LMFDB - Embedded newform 144.3.m.c.19.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(19,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, 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("144.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.m (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:	$3.92371580679$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			19.7
Root			$1.80398 - 0.863518i$ of defining polynomial
Character	$\chi$	$=$	144.19
Dual form			144.3.m.c.91.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +O(q^{10})$	\(q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +(-17.3247 + 6.10803i) q^{10} +(-4.31091 - 4.31091i) q^{11} +(4.06281 + 4.06281i) q^{13} +(7.11259 + 3.40462i) q^{14} +(-3.41312 + 15.6317i) q^{16} +14.5538 q^{17} +(4.94805 - 4.94805i) q^{19} +(-36.5277 - 3.94140i) q^{20} +(-4.05424 - 11.4993i) q^{22} +43.6717 q^{23} -59.3629i q^{25} +(3.82091 + 10.8375i) q^{26} +(9.89101 + 12.2837i) q^{28} +(-25.0979 - 25.0979i) q^{29} +32.5024i q^{31} +(-19.6555 + 25.2520i) q^{32} +(26.2547 + 12.5675i) q^{34} +(-25.6069 + 25.6069i) q^{35} +(4.14345 - 4.14345i) q^{37} +(13.1989 - 4.65344i) q^{38} +(-62.4917 - 38.6525i) q^{40} -55.3348i q^{41} +(-16.1189 - 16.1189i) q^{43} +(2.61613 - 24.2455i) q^{44} +(78.7828 + 37.7113i) q^{46} +7.92420i q^{47} -33.4549 q^{49} +(51.2610 - 107.089i) q^{50} +(-2.46556 + 22.8501i) q^{52} +(31.5748 - 31.5748i) q^{53} +55.9964 q^{55} +(7.23597 + 30.7006i) q^{56} +(-23.6036 - 66.9485i) q^{58} +(49.7172 + 49.7172i) q^{59} +(44.4711 + 44.4711i) q^{61} +(-28.0664 + 58.6336i) q^{62} +(-57.2636 + 28.5812i) q^{64} -52.7736 q^{65} +(-1.64068 + 1.64068i) q^{67} +(36.5107 + 45.3429i) q^{68} +(-68.3064 + 24.0823i) q^{70} -24.1145 q^{71} +10.7741i q^{73} +(11.0526 - 3.89675i) q^{74} +(27.8288 + 3.00278i) q^{76} +(-16.9967 - 16.9967i) q^{77} -72.0517i q^{79} +(-79.3565 - 123.691i) q^{80} +(47.7826 - 99.8227i) q^{82} +(-42.0499 + 42.0499i) q^{83} +(-94.5229 + 94.5229i) q^{85} +(-15.1592 - 42.9971i) q^{86} +(25.6558 - 41.4792i) q^{88} +28.9853i q^{89} +(16.0185 + 16.0185i) q^{91} +(109.558 + 136.061i) q^{92} +(-6.84269 + 14.2951i) q^{94} +64.2724i q^{95} -54.2698 q^{97} +(-60.3519 - 28.8889i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) $ 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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
$3$		0			0
$3$		0			0
$4$	2.50867	+	3.11554i	0.627168	+	0.778884i
$5$	−6.49473	+	6.49473i	−1.29895	+	1.29895i	−0.369856	+	0.929089i	$0.620593\pi$
$5$	−6.49473	+	6.49473i	−1.29895	+	1.29895i	−0.929089	+	0.369856i	$0.879407\pi$
$6$		0			0
$7$	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
$9$		0			0
$10$	−17.3247	+	6.10803i	−1.73247	+	0.610803i
$11$	−4.31091	−	4.31091i	−0.391901	−	0.391901i	0.483464	−	0.875364i	$-0.339379\pi$
$11$	−4.31091	−	4.31091i	−0.391901	−	0.391901i	−0.875364	+	0.483464i	$0.839379\pi$
$12$		0			0
$13$	4.06281	+	4.06281i	0.312524	+	0.312524i	0.845887	−	0.533363i	$-0.179072\pi$
$13$	4.06281	+	4.06281i	0.312524	+	0.312524i	−0.533363	+	0.845887i	$0.679072\pi$
$14$	7.11259	+	3.40462i	0.508042	+	0.243187i
$15$		0			0
$16$	−3.41312	+	15.6317i	−0.213320	+	0.976982i
$17$	14.5538			0.856106			0.428053	−	0.903754i	$-0.359200\pi$
$17$	14.5538			0.856106			0.428053	+	0.903754i	$0.359200\pi$
$18$		0			0
$19$	4.94805	−	4.94805i	0.260423	−	0.260423i	−0.564803	−	0.825226i	$-0.691048\pi$
$19$	4.94805	−	4.94805i	0.260423	−	0.260423i	0.825226	+	0.564803i	$0.191048\pi$
$20$	−36.5277	−	3.94140i	−1.82638	−	0.197070i
$21$		0			0
$22$	−4.05424	−	11.4993i	−0.184284	−	0.522697i
$23$	43.6717			1.89877			0.949385	−	0.314115i	$-0.101708\pi$
$23$	43.6717			1.89877			0.949385	+	0.314115i	$0.101708\pi$
$24$		0			0
$25$		−	59.3629i		−	2.37452i
$26$	3.82091	+	10.8375i	0.146958	+	0.416828i
$27$		0			0
$28$	9.89101	+	12.2837i	0.353250	+	0.438704i
$29$	−25.0979	−	25.0979i	−0.865445	−	0.865445i	0.126519	−	0.991964i	$-0.459619\pi$
$29$	−25.0979	−	25.0979i	−0.865445	−	0.865445i	−0.991964	+	0.126519i	$0.959619\pi$
$30$		0			0
$31$			32.5024i			1.04846i	0.851576	+	0.524232i	$0.175648\pi$
$31$			32.5024i			1.04846i	−0.851576	+	0.524232i	$0.824352\pi$
$32$	−19.6555	+	25.2520i	−0.614233	+	0.789125i
$33$		0			0
$34$	26.2547	+	12.5675i	0.772198	+	0.369631i
$35$	−25.6069	+	25.6069i	−0.731627	+	0.731627i
$36$		0			0
$37$	4.14345	−	4.14345i	0.111985	−	0.111985i	−0.648894	−	0.760879i	$-0.724768\pi$
$37$	4.14345	−	4.14345i	0.111985	−	0.111985i	0.760879	+	0.648894i	$0.224768\pi$
$38$	13.1989	−	4.65344i	0.347339	−	0.122459i
$39$		0			0
$40$	−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	$-0.235776\pi$
$42$		0			0
$43$	−16.1189	−	16.1189i	−0.374858	−	0.374858i	0.494385	−	0.869243i	$-0.335393\pi$
$43$	−16.1189	−	16.1189i	−0.374858	−	0.374858i	−0.869243	+	0.494385i	$0.835393\pi$
$44$	2.61613	−	24.2455i	0.0594574	−	0.551033i
$45$		0			0
$46$	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	$0.973135\pi$
$48$		0			0
$49$	−33.4549			−0.682753
$50$	51.2610	−	107.089i	1.02522	−	2.14179i
$51$		0			0
$52$	−2.46556	+	22.8501i	−0.0474147	+	0.439424i
$53$	31.5748	−	31.5748i	0.595750	−	0.595750i	−0.343429	−	0.939179i	$-0.611588\pi$
$53$	31.5748	−	31.5748i	0.595750	−	0.595750i	0.939179	+	0.343429i	$0.111588\pi$
$54$		0			0
$55$	55.9964			1.01812
$56$	7.23597	+	30.7006i	0.129214	+	0.548225i
$57$		0			0
$58$	−23.6036	−	66.9485i	−0.406958	−	1.15429i
$59$	49.7172	+	49.7172i	0.842665	+	0.842665i	0.989205	−	0.146540i	$-0.0468137\pi$
$59$	49.7172	+	49.7172i	0.842665	+	0.842665i	−0.146540	+	0.989205i	$0.546814\pi$
$60$		0			0
$61$	44.4711	+	44.4711i	0.729035	+	0.729035i	0.970427	−	0.241393i	$-0.0776043\pi$
$61$	44.4711	+	44.4711i	0.729035	+	0.729035i	−0.241393	+	0.970427i	$0.577604\pi$
$62$	−28.0664	+	58.6336i	−0.452684	+	0.945703i
$63$		0			0
$64$	−57.2636	+	28.5812i	−0.894743	+	0.446581i
$65$	−52.7736			−0.811902
$66$		0			0
$67$	−1.64068	+	1.64068i	−0.0244878	+	0.0244878i	−0.719245	−	0.694757i	$-0.755512\pi$
$67$	−1.64068	+	1.64068i	−0.0244878	+	0.0244878i	0.694757	+	0.719245i	$0.255512\pi$
$68$	36.5107	+	45.3429i	0.536922	+	0.666807i
$69$		0			0
$70$	−68.3064	+	24.0823i	−0.975805	+	0.344033i
$71$	−24.1145			−0.339641			−0.169821	−	0.985475i	$-0.554319\pi$
$71$	−24.1145			−0.339641			−0.169821	+	0.985475i	$0.554319\pi$
$72$		0			0
$73$			10.7741i			0.147591i	0.997273	+	0.0737955i	$0.0235112\pi$
$73$			10.7741i			0.147591i	−0.997273	+	0.0737955i	$0.976489\pi$
$74$	11.0526	−	3.89675i	0.149360	−	0.0526588i
$75$		0			0
$76$	27.8288	+	3.00278i	0.366169	+	0.0395103i
$77$	−16.9967	−	16.9967i	−0.220737	−	0.220737i
$78$		0			0
$79$		−	72.0517i		−	0.912047i	−0.889968	−	0.456024i	$-0.849273\pi$
$79$		−	72.0517i		−	0.912047i	0.889968	−	0.456024i	$-0.150727\pi$
$80$	−79.3565	−	123.691i	−0.991956	−	1.54614i
$81$		0			0
$82$	47.7826	−	99.8227i	0.582714	−	1.21735i
$83$	−42.0499	+	42.0499i	−0.506625	+	0.506625i	−0.913489	−	0.406864i	$-0.866622\pi$
$83$	−42.0499	+	42.0499i	−0.506625	+	0.506625i	0.406864	+	0.913489i	$0.366622\pi$
$84$		0			0
$85$	−94.5229	+	94.5229i	−1.11203	+	1.11203i
$86$	−15.1592	−	42.9971i	−0.176269	−	0.499966i
$87$		0			0
$88$	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	$0.947935\pi$
$90$		0			0
$91$	16.0185	+	16.0185i	0.176028	+	0.176028i
$92$	109.558	+	136.061i	1.19085	+	1.47892i
$93$		0			0
$94$	−6.84269	+	14.2951i	−0.0727946	+	0.152075i
$95$			64.2724i			0.676552i
$96$		0			0
$97$	−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
$99$		0			0
$100$	184.947	−	148.922i	1.84947	−	1.48922i
$101$	−57.0829	+	57.0829i	−0.565177	+	0.565177i	−0.930773	−	0.365597i	$-0.880865\pi$
$101$	−57.0829	+	57.0829i	−0.565177	+	0.565177i	0.365597	+	0.930773i	$0.380865\pi$
$102$		0			0
$103$	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
$105$		0			0
$106$	84.2255	−	29.6948i	0.794581	−	0.280140i
$107$	−25.6981	−	25.6981i	−0.240169	−	0.240169i	0.576751	−	0.816920i	$-0.304320\pi$
$107$	−25.6981	−	25.6981i	−0.240169	−	0.240169i	−0.816920	+	0.576751i	$0.804320\pi$
$108$		0			0
$109$	−9.66133	−	9.66133i	−0.0886360	−	0.0886360i	0.661399	−	0.750035i	$-0.269963\pi$
$109$	−9.66133	−	9.66133i	−0.0886360	−	0.0886360i	−0.750035	+	0.661399i	$0.769963\pi$
$110$	101.016	+	48.3539i	0.918329	+	0.439581i
$111$		0			0
$112$	−13.4570	+	61.6316i	−0.120152	+	0.550282i
$113$	−64.2927			−0.568962			−0.284481	−	0.958682i	$-0.591821\pi$
$113$	−64.2927			−0.568962			−0.284481	+	0.958682i	$0.591821\pi$
$114$		0			0
$115$	−283.636	+	283.636i	−2.46640	+	2.46640i
$116$	15.2310	−	141.156i	0.131301	−	1.21686i
$117$		0			0
$118$	46.7571	+	132.620i	0.396246	+	1.12390i
$119$	57.3816			0.482199
$120$		0			0
$121$		−	83.8321i		−	0.692827i
$122$	41.8233	+	118.627i	0.342814	+	0.972348i
$123$		0			0
$124$	−101.262	+	81.5379i	−0.816632	+	0.657563i
$125$	223.178	+	223.178i	1.78542	+	1.78542i
$126$		0			0
$127$			129.668i			1.02101i	0.859875	+	0.510504i	$0.170541\pi$
$127$			129.668i			1.02101i	−0.859875	+	0.510504i	$0.829459\pi$
$128$	−127.983	+	2.11172i	−0.999864	+	0.0164978i
$129$		0			0
$130$	−95.2025	−	45.5710i	−0.732327	−	0.350546i
$131$	118.504	−	118.504i	0.904613	−	0.904613i	−0.0912183	−	0.995831i	$-0.529076\pi$
$131$	118.504	−	118.504i	0.904613	−	0.904613i	0.995831	+	0.0912183i	$0.0290761\pi$
$132$		0			0
$133$	19.5088	−	19.5088i	0.146683	−	0.146683i
$134$	−4.37651	+	1.54299i	−0.0326605	+	0.0115149i
$135$		0			0
$136$	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	$-0.194888\pi$
$138$		0			0
$139$	−118.943	−	118.943i	−0.855703	−	0.855703i	0.135125	−	0.990829i	$-0.456856\pi$
$139$	−118.943	−	118.943i	−0.855703	−	0.855703i	−0.990829	+	0.135125i	$0.956856\pi$
$140$	−144.019	−	15.5399i	−1.02871	−	0.110999i
$141$		0			0
$142$	−43.5021	−	20.8233i	−0.306353	−	0.146643i
$143$		−	35.0288i		−	0.244957i
$144$		0			0
$145$	326.008			2.24833
$146$	−9.30367	+	19.4363i	−0.0637238	+	0.133125i
$147$		0			0
$148$	23.3036	+	2.51450i	0.157457	+	0.0169899i
$149$	−99.5402	+	99.5402i	−0.668055	+	0.668055i	−0.957266	−	0.289210i	$-0.906607\pi$
$149$	−99.5402	+	99.5402i	−0.668055	+	0.668055i	0.289210	+	0.957266i	$0.406607\pi$
$150$		0			0
$151$	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
$153$		0			0
$154$	−15.9848	−	45.3387i	−0.103797	−	0.294407i
$155$	−211.094	−	211.094i	−1.36190	−	1.36190i
$156$		0			0
$157$	−75.8792	−	75.8792i	−0.483307	−	0.483307i	0.422879	−	0.906186i	$-0.361019\pi$
$157$	−75.8792	−	75.8792i	−0.483307	−	0.483307i	−0.906186	+	0.422879i	$0.861019\pi$
$158$	62.2180	−	129.980i	0.393785	−	0.822657i
$159$		0			0
$160$	−36.3479	−	291.662i	−0.227175	−	1.82288i
$161$	172.186			1.06948
$162$		0			0
$163$	177.242	−	177.242i	1.08737	−	1.08737i	0.0915766	−	0.995798i	$-0.470809\pi$
$163$	177.242	−	177.242i	1.08737	−	1.08737i	0.995798	−	0.0915766i	$-0.0291906\pi$
$164$	172.397	−	138.817i	1.05120	−	0.846444i
$165$		0			0
$166$	−112.168	+	39.5462i	−0.675710	+	0.238230i
$167$	−61.6774			−0.369326			−0.184663	−	0.982802i	$-0.559119\pi$
$167$	−61.6774			−0.369326			−0.184663	+	0.982802i	$0.559119\pi$
$168$		0			0
$169$		−	135.987i		−	0.804658i
$170$	−252.140	+	88.8950i	−1.48317	+	0.522912i
$171$		0			0
$172$	9.78193	−	90.6560i	0.0568717	−	0.527069i
$173$	−69.7012	−	69.7012i	−0.402897	−	0.402897i	0.476355	−	0.879253i	$-0.341958\pi$
$173$	−69.7012	−	69.7012i	−0.402897	−	0.402897i	−0.879253	+	0.476355i	$0.841958\pi$
$174$		0			0
$175$		−	234.052i		−	1.33744i
$176$	82.1006	−	52.6733i	0.466481	−	0.299280i
$177$		0			0
$178$	−25.0293	+	52.2888i	−0.140614	+	0.293757i
$179$	−43.6228	+	43.6228i	−0.243703	+	0.243703i	−0.818380	−	0.574677i	$-0.805128\pi$
$179$	−43.6228	+	43.6228i	−0.243703	+	0.243703i	0.574677	+	0.818380i	$0.305128\pi$
$180$		0			0
$181$	−44.7291	+	44.7291i	−0.247122	+	0.247122i	−0.819788	−	0.572666i	$-0.805909\pi$
$181$	−44.7291	+	44.7291i	−0.247122	+	0.247122i	0.572666	+	0.819788i	$0.305909\pi$
$182$	15.0648	+	42.7294i	0.0827736	+	0.234777i
$183$		0			0
$184$	80.1494	+	340.056i	0.435595	+	1.84813i
$185$			53.8211i			0.290925i
$186$		0			0
$187$	−62.7401	−	62.7401i	−0.335509	−	0.335509i
$188$	−24.6881	+	19.8792i	−0.131320	+	0.105741i
$189$		0			0
$190$	−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	$-0.148445\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−83.9274	−	104.230i	−0.428201	−	0.531785i
$197$	18.3354	−	18.3354i	0.0930731	−	0.0930731i	−0.659037	−	0.752110i	$-0.729036\pi$
$197$	18.3354	−	18.3354i	0.0930731	−	0.0930731i	0.752110	+	0.659037i	$0.229036\pi$
$198$		0			0
$199$	−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
$201$		0			0
$202$	−152.268	+	53.6842i	−0.753804	+	0.265763i
$203$	−98.9542	−	98.9542i	−0.487459	−	0.487459i
$204$		0			0
$205$	359.384	+	359.384i	1.75309	+	1.75309i
$206$	70.9051	+	33.9404i	0.344199	+	0.164759i
$207$		0			0
$208$	−77.3755	+	49.6418i	−0.371998	+	0.238663i
$209$	−42.6612			−0.204120
$210$		0			0
$211$	190.206	−	190.206i	0.901451	−	0.901451i	−0.0941112	−	0.995562i	$-0.530001\pi$
$211$	190.206	−	190.206i	0.901451	−	0.901451i	0.995562	+	0.0941112i	$0.0300009\pi$
$212$	177.583	+	19.1615i	0.837656	+	0.0903845i
$213$		0			0
$214$	−24.1680	−	68.5496i	−0.112935	−	0.320325i
$215$	209.375			0.973839
$216$		0			0
$217$			128.148i			0.590544i
$218$	−9.08609	−	25.7716i	−0.0416793	−	0.118218i
$219$		0			0
$220$	140.477	+	174.459i	0.638530	+	0.792994i
$221$	59.1293	+	59.1293i	0.267553	+	0.267553i
$222$		0			0
$223$		−	154.401i		−	0.692379i	−0.938165	−	0.346190i	$-0.887475\pi$
$223$		−	154.401i		−	0.692379i	0.938165	−	0.346190i	$-0.112525\pi$
$224$	−77.4961	+	99.5617i	−0.345965	+	0.444472i
$225$		0			0
$226$	−115.983	−	55.5179i	−0.513197	−	0.245654i
$227$	36.8204	−	36.8204i	0.162204	−	0.162204i	−0.621338	−	0.783543i	$-0.713411\pi$
$227$	36.8204	−	36.8204i	0.162204	−	0.162204i	0.783543	+	0.621338i	$0.213411\pi$
$228$		0			0
$229$	17.9692	−	17.9692i	0.0784683	−	0.0784683i	−0.666783	−	0.745252i	$-0.732329\pi$
$229$	17.9692	−	17.9692i	0.0784683	−	0.0784683i	0.745252	+	0.666783i	$0.232329\pi$
$230$	−756.597	+	266.748i	−3.28955	+	1.15977i
$231$		0			0
$232$	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	$0.882844\pi$
$234$		0			0
$235$	−51.4655	−	51.4655i	−0.219002	−	0.219002i
$236$	−30.1715	+	279.620i	−0.127845	+	1.18483i
$237$		0			0
$238$	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	$0.980175\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	−26.9878	+	250.115i	−0.110606	+	1.02506i
$245$	217.280	−	217.280i	0.886859	−	0.886859i
$246$		0			0
$247$	40.2059			0.162777
$248$	−253.084	+	59.6507i	−1.02050	+	0.240527i
$249$		0			0
$250$	209.890	+	595.326i	0.839559	+	2.38130i
$251$	342.946	+	342.946i	1.36632	+	1.36632i	0.865623	+	0.500697i	$0.166923\pi$
$251$	342.946	+	342.946i	1.36632	+	1.36632i	0.500697	+	0.865623i	$0.333077\pi$
$252$		0			0
$253$	−188.265	−	188.265i	−0.744130	−	0.744130i
$254$	−111.971	+	233.918i	−0.440829	+	0.920938i
$255$		0			0
$256$	−232.701	−	106.706i	−0.908989	−	0.416819i
$257$	393.565			1.53138			0.765691	−	0.643209i	$-0.222397\pi$
$257$	393.565			1.53138			0.765691	+	0.643209i	$0.222397\pi$
$258$		0			0
$259$	16.3365	−	16.3365i	0.0630753	−	0.0630753i
$260$	−132.392	−	164.418i	−0.509199	−	0.632377i
$261$		0			0
$262$	316.110	−	111.449i	1.20653	−	0.425376i
$263$	−413.800			−1.57338			−0.786692	−	0.617346i	$-0.788208\pi$
$263$	−413.800			−1.57338			−0.786692	+	0.617346i	$0.788208\pi$
$264$		0			0
$265$			410.139i			1.54769i
$266$	52.0396	−	18.3472i	0.195638	−	0.0689746i
$267$		0			0
$268$	−9.22752	−	0.995666i	−0.0344311	−	0.00371517i
$269$	−165.389	−	165.389i	−0.614830	−	0.614830i	0.329371	−	0.944201i	$-0.393163\pi$
$269$	−165.389	−	165.389i	−0.614830	−	0.614830i	−0.944201	+	0.329371i	$0.893163\pi$
$270$		0			0
$271$			309.821i			1.14325i	0.820514	+	0.571626i	$0.193687\pi$
$271$			309.821i			1.14325i	−0.820514	+	0.571626i	$0.806313\pi$
$272$	−49.6738	+	227.501i	−0.182624	+	0.836400i
$273$		0			0
$274$	135.980	−	284.076i	0.496278	−	1.03678i
$275$	−255.908	+	255.908i	−0.930575	+	0.930575i
$276$		0			0
$277$	157.397	−	157.397i	0.568221	−	0.568221i	−0.363409	−	0.931630i	$-0.618387\pi$
$277$	157.397	−	157.397i	0.568221	−	0.568221i	0.931630	+	0.363409i	$0.118387\pi$
$278$	−111.861	−	317.279i	−0.402377	−	1.14129i
$279$		0			0
$280$	−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	$0.738789\pi$
$282$		0			0
$283$	343.521	+	343.521i	1.21385	+	1.21385i	0.969748	+	0.244106i	$0.0784946\pi$
$283$	343.521	+	343.521i	1.21385	+	1.21385i	0.244106	+	0.969748i	$0.421505\pi$
$284$	−60.4955	−	75.1297i	−0.213012	−	0.264541i
$285$		0			0
$286$	30.2480	−	63.1912i	0.105762	−	0.220948i
$287$		−	218.170i		−	0.760174i
$288$		0			0
$289$	−77.1870			−0.267083
$290$	588.111	+	281.514i	2.02797	+	0.970737i
$291$		0			0
$292$	−33.5672	+	27.0288i	−0.114956	+	0.0925644i
$293$	−35.1386	+	35.1386i	−0.119927	+	0.119927i	−0.764523	−	0.644596i	$-0.777025\pi$
$293$	−35.1386	+	35.1386i	−0.119927	+	0.119927i	0.644596	+	0.764523i	$0.277025\pi$
$294$		0			0
$295$	−645.799			−2.18915
$296$	39.8679	+	24.6592i	0.134689	+	0.0833081i
$297$		0			0
$298$	−265.523	+	93.6136i	−0.891017	+	0.314140i
$299$	177.430	+	177.430i	0.593410	+	0.593410i
$300$		0			0
$301$	−63.5524	−	63.5524i	−0.211137	−	0.211137i
$302$	493.758	+	236.349i	1.63496	+	0.782613i
$303$		0			0
$304$	60.4582	+	94.2347i	0.198876	+	0.309983i
$305$	−577.655			−1.89395
$306$		0			0
$307$	−16.4432	+	16.4432i	−0.0535609	+	0.0535609i	−0.733380	−	0.679819i	$-0.762058\pi$
$307$	−16.4432	+	16.4432i	−0.0535609	+	0.0535609i	0.679819	+	0.733380i	$0.262058\pi$
$308$	10.3147	−	95.5932i	0.0334892	−	0.310368i
$309$		0			0
$310$	−198.526	−	563.093i	−0.640405	−	1.81643i
$311$	−39.8016			−0.127980			−0.0639898	−	0.997951i	$-0.520382\pi$
$311$	−39.8016			−0.127980			−0.0639898	+	0.997951i	$0.520382\pi$
$312$		0			0
$313$		−	431.885i		−	1.37982i	−0.723894	−	0.689911i	$-0.757649\pi$
$313$		−	431.885i		−	1.37982i	0.723894	−	0.689911i	$-0.242351\pi$
$314$	−71.3613	−	202.407i	−0.227265	−	0.644610i
$315$		0			0
$316$	224.480	−	180.754i	0.710379	−	0.572007i
$317$	−255.063	−	255.063i	−0.804615	−	0.804615i	0.179198	−	0.983813i	$-0.442650\pi$
$317$	−255.063	−	255.063i	−0.804615	−	0.804615i	−0.983813	+	0.179198i	$0.942650\pi$
$318$		0			0
$319$			216.390i			0.678337i
$320$	186.284	−	557.538i	0.582138	−	1.74231i
$321$		0			0
$322$	310.619	+	148.685i	0.964656	+	0.461756i
$323$	72.0128	−	72.0128i	0.222950	−	0.222950i
$324$		0			0
$325$	241.180	−	241.180i	0.742092	−	0.742092i
$326$	472.792	−	166.689i	1.45028	−	0.511316i
$327$		0			0
$328$	430.872	−	101.554i	1.31363	−	0.309617i
$329$			31.2430i			0.0949635i
$330$		0			0
$331$	205.897	+	205.897i	0.622045	+	0.622045i	0.946054	−	0.324009i	$-0.105031\pi$
$331$	205.897	+	205.897i	0.622045	+	0.622045i	−0.324009	+	0.946054i	$0.605031\pi$
$332$	−236.497	−	25.5185i	−0.712341	−	0.0768628i
$333$		0			0
$334$	−111.265	−	53.2596i	−0.333128	−	0.159460i
$335$		−	21.3115i		−	0.0636165i
$336$		0			0
$337$	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
$339$		0			0
$340$	−531.617	−	57.3623i	−1.56358	−	0.168713i
$341$	140.115	−	140.115i	0.410894	−	0.410894i
$342$		0			0
$343$	−325.097			−0.947805
$344$	95.9294	−	155.094i	0.278865	−	0.450856i
$345$		0			0
$346$	−65.5512	−	185.928i	−0.189454	−	0.537363i
$347$	−296.512	−	296.512i	−0.854500	−	0.854500i	0.136183	−	0.990684i	$-0.456516\pi$
$347$	−296.512	−	296.512i	−0.854500	−	0.854500i	−0.990684	+	0.136183i	$0.956516\pi$
$348$		0			0
$349$	−198.107	−	198.107i	−0.567641	−	0.567641i	0.363826	−	0.931467i	$-0.381470\pi$
$349$	−198.107	−	198.107i	−0.567641	−	0.567641i	−0.931467	+	0.363826i	$0.881470\pi$
$350$	202.108	−	422.224i	0.577451	−	1.20636i
$351$		0			0
$352$	193.592	−	24.1261i	0.549977	−	0.0685402i
$353$	−85.4490			−0.242065			−0.121033	−	0.992649i	$-0.538621\pi$
$353$	−85.4490			−0.242065			−0.121033	+	0.992649i	$0.538621\pi$
$354$		0			0
$355$	156.617	−	156.617i	0.441176	−	0.441176i
$356$	−90.3046	+	72.7145i	−0.253665	+	0.204254i
$357$		0			0
$358$	−116.364	+	41.0255i	−0.325038	+	0.114596i
$359$	302.214			0.841823			0.420911	−	0.907102i	$-0.361710\pi$
$359$	302.214			0.841823			0.420911	+	0.907102i	$0.361710\pi$
$360$		0			0
$361$			312.034i			0.864359i
$362$	−119.315	+	42.0659i	−0.329599	+	0.116204i
$363$		0			0
$364$	−9.72104	+	90.0916i	−0.0267061	+	0.247504i
$365$	−69.9751	−	69.9751i	−0.191713	−	0.191713i
$366$		0			0
$367$			372.554i			1.01513i	0.861612	+	0.507567i	$0.169455\pi$
$367$			372.554i			1.01513i	−0.861612	+	0.507567i	$0.830545\pi$
$368$	−149.057	+	682.664i	−0.405045	+	1.85507i
$369$		0			0
$370$	−46.4755	+	97.0921i	−0.125610	+	0.262411i
$371$	124.491	−	124.491i	0.335554	−	0.335554i
$372$		0			0
$373$	−407.130	+	407.130i	−1.09150	+	1.09150i	−0.0961318	+	0.995369i	$0.530647\pi$
$373$	−407.130	+	407.130i	−1.09150	+	1.09150i	−0.995369	+	0.0961318i	$0.969353\pi$
$374$	−59.0046	−	167.359i	−0.157766	−	0.447484i
$375$		0			0
$376$	−61.7029	+	14.5431i	−0.164104	+	0.0386784i
$377$		−	203.936i		−	0.540944i
$378$		0			0
$379$	−117.854	−	117.854i	−0.310961	−	0.310961i	0.534321	−	0.845282i	$-0.320567\pi$
$379$	−117.854	−	117.854i	−0.310961	−	0.310961i	−0.845282	+	0.534321i	$0.820567\pi$
$380$	−200.243	+	161.238i	−0.526955	+	0.424312i
$381$		0			0
$382$	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	$0.821209\pi$
$384$		0			0
$385$	220.778			0.573450
$386$	−388.548	−	185.988i	−1.00660	−	0.481834i
$387$		0			0
$388$	−136.145	−	169.080i	−0.350890	−	0.435772i
$389$	−458.508	+	458.508i	−1.17868	+	1.17868i	−0.198605	+	0.980080i	$0.563641\pi$
$389$	−458.508	+	458.508i	−1.17868	+	1.17868i	−0.980080	+	0.198605i	$0.936359\pi$
$390$		0			0
$391$	635.589			1.62555
$392$	−61.3988	−	260.501i	−0.156630	−	0.664544i
$393$		0			0
$394$	48.9096	−	17.2437i	0.124136	−	0.0437658i
$395$	467.956	+	467.956i	1.18470	+	1.18470i
$396$		0			0
$397$	−259.865	−	259.865i	−0.654573	−	0.654573i	0.299518	−	0.954091i	$-0.403174\pi$
$397$	−259.865	−	259.865i	−0.654573	−	0.654573i	−0.954091	+	0.299518i	$0.903174\pi$
$398$	−409.705	−	196.115i	−1.02941	−	0.492752i
$399$		0			0
$400$	927.944	+	202.613i	2.31986	+	0.506531i
$401$	499.197			1.24488			0.622441	−	0.782667i	$-0.286141\pi$
$401$	499.197			1.24488			0.622441	+	0.782667i	$0.286141\pi$
$402$		0			0
$403$	−132.051	+	132.051i	−0.327670	+	0.327670i
$404$	−321.046	−	34.6414i	−0.794668	−	0.0857461i
$405$		0			0
$406$	−93.0624	−	263.960i	−0.229218	−	0.650147i
$407$	−35.7241			−0.0877741
$408$		0			0
$409$			494.949i			1.21014i	0.796171	+	0.605072i	$0.206856\pi$
$409$			494.949i			1.21014i	−0.796171	+	0.605072i	$0.793144\pi$
$410$	337.986	+	958.656i	0.824357	+	2.33819i
$411$		0			0
$412$	98.6030	+	122.456i	0.239328	+	0.297222i
$413$	196.021	+	196.021i	0.474628	+	0.474628i
$414$		0			0
$415$		−	546.205i		−	1.31616i
$416$	−182.450	+	22.7376i	−0.438582	+	0.0546577i
$417$		0			0
$418$	−76.9598	−	36.8387i	−0.184114	−	0.0881308i
$419$	560.555	−	560.555i	1.33784	−	1.33784i	0.439693	−	0.898148i	$-0.355087\pi$
$419$	560.555	−	560.555i	1.33784	−	1.33784i	0.898148	−	0.439693i	$-0.144913\pi$
$420$		0			0
$421$	397.946	−	397.946i	0.945239	−	0.945239i	−0.0533373	−	0.998577i	$-0.516986\pi$
$421$	397.946	−	397.946i	0.945239	−	0.945239i	0.998577	+	0.0533373i	$0.0169858\pi$
$422$	507.374	−	178.881i	1.20231	−	0.423889i
$423$		0			0
$424$	303.810	+	187.913i	0.716532	+	0.443191i
$425$		−	863.956i		−	2.03284i
$426$		0			0
$427$	175.337	+	175.337i	0.410626	+	0.410626i
$428$	15.5952	−	144.531i	0.0364374	−	0.337690i
$429$		0			0
$430$	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	$0.720757\pi$
$432$		0			0
$433$	−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
$435$		0			0
$436$	5.86309	−	54.3373i	0.0134475	−	0.124627i
$437$	216.090	−	216.090i	0.494484	−	0.494484i
$438$		0			0
$439$	−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
$441$		0			0
$442$	55.6087	+	157.727i	0.125812	+	0.356849i
$443$	−421.096	−	421.096i	−0.950555	−	0.950555i	0.0482792	−	0.998834i	$-0.484626\pi$
$443$	−421.096	−	421.096i	−0.950555	−	0.950555i	−0.998834	+	0.0482792i	$0.984626\pi$
$444$		0			0
$445$	−188.251	−	188.251i	−0.423037	−	0.423037i
$446$	133.328	−	278.535i	0.298941	−	0.624518i
$447$		0			0
$448$	−225.775	+	112.688i	−0.503961	+	0.251535i
$449$	−492.636			−1.09718			−0.548592	−	0.836090i	$-0.684836\pi$
$449$	−492.636			−1.09718			−0.548592	+	0.836090i	$0.684836\pi$
$450$		0			0
$451$	−238.543	+	238.543i	−0.528921	+	0.528921i
$452$	−161.289	−	200.306i	−0.356835	−	0.443155i
$453$		0			0
$454$	98.2182	−	34.6281i	0.216340	−	0.0762733i
$455$	−208.072			−0.457301
$456$		0			0
$457$			516.831i			1.13092i	0.824775	+	0.565461i	$0.191302\pi$
$457$			516.831i			1.13092i	−0.824775	+	0.565461i	$0.808698\pi$
$458$	47.9329	−	16.8994i	0.104657	−	0.0368981i
$459$		0			0
$460$	−1595.23	−	172.128i	−3.46788	−	0.374191i
$461$	27.5260	+	27.5260i	0.0597093	+	0.0597093i	0.736331	−	0.676622i	$-0.236557\pi$
$461$	27.5260	+	27.5260i	0.0597093	+	0.0597093i	−0.676622	+	0.736331i	$0.736557\pi$
$462$		0			0
$463$		−	122.111i		−	0.263740i	−0.991267	−	0.131870i	$-0.957902\pi$
$463$		−	122.111i		−	0.263740i	0.991267	−	0.131870i	$-0.0420981\pi$
$464$	477.985	−	306.661i	1.03014	−	0.660908i
$465$		0			0
$466$	−144.785	+	302.471i	−0.310697	+	0.649079i
$467$	−267.964	+	267.964i	−0.573798	+	0.573798i	−0.933188	−	0.359390i	$-0.882985\pi$
$467$	−267.964	+	267.964i	−0.573798	+	0.573798i	0.359390	+	0.933188i	$0.382985\pi$
$468$		0			0
$469$	−6.46875	+	6.46875i	−0.0137926	+	0.0137926i
$470$	−48.4013	−	137.284i	−0.102981	−	0.292094i
$471$		0			0
$472$	−295.886	+	478.375i	−0.626876	+	1.01351i
$473$			138.974i			0.293814i
$474$		0			0
$475$	−293.730	−	293.730i	−0.618380	−	0.618380i
$476$	143.952	+	178.775i	0.302420	+	0.375577i
$477$		0			0
$478$	−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	$0.855879\pi$
$480$		0			0
$481$	33.6681			0.0699960
$482$	−193.699	−	92.7186i	−0.401864	−	0.192362i
$483$		0			0
$484$	261.182	−	210.307i	0.539632	−	0.434519i
$485$	352.468	−	352.468i	0.726738	−	0.726738i
$486$		0			0
$487$	−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
$489$		0			0
$490$	579.595	−	204.344i	1.18285	−	0.417028i
$491$	301.955	+	301.955i	0.614979	+	0.614979i	0.944239	−	0.329260i	$-0.106799\pi$
$491$	301.955	+	301.955i	0.614979	+	0.614979i	−0.329260	+	0.944239i	$0.606799\pi$
$492$		0			0
$493$	−365.270	−	365.270i	−0.740912	−	0.740912i
$494$	72.5306	+	34.7185i	0.146823	+	0.0702804i
$495$		0			0
$496$	−508.068	−	110.934i	−1.02433	−	0.223658i
$497$	−95.0771			−0.191302
$498$		0			0
$499$	619.990	−	619.990i	1.24247	−	1.24247i	0.283491	−	0.958975i	$-0.408507\pi$
$499$	619.990	−	619.990i	1.24247	−	1.24247i	0.958975	−	0.283491i	$-0.0914925\pi$
$500$	−135.438	+	1255.20i	−0.270876	+	2.51040i
$501$		0			0
$502$	322.527	+	914.808i	0.642484	+	1.82233i
$503$	−222.446			−0.442239			−0.221120	−	0.975247i	$-0.570971\pi$
$503$	−222.446			−0.442239			−0.221120	+	0.975247i	$0.570971\pi$
$504$		0			0
$505$		−	741.475i		−	1.46827i
$506$	−177.056	−	502.196i	−0.349912	−	0.992482i
$507$		0			0
$508$	−403.985	+	325.295i	−0.795246	+	0.640344i
$509$	−489.873	−	489.873i	−0.962421	−	0.962421i	0.0368976	−	0.999319i	$-0.488252\pi$
$509$	−489.873	−	489.873i	−0.962421	−	0.962421i	−0.999319	+	0.0368976i	$0.988252\pi$
$510$		0			0
$511$			42.4795i			0.0831302i
$512$	−327.646	−	393.437i	−0.639933	−	0.768431i
$513$		0			0
$514$	709.983	+	339.850i	1.38129	+	0.661188i
$515$	−255.274	+	255.274i	−0.495678	+	0.495678i
$516$		0			0
$517$	34.1605	−	34.1605i	0.0660745	−	0.0660745i
$518$	43.5775	−	15.3638i	0.0841265	−	0.0296599i
$519$		0			0
$520$	−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	$0.939409\pi$
$522$		0			0
$523$	621.874	+	621.874i	1.18905	+	1.18905i	0.977330	+	0.211721i	$0.0679067\pi$
$523$	621.874	+	621.874i	1.18905	+	1.18905i	0.211721	+	0.977330i	$0.432093\pi$
$524$	666.493	+	71.9157i	1.27193	+	0.137244i
$525$		0			0
$526$	−746.486	−	357.324i	−1.41918	−	0.679323i
$527$			473.033i			0.897596i
$528$		0			0
$529$	1378.22			2.60533
$530$	−354.162	+	739.881i	−0.668231	+	1.39600i
$531$		0			0
$532$	109.722	+	11.8391i	0.206243	+	0.0222540i
$533$	224.815	−	224.815i	0.421791	−	0.421791i
$534$		0			0
$535$	333.804			0.623933
$536$	−15.7865	−	9.76429i	−0.0294524	−	0.0182170i
$537$		0			0
$538$	−155.542	−	441.175i	−0.289111	−	0.820028i
$539$	144.221	+	144.221i	0.267572	+	0.267572i
$540$		0			0
$541$	423.563	+	423.563i	0.782925	+	0.782925i	0.980323	−	0.197398i	$-0.0632492\pi$
$541$	423.563	+	423.563i	0.782925	+	0.782925i	−0.197398	+	0.980323i	$0.563249\pi$
$542$	−267.536	+	558.911i	−0.493609	+	1.03120i
$543$		0			0
$544$	−286.062	+	367.512i	−0.525848	+	0.675574i
$545$	125.495			0.230267
$546$		0			0
$547$	−14.5553	+	14.5553i	−0.0266093	+	0.0266093i	−0.720286	−	0.693677i	$-0.755990\pi$
$547$	−14.5553	+	14.5553i	−0.0266093	+	0.0266093i	0.693677	+	0.720286i	$0.255990\pi$
$548$	490.610	−	395.046i	0.895274	−	0.720888i
$549$		0			0
$550$	−682.634	+	240.671i	−1.24115	+	0.437584i
$551$	−248.371			−0.450764
$552$		0			0
$553$		−	284.080i		−	0.513708i
$554$	419.856	−	148.026i	0.757863	−	0.267194i
$555$		0			0
$556$	72.1818	−	668.959i	0.129823	−	1.20316i
$557$	351.991	+	351.991i	0.631941	+	0.631941i	0.948554	−	0.316614i	$-0.102546\pi$
$557$	351.991	+	351.991i	0.631941	+	0.631941i	−0.316614	+	0.948554i	$0.602546\pi$
$558$		0			0
$559$		−	130.976i		−	0.234304i
$560$	−312.881	−	487.680i	−0.558716	−	0.870857i
$561$		0			0
$562$	−355.027	+	741.689i	−0.631721	+	1.31973i
$563$	150.902	−	150.902i	0.268031	−	0.268031i	−0.560275	−	0.828307i	$-0.689305\pi$
$563$	150.902	−	150.902i	0.268031	−	0.268031i	0.828307	+	0.560275i	$0.189305\pi$
$564$		0			0
$565$	417.563	−	417.563i	0.739050	−	0.739050i
$566$	323.068	+	916.341i	0.570791	+	1.61898i
$567$		0			0
$568$	−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	$0.968256\pi$
$570$		0			0
$571$	−207.486	−	207.486i	−0.363373	−	0.363373i	0.501680	−	0.865053i	$-0.332715\pi$
$571$	−207.486	−	207.486i	−0.363373	−	0.363373i	−0.865053	+	0.501680i	$0.832715\pi$
$572$	109.133	−	87.8758i	0.190793	−	0.153629i
$573$		0			0
$574$	188.394	−	393.574i	0.328212	−	0.685669i
$575$		−	2592.48i		−	4.50866i
$576$		0			0
$577$	−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
$579$		0			0
$580$	817.847	+	1015.69i	1.41008	+	1.75119i
$581$	−165.791	+	165.791i	−0.285355	+	0.285355i
$582$		0			0
$583$	−272.232			−0.466950
$584$	−83.8944	+	19.7735i	−0.143655	+	0.0338587i
$585$		0			0
$586$	−93.7320	+	33.0464i	−0.159952	+	0.0563932i
$587$	540.404	+	540.404i	0.920619	+	0.920619i	0.997073	−	0.0764537i	$-0.0243597\pi$
$587$	540.404	+	540.404i	0.920619	+	0.920619i	−0.0764537	+	0.997073i	$0.524360\pi$
$588$		0			0
$589$	160.823	+	160.823i	0.273045	+	0.273045i
$590$	−1165.01	−	557.659i	−1.97459	−	0.945185i
$591$		0			0
$592$	50.6272	+	78.9113i	0.0855189	+	0.133296i
$593$	−411.176			−0.693383			−0.346692	−	0.937979i	$-0.612695\pi$
$593$	−411.176			−0.693383			−0.346692	+	0.937979i	$0.612695\pi$
$594$		0			0
$595$	−372.678	+	372.678i	−0.626350	+	0.626350i
$596$	−559.835	−	60.4072i	−0.939320	−	0.101354i
$597$		0			0
$598$	166.866	+	473.293i	0.279039	+	0.791460i
$599$	552.839			0.922936			0.461468	−	0.887157i	$-0.347323\pi$
$599$	552.839			0.922936			0.461468	+	0.887157i	$0.347323\pi$
$600$		0			0
$601$			881.159i			1.46615i	0.680145	+	0.733077i	$0.261917\pi$
$601$			881.159i			1.46615i	−0.680145	+	0.733077i	$0.738083\pi$
$602$	−59.7684	−	169.526i	−0.0992831	−	0.281604i
$603$		0			0
$604$	686.637	+	852.738i	1.13682	+	1.41182i
$605$	544.467	+	544.467i	0.899945	+	0.899945i
$606$		0			0
$607$		−	1175.08i		−	1.93588i	−0.251186	−	0.967939i	$-0.580820\pi$
$607$		−	1175.08i		−	1.93588i	0.251186	−	0.967939i	$-0.419180\pi$
$608$	27.6919	+	222.204i	0.0455459	+	0.365467i
$609$		0			0
$610$	−1042.08	−	498.816i	−1.70832	−	0.817731i
$611$	−32.1945	+	32.1945i	−0.0526915	+	0.0526915i
$612$		0			0
$613$	−496.928	+	496.928i	−0.810649	+	0.810649i	−0.984731	−	0.174082i	$-0.944304\pi$
$613$	−496.928	+	496.928i	−0.810649	+	0.810649i	0.174082	+	0.984731i	$0.444304\pi$
$614$	−43.8622	+	15.4642i	−0.0714367	+	0.0251859i
$615$		0			0
$616$	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	$0.831453\pi$
$618$		0			0
$619$	7.45302	+	7.45302i	0.0120404	+	0.0120404i	0.713101	−	0.701061i	$-0.247290\pi$
$619$	7.45302	+	7.45302i	0.0120404	+	0.0120404i	−0.701061	+	0.713101i	$0.747290\pi$
$620$	128.105	−	1187.24i	0.206621	−	1.91490i
$621$		0			0
$622$	−71.8013	−	34.3694i	−0.115436	−	0.0552563i
$623$			114.281i			0.183437i
$624$		0			0
$625$	−1414.88			−2.26381
$626$	372.940	−	779.110i	0.595751	−	1.24458i
$627$		0			0
$628$	46.0482	−	426.760i	0.0733251	−	0.679555i
$629$	60.3029	−	60.3029i	0.0958711	−	0.0958711i
$630$		0			0
$631$	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
$633$		0			0
$634$	−239.877	−	680.379i	−0.378354	−	1.07315i
$635$	−842.158	−	842.158i	−1.32623	−	1.32623i
$636$		0			0
$637$	−135.921	−	135.921i	−0.213376	−	0.213376i
$638$	−186.856	+	390.362i	−0.292878	+	0.611853i
$639$		0			0
$640$	817.497	−	844.927i	1.27734	−	1.32020i
$641$	782.691			1.22105			0.610523	−	0.791998i	$-0.290959\pi$
$641$	782.691			1.22105			0.610523	+	0.791998i	$0.290959\pi$
$642$		0			0
$643$	126.760	−	126.760i	0.197138	−	0.197138i	−0.601634	−	0.798772i	$-0.705483\pi$
$643$	126.760	−	126.760i	0.197138	−	0.197138i	0.798772	+	0.601634i	$0.205483\pi$
$644$	431.958	+	536.450i	0.670741	+	0.832998i
$645$		0			0
$646$	192.094	−	67.7252i	0.297359	−	0.104838i
$647$	−1226.09			−1.89504			−0.947520	−	0.319697i	$-0.896419\pi$
$647$	−1226.09			−1.89504			−0.947520	+	0.319697i	$0.896419\pi$
$648$		0			0
$649$		−	428.653i		−	0.660482i
$650$	643.347	−	226.820i	0.989764	−	0.348954i
$651$		0			0
$652$	996.846	+	107.561i	1.52891	+	0.164972i
$653$	−326.300	−	326.300i	−0.499694	−	0.499694i	0.411649	−	0.911343i	$-0.364953\pi$
$653$	−326.300	−	326.300i	−0.499694	−	0.499694i	−0.911343	+	0.411649i	$0.864953\pi$
$654$		0			0
$655$			1539.31i			2.35008i
$656$	864.978	+	188.864i	1.31856	+	0.287903i
$657$		0			0
$658$	−26.9789	+	56.3616i	−0.0410013	+	0.0856560i
$659$	574.901	−	574.901i	0.872384	−	0.872384i	−0.120347	−	0.992732i	$-0.538401\pi$
$659$	574.901	−	574.901i	0.872384	−	0.872384i	0.992732	+	0.120347i	$0.0384009\pi$
$660$		0			0
$661$	52.8795	−	52.8795i	0.0799993	−	0.0799993i	−0.665975	−	0.745974i	$-0.731984\pi$
$661$	52.8795	−	52.8795i	0.0799993	−	0.0799993i	0.745974	+	0.665975i	$0.231984\pi$
$662$	193.638	+	549.229i	0.292504	+	0.829651i
$663$		0			0
$664$	−404.600	−	250.254i	−0.609338	−	0.376889i
$665$			253.409i			0.381065i
$666$		0			0
$667$	−1096.07	−	1096.07i	−1.64328	−	1.64328i
$668$	−154.729	−	192.158i	−0.231630	−	0.287662i
$669$		0			0
$670$	18.4029	−	38.4455i	0.0274670	−	0.0573814i
$671$		−	383.422i		−	0.571419i
$672$		0			0
$673$	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
$675$		0			0
$676$	423.673	−	341.147i	0.626735	−	0.504656i
$677$	−107.154	+	107.154i	−0.158278	+	0.158278i	−0.781803	−	0.623525i	$-0.785700\pi$
$677$	−107.154	+	107.154i	−0.158278	+	0.158278i	0.623525	+	0.781803i	$0.285700\pi$
$678$		0			0
$679$	−213.971			−0.315127
$680$	−909.491	−	562.541i	−1.33749	−	0.827266i
$681$		0			0
$682$	373.756	−	131.772i	0.548029	−	0.193215i
$683$	−724.233	−	724.233i	−1.06037	−	1.06037i	−0.998057	−	0.0623142i	$-0.980152\pi$
$683$	−724.233	−	724.233i	−1.06037	−	1.06037i	−0.0623142	−	0.998057i	$-0.519848\pi$
$684$		0			0
$685$	1022.74	+	1022.74i	1.49305	+	1.49305i
$686$	−586.468	−	280.727i	−0.854910	−	0.409223i
$687$		0			0
$688$	306.981	−	196.950i	0.446194	−	0.286265i
$689$	256.564			0.372372
$690$		0			0
$691$	162.528	−	162.528i	0.235207	−	0.235207i	−0.579655	−	0.814862i	$-0.696813\pi$
$691$	162.528	−	162.528i	0.235207	−	0.235207i	0.814862	+	0.579655i	$0.196813\pi$
$692$	42.2990	−	392.014i	0.0611257	−	0.566495i
$693$		0			0
$694$	−278.857	−	790.943i	−0.401812	−	1.13969i
$695$	1545.00			2.22302
$696$		0			0
$697$		−	805.331i		−	1.15543i
$698$	−186.312	−	528.449i	−0.266922	−	0.757090i
$699$		0			0
$700$	729.197	−	587.159i	1.04171	−	0.838799i
$701$	301.659	+	301.659i	0.430327	+	0.430327i	0.888740	−	0.458412i	$-0.151582\pi$
$701$	301.659	+	301.659i	0.430327	+	0.430327i	−0.458412	+	0.888740i	$0.651582\pi$
$702$		0			0
$703$		−	41.0040i		−	0.0583271i
$704$	370.069	+	123.647i	0.525666	+	0.175635i
$705$		0			0
$706$	−154.148	−	73.7867i	−0.218340	−	0.104514i
$707$	−225.062	+	225.062i	−0.318334	+	0.318334i
$708$		0			0
$709$	−629.100	+	629.100i	−0.887306	+	0.887306i	−0.994264	−	0.106958i	$-0.965889\pi$
$709$	−629.100	+	629.100i	−0.887306	+	0.887306i	0.106958	+	0.994264i	$0.465889\pi$
$710$	417.776	−	147.292i	0.588417	−	0.207454i
$711$		0			0
$712$	−225.698	+	53.1958i	−0.316991	+	0.0747132i
$713$			1419.43i			1.99079i
$714$		0			0
$715$	227.502	+	227.502i	0.318185	+	0.318185i
$716$	−245.344	−	26.4730i	−0.342659	−	0.0369735i
$717$		0			0
$718$	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	$-0.0322718\pi$
$720$		0			0
$721$	154.968			0.214935
$722$	−269.447	+	562.902i	−0.373195	+	0.779643i
$723$		0			0
$724$	−251.566	−	27.1444i	−0.347466	−	0.0374922i
$725$	−1489.88	+	1489.88i	−2.05501	+	2.05501i
$726$		0			0
$727$	−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
$729$		0			0
$730$	−65.8088	−	186.658i	−0.0901490	−	0.255696i
$731$	−234.591	−	234.591i	−0.320918	−	0.320918i
$732$		0			0
$733$	692.101	+	692.101i	0.944203	+	0.944203i	0.998524	−	0.0543203i	$-0.0172992\pi$
$733$	692.101	+	692.101i	0.944203	+	0.944203i	−0.0543203	+	0.998524i	$0.517299\pi$
$734$	−321.707	+	672.080i	−0.438294	+	0.915640i
$735$		0			0
$736$	−858.388	+	1102.80i	−1.16629	+	1.49837i
$737$	14.1456			0.0191935
$738$		0			0
$739$	−440.389	+	440.389i	−0.595926	+	0.595926i	−0.939226	−	0.343300i	$-0.888455\pi$
$739$	−440.389	+	440.389i	−0.595926	+	0.595926i	0.343300	+	0.939226i	$0.388455\pi$
$740$	−167.682	+	135.020i	−0.226597	+	0.182459i
$741$		0			0
$742$	332.078	−	117.078i	0.447545	−	0.157788i
$743$	1010.54			1.36008			0.680039	−	0.733176i	$-0.261963\pi$
$743$	1010.54			1.36008			0.680039	+	0.733176i	$0.261963\pi$
$744$		0			0
$745$		−	1292.97i		−	1.73553i
$746$	−1086.02	+	382.889i	−1.45579	+	0.513256i
$747$		0			0
$748$	38.0746	−	352.863i	0.0509018	−	0.471743i
$749$	−101.321	−	101.321i	−0.135275	−	0.135275i
$750$		0			0
$751$			776.971i			1.03458i	0.855810	+	0.517291i	$0.173060\pi$
$751$			776.971i			1.03458i	−0.855810	+	0.517291i	$0.826940\pi$
$752$	−123.869	−	27.0462i	−0.164719	−	0.0359657i
$753$		0			0
$754$	176.102	−	367.896i	0.233557	−	0.487925i
$755$	−1777.64	+	1777.64i	−2.35449	+	2.35449i
$756$		0			0
$757$	375.481	−	375.481i	0.496012	−	0.496012i	−0.414182	−	0.910194i	$-0.635932\pi$
$757$	375.481	−	375.481i	0.496012	−	0.496012i	0.910194	+	0.414182i	$0.135932\pi$
$758$	−110.837	−	314.376i	−0.146223	−	0.414744i
$759$		0			0
$760$	−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	$-0.448621\pi$
$762$		0			0
$763$	−38.0920	−	38.0920i	−0.0499239	−	0.0499239i
$764$	535.122	−	430.888i	0.700421	−	0.563989i
$765$		0			0
$766$	−352.301	+	735.993i	−0.459923	+	0.960827i
$767$			403.983i			0.526705i
$768$		0			0
$769$	−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
$771$		0			0
$772$	−540.328	−	671.036i	−0.699906	−	0.869218i
$773$	748.271	−	748.271i	0.968009	−	0.968009i	−0.0314945	−	0.999504i	$-0.510027\pi$
$773$	748.271	−	748.271i	0.968009	−	0.968009i	0.999504	+	0.0314945i	$0.0100267\pi$
$774$		0			0
$775$	1929.44			2.48960
$776$	−99.5999	−	422.580i	−0.128350	−	0.544562i
$777$		0			0
$778$	−1223.07	+	431.209i	−1.57207	+	0.554253i
$779$	−273.799	−	273.799i	−0.351475	−	0.351475i
$780$		0			0
$781$	103.956	+	103.956i	0.133106	+	0.133106i
$782$	1146.59	+	548.843i	1.46623	+	0.701845i
$783$		0			0
$784$	114.185	−	522.958i	0.145645	−	0.667038i
$785$	985.629			1.25558
$786$		0			0
$787$	−735.839	+	735.839i	−0.934992	+	0.934992i	−0.998012	−	0.0630203i	$-0.979927\pi$
$787$	−735.839	+	735.839i	−0.934992	+	0.934992i	0.0630203	+	0.998012i	$0.479927\pi$
$788$	103.122	+	11.1271i	0.130866	+	0.0141206i
$789$		0			0
$790$	440.094	+	1248.27i	0.557081	+	1.58009i
$791$	−253.488			−0.320466
$792$		0			0
$793$			361.355i			0.455681i
$794$	−244.393	−	693.190i	−0.307800	−	0.873035i
$795$		0			0
$796$	−569.750	−	707.576i	−0.715767	−	0.888914i
$797$	−212.043	−	212.043i	−0.266051	−	0.266051i	0.561455	−	0.827507i	$-0.310242\pi$
$797$	−212.043	−	212.043i	−0.266051	−	0.266051i	−0.827507	+	0.561455i	$0.810242\pi$
$798$		0			0
$799$			115.327i			0.144340i
$800$	1499.03	+	1166.81i	1.87379	+	1.45851i
$801$		0			0
$802$	900.541	+	431.066i	1.12287	+	0.537489i
$803$	46.4464	−	46.4464i	0.0578411	−	0.0578411i
$804$		0			0
$805$	−1118.30	+	1118.30i	−1.38919	+	1.38919i
$806$	−352.245	+	124.189i	−0.437029	+	0.154080i
$807$		0			0
$808$	−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	$-0.170883\pi$
$810$		0			0
$811$	112.908	+	112.908i	0.139221	+	0.139221i	0.773283	−	0.634062i	$-0.218613\pi$
$811$	112.908	+	112.908i	0.139221	+	0.139221i	−0.634062	+	0.773283i	$0.718613\pi$
$812$	60.0515	−	556.539i	0.0739550	−	0.685393i
$813$		0			0
$814$	−64.4454	−	30.8484i	−0.0791713	−	0.0378973i
$815$			2302.28i			2.82488i
$816$		0			0
$817$	−159.514			−0.195243
$818$	−427.397	+	892.877i	−0.522491	+	1.09154i
$819$		0			0
$820$	−218.097	+	2021.25i	−0.265971	+	2.46494i
$821$	−555.298	+	555.298i	−0.676368	+	0.676368i	−0.959176	−	0.282808i	$-0.908734\pi$
$821$	−555.298	+	555.298i	−0.676368	+	0.676368i	0.282808	+	0.959176i	$0.408734\pi$
$822$		0			0
$823$	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
$825$		0			0
$826$	184.350	+	522.886i	0.223184	+	0.633034i
$827$	−116.947	−	116.947i	−0.141411	−	0.141411i	0.632858	−	0.774268i	$-0.281882\pi$
$827$	−116.947	−	116.947i	−0.141411	−	0.141411i	−0.774268	+	0.632858i	$0.781882\pi$
$828$		0			0
$829$	181.419	+	181.419i	0.218841	+	0.218841i	0.808010	−	0.589169i	$-0.200545\pi$
$829$	181.419	+	181.419i	0.218841	+	0.218841i	−0.589169	+	0.808010i	$0.700545\pi$
$830$	471.658	−	985.341i	0.568262	−	1.18716i
$831$		0			0
$832$	−348.771	−	116.531i	−0.419195	−	0.140061i
$833$	−486.896			−0.584509
$834$		0			0
$835$	400.578	−	400.578i	0.479734	−	0.479734i
$836$	−107.023	−	132.912i	−0.128018	−	0.158986i
$837$		0			0
$838$	1495.28	−	527.180i	1.78434	−	0.629093i
$839$	−521.472			−0.621540			−0.310770	−	0.950485i	$-0.600587\pi$
$839$	−521.472			−0.621540			−0.310770	+	0.950485i	$0.600587\pi$
$840$		0			0
$841$			418.809i			0.497989i
$842$	1061.52	−	374.252i	1.26071	−	0.444480i
$843$		0			0
$844$	1069.76	+	115.429i	1.26749	+	0.136764i
$845$	883.200	+	883.200i	1.04521	+	1.04521i
$846$		0			0
$847$		−	330.527i		−	0.390233i
$848$	385.799	+	601.336i	0.454952	+	0.709123i
$849$		0			0
$850$	746.041	−	1558.56i	0.877696	−	1.83360i
$851$	180.952	−	180.952i	0.212634	−	0.212634i
$852$		0			0
$853$	−644.278	+	644.278i	−0.755309	+	0.755309i	−0.975465	−	0.220156i	$-0.929343\pi$
$853$	−644.278	+	644.278i	−0.755309	+	0.755309i	0.220156	+	0.975465i	$0.429343\pi$
$854$	164.898	+	467.712i	0.193089	+	0.547672i
$855$		0			0
$856$	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	$-0.145649\pi$
$858$		0			0
$859$	−1011.32	−	1011.32i	−1.17732	−	1.17732i	−0.980425	−	0.196894i	$-0.936915\pi$
$859$	−1011.32	−	1011.32i	−1.17732	−	1.17732i	−0.196894	−	0.980425i	$-0.563085\pi$
$860$	525.255	+	652.316i	0.610761	+	0.758508i
$861$		0			0
$862$	−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	$-0.112655\pi$
$864$		0			0
$865$	905.381			1.04668
$866$	−611.187	−	292.560i	−0.705759	−	0.337829i
$867$		0			0
$868$	−399.250	+	321.482i	−0.459965	+	0.370370i
$869$	−310.609	+	310.609i	−0.357432	+	0.357432i
$870$		0			0
$871$	−13.3315			−0.0153060
$872$	57.4981	−	92.9604i	0.0659382	−	0.106606i
$873$		0			0
$874$	576.418	−	203.224i	0.659517	−	0.232521i
$875$	879.929	+	879.929i	1.00563	+	1.00563i
$876$		0			0
$877$	−664.587	−	664.587i	−0.757796	−	0.757796i	0.218125	−	0.975921i	$-0.430006\pi$
$877$	−664.587	−	664.587i	−0.757796	−	0.757796i	−0.975921	+	0.218125i	$0.930006\pi$
$878$	−423.152	−	202.552i	−0.481950	−	0.230697i
$879$		0			0
$880$	−191.122	+	875.319i	−0.217184	+	0.994681i
$881$	−772.898			−0.877296			−0.438648	−	0.898659i	$-0.644542\pi$
$881$	−772.898			−0.877296			−0.438648	+	0.898659i	$0.644542\pi$
$882$		0			0
$883$	−321.603	+	321.603i	−0.364216	+	0.364216i	−0.865363	−	0.501146i	$-0.832912\pi$
$883$	−321.603	+	321.603i	−0.364216	+	0.364216i	0.501146	+	0.865363i	$0.332912\pi$
$884$	−35.8833	+	332.555i	−0.0405920	+	0.376194i
$885$		0			0
$886$	−396.024	−	1123.27i	−0.446979	−	1.26780i
$887$	−762.665			−0.859825			−0.429912	−	0.902871i	$-0.641456\pi$
$887$	−762.665			−0.859825			−0.429912	+	0.902871i	$0.641456\pi$
$888$		0			0
$889$			511.245i			0.575079i
$890$	−177.043	−	502.160i	−0.198925	−	0.564224i
$891$		0			0
$892$	481.040	−	387.341i	0.539283	−	0.434238i
$893$	39.2093	+	39.2093i	0.0439074	+	0.0439074i
$894$		0			0
$895$		−	566.637i		−	0.633114i
$896$	−504.600	+	8.32594i	−0.563170	+	0.00929234i
$897$		0			0
$898$	−888.704	−	425.400i	−0.989648	−	0.473719i
$899$	815.741	−	815.741i	0.907388	−	0.907388i
$900$		0			0
$901$	459.533	−	459.533i	0.510025	−	0.510025i
$902$	−636.313	+	224.340i	−0.705447	+	0.248714i
$903$		0			0
$904$	−117.994	−	500.624i	−0.130525	−	0.553787i
$905$		−	581.006i		−	0.641996i
$906$		0			0
$907$	−729.007	−	729.007i	−0.803756	−	0.803756i	0.179924	−	0.983680i	$-0.442415\pi$
$907$	−729.007	−	729.007i	−0.803756	−	0.803756i	−0.983680	+	0.179924i	$0.942415\pi$
$908$	207.086	+	22.3449i	0.228068	+	0.0246089i
$909$		0			0
$910$	−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	$-0.161554\pi$
$912$		0			0
$913$	362.546			0.397094
$914$	−446.293	+	932.352i	−0.488286	+	1.02008i
$915$		0			0
$916$	101.063	+	10.9048i	0.110331	+	0.0119049i
$917$	467.230	−	467.230i	0.509520	−	0.509520i
$918$		0			0
$919$	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
$921$		0			0
$922$	25.8871	+	73.4255i	0.0280771	+	0.0796371i
$923$	−97.9727	−	97.9727i	−0.106146	−	0.106146i
$924$		0			0
$925$	−245.967	−	245.967i	−0.265911	−	0.265911i
$926$	105.445	−	220.286i	0.113872	−	0.237890i
$927$		0			0
$928$	1127.08	−	140.461i	1.21453	−	0.151359i
$929$	−585.585			−0.630339			−0.315170	−	0.949035i	$-0.602061\pi$
$929$	−585.585			−0.630339			−0.315170	+	0.949035i	$0.602061\pi$
$930$		0			0
$931$	−165.536	+	165.536i	−0.177805	+	0.177805i
$932$	−522.378	+	420.626i	−0.560491	+	0.451315i
$933$		0			0
$934$	−714.792	+	252.009i	−0.765302	+	0.269817i
$935$	814.960			0.871614
$936$		0			0
$937$		−	1423.91i		−	1.51965i	−0.650129	−	0.759824i	$-0.725285\pi$
$937$		−	1423.91i		−	1.51965i	0.650129	−	0.759824i	$-0.274715\pi$
$938$	−17.2554	+	6.08360i	−0.0183959	+	0.00648572i
$939$		0			0
$940$	31.2325	−	289.453i	0.0332260	−	0.307929i
$941$	−142.471	−	142.471i	−0.151404	−	0.151404i	0.627341	−	0.778745i	$-0.284143\pi$
$941$	−142.471	−	142.471i	−0.151404	−	0.151404i	−0.778745	+	0.627341i	$0.784143\pi$
$942$		0			0
$943$		−	2416.56i		−	2.56264i
$944$	−946.856	+	607.475i	−1.00303	+	0.643511i
$945$		0			0
$946$	−120.007	+	250.706i	−0.126857	+	0.265017i
$947$	−174.352	+	174.352i	−0.184110	+	0.184110i	−0.793144	−	0.609034i	$-0.791557\pi$
$947$	−174.352	+	174.352i	−0.184110	+	0.184110i	0.609034	+	0.793144i	$0.291557\pi$
$948$		0			0
$949$	−43.7733	+	43.7733i	−0.0461257	+	0.0461257i
$950$	−276.242	−	783.525i	−0.290781	−	0.824763i
$951$		0			0
$952$	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	$0.988824\pi$
$954$		0			0
$955$	1115.53	+	1115.53i	1.16809	+	1.16809i
$956$	−92.6899	+	74.6352i	−0.0969559	+	0.0780703i
$957$		0			0
$958$	−361.887	+	756.019i	−0.377752	+	0.789163i
$959$		−	620.870i		−	0.647414i
$960$		0			0
$961$	−95.4048			−0.0992766
$962$	60.7365	+	29.0730i	0.0631356	+	0.0302214i
$963$		0			0
$964$	−269.364	−	334.525i	−0.279423	−	0.347017i
$965$	1398.86	−	1398.86i	1.44959	−	1.44959i
$966$		0			0
$967$	−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
$969$		0			0
$970$	940.206	−	331.482i	0.969285	−	0.341734i
$971$	801.089	+	801.089i	0.825015	+	0.825015i	0.986822	−	0.161808i	$-0.0517324\pi$
$971$	801.089	+	801.089i	0.825015	+	0.825015i	−0.161808	+	0.986822i	$0.551732\pi$
$972$		0			0
$973$	−468.959	−	468.959i	−0.481972	−	0.481972i
$974$	−103.256	−	49.4258i	−0.106012	−	0.0507452i
$975$		0			0
$976$	−846.945	+	543.375i	−0.867771	+	0.556736i
$977$	1591.49			1.62896			0.814479	−	0.580194i	$-0.197023\pi$
$977$	1591.49			1.62896			0.814479	+	0.580194i	$0.197023\pi$
$978$		0			0
$979$	124.953	−	124.953i	0.127633	−	0.127633i
$980$	1222.03	+	131.859i	1.24697	+	0.134550i
$981$		0			0
$982$	283.976	+	805.463i	0.289182	+	0.820227i
$983$	1699.86			1.72926			0.864631	−	0.502408i	$-0.167552\pi$
$983$	1699.86			1.72926			0.864631	+	0.502408i	$0.167552\pi$
$984$		0			0
$985$			238.167i			0.241794i
$986$	−343.522	−	974.355i	−0.348399	−	0.988190i
$987$		0			0
$988$	100.863	+	125.263i	0.102089	+	0.126784i
$989$	−703.939	−	703.939i	−0.711769	−	0.711769i
$990$		0			0
$991$		−	228.875i		−	0.230954i	−0.993310	−	0.115477i	$-0.963160\pi$
$991$		−	228.875i		−	0.230954i	0.993310	−	0.115477i	$-0.0368397\pi$
$992$	−820.750	−	638.849i	−0.827369	−	0.644001i
$993$		0			0
$994$	−171.517	−	82.1008i	−0.172552	−	0.0825963i
$995$	1475.03	−	1475.03i	1.48244	−	1.48244i
$996$		0			0
$997$	1020.63	−	1020.63i	1.02370	−	1.02370i	0.0239926	−	0.999712i	$-0.492362\pi$
$997$	1020.63	−	1020.63i	1.02370	−	1.02370i	0.999712	−	0.0239926i	$-0.00763781\pi$
$998$	1653.82	−	583.076i	1.65714	−	0.584245i
$999$		0			0

Twists

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

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

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +O(q^{10})\)	\(q+(1.80398 + 0.863518i) q^{2} +(2.50867 + 3.11554i) q^{4} +(-6.49473 + 6.49473i) q^{5} +3.94273 q^{7} +(1.83527 + 7.78664i) q^{8} +(-17.3247 + 6.10803i) q^{10} +(-4.31091 - 4.31091i) q^{11} +(4.06281 + 4.06281i) q^{13} +(7.11259 + 3.40462i) q^{14} +(-3.41312 + 15.6317i) q^{16} +14.5538 q^{17} +(4.94805 - 4.94805i) q^{19} +(-36.5277 - 3.94140i) q^{20} +(-4.05424 - 11.4993i) q^{22} +43.6717 q^{23} -59.3629i q^{25} +(3.82091 + 10.8375i) q^{26} +(9.89101 + 12.2837i) q^{28} +(-25.0979 - 25.0979i) q^{29} +32.5024i q^{31} +(-19.6555 + 25.2520i) q^{32} +(26.2547 + 12.5675i) q^{34} +(-25.6069 + 25.6069i) q^{35} +(4.14345 - 4.14345i) q^{37} +(13.1989 - 4.65344i) q^{38} +(-62.4917 - 38.6525i) q^{40} -55.3348i q^{41} +(-16.1189 - 16.1189i) q^{43} +(2.61613 - 24.2455i) q^{44} +(78.7828 + 37.7113i) q^{46} +7.92420i q^{47} -33.4549 q^{49} +(51.2610 - 107.089i) q^{50} +(-2.46556 + 22.8501i) q^{52} +(31.5748 - 31.5748i) q^{53} +55.9964 q^{55} +(7.23597 + 30.7006i) q^{56} +(-23.6036 - 66.9485i) q^{58} +(49.7172 + 49.7172i) q^{59} +(44.4711 + 44.4711i) q^{61} +(-28.0664 + 58.6336i) q^{62} +(-57.2636 + 28.5812i) q^{64} -52.7736 q^{65} +(-1.64068 + 1.64068i) q^{67} +(36.5107 + 45.3429i) q^{68} +(-68.3064 + 24.0823i) q^{70} -24.1145 q^{71} +10.7741i q^{73} +(11.0526 - 3.89675i) q^{74} +(27.8288 + 3.00278i) q^{76} +(-16.9967 - 16.9967i) q^{77} -72.0517i q^{79} +(-79.3565 - 123.691i) q^{80} +(47.7826 - 99.8227i) q^{82} +(-42.0499 + 42.0499i) q^{83} +(-94.5229 + 94.5229i) q^{85} +(-15.1592 - 42.9971i) q^{86} +(25.6558 - 41.4792i) q^{88} +28.9853i q^{89} +(16.0185 + 16.0185i) q^{91} +(109.558 + 136.061i) q^{92} +(-6.84269 + 14.2951i) q^{94} +64.2724i q^{95} -54.2698 q^{97} +(-60.3519 - 28.8889i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 16 * q + 12 * q^4 + 12 * q^8	\( 16 q + 12 q^{4} + 12 q^{8} - 56 q^{10} - 32 q^{11} + 44 q^{14} + 32 q^{16} - 32 q^{19} - 80 q^{20} + 32 q^{22} + 128 q^{23} + 100 q^{26} - 120 q^{28} - 32 q^{29} - 160 q^{32} + 96 q^{34} - 96 q^{35} - 96 q^{37} - 168 q^{38} + 48 q^{40} + 160 q^{43} - 88 q^{44} + 136 q^{46} + 112 q^{49} + 236 q^{50} - 48 q^{52} + 160 q^{53} - 256 q^{55} + 224 q^{56} + 144 q^{58} + 128 q^{59} - 32 q^{61} + 276 q^{62} - 408 q^{64} + 32 q^{65} + 320 q^{67} + 448 q^{68} - 384 q^{70} - 512 q^{71} - 348 q^{74} + 72 q^{76} - 224 q^{77} - 552 q^{80} - 40 q^{82} + 160 q^{83} + 160 q^{85} - 528 q^{86} + 480 q^{88} - 480 q^{91} - 496 q^{92} + 312 q^{94} + 440 q^{98}+O(q^{100}) \) 16 * q + 12 * q^4 + 12 * q^8 - 56 * q^10 - 32 * q^11 + 44 * q^14 + 32 * q^16 - 32 * q^19 - 80 * q^20 + 32 * q^22 + 128 * q^23 + 100 * q^26 - 120 * q^28 - 32 * q^29 - 160 * q^32 + 96 * q^34 - 96 * q^35 - 96 * q^37 - 168 * q^38 + 48 * q^40 + 160 * q^43 - 88 * q^44 + 136 * q^46 + 112 * q^49 + 236 * q^50 - 48 * q^52 + 160 * q^53 - 256 * q^55 + 224 * q^56 + 144 * q^58 + 128 * q^59 - 32 * q^61 + 276 * q^62 - 408 * q^64 + 32 * q^65 + 320 * q^67 + 448 * q^68 - 384 * q^70 - 512 * q^71 - 348 * q^74 + 72 * q^76 - 224 * q^77 - 552 * q^80 - 40 * q^82 + 160 * q^83 + 160 * q^85 - 528 * q^86 + 480 * q^88 - 480 * q^91 - 496 * q^92 + 312 * q^94 + 440 * q^98

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