LMFDB - Embedded newform 252.4.w.a.5.5

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			5.5
Character	$\chi$	$=$	252.5
Dual form			252.4.w.a.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.59055 + 2.43451i) q^{3} +(1.72890 + 2.99454i) q^{5} +(-17.7636 + 5.23980i) q^{7} +(15.1463 - 22.3515i) q^{9} +O(q^{10})$	\(q+(-4.59055 + 2.43451i) q^{3} +(1.72890 + 2.99454i) q^{5} +(-17.7636 + 5.23980i) q^{7} +(15.1463 - 22.3515i) q^{9} +(-26.9308 - 15.5485i) q^{11} +(-2.16207 - 1.24827i) q^{13} +(-15.2268 - 9.53756i) q^{15} +(0.621716 + 1.07684i) q^{17} +(76.0352 + 43.8990i) q^{19} +(68.7882 - 67.2992i) q^{21} +(-43.0633 + 24.8626i) q^{23} +(56.5218 - 97.8987i) q^{25} +(-15.1150 + 139.480i) q^{27} +(228.650 - 132.011i) q^{29} -257.043i q^{31} +(161.480 + 5.81287i) q^{33} +(-46.4022 - 44.1346i) q^{35} +(-47.7268 + 82.6653i) q^{37} +(12.9640 + 0.466672i) q^{39} +(93.9702 - 162.761i) q^{41} +(-133.204 - 230.716i) q^{43} +(93.1188 + 6.71278i) q^{45} +571.849 q^{47} +(288.089 - 186.155i) q^{49} +(-5.47561 - 3.42973i) q^{51} +(167.674 - 96.8064i) q^{53} -107.527i q^{55} +(-455.916 - 16.4118i) q^{57} +291.060 q^{59} -158.882i q^{61} +(-151.935 + 476.406i) q^{63} -8.63255i q^{65} -443.977 q^{67} +(137.156 - 218.971i) q^{69} +405.345i q^{71} +(-505.536 + 291.872i) q^{73} +(-21.1309 + 587.012i) q^{75} +(559.858 + 135.085i) q^{77} -1287.12 q^{79} +(-270.178 - 677.085i) q^{81} +(-610.720 - 1057.80i) q^{83} +(-2.14977 + 3.72351i) q^{85} +(-728.248 + 1162.66i) q^{87} +(-406.886 + 704.748i) q^{89} +(44.9468 + 10.8450i) q^{91} +(625.774 + 1179.97i) q^{93} +303.587i q^{95} +(496.443 - 286.621i) q^{97} +(-755.434 + 366.441i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−4.59055	+	2.43451i	−0.883452	+	0.468522i
$3$	−4.59055	+	2.43451i	−0.883452	+	0.468522i
$4$		0			0
$5$	1.72890	+	2.99454i	0.154637	+	0.267840i	0.932927	−	0.360066i	$-0.117246\pi$
$5$	1.72890	+	2.99454i	0.154637	+	0.267840i	−0.778290	+	0.627906i	$0.783912\pi$
$6$		0			0
$7$	−17.7636	+	5.23980i	−0.959143	+	0.282923i
$7$	−17.7636	+	5.23980i	−0.959143	+	0.282923i
$8$		0			0
$9$	15.1463	−	22.3515i	0.560975	−	0.827833i
$10$		0			0
$11$	−26.9308	−	15.5485i	−0.738176	−	0.426186i	0.0832299	−	0.996530i	$-0.473476\pi$
$11$	−26.9308	−	15.5485i	−0.738176	−	0.426186i	−0.821406	+	0.570344i	$0.806810\pi$
$12$		0			0
$13$	−2.16207	−	1.24827i	−0.0461270	−	0.0266314i	0.476759	−	0.879034i	$-0.341811\pi$
$13$	−2.16207	−	1.24827i	−0.0461270	−	0.0266314i	−0.522886	+	0.852403i	$0.675145\pi$
$14$		0			0
$15$	−15.2268	−	9.53756i	−0.262103	−	0.164173i
$16$		0			0
$17$	0.621716	+	1.07684i	0.00886990	+	0.0153631i	0.870426	−	0.492299i	$-0.163843\pi$
$17$	0.621716	+	1.07684i	0.00886990	+	0.0153631i	−0.861556	+	0.507662i	$0.830510\pi$
$18$		0			0
$19$	76.0352	+	43.8990i	0.918088	+	0.530059i	0.883025	−	0.469326i	$-0.155503\pi$
$19$	76.0352	+	43.8990i	0.918088	+	0.530059i	0.0350638	+	0.999385i	$0.488837\pi$
$20$		0			0
$21$	68.7882	−	67.2992i	0.714801	−	0.699328i
$22$		0			0
$23$	−43.0633	+	24.8626i	−0.390405	+	0.225401i	−0.682336	−	0.731039i	$-0.739036\pi$
$23$	−43.0633	+	24.8626i	−0.390405	+	0.225401i	0.291930	+	0.956440i	$0.405702\pi$
$24$		0			0
$25$	56.5218	−	97.8987i	0.452175	−	0.783189i
$26$		0			0
$27$	−15.1150	+	139.480i	−0.107736	+	0.994180i
$28$		0			0
$29$	228.650	−	132.011i	1.46411	−	0.845307i	0.464917	−	0.885354i	$-0.346084\pi$
$29$	228.650	−	132.011i	1.46411	−	0.845307i	0.999198	+	0.0400471i	$0.0127508\pi$
$30$		0			0
$31$		−	257.043i		−	1.48924i	−0.667491	−	0.744618i	$-0.732632\pi$
$31$		−	257.043i		−	1.48924i	0.667491	−	0.744618i	$-0.267368\pi$
$32$		0			0
$33$	161.480	+	5.81287i	0.851820	+	0.0306634i
$34$		0			0
$35$	−46.4022	−	44.1346i	−0.224097	−	0.213146i
$36$		0			0
$37$	−47.7268	+	82.6653i	−0.212061	+	0.367300i	−0.952359	−	0.304978i	$-0.901351\pi$
$37$	−47.7268	+	82.6653i	−0.212061	+	0.367300i	0.740299	+	0.672278i	$0.234684\pi$
$38$		0			0
$39$	12.9640	+	0.466672i	0.0532284	+	0.00191609i
$40$		0			0
$41$	93.9702	−	162.761i	0.357944	−	0.619976i	−0.629674	−	0.776860i	$-0.716811\pi$
$41$	93.9702	−	162.761i	0.357944	−	0.619976i	0.987617	+	0.156883i	$0.0501447\pi$
$42$		0			0
$43$	−133.204	−	230.716i	−0.472405	−	0.818230i	0.527096	−	0.849806i	$-0.323281\pi$
$43$	−133.204	−	230.716i	−0.472405	−	0.818230i	−0.999501	+	0.0315755i	$0.989948\pi$
$44$		0			0
$45$	93.1188	+	6.71278i	0.308474	+	0.0222374i
$46$		0			0
$47$	571.849			1.77474			0.887369	−	0.461059i	$-0.152530\pi$
$47$	571.849			1.77474			0.887369	+	0.461059i	$0.152530\pi$
$48$		0			0
$49$	288.089	−	186.155i	0.839910	−	0.542726i
$50$		0			0
$51$	−5.47561	−	3.42973i	−0.0150341	−	0.00941684i
$52$		0			0
$53$	167.674	−	96.8064i	0.434561	−	0.250894i	−0.266727	−	0.963772i	$-0.585942\pi$
$53$	167.674	−	96.8064i	0.434561	−	0.250894i	0.701288	+	0.712878i	$0.252609\pi$
$54$		0			0
$55$		−	107.527i		−	0.263617i
$56$		0			0
$57$	−455.916	−	16.4118i	−1.05943	−	0.0381368i
$58$		0			0
$59$	291.060			0.642250			0.321125	−	0.947037i	$-0.395939\pi$
$59$	291.060			0.642250			0.321125	+	0.947037i	$0.395939\pi$
$60$		0			0
$61$		−	158.882i		−	0.333488i	−0.986000	−	0.166744i	$-0.946675\pi$
$61$		−	158.882i		−	0.333488i	0.986000	−	0.166744i	$-0.0533253\pi$
$62$		0			0
$63$	−151.935	+	476.406i	−0.303842	+	0.952722i
$64$		0			0
$65$		−	8.63255i		−	0.0164729i
$66$		0			0
$67$	−443.977			−0.809559			−0.404780	−	0.914414i	$-0.632652\pi$
$67$	−443.977			−0.809559			−0.404780	+	0.914414i	$0.632652\pi$
$68$		0			0
$69$	137.156	−	218.971i	0.239299	−	0.382044i
$70$		0			0
$71$			405.345i			0.677543i	0.940869	+	0.338772i	$0.110011\pi$
$71$			405.345i			0.677543i	−0.940869	+	0.338772i	$0.889989\pi$
$72$		0			0
$73$	−505.536	+	291.872i	−0.810528	+	0.467959i	−0.847139	−	0.531371i	$-0.821677\pi$
$73$	−505.536	+	291.872i	−0.810528	+	0.467959i	0.0366111	+	0.999330i	$0.488344\pi$
$74$		0			0
$75$	−21.1309	+	587.012i	−0.0325332	+	0.903764i
$76$		0			0
$77$	559.858	+	135.085i	0.828593	+	0.199927i
$78$		0			0
$79$	−1287.12			−1.83307			−0.916533	−	0.399959i	$-0.869024\pi$
$79$	−1287.12			−1.83307			−0.916533	+	0.399959i	$0.869024\pi$
$80$		0			0
$81$	−270.178	−	677.085i	−0.370615	−	0.928787i
$82$		0			0
$83$	−610.720	−	1057.80i	−0.807653	−	1.39890i	−0.914485	−	0.404619i	$-0.867404\pi$
$83$	−610.720	−	1057.80i	−0.807653	−	1.39890i	0.106832	−	0.994277i	$-0.465929\pi$
$84$		0			0
$85$	−2.14977	+	3.72351i	−0.00274324	+	0.00475142i
$86$		0			0
$87$	−728.248	+	1162.66i	−0.897430	+	1.43276i
$88$		0			0
$89$	−406.886	+	704.748i	−0.484605	+	0.839361i	−0.999844	−	0.0176859i	$-0.994370\pi$
$89$	−406.886	+	704.748i	−0.484605	+	0.839361i	0.515238	+	0.857047i	$0.327703\pi$
$90$		0			0
$91$	44.9468	+	10.8450i	0.0517770	+	0.0124930i
$92$		0			0
$93$	625.774	+	1179.97i	0.697739	+	1.31567i
$94$		0			0
$95$			303.587i			0.327867i
$96$		0			0
$97$	496.443	−	286.621i	0.519651	−	0.300021i	−0.217141	−	0.976140i	$-0.569673\pi$
$97$	496.443	−	286.621i	0.519651	−	0.300021i	0.736792	+	0.676120i	$0.236340\pi$
$98$		0			0
$99$	−755.434	+	366.441i	−0.766909	+	0.372007i
$100$		0			0
$101$	507.488	−	878.995i	0.499970	−	0.865973i	−0.500030	−	0.866008i	$-0.666678\pi$
$101$	507.488	−	878.995i	0.499970	−	0.865973i	1.00000		3.46559e-5i	$1.10313e-5\pi$
$102$		0			0
$103$	684.671	−	395.295i	0.654977	−	0.378151i	−0.135383	−	0.990793i	$-0.543227\pi$
$103$	684.671	−	395.295i	0.654977	−	0.378151i	0.790360	+	0.612642i	$0.209893\pi$
$104$		0			0
$105$	320.458	+	89.6357i	0.297843	+	0.0833099i
$106$		0			0
$107$	739.624	+	427.022i	0.668244	+	0.385811i	0.795411	−	0.606070i	$-0.207255\pi$
$107$	739.624	+	427.022i	0.668244	+	0.385811i	−0.127167	+	0.991881i	$0.540588\pi$
$108$		0			0
$109$	−51.1159	−	88.5354i	−0.0449176	−	0.0777996i	0.842693	−	0.538395i	$-0.180969\pi$
$109$	−51.1159	−	88.5354i	−0.0449176	−	0.0777996i	−0.887610	+	0.460596i	$0.847636\pi$
$110$		0			0
$111$	17.8429	−	495.671i	0.0152574	−	0.423847i
$112$		0			0
$113$	−459.268	−	265.159i	−0.382339	−	0.220743i	0.296496	−	0.955034i	$-0.404182\pi$
$113$	−459.268	−	265.159i	−0.382339	−	0.220743i	−0.678835	+	0.734290i	$0.737515\pi$
$114$		0			0
$115$	−148.904	−	85.9698i	−0.120742	−	0.0697107i
$116$		0			0
$117$	−60.6482	+	29.4188i	−0.0479225	+	0.0232459i
$118$		0			0
$119$	−16.6863	−	15.8709i	−0.0128541	−	0.0122259i
$120$		0			0
$121$	−181.989	−	315.214i	−0.136731	−	0.236825i
$122$		0			0
$123$	−35.1312	+	975.935i	−0.0257534	+	0.715424i
$124$		0			0
$125$	823.106			0.588967
$126$		0			0
$127$	−2163.65			−1.51176			−0.755878	−	0.654713i	$-0.772790\pi$
$127$	−2163.65			−1.51176			−0.755878	+	0.654713i	$0.772790\pi$
$128$		0			0
$129$	1173.16	+	734.828i	0.800706	+	0.501535i
$130$		0			0
$131$	1285.28	+	2226.16i	0.857215	+	1.48474i	0.874575	+	0.484890i	$0.161140\pi$
$131$	1285.28	+	2226.16i	0.857215	+	1.48474i	−0.0173605	+	0.999849i	$0.505526\pi$
$132$		0			0
$133$	−1580.68	−	381.393i	−1.03054	−	0.248654i
$134$		0			0
$135$	−443.809	+	195.883i	−0.282941	+	0.124881i
$136$		0			0
$137$	−536.065	−	309.497i	−0.334300	−	0.193008i	0.323449	−	0.946246i	$-0.395158\pi$
$137$	−536.065	−	309.497i	−0.334300	−	0.193008i	−0.657749	+	0.753238i	$0.728491\pi$
$138$		0			0
$139$	−977.790	−	564.527i	−0.596655	−	0.344479i	0.171070	−	0.985259i	$-0.445278\pi$
$139$	−977.790	−	564.527i	−0.596655	−	0.344479i	−0.767724	+	0.640780i	$0.778611\pi$
$140$		0			0
$141$	−2625.10	+	1392.17i	−1.56790	+	0.831504i
$142$		0			0
$143$	38.8175	+	67.2339i	0.0226999	+	0.0393174i
$144$		0			0
$145$	790.627	+	456.469i	0.452814	+	0.261432i
$146$		0			0
$147$	−869.291	+	1555.91i	−0.487741	+	0.872989i
$148$		0			0
$149$	1168.34	−	674.540i	0.642375	−	0.370875i	−0.143154	−	0.989700i	$-0.545724\pi$
$149$	1168.34	−	674.540i	0.642375	−	0.370875i	0.785529	+	0.618825i	$0.212391\pi$
$150$		0			0
$151$	212.158	−	367.468i	0.114339	−	0.198040i	−0.803177	−	0.595741i	$-0.796858\pi$
$151$	212.158	−	367.468i	0.114339	−	0.198040i	0.917515	+	0.397701i	$0.130192\pi$
$152$		0			0
$153$	33.4858	+	2.41393i	0.0176939	+	0.00127552i
$154$		0			0
$155$	769.726	−	444.401i	0.398876	−	0.230291i
$156$		0			0
$157$		−	1014.13i		−	0.515517i	−0.966209	−	0.257758i	$-0.917016\pi$
$157$		−	1014.13i		−	0.515517i	0.966209	−	0.257758i	$-0.0829838\pi$
$158$		0			0
$159$	−534.038	+	852.598i	−0.266365	+	0.425254i
$160$		0			0
$161$	634.683	−	667.292i	0.310683	−	0.326646i
$162$		0			0
$163$	−40.6443	+	70.3980i	−0.0195307	+	0.0338282i	−0.875626	−	0.482991i	$-0.839551\pi$
$163$	−40.6443	+	70.3980i	−0.0195307	+	0.0338282i	0.856095	+	0.516819i	$0.172884\pi$
$164$		0			0
$165$	261.776	+	493.608i	0.123510	+	0.232893i
$166$		0			0
$167$	240.081	−	415.832i	0.111245	−	0.192683i	−0.805027	−	0.593238i	$-0.797849\pi$
$167$	240.081	−	415.832i	0.111245	−	0.192683i	0.916273	+	0.400555i	$0.131183\pi$
$168$		0			0
$169$	−1095.38	−	1897.26i	−0.498582	−	0.863569i
$170$		0			0
$171$	2132.86	−	1034.59i	0.953824	−	0.462675i
$172$		0			0
$173$	891.966			0.391994			0.195997	−	0.980605i	$-0.437206\pi$
$173$	891.966			0.391994			0.195997	+	0.980605i	$0.437206\pi$
$174$		0			0
$175$	−491.060	+	2035.19i	−0.212118	+	0.879121i
$176$		0			0
$177$	−1336.13	+	708.589i	−0.567397	+	0.300908i
$178$		0			0
$179$	777.039	−	448.624i	0.324462	−	0.187328i	−0.328918	−	0.944359i	$-0.606684\pi$
$179$	777.039	−	448.624i	0.324462	−	0.187328i	0.653380	+	0.757031i	$0.273351\pi$
$180$		0			0
$181$		−	2318.80i		−	0.952240i	−0.879380	−	0.476120i	$-0.842043\pi$
$181$		−	2318.80i		−	0.952240i	0.879380	−	0.476120i	$-0.157957\pi$
$182$		0			0
$183$	386.800	+	729.355i	0.156246	+	0.294620i
$184$		0			0
$185$	−330.059			−0.131170
$186$		0			0
$187$		−	38.6670i		−	0.0151209i
$188$		0			0
$189$	−462.349	−	2556.85i	−0.177941	−	0.984041i
$190$		0			0
$191$		−	2042.71i		−	0.773850i	−0.922111	−	0.386925i	$-0.873537\pi$
$191$		−	2042.71i		−	0.773850i	0.922111	−	0.386925i	$-0.126463\pi$
$192$		0			0
$193$	485.529			0.181083			0.0905417	−	0.995893i	$-0.471140\pi$
$193$	485.529			0.181083			0.0905417	+	0.995893i	$0.471140\pi$
$194$		0			0
$195$	21.0160	+	39.6282i	0.00771790	+	0.0145530i
$196$		0			0
$197$			2212.99i			0.800351i	0.916439	+	0.400175i	$0.131051\pi$
$197$			2212.99i			0.800351i	−0.916439	+	0.400175i	$0.868949\pi$
$198$		0			0
$199$	930.187	−	537.044i	0.331353	−	0.191307i	−0.325089	−	0.945684i	$-0.605394\pi$
$199$	930.187	−	537.044i	0.331353	−	0.191307i	0.656442	+	0.754377i	$0.272061\pi$
$200$		0			0
$201$	2038.10	−	1080.87i	0.715206	−	0.379296i
$202$		0			0
$203$	−3369.94	+	3543.08i	−1.16514	+	1.22500i
$204$		0			0
$205$	649.860			0.221406
$206$		0			0
$207$	−96.5339	+	1339.11i	−0.0324134	+	0.449634i
$208$		0			0
$209$	−1365.13	−	2364.47i	−0.451807	−	0.782553i
$210$		0			0
$211$	1512.38	−	2619.51i	0.493442	−	0.854666i	−0.506530	−	0.862223i	$-0.669072\pi$
$211$	1512.38	−	2619.51i	0.493442	−	0.854666i	0.999971	+	0.00755635i	$0.00240528\pi$
$212$		0			0
$213$	−986.816	−	1860.76i	−0.317444	−	0.598577i
$214$		0			0
$215$	460.593	−	797.770i	0.146103	−	0.253058i
$216$		0			0
$217$	1346.85	+	4566.00i	0.421338	+	1.42839i
$218$		0			0
$219$	1610.13	−	2570.59i	0.496814	−	0.793169i
$220$		0			0
$221$		−	3.10429i		−	0.000944873i
$222$		0			0
$223$	−1185.83	+	684.638i	−0.356094	+	0.205591i	−0.667366	−	0.744730i	$-0.732578\pi$
$223$	−1185.83	+	684.638i	−0.356094	+	0.205591i	0.311272	+	0.950321i	$0.399245\pi$
$224$		0			0
$225$	−1332.08	−	2746.15i	−0.394692	−	0.813674i
$226$		0			0
$227$	3019.13	−	5229.28i	0.882760	−	1.52898i	0.0344994	−	0.999405i	$-0.489016\pi$
$227$	3019.13	−	5229.28i	0.882760	−	1.52898i	0.848260	−	0.529580i	$-0.177650\pi$
$228$		0			0
$229$	2244.60	−	1295.92i	0.647719	−	0.373961i	−0.139863	−	0.990171i	$-0.544666\pi$
$229$	2244.60	−	1295.92i	0.647719	−	0.373961i	0.787582	+	0.616210i	$0.211333\pi$
$230$		0			0
$231$	−2898.92	+	742.866i	−0.825692	+	0.211589i
$232$		0			0
$233$	1457.96	+	841.752i	0.409931	+	0.236674i	0.690760	−	0.723084i	$-0.257276\pi$
$233$	1457.96	+	841.752i	0.409931	+	0.236674i	−0.280829	+	0.959758i	$0.590609\pi$
$234$		0			0
$235$	988.668	+	1712.42i	0.274441	+	0.475346i
$236$		0			0
$237$	5908.59	−	3133.51i	1.61943	−	0.858831i
$238$		0			0
$239$	−3631.74	−	2096.79i	−0.982920	−	0.567489i	−0.0797694	−	0.996813i	$-0.525418\pi$
$239$	−3631.74	−	2096.79i	−0.982920	−	0.567489i	−0.903150	+	0.429324i	$0.858752\pi$
$240$		0			0
$241$	3280.56	+	1894.03i	0.876844	+	0.506246i	0.869617	−	0.493727i	$-0.164366\pi$
$241$	3280.56	+	1894.03i	0.876844	+	0.506246i	0.00722781	+	0.999974i	$0.497699\pi$
$242$		0			0
$243$	2888.64	+	2450.44i	0.762577	+	0.646897i
$244$		0			0
$245$	1055.53	+	540.851i	0.275245	+	0.141035i
$246$		0			0
$247$	−109.596	−	189.826i	−0.0282325	−	0.0489000i
$248$		0			0
$249$	5378.76	+	3369.07i	1.36894	+	0.857455i
$250$		0			0
$251$	3435.63			0.863966			0.431983	−	0.901882i	$-0.357814\pi$
$251$	3435.63			0.863966			0.431983	+	0.901882i	$0.357814\pi$
$252$		0			0
$253$	1546.30			0.384250
$254$		0			0
$255$	0.803700	−	22.3266i	0.000197371	−	0.00548292i
$256$		0			0
$257$	−1665.56	−	2884.84i	−0.404260	−	0.700199i	0.589975	−	0.807421i	$-0.299138\pi$
$257$	−1665.56	−	2884.84i	−0.404260	−	0.700199i	−0.994235	+	0.107223i	$0.965804\pi$
$258$		0			0
$259$	414.649	−	1718.51i	0.0994790	−	0.412290i
$260$		0			0
$261$	512.560	−	7110.17i	0.121558	−	1.68624i
$262$		0			0
$263$	5119.17	+	2955.56i	1.20024	+	0.692956i	0.960607	−	0.277909i	$-0.0896413\pi$
$263$	5119.17	+	2955.56i	1.20024	+	0.692956i	0.239628	+	0.970865i	$0.422975\pi$
$264$		0			0
$265$	579.781	+	334.737i	0.134399	+	0.0775952i
$266$		0			0
$267$	152.116	−	4225.75i	0.0348665	−	0.968583i
$268$		0			0
$269$	460.264	+	797.201i	0.104323	+	0.180692i	0.913461	−	0.406926i	$-0.133399\pi$
$269$	460.264	+	797.201i	0.104323	+	0.180692i	−0.809139	+	0.587618i	$0.800066\pi$
$270$		0			0
$271$	−2199.30	−	1269.77i	−0.492981	−	0.284623i	0.232829	−	0.972518i	$-0.425202\pi$
$271$	−2199.30	−	1269.77i	−0.492981	−	0.284623i	−0.725810	+	0.687895i	$0.758535\pi$
$272$		0			0
$273$	−232.733	+	59.6392i	−0.0515958	+	0.0132217i
$274$		0			0
$275$	−3044.35	+	1757.66i	−0.667569	+	0.385421i
$276$		0			0
$277$	−1439.58	+	2493.43i	−0.312260	+	0.540850i	−0.978851	−	0.204573i	$-0.934419\pi$
$277$	−1439.58	+	2493.43i	−0.312260	+	0.540850i	0.666591	+	0.745423i	$0.267753\pi$
$278$		0			0
$279$	−5745.30	−	3893.26i	−1.23284	−	0.835423i
$280$		0			0
$281$	−6811.30	+	3932.50i	−1.44601	+	0.834852i	−0.998240	−	0.0592980i	$-0.981114\pi$
$281$	−6811.30	+	3932.50i	−1.44601	+	0.834852i	−0.447767	+	0.894150i	$0.647780\pi$
$282$		0			0
$283$			5461.46i			1.14717i	0.819145	+	0.573586i	$0.194448\pi$
$283$			5461.46i			1.14717i	−0.819145	+	0.573586i	$0.805552\pi$
$284$		0			0
$285$	−739.087	−	1393.63i	−0.153613	−	0.289655i
$286$		0			0
$287$	−816.411	+	3383.61i	−0.167914	+	0.695916i
$288$		0			0
$289$	2455.73	−	4253.44i	0.499843	−	0.865753i
$290$		0			0
$291$	−1581.16	+	2524.35i	−0.318520	+	0.508522i
$292$		0			0
$293$	−411.644	+	712.989i	−0.0820768	+	0.142161i	−0.904142	−	0.427232i	$-0.859489\pi$
$293$	−411.644	+	712.989i	−0.0820768	+	0.142161i	0.822065	+	0.569394i	$0.192822\pi$
$294$		0			0
$295$	503.213	+	871.590i	0.0993159	+	0.172020i
$296$		0			0
$297$	2575.75	−	3521.28i	0.503234	−	0.687964i
$298$		0			0
$299$	124.141			0.0240110
$300$		0			0
$301$	3575.09	+	3400.38i	0.684600	+	0.651146i
$302$		0			0
$303$	−189.727	+	5270.56i	−0.0359720	+	0.999293i
$304$		0			0
$305$	475.778	−	274.691i	0.0893212	−	0.0515696i
$306$		0			0
$307$		−	9015.37i		−	1.67601i	−0.545665	−	0.838004i	$-0.683723\pi$
$307$		−	9015.37i		−	1.67601i	0.545665	−	0.838004i	$-0.316277\pi$
$308$		0			0
$309$	−2180.67	+	3481.46i	−0.401469	+	0.640950i
$310$		0			0
$311$	−10641.5			−1.94026			−0.970132	−	0.242579i	$-0.922007\pi$
$311$	−10641.5			−1.94026			−0.970132	+	0.242579i	$0.922007\pi$
$312$		0			0
$313$			7800.48i			1.40866i	0.709875	+	0.704328i	$0.248751\pi$
$313$			7800.48i			1.40866i	−0.709875	+	0.704328i	$0.751249\pi$
$314$		0			0
$315$	−1689.30	+	368.681i	−0.302162	+	0.0659455i
$316$		0			0
$317$		−	7802.28i		−	1.38240i	−0.722665	−	0.691198i	$-0.757083\pi$
$317$		−	7802.28i		−	1.38240i	0.722665	−	0.691198i	$-0.242917\pi$
$318$		0			0
$319$	−8210.31			−1.44103
$320$		0			0
$321$	−4434.87	−	159.644i	−0.771122	−	0.0277584i
$322$		0			0
$323$			109.171i			0.0188063i
$324$		0			0
$325$	−244.409	+	141.109i	−0.0417149	+	0.0240841i
$326$		0			0
$327$	450.191	+	281.984i	0.0761333	+	0.0476873i
$328$		0			0
$329$	−10158.1	+	2996.37i	−1.70223	+	0.502114i
$330$		0			0
$331$	7233.88			1.20124			0.600620	−	0.799535i	$-0.294921\pi$
$331$	7233.88			1.20124			0.600620	+	0.799535i	$0.294921\pi$
$332$		0			0
$333$	1124.81	+	2318.84i	0.185102	+	0.381597i
$334$		0			0
$335$	−767.591	−	1329.51i	−0.125188	−	0.216832i
$336$		0			0
$337$	−3328.34	+	5764.85i	−0.538001	+	0.931844i	0.461011	+	0.887394i	$0.347487\pi$
$337$	−3328.34	+	5764.85i	−0.538001	+	0.931844i	−0.999012	+	0.0444499i	$0.985846\pi$
$338$		0			0
$339$	2753.82	+	99.1307i	0.441201	+	0.0158821i
$340$		0			0
$341$	−3996.63	+	6922.37i	−0.634691	+	1.09932i
$342$		0			0
$343$	−4142.07	+	4816.31i	−0.652044	+	0.758181i
$344$		0			0
$345$	892.846	+	32.1402i	0.139331	+	0.00501556i
$346$		0			0
$347$		−	4949.20i		−	0.765669i	−0.923817	−	0.382834i	$-0.874948\pi$
$347$		−	4949.20i		−	0.765669i	0.923817	−	0.382834i	$-0.125052\pi$
$348$		0			0
$349$	4149.53	−	2395.73i	0.636444	−	0.367451i	−0.146799	−	0.989166i	$-0.546897\pi$
$349$	4149.53	−	2395.73i	0.636444	−	0.367451i	0.783244	+	0.621715i	$0.213564\pi$
$350$		0			0
$351$	206.788	−	282.697i	0.0314460	−	0.0429894i
$352$		0			0
$353$	−4480.46	+	7760.39i	−0.675555	+	1.17010i	0.300751	+	0.953703i	$0.402763\pi$
$353$	−4480.46	+	7760.39i	−0.675555	+	1.17010i	−0.976306	+	0.216393i	$0.930571\pi$
$354$		0			0
$355$	−1213.82	+	700.800i	−0.181473	+	0.104773i
$356$		0			0
$357$	115.237	+	32.2332i	0.0170841	+	0.00477861i
$358$		0			0
$359$	11505.1	+	6642.48i	1.69141	+	0.976536i	0.953382	+	0.301767i	$0.0975764\pi$
$359$	11505.1	+	6642.48i	1.69141	+	0.976536i	0.738029	+	0.674769i	$0.235757\pi$
$360$		0			0
$361$	424.739	+	735.669i	0.0619243	+	0.107256i
$362$		0			0
$363$	1602.82	+	1003.95i	0.231753	+	0.145162i
$364$		0			0
$365$	−1748.04	−	1009.23i	−0.250676	−	0.144728i
$366$		0			0
$367$	6096.85	+	3520.02i	0.867175	+	0.500664i	0.866408	−	0.499336i	$-0.166423\pi$
$367$	6096.85	+	3520.02i	0.867175	+	0.500664i	0.000766372		1.00000i	$0.499756\pi$
$368$		0			0
$369$	−2214.65	−	4565.61i	−0.312440	−	0.644109i
$370$		0			0
$371$	−2471.24	+	2598.20i	−0.345823	+	0.363590i
$372$		0			0
$373$	−1267.88	−	2196.04i	−0.176001	−	0.304843i	0.764506	−	0.644617i	$-0.222983\pi$
$373$	−1267.88	−	2196.04i	−0.176001	−	0.304843i	−0.940507	+	0.339773i	$0.889650\pi$
$374$		0			0
$375$	−3778.51	+	2003.86i	−0.520324	+	0.275944i
$376$		0			0
$377$	−659.145			−0.0900470
$378$		0			0
$379$	−5227.61			−0.708507			−0.354254	−	0.935149i	$-0.615265\pi$
$379$	−5227.61			−0.708507			−0.354254	+	0.935149i	$0.615265\pi$
$380$		0			0
$381$	9932.35	−	5267.43i	1.33556	−	0.708291i
$382$		0			0
$383$	1786.90	+	3095.00i	0.238398	+	0.412917i	0.960255	−	0.279125i	$-0.0900445\pi$
$383$	1786.90	+	3095.00i	0.238398	+	0.412917i	−0.721857	+	0.692042i	$0.756711\pi$
$384$		0			0
$385$	563.420	+	1910.06i	0.0745832	+	0.252846i
$386$		0			0
$387$	−7174.40	−	517.191i	−0.942366	−	0.0679335i
$388$		0			0
$389$	−9192.22	−	5307.13i	−1.19811	−	0.691728i	−0.237975	−	0.971271i	$-0.576484\pi$
$389$	−9192.22	−	5307.13i	−1.19811	−	0.691728i	−0.960133	+	0.279543i	$0.909817\pi$
$390$		0			0
$391$	−53.5463	−	30.9150i	−0.00692571	−	0.00399856i
$392$		0			0
$393$	−11319.7	−	7090.30i	−1.45294	−	0.910072i
$394$		0			0
$395$	−2225.30	−	3854.33i	−0.283460	−	0.490968i
$396$		0			0
$397$	12393.1	+	7155.16i	1.56673	+	0.904552i	0.996547	+	0.0830338i	$0.0264610\pi$
$397$	12393.1	+	7155.16i	1.56673	+	0.904552i	0.570183	+	0.821518i	$0.306872\pi$
$398$		0			0
$399$	8184.69	−	2097.38i	1.02694	−	0.263158i
$400$		0			0
$401$	−10113.4	+	5838.97i	−1.25945	+	0.727142i	−0.972967	−	0.230944i	$-0.925819\pi$
$401$	−10113.4	+	5838.97i	−1.25945	+	0.727142i	−0.286480	+	0.958086i	$0.592485\pi$
$402$		0			0
$403$	−320.860	+	555.746i	−0.0396605	+	0.0686940i
$404$		0			0
$405$	1560.45	−	1979.67i	0.191455	−	0.242891i
$406$		0			0
$407$	2570.64	−	1484.16i	0.313076	−	0.180754i
$408$		0			0
$409$			8501.23i			1.02777i	0.857858	+	0.513886i	$0.171795\pi$
$409$			8501.23i			1.02777i	−0.857858	+	0.513886i	$0.828205\pi$
$410$		0			0
$411$	3214.31	+	115.707i	0.385767	+	0.0138866i
$412$		0			0
$413$	−5170.26	+	1525.10i	−0.616010	+	0.181707i
$414$		0			0
$415$	2111.74	−	3657.65i	0.249787	−	0.432643i
$416$		0			0
$417$	5862.94	+	211.051i	0.688512	+	0.0247847i
$418$		0			0
$419$	2317.23	−	4013.55i	0.270176	−	0.467959i	−0.698730	−	0.715385i	$-0.746251\pi$
$419$	2317.23	−	4013.55i	0.270176	−	0.467959i	0.968907	+	0.247426i	$0.0795846\pi$
$420$		0			0
$421$	3934.88	+	6815.41i	0.455521	+	0.788985i	0.998718	−	0.0506201i	$-0.0161198\pi$
$421$	3934.88	+	6815.41i	0.455521	+	0.788985i	−0.543197	+	0.839605i	$0.682786\pi$
$422$		0			0
$423$	8661.40	−	12781.7i	0.995583	−	1.46919i
$424$		0			0
$425$	140.562			0.0160430
$426$		0			0
$427$	832.509	+	2822.31i	0.0943512	+	0.319862i
$428$		0			0
$429$	−341.876	−	214.139i	−0.0384753	−	0.0240996i
$430$		0			0
$431$	14037.4	−	8104.49i	1.56881	−	0.905753i	0.572502	−	0.819903i	$-0.305973\pi$
$431$	14037.4	−	8104.49i	1.56881	−	0.905753i	0.996308	−	0.0858498i	$-0.0273605\pi$
$432$		0			0
$433$			12760.5i			1.41624i	0.706094	+	0.708118i	$0.250455\pi$
$433$			12760.5i			1.41624i	−0.706094	+	0.708118i	$0.749545\pi$
$434$		0			0
$435$	−4740.69	−	170.653i	−0.522526	−	0.0188096i
$436$		0			0
$437$	−4365.77			−0.477902
$438$		0			0
$439$		−	5660.16i		−	0.615364i	−0.951489	−	0.307682i	$-0.900447\pi$
$439$		−	5660.16i		−	0.615364i	0.951489	−	0.307682i	$-0.0995533\pi$
$440$		0			0
$441$	202.642	−	9258.78i	0.0218813	−	0.999761i
$442$		0			0
$443$			5933.49i			0.636363i	0.948030	+	0.318182i	$0.103072\pi$
$443$			5933.49i			0.636363i	−0.948030	+	0.318182i	$0.896928\pi$
$444$		0			0
$445$	−2813.86			−0.299752
$446$		0			0
$447$	−3721.14	+	5940.84i	−0.393744	+	0.628617i
$448$		0			0
$449$			11706.5i			1.23043i	0.788358	+	0.615216i	$0.210931\pi$
$449$			11706.5i			1.23043i	−0.788358	+	0.615216i	$0.789069\pi$
$450$		0			0
$451$	−5061.38	+	2922.19i	−0.528451	+	0.305101i
$452$		0			0
$453$	−79.3160	+	2203.38i	−0.00822647	+	0.228529i
$454$		0			0
$455$	45.2328	+	153.345i	0.00466054	+	0.0157998i
$456$		0			0
$457$	−14843.3			−1.51935			−0.759675	−	0.650303i	$-0.774642\pi$
$457$	−14843.3			−1.51935			−0.759675	+	0.650303i	$0.774642\pi$
$458$		0			0
$459$	−159.595	+	70.4402i	−0.0162293	+	0.00716311i
$460$		0			0
$461$	−4515.51	−	7821.10i	−0.456200	−	0.790162i	0.542556	−	0.840020i	$-0.317457\pi$
$461$	−4515.51	−	7821.10i	−0.456200	−	0.790162i	−0.998756	+	0.0498575i	$0.984123\pi$
$462$		0			0
$463$	7326.56	−	12690.0i	0.735408	−	1.27376i	−0.219136	−	0.975694i	$-0.570324\pi$
$463$	7326.56	−	12690.0i	0.735408	−	1.27376i	0.954544	−	0.298070i	$-0.0963429\pi$
$464$		0			0
$465$	−2451.56	+	3913.95i	−0.244492	+	0.390334i
$466$		0			0
$467$	3535.45	−	6123.57i	0.350323	−	0.606778i	−0.635983	−	0.771703i	$-0.719405\pi$
$467$	3535.45	−	6123.57i	0.350323	−	0.606778i	0.986306	+	0.164926i	$0.0527384\pi$
$468$		0			0
$469$	7886.62	−	2326.35i	0.776483	−	0.229043i
$470$		0			0
$471$	2468.90	+	4655.40i	0.241531	+	0.455434i
$472$		0			0
$473$			8284.49i			0.805330i
$474$		0			0
$475$	8595.30	−	4962.50i	0.830273	−	0.479358i
$476$		0			0
$477$	375.870	−	5214.02i	0.0360794	−	0.500489i
$478$		0			0
$479$	6568.54	−	11377.0i	0.626564	−	1.08524i	−0.361672	−	0.932305i	$-0.617794\pi$
$479$	6568.54	−	11377.0i	0.626564	−	1.08524i	0.988236	−	0.152935i	$-0.0488726\pi$
$480$		0			0
$481$	206.378	−	119.152i	0.0195634	−	0.0112950i
$482$		0			0
$483$	−1289.02	+	4608.38i	−0.121433	+	0.434138i
$484$		0			0
$485$	1716.60	+	991.079i	0.160715	+	0.0927888i
$486$		0			0
$487$	−10134.9	−	17554.1i	−0.943027	−	1.63337i	−0.759654	−	0.650328i	$-0.774632\pi$
$487$	−10134.9	−	17554.1i	−0.943027	−	1.63337i	−0.183374	−	0.983043i	$-0.558702\pi$
$488$		0			0
$489$	15.1950	−	422.114i	0.00140520	−	0.0390361i
$490$		0			0
$491$	3894.03	+	2248.22i	0.357913	+	0.206641i	0.668165	−	0.744013i	$-0.267080\pi$
$491$	3894.03	+	2248.22i	0.357913	+	0.206641i	−0.310252	+	0.950654i	$0.600413\pi$
$492$		0			0
$493$	284.311	+	164.147i	0.0259731	+	0.0149956i
$494$		0			0
$495$	−2403.39	−	1628.64i	−0.218231	−	0.147882i
$496$		0			0
$497$	−2123.92	−	7200.37i	−0.191692	−	0.649861i
$498$		0			0
$499$	2780.67	+	4816.27i	0.249459	+	0.432076i	0.963376	−	0.268155i	$-0.0864139\pi$
$499$	2780.67	+	4816.27i	0.249459	+	0.432076i	−0.713917	+	0.700231i	$0.753081\pi$
$500$		0			0
$501$	−89.7552	+	2493.38i	−0.00800392	+	0.222347i
$502$		0			0
$503$	6642.04			0.588775			0.294388	−	0.955686i	$-0.404884\pi$
$503$	6642.04			0.588775			0.294388	+	0.955686i	$0.404884\pi$
$504$		0			0
$505$	3509.58			0.309256
$506$		0			0
$507$	9647.31	+	6042.75i	0.845074	+	0.529325i
$508$		0			0
$509$	1766.24	+	3059.22i	0.153806	+	0.266400i	0.932624	−	0.360851i	$-0.117514\pi$
$509$	1766.24	+	3059.22i	0.153806	+	0.266400i	−0.778818	+	0.627250i	$0.784180\pi$
$510$		0			0
$511$	7450.78	−	7833.59i	0.645016	−	0.678156i
$512$		0			0
$513$	−7272.28	+	9941.83i	−0.625885	+	0.855638i
$514$		0			0
$515$	2367.45	+	1366.85i	0.202568	+	0.116953i
$516$		0			0
$517$	−15400.3	−	8891.38i	−1.31007	−	0.756369i
$518$		0			0
$519$	−4094.62	+	2171.50i	−0.346308	+	0.183658i
$520$		0			0
$521$	−5551.90	−	9616.17i	−0.466858	−	0.808622i	0.532425	−	0.846477i	$-0.321281\pi$
$521$	−5551.90	−	9616.17i	−0.466858	−	0.808622i	−0.999283	+	0.0378554i	$0.987947\pi$
$522$		0			0
$523$	2636.38	+	1522.11i	0.220422	+	0.127261i	0.606146	−	0.795354i	$-0.292715\pi$
$523$	2636.38	+	1522.11i	0.220422	+	0.127261i	−0.385724	+	0.922614i	$0.626048\pi$
$524$		0			0
$525$	−2700.46	−	10538.1i	−0.224491	−	0.876043i
$526$		0			0
$527$	276.795	−	159.808i	0.0228793	−	0.0132094i
$528$		0			0
$529$	−4847.20	+	8395.60i	−0.398389	+	0.690030i
$530$		0			0
$531$	4408.49	−	6505.62i	0.360286	−	0.531676i
$532$		0			0
$533$	−406.341	+	234.601i	−0.0330217	+	0.0190651i
$534$		0			0
$535$			2953.11i			0.238643i
$536$		0			0
$537$	−2474.86	+	3951.14i	−0.198879	+	0.317513i
$538$		0			0
$539$	−10652.9	+	533.952i	−0.851303	+	0.0426696i
$540$		0			0
$541$	1771.35	−	3068.07i	0.140770	−	0.243820i	−0.787017	−	0.616931i	$-0.788376\pi$
$541$	1771.35	−	3068.07i	0.140770	−	0.243820i	0.927787	+	0.373111i	$0.121709\pi$
$542$		0			0
$543$	5645.15	+	10644.6i	0.446145	+	0.841258i
$544$		0			0
$545$	176.748	−	306.137i	0.0138919	−	0.0240614i
$546$		0			0
$547$	−8883.45	−	15386.6i	−0.694385	−	1.20271i	−0.970387	−	0.241554i	$-0.922343\pi$
$547$	−8883.45	−	15386.6i	−0.694385	−	1.20271i	0.276002	−	0.961157i	$-0.410990\pi$
$548$		0			0
$549$	−3551.25	−	2406.48i	−0.276072	−	0.187078i
$550$		0			0
$551$	23180.7			1.79225
$552$		0			0
$553$	22863.8	−	6744.24i	1.75817	−	0.518616i
$554$		0			0
$555$	1515.15	−	803.533i	0.115882	−	0.0614560i
$556$		0			0
$557$	18571.9	−	10722.5i	1.41277	−	0.815665i	0.417124	−	0.908849i	$-0.363038\pi$
$557$	18571.9	−	10722.5i	1.41277	−	0.815665i	0.995649	+	0.0931845i	$0.0297047\pi$
$558$		0			0
$559$			665.101i			0.0503234i
$560$		0			0
$561$	94.1352	+	177.503i	0.00708448	+	0.0133586i
$562$		0			0
$563$	−9030.57			−0.676009			−0.338005	−	0.941144i	$-0.609752\pi$
$563$	−9030.57			−0.676009			−0.338005	+	0.941144i	$0.609752\pi$
$564$		0			0
$565$		−	1833.73i		−	0.136541i
$566$		0			0
$567$	8347.12	+	10611.8i	0.618247	+	0.785984i
$568$		0			0
$569$		−	10810.6i		−	0.796494i	−0.917278	−	0.398247i	$-0.869619\pi$
$569$		−	10810.6i		−	0.796494i	0.917278	−	0.398247i	$-0.130381\pi$
$570$		0			0
$571$	−11040.5			−0.809164			−0.404582	−	0.914502i	$-0.632583\pi$
$571$	−11040.5			−0.809164			−0.404582	+	0.914502i	$0.632583\pi$
$572$		0			0
$573$	4973.00	+	9377.17i	0.362566	+	0.683659i
$574$		0			0
$575$			5621.12i			0.407682i
$576$		0			0
$577$	−11806.0	+	6816.19i	−0.851802	+	0.491788i	−0.861258	−	0.508167i	$-0.830323\pi$
$577$	−11806.0	+	6816.19i	−0.851802	+	0.491788i	0.00945662	+	0.999955i	$0.496990\pi$
$578$		0			0
$579$	−2228.84	+	1182.02i	−0.159979	+	0.0848416i
$580$		0			0
$581$	16391.2	+	15590.2i	1.17043	+	1.11324i
$582$		0			0
$583$	−6020.77			−0.427710
$584$		0			0
$585$	−192.950	−	130.751i	−0.0136368	−	0.00924086i
$586$		0			0
$587$	7427.33	+	12864.5i	0.522247	+	0.904558i	0.999665	+	0.0258815i	$0.00823926\pi$
$587$	7427.33	+	12864.5i	0.522247	+	0.904558i	−0.477418	+	0.878676i	$0.658427\pi$
$588$		0			0
$589$	11283.9	−	19544.3i	0.789382	−	1.36725i
$590$		0			0
$591$	−5387.55	−	10158.8i	−0.374982	−	0.707071i
$592$		0			0
$593$	−5557.23	+	9625.41i	−0.384837	+	0.666557i	−0.991747	−	0.128214i	$-0.959076\pi$
$593$	−5557.23	+	9625.41i	−0.384837	+	0.666557i	0.606910	+	0.794771i	$0.292409\pi$
$594$		0			0
$595$	18.6771	−	77.4071i	0.00128687	−	0.00533342i
$596$		0			0
$597$	−2962.63	+	4729.88i	−0.203103	+	0.324256i
$598$		0			0
$599$		−	26966.4i		−	1.83943i	−0.392592	−	0.919713i	$-0.628422\pi$
$599$		−	26966.4i		−	1.83943i	0.392592	−	0.919713i	$-0.371578\pi$
$600$		0			0
$601$	−10479.2	+	6050.20i	−0.711244	+	0.410637i	−0.811521	−	0.584323i	$-0.801360\pi$
$601$	−10479.2	+	6050.20i	−0.711244	+	0.410637i	0.100278	+	0.994959i	$0.468027\pi$
$602$		0			0
$603$	−6724.62	+	9923.55i	−0.454142	+	0.670180i
$604$		0			0
$605$	629.281	−	1089.95i	0.0422875	−	0.0732440i
$606$		0			0
$607$	12203.2	−	7045.51i	0.815999	−	0.471117i	−0.0330356	−	0.999454i	$-0.510517\pi$
$607$	12203.2	−	7045.51i	0.815999	−	0.471117i	0.849035	+	0.528337i	$0.177184\pi$
$608$		0			0
$609$	6844.20	−	24468.8i	0.455404	−	1.62812i
$610$		0			0
$611$	−1236.38	−	713.824i	−0.0818634	−	0.0472639i
$612$		0			0
$613$	−1054.90	−	1827.14i	−0.0695059	−	0.120388i	0.829178	−	0.558985i	$-0.188809\pi$
$613$	−1054.90	−	1827.14i	−0.0695059	−	0.120388i	−0.898684	+	0.438597i	$0.855476\pi$
$614$		0			0
$615$	−2983.21	+	1582.09i	−0.195601	+	0.103733i
$616$		0			0
$617$	19738.2	+	11395.8i	1.28789	+	0.743565i	0.978278	−	0.207297i	$-0.0664668\pi$
$617$	19738.2	+	11395.8i	1.28789	+	0.743565i	0.309614	+	0.950862i	$0.399800\pi$
$618$		0			0
$619$	−17495.3	−	10100.9i	−1.13602	−	0.655879i	−0.190575	−	0.981673i	$-0.561035\pi$
$619$	−17495.3	−	10100.9i	−1.13602	−	0.655879i	−0.945441	+	0.325793i	$0.894369\pi$
$620$		0			0
$621$	−2816.92	−	6382.25i	−0.182028	−	0.412417i
$622$		0			0
$623$	3535.02	−	14650.8i	0.227332	−	0.942173i
$624$		0			0
$625$	−5642.16	−	9772.51i	−0.361098	−	0.625441i
$626$		0			0
$627$	12023.0	+	7530.79i	0.765793	+	0.479666i
$628$		0			0
$629$	−118.690			−0.00752383
$630$		0			0
$631$	16687.2			1.05278			0.526392	−	0.850242i	$-0.323544\pi$
$631$	16687.2			1.05278			0.526392	+	0.850242i	$0.323544\pi$
$632$		0			0
$633$	−565.408	+	15706.9i	−0.0355023	+	0.986245i
$634$		0			0
$635$	−3740.73	−	6479.14i	−0.233774	−	0.404908i
$636$		0			0
$637$	−855.242	+	42.8671i	−0.0531961	+	0.00266633i
$638$		0			0
$639$	9060.06	+	6139.48i	0.560893	+	0.380084i
$640$		0			0
$641$	3419.39	+	1974.18i	0.210698	+	0.121647i	0.601636	−	0.798770i	$-0.294516\pi$
$641$	3419.39	+	1974.18i	0.210698	+	0.121647i	−0.390938	+	0.920417i	$0.627849\pi$
$642$		0			0
$643$	6034.19	+	3483.84i	0.370086	+	0.213669i	0.673496	−	0.739191i	$-0.264792\pi$
$643$	6034.19	+	3483.84i	0.370086	+	0.213669i	−0.303410	+	0.952860i	$0.598125\pi$
$644$		0			0
$645$	−172.195	+	4783.52i	−0.0105119	+	0.292017i
$646$		0			0
$647$	−799.396	−	1384.60i	−0.0485742	−	0.0841330i	0.840716	−	0.541476i	$-0.182134\pi$
$647$	−799.396	−	1384.60i	−0.0485742	−	0.0841330i	−0.889290	+	0.457343i	$0.848801\pi$
$648$		0			0
$649$	−7838.47	−	4525.54i	−0.474094	−	0.273718i
$650$		0			0
$651$	−17298.8	−	17681.5i	−1.04146	−	1.06451i
$652$		0			0
$653$	19004.0	−	10972.0i	1.13887	−	0.657528i	0.192721	−	0.981253i	$-0.438269\pi$
$653$	19004.0	−	10972.0i	1.13887	−	0.657528i	0.946151	+	0.323725i	$0.104935\pi$
$654$		0			0
$655$	−4444.22	+	7697.62i	−0.265115	+	0.459192i
$656$		0			0
$657$	−1133.25	+	15720.3i	−0.0672941	+	0.933495i
$658$		0			0
$659$	15961.3	−	9215.25i	0.943495	−	0.544727i	0.0524411	−	0.998624i	$-0.483300\pi$
$659$	15961.3	−	9215.25i	0.943495	−	0.544727i	0.891054	+	0.453897i	$0.149966\pi$
$660$		0			0
$661$			19596.1i			1.15310i	0.817062	+	0.576551i	$0.195602\pi$
$661$			19596.1i			1.15310i	−0.817062	+	0.576551i	$0.804398\pi$
$662$		0			0
$663$	7.55742	+	14.2504i	0.000442694	+	0.000834750i
$664$		0			0
$665$	−1590.74	−	5392.80i	−0.0927611	−	0.314472i
$666$		0			0
$667$	−6564.30	+	11369.7i	−0.381065	+	0.660025i
$668$		0			0
$669$	3776.85	−	6029.78i	0.218268	−	0.348467i
$670$		0			0
$671$	−2470.37	+	4278.81i	−0.142128	+	0.246172i
$672$		0			0
$673$	−4893.95	−	8476.57i	−0.280309	−	0.485510i	0.691152	−	0.722710i	$-0.257104\pi$
$673$	−4893.95	−	8476.57i	−0.280309	−	0.485510i	−0.971461	+	0.237200i	$0.923770\pi$
$674$		0			0
$675$	12800.5	+	9363.37i	0.729915	+	0.533921i
$676$		0			0
$677$	−27541.6			−1.56353			−0.781764	−	0.623574i	$-0.785680\pi$
$677$	−27541.6			−1.56353			−0.781764	+	0.623574i	$0.785680\pi$
$678$		0			0
$679$	−7316.76	+	7692.68i	−0.413537	+	0.434784i
$680$		0			0
$681$	−1128.71	+	31355.4i	−0.0635130	+	1.76438i
$682$		0			0
$683$	−20518.2	+	11846.2i	−1.14950	+	0.663663i	−0.948765	−	0.315983i	$-0.897666\pi$
$683$	−20518.2	+	11846.2i	−1.14950	+	0.663663i	−0.200733	+	0.979646i	$0.564332\pi$
$684$		0			0
$685$		−	2140.36i		−	0.119385i
$686$		0			0
$687$	−7149.03	+	11413.5i	−0.397020	+	0.633847i
$688$		0			0
$689$	−483.364			−0.0267267
$690$		0			0
$691$		−	11942.6i		−	0.657478i	−0.944421	−	0.328739i	$-0.893376\pi$
$691$		−	11942.6i		−	0.657478i	0.944421	−	0.328739i	$-0.106624\pi$
$692$		0			0
$693$	11499.1	−	10467.6i	0.630326	−	0.573783i
$694$		0			0
$695$		−	3904.04i		−	0.213077i
$696$		0			0
$697$	233.691			0.0126997
$698$		0			0
$699$	−8742.08	−	314.693i	−0.473041	−	0.0170283i
$700$		0			0
$701$			23013.5i			1.23995i	0.784620	+	0.619977i	$0.212858\pi$
$701$			23013.5i			1.23995i	−0.784620	+	0.619977i	$0.787142\pi$
$702$		0			0
$703$	−7257.84	+	4190.32i	−0.389381	+	0.224809i
$704$		0			0
$705$	−8707.45	−	5454.04i	−0.465165	−	0.291363i
$706$		0			0
$707$	−4409.04	+	18273.2i	−0.234539	+	0.972045i
$708$		0			0
$709$	7660.84			0.405795			0.202898	−	0.979200i	$-0.434964\pi$
$709$	7660.84			0.405795			0.202898	+	0.979200i	$0.434964\pi$
$710$		0			0
$711$	−19495.1	+	28769.0i	−1.02830	+	1.51747i
$712$		0			0
$713$	6390.76	+	11069.1i	0.335675	+	0.581405i
$714$		0			0
$715$	−134.223	+	232.481i	−0.00702050	+	0.0121599i
$716$		0			0
$717$	21776.3	+	783.893i	1.13424	+	0.0408299i
$718$		0			0
$719$	−12056.5	+	20882.5i	−0.625358	+	1.08315i	0.363114	+	0.931745i	$0.381714\pi$
$719$	−12056.5	+	20882.5i	−0.625358	+	1.08315i	−0.988472	+	0.151406i	$0.951620\pi$
$720$		0			0
$721$	−10090.9	+	10609.4i	−0.521229	+	0.548009i
$722$		0			0
$723$	−19670.6	−	708.092i	−1.01184	−	0.0364236i
$724$		0			0
$725$		−	29846.1i		−	1.52891i
$726$		0			0
$727$	−19496.3	+	11256.2i	−0.994606	+	0.574236i	−0.906648	−	0.421888i	$-0.861368\pi$
$727$	−19496.3	+	11256.2i	−0.994606	+	0.574236i	−0.0879583	+	0.996124i	$0.528034\pi$
$728$		0			0
$729$	−19226.1	−	4216.46i	−0.976786	−	0.214218i
$730$		0			0
$731$	165.630	−	286.880i	0.00838038	−	0.0145152i
$732$		0			0
$733$	−8289.73	+	4786.08i	−0.417719	+	0.241170i	−0.694101	−	0.719878i	$-0.744198\pi$
$733$	−8289.73	+	4786.08i	−0.417719	+	0.241170i	0.276382	+	0.961048i	$0.410865\pi$
$734$		0			0
$735$	−6162.15	+	86.8853i	−0.309244	+	0.00436029i
$736$		0			0
$737$	11956.6	+	6903.18i	0.597597	+	0.345023i
$738$		0			0
$739$	−17009.8	−	29461.8i	−0.846705	−	1.46654i	−0.884132	−	0.467237i	$-0.845249\pi$
$739$	−17009.8	−	29461.8i	−0.846705	−	1.46654i	0.0374266	−	0.999299i	$-0.488084\pi$
$740$		0			0
$741$	965.238	+	604.592i	0.0478528	+	0.0299733i
$742$		0			0
$743$	27100.0	+	15646.2i	1.33809	+	0.772548i	0.986524	−	0.163615i	$-0.0523154\pi$
$743$	27100.0	+	15646.2i	1.33809	+	0.772548i	0.351568	+	0.936163i	$0.385649\pi$
$744$		0			0
$745$	4039.87	+	2332.42i	0.198670	+	0.114702i
$746$		0			0
$747$	−32893.5	−	2371.24i	−1.61113	−	0.116143i
$748$		0			0
$749$	−15375.9	−	3709.96i	−0.750096	−	0.180986i
$750$		0			0
$751$	−13068.1	−	22634.6i	−0.634969	−	1.09980i	−0.986522	−	0.163630i	$-0.947680\pi$
$751$	−13068.1	−	22634.6i	−0.634969	−	1.09980i	0.351553	−	0.936168i	$-0.385654\pi$
$752$		0			0
$753$	−15771.5	+	8364.09i	−0.763272	+	0.404787i
$754$		0			0
$755$	1467.20			0.0707241
$756$		0			0
$757$	19034.4			0.913893			0.456946	−	0.889494i	$-0.348943\pi$
$757$	19034.4			0.913893			0.456946	+	0.889494i	$0.348943\pi$
$758$		0			0
$759$	−7098.39	+	3764.49i	−0.339467	+	0.180030i
$760$		0			0
$761$	−991.469	−	1717.27i	−0.0472283	−	0.0818017i	0.841445	−	0.540343i	$-0.181705\pi$
$761$	−991.469	−	1717.27i	−0.0472283	−	0.0818017i	−0.888673	+	0.458541i	$0.848372\pi$
$762$		0			0
$763$	1371.91	+	1304.87i	0.0650936	+	0.0619127i
$764$		0			0
$765$	50.6649	+	104.448i	0.00239450	+	0.00493637i
$766$		0			0
$767$	−629.293	−	363.322i	−0.0296251	−	0.0171041i
$768$		0			0
$769$	−6456.22	−	3727.50i	−0.302753	−	0.174795i	0.340926	−	0.940090i	$-0.389260\pi$
$769$	−6456.22	−	3727.50i	−0.302753	−	0.174795i	−0.643679	+	0.765295i	$0.722593\pi$
$770$		0			0
$771$	14669.0	+	9188.16i	0.685203	+	0.429187i
$772$		0			0
$773$	−18980.1	−	32874.5i	−0.883139	−	1.52964i	−0.847832	−	0.530265i	$-0.822092\pi$
$773$	−18980.1	−	32874.5i	−0.883139	−	1.52964i	−0.0353072	−	0.999377i	$-0.511241\pi$
$774$		0			0
$775$	−25164.2	−	14528.5i	−1.16635	−	0.673394i
$776$		0			0
$777$	2280.26	+	8898.37i	0.105282	+	0.410846i
$778$		0			0
$779$	14290.1	−	8250.39i	0.657248	−	0.379462i
$780$		0			0
$781$	6302.50	−	10916.2i	0.288759	−	0.500146i
$782$		0			0
$783$	14956.8	+	33887.4i	0.682649	+	1.54666i
$784$		0			0
$785$	3036.84	−	1753.32i	0.138076	−	0.0797181i
$786$		0			0
$787$			33851.9i			1.53328i	0.642078	+	0.766640i	$0.278073\pi$
$787$			33851.9i			1.53328i	−0.642078	+	0.766640i	$0.721927\pi$
$788$		0			0
$789$	−30695.2	−	1104.95i	−1.38501	−	0.0498570i
$790$		0			0
$791$	9547.62	+	2303.69i	0.429171	+	0.103552i
$792$		0			0
$793$	−198.328	+	343.514i	−0.00888126	+	0.0153828i
$794$		0			0
$795$	−3476.44	−	125.143i	−0.155090	−	0.00558284i
$796$		0			0
$797$	−1396.19	+	2418.28i	−0.0620523	+	0.107478i	−0.895383	−	0.445298i	$-0.853098\pi$
$797$	−1396.19	+	2418.28i	−0.0620523	+	0.107478i	0.833330	+	0.552775i	$0.186431\pi$
$798$		0			0
$799$	355.528	+	615.792i	0.0157418	+	0.0272655i
$800$		0			0
$801$	9589.34	+	19768.9i	0.423000	+	0.872033i
$802$		0			0
$803$	18152.6			0.797750
$804$		0			0
$805$	3095.53	+	746.904i	0.135532	+	0.0327017i
$806$		0			0
$807$	−4053.66	−	2539.07i	−0.176822	−	0.110755i
$808$		0			0
$809$	25463.7	−	14701.5i	1.10662	−	0.638909i	0.168670	−	0.985673i	$-0.446053\pi$
$809$	25463.7	−	14701.5i	1.10662	−	0.638909i	0.937952	+	0.346764i	$0.112720\pi$
$810$		0			0
$811$			42354.1i			1.83385i	0.399059	+	0.916925i	$0.369337\pi$
$811$			42354.1i			1.83385i	−0.399059	+	0.916925i	$0.630663\pi$
$812$		0			0
$813$	13187.2	+	474.707i	0.568877	+	0.0204781i
$814$		0			0
$815$	−281.079			−0.0120807
$816$		0			0
$817$		−	23390.1i		−	1.00161i
$818$		0			0
$819$	923.180	−	840.368i	0.0393877	−	0.0358545i
$820$		0			0
$821$			5826.12i			0.247665i	0.992303	+	0.123833i	$0.0395186\pi$
$821$			5826.12i			0.247665i	−0.992303	+	0.123833i	$0.960481\pi$
$822$		0			0
$823$	−39444.3			−1.67064			−0.835322	−	0.549761i	$-0.814719\pi$
$823$	−39444.3			−1.67064			−0.835322	+	0.549761i	$0.814719\pi$
$824$		0			0
$825$	9696.22	−	15480.1i	0.409187	−	0.653271i
$826$		0			0
$827$			8871.60i			0.373030i	0.982452	+	0.186515i	$0.0597193\pi$
$827$			8871.60i			0.373030i	−0.982452	+	0.186515i	$0.940281\pi$
$828$		0			0
$829$	−11452.9	+	6612.31i	−0.479824	+	0.277027i	−0.720343	−	0.693618i	$-0.756016\pi$
$829$	−11452.9	+	6612.31i	−0.479824	+	0.277027i	0.240519	+	0.970644i	$0.422682\pi$
$830$		0			0
$831$	538.193	−	14950.9i	0.0224666	−	0.624116i
$832$		0			0
$833$	379.570	+	194.491i	0.0157879	+	0.00808970i
$834$		0			0
$835$	1660.30			0.0688108
$836$		0			0
$837$	35852.2	+	3885.20i	1.48057	+	0.160445i
$838$		0			0
$839$	7504.38	+	12998.0i	0.308796	+	0.534850i	0.978099	−	0.208139i	$-0.0667406\pi$
$839$	7504.38	+	12998.0i	0.308796	+	0.534850i	−0.669303	+	0.742989i	$0.733407\pi$
$840$		0			0
$841$	22659.5	−	39247.5i	0.929088	−	1.60923i
$842$		0			0
$843$	21693.9	−	34634.5i	0.886331	−	1.41504i
$844$		0			0
$845$	3787.61	−	6560.34i	0.154199	−	0.267080i
$846$		0			0
$847$	4884.44	+	4645.75i	0.198148	+	0.188465i
$848$		0			0
$849$	−13296.0	−	25071.1i	−0.537475	−	1.01347i
$850$		0			0
$851$		−	4746.45i		−	0.191194i
$852$		0			0
$853$	817.893	−	472.211i	0.0328302	−	0.0189545i	−0.483495	−	0.875347i	$-0.660633\pi$
$853$	817.893	−	472.211i	0.0328302	−	0.0189545i	0.516325	+	0.856393i	$0.327300\pi$
$854$		0			0
$855$	6785.63	+	4598.23i	0.271419	+	0.183925i
$856$		0			0
$857$	−16903.3	+	29277.4i	−0.673752	+	1.16697i	0.303080	+	0.952965i	$0.401985\pi$
$857$	−16903.3	+	29277.4i	−0.673752	+	1.16697i	−0.976832	+	0.214008i	$0.931348\pi$
$858$		0			0
$859$	18861.4	−	10889.6i	0.749177	−	0.432537i	−0.0762198	−	0.997091i	$-0.524285\pi$
$859$	18861.4	−	10889.6i	0.749177	−	0.432537i	0.825396	+	0.564554i	$0.190952\pi$
$860$		0			0
$861$	−4489.65	−	17520.2i	−0.177708	−	0.693480i
$862$		0			0
$863$	8670.13	+	5005.70i	0.341987	+	0.197446i	0.661150	−	0.750253i	$-0.270069\pi$
$863$	8670.13	+	5005.70i	0.341987	+	0.197446i	−0.319163	+	0.947700i	$0.603402\pi$
$864$		0			0
$865$	1542.12	+	2671.03i	0.0606169	+	0.104992i
$866$		0			0
$867$	−918.084	+	25504.1i	−0.0359628	+	0.999038i
$868$		0			0
$869$	34663.1	+	20012.8i	1.35312	+	0.781227i
$870$		0			0
$871$	959.911	+	554.205i	0.0373425	+	0.0215597i
$872$		0			0
$873$	1112.86	−	15437.5i	0.0431440	−	0.598488i
$874$		0			0
$875$	−14621.3	+	4312.91i	−0.564903	+	0.166632i
$876$		0			0
$877$	−3048.14	−	5279.54i	−0.117364	−	0.203281i	0.801358	−	0.598185i	$-0.204111\pi$
$877$	−3048.14	−	5279.54i	−0.117364	−	0.203281i	−0.918722	+	0.394904i	$0.870778\pi$
$878$		0			0
$879$	153.895	−	4275.16i	0.00590529	−	0.164047i
$880$		0			0
$881$	−27623.6			−1.05637			−0.528185	−	0.849130i	$-0.677127\pi$
$881$	−27623.6			−1.05637			−0.528185	+	0.849130i	$0.677127\pi$
$882$		0			0
$883$	45677.7			1.74086			0.870428	−	0.492295i	$-0.163842\pi$
$883$	45677.7			1.74086			0.870428	+	0.492295i	$0.163842\pi$
$884$		0			0
$885$	−4431.92	−	2776.00i	−0.168336	−	0.105440i
$886$		0			0
$887$	−11424.2	−	19787.4i	−0.432456	−	0.749036i	0.564628	−	0.825346i	$-0.309020\pi$
$887$	−11424.2	−	19787.4i	−0.432456	−	0.749036i	−0.997084	+	0.0763093i	$0.975686\pi$
$888$		0			0
$889$	38434.2	−	11337.1i	1.44999	−	0.427710i
$890$		0			0
$891$	−3251.54	+	22435.3i	−0.122257	+	0.843559i
$892$		0			0
$893$	43480.7	+	25103.6i	1.62937	+	0.940716i
$894$		0			0
$895$	2686.84	+	1551.25i	0.100348	+	0.0579358i
$896$		0			0
$897$	−569.877	+	302.223i	−0.0212125	+	0.0112497i
$898$		0			0
$899$	−33932.6	−	58773.0i	−1.25886	−	2.18041i
$900$		0			0
$901$	208.491	+	120.372i	0.00770903	+	0.00445081i
$902$		0			0
$903$	−24689.9	−	6906.04i	−0.909887	−	0.254506i
$904$		0			0
$905$	6943.75	−	4008.98i	0.255048	−	0.147252i
$906$		0			0
$907$	−18407.1	+	31882.1i	−0.673869	+	1.16718i	0.302929	+	0.953013i	$0.402035\pi$
$907$	−18407.1	+	31882.1i	−0.673869	+	1.16718i	−0.976798	+	0.214162i	$0.931298\pi$
$908$		0			0
$909$	−11960.3	−	24656.7i	−0.436411	−	0.899681i
$910$		0			0
$911$	−18246.8	+	10534.8i	−0.663604	+	0.383132i	−0.793649	−	0.608376i	$-0.791821\pi$
$911$	−18246.8	+	10534.8i	−0.663604	+	0.383132i	0.130045	+	0.991508i	$0.458488\pi$
$912$		0			0
$913$			37983.1i			1.37684i
$914$		0			0
$915$	−1515.35	+	2419.27i	−0.0547495	+	0.0874082i
$916$		0			0
$917$	−34495.8	−	32810.0i	−1.24226	−	1.18155i
$918$		0			0
$919$	15269.0	−	26446.7i	0.548073	−	0.949289i	−0.450334	−	0.892860i	$-0.648695\pi$
$919$	15269.0	−	26446.7i	0.548073	−	0.949289i	0.998407	−	0.0564293i	$-0.0179716\pi$
$920$		0			0
$921$	21948.0	+	41385.5i	0.785246	+	1.48067i
$922$		0			0
$923$	505.981	−	876.385i	0.0180440	−	0.0312530i
$924$		0			0
$925$	5395.21	+	9344.78i	0.191777	+	0.332167i
$926$		0			0
$927$	1534.81	−	21290.7i	0.0543794	−	0.754345i
$928$		0			0
$929$	−39564.4			−1.39727			−0.698637	−	0.715477i	$-0.746210\pi$
$929$	−39564.4			−1.39727			−0.698637	+	0.715477i	$0.746210\pi$
$930$		0			0
$931$	30076.9	−	1507.54i	1.05879	−	0.0530693i
$932$		0			0
$933$	48850.2	−	25906.8i	1.71413	−	0.909056i
$934$		0			0
$935$	115.790	−	66.8513i	0.00404998	−	0.00233826i
$936$		0			0
$937$		−	17421.8i		−	0.607412i	−0.952766	−	0.303706i	$-0.901776\pi$
$937$		−	17421.8i		−	0.607412i	0.952766	−	0.303706i	$-0.0982241\pi$
$938$		0			0
$939$	−18990.4	−	35808.5i	−0.659986	−	1.24448i
$940$		0			0
$941$	−5478.36			−0.189787			−0.0948935	−	0.995487i	$-0.530251\pi$
$941$	−5478.36			−0.189787			−0.0948935	+	0.995487i	$0.530251\pi$
$942$		0			0
$943$			9345.38i			0.322723i
$944$		0			0
$945$	6857.25	−	5805.06i	0.236049	−	0.199829i
$946$		0			0
$947$			10172.1i			0.349050i	0.984653	+	0.174525i	$0.0558390\pi$
$947$			10172.1i			0.349050i	−0.984653	+	0.174525i	$0.944161\pi$
$948$		0			0
$949$	1457.34			0.0498497
$950$		0			0
$951$	18994.7	+	35816.8i	0.647683	+	1.22128i
$952$		0			0
$953$		−	34572.9i		−	1.17516i	−0.809166	−	0.587580i	$-0.800081\pi$
$953$		−	34572.9i		−	1.17516i	0.809166	−	0.587580i	$-0.199919\pi$
$954$		0			0
$955$	6116.98	−	3531.64i	0.207268	−	0.119666i
$956$		0			0
$957$	37689.9	−	19988.1i	1.27308	−	0.675155i
$958$		0			0
$959$	11144.1	+	2688.90i	0.375248	+	0.0905414i
$960$		0			0
$961$	−36280.1			−1.21782
$962$		0			0
$963$	20747.1	−	10063.9i	0.694255	−	0.336764i
$964$		0			0
$965$	839.429	+	1453.93i	0.0280023	+	0.0485014i
$966$		0			0
$967$	2296.74	−	3978.07i	0.0763787	−	0.132292i	−0.825306	−	0.564685i	$-0.808998\pi$
$967$	2296.74	−	3978.07i	0.0763787	−	0.132292i	0.901685	+	0.432394i	$0.142331\pi$
$968$		0			0
$969$	−265.778	−	501.154i	−0.00881115	−	0.0166144i
$970$		0			0
$971$	−16400.0	+	28405.6i	−0.542018	+	0.938803i	0.456770	+	0.889585i	$0.349006\pi$
$971$	−16400.0	+	28405.6i	−0.542018	+	0.938803i	−0.998788	+	0.0492181i	$0.984327\pi$
$972$		0			0
$973$	20327.0	+	4904.60i	0.669738	+	0.161597i
$974$		0			0
$975$	778.438	−	1242.79i	0.0255692	−	0.0408215i
$976$		0			0
$977$		−	11227.3i		−	0.367650i	−0.982959	−	0.183825i	$-0.941152\pi$
$977$		−	11227.3i		−	0.367650i	0.982959	−	0.183825i	$-0.0588480\pi$
$978$		0			0
$979$	21915.5	−	12652.9i	0.715448	−	0.413064i
$980$		0			0
$981$	−2753.12	−	198.467i	−0.0896027	−	0.00645930i
$982$		0			0
$983$	−8084.28	+	14002.4i	−0.262308	+	0.454330i	−0.966855	−	0.255327i	$-0.917817\pi$
$983$	−8084.28	+	14002.4i	−0.262308	+	0.454330i	0.704547	+	0.709657i	$0.251150\pi$
$984$		0			0
$985$	−6626.89	+	3826.04i	−0.214366	+	0.123764i
$986$		0			0
$987$	39336.5	−	38484.9i	1.26859	−	1.24112i
$988$		0			0
$989$	11472.4	+	6623.60i	0.368859	+	0.212961i
$990$		0			0
$991$	8490.45	+	14705.9i	0.272158	+	0.471391i	0.969414	−	0.245431i	$-0.0789295\pi$
$991$	8490.45	+	14705.9i	0.272158	+	0.471391i	−0.697257	+	0.716822i	$0.745596\pi$
$992$		0			0
$993$	−33207.5	+	17611.0i	−1.06124	+	0.562807i
$994$		0			0
$995$	3216.40	+	1856.99i	0.102479	+	0.0591663i
$996$		0			0
$997$	31141.4	+	17979.5i	0.989227	+	0.571130i	0.905043	−	0.425320i	$-0.139838\pi$
$997$	31141.4	+	17979.5i	0.989227	+	0.571130i	0.0841837	+	0.996450i	$0.473172\pi$
$998$		0			0
$999$	−10808.7	−	7906.40i	−0.342315	−	0.250398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.w.a.5.5	✓	48
3.2	odd	2		756.4.w.a.341.11		48
7.3	odd	6		252.4.bm.a.185.4	yes	48
9.2	odd	6		252.4.bm.a.173.4	yes	48
9.7	even	3		756.4.bm.a.89.11		48
21.17	even	6		756.4.bm.a.17.11		48
63.38	even	6	inner	252.4.w.a.101.5	yes	48
63.52	odd	6		756.4.w.a.521.11		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.w.a.5.5	✓	48	1.1	even	1	trivial
252.4.w.a.101.5	yes	48	63.38	even	6	inner
252.4.bm.a.173.4	yes	48	9.2	odd	6
252.4.bm.a.185.4	yes	48	7.3	odd	6
756.4.w.a.341.11		48	3.2	odd	2
756.4.w.a.521.11		48	63.52	odd	6
756.4.bm.a.17.11		48	21.17	even	6
756.4.bm.a.89.11		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)

\(f(q)\)	\(=\)	\(q+(-4.59055 + 2.43451i) q^{3} +(1.72890 + 2.99454i) q^{5} +(-17.7636 + 5.23980i) q^{7} +(15.1463 - 22.3515i) q^{9} +O(q^{10})\)	\(q+(-4.59055 + 2.43451i) q^{3} +(1.72890 + 2.99454i) q^{5} +(-17.7636 + 5.23980i) q^{7} +(15.1463 - 22.3515i) q^{9} +(-26.9308 - 15.5485i) q^{11} +(-2.16207 - 1.24827i) q^{13} +(-15.2268 - 9.53756i) q^{15} +(0.621716 + 1.07684i) q^{17} +(76.0352 + 43.8990i) q^{19} +(68.7882 - 67.2992i) q^{21} +(-43.0633 + 24.8626i) q^{23} +(56.5218 - 97.8987i) q^{25} +(-15.1150 + 139.480i) q^{27} +(228.650 - 132.011i) q^{29} -257.043i q^{31} +(161.480 + 5.81287i) q^{33} +(-46.4022 - 44.1346i) q^{35} +(-47.7268 + 82.6653i) q^{37} +(12.9640 + 0.466672i) q^{39} +(93.9702 - 162.761i) q^{41} +(-133.204 - 230.716i) q^{43} +(93.1188 + 6.71278i) q^{45} +571.849 q^{47} +(288.089 - 186.155i) q^{49} +(-5.47561 - 3.42973i) q^{51} +(167.674 - 96.8064i) q^{53} -107.527i q^{55} +(-455.916 - 16.4118i) q^{57} +291.060 q^{59} -158.882i q^{61} +(-151.935 + 476.406i) q^{63} -8.63255i q^{65} -443.977 q^{67} +(137.156 - 218.971i) q^{69} +405.345i q^{71} +(-505.536 + 291.872i) q^{73} +(-21.1309 + 587.012i) q^{75} +(559.858 + 135.085i) q^{77} -1287.12 q^{79} +(-270.178 - 677.085i) q^{81} +(-610.720 - 1057.80i) q^{83} +(-2.14977 + 3.72351i) q^{85} +(-728.248 + 1162.66i) q^{87} +(-406.886 + 704.748i) q^{89} +(44.9468 + 10.8450i) q^{91} +(625.774 + 1179.97i) q^{93} +303.587i q^{95} +(496.443 - 286.621i) q^{97} +(-755.434 + 366.441i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 12 q^{9}+O(q^{10}) \) 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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