LMFDB - Embedded newform 36.3.g.a.29.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,3,Mod(5,36)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("36.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	36.g (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:	$0.980928951697$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.2
Root			$1.68614 + 0.396143i$ of defining polynomial
Character	$\chi$	$=$	36.29
Dual form			36.3.g.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.18614 + 2.05446i) q^{3} +(-2.05842 + 1.18843i) q^{5} +(4.05842 - 7.02939i) q^{7} +(0.558422 + 8.98266i) q^{9} +O(q^{10})$	\(q+(2.18614 + 2.05446i) q^{3} +(-2.05842 + 1.18843i) q^{5} +(4.05842 - 7.02939i) q^{7} +(0.558422 + 8.98266i) q^{9} +(-17.6168 - 10.1711i) q^{11} +(-3.05842 - 5.29734i) q^{13} +(-6.94158 - 1.63086i) q^{15} +17.9653i q^{17} +9.11684 q^{19} +(23.3139 - 7.02939i) q^{21} +(29.0584 - 16.7769i) q^{23} +(-9.67527 + 16.7581i) q^{25} +(-17.2337 + 20.7846i) q^{27} +(14.4090 + 8.31901i) q^{29} +(11.1753 + 19.3561i) q^{31} +(-17.6168 - 58.4285i) q^{33} +19.2926i q^{35} -50.4674 q^{37} +(4.19702 - 17.8641i) q^{39} +(29.9674 - 17.3017i) q^{41} +(-11.5000 + 19.9186i) q^{43} +(-11.8247 - 17.8265i) q^{45} +(-33.1753 - 19.1537i) q^{47} +(-8.44158 - 14.6212i) q^{49} +(-36.9090 + 39.2747i) q^{51} +19.0149i q^{53} +48.3505 q^{55} +(19.9307 + 18.7302i) q^{57} +(-2.96738 + 1.71322i) q^{59} +(23.1753 - 40.1407i) q^{61} +(65.4090 + 32.5301i) q^{63} +(12.5910 + 7.26944i) q^{65} +(3.14947 + 5.45504i) q^{67} +(97.9932 + 23.0226i) q^{69} -35.9306i q^{71} +47.3505 q^{73} +(-55.5802 + 16.7581i) q^{75} +(-142.993 + 82.5571i) q^{77} +(42.2921 - 73.2521i) q^{79} +(-80.3763 + 10.0322i) q^{81} +(-33.1753 - 19.1537i) q^{83} +(-21.3505 - 36.9802i) q^{85} +(14.4090 + 47.7891i) q^{87} -143.723i q^{89} -49.6495 q^{91} +(-15.3356 + 65.2743i) q^{93} +(-18.7663 + 10.8347i) q^{95} +(-40.3832 + 69.9457i) q^{97} +(81.5258 - 163.926i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{3} + 9 q^{5} - q^{7} - 15 q^{9}+O(q^{10}) $ 4 * q + 3 * q^3 + 9 * q^5 - q^7 - 15 * q^9	$ 4 q + 3 q^{3} + 9 q^{5} - q^{7} - 15 q^{9} - 36 q^{11} + 5 q^{13} - 45 q^{15} + 2 q^{19} + 99 q^{21} + 99 q^{23} + 13 q^{25} - 63 q^{29} - 7 q^{31} - 36 q^{33} - 64 q^{37} + 57 q^{39} - 18 q^{41} - 46 q^{43} - 99 q^{45} - 81 q^{47} - 51 q^{49} - 27 q^{51} + 90 q^{55} + 51 q^{57} + 126 q^{59} + 41 q^{61} + 141 q^{63} + 171 q^{65} + 116 q^{67} + 99 q^{69} + 86 q^{73} - 297 q^{75} - 279 q^{77} + 83 q^{79} - 63 q^{81} - 81 q^{83} + 18 q^{85} - 63 q^{87} - 302 q^{91} - 159 q^{93} - 144 q^{95} - 196 q^{97} + 171 q^{99}+O(q^{100}) $ 4 * q + 3 * q^3 + 9 * q^5 - q^7 - 15 * q^9 - 36 * q^11 + 5 * q^13 - 45 * q^15 + 2 * q^19 + 99 * q^21 + 99 * q^23 + 13 * q^25 - 63 * q^29 - 7 * q^31 - 36 * q^33 - 64 * q^37 + 57 * q^39 - 18 * q^41 - 46 * q^43 - 99 * q^45 - 81 * q^47 - 51 * q^49 - 27 * q^51 + 90 * q^55 + 51 * q^57 + 126 * q^59 + 41 * q^61 + 141 * q^63 + 171 * q^65 + 116 * q^67 + 99 * q^69 + 86 * q^73 - 297 * q^75 - 279 * q^77 + 83 * q^79 - 63 * q^81 - 81 * q^83 + 18 * q^85 - 63 * q^87 - 302 * q^91 - 159 * q^93 - 144 * q^95 - 196 * q^97 + 171 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	2.18614	+	2.05446i	0.728714	+	0.684819i
$3$	2.18614	+	2.05446i	0.728714	+	0.684819i
$4$		0			0
$5$	−2.05842	+	1.18843i	−0.411684	+	0.237686i	−0.691513	−	0.722364i	$-0.743056\pi$
$5$	−2.05842	+	1.18843i	−0.411684	+	0.237686i	0.279829	+	0.960050i	$0.409722\pi$
$6$		0			0
$7$	4.05842	−	7.02939i	0.579775	−	1.00420i	−0.415730	−	0.909488i	$-0.636474\pi$
$7$	4.05842	−	7.02939i	0.579775	−	1.00420i	0.995505	−	0.0947110i	$-0.0301927\pi$
$8$		0			0
$9$	0.558422	+	8.98266i	0.0620469	+	0.998073i
$10$		0			0
$11$	−17.6168	−	10.1711i	−1.60153	−	0.924645i	−0.991181	−	0.132513i	$-0.957695\pi$
$11$	−17.6168	−	10.1711i	−1.60153	−	0.924645i	−0.610350	−	0.792132i	$-0.708971\pi$
$12$		0			0
$13$	−3.05842	−	5.29734i	−0.235263	−	0.407488i	0.724086	−	0.689710i	$-0.242262\pi$
$13$	−3.05842	−	5.29734i	−0.235263	−	0.407488i	−0.959349	+	0.282222i	$0.908929\pi$
$14$		0			0
$15$	−6.94158	−	1.63086i	−0.462772	−	0.108724i
$16$		0			0
$17$			17.9653i			1.05678i	0.849001	+	0.528392i	$0.177205\pi$
$17$			17.9653i			1.05678i	−0.849001	+	0.528392i	$0.822795\pi$
$18$		0			0
$19$	9.11684			0.479834			0.239917	−	0.970793i	$-0.422880\pi$
$19$	9.11684			0.479834			0.239917	+	0.970793i	$0.422880\pi$
$20$		0			0
$21$	23.3139	−	7.02939i	1.11018	−	0.334733i
$22$		0			0
$23$	29.0584	−	16.7769i	1.26341	−	0.729430i	0.289677	−	0.957124i	$-0.406452\pi$
$23$	29.0584	−	16.7769i	1.26341	−	0.729430i	0.973733	+	0.227695i	$0.0731188\pi$
$24$		0			0
$25$	−9.67527	+	16.7581i	−0.387011	+	0.670322i
$26$		0			0
$27$	−17.2337	+	20.7846i	−0.638285	+	0.769800i
$28$		0			0
$29$	14.4090	+	8.31901i	0.496860	+	0.286863i	0.727416	−	0.686197i	$-0.240721\pi$
$29$	14.4090	+	8.31901i	0.496860	+	0.286863i	−0.230556	+	0.973059i	$0.574054\pi$
$30$		0			0
$31$	11.1753	+	19.3561i	0.360492	+	0.624391i	0.988042	−	0.154185i	$-0.0492753\pi$
$31$	11.1753	+	19.3561i	0.360492	+	0.624391i	−0.627549	+	0.778577i	$0.715942\pi$
$32$		0			0
$33$	−17.6168	−	58.4285i	−0.533844	−	1.77056i
$34$		0			0
$35$			19.2926i			0.551217i
$36$		0			0
$37$	−50.4674			−1.36398			−0.681992	−	0.731360i	$-0.738886\pi$
$37$	−50.4674			−1.36398			−0.681992	+	0.731360i	$0.738886\pi$
$38$		0			0
$39$	4.19702	−	17.8641i	0.107616	−	0.458055i
$40$		0			0
$41$	29.9674	−	17.3017i	0.730912	−	0.421992i	−0.0878440	−	0.996134i	$-0.527998\pi$
$41$	29.9674	−	17.3017i	0.730912	−	0.421992i	0.818756	+	0.574142i	$0.194664\pi$
$42$		0			0
$43$	−11.5000	+	19.9186i	−0.267442	+	0.463223i	−0.968200	−	0.250176i	$-0.919512\pi$
$43$	−11.5000	+	19.9186i	−0.267442	+	0.463223i	0.700759	+	0.713398i	$0.252845\pi$
$44$		0			0
$45$	−11.8247	−	17.8265i	−0.262772	−	0.396143i
$46$		0			0
$47$	−33.1753	−	19.1537i	−0.705857	−	0.407527i	0.103668	−	0.994612i	$-0.466942\pi$
$47$	−33.1753	−	19.1537i	−0.705857	−	0.407527i	−0.809525	+	0.587085i	$0.800275\pi$
$48$		0			0
$49$	−8.44158	−	14.6212i	−0.172277	−	0.298393i
$50$		0			0
$51$	−36.9090	+	39.2747i	−0.723705	+	0.770092i
$52$		0			0
$53$			19.0149i			0.358771i	0.983779	+	0.179386i	$0.0574110\pi$
$53$			19.0149i			0.358771i	−0.983779	+	0.179386i	$0.942589\pi$
$54$		0			0
$55$	48.3505			0.879101
$56$		0			0
$57$	19.9307	+	18.7302i	0.349661	+	0.328599i
$58$		0			0
$59$	−2.96738	+	1.71322i	−0.0502945	+	0.0290375i	−0.524936	−	0.851141i	$-0.675911\pi$
$59$	−2.96738	+	1.71322i	−0.0502945	+	0.0290375i	0.474642	+	0.880179i	$0.342578\pi$
$60$		0			0
$61$	23.1753	−	40.1407i	0.379922	−	0.658045i	−0.611128	−	0.791532i	$-0.709284\pi$
$61$	23.1753	−	40.1407i	0.379922	−	0.658045i	0.991051	+	0.133487i	$0.0426174\pi$
$62$		0			0
$63$	65.4090	+	32.5301i	1.03824	+	0.516350i
$64$		0			0
$65$	12.5910	+	7.26944i	0.193708	+	0.111838i
$66$		0			0
$67$	3.14947	+	5.45504i	0.0470070	+	0.0814185i	0.888572	−	0.458738i	$-0.151698\pi$
$67$	3.14947	+	5.45504i	0.0470070	+	0.0814185i	−0.841565	+	0.540157i	$0.818365\pi$
$68$		0			0
$69$	97.9932	+	23.0226i	1.42019	+	0.333661i
$70$		0			0
$71$		−	35.9306i		−	0.506065i	−0.967458	−	0.253033i	$-0.918572\pi$
$71$		−	35.9306i		−	0.506065i	0.967458	−	0.253033i	$-0.0814280\pi$
$72$		0			0
$73$	47.3505			0.648637			0.324319	−	0.945948i	$-0.394865\pi$
$73$	47.3505			0.648637			0.324319	+	0.945948i	$0.394865\pi$
$74$		0			0
$75$	−55.5802	+	16.7581i	−0.741069	+	0.223441i
$76$		0			0
$77$	−142.993	+	82.5571i	−1.85705	+	1.07217i
$78$		0			0
$79$	42.2921	−	73.2521i	0.535343	−	0.927242i	−0.463803	−	0.885938i	$-0.653516\pi$
$79$	42.2921	−	73.2521i	0.535343	−	0.927242i	0.999147	−	0.0413035i	$-0.0131510\pi$
$80$		0			0
$81$	−80.3763	+	10.0322i	−0.992300	+	0.123855i
$82$		0			0
$83$	−33.1753	−	19.1537i	−0.399702	−	0.230768i	0.286653	−	0.958034i	$-0.407457\pi$
$83$	−33.1753	−	19.1537i	−0.399702	−	0.230768i	−0.686355	+	0.727266i	$0.740791\pi$
$84$		0			0
$85$	−21.3505	−	36.9802i	−0.251183	−	0.435061i
$86$		0			0
$87$	14.4090	+	47.7891i	0.165620	+	0.549300i
$88$		0			0
$89$		−	143.723i		−	1.61486i	−0.589963	−	0.807430i	$-0.700858\pi$
$89$		−	143.723i		−	1.61486i	0.589963	−	0.807430i	$-0.299142\pi$
$90$		0			0
$91$	−49.6495			−0.545599
$92$		0			0
$93$	−15.3356	+	65.2743i	−0.164899	+	0.701874i
$94$		0			0
$95$	−18.7663	+	10.8347i	−0.197540	+	0.114050i
$96$		0			0
$97$	−40.3832	+	69.9457i	−0.416321	+	0.721089i	−0.995566	−	0.0940641i	$-0.970014\pi$
$97$	−40.3832	+	69.9457i	−0.416321	+	0.721089i	0.579245	+	0.815154i	$0.303347\pi$
$98$		0			0
$99$	81.5258	−	163.926i	0.823493	−	1.65582i
$100$		0			0
$101$	105.942	+	61.1654i	1.04893	+	0.605598i	0.922349	−	0.386359i	$-0.126267\pi$
$101$	105.942	+	61.1654i	1.04893	+	0.605598i	0.126578	+	0.991957i	$0.459601\pi$
$102$		0			0
$103$	−36.8247	−	63.7823i	−0.357522	−	0.619246i	0.630024	−	0.776575i	$-0.283045\pi$
$103$	−36.8247	−	63.7823i	−0.357522	−	0.619246i	−0.987546	+	0.157330i	$0.949712\pi$
$104$		0			0
$105$	−39.6358	+	42.1764i	−0.377484	+	0.401680i
$106$		0			0
$107$			72.9108i			0.681410i	0.940170	+	0.340705i	$0.110666\pi$
$107$			72.9108i			0.681410i	−0.940170	+	0.340705i	$0.889334\pi$
$108$		0			0
$109$	31.2989			0.287146			0.143573	−	0.989640i	$-0.454141\pi$
$109$	31.2989			0.287146			0.143573	+	0.989640i	$0.454141\pi$
$110$		0			0
$111$	−110.329	−	103.683i	−0.993953	−	0.934081i
$112$		0			0
$113$	16.2269	−	9.36858i	0.143601	−	0.0829078i	−0.426478	−	0.904498i	$-0.640246\pi$
$113$	16.2269	−	9.36858i	0.143601	−	0.0829078i	0.570079	+	0.821590i	$0.306913\pi$
$114$		0			0
$115$	−39.8763	+	69.0678i	−0.346751	+	0.600590i
$116$		0			0
$117$	45.8763	−	30.4309i	0.392105	−	0.260093i
$118$		0			0
$119$	126.285	+	72.9108i	1.06122	+	0.612696i
$120$		0			0
$121$	146.402	+	253.576i	1.20993	+	2.09567i
$122$		0			0
$123$	101.058	+	23.7428i	0.821613	+	0.193031i
$124$		0			0
$125$		−	105.415i		−	0.843320i
$126$		0			0
$127$	−126.103			−0.992939			−0.496469	−	0.868054i	$-0.665370\pi$
$127$	−126.103			−0.992939			−0.496469	+	0.868054i	$0.665370\pi$
$128$		0			0
$129$	−66.0625	+	19.9186i	−0.512112	+	0.154408i
$130$		0			0
$131$	140.694	−	81.2299i	1.07400	−	0.620075i	0.144730	−	0.989471i	$-0.453769\pi$
$131$	140.694	−	81.2299i	1.07400	−	0.620075i	0.929272	+	0.369396i	$0.120435\pi$
$132$		0			0
$133$	37.0000	−	64.0859i	0.278195	−	0.481849i
$134$		0			0
$135$	10.7731	−	63.2645i	0.0798010	−	0.468626i
$136$		0			0
$137$	90.3832	+	52.1827i	0.659731	+	0.380896i	0.792174	−	0.610295i	$-0.208949\pi$
$137$	90.3832	+	52.1827i	0.659731	+	0.380896i	−0.132443	+	0.991191i	$0.542282\pi$
$138$		0			0
$139$	−30.6168	−	53.0299i	−0.220265	−	0.381510i	0.734623	−	0.678475i	$-0.237359\pi$
$139$	−30.6168	−	53.0299i	−0.220265	−	0.381510i	−0.954888	+	0.296965i	$0.904026\pi$
$140$		0			0
$141$	−33.1753	−	110.030i	−0.235286	−	0.780354i
$142$		0			0
$143$			124.430i			0.870139i
$144$		0			0
$145$	−39.5463			−0.272733
$146$		0			0
$147$	11.5842	−	49.3069i	0.0788042	−	0.335421i
$148$		0			0
$149$	−128.344	+	74.0993i	−0.861367	+	0.497311i	−0.864470	−	0.502685i	$-0.832346\pi$
$149$	−128.344	+	74.0993i	−0.861367	+	0.497311i	0.00310272	+	0.999995i	$0.499012\pi$
$150$		0			0
$151$	−127.526	+	220.881i	−0.844542	+	1.46279i	0.0414769	+	0.999139i	$0.486794\pi$
$151$	−127.526	+	220.881i	−0.844542	+	1.46279i	−0.886019	+	0.463650i	$0.846540\pi$
$152$		0			0
$153$	−161.376	+	10.0322i	−1.05475	+	0.0655701i
$154$		0			0
$155$	−46.0068	−	26.5621i	−0.296818	−	0.171368i
$156$		0			0
$157$	−146.227	−	253.272i	−0.931381	−	1.61320i	−0.780963	−	0.624577i	$-0.785271\pi$
$157$	−146.227	−	253.272i	−0.931381	−	1.61320i	−0.150418	−	0.988622i	$-0.548062\pi$
$158$		0			0
$159$	−39.0652	+	41.5692i	−0.245693	+	0.261442i
$160$		0			0
$161$		−	272.351i		−	1.69162i
$162$		0			0
$163$	93.5326			0.573820			0.286910	−	0.957958i	$-0.407372\pi$
$163$	93.5326			0.573820			0.286910	+	0.957958i	$0.407372\pi$
$164$		0			0
$165$	105.701	+	99.3340i	0.640613	+	0.602024i
$166$		0			0
$167$	−97.2269	+	56.1340i	−0.582197	+	0.336131i	−0.762006	−	0.647570i	$-0.775785\pi$
$167$	−97.2269	+	56.1340i	−0.582197	+	0.336131i	0.179809	+	0.983702i	$0.442452\pi$
$168$		0			0
$169$	65.7921	−	113.955i	0.389302	−	0.674292i
$170$		0			0
$171$	5.09105	+	81.8935i	0.0297722	+	0.478909i
$172$		0			0
$173$	−205.227	−	118.488i	−1.18628	−	0.684900i	−0.228823	−	0.973468i	$-0.573488\pi$
$173$	−205.227	−	118.488i	−1.18628	−	0.684900i	−0.957460	+	0.288568i	$0.906821\pi$
$174$		0			0
$175$	78.5326	+	136.022i	0.448758	+	0.777271i
$176$		0			0
$177$	−10.0068	−	2.35101i	−0.0565357	−	0.0132826i
$178$		0			0
$179$			234.599i			1.31061i	0.755366	+	0.655304i	$0.227459\pi$
$179$			234.599i			1.31061i	−0.755366	+	0.655304i	$0.772541\pi$
$180$		0			0
$181$	221.636			1.22451			0.612254	−	0.790661i	$-0.290263\pi$
$181$	221.636			1.22451			0.612254	+	0.790661i	$0.290263\pi$
$182$		0			0
$183$	133.132	−	40.1407i	0.727496	−	0.219348i
$184$		0			0
$185$	103.883	−	59.9770i	0.561531	−	0.324200i
$186$		0			0
$187$	182.727	−	316.492i	0.977149	−	1.69247i
$188$		0			0
$189$	76.1616	+	205.495i	0.402971	+	1.08728i
$190$		0			0
$191$	−130.162	−	75.1488i	−0.681474	−	0.393449i	0.118936	−	0.992902i	$-0.462052\pi$
$191$	−130.162	−	75.1488i	−0.681474	−	0.393449i	−0.800410	+	0.599452i	$0.795385\pi$
$192$		0			0
$193$	24.5000	+	42.4352i	0.126943	+	0.219872i	0.922491	−	0.386019i	$-0.126150\pi$
$193$	24.5000	+	42.4352i	0.126943	+	0.219872i	−0.795548	+	0.605891i	$0.792817\pi$
$194$		0			0
$195$	12.5910	+	41.7598i	0.0645695	+	0.214153i
$196$		0			0
$197$			276.827i			1.40521i	0.711579	+	0.702606i	$0.247980\pi$
$197$			276.827i			1.40521i	−0.711579	+	0.702606i	$0.752020\pi$
$198$		0			0
$199$	−198.935			−0.999672			−0.499836	−	0.866120i	$-0.666606\pi$
$199$	−198.935			−0.999672			−0.499836	+	0.866120i	$0.666606\pi$
$200$		0			0
$201$	−4.32196	+	18.3959i	−0.0215023	+	0.0915220i
$202$		0			0
$203$	116.955	−	67.5241i	0.576134	−	0.332631i
$204$		0			0
$205$	−41.1237	+	71.2283i	−0.200603	+	0.347455i
$206$		0			0
$207$	166.928	+	251.653i	0.806415	+	1.21572i
$208$		0			0
$209$	−160.610	−	92.7282i	−0.768469	−	0.443676i
$210$		0			0
$211$	−47.0068	−	81.4182i	−0.222781	−	0.385868i	0.732870	−	0.680368i	$-0.238180\pi$
$211$	−47.0068	−	81.4182i	−0.222781	−	0.385868i	−0.955651	+	0.294500i	$0.904847\pi$
$212$		0			0
$213$	73.8179	−	78.5494i	0.346563	−	0.368777i
$214$		0			0
$215$		−	54.6678i		−	0.254269i
$216$		0			0
$217$	181.416			0.836017
$218$		0			0
$219$	103.515	+	97.2796i	0.472671	+	0.444199i
$220$		0			0
$221$	95.1684	−	54.9455i	0.430626	−	0.248622i
$222$		0			0
$223$	77.8763	−	134.886i	0.349221	−	0.604869i	−0.636890	−	0.770955i	$-0.719780\pi$
$223$	77.8763	−	134.886i	0.349221	−	0.604869i	0.986111	+	0.166086i	$0.0531128\pi$
$224$		0			0
$225$	−155.935	−	77.5516i	−0.693043	−	0.344674i
$226$		0			0
$227$	−138.448	−	79.9332i	−0.609905	−	0.352129i	0.163023	−	0.986622i	$-0.447875\pi$
$227$	−138.448	−	79.9332i	−0.609905	−	0.352129i	−0.772928	+	0.634493i	$0.781209\pi$
$228$		0			0
$229$	19.1237	+	33.1232i	0.0835095	+	0.144643i	0.904755	−	0.425932i	$-0.140054\pi$
$229$	19.1237	+	33.1232i	0.0835095	+	0.144643i	−0.821246	+	0.570575i	$0.806720\pi$
$230$		0			0
$231$	−482.213	−	113.292i	−2.08750	−	0.490440i
$232$		0			0
$233$			157.490i			0.675921i	0.941160	+	0.337960i	$0.109737\pi$
$233$			157.490i			0.675921i	−0.941160	+	0.337960i	$0.890263\pi$
$234$		0			0
$235$	91.0516			0.387454
$236$		0			0
$237$	242.950	−	73.2521i	1.02510	−	0.309081i
$238$		0			0
$239$	−62.4742	+	36.0695i	−0.261398	+	0.150918i	−0.624972	−	0.780647i	$-0.714890\pi$
$239$	−62.4742	+	36.0695i	−0.261398	+	0.150918i	0.363574	+	0.931565i	$0.381556\pi$
$240$		0			0
$241$	−113.370	+	196.362i	−0.470413	+	0.814779i	−0.999427	−	0.0338337i	$-0.989228\pi$
$241$	−113.370	+	196.362i	−0.470413	+	0.814779i	0.529015	+	0.848613i	$0.322562\pi$
$242$		0			0
$243$	−196.325	−	143.198i	−0.807921	−	0.589291i
$244$		0			0
$245$	34.7527	+	20.0645i	0.141848	+	0.0818957i
$246$		0			0
$247$	−27.8832	−	48.2950i	−0.112887	−	0.195526i
$248$		0			0
$249$	−33.1753	−	110.030i	−0.133234	−	0.441887i
$250$		0			0
$251$		−	222.931i		−	0.888171i	−0.895985	−	0.444085i	$-0.853529\pi$
$251$		−	222.931i		−	0.888171i	0.895985	−	0.444085i	$-0.146471\pi$
$252$		0			0
$253$	−682.557			−2.69785
$254$		0			0
$255$	29.2989	−	124.708i	0.114898	−	0.489050i
$256$		0			0
$257$	92.2011	−	53.2323i	0.358759	−	0.207130i	−0.309777	−	0.950809i	$-0.600254\pi$
$257$	92.2011	−	53.2323i	0.358759	−	0.207130i	0.668536	+	0.743680i	$0.266921\pi$
$258$		0			0
$259$	−204.818	+	354.755i	−0.790803	+	1.36971i
$260$		0			0
$261$	−66.6806	+	134.076i	−0.255481	+	0.513702i
$262$		0			0
$263$	155.344	+	89.6877i	0.590660	+	0.341018i	0.765359	−	0.643604i	$-0.222562\pi$
$263$	155.344	+	89.6877i	0.590660	+	0.341018i	−0.174698	+	0.984622i	$0.555895\pi$
$264$		0			0
$265$	−22.5979	−	39.1407i	−0.0852750	−	0.147701i
$266$		0			0
$267$	295.272	−	314.198i	1.10589	−	1.17677i
$268$		0			0
$269$			416.351i			1.54777i	0.633324	+	0.773887i	$0.281690\pi$
$269$			416.351i			1.54777i	−0.633324	+	0.773887i	$0.718310\pi$
$270$		0			0
$271$	396.907			1.46460			0.732302	−	0.680980i	$-0.238446\pi$
$271$	396.907			1.46460			0.732302	+	0.680980i	$0.238446\pi$
$272$		0			0
$273$	−108.541	−	102.003i	−0.397585	−	0.373636i
$274$		0			0
$275$	340.895	−	196.816i	1.23962	−	0.715695i
$276$		0			0
$277$	57.7731	−	100.066i	0.208567	−	0.361249i	−0.742696	−	0.669629i	$-0.766453\pi$
$277$	57.7731	−	100.066i	0.208567	−	0.361249i	0.951263	+	0.308379i	$0.0997866\pi$
$278$		0			0
$279$	−167.629	+	111.192i	−0.600821	+	0.398539i
$280$		0			0
$281$	422.564	+	243.967i	1.50379	+	0.868211i	0.999990	+	0.00438786i	$0.00139670\pi$
$281$	422.564	+	243.967i	1.50379	+	0.868211i	0.503795	+	0.863823i	$0.331937\pi$
$282$		0			0
$283$	169.825	+	294.145i	0.600087	+	1.03938i	0.992807	+	0.119724i	$0.0382009\pi$
$283$	169.825	+	294.145i	0.600087	+	1.03938i	−0.392720	+	0.919658i	$0.628466\pi$
$284$		0			0
$285$	−63.2853	−	14.8683i	−0.222054	−	0.0521695i
$286$		0			0
$287$		−	280.870i		−	0.978641i
$288$		0			0
$289$	−33.7527			−0.116791
$290$		0			0
$291$	−231.984	+	69.9457i	−0.797194	+	0.240363i
$292$		0			0
$293$	122.409	−	70.6728i	0.417778	−	0.241204i	−0.276348	−	0.961058i	$-0.589124\pi$
$293$	122.409	−	70.6728i	0.417778	−	0.241204i	0.694126	+	0.719853i	$0.255791\pi$
$294$		0			0
$295$	4.07207	−	7.05304i	0.0138036	−	0.0239086i
$296$		0			0
$297$	515.005	−	190.874i	1.73402	−	0.642673i
$298$		0			0
$299$	−177.746	−	102.622i	−0.594468	−	0.343216i
$300$		0			0
$301$	93.3437	+	161.676i	0.310112	+	0.537130i
$302$		0			0
$303$	105.942	+	351.368i	0.349642	+	1.15963i
$304$		0			0
$305$			110.169i			0.361209i
$306$		0			0
$307$	−120.649			−0.392995			−0.196498	−	0.980504i	$-0.562957\pi$
$307$	−120.649			−0.392995			−0.196498	+	0.980504i	$0.562957\pi$
$308$		0			0
$309$	50.5339	−	215.092i	0.163540	−	0.696090i
$310$		0			0
$311$	−119.254	+	68.8514i	−0.383454	+	0.221387i	−0.679320	−	0.733842i	$-0.737725\pi$
$311$	−119.254	+	68.8514i	−0.383454	+	0.221387i	0.295866	+	0.955229i	$0.404392\pi$
$312$		0			0
$313$	−129.266	+	223.896i	−0.412991	+	0.715322i	−0.995215	−	0.0977064i	$-0.968849\pi$
$313$	−129.266	+	223.896i	−0.412991	+	0.715322i	0.582224	+	0.813029i	$0.302183\pi$
$314$		0			0
$315$	−173.299	+	10.7734i	−0.550155	+	0.0342013i
$316$		0			0
$317$	−16.7079	−	9.64630i	−0.0527063	−	0.0304300i	0.473415	−	0.880839i	$-0.343021\pi$
$317$	−16.7079	−	9.64630i	−0.0527063	−	0.0304300i	−0.526122	+	0.850409i	$0.676354\pi$
$318$		0			0
$319$	−169.227	−	293.110i	−0.530492	−	0.918839i
$320$		0			0
$321$	−149.792	+	159.393i	−0.466642	+	0.496553i
$322$		0			0
$323$			163.787i			0.507081i
$324$		0			0
$325$	118.364			0.364197
$326$		0			0
$327$	68.4239	+	64.3023i	0.209247	+	0.196643i
$328$		0			0
$329$	−269.278	+	155.468i	−0.818476	+	0.472547i
$330$		0			0
$331$	98.3953	−	170.426i	0.297267	−	0.514881i	−0.678243	−	0.734838i	$-0.737258\pi$
$331$	98.3953	−	170.426i	0.297267	−	0.514881i	0.975510	+	0.219957i	$0.0705916\pi$
$332$		0			0
$333$	−28.1821	−	453.331i	−0.0846309	−	1.36136i
$334$		0			0
$335$	−12.9659	−	7.48585i	−0.0387041	−	0.0223458i
$336$		0			0
$337$	−158.720	−	274.911i	−0.470979	−	0.815760i	0.528470	−	0.848952i	$-0.322766\pi$
$337$	−158.720	−	274.911i	−0.470979	−	0.815760i	−0.999449	+	0.0331921i	$0.989433\pi$
$338$		0			0
$339$	54.7215	+	12.8563i	0.161420	+	0.0379243i
$340$		0			0
$341$		−	454.659i		−	1.33331i
$342$		0			0
$343$	260.687			0.760022
$344$		0			0
$345$	−229.072	+	69.0678i	−0.663977	+	0.200197i
$346$		0			0
$347$	−537.407	+	310.272i	−1.54872	+	0.894157i	−0.550485	+	0.834845i	$0.685557\pi$
$347$	−537.407	+	310.272i	−1.54872	+	0.894157i	−0.998240	+	0.0593116i	$0.981109\pi$
$348$		0			0
$349$	189.512	−	328.245i	0.543015	−	0.940529i	−0.455714	−	0.890126i	$-0.650616\pi$
$349$	189.512	−	328.245i	0.543015	−	0.940529i	0.998729	−	0.0504030i	$-0.0160506\pi$
$350$		0			0
$351$	162.811	+	27.7246i	0.463849	+	0.0789876i
$352$		0			0
$353$	−213.514	−	123.272i	−0.604855	−	0.349213i	0.166094	−	0.986110i	$-0.446884\pi$
$353$	−213.514	−	123.272i	−0.604855	−	0.349213i	−0.770949	+	0.636897i	$0.780218\pi$
$354$		0			0
$355$	42.7011	+	73.9604i	0.120285	+	0.208339i
$356$		0			0
$357$	126.285	+	418.841i	0.353740	+	1.17322i
$358$		0			0
$359$		−	572.791i		−	1.59552i	−0.602976	−	0.797759i	$-0.706019\pi$
$359$		−	572.791i		−	1.59552i	0.602976	−	0.797759i	$-0.293981\pi$
$360$		0			0
$361$	−277.883			−0.769759
$362$		0			0
$363$	−200.905	+	855.129i	−0.553457	+	2.35573i
$364$		0			0
$365$	−97.4674	+	56.2728i	−0.267034	+	0.154172i
$366$		0			0
$367$	93.9279	−	162.688i	0.255934	−	0.443291i	−0.709214	−	0.704993i	$-0.750950\pi$
$367$	93.9279	−	162.688i	0.255934	−	0.443291i	0.965149	+	0.261701i	$0.0842836\pi$
$368$		0			0
$369$	172.149	+	259.525i	0.466530	+	0.703320i
$370$		0			0
$371$	133.663	+	77.1704i	0.360278	+	0.208007i
$372$		0			0
$373$	−75.0584	−	130.005i	−0.201229	−	0.348539i	0.747696	−	0.664042i	$-0.231160\pi$
$373$	−75.0584	−	130.005i	−0.201229	−	0.348539i	−0.948925	+	0.315503i	$0.897827\pi$
$374$		0			0
$375$	216.571	−	230.452i	0.577522	−	0.614539i
$376$		0			0
$377$		−	101.772i		−	0.269953i
$378$		0			0
$379$	−26.6222			−0.0702432			−0.0351216	−	0.999383i	$-0.511182\pi$
$379$	−26.6222			−0.0702432			−0.0351216	+	0.999383i	$0.511182\pi$
$380$		0			0
$381$	−275.679	−	259.073i	−0.723568	−	0.679983i
$382$		0			0
$383$	−444.966	+	256.901i	−1.16179	+	0.670760i	−0.951733	−	0.306929i	$-0.900699\pi$
$383$	−444.966	+	256.901i	−1.16179	+	0.670760i	−0.210058	+	0.977689i	$0.567365\pi$
$384$		0			0
$385$	196.227	−	339.875i	0.509680	−	0.882792i
$386$		0			0
$387$	−185.344	−	92.1776i	−0.478924	−	0.238185i
$388$		0			0
$389$	−22.1616	−	12.7950i	−0.0569707	−	0.0328921i	0.471244	−	0.882003i	$-0.343805\pi$
$389$	−22.1616	−	12.7950i	−0.0569707	−	0.0328921i	−0.528215	+	0.849111i	$0.677138\pi$
$390$		0			0
$391$	301.402	+	522.044i	0.770849	+	1.33515i
$392$		0			0
$393$	474.461	+	111.470i	1.20728	+	0.283639i
$394$		0			0
$395$			201.045i			0.508975i
$396$		0			0
$397$	388.804			0.979356			0.489678	−	0.871903i	$-0.337114\pi$
$397$	388.804			0.979356			0.489678	+	0.871903i	$0.337114\pi$
$398$		0			0
$399$	212.549	−	64.0859i	0.532704	−	0.160616i
$400$		0			0
$401$	−34.0842	+	19.6785i	−0.0849981	+	0.0490736i	−0.541897	−	0.840445i	$-0.682294\pi$
$401$	−34.0842	+	19.6785i	−0.0849981	+	0.0490736i	0.456899	+	0.889519i	$0.348960\pi$
$402$		0			0
$403$	68.3574	−	118.398i	0.169621	−	0.293793i
$404$		0			0
$405$	153.526	−	116.172i	0.379076	−	0.286845i
$406$		0			0
$407$	889.076	+	513.308i	2.18446	+	1.26120i
$408$		0			0
$409$	−86.7200	−	150.204i	−0.212029	−	0.367246i	0.740320	−	0.672255i	$-0.234674\pi$
$409$	−86.7200	−	150.204i	−0.212029	−	0.367246i	−0.952350	+	0.305009i	$0.901341\pi$
$410$		0			0
$411$	90.3832	+	299.767i	0.219910	+	0.729360i
$412$		0			0
$413$			27.8118i			0.0673409i
$414$		0			0
$415$	91.0516			0.219401
$416$		0			0
$417$	42.0149	−	178.832i	0.100755	−	0.428853i
$418$		0			0
$419$	115.031	−	66.4132i	0.274537	−	0.158504i	−0.356411	−	0.934329i	$-0.616000\pi$
$419$	115.031	−	66.4132i	0.274537	−	0.158504i	0.630948	+	0.775825i	$0.282666\pi$
$420$		0			0
$421$	−317.447	+	549.834i	−0.754031	+	1.30602i	0.191824	+	0.981429i	$0.438560\pi$
$421$	−317.447	+	549.834i	−0.754031	+	1.30602i	−0.945855	+	0.324590i	$0.894774\pi$
$422$		0			0
$423$	153.526	−	308.698i	0.362945	−	0.729782i
$424$		0			0
$425$	−301.064	−	173.819i	−0.708385	−	0.408986i
$426$		0			0
$427$	−188.110	−	325.816i	−0.440539	−	0.763035i
$428$		0			0
$429$	−255.636	+	272.021i	−0.595888	+	0.634082i
$430$		0			0
$431$		−	602.424i		−	1.39774i	−0.715251	−	0.698868i	$-0.753687\pi$
$431$		−	602.424i		−	1.39774i	0.715251	−	0.698868i	$-0.246313\pi$
$432$		0			0
$433$	266.155			0.614676			0.307338	−	0.951600i	$-0.400562\pi$
$433$	266.155			0.614676			0.307338	+	0.951600i	$0.400562\pi$
$434$		0			0
$435$	−86.4537	−	81.2461i	−0.198744	−	0.186773i
$436$		0			0
$437$	264.921	−	152.952i	0.606227	−	0.350005i
$438$		0			0
$439$	−250.330	+	433.584i	−0.570228	+	0.987664i	0.426314	+	0.904575i	$0.359812\pi$
$439$	−250.330	+	433.584i	−0.570228	+	0.987664i	−0.996542	+	0.0830886i	$0.973522\pi$
$440$		0			0
$441$	126.624	−	83.9926i	0.287129	−	0.190460i
$442$		0			0
$443$	−261.098	−	150.745i	−0.589386	−	0.340282i	0.175469	−	0.984485i	$-0.443856\pi$
$443$	−261.098	−	150.745i	−0.589386	−	0.340282i	−0.764855	+	0.644203i	$0.777189\pi$
$444$		0			0
$445$	170.804	+	295.842i	0.383830	+	0.664813i
$446$		0			0
$447$	−432.811	−	101.685i	−0.968257	−	0.227483i
$448$		0			0
$449$			565.321i			1.25907i	0.776973	+	0.629534i	$0.216754\pi$
$449$			565.321i			1.25907i	−0.776973	+	0.629534i	$0.783246\pi$
$450$		0			0
$451$	−703.907			−1.56077
$452$		0			0
$453$	−732.580	+	220.881i	−1.61717	+	0.487596i
$454$		0			0
$455$	102.200	−	59.0049i	0.224614	−	0.129681i
$456$		0			0
$457$	−26.1495	+	45.2922i	−0.0572198	+	0.0991077i	−0.893216	−	0.449627i	$-0.851557\pi$
$457$	−26.1495	+	45.2922i	−0.0572198	+	0.0991077i	0.835997	+	0.548735i	$0.184890\pi$
$458$		0			0
$459$	−373.402	−	309.609i	−0.813512	−	0.674529i
$460$		0			0
$461$	166.357	+	96.0465i	0.360862	+	0.208344i	0.669459	−	0.742849i	$-0.266526\pi$
$461$	166.357	+	96.0465i	0.360862	+	0.208344i	−0.308597	+	0.951193i	$0.599859\pi$
$462$		0			0
$463$	−283.110	−	490.361i	−0.611469	−	1.05909i	−0.990993	−	0.133913i	$-0.957246\pi$
$463$	−283.110	−	490.361i	−0.611469	−	1.05909i	0.379524	−	0.925182i	$-0.376088\pi$
$464$		0			0
$465$	−46.0068	−	152.587i	−0.0989394	−	0.328145i
$466$		0			0
$467$			174.405i			0.373459i	0.982411	+	0.186729i	$0.0597888\pi$
$467$			174.405i			0.373459i	−0.982411	+	0.186729i	$0.940211\pi$
$468$		0			0
$469$	51.1275			0.109014
$470$		0			0
$471$	200.664	−	854.106i	0.426039	−	1.81339i
$472$		0			0
$473$	405.187	−	233.935i	0.856633	−	0.494577i
$474$		0			0
$475$	−88.2079	+	152.781i	−0.185701	+	0.321643i
$476$		0			0
$477$	−170.804	+	10.6183i	−0.358080	+	0.0222607i
$478$		0			0
$479$	473.784	+	273.539i	0.989110	+	0.571063i	0.905008	−	0.425394i	$-0.139865\pi$
$479$	473.784	+	273.539i	0.989110	+	0.571063i	0.0841020	+	0.996457i	$0.473198\pi$
$480$		0			0
$481$	154.351	+	267.343i	0.320895	+	0.555807i
$482$		0			0
$483$	559.533	−	595.397i	1.15845	−	1.23271i
$484$		0			0
$485$		−	191.970i		−	0.395815i
$486$		0			0
$487$	−769.945			−1.58100			−0.790498	−	0.612464i	$-0.790178\pi$
$487$	−769.945			−1.58100			−0.790498	+	0.612464i	$0.790178\pi$
$488$		0			0
$489$	204.475	+	192.159i	0.418150	+	0.392962i
$490$		0			0
$491$	−154.916	+	89.4407i	−0.315511	+	0.182160i	−0.649390	−	0.760456i	$-0.724976\pi$
$491$	−154.916	+	89.4407i	−0.315511	+	0.182160i	0.333879	+	0.942616i	$0.391642\pi$
$492$		0			0
$493$	−149.454	+	258.861i	−0.303152	+	0.525074i
$494$		0			0
$495$	27.0000	+	434.316i	0.0545455	+	0.877407i
$496$		0			0
$497$	−252.571	−	145.822i	−0.508190	−	0.293404i
$498$		0			0
$499$	192.655	+	333.688i	0.386082	+	0.668713i	0.991919	−	0.126876i	$-0.0404949\pi$
$499$	192.655	+	333.688i	0.386082	+	0.668713i	−0.605837	+	0.795589i	$0.707162\pi$
$500$		0			0
$501$	−327.876	−	77.0316i	−0.654444	−	0.153756i
$502$		0			0
$503$			67.6630i			0.134519i	0.997736	+	0.0672594i	$0.0214255\pi$
$503$			67.6630i			0.134519i	−0.997736	+	0.0672594i	$0.978574\pi$
$504$		0			0
$505$	−290.763			−0.575769
$506$		0			0
$507$	377.947	−	113.955i	0.745457	−	0.224764i
$508$		0			0
$509$	523.292	−	302.123i	1.02808	−	0.593562i	0.111645	−	0.993748i	$-0.464388\pi$
$509$	523.292	−	302.123i	1.02808	−	0.593562i	0.916434	+	0.400187i	$0.131055\pi$
$510$		0			0
$511$	192.168	−	332.846i	0.376063	−	0.651361i
$512$		0			0
$513$	−157.117	+	189.490i	−0.306271	+	0.369376i
$514$		0			0
$515$	151.602	+	87.5273i	0.294372	+	0.169956i
$516$		0			0
$517$	389.629	+	674.857i	0.753634	+	1.30533i
$518$		0			0
$519$	−205.227	−	680.660i	−0.395427	−	1.31148i
$520$		0			0
$521$			273.678i			0.525294i	0.964892	+	0.262647i	$0.0845954\pi$
$521$			273.678i			0.525294i	−0.964892	+	0.262647i	$0.915405\pi$
$522$		0			0
$523$	687.402			1.31434			0.657172	−	0.753740i	$-0.271752\pi$
$523$	687.402			1.31434			0.657172	+	0.753740i	$0.271752\pi$
$524$		0			0
$525$	−107.769	+	458.706i	−0.205274	+	0.873726i
$526$		0			0
$527$	−347.739	+	200.767i	−0.659846	+	0.380962i
$528$		0			0
$529$	298.428	−	516.892i	0.564136	−	0.977112i
$530$		0			0
$531$	−17.0463	−	25.6982i	−0.0321022	−	0.0483959i
$532$		0			0
$533$	−183.306	−	105.832i	−0.343913	−	0.198558i
$534$		0			0
$535$	−86.6495	−	150.081i	−0.161962	−	0.280526i
$536$		0			0
$537$	−481.973	+	512.866i	−0.897528	+	0.955057i
$538$		0			0
$539$			343.440i			0.637180i
$540$		0			0
$541$	664.543			1.22836			0.614180	−	0.789166i	$-0.289487\pi$
$541$	664.543			1.22836			0.614180	+	0.789166i	$0.289487\pi$
$542$		0			0
$543$	484.527	+	455.341i	0.892315	+	0.838565i
$544$		0			0
$545$	−64.4264	+	37.1966i	−0.118214	+	0.0682507i
$546$		0			0
$547$	−259.603	+	449.646i	−0.474594	+	0.822022i	−0.999577	−	0.0290914i	$-0.990739\pi$
$547$	−259.603	+	449.646i	−0.474594	+	0.822022i	0.524982	+	0.851113i	$0.324072\pi$
$548$		0			0
$549$	373.512	+	185.760i	0.680350	+	0.338361i
$550$		0			0
$551$	131.364	+	75.8431i	0.238410	+	0.137646i
$552$		0			0
$553$	−343.278	−	594.576i	−0.620757	−	1.07518i
$554$		0			0
$555$	350.323	+	82.3053i	0.631213	+	0.148298i
$556$		0			0
$557$		−	422.648i		−	0.758794i	−0.925234	−	0.379397i	$-0.876131\pi$
$557$		−	422.648i		−	0.758794i	0.925234	−	0.379397i	$-0.123869\pi$
$558$		0			0
$559$	140.687			0.251677
$560$		0			0
$561$	1049.69	−	316.492i	1.87110	−	0.564157i
$562$		0			0
$563$	798.799	−	461.187i	1.41883	−	0.819159i	0.422630	−	0.906302i	$-0.361107\pi$
$563$	798.799	−	461.187i	1.41883	−	0.819159i	0.996196	+	0.0871428i	$0.0277737\pi$
$564$		0			0
$565$	−22.2678	+	38.5690i	−0.0394121	+	0.0682637i
$566$		0			0
$567$	−255.681	+	605.712i	−0.450936	+	1.06827i
$568$		0			0
$569$	−914.445	−	527.955i	−1.60711	−	0.927865i	−0.990013	−	0.140978i	$-0.954975\pi$
$569$	−914.445	−	527.955i	−1.60711	−	0.927865i	−0.617097	−	0.786887i	$-0.711691\pi$
$570$		0			0
$571$	−401.524	−	695.460i	−0.703195	−	1.21797i	−0.967339	−	0.253486i	$-0.918423\pi$
$571$	−401.524	−	695.460i	−0.703195	−	1.21797i	0.264144	−	0.964483i	$-0.414911\pi$
$572$		0			0
$573$	−130.162	−	431.697i	−0.227158	−	0.753398i
$574$		0			0
$575$			649.283i			1.12919i
$576$		0			0
$577$	−96.6495			−0.167503			−0.0837517	−	0.996487i	$-0.526690\pi$
$577$	−96.6495			−0.167503			−0.0837517	+	0.996487i	$0.526690\pi$
$578$		0			0
$579$	−33.6209	+	143.104i	−0.0580672	+	0.247156i
$580$		0			0
$581$	−269.278	+	155.468i	−0.463474	+	0.267587i
$582$		0			0
$583$	193.402	−	334.982i	0.331736	−	0.574584i
$584$		0			0
$585$	−58.2678	+	117.160i	−0.0996031	+	0.200274i
$586$		0			0
$587$	−870.497	−	502.582i	−1.48296	−	0.856187i	−0.483146	−	0.875540i	$-0.660506\pi$
$587$	−870.497	−	502.582i	−1.48296	−	0.856187i	−0.999813	+	0.0193528i	$0.993839\pi$
$588$		0			0
$589$	101.883	+	176.467i	0.172976	+	0.299604i
$590$		0			0
$591$	−568.728	+	605.182i	−0.962315	+	1.02400i
$592$		0			0
$593$			752.444i			1.26888i	0.772973	+	0.634439i	$0.218769\pi$
$593$			752.444i			1.26888i	−0.772973	+	0.634439i	$0.781231\pi$
$594$		0			0
$595$	−346.598			−0.582517
$596$		0			0
$597$	−434.899	−	408.703i	−0.728475	−	0.684594i
$598$		0			0
$599$	−24.0857	+	13.9059i	−0.0402099	+	0.0232152i	−0.519970	−	0.854184i	$-0.674057\pi$
$599$	−24.0857	+	13.9059i	−0.0402099	+	0.0232152i	0.479760	+	0.877400i	$0.340724\pi$
$600$		0			0
$601$	475.356	−	823.340i	0.790942	−	1.36995i	−0.134443	−	0.990921i	$-0.542925\pi$
$601$	475.356	−	823.340i	0.790942	−	1.36995i	0.925385	−	0.379030i	$-0.123742\pi$
$602$		0			0
$603$	−47.2420	+	31.3368i	−0.0783450	+	0.0519682i
$604$		0			0
$605$	−602.715	−	347.978i	−0.996223	−	0.575169i
$606$		0			0
$607$	161.306	+	279.390i	0.265743	+	0.460280i	0.967758	−	0.251882i	$-0.0810495\pi$
$607$	161.306	+	279.390i	0.265743	+	0.460280i	−0.702015	+	0.712162i	$0.747716\pi$
$608$		0			0
$609$	394.406	+	92.6621i	0.647629	+	0.152155i
$610$		0			0
$611$			234.321i			0.383504i
$612$		0			0
$613$	138.206			0.225459			0.112730	−	0.993626i	$-0.464041\pi$
$613$	138.206			0.225459			0.112730	+	0.993626i	$0.464041\pi$
$614$		0			0
$615$	−236.237	+	71.2283i	−0.384126	+	0.115818i
$616$		0			0
$617$	−682.084	+	393.802i	−1.10548	+	0.638252i	−0.937656	−	0.347564i	$-0.887009\pi$
$617$	−682.084	+	393.802i	−1.10548	+	0.638252i	−0.167829	+	0.985816i	$0.553676\pi$
$618$		0			0
$619$	121.747	−	210.873i	0.196684	−	0.340667i	−0.750767	−	0.660567i	$-0.770316\pi$
$619$	121.747	−	210.873i	0.196684	−	0.340667i	0.947451	+	0.319900i	$0.103649\pi$
$620$		0			0
$621$	−152.083	+	893.096i	−0.244900	+	1.43816i
$622$		0			0
$623$	−1010.28	−	583.287i	−1.62164	−	0.936255i
$624$		0			0
$625$	−116.603	−	201.963i	−0.186565	−	0.323140i
$626$		0			0
$627$	−160.610	−	532.683i	−0.256156	−	0.849574i
$628$		0			0
$629$		−	906.662i		−	1.44143i
$630$		0			0
$631$	111.924			0.177376			0.0886879	−	0.996059i	$-0.471733\pi$
$631$	111.924			0.177376			0.0886879	+	0.996059i	$0.471733\pi$
$632$		0			0
$633$	64.5066	−	274.565i	0.101906	−	0.433752i
$634$		0			0
$635$	259.574	−	149.865i	0.408777	−	0.236008i
$636$		0			0
$637$	−51.6358	+	89.4359i	−0.0810609	+	0.140402i
$638$		0			0
$639$	322.753	−	20.0645i	0.505090	−	0.0313998i
$640$		0			0
$641$	632.095	+	364.940i	0.986107	+	0.569329i	0.904108	−	0.427303i	$-0.140536\pi$
$641$	632.095	+	364.940i	0.986107	+	0.569329i	0.0819990	+	0.996632i	$0.473870\pi$
$642$		0			0
$643$	288.500	+	499.697i	0.448678	+	0.777133i	0.998300	−	0.0582801i	$-0.0185617\pi$
$643$	288.500	+	499.697i	0.448678	+	0.777133i	−0.549622	+	0.835413i	$0.685228\pi$
$644$		0			0
$645$	112.313	−	119.512i	0.174128	−	0.185289i
$646$		0			0
$647$			129.029i			0.199426i	0.995016	+	0.0997130i	$0.0317925\pi$
$647$			129.029i			0.199426i	−0.995016	+	0.0997130i	$0.968208\pi$
$648$		0			0
$649$	69.7011			0.107398
$650$		0			0
$651$	396.600	+	372.711i	0.609217	+	0.572520i
$652$		0			0
$653$	1026.62	−	592.717i	1.57215	−	0.907682i	0.576247	−	0.817275i	$-0.304517\pi$
$653$	1026.62	−	592.717i	1.57215	−	0.907682i	0.995905	−	0.0904070i	$-0.0288168\pi$
$654$		0			0
$655$	−193.072	+	334.411i	−0.294767	+	0.510551i
$656$		0			0
$657$	26.4416	+	425.334i	0.0402459	+	0.647388i
$658$		0			0
$659$	947.808	+	547.217i	1.43825	+	0.830375i	0.997728	−	0.0673658i	$-0.0214595\pi$
$659$	947.808	+	547.217i	1.43825	+	0.830375i	0.440524	+	0.897741i	$0.354793\pi$
$660$		0			0
$661$	−604.876	−	1047.68i	−0.915093	−	1.58499i	−0.806765	−	0.590872i	$-0.798784\pi$
$661$	−604.876	−	1047.68i	−0.915093	−	1.58499i	−0.108327	−	0.994115i	$-0.534549\pi$
$662$		0			0
$663$	320.935	+	75.4007i	0.484064	+	0.113727i
$664$		0			0
$665$			175.888i			0.264493i
$666$		0			0
$667$	558.269			0.836984
$668$		0			0
$669$	447.365	−	134.886i	0.668708	−	0.201623i
$670$		0			0
$671$	−816.550	+	471.435i	−1.21692	+	0.702586i
$672$		0			0
$673$	−508.615	+	880.948i	−0.755743	+	1.30899i	0.189260	+	0.981927i	$0.439391\pi$
$673$	−508.615	+	880.948i	−0.755743	+	1.30899i	−0.945004	+	0.327059i	$0.893942\pi$
$674$		0			0
$675$	−181.569	−	489.900i	−0.268991	−	0.725777i
$676$		0			0
$677$	689.890	+	398.308i	1.01904	+	0.588343i	0.913826	−	0.406107i	$-0.133114\pi$
$677$	689.890	+	398.308i	1.01904	+	0.588343i	0.105214	+	0.994450i	$0.466447\pi$
$678$		0			0
$679$	327.784	+	567.738i	0.482745	+	0.836139i
$680$		0			0
$681$	−138.448	−	459.181i	−0.203302	−	0.674275i
$682$		0			0
$683$			400.485i			0.586361i	0.956057	+	0.293181i	$0.0947138\pi$
$683$			400.485i			0.586361i	−0.956057	+	0.293181i	$0.905286\pi$
$684$		0			0
$685$	−248.062			−0.362135
$686$		0			0
$687$	−26.2431	+	111.701i	−0.0381995	+	0.162592i
$688$		0			0
$689$	100.728	−	58.1556i	0.146195	−	0.0844057i
$690$		0			0
$691$	216.423	−	374.855i	0.313202	−	0.542482i	−0.665852	−	0.746084i	$-0.731932\pi$
$691$	216.423	−	374.855i	0.313202	−	0.542482i	0.979054	+	0.203602i	$0.0652650\pi$
$692$		0			0
$693$	−821.433	−	1238.36i	−1.18533	−	1.78695i
$694$		0			0
$695$	126.045	+	72.7720i	0.181359	+	0.104708i
$696$		0			0
$697$	310.830	+	538.373i	0.445954	+	0.772415i
$698$		0			0
$699$	−323.555	+	344.294i	−0.462883	+	0.492553i
$700$		0			0
$701$			65.4412i			0.0933541i	0.998910	+	0.0466770i	$0.0148632\pi$
$701$			65.4412i			0.0933541i	−0.998910	+	0.0466770i	$0.985137\pi$
$702$		0			0
$703$	−460.103			−0.654485
$704$		0			0
$705$	199.052	+	187.061i	0.282343	+	0.265335i
$706$		0			0
$707$	859.911	−	496.470i	1.21628	−	0.702221i
$708$		0			0
$709$	−100.461	+	174.003i	−0.141693	+	0.245420i	−0.928134	−	0.372245i	$-0.878588\pi$
$709$	−100.461	+	174.003i	−0.141693	+	0.245420i	0.786441	+	0.617665i	$0.211921\pi$
$710$		0			0
$711$	681.615	+	338.990i	0.958671	+	0.476779i
$712$		0			0
$713$	649.471	+	374.972i	0.910899	+	0.525908i
$714$		0			0
$715$	−147.876	−	256.129i	−0.206820	−	0.358223i
$716$		0			0
$717$	−210.681	−	49.4975i	−0.293836	−	0.0690342i
$718$		0			0
$719$		−	1062.98i		−	1.47841i	−0.673478	−	0.739207i	$-0.735200\pi$
$719$		−	1062.98i		−	1.47841i	0.673478	−	0.739207i	$-0.264800\pi$
$720$		0			0
$721$	−597.801			−0.829128
$722$		0			0
$723$	−651.258	+	196.362i	−0.900772	+	0.271593i
$724$		0			0
$725$	−278.821	+	160.977i	−0.384581	+	0.222038i
$726$		0			0
$727$	−495.629	+	858.455i	−0.681746	+	1.18082i	0.292702	+	0.956204i	$0.405446\pi$
$727$	−495.629	+	858.455i	−0.681746	+	1.18082i	−0.974448	+	0.224614i	$0.927888\pi$
$728$		0			0
$729$	−135.000	−	716.391i	−0.185185	−	0.982704i
$730$		0			0
$731$	−357.844	−	206.601i	−0.489526	−	0.282628i
$732$		0			0
$733$	590.134	+	1022.14i	0.805095	+	1.39446i	0.916227	+	0.400659i	$0.131219\pi$
$733$	590.134	+	1022.14i	0.805095	+	1.39446i	−0.111133	+	0.993806i	$0.535448\pi$
$734$		0			0
$735$	34.7527	+	115.262i	0.0472825	+	0.156818i
$736$		0			0
$737$		−	128.134i		−	0.173859i
$738$		0			0
$739$	599.351			0.811029			0.405515	−	0.914089i	$-0.367092\pi$
$739$	599.351			0.811029			0.405515	+	0.914089i	$0.367092\pi$
$740$		0			0
$741$	38.2635	−	162.864i	0.0516377	−	0.219790i
$742$		0			0
$743$	287.083	−	165.747i	0.386383	−	0.223078i	−0.294209	−	0.955741i	$-0.595056\pi$
$743$	287.083	−	165.747i	0.386383	−	0.223078i	0.680592	+	0.732663i	$0.261723\pi$
$744$		0			0
$745$	176.124	−	305.055i	0.236408	−	0.409470i
$746$		0			0
$747$	153.526	−	308.698i	0.205523	−	0.413250i
$748$		0			0
$749$	512.519	+	295.903i	0.684271	+	0.395064i
$750$		0			0
$751$	−76.0448	−	131.713i	−0.101258	−	0.175384i	0.810945	−	0.585122i	$-0.198953\pi$
$751$	−76.0448	−	131.713i	−0.101258	−	0.175384i	−0.912203	+	0.409738i	$0.865620\pi$
$752$		0			0
$753$	458.002	−	487.358i	0.608236	−	0.647222i
$754$		0			0
$755$		−	606.222i		−	0.802943i
$756$		0			0
$757$	−1179.61			−1.55827			−0.779134	−	0.626858i	$-0.784341\pi$
$757$	−1179.61			−1.55827			−0.779134	+	0.626858i	$0.784341\pi$
$758$		0			0
$759$	−1492.17	−	1402.28i	−1.96596	−	1.84754i
$760$		0			0
$761$	−1162.58	+	671.214i	−1.52770	+	0.882016i	−0.528239	+	0.849096i	$0.677147\pi$
$761$	−1162.58	+	671.214i	−1.52770	+	0.882016i	−0.999458	+	0.0329205i	$0.989519\pi$
$762$		0			0
$763$	127.024	−	220.013i	0.166480	−	0.288352i
$764$		0			0
$765$	320.258	−	212.435i	0.418638	−	0.277693i
$766$		0			0
$767$	18.1510	+	10.4795i	0.0236649	+	0.0136629i
$768$		0			0
$769$	−548.512	−	950.051i	−0.713280	−	1.23544i	−0.963619	−	0.267279i	$-0.913876\pi$
$769$	−548.512	−	950.051i	−0.713280	−	1.23544i	0.250339	−	0.968158i	$-0.419458\pi$
$770$		0			0
$771$	310.928	+	73.0497i	0.403279	+	0.0947467i
$772$		0			0
$773$			1181.39i			1.52832i	0.645028	+	0.764159i	$0.276846\pi$
$773$			1181.39i			1.52832i	−0.645028	+	0.764159i	$0.723154\pi$
$774$		0			0
$775$	−432.495			−0.558058
$776$		0			0
$777$	−1176.59	+	354.755i	−1.51427	+	0.456570i
$778$		0			0
$779$	273.208	−	157.737i	0.350716	−	0.202486i
$780$		0			0
$781$	−365.454	+	632.984i	−0.467931	+	0.810479i
$782$		0			0
$783$	−421.227	+	156.117i	−0.537965	+	0.199383i
$784$		0			0
$785$	601.993	+	347.561i	0.766870	+	0.442753i
$786$		0			0
$787$	18.0311	+	31.2308i	0.0229112	+	0.0396834i	0.877254	−	0.480027i	$-0.159373\pi$
$787$	18.0311	+	31.2308i	0.0229112	+	0.0396834i	−0.854342	+	0.519710i	$0.826040\pi$
$788$		0			0
$789$	155.344	+	515.217i	0.196887	+	0.653000i
$790$		0			0
$791$		−	152.087i		−	0.192271i
$792$		0			0
$793$	−283.519			−0.357527
$794$		0			0
$795$	31.0106	−	131.993i	0.0390071	−	0.166029i
$796$		0			0
$797$	−115.618	+	66.7523i	−0.145067	+	0.0837544i	−0.570777	−	0.821105i	$-0.693358\pi$
$797$	−115.618	+	66.7523i	−0.145067	+	0.0837544i	0.425710	+	0.904860i	$0.360024\pi$
$798$		0			0
$799$	344.103	−	596.004i	0.430667	−	0.745938i
$800$		0			0
$801$	1291.01	−	80.2578i	1.61175	−	0.100197i
$802$		0			0
$803$	−834.167	−	481.607i	−1.03881	−	0.599759i
$804$		0			0
$805$	323.670	+	560.613i	0.402074	+	0.696413i
$806$		0			0
$807$	−855.375	+	910.202i	−1.05994	+	1.12788i
$808$		0			0
$809$		−	1053.66i		−	1.30242i	−0.758898	−	0.651209i	$-0.774262\pi$
$809$		−	1053.66i		−	1.30242i	0.758898	−	0.651209i	$-0.225738\pi$
$810$		0			0
$811$	434.464			0.535714			0.267857	−	0.963459i	$-0.413684\pi$
$811$	434.464			0.535714			0.267857	+	0.963459i	$0.413684\pi$
$812$		0			0
$813$	867.696	+	815.429i	1.06728	+	1.00299i
$814$		0			0
$815$	−192.530	+	111.157i	−0.236233	+	0.136389i
$816$		0			0
$817$	−104.844	+	181.595i	−0.128328	+	0.222270i
$818$		0			0
$819$	−27.7254	−	445.984i	−0.0338527	−	0.544547i
$820$		0			0
$821$	252.436	+	145.744i	0.307474	+	0.177520i	0.645796	−	0.763510i	$-0.276526\pi$
$821$	252.436	+	145.744i	0.307474	+	0.177520i	−0.338322	+	0.941031i	$0.609859\pi$
$822$		0			0
$823$	−168.409	−	291.693i	−0.204628	−	0.354426i	0.745386	−	0.666633i	$-0.232265\pi$
$823$	−168.409	−	291.693i	−0.204628	−	0.354426i	−0.950014	+	0.312207i	$0.898932\pi$
$824$		0			0
$825$	1149.59	+	270.087i	1.39345	+	0.327378i
$826$		0			0
$827$		−	1029.27i		−	1.24458i	−0.782785	−	0.622292i	$-0.786202\pi$
$827$		−	1029.27i		−	1.24458i	0.782785	−	0.622292i	$-0.213798\pi$
$828$		0			0
$829$	790.674			0.953768			0.476884	−	0.878966i	$-0.341766\pi$
$829$	790.674			0.953768			0.476884	+	0.878966i	$0.341766\pi$
$830$		0			0
$831$	331.881	−	100.066i	0.399376	−	0.120416i
$832$		0			0
$833$	262.675	−	151.656i	0.315336	−	0.182060i
$834$		0			0
$835$	133.423	−	231.095i	0.159788	−	0.276760i
$836$		0			0
$837$	−594.901	−	101.304i	−0.710753	−	0.121032i
$838$		0			0
$839$	655.031	+	378.182i	0.780728	+	0.450754i	0.836688	−	0.547679i	$-0.184489\pi$
$839$	655.031	+	378.182i	0.780728	+	0.450754i	−0.0559600	+	0.998433i	$0.517822\pi$
$840$		0			0
$841$	−282.088	−	488.591i	−0.335420	−	0.580964i
$842$		0			0
$843$	422.564	+	1401.49i	0.501262	+	1.66250i
$844$		0			0
$845$			312.757i			0.370127i
$846$		0			0
$847$	2376.65			2.80596
$848$		0			0
$849$	−233.047	+	991.940i	−0.274496	+	1.16836i
$850$		0			0
$851$	−1466.50	+	846.686i	−1.72327	+	0.994930i
$852$		0			0
$853$	599.175	−	1037.80i	0.702433	−	1.21665i	−0.265177	−	0.964200i	$-0.585430\pi$
$853$	599.175	−	1037.80i	0.702433	−	1.21665i	0.967610	−	0.252450i	$-0.0812362\pi$
$854$		0			0
$855$	−107.804	−	162.521i	−0.126087	−	0.190083i
$856$		0			0
$857$	605.629	+	349.660i	0.706685	+	0.408005i	0.809832	−	0.586661i	$-0.199558\pi$
$857$	605.629	+	349.660i	0.706685	+	0.408005i	−0.103147	+	0.994666i	$0.532891\pi$
$858$		0			0
$859$	278.734	+	482.781i	0.324486	+	0.562027i	0.981408	−	0.191932i	$-0.0614753\pi$
$859$	278.734	+	482.781i	0.324486	+	0.562027i	−0.656922	+	0.753959i	$0.728142\pi$
$860$		0			0
$861$	577.035	−	614.021i	0.670192	−	0.713149i
$862$		0			0
$863$			99.3954i			0.115174i	0.998340	+	0.0575871i	$0.0183407\pi$
$863$			99.3954i			0.115174i	−0.998340	+	0.0575871i	$0.981659\pi$
$864$		0			0
$865$	563.258			0.651165
$866$		0			0
$867$	−73.7881	−	69.3434i	−0.0851073	−	0.0799808i
$868$		0			0
$869$	−1490.11	+	860.314i	−1.71474	+	0.990004i
$870$		0			0
$871$	19.2648	−	33.3676i	0.0221180	−	0.0383096i
$872$		0			0
$873$	−650.849	−	323.689i	−0.745532	−	0.370778i
$874$		0			0
$875$	−741.004	−	427.819i	−0.846861	−	0.488936i
$876$		0			0
$877$	−401.292	−	695.058i	−0.457574	−	0.792541i	0.541258	−	0.840856i	$-0.317948\pi$
$877$	−401.292	−	695.058i	−0.457574	−	0.792541i	−0.998832	+	0.0483154i	$0.984615\pi$
$878$		0			0
$879$	412.797	+	96.9830i	0.469622	+	0.110333i
$880$		0			0
$881$		−	524.266i		−	0.595080i	−0.954709	−	0.297540i	$-0.903834\pi$
$881$		−	524.266i		−	0.595080i	0.954709	−	0.297540i	$-0.0961662\pi$
$882$		0			0
$883$	−993.894			−1.12559			−0.562794	−	0.826597i	$-0.690273\pi$
$883$	−993.894			−1.12559			−0.562794	+	0.826597i	$0.690273\pi$
$884$		0			0
$885$	23.3923	−	7.05304i	0.0264320	−	0.00796954i
$886$		0			0
$887$	616.643	−	356.019i	0.695200	−	0.401374i	−0.110357	−	0.993892i	$-0.535199\pi$
$887$	616.643	−	356.019i	0.695200	−	0.401374i	0.805557	+	0.592518i	$0.201866\pi$
$888$		0			0
$889$	−511.780	+	886.429i	−0.575681	+	0.997108i
$890$		0			0
$891$	1518.02	+	640.779i	1.70372	+	0.719168i
$892$		0			0
$893$	−302.454	−	174.622i	−0.338694	−	0.195545i
$894$		0			0
$895$	−278.804	−	482.903i	−0.311513	−	0.539557i
$896$		0			0
$897$	−177.746	−	589.516i	−0.198156	−	0.657209i
$898$		0			0
$899$			371.869i			0.413647i
$900$		0			0
$901$	−341.609			−0.379144
$902$		0			0
$903$	−128.094	+	545.217i	−0.141854	+	0.603784i
$904$		0			0
$905$	−456.220	+	263.399i	−0.504111	+	0.291048i
$906$		0			0
$907$	374.473	−	648.606i	0.412870	−	0.715111i	−0.582333	−	0.812951i	$-0.697860\pi$
$907$	374.473	−	648.606i	0.412870	−	0.715111i	0.995202	+	0.0978396i	$0.0311932\pi$
$908$		0			0
$909$	−490.268	+	985.793i	−0.539349	+	1.08448i
$910$		0			0
$911$	−3.87633	−	2.23800i	−0.00425503	−	0.00245664i	0.497871	−	0.867251i	$-0.334115\pi$
$911$	−3.87633	−	2.23800i	−0.00425503	−	0.00245664i	−0.502126	+	0.864794i	$0.667449\pi$
$912$		0			0
$913$	389.629	+	674.857i	0.426757	+	0.739165i
$914$		0			0
$915$	−226.337	+	240.844i	−0.247363	+	0.263218i
$916$		0			0
$917$		−	1318.66i		−	1.43802i
$918$		0			0
$919$	−1592.91			−1.73331			−0.866653	−	0.498912i	$-0.833733\pi$
$919$	−1592.91			−1.73331			−0.866653	+	0.498912i	$0.833733\pi$
$920$		0			0
$921$	−263.757	−	247.869i	−0.286381	−	0.269130i
$922$		0			0
$923$	−190.337	+	109.891i	−0.206215	+	0.119059i
$924$		0			0
$925$	488.285	−	845.735i	0.527876	−	0.914308i
$926$		0			0
$927$	552.371	−	366.401i	0.595869	−	0.395255i
$928$		0			0
$929$	−770.784	−	445.012i	−0.829692	−	0.479023i	0.0240553	−	0.999711i	$-0.492342\pi$
$929$	−770.784	−	445.012i	−0.829692	−	0.479023i	−0.853747	+	0.520688i	$0.825676\pi$
$930$		0			0
$931$	−76.9605	−	133.300i	−0.0826644	−	0.143179i
$932$		0			0
$933$	−402.159	−	94.4835i	−0.431038	−	0.101269i
$934$		0			0
$935$			868.633i			0.929019i
$936$		0			0
$937$	443.554			0.473377			0.236688	−	0.971586i	$-0.423938\pi$
$937$	443.554			0.473377			0.236688	+	0.971586i	$0.423938\pi$
$938$		0			0
$939$	−742.578	+	223.896i	−0.790818	+	0.238441i
$940$		0			0
$941$	−69.7458	+	40.2678i	−0.0741188	+	0.0427925i	−0.536601	−	0.843836i	$-0.680292\pi$
$941$	−69.7458	+	40.2678i	−0.0741188	+	0.0427925i	0.462483	+	0.886628i	$0.346959\pi$
$942$		0			0
$943$	580.536	−	1005.52i	0.615627	−	1.06630i
$944$		0			0
$945$	−400.989	−	332.483i	−0.424327	−	0.351834i
$946$		0			0
$947$	245.861	+	141.948i	0.259621	+	0.149892i	0.624162	−	0.781295i	$-0.285441\pi$
$947$	245.861	+	141.948i	0.259621	+	0.149892i	−0.364541	+	0.931187i	$0.618774\pi$
$948$		0			0
$949$	−144.818	−	250.832i	−0.152601	−	0.264312i
$950$		0			0
$951$	−16.7079	−	55.4138i	−0.0175688	−	0.0582690i
$952$		0			0
$953$		−	1123.17i		−	1.17857i	−0.807927	−	0.589283i	$-0.799410\pi$
$953$		−	1123.17i		−	1.17857i	0.807927	−	0.589283i	$-0.200590\pi$
$954$		0			0
$955$	357.237			0.374070
$956$		0			0
$957$	232.227	−	988.448i	0.242661	−	1.03286i
$958$		0			0
$959$	733.626	−	423.559i	0.764991	−	0.441668i
$960$		0			0
$961$	230.727	−	399.631i	0.240090	−	0.415849i
$962$		0			0
$963$	−654.933	+	40.7150i	−0.680097	+	0.0422794i
$964$		0			0
$965$	−100.863	−	58.2331i	−0.104521	−	0.0603452i
$966$		0			0
$967$	699.536	+	1211.63i	0.723409	+	1.25298i	0.959626	+	0.281281i	$0.0907592\pi$
$967$	699.536	+	1211.63i	0.723409	+	1.25298i	−0.236217	+	0.971700i	$0.575907\pi$
$968$		0			0
$969$	−336.493	+	358.061i	−0.347258	+	0.369516i
$970$		0			0
$971$			1705.41i			1.75634i	0.478345	+	0.878172i	$0.341237\pi$
$971$			1705.41i			1.75634i	−0.478345	+	0.878172i	$0.658763\pi$
$972$		0			0
$973$	−497.024			−0.510816
$974$		0			0
$975$	258.761	+	243.174i	0.265396	+	0.249409i
$976$		0			0
$977$	1005.50	−	580.524i	1.02917	−	0.594190i	0.112422	−	0.993661i	$-0.464139\pi$
$977$	1005.50	−	580.524i	1.02917	−	0.594190i	0.916746	+	0.399470i	$0.130806\pi$
$978$		0			0
$979$	−1461.81	+	2531.94i	−1.49317	+	2.58625i
$980$		0			0
$981$	17.4780	+	281.148i	0.0178165	+	0.286593i
$982$		0			0
$983$	−1023.46	−	590.895i	−1.04116	−	0.601114i	−0.120999	−	0.992653i	$-0.538610\pi$
$983$	−1023.46	−	590.895i	−1.04116	−	0.601114i	−0.920162	+	0.391539i	$0.871943\pi$
$984$		0			0
$985$	−328.989	−	569.826i	−0.333999	−	0.578504i
$986$		0			0
$987$	−908.083	−	213.346i	−0.920043	−	0.216156i
$988$		0			0
$989$			771.737i			0.780320i
$990$		0			0
$991$	−969.527			−0.978332			−0.489166	−	0.872191i	$-0.662699\pi$
$991$	−969.527			−0.978332			−0.489166	+	0.872191i	$0.662699\pi$
$992$		0			0
$993$	565.238	−	170.426i	0.569223	−	0.171627i
$994$		0			0
$995$	409.492	−	236.420i	0.411549	−	0.237608i
$996$		0			0
$997$	−390.124	+	675.714i	−0.391298	+	0.677747i	−0.992621	−	0.121258i	$-0.961307\pi$
$997$	−390.124	+	675.714i	−0.391298	+	0.677747i	0.601323	+	0.799006i	$0.294640\pi$
$998$		0			0
$999$	869.739	−	1048.94i	0.870610	−	1.04999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.g.a.29.2	yes	4
3.2	odd	2		108.3.g.a.89.2		4
4.3	odd	2		144.3.q.b.65.1		4
5.2	odd	4		900.3.u.a.749.3		8
5.3	odd	4		900.3.u.a.749.2		8
5.4	even	2		900.3.p.a.101.1		4
8.3	odd	2		576.3.q.g.65.2		4
8.5	even	2		576.3.q.d.65.1		4
9.2	odd	6		324.3.c.b.161.3		4
9.4	even	3		108.3.g.a.17.2		4
9.5	odd	6	inner	36.3.g.a.5.2	✓	4
9.7	even	3		324.3.c.b.161.2		4
12.11	even	2		432.3.q.b.305.2		4
15.2	even	4		2700.3.u.b.2249.3		8
15.8	even	4		2700.3.u.b.2249.2		8
15.14	odd	2		2700.3.p.b.1601.1		4
24.5	odd	2		1728.3.q.g.1601.1		4
24.11	even	2		1728.3.q.h.1601.1		4
36.7	odd	6		1296.3.e.e.161.2		4
36.11	even	6		1296.3.e.e.161.3		4
36.23	even	6		144.3.q.b.113.1		4
36.31	odd	6		432.3.q.b.17.2		4
45.4	even	6		2700.3.p.b.2501.1		4
45.13	odd	12		2700.3.u.b.449.3		8
45.14	odd	6		900.3.p.a.401.1		4
45.22	odd	12		2700.3.u.b.449.2		8
45.23	even	12		900.3.u.a.149.3		8
45.32	even	12		900.3.u.a.149.2		8
72.5	odd	6		576.3.q.d.257.1		4
72.13	even	6		1728.3.q.g.449.1		4
72.59	even	6		576.3.q.g.257.2		4
72.67	odd	6		1728.3.q.h.449.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.g.a.5.2	✓	4	9.5	odd	6	inner
36.3.g.a.29.2	yes	4	1.1	even	1	trivial
108.3.g.a.17.2		4	9.4	even	3
108.3.g.a.89.2		4	3.2	odd	2
144.3.q.b.65.1		4	4.3	odd	2
144.3.q.b.113.1		4	36.23	even	6
324.3.c.b.161.2		4	9.7	even	3
324.3.c.b.161.3		4	9.2	odd	6
432.3.q.b.17.2		4	36.31	odd	6
432.3.q.b.305.2		4	12.11	even	2
576.3.q.d.65.1		4	8.5	even	2
576.3.q.d.257.1		4	72.5	odd	6
576.3.q.g.65.2		4	8.3	odd	2
576.3.q.g.257.2		4	72.59	even	6
900.3.p.a.101.1		4	5.4	even	2
900.3.p.a.401.1		4	45.14	odd	6
900.3.u.a.149.2		8	45.32	even	12
900.3.u.a.149.3		8	45.23	even	12
900.3.u.a.749.2		8	5.3	odd	4
900.3.u.a.749.3		8	5.2	odd	4
1296.3.e.e.161.2		4	36.7	odd	6
1296.3.e.e.161.3		4	36.11	even	6
1728.3.q.g.449.1		4	72.13	even	6
1728.3.q.g.1601.1		4	24.5	odd	2
1728.3.q.h.449.1		4	72.67	odd	6
1728.3.q.h.1601.1		4	24.11	even	2
2700.3.p.b.1601.1		4	15.14	odd	2
2700.3.p.b.2501.1		4	45.4	even	6
2700.3.u.b.449.2		8	45.22	odd	12
2700.3.u.b.449.3		8	45.13	odd	12
2700.3.u.b.2249.2		8	15.8	even	4
2700.3.u.b.2249.3		8	15.2	even	4

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	36.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18614 + 2.05446i) q^{3} +(-2.05842 + 1.18843i) q^{5} +(4.05842 - 7.02939i) q^{7} +(0.558422 + 8.98266i) q^{9} +O(q^{10})\)	\(q+(2.18614 + 2.05446i) q^{3} +(-2.05842 + 1.18843i) q^{5} +(4.05842 - 7.02939i) q^{7} +(0.558422 + 8.98266i) q^{9} +(-17.6168 - 10.1711i) q^{11} +(-3.05842 - 5.29734i) q^{13} +(-6.94158 - 1.63086i) q^{15} +17.9653i q^{17} +9.11684 q^{19} +(23.3139 - 7.02939i) q^{21} +(29.0584 - 16.7769i) q^{23} +(-9.67527 + 16.7581i) q^{25} +(-17.2337 + 20.7846i) q^{27} +(14.4090 + 8.31901i) q^{29} +(11.1753 + 19.3561i) q^{31} +(-17.6168 - 58.4285i) q^{33} +19.2926i q^{35} -50.4674 q^{37} +(4.19702 - 17.8641i) q^{39} +(29.9674 - 17.3017i) q^{41} +(-11.5000 + 19.9186i) q^{43} +(-11.8247 - 17.8265i) q^{45} +(-33.1753 - 19.1537i) q^{47} +(-8.44158 - 14.6212i) q^{49} +(-36.9090 + 39.2747i) q^{51} +19.0149i q^{53} +48.3505 q^{55} +(19.9307 + 18.7302i) q^{57} +(-2.96738 + 1.71322i) q^{59} +(23.1753 - 40.1407i) q^{61} +(65.4090 + 32.5301i) q^{63} +(12.5910 + 7.26944i) q^{65} +(3.14947 + 5.45504i) q^{67} +(97.9932 + 23.0226i) q^{69} -35.9306i q^{71} +47.3505 q^{73} +(-55.5802 + 16.7581i) q^{75} +(-142.993 + 82.5571i) q^{77} +(42.2921 - 73.2521i) q^{79} +(-80.3763 + 10.0322i) q^{81} +(-33.1753 - 19.1537i) q^{83} +(-21.3505 - 36.9802i) q^{85} +(14.4090 + 47.7891i) q^{87} -143.723i q^{89} -49.6495 q^{91} +(-15.3356 + 65.2743i) q^{93} +(-18.7663 + 10.8347i) q^{95} +(-40.3832 + 69.9457i) q^{97} +(81.5258 - 163.926i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{3} + 9 q^{5} - q^{7} - 15 q^{9}+O(q^{10}) \) 4 * q + 3 * q^3 + 9 * q^5 - q^7 - 15 * q^9	\( 4 q + 3 q^{3} + 9 q^{5} - q^{7} - 15 q^{9} - 36 q^{11} + 5 q^{13} - 45 q^{15} + 2 q^{19} + 99 q^{21} + 99 q^{23} + 13 q^{25} - 63 q^{29} - 7 q^{31} - 36 q^{33} - 64 q^{37} + 57 q^{39} - 18 q^{41} - 46 q^{43} - 99 q^{45} - 81 q^{47} - 51 q^{49} - 27 q^{51} + 90 q^{55} + 51 q^{57} + 126 q^{59} + 41 q^{61} + 141 q^{63} + 171 q^{65} + 116 q^{67} + 99 q^{69} + 86 q^{73} - 297 q^{75} - 279 q^{77} + 83 q^{79} - 63 q^{81} - 81 q^{83} + 18 q^{85} - 63 q^{87} - 302 q^{91} - 159 q^{93} - 144 q^{95} - 196 q^{97} + 171 q^{99}+O(q^{100}) \) 4 * q + 3 * q^3 + 9 * q^5 - q^7 - 15 * q^9 - 36 * q^11 + 5 * q^13 - 45 * q^15 + 2 * q^19 + 99 * q^21 + 99 * q^23 + 13 * q^25 - 63 * q^29 - 7 * q^31 - 36 * q^33 - 64 * q^37 + 57 * q^39 - 18 * q^41 - 46 * q^43 - 99 * q^45 - 81 * q^47 - 51 * q^49 - 27 * q^51 + 90 * q^55 + 51 * q^57 + 126 * q^59 + 41 * q^61 + 141 * q^63 + 171 * q^65 + 116 * q^67 + 99 * q^69 + 86 * q^73 - 297 * q^75 - 279 * q^77 + 83 * q^79 - 63 * q^81 - 81 * q^83 + 18 * q^85 - 63 * q^87 - 302 * q^91 - 159 * q^93 - 144 * q^95 - 196 * q^97 + 171 * q^99

Introduction

L-functions

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