LMFDB - Embedded newform 900.3.p.d.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 10 x^{14} - 12 x^{13} + 6 x^{12} - 27 x^{11} - 585 x^{10} + 3618 x^{9} + \cdots + 43046721 $ x^16 - 2x^15 + 10x^14 - 12x^13 + 6x^12 - 27x^11 - 585x^10 + 3618x^9 - 12150x^8 + 32562x^7 - 47385x^6 - 19683x^5 + 39366x^4 - 708588x^3 + 5314410x^2 - 9565938*x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{41}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.4
Root			$-2.99949 + 0.0553819i$ of defining polynomial
Character	$\chi$	$=$	900.101
Dual form			900.3.p.d.401.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54771 - 2.56994i) q^{3} +(-0.725042 + 1.25581i) q^{7} +(-4.20921 + 7.95503i) q^{9} +O(q^{10})$	\(q+(-1.54771 - 2.56994i) q^{3} +(-0.725042 + 1.25581i) q^{7} +(-4.20921 + 7.95503i) q^{9} +(8.07235 + 4.66057i) q^{11} +(-5.60207 - 9.70307i) q^{13} +4.16234i q^{17} +3.14773 q^{19} +(4.34951 - 0.0803085i) q^{21} +(11.5999 - 6.69719i) q^{23} +(26.9586 - 1.49463i) q^{27} +(12.6968 + 7.33048i) q^{29} +(7.07498 + 12.2542i) q^{31} +(-0.516223 - 27.9587i) q^{33} +18.0321 q^{37} +(-16.2660 + 29.4145i) q^{39} +(17.6468 - 10.1884i) q^{41} +(16.7364 - 28.9883i) q^{43} +(-1.63903 - 0.946292i) q^{47} +(23.4486 + 40.6142i) q^{49} +(10.6970 - 6.44209i) q^{51} -97.8498i q^{53} +(-4.87176 - 8.08948i) q^{57} +(-28.9968 + 16.7413i) q^{59} +(29.6385 - 51.3354i) q^{61} +(-6.93816 - 11.0537i) q^{63} +(-47.9406 - 83.0356i) q^{67} +(-35.1646 - 19.4457i) q^{69} -97.3685i q^{71} +90.1349 q^{73} +(-11.7056 + 6.75822i) q^{77} +(-66.7654 + 115.641i) q^{79} +(-45.5651 - 66.9688i) q^{81} +(-6.48602 - 3.74470i) q^{83} +(-0.811952 - 43.9754i) q^{87} -100.406i q^{89} +16.2469 q^{91} +(20.5426 - 37.1482i) q^{93} +(32.4085 - 56.1332i) q^{97} +(-71.0532 + 44.5985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9	$ 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.54771	−	2.56994i	−0.515902	−	0.856648i
$3$	−1.54771	−	2.56994i	−0.515902	−	0.856648i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.725042	+	1.25581i	−0.103577	+	0.179401i	−0.913156	−	0.407610i	$-0.866362\pi$
$7$	−0.725042	+	1.25581i	−0.103577	+	0.179401i	0.809579	+	0.587011i	$0.199696\pi$
$8$		0			0
$9$	−4.20921	+	7.95503i	−0.467690	+	0.883893i
$10$		0			0
$11$	8.07235	+	4.66057i	0.733850	+	0.423688i	0.819829	−	0.572609i	$-0.194069\pi$
$11$	8.07235	+	4.66057i	0.733850	+	0.423688i	−0.0859792	+	0.996297i	$0.527402\pi$
$12$		0			0
$13$	−5.60207	−	9.70307i	−0.430928	−	0.746390i	0.566025	−	0.824388i	$-0.308480\pi$
$13$	−5.60207	−	9.70307i	−0.430928	−	0.746390i	−0.996953	+	0.0779982i	$0.975147\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			4.16234i			0.244844i	0.992478	+	0.122422i	$0.0390661\pi$
$17$			4.16234i			0.244844i	−0.992478	+	0.122422i	$0.960934\pi$
$18$		0			0
$19$	3.14773			0.165670			0.0828350	−	0.996563i	$-0.473603\pi$
$19$	3.14773			0.165670			0.0828350	+	0.996563i	$0.473603\pi$
$20$		0			0
$21$	4.34951	−	0.0803085i	0.207120	−	0.00382421i
$22$		0			0
$23$	11.5999	−	6.69719i	0.504342	−	0.291182i	−0.226163	−	0.974090i	$-0.572618\pi$
$23$	11.5999	−	6.69719i	0.504342	−	0.291182i	0.730505	+	0.682907i	$0.239285\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	26.9586	−	1.49463i	0.998467	−	0.0553568i
$28$		0			0
$29$	12.6968	+	7.33048i	0.437819	+	0.252775i	0.702672	−	0.711514i	$-0.251990\pi$
$29$	12.6968	+	7.33048i	0.437819	+	0.252775i	−0.264853	+	0.964289i	$0.585323\pi$
$30$		0			0
$31$	7.07498	+	12.2542i	0.228225	+	0.395297i	0.957282	−	0.289156i	$-0.0933745\pi$
$31$	7.07498	+	12.2542i	0.228225	+	0.395297i	−0.729057	+	0.684453i	$0.760041\pi$
$32$		0			0
$33$	−0.516223	−	27.9587i	−0.0156431	−	0.847232i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	18.0321			0.487354			0.243677	−	0.969856i	$-0.421646\pi$
$37$	18.0321			0.487354			0.243677	+	0.969856i	$0.421646\pi$
$38$		0			0
$39$	−16.2660	+	29.4145i	−0.417076	+	0.754218i
$40$		0			0
$41$	17.6468	−	10.1884i	0.430411	−	0.248498i	−0.269111	−	0.963109i	$-0.586730\pi$
$41$	17.6468	−	10.1884i	0.430411	−	0.248498i	0.699522	+	0.714612i	$0.253396\pi$
$42$		0			0
$43$	16.7364	−	28.9883i	0.389219	−	0.674147i	−0.603126	−	0.797646i	$-0.706078\pi$
$43$	16.7364	−	28.9883i	0.389219	−	0.674147i	0.992345	+	0.123499i	$0.0394117\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.63903	−	0.946292i	−0.0348729	−	0.0201339i	0.482462	−	0.875917i	$-0.339743\pi$
$47$	−1.63903	−	0.946292i	−0.0348729	−	0.0201339i	−0.517335	+	0.855783i	$0.673076\pi$
$48$		0			0
$49$	23.4486	+	40.6142i	0.478543	+	0.828861i
$50$		0			0
$51$	10.6970	−	6.44209i	0.209745	−	0.126315i
$52$		0			0
$53$		−	97.8498i		−	1.84622i	−0.384532	−	0.923112i	$-0.625637\pi$
$53$		−	97.8498i		−	1.84622i	0.384532	−	0.923112i	$-0.374363\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.87176	−	8.08948i	−0.0854695	−	0.141921i
$58$		0			0
$59$	−28.9968	+	16.7413i	−0.491472	+	0.283751i	−0.725185	−	0.688554i	$-0.758246\pi$
$59$	−28.9968	+	16.7413i	−0.491472	+	0.283751i	0.233713	+	0.972306i	$0.424912\pi$
$60$		0			0
$61$	29.6385	−	51.3354i	0.485877	−	0.841564i	−0.513991	−	0.857795i	$-0.671834\pi$
$61$	29.6385	−	51.3354i	0.485877	−	0.841564i	0.999868	+	0.0162318i	$0.00516697\pi$
$62$		0			0
$63$	−6.93816	−	11.0537i	−0.110129	−	0.175456i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−47.9406	−	83.0356i	−0.715532	−	1.23934i	−0.962754	−	0.270379i	$-0.912851\pi$
$67$	−47.9406	−	83.0356i	−0.715532	−	1.23934i	0.247222	−	0.968959i	$-0.420482\pi$
$68$		0			0
$69$	−35.1646	−	19.4457i	−0.509632	−	0.281822i
$70$		0			0
$71$		−	97.3685i		−	1.37139i	−0.727890	−	0.685693i	$-0.759499\pi$
$71$		−	97.3685i		−	1.37139i	0.727890	−	0.685693i	$-0.240501\pi$
$72$		0			0
$73$	90.1349			1.23473			0.617363	−	0.786679i	$-0.288201\pi$
$73$	90.1349			1.23473			0.617363	+	0.786679i	$0.288201\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−11.7056	+	6.75822i	−0.152021	+	0.0877691i
$78$		0			0
$79$	−66.7654	+	115.641i	−0.845132	+	1.46381i	0.0403753	+	0.999185i	$0.487145\pi$
$79$	−66.7654	+	115.641i	−0.845132	+	1.46381i	−0.885507	+	0.464626i	$0.846189\pi$
$80$		0			0
$81$	−45.5651	−	66.9688i	−0.562532	−	0.826775i
$82$		0			0
$83$	−6.48602	−	3.74470i	−0.0781448	−	0.0451169i	0.460418	−	0.887702i	$-0.347699\pi$
$83$	−6.48602	−	3.74470i	−0.0781448	−	0.0451169i	−0.538563	+	0.842585i	$0.681033\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.811952	−	43.9754i	−0.00933278	−	0.505464i
$88$		0			0
$89$		−	100.406i		−	1.12816i	−0.825719	−	0.564081i	$-0.809230\pi$
$89$		−	100.406i		−	1.12816i	0.825719	−	0.564081i	$-0.190770\pi$
$90$		0			0
$91$	16.2469			0.178538
$92$		0			0
$93$	20.5426	−	37.1482i	0.220889	−	0.399443i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	32.4085	−	56.1332i	0.334109	−	0.578693i	−0.649205	−	0.760614i	$-0.724898\pi$
$97$	32.4085	−	56.1332i	0.334109	−	0.578693i	0.983313	+	0.181921i	$0.0582315\pi$
$98$		0			0
$99$	−71.0532	+	44.5985i	−0.717709	+	0.450490i
$100$		0			0
$101$	−71.9956	−	41.5667i	−0.712828	−	0.411551i	0.0992793	−	0.995060i	$-0.468346\pi$
$101$	−71.9956	−	41.5667i	−0.712828	−	0.411551i	−0.812107	+	0.583508i	$0.801680\pi$
$102$		0			0
$103$	19.7330	+	34.1786i	0.191583	+	0.331831i	0.945775	−	0.324823i	$-0.105305\pi$
$103$	19.7330	+	34.1786i	0.191583	+	0.331831i	−0.754192	+	0.656654i	$0.771971\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	18.8472i		−	0.176142i	−0.996114	−	0.0880708i	$-0.971930\pi$
$107$		−	18.8472i		−	0.176142i	0.996114	−	0.0880708i	$-0.0280702\pi$
$108$		0			0
$109$	109.284			1.00260			0.501302	−	0.865273i	$-0.332855\pi$
$109$	109.284			1.00260			0.501302	+	0.865273i	$0.332855\pi$
$110$		0			0
$111$	−27.9084	−	46.3415i	−0.251427	−	0.417491i
$112$		0			0
$113$	150.577	−	86.9358i	1.33254	−	0.769343i	0.346853	−	0.937920i	$-0.387250\pi$
$113$	150.577	−	86.9358i	1.33254	−	0.769343i	0.985689	+	0.168576i	$0.0539170\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	100.768	−	3.72240i	0.861269	−	0.0318154i
$118$		0			0
$119$	−5.22712	−	3.01788i	−0.0439253	−	0.0253603i
$120$		0			0
$121$	−17.0581	−	29.5456i	−0.140976	−	0.244178i
$122$		0			0
$123$	−53.4957	−	29.5827i	−0.434925	−	0.240510i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−112.817			−0.888321			−0.444160	−	0.895947i	$-0.646498\pi$
$127$	−112.817			−0.888321			−0.444160	+	0.895947i	$0.646498\pi$
$128$		0			0
$129$	−100.401	+	1.85379i	−0.778305	+	0.0143705i
$130$		0			0
$131$	111.050	−	64.1149i	0.847711	−	0.489426i	−0.0121666	−	0.999926i	$-0.503873\pi$
$131$	111.050	−	64.1149i	0.847711	−	0.489426i	0.859878	+	0.510500i	$0.170540\pi$
$132$		0			0
$133$	−2.28224	+	3.95295i	−0.0171597	+	0.0297214i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	88.6320	+	51.1717i	0.646949	+	0.373516i	0.787286	−	0.616587i	$-0.211485\pi$
$137$	88.6320	+	51.1717i	0.646949	+	0.373516i	−0.140337	+	0.990104i	$0.544819\pi$
$138$		0			0
$139$	99.2000	+	171.819i	0.713669	+	1.23611i	0.963471	+	0.267814i	$0.0863014\pi$
$139$	99.2000	+	171.819i	0.713669	+	1.23611i	−0.249801	+	0.968297i	$0.580365\pi$
$140$		0			0
$141$	0.104815	+	5.67679i	0.000743368	+	0.0402609i
$142$		0			0
$143$		−	104.435i		−	0.730317i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	68.0846	−	123.121i	0.463161	−	0.837554i
$148$		0			0
$149$	171.716	−	99.1403i	1.15246	−	0.665371i	0.202972	−	0.979185i	$-0.434940\pi$
$149$	171.716	−	99.1403i	1.15246	−	0.665371i	0.949485	+	0.313813i	$0.101607\pi$
$150$		0			0
$151$	−24.6929	+	42.7694i	−0.163529	+	0.283241i	−0.936132	−	0.351649i	$-0.885621\pi$
$151$	−24.6929	+	42.7694i	−0.163529	+	0.283241i	0.772603	+	0.634890i	$0.218954\pi$
$152$		0			0
$153$	−33.1116	−	17.5202i	−0.216416	−	0.114511i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−40.1577	−	69.5551i	−0.255781	−	0.443026i	0.709326	−	0.704880i	$-0.248999\pi$
$157$	−40.1577	−	69.5551i	−0.255781	−	0.443026i	−0.965107	+	0.261854i	$0.915666\pi$
$158$		0			0
$159$	−251.468	+	151.443i	−1.58156	+	0.952471i
$160$		0			0
$161$			19.4230i			0.120640i
$162$		0			0
$163$	2.54453			0.0156106			0.00780530	−	0.999970i	$-0.497515\pi$
$163$	2.54453			0.0156106			0.00780530	+	0.999970i	$0.497515\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−249.194	+	143.872i	−1.49218	+	0.861512i	−0.999960	−	0.00895792i	$-0.997149\pi$
$167$	−249.194	+	143.872i	−1.49218	+	0.861512i	−0.492222	+	0.870470i	$0.663815\pi$
$168$		0			0
$169$	21.7337	−	37.6438i	0.128602	−	0.222744i
$170$		0			0
$171$	−13.2495	+	25.0403i	−0.0774822	+	0.146434i
$172$		0			0
$173$	8.88298	+	5.12859i	0.0513467	+	0.0296450i	0.525454	−	0.850822i	$-0.323896\pi$
$173$	8.88298	+	5.12859i	0.0513467	+	0.0296450i	−0.474107	+	0.880467i	$0.657229\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	87.9029	+	48.6095i	0.496626	+	0.274630i
$178$		0			0
$179$		−	227.398i		−	1.27038i	−0.772355	−	0.635191i	$-0.780921\pi$
$179$		−	227.398i		−	1.27038i	0.772355	−	0.635191i	$-0.219079\pi$
$180$		0			0
$181$	132.277			0.730813			0.365406	−	0.930848i	$-0.380930\pi$
$181$	132.277			0.730813			0.365406	+	0.930848i	$0.380930\pi$
$182$		0			0
$183$	−177.801	+	3.28287i	−0.971588	+	0.0179392i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−19.3989	+	33.5999i	−0.103737	+	0.179679i
$188$		0			0
$189$	−17.6692	+	34.9386i	−0.0934876	+	0.184860i
$190$		0			0
$191$	106.079	+	61.2445i	0.555385	+	0.320652i	0.751291	−	0.659971i	$-0.229431\pi$
$191$	106.079	+	61.2445i	0.555385	+	0.320652i	−0.195906	+	0.980623i	$0.562765\pi$
$192$		0			0
$193$	91.5875	+	158.634i	0.474547	+	0.821939i	0.999575	−	0.0291456i	$-0.00927864\pi$
$193$	91.5875	+	158.634i	0.474547	+	0.821939i	−0.525028	+	0.851085i	$0.675945\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			140.366i			0.712520i	0.934387	+	0.356260i	$0.115948\pi$
$197$			140.366i			0.712520i	−0.934387	+	0.356260i	$0.884052\pi$
$198$		0			0
$199$	103.130			0.518242			0.259121	−	0.965845i	$-0.416567\pi$
$199$	103.130			0.518242			0.259121	+	0.965845i	$0.416567\pi$
$200$		0			0
$201$	−139.199	+	251.719i	−0.692531	+	1.25234i
$202$		0			0
$203$	−18.4114	+	10.6298i	−0.0906964	+	0.0523636i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.45008	+	120.467i	0.0214980	+	0.581967i
$208$		0			0
$209$	25.4096	+	14.6702i	0.121577	+	0.0701924i
$210$		0			0
$211$	149.075	+	258.206i	0.706517	+	1.22372i	0.966141	+	0.258013i	$0.0830679\pi$
$211$	149.075	+	258.206i	0.706517	+	1.22372i	−0.259624	+	0.965710i	$0.583599\pi$
$212$		0			0
$213$	−250.231	+	150.698i	−1.17480	+	0.707501i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−20.5186			−0.0945559
$218$		0			0
$219$	−139.502	−	231.642i	−0.636997	−	1.05772i
$220$		0			0
$221$	40.3875	−	23.3177i	0.182749	−	0.105510i
$222$		0			0
$223$	−62.1214	+	107.597i	−0.278571	+	0.482499i	−0.971030	−	0.238958i	$-0.923194\pi$
$223$	−62.1214	+	107.597i	−0.278571	+	0.482499i	0.692459	+	0.721457i	$0.256527\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	175.493	+	101.321i	0.773098	+	0.446349i	0.833979	−	0.551797i	$-0.186058\pi$
$227$	175.493	+	101.321i	0.773098	+	0.446349i	−0.0608804	+	0.998145i	$0.519391\pi$
$228$		0			0
$229$	179.663	+	311.186i	0.784556	+	1.35889i	0.929264	+	0.369416i	$0.120442\pi$
$229$	179.663	+	311.186i	0.784556	+	1.35889i	−0.144709	+	0.989474i	$0.546224\pi$
$230$		0			0
$231$	35.4851	+	19.6229i	0.153615	+	0.0849478i
$232$		0			0
$233$		−	124.960i		−	0.536309i	−0.963376	−	0.268154i	$-0.913586\pi$
$233$		−	124.960i		−	0.536309i	0.963376	−	0.268154i	$-0.0864137\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	400.524	−	7.39519i	1.68998	−	0.0312033i
$238$		0			0
$239$	257.359	−	148.586i	1.07682	−	0.621700i	0.146781	−	0.989169i	$-0.453109\pi$
$239$	257.359	−	148.586i	1.07682	−	0.621700i	0.930036	+	0.367469i	$0.119775\pi$
$240$		0			0
$241$	−139.411	+	241.467i	−0.578469	+	1.00194i	0.417186	+	0.908821i	$0.363016\pi$
$241$	−139.411	+	241.467i	−0.578469	+	1.00194i	−0.995655	+	0.0931168i	$0.970317\pi$
$242$		0			0
$243$	−101.585	+	220.748i	−0.418043	+	0.908427i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.6338	−	30.5426i	−0.0713919	−	0.123654i
$248$		0			0
$249$	0.414778	+	22.4644i	0.00166577	+	0.0902184i
$250$		0			0
$251$			157.274i			0.626590i	0.949656	+	0.313295i	$0.101433\pi$
$251$			157.274i			0.626590i	−0.949656	+	0.313295i	$0.898567\pi$
$252$		0			0
$253$	124.851			0.493482
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−249.263	+	143.912i	−0.969895	+	0.559969i	−0.899204	−	0.437529i	$-0.855854\pi$
$257$	−249.263	+	143.912i	−0.969895	+	0.559969i	−0.0706910	+	0.997498i	$0.522520\pi$
$258$		0			0
$259$	−13.0740	+	22.6449i	−0.0504789	+	0.0874320i
$260$		0			0
$261$	−111.757	+	70.1476i	−0.428190	+	0.268765i
$262$		0			0
$263$	−148.598	−	85.7929i	−0.565010	−	0.326209i	0.190144	−	0.981756i	$-0.439105\pi$
$263$	−148.598	−	85.7929i	−0.565010	−	0.326209i	−0.755154	+	0.655547i	$0.772438\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−258.039	+	155.400i	−0.966438	+	0.582022i
$268$		0			0
$269$		−	509.332i		−	1.89343i	−0.322076	−	0.946714i	$-0.604381\pi$
$269$		−	509.332i		−	1.89343i	0.322076	−	0.946714i	$-0.395619\pi$
$270$		0			0
$271$	100.133			0.369495			0.184747	−	0.982786i	$-0.440853\pi$
$271$	100.133			0.369495			0.184747	+	0.982786i	$0.440853\pi$
$272$		0			0
$273$	−25.1455	−	41.7537i	−0.0921081	−	0.152944i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	148.986	−	258.051i	0.537855	−	0.931592i	−0.461164	−	0.887315i	$-0.652568\pi$
$277$	148.986	−	258.051i	0.537855	−	0.931592i	0.999019	−	0.0442774i	$-0.0140985\pi$
$278$		0			0
$279$	−127.263	+	4.70111i	−0.456139	+	0.0168498i
$280$		0			0
$281$	−427.177	−	246.631i	−1.52020	−	0.877689i	−0.999716	−	0.0238186i	$-0.992418\pi$
$281$	−427.177	−	246.631i	−1.52020	−	0.877689i	−0.520486	−	0.853870i	$-0.674249\pi$
$282$		0			0
$283$	233.433	+	404.318i	0.824851	+	1.42868i	0.902033	+	0.431667i	$0.142075\pi$
$283$	233.433	+	404.318i	0.824851	+	1.42868i	−0.0771816	+	0.997017i	$0.524592\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			29.5481i			0.102955i
$288$		0			0
$289$	271.675			0.940052
$290$		0			0
$291$	−194.418	+	3.58969i	−0.668103	+	0.0123357i
$292$		0			0
$293$	−142.708	+	82.3923i	−0.487057	+	0.281202i	−0.723353	−	0.690479i	$-0.757400\pi$
$293$	−142.708	+	82.3923i	−0.487057	+	0.281202i	0.236296	+	0.971681i	$0.424067\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	224.585	+	113.577i	0.756178	+	0.382415i
$298$		0			0
$299$	−129.967	−	75.0362i	−0.434671	−	0.250957i
$300$		0			0
$301$	24.2692	+	42.0355i	0.0806286	+	0.139653i
$302$		0			0
$303$	4.60409	+	249.358i	0.0151950	+	0.822962i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−532.817			−1.73556			−0.867781	−	0.496947i	$-0.834454\pi$
$307$	−532.817			−1.73556			−0.867781	+	0.496947i	$0.834454\pi$
$308$		0			0
$309$	57.2961	−	103.611i	0.185424	−	0.335311i
$310$		0			0
$311$	273.525	−	157.920i	0.879501	−	0.507780i	0.00900684	−	0.999959i	$-0.497133\pi$
$311$	273.525	−	157.920i	0.879501	−	0.507780i	0.870494	+	0.492180i	$0.163800\pi$
$312$		0			0
$313$	−243.203	+	421.241i	−0.777008	+	1.34582i	0.156651	+	0.987654i	$0.449930\pi$
$313$	−243.203	+	421.241i	−0.777008	+	1.34582i	−0.933659	+	0.358163i	$0.883403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	187.590	+	108.305i	0.591767	+	0.341657i	0.765796	−	0.643084i	$-0.222345\pi$
$317$	187.590	+	108.305i	0.591767	+	0.341657i	−0.174029	+	0.984741i	$0.555679\pi$
$318$		0			0
$319$	68.3284	+	118.348i	0.214196	+	0.370998i
$320$		0			0
$321$	−48.4361	+	29.1699i	−0.150891	+	0.0908719i
$322$		0			0
$323$			13.1019i			0.0405633i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−169.139	−	280.853i	−0.517245	−	0.858877i
$328$		0			0
$329$	2.37673	−	1.37220i	0.00722409	−	0.00417083i
$330$		0			0
$331$	−41.1383	+	71.2537i	−0.124285	+	0.215268i	−0.921453	−	0.388489i	$-0.872997\pi$
$331$	−41.1383	+	71.2537i	−0.124285	+	0.215268i	0.797168	+	0.603757i	$0.206330\pi$
$332$		0			0
$333$	−75.9009	+	143.446i	−0.227931	+	0.430769i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−148.939	−	257.971i	−0.441957	−	0.765492i	0.555878	−	0.831264i	$-0.312382\pi$
$337$	−148.939	−	257.971i	−0.441957	−	0.765492i	−0.997835	+	0.0657724i	$0.979049\pi$
$338$		0			0
$339$	−456.469	−	252.424i	−1.34652	−	0.744612i
$340$		0			0
$341$			131.894i			0.386785i
$342$		0			0
$343$	−139.059			−0.405420
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−490.844	+	283.389i	−1.41454	+	0.816683i	−0.995812	−	0.0914296i	$-0.970856\pi$
$347$	−490.844	+	283.389i	−1.41454	+	0.816683i	−0.418725	+	0.908113i	$0.637523\pi$
$348$		0			0
$349$	67.0512	−	116.136i	0.192124	−	0.332768i	−0.753830	−	0.657069i	$-0.771796\pi$
$349$	67.0512	−	116.136i	0.192124	−	0.332768i	0.945954	+	0.324301i	$0.105129\pi$
$350$		0			0
$351$	−165.526	−	253.208i	−0.471585	−	0.721390i
$352$		0			0
$353$	548.536	+	316.697i	1.55393	+	0.897160i	0.997816	+	0.0660508i	$0.0210399\pi$
$353$	548.536	+	316.697i	1.55393	+	0.897160i	0.556110	+	0.831109i	$0.312293\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.334272	+	18.1042i	0.000936335	+	0.0507120i
$358$		0			0
$359$		−	669.069i		−	1.86370i	−0.362843	−	0.931850i	$-0.618194\pi$
$359$		−	669.069i		−	1.86370i	0.362843	−	0.931850i	$-0.381806\pi$
$360$		0			0
$361$	−351.092			−0.972553
$362$		0			0
$363$	−49.5294	+	89.5663i	−0.136445	+	0.246739i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−130.592	+	226.191i	−0.355836	+	0.616325i	−0.987261	−	0.159112i	$-0.949137\pi$
$367$	−130.592	+	226.191i	−0.355836	+	0.616325i	0.631425	+	0.775437i	$0.282470\pi$
$368$		0			0
$369$	6.76989	+	183.266i	0.0183466	+	0.496657i
$370$		0			0
$371$	122.881	+	70.9453i	0.331215	+	0.191227i
$372$		0			0
$373$	153.422	+	265.735i	0.411320	+	0.712427i	0.995034	−	0.0995321i	$-0.0317346\pi$
$373$	153.422	+	265.735i	0.411320	+	0.712427i	−0.583714	+	0.811959i	$0.698401\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	164.263i		−	0.435712i
$378$		0			0
$379$	102.483			0.270403			0.135201	−	0.990818i	$-0.456832\pi$
$379$	102.483			0.270403			0.135201	+	0.990818i	$0.456832\pi$
$380$		0			0
$381$	174.607	+	289.932i	0.458287	+	0.760978i
$382$		0			0
$383$	−182.438	+	105.331i	−0.476341	+	0.275015i	−0.718890	−	0.695124i	$-0.755350\pi$
$383$	−182.438	+	105.331i	−0.476341	+	0.275015i	0.242550	+	0.970139i	$0.422016\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	160.156	+	255.157i	0.413840	+	0.659319i
$388$		0			0
$389$	287.637	+	166.067i	0.739426	+	0.426908i	0.821861	−	0.569689i	$-0.192936\pi$
$389$	287.637	+	166.067i	0.739426	+	0.426908i	−0.0824347	+	0.996596i	$0.526270\pi$
$390$		0			0
$391$	27.8760	+	48.2827i	0.0712941	+	0.123485i
$392$		0			0
$393$	−336.645	−	186.162i	−0.856602	−	0.473694i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	314.165			0.791348			0.395674	−	0.918391i	$-0.370511\pi$
$397$	314.165			0.791348			0.395674	+	0.918391i	$0.370511\pi$
$398$		0			0
$399$	13.6911	−	0.252789i	0.0343135	−	0.000633557i
$400$		0			0
$401$	−228.530	+	131.942i	−0.569901	+	0.329032i	−0.757110	−	0.653288i	$-0.773389\pi$
$401$	−228.530	+	131.942i	−0.569901	+	0.329032i	0.187209	+	0.982320i	$0.440056\pi$
$402$		0			0
$403$	79.2690	−	137.298i	0.196697	−	0.340690i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	145.561	+	84.0399i	0.357645	+	0.206486i
$408$		0			0
$409$	−9.96171	−	17.2542i	−0.0243563	−	0.0421863i	0.853590	−	0.520945i	$-0.174420\pi$
$409$	−9.96171	−	17.2542i	−0.0243563	−	0.0421863i	−0.877947	+	0.478759i	$0.841087\pi$
$410$		0			0
$411$	−5.66798	−	306.978i	−0.0137907	−	0.746905i
$412$		0			0
$413$		−	48.5527i		−	0.117561i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	288.034	−	520.864i	0.690728	−	1.24908i
$418$		0			0
$419$	−52.3156	+	30.2044i	−0.124858	+	0.0720870i	−0.561128	−	0.827729i	$-0.689633\pi$
$419$	−52.3156	+	30.2044i	−0.124858	+	0.0720870i	0.436270	+	0.899816i	$0.356299\pi$
$420$		0			0
$421$	120.897	−	209.400i	0.287167	−	0.497387i	−0.685966	−	0.727634i	$-0.740620\pi$
$421$	120.897	−	209.400i	0.287167	−	0.497387i	0.973132	+	0.230247i	$0.0739533\pi$
$422$		0			0
$423$	14.4268	−	9.05537i	0.0341059	−	0.0214075i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	42.9783	+	74.4407i	0.100652	+	0.174334i
$428$		0			0
$429$	−268.393	+	161.635i	−0.625624	+	0.376772i
$430$		0			0
$431$		−	136.406i		−	0.316488i	−0.987400	−	0.158244i	$-0.949417\pi$
$431$		−	136.406i		−	0.316488i	0.987400	−	0.158244i	$-0.0505832\pi$
$432$		0			0
$433$	211.026			0.487357			0.243679	−	0.969856i	$-0.421646\pi$
$433$	211.026			0.487357			0.243679	+	0.969856i	$0.421646\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	36.5133	−	21.0809i	0.0835543	−	0.0482401i
$438$		0			0
$439$	−94.6528	+	163.943i	−0.215610	+	0.373447i	−0.953461	−	0.301516i	$-0.902507\pi$
$439$	−94.6528	+	163.943i	−0.215610	+	0.373447i	0.737851	+	0.674963i	$0.235841\pi$
$440$		0			0
$441$	−421.788	+	15.5809i	−0.956434	+	0.0353308i
$442$		0			0
$443$	1.76983	+	1.02181i	0.00399509	+	0.00230657i	0.501996	−	0.864870i	$-0.332599\pi$
$443$	1.76983	+	1.02181i	0.00399509	+	0.00230657i	−0.498001	+	0.867176i	$0.665932\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−520.551	−	287.860i	−1.16454	−	0.643983i
$448$		0			0
$449$		−	80.3898i		−	0.179042i	−0.995985	−	0.0895210i	$-0.971466\pi$
$449$		−	80.3898i		−	0.179042i	0.995985	−	0.0895210i	$-0.0285336\pi$
$450$		0			0
$451$	189.935			0.421142
$452$		0			0
$453$	148.132	−	2.73508i	0.327003	−	0.00603771i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.4675	−	23.3265i	0.0294694	−	0.0510426i	−0.850915	−	0.525304i	$-0.823952\pi$
$457$	13.4675	−	23.3265i	0.0294694	−	0.0510426i	0.880384	+	0.474262i	$0.157285\pi$
$458$		0			0
$459$	6.22117	+	112.211i	0.0135538	+	0.244468i
$460$		0			0
$461$	−328.251	−	189.516i	−0.712042	−	0.411097i	0.0997749	−	0.995010i	$-0.468188\pi$
$461$	−328.251	−	189.516i	−0.712042	−	0.411097i	−0.811817	+	0.583913i	$0.801521\pi$
$462$		0			0
$463$	−363.508	−	629.614i	−0.785114	−	1.35986i	−0.928931	−	0.370254i	$-0.879271\pi$
$463$	−363.508	−	629.614i	−0.785114	−	1.35986i	0.143816	−	0.989604i	$-0.454063\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	167.449i		−	0.358564i	−0.983798	−	0.179282i	$-0.942623\pi$
$467$		−	167.449i		−	0.358564i	0.983798	−	0.179282i	$-0.0573774\pi$
$468$		0			0
$469$	139.036			0.296452
$470$		0			0
$471$	−116.600	+	210.854i	−0.247559	+	0.447672i
$472$		0			0
$473$	270.204	−	156.002i	0.571256	−	0.329815i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	778.399	+	411.870i	1.63186	+	0.863460i
$478$		0			0
$479$	549.652	+	317.342i	1.14750	+	0.662509i	0.948277	−	0.317445i	$-0.102825\pi$
$479$	549.652	+	317.342i	1.14750	+	0.662509i	0.199223	+	0.979954i	$0.436158\pi$
$480$		0			0
$481$	−101.017	−	174.967i	−0.210015	−	0.363756i
$482$		0			0
$483$	49.9159	−	30.0611i	0.103346	−	0.0622383i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	22.0173			0.0452100			0.0226050	−	0.999744i	$-0.492804\pi$
$487$	22.0173			0.0452100			0.0226050	+	0.999744i	$0.492804\pi$
$488$		0			0
$489$	−3.93818	−	6.53929i	−0.00805355	−	0.0133728i
$490$		0			0
$491$	748.480	−	432.135i	1.52440	−	0.880112i	0.524816	−	0.851216i	$-0.324134\pi$
$491$	748.480	−	432.135i	1.52440	−	0.880112i	0.999582	−	0.0288958i	$-0.00919911\pi$
$492$		0			0
$493$	−30.5120	+	52.8483i	−0.0618904	+	0.107197i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	122.276	+	70.5963i	0.246029	+	0.142045i
$498$		0			0
$499$	−116.676	−	202.089i	−0.233820	−	0.404989i	0.725109	−	0.688634i	$-0.241789\pi$
$499$	−116.676	−	202.089i	−0.233820	−	0.404989i	−0.958929	+	0.283645i	$0.908456\pi$
$500$		0			0
$501$	755.424	+	417.743i	1.50783	+	0.833818i
$502$		0			0
$503$		−	892.050i		−	1.77346i	−0.462289	−	0.886729i	$-0.652972\pi$
$503$		−	892.050i		−	1.77346i	0.462289	−	0.886729i	$-0.347028\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−130.380	+	2.40730i	−0.257159	+	0.00474813i
$508$		0			0
$509$	−520.901	+	300.742i	−1.02338	+	0.590850i	−0.915082	−	0.403269i	$-0.867874\pi$
$509$	−520.901	+	300.742i	−1.02338	+	0.590850i	−0.108300	+	0.994118i	$0.534541\pi$
$510$		0			0
$511$	−65.3517	+	113.192i	−0.127890	+	0.221512i
$512$		0			0
$513$	84.8584	−	4.70470i	0.165416	−	0.00917095i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−8.82052	−	15.2776i	−0.0170610	−	0.0295505i
$518$		0			0
$519$	−0.568062	−	30.7663i	−0.00109453	−	0.0592799i
$520$		0			0
$521$			647.461i			1.24273i	0.783522	+	0.621363i	$0.213421\pi$
$521$			647.461i			1.24273i	−0.783522	+	0.621363i	$0.786579\pi$
$522$		0			0
$523$	367.715			0.703088			0.351544	−	0.936171i	$-0.385657\pi$
$523$	367.715			0.703088			0.351544	+	0.936171i	$0.385657\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−51.0063	+	29.4485i	−0.0967861	+	0.0558795i
$528$		0			0
$529$	−174.795	+	302.754i	−0.330426	+	0.572315i
$530$		0			0
$531$	−11.1241	−	301.139i	−0.0209494	−	0.567116i
$532$		0			0
$533$	−197.718	−	114.152i	−0.370952	−	0.214169i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−584.401	+	351.946i	−1.08827	+	0.655393i
$538$		0			0
$539$			437.136i			0.811013i
$540$		0			0
$541$	533.836			0.986757			0.493379	−	0.869815i	$-0.335762\pi$
$541$	533.836			0.986757			0.493379	+	0.869815i	$0.335762\pi$
$542$		0			0
$543$	−204.726	−	339.944i	−0.377028	−	0.626049i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−185.624	+	321.510i	−0.339349	+	0.587770i	−0.984310	−	0.176445i	$-0.943540\pi$
$547$	−185.624	+	321.510i	−0.339349	+	0.587770i	0.644961	+	0.764215i	$0.276874\pi$
$548$		0			0
$549$	283.620	+	451.857i	0.516612	+	0.823054i
$550$		0			0
$551$	39.9660	+	23.0744i	0.0725335	+	0.0418772i
$552$		0			0
$553$	−96.8155	−	167.689i	−0.175073	−	0.303236i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	677.311i		−	1.21600i	−0.793938	−	0.607999i	$-0.791972\pi$
$557$		−	677.311i		−	1.21600i	0.793938	−	0.607999i	$-0.208028\pi$
$558$		0			0
$559$	−375.034			−0.670902
$560$		0			0
$561$	116.374	−	2.14870i	0.207440	−	0.00383012i
$562$		0			0
$563$	−551.268	+	318.275i	−0.979162	+	0.565319i	−0.902017	−	0.431701i	$-0.857914\pi$
$563$	−551.268	+	318.275i	−0.979162	+	0.565319i	−0.0771448	+	0.997020i	$0.524580\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	117.137	−	8.66593i	0.206590	−	0.0152838i
$568$		0			0
$569$	190.767	+	110.139i	0.335267	+	0.193566i	0.658177	−	0.752863i	$-0.271328\pi$
$569$	190.767	+	110.139i	0.335267	+	0.193566i	−0.322910	+	0.946430i	$0.604661\pi$
$570$		0			0
$571$	302.443	+	523.847i	0.529672	+	0.917420i	0.999401	+	0.0346087i	$0.0110185\pi$
$571$	302.443	+	523.847i	0.529672	+	0.917420i	−0.469728	+	0.882811i	$0.655648\pi$
$572$		0			0
$573$	−6.78368	−	367.404i	−0.0118389	−	0.641194i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	633.656			1.09819			0.549095	−	0.835760i	$-0.314972\pi$
$577$	633.656			1.09819			0.549095	+	0.835760i	$0.314972\pi$
$578$		0			0
$579$	265.930	−	480.894i	0.459292	−	0.830560i
$580$		0			0
$581$	9.40527	−	5.43014i	0.0161881	−	0.00934619i
$582$		0			0
$583$	456.036	−	789.878i	0.782223	−	1.35485i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	717.643	+	414.331i	1.22256	+	0.705845i	0.965463	−	0.260540i	$-0.0839007\pi$
$587$	717.643	+	414.331i	1.22256	+	0.705845i	0.257097	+	0.966386i	$0.417234\pi$
$588$		0			0
$589$	22.2701	+	38.5730i	0.0378100	+	0.0654889i
$590$		0			0
$591$	360.734	−	217.246i	0.610378	−	0.367591i
$592$		0			0
$593$		−	304.718i		−	0.513858i	−0.966430	−	0.256929i	$-0.917289\pi$
$593$		−	304.718i		−	0.513858i	0.966430	−	0.256929i	$-0.0827106\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−159.615	−	265.039i	−0.267362	−	0.443951i
$598$		0			0
$599$	−690.368	+	398.584i	−1.15253	+	0.665416i	−0.949504	−	0.313756i	$-0.898413\pi$
$599$	−690.368	+	398.584i	−1.15253	+	0.665416i	−0.203031	+	0.979172i	$0.565079\pi$
$600$		0			0
$601$	432.523	−	749.152i	0.719672	−	1.24651i	−0.241457	−	0.970411i	$-0.577625\pi$
$601$	432.523	−	749.152i	0.719672	−	1.24651i	0.961130	−	0.276098i	$-0.0890413\pi$
$602$		0			0
$603$	862.343	−	31.8551i	1.43009	−	0.0528277i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−72.7532	−	126.012i	−0.119857	−	0.207598i	0.799854	−	0.600195i	$-0.204910\pi$
$607$	−72.7532	−	126.012i	−0.119857	−	0.207598i	−0.919711	+	0.392596i	$0.871577\pi$
$608$		0			0
$609$	55.8134	+	30.8643i	0.0916476	+	0.0506804i
$610$		0			0
$611$			21.2048i			0.0347050i
$612$		0			0
$613$	−577.301			−0.941764			−0.470882	−	0.882196i	$-0.656064\pi$
$613$	−577.301			−0.941764			−0.470882	+	0.882196i	$0.656064\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−467.989	+	270.194i	−0.758491	+	0.437915i	−0.828754	−	0.559613i	$-0.810950\pi$
$617$	−467.989	+	270.194i	−0.758491	+	0.437915i	0.0702626	+	0.997529i	$0.477616\pi$
$618$		0			0
$619$	−230.899	+	399.930i	−0.373020	+	0.646090i	−0.990029	−	0.140867i	$-0.955011\pi$
$619$	−230.899	+	399.930i	−0.373020	+	0.646090i	0.617008	+	0.786957i	$0.288344\pi$
$620$		0			0
$621$	302.706	−	197.884i	0.487450	−	0.318654i
$622$		0			0
$623$	126.091	+	72.7989i	0.202394	+	0.116852i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.62493	−	88.0063i	−0.00259159	−	0.140361i
$628$		0			0
$629$			75.0558i			0.119326i
$630$		0			0
$631$	−752.449			−1.19247			−0.596235	−	0.802810i	$-0.703338\pi$
$631$	−752.449			−1.19247			−0.596235	+	0.802810i	$0.703338\pi$
$632$		0			0
$633$	432.849	−	782.741i	0.683806	−	1.23656i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	262.722	−	455.047i	0.412436	−	0.714360i
$638$		0			0
$639$	774.569	+	409.844i	1.21216	+	0.641384i
$640$		0			0
$641$	−662.504	−	382.497i	−1.03355	−	0.596719i	−0.115549	−	0.993302i	$-0.536863\pi$
$641$	−662.504	−	382.497i	−1.03355	−	0.596719i	−0.917999	+	0.396583i	$0.870196\pi$
$642$		0			0
$643$	−187.638	−	324.999i	−0.291817	−	0.505441i	0.682423	−	0.730958i	$-0.260926\pi$
$643$	−187.638	−	324.999i	−0.291817	−	0.505441i	−0.974239	+	0.225517i	$0.927593\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1241.27i		−	1.91850i	−0.282557	−	0.959251i	$-0.591183\pi$
$647$		−	1241.27i		−	1.91850i	0.282557	−	0.959251i	$-0.408817\pi$
$648$		0			0
$649$	−312.097			−0.480889
$650$		0			0
$651$	31.7568	+	52.7317i	0.0487816	+	0.0810011i
$652$		0			0
$653$	725.975	−	419.142i	1.11175	−	0.641871i	0.172470	−	0.985015i	$-0.444825\pi$
$653$	725.975	−	419.142i	1.11175	−	0.641871i	0.939283	+	0.343144i	$0.111492\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−379.397	+	717.027i	−0.577469	+	1.09136i
$658$		0			0
$659$	−173.535	−	100.190i	−0.263330	−	0.152034i	0.362523	−	0.931975i	$-0.381916\pi$
$659$	−173.535	−	100.190i	−0.263330	−	0.152034i	−0.625853	+	0.779941i	$0.715249\pi$
$660$		0			0
$661$	−550.664	−	953.778i	−0.833077	−	1.44293i	−0.895586	−	0.444888i	$-0.853244\pi$
$661$	−550.664	−	953.778i	−0.833077	−	1.44293i	0.0625092	−	0.998044i	$-0.480090\pi$
$662$		0			0
$663$	−122.433	−	67.7046i	−0.184666	−	0.102118i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	196.374			0.294414
$668$		0			0
$669$	372.665	−	6.88080i	0.557047	−	0.0102852i
$670$		0			0
$671$	478.504	−	276.265i	0.713121	−	0.411721i
$672$		0			0
$673$	241.487	−	418.267i	0.358821	−	0.621497i	−0.628943	−	0.777451i	$-0.716512\pi$
$673$	241.487	−	418.267i	0.358821	−	0.621497i	0.987764	+	0.155955i	$0.0498455\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	457.500	+	264.138i	0.675776	+	0.390159i	0.798262	−	0.602311i	$-0.205753\pi$
$677$	457.500	+	264.138i	0.675776	+	0.390159i	−0.122486	+	0.992470i	$0.539087\pi$
$678$		0			0
$679$	46.9951	+	81.3979i	0.0692122	+	0.119879i
$680$		0			0
$681$	−11.2227	−	607.823i	−0.0164798	−	0.892545i
$682$		0			0
$683$			620.705i			0.908792i	0.890800	+	0.454396i	$0.150145\pi$
$683$			620.705i			0.908792i	−0.890800	+	0.454396i	$0.849855\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	521.664	−	943.349i	0.759336	−	1.37314i
$688$		0			0
$689$	−949.444	+	548.161i	−1.37800	+	0.795590i
$690$		0			0
$691$	−245.260	+	424.802i	−0.354934	+	0.614764i	−0.987107	−	0.160063i	$-0.948830\pi$
$691$	−245.260	+	424.802i	−0.354934	+	0.614764i	0.632172	+	0.774828i	$0.282163\pi$
$692$		0			0
$693$	−4.49064	−	121.565i	−0.00647999	−	0.175419i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	42.4077	+	73.4522i	0.0608431	+	0.105383i
$698$		0			0
$699$	−321.140	+	193.401i	−0.459427	+	0.276683i
$700$		0			0
$701$			204.463i			0.291674i	0.989309	+	0.145837i	$0.0465874\pi$
$701$			204.463i			0.291674i	−0.989309	+	0.145837i	$0.953413\pi$
$702$		0			0
$703$	56.7602			0.0807399
$704$		0			0
$705$		0			0
$706$		0			0
$707$	104.400	−	60.2752i	0.147666	−	0.0852549i
$708$		0			0
$709$	603.753	−	1045.73i	0.851556	−	1.47494i	−0.0282478	−	0.999601i	$-0.508993\pi$
$709$	603.753	−	1045.73i	0.851556	−	1.47494i	0.879804	−	0.475337i	$-0.157674\pi$
$710$		0			0
$711$	−638.899	−	1017.88i	−0.898592	−	1.43162i
$712$		0			0
$713$	164.138	+	94.7649i	0.230207	+	0.132910i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−780.175	−	431.430i	−1.08811	−	0.601716i
$718$		0			0
$719$			890.720i			1.23883i	0.785063	+	0.619416i	$0.212630\pi$
$719$			890.720i			1.23883i	−0.785063	+	0.619416i	$0.787370\pi$
$720$		0			0
$721$	−57.2291			−0.0793746
$722$		0			0
$723$	836.324	−	15.4417i	1.15674	−	0.0213578i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−46.9200	+	81.2678i	−0.0645392	+	0.111785i	−0.896489	−	0.443065i	$-0.853891\pi$
$727$	−46.9200	+	81.2678i	−0.0645392	+	0.111785i	0.831950	+	0.554850i	$0.187224\pi$
$728$		0			0
$729$	724.532	−	80.5864i	0.993871	−	0.110544i
$730$		0			0
$731$	120.659	+	69.6627i	0.165061	+	0.0952978i
$732$		0			0
$733$	−81.8500	−	141.768i	−0.111664	−	0.193409i	0.804777	−	0.593577i	$-0.202285\pi$
$733$	−81.8500	−	141.768i	−0.111664	−	0.193409i	−0.916441	+	0.400169i	$0.868952\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	893.723i		−	1.21265i
$738$		0			0
$739$	−808.628			−1.09422			−0.547109	−	0.837061i	$-0.684272\pi$
$739$	−808.628			−1.09422			−0.547109	+	0.837061i	$0.684272\pi$
$740$		0			0
$741$	−51.2009	+	92.5889i	−0.0690970	+	0.124951i
$742$		0			0
$743$	−928.259	+	535.931i	−1.24934	+	0.721307i	−0.970978	−	0.239170i	$-0.923125\pi$
$743$	−928.259	+	535.931i	−1.24934	+	0.721307i	−0.278362	+	0.960476i	$0.589791\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	57.0902	−	35.8342i	0.0764260	−	0.0479709i
$748$		0			0
$749$	23.6685	+	13.6650i	0.0316001	+	0.0182443i
$750$		0			0
$751$	−212.693	−	368.396i	−0.283214	−	0.490540i	0.688961	−	0.724799i	$-0.258067\pi$
$751$	−212.693	−	368.396i	−0.283214	−	0.490540i	−0.972174	+	0.234258i	$0.924734\pi$
$752$		0			0
$753$	404.185	−	243.414i	0.536767	−	0.323259i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−367.915			−0.486017			−0.243008	−	0.970024i	$-0.578134\pi$
$757$	−367.915			−0.486017			−0.243008	+	0.970024i	$0.578134\pi$
$758$		0			0
$759$	−193.233	−	320.860i	−0.254588	−	0.422740i
$760$		0			0
$761$	−221.377	+	127.812i	−0.290902	+	0.167953i	−0.638349	−	0.769747i	$-0.720382\pi$
$761$	−221.377	+	127.812i	−0.290902	+	0.167953i	0.347446	+	0.937700i	$0.387049\pi$
$762$		0			0
$763$	−79.2354	+	137.240i	−0.103847	+	0.179868i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	324.885	+	187.572i	0.423578	+	0.244553i
$768$		0			0
$769$	−753.541	−	1305.17i	−0.979898	−	1.69723i	−0.662722	−	0.748865i	$-0.730599\pi$
$769$	−753.541	−	1305.17i	−0.979898	−	1.69723i	−0.317175	−	0.948367i	$-0.602734\pi$
$770$		0			0
$771$	755.632	+	417.858i	0.980067	+	0.541969i
$772$		0			0
$773$			409.392i			0.529614i	0.964301	+	0.264807i	$0.0853083\pi$
$773$			409.392i			0.529614i	−0.964301	+	0.264807i	$0.914692\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	78.4308	−	1.44813i	0.100941	−	0.00186375i
$778$		0			0
$779$	55.5475	−	32.0703i	0.0713061	−	0.0411686i
$780$		0			0
$781$	453.793	−	785.992i	0.581041	−	1.00639i
$782$		0			0
$783$	353.243	+	178.642i	0.451141	+	0.228151i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	572.046	+	990.812i	0.726869	+	1.25897i	0.958200	+	0.286098i	$0.0923584\pi$
$787$	572.046	+	990.812i	0.726869	+	1.25897i	−0.231332	+	0.972875i	$0.574308\pi$
$788$		0			0
$789$	9.50275	+	514.670i	0.0120440	+	0.652306i
$790$		0			0
$791$			252.128i			0.318747i
$792$		0			0
$793$	−664.147			−0.837513
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−966.792	+	558.177i	−1.21304	+	0.700348i	−0.963420	−	0.267996i	$-0.913639\pi$
$797$	−966.792	+	558.177i	−1.21304	+	0.700348i	−0.249619	+	0.968344i	$0.580305\pi$
$798$		0			0
$799$	3.93879	−	6.82219i	0.00492965	−	0.00853841i
$800$		0			0
$801$	798.737	+	422.632i	0.997175	+	0.527630i
$802$		0			0
$803$	727.601	+	420.080i	0.906103	+	0.523139i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1308.95	+	788.296i	−1.62200	+	0.976823i
$808$		0			0
$809$			352.291i			0.435465i	0.976009	+	0.217732i	$0.0698660\pi$
$809$			352.291i			0.435465i	−0.976009	+	0.217732i	$0.930134\pi$
$810$		0			0
$811$	−241.622			−0.297931			−0.148965	−	0.988842i	$-0.547594\pi$
$811$	−241.622			−0.297931			−0.148965	+	0.988842i	$0.547594\pi$
$812$		0			0
$813$	−154.977	−	257.336i	−0.190623	−	0.316527i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	52.6817	−	91.2474i	0.0644819	−	0.111686i
$818$		0			0
$819$	−68.3868	+	129.245i	−0.0835004	+	0.157808i
$820$		0			0
$821$	−356.746	−	205.967i	−0.434526	−	0.250874i	0.266747	−	0.963767i	$-0.414051\pi$
$821$	−356.746	−	205.967i	−0.434526	−	0.250874i	−0.701273	+	0.712893i	$0.747385\pi$
$822$		0			0
$823$	−424.417	−	735.112i	−0.515695	−	0.893211i	−0.999834	−	0.0182193i	$-0.994200\pi$
$823$	−424.417	−	735.112i	−0.515695	−	0.893211i	0.484139	−	0.874991i	$-0.339133\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1554.56i		−	1.87976i	−0.341500	−	0.939882i	$-0.610935\pi$
$827$		−	1554.56i		−	1.87976i	0.341500	−	0.939882i	$-0.389065\pi$
$828$		0			0
$829$	−354.980			−0.428202			−0.214101	−	0.976811i	$-0.568682\pi$
$829$	−354.980			−0.428202			−0.214101	+	0.976811i	$0.568682\pi$
$830$		0			0
$831$	−893.763	+	16.5022i	−1.07553	+	0.0198583i
$832$		0			0
$833$	−169.050	+	97.6013i	−0.202942	+	0.117168i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	209.047	+	319.782i	0.249757	+	0.382057i
$838$		0			0
$839$	855.669	+	494.021i	1.01987	+	0.588821i	0.914066	−	0.405566i	$-0.132926\pi$
$839$	855.669	+	494.021i	1.01987	+	0.588821i	0.105802	+	0.994387i	$0.466259\pi$
$840$		0			0
$841$	−313.028	−	542.181i	−0.372210	−	0.644686i
$842$		0			0
$843$	27.3178	+	1479.53i	0.0324054	+	1.75508i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	49.4715			0.0584079
$848$		0			0
$849$	677.788	−	1225.67i	0.798336	−	1.44367i
$850$		0			0
$851$	209.170	−	120.764i	0.245793	−	0.141909i
$852$		0			0
$853$	−21.7215	+	37.6227i	−0.0254648	+	0.0441064i	−0.878477	−	0.477785i	$-0.841440\pi$
$853$	−21.7215	+	37.6227i	−0.0254648	+	0.0441064i	0.853012	+	0.521891i	$0.174773\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−677.278	−	391.027i	−0.790289	−	0.456274i	0.0497751	−	0.998760i	$-0.484150\pi$
$857$	−677.278	−	391.027i	−0.790289	−	0.456274i	−0.840064	+	0.542487i	$0.817483\pi$
$858$		0			0
$859$	−543.576	−	941.502i	−0.632801	−	1.09604i	−0.986976	−	0.160865i	$-0.948572\pi$
$859$	−543.576	−	941.502i	−0.632801	−	1.09604i	0.354175	−	0.935179i	$-0.384762\pi$
$860$		0			0
$861$	75.9369	−	45.7318i	0.0881962	−	0.0531147i
$862$		0			0
$863$		−	62.4433i		−	0.0723561i	−0.999345	−	0.0361780i	$-0.988482\pi$
$863$		−	62.4433i		−	0.0723561i	0.999345	−	0.0361780i	$-0.0115183\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−420.473	−	698.189i	−0.484975	−	0.805293i
$868$		0			0
$869$	−1077.91	+	622.330i	−1.24040	+	0.716145i
$870$		0			0
$871$	−537.133	+	930.342i	−0.616686	+	1.06813i
$872$		0			0
$873$	310.127	+	494.087i	0.355243	+	0.565965i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	366.136	+	634.167i	0.417487	+	0.723109i	0.995686	−	0.0927866i	$-0.0295774\pi$
$877$	366.136	+	634.167i	0.417487	+	0.723109i	−0.578199	+	0.815896i	$0.696244\pi$
$878$		0			0
$879$	432.613	+	239.231i	0.492165	+	0.272163i
$880$		0			0
$881$			618.530i			0.702077i	0.936361	+	0.351038i	$0.114171\pi$
$881$			618.530i			0.702077i	−0.936361	+	0.351038i	$0.885829\pi$
$882$		0			0
$883$	291.483			0.330106			0.165053	−	0.986285i	$-0.447221\pi$
$883$	291.483			0.330106			0.165053	+	0.986285i	$0.447221\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	861.262	−	497.250i	0.970983	−	0.560597i	0.0714472	−	0.997444i	$-0.477238\pi$
$887$	861.262	−	497.250i	0.970983	−	0.560597i	0.899536	+	0.436847i	$0.143905\pi$
$888$		0			0
$889$	81.7969	−	141.676i	0.0920100	−	0.159366i
$890$		0			0
$891$	−55.7046	−	752.955i	−0.0625192	−	0.845067i
$892$		0			0
$893$	−5.15921	−	2.97867i	−0.00577739	−	0.00333558i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	8.31130	+	450.141i	0.00926566	+	0.501829i
$898$		0			0
$899$			207.452i			0.230758i
$900$		0			0
$901$	407.285			0.452036
$902$		0			0
$903$	70.4672	−	127.429i	0.0780368	−	0.141118i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−144.475	+	250.238i	−0.159289	+	0.275896i	−0.934612	−	0.355668i	$-0.884253\pi$
$907$	−144.475	+	250.238i	−0.159289	+	0.275896i	0.775324	+	0.631564i	$0.217587\pi$
$908$		0			0
$909$	633.709	−	397.765i	0.697150	−	0.437585i
$910$		0			0
$911$	−361.910	−	208.949i	−0.397267	−	0.229362i	0.288037	−	0.957619i	$-0.406997\pi$
$911$	−361.910	−	208.949i	−0.397267	−	0.229362i	−0.685304	+	0.728257i	$0.740331\pi$
$912$		0			0
$913$	−34.9049	−	60.4571i	−0.0382310	−	0.0662181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			185.944i			0.202774i
$918$		0			0
$919$	−200.015			−0.217644			−0.108822	−	0.994061i	$-0.534708\pi$
$919$	−200.015			−0.217644			−0.108822	+	0.994061i	$0.534708\pi$
$920$		0			0
$921$	824.645	+	1369.31i	0.895380	+	1.48676i
$922$		0			0
$923$	−944.773	+	545.465i	−1.02359	+	0.590969i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−354.952	+	13.1120i	−0.382904	+	0.0141445i
$928$		0			0
$929$	895.535	+	517.037i	0.963978	+	0.556553i	0.897395	−	0.441228i	$-0.145457\pi$
$929$	895.535	+	517.037i	0.963978	+	0.556553i	0.0665827	+	0.997781i	$0.478790\pi$
$930$		0			0
$931$	73.8099	+	127.843i	0.0792803	+	0.137317i
$932$		0			0
$933$	−829.180	−	458.530i	−0.888725	−	0.491457i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−14.6999			−0.0156883			−0.00784415	−	0.999969i	$-0.502497\pi$
$937$	−14.6999			−0.0156883			−0.00784415	+	0.999969i	$0.502497\pi$
$938$		0			0
$939$	1458.97	−	26.9382i	1.55375	−	0.0286881i
$940$		0			0
$941$	−592.727	+	342.211i	−0.629890	+	0.363667i	−0.780710	−	0.624894i	$-0.785142\pi$
$941$	−592.727	+	342.211i	−0.629890	+	0.363667i	0.150819	+	0.988561i	$0.451809\pi$
$942$		0			0
$943$	136.467	−	236.368i	0.144716	−	0.250656i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1498.65	+	865.244i	1.58252	+	0.913669i	0.994490	+	0.104830i	$0.0334298\pi$
$947$	1498.65	+	865.244i	1.58252	+	0.913669i	0.588030	+	0.808839i	$0.299904\pi$
$948$		0			0
$949$	−504.942	−	874.585i	−0.532078	−	0.921586i
$950$		0			0
$951$	−11.9963	−	649.721i	−0.0126144	−	0.683198i
$952$		0			0
$953$			1253.61i			1.31544i	0.753264	+	0.657719i	$0.228478\pi$
$953$			1253.61i			1.31544i	−0.753264	+	0.657719i	$0.771522\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	198.396	−	358.769i	0.207310	−	0.374889i
$958$		0			0
$959$	−128.524	+	74.2034i	−0.134019	+	0.0773758i
$960$		0			0
$961$	380.389	−	658.854i	0.395827	−	0.685592i
$962$		0			0
$963$	149.930	+	79.3316i	0.155690	+	0.0823797i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	551.906	+	955.930i	0.570741	+	0.988552i	0.996490	+	0.0837107i	$0.0266772\pi$
$967$	551.906	+	955.930i	0.570741	+	0.988552i	−0.425749	+	0.904841i	$0.639990\pi$
$968$		0			0
$969$	33.6712	−	20.2779i	0.0347484	−	0.0209267i
$970$		0			0
$971$			1839.18i			1.89411i	0.321072	+	0.947055i	$0.395957\pi$
$971$			1839.18i			1.89411i	−0.321072	+	0.947055i	$0.604043\pi$
$972$		0			0
$973$	−287.697			−0.295680
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−678.313	+	391.624i	−0.694281	+	0.400843i	−0.805214	−	0.592984i	$-0.797950\pi$
$977$	−678.313	+	391.624i	−0.694281	+	0.400843i	0.110933	+	0.993828i	$0.464616\pi$
$978$		0			0
$979$	467.952	−	810.516i	0.477989	−	0.827902i
$980$		0			0
$981$	−459.998	+	869.356i	−0.468907	+	0.886194i
$982$		0			0
$983$	−523.845	−	302.442i	−0.532904	−	0.307672i	0.209294	−	0.977853i	$-0.432883\pi$
$983$	−523.845	−	302.442i	−0.532904	−	0.307672i	−0.742198	+	0.670180i	$0.766217\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−7.20496	−	3.98428i	−0.00729986	−	0.00403676i
$988$		0			0
$989$		−	448.348i		−	0.453334i
$990$		0			0
$991$	−336.871			−0.339931			−0.169965	−	0.985450i	$-0.554366\pi$
$991$	−336.871			−0.339931			−0.169965	+	0.985450i	$0.554366\pi$
$992$		0			0
$993$	246.788	−	4.55664i	0.248528	−	0.00458876i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−172.046	+	297.993i	−0.172564	+	0.298890i	−0.939316	−	0.343054i	$-0.888539\pi$
$997$	−172.046	+	297.993i	−0.172564	+	0.298890i	0.766752	+	0.641944i	$0.221872\pi$
$998$		0			0
$999$	486.120	−	26.9514i	0.486607	−	0.0269783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.d.101.4	✓	16
3.2	odd	2		2700.3.p.e.1601.4		16
5.2	odd	4		900.3.u.d.749.3		32
5.3	odd	4		900.3.u.d.749.14		32
5.4	even	2		900.3.p.e.101.5	yes	16
9.4	even	3		2700.3.p.e.2501.4		16
9.5	odd	6	inner	900.3.p.d.401.4	yes	16
15.2	even	4		2700.3.u.d.2249.8		32
15.8	even	4		2700.3.u.d.2249.9		32
15.14	odd	2		2700.3.p.d.1601.5		16
45.4	even	6		2700.3.p.d.2501.5		16
45.13	odd	12		2700.3.u.d.449.8		32
45.14	odd	6		900.3.p.e.401.5	yes	16
45.22	odd	12		2700.3.u.d.449.9		32
45.23	even	12		900.3.u.d.149.3		32
45.32	even	12		900.3.u.d.149.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.4	✓	16	1.1	even	1	trivial
900.3.p.d.401.4	yes	16	9.5	odd	6	inner
900.3.p.e.101.5	yes	16	5.4	even	2
900.3.p.e.401.5	yes	16	45.14	odd	6
900.3.u.d.149.3		32	45.23	even	12
900.3.u.d.149.14		32	45.32	even	12
900.3.u.d.749.3		32	5.2	odd	4
900.3.u.d.749.14		32	5.3	odd	4
2700.3.p.d.1601.5		16	15.14	odd	2
2700.3.p.d.2501.5		16	45.4	even	6
2700.3.p.e.1601.4		16	3.2	odd	2
2700.3.p.e.2501.4		16	9.4	even	3
2700.3.u.d.449.8		32	45.13	odd	12
2700.3.u.d.449.9		32	45.22	odd	12
2700.3.u.d.2249.8		32	15.2	even	4
2700.3.u.d.2249.9		32	15.8	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54771 - 2.56994i) q^{3} +(-0.725042 + 1.25581i) q^{7} +(-4.20921 + 7.95503i) q^{9} +O(q^{10})\)	\(q+(-1.54771 - 2.56994i) q^{3} +(-0.725042 + 1.25581i) q^{7} +(-4.20921 + 7.95503i) q^{9} +(8.07235 + 4.66057i) q^{11} +(-5.60207 - 9.70307i) q^{13} +4.16234i q^{17} +3.14773 q^{19} +(4.34951 - 0.0803085i) q^{21} +(11.5999 - 6.69719i) q^{23} +(26.9586 - 1.49463i) q^{27} +(12.6968 + 7.33048i) q^{29} +(7.07498 + 12.2542i) q^{31} +(-0.516223 - 27.9587i) q^{33} +18.0321 q^{37} +(-16.2660 + 29.4145i) q^{39} +(17.6468 - 10.1884i) q^{41} +(16.7364 - 28.9883i) q^{43} +(-1.63903 - 0.946292i) q^{47} +(23.4486 + 40.6142i) q^{49} +(10.6970 - 6.44209i) q^{51} -97.8498i q^{53} +(-4.87176 - 8.08948i) q^{57} +(-28.9968 + 16.7413i) q^{59} +(29.6385 - 51.3354i) q^{61} +(-6.93816 - 11.0537i) q^{63} +(-47.9406 - 83.0356i) q^{67} +(-35.1646 - 19.4457i) q^{69} -97.3685i q^{71} +90.1349 q^{73} +(-11.7056 + 6.75822i) q^{77} +(-66.7654 + 115.641i) q^{79} +(-45.5651 - 66.9688i) q^{81} +(-6.48602 - 3.74470i) q^{83} +(-0.811952 - 43.9754i) q^{87} -100.406i q^{89} +16.2469 q^{91} +(20.5426 - 37.1482i) q^{93} +(32.4085 - 56.1332i) q^{97} +(-71.0532 + 44.5985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9}+O(q^{10}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9	\( 16 q - 2 q^{3} + q^{7} + 14 q^{9} + 10 q^{13} + 2 q^{19} + q^{21} - 27 q^{23} + 16 q^{27} + 9 q^{29} + 8 q^{31} - 36 q^{33} + 22 q^{37} + 19 q^{39} + 54 q^{41} - 44 q^{43} + 108 q^{47} - 45 q^{49} + 90 q^{51} + 68 q^{57} + 9 q^{59} - 55 q^{61} + 107 q^{63} + 28 q^{67} - 147 q^{69} - 86 q^{73} - 342 q^{77} + 11 q^{79} - 130 q^{81} + 306 q^{83} - 375 q^{87} - 134 q^{91} + 83 q^{93} - 41 q^{97} + 252 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 + q^7 + 14 * q^9 + 10 * q^13 + 2 * q^19 + q^21 - 27 * q^23 + 16 * q^27 + 9 * q^29 + 8 * q^31 - 36 * q^33 + 22 * q^37 + 19 * q^39 + 54 * q^41 - 44 * q^43 + 108 * q^47 - 45 * q^49 + 90 * q^51 + 68 * q^57 + 9 * q^59 - 55 * q^61 + 107 * q^63 + 28 * q^67 - 147 * q^69 - 86 * q^73 - 342 * q^77 + 11 * q^79 - 130 * q^81 + 306 * q^83 - 375 * q^87 - 134 * q^91 + 83 * q^93 - 41 * q^97 + 252 * q^99

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