LMFDB - Embedded newform 48.3.l.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,3,Mod(19,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	48.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.30790526893$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 $ x^16 - 6x^14 - 4x^13 + 10x^12 + 56x^11 + 88x^10 - 128x^9 - 496x^8 - 512x^7 + 1408x^6 + 3584x^5 + 2560x^4 - 4096x^3 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Root			$1.80398 + 0.863518i$ of defining polynomial
Character	$\chi$	$=$	48.43
Dual form			48.3.l.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.80398 + 0.863518i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50867 - 3.11554i) q^{4} +(6.49473 + 6.49473i) q^{5} +(3.26700 + 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 + 7.78664i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.80398 + 0.863518i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50867 - 3.11554i) q^{4} +(6.49473 + 6.49473i) q^{5} +(3.26700 + 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 + 7.78664i) q^{8} +3.00000i q^{9} +(-17.3247 - 6.10803i) q^{10} +(4.31091 - 4.31091i) q^{11} +(-6.88822 + 0.743251i) q^{12} +(4.06281 - 4.06281i) q^{13} +(-7.11259 + 3.40462i) q^{14} -15.9088i q^{15} +(-3.41312 - 15.6317i) q^{16} -14.5538 q^{17} +(-2.59055 - 5.41193i) q^{18} +(4.94805 + 4.94805i) q^{19} +(36.5277 - 3.94140i) q^{20} +(-4.82883 - 4.82883i) q^{21} +(-4.05424 + 11.4993i) q^{22} -43.6717 q^{23} +(11.7844 - 7.28891i) q^{24} +59.3629i q^{25} +(-3.82091 + 10.8375i) q^{26} +(3.67423 - 3.67423i) q^{27} +(9.89101 - 12.2837i) q^{28} +(25.0979 - 25.0979i) q^{29} +(13.7375 + 28.6991i) q^{30} -32.5024i q^{31} +(19.6555 + 25.2520i) q^{32} -10.5595 q^{33} +(26.2547 - 12.5675i) q^{34} +(25.6069 + 25.6069i) q^{35} +(9.34661 + 7.52602i) q^{36} +(4.14345 + 4.14345i) q^{37} +(-13.1989 - 4.65344i) q^{38} -9.95180 q^{39} +(-62.4917 + 38.6525i) q^{40} -55.3348i q^{41} +(12.8809 + 4.54133i) q^{42} +(-16.1189 + 16.1189i) q^{43} +(-2.61613 - 24.2455i) q^{44} +(-19.4842 + 19.4842i) q^{45} +(78.7828 - 37.7113i) q^{46} +7.92420i q^{47} +(-14.9647 + 23.3251i) q^{48} -33.4549 q^{49} +(-51.2610 - 107.089i) q^{50} +(17.8247 + 17.8247i) q^{51} +(-2.46556 - 22.8501i) q^{52} +(-31.5748 - 31.5748i) q^{53} +(-3.45547 + 9.80101i) q^{54} +55.9964 q^{55} +(-7.23597 + 30.7006i) q^{56} -12.1202i q^{57} +(-23.6036 + 66.9485i) q^{58} +(-49.7172 + 49.7172i) q^{59} +(-49.5643 - 39.9099i) q^{60} +(44.4711 - 44.4711i) q^{61} +(28.0664 + 58.6336i) q^{62} +11.8282i q^{63} +(-57.2636 - 28.5812i) q^{64} +52.7736 q^{65} +(19.0492 - 9.11834i) q^{66} +(-1.64068 - 1.64068i) q^{67} +(-36.5107 + 45.3429i) q^{68} +(53.4867 + 53.4867i) q^{69} +(-68.3064 - 24.0823i) q^{70} +24.1145 q^{71} +(-23.3599 - 5.50581i) q^{72} -10.7741i q^{73} +(-11.0526 - 3.89675i) q^{74} +(72.7044 - 72.7044i) q^{75} +(27.8288 - 3.00278i) q^{76} +(16.9967 - 16.9967i) q^{77} +(17.9528 - 8.59356i) q^{78} +72.0517i q^{79} +(79.3565 - 123.691i) q^{80} -9.00000 q^{81} +(47.7826 + 99.8227i) q^{82} +(42.0499 + 42.0499i) q^{83} +(-27.1584 + 2.93044i) q^{84} +(-94.5229 - 94.5229i) q^{85} +(15.1592 - 42.9971i) q^{86} -61.4770 q^{87} +(25.6558 + 41.4792i) q^{88} +28.9853i q^{89} +(18.3241 - 51.9740i) q^{90} +(16.0185 - 16.0185i) q^{91} +(-109.558 + 136.061i) q^{92} +(-39.8071 + 39.8071i) q^{93} +(-6.84269 - 14.2951i) q^{94} +64.2724i q^{95} +(6.85432 - 55.0002i) q^{96} -54.2698 q^{97} +(60.3519 - 28.8889i) q^{98} +(12.9327 + 12.9327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) $ 16 * q + 12 * q^4 - 12 * q^8	$ 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) $ 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.80398	+	0.863518i	−0.901989	+	0.431759i
$2$	−1.80398	+	0.863518i	−0.901989	+	0.431759i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$	2.50867	−	3.11554i	0.627168	−	0.778884i
$5$	6.49473	+	6.49473i	1.29895	+	1.29895i	0.929089	+	0.369856i	$0.120593\pi$
$5$	6.49473	+	6.49473i	1.29895	+	1.29895i	0.369856	+	0.929089i	$0.379407\pi$
$6$	3.26700	+	1.15182i	0.544500	+	0.191971i
$7$	3.94273			0.563247			0.281623	−	0.959525i	$-0.409127\pi$
$7$	3.94273			0.563247			0.281623	+	0.959525i	$0.409127\pi$
$8$	−1.83527	+	7.78664i	−0.229409	+	0.973330i
$9$			3.00000i			0.333333i
$10$	−17.3247	−	6.10803i	−1.73247	−	0.610803i
$11$	4.31091	−	4.31091i	0.391901	−	0.391901i	−0.483464	−	0.875364i	$-0.660621\pi$
$11$	4.31091	−	4.31091i	0.391901	−	0.391901i	0.875364	+	0.483464i	$0.160621\pi$
$12$	−6.88822	+	0.743251i	−0.574018	+	0.0619376i
$13$	4.06281	−	4.06281i	0.312524	−	0.312524i	−0.533363	−	0.845887i	$-0.679072\pi$
$13$	4.06281	−	4.06281i	0.312524	−	0.312524i	0.845887	+	0.533363i	$0.179072\pi$
$14$	−7.11259	+	3.40462i	−0.508042	+	0.243187i
$15$		−	15.9088i		−	1.06058i
$16$	−3.41312	−	15.6317i	−0.213320	−	0.976982i
$17$	−14.5538			−0.856106			−0.428053	−	0.903754i	$-0.640800\pi$
$17$	−14.5538			−0.856106			−0.428053	+	0.903754i	$0.640800\pi$
$18$	−2.59055	−	5.41193i	−0.143920	−	0.300663i
$19$	4.94805	+	4.94805i	0.260423	+	0.260423i	0.825226	−	0.564803i	$-0.191048\pi$
$19$	4.94805	+	4.94805i	0.260423	+	0.260423i	−0.564803	+	0.825226i	$0.691048\pi$
$20$	36.5277	−	3.94140i	1.82638	−	0.197070i
$21$	−4.82883	−	4.82883i	−0.229945	−	0.229945i
$22$	−4.05424	+	11.4993i	−0.184284	+	0.522697i
$23$	−43.6717			−1.89877			−0.949385	−	0.314115i	$-0.898292\pi$
$23$	−43.6717			−1.89877			−0.949385	+	0.314115i	$0.898292\pi$
$24$	11.7844	−	7.28891i	0.491016	−	0.303705i
$25$			59.3629i			2.37452i
$26$	−3.82091	+	10.8375i	−0.146958	+	0.416828i
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	9.89101	−	12.2837i	0.353250	−	0.438704i
$29$	25.0979	−	25.0979i	0.865445	−	0.865445i	−0.126519	−	0.991964i	$-0.540381\pi$
$29$	25.0979	−	25.0979i	0.865445	−	0.865445i	0.991964	+	0.126519i	$0.0403806\pi$
$30$	13.7375	+	28.6991i	0.457917	+	0.956635i
$31$		−	32.5024i		−	1.04846i	−0.851576	−	0.524232i	$-0.824352\pi$
$31$		−	32.5024i		−	1.04846i	0.851576	−	0.524232i	$-0.175648\pi$
$32$	19.6555	+	25.2520i	0.614233	+	0.789125i
$33$	−10.5595			−0.319986
$34$	26.2547	−	12.5675i	0.772198	−	0.369631i
$35$	25.6069	+	25.6069i	0.731627	+	0.731627i
$36$	9.34661	+	7.52602i	0.259628	+	0.209056i
$37$	4.14345	+	4.14345i	0.111985	+	0.111985i	0.760879	−	0.648894i	$-0.224768\pi$
$37$	4.14345	+	4.14345i	0.111985	+	0.111985i	−0.648894	+	0.760879i	$0.724768\pi$
$38$	−13.1989	−	4.65344i	−0.347339	−	0.122459i
$39$	−9.95180			−0.255174
$40$	−62.4917	+	38.6525i	−1.56229	+	0.966313i
$41$		−	55.3348i		−	1.34963i	−0.737987	−	0.674814i	$-0.764224\pi$
$41$		−	55.3348i		−	1.34963i	0.737987	−	0.674814i	$-0.235776\pi$
$42$	12.8809	+	4.54133i	0.306688	+	0.108127i
$43$	−16.1189	+	16.1189i	−0.374858	+	0.374858i	−0.869243	−	0.494385i	$-0.835393\pi$
$43$	−16.1189	+	16.1189i	−0.374858	+	0.374858i	0.494385	+	0.869243i	$0.335393\pi$
$44$	−2.61613	−	24.2455i	−0.0594574	−	0.551033i
$45$	−19.4842	+	19.4842i	−0.432982	+	0.432982i
$46$	78.7828	−	37.7113i	1.71267	−	0.819811i
$47$			7.92420i			0.168600i	0.996440	+	0.0843001i	$0.0268654\pi$
$47$			7.92420i			0.168600i	−0.996440	+	0.0843001i	$0.973135\pi$
$48$	−14.9647	+	23.3251i	−0.311764	+	0.485939i
$49$	−33.4549			−0.682753
$50$	−51.2610	−	107.089i	−1.02522	−	2.14179i
$51$	17.8247	+	17.8247i	0.349504	+	0.349504i
$52$	−2.46556	−	22.8501i	−0.0474147	−	0.439424i
$53$	−31.5748	−	31.5748i	−0.595750	−	0.595750i	0.343429	−	0.939179i	$-0.388412\pi$
$53$	−31.5748	−	31.5748i	−0.595750	−	0.595750i	−0.939179	+	0.343429i	$0.888412\pi$
$54$	−3.45547	+	9.80101i	−0.0639902	+	0.181500i
$55$	55.9964			1.01812
$56$	−7.23597	+	30.7006i	−0.129214	+	0.548225i
$57$		−	12.1202i		−	0.212635i
$58$	−23.6036	+	66.9485i	−0.406958	+	1.15429i
$59$	−49.7172	+	49.7172i	−0.842665	+	0.842665i	−0.989205	−	0.146540i	$-0.953186\pi$
$59$	−49.7172	+	49.7172i	−0.842665	+	0.842665i	0.146540	+	0.989205i	$0.453186\pi$
$60$	−49.5643	−	39.9099i	−0.826072	−	0.665165i
$61$	44.4711	−	44.4711i	0.729035	−	0.729035i	−0.241393	−	0.970427i	$-0.577604\pi$
$61$	44.4711	−	44.4711i	0.729035	−	0.729035i	0.970427	+	0.241393i	$0.0776043\pi$
$62$	28.0664	+	58.6336i	0.452684	+	0.945703i
$63$			11.8282i			0.187749i
$64$	−57.2636	−	28.5812i	−0.894743	−	0.446581i
$65$	52.7736			0.811902
$66$	19.0492	−	9.11834i	0.288624	−	0.138157i
$67$	−1.64068	−	1.64068i	−0.0244878	−	0.0244878i	0.694757	−	0.719245i	$-0.255512\pi$
$67$	−1.64068	−	1.64068i	−0.0244878	−	0.0244878i	−0.719245	+	0.694757i	$0.755512\pi$
$68$	−36.5107	+	45.3429i	−0.536922	+	0.666807i
$69$	53.4867	+	53.4867i	0.775170	+	0.775170i
$70$	−68.3064	−	24.0823i	−0.975805	−	0.344033i
$71$	24.1145			0.339641			0.169821	−	0.985475i	$-0.445681\pi$
$71$	24.1145			0.339641			0.169821	+	0.985475i	$0.445681\pi$
$72$	−23.3599	−	5.50581i	−0.324443	−	0.0764696i
$73$		−	10.7741i		−	0.147591i	−0.997273	−	0.0737955i	$-0.976489\pi$
$73$		−	10.7741i		−	0.147591i	0.997273	−	0.0737955i	$-0.0235112\pi$
$74$	−11.0526	−	3.89675i	−0.149360	−	0.0526588i
$75$	72.7044	−	72.7044i	0.969392	−	0.969392i
$76$	27.8288	−	3.00278i	0.366169	−	0.0395103i
$77$	16.9967	−	16.9967i	0.220737	−	0.220737i
$78$	17.9528	−	8.59356i	0.230165	−	0.110174i
$79$			72.0517i			0.912047i	0.889968	+	0.456024i	$0.150727\pi$
$79$			72.0517i			0.912047i	−0.889968	+	0.456024i	$0.849273\pi$
$80$	79.3565	−	123.691i	0.991956	−	1.54614i
$81$	−9.00000			−0.111111
$82$	47.7826	+	99.8227i	0.582714	+	1.21735i
$83$	42.0499	+	42.0499i	0.506625	+	0.506625i	0.913489	−	0.406864i	$-0.133378\pi$
$83$	42.0499	+	42.0499i	0.506625	+	0.506625i	−0.406864	+	0.913489i	$0.633378\pi$
$84$	−27.1584	+	2.93044i	−0.323314	+	0.0348861i
$85$	−94.5229	−	94.5229i	−1.11203	−	1.11203i
$86$	15.1592	−	42.9971i	0.176269	−	0.499966i
$87$	−61.4770			−0.706633
$88$	25.6558	+	41.4792i	0.291543	+	0.471354i
$89$			28.9853i			0.325677i	0.986653	+	0.162839i	$0.0520650\pi$
$89$			28.9853i			0.325677i	−0.986653	+	0.162839i	$0.947935\pi$
$90$	18.3241	−	51.9740i	0.203601	−	0.577488i
$91$	16.0185	−	16.0185i	0.176028	−	0.176028i
$92$	−109.558	+	136.061i	−1.19085	+	1.47892i
$93$	−39.8071	+	39.8071i	−0.428034	+	0.428034i
$94$	−6.84269	−	14.2951i	−0.0727946	−	0.152075i
$95$			64.2724i			0.676552i
$96$	6.85432	−	55.0002i	0.0713992	−	0.572918i
$97$	−54.2698			−0.559483			−0.279741	−	0.960075i	$-0.590249\pi$
$97$	−54.2698			−0.559483			−0.279741	+	0.960075i	$0.590249\pi$
$98$	60.3519	−	28.8889i	0.615836	−	0.294785i
$99$	12.9327	+	12.9327i	0.130634	+	0.130634i
$100$	184.947	+	148.922i	1.84947	+	1.48922i
$101$	57.0829	+	57.0829i	0.565177	+	0.565177i	0.930773	−	0.365597i	$-0.119135\pi$
$101$	57.0829	+	57.0829i	0.565177	+	0.565177i	−0.365597	+	0.930773i	$0.619135\pi$
$102$	−47.5473	−	16.7634i	−0.466150	−	0.164347i
$103$	39.3048			0.381600			0.190800	−	0.981629i	$-0.438892\pi$
$103$	39.3048			0.381600			0.190800	+	0.981629i	$0.438892\pi$
$104$	24.1793	+	39.0920i	0.232493	+	0.375884i
$105$		−	62.7239i		−	0.597371i
$106$	84.2255	+	29.6948i	0.794581	+	0.280140i
$107$	25.6981	−	25.6981i	0.240169	−	0.240169i	−0.576751	−	0.816920i	$-0.695680\pi$
$107$	25.6981	−	25.6981i	0.240169	−	0.240169i	0.816920	+	0.576751i	$0.195680\pi$
$108$	−2.22975	−	20.6647i	−0.0206459	−	0.191339i
$109$	−9.66133	+	9.66133i	−0.0886360	+	0.0886360i	−0.750035	−	0.661399i	$-0.769963\pi$
$109$	−9.66133	+	9.66133i	−0.0886360	+	0.0886360i	0.661399	+	0.750035i	$0.269963\pi$
$110$	−101.016	+	48.3539i	−0.918329	+	0.439581i
$111$		−	10.1493i		−	0.0914355i
$112$	−13.4570	−	61.6316i	−0.120152	−	0.550282i
$113$	64.2927			0.568962			0.284481	−	0.958682i	$-0.408179\pi$
$113$	64.2927			0.568962			0.284481	+	0.958682i	$0.408179\pi$
$114$	10.4660	+	21.8645i	0.0918070	+	0.191794i
$115$	−283.636	−	283.636i	−2.46640	−	2.46640i
$116$	−15.2310	−	141.156i	−0.131301	−	1.21686i
$117$	12.1884	+	12.1884i	0.104175	+	0.104175i
$118$	46.7571	−	132.620i	0.396246	−	1.12390i
$119$	−57.3816			−0.482199
$120$	123.876	+	29.1969i	1.03230	+	0.243307i
$121$			83.8321i			0.692827i
$122$	−41.8233	+	118.627i	−0.342814	+	0.972348i
$123$	−67.7710	+	67.7710i	−0.550984	+	0.550984i
$124$	−101.262	−	81.5379i	−0.816632	−	0.657563i
$125$	−223.178	+	223.178i	−1.78542	+	1.78542i
$126$	−10.2138	−	21.3378i	−0.0810623	−	0.169347i
$127$		−	129.668i		−	1.02101i	−0.859875	−	0.510504i	$-0.829459\pi$
$127$		−	129.668i		−	1.02101i	0.859875	−	0.510504i	$-0.170541\pi$
$128$	127.983	+	2.11172i	0.999864	+	0.0164978i
$129$	39.4830			0.306070
$130$	−95.2025	+	45.5710i	−0.732327	+	0.350546i
$131$	−118.504	−	118.504i	−0.904613	−	0.904613i	0.0912183	−	0.995831i	$-0.470924\pi$
$131$	−118.504	−	118.504i	−0.904613	−	0.904613i	−0.995831	+	0.0912183i	$0.970924\pi$
$132$	−26.4904	+	32.8986i	−0.200685	+	0.249232i
$133$	19.5088	+	19.5088i	0.146683	+	0.146683i
$134$	4.37651	+	1.54299i	0.0326605	+	0.0115149i
$135$	47.7263			0.353528
$136$	26.7102	−	113.325i	0.196398	−	0.833273i
$137$		−	157.472i		−	1.14943i	−0.818353	−	0.574716i	$-0.805112\pi$
$137$		−	157.472i		−	1.14943i	0.818353	−	0.574716i	$-0.194888\pi$
$138$	−142.676	−	50.3021i	−1.03388	−	0.364508i
$139$	−118.943	+	118.943i	−0.855703	+	0.855703i	−0.990829	−	0.135125i	$-0.956856\pi$
$139$	−118.943	+	118.943i	−0.855703	+	0.855703i	0.135125	+	0.990829i	$0.456856\pi$
$140$	144.019	−	15.5399i	1.02871	−	0.110999i
$141$	9.70513	−	9.70513i	0.0688307	−	0.0688307i
$142$	−43.5021	+	20.8233i	−0.306353	+	0.146643i
$143$		−	35.0288i		−	0.244957i
$144$	46.8952	−	10.2394i	0.325661	−	0.0711066i
$145$	326.008			2.24833
$146$	9.30367	+	19.4363i	0.0637238	+	0.133125i
$147$	40.9737	+	40.9737i	0.278733	+	0.278733i
$148$	23.3036	−	2.51450i	0.157457	−	0.0169899i
$149$	99.5402	+	99.5402i	0.668055	+	0.668055i	0.957266	−	0.289210i	$-0.0933927\pi$
$149$	99.5402	+	99.5402i	0.668055	+	0.668055i	−0.289210	+	0.957266i	$0.593393\pi$
$150$	−68.3756	+	193.939i	−0.455837	+	1.29293i
$151$	273.705			1.81262			0.906308	−	0.422618i	$-0.138889\pi$
$151$	273.705			1.81262			0.906308	+	0.422618i	$0.138889\pi$
$152$	−47.6097	+	29.4477i	−0.313221	+	0.193735i
$153$		−	43.6614i		−	0.285369i
$154$	−15.9848	+	45.3387i	−0.103797	+	0.294407i
$155$	211.094	−	211.094i	1.36190	−	1.36190i
$156$	−24.9658	+	31.0052i	−0.160037	+	0.198751i
$157$	−75.8792	+	75.8792i	−0.483307	+	0.483307i	−0.906186	−	0.422879i	$-0.861019\pi$
$157$	−75.8792	+	75.8792i	−0.483307	+	0.483307i	0.422879	+	0.906186i	$0.361019\pi$
$158$	−62.2180	−	129.980i	−0.393785	−	0.822657i
$159$			77.3420i			0.486428i
$160$	−36.3479	+	291.662i	−0.227175	+	1.82288i
$161$	−172.186			−1.06948
$162$	16.2358	−	7.77166i	0.100221	−	0.0479732i
$163$	177.242	+	177.242i	1.08737	+	1.08737i	0.995798	+	0.0915766i	$0.0291906\pi$
$163$	177.242	+	177.242i	1.08737	+	1.08737i	0.0915766	+	0.995798i	$0.470809\pi$
$164$	−172.397	−	138.817i	−1.05120	−	0.846444i
$165$	−68.5812	−	68.5812i	−0.415644	−	0.415644i
$166$	−112.168	−	39.5462i	−0.675710	−	0.238230i
$167$	61.6774			0.369326			0.184663	−	0.982802i	$-0.440881\pi$
$167$	61.6774			0.369326			0.184663	+	0.982802i	$0.440881\pi$
$168$	46.4626	−	28.7382i	0.276563	−	0.171061i
$169$			135.987i			0.804658i
$170$	252.140	+	88.8950i	1.48317	+	0.522912i
$171$	−14.8441	+	14.8441i	−0.0868078	+	0.0868078i
$172$	9.78193	+	90.6560i	0.0568717	+	0.527069i
$173$	69.7012	−	69.7012i	0.402897	−	0.402897i	−0.476355	−	0.879253i	$-0.658042\pi$
$173$	69.7012	−	69.7012i	0.402897	−	0.402897i	0.879253	+	0.476355i	$0.158042\pi$
$174$	110.903	−	53.0865i	0.637375	−	0.305095i
$175$			234.052i			1.33744i
$176$	−82.1006	−	52.6733i	−0.466481	−	0.299280i
$177$	121.782			0.688033
$178$	−25.0293	−	52.2888i	−0.140614	−	0.293757i
$179$	43.6228	+	43.6228i	0.243703	+	0.243703i	0.818380	−	0.574677i	$-0.194872\pi$
$179$	43.6228	+	43.6228i	0.243703	+	0.243703i	−0.574677	+	0.818380i	$0.694872\pi$
$180$	11.8242	+	109.583i	0.0656900	+	0.608795i
$181$	−44.7291	−	44.7291i	−0.247122	−	0.247122i	0.572666	−	0.819788i	$-0.305909\pi$
$181$	−44.7291	−	44.7291i	−0.247122	−	0.247122i	−0.819788	+	0.572666i	$0.805909\pi$
$182$	−15.0648	+	42.7294i	−0.0827736	+	0.234777i
$183$	−108.932			−0.595254
$184$	80.1494	−	340.056i	0.435595	−	1.84813i
$185$			53.8211i			0.290925i
$186$	37.4370	−	106.185i	0.201274	−	0.570889i
$187$	−62.7401	+	62.7401i	−0.335509	+	0.335509i
$188$	24.6881	+	19.8792i	0.131320	+	0.105741i
$189$	14.4865	−	14.4865i	0.0766482	−	0.0766482i
$190$	−55.5004	−	115.946i	−0.292107	−	0.610242i
$191$		−	171.759i		−	0.899263i	−0.893214	−	0.449632i	$-0.851555\pi$
$191$		−	171.759i		−	0.899263i	0.893214	−	0.449632i	$-0.148445\pi$
$192$	35.1286	+	105.138i	0.182961	+	0.547593i
$193$	−215.384			−1.11598			−0.557989	−	0.829848i	$-0.688427\pi$
$193$	−215.384			−1.11598			−0.557989	+	0.829848i	$0.688427\pi$
$194$	97.9016	−	46.8630i	0.504647	−	0.241562i
$195$	−64.6342	−	64.6342i	−0.331458	−	0.331458i
$196$	−83.9274	+	104.230i	−0.428201	+	0.531785i
$197$	−18.3354	−	18.3354i	−0.0930731	−	0.0930731i	0.659037	−	0.752110i	$-0.270964\pi$
$197$	−18.3354	−	18.3354i	−0.0930731	−	0.0930731i	−0.752110	+	0.659037i	$0.770964\pi$
$198$	−34.4980	−	12.1627i	−0.174232	−	0.0614279i
$199$	−227.112			−1.14127			−0.570634	−	0.821205i	$-0.693302\pi$
$199$	−227.112			−1.14127			−0.570634	+	0.821205i	$0.693302\pi$
$200$	−462.238	−	108.947i	−2.31119	−	0.544735i
$201$			4.01883i			0.0199942i
$202$	−152.268	−	53.6842i	−0.753804	−	0.265763i
$203$	98.9542	−	98.9542i	0.487459	−	0.487459i
$204$	100.250	−	10.8171i	0.491420	−	0.0530251i
$205$	359.384	−	359.384i	1.75309	−	1.75309i
$206$	−70.9051	+	33.9404i	−0.344199	+	0.164759i
$207$		−	131.015i		−	0.632923i
$208$	−77.3755	−	49.6418i	−0.371998	−	0.238663i
$209$	42.6612			0.204120
$210$	54.1632	+	113.153i	0.257920	+	0.538822i
$211$	190.206	+	190.206i	0.901451	+	0.901451i	0.995562	−	0.0941112i	$-0.0300009\pi$
$211$	190.206	+	190.206i	0.901451	+	0.901451i	−0.0941112	+	0.995562i	$0.530001\pi$
$212$	−177.583	+	19.1615i	−0.837656	+	0.0903845i
$213$	−29.5342	−	29.5342i	−0.138658	−	0.138658i
$214$	−24.1680	+	68.5496i	−0.112935	+	0.320325i
$215$	−209.375			−0.973839
$216$	21.8667	+	35.3532i	0.101235	+	0.163672i
$217$		−	128.148i		−	0.590544i
$218$	9.08609	−	25.7716i	0.0416793	−	0.118218i
$219$	−13.1956	+	13.1956i	−0.0602538	+	0.0602538i
$220$	140.477	−	174.459i	0.638530	−	0.792994i
$221$	−59.1293	+	59.1293i	−0.267553	+	0.267553i
$222$	8.76414	+	18.3092i	0.0394781	+	0.0824738i
$223$			154.401i			0.692379i	0.938165	+	0.346190i	$0.112525\pi$
$223$			154.401i			0.692379i	−0.938165	+	0.346190i	$0.887475\pi$
$224$	77.4961	+	99.5617i	0.345965	+	0.444472i
$225$	−178.089			−0.791506
$226$	−115.983	+	55.5179i	−0.513197	+	0.245654i
$227$	−36.8204	−	36.8204i	−0.162204	−	0.162204i	0.621338	−	0.783543i	$-0.286589\pi$
$227$	−36.8204	−	36.8204i	−0.162204	−	0.162204i	−0.783543	+	0.621338i	$0.786589\pi$
$228$	−37.7609	−	30.4056i	−0.165618	−	0.133358i
$229$	17.9692	+	17.9692i	0.0784683	+	0.0784683i	0.745252	−	0.666783i	$-0.232329\pi$
$229$	17.9692	+	17.9692i	0.0784683	+	0.0784683i	−0.666783	+	0.745252i	$0.732329\pi$
$230$	756.597	+	266.748i	3.28955	+	1.15977i
$231$	−41.6333			−0.180231
$232$	149.367	+	241.490i	0.643823	+	1.04090i
$233$			167.669i			0.719608i	0.933028	+	0.359804i	$0.117156\pi$
$233$			167.669i			0.719608i	−0.933028	+	0.359804i	$0.882844\pi$
$234$	−32.5126	−	11.4627i	−0.138943	−	0.0489860i
$235$	−51.4655	+	51.4655i	−0.219002	+	0.219002i
$236$	30.1715	+	279.620i	0.127845	+	1.18483i
$237$	88.2450	−	88.2450i	0.372342	−	0.372342i
$238$	103.515	−	49.5501i	0.434938	−	0.208194i
$239$			29.7509i			0.124481i	0.998061	+	0.0622403i	$0.0198245\pi$
$239$			29.7509i			0.124481i	−0.998061	+	0.0622403i	$0.980175\pi$
$240$	−248.681	+	54.2985i	−1.03617	+	0.226244i
$241$	−107.373			−0.445531			−0.222766	−	0.974872i	$-0.571508\pi$
$241$	−107.373			−0.445531			−0.222766	+	0.974872i	$0.571508\pi$
$242$	−72.3905	−	151.231i	−0.299134	−	0.624923i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	−26.9878	−	250.115i	−0.110606	−	1.02506i
$245$	−217.280	−	217.280i	−0.886859	−	0.886859i
$246$	63.7359	−	180.779i	0.259089	−	0.734873i
$247$	40.2059			0.162777
$248$	253.084	+	59.6507i	1.02050	+	0.240527i
$249$		−	103.001i		−	0.413658i
$250$	209.890	−	595.326i	0.839559	−	2.38130i
$251$	−342.946	+	342.946i	−1.36632	+	1.36632i	−0.500697	+	0.865623i	$0.666923\pi$
$251$	−342.946	+	342.946i	−1.36632	+	1.36632i	−0.865623	+	0.500697i	$0.833077\pi$
$252$	36.8511	+	29.6730i	0.146235	+	0.117750i
$253$	−188.265	+	188.265i	−0.744130	+	0.744130i
$254$	111.971	+	233.918i	0.440829	+	0.920938i
$255$			231.533i			0.907972i
$256$	−232.701	+	106.706i	−0.908989	+	0.416819i
$257$	−393.565			−1.53138			−0.765691	−	0.643209i	$-0.777603\pi$
$257$	−393.565			−1.53138			−0.765691	+	0.643209i	$0.777603\pi$
$258$	−71.2265	+	34.0943i	−0.276072	+	0.132149i
$259$	16.3365	+	16.3365i	0.0630753	+	0.0630753i
$260$	132.392	−	164.418i	0.509199	−	0.632377i
$261$	75.2937	+	75.2937i	0.288482	+	0.288482i
$262$	316.110	+	111.449i	1.20653	+	0.425376i
$263$	413.800			1.57338			0.786692	−	0.617346i	$-0.211792\pi$
$263$	413.800			1.57338			0.786692	+	0.617346i	$0.211792\pi$
$264$	19.3796	−	82.2233i	0.0734076	−	0.311452i
$265$		−	410.139i		−	1.54769i
$266$	−52.0396	−	18.3472i	−0.195638	−	0.0689746i
$267$	35.4995	−	35.4995i	0.132957	−	0.132957i
$268$	−9.22752	+	0.995666i	−0.0344311	+	0.00371517i
$269$	165.389	−	165.389i	0.614830	−	0.614830i	−0.329371	−	0.944201i	$-0.606837\pi$
$269$	165.389	−	165.389i	0.614830	−	0.614830i	0.944201	+	0.329371i	$0.106837\pi$
$270$	−86.0972	+	41.2125i	−0.318878	+	0.152639i
$271$		−	309.821i		−	1.14325i	−0.820514	−	0.571626i	$-0.806313\pi$
$271$		−	309.821i		−	1.14325i	0.820514	−	0.571626i	$-0.193687\pi$
$272$	49.6738	+	227.501i	0.182624	+	0.836400i
$273$	−39.2372			−0.143726
$274$	135.980	+	284.076i	0.496278	+	1.03678i
$275$	255.908	+	255.908i	0.930575	+	0.930575i
$276$	300.820	−	32.4590i	1.08993	−	0.117605i
$277$	157.397	+	157.397i	0.568221	+	0.568221i	0.931630	−	0.363409i	$-0.118387\pi$
$277$	157.397	+	157.397i	0.568221	+	0.568221i	−0.363409	+	0.931630i	$0.618387\pi$
$278$	111.861	−	317.279i	0.402377	−	1.14129i
$279$	97.5071			0.349488
$280$	−246.388	+	152.396i	−0.879956	+	0.544273i
$281$			411.141i			1.46313i	0.681769	+	0.731567i	$0.261211\pi$
$281$			411.141i			1.46313i	−0.681769	+	0.731567i	$0.738789\pi$
$282$	−9.12729	+	25.8884i	−0.0323663	+	0.0918028i
$283$	343.521	−	343.521i	1.21385	−	1.21385i	0.244106	−	0.969748i	$-0.421505\pi$
$283$	343.521	−	343.521i	1.21385	−	1.21385i	0.969748	−	0.244106i	$-0.0784946\pi$
$284$	60.4955	−	75.1297i	0.213012	−	0.264541i
$285$	78.7173	−	78.7173i	0.276201	−	0.276201i
$286$	30.2480	+	63.1912i	0.105762	+	0.220948i
$287$		−	218.170i		−	0.760174i
$288$	−75.7560	+	58.9664i	−0.263042	+	0.204744i
$289$	−77.1870			−0.267083
$290$	−588.111	+	281.514i	−2.02797	+	0.970737i
$291$	66.4667	+	66.4667i	0.228408	+	0.228408i
$292$	−33.5672	−	27.0288i	−0.114956	−	0.0925644i
$293$	35.1386	+	35.1386i	0.119927	+	0.119927i	0.764523	−	0.644596i	$-0.222975\pi$
$293$	35.1386	+	35.1386i	0.119927	+	0.119927i	−0.644596	+	0.764523i	$0.722975\pi$
$294$	−109.297	−	38.5341i	−0.371759	−	0.131069i
$295$	−645.799			−2.18915
$296$	−39.8679	+	24.6592i	−0.134689	+	0.0833081i
$297$		−	31.6786i		−	0.106662i
$298$	−265.523	−	93.6136i	−0.891017	−	0.314140i
$299$	−177.430	+	177.430i	−0.593410	+	0.593410i
$300$	−44.1215	−	408.905i	−0.147072	−	1.36302i
$301$	−63.5524	+	63.5524i	−0.211137	+	0.211137i
$302$	−493.758	+	236.349i	−1.63496	+	0.782613i
$303$		−	139.824i		−	0.461465i
$304$	60.4582	−	94.2347i	0.198876	−	0.309983i
$305$	577.655			1.89395
$306$	37.7024	+	78.7642i	0.123210	+	0.257399i
$307$	−16.4432	−	16.4432i	−0.0535609	−	0.0535609i	0.679819	−	0.733380i	$-0.262058\pi$
$307$	−16.4432	−	16.4432i	−0.0535609	−	0.0535609i	−0.733380	+	0.679819i	$0.762058\pi$
$308$	−10.3147	−	95.5932i	−0.0334892	−	0.310368i
$309$	−48.1384	−	48.1384i	−0.155788	−	0.155788i
$310$	−198.526	+	563.093i	−0.640405	+	1.81643i
$311$	39.8016			0.127980			0.0639898	−	0.997951i	$-0.479618\pi$
$311$	39.8016			0.127980			0.0639898	+	0.997951i	$0.479618\pi$
$312$	18.2643	−	77.4911i	0.0585393	−	0.248369i
$313$			431.885i			1.37982i	0.723894	+	0.689911i	$0.242351\pi$
$313$			431.885i			1.37982i	−0.723894	+	0.689911i	$0.757649\pi$
$314$	71.3613	−	202.407i	0.227265	−	0.644610i
$315$	−76.8208	+	76.8208i	−0.243876	+	0.243876i
$316$	224.480	+	180.754i	0.710379	+	0.572007i
$317$	255.063	−	255.063i	0.804615	−	0.804615i	−0.179198	−	0.983813i	$-0.557350\pi$
$317$	255.063	−	255.063i	0.804615	−	0.804615i	0.983813	+	0.179198i	$0.0573503\pi$
$318$	−66.7862	−	139.523i	−0.210020	−	0.438753i
$319$		−	216.390i		−	0.678337i
$320$	−186.284	−	557.538i	−0.582138	−	1.74231i
$321$	−62.9472			−0.196097
$322$	310.619	−	148.685i	0.964656	−	0.461756i
$323$	−72.0128	−	72.0128i	−0.222950	−	0.222950i
$324$	−22.5781	+	28.0398i	−0.0696854	+	0.0865426i
$325$	241.180	+	241.180i	0.742092	+	0.742092i
$326$	−472.792	−	166.689i	−1.45028	−	0.511316i
$327$	23.6653			0.0723710
$328$	430.872	+	101.554i	1.31363	+	0.309617i
$329$			31.2430i			0.0949635i
$330$	182.940	+	64.4979i	0.554364	+	0.195448i
$331$	205.897	−	205.897i	0.622045	−	0.622045i	−0.324009	−	0.946054i	$-0.605031\pi$
$331$	205.897	−	205.897i	0.622045	−	0.622045i	0.946054	+	0.324009i	$0.105031\pi$
$332$	236.497	−	25.5185i	0.712341	−	0.0768628i
$333$	−12.4303	+	12.4303i	−0.0373284	+	0.0373284i
$334$	−111.265	+	53.2596i	−0.333128	+	0.159460i
$335$		−	21.3115i		−	0.0636165i
$336$	−59.0016	+	91.9644i	−0.175600	+	0.273703i
$337$	45.7312			0.135701			0.0678504	−	0.997696i	$-0.478386\pi$
$337$	45.7312			0.135701			0.0678504	+	0.997696i	$0.478386\pi$
$338$	−117.427	−	245.318i	−0.347418	−	0.725793i
$339$	−78.7421	−	78.7421i	−0.232278	−	0.232278i
$340$	−531.617	+	57.3623i	−1.56358	+	0.168713i
$341$	−140.115	−	140.115i	−0.410894	−	0.410894i
$342$	13.9603	−	39.5967i	0.0408196	−	0.115780i
$343$	−325.097			−0.947805
$344$	−95.9294	−	155.094i	−0.278865	−	0.450856i
$345$			694.763i			2.01381i
$346$	−65.5512	+	185.928i	−0.189454	+	0.537363i
$347$	296.512	−	296.512i	0.854500	−	0.854500i	−0.136183	−	0.990684i	$-0.543484\pi$
$347$	296.512	−	296.512i	0.854500	−	0.854500i	0.990684	+	0.136183i	$0.0434836\pi$
$348$	−154.226	+	191.534i	−0.443178	+	0.550385i
$349$	−198.107	+	198.107i	−0.567641	+	0.567641i	−0.931467	−	0.363826i	$-0.881470\pi$
$349$	−198.107	+	198.107i	−0.567641	+	0.567641i	0.363826	+	0.931467i	$0.381470\pi$
$350$	−202.108	−	422.224i	−0.577451	−	1.20636i
$351$		−	29.8554i		−	0.0850581i
$352$	193.592	+	24.1261i	0.549977	+	0.0685402i
$353$	85.4490			0.242065			0.121033	−	0.992649i	$-0.461379\pi$
$353$	85.4490			0.242065			0.121033	+	0.992649i	$0.461379\pi$
$354$	−219.692	+	105.161i	−0.620598	+	0.297064i
$355$	156.617	+	156.617i	0.441176	+	0.441176i
$356$	90.3046	+	72.7145i	0.253665	+	0.204254i
$357$	70.2779	+	70.2779i	0.196857	+	0.196857i
$358$	−116.364	−	41.0255i	−0.325038	−	0.114596i
$359$	−302.214			−0.841823			−0.420911	−	0.907102i	$-0.638290\pi$
$359$	−302.214			−0.841823			−0.420911	+	0.907102i	$0.638290\pi$
$360$	−115.958	−	187.475i	−0.322104	−	0.520764i
$361$		−	312.034i		−	0.864359i
$362$	119.315	+	42.0659i	0.329599	+	0.116204i
$363$	102.673	−	102.673i	0.282846	−	0.282846i
$364$	−9.72104	−	90.0916i	−0.0267061	−	0.247504i
$365$	69.9751	−	69.9751i	0.191713	−	0.191713i
$366$	196.510	−	94.0643i	0.536913	−	0.257006i
$367$		−	372.554i		−	1.01513i	−0.861612	−	0.507567i	$-0.830545\pi$
$367$		−	372.554i		−	1.01513i	0.861612	−	0.507567i	$-0.169455\pi$
$368$	149.057	+	682.664i	0.405045	+	1.85507i
$369$	166.004			0.449876
$370$	−46.4755	−	97.0921i	−0.125610	−	0.262411i
$371$	−124.491	−	124.491i	−0.335554	−	0.335554i
$372$	24.1574	+	223.884i	0.0649393	+	0.601838i
$373$	−407.130	−	407.130i	−1.09150	−	1.09150i	−0.995369	−	0.0961318i	$-0.969353\pi$
$373$	−407.130	−	407.130i	−1.09150	−	1.09150i	−0.0961318	−	0.995369i	$-0.530647\pi$
$374$	59.0046	−	167.359i	0.157766	−	0.447484i
$375$	546.672			1.45779
$376$	−61.7029	−	14.5431i	−0.164104	−	0.0386784i
$377$		−	203.936i		−	0.540944i
$378$	−13.6240	+	38.6427i	−0.0360423	+	0.102229i
$379$	−117.854	+	117.854i	−0.310961	+	0.310961i	−0.845282	−	0.534321i	$-0.820567\pi$
$379$	−117.854	+	117.854i	−0.310961	+	0.310961i	0.534321	+	0.845282i	$0.320567\pi$
$380$	200.243	+	161.238i	0.526955	+	0.424312i
$381$	−158.810	+	158.810i	−0.416825	+	0.416825i
$382$	148.317	+	309.850i	0.388265	+	0.811126i
$383$			407.983i			1.06523i	0.846357	+	0.532615i	$0.178791\pi$
$383$			407.983i			1.06523i	−0.846357	+	0.532615i	$0.821209\pi$
$384$	−154.160	−	159.332i	−0.401458	−	0.414928i
$385$	220.778			0.573450
$386$	388.548	−	185.988i	1.00660	−	0.481834i
$387$	−48.3566	−	48.3566i	−0.124953	−	0.124953i
$388$	−136.145	+	169.080i	−0.350890	+	0.435772i
$389$	458.508	+	458.508i	1.17868	+	1.17868i	0.980080	+	0.198605i	$0.0636411\pi$
$389$	458.508	+	458.508i	1.17868	+	1.17868i	0.198605	+	0.980080i	$0.436359\pi$
$390$	172.412	+	60.7859i	0.442081	+	0.155861i
$391$	635.589			1.62555
$392$	61.3988	−	260.501i	0.156630	−	0.664544i
$393$			290.275i			0.738613i
$394$	48.9096	+	17.2437i	0.124136	+	0.0437658i
$395$	−467.956	+	467.956i	−1.18470	+	1.18470i
$396$	72.7364	−	7.84838i	0.183678	−	0.0198191i
$397$	−259.865	+	259.865i	−0.654573	+	0.654573i	−0.954091	−	0.299518i	$-0.903174\pi$
$397$	−259.865	+	259.865i	−0.654573	+	0.654573i	0.299518	+	0.954091i	$0.403174\pi$
$398$	409.705	−	196.115i	1.02941	−	0.492752i
$399$		−	47.7866i		−	0.119766i
$400$	927.944	−	202.613i	2.31986	−	0.506531i
$401$	−499.197			−1.24488			−0.622441	−	0.782667i	$-0.713859\pi$
$401$	−499.197			−1.24488			−0.622441	+	0.782667i	$0.713859\pi$
$402$	−3.47033	−	7.24988i	−0.00863266	−	0.0180345i
$403$	−132.051	−	132.051i	−0.327670	−	0.327670i
$404$	321.046	−	34.6414i	0.794668	−	0.0857461i
$405$	−58.4525	−	58.4525i	−0.144327	−	0.144327i
$406$	−93.0624	+	263.960i	−0.229218	+	0.650147i
$407$	35.7241			0.0877741
$408$	−171.508	+	106.081i	−0.420362	+	0.260003i
$409$		−	494.949i		−	1.21014i	−0.796171	−	0.605072i	$-0.793144\pi$
$409$		−	494.949i		−	1.21014i	0.796171	−	0.605072i	$-0.206856\pi$
$410$	−337.986	+	958.656i	−0.824357	+	2.33819i
$411$	−192.863	+	192.863i	−0.469254	+	0.469254i
$412$	98.6030	−	122.456i	0.239328	−	0.297222i
$413$	−196.021	+	196.021i	−0.474628	+	0.474628i
$414$	113.134	+	236.348i	0.273270	+	0.570890i
$415$			546.205i			1.31616i
$416$	182.450	+	22.7376i	0.438582	+	0.0546577i
$417$	291.349			0.698679
$418$	−76.9598	+	36.8387i	−0.184114	+	0.0881308i
$419$	−560.555	−	560.555i	−1.33784	−	1.33784i	−0.898148	−	0.439693i	$-0.855087\pi$
$419$	−560.555	−	560.555i	−1.33784	−	1.33784i	−0.439693	−	0.898148i	$-0.644913\pi$
$420$	−195.419	−	157.354i	−0.465282	−	0.374652i
$421$	397.946	+	397.946i	0.945239	+	0.945239i	0.998577	−	0.0533373i	$-0.0169858\pi$
$421$	397.946	+	397.946i	0.945239	+	0.945239i	−0.0533373	+	0.998577i	$0.516986\pi$
$422$	−507.374	−	178.881i	−1.20231	−	0.423889i
$423$	−23.7726			−0.0562000
$424$	303.810	−	187.913i	0.716532	−	0.443191i
$425$		−	863.956i		−	2.03284i
$426$	78.7823	+	27.7757i	0.184935	+	0.0652012i
$427$	175.337	−	175.337i	0.410626	−	0.410626i
$428$	−15.5952	−	144.531i	−0.0364374	−	0.337690i
$429$	−42.9013	+	42.9013i	−0.100003	+	0.100003i
$430$	377.709	−	180.799i	0.878392	−	0.420464i
$431$			662.874i			1.53799i	0.639255	+	0.768995i	$0.279243\pi$
$431$			662.874i			1.53799i	−0.639255	+	0.768995i	$0.720757\pi$
$432$	−69.9752	−	44.8940i	−0.161980	−	0.103921i
$433$	−338.800			−0.782448			−0.391224	−	0.920296i	$-0.627948\pi$
$433$	−338.800			−0.782448			−0.391224	+	0.920296i	$0.627948\pi$
$434$	110.658	+	231.176i	0.254973	+	0.532664i
$435$	−399.277	−	399.277i	−0.917877	−	0.917877i
$436$	5.86309	+	54.3373i	0.0134475	+	0.124627i
$437$	−216.090	−	216.090i	−0.494484	−	0.494484i
$438$	12.4099	−	35.1992i	0.0283331	−	0.0803634i
$439$	−234.566			−0.534319			−0.267160	−	0.963652i	$-0.586085\pi$
$439$	−234.566			−0.534319			−0.267160	+	0.963652i	$0.586085\pi$
$440$	−102.768	+	436.024i	−0.233565	+	0.990963i
$441$		−	100.365i		−	0.227584i
$442$	55.6087	−	157.727i	0.125812	−	0.356849i
$443$	421.096	−	421.096i	0.950555	−	0.950555i	−0.0482792	−	0.998834i	$-0.515374\pi$
$443$	421.096	−	421.096i	0.950555	−	0.950555i	0.998834	+	0.0482792i	$0.0153737\pi$
$444$	−31.6206	−	25.4614i	−0.0712176	−	0.0573454i
$445$	−188.251	+	188.251i	−0.423037	+	0.423037i
$446$	−133.328	−	278.535i	−0.298941	−	0.624518i
$447$		−	243.823i		−	0.545465i
$448$	−225.775	−	112.688i	−0.503961	−	0.251535i
$449$	492.636			1.09718			0.548592	−	0.836090i	$-0.315164\pi$
$449$	492.636			1.09718			0.548592	+	0.836090i	$0.315164\pi$
$450$	321.268	−	153.783i	0.713929	−	0.341740i
$451$	−238.543	−	238.543i	−0.528921	−	0.528921i
$452$	161.289	−	200.306i	0.356835	−	0.443155i
$453$	−335.219	−	335.219i	−0.739997	−	0.739997i
$454$	98.2182	+	34.6281i	0.216340	+	0.0762733i
$455$	208.072			0.457301
$456$	94.3755	+	22.2438i	0.206964	+	0.0487803i
$457$		−	516.831i		−	1.13092i	−0.824775	−	0.565461i	$-0.808698\pi$
$457$		−	516.831i		−	1.13092i	0.824775	−	0.565461i	$-0.191302\pi$
$458$	−47.9329	−	16.8994i	−0.104657	−	0.0368981i
$459$	−53.4741	+	53.4741i	−0.116501	+	0.116501i
$460$	−1595.23	+	172.128i	−3.46788	+	0.374191i
$461$	−27.5260	+	27.5260i	−0.0597093	+	0.0597093i	−0.736331	−	0.676622i	$-0.763443\pi$
$461$	−27.5260	+	27.5260i	−0.0597093	+	0.0597093i	0.676622	+	0.736331i	$0.263443\pi$
$462$	75.1056	−	35.9511i	0.162566	−	0.0778163i
$463$			122.111i			0.263740i	0.991267	+	0.131870i	$0.0420981\pi$
$463$			122.111i			0.263740i	−0.991267	+	0.131870i	$0.957902\pi$
$464$	−477.985	−	306.661i	−1.03014	−	0.660908i
$465$	−517.073			−1.11198
$466$	−144.785	−	302.471i	−0.310697	−	0.649079i
$467$	267.964	+	267.964i	0.573798	+	0.573798i	0.933188	−	0.359390i	$-0.117015\pi$
$467$	267.964	+	267.964i	0.573798	+	0.573798i	−0.359390	+	0.933188i	$0.617015\pi$
$468$	68.5502	−	7.39669i	0.146475	−	0.0158049i
$469$	−6.46875	−	6.46875i	−0.0137926	−	0.0137926i
$470$	48.4013	−	137.284i	0.102981	−	0.292094i
$471$	185.865			0.394618
$472$	−295.886	−	478.375i	−0.626876	−	1.01351i
$473$			138.974i			0.293814i
$474$	−82.9909	+	235.393i	−0.175086	+	0.496610i
$475$	−293.730	+	293.730i	−0.618380	+	0.618380i
$476$	−143.952	+	178.775i	−0.302420	+	0.375577i
$477$	94.7243	−	94.7243i	0.198583	−	0.198583i
$478$	−25.6904	−	53.6699i	−0.0537456	−	0.112280i
$479$			419.084i			0.874915i	0.899239	+	0.437457i	$0.144121\pi$
$479$			419.084i			0.874915i	−0.899239	+	0.437457i	$0.855879\pi$
$480$	401.728	−	312.694i	0.836933	−	0.651446i
$481$	33.6681			0.0699960
$482$	193.699	−	92.7186i	0.401864	−	0.192362i
$483$	210.883	+	210.883i	0.436612	+	0.436612i
$484$	261.182	+	210.307i	0.539632	+	0.434519i
$485$	−352.468	−	352.468i	−0.726738	−	0.726738i
$486$	−29.4030	−	10.3664i	−0.0605000	−	0.0213301i
$487$	−57.2378			−0.117531			−0.0587657	−	0.998272i	$-0.518716\pi$
$487$	−57.2378			−0.117531			−0.0587657	+	0.998272i	$0.518716\pi$
$488$	264.664	+	427.897i	0.542344	+	0.876838i
$489$		−	434.153i		−	0.887838i
$490$	579.595	+	204.344i	1.18285	+	0.417028i
$491$	−301.955	+	301.955i	−0.614979	+	0.614979i	−0.944239	−	0.329260i	$-0.893201\pi$
$491$	−301.955	+	301.955i	−0.614979	+	0.614979i	0.329260	+	0.944239i	$0.393201\pi$
$492$	41.1276	+	381.158i	0.0835927	+	0.774712i
$493$	−365.270	+	365.270i	−0.740912	+	0.740912i
$494$	−72.5306	+	34.7185i	−0.146823	+	0.0702804i
$495$			167.989i			0.339372i
$496$	−508.068	+	110.934i	−1.02433	+	0.223658i
$497$	95.0771			0.191302
$498$	88.9430	+	185.811i	0.178600	+	0.373115i
$499$	619.990	+	619.990i	1.24247	+	1.24247i	0.958975	+	0.283491i	$0.0914925\pi$
$499$	619.990	+	619.990i	1.24247	+	1.24247i	0.283491	+	0.958975i	$0.408507\pi$
$500$	135.438	+	1255.20i	0.270876	+	2.51040i
$501$	−75.5391	−	75.5391i	−0.150777	−	0.150777i
$502$	322.527	−	914.808i	0.642484	−	1.82233i
$503$	222.446			0.442239			0.221120	−	0.975247i	$-0.429029\pi$
$503$	222.446			0.442239			0.221120	+	0.975247i	$0.429029\pi$
$504$	−92.1018	−	21.7079i	−0.182742	−	0.0430713i
$505$			741.475i			1.46827i
$506$	177.056	−	502.196i	0.349912	−	0.992482i
$507$	166.550	−	166.550i	0.328500	−	0.328500i
$508$	−403.985	−	325.295i	−0.795246	−	0.640344i
$509$	489.873	−	489.873i	0.962421	−	0.962421i	−0.0368976	−	0.999319i	$-0.511748\pi$
$509$	489.873	−	489.873i	0.962421	−	0.962421i	0.999319	+	0.0368976i	$0.0117475\pi$
$510$	−199.933	−	417.680i	−0.392025	−	0.818981i
$511$		−	42.4795i		−	0.0831302i
$512$	327.646	−	393.437i	0.639933	−	0.768431i
$513$	36.3606			0.0708783
$514$	709.983	−	339.850i	1.38129	−	0.661188i
$515$	255.274	+	255.274i	0.495678	+	0.495678i
$516$	99.0500	−	123.011i	0.191957	−	0.238393i
$517$	34.1605	+	34.1605i	0.0660745	+	0.0660745i
$518$	−43.5775	−	15.3638i	−0.0841265	−	0.0296599i
$519$	−170.732			−0.328964
$520$	−96.8539	+	410.929i	−0.186257	+	0.790249i
$521$			197.152i			0.378412i	0.981937	+	0.189206i	$0.0605913\pi$
$521$			197.152i			0.378412i	−0.981937	+	0.189206i	$0.939409\pi$
$522$	−200.846	−	70.8107i	−0.384762	−	0.135653i
$523$	621.874	−	621.874i	1.18905	−	1.18905i	0.211721	−	0.977330i	$-0.432093\pi$
$523$	621.874	−	621.874i	1.18905	−	1.18905i	0.977330	−	0.211721i	$-0.0679067\pi$
$524$	−666.493	+	71.9157i	−1.27193	+	0.137244i
$525$	286.654	−	286.654i	0.546007	−	0.546007i
$526$	−746.486	+	357.324i	−1.41918	+	0.679323i
$527$			473.033i			0.897596i
$528$	36.0409	+	165.064i	0.0682593	+	0.312620i
$529$	1378.22			2.60533
$530$	354.162	+	739.881i	0.668231	+	1.39600i
$531$	−149.152	−	149.152i	−0.280888	−	0.280888i
$532$	109.722	−	11.8391i	0.206243	−	0.0222540i
$533$	−224.815	−	224.815i	−0.421791	−	0.421791i
$534$	−33.3859	+	94.6949i	−0.0625204	+	0.177331i
$535$	333.804			0.623933
$536$	15.7865	−	9.76429i	0.0294524	−	0.0182170i
$537$		−	106.854i		−	0.198983i
$538$	−155.542	+	441.175i	−0.289111	+	0.820028i
$539$	−144.221	+	144.221i	−0.267572	+	0.267572i
$540$	119.730	−	148.693i	0.221722	−	0.275357i
$541$	423.563	−	423.563i	0.782925	−	0.782925i	−0.197398	−	0.980323i	$-0.563249\pi$
$541$	423.563	−	423.563i	0.782925	−	0.782925i	0.980323	+	0.197398i	$0.0632492\pi$
$542$	267.536	+	558.911i	0.493609	+	1.03120i
$543$			109.563i			0.201774i
$544$	−286.062	−	367.512i	−0.525848	−	0.675574i
$545$	−125.495			−0.230267
$546$	70.7831	−	33.8821i	0.129639	−	0.0620551i
$547$	−14.5553	−	14.5553i	−0.0266093	−	0.0266093i	0.693677	−	0.720286i	$-0.255990\pi$
$547$	−14.5553	−	14.5553i	−0.0266093	−	0.0266093i	−0.720286	+	0.693677i	$0.755990\pi$
$548$	−490.610	−	395.046i	−0.895274	−	0.720888i
$549$	133.413	+	133.413i	0.243012	+	0.243012i
$550$	−682.634	−	240.671i	−1.24115	−	0.437584i
$551$	248.371			0.450764
$552$	−514.644	+	318.319i	−0.932327	+	0.576665i
$553$			284.080i			0.513708i
$554$	−419.856	−	148.026i	−0.757863	−	0.267194i
$555$	65.9172	−	65.9172i	0.118770	−	0.118770i
$556$	72.1818	+	668.959i	0.129823	+	1.20316i
$557$	−351.991	+	351.991i	−0.631941	+	0.631941i	−0.948554	−	0.316614i	$-0.897454\pi$
$557$	−351.991	+	351.991i	−0.631941	+	0.631941i	0.316614	+	0.948554i	$0.397454\pi$
$558$	−175.901	+	84.1992i	−0.315234	+	0.150895i
$559$			130.976i			0.234304i
$560$	312.881	−	487.680i	0.558716	−	0.870857i
$561$	153.681			0.273942
$562$	−355.027	−	741.689i	−0.631721	−	1.31973i
$563$	−150.902	−	150.902i	−0.268031	−	0.268031i	0.560275	−	0.828307i	$-0.310695\pi$
$563$	−150.902	−	150.902i	−0.268031	−	0.268031i	−0.828307	+	0.560275i	$0.810695\pi$
$564$	−5.88967	−	54.5837i	−0.0104427	−	0.0967796i
$565$	417.563	+	417.563i	0.739050	+	0.739050i
$566$	−323.068	+	916.341i	−0.570791	+	1.61898i
$567$	−35.4845			−0.0625830
$568$	−44.2567	+	187.771i	−0.0779168	+	0.330583i
$569$			113.300i			0.199121i	0.995032	+	0.0995603i	$0.0317436\pi$
$569$			113.300i			0.199121i	−0.995032	+	0.0995603i	$0.968256\pi$
$570$	−74.0305	+	209.978i	−0.129878	+	0.368383i
$571$	−207.486	+	207.486i	−0.363373	+	0.363373i	−0.865053	−	0.501680i	$-0.832715\pi$
$571$	−207.486	+	207.486i	−0.363373	+	0.363373i	0.501680	+	0.865053i	$0.332715\pi$
$572$	−109.133	−	87.8758i	−0.190793	−	0.153629i
$573$	−210.361	+	210.361i	−0.367123	+	0.367123i
$574$	188.394	+	393.574i	0.328212	+	0.685669i
$575$		−	2592.48i		−	4.50866i
$576$	85.7436	−	171.791i	0.148860	−	0.298248i
$577$	−484.715			−0.840061			−0.420031	−	0.907510i	$-0.637981\pi$
$577$	−484.715			−0.840061			−0.420031	+	0.907510i	$0.637981\pi$
$578$	139.244	−	66.6524i	0.240906	−	0.115316i
$579$	263.790	+	263.790i	0.455596	+	0.455596i
$580$	817.847	−	1015.69i	1.41008	−	1.75119i
$581$	165.791	+	165.791i	0.285355	+	0.285355i
$582$	−177.300	−	62.5093i	−0.304639	−	0.107404i
$583$	−272.232			−0.466950
$584$	83.8944	+	19.7735i	0.143655	+	0.0338587i
$585$			158.321i			0.270634i
$586$	−93.7320	−	33.0464i	−0.159952	−	0.0563932i
$587$	−540.404	+	540.404i	−0.920619	+	0.920619i	−0.997073	−	0.0764537i	$-0.975640\pi$
$587$	−540.404	+	540.404i	−0.920619	+	0.920619i	0.0764537	+	0.997073i	$0.475640\pi$
$588$	230.445	−	24.8654i	0.391913	−	0.0422881i
$589$	160.823	−	160.823i	0.273045	−	0.273045i
$590$	1165.01	−	557.659i	1.97459	−	0.945185i
$591$			44.9124i			0.0759939i
$592$	50.6272	−	78.9113i	0.0855189	−	0.133296i
$593$	411.176			0.693383			0.346692	−	0.937979i	$-0.387305\pi$
$593$	411.176			0.693383			0.346692	+	0.937979i	$0.387305\pi$
$594$	27.3550	+	57.1475i	0.0460522	+	0.0962079i
$595$	−372.678	−	372.678i	−0.626350	−	0.626350i
$596$	559.835	−	60.4072i	0.939320	−	0.101354i
$597$	278.154	+	278.154i	0.465920	+	0.465920i
$598$	166.866	−	473.293i	0.279039	−	0.791460i
$599$	−552.839			−0.922936			−0.461468	−	0.887157i	$-0.652677\pi$
$599$	−552.839			−0.922936			−0.461468	+	0.887157i	$0.652677\pi$
$600$	432.691	+	699.556i	0.721152	+	1.16593i
$601$		−	881.159i		−	1.46615i	−0.680145	−	0.733077i	$-0.738083\pi$
$601$		−	881.159i		−	1.46615i	0.680145	−	0.733077i	$-0.261917\pi$
$602$	59.7684	−	169.526i	0.0992831	−	0.281604i
$603$	4.92204	−	4.92204i	0.00816259	−	0.00816259i
$604$	686.637	−	852.738i	1.13682	−	1.41182i
$605$	−544.467	+	544.467i	−0.899945	+	0.899945i
$606$	120.740	+	252.239i	0.199242	+	0.416236i
$607$			1175.08i			1.93588i	0.251186	+	0.967939i	$0.419180\pi$
$607$			1175.08i			1.93588i	−0.251186	+	0.967939i	$0.580820\pi$
$608$	−27.6919	+	222.204i	−0.0455459	+	0.365467i
$609$	−242.387			−0.398009
$610$	−1042.08	+	498.816i	−1.70832	+	0.817731i
$611$	32.1945	+	32.1945i	0.0526915	+	0.0526915i
$612$	−136.029	−	109.532i	−0.222269	−	0.178974i
$613$	−496.928	−	496.928i	−0.810649	−	0.810649i	0.174082	−	0.984731i	$-0.444304\pi$
$613$	−496.928	−	496.928i	−0.810649	−	0.810649i	−0.984731	+	0.174082i	$0.944304\pi$
$614$	43.8622	+	15.4642i	0.0714367	+	0.0251859i
$615$	−880.308			−1.43140
$616$	101.154	+	163.541i	0.164211	+	0.265489i
$617$			623.301i			1.01021i	0.863057	+	0.505106i	$0.168547\pi$
$617$			623.301i			1.01021i	−0.863057	+	0.505106i	$0.831453\pi$
$618$	128.409	+	45.2722i	0.207781	+	0.0732560i
$619$	7.45302	−	7.45302i	0.0120404	−	0.0120404i	−0.701061	−	0.713101i	$-0.747290\pi$
$619$	7.45302	−	7.45302i	0.0120404	−	0.0120404i	0.713101	+	0.701061i	$0.247290\pi$
$620$	−128.105	−	1187.24i	−0.206621	−	1.91490i
$621$	−160.460	+	160.460i	−0.258390	+	0.258390i
$622$	−71.8013	+	34.3694i	−0.115436	+	0.0552563i
$623$			114.281i			0.183437i
$624$	33.9667	+	155.564i	0.0544338	+	0.249301i
$625$	−1414.88			−2.26381
$626$	−372.940	−	779.110i	−0.595751	−	1.24458i
$627$	−52.2490	−	52.2490i	−0.0833318	−	0.0833318i
$628$	46.0482	+	426.760i	0.0733251	+	0.679555i
$629$	−60.3029	−	60.3029i	−0.0958711	−	0.0958711i
$630$	72.2469	−	204.919i	0.114678	−	0.325268i
$631$	147.833			0.234284			0.117142	−	0.993115i	$-0.462627\pi$
$631$	147.833			0.234284			0.117142	+	0.993115i	$0.462627\pi$
$632$	−561.041	−	132.234i	−0.887723	−	0.209232i
$633$		−	465.908i		−	0.736031i
$634$	−239.877	+	680.379i	−0.378354	+	1.07315i
$635$	842.158	−	842.158i	1.32623	−	1.32623i
$636$	240.962	+	194.026i	0.378871	+	0.305072i
$637$	−135.921	+	135.921i	−0.213376	+	0.213376i
$638$	186.856	+	390.362i	0.292878	+	0.611853i
$639$			72.3436i			0.113214i
$640$	817.497	+	844.927i	1.27734	+	1.32020i
$641$	−782.691			−1.22105			−0.610523	−	0.791998i	$-0.709041\pi$
$641$	−782.691			−1.22105			−0.610523	+	0.791998i	$0.709041\pi$
$642$	113.555	−	54.3561i	0.176878	−	0.0846668i
$643$	126.760	+	126.760i	0.197138	+	0.197138i	0.798772	−	0.601634i	$-0.205483\pi$
$643$	126.760	+	126.760i	0.197138	+	0.197138i	−0.601634	+	0.798772i	$0.705483\pi$
$644$	−431.958	+	536.450i	−0.670741	+	0.832998i
$645$	256.431	+	256.431i	0.397568	+	0.397568i
$646$	192.094	+	67.7252i	0.297359	+	0.104838i
$647$	1226.09			1.89504			0.947520	−	0.319697i	$-0.103581\pi$
$647$	1226.09			1.89504			0.947520	+	0.319697i	$0.103581\pi$
$648$	16.5174	−	70.0798i	0.0254899	−	0.108148i
$649$			428.653i			0.660482i
$650$	−643.347	−	226.820i	−0.989764	−	0.348954i
$651$	−156.949	+	156.949i	−0.241089	+	0.241089i
$652$	996.846	−	107.561i	1.52891	−	0.164972i
$653$	326.300	−	326.300i	0.499694	−	0.499694i	−0.411649	−	0.911343i	$-0.635047\pi$
$653$	326.300	−	326.300i	0.499694	−	0.499694i	0.911343	+	0.411649i	$0.135047\pi$
$654$	−42.6917	+	20.4354i	−0.0652779	+	0.0312468i
$655$		−	1539.31i		−	2.35008i
$656$	−864.978	+	188.864i	−1.31856	+	0.287903i
$657$	32.3224			0.0491970
$658$	−26.9789	−	56.3616i	−0.0410013	−	0.0856560i
$659$	−574.901	−	574.901i	−0.872384	−	0.872384i	0.120347	−	0.992732i	$-0.461599\pi$
$659$	−574.901	−	574.901i	−0.872384	−	0.872384i	−0.992732	+	0.120347i	$0.961599\pi$
$660$	−385.715	+	41.6193i	−0.584417	+	0.0630596i
$661$	52.8795	+	52.8795i	0.0799993	+	0.0799993i	0.745974	−	0.665975i	$-0.231984\pi$
$661$	52.8795	+	52.8795i	0.0799993	+	0.0799993i	−0.665975	+	0.745974i	$0.731984\pi$
$662$	−193.638	+	549.229i	−0.292504	+	0.829651i
$663$	144.837			0.218456
$664$	−404.600	+	250.254i	−0.609338	+	0.376889i
$665$			253.409i			0.381065i
$666$	11.6902	−	33.1579i	0.0175529	−	0.0497866i
$667$	−1096.07	+	1096.07i	−1.64328	+	1.64328i
$668$	154.729	−	192.158i	0.231630	−	0.287662i
$669$	189.101	−	189.101i	0.282663	−	0.282663i
$670$	18.4029	+	38.4455i	0.0274670	+	0.0573814i
$671$		−	383.422i		−	0.571419i
$672$	27.0247	−	216.851i	0.0402154	−	0.322694i
$673$	342.318			0.508645			0.254322	−	0.967119i	$-0.418148\pi$
$673$	342.318			0.508645			0.254322	+	0.967119i	$0.418148\pi$
$674$	−82.4981	+	39.4897i	−0.122401	+	0.0585901i
$675$	218.113	+	218.113i	0.323131	+	0.323131i
$676$	423.673	+	341.147i	0.626735	+	0.504656i
$677$	107.154	+	107.154i	0.158278	+	0.158278i	0.781803	−	0.623525i	$-0.214300\pi$
$677$	107.154	+	107.154i	0.158278	+	0.158278i	−0.623525	+	0.781803i	$0.714300\pi$
$678$	210.044	+	74.0538i	0.309800	+	0.109224i
$679$	−213.971			−0.315127
$680$	909.491	−	562.541i	1.33749	−	0.827266i
$681$			90.1911i			0.132439i
$682$	373.756	+	131.772i	0.548029	+	0.193215i
$683$	724.233	−	724.233i	1.06037	−	1.06037i	0.0623142	−	0.998057i	$-0.480152\pi$
$683$	724.233	−	724.233i	1.06037	−	1.06037i	0.998057	−	0.0623142i	$-0.0198481\pi$
$684$	9.00834	+	83.4865i	0.0131701	+	0.122056i
$685$	1022.74	−	1022.74i	1.49305	−	1.49305i
$686$	586.468	−	280.727i	0.854910	−	0.409223i
$687$		−	44.0155i		−	0.0640691i
$688$	306.981	+	196.950i	0.446194	+	0.286265i
$689$	−256.564			−0.372372
$690$	−599.940	−	1253.34i	−0.869479	−	1.81643i
$691$	162.528	+	162.528i	0.235207	+	0.235207i	0.814862	−	0.579655i	$-0.196813\pi$
$691$	162.528	+	162.528i	0.235207	+	0.235207i	−0.579655	+	0.814862i	$0.696813\pi$
$692$	−42.2990	−	392.014i	−0.0611257	−	0.566495i
$693$	50.9902	+	50.9902i	0.0735790	+	0.0735790i
$694$	−278.857	+	790.943i	−0.401812	+	1.13969i
$695$	−1545.00			−2.22302
$696$	112.827	−	478.700i	0.162108	−	0.687787i
$697$			805.331i			1.15543i
$698$	186.312	−	528.449i	0.266922	−	0.757090i
$699$	205.351	−	205.351i	0.293779	−	0.293779i
$700$	729.197	+	587.159i	1.04171	+	0.838799i
$701$	−301.659	+	301.659i	−0.430327	+	0.430327i	−0.888740	−	0.458412i	$-0.848418\pi$
$701$	−301.659	+	301.659i	−0.430327	+	0.430327i	0.458412	+	0.888740i	$0.348418\pi$
$702$	25.7807	+	53.8585i	0.0367246	+	0.0767215i
$703$			41.0040i			0.0583271i
$704$	−370.069	+	123.647i	−0.525666	+	0.175635i
$705$	126.064			0.178815
$706$	−154.148	+	73.7867i	−0.218340	+	0.104514i
$707$	225.062	+	225.062i	0.318334	+	0.318334i
$708$	305.511	−	379.415i	0.431512	−	0.535898i
$709$	−629.100	−	629.100i	−0.887306	−	0.887306i	0.106958	−	0.994264i	$-0.465889\pi$
$709$	−629.100	−	629.100i	−0.887306	−	0.887306i	−0.994264	+	0.106958i	$0.965889\pi$
$710$	−417.776	−	147.292i	−0.588417	−	0.207454i
$711$	−216.155			−0.304016
$712$	−225.698	−	53.1958i	−0.316991	−	0.0747132i
$713$			1419.43i			1.99079i
$714$	−187.466	−	66.0935i	−0.262557	−	0.0925680i
$715$	227.502	−	227.502i	0.318185	−	0.318185i
$716$	245.344	−	26.4730i	0.342659	−	0.0369735i
$717$	36.4372	−	36.4372i	0.0508190	−	0.0508190i
$718$	545.188	−	260.968i	0.759315	−	0.363465i
$719$		−	145.542i		−	0.202422i	−0.994865	−	0.101211i	$-0.967728\pi$
$719$		−	145.542i		−	0.202422i	0.994865	−	0.101211i	$-0.0322718\pi$
$720$	371.073	+	238.069i	0.515379	+	0.330652i
$721$	154.968			0.214935
$722$	269.447	+	562.902i	0.373195	+	0.779643i
$723$	131.505	+	131.505i	0.181887	+	0.181887i
$724$	−251.566	+	27.1444i	−0.347466	+	0.0374922i
$725$	1489.88	+	1489.88i	2.05501	+	2.05501i
$726$	−96.5598	+	273.880i	−0.133002	+	0.377245i
$727$	−938.214			−1.29053			−0.645264	−	0.763960i	$-0.723253\pi$
$727$	−938.214			−1.29053			−0.645264	+	0.763960i	$0.723253\pi$
$728$	95.3322	+	154.129i	0.130951	+	0.211716i
$729$		−	27.0000i		−	0.0370370i
$730$	−65.8088	+	186.658i	−0.0901490	+	0.255696i
$731$	234.591	−	234.591i	0.320918	−	0.320918i
$732$	−273.274	+	339.380i	−0.373325	+	0.463634i
$733$	692.101	−	692.101i	0.944203	−	0.944203i	−0.0543203	−	0.998524i	$-0.517299\pi$
$733$	692.101	−	692.101i	0.944203	−	0.944203i	0.998524	+	0.0543203i	$0.0172992\pi$
$734$	321.707	+	672.080i	0.438294	+	0.915640i
$735$			532.226i			0.724117i
$736$	−858.388	−	1102.80i	−1.16629	−	1.49837i
$737$	−14.1456			−0.0191935
$738$	−299.468	+	143.348i	−0.405783	+	0.194238i
$739$	−440.389	−	440.389i	−0.595926	−	0.595926i	0.343300	−	0.939226i	$-0.388455\pi$
$739$	−440.389	−	440.389i	−0.595926	−	0.595926i	−0.939226	+	0.343300i	$0.888455\pi$
$740$	167.682	+	135.020i	0.226597	+	0.182459i
$741$	−49.2420	−	49.2420i	−0.0664534	−	0.0664534i
$742$	332.078	+	117.078i	0.447545	+	0.157788i
$743$	−1010.54			−1.36008			−0.680039	−	0.733176i	$-0.738037\pi$
$743$	−1010.54			−1.36008			−0.680039	+	0.733176i	$0.738037\pi$
$744$	−236.907	−	383.021i	−0.318423	−	0.514813i
$745$			1292.97i			1.73553i
$746$	1086.02	+	382.889i	1.45579	+	0.513256i
$747$	−126.150	+	126.150i	−0.168875	+	0.168875i
$748$	38.0746	+	352.863i	0.0509018	+	0.471743i
$749$	101.321	−	101.321i	0.135275	−	0.135275i
$750$	−986.183	+	472.061i	−1.31491	+	0.629414i
$751$		−	776.971i		−	1.03458i	−0.855810	−	0.517291i	$-0.826940\pi$
$751$		−	776.971i		−	1.03458i	0.855810	−	0.517291i	$-0.173060\pi$
$752$	123.869	−	27.0462i	0.164719	−	0.0359657i
$753$	840.043			1.11560
$754$	176.102	+	367.896i	0.233557	+	0.487925i
$755$	1777.64	+	1777.64i	2.35449	+	2.35449i
$756$	−8.79131	−	81.4751i	−0.0116287	−	0.107771i
$757$	375.481	+	375.481i	0.496012	+	0.496012i	0.910194	−	0.414182i	$-0.135932\pi$
$757$	375.481	+	375.481i	0.496012	+	0.496012i	−0.414182	+	0.910194i	$0.635932\pi$
$758$	110.837	−	314.376i	0.146223	−	0.414744i
$759$	461.153			0.607579
$760$	−500.466	−	117.957i	−0.658508	−	0.155207i
$761$		−	1502.22i		−	1.97400i	−0.160711	−	0.987001i	$-0.551379\pi$
$761$		−	1502.22i		−	1.97400i	0.160711	−	0.987001i	$-0.448621\pi$
$762$	149.355	−	423.626i	0.196003	−	0.555939i
$763$	−38.0920	+	38.0920i	−0.0499239	+	0.0499239i
$764$	−535.122	−	430.888i	−0.700421	−	0.563989i
$765$	283.569	−	283.569i	0.370678	−	0.370678i
$766$	−352.301	−	735.993i	−0.459923	−	0.960827i
$767$			403.983i			0.526705i
$768$	415.687	+	154.312i	0.541259	+	0.200928i
$769$	−293.930			−0.382223			−0.191112	−	0.981568i	$-0.561209\pi$
$769$	−293.930			−0.382223			−0.191112	+	0.981568i	$0.561209\pi$
$770$	−398.279	+	190.646i	−0.517246	+	0.247592i
$771$	482.017	+	482.017i	0.625184	+	0.625184i
$772$	−540.328	+	671.036i	−0.699906	+	0.869218i
$773$	−748.271	−	748.271i	−0.968009	−	0.968009i	0.0314945	−	0.999504i	$-0.489973\pi$
$773$	−748.271	−	748.271i	−0.968009	−	0.968009i	−0.999504	+	0.0314945i	$0.989973\pi$
$774$	128.991	+	45.4775i	0.166655	+	0.0587564i
$775$	1929.44			2.48960
$776$	99.5999	−	422.580i	0.128350	−	0.544562i
$777$		−	40.0161i		−	0.0515007i
$778$	−1223.07	−	431.209i	−1.57207	−	0.554253i
$779$	273.799	−	273.799i	0.351475	−	0.351475i
$780$	−363.516	+	39.2240i	−0.466047	+	0.0502872i
$781$	103.956	−	103.956i	0.133106	−	0.133106i
$782$	−1146.59	+	548.843i	−1.46623	+	0.701845i
$783$		−	184.431i		−	0.235544i
$784$	114.185	+	522.958i	0.145645	+	0.667038i
$785$	−985.629			−1.25558
$786$	−250.658	−	523.650i	−0.318903	−	0.666221i
$787$	−735.839	−	735.839i	−0.934992	−	0.934992i	0.0630203	−	0.998012i	$-0.479927\pi$
$787$	−735.839	−	735.839i	−0.934992	−	0.934992i	−0.998012	+	0.0630203i	$0.979927\pi$
$788$	−103.122	+	11.1271i	−0.130866	+	0.0141206i
$789$	−506.799	−	506.799i	−0.642331	−	0.642331i
$790$	440.094	−	1248.27i	0.557081	−	1.58009i
$791$	253.488			0.320466
$792$	−124.438	+	76.9675i	−0.157118	+	0.0971811i
$793$		−	361.355i		−	0.455681i
$794$	244.393	−	693.190i	0.307800	−	0.873035i
$795$	−502.315	+	502.315i	−0.631843	+	0.631843i
$796$	−569.750	+	707.576i	−0.715767	+	0.888914i
$797$	212.043	−	212.043i	0.266051	−	0.266051i	−0.561455	−	0.827507i	$-0.689758\pi$
$797$	212.043	−	212.043i	0.266051	−	0.266051i	0.827507	+	0.561455i	$0.189758\pi$
$798$	41.2646	+	86.2060i	0.0517100	+	0.108028i
$799$		−	115.327i		−	0.144340i
$800$	−1499.03	+	1166.81i	−1.87379	+	1.45851i
$801$	−86.9558			−0.108559
$802$	900.541	−	431.066i	1.12287	−	0.537489i
$803$	−46.4464	−	46.4464i	−0.0578411	−	0.0578411i
$804$	12.5208	+	10.0819i	0.0155731	+	0.0125397i
$805$	−1118.30	−	1118.30i	−1.38919	−	1.38919i
$806$	352.245	+	124.189i	0.437029	+	0.154080i
$807$	−405.119			−0.502006
$808$	−549.246	+	339.721i	−0.679760	+	0.420447i
$809$		−	827.491i		−	1.02286i	−0.859326	−	0.511428i	$-0.829117\pi$
$809$		−	827.491i		−	1.02286i	0.859326	−	0.511428i	$-0.170883\pi$
$810$	155.922	+	54.9723i	0.192496	+	0.0678670i
$811$	112.908	−	112.908i	0.139221	−	0.139221i	−0.634062	−	0.773283i	$-0.718613\pi$
$811$	112.908	−	112.908i	0.139221	−	0.139221i	0.773283	+	0.634062i	$0.218613\pi$
$812$	−60.0515	−	556.539i	−0.0739550	−	0.685393i
$813$	−379.452	+	379.452i	−0.466731	+	0.466731i
$814$	−64.4454	+	30.8484i	−0.0791713	+	0.0378973i
$815$			2302.28i			2.82488i
$816$	217.793	−	339.468i	0.266903	−	0.416015i
$817$	−159.514			−0.195243
$818$	427.397	+	892.877i	0.522491	+	1.09154i
$819$	48.0556	+	48.0556i	0.0586760	+	0.0586760i
$820$	−218.097	−	2021.25i	−0.265971	−	2.46494i
$821$	555.298	+	555.298i	0.676368	+	0.676368i	0.959176	−	0.282808i	$-0.0912661\pi$
$821$	555.298	+	555.298i	0.676368	+	0.676368i	−0.282808	+	0.959176i	$0.591266\pi$
$822$	181.380	−	514.462i	0.220657	−	0.625866i
$823$	763.799			0.928067			0.464034	−	0.885818i	$-0.346402\pi$
$823$	763.799			0.928067			0.464034	+	0.885818i	$0.346402\pi$
$824$	−72.1350	+	306.053i	−0.0875425	+	0.371423i
$825$		−	626.844i		−	0.759812i
$826$	184.350	−	522.886i	0.223184	−	0.633034i
$827$	116.947	−	116.947i	0.141411	−	0.141411i	−0.632858	−	0.774268i	$-0.718118\pi$
$827$	116.947	−	116.947i	0.141411	−	0.141411i	0.774268	+	0.632858i	$0.218118\pi$
$828$	−408.182	−	328.674i	−0.492974	−	0.396949i
$829$	181.419	−	181.419i	0.218841	−	0.218841i	−0.589169	−	0.808010i	$-0.700545\pi$
$829$	181.419	−	181.419i	0.218841	−	0.218841i	0.808010	+	0.589169i	$0.200545\pi$
$830$	−471.658	−	985.341i	−0.568262	−	1.18716i
$831$		−	385.543i		−	0.463950i
$832$	−348.771	+	116.531i	−0.419195	+	0.140061i
$833$	486.896			0.584509
$834$	−525.587	+	251.585i	−0.630201	+	0.301661i
$835$	400.578	+	400.578i	0.479734	+	0.479734i
$836$	107.023	−	132.912i	0.128018	−	0.158986i
$837$	−119.421	−	119.421i	−0.142678	−	0.142678i
$838$	1495.28	+	527.180i	1.78434	+	0.629093i
$839$	521.472			0.621540			0.310770	−	0.950485i	$-0.399413\pi$
$839$	521.472			0.621540			0.310770	+	0.950485i	$0.399413\pi$
$840$	488.409	+	115.115i	0.581439	+	0.137042i
$841$		−	418.809i		−	0.497989i
$842$	−1061.52	−	374.252i	−1.26071	−	0.444480i
$843$	503.542	−	503.542i	0.597322	−	0.597322i
$844$	1069.76	−	115.429i	1.26749	−	0.136764i
$845$	−883.200	+	883.200i	−1.04521	+	1.04521i
$846$	42.8853	−	20.5281i	0.0506918	−	0.0242649i
$847$			330.527i			0.390233i
$848$	−385.799	+	601.336i	−0.454952	+	0.709123i
$849$	−841.451			−0.991108
$850$	746.041	+	1558.56i	0.877696	+	1.83360i
$851$	−180.952	−	180.952i	−0.212634	−	0.212634i
$852$	−166.106	+	17.9232i	−0.194960	+	0.0210366i
$853$	−644.278	−	644.278i	−0.755309	−	0.755309i	0.220156	−	0.975465i	$-0.429343\pi$
$853$	−644.278	−	644.278i	−0.755309	−	0.755309i	−0.975465	+	0.220156i	$0.929343\pi$
$854$	−164.898	+	467.712i	−0.193089	+	0.547672i
$855$	−192.817			−0.225517
$856$	152.939	+	247.265i	0.178667	+	0.288861i
$857$		−	757.190i		−	0.883536i	−0.897129	−	0.441768i	$-0.854351\pi$
$857$		−	757.190i		−	0.883536i	0.897129	−	0.441768i	$-0.145649\pi$
$858$	40.3470	−	114.439i	0.0470245	−	0.133379i
$859$	−1011.32	+	1011.32i	−1.17732	+	1.17732i	−0.196894	+	0.980425i	$0.563085\pi$
$859$	−1011.32	+	1011.32i	−1.17732	+	1.17732i	−0.980425	+	0.196894i	$0.936915\pi$
$860$	−525.255	+	652.316i	−0.610761	+	0.758508i
$861$	−267.203	+	267.203i	−0.310340	+	0.310340i
$862$	−572.403	−	1195.81i	−0.664041	−	1.38725i
$863$		−	598.188i		−	0.693149i	−0.938022	−	0.346575i	$-0.887345\pi$
$863$		−	598.188i		−	0.693149i	0.938022	−	0.346575i	$-0.112655\pi$
$864$	165.000	+	20.5630i	0.190973	+	0.0237997i
$865$	905.381			1.04668
$866$	611.187	−	292.560i	0.705759	−	0.337829i
$867$	94.5344	+	94.5344i	0.109036	+	0.109036i
$868$	−399.250	−	321.482i	−0.459965	−	0.370370i
$869$	310.609	+	310.609i	0.357432	+	0.357432i
$870$	1065.07	+	375.504i	1.22422	+	0.431613i
$871$	−13.3315			−0.0153060
$872$	−57.4981	−	92.9604i	−0.0659382	−	0.106606i
$873$		−	162.810i		−	0.186494i
$874$	576.418	+	203.224i	0.659517	+	0.232521i
$875$	−879.929	+	879.929i	−1.00563	+	1.00563i
$876$	8.00789	+	74.2147i	0.00914143	+	0.0847200i
$877$	−664.587	+	664.587i	−0.757796	+	0.757796i	−0.975921	−	0.218125i	$-0.930006\pi$
$877$	−664.587	+	664.587i	−0.757796	+	0.757796i	0.218125	+	0.975921i	$0.430006\pi$
$878$	423.152	−	202.552i	0.481950	−	0.230697i
$879$		−	86.0716i		−	0.0979199i
$880$	−191.122	−	875.319i	−0.217184	−	0.994681i
$881$	772.898			0.877296			0.438648	−	0.898659i	$-0.355458\pi$
$881$	772.898			0.877296			0.438648	+	0.898659i	$0.355458\pi$
$882$	86.6667	+	181.056i	0.0982616	+	0.205279i
$883$	−321.603	−	321.603i	−0.364216	−	0.364216i	0.501146	−	0.865363i	$-0.332912\pi$
$883$	−321.603	−	321.603i	−0.364216	−	0.364216i	−0.865363	+	0.501146i	$0.832912\pi$
$884$	35.8833	+	332.555i	0.0405920	+	0.376194i
$885$	790.939	+	790.939i	0.893717	+	0.893717i
$886$	−396.024	+	1123.27i	−0.446979	+	1.26780i
$887$	762.665			0.859825			0.429912	−	0.902871i	$-0.358544\pi$
$887$	762.665			0.859825			0.429912	+	0.902871i	$0.358544\pi$
$888$	79.0292	+	18.6268i	0.0889969	+	0.0209761i
$889$		−	511.245i		−	0.575079i
$890$	177.043	−	502.160i	0.198925	−	0.564224i
$891$	−38.7982	+	38.7982i	−0.0435445	+	0.0435445i
$892$	481.040	+	387.341i	0.539283	+	0.434238i
$893$	−39.2093	+	39.2093i	−0.0439074	+	0.0439074i
$894$	210.545	+	439.851i	0.235509	+	0.492003i
$895$			566.637i			0.633114i
$896$	504.600	+	8.32594i	0.563170	+	0.00929234i
$897$	434.612			0.484518
$898$	−888.704	+	425.400i	−0.989648	+	0.473719i
$899$	−815.741	−	815.741i	−0.907388	−	0.907388i
$900$	−446.767	+	554.842i	−0.496407	+	0.616491i
$901$	459.533	+	459.533i	0.510025	+	0.510025i
$902$	636.313	+	224.340i	0.705447	+	0.248714i
$903$	155.671			0.172393
$904$	−117.994	+	500.624i	−0.130525	+	0.553787i
$905$		−	581.006i		−	0.641996i
$906$	894.195	+	315.260i	0.986970	+	0.347969i
$907$	−729.007	+	729.007i	−0.803756	+	0.803756i	−0.983680	−	0.179924i	$-0.942415\pi$
$907$	−729.007	+	729.007i	−0.803756	+	0.803756i	0.179924	+	0.983680i	$0.442415\pi$
$908$	−207.086	+	22.3449i	−0.228068	+	0.0246089i
$909$	−171.249	+	171.249i	−0.188392	+	0.188392i
$910$	−375.357	+	179.674i	−0.412481	+	0.197444i
$911$		−	885.541i		−	0.972054i	−0.873944	−	0.486027i	$-0.838446\pi$
$911$		−	885.541i		−	0.972054i	0.873944	−	0.486027i	$-0.161554\pi$
$912$	−189.459	+	41.3676i	−0.207741	+	0.0453592i
$913$	362.546			0.397094
$914$	446.293	+	932.352i	0.488286	+	1.02008i
$915$	−707.480	−	707.480i	−0.773203	−	0.773203i
$916$	101.063	−	10.9048i	0.110331	−	0.0119049i
$917$	−467.230	−	467.230i	−0.509520	−	0.509520i
$918$	50.2902	−	142.642i	0.0547824	−	0.155383i
$919$	714.964			0.777980			0.388990	−	0.921242i	$-0.372824\pi$
$919$	714.964			0.777980			0.388990	+	0.921242i	$0.372824\pi$
$920$	2729.12	−	1688.02i	2.96643	−	1.83481i
$921$			40.2774i			0.0437323i
$922$	25.8871	−	73.4255i	0.0280771	−	0.0796371i
$923$	97.9727	−	97.9727i	0.106146	−	0.106146i
$924$	−104.444	+	129.710i	−0.113035	+	0.140379i
$925$	−245.967	+	245.967i	−0.265911	+	0.265911i
$926$	−105.445	−	220.286i	−0.113872	−	0.237890i
$927$			117.914i			0.127200i
$928$	1127.08	+	140.461i	1.21453	+	0.151359i
$929$	585.585			0.630339			0.315170	−	0.949035i	$-0.397939\pi$
$929$	585.585			0.630339			0.315170	+	0.949035i	$0.397939\pi$
$930$	932.788	−	446.502i	1.00300	−	0.480109i
$931$	−165.536	−	165.536i	−0.177805	−	0.177805i
$932$	522.378	+	420.626i	0.560491	+	0.451315i
$933$	−48.7468	−	48.7468i	−0.0522474	−	0.0522474i
$934$	−714.792	−	252.009i	−0.765302	−	0.269817i
$935$	−814.960			−0.871614
$936$	−117.276	+	72.5378i	−0.125295	+	0.0774977i
$937$			1423.91i			1.51965i	0.650129	+	0.759824i	$0.274715\pi$
$937$			1423.91i			1.51965i	−0.650129	+	0.759824i	$0.725285\pi$
$938$	17.2554	+	6.08360i	0.0183959	+	0.00648572i
$939$	528.948	−	528.948i	0.563310	−	0.563310i
$940$	31.2325	+	289.453i	0.0332260	+	0.307929i
$941$	142.471	−	142.471i	0.151404	−	0.151404i	−0.627341	−	0.778745i	$-0.715857\pi$
$941$	142.471	−	142.471i	0.151404	−	0.151404i	0.778745	+	0.627341i	$0.215857\pi$
$942$	−335.297	+	160.498i	−0.355941	+	0.170380i
$943$			2416.56i			2.56264i
$944$	946.856	+	607.475i	1.00303	+	0.643511i
$945$	188.172			0.199124
$946$	−120.007	−	250.706i	−0.126857	−	0.265017i
$947$	174.352	+	174.352i	0.184110	+	0.184110i	0.793144	−	0.609034i	$-0.208443\pi$
$947$	174.352	+	174.352i	0.184110	+	0.184110i	−0.609034	+	0.793144i	$0.708443\pi$
$948$	−53.5525	−	496.308i	−0.0564900	−	0.523532i
$949$	−43.7733	−	43.7733i	−0.0461257	−	0.0461257i
$950$	276.242	−	783.525i	0.290781	−	0.824763i
$951$	−624.774			−0.656965
$952$	105.311	−	446.810i	0.110621	−	0.469339i
$953$			66.9080i			0.0702078i	0.999384	+	0.0351039i	$0.0111762\pi$
$953$			66.9080i			0.0702078i	−0.999384	+	0.0351039i	$0.988824\pi$
$954$	−89.0844	+	252.677i	−0.0933799	+	0.264860i
$955$	1115.53	−	1115.53i	1.16809	−	1.16809i
$956$	92.6899	+	74.6352i	0.0969559	+	0.0780703i
$957$	−265.022	+	265.022i	−0.276930	+	0.276930i
$958$	−361.887	−	756.019i	−0.377752	−	0.789163i
$959$		−	620.870i		−	0.647414i
$960$	−454.691	+	910.992i	−0.473637	+	0.948950i
$961$	−95.4048			−0.0992766
$962$	−60.7365	+	29.0730i	−0.0631356	+	0.0302214i
$963$	77.0943	+	77.0943i	0.0800564	+	0.0800564i
$964$	−269.364	+	334.525i	−0.279423	+	0.347017i
$965$	−1398.86	−	1398.86i	−1.44959	−	1.44959i
$966$	−562.531	−	198.327i	−0.582330	−	0.205308i
$967$	−128.892			−0.133290			−0.0666451	−	0.997777i	$-0.521230\pi$
$967$	−128.892			−0.133290			−0.0666451	+	0.997777i	$0.521230\pi$
$968$	−652.771	−	153.855i	−0.674350	−	0.158941i
$969$			176.395i			0.182038i
$970$	940.206	+	331.482i	0.969285	+	0.341734i
$971$	−801.089	+	801.089i	−0.825015	+	0.825015i	−0.986822	−	0.161808i	$-0.948268\pi$
$971$	−801.089	+	801.089i	−0.825015	+	0.825015i	0.161808	+	0.986822i	$0.448268\pi$
$972$	61.9940	−	6.68926i	0.0637798	−	0.00688195i
$973$	−468.959	+	468.959i	−0.481972	+	0.481972i
$974$	103.256	−	49.4258i	0.106012	−	0.0507452i
$975$		−	590.768i		−	0.605916i
$976$	−846.945	−	543.375i	−0.867771	−	0.556736i
$977$	−1591.49			−1.62896			−0.814479	−	0.580194i	$-0.802977\pi$
$977$	−1591.49			−1.62896			−0.814479	+	0.580194i	$0.802977\pi$
$978$	374.899	+	783.202i	0.383332	+	0.800820i
$979$	124.953	+	124.953i	0.127633	+	0.127633i
$980$	−1222.03	+	131.859i	−1.24697	+	0.134550i
$981$	−28.9840	−	28.9840i	−0.0295453	−	0.0295453i
$982$	283.976	−	805.463i	0.289182	−	0.820227i
$983$	−1699.86			−1.72926			−0.864631	−	0.502408i	$-0.832448\pi$
$983$	−1699.86			−1.72926			−0.864631	+	0.502408i	$0.832448\pi$
$984$	−403.330	−	652.087i	−0.409889	−	0.662690i
$985$		−	238.167i		−	0.241794i
$986$	343.522	−	974.355i	0.348399	−	0.988190i
$987$	38.2647	−	38.2647i	0.0387687	−	0.0387687i
$988$	100.863	−	125.263i	0.102089	−	0.126784i
$989$	703.939	−	703.939i	0.711769	−	0.711769i
$990$	−145.062	−	303.049i	−0.146527	−	0.306110i
$991$			228.875i			0.230954i	0.993310	+	0.115477i	$0.0368397\pi$
$991$			228.875i			0.230954i	−0.993310	+	0.115477i	$0.963160\pi$
$992$	820.750	−	638.849i	0.827369	−	0.644001i
$993$	−504.342			−0.507898
$994$	−171.517	+	82.1008i	−0.172552	+	0.0825963i
$995$	−1475.03	−	1475.03i	−1.48244	−	1.48244i
$996$	−320.902	−	258.395i	−0.322191	−	0.259433i
$997$	1020.63	+	1020.63i	1.02370	+	1.02370i	0.999712	+	0.0239926i	$0.00763781\pi$
$997$	1020.63	+	1020.63i	1.02370	+	1.02370i	0.0239926	+	0.999712i	$0.492362\pi$
$998$	−1653.82	−	583.076i	−1.65714	−	0.584245i
$999$	30.4480			0.0304785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.3.l.a.43.2	yes	16
3.2	odd	2		144.3.m.c.91.7		16
4.3	odd	2		192.3.l.a.79.8		16
8.3	odd	2		384.3.l.b.31.1		16
8.5	even	2		384.3.l.a.31.5		16
12.11	even	2		576.3.m.c.271.1		16
16.3	odd	4	inner	48.3.l.a.19.2	✓	16
16.5	even	4		384.3.l.b.223.1		16
16.11	odd	4		384.3.l.a.223.5		16
16.13	even	4		192.3.l.a.175.8		16
24.5	odd	2		1152.3.m.f.415.8		16
24.11	even	2		1152.3.m.c.415.8		16
48.5	odd	4		1152.3.m.c.991.8		16
48.11	even	4		1152.3.m.f.991.8		16
48.29	odd	4		576.3.m.c.559.1		16
48.35	even	4		144.3.m.c.19.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.2	✓	16	16.3	odd	4	inner
48.3.l.a.43.2	yes	16	1.1	even	1	trivial
144.3.m.c.19.7		16	48.35	even	4
144.3.m.c.91.7		16	3.2	odd	2
192.3.l.a.79.8		16	4.3	odd	2
192.3.l.a.175.8		16	16.13	even	4
384.3.l.a.31.5		16	8.5	even	2
384.3.l.a.223.5		16	16.11	odd	4
384.3.l.b.31.1		16	8.3	odd	2
384.3.l.b.223.1		16	16.5	even	4
576.3.m.c.271.1		16	12.11	even	2
576.3.m.c.559.1		16	48.29	odd	4
1152.3.m.c.415.8		16	24.11	even	2
1152.3.m.c.991.8		16	48.5	odd	4
1152.3.m.f.415.8		16	24.5	odd	2
1152.3.m.f.991.8		16	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80398 + 0.863518i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50867 - 3.11554i) q^{4} +(6.49473 + 6.49473i) q^{5} +(3.26700 + 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 + 7.78664i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.80398 + 0.863518i) q^{2} +(-1.22474 - 1.22474i) q^{3} +(2.50867 - 3.11554i) q^{4} +(6.49473 + 6.49473i) q^{5} +(3.26700 + 1.15182i) q^{6} +3.94273 q^{7} +(-1.83527 + 7.78664i) q^{8} +3.00000i q^{9} +(-17.3247 - 6.10803i) q^{10} +(4.31091 - 4.31091i) q^{11} +(-6.88822 + 0.743251i) q^{12} +(4.06281 - 4.06281i) q^{13} +(-7.11259 + 3.40462i) q^{14} -15.9088i q^{15} +(-3.41312 - 15.6317i) q^{16} -14.5538 q^{17} +(-2.59055 - 5.41193i) q^{18} +(4.94805 + 4.94805i) q^{19} +(36.5277 - 3.94140i) q^{20} +(-4.82883 - 4.82883i) q^{21} +(-4.05424 + 11.4993i) q^{22} -43.6717 q^{23} +(11.7844 - 7.28891i) q^{24} +59.3629i q^{25} +(-3.82091 + 10.8375i) q^{26} +(3.67423 - 3.67423i) q^{27} +(9.89101 - 12.2837i) q^{28} +(25.0979 - 25.0979i) q^{29} +(13.7375 + 28.6991i) q^{30} -32.5024i q^{31} +(19.6555 + 25.2520i) q^{32} -10.5595 q^{33} +(26.2547 - 12.5675i) q^{34} +(25.6069 + 25.6069i) q^{35} +(9.34661 + 7.52602i) q^{36} +(4.14345 + 4.14345i) q^{37} +(-13.1989 - 4.65344i) q^{38} -9.95180 q^{39} +(-62.4917 + 38.6525i) q^{40} -55.3348i q^{41} +(12.8809 + 4.54133i) q^{42} +(-16.1189 + 16.1189i) q^{43} +(-2.61613 - 24.2455i) q^{44} +(-19.4842 + 19.4842i) q^{45} +(78.7828 - 37.7113i) q^{46} +7.92420i q^{47} +(-14.9647 + 23.3251i) q^{48} -33.4549 q^{49} +(-51.2610 - 107.089i) q^{50} +(17.8247 + 17.8247i) q^{51} +(-2.46556 - 22.8501i) q^{52} +(-31.5748 - 31.5748i) q^{53} +(-3.45547 + 9.80101i) q^{54} +55.9964 q^{55} +(-7.23597 + 30.7006i) q^{56} -12.1202i q^{57} +(-23.6036 + 66.9485i) q^{58} +(-49.7172 + 49.7172i) q^{59} +(-49.5643 - 39.9099i) q^{60} +(44.4711 - 44.4711i) q^{61} +(28.0664 + 58.6336i) q^{62} +11.8282i q^{63} +(-57.2636 - 28.5812i) q^{64} +52.7736 q^{65} +(19.0492 - 9.11834i) q^{66} +(-1.64068 - 1.64068i) q^{67} +(-36.5107 + 45.3429i) q^{68} +(53.4867 + 53.4867i) q^{69} +(-68.3064 - 24.0823i) q^{70} +24.1145 q^{71} +(-23.3599 - 5.50581i) q^{72} -10.7741i q^{73} +(-11.0526 - 3.89675i) q^{74} +(72.7044 - 72.7044i) q^{75} +(27.8288 - 3.00278i) q^{76} +(16.9967 - 16.9967i) q^{77} +(17.9528 - 8.59356i) q^{78} +72.0517i q^{79} +(79.3565 - 123.691i) q^{80} -9.00000 q^{81} +(47.7826 + 99.8227i) q^{82} +(42.0499 + 42.0499i) q^{83} +(-27.1584 + 2.93044i) q^{84} +(-94.5229 - 94.5229i) q^{85} +(15.1592 - 42.9971i) q^{86} -61.4770 q^{87} +(25.6558 + 41.4792i) q^{88} +28.9853i q^{89} +(18.3241 - 51.9740i) q^{90} +(16.0185 - 16.0185i) q^{91} +(-109.558 + 136.061i) q^{92} +(-39.8071 + 39.8071i) q^{93} +(-6.84269 - 14.2951i) q^{94} +64.2724i q^{95} +(6.85432 - 55.0002i) q^{96} -54.2698 q^{97} +(60.3519 - 28.8889i) q^{98} +(12.9327 + 12.9327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} - 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 - 12 * q^8	\( 16 q + 12 q^{4} - 12 q^{8} - 56 q^{10} + 32 q^{11} - 24 q^{12} - 44 q^{14} + 32 q^{16} + 12 q^{18} - 32 q^{19} + 80 q^{20} + 32 q^{22} - 128 q^{23} + 36 q^{24} - 100 q^{26} - 120 q^{28} + 32 q^{29} + 72 q^{30} + 160 q^{32} + 96 q^{34} + 96 q^{35} + 12 q^{36} - 96 q^{37} + 168 q^{38} + 48 q^{40} - 60 q^{42} + 160 q^{43} + 88 q^{44} + 136 q^{46} - 144 q^{48} + 112 q^{49} - 236 q^{50} - 96 q^{51} - 48 q^{52} - 160 q^{53} - 36 q^{54} - 256 q^{55} - 224 q^{56} + 144 q^{58} - 128 q^{59} - 72 q^{60} - 32 q^{61} - 276 q^{62} - 408 q^{64} - 32 q^{65} + 72 q^{66} + 320 q^{67} - 448 q^{68} + 96 q^{69} - 384 q^{70} + 512 q^{71} + 60 q^{72} + 348 q^{74} + 192 q^{75} + 72 q^{76} + 224 q^{77} + 396 q^{78} + 552 q^{80} - 144 q^{81} - 40 q^{82} - 160 q^{83} + 72 q^{84} + 160 q^{85} + 528 q^{86} + 480 q^{88} - 24 q^{90} - 480 q^{91} + 496 q^{92} + 312 q^{94} - 480 q^{96} - 440 q^{98} + 96 q^{99}+O(q^{100}) \) 16 * q + 12 * q^4 - 12 * q^8 - 56 * q^10 + 32 * q^11 - 24 * q^12 - 44 * q^14 + 32 * q^16 + 12 * q^18 - 32 * q^19 + 80 * q^20 + 32 * q^22 - 128 * q^23 + 36 * q^24 - 100 * q^26 - 120 * q^28 + 32 * q^29 + 72 * q^30 + 160 * q^32 + 96 * q^34 + 96 * q^35 + 12 * q^36 - 96 * q^37 + 168 * q^38 + 48 * q^40 - 60 * q^42 + 160 * q^43 + 88 * q^44 + 136 * q^46 - 144 * q^48 + 112 * q^49 - 236 * q^50 - 96 * q^51 - 48 * q^52 - 160 * q^53 - 36 * q^54 - 256 * q^55 - 224 * q^56 + 144 * q^58 - 128 * q^59 - 72 * q^60 - 32 * q^61 - 276 * q^62 - 408 * q^64 - 32 * q^65 + 72 * q^66 + 320 * q^67 - 448 * q^68 + 96 * q^69 - 384 * q^70 + 512 * q^71 + 60 * q^72 + 348 * q^74 + 192 * q^75 + 72 * q^76 + 224 * q^77 + 396 * q^78 + 552 * q^80 - 144 * q^81 - 40 * q^82 - 160 * q^83 + 72 * q^84 + 160 * q^85 + 528 * q^86 + 480 * q^88 - 24 * q^90 - 480 * q^91 + 496 * q^92 + 312 * q^94 - 480 * q^96 - 440 * q^98 + 96 * q^99

Introduction

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