LMFDB - Embedded newform 144.3.m.c.91.7

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			91.7
Root			$1.80398 + 0.863518i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.c.19.7

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	−0.929089	−	0.369856i	$-0.879407\pi$
$5$	−6.49473	−	6.49473i	−1.29895	−	1.29895i	−0.369856	−	0.929089i	$-0.620593\pi$
$6$		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	−0.875364	−	0.483464i	$-0.839379\pi$
$11$	−4.31091	+	4.31091i	−0.391901	+	0.391901i	0.483464	+	0.875364i	$0.339379\pi$
$12$		0			0
$13$	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
$15$		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	0.825226	−	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
$21$		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	−0.991964	−	0.126519i	$-0.959619\pi$
$29$	−25.0979	+	25.0979i	−0.865445	+	0.865445i	0.126519	+	0.991964i	$0.459619\pi$
$30$		0			0
$31$		−	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
$33$		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	0.760879	−	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
$39$		0			0
$40$	−62.4917	+	38.6525i	−1.56229	+	0.966313i
$41$			55.3348i			1.34963i	0.737987	+	0.674814i	$0.235776\pi$
$41$			55.3348i			1.34963i	−0.737987	+	0.674814i	$0.764224\pi$
$42$		0			0
$43$	−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
$45$		0			0
$46$	78.7828	−	37.7113i	1.71267	−	0.819811i
$47$		−	7.92420i		−	0.168600i	−0.996440	−	0.0843001i	$-0.973135\pi$
$47$		−	7.92420i		−	0.168600i	0.996440	−	0.0843001i	$-0.0268654\pi$
$48$		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	0.939179	−	0.343429i	$-0.111588\pi$
$53$	31.5748	+	31.5748i	0.595750	+	0.595750i	−0.343429	+	0.939179i	$0.611588\pi$
$54$		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	−0.146540	−	0.989205i	$-0.546814\pi$
$59$	49.7172	−	49.7172i	0.842665	−	0.842665i	0.989205	+	0.146540i	$0.0468137\pi$
$60$		0			0
$61$	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
$63$		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	0.694757	−	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
$69$		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	$-0.976489\pi$
$73$		−	10.7741i		−	0.147591i	0.997273	−	0.0737955i	$-0.0235112\pi$
$74$	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	$0.150727\pi$
$79$			72.0517i			0.912047i	−0.889968	+	0.456024i	$0.849273\pi$
$80$	−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	0.406864	−	0.913489i	$-0.366622\pi$
$83$	−42.0499	−	42.0499i	−0.506625	−	0.506625i	−0.913489	+	0.406864i	$0.866622\pi$
$84$		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	$-0.947935\pi$
$89$		−	28.9853i		−	0.325677i	0.986653	−	0.162839i	$-0.0520650\pi$
$90$		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	0.365597	−	0.930773i	$-0.380865\pi$
$101$	−57.0829	−	57.0829i	−0.565177	−	0.565177i	−0.930773	+	0.365597i	$0.880865\pi$
$102$		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	−0.816920	−	0.576751i	$-0.804320\pi$
$107$	−25.6981	+	25.6981i	−0.240169	+	0.240169i	0.576751	+	0.816920i	$0.304320\pi$
$108$		0			0
$109$	−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
$111$		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	$-0.829459\pi$
$127$		−	129.668i		−	1.02101i	0.859875	−	0.510504i	$-0.170541\pi$
$128$	−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	0.995831	−	0.0912183i	$-0.0290761\pi$
$131$	118.504	+	118.504i	0.904613	+	0.904613i	−0.0912183	+	0.995831i	$0.529076\pi$
$132$		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	$0.194888\pi$
$137$			157.472i			1.14943i	−0.818353	+	0.574716i	$0.805112\pi$
$138$		0			0
$139$	−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
$141$		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	0.289210	−	0.957266i	$-0.406607\pi$
$149$	−99.5402	−	99.5402i	−0.668055	−	0.668055i	−0.957266	+	0.289210i	$0.906607\pi$
$150$		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	−0.906186	−	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
$159$		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	0.995798	+	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
$165$		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	−0.879253	−	0.476355i	$-0.841958\pi$
$173$	−69.7012	+	69.7012i	−0.402897	+	0.402897i	0.476355	+	0.879253i	$0.341958\pi$
$174$		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	0.574677	−	0.818380i	$-0.305128\pi$
$179$	−43.6228	−	43.6228i	−0.243703	−	0.243703i	−0.818380	+	0.574677i	$0.805128\pi$
$180$		0			0
$181$	−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
$183$		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	$0.148445\pi$
$191$			171.759i			0.899263i	−0.893214	+	0.449632i	$0.851555\pi$
$192$		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	0.752110	−	0.659037i	$-0.229036\pi$
$197$	18.3354	+	18.3354i	0.0930731	+	0.0930731i	−0.659037	+	0.752110i	$0.729036\pi$
$198$		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	0.995562	−	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
$213$		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	$0.112525\pi$
$223$			154.401i			0.692379i	−0.938165	+	0.346190i	$0.887475\pi$
$224$	−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	0.783543	−	0.621338i	$-0.213411\pi$
$227$	36.8204	+	36.8204i	0.162204	+	0.162204i	−0.621338	+	0.783543i	$0.713411\pi$
$228$		0			0
$229$	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
$231$		0			0
$232$	149.367	+	241.490i	0.643823	+	1.04090i
$233$		−	167.669i		−	0.719608i	−0.933028	−	0.359804i	$-0.882844\pi$
$233$		−	167.669i		−	0.719608i	0.933028	−	0.359804i	$-0.117156\pi$
$234$		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	$-0.980175\pi$
$239$		−	29.7509i		−	0.124481i	0.998061	−	0.0622403i	$-0.0198245\pi$
$240$		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	0.500697	−	0.865623i	$-0.333077\pi$
$251$	342.946	−	342.946i	1.36632	−	1.36632i	0.865623	−	0.500697i	$-0.166923\pi$
$252$		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	−0.944201	−	0.329371i	$-0.893163\pi$
$269$	−165.389	+	165.389i	−0.614830	+	0.614830i	0.329371	+	0.944201i	$0.393163\pi$
$270$		0			0
$271$		−	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
$273$		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	0.931630	−	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
$279$		0			0
$280$	−246.388	+	152.396i	−0.879956	+	0.544273i
$281$		−	411.141i		−	1.46313i	−0.681769	−	0.731567i	$-0.738789\pi$
$281$		−	411.141i		−	1.46313i	0.681769	−	0.731567i	$-0.261211\pi$
$282$		0			0
$283$	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
$285$		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	0.644596	−	0.764523i	$-0.277025\pi$
$293$	−35.1386	−	35.1386i	−0.119927	−	0.119927i	−0.764523	+	0.644596i	$0.777025\pi$
$294$		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	0.679819	−	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
$309$		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	$0.242351\pi$
$313$			431.885i			1.37982i	−0.723894	+	0.689911i	$0.757649\pi$
$314$	−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	−0.983813	−	0.179198i	$-0.942650\pi$
$317$	−255.063	+	255.063i	−0.804615	+	0.804615i	0.179198	+	0.983813i	$0.442650\pi$
$318$		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	−0.324009	−	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
$333$		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	−0.990684	−	0.136183i	$-0.956516\pi$
$347$	−296.512	+	296.512i	−0.854500	+	0.854500i	0.136183	+	0.990684i	$0.456516\pi$
$348$		0			0
$349$	−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
$351$		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	$-0.830545\pi$
$367$		−	372.554i		−	1.01513i	0.861612	−	0.507567i	$-0.169455\pi$
$368$	−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	−0.995369	−	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
$375$		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	−0.845282	−	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
$381$		0			0
$382$	148.317	+	309.850i	0.388265	+	0.811126i
$383$		−	407.983i		−	1.06523i	−0.846357	−	0.532615i	$-0.821209\pi$
$383$		−	407.983i		−	1.06523i	0.846357	−	0.532615i	$-0.178791\pi$
$384$		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	−0.980080	−	0.198605i	$-0.936359\pi$
$389$	−458.508	−	458.508i	−1.17868	−	1.17868i	−0.198605	−	0.980080i	$-0.563641\pi$
$390$		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	−0.954091	−	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
$399$		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	$-0.793144\pi$
$409$		−	494.949i		−	1.21014i	0.796171	−	0.605072i	$-0.206856\pi$
$410$	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	0.898148	+	0.439693i	$0.144913\pi$
$419$	560.555	+	560.555i	1.33784	+	1.33784i	0.439693	+	0.898148i	$0.355087\pi$
$420$		0			0
$421$	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
$423$		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	$-0.720757\pi$
$431$		−	662.874i		−	1.53799i	0.639255	−	0.768995i	$-0.279243\pi$
$432$		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	−0.998834	−	0.0482792i	$-0.984626\pi$
$443$	−421.096	+	421.096i	−0.950555	+	0.950555i	0.0482792	+	0.998834i	$0.484626\pi$
$444$		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	$-0.808698\pi$
$457$		−	516.831i		−	1.13092i	0.824775	−	0.565461i	$-0.191302\pi$
$458$	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	−0.676622	−	0.736331i	$-0.736557\pi$
$461$	27.5260	−	27.5260i	0.0597093	−	0.0597093i	0.736331	+	0.676622i	$0.236557\pi$
$462$		0			0
$463$			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
$465$		0			0
$466$	−144.785	−	302.471i	−0.310697	−	0.649079i
$467$	−267.964	−	267.964i	−0.573798	−	0.573798i	0.359390	−	0.933188i	$-0.382985\pi$
$467$	−267.964	−	267.964i	−0.573798	−	0.573798i	−0.933188	+	0.359390i	$0.882985\pi$
$468$		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	$-0.855879\pi$
$479$		−	419.084i		−	0.874915i	0.899239	−	0.437457i	$-0.144121\pi$
$480$		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	−0.329260	−	0.944239i	$-0.606799\pi$
$491$	301.955	−	301.955i	0.614979	−	0.614979i	0.944239	+	0.329260i	$0.106799\pi$
$492$		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	0.958975	+	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
$501$		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	−0.999319	−	0.0368976i	$-0.988252\pi$
$509$	−489.873	+	489.873i	−0.962421	+	0.962421i	0.0368976	+	0.999319i	$0.488252\pi$
$510$		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	$-0.939409\pi$
$521$		−	197.152i		−	0.378412i	0.981937	−	0.189206i	$-0.0605913\pi$
$522$		0			0
$523$	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
$525$		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	−0.197398	−	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
$543$		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	0.693677	−	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
$549$		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	−0.316614	−	0.948554i	$-0.602546\pi$
$557$	351.991	−	351.991i	0.631941	−	0.631941i	0.948554	+	0.316614i	$0.102546\pi$
$558$		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	0.828307	−	0.560275i	$-0.189305\pi$
$563$	150.902	+	150.902i	0.268031	+	0.268031i	−0.560275	+	0.828307i	$0.689305\pi$
$564$		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	$-0.968256\pi$
$569$		−	113.300i		−	0.199121i	0.995032	−	0.0995603i	$-0.0317436\pi$
$570$		0			0
$571$	−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
$573$		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	−0.0764537	−	0.997073i	$-0.524360\pi$
$587$	540.404	−	540.404i	0.920619	−	0.920619i	0.997073	+	0.0764537i	$0.0243597\pi$
$588$		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	$-0.738083\pi$
$601$		−	881.159i		−	1.46615i	0.680145	−	0.733077i	$-0.261917\pi$
$602$	−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	$0.419180\pi$
$607$			1175.08i			1.93588i	−0.251186	+	0.967939i	$0.580820\pi$
$608$	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	0.174082	−	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
$615$		0			0
$616$	101.154	+	163.541i	0.164211	+	0.265489i
$617$		−	623.301i		−	1.01021i	−0.863057	−	0.505106i	$-0.831453\pi$
$617$		−	623.301i		−	1.01021i	0.863057	−	0.505106i	$-0.168547\pi$
$618$		0			0
$619$	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
$621$		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	0.798772	−	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
$645$		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	−0.911343	−	0.411649i	$-0.864953\pi$
$653$	−326.300	+	326.300i	−0.499694	+	0.499694i	0.411649	+	0.911343i	$0.364953\pi$
$654$		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	0.992732	−	0.120347i	$-0.0384009\pi$
$659$	574.901	+	574.901i	0.872384	+	0.872384i	−0.120347	+	0.992732i	$0.538401\pi$
$660$		0			0
$661$	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
$663$		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	0.623525	−	0.781803i	$-0.285700\pi$
$677$	−107.154	−	107.154i	−0.158278	−	0.158278i	−0.781803	+	0.623525i	$0.785700\pi$
$678$		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	−0.0623142	+	0.998057i	$0.519848\pi$
$683$	−724.233	+	724.233i	−1.06037	+	1.06037i	−0.998057	+	0.0623142i	$0.980152\pi$
$684$		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	0.814862	−	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
$693$		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	−0.458412	−	0.888740i	$-0.651582\pi$
$701$	301.659	−	301.659i	0.430327	−	0.430327i	0.888740	+	0.458412i	$0.151582\pi$
$702$		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	0.106958	−	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
$711$		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	$0.0322718\pi$
$719$			145.542i			0.202422i	−0.994865	+	0.101211i	$0.967728\pi$
$720$		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	−0.0543203	−	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
$735$		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	0.343300	−	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
$741$		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	$-0.826940\pi$
$751$		−	776.971i		−	1.03458i	0.855810	−	0.517291i	$-0.173060\pi$
$752$	−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	0.910194	−	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
$759$		0			0
$760$	−500.466	−	117.957i	−0.658508	−	0.155207i
$761$			1502.22i			1.97400i	0.160711	+	0.987001i	$0.448621\pi$
$761$			1502.22i			1.97400i	−0.160711	+	0.987001i	$0.551379\pi$
$762$		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	0.999504	−	0.0314945i	$-0.0100267\pi$
$773$	748.271	+	748.271i	0.968009	+	0.968009i	−0.0314945	+	0.999504i	$0.510027\pi$
$774$		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	0.0630203	−	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
$789$		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	−0.827507	−	0.561455i	$-0.810242\pi$
$797$	−212.043	+	212.043i	−0.266051	+	0.266051i	0.561455	+	0.827507i	$0.310242\pi$
$798$		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	$0.170883\pi$
$809$			827.491i			1.02286i	−0.859326	+	0.511428i	$0.829117\pi$
$810$		0			0
$811$	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
$813$		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	0.282808	−	0.959176i	$-0.408734\pi$
$821$	−555.298	−	555.298i	−0.676368	−	0.676368i	−0.959176	+	0.282808i	$0.908734\pi$
$822$		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	−0.774268	−	0.632858i	$-0.781882\pi$
$827$	−116.947	+	116.947i	−0.141411	+	0.141411i	0.632858	+	0.774268i	$0.281882\pi$
$828$		0			0
$829$	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
$831$		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	0.220156	−	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
$855$		0			0
$856$	152.939	+	247.265i	0.178667	+	0.288861i
$857$			757.190i			0.883536i	0.897129	+	0.441768i	$0.145649\pi$
$857$			757.190i			0.883536i	−0.897129	+	0.441768i	$0.854351\pi$
$858$		0			0
$859$	−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
$861$		0			0
$862$	−572.403	−	1195.81i	−0.664041	−	1.38725i
$863$			598.188i			0.693149i	0.938022	+	0.346575i	$0.112655\pi$
$863$			598.188i			0.693149i	−0.938022	+	0.346575i	$0.887345\pi$
$864$		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	−0.975921	−	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
$879$		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	0.501146	−	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
$885$		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	−0.983680	−	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
$909$		0			0
$910$	−375.357	+	179.674i	−0.412481	+	0.197444i
$911$			885.541i			0.972054i	0.873944	+	0.486027i	$0.161554\pi$
$911$			885.541i			0.972054i	−0.873944	+	0.486027i	$0.838446\pi$
$912$		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	$0.274715\pi$
$937$			1423.91i			1.51965i	−0.650129	+	0.759824i	$0.725285\pi$
$938$	−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	−0.778745	−	0.627341i	$-0.784143\pi$
$941$	−142.471	+	142.471i	−0.151404	+	0.151404i	0.627341	+	0.778745i	$0.284143\pi$
$942$		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	0.609034	−	0.793144i	$-0.291557\pi$
$947$	−174.352	−	174.352i	−0.184110	−	0.184110i	−0.793144	+	0.609034i	$0.791557\pi$
$948$		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	$-0.988824\pi$
$953$		−	66.9080i		−	0.0702078i	0.999384	−	0.0351039i	$-0.0111762\pi$
$954$		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	−0.161808	−	0.986822i	$-0.551732\pi$
$971$	801.089	−	801.089i	0.825015	−	0.825015i	0.986822	+	0.161808i	$0.0517324\pi$
$972$		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	$0.0368397\pi$
$991$			228.875i			0.230954i	−0.993310	+	0.115477i	$0.963160\pi$
$992$	−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	0.999712	+	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.2	✓	16	48.35	even	4
48.3.l.a.43.2	yes	16	3.2	odd	2
144.3.m.c.19.7		16	16.3	odd	4	inner
144.3.m.c.91.7		16	1.1	even	1	trivial
192.3.l.a.79.8		16	12.11	even	2
192.3.l.a.175.8		16	48.29	odd	4
384.3.l.a.31.5		16	24.5	odd	2
384.3.l.a.223.5		16	48.11	even	4
384.3.l.b.31.1		16	24.11	even	2
384.3.l.b.223.1		16	48.5	odd	4
576.3.m.c.271.1		16	4.3	odd	2
576.3.m.c.559.1		16	16.13	even	4
1152.3.m.c.415.8		16	8.3	odd	2
1152.3.m.c.991.8		16	16.5	even	4
1152.3.m.f.415.8		16	8.5	even	2
1152.3.m.f.991.8		16	16.11	odd	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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
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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