LMFDB - Embedded newform 432.3.bc.a.353.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,3,Mod(65,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 0, 13])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.65"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	432.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,6,0,-15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.7711474204$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			353.1
Character	$\chi$	$=$	432.353
Dual form			432.3.bc.a.257.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.32380 + 1.89736i) q^{3} +(3.98394 + 4.74788i) q^{5} +(7.49258 - 2.72708i) q^{7} +(1.80008 - 8.81815i) q^{9} +(7.35571 - 8.76619i) q^{11} +(-1.43358 - 8.13025i) q^{13} +(-18.2663 - 3.47416i) q^{15} +(20.7128 - 11.9585i) q^{17} +(-6.12102 + 10.6019i) q^{19} +(-12.2370 + 20.5533i) q^{21} +(5.04566 - 13.8628i) q^{23} +(-2.32934 + 13.2103i) q^{25} +(12.5481 + 23.9070i) q^{27} +(-17.5228 - 3.08975i) q^{29} +(12.2356 + 4.45339i) q^{31} +(-0.460606 + 34.3273i) q^{33} +(42.7978 + 24.7093i) q^{35} +(8.53500 + 14.7831i) q^{37} +(18.7573 + 16.1730i) q^{39} +(30.2688 - 5.33721i) q^{41} +(30.5116 + 25.6022i) q^{43} +(49.0389 - 26.5844i) q^{45} +(-19.9668 - 54.8583i) q^{47} +(11.1657 - 9.36910i) q^{49} +(-25.4428 + 67.0888i) q^{51} +91.2612i q^{53} +70.9255 q^{55} +(-5.89158 - 36.2505i) q^{57} +(13.2814 + 15.8282i) q^{59} +(32.8508 - 11.9567i) q^{61} +(-10.5605 - 70.9797i) q^{63} +(32.8901 - 39.1969i) q^{65} +(-8.95370 - 50.7790i) q^{67} +(14.5776 + 41.7879i) q^{69} +(-2.28181 + 1.31740i) q^{71} +(-34.5072 + 59.7683i) q^{73} +(-19.6518 - 35.1177i) q^{75} +(31.2072 - 85.7410i) q^{77} +(-26.2964 + 149.134i) q^{79} +(-74.5194 - 31.7468i) q^{81} +(-53.2469 - 9.38886i) q^{83} +(139.296 + 50.6997i) q^{85} +(46.5819 - 26.0671i) q^{87} +(-141.225 - 81.5361i) q^{89} +(-32.9130 - 57.0070i) q^{91} +(-36.8828 + 12.8665i) q^{93} +(-74.7224 + 13.1756i) q^{95} +(43.6738 + 36.6467i) q^{97} +(-64.0607 - 80.6436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37}+ \cdots - 513 q^{99}+O(q^{100}) $ 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{18}\right)$

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
$3$	−2.32380	+	1.89736i	−0.774600	+	0.632452i
$3$	−2.32380	+	1.89736i	−0.774600	+	0.632452i
$4$		0			0
$5$	3.98394	+	4.74788i	0.796788	+	0.949575i	0.999560	−	0.0296506i	$-0.00943948\pi$
$5$	3.98394	+	4.74788i	0.796788	+	0.949575i	−0.202772	+	0.979226i	$0.564995\pi$
$6$		0			0
$7$	7.49258	−	2.72708i	1.07037	−	0.389582i	0.254054	−	0.967190i	$-0.418236\pi$
$7$	7.49258	−	2.72708i	1.07037	−	0.389582i	0.816315	+	0.577608i	$0.196014\pi$
$8$		0			0
$9$	1.80008	−	8.81815i	0.200009	−	0.979794i
$10$		0			0
$11$	7.35571	−	8.76619i	0.668701	−	0.796927i	−0.319906	−	0.947449i	$-0.603651\pi$
$11$	7.35571	−	8.76619i	0.668701	−	0.796927i	0.988607	+	0.150523i	$0.0480957\pi$
$12$		0			0
$13$	−1.43358	−	8.13025i	−0.110276	−	0.625403i	−0.988981	−	0.148040i	$-0.952704\pi$
$13$	−1.43358	−	8.13025i	−0.110276	−	0.625403i	0.878706	−	0.477364i	$-0.158408\pi$
$14$		0			0
$15$	−18.2663	−	3.47416i	−1.21775	−	0.231611i
$16$		0			0
$17$	20.7128	−	11.9585i	1.21840	−	0.703443i	0.253824	−	0.967250i	$-0.418311\pi$
$17$	20.7128	−	11.9585i	1.21840	−	0.703443i	0.964576	+	0.263807i	$0.0849782\pi$
$18$		0			0
$19$	−6.12102	+	10.6019i	−0.322159	+	0.557995i	−0.980933	−	0.194345i	$-0.937742\pi$
$19$	−6.12102	+	10.6019i	−0.322159	+	0.557995i	0.658774	+	0.752341i	$0.271075\pi$
$20$		0			0
$21$	−12.2370	+	20.5533i	−0.582715	+	0.978727i
$22$		0			0
$23$	5.04566	−	13.8628i	0.219377	−	0.602732i	−0.780368	−	0.625320i	$-0.784968\pi$
$23$	5.04566	−	13.8628i	0.219377	−	0.602732i	0.999745	+	0.0225880i	$0.00719059\pi$
$24$		0			0
$25$	−2.32934	+	13.2103i	−0.0931735	+	0.528413i
$26$		0			0
$27$	12.5481	+	23.9070i	0.464745	+	0.885444i
$28$		0			0
$29$	−17.5228	−	3.08975i	−0.604235	−	0.106543i	−0.136843	−	0.990593i	$-0.543695\pi$
$29$	−17.5228	−	3.08975i	−0.604235	−	0.106543i	−0.467393	+	0.884050i	$0.654807\pi$
$30$		0			0
$31$	12.2356	+	4.45339i	0.394697	+	0.143658i	0.531741	−	0.846907i	$-0.321538\pi$
$31$	12.2356	+	4.45339i	0.394697	+	0.143658i	−0.137044	+	0.990565i	$0.543760\pi$
$32$		0			0
$33$	−0.460606	+	34.3273i	−0.0139578	+	1.04022i
$34$		0			0
$35$	42.7978	+	24.7093i	1.22280	+	0.705981i
$36$		0			0
$37$	8.53500	+	14.7831i	0.230676	+	0.399542i	0.958007	−	0.286744i	$-0.0925730\pi$
$37$	8.53500	+	14.7831i	0.230676	+	0.399542i	−0.727331	+	0.686286i	$0.759240\pi$
$38$		0			0
$39$	18.7573	+	16.1730i	0.480957	+	0.414693i
$40$		0			0
$41$	30.2688	−	5.33721i	0.738265	−	0.130176i	0.208144	−	0.978098i	$-0.433258\pi$
$41$	30.2688	−	5.33721i	0.738265	−	0.130176i	0.530121	+	0.847922i	$0.322147\pi$
$42$		0			0
$43$	30.5116	+	25.6022i	0.709571	+	0.595401i	0.924479	−	0.381233i	$-0.124501\pi$
$43$	30.5116	+	25.6022i	0.709571	+	0.595401i	−0.214908	+	0.976634i	$0.568945\pi$
$44$		0			0
$45$	49.0389	−	26.5844i	1.08975	−	0.590764i
$46$		0			0
$47$	−19.9668	−	54.8583i	−0.424825	−	1.16720i	−0.948914	−	0.315534i	$-0.897816\pi$
$47$	−19.9668	−	54.8583i	−0.424825	−	1.16720i	0.524089	−	0.851663i	$-0.324406\pi$
$48$		0			0
$49$	11.1657	−	9.36910i	0.227871	−	0.191206i
$50$		0			0
$51$	−25.4428	+	67.0888i	−0.498878	+	1.31547i
$52$		0			0
$53$			91.2612i			1.72191i	0.508681	+	0.860955i	$0.330133\pi$
$53$			91.2612i			1.72191i	−0.508681	+	0.860955i	$0.669867\pi$
$54$		0			0
$55$	70.9255			1.28956
$56$		0			0
$57$	−5.89158	−	36.2505i	−0.103361	−	0.635973i
$58$		0			0
$59$	13.2814	+	15.8282i	0.225109	+	0.268274i	0.866764	−	0.498719i	$-0.166196\pi$
$59$	13.2814	+	15.8282i	0.225109	+	0.268274i	−0.641655	+	0.766994i	$0.721752\pi$
$60$		0			0
$61$	32.8508	−	11.9567i	0.538538	−	0.196012i	−0.0584084	−	0.998293i	$-0.518603\pi$
$61$	32.8508	−	11.9567i	0.538538	−	0.196012i	0.596947	+	0.802281i	$0.296380\pi$
$62$		0			0
$63$	−10.5605	−	70.9797i	−0.167627	−	1.12666i
$64$		0			0
$65$	32.8901	−	39.1969i	0.506001	−	0.603029i
$66$		0			0
$67$	−8.95370	−	50.7790i	−0.133637	−	0.757895i	−0.975799	−	0.218670i	$-0.929828\pi$
$67$	−8.95370	−	50.7790i	−0.133637	−	0.757895i	0.842162	−	0.539225i	$-0.181283\pi$
$68$		0			0
$69$	14.5776	+	41.7879i	0.211270	+	0.605621i
$70$		0			0
$71$	−2.28181	+	1.31740i	−0.0321381	+	0.0185549i	−0.515983	−	0.856599i	$-0.672573\pi$
$71$	−2.28181	+	1.31740i	−0.0321381	+	0.0185549i	0.483845	+	0.875154i	$0.339240\pi$
$72$		0			0
$73$	−34.5072	+	59.7683i	−0.472702	+	0.818743i	−0.999512	−	0.0312395i	$-0.990055\pi$
$73$	−34.5072	+	59.7683i	−0.472702	+	0.818743i	0.526810	+	0.849983i	$0.323388\pi$
$74$		0			0
$75$	−19.6518	−	35.1177i	−0.262024	−	0.468237i
$76$		0			0
$77$	31.2072	−	85.7410i	0.405288	−	1.11352i
$78$		0			0
$79$	−26.2964	+	149.134i	−0.332866	+	1.88778i	0.114494	+	0.993424i	$0.463475\pi$
$79$	−26.2964	+	149.134i	−0.332866	+	1.88778i	−0.447360	+	0.894354i	$0.647636\pi$
$80$		0			0
$81$	−74.5194	−	31.7468i	−0.919993	−	0.391936i
$82$		0			0
$83$	−53.2469	−	9.38886i	−0.641529	−	0.113119i	−0.156585	−	0.987664i	$-0.550049\pi$
$83$	−53.2469	−	9.38886i	−0.641529	−	0.113119i	−0.484943	+	0.874546i	$0.661160\pi$
$84$		0			0
$85$	139.296	+	50.6997i	1.63878	+	0.596467i
$86$		0			0
$87$	46.5819	−	26.0671i	0.535424	−	0.299622i
$88$		0			0
$89$	−141.225	−	81.5361i	−1.58679	−	0.916136i	−0.993831	−	0.110906i	$-0.964625\pi$
$89$	−141.225	−	81.5361i	−1.58679	−	0.916136i	−0.592962	−	0.805230i	$-0.702042\pi$
$90$		0			0
$91$	−32.9130	−	57.0070i	−0.361682	−	0.626451i
$92$		0			0
$93$	−36.8828	+	12.8665i	−0.396589	+	0.138349i
$94$		0			0
$95$	−74.7224	+	13.1756i	−0.786551	+	0.138690i
$96$		0			0
$97$	43.6738	+	36.6467i	0.450246	+	0.377801i	0.839527	−	0.543318i	$-0.182832\pi$
$97$	43.6738	+	36.6467i	0.450246	+	0.377801i	−0.389281	+	0.921119i	$0.627277\pi$
$98$		0			0
$99$	−64.0607	−	80.6436i	−0.647078	−	0.814582i
$100$		0			0
$101$	−9.49911	−	26.0986i	−0.0940506	−	0.258402i	0.883743	−	0.467973i	$-0.155016\pi$
$101$	−9.49911	−	26.0986i	−0.0940506	−	0.258402i	−0.977793	+	0.209571i	$0.932793\pi$
$102$		0			0
$103$	−62.8906	+	52.7715i	−0.610589	+	0.512345i	−0.894829	−	0.446408i	$-0.852703\pi$
$103$	−62.8906	+	52.7715i	−0.610589	+	0.512345i	0.284241	+	0.958753i	$0.408258\pi$
$104$		0			0
$105$	−146.336	+	23.7832i	−1.39368	+	0.226506i
$106$		0			0
$107$			35.8639i			0.335177i	0.985857	+	0.167588i	$0.0535980\pi$
$107$			35.8639i			0.335177i	−0.985857	+	0.167588i	$0.946402\pi$
$108$		0			0
$109$	1.41546			0.0129859			0.00649295	−	0.999979i	$-0.497933\pi$
$109$	1.41546			0.0129859			0.00649295	+	0.999979i	$0.497933\pi$
$110$		0			0
$111$	−47.8823	−	18.1589i	−0.431372	−	0.163594i
$112$		0			0
$113$	−95.7961	−	114.165i	−0.847753	−	1.01031i	−0.999759	−	0.0219332i	$-0.993018\pi$
$113$	−95.7961	−	114.165i	−0.847753	−	1.01031i	0.152006	−	0.988380i	$-0.451427\pi$
$114$		0			0
$115$	85.9207	−	31.2726i	0.747136	−	0.271935i
$116$		0			0
$117$	−74.2743	−	1.99359i	−0.634823	−	0.0170393i
$118$		0			0
$119$	122.580	−	146.086i	1.03009	−	1.22761i
$120$		0			0
$121$	−1.72825	−	9.80142i	−0.0142831	−	0.0810035i
$122$		0			0
$123$	−60.2121	+	69.8334i	−0.489530	+	0.567751i
$124$		0			0
$125$	62.1878	−	35.9041i	0.497502	−	0.287233i
$126$		0			0
$127$	8.57044	−	14.8444i	0.0674838	−	0.116885i	−0.830309	−	0.557303i	$-0.811836\pi$
$127$	8.57044	−	14.8444i	0.0674838	−	0.116885i	0.897793	+	0.440417i	$0.145170\pi$
$128$		0			0
$129$	−119.479	−	1.60318i	−0.926196	−	0.0124278i
$130$		0			0
$131$	49.9104	−	137.128i	0.380995	−	1.04678i	−0.589943	−	0.807445i	$-0.700850\pi$
$131$	49.9104	−	137.128i	0.380995	−	1.04678i	0.970938	−	0.239331i	$-0.0769282\pi$
$132$		0			0
$133$	−16.9500	+	96.1282i	−0.127444	+	0.722768i
$134$		0			0
$135$	−63.5165	+	154.821i	−0.470493	+	1.14682i
$136$		0			0
$137$	85.6934	+	15.1101i	0.625499	+	0.110292i	0.477409	−	0.878681i	$-0.341576\pi$
$137$	85.6934	+	15.1101i	0.625499	+	0.110292i	0.148091	+	0.988974i	$0.452687\pi$
$138$		0			0
$139$	34.6380	+	12.6072i	0.249194	+	0.0906992i	0.463597	−	0.886046i	$-0.346558\pi$
$139$	34.6380	+	12.6072i	0.249194	+	0.0906992i	−0.214403	+	0.976745i	$0.568781\pi$
$140$		0			0
$141$	150.484	+	89.5955i	1.06727	+	0.635429i
$142$		0			0
$143$	−81.8163	−	47.2367i	−0.572142	−	0.330326i
$144$		0			0
$145$	−55.1402	−	95.5056i	−0.380277	−	0.658659i
$146$		0			0
$147$	−8.17024	+	42.9571i	−0.0555798	+	0.292225i
$148$		0			0
$149$	63.6158	−	11.2172i	0.426952	−	0.0752832i	0.0439567	−	0.999033i	$-0.486004\pi$
$149$	63.6158	−	11.2172i	0.426952	−	0.0752832i	0.382995	+	0.923750i	$0.374893\pi$
$150$		0			0
$151$	118.320	+	99.2826i	0.783579	+	0.657501i	0.944147	−	0.329524i	$-0.106888\pi$
$151$	118.320	+	99.2826i	0.783579	+	0.657501i	−0.160568	+	0.987025i	$0.551333\pi$
$152$		0			0
$153$	−68.1674	−	204.175i	−0.445538	−	1.33448i
$154$		0			0
$155$	27.6018	+	75.8352i	0.178076	+	0.489259i
$156$		0			0
$157$	−147.505	+	123.771i	−0.939522	+	0.788352i	−0.977502	−	0.210926i	$-0.932352\pi$
$157$	−147.505	+	123.771i	−0.939522	+	0.788352i	0.0379802	+	0.999278i	$0.487908\pi$
$158$		0			0
$159$	−173.155	−	212.073i	−1.08902	−	1.33379i
$160$		0			0
$161$		−	117.628i		−	0.730611i
$162$		0			0
$163$	−171.309			−1.05098			−0.525488	−	0.850801i	$-0.676117\pi$
$163$	−171.309			−1.05098			−0.525488	+	0.850801i	$0.676117\pi$
$164$		0			0
$165$	−164.817	+	134.571i	−0.998889	+	0.815581i
$166$		0			0
$167$	−101.164	−	120.563i	−0.605773	−	0.721932i	0.372782	−	0.927919i	$-0.378404\pi$
$167$	−101.164	−	120.563i	−0.605773	−	0.721932i	−0.978555	+	0.205987i	$0.933960\pi$
$168$		0			0
$169$	94.7623	−	34.4907i	0.560724	−	0.204087i
$170$		0			0
$171$	82.4709	+	73.0604i	0.482286	+	0.427254i
$172$		0			0
$173$	33.7496	−	40.2212i	0.195084	−	0.232492i	−0.659631	−	0.751590i	$-0.729287\pi$
$173$	33.7496	−	40.2212i	0.195084	−	0.232492i	0.854715	+	0.519097i	$0.173732\pi$
$174$		0			0
$175$	18.5728	+	105.332i	0.106130	+	0.601896i
$176$		0			0
$177$	−60.8951	−	11.5819i	−0.344040	−	0.0654347i
$178$		0			0
$179$	57.9711	−	33.4697i	0.323861	−	0.186981i	−0.329251	−	0.944242i	$-0.606796\pi$
$179$	57.9711	−	33.4697i	0.323861	−	0.186981i	0.653112	+	0.757261i	$0.273463\pi$
$180$		0			0
$181$	64.7294	−	112.115i	0.357621	−	0.619418i	−0.629942	−	0.776642i	$-0.716921\pi$
$181$	64.7294	−	112.115i	0.357621	−	0.619418i	0.987563	+	0.157225i	$0.0502547\pi$
$182$		0			0
$183$	−53.6526	+	90.1147i	−0.293184	+	0.492430i
$184$		0			0
$185$	−36.1852	+	99.4180i	−0.195596	+	0.537394i
$186$		0			0
$187$	47.5265	−	269.536i	0.254152	−	1.44137i
$188$		0			0
$189$	159.214	+	144.905i	0.842402	+	0.766696i
$190$		0			0
$191$	267.225	+	47.1189i	1.39908	+	0.246696i	0.821766	−	0.569825i	$-0.192989\pi$
$191$	267.225	+	47.1189i	1.39908	+	0.246696i	0.577315	+	0.816521i	$0.304100\pi$
$192$		0			0
$193$	−194.971	−	70.9637i	−1.01021	−	0.367688i	−0.216699	−	0.976238i	$-0.569529\pi$
$193$	−194.971	−	70.9637i	−1.01021	−	0.367688i	−0.793515	+	0.608551i	$0.791751\pi$
$194$		0			0
$195$	−2.05954	+	153.490i	−0.0105617	+	0.787128i
$196$		0			0
$197$	154.871	+	89.4146i	0.786145	+	0.453881i	0.838604	−	0.544742i	$-0.183372\pi$
$197$	154.871	+	89.4146i	0.786145	+	0.453881i	−0.0524583	+	0.998623i	$0.516706\pi$
$198$		0			0
$199$	−12.8040	−	22.1772i	−0.0643418	−	0.111443i	0.832060	−	0.554686i	$-0.187161\pi$
$199$	−12.8040	−	22.1772i	−0.0643418	−	0.111443i	−0.896402	+	0.443242i	$0.853828\pi$
$200$		0			0
$201$	117.152	+	101.012i	0.582848	+	0.502546i
$202$		0			0
$203$	−139.717	+	24.6359i	−0.688262	+	0.121359i
$204$		0			0
$205$	145.930	+	122.450i	0.711853	+	0.597315i
$206$		0			0
$207$	−113.162	−	69.4477i	−0.546676	−	0.335496i
$208$		0			0
$209$	47.9140	+	131.643i	0.229254	+	0.629869i
$210$		0			0
$211$	−275.995	+	231.587i	−1.30803	+	1.09757i	−0.319335	+	0.947642i	$0.603460\pi$
$211$	−275.995	+	231.587i	−1.30803	+	1.09757i	−0.988697	+	0.149928i	$0.952096\pi$
$212$		0			0
$213$	2.80288	−	7.39077i	0.0131591	−	0.0346985i
$214$		0			0
$215$			246.863i			1.14820i
$216$		0			0
$217$	103.821			0.478438
$218$		0			0
$219$	−33.2138	−	204.362i	−0.151661	−	0.933159i
$220$		0			0
$221$	−126.919	−	151.257i	−0.574296	−	0.684419i
$222$		0			0
$223$	8.44446	−	3.07353i	0.0378675	−	0.0137827i	−0.323017	−	0.946393i	$-0.604697\pi$
$223$	8.44446	−	3.07353i	0.0378675	−	0.0137827i	0.360884	+	0.932611i	$0.382475\pi$
$224$		0			0
$225$	112.298	+	44.3202i	0.499101	+	0.196978i
$226$		0			0
$227$	−46.1393	+	54.9867i	−0.203257	+	0.242232i	−0.858038	−	0.513587i	$-0.828316\pi$
$227$	−46.1393	+	54.9867i	−0.203257	+	0.242232i	0.654781	+	0.755819i	$0.272761\pi$
$228$		0			0
$229$	9.36599	+	53.1172i	0.0408995	+	0.231953i	0.998405	−	0.0564635i	$-0.0179825\pi$
$229$	9.36599	+	53.1172i	0.0408995	+	0.231953i	−0.957505	+	0.288416i	$0.906871\pi$
$230$		0			0
$231$	90.1620	+	258.456i	0.390312	+	1.11886i
$232$		0			0
$233$	−314.078	+	181.333i	−1.34798	+	0.778254i	−0.987962	−	0.154694i	$-0.950561\pi$
$233$	−314.078	+	181.333i	−1.34798	+	0.778254i	−0.360013	+	0.932947i	$0.617228\pi$
$234$		0			0
$235$	180.914	−	313.352i	0.769846	−	1.33341i
$236$		0			0
$237$	−221.853	−	396.452i	−0.936091	−	1.67279i
$238$		0			0
$239$	86.0424	−	236.399i	0.360010	−	0.989119i	−0.619015	−	0.785379i	$-0.712468\pi$
$239$	86.0424	−	236.399i	0.360010	−	0.989119i	0.979025	−	0.203740i	$-0.0653097\pi$
$240$		0			0
$241$	69.9633	−	396.781i	0.290304	−	1.64640i	−0.395395	−	0.918511i	$-0.629392\pi$
$241$	69.9633	−	396.781i	0.290304	−	1.64640i	0.685699	−	0.727885i	$-0.259497\pi$
$242$		0			0
$243$	233.403	−	67.6166i	0.960507	−	0.278257i
$244$		0			0
$245$	88.9667	+	15.6872i	0.363129	+	0.0640295i
$246$		0			0
$247$	94.9711	+	34.5667i	0.384499	+	0.139946i
$248$		0			0
$249$	141.549	−	79.2104i	0.568470	−	0.318114i
$250$		0			0
$251$	−329.280	−	190.110i	−1.31187	−	0.757409i	−0.329465	−	0.944168i	$-0.606868\pi$
$251$	−329.280	−	190.110i	−1.31187	−	0.757409i	−0.982406	+	0.186759i	$0.940202\pi$
$252$		0			0
$253$	−84.4099	−	146.202i	−0.333636	−	0.577875i
$254$		0			0
$255$	−419.892	+	146.479i	−1.64663	+	0.574426i
$256$		0			0
$257$	−21.3590	+	3.76618i	−0.0831091	+	0.0146544i	−0.215048	−	0.976603i	$-0.568991\pi$
$257$	−21.3590	+	3.76618i	−0.0831091	+	0.0146544i	0.131939	+	0.991258i	$0.457880\pi$
$258$		0			0
$259$	104.264	+	87.4877i	0.402563	+	0.337790i
$260$		0			0
$261$	−58.7884	+	148.957i	−0.225243	+	0.570716i
$262$		0			0
$263$	23.2155	+	63.7841i	0.0882719	+	0.242525i	0.975972	−	0.217898i	$-0.0699200\pi$
$263$	23.2155	+	63.7841i	0.0882719	+	0.242525i	−0.887700	+	0.460423i	$0.847698\pi$
$264$		0			0
$265$	−433.297	+	363.579i	−1.63508	+	1.37200i
$266$		0			0
$267$	482.881	−	78.4799i	1.80854	−	0.293932i
$268$		0			0
$269$			290.581i			1.08023i	0.841592	+	0.540113i	$0.181619\pi$
$269$			290.581i			1.08023i	−0.841592	+	0.540113i	$0.818381\pi$
$270$		0			0
$271$	414.644			1.53005			0.765026	−	0.644000i	$-0.222726\pi$
$271$	414.644			1.53005			0.765026	+	0.644000i	$0.222726\pi$
$272$		0			0
$273$	184.646	+	70.0252i	0.676359	+	0.256503i
$274$		0			0
$275$	98.6704	+	117.591i	0.358801	+	0.427603i
$276$		0			0
$277$	−164.568	+	59.8978i	−0.594108	+	0.216238i	−0.621535	−	0.783386i	$-0.713491\pi$
$277$	−164.568	+	59.8978i	−0.594108	+	0.216238i	0.0274272	+	0.999624i	$0.491269\pi$
$278$		0			0
$279$	61.2958	−	99.8788i	0.219698	−	0.357989i
$280$		0			0
$281$	241.214	−	287.468i	0.858414	−	1.02302i	−0.141041	−	0.990004i	$-0.545045\pi$
$281$	241.214	−	287.468i	0.858414	−	1.02302i	0.999455	−	0.0330139i	$-0.0105106\pi$
$282$		0			0
$283$	−2.56593	−	14.5521i	−0.00906688	−	0.0514208i	0.979939	−	0.199299i	$-0.0638666\pi$
$283$	−2.56593	−	14.5521i	−0.00906688	−	0.0514208i	−0.989006	+	0.147879i	$0.952756\pi$
$284$		0			0
$285$	148.641	−	172.392i	0.521547	−	0.604885i
$286$		0			0
$287$	212.237	−	122.535i	0.739501	−	0.426951i
$288$		0			0
$289$	141.513	−	245.108i	0.489665	−	0.848125i
$290$		0			0
$291$	−171.021	−	2.29477i	−0.587701	−	0.00788582i
$292$		0			0
$293$	−45.4702	+	124.928i	−0.155188	+	0.426376i	−0.992784	−	0.119914i	$-0.961738\pi$
$293$	−45.4702	+	124.928i	−0.155188	+	0.426376i	0.837596	+	0.546290i	$0.183960\pi$
$294$		0			0
$295$	−22.2379	+	126.117i	−0.0753826	+	0.427516i
$296$		0			0
$297$	301.874	+	65.8537i	1.01641	+	0.221730i
$298$		0			0
$299$	−119.942	−	21.1490i	−0.401143	−	0.0707323i
$300$		0			0
$301$	298.430	+	108.620i	0.991461	+	0.360862i
$302$		0			0
$303$	71.5924	+	42.6247i	0.236278	+	0.140676i
$304$		0			0
$305$	187.645	+	108.337i	0.615229	+	0.355203i
$306$		0			0
$307$	35.2589	+	61.0701i	0.114850	+	0.198926i	0.917720	−	0.397229i	$-0.130028\pi$
$307$	35.2589	+	61.0701i	0.114850	+	0.198926i	−0.802870	+	0.596154i	$0.796695\pi$
$308$		0			0
$309$	46.0189	−	241.956i	0.148928	−	0.783030i
$310$		0			0
$311$	−60.0519	+	10.5888i	−0.193093	+	0.0340475i	−0.269358	−	0.963040i	$-0.586812\pi$
$311$	−60.0519	+	10.5888i	−0.193093	+	0.0340475i	0.0762652	+	0.997088i	$0.475700\pi$
$312$		0			0
$313$	161.890	+	135.842i	0.517221	+	0.434000i	0.863662	−	0.504072i	$-0.168165\pi$
$313$	161.890	+	135.842i	0.517221	+	0.434000i	−0.346441	+	0.938072i	$0.612610\pi$
$314$		0			0
$315$	294.930	−	332.919i	0.936287	−	1.05688i
$316$		0			0
$317$	45.7588	+	125.721i	0.144349	+	0.396597i	0.990706	−	0.136020i	$-0.0434310\pi$
$317$	45.7588	+	125.721i	0.144349	+	0.396597i	−0.846357	+	0.532617i	$0.821209\pi$
$318$		0			0
$319$	−155.978	+	130.881i	−0.488960	+	0.410286i
$320$		0			0
$321$	−68.0466	−	83.3405i	−0.211983	−	0.259628i
$322$		0			0
$323$			292.794i			0.906482i
$324$		0			0
$325$	110.743			0.340746
$326$		0			0
$327$	−3.28925	+	2.68564i	−0.0100589	+	0.00821296i
$328$		0			0
$329$	−299.206	−	356.579i	−0.909439	−	1.08383i
$330$		0			0
$331$	−82.8821	+	30.1666i	−0.250399	+	0.0911378i	−0.464170	−	0.885746i	$-0.653647\pi$
$331$	−82.8821	+	30.1666i	−0.250399	+	0.0911378i	0.213771	+	0.976884i	$0.431425\pi$
$332$		0			0
$333$	145.723	−	48.6521i	0.437606	−	0.146103i
$334$		0			0
$335$	205.421	−	244.812i	0.613198	−	0.730781i
$336$		0			0
$337$	7.15157	+	40.5586i	0.0212213	+	0.120352i	0.993578	−	0.113148i	$-0.0360934\pi$
$337$	7.15157	+	40.5586i	0.0212213	+	0.120352i	−0.972357	+	0.233500i	$0.924982\pi$
$338$		0			0
$339$	439.223	+	83.5381i	1.29564	+	0.246425i
$340$		0			0
$341$	129.041	−	74.5018i	0.378419	−	0.218480i
$342$		0			0
$343$	−137.240	+	237.706i	−0.400116	+	0.693022i
$344$		0			0
$345$	−140.327	+	235.693i	−0.406746	+	0.683169i
$346$		0			0
$347$	−117.292	+	322.257i	−0.338017	+	0.928695i	0.647939	+	0.761692i	$0.275631\pi$
$347$	−117.292	+	322.257i	−0.338017	+	0.928695i	−0.985956	+	0.167003i	$0.946591\pi$
$348$		0			0
$349$	−102.322	+	580.297i	−0.293186	+	1.66274i	0.381298	+	0.924452i	$0.375477\pi$
$349$	−102.322	+	580.297i	−0.293186	+	1.66274i	−0.674484	+	0.738289i	$0.735634\pi$
$350$		0			0
$351$	176.381	−	136.292i	0.502510	−	0.388296i
$352$		0			0
$353$	124.087	+	21.8798i	0.351521	+	0.0619826i	0.346621	−	0.938005i	$-0.387329\pi$
$353$	124.087	+	21.8798i	0.351521	+	0.0619826i	0.00490000	+	0.999988i	$0.498440\pi$
$354$		0			0
$355$	−15.3454	−	5.58528i	−0.0432266	−	0.0157332i
$356$		0			0
$357$	−7.67585	+	572.053i	−0.0215010	+	1.60239i
$358$		0			0
$359$	298.332	+	172.242i	0.831007	+	0.479782i	0.854197	−	0.519949i	$-0.174049\pi$
$359$	298.332	+	172.242i	0.831007	+	0.479782i	−0.0231901	+	0.999731i	$0.507382\pi$
$360$		0			0
$361$	105.566	+	182.846i	0.292427	+	0.506499i
$362$		0			0
$363$	22.6129	+	19.4974i	0.0622945	+	0.0537119i
$364$		0			0
$365$	−421.247	+	74.2772i	−1.15410	+	0.203499i
$366$		0			0
$367$	−258.712	−	217.085i	−0.704937	−	0.591513i	0.218236	−	0.975896i	$-0.429970\pi$
$367$	−258.712	−	217.085i	−0.704937	−	0.591513i	−0.923174	+	0.384383i	$0.874414\pi$
$368$		0			0
$369$	7.42214	−	276.523i	0.0201142	−	0.749384i
$370$		0			0
$371$	248.876	+	683.782i	0.670826	+	1.84308i
$372$		0			0
$373$	75.9155	−	63.7007i	0.203527	−	0.170779i	−0.535327	−	0.844645i	$-0.679812\pi$
$373$	75.9155	−	63.7007i	0.203527	−	0.170779i	0.738854	+	0.673865i	$0.235367\pi$
$374$		0			0
$375$	−76.3890	+	201.426i	−0.203704	+	0.537137i
$376$		0			0
$377$			146.894i			0.389640i
$378$		0			0
$379$	−599.859			−1.58274			−0.791370	−	0.611337i	$-0.790632\pi$
$379$	−599.859			−1.58274			−0.791370	+	0.611337i	$0.790632\pi$
$380$		0			0
$381$	8.24920	+	50.7567i	0.0216514	+	0.133220i
$382$		0			0
$383$	−73.0625	−	87.0726i	−0.190764	−	0.227343i	0.662182	−	0.749343i	$-0.269631\pi$
$383$	−73.0625	−	87.0726i	−0.190764	−	0.227343i	−0.852946	+	0.522000i	$0.825186\pi$
$384$		0			0
$385$	531.415	−	193.419i	1.38030	−	0.502388i
$386$		0			0
$387$	280.688	−	222.969i	0.725291	−	0.576148i
$388$		0			0
$389$	233.254	−	277.981i	0.599624	−	0.714604i	−0.377801	−	0.925887i	$-0.623320\pi$
$389$	233.254	−	277.981i	0.599624	−	0.714604i	0.977425	+	0.211283i	$0.0677640\pi$
$390$		0			0
$391$	−61.2696	−	347.477i	−0.156700	−	0.888688i
$392$		0			0
$393$	144.198	+	413.355i	0.366917	+	1.05179i
$394$		0			0
$395$	−812.835	+	469.291i	−2.05781	+	1.18808i
$396$		0			0
$397$	239.208	−	414.320i	0.602539	−	1.04363i	−0.389896	−	0.920859i	$-0.627489\pi$
$397$	239.208	−	414.320i	0.602539	−	1.04363i	0.992435	−	0.122769i	$-0.0391775\pi$
$398$		0			0
$399$	−143.001	−	255.543i	−0.358398	−	0.640458i
$400$		0			0
$401$	−218.214	+	599.538i	−0.544174	+	1.49511i	0.297286	+	0.954788i	$0.403919\pi$
$401$	−218.214	+	599.538i	−0.544174	+	1.49511i	−0.841461	+	0.540319i	$0.818304\pi$
$402$		0			0
$403$	18.6665	−	105.863i	0.0463188	−	0.262687i
$404$		0			0
$405$	−146.151	−	480.286i	−0.360867	−	1.18589i
$406$		0			0
$407$	192.372	+	33.9204i	0.472659	+	0.0833425i
$408$		0			0
$409$	−575.541	−	209.480i	−1.40719	−	0.512175i	−0.476886	−	0.878965i	$-0.658235\pi$
$409$	−575.541	−	209.480i	−1.40719	−	0.512175i	−0.930304	+	0.366790i	$0.880457\pi$
$410$		0			0
$411$	−227.803	+	127.478i	−0.554266	+	0.310166i
$412$		0			0
$413$	142.677	+	82.3746i	0.345465	+	0.199454i
$414$		0			0
$415$	−167.555	−	290.214i	−0.403748	−	0.699311i
$416$		0			0
$417$	−104.412	+	36.4239i	−0.250388	+	0.0873476i
$418$		0			0
$419$	−516.661	+	91.1012i	−1.23308	+	0.217425i	−0.751948	−	0.659223i	$-0.770886\pi$
$419$	−516.661	+	91.1012i	−1.23308	+	0.217425i	−0.481132	+	0.876648i	$0.659774\pi$
$420$		0			0
$421$	−282.105	−	236.715i	−0.670084	−	0.562267i	0.243006	−	0.970025i	$-0.421866\pi$
$421$	−282.105	−	236.715i	−0.670084	−	0.562267i	−0.913090	+	0.407757i	$0.866311\pi$
$422$		0			0
$423$	−519.690	+	77.3205i	−1.22858	+	0.182791i
$424$		0			0
$425$	109.729	+	301.478i	0.258186	+	0.709361i
$426$		0			0
$427$	213.531	−	179.174i	0.500072	−	0.419610i
$428$		0			0
$429$	279.749	−	45.4661i	0.652097	−	0.105982i
$430$		0			0
$431$		−	178.021i		−	0.413043i	−0.978442	−	0.206521i	$-0.933786\pi$
$431$		−	178.021i		−	0.413043i	0.978442	−	0.206521i	$-0.0662143\pi$
$432$		0			0
$433$	−710.746			−1.64144			−0.820722	−	0.571327i	$-0.806429\pi$
$433$	−710.746			−1.64144			−0.820722	+	0.571327i	$0.806429\pi$
$434$		0			0
$435$	309.343	+	117.315i	0.711133	+	0.269690i
$436$		0			0
$437$	116.088	+	138.348i	0.265648	+	0.316587i
$438$		0			0
$439$	598.391	−	217.797i	1.36308	−	0.496120i	0.446073	−	0.894996i	$-0.352822\pi$
$439$	598.391	−	217.797i	1.36308	−	0.496120i	0.917005	+	0.398877i	$0.130600\pi$
$440$		0			0
$441$	−62.5190	−	115.326i	−0.141766	−	0.261509i
$442$		0			0
$443$	207.534	−	247.329i	0.468473	−	0.558305i	−0.479134	−	0.877742i	$-0.659049\pi$
$443$	207.534	−	247.329i	0.468473	−	0.558305i	0.947608	+	0.319437i	$0.103494\pi$
$444$		0			0
$445$	−175.507	−	995.352i	−0.394399	−	2.23675i
$446$		0			0
$447$	−126.547	+	146.768i	−0.283104	+	0.328341i
$448$		0			0
$449$	22.4287	−	12.9492i	0.0499526	−	0.0288401i	−0.474816	−	0.880085i	$-0.657485\pi$
$449$	22.4287	−	12.9492i	0.0499526	−	0.0288401i	0.524768	+	0.851245i	$0.324152\pi$
$450$		0			0
$451$	175.862	−	304.602i	0.389938	−	0.675392i
$452$		0			0
$453$	−463.327	−	6.21696i	−1.02280	−	0.0137240i
$454$		0			0
$455$	139.539	−	383.380i	0.306679	−	0.842593i
$456$		0			0
$457$	−68.6711	+	389.453i	−0.150265	+	0.852195i	0.812723	+	0.582650i	$0.197984\pi$
$457$	−68.6711	+	389.453i	−0.150265	+	0.852195i	−0.962988	+	0.269544i	$0.913127\pi$
$458$		0			0
$459$	545.800	+	345.124i	1.18911	+	0.751903i
$460$		0			0
$461$	−883.267	−	155.744i	−1.91598	−	0.337839i	−0.917743	−	0.397175i	$-0.869991\pi$
$461$	−883.267	−	155.744i	−1.91598	−	0.337839i	−0.998238	+	0.0593356i	$0.981102\pi$
$462$		0			0
$463$	−279.650	−	101.784i	−0.603997	−	0.219837i	0.0218778	−	0.999761i	$-0.493036\pi$
$463$	−279.650	−	101.784i	−0.603997	−	0.219837i	−0.625874	+	0.779924i	$0.715258\pi$
$464$		0			0
$465$	−208.027	−	123.855i	−0.447370	−	0.266356i
$466$		0			0
$467$	684.460	+	395.173i	1.46565	+	0.846196i	0.999263	−	0.0383833i	$-0.0122208\pi$
$467$	684.460	+	395.173i	1.46565	+	0.846196i	0.466391	+	0.884579i	$0.345554\pi$
$468$		0			0
$469$	−205.565	−	356.048i	−0.438304	−	0.759165i
$470$		0			0
$471$	107.934	−	567.489i	0.229158	−	1.20486i
$472$		0			0
$473$	448.868	−	79.1476i	0.948982	−	0.167331i
$474$		0			0
$475$	−125.797	−	105.556i	−0.264836	−	0.222223i
$476$		0			0
$477$	804.755	+	164.278i	1.68712	+	0.344398i
$478$		0			0
$479$	0.369996	+	1.01656i	0.000772435	+	0.00212225i	0.940078	−	0.340959i	$-0.110752\pi$
$479$	0.369996	+	1.01656i	0.000772435	+	0.00212225i	−0.939306	+	0.343081i	$0.888529\pi$
$480$		0			0
$481$	107.954	−	90.5844i	0.224437	−	0.188325i
$482$		0			0
$483$	223.183	+	273.345i	0.462076	+	0.565931i
$484$		0			0
$485$			353.356i			0.728569i
$486$		0			0
$487$	−647.606			−1.32979			−0.664893	−	0.746939i	$-0.731523\pi$
$487$	−647.606			−1.32979			−0.664893	+	0.746939i	$0.731523\pi$
$488$		0			0
$489$	398.088	−	325.034i	0.814086	−	0.664692i
$490$		0			0
$491$	−200.752	−	239.247i	−0.408863	−	0.487264i	0.521838	−	0.853045i	$-0.325247\pi$
$491$	−200.752	−	239.247i	−0.408863	−	0.487264i	−0.930701	+	0.365781i	$0.880802\pi$
$492$		0			0
$493$	−399.896	+	145.550i	−0.811147	+	0.295233i
$494$		0			0
$495$	127.672	−	625.432i	0.257923	−	1.26350i
$496$		0			0
$497$	−13.5040	+	16.0934i	−0.0271709	+	0.0323811i
$498$		0			0
$499$	−7.96919	−	45.1955i	−0.0159703	−	0.0905722i	0.975781	−	0.218751i	$-0.0701981\pi$
$499$	−7.96919	−	45.1955i	−0.0159703	−	0.0905722i	−0.991751	+	0.128178i	$0.959087\pi$
$500$		0			0
$501$	463.835	+	88.2192i	0.925819	+	0.176086i
$502$		0			0
$503$	−493.829	+	285.113i	−0.981768	+	0.566824i	−0.902803	−	0.430053i	$-0.858495\pi$
$503$	−493.829	+	285.113i	−0.981768	+	0.566824i	−0.0789646	+	0.996877i	$0.525161\pi$
$504$		0			0
$505$	86.0690	−	149.076i	0.170434	−	0.295200i
$506$		0			0
$507$	−154.768	+	259.947i	−0.305261	+	0.512716i
$508$		0			0
$509$	177.877	−	488.713i	0.349464	−	0.960144i	−0.633076	−	0.774090i	$-0.718208\pi$
$509$	177.877	−	488.713i	0.349464	−	0.960144i	0.982540	−	0.186054i	$-0.0595700\pi$
$510$		0			0
$511$	−95.5556	+	541.923i	−0.186997	+	1.06051i
$512$		0			0
$513$	−330.267	−	13.3010i	−0.643796	−	0.0259280i
$514$		0			0
$515$	−501.105	−	88.3583i	−0.973020	−	0.171570i
$516$		0			0
$517$	−627.768	−	228.489i	−1.21425	−	0.441952i
$518$		0			0
$519$	−2.11336	+	157.501i	−0.00407199	+	0.303470i
$520$		0			0
$521$	−365.719	−	211.148i	−0.701956	−	0.405275i	0.106119	−	0.994353i	$-0.466157\pi$
$521$	−365.719	−	211.148i	−0.701956	−	0.405275i	−0.808076	+	0.589079i	$0.799491\pi$
$522$		0			0
$523$	−500.529	−	866.942i	−0.957035	−	1.65763i	−0.729641	−	0.683831i	$-0.760313\pi$
$523$	−500.529	−	866.942i	−0.957035	−	1.65763i	−0.227394	−	0.973803i	$-0.573021\pi$
$524$		0			0
$525$	−243.011	−	209.531i	−0.462879	−	0.399106i
$526$		0			0
$527$	306.690	−	54.0777i	0.581954	−	0.102614i
$528$		0			0
$529$	238.518	+	200.140i	0.450884	+	0.378337i
$530$		0			0
$531$	163.483	−	88.6255i	0.307878	−	0.166903i
$532$		0			0
$533$	−86.7857	−	238.442i	−0.162825	−	0.447358i
$534$		0			0
$535$	−170.277	+	142.880i	−0.318276	+	0.267065i
$536$		0			0
$537$	−71.2094	+	187.769i	−0.132606	+	0.349662i
$538$		0			0
$539$		−	166.797i		−	0.309456i
$540$		0			0
$541$	−192.818			−0.356410			−0.178205	−	0.983993i	$-0.557029\pi$
$541$	−192.818			−0.356410			−0.178205	+	0.983993i	$0.557029\pi$
$542$		0			0
$543$	62.3031	+	383.346i	0.114739	+	0.705979i
$544$		0			0
$545$	5.63912	+	6.72044i	0.0103470	+	0.0123311i
$546$		0			0
$547$	−710.023	+	258.427i	−1.29803	+	0.472444i	−0.896355	−	0.443338i	$-0.853794\pi$
$547$	−710.023	+	258.427i	−1.29803	+	0.472444i	−0.401676	+	0.915782i	$0.631572\pi$
$548$		0			0
$549$	−46.3019	−	311.207i	−0.0843386	−	0.566861i
$550$		0			0
$551$	140.015	−	166.863i	0.254110	−	0.302837i
$552$		0			0
$553$	209.673	+	1189.11i	0.379155	+	2.15030i
$554$		0			0
$555$	−104.544	−	299.684i	−0.188368	−	0.539970i
$556$		0			0
$557$	−741.183	+	427.922i	−1.33067	+	0.768262i	−0.985402	−	0.170242i	$-0.945545\pi$
$557$	−741.183	+	427.922i	−1.33067	+	0.768262i	−0.345267	+	0.938505i	$0.612212\pi$
$558$		0			0
$559$	164.412	−	284.769i	0.294118	−	0.509427i
$560$		0			0
$561$	400.964	+	716.522i	0.714730	+	1.27722i
$562$		0			0
$563$	−53.2716	+	146.362i	−0.0946209	+	0.259969i	−0.977970	−	0.208748i	$-0.933061\pi$
$563$	−53.2716	+	146.362i	−0.0946209	+	0.259969i	0.883349	+	0.468717i	$0.155283\pi$
$564$		0			0
$565$	160.397	−	909.656i	0.283888	−	1.61001i
$566$		0			0
$567$	−644.919	−	34.6455i	−1.13742	−	0.0611031i
$568$		0			0
$569$	626.354	+	110.443i	1.10080	+	0.194100i	0.694395	−	0.719594i	$-0.255672\pi$
$569$	626.354	+	110.443i	1.10080	+	0.194100i	0.406402	+	0.913694i	$0.366783\pi$
$570$		0			0
$571$	−943.621	−	343.450i	−1.65258	−	0.601488i	−0.663406	−	0.748260i	$-0.730890\pi$
$571$	−943.621	−	343.450i	−1.65258	−	0.601488i	−0.989170	+	0.146772i	$0.953112\pi$
$572$		0			0
$573$	−710.377	+	397.525i	−1.23975	+	0.693761i
$574$		0			0
$575$	171.380	+	98.9461i	0.298052	+	0.172080i
$576$		0			0
$577$	−414.908	−	718.642i	−0.719079	−	1.24548i	−0.961365	−	0.275276i	$-0.911231\pi$
$577$	−414.908	−	718.642i	−0.719079	−	1.24548i	0.242287	−	0.970205i	$-0.422103\pi$
$578$		0			0
$579$	587.718	−	205.024i	1.01506	−	0.354101i
$580$		0			0
$581$	−424.561	+	74.8615i	−0.730741	+	0.128849i
$582$		0			0
$583$	800.013	+	671.291i	1.37224	+	1.15144i
$584$		0			0
$585$	−286.439	−	360.587i	−0.489639	−	0.616389i
$586$		0			0
$587$	−100.401	−	275.849i	−0.171040	−	0.469930i	0.824323	−	0.566120i	$-0.191556\pi$
$587$	−100.401	−	275.849i	−0.171040	−	0.469930i	−0.995363	+	0.0961909i	$0.969334\pi$
$588$		0			0
$589$	−122.109	+	102.461i	−0.207316	+	0.173958i
$590$		0			0
$591$	−529.540	+	86.0631i	−0.896006	+	0.145623i
$592$		0			0
$593$			720.027i			1.21421i	0.794621	+	0.607106i	$0.207670\pi$
$593$			720.027i			1.21421i	−0.794621	+	0.607106i	$0.792330\pi$
$594$		0			0
$595$	1181.95			1.98647
$596$		0			0
$597$	71.8320	+	27.2416i	0.120322	+	0.0456308i
$598$		0			0
$599$	297.913	+	355.039i	0.497351	+	0.592719i	0.955071	−	0.296377i	$-0.0957784\pi$
$599$	297.913	+	355.039i	0.497351	+	0.592719i	−0.457721	+	0.889096i	$0.651334\pi$
$600$		0			0
$601$	512.198	−	186.425i	0.852244	−	0.310191i	0.121289	−	0.992617i	$-0.461297\pi$
$601$	512.198	−	186.425i	0.852244	−	0.310191i	0.730955	+	0.682426i	$0.239075\pi$
$602$		0			0
$603$	−463.894	−	12.4514i	−0.769310	−	0.0206490i
$604$		0			0
$605$	39.6507	−	47.2538i	0.0655383	−	0.0781055i
$606$		0			0
$607$	176.997	+	1003.80i	0.291593	+	1.65371i	0.680735	+	0.732529i	$0.261660\pi$
$607$	176.997	+	1003.80i	0.291593	+	1.65371i	−0.389142	+	0.921178i	$0.627229\pi$
$608$		0			0
$609$	277.932	−	322.342i	0.456374	−	0.529297i
$610$		0			0
$611$	−417.387	+	240.979i	−0.683122	+	0.394400i
$612$		0			0
$613$	−496.963	+	860.765i	−0.810706	+	1.40418i	0.101664	+	0.994819i	$0.467583\pi$
$613$	−496.963	+	860.765i	−0.810706	+	1.40418i	−0.912370	+	0.409366i	$0.865750\pi$
$614$		0			0
$615$	−571.442	−	7.66765i	−0.929174	−	0.0124677i
$616$		0			0
$617$	323.050	−	887.573i	0.523582	−	1.43853i	−0.342924	−	0.939363i	$-0.611417\pi$
$617$	323.050	−	887.573i	0.523582	−	1.43853i	0.866506	−	0.499166i	$-0.166360\pi$
$618$		0			0
$619$	81.4780	−	462.084i	0.131628	−	0.746502i	−0.845520	−	0.533944i	$-0.820709\pi$
$619$	81.4780	−	462.084i	0.131628	−	0.746502i	0.977148	−	0.212558i	$-0.0681794\pi$
$620$		0			0
$621$	394.733	−	53.3260i	0.635640	−	0.0858712i
$622$		0			0
$623$	−1280.49	−	225.785i	−2.05536	−	0.362416i
$624$		0			0
$625$	733.350	+	266.917i	1.17336	+	0.427068i
$626$		0			0
$627$	−361.115	−	215.001i	−0.575942	−	0.342905i
$628$		0			0
$629$	353.568	+	204.132i	0.562111	+	0.324535i
$630$		0			0
$631$	510.282	+	883.835i	0.808689	+	1.40069i	0.913773	+	0.406226i	$0.133156\pi$
$631$	510.282	+	883.835i	0.808689	+	1.40069i	−0.105084	+	0.994463i	$0.533511\pi$
$632$		0			0
$633$	201.953	−	1061.82i	0.319042	−	1.67744i
$634$		0			0
$635$	104.624	−	18.4480i	0.164762	−	0.0290520i
$636$		0			0
$637$	−92.1800	−	77.3482i	−0.144710	−	0.121426i
$638$		0			0
$639$	7.50959	+	22.4927i	0.0117521	+	0.0351999i
$640$		0			0
$641$	384.982	+	1057.73i	0.600596	+	1.65012i	0.750069	+	0.661359i	$0.230020\pi$
$641$	384.982	+	1057.73i	0.600596	+	1.65012i	−0.149473	+	0.988766i	$0.547758\pi$
$642$		0			0
$643$	163.564	−	137.247i	0.254377	−	0.213448i	−0.506677	−	0.862136i	$-0.669126\pi$
$643$	163.564	−	137.247i	0.254377	−	0.213448i	0.761054	+	0.648688i	$0.224682\pi$
$644$		0			0
$645$	−468.387	−	573.660i	−0.726181	−	0.889395i
$646$		0			0
$647$		−	267.943i		−	0.414132i	−0.978327	−	0.207066i	$-0.933609\pi$
$647$		−	267.943i		−	0.414132i	0.978327	−	0.207066i	$-0.0663914\pi$
$648$		0			0
$649$	236.447			0.364326
$650$		0			0
$651$	−241.259	+	196.985i	−0.370598	+	0.302589i
$652$		0			0
$653$	34.1737	+	40.7266i	0.0523333	+	0.0623684i	0.791576	−	0.611071i	$-0.209261\pi$
$653$	34.1737	+	40.7266i	0.0523333	+	0.0623684i	−0.739243	+	0.673439i	$0.764816\pi$
$654$		0			0
$655$	849.906	−	309.340i	1.29757	−	0.472275i
$656$		0			0
$657$	464.929	+	411.878i	0.707655	+	0.626907i
$658$		0			0
$659$	322.292	−	384.092i	0.489062	−	0.582841i	−0.463917	−	0.885879i	$-0.653556\pi$
$659$	322.292	−	384.092i	0.489062	−	0.582841i	0.952979	+	0.303038i	$0.0980008\pi$
$660$		0			0
$661$	100.807	+	571.703i	0.152506	+	0.864906i	0.961030	+	0.276443i	$0.0891557\pi$
$661$	100.807	+	571.703i	0.152506	+	0.864906i	−0.808524	+	0.588463i	$0.799733\pi$
$662$		0			0
$663$	581.923	+	110.679i	0.877711	+	0.166936i
$664$		0			0
$665$	−523.933	+	302.493i	−0.787869	+	0.454876i
$666$		0			0
$667$	−131.247	+	227.326i	−0.196772	+	0.340819i
$668$		0			0
$669$	−13.7916	+	23.1644i	−0.0206153	+	0.0346254i
$670$		0			0
$671$	136.826	−	375.927i	0.203914	−	0.560249i
$672$		0			0
$673$	−20.6831	+	117.300i	−0.0307327	+	0.174294i	−0.996311	−	0.0858201i	$-0.972649\pi$
$673$	−20.6831	+	117.300i	−0.0307327	+	0.174294i	0.965578	+	0.260114i	$0.0837601\pi$
$674$		0			0
$675$	−345.048	+	110.077i	−0.511183	+	0.163078i
$676$		0			0
$677$	−460.585	−	81.2136i	−0.680333	−	0.119961i	−0.177206	−	0.984174i	$-0.556706\pi$
$677$	−460.585	−	81.2136i	−0.680333	−	0.119961i	−0.503127	+	0.864213i	$0.667817\pi$
$678$		0			0
$679$	427.168	+	155.476i	0.629113	+	0.228979i
$680$		0			0
$681$	2.88919	−	215.321i	0.00424257	−	0.316183i
$682$		0			0
$683$	271.489	+	156.744i	0.397495	+	0.229494i	0.685402	−	0.728164i	$-0.259626\pi$
$683$	271.489	+	156.744i	0.397495	+	0.229494i	−0.287908	+	0.957658i	$0.592960\pi$
$684$		0			0
$685$	269.657	+	467.059i	0.393660	+	0.681839i
$686$		0			0
$687$	−122.547	−	105.663i	−0.178380	−	0.153803i
$688$		0			0
$689$	741.976	−	130.830i	1.07689	−	0.189884i
$690$		0			0
$691$	515.245	+	432.342i	0.745651	+	0.625675i	0.934349	−	0.356360i	$-0.115982\pi$
$691$	515.245	+	432.342i	0.745651	+	0.625675i	−0.188698	+	0.982035i	$0.560427\pi$
$692$		0			0
$693$	−699.901	−	429.530i	−1.00996	−	0.619813i
$694$		0			0
$695$	78.1382	+	214.683i	0.112429	+	0.308896i
$696$		0			0
$697$	563.127	−	472.520i	0.807930	−	0.677934i
$698$		0			0
$699$	385.801	−	1017.30i	0.551933	−	1.45536i
$700$		0			0
$701$		−	906.580i		−	1.29327i	−0.762801	−	0.646633i	$-0.776176\pi$
$701$		−	906.580i		−	1.29327i	0.762801	−	0.646633i	$-0.223824\pi$
$702$		0			0
$703$	−208.972			−0.297257
$704$		0			0
$705$	174.133	+	1071.43i	0.246997	+	1.51975i
$706$		0			0
$707$	−142.346	−	169.641i	−0.201338	−	0.239945i
$708$		0			0
$709$	27.2901	−	9.93278i	0.0384910	−	0.0140096i	−0.322703	−	0.946500i	$-0.604591\pi$
$709$	27.2901	−	9.93278i	0.0384910	−	0.0140096i	0.361194	+	0.932491i	$0.382369\pi$
$710$		0			0
$711$	1267.75	+	500.340i	1.78306	+	0.703714i
$712$		0			0
$713$	123.473	−	147.150i	0.173175	−	0.206381i
$714$		0			0
$715$	−101.678	−	576.642i	−0.142206	−	0.806492i
$716$		0			0
$717$	248.589	+	712.598i	0.346707	+	0.993860i
$718$		0			0
$719$	837.314	−	483.423i	1.16455	−	0.672355i	0.212162	−	0.977234i	$-0.431949\pi$
$719$	837.314	−	483.423i	1.16455	−	0.672355i	0.952391	+	0.304879i	$0.0986161\pi$
$720$		0			0
$721$	−327.301	+	566.902i	−0.453955	+	0.786272i
$722$		0			0
$723$	590.255	+	1054.79i	0.816397	+	1.45890i
$724$		0			0
$725$	81.6331	−	224.285i	0.112597	−	0.309359i
$726$		0			0
$727$	−152.352	+	864.032i	−0.209563	+	1.18849i	0.680533	+	0.732717i	$0.261748\pi$
$727$	−152.352	+	864.032i	−0.209563	+	1.18849i	−0.890096	+	0.455773i	$0.849363\pi$
$728$		0			0
$729$	−414.089	+	599.976i	−0.568024	+	0.823012i
$730$		0			0
$731$	938.145	+	165.420i	1.28337	+	0.226293i
$732$		0			0
$733$	−34.0124	−	12.3795i	−0.0464017	−	0.0168888i	0.318715	−	0.947851i	$-0.396749\pi$
$733$	−34.0124	−	12.3795i	−0.0464017	−	0.0168888i	−0.365117	+	0.930962i	$0.618971\pi$
$734$		0			0
$735$	−236.505	+	132.347i	−0.321775	+	0.180065i
$736$		0			0
$737$	−510.999	−	295.026i	−0.693350	−	0.400306i
$738$		0			0
$739$	−237.815	−	411.907i	−0.321806	−	0.557384i	0.659055	−	0.752095i	$-0.270957\pi$
$739$	−237.815	−	411.907i	−0.321806	−	0.557384i	−0.980861	+	0.194711i	$0.937623\pi$
$740$		0			0
$741$	−286.279	+	99.8680i	−0.386342	+	0.134775i
$742$		0			0
$743$	−50.1096	+	8.83567i	−0.0674422	+	0.0118919i	−0.207267	−	0.978284i	$-0.566457\pi$
$743$	−50.1096	+	8.83567i	−0.0674422	+	0.0118919i	0.139825	+	0.990176i	$0.455346\pi$
$744$		0			0
$745$	306.700	+	257.352i	0.411677	+	0.345438i
$746$		0			0
$747$	−178.641	+	452.638i	−0.239145	+	0.605941i
$748$		0			0
$749$	97.8037	+	268.713i	0.130579	+	0.358763i
$750$		0			0
$751$	−36.1543	+	30.3371i	−0.0481416	+	0.0403956i	−0.666541	−	0.745468i	$-0.732226\pi$
$751$	−36.1543	+	30.3371i	−0.0481416	+	0.0403956i	0.618399	+	0.785864i	$0.287781\pi$
$752$		0			0
$753$	1125.89	−	182.984i	1.49520	−	0.243006i
$754$		0			0
$755$			957.307i			1.26796i
$756$		0			0
$757$	973.584			1.28611			0.643054	−	0.765821i	$-0.277667\pi$
$757$	973.584			1.28611			0.643054	+	0.765821i	$0.277667\pi$
$758$		0			0
$759$	473.549	+	179.589i	0.623912	+	0.236613i
$760$		0			0
$761$	−10.4814	−	12.4913i	−0.0137733	−	0.0164143i	0.759114	−	0.650958i	$-0.225633\pi$
$761$	−10.4814	−	12.4913i	−0.0137733	−	0.0164143i	−0.772887	+	0.634544i	$0.781188\pi$
$762$		0			0
$763$	10.6055	−	3.86008i	0.0138997	−	0.00505908i
$764$		0			0
$765$	697.822	−	1137.07i	0.912186	−	1.48637i
$766$		0			0
$767$	109.647	−	130.672i	0.142956	−	0.170368i
$768$		0			0
$769$	24.6634	+	139.873i	0.0320720	+	0.181890i	0.996636	−	0.0819614i	$-0.0261184\pi$
$769$	24.6634	+	139.873i	0.0320720	+	0.181890i	−0.964563	+	0.263851i	$0.915007\pi$
$770$		0			0
$771$	42.4884	−	49.2775i	0.0551081	−	0.0639138i
$772$		0			0
$773$	991.099	−	572.211i	1.28215	−	0.740248i	0.304906	−	0.952382i	$-0.401375\pi$
$773$	991.099	−	572.211i	1.28215	−	0.740248i	0.977240	+	0.212135i	$0.0680416\pi$
$774$		0			0
$775$	−87.3317	+	151.263i	−0.112686	+	0.195178i
$776$		0			0
$777$	−408.283	−	5.47838i	−0.525461	−	0.00705068i
$778$		0			0
$779$	−128.691	+	353.577i	−0.165201	+	0.453886i
$780$		0			0
$781$	−5.23571	+	29.6932i	−0.00670385	+	0.0380194i
$782$		0			0
$783$	−146.012	−	457.689i	−0.186478	−	0.584532i
$784$		0			0
$785$	−1175.30	−	207.237i	−1.49720	−	0.263997i
$786$		0			0
$787$	−243.549	−	88.6445i	−0.309465	−	0.112636i	0.182619	−	0.983184i	$-0.441542\pi$
$787$	−243.549	−	88.6445i	−0.309465	−	0.112636i	−0.492084	+	0.870548i	$0.663765\pi$
$788$		0			0
$789$	−174.969	−	104.173i	−0.221761	−	0.132032i
$790$		0			0
$791$	−1029.10	−	594.150i	−1.30101	−	0.751138i
$792$		0			0
$793$	−144.305	−	249.944i	−0.181974	−	0.315188i
$794$		0			0
$795$	317.056	−	1667.00i	0.398812	−	2.09686i
$796$		0			0
$797$	−1045.29	+	184.314i	−1.31154	+	0.231259i	−0.785319	−	0.619091i	$-0.787501\pi$
$797$	−1045.29	+	184.314i	−1.31154	+	0.231259i	−0.526217	+	0.850350i	$0.676390\pi$
$798$		0			0
$799$	−1069.59	−	897.495i	−1.33866	−	1.12327i
$800$		0			0
$801$	−973.213	+	1098.57i	−1.21500	+	1.37149i
$802$		0			0
$803$	270.115	+	742.135i	0.336382	+	0.924203i
$804$		0			0
$805$	558.485	−	468.625i	0.693770	−	0.582142i
$806$		0			0
$807$	−551.335	−	675.252i	−0.683191	−	0.836743i
$808$		0			0
$809$		−	1471.80i		−	1.81928i	−0.415398	−	0.909640i	$-0.636358\pi$
$809$		−	1471.80i		−	1.81928i	0.415398	−	0.909640i	$-0.363642\pi$
$810$		0			0
$811$	−128.574			−0.158537			−0.0792685	−	0.996853i	$-0.525258\pi$
$811$	−128.574			−0.158537			−0.0792685	+	0.996853i	$0.525258\pi$
$812$		0			0
$813$	−963.549	+	786.727i	−1.18518	+	0.967684i
$814$		0			0
$815$	−682.486	−	813.355i	−0.837406	−	0.997981i
$816$		0			0
$817$	−458.195	+	166.769i	−0.560826	+	0.204124i
$818$		0			0
$819$	−561.943	+	187.614i	−0.686133	+	0.229077i
$820$		0			0
$821$	956.042	−	1139.37i	1.16448	−	1.38778i	0.257678	−	0.966231i	$-0.417043\pi$
$821$	956.042	−	1139.37i	1.16448	−	1.38778i	0.906806	−	0.421547i	$-0.138513\pi$
$822$		0			0
$823$	208.329	+	1181.49i	0.253134	+	1.43559i	0.800818	+	0.598907i	$0.204398\pi$
$823$	208.329	+	1181.49i	0.253134	+	1.43559i	−0.547685	+	0.836685i	$0.684491\pi$
$824$		0			0
$825$	−452.402	−	86.0446i	−0.548366	−	0.104296i
$826$		0			0
$827$	609.332	−	351.798i	0.736798	−	0.425391i	−0.0841057	−	0.996457i	$-0.526803\pi$
$827$	609.332	−	351.798i	0.736798	−	0.425391i	0.820904	+	0.571066i	$0.193470\pi$
$828$		0			0
$829$	112.799	−	195.374i	0.136066	−	0.235674i	−0.789938	−	0.613187i	$-0.789887\pi$
$829$	112.799	−	195.374i	0.136066	−	0.235674i	0.926004	+	0.377513i	$0.123221\pi$
$830$		0			0
$831$	268.775	−	451.434i	0.323436	−	0.543242i
$832$		0			0
$833$	119.231	−	327.585i	0.143135	−	0.393260i
$834$		0			0
$835$	169.385	−	960.629i	0.202856	−	1.15045i
$836$		0			0
$837$	47.0665	+	348.398i	0.0562324	+	0.416246i
$838$		0			0
$839$	703.465	+	124.040i	0.838456	+	0.147842i	0.576356	−	0.817198i	$-0.304474\pi$
$839$	703.465	+	124.040i	0.838456	+	0.147842i	0.262100	+	0.965041i	$0.415585\pi$
$840$		0			0
$841$	−492.779	−	179.357i	−0.585944	−	0.213266i
$842$		0			0
$843$	−15.1046	+	1125.69i	−0.0179176	+	1.33533i
$844$		0			0
$845$	541.285	+	312.511i	0.640574	+	0.369836i
$846$		0			0
$847$	−39.6783	−	68.7249i	−0.0468457	−	0.0811392i
$848$		0			0
$849$	33.5732	+	28.9477i	0.0395444	+	0.0340962i
$850$		0			0
$851$	248.000	−	43.7291i	0.291422	−	0.0513855i
$852$		0			0
$853$	199.629	+	167.509i	0.234032	+	0.196376i	0.752260	−	0.658866i	$-0.228964\pi$
$853$	199.629	+	167.509i	0.234032	+	0.196376i	−0.518228	+	0.855242i	$0.673408\pi$
$854$		0			0
$855$	−18.3225	+	682.630i	−0.0214298	+	0.798397i
$856$		0			0
$857$	354.046	+	972.733i	0.413122	+	1.13504i	0.955521	+	0.294923i	$0.0952940\pi$
$857$	354.046	+	972.733i	0.413122	+	1.13504i	−0.542399	+	0.840121i	$0.682484\pi$
$858$		0			0
$859$	427.947	−	359.090i	0.498192	−	0.418033i	−0.358759	−	0.933430i	$-0.616800\pi$
$859$	427.947	−	359.090i	0.498192	−	0.418033i	0.856951	+	0.515397i	$0.172356\pi$
$860$		0			0
$861$	−260.703	+	687.435i	−0.302791	+	0.798415i
$862$		0			0
$863$		−	251.585i		−	0.291523i	−0.989320	−	0.145762i	$-0.953437\pi$
$863$		−	251.585i		−	0.291523i	0.989320	−	0.145762i	$-0.0465633\pi$
$864$		0			0
$865$	325.422			0.376210
$866$		0			0
$867$	136.209	+	838.083i	0.157104	+	0.966647i
$868$		0			0
$869$	1113.91	+	1327.51i	1.28183	+	1.52763i
$870$		0			0
$871$	−400.010	+	145.592i	−0.459253	+	0.167155i
$872$		0			0
$873$	401.772	−	319.155i	0.460220	−	0.365584i
$874$		0			0
$875$	368.034	−	438.605i	0.420610	−	0.501263i
$876$		0			0
$877$	−84.6067	−	479.828i	−0.0964729	−	0.547125i	−0.994286	−	0.106748i	$-0.965956\pi$
$877$	−84.6067	−	479.828i	−0.0964729	−	0.547125i	0.897813	−	0.440376i	$-0.145155\pi$
$878$		0			0
$879$	−131.370	−	376.581i	−0.149454	−	0.428420i
$880$		0			0
$881$	−53.6224	+	30.9589i	−0.0608654	+	0.0351407i	−0.530124	−	0.847920i	$-0.677855\pi$
$881$	−53.6224	+	30.9589i	−0.0608654	+	0.0351407i	0.469258	+	0.883061i	$0.344521\pi$
$882$		0			0
$883$	−50.9265	+	88.2073i	−0.0576744	+	0.0998950i	−0.893421	−	0.449220i	$-0.851702\pi$
$883$	−50.9265	+	88.2073i	−0.0576744	+	0.0998950i	0.835747	+	0.549115i	$0.185035\pi$
$884$		0			0
$885$	−187.613	−	335.264i	−0.211992	−	0.378830i
$886$		0			0
$887$	−430.135	+	1181.79i	−0.484933	+	1.33234i	0.420284	+	0.907393i	$0.361930\pi$
$887$	−430.135	+	1181.79i	−0.484933	+	1.33234i	−0.905217	+	0.424950i	$0.860292\pi$
$888$		0			0
$889$	23.7328	−	134.595i	0.0266961	−	0.151401i
$890$		0			0
$891$	−826.442	+	419.731i	−0.927544	+	0.471079i
$892$		0			0
$893$	703.820	+	124.102i	0.788152	+	0.138972i
$894$		0			0
$895$	389.863	+	141.899i	0.435602	+	0.158546i
$896$		0			0
$897$	318.847	−	178.426i	0.355460	−	0.198914i
$898$		0			0
$899$	−200.642	−	115.841i	−0.223184	−	0.128855i
$900$		0			0
$901$	1091.35	+	1890.27i	1.21127	+	2.09797i
$902$		0			0
$903$	−899.581	+	313.817i	−0.996213	+	0.347527i
$904$		0			0
$905$	790.184	−	139.331i	0.873132	−	0.153957i
$906$		0			0
$907$	639.102	+	536.271i	0.704633	+	0.591258i	0.923088	−	0.384590i	$-0.125657\pi$
$907$	639.102	+	536.271i	0.704633	+	0.591258i	−0.218454	+	0.975847i	$0.570101\pi$
$908$		0			0
$909$	−247.240	+	36.7849i	−0.271992	+	0.0404674i
$910$		0			0
$911$	244.801	+	672.586i	0.268717	+	0.738294i	0.998507	+	0.0546228i	$0.0173956\pi$
$911$	244.801	+	672.586i	0.268717	+	0.738294i	−0.729790	+	0.683671i	$0.760382\pi$
$912$		0			0
$913$	−473.973	+	397.711i	−0.519138	+	0.435609i
$914$		0			0
$915$	−641.602	+	104.276i	−0.701205	+	0.113963i
$916$		0			0
$917$		−	1163.55i		−	1.26887i
$918$		0			0
$919$	714.401			0.777367			0.388684	−	0.921371i	$-0.372930\pi$
$919$	714.401			0.777367			0.388684	+	0.921371i	$0.372930\pi$
$920$		0			0
$921$	−197.806	−	75.0162i	−0.214773	−	0.0814508i
$922$		0			0
$923$	13.9819	+	16.6630i	0.0151484	+	0.0180531i
$924$		0			0
$925$	−215.170	+	78.3155i	−0.232616	+	0.0846654i
$926$		0			0
$927$	352.138	+	649.572i	0.379869	+	0.700725i
$928$		0			0
$929$	−207.867	+	247.726i	−0.223753	+	0.266659i	−0.866229	−	0.499647i	$-0.833463\pi$
$929$	−207.867	+	247.726i	−0.223753	+	0.266659i	0.642476	+	0.766306i	$0.277907\pi$
$930$		0			0
$931$	30.9852	+	175.726i	0.0332816	+	0.188750i
$932$		0			0
$933$	119.458	−	138.546i	0.128036	−	0.148495i
$934$		0			0
$935$	1469.07	−	848.166i	1.57119	−	0.907129i
$936$		0			0
$937$	530.062	−	918.094i	0.565701	−	0.979823i	−0.431283	−	0.902217i	$-0.641939\pi$
$937$	530.062	−	918.094i	0.565701	−	0.979823i	0.996984	−	0.0776063i	$-0.0247277\pi$
$938$		0			0
$939$	−633.941	−	8.50627i	−0.675124	−	0.00905886i
$940$		0			0
$941$	−444.757	+	1221.96i	−0.472643	+	1.29858i	0.442977	+	0.896533i	$0.353922\pi$
$941$	−444.757	+	1221.96i	−0.472643	+	1.29858i	−0.915620	+	0.402044i	$0.868300\pi$
$942$		0			0
$943$	78.7374	−	446.542i	0.0834967	−	0.473533i
$944$		0			0
$945$	−53.6937	+	1333.22i	−0.0568187	+	1.41082i
$946$		0			0
$947$	−1618.54	−	285.392i	−1.70912	−	0.301364i	−0.768254	−	0.640145i	$-0.778874\pi$
$947$	−1618.54	−	285.392i	−1.70912	−	0.301364i	−0.940865	+	0.338781i	$0.889985\pi$
$948$		0			0
$949$	535.400	+	194.870i	0.564172	+	0.205342i
$950$		0			0
$951$	−344.872	−	205.330i	−0.362641	−	0.215910i
$952$		0			0
$953$	404.262	+	233.401i	0.424199	+	0.244912i	0.696872	−	0.717195i	$-0.254574\pi$
$953$	404.262	+	233.401i	0.424199	+	0.244912i	−0.272673	+	0.962107i	$0.587908\pi$
$954$		0			0
$955$	840.892	+	1456.47i	0.880515	+	1.52510i
$956$		0			0
$957$	114.134	−	600.087i	0.119262	−	0.627051i
$958$		0			0
$959$	683.271	−	120.479i	0.712483	−	0.125630i
$960$		0			0
$961$	−606.291	−	508.739i	−0.630896	−	0.529385i
$962$		0			0
$963$	316.253	+	64.5581i	0.328404	+	0.0670385i
$964$		0			0
$965$	−439.827	−	1208.41i	−0.455779	−	1.25224i
$966$		0			0
$967$	878.060	−	736.780i	0.908025	−	0.761923i	−0.0637176	−	0.997968i	$-0.520296\pi$
$967$	878.060	−	736.780i	0.908025	−	0.761923i	0.971742	+	0.236045i	$0.0758512\pi$
$968$		0			0
$969$	−555.534	−	680.394i	−0.573306	−	0.702161i
$970$		0			0
$971$		−	1439.65i		−	1.48264i	−0.671150	−	0.741322i	$-0.734199\pi$
$971$		−	1439.65i		−	1.48264i	0.671150	−	0.741322i	$-0.265801\pi$
$972$		0			0
$973$	293.908			0.302064
$974$		0			0
$975$	−257.343	+	210.118i	−0.263942	+	0.215506i
$976$		0			0
$977$	−885.175	−	1054.91i	−0.906013	−	1.07974i	−0.996479	−	0.0838447i	$-0.973280\pi$
$977$	−885.175	−	1054.91i	−0.906013	−	1.07974i	0.0904659	−	0.995900i	$-0.471164\pi$
$978$		0			0
$979$	−1753.57	+	638.247i	−1.79118	+	0.651937i
$980$		0			0
$981$	2.54795	−	12.4818i	0.00259730	−	0.0127235i
$982$		0			0
$983$	792.551	−	944.525i	0.806257	−	0.960860i	−0.193538	−	0.981093i	$-0.561996\pi$
$983$	792.551	−	944.525i	0.806257	−	0.960860i	0.999795	+	0.0202328i	$0.00644073\pi$
$984$		0			0
$985$	192.466	+	1091.53i	0.195397	+	1.10815i
$986$		0			0
$987$	1371.85	+	260.919i	1.38992	+	0.264356i
$988$		0			0
$989$	508.871	−	293.797i	0.514531	−	0.297064i
$990$		0			0
$991$	−25.7878	+	44.6657i	−0.0260220	+	0.0450714i	−0.878743	−	0.477295i	$-0.841617\pi$
$991$	−25.7878	+	44.6657i	−0.0260220	+	0.0450714i	0.852721	+	0.522366i	$0.174951\pi$
$992$		0			0
$993$	135.365	−	227.358i	0.136319	−	0.228961i
$994$		0			0
$995$	54.2842	−	149.145i	0.0545570	−	0.149894i
$996$		0			0
$997$	−143.357	+	813.019i	−0.143789	+	0.815465i	0.824543	+	0.565799i	$0.191432\pi$
$997$	−143.357	+	813.019i	−0.143789	+	0.815465i	−0.968332	+	0.249667i	$0.919679\pi$
$998$		0			0
$999$	−246.320	+	389.546i	−0.246567	+	0.389936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.3.bc.a.353.1		30
4.3	odd	2		27.3.f.a.2.3	✓	30
12.11	even	2		81.3.f.a.8.3		30
27.14	odd	18	inner	432.3.bc.a.257.1		30
36.7	odd	6		243.3.f.c.188.3		30
36.11	even	6		243.3.f.b.188.3		30
36.23	even	6		243.3.f.a.107.3		30
36.31	odd	6		243.3.f.d.107.3		30
108.11	even	18		729.3.b.a.728.15		30
108.23	even	18		243.3.f.d.134.3		30
108.31	odd	18		243.3.f.a.134.3		30
108.43	odd	18		729.3.b.a.728.16		30
108.59	even	18		243.3.f.c.53.3		30
108.67	odd	18		81.3.f.a.71.3		30
108.95	even	18		27.3.f.a.14.3	yes	30
108.103	odd	18		243.3.f.b.53.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.3	✓	30	4.3	odd	2
27.3.f.a.14.3	yes	30	108.95	even	18
81.3.f.a.8.3		30	12.11	even	2
81.3.f.a.71.3		30	108.67	odd	18
243.3.f.a.107.3		30	36.23	even	6
243.3.f.a.134.3		30	108.31	odd	18
243.3.f.b.53.3		30	108.103	odd	18
243.3.f.b.188.3		30	36.11	even	6
243.3.f.c.53.3		30	108.59	even	18
243.3.f.c.188.3		30	36.7	odd	6
243.3.f.d.107.3		30	36.31	odd	6
243.3.f.d.134.3		30	108.23	even	18
432.3.bc.a.257.1		30	27.14	odd	18	inner
432.3.bc.a.353.1		30	1.1	even	1	trivial
729.3.b.a.728.15		30	108.11	even	18
729.3.b.a.728.16		30	108.43	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	432.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.32380 + 1.89736i) q^{3} +(3.98394 + 4.74788i) q^{5} +(7.49258 - 2.72708i) q^{7} +(1.80008 - 8.81815i) q^{9} +(7.35571 - 8.76619i) q^{11} +(-1.43358 - 8.13025i) q^{13} +(-18.2663 - 3.47416i) q^{15} +(20.7128 - 11.9585i) q^{17} +(-6.12102 + 10.6019i) q^{19} +(-12.2370 + 20.5533i) q^{21} +(5.04566 - 13.8628i) q^{23} +(-2.32934 + 13.2103i) q^{25} +(12.5481 + 23.9070i) q^{27} +(-17.5228 - 3.08975i) q^{29} +(12.2356 + 4.45339i) q^{31} +(-0.460606 + 34.3273i) q^{33} +(42.7978 + 24.7093i) q^{35} +(8.53500 + 14.7831i) q^{37} +(18.7573 + 16.1730i) q^{39} +(30.2688 - 5.33721i) q^{41} +(30.5116 + 25.6022i) q^{43} +(49.0389 - 26.5844i) q^{45} +(-19.9668 - 54.8583i) q^{47} +(11.1657 - 9.36910i) q^{49} +(-25.4428 + 67.0888i) q^{51} +91.2612i q^{53} +70.9255 q^{55} +(-5.89158 - 36.2505i) q^{57} +(13.2814 + 15.8282i) q^{59} +(32.8508 - 11.9567i) q^{61} +(-10.5605 - 70.9797i) q^{63} +(32.8901 - 39.1969i) q^{65} +(-8.95370 - 50.7790i) q^{67} +(14.5776 + 41.7879i) q^{69} +(-2.28181 + 1.31740i) q^{71} +(-34.5072 + 59.7683i) q^{73} +(-19.6518 - 35.1177i) q^{75} +(31.2072 - 85.7410i) q^{77} +(-26.2964 + 149.134i) q^{79} +(-74.5194 - 31.7468i) q^{81} +(-53.2469 - 9.38886i) q^{83} +(139.296 + 50.6997i) q^{85} +(46.5819 - 26.0671i) q^{87} +(-141.225 - 81.5361i) q^{89} +(-32.9130 - 57.0070i) q^{91} +(-36.8828 + 12.8665i) q^{93} +(-74.7224 + 13.1756i) q^{95} +(43.6738 + 36.6467i) q^{97} +(-64.0607 - 80.6436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 6 q^{3} - 15 q^{5} + 6 q^{7} + 6 q^{11} - 6 q^{13} + 9 q^{15} - 9 q^{17} + 3 q^{19} + 132 q^{21} - 120 q^{23} - 15 q^{25} + 90 q^{27} - 168 q^{29} - 39 q^{31} - 207 q^{33} + 252 q^{35} - 3 q^{37}+ \cdots - 513 q^{99}+O(q^{100}) \) 30 * q + 6 * q^3 - 15 * q^5 + 6 * q^7 + 6 * q^11 - 6 * q^13 + 9 * q^15 - 9 * q^17 + 3 * q^19 + 132 * q^21 - 120 * q^23 - 15 * q^25 + 90 * q^27 - 168 * q^29 - 39 * q^31 - 207 * q^33 + 252 * q^35 - 3 * q^37 - 15 * q^39 + 228 * q^41 + 96 * q^43 + 477 * q^45 - 399 * q^47 - 78 * q^49 - 36 * q^51 + 12 * q^55 - 192 * q^57 + 474 * q^59 + 138 * q^61 + 585 * q^63 - 411 * q^65 - 354 * q^67 + 99 * q^69 - 315 * q^71 - 66 * q^73 - 255 * q^75 + 201 * q^77 - 30 * q^79 + 36 * q^81 + 33 * q^83 - 261 * q^85 + 279 * q^87 + 72 * q^89 - 96 * q^91 + 591 * q^93 - 681 * q^95 - 582 * q^97 - 513 * q^99

Introduction

L-functions

Modular forms

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