−	2.13299i	0.203738	−	0.0699434i
$931$	8.11230	−	22.9833i	0.265870	−	0.753246i
$932$	−22.2021	−	7.62199i	−0.727254	−	0.249667i
$933$	6.19141	+	3.80585i	0.202698	+	0.124598i
$934$	−4.56695	−	23.3803i	−0.149435	−	0.765025i
$935$	12.1489	−	10.5805i	0.397313	−	0.346020i
$936$	−5.92275	+	1.67479i	−0.193591	+	0.0547423i
$937$	−41.2630	+	16.7596i	−1.34800	+	0.547512i	−0.932201	−	0.361942i	$-0.882114\pi$
$937$	−41.2630	+	16.7596i	−1.34800	+	0.547512i	−0.415804	+	0.909454i	$0.636500\pi$
$938$	3.38191	−	13.3549i	0.110423	−	0.436052i
$939$	−0.431097	+	0.982802i	−0.0140683	+	0.0320725i
$940$	−4.17666	+	0.936012i	−0.136228	+	0.0305293i
$941$	29.1172	−	17.8983i	0.949194	−	0.583467i	0.0397121	−	0.999211i	$-0.487356\pi$
$941$	29.1172	−	17.8983i	0.949194	−	0.583467i	0.909482	+	0.415744i	$0.136479\pi$
$942$	1.43207	+	1.55564i	0.0466593	+	0.0506855i
$943$	−11.2055	−	6.06410i	−0.364900	−	0.197474i
$944$	−1.82664	+	2.21797i	−0.0594521	+	0.0721886i
$945$	6.76589	+	2.74807i	0.220094	+	0.0893946i
$946$	−23.1732	−	2.56481i	−0.753426	−	0.0833892i
$947$	−29.6426	−	12.0398i	−0.963254	−	0.391240i	−0.160159	−	0.987091i	$-0.551201\pi$
$947$	−29.6426	−	12.0398i	−0.963254	−	0.391240i	−0.803095	+	0.595851i	$0.796815\pi$
$948$	5.30081	−	7.21201i	0.172162	−	0.234235i
$949$	20.0886	+	10.8714i	0.652104	+	0.352901i
$950$	14.4923	−	6.20849i	0.470192	−	0.201430i
$951$	−30.1417	+	16.3119i	−0.977411	+	0.528949i
$952$	0.379002	−	2.73316i	0.0122835	−	0.0885823i
$953$	−28.1509	−	1.55313i	−0.911896	−	0.0503107i	−0.406939	−	0.913455i	$-0.633404\pi$
$953$	−28.1509	−	1.55313i	−0.911896	−	0.0503107i	−0.504957	+	0.863145i	$0.668492\pi$
$954$	0.237929	+	1.71582i	0.00770323	+	0.0555517i
$955$	−27.8503	+	13.1429i	−0.901215	+	0.425294i
$956$	0.517722	−	0.896721i	0.0167443	−	0.0290020i
$957$	−6.68077	+	10.2257i	−0.215959	+	0.330549i
$958$	−2.86820	−	34.6141i	−0.0926674	−	1.11833i
$959$	−2.17974	−	15.7191i	−0.0703874	−	0.507597i
$960$	−0.755577	−	1.02800i	−0.0243861	−	0.0331785i
$961$	−1.10171	−	4.35056i	−0.0355391	−	0.140341i
$962$	−35.0345	−	5.84622i	−1.12956	−	0.188490i
$963$	11.8911	−	2.66487i	0.383187	−	0.0858742i
$964$	−3.63991	−	2.23745i	−0.117234	−	0.0720633i
$965$	−12.6572	−	25.0112i	−0.407448	−	0.805140i
$966$	−0.456041	+	3.28873i	−0.0146729	+	0.105813i
$967$	29.3549	+	50.8442i	0.943990	+	1.63504i	0.757762	+	0.652532i	$0.226293\pi$
$967$	29.3549	+	50.8442i	0.943990	+	1.63504i	0.186228	+	0.982507i	$0.440374\pi$
$968$	−5.82202	−	22.9907i	−0.187127	−	0.738948i
$969$	3.08275	−	10.5535i	0.0990322	−	0.339029i
$970$	3.43710	−	13.5728i	0.110359	−	0.435797i
$971$	−5.34124	+	1.51036i	−0.171408	+	0.0484697i	−0.356726	−	0.934209i	$-0.616107\pi$
$971$	−5.34124	+	1.51036i	−0.171408	+	0.0484697i	0.185318	+	0.982679i	$0.440669\pi$
$972$	4.61873	−	14.7669i	0.148146	−	0.473649i
$973$	6.50817	+	3.07128i	0.208642	+	0.0984607i
$974$	25.5090	−	17.6876i	0.817362	−	0.566746i
$975$	1.81963	+	13.1223i	0.0582749	+	0.420248i
$976$	1.38540	−	1.07830i	0.0443456	−	0.0345155i
$977$	−7.16806	−	10.9715i	−0.229327	−	0.351011i	0.703900	−	0.710299i	$-0.251440\pi$
$977$	−7.16806	−	10.9715i	−0.229327	−	0.351011i	−0.933226	+	0.359289i	$0.883019\pi$
$978$	8.35006	−	0.460686i	0.267006	−	0.0147311i
$979$	69.5027	−	60.5300i	2.22132	−	1.93455i
$980$	1.61424	−	6.37448i	0.0515649	−	0.203625i
$981$	−17.4310	+	2.90873i	−0.556531	+	0.0928685i
$982$	−0.493408	−	0.232845i	−0.0157453	−	0.00743038i
$983$	−15.7544	−	13.7205i	−0.502488	−	0.437617i	0.367986	−	0.929831i	$-0.380047\pi$
$983$	−15.7544	−	13.7205i	−0.502488	−	0.437617i	−0.870474	+	0.492214i	$0.836188\pi$
$984$	2.67999	−	4.64189i	0.0854351	−	0.147978i
$985$	−1.31635	+	0.145693i	−0.0419422	+	0.00464217i
$986$	−4.41594	+	0.488756i	−0.140632	+	0.0155652i
$987$	−2.56303	+	3.92300i	−0.0815820	+	0.124871i
$988$	−3.88213	−	14.1950i	−0.123507	−	0.451604i
$989$	5.58119	+	8.54264i	0.177471	+	0.271640i
$990$	8.03067	+	9.75110i	0.255231	+	0.309910i
$991$	−7.11531	−	4.37376i	−0.226025	−	0.138937i	0.406032	−	0.913859i	$-0.366912\pi$
$991$	−7.11531	−	4.37376i	−0.226025	−	0.138937i	−0.632057	+	0.774922i	$0.717789\pi$
$992$	4.38653	−	2.69639i	0.139272	−	0.0856104i
$993$	−26.1580	+	25.4469i	−0.830099	+	0.807532i
$994$	−3.22913	−	3.14134i	−0.102422	−	0.0996374i
$995$	−5.10863	+	1.75379i	−0.161954	+	0.0555990i
$996$	4.34224	+	2.34990i	0.137589	+	0.0744595i
$997$	1.15893	−	42.0438i	0.0367037	−	1.33154i	−0.727296	−	0.686324i	$-0.759223\pi$
$997$	1.15893	−	42.0438i	0.0367037	−	1.33154i	0.763999	−	0.645217i	$-0.223233\pi$
$998$	0.502411	+	0.488753i	0.0159035	+	0.0154712i
$999$	37.2825	−	40.4996i	1.17957	−	1.28135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.i.a.501.5	yes	576
361.49	even	57	inner	722.2.i.a.49.5	✓	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.i.a.49.5	✓	576	361.49	even	57	inner
722.2.i.a.501.5	yes	576	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.i (of order \(57\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.926494 + 0.376309i) q^{2} +(-1.05860 - 0.237238i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0324042 - 1.17556i) q^{5} +(-0.891514 - 0.618162i) q^{6} +(0.291339 + 1.15047i) q^{7} +(0.401695 + 0.915773i) q^{8} +(-1.64871 - 0.778047i) q^{9} +O(q^{10})\)	\(q+(0.926494 + 0.376309i) q^{2} +(-1.05860 - 0.237238i) q^{3} +(0.716783 + 0.697297i) q^{4} +(-0.0324042 - 1.17556i) q^{5} +(-0.891514 - 0.618162i) q^{6} +(0.291339 + 1.15047i) q^{7} +(0.401695 + 0.915773i) q^{8} +(-1.64871 - 0.778047i) q^{9} +(0.412353 - 1.10135i) q^{10} +(0.486562 - 5.87194i) q^{11} +(-0.593362 - 0.908208i) q^{12} +(-1.00783 - 3.22221i) q^{13} +(-0.163010 + 1.17554i) q^{14} +(-0.244585 + 1.25214i) q^{15} +(0.0275543 + 0.999620i) q^{16} +(-1.66654 + 1.62123i) q^{17} +(-1.23474 - 1.34128i) q^{18} +(3.23228 - 2.92445i) q^{19} +(0.796489 - 0.865218i) q^{20} +(-0.0354762 - 1.28701i) q^{21} +(2.66046 - 5.25722i) q^{22} +(-2.51638 + 0.563934i) q^{23} +(-0.207979 - 1.06474i) q^{24} +(3.61151 - 0.199253i) q^{25} +(0.278800 - 3.36462i) q^{26} +(4.12907 + 3.21379i) q^{27} +(-0.593394 + 1.02779i) q^{28} +(1.83880 + 0.519964i) q^{29} +(-0.697799 + 1.06806i) q^{30} +(-4.06328 - 3.16258i) q^{31} +(-0.350638 + 0.936511i) q^{32} +(-1.90812 + 6.10061i) q^{33} +(-2.15412 + 0.874929i) q^{34} +(1.34301 - 0.379768i) q^{35} +(-0.639240 - 1.70733i) q^{36} +(0.868779 - 10.4846i) q^{37} +(4.09518 - 1.49315i) q^{38} +(0.302459 + 3.65014i) q^{39} +(1.06353 - 0.501893i) q^{40} +(3.72583 + 3.24483i) q^{41} +(0.451446 - 1.20576i) q^{42} +(-1.38746 - 3.70575i) q^{43} +(4.44324 - 3.86962i) q^{44} +(-0.861218 + 1.96338i) q^{45} +(-2.54363 - 0.424456i) q^{46} +(-2.99098 - 2.07390i) q^{47} +(0.207979 - 1.06474i) q^{48} +(4.91761 - 2.66128i) q^{49} +(3.42102 + 1.17444i) q^{50} +(2.14882 - 1.32087i) q^{51} +(1.52444 - 3.01238i) q^{52} +(-0.780829 - 0.541415i) q^{53} +(2.61618 + 4.53136i) q^{54} +(-6.91859 - 0.381709i) q^{55} +(-0.936543 + 0.728941i) q^{56} +(-4.11549 + 2.32901i) q^{57} +(1.50797 + 1.17370i) q^{58} +(2.16679 + 1.88706i) q^{59} +(-1.04843 + 0.726964i) q^{60} +(-1.03972 - 1.41459i) q^{61} +(-2.57450 - 4.45916i) q^{62} +(0.414787 - 2.12348i) q^{63} +(-0.677282 + 0.735724i) q^{64} +(-3.75526 + 1.28918i) q^{65} +(-4.06358 + 4.93414i) q^{66} +(-11.5377 - 1.27699i) q^{67} -2.32503 q^{68} +2.79763 q^{69} +(1.38720 + 0.153536i) q^{70} +(-2.24812 + 3.05867i) q^{71} +(0.0502337 - 1.82239i) q^{72} +(-4.84945 + 4.71762i) q^{73} +(4.75037 - 9.38699i) q^{74} +(-3.87042 - 0.645860i) q^{75} +(4.35605 + 0.157663i) q^{76} +(6.89726 - 1.15095i) q^{77} +(-1.09336 + 3.49565i) q^{78} +(2.89289 + 7.72657i) q^{79} +(1.17422 - 0.0647837i) q^{80} +(-0.131688 - 0.159900i) q^{81} +(2.23090 + 4.40838i) q^{82} +(-4.00258 + 2.16609i) q^{83} +(0.872000 - 0.947244i) q^{84} +(1.95986 + 1.90659i) q^{85} +(0.109032 - 3.95547i) q^{86} +(-1.82321 - 0.986670i) q^{87} +(5.57281 - 1.91315i) q^{88} +(11.2122 + 10.9074i) q^{89} +(-1.53675 + 1.49497i) q^{90} +(3.41345 - 2.09824i) q^{91} +(-2.19693 - 1.35045i) q^{92} +(3.55111 + 4.31188i) q^{93} +(-1.99070 - 3.04699i) q^{94} +(-3.54261 - 3.70498i) q^{95} +(0.593362 - 0.908208i) q^{96} +(11.8335 - 1.30973i) q^{97} +(5.55760 - 0.615115i) q^{98} +(-5.37084 + 9.30258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9}+O(q^{10}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9	\( 576 q - 16 q^{2} + q^{3} + 16 q^{4} - q^{5} - q^{6} + 10 q^{7} + 32 q^{8} + 13 q^{9} + q^{10} + 34 q^{11} - 2 q^{12} + 2 q^{13} - 14 q^{14} + 38 q^{15} + 16 q^{16} + 12 q^{17} + 26 q^{18} + 7 q^{19} + 2 q^{20} + 75 q^{21} + 36 q^{22} - 45 q^{23} - q^{24} + 9 q^{25} + 4 q^{26} - 110 q^{27} + 33 q^{28} - 36 q^{29} - 57 q^{30} - 4 q^{31} - 16 q^{32} + 81 q^{33} + 7 q^{34} - 2 q^{35} + 13 q^{36} + 14 q^{37} - 30 q^{38} + 40 q^{39} + q^{40} + 11 q^{41} + q^{42} - 9 q^{43} + 2 q^{44} - 85 q^{45} - 33 q^{46} - 213 q^{47} + q^{48} - 76 q^{49} - 20 q^{50} - 3 q^{51} + 2 q^{52} - 144 q^{53} + 78 q^{54} - 6 q^{55} - 29 q^{56} - 8 q^{57} + 4 q^{58} - 5 q^{59} + 69 q^{61} - 2 q^{62} - 95 q^{63} - 32 q^{64} - 84 q^{65} - 5 q^{66} - 5 q^{67} - 62 q^{68} + 2 q^{69} + 211 q^{70} + 129 q^{71} - 13 q^{72} - 8 q^{73} - 31 q^{74} - 36 q^{75} - 18 q^{76} - 10 q^{77} + q^{78} - 2 q^{79} - q^{80} - 64 q^{81} - 49 q^{82} - 72 q^{83} + 2 q^{84} - 6 q^{85} - 10 q^{86} - 81 q^{87} + 4 q^{88} - 7 q^{89} + 81 q^{90} + 35 q^{91} - 7 q^{92} - 80 q^{93} - 27 q^{94} + 285 q^{95} + 2 q^{96} + 38 q^{97} - 171 q^{98} + 84 q^{99}+O(q^{100}) \) 576 * q - 16 * q^2 + q^3 + 16 * q^4 - q^5 - q^6 + 10 * q^7 + 32 * q^8 + 13 * q^9 + q^10 + 34 * q^11 - 2 * q^12 + 2 * q^13 - 14 * q^14 + 38 * q^15 + 16 * q^16 + 12 * q^17 + 26 * q^18 + 7 * q^19 + 2 * q^20 + 75 * q^21 + 36 * q^22 - 45 * q^23 - q^24 + 9 * q^25 + 4 * q^26 - 110 * q^27 + 33 * q^28 - 36 * q^29 - 57 * q^30 - 4 * q^31 - 16 * q^32 + 81 * q^33 + 7 * q^34 - 2 * q^35 + 13 * q^36 + 14 * q^37 - 30 * q^38 + 40 * q^39 + q^40 + 11 * q^41 + q^42 - 9 * q^43 + 2 * q^44 - 85 * q^45 - 33 * q^46 - 213 * q^47 + q^48 - 76 * q^49 - 20 * q^50 - 3 * q^51 + 2 * q^52 - 144 * q^53 + 78 * q^54 - 6 * q^55 - 29 * q^56 - 8 * q^57 + 4 * q^58 - 5 * q^59 + 69 * q^61 - 2 * q^62 - 95 * q^63 - 32 * q^64 - 84 * q^65 - 5 * q^66 - 5 * q^67 - 62 * q^68 + 2 * q^69 + 211 * q^70 + 129 * q^71 - 13 * q^72 - 8 * q^73 - 31 * q^74 - 36 * q^75 - 18 * q^76 - 10 * q^77 + q^78 - 2 * q^79 - q^80 - 64 * q^81 - 49 * q^82 - 72 * q^83 + 2 * q^84 - 6 * q^85 - 10 * q^86 - 81 * q^87 + 4 * q^88 - 7 * q^89 + 81 * q^90 + 35 * q^91 - 7 * q^92 - 80 * q^93 - 27 * q^94 + 285 * q^95 + 2 * q^96 + 38 * q^97 - 171 * q^98 + 84 * q^99

Introduction

L-functions

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