LMFDB - Embedded newform 252.3.bh.a.137.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(137,252)]

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, 1, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("252.137");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.bh (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:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.6
Character	$\chi$	$=$	252.137
Dual form			252.3.bh.a.149.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40238 - 2.65204i) q^{3} +(6.97157 + 4.02504i) q^{5} +(1.23048 + 6.89100i) q^{7} +(-5.06667 + 7.43834i) q^{9} +O(q^{10})$	\(q+(-1.40238 - 2.65204i) q^{3} +(6.97157 + 4.02504i) q^{5} +(1.23048 + 6.89100i) q^{7} +(-5.06667 + 7.43834i) q^{9} +(-16.6393 + 9.60669i) q^{11} +(0.782606 + 1.35551i) q^{13} +(0.897800 - 24.1335i) q^{15} +(8.39721 + 4.84813i) q^{17} +(5.84871 + 10.1303i) q^{19} +(16.5496 - 12.9271i) q^{21} +(-1.79731 - 1.03768i) q^{23} +(19.9019 + 34.4710i) q^{25} +(26.8322 + 3.00568i) q^{27} +(40.2492 + 23.2379i) q^{29} -22.3494 q^{31} +(48.8119 + 30.6559i) q^{33} +(-19.1582 + 52.9938i) q^{35} +(-30.6213 - 53.0376i) q^{37} +(2.49737 - 3.97645i) q^{39} +(48.9545 - 28.2639i) q^{41} +(21.6300 - 37.4643i) q^{43} +(-65.2622 + 31.4633i) q^{45} -6.35293i q^{47} +(-45.9718 + 16.9585i) q^{49} +(1.08139 - 29.0687i) q^{51} +(55.3510 + 31.9569i) q^{53} -154.669 q^{55} +(18.6638 - 29.7175i) q^{57} -32.0773i q^{59} -74.5416 q^{61} +(-57.4920 - 25.7617i) q^{63} +12.6001i q^{65} +4.76192 q^{67} +(-0.231458 + 6.22176i) q^{69} +33.1772i q^{71} +(6.60726 - 11.4441i) q^{73} +(63.5088 - 101.122i) q^{75} +(-86.6740 - 102.840i) q^{77} +46.2460 q^{79} +(-29.6577 - 75.3752i) q^{81} +(81.0445 + 46.7910i) q^{83} +(39.0278 + 67.5982i) q^{85} +(5.18329 - 139.331i) q^{87} +(-55.9009 + 32.2744i) q^{89} +(-8.37786 + 7.06087i) q^{91} +(31.3423 + 59.2716i) q^{93} +94.1651i q^{95} +(-96.6875 + 167.468i) q^{97} +(12.8480 - 172.442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{7} - 14 q^{9}+O(q^{10}) $ 32 * q - q^7 - 14 * q^9	$ 32 q - q^{7} - 14 q^{9} + 18 q^{11} - 5 q^{13} - 29 q^{15} + 27 q^{17} - 14 q^{19} - 8 q^{21} - 45 q^{23} + 80 q^{25} + 45 q^{27} + 36 q^{29} + 16 q^{31} + 116 q^{33} + 45 q^{35} - 11 q^{37} + 55 q^{39} + 72 q^{41} + 16 q^{43} - 154 q^{45} - 37 q^{49} - 133 q^{51} - 180 q^{53} - 24 q^{55} + 57 q^{57} + 82 q^{61} - 99 q^{63} + 70 q^{67} - 97 q^{69} - 98 q^{73} - 149 q^{75} - 135 q^{77} + 142 q^{79} - 98 q^{81} - 30 q^{85} - 86 q^{87} + 189 q^{89} + 109 q^{91} + 109 q^{93} + 19 q^{97} - 101 q^{99}+O(q^{100}) $ 32 * q - q^7 - 14 * q^9 + 18 * q^11 - 5 * q^13 - 29 * q^15 + 27 * q^17 - 14 * q^19 - 8 * q^21 - 45 * q^23 + 80 * q^25 + 45 * q^27 + 36 * q^29 + 16 * q^31 + 116 * q^33 + 45 * q^35 - 11 * q^37 + 55 * q^39 + 72 * q^41 + 16 * q^43 - 154 * q^45 - 37 * q^49 - 133 * q^51 - 180 * q^53 - 24 * q^55 + 57 * q^57 + 82 * q^61 - 99 * q^63 + 70 * q^67 - 97 * q^69 - 98 * q^73 - 149 * q^75 - 135 * q^77 + 142 * q^79 - 98 * q^81 - 30 * q^85 - 86 * q^87 + 189 * q^89 + 109 * q^91 + 109 * q^93 + 19 * q^97 - 101 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.40238	−	2.65204i	−0.467459	−	0.884015i
$3$	−1.40238	−	2.65204i	−0.467459	−	0.884015i
$4$		0			0
$5$	6.97157	+	4.02504i	1.39431	+	0.805008i	0.993789	−	0.111278i	$-0.0354945\pi$
$5$	6.97157	+	4.02504i	1.39431	+	0.805008i	0.400525	+	0.916286i	$0.368828\pi$
$6$		0			0
$7$	1.23048	+	6.89100i	0.175783	+	0.984429i
$7$	1.23048	+	6.89100i	0.175783	+	0.984429i
$8$		0			0
$9$	−5.06667	+	7.43834i	−0.562964	+	0.826482i
$10$		0			0
$11$	−16.6393	+	9.60669i	−1.51266	+	0.873335i	−0.512771	+	0.858526i	$0.671381\pi$
$11$	−16.6393	+	9.60669i	−1.51266	+	0.873335i	−0.999890	+	0.0148098i	$0.995286\pi$
$12$		0			0
$13$	0.782606	+	1.35551i	0.0602005	+	0.104270i	0.894555	−	0.446958i	$-0.147493\pi$
$13$	0.782606	+	1.35551i	0.0602005	+	0.104270i	−0.834354	+	0.551228i	$0.814159\pi$
$14$		0			0
$15$	0.897800	−	24.1335i	0.0598533	−	1.60890i
$16$		0			0
$17$	8.39721	+	4.84813i	0.493953	+	0.285184i	0.726213	−	0.687470i	$-0.241279\pi$
$17$	8.39721	+	4.84813i	0.493953	+	0.285184i	−0.232260	+	0.972654i	$0.574612\pi$
$18$		0			0
$19$	5.84871	+	10.1303i	0.307827	+	0.533172i	0.977887	−	0.209135i	$-0.0670649\pi$
$19$	5.84871	+	10.1303i	0.307827	+	0.533172i	−0.670060	+	0.742307i	$0.733732\pi$
$20$		0			0
$21$	16.5496	−	12.9271i	0.788078	−	0.615575i
$22$		0			0
$23$	−1.79731	−	1.03768i	−0.0781439	−	0.0451164i	0.460419	−	0.887702i	$-0.347699\pi$
$23$	−1.79731	−	1.03768i	−0.0781439	−	0.0451164i	−0.538563	+	0.842585i	$0.681033\pi$
$24$		0			0
$25$	19.9019	+	34.4710i	0.796075	+	1.37884i
$26$		0			0
$27$	26.8322	+	3.00568i	0.993784	+	0.111321i
$28$		0			0
$29$	40.2492	+	23.2379i	1.38790	+	0.801306i	0.993079	−	0.117451i	$-0.0374725\pi$
$29$	40.2492	+	23.2379i	1.38790	+	0.801306i	0.394823	+	0.918757i	$0.370806\pi$
$30$		0			0
$31$	−22.3494			−0.720949			−0.360474	−	0.932769i	$-0.617385\pi$
$31$	−22.3494			−0.720949			−0.360474	+	0.932769i	$0.617385\pi$
$32$		0			0
$33$	48.8119	+	30.6559i	1.47915	+	0.928966i
$34$		0			0
$35$	−19.1582	+	52.9938i	−0.547376	+	1.51411i
$36$		0			0
$37$	−30.6213	−	53.0376i	−0.827603	−	1.43345i	−0.899914	−	0.436068i	$-0.856371\pi$
$37$	−30.6213	−	53.0376i	−0.827603	−	1.43345i	0.0723114	−	0.997382i	$-0.476962\pi$
$38$		0			0
$39$	2.49737	−	3.97645i	0.0640352	−	0.101960i
$40$		0			0
$41$	48.9545	−	28.2639i	1.19401	−	0.689363i	0.234797	−	0.972044i	$-0.424557\pi$
$41$	48.9545	−	28.2639i	1.19401	−	0.689363i	0.959214	+	0.282682i	$0.0912240\pi$
$42$		0			0
$43$	21.6300	−	37.4643i	0.503023	−	0.871262i	−0.496971	−	0.867767i	$-0.665554\pi$
$43$	21.6300	−	37.4643i	0.503023	−	0.871262i	0.999994	−	0.00349442i	$-0.00111231\pi$
$44$		0			0
$45$	−65.2622	+	31.4633i	−1.45027	+	0.699185i
$46$		0			0
$47$		−	6.35293i		−	0.135169i	−0.997714	−	0.0675844i	$-0.978471\pi$
$47$		−	6.35293i		−	0.135169i	0.997714	−	0.0675844i	$-0.0215292\pi$
$48$		0			0
$49$	−45.9718	+	16.9585i	−0.938201	+	0.346091i
$50$		0			0
$51$	1.08139	−	29.0687i	0.0212038	−	0.569974i
$52$		0			0
$53$	55.3510	+	31.9569i	1.04436	+	0.602960i	0.921065	−	0.389410i	$-0.127321\pi$
$53$	55.3510	+	31.9569i	1.04436	+	0.602960i	0.123293	+	0.992370i	$0.460654\pi$
$54$		0			0
$55$	−154.669			−2.81217
$56$		0			0
$57$	18.6638	−	29.7175i	0.327435	−	0.521359i
$58$		0			0
$59$		−	32.0773i		−	0.543683i	−0.962342	−	0.271842i	$-0.912367\pi$
$59$		−	32.0773i		−	0.543683i	0.962342	−	0.271842i	$-0.0876327\pi$
$60$		0			0
$61$	−74.5416			−1.22199			−0.610997	−	0.791633i	$-0.709231\pi$
$61$	−74.5416			−1.22199			−0.610997	+	0.791633i	$0.709231\pi$
$62$		0			0
$63$	−57.4920	−	25.7617i	−0.912572	−	0.408916i
$64$		0			0
$65$			12.6001i			0.193847i
$66$		0			0
$67$	4.76192			0.0710734			0.0355367	−	0.999368i	$-0.488686\pi$
$67$	4.76192			0.0710734			0.0355367	+	0.999368i	$0.488686\pi$
$68$		0			0
$69$	−0.231458	+	6.22176i	−0.00335446	+	0.0901704i
$70$		0			0
$71$			33.1772i			0.467284i	0.972323	+	0.233642i	$0.0750644\pi$
$71$			33.1772i			0.467284i	−0.972323	+	0.233642i	$0.924936\pi$
$72$		0			0
$73$	6.60726	−	11.4441i	0.0905104	−	0.156769i	−0.817216	−	0.576332i	$-0.804483\pi$
$73$	6.60726	−	11.4441i	0.0905104	−	0.156769i	0.907726	+	0.419563i	$0.137817\pi$
$74$		0			0
$75$	63.5088	−	101.122i	0.846784	−	1.34829i
$76$		0			0
$77$	−86.6740	−	102.840i	−1.12564	−	1.33559i
$78$		0			0
$79$	46.2460			0.585393			0.292696	−	0.956205i	$-0.405448\pi$
$79$	46.2460			0.585393			0.292696	+	0.956205i	$0.405448\pi$
$80$		0			0
$81$	−29.6577	−	75.3752i	−0.366144	−	0.930558i
$82$		0			0
$83$	81.0445	+	46.7910i	0.976439	+	0.563748i	0.901193	−	0.433417i	$-0.142692\pi$
$83$	81.0445	+	46.7910i	0.976439	+	0.563748i	0.0752462	+	0.997165i	$0.476026\pi$
$84$		0			0
$85$	39.0278	+	67.5982i	0.459151	+	0.795273i
$86$		0			0
$87$	5.18329	−	139.331i	0.0595781	−	1.60150i
$88$		0			0
$89$	−55.9009	+	32.2744i	−0.628099	+	0.362633i	−0.780016	−	0.625760i	$-0.784789\pi$
$89$	−55.9009	+	32.2744i	−0.628099	+	0.362633i	0.151916	+	0.988393i	$0.451456\pi$
$90$		0			0
$91$	−8.37786	+	7.06087i	−0.0920644	+	0.0775920i
$92$		0			0
$93$	31.3423	+	59.2716i	0.337014	+	0.637329i
$94$		0			0
$95$			94.1651i			0.991212i
$96$		0			0
$97$	−96.6875	+	167.468i	−0.996779	+	1.72647i	−0.428933	+	0.903337i	$0.641110\pi$
$97$	−96.6875	+	167.468i	−0.996779	+	1.72647i	−0.567846	+	0.823135i	$0.692223\pi$
$98$		0			0
$99$	12.8480	−	172.442i	0.129777	−	1.74184i
$100$		0			0
$101$	−58.3858	+	33.7091i	−0.578077	+	0.333753i	−0.760369	−	0.649491i	$-0.774982\pi$
$101$	−58.3858	+	33.7091i	−0.578077	+	0.333753i	0.182292	+	0.983245i	$0.441649\pi$
$102$		0			0
$103$	40.1420	−	69.5280i	0.389728	−	0.675029i	−0.602685	−	0.797979i	$-0.705902\pi$
$103$	40.1420	−	69.5280i	0.389728	−	0.675029i	0.992413	+	0.122951i	$0.0392357\pi$
$104$		0			0
$105$	167.409	−	23.5091i	1.59437	−	0.223896i
$106$		0			0
$107$	108.086	−	62.4035i	1.01015	−	0.583210i	0.0989143	−	0.995096i	$-0.468463\pi$
$107$	108.086	−	62.4035i	1.01015	−	0.583210i	0.911236	+	0.411886i	$0.135130\pi$
$108$		0			0
$109$	80.8079	−	139.963i	0.741357	−	1.28407i	−0.210521	−	0.977589i	$-0.567516\pi$
$109$	80.8079	−	139.963i	0.741357	−	1.28407i	0.951878	−	0.306478i	$-0.0991506\pi$
$110$		0			0
$111$	−97.7155	+	155.588i	−0.880320	+	1.40169i
$112$		0			0
$113$	28.7804	−	16.6164i	0.254694	−	0.147048i	−0.367218	−	0.930135i	$-0.619690\pi$
$113$	28.7804	−	16.6164i	0.254694	−	0.147048i	0.621912	+	0.783087i	$0.286356\pi$
$114$		0			0
$115$	−8.35338	−	14.4685i	−0.0726381	−	0.125813i
$116$		0			0
$117$	−14.0480	−	1.04666i	−0.120068	−	0.00894577i
$118$		0			0
$119$	−23.0759	+	63.8307i	−0.193915	+	0.536393i
$120$		0			0
$121$	124.077	−	214.908i	1.02543	−	1.77610i
$122$		0			0
$123$	−143.610	−	90.1927i	−1.16756	−	0.733274i
$124$		0			0
$125$			119.171i			0.953370i
$126$		0			0
$127$	−194.763			−1.53357			−0.766785	−	0.641904i	$-0.778145\pi$
$127$	−194.763			−1.53357			−0.766785	+	0.641904i	$0.778145\pi$
$128$		0			0
$129$	−129.690	−	4.82465i	−1.00535	−	0.0374004i
$130$		0			0
$131$	−101.363	−	58.5218i	−0.773761	−	0.446731i	0.0604533	−	0.998171i	$-0.480745\pi$
$131$	−101.363	−	58.5218i	−0.773761	−	0.446731i	−0.834215	+	0.551440i	$0.814079\pi$
$132$		0			0
$133$	−62.6109	+	52.7686i	−0.470759	+	0.396756i
$134$		0			0
$135$	174.964	+	128.955i	1.29603	+	0.955221i
$136$		0			0
$137$	−69.1202	+	39.9066i	−0.504527	+	0.291289i	−0.730581	−	0.682826i	$-0.760751\pi$
$137$	−69.1202	+	39.9066i	−0.504527	+	0.291289i	0.226054	+	0.974115i	$0.427417\pi$
$138$		0			0
$139$	−37.9101	−	65.6622i	−0.272734	−	0.472390i	0.696827	−	0.717240i	$-0.254595\pi$
$139$	−37.9101	−	65.6622i	−0.272734	−	0.472390i	−0.969561	+	0.244850i	$0.921261\pi$
$140$		0			0
$141$	−16.8483	+	8.90922i	−0.119491	+	0.0631859i
$142$		0			0
$143$	−26.0440	−	15.0365i	−0.182126	−	0.105150i
$144$		0			0
$145$	187.067	+	324.009i	1.29011	+	2.23454i
$146$		0			0
$147$	109.445	+	98.1371i	0.744521	+	0.667599i
$148$		0			0
$149$	94.3571	+	54.4771i	0.633269	+	0.365618i	0.782017	−	0.623257i	$-0.214191\pi$
$149$	94.3571	+	54.4771i	0.633269	+	0.365618i	−0.148748	+	0.988875i	$0.547524\pi$
$150$		0			0
$151$	−81.7169	−	141.538i	−0.541172	−	0.937337i	−0.998837	−	0.0482125i	$-0.984648\pi$
$151$	−81.7169	−	141.538i	−0.541172	−	0.937337i	0.457665	−	0.889125i	$-0.348686\pi$
$152$		0			0
$153$	−78.6079	+	37.8974i	−0.513777	+	0.247695i
$154$		0			0
$155$	−155.811	−	89.9573i	−1.00523	−	0.580369i
$156$		0			0
$157$	−31.5130			−0.200720			−0.100360	−	0.994951i	$-0.531999\pi$
$157$	−31.5130			−0.200720			−0.100360	+	0.994951i	$0.531999\pi$
$158$		0			0
$159$	7.12811	−	191.609i	0.0448309	−	1.20509i
$160$		0			0
$161$	4.93908	−	13.6621i	0.0306775	−	0.0848578i
$162$		0			0
$163$	149.467	+	258.884i	0.916974	+	1.58824i	0.803986	+	0.594648i	$0.202709\pi$
$163$	149.467	+	258.884i	0.916974	+	1.58824i	0.112988	+	0.993596i	$0.463958\pi$
$164$		0			0
$165$	216.905	+	410.189i	1.31457	+	2.48600i
$166$		0			0
$167$	226.397	−	130.710i	1.35567	−	0.782695i	0.366632	−	0.930366i	$-0.380511\pi$
$167$	226.397	−	130.710i	1.35567	−	0.782695i	0.989037	+	0.147671i	$0.0471776\pi$
$168$		0			0
$169$	83.2751	−	144.237i	0.492752	−	0.853471i
$170$		0			0
$171$	−104.986	−	7.82205i	−0.613952	−	0.0457430i
$172$		0			0
$173$			192.482i			1.11261i	0.830977	+	0.556307i	$0.187782\pi$
$173$			192.482i			1.11261i	−0.830977	+	0.556307i	$0.812218\pi$
$174$		0			0
$175$	−213.051	+	179.560i	−1.21744	+	1.02606i
$176$		0			0
$177$	−85.0705	+	44.9845i	−0.480624	+	0.254150i
$178$		0			0
$179$	303.708	+	175.346i	1.69669	+	0.979585i	0.948860	+	0.315696i	$0.102238\pi$
$179$	303.708	+	175.346i	1.69669	+	0.979585i	0.747831	+	0.663889i	$0.231095\pi$
$180$		0			0
$181$	227.913			1.25919			0.629594	−	0.776925i	$-0.283221\pi$
$181$	227.913			1.25919			0.629594	+	0.776925i	$0.283221\pi$
$182$		0			0
$183$	104.535	+	197.688i	0.571232	+	1.08026i
$184$		0			0
$185$		−	493.008i		−	2.66491i
$186$		0			0
$187$	−186.298			−0.996246
$188$		0			0
$189$	12.3043	+	188.599i	0.0651023	+	0.997879i
$190$		0			0
$191$		−	187.619i		−	0.982298i	−0.871076	−	0.491149i	$-0.836577\pi$
$191$		−	187.619i		−	0.982298i	0.871076	−	0.491149i	$-0.163423\pi$
$192$		0			0
$193$	−35.8113			−0.185551			−0.0927753	−	0.995687i	$-0.529574\pi$
$193$	−35.8113			−0.185551			−0.0927753	+	0.995687i	$0.529574\pi$
$194$		0			0
$195$	33.4160	−	17.6701i	0.171364	−	0.0906157i
$196$		0			0
$197$		−	110.071i		−	0.558736i	−0.960184	−	0.279368i	$-0.909875\pi$
$197$		−	110.071i		−	0.558736i	0.960184	−	0.279368i	$-0.0901250\pi$
$198$		0			0
$199$	34.5156	−	59.7829i	0.173445	−	0.300416i	−0.766177	−	0.642630i	$-0.777843\pi$
$199$	34.5156	−	59.7829i	0.173445	−	0.300416i	0.939622	+	0.342214i	$0.111177\pi$
$200$		0			0
$201$	−6.67801	−	12.6288i	−0.0332239	−	0.0628300i
$202$		0			0
$203$	−110.606	+	305.951i	−0.544859	+	1.50715i
$204$		0			0
$205$	455.053			2.21977
$206$		0			0
$207$	16.8250	−	8.11142i	0.0812800	−	0.0391856i
$208$		0			0
$209$	−194.637	−	112.373i	−0.931275	−	0.537672i
$210$		0			0
$211$	122.482	+	212.145i	0.580484	+	1.00543i	0.995422	+	0.0955775i	$0.0304698\pi$
$211$	122.482	+	212.145i	0.580484	+	1.00543i	−0.414938	+	0.909849i	$0.636197\pi$
$212$		0			0
$213$	87.9874	−	46.5270i	0.413086	−	0.218436i
$214$		0			0
$215$	301.590	−	174.123i	1.40274	−	0.809875i
$216$		0			0
$217$	−27.5005	−	154.010i	−0.126730	−	0.709723i
$218$		0			0
$219$	−39.6162	−	1.47377i	−0.180896	−	0.00672956i
$220$		0			0
$221$			15.1767i			0.0686729i
$222$		0			0
$223$	−50.2344	+	87.0085i	−0.225266	+	0.390173i	−0.956399	−	0.292062i	$-0.905659\pi$
$223$	−50.2344	+	87.0085i	−0.225266	+	0.390173i	0.731133	+	0.682235i	$0.238992\pi$
$224$		0			0
$225$	−357.243	−	26.6167i	−1.58775	−	0.118297i
$226$		0			0
$227$	−144.520	+	83.4386i	−0.636651	+	0.367571i	−0.783323	−	0.621614i	$-0.786477\pi$
$227$	−144.520	+	83.4386i	−0.636651	+	0.367571i	0.146672	+	0.989185i	$0.453144\pi$
$228$		0			0
$229$	138.765	−	240.347i	0.605959	−	1.04955i	−0.385941	−	0.922524i	$-0.626123\pi$
$229$	138.765	−	240.347i	0.605959	−	1.04955i	0.991899	−	0.127027i	$-0.0405436\pi$
$230$		0			0
$231$	−151.188	+	374.084i	−0.654492	+	1.61941i
$232$		0			0
$233$	−41.2378	+	23.8087i	−0.176986	+	0.102183i	−0.585876	−	0.810401i	$-0.699249\pi$
$233$	−41.2378	+	23.8087i	−0.176986	+	0.102183i	0.408890	+	0.912584i	$0.365916\pi$
$234$		0			0
$235$	25.5708	−	44.2899i	0.108812	−	0.188468i
$236$		0			0
$237$	−64.8544	−	122.646i	−0.273647	−	0.517496i
$238$		0			0
$239$	199.849	−	115.383i	0.836187	−	0.482773i	−0.0197796	−	0.999804i	$-0.506296\pi$
$239$	199.849	−	115.383i	0.836187	−	0.482773i	0.855966	+	0.517032i	$0.172963\pi$
$240$		0			0
$241$	−148.738	−	257.623i	−0.617172	−	1.06897i	−0.989999	−	0.141073i	$-0.954945\pi$
$241$	−148.738	−	257.623i	−0.617172	−	1.06897i	0.372827	−	0.927901i	$-0.378388\pi$
$242$		0			0
$243$	−158.307	+	184.358i	−0.651470	+	0.758675i
$244$		0			0
$245$	−388.754	−	66.8111i	−1.58675	−	0.272699i
$246$		0			0
$247$	−9.15447	+	15.8560i	−0.0370626	+	0.0641943i
$248$		0			0
$249$	10.4369	−	280.552i	0.0419154	−	1.12672i
$250$		0			0
$251$			85.2548i			0.339661i	0.985473	+	0.169830i	$0.0543220\pi$
$251$			85.2548i			0.339661i	−0.985473	+	0.169830i	$0.945678\pi$
$252$		0			0
$253$	39.8746			0.157607
$254$		0			0
$255$	124.542	−	198.302i	0.488398	−	0.777654i
$256$		0			0
$257$	62.1430	+	35.8783i	0.241802	+	0.139604i	0.616004	−	0.787743i	$-0.288750\pi$
$257$	62.1430	+	35.8783i	0.241802	+	0.139604i	−0.374203	+	0.927347i	$0.622084\pi$
$258$		0			0
$259$	327.804	−	276.273i	1.26565	−	1.06669i
$260$		0			0
$261$	−376.780	+	181.648i	−1.44360	+	0.695970i
$262$		0			0
$263$	−295.596	+	170.662i	−1.12394	+	0.648906i	−0.942403	−	0.334479i	$-0.891440\pi$
$263$	−295.596	+	170.662i	−1.12394	+	0.648906i	−0.181534	+	0.983385i	$0.558106\pi$
$264$		0			0
$265$	257.255	+	445.580i	0.970775	+	1.68143i
$266$		0			0
$267$	163.987	+	102.991i	0.614184	+	0.385733i
$268$		0			0
$269$	−182.681	−	105.471i	−0.679111	−	0.392085i	0.120409	−	0.992724i	$-0.461579\pi$
$269$	−182.681	−	105.471i	−0.679111	−	0.392085i	−0.799520	+	0.600639i	$0.794913\pi$
$270$		0			0
$271$	−129.425	−	224.171i	−0.477584	−	0.827199i	0.522086	−	0.852893i	$-0.325154\pi$
$271$	−129.425	−	224.171i	−0.477584	−	0.827199i	−0.999670	+	0.0256934i	$0.991821\pi$
$272$		0			0
$273$	30.4747	+	12.3165i	0.111629	+	0.0451152i
$274$		0			0
$275$	−662.305	−	382.382i	−2.40838	−	1.39048i
$276$		0			0
$277$	204.629	+	354.427i	0.738731	+	1.27952i	0.953067	+	0.302760i	$0.0979080\pi$
$277$	204.629	+	354.427i	0.738731	+	1.27952i	−0.214336	+	0.976760i	$0.568759\pi$
$278$		0			0
$279$	113.237	−	166.242i	0.405868	−	0.595851i
$280$		0			0
$281$	−277.104	−	159.986i	−0.986134	−	0.569344i	−0.0820173	−	0.996631i	$-0.526136\pi$
$281$	−277.104	−	159.986i	−0.986134	−	0.569344i	−0.904116	+	0.427286i	$0.859470\pi$
$282$		0			0
$283$	123.768			0.437341			0.218671	−	0.975799i	$-0.429828\pi$
$283$	123.768			0.437341			0.218671	+	0.975799i	$0.429828\pi$
$284$		0			0
$285$	249.730	−	132.055i	0.876246	−	0.463351i
$286$		0			0
$287$	255.004	+	302.567i	0.888515	+	1.05424i
$288$		0			0
$289$	−97.4913	−	168.860i	−0.337340	−	0.584290i
$290$		0			0
$291$	579.724	+	21.5665i	1.99218	+	0.0741118i
$292$		0			0
$293$	16.0474	−	9.26498i	0.0547693	−	0.0316211i	−0.472365	−	0.881403i	$-0.656600\pi$
$293$	16.0474	−	9.26498i	0.0547693	−	0.0316211i	0.527135	+	0.849782i	$0.323266\pi$
$294$		0			0
$295$	129.112	−	223.629i	0.437669	−	0.758066i
$296$		0			0
$297$	−475.343	+	207.756i	−1.60048	+	0.699515i
$298$		0			0
$299$		−	3.24837i		−	0.0108641i
$300$		0			0
$301$	284.782	+	102.953i	0.946118	+	0.342038i
$302$		0			0
$303$	171.277	+	107.569i	0.565270	+	0.355013i
$304$		0			0
$305$	−519.672	−	300.033i	−1.70384	−	0.983714i
$306$		0			0
$307$	363.739			1.18482			0.592408	−	0.805638i	$-0.298177\pi$
$307$	363.739			1.18482			0.592408	+	0.805638i	$0.298177\pi$
$308$		0			0
$309$	−240.685	−	8.95382i	−0.778917	−	0.0289768i
$310$		0			0
$311$			150.188i			0.482921i	0.970411	+	0.241460i	$0.0776264\pi$
$311$			150.188i			0.482921i	−0.970411	+	0.241460i	$0.922374\pi$
$312$		0			0
$313$	−234.215			−0.748290			−0.374145	−	0.927370i	$-0.622064\pi$
$313$	−234.215			−0.748290			−0.374145	+	0.927370i	$0.622064\pi$
$314$		0			0
$315$	−297.118	−	411.007i	−0.943231	−	1.30479i
$316$		0			0
$317$		−	392.685i		−	1.23875i	−0.785094	−	0.619377i	$-0.787385\pi$
$317$		−	392.685i		−	1.23875i	0.785094	−	0.619377i	$-0.212615\pi$
$318$		0			0
$319$	−892.956			−2.79923
$320$		0			0
$321$	−317.074	−	199.136i	−0.987770	−	0.620360i
$322$		0			0
$323$			113.421i			0.351149i
$324$		0			0
$325$	−31.1506	+	53.9545i	−0.0958481	+	0.166014i
$326$		0			0
$327$	−484.512	−	18.0245i	−1.48169	−	0.0551208i
$328$		0			0
$329$	43.7781	−	7.81716i	0.133064	−	0.0237604i
$330$		0			0
$331$	152.027			0.459295			0.229648	−	0.973274i	$-0.426243\pi$
$331$	152.027			0.459295			0.229648	+	0.973274i	$0.426243\pi$
$332$		0			0
$333$	549.660	+	40.9529i	1.65063	+	0.122982i
$334$		0			0
$335$	33.1981	+	19.1669i	0.0990987	+	0.0572147i
$336$		0			0
$337$	−142.286	−	246.447i	−0.422214	−	0.731295i	0.573942	−	0.818896i	$-0.305413\pi$
$337$	−142.286	−	246.447i	−0.422214	−	0.731295i	−0.996156	+	0.0876006i	$0.972080\pi$
$338$		0			0
$339$	−84.4284	−	53.0245i	−0.249051	−	0.156414i
$340$		0			0
$341$	371.878	−	214.704i	1.09055	−	0.629630i
$342$		0			0
$343$	−173.428	−	295.925i	−0.505622	−	0.862755i
$344$		0			0
$345$	−26.6564	+	42.4438i	−0.0772651	+	0.123026i
$346$		0			0
$347$		−	133.781i		−	0.385537i	−0.981244	−	0.192768i	$-0.938253\pi$
$347$		−	133.781i		−	0.385537i	0.981244	−	0.192768i	$-0.0617466\pi$
$348$		0			0
$349$	−231.018	+	400.135i	−0.661943	+	1.14652i	0.318162	+	0.948036i	$0.396934\pi$
$349$	−231.018	+	400.135i	−0.661943	+	1.14652i	−0.980105	+	0.198482i	$0.936399\pi$
$350$		0			0
$351$	16.9248	+	38.7236i	0.0482188	+	0.110324i
$352$		0			0
$353$	557.892	−	322.099i	1.58043	−	0.912462i	0.585636	−	0.810575i	$-0.300845\pi$
$353$	557.892	−	322.099i	1.58043	−	0.912462i	0.994796	−	0.101888i	$-0.0324883\pi$
$354$		0			0
$355$	−133.539	+	231.297i	−0.376168	+	0.651541i
$356$		0			0
$357$	201.643	−	28.3165i	0.564826	−	0.0793180i
$358$		0			0
$359$	157.335	−	90.8373i	0.438259	−	0.253029i	−0.264600	−	0.964358i	$-0.585240\pi$
$359$	157.335	−	90.8373i	0.438259	−	0.253029i	0.702859	+	0.711329i	$0.251907\pi$
$360$		0			0
$361$	112.085	−	194.137i	0.310485	−	0.537776i
$362$		0			0
$363$	−743.947	−	27.6758i	−2.04944	−	0.0762420i
$364$		0			0
$365$	92.1260	−	53.1889i	0.252400	−	0.145723i
$366$		0			0
$367$	281.621	+	487.782i	0.767360	+	1.32911i	0.938990	+	0.343945i	$0.111763\pi$
$367$	281.621	+	487.782i	0.767360	+	1.32911i	−0.171630	+	0.985161i	$0.554903\pi$
$368$		0			0
$369$	−37.8000	+	507.343i	−0.102439	+	1.37491i
$370$		0			0
$371$	−152.107	+	420.746i	−0.409991	+	1.13409i
$372$		0			0
$373$	22.0770	−	38.2385i	0.0591877	−	0.102516i	−0.834913	−	0.550381i	$-0.814482\pi$
$373$	22.0770	−	38.2385i	0.0591877	−	0.102516i	0.894101	+	0.447865i	$0.147816\pi$
$374$		0			0
$375$	316.047	−	167.123i	0.842793	−	0.445662i
$376$		0			0
$377$			72.7444i			0.192956i
$378$		0			0
$379$	106.066			0.279857			0.139928	−	0.990162i	$-0.455313\pi$
$379$	106.066			0.279857			0.139928	+	0.990162i	$0.455313\pi$
$380$		0			0
$381$	273.132	+	516.521i	0.716881	+	1.35570i
$382$		0			0
$383$	271.781	+	156.913i	0.709612	+	0.409695i	0.810917	−	0.585161i	$-0.198969\pi$
$383$	271.781	+	156.913i	0.709612	+	0.409695i	−0.101305	+	0.994855i	$0.532302\pi$
$384$		0			0
$385$	−190.317	−	1065.83i	−0.494331	−	2.76838i
$386$		0			0
$387$	169.080	+	350.710i	0.436898	+	0.906228i
$388$		0			0
$389$	53.2693	−	30.7550i	0.136939	−	0.0790618i	−0.429965	−	0.902845i	$-0.641474\pi$
$389$	53.2693	−	30.7550i	0.136939	−	0.0790618i	0.566904	+	0.823784i	$0.308141\pi$
$390$		0			0
$391$	−10.0616	−	17.4272i	−0.0257330	−	0.0445708i
$392$		0			0
$393$	−13.0535	+	350.888i	−0.0332150	+	0.892845i
$394$		0			0
$395$	322.407	+	186.142i	0.816221	+	0.471245i
$396$		0			0
$397$	−65.6615	−	113.729i	−0.165394	−	0.286471i	0.771401	−	0.636349i	$-0.219556\pi$
$397$	−65.6615	−	113.729i	−0.165394	−	0.286471i	−0.936795	+	0.349878i	$0.886223\pi$
$398$		0			0
$399$	227.749	+	92.0455i	0.570799	+	0.230690i
$400$		0			0
$401$	−181.577	−	104.834i	−0.452811	−	0.261431i	0.256206	−	0.966622i	$-0.417528\pi$
$401$	−181.577	−	104.834i	−0.452811	−	0.261431i	−0.709017	+	0.705192i	$0.750861\pi$
$402$		0			0
$403$	−17.4908	−	30.2949i	−0.0434015	−	0.0751735i
$404$		0			0
$405$	96.6276	−	644.857i	0.238587	−	1.59224i
$406$		0			0
$407$	1019.03	+	588.338i	2.50376	+	1.44555i
$408$		0			0
$409$	272.976			0.667423			0.333711	−	0.942675i	$-0.391699\pi$
$409$	272.976			0.667423			0.333711	+	0.942675i	$0.391699\pi$
$410$		0			0
$411$	202.767	+	127.346i	0.493350	+	0.309844i
$412$		0			0
$413$	221.045	−	39.4705i	0.535218	−	0.0955702i
$414$		0			0
$415$	376.672	+	652.414i	0.907642	+	1.57208i
$416$		0			0
$417$	−120.975	+	192.622i	−0.290107	+	0.461924i
$418$		0			0
$419$	93.8050	−	54.1584i	0.223878	−	0.129256i	−0.383866	−	0.923389i	$-0.625408\pi$
$419$	93.8050	−	54.1584i	0.223878	−	0.129256i	0.607745	+	0.794132i	$0.292074\pi$
$420$		0			0
$421$	−268.137	+	464.427i	−0.636905	+	1.10315i	0.349203	+	0.937047i	$0.386452\pi$
$421$	−268.137	+	464.427i	−0.636905	+	1.10315i	−0.986108	+	0.166104i	$0.946881\pi$
$422$		0			0
$423$	47.2553	+	32.1882i	0.111715	+	0.0760951i
$424$		0			0
$425$			385.947i			0.908112i
$426$		0			0
$427$	−91.7220	−	513.666i	−0.214806	−	1.20297i
$428$		0			0
$429$	−3.35395	+	90.1566i	−0.00781806	+	0.210155i
$430$		0			0
$431$	−235.401	−	135.909i	−0.546173	−	0.315333i	0.201404	−	0.979508i	$-0.435450\pi$
$431$	−235.401	−	135.909i	−0.546173	−	0.315333i	−0.747577	+	0.664175i	$0.768783\pi$
$432$		0			0
$433$	−428.323			−0.989199			−0.494600	−	0.869121i	$-0.664685\pi$
$433$	−428.323			−0.989199			−0.494600	+	0.869121i	$0.664685\pi$
$434$		0			0
$435$	596.947	−	950.492i	1.37229	−	2.18504i
$436$		0			0
$437$		−	24.2763i		−	0.0555521i
$438$		0			0
$439$	−306.579			−0.698358			−0.349179	−	0.937056i	$-0.613539\pi$
$439$	−306.579			−0.698358			−0.349179	+	0.937056i	$0.613539\pi$
$440$		0			0
$441$	106.781	−	427.877i	0.242135	−	0.970243i
$442$		0			0
$443$		−	290.777i		−	0.656381i	−0.944612	−	0.328191i	$-0.893561\pi$
$443$		−	290.777i		−	0.656381i	0.944612	−	0.328191i	$-0.106439\pi$
$444$		0			0
$445$	−519.622			−1.16769
$446$		0			0
$447$	12.1513	−	326.637i	0.0271842	−	0.730731i
$448$		0			0
$449$		−	278.892i		−	0.621140i	−0.950550	−	0.310570i	$-0.899480\pi$
$449$		−	278.892i		−	0.621140i	0.950550	−	0.310570i	$-0.100520\pi$
$450$		0			0
$451$	−543.044	+	940.580i	−1.20409	+	2.08554i
$452$		0			0
$453$	−260.767	+	415.207i	−0.575644	+	0.916571i
$454$		0			0
$455$	−86.8272	+	15.5041i	−0.190829	+	0.0340750i
$456$		0			0
$457$	443.216			0.969838			0.484919	−	0.874559i	$-0.338849\pi$
$457$	443.216			0.969838			0.484919	+	0.874559i	$0.338849\pi$
$458$		0			0
$459$	210.743	+	155.325i	0.459136	+	0.338399i
$460$		0			0
$461$	134.497	+	77.6519i	0.291751	+	0.168442i	0.638731	−	0.769430i	$-0.279460\pi$
$461$	134.497	+	77.6519i	0.291751	+	0.168442i	−0.346980	+	0.937872i	$0.612793\pi$
$462$		0			0
$463$	201.958	+	349.802i	0.436195	+	0.755511i	0.997392	−	0.0721704i	$-0.0229925\pi$
$463$	201.958	+	349.802i	0.436195	+	0.755511i	−0.561198	+	0.827682i	$0.689659\pi$
$464$		0			0
$465$	−20.0653	+	539.370i	−0.0431512	+	1.15994i
$466$		0			0
$467$	−358.548	+	207.008i	−0.767769	+	0.443272i	−0.832078	−	0.554658i	$-0.812849\pi$
$467$	−358.548	+	207.008i	−0.767769	+	0.443272i	0.0643092	+	0.997930i	$0.479516\pi$
$468$		0			0
$469$	5.85945	+	32.8144i	0.0124935	+	0.0699668i
$470$		0			0
$471$	44.1931	+	83.5738i	0.0938282	+	0.177439i
$472$		0			0
$473$			831.171i			1.75723i
$474$		0			0
$475$	−232.800	+	403.222i	−0.490106	+	0.848889i
$476$		0			0
$477$	−518.151	+	249.804i	−1.08627	+	0.523698i
$478$		0			0
$479$	−721.242	+	416.409i	−1.50572	+	0.869330i	−0.505746	+	0.862682i	$0.668783\pi$
$479$	−721.242	+	416.409i	−1.50572	+	0.869330i	−0.999978	+	0.00664795i	$0.997884\pi$
$480$		0			0
$481$	47.9288	−	83.0151i	0.0996441	−	0.172589i
$482$		0			0
$483$	−43.1590	+	6.06077i	−0.0893560	+	0.0125482i
$484$		0			0
$485$	−1348.13	+	778.342i	−2.77965	+	1.60483i
$486$		0			0
$487$	90.7601	−	157.201i	0.186366	−	0.322795i	−0.757670	−	0.652638i	$-0.773662\pi$
$487$	90.7601	−	157.201i	0.186366	−	0.322795i	0.944036	+	0.329843i	$0.106996\pi$
$488$		0			0
$489$	476.963	−	759.445i	0.975384	−	1.55306i
$490$		0			0
$491$	−213.443	+	123.232i	−0.434712	+	0.250981i	−0.701352	−	0.712815i	$-0.747420\pi$
$491$	−213.443	+	123.232i	−0.434712	+	0.250981i	0.266640	+	0.963796i	$0.414086\pi$
$492$		0			0
$493$	225.320	+	390.266i	0.457039	+	0.791615i
$494$		0			0
$495$	783.658	−	1150.48i	1.58315	−	2.32420i
$496$		0			0
$497$	−228.624	+	40.8239i	−0.460008	+	0.0821406i
$498$		0			0
$499$	463.819	−	803.358i	0.929497	−	1.60994i	0.145333	−	0.989383i	$-0.453575\pi$
$499$	463.819	−	803.358i	0.929497	−	1.60994i	0.784164	−	0.620554i	$-0.213092\pi$
$500$		0			0
$501$	−664.143	−	417.109i	−1.32563	−	0.832552i
$502$		0			0
$503$			569.020i			1.13125i	0.824662	+	0.565626i	$0.191366\pi$
$503$			569.020i			1.13125i	−0.824662	+	0.565626i	$0.808634\pi$
$504$		0			0
$505$	−542.721			−1.07470
$506$		0			0
$507$	−499.305	−	18.5748i	−0.984822	−	0.0366367i
$508$		0			0
$509$	547.002	+	315.812i	1.07466	+	0.620456i	0.929451	−	0.368945i	$-0.120281\pi$
$509$	547.002	+	315.812i	1.07466	+	0.620456i	0.145210	+	0.989401i	$0.453614\pi$
$510$		0			0
$511$	86.9915	+	31.4489i	0.170238	+	0.0615438i
$512$		0			0
$513$	126.485	+	289.396i	0.246560	+	0.564125i
$514$		0			0
$515$	559.705	−	323.146i	1.08681	−	0.627468i
$516$		0			0
$517$	61.0307	+	105.708i	0.118048	+	0.204465i
$518$		0			0
$519$	510.472	−	269.933i	0.983568	−	0.520102i
$520$		0			0
$521$	278.992	+	161.076i	0.535494	+	0.309168i	0.743251	−	0.669013i	$-0.233283\pi$
$521$	278.992	+	161.076i	0.535494	+	0.309168i	−0.207757	+	0.978181i	$0.566616\pi$
$522$		0			0
$523$	−204.092	−	353.498i	−0.390233	−	0.675904i	0.602247	−	0.798310i	$-0.294272\pi$
$523$	−204.092	−	353.498i	−0.390233	−	0.675904i	−0.992480	+	0.122406i	$0.960939\pi$
$524$		0			0
$525$	774.979	+	313.211i	1.47615	+	0.596591i
$526$		0			0
$527$	−187.673	−	108.353i	−0.356115	−	0.205603i
$528$		0			0
$529$	−262.346	−	454.397i	−0.495929	−	0.858974i
$530$		0			0
$531$	238.602	+	162.525i	0.449344	+	0.306074i
$532$		0			0
$533$	76.6241	+	44.2389i	0.143760	+	0.0829999i
$534$		0			0
$535$	1004.71			1.87795
$536$		0			0
$537$	39.1115	−	1051.35i	0.0728334	−	1.95782i
$538$		0			0
$539$	602.023	−	723.814i	1.11693	−	1.34288i
$540$		0			0
$541$	−182.747	−	316.528i	−0.337795	−	0.585079i	0.646222	−	0.763149i	$-0.276348\pi$
$541$	−182.747	−	316.528i	−0.337795	−	0.585079i	−0.984018	+	0.178070i	$0.943015\pi$
$542$		0			0
$543$	−319.620	−	604.435i	−0.588619	−	1.11314i
$544$		0			0
$545$	1126.72	−	650.510i	2.06737	−	1.19360i
$546$		0			0
$547$	−294.880	+	510.747i	−0.539086	+	0.933724i	0.459868	+	0.887987i	$0.347897\pi$
$547$	−294.880	+	510.747i	−0.539086	+	0.933724i	−0.998954	+	0.0457367i	$0.985436\pi$
$548$		0			0
$549$	377.678	−	554.465i	0.687938	−	1.00996i
$550$		0			0
$551$			543.646i			0.986653i
$552$		0			0
$553$	56.9048	+	318.681i	0.102902	+	0.576277i
$554$		0			0
$555$	−1307.48	+	691.383i	−2.35582	+	1.24574i
$556$		0			0
$557$	426.103	+	246.011i	0.764996	+	0.441671i	0.831087	−	0.556143i	$-0.187719\pi$
$557$	426.103	+	246.011i	0.764996	+	0.441671i	−0.0660907	+	0.997814i	$0.521053\pi$
$558$		0			0
$559$	67.7111			0.121129
$560$		0			0
$561$	261.260	+	494.070i	0.465704	+	0.880696i
$562$		0			0
$563$			21.1519i			0.0375699i	0.999824	+	0.0187850i	$0.00597979\pi$
$563$			21.1519i			0.0375699i	−0.999824	+	0.0187850i	$0.994020\pi$
$564$		0			0
$565$	267.526			0.473498
$566$		0			0
$567$	482.918	−	297.119i	0.851707	−	0.524019i
$568$		0			0
$569$		−	154.080i		−	0.270791i	−0.990792	−	0.135396i	$-0.956769\pi$
$569$		−	154.080i		−	0.270791i	0.990792	−	0.135396i	$-0.0432306\pi$
$570$		0			0
$571$	45.1693			0.0791056			0.0395528	−	0.999217i	$-0.487407\pi$
$571$	45.1693			0.0791056			0.0395528	+	0.999217i	$0.487407\pi$
$572$		0			0
$573$	−497.574	+	263.113i	−0.868366	+	0.459184i
$574$		0			0
$575$		−	82.6069i		−	0.143664i
$576$		0			0
$577$	13.1264	−	22.7356i	0.0227494	−	0.0394032i	−0.854427	−	0.519572i	$-0.826091\pi$
$577$	13.1264	−	22.7356i	0.0227494	−	0.0394032i	0.877176	+	0.480169i	$0.159425\pi$
$578$		0			0
$579$	50.2209	+	94.9730i	0.0867373	+	0.164029i
$580$		0			0
$581$	−222.714	+	616.053i	−0.383328	+	1.06033i
$582$		0			0
$583$	−1228.00			−2.10635
$584$		0			0
$585$	−93.7236	−	63.8404i	−0.160211	−	0.109129i
$586$		0			0
$587$	606.599	+	350.220i	1.03339	+	0.596627i	0.917953	−	0.396688i	$-0.129841\pi$
$587$	606.599	+	350.220i	1.03339	+	0.596627i	0.115434	+	0.993315i	$0.463174\pi$
$588$		0			0
$589$	−130.715	−	226.405i	−0.221927	−	0.384389i
$590$		0			0
$591$	−291.913	+	154.361i	−0.493931	+	0.261186i
$592$		0			0
$593$	−679.184	+	392.127i	−1.14534	+	0.661260i	−0.947746	−	0.319025i	$-0.896645\pi$
$593$	−679.184	+	392.127i	−1.14534	+	0.661260i	−0.197589	+	0.980285i	$0.563311\pi$
$594$		0			0
$595$	−417.796	+	352.119i	−0.702179	+	0.591797i
$596$		0			0
$597$	−206.951	−	7.69885i	−0.346651	−	0.0128959i
$598$		0			0
$599$			518.783i			0.866081i	0.901374	+	0.433041i	$0.142559\pi$
$599$			518.783i			0.866081i	−0.901374	+	0.433041i	$0.857441\pi$
$600$		0			0
$601$	1.71229	−	2.96577i	0.00284907	−	0.00493473i	−0.864597	−	0.502465i	$-0.832426\pi$
$601$	1.71229	−	2.96577i	0.00284907	−	0.00493473i	0.867446	+	0.497531i	$0.165760\pi$
$602$		0			0
$603$	−24.1271	+	35.4208i	−0.0400118	+	0.0587409i
$604$		0			0
$605$	1730.02	−	998.829i	2.85954	−	1.65096i
$606$		0			0
$607$	−219.639	+	380.425i	−0.361843	+	0.626730i	−0.988264	−	0.152754i	$-0.951186\pi$
$607$	−219.639	+	380.425i	−0.361843	+	0.626730i	0.626421	+	0.779485i	$0.284519\pi$
$608$		0			0
$609$	966.507	−	135.726i	1.58704	−	0.222866i
$610$		0			0
$611$	8.61149	−	4.97184i	0.0140941	−	0.00813722i
$612$		0			0
$613$	56.2801	−	97.4800i	0.0918109	−	0.159021i	−0.816462	−	0.577399i	$-0.804068\pi$
$613$	56.2801	−	97.4800i	0.0918109	−	0.159021i	0.908273	+	0.418378i	$0.137401\pi$
$614$		0			0
$615$	−638.156	−	1206.82i	−1.03765	−	1.96231i
$616$		0			0
$617$	−259.198	+	149.648i	−0.420094	+	0.242541i	−0.695117	−	0.718896i	$-0.744648\pi$
$617$	−259.198	+	149.648i	−0.420094	+	0.242541i	0.275024	+	0.961437i	$0.411314\pi$
$618$		0			0
$619$	−143.491	−	248.533i	−0.231811	−	0.401508i	0.726530	−	0.687134i	$-0.241132\pi$
$619$	−143.491	−	248.533i	−0.231811	−	0.401508i	−0.958341	+	0.285627i	$0.907798\pi$
$620$		0			0
$621$	−45.1068	−	33.2453i	−0.0726358	−	0.0535351i
$622$		0			0
$623$	−291.188	−	345.500i	−0.467396	−	0.554575i
$624$		0			0
$625$	17.8780	−	30.9655i	0.0286047	−	0.0495449i
$626$		0			0
$627$	−25.0653	+	673.775i	−0.0399766	+	1.07460i
$628$		0			0
$629$		−	593.824i		−	0.944077i
$630$		0			0
$631$	−263.760			−0.418003			−0.209001	−	0.977915i	$-0.567021\pi$
$631$	−263.760			−0.418003			−0.209001	+	0.977915i	$0.567021\pi$
$632$		0			0
$633$	390.852	−	622.335i	0.617460	−	0.983152i
$634$		0			0
$635$	−1357.81	−	783.930i	−2.13828	−	1.23454i
$636$		0			0
$637$	−58.9653	−	49.0436i	−0.0925672	−	0.0769916i
$638$		0			0
$639$	−246.783	−	168.098i	−0.386202	−	0.263064i
$640$		0			0
$641$	−104.470	+	60.3156i	−0.162979	+	0.0940960i	−0.579271	−	0.815135i	$-0.696663\pi$
$641$	−104.470	+	60.3156i	−0.162979	+	0.0940960i	0.416292	+	0.909231i	$0.363329\pi$
$642$		0			0
$643$	−477.894	−	827.737i	−0.743226	−	1.28730i	−0.951019	−	0.309132i	$-0.899962\pi$
$643$	−477.894	−	827.737i	−0.743226	−	1.28730i	0.207794	−	0.978173i	$-0.433372\pi$
$644$		0			0
$645$	−884.726	−	555.644i	−1.37167	−	0.861463i
$646$		0			0
$647$	−340.484	−	196.578i	−0.526250	−	0.303831i	0.213238	−	0.977000i	$-0.431599\pi$
$647$	−340.484	−	196.578i	−0.526250	−	0.303831i	−0.739488	+	0.673170i	$0.764932\pi$
$648$		0			0
$649$	308.157	+	533.743i	0.474818	+	0.822409i
$650$		0			0
$651$	−369.875	+	288.913i	−0.568164	+	0.443798i
$652$		0			0
$653$	−600.236	−	346.547i	−0.919198	−	0.530699i	−0.0358191	−	0.999358i	$-0.511404\pi$
$653$	−600.236	−	346.547i	−0.919198	−	0.530699i	−0.883379	+	0.468659i	$0.844737\pi$
$654$		0			0
$655$	−471.105	−	815.978i	−0.719244	−	1.24577i
$656$		0			0
$657$	51.6483	+	107.131i	0.0786123	+	0.163060i
$658$		0			0
$659$	−120.779	−	69.7321i	−0.183277	−	0.105815i	0.405554	−	0.914071i	$-0.367078\pi$
$659$	−120.779	−	69.7321i	−0.183277	−	0.105815i	−0.588831	+	0.808256i	$0.700412\pi$
$660$		0			0
$661$	−202.532			−0.306402			−0.153201	−	0.988195i	$-0.548958\pi$
$661$	−202.532			−0.306402			−0.153201	+	0.988195i	$0.548958\pi$
$662$		0			0
$663$	40.2493	−	21.2835i	0.0607078	−	0.0321018i
$664$		0			0
$665$	−648.892	+	115.868i	−0.975778	+	0.174238i
$666$		0			0
$667$	−48.2268	−	83.5313i	−0.0723040	−	0.125234i
$668$		0			0
$669$	301.198	+	11.2050i	0.450221	+	0.0167488i
$670$		0			0
$671$	1240.32	−	716.098i	1.84846	−	1.06721i
$672$		0			0
$673$	−319.572	+	553.515i	−0.474847	+	0.822459i	−0.999585	−	0.0288047i	$-0.990830\pi$
$673$	−319.572	+	553.515i	−0.474847	+	0.822459i	0.524738	+	0.851264i	$0.324163\pi$
$674$		0			0
$675$	430.402	+	984.752i	0.637632	+	1.45889i
$676$		0			0
$677$		−	344.793i		−	0.509295i	−0.967034	−	0.254647i	$-0.918041\pi$
$677$		−	344.793i		−	0.509295i	0.967034	−	0.254647i	$-0.0819594\pi$
$678$		0			0
$679$	−1272.99	−	460.208i	−1.87480	−	0.677774i
$680$		0			0
$681$	423.954	+	266.261i	0.622547	+	0.390985i
$682$		0			0
$683$	−392.616	−	226.677i	−0.574840	−	0.331884i	0.184240	−	0.982881i	$-0.441018\pi$
$683$	−392.616	−	226.677i	−0.574840	−	0.331884i	−0.759080	+	0.650997i	$0.774351\pi$
$684$		0			0
$685$	−642.502			−0.937959
$686$		0			0
$687$	−832.012	−	30.9520i	−1.21108	−	0.0450538i
$688$		0			0
$689$			100.039i			0.145194i
$690$		0			0
$691$	−21.6872			−0.0313852			−0.0156926	−	0.999877i	$-0.504995\pi$
$691$	−21.6872			−0.0313852			−0.0156926	+	0.999877i	$0.504995\pi$
$692$		0			0
$693$	1204.11	−	123.652i	1.73753	−	0.178429i
$694$		0			0
$695$		−	610.358i		−	0.878213i
$696$		0			0
$697$	548.108			0.786381
$698$		0			0
$699$	120.973	+	75.9757i	0.173065	+	0.108692i
$700$		0			0
$701$			988.932i			1.41074i	0.708837	+	0.705372i	$0.249220\pi$
$701$			988.932i			1.41074i	−0.708837	+	0.705372i	$0.750780\pi$
$702$		0			0
$703$	358.190	−	620.403i	0.509516	−	0.882508i
$704$		0			0
$705$	−153.319	−	5.70367i	−0.217473	−	0.00809031i
$706$		0			0
$707$	−304.132	−	360.858i	−0.430172	−	0.510408i
$708$		0			0
$709$	657.215			0.926960			0.463480	−	0.886107i	$-0.346601\pi$
$709$	657.215			0.926960			0.463480	+	0.886107i	$0.346601\pi$
$710$		0			0
$711$	−234.313	+	343.993i	−0.329555	+	0.483816i
$712$		0			0
$713$	40.1688	+	23.1915i	0.0563378	+	0.0325266i
$714$		0			0
$715$	−121.045	−	209.656i	−0.169294	−	0.293225i
$716$		0			0
$717$	−586.263	−	368.197i	−0.817661	−	0.513525i
$718$		0			0
$719$	490.350	−	283.104i	0.681988	−	0.393746i	−0.118615	−	0.992940i	$-0.537846\pi$
$719$	490.350	−	283.104i	0.681988	−	0.393746i	0.800604	+	0.599194i	$0.204512\pi$
$720$		0			0
$721$	528.511	+	191.066i	0.733025	+	0.265001i
$722$		0			0
$723$	−474.639	+	755.745i	−0.656485	+	1.04529i
$724$		0			0
$725$			1849.91i			2.55160i
$726$		0			0
$727$	61.6116	−	106.714i	0.0847478	−	0.146787i	−0.820536	−	0.571595i	$-0.806325\pi$
$727$	61.6116	−	106.714i	0.0847478	−	0.146787i	0.905284	+	0.424807i	$0.139658\pi$
$728$		0			0
$729$	710.932	+	161.298i	0.975215	+	0.221259i
$730$		0			0
$731$	363.263	−	209.730i	0.496940	−	0.286908i
$732$		0			0
$733$	−518.567	+	898.184i	−0.707458	+	1.22535i	0.258339	+	0.966054i	$0.416825\pi$
$733$	−518.567	+	898.184i	−0.707458	+	1.22535i	−0.965797	+	0.259299i	$0.916509\pi$
$734$		0			0
$735$	367.995	+	1124.69i	0.500673	+	1.53019i
$736$		0			0
$737$	−79.2349	+	45.7463i	−0.107510	+	0.0620709i
$738$		0			0
$739$	536.011	−	928.397i	0.725319	−	1.25629i	−0.233524	−	0.972351i	$-0.575026\pi$
$739$	536.011	−	928.397i	0.725319	−	1.25629i	0.958843	−	0.283938i	$-0.0916409\pi$
$740$		0			0
$741$	54.8888	+	2.04194i	0.0740740	+	0.00275565i
$742$		0			0
$743$	−645.464	+	372.659i	−0.868727	+	0.501560i	−0.866925	−	0.498439i	$-0.833907\pi$
$743$	−645.464	+	372.659i	−0.868727	+	0.501560i	−0.00180187	+	0.999998i	$0.500574\pi$
$744$		0			0
$745$	438.545	+	759.582i	0.588651	+	1.01957i
$746$		0			0
$747$	−758.673	+	365.761i	−1.01563	+	0.489640i
$748$		0			0
$749$	563.020	+	668.035i	0.751696	+	0.891902i
$750$		0			0
$751$	3.18917	−	5.52381i	0.00424657	−	0.00735527i	−0.863894	−	0.503673i	$-0.831982\pi$
$751$	3.18917	−	5.52381i	0.00424657	−	0.00735527i	0.868141	+	0.496318i	$0.165315\pi$
$752$		0			0
$753$	226.099	−	119.559i	0.300265	−	0.158777i
$754$		0			0
$755$		−	1315.66i		−	1.74259i
$756$		0			0
$757$	1187.30			1.56843			0.784216	−	0.620488i	$-0.213066\pi$
$757$	1187.30			1.56843			0.784216	+	0.620488i	$0.213066\pi$
$758$		0			0
$759$	−55.9192	−	105.749i	−0.0736748	−	0.139327i
$760$		0			0
$761$	234.723	+	135.518i	0.308441	+	0.178078i	0.646228	−	0.763144i	$-0.276345\pi$
$761$	234.723	+	135.518i	0.308441	+	0.178078i	−0.337788	+	0.941222i	$0.609679\pi$
$762$		0			0
$763$	1063.92	+	384.625i	1.39439	+	0.504096i
$764$		0			0
$765$	−700.559	−	52.1957i	−0.915764	−	0.0682297i
$766$		0			0
$767$	43.4812	−	25.1039i	0.0566900	−	0.0327300i
$768$		0			0
$769$	−12.4068	−	21.4892i	−0.0161337	−	0.0279443i	0.857846	−	0.513907i	$-0.171802\pi$
$769$	−12.4068	−	21.4892i	−0.0161337	−	0.0279443i	−0.873980	+	0.485963i	$0.838469\pi$
$770$		0			0
$771$	8.00279	−	215.121i	0.0103798	−	0.279015i
$772$		0			0
$773$	−780.685	−	450.729i	−1.00994	−	0.583090i	−0.0987672	−	0.995111i	$-0.531490\pi$
$773$	−780.685	−	450.729i	−1.00994	−	0.583090i	−0.911175	+	0.412020i	$0.864823\pi$
$774$		0			0
$775$	−444.795	−	770.408i	−0.573929	−	0.994075i
$776$		0			0
$777$	−1192.39	−	481.910i	−1.53461	−	0.620219i
$778$		0			0
$779$	572.641	+	330.614i	0.735097	+	0.424409i
$780$		0			0
$781$	−318.723	−	552.044i	−0.408096	−	0.706843i
$782$		0			0
$783$	1010.13	+	744.499i	1.29007	+	0.950828i
$784$		0			0
$785$	−219.695	−	126.841i	−0.279866	−	0.161581i
$786$		0			0
$787$	778.855			0.989651			0.494825	−	0.868992i	$-0.335232\pi$
$787$	778.855			0.989651			0.494825	+	0.868992i	$0.335232\pi$
$788$		0			0
$789$	867.140	+	544.599i	1.09904	+	0.690240i
$790$		0			0
$791$	149.917	+	177.880i	0.189529	+	0.224880i
$792$		0			0
$793$	−58.3367	−	101.042i	−0.0735646	−	0.127418i
$794$		0			0
$795$	820.927	−	1307.12i	1.03261	−	1.64418i
$796$		0			0
$797$	492.791	−	284.513i	0.618307	−	0.356980i	−0.157903	−	0.987455i	$-0.550473\pi$
$797$	492.791	−	284.513i	0.618307	−	0.356980i	0.776210	+	0.630475i	$0.217140\pi$
$798$		0			0
$799$	30.7999	−	53.3469i	0.0385480	−	0.0667671i
$800$		0			0
$801$	43.1637	−	579.333i	0.0538872	−	0.723262i
$802$		0			0
$803$			253.896i			0.316184i
$804$		0			0
$805$	89.4237	−	75.3663i	0.111085	−	0.0936228i
$806$		0			0
$807$	−23.5257	+	632.388i	−0.0291520	+	0.783628i
$808$		0			0
$809$	−888.209	−	512.808i	−1.09791	−	0.633878i	−0.162238	−	0.986752i	$-0.551871\pi$
$809$	−888.209	−	512.808i	−1.09791	−	0.633878i	−0.935671	+	0.352873i	$0.885205\pi$
$810$		0			0
$811$	−276.040			−0.340370			−0.170185	−	0.985412i	$-0.554437\pi$
$811$	−276.040			−0.340370			−0.170185	+	0.985412i	$0.554437\pi$
$812$		0			0
$813$	−413.008	+	657.614i	−0.508005	+	0.808873i
$814$		0			0
$815$			2406.44i			2.95268i
$816$		0			0
$817$	506.030			0.619376
$818$		0			0
$819$	−10.0732	−	98.0925i	−0.0122994	−	0.119771i
$820$		0			0
$821$		−	203.452i		−	0.247810i	−0.992294	−	0.123905i	$-0.960458\pi$
$821$		−	203.452i		−	0.247810i	0.992294	−	0.123905i	$-0.0395418\pi$
$822$		0			0
$823$	820.361			0.996794			0.498397	−	0.866949i	$-0.333922\pi$
$823$	820.361			0.996794			0.498397	+	0.866949i	$0.333922\pi$
$824$		0			0
$825$	−85.2918	+	2292.71i	−0.103384	+	2.77904i
$826$		0			0
$827$		−	1580.90i		−	1.91161i	−0.293998	−	0.955806i	$-0.594986\pi$
$827$		−	1580.90i		−	1.91161i	0.293998	−	0.955806i	$-0.405014\pi$
$828$		0			0
$829$	51.7377	−	89.6124i	0.0624098	−	0.108097i	−0.833132	−	0.553074i	$-0.813455\pi$
$829$	51.7377	−	89.6124i	0.0624098	−	0.108097i	0.895542	+	0.444977i	$0.146788\pi$
$830$		0			0
$831$	652.989	−	1039.72i	0.785788	−	1.25117i
$832$		0			0
$833$	−468.252	−	80.4736i	−0.562127	−	0.0966069i
$834$		0			0
$835$	2104.45			2.52030
$836$		0			0
$837$	−599.684	−	67.1751i	−0.716468	−	0.0802570i
$838$		0			0
$839$	−1258.61	−	726.657i	−1.50013	−	0.866099i	−1.00000		0.000147057i	$-0.999953\pi$
$839$	−1258.61	−	726.657i	−1.50013	−	0.866099i	−0.500127	−	0.865952i	$-0.666713\pi$
$840$		0			0
$841$	659.496	+	1142.28i	0.784181	+	1.35824i
$842$		0			0
$843$	−35.6854	+	959.251i	−0.0423315	+	1.13790i
$844$		0			0
$845$	1161.12	−	670.371i	1.37410	−	0.793338i
$846$		0			0
$847$	1633.60	+	590.575i	1.92869	+	0.697255i
$848$		0			0
$849$	−173.569	−	328.237i	−0.204439	−	0.386616i
$850$		0			0
$851$			127.100i			0.149354i
$852$		0			0
$853$	−52.3396	+	90.6549i	−0.0613595	+	0.106278i	−0.895073	−	0.445919i	$-0.852877\pi$
$853$	−52.3396	+	90.6549i	−0.0613595	+	0.106278i	0.833714	+	0.552197i	$0.186210\pi$
$854$		0			0
$855$	−700.432	−	477.104i	−0.819218	−	0.558016i
$856$		0			0
$857$	−195.478	+	112.859i	−0.228096	+	0.131691i	−0.609693	−	0.792637i	$-0.708707\pi$
$857$	−195.478	+	112.859i	−0.228096	+	0.131691i	0.381598	+	0.924329i	$0.375374\pi$
$858$		0			0
$859$	−291.619	+	505.099i	−0.339486	+	0.588008i	−0.984336	−	0.176302i	$-0.943587\pi$
$859$	−291.619	+	505.099i	−0.339486	+	0.588008i	0.644850	+	0.764309i	$0.276920\pi$
$860$		0			0
$861$	444.810	−	1100.59i	0.516620	−	1.27828i
$862$		0			0
$863$	306.120	−	176.739i	0.354716	−	0.204796i	−0.312044	−	0.950068i	$-0.601014\pi$
$863$	306.120	−	176.739i	0.354716	−	0.204796i	0.666761	+	0.745272i	$0.267680\pi$
$864$		0			0
$865$	−774.749	+	1341.90i	−0.895664	+	1.55133i
$866$		0			0
$867$	−311.104	+	495.356i	−0.358828	+	0.571345i
$868$		0			0
$869$	−769.500	+	444.271i	−0.885500	+	0.511244i
$870$		0			0
$871$	3.72671	+	6.45485i	0.00427865	+	0.00741084i
$872$		0			0
$873$	−755.797	−	1567.70i	−0.865747	−	1.79576i
$874$		0			0
$875$	−821.209	+	146.638i	−0.938525	+	0.167586i
$876$		0			0
$877$	−458.091	+	793.437i	−0.522339	+	0.904718i	0.477323	+	0.878728i	$0.341607\pi$
$877$	−458.091	+	793.437i	−0.522339	+	0.904718i	−0.999662	+	0.0259898i	$0.991726\pi$
$878$		0			0
$879$	−47.0757	−	29.5654i	−0.0535559	−	0.0336353i
$880$		0			0
$881$			1041.09i			1.18172i	0.806775	+	0.590859i	$0.201211\pi$
$881$			1041.09i			1.18172i	−0.806775	+	0.590859i	$0.798789\pi$
$882$		0			0
$883$	247.115			0.279858			0.139929	−	0.990162i	$-0.455313\pi$
$883$	247.115			0.279858			0.139929	+	0.990162i	$0.455313\pi$
$884$		0			0
$885$	−774.139	−	28.7990i	−0.874734	−	0.0325413i
$886$		0			0
$887$	−933.499	−	538.956i	−1.05242	−	0.607616i	−0.129096	−	0.991632i	$-0.541207\pi$
$887$	−933.499	−	538.956i	−1.05242	−	0.607616i	−0.923327	+	0.384016i	$0.874541\pi$
$888$		0			0
$889$	−239.652	−	1342.11i	−0.269575	−	1.50969i
$890$		0			0
$891$	1217.59	+	969.277i	1.36654	+	1.08785i
$892$		0			0
$893$	64.3569	−	37.1565i	0.0720682	−	0.0416086i
$894$		0			0
$895$	1411.55	+	2444.87i	1.57715	+	2.73170i
$896$		0			0
$897$	−8.61482	+	4.55544i	−0.00960403	+	0.00507853i
$898$		0			0
$899$	−899.545	−	519.353i	−1.00061	−	0.577700i
$900$		0			0
$901$	309.862	+	536.697i	0.343909	+	0.595669i
$902$		0			0
$903$	−126.335	−	899.633i	−0.139905	−	0.996271i
$904$		0			0
$905$	1588.91	+	917.358i	1.75570	+	1.01366i
$906$		0			0
$907$	433.640	+	751.087i	0.478104	+	0.828100i	0.999685	−	0.0251017i	$-0.00799095\pi$
$907$	433.640	+	751.087i	0.478104	+	0.828100i	−0.521581	+	0.853202i	$0.674658\pi$
$908$		0			0
$909$	45.0824	−	605.086i	0.0495956	−	0.665661i
$910$		0			0
$911$	987.899	+	570.364i	1.08441	+	0.626085i	0.932083	−	0.362245i	$-0.117990\pi$
$911$	987.899	+	570.364i	1.08441	+	0.626085i	0.152328	+	0.988330i	$0.451323\pi$
$912$		0			0
$913$	−1798.03			−1.96936
$914$		0			0
$915$	−66.9235	+	1798.95i	−0.0731404	+	1.96607i
$916$		0			0
$917$	278.549	−	770.501i	0.303761	−	0.840241i
$918$		0			0
$919$	308.533	+	534.394i	0.335726	+	0.581495i	0.983624	−	0.180232i	$-0.0576849\pi$
$919$	308.533	+	534.394i	0.335726	+	0.581495i	−0.647898	+	0.761727i	$0.724352\pi$
$920$		0			0
$921$	−510.099	−	964.651i	−0.553853	−	1.04739i
$922$		0			0
$923$	−44.9721	+	25.9647i	−0.0487239	+	0.0281307i
$924$		0			0
$925$	1218.84	−	2111.10i	1.31767	−	2.28227i
$926$		0			0
$927$	313.786	+	650.865i	0.338496	+	0.702120i
$928$		0			0
$929$		−	532.241i		−	0.572918i	−0.958093	−	0.286459i	$-0.907522\pi$
$929$		−	532.241i		−	0.572918i	0.958093	−	0.286459i	$-0.0924782\pi$
$930$		0			0
$931$	−440.670	−	366.521i	−0.473329	−	0.393686i
$932$		0			0
$933$	398.306	−	210.621i	0.426909	−	0.225746i
$934$		0			0
$935$	−1298.79	−	749.856i	−1.38908	−	0.801985i
$936$		0			0
$937$	−1506.24			−1.60751			−0.803755	−	0.594960i	$-0.797168\pi$
$937$	−1506.24			−1.60751			−0.803755	+	0.594960i	$0.797168\pi$
$938$		0			0
$939$	328.458	+	621.148i	0.349795	+	0.661499i
$940$		0			0
$941$		−	204.118i		−	0.216916i	−0.994101	−	0.108458i	$-0.965409\pi$
$941$		−	204.118i		−	0.216916i	0.994101	−	0.108458i	$-0.0345913\pi$
$942$		0			0
$943$	−117.315			−0.124406
$944$		0			0
$945$	−673.338	+	1364.36i	−0.712527	+	1.44376i
$946$		0			0
$947$		−	497.276i		−	0.525106i	−0.964918	−	0.262553i	$-0.915435\pi$
$947$		−	497.276i		−	0.525106i	0.964918	−	0.262553i	$-0.0845645\pi$
$948$		0			0
$949$	20.6835			0.0217951
$950$		0			0
$951$	−1041.42	+	550.693i	−1.09508	+	0.579067i
$952$		0			0
$953$		−	582.144i		−	0.610854i	−0.952215	−	0.305427i	$-0.901201\pi$
$953$		−	582.144i		−	0.610854i	0.952215	−	0.305427i	$-0.0987992\pi$
$954$		0			0
$955$	755.174	−	1308.00i	0.790758	−	1.36963i
$956$		0			0
$957$	1252.26	+	2368.16i	1.30853	+	2.47456i
$958$		0			0
$959$	−360.047	−	427.203i	−0.375441	−	0.445468i
$960$		0			0
$961$	−461.504			−0.480233
$962$		0			0
$963$	−83.4583	+	1120.16i	−0.0866649	+	1.16320i
$964$		0			0
$965$	−249.661	−	144.142i	−0.258716	−	0.149370i
$966$		0			0
$967$	−239.897	−	415.514i	−0.248084	−	0.429694i	0.714910	−	0.699216i	$-0.246468\pi$
$967$	−239.897	−	415.514i	−0.248084	−	0.429694i	−0.962994	+	0.269522i	$0.913134\pi$
$968$		0			0
$969$	300.798	−	159.059i	0.310421	−	0.164148i
$970$		0			0
$971$	311.099	−	179.613i	0.320391	−	0.184978i	−0.331176	−	0.943569i	$-0.607445\pi$
$971$	311.099	−	179.613i	0.320391	−	0.184978i	0.651567	+	0.758591i	$0.274112\pi$
$972$		0			0
$973$	405.831	−	342.034i	0.417092	−	0.351526i
$974$		0			0
$975$	186.775	+	6.94827i	0.191564	+	0.00712643i
$976$		0			0
$977$		−	9.86558i		−	0.0100978i	−0.999987	−	0.00504892i	$-0.998393\pi$
$977$		−	9.86558i		−	0.0100978i	0.999987	−	0.00504892i	$-0.00160713\pi$
$978$		0			0
$979$	620.100	−	1074.04i	0.633401	−	1.09708i
$980$		0			0
$981$	631.667	+	1310.22i	0.643901	+	1.33560i
$982$		0			0
$983$	177.778	−	102.640i	0.180853	−	0.104415i	−0.406840	−	0.913499i	$-0.633370\pi$
$983$	177.778	−	102.640i	0.180853	−	0.104415i	0.587693	+	0.809084i	$0.300036\pi$
$984$		0			0
$985$	443.040	−	767.368i	0.449787	−	0.779054i
$986$		0			0
$987$	−82.1249	−	105.139i	−0.0832066	−	0.106524i
$988$		0			0
$989$	−77.7516	+	44.8899i	−0.0786164	+	0.0453892i
$990$		0			0
$991$	−204.103	+	353.517i	−0.205957	+	0.356728i	−0.950437	−	0.310917i	$-0.899364\pi$
$991$	−204.103	+	353.517i	−0.205957	+	0.356728i	0.744480	+	0.667645i	$0.232697\pi$
$992$		0			0
$993$	−213.199	−	403.182i	−0.214702	−	0.406024i
$994$		0			0
$995$	481.257	−	277.854i	0.483675	−	0.279250i
$996$		0			0
$997$	325.326	+	563.482i	0.326305	+	0.565177i	0.981776	−	0.190044i	$-0.0608630\pi$
$997$	325.326	+	563.482i	0.326305	+	0.565177i	−0.655471	+	0.755221i	$0.727530\pi$
$998$		0			0
$999$	−662.222	−	1515.15i	−0.662885	−	1.51667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.bh.a.137.6	yes	32
3.2	odd	2		756.3.bh.a.305.2		32
7.2	even	3		252.3.m.a.65.16	✓	32
9.4	even	3		756.3.m.a.557.2		32
9.5	odd	6		252.3.m.a.221.16	yes	32
21.2	odd	6		756.3.m.a.737.15		32
63.23	odd	6	inner	252.3.bh.a.149.6	yes	32
63.58	even	3		756.3.bh.a.233.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.3.m.a.65.16	✓	32	7.2	even	3
252.3.m.a.221.16	yes	32	9.5	odd	6
252.3.bh.a.137.6	yes	32	1.1	even	1	trivial
252.3.bh.a.149.6	yes	32	63.23	odd	6	inner
756.3.m.a.557.2		32	9.4	even	3
756.3.m.a.737.15		32	21.2	odd	6
756.3.bh.a.233.2		32	63.58	even	3
756.3.bh.a.305.2		32	3.2	odd	2

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40238 - 2.65204i) q^{3} +(6.97157 + 4.02504i) q^{5} +(1.23048 + 6.89100i) q^{7} +(-5.06667 + 7.43834i) q^{9} +O(q^{10})\)	\(q+(-1.40238 - 2.65204i) q^{3} +(6.97157 + 4.02504i) q^{5} +(1.23048 + 6.89100i) q^{7} +(-5.06667 + 7.43834i) q^{9} +(-16.6393 + 9.60669i) q^{11} +(0.782606 + 1.35551i) q^{13} +(0.897800 - 24.1335i) q^{15} +(8.39721 + 4.84813i) q^{17} +(5.84871 + 10.1303i) q^{19} +(16.5496 - 12.9271i) q^{21} +(-1.79731 - 1.03768i) q^{23} +(19.9019 + 34.4710i) q^{25} +(26.8322 + 3.00568i) q^{27} +(40.2492 + 23.2379i) q^{29} -22.3494 q^{31} +(48.8119 + 30.6559i) q^{33} +(-19.1582 + 52.9938i) q^{35} +(-30.6213 - 53.0376i) q^{37} +(2.49737 - 3.97645i) q^{39} +(48.9545 - 28.2639i) q^{41} +(21.6300 - 37.4643i) q^{43} +(-65.2622 + 31.4633i) q^{45} -6.35293i q^{47} +(-45.9718 + 16.9585i) q^{49} +(1.08139 - 29.0687i) q^{51} +(55.3510 + 31.9569i) q^{53} -154.669 q^{55} +(18.6638 - 29.7175i) q^{57} -32.0773i q^{59} -74.5416 q^{61} +(-57.4920 - 25.7617i) q^{63} +12.6001i q^{65} +4.76192 q^{67} +(-0.231458 + 6.22176i) q^{69} +33.1772i q^{71} +(6.60726 - 11.4441i) q^{73} +(63.5088 - 101.122i) q^{75} +(-86.6740 - 102.840i) q^{77} +46.2460 q^{79} +(-29.6577 - 75.3752i) q^{81} +(81.0445 + 46.7910i) q^{83} +(39.0278 + 67.5982i) q^{85} +(5.18329 - 139.331i) q^{87} +(-55.9009 + 32.2744i) q^{89} +(-8.37786 + 7.06087i) q^{91} +(31.3423 + 59.2716i) q^{93} +94.1651i q^{95} +(-96.6875 + 167.468i) q^{97} +(12.8480 - 172.442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{7} - 14 q^{9}+O(q^{10}) \) 32 * q - q^7 - 14 * q^9	\( 32 q - q^{7} - 14 q^{9} + 18 q^{11} - 5 q^{13} - 29 q^{15} + 27 q^{17} - 14 q^{19} - 8 q^{21} - 45 q^{23} + 80 q^{25} + 45 q^{27} + 36 q^{29} + 16 q^{31} + 116 q^{33} + 45 q^{35} - 11 q^{37} + 55 q^{39} + 72 q^{41} + 16 q^{43} - 154 q^{45} - 37 q^{49} - 133 q^{51} - 180 q^{53} - 24 q^{55} + 57 q^{57} + 82 q^{61} - 99 q^{63} + 70 q^{67} - 97 q^{69} - 98 q^{73} - 149 q^{75} - 135 q^{77} + 142 q^{79} - 98 q^{81} - 30 q^{85} - 86 q^{87} + 189 q^{89} + 109 q^{91} + 109 q^{93} + 19 q^{97} - 101 q^{99}+O(q^{100}) \) 32 * q - q^7 - 14 * q^9 + 18 * q^11 - 5 * q^13 - 29 * q^15 + 27 * q^17 - 14 * q^19 - 8 * q^21 - 45 * q^23 + 80 * q^25 + 45 * q^27 + 36 * q^29 + 16 * q^31 + 116 * q^33 + 45 * q^35 - 11 * q^37 + 55 * q^39 + 72 * q^41 + 16 * q^43 - 154 * q^45 - 37 * q^49 - 133 * q^51 - 180 * q^53 - 24 * q^55 + 57 * q^57 + 82 * q^61 - 99 * q^63 + 70 * q^67 - 97 * q^69 - 98 * q^73 - 149 * q^75 - 135 * q^77 + 142 * q^79 - 98 * q^81 - 30 * q^85 - 86 * q^87 + 189 * q^89 + 109 * q^91 + 109 * q^93 + 19 * q^97 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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