LMFDB - Embedded newform 144.3.m.b.91.6

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} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 $ x^16 - 6x^14 + 10x^12 + 88x^10 - 752x^8 + 1408x^6 + 2560x^4 - 24576*x^2 + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			91.6
Root			$1.66730 - 1.10459i$ of defining polynomial
Character	$\chi$	$=$	144.91
Dual form			144.3.m.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10459 + 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(4.23991 + 4.23991i) q^{5} -0.262225 q^{7} +(-7.86415 + 1.46802i) q^{8} +O(q^{10})$	\(q+(1.10459 + 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(4.23991 + 4.23991i) q^{5} -0.262225 q^{7} +(-7.86415 + 1.46802i) q^{8} +(-2.38583 + 11.7525i) q^{10} +(8.60531 - 8.60531i) q^{11} +(-15.9957 + 15.9957i) q^{13} +(-0.289652 - 0.437208i) q^{14} +(-11.1343 - 11.4903i) q^{16} +3.51534 q^{17} +(10.7566 + 10.7566i) q^{19} +(-22.2304 + 9.00387i) q^{20} +(23.8530 + 4.84227i) q^{22} +16.4968 q^{23} +10.9536i q^{25} +(-44.3382 - 9.00087i) q^{26} +(0.409009 - 0.965871i) q^{28} +(25.9522 - 25.9522i) q^{29} -46.2072i q^{31} +(6.85895 - 31.2563i) q^{32} +(3.88301 + 5.86112i) q^{34} +(-1.11181 - 1.11181i) q^{35} +(-2.99313 - 2.99313i) q^{37} +(-6.05283 + 29.8162i) q^{38} +(-39.5676 - 27.1190i) q^{40} -21.9026i q^{41} +(48.7016 - 48.7016i) q^{43} +(18.2742 + 45.1187i) q^{44} +(18.2222 + 27.5051i) q^{46} +70.7760i q^{47} -48.9312 q^{49} +(-18.2630 + 12.0993i) q^{50} +(-33.9684 - 83.8672i) q^{52} +(52.8193 + 52.8193i) q^{53} +72.9715 q^{55} +(2.06218 - 0.384952i) q^{56} +(71.9366 + 14.6035i) q^{58} +(61.7726 - 61.7726i) q^{59} +(-22.9004 + 22.9004i) q^{61} +(77.0411 - 51.0400i) q^{62} +(59.6898 - 23.0895i) q^{64} -135.640 q^{65} +(-54.9939 - 54.9939i) q^{67} +(-5.48309 + 12.9483i) q^{68} +(0.625624 - 3.08182i) q^{70} -84.2532 q^{71} +78.0341i q^{73} +(1.68426 - 8.29663i) q^{74} +(-56.3983 + 22.8428i) q^{76} +(-2.25653 + 2.25653i) q^{77} +59.2887i q^{79} +(1.50953 - 95.9263i) q^{80} +(36.5181 - 24.1934i) q^{82} +(-111.661 - 111.661i) q^{83} +(14.9047 + 14.9047i) q^{85} +(134.995 + 27.4047i) q^{86} +(-55.0407 + 80.3063i) q^{88} +34.5426i q^{89} +(4.19447 - 4.19447i) q^{91} +(-25.7311 + 60.7637i) q^{92} +(-118.005 + 78.1784i) q^{94} +91.2142i q^{95} -66.0805 q^{97} +(-54.0490 - 81.5829i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{4}+O(q^{10}) $ 16 * q - 12 * q^4	$ 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) $ 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

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 $

$2$	1.10459	+	1.66730i	0.552295	+	0.833649i
$2$	1.10459	+	1.66730i	0.552295	+	0.833649i
$3$		0			0
$3$		0			0
$4$	−1.55976	+	3.68336i	−0.389940	+	0.920840i
$5$	4.23991	+	4.23991i	0.847982	+	0.847982i	0.989881	−	0.141900i	$-0.0453210\pi$
$5$	4.23991	+	4.23991i	0.847982	+	0.847982i	−0.141900	+	0.989881i	$0.545321\pi$
$6$		0			0
$7$	−0.262225			−0.0374608			−0.0187304	−	0.999825i	$-0.505962\pi$
$7$	−0.262225			−0.0374608			−0.0187304	+	0.999825i	$0.505962\pi$
$8$	−7.86415	+	1.46802i	−0.983019	+	0.183503i
$9$		0			0
$10$	−2.38583	+	11.7525i	−0.238583	+	1.17525i
$11$	8.60531	−	8.60531i	0.782301	−	0.782301i	−0.197917	−	0.980219i	$-0.563418\pi$
$11$	8.60531	−	8.60531i	0.782301	−	0.782301i	0.980219	+	0.197917i	$0.0634178\pi$
$12$		0			0
$13$	−15.9957	+	15.9957i	−1.23044	+	1.23044i	−0.266640	+	0.963796i	$0.585913\pi$
$13$	−15.9957	+	15.9957i	−1.23044	+	1.23044i	−0.963796	+	0.266640i	$0.914087\pi$
$14$	−0.289652	−	0.437208i	−0.0206894	−	0.0312291i
$15$		0			0
$16$	−11.1343	−	11.4903i	−0.695893	−	0.718145i
$17$	3.51534			0.206785			0.103392	−	0.994641i	$-0.467030\pi$
$17$	3.51534			0.206785			0.103392	+	0.994641i	$0.467030\pi$
$18$		0			0
$19$	10.7566	+	10.7566i	0.566138	+	0.566138i	0.931044	−	0.364906i	$-0.118899\pi$
$19$	10.7566	+	10.7566i	0.566138	+	0.566138i	−0.364906	+	0.931044i	$0.618899\pi$
$20$	−22.2304	+	9.00387i	−1.11152	+	0.450193i
$21$		0			0
$22$	23.8530	+	4.84227i	1.08423	+	0.220103i
$23$	16.4968			0.717253			0.358626	−	0.933481i	$-0.383245\pi$
$23$	16.4968			0.717253			0.358626	+	0.933481i	$0.383245\pi$
$24$		0			0
$25$			10.9536i			0.438145i
$26$	−44.3382	−	9.00087i	−1.70532	−	0.346187i
$27$		0			0
$28$	0.409009	−	0.965871i	0.0146075	−	0.0344954i
$29$	25.9522	−	25.9522i	0.894903	−	0.894903i	−0.100077	−	0.994980i	$-0.531909\pi$
$29$	25.9522	−	25.9522i	0.894903	−	0.894903i	0.994980	+	0.100077i	$0.0319088\pi$
$30$		0			0
$31$		−	46.2072i		−	1.49055i	−0.666755	−	0.745277i	$-0.732317\pi$
$31$		−	46.2072i		−	1.49055i	0.666755	−	0.745277i	$-0.267683\pi$
$32$	6.85895	−	31.2563i	0.214342	−	0.976759i
$33$		0			0
$34$	3.88301	+	5.86112i	0.114206	+	0.172386i
$35$	−1.11181	−	1.11181i	−0.0317660	−	0.0317660i
$36$		0			0
$37$	−2.99313	−	2.99313i	−0.0808955	−	0.0808955i	0.665501	−	0.746397i	$-0.268218\pi$
$37$	−2.99313	−	2.99313i	−0.0808955	−	0.0808955i	−0.746397	+	0.665501i	$0.768218\pi$
$38$	−6.05283	+	29.8162i	−0.159285	+	0.784636i
$39$		0			0
$40$	−39.5676	−	27.1190i	−0.989189	−	0.677975i
$41$		−	21.9026i		−	0.534210i	−0.963667	−	0.267105i	$-0.913933\pi$
$41$		−	21.9026i		−	0.534210i	0.963667	−	0.267105i	$-0.0860670\pi$
$42$		0			0
$43$	48.7016	−	48.7016i	1.13260	−	1.13260i	0.142851	−	0.989744i	$-0.454373\pi$
$43$	48.7016	−	48.7016i	1.13260	−	1.13260i	0.989744	−	0.142851i	$-0.0456270\pi$
$44$	18.2742	+	45.1187i	0.415324	+	1.02543i
$45$		0			0
$46$	18.2222	+	27.5051i	0.396135	+	0.597937i
$47$			70.7760i			1.50587i	0.658094	+	0.752936i	$0.271363\pi$
$47$			70.7760i			1.50587i	−0.658094	+	0.752936i	$0.728637\pi$
$48$		0			0
$49$	−48.9312			−0.998597
$50$	−18.2630	+	12.0993i	−0.365259	+	0.241986i
$51$		0			0
$52$	−33.9684	−	83.8672i	−0.653239	−	1.61283i
$53$	52.8193	+	52.8193i	0.996590	+	0.996590i	0.999994	−	0.00340427i	$-0.00108361\pi$
$53$	52.8193	+	52.8193i	0.996590	+	0.996590i	−0.00340427	+	0.999994i	$0.501084\pi$
$54$		0			0
$55$	72.9715			1.32675
$56$	2.06218	−	0.384952i	0.0368247	−	0.00687415i
$57$		0			0
$58$	71.9366	+	14.6035i	1.24029	+	0.251784i
$59$	61.7726	−	61.7726i	1.04699	−	1.04699i	0.0481541	−	0.998840i	$-0.484666\pi$
$59$	61.7726	−	61.7726i	1.04699	−	1.04699i	0.998840	−	0.0481541i	$-0.0153339\pi$
$60$		0			0
$61$	−22.9004	+	22.9004i	−0.375416	+	0.375416i	−0.869445	−	0.494029i	$-0.835524\pi$
$61$	−22.9004	+	22.9004i	−0.375416	+	0.375416i	0.494029	+	0.869445i	$0.335524\pi$
$62$	77.0411	−	51.0400i	1.24260	−	0.823226i
$63$		0			0
$64$	59.6898	−	23.0895i	0.932654	−	0.360773i
$65$	−135.640			−2.08677
$66$		0			0
$67$	−54.9939	−	54.9939i	−0.820804	−	0.820804i	0.165419	−	0.986223i	$-0.447102\pi$
$67$	−54.9939	−	54.9939i	−0.820804	−	0.820804i	−0.986223	+	0.165419i	$0.947102\pi$
$68$	−5.48309	+	12.9483i	−0.0806337	+	0.190416i
$69$		0			0
$70$	0.625624	−	3.08182i	0.00893749	−	0.0440260i
$71$	−84.2532			−1.18666			−0.593332	−	0.804958i	$-0.702188\pi$
$71$	−84.2532			−1.18666			−0.593332	+	0.804958i	$0.702188\pi$
$72$		0			0
$73$			78.0341i			1.06896i	0.845181	+	0.534480i	$0.179493\pi$
$73$			78.0341i			1.06896i	−0.845181	+	0.534480i	$0.820507\pi$
$74$	1.68426	−	8.29663i	0.0227602	−	0.112117i
$75$		0			0
$76$	−56.3983	+	22.8428i	−0.742083	+	0.300563i
$77$	−2.25653	+	2.25653i	−0.0293056	+	0.0293056i
$78$		0			0
$79$			59.2887i			0.750490i	0.926926	+	0.375245i	$0.122441\pi$
$79$			59.2887i			0.750490i	−0.926926	+	0.375245i	$0.877559\pi$
$80$	1.50953	−	95.9263i	0.0188691	−	1.19908i
$81$		0			0
$82$	36.5181	−	24.1934i	0.445343	−	0.295041i
$83$	−111.661	−	111.661i	−1.34531	−	1.34531i	−0.890676	−	0.454638i	$-0.849769\pi$
$83$	−111.661	−	111.661i	−1.34531	−	1.34531i	−0.454638	−	0.890676i	$-0.650231\pi$
$84$		0			0
$85$	14.9047	+	14.9047i	0.175350	+	0.175350i
$86$	134.995	+	27.4047i	1.56971	+	0.318660i
$87$		0			0
$88$	−55.0407	+	80.3063i	−0.625463	+	0.912571i
$89$			34.5426i			0.388119i	0.980990	+	0.194060i	$0.0621655\pi$
$89$			34.5426i			0.388119i	−0.980990	+	0.194060i	$0.937834\pi$
$90$		0			0
$91$	4.19447	−	4.19447i	0.0460931	−	0.0460931i
$92$	−25.7311	+	60.7637i	−0.279686	+	0.660475i
$93$		0			0
$94$	−118.005	+	78.1784i	−1.25537	+	0.831686i
$95$			91.2142i			0.960150i
$96$		0			0
$97$	−66.0805			−0.681242			−0.340621	−	0.940201i	$-0.610637\pi$
$97$	−66.0805			−0.681242			−0.340621	+	0.940201i	$0.610637\pi$
$98$	−54.0490	−	81.5829i	−0.551520	−	0.832479i
$99$		0			0
$100$	−40.3462	−	17.0850i	−0.403462	−	0.170850i
$101$	25.5254	+	25.5254i	0.252727	+	0.252727i	0.822088	−	0.569361i	$-0.192809\pi$
$101$	25.5254	+	25.5254i	0.252727	+	0.252727i	−0.569361	+	0.822088i	$0.692809\pi$
$102$		0			0
$103$	−14.2072			−0.137934			−0.0689670	−	0.997619i	$-0.521970\pi$
$103$	−14.2072			−0.137934			−0.0689670	+	0.997619i	$0.521970\pi$
$104$	102.310	−	149.274i	0.983754	−	1.43533i
$105$		0			0
$106$	−29.7218	+	146.409i	−0.280394	+	1.38122i
$107$	−21.8489	+	21.8489i	−0.204195	+	0.204195i	−0.801795	−	0.597600i	$-0.796121\pi$
$107$	−21.8489	+	21.8489i	−0.204195	+	0.204195i	0.597600	+	0.801795i	$0.296121\pi$
$108$		0			0
$109$	17.8979	−	17.8979i	0.164201	−	0.164201i	−0.620224	−	0.784425i	$-0.712958\pi$
$109$	17.8979	−	17.8979i	0.164201	−	0.164201i	0.784425	+	0.620224i	$0.212958\pi$
$110$	80.6036	+	121.665i	0.732760	+	1.10605i
$111$		0			0
$112$	2.91970	+	3.01305i	0.0260687	+	0.0269023i
$113$	−174.546			−1.54465			−0.772325	−	0.635227i	$-0.780907\pi$
$113$	−174.546			−1.54465			−0.772325	+	0.635227i	$0.780907\pi$
$114$		0			0
$115$	69.9450	+	69.9450i	0.608217	+	0.608217i
$116$	55.1121	+	136.070i	0.475104	+	1.17302i
$117$		0			0
$118$	171.227	+	34.7599i	1.45107	+	0.294575i
$119$	−0.921813			−0.00774632
$120$		0			0
$121$		−	27.1029i		−	0.223991i
$122$	−63.4773	−	12.8862i	−0.520306	−	0.105625i
$123$		0			0
$124$	170.198	+	72.0722i	1.37256	+	0.581227i
$125$	59.5553	−	59.5553i	0.476442	−	0.476442i
$126$		0			0
$127$		−	45.3438i		−	0.357037i	−0.983937	−	0.178519i	$-0.942869\pi$
$127$		−	45.3438i		−	0.357037i	0.983937	−	0.178519i	$-0.0571305\pi$
$128$	104.430	+	74.0163i	0.815858	+	0.578252i
$129$		0			0
$130$	−149.827	−	226.153i	−1.15252	−	1.73964i
$131$	32.6213	+	32.6213i	0.249017	+	0.249017i	0.820567	−	0.571550i	$-0.193658\pi$
$131$	32.6213	+	32.6213i	0.249017	+	0.249017i	−0.571550	+	0.820567i	$0.693658\pi$
$132$		0			0
$133$	−2.82066	−	2.82066i	−0.0212080	−	0.0212080i
$134$	30.9454	−	152.437i	0.230936	−	1.13759i
$135$		0			0
$136$	−27.6452	+	5.16059i	−0.203274	+	0.0379455i
$137$		−	115.159i		−	0.840577i	−0.907390	−	0.420289i	$-0.861929\pi$
$137$		−	115.159i		−	0.840577i	0.907390	−	0.420289i	$-0.138071\pi$
$138$		0			0
$139$	−122.841	+	122.841i	−0.883748	+	0.883748i	−0.993913	−	0.110165i	$-0.964862\pi$
$139$	−122.841	+	122.841i	−0.883748	+	0.883748i	0.110165	+	0.993913i	$0.464862\pi$
$140$	5.82936	−	2.36104i	0.0416383	−	0.0168646i
$141$		0			0
$142$	−93.0652	−	140.475i	−0.655389	−	0.989261i
$143$			275.296i			1.92514i
$144$		0			0
$145$	220.070			1.51772
$146$	−130.106	+	86.1957i	−0.891137	+	0.590382i
$147$		0			0
$148$	15.6934	−	6.35622i	0.106036	−	0.0429474i
$149$	99.9710	+	99.9710i	0.670946	+	0.670946i	0.957934	−	0.286988i	$-0.0926540\pi$
$149$	99.9710	+	99.9710i	0.670946	+	0.670946i	−0.286988	+	0.957934i	$0.592654\pi$
$150$		0			0
$151$	−222.762			−1.47525			−0.737623	−	0.675212i	$-0.764052\pi$
$151$	−222.762			−1.47525			−0.737623	+	0.675212i	$0.764052\pi$
$152$	−100.383	−	68.8008i	−0.660413	−	0.452637i
$153$		0			0
$154$	−6.25485	−	1.26977i	−0.0406159	−	0.00824524i
$155$	195.914	−	195.914i	1.26396	−	1.26396i
$156$		0			0
$157$	45.9080	−	45.9080i	0.292408	−	0.292408i	−0.545623	−	0.838031i	$-0.683707\pi$
$157$	45.9080	−	45.9080i	0.292408	−	0.292408i	0.838031	+	0.545623i	$0.183707\pi$
$158$	−98.8519	+	65.4898i	−0.625645	+	0.414492i
$159$		0			0
$160$	161.605	−	103.442i	1.01003	−	0.646515i
$161$	−4.32588			−0.0268689
$162$		0			0
$163$	37.3289	+	37.3289i	0.229012	+	0.229012i	0.812280	−	0.583268i	$-0.198226\pi$
$163$	37.3289	+	37.3289i	0.229012	+	0.229012i	−0.583268	+	0.812280i	$0.698226\pi$
$164$	80.6752	+	34.1628i	0.491922	+	0.208310i
$165$		0			0
$166$	62.8325	−	309.512i	0.378509	−	1.86453i
$167$	−71.6232			−0.428882			−0.214441	−	0.976737i	$-0.568793\pi$
$167$	−71.6232			−0.428882			−0.214441	+	0.976737i	$0.568793\pi$
$168$		0			0
$169$		−	342.723i		−	2.02795i
$170$	−8.38700	+	41.3142i	−0.0493353	+	0.243025i
$171$		0			0
$172$	103.423	+	255.348i	0.601295	+	1.48458i
$173$	100.398	−	100.398i	0.580334	−	0.580334i	−0.354661	−	0.934995i	$-0.615404\pi$
$173$	100.398	−	100.398i	0.580334	−	0.580334i	0.934995	+	0.354661i	$0.115404\pi$
$174$		0			0
$175$		−	2.87232i		−	0.0164133i
$176$	−194.692	−	3.06373i	−1.10620	−	0.0174076i
$177$		0			0
$178$	−57.5928	+	38.1554i	−0.323555	+	0.214356i
$179$	−64.4199	−	64.4199i	−0.359888	−	0.359888i	0.503884	−	0.863771i	$-0.331904\pi$
$179$	−64.4199	−	64.4199i	−0.359888	−	0.359888i	−0.863771	+	0.503884i	$0.831904\pi$
$180$		0			0
$181$	−79.0033	−	79.0033i	−0.436482	−	0.436482i	0.454344	−	0.890826i	$-0.349874\pi$
$181$	−79.0033	−	79.0033i	−0.436482	−	0.436482i	−0.890826	+	0.454344i	$0.849874\pi$
$182$	11.6266	+	2.36026i	0.0638824	+	0.0129685i
$183$		0			0
$184$	−129.733	+	24.2177i	−0.705073	+	0.131618i
$185$		−	25.3812i		−	0.137196i
$186$		0			0
$187$	30.2506	−	30.2506i	0.161768	−	0.161768i
$188$	−260.693	−	110.394i	−1.38667	−	0.587200i
$189$		0			0
$190$	−152.081	+	100.754i	−0.800427	+	0.530286i
$191$		−	304.422i		−	1.59383i	−0.604089	−	0.796917i	$-0.706463\pi$
$191$		−	304.422i		−	1.59383i	0.604089	−	0.796917i	$-0.293537\pi$
$192$		0			0
$193$	253.689			1.31445			0.657225	−	0.753695i	$-0.271730\pi$
$193$	253.689			1.31445			0.657225	+	0.753695i	$0.271730\pi$
$194$	−72.9919	−	110.176i	−0.376247	−	0.567917i
$195$		0			0
$196$	76.3210	−	180.231i	0.389393	−	0.919548i
$197$	89.4218	+	89.4218i	0.453918	+	0.453918i	0.896653	−	0.442735i	$-0.145992\pi$
$197$	89.4218	+	89.4218i	0.453918	+	0.453918i	−0.442735	+	0.896653i	$0.645992\pi$
$198$		0			0
$199$	117.278			0.589339			0.294670	−	0.955599i	$-0.404790\pi$
$199$	117.278			0.589339			0.294670	+	0.955599i	$0.404790\pi$
$200$	−16.0802	−	86.1411i	−0.0804008	−	0.430705i
$201$		0			0
$202$	−14.3633	+	70.7536i	−0.0711056	+	0.350265i
$203$	−6.80533	+	6.80533i	−0.0335238	+	0.0335238i
$204$		0			0
$205$	92.8650	−	92.8650i	0.453000	−	0.453000i
$206$	−15.6931	−	23.6876i	−0.0761802	−	0.114988i
$207$		0			0
$208$	361.896	+	5.69491i	1.73988	+	0.0273794i
$209$	185.128			0.885781
$210$		0			0
$211$	−80.8941	−	80.8941i	−0.383384	−	0.383384i	0.488936	−	0.872320i	$-0.337385\pi$
$211$	−80.8941	−	80.8941i	−0.383384	−	0.383384i	−0.872320	+	0.488936i	$0.837385\pi$
$212$	−276.938	+	112.167i	−1.30631	+	0.529090i
$213$		0			0
$214$	−60.5626	−	12.2945i	−0.283003	−	0.0574510i
$215$	412.981			1.92084
$216$		0			0
$217$			12.1167i			0.0558373i
$218$	49.6109	+	10.0713i	0.227573	+	0.0461984i
$219$		0			0
$220$	−113.818	+	268.780i	−0.517355	+	1.22173i
$221$	−56.2303	+	56.2303i	−0.254436	+	0.254436i
$222$		0			0
$223$			263.109i			1.17986i	0.807453	+	0.589931i	$0.200845\pi$
$223$			263.109i			1.17986i	−0.807453	+	0.589931i	$0.799155\pi$
$224$	−1.79859	+	8.19619i	−0.00802943	+	0.0365901i
$225$		0			0
$226$	−192.801	−	291.019i	−0.853103	−	1.28770i
$227$	112.085	+	112.085i	0.493765	+	0.493765i	0.909490	−	0.415725i	$-0.136472\pi$
$227$	112.085	+	112.085i	0.493765	+	0.493765i	−0.415725	+	0.909490i	$0.636472\pi$
$228$		0			0
$229$	100.869	+	100.869i	0.440477	+	0.440477i	0.892172	−	0.451695i	$-0.149180\pi$
$229$	100.869	+	100.869i	0.440477	+	0.440477i	−0.451695	+	0.892172i	$0.649180\pi$
$230$	−39.3585	+	193.880i	−0.171124	+	0.842955i
$231$		0			0
$232$	−165.994	+	242.190i	−0.715490	+	1.04392i
$233$			325.669i			1.39772i	0.715259	+	0.698860i	$0.246309\pi$
$233$			325.669i			1.39772i	−0.715259	+	0.698860i	$0.753691\pi$
$234$		0			0
$235$	−300.084	+	300.084i	−1.27695	+	1.27695i
$236$	131.180	+	323.881i	0.555849	+	1.37238i
$237$		0			0
$238$	−1.01823	−	1.53694i	−0.00427826	−	0.00645771i
$239$		−	25.2269i		−	0.105552i	−0.998606	−	0.0527760i	$-0.983193\pi$
$239$		−	25.2269i		−	0.105552i	0.998606	−	0.0527760i	$-0.0168069\pi$
$240$		0			0
$241$	−305.987			−1.26966			−0.634828	−	0.772653i	$-0.718929\pi$
$241$	−305.987			−1.26966			−0.634828	+	0.772653i	$0.718929\pi$
$242$	45.1885	−	29.9376i	0.186730	−	0.123709i
$243$		0			0
$244$	−48.6313	−	120.070i	−0.199309	−	0.492088i
$245$	−207.464	−	207.464i	−0.846792	−	0.846792i
$246$		0			0
$247$	−344.119			−1.39319
$248$	67.8331	+	363.381i	0.273521	+	1.46524i
$249$		0			0
$250$	165.081	+	33.5122i	0.660322	+	0.134049i
$251$	−99.5293	+	99.5293i	−0.396531	+	0.396531i	−0.877008	−	0.480476i	$-0.840464\pi$
$251$	−99.5293	+	99.5293i	−0.396531	+	0.396531i	0.480476	+	0.877008i	$0.340464\pi$
$252$		0			0
$253$	141.960	−	141.960i	0.561108	−	0.561108i
$254$	75.6015	−	50.0863i	0.297644	−	0.197190i
$255$		0			0
$256$	−8.05500	+	255.873i	−0.0314648	+	0.999505i
$257$	265.635			1.03360			0.516799	−	0.856107i	$-0.327124\pi$
$257$	265.635			1.03360			0.516799	+	0.856107i	$0.327124\pi$
$258$		0			0
$259$	0.784876	+	0.784876i	0.00303041	+	0.00303041i
$260$	211.566	−	499.612i	0.813717	−	1.92159i
$261$		0			0
$262$	−18.3562	+	90.4225i	−0.0700619	+	0.345124i
$263$	−206.692			−0.785901			−0.392950	−	0.919560i	$-0.628546\pi$
$263$	−206.692			−0.785901			−0.392950	+	0.919560i	$0.628546\pi$
$264$		0			0
$265$			447.898i			1.69018i
$266$	1.58721	−	7.81856i	0.00596694	−	0.0293931i
$267$		0			0
$268$	288.340	−	116.785i	1.07589	−	0.435765i
$269$	−8.03470	+	8.03470i	−0.0298688	+	0.0298688i	−0.721883	−	0.692015i	$-0.756723\pi$
$269$	−8.03470	+	8.03470i	−0.0298688	+	0.0298688i	0.692015	+	0.721883i	$0.256723\pi$
$270$		0			0
$271$			216.666i			0.799507i	0.916623	+	0.399754i	$0.130904\pi$
$271$			216.666i			0.799507i	−0.916623	+	0.399754i	$0.869096\pi$
$272$	−39.1409	−	40.3924i	−0.143900	−	0.148502i
$273$		0			0
$274$	192.004	−	127.204i	0.700746	−	0.464247i
$275$	94.2595	+	94.2595i	0.342762	+	0.342762i
$276$		0			0
$277$	65.0909	+	65.0909i	0.234985	+	0.234985i	0.814770	−	0.579785i	$-0.196863\pi$
$277$	65.0909	+	65.0909i	0.234985	+	0.234985i	−0.579785	+	0.814770i	$0.696863\pi$
$278$	−340.502	−	69.1235i	−1.22483	−	0.248646i
$279$		0			0
$280$	10.3756	+	7.11130i	0.0370558	+	0.0253975i
$281$		−	403.952i		−	1.43755i	−0.695242	−	0.718776i	$-0.744703\pi$
$281$		−	403.952i		−	1.43755i	0.695242	−	0.718776i	$-0.255297\pi$
$282$		0			0
$283$	245.705	−	245.705i	0.868214	−	0.868214i	−0.124061	−	0.992275i	$-0.539592\pi$
$283$	245.705	−	245.705i	0.868214	−	0.868214i	0.992275	+	0.124061i	$0.0395917\pi$
$284$	131.415	−	310.335i	0.462728	−	1.09273i
$285$		0			0
$286$	−458.999	+	304.089i	−1.60489	+	1.06325i
$287$			5.74342i			0.0200119i
$288$		0			0
$289$	−276.642			−0.957240
$290$	243.087	+	366.922i	0.838231	+	1.26525i
$291$		0			0
$292$	−287.428	−	121.715i	−0.984342	−	0.416831i
$293$	−67.6849	−	67.6849i	−0.231007	−	0.231007i	0.582106	−	0.813113i	$-0.302229\pi$
$293$	−67.6849	−	67.6849i	−0.231007	−	0.231007i	−0.813113	+	0.582106i	$0.802229\pi$
$294$		0			0
$295$	523.821			1.77566
$296$	27.9324	+	19.1445i	0.0943664	+	0.0646773i
$297$		0			0
$298$	−56.2544	+	277.108i	−0.188773	+	0.929894i
$299$	−263.878	+	263.878i	−0.882534	+	0.882534i
$300$		0			0
$301$	−12.7708	+	12.7708i	−0.0424279	+	0.0424279i
$302$	−246.061	−	371.411i	−0.814772	−	1.22984i
$303$		0			0
$304$	3.82966	−	243.365i	0.0125976	−	0.800541i
$305$	−194.191			−0.636692
$306$		0			0
$307$	−4.98162	−	4.98162i	−0.0162268	−	0.0162268i	0.698947	−	0.715174i	$-0.253652\pi$
$307$	−4.98162	−	4.98162i	−0.0162268	−	0.0162268i	−0.715174	+	0.698947i	$0.753652\pi$
$308$	−4.79197	−	11.8313i	−0.0155584	−	0.0384132i
$309$		0			0
$310$	543.052	+	110.242i	1.75178	+	0.355620i
$311$	−380.390			−1.22312			−0.611560	−	0.791198i	$-0.709458\pi$
$311$	−380.390			−1.22312			−0.611560	+	0.791198i	$0.709458\pi$
$312$		0			0
$313$		−	145.761i		−	0.465691i	−0.972514	−	0.232845i	$-0.925196\pi$
$313$		−	145.761i		−	0.465691i	0.972514	−	0.232845i	$-0.0748036\pi$
$314$	127.252	+	25.8328i	0.405261	+	0.0822699i
$315$		0			0
$316$	−218.382	−	92.4762i	−0.691082	−	0.292646i
$317$	−283.175	+	283.175i	−0.893295	+	0.893295i	−0.994832	−	0.101537i	$-0.967624\pi$
$317$	−283.175	+	283.175i	−0.893295	+	0.893295i	0.101537	+	0.994832i	$0.467624\pi$
$318$		0			0
$319$		−	446.654i		−	1.40017i
$320$	350.977	+	155.182i	1.09680	+	0.484944i
$321$		0			0
$322$	−4.77833	−	7.21254i	−0.0148395	−	0.0223992i
$323$	37.8132	+	37.8132i	0.117069	+	0.117069i
$324$		0			0
$325$	−175.211	−	175.211i	−0.539110	−	0.539110i
$326$	−21.0052	+	103.472i	−0.0644333	+	0.317397i
$327$		0			0
$328$	32.1535	+	172.245i	0.0980288	+	0.525139i
$329$		−	18.5593i		−	0.0564111i
$330$		0			0
$331$	105.963	−	105.963i	0.320131	−	0.320131i	−0.528687	−	0.848817i	$-0.677315\pi$
$331$	105.963	−	105.963i	0.320131	−	0.320131i	0.848817	+	0.528687i	$0.177315\pi$
$332$	585.453	−	237.124i	1.76341	−	0.714227i
$333$		0			0
$334$	−79.1143	−	119.417i	−0.236869	−	0.357537i
$335$		−	466.338i		−	1.39205i
$336$		0			0
$337$	249.581			0.740595			0.370298	−	0.928913i	$-0.379256\pi$
$337$	249.581			0.740595			0.370298	+	0.928913i	$0.379256\pi$
$338$	571.421	−	378.568i	1.69059	−	1.12002i
$339$		0			0
$340$	−78.1473	+	31.6517i	−0.229845	+	0.0930932i
$341$	−397.627	−	397.627i	−1.16606	−	1.16606i
$342$		0			0
$343$	25.6801			0.0748690
$344$	−311.502	+	454.492i	−0.905529	+	1.32120i
$345$		0			0
$346$	278.291	+	56.4945i	0.804310	+	0.163279i
$347$	−297.586	+	297.586i	−0.857597	+	0.857597i	−0.991054	−	0.133458i	$-0.957392\pi$
$347$	−297.586	+	297.586i	−0.857597	+	0.857597i	0.133458	+	0.991054i	$0.457392\pi$
$348$		0			0
$349$	−288.797	+	288.797i	−0.827498	+	0.827498i	−0.987170	−	0.159672i	$-0.948956\pi$
$349$	−288.797	+	288.797i	−0.827498	+	0.827498i	0.159672	+	0.987170i	$0.448956\pi$
$350$	4.78901	−	3.17274i	0.0136829	−	0.00906497i
$351$		0			0
$352$	−209.947	−	327.994i	−0.596439	−	0.931800i
$353$	255.362			0.723404			0.361702	−	0.932294i	$-0.382196\pi$
$353$	255.362			0.723404			0.361702	+	0.932294i	$0.382196\pi$
$354$		0			0
$355$	−357.226	−	357.226i	−1.00627	−	1.00627i
$356$	−127.233	−	53.8782i	−0.357396	−	0.151343i
$357$		0			0
$358$	36.2495	−	178.565i	0.101256	−	0.498784i
$359$	381.798			1.06350			0.531752	−	0.846900i	$-0.321534\pi$
$359$	381.798			1.06350			0.531752	+	0.846900i	$0.321534\pi$
$360$		0			0
$361$		−	129.590i		−	0.358975i
$362$	44.4557	−	218.988i	0.122806	−	0.604940i
$363$		0			0
$364$	8.90738	+	21.9921i	0.0244708	+	0.0604179i
$365$	−330.857	+	330.857i	−0.906459	+	0.906459i
$366$		0			0
$367$			18.6026i			0.0506884i	0.999679	+	0.0253442i	$0.00806817\pi$
$367$			18.6026i			0.0506884i	−0.999679	+	0.0253442i	$0.991932\pi$
$368$	−183.680	−	189.554i	−0.499131	−	0.515092i
$369$		0			0
$370$	42.3180	−	28.0358i	0.114373	−	0.0757726i
$371$	−13.8506	−	13.8506i	−0.0373330	−	0.0373330i
$372$		0			0
$373$	150.079	+	150.079i	0.402357	+	0.402357i	0.879063	−	0.476706i	$-0.158169\pi$
$373$	150.079	+	150.079i	0.402357	+	0.402357i	−0.476706	+	0.879063i	$0.658169\pi$
$374$	83.8514	+	17.0222i	0.224202	+	0.0455140i
$375$		0			0
$376$	−103.901	−	556.593i	−0.276331	−	1.48030i
$377$			830.245i			2.20224i
$378$		0			0
$379$	379.359	−	379.359i	1.00095	−	1.00095i	0.000948851	−	1.00000i	$-0.499698\pi$
$379$	379.359	−	379.359i	1.00095	−	1.00095i	1.00000		0.000948851i	$-0.000302029\pi$
$380$	−335.975	−	142.272i	−0.884144	−	0.374401i
$381$		0			0
$382$	507.562	−	336.262i	1.32870	−	0.880267i
$383$		−	427.421i		−	1.11598i	−0.829847	−	0.557991i	$-0.811572\pi$
$383$		−	427.421i		−	1.11598i	0.829847	−	0.557991i	$-0.188428\pi$
$384$		0			0
$385$	−19.1350			−0.0497012
$386$	280.222	+	422.975i	0.725964	+	1.09579i
$387$		0			0
$388$	103.070	−	243.398i	0.265644	−	0.627315i
$389$	−236.247	−	236.247i	−0.607318	−	0.607318i	0.334926	−	0.942244i	$-0.391289\pi$
$389$	−236.247	−	236.247i	−0.607318	−	0.607318i	−0.942244	+	0.334926i	$0.891289\pi$
$390$		0			0
$391$	57.9920			0.148317
$392$	384.803	−	71.8320i	0.981640	−	0.183245i
$393$		0			0
$394$	−50.3183	+	247.867i	−0.127711	+	0.629105i
$395$	−251.379	+	251.379i	−0.636402	+	0.636402i
$396$		0			0
$397$	−427.593	+	427.593i	−1.07706	+	1.07706i	−0.0802895	+	0.996772i	$0.525584\pi$
$397$	−427.593	+	427.593i	−1.07706	+	1.07706i	−0.996772	+	0.0802895i	$0.974416\pi$
$398$	129.545	+	195.538i	0.325489	+	0.491302i
$399$		0			0
$400$	125.861	−	121.961i	0.314652	−	0.304902i
$401$	638.396			1.59201			0.796005	−	0.605290i	$-0.206943\pi$
$401$	638.396			1.59201			0.796005	+	0.605290i	$0.206943\pi$
$402$		0			0
$403$	739.115	+	739.115i	1.83403	+	1.83403i
$404$	−133.833	+	54.2058i	−0.331270	+	0.134173i
$405$		0			0
$406$	−18.8636	−	3.82940i	−0.0464621	−	0.00943203i
$407$	−51.5137			−0.126569
$408$		0			0
$409$			273.582i			0.668905i	0.942413	+	0.334453i	$0.108551\pi$
$409$			273.582i			0.668905i	−0.942413	+	0.334453i	$0.891449\pi$
$410$	257.411	+	52.2558i	0.627833	+	0.127453i
$411$		0			0
$412$	22.1598	−	52.3302i	0.0537860	−	0.127015i
$413$	−16.1984	+	16.1984i	−0.0392212	+	0.0392212i
$414$		0			0
$415$		−	946.865i		−	2.28160i
$416$	390.252	+	609.679i	0.938105	+	1.46557i
$417$		0			0
$418$	204.491	+	308.664i	0.489213	+	0.738430i
$419$	150.314	+	150.314i	0.358745	+	0.358745i	0.863350	−	0.504606i	$-0.168362\pi$
$419$	150.314	+	150.314i	0.358745	+	0.358745i	−0.504606	+	0.863350i	$0.668362\pi$
$420$		0			0
$421$	−220.826	−	220.826i	−0.524527	−	0.524527i	0.394408	−	0.918935i	$-0.370950\pi$
$421$	−220.826	−	220.826i	−0.524527	−	0.524527i	−0.918935	+	0.394408i	$0.870950\pi$
$422$	45.5196	−	224.229i	0.107866	−	0.531349i
$423$		0			0
$424$	−492.919	−	337.839i	−1.16254	−	0.796790i
$425$			38.5058i			0.0906018i
$426$		0			0
$427$	6.00507	−	6.00507i	0.0140634	−	0.0140634i
$428$	−46.3983	−	114.556i	−0.108407	−	0.267655i
$429$		0			0
$430$	456.174	+	688.561i	1.06087	+	1.60131i
$431$		−	463.722i		−	1.07592i	−0.842970	−	0.537960i	$-0.819195\pi$
$431$		−	463.722i		−	1.07592i	0.842970	−	0.537960i	$-0.180805\pi$
$432$		0			0
$433$	−310.114			−0.716199			−0.358099	−	0.933683i	$-0.616575\pi$
$433$	−310.114			−0.716199			−0.358099	+	0.933683i	$0.616575\pi$
$434$	−20.2021	+	13.3840i	−0.0465487	+	0.0308387i
$435$		0			0
$436$	38.0079	+	93.8407i	0.0871741	+	0.215231i
$437$	177.450	+	177.450i	0.406064	+	0.406064i
$438$		0			0
$439$	89.9103			0.204807			0.102404	−	0.994743i	$-0.467347\pi$
$439$	89.9103			0.204807			0.102404	+	0.994743i	$0.467347\pi$
$440$	−573.859	+	107.124i	−1.30422	+	0.243463i
$441$		0			0
$442$	−155.864	−	31.6412i	−0.352633	−	0.0715864i
$443$	−78.9267	+	78.9267i	−0.178164	+	0.178164i	−0.790555	−	0.612391i	$-0.790208\pi$
$443$	−78.9267	+	78.9267i	−0.178164	+	0.178164i	0.612391	+	0.790555i	$0.290208\pi$
$444$		0			0
$445$	−146.458	+	146.458i	−0.329118	+	0.329118i
$446$	−438.682	+	290.628i	−0.983591	+	0.651632i
$447$		0			0
$448$	−15.6522	+	6.05465i	−0.0349379	+	0.0135148i
$449$	187.048			0.416587			0.208294	−	0.978066i	$-0.433209\pi$
$449$	187.048			0.416587			0.208294	+	0.978066i	$0.433209\pi$
$450$		0			0
$451$	−188.479	−	188.479i	−0.417913	−	0.417913i
$452$	272.249	−	642.914i	0.602321	−	1.42238i
$453$		0			0
$454$	−63.0709	+	310.686i	−0.138923	+	0.684331i
$455$	35.5683			0.0781722
$456$		0			0
$457$			153.318i			0.335489i	0.985831	+	0.167744i	$0.0536483\pi$
$457$			153.318i			0.335489i	−0.985831	+	0.167744i	$0.946352\pi$
$458$	−56.7599	+	279.598i	−0.123930	+	0.610477i
$459$		0			0
$460$	−366.730	+	148.535i	−0.797239	+	0.322903i
$461$	99.6025	−	99.6025i	0.216057	−	0.216057i	−0.590777	−	0.806835i	$-0.701179\pi$
$461$	99.6025	−	99.6025i	0.216057	−	0.216057i	0.806835	+	0.590777i	$0.201179\pi$
$462$		0			0
$463$			255.682i			0.552229i	0.961125	+	0.276114i	$0.0890469\pi$
$463$			255.682i			0.552229i	−0.961125	+	0.276114i	$0.910953\pi$
$464$	−587.158	−	9.23971i	−1.26543	−	0.0199132i
$465$		0			0
$466$	−542.986	+	359.730i	−1.16521	+	0.771954i
$467$	285.533	+	285.533i	0.611420	+	0.611420i	0.943316	−	0.331896i	$-0.107688\pi$
$467$	285.533	+	285.533i	0.611420	+	0.611420i	−0.331896	+	0.943316i	$0.607688\pi$
$468$		0			0
$469$	14.4208	+	14.4208i	0.0307480	+	0.0307480i
$470$	−831.798	−	168.859i	−1.76978	−	0.359275i
$471$		0			0
$472$	−395.106	+	576.473i	−0.837089	+	1.22134i
$473$		−	838.185i		−	1.77206i
$474$		0			0
$475$	−117.824	+	117.824i	−0.248051	+	0.248051i
$476$	1.43781	−	3.39537i	0.00302060	−	0.00713313i
$477$		0			0
$478$	42.0608	−	27.8654i	0.0879933	−	0.0582959i
$479$			418.575i			0.873852i	0.899498	+	0.436926i	$0.143933\pi$
$479$			418.575i			0.873852i	−0.899498	+	0.436926i	$0.856067\pi$
$480$		0			0
$481$	95.7543			0.199073
$482$	−337.991	−	510.172i	−0.701225	−	1.05845i
$483$		0			0
$484$	99.8297	+	42.2740i	0.206260	+	0.0873430i
$485$	−280.175	−	280.175i	−0.577681	−	0.577681i
$486$		0			0
$487$	−162.560			−0.333800			−0.166900	−	0.985974i	$-0.553376\pi$
$487$	−162.560			−0.333800			−0.166900	+	0.985974i	$0.553376\pi$
$488$	146.474	−	213.711i	0.300152	−	0.437931i
$489$		0			0
$490$	116.741	−	575.067i	0.238248	−	1.17361i
$491$	559.393	−	559.393i	1.13929	−	1.13929i	0.150715	−	0.988577i	$-0.451842\pi$
$491$	559.393	−	559.393i	1.13929	−	1.13929i	0.988577	−	0.150715i	$-0.0481577\pi$
$492$		0			0
$493$	91.2309	−	91.2309i	0.185052	−	0.185052i
$494$	−380.110	−	573.748i	−0.769454	−	1.16143i
$495$		0			0
$496$	−530.936	+	514.485i	−1.07043	+	1.03727i
$497$	22.0933			0.0444534
$498$		0			0
$499$	247.957	+	247.957i	0.496908	+	0.496908i	0.910474	−	0.413566i	$-0.135717\pi$
$499$	247.957	+	247.957i	0.496908	+	0.496908i	−0.413566	+	0.910474i	$0.635717\pi$
$500$	126.472	+	312.256i	0.252943	+	0.624511i
$501$		0			0
$502$	−275.884	−	56.0059i	−0.549570	−	0.111565i
$503$	260.971			0.518829			0.259415	−	0.965766i	$-0.416470\pi$
$503$	260.971			0.518829			0.259415	+	0.965766i	$0.416470\pi$
$504$		0			0
$505$			216.451i			0.428616i
$506$	393.498	+	79.8820i	0.777664	+	0.157870i
$507$		0			0
$508$	167.017	+	70.7254i	0.328774	+	0.139223i
$509$	149.941	−	149.941i	0.294580	−	0.294580i	−0.544306	−	0.838886i	$-0.683207\pi$
$509$	149.941	−	149.941i	0.294580	−	0.294580i	0.838886	+	0.544306i	$0.183207\pi$
$510$		0			0
$511$		−	20.4625i		−	0.0400441i
$512$	−435.514	+	269.205i	−0.850614	+	0.525791i
$513$		0			0
$514$	293.417	+	442.892i	0.570851	+	0.861657i
$515$	−60.2372	−	60.2372i	−0.116965	−	0.116965i
$516$		0			0
$517$	609.049	+	609.049i	1.17805	+	1.17805i
$518$	−0.441655	+	2.17559i	−0.000852616	+	0.00419998i
$519$		0			0
$520$	1066.70	−	199.123i	2.05134	−	0.382928i
$521$		−	391.686i		−	0.751797i	−0.926661	−	0.375899i	$-0.877334\pi$
$521$		−	391.686i		−	0.751797i	0.926661	−	0.375899i	$-0.122666\pi$
$522$		0			0
$523$	−128.962	+	128.962i	−0.246582	+	0.246582i	−0.819566	−	0.572985i	$-0.805786\pi$
$523$	−128.962	+	128.962i	−0.246582	+	0.246582i	0.572985	+	0.819566i	$0.305786\pi$
$524$	−171.037	+	69.2745i	−0.326407	+	0.132203i
$525$		0			0
$526$	−228.310	−	344.617i	−0.434049	−	0.655165i
$527$		−	162.434i		−	0.308224i
$528$		0			0
$529$	−256.855			−0.485548
$530$	−746.779	+	494.743i	−1.40902	+	0.933478i
$531$		0			0
$532$	14.7891	−	5.98996i	0.0277990	−	0.0112593i
$533$	350.347	+	350.347i	0.657311	+	0.657311i
$534$		0			0
$535$	−185.274			−0.346307
$536$	513.212	+	351.748i	0.957486	+	0.656247i
$537$		0			0
$538$	−22.2713	−	4.52118i	−0.0413965	−	0.00840369i
$539$	−421.069	+	421.069i	−0.781204	+	0.781204i
$540$		0			0
$541$	71.0166	−	71.0166i	0.131269	−	0.131269i	−0.638420	−	0.769689i	$-0.720411\pi$
$541$	71.0166	−	71.0166i	0.131269	−	0.131269i	0.769689	+	0.638420i	$0.220411\pi$
$542$	−361.247	+	239.328i	−0.666508	+	0.441564i
$543$		0			0
$544$	24.1116	−	109.877i	0.0443227	−	0.201979i
$545$	151.771			0.278478
$546$		0			0
$547$	−672.846	−	672.846i	−1.23007	−	1.23007i	−0.963938	−	0.266128i	$-0.914255\pi$
$547$	−672.846	−	672.846i	−1.23007	−	1.23007i	−0.266128	−	0.963938i	$-0.585745\pi$
$548$	424.172	+	179.621i	0.774037	+	0.327775i
$549$		0			0
$550$	−53.0405	+	261.277i	−0.0964372	+	0.475048i
$551$	558.316			1.01328
$552$		0			0
$553$		−	15.5470i		−	0.0281140i
$554$	−36.6271	+	180.425i	−0.0661139	+	0.325676i
$555$		0			0
$556$	−260.865	−	644.070i	−0.469182	−	1.15840i
$557$	294.546	−	294.546i	0.528809	−	0.528809i	−0.391408	−	0.920217i	$-0.628012\pi$
$557$	294.546	−	294.546i	0.528809	−	0.528809i	0.920217	+	0.391408i	$0.128012\pi$
$558$		0			0
$559$			1558.03i			2.78717i
$560$	−0.395836	+	25.1543i	−0.000706850	+	0.0449184i
$561$		0			0
$562$	673.508	−	446.201i	1.19841	−	0.793953i
$563$	613.943	+	613.943i	1.09048	+	1.09048i	0.995477	+	0.0950080i	$0.0302877\pi$
$563$	613.943	+	613.943i	1.09048	+	1.09048i	0.0950080	+	0.995477i	$0.469712\pi$
$564$		0			0
$565$	−740.057	−	740.057i	−1.30984	−	1.30984i
$566$	681.065	+	138.260i	1.20330	+	0.244275i
$567$		0			0
$568$	662.580	−	123.685i	1.16651	−	0.217756i
$569$			1044.74i			1.83610i	0.396460	+	0.918052i	$0.370239\pi$
$569$			1044.74i			1.83610i	−0.396460	+	0.918052i	$0.629761\pi$
$570$		0			0
$571$	131.781	−	131.781i	0.230789	−	0.230789i	−0.582233	−	0.813022i	$-0.697821\pi$
$571$	131.781	−	131.781i	0.230789	−	0.230789i	0.813022	+	0.582233i	$0.197821\pi$
$572$	−1014.01	−	429.395i	−1.77275	−	0.750691i
$573$		0			0
$574$	−9.57599	+	6.34413i	−0.0166829	+	0.0110525i
$575$			180.700i			0.314261i
$576$		0			0
$577$	−114.453			−0.198359			−0.0991794	−	0.995070i	$-0.531622\pi$
$577$	−114.453			−0.198359			−0.0991794	+	0.995070i	$0.531622\pi$
$578$	−305.576	−	461.245i	−0.528679	−	0.798002i
$579$		0			0
$580$	−343.256	+	810.596i	−0.591821	+	1.39758i
$581$	29.2804	+	29.2804i	0.0503965	+	0.0503965i
$582$		0			0
$583$	909.053			1.55927
$584$	−114.556	−	613.672i	−0.196157	−	1.05081i
$585$		0			0
$586$	38.0868	−	187.615i	0.0649945	−	0.320162i
$587$	308.249	−	308.249i	0.525125	−	0.525125i	−0.393990	−	0.919115i	$-0.628905\pi$
$587$	308.249	−	308.249i	0.525125	−	0.525125i	0.919115	+	0.393990i	$0.128905\pi$
$588$		0			0
$589$	497.034	−	497.034i	0.843860	−	0.843860i
$590$	578.607	+	873.365i	0.980690	+	1.48028i
$591$		0			0
$592$	−1.06564	+	67.7185i	−0.00180007	+	0.114389i
$593$	646.173			1.08967			0.544834	−	0.838544i	$-0.316593\pi$
$593$	646.173			1.08967			0.544834	+	0.838544i	$0.316593\pi$
$594$		0			0
$595$	−3.90840	−	3.90840i	−0.00656874	−	0.00656874i
$596$	−524.160	+	212.298i	−0.879463	+	0.356205i
$597$		0			0
$598$	−731.439	−	148.486i	−1.22314	−	0.248304i
$599$	−528.055			−0.881561			−0.440780	−	0.897615i	$-0.645298\pi$
$599$	−528.055			−0.881561			−0.440780	+	0.897615i	$0.645298\pi$
$600$		0			0
$601$		−	280.764i		−	0.467161i	−0.972338	−	0.233580i	$-0.924956\pi$
$601$		−	280.764i		−	0.467161i	0.972338	−	0.233580i	$-0.0750442\pi$
$602$	−35.3992	−	7.18622i	−0.0588027	−	0.0119372i
$603$		0			0
$604$	347.456	−	820.514i	0.575258	−	1.35847i
$605$	114.914	−	114.914i	0.189940	−	0.189940i
$606$		0			0
$607$		−	662.871i		−	1.09204i	−0.837771	−	0.546022i	$-0.816141\pi$
$607$		−	662.871i		−	1.09204i	0.837771	−	0.546022i	$-0.183859\pi$
$608$	409.991	−	262.433i	0.674328	−	0.431633i
$609$		0			0
$610$	−214.502	−	323.774i	−0.351642	−	0.530778i
$611$	−1132.11	−	1132.11i	−1.85288	−	1.85288i
$612$		0			0
$613$	128.389	+	128.389i	0.209443	+	0.209443i	0.804031	−	0.594588i	$-0.202685\pi$
$613$	128.389	+	128.389i	0.209443	+	0.209443i	−0.594588	+	0.804031i	$0.702685\pi$
$614$	2.80319	−	13.8085i	0.00456546	−	0.0224894i
$615$		0			0
$616$	14.4331	−	21.0584i	0.0234303	−	0.0341856i
$617$			20.8646i			0.0338162i	0.999857	+	0.0169081i	$0.00538228\pi$
$617$			20.8646i			0.0338162i	−0.999857	+	0.0169081i	$0.994618\pi$
$618$		0			0
$619$	−472.367	+	472.367i	−0.763113	+	0.763113i	−0.976884	−	0.213771i	$-0.931425\pi$
$619$	−472.367	+	472.367i	−0.763113	+	0.763113i	0.213771	+	0.976884i	$0.431425\pi$
$620$	416.044	+	1027.20i	0.671038	+	1.65678i
$621$		0			0
$622$	−420.175	−	634.224i	−0.675523	−	1.01965i
$623$		−	9.05795i		−	0.0145393i
$624$		0			0
$625$	778.859			1.24617
$626$	243.027	−	161.006i	0.388222	−	0.257199i
$627$		0			0
$628$	97.4903	+	240.701i	0.155239	+	0.383282i
$629$	−10.5219	−	10.5219i	−0.0167280	−	0.0167280i
$630$		0			0
$631$	−906.653			−1.43685			−0.718426	−	0.695604i	$-0.755137\pi$
$631$	−906.653			−1.43685			−0.718426	+	0.695604i	$0.755137\pi$
$632$	−87.0370	−	466.256i	−0.137717	−	0.737746i
$633$		0			0
$634$	−784.928	−	159.344i	−1.23806	−	0.251332i
$635$	192.253	−	192.253i	0.302761	−	0.302761i
$636$		0			0
$637$	782.688	−	782.688i	1.22871	−	1.22871i
$638$	744.704	−	493.369i	1.16725	−	0.773306i
$639$		0			0
$640$	128.951	+	756.595i	0.201485	+	1.18218i
$641$	−1125.11			−1.75524			−0.877622	−	0.479353i	$-0.840871\pi$
$641$	−1125.11			−1.75524			−0.877622	+	0.479353i	$0.840871\pi$
$642$		0			0
$643$	−607.794	−	607.794i	−0.945247	−	0.945247i	0.0533302	−	0.998577i	$-0.483016\pi$
$643$	−607.794	−	607.794i	−0.945247	−	0.945247i	−0.998577	+	0.0533302i	$0.983016\pi$
$644$	6.74734	−	15.9338i	0.0104772	−	0.0247419i
$645$		0			0
$646$	−21.2778	+	104.814i	−0.0329377	+	0.162251i
$647$	383.377			0.592545			0.296273	−	0.955103i	$-0.404256\pi$
$647$	383.377			0.592545			0.296273	+	0.955103i	$0.404256\pi$
$648$		0			0
$649$		−	1063.15i		−	1.63813i
$650$	98.5923	−	485.664i	0.151680	−	0.747176i
$651$		0			0
$652$	−195.720	+	79.2717i	−0.300184	+	0.121582i
$653$	−755.121	+	755.121i	−1.15639	+	1.15639i	−0.171141	+	0.985246i	$0.554746\pi$
$653$	−755.121	+	755.121i	−1.15639	+	1.15639i	−0.985246	+	0.171141i	$0.945254\pi$
$654$		0			0
$655$			276.622i			0.422324i
$656$	−251.668	+	243.870i	−0.383640	+	0.371753i
$657$		0			0
$658$	30.9438	−	20.5004i	0.0470271	−	0.0311556i
$659$	−31.8233	−	31.8233i	−0.0482902	−	0.0482902i	0.682549	−	0.730840i	$-0.260871\pi$
$659$	−31.8233	−	31.8233i	−0.0482902	−	0.0482902i	−0.730840	+	0.682549i	$0.760871\pi$
$660$		0			0
$661$	579.890	+	579.890i	0.877292	+	0.877292i	0.993254	−	0.115961i	$-0.0369949\pi$
$661$	579.890	+	579.890i	0.877292	+	0.877292i	−0.115961	+	0.993254i	$0.536995\pi$
$662$	293.718	+	59.6263i	0.443683	+	0.0900699i
$663$		0			0
$664$	1042.04	+	714.199i	1.56934	+	1.07560i
$665$		−	23.9187i		−	0.0359680i
$666$		0			0
$667$	428.129	−	428.129i	0.641872	−	0.641872i
$668$	111.715	−	263.814i	0.167238	−	0.394931i
$669$		0			0
$670$	777.524	−	515.112i	1.16048	−	0.768824i
$671$			394.130i			0.587377i
$672$		0			0
$673$	262.375			0.389859			0.194930	−	0.980817i	$-0.437552\pi$
$673$	262.375			0.389859			0.194930	+	0.980817i	$0.437552\pi$
$674$	275.684	+	416.125i	0.409027	+	0.617396i
$675$		0			0
$676$	1262.37	+	534.566i	1.86741	+	0.790777i
$677$	574.436	+	574.436i	0.848502	+	0.848502i	0.989946	−	0.141444i	$-0.0451746\pi$
$677$	574.436	+	574.436i	0.848502	+	0.848502i	−0.141444	+	0.989946i	$0.545175\pi$
$678$		0			0
$679$	17.3280			0.0255199
$680$	−139.094	−	95.3327i	−0.204549	−	0.140195i
$681$		0			0
$682$	223.748	−	1102.18i	0.328076	−	1.61610i
$683$	253.790	−	253.790i	0.371582	−	0.371582i	−0.496471	−	0.868053i	$-0.665371\pi$
$683$	253.790	−	253.790i	0.371582	−	0.371582i	0.868053	+	0.496471i	$0.165371\pi$
$684$		0			0
$685$	488.264	−	488.264i	0.712794	−	0.712794i
$686$	28.3659	+	42.8163i	0.0413498	+	0.0624144i
$687$		0			0
$688$	−1101.85	−	17.3391i	−1.60153	−	0.0252022i
$689$	−1689.76			−2.45248
$690$		0			0
$691$	734.512	+	734.512i	1.06297	+	1.06297i	0.997879	+	0.0650902i	$0.0207335\pi$
$691$	734.512	+	734.512i	1.06297	+	1.06297i	0.0650902	+	0.997879i	$0.479266\pi$
$692$	213.205	+	526.398i	0.308099	+	0.760690i
$693$		0			0
$694$	−824.875	−	167.454i	−1.18858	−	0.241288i
$695$	−1041.67			−1.49880
$696$		0			0
$697$		−	76.9952i		−	0.110467i
$698$	−800.513	−	162.508i	−1.14687	−	0.232820i
$699$		0			0
$700$	10.5798	+	4.48013i	0.0151140	+	0.00640019i
$701$	745.410	−	745.410i	1.06335	−	1.06335i	0.0655005	−	0.997853i	$-0.479136\pi$
$701$	745.410	−	745.410i	1.06335	−	1.06335i	0.997853	−	0.0655005i	$-0.0208644\pi$
$702$		0			0
$703$		−	64.3920i		−	0.0915961i
$704$	314.958	−	712.342i	0.447383	−	1.01185i
$705$		0			0
$706$	282.070	+	425.764i	0.399533	+	0.603065i
$707$	−6.69342	−	6.69342i	−0.00946735	−	0.00946735i
$708$		0			0
$709$	−809.881	−	809.881i	−1.14229	−	1.14229i	−0.988031	−	0.154255i	$-0.950702\pi$
$709$	−809.881	−	809.881i	−1.14229	−	1.14229i	−0.154255	−	0.988031i	$-0.549298\pi$
$710$	201.013	−	990.189i	0.283117	−	1.39463i
$711$		0			0
$712$	−50.7093	−	271.648i	−0.0712209	−	0.381529i
$713$		−	762.272i		−	1.06910i
$714$		0			0
$715$	−1167.23	+	1167.23i	−1.63249	+	1.63249i
$716$	337.761	−	136.802i	0.471734	−	0.191064i
$717$		0			0
$718$	421.730	+	636.570i	0.587368	+	0.886588i
$719$			662.400i			0.921280i	0.887587	+	0.460640i	$0.152380\pi$
$719$			662.400i			0.921280i	−0.887587	+	0.460640i	$0.847620\pi$
$720$		0			0
$721$	3.72549			0.00516711
$722$	216.065	−	143.144i	0.299259	−	0.198260i
$723$		0			0
$724$	414.224	−	167.771i	0.572132	−	0.231728i
$725$	284.271	+	284.271i	0.392098	+	0.392098i
$726$		0			0
$727$	−1253.93			−1.72481			−0.862403	−	0.506222i	$-0.831042\pi$
$727$	−1253.93			−1.72481			−0.862403	+	0.506222i	$0.831042\pi$
$728$	−26.8284	+	39.1435i	−0.0368522	+	0.0537686i
$729$		0			0
$730$	−917.100	−	186.176i	−1.25630	−	0.255035i
$731$	171.203	−	171.203i	0.234204	−	0.234204i
$732$		0			0
$733$	−509.300	+	509.300i	−0.694816	+	0.694816i	−0.963288	−	0.268472i	$-0.913481\pi$
$733$	−509.300	+	509.300i	−0.694816	+	0.694816i	0.268472	+	0.963288i	$0.413481\pi$
$734$	−31.0161	+	20.5483i	−0.0422563	+	0.0279949i
$735$		0			0
$736$	113.151	−	515.629i	0.153738	−	0.700583i
$737$	−946.479			−1.28423
$738$		0			0
$739$	818.847	+	818.847i	1.10805	+	1.10805i	0.993407	+	0.114640i	$0.0365716\pi$
$739$	818.847	+	818.847i	1.10805	+	1.10805i	0.114640	+	0.993407i	$0.463428\pi$
$740$	93.4882	+	39.5886i	0.126335	+	0.0534981i
$741$		0			0
$742$	7.79381	−	38.3922i	0.0105038	−	0.0517415i
$743$	−1110.03			−1.49398			−0.746991	−	0.664834i	$-0.768502\pi$
$743$	−1110.03			−1.49398			−0.746991	+	0.664834i	$0.768502\pi$
$744$		0			0
$745$			847.736i			1.13790i
$746$	−84.4506	+	416.002i	−0.113205	+	0.557644i
$747$		0			0
$748$	64.2403	+	158.608i	0.0858827	+	0.212042i
$749$	5.72933	−	5.72933i	0.00764931	−	0.00764931i
$750$		0			0
$751$			34.0597i			0.0453525i	0.999743	+	0.0226762i	$0.00721869\pi$
$751$			34.0597i			0.0453525i	−0.999743	+	0.0226762i	$0.992781\pi$
$752$	813.239	−	788.040i	1.08143	−	1.04793i
$753$		0			0
$754$	−1384.27	+	917.081i	−1.83590	+	1.21629i
$755$	−944.491	−	944.491i	−1.25098	−	1.25098i
$756$		0			0
$757$	398.543	+	398.543i	0.526477	+	0.526477i	0.919520	−	0.393043i	$-0.128578\pi$
$757$	398.543	+	398.543i	0.526477	+	0.526477i	−0.393043	+	0.919520i	$0.628578\pi$
$758$	1051.54	+	213.468i	1.38726	+	0.281620i
$759$		0			0
$760$	−133.904	−	717.323i	−0.176190	−	0.943845i
$761$		−	903.338i		−	1.18704i	−0.804819	−	0.593520i	$-0.797738\pi$
$761$		−	903.338i		−	1.18704i	0.804819	−	0.593520i	$-0.202262\pi$
$762$		0			0
$763$	−4.69328	+	4.69328i	−0.00615108	+	0.00615108i
$764$	1121.30	+	474.826i	1.46767	+	0.621500i
$765$		0			0
$766$	712.638	−	472.125i	0.930337	−	0.616352i
$767$			1976.19i			2.57652i
$768$		0			0
$769$	−98.9621			−0.128689			−0.0643447	−	0.997928i	$-0.520496\pi$
$769$	−98.9621			−0.128689			−0.0643447	+	0.997928i	$0.520496\pi$
$770$	−21.1363	−	31.9037i	−0.0274498	−	0.0414334i
$771$		0			0
$772$	−395.694	+	934.427i	−0.512557	+	1.21040i
$773$	−111.945	−	111.945i	−0.144818	−	0.144818i	0.630980	−	0.775799i	$-0.282653\pi$
$773$	−111.945	−	111.945i	−0.144818	−	0.144818i	−0.775799	+	0.630980i	$0.782653\pi$
$774$		0			0
$775$	506.137			0.653080
$776$	519.667	−	97.0075i	0.669674	−	0.125010i
$777$		0			0
$778$	132.938	−	654.849i	0.170871	−	0.841709i
$779$	235.598	−	235.598i	0.302437	−	0.302437i
$780$		0			0
$781$	−725.025	+	725.025i	−0.928329	+	0.928329i
$782$	64.0574	+	96.6899i	0.0819148	+	0.123644i
$783$		0			0
$784$	544.815	+	562.236i	0.694917	+	0.717137i
$785$	389.291			0.495913
$786$		0			0
$787$	−163.931	−	163.931i	−0.208299	−	0.208299i	0.595245	−	0.803544i	$-0.297055\pi$
$787$	−163.931	−	163.931i	−0.208299	−	0.208299i	−0.803544	+	0.595245i	$0.797055\pi$
$788$	−468.850	+	189.896i	−0.594987	+	0.240985i
$789$		0			0
$790$	−696.794	−	141.453i	−0.882017	−	0.179054i
$791$	45.7703			0.0578638
$792$		0			0
$793$		−	732.614i		−	0.923852i
$794$	−1185.24	−	240.610i	−1.49275	−	0.303035i
$795$		0			0
$796$	−182.926	+	431.979i	−0.229807	+	0.542687i
$797$	−271.277	+	271.277i	−0.340373	+	0.340373i	−0.856507	−	0.516135i	$-0.827370\pi$
$797$	−271.277	+	271.277i	−0.340373	+	0.340373i	0.516135	+	0.856507i	$0.327370\pi$
$798$		0			0
$799$			248.802i			0.311392i
$800$	342.370	+	75.1304i	0.427962	+	0.0939130i
$801$		0			0
$802$	705.166	+	1064.40i	0.879260	+	1.32718i
$803$	671.508	+	671.508i	0.836249	+	0.836249i
$804$		0			0
$805$	−18.3414	−	18.3414i	−0.0227843	−	0.0227843i
$806$	−415.905	+	2048.74i	−0.516011	+	2.54187i
$807$		0			0
$808$	−238.208	−	163.264i	−0.294811	−	0.202059i
$809$			1505.90i			1.86144i	0.365736	+	0.930718i	$0.380817\pi$
$809$			1505.90i			1.86144i	−0.365736	+	0.930718i	$0.619183\pi$
$810$		0			0
$811$	−492.677	+	492.677i	−0.607493	+	0.607493i	−0.942290	−	0.334797i	$-0.891332\pi$
$811$	−492.677	+	492.677i	−0.607493	+	0.607493i	0.334797	+	0.942290i	$0.391332\pi$
$812$	−14.4518	−	35.6811i	−0.0177978	−	0.0439423i
$813$		0			0
$814$	−56.9015	−	85.8887i	−0.0699036	−	0.105514i
$815$			316.542i			0.388396i
$816$		0			0
$817$	1047.73			1.28241
$818$	−456.143	+	302.196i	−0.557632	+	0.369433i
$819$		0			0
$820$	197.208	+	486.903i	0.240498	+	0.593784i
$821$	139.500	+	139.500i	0.169914	+	0.169914i	0.786942	−	0.617027i	$-0.211663\pi$
$821$	139.500	+	139.500i	0.169914	+	0.169914i	−0.617027	+	0.786942i	$0.711663\pi$
$822$		0			0
$823$	−1262.09			−1.53353			−0.766763	−	0.641931i	$-0.778134\pi$
$823$	−1262.09			−1.53353			−0.766763	+	0.641931i	$0.778134\pi$
$824$	111.728	−	20.8564i	0.135592	−	0.0253112i
$825$		0			0
$826$	−44.9000	−	9.11493i	−0.0543584	−	0.0110350i
$827$	−179.936	+	179.936i	−0.217577	+	0.217577i	−0.807477	−	0.589900i	$-0.799167\pi$
$827$	−179.936	+	179.936i	−0.217577	+	0.217577i	0.589900	+	0.807477i	$0.299167\pi$
$828$		0			0
$829$	−144.901	+	144.901i	−0.174790	+	0.174790i	−0.789080	−	0.614290i	$-0.789443\pi$
$829$	−144.901	+	144.901i	−0.174790	+	0.174790i	0.614290	+	0.789080i	$0.289443\pi$
$830$	1578.71	−	1045.90i	1.90206	−	1.26012i
$831$		0			0
$832$	−585.447	+	1324.11i	−0.703663	+	1.59148i
$833$	−172.010			−0.206495
$834$		0			0
$835$	−303.676	−	303.676i	−0.363684	−	0.363684i
$836$	−288.756	+	681.894i	−0.345402	+	0.815663i
$837$		0			0
$838$	−84.5827	+	416.653i	−0.100934	+	0.497200i
$839$	1006.03			1.19908			0.599540	−	0.800345i	$-0.295350\pi$
$839$	1006.03			1.19908			0.599540	+	0.800345i	$0.295350\pi$
$840$		0			0
$841$		−	506.033i		−	0.601703i
$842$	124.260	−	612.105i	0.147578	−	0.726965i
$843$		0			0
$844$	424.137	−	171.787i	0.502532	−	0.203539i
$845$	1453.11	−	1453.11i	1.71966	−	1.71966i
$846$		0			0
$847$			7.10706i			0.00839087i
$848$	18.8051	−	1195.02i	0.0221759	−	1.40922i
$849$		0			0
$850$	−64.2006	+	42.5331i	−0.0755301	+	0.0500390i
$851$	−49.3772	−	49.3772i	−0.0580225	−	0.0580225i
$852$		0			0
$853$	77.4150	+	77.4150i	0.0907561	+	0.0907561i	0.751027	−	0.660271i	$-0.229559\pi$
$853$	77.4150	+	77.4150i	0.0907561	+	0.0907561i	−0.660271	+	0.751027i	$0.729559\pi$
$854$	16.6454	+	3.37909i	0.0194911	+	0.00395678i
$855$		0			0
$856$	139.748	−	203.898i	0.163257	−	0.238198i
$857$		−	175.567i		−	0.204863i	−0.994740	−	0.102431i	$-0.967338\pi$
$857$		−	175.567i		−	0.204863i	0.994740	−	0.102431i	$-0.0326622\pi$
$858$		0			0
$859$	1058.18	−	1058.18i	1.23188	−	1.23188i	0.268634	−	0.963242i	$-0.413428\pi$
$859$	1058.18	−	1058.18i	1.23188	−	1.23188i	0.963242	−	0.268634i	$-0.0865722\pi$
$860$	−644.151	+	1521.16i	−0.749013	+	1.76879i
$861$		0			0
$862$	773.162	−	512.222i	0.896939	−	0.594225i
$863$		−	569.219i		−	0.659581i	−0.944054	−	0.329791i	$-0.893022\pi$
$863$		−	569.219i		−	0.659581i	0.944054	−	0.329791i	$-0.106978\pi$
$864$		0			0
$865$	851.355			0.984225
$866$	−342.549	−	517.052i	−0.395553	−	0.597058i
$867$		0			0
$868$	−44.6302	−	18.8992i	−0.0514173	−	0.0217732i
$869$	510.198	+	510.198i	0.587110	+	0.587110i
$870$		0			0
$871$	1759.33			2.01989
$872$	−114.477	+	167.026i	−0.131281	+	0.191544i
$873$		0			0
$874$	−99.8524	+	491.872i	−0.114248	+	0.562782i
$875$	−15.6169	+	15.6169i	−0.0178479	+	0.0178479i
$876$		0			0
$877$	−166.695	+	166.695i	−0.190074	+	0.190074i	−0.795728	−	0.605654i	$-0.792912\pi$
$877$	−166.695	+	166.695i	−0.190074	+	0.190074i	0.605654	+	0.795728i	$0.292912\pi$
$878$	99.3141	+	149.907i	0.113114	+	0.170737i
$879$		0			0
$880$	−812.486	−	838.466i	−0.923279	−	0.952802i
$881$	−1495.53			−1.69754			−0.848771	−	0.528761i	$-0.822657\pi$
$881$	−1495.53			−1.69754			−0.848771	+	0.528761i	$0.822657\pi$
$882$		0			0
$883$	134.367	+	134.367i	0.152171	+	0.152171i	0.779087	−	0.626916i	$-0.215683\pi$
$883$	134.367	+	134.367i	0.152171	+	0.152171i	−0.626916	+	0.779087i	$0.715683\pi$
$884$	−119.411	−	294.822i	−0.135080	−	0.333509i
$885$		0			0
$886$	−218.776	−	44.4126i	−0.246926	−	0.0501271i
$887$	414.255			0.467030			0.233515	−	0.972353i	$-0.424977\pi$
$887$	414.255			0.467030			0.233515	+	0.972353i	$0.424977\pi$
$888$		0			0
$889$			11.8903i			0.0133749i
$890$	−405.964	−	82.4127i	−0.456139	−	0.0925985i
$891$		0			0
$892$	−969.127	−	410.388i	−1.08646	−	0.460076i
$893$	−761.311	+	761.311i	−0.852531	+	0.852531i
$894$		0			0
$895$		−	546.269i		−	0.610356i
$896$	−27.3842	−	19.4090i	−0.0305627	−	0.0216618i
$897$		0			0
$898$	206.611	+	311.864i	0.230079	+	0.347287i
$899$	−1199.18	−	1199.18i	−1.33390	−	1.33390i
$900$		0			0
$901$	185.678	+	185.678i	0.206080	+	0.206080i
$902$	106.058	−	522.442i	0.117581	−	0.579204i
$903$		0			0
$904$	1372.65	−	256.236i	1.51842	−	0.283447i
$905$		−	669.933i		−	0.740258i
$906$		0			0
$907$	−312.683	+	312.683i	−0.344744	+	0.344744i	−0.858148	−	0.513403i	$-0.828385\pi$
$907$	−312.683	+	312.683i	−0.344744	+	0.344744i	0.513403	+	0.858148i	$0.328385\pi$
$908$	−587.674	+	238.023i	−0.647218	+	0.262140i
$909$		0			0
$910$	39.2884	+	59.3030i	0.0431741	+	0.0651681i
$911$		−	391.366i		−	0.429601i	−0.976658	−	0.214800i	$-0.931090\pi$
$911$		−	391.366i		−	0.429601i	0.976658	−	0.214800i	$-0.0689101\pi$
$912$		0			0
$913$	−1921.76			−2.10488
$914$	−255.627	+	169.354i	−0.279680	+	0.185289i
$915$		0			0
$916$	−528.870	+	214.206i	−0.577369	+	0.233850i
$917$	−8.55413	−	8.55413i	−0.00932838	−	0.00932838i
$918$		0			0
$919$	294.161			0.320088			0.160044	−	0.987110i	$-0.448836\pi$
$919$	294.161			0.320088			0.160044	+	0.987110i	$0.448836\pi$
$920$	−652.739	−	447.377i	−0.709499	−	0.486280i
$921$		0			0
$922$	276.087	+	56.0470i	0.299443	+	0.0607885i
$923$	1347.69	−	1347.69i	1.46011	−	1.46011i
$924$		0			0
$925$	32.7857	−	32.7857i	0.0354440	−	0.0354440i
$926$	−426.298	+	282.424i	−0.460365	+	0.304993i
$927$		0			0
$928$	−633.164	−	989.174i	−0.682289	−	1.06592i
$929$	1015.40			1.09300			0.546501	−	0.837458i	$-0.315959\pi$
$929$	1015.40			1.09300			0.546501	+	0.837458i	$0.315959\pi$
$930$		0			0
$931$	−526.335	−	526.335i	−0.565344	−	0.565344i
$932$	−1199.55	−	507.965i	−1.28708	−	0.545027i
$933$		0			0
$934$	−160.672	+	791.466i	−0.172025	+	0.847394i
$935$	256.520			0.274353
$936$		0			0
$937$			1582.09i			1.68846i	0.535977	+	0.844232i	$0.319943\pi$
$937$			1582.09i			1.68846i	−0.535977	+	0.844232i	$0.680057\pi$
$938$	−8.11468	+	39.9728i	−0.00865105	+	0.0426149i
$939$		0			0
$940$	−637.257	−	1573.37i	−0.677933	−	1.67380i
$941$	113.842	−	113.842i	0.120980	−	0.120980i	−0.644025	−	0.765005i	$-0.722737\pi$
$941$	113.842	−	113.842i	0.120980	−	0.120980i	0.765005	+	0.644025i	$0.222737\pi$
$942$		0			0
$943$		−	361.323i		−	0.383163i
$944$	−1397.58	−	21.9928i	−1.48049	−	0.0232974i
$945$		0			0
$946$	1397.50	−	925.851i	1.47728	−	0.978701i
$947$	388.664	+	388.664i	0.410416	+	0.410416i	0.881884	−	0.471467i	$-0.156275\pi$
$947$	388.664	+	388.664i	0.410416	+	0.410416i	−0.471467	+	0.881884i	$0.656275\pi$
$948$		0			0
$949$	−1248.21	−	1248.21i	−1.31529	−	1.31529i
$950$	−326.595	−	66.3005i	−0.343785	−	0.0697900i
$951$		0			0
$952$	7.24928	−	1.35324i	0.00761479	−	0.00142147i
$953$			211.977i			0.222431i	0.993796	+	0.111215i	$0.0354744\pi$
$953$			211.977i			0.222431i	−0.993796	+	0.111215i	$0.964526\pi$
$954$		0			0
$955$	1290.72	−	1290.72i	1.35154	−	1.35154i
$956$	92.9199	+	39.3480i	0.0971966	+	0.0411590i
$957$		0			0
$958$	−697.889	+	462.354i	−0.728485	+	0.482624i
$959$			30.1976i			0.0314887i
$960$		0			0
$961$	−1174.11			−1.22175
$962$	105.769	+	159.651i	0.109947	+	0.165957i
$963$		0			0
$964$	477.267	−	1127.06i	0.495090	−	1.16915i
$965$	1075.62	+	1075.62i	1.11463	+	1.11463i
$966$		0			0
$967$	516.501			0.534127			0.267063	−	0.963679i	$-0.413947\pi$
$967$	516.501			0.534127			0.267063	+	0.963679i	$0.413947\pi$
$968$	39.7876	+	213.141i	0.0411029	+	0.220187i
$969$		0			0
$970$	157.657	−	776.614i	0.162532	−	0.800633i
$971$	795.556	−	795.556i	0.819316	−	0.819316i	−0.166693	−	0.986009i	$-0.553309\pi$
$971$	795.556	−	795.556i	0.819316	−	0.819316i	0.986009	+	0.166693i	$0.0533089\pi$
$972$		0			0
$973$	32.2120	−	32.2120i	0.0331059	−	0.0331059i
$974$	−179.563	−	271.037i	−0.184356	−	0.278272i
$975$		0			0
$976$	518.113	+	8.15318i	0.530853	+	0.00835367i
$977$	512.430			0.524493			0.262246	−	0.965001i	$-0.415537\pi$
$977$	512.430			0.524493			0.262246	+	0.965001i	$0.415537\pi$
$978$		0			0
$979$	297.250	+	297.250i	0.303626	+	0.303626i
$980$	1087.76	−	440.570i	1.10996	−	0.449562i
$981$		0			0
$982$	1550.57	+	314.774i	1.57900	+	0.320544i
$983$	−722.200			−0.734690			−0.367345	−	0.930085i	$-0.619733\pi$
$983$	−722.200			−0.734690			−0.367345	+	0.930085i	$0.619733\pi$
$984$		0			0
$985$			758.281i			0.769828i
$986$	252.882	+	51.3363i	0.256472	+	0.0520652i
$987$		0			0
$988$	536.743	−	1267.51i	0.543262	−	1.28291i
$989$	803.421	−	803.421i	0.812357	−	0.812357i
$990$		0			0
$991$		−	794.715i		−	0.801932i	−0.916093	−	0.400966i	$-0.868675\pi$
$991$		−	794.715i		−	0.801932i	0.916093	−	0.400966i	$-0.131325\pi$
$992$	−1444.26	−	316.933i	−1.45591	−	0.319489i
$993$		0			0
$994$	24.4041	+	36.8361i	0.0245514	+	0.0370585i
$995$	497.250	+	497.250i	0.499749	+	0.499749i
$996$		0			0
$997$	1080.18	+	1080.18i	1.08343	+	1.08343i	0.996187	+	0.0872401i	$0.0278047\pi$
$997$	1080.18	+	1080.18i	1.08343	+	1.08343i	0.0872401	+	0.996187i	$0.472195\pi$
$998$	−139.527	+	687.310i	−0.139807	+	0.688687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.m.b.91.6	yes	16
3.2	odd	2	inner	144.3.m.b.91.3	yes	16
4.3	odd	2		576.3.m.b.271.7		16
8.3	odd	2		1152.3.m.d.415.2		16
8.5	even	2		1152.3.m.e.415.2		16
12.11	even	2		576.3.m.b.271.2		16
16.3	odd	4	inner	144.3.m.b.19.6	yes	16
16.5	even	4		1152.3.m.d.991.2		16
16.11	odd	4		1152.3.m.e.991.2		16
16.13	even	4		576.3.m.b.559.7		16
24.5	odd	2		1152.3.m.e.415.7		16
24.11	even	2		1152.3.m.d.415.7		16
48.5	odd	4		1152.3.m.d.991.7		16
48.11	even	4		1152.3.m.e.991.7		16
48.29	odd	4		576.3.m.b.559.2		16
48.35	even	4	inner	144.3.m.b.19.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.m.b.19.3	✓	16	48.35	even	4	inner
144.3.m.b.19.6	yes	16	16.3	odd	4	inner
144.3.m.b.91.3	yes	16	3.2	odd	2	inner
144.3.m.b.91.6	yes	16	1.1	even	1	trivial
576.3.m.b.271.2		16	12.11	even	2
576.3.m.b.271.7		16	4.3	odd	2
576.3.m.b.559.2		16	48.29	odd	4
576.3.m.b.559.7		16	16.13	even	4
1152.3.m.d.415.2		16	8.3	odd	2
1152.3.m.d.415.7		16	24.11	even	2
1152.3.m.d.991.2		16	16.5	even	4
1152.3.m.d.991.7		16	48.5	odd	4
1152.3.m.e.415.2		16	8.5	even	2
1152.3.m.e.415.7		16	24.5	odd	2
1152.3.m.e.991.2		16	16.11	odd	4
1152.3.m.e.991.7		16	48.11	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.10459 + 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(4.23991 + 4.23991i) q^{5} -0.262225 q^{7} +(-7.86415 + 1.46802i) q^{8} +O(q^{10})\)	\(q+(1.10459 + 1.66730i) q^{2} +(-1.55976 + 3.68336i) q^{4} +(4.23991 + 4.23991i) q^{5} -0.262225 q^{7} +(-7.86415 + 1.46802i) q^{8} +(-2.38583 + 11.7525i) q^{10} +(8.60531 - 8.60531i) q^{11} +(-15.9957 + 15.9957i) q^{13} +(-0.289652 - 0.437208i) q^{14} +(-11.1343 - 11.4903i) q^{16} +3.51534 q^{17} +(10.7566 + 10.7566i) q^{19} +(-22.2304 + 9.00387i) q^{20} +(23.8530 + 4.84227i) q^{22} +16.4968 q^{23} +10.9536i q^{25} +(-44.3382 - 9.00087i) q^{26} +(0.409009 - 0.965871i) q^{28} +(25.9522 - 25.9522i) q^{29} -46.2072i q^{31} +(6.85895 - 31.2563i) q^{32} +(3.88301 + 5.86112i) q^{34} +(-1.11181 - 1.11181i) q^{35} +(-2.99313 - 2.99313i) q^{37} +(-6.05283 + 29.8162i) q^{38} +(-39.5676 - 27.1190i) q^{40} -21.9026i q^{41} +(48.7016 - 48.7016i) q^{43} +(18.2742 + 45.1187i) q^{44} +(18.2222 + 27.5051i) q^{46} +70.7760i q^{47} -48.9312 q^{49} +(-18.2630 + 12.0993i) q^{50} +(-33.9684 - 83.8672i) q^{52} +(52.8193 + 52.8193i) q^{53} +72.9715 q^{55} +(2.06218 - 0.384952i) q^{56} +(71.9366 + 14.6035i) q^{58} +(61.7726 - 61.7726i) q^{59} +(-22.9004 + 22.9004i) q^{61} +(77.0411 - 51.0400i) q^{62} +(59.6898 - 23.0895i) q^{64} -135.640 q^{65} +(-54.9939 - 54.9939i) q^{67} +(-5.48309 + 12.9483i) q^{68} +(0.625624 - 3.08182i) q^{70} -84.2532 q^{71} +78.0341i q^{73} +(1.68426 - 8.29663i) q^{74} +(-56.3983 + 22.8428i) q^{76} +(-2.25653 + 2.25653i) q^{77} +59.2887i q^{79} +(1.50953 - 95.9263i) q^{80} +(36.5181 - 24.1934i) q^{82} +(-111.661 - 111.661i) q^{83} +(14.9047 + 14.9047i) q^{85} +(134.995 + 27.4047i) q^{86} +(-55.0407 + 80.3063i) q^{88} +34.5426i q^{89} +(4.19447 - 4.19447i) q^{91} +(-25.7311 + 60.7637i) q^{92} +(-118.005 + 78.1784i) q^{94} +91.2142i q^{95} -66.0805 q^{97} +(-54.0490 - 81.5829i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{4}+O(q^{10}) \) 16 * q - 12 * q^4	\( 16 q - 12 q^{4} + 16 q^{10} + 32 q^{16} - 32 q^{19} + 104 q^{22} - 24 q^{34} + 96 q^{37} - 312 q^{40} - 32 q^{43} - 224 q^{46} + 112 q^{49} - 264 q^{52} - 256 q^{55} + 312 q^{58} - 32 q^{61} + 456 q^{64} - 256 q^{67} + 744 q^{70} + 264 q^{76} - 280 q^{82} + 160 q^{85} - 912 q^{88} + 288 q^{91} - 1104 q^{94}+O(q^{100}) \) 16 * q - 12 * q^4 + 16 * q^10 + 32 * q^16 - 32 * q^19 + 104 * q^22 - 24 * q^34 + 96 * q^37 - 312 * q^40 - 32 * q^43 - 224 * q^46 + 112 * q^49 - 264 * q^52 - 256 * q^55 + 312 * q^58 - 32 * q^61 + 456 * q^64 - 256 * q^67 + 744 * q^70 + 264 * q^76 - 280 * q^82 + 160 * q^85 - 912 * q^88 + 288 * q^91 - 1104 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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