LMFDB - Embedded newform 390.2.bh.b.371.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(11,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("390.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bh (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			371.4
Character	$\chi$	$=$	390.371
Dual form			390.2.bh.b.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.46331 - 0.926670i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.27383 - 1.17361i) q^{6} +(2.90548 + 0.778522i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.28257 - 2.71201i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.46331 - 0.926670i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.27383 - 1.17361i) q^{6} +(2.90548 + 0.778522i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.28257 - 2.71201i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-0.227597 + 0.0609843i) q^{11} +(-0.803931 + 1.53418i) q^{12} +(2.63314 - 2.46304i) q^{13} -3.00798i q^{14} +(-0.379464 + 1.68997i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.157921 + 0.273528i) q^{17} +(-2.95156 - 0.536943i) q^{18} +(0.974755 - 3.63784i) q^{19} +(0.258819 - 0.965926i) q^{20} +(4.97306 - 1.55320i) q^{21} +(0.117813 + 0.204058i) q^{22} +(-1.42400 + 2.46643i) q^{23} +(1.68997 + 0.379464i) q^{24} -1.00000i q^{25} +(-3.06062 - 1.90593i) q^{26} +(-0.636346 - 5.15704i) q^{27} +(-2.90548 + 0.778522i) q^{28} +(-4.09336 - 2.36330i) q^{29} +(1.73060 - 0.0708632i) q^{30} +(2.01527 + 2.01527i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.276533 + 0.300146i) q^{33} +(0.223334 - 0.223334i) q^{34} +(-2.60498 + 1.50399i) q^{35} +(0.245272 + 2.98996i) q^{36} +(0.951577 + 3.55133i) q^{37} -3.76616 q^{38} +(1.57068 - 6.04425i) q^{39} -1.00000 q^{40} +(2.31421 + 8.63675i) q^{41} +(-2.78740 - 4.40161i) q^{42} +(-10.5470 + 6.08931i) q^{43} +(0.166612 - 0.166612i) q^{44} +(1.01077 + 2.82460i) q^{45} +(2.75095 + 0.737115i) q^{46} +(-0.913385 - 0.913385i) q^{47} +(-0.0708632 - 1.73060i) q^{48} +(1.77356 + 1.02396i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(0.484558 + 0.253915i) q^{51} +(-1.04884 + 3.44963i) q^{52} -8.08755i q^{53} +(-4.81662 + 1.94940i) q^{54} +(0.117813 - 0.204058i) q^{55} +(1.50399 + 2.60498i) q^{56} +(-1.94470 - 6.22657i) q^{57} +(-1.22333 + 4.56555i) q^{58} +(1.51543 - 5.65567i) q^{59} +(-0.516361 - 1.65329i) q^{60} +(5.17260 + 8.95920i) q^{61} +(1.42501 - 2.46819i) q^{62} +(5.83784 - 6.88121i) q^{63} +1.00000i q^{64} +(-0.120274 + 3.60354i) q^{65} +(0.361491 + 0.189427i) q^{66} +(-10.5440 + 2.82526i) q^{67} +(-0.273528 - 0.157921i) q^{68} +(0.201818 + 4.92874i) q^{69} +(2.12696 + 2.12696i) q^{70} +(12.3084 + 3.29804i) q^{71} +(2.82460 - 1.01077i) q^{72} +(0.383119 - 0.383119i) q^{73} +(3.18404 - 1.83831i) q^{74} +(-0.926670 - 1.46331i) q^{75} +(0.974755 + 3.63784i) q^{76} -0.708756 q^{77} +(-6.24482 + 0.0472118i) q^{78} +0.0348413 q^{79} +(0.258819 + 0.965926i) q^{80} +(-5.71005 - 6.95668i) q^{81} +(7.74350 - 4.47071i) q^{82} +(6.34642 - 6.34642i) q^{83} +(-3.53020 + 3.83164i) q^{84} +(-0.305080 - 0.0817460i) q^{85} +(8.61159 + 8.61159i) q^{86} +(-8.17986 + 0.334942i) q^{87} +(-0.204058 - 0.117813i) q^{88} +(-8.55102 + 2.29124i) q^{89} +(2.46674 - 1.70739i) q^{90} +(9.56807 - 5.10638i) q^{91} -2.84799i q^{92} +(4.81646 + 1.08148i) q^{93} +(-0.645861 + 1.11866i) q^{94} +(1.88308 + 3.26159i) q^{95} +(-1.65329 + 0.516361i) q^{96} +(-3.65939 + 13.6570i) q^{97} +(0.530043 - 1.97815i) q^{98} +(-0.126517 + 0.695462i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{6} + 4 q^{9}+O(q^{10}) $ 32 * q - 8 * q^6 + 4 * q^9	$ 32 q - 8 q^{6} + 4 q^{9} + 16 q^{13} + 4 q^{15} + 16 q^{16} + 24 q^{18} + 32 q^{19} + 36 q^{21} + 8 q^{22} - 8 q^{24} + 12 q^{30} - 24 q^{31} - 28 q^{33} - 8 q^{34} - 12 q^{36} + 16 q^{37} - 4 q^{39} - 32 q^{40} - 12 q^{42} + 48 q^{43} - 24 q^{45} + 24 q^{46} - 48 q^{49} - 16 q^{52} - 20 q^{54} + 8 q^{55} + 4 q^{57} - 24 q^{58} + 4 q^{60} + 32 q^{61} - 48 q^{63} - 48 q^{66} - 64 q^{67} - 36 q^{69} - 40 q^{73} - 12 q^{75} + 32 q^{76} + 4 q^{78} - 32 q^{79} + 16 q^{81} + 12 q^{84} + 40 q^{85} - 72 q^{87} - 48 q^{88} - 144 q^{91} + 56 q^{94} - 4 q^{96} + 112 q^{97} + 72 q^{99}+O(q^{100}) $ 32 * q - 8 * q^6 + 4 * q^9 + 16 * q^13 + 4 * q^15 + 16 * q^16 + 24 * q^18 + 32 * q^19 + 36 * q^21 + 8 * q^22 - 8 * q^24 + 12 * q^30 - 24 * q^31 - 28 * q^33 - 8 * q^34 - 12 * q^36 + 16 * q^37 - 4 * q^39 - 32 * q^40 - 12 * q^42 + 48 * q^43 - 24 * q^45 + 24 * q^46 - 48 * q^49 - 16 * q^52 - 20 * q^54 + 8 * q^55 + 4 * q^57 - 24 * q^58 + 4 * q^60 + 32 * q^61 - 48 * q^63 - 48 * q^66 - 64 * q^67 - 36 * q^69 - 40 * q^73 - 12 * q^75 + 32 * q^76 + 4 * q^78 - 32 * q^79 + 16 * q^81 + 12 * q^84 + 40 * q^85 - 72 * q^87 - 48 * q^88 - 144 * q^91 + 56 * q^94 - 4 * q^96 + 112 * q^97 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.46331	−	0.926670i	0.844844	−	0.535013i
$3$	1.46331	−	0.926670i	0.844844	−	0.535013i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$5$	−0.707107	+	0.707107i	−0.316228	+	0.316228i
$6$	−1.27383	−	1.17361i	−0.520038	−	0.479125i
$7$	2.90548	+	0.778522i	1.09817	+	0.294254i	0.762019	−	0.647555i	$-0.224208\pi$
$7$	2.90548	+	0.778522i	1.09817	+	0.294254i	0.336150	+	0.941808i	$0.390875\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.28257	−	2.71201i	0.427522	−	0.904005i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$	−0.227597	+	0.0609843i	−0.0686230	+	0.0183875i	−0.292967	−	0.956122i	$-0.594643\pi$
$11$	−0.227597	+	0.0609843i	−0.0686230	+	0.0183875i	0.224344	+	0.974510i	$0.427976\pi$
$12$	−0.803931	+	1.53418i	−0.232075	+	0.442878i
$13$	2.63314	−	2.46304i	0.730301	−	0.683125i
$13$	2.63314	−	2.46304i	0.730301	−	0.683125i
$14$		−	3.00798i		−	0.803916i
$15$	−0.379464	+	1.68997i	−0.0979771	+	0.436349i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.157921	+	0.273528i	0.0383015	+	0.0663402i	0.884541	−	0.466463i	$-0.154472\pi$
$17$	0.157921	+	0.273528i	0.0383015	+	0.0663402i	−0.846239	+	0.532803i	$0.821139\pi$
$18$	−2.95156	−	0.536943i	−0.695689	−	0.126559i
$19$	0.974755	−	3.63784i	0.223624	−	0.834577i	−0.759327	−	0.650709i	$-0.774472\pi$
$19$	0.974755	−	3.63784i	0.223624	−	0.834577i	0.982951	−	0.183867i	$-0.0588617\pi$
$20$	0.258819	−	0.965926i	0.0578737	−	0.215988i
$21$	4.97306	−	1.55320i	1.08521	−	0.338937i
$22$	0.117813	+	0.204058i	0.0251177	+	0.0435052i
$23$	−1.42400	+	2.46643i	−0.296924	+	0.514287i	−0.975431	−	0.220307i	$-0.929294\pi$
$23$	−1.42400	+	2.46643i	−0.296924	+	0.514287i	0.678507	+	0.734594i	$0.262627\pi$
$24$	1.68997	+	0.379464i	0.344964	+	0.0774577i
$25$		−	1.00000i		−	0.200000i
$26$	−3.06062	−	1.90593i	−0.600238	−	0.373784i
$27$	−0.636346	−	5.15704i	−0.122465	−	0.992473i
$28$	−2.90548	+	0.778522i	−0.549085	+	0.147127i
$29$	−4.09336	−	2.36330i	−0.760117	−	0.438854i	0.0692206	−	0.997601i	$-0.477949\pi$
$29$	−4.09336	−	2.36330i	−0.760117	−	0.438854i	−0.829338	+	0.558748i	$0.811282\pi$
$30$	1.73060	−	0.0708632i	0.315963	−	0.0129378i
$31$	2.01527	+	2.01527i	0.361953	+	0.361953i	0.864532	−	0.502578i	$-0.167615\pi$
$31$	2.01527	+	2.01527i	0.361953	+	0.361953i	−0.502578	+	0.864532i	$0.667615\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.276533	+	0.300146i	−0.0481382	+	0.0522487i
$34$	0.223334	−	0.223334i	0.0383015	−	0.0383015i
$35$	−2.60498	+	1.50399i	−0.440323	+	0.254220i
$36$	0.245272	+	2.98996i	0.0408787	+	0.498326i
$37$	0.951577	+	3.55133i	0.156438	+	0.583836i	0.998978	+	0.0452012i	$0.0143929\pi$
$37$	0.951577	+	3.55133i	0.156438	+	0.583836i	−0.842540	+	0.538634i	$0.818940\pi$
$38$	−3.76616			−0.610953
$39$	1.57068	−	6.04425i	0.251509	−	0.967855i
$40$	−1.00000			−0.158114
$41$	2.31421	+	8.63675i	0.361419	+	1.34883i	0.872211	+	0.489129i	$0.162685\pi$
$41$	2.31421	+	8.63675i	0.361419	+	1.34883i	−0.510792	+	0.859704i	$0.670648\pi$
$42$	−2.78740	−	4.40161i	−0.430105	−	0.679183i
$43$	−10.5470	+	6.08931i	−1.60840	+	0.928611i	−0.618674	+	0.785648i	$0.712330\pi$
$43$	−10.5470	+	6.08931i	−1.60840	+	0.928611i	−0.989728	+	0.142964i	$0.954337\pi$
$44$	0.166612	−	0.166612i	0.0251177	−	0.0251177i
$45$	1.01077	+	2.82460i	0.150677	+	0.421066i
$46$	2.75095	+	0.737115i	0.405606	+	0.108682i
$47$	−0.913385	−	0.913385i	−0.133231	−	0.133231i	0.637346	−	0.770577i	$-0.280032\pi$
$47$	−0.913385	−	0.913385i	−0.133231	−	0.133231i	−0.770577	+	0.637346i	$0.780032\pi$
$48$	−0.0708632	−	1.73060i	−0.0102282	−	0.249791i
$49$	1.77356	+	1.02396i	0.253365	+	0.146281i
$50$	−0.965926	+	0.258819i	−0.136603	+	0.0366025i
$51$	0.484558	+	0.253915i	0.0678517	+	0.0355553i
$52$	−1.04884	+	3.44963i	−0.145448	+	0.478377i
$53$		−	8.08755i		−	1.11091i	−0.831546	−	0.555456i	$-0.812544\pi$
$53$		−	8.08755i		−	1.11091i	0.831546	−	0.555456i	$-0.187456\pi$
$54$	−4.81662	+	1.94940i	−0.655459	+	0.265280i
$55$	0.117813	−	0.204058i	0.0158859	−	0.0275151i
$56$	1.50399	+	2.60498i	0.200979	+	0.348106i
$57$	−1.94470	−	6.22657i	−0.257582	−	0.824729i
$58$	−1.22333	+	4.56555i	−0.160632	+	0.599486i
$59$	1.51543	−	5.65567i	0.197292	−	0.736306i	−0.794369	−	0.607436i	$-0.792198\pi$
$59$	1.51543	−	5.65567i	0.197292	−	0.736306i	0.991661	−	0.128870i	$-0.0411350\pi$
$60$	−0.516361	−	1.65329i	−0.0666619	−	0.213439i
$61$	5.17260	+	8.95920i	0.662283	+	1.14711i	0.980014	+	0.198927i	$0.0637457\pi$
$61$	5.17260	+	8.95920i	0.662283	+	1.14711i	−0.317731	+	0.948181i	$0.602921\pi$
$62$	1.42501	−	2.46819i	0.180977	−	0.313461i
$63$	5.83784	−	6.88121i	0.735498	−	0.866950i
$64$			1.00000i			0.125000i
$65$	−0.120274	+	3.60354i	−0.0149182	+	0.446965i
$66$	0.361491	+	0.189427i	0.0444964	+	0.0233168i
$67$	−10.5440	+	2.82526i	−1.28816	+	0.345161i	−0.836960	−	0.547264i	$-0.815669\pi$
$67$	−10.5440	+	2.82526i	−1.28816	+	0.345161i	−0.451197	+	0.892425i	$0.649003\pi$
$68$	−0.273528	−	0.157921i	−0.0331701	−	0.0191508i
$69$	0.201818	+	4.92874i	0.0242960	+	0.593350i
$70$	2.12696	+	2.12696i	0.254220	+	0.254220i
$71$	12.3084	+	3.29804i	1.46074	+	0.391405i	0.899746	−	0.436413i	$-0.143751\pi$
$71$	12.3084	+	3.29804i	1.46074	+	0.391405i	0.560997	+	0.827818i	$0.310418\pi$
$72$	2.82460	−	1.01077i	0.332882	−	0.119121i
$73$	0.383119	−	0.383119i	0.0448407	−	0.0448407i	−0.684331	−	0.729172i	$-0.739906\pi$
$73$	0.383119	−	0.383119i	0.0448407	−	0.0448407i	0.729172	+	0.684331i	$0.239906\pi$
$74$	3.18404	−	1.83831i	0.370137	−	0.213699i
$75$	−0.926670	−	1.46331i	−0.107003	−	0.168969i
$76$	0.974755	+	3.63784i	0.111812	+	0.417288i
$77$	−0.708756			−0.0807702
$78$	−6.24482	+	0.0472118i	−0.707087	+	0.00534569i
$79$	0.0348413			0.00391995			0.00195997	−	0.999998i	$-0.499376\pi$
$79$	0.0348413			0.00391995			0.00195997	+	0.999998i	$0.499376\pi$
$80$	0.258819	+	0.965926i	0.0289368	+	0.107994i
$81$	−5.71005	−	6.95668i	−0.634449	−	0.772964i
$82$	7.74350	−	4.47071i	0.855126	−	0.493707i
$83$	6.34642	−	6.34642i	0.696610	−	0.696610i	−0.267068	−	0.963678i	$-0.586055\pi$
$83$	6.34642	−	6.34642i	0.696610	−	0.696610i	0.963678	+	0.267068i	$0.0860548\pi$
$84$	−3.53020	+	3.83164i	−0.385176	+	0.418067i
$85$	−0.305080	−	0.0817460i	−0.0330906	−	0.00886660i
$86$	8.61159	+	8.61159i	0.928611	+	0.928611i
$87$	−8.17986	+	0.334942i	−0.876973	+	0.0359096i
$88$	−0.204058	−	0.117813i	−0.0217526	−	0.0125589i
$89$	−8.55102	+	2.29124i	−0.906406	+	0.242871i	−0.681765	−	0.731571i	$-0.738787\pi$
$89$	−8.55102	+	2.29124i	−0.906406	+	0.242871i	−0.224641	+	0.974442i	$0.572121\pi$
$90$	2.46674	−	1.70739i	0.260017	−	0.179975i
$91$	9.56807	−	5.10638i	1.00301	−	0.535294i
$92$		−	2.84799i		−	0.296924i
$93$	4.81646	+	1.08148i	0.499444	+	0.112144i
$94$	−0.645861	+	1.11866i	−0.0666155	+	0.115381i
$95$	1.88308	+	3.26159i	0.193200	+	0.334632i
$96$	−1.65329	+	0.516361i	−0.168738	+	0.0527009i
$97$	−3.65939	+	13.6570i	−0.371555	+	1.38666i	0.486759	+	0.873537i	$0.338179\pi$
$97$	−3.65939	+	13.6570i	−0.371555	+	1.38666i	−0.858314	+	0.513126i	$0.828488\pi$
$98$	0.530043	−	1.97815i	0.0535424	−	0.199823i
$99$	−0.126517	+	0.695462i	−0.0127155	+	0.0698965i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−6.70143	+	11.6072i	−0.666817	+	1.15496i	0.311972	+	0.950091i	$0.399011\pi$
$101$	−6.70143	+	11.6072i	−0.666817	+	1.15496i	−0.978789	+	0.204870i	$0.934323\pi$
$102$	0.119851	−	0.533765i	0.0118670	−	0.0528506i
$103$			6.01359i			0.592537i	0.955105	+	0.296268i	$0.0957423\pi$
$103$			6.01359i			0.592537i	−0.955105	+	0.296268i	$0.904258\pi$
$104$	3.60354	+	0.120274i	0.353357	+	0.0117939i
$105$	−2.41821	+	4.61477i	−0.235993	+	0.450355i
$106$	−7.81198	+	2.09321i	−0.758766	+	0.203311i
$107$	9.77103	+	5.64131i	0.944601	+	0.545366i	0.891400	−	0.453218i	$-0.149724\pi$
$107$	9.77103	+	5.64131i	0.944601	+	0.545366i	0.0532015	+	0.998584i	$0.483057\pi$
$108$	3.12961	+	4.14795i	0.301147	+	0.399137i
$109$	4.20673	+	4.20673i	0.402931	+	0.402931i	0.879265	−	0.476333i	$-0.158034\pi$
$109$	4.20673	+	4.20673i	0.402931	+	0.402931i	−0.476333	+	0.879265i	$0.658034\pi$
$110$	−0.227597	−	0.0609843i	−0.0217005	−	0.00581463i
$111$	4.68337	+	4.31491i	0.444526	+	0.409553i
$112$	2.12696	−	2.12696i	0.200979	−	0.200979i
$113$	−18.3753	+	10.6090i	−1.72860	+	0.998007i	−0.832744	+	0.553658i	$0.813232\pi$
$113$	−18.3753	+	10.6090i	−1.72860	+	0.998007i	−0.895854	+	0.444349i	$0.853435\pi$
$114$	−5.51108	+	3.48999i	−0.516159	+	0.326868i
$115$	−0.737115	−	2.75095i	−0.0687363	−	0.256527i
$116$	4.72660			0.438854
$117$	−3.30264	−	10.3001i	−0.305329	−	0.952247i
$118$	−5.85518			−0.539013
$119$	0.245890	+	0.917675i	0.0225407	+	0.0841231i
$120$	−1.46331	+	0.926670i	−0.133582	+	0.0845930i
$121$	−9.47820	+	5.47224i	−0.861654	+	0.497476i
$122$	7.31515	−	7.31515i	0.662283	−	0.662283i
$123$	11.3898	+	10.4938i	1.02699	+	0.946190i
$124$	−2.75291	−	0.737640i	−0.247219	−	0.0662420i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−8.15768	−	3.85793i	−0.726744	−	0.343692i
$127$	−16.8026	−	9.70098i	−1.49099	−	0.860823i	−0.491042	−	0.871136i	$-0.663384\pi$
$127$	−16.8026	−	9.70098i	−1.49099	−	0.860823i	−0.999947	+	0.0103131i	$0.996717\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−9.79077	+	18.6841i	−0.862029	+	1.64505i
$130$	3.51189	−	0.816490i	0.308013	−	0.0716109i
$131$		−	2.38021i		−	0.207960i	−0.994579	−	0.103980i	$-0.966842\pi$
$131$		−	2.38021i		−	0.207960i	0.994579	−	0.103980i	$-0.0331578\pi$
$132$	0.0894113	−	0.398200i	0.00778225	−	0.0346589i
$133$	5.66427	−	9.81080i	0.491154	−	0.850704i
$134$	5.45799	+	9.45351i	0.471498	+	0.816659i
$135$	4.09654	+	3.19661i	0.352574	+	0.275121i
$136$	−0.0817460	+	0.305080i	−0.00700966	+	0.0261604i
$137$	4.43351	−	16.5461i	0.378780	−	1.41363i	−0.468962	−	0.883218i	$-0.655372\pi$
$137$	4.43351	−	16.5461i	0.378780	−	1.41363i	0.847742	−	0.530408i	$-0.177961\pi$
$138$	4.70856	−	1.47059i	0.400819	−	0.125185i
$139$	2.76742	+	4.79332i	0.234730	+	0.406564i	0.959194	−	0.282748i	$-0.0912461\pi$
$139$	2.76742	+	4.79332i	0.234730	+	0.406564i	−0.724464	+	0.689312i	$0.757913\pi$
$140$	1.50399	−	2.60498i	0.127110	−	0.220161i
$141$	−2.18297	−	0.490162i	−0.183840	−	0.0412790i
$142$		−	12.7426i		−	1.06934i
$143$	−0.449086	+	0.721161i	−0.0375545	+	0.0603065i
$144$	−1.70739	−	2.46674i	−0.142283	−	0.205562i
$145$	4.56555	−	1.22333i	0.379148	−	0.101592i
$146$	−0.469223	−	0.270906i	−0.0388332	−	0.0224204i
$147$	3.54414	−	0.145123i	0.292316	−	0.0119695i
$148$	−2.59976	−	2.59976i	−0.213699	−	0.213699i
$149$	1.30794	+	0.350461i	0.107151	+	0.0287109i	0.311996	−	0.950083i	$-0.399002\pi$
$149$	1.30794	+	0.350461i	0.107151	+	0.0287109i	−0.204845	+	0.978794i	$0.565669\pi$
$150$	−1.17361	+	1.27383i	−0.0958250	+	0.104008i
$151$	6.65088	−	6.65088i	0.541241	−	0.541241i	−0.382652	−	0.923893i	$-0.624989\pi$
$151$	6.65088	−	6.65088i	0.541241	−	0.541241i	0.923893	+	0.382652i	$0.124989\pi$
$152$	3.26159	−	1.88308i	0.264550	−	0.152738i
$153$	0.944355	−	0.0774673i	0.0763466	−	0.00626286i
$154$	0.183439	+	0.684606i	0.0147820	+	0.0551671i
$155$	−2.85002			−0.228919
$156$	1.66188	+	6.01981i	0.133057	+	0.481971i
$157$	−15.1629			−1.21013			−0.605066	−	0.796175i	$-0.706853\pi$
$157$	−15.1629			−1.21013			−0.605066	+	0.796175i	$0.706853\pi$
$158$	−0.00901758	−	0.0336541i	−0.000717400	−	0.00267737i
$159$	−7.49449	−	11.8346i	−0.594352	−	0.938546i
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−6.05757	+	6.05757i	−0.477404	+	0.477404i
$162$	−5.24177	+	7.31600i	−0.411832	+	0.574799i
$163$	14.5667	+	3.90314i	1.14095	+	0.305717i	0.779334	−	0.626609i	$-0.215558\pi$
$163$	14.5667	+	3.90314i	1.14095	+	0.305717i	0.361618	+	0.932326i	$0.382224\pi$
$164$	−6.32254	−	6.32254i	−0.493707	−	0.493707i
$165$	−0.0166972	−	0.407773i	−0.00129987	−	0.0317451i
$166$	−7.77274	−	4.48760i	−0.603282	−	0.348305i
$167$	3.27641	−	0.877911i	0.253536	−	0.0679348i	−0.129812	−	0.991539i	$-0.541438\pi$
$167$	3.27641	−	0.877911i	0.253536	−	0.0679348i	0.383348	+	0.923604i	$0.374771\pi$
$168$	4.61477	+	2.41821i	0.356037	+	0.186569i
$169$	0.866829	−	12.9711i	0.0666791	−	0.997774i
$170$			0.315842i			0.0242240i
$171$	−8.61567	−	7.30932i	−0.658857	−	0.558957i
$172$	6.08931	−	10.5470i	0.464306	−	0.804201i
$173$	−11.8692	−	20.5581i	−0.902400	−	1.56300i	−0.824370	−	0.566051i	$-0.808470\pi$
$173$	−11.8692	−	20.5581i	−0.902400	−	1.56300i	−0.0780299	−	0.996951i	$-0.524863\pi$
$174$	2.44063	+	7.81445i	0.185024	+	0.592412i
$175$	0.778522	−	2.90548i	0.0588507	−	0.219634i
$176$	−0.0609843	+	0.227597i	−0.00459687	+	0.0171557i
$177$	−3.02339	−	9.68032i	−0.227252	−	0.727617i
$178$	4.42633	+	7.66663i	0.331768	+	0.574638i
$179$	−0.663781	+	1.14970i	−0.0496133	+	0.0859328i	−0.889766	−	0.456418i	$-0.849132\pi$
$179$	−0.663781	+	1.14970i	−0.0496133	+	0.0859328i	0.840152	+	0.542351i	$0.182466\pi$
$180$	−2.28765	−	1.94079i	−0.170512	−	0.144658i
$181$		−	14.9601i		−	1.11197i	−0.831191	−	0.555987i	$-0.812340\pi$
$181$		−	14.9601i		−	1.11197i	0.831191	−	0.555987i	$-0.187660\pi$
$182$	−7.40878	−	7.92042i	−0.549175	−	0.587100i
$183$	15.8713	+	8.31682i	1.17324	+	0.614797i
$184$	−2.75095	+	0.737115i	−0.202803	+	0.0543408i
$185$	−3.18404	−	1.83831i	−0.234095	−	0.135155i
$186$	−0.201962	−	4.93225i	−0.0148086	−	0.361650i
$187$	−0.0526232	−	0.0526232i	−0.00384819	−	0.00384819i
$188$	1.24771	+	0.334322i	0.0909984	+	0.0243829i
$189$	2.16598	−	15.4791i	0.157552	−	1.12594i
$190$	2.66308	−	2.66308i	0.193200	−	0.193200i
$191$	−1.64675	+	0.950752i	−0.119155	+	0.0687940i	−0.558393	−	0.829577i	$-0.688582\pi$
$191$	−1.64675	+	0.950752i	−0.119155	+	0.0687940i	0.439238	+	0.898371i	$0.355248\pi$
$192$	0.926670	+	1.46331i	0.0668766	+	0.105605i
$193$	1.44346	+	5.38708i	0.103903	+	0.387771i	0.998218	−	0.0596662i	$-0.0190036\pi$
$193$	1.44346	+	5.38708i	0.103903	+	0.387771i	−0.894316	+	0.447437i	$0.852337\pi$
$194$	14.1388			1.01511
$195$	3.16330	+	5.38457i	0.226528	+	0.385597i
$196$	−2.04793			−0.146281
$197$	2.45641	+	9.16744i	0.175012	+	0.653153i	0.996550	+	0.0829990i	$0.0264498\pi$
$197$	2.45641	+	9.16744i	0.175012	+	0.653153i	−0.821538	+	0.570154i	$0.806884\pi$
$198$	0.704510	−	0.0577923i	0.0500673	−	0.00410712i
$199$	21.2079	−	12.2444i	1.50339	−	0.867981i	0.503395	−	0.864056i	$-0.332084\pi$
$199$	21.2079	−	12.2444i	1.50339	−	0.867981i	0.999992	−	0.00392521i	$-0.00124944\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$	−12.8111	+	13.9051i	−0.903626	+	0.980787i
$202$	12.9462	+	3.46892i	0.910890	+	0.244072i
$203$	−10.0533	−	10.0533i	−0.705603	−	0.705603i
$204$	−0.546597	+	0.0223816i	−0.0382694	+	0.00156703i
$205$	−7.74350	−	4.47071i	−0.540829	−	0.312248i
$206$	5.80869	−	1.55643i	0.404710	−	0.108442i
$207$	4.86264	+	7.02527i	0.337977	+	0.488290i
$208$	−0.816490	−	3.51189i	−0.0566134	−	0.243505i
$209$			0.887404i			0.0613830i
$210$	5.08340	+	1.14142i	0.350788	+	0.0787654i
$211$	5.19586	−	8.99950i	0.357698	−	0.619551i	−0.629878	−	0.776694i	$-0.716895\pi$
$211$	5.19586	−	8.99950i	0.357698	−	0.619551i	0.987576	+	0.157143i	$0.0502285\pi$
$212$	4.04378	+	7.00403i	0.277728	+	0.481039i
$213$	21.0673	−	6.57980i	1.44351	−	0.450840i
$214$	2.92016	−	10.8982i	0.199618	−	0.744983i
$215$	3.15206	−	11.7636i	0.214969	−	0.802274i
$216$	3.19661	−	4.09654i	0.217502	−	0.278734i
$217$	4.28640	+	7.42427i	0.290980	+	0.503992i
$218$	2.97461	−	5.15217i	0.201466	−	0.348949i
$219$	0.205598	−	0.915648i	0.0138930	−	0.0618738i
$220$			0.235625i			0.0158859i
$221$	1.08954	+	0.331269i	0.0732903	+	0.0222836i
$222$	2.95574	−	5.64057i	0.198376	−	0.378570i
$223$	−6.63395	+	1.77756i	−0.444242	+	0.119034i	−0.474004	−	0.880523i	$-0.657192\pi$
$223$	−6.63395	+	1.77756i	−0.444242	+	0.119034i	0.0297620	+	0.999557i	$0.490525\pi$
$224$	−2.60498	−	1.50399i	−0.174053	−	0.100489i
$225$	−2.71201	−	1.28257i	−0.180801	−	0.0855044i
$226$	15.0033	+	15.0033i	0.998007	+	0.998007i
$227$	−12.6328	−	3.38494i	−0.838465	−	0.224666i	−0.186062	−	0.982538i	$-0.559572\pi$
$227$	−12.6328	−	3.38494i	−0.838465	−	0.224666i	−0.652403	+	0.757872i	$0.726239\pi$
$228$	4.79744	+	4.42001i	0.317718	+	0.292723i
$229$	−6.48520	+	6.48520i	−0.428554	+	0.428554i	−0.888136	−	0.459582i	$-0.847999\pi$
$229$	−6.48520	+	6.48520i	−0.428554	+	0.428554i	0.459582	+	0.888136i	$0.347999\pi$
$230$	−2.46643	+	1.42400i	−0.162632	+	0.0938956i
$231$	−1.03713	+	0.656782i	−0.0682382	+	0.0432131i
$232$	−1.22333	−	4.56555i	−0.0803158	−	0.299743i
$233$	−22.2151			−1.45536			−0.727681	−	0.685916i	$-0.759402\pi$
$233$	−22.2151			−1.45536			−0.727681	+	0.685916i	$0.759402\pi$
$234$	−9.09437	+	5.85597i	−0.594518	+	0.382817i
$235$	1.29172			0.0842626
$236$	1.51543	+	5.65567i	0.0986462	+	0.368153i
$237$	0.0509836	−	0.0322863i	0.00331174	−	0.00209722i
$238$	0.822765	−	0.475023i	0.0533319	−	0.0307912i
$239$	10.4517	−	10.4517i	0.676065	−	0.676065i	−0.283043	−	0.959107i	$-0.591344\pi$
$239$	10.4517	−	10.4517i	0.676065	−	0.676065i	0.959107	+	0.283043i	$0.0913438\pi$
$240$	1.27383	+	1.17361i	0.0822252	+	0.0757563i
$241$	−14.8718	−	3.98489i	−0.957978	−	0.256689i	−0.254233	−	0.967143i	$-0.581823\pi$
$241$	−14.8718	−	3.98489i	−0.957978	−	0.256689i	−0.703744	+	0.710454i	$0.748490\pi$
$242$	7.73892	+	7.73892i	0.497476	+	0.497476i
$243$	−14.8021	−	4.88847i	−0.949557	−	0.313595i
$244$	−8.95920	−	5.17260i	−0.573554	−	0.331141i
$245$	−1.97815	+	0.530043i	−0.126379	+	0.0338632i
$246$	7.18828	−	13.7177i	0.458308	−	0.874609i
$247$	−6.39348	−	11.9798i	−0.406808	−	0.762256i
$248$			2.85002i			0.180977i
$249$	3.40576	−	15.1678i	0.215831	−	0.961222i
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−7.54611	−	13.0702i	−0.476306	−	0.824986i	0.523325	−	0.852133i	$-0.324691\pi$
$251$	−7.54611	−	13.0702i	−0.476306	−	0.824986i	−0.999631	+	0.0271465i	$0.991358\pi$
$252$	−1.61511	+	8.87822i	−0.101743	+	0.559275i
$253$	0.173683	−	0.648194i	0.0109194	−	0.0407516i
$254$	−5.02160	+	18.7409i	−0.315083	+	1.17591i
$255$	−0.522179	+	0.163089i	−0.0327001	+	0.0102130i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.9599	+	25.9113i	−0.933174	+	1.61630i	−0.155315	+	0.987865i	$0.549639\pi$
$257$	−14.9599	+	25.9113i	−0.933174	+	1.61630i	−0.777859	+	0.628439i	$0.783694\pi$
$258$	20.5815	+	4.62135i	1.28135	+	0.287712i
$259$			11.0592i			0.687183i
$260$	−1.69761	−	3.18090i	−0.105281	−	0.197271i
$261$	−11.6593	+	8.07015i	−0.721693	+	0.499530i
$262$	−2.29911	+	0.616044i	−0.142039	+	0.0380593i
$263$	−6.33347	−	3.65663i	−0.390538	−	0.225477i	0.291855	−	0.956463i	$-0.405727\pi$
$263$	−6.33347	−	3.65663i	−0.390538	−	0.225477i	−0.682393	+	0.730985i	$0.739061\pi$
$264$	−0.407773	+	0.0166972i	−0.0250967	+	0.00102764i
$265$	5.71876	+	5.71876i	0.351301	+	0.351301i
$266$	−10.9425	−	2.93204i	−0.670929	−	0.179775i
$267$	−10.3896	+	11.2768i	−0.635832	+	0.690127i
$268$	7.71876	−	7.71876i	0.471498	−	0.471498i
$269$	15.8402	−	9.14533i	0.965793	−	0.557601i	0.0678419	−	0.997696i	$-0.478389\pi$
$269$	15.8402	−	9.14533i	0.965793	−	0.557601i	0.897951	+	0.440095i	$0.145055\pi$
$270$	2.02743	−	4.78430i	0.123385	−	0.291163i
$271$	−0.171023	−	0.638265i	−0.0103889	−	0.0387718i	0.960537	−	0.278153i	$-0.0897222\pi$
$271$	−0.171023	−	0.638265i	−0.0103889	−	0.0387718i	−0.970926	+	0.239381i	$0.923056\pi$
$272$	0.315842			0.0191508
$273$	9.26915	−	16.3387i	0.560995	−	0.988861i
$274$	−17.1298			−1.03485
$275$	0.0609843	+	0.227597i	0.00367749	+	0.0137246i
$276$	−2.63915	−	4.16750i	−0.158858	−	0.250854i
$277$	16.3162	−	9.42014i	0.980343	−	0.566001i	0.0779694	−	0.996956i	$-0.475156\pi$
$277$	16.3162	−	9.42014i	0.980343	−	0.566001i	0.902374	+	0.430954i	$0.141823\pi$
$278$	3.91373	−	3.91373i	0.234730	−	0.234730i
$279$	8.05016	−	2.88072i	0.481951	−	0.172464i
$280$	−2.90548	−	0.778522i	−0.173636	−	0.0465256i
$281$	19.4137	+	19.4137i	1.15813	+	1.15813i	0.984878	+	0.173247i	$0.0554260\pi$
$281$	19.4137	+	19.4137i	1.15813	+	1.15813i	0.173247	+	0.984878i	$0.444574\pi$
$282$	0.0915356	+	2.23545i	0.00545086	+	0.133119i
$283$	−13.7333	−	7.92894i	−0.816361	−	0.471326i	0.0327989	−	0.999462i	$-0.489558\pi$
$283$	−13.7333	−	7.92894i	−0.816361	−	0.471326i	−0.849160	+	0.528136i	$0.822891\pi$
$284$	−12.3084	+	3.29804i	−0.730372	+	0.195702i
$285$	5.77796	+	3.02774i	0.342257	+	0.179348i
$286$	0.812820	+	0.247134i	0.0480630	+	0.0146133i
$287$			26.8956i			1.58760i
$288$	−1.94079	+	2.28765i	−0.114362	+	0.134801i
$289$	8.45012	−	14.6360i	0.497066	−	0.860944i
$290$	−2.36330	−	4.09336i	−0.138778	−	0.240370i
$291$	7.30073	+	23.3756i	0.427976	+	1.37030i
$292$	−0.140231	+	0.523350i	−0.00820642	+	0.0306268i
$293$	−0.672444	+	2.50959i	−0.0392846	+	0.146612i	−0.982782	−	0.184767i	$-0.940847\pi$
$293$	−0.672444	+	2.50959i	−0.0392846	+	0.146612i	0.943498	+	0.331379i	$0.107514\pi$
$294$	−1.05747	−	3.38582i	−0.0616729	−	0.197465i
$295$	2.92759	+	5.07074i	0.170451	+	0.295230i
$296$	−1.83831	+	3.18404i	−0.106849	+	0.185068i
$297$	0.459329	+	1.13492i	0.0266530	+	0.0658546i
$298$		−	1.35408i		−	0.0784397i
$299$	2.32536	+	10.0018i	0.134479	+	0.578421i
$300$	1.53418	+	0.803931i	0.0885757	+	0.0464150i
$301$	−35.3848	+	9.48132i	−2.03954	+	0.546494i
$302$	−8.14563	−	4.70288i	−0.468728	−	0.270620i
$303$	0.949770	+	23.1950i	0.0545629	+	1.33252i
$304$	−2.66308	−	2.66308i	−0.152738	−	0.152738i
$305$	−9.99269	−	2.67753i	−0.572180	−	0.153315i
$306$	−0.319245	−	0.892127i	−0.0182500	−	0.0509995i
$307$	−8.76237	+	8.76237i	−0.500095	+	0.500095i	−0.911467	−	0.411372i	$-0.865050\pi$
$307$	−8.76237	+	8.76237i	−0.500095	+	0.500095i	0.411372	+	0.911467i	$0.365050\pi$
$308$	0.613801	−	0.354378i	0.0349745	−	0.0201926i
$309$	5.57261	+	8.79977i	0.317015	+	0.500601i
$310$	0.737640	+	2.75291i	0.0418951	+	0.156355i
$311$	32.8499			1.86275			0.931373	−	0.364066i	$-0.118612\pi$
$311$	32.8499			1.86275			0.931373	+	0.364066i	$0.118612\pi$
$312$	5.38457	−	3.16330i	0.304841	−	0.179086i
$313$	16.0388			0.906569			0.453285	−	0.891366i	$-0.350252\pi$
$313$	16.0388			0.906569			0.453285	+	0.891366i	$0.350252\pi$
$314$	3.92445	+	14.6462i	0.221470	+	0.826535i
$315$	0.737772	+	8.99372i	0.0415688	+	0.506739i
$316$	−0.0301734	+	0.0174206i	−0.00169739	+	0.000979987i
$317$	5.51295	−	5.51295i	0.309638	−	0.309638i	−0.535131	−	0.844769i	$-0.679738\pi$
$317$	5.51295	−	5.51295i	0.309638	−	0.309638i	0.844769	+	0.535131i	$0.179738\pi$
$318$	−9.49165	+	10.3021i	−0.532265	+	0.577716i
$319$	1.07576	+	0.288249i	0.0602309	+	0.0161388i
$320$	−0.707107	−	0.707107i	−0.0395285	−	0.0395285i
$321$	19.5257	−	0.799523i	1.08982	−	0.0446250i
$322$	7.41898	+	4.28335i	0.413444	+	0.238702i
$323$	1.14898	−	0.307869i	0.0639311	−	0.0171303i
$324$	8.42338	+	3.16964i	0.467966	+	0.176091i
$325$	−2.46304	−	2.63314i	−0.136625	−	0.146060i
$326$		−	15.0806i		−	0.835235i
$327$	10.0540	+	2.25751i	0.555988	+	0.124841i
$328$	−4.47071	+	7.74350i	−0.246854	+	0.427563i
$329$	−1.94273	−	3.36491i	−0.107106	−	0.185514i
$330$	−0.389557	+	0.121668i	−0.0214444	+	0.00669759i
$331$	8.44404	−	31.5136i	0.464127	−	1.73214i	−0.195642	−	0.980675i	$-0.562679\pi$
$331$	8.44404	−	31.5136i	0.464127	−	1.73214i	0.659769	−	0.751469i	$-0.270654\pi$
$332$	−2.32295	+	8.66937i	−0.127488	+	0.475793i
$333$	10.8517	+	1.97413i	0.594671	+	0.108182i
$334$	−1.69599	−	2.93755i	−0.0928006	−	0.160735i
$335$	5.45799	−	9.45351i	0.298202	−	0.516500i
$336$	1.14142	−	5.08340i	0.0622695	−	0.277322i
$337$			34.6249i			1.88614i	0.332593	+	0.943070i	$0.392076\pi$
$337$			34.6249i			1.88614i	−0.332593	+	0.943070i	$0.607924\pi$
$338$	−12.7534	+	2.51987i	−0.693696	+	0.137063i
$339$	−17.0577	+	32.5520i	−0.926449	+	1.76798i
$340$	0.305080	−	0.0817460i	0.0165453	−	0.00443330i
$341$	−0.581569	−	0.335769i	−0.0314937	−	0.0181829i
$342$	−4.83036	+	10.2139i	−0.261196	+	0.552304i
$343$	−10.5329	−	10.5329i	−0.568721	−	0.568721i
$344$	−11.7636	−	3.15206i	−0.634253	−	0.169948i
$345$	−3.62785	−	3.34244i	−0.195317	−	0.179951i
$346$	−16.7856	+	16.7856i	−0.902400	+	0.902400i
$347$	24.3786	−	14.0750i	1.30871	−	0.755586i	0.326832	−	0.945082i	$-0.394019\pi$
$347$	24.3786	−	14.0750i	1.30871	−	0.755586i	0.981881	+	0.189496i	$0.0606855\pi$
$348$	6.91649	−	4.38000i	0.370763	−	0.234793i
$349$	0.701977	+	2.61981i	0.0375760	+	0.140235i	0.982165	−	0.188018i	$-0.0602065\pi$
$349$	0.701977	+	2.61981i	0.0375760	+	0.140235i	−0.944590	+	0.328254i	$0.893540\pi$
$350$	−3.00798			−0.160783
$351$	−14.3776	−	12.0118i	−0.767420	−	0.641145i
$352$	0.235625			0.0125589
$353$	5.17251	+	19.3041i	0.275305	+	1.02745i	0.955637	+	0.294547i	$0.0951689\pi$
$353$	5.17251	+	19.3041i	0.275305	+	1.02745i	−0.680332	+	0.732904i	$0.738164\pi$
$354$	−8.56796	+	5.42582i	−0.455382	+	0.288379i
$355$	−11.0354	+	6.37132i	−0.585701	+	0.338154i
$356$	6.25978	−	6.25978i	0.331768	−	0.331768i
$357$	1.21020	+	1.11499i	0.0640503	+	0.0590113i
$358$	1.28233	+	0.343598i	0.0677731	+	0.0181597i
$359$	−3.15227	−	3.15227i	−0.166370	−	0.166370i	0.619012	−	0.785382i	$-0.287533\pi$
$359$	−3.15227	−	3.15227i	−0.166370	−	0.166370i	−0.785382	+	0.619012i	$0.787533\pi$
$360$	−1.28257	+	2.71201i	−0.0675972	+	0.142936i
$361$	4.17078	+	2.40800i	0.219515	+	0.126737i
$362$	−14.4503	+	3.87196i	−0.759493	+	0.203506i
$363$	−8.79861	+	16.7908i	−0.461807	+	0.881286i
$364$	−5.73300	+	9.20629i	−0.300491	+	0.482541i
$365$			0.541812i			0.0283598i
$366$	3.92562	−	17.4831i	0.205196	−	0.913856i
$367$	12.3353	−	21.3653i	0.643896	−	1.11526i	−0.340659	−	0.940187i	$-0.610650\pi$
$367$	12.3353	−	21.3653i	0.643896	−	1.11526i	0.984555	−	0.175074i	$-0.0560165\pi$
$368$	1.42400	+	2.46643i	0.0742310	+	0.128572i
$369$	26.3911	+	4.80104i	1.37387	+	0.249932i
$370$	−0.951577	+	3.55133i	−0.0494701	+	0.184625i
$371$	6.29634	−	23.4983i	0.326890	−	1.21997i
$372$	−4.71192	+	1.47164i	−0.244301	+	0.0763010i
$373$	−1.16145	−	2.01170i	−0.0601377	−	0.104162i	0.834389	−	0.551176i	$-0.185821\pi$
$373$	−1.16145	−	2.01170i	−0.0601377	−	0.104162i	−0.894527	+	0.447014i	$0.852487\pi$
$374$	−0.0372102	+	0.0644500i	−0.00192410	+	0.00333263i
$375$	1.68997	+	0.379464i	0.0872698	+	0.0195954i
$376$		−	1.29172i		−	0.0666155i
$377$	−16.5993	+	3.85922i	−0.854907	+	0.198760i
$378$	−15.5123	+	1.91411i	−0.797865	+	0.0984514i
$379$	−16.3228	+	4.37368i	−0.838446	+	0.224661i	−0.652395	−	0.757879i	$-0.726236\pi$
$379$	−16.3228	+	4.37368i	−0.838446	+	0.224661i	−0.186051	+	0.982540i	$0.559569\pi$
$380$	−3.26159	−	1.88308i	−0.167316	−	0.0966001i
$381$	−33.5770	+	1.37489i	−1.72020	+	0.0704375i
$382$	1.34457	+	1.34457i	0.0687940	+	0.0687940i
$383$	26.6839	+	7.14993i	1.36348	+	0.365344i	0.865095	−	0.501609i	$-0.167258\pi$
$383$	26.6839	+	7.14993i	1.36348	+	0.365344i	0.498389	+	0.866953i	$0.333925\pi$
$384$	1.17361	−	1.27383i	0.0598906	−	0.0650047i
$385$	0.501166	−	0.501166i	0.0255418	−	0.0255418i
$386$	4.82992	−	2.78856i	0.245837	−	0.141934i
$387$	2.98707	+	36.4136i	0.151842	+	1.85101i
$388$	−3.65939	−	13.6570i	−0.185777	−	0.693331i
$389$	9.04744			0.458723			0.229362	−	0.973341i	$-0.426336\pi$
$389$	9.04744			0.458723			0.229362	+	0.973341i	$0.426336\pi$
$390$	4.38237	−	4.44914i	0.221910	−	0.225291i
$391$	−0.899517			−0.0454905
$392$	0.530043	+	1.97815i	0.0267712	+	0.0999115i
$393$	−2.20567	−	3.48299i	−0.111261	−	0.175694i
$394$	8.21930	−	4.74542i	0.414082	−	0.239071i
$395$	−0.0246365	+	0.0246365i	−0.00123960	+	0.00123960i
$396$	−0.238164	−	0.665546i	−0.0119682	−	0.0334450i
$397$	9.07149	+	2.43070i	0.455285	+	0.121993i	0.479171	−	0.877721i	$-0.340937\pi$
$397$	9.07149	+	2.43070i	0.455285	+	0.121993i	−0.0238862	+	0.999715i	$0.507604\pi$
$398$	−17.3162	−	17.3162i	−0.867981	−	0.867981i
$399$	−0.802777	−	19.6052i	−0.0401891	−	0.981486i
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	−14.1236	+	3.78441i	−0.705299	+	0.188984i	−0.593603	−	0.804758i	$-0.702295\pi$
$401$	−14.1236	+	3.78441i	−0.705299	+	0.188984i	−0.111696	+	0.993742i	$0.535628\pi$
$402$	16.7470	+	8.77569i	0.835265	+	0.437691i
$403$	10.2702	+	0.342785i	0.511594	+	0.0170753i
$404$		−	13.4029i		−	0.666817i
$405$	8.95673	+	0.881503i	0.445063	+	0.0438022i
$406$	−7.10875	+	12.3127i	−0.352802	+	0.611070i
$407$	−0.433151	−	0.750240i	−0.0214705	−	0.0371880i
$408$	0.163089	+	0.522179i	0.00807409	+	0.0258517i
$409$	4.78718	−	17.8660i	0.236711	−	0.883416i	−0.740660	−	0.671880i	$-0.765487\pi$
$409$	4.78718	−	17.8660i	0.236711	−	0.883416i	0.977370	−	0.211536i	$-0.0678464\pi$
$410$	−2.31421	+	8.63675i	−0.114291	+	0.426539i
$411$	−8.84514	−	28.3205i	−0.436298	−	1.39695i
$412$	−3.00680	−	5.20792i	−0.148134	−	0.256576i
$413$	8.80613	−	15.2527i	0.433321	−	0.750534i
$414$	5.52734	−	6.51522i	0.271654	−	0.320206i
$415$			8.97519i			0.440575i
$416$	−3.18090	+	1.69761i	−0.155956	+	0.0832323i
$417$	8.49143	+	4.44964i	0.415827	+	0.217900i
$418$	0.857166	−	0.229677i	0.0419254	−	0.0112339i
$419$	0.797451	+	0.460408i	0.0389580	+	0.0224924i	0.519353	−	0.854560i	$-0.326173\pi$
$419$	0.797451	+	0.460408i	0.0389580	+	0.0224924i	−0.480394	+	0.877053i	$0.659507\pi$
$420$	−0.213155	−	5.20561i	−0.0104009	−	0.254008i
$421$	−3.18235	−	3.18235i	−0.155098	−	0.155098i	0.625292	−	0.780391i	$-0.284980\pi$
$421$	−3.18235	−	3.18235i	−0.155098	−	0.155098i	−0.780391	+	0.625292i	$0.784980\pi$
$422$	−10.0376	−	2.68958i	−0.488624	−	0.130926i
$423$	−3.64859	+	1.30564i	−0.177401	+	0.0634822i
$424$	5.71876	−	5.71876i	0.277728	−	0.277728i
$425$	0.273528	−	0.157921i	0.0132680	−	0.00766030i
$426$	−11.8082	−	18.6465i	−0.572110	−	0.903424i
$427$	8.05396	+	30.0578i	0.389758	+	1.45460i
$428$	−11.2826			−0.545366
$429$	0.0111243	+	1.47144i	0.000537087	+	0.0710417i
$430$	−12.1786			−0.587305
$431$	−9.55356	−	35.6544i	−0.460179	−	1.71741i	−0.672399	−	0.740189i	$-0.734736\pi$
$431$	−9.55356	−	35.6544i	−0.460179	−	1.71741i	0.212220	−	0.977222i	$-0.431931\pi$
$432$	−4.78430	−	2.02743i	−0.230185	−	0.0975447i
$433$	3.23172	−	1.86584i	0.155307	−	0.0896663i	−0.420333	−	0.907370i	$-0.638087\pi$
$433$	3.23172	−	1.86584i	0.155307	−	0.0896663i	0.575639	+	0.817704i	$0.304753\pi$
$434$	6.06189	−	6.06189i	0.290980	−	0.290980i
$435$	5.54719	−	6.02087i	0.265968	−	0.288679i
$436$	−5.74650	−	1.53977i	−0.275207	−	0.0737416i
$437$	7.58444	+	7.58444i	0.362813	+	0.362813i
$438$	−0.937661	+	0.0383946i	−0.0448032	+	0.00183456i
$439$	10.4717	+	6.04582i	0.499786	+	0.288551i	0.728625	−	0.684913i	$-0.240160\pi$
$439$	10.4717	+	6.04582i	0.499786	+	0.288551i	−0.228839	+	0.973464i	$0.573493\pi$
$440$	0.227597	−	0.0609843i	0.0108502	−	0.00290731i
$441$	5.05171	−	3.49661i	0.240558	−	0.166505i
$442$	0.0379878	−	1.13815i	0.00180689	−	0.0541364i
$443$			14.0318i			0.666672i	0.942808	+	0.333336i	$0.108174\pi$
$443$			14.0318i			0.666672i	−0.942808	+	0.333336i	$0.891826\pi$
$444$	−6.21337	−	1.39514i	−0.294874	−	0.0662104i
$445$	4.42633	−	7.66663i	0.209828	−	0.363433i
$446$	3.43398	+	5.94783i	0.162604	+	0.281638i
$447$	2.23869	−	0.699193i	0.105886	−	0.0330707i
$448$	−0.778522	+	2.90548i	−0.0367817	+	0.137271i
$449$	−9.91117	+	36.9890i	−0.467737	+	1.74562i	0.179915	+	0.983682i	$0.442418\pi$
$449$	−9.91117	+	36.9890i	−0.467737	+	1.74562i	−0.647652	+	0.761937i	$0.724249\pi$
$450$	−0.536943	+	2.95156i	−0.0253117	+	0.139138i
$451$	−1.05341	−	1.82456i	−0.0496033	−	0.0859154i
$452$	10.6090	−	18.3753i	0.499003	−	0.864299i
$453$	3.56915	−	15.8955i	0.167693	−	0.746835i
$454$			13.0784i			0.613799i
$455$	−3.15489	+	10.3764i	−0.147904	+	0.486453i
$456$	3.02774	−	5.77796i	0.141787	−	0.270578i
$457$	−9.94765	+	2.66546i	−0.465331	+	0.124685i	−0.483864	−	0.875143i	$-0.660767\pi$
$457$	−9.94765	+	2.66546i	−0.465331	+	0.124685i	0.0185328	+	0.999828i	$0.494100\pi$
$458$	7.94271	+	4.58573i	0.371139	+	0.214277i
$459$	1.31010	−	0.988464i	0.0611502	−	0.0461375i
$460$	2.01384	+	2.01384i	0.0938956	+	0.0938956i
$461$	25.8963	+	6.93889i	1.20611	+	0.323176i	0.805235	−	0.592956i	$-0.202039\pi$
$461$	25.8963	+	6.93889i	1.20611	+	0.323176i	0.400876	+	0.916132i	$0.368706\pi$
$462$	0.902832	+	0.831804i	0.0420036	+	0.0386990i
$463$	−29.8128	+	29.8128i	−1.38552	+	1.38552i	−0.551042	+	0.834478i	$0.685770\pi$
$463$	−29.8128	+	29.8128i	−1.38552	+	1.38552i	−0.834478	+	0.551042i	$0.814230\pi$
$464$	−4.09336	+	2.36330i	−0.190029	+	0.109713i
$465$	−4.17047	+	2.64103i	−0.193401	+	0.122475i
$466$	5.74970	+	21.4582i	0.266350	+	0.994030i
$467$	6.85301			0.317119			0.158560	−	0.987349i	$-0.449315\pi$
$467$	6.85301			0.317119			0.158560	+	0.987349i	$0.449315\pi$
$468$	8.01023	+	7.26885i	0.370273	+	0.336003i
$469$	−32.8350			−1.51618
$470$	−0.334322	−	1.24771i	−0.0154211	−	0.0575524i
$471$	−22.1881	+	14.0510i	−1.02237	+	0.647436i
$472$	5.07074	−	2.92759i	0.233400	−	0.134753i
$473$	2.02911	−	2.02911i	0.0932985	−	0.0932985i
$474$	−0.0443817	−	0.0408901i	−0.00203852	−	0.00187814i
$475$	−3.63784	−	0.974755i	−0.166915	−	0.0447248i
$476$	−0.671784	−	0.671784i	−0.0307912	−	0.0307912i
$477$	−21.9336	−	10.3728i	−1.00427	−	0.474939i
$478$	−12.8007	−	7.39047i	−0.585489	−	0.338032i
$479$	−6.65578	+	1.78341i	−0.304110	+	0.0814861i	−0.407647	−	0.913139i	$-0.633651\pi$
$479$	−6.65578	+	1.78341i	−0.304110	+	0.0814861i	0.103537	+	0.994626i	$0.466984\pi$
$480$	0.803931	−	1.53418i	0.0366943	−	0.0700252i
$481$	11.2527	+	7.00737i	0.513080	+	0.319509i
$482$			15.3964i			0.701288i
$483$	−3.25075	+	14.4775i	−0.147914	+	0.658748i
$484$	5.47224	−	9.47820i	0.248738	−	0.430827i
$485$	−7.06940	−	12.2446i	−0.321005	−	0.555997i
$486$	−0.890827	+	15.5630i	−0.0404087	+	0.705951i
$487$	3.88503	−	14.4991i	0.176047	−	0.657017i	−0.820324	−	0.571900i	$-0.806207\pi$
$487$	3.88503	−	14.4991i	0.176047	−	0.657017i	0.996371	−	0.0851178i	$-0.0271267\pi$
$488$	−2.67753	+	9.99269i	−0.121206	+	0.452348i
$489$	24.9326	−	7.78701i	1.12749	−	0.352141i
$490$	1.02396	+	1.77356i	0.0462580	+	0.0801211i
$491$	0.858837	−	1.48755i	0.0387588	−	0.0671322i	−0.845995	−	0.533190i	$-0.820993\pi$
$491$	0.858837	−	1.48755i	0.0387588	−	0.0671322i	0.884754	+	0.466058i	$0.154326\pi$
$492$	−15.1108	−	3.39294i	−0.681245	−	0.152966i
$493$		−	1.49286i		−	0.0672351i
$494$	−9.91683	+	9.27623i	−0.446179	+	0.417357i
$495$	−0.402304	−	0.581227i	−0.0180822	−	0.0261242i
$496$	2.75291	−	0.737640i	0.123609	−	0.0331210i
$497$	33.1944	+	19.1648i	1.48897	+	0.859658i
$498$	−15.5325	+	0.636011i	−0.696027	+	0.0285003i
$499$	17.3844	+	17.3844i	0.778231	+	0.778231i	0.979530	−	0.201299i	$-0.0645162\pi$
$499$	17.3844	+	17.3844i	0.778231	+	0.778231i	−0.201299	+	0.979530i	$0.564516\pi$
$500$	−0.965926	−	0.258819i	−0.0431975	−	0.0115747i
$501$	3.98088	−	4.32081i	0.177852	−	0.193039i
$502$	−10.6718	+	10.6718i	−0.476306	+	0.476306i
$503$	−3.29157	+	1.90039i	−0.146764	+	0.0847341i	−0.571584	−	0.820544i	$-0.693671\pi$
$503$	−3.29157	+	1.90039i	−0.146764	+	0.0847341i	0.424820	+	0.905278i	$0.360337\pi$
$504$	8.99372	−	0.737772i	0.400612	−	0.0328630i
$505$	−3.46892	−	12.9462i	−0.154365	−	0.576097i
$506$	−0.671060			−0.0298322
$507$	−10.7515	−	19.7840i	−0.477489	−	0.878638i
$508$	19.4020			0.860823
$509$	1.41966	+	5.29826i	0.0629255	+	0.234841i	0.990225	−	0.139479i	$-0.0445428\pi$
$509$	1.41966	+	5.29826i	0.0629255	+	0.234841i	−0.927300	+	0.374320i	$0.877876\pi$
$510$	0.292682	+	0.462176i	0.0129602	+	0.0204655i
$511$	1.41141	−	0.814880i	0.0624372	−	0.0360481i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−19.3807	−	2.71193i	−0.855681	−	0.119735i
$514$	28.9003	+	7.74382i	1.27474	+	0.341565i
$515$	−4.25225	−	4.25225i	−0.187377	−	0.187377i
$516$	−0.863017	−	21.0763i	−0.0379922	−	0.927834i
$517$	0.263586	+	0.152181i	0.0115925	+	0.00669292i
$518$	10.6823	−	2.86232i	0.469355	−	0.125763i
$519$	−36.4189	−	19.0841i	−1.59861	−	0.837697i
$520$	−2.63314	+	2.46304i	−0.115471	+	0.108012i
$521$		−	25.1040i		−	1.09983i	−0.835222	−	0.549913i	$-0.814661\pi$
$521$		−	25.1040i		−	1.09983i	0.835222	−	0.549913i	$-0.185339\pi$
$522$	10.8128	+	9.17332i	0.473264	+	0.401505i
$523$	6.65226	−	11.5221i	0.290883	−	0.503824i	−0.683136	−	0.730292i	$-0.739384\pi$
$523$	6.65226	−	11.5221i	0.290883	−	0.503824i	0.974019	+	0.226467i	$0.0727176\pi$
$524$	1.19011	+	2.06132i	0.0519900	+	0.0900493i
$525$	−1.55320	−	4.97306i	−0.0677873	−	0.217042i
$526$	−1.89281	+	7.06406i	−0.0825304	+	0.308008i
$527$	−0.232978	+	0.869486i	−0.0101487	+	0.0378754i
$528$	0.121668	+	0.389557i	0.00529491	+	0.0169533i
$529$	7.44447	+	12.8942i	0.323672	+	0.560617i
$530$	4.04378	−	7.00403i	0.175650	−	0.304236i
$531$	−13.3946	−	11.3636i	−0.581277	−	0.493140i
$532$			11.3285i			0.491154i
$533$	27.3663	+	17.0417i	1.18537	+	0.738160i
$534$	13.5815	+	7.11693i	0.587731	+	0.307980i
$535$	−10.8982	+	2.92016i	−0.471169	+	0.126249i
$536$	−9.45351	−	5.45799i	−0.408329	−	0.235749i
$537$	0.0940753	+	2.29748i	0.00405965	+	0.0991436i
$538$	−12.9335	−	12.9335i	−0.557601	−	0.557601i
$539$	−0.466101	−	0.124891i	−0.0200764	−	0.00537946i
$540$	−5.14602	−	0.720077i	−0.221449	−	0.0309872i
$541$	27.7903	−	27.7903i	1.19480	−	1.19480i	0.219095	−	0.975704i	$-0.429690\pi$
$541$	27.7903	−	27.7903i	1.19480	−	1.19480i	0.975704	−	0.219095i	$-0.0703103\pi$
$542$	−0.572253	+	0.330390i	−0.0245804	+	0.0141915i
$543$	−13.8631	−	21.8913i	−0.594921	−	0.939445i
$544$	−0.0817460	−	0.305080i	−0.00350483	−	0.0130802i
$545$	−5.94921			−0.254836
$546$	−18.1810	−	4.72456i	−0.778074	−	0.202192i
$547$	40.2659			1.72164			0.860822	−	0.508906i	$-0.169950\pi$
$547$	40.2659			1.72164			0.860822	+	0.508906i	$0.169950\pi$
$548$	4.43351	+	16.5461i	0.189390	+	0.706813i
$549$	30.9317	−	2.53738i	1.32013	−	0.108293i
$550$	0.204058	−	0.117813i	0.00870104	−	0.00502355i
$551$	−12.5873	+	12.5873i	−0.536238	+	0.536238i
$552$	−3.34244	+	3.62785i	−0.142264	+	0.154412i
$553$	0.101231	+	0.0271247i	0.00430477	+	0.00115346i
$554$	−13.3221	−	13.3221i	−0.566001	−	0.566001i
$555$	−6.36274	+	0.260537i	−0.270083	+	0.0110592i
$556$	−4.79332	−	2.76742i	−0.203282	−	0.117365i
$557$	−15.1918	+	4.07062i	−0.643696	+	0.172478i	−0.565877	−	0.824490i	$-0.691462\pi$
$557$	−15.1918	+	4.07062i	−0.643696	+	0.172478i	−0.0778191	+	0.996967i	$0.524796\pi$
$558$	−4.86610	−	7.03027i	−0.205998	−	0.297615i
$559$	−12.7735	+	42.0117i	−0.540260	+	1.77691i
$560$			3.00798i			0.127110i
$561$	−0.125769	−	0.0282399i	−0.00530995	−	0.00119229i
$562$	13.7276	−	23.7769i	0.579063	−	1.00297i
$563$	−13.0055	−	22.5261i	−0.548115	−	0.949363i	−0.998404	−	0.0564797i	$-0.982012\pi$
$563$	−13.0055	−	22.5261i	−0.548115	−	0.949363i	0.450289	−	0.892883i	$-0.351321\pi$
$564$	2.13559	−	0.666995i	0.0899246	−	0.0280855i
$565$	5.49160	−	20.4949i	0.231033	−	0.862228i
$566$	−4.10432	+	15.3175i	−0.172517	+	0.643844i
$567$	−11.1745	−	24.6579i	−0.469285	−	1.03553i
$568$	6.37132	+	11.0354i	0.267335	+	0.463037i
$569$	2.87286	−	4.97594i	0.120437	−	0.208602i	−0.799503	−	0.600662i	$-0.794904\pi$
$569$	2.87286	−	4.97594i	0.120437	−	0.208602i	0.919940	+	0.392059i	$0.128237\pi$
$570$	1.42912	−	6.36471i	0.0598594	−	0.266589i
$571$		−	23.8513i		−	0.998147i	−0.866560	−	0.499074i	$-0.833674\pi$
$571$		−	23.8513i		−	0.998147i	0.866560	−	0.499074i	$-0.166326\pi$
$572$	0.0283397	−	0.849087i	0.00118494	−	0.0355021i
$573$	−1.52868	+	2.91724i	−0.0638614	+	0.121869i
$574$	25.9791	−	6.96109i	1.08435	−	0.290550i
$575$	2.46643	+	1.42400i	0.102857	+	0.0593848i
$576$	2.71201	+	1.28257i	0.113001	+	0.0534403i
$577$	−10.5626	−	10.5626i	−0.439728	−	0.439728i	0.452192	−	0.891920i	$-0.350642\pi$
$577$	−10.5626	−	10.5626i	−0.439728	−	0.439728i	−0.891920	+	0.452192i	$0.850642\pi$
$578$	−16.3244	−	4.37410i	−0.679005	−	0.181939i
$579$	7.10428	+	6.54537i	0.295244	+	0.272016i
$580$	−3.34221	+	3.34221i	−0.138778	+	0.138778i
$581$	23.3802	−	13.4986i	0.969976	−	0.560016i
$582$	20.6895	−	13.1020i	0.857607	−	0.543095i
$583$	0.493214	+	1.84070i	0.0204268	+	0.0762340i
$584$	0.541812			0.0224204
$585$	9.61861	+	4.94797i	0.397680	+	0.204573i
$586$	2.59812			0.107328
$587$	−9.40166	−	35.0875i	−0.388048	−	1.44821i	−0.833306	−	0.552812i	$-0.813555\pi$
$587$	−9.40166	−	35.0875i	−0.388048	−	1.44821i	0.445258	−	0.895402i	$-0.353112\pi$
$588$	−2.99676	+	1.89775i	−0.123584	+	0.0782620i
$589$	9.29562	−	5.36683i	0.383019	−	0.221136i
$590$	4.14024	−	4.14024i	0.170451	−	0.170451i
$591$	12.0897	+	11.1385i	0.497303	+	0.458179i
$592$	3.55133	+	0.951577i	0.145959	+	0.0391096i
$593$	−20.0829	−	20.0829i	−0.824704	−	0.824704i	0.162075	−	0.986779i	$-0.448181\pi$
$593$	−20.0829	−	20.0829i	−0.824704	−	0.824704i	−0.986779	+	0.162075i	$0.948181\pi$
$594$	0.977363	−	0.737416i	0.0401017	−	0.0302565i
$595$	−0.822765	−	0.475023i	−0.0337301	−	0.0194741i
$596$	−1.30794	+	0.350461i	−0.0535753	+	0.0143555i
$597$	19.6873	−	37.5701i	0.805747	−	1.53764i
$598$	9.05918	−	4.83479i	0.370457	−	0.197709i
$599$			11.8335i			0.483504i	0.970338	+	0.241752i	$0.0777221\pi$
$599$			11.8335i			0.483504i	−0.970338	+	0.241752i	$0.922278\pi$
$600$	0.379464	−	1.68997i	0.0154915	−	0.0689928i
$601$	−1.72111	+	2.98105i	−0.0702056	+	0.121600i	−0.898991	−	0.437966i	$-0.855699\pi$
$601$	−1.72111	+	2.98105i	−0.0702056	+	0.121600i	0.828786	+	0.559566i	$0.189032\pi$
$602$	18.3165	+	31.7251i	0.746525	+	1.29302i
$603$	−5.86126	+	32.2191i	−0.238689	+	1.31206i
$604$	−2.43439	+	9.08527i	−0.0990539	+	0.369674i
$605$	2.83264	−	10.5716i	0.115163	−	0.429795i
$606$	22.1588	−	6.92072i	0.900141	−	0.281135i
$607$	4.27256	+	7.40029i	0.173418	+	0.300369i	0.939613	−	0.342240i	$-0.111186\pi$
$607$	4.27256	+	7.40029i	0.173418	+	0.300369i	−0.766195	+	0.642608i	$0.777852\pi$
$608$	−1.88308	+	3.26159i	−0.0763691	+	0.132275i
$609$	−24.0272	−	5.39503i	−0.973631	−	0.218618i
$610$			10.3452i			0.418865i
$611$	−4.65478	−	0.155361i	−0.188312	−	0.00628524i
$612$	−0.779102	+	0.539266i	−0.0314933	+	0.0217985i
$613$	15.1454	−	4.05819i	0.611716	−	0.163909i	0.0603571	−	0.998177i	$-0.480776\pi$
$613$	15.1454	−	4.05819i	0.611716	−	0.163909i	0.551359	+	0.834268i	$0.314109\pi$
$614$	10.7317	+	6.19593i	0.433095	+	0.250047i
$615$	−15.4740	+	0.633618i	−0.623973	+	0.0255499i
$616$	−0.501166	−	0.501166i	−0.0201926	−	0.0201926i
$617$	41.8141	+	11.2041i	1.68337	+	0.451058i	0.968666	−	0.248367i	$-0.0798937\pi$
$617$	41.8141	+	11.2041i	1.68337	+	0.451058i	0.714706	+	0.699425i	$0.246560\pi$
$618$	7.05762	−	7.66028i	0.283899	−	0.308142i
$619$	−23.3540	+	23.3540i	−0.938677	+	0.938677i	−0.998225	−	0.0595480i	$-0.981034\pi$
$619$	−23.3540	+	23.3540i	−0.938677	+	0.938677i	0.0595480	+	0.998225i	$0.481034\pi$
$620$	2.46819	−	1.42501i	0.0991250	−	0.0572298i
$621$	13.6257	+	5.77410i	0.546779	+	0.231707i
$622$	−8.50218	−	31.7306i	−0.340906	−	1.27228i
$623$	−26.6286			−1.06685
$624$	−4.44914	−	4.38237i	−0.178108	−	0.175435i
$625$	−1.00000			−0.0400000
$626$	−4.15116	−	15.4923i	−0.165914	−	0.619198i
$627$	0.822330	+	1.29855i	0.0328407	+	0.0518591i
$628$	13.1315	−	7.58145i	0.524002	−	0.302533i
$629$	−0.821113	+	0.821113i	−0.0327399	+	0.0327399i
$630$	8.49632	−	3.04038i	0.338501	−	0.121132i
$631$	33.2854	+	8.91879i	1.32507	+	0.355051i	0.850875	−	0.525369i	$-0.176073\pi$
$631$	33.2854	+	8.91879i	1.32507	+	0.355051i	0.474195	+	0.880420i	$0.342739\pi$
$632$	0.0246365	+	0.0246365i	0.000979987	+	0.000979987i
$633$	−0.736391	−	17.9839i	−0.0292689	−	0.714797i
$634$	−6.75195	−	3.89824i	−0.268154	−	0.154819i
$635$	18.7409	−	5.02160i	0.743708	−	0.199276i
$636$	12.4077	+	6.50184i	0.491998	+	0.257815i
$637$	7.19209	−	1.67211i	0.284961	−	0.0662515i
$638$		−	1.11371i		−	0.0440921i
$639$	24.7307	−	29.1507i	0.978332	−	1.15318i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	3.91216	+	6.77606i	0.154521	+	0.267638i	0.932885	−	0.360176i	$-0.117283\pi$
$641$	3.91216	+	6.77606i	0.154521	+	0.267638i	−0.778363	+	0.627814i	$0.783950\pi$
$642$	−5.82590	−	18.6534i	−0.229930	−	0.736193i
$643$	−3.66632	+	13.6829i	−0.144586	+	0.539601i	0.855188	+	0.518318i	$0.173442\pi$
$643$	−3.66632	+	13.6829i	−0.144586	+	0.539601i	−0.999773	+	0.0212828i	$0.993225\pi$
$644$	2.21723	−	8.27480i	0.0873709	−	0.326073i
$645$	−6.28857	−	20.1348i	−0.247612	−	0.792807i
$646$	−0.594757	−	1.03015i	−0.0234004	−	0.0405307i
$647$	−0.642158	+	1.11225i	−0.0252458	+	0.0437271i	−0.878372	−	0.477977i	$-0.841370\pi$
$647$	−0.642158	+	1.11225i	−0.0252458	+	0.0437271i	0.853126	+	0.521704i	$0.174704\pi$
$648$	0.881503	−	8.95673i	0.0346287	−	0.351853i
$649$			1.37963i			0.0541552i
$650$	−1.90593	+	3.06062i	−0.0747568	+	0.120048i
$651$	13.1522	+	6.89194i	0.515475	+	0.270116i
$652$	−14.5667	+	3.90314i	−0.570476	+	0.152859i
$653$	−4.05541	−	2.34139i	−0.158700	−	0.0916256i	0.418547	−	0.908195i	$-0.362540\pi$
$653$	−4.05541	−	2.34139i	−0.158700	−	0.0916256i	−0.577247	+	0.816570i	$0.695873\pi$
$654$	−0.421580	−	10.2957i	−0.0164851	−	0.402594i
$655$	1.68306	+	1.68306i	0.0657627	+	0.0657627i
$656$	8.63675	+	2.31421i	0.337208	+	0.0903547i
$657$	−0.547649	−	1.53040i	−0.0213658	−	0.0597066i
$658$	−2.74744	+	2.74744i	−0.107106	+	0.107106i
$659$	−1.76921	+	1.02145i	−0.0689185	+	0.0397901i	−0.534063	−	0.845445i	$-0.679336\pi$
$659$	−1.76921	+	1.02145i	−0.0689185	+	0.0397901i	0.465145	+	0.885235i	$0.346002\pi$
$660$	0.218347	+	0.344794i	0.00849914	+	0.0134211i
$661$	8.07328	+	30.1299i	0.314014	+	1.17192i	0.924904	+	0.380201i	$0.124145\pi$
$661$	8.07328	+	30.1299i	0.314014	+	1.17192i	−0.610890	+	0.791716i	$0.709188\pi$
$662$	−32.6253			−1.26802
$663$	1.90131	−	0.524893i	0.0738408	−	0.0203851i
$664$	8.97519			0.348305
$665$	2.93204	+	10.9425i	0.113700	+	0.424333i
$666$	−0.901769	−	10.9929i	−0.0349429	−	0.425966i
$667$	11.6579	−	6.73066i	0.451394	−	0.260612i
$668$	−2.39850	+	2.39850i	−0.0928006	+	0.0928006i
$669$	−8.06032	+	8.74860i	−0.311630	+	0.338240i
$670$	−10.5440	−	2.82526i	−0.407351	−	0.109149i
$671$	−1.72364	−	1.72364i	−0.0665402	−	0.0665402i
$672$	−5.20561	+	0.213155i	−0.200811	+	0.00822263i
$673$	11.5534	+	6.67038i	0.445352	+	0.257124i	0.705865	−	0.708346i	$-0.250558\pi$
$673$	11.5534	+	6.67038i	0.445352	+	0.257124i	−0.260513	+	0.965470i	$0.583892\pi$
$674$	33.4451	−	8.96160i	1.28826	−	0.345188i
$675$	−5.15704	+	0.636346i	−0.198495	+	0.0244930i
$676$	5.73484	+	11.6667i	0.220571	+	0.448719i
$677$		−	33.8356i		−	1.30041i	−0.759760	−	0.650204i	$-0.774683\pi$
$677$		−	33.8356i		−	1.30041i	0.759760	−	0.650204i	$-0.225317\pi$
$678$	35.8577	+	8.05143i	1.37711	+	0.309213i
$679$	−21.2646	+	36.8314i	−0.816061	+	1.41346i
$680$	−0.157921	−	0.273528i	−0.00605600	−	0.0104893i
$681$	−21.6224	+	6.75317i	−0.828571	+	0.258782i
$682$	−0.173807	+	0.648656i	−0.00665540	+	0.0248383i
$683$	9.64474	−	35.9947i	0.369046	−	1.37730i	−0.492807	−	0.870139i	$-0.664029\pi$
$683$	9.64474	−	35.9947i	0.369046	−	1.37730i	0.861853	−	0.507158i	$-0.169304\pi$
$684$	11.1161	+	2.02222i	0.425033	+	0.0773214i
$685$	8.56488	+	14.8348i	0.327247	+	0.566809i
$686$	−7.44786	+	12.9001i	−0.284361	+	0.492527i
$687$	−3.48024	+	15.4995i	−0.132779	+	0.591343i
$688$			12.1786i			0.464306i
$689$	−19.9200	−	21.2956i	−0.758892	−	0.811299i
$690$	−2.28959	+	4.36932i	−0.0871632	+	0.166337i
$691$	−14.8688	+	3.98409i	−0.565637	+	0.151562i	−0.530295	−	0.847813i	$-0.677919\pi$
$691$	−14.8688	+	3.98409i	−0.565637	+	0.151562i	−0.0353421	+	0.999375i	$0.511252\pi$
$692$	20.5581	+	11.8692i	0.781501	+	0.451200i
$693$	−0.909027	+	1.92216i	−0.0345311	+	0.0730167i
$694$	−19.9051	−	19.9051i	−0.755586	−	0.755586i
$695$	−5.34625	−	1.43252i	−0.202795	−	0.0543387i
$696$	−6.02087	−	5.54719i	−0.228221	−	0.210266i
$697$	−1.99693	+	1.99693i	−0.0756390	+	0.0756390i
$698$	2.34886	−	1.35612i	0.0889057	−	0.0513297i
$699$	−32.5077	+	20.5861i	−1.22955	+	0.778637i
$700$	0.778522	+	2.90548i	0.0294254	+	0.109817i
$701$	17.4016			0.657250			0.328625	−	0.944461i	$-0.393415\pi$
$701$	17.4016			0.657250			0.328625	+	0.944461i	$0.393415\pi$
$702$	−7.88136	+	16.9966i	−0.297463	+	0.641495i
$703$	13.8467			0.522239
$704$	−0.0609843	−	0.227597i	−0.00229843	−	0.00857787i
$705$	1.89019	−	1.19700i	0.0711888	−	0.0450816i
$706$	17.3075	−	9.99252i	0.651378	−	0.376073i
$707$	−28.5074	+	28.5074i	−1.07213	+	1.07213i
$708$	7.45849	+	6.87171i	0.280307	+	0.258255i
$709$	−30.2103	−	8.09484i	−1.13457	−	0.304008i	−0.357806	−	0.933796i	$-0.616475\pi$
$709$	−30.2103	−	8.09484i	−1.13457	−	0.304008i	−0.776767	+	0.629788i	$0.783142\pi$
$710$	9.01040	+	9.01040i	0.338154	+	0.338154i
$711$	0.0446862	−	0.0944900i	0.00167586	−	0.00354365i
$712$	−7.66663	−	4.42633i	−0.287319	−	0.165884i
$713$	−7.84027	+	2.10079i	−0.293620	+	0.0786754i
$714$	0.763772	−	1.45754i	0.0285834	−	0.0545470i
$715$	−0.192386	−	0.827489i	−0.00719482	−	0.0309464i
$716$		−	1.32756i		−	0.0496133i
$717$	5.60883	−	24.9794i	0.209466	−	0.932872i
$718$	−2.22899	+	3.86072i	−0.0831851	+	0.144081i
$719$	−19.3424	−	33.5021i	−0.721351	−	1.24942i	−0.960458	−	0.278424i	$-0.910188\pi$
$719$	−19.3424	−	33.5021i	−0.721351	−	1.24942i	0.239107	−	0.970993i	$-0.423145\pi$
$720$	2.95156	+	0.536943i	0.109998	+	0.0200107i
$721$	−4.68171	+	17.4724i	−0.174356	+	0.650706i
$722$	1.24647	−	4.65191i	0.0463890	−	0.173126i
$723$	−25.4548	+	7.95012i	−0.946674	+	0.295668i
$724$	7.48005	+	12.9558i	0.277994	+	0.481499i
$725$	−2.36330	+	4.09336i	−0.0877708	+	0.152023i
$726$	18.4959	+	4.15303i	0.686446	+	0.154134i
$727$		−	2.39169i		−	0.0887029i	−0.999016	−	0.0443515i	$-0.985878\pi$
$727$		−	2.39169i		−	0.0887029i	0.999016	−	0.0443515i	$-0.0141221\pi$
$728$	10.3764	+	3.15489i	0.384575	+	0.116928i
$729$	−26.1901	+	6.56332i	−0.970005	+	0.243086i
$730$	0.523350	−	0.140231i	0.0193701	−	0.00519019i
$731$	−3.33119	−	1.92326i	−0.123208	−	0.0711344i
$732$	−17.9034	+	0.733094i	−0.661728	+	0.0270959i
$733$	−23.2755	−	23.2755i	−0.859702	−	0.859702i	0.131601	−	0.991303i	$-0.457988\pi$
$733$	−23.2755	−	23.2755i	−0.859702	−	0.859702i	−0.991303	+	0.131601i	$0.957988\pi$
$734$	−23.8299	−	6.38521i	−0.879578	−	0.235682i
$735$	−2.40347	+	2.60871i	−0.0886534	+	0.0962236i
$736$	2.01384	−	2.01384i	0.0742310	−	0.0742310i
$737$	2.22749	−	1.28604i	0.0820505	−	0.0473719i
$738$	−2.19308	−	26.7345i	−0.0807284	−	0.984109i
$739$	−8.60065	−	32.0981i	−0.316380	−	1.18075i	−0.922698	−	0.385524i	$-0.874021\pi$
$739$	−8.60065	−	32.0981i	−0.316380	−	1.18075i	0.606318	−	0.795222i	$-0.292646\pi$
$740$	3.67661			0.135155
$741$	−20.4570	−	11.6055i	−0.751506	−	0.426340i
$742$	−24.3272			−0.893079
$743$	11.1382	+	41.5683i	0.408621	+	1.52499i	0.797279	+	0.603611i	$0.206272\pi$
$743$	11.1382	+	41.5683i	0.408621	+	1.52499i	−0.388659	+	0.921382i	$0.627061\pi$
$744$	2.64103	+	4.17047i	0.0968248	+	0.152897i
$745$	−1.17267	+	0.677039i	−0.0429632	+	0.0248048i
$746$	−1.64254	+	1.64254i	−0.0601377	+	0.0601377i
$747$	−9.07187	−	25.3513i	−0.331923	−	0.927555i
$748$	0.0718847	+	0.0192614i	0.00262836	+	0.000704268i
$749$	23.9977	+	23.9977i	0.876856	+	0.876856i
$750$	−0.0708632	−	1.73060i	−0.00258756	−	0.0631926i
$751$	−2.97565	−	1.71799i	−0.108583	−	0.0626903i	0.444725	−	0.895667i	$-0.353301\pi$
$751$	−2.97565	−	1.71799i	−0.108583	−	0.0626903i	−0.553308	+	0.832977i	$0.686635\pi$
$752$	−1.24771	+	0.334322i	−0.0454992	+	0.0121915i
$753$	−23.1541	−	12.1331i	−0.843783	−	0.442155i
$754$	8.02393	+	15.0348i	0.292214	+	0.547536i
$755$			9.40576i			0.342311i
$756$	5.86376	+	14.4883i	0.213263	+	0.526934i
$757$	−5.42139	+	9.39012i	−0.197044	+	0.341290i	−0.947569	−	0.319552i	$-0.896467\pi$
$757$	−5.42139	+	9.39012i	−0.197044	+	0.341290i	0.750525	+	0.660842i	$0.229801\pi$
$758$	8.44930	+	14.6346i	0.306892	+	0.531553i
$759$	−0.346509	−	1.10946i	−0.0125775	−	0.0402707i
$760$	−0.974755	+	3.63784i	−0.0353581	+	0.131958i
$761$	4.52860	−	16.9010i	0.164162	−	0.612660i	−0.833984	−	0.551789i	$-0.813945\pi$
$761$	4.52860	−	16.9010i	0.164162	−	0.612660i	0.998146	−	0.0608711i	$-0.0193878\pi$
$762$	10.0184	+	32.0771i	0.362929	+	1.16203i
$763$	8.94755	+	15.4976i	0.323923	+	0.561051i
$764$	0.950752	−	1.64675i	0.0343970	−	0.0595773i
$765$	−0.612982	+	0.722538i	−0.0221624	+	0.0261234i
$766$		−	27.6252i		−	0.998140i
$767$	−9.93982	−	18.6247i	−0.358906	−	0.672500i
$768$	−1.53418	−	0.803931i	−0.0553598	−	0.0290094i
$769$	−9.63566	+	2.58187i	−0.347471	+	0.0931045i	−0.428333	−	0.903621i	$-0.640899\pi$
$769$	−9.63566	+	2.58187i	−0.347471	+	0.0931045i	0.0808627	+	0.996725i	$0.474232\pi$
$770$	−0.613801	−	0.354378i	−0.0221198	−	0.0127709i
$771$	2.12022	+	51.7793i	0.0763577	+	1.86478i
$772$	−3.94362	−	3.94362i	−0.141934	−	0.141934i
$773$	32.6203	+	8.74057i	1.17327	+	0.314376i	0.792253	−	0.610192i	$-0.208908\pi$
$773$	32.6203	+	8.74057i	1.17327	+	0.314376i	0.381016	+	0.924569i	$0.375574\pi$
$774$	34.3997	−	12.3098i	1.23647	−	0.442467i
$775$	2.01527	−	2.01527i	0.0723906	−	0.0723906i
$776$	−12.2446	+	7.06940i	−0.439554	+	0.253777i
$777$	10.2482	+	16.1830i	0.367652	+	0.580562i
$778$	−2.34165	−	8.73916i	−0.0839522	−	0.313314i
$779$	33.6749			1.20653
$780$	−5.43178	−	3.08152i	−0.194489	−	0.110336i
$781$	−3.00249			−0.107437
$782$	0.232812	+	0.868867i	0.00832535	+	0.0310706i
$783$	−9.58285	+	22.6135i	−0.342463	+	0.808140i
$784$	1.77356	−	1.02396i	0.0633413	−	0.0365701i
$785$	10.7218	−	10.7218i	0.382677	−	0.382677i
$786$	−2.79344	+	3.03198i	−0.0996388	+	0.108147i
$787$	−29.8480	−	7.99775i	−1.06397	−	0.285089i	−0.315955	−	0.948774i	$-0.602325\pi$
$787$	−29.8480	−	7.99775i	−1.06397	−	0.285089i	−0.748012	+	0.663685i	$0.768991\pi$
$788$	−6.71103	−	6.71103i	−0.239071	−	0.239071i
$789$	−12.6563	+	0.518241i	−0.450577	+	0.0184499i
$790$	0.0301734	+	0.0174206i	0.00107352	+	0.000619798i
$791$	−61.6483	+	16.5186i	−2.19196	+	0.587334i
$792$	−0.581227	+	0.402304i	−0.0206530	+	0.0142953i
$793$	35.6871	+	10.8505i	1.26728	+	0.385312i
$794$		−	9.39150i		−	0.333292i
$795$	13.6677	+	3.06893i	0.484745	+	0.108844i
$796$	−12.2444	+	21.2079i	−0.433991	+	0.751694i
$797$	−0.742989	−	1.28689i	−0.0263180	−	0.0455841i	0.852566	−	0.522619i	$-0.175045\pi$
$797$	−0.742989	−	1.28689i	−0.0263180	−	0.0455841i	−0.878884	+	0.477035i	$0.841712\pi$
$798$	−18.7294	+	5.84961i	−0.663012	+	0.207074i
$799$	0.105593	−	0.394079i	0.00373562	−	0.0139415i
$800$	−0.258819	+	0.965926i	−0.00915064	+	0.0341506i
$801$	−4.75338	+	26.1291i	−0.167952	+	0.923228i
$802$	7.31091	+	12.6629i	0.258157	+	0.447142i
$803$	−0.0638324	+	0.110561i	−0.00225260	+	0.00390161i
$804$	4.14222	−	18.4477i	0.146085	−	0.650600i
$805$		−	8.56670i		−	0.301936i
$806$	−2.32701	−	10.0090i	−0.0819656	−	0.352550i
$807$	14.7044	−	28.0611i	0.517621	−	0.987797i
$808$	−12.9462	+	3.46892i	−0.455445	+	0.122036i
$809$	−11.0497	−	6.37953i	−0.388486	−	0.224292i	0.293018	−	0.956107i	$-0.405340\pi$
$809$	−11.0497	−	6.37953i	−0.388486	−	0.224292i	−0.681504	+	0.731815i	$0.738674\pi$
$810$	−1.46670	−	8.87968i	−0.0515348	−	0.312000i
$811$	−8.39248	−	8.39248i	−0.294700	−	0.294700i	0.544234	−	0.838934i	$-0.316820\pi$
$811$	−8.39248	−	8.39248i	−0.294700	−	0.294700i	−0.838934	+	0.544234i	$0.816820\pi$
$812$	13.7331	+	3.67976i	0.481936	+	0.129134i
$813$	−0.841720	−	0.775500i	−0.0295204	−	0.0271980i
$814$	−0.612569	+	0.612569i	−0.0214705	+	0.0214705i
$815$	−13.0601	+	7.54028i	−0.457477	+	0.264125i
$816$	0.462176	−	0.292682i	0.0161794	−	0.0102459i
$817$	11.8712	+	44.3038i	0.415320	+	1.54999i
$818$	−18.4962			−0.646705
$819$	−1.57688	−	32.4980i	−0.0551007	−	1.13557i
$820$	8.94142			0.312248
$821$	−1.85492	−	6.92267i	−0.0647373	−	0.241603i	0.925974	−	0.377588i	$-0.123247\pi$
$821$	−1.85492	−	6.92267i	−0.0647373	−	0.241603i	−0.990711	+	0.135986i	$0.956580\pi$
$822$	−25.0662	+	15.8736i	−0.874284	+	0.553656i
$823$	−5.58084	+	3.22210i	−0.194536	+	0.112315i	−0.594104	−	0.804388i	$-0.702493\pi$
$823$	−5.58084	+	3.22210i	−0.194536	+	0.112315i	0.399568	+	0.916703i	$0.369160\pi$
$824$	−4.25225	+	4.25225i	−0.148134	+	0.148134i
$825$	0.300146	+	0.276533i	0.0104497	+	0.00962763i
$826$	−17.0121	−	4.55839i	−0.591928	−	0.158607i
$827$	−14.8707	−	14.8707i	−0.517104	−	0.517104i	0.399590	−	0.916694i	$-0.369153\pi$
$827$	−14.8707	−	14.8707i	−0.517104	−	0.517104i	−0.916694	+	0.399590i	$0.869153\pi$
$828$	−7.72380	−	3.65274i	−0.268421	−	0.126942i
$829$	13.6343	+	7.87174i	0.473537	+	0.273397i	0.717719	−	0.696333i	$-0.245186\pi$
$829$	13.6343	+	7.87174i	0.473537	+	0.273397i	−0.244182	+	0.969729i	$0.578519\pi$
$830$	8.66937	−	2.32295i	0.300918	−	0.0806308i
$831$	15.1463	−	28.9043i	0.525419	−	1.00268i
$832$	2.46304	+	2.63314i	0.0853907	+	0.0912876i
$833$			0.646822i			0.0224111i
$834$	2.10027	−	9.35374i	0.0727265	−	0.323894i
$835$	−1.69599	+	2.93755i	−0.0586923	+	0.101658i
$836$	−0.443702	−	0.768514i	−0.0153458	−	0.0265796i
$837$	9.11042	−	11.6752i	0.314902	−	0.403555i
$838$	0.238325	−	0.889441i	0.00823280	−	0.0307252i
$839$	−12.8147	+	47.8251i	−0.442413	+	1.65111i	0.280266	+	0.959922i	$0.409577\pi$
$839$	−12.8147	+	47.8251i	−0.442413	+	1.65111i	−0.722679	+	0.691184i	$0.757089\pi$
$840$	−4.97306	+	1.55320i	−0.171587	+	0.0535906i
$841$	−3.32962	−	5.76708i	−0.114815	−	0.198865i
$842$	−2.25026	+	3.89757i	−0.0775491	+	0.134319i
$843$	46.3985	+	10.4182i	1.59805	+	0.358823i
$844$			10.3917i			0.357698i
$845$	8.55899	+	9.78487i	0.294438	+	0.336610i
$846$	2.20547	+	3.18634i	0.0758257	+	0.109549i
$847$	−31.7990	+	8.52052i	−1.09263	+	0.292768i
$848$	−7.00403	−	4.04378i	−0.240519	−	0.138864i
$849$	−27.4436	+	1.12374i	−0.941863	+	0.0385667i
$850$	−0.223334	−	0.223334i	−0.00766030	−	0.00766030i
$851$	−10.1142	−	2.71008i	−0.346709	−	0.0929005i
$852$	−14.9549	+	16.2319i	−0.512347	+	0.556096i
$853$	−9.01682	+	9.01682i	−0.308730	+	0.308730i	−0.844417	−	0.535687i	$-0.820053\pi$
$853$	−9.01682	+	9.01682i	−0.308730	+	0.308730i	0.535687	+	0.844417i	$0.320053\pi$
$854$	26.9491	−	15.5590i	0.922178	−	0.532420i
$855$	11.2607	−	0.923734i	0.385107	−	0.0315910i
$856$	2.92016	+	10.8982i	0.0998089	+	0.372492i
$857$	−29.2149			−0.997963			−0.498981	−	0.866613i	$-0.666292\pi$
$857$	−29.2149			−0.997963			−0.498981	+	0.866613i	$0.666292\pi$
$858$	1.41842	−	0.391581i	0.0484241	−	0.0133684i
$859$	23.0414			0.786162			0.393081	−	0.919504i	$-0.371409\pi$
$859$	23.0414			0.786162			0.393081	+	0.919504i	$0.371409\pi$
$860$	3.15206	+	11.7636i	0.107484	+	0.401137i
$861$	24.9233	+	39.3567i	0.849385	+	1.34127i
$862$	−31.9668	+	18.4561i	−1.08879	+	0.628616i
$863$	−18.3785	+	18.3785i	−0.625611	+	0.625611i	−0.946961	−	0.321350i	$-0.895864\pi$
$863$	−18.3785	+	18.3785i	−0.625611	+	0.625611i	0.321350	+	0.946961i	$0.395864\pi$
$864$	−0.720077	+	5.14602i	−0.0244975	+	0.175071i
$865$	22.9296	+	6.14396i	0.779629	+	0.208901i
$866$	−2.63869	−	2.63869i	−0.0896663	−	0.0896663i
$867$	−1.19761	−	29.2476i	−0.0406728	−	0.993300i
$868$	−7.42427	−	4.28640i	−0.251996	−	0.145490i
$869$	−0.00792975	+	0.00212477i	−0.000268998	+	7.20779e-5i
$870$	−7.25144	−	3.79986i	−0.245847	−	0.128827i
$871$	−20.8051	+	33.4097i	−0.704954	+	1.13204i
$872$			5.94921i			0.201466i
$873$	32.3447	+	27.4404i	1.09470	+	0.928716i
$874$	5.36301	−	9.28900i	0.181406	−	0.314205i
$875$	1.50399	+	2.60498i	0.0508441	+	0.0880646i
$876$	0.279771	+	0.895773i	0.00945258	+	0.0302654i
$877$	1.00334	−	3.74452i	0.0338804	−	0.126443i	−0.946914	−	0.321486i	$-0.895818\pi$
$877$	1.00334	−	3.74452i	0.0338804	−	0.126443i	0.980795	+	0.195042i	$0.0624844\pi$
$878$	3.12955	−	11.6796i	0.105617	−	0.394169i
$879$	1.34157	+	4.29545i	0.0452500	+	0.144882i
$880$	−0.117813	−	0.204058i	−0.00397146	−	0.00687878i
$881$	−19.7652	+	34.2344i	−0.665907	+	1.15338i	0.313131	+	0.949710i	$0.398622\pi$
$881$	−19.7652	+	34.2344i	−0.665907	+	1.15338i	−0.979039	+	0.203675i	$0.934711\pi$
$882$	−4.68495	−	3.97459i	−0.157750	−	0.133831i
$883$		−	27.3175i		−	0.919307i	−0.888098	−	0.459654i	$-0.847974\pi$
$883$		−	27.3175i		−	0.919307i	0.888098	−	0.459654i	$-0.152026\pi$
$884$	−1.10920	+	0.257882i	−0.0373065	+	0.00867351i
$885$	8.98288	+	4.70716i	0.301956	+	0.158229i
$886$	13.5537	−	3.63170i	0.455345	−	0.122009i
$887$	−25.1304	−	14.5090i	−0.843795	−	0.487165i	0.0147573	−	0.999891i	$-0.495302\pi$
$887$	−25.1304	−	14.5090i	−0.843795	−	0.487165i	−0.858552	+	0.512726i	$0.828636\pi$
$888$	0.260537	+	6.36274i	0.00874303	+	0.213520i
$889$	−41.2672	−	41.2672i	−1.38406	−	1.38406i
$890$	−8.55102	−	2.29124i	−0.286631	−	0.0768025i
$891$	1.72384	+	1.23509i	0.0577507	+	0.0413772i
$892$	4.85638	−	4.85638i	0.162604	−	0.162604i
$893$	−4.21307	+	2.43242i	−0.140985	+	0.0813978i
$894$	−1.25478	−	1.98144i	−0.0419662	−	0.0662693i
$895$	−0.343598	−	1.28233i	−0.0114852	−	0.0428634i
$896$	3.00798			0.100489
$897$	12.6711	+	12.4810i	0.423076	+	0.416727i
$898$	38.2938			1.27788
$899$	−3.48653	−	13.0119i	−0.116282	−	0.433971i
$900$	2.98996	−	0.245272i	0.0996652	−	0.00817573i
$901$	2.21217	−	1.27720i	0.0736980	−	0.0425496i
$902$	−1.48975	+	1.48975i	−0.0496033	+	0.0496033i
$903$	−42.9929	+	46.6641i	−1.43072	+	1.55289i
$904$	−20.4949	−	5.49160i	−0.681651	−	0.182648i
$905$	10.5784	+	10.5784i	0.351637	+	0.351637i
$906$	−16.2776	+	0.666523i	−0.540788	+	0.0221437i
$907$	34.2329	+	19.7644i	1.13669	+	0.656266i	0.945608	−	0.325309i	$-0.105468\pi$
$907$	34.2329	+	19.7644i	1.13669	+	0.656266i	0.191078	+	0.981575i	$0.438802\pi$
$908$	12.6328	−	3.38494i	0.419233	−	0.112333i
$909$	22.8839	+	33.0614i	0.759012	+	1.09658i
$910$	10.8394	+	0.361783i	0.359322	+	0.0119930i
$911$			25.3787i			0.840833i	0.907331	+	0.420416i	$0.138116\pi$
$911$			25.3787i			0.840833i	−0.907331	+	0.420416i	$0.861884\pi$
$912$	−6.36471	−	1.42912i	−0.210757	−	0.0473230i
$913$	−1.05739	+	1.83146i	−0.0349945	+	0.0606123i
$914$	5.14928	+	8.91882i	0.170323	+	0.295008i
$915$	−17.1036	+	5.34185i	−0.565428	+	0.176596i
$916$	2.37375	−	8.85895i	0.0784308	−	0.292708i
$917$	1.85305	−	6.91566i	0.0611930	−	0.228375i
$918$	−1.29386	−	1.00963i	−0.0427038	−	0.0333226i
$919$	3.16313	+	5.47870i	0.104342	+	0.180726i	0.913469	−	0.406908i	$-0.133393\pi$
$919$	3.16313	+	5.47870i	0.104342	+	0.180726i	−0.809127	+	0.587634i	$0.800060\pi$
$920$	1.42400	−	2.46643i	0.0469478	−	0.0813159i
$921$	−4.70226	+	20.9419i	−0.154945	+	0.690059i
$922$		−	26.8098i		−	0.882935i
$923$	40.5330	−	21.6320i	1.33416	−	0.712027i
$924$	0.569791	−	1.08736i	0.0187447	−	0.0357714i
$925$	3.55133	−	0.951577i	0.116767	−	0.0312877i
$926$	36.5131	+	21.0809i	1.19990	+	0.692760i
$927$	16.3090	+	7.71283i	0.535656	+	0.253323i
$928$	3.34221	+	3.34221i	0.109713	+	0.109713i
$929$	14.8052	+	3.96703i	0.485741	+	0.130154i	0.493375	−	0.869817i	$-0.335763\pi$
$929$	14.8052	+	3.96703i	0.485741	+	0.130154i	−0.00763335	+	0.999971i	$0.502430\pi$
$930$	3.63044	+	3.34482i	0.119047	+	0.109681i
$931$	5.45380	−	5.45380i	0.178741	−	0.178741i
$932$	19.2389	−	11.1076i	0.630190	−	0.363840i
$933$	48.0697	−	30.4410i	1.57373	−	0.996594i
$934$	−1.77369	−	6.61950i	−0.0580369	−	0.216597i
$935$	0.0744205			0.00243381
$936$	4.94797	−	9.61861i	0.161730	−	0.314394i
$937$	−25.1329			−0.821056			−0.410528	−	0.911848i	$-0.634656\pi$
$937$	−25.1329			−0.821056			−0.410528	+	0.911848i	$0.634656\pi$
$938$	8.49832	+	31.7162i	0.277480	+	1.03557i
$939$	23.4698	−	14.8627i	0.765909	−	0.485026i
$940$	−1.11866	+	0.645861i	−0.0364868	+	0.0210657i
$941$	−32.2736	+	32.2736i	−1.05209	+	1.05209i	−0.0535227	+	0.998567i	$0.517045\pi$
$941$	−32.2736	+	32.2736i	−1.05209	+	1.05209i	−0.998567	+	0.0535227i	$0.982955\pi$
$942$	19.3149	+	17.7954i	0.629314	+	0.579804i
$943$	−24.5974	−	6.59085i	−0.801002	−	0.214628i
$944$	−4.14024	−	4.14024i	−0.134753	−	0.134753i
$945$	9.41380	+	12.4770i	0.306231	+	0.405875i
$946$	−2.48514	−	1.43480i	−0.0807989	−	0.0466493i
$947$	46.9552	−	12.5816i	1.52584	−	0.408847i	0.604180	−	0.796848i	$-0.293501\pi$
$947$	46.9552	−	12.5816i	1.52584	−	0.408847i	0.921659	+	0.388001i	$0.126834\pi$
$948$	−0.0280100	+	0.0534526i	−0.000909721	+	0.00173606i
$949$	0.0651662	−	1.95244i	0.00211538	−	0.0633790i
$950$			3.76616i			0.122191i
$951$	2.95848	−	13.1758i	0.0959354	−	0.427256i
$952$	−0.475023	+	0.822765i	−0.0153956	+	0.0266660i
$953$	−10.5502	−	18.2734i	−0.341754	−	0.591935i	0.643005	−	0.765862i	$-0.277688\pi$
$953$	−10.5502	−	18.2734i	−0.341754	−	0.591935i	−0.984758	+	0.173927i	$0.944354\pi$
$954$	−4.34256	+	23.8709i	−0.140596	+	0.772848i
$955$	0.492145	−	1.83671i	0.0159254	−	0.0594346i
$956$	−3.82559	+	14.2773i	−0.123728	+	0.461761i
$957$	1.84128	−	0.575075i	0.0595202	−	0.0185895i
$958$	3.44529	+	5.96741i	0.111312	+	0.192798i
$959$	25.7630	−	44.6228i	0.831929	−	1.44094i
$960$	−1.68997	−	0.379464i	−0.0545436	−	0.0122471i
$961$		−	22.8774i		−	0.737980i
$962$	3.85618	−	12.6829i	0.124328	−	0.408914i
$963$	27.8313	−	19.2638i	0.896851	−	0.620768i
$964$	14.8718	−	3.98489i	0.478989	−	0.128345i
$965$	−4.82992	−	2.78856i	−0.155481	−	0.0897669i
$966$	14.8255	−	0.607064i	0.477004	−	0.0195320i
$967$	26.3930	+	26.3930i	0.848743	+	0.848743i	0.989976	−	0.141233i	$-0.0451067\pi$
$967$	26.3930	+	26.3930i	0.848743	+	0.848743i	−0.141233	+	0.989976i	$0.545107\pi$
$968$	−10.5716	−	2.83264i	−0.339783	−	0.0910445i
$969$	1.39603	−	1.51524i	0.0448469	−	0.0486764i
$970$	−9.99765	+	9.99765i	−0.321005	+	0.321005i
$971$	−10.2052	+	5.89200i	−0.327502	+	0.189083i	−0.654732	−	0.755862i	$-0.727218\pi$
$971$	−10.2052	+	5.89200i	−0.327502	+	0.189083i	0.327230	+	0.944945i	$0.393885\pi$
$972$	15.2632	−	3.16752i	0.489569	−	0.101598i
$973$	4.30900	+	16.0814i	0.138140	+	0.515546i
$974$	−15.0106			−0.480970
$975$	−6.04425	−	1.57068i	−0.193571	−	0.0503019i
$976$	10.3452			0.331141
$977$	−11.2246	−	41.8907i	−0.359106	−	1.34020i	−0.875238	−	0.483693i	$-0.839295\pi$
$977$	−11.2246	−	41.8907i	−0.359106	−	1.34020i	0.516132	−	0.856509i	$-0.327371\pi$
$978$	−13.9747	−	22.0676i	−0.446862	−	0.705643i
$979$	1.80645	−	1.04296i	0.0577345	−	0.0333330i
$980$	1.44810	−	1.44810i	0.0462580	−	0.0462580i
$981$	16.8041	−	6.01330i	0.536514	−	0.191990i
$982$	−1.65915	−	0.444567i	−0.0529455	−	0.0141867i
$983$	37.0008	+	37.0008i	1.18014	+	1.18014i	0.979707	+	0.200435i	$0.0642355\pi$
$983$	37.0008	+	37.0008i	1.18014	+	1.18014i	0.200435	+	0.979707i	$0.435765\pi$
$984$	0.633618	+	15.4740i	0.0201990	+	0.493294i
$985$	−8.21930	−	4.74542i	−0.261889	−	0.151202i
$986$	−1.44199	+	0.386381i	−0.0459224	+	0.0123049i
$987$	−5.96099	−	3.12365i	−0.189740	−	0.0994268i
$988$	11.5268	+	7.17806i	0.366717	+	0.228364i
$989$		−	34.6846i		−	1.10291i
$990$	−0.457298	+	0.539029i	−0.0145339	+	0.0171315i
$991$	19.8833	−	34.4389i	0.631614	−	1.09399i	−0.355608	−	0.934635i	$-0.615726\pi$
$991$	19.8833	−	34.4389i	0.631614	−	1.09399i	0.987222	−	0.159352i	$-0.0509405\pi$
$992$	−1.42501	−	2.46819i	−0.0452442	−	0.0783652i
$993$	−16.8464	−	53.9391i	−0.534605	−	1.71170i
$994$	9.92042	−	37.0235i	0.314657	−	1.17431i
$995$	−6.33816	+	23.6543i	−0.200933	+	0.749893i
$996$	4.63444	+	14.8386i	0.146848	+	0.470179i
$997$	−21.5514	−	37.3281i	−0.682539	−	1.18219i	−0.974204	−	0.225671i	$-0.927543\pi$
$997$	−21.5514	−	37.3281i	−0.682539	−	1.18219i	0.291665	−	0.956521i	$-0.405791\pi$
$998$	12.2926	−	21.2914i	0.389116	−	0.673968i
$999$	17.7088	−	7.16720i	0.560283	−	0.226760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bh.b.371.4	yes	32
3.2	odd	2	inner	390.2.bh.b.371.6	yes	32
13.2	odd	12	inner	390.2.bh.b.41.6	yes	32
39.2	even	12	inner	390.2.bh.b.41.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bh.b.41.4	✓	32	39.2	even	12	inner
390.2.bh.b.41.6	yes	32	13.2	odd	12	inner
390.2.bh.b.371.4	yes	32	1.1	even	1	trivial
390.2.bh.b.371.6	yes	32	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bh (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.46331 - 0.926670i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.27383 - 1.17361i) q^{6} +(2.90548 + 0.778522i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.28257 - 2.71201i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.46331 - 0.926670i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.27383 - 1.17361i) q^{6} +(2.90548 + 0.778522i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.28257 - 2.71201i) q^{9} +(0.866025 + 0.500000i) q^{10} +(-0.227597 + 0.0609843i) q^{11} +(-0.803931 + 1.53418i) q^{12} +(2.63314 - 2.46304i) q^{13} -3.00798i q^{14} +(-0.379464 + 1.68997i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.157921 + 0.273528i) q^{17} +(-2.95156 - 0.536943i) q^{18} +(0.974755 - 3.63784i) q^{19} +(0.258819 - 0.965926i) q^{20} +(4.97306 - 1.55320i) q^{21} +(0.117813 + 0.204058i) q^{22} +(-1.42400 + 2.46643i) q^{23} +(1.68997 + 0.379464i) q^{24} -1.00000i q^{25} +(-3.06062 - 1.90593i) q^{26} +(-0.636346 - 5.15704i) q^{27} +(-2.90548 + 0.778522i) q^{28} +(-4.09336 - 2.36330i) q^{29} +(1.73060 - 0.0708632i) q^{30} +(2.01527 + 2.01527i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.276533 + 0.300146i) q^{33} +(0.223334 - 0.223334i) q^{34} +(-2.60498 + 1.50399i) q^{35} +(0.245272 + 2.98996i) q^{36} +(0.951577 + 3.55133i) q^{37} -3.76616 q^{38} +(1.57068 - 6.04425i) q^{39} -1.00000 q^{40} +(2.31421 + 8.63675i) q^{41} +(-2.78740 - 4.40161i) q^{42} +(-10.5470 + 6.08931i) q^{43} +(0.166612 - 0.166612i) q^{44} +(1.01077 + 2.82460i) q^{45} +(2.75095 + 0.737115i) q^{46} +(-0.913385 - 0.913385i) q^{47} +(-0.0708632 - 1.73060i) q^{48} +(1.77356 + 1.02396i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(0.484558 + 0.253915i) q^{51} +(-1.04884 + 3.44963i) q^{52} -8.08755i q^{53} +(-4.81662 + 1.94940i) q^{54} +(0.117813 - 0.204058i) q^{55} +(1.50399 + 2.60498i) q^{56} +(-1.94470 - 6.22657i) q^{57} +(-1.22333 + 4.56555i) q^{58} +(1.51543 - 5.65567i) q^{59} +(-0.516361 - 1.65329i) q^{60} +(5.17260 + 8.95920i) q^{61} +(1.42501 - 2.46819i) q^{62} +(5.83784 - 6.88121i) q^{63} +1.00000i q^{64} +(-0.120274 + 3.60354i) q^{65} +(0.361491 + 0.189427i) q^{66} +(-10.5440 + 2.82526i) q^{67} +(-0.273528 - 0.157921i) q^{68} +(0.201818 + 4.92874i) q^{69} +(2.12696 + 2.12696i) q^{70} +(12.3084 + 3.29804i) q^{71} +(2.82460 - 1.01077i) q^{72} +(0.383119 - 0.383119i) q^{73} +(3.18404 - 1.83831i) q^{74} +(-0.926670 - 1.46331i) q^{75} +(0.974755 + 3.63784i) q^{76} -0.708756 q^{77} +(-6.24482 + 0.0472118i) q^{78} +0.0348413 q^{79} +(0.258819 + 0.965926i) q^{80} +(-5.71005 - 6.95668i) q^{81} +(7.74350 - 4.47071i) q^{82} +(6.34642 - 6.34642i) q^{83} +(-3.53020 + 3.83164i) q^{84} +(-0.305080 - 0.0817460i) q^{85} +(8.61159 + 8.61159i) q^{86} +(-8.17986 + 0.334942i) q^{87} +(-0.204058 - 0.117813i) q^{88} +(-8.55102 + 2.29124i) q^{89} +(2.46674 - 1.70739i) q^{90} +(9.56807 - 5.10638i) q^{91} -2.84799i q^{92} +(4.81646 + 1.08148i) q^{93} +(-0.645861 + 1.11866i) q^{94} +(1.88308 + 3.26159i) q^{95} +(-1.65329 + 0.516361i) q^{96} +(-3.65939 + 13.6570i) q^{97} +(0.530043 - 1.97815i) q^{98} +(-0.126517 + 0.695462i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{6} + 4 q^{9}+O(q^{10}) \) 32 * q - 8 * q^6 + 4 * q^9	\( 32 q - 8 q^{6} + 4 q^{9} + 16 q^{13} + 4 q^{15} + 16 q^{16} + 24 q^{18} + 32 q^{19} + 36 q^{21} + 8 q^{22} - 8 q^{24} + 12 q^{30} - 24 q^{31} - 28 q^{33} - 8 q^{34} - 12 q^{36} + 16 q^{37} - 4 q^{39} - 32 q^{40} - 12 q^{42} + 48 q^{43} - 24 q^{45} + 24 q^{46} - 48 q^{49} - 16 q^{52} - 20 q^{54} + 8 q^{55} + 4 q^{57} - 24 q^{58} + 4 q^{60} + 32 q^{61} - 48 q^{63} - 48 q^{66} - 64 q^{67} - 36 q^{69} - 40 q^{73} - 12 q^{75} + 32 q^{76} + 4 q^{78} - 32 q^{79} + 16 q^{81} + 12 q^{84} + 40 q^{85} - 72 q^{87} - 48 q^{88} - 144 q^{91} + 56 q^{94} - 4 q^{96} + 112 q^{97} + 72 q^{99}+O(q^{100}) \) 32 * q - 8 * q^6 + 4 * q^9 + 16 * q^13 + 4 * q^15 + 16 * q^16 + 24 * q^18 + 32 * q^19 + 36 * q^21 + 8 * q^22 - 8 * q^24 + 12 * q^30 - 24 * q^31 - 28 * q^33 - 8 * q^34 - 12 * q^36 + 16 * q^37 - 4 * q^39 - 32 * q^40 - 12 * q^42 + 48 * q^43 - 24 * q^45 + 24 * q^46 - 48 * q^49 - 16 * q^52 - 20 * q^54 + 8 * q^55 + 4 * q^57 - 24 * q^58 + 4 * q^60 + 32 * q^61 - 48 * q^63 - 48 * q^66 - 64 * q^67 - 36 * q^69 - 40 * q^73 - 12 * q^75 + 32 * q^76 + 4 * q^78 - 32 * q^79 + 16 * q^81 + 12 * q^84 + 40 * q^85 - 72 * q^87 - 48 * q^88 - 144 * q^91 + 56 * q^94 - 4 * q^96 + 112 * q^97 + 72 * q^99

Introduction

L-functions

Modular forms

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