LMFDB - Embedded newform 252.4.x.a.209.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (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			209.8
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.66558 + 3.68287i) q^{3} +(8.29874 + 14.3738i) q^{5} +(18.2297 - 3.26749i) q^{7} +(-0.127054 - 26.9997i) q^{9} +O(q^{10})$	\(q+(-3.66558 + 3.68287i) q^{3} +(8.29874 + 14.3738i) q^{5} +(18.2297 - 3.26749i) q^{7} +(-0.127054 - 26.9997i) q^{9} +(46.2764 + 26.7177i) q^{11} +(11.0474 - 6.37824i) q^{13} +(-83.3566 - 22.1253i) q^{15} +96.7463 q^{17} -54.6996i q^{19} +(-54.7888 + 79.1150i) q^{21} +(-55.6727 + 32.1426i) q^{23} +(-75.2381 + 130.316i) q^{25} +(99.9021 + 98.5016i) q^{27} +(-112.711 - 65.0740i) q^{29} +(-190.618 + 110.053i) q^{31} +(-268.027 + 72.4940i) q^{33} +(198.250 + 234.915i) q^{35} +279.735 q^{37} +(-17.0050 + 64.0662i) q^{39} +(185.308 + 320.963i) q^{41} +(-153.876 + 266.520i) q^{43} +(387.035 - 225.890i) q^{45} +(-163.683 + 283.506i) q^{47} +(321.647 - 119.131i) q^{49} +(-354.631 + 356.304i) q^{51} -451.749i q^{53} +886.892i q^{55} +(201.451 + 200.506i) q^{57} +(-258.739 - 448.148i) q^{59} +(-234.511 - 135.395i) q^{61} +(-90.5373 - 491.782i) q^{63} +(183.360 + 105.863i) q^{65} +(-370.881 - 642.385i) q^{67} +(85.6955 - 322.857i) q^{69} -914.198i q^{71} +337.210i q^{73} +(-204.146 - 754.777i) q^{75} +(930.906 + 335.849i) q^{77} +(-498.583 + 863.570i) q^{79} +(-728.968 + 6.86085i) q^{81} +(-17.0271 + 29.4917i) q^{83} +(802.872 + 1390.61i) q^{85} +(652.812 - 176.568i) q^{87} +208.953 q^{89} +(180.551 - 152.371i) q^{91} +(293.413 - 1105.43i) q^{93} +(786.243 - 453.937i) q^{95} +(-1100.94 - 635.630i) q^{97} +(715.489 - 1252.84i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−3.66558	+	3.68287i	−0.705441	+	0.708769i
$3$	−3.66558	+	3.68287i	−0.705441	+	0.708769i
$4$		0			0
$5$	8.29874	+	14.3738i	0.742262	+	1.28564i	0.951463	+	0.307762i	$0.0995802\pi$
$5$	8.29874	+	14.3738i	0.742262	+	1.28564i	−0.209202	+	0.977873i	$0.567086\pi$
$6$		0			0
$7$	18.2297	−	3.26749i	0.984314	−	0.176428i
$7$	18.2297	−	3.26749i	0.984314	−	0.176428i
$8$		0			0
$9$	−0.127054	−	26.9997i	−0.00470571	−	0.999989i
$10$		0			0
$11$	46.2764	+	26.7177i	1.26844	+	0.732334i	0.974693	−	0.223548i	$-0.0717641\pi$
$11$	46.2764	+	26.7177i	1.26844	+	0.732334i	0.293748	+	0.955883i	$0.405097\pi$
$12$		0			0
$13$	11.0474	−	6.37824i	0.235693	−	0.136077i	−0.377503	−	0.926009i	$-0.623217\pi$
$13$	11.0474	−	6.37824i	0.235693	−	0.136077i	0.613196	+	0.789931i	$0.289884\pi$
$14$		0			0
$15$	−83.3566	−	22.1253i	−1.43484	−	0.380848i
$16$		0			0
$17$	96.7463			1.38026			0.690130	−	0.723686i	$-0.257553\pi$
$17$	96.7463			1.38026			0.690130	+	0.723686i	$0.257553\pi$
$18$		0			0
$19$		−	54.6996i		−	0.660471i	−0.943899	−	0.330235i	$-0.892872\pi$
$19$		−	54.6996i		−	0.660471i	0.943899	−	0.330235i	$-0.107128\pi$
$20$		0			0
$21$	−54.7888	+	79.1150i	−0.569329	+	0.822110i
$22$		0			0
$23$	−55.6727	+	32.1426i	−0.504720	+	0.291400i	−0.730660	−	0.682741i	$-0.760788\pi$
$23$	−55.6727	+	32.1426i	−0.504720	+	0.291400i	0.225941	+	0.974141i	$0.427454\pi$
$24$		0			0
$25$	−75.2381	+	130.316i	−0.601905	+	1.04253i
$26$		0			0
$27$	99.9021	+	98.5016i	0.712080	+	0.702098i
$28$		0			0
$29$	−112.711	−	65.0740i	−0.721724	−	0.416688i	0.0936628	−	0.995604i	$-0.470142\pi$
$29$	−112.711	−	65.0740i	−0.721724	−	0.416688i	−0.815387	+	0.578916i	$0.803476\pi$
$30$		0			0
$31$	−190.618	+	110.053i	−1.10439	+	0.637618i	−0.937370	−	0.348336i	$-0.886747\pi$
$31$	−190.618	+	110.053i	−1.10439	+	0.637618i	−0.167017	+	0.985954i	$0.553413\pi$
$32$		0			0
$33$	−268.027	+	72.4940i	−1.41387	+	0.382412i
$34$		0			0
$35$	198.250	+	234.915i	0.957440	+	1.13451i
$36$		0			0
$37$	279.735			1.24292			0.621462	−	0.783445i	$-0.286539\pi$
$37$	279.735			1.24292			0.621462	+	0.783445i	$0.286539\pi$
$38$		0			0
$39$	−17.0050	+	64.0662i	−0.0698201	+	0.263046i
$40$		0			0
$41$	185.308	+	320.963i	0.705861	+	1.22259i	0.966380	+	0.257118i	$0.0827729\pi$
$41$	185.308	+	320.963i	0.705861	+	1.22259i	−0.260519	+	0.965469i	$0.583894\pi$
$42$		0			0
$43$	−153.876	+	266.520i	−0.545717	+	0.945209i	0.452845	+	0.891589i	$0.350409\pi$
$43$	−153.876	+	266.520i	−0.545717	+	0.945209i	−0.998561	+	0.0536194i	$0.982924\pi$
$44$		0			0
$45$	387.035	−	225.890i	1.28213	−	0.748303i
$46$		0			0
$47$	−163.683	+	283.506i	−0.507990	+	0.879865i	0.491967	+	0.870614i	$0.336278\pi$
$47$	−163.683	+	283.506i	−0.507990	+	0.879865i	−0.999957	+	0.00925130i	$0.997055\pi$
$48$		0			0
$49$	321.647	−	119.131i	0.937747	−	0.347320i
$50$		0			0
$51$	−354.631	+	356.304i	−0.973692	+	0.978285i
$52$		0			0
$53$		−	451.749i		−	1.17080i	−0.810744	−	0.585401i	$-0.800937\pi$
$53$		−	451.749i		−	1.17080i	0.810744	−	0.585401i	$-0.199063\pi$
$54$		0			0
$55$			886.892i			2.17434i
$56$		0			0
$57$	201.451	+	200.506i	0.468121	+	0.465923i
$58$		0			0
$59$	−258.739	−	448.148i	−0.570930	−	0.988880i	−0.996471	−	0.0839410i	$-0.973249\pi$
$59$	−258.739	−	448.148i	−0.570930	−	0.988880i	0.425540	−	0.904939i	$-0.360084\pi$
$60$		0			0
$61$	−234.511	−	135.395i	−0.492230	−	0.284189i	0.233269	−	0.972412i	$-0.425058\pi$
$61$	−234.511	−	135.395i	−0.492230	−	0.284189i	−0.725499	+	0.688223i	$0.758391\pi$
$62$		0			0
$63$	−90.5373	−	491.782i	−0.181058	−	0.983472i
$64$		0			0
$65$	183.360	+	105.863i	0.349892	+	0.202010i
$66$		0			0
$67$	−370.881	−	642.385i	−0.676274	−	1.17134i	−0.976095	−	0.217345i	$-0.930260\pi$
$67$	−370.881	−	642.385i	−0.676274	−	1.17134i	0.299821	−	0.953996i	$-0.403073\pi$
$68$		0			0
$69$	85.6955	−	322.857i	0.149515	−	0.563295i
$70$		0			0
$71$		−	914.198i		−	1.52810i	−0.645155	−	0.764051i	$-0.723207\pi$
$71$		−	914.198i		−	1.52810i	0.645155	−	0.764051i	$-0.276793\pi$
$72$		0			0
$73$			337.210i			0.540650i	0.962769	+	0.270325i	$0.0871311\pi$
$73$			337.210i			0.540650i	−0.962769	+	0.270325i	$0.912869\pi$
$74$		0			0
$75$	−204.146	−	754.777i	−0.314304	−	1.16205i
$76$		0			0
$77$	930.906	+	335.849i	1.37775	+	0.497059i
$78$		0			0
$79$	−498.583	+	863.570i	−0.710062	+	1.22986i	0.254771	+	0.967001i	$0.418000\pi$
$79$	−498.583	+	863.570i	−0.710062	+	1.22986i	−0.964833	+	0.262863i	$0.915333\pi$
$80$		0			0
$81$	−728.968	+	6.86085i	−0.999956	+	0.00941131i
$82$		0			0
$83$	−17.0271	+	29.4917i	−0.0225176	+	0.0390016i	−0.877065	−	0.480372i	$-0.840502\pi$
$83$	−17.0271	+	29.4917i	−0.0225176	+	0.0390016i	0.854547	+	0.519374i	$0.173835\pi$
$84$		0			0
$85$	802.872	+	1390.61i	1.02451	+	1.77451i
$86$		0			0
$87$	652.812	−	176.568i	0.804469	−	0.217587i
$88$		0			0
$89$	208.953			0.248865			0.124433	−	0.992228i	$-0.460289\pi$
$89$	208.953			0.248865			0.124433	+	0.992228i	$0.460289\pi$
$90$		0			0
$91$	180.551	−	152.371i	0.207988	−	0.175526i
$92$		0			0
$93$	293.413	−	1105.43i	0.327156	−	1.23256i
$94$		0			0
$95$	786.243	−	453.937i	0.849124	−	0.490242i
$96$		0			0
$97$	−1100.94	−	635.630i	−1.15241	−	0.665345i	−0.202937	−	0.979192i	$-0.565049\pi$
$97$	−1100.94	−	635.630i	−1.15241	−	0.665345i	−0.949474	+	0.313847i	$0.898382\pi$
$98$		0			0
$99$	715.489	−	1252.84i	0.726357	−	1.27187i
$100$		0			0
$101$	307.124	−	531.954i	0.302574	−	0.524073i	−0.674144	−	0.738600i	$-0.735487\pi$
$101$	307.124	−	531.954i	0.302574	−	0.524073i	0.976718	+	0.214526i	$0.0688208\pi$
$102$		0			0
$103$	−903.410	+	521.584i	−0.864229	+	0.498963i	−0.865426	−	0.501036i	$-0.832952\pi$
$103$	−903.410	+	521.584i	−0.864229	+	0.498963i	0.00119716	+	0.999999i	$0.499619\pi$
$104$		0			0
$105$	−1591.86	−	130.971i	−1.47952	−	0.121729i
$106$		0			0
$107$		−	1128.83i		−	1.01989i	−0.860207	−	0.509945i	$-0.829666\pi$
$107$		−	1128.83i		−	1.01989i	0.860207	−	0.509945i	$-0.170334\pi$
$108$		0			0
$109$	1555.72			1.36707			0.683535	−	0.729918i	$-0.260442\pi$
$109$	1555.72			1.36707			0.683535	+	0.729918i	$0.260442\pi$
$110$		0			0
$111$	−1025.39	+	1030.23i	−0.876809	+	0.880945i
$112$		0			0
$113$	223.834	−	129.231i	0.186341	−	0.107584i	−0.403927	−	0.914791i	$-0.632355\pi$
$113$	223.834	−	129.231i	0.186341	−	0.107584i	0.590269	+	0.807207i	$0.299022\pi$
$114$		0			0
$115$	−924.026	−	533.487i	−0.749268	−	0.432590i
$116$		0			0
$117$	−173.614	−	297.467i	−0.137185	−	0.235050i
$118$		0			0
$119$	1763.66	−	316.117i	1.35861	−	0.243516i
$120$		0			0
$121$	762.167	+	1320.11i	0.572628	+	0.991820i
$122$		0			0
$123$	−1861.33	−	494.050i	−1.36447	−	0.362171i
$124$		0			0
$125$	−422.841			−0.302560
$126$		0			0
$127$	−586.759			−0.409972			−0.204986	−	0.978765i	$-0.565715\pi$
$127$	−586.759			−0.409972			−0.204986	+	0.978765i	$0.565715\pi$
$128$		0			0
$129$	−417.516	−	1543.66i	−0.284963	−	1.05358i
$130$		0			0
$131$	1132.43	+	1961.43i	0.755275	+	1.30817i	0.945237	+	0.326384i	$0.105830\pi$
$131$	1132.43	+	1961.43i	0.755275	+	1.30817i	−0.189962	+	0.981791i	$0.560837\pi$
$132$		0			0
$133$	−178.730	−	997.159i	−0.116525	−	0.650110i
$134$		0			0
$135$	−586.785	+	2253.42i	−0.374092	+	1.43662i
$136$		0			0
$137$	1654.71	+	955.347i	1.03191	+	0.595772i	0.917531	−	0.397665i	$-0.130179\pi$
$137$	1654.71	+	955.347i	1.03191	+	0.595772i	0.114377	+	0.993437i	$0.463513\pi$
$138$		0			0
$139$	−1469.79	+	848.585i	−0.896879	+	0.517813i	−0.876186	−	0.481973i	$-0.839920\pi$
$139$	−1469.79	+	848.585i	−0.896879	+	0.517813i	−0.0206927	+	0.999786i	$0.506587\pi$
$140$		0			0
$141$	−444.126	−	1642.04i	−0.265263	−	0.980741i
$142$		0			0
$143$	681.647			0.398617
$144$		0			0
$145$		−	2160.13i		−	1.23717i
$146$		0			0
$147$	−740.280	+	1621.27i	−0.415355	+	0.909659i
$148$		0			0
$149$	−140.294	+	80.9987i	−0.0771364	+	0.0445347i	−0.538072	−	0.842899i	$-0.680847\pi$
$149$	−140.294	+	80.9987i	−0.0771364	+	0.0445347i	0.460936	+	0.887434i	$0.347514\pi$
$150$		0			0
$151$	1536.40	−	2661.13i	0.828017	−	1.43417i	−0.0715744	−	0.997435i	$-0.522802\pi$
$151$	1536.40	−	2661.13i	0.828017	−	1.43417i	0.899591	−	0.436732i	$-0.143864\pi$
$152$		0			0
$153$	−12.2920	−	2612.12i	−0.00649510	−	1.38024i
$154$		0			0
$155$	−3163.77	−	1826.61i	−1.63949	−	0.946558i
$156$		0			0
$157$	877.841	−	506.822i	0.446238	−	0.257636i	−0.260002	−	0.965608i	$-0.583723\pi$
$157$	877.841	−	506.822i	0.446238	−	0.257636i	0.706240	+	0.707972i	$0.250390\pi$
$158$		0			0
$159$	1663.73	+	1655.92i	0.829828	+	0.825932i
$160$		0			0
$161$	−909.873	+	767.862i	−0.445391	+	0.375876i
$162$		0			0
$163$	1297.23			0.623356			0.311678	−	0.950188i	$-0.399109\pi$
$163$	1297.23			0.623356			0.311678	+	0.950188i	$0.399109\pi$
$164$		0			0
$165$	−3266.31	−	3250.97i	−1.54110	−	1.53387i
$166$		0			0
$167$	716.233	+	1240.55i	0.331879	+	0.574831i	0.982880	−	0.184246i	$-0.0589842\pi$
$167$	716.233	+	1240.55i	0.331879	+	0.574831i	−0.651001	+	0.759077i	$0.725651\pi$
$168$		0			0
$169$	−1017.14	+	1761.73i	−0.462966	+	0.801880i
$170$		0			0
$171$	−1476.87	+	6.94981i	−0.660463	+	0.00310798i
$172$		0			0
$173$	987.659	−	1710.68i	0.434048	−	0.751793i	−0.563169	−	0.826341i	$-0.690418\pi$
$173$	987.659	−	1710.68i	0.434048	−	0.751793i	0.997217	+	0.0745483i	$0.0237515\pi$
$174$		0			0
$175$	−945.765	+	2621.47i	−0.408532	+	1.13237i
$176$		0			0
$177$	2598.90	+	689.823i	1.10365	+	0.292939i
$178$		0			0
$179$		−	2310.07i		−	0.964595i	−0.876007	−	0.482298i	$-0.839802\pi$
$179$		−	2310.07i		−	0.964595i	0.876007	−	0.482298i	$-0.160198\pi$
$180$		0			0
$181$			423.545i			0.173933i	0.996211	+	0.0869665i	$0.0277173\pi$
$181$			423.545i			0.173933i	−0.996211	+	0.0869665i	$0.972283\pi$
$182$		0			0
$183$	1358.26	−	367.372i	0.548663	−	0.148398i
$184$		0			0
$185$	2321.45	+	4020.87i	0.922574	+	1.59795i
$186$		0			0
$187$	4477.06	+	2584.83i	1.75078	+	1.01081i
$188$		0			0
$189$	2143.04	+	1469.23i	0.824780	+	0.565454i
$190$		0			0
$191$	2030.43	+	1172.27i	0.769197	+	0.444096i	0.832588	−	0.553893i	$-0.186858\pi$
$191$	2030.43	+	1172.27i	0.769197	+	0.444096i	−0.0633911	+	0.997989i	$0.520192\pi$
$192$		0			0
$193$	−2025.36	−	3508.02i	−0.755380	−	1.30836i	−0.945185	−	0.326535i	$-0.894119\pi$
$193$	−2025.36	−	3508.02i	−0.755380	−	1.30836i	0.189805	−	0.981822i	$-0.439214\pi$
$194$		0			0
$195$	−1062.00	+	287.241i	−0.390006	+	0.105486i
$196$		0			0
$197$		−	3659.21i		−	1.32339i	−0.749773	−	0.661695i	$-0.769837\pi$
$197$		−	3659.21i		−	1.32339i	0.749773	−	0.661695i	$-0.230163\pi$
$198$		0			0
$199$			557.050i			0.198433i	0.995066	+	0.0992166i	$0.0316337\pi$
$199$			557.050i			0.198433i	−0.995066	+	0.0992166i	$0.968366\pi$
$200$		0			0
$201$	3725.32	+	988.807i	1.30728	+	0.346990i
$202$		0			0
$203$	−2267.33	−	817.999i	−0.783918	−	0.282819i
$204$		0			0
$205$	−3075.65	+	5327.18i	−1.04787	+	1.81496i
$206$		0			0
$207$	874.915	+	1499.06i	0.293772	+	0.503343i
$208$		0			0
$209$	1461.45	−	2531.30i	0.483685	−	0.837768i
$210$		0			0
$211$	2195.03	+	3801.91i	0.716173	+	1.24045i	0.962505	+	0.271262i	$0.0874410\pi$
$211$	2195.03	+	3801.91i	0.716173	+	1.24045i	−0.246333	+	0.969185i	$0.579226\pi$
$212$		0			0
$213$	3366.87	+	3351.06i	1.08307	+	1.07799i
$214$		0			0
$215$	−5107.89			−1.62026
$216$		0			0
$217$	−3115.32	+	2629.08i	−0.974569	+	0.822460i
$218$		0			0
$219$	−1241.90	−	1236.07i	−0.383196	−	0.381397i
$220$		0			0
$221$	1068.80	−	617.071i	0.325318	−	0.187822i
$222$		0			0
$223$	2171.75	+	1253.86i	0.652157	+	0.376523i	0.789282	−	0.614030i	$-0.210453\pi$
$223$	2171.75	+	1253.86i	0.652157	+	0.376523i	−0.137125	+	0.990554i	$0.543786\pi$
$224$		0			0
$225$	3528.06	+	2014.85i	1.04535	+	0.596992i
$226$		0			0
$227$	−1344.84	+	2329.34i	−0.393218	+	0.681073i	−0.992872	−	0.119186i	$-0.961971\pi$
$227$	−1344.84	+	2329.34i	−0.393218	+	0.681073i	0.599654	+	0.800259i	$0.295305\pi$
$228$		0			0
$229$	−3562.03	+	2056.54i	−1.02788	+	0.593449i	−0.916378	−	0.400314i	$-0.868901\pi$
$229$	−3562.03	+	2056.54i	−1.02788	+	0.593449i	−0.111507	+	0.993764i	$0.535568\pi$
$230$		0			0
$231$	−4649.20	+	2197.32i	−1.32422	+	0.625858i
$232$		0			0
$233$			2621.07i			0.736960i	0.929636	+	0.368480i	$0.120122\pi$
$233$			2621.07i			0.736960i	−0.929636	+	0.368480i	$0.879878\pi$
$234$		0			0
$235$	−5433.43			−1.50825
$236$		0			0
$237$	−1352.82	−	5001.70i	−0.370782	−	1.37087i
$238$		0			0
$239$	−4446.09	+	2566.95i	−1.20332	+	0.694738i	−0.961292	−	0.275531i	$-0.911146\pi$
$239$	−4446.09	+	2566.95i	−1.20332	+	0.694738i	−0.242029	+	0.970269i	$0.577813\pi$
$240$		0			0
$241$	−568.896	−	328.452i	−0.152057	−	0.0877903i	0.422041	−	0.906577i	$-0.361314\pi$
$241$	−568.896	−	328.452i	−0.152057	−	0.0877903i	−0.574098	+	0.818786i	$0.694647\pi$
$242$		0			0
$243$	2646.82	−	2709.84i	0.698739	−	0.715376i
$244$		0			0
$245$	4381.63	+	3634.67i	1.14258	+	0.947797i
$246$		0			0
$247$	−348.887	−	604.290i	−0.0898752	−	0.155668i
$248$		0			0
$249$	−46.2001	−	170.813i	−0.0117583	−	0.0434731i
$250$		0			0
$251$	1807.27			0.454479			0.227239	−	0.973839i	$-0.427030\pi$
$251$	1807.27			0.454479			0.227239	+	0.973839i	$0.427030\pi$
$252$		0			0
$253$	−3435.10			−0.853609
$254$		0			0
$255$	−8064.44	−	2140.54i	−1.98045	−	0.525669i
$256$		0			0
$257$	−1044.71	−	1809.50i	−0.253570	−	0.439196i	0.710936	−	0.703256i	$-0.248271\pi$
$257$	−1044.71	−	1809.50i	−0.253570	−	0.439196i	−0.964506	+	0.264061i	$0.914938\pi$
$258$		0			0
$259$	5099.50	−	914.030i	1.22343	−	0.219286i
$260$		0			0
$261$	−1742.66	+	3051.44i	−0.413287	+	0.723677i
$262$		0			0
$263$	−4219.35	−	2436.05i	−0.989265	−	0.571152i	−0.0842101	−	0.996448i	$-0.526837\pi$
$263$	−4219.35	−	2436.05i	−0.989265	−	0.571152i	−0.905054	+	0.425296i	$0.860170\pi$
$264$		0			0
$265$	6493.37	−	3748.95i	1.50522	−	0.869042i
$266$		0			0
$267$	−765.935	+	769.548i	−0.175560	+	0.176388i
$268$		0			0
$269$	−4640.31			−1.05176			−0.525882	−	0.850557i	$-0.676265\pi$
$269$	−4640.31			−1.05176			−0.525882	+	0.850557i	$0.676265\pi$
$270$		0			0
$271$		−	5685.82i		−	1.27450i	−0.770658	−	0.637249i	$-0.780072\pi$
$271$		−	5685.82i		−	1.27450i	0.770658	−	0.637249i	$-0.219928\pi$
$272$		0			0
$273$	−100.662	+	1223.47i	−0.0223163	+	0.271238i
$274$		0			0
$275$	−6963.49	+	4020.37i	−1.52696	+	0.881591i
$276$		0			0
$277$	2507.59	−	4343.28i	0.543923	−	0.942103i	−0.454751	−	0.890619i	$-0.650272\pi$
$277$	2507.59	−	4343.28i	0.543923	−	0.942103i	0.998674	−	0.0514839i	$-0.0163951\pi$
$278$		0			0
$279$	2995.62	+	5132.64i	0.642808	+	1.10137i
$280$		0			0
$281$	4421.84	+	2552.95i	0.938736	+	0.541979i	0.889564	−	0.456811i	$-0.151008\pi$
$281$	4421.84	+	2552.95i	0.938736	+	0.541979i	0.0491721	+	0.998790i	$0.484342\pi$
$282$		0			0
$283$	5499.39	−	3175.07i	1.15514	−	0.666921i	0.205006	−	0.978761i	$-0.434279\pi$
$283$	5499.39	−	3175.07i	1.15514	−	0.666921i	0.950135	+	0.311840i	$0.100945\pi$
$284$		0			0
$285$	−1210.24	+	4559.57i	−0.251539	+	0.947670i
$286$		0			0
$287$	4426.87	+	5245.59i	0.910486	+	1.07888i
$288$		0			0
$289$	4446.84			0.905117
$290$		0			0
$291$	6376.54	−	1724.68i	1.28453	−	0.347431i
$292$		0			0
$293$	762.297	+	1320.34i	0.151993	+	0.263259i	0.931960	−	0.362561i	$-0.118098\pi$
$293$	762.297	+	1320.34i	0.151993	+	0.263259i	−0.779967	+	0.625820i	$0.784764\pi$
$294$		0			0
$295$	4294.41	−	7438.13i	0.847560	−	1.46802i
$296$		0			0
$297$	1991.37	+	7227.45i	0.389061	+	1.41205i
$298$		0			0
$299$	−410.027	+	710.188i	−0.0793059	+	0.137362i
$300$		0			0
$301$	−1934.26	+	5361.38i	−0.370395	+	1.02666i
$302$		0			0
$303$	833.330	+	3081.02i	0.157999	+	0.584158i
$304$		0			0
$305$		−	4494.43i		−	0.843771i
$306$		0			0
$307$			633.080i			0.117693i	0.998267	+	0.0588466i	$0.0187423\pi$
$307$			633.080i			0.117693i	−0.998267	+	0.0588466i	$0.981258\pi$
$308$		0			0
$309$	1390.59	−	5239.05i	0.256013	−	0.964527i
$310$		0			0
$311$	−2222.36	−	3849.24i	−0.405204	−	0.701833i	0.589142	−	0.808030i	$-0.299466\pi$
$311$	−2222.36	−	3849.24i	−0.405204	−	0.701833i	−0.994345	+	0.106197i	$0.966133\pi$
$312$		0			0
$313$	−8892.94	−	5134.34i	−1.60594	−	0.927189i	−0.990266	−	0.139187i	$-0.955551\pi$
$313$	−8892.94	−	5134.34i	−1.60594	−	0.927189i	−0.615673	−	0.788002i	$-0.711116\pi$
$314$		0			0
$315$	6317.46	−	5382.54i	1.12999	−	0.962768i
$316$		0			0
$317$	1625.88	+	938.700i	0.288070	+	0.166318i	0.637071	−	0.770805i	$-0.280146\pi$
$317$	1625.88	+	938.700i	0.288070	+	0.166318i	−0.349001	+	0.937122i	$0.613479\pi$
$318$		0			0
$319$	−3477.25	−	6022.78i	−0.610309	−	1.05709i
$320$		0			0
$321$	4157.34	+	4137.82i	0.722866	+	0.719472i
$322$		0			0
$323$		−	5291.98i		−	0.911621i
$324$		0			0
$325$			1919.55i			0.327623i
$326$		0			0
$327$	−5702.60	+	5729.50i	−0.964387	+	0.968936i
$328$		0			0
$329$	−2057.54	+	5703.08i	−0.344789	+	0.955687i
$330$		0			0
$331$	1549.03	−	2683.00i	0.257228	−	0.445531i	−0.708271	−	0.705941i	$-0.750524\pi$
$331$	1549.03	−	2683.00i	0.257228	−	0.445531i	0.965498	+	0.260410i	$0.0838576\pi$
$332$		0			0
$333$	−35.5415	−	7552.76i	−0.00584883	−	1.24291i
$334$		0			0
$335$	6155.69	−	10662.0i	1.00394	−	1.73888i
$336$		0			0
$337$	−5445.10	−	9431.18i	−0.880158	−	1.52448i	−0.851165	−	0.524899i	$-0.824103\pi$
$337$	−5445.10	−	9431.18i	−0.880158	−	1.52448i	−0.0289934	−	0.999580i	$-0.509230\pi$
$338$		0			0
$339$	−344.542	+	1298.06i	−0.0552005	+	0.207967i
$340$		0			0
$341$	−11761.5			−1.86780
$342$		0			0
$343$	5474.29	−	3222.70i	0.861760	−	0.507317i
$344$		0			0
$345$	5351.85	−	1447.53i	0.835171	−	0.225891i
$346$		0			0
$347$	−3226.80	+	1862.99i	−0.499203	+	0.288215i	−0.728385	−	0.685169i	$-0.759729\pi$
$347$	−3226.80	+	1862.99i	−0.499203	+	0.288215i	0.229181	+	0.973384i	$0.426395\pi$
$348$		0			0
$349$	−529.889	−	305.931i	−0.0812730	−	0.0469230i	0.458813	−	0.888533i	$-0.348275\pi$
$349$	−529.889	−	305.931i	−0.0812730	−	0.0469230i	−0.540086	+	0.841610i	$0.681608\pi$
$350$		0			0
$351$	1731.93	+	450.991i	0.263372	+	0.0685815i
$352$		0			0
$353$	2592.39	−	4490.16i	0.390876	−	0.677017i	−0.601689	−	0.798730i	$-0.705505\pi$
$353$	2592.39	−	4490.16i	0.390876	−	0.677017i	0.992565	+	0.121713i	$0.0388388\pi$
$354$		0			0
$355$	13140.5	−	7586.69i	1.96458	−	1.13425i
$356$		0			0
$357$	−5300.62	+	7654.08i	−0.785822	+	1.13473i
$358$		0			0
$359$			10228.9i			1.50379i	0.659280	+	0.751897i	$0.270861\pi$
$359$			10228.9i			1.50379i	−0.659280	+	0.751897i	$0.729139\pi$
$360$		0			0
$361$	3866.96			0.563778
$362$		0			0
$363$	−7655.59	−	2032.01i	−1.10693	−	0.293810i
$364$		0			0
$365$	−4847.00	+	2798.42i	−0.695078	+	0.401304i
$366$		0			0
$367$	−8636.46	−	4986.26i	−1.22839	−	0.709212i	−0.261698	−	0.965150i	$-0.584282\pi$
$367$	−8636.46	−	4986.26i	−1.22839	−	0.709212i	−0.966693	+	0.255938i	$0.917616\pi$
$368$		0			0
$369$	8642.37	−	5044.05i	1.21925	−	0.711606i
$370$		0			0
$371$	−1476.08	−	8235.27i	−0.206562	−	1.15244i
$372$		0			0
$373$	−4230.45	−	7327.36i	−0.587251	−	1.01715i	−0.994591	−	0.103872i	$-0.966877\pi$
$373$	−4230.45	−	7327.36i	−0.587251	−	1.01715i	0.407340	−	0.913277i	$-0.366457\pi$
$374$		0			0
$375$	1549.96	−	1557.27i	0.213439	−	0.214445i
$376$		0			0
$377$	−1660.23			−0.226807
$378$		0			0
$379$	−1.71044			−0.000231819			−0.000115910	−	1.00000i	$-0.500037\pi$
$379$	−1.71044			−0.000231819			−0.000115910		1.00000i	$0.500037\pi$
$380$		0			0
$381$	2150.81	−	2160.96i	0.289211	−	0.290575i
$382$		0			0
$383$	−1278.28	−	2214.04i	−0.170540	−	0.295384i	0.768069	−	0.640367i	$-0.221218\pi$
$383$	−1278.28	−	2214.04i	−0.170540	−	0.295384i	−0.938609	+	0.344983i	$0.887885\pi$
$384$		0			0
$385$	2897.91	+	16167.8i	0.383613	+	2.14023i
$386$		0			0
$387$	7215.52	+	4120.73i	0.947766	+	0.541263i
$388$		0			0
$389$	2061.39	+	1190.14i	0.268680	+	0.155123i	0.628288	−	0.777981i	$-0.283756\pi$
$389$	2061.39	+	1190.14i	0.268680	+	0.155123i	−0.359607	+	0.933104i	$0.617089\pi$
$390$		0			0
$391$	−5386.12	+	3109.68i	−0.696644	+	0.402208i
$392$		0			0
$393$	−11374.7	−	3019.18i	−1.46000	−	0.387525i
$394$		0			0
$395$	−16550.4			−2.10821
$396$		0			0
$397$		−	12885.5i		−	1.62898i	−0.580177	−	0.814491i	$-0.697017\pi$
$397$		−	12885.5i		−	1.62898i	0.580177	−	0.814491i	$-0.302983\pi$
$398$		0			0
$399$	4327.56	+	2996.93i	0.542979	+	0.376025i
$400$		0			0
$401$	6388.40	−	3688.35i	0.795565	−	0.459320i	−0.0463529	−	0.998925i	$-0.514760\pi$
$401$	6388.40	−	3688.35i	0.795565	−	0.459320i	0.841918	+	0.539605i	$0.181427\pi$
$402$		0			0
$403$	−1403.89	+	2431.61i	−0.173531	+	0.300564i
$404$		0			0
$405$	−6148.13	−	10421.1i	−0.754328	−	1.27859i
$406$		0			0
$407$	12945.1	+	7473.87i	1.57657	+	0.910236i
$408$		0			0
$409$	5869.30	−	3388.64i	0.709580	−	0.409676i	−0.101325	−	0.994853i	$-0.532308\pi$
$409$	5869.30	−	3388.64i	0.709580	−	0.409676i	0.810906	+	0.585177i	$0.198975\pi$
$410$		0			0
$411$	−9583.88	+	2592.18i	−1.15021	+	0.311101i
$412$		0			0
$413$	−6181.06	−	7324.20i	−0.736440	−	0.872641i
$414$		0			0
$415$	−565.212			−0.0668558
$416$		0			0
$417$	2262.41	−	8523.61i	0.265686	−	1.00097i
$418$		0			0
$419$	−2707.65	−	4689.79i	−0.315698	−	0.546804i	0.663888	−	0.747832i	$-0.268905\pi$
$419$	−2707.65	−	4689.79i	−0.315698	−	0.546804i	−0.979586	+	0.201028i	$0.935572\pi$
$420$		0			0
$421$	−409.136	+	708.644i	−0.0473636	+	0.0820361i	−0.888735	−	0.458421i	$-0.848415\pi$
$421$	−409.136	+	708.644i	−0.0473636	+	0.0820361i	0.841372	+	0.540457i	$0.181749\pi$
$422$		0			0
$423$	7675.39	+	4383.36i	0.882246	+	0.503844i
$424$		0			0
$425$	−7279.01	+	12607.6i	−0.830785	+	1.43896i
$426$		0			0
$427$	−4717.47	−	1701.95i	−0.534647	−	0.192888i
$428$		0			0
$429$	−2498.63	+	2510.42i	−0.281201	+	0.282527i
$430$		0			0
$431$		−	10300.0i		−	1.15113i	−0.817757	−	0.575564i	$-0.804783\pi$
$431$		−	10300.0i		−	1.15113i	0.817757	−	0.575564i	$-0.195217\pi$
$432$		0			0
$433$			16119.3i			1.78902i	0.447047	+	0.894511i	$0.352476\pi$
$433$			16119.3i			1.78902i	−0.447047	+	0.894511i	$0.647524\pi$
$434$		0			0
$435$	7955.47	+	7918.12i	0.876864	+	0.872747i
$436$		0			0
$437$	1758.19	+	3045.27i	0.192461	+	0.333353i
$438$		0			0
$439$	8192.95	+	4730.20i	0.890725	+	0.514260i	0.874180	−	0.485603i	$-0.161400\pi$
$439$	8192.95	+	4730.20i	0.890725	+	0.514260i	0.0165456	+	0.999863i	$0.494733\pi$
$440$		0			0
$441$	−3257.36	−	8669.24i	−0.351729	−	0.936102i
$442$		0			0
$443$	3327.36	+	1921.05i	0.356857	+	0.206032i	0.667701	−	0.744429i	$-0.267278\pi$
$443$	3327.36	+	1921.05i	0.356857	+	0.206032i	−0.310844	+	0.950461i	$0.600612\pi$
$444$		0			0
$445$	1734.05	+	3003.46i	0.184723	+	0.319950i
$446$		0			0
$447$	215.951	−	813.591i	0.0228504	−	0.0860885i
$448$		0			0
$449$			15663.0i			1.64628i	0.567837	+	0.823141i	$0.307780\pi$
$449$			15663.0i			1.64628i	−0.567837	+	0.823141i	$0.692220\pi$
$450$		0			0
$451$			19804.0i			2.06770i
$452$		0			0
$453$	4168.78	+	15412.9i	0.432376	+	1.59859i
$454$		0			0
$455$	3688.50	+	1330.73i	0.380043	+	0.137111i
$456$		0			0
$457$	−2476.59	+	4289.58i	−0.253501	+	0.439077i	−0.964487	−	0.264129i	$-0.914915\pi$
$457$	−2476.59	+	4289.58i	−0.253501	+	0.439077i	0.710986	+	0.703206i	$0.248249\pi$
$458$		0			0
$459$	9665.15	+	9529.66i	0.982856	+	0.969078i
$460$		0			0
$461$	−1755.21	+	3040.12i	−0.177329	+	0.307142i	−0.940965	−	0.338505i	$-0.890079\pi$
$461$	−1755.21	+	3040.12i	−0.177329	+	0.307142i	0.763636	+	0.645647i	$0.223412\pi$
$462$		0			0
$463$	−7086.75	−	12274.6i	−0.711338	−	1.23207i	−0.964355	−	0.264611i	$-0.914756\pi$
$463$	−7086.75	−	12274.6i	−0.711338	−	1.23207i	0.253017	−	0.967462i	$-0.418577\pi$
$464$		0			0
$465$	18324.2	−	4956.20i	1.82745	−	0.494276i
$466$		0			0
$467$	−1922.47			−0.190495			−0.0952474	−	0.995454i	$-0.530364\pi$
$467$	−1922.47			−0.190495			−0.0952474	+	0.995454i	$0.530364\pi$
$468$		0			0
$469$	−8860.05	−	10498.7i	−0.872323	−	1.03365i
$470$		0			0
$471$	−1351.24	+	5090.77i	−0.132191	+	0.498026i
$472$		0			0
$473$	−14241.6	+	8222.39i	−1.38442	+	0.799294i
$474$		0			0
$475$	7128.24	+	4115.49i	0.688560	+	0.397541i
$476$		0			0
$477$	−12197.1	+	57.3966i	−1.17079	+	0.00550945i
$478$		0			0
$479$	8556.48	−	14820.3i	0.816192	−	1.41369i	−0.0922775	−	0.995733i	$-0.529415\pi$
$479$	8556.48	−	14820.3i	0.816192	−	1.41369i	0.908469	−	0.417952i	$-0.137252\pi$
$480$		0			0
$481$	3090.36	−	1784.22i	0.292948	−	0.169134i
$482$		0			0
$483$	507.277	−	6165.60i	0.0477887	−	0.580838i
$484$		0			0
$485$		−	21099.7i		−	1.97544i
$486$		0			0
$487$	3067.21			0.285397			0.142699	−	0.989766i	$-0.454422\pi$
$487$	3067.21			0.285397			0.142699	+	0.989766i	$0.454422\pi$
$488$		0			0
$489$	−4755.11	+	4777.54i	−0.439741	+	0.441815i
$490$		0			0
$491$	7470.97	−	4313.37i	0.686681	−	0.396455i	−0.115687	−	0.993286i	$-0.536907\pi$
$491$	7470.97	−	4313.37i	0.686681	−	0.396455i	0.802367	+	0.596831i	$0.203574\pi$
$492$		0			0
$493$	−10904.4	−	6295.67i	−0.996167	−	0.575137i
$494$		0			0
$495$	23945.8	−	112.683i	2.17431	−	0.0102318i
$496$		0			0
$497$	−2987.13	−	16665.6i	−0.269600	−	1.50413i
$498$		0			0
$499$	6142.19	+	10638.6i	0.551026	+	0.954406i	0.998201	+	0.0599589i	$0.0190970\pi$
$499$	6142.19	+	10638.6i	0.551026	+	0.954406i	−0.447174	+	0.894447i	$0.647570\pi$
$500$		0			0
$501$	−7194.20	−	1909.55i	−0.641543	−	0.170284i
$502$		0			0
$503$	−3977.87			−0.352613			−0.176307	−	0.984335i	$-0.556415\pi$
$503$	−3977.87			−0.352613			−0.176307	+	0.984335i	$0.556415\pi$
$504$		0			0
$505$	10195.0			0.898356
$506$		0			0
$507$	−2759.83	−	10203.7i	−0.241752	−	0.893815i
$508$		0			0
$509$	8362.32	+	14484.0i	0.728199	+	1.26128i	0.957644	+	0.287956i	$0.0929758\pi$
$509$	8362.32	+	14484.0i	0.728199	+	1.26128i	−0.229444	+	0.973322i	$0.573691\pi$
$510$		0			0
$511$	1101.83	+	6147.25i	0.0953856	+	0.532169i
$512$		0			0
$513$	5388.00	−	5464.60i	0.463715	−	0.470308i
$514$		0			0
$515$	−14994.3	−	8656.97i	−1.28297	−	0.740722i
$516$		0			0
$517$	−15149.3	+	8746.43i	−1.28871	+	0.744038i
$518$		0			0
$519$	2679.85	+	9908.03i	0.226652	+	0.837985i
$520$		0			0
$521$	9088.77			0.764273			0.382137	−	0.924106i	$-0.375188\pi$
$521$	9088.77			0.764273			0.382137	+	0.924106i	$0.375188\pi$
$522$		0			0
$523$		−	13218.7i		−	1.10519i	−0.833450	−	0.552596i	$-0.813637\pi$
$523$		−	13218.7i		−	1.10519i	0.833450	−	0.552596i	$-0.186363\pi$
$524$		0			0
$525$	−6187.76	−	13092.3i	−0.514392	−	1.08837i
$526$		0			0
$527$	−18441.6	+	10647.2i	−1.52434	+	0.880078i
$528$		0			0
$529$	−4017.20	+	6958.00i	−0.330172	+	0.571875i
$530$		0			0
$531$	−12067.0	+	7042.80i	−0.986183	+	0.575577i
$532$		0			0
$533$	4094.36	+	2363.88i	0.332733	+	0.192103i
$534$		0			0
$535$	16225.6	−	9367.87i	1.31121	−	0.757025i
$536$		0			0
$537$	8507.68	+	8467.74i	0.683675	+	0.680465i
$538$		0			0
$539$	18067.6	+	3080.72i	1.44383	+	0.246189i
$540$		0			0
$541$	−20011.9			−1.59035			−0.795174	−	0.606382i	$-0.792620\pi$
$541$	−20011.9			−1.59035			−0.795174	+	0.606382i	$0.792620\pi$
$542$		0			0
$543$	−1559.86	−	1552.54i	−0.123278	−	0.122699i
$544$		0			0
$545$	12910.5	+	22361.6i	1.01472	+	1.75755i
$546$		0			0
$547$	8725.59	−	15113.2i	0.682046	−	1.18134i	−0.292309	−	0.956324i	$-0.594424\pi$
$547$	8725.59	−	15113.2i	0.682046	−	1.18134i	0.974355	−	0.225015i	$-0.0722430\pi$
$548$		0			0
$549$	−3625.82	+	6348.92i	−0.281870	+	0.493562i
$550$		0			0
$551$	−3559.52	+	6165.27i	−0.275210	+	0.476678i
$552$		0			0
$553$	−6267.33	+	17371.8i	−0.481942	+	1.33585i
$554$		0			0
$555$	−23317.8	−	6189.21i	−1.78340	−	0.473365i
$556$		0			0
$557$			15169.7i			1.15397i	0.816754	+	0.576986i	$0.195771\pi$
$557$			15169.7i			1.15397i	−0.816754	+	0.576986i	$0.804229\pi$
$558$		0			0
$559$			3925.82i			0.297039i
$560$		0			0
$561$	−25930.6	+	7013.53i	−1.95150	+	0.527828i
$562$		0			0
$563$	3488.62	+	6042.47i	0.261151	+	0.452326i	0.966548	−	0.256486i	$-0.0825647\pi$
$563$	3488.62	+	6042.47i	0.261151	+	0.452326i	−0.705397	+	0.708812i	$0.749231\pi$
$564$		0			0
$565$	3715.08	+	2144.90i	0.276628	+	0.159711i
$566$		0			0
$567$	−13266.5	+	2506.96i	−0.982610	+	0.185684i
$568$		0			0
$569$	17354.8	+	10019.8i	1.27865	+	0.738227i	0.976600	−	0.215066i	$-0.0689967\pi$
$569$	17354.8	+	10019.8i	1.27865	+	0.738227i	0.302047	+	0.953293i	$0.402330\pi$
$570$		0			0
$571$	8327.71	+	14424.0i	0.610339	+	1.05714i	0.991183	+	0.132500i	$0.0423003\pi$
$571$	8327.71	+	14424.0i	0.610339	+	1.05714i	−0.380844	+	0.924639i	$0.624366\pi$
$572$		0			0
$573$	−11760.0	+	3180.76i	−0.857385	+	0.231899i
$574$		0			0
$575$		−	9673.40i		−	0.701580i
$576$		0			0
$577$		−	8678.08i		−	0.626123i	−0.949733	−	0.313062i	$-0.898645\pi$
$577$		−	8678.08i		−	0.626123i	0.949733	−	0.313062i	$-0.101355\pi$
$578$		0			0
$579$	20343.7	+	5399.81i	1.46020	+	0.387579i
$580$		0			0
$581$	−214.035	+	593.262i	−0.0152834	+	0.0423626i
$582$		0			0
$583$	12069.7	−	20905.3i	0.857419	−	1.48509i
$584$		0			0
$585$	2834.97	−	4964.11i	0.200361	−	0.350839i
$586$		0			0
$587$	5941.85	−	10291.6i	0.417796	−	0.723645i	−0.577921	−	0.816093i	$-0.696136\pi$
$587$	5941.85	−	10291.6i	0.417796	−	0.723645i	0.995718	+	0.0924479i	$0.0294692\pi$
$588$		0			0
$589$	6019.87	+	10426.7i	0.421128	+	0.729415i
$590$		0			0
$591$	13476.4	+	13413.1i	0.937977	+	0.933574i
$592$		0			0
$593$	−12702.9			−0.879675			−0.439838	−	0.898077i	$-0.644964\pi$
$593$	−12702.9			−0.879675			−0.439838	+	0.898077i	$0.644964\pi$
$594$		0			0
$595$	19180.0	+	22727.2i	1.32152	+	1.56592i
$596$		0			0
$597$	−2051.54	−	2041.91i	−0.140643	−	0.139983i
$598$		0			0
$599$	20674.6	−	11936.5i	1.41025	−	0.814209i	0.414840	−	0.909894i	$-0.363838\pi$
$599$	20674.6	−	11936.5i	1.41025	−	0.814209i	0.995412	+	0.0956853i	$0.0305042\pi$
$600$		0			0
$601$	−9016.55	−	5205.71i	−0.611968	−	0.353320i	0.161767	−	0.986829i	$-0.448281\pi$
$601$	−9016.55	−	5205.71i	−0.611968	−	0.353320i	−0.773735	+	0.633509i	$0.781614\pi$
$602$		0			0
$603$	−17297.1	+	10095.3i	−1.16815	+	0.681778i
$604$		0			0
$605$	−12650.1	+	21910.5i	−0.850079	+	1.47238i
$606$		0			0
$607$	−13446.8	+	7763.51i	−0.899158	+	0.519129i	−0.876927	−	0.480624i	$-0.840410\pi$
$607$	−13446.8	+	7763.51i	−0.899158	+	0.519129i	−0.0222310	+	0.999753i	$0.507077\pi$
$608$		0			0
$609$	11323.7	−	5351.84i	0.753461	−	0.356104i
$610$		0			0
$611$			4176.03i			0.276504i
$612$		0			0
$613$	−9275.88			−0.611173			−0.305587	−	0.952164i	$-0.598853\pi$
$613$	−9275.88			−0.611173			−0.305587	+	0.952164i	$0.598853\pi$
$614$		0			0
$615$	−8345.27	−	30854.4i	−0.547177	−	2.02304i
$616$		0			0
$617$	2687.23	−	1551.47i	0.175338	−	0.101232i	−0.409762	−	0.912192i	$-0.634388\pi$
$617$	2687.23	−	1551.47i	0.175338	−	0.101232i	0.585101	+	0.810961i	$0.301055\pi$
$618$		0			0
$619$	−5859.30	−	3382.87i	−0.380460	−	0.219659i	0.297558	−	0.954704i	$-0.403828\pi$
$619$	−5859.30	−	3382.87i	−0.380460	−	0.219659i	−0.678019	+	0.735045i	$0.737161\pi$
$620$		0			0
$621$	−8727.92	−	2272.73i	−0.563992	−	0.146862i
$622$		0			0
$623$	3809.17	−	682.752i	0.244962	−	0.0439067i
$624$		0			0
$625$	5895.72	+	10211.7i	0.377326	+	0.653548i
$626$		0			0
$627$	3965.39	+	14661.0i	0.252572	+	0.933817i
$628$		0			0
$629$	27063.3			1.71556
$630$		0			0
$631$	−4096.60			−0.258452			−0.129226	−	0.991615i	$-0.541249\pi$
$631$	−4096.60			−0.258452			−0.129226	+	0.991615i	$0.541249\pi$
$632$		0			0
$633$	−22048.0	−	5852.18i	−1.38441	−	0.367462i
$634$		0			0
$635$	−4869.36	−	8433.98i	−0.304307	−	0.527075i
$636$		0			0
$637$	2793.53	−	3367.63i	0.173758	−	0.209467i
$638$		0			0
$639$	−24683.1	+	116.153i	−1.52809	+	0.00719081i
$640$		0			0
$641$	15136.8	+	8739.26i	0.932713	+	0.538502i	0.887669	−	0.460483i	$-0.152324\pi$
$641$	15136.8	+	8739.26i	0.932713	+	0.538502i	0.0450444	+	0.998985i	$0.485657\pi$
$642$		0			0
$643$	−8965.15	+	5176.03i	−0.549846	+	0.317454i	−0.749060	−	0.662502i	$-0.769495\pi$
$643$	−8965.15	+	5176.03i	−0.549846	+	0.317454i	0.199214	+	0.979956i	$0.436161\pi$
$644$		0			0
$645$	18723.4	−	18811.7i	1.14300	−	1.14839i
$646$		0			0
$647$	13536.7			0.822539			0.411269	−	0.911514i	$-0.365086\pi$
$647$	13536.7			0.822539			0.411269	+	0.911514i	$0.365086\pi$
$648$		0			0
$649$		−	27651.6i		−	1.67245i
$650$		0			0
$651$	1736.87	−	21110.4i	0.104567	−	1.27094i
$652$		0			0
$653$	20174.8	−	11647.9i	1.20904	−	0.698039i	0.246490	−	0.969145i	$-0.420723\pi$
$653$	20174.8	−	11647.9i	1.20904	−	0.698039i	0.962549	+	0.271106i	$0.0873895\pi$
$654$		0			0
$655$	−18795.5	+	32554.8i	−1.12122	+	1.94202i
$656$		0			0
$657$	9104.57	−	42.8439i	0.540644	−	0.00254414i
$658$		0			0
$659$	−1032.74	−	596.254i	−0.0610469	−	0.0352454i	0.469166	−	0.883110i	$-0.344555\pi$
$659$	−1032.74	−	596.254i	−0.0610469	−	0.0352454i	−0.530213	+	0.847865i	$0.677888\pi$
$660$		0			0
$661$	10922.7	−	6306.24i	0.642731	−	0.371081i	−0.142935	−	0.989732i	$-0.545654\pi$
$661$	10922.7	−	6306.24i	0.642731	−	0.371081i	0.785666	+	0.618651i	$0.212321\pi$
$662$		0			0
$663$	−1645.17	+	6198.17i	−0.0963699	+	0.363072i
$664$		0			0
$665$	12849.8	−	10844.2i	0.749312	−	0.632361i
$666$		0			0
$667$	8366.60			0.485691
$668$		0			0
$669$	−12578.5	+	3402.15i	−0.726927	+	0.196614i
$670$		0			0
$671$	−7234.87	−	12531.2i	−0.416243	−	0.720954i
$672$		0			0
$673$	−12824.0	+	22211.8i	−0.734515	+	1.27222i	0.220421	+	0.975405i	$0.429257\pi$
$673$	−12824.0	+	22211.8i	−0.734515	+	1.27222i	−0.954936	+	0.296813i	$0.904076\pi$
$674$		0			0
$675$	−20352.8	+	5607.79i	−1.16056	+	0.319769i
$676$		0			0
$677$	−7049.87	+	12210.7i	−0.400220	+	0.693201i	−0.993752	−	0.111609i	$-0.964399\pi$
$677$	−7049.87	+	12210.7i	−0.400220	+	0.693201i	0.593533	+	0.804810i	$0.297733\pi$
$678$		0			0
$679$	−22146.8	−	7990.05i	−1.25172	−	0.451591i
$680$		0			0
$681$	−3649.01	−	13491.3i	−0.205331	−	0.759157i
$682$		0			0
$683$		−	6066.68i		−	0.339875i	−0.985455	−	0.169938i	$-0.945643\pi$
$683$		−	6066.68i		−	0.339875i	0.985455	−	0.169938i	$-0.0543567\pi$
$684$		0			0
$685$			31712.7i			1.76888i
$686$		0			0
$687$	5482.94	−	20656.9i	0.304494	−	1.14718i
$688$		0			0
$689$	−2881.37	−	4990.67i	−0.159320	−	0.275950i
$690$		0			0
$691$	−27362.7	−	15797.9i	−1.50641	−	0.869725i	−0.999972	−	0.00744663i	$-0.997630\pi$
$691$	−27362.7	−	15797.9i	−1.50641	−	0.869725i	−0.506435	−	0.862278i	$-0.669037\pi$
$692$		0			0
$693$	8949.54	−	25176.8i	0.490570	−	1.38007i
$694$		0			0
$695$	−24394.8	−	14084.4i	−1.33144	−	0.768706i
$696$		0			0
$697$	17927.9	+	31052.0i	0.974271	+	1.68749i
$698$		0			0
$699$	−9653.04	−	9607.73i	−0.522334	−	0.519882i
$700$		0			0
$701$		−	14828.2i		−	0.798936i	−0.916747	−	0.399468i	$-0.869195\pi$
$701$		−	14828.2i		−	0.798936i	0.916747	−	0.399468i	$-0.130805\pi$
$702$		0			0
$703$		−	15301.4i		−	0.820914i
$704$		0			0
$705$	19916.7	−	20010.6i	1.06398	−	1.06900i
$706$		0			0
$707$	3860.63	−	10700.9i	0.205366	−	0.569235i
$708$		0			0
$709$	10513.5	−	18210.0i	0.556903	−	0.964584i	−0.440850	−	0.897581i	$-0.645323\pi$
$709$	10513.5	−	18210.0i	0.556903	−	0.964584i	0.997753	−	0.0670034i	$-0.0213438\pi$
$710$		0			0
$711$	23379.5	+	13351.9i	1.23319	+	0.704267i
$712$		0			0
$713$	7074.80	−	12253.9i	0.371604	−	0.643636i
$714$		0			0
$715$	5656.81	+	9797.88i	0.295878	+	0.512476i
$716$		0			0
$717$	6843.75	−	25783.7i	0.356464	−	1.34297i
$718$		0			0
$719$	−36268.4			−1.88120			−0.940601	−	0.339514i	$-0.889738\pi$
$719$	−36268.4			−1.88120			−0.940601	+	0.339514i	$0.889738\pi$
$720$		0			0
$721$	−14764.7	+	12460.2i	−0.762642	+	0.643610i
$722$		0			0
$723$	3294.98	−	891.202i	0.169491	−	0.0458425i
$724$		0			0
$725$	16960.4	−	9792.09i	0.868819	−	0.501613i
$726$		0			0
$727$	20411.1	+	11784.3i	1.04127	+	0.601178i	0.920193	−	0.391465i	$-0.128032\pi$
$727$	20411.1	+	11784.3i	1.04127	+	0.601178i	0.121078	+	0.992643i	$0.461365\pi$
$728$		0			0
$729$	277.859	+	19681.0i	0.0141167	+	0.999900i
$730$		0			0
$731$	−14886.9	+	25784.8i	−0.753231	+	1.30463i
$732$		0			0
$733$	−15961.7	+	9215.47i	−0.804307	+	0.464367i	−0.844975	−	0.534806i	$-0.820385\pi$
$733$	−15961.7	+	9215.47i	−0.804307	+	0.464367i	0.0406678	+	0.999173i	$0.487051\pi$
$734$		0			0
$735$	−29447.2	+	2813.82i	−1.47779	+	0.141210i
$736$		0			0
$737$		−	39636.3i		−	1.98104i
$738$		0			0
$739$	−2029.42			−0.101020			−0.0505098	−	0.998724i	$-0.516085\pi$
$739$	−2029.42			−0.101020			−0.0505098	+	0.998724i	$0.516085\pi$
$740$		0			0
$741$	3504.40	+	930.168i	0.173734	+	0.0461142i
$742$		0			0
$743$	1592.75	−	919.575i	0.0786438	−	0.0454050i	−0.460162	−	0.887835i	$-0.652209\pi$
$743$	1592.75	−	919.575i	0.0786438	−	0.0454050i	0.538806	+	0.842430i	$0.318875\pi$
$744$		0			0
$745$	−2328.52	−	1344.37i	−0.114511	−	0.0661128i
$746$		0			0
$747$	798.431	+	455.978i	0.0391072	+	0.0223338i
$748$		0			0
$749$	−3688.44	−	20578.3i	−0.179937	−	1.00389i
$750$		0			0
$751$	1091.30	+	1890.19i	0.0530254	+	0.0918427i	0.891320	−	0.453375i	$-0.149780\pi$
$751$	1091.30	+	1890.19i	0.0530254	+	0.0918427i	−0.838294	+	0.545218i	$0.816447\pi$
$752$		0			0
$753$	−6624.71	+	6655.95i	−0.320608	+	0.322120i
$754$		0			0
$755$	51000.8			2.45842
$756$		0			0
$757$	14605.5			0.701250			0.350625	−	0.936516i	$-0.385969\pi$
$757$	14605.5			0.701250			0.350625	+	0.936516i	$0.385969\pi$
$758$		0			0
$759$	12591.6	−	12651.0i	0.602171	−	0.605011i
$760$		0			0
$761$	−8971.11	−	15538.4i	−0.427336	−	0.740167i	0.569300	−	0.822130i	$-0.307214\pi$
$761$	−8971.11	−	15538.4i	−0.427336	−	0.740167i	−0.996635	+	0.0819631i	$0.973881\pi$
$762$		0			0
$763$	28360.3	−	5083.28i	1.34563	−	0.241189i
$764$		0			0
$765$	37444.2	−	21854.0i	1.76967	−	1.03285i
$766$		0			0
$767$	−5716.80	−	3300.60i	−0.269129	−	0.155381i
$768$		0			0
$769$	4600.21	−	2655.93i	0.215719	−	0.124545i	−0.388248	−	0.921555i	$-0.626919\pi$
$769$	4600.21	−	2655.93i	0.215719	−	0.124545i	0.603966	+	0.797010i	$0.293586\pi$
$770$		0			0
$771$	10493.6	+	2785.31i	0.490167	+	0.130104i
$772$		0			0
$773$	−21593.6			−1.00475			−0.502373	−	0.864651i	$-0.667540\pi$
$773$	−21593.6			−1.00475			−0.502373	+	0.864651i	$0.667540\pi$
$774$		0			0
$775$		−	33120.8i		−	1.53514i
$776$		0			0
$777$	−15326.4	+	22131.2i	−0.707632	+	1.02182i
$778$		0			0
$779$	17556.6	−	10136.3i	0.807483	−	0.466200i
$780$		0			0
$781$	24425.2	−	42305.7i	1.11908	−	1.93831i
$782$		0			0
$783$	−4850.22	−	17603.3i	−0.221370	−	0.803436i
$784$		0			0
$785$	14569.9	+	8411.96i	0.662451	+	0.382466i
$786$		0			0
$787$	−30052.6	+	17350.9i	−1.36120	+	0.785887i	−0.989783	−	0.142581i	$-0.954460\pi$
$787$	−30052.6	+	17350.9i	−1.36120	+	0.785887i	−0.371413	+	0.928468i	$0.621126\pi$
$788$		0			0
$789$	24438.0	−	6609.81i	1.10268	−	0.298245i
$790$		0			0
$791$	3658.18	−	3087.22i	0.164437	−	0.138772i
$792$		0			0
$793$	−3454.33			−0.154687
$794$		0			0
$795$	−9995.07	+	37656.3i	−0.445898	+	1.67991i
$796$		0			0
$797$	−5560.35	−	9630.81i	−0.247124	−	0.428031i	0.715603	−	0.698508i	$-0.246152\pi$
$797$	−5560.35	−	9630.81i	−0.247124	−	0.428031i	−0.962727	+	0.270476i	$0.912819\pi$
$798$		0			0
$799$	−15835.7	+	27428.2i	−0.701159	+	1.21444i
$800$		0			0
$801$	−26.5484	−	5641.68i	−0.00117109	−	0.248863i
$802$		0			0
$803$	−9009.46	+	15604.8i	−0.395936	+	0.685782i
$804$		0			0
$805$	−18587.9	−	6706.08i	−0.813836	−	0.293613i
$806$		0			0
$807$	17009.4	−	17089.7i	0.741958	−	0.745458i
$808$		0			0
$809$			39619.1i			1.72180i	0.508777	+	0.860898i	$0.330098\pi$
$809$			39619.1i			1.72180i	−0.508777	+	0.860898i	$0.669902\pi$
$810$		0			0
$811$			2483.62i			0.107536i	0.998553	+	0.0537679i	$0.0171231\pi$
$811$			2483.62i			0.107536i	−0.998553	+	0.0537679i	$0.982877\pi$
$812$		0			0
$813$	20940.1	+	20841.8i	0.903324	+	0.899083i
$814$		0			0
$815$	10765.4	+	18646.2i	0.462693	+	0.801408i
$816$		0			0
$817$	14578.6	+	8416.93i	0.624283	+	0.360430i
$818$		0			0
$819$	−4136.91	−	4855.47i	−0.176502	−	0.207160i
$820$		0			0
$821$	−4241.97	−	2449.10i	−0.180324	−	0.104110i	0.407121	−	0.913374i	$-0.366533\pi$
$821$	−4241.97	−	2449.10i	−0.180324	−	0.104110i	−0.587445	+	0.809264i	$0.699866\pi$
$822$		0			0
$823$	−7968.20	−	13801.3i	−0.337490	−	0.584549i	0.646470	−	0.762939i	$-0.276245\pi$
$823$	−7968.20	−	13801.3i	−0.337490	−	0.584549i	−0.983960	+	0.178390i	$0.942911\pi$
$824$		0			0
$825$	10718.7	−	40382.6i	0.452337	−	1.70417i
$826$		0			0
$827$		−	11183.9i		−	0.470256i	−0.971964	−	0.235128i	$-0.924449\pi$
$827$		−	11183.9i		−	0.470256i	0.971964	−	0.235128i	$-0.0755509\pi$
$828$		0			0
$829$		−	6180.21i		−	0.258924i	−0.991584	−	0.129462i	$-0.958675\pi$
$829$		−	6180.21i		−	0.258924i	0.991584	−	0.129462i	$-0.0413250\pi$
$830$		0			0
$831$	6803.95	+	25155.8i	0.284027	+	1.05011i
$832$		0			0
$833$	31118.2	−	11525.5i	1.29433	−	0.479392i
$834$		0			0
$835$	−11887.7	+	20590.0i	−0.492682	+	0.853350i
$836$		0			0
$837$	−29883.5	−	7781.61i	−1.23408	−	0.321352i
$838$		0			0
$839$	−10159.7	+	17597.1i	−0.418059	+	0.724100i	−0.995744	−	0.0921599i	$-0.970623\pi$
$839$	−10159.7	+	17597.1i	−0.418059	+	0.724100i	0.577685	+	0.816260i	$0.303956\pi$
$840$		0			0
$841$	−3725.25	−	6452.32i	−0.152743	−	0.264558i
$842$		0			0
$843$	−25610.8	+	6927.01i	−1.04636	+	0.283012i
$844$		0			0
$845$	−33763.8			−1.37457
$846$		0			0
$847$	18207.6	+	21574.9i	0.738630	+	0.875235i
$848$		0			0
$849$	−8465.06	+	31892.0i	−0.342191	+	1.28920i
$850$		0			0
$851$	−15573.6	+	8991.42i	−0.627328	+	0.362188i
$852$		0			0
$853$	−21731.2	−	12546.5i	−0.872289	−	0.503616i	−0.00418087	−	0.999991i	$-0.501331\pi$
$853$	−21731.2	−	12546.5i	−0.872289	−	0.503616i	−0.868108	+	0.496375i	$0.834664\pi$
$854$		0			0
$855$	−12356.1	−	21170.6i	−0.494232	−	0.846808i
$856$		0			0
$857$	8181.75	−	14171.2i	0.326118	−	0.564853i	−0.655620	−	0.755091i	$-0.727593\pi$
$857$	8181.75	−	14171.2i	0.326118	−	0.564853i	0.981738	+	0.190238i	$0.0609260\pi$
$858$		0			0
$859$	30710.8	−	17730.9i	1.21984	−	0.704273i	0.254954	−	0.966953i	$-0.417940\pi$
$859$	30710.8	−	17730.9i	1.21984	−	0.704273i	0.964883	+	0.262680i	$0.0846064\pi$
$860$		0			0
$861$	−35545.8	−	2924.55i	−1.40697	−	0.115759i
$862$		0			0
$863$			33166.4i			1.30822i	0.756398	+	0.654111i	$0.226957\pi$
$863$			33166.4i			1.30822i	−0.756398	+	0.654111i	$0.773043\pi$
$864$		0			0
$865$	32785.3			1.28871
$866$		0			0
$867$	−16300.2	+	16377.1i	−0.638507	+	0.641518i
$868$		0			0
$869$	−46145.2	+	26641.9i	−1.80134	+	1.04001i
$870$		0			0
$871$	−8194.58	−	4731.14i	−0.318786	−	0.184051i
$872$		0			0
$873$	−17021.9	+	29805.9i	−0.659914	+	1.15553i
$874$		0			0
$875$	−7708.28	+	1381.63i	−0.297814	+	0.0533800i
$876$		0			0
$877$	−5617.94	−	9730.56i	−0.216311	−	0.374661i	0.737367	−	0.675493i	$-0.236069\pi$
$877$	−5617.94	−	9730.56i	−0.216311	−	0.374661i	−0.953677	+	0.300832i	$0.902736\pi$
$878$		0			0
$879$	−7656.89	−	2032.36i	−0.293812	−	0.0779862i
$880$		0			0
$881$	25537.5			0.976597			0.488298	−	0.872677i	$-0.337618\pi$
$881$	25537.5			0.976597			0.488298	+	0.872677i	$0.337618\pi$
$882$		0			0
$883$	17936.9			0.683606			0.341803	−	0.939772i	$-0.388962\pi$
$883$	17936.9			0.683606			0.341803	+	0.939772i	$0.388962\pi$
$884$		0			0
$885$	11652.2	+	43080.8i	0.442580	+	1.63632i
$886$		0			0
$887$	−2646.98	−	4584.71i	−0.100200	−	0.173551i	0.811567	−	0.584259i	$-0.198615\pi$
$887$	−2646.98	−	4584.71i	−0.100200	−	0.173551i	−0.911767	+	0.410708i	$0.865281\pi$
$888$		0			0
$889$	−10696.5	+	1917.23i	−0.403541	+	0.0723304i
$890$		0			0
$891$	−33917.3	−	19158.8i	−1.27528	−	0.720364i
$892$		0			0
$893$	15507.7	+	8953.37i	0.581125	+	0.335513i
$894$		0			0
$895$	33204.5	−	19170.6i	1.24012	−	0.715982i
$896$		0			0
$897$	−1112.54	−	4113.33i	−0.0414121	−	0.153110i
$898$		0			0
$899$	28646.4			1.06275
$900$		0			0
$901$		−	43705.0i		−	1.61601i
$902$		0			0
$903$	−12655.1	−	26776.2i	−0.466373	−	0.986774i
$904$		0			0
$905$	−6087.97	+	3514.89i	−0.223614	+	0.129104i
$906$		0			0
$907$	−6770.38	+	11726.6i	−0.247857	+	0.429302i	−0.962931	−	0.269747i	$-0.913060\pi$
$907$	−6770.38	+	11726.6i	−0.247857	+	0.429302i	0.715074	+	0.699049i	$0.246393\pi$
$908$		0			0
$909$	−14401.6	−	8224.66i	−0.525491	−	0.300104i
$910$		0			0
$911$	−23505.1	−	13570.7i	−0.854840	−	0.493542i	0.00744116	−	0.999972i	$-0.497631\pi$
$911$	−23505.1	−	13570.7i	−0.854840	−	0.493542i	−0.862281	+	0.506430i	$0.830965\pi$
$912$		0			0
$913$	−1575.90	+	909.846i	−0.0571245	+	0.0329808i
$914$		0			0
$915$	16552.4	+	16474.7i	0.598038	+	0.595231i
$916$		0			0
$917$	27052.9	+	32056.2i	0.974226	+	1.15440i
$918$		0			0
$919$	−32872.5			−1.17994			−0.589969	−	0.807426i	$-0.700860\pi$
$919$	−32872.5			−1.17994			−0.589969	+	0.807426i	$0.700860\pi$
$920$		0			0
$921$	−2331.55	−	2320.61i	−0.0834172	−	0.0830256i
$922$		0			0
$923$	−5830.98	−	10099.5i	−0.207940	−	0.360163i
$924$		0			0
$925$	−21046.7	+	36454.0i	−0.748122	+	1.29578i
$926$		0			0
$927$	14197.4	+	24325.5i	0.503024	+	0.861872i
$928$		0			0
$929$	−11828.2	+	20487.0i	−0.417729	+	0.723528i	−0.995711	−	0.0925216i	$-0.970507\pi$
$929$	−11828.2	+	20487.0i	−0.417729	+	0.723528i	0.577981	+	0.816050i	$0.303841\pi$
$930$		0			0
$931$	−6516.41	−	17594.0i	−0.229395	−	0.619354i
$932$		0			0
$933$	22322.5	+	5925.03i	0.783285	+	0.207906i
$934$		0			0
$935$			85803.5i			3.00115i
$936$		0			0
$937$			26716.0i			0.931456i	0.884928	+	0.465728i	$0.154207\pi$
$937$			26716.0i			0.931456i	−0.884928	+	0.465728i	$0.845793\pi$
$938$		0			0
$939$	51506.9	−	13931.2i	1.79006	−	0.484162i
$940$		0			0
$941$	−19766.0	−	34235.6i	−0.684752	−	1.18603i	−0.973515	−	0.228625i	$-0.926577\pi$
$941$	−19766.0	−	34235.6i	−0.684752	−	1.18603i	0.288762	−	0.957401i	$-0.406756\pi$
$942$		0			0
$943$	−20633.2	−	11912.6i	−0.712524	−	0.411376i
$944$		0			0
$945$	−3333.93	+	42996.5i	−0.114765	+	1.48008i
$946$		0			0
$947$	−38984.8	−	22507.9i	−1.33774	−	0.772343i	−0.351265	−	0.936276i	$-0.614248\pi$
$947$	−38984.8	−	22507.9i	−1.33774	−	0.772343i	−0.986471	+	0.163933i	$0.947582\pi$
$948$		0			0
$949$	2150.81	+	3725.31i	0.0735702	+	0.127427i
$950$		0			0
$951$	−9416.89	+	2547.01i	−0.321097	+	0.0868480i
$952$		0			0
$953$		−	9240.19i		−	0.314081i	−0.987592	−	0.157040i	$-0.949805\pi$
$953$		−	9240.19i		−	0.314081i	0.987592	−	0.157040i	$-0.0501953\pi$
$954$		0			0
$955$			38913.4i			1.31854i
$956$		0			0
$957$	34927.2	+	9270.70i	1.17977	+	0.313144i
$958$		0			0
$959$	33286.5	+	12009.0i	1.12083	+	0.404370i
$960$		0			0
$961$	9327.94	−	16156.5i	0.313113	−	0.542327i
$962$		0			0
$963$	−30478.1	+	143.423i	−1.01988	+	0.00479930i
$964$		0			0
$965$	33615.8	−	58224.3i	1.12138	−	1.94229i
$966$		0			0
$967$	12391.8	+	21463.2i	0.412093	+	0.713766i	0.995118	−	0.0986881i	$-0.0314646\pi$
$967$	12391.8	+	21463.2i	0.412093	+	0.713766i	−0.583026	+	0.812454i	$0.698131\pi$
$968$		0			0
$969$	19489.7	+	19398.2i	0.646128	+	0.643095i
$970$		0			0
$971$	37516.1			1.23991			0.619953	−	0.784639i	$-0.287152\pi$
$971$	37516.1			1.23991			0.619953	+	0.784639i	$0.287152\pi$
$972$		0			0
$973$	−24021.2	+	20272.0i	−0.791454	+	0.667925i
$974$		0			0
$975$	−7069.44	−	7036.26i	−0.232209	−	0.231118i
$976$		0			0
$977$	14175.0	−	8183.92i	0.464173	−	0.267991i	−0.249624	−	0.968343i	$-0.580307\pi$
$977$	14175.0	−	8183.92i	0.464173	−	0.267991i	0.713797	+	0.700352i	$0.246974\pi$
$978$		0			0
$979$	9669.60	+	5582.75i	0.315671	+	0.182253i
$980$		0			0
$981$	−197.660	−	42003.9i	−0.00643303	−	1.36705i
$982$		0			0
$983$	−14758.1	+	25561.7i	−0.478850	+	0.829393i	−0.999706	−	0.0242520i	$-0.992280\pi$
$983$	−14758.1	+	25561.7i	−0.478850	+	0.829393i	0.520856	+	0.853645i	$0.325613\pi$
$984$		0			0
$985$	52596.9	−	30366.8i	1.70140	−	0.982302i
$986$		0			0
$987$	−13461.6	−	28482.7i	−0.434132	−	0.918557i
$988$		0			0
$989$		−	19783.9i		−	0.636087i
$990$		0			0
$991$	−13893.1			−0.445336			−0.222668	−	0.974894i	$-0.571477\pi$
$991$	−13893.1			−0.445336			−0.222668	+	0.974894i	$0.571477\pi$
$992$		0			0
$993$	4203.04	+	15539.6i	0.134320	+	0.496611i
$994$		0			0
$995$	−8006.95	+	4622.81i	−0.255113	+	0.147289i
$996$		0			0
$997$	17139.3	+	9895.40i	0.544441	+	0.314333i	0.746877	−	0.664962i	$-0.231552\pi$
$997$	17139.3	+	9895.40i	0.544441	+	0.314333i	−0.202436	+	0.979296i	$0.564886\pi$
$998$		0			0
$999$	27946.1	+	27554.4i	0.885061	+	0.872654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.8	yes	48
3.2	odd	2		756.4.x.a.629.3		48
7.6	odd	2	inner	252.4.x.a.209.17	yes	48
9.2	odd	6		2268.4.f.a.1133.44		48
9.4	even	3		756.4.x.a.125.22		48
9.5	odd	6	inner	252.4.x.a.41.17	yes	48
9.7	even	3		2268.4.f.a.1133.5		48
21.20	even	2		756.4.x.a.629.22		48
63.13	odd	6		756.4.x.a.125.3		48
63.20	even	6		2268.4.f.a.1133.6		48
63.34	odd	6		2268.4.f.a.1133.43		48
63.41	even	6	inner	252.4.x.a.41.8	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.8	✓	48	63.41	even	6	inner
252.4.x.a.41.17	yes	48	9.5	odd	6	inner
252.4.x.a.209.8	yes	48	1.1	even	1	trivial
252.4.x.a.209.17	yes	48	7.6	odd	2	inner
756.4.x.a.125.3		48	63.13	odd	6
756.4.x.a.125.22		48	9.4	even	3
756.4.x.a.629.3		48	3.2	odd	2
756.4.x.a.629.22		48	21.20	even	2
2268.4.f.a.1133.5		48	9.7	even	3
2268.4.f.a.1133.6		48	63.20	even	6
2268.4.f.a.1133.43		48	63.34	odd	6
2268.4.f.a.1133.44		48	9.2	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.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.66558 + 3.68287i) q^{3} +(8.29874 + 14.3738i) q^{5} +(18.2297 - 3.26749i) q^{7} +(-0.127054 - 26.9997i) q^{9} +O(q^{10})\)	\(q+(-3.66558 + 3.68287i) q^{3} +(8.29874 + 14.3738i) q^{5} +(18.2297 - 3.26749i) q^{7} +(-0.127054 - 26.9997i) q^{9} +(46.2764 + 26.7177i) q^{11} +(11.0474 - 6.37824i) q^{13} +(-83.3566 - 22.1253i) q^{15} +96.7463 q^{17} -54.6996i q^{19} +(-54.7888 + 79.1150i) q^{21} +(-55.6727 + 32.1426i) q^{23} +(-75.2381 + 130.316i) q^{25} +(99.9021 + 98.5016i) q^{27} +(-112.711 - 65.0740i) q^{29} +(-190.618 + 110.053i) q^{31} +(-268.027 + 72.4940i) q^{33} +(198.250 + 234.915i) q^{35} +279.735 q^{37} +(-17.0050 + 64.0662i) q^{39} +(185.308 + 320.963i) q^{41} +(-153.876 + 266.520i) q^{43} +(387.035 - 225.890i) q^{45} +(-163.683 + 283.506i) q^{47} +(321.647 - 119.131i) q^{49} +(-354.631 + 356.304i) q^{51} -451.749i q^{53} +886.892i q^{55} +(201.451 + 200.506i) q^{57} +(-258.739 - 448.148i) q^{59} +(-234.511 - 135.395i) q^{61} +(-90.5373 - 491.782i) q^{63} +(183.360 + 105.863i) q^{65} +(-370.881 - 642.385i) q^{67} +(85.6955 - 322.857i) q^{69} -914.198i q^{71} +337.210i q^{73} +(-204.146 - 754.777i) q^{75} +(930.906 + 335.849i) q^{77} +(-498.583 + 863.570i) q^{79} +(-728.968 + 6.86085i) q^{81} +(-17.0271 + 29.4917i) q^{83} +(802.872 + 1390.61i) q^{85} +(652.812 - 176.568i) q^{87} +208.953 q^{89} +(180.551 - 152.371i) q^{91} +(293.413 - 1105.43i) q^{93} +(786.243 - 453.937i) q^{95} +(-1100.94 - 635.630i) q^{97} +(715.489 - 1252.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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