LMFDB - Embedded newform 144.3.m.c.91.1

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			91.1
Root			$-1.96679 - 0.362960i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.c.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +O(q^{10})$	\(q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +(3.95895 + 2.72539i) q^{10} +(5.59560 - 5.59560i) q^{11} +(-13.5782 + 13.5782i) q^{13} +(11.2949 - 2.08441i) q^{14} +(11.9232 - 10.6695i) q^{16} -19.7023 q^{17} +(-21.6943 - 21.6943i) q^{19} +(-8.77563 - 3.92333i) q^{20} +(-8.97439 + 13.0363i) q^{22} -24.9257 q^{23} -19.2247i q^{25} +(21.7771 - 31.6337i) q^{26} +(-21.4581 + 8.19918i) q^{28} +(-1.50581 + 1.50581i) q^{29} +2.20037i q^{31} +(-19.5777 + 25.3123i) q^{32} +(38.7504 - 7.15116i) q^{34} +(9.75877 + 9.75877i) q^{35} +(27.6956 + 27.6956i) q^{37} +(50.5423 + 34.7940i) q^{38} +(18.6838 + 4.53116i) q^{40} +51.3127i q^{41} +(21.4400 - 21.4400i) q^{43} +(12.9191 - 28.8971i) q^{44} +(49.0236 - 9.04703i) q^{46} -76.5216i q^{47} -16.0202 q^{49} +(6.97781 + 37.8110i) q^{50} +(-31.3491 + 70.1211i) q^{52} +(56.5145 + 56.5145i) q^{53} -19.0173 q^{55} +(39.2276 - 23.9145i) q^{56} +(2.41506 - 3.50816i) q^{58} +(48.0041 - 48.0041i) q^{59} +(-51.5587 + 51.5587i) q^{61} +(-0.798646 - 4.32766i) q^{62} +(29.3180 - 56.8899i) q^{64} +46.1469 q^{65} +(63.4445 + 63.4445i) q^{67} +(-73.6182 + 28.1297i) q^{68} +(-22.7355 - 15.6514i) q^{70} -43.4856 q^{71} -73.9992i q^{73} +(-64.5239 - 44.4190i) q^{74} +(-112.035 - 50.0876i) q^{76} +(-32.1344 + 32.1344i) q^{77} +4.12659i q^{79} +(-38.3918 - 2.13036i) q^{80} +(-18.6245 - 100.921i) q^{82} +(-38.4428 - 38.4428i) q^{83} +(33.4803 + 33.4803i) q^{85} +(-34.3862 + 49.9499i) q^{86} +(-14.9206 + 61.5236i) q^{88} -52.9839i q^{89} +(77.9767 - 77.9767i) q^{91} +(-93.1353 + 35.5872i) q^{92} +(27.7743 + 150.502i) q^{94} +73.7305i q^{95} +23.1008 q^{97} +(31.5084 - 5.81471i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.96679	+	0.362960i	−0.983395	+	0.181480i
$2$	−1.96679	+	0.362960i	−0.983395	+	0.181480i
$3$		0			0
$3$		0			0
$4$	3.73652	−	1.42773i	0.934130	−	0.356933i
$5$	−1.69930	−	1.69930i	−0.339861	−	0.339861i	0.516454	−	0.856315i	$-0.327252\pi$
$5$	−1.69930	−	1.69930i	−0.339861	−	0.339861i	−0.856315	+	0.516454i	$0.827252\pi$
$6$		0			0
$7$	−5.74280			−0.820400			−0.410200	−	0.911996i	$-0.634541\pi$
$7$	−5.74280			−0.820400			−0.410200	+	0.911996i	$0.634541\pi$
$8$	−6.83074	+	4.16426i	−0.853842	+	0.520532i
$9$		0			0
$10$	3.95895	+	2.72539i	0.395895	+	0.272539i
$11$	5.59560	−	5.59560i	0.508691	−	0.508691i	−0.405434	−	0.914125i	$-0.632879\pi$
$11$	5.59560	−	5.59560i	0.508691	−	0.508691i	0.914125	+	0.405434i	$0.132879\pi$
$12$		0			0
$13$	−13.5782	+	13.5782i	−1.04447	+	1.04447i	−0.0455110	+	0.998964i	$0.514492\pi$
$13$	−13.5782	+	13.5782i	−1.04447	+	1.04447i	−0.998964	+	0.0455110i	$0.985508\pi$
$14$	11.2949	−	2.08441i	0.806777	−	0.148886i
$15$		0			0
$16$	11.9232	−	10.6695i	0.745198	−	0.666844i
$17$	−19.7023			−1.15896			−0.579481	−	0.814986i	$-0.696745\pi$
$17$	−19.7023			−1.15896			−0.579481	+	0.814986i	$0.696745\pi$
$18$		0			0
$19$	−21.6943	−	21.6943i	−1.14181	−	1.14181i	−0.988120	−	0.153687i	$-0.950885\pi$
$19$	−21.6943	−	21.6943i	−1.14181	−	1.14181i	−0.153687	−	0.988120i	$-0.549115\pi$
$20$	−8.77563	−	3.92333i	−0.438782	−	0.196167i
$21$		0			0
$22$	−8.97439	+	13.0363i	−0.407927	+	0.592561i
$23$	−24.9257			−1.08373			−0.541863	−	0.840467i	$-0.682281\pi$
$23$	−24.9257			−1.08373			−0.541863	+	0.840467i	$0.682281\pi$
$24$		0			0
$25$		−	19.2247i		−	0.768989i
$26$	21.7771	−	31.6337i	0.837580	−	1.21668i
$27$		0			0
$28$	−21.4581	+	8.19918i	−0.766360	+	0.292828i
$29$	−1.50581	+	1.50581i	−0.0519245	+	0.0519245i	−0.732592	−	0.680668i	$-0.761690\pi$
$29$	−1.50581	+	1.50581i	−0.0519245	+	0.0519245i	0.680668	+	0.732592i	$0.261690\pi$
$30$		0			0
$31$			2.20037i			0.0709796i	0.999370	+	0.0354898i	$0.0112991\pi$
$31$			2.20037i			0.0709796i	−0.999370	+	0.0354898i	$0.988701\pi$
$32$	−19.5777	+	25.3123i	−0.611805	+	0.791009i
$33$		0			0
$34$	38.7504	−	7.15116i	1.13972	−	0.210328i
$35$	9.75877	+	9.75877i	0.278822	+	0.278822i
$36$		0			0
$37$	27.6956	+	27.6956i	0.748530	+	0.748530i	0.974203	−	0.225673i	$-0.0724580\pi$
$37$	27.6956	+	27.6956i	0.748530	+	0.748530i	−0.225673	+	0.974203i	$0.572458\pi$
$38$	50.5423	+	34.7940i	1.33006	+	0.915631i
$39$		0			0
$40$	18.6838	+	4.53116i	0.467096	+	0.113279i
$41$			51.3127i			1.25153i	0.780012	+	0.625764i	$0.215213\pi$
$41$			51.3127i			1.25153i	−0.780012	+	0.625764i	$0.784787\pi$
$42$		0			0
$43$	21.4400	−	21.4400i	0.498606	−	0.498606i	−0.412398	−	0.911004i	$-0.635309\pi$
$43$	21.4400	−	21.4400i	0.498606	−	0.498606i	0.911004	+	0.412398i	$0.135309\pi$
$44$	12.9191	−	28.8971i	0.293615	−	0.656752i
$45$		0			0
$46$	49.0236	−	9.04703i	1.06573	−	0.196675i
$47$		−	76.5216i		−	1.62812i	−0.580781	−	0.814060i	$-0.697253\pi$
$47$		−	76.5216i		−	1.62812i	0.580781	−	0.814060i	$-0.302747\pi$
$48$		0			0
$49$	−16.0202			−0.326944
$50$	6.97781	+	37.8110i	0.139556	+	0.756220i
$51$		0			0
$52$	−31.3491	+	70.1211i	−0.602868	+	1.34848i
$53$	56.5145	+	56.5145i	1.06631	+	1.06631i	0.997639	+	0.0686712i	$0.0218759\pi$
$53$	56.5145	+	56.5145i	1.06631	+	1.06631i	0.0686712	+	0.997639i	$0.478124\pi$
$54$		0			0
$55$	−19.0173			−0.345768
$56$	39.2276	−	23.9145i	0.700492	−	0.427044i
$57$		0			0
$58$	2.41506	−	3.50816i	0.0416390	−	0.0604855i
$59$	48.0041	−	48.0041i	0.813628	−	0.813628i	−0.171547	−	0.985176i	$-0.554877\pi$
$59$	48.0041	−	48.0041i	0.813628	−	0.813628i	0.985176	+	0.171547i	$0.0548767\pi$
$60$		0			0
$61$	−51.5587	+	51.5587i	−0.845224	+	0.845224i	−0.989533	−	0.144308i	$-0.953904\pi$
$61$	−51.5587	+	51.5587i	−0.845224	+	0.845224i	0.144308	+	0.989533i	$0.453904\pi$
$62$	−0.798646	−	4.32766i	−0.0128814	−	0.0698010i
$63$		0			0
$64$	29.3180	−	56.8899i	0.458093	−	0.888904i
$65$	46.1469			0.709952
$66$		0			0
$67$	63.4445	+	63.4445i	0.946934	+	0.946934i	0.998661	−	0.0517277i	$-0.0164728\pi$
$67$	63.4445	+	63.4445i	0.946934	+	0.946934i	−0.0517277	+	0.998661i	$0.516473\pi$
$68$	−73.6182	+	28.1297i	−1.08262	+	0.413672i
$69$		0			0
$70$	−22.7355	−	15.6514i	−0.324793	−	0.223591i
$71$	−43.4856			−0.612473			−0.306237	−	0.951955i	$-0.599070\pi$
$71$	−43.4856			−0.612473			−0.306237	+	0.951955i	$0.599070\pi$
$72$		0			0
$73$		−	73.9992i		−	1.01369i	−0.862038	−	0.506844i	$-0.830812\pi$
$73$		−	73.9992i		−	1.01369i	0.862038	−	0.506844i	$-0.169188\pi$
$74$	−64.5239	−	44.4190i	−0.871944	−	0.600257i
$75$		0			0
$76$	−112.035	−	50.0876i	−1.47414	−	0.659047i
$77$	−32.1344	+	32.1344i	−0.417330	+	0.417330i
$78$		0			0
$79$			4.12659i			0.0522354i	0.999659	+	0.0261177i	$0.00831446\pi$
$79$			4.12659i			0.0522354i	−0.999659	+	0.0261177i	$0.991686\pi$
$80$	−38.3918	−	2.13036i	−0.479898	−	0.0266295i
$81$		0			0
$82$	−18.6245	−	100.921i	−0.227127	−	1.23075i
$83$	−38.4428	−	38.4428i	−0.463166	−	0.463166i	0.436526	−	0.899692i	$-0.356209\pi$
$83$	−38.4428	−	38.4428i	−0.463166	−	0.463166i	−0.899692	+	0.436526i	$0.856209\pi$
$84$		0			0
$85$	33.4803	+	33.4803i	0.393886	+	0.393886i
$86$	−34.3862	+	49.9499i	−0.399839	+	0.580813i
$87$		0			0
$88$	−14.9206	+	61.5236i	−0.169552	+	0.699132i
$89$		−	52.9839i		−	0.595325i	−0.954671	−	0.297662i	$-0.903793\pi$
$89$		−	52.9839i		−	0.595325i	0.954671	−	0.297662i	$-0.0962070\pi$
$90$		0			0
$91$	77.9767	−	77.9767i	0.856887	−	0.856887i
$92$	−93.1353	+	35.5872i	−1.01234	+	0.386817i
$93$		0			0
$94$	27.7743	+	150.502i	0.295471	+	1.60108i
$95$			73.7305i			0.776111i
$96$		0			0
$97$	23.1008			0.238153			0.119077	−	0.992885i	$-0.462007\pi$
$97$	23.1008			0.238153			0.119077	+	0.992885i	$0.462007\pi$
$98$	31.5084	−	5.81471i	0.321515	−	0.0593337i
$99$		0			0
$100$	−27.4478	−	71.8336i	−0.274478	−	0.718336i
$101$	−16.1216	−	16.1216i	−0.159619	−	0.159619i	0.622779	−	0.782398i	$-0.286004\pi$
$101$	−16.1216	−	16.1216i	−0.159619	−	0.159619i	−0.782398	+	0.622779i	$0.786004\pi$
$102$		0			0
$103$	−98.8380			−0.959592			−0.479796	−	0.877380i	$-0.659289\pi$
$103$	−98.8380			−0.959592			−0.479796	+	0.877380i	$0.659289\pi$
$104$	36.2060	−	149.292i	0.348134	−	1.43550i
$105$		0			0
$106$	−131.665	−	90.6395i	−1.24212	−	0.855090i
$107$	−15.6655	+	15.6655i	−0.146406	+	0.146406i	−0.776511	−	0.630104i	$-0.783012\pi$
$107$	−15.6655	+	15.6655i	−0.146406	+	0.146406i	0.630104	+	0.776511i	$0.283012\pi$
$108$		0			0
$109$	84.6938	−	84.6938i	0.777008	−	0.777008i	−0.202313	−	0.979321i	$-0.564846\pi$
$109$	84.6938	−	84.6938i	0.777008	−	0.777008i	0.979321	+	0.202313i	$0.0648459\pi$
$110$	37.4029	−	6.90250i	0.340027	−	0.0627500i
$111$		0			0
$112$	−68.4724	+	61.2728i	−0.611360	+	0.547079i
$113$	−63.8537			−0.565077			−0.282538	−	0.959256i	$-0.591176\pi$
$113$	−63.8537			−0.565077			−0.282538	+	0.959256i	$0.591176\pi$
$114$		0			0
$115$	42.3563	+	42.3563i	0.368316	+	0.368316i
$116$	−3.47659	+	7.77638i	−0.0299706	+	0.0670377i
$117$		0			0
$118$	−76.9903	+	111.837i	−0.652461	+	0.947775i
$119$	113.147			0.950812
$120$		0			0
$121$			58.3785i			0.482467i
$122$	82.6913	−	120.119i	0.677798	−	0.984580i
$123$		0			0
$124$	3.14154	+	8.22172i	0.0253350	+	0.0663042i
$125$	−75.1513	+	75.1513i	−0.601210	+	0.601210i
$126$		0			0
$127$		−	36.8901i		−	0.290473i	−0.989397	−	0.145237i	$-0.953606\pi$
$127$		−	36.8901i		−	0.290473i	0.989397	−	0.145237i	$-0.0463944\pi$
$128$	−37.0135	+	122.532i	−0.289168	+	0.957278i
$129$		0			0
$130$	−90.7612	+	16.7495i	−0.698163	+	0.128842i
$131$	40.4136	+	40.4136i	0.308500	+	0.308500i	0.844328	−	0.535827i	$-0.180000\pi$
$131$	40.4136	+	40.4136i	0.308500	+	0.308500i	−0.535827	+	0.844328i	$0.680000\pi$
$132$		0			0
$133$	124.586	+	124.586i	0.936738	+	0.936738i
$134$	−147.810	−	101.754i	−1.10306	−	0.759360i
$135$		0			0
$136$	134.582	−	82.0456i	0.989570	−	0.603276i
$137$		−	253.499i		−	1.85036i	−0.379531	−	0.925179i	$-0.623915\pi$
$137$		−	253.499i		−	1.85036i	0.379531	−	0.925179i	$-0.376085\pi$
$138$		0			0
$139$	67.8065	−	67.8065i	0.487816	−	0.487816i	−0.419800	−	0.907617i	$-0.637900\pi$
$139$	67.8065	−	67.8065i	0.487816	−	0.487816i	0.907617	+	0.419800i	$0.137900\pi$
$140$	50.3967	+	22.5309i	0.359977	+	0.160935i
$141$		0			0
$142$	85.5270	−	15.7835i	0.602303	−	0.111152i
$143$			151.956i			1.06263i
$144$		0			0
$145$	5.11766			0.0352942
$146$	26.8588	+	145.541i	0.183964	+	0.996856i
$147$		0			0
$148$	143.027	+	63.9433i	0.966400	+	0.432049i
$149$	43.9337	+	43.9337i	0.294857	+	0.294857i	0.838996	−	0.544138i	$-0.183143\pi$
$149$	43.9337	+	43.9337i	0.294857	+	0.294857i	−0.544138	+	0.838996i	$0.683143\pi$
$150$		0			0
$151$	−223.084			−1.47738			−0.738688	−	0.674047i	$-0.764554\pi$
$151$	−223.084			−1.47738			−0.738688	+	0.674047i	$0.764554\pi$
$152$	238.529	+	57.8475i	1.56927	+	0.380576i
$153$		0			0
$154$	51.5381	−	74.8651i	0.334663	−	0.486137i
$155$	3.73909	−	3.73909i	0.0241232	−	0.0241232i
$156$		0			0
$157$	−78.8526	+	78.8526i	−0.502246	+	0.502246i	−0.912135	−	0.409889i	$-0.865567\pi$
$157$	−78.8526	+	78.8526i	−0.502246	+	0.502246i	0.409889	+	0.912135i	$0.365567\pi$
$158$	−1.49779	−	8.11614i	−0.00947968	−	0.0513680i
$159$		0			0
$160$	76.2818	−	9.74473i	0.476761	−	0.0609045i
$161$	143.143			0.889089
$162$		0			0
$163$	52.2425	+	52.2425i	0.320506	+	0.320506i	0.848961	−	0.528455i	$-0.177228\pi$
$163$	52.2425	+	52.2425i	0.320506	+	0.320506i	−0.528455	+	0.848961i	$0.677228\pi$
$164$	73.2607	+	191.731i	0.446712	+	1.16909i
$165$		0			0
$166$	89.5620	+	61.6556i	0.539530	+	0.371419i
$167$	−96.5201			−0.577965			−0.288982	−	0.957334i	$-0.593317\pi$
$167$	−96.5201			−0.577965			−0.288982	+	0.957334i	$0.593317\pi$
$168$		0			0
$169$		−	199.734i		−	1.18186i
$170$	−78.0006	−	53.6966i	−0.458827	−	0.315863i
$171$		0			0
$172$	49.5005	−	110.722i	0.287794	−	0.643731i
$173$	46.3076	−	46.3076i	0.267674	−	0.267674i	−0.560488	−	0.828162i	$-0.689386\pi$
$173$	46.3076	−	46.3076i	0.267674	−	0.267674i	0.828162	+	0.560488i	$0.189386\pi$
$174$		0			0
$175$			110.404i			0.630879i
$176$	7.01501	−	126.419i	0.0398580	−	0.718293i
$177$		0			0
$178$	19.2310	+	104.208i	0.108040	+	0.585439i
$179$	93.5440	+	93.5440i	0.522592	+	0.522592i	0.918353	−	0.395761i	$-0.129519\pi$
$179$	93.5440	+	93.5440i	0.522592	+	0.522592i	−0.395761	+	0.918353i	$0.629519\pi$
$180$		0			0
$181$	−115.810	−	115.810i	−0.639836	−	0.639836i	0.310679	−	0.950515i	$-0.399444\pi$
$181$	−115.810	−	115.810i	−0.639836	−	0.639836i	−0.950515	+	0.310679i	$0.899444\pi$
$182$	−125.061	+	181.666i	−0.687150	+	0.998166i
$183$		0			0
$184$	170.261	−	103.797i	0.925331	−	0.564114i
$185$		−	94.1266i		−	0.508792i
$186$		0			0
$187$	−110.246	+	110.246i	−0.589553	+	0.589553i
$188$	−109.252	−	285.925i	−0.581130	−	1.52088i
$189$		0			0
$190$	−26.7612	−	145.012i	−0.140849	−	0.763223i
$191$			35.2964i			0.184798i	0.995722	+	0.0923991i	$0.0294535\pi$
$191$			35.2964i			0.184798i	−0.995722	+	0.0923991i	$0.970546\pi$
$192$		0			0
$193$	−364.339			−1.88777			−0.943884	−	0.330277i	$-0.892858\pi$
$193$	−364.339			−1.88777			−0.943884	+	0.330277i	$0.892858\pi$
$194$	−45.4345	+	8.38468i	−0.234198	+	0.0432200i
$195$		0			0
$196$	−59.8599	+	22.8726i	−0.305408	+	0.116697i
$197$	−130.582	−	130.582i	−0.662851	−	0.662851i	0.293200	−	0.956051i	$-0.405280\pi$
$197$	−130.582	−	130.582i	−0.662851	−	0.662851i	−0.956051	+	0.293200i	$0.905280\pi$
$198$		0			0
$199$	−12.7493			−0.0640670			−0.0320335	−	0.999487i	$-0.510198\pi$
$199$	−12.7493			−0.0640670			−0.0320335	+	0.999487i	$0.510198\pi$
$200$	80.0567	+	131.319i	0.400283	+	0.656595i
$201$		0			0
$202$	37.5592	+	25.8562i	0.185937	+	0.128001i
$203$	8.64756	−	8.64756i	0.0425988	−	0.0425988i
$204$		0			0
$205$	87.1958	−	87.1958i	0.425346	−	0.425346i
$206$	194.394	−	35.8743i	0.943658	−	0.174147i
$207$		0			0
$208$	−17.0225	+	306.767i	−0.0818388	+	1.47484i
$209$	−242.786			−1.16165
$210$		0			0
$211$	8.59499	+	8.59499i	0.0407345	+	0.0407345i	0.727181	−	0.686446i	$-0.240830\pi$
$211$	8.59499	+	8.59499i	0.0407345	+	0.0407345i	−0.686446	+	0.727181i	$0.740830\pi$
$212$	291.855	+	130.480i	1.37667	+	0.615471i
$213$		0			0
$214$	25.1247	−	36.4966i	0.117405	−	0.170545i
$215$	−72.8663			−0.338913
$216$		0			0
$217$		−	12.6363i		−	0.0582317i
$218$	−135.834	+	197.315i	−0.623094	+	0.905117i
$219$		0			0
$220$	−71.0583	+	27.1515i	−0.322992	+	0.123416i
$221$	267.522	−	267.522i	1.21051	−	1.21051i
$222$		0			0
$223$			50.5909i			0.226865i	0.993546	+	0.113433i	$0.0361846\pi$
$223$			50.5909i			0.226865i	−0.993546	+	0.113433i	$0.963815\pi$
$224$	112.431	−	145.363i	0.501925	−	0.648944i
$225$		0			0
$226$	125.587	−	23.1763i	0.555693	−	0.102550i
$227$	−31.7175	−	31.7175i	−0.139725	−	0.139725i	0.633785	−	0.773509i	$-0.281501\pi$
$227$	−31.7175	−	31.7175i	−0.139725	−	0.139725i	−0.773509	+	0.633785i	$0.781501\pi$
$228$		0			0
$229$	−169.826	−	169.826i	−0.741599	−	0.741599i	0.231287	−	0.972886i	$-0.425706\pi$
$229$	−169.826	−	169.826i	−0.741599	−	0.741599i	−0.972886	+	0.231287i	$0.925706\pi$
$230$	−98.6796	−	67.9323i	−0.429042	−	0.295358i
$231$		0			0
$232$	4.01521	−	16.5564i	0.0173070	−	0.0713636i
$233$			363.082i			1.55829i	0.626844	+	0.779145i	$0.284346\pi$
$233$			363.082i			1.55829i	−0.626844	+	0.779145i	$0.715654\pi$
$234$		0			0
$235$	−130.033	+	130.033i	−0.553334	+	0.553334i
$236$	110.831	−	247.905i	0.469624	−	1.05045i
$237$		0			0
$238$	−222.536	+	41.0677i	−0.935024	+	0.172553i
$239$		−	27.6282i		−	0.115599i	−0.998328	−	0.0577996i	$-0.981592\pi$
$239$		−	27.6282i		−	0.115599i	0.998328	−	0.0577996i	$-0.0184084\pi$
$240$		0			0
$241$	368.121			1.52747			0.763737	−	0.645527i	$-0.223362\pi$
$241$	368.121			1.52747			0.763737	+	0.645527i	$0.223362\pi$
$242$	−21.1891	−	114.818i	−0.0875581	−	0.474456i
$243$		0			0
$244$	−119.038	+	266.262i	−0.487861	+	1.09124i
$245$	27.2233	+	27.2233i	0.111115	+	0.111115i
$246$		0			0
$247$	589.139			2.38518
$248$	−9.16290	−	15.0301i	−0.0369472	−	0.0606054i
$249$		0			0
$250$	120.530	−	175.084i	0.482119	−	0.700334i
$251$	−329.839	+	329.839i	−1.31410	+	1.31410i	−0.395734	+	0.918365i	$0.629510\pi$
$251$	−329.839	+	329.839i	−1.31410	+	1.31410i	−0.918365	+	0.395734i	$0.870490\pi$
$252$		0			0
$253$	−139.474	+	139.474i	−0.551281	+	0.551281i
$254$	13.3896	+	72.5551i	0.0527151	+	0.285650i
$255$		0			0
$256$	28.3236	−	254.428i	0.110639	−	0.993861i
$257$	−23.6762			−0.0921252			−0.0460626	−	0.998939i	$-0.514667\pi$
$257$	−23.6762			−0.0921252			−0.0460626	+	0.998939i	$0.514667\pi$
$258$		0			0
$259$	−159.050	−	159.050i	−0.614094	−	0.614094i
$260$	172.429	−	65.8854i	0.663188	−	0.253405i
$261$		0			0
$262$	−94.1535	−	64.8164i	−0.359364	−	0.247391i
$263$	−243.854			−0.927202			−0.463601	−	0.886044i	$-0.653443\pi$
$263$	−243.854			−0.927202			−0.463601	+	0.886044i	$0.653443\pi$
$264$		0			0
$265$		−	192.071i		−	0.724794i
$266$	−290.255	−	199.815i	−1.09118	−	0.751184i
$267$		0			0
$268$	327.644	+	146.480i	1.22255	+	0.546567i
$269$	−234.293	+	234.293i	−0.870976	+	0.870976i	−0.992579	−	0.121603i	$-0.961197\pi$
$269$	−234.293	+	234.293i	−0.870976	+	0.870976i	0.121603	+	0.992579i	$0.461197\pi$
$270$		0			0
$271$			30.9533i			0.114219i	0.998368	+	0.0571094i	$0.0181884\pi$
$271$			30.9533i			0.114219i	−0.998368	+	0.0571094i	$0.981812\pi$
$272$	−234.914	+	210.214i	−0.863655	+	0.772846i
$273$		0			0
$274$	92.0100	+	498.579i	0.335803	+	1.81963i
$275$	−107.574	−	107.574i	−0.391178	−	0.391178i
$276$		0			0
$277$	−41.4479	−	41.4479i	−0.149631	−	0.149631i	0.628322	−	0.777953i	$-0.283742\pi$
$277$	−41.4479	−	41.4479i	−0.149631	−	0.149631i	−0.777953	+	0.628322i	$0.783742\pi$
$278$	−108.750	+	157.972i	−0.391187	+	0.568245i
$279$		0			0
$280$	−107.298	−	26.0216i	−0.383206	−	0.0929342i
$281$		−	93.3971i		−	0.332374i	−0.986094	−	0.166187i	$-0.946854\pi$
$281$		−	93.3971i		−	0.332374i	0.986094	−	0.166187i	$-0.0531455\pi$
$282$		0			0
$283$	40.0982	−	40.0982i	0.141690	−	0.141690i	−0.632704	−	0.774394i	$-0.718055\pi$
$283$	40.0982	−	40.0982i	0.141690	−	0.141690i	0.774394	+	0.632704i	$0.218055\pi$
$284$	−162.485	+	62.0858i	−0.572130	+	0.218612i
$285$		0			0
$286$	−55.1540	−	298.866i	−0.192846	−	1.04498i
$287$		−	294.678i		−	1.02675i
$288$		0			0
$289$	99.1824			0.343192
$290$	−10.0654	+	1.85750i	−0.0347081	+	0.00640519i
$291$		0			0
$292$	−105.651	−	276.500i	−0.361819	−	0.946917i
$293$	−141.326	−	141.326i	−0.482340	−	0.482340i	0.423538	−	0.905878i	$-0.360788\pi$
$293$	−141.326	−	141.326i	−0.482340	−	0.482340i	−0.905878	+	0.423538i	$0.860788\pi$
$294$		0			0
$295$	−163.147			−0.553041
$296$	−304.513	−	73.8499i	−1.02876	−	0.249493i
$297$		0			0
$298$	−102.355	−	70.4622i	−0.343472	−	0.236450i
$299$	338.445	−	338.445i	1.13192	−	1.13192i
$300$		0			0
$301$	−123.126	+	123.126i	−0.409056	+	0.409056i
$302$	438.759	−	80.9705i	1.45284	−	0.268114i
$303$		0			0
$304$	−490.133	−	27.1974i	−1.61228	−	0.0894652i
$305$	175.228			0.574517
$306$		0			0
$307$	−285.548	−	285.548i	−0.930125	−	0.930125i	0.0675885	−	0.997713i	$-0.478470\pi$
$307$	−285.548	−	285.548i	−0.930125	−	0.930125i	−0.997713	+	0.0675885i	$0.978470\pi$
$308$	−74.1916	+	165.950i	−0.240882	+	0.538799i
$309$		0			0
$310$	−5.99687	+	8.71115i	−0.0193447	+	0.0281005i
$311$	365.454			1.17509			0.587547	−	0.809190i	$-0.300094\pi$
$311$	365.454			1.17509			0.587547	+	0.809190i	$0.300094\pi$
$312$		0			0
$313$			461.508i			1.47447i	0.675638	+	0.737234i	$0.263868\pi$
$313$			461.508i			1.47447i	−0.675638	+	0.737234i	$0.736132\pi$
$314$	126.466	−	183.707i	0.402758	−	0.585054i
$315$		0			0
$316$	5.89167	+	15.4191i	0.0186445	+	0.0487946i
$317$	319.216	−	319.216i	1.00699	−	1.00699i	0.00701388	−	0.999975i	$-0.497767\pi$
$317$	319.216	−	319.216i	1.00699	−	1.00699i	0.999975	−	0.00701388i	$-0.00223261\pi$
$318$		0			0
$319$			16.8518i			0.0528270i
$320$	−146.493	+	46.8531i	−0.457792	+	0.146416i
$321$		0			0
$322$	−281.533	+	51.9553i	−0.874325	+	0.161352i
$323$	427.429	+	427.429i	1.32331	+	1.32331i
$324$		0			0
$325$	261.037	+	261.037i	0.803190	+	0.803190i
$326$	−121.712	−	83.7881i	−0.373350	−	0.257019i
$327$		0			0
$328$	−213.679	−	350.503i	−0.651461	−	1.06861i
$329$			439.448i			1.33571i
$330$		0			0
$331$	−85.7864	+	85.7864i	−0.259173	+	0.259173i	−0.824718	−	0.565544i	$-0.808666\pi$
$331$	−85.7864	+	85.7864i	−0.259173	+	0.259173i	0.565544	+	0.824718i	$0.308666\pi$
$332$	−198.528	−	88.7562i	−0.597976	−	0.267338i
$333$		0			0
$334$	189.835	−	35.0329i	0.568367	−	0.104889i
$335$		−	215.623i		−	0.643651i
$336$		0			0
$337$	258.256			0.766339			0.383170	−	0.923678i	$-0.374832\pi$
$337$	258.256			0.766339			0.383170	+	0.923678i	$0.374832\pi$
$338$	72.4953	+	392.834i	0.214483	+	1.16223i
$339$		0			0
$340$	172.901	+	77.2989i	0.508531	+	0.227350i
$341$	12.3124	+	12.3124i	0.0361067	+	0.0361067i
$342$		0			0
$343$	373.398			1.08862
$344$	−57.1695	+	235.733i	−0.166190	+	0.685271i
$345$		0			0
$346$	−74.2695	+	107.885i	−0.214652	+	0.311807i
$347$	−27.7237	+	27.7237i	−0.0798953	+	0.0798953i	−0.745925	−	0.666030i	$-0.767992\pi$
$347$	−27.7237	+	27.7237i	−0.0798953	+	0.0798953i	0.666030	+	0.745925i	$0.267992\pi$
$348$		0			0
$349$	321.089	−	321.089i	0.920027	−	0.920027i	−0.0770037	−	0.997031i	$-0.524535\pi$
$349$	321.089	−	321.089i	0.920027	−	0.920027i	0.997031	+	0.0770037i	$0.0245353\pi$
$350$	−40.0722	−	217.141i	−0.114492	−	0.620403i
$351$		0			0
$352$	32.0882	+	251.187i	0.0911596	+	0.713599i
$353$	241.363			0.683748			0.341874	−	0.939746i	$-0.388938\pi$
$353$	241.363			0.683748			0.341874	+	0.939746i	$0.388938\pi$
$354$		0			0
$355$	73.8953	+	73.8953i	0.208156	+	0.208156i
$356$	−75.6468	−	197.975i	−0.212491	−	0.556111i
$357$		0			0
$358$	−217.934	−	150.029i	−0.608754	−	0.419074i
$359$	363.821			1.01343			0.506714	−	0.862114i	$-0.330860\pi$
$359$	363.821			1.01343			0.506714	+	0.862114i	$0.330860\pi$
$360$		0			0
$361$			580.287i			1.60744i
$362$	269.809	+	185.740i	0.745329	+	0.513094i
$363$		0			0
$364$	180.032	−	402.692i	0.494593	−	1.10630i
$365$	−125.747	+	125.747i	−0.344513	+	0.344513i
$366$		0			0
$367$		−	411.402i		−	1.12099i	−0.828159	−	0.560493i	$-0.810612\pi$
$367$		−	411.402i		−	1.12099i	0.828159	−	0.560493i	$-0.189388\pi$
$368$	−297.193	+	265.945i	−0.807590	+	0.722676i
$369$		0			0
$370$	34.1642	+	185.127i	0.0923356	+	0.500344i
$371$	−324.551	−	324.551i	−0.874801	−	0.874801i
$372$		0			0
$373$	−225.677	−	225.677i	−0.605033	−	0.605033i	0.336611	−	0.941644i	$-0.390719\pi$
$373$	−225.677	−	225.677i	−0.605033	−	0.605033i	−0.941644	+	0.336611i	$0.890719\pi$
$374$	176.816	−	256.847i	0.472771	−	0.686756i
$375$		0			0
$376$	318.656	+	522.699i	0.847488	+	1.39016i
$377$		−	40.8923i		−	0.108468i
$378$		0			0
$379$	−157.180	+	157.180i	−0.414724	+	0.414724i	−0.883381	−	0.468656i	$-0.844738\pi$
$379$	−157.180	+	157.180i	−0.414724	+	0.414724i	0.468656	+	0.883381i	$0.344738\pi$
$380$	105.267	+	275.496i	0.277019	+	0.724988i
$381$		0			0
$382$	−12.8112	−	69.4207i	−0.0335372	−	0.181729i
$383$			703.356i			1.83644i	0.396072	+	0.918219i	$0.370373\pi$
$383$			703.356i			1.83644i	−0.396072	+	0.918219i	$0.629627\pi$
$384$		0			0
$385$	109.212			0.283668
$386$	716.578	−	132.241i	1.85642	−	0.342592i
$387$		0			0
$388$	86.3168	−	32.9818i	0.222466	−	0.0850047i
$389$	−10.7401	−	10.7401i	−0.0276095	−	0.0276095i	0.693167	−	0.720777i	$-0.256215\pi$
$389$	−10.7401	−	10.7401i	−0.0276095	−	0.0276095i	−0.720777	+	0.693167i	$0.756215\pi$
$390$		0			0
$391$	491.095			1.25600
$392$	109.430	−	66.7124i	0.279158	−	0.170185i
$393$		0			0
$394$	304.222	+	209.431i	0.772138	+	0.531550i
$395$	7.01234	−	7.01234i	0.0177528	−	0.0177528i
$396$		0			0
$397$	365.020	−	365.020i	0.919446	−	0.919446i	−0.0775433	−	0.996989i	$-0.524708\pi$
$397$	365.020	−	365.020i	0.919446	−	0.919446i	0.996989	+	0.0775433i	$0.0247076\pi$
$398$	25.0753	−	4.62750i	0.0630032	−	0.0116269i
$399$		0			0
$400$	−205.118	−	229.220i	−0.512796	−	0.573049i
$401$	−341.735			−0.852207			−0.426104	−	0.904674i	$-0.640114\pi$
$401$	−341.735			−0.852207			−0.426104	+	0.904674i	$0.640114\pi$
$402$		0			0
$403$	−29.8770	−	29.8770i	−0.0741364	−	0.0741364i
$404$	−83.2558	−	37.2213i	−0.206079	−	0.0921318i
$405$		0			0
$406$	−13.8692	+	20.1467i	−0.0341606	+	0.0496223i
$407$	309.947			0.761541
$408$		0			0
$409$			368.259i			0.900389i	0.892931	+	0.450194i	$0.148645\pi$
$409$			368.259i			0.900389i	−0.892931	+	0.450194i	$0.851355\pi$
$410$	−139.847	+	203.144i	−0.341091	+	0.495474i
$411$		0			0
$412$	−369.310	+	141.114i	−0.896384	+	0.342510i
$413$	−275.678	+	275.678i	−0.667501	+	0.667501i
$414$		0			0
$415$			130.652i			0.314824i
$416$	−77.8646	−	609.525i	−0.187174	−	1.46520i
$417$		0			0
$418$	477.508	−	88.1215i	1.14236	−	0.210817i
$419$	−407.140	−	407.140i	−0.971694	−	0.971694i	0.0279165	−	0.999610i	$-0.491113\pi$
$419$	−407.140	−	407.140i	−0.971694	−	0.971694i	−0.999610	+	0.0279165i	$0.991113\pi$
$420$		0			0
$421$	57.5576	+	57.5576i	0.136716	+	0.136716i	0.772153	−	0.635437i	$-0.219180\pi$
$421$	57.5576	+	57.5576i	0.136716	+	0.136716i	−0.635437	+	0.772153i	$0.719180\pi$
$422$	−20.0242	−	13.7849i	−0.0474506	−	0.0326656i
$423$		0			0
$424$	−621.376	−	150.695i	−1.46551	−	0.355412i
$425$			378.772i			0.891229i
$426$		0			0
$427$	296.091	−	296.091i	0.693422	−	0.693422i
$428$	−36.1683	+	80.9005i	−0.0845053	+	0.189020i
$429$		0			0
$430$	143.313	−	26.4476i	0.333285	−	0.0615060i
$431$		−	796.565i		−	1.84818i	−0.382177	−	0.924089i	$-0.624826\pi$
$431$		−	796.565i		−	1.84818i	0.382177	−	0.924089i	$-0.375174\pi$
$432$		0			0
$433$	−335.804			−0.775529			−0.387764	−	0.921758i	$-0.626753\pi$
$433$	−335.804			−0.775529			−0.387764	+	0.921758i	$0.626753\pi$
$434$	4.58646	+	24.8529i	0.0105679	+	0.0572647i
$435$		0			0
$436$	195.540	−	437.380i	0.448487	−	1.00317i
$437$	540.746	+	540.746i	1.23741	+	1.23741i
$438$		0			0
$439$	−285.630			−0.650638			−0.325319	−	0.945604i	$-0.605472\pi$
$439$	−285.630			−0.650638			−0.325319	+	0.945604i	$0.605472\pi$
$440$	129.902	−	79.1927i	0.295232	−	0.179983i
$441$		0			0
$442$	−429.059	+	623.259i	−0.970722	+	1.41009i
$443$	−111.596	+	111.596i	−0.251909	+	0.251909i	−0.821753	−	0.569844i	$-0.807004\pi$
$443$	−111.596	+	111.596i	−0.251909	+	0.251909i	0.569844	+	0.821753i	$0.307004\pi$
$444$		0			0
$445$	−90.0358	+	90.0358i	−0.202328	+	0.202328i
$446$	−18.3625	−	99.5017i	−0.0411715	−	0.223098i
$447$		0			0
$448$	−168.367	+	326.707i	−0.375820	+	0.729257i
$449$	99.6741			0.221991			0.110996	−	0.993821i	$-0.464596\pi$
$449$	99.6741			0.221991			0.110996	+	0.993821i	$0.464596\pi$
$450$		0			0
$451$	287.125	+	287.125i	0.636641	+	0.636641i
$452$	−238.591	+	91.1659i	−0.527855	+	0.201695i
$453$		0			0
$454$	73.8939	+	50.8695i	0.162762	+	0.112047i
$455$	−265.012			−0.582445
$456$		0			0
$457$		−	32.1643i		−	0.0703813i	−0.999381	−	0.0351907i	$-0.988796\pi$
$457$		−	32.1643i		−	0.0703813i	0.999381	−	0.0351907i	$-0.0112039\pi$
$458$	395.652	+	272.372i	0.863870	+	0.594699i
$459$		0			0
$460$	218.739	+	97.7918i	0.475519	+	0.212591i
$461$	−165.361	+	165.361i	−0.358701	+	0.358701i	−0.863334	−	0.504633i	$-0.831628\pi$
$461$	−165.361	+	165.361i	−0.358701	+	0.358701i	0.504633	+	0.863334i	$0.331628\pi$
$462$		0			0
$463$		−	923.215i		−	1.99398i	−0.0774991	−	0.996992i	$-0.524693\pi$
$463$		−	923.215i		−	1.99398i	0.0774991	−	0.996992i	$-0.475307\pi$
$464$	−1.88778	+	34.0202i	−0.00406849	+	0.0733195i
$465$		0			0
$466$	−131.784	−	714.105i	−0.282798	−	1.53241i
$467$	−507.842	−	507.842i	−1.08746	−	1.08746i	−0.995790	−	0.0916660i	$-0.970781\pi$
$467$	−507.842	−	507.842i	−1.08746	−	1.08746i	−0.0916660	−	0.995790i	$-0.529219\pi$
$468$		0			0
$469$	−364.349	−	364.349i	−0.776864	−	0.776864i
$470$	208.551	−	302.945i	0.443727	−	0.644565i
$471$		0			0
$472$	−128.002	+	527.805i	−0.271191	+	1.11823i
$473$		−	239.940i		−	0.507272i
$474$		0			0
$475$	−417.068	+	417.068i	−0.878037	+	0.878037i
$476$	422.775	−	161.543i	0.888182	−	0.339376i
$477$		0			0
$478$	10.0279	+	54.3389i	0.0209789	+	0.113680i
$479$		−	52.3866i		−	0.109367i	−0.998504	−	0.0546833i	$-0.982585\pi$
$479$		−	52.3866i		−	0.109367i	0.998504	−	0.0546833i	$-0.0174149\pi$
$480$		0			0
$481$	−752.112			−1.56364
$482$	−724.017	+	133.613i	−1.50211	+	0.277206i
$483$		0			0
$484$	83.3489	+	218.132i	0.172208	+	0.450687i
$485$	−39.2554	−	39.2554i	−0.0809389	−	0.0809389i
$486$		0			0
$487$	−715.733			−1.46968			−0.734839	−	0.678241i	$-0.762742\pi$
$487$	−715.733			−1.46968			−0.734839	+	0.678241i	$0.762742\pi$
$488$	137.480	−	566.887i	0.281722	−	1.16165i
$489$		0			0
$490$	−63.4234	−	43.6614i	−0.129435	−	0.0891050i
$491$	22.3258	−	22.3258i	0.0454701	−	0.0454701i	−0.684006	−	0.729476i	$-0.739764\pi$
$491$	22.3258	−	22.3258i	0.0454701	−	0.0454701i	0.729476	+	0.684006i	$0.239764\pi$
$492$		0			0
$493$	29.6680	−	29.6680i	0.0601784	−	0.0601784i
$494$	−1158.71	+	213.834i	−2.34557	+	0.432862i
$495$		0			0
$496$	23.4768	+	26.2353i	0.0473323	+	0.0528938i
$497$	249.729			0.502473
$498$		0			0
$499$	84.0984	+	84.0984i	0.168534	+	0.168534i	0.786335	−	0.617801i	$-0.211976\pi$
$499$	84.0984	+	84.0984i	0.168534	+	0.168534i	−0.617801	+	0.786335i	$0.711976\pi$
$500$	−173.508	+	388.100i	−0.347017	+	0.776200i
$501$		0			0
$502$	529.005	−	768.442i	1.05380	−	1.53076i
$503$	−327.870			−0.651829			−0.325914	−	0.945399i	$-0.605672\pi$
$503$	−327.870			−0.651829			−0.325914	+	0.945399i	$0.605672\pi$
$504$		0			0
$505$			54.7909i			0.108497i
$506$	223.693	−	324.940i	0.442081	−	0.642174i
$507$		0			0
$508$	−52.6692	−	137.841i	−0.103680	−	0.271340i
$509$	−34.6224	+	34.6224i	−0.0680205	+	0.0680205i	−0.740299	−	0.672278i	$-0.765316\pi$
$509$	−34.6224	+	34.6224i	−0.0680205	+	0.0680205i	0.672278	+	0.740299i	$0.265316\pi$
$510$		0			0
$511$			424.963i			0.831630i
$512$	36.6407	+	510.687i	0.0715639	+	0.997436i
$513$		0			0
$514$	46.5661	−	8.59351i	0.0905954	−	0.0167189i
$515$	167.956	+	167.956i	0.326128	+	0.326128i
$516$		0			0
$517$	−428.184	−	428.184i	−0.828210	−	0.828210i
$518$	370.548	+	255.090i	0.715343	+	0.492451i
$519$		0			0
$520$	−315.217	+	192.167i	−0.606187	+	0.369553i
$521$		−	235.719i		−	0.452436i	−0.974077	−	0.226218i	$-0.927364\pi$
$521$		−	235.719i		−	0.452436i	0.974077	−	0.226218i	$-0.0726362\pi$
$522$		0			0
$523$	−185.851	+	185.851i	−0.355356	+	0.355356i	−0.862098	−	0.506742i	$-0.830850\pi$
$523$	−185.851	+	185.851i	−0.355356	+	0.355356i	0.506742	+	0.862098i	$0.330850\pi$
$524$	208.706	+	93.3063i	0.398294	+	0.178066i
$525$		0			0
$526$	479.610	−	88.5093i	0.911805	−	0.168269i
$527$		−	43.3524i		−	0.0822626i
$528$		0			0
$529$	92.2900			0.174461
$530$	69.7139	+	377.762i	0.131536	+	0.712759i
$531$		0			0
$532$	643.394	+	287.643i	1.20939	+	0.540683i
$533$	−696.732	−	696.732i	−1.30719	−	1.30719i
$534$		0			0
$535$	53.2408			0.0995155
$536$	−697.572	−	169.174i	−1.30144	−	0.315623i
$537$		0			0
$538$	375.765	−	545.843i	0.698448	−	1.01458i
$539$	−89.6428	+	89.6428i	−0.166313	+	0.166313i
$540$		0			0
$541$	−315.952	+	315.952i	−0.584015	+	0.584015i	−0.936004	−	0.351989i	$-0.885506\pi$
$541$	−315.952	+	315.952i	−0.584015	+	0.584015i	0.351989	+	0.936004i	$0.385506\pi$
$542$	−11.2348	−	60.8786i	−0.0207284	−	0.112322i
$543$		0			0
$544$	385.728	−	498.711i	0.709058	−	0.916749i
$545$	−287.841			−0.528149
$546$		0			0
$547$	−550.957	−	550.957i	−1.00723	−	1.00723i	−0.999974	−	0.00725954i	$-0.997689\pi$
$547$	−550.957	−	550.957i	−1.00723	−	1.00723i	−0.00725954	−	0.999974i	$-0.502311\pi$
$548$	−361.929	−	947.204i	−0.660454	−	1.72847i
$549$		0			0
$550$	250.620	+	172.530i	0.455673	+	0.313691i
$551$	65.3350			0.118575
$552$		0			0
$553$		−	23.6982i		−	0.0428539i
$554$	96.5631	+	66.4753i	0.174302	+	0.119992i
$555$		0			0
$556$	156.551	−	350.170i	0.281566	−	0.629802i
$557$	−2.35545	+	2.35545i	−0.00422882	+	0.00422882i	−0.709218	−	0.704989i	$-0.750952\pi$
$557$	−2.35545	+	2.35545i	−0.00422882	+	0.00422882i	0.704989	+	0.709218i	$0.250952\pi$
$558$		0			0
$559$			582.233i			1.04156i
$560$	220.476	+	12.2342i	0.393708	+	0.0218468i
$561$		0			0
$562$	33.8994	+	183.692i	0.0603192	+	0.326855i
$563$	−269.210	−	269.210i	−0.478170	−	0.478170i	0.426376	−	0.904546i	$-0.359790\pi$
$563$	−269.210	−	269.210i	−0.478170	−	0.478170i	−0.904546	+	0.426376i	$0.859790\pi$
$564$		0			0
$565$	108.507	+	108.507i	0.192047	+	0.192047i
$566$	−64.3106	+	93.4187i	−0.113623	+	0.165051i
$567$		0			0
$568$	297.039	−	181.085i	0.522956	−	0.318812i
$569$			342.558i			0.602035i	0.953619	+	0.301018i	$0.0973263\pi$
$569$			342.558i			0.602035i	−0.953619	+	0.301018i	$0.902674\pi$
$570$		0			0
$571$	153.948	−	153.948i	0.269610	−	0.269610i	−0.559333	−	0.828943i	$-0.688943\pi$
$571$	153.948	−	153.948i	0.269610	−	0.269610i	0.828943	+	0.559333i	$0.188943\pi$
$572$	216.953	+	567.787i	0.379288	+	0.992634i
$573$		0			0
$574$	106.957	+	579.570i	0.186335	+	1.00970i
$575$			479.190i			0.833373i
$576$		0			0
$577$	563.693			0.976938			0.488469	−	0.872581i	$-0.337556\pi$
$577$	563.693			0.976938			0.488469	+	0.872581i	$0.337556\pi$
$578$	−195.071	+	35.9992i	−0.337493	+	0.0622824i
$579$		0			0
$580$	19.1222	−	7.30664i	0.0329693	−	0.0125977i
$581$	220.769	+	220.769i	0.379981	+	0.379981i
$582$		0			0
$583$	632.465			1.08484
$584$	308.152	+	505.469i	0.527657	+	0.865530i
$585$		0			0
$586$	329.253	+	226.662i	0.561866	+	0.386796i
$587$	−176.603	+	176.603i	−0.300857	+	0.300857i	−0.841349	−	0.540492i	$-0.818238\pi$
$587$	−176.603	+	176.603i	−0.300857	+	0.300857i	0.540492	+	0.841349i	$0.318238\pi$
$588$		0			0
$589$	47.7355	−	47.7355i	0.0810450	−	0.0810450i
$590$	320.876	−	59.2159i	0.543857	−	0.100366i
$591$		0			0
$592$	625.718	+	34.7210i	1.05696	+	0.0586504i
$593$	996.597			1.68060			0.840301	−	0.542120i	$-0.182378\pi$
$593$	996.597			1.68060			0.840301	+	0.542120i	$0.182378\pi$
$594$		0			0
$595$	−192.271	−	192.271i	−0.323144	−	0.323144i
$596$	226.885	+	101.434i	0.380679	+	0.170191i
$597$		0			0
$598$	−542.808	+	788.493i	−0.907707	+	1.31855i
$599$	854.031			1.42576			0.712880	−	0.701286i	$-0.247390\pi$
$599$	854.031			1.42576			0.712880	+	0.701286i	$0.247390\pi$
$600$		0			0
$601$		−	345.733i		−	0.575263i	−0.957741	−	0.287631i	$-0.907132\pi$
$601$		−	345.733i		−	0.575263i	0.957741	−	0.287631i	$-0.0928678\pi$
$602$	197.473	−	286.853i	0.328028	−	0.476499i
$603$		0			0
$604$	−833.557	+	318.504i	−1.38006	+	0.527325i
$605$	99.2029	−	99.2029i	0.163972	−	0.163972i
$606$		0			0
$607$			526.354i			0.867141i	0.901120	+	0.433570i	$0.142746\pi$
$607$			526.354i			0.867141i	−0.901120	+	0.433570i	$0.857254\pi$
$608$	973.859	−	124.407i	1.60174	−	0.204617i
$609$		0			0
$610$	−344.636	+	63.6007i	−0.564977	+	0.104263i
$611$	1039.02	+	1039.02i	1.70053	+	1.70053i
$612$		0			0
$613$	410.567	+	410.567i	0.669767	+	0.669767i	0.957662	−	0.287895i	$-0.0929554\pi$
$613$	410.567	+	410.567i	0.669767	+	0.669767i	−0.287895	+	0.957662i	$0.592955\pi$
$614$	665.256	+	457.971i	1.08348	+	0.745881i
$615$		0			0
$616$	85.6859	−	353.318i	0.139100	−	0.573568i
$617$		−	514.755i		−	0.834287i	−0.908841	−	0.417144i	$-0.863031\pi$
$617$		−	514.755i		−	0.834287i	0.908841	−	0.417144i	$-0.136969\pi$
$618$		0			0
$619$	314.214	−	314.214i	0.507615	−	0.507615i	−0.406179	−	0.913794i	$-0.633139\pi$
$619$	314.214	−	314.214i	0.507615	−	0.507615i	0.913794	+	0.406179i	$0.133139\pi$
$620$	8.63278	−	19.3096i	0.0139238	−	0.0311446i
$621$		0			0
$622$	−718.772	+	132.645i	−1.15558	+	0.213256i
$623$			304.276i			0.488404i
$624$		0			0
$625$	−225.209			−0.360334
$626$	−167.509	−	907.690i	−0.267586	−	1.44998i
$627$		0			0
$628$	−182.054	+	407.215i	−0.289895	+	0.648431i
$629$	−545.669	−	545.669i	−0.867518	−	0.867518i
$630$		0			0
$631$	−230.081			−0.364629			−0.182315	−	0.983240i	$-0.558359\pi$
$631$	−230.081			−0.364629			−0.182315	+	0.983240i	$0.558359\pi$
$632$	−17.1842	−	28.1877i	−0.0271902	−	0.0446008i
$633$		0			0
$634$	−511.967	+	743.692i	−0.807519	+	1.17302i
$635$	−62.6875	+	62.6875i	−0.0987205	+	0.0987205i
$636$		0			0
$637$	217.526	−	217.526i	0.341484	−	0.341484i
$638$	−6.11654	−	33.1440i	−0.00958705	−	0.0519498i
$639$		0			0
$640$	271.116	−	145.321i	0.423618	−	0.227065i
$641$	−746.825			−1.16509			−0.582547	−	0.812797i	$-0.697944\pi$
$641$	−746.825			−1.16509			−0.582547	+	0.812797i	$0.697944\pi$
$642$		0			0
$643$	548.092	+	548.092i	0.852398	+	0.852398i	0.990428	−	0.138030i	$-0.0440772\pi$
$643$	548.092	+	548.092i	0.852398	+	0.852398i	−0.138030	+	0.990428i	$0.544077\pi$
$644$	534.858	−	204.370i	0.830524	−	0.317345i
$645$		0			0
$646$	−995.803	−	685.523i	−1.54149	−	1.06118i
$647$	−1055.00			−1.63060			−0.815302	−	0.579036i	$-0.803429\pi$
$647$	−1055.00			−1.63060			−0.815302	+	0.579036i	$0.803429\pi$
$648$		0			0
$649$		−	537.223i		−	0.827771i
$650$	−608.150	−	418.658i	−0.935616	−	0.644090i
$651$		0			0
$652$	269.794	+	120.617i	0.413794	+	0.184995i
$653$	854.888	−	854.888i	1.30917	−	1.30917i	0.387155	−	0.922015i	$-0.373458\pi$
$653$	854.888	−	854.888i	1.30917	−	1.30917i	0.922015	−	0.387155i	$-0.126542\pi$
$654$		0			0
$655$		−	137.350i		−	0.209694i
$656$	547.480	+	611.809i	0.834574	+	0.932636i
$657$		0			0
$658$	−159.502	−	864.302i	−0.242405	−	1.31353i
$659$	768.766	+	768.766i	1.16656	+	1.16656i	0.983009	+	0.183556i	$0.0587607\pi$
$659$	768.766	+	768.766i	1.16656	+	1.16656i	0.183556	+	0.983009i	$0.441239\pi$
$660$		0			0
$661$	312.323	+	312.323i	0.472500	+	0.472500i	0.902723	−	0.430223i	$-0.141565\pi$
$661$	312.323	+	312.323i	0.472500	+	0.472500i	−0.430223	+	0.902723i	$0.641565\pi$
$662$	137.587	−	199.861i	0.207835	−	0.301904i
$663$		0			0
$664$	422.678	+	102.507i	0.636563	+	0.154378i
$665$		−	423.420i		−	0.636721i
$666$		0			0
$667$	37.5333	−	37.5333i	0.0562719	−	0.0562719i
$668$	−360.649	+	137.805i	−0.539894	+	0.206295i
$669$		0			0
$670$	78.2626	+	424.085i	0.116810	+	0.632963i
$671$			577.004i			0.859916i
$672$		0			0
$673$	740.565			1.10039			0.550197	−	0.835035i	$-0.314553\pi$
$673$	740.565			1.10039			0.550197	+	0.835035i	$0.314553\pi$
$674$	−507.936	+	93.7367i	−0.753614	+	0.139075i
$675$		0			0
$676$	−285.166	−	746.308i	−0.421843	−	1.10401i
$677$	547.118	+	547.118i	0.808151	+	0.808151i	0.984354	−	0.176203i	$-0.0563814\pi$
$677$	547.118	+	547.118i	0.808151	+	0.808151i	−0.176203	+	0.984354i	$0.556381\pi$
$678$		0			0
$679$	−132.664			−0.195381
$680$	−368.115	−	89.2746i	−0.541346	−	0.131286i
$681$		0			0
$682$	−28.6848	−	19.7470i	−0.0420598	−	0.0289545i
$683$	407.623	−	407.623i	0.596813	−	0.596813i	−0.342650	−	0.939463i	$-0.611324\pi$
$683$	407.623	−	407.623i	0.596813	−	0.596813i	0.939463	+	0.342650i	$0.111324\pi$
$684$		0			0
$685$	−430.772	+	430.772i	−0.628864	+	0.628864i
$686$	−734.396	+	135.529i	−1.07055	+	0.197564i
$687$		0			0
$688$	26.8786	−	484.388i	0.0390678	−	0.704052i
$689$	−1534.73			−2.22747
$690$		0			0
$691$	17.6037	+	17.6037i	0.0254757	+	0.0254757i	0.719730	−	0.694254i	$-0.244266\pi$
$691$	17.6037	+	17.6037i	0.0254757	+	0.0254757i	−0.694254	+	0.719730i	$0.744266\pi$
$692$	106.915	−	239.144i	0.154501	−	0.345584i
$693$		0			0
$694$	44.4640	−	64.5892i	0.0640692	−	0.0930680i
$695$	−230.448			−0.331579
$696$		0			0
$697$		−	1010.98i		−	1.45047i
$698$	−514.973	+	748.058i	−0.737783	+	1.07172i
$699$		0			0
$700$	157.627	+	412.526i	0.225181	+	0.589323i
$701$	−164.273	+	164.273i	−0.234341	+	0.234341i	−0.814502	−	0.580161i	$-0.802990\pi$
$701$	−164.273	+	164.273i	−0.234341	+	0.234341i	0.580161	+	0.814502i	$0.302990\pi$
$702$		0			0
$703$		−	1201.68i		−	1.70935i
$704$	−154.281	−	482.385i	−0.219150	−	0.685205i
$705$		0			0
$706$	−474.710	+	87.6051i	−0.672394	+	0.124087i
$707$	92.5829	+	92.5829i	0.130952	+	0.130952i
$708$		0			0
$709$	422.796	+	422.796i	0.596327	+	0.596327i	0.939333	−	0.343006i	$-0.111445\pi$
$709$	422.796	+	422.796i	0.596327	+	0.596327i	−0.343006	+	0.939333i	$0.611445\pi$
$710$	−172.157	−	118.515i	−0.242475	−	0.166923i
$711$		0			0
$712$	220.638	+	361.919i	0.309886	+	0.508313i
$713$		−	54.8457i		−	0.0769224i
$714$		0			0
$715$	258.220	−	258.220i	0.361146	−	0.361146i
$716$	483.085	+	215.973i	0.674699	+	0.301639i
$717$		0			0
$718$	−715.559	+	132.052i	−0.996601	+	0.183917i
$719$		−	1029.00i		−	1.43115i	−0.698534	−	0.715577i	$-0.746164\pi$
$719$		−	1029.00i		−	1.43115i	0.698534	−	0.715577i	$-0.253836\pi$
$720$		0			0
$721$	567.607			0.787250
$722$	−210.621	−	1141.30i	−0.291719	−	1.58075i
$723$		0			0
$724$	−598.074	−	267.381i	−0.826068	−	0.369311i
$725$	28.9488	+	28.9488i	0.0399293	+	0.0399293i
$726$		0			0
$727$	−475.001			−0.653372			−0.326686	−	0.945133i	$-0.605932\pi$
$727$	−475.001			−0.653372			−0.326686	+	0.945133i	$0.605932\pi$
$728$	−207.924	+	857.354i	−0.285609	+	1.17768i
$729$		0			0
$730$	201.677	−	292.960i	0.276270	−	0.401314i
$731$	−422.419	+	422.419i	−0.577865	+	0.577865i
$732$		0			0
$733$	−344.939	+	344.939i	−0.470586	+	0.470586i	−0.902104	−	0.431519i	$-0.857978\pi$
$733$	−344.939	+	344.939i	−0.470586	+	0.470586i	0.431519	+	0.902104i	$0.357978\pi$
$734$	149.322	+	809.141i	0.203437	+	1.10237i
$735$		0			0
$736$	487.989	−	630.926i	0.663028	−	0.857237i
$737$	710.021			0.963393
$738$		0			0
$739$	363.340	+	363.340i	0.491665	+	0.491665i	0.908831	−	0.417166i	$-0.136976\pi$
$739$	363.340	+	363.340i	0.491665	+	0.491665i	−0.417166	+	0.908831i	$0.636976\pi$
$740$	−134.388	−	351.706i	−0.181605	−	0.475278i
$741$		0			0
$742$	756.123	+	520.525i	1.01903	+	0.701516i
$743$	−271.667			−0.365636			−0.182818	−	0.983147i	$-0.558522\pi$
$743$	−271.667			−0.365636			−0.182818	+	0.983147i	$0.558522\pi$
$744$		0			0
$745$		−	149.314i		−	0.200421i
$746$	525.771	+	361.948i	0.704787	+	0.485185i
$747$		0			0
$748$	−254.536	+	569.340i	−0.340288	+	0.761150i
$749$	89.9637	−	89.9637i	0.120112	−	0.120112i
$750$		0			0
$751$			1105.27i			1.47173i	0.677128	+	0.735866i	$0.263224\pi$
$751$			1105.27i			1.47173i	−0.677128	+	0.735866i	$0.736776\pi$
$752$	−816.447	−	912.380i	−1.08570	−	1.21327i
$753$		0			0
$754$	14.8423	+	80.4265i	0.0196847	+	0.106666i
$755$	379.087	+	379.087i	0.502102	+	0.502102i
$756$		0			0
$757$	554.565	+	554.565i	0.732583	+	0.732583i	0.971131	−	0.238548i	$-0.0766713\pi$
$757$	554.565	+	554.565i	0.732583	+	0.732583i	−0.238548	+	0.971131i	$0.576671\pi$
$758$	252.091	−	366.191i	0.332573	−	0.483102i
$759$		0			0
$760$	−307.033	−	503.634i	−0.403990	−	0.662676i
$761$			188.496i			0.247695i	0.992301	+	0.123847i	$0.0395234\pi$
$761$			188.496i			0.247695i	−0.992301	+	0.123847i	$0.960477\pi$
$762$		0			0
$763$	−486.380	+	486.380i	−0.637457	+	0.637457i
$764$	50.3939	+	131.886i	0.0659605	+	0.172625i
$765$		0			0
$766$	−255.290	−	1383.35i	−0.333277	−	1.80594i
$767$			1303.62i			1.69963i
$768$		0			0
$769$	−593.354			−0.771592			−0.385796	−	0.922584i	$-0.626073\pi$
$769$	−593.354			−0.771592			−0.385796	+	0.922584i	$0.626073\pi$
$770$	−214.798	+	39.6397i	−0.278958	+	0.0514801i
$771$		0			0
$772$	−1361.36	+	520.179i	−1.76342	+	0.673807i
$773$	−514.720	−	514.720i	−0.665873	−	0.665873i	0.290885	−	0.956758i	$-0.406050\pi$
$773$	−514.720	−	514.720i	−0.665873	−	0.665873i	−0.956758	+	0.290885i	$0.906050\pi$
$774$		0			0
$775$	42.3015			0.0545826
$776$	−157.796	+	96.1978i	−0.203345	+	0.123966i
$777$		0			0
$778$	25.0218	+	17.2253i	0.0321616	+	0.0221405i
$779$	1113.19	−	1113.19i	1.42900	−	1.42900i
$780$		0			0
$781$	−243.328	+	243.328i	−0.311560	+	0.311560i
$782$	−965.879	+	178.248i	−1.23514	+	0.227938i
$783$		0			0
$784$	−191.012	+	170.928i	−0.243638	+	0.218020i
$785$	267.989			0.341387
$786$		0			0
$787$	96.1835	+	96.1835i	0.122215	+	0.122215i	0.765569	−	0.643354i	$-0.222458\pi$
$787$	96.1835	+	96.1835i	0.122215	+	0.122215i	−0.643354	+	0.765569i	$0.722458\pi$
$788$	−674.356	−	301.485i	−0.855782	−	0.382595i
$789$		0			0
$790$	−11.2466	+	16.3370i	−0.0142362	+	0.0206797i
$791$	366.699			0.463589
$792$		0			0
$793$		−	1400.15i		−	1.76563i
$794$	−585.430	+	850.405i	−0.737317	+	1.07104i
$795$		0			0
$796$	−47.6382	+	18.2026i	−0.0598469	+	0.0228676i
$797$	664.410	−	664.410i	0.833639	−	0.833639i	−0.154374	−	0.988013i	$-0.549336\pi$
$797$	664.410	−	664.410i	0.833639	−	0.833639i	0.988013	+	0.154374i	$0.0493359\pi$
$798$		0			0
$799$			1507.66i			1.88693i
$800$	486.622	+	376.377i	0.608277	+	0.470471i
$801$		0			0
$802$	672.121	−	124.036i	0.838056	−	0.154659i
$803$	−414.070	−	414.070i	−0.515654	−	0.515654i
$804$		0			0
$805$	−243.244	−	243.244i	−0.302166	−	0.302166i
$806$	69.6059	+	47.9176i	0.0863596	+	0.0594511i
$807$		0			0
$808$	177.256	+	42.9878i	0.219377	+	0.0532028i
$809$		−	1371.63i		−	1.69547i	−0.530422	−	0.847734i	$-0.677966\pi$
$809$		−	1371.63i		−	1.69547i	0.530422	−	0.847734i	$-0.322034\pi$
$810$		0			0
$811$	809.783	−	809.783i	0.998500	−	0.998500i	−0.00149916	−	0.999999i	$-0.500477\pi$
$811$	809.783	−	809.783i	0.998500	−	0.998500i	0.999999	+	0.00149916i	$0.000477196\pi$
$812$	19.9654	−	44.6582i	0.0245879	−	0.0549978i
$813$		0			0
$814$	−609.601	+	112.498i	−0.748895	+	0.138205i
$815$		−	177.552i		−	0.217855i
$816$		0			0
$817$	−930.255			−1.13862
$818$	−133.663	−	724.288i	−0.163403	−	0.885437i
$819$		0			0
$820$	201.317	−	450.301i	0.245508	−	0.549148i
$821$	1144.74	+	1144.74i	1.39432	+	1.39432i	0.815342	+	0.578980i	$0.196549\pi$
$821$	1144.74	+	1144.74i	1.39432	+	1.39432i	0.578980	+	0.815342i	$0.303451\pi$
$822$		0			0
$823$	439.361			0.533853			0.266926	−	0.963717i	$-0.413992\pi$
$823$	439.361			0.533853			0.266926	+	0.963717i	$0.413992\pi$
$824$	675.137	−	411.587i	0.819340	−	0.499498i
$825$		0			0
$826$	442.140	−	642.260i	0.535279	−	0.777555i
$827$	−911.996	+	911.996i	−1.10278	+	1.10278i	−0.108701	+	0.994074i	$0.534669\pi$
$827$	−911.996	+	911.996i	−1.10278	+	1.10278i	−0.994074	+	0.108701i	$0.965331\pi$
$828$		0			0
$829$	470.575	−	470.575i	0.567642	−	0.567642i	−0.363825	−	0.931467i	$-0.618529\pi$
$829$	470.575	−	470.575i	0.567642	−	0.567642i	0.931467	+	0.363825i	$0.118529\pi$
$830$	−47.4214	−	256.965i	−0.0571342	−	0.309596i
$831$		0			0
$832$	374.376	+	1170.54i	0.449972	+	1.40690i
$833$	315.636			0.378915
$834$		0			0
$835$	164.017	+	164.017i	0.196428	+	0.196428i
$836$	−907.173	+	346.633i	−1.08514	+	0.414632i
$837$		0			0
$838$	948.533	+	652.983i	1.13190	+	0.779215i
$839$	−1432.91			−1.70787			−0.853937	−	0.520376i	$-0.825792\pi$
$839$	−1432.91			−1.70787			−0.853937	+	0.520376i	$0.825792\pi$
$840$		0			0
$841$			836.465i			0.994608i
$842$	−134.095	−	92.3126i	−0.159258	−	0.109635i
$843$		0			0
$844$	44.3867	+	19.8440i	0.0525909	+	0.0235119i
$845$	−339.408	+	339.408i	−0.401666	+	0.401666i
$846$		0			0
$847$		−	335.256i		−	0.395816i
$848$	1276.81	+	70.8502i	1.50567	+	0.0835498i
$849$		0			0
$850$	−137.479	−	744.965i	−0.161740	−	0.876430i
$851$	−690.332	−	690.332i	−0.811201	−	0.811201i
$852$		0			0
$853$	211.443	+	211.443i	0.247881	+	0.247881i	0.820101	−	0.572219i	$-0.193917\pi$
$853$	211.443	+	211.443i	0.247881	+	0.247881i	−0.572219	+	0.820101i	$0.693917\pi$
$854$	−474.880	+	689.818i	−0.556065	+	0.807750i
$855$		0			0
$856$	41.7717	−	172.242i	0.0487987	−	0.201217i
$857$			710.925i			0.829551i	0.909924	+	0.414775i	$0.136140\pi$
$857$			710.925i			0.829551i	−0.909924	+	0.414775i	$0.863860\pi$
$858$		0			0
$859$	348.557	−	348.557i	0.405771	−	0.405771i	−0.474490	−	0.880261i	$-0.657368\pi$
$859$	348.557	−	348.557i	0.405771	−	0.405771i	0.880261	+	0.474490i	$0.157368\pi$
$860$	−272.266	+	104.034i	−0.316589	+	0.120969i
$861$		0			0
$862$	289.121	+	1566.68i	0.335407	+	1.81749i
$863$		−	1493.19i		−	1.73023i	−0.501571	−	0.865116i	$-0.667245\pi$
$863$		−	1493.19i		−	1.73023i	0.501571	−	0.865116i	$-0.332755\pi$
$864$		0			0
$865$	−157.382			−0.181944
$866$	660.456	−	121.883i	0.762651	−	0.140743i
$867$		0			0
$868$	−18.0412	−	47.2157i	−0.0207848	−	0.0543960i
$869$	23.0908	+	23.0908i	0.0265717	+	0.0265717i
$870$		0			0
$871$	−1722.92			−1.97810
$872$	−225.835	+	931.208i	−0.258985	+	1.06790i
$873$		0			0
$874$	−1259.80	−	867.264i	−1.44142	−	0.992293i
$875$	431.579	−	431.579i	0.493233	−	0.493233i
$876$		0			0
$877$	−332.929	+	332.929i	−0.379623	+	0.379623i	−0.870966	−	0.491343i	$-0.836506\pi$
$877$	−332.929	+	332.929i	−0.379623	+	0.379623i	0.491343	+	0.870966i	$0.336506\pi$
$878$	561.774	−	103.672i	0.639834	−	0.118078i
$879$		0			0
$880$	−226.746	+	202.905i	−0.257666	+	0.230573i
$881$	637.491			0.723599			0.361799	−	0.932256i	$-0.382162\pi$
$881$	637.491			0.723599			0.361799	+	0.932256i	$0.382162\pi$
$882$		0			0
$883$	134.646	+	134.646i	0.152487	+	0.152487i	0.779228	−	0.626741i	$-0.215612\pi$
$883$	134.646	+	134.646i	0.152487	+	0.152487i	−0.626741	+	0.779228i	$0.715612\pi$
$884$	617.651	−	1381.55i	0.698700	−	1.56284i
$885$		0			0
$886$	178.980	−	259.990i	0.202010	−	0.293442i
$887$	−3.90891			−0.00440688			−0.00220344	−	0.999998i	$-0.500701\pi$
$887$	−3.90891			−0.00440688			−0.00220344	+	0.999998i	$0.500701\pi$
$888$		0			0
$889$			211.853i			0.238304i
$890$	144.402	−	209.761i	0.162249	−	0.235686i
$891$		0			0
$892$	72.2303	+	189.034i	0.0809756	+	0.211922i
$893$	−1660.08	+	1660.08i	−1.85900	+	1.85900i
$894$		0			0
$895$		−	317.919i		−	0.355217i
$896$	212.561	−	703.675i	0.237233	−	0.785351i
$897$		0			0
$898$	−196.038	+	36.1777i	−0.218305	+	0.0402870i
$899$	−3.31333	−	3.31333i	−0.00368558	−	0.00368558i
$900$		0			0
$901$	−1113.47	−	1113.47i	−1.23581	−	1.23581i
$902$	−668.930	−	460.500i	−0.741607	−	0.510532i
$903$		0			0
$904$	436.168	−	265.903i	0.482486	−	0.294140i
$905$			393.594i			0.434910i
$906$		0			0
$907$	697.707	−	697.707i	0.769247	−	0.769247i	−0.208727	−	0.977974i	$-0.566932\pi$
$907$	697.707	−	697.707i	0.769247	−	0.769247i	0.977974	+	0.208727i	$0.0669319\pi$
$908$	−163.797	−	73.2290i	−0.180393	−	0.0806487i
$909$		0			0
$910$	521.224	−	96.1889i	0.572773	−	0.105702i
$911$			796.856i			0.874705i	0.899290	+	0.437353i	$0.144084\pi$
$911$			796.856i			0.874705i	−0.899290	+	0.437353i	$0.855916\pi$
$912$		0			0
$913$	−430.221			−0.471216
$914$	11.6743	+	63.2603i	0.0127728	+	0.0692126i
$915$		0			0
$916$	−877.025	−	392.093i	−0.957451	−	0.428049i
$917$	−232.087	−	232.087i	−0.253094	−	0.253094i
$918$		0			0
$919$	420.532			0.457597			0.228798	−	0.973474i	$-0.426520\pi$
$919$	420.532			0.457597			0.228798	+	0.973474i	$0.426520\pi$
$920$	−465.708	−	112.942i	−0.506204	−	0.122763i
$921$		0			0
$922$	265.211	−	385.250i	0.287647	−	0.417841i
$923$	590.455	−	590.455i	0.639713	−	0.639713i
$924$		0			0
$925$	532.441	−	532.441i	0.575612	−	0.575612i
$926$	335.090	+	1815.77i	0.361868	+	1.96087i
$927$		0			0
$928$	−8.63512	−	67.5958i	−0.00930509	−	0.0728403i
$929$	−1178.38			−1.26843			−0.634217	−	0.773155i	$-0.718677\pi$
$929$	−1178.38			−1.26843			−0.634217	+	0.773155i	$0.718677\pi$
$930$		0			0
$931$	347.548	+	347.548i	0.373306	+	0.373306i
$932$	518.383	+	1356.66i	0.556205	+	1.45565i
$933$		0			0
$934$	1183.14	+	814.492i	1.26675	+	0.872047i
$935$	374.684			0.400732
$936$		0			0
$937$		−	405.962i		−	0.433257i	−0.976254	−	0.216629i	$-0.930494\pi$
$937$		−	405.962i		−	0.433257i	0.976254	−	0.216629i	$-0.0695061\pi$
$938$	848.843	+	584.354i	0.904950	+	0.622979i
$939$		0			0
$940$	−300.220	+	671.526i	−0.319383	+	0.714389i
$941$	−429.859	+	429.859i	−0.456810	+	0.456810i	−0.897607	−	0.440797i	$-0.854696\pi$
$941$	−429.859	+	429.859i	−0.456810	+	0.456810i	0.440797	+	0.897607i	$0.354696\pi$
$942$		0			0
$943$		−	1279.00i		−	1.35631i
$944$	60.1810	−	1084.54i	0.0637511	−	1.14888i
$945$		0			0
$946$	87.0886	+	471.911i	0.0920598	+	0.498849i
$947$	−661.681	−	661.681i	−0.698713	−	0.698713i	0.265420	−	0.964133i	$-0.414489\pi$
$947$	−661.681	−	661.681i	−0.698713	−	0.698713i	−0.964133	+	0.265420i	$0.914489\pi$
$948$		0			0
$949$	1004.77	+	1004.77i	1.05877	+	1.05877i
$950$	668.905	−	971.663i	0.704111	−	1.02280i
$951$		0			0
$952$	−772.875	+	471.172i	−0.811844	+	0.494928i
$953$			31.1854i			0.0327234i	0.999866	+	0.0163617i	$0.00520833\pi$
$953$			31.1854i			0.0327234i	−0.999866	+	0.0163617i	$0.994792\pi$
$954$		0			0
$955$	59.9794	−	59.9794i	0.0628056	−	0.0628056i
$956$	−39.4457	−	103.233i	−0.0412612	−	0.107985i
$957$		0			0
$958$	19.0142	+	103.033i	0.0198478	+	0.107550i
$959$			1455.79i			1.51803i
$960$		0			0
$961$	956.158			0.994962
$962$	1479.25	−	272.987i	1.53768	−	0.283770i
$963$		0			0
$964$	1375.49	−	525.579i	1.42686	−	0.545206i
$965$	619.123	+	619.123i	0.641578	+	0.641578i
$966$		0			0
$967$	−1312.55			−1.35734			−0.678672	−	0.734442i	$-0.737444\pi$
$967$	−1312.55			−1.35734			−0.678672	+	0.734442i	$0.737444\pi$
$968$	−243.103	−	398.768i	−0.251140	−	0.411951i
$969$		0			0
$970$	91.4551	+	62.9589i	0.0942837	+	0.0649061i
$971$	−318.758	+	318.758i	−0.328278	+	0.328278i	−0.851931	−	0.523653i	$-0.824569\pi$
$971$	−318.758	+	318.758i	−0.328278	+	0.328278i	0.523653	+	0.851931i	$0.324569\pi$
$972$		0			0
$973$	−389.399	+	389.399i	−0.400205	+	0.400205i
$974$	1407.70	−	259.783i	1.44527	−	0.266717i
$975$		0			0
$976$	−64.6373	+	1164.85i	−0.0662268	+	1.19349i
$977$	531.045			0.543546			0.271773	−	0.962361i	$-0.412390\pi$
$977$	531.045			0.543546			0.271773	+	0.962361i	$0.412390\pi$
$978$		0			0
$979$	−296.477	−	296.477i	−0.302836	−	0.302836i
$980$	140.588	+	62.8527i	0.143457	+	0.0641354i
$981$		0			0
$982$	−35.8068	+	52.0135i	−0.0364631	+	0.0529669i
$983$	1796.17			1.82723			0.913614	−	0.406582i	$-0.133279\pi$
$983$	1796.17			1.82723			0.913614	+	0.406582i	$0.133279\pi$
$984$		0			0
$985$			443.796i			0.450554i
$986$	−47.5824	+	69.1189i	−0.0482580	+	0.0701003i
$987$		0			0
$988$	2201.33	−	841.132i	2.22806	−	0.851348i
$989$	−534.408	+	534.408i	−0.540352	+	0.540352i
$990$		0			0
$991$			506.064i			0.510660i	0.966854	+	0.255330i	$0.0821841\pi$
$991$			506.064i			0.510660i	−0.966854	+	0.255330i	$0.917816\pi$
$992$	−55.6964	−	43.0783i	−0.0561455	−	0.0434257i
$993$		0			0
$994$	−491.165	+	90.6417i	−0.494129	+	0.0911889i
$995$	21.6650	+	21.6650i	0.0217739	+	0.0217739i
$996$		0			0
$997$	−249.068	−	249.068i	−0.249817	−	0.249817i	0.571078	−	0.820896i	$-0.306525\pi$
$997$	−249.068	−	249.068i	−0.249817	−	0.249817i	−0.820896	+	0.571078i	$0.806525\pi$
$998$	−195.928	−	134.879i	−0.196321	−	0.135150i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.c.91.1		16
3.2	odd	2		48.3.l.a.43.8	yes	16
4.3	odd	2		576.3.m.c.271.3		16
8.3	odd	2		1152.3.m.c.415.6		16
8.5	even	2		1152.3.m.f.415.6		16
12.11	even	2		192.3.l.a.79.7		16
16.3	odd	4	inner	144.3.m.c.19.1		16
16.5	even	4		1152.3.m.c.991.6		16
16.11	odd	4		1152.3.m.f.991.6		16
16.13	even	4		576.3.m.c.559.3		16
24.5	odd	2		384.3.l.a.31.6		16
24.11	even	2		384.3.l.b.31.2		16
48.5	odd	4		384.3.l.b.223.2		16
48.11	even	4		384.3.l.a.223.6		16
48.29	odd	4		192.3.l.a.175.7		16
48.35	even	4		48.3.l.a.19.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.3.l.a.19.8	✓	16	48.35	even	4
48.3.l.a.43.8	yes	16	3.2	odd	2
144.3.m.c.19.1		16	16.3	odd	4	inner
144.3.m.c.91.1		16	1.1	even	1	trivial
192.3.l.a.79.7		16	12.11	even	2
192.3.l.a.175.7		16	48.29	odd	4
384.3.l.a.31.6		16	24.5	odd	2
384.3.l.a.223.6		16	48.11	even	4
384.3.l.b.31.2		16	24.11	even	2
384.3.l.b.223.2		16	48.5	odd	4
576.3.m.c.271.3		16	4.3	odd	2
576.3.m.c.559.3		16	16.13	even	4
1152.3.m.c.415.6		16	8.3	odd	2
1152.3.m.c.991.6		16	16.5	even	4
1152.3.m.f.415.6		16	8.5	even	2
1152.3.m.f.991.6		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)

\(f(q)\)	\(=\)	\(q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +O(q^{10})\)	\(q+(-1.96679 + 0.362960i) q^{2} +(3.73652 - 1.42773i) q^{4} +(-1.69930 - 1.69930i) q^{5} -5.74280 q^{7} +(-6.83074 + 4.16426i) q^{8} +(3.95895 + 2.72539i) q^{10} +(5.59560 - 5.59560i) q^{11} +(-13.5782 + 13.5782i) q^{13} +(11.2949 - 2.08441i) q^{14} +(11.9232 - 10.6695i) q^{16} -19.7023 q^{17} +(-21.6943 - 21.6943i) q^{19} +(-8.77563 - 3.92333i) q^{20} +(-8.97439 + 13.0363i) q^{22} -24.9257 q^{23} -19.2247i q^{25} +(21.7771 - 31.6337i) q^{26} +(-21.4581 + 8.19918i) q^{28} +(-1.50581 + 1.50581i) q^{29} +2.20037i q^{31} +(-19.5777 + 25.3123i) q^{32} +(38.7504 - 7.15116i) q^{34} +(9.75877 + 9.75877i) q^{35} +(27.6956 + 27.6956i) q^{37} +(50.5423 + 34.7940i) q^{38} +(18.6838 + 4.53116i) q^{40} +51.3127i q^{41} +(21.4400 - 21.4400i) q^{43} +(12.9191 - 28.8971i) q^{44} +(49.0236 - 9.04703i) q^{46} -76.5216i q^{47} -16.0202 q^{49} +(6.97781 + 37.8110i) q^{50} +(-31.3491 + 70.1211i) q^{52} +(56.5145 + 56.5145i) q^{53} -19.0173 q^{55} +(39.2276 - 23.9145i) q^{56} +(2.41506 - 3.50816i) q^{58} +(48.0041 - 48.0041i) q^{59} +(-51.5587 + 51.5587i) q^{61} +(-0.798646 - 4.32766i) q^{62} +(29.3180 - 56.8899i) q^{64} +46.1469 q^{65} +(63.4445 + 63.4445i) q^{67} +(-73.6182 + 28.1297i) q^{68} +(-22.7355 - 15.6514i) q^{70} -43.4856 q^{71} -73.9992i q^{73} +(-64.5239 - 44.4190i) q^{74} +(-112.035 - 50.0876i) q^{76} +(-32.1344 + 32.1344i) q^{77} +4.12659i q^{79} +(-38.3918 - 2.13036i) q^{80} +(-18.6245 - 100.921i) q^{82} +(-38.4428 - 38.4428i) q^{83} +(33.4803 + 33.4803i) q^{85} +(-34.3862 + 49.9499i) q^{86} +(-14.9206 + 61.5236i) q^{88} -52.9839i q^{89} +(77.9767 - 77.9767i) q^{91} +(-93.1353 + 35.5872i) q^{92} +(27.7743 + 150.502i) q^{94} +73.7305i q^{95} +23.1008 q^{97} +(31.5084 - 5.81471i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{4} + 12 q^{8}+O(q^{10}) \) 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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