LMFDB - Embedded newform 900.3.u.d.749.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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, 5, 3]))

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

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

chi := DirichletCharacter("900.149");

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.u (of order $6$, degree $2$, not 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.3
Character	$\chi$	$=$	900.749
Dual form			900.3.u.d.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.56994 + 1.54771i) q^{3} +(-1.25581 - 0.725042i) q^{7} +(4.20921 - 7.95503i) q^{9} +O(q^{10})$	\(q+(-2.56994 + 1.54771i) q^{3} +(-1.25581 - 0.725042i) q^{7} +(4.20921 - 7.95503i) q^{9} +(8.07235 + 4.66057i) q^{11} +(-9.70307 + 5.60207i) q^{13} -4.16234 q^{17} -3.14773 q^{19} +(4.34951 - 0.0803085i) q^{21} +(-6.69719 - 11.5999i) q^{23} +(1.49463 + 26.9586i) q^{27} +(-12.6968 - 7.33048i) q^{29} +(7.07498 + 12.2542i) q^{31} +(-27.9587 + 0.516223i) q^{33} +18.0321i q^{37} +(16.2660 - 29.4145i) q^{39} +(17.6468 - 10.1884i) q^{41} +(-28.9883 - 16.7364i) q^{43} +(0.946292 - 1.63903i) q^{47} +(-23.4486 - 40.6142i) q^{49} +(10.6970 - 6.44209i) q^{51} -97.8498 q^{53} +(8.08948 - 4.87176i) q^{57} +(28.9968 - 16.7413i) q^{59} +(29.6385 - 51.3354i) q^{61} +(-11.0537 + 6.93816i) q^{63} +(83.0356 - 47.9406i) q^{67} +(35.1646 + 19.4457i) q^{69} -97.3685i q^{71} -90.1349i q^{73} +(-6.75822 - 11.7056i) q^{77} +(66.7654 - 115.641i) q^{79} +(-45.5651 - 66.9688i) q^{81} +(-3.74470 + 6.48602i) q^{83} +(43.9754 - 0.811952i) q^{87} +100.406i q^{89} +16.2469 q^{91} +(-37.1482 - 20.5426i) q^{93} +(56.1332 + 32.4085i) q^{97} +(71.0532 - 44.5985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 28 q^{9}+O(q^{10}) $ 32 * q - 28 * q^9	$ 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) $ 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * 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
$3$	−2.56994	+	1.54771i	−0.856648	+	0.515902i
$3$	−2.56994	+	1.54771i	−0.856648	+	0.515902i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.25581	−	0.725042i	−0.179401	−	0.103577i	0.407610	−	0.913156i	$-0.366362\pi$
$7$	−1.25581	−	0.725042i	−0.179401	−	0.103577i	−0.587011	+	0.809579i	$0.699696\pi$
$8$		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
$13$	−9.70307	+	5.60207i	−0.746390	+	0.430928i	−0.824388	−	0.566025i	$-0.808480\pi$
$13$	−9.70307	+	5.60207i	−0.746390	+	0.430928i	0.0779982	+	0.996953i	$0.475147\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.16234			−0.244844			−0.122422	−	0.992478i	$-0.539066\pi$
$17$	−4.16234			−0.244844			−0.122422	+	0.992478i	$0.539066\pi$
$18$		0			0
$19$	−3.14773			−0.165670			−0.0828350	−	0.996563i	$-0.526397\pi$
$19$	−3.14773			−0.165670			−0.0828350	+	0.996563i	$0.526397\pi$
$20$		0			0
$21$	4.34951	−	0.0803085i	0.207120	−	0.00382421i
$22$		0			0
$23$	−6.69719	−	11.5999i	−0.291182	−	0.504342i	0.682907	−	0.730505i	$-0.260715\pi$
$23$	−6.69719	−	11.5999i	−0.291182	−	0.504342i	−0.974090	+	0.226163i	$0.927382\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.49463	+	26.9586i	0.0553568	+	0.998467i
$28$		0			0
$29$	−12.6968	−	7.33048i	−0.437819	−	0.252775i	0.264853	−	0.964289i	$-0.414677\pi$
$29$	−12.6968	−	7.33048i	−0.437819	−	0.252775i	−0.702672	+	0.711514i	$0.748010\pi$
$30$		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
$33$	−27.9587	+	0.516223i	−0.847232	+	0.0156431i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			18.0321i			0.487354i	0.969856	+	0.243677i	$0.0783537\pi$
$37$			18.0321i			0.487354i	−0.969856	+	0.243677i	$0.921646\pi$
$38$		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
$43$	−28.9883	−	16.7364i	−0.674147	−	0.389219i	0.123499	−	0.992345i	$-0.460588\pi$
$43$	−28.9883	−	16.7364i	−0.674147	−	0.389219i	−0.797646	+	0.603126i	$0.793922\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.946292	−	1.63903i	0.0201339	−	0.0348729i	−0.855783	−	0.517335i	$-0.826924\pi$
$47$	0.946292	−	1.63903i	0.0201339	−	0.0348729i	0.875917	+	0.482462i	$0.160257\pi$
$48$		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
$53$	−97.8498			−1.84622			−0.923112	−	0.384532i	$-0.874363\pi$
$53$	−97.8498			−1.84622			−0.923112	+	0.384532i	$0.874363\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	8.08948	−	4.87176i	0.141921	−	0.0854695i
$58$		0			0
$59$	28.9968	−	16.7413i	0.491472	−	0.283751i	−0.233713	−	0.972306i	$-0.575088\pi$
$59$	28.9968	−	16.7413i	0.491472	−	0.283751i	0.725185	+	0.688554i	$0.241754\pi$
$60$		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
$63$	−11.0537	+	6.93816i	−0.175456	+	0.110129i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	83.0356	−	47.9406i	1.23934	−	0.715532i	0.270379	−	0.962754i	$-0.412851\pi$
$67$	83.0356	−	47.9406i	1.23934	−	0.715532i	0.968959	+	0.247222i	$0.0795178\pi$
$68$		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
$73$		−	90.1349i		−	1.23473i	−0.786679	−	0.617363i	$-0.788201\pi$
$73$		−	90.1349i		−	1.23473i	0.786679	−	0.617363i	$-0.211799\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.75822	−	11.7056i	−0.0877691	−	0.152021i
$78$		0			0
$79$	66.7654	−	115.641i	0.845132	−	1.46381i	−0.0403753	−	0.999185i	$-0.512855\pi$
$79$	66.7654	−	115.641i	0.845132	−	1.46381i	0.885507	−	0.464626i	$-0.153811\pi$
$80$		0			0
$81$	−45.5651	−	66.9688i	−0.562532	−	0.826775i
$82$		0			0
$83$	−3.74470	+	6.48602i	−0.0451169	+	0.0781448i	−0.887702	−	0.460418i	$-0.847699\pi$
$83$	−3.74470	+	6.48602i	−0.0451169	+	0.0781448i	0.842585	+	0.538563i	$0.181033\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	43.9754	−	0.811952i	0.505464	−	0.00933278i
$88$		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
$93$	−37.1482	−	20.5426i	−0.399443	−	0.220889i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	56.1332	+	32.4085i	0.578693	+	0.334109i	0.760614	−	0.649205i	$-0.224898\pi$
$97$	56.1332	+	32.4085i	0.578693	+	0.334109i	−0.181921	+	0.983313i	$0.558231\pi$
$98$		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
$103$	34.1786	−	19.7330i	0.331831	−	0.191583i	−0.324823	−	0.945775i	$-0.605305\pi$
$103$	34.1786	−	19.7330i	0.331831	−	0.191583i	0.656654	+	0.754192i	$0.271971\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	18.8472			0.176142			0.0880708	−	0.996114i	$-0.471930\pi$
$107$	18.8472			0.176142			0.0880708	+	0.996114i	$0.471930\pi$
$108$		0			0
$109$	−109.284			−1.00260			−0.501302	−	0.865273i	$-0.667145\pi$
$109$	−109.284			−1.00260			−0.501302	+	0.865273i	$0.667145\pi$
$110$		0			0
$111$	−27.9084	−	46.3415i	−0.251427	−	0.417491i
$112$		0			0
$113$	−86.9358	−	150.577i	−0.769343	−	1.33254i	−0.937920	−	0.346853i	$-0.887250\pi$
$113$	−86.9358	−	150.577i	−0.769343	−	1.33254i	0.168576	−	0.985689i	$-0.446083\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.72240	+	100.768i	0.0318154	+	0.861269i
$118$		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
$123$	−29.5827	+	53.4957i	−0.240510	+	0.434925i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	112.817i		−	0.888321i	−0.895947	−	0.444160i	$-0.853502\pi$
$127$		−	112.817i		−	0.888321i	0.895947	−	0.444160i	$-0.146498\pi$
$128$		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
$133$	3.95295	+	2.28224i	0.0297214	+	0.0171597i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−51.1717	+	88.6320i	−0.373516	+	0.646949i	−0.990104	−	0.140337i	$-0.955181\pi$
$137$	−51.1717	+	88.6320i	−0.373516	+	0.646949i	0.616587	+	0.787286i	$0.288515\pi$
$138$		0			0
$139$	−99.2000	−	171.819i	−0.713669	−	1.23611i	−0.963471	−	0.267814i	$-0.913699\pi$
$139$	−99.2000	−	171.819i	−0.713669	−	1.23611i	0.249801	−	0.968297i	$-0.419635\pi$
$140$		0			0
$141$	0.104815	+	5.67679i	0.000743368	+	0.0402609i
$142$		0			0
$143$	−104.435			−0.730317
$144$		0			0
$145$		0			0
$146$		0			0
$147$	123.121	+	68.0846i	0.837554	+	0.463161i
$148$		0			0
$149$	−171.716	+	99.1403i	−1.15246	+	0.665371i	−0.949485	−	0.313813i	$-0.898393\pi$
$149$	−171.716	+	99.1403i	−1.15246	+	0.665371i	−0.202972	+	0.979185i	$0.565060\pi$
$150$		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
$153$	−17.5202	+	33.1116i	−0.114511	+	0.216416i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	69.5551	−	40.1577i	0.443026	−	0.255781i	−0.261854	−	0.965107i	$-0.584334\pi$
$157$	69.5551	−	40.1577i	0.443026	−	0.255781i	0.704880	+	0.709326i	$0.251001\pi$
$158$		0			0
$159$	251.468	−	151.443i	1.58156	−	0.952471i
$160$		0			0
$161$			19.4230i			0.120640i
$162$		0			0
$163$		−	2.54453i		−	0.0156106i	−0.999970	−	0.00780530i	$-0.997515\pi$
$163$		−	2.54453i		−	0.0156106i	0.999970	−	0.00780530i	$-0.00248453\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−143.872	−	249.194i	−0.861512	−	1.49218i	−0.870470	−	0.492222i	$-0.836185\pi$
$167$	−143.872	−	249.194i	−0.861512	−	1.49218i	0.00895792	−	0.999960i	$-0.497149\pi$
$168$		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
$173$	5.12859	−	8.88298i	0.0296450	−	0.0513467i	−0.850822	−	0.525454i	$-0.823896\pi$
$173$	5.12859	−	8.88298i	0.0296450	−	0.0513467i	0.880467	+	0.474107i	$0.157229\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−48.6095	+	87.9029i	−0.274630	+	0.496626i
$178$		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
$183$	3.28287	+	177.801i	0.0179392	+	0.971588i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−33.5999	−	19.3989i	−0.179679	−	0.103737i
$188$		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
$193$	158.634	−	91.5875i	0.821939	−	0.474547i	−0.0291456	−	0.999575i	$-0.509279\pi$
$193$	158.634	−	91.5875i	0.821939	−	0.474547i	0.851085	+	0.525028i	$0.175945\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−140.366			−0.712520			−0.356260	−	0.934387i	$-0.615948\pi$
$197$	−140.366			−0.712520			−0.356260	+	0.934387i	$0.615948\pi$
$198$		0			0
$199$	−103.130			−0.518242			−0.259121	−	0.965845i	$-0.583433\pi$
$199$	−103.130			−0.518242			−0.259121	+	0.965845i	$0.583433\pi$
$200$		0			0
$201$	−139.199	+	251.719i	−0.692531	+	1.25234i
$202$		0			0
$203$	10.6298	+	18.4114i	0.0523636	+	0.0906964i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−120.467	+	4.45008i	−0.581967	+	0.0214980i
$208$		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
$213$	150.698	+	250.231i	0.707501	+	1.17480i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	20.5186i		−	0.0945559i
$218$		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
$223$	107.597	+	62.1214i	0.482499	+	0.278571i	0.721457	−	0.692459i	$-0.243473\pi$
$223$	107.597	+	62.1214i	0.482499	+	0.278571i	−0.238958	+	0.971030i	$0.576806\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−101.321	+	175.493i	−0.446349	+	0.773098i	−0.998145	−	0.0608804i	$-0.980609\pi$
$227$	−101.321	+	175.493i	−0.446349	+	0.773098i	0.551797	+	0.833979i	$0.313942\pi$
$228$		0			0
$229$	−179.663	−	311.186i	−0.784556	−	1.35889i	−0.929264	−	0.369416i	$-0.879558\pi$
$229$	−179.663	−	311.186i	−0.784556	−	1.35889i	0.144709	−	0.989474i	$-0.453776\pi$
$230$		0			0
$231$	35.4851	+	19.6229i	0.153615	+	0.0849478i
$232$		0			0
$233$	−124.960			−0.536309			−0.268154	−	0.963376i	$-0.586414\pi$
$233$	−124.960			−0.536309			−0.268154	+	0.963376i	$0.586414\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	7.39519	+	400.524i	0.0312033	+	1.68998i
$238$		0			0
$239$	−257.359	+	148.586i	−1.07682	+	0.621700i	−0.930036	−	0.367469i	$-0.880225\pi$
$239$	−257.359	+	148.586i	−1.07682	+	0.621700i	−0.146781	+	0.989169i	$0.546891\pi$
$240$		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
$243$	220.748	+	101.585i	0.908427	+	0.418043i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	30.5426	−	17.6338i	0.123654	−	0.0713919i
$248$		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
$253$		−	124.851i		−	0.493482i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−143.912	−	249.263i	−0.559969	−	0.969895i	−0.997498	−	0.0706910i	$-0.977480\pi$
$257$	−143.912	−	249.263i	−0.559969	−	0.969895i	0.437529	−	0.899204i	$-0.355854\pi$
$258$		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
$263$	−85.7929	+	148.598i	−0.326209	+	0.565010i	−0.981756	−	0.190144i	$-0.939105\pi$
$263$	−85.7929	+	148.598i	−0.326209	+	0.565010i	0.655547	+	0.755154i	$0.272438\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−155.400	−	258.039i	−0.582022	−	0.966438i
$268$		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
$273$	−41.7537	+	25.1455i	−0.152944	+	0.0921081i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	258.051	+	148.986i	0.931592	+	0.537855i	0.887315	−	0.461164i	$-0.152568\pi$
$277$	258.051	+	148.986i	0.931592	+	0.537855i	0.0442774	+	0.999019i	$0.485901\pi$
$278$		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
$283$	404.318	−	233.433i	1.42868	−	0.824851i	0.431667	−	0.902033i	$-0.357925\pi$
$283$	404.318	−	233.433i	1.42868	−	0.824851i	0.997017	+	0.0771816i	$0.0245921\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−29.5481			−0.102955
$288$		0			0
$289$	−271.675			−0.940052
$290$		0			0
$291$	−194.418	+	3.58969i	−0.668103	+	0.0123357i
$292$		0			0
$293$	82.3923	+	142.708i	0.281202	+	0.487057i	0.971681	−	0.236296i	$-0.0759335\pi$
$293$	82.3923	+	142.708i	0.281202	+	0.487057i	−0.690479	+	0.723353i	$0.742600\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−113.577	+	224.585i	−0.382415	+	0.756178i
$298$		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
$303$	249.358	−	4.60409i	0.822962	−	0.0151950i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	532.817i		−	1.73556i	−0.496947	−	0.867781i	$-0.665546\pi$
$307$		−	532.817i		−	1.73556i	0.496947	−	0.867781i	$-0.334454\pi$
$308$		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
$313$	421.241	+	243.203i	1.34582	+	0.777008i	0.987654	−	0.156651i	$-0.0500698\pi$
$313$	421.241	+	243.203i	1.34582	+	0.777008i	0.358163	+	0.933659i	$0.383403\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−108.305	+	187.590i	−0.341657	+	0.591767i	−0.984741	−	0.174029i	$-0.944321\pi$
$317$	−108.305	+	187.590i	−0.341657	+	0.591767i	0.643084	+	0.765796i	$0.277655\pi$
$318$		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
$323$	13.1019			0.0405633
$324$		0			0
$325$		0			0
$326$		0			0
$327$	280.853	−	169.139i	0.858877	−	0.517245i
$328$		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
$333$	143.446	+	75.9009i	0.430769	+	0.227931i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	257.971	−	148.939i	0.765492	−	0.441957i	−0.0657724	−	0.997835i	$-0.520951\pi$
$337$	257.971	−	148.939i	0.765492	−	0.441957i	0.831264	+	0.555878i	$0.187618\pi$
$338$		0			0
$339$	456.469	+	252.424i	1.34652	+	0.744612i
$340$		0			0
$341$			131.894i			0.386785i
$342$		0			0
$343$			139.059i			0.405420i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−283.389	−	490.844i	−0.816683	−	1.41454i	−0.908113	−	0.418725i	$-0.862477\pi$
$347$	−283.389	−	490.844i	−0.816683	−	1.41454i	0.0914296	−	0.995812i	$-0.470856\pi$
$348$		0			0
$349$	−67.0512	+	116.136i	−0.192124	+	0.332768i	−0.945954	−	0.324301i	$-0.894871\pi$
$349$	−67.0512	+	116.136i	−0.192124	+	0.332768i	0.753830	+	0.657069i	$0.228204\pi$
$350$		0			0
$351$	−165.526	−	253.208i	−0.471585	−	0.721390i
$352$		0			0
$353$	316.697	−	548.536i	0.897160	−	1.55393i	0.0660508	−	0.997816i	$-0.478960\pi$
$353$	316.697	−	548.536i	0.897160	−	1.55393i	0.831109	−	0.556110i	$-0.187707\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−18.1042	+	0.334272i	−0.0507120	+	0.000936335i
$358$		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
$363$	89.5663	+	49.5294i	0.246739	+	0.136445i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−226.191	−	130.592i	−0.616325	−	0.355836i	0.159112	−	0.987261i	$-0.449137\pi$
$367$	−226.191	−	130.592i	−0.616325	−	0.355836i	−0.775437	+	0.631425i	$0.782470\pi$
$368$		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
$373$	265.735	−	153.422i	0.712427	−	0.411320i	−0.0995321	−	0.995034i	$-0.531735\pi$
$373$	265.735	−	153.422i	0.712427	−	0.411320i	0.811959	+	0.583714i	$0.198401\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	164.263			0.435712
$378$		0			0
$379$	−102.483			−0.270403			−0.135201	−	0.990818i	$-0.543168\pi$
$379$	−102.483			−0.270403			−0.135201	+	0.990818i	$0.543168\pi$
$380$		0			0
$381$	174.607	+	289.932i	0.458287	+	0.760978i
$382$		0			0
$383$	105.331	+	182.438i	0.275015	+	0.476341i	0.970139	−	0.242550i	$-0.0779837\pi$
$383$	105.331	+	182.438i	0.275015	+	0.476341i	−0.695124	+	0.718890i	$0.744650\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−255.157	+	160.156i	−0.659319	+	0.413840i
$388$		0			0
$389$	−287.637	−	166.067i	−0.739426	−	0.426908i	0.0824347	−	0.996596i	$-0.473730\pi$
$389$	−287.637	−	166.067i	−0.739426	−	0.426908i	−0.821861	+	0.569689i	$0.807064\pi$
$390$		0			0
$391$	27.8760	+	48.2827i	0.0712941	+	0.123485i
$392$		0			0
$393$	−186.162	+	336.645i	−0.473694	+	0.856602i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			314.165i			0.791348i	0.918391	+	0.395674i	$0.129489\pi$
$397$			314.165i			0.791348i	−0.918391	+	0.395674i	$0.870511\pi$
$398$		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
$403$	−137.298	−	79.2690i	−0.340690	−	0.196697i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−84.0399	+	145.561i	−0.206486	+	0.357645i
$408$		0			0
$409$	9.96171	+	17.2542i	0.0243563	+	0.0421863i	0.877947	−	0.478759i	$-0.158913\pi$
$409$	9.96171	+	17.2542i	0.0243563	+	0.0421863i	−0.853590	+	0.520945i	$0.825580\pi$
$410$		0			0
$411$	−5.66798	−	306.978i	−0.0137907	−	0.746905i
$412$		0			0
$413$	−48.5527			−0.117561
$414$		0			0
$415$		0			0
$416$		0			0
$417$	520.864	+	288.034i	1.24908	+	0.690728i
$418$		0			0
$419$	52.3156	−	30.2044i	0.124858	−	0.0720870i	−0.436270	−	0.899816i	$-0.643701\pi$
$419$	52.3156	−	30.2044i	0.124858	−	0.0720870i	0.561128	+	0.827729i	$0.310367\pi$
$420$		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
$423$	−9.05537	−	14.4268i	−0.0214075	−	0.0341059i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−74.4407	+	42.9783i	−0.174334	+	0.100652i
$428$		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
$433$		−	211.026i		−	0.487357i	−0.969856	−	0.243679i	$-0.921646\pi$
$433$		−	211.026i		−	0.487357i	0.969856	−	0.243679i	$-0.0783542\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	21.0809	+	36.5133i	0.0482401	+	0.0835543i
$438$		0			0
$439$	94.6528	−	163.943i	0.215610	−	0.373447i	−0.737851	−	0.674963i	$-0.764159\pi$
$439$	94.6528	−	163.943i	0.215610	−	0.373447i	0.953461	+	0.301516i	$0.0974927\pi$
$440$		0			0
$441$	−421.788	+	15.5809i	−0.956434	+	0.0353308i
$442$		0			0
$443$	1.02181	−	1.76983i	0.00230657	−	0.00399509i	−0.864870	−	0.501996i	$-0.832599\pi$
$443$	1.02181	−	1.76983i	0.00230657	−	0.00399509i	0.867176	+	0.498001i	$0.165932\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	287.860	−	520.551i	0.643983	−	1.16454i
$448$		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
$453$	−2.73508	−	148.132i	−0.00603771	−	0.327003i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	23.3265	+	13.4675i	0.0510426	+	0.0294694i	0.525304	−	0.850915i	$-0.323952\pi$
$457$	23.3265	+	13.4675i	0.0510426	+	0.0294694i	−0.474262	+	0.880384i	$0.657285\pi$
$458$		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
$463$	−629.614	+	363.508i	−1.35986	+	0.785114i	−0.989604	−	0.143816i	$-0.954063\pi$
$463$	−629.614	+	363.508i	−1.35986	+	0.785114i	−0.370254	+	0.928931i	$0.620729\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	167.449			0.358564			0.179282	−	0.983798i	$-0.442623\pi$
$467$	167.449			0.358564			0.179282	+	0.983798i	$0.442623\pi$
$468$		0			0
$469$	−139.036			−0.296452
$470$		0			0
$471$	−116.600	+	210.854i	−0.247559	+	0.447672i
$472$		0			0
$473$	−156.002	−	270.204i	−0.329815	−	0.571256i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−411.870	+	778.399i	−0.863460	+	1.63186i
$478$		0			0
$479$	−549.652	−	317.342i	−1.14750	−	0.662509i	−0.199223	−	0.979954i	$-0.563842\pi$
$479$	−549.652	−	317.342i	−1.14750	−	0.662509i	−0.948277	+	0.317445i	$0.897175\pi$
$480$		0			0
$481$	−101.017	−	174.967i	−0.210015	−	0.363756i
$482$		0			0
$483$	−30.0611	−	49.9159i	−0.0622383	−	0.103346i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			22.0173i			0.0452100i	0.999744	+	0.0226050i	$0.00719601\pi$
$487$			22.0173i			0.0452100i	−0.999744	+	0.0226050i	$0.992804\pi$
$488$		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
$493$	52.8483	+	30.5120i	0.107197	+	0.0618904i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−70.5963	+	122.276i	−0.142045	+	0.246029i
$498$		0			0
$499$	116.676	+	202.089i	0.233820	+	0.404989i	0.958929	−	0.283645i	$-0.0915439\pi$
$499$	116.676	+	202.089i	0.233820	+	0.404989i	−0.725109	+	0.688634i	$0.758211\pi$
$500$		0			0
$501$	755.424	+	417.743i	1.50783	+	0.833818i
$502$		0			0
$503$	−892.050			−1.77346			−0.886729	−	0.462289i	$-0.847028\pi$
$503$	−892.050			−1.77346			−0.886729	+	0.462289i	$0.847028\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.40730	−	130.380i	−0.00474813	−	0.257159i
$508$		0			0
$509$	520.901	−	300.742i	1.02338	−	0.590850i	0.108300	−	0.994118i	$-0.465459\pi$
$509$	520.901	−	300.742i	1.02338	−	0.590850i	0.915082	+	0.403269i	$0.132126\pi$
$510$		0			0
$511$	−65.3517	+	113.192i	−0.127890	+	0.221512i
$512$		0			0
$513$	−4.70470	−	84.8584i	−0.00917095	−	0.165416i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	15.2776	−	8.82052i	0.0295505	−	0.0170610i
$518$		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
$523$		−	367.715i		−	0.703088i	−0.936171	−	0.351544i	$-0.885657\pi$
$523$		−	367.715i		−	0.703088i	0.936171	−	0.351544i	$-0.114343\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−29.4485	−	51.0063i	−0.0558795	−	0.0967861i
$528$		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
$533$	−114.152	+	197.718i	−0.214169	+	0.370952i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−351.946	−	584.401i	−0.655393	−	1.08827i
$538$		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
$543$	−339.944	+	204.726i	−0.626049	+	0.377028i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−321.510	−	185.624i	−0.587770	−	0.339349i	0.176445	−	0.984310i	$-0.443540\pi$
$547$	−321.510	−	185.624i	−0.587770	−	0.339349i	−0.764215	+	0.644961i	$0.776874\pi$
$548$		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
$553$	−167.689	+	96.8155i	−0.303236	+	0.175073i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	677.311			1.21600			0.607999	−	0.793938i	$-0.291972\pi$
$557$	677.311			1.21600			0.607999	+	0.793938i	$0.291972\pi$
$558$		0			0
$559$	375.034			0.670902
$560$		0			0
$561$	116.374	−	2.14870i	0.207440	−	0.00383012i
$562$		0			0
$563$	318.275	+	551.268i	0.565319	+	0.979162i	0.997020	+	0.0771448i	$0.0245804\pi$
$563$	318.275	+	551.268i	0.565319	+	0.979162i	−0.431701	+	0.902017i	$0.642086\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	8.66593	+	117.137i	0.0152838	+	0.206590i
$568$		0			0
$569$	−190.767	−	110.139i	−0.335267	−	0.193566i	0.322910	−	0.946430i	$-0.395339\pi$
$569$	−190.767	−	110.139i	−0.335267	−	0.193566i	−0.658177	+	0.752863i	$0.728672\pi$
$570$		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
$573$	−367.404	+	6.78368i	−0.641194	+	0.0118389i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			633.656i			1.09819i	0.835760	+	0.549095i	$0.185028\pi$
$577$			633.656i			1.09819i	−0.835760	+	0.549095i	$0.814972\pi$
$578$		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
$583$	−789.878	−	456.036i	−1.35485	−	0.782223i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−414.331	+	717.643i	−0.705845	+	1.22256i	0.260540	+	0.965463i	$0.416099\pi$
$587$	−414.331	+	717.643i	−0.705845	+	1.22256i	−0.966386	+	0.257097i	$0.917234\pi$
$588$		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
$593$	−304.718			−0.513858			−0.256929	−	0.966430i	$-0.582711\pi$
$593$	−304.718			−0.513858			−0.256929	+	0.966430i	$0.582711\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	265.039	−	159.615i	0.443951	−	0.267362i
$598$		0			0
$599$	690.368	−	398.584i	1.15253	−	0.665416i	0.203031	−	0.979172i	$-0.434921\pi$
$599$	690.368	−	398.584i	1.15253	−	0.665416i	0.949504	+	0.313756i	$0.101587\pi$
$600$		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
$603$	−31.8551	−	862.343i	−0.0528277	−	1.43009i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	126.012	−	72.7532i	0.207598	−	0.119857i	−0.392596	−	0.919711i	$-0.628423\pi$
$607$	126.012	−	72.7532i	0.207598	−	0.119857i	0.600195	+	0.799854i	$0.295090\pi$
$608$		0			0
$609$	−55.8134	−	30.8643i	−0.0916476	−	0.0506804i
$610$		0			0
$611$			21.2048i			0.0347050i
$612$		0			0
$613$			577.301i			0.941764i	0.882196	+	0.470882i	$0.156064\pi$
$613$			577.301i			0.941764i	−0.882196	+	0.470882i	$0.843936\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−270.194	−	467.989i	−0.437915	−	0.758491i	0.559613	−	0.828754i	$-0.310950\pi$
$617$	−270.194	−	467.989i	−0.437915	−	0.758491i	−0.997529	+	0.0702626i	$0.977616\pi$
$618$		0			0
$619$	230.899	−	399.930i	0.373020	−	0.646090i	−0.617008	−	0.786957i	$-0.711656\pi$
$619$	230.899	−	399.930i	0.373020	−	0.646090i	0.990029	+	0.140867i	$0.0449889\pi$
$620$		0			0
$621$	302.706	−	197.884i	0.487450	−	0.318654i
$622$		0			0
$623$	72.7989	−	126.091i	0.116852	−	0.202394i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	88.0063	−	1.62493i	0.140361	−	0.00259159i
$628$		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
$633$	−782.741	−	432.849i	−1.23656	−	0.683806i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	455.047	+	262.722i	0.714360	+	0.412436i
$638$		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
$643$	−324.999	+	187.638i	−0.505441	+	0.291817i	−0.730958	−	0.682423i	$-0.760926\pi$
$643$	−324.999	+	187.638i	−0.505441	+	0.291817i	0.225517	+	0.974239i	$0.427593\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1241.27			1.91850			0.959251	−	0.282557i	$-0.0911826\pi$
$647$	1241.27			1.91850			0.959251	+	0.282557i	$0.0911826\pi$
$648$		0			0
$649$	312.097			0.480889
$650$		0			0
$651$	31.7568	+	52.7317i	0.0487816	+	0.0810011i
$652$		0			0
$653$	−419.142	−	725.975i	−0.641871	−	1.11175i	−0.985015	−	0.172470i	$-0.944825\pi$
$653$	−419.142	−	725.975i	−0.641871	−	1.11175i	0.343144	−	0.939283i	$-0.388508\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−717.027	−	379.397i	−1.09136	−	0.577469i
$658$		0			0
$659$	173.535	+	100.190i	0.263330	+	0.152034i	0.625853	−	0.779941i	$-0.284751\pi$
$659$	173.535	+	100.190i	0.263330	+	0.152034i	−0.362523	+	0.931975i	$0.618084\pi$
$660$		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
$663$	−67.7046	+	122.433i	−0.102118	+	0.184666i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			196.374i			0.294414i
$668$		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
$673$	−418.267	−	241.487i	−0.621497	−	0.358821i	0.155955	−	0.987764i	$-0.450155\pi$
$673$	−418.267	−	241.487i	−0.621497	−	0.358821i	−0.777451	+	0.628943i	$0.783488\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−264.138	+	457.500i	−0.390159	+	0.675776i	−0.992470	−	0.122486i	$-0.960913\pi$
$677$	−264.138	+	457.500i	−0.390159	+	0.675776i	0.602311	+	0.798262i	$0.294247\pi$
$678$		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
$683$	620.705			0.908792			0.454396	−	0.890800i	$-0.349855\pi$
$683$	620.705			0.908792			0.454396	+	0.890800i	$0.349855\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	943.349	+	521.664i	1.37314	+	0.759336i
$688$		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
$693$	−121.565	+	4.49064i	−0.175419	+	0.00647999i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−73.4522	+	42.4077i	−0.105383	+	0.0608431i
$698$		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
$703$		−	56.7602i		−	0.0807399i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	60.2752	+	104.400i	0.0852549	+	0.147666i
$708$		0			0
$709$	−603.753	+	1045.73i	−0.851556	+	1.47494i	0.0282478	+	0.999601i	$0.491007\pi$
$709$	−603.753	+	1045.73i	−0.851556	+	1.47494i	−0.879804	+	0.475337i	$0.842326\pi$
$710$		0			0
$711$	−638.899	−	1017.88i	−0.898592	−	1.43162i
$712$		0			0
$713$	94.7649	−	164.138i	0.132910	−	0.230207i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	431.430	−	780.175i	0.601716	−	1.08811i
$718$		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
$723$	−15.4417	−	836.324i	−0.0213578	−	1.15674i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−81.2678	−	46.9200i	−0.111785	−	0.0645392i	0.443065	−	0.896489i	$-0.353891\pi$
$727$	−81.2678	−	46.9200i	−0.111785	−	0.0645392i	−0.554850	+	0.831950i	$0.687224\pi$
$728$		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
$733$	−141.768	+	81.8500i	−0.193409	+	0.111664i	−0.593577	−	0.804777i	$-0.702285\pi$
$733$	−141.768	+	81.8500i	−0.193409	+	0.111664i	0.400169	+	0.916441i	$0.368952\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	893.723			1.21265
$738$		0			0
$739$	808.628			1.09422			0.547109	−	0.837061i	$-0.315728\pi$
$739$	808.628			1.09422			0.547109	+	0.837061i	$0.315728\pi$
$740$		0			0
$741$	−51.2009	+	92.5889i	−0.0690970	+	0.124951i
$742$		0			0
$743$	535.931	+	928.259i	0.721307	+	1.24934i	0.960476	+	0.278362i	$0.0897915\pi$
$743$	535.931	+	928.259i	0.721307	+	1.24934i	−0.239170	+	0.970978i	$0.576875\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	35.8342	+	57.0902i	0.0479709	+	0.0764260i
$748$		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
$753$	−243.414	−	404.185i	−0.323259	−	0.536767i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	367.915i		−	0.486017i	−0.970024	−	0.243008i	$-0.921866\pi$
$757$		−	367.915i		−	0.486017i	0.970024	−	0.243008i	$-0.0781343\pi$
$758$		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
$763$	137.240	+	79.2354i	0.179868	+	0.103847i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−187.572	+	324.885i	−0.244553	+	0.423578i
$768$		0			0
$769$	753.541	+	1305.17i	0.979898	+	1.69723i	0.662722	+	0.748865i	$0.269401\pi$
$769$	753.541	+	1305.17i	0.979898	+	1.69723i	0.317175	+	0.948367i	$0.397266\pi$
$770$		0			0
$771$	755.632	+	417.858i	0.980067	+	0.541969i
$772$		0			0
$773$	409.392			0.529614			0.264807	−	0.964301i	$-0.414692\pi$
$773$	409.392			0.529614			0.264807	+	0.964301i	$0.414692\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.44813	+	78.4308i	0.00186375	+	0.100941i
$778$		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
$783$	178.642	−	353.243i	0.228151	−	0.451141i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−990.812	+	572.046i	−1.25897	+	0.726869i	−0.972875	−	0.231332i	$-0.925692\pi$
$787$	−990.812	+	572.046i	−1.25897	+	0.726869i	−0.286098	+	0.958200i	$0.592358\pi$
$788$		0			0
$789$	−9.50275	−	514.670i	−0.0120440	−	0.652306i
$790$		0			0
$791$			252.128i			0.318747i
$792$		0			0
$793$			664.147i			0.837513i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−558.177	−	966.792i	−0.700348	−	1.21304i	−0.968344	−	0.249619i	$-0.919695\pi$
$797$	−558.177	−	966.792i	−0.700348	−	1.21304i	0.267996	−	0.963420i	$-0.413639\pi$
$798$		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
$803$	420.080	−	727.601i	0.523139	−	0.906103i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−788.296	−	1308.95i	−0.976823	−	1.62200i
$808$		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
$813$	−257.336	+	154.977i	−0.316527	+	0.190623i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	91.2474	+	52.6817i	0.111686	+	0.0644819i
$818$		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
$823$	−735.112	+	424.417i	−0.893211	+	0.515695i	−0.874991	−	0.484139i	$-0.839133\pi$
$823$	−735.112	+	424.417i	−0.893211	+	0.515695i	−0.0182193	+	0.999834i	$0.505800\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1554.56			1.87976			0.939882	−	0.341500i	$-0.110935\pi$
$827$	1554.56			1.87976			0.939882	+	0.341500i	$0.110935\pi$
$828$		0			0
$829$	354.980			0.428202			0.214101	−	0.976811i	$-0.431318\pi$
$829$	354.980			0.428202			0.214101	+	0.976811i	$0.431318\pi$
$830$		0			0
$831$	−893.763	+	16.5022i	−1.07553	+	0.0198583i
$832$		0			0
$833$	97.6013	+	169.050i	0.117168	+	0.202942i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−319.782	+	209.047i	−0.382057	+	0.249757i
$838$		0			0
$839$	−855.669	−	494.021i	−1.01987	−	0.588821i	−0.105802	−	0.994387i	$-0.533741\pi$
$839$	−855.669	−	494.021i	−1.01987	−	0.588821i	−0.914066	+	0.405566i	$0.867074\pi$
$840$		0			0
$841$	−313.028	−	542.181i	−0.372210	−	0.644686i
$842$		0			0
$843$	1479.53	−	27.3178i	1.75508	−	0.0324054i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			49.4715i			0.0584079i
$848$		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
$853$	37.6227	+	21.7215i	0.0441064	+	0.0254648i	0.521891	−	0.853012i	$-0.325227\pi$
$853$	37.6227	+	21.7215i	0.0441064	+	0.0254648i	−0.477785	+	0.878477i	$0.658560\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	391.027	−	677.278i	0.456274	−	0.790289i	−0.542487	−	0.840064i	$-0.682517\pi$
$857$	391.027	−	677.278i	0.456274	−	0.790289i	0.998760	+	0.0497751i	$0.0158505\pi$
$858$		0			0
$859$	543.576	+	941.502i	0.632801	+	1.09604i	0.986976	+	0.160865i	$0.0514283\pi$
$859$	543.576	+	941.502i	0.632801	+	1.09604i	−0.354175	+	0.935179i	$0.615238\pi$
$860$		0			0
$861$	75.9369	−	45.7318i	0.0881962	−	0.0531147i
$862$		0			0
$863$	−62.4433			−0.0723561			−0.0361780	−	0.999345i	$-0.511518\pi$
$863$	−62.4433			−0.0723561			−0.0361780	+	0.999345i	$0.511518\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	698.189	−	420.473i	0.805293	−	0.484975i
$868$		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
$873$	494.087	−	310.127i	0.565965	−	0.355243i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−634.167	+	366.136i	−0.723109	+	0.417487i	−0.815896	−	0.578199i	$-0.803756\pi$
$877$	−634.167	+	366.136i	−0.723109	+	0.417487i	0.0927866	+	0.995686i	$0.470423\pi$
$878$		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
$883$		−	291.483i		−	0.330106i	−0.986285	−	0.165053i	$-0.947221\pi$
$883$		−	291.483i		−	0.330106i	0.986285	−	0.165053i	$-0.0527795\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	497.250	+	861.262i	0.560597	+	0.970983i	0.997444	+	0.0714472i	$0.0227617\pi$
$887$	497.250	+	861.262i	0.560597	+	0.970983i	−0.436847	+	0.899536i	$0.643905\pi$
$888$		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
$893$	−2.97867	+	5.15921i	−0.00333558	+	0.00577739i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−450.141	+	8.31130i	−0.501829	+	0.00926566i
$898$		0			0
$899$		−	207.452i		−	0.230758i
$900$		0			0
$901$	407.285			0.452036
$902$		0			0
$903$	−127.429	−	70.4672i	−0.141118	−	0.0780368i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−250.238	−	144.475i	−0.275896	−	0.159289i	0.355668	−	0.934612i	$-0.384253\pi$
$907$	−250.238	−	144.475i	−0.275896	−	0.159289i	−0.631564	+	0.775324i	$0.717587\pi$
$908$		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
$913$	−60.4571	+	34.9049i	−0.0662181	+	0.0382310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−185.944			−0.202774
$918$		0			0
$919$	200.015			0.217644			0.108822	−	0.994061i	$-0.465292\pi$
$919$	200.015			0.217644			0.108822	+	0.994061i	$0.465292\pi$
$920$		0			0
$921$	824.645	+	1369.31i	0.895380	+	1.48676i
$922$		0			0
$923$	545.465	+	944.773i	0.590969	+	1.02359i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−13.1120	−	354.952i	−0.0141445	−	0.382904i
$928$		0			0
$929$	−895.535	−	517.037i	−0.963978	−	0.556553i	−0.0665827	−	0.997781i	$-0.521210\pi$
$929$	−895.535	−	517.037i	−0.963978	−	0.556553i	−0.897395	+	0.441228i	$0.854543\pi$
$930$		0			0
$931$	73.8099	+	127.843i	0.0792803	+	0.137317i
$932$		0			0
$933$	−458.530	+	829.180i	−0.491457	+	0.888725i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	14.6999i		−	0.0156883i	−0.999969	−	0.00784415i	$-0.997503\pi$
$937$		−	14.6999i		−	0.0156883i	0.999969	−	0.00784415i	$-0.00249690\pi$
$938$		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
$943$	−236.368	−	136.467i	−0.250656	−	0.144716i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−865.244	+	1498.65i	−0.913669	+	1.58252i	−0.104830	+	0.994490i	$0.533430\pi$
$947$	−865.244	+	1498.65i	−0.913669	+	1.58252i	−0.808839	+	0.588030i	$0.799904\pi$
$948$		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
$953$	1253.61			1.31544			0.657719	−	0.753264i	$-0.271522\pi$
$953$	1253.61			1.31544			0.657719	+	0.753264i	$0.271522\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	358.769	+	198.396i	0.374889	+	0.207310i
$958$		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
$963$	79.3316	−	149.930i	0.0823797	−	0.155690i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−955.930	+	551.906i	−0.988552	+	0.570741i	−0.904841	−	0.425749i	$-0.860010\pi$
$967$	−955.930	+	551.906i	−0.988552	+	0.570741i	−0.0837107	+	0.996490i	$0.526677\pi$
$968$		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
$973$			287.697i			0.295680i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−391.624	−	678.313i	−0.400843	−	0.694281i	0.592984	−	0.805214i	$-0.297950\pi$
$977$	−391.624	−	678.313i	−0.400843	−	0.694281i	−0.993828	+	0.110933i	$0.964616\pi$
$978$		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
$983$	−302.442	+	523.845i	−0.307672	+	0.532904i	−0.977853	−	0.209294i	$-0.932883\pi$
$983$	−302.442	+	523.845i	−0.307672	+	0.532904i	0.670180	+	0.742198i	$0.266217\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.98428	−	7.20496i	0.00403676	−	0.00729986i
$988$		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
$993$	−4.55664	−	246.788i	−0.00458876	−	0.248528i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−297.993	−	172.046i	−0.298890	−	0.172564i	0.343054	−	0.939316i	$-0.388539\pi$
$997$	−297.993	−	172.046i	−0.298890	−	0.172564i	−0.641944	+	0.766752i	$0.721872\pi$
$998$		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.u.d.749.3		32
3.2	odd	2		2700.3.u.d.2249.8		32
5.2	odd	4		900.3.p.e.101.5	yes	16
5.3	odd	4		900.3.p.d.101.4	✓	16
5.4	even	2	inner	900.3.u.d.749.14		32
9.4	even	3		2700.3.u.d.449.9		32
9.5	odd	6	inner	900.3.u.d.149.14		32
15.2	even	4		2700.3.p.d.1601.5		16
15.8	even	4		2700.3.p.e.1601.4		16
15.14	odd	2		2700.3.u.d.2249.9		32
45.4	even	6		2700.3.u.d.449.8		32
45.13	odd	12		2700.3.p.e.2501.4		16
45.14	odd	6	inner	900.3.u.d.149.3		32
45.22	odd	12		2700.3.p.d.2501.5		16
45.23	even	12		900.3.p.d.401.4	yes	16
45.32	even	12		900.3.p.e.401.5	yes	16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.56994 + 1.54771i) q^{3} +(-1.25581 - 0.725042i) q^{7} +(4.20921 - 7.95503i) q^{9} +O(q^{10})\)	\(q+(-2.56994 + 1.54771i) q^{3} +(-1.25581 - 0.725042i) q^{7} +(4.20921 - 7.95503i) q^{9} +(8.07235 + 4.66057i) q^{11} +(-9.70307 + 5.60207i) q^{13} -4.16234 q^{17} -3.14773 q^{19} +(4.34951 - 0.0803085i) q^{21} +(-6.69719 - 11.5999i) q^{23} +(1.49463 + 26.9586i) q^{27} +(-12.6968 - 7.33048i) q^{29} +(7.07498 + 12.2542i) q^{31} +(-27.9587 + 0.516223i) q^{33} +18.0321i q^{37} +(16.2660 - 29.4145i) q^{39} +(17.6468 - 10.1884i) q^{41} +(-28.9883 - 16.7364i) q^{43} +(0.946292 - 1.63903i) q^{47} +(-23.4486 - 40.6142i) q^{49} +(10.6970 - 6.44209i) q^{51} -97.8498 q^{53} +(8.08948 - 4.87176i) q^{57} +(28.9968 - 16.7413i) q^{59} +(29.6385 - 51.3354i) q^{61} +(-11.0537 + 6.93816i) q^{63} +(83.0356 - 47.9406i) q^{67} +(35.1646 + 19.4457i) q^{69} -97.3685i q^{71} -90.1349i q^{73} +(-6.75822 - 11.7056i) q^{77} +(66.7654 - 115.641i) q^{79} +(-45.5651 - 66.9688i) q^{81} +(-3.74470 + 6.48602i) q^{83} +(43.9754 - 0.811952i) q^{87} +100.406i q^{89} +16.2469 q^{91} +(-37.1482 - 20.5426i) q^{93} +(56.1332 + 32.4085i) q^{97} +(71.0532 - 44.5985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 28 q^{9}+O(q^{10}) \) 32 * q - 28 * q^9	\( 32 q - 28 q^{9} - 4 q^{19} + 2 q^{21} - 18 q^{29} + 16 q^{31} - 38 q^{39} + 108 q^{41} + 90 q^{49} + 180 q^{51} - 18 q^{59} - 110 q^{61} + 294 q^{69} - 22 q^{79} - 260 q^{81} - 268 q^{91} - 504 q^{99}+O(q^{100}) \) 32 * q - 28 * q^9 - 4 * q^19 + 2 * q^21 - 18 * q^29 + 16 * q^31 - 38 * q^39 + 108 * q^41 + 90 * q^49 + 180 * q^51 - 18 * q^59 - 110 * q^61 + 294 * q^69 - 22 * q^79 - 260 * q^81 - 268 * q^91 - 504 * q^99

Introduction

L-functions

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