LMFDB - Embedded newform 252.4.i.a.25.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.i (of order $3$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.33327 + 2.86754i) q^{3} +(0.863703 - 1.49598i) q^{5} +(-16.5772 - 8.25811i) q^{7} +(10.5544 - 24.8517i) q^{9} +O(q^{10})$	\(q+(-4.33327 + 2.86754i) q^{3} +(0.863703 - 1.49598i) q^{5} +(-16.5772 - 8.25811i) q^{7} +(10.5544 - 24.8517i) q^{9} +(28.7488 + 49.7944i) q^{11} +(-31.7458 - 54.9853i) q^{13} +(0.547124 + 8.95917i) q^{15} +(27.1843 - 47.0846i) q^{17} +(30.6466 + 53.0815i) q^{19} +(95.5139 - 11.7513i) q^{21} +(41.0630 - 71.1231i) q^{23} +(61.0080 + 105.669i) q^{25} +(25.5282 + 137.954i) q^{27} +(-97.6997 + 169.221i) q^{29} +305.894 q^{31} +(-267.364 - 133.334i) q^{33} +(-26.6717 + 17.6666i) q^{35} +(125.575 + 217.502i) q^{37} +(295.235 + 147.233i) q^{39} +(-23.5059 - 40.7134i) q^{41} +(-48.6627 + 84.2862i) q^{43} +(-28.0616 - 37.2536i) q^{45} +635.287 q^{47} +(206.607 + 273.793i) q^{49} +(17.2203 + 281.982i) q^{51} +(304.837 - 527.993i) q^{53} +99.3217 q^{55} +(-285.013 - 142.136i) q^{57} +372.384 q^{59} +187.055 q^{61} +(-380.190 + 324.812i) q^{63} -109.676 q^{65} -1011.05 q^{67} +(26.0119 + 425.945i) q^{69} -772.524 q^{71} +(139.034 - 240.814i) q^{73} +(-567.375 - 282.949i) q^{75} +(-65.3674 - 1062.86i) q^{77} +1133.09 q^{79} +(-506.210 - 524.588i) q^{81} +(140.156 - 242.758i) q^{83} +(-46.9584 - 81.3343i) q^{85} +(-61.8892 - 1013.44i) q^{87} +(-368.603 - 638.439i) q^{89} +(72.1817 + 1173.66i) q^{91} +(-1325.52 + 877.164i) q^{93} +105.878 q^{95} +(167.778 - 290.601i) q^{97} +(1540.90 - 188.906i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−4.33327	+	2.86754i	−0.833937	+	0.551859i
$3$	−4.33327	+	2.86754i	−0.833937	+	0.551859i
$4$		0			0
$5$	0.863703	−	1.49598i	0.0772519	−	0.133804i	−0.824811	−	0.565408i	$-0.808719\pi$
$5$	0.863703	−	1.49598i	0.0772519	−	0.133804i	0.902063	+	0.431604i	$0.142052\pi$
$6$		0			0
$7$	−16.5772	−	8.25811i	−0.895085	−	0.445896i
$7$	−16.5772	−	8.25811i	−0.895085	−	0.445896i
$8$		0			0
$9$	10.5544	−	24.8517i	0.390903	−	0.920432i
$10$		0			0
$11$	28.7488	+	49.7944i	0.788008	+	1.36487i	0.927185	+	0.374603i	$0.122221\pi$
$11$	28.7488	+	49.7944i	0.788008	+	1.36487i	−0.139177	+	0.990267i	$0.544446\pi$
$12$		0			0
$13$	−31.7458	−	54.9853i	−0.677284	−	1.17309i	−0.975796	−	0.218684i	$-0.929824\pi$
$13$	−31.7458	−	54.9853i	−0.677284	−	1.17309i	0.298512	−	0.954406i	$-0.403510\pi$
$14$		0			0
$15$	0.547124	+	8.95917i	0.00941780	+	0.154217i
$16$		0			0
$17$	27.1843	−	47.0846i	0.387833	−	0.671747i	−0.604324	−	0.796738i	$-0.706557\pi$
$17$	27.1843	−	47.0846i	0.387833	−	0.671747i	0.992158	+	0.124991i	$0.0398903\pi$
$18$		0			0
$19$	30.6466	+	53.0815i	0.370043	+	0.640933i	0.989572	−	0.144041i	$-0.0460097\pi$
$19$	30.6466	+	53.0815i	0.370043	+	0.640933i	−0.619529	+	0.784974i	$0.712676\pi$
$20$		0			0
$21$	95.5139	−	11.7513i	0.992516	−	0.122111i
$22$		0			0
$23$	41.0630	−	71.1231i	0.372270	−	0.644791i	−0.617644	−	0.786458i	$-0.711913\pi$
$23$	41.0630	−	71.1231i	0.372270	−	0.644791i	0.989914	+	0.141667i	$0.0452461\pi$
$24$		0			0
$25$	61.0080	+	105.669i	0.488064	+	0.845352i
$26$		0			0
$27$	25.5282	+	137.954i	0.181959	+	0.983306i
$28$		0			0
$29$	−97.6997	+	169.221i	−0.625599	+	1.08357i	0.362825	+	0.931857i	$0.381812\pi$
$29$	−97.6997	+	169.221i	−0.625599	+	1.08357i	−0.988425	+	0.151713i	$0.951521\pi$
$30$		0			0
$31$	305.894			1.77226			0.886132	−	0.463432i	$-0.153382\pi$
$31$	305.894			1.77226			0.886132	+	0.463432i	$0.153382\pi$
$32$		0			0
$33$	−267.364	−	133.334i	−1.41037	−	0.703347i
$34$		0			0
$35$	−26.6717	+	17.6666i	−0.128810	+	0.0853199i
$36$		0			0
$37$	125.575	+	217.502i	0.557957	+	0.966409i	0.997667	+	0.0682695i	$0.0217478\pi$
$37$	125.575	+	217.502i	0.557957	+	0.966409i	−0.439710	+	0.898140i	$0.644919\pi$
$38$		0			0
$39$	295.235	+	147.233i	1.21219	+	0.604519i
$40$		0			0
$41$	−23.5059	−	40.7134i	−0.0895367	−	0.155082i	0.817779	−	0.575533i	$-0.195205\pi$
$41$	−23.5059	−	40.7134i	−0.0895367	−	0.155082i	−0.907315	+	0.420451i	$0.861872\pi$
$42$		0			0
$43$	−48.6627	+	84.2862i	−0.172581	+	0.298919i	−0.939321	−	0.343038i	$-0.888544\pi$
$43$	−48.6627	+	84.2862i	−0.172581	+	0.298919i	0.766740	+	0.641957i	$0.221877\pi$
$44$		0			0
$45$	−28.0616	−	37.2536i	−0.0929596	−	0.123410i
$46$		0			0
$47$	635.287			1.97162			0.985810	−	0.167867i	$-0.0536878\pi$
$47$	635.287			1.97162			0.985810	+	0.167867i	$0.0536878\pi$
$48$		0			0
$49$	206.607	+	273.793i	0.602354	+	0.798229i
$50$		0			0
$51$	17.2203	+	281.982i	0.0472808	+	0.774224i
$52$		0			0
$53$	304.837	−	527.993i	0.790049	−	1.36841i	−0.135887	−	0.990724i	$-0.543388\pi$
$53$	304.837	−	527.993i	0.790049	−	1.36841i	0.925936	−	0.377681i	$-0.123278\pi$
$54$		0			0
$55$	99.3217			0.243501
$56$		0			0
$57$	−285.013	−	142.136i	−0.662297	−	0.330287i
$58$		0			0
$59$	372.384			0.821699			0.410850	−	0.911703i	$-0.365232\pi$
$59$	372.384			0.821699			0.410850	+	0.911703i	$0.365232\pi$
$60$		0			0
$61$	187.055			0.392621			0.196311	−	0.980542i	$-0.437104\pi$
$61$	187.055			0.392621			0.196311	+	0.980542i	$0.437104\pi$
$62$		0			0
$63$	−380.190	+	324.812i	−0.760308	+	0.649562i
$64$		0			0
$65$	−109.676			−0.209286
$66$		0			0
$67$	−1011.05			−1.84357			−0.921787	−	0.387696i	$-0.873271\pi$
$67$	−1011.05			−1.84357			−0.921787	+	0.387696i	$0.873271\pi$
$68$		0			0
$69$	26.0119	+	425.945i	0.0453835	+	0.743156i
$70$		0			0
$71$	−772.524			−1.29129			−0.645646	−	0.763637i	$-0.723412\pi$
$71$	−772.524			−1.29129			−0.645646	+	0.763637i	$0.723412\pi$
$72$		0			0
$73$	139.034	−	240.814i	0.222914	−	0.386098i	−0.732778	−	0.680468i	$-0.761777\pi$
$73$	139.034	−	240.814i	0.222914	−	0.386098i	0.955691	+	0.294370i	$0.0951098\pi$
$74$		0			0
$75$	−567.375	−	282.949i	−0.873530	−	0.435628i
$76$		0			0
$77$	−65.3674	−	1062.86i	−0.0967442	−	1.57304i
$78$		0			0
$79$	1133.09			1.61370			0.806850	−	0.590756i	$-0.201170\pi$
$79$	1133.09			1.61370			0.806850	+	0.590756i	$0.201170\pi$
$80$		0			0
$81$	−506.210	−	524.588i	−0.694389	−	0.719600i
$82$		0			0
$83$	140.156	−	242.758i	0.185351	−	0.321038i	−0.758344	−	0.651855i	$-0.773991\pi$
$83$	140.156	−	242.758i	0.185351	−	0.321038i	0.943695	+	0.330817i	$0.107324\pi$
$84$		0			0
$85$	−46.9584	−	81.3343i	−0.0599218	−	0.103788i
$86$		0			0
$87$	−61.8892	−	1013.44i	−0.0762669	−	1.24887i
$88$		0			0
$89$	−368.603	−	638.439i	−0.439009	−	0.760386i	0.558604	−	0.829434i	$-0.311337\pi$
$89$	−368.603	−	638.439i	−0.439009	−	0.760386i	−0.997613	+	0.0690483i	$0.978004\pi$
$90$		0			0
$91$	72.1817	+	1173.66i	0.0831505	+	1.35201i
$92$		0			0
$93$	−1325.52	+	877.164i	−1.47796	+	0.978040i
$94$		0			0
$95$	105.878			0.114346
$96$		0			0
$97$	167.778	−	290.601i	0.175622	−	0.304186i	−0.764755	−	0.644322i	$-0.777140\pi$
$97$	167.778	−	290.601i	0.175622	−	0.304186i	0.940376	+	0.340136i	$0.110473\pi$
$98$		0			0
$99$	1540.90	−	188.906i	1.56430	−	0.191775i
$100$		0			0
$101$	−41.1266	−	71.2334i	−0.0405174	−	0.0701781i	0.845056	−	0.534678i	$-0.179567\pi$
$101$	−41.1266	−	71.2334i	−0.0405174	−	0.0701781i	−0.885573	+	0.464500i	$0.846234\pi$
$102$		0			0
$103$	−295.688	+	512.146i	−0.282864	+	0.489935i	−0.972089	−	0.234613i	$-0.924618\pi$
$103$	−295.688	+	512.146i	−0.282864	+	0.489935i	0.689225	+	0.724547i	$0.257951\pi$
$104$		0			0
$105$	64.9160	−	153.036i	0.0603348	−	0.142236i
$106$		0			0
$107$	576.158	+	997.935i	0.520554	+	0.901626i	0.999714	+	0.0238989i	$0.00760796\pi$
$107$	576.158	+	997.935i	0.520554	+	0.901626i	−0.479160	+	0.877727i	$0.659059\pi$
$108$		0			0
$109$	−354.671	+	614.309i	−0.311664	+	0.539817i	−0.978723	−	0.205188i	$-0.934220\pi$
$109$	−354.671	+	614.309i	−0.311664	+	0.539817i	0.667059	+	0.745005i	$0.267553\pi$
$110$		0			0
$111$	−1167.85	−	582.403i	−0.998622	−	0.498012i
$112$		0			0
$113$	−568.902	−	985.367i	−0.473609	−	0.820314i	0.525935	−	0.850525i	$-0.323716\pi$
$113$	−568.902	−	985.367i	−0.473609	−	0.820314i	−0.999544	+	0.0302106i	$0.990382\pi$
$114$		0			0
$115$	−70.9324	−	122.858i	−0.0575172	−	0.0996227i
$116$		0			0
$117$	−1701.53	+	208.598i	−1.34450	+	0.164828i
$118$		0			0
$119$	−839.470	+	556.040i	−0.646673	+	0.428337i
$120$		0			0
$121$	−987.487	+	1710.38i	−0.741914	+	1.28503i
$122$		0			0
$123$	218.605	+	109.018i	0.160251	+	0.0799172i
$124$		0			0
$125$	426.697			0.305319
$126$		0			0
$127$	1467.56			1.02539			0.512697	−	0.858570i	$-0.328646\pi$
$127$	1467.56			1.02539			0.512697	+	0.858570i	$0.328646\pi$
$128$		0			0
$129$	−30.8260	−	504.777i	−0.0210394	−	0.344520i
$130$		0			0
$131$	334.245	−	578.930i	0.222925	−	0.386117i	−0.732770	−	0.680476i	$-0.761773\pi$
$131$	334.245	−	578.930i	0.222925	−	0.386117i	0.955695	+	0.294359i	$0.0951062\pi$
$132$		0			0
$133$	−69.6825	−	1133.03i	−0.0454304	−	0.738690i
$134$		0			0
$135$	228.425	+	80.9617i	0.145627	+	0.0516154i
$136$		0			0
$137$	193.257	+	334.731i	0.120519	+	0.208745i	0.919972	−	0.391983i	$-0.128211\pi$
$137$	193.257	+	334.731i	0.120519	+	0.208745i	−0.799454	+	0.600728i	$0.794878\pi$
$138$		0			0
$139$	−380.559	−	659.148i	−0.232220	−	0.402217i	0.726241	−	0.687440i	$-0.241266\pi$
$139$	−380.559	−	659.148i	−0.232220	−	0.402217i	−0.958461	+	0.285223i	$0.907932\pi$
$140$		0			0
$141$	−2752.87	+	1821.71i	−1.64421	+	1.08806i
$142$		0			0
$143$	1825.30	−	3161.52i	1.06741	−	1.84881i
$144$		0			0
$145$	168.767	+	292.313i	0.0966575	+	0.167416i
$146$		0			0
$147$	−1680.40	−	593.961i	−0.942835	−	0.333259i
$148$		0			0
$149$	1259.85	−	2182.13i	0.692692	−	1.19978i	−0.278260	−	0.960506i	$-0.589758\pi$
$149$	1259.85	−	2182.13i	0.692692	−	1.19978i	0.970952	−	0.239273i	$-0.0769090\pi$
$150$		0			0
$151$	−131.848	−	228.367i	−0.0710571	−	0.123075i	0.828308	−	0.560273i	$-0.189304\pi$
$151$	−131.848	−	228.367i	−0.0710571	−	0.123075i	−0.899365	+	0.437199i	$0.855971\pi$
$152$		0			0
$153$	−883.217	−	1172.53i	−0.466692	−	0.619562i
$154$		0			0
$155$	264.202	−	457.611i	0.136911	−	0.237137i
$156$		0			0
$157$	1356.24			0.689427			0.344713	−	0.938708i	$-0.387976\pi$
$157$	1356.24			0.689427			0.344713	+	0.938708i	$0.387976\pi$
$158$		0			0
$159$	193.103	+	3162.07i	0.0963150	+	1.57716i
$160$		0			0
$161$	−1268.05	+	839.920i	−0.620723	+	0.411149i
$162$		0			0
$163$	1454.23	+	2518.80i	0.698799	+	1.21036i	0.968883	+	0.247519i	$0.0796153\pi$
$163$	1454.23	+	2518.80i	0.698799	+	1.21036i	−0.270084	+	0.962837i	$0.587051\pi$
$164$		0			0
$165$	−430.387	+	284.809i	−0.203064	+	0.134378i
$166$		0			0
$167$	−1490.48	−	2581.59i	−0.690639	−	1.19622i	−0.971629	−	0.236511i	$-0.923996\pi$
$167$	−1490.48	−	2581.59i	−0.690639	−	1.19622i	0.280990	−	0.959711i	$-0.409337\pi$
$168$		0			0
$169$	−917.086	+	1588.44i	−0.417427	+	0.723004i
$170$		0			0
$171$	1642.62	−	201.376i	0.734586	−	0.0900562i
$172$		0			0
$173$	−501.558			−0.220421			−0.110210	−	0.993908i	$-0.535152\pi$
$173$	−501.558			−0.220421			−0.110210	+	0.993908i	$0.535152\pi$
$174$		0			0
$175$	−138.717	−	2255.51i	−0.0599199	−	0.974288i
$176$		0			0
$177$	−1613.64	+	1067.83i	−0.685246	+	0.453462i
$178$		0			0
$179$	−1584.68	+	2744.75i	−0.661703	+	1.14610i	0.318465	+	0.947935i	$0.396833\pi$
$179$	−1584.68	+	2744.75i	−0.661703	+	1.14610i	−0.980168	+	0.198168i	$0.936501\pi$
$180$		0			0
$181$	862.775			0.354307			0.177153	−	0.984183i	$-0.443311\pi$
$181$	862.775			0.354307			0.177153	+	0.984183i	$0.443311\pi$
$182$		0			0
$183$	−810.557	+	536.387i	−0.327421	+	0.216671i
$184$		0			0
$185$	433.838			0.172413
$186$		0			0
$187$	3126.07			1.22246
$188$		0			0
$189$	716.053	−	2497.71i	0.275583	−	0.961277i
$190$		0			0
$191$	−1871.53			−0.709000			−0.354500	−	0.935056i	$-0.615349\pi$
$191$	−1871.53			−0.709000			−0.354500	+	0.935056i	$0.615349\pi$
$192$		0			0
$193$	3108.46			1.15934			0.579668	−	0.814853i	$-0.303182\pi$
$193$	3108.46			1.15934			0.579668	+	0.814853i	$0.303182\pi$
$194$		0			0
$195$	475.254	−	314.500i	0.174531	−	0.115496i
$196$		0			0
$197$	5258.12			1.90165			0.950825	−	0.309727i	$-0.100238\pi$
$197$	5258.12			1.90165			0.950825	+	0.309727i	$0.100238\pi$
$198$		0			0
$199$	−779.536	+	1350.20i	−0.277687	+	0.480969i	−0.970810	−	0.239851i	$-0.922901\pi$
$199$	−779.536	+	1350.20i	−0.277687	+	0.480969i	0.693122	+	0.720820i	$0.256235\pi$
$200$		0			0
$201$	4381.15	−	2899.23i	1.53743	−	1.01739i
$202$		0			0
$203$	3017.03	−	1998.39i	1.04312	−	0.690935i
$204$		0			0
$205$	−81.2084			−0.0276675
$206$		0			0
$207$	−1334.13	−	1771.14i	−0.447964	−	0.594700i
$208$		0			0
$209$	−1762.11	+	3052.06i	−0.583193	+	1.01012i
$210$		0			0
$211$	−229.128	−	396.861i	−0.0747574	−	0.129484i	0.826223	−	0.563343i	$-0.190485\pi$
$211$	−229.128	−	396.861i	−0.0747574	−	0.129484i	−0.900981	+	0.433859i	$0.857152\pi$
$212$		0			0
$213$	3347.55	−	2215.25i	1.07686	−	0.712611i
$214$		0			0
$215$	84.0601	+	145.596i	0.0266644	+	0.0461842i
$216$		0			0
$217$	−5070.87	−	2526.11i	−1.58633	−	0.790245i
$218$		0			0
$219$	88.0730	+	1442.20i	0.0271755	+	0.444998i
$220$		0			0
$221$	−3451.95			−1.05069
$222$		0			0
$223$	−2311.57	+	4003.76i	−0.694144	+	1.20229i	0.276324	+	0.961064i	$0.410884\pi$
$223$	−2311.57	+	4003.76i	−0.694144	+	1.20229i	−0.970468	+	0.241228i	$0.922450\pi$
$224$		0			0
$225$	3269.95	−	400.878i	0.968875	−	0.118779i
$226$		0			0
$227$	3233.36	+	5600.35i	0.945400	+	1.63748i	0.754949	+	0.655783i	$0.227661\pi$
$227$	3233.36	+	5600.35i	0.945400	+	1.63748i	0.190450	+	0.981697i	$0.439005\pi$
$228$		0			0
$229$	−2748.43	+	4760.43i	−0.793108	+	1.37370i	0.130926	+	0.991392i	$0.458205\pi$
$229$	−2748.43	+	4760.43i	−0.793108	+	1.37370i	−0.924034	+	0.382311i	$0.875128\pi$
$230$		0			0
$231$	3331.06	+	4418.22i	0.948777	+	1.25843i
$232$		0			0
$233$	−146.929	−	254.489i	−0.0413118	−	0.0715542i	0.844630	−	0.535350i	$-0.179820\pi$
$233$	−146.929	−	254.489i	−0.0413118	−	0.0715542i	−0.885942	+	0.463796i	$0.846487\pi$
$234$		0			0
$235$	548.699	−	950.375i	0.152311	−	0.263811i
$236$		0			0
$237$	−4909.97	+	3249.18i	−1.34573	+	0.890535i
$238$		0			0
$239$	1996.26	+	3457.62i	0.540282	+	0.935795i	0.998888	+	0.0471556i	$0.0150157\pi$
$239$	1996.26	+	3457.62i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$240$		0			0
$241$	−391.288	−	677.731i	−0.104585	−	0.181147i	0.808983	−	0.587832i	$-0.200018\pi$
$241$	−391.288	−	677.731i	−0.104585	−	0.181147i	−0.913569	+	0.406684i	$0.866685\pi$
$242$		0			0
$243$	3697.82	+	821.603i	0.976195	+	0.216897i
$244$		0			0
$245$	588.035	−	72.6044i	0.153339	−	0.0189328i
$246$		0			0
$247$	1945.80	−	3370.22i	0.501248	−	0.868187i
$248$		0			0
$249$	88.7840	+	1453.84i	0.0225962	+	0.370013i
$250$		0			0
$251$	1485.08			0.373455			0.186728	−	0.982412i	$-0.440212\pi$
$251$	1485.08			0.373455			0.186728	+	0.982412i	$0.440212\pi$
$252$		0			0
$253$	4722.04			1.17341
$254$		0			0
$255$	436.713	+	217.788i	0.107247	+	0.0534840i
$256$		0			0
$257$	−592.322	+	1025.93i	−0.143767	+	0.249011i	−0.928912	−	0.370300i	$-0.879255\pi$
$257$	−592.322	+	1025.93i	−0.143767	+	0.249011i	0.785145	+	0.619311i	$0.212588\pi$
$258$		0			0
$259$	−285.525	−	4642.59i	−0.0685006	−	1.11381i
$260$		0			0
$261$	3174.26	+	4214.02i	0.752803	+	0.999393i
$262$		0			0
$263$	1693.08	+	2932.51i	0.396958	+	0.687551i	0.993349	−	0.115143i	$-0.0367325\pi$
$263$	1693.08	+	2932.51i	0.396958	+	0.687551i	−0.596391	+	0.802694i	$0.703399\pi$
$264$		0			0
$265$	−526.577	−	912.059i	−0.122066	−	0.211424i
$266$		0			0
$267$	3428.00	+	1709.54i	0.785732	+	0.391843i
$268$		0			0
$269$	3078.57	−	5332.25i	0.697784	−	1.20860i	−0.271449	−	0.962453i	$-0.587503\pi$
$269$	3078.57	−	5332.25i	0.697784	−	1.20860i	0.969233	−	0.246145i	$-0.0791639\pi$
$270$		0			0
$271$	−3202.25	−	5546.45i	−0.717795	−	1.24326i	−0.961871	−	0.273502i	$-0.911818\pi$
$271$	−3202.25	−	5546.45i	−0.717795	−	1.24326i	0.244076	−	0.969756i	$-0.421515\pi$
$272$		0			0
$273$	−3678.31	−	4878.81i	−0.815463	−	1.08161i
$274$		0			0
$275$	−3507.82	+	6075.71i	−0.769197	+	1.33229i
$276$		0			0
$277$	1076.73	+	1864.95i	0.233554	+	0.404527i	0.958851	−	0.283908i	$-0.0916311\pi$
$277$	1076.73	+	1864.95i	0.233554	+	0.404527i	−0.725297	+	0.688436i	$0.758298\pi$
$278$		0			0
$279$	3228.53	−	7601.97i	0.692784	−	1.63125i
$280$		0			0
$281$	470.197	−	814.406i	0.0998207	−	0.172895i	−0.811790	−	0.583950i	$-0.801506\pi$
$281$	470.197	−	814.406i	0.0998207	−	0.172895i	0.911610	+	0.411055i	$0.134840\pi$
$282$		0			0
$283$	6766.92			1.42138			0.710692	−	0.703503i	$-0.248382\pi$
$283$	6766.92			1.42138			0.710692	+	0.703503i	$0.248382\pi$
$284$		0			0
$285$	−458.799	+	303.610i	−0.0953575	+	0.0631029i
$286$		0			0
$287$	53.4464	+	869.029i	0.0109925	+	0.178736i
$288$		0			0
$289$	978.525	+	1694.85i	0.199171	+	0.344974i
$290$		0			0
$291$	106.282	+	1740.36i	0.0214101	+	0.350590i
$292$		0			0
$293$	−2281.54	−	3951.74i	−0.454911	−	0.787929i	0.543772	−	0.839233i	$-0.316996\pi$
$293$	−2281.54	−	3951.74i	−0.454911	−	0.787929i	−0.998683	+	0.0513040i	$0.983662\pi$
$294$		0			0
$295$	321.629	−	557.078i	0.0634779	−	0.109947i
$296$		0			0
$297$	−6135.43	+	5237.17i	−1.19870	+	1.02320i
$298$		0			0
$299$	−5214.30			−1.00853
$300$		0			0
$301$	1502.73	−	995.368i	0.287761	−	0.190605i
$302$		0			0
$303$	382.478	+	190.741i	0.0725174	+	0.0361643i
$304$		0			0
$305$	161.560	−	279.829i	0.0303307	−	0.0525344i
$306$		0			0
$307$	−9374.15			−1.74271			−0.871354	−	0.490655i	$-0.836757\pi$
$307$	−9374.15			−1.74271			−0.871354	+	0.490655i	$0.836757\pi$
$308$		0			0
$309$	−187.307	−	3067.16i	−0.0344840	−	0.564676i
$310$		0			0
$311$	−3661.65			−0.667630			−0.333815	−	0.942639i	$-0.608336\pi$
$311$	−3661.65			−0.667630			−0.333815	+	0.942639i	$0.608336\pi$
$312$		0			0
$313$	−5424.28			−0.979548			−0.489774	−	0.871849i	$-0.662921\pi$
$313$	−5424.28			−0.979548			−0.489774	+	0.871849i	$0.662921\pi$
$314$		0			0
$315$	157.540	+	849.296i	0.0281789	+	0.151912i
$316$		0			0
$317$	−4805.81			−0.851486			−0.425743	−	0.904844i	$-0.639987\pi$
$317$	−4805.81			−0.851486			−0.425743	+	0.904844i	$0.639987\pi$
$318$		0			0
$319$	−11235.0			−1.97191
$320$		0			0
$321$	−5358.27	−	2672.16i	−0.931680	−	0.464628i
$322$		0			0
$323$	3332.43			0.574060
$324$		0			0
$325$	3873.49	−	6709.09i	0.661116	−	1.14509i
$326$		0			0
$327$	−224.671	−	3679.00i	−0.0379950	−	0.622168i
$328$		0			0
$329$	−10531.3	−	5246.27i	−1.76477	−	0.879137i
$330$		0			0
$331$	−325.032			−0.0539739			−0.0269870	−	0.999636i	$-0.508591\pi$
$331$	−325.032			−0.0539739			−0.0269870	+	0.999636i	$0.508591\pi$
$332$		0			0
$333$	6730.66	−	825.141i	1.10762	−	0.135788i
$334$		0			0
$335$	−873.247	+	1512.51i	−0.142420	+	0.246678i
$336$		0			0
$337$	442.683	+	766.750i	0.0715564	+	0.123939i	0.899584	−	0.436749i	$-0.143870\pi$
$337$	442.683	+	766.750i	0.0715564	+	0.123939i	−0.828027	+	0.560688i	$0.810537\pi$
$338$		0			0
$339$	5290.78	+	2638.51i	0.847658	+	0.422726i
$340$		0			0
$341$	8794.09	+	15231.8i	1.39656	+	2.41891i
$342$		0			0
$343$	−1163.96	−	6244.90i	−0.183231	−	0.983070i
$344$		0			0
$345$	659.671	+	328.977i	0.102943	+	0.0513377i
$346$		0			0
$347$	−8306.66			−1.28509			−0.642543	−	0.766250i	$-0.722121\pi$
$347$	−8306.66			−1.28509			−0.642543	+	0.766250i	$0.722121\pi$
$348$		0			0
$349$	−487.113	+	843.705i	−0.0747123	+	0.129405i	−0.900961	−	0.433900i	$-0.857137\pi$
$349$	−487.113	+	843.705i	−0.0747123	+	0.129405i	0.826249	+	0.563305i	$0.190470\pi$
$350$		0			0
$351$	6775.03	−	5783.13i	1.03027	−	0.879432i
$352$		0			0
$353$	−4680.90	−	8107.56i	−0.705777	−	1.22244i	−0.966411	−	0.257003i	$-0.917265\pi$
$353$	−4680.90	−	8107.56i	−0.705777	−	1.22244i	0.260634	−	0.965438i	$-0.416068\pi$
$354$		0			0
$355$	−667.231	+	1155.68i	−0.0997548	+	0.172780i
$356$		0			0
$357$	2043.18	−	4816.69i	0.302903	−	0.714079i
$358$		0			0
$359$	552.866	+	957.593i	0.0812790	+	0.140779i	0.903800	−	0.427956i	$-0.140766\pi$
$359$	552.866	+	957.593i	0.0812790	+	0.140779i	−0.822521	+	0.568735i	$0.807433\pi$
$360$		0			0
$361$	1551.07	−	2686.54i	0.226137	−	0.391680i
$362$		0			0
$363$	−625.537	−	10243.2i	−0.0904468	−	1.48107i
$364$		0			0
$365$	−240.168	−	415.984i	−0.0344410	−	0.0596536i
$366$		0			0
$367$	757.648	+	1312.29i	0.107763	+	0.186651i	0.914864	−	0.403763i	$-0.132298\pi$
$367$	757.648	+	1312.29i	0.107763	+	0.186651i	−0.807101	+	0.590414i	$0.798965\pi$
$368$		0			0
$369$	−1259.89	+	154.455i	−0.177743	+	0.0217903i
$370$		0			0
$371$	−9413.57	+	6235.28i	−1.31733	+	0.872559i
$372$		0			0
$373$	928.740	−	1608.62i	0.128923	−	0.223301i	−0.794337	−	0.607478i	$-0.792181\pi$
$373$	928.740	−	1608.62i	0.128923	−	0.223301i	0.923260	+	0.384177i	$0.125515\pi$
$374$		0			0
$375$	−1848.99	+	1223.57i	−0.254617	+	0.168493i
$376$		0			0
$377$	12406.2			1.69483
$378$		0			0
$379$	−5876.07			−0.796395			−0.398197	−	0.917300i	$-0.630364\pi$
$379$	−5876.07			−0.796395			−0.398197	+	0.917300i	$0.630364\pi$
$380$		0			0
$381$	−6359.33	+	4208.30i	−0.855114	+	0.565873i
$382$		0			0
$383$	−356.716	+	617.850i	−0.0475909	+	0.0824299i	−0.888840	−	0.458218i	$-0.848488\pi$
$383$	−356.716	+	617.850i	−0.0475909	+	0.0824299i	0.841249	+	0.540648i	$0.181821\pi$
$384$		0			0
$385$	−1646.48	−	820.209i	−0.217954	−	0.108576i
$386$		0			0
$387$	1581.05	+	2098.94i	0.207672	+	0.275698i
$388$		0			0
$389$	3281.02	+	5682.89i	0.427646	+	0.740704i	0.996663	−	0.0816211i	$-0.0260097\pi$
$389$	3281.02	+	5682.89i	0.427646	+	0.740704i	−0.569018	+	0.822325i	$0.692676\pi$
$390$		0			0
$391$	−2232.54	−	3866.87i	−0.288758	−	0.500143i
$392$		0			0
$393$	211.732	+	3467.12i	0.0271768	+	0.445020i
$394$		0			0
$395$	978.651	−	1695.07i	0.124662	−	0.215920i
$396$		0			0
$397$	1080.78	+	1871.97i	0.136632	+	0.236654i	0.926220	−	0.376984i	$-0.123039\pi$
$397$	1080.78	+	1871.97i	0.136632	+	0.236654i	−0.789588	+	0.613638i	$0.789705\pi$
$398$		0			0
$399$	3550.95	+	4709.88i	0.445539	+	0.590950i
$400$		0			0
$401$	776.059	−	1344.17i	0.0966448	−	0.167394i	−0.813649	−	0.581356i	$-0.802522\pi$
$401$	776.059	−	1344.17i	0.0966448	−	0.167394i	0.910294	+	0.413963i	$0.135856\pi$
$402$		0			0
$403$	−9710.84	−	16819.7i	−1.20033	−	2.07903i
$404$		0			0
$405$	−1221.99	+	304.189i	−0.149928	+	0.0373217i
$406$		0			0
$407$	−7220.26	+	12505.9i	−0.879349	+	1.52308i
$408$		0			0
$409$	2080.52			0.251528			0.125764	−	0.992060i	$-0.459862\pi$
$409$	2080.52			0.251528			0.125764	+	0.992060i	$0.459862\pi$
$410$		0			0
$411$	−1797.29	−	896.307i	−0.215703	−	0.107571i
$412$		0			0
$413$	−6173.09	−	3075.19i	−0.735491	−	0.366392i
$414$		0			0
$415$	−242.107	−	419.341i	−0.0286375	−	0.0496016i
$416$		0			0
$417$	3539.20	+	1764.99i	0.415624	+	0.207271i
$418$		0			0
$419$	4013.42	+	6951.45i	0.467944	+	0.810503i	0.999329	−	0.0366276i	$-0.0116615\pi$
$419$	4013.42	+	6951.45i	0.467944	+	0.810503i	−0.531385	+	0.847131i	$0.678328\pi$
$420$		0			0
$421$	−4536.14	+	7856.83i	−0.525126	+	0.909545i	0.474446	+	0.880285i	$0.342649\pi$
$421$	−4536.14	+	7856.83i	−0.525126	+	0.909545i	−0.999572	+	0.0292605i	$0.990685\pi$
$422$		0			0
$423$	6705.07	−	15787.9i	0.770713	−	1.81474i
$424$		0			0
$425$	6633.85			0.757150
$426$		0			0
$427$	−3100.84	−	1544.72i	−0.351429	−	0.175068i
$428$		0			0
$429$	1156.26	+	18933.9i	0.130128	+	2.13085i
$430$		0			0
$431$	−215.061	+	372.496i	−0.0240351	+	0.0416300i	−0.877793	−	0.479041i	$-0.840985\pi$
$431$	−215.061	+	372.496i	−0.0240351	+	0.0416300i	0.853758	+	0.520671i	$0.174318\pi$
$432$		0			0
$433$	−7449.81			−0.826825			−0.413412	−	0.910544i	$-0.635663\pi$
$433$	−7449.81			−0.826825			−0.413412	+	0.910544i	$0.635663\pi$
$434$		0			0
$435$	−1569.53	−	782.724i	−0.172996	−	0.0862729i
$436$		0			0
$437$	5033.76			0.551024
$438$		0			0
$439$	−1398.34			−0.152025			−0.0760125	−	0.997107i	$-0.524219\pi$
$439$	−1398.34			−0.152025			−0.0760125	+	0.997107i	$0.524219\pi$
$440$		0			0
$441$	8984.82	−	2244.82i	0.970178	−	0.242395i
$442$		0			0
$443$	−10005.9			−1.07312			−0.536562	−	0.843861i	$-0.680277\pi$
$443$	−10005.9			−1.07312			−0.536562	+	0.843861i	$0.680277\pi$
$444$		0			0
$445$	−1273.45			−0.135657
$446$		0			0
$447$	798.071	+	13068.4i	0.0844463	+	1.38281i
$448$		0			0
$449$	4372.22			0.459550			0.229775	−	0.973244i	$-0.426201\pi$
$449$	4372.22			0.459550			0.229775	+	0.973244i	$0.426201\pi$
$450$		0			0
$451$	1351.53	−	2340.92i	0.141111	−	0.244412i
$452$		0			0
$453$	1226.18	+	611.496i	0.127177	+	0.0634230i
$454$		0			0
$455$	1818.11	+	905.713i	0.187329	+	0.0933197i
$456$		0			0
$457$	7330.24			0.750315			0.375158	−	0.926961i	$-0.377589\pi$
$457$	7330.24			0.750315			0.375158	+	0.926961i	$0.377589\pi$
$458$		0			0
$459$	7189.48	+	2548.20i	0.731103	+	0.259128i
$460$		0			0
$461$	5301.11	−	9181.80i	0.535569	−	0.927633i	−0.463566	−	0.886062i	$-0.653430\pi$
$461$	5301.11	−	9181.80i	0.535569	−	0.927633i	0.999136	−	0.0415709i	$-0.0132363\pi$
$462$		0			0
$463$	−1192.73	−	2065.87i	−0.119721	−	0.207363i	0.799936	−	0.600085i	$-0.204867\pi$
$463$	−1192.73	−	2065.87i	−0.119721	−	0.207363i	−0.919657	+	0.392722i	$0.871533\pi$
$464$		0			0
$465$	167.362	+	2740.56i	0.0166908	+	0.273313i
$466$		0			0
$467$	1267.01	+	2194.53i	0.125547	+	0.217454i	0.921947	−	0.387317i	$-0.126598\pi$
$467$	1267.01	+	2194.53i	0.125547	+	0.217454i	−0.796400	+	0.604771i	$0.793265\pi$
$468$		0			0
$469$	16760.4	+	8349.36i	1.65016	+	0.822042i
$470$		0			0
$471$	−5876.96	+	3889.08i	−0.574939	+	0.380466i
$472$		0			0
$473$	−5595.97			−0.543981
$474$		0			0
$475$	−3739.38	+	6476.79i	−0.361209	+	0.625633i
$476$		0			0
$477$	−9904.14	−	13148.4i	−0.950690	−	1.26210i
$478$		0			0
$479$	−2715.76	−	4703.83i	−0.259053	−	0.448692i	0.706936	−	0.707278i	$-0.250077\pi$
$479$	−2715.76	−	4703.83i	−0.259053	−	0.448692i	−0.965988	+	0.258586i	$0.916744\pi$
$480$		0			0
$481$	7972.94	−	13809.5i	0.755790	−	1.30907i
$482$		0			0
$483$	3086.30	−	7275.79i	0.290748	−	0.685424i
$484$		0			0
$485$	−289.821	−	501.985i	−0.0271342	−	0.0469979i
$486$		0			0
$487$	−3258.44	+	5643.78i	−0.303191	+	0.525142i	−0.976857	−	0.213894i	$-0.931385\pi$
$487$	−3258.44	+	5643.78i	−0.303191	+	0.525142i	0.673666	+	0.739036i	$0.264719\pi$
$488$		0			0
$489$	−13524.4	−	6744.58i	−1.25070	−	0.623723i
$490$		0			0
$491$	−7171.66	−	12421.7i	−0.659170	−	1.14172i	−0.980831	−	0.194861i	$-0.937574\pi$
$491$	−7171.66	−	12421.7i	−0.659170	−	1.14172i	0.321661	−	0.946855i	$-0.395759\pi$
$492$		0			0
$493$	5311.80	+	9200.31i	0.485257	+	0.840489i
$494$		0			0
$495$	1048.28	−	2468.31i	0.0951852	−	0.224126i
$496$		0			0
$497$	12806.3	+	6379.58i	1.15582	+	0.575782i
$498$		0			0
$499$	5461.79	−	9460.10i	0.489987	−	0.848682i	−0.509947	−	0.860206i	$-0.670335\pi$
$499$	5461.79	−	9460.10i	0.489987	−	0.848682i	0.999934	+	0.0115240i	$0.00366829\pi$
$500$		0			0
$501$	13861.5	+	6912.69i	1.23610	+	0.616439i
$502$		0			0
$503$	490.063			0.0434410			0.0217205	−	0.999764i	$-0.493086\pi$
$503$	490.063			0.0434410			0.0217205	+	0.999764i	$0.493086\pi$
$504$		0			0
$505$	−142.085			−0.0125202
$506$		0			0
$507$	−580.941	−	9512.92i	−0.0508886	−	0.833301i
$508$		0			0
$509$	1705.73	−	2954.41i	0.148537	−	0.257273i	−0.782150	−	0.623090i	$-0.785877\pi$
$509$	1705.73	−	2954.41i	0.148537	−	0.257273i	0.930687	+	0.365817i	$0.119210\pi$
$510$		0			0
$511$	−4293.46	+	2843.87i	−0.371686	+	0.246194i
$512$		0			0
$513$	−6540.45	+	5582.90i	−0.562900	+	0.480489i
$514$		0			0
$515$	510.773	+	884.684i	0.0437036	+	0.0756968i
$516$		0			0
$517$	18263.7	+	31633.7i	1.55365	+	2.69100i
$518$		0			0
$519$	2173.38	−	1438.24i	0.183817	−	0.121641i
$520$		0			0
$521$	−1470.21	+	2546.49i	−0.123630	+	0.214134i	−0.921197	−	0.389097i	$-0.872787\pi$
$521$	−1470.21	+	2546.49i	−0.123630	+	0.214134i	0.797567	+	0.603231i	$0.206120\pi$
$522$		0			0
$523$	−4855.29	−	8409.62i	−0.405941	−	0.703111i	0.588489	−	0.808505i	$-0.299723\pi$
$523$	−4855.29	−	8409.62i	−0.405941	−	0.703111i	−0.994431	+	0.105394i	$0.966390\pi$
$524$		0			0
$525$	7068.86	+	9375.94i	0.587639	+	0.779428i
$526$		0			0
$527$	8315.52	−	14402.9i	0.687343	−	1.19051i
$528$		0			0
$529$	2711.17	+	4695.88i	0.222830	+	0.385952i
$530$		0			0
$531$	3930.29	−	9254.36i	0.321205	−	0.756318i
$532$		0			0
$533$	−1492.43	+	2584.96i	−0.121284	+	0.210069i
$534$		0			0
$535$	1990.52			0.160855
$536$		0			0
$537$	−1003.84	−	16437.9i	−0.0806683	−	1.32094i
$538$		0			0
$539$	−7693.62	+	18159.1i	−0.614820	+	1.45115i
$540$		0			0
$541$	3660.36	+	6339.92i	0.290889	+	0.503835i	0.974020	−	0.226461i	$-0.0727156\pi$
$541$	3660.36	+	6339.92i	0.290889	+	0.503835i	−0.683131	+	0.730296i	$0.739382\pi$
$542$		0			0
$543$	−3738.63	+	2474.04i	−0.295470	+	0.195527i
$544$		0			0
$545$	612.661	+	1061.16i	0.0481533	+	0.0834039i
$546$		0			0
$547$	3955.06	−	6850.37i	0.309152	−	0.535468i	−0.669025	−	0.743240i	$-0.733288\pi$
$547$	3955.06	−	6850.37i	0.309152	−	0.535468i	0.978177	+	0.207772i	$0.0666214\pi$
$548$		0			0
$549$	1974.25	−	4648.62i	0.153477	−	0.361381i
$550$		0			0
$551$	−11976.7			−0.925994
$552$		0			0
$553$	−18783.4	−	9357.16i	−1.44440	−	0.719543i
$554$		0			0
$555$	−1879.93	+	1244.05i	−0.143782	+	0.0951476i
$556$		0			0
$557$	4721.25	−	8177.44i	0.359148	−	0.622063i	−0.628670	−	0.777672i	$-0.716401\pi$
$557$	4721.25	−	8177.44i	0.359148	−	0.622063i	0.987819	+	0.155609i	$0.0497339\pi$
$558$		0			0
$559$	6179.33			0.467545
$560$		0			0
$561$	−13546.1	+	8964.13i	−1.01946	+	0.674627i
$562$		0			0
$563$	26139.3			1.95673			0.978364	−	0.206890i	$-0.0663341\pi$
$563$	26139.3			1.95673			0.978364	+	0.206890i	$0.0663341\pi$
$564$		0			0
$565$	−1965.45			−0.146349
$566$		0			0
$567$	4059.43	+	12876.5i	0.300670	+	0.953728i
$568$		0			0
$569$	7130.09			0.525323			0.262661	−	0.964888i	$-0.415400\pi$
$569$	7130.09			0.525323			0.262661	+	0.964888i	$0.415400\pi$
$570$		0			0
$571$	4992.03			0.365867			0.182934	−	0.983125i	$-0.441441\pi$
$571$	4992.03			0.365867			0.182934	+	0.983125i	$0.441441\pi$
$572$		0			0
$573$	8109.83	−	5366.69i	0.591262	−	0.391268i
$574$		0			0
$575$	10020.7			0.726767
$576$		0			0
$577$	−6242.85	+	10812.9i	−0.450422	+	0.780153i	−0.998412	−	0.0563314i	$-0.982060\pi$
$577$	−6242.85	+	10812.9i	−0.450422	+	0.780153i	0.547990	+	0.836485i	$0.315393\pi$
$578$		0			0
$579$	−13469.8	+	8913.64i	−0.966813	+	0.639790i
$580$		0			0
$581$	−4328.12	+	2866.82i	−0.309055	+	0.204709i
$582$		0			0
$583$	35054.8			2.49026
$584$		0			0
$585$	−1157.56	+	2725.62i	−0.0818106	+	0.192633i
$586$		0			0
$587$	3699.04	−	6406.92i	0.260095	−	0.450497i	−0.706172	−	0.708040i	$-0.749580\pi$
$587$	3699.04	−	6406.92i	0.260095	−	0.450497i	0.966267	+	0.257543i	$0.0829129\pi$
$588$		0			0
$589$	9374.61	+	16237.3i	0.655814	+	1.13590i
$590$		0			0
$591$	−22784.8	+	15077.9i	−1.58586	+	1.04944i
$592$		0			0
$593$	−6646.95	−	11512.9i	−0.460299	−	0.797262i	0.538676	−	0.842513i	$-0.318925\pi$
$593$	−6646.95	−	11512.9i	−0.460299	−	0.797262i	−0.998976	+	0.0452510i	$0.985591\pi$
$594$		0			0
$595$	106.771	+	1736.08i	0.00735663	+	0.119617i
$596$		0			0
$597$	−493.808	−	8086.11i	−0.0338529	−	0.554342i
$598$		0			0
$599$	14781.5			1.00827			0.504135	−	0.863625i	$-0.331811\pi$
$599$	14781.5			1.00827			0.504135	+	0.863625i	$0.331811\pi$
$600$		0			0
$601$	804.342	−	1393.16i	0.0545920	−	0.0945561i	−0.837438	−	0.546532i	$-0.815948\pi$
$601$	804.342	−	1393.16i	0.0545920	−	0.0945561i	0.892030	+	0.451976i	$0.149281\pi$
$602$		0			0
$603$	−10671.0	+	25126.3i	−0.720660	+	1.69688i
$604$		0			0
$605$	1705.79	+	2954.52i	0.114629	+	0.198542i
$606$		0			0
$607$	−9209.97	+	15952.1i	−0.615850	+	1.06668i	0.374384	+	0.927274i	$0.377854\pi$
$607$	−9209.97	+	15952.1i	−0.615850	+	1.06668i	−0.990235	+	0.139411i	$0.955479\pi$
$608$		0			0
$609$	−7343.12	+	17311.0i	−0.488602	+	1.15185i
$610$		0			0
$611$	−20167.7	−	34931.4i	−1.33535	−	2.31289i
$612$		0			0
$613$	9683.71	−	16772.7i	0.638045	−	1.10513i	−0.347817	−	0.937562i	$-0.613077\pi$
$613$	9683.71	−	16772.7i	0.638045	−	1.10513i	0.985861	−	0.167563i	$-0.0535898\pi$
$614$		0			0
$615$	351.898	−	232.869i	0.0230730	−	0.0152686i
$616$		0			0
$617$	−7593.11	−	13151.6i	−0.495441	−	0.858129i	0.504545	−	0.863385i	$-0.331660\pi$
$617$	−7593.11	−	13151.6i	−0.495441	−	0.858129i	−0.999986	+	0.00525646i	$0.998327\pi$
$618$		0			0
$619$	3199.19	+	5541.17i	0.207733	+	0.359803i	0.951000	−	0.309191i	$-0.100058\pi$
$619$	3199.19	+	5541.17i	0.207733	+	0.359803i	−0.743267	+	0.668995i	$0.766725\pi$
$620$		0			0
$621$	10860.0	+	3849.15i	0.701765	+	0.248730i
$622$		0			0
$623$	838.108	+	13627.5i	0.0538974	+	0.876362i
$624$		0			0
$625$	−7257.46	+	12570.3i	−0.464478	+	0.804499i
$626$		0			0
$627$	−1116.23	−	18278.3i	−0.0710972	−	1.16422i
$628$		0			0
$629$	13654.7			0.865577
$630$		0			0
$631$	−7850.80			−0.495302			−0.247651	−	0.968849i	$-0.579659\pi$
$631$	−7850.80			−0.495302			−0.247651	+	0.968849i	$0.579659\pi$
$632$		0			0
$633$	2130.89	+	1062.67i	0.133800	+	0.0667257i
$634$		0			0
$635$	1267.54	−	2195.44i	0.0792137	−	0.137202i
$636$		0			0
$637$	8495.65	−	20052.1i	0.528430	−	1.24724i
$638$		0			0
$639$	−8153.52	+	19198.5i	−0.504770	+	1.18855i
$640$		0			0
$641$	12509.7	+	21667.5i	0.770833	+	1.33512i	0.937107	+	0.349043i	$0.113493\pi$
$641$	12509.7	+	21667.5i	0.770833	+	1.33512i	−0.166273	+	0.986080i	$0.553173\pi$
$642$		0			0
$643$	−9592.10	−	16614.0i	−0.588298	−	1.01896i	−0.994455	−	0.105159i	$-0.966465\pi$
$643$	−9592.10	−	16614.0i	−0.588298	−	1.01896i	0.406157	−	0.913803i	$-0.366868\pi$
$644$		0			0
$645$	−781.759	−	389.862i	−0.0477236	−	0.0237997i
$646$		0			0
$647$	5635.13	−	9760.33i	0.342411	−	0.593073i	−0.642469	−	0.766312i	$-0.722090\pi$
$647$	5635.13	−	9760.33i	0.342411	−	0.593073i	0.984880	+	0.173239i	$0.0554232\pi$
$648$		0			0
$649$	10705.6	+	18542.6i	0.647506	+	1.12151i
$650$		0			0
$651$	29217.1	−	3594.64i	1.75900	−	0.216413i
$652$		0			0
$653$	5203.53	−	9012.78i	0.311838	−	0.540119i	−0.666923	−	0.745127i	$-0.732389\pi$
$653$	5203.53	−	9012.78i	0.311838	−	0.540119i	0.978760	+	0.205008i	$0.0657222\pi$
$654$		0			0
$655$	−577.377	−	1000.05i	−0.0344427	−	0.0596566i
$656$		0			0
$657$	−4517.21	−	5996.87i	−0.268239	−	0.356104i
$658$		0			0
$659$	3811.66	−	6601.98i	0.225313	−	0.390253i	−0.731101	−	0.682270i	$-0.760993\pi$
$659$	3811.66	−	6601.98i	0.225313	−	0.390253i	0.956413	+	0.292017i	$0.0943263\pi$
$660$		0			0
$661$	−16073.1			−0.945795			−0.472897	−	0.881117i	$-0.656792\pi$
$661$	−16073.1			−0.945795			−0.472897	+	0.881117i	$0.656792\pi$
$662$		0			0
$663$	14958.2	−	9898.61i	0.876212	−	0.579834i
$664$		0			0
$665$	−1755.16	−	874.354i	−0.102349	−	0.0509864i
$666$		0			0
$667$	8023.68	+	13897.4i	0.465784	+	0.806762i
$668$		0			0
$669$	−1464.30	−	23977.9i	−0.0846232	−	1.38571i
$670$		0			0
$671$	5377.60	+	9314.27i	0.309389	+	0.535877i
$672$		0			0
$673$	−1169.63	+	2025.86i	−0.0669925	+	0.116034i	−0.897576	−	0.440860i	$-0.854674\pi$
$673$	−1169.63	+	2025.86i	−0.0669925	+	0.116034i	0.830584	+	0.556894i	$0.188007\pi$
$674$		0			0
$675$	−13020.0	+	11113.8i	−0.742432	+	0.633736i
$676$		0			0
$677$	5316.99			0.301844			0.150922	−	0.988546i	$-0.451776\pi$
$677$	5316.99			0.301844			0.150922	+	0.988546i	$0.451776\pi$
$678$		0			0
$679$	−5181.11	+	3431.81i	−0.292832	+	0.193963i
$680$		0			0
$681$	−30070.2	−	14996.0i	−1.69206	−	0.843829i
$682$		0			0
$683$	−16690.5	+	28908.8i	−0.935056	+	1.61957i	−0.160523	+	0.987032i	$0.551318\pi$
$683$	−16690.5	+	28908.8i	−0.935056	+	1.61957i	−0.774533	+	0.632533i	$0.782015\pi$
$684$		0			0
$685$	667.667			0.0372413
$686$		0			0
$687$	−1741.03	−	28509.5i	−0.0966879	−	1.58327i
$688$		0			0
$689$	−38709.1			−2.14035
$690$		0			0
$691$	−21445.5			−1.18064			−0.590321	−	0.807169i	$-0.700999\pi$
$691$	−21445.5			−1.18064			−0.590321	+	0.807169i	$0.700999\pi$
$692$		0			0
$693$	−27103.8	−	9593.38i	−1.48570	−	0.525862i
$694$		0			0
$695$	−1314.76			−0.0717578
$696$		0			0
$697$	−2555.97			−0.138901
$698$		0			0
$699$	1366.44	+	681.443i	0.0739393	+	0.0368734i
$700$		0			0
$701$	7971.18			0.429483			0.214741	−	0.976671i	$-0.431109\pi$
$701$	7971.18			0.429483			0.214741	+	0.976671i	$0.431109\pi$
$702$		0			0
$703$	−7696.89	+	13331.4i	−0.412936	+	0.715225i
$704$		0			0
$705$	347.581	+	5691.64i	0.0185683	+	0.304056i
$706$		0			0
$707$	93.5114	+	1520.48i	0.00497434	+	0.0808819i
$708$		0			0
$709$	19978.9			1.05829			0.529143	−	0.848533i	$-0.322514\pi$
$709$	19978.9			1.05829			0.529143	+	0.848533i	$0.322514\pi$
$710$		0			0
$711$	11959.1	−	28159.1i	0.630801	−	1.48530i
$712$		0			0
$713$	12560.9	−	21756.1i	0.659761	−	1.14274i
$714$		0			0
$715$	−3153.04	−	5461.23i	−0.164919	−	0.285648i
$716$		0			0
$717$	−18565.2	−	9258.44i	−0.966988	−	0.482236i
$718$		0			0
$719$	3680.97	+	6375.62i	0.190928	+	0.330696i	0.945558	−	0.325454i	$-0.105517\pi$
$719$	3680.97	+	6375.62i	0.190928	+	0.330696i	−0.754630	+	0.656150i	$0.772184\pi$
$720$		0			0
$721$	9131.03	−	6048.13i	0.471647	−	0.312405i
$722$		0			0
$723$	3638.98	+	1814.75i	0.187186	+	0.0933491i
$724$		0			0
$725$	−23841.9			−1.22133
$726$		0			0
$727$	−14773.9	+	25589.2i	−0.753694	+	1.30544i	0.192328	+	0.981331i	$0.438396\pi$
$727$	−14773.9	+	25589.2i	−0.753694	+	1.30544i	−0.946021	+	0.324105i	$0.894937\pi$
$728$		0			0
$729$	−18379.6	+	7043.43i	−0.933782	+	0.357843i
$730$		0			0
$731$	2645.72	+	4582.53i	0.133865	+	0.231862i
$732$		0			0
$733$	4863.32	−	8423.51i	0.245062	−	0.424460i	−0.717087	−	0.696984i	$-0.754525\pi$
$733$	4863.32	−	8423.51i	0.245062	−	0.424460i	0.962149	+	0.272524i	$0.0878583\pi$
$734$		0			0
$735$	−2339.92	+	2000.83i	−0.117427	+	0.100410i
$736$		0			0
$737$	−29066.5	−	50344.6i	−1.45275	−	2.51624i
$738$		0			0
$739$	−6774.53	+	11733.8i	−0.337219	+	0.584081i	−0.983909	−	0.178673i	$-0.942820\pi$
$739$	−6774.53	+	11733.8i	−0.337219	+	0.584081i	0.646689	+	0.762753i	$0.276153\pi$
$740$		0			0
$741$	1232.59	+	20183.7i	0.0611072	+	1.00063i
$742$		0			0
$743$	−7302.28	−	12647.9i	−0.360558	−	0.624505i	0.627495	−	0.778621i	$-0.284080\pi$
$743$	−7302.28	−	12647.9i	−0.360558	−	0.624505i	−0.988053	+	0.154116i	$0.950747\pi$
$744$		0			0
$745$	−2176.28	−	3769.42i	−0.107024	−	0.185370i
$746$		0			0
$747$	−4553.67	−	6045.28i	−0.223039	−	0.296098i
$748$		0			0
$749$	−1310.04	−	21300.9i	−0.0639087	−	1.03915i
$750$		0			0
$751$	13860.4	−	24007.0i	0.673469	−	1.16648i	−0.303445	−	0.952849i	$-0.598137\pi$
$751$	13860.4	−	24007.0i	0.673469	−	1.16648i	0.976914	−	0.213633i	$-0.0685297\pi$
$752$		0			0
$753$	−6435.24	+	4258.52i	−0.311438	+	0.206095i
$754$		0			0
$755$	−455.509			−0.0219572
$756$		0			0
$757$	−17403.7			−0.835599			−0.417799	−	0.908539i	$-0.637198\pi$
$757$	−17403.7			−0.835599			−0.417799	+	0.908539i	$0.637198\pi$
$758$		0			0
$759$	−20461.9	+	13540.7i	−0.978549	+	0.647556i
$760$		0			0
$761$	16975.3	−	29402.0i	0.808612	−	1.40056i	−0.105214	−	0.994450i	$-0.533553\pi$
$761$	16975.3	−	29402.0i	0.808612	−	1.40056i	0.913826	−	0.406107i	$-0.133114\pi$
$762$		0			0
$763$	10952.5	−	7254.61i	0.519668	−	0.344213i
$764$		0			0
$765$	−2516.91	+	308.559i	−0.118953	+	0.0145830i
$766$		0			0
$767$	−11821.6	−	20475.6i	−0.556524	−	0.963927i
$768$		0			0
$769$	17577.3	+	30444.7i	0.824256	+	1.42765i	0.902487	+	0.430717i	$0.141739\pi$
$769$	17577.3	+	30444.7i	0.824256	+	1.42765i	−0.0782314	+	0.996935i	$0.524927\pi$
$770$		0			0
$771$	−375.215	−	6144.15i	−0.0175266	−	0.286999i
$772$		0			0
$773$	7859.85	−	13613.7i	0.365717	−	0.633440i	−0.623174	−	0.782083i	$-0.714157\pi$
$773$	7859.85	−	13613.7i	0.365717	−	0.633440i	0.988891	+	0.148643i	$0.0474906\pi$
$774$		0			0
$775$	18662.0	+	32323.5i	0.864979	+	1.49819i
$776$		0			0
$777$	14550.1	+	19298.8i	0.671790	+	0.891044i
$778$		0			0
$779$	1440.75	−	2495.46i	0.0662648	−	0.114774i
$780$		0			0
$781$	−22209.1	−	38467.3i	−1.01755	−	1.76245i
$782$		0			0
$783$	−25838.8	−	9158.17i	−1.17931	−	0.417990i
$784$		0			0
$785$	1171.39	−	2028.91i	0.0532595	−	0.0922482i
$786$		0			0
$787$	−26887.2			−1.21782			−0.608911	−	0.793238i	$-0.708393\pi$
$787$	−26887.2			−1.21782			−0.608911	+	0.793238i	$0.708393\pi$
$788$		0			0
$789$	−15745.7	−	7852.34i	−0.710470	−	0.354310i
$790$		0			0
$791$	1293.54	+	21032.7i	0.0581452	+	0.945431i
$792$		0			0
$793$	−5938.19	−	10285.2i	−0.265916	−	0.460580i
$794$		0			0
$795$	4897.17	+	2442.21i	0.218471	+	0.108951i
$796$		0			0
$797$	14304.6	+	24776.4i	0.635755	+	1.10116i	0.986355	+	0.164634i	$0.0526444\pi$
$797$	14304.6	+	24776.4i	0.635755	+	1.10116i	−0.350600	+	0.936525i	$0.614022\pi$
$798$		0			0
$799$	17269.8	−	29912.2i	0.764660	−	1.32443i
$800$		0			0
$801$	−19756.6	+	2422.05i	−0.871494	+	0.106840i
$802$		0			0
$803$	15988.2			0.702631
$804$		0			0
$805$	161.282	+	2622.42i	0.00706142	+	0.114817i
$806$		0			0
$807$	1950.17	+	31934.0i	0.0850670	+	1.39297i
$808$		0			0
$809$	−10203.3	+	17672.6i	−0.443422	+	0.768030i	−0.997941	−	0.0641414i	$-0.979569\pi$
$809$	−10203.3	+	17672.6i	−0.443422	+	0.768030i	0.554518	+	0.832171i	$0.312902\pi$
$810$		0			0
$811$	33253.2			1.43980			0.719901	−	0.694077i	$-0.244187\pi$
$811$	33253.2			1.43980			0.719901	+	0.694077i	$0.244187\pi$
$812$		0			0
$813$	29780.9	+	14851.7i	1.28470	+	0.640678i
$814$		0			0
$815$	5024.10			0.215934
$816$		0			0
$817$	−5965.38			−0.255449
$818$		0			0
$819$	29929.3	+	10593.5i	1.27694	+	0.451972i
$820$		0			0
$821$	−15056.8			−0.640056			−0.320028	−	0.947408i	$-0.603692\pi$
$821$	−15056.8			−0.640056			−0.320028	+	0.947408i	$0.603692\pi$
$822$		0			0
$823$	13824.4			0.585526			0.292763	−	0.956185i	$-0.405425\pi$
$823$	13824.4			0.585526			0.292763	+	0.956185i	$0.405425\pi$
$824$		0			0
$825$	−2222.07	−	36386.5i	−0.0937730	−	1.53553i
$826$		0			0
$827$	−7657.73			−0.321989			−0.160995	−	0.986955i	$-0.551470\pi$
$827$	−7657.73			−0.321989			−0.160995	+	0.986955i	$0.551470\pi$
$828$		0			0
$829$	−10488.5	+	18166.6i	−0.439422	+	0.761101i	−0.997645	−	0.0685901i	$-0.978150\pi$
$829$	−10488.5	+	18166.6i	−0.439422	+	0.761101i	0.558223	+	0.829691i	$0.311483\pi$
$830$		0			0
$831$	−10013.6	−	4993.76i	−0.418012	−	0.208462i
$832$		0			0
$833$	18507.9	−	2285.16i	0.769821	−	0.0950495i
$834$		0			0
$835$	−5149.32			−0.213413
$836$		0			0
$837$	7808.92	+	42199.3i	0.322480	+	1.74268i
$838$		0			0
$839$	11874.5	−	20567.2i	0.488620	−	0.846315i	−0.511294	−	0.859406i	$-0.670834\pi$
$839$	11874.5	−	20567.2i	0.488620	−	0.846315i	0.999914	+	0.0130911i	$0.00416713\pi$
$840$		0			0
$841$	−6895.97	−	11944.2i	−0.282749	−	0.489736i
$842$		0			0
$843$	297.853	+	4877.35i	0.0121692	+	0.199270i
$844$		0			0
$845$	1584.18	+	2743.88i	0.0644940	+	0.111707i
$846$		0			0
$847$	30494.3	−	20198.5i	1.23707	−	0.819397i
$848$		0			0
$849$	−29322.9	+	19404.4i	−1.18535	+	0.784403i
$850$		0			0
$851$	20625.9			0.830843
$852$		0			0
$853$	−23325.5	+	40401.0i	−0.936284	+	1.62169i	−0.163955	+	0.986468i	$0.552425\pi$
$853$	−23325.5	+	40401.0i	−0.936284	+	1.62169i	−0.772329	+	0.635223i	$0.780908\pi$
$854$		0			0
$855$	1117.48	−	2631.25i	0.0446983	−	0.105248i
$856$		0			0
$857$	−11472.3	−	19870.6i	−0.457276	−	0.792026i	0.541540	−	0.840675i	$-0.317842\pi$
$857$	−11472.3	−	19870.6i	−0.457276	−	0.792026i	−0.998816	+	0.0486496i	$0.984508\pi$
$858$		0			0
$859$	−8492.22	+	14709.0i	−0.337312	+	0.584241i	−0.983926	−	0.178576i	$-0.942851\pi$
$859$	−8492.22	+	14709.0i	−0.337312	+	0.584241i	0.646614	+	0.762817i	$0.276184\pi$
$860$		0			0
$861$	−2723.57	−	3612.47i	−0.107804	−	0.142988i
$862$		0			0
$863$	−17340.0	−	30033.7i	−0.683963	−	1.18466i	−0.973761	−	0.227571i	$-0.926922\pi$
$863$	−17340.0	−	30033.7i	−0.683963	−	1.18466i	0.289798	−	0.957088i	$-0.406412\pi$
$864$		0			0
$865$	−433.197	+	750.319i	−0.0170279	+	0.0294932i
$866$		0			0
$867$	−9100.28	−	4538.30i	−0.356472	−	0.177772i
$868$		0			0
$869$	32574.9	+	56421.4i	1.27161	+	2.20249i
$870$		0			0
$871$	32096.6	+	55592.9i	1.24862	+	2.16268i
$872$		0			0
$873$	−5451.11	−	7236.68i	−0.211331	−	0.280555i
$874$		0			0
$875$	−7073.44	−	3523.71i	−0.273287	−	0.136141i
$876$		0			0
$877$	19354.2	−	33522.5i	0.745205	−	1.29073i	−0.204894	−	0.978784i	$-0.565685\pi$
$877$	19354.2	−	33522.5i	0.745205	−	1.29073i	0.950099	−	0.311949i	$-0.100982\pi$
$878$		0			0
$879$	21218.3	+	10581.5i	0.814193	+	0.406037i
$880$		0			0
$881$	71.2129			0.00272330			0.00136165	−	0.999999i	$-0.499567\pi$
$881$	71.2129			0.00272330			0.00136165	+	0.999999i	$0.499567\pi$
$882$		0			0
$883$	2766.21			0.105425			0.0527125	−	0.998610i	$-0.483213\pi$
$883$	2766.21			0.105425			0.0527125	+	0.998610i	$0.483213\pi$
$884$		0			0
$885$	203.740	+	3336.25i	0.00773860	+	0.126720i
$886$		0			0
$887$	−16174.5	+	28015.1i	−0.612275	+	1.06049i	0.378581	+	0.925568i	$0.376412\pi$
$887$	−16174.5	+	28015.1i	−0.612275	+	1.06049i	−0.990856	+	0.134924i	$0.956921\pi$
$888$		0			0
$889$	−24328.1	−	12119.3i	−0.917815	−	0.457219i
$890$		0			0
$891$	11568.6	−	40287.7i	0.434976	−	1.51480i
$892$		0			0
$893$	19469.4	+	33722.0i	0.729583	+	1.26368i
$894$		0			0
$895$	2737.39	+	4741.30i	0.102236	+	0.177077i
$896$		0			0
$897$	22594.9	−	14952.2i	0.841051	−	0.556567i
$898$		0			0
$899$	−29885.8	+	51763.7i	−1.10873	+	1.92037i
$900$		0			0
$901$	−16573.6	−	28706.3i	−0.612815	−	1.06143i
$902$		0			0
$903$	−3657.49	+	8622.35i	−0.134788	+	0.317756i
$904$		0			0
$905$	745.181	−	1290.69i	0.0273709	−	0.0474078i
$906$		0			0
$907$	−9794.94	−	16965.3i	−0.358584	−	0.621086i	0.629140	−	0.777292i	$-0.283407\pi$
$907$	−9794.94	−	16965.3i	−0.358584	−	0.621086i	−0.987725	+	0.156206i	$0.950074\pi$
$908$		0			0
$909$	−2204.34	+	270.239i	−0.0804325	+	0.00986059i
$910$		0			0
$911$	11209.5	−	19415.4i	0.407670	−	0.706105i	−0.586958	−	0.809617i	$-0.699675\pi$
$911$	11209.5	−	19415.4i	0.407670	−	0.706105i	0.994628	+	0.103512i	$0.0330081\pi$
$912$		0			0
$913$	16117.3			0.584233
$914$		0			0
$915$	102.342	+	1675.85i	0.00369763	+	0.0605487i
$916$		0			0
$917$	−10321.7	+	6836.80i	−0.371705	+	0.246206i
$918$		0			0
$919$	−22376.6	−	38757.5i	−0.803196	−	1.39118i	−0.917502	−	0.397731i	$-0.869798\pi$
$919$	−22376.6	−	38757.5i	−0.803196	−	1.39118i	0.114306	−	0.993446i	$-0.463535\pi$
$920$		0			0
$921$	40620.7	−	26880.8i	1.45331	−	0.961729i
$922$		0			0
$923$	24524.4	+	42477.4i	0.874571	+	1.51480i
$924$		0			0
$925$	−15322.2	+	26538.8i	−0.544637	+	0.943340i
$926$		0			0
$927$	9606.88	+	12753.7i	0.340379	+	0.451874i
$928$		0			0
$929$	11702.7			0.413299			0.206649	−	0.978415i	$-0.433744\pi$
$929$	11702.7			0.413299			0.206649	+	0.978415i	$0.433744\pi$
$930$		0			0
$931$	−8201.50	+	19357.8i	−0.288715	+	0.681447i
$932$		0			0
$933$	15866.9	−	10499.9i	0.556762	−	0.368437i
$934$		0			0
$935$	2699.99	−	4676.52i	0.0944377	−	0.163571i
$936$		0			0
$937$	−34273.5			−1.19495			−0.597473	−	0.801889i	$-0.703829\pi$
$937$	−34273.5			−1.19495			−0.597473	+	0.801889i	$0.703829\pi$
$938$		0			0
$939$	23504.9	−	15554.4i	0.816882	−	0.540572i
$940$		0			0
$941$	−17899.0			−0.620074			−0.310037	−	0.950725i	$-0.600341\pi$
$941$	−17899.0			−0.620074			−0.310037	+	0.950725i	$0.600341\pi$
$942$		0			0
$943$	−3860.89			−0.133327
$944$		0			0
$945$	−3118.05	−	3228.48i	−0.107334	−	0.111135i
$946$		0			0
$947$	15705.8			0.538934			0.269467	−	0.963010i	$-0.413152\pi$
$947$	15705.8			0.538934			0.269467	+	0.963010i	$0.413152\pi$
$948$		0			0
$949$	−17655.0			−0.603903
$950$		0			0
$951$	20824.8	−	13780.9i	0.710086	−	0.469900i
$952$		0			0
$953$	−40625.1			−1.38088			−0.690438	−	0.723391i	$-0.742582\pi$
$953$	−40625.1			−1.38088			−0.690438	+	0.723391i	$0.742582\pi$
$954$		0			0
$955$	−1616.44	+	2799.76i	−0.0547716	+	0.0948672i
$956$		0			0
$957$	48684.2	−	32216.8i	1.64445	−	1.08822i
$958$		0			0
$959$	−439.417	−	7144.85i	−0.0147962	−	0.240583i
$960$		0			0
$961$	63780.2			2.14092
$962$		0			0
$963$	30881.3	−	3785.88i	1.03337	−	0.126686i
$964$		0			0
$965$	2684.78	−	4650.18i	0.0895609	−	0.155124i
$966$		0			0
$967$	11516.0	+	19946.3i	0.382968	+	0.663320i	0.991485	−	0.130221i	$-0.0415687\pi$
$967$	11516.0	+	19946.3i	0.382968	+	0.663320i	−0.608517	+	0.793541i	$0.708235\pi$
$968$		0			0
$969$	−14440.3	+	9555.88i	−0.478730	+	0.316800i
$970$		0			0
$971$	19333.5	+	33486.6i	0.638972	+	1.10673i	0.985659	+	0.168751i	$0.0539735\pi$
$971$	19333.5	+	33486.6i	0.638972	+	1.10673i	−0.346686	+	0.937981i	$0.612693\pi$
$972$		0			0
$973$	865.293	+	14069.5i	0.0285098	+	0.463564i
$974$		0			0
$975$	2453.72	+	40179.7i	0.0805968	+	1.31977i
$976$		0			0
$977$	−465.560			−0.0152452			−0.00762262	−	0.999971i	$-0.502426\pi$
$977$	−465.560			−0.0152452			−0.00762262	+	0.999971i	$0.502426\pi$
$978$		0			0
$979$	21193.8	−	36708.7i	0.691885	−	1.19838i
$980$		0			0
$981$	11523.2	+	15297.8i	0.375035	+	0.497882i
$982$		0			0
$983$	−6633.44	−	11489.5i	−0.215233	−	0.372794i	0.738112	−	0.674678i	$-0.235718\pi$
$983$	−6633.44	−	11489.5i	−0.215233	−	0.372794i	−0.953345	+	0.301884i	$0.902384\pi$
$984$		0			0
$985$	4541.45	−	7866.02i	0.146906	−	0.254449i
$986$		0			0
$987$	60678.7	−	7465.43i	1.95686	−	0.240757i
$988$		0			0
$989$	3996.46	+	6922.08i	0.128494	+	0.222557i
$990$		0			0
$991$	1082.34	−	1874.67i	0.0346940	−	0.0600918i	−0.848157	−	0.529745i	$-0.822288\pi$
$991$	1082.34	−	1874.67i	0.0346940	−	0.0600918i	0.882851	+	0.469653i	$0.155621\pi$
$992$		0			0
$993$	1408.45	−	932.043i	0.0450109	−	0.0297860i
$994$		0			0
$995$	1346.57	+	2332.33i	0.0429038	+	0.0743115i
$996$		0			0
$997$	4091.16	+	7086.09i	0.129958	+	0.225094i	0.923660	−	0.383213i	$-0.125182\pi$
$997$	4091.16	+	7086.09i	0.129958	+	0.225094i	−0.793702	+	0.608307i	$0.791849\pi$
$998$		0			0
$999$	−26799.6	+	22876.0i	−0.848751	+	0.724489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.5	✓	48
3.2	odd	2		756.4.i.a.613.13		48
7.2	even	3		252.4.l.a.205.11	yes	48
9.4	even	3		252.4.l.a.193.11	yes	48
9.5	odd	6		756.4.l.a.361.12		48
21.2	odd	6		756.4.l.a.289.12		48
63.23	odd	6		756.4.i.a.37.13		48
63.58	even	3	inner	252.4.i.a.121.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.5	✓	48	1.1	even	1	trivial
252.4.i.a.121.5	yes	48	63.58	even	3	inner
252.4.l.a.193.11	yes	48	9.4	even	3
252.4.l.a.205.11	yes	48	7.2	even	3
756.4.i.a.37.13		48	63.23	odd	6
756.4.i.a.613.13		48	3.2	odd	2
756.4.l.a.289.12		48	21.2	odd	6
756.4.l.a.361.12		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.33327 + 2.86754i) q^{3} +(0.863703 - 1.49598i) q^{5} +(-16.5772 - 8.25811i) q^{7} +(10.5544 - 24.8517i) q^{9} +O(q^{10})\)	\(q+(-4.33327 + 2.86754i) q^{3} +(0.863703 - 1.49598i) q^{5} +(-16.5772 - 8.25811i) q^{7} +(10.5544 - 24.8517i) q^{9} +(28.7488 + 49.7944i) q^{11} +(-31.7458 - 54.9853i) q^{13} +(0.547124 + 8.95917i) q^{15} +(27.1843 - 47.0846i) q^{17} +(30.6466 + 53.0815i) q^{19} +(95.5139 - 11.7513i) q^{21} +(41.0630 - 71.1231i) q^{23} +(61.0080 + 105.669i) q^{25} +(25.5282 + 137.954i) q^{27} +(-97.6997 + 169.221i) q^{29} +305.894 q^{31} +(-267.364 - 133.334i) q^{33} +(-26.6717 + 17.6666i) q^{35} +(125.575 + 217.502i) q^{37} +(295.235 + 147.233i) q^{39} +(-23.5059 - 40.7134i) q^{41} +(-48.6627 + 84.2862i) q^{43} +(-28.0616 - 37.2536i) q^{45} +635.287 q^{47} +(206.607 + 273.793i) q^{49} +(17.2203 + 281.982i) q^{51} +(304.837 - 527.993i) q^{53} +99.3217 q^{55} +(-285.013 - 142.136i) q^{57} +372.384 q^{59} +187.055 q^{61} +(-380.190 + 324.812i) q^{63} -109.676 q^{65} -1011.05 q^{67} +(26.0119 + 425.945i) q^{69} -772.524 q^{71} +(139.034 - 240.814i) q^{73} +(-567.375 - 282.949i) q^{75} +(-65.3674 - 1062.86i) q^{77} +1133.09 q^{79} +(-506.210 - 524.588i) q^{81} +(140.156 - 242.758i) q^{83} +(-46.9584 - 81.3343i) q^{85} +(-61.8892 - 1013.44i) q^{87} +(-368.603 - 638.439i) q^{89} +(72.1817 + 1173.66i) q^{91} +(-1325.52 + 877.164i) q^{93} +105.878 q^{95} +(167.778 - 290.601i) q^{97} +(1540.90 - 188.906i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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