LMFDB - Embedded newform 900.3.p.e.401.5

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			401.5
Root			$-2.99949 - 0.0553819i$ of defining polynomial
Character	$\chi$	$=$	900.401
Dual form			900.3.p.e.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54771 - 2.56994i) q^{3} +(0.725042 + 1.25581i) q^{7} +(-4.20921 - 7.95503i) q^{9} +O(q^{10})$	\(q+(1.54771 - 2.56994i) q^{3} +(0.725042 + 1.25581i) q^{7} +(-4.20921 - 7.95503i) q^{9} +(8.07235 - 4.66057i) q^{11} +(5.60207 - 9.70307i) q^{13} +4.16234i q^{17} +3.14773 q^{19} +(4.34951 + 0.0803085i) q^{21} +(-11.5999 - 6.69719i) q^{23} +(-26.9586 - 1.49463i) q^{27} +(12.6968 - 7.33048i) q^{29} +(7.07498 - 12.2542i) q^{31} +(0.516223 - 27.9587i) q^{33} -18.0321 q^{37} +(-16.2660 - 29.4145i) q^{39} +(17.6468 + 10.1884i) q^{41} +(-16.7364 - 28.9883i) q^{43} +(1.63903 - 0.946292i) q^{47} +(23.4486 - 40.6142i) q^{49} +(10.6970 + 6.44209i) q^{51} -97.8498i q^{53} +(4.87176 - 8.08948i) q^{57} +(-28.9968 - 16.7413i) q^{59} +(29.6385 + 51.3354i) q^{61} +(6.93816 - 11.0537i) q^{63} +(47.9406 - 83.0356i) q^{67} +(-35.1646 + 19.4457i) q^{69} +97.3685i q^{71} -90.1349 q^{73} +(11.7056 + 6.75822i) q^{77} +(-66.7654 - 115.641i) q^{79} +(-45.5651 + 66.9688i) q^{81} +(6.48602 - 3.74470i) q^{83} +(0.811952 - 43.9754i) q^{87} +100.406i q^{89} +16.2469 q^{91} +(-20.5426 - 37.1482i) q^{93} +(-32.4085 - 56.1332i) q^{97} +(-71.0532 - 44.5985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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	$-0.133638\pi$
$7$	0.725042	+	1.25581i	0.103577	+	0.179401i	−0.809579	+	0.587011i	$0.800304\pi$
$8$		0			0
$9$	−4.20921	−	7.95503i	−0.467690	−	0.883893i
$10$		0			0
$11$	8.07235	−	4.66057i	0.733850	−	0.423688i	−0.0859792	−	0.996297i	$-0.527402\pi$
$11$	8.07235	−	4.66057i	0.733850	−	0.423688i	0.819829	+	0.572609i	$0.194069\pi$
$12$		0			0
$13$	5.60207	−	9.70307i	0.430928	−	0.746390i	−0.566025	−	0.824388i	$-0.691520\pi$
$13$	5.60207	−	9.70307i	0.430928	−	0.746390i	0.996953	+	0.0779982i	$0.0248528\pi$
$14$		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	$-0.427382\pi$
$23$	−11.5999	−	6.69719i	−0.504342	−	0.291182i	−0.730505	+	0.682907i	$0.760715\pi$
$24$		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	−0.264853	−	0.964289i	$-0.585323\pi$
$29$	12.6968	−	7.33048i	0.437819	−	0.252775i	0.702672	+	0.711514i	$0.251990\pi$
$30$		0			0
$31$	7.07498	−	12.2542i	0.228225	−	0.395297i	−0.729057	−	0.684453i	$-0.760041\pi$
$31$	7.07498	−	12.2542i	0.228225	−	0.395297i	0.957282	+	0.289156i	$0.0933745\pi$
$32$		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	$-0.578354\pi$
$37$	−18.0321			−0.487354			−0.243677	+	0.969856i	$0.578354\pi$
$38$		0			0
$39$	−16.2660	−	29.4145i	−0.417076	−	0.754218i
$40$		0			0
$41$	17.6468	+	10.1884i	0.430411	+	0.248498i	0.699522	−	0.714612i	$-0.253396\pi$
$41$	17.6468	+	10.1884i	0.430411	+	0.248498i	−0.269111	+	0.963109i	$0.586730\pi$
$42$		0			0
$43$	−16.7364	−	28.9883i	−0.389219	−	0.674147i	0.603126	−	0.797646i	$-0.293922\pi$
$43$	−16.7364	−	28.9883i	−0.389219	−	0.674147i	−0.992345	+	0.123499i	$0.960588\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.63903	−	0.946292i	0.0348729	−	0.0201339i	−0.482462	−	0.875917i	$-0.660257\pi$
$47$	1.63903	−	0.946292i	0.0348729	−	0.0201339i	0.517335	+	0.855783i	$0.326924\pi$
$48$		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	0.233713	−	0.972306i	$-0.424912\pi$
$59$	−28.9968	−	16.7413i	−0.491472	−	0.283751i	−0.725185	+	0.688554i	$0.758246\pi$
$60$		0			0
$61$	29.6385	+	51.3354i	0.485877	+	0.841564i	0.999868	−	0.0162318i	$-0.00516697\pi$
$61$	29.6385	+	51.3354i	0.485877	+	0.841564i	−0.513991	+	0.857795i	$0.671834\pi$
$62$		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	−0.247222	−	0.968959i	$-0.579518\pi$
$67$	47.9406	−	83.0356i	0.715532	−	1.23934i	0.962754	−	0.270379i	$-0.0871488\pi$
$68$		0			0
$69$	−35.1646	+	19.4457i	−0.509632	+	0.281822i
$70$		0			0
$71$			97.3685i			1.37139i	0.727890	+	0.685693i	$0.240501\pi$
$71$			97.3685i			1.37139i	−0.727890	+	0.685693i	$0.759499\pi$
$72$		0			0
$73$	−90.1349			−1.23473			−0.617363	−	0.786679i	$-0.711799\pi$
$73$	−90.1349			−1.23473			−0.617363	+	0.786679i	$0.711799\pi$
$74$		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	−0.885507	−	0.464626i	$-0.846189\pi$
$79$	−66.7654	−	115.641i	−0.845132	−	1.46381i	0.0403753	−	0.999185i	$-0.487145\pi$
$80$		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	$-0.652301\pi$
$83$	6.48602	−	3.74470i	0.0781448	−	0.0451169i	0.538563	+	0.842585i	$0.318967\pi$
$84$		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	$0.190770\pi$
$89$			100.406i			1.12816i	−0.825719	+	0.564081i	$0.809230\pi$
$90$		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	$-0.275102\pi$
$97$	−32.4085	−	56.1332i	−0.334109	−	0.578693i	−0.983313	+	0.181921i	$0.941769\pi$
$98$		0			0
$99$	−71.0532	−	44.5985i	−0.717709	−	0.450490i
$100$		0			0
$101$	−71.9956	+	41.5667i	−0.712828	+	0.411551i	−0.812107	−	0.583508i	$-0.801680\pi$
$101$	−71.9956	+	41.5667i	−0.712828	+	0.411551i	0.0992793	+	0.995060i	$0.468346\pi$
$102$		0			0
$103$	−19.7330	+	34.1786i	−0.191583	+	0.331831i	−0.945775	−	0.324823i	$-0.894695\pi$
$103$	−19.7330	+	34.1786i	−0.191583	+	0.331831i	0.754192	+	0.656654i	$0.228029\pi$
$104$		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	$-0.612750\pi$
$113$	−150.577	−	86.9358i	−1.33254	−	0.769343i	−0.985689	+	0.168576i	$0.946083\pi$
$114$		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	$-0.353502\pi$
$127$	112.817			0.888321			0.444160	+	0.895947i	$0.353502\pi$
$128$		0			0
$129$	−100.401	−	1.85379i	−0.778305	−	0.0143705i
$130$		0			0
$131$	111.050	+	64.1149i	0.847711	+	0.489426i	0.859878	−	0.510500i	$-0.170540\pi$
$131$	111.050	+	64.1149i	0.847711	+	0.489426i	−0.0121666	+	0.999926i	$0.503873\pi$
$132$		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	$-0.788515\pi$
$137$	−88.6320	+	51.1717i	−0.646949	+	0.373516i	0.140337	+	0.990104i	$0.455181\pi$
$138$		0			0
$139$	99.2000	−	171.819i	0.713669	−	1.23611i	−0.249801	−	0.968297i	$-0.580365\pi$
$139$	99.2000	−	171.819i	0.713669	−	1.23611i	0.963471	−	0.267814i	$-0.0863014\pi$
$140$		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	0.949485	−	0.313813i	$-0.101607\pi$
$149$	171.716	+	99.1403i	1.15246	+	0.665371i	0.202972	+	0.979185i	$0.434940\pi$
$150$		0			0
$151$	−24.6929	−	42.7694i	−0.163529	−	0.283241i	0.772603	−	0.634890i	$-0.218954\pi$
$151$	−24.6929	−	42.7694i	−0.163529	−	0.283241i	−0.936132	+	0.351649i	$0.885621\pi$
$152$		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	$-0.751001\pi$
$157$	40.1577	−	69.5551i	0.255781	−	0.443026i	0.965107	+	0.261854i	$0.0843340\pi$
$158$		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	$-0.502485\pi$
$163$	−2.54453			−0.0156106			−0.00780530	+	0.999970i	$0.502485\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	249.194	+	143.872i	1.49218	+	0.861512i	0.999960	−	0.00895792i	$-0.00285143\pi$
$167$	249.194	+	143.872i	1.49218	+	0.861512i	0.492222	+	0.870470i	$0.336185\pi$
$168$		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	$-0.676104\pi$
$173$	−8.88298	+	5.12859i	−0.0513467	+	0.0296450i	0.474107	+	0.880467i	$0.342771\pi$
$174$		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	$0.219079\pi$
$179$			227.398i			1.27038i	−0.772355	+	0.635191i	$0.780921\pi$
$180$		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	−0.195906	−	0.980623i	$-0.562765\pi$
$191$	106.079	−	61.2445i	0.555385	−	0.320652i	0.751291	+	0.659971i	$0.229431\pi$
$192$		0			0
$193$	−91.5875	+	158.634i	−0.474547	+	0.821939i	−0.999575	−	0.0291456i	$-0.990721\pi$
$193$	−91.5875	+	158.634i	−0.474547	+	0.821939i	0.525028	+	0.851085i	$0.324055\pi$
$194$		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	−0.259624	−	0.965710i	$-0.583599\pi$
$211$	149.075	−	258.206i	0.706517	−	1.22372i	0.966141	−	0.258013i	$-0.0830679\pi$
$212$		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	$-0.0768059\pi$
$223$	62.1214	+	107.597i	0.278571	+	0.482499i	−0.692459	+	0.721457i	$0.743473\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−175.493	+	101.321i	−0.773098	+	0.446349i	−0.833979	−	0.551797i	$-0.813942\pi$
$227$	−175.493	+	101.321i	−0.773098	+	0.446349i	0.0608804	+	0.998145i	$0.480609\pi$
$228$		0			0
$229$	179.663	−	311.186i	0.784556	−	1.35889i	−0.144709	−	0.989474i	$-0.546224\pi$
$229$	179.663	−	311.186i	0.784556	−	1.35889i	0.929264	−	0.369416i	$-0.120442\pi$
$230$		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	0.930036	−	0.367469i	$-0.119775\pi$
$239$	257.359	+	148.586i	1.07682	+	0.621700i	0.146781	+	0.989169i	$0.453109\pi$
$240$		0			0
$241$	−139.411	−	241.467i	−0.578469	−	1.00194i	−0.995655	−	0.0931168i	$-0.970317\pi$
$241$	−139.411	−	241.467i	−0.578469	−	1.00194i	0.417186	−	0.908821i	$-0.363016\pi$
$242$		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	$-0.898567\pi$
$251$		−	157.274i		−	0.626590i	0.949656	−	0.313295i	$-0.101433\pi$
$252$		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	$-0.144146\pi$
$257$	249.263	+	143.912i	0.969895	+	0.559969i	0.0706910	+	0.997498i	$0.477480\pi$
$258$		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	$-0.560895\pi$
$263$	148.598	−	85.7929i	0.565010	−	0.326209i	0.755154	+	0.655547i	$0.227562\pi$
$264$		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	$0.395619\pi$
$269$			509.332i			1.89343i	−0.322076	+	0.946714i	$0.604381\pi$
$270$		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	−0.999019	−	0.0442774i	$-0.985901\pi$
$277$	−148.986	−	258.051i	−0.537855	−	0.931592i	0.461164	−	0.887315i	$-0.347432\pi$
$278$		0			0
$279$	−127.263	−	4.70111i	−0.456139	−	0.0168498i
$280$		0			0
$281$	−427.177	+	246.631i	−1.52020	+	0.877689i	−0.520486	+	0.853870i	$0.674249\pi$
$281$	−427.177	+	246.631i	−1.52020	+	0.877689i	−0.999716	+	0.0238186i	$0.992418\pi$
$282$		0			0
$283$	−233.433	+	404.318i	−0.824851	+	1.42868i	0.0771816	+	0.997017i	$0.475408\pi$
$283$	−233.433	+	404.318i	−0.824851	+	1.42868i	−0.902033	+	0.431667i	$0.857925\pi$
$284$		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	$-0.242600\pi$
$293$	142.708	+	82.3923i	0.487057	+	0.281202i	−0.236296	+	0.971681i	$0.575933\pi$
$294$		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	$-0.165546\pi$
$307$	532.817			1.73556			0.867781	+	0.496947i	$0.165546\pi$
$308$		0			0
$309$	57.2961	+	103.611i	0.185424	+	0.335311i
$310$		0			0
$311$	273.525	+	157.920i	0.879501	+	0.507780i	0.870494	−	0.492180i	$-0.163800\pi$
$311$	273.525	+	157.920i	0.879501	+	0.507780i	0.00900684	+	0.999959i	$0.497133\pi$
$312$		0			0
$313$	243.203	+	421.241i	0.777008	+	1.34582i	0.933659	+	0.358163i	$0.116597\pi$
$313$	243.203	+	421.241i	0.777008	+	1.34582i	−0.156651	+	0.987654i	$0.550070\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−187.590	+	108.305i	−0.591767	+	0.341657i	−0.765796	−	0.643084i	$-0.777655\pi$
$317$	−187.590	+	108.305i	−0.591767	+	0.341657i	0.174029	+	0.984741i	$0.444321\pi$
$318$		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	0.797168	−	0.603757i	$-0.206330\pi$
$331$	−41.1383	−	71.2537i	−0.124285	−	0.215268i	−0.921453	+	0.388489i	$0.872997\pi$
$332$		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	$-0.687618\pi$
$337$	148.939	−	257.971i	0.441957	−	0.765492i	0.997835	+	0.0657724i	$0.0209511\pi$
$338$		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	$-0.0291437\pi$
$347$	490.844	+	283.389i	1.41454	+	0.816683i	0.418725	+	0.908113i	$0.362477\pi$
$348$		0			0
$349$	67.0512	+	116.136i	0.192124	+	0.332768i	0.945954	−	0.324301i	$-0.105129\pi$
$349$	67.0512	+	116.136i	0.192124	+	0.332768i	−0.753830	+	0.657069i	$0.771796\pi$
$350$		0			0
$351$	−165.526	+	253.208i	−0.471585	+	0.721390i
$352$		0			0
$353$	−548.536	+	316.697i	−1.55393	+	0.897160i	−0.556110	+	0.831109i	$0.687707\pi$
$353$	−548.536	+	316.697i	−1.55393	+	0.897160i	−0.997816	+	0.0660508i	$0.978960\pi$
$354$		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	$0.381806\pi$
$359$			669.069i			1.86370i	−0.362843	+	0.931850i	$0.618194\pi$
$360$		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	$-0.0508630\pi$
$367$	130.592	+	226.191i	0.355836	+	0.616325i	−0.631425	+	0.775437i	$0.717530\pi$
$368$		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	$-0.968265\pi$
$373$	−153.422	+	265.735i	−0.411320	+	0.712427i	0.583714	+	0.811959i	$0.301599\pi$
$374$		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	$-0.244650\pi$
$383$	182.438	+	105.331i	0.476341	+	0.275015i	−0.242550	+	0.970139i	$0.577984\pi$
$384$		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	−0.0824347	−	0.996596i	$-0.526270\pi$
$389$	287.637	−	166.067i	0.739426	−	0.426908i	0.821861	+	0.569689i	$0.192936\pi$
$390$		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	$-0.629489\pi$
$397$	−314.165			−0.791348			−0.395674	+	0.918391i	$0.629489\pi$
$398$		0			0
$399$	13.6911	+	0.252789i	0.0343135	+	0.000633557i
$400$		0			0
$401$	−228.530	−	131.942i	−0.569901	−	0.329032i	0.187209	−	0.982320i	$-0.440056\pi$
$401$	−228.530	−	131.942i	−0.569901	−	0.329032i	−0.757110	+	0.653288i	$0.773389\pi$
$402$		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	−0.877947	−	0.478759i	$-0.841087\pi$
$409$	−9.96171	+	17.2542i	−0.0243563	+	0.0421863i	0.853590	+	0.520945i	$0.174420\pi$
$410$		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	0.436270	−	0.899816i	$-0.356299\pi$
$419$	−52.3156	−	30.2044i	−0.124858	−	0.0720870i	−0.561128	+	0.827729i	$0.689633\pi$
$420$		0			0
$421$	120.897	+	209.400i	0.287167	+	0.497387i	0.973132	−	0.230247i	$-0.0739533\pi$
$421$	120.897	+	209.400i	0.287167	+	0.497387i	−0.685966	+	0.727634i	$0.740620\pi$
$422$		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	$0.0505832\pi$
$431$			136.406i			0.316488i	−0.987400	+	0.158244i	$0.949417\pi$
$432$		0			0
$433$	−211.026			−0.487357			−0.243679	−	0.969856i	$-0.578354\pi$
$433$	−211.026			−0.487357			−0.243679	+	0.969856i	$0.578354\pi$
$434$		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	0.737851	−	0.674963i	$-0.235841\pi$
$439$	−94.6528	−	163.943i	−0.215610	−	0.373447i	−0.953461	+	0.301516i	$0.902507\pi$
$440$		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	$-0.667401\pi$
$443$	−1.76983	+	1.02181i	−0.00399509	+	0.00230657i	0.498001	+	0.867176i	$0.334068\pi$
$444$		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	$0.0285336\pi$
$449$			80.3898i			0.179042i	−0.995985	+	0.0895210i	$0.971466\pi$
$450$		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	$-0.176048\pi$
$457$	−13.4675	−	23.3265i	−0.0294694	−	0.0510426i	−0.880384	+	0.474262i	$0.842715\pi$
$458$		0			0
$459$	6.22117	−	112.211i	0.0135538	−	0.244468i
$460$		0			0
$461$	−328.251	+	189.516i	−0.712042	+	0.411097i	−0.811817	−	0.583913i	$-0.801521\pi$
$461$	−328.251	+	189.516i	−0.712042	+	0.411097i	0.0997749	+	0.995010i	$0.468188\pi$
$462$		0			0
$463$	363.508	−	629.614i	0.785114	−	1.35986i	−0.143816	−	0.989604i	$-0.545937\pi$
$463$	363.508	−	629.614i	0.785114	−	1.35986i	0.928931	−	0.370254i	$-0.120729\pi$
$464$		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	0.199223	−	0.979954i	$-0.436158\pi$
$479$	549.652	−	317.342i	1.14750	−	0.662509i	0.948277	+	0.317445i	$0.102825\pi$
$480$		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	$-0.507196\pi$
$487$	−22.0173			−0.0452100			−0.0226050	+	0.999744i	$0.507196\pi$
$488$		0			0
$489$	−3.93818	+	6.53929i	−0.00805355	+	0.0133728i
$490$		0			0
$491$	748.480	+	432.135i	1.52440	+	0.880112i	0.999582	+	0.0288958i	$0.00919911\pi$
$491$	748.480	+	432.135i	1.52440	+	0.880112i	0.524816	+	0.851216i	$0.324134\pi$
$492$		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	−0.958929	−	0.283645i	$-0.908456\pi$
$499$	−116.676	+	202.089i	−0.233820	+	0.404989i	0.725109	+	0.688634i	$0.241789\pi$
$500$		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	−0.108300	−	0.994118i	$-0.534541\pi$
$509$	−520.901	−	300.742i	−1.02338	−	0.590850i	−0.915082	+	0.403269i	$0.867874\pi$
$510$		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	$-0.786579\pi$
$521$		−	647.461i		−	1.24273i	0.783522	−	0.621363i	$-0.213421\pi$
$522$		0			0
$523$	−367.715			−0.703088			−0.351544	−	0.936171i	$-0.614343\pi$
$523$	−367.715			−0.703088			−0.351544	+	0.936171i	$0.614343\pi$
$524$		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	$-0.0564598\pi$
$547$	185.624	+	321.510i	0.339349	+	0.587770i	−0.644961	+	0.764215i	$0.723126\pi$
$548$		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	$-0.142086\pi$
$563$	551.268	+	318.275i	0.979162	+	0.565319i	0.0771448	+	0.997020i	$0.475420\pi$
$564$		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	−0.322910	−	0.946430i	$-0.604661\pi$
$569$	190.767	−	110.139i	0.335267	−	0.193566i	0.658177	+	0.752863i	$0.271328\pi$
$570$		0			0
$571$	302.443	−	523.847i	0.529672	−	0.917420i	−0.469728	−	0.882811i	$-0.655648\pi$
$571$	302.443	−	523.847i	0.529672	−	0.917420i	0.999401	−	0.0346087i	$-0.0110185\pi$
$572$		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	$-0.685028\pi$
$577$	−633.656			−1.09819			−0.549095	+	0.835760i	$0.685028\pi$
$578$		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	$-0.916099\pi$
$587$	−717.643	+	414.331i	−1.22256	+	0.705845i	−0.257097	+	0.966386i	$0.582766\pi$
$588$		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	−0.203031	−	0.979172i	$-0.565079\pi$
$599$	−690.368	−	398.584i	−1.15253	−	0.665416i	−0.949504	+	0.313756i	$0.898413\pi$
$600$		0			0
$601$	432.523	+	749.152i	0.719672	+	1.24651i	0.961130	+	0.276098i	$0.0890413\pi$
$601$	432.523	+	749.152i	0.719672	+	1.24651i	−0.241457	+	0.970411i	$0.577625\pi$
$602$		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	$-0.795090\pi$
$607$	72.7532	−	126.012i	0.119857	−	0.207598i	0.919711	+	0.392596i	$0.128423\pi$
$608$		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	$-0.343936\pi$
$613$	577.301			0.941764			0.470882	+	0.882196i	$0.343936\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	467.989	+	270.194i	0.758491	+	0.437915i	0.828754	−	0.559613i	$-0.189050\pi$
$617$	467.989	+	270.194i	0.758491	+	0.437915i	−0.0702626	+	0.997529i	$0.522384\pi$
$618$		0			0
$619$	−230.899	−	399.930i	−0.373020	−	0.646090i	0.617008	−	0.786957i	$-0.288344\pi$
$619$	−230.899	−	399.930i	−0.373020	−	0.646090i	−0.990029	+	0.140867i	$0.955011\pi$
$620$		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	−0.917999	−	0.396583i	$-0.870196\pi$
$641$	−662.504	+	382.497i	−1.03355	+	0.596719i	−0.115549	+	0.993302i	$0.536863\pi$
$642$		0			0
$643$	187.638	−	324.999i	0.291817	−	0.505441i	−0.682423	−	0.730958i	$-0.739074\pi$
$643$	187.638	−	324.999i	0.291817	−	0.505441i	0.974239	+	0.225517i	$0.0724070\pi$
$644$		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	$-0.555175\pi$
$653$	−725.975	−	419.142i	−1.11175	−	0.641871i	−0.939283	+	0.343144i	$0.888508\pi$
$654$		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	−0.625853	−	0.779941i	$-0.715249\pi$
$659$	−173.535	+	100.190i	−0.263330	+	0.152034i	0.362523	+	0.931975i	$0.381916\pi$
$660$		0			0
$661$	−550.664	+	953.778i	−0.833077	+	1.44293i	0.0625092	+	0.998044i	$0.480090\pi$
$661$	−550.664	+	953.778i	−0.833077	+	1.44293i	−0.895586	+	0.444888i	$0.853244\pi$
$662$		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	$-0.283488\pi$
$673$	−241.487	−	418.267i	−0.358821	−	0.621497i	−0.987764	+	0.155955i	$0.950155\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−457.500	+	264.138i	−0.675776	+	0.390159i	−0.798262	−	0.602311i	$-0.794247\pi$
$677$	−457.500	+	264.138i	−0.675776	+	0.390159i	0.122486	+	0.992470i	$0.460913\pi$
$678$		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	0.632172	−	0.774828i	$-0.282163\pi$
$691$	−245.260	−	424.802i	−0.354934	−	0.614764i	−0.987107	+	0.160063i	$0.948830\pi$
$692$		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	$-0.953413\pi$
$701$		−	204.463i		−	0.291674i	0.989309	−	0.145837i	$-0.0465874\pi$
$702$		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	0.879804	+	0.475337i	$0.157674\pi$
$709$	603.753	+	1045.73i	0.851556	+	1.47494i	−0.0282478	+	0.999601i	$0.508993\pi$
$710$		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	$-0.787370\pi$
$719$		−	890.720i		−	1.23883i	0.785063	−	0.619416i	$-0.212630\pi$
$720$		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	$-0.146109\pi$
$727$	46.9200	+	81.2678i	0.0645392	+	0.111785i	−0.831950	+	0.554850i	$0.812776\pi$
$728$		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	$-0.797715\pi$
$733$	81.8500	−	141.768i	0.111664	−	0.193409i	0.916441	+	0.400169i	$0.131048\pi$
$734$		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	$-0.0768752\pi$
$743$	928.259	+	535.931i	1.24934	+	0.721307i	0.278362	+	0.960476i	$0.410209\pi$
$744$		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	−0.972174	−	0.234258i	$-0.924734\pi$
$751$	−212.693	+	368.396i	−0.283214	+	0.490540i	0.688961	+	0.724799i	$0.258067\pi$
$752$		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	$-0.421866\pi$
$757$	367.915			0.486017			0.243008	+	0.970024i	$0.421866\pi$
$758$		0			0
$759$	−193.233	+	320.860i	−0.254588	+	0.422740i
$760$		0			0
$761$	−221.377	−	127.812i	−0.290902	−	0.167953i	0.347446	−	0.937700i	$-0.387049\pi$
$761$	−221.377	−	127.812i	−0.290902	−	0.167953i	−0.638349	+	0.769747i	$0.720382\pi$
$762$		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	−0.317175	+	0.948367i	$0.602734\pi$
$769$	−753.541	+	1305.17i	−0.979898	+	1.69723i	−0.662722	+	0.748865i	$0.730599\pi$
$770$		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	0.231332	+	0.972875i	$0.425692\pi$
$787$	−572.046	+	990.812i	−0.726869	+	1.25897i	−0.958200	+	0.286098i	$0.907642\pi$
$788$		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	$-0.0863614\pi$
$797$	966.792	+	558.177i	1.21304	+	0.700348i	0.249619	+	0.968344i	$0.419695\pi$
$798$		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	$-0.930134\pi$
$809$		−	352.291i		−	0.435465i	0.976009	−	0.217732i	$-0.0698660\pi$
$810$		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	−0.701273	−	0.712893i	$-0.747385\pi$
$821$	−356.746	+	205.967i	−0.434526	+	0.250874i	0.266747	+	0.963767i	$0.414051\pi$
$822$		0			0
$823$	424.417	−	735.112i	0.515695	−	0.893211i	−0.484139	−	0.874991i	$-0.660867\pi$
$823$	424.417	−	735.112i	0.515695	−	0.893211i	0.999834	−	0.0182193i	$-0.00579971\pi$
$824$		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	0.105802	−	0.994387i	$-0.466259\pi$
$839$	855.669	−	494.021i	1.01987	−	0.588821i	0.914066	+	0.405566i	$0.132926\pi$
$840$		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	$-0.158560\pi$
$853$	21.7215	+	37.6227i	0.0254648	+	0.0441064i	−0.853012	+	0.521891i	$0.825227\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	677.278	−	391.027i	0.790289	−	0.456274i	−0.0497751	−	0.998760i	$-0.515850\pi$
$857$	677.278	−	391.027i	0.790289	−	0.456274i	0.840064	+	0.542487i	$0.182517\pi$
$858$		0			0
$859$	−543.576	+	941.502i	−0.632801	+	1.09604i	0.354175	+	0.935179i	$0.384762\pi$
$859$	−543.576	+	941.502i	−0.632801	+	1.09604i	−0.986976	+	0.160865i	$0.948572\pi$
$860$		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	$-0.970423\pi$
$877$	−366.136	+	634.167i	−0.417487	+	0.723109i	0.578199	+	0.815896i	$0.303756\pi$
$878$		0			0
$879$	432.613	−	239.231i	0.492165	−	0.272163i
$880$		0			0
$881$		−	618.530i		−	0.702077i	−0.936361	−	0.351038i	$-0.885829\pi$
$881$		−	618.530i		−	0.702077i	0.936361	−	0.351038i	$-0.114171\pi$
$882$		0			0
$883$	−291.483			−0.330106			−0.165053	−	0.986285i	$-0.552779\pi$
$883$	−291.483			−0.330106			−0.165053	+	0.986285i	$0.552779\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−861.262	−	497.250i	−0.970983	−	0.560597i	−0.0714472	−	0.997444i	$-0.522762\pi$
$887$	−861.262	−	497.250i	−0.970983	−	0.560597i	−0.899536	+	0.436847i	$0.856095\pi$
$888$		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	$-0.115747\pi$
$907$	144.475	+	250.238i	0.159289	+	0.275896i	−0.775324	+	0.631564i	$0.782413\pi$
$908$		0			0
$909$	633.709	+	397.765i	0.697150	+	0.437585i
$910$		0			0
$911$	−361.910	+	208.949i	−0.397267	+	0.229362i	−0.685304	−	0.728257i	$-0.740331\pi$
$911$	−361.910	+	208.949i	−0.397267	+	0.229362i	0.288037	+	0.957619i	$0.406997\pi$
$912$		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	0.0665827	−	0.997781i	$-0.478790\pi$
$929$	895.535	−	517.037i	0.963978	−	0.556553i	0.897395	+	0.441228i	$0.145457\pi$
$930$		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	$-0.497503\pi$
$937$	14.6999			0.0156883			0.00784415	+	0.999969i	$0.497503\pi$
$938$		0			0
$939$	1458.97	+	26.9382i	1.55375	+	0.0286881i
$940$		0			0
$941$	−592.727	−	342.211i	−0.629890	−	0.363667i	0.150819	−	0.988561i	$-0.451809\pi$
$941$	−592.727	−	342.211i	−0.629890	−	0.363667i	−0.780710	+	0.624894i	$0.785142\pi$
$942$		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	−0.588030	+	0.808839i	$0.700096\pi$
$947$	−1498.65	+	865.244i	−1.58252	+	0.913669i	−0.994490	+	0.104830i	$0.966570\pi$
$948$		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	0.425749	+	0.904841i	$0.360010\pi$
$967$	−551.906	+	955.930i	−0.570741	+	0.988552i	−0.996490	+	0.0837107i	$0.973323\pi$
$968$		0			0
$969$	33.6712	+	20.2779i	0.0347484	+	0.0209267i
$970$		0			0
$971$		−	1839.18i		−	1.89411i	−0.321072	−	0.947055i	$-0.604043\pi$
$971$		−	1839.18i		−	1.89411i	0.321072	−	0.947055i	$-0.395957\pi$
$972$		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	$-0.202050\pi$
$977$	678.313	+	391.624i	0.694281	+	0.400843i	−0.110933	+	0.993828i	$0.535384\pi$
$978$		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	$-0.567117\pi$
$983$	523.845	−	302.442i	0.532904	−	0.307672i	0.742198	+	0.670180i	$0.233783\pi$
$984$		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	$-0.111461\pi$
$997$	172.046	+	297.993i	0.172564	+	0.298890i	−0.766752	+	0.641944i	$0.778128\pi$
$998$		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.e.401.5	yes	16
3.2	odd	2		2700.3.p.d.2501.5		16
5.2	odd	4		900.3.u.d.149.3		32
5.3	odd	4		900.3.u.d.149.14		32
5.4	even	2		900.3.p.d.401.4	yes	16
9.2	odd	6	inner	900.3.p.e.101.5	yes	16
9.7	even	3		2700.3.p.d.1601.5		16
15.2	even	4		2700.3.u.d.449.8		32
15.8	even	4		2700.3.u.d.449.9		32
15.14	odd	2		2700.3.p.e.2501.4		16
45.2	even	12		900.3.u.d.749.14		32
45.7	odd	12		2700.3.u.d.2249.9		32
45.29	odd	6		900.3.p.d.101.4	✓	16
45.34	even	6		2700.3.p.e.1601.4		16
45.38	even	12		900.3.u.d.749.3		32
45.43	odd	12		2700.3.u.d.2249.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.3.p.d.101.4	✓	16	45.29	odd	6
900.3.p.d.401.4	yes	16	5.4	even	2
900.3.p.e.101.5	yes	16	9.2	odd	6	inner
900.3.p.e.401.5	yes	16	1.1	even	1	trivial
900.3.u.d.149.3		32	5.2	odd	4
900.3.u.d.149.14		32	5.3	odd	4
900.3.u.d.749.3		32	45.38	even	12
900.3.u.d.749.14		32	45.2	even	12
2700.3.p.d.1601.5		16	9.7	even	3
2700.3.p.d.2501.5		16	3.2	odd	2
2700.3.p.e.1601.4		16	45.34	even	6
2700.3.p.e.2501.4		16	15.14	odd	2
2700.3.u.d.449.8		32	15.2	even	4
2700.3.u.d.449.9		32	15.8	even	4
2700.3.u.d.2249.8		32	45.43	odd	12
2700.3.u.d.2249.9		32	45.7	odd	12

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more