LMFDB - Embedded newform 252.4.w.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(5,252)]

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, 5, 5]))

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

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

chi := DirichletCharacter("252.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.w (of order $6$, 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 $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.569877 + 5.16481i) q^{3} +(8.28296 + 14.3465i) q^{5} +(-3.56863 + 18.1732i) q^{7} +(-26.3505 + 5.88661i) q^{9} +O(q^{10})$	\(q+(0.569877 + 5.16481i) q^{3} +(8.28296 + 14.3465i) q^{5} +(-3.56863 + 18.1732i) q^{7} +(-26.3505 + 5.88661i) q^{9} +(21.0059 + 12.1278i) q^{11} +(21.6559 + 12.5031i) q^{13} +(-69.3767 + 50.9556i) q^{15} +(-38.0407 - 65.8884i) q^{17} +(22.4541 + 12.9639i) q^{19} +(-95.8947 - 8.07482i) q^{21} +(59.2174 - 34.1892i) q^{23} +(-74.7148 + 129.410i) q^{25} +(-45.4197 - 132.741i) q^{27} +(72.7435 - 41.9985i) q^{29} -174.443i q^{31} +(-50.6668 + 115.403i) q^{33} +(-290.281 + 99.3304i) q^{35} +(2.25533 - 3.90635i) q^{37} +(-52.2347 + 118.974i) q^{39} +(-176.556 + 305.803i) q^{41} +(210.288 + 364.230i) q^{43} +(-302.712 - 329.279i) q^{45} -526.888 q^{47} +(-317.530 - 129.707i) q^{49} +(318.622 - 234.021i) q^{51} +(-263.120 + 151.913i) q^{53} +401.815i q^{55} +(-54.1600 + 123.359i) q^{57} +611.471 q^{59} -698.018i q^{61} +(-12.9432 - 499.879i) q^{63} +414.249i q^{65} +1037.61 q^{67} +(210.327 + 286.363i) q^{69} +486.628i q^{71} +(-397.291 + 229.376i) q^{73} +(-710.955 - 312.140i) q^{75} +(-295.363 + 338.465i) q^{77} -5.23947 q^{79} +(659.696 - 310.230i) q^{81} +(-69.2400 - 119.927i) q^{83} +(630.179 - 1091.50i) q^{85} +(258.369 + 351.772i) q^{87} +(-610.904 + 1058.12i) q^{89} +(-304.503 + 348.939i) q^{91} +(900.964 - 99.4109i) q^{93} +429.518i q^{95} +(793.532 - 458.146i) q^{97} +(-624.907 - 195.919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 12 * q^9	$ 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.569877	+	5.16481i	0.109673	+	0.993968i
$3$	0.569877	+	5.16481i	0.109673	+	0.993968i
$4$		0			0
$5$	8.28296	+	14.3465i	0.740850	+	1.28319i	0.952109	+	0.305760i	$0.0989105\pi$
$5$	8.28296	+	14.3465i	0.740850	+	1.28319i	−0.211258	+	0.977430i	$0.567756\pi$
$6$		0			0
$7$	−3.56863	+	18.1732i	−0.192688	+	0.981260i
$7$	−3.56863	+	18.1732i	−0.192688	+	0.981260i
$8$		0			0
$9$	−26.3505	+	5.88661i	−0.975944	+	0.218022i
$10$		0			0
$11$	21.0059	+	12.1278i	0.575774	+	0.332424i	0.759452	−	0.650563i	$-0.225467\pi$
$11$	21.0059	+	12.1278i	0.575774	+	0.332424i	−0.183678	+	0.982986i	$0.558800\pi$
$12$		0			0
$13$	21.6559	+	12.5031i	0.462021	+	0.266748i	0.712894	−	0.701272i	$-0.247384\pi$
$13$	21.6559	+	12.5031i	0.462021	+	0.266748i	−0.250873	+	0.968020i	$0.580718\pi$
$14$		0			0
$15$	−69.3767	+	50.9556i	−1.19420	+	0.877112i
$16$		0			0
$17$	−38.0407	−	65.8884i	−0.542719	−	0.940017i	−0.998747	−	0.0500511i	$-0.984062\pi$
$17$	−38.0407	−	65.8884i	−0.542719	−	0.940017i	0.456028	−	0.889966i	$-0.349272\pi$
$18$		0			0
$19$	22.4541	+	12.9639i	0.271123	+	0.156533i	0.629398	−	0.777083i	$-0.283302\pi$
$19$	22.4541	+	12.9639i	0.271123	+	0.156533i	−0.358275	+	0.933616i	$0.616635\pi$
$20$		0			0
$21$	−95.8947	−	8.07482i	−0.996473	−	0.0839082i
$22$		0			0
$23$	59.2174	−	34.1892i	0.536856	−	0.309954i	−0.206948	−	0.978352i	$-0.566353\pi$
$23$	59.2174	−	34.1892i	0.536856	−	0.309954i	0.743804	+	0.668398i	$0.233020\pi$
$24$		0			0
$25$	−74.7148	+	129.410i	−0.597718	+	1.03528i
$26$		0			0
$27$	−45.4197	−	132.741i	−0.323742	−	0.946145i
$28$		0			0
$29$	72.7435	−	41.9985i	0.465797	−	0.268928i	−0.248682	−	0.968585i	$-0.579997\pi$
$29$	72.7435	−	41.9985i	0.465797	−	0.268928i	0.714479	+	0.699657i	$0.246664\pi$
$30$		0			0
$31$		−	174.443i		−	1.01067i	−0.862922	−	0.505336i	$-0.831368\pi$
$31$		−	174.443i		−	1.01067i	0.862922	−	0.505336i	$-0.168632\pi$
$32$		0			0
$33$	−50.6668	+	115.403i	−0.267271	+	0.608759i
$34$		0			0
$35$	−290.281	+	99.3304i	−1.40190	+	0.479711i
$36$		0			0
$37$	2.25533	−	3.90635i	0.0100209	−	0.0173568i	−0.860971	−	0.508653i	$-0.830144\pi$
$37$	2.25533	−	3.90635i	0.0100209	−	0.0173568i	0.870992	+	0.491297i	$0.163477\pi$
$38$		0			0
$39$	−52.2347	+	118.974i	−0.214468	+	0.488489i
$40$		0			0
$41$	−176.556	+	305.803i	−0.672520	+	1.16484i	0.304667	+	0.952459i	$0.401455\pi$
$41$	−176.556	+	305.803i	−0.672520	+	1.16484i	−0.977187	+	0.212380i	$0.931878\pi$
$42$		0			0
$43$	210.288	+	364.230i	0.745783	+	1.29173i	0.949828	+	0.312773i	$0.101258\pi$
$43$	210.288	+	364.230i	0.745783	+	1.29173i	−0.204044	+	0.978962i	$0.565409\pi$
$44$		0			0
$45$	−302.712	−	329.279i	−1.00279	−	1.09080i
$46$		0			0
$47$	−526.888			−1.63520			−0.817601	−	0.575785i	$-0.804696\pi$
$47$	−526.888			−1.63520			−0.817601	+	0.575785i	$0.804696\pi$
$48$		0			0
$49$	−317.530	−	129.707i	−0.925743	−	0.378154i
$50$		0			0
$51$	318.622	−	234.021i	0.874825	−	0.642539i
$52$		0			0
$53$	−263.120	+	151.913i	−0.681931	+	0.393713i	−0.800582	−	0.599223i	$-0.795476\pi$
$53$	−263.120	+	151.913i	−0.681931	+	0.393713i	0.118651	+	0.992936i	$0.462143\pi$
$54$		0			0
$55$			401.815i			0.985104i
$56$		0			0
$57$	−54.1600	+	123.359i	−0.125854	+	0.286655i
$58$		0			0
$59$	611.471			1.34927			0.674633	−	0.738153i	$-0.264302\pi$
$59$	611.471			1.34927			0.674633	+	0.738153i	$0.264302\pi$
$60$		0			0
$61$		−	698.018i		−	1.46512i	−0.680705	−	0.732558i	$-0.738326\pi$
$61$		−	698.018i		−	1.46512i	0.680705	−	0.732558i	$-0.261674\pi$
$62$		0			0
$63$	−12.9432	−	499.879i	−0.0258841	−	0.999665i
$64$		0			0
$65$			414.249i			0.790481i
$66$		0			0
$67$	1037.61			1.89200			0.946001	−	0.324163i	$-0.105083\pi$
$67$	1037.61			1.89200			0.946001	+	0.324163i	$0.105083\pi$
$68$		0			0
$69$	210.327	+	286.363i	0.366962	+	0.499624i
$70$		0			0
$71$			486.628i			0.813410i	0.913560	+	0.406705i	$0.133322\pi$
$71$			486.628i			0.813410i	−0.913560	+	0.406705i	$0.866678\pi$
$72$		0			0
$73$	−397.291	+	229.376i	−0.636978	+	0.367759i	−0.783449	−	0.621455i	$-0.786542\pi$
$73$	−397.291	+	229.376i	−0.636978	+	0.367759i	0.146472	+	0.989215i	$0.453208\pi$
$74$		0			0
$75$	−710.955	−	312.140i	−1.09459	−	0.480571i
$76$		0			0
$77$	−295.363	+	338.465i	−0.437139	+	0.500930i
$78$		0			0
$79$	−5.23947			−0.00746185			−0.00373093	−	0.999993i	$-0.501188\pi$
$79$	−5.23947			−0.00746185			−0.00373093	+	0.999993i	$0.501188\pi$
$80$		0			0
$81$	659.696	−	310.230i	0.904932	−	0.425555i
$82$		0			0
$83$	−69.2400	−	119.927i	−0.0915671	−	0.158599i	0.816604	−	0.577199i	$-0.195854\pi$
$83$	−69.2400	−	119.927i	−0.0915671	−	0.158599i	−0.908171	+	0.418600i	$0.862521\pi$
$84$		0			0
$85$	630.179	−	1091.50i	0.804147	−	1.39282i
$86$		0			0
$87$	258.369	+	351.772i	0.318391	+	0.433493i
$88$		0			0
$89$	−610.904	+	1058.12i	−0.727592	+	1.26023i	0.230307	+	0.973118i	$0.426027\pi$
$89$	−610.904	+	1058.12i	−0.727592	+	1.26023i	−0.957898	+	0.287108i	$0.907306\pi$
$90$		0			0
$91$	−304.503	+	348.939i	−0.350775	+	0.401964i
$92$		0			0
$93$	900.964	−	99.4109i	1.00458	−	0.110843i
$94$		0			0
$95$			429.518i			0.463869i
$96$		0			0
$97$	793.532	−	458.146i	0.830629	−	0.479564i	−0.0234391	−	0.999725i	$-0.507462\pi$
$97$	793.532	−	458.146i	0.830629	−	0.479564i	0.854068	+	0.520162i	$0.174128\pi$
$98$		0			0
$99$	−624.907	−	195.919i	−0.634399	−	0.198895i
$100$		0			0
$101$	295.074	−	511.084i	0.290703	−	0.503512i	−0.683273	−	0.730163i	$-0.739444\pi$
$101$	295.074	−	511.084i	0.290703	−	0.503512i	0.973976	+	0.226651i	$0.0727776\pi$
$102$		0			0
$103$	1313.11	−	758.123i	1.25616	−	0.725244i	0.283834	−	0.958874i	$-0.408394\pi$
$103$	1313.11	−	758.123i	1.25616	−	0.725244i	0.972326	+	0.233630i	$0.0750603\pi$
$104$		0			0
$105$	−678.446	−	1442.64i	−0.630568	−	1.34083i
$106$		0			0
$107$	615.020	+	355.082i	0.555665	+	0.320813i	0.751404	−	0.659843i	$-0.229377\pi$
$107$	615.020	+	355.082i	0.555665	+	0.320813i	−0.195739	+	0.980656i	$0.562710\pi$
$108$		0			0
$109$	185.712	+	321.663i	0.163193	+	0.282658i	0.936012	−	0.351968i	$-0.114487\pi$
$109$	185.712	+	321.663i	0.163193	+	0.282658i	−0.772819	+	0.634626i	$0.781154\pi$
$110$		0			0
$111$	21.4608	+	9.42222i	0.0183511	+	0.00805692i
$112$		0			0
$113$	689.320	+	397.979i	0.573856	+	0.331316i	0.758688	−	0.651454i	$-0.225841\pi$
$113$	689.320	+	397.979i	0.573856	+	0.331316i	−0.184832	+	0.982770i	$0.559174\pi$
$114$		0			0
$115$	980.990	+	566.375i	0.795459	+	0.459259i
$116$		0			0
$117$	−644.245	−	201.982i	−0.509064	−	0.159600i
$118$		0			0
$119$	1333.16	−	456.189i	1.02698	−	0.351418i
$120$		0			0
$121$	−371.335	−	643.170i	−0.278989	−	0.483223i
$122$		0			0
$123$	−1680.03	−	737.605i	−1.23157	−	0.540712i
$124$		0			0
$125$	−404.698			−0.289578
$126$		0			0
$127$	1811.93			1.26600			0.633002	−	0.774150i	$-0.281822\pi$
$127$	1811.93			1.26600			0.633002	+	0.774150i	$0.281822\pi$
$128$		0			0
$129$	−1761.34	+	1293.67i	−1.20215	+	0.882953i
$130$		0			0
$131$	−1359.00	−	2353.86i	−0.906386	−	1.56991i	−0.819045	−	0.573729i	$-0.805496\pi$
$131$	−1359.00	−	2353.86i	−0.906386	−	1.56991i	−0.0873411	−	0.996178i	$-0.527837\pi$
$132$		0			0
$133$	−315.726	+	361.800i	−0.205841	+	0.235880i
$134$		0			0
$135$	1528.15	−	1751.10i	0.974240	−	1.11637i
$136$		0			0
$137$	−294.385	−	169.963i	−0.183584	−	0.105992i	0.405392	−	0.914143i	$-0.367135\pi$
$137$	−294.385	−	169.963i	−0.183584	−	0.105992i	−0.588975	+	0.808151i	$0.700469\pi$
$138$		0			0
$139$	2496.59	+	1441.41i	1.52344	+	0.879558i	0.999615	+	0.0277314i	$0.00882830\pi$
$139$	2496.59	+	1441.41i	1.52344	+	0.879558i	0.523824	+	0.851827i	$0.324505\pi$
$140$		0			0
$141$	−300.261	−	2721.27i	−0.179337	−	1.62534i
$142$		0			0
$143$	303.268	+	525.276i	0.177347	+	0.307173i
$144$		0			0
$145$	1205.06	+	695.743i	0.690172	+	0.398471i
$146$		0			0
$147$	488.958	−	1713.90i	0.274344	−	0.961632i
$148$		0			0
$149$	−1748.78	+	1009.66i	−0.961515	+	0.555131i	−0.896639	−	0.442762i	$-0.853999\pi$
$149$	−1748.78	+	1009.66i	−0.961515	+	0.555131i	−0.0648760	+	0.997893i	$0.520665\pi$
$150$		0			0
$151$	−137.925	+	238.892i	−0.0743321	+	0.128747i	−0.900796	−	0.434243i	$-0.857016\pi$
$151$	−137.925	+	238.892i	−0.0743321	+	0.128747i	0.826464	+	0.562990i	$0.190349\pi$
$152$		0			0
$153$	1390.25	+	1512.26i	0.734608	+	0.799078i
$154$		0			0
$155$	2502.65	−	1444.90i	1.29689	−	0.748757i
$156$		0			0
$157$			3568.45i			1.81397i	0.421162	+	0.906985i	$0.361622\pi$
$157$			3568.45i			1.81397i	−0.421162	+	0.906985i	$0.638378\pi$
$158$		0			0
$159$	−934.545	−	1272.39i	−0.466127	−	0.634638i
$160$		0			0
$161$	410.001	+	1198.18i	0.200700	+	0.586519i
$162$		0			0
$163$	1307.22	−	2264.16i	0.628153	−	1.08799i	−0.359769	−	0.933042i	$-0.617144\pi$
$163$	1307.22	−	2264.16i	0.628153	−	1.08799i	0.987922	−	0.154952i	$-0.0495223\pi$
$164$		0			0
$165$	−2075.30	+	228.985i	−0.979162	+	0.108039i
$166$		0			0
$167$	−296.022	+	512.725i	−0.137167	+	0.237580i	−0.926423	−	0.376484i	$-0.877133\pi$
$167$	−296.022	+	512.725i	−0.137167	+	0.237580i	0.789256	+	0.614064i	$0.210466\pi$
$168$		0			0
$169$	−785.847	−	1361.13i	−0.357691	−	0.619539i
$170$		0			0
$171$	−667.991	−	209.426i	−0.298728	−	0.0936563i
$172$		0			0
$173$	−1840.30			−0.808761			−0.404381	−	0.914591i	$-0.632513\pi$
$173$	−1840.30			−0.808761			−0.404381	+	0.914591i	$0.632513\pi$
$174$		0			0
$175$	−2085.16	−	1819.62i	−0.900704	−	0.786003i
$176$		0			0
$177$	348.463	+	3158.13i	0.147978	+	1.34113i
$178$		0			0
$179$	−3103.60	+	1791.87i	−1.29595	+	0.748214i	−0.979701	−	0.200464i	$-0.935755\pi$
$179$	−3103.60	+	1791.87i	−1.29595	+	0.748214i	−0.316244	+	0.948678i	$0.602422\pi$
$180$		0			0
$181$			3358.77i			1.37931i	0.724137	+	0.689656i	$0.242238\pi$
$181$			3358.77i			1.37931i	−0.724137	+	0.689656i	$0.757762\pi$
$182$		0			0
$183$	3605.13	−	397.784i	1.45628	−	0.160683i
$184$		0			0
$185$	74.7233			0.0296960
$186$		0			0
$187$		−	1845.39i		−	0.721650i
$188$		0			0
$189$	2574.41	−	351.719i	0.990796	−	0.135364i
$190$		0			0
$191$			2838.61i			1.07536i	0.843148	+	0.537682i	$0.180700\pi$
$191$			2838.61i			1.07536i	−0.843148	+	0.537682i	$0.819300\pi$
$192$		0			0
$193$	−100.042			−0.0373119			−0.0186560	−	0.999826i	$-0.505939\pi$
$193$	−100.042			−0.0373119			−0.0186560	+	0.999826i	$0.505939\pi$
$194$		0			0
$195$	−2139.52	+	236.071i	−0.785713	+	0.0866943i
$196$		0			0
$197$			693.739i			0.250898i	0.992100	+	0.125449i	$0.0400371\pi$
$197$			693.739i			0.250898i	−0.992100	+	0.125449i	$0.959963\pi$
$198$		0			0
$199$	−468.970	+	270.760i	−0.167057	+	0.0964506i	−0.581198	−	0.813763i	$-0.697416\pi$
$199$	−468.970	+	270.760i	−0.167057	+	0.0964506i	0.414140	+	0.910213i	$0.364082\pi$
$200$		0			0
$201$	591.309	+	5359.05i	0.207501	+	1.88059i
$202$		0			0
$203$	503.651	+	1471.86i	0.174135	+	0.508887i
$204$		0			0
$205$	−5849.61			−1.99295
$206$		0			0
$207$	−1359.15	+	1249.49i	−0.456364	+	0.419544i
$208$		0			0
$209$	314.446	+	544.637i	0.104070	+	0.180255i
$210$		0			0
$211$	−58.9096	+	102.034i	−0.0192204	+	0.0332907i	−0.875476	−	0.483262i	$-0.839452\pi$
$211$	−58.9096	+	102.034i	−0.0192204	+	0.0332907i	0.856255	+	0.516553i	$0.172785\pi$
$212$		0			0
$213$	−2513.34	+	277.318i	−0.808503	+	0.0892090i
$214$		0			0
$215$	−3483.62	+	6033.81i	−1.10503	+	1.91396i
$216$		0			0
$217$	3170.18	+	622.522i	0.991733	+	0.194745i
$218$		0			0
$219$	−1411.09	−	1921.22i	−0.435400	−	0.592802i
$220$		0			0
$221$		−	1902.50i		−	0.579077i
$222$		0			0
$223$	1479.94	−	854.442i	0.444412	−	0.256581i	−0.261055	−	0.965324i	$-0.584070\pi$
$223$	1479.94	−	854.442i	0.444412	−	0.256581i	0.705467	+	0.708742i	$0.250737\pi$
$224$		0			0
$225$	1206.99	−	3849.83i	0.357625	−	1.14069i
$226$		0			0
$227$	1469.35	−	2545.00i	0.429623	−	0.744129i	−0.567217	−	0.823569i	$-0.691980\pi$
$227$	1469.35	−	2545.00i	0.429623	−	0.744129i	0.996840	+	0.0794396i	$0.0253131\pi$
$228$		0			0
$229$	−1787.97	+	1032.28i	−0.515949	+	0.297883i	−0.735276	−	0.677768i	$-0.762947\pi$
$229$	−1787.97	+	1032.28i	−0.515949	+	0.297883i	0.219327	+	0.975651i	$0.429614\pi$
$230$		0			0
$231$	−1916.43	−	1332.61i	−0.545851	−	0.379563i
$232$		0			0
$233$	−462.421	−	266.979i	−0.130018	−	0.0750659i	0.433580	−	0.901115i	$-0.357250\pi$
$233$	−462.421	−	266.979i	−0.130018	−	0.0750659i	−0.563598	+	0.826049i	$0.690583\pi$
$234$		0			0
$235$	−4364.19	−	7559.00i	−1.21144	−	2.09828i
$236$		0			0
$237$	−2.98585	−	27.0608i	−0.000818362	−	0.00741684i
$238$		0			0
$239$	−1393.03	−	804.268i	−0.377020	−	0.217673i	0.299501	−	0.954096i	$-0.403180\pi$
$239$	−1393.03	−	804.268i	−0.377020	−	0.217673i	−0.676521	+	0.736423i	$0.736513\pi$
$240$		0			0
$241$	−3534.34	−	2040.55i	−0.944675	−	0.545409i	−0.0532525	−	0.998581i	$-0.516959\pi$
$241$	−3534.34	−	2040.55i	−0.944675	−	0.545409i	−0.891423	+	0.453173i	$0.850292\pi$
$242$		0			0
$243$	1978.22	+	3230.41i	0.522235	+	0.852802i
$244$		0			0
$245$	−769.245	−	5629.80i	−0.200593	−	1.46806i
$246$		0			0
$247$	324.177	+	561.491i	0.0835096	+	0.144643i
$248$		0			0
$249$	579.942	−	425.955i	0.147600	−	0.108409i
$250$		0			0
$251$	3954.86			0.994537			0.497269	−	0.867597i	$-0.334336\pi$
$251$	3954.86			0.994537			0.497269	+	0.867597i	$0.334336\pi$
$252$		0			0
$253$	1658.55			0.412144
$254$		0			0
$255$	5996.52	+	2632.73i	1.47261	+	0.646541i
$256$		0			0
$257$	−1646.27	−	2851.42i	−0.399577	−	0.692088i	0.594096	−	0.804394i	$-0.297510\pi$
$257$	−1646.27	−	2851.42i	−0.399577	−	0.692088i	−0.993674	+	0.112306i	$0.964176\pi$
$258$		0			0
$259$	62.9424	+	54.9269i	0.0151006	+	0.0131776i
$260$		0			0
$261$	−1669.60	+	1534.89i	−0.395960	+	0.364013i
$262$		0			0
$263$	3512.67	+	2028.04i	0.823576	+	0.475492i	0.851648	−	0.524114i	$-0.175603\pi$
$263$	3512.67	+	2028.04i	0.823576	+	0.475492i	−0.0280719	+	0.999606i	$0.508937\pi$
$264$		0			0
$265$	−4358.83	−	2516.57i	−1.01042	−	0.583365i
$266$		0			0
$267$	−5813.11	−	2552.20i	−1.33242	−	0.584990i
$268$		0			0
$269$	343.142	+	594.339i	0.0777759	+	0.134712i	0.902290	−	0.431130i	$-0.141885\pi$
$269$	343.142	+	594.339i	0.0777759	+	0.134712i	−0.824514	+	0.565841i	$0.808551\pi$
$270$		0			0
$271$	−3127.32	−	1805.56i	−0.701000	−	0.404723i	0.106720	−	0.994289i	$-0.465965\pi$
$271$	−3127.32	−	1805.56i	−0.701000	−	0.404723i	−0.807720	+	0.589566i	$0.799299\pi$
$272$		0			0
$273$	−1975.73	−	1373.85i	−0.438010	−	0.304575i
$274$		0			0
$275$	−3138.90	+	1812.25i	−0.688302	+	0.397391i
$276$		0			0
$277$	−22.4974	+	38.9667i	−0.00487993	+	0.00845228i	−0.868455	−	0.495768i	$-0.834887\pi$
$277$	−22.4974	+	38.9667i	−0.00487993	+	0.00845228i	0.863575	+	0.504220i	$0.168220\pi$
$278$		0			0
$279$	1026.88	+	4596.65i	0.220349	+	0.986360i
$280$		0			0
$281$	2639.36	−	1523.83i	0.560323	−	0.323503i	−0.192952	−	0.981208i	$-0.561806\pi$
$281$	2639.36	−	1523.83i	0.560323	−	0.323503i	0.753275	+	0.657705i	$0.228473\pi$
$282$		0			0
$283$			4584.25i			0.962917i	0.876469	+	0.481459i	$0.159893\pi$
$283$			4584.25i			0.962917i	−0.876469	+	0.481459i	$0.840107\pi$
$284$		0			0
$285$	−2218.38	+	244.772i	−0.461071	+	0.0508739i
$286$		0			0
$287$	−4927.36	−	4299.88i	−1.01342	−	0.884368i
$288$		0			0
$289$	−437.687	+	758.096i	−0.0890875	+	0.154304i
$290$		0			0
$291$	2818.45	+	3837.35i	0.567768	+	0.773023i
$292$		0			0
$293$	3189.17	−	5523.81i	0.635882	−	1.10138i	−0.350445	−	0.936583i	$-0.613970\pi$
$293$	3189.17	−	5523.81i	0.635882	−	1.10138i	0.986327	−	0.164797i	$-0.0526970\pi$
$294$		0			0
$295$	5064.79	+	8772.47i	0.999605	+	1.73137i
$296$		0			0
$297$	655.764	−	3339.17i	0.128119	−	0.652386i
$298$		0			0
$299$	1709.88			0.330718
$300$		0			0
$301$	−7369.67	+	2521.81i	−1.41123	+	0.482906i
$302$		0			0
$303$	2807.80	+	1232.75i	0.532357	+	0.233728i
$304$		0			0
$305$	10014.1	−	5781.65i	1.88002	−	1.08543i
$306$		0			0
$307$			7269.83i			1.35150i	0.737130	+	0.675751i	$0.236180\pi$
$307$			7269.83i			1.35150i	−0.737130	+	0.675751i	$0.763820\pi$
$308$		0			0
$309$	4663.87	+	6349.92i	0.858636	+	1.16904i
$310$		0			0
$311$	−7861.00			−1.43330			−0.716650	−	0.697433i	$-0.754325\pi$
$311$	−7861.00			−1.43330			−0.716650	+	0.697433i	$0.754325\pi$
$312$		0			0
$313$			9289.73i			1.67759i	0.544445	+	0.838796i	$0.316740\pi$
$313$			9289.73i			1.67759i	−0.544445	+	0.838796i	$0.683260\pi$
$314$		0			0
$315$	7064.31	−	4326.17i	1.26358	−	0.773816i
$316$		0			0
$317$			3993.82i			0.707620i	0.935317	+	0.353810i	$0.115114\pi$
$317$			3993.82i			0.707620i	−0.935317	+	0.353810i	$0.884886\pi$
$318$		0			0
$319$	2037.39			0.357592
$320$		0			0
$321$	−1483.44	+	3378.81i	−0.257937	+	0.587498i
$322$		0			0
$323$		−	1972.62i		−	0.339813i
$324$		0			0
$325$	−3236.04	+	1868.33i	−0.552317	+	0.318880i
$326$		0			0
$327$	−1555.49	+	1142.48i	−0.263055	+	0.193208i
$328$		0			0
$329$	1880.27	−	9575.23i	0.315084	−	1.60456i
$330$		0			0
$331$	7236.97			1.20175			0.600876	−	0.799342i	$-0.294818\pi$
$331$	7236.97			1.20175			0.600876	+	0.799342i	$0.294818\pi$
$332$		0			0
$333$	−36.4340	+	116.211i	−0.00599570	+	0.0191240i
$334$		0			0
$335$	8594.47	+	14886.1i	1.40169	+	2.42780i
$336$		0			0
$337$	4995.54	−	8652.52i	0.807490	−	1.39861i	−0.107107	−	0.994248i	$-0.534159\pi$
$337$	4995.54	−	8652.52i	0.807490	−	1.39861i	0.914597	−	0.404367i	$-0.132508\pi$
$338$		0			0
$339$	−1662.66	+	3787.00i	−0.266381	+	0.606731i
$340$		0			0
$341$	2115.60	−	3664.33i	0.335971	−	0.581920i
$342$		0			0
$343$	3490.33	−	5307.65i	0.549447	−	0.835528i
$344$		0			0
$345$	−2366.17	+	5389.39i	−0.369248	+	0.841029i
$346$		0			0
$347$		−	7538.38i		−	1.16623i	−0.812390	−	0.583115i	$-0.801834\pi$
$347$		−	7538.38i		−	1.16623i	0.812390	−	0.583115i	$-0.198166\pi$
$348$		0			0
$349$	10542.5	−	6086.71i	1.61698	−	0.933565i	0.629287	−	0.777173i	$-0.283347\pi$
$349$	10542.5	−	6086.71i	1.61698	−	0.933565i	0.987695	−	0.156392i	$-0.0499864\pi$
$350$		0			0
$351$	676.056	−	3442.51i	0.102807	−	0.523497i
$352$		0			0
$353$	5800.04	−	10046.0i	0.874518	−	1.51471i	0.0172420	−	0.999851i	$-0.494511\pi$
$353$	5800.04	−	10046.0i	0.874518	−	1.51471i	0.857276	−	0.514858i	$-0.172155\pi$
$354$		0			0
$355$	−6981.41	+	4030.72i	−1.04376	+	0.602615i
$356$		0			0
$357$	3115.86	+	6625.52i	0.461930	+	0.982240i
$358$		0			0
$359$	4778.44	+	2758.83i	0.702496	+	0.405586i	0.808276	−	0.588803i	$-0.200401\pi$
$359$	4778.44	+	2758.83i	0.702496	+	0.405586i	−0.105780	+	0.994390i	$0.533734\pi$
$360$		0			0
$361$	−3093.37	−	5357.88i	−0.450995	−	0.781146i
$362$		0			0
$363$	3110.24	−	2284.40i	0.449711	−	0.330303i
$364$		0			0
$365$	−6581.49	−	3799.82i	−0.943811	−	0.544909i
$366$		0			0
$367$	−7273.98	−	4199.64i	−1.03460	−	0.597328i	−0.116302	−	0.993214i	$-0.537104\pi$
$367$	−7273.98	−	4199.64i	−1.03460	−	0.597328i	−0.918300	+	0.395886i	$0.870437\pi$
$368$		0			0
$369$	2852.18	−	9097.37i	0.402381	−	1.28344i
$370$		0			0
$371$	−1821.76	−	5323.85i	−0.254935	−	0.745015i
$372$		0			0
$373$	2673.53	+	4630.68i	0.371126	+	0.642809i	0.989739	−	0.142887i	$-0.0456385\pi$
$373$	2673.53	+	4630.68i	0.371126	+	0.642809i	−0.618613	+	0.785696i	$0.712305\pi$
$374$		0			0
$375$	−230.628	−	2090.19i	−0.0317589	−	0.287831i
$376$		0			0
$377$	2100.44			0.286944
$378$		0			0
$379$	−8330.90			−1.12910			−0.564551	−	0.825398i	$-0.690951\pi$
$379$	−8330.90			−1.12910			−0.564551	+	0.825398i	$0.690951\pi$
$380$		0			0
$381$	1032.58	+	9358.26i	0.138846	+	1.25837i
$382$		0			0
$383$	−2914.20	−	5047.55i	−0.388796	−	0.673414i	0.603492	−	0.797369i	$-0.293776\pi$
$383$	−2914.20	−	5047.55i	−0.388796	−	0.673414i	−0.992288	+	0.123955i	$0.960442\pi$
$384$		0			0
$385$	−7302.26	−	1433.93i	−0.966643	−	0.189818i
$386$		0			0
$387$	−7685.28	−	8359.76i	−1.00947	−	1.09806i
$388$		0			0
$389$	3655.54	+	2110.53i	0.476461	+	0.275085i	0.718940	−	0.695072i	$-0.244627\pi$
$389$	3655.54	+	2110.53i	0.476461	+	0.275085i	−0.242480	+	0.970157i	$0.577961\pi$
$390$		0			0
$391$	−4505.34	−	2601.16i	−0.582723	−	0.336435i
$392$		0			0
$393$	11382.8	−	8360.40i	1.46103	−	1.07310i
$394$		0			0
$395$	−43.3983	−	75.1680i	−0.00552811	−	0.00957497i
$396$		0			0
$397$	−7332.34	−	4233.33i	−0.926951	−	0.535175i	−0.0411048	−	0.999155i	$-0.513088\pi$
$397$	−7332.34	−	4233.33i	−0.926951	−	0.535175i	−0.885846	+	0.463980i	$0.846421\pi$
$398$		0			0
$399$	−2048.55	−	1424.48i	−0.257032	−	0.178730i
$400$		0			0
$401$	8038.85	−	4641.23i	1.00110	−	0.577985i	0.0925262	−	0.995710i	$-0.470506\pi$
$401$	8038.85	−	4641.23i	1.00110	−	0.577985i	0.908573	+	0.417725i	$0.137172\pi$
$402$		0			0
$403$	2181.07	−	3777.72i	0.269595	−	0.466952i
$404$		0			0
$405$	9914.95	+	6894.71i	1.21649	+	0.845928i
$406$		0			0
$407$	94.7506	−	54.7043i	0.0115396	−	0.00666239i
$408$		0			0
$409$		−	6311.32i		−	0.763019i	−0.924365	−	0.381510i	$-0.875404\pi$
$409$		−	6311.32i		−	0.763019i	0.924365	−	0.381510i	$-0.124596\pi$
$410$		0			0
$411$	710.063	−	1617.30i	0.0852186	−	0.194101i
$412$		0			0
$413$	−2182.11	+	11112.4i	−0.259988	+	1.32398i
$414$		0			0
$415$	1147.02	−	1986.70i	0.135675	−	0.234996i
$416$		0			0
$417$	−6021.84	+	13715.8i	−0.707172	+	1.61071i
$418$		0			0
$419$	−4816.45	+	8342.34i	−0.561573	+	0.972673i	0.435786	+	0.900050i	$0.356470\pi$
$419$	−4816.45	+	8342.34i	−0.561573	+	0.972673i	−0.997359	+	0.0726232i	$0.976863\pi$
$420$		0			0
$421$	1947.19	+	3372.63i	0.225416	+	0.390432i	0.956444	−	0.291915i	$-0.0942925\pi$
$421$	1947.19	+	3372.63i	0.225416	+	0.390432i	−0.731028	+	0.682347i	$0.760959\pi$
$422$		0			0
$423$	13883.7	−	3101.58i	1.59587	−	0.356511i
$424$		0			0
$425$	11368.8			1.29757
$426$		0			0
$427$	12685.2	+	2490.97i	1.43766	+	0.282310i
$428$		0			0
$429$	−2540.12	+	1865.67i	−0.285870	+	0.209965i
$430$		0			0
$431$	1440.36	−	831.595i	0.160974	−	0.0929386i	−0.417349	−	0.908746i	$-0.637041\pi$
$431$	1440.36	−	831.595i	0.160974	−	0.0929386i	0.578323	+	0.815808i	$0.303707\pi$
$432$		0			0
$433$		−	5804.60i		−	0.644230i	−0.946701	−	0.322115i	$-0.895606\pi$
$433$		−	5804.60i		−	0.644230i	0.946701	−	0.322115i	$-0.104394\pi$
$434$		0			0
$435$	−2906.64	+	6620.40i	−0.320374	+	0.729710i
$436$		0			0
$437$	1772.90			0.194072
$438$		0			0
$439$			1907.86i			0.207419i	0.994608	+	0.103710i	$0.0330712\pi$
$439$			1907.86i			0.207419i	−0.994608	+	0.103710i	$0.966929\pi$
$440$		0			0
$441$	9130.59	+	1548.67i	0.985919	+	0.167224i
$442$		0			0
$443$		−	16313.2i		−	1.74958i	−0.484503	−	0.874790i	$-0.661000\pi$
$443$		−	16313.2i		−	1.74958i	0.484503	−	0.874790i	$-0.339000\pi$
$444$		0			0
$445$	−20240.4			−2.15615
$446$		0			0
$447$	−6211.29	−	8456.74i	−0.657234	−	0.894832i
$448$		0			0
$449$			12238.3i			1.28632i	0.765731	+	0.643161i	$0.222377\pi$
$449$			12238.3i			1.28632i	−0.765731	+	0.643161i	$0.777623\pi$
$450$		0			0
$451$	−7417.42	+	4282.45i	−0.774440	+	0.447123i
$452$		0			0
$453$	−1312.43	−	576.215i	−0.136123	−	0.0597637i
$454$		0			0
$455$	−7528.23	−	1478.30i	−0.775668	−	0.152316i
$456$		0			0
$457$	4137.78			0.423539			0.211770	−	0.977320i	$-0.432077\pi$
$457$	4137.78			0.423539			0.211770	+	0.977320i	$0.432077\pi$
$458$		0			0
$459$	−7018.26	+	8042.17i	−0.713692	+	0.817814i
$460$		0			0
$461$	−5820.95	−	10082.2i	−0.588089	−	1.01860i	−0.994483	−	0.104901i	$-0.966547\pi$
$461$	−5820.95	−	10082.2i	−0.588089	−	1.01860i	0.406394	−	0.913698i	$-0.366786\pi$
$462$		0			0
$463$	8003.80	−	13863.0i	0.803387	−	1.39151i	−0.113987	−	0.993482i	$-0.536362\pi$
$463$	8003.80	−	13863.0i	0.803387	−	1.39151i	0.917374	−	0.398025i	$-0.130304\pi$
$464$		0			0
$465$	8888.84	+	12102.3i	0.886474	+	1.20694i
$466$		0			0
$467$	−5194.75	+	8997.57i	−0.514741	+	0.891558i	0.485112	+	0.874452i	$0.338779\pi$
$467$	−5194.75	+	8997.57i	−0.514741	+	0.891558i	−0.999854	+	0.0171065i	$0.994555\pi$
$468$		0			0
$469$	−3702.85	+	18856.7i	−0.364566	+	1.85655i
$470$		0			0
$471$	−18430.4	+	2033.58i	−1.80303	+	0.198943i
$472$		0			0
$473$			10201.3i			0.991664i
$474$		0			0
$475$	−3355.31	+	1937.19i	−0.324110	+	0.187125i
$476$		0			0
$477$	6039.09	−	5551.85i	0.579688	−	0.532918i
$478$		0			0
$479$	−6845.88	+	11857.4i	−0.653020	+	1.13106i	0.329367	+	0.944202i	$0.393165\pi$
$479$	−6845.88	+	11857.4i	−0.653020	+	1.13106i	−0.982386	+	0.186861i	$0.940169\pi$
$480$		0			0
$481$	97.6827	−	56.3971i	0.00925977	−	0.00534613i
$482$		0			0
$483$	−5954.71	+	2800.39i	−0.560970	+	0.263814i
$484$		0			0
$485$	13145.6	+	7589.61i	1.23074	+	0.710570i
$486$		0			0
$487$	−2764.08	−	4787.53i	−0.257192	−	0.445470i	0.708297	−	0.705915i	$-0.249464\pi$
$487$	−2764.08	−	4787.53i	−0.257192	−	0.445470i	−0.965489	+	0.260445i	$0.916131\pi$
$488$		0			0
$489$	12438.9	+	5461.22i	1.15032	+	0.505041i
$490$		0			0
$491$	−10923.1	−	6306.47i	−1.00398	−	0.579647i	−0.0945556	−	0.995520i	$-0.530143\pi$
$491$	−10923.1	−	6306.47i	−1.00398	−	0.579647i	−0.909423	+	0.415872i	$0.863476\pi$
$492$		0			0
$493$	−5534.42	−	3195.30i	−0.505594	−	0.291905i
$494$		0			0
$495$	−2365.33	−	10588.0i	−0.214775	−	0.961406i
$496$		0			0
$497$	−8843.58	−	1736.60i	−0.798167	−	0.156734i
$498$		0			0
$499$	6458.48	+	11186.4i	0.579401	+	1.00355i	0.995548	+	0.0942548i	$0.0300468\pi$
$499$	6458.48	+	11186.4i	0.579401	+	1.00355i	−0.416147	+	0.909297i	$0.636620\pi$
$500$		0			0
$501$	−2816.82	−	1236.71i	−0.251190	−	0.110283i
$502$		0			0
$503$	−6725.58			−0.596181			−0.298090	−	0.954538i	$-0.596350\pi$
$503$	−6725.58			−0.596181			−0.298090	+	0.954538i	$0.596350\pi$
$504$		0			0
$505$	9776.35			0.861469
$506$		0			0
$507$	6582.12	−	4834.42i	0.576573	−	0.423480i
$508$		0			0
$509$	−3790.75	−	6565.78i	−0.330103	−	0.571755i	0.652429	−	0.757850i	$-0.273750\pi$
$509$	−3790.75	−	6565.78i	−0.330103	−	0.571755i	−0.982532	+	0.186095i	$0.940417\pi$
$510$		0			0
$511$	−2750.71	−	8038.60i	−0.238130	−	0.695904i
$512$		0			0
$513$	700.975	−	3569.39i	0.0603290	−	0.307198i
$514$		0			0
$515$	21752.8	+	12559.0i	1.86125	+	1.07459i
$516$		0			0
$517$	−11067.8	−	6389.97i	−0.941507	−	0.543580i
$518$		0			0
$519$	−1048.75	−	9504.81i	−0.0886991	−	0.803882i
$520$		0			0
$521$	−5844.68	−	10123.3i	−0.491478	−	0.851265i	0.508474	−	0.861077i	$-0.330210\pi$
$521$	−5844.68	−	10123.3i	−0.491478	−	0.851265i	−0.999952	+	0.00981258i	$0.996877\pi$
$522$		0			0
$523$	4727.32	+	2729.32i	0.395242	+	0.228193i	0.684429	−	0.729080i	$-0.260052\pi$
$523$	4727.32	+	2729.32i	0.395242	+	0.228193i	−0.289187	+	0.957273i	$0.593385\pi$
$524$		0			0
$525$	8209.71	−	11806.4i	0.682479	−	0.981474i
$526$		0			0
$527$	−11493.8	+	6635.93i	−0.950049	+	0.548511i
$528$		0			0
$529$	−3745.70	+	6487.74i	−0.307857	+	0.533225i
$530$		0			0
$531$	−16112.6	+	3599.49i	−1.31681	+	0.294170i
$532$		0			0
$533$	−7646.95	+	4414.97i	−0.621437	+	0.358787i
$534$		0			0
$535$			11764.5i			0.950699i
$536$		0			0
$537$	−11023.3	−	15008.4i	−0.885831	−	1.20607i
$538$		0			0
$539$	−5096.94	−	6575.54i	−0.407312	−	0.525470i
$540$		0			0
$541$	11741.7	−	20337.3i	0.933117	−	1.61621i	0.155158	−	0.987890i	$-0.450411\pi$
$541$	11741.7	−	20337.3i	0.933117	−	1.61621i	0.777958	−	0.628316i	$-0.216255\pi$
$542$		0			0
$543$	−17347.4	+	1914.08i	−1.37099	+	0.151273i
$544$		0			0
$545$	−3076.49	+	5328.64i	−0.241803	+	0.418815i
$546$		0			0
$547$	12361.8	+	21411.3i	0.966279	+	1.67364i	0.706140	+	0.708072i	$0.250435\pi$
$547$	12361.8	+	21411.3i	0.966279	+	1.67364i	0.260139	+	0.965571i	$0.416232\pi$
$548$		0			0
$549$	4108.96	+	18393.1i	0.319428	+	1.42987i
$550$		0			0
$551$	2177.85			0.168384
$552$		0			0
$553$	18.6977	−	95.2178i	0.00143781	−	0.00732202i
$554$		0			0
$555$	42.5831	+	385.932i	0.00325685	+	0.0295169i
$556$		0			0
$557$	−19751.9	+	11403.8i	−1.50254	+	0.867494i	−0.502548	+	0.864550i	$0.667604\pi$
$557$	−19751.9	+	11403.8i	−1.50254	+	0.867494i	−0.999996	+	0.00294428i	$0.999063\pi$
$558$		0			0
$559$			10517.0i			0.795745i
$560$		0			0
$561$	9531.10	−	1051.65i	0.717297	−	0.0791454i
$562$		0			0
$563$	13196.6			0.987871			0.493936	−	0.869498i	$-0.335558\pi$
$563$	13196.6			0.987871			0.493936	+	0.869498i	$0.335558\pi$
$564$		0			0
$565$			13185.8i			0.981822i
$566$		0			0
$567$	3283.65	+	13095.9i	0.243211	+	0.969973i
$568$		0			0
$569$		−	24631.7i		−	1.81479i	−0.420283	−	0.907393i	$-0.638069\pi$
$569$		−	24631.7i		−	1.81479i	0.420283	−	0.907393i	$-0.361931\pi$
$570$		0			0
$571$	12032.2			0.881840			0.440920	−	0.897546i	$-0.354652\pi$
$571$	12032.2			0.881840			0.440920	+	0.897546i	$0.354652\pi$
$572$		0			0
$573$	−14660.9	+	1617.66i	−1.06888	+	0.117938i
$574$		0			0
$575$			10217.7i			0.741060i
$576$		0			0
$577$	−1354.20	+	781.847i	−0.0977054	+	0.0564102i	−0.548057	−	0.836441i	$-0.684632\pi$
$577$	−1354.20	+	781.847i	−0.0977054	+	0.0564102i	0.450351	+	0.892852i	$0.351299\pi$
$578$		0			0
$579$	−57.0118	−	516.699i	−0.00409211	−	0.0370869i
$580$		0			0
$581$	2426.55	−	830.335i	0.173271	−	0.0592911i
$582$		0			0
$583$	−7369.44			−0.523518
$584$		0			0
$585$	−2438.52	−	10915.7i	−0.172343	−	0.771465i
$586$		0			0
$587$	6210.23	+	10756.4i	0.436667	+	0.756330i	0.997430	−	0.0716464i	$-0.0228253\pi$
$587$	6210.23	+	10756.4i	0.436667	+	0.756330i	−0.560763	+	0.827977i	$0.689492\pi$
$588$		0			0
$589$	2261.46	−	3916.96i	0.158203	−	0.274016i
$590$		0			0
$591$	−3583.03	+	395.346i	−0.249384	+	0.0275167i
$592$		0			0
$593$	2504.15	−	4337.31i	0.173411	−	0.300357i	−0.766199	−	0.642603i	$-0.777854\pi$
$593$	2504.15	−	4337.31i	0.173411	−	0.300357i	0.939610	+	0.342246i	$0.111188\pi$
$594$		0			0
$595$	17587.2	+	15347.5i	1.21177	+	1.05746i
$596$		0			0
$597$	−1665.68	−	2267.84i	−0.114190	−	0.155472i
$598$		0			0
$599$			2117.31i			0.144425i	0.997389	+	0.0722127i	$0.0230060\pi$
$599$			2117.31i			0.144425i	−0.997389	+	0.0722127i	$0.976994\pi$
$600$		0			0
$601$	−4424.32	+	2554.38i	−0.300286	+	0.173370i	−0.642571	−	0.766226i	$-0.722132\pi$
$601$	−4424.32	+	2554.38i	−0.300286	+	0.173370i	0.342286	+	0.939596i	$0.388799\pi$
$602$		0			0
$603$	−27341.5	+	6108.00i	−1.84649	+	0.412499i
$604$		0			0
$605$	6151.50	−	10654.7i	0.413378	−	0.715992i
$606$		0			0
$607$	3369.87	−	1945.60i	0.225336	−	0.130098i	−0.383083	−	0.923714i	$-0.625138\pi$
$607$	3369.87	−	1945.60i	0.225336	−	0.130098i	0.608419	+	0.793616i	$0.291804\pi$
$608$		0			0
$609$	−7314.84	+	3440.04i	−0.486720	+	0.228896i
$610$		0			0
$611$	−11410.2	−	6587.71i	−0.755498	−	0.436187i
$612$		0			0
$613$	1258.27	+	2179.39i	0.0829056	+	0.143597i	0.904497	−	0.426480i	$-0.140247\pi$
$613$	1258.27	+	2179.39i	0.0829056	+	0.143597i	−0.821591	+	0.570077i	$0.806913\pi$
$614$		0			0
$615$	−3333.55	−	30212.1i	−0.218572	−	1.98093i
$616$		0			0
$617$	15584.3	+	8997.61i	1.01686	+	0.587083i	0.913192	−	0.407529i	$-0.133610\pi$
$617$	15584.3	+	8997.61i	1.01686	+	0.587083i	0.103665	+	0.994612i	$0.466943\pi$
$618$		0			0
$619$	−11116.8	−	6418.30i	−0.721846	−	0.416758i	0.0935856	−	0.995611i	$-0.470167\pi$
$619$	−11116.8	−	6418.30i	−0.721846	−	0.416758i	−0.815432	+	0.578853i	$0.803500\pi$
$620$		0			0
$621$	−7227.93	−	6307.68i	−0.467064	−	0.407598i
$622$		0			0
$623$	−17049.3	−	14878.1i	−1.09641	−	0.956787i
$624$		0			0
$625$	5987.25	+	10370.2i	0.383184	+	0.663694i
$626$		0			0
$627$	−2633.75	+	1934.43i	−0.167754	+	0.123212i
$628$		0			0
$629$	−343.178			−0.0217542
$630$		0			0
$631$	13484.9			0.850756			0.425378	−	0.905016i	$-0.360141\pi$
$631$	13484.9			0.850756			0.425378	+	0.905016i	$0.360141\pi$
$632$		0			0
$633$	−560.559	−	246.110i	−0.0351978	−	0.0154534i
$634$		0			0
$635$	15008.1	+	25994.8i	0.937920	+	1.62453i
$636$		0			0
$637$	−5254.67	−	6779.02i	−0.326841	−	0.421655i
$638$		0			0
$639$	−2864.59	−	12822.9i	−0.177342	−	0.793843i
$640$		0			0
$641$	12522.6	+	7229.90i	0.771624	+	0.445498i	0.833454	−	0.552589i	$-0.186360\pi$
$641$	12522.6	+	7229.90i	0.771624	+	0.445498i	−0.0618294	+	0.998087i	$0.519693\pi$
$642$		0			0
$643$	−9141.29	−	5277.73i	−0.560649	−	0.323691i	0.192757	−	0.981247i	$-0.438257\pi$
$643$	−9141.29	−	5277.73i	−0.560649	−	0.323691i	−0.753406	+	0.657556i	$0.771590\pi$
$644$		0			0
$645$	−33148.7	−	14553.7i	−2.02361	−	0.888452i
$646$		0			0
$647$	−3540.21	−	6131.82i	−0.215116	−	0.372592i	0.738193	−	0.674590i	$-0.235680\pi$
$647$	−3540.21	−	6131.82i	−0.215116	−	0.372592i	−0.953308	+	0.301998i	$0.902346\pi$
$648$		0			0
$649$	12844.5	+	7415.78i	0.776873	+	0.448528i
$650$		0			0
$651$	−1408.60	+	16728.1i	−0.0848037	+	1.00711i
$652$		0			0
$653$	4299.92	−	2482.56i	0.257686	−	0.148775i	−0.365593	−	0.930775i	$-0.619134\pi$
$653$	4299.92	−	2482.56i	0.257686	−	0.148775i	0.623278	+	0.782000i	$0.285800\pi$
$654$		0			0
$655$	22513.1	−	38993.9i	1.34299	−	2.32613i
$656$		0			0
$657$	9118.56	−	8382.86i	0.541475	−	0.497788i
$658$		0			0
$659$	−23711.6	+	13689.9i	−1.40163	+	0.809231i	−0.994560	−	0.104166i	$-0.966783\pi$
$659$	−23711.6	+	13689.9i	−1.40163	+	0.809231i	−0.407070	+	0.913397i	$0.633449\pi$
$660$		0			0
$661$		−	13997.9i		−	0.823686i	−0.911255	−	0.411843i	$-0.864885\pi$
$661$		−	13997.9i		−	0.823686i	0.911255	−	0.411843i	$-0.135115\pi$
$662$		0			0
$663$	9826.04	−	1084.19i	0.575584	−	0.0635090i
$664$		0			0
$665$	−7805.71	−	1532.79i	−0.455176	−	0.0893821i
$666$		0			0
$667$	2871.78	−	4974.08i	0.166711	−	0.288751i
$668$		0			0
$669$	5256.41	+	7156.66i	0.303774	+	0.413591i
$670$		0			0
$671$	8465.40	−	14662.5i	0.487039	−	0.843576i
$672$		0			0
$673$	−6547.88	−	11341.3i	−0.375040	−	0.649589i	0.615293	−	0.788299i	$-0.289038\pi$
$673$	−6547.88	−	11341.3i	−0.375040	−	0.649589i	−0.990333	+	0.138710i	$0.955704\pi$
$674$		0			0
$675$	20571.4	+	4039.92i	1.17303	+	0.230366i
$676$		0			0
$677$	−10079.6			−0.572217			−0.286109	−	0.958197i	$-0.592362\pi$
$677$	−10079.6			−0.572217			−0.286109	+	0.958197i	$0.592362\pi$
$678$		0			0
$679$	5494.15	+	16056.0i	0.310525	+	0.907469i
$680$		0			0
$681$	13981.8	+	6138.60i	0.786758	+	0.345421i
$682$		0			0
$683$	17038.3	−	9837.05i	0.954541	−	0.551104i	0.0600521	−	0.998195i	$-0.480873\pi$
$683$	17038.3	−	9837.05i	0.954541	−	0.551104i	0.894489	+	0.447091i	$0.147540\pi$
$684$		0			0
$685$		−	5631.19i		−	0.314097i
$686$		0			0
$687$	−6350.47	−	8646.24i	−0.352672	−	0.480167i
$688$		0			0
$689$	−7597.49			−0.420089
$690$		0			0
$691$		−	23079.9i		−	1.27062i	−0.772257	−	0.635311i	$-0.780872\pi$
$691$		−	23079.9i		−	1.27062i	0.772257	−	0.635311i	$-0.219128\pi$
$692$		0			0
$693$	5790.54	−	10657.4i	0.317409	−	0.584186i
$694$		0			0
$695$			47756.5i			2.60648i
$696$		0			0
$697$	26865.2			1.45996
$698$		0			0
$699$	1115.37	−	2540.46i	0.0603537	−	0.137466i
$700$		0			0
$701$			27514.6i			1.48247i	0.671244	+	0.741237i	$0.265760\pi$
$701$			27514.6i			1.48247i	−0.671244	+	0.741237i	$0.734240\pi$
$702$		0			0
$703$	101.283	−	58.4758i	0.00543380	−	0.00313721i
$704$		0			0
$705$	36553.7	−	26847.9i	1.95276	−	1.43426i
$706$		0			0
$707$	8235.01	+	7186.31i	0.438061	+	0.382276i
$708$		0			0
$709$	1563.56			0.0828221			0.0414111	−	0.999142i	$-0.486815\pi$
$709$	1563.56			0.0828221			0.0414111	+	0.999142i	$0.486815\pi$
$710$		0			0
$711$	138.062	−	30.8427i	0.00728235	−	0.00162685i
$712$		0			0
$713$	−5964.06	−	10330.0i	−0.313262	−	0.542585i
$714$		0			0
$715$	−5023.92	+	8701.68i	−0.262775	+	0.455139i
$716$		0			0
$717$	3360.03	−	7653.08i	0.175011	−	0.398619i
$718$		0			0
$719$	−13996.9	+	24243.3i	−0.726001	+	1.25747i	0.232560	+	0.972582i	$0.425290\pi$
$719$	−13996.9	+	24243.3i	−0.726001	+	1.25747i	−0.958561	+	0.284889i	$0.908043\pi$
$720$		0			0
$721$	9091.52	+	26568.8i	0.469606	+	1.37236i
$722$		0			0
$723$	8524.92	−	19417.0i	0.438513	−	0.998793i
$724$		0			0
$725$			12551.6i			0.642973i
$726$		0			0
$727$	19002.0	−	10970.8i	0.969388	−	0.559676i	0.0703383	−	0.997523i	$-0.477592\pi$
$727$	19002.0	−	10970.8i	0.969388	−	0.559676i	0.899050	+	0.437847i	$0.144259\pi$
$728$		0			0
$729$	−15557.1	+	12058.1i	−0.790383	+	0.612614i
$730$		0			0
$731$	15999.0	−	27711.1i	0.809501	−	1.40210i
$732$		0			0
$733$	30328.0	−	17509.9i	1.52823	−	0.882323i	0.528791	−	0.848752i	$-0.322645\pi$
$733$	30328.0	−	17509.9i	1.52823	−	0.882323i	0.999436	−	0.0335708i	$-0.0106879\pi$
$734$		0			0
$735$	28638.4	−	7181.29i	1.43720	−	0.360389i
$736$		0			0
$737$	21795.9	+	12583.9i	1.08937	+	0.628946i
$738$		0			0
$739$	−12337.0	−	21368.3i	−0.614105	−	1.06366i	−0.990541	−	0.137219i	$-0.956184\pi$
$739$	−12337.0	−	21368.3i	−0.614105	−	1.06366i	0.376435	−	0.926443i	$-0.377150\pi$
$740$		0			0
$741$	−2715.25	+	1994.29i	−0.134612	+	0.0988693i
$742$		0			0
$743$	−1374.00	−	793.278i	−0.0678426	−	0.0391690i	0.465695	−	0.884945i	$-0.345804\pi$
$743$	−1374.00	−	793.278i	−0.0678426	−	0.0391690i	−0.533538	+	0.845776i	$0.679138\pi$
$744$		0			0
$745$	−28970.2	−	16725.9i	−1.42468	−	0.822538i
$746$		0			0
$747$	2530.47	+	2752.55i	0.123943	+	0.134820i
$748$		0			0
$749$	−8647.75	+	9909.71i	−0.421871	+	0.483435i
$750$		0			0
$751$	−3275.32	−	5673.02i	−0.159145	−	0.275648i	0.775415	−	0.631452i	$-0.217541\pi$
$751$	−3275.32	−	5673.02i	−0.159145	−	0.275648i	−0.934561	+	0.355804i	$0.884207\pi$
$752$		0			0
$753$	2253.78	+	20426.1i	0.109074	+	0.988538i
$754$		0			0
$755$	−4569.70			−0.220276
$756$		0			0
$757$	−20793.6			−0.998357			−0.499179	−	0.866499i	$-0.666365\pi$
$757$	−20793.6			−0.998357			−0.499179	+	0.866499i	$0.666365\pi$
$758$		0			0
$759$	945.171	+	8566.11i	0.0452009	+	0.409657i
$760$		0			0
$761$	−2391.74	−	4142.62i	−0.113930	−	0.197332i	0.803422	−	0.595410i	$-0.203011\pi$
$761$	−2391.74	−	4142.62i	−0.113930	−	0.197332i	−0.917351	+	0.398078i	$0.869677\pi$
$762$		0			0
$763$	−6508.38	+	2227.09i	−0.308806	+	0.105670i
$764$		0			0
$765$	−10180.3	+	32471.2i	−0.481135	+	1.53464i
$766$		0			0
$767$	13242.0	+	7645.26i	0.623390	+	0.359914i
$768$		0			0
$769$	35756.0	+	20643.7i	1.67671	+	0.968051i	0.963733	+	0.266867i	$0.0859884\pi$
$769$	35756.0	+	20643.7i	1.67671	+	0.968051i	0.712980	+	0.701184i	$0.247345\pi$
$770$		0			0
$771$	13788.9	−	10127.6i	0.644091	−	0.473070i
$772$		0			0
$773$	−19733.6	−	34179.7i	−0.918201	−	1.59037i	−0.802146	−	0.597128i	$-0.796308\pi$
$773$	−19733.6	−	34179.7i	−0.918201	−	1.59037i	−0.116055	−	0.993243i	$-0.537025\pi$
$774$		0			0
$775$	22574.6	+	13033.5i	1.04633	+	0.604098i
$776$		0			0
$777$	−247.818	+	356.387i	−0.0114420	+	0.0164547i
$778$		0			0
$779$	−7928.80	+	4577.70i	−0.364671	+	0.210543i
$780$		0			0
$781$	−5901.71	+	10222.1i	−0.270397	+	0.468341i
$782$		0			0
$783$	−8878.88	−	7748.45i	−0.405243	−	0.353649i
$784$		0			0
$785$	−51194.8	+	29557.3i	−2.32767	+	1.34388i
$786$		0			0
$787$		−	1106.90i		−	0.0501355i	−0.999686	−	0.0250677i	$-0.992020\pi$
$787$		−	1106.90i		−	0.0501355i	0.999686	−	0.0250677i	$-0.00798015\pi$
$788$		0			0
$789$	−8472.65	+	19298.0i	−0.382300	+	0.870757i
$790$		0			0
$791$	−9692.48	+	11106.9i	−0.435682	+	0.499261i
$792$		0			0
$793$	8727.36	−	15116.2i	0.390817	−	0.676914i
$794$		0			0
$795$	10513.6	−	23946.6i	0.469030	−	1.06830i
$796$		0			0
$797$	5430.88	−	9406.56i	0.241370	−	0.418065i	−0.719735	−	0.694249i	$-0.755737\pi$
$797$	5430.88	−	9406.56i	0.241370	−	0.418065i	0.961105	+	0.276184i	$0.0890700\pi$
$798$		0			0
$799$	20043.2	+	34715.8i	0.887455	+	1.53712i
$800$		0			0
$801$	9868.89	−	31478.0i	0.435331	−	1.38854i
$802$		0			0
$803$	−11127.3			−0.489008
$804$		0			0
$805$	−13793.6	+	15806.5i	−0.603928	+	0.692059i
$806$		0			0
$807$	−2874.10	+	2110.96i	−0.125369	+	0.0920809i
$808$		0			0
$809$	32491.6	−	18759.0i	1.41204	−	0.815244i	0.416463	−	0.909153i	$-0.363270\pi$
$809$	32491.6	−	18759.0i	1.41204	−	0.815244i	0.995581	+	0.0939092i	$0.0299363\pi$
$810$		0			0
$811$		−	8338.36i		−	0.361035i	−0.983572	−	0.180518i	$-0.942223\pi$
$811$		−	8338.36i		−	0.361035i	0.983572	−	0.180518i	$-0.0577772\pi$
$812$		0			0
$813$	7543.18	−	17180.9i	0.325401	−	0.741159i
$814$		0			0
$815$	43310.4			1.86147
$816$		0			0
$817$			10904.6i			0.466958i
$818$		0			0
$819$	5969.72	−	10987.2i	0.254700	−	0.468771i
$820$		0			0
$821$			15309.0i			0.650778i	0.945580	+	0.325389i	$0.105495\pi$
$821$			15309.0i			0.650778i	−0.945580	+	0.325389i	$0.894505\pi$
$822$		0			0
$823$	−4298.57			−0.182064			−0.0910321	−	0.995848i	$-0.529017\pi$
$823$	−4298.57			−0.182064			−0.0910321	+	0.995848i	$0.529017\pi$
$824$		0			0
$825$	−11148.7	−	15179.1i	−0.470482	−	0.640567i
$826$		0			0
$827$		−	6205.21i		−	0.260915i	−0.991454	−	0.130457i	$-0.958355\pi$
$827$		−	6205.21i		−	0.260915i	0.991454	−	0.130457i	$-0.0416445\pi$
$828$		0			0
$829$	−33605.2	+	19401.9i	−1.40791	+	0.812856i	−0.995186	−	0.0980018i	$-0.968755\pi$
$829$	−33605.2	+	19401.9i	−1.40791	+	0.812856i	−0.412721	+	0.910857i	$0.635422\pi$
$830$		0			0
$831$	−214.076	−	93.9888i	−0.00893649	−	0.00392351i
$832$		0			0
$833$	3532.87	+	25855.7i	0.146947	+	1.07544i
$834$		0			0
$835$	−9807.75			−0.406481
$836$		0			0
$837$	−23155.6	+	7923.15i	−0.956244	+	0.327197i
$838$		0			0
$839$	−12579.3	−	21788.0i	−0.517624	−	0.896551i	−0.999790	−	0.0204713i	$-0.993483\pi$
$839$	−12579.3	−	21788.0i	−0.517624	−	0.896551i	0.482167	−	0.876080i	$-0.339850\pi$
$840$		0			0
$841$	−8666.76	+	15011.3i	−0.355355	+	0.615493i
$842$		0			0
$843$	9374.41	+	12763.4i	0.383004	+	0.521464i
$844$		0			0
$845$	13018.3	−	22548.3i	0.529991	−	0.917971i
$846$		0			0
$847$	13013.6	−	4453.10i	0.527926	−	0.180650i
$848$		0			0
$849$	−23676.8	+	2612.46i	−0.957109	+	0.105606i
$850$		0			0
$851$		−	308.432i		−	0.0124241i
$852$		0			0
$853$	10159.4	−	5865.53i	0.407797	−	0.235442i	−0.282046	−	0.959401i	$-0.591013\pi$
$853$	10159.4	−	5865.53i	0.407797	−	0.235442i	0.689843	+	0.723959i	$0.257680\pi$
$854$		0			0
$855$	−2528.40	−	11318.0i	−0.101134	−	0.452710i
$856$		0			0
$857$	20374.2	−	35289.2i	0.812101	−	1.40660i	−0.0992903	−	0.995059i	$-0.531657\pi$
$857$	20374.2	−	35289.2i	0.812101	−	1.40660i	0.911391	−	0.411541i	$-0.135009\pi$
$858$		0			0
$859$	21932.7	−	12662.8i	0.871168	−	0.502969i	0.00343199	−	0.999994i	$-0.498908\pi$
$859$	21932.7	−	12662.8i	0.871168	−	0.502969i	0.867736	+	0.497025i	$0.165574\pi$
$860$		0			0
$861$	19400.0	−	27899.2i	0.767888	−	1.10430i
$862$		0			0
$863$	−15407.9	−	8895.75i	−0.607753	−	0.350886i	0.164333	−	0.986405i	$-0.447453\pi$
$863$	−15407.9	−	8895.75i	−0.607753	−	0.350886i	−0.772085	+	0.635519i	$0.780786\pi$
$864$		0			0
$865$	−15243.2	−	26401.9i	−0.599171	−	1.03779i
$866$		0			0
$867$	−4164.85	−	1828.55i	−0.163144	−	0.0716271i
$868$		0			0
$869$	−110.060	−	63.5430i	−0.00429634	−	0.00248049i
$870$		0			0
$871$	22470.4	+	12973.3i	0.874145	+	0.504688i
$872$		0			0
$873$	−18213.0	+	16743.6i	−0.706091	+	0.649123i
$874$		0			0
$875$	1444.22	−	7354.65i	0.0557983	−	0.284152i
$876$		0			0
$877$	−17605.0	−	30492.7i	−0.677853	−	1.17408i	−0.975626	−	0.219440i	$-0.929577\pi$
$877$	−17605.0	−	30492.7i	−0.677853	−	1.17408i	0.297773	−	0.954637i	$-0.403756\pi$
$878$		0			0
$879$	30346.9	+	13323.6i	1.16448	+	0.511255i
$880$		0			0
$881$	−19971.8			−0.763755			−0.381878	−	0.924213i	$-0.624722\pi$
$881$	−19971.8			−0.763755			−0.381878	+	0.924213i	$0.624722\pi$
$882$		0			0
$883$	5583.77			0.212807			0.106404	−	0.994323i	$-0.466066\pi$
$883$	5583.77			0.212807			0.106404	+	0.994323i	$0.466066\pi$
$884$		0			0
$885$	−42421.8	+	31157.9i	−1.61129	+	1.18346i
$886$		0			0
$887$	−8743.47	−	15144.1i	−0.330977	−	0.573270i	0.651726	−	0.758454i	$-0.274045\pi$
$887$	−8743.47	−	15144.1i	−0.330977	−	0.573270i	−0.982704	+	0.185185i	$0.940712\pi$
$888$		0			0
$889$	−6466.11	+	32928.5i	−0.243944	+	1.24228i
$890$		0			0
$891$	17619.9	+	1483.98i	0.662502	+	0.0557969i
$892$		0			0
$893$	−11830.8	−	6830.52i	−0.443340	−	0.255963i
$894$		0			0
$895$	−51414.0	−	29683.9i	−1.92020	−	1.10863i
$896$		0			0
$897$	974.419	+	8831.19i	0.0362708	+	0.328723i
$898$		0			0
$899$	−7326.33	−	12689.6i	−0.271798	−	0.470769i
$900$		0			0
$901$	20018.5	+	11557.7i	0.740194	+	0.427351i
$902$		0			0
$903$	−17224.5	−	36625.8i	−0.634766	−	1.34976i
$904$		0			0
$905$	−48186.6	+	27820.6i	−1.76992	+	1.02186i
$906$		0			0
$907$	10253.5	−	17759.7i	0.375373	−	0.650165i	−0.615010	−	0.788519i	$-0.710848\pi$
$907$	10253.5	−	17759.7i	0.375373	−	0.650165i	0.990383	+	0.138355i	$0.0441813\pi$
$908$		0			0
$909$	−4766.80	+	15204.3i	−0.173933	+	0.554779i
$910$		0			0
$911$	9542.12	−	5509.15i	0.347030	−	0.200358i	−0.316346	−	0.948644i	$-0.602456\pi$
$911$	9542.12	−	5509.15i	0.347030	−	0.200358i	0.663377	+	0.748286i	$0.269123\pi$
$912$		0			0
$913$		−	3358.90i		−	0.121756i
$914$		0			0
$915$	35567.9	+	48426.2i	1.28507	+	1.74964i
$916$		0			0
$917$	47627.0	−	16297.3i	1.71514	−	0.586898i
$918$		0			0
$919$	−5307.19	+	9192.33i	−0.190499	+	0.329953i	−0.945416	−	0.325867i	$-0.894344\pi$
$919$	−5307.19	+	9192.33i	−0.190499	+	0.329953i	0.754917	+	0.655820i	$0.227677\pi$
$920$		0			0
$921$	−37547.3	+	4142.90i	−1.34335	+	0.148223i
$922$		0			0
$923$	−6084.34	+	10538.4i	−0.216976	+	0.375813i
$924$		0			0
$925$	337.013	+	583.724i	0.0119794	+	0.0207489i
$926$		0			0
$927$	−30138.3	+	27706.7i	−1.06782	+	0.981668i
$928$		0			0
$929$	16808.5			0.593616			0.296808	−	0.954937i	$-0.404078\pi$
$929$	16808.5			0.593616			0.296808	+	0.954937i	$0.404078\pi$
$930$		0			0
$931$	−5448.35	−	7028.88i	−0.191796	−	0.247435i
$932$		0			0
$933$	−4479.80	−	40600.5i	−0.157194	−	1.42465i
$934$		0			0
$935$	26474.9	−	15285.3i	0.926014	−	0.534635i
$936$		0			0
$937$		−	34975.7i		−	1.21943i	−0.792620	−	0.609715i	$-0.791284\pi$
$937$		−	34975.7i		−	1.21943i	0.792620	−	0.609715i	$-0.208716\pi$
$938$		0			0
$939$	−47979.7	+	5294.00i	−1.66747	+	0.183986i
$940$		0			0
$941$	28439.5			0.985231			0.492616	−	0.870247i	$-0.336041\pi$
$941$	28439.5			0.985231			0.492616	+	0.870247i	$0.336041\pi$
$942$		0			0
$943$			24145.1i			0.833801i
$944$		0			0
$945$	26369.6	+	34020.4i	0.907729	+	1.17110i
$946$		0			0
$947$		−	2102.67i		−	0.0721515i	−0.999349	−	0.0360758i	$-0.988514\pi$
$947$		−	2102.67i		−	0.0721515i	0.999349	−	0.0360758i	$-0.0114858\pi$
$948$		0			0
$949$	−11471.6			−0.392396
$950$		0			0
$951$	−20627.3	+	2275.99i	−0.703351	+	0.0776066i
$952$		0			0
$953$		−	15679.1i		−	0.532944i	−0.963843	−	0.266472i	$-0.914142\pi$
$953$		−	15679.1i		−	0.532944i	0.963843	−	0.266472i	$-0.0858579\pi$
$954$		0			0
$955$	−40724.1	+	23512.1i	−1.37990	+	0.796684i
$956$		0			0
$957$	1161.06	+	10522.7i	0.0392181	+	0.355435i
$958$		0			0
$959$	4139.32	−	4743.37i	0.139380	−	0.159720i
$960$		0			0
$961$	−639.312			−0.0214599
$962$		0			0
$963$	−18296.3	−	5736.20i	−0.612243	−	0.191948i
$964$		0			0
$965$	−828.646	−	1435.26i	−0.0276426	−	0.0478783i
$966$		0			0
$967$	−4592.18	+	7953.89i	−0.152714	+	0.264509i	−0.932224	−	0.361881i	$-0.882135\pi$
$967$	−4592.18	+	7953.89i	−0.152714	+	0.264509i	0.779510	+	0.626390i	$0.215468\pi$
$968$		0			0
$969$	10188.2	−	1124.15i	0.337763	−	0.0372683i
$970$		0			0
$971$	−15054.2	+	26074.6i	−0.497540	+	0.861765i	−0.999996	−	0.00283768i	$-0.999097\pi$
$971$	−15054.2	+	26074.6i	−0.497540	+	0.861765i	0.502455	+	0.864603i	$0.332430\pi$
$972$		0			0
$973$	−35104.4	+	40227.2i	−1.15662	+	1.32541i
$974$		0			0
$975$	−11493.7	−	15648.8i	−0.377531	−	0.514013i
$976$		0			0
$977$			14207.8i			0.465247i	0.972567	+	0.232624i	$0.0747310\pi$
$977$			14207.8i			0.465247i	−0.972567	+	0.232624i	$0.925269\pi$
$978$		0			0
$979$	−25665.2	+	14817.8i	−0.837857	+	0.483737i
$980$		0			0
$981$	−6787.11	−	7382.76i	−0.220893	−	0.240279i
$982$		0			0
$983$	−2203.18	+	3816.02i	−0.0714858	+	0.123817i	−0.899553	−	0.436812i	$-0.856107\pi$
$983$	−2203.18	+	3816.02i	−0.0714858	+	0.123817i	0.828067	+	0.560629i	$0.189441\pi$
$984$		0			0
$985$	−9952.73	+	5746.21i	−0.321950	+	0.185878i
$986$		0			0
$987$	50525.8	+	4254.53i	1.62944	+	0.137207i
$988$		0			0
$989$	24905.5	+	14379.2i	0.800756	+	0.462317i
$990$		0			0
$991$	−233.806	−	404.965i	−0.00749456	−	0.0129810i	0.862254	−	0.506476i	$-0.169052\pi$
$991$	−233.806	−	404.965i	−0.00749456	−	0.0129810i	−0.869748	+	0.493495i	$0.835719\pi$
$992$		0			0
$993$	4124.18	+	37377.6i	0.131800	+	1.19450i
$994$		0			0
$995$	−7768.92	−	4485.39i	−0.247529	−	0.142911i
$996$		0			0
$997$	38136.5	+	22018.1i	1.21143	+	0.699420i	0.963071	−	0.269248i	$-0.0867752\pi$
$997$	38136.5	+	22018.1i	1.21143	+	0.699420i	0.248360	+	0.968668i	$0.420109\pi$
$998$		0			0
$999$	−620.968	−	121.949i	−0.0196662	−	0.00386215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.13	✓	48
3.2	odd	2		756.4.w.a.341.4		48
7.3	odd	6		252.4.bm.a.185.5	yes	48
9.2	odd	6		252.4.bm.a.173.5	yes	48
9.7	even	3		756.4.bm.a.89.4		48
21.17	even	6		756.4.bm.a.17.4		48
63.38	even	6	inner	252.4.w.a.101.13	yes	48
63.52	odd	6		756.4.w.a.521.4		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.13	✓	48	1.1	even	1	trivial
252.4.w.a.101.13	yes	48	63.38	even	6	inner
252.4.bm.a.173.5	yes	48	9.2	odd	6
252.4.bm.a.185.5	yes	48	7.3	odd	6
756.4.w.a.341.4		48	3.2	odd	2
756.4.w.a.521.4		48	63.52	odd	6
756.4.bm.a.17.4		48	21.17	even	6
756.4.bm.a.89.4		48	9.7	even	3

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.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.569877 + 5.16481i) q^{3} +(8.28296 + 14.3465i) q^{5} +(-3.56863 + 18.1732i) q^{7} +(-26.3505 + 5.88661i) q^{9} +O(q^{10})\)	\(q+(0.569877 + 5.16481i) q^{3} +(8.28296 + 14.3465i) q^{5} +(-3.56863 + 18.1732i) q^{7} +(-26.3505 + 5.88661i) q^{9} +(21.0059 + 12.1278i) q^{11} +(21.6559 + 12.5031i) q^{13} +(-69.3767 + 50.9556i) q^{15} +(-38.0407 - 65.8884i) q^{17} +(22.4541 + 12.9639i) q^{19} +(-95.8947 - 8.07482i) q^{21} +(59.2174 - 34.1892i) q^{23} +(-74.7148 + 129.410i) q^{25} +(-45.4197 - 132.741i) q^{27} +(72.7435 - 41.9985i) q^{29} -174.443i q^{31} +(-50.6668 + 115.403i) q^{33} +(-290.281 + 99.3304i) q^{35} +(2.25533 - 3.90635i) q^{37} +(-52.2347 + 118.974i) q^{39} +(-176.556 + 305.803i) q^{41} +(210.288 + 364.230i) q^{43} +(-302.712 - 329.279i) q^{45} -526.888 q^{47} +(-317.530 - 129.707i) q^{49} +(318.622 - 234.021i) q^{51} +(-263.120 + 151.913i) q^{53} +401.815i q^{55} +(-54.1600 + 123.359i) q^{57} +611.471 q^{59} -698.018i q^{61} +(-12.9432 - 499.879i) q^{63} +414.249i q^{65} +1037.61 q^{67} +(210.327 + 286.363i) q^{69} +486.628i q^{71} +(-397.291 + 229.376i) q^{73} +(-710.955 - 312.140i) q^{75} +(-295.363 + 338.465i) q^{77} -5.23947 q^{79} +(659.696 - 310.230i) q^{81} +(-69.2400 - 119.927i) q^{83} +(630.179 - 1091.50i) q^{85} +(258.369 + 351.772i) q^{87} +(-610.904 + 1058.12i) q^{89} +(-304.503 + 348.939i) q^{91} +(900.964 - 99.4109i) q^{93} +429.518i q^{95} +(793.532 - 458.146i) q^{97} +(-624.907 - 195.919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 12 * q^9	\( 48 q + 6 q^{7} + 12 q^{9} + 12 q^{11} - 36 q^{13} + 66 q^{15} - 72 q^{17} + 24 q^{21} + 30 q^{23} - 600 q^{25} - 396 q^{27} + 42 q^{29} + 390 q^{35} + 84 q^{37} - 840 q^{39} - 618 q^{41} - 42 q^{43} + 366 q^{45} + 396 q^{47} + 318 q^{49} - 738 q^{51} - 1620 q^{53} + 492 q^{57} + 1500 q^{59} + 672 q^{63} - 588 q^{67} - 924 q^{69} + 564 q^{75} - 2472 q^{77} + 1608 q^{79} + 2592 q^{81} - 360 q^{85} + 2640 q^{87} + 1722 q^{89} + 540 q^{91} + 660 q^{93} - 792 q^{97} - 54 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 12 * q^9 + 12 * q^11 - 36 * q^13 + 66 * q^15 - 72 * q^17 + 24 * q^21 + 30 * q^23 - 600 * q^25 - 396 * q^27 + 42 * q^29 + 390 * q^35 + 84 * q^37 - 840 * q^39 - 618 * q^41 - 42 * q^43 + 366 * q^45 + 396 * q^47 + 318 * q^49 - 738 * q^51 - 1620 * q^53 + 492 * q^57 + 1500 * q^59 + 672 * q^63 - 588 * q^67 - 924 * q^69 + 564 * q^75 - 2472 * q^77 + 1608 * q^79 + 2592 * q^81 - 360 * q^85 + 2640 * q^87 + 1722 * q^89 + 540 * q^91 + 660 * q^93 - 792 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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