LMFDB - Embedded newform 675.2.e.d.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(226,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("675.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.e (of order $3$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	675.226
Dual form			675.2.e.d.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 1.67303i) q^{2} +(-0.866025 + 1.50000i) q^{4} +(0.448288 + 0.776457i) q^{7} -0.517638 q^{8} +O(q^{10})$	\(q+(-0.965926 - 1.67303i) q^{2} +(-0.866025 + 1.50000i) q^{4} +(0.448288 + 0.776457i) q^{7} -0.517638 q^{8} +(2.36603 + 4.09808i) q^{11} +(1.22474 - 2.12132i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.23205 + 3.86603i) q^{16} +0.378937 q^{17} +2.73205 q^{19} +(4.57081 - 7.91688i) q^{22} +(0.965926 - 1.67303i) q^{23} -4.73205 q^{26} -1.55291 q^{28} +(3.23205 + 5.59808i) q^{29} +(1.36603 - 2.36603i) q^{31} +(3.79435 - 6.57201i) q^{32} +(-0.366025 - 0.633975i) q^{34} +4.24264 q^{37} +(-2.63896 - 4.57081i) q^{38} +(2.13397 - 3.69615i) q^{41} +(4.57081 + 7.91688i) q^{43} -8.19615 q^{44} -3.73205 q^{46} +(-2.19067 - 3.79435i) q^{47} +(3.09808 - 5.36603i) q^{49} +(2.12132 + 3.67423i) q^{52} +3.86370 q^{53} +(-0.232051 - 0.401924i) q^{56} +(6.24384 - 10.8147i) q^{58} +(1.26795 - 2.19615i) q^{59} +(-5.33013 - 9.23205i) q^{61} -5.27792 q^{62} -5.73205 q^{64} +(-2.56961 + 4.45069i) q^{67} +(-0.328169 + 0.568406i) q^{68} -3.80385 q^{71} -8.48528 q^{73} +(-4.09808 - 7.09808i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(-2.12132 + 3.67423i) q^{77} +(-0.267949 - 0.464102i) q^{79} -8.24504 q^{82} +(5.20857 + 9.02150i) q^{83} +(8.83013 - 15.2942i) q^{86} +(-1.22474 - 2.12132i) q^{88} +7.39230 q^{89} +2.19615 q^{91} +(1.67303 + 2.89778i) q^{92} +(-4.23205 + 7.33013i) q^{94} +(-5.13922 - 8.90138i) q^{97} -11.9700 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q + 12 q^{11} + 4 q^{16} + 8 q^{19} - 24 q^{26} + 12 q^{29} + 4 q^{31} + 4 q^{34} + 24 q^{41} - 24 q^{44} - 16 q^{46} + 4 q^{49} + 12 q^{56} + 24 q^{59} - 8 q^{61} - 32 q^{64} - 72 q^{71} - 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{86} - 24 q^{89} - 24 q^{91} - 20 q^{94}+O(q^{100}) $ 8 * q + 12 * q^11 + 4 * q^16 + 8 * q^19 - 24 * q^26 + 12 * q^29 + 4 * q^31 + 4 * q^34 + 24 * q^41 - 24 * q^44 - 16 * q^46 + 4 * q^49 + 12 * q^56 + 24 * q^59 - 8 * q^61 - 32 * q^64 - 72 * q^71 - 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^86 - 24 * q^89 - 24 * q^91 - 20 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.965926	−	1.67303i	−0.683013	−	1.18301i	−0.974057	−	0.226303i	$-0.927336\pi$
$2$	−0.965926	−	1.67303i	−0.683013	−	1.18301i	0.291044	−	0.956710i	$-0.405997\pi$
$3$		0			0
$3$		0			0
$4$	−0.866025	+	1.50000i	−0.433013	+	0.750000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.448288	+	0.776457i	0.169437	+	0.293473i	0.938222	−	0.346034i	$-0.112472\pi$
$7$	0.448288	+	0.776457i	0.169437	+	0.293473i	−0.768785	+	0.639507i	$0.779138\pi$
$8$	−0.517638			−0.183013
$9$		0			0
$10$		0			0
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	0.963580	+	0.267421i	$0.0861715\pi$
$11$	2.36603	+	4.09808i	0.713384	+	1.23562i	−0.250196	+	0.968195i	$0.580495\pi$
$12$		0			0
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	−0.644690	−	0.764444i	$-0.723014\pi$
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	0.984373	+	0.176096i	$0.0563468\pi$
$14$	0.866025	−	1.50000i	0.231455	−	0.400892i
$15$		0			0
$16$	2.23205	+	3.86603i	0.558013	+	0.966506i
$17$	0.378937			0.0919058			0.0459529	−	0.998944i	$-0.485368\pi$
$17$	0.378937			0.0919058			0.0459529	+	0.998944i	$0.485368\pi$
$18$		0			0
$19$	2.73205			0.626775			0.313388	−	0.949625i	$-0.398536\pi$
$19$	2.73205			0.626775			0.313388	+	0.949625i	$0.398536\pi$
$20$		0			0
$21$		0			0
$22$	4.57081	−	7.91688i	0.974500	−	1.68788i
$23$	0.965926	−	1.67303i	0.201409	−	0.348851i	−0.747573	−	0.664179i	$-0.768781\pi$
$23$	0.965926	−	1.67303i	0.201409	−	0.348851i	0.948983	+	0.315328i	$0.102114\pi$
$24$		0			0
$25$		0			0
$26$	−4.73205			−0.928032
$27$		0			0
$28$	−1.55291			−0.293473
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	0.992794	+	0.119835i	$0.0382364\pi$
$29$	3.23205	+	5.59808i	0.600177	+	1.03954i	−0.392617	+	0.919702i	$0.628430\pi$
$30$		0			0
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	−0.716883	−	0.697193i	$-0.754432\pi$
$31$	1.36603	−	2.36603i	0.245345	−	0.424951i	0.962229	+	0.272243i	$0.0877653\pi$
$32$	3.79435	−	6.57201i	0.670753	−	1.16178i
$33$		0			0
$34$	−0.366025	−	0.633975i	−0.0627728	−	0.108726i
$35$		0			0
$36$		0			0
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	−2.63896	−	4.57081i	−0.428096	−	0.741483i
$39$		0			0
$40$		0			0
$41$	2.13397	−	3.69615i	0.333271	−	0.577242i	−0.649880	−	0.760037i	$-0.725181\pi$
$41$	2.13397	−	3.69615i	0.333271	−	0.577242i	0.983151	+	0.182795i	$0.0585143\pi$
$42$		0			0
$43$	4.57081	+	7.91688i	0.697042	+	1.20731i	0.969487	+	0.245141i	$0.0788342\pi$
$43$	4.57081	+	7.91688i	0.697042	+	1.20731i	−0.272445	+	0.962171i	$0.587832\pi$
$44$	−8.19615			−1.23562
$45$		0			0
$46$	−3.73205			−0.550261
$47$	−2.19067	−	3.79435i	−0.319542	−	0.553463i	0.660850	−	0.750518i	$-0.270196\pi$
$47$	−2.19067	−	3.79435i	−0.319542	−	0.553463i	−0.980393	+	0.197054i	$0.936862\pi$
$48$		0			0
$49$	3.09808	−	5.36603i	0.442582	−	0.766575i
$50$		0			0
$51$		0			0
$52$	2.12132	+	3.67423i	0.294174	+	0.509525i
$53$	3.86370			0.530720			0.265360	−	0.964149i	$-0.414509\pi$
$53$	3.86370			0.530720			0.265360	+	0.964149i	$0.414509\pi$
$54$		0			0
$55$		0			0
$56$	−0.232051	−	0.401924i	−0.0310091	−	0.0537093i
$57$		0			0
$58$	6.24384	−	10.8147i	0.819857	−	1.42003i
$59$	1.26795	−	2.19615i	0.165073	−	0.285915i	−0.771608	−	0.636098i	$-0.780547\pi$
$59$	1.26795	−	2.19615i	0.165073	−	0.285915i	0.936681	+	0.350183i	$0.113881\pi$
$60$		0			0
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	−0.974230	−	0.225557i	$-0.927580\pi$
$61$	−5.33013	−	9.23205i	−0.682453	−	1.18204i	0.291777	−	0.956486i	$-0.405753\pi$
$62$	−5.27792			−0.670296
$63$		0			0
$64$	−5.73205			−0.716506
$65$		0			0
$66$		0			0
$67$	−2.56961	+	4.45069i	−0.313928	+	0.543739i	−0.979209	−	0.202854i	$-0.934978\pi$
$67$	−2.56961	+	4.45069i	−0.313928	+	0.543739i	0.665281	+	0.746593i	$0.268312\pi$
$68$	−0.328169	+	0.568406i	−0.0397964	+	0.0689294i
$69$		0			0
$70$		0			0
$71$	−3.80385			−0.451434			−0.225717	−	0.974193i	$-0.572472\pi$
$71$	−3.80385			−0.451434			−0.225717	+	0.974193i	$0.572472\pi$
$72$		0			0
$73$	−8.48528			−0.993127			−0.496564	−	0.868000i	$-0.665405\pi$
$73$	−8.48528			−0.993127			−0.496564	+	0.868000i	$0.665405\pi$
$74$	−4.09808	−	7.09808i	−0.476392	−	0.825135i
$75$		0			0
$76$	−2.36603	+	4.09808i	−0.271402	+	0.470082i
$77$	−2.12132	+	3.67423i	−0.241747	+	0.418718i
$78$		0			0
$79$	−0.267949	−	0.464102i	−0.0301466	−	0.0522155i	0.850558	−	0.525880i	$-0.176264\pi$
$79$	−0.267949	−	0.464102i	−0.0301466	−	0.0522155i	−0.880705	+	0.473665i	$0.842931\pi$
$80$		0			0
$81$		0			0
$82$	−8.24504			−0.910513
$83$	5.20857	+	9.02150i	0.571714	+	0.990238i	0.996390	+	0.0848929i	$0.0270548\pi$
$83$	5.20857	+	9.02150i	0.571714	+	0.990238i	−0.424676	+	0.905346i	$0.639612\pi$
$84$		0			0
$85$		0			0
$86$	8.83013	−	15.2942i	0.952177	−	1.64922i
$87$		0			0
$88$	−1.22474	−	2.12132i	−0.130558	−	0.226134i
$89$	7.39230			0.783583			0.391791	−	0.920054i	$-0.371856\pi$
$89$	7.39230			0.783583			0.391791	+	0.920054i	$0.371856\pi$
$90$		0			0
$91$	2.19615			0.230219
$92$	1.67303	+	2.89778i	0.174426	+	0.302114i
$93$		0			0
$94$	−4.23205	+	7.33013i	−0.436503	+	0.756045i
$95$		0			0
$96$		0			0
$97$	−5.13922	−	8.90138i	−0.521808	−	0.903799i	−0.999678	−	0.0253679i	$-0.991924\pi$
$97$	−5.13922	−	8.90138i	−0.521808	−	0.903799i	0.477870	−	0.878431i	$-0.341409\pi$
$98$	−11.9700			−1.20916
$99$		0			0
$100$		0			0
$101$	1.26795	+	2.19615i	0.126166	+	0.218525i	0.922188	−	0.386742i	$-0.126400\pi$
$101$	1.26795	+	2.19615i	0.126166	+	0.218525i	−0.796022	+	0.605267i	$0.793066\pi$
$102$		0			0
$103$	−4.57081	+	7.91688i	−0.450375	+	0.780073i	−0.998409	−	0.0563832i	$-0.982043\pi$
$103$	−4.57081	+	7.91688i	−0.450375	+	0.780073i	0.548034	+	0.836456i	$0.315376\pi$
$104$	−0.633975	+	1.09808i	−0.0621663	+	0.107675i
$105$		0			0
$106$	−3.73205	−	6.46410i	−0.362489	−	0.627849i
$107$	11.7298			1.13396			0.566982	−	0.823730i	$-0.308111\pi$
$107$	11.7298			1.13396			0.566982	+	0.823730i	$0.308111\pi$
$108$		0			0
$109$	−4.66025			−0.446371			−0.223186	−	0.974776i	$-0.571646\pi$
$109$	−4.66025			−0.446371			−0.223186	+	0.974776i	$0.571646\pi$
$110$		0			0
$111$		0			0
$112$	−2.00120	+	3.46618i	−0.189096	+	0.327524i
$113$	−1.27551	+	2.20925i	−0.119990	+	0.207829i	−0.919764	−	0.392473i	$-0.871620\pi$
$113$	−1.27551	+	2.20925i	−0.119990	+	0.207829i	0.799773	+	0.600302i	$0.204953\pi$
$114$		0			0
$115$		0			0
$116$	−11.1962			−1.03954
$117$		0			0
$118$	−4.89898			−0.450988
$119$	0.169873	+	0.294229i	0.0155722	+	0.0269719i
$120$		0			0
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	−10.2970	+	17.8350i	−0.932248	+	1.61470i
$123$		0			0
$124$	2.36603	+	4.09808i	0.212475	+	0.368018i
$125$		0			0
$126$		0			0
$127$	4.65874			0.413397			0.206698	−	0.978405i	$-0.433728\pi$
$127$	4.65874			0.413397			0.206698	+	0.978405i	$0.433728\pi$
$128$	−2.05197	−	3.55412i	−0.181370	−	0.314142i
$129$		0			0
$130$		0			0
$131$	−0.464102	+	0.803848i	−0.0405487	+	0.0702325i	−0.885588	−	0.464473i	$-0.846244\pi$
$131$	−0.464102	+	0.803848i	−0.0405487	+	0.0702325i	0.845039	+	0.534705i	$0.179577\pi$
$132$		0			0
$133$	1.22474	+	2.12132i	0.106199	+	0.183942i
$134$	9.92820			0.857666
$135$		0			0
$136$	−0.196152			−0.0168199
$137$	9.28032	+	16.0740i	0.792871	+	1.37329i	0.924182	+	0.381952i	$0.124748\pi$
$137$	9.28032	+	16.0740i	0.792871	+	1.37329i	−0.131311	+	0.991341i	$0.541919\pi$
$138$		0			0
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		0			0
$141$		0			0
$142$	3.67423	+	6.36396i	0.308335	+	0.534052i
$143$	11.5911			0.969297
$144$		0			0
$145$		0			0
$146$	8.19615	+	14.1962i	0.678318	+	1.17488i
$147$		0			0
$148$	−3.67423	+	6.36396i	−0.302020	+	0.523114i
$149$	3.86603	−	6.69615i	0.316717	−	0.548570i	−0.663084	−	0.748545i	$-0.730753\pi$
$149$	3.86603	−	6.69615i	0.316717	−	0.548570i	0.979801	+	0.199975i	$0.0640861\pi$
$150$		0			0
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.800768	+	0.598975i	$0.204425\pi$
$151$	11.2942	+	19.5622i	0.919111	+	1.59195i	0.118343	+	0.992973i	$0.462242\pi$
$152$	−1.41421			−0.114708
$153$		0			0
$154$	8.19615			0.660465
$155$		0			0
$156$		0			0
$157$	−10.6945	+	18.5235i	−0.853517	+	1.47833i	0.0244975	+	0.999700i	$0.492201\pi$
$157$	−10.6945	+	18.5235i	−0.853517	+	1.47833i	−0.878014	+	0.478635i	$0.841132\pi$
$158$	−0.517638	+	0.896575i	−0.0411811	+	0.0713277i
$159$		0			0
$160$		0			0
$161$	1.73205			0.136505
$162$		0			0
$163$	18.9396			1.48346			0.741731	−	0.670697i	$-0.234005\pi$
$163$	18.9396			1.48346			0.741731	+	0.670697i	$0.234005\pi$
$164$	3.69615	+	6.40192i	0.288621	+	0.499906i
$165$		0			0
$166$	10.0622	−	17.4282i	0.780976	−	1.35269i
$167$	8.50386	−	14.7291i	0.658049	−	1.13977i	−0.323071	−	0.946375i	$-0.604715\pi$
$167$	8.50386	−	14.7291i	0.658049	−	1.13977i	0.981120	−	0.193399i	$-0.0619513\pi$
$168$		0			0
$169$	3.50000	+	6.06218i	0.269231	+	0.466321i
$170$		0			0
$171$		0			0
$172$	−15.8338			−1.20731
$173$	−0.378937	−	0.656339i	−0.0288101	−	0.0499005i	0.851261	−	0.524743i	$-0.175838\pi$
$173$	−0.378937	−	0.656339i	−0.0288101	−	0.0499005i	−0.880071	+	0.474842i	$0.842505\pi$
$174$		0			0
$175$		0			0
$176$	−10.5622	+	18.2942i	−0.796154	+	1.37898i
$177$		0			0
$178$	−7.14042	−	12.3676i	−0.535197	−	0.926988i
$179$	−24.5885			−1.83783			−0.918914	−	0.394458i	$-0.870932\pi$
$179$	−24.5885			−1.83783			−0.918914	+	0.394458i	$0.870932\pi$
$180$		0			0
$181$	8.46410			0.629132			0.314566	−	0.949236i	$-0.398141\pi$
$181$	8.46410			0.629132			0.314566	+	0.949236i	$0.398141\pi$
$182$	−2.12132	−	3.67423i	−0.157243	−	0.272352i
$183$		0			0
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$		0			0
$186$		0			0
$187$	0.896575	+	1.55291i	0.0655641	+	0.113560i
$188$	7.58871			0.553463
$189$		0			0
$190$		0			0
$191$	0.169873	+	0.294229i	0.0122916	+	0.0212896i	0.872106	−	0.489317i	$-0.162754\pi$
$191$	0.169873	+	0.294229i	0.0122916	+	0.0212896i	−0.859814	+	0.510607i	$0.829421\pi$
$192$		0			0
$193$	−10.3664	+	17.9551i	−0.746187	+	1.29243i	0.203451	+	0.979085i	$0.434784\pi$
$193$	−10.3664	+	17.9551i	−0.746187	+	1.29243i	−0.949638	+	0.313349i	$0.898549\pi$
$194$	−9.92820	+	17.1962i	−0.712803	+	1.23461i
$195$		0			0
$196$	5.36603	+	9.29423i	0.383288	+	0.663873i
$197$	−20.8343			−1.48438			−0.742190	−	0.670190i	$-0.766213\pi$
$197$	−20.8343			−1.48438			−0.742190	+	0.670190i	$0.766213\pi$
$198$		0			0
$199$	4.58846			0.325267			0.162634	−	0.986687i	$-0.448001\pi$
$199$	4.58846			0.325267			0.162634	+	0.986687i	$0.448001\pi$
$200$		0			0
$201$		0			0
$202$	2.44949	−	4.24264i	0.172345	−	0.298511i
$203$	−2.89778	+	5.01910i	−0.203384	+	0.352272i
$204$		0			0
$205$		0			0
$206$	17.6603			1.23045
$207$		0			0
$208$	10.9348			0.758190
$209$	6.46410	+	11.1962i	0.447131	+	0.774454i
$210$		0			0
$211$	6.56218	−	11.3660i	0.451759	−	0.782469i	−0.546736	−	0.837305i	$-0.684130\pi$
$211$	6.56218	−	11.3660i	0.451759	−	0.782469i	0.998495	+	0.0548353i	$0.0174634\pi$
$212$	−3.34607	+	5.79555i	−0.229809	+	0.398040i
$213$		0			0
$214$	−11.3301	−	19.6244i	−0.774512	−	1.34149i
$215$		0			0
$216$		0			0
$217$	2.44949			0.166282
$218$	4.50146	+	7.79676i	0.304877	+	0.528063i
$219$		0			0
$220$		0			0
$221$	0.464102	−	0.803848i	0.0312189	−	0.0540726i
$222$		0			0
$223$	−8.36516	−	14.4889i	−0.560173	−	0.970248i	−0.997481	−	0.0709359i	$-0.977401\pi$
$223$	−8.36516	−	14.4889i	−0.560173	−	0.970248i	0.437308	−	0.899312i	$-0.355932\pi$
$224$	6.80385			0.454601
$225$		0			0
$226$	4.92820			0.327819
$227$	0.947343	+	1.64085i	0.0628774	+	0.108907i	0.895750	−	0.444557i	$-0.146639\pi$
$227$	0.947343	+	1.64085i	0.0628774	+	0.108907i	−0.832873	+	0.553464i	$0.813306\pi$
$228$		0			0
$229$	−9.96410	+	17.2583i	−0.658446	+	1.14046i	0.322571	+	0.946545i	$0.395453\pi$
$229$	−9.96410	+	17.2583i	−0.658446	+	1.14046i	−0.981018	+	0.193917i	$0.937881\pi$
$230$		0			0
$231$		0			0
$232$	−1.67303	−	2.89778i	−0.109840	−	0.190248i
$233$	−7.07107			−0.463241			−0.231621	−	0.972806i	$-0.574403\pi$
$233$	−7.07107			−0.463241			−0.231621	+	0.972806i	$0.574403\pi$
$234$		0			0
$235$		0			0
$236$	2.19615	+	3.80385i	0.142957	+	0.247609i
$237$		0			0
$238$	0.328169	−	0.568406i	0.0212721	−	0.0368443i
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	−0.577623	−	0.816304i	$-0.696020\pi$
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	0.995751	+	0.0920846i	$0.0293530\pi$
$240$		0			0
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	0.747256	−	0.664536i	$-0.231371\pi$
$241$	−3.13397	−	5.42820i	−0.201877	−	0.349661i	−0.949133	+	0.314875i	$0.898037\pi$
$242$	22.0082			1.41474
$243$		0			0
$244$	18.4641			1.18204
$245$		0			0
$246$		0			0
$247$	3.34607	−	5.79555i	0.212905	−	0.368762i
$248$	−0.707107	+	1.22474i	−0.0449013	+	0.0777714i
$249$		0			0
$250$		0			0
$251$	−18.5885			−1.17329			−0.586647	−	0.809843i	$-0.699552\pi$
$251$	−18.5885			−1.17329			−0.586647	+	0.809843i	$0.699552\pi$
$252$		0			0
$253$	9.14162			0.574729
$254$	−4.50000	−	7.79423i	−0.282355	−	0.489053i
$255$		0			0
$256$	−9.69615	+	16.7942i	−0.606010	+	1.04964i
$257$	−11.2122	+	19.4201i	−0.699396	+	1.21139i	0.269280	+	0.963062i	$0.413214\pi$
$257$	−11.2122	+	19.4201i	−0.699396	+	1.21139i	−0.968676	+	0.248328i	$0.920119\pi$
$258$		0			0
$259$	1.90192	+	3.29423i	0.118180	+	0.204693i
$260$		0			0
$261$		0			0
$262$	1.79315			0.110781
$263$	−3.81294	−	6.60420i	−0.235116	−	0.407232i	0.724191	−	0.689600i	$-0.242214\pi$
$263$	−3.81294	−	6.60420i	−0.235116	−	0.407232i	−0.959306	+	0.282368i	$0.908880\pi$
$264$		0			0
$265$		0			0
$266$	2.36603	−	4.09808i	0.145070	−	0.251269i
$267$		0			0
$268$	−4.45069	−	7.70882i	−0.271869	−	0.470891i
$269$	−17.1962			−1.04847			−0.524234	−	0.851574i	$-0.675648\pi$
$269$	−17.1962			−1.04847			−0.524234	+	0.851574i	$0.675648\pi$
$270$		0			0
$271$	−23.5167			−1.42854			−0.714268	−	0.699873i	$-0.753240\pi$
$271$	−23.5167			−1.42854			−0.714268	+	0.699873i	$0.753240\pi$
$272$	0.845807	+	1.46498i	0.0512846	+	0.0888276i
$273$		0			0
$274$	17.9282	−	31.0526i	1.08308	−	1.87595i
$275$		0			0
$276$		0			0
$277$	−6.12372	−	10.6066i	−0.367939	−	0.637289i	0.621304	−	0.783569i	$-0.286603\pi$
$277$	−6.12372	−	10.6066i	−0.367939	−	0.637289i	−0.989243	+	0.146281i	$0.953270\pi$
$278$	−15.4548			−0.926918
$279$		0			0
$280$		0			0
$281$	−8.13397	−	14.0885i	−0.485232	−	0.840447i	0.514624	−	0.857416i	$-0.327932\pi$
$281$	−8.13397	−	14.0885i	−0.485232	−	0.840447i	−0.999856	+	0.0169692i	$0.994598\pi$
$282$		0			0
$283$	−2.24144	+	3.88229i	−0.133240	+	0.230778i	−0.924924	−	0.380153i	$-0.875871\pi$
$283$	−2.24144	+	3.88229i	−0.133240	+	0.230778i	0.791684	+	0.610931i	$0.209205\pi$
$284$	3.29423	−	5.70577i	0.195477	−	0.338575i
$285$		0			0
$286$	−11.1962	−	19.3923i	−0.662042	−	1.14669i
$287$	3.82654			0.225873
$288$		0			0
$289$	−16.8564			−0.991553
$290$		0			0
$291$		0			0
$292$	7.34847	−	12.7279i	0.430037	−	0.744845i
$293$	4.43211	−	7.67664i	0.258927	−	0.448474i	−0.707028	−	0.707186i	$-0.749965\pi$
$293$	4.43211	−	7.67664i	0.258927	−	0.448474i	0.965955	+	0.258711i	$0.0832979\pi$
$294$		0			0
$295$		0			0
$296$	−2.19615			−0.127649
$297$		0			0
$298$	−14.9372			−0.865287
$299$	−2.36603	−	4.09808i	−0.136831	−	0.236998i
$300$		0			0
$301$	−4.09808	+	7.09808i	−0.236209	+	0.409126i
$302$	21.8188	−	37.7912i	1.25553	−	2.17464i
$303$		0			0
$304$	6.09808	+	10.5622i	0.349749	+	0.605782i
$305$		0			0
$306$		0			0
$307$	25.8719			1.47659			0.738295	−	0.674478i	$-0.235631\pi$
$307$	25.8719			1.47659			0.738295	+	0.674478i	$0.235631\pi$
$308$	−3.67423	−	6.36396i	−0.209359	−	0.362620i
$309$		0			0
$310$		0			0
$311$	14.0263	−	24.2942i	0.795357	−	1.37760i	−0.127255	−	0.991870i	$-0.540617\pi$
$311$	14.0263	−	24.2942i	0.795357	−	1.37760i	0.922612	−	0.385729i	$-0.126050\pi$
$312$		0			0
$313$	−2.77766	−	4.81105i	−0.157003	−	0.271936i	0.776784	−	0.629767i	$-0.216850\pi$
$313$	−2.77766	−	4.81105i	−0.157003	−	0.271936i	−0.933786	+	0.357831i	$0.883516\pi$
$314$	41.3205			2.33185
$315$		0			0
$316$	0.928203			0.0522155
$317$	−17.5761	−	30.4428i	−0.987174	−	1.70984i	−0.631846	−	0.775094i	$-0.717703\pi$
$317$	−17.5761	−	30.4428i	−0.987174	−	1.70984i	−0.355328	−	0.934742i	$-0.615631\pi$
$318$		0			0
$319$	−15.2942	+	26.4904i	−0.856312	+	1.48318i
$320$		0			0
$321$		0			0
$322$	−1.67303	−	2.89778i	−0.0932345	−	0.161487i
$323$	1.03528			0.0576043
$324$		0			0
$325$		0			0
$326$	−18.2942	−	31.6865i	−1.01322	−	1.75495i
$327$		0			0
$328$	−1.10463	+	1.91327i	−0.0609928	+	0.105643i
$329$	1.96410	−	3.40192i	0.108284	−	0.187554i
$330$		0			0
$331$	−6.19615	−	10.7321i	−0.340571	−	0.589887i	0.643968	−	0.765053i	$-0.277287\pi$
$331$	−6.19615	−	10.7321i	−0.340571	−	0.589887i	−0.984539	+	0.175166i	$0.943954\pi$
$332$	−18.0430			−0.990238
$333$		0			0
$334$	−32.8564			−1.79782
$335$		0			0
$336$		0			0
$337$	0.896575	−	1.55291i	0.0488396	−	0.0845926i	−0.840572	−	0.541700i	$-0.817781\pi$
$337$	0.896575	−	1.55291i	0.0488396	−	0.0845926i	0.889412	+	0.457107i	$0.151114\pi$
$338$	6.76148	−	11.7112i	0.367776	−	0.637007i
$339$		0			0
$340$		0			0
$341$	12.9282			0.700101
$342$		0			0
$343$	11.8313			0.638833
$344$	−2.36603	−	4.09808i	−0.127568	−	0.220953i
$345$		0			0
$346$	−0.732051	+	1.26795i	−0.0393553	+	0.0681654i
$347$	4.94975	−	8.57321i	0.265716	−	0.460234i	−0.702035	−	0.712143i	$-0.747725\pi$
$347$	4.94975	−	8.57321i	0.265716	−	0.460234i	0.967751	+	0.251909i	$0.0810582\pi$
$348$		0			0
$349$	−10.7679	−	18.6506i	−0.576395	−	0.998346i	−0.995889	−	0.0905872i	$-0.971126\pi$
$349$	−10.7679	−	18.6506i	−0.576395	−	0.998346i	0.419493	−	0.907758i	$-0.362208\pi$
$350$		0			0
$351$		0			0
$352$	35.9101			1.91402
$353$	4.52004	+	7.82894i	0.240578	+	0.416693i	0.960879	−	0.276969i	$-0.0893298\pi$
$353$	4.52004	+	7.82894i	0.240578	+	0.416693i	−0.720301	+	0.693661i	$0.755996\pi$
$354$		0			0
$355$		0			0
$356$	−6.40192	+	11.0885i	−0.339301	+	0.587687i
$357$		0			0
$358$	23.7506	+	41.1373i	1.25526	+	2.17417i
$359$	−9.80385			−0.517427			−0.258714	−	0.965954i	$-0.583299\pi$
$359$	−9.80385			−0.517427			−0.258714	+	0.965954i	$0.583299\pi$
$360$		0			0
$361$	−11.5359			−0.607153
$362$	−8.17569	−	14.1607i	−0.429705	−	0.744271i
$363$		0			0
$364$	−1.90192	+	3.29423i	−0.0996879	+	0.172664i
$365$		0			0
$366$		0			0
$367$	12.3998	+	21.4770i	0.647262	+	1.12109i	0.983774	+	0.179411i	$0.0574193\pi$
$367$	12.3998	+	21.4770i	0.647262	+	1.12109i	−0.336512	+	0.941679i	$0.609247\pi$
$368$	8.62398			0.449556
$369$		0			0
$370$		0			0
$371$	1.73205	+	3.00000i	0.0899236	+	0.155752i
$372$		0			0
$373$	16.0740	−	27.8410i	0.832280	−	1.44155i	−0.0639468	−	0.997953i	$-0.520369\pi$
$373$	16.0740	−	27.8410i	0.832280	−	1.44155i	0.896226	−	0.443597i	$-0.146298\pi$
$374$	1.73205	−	3.00000i	0.0895622	−	0.155126i
$375$		0			0
$376$	1.13397	+	1.96410i	0.0584803	+	0.101291i
$377$	15.8338			0.815480
$378$		0			0
$379$	12.5359			0.643926			0.321963	−	0.946752i	$-0.395657\pi$
$379$	12.5359			0.643926			0.321963	+	0.946752i	$0.395657\pi$
$380$		0			0
$381$		0			0
$382$	0.328169	−	0.568406i	0.0167906	−	0.0290822i
$383$	10.2277	−	17.7148i	0.522609	−	0.905186i	−0.477045	−	0.878879i	$-0.658292\pi$
$383$	10.2277	−	17.7148i	0.522609	−	0.905186i	0.999654	−	0.0263067i	$-0.00837465\pi$
$384$		0			0
$385$		0			0
$386$	40.0526			2.03862
$387$		0			0
$388$	17.8028			0.903799
$389$	−12.0622	−	20.8923i	−0.611577	−	1.05928i	−0.990975	−	0.134048i	$-0.957202\pi$
$389$	−12.0622	−	20.8923i	−0.611577	−	1.05928i	0.379398	−	0.925234i	$-0.376131\pi$
$390$		0			0
$391$	0.366025	−	0.633975i	0.0185107	−	0.0320615i
$392$	−1.60368	+	2.77766i	−0.0809982	+	0.140293i
$393$		0			0
$394$	20.1244	+	34.8564i	1.01385	+	1.75604i
$395$		0			0
$396$		0			0
$397$	−29.3939			−1.47524			−0.737618	−	0.675218i	$-0.764050\pi$
$397$	−29.3939			−1.47524			−0.737618	+	0.675218i	$0.764050\pi$
$398$	−4.43211	−	7.67664i	−0.222162	−	0.384795i
$399$		0			0
$400$		0			0
$401$	−15.4641	+	26.7846i	−0.772240	+	1.33756i	0.164092	+	0.986445i	$0.447531\pi$
$401$	−15.4641	+	26.7846i	−0.772240	+	1.33756i	−0.936333	+	0.351115i	$0.885803\pi$
$402$		0			0
$403$	−3.34607	−	5.79555i	−0.166679	−	0.288697i
$404$	−4.39230			−0.218525
$405$		0			0
$406$	11.1962			0.555656
$407$	10.0382	+	17.3867i	0.497575	+	0.861825i
$408$		0			0
$409$	11.7321	−	20.3205i	0.580113	−	1.00478i	−0.415353	−	0.909660i	$-0.636342\pi$
$409$	11.7321	−	20.3205i	0.580113	−	1.00478i	0.995465	−	0.0951241i	$-0.0303248\pi$
$410$		0			0
$411$		0			0
$412$	−7.91688	−	13.7124i	−0.390036	−	0.675563i
$413$	2.27362			0.111878
$414$		0			0
$415$		0			0
$416$	−9.29423	−	16.0981i	−0.455687	−	0.789273i
$417$		0			0
$418$	12.4877	−	21.6293i	0.610793	−	1.05792i
$419$	−8.02628	+	13.9019i	−0.392109	+	0.679153i	−0.992728	−	0.120383i	$-0.961588\pi$
$419$	−8.02628	+	13.9019i	−0.392109	+	0.679153i	0.600618	+	0.799536i	$0.294921\pi$
$420$		0			0
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	0.977368	−	0.211545i	$-0.0678494\pi$
$421$	6.26795	+	10.8564i	0.305481	+	0.529109i	−0.671887	+	0.740653i	$0.734516\pi$
$422$	−25.3543			−1.23423
$423$		0			0
$424$	−2.00000			−0.0971286
$425$		0			0
$426$		0			0
$427$	4.77886	−	8.27723i	0.231265	−	0.400563i
$428$	−10.1583	+	17.5947i	−0.491021	+	0.850473i
$429$		0			0
$430$		0			0
$431$	6.00000			0.289010			0.144505	−	0.989504i	$-0.453841\pi$
$431$	6.00000			0.289010			0.144505	+	0.989504i	$0.453841\pi$
$432$		0			0
$433$	−30.5307			−1.46721			−0.733606	−	0.679575i	$-0.762164\pi$
$433$	−30.5307			−1.46721			−0.733606	+	0.679575i	$0.762164\pi$
$434$	−2.36603	−	4.09808i	−0.113573	−	0.196714i
$435$		0			0
$436$	4.03590	−	6.99038i	0.193284	−	0.334779i
$437$	2.63896	−	4.57081i	0.126239	−	0.218651i
$438$		0			0
$439$	−4.66025	−	8.07180i	−0.222422	−	0.385246i	0.733121	−	0.680098i	$-0.238063\pi$
$439$	−4.66025	−	8.07180i	−0.222422	−	0.385246i	−0.955543	+	0.294852i	$0.904730\pi$
$440$		0			0
$441$		0			0
$442$	−1.79315			−0.0852915
$443$	−6.95095	−	12.0394i	−0.330250	−	0.572009i	0.652311	−	0.757951i	$-0.273800\pi$
$443$	−6.95095	−	12.0394i	−0.330250	−	0.572009i	−0.982561	+	0.185942i	$0.940466\pi$
$444$		0			0
$445$		0			0
$446$	−16.1603	+	27.9904i	−0.765210	+	1.32538i
$447$		0			0
$448$	−2.56961	−	4.45069i	−0.121403	−	0.210275i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$	20.1962			0.951000
$452$	−2.20925	−	3.82654i	−0.103915	−	0.179985i
$453$		0			0
$454$	1.83013	−	3.16987i	0.0858921	−	0.148770i
$455$		0			0
$456$		0			0
$457$	−17.2987	−	29.9623i	−0.809201	−	1.40158i	−0.913418	−	0.407022i	$-0.866567\pi$
$457$	−17.2987	−	29.9623i	−0.809201	−	1.40158i	0.104218	−	0.994554i	$-0.466766\pi$
$458$	38.4983			1.79891
$459$		0			0
$460$		0			0
$461$	9.35641	+	16.2058i	0.435771	+	0.754778i	0.997358	−	0.0726397i	$-0.0231423\pi$
$461$	9.35641	+	16.2058i	0.435771	+	0.754778i	−0.561587	+	0.827418i	$0.689809\pi$
$462$		0			0
$463$	0.0879327	−	0.152304i	0.00408658	−	0.00707816i	−0.863975	−	0.503535i	$-0.832033\pi$
$463$	0.0879327	−	0.152304i	0.00408658	−	0.00707816i	0.868061	+	0.496457i	$0.165366\pi$
$464$	−14.4282	+	24.9904i	−0.669813	+	1.16015i
$465$		0			0
$466$	6.83013	+	11.8301i	0.316400	+	0.548020i
$467$	5.75839			0.266467			0.133233	−	0.991085i	$-0.457464\pi$
$467$	5.75839			0.266467			0.133233	+	0.991085i	$0.457464\pi$
$468$		0			0
$469$	−4.60770			−0.212764
$470$		0			0
$471$		0			0
$472$	−0.656339	+	1.13681i	−0.0302104	+	0.0523260i
$473$	−21.6293	+	37.4631i	−0.994517	+	1.72255i
$474$		0			0
$475$		0			0
$476$	−0.588457			−0.0269719
$477$		0			0
$478$	−24.9754			−1.14235
$479$	15.9282	+	27.5885i	0.727778	+	1.26055i	0.957820	+	0.287368i	$0.0927803\pi$
$479$	15.9282	+	27.5885i	0.727778	+	1.26055i	−0.230042	+	0.973181i	$0.573886\pi$
$480$		0			0
$481$	5.19615	−	9.00000i	0.236924	−	0.410365i
$482$	−6.05437	+	10.4865i	−0.275769	+	0.477646i
$483$		0			0
$484$	−9.86603	−	17.0885i	−0.448456	−	0.776748i
$485$		0			0
$486$		0			0
$487$	−1.13681			−0.0515139			−0.0257569	−	0.999668i	$-0.508200\pi$
$487$	−1.13681			−0.0515139			−0.0257569	+	0.999668i	$0.508200\pi$
$488$	2.75908	+	4.77886i	0.124898	+	0.216329i
$489$		0			0
$490$		0			0
$491$	−10.8564	+	18.8038i	−0.489943	+	0.848606i	−0.999933	−	0.0115744i	$-0.996316\pi$
$491$	−10.8564	+	18.8038i	−0.489943	+	0.848606i	0.509990	+	0.860180i	$0.329649\pi$
$492$		0			0
$493$	1.22474	+	2.12132i	0.0551597	+	0.0955395i
$494$	−12.9282			−0.581667
$495$		0			0
$496$	12.1962			0.547623
$497$	−1.70522	−	2.95352i	−0.0764895	−	0.132484i
$498$		0			0
$499$	1.92820	−	3.33975i	0.0863182	−	0.149508i	−0.819634	−	0.572888i	$-0.805823\pi$
$499$	1.92820	−	3.33975i	0.0863182	−	0.149508i	0.905952	+	0.423380i	$0.139156\pi$
$500$		0			0
$501$		0			0
$502$	17.9551	+	31.0991i	0.801374	+	1.38802i
$503$	−29.3567			−1.30895			−0.654476	−	0.756083i	$-0.727111\pi$
$503$	−29.3567			−1.30895			−0.654476	+	0.756083i	$0.727111\pi$
$504$		0			0
$505$		0			0
$506$	−8.83013	−	15.2942i	−0.392547	−	0.679911i
$507$		0			0
$508$	−4.03459	+	6.98811i	−0.179006	+	0.310047i
$509$	−5.42820	+	9.40192i	−0.240601	+	0.416733i	−0.960886	−	0.276946i	$-0.910678\pi$
$509$	−5.42820	+	9.40192i	−0.240601	+	0.416733i	0.720285	+	0.693679i	$0.244011\pi$
$510$		0			0
$511$	−3.80385	−	6.58846i	−0.168272	−	0.291456i
$512$	29.2552			1.29291
$513$		0			0
$514$	43.3205			1.91079
$515$		0			0
$516$		0			0
$517$	10.3664	−	17.9551i	0.455912	−	0.789663i
$518$	3.67423	−	6.36396i	0.161437	−	0.279616i
$519$		0			0
$520$		0			0
$521$	−1.39230			−0.0609980			−0.0304990	−	0.999535i	$-0.509710\pi$
$521$	−1.39230			−0.0609980			−0.0304990	+	0.999535i	$0.509710\pi$
$522$		0			0
$523$	−30.9468			−1.35321			−0.676604	−	0.736347i	$-0.736549\pi$
$523$	−30.9468			−1.35321			−0.676604	+	0.736347i	$0.736549\pi$
$524$	−0.803848	−	1.39230i	−0.0351162	−	0.0608231i
$525$		0			0
$526$	−7.36603	+	12.7583i	−0.321174	+	0.556290i
$527$	0.517638	−	0.896575i	0.0225487	−	0.0390554i
$528$		0			0
$529$	9.63397	+	16.6865i	0.418868	+	0.725501i
$530$		0			0
$531$		0			0
$532$	−4.24264			−0.183942
$533$	−5.22715	−	9.05369i	−0.226413	−	0.392159i
$534$		0			0
$535$		0			0
$536$	1.33013	−	2.30385i	0.0574527	−	0.0995111i
$537$		0			0
$538$	16.6102	+	28.7697i	0.716117	+	1.24035i
$539$	29.3205			1.26292
$540$		0			0
$541$	21.3923			0.919727			0.459864	−	0.887990i	$-0.347898\pi$
$541$	21.3923			0.919727			0.459864	+	0.887990i	$0.347898\pi$
$542$	22.7153	+	39.3441i	0.975708	+	1.68998i
$543$		0			0
$544$	1.43782	−	2.49038i	0.0616461	−	0.106774i
$545$		0			0
$546$		0			0
$547$	15.1452	+	26.2323i	0.647563	+	1.12161i	0.983703	+	0.179800i	$0.0575451\pi$
$547$	15.1452	+	26.2323i	0.647563	+	1.12161i	−0.336140	+	0.941812i	$0.609122\pi$
$548$	−32.1480			−1.37329
$549$		0			0
$550$		0			0
$551$	8.83013	+	15.2942i	0.376176	+	0.651556i
$552$		0			0
$553$	0.240237	−	0.416102i	0.0102159	−	0.0176945i
$554$	−11.8301	+	20.4904i	−0.502614	+	0.870553i
$555$		0			0
$556$	6.92820	+	12.0000i	0.293821	+	0.508913i
$557$	−31.1127			−1.31829			−0.659144	−	0.752017i	$-0.729081\pi$
$557$	−31.1127			−1.31829			−0.659144	+	0.752017i	$0.729081\pi$
$558$		0			0
$559$	22.3923			0.947094
$560$		0			0
$561$		0			0
$562$	−15.7136	+	27.2168i	−0.662840	+	1.14807i
$563$	13.7818	−	23.8707i	0.580833	−	1.00603i	−0.414548	−	0.910027i	$-0.636060\pi$
$563$	13.7818	−	23.8707i	0.580833	−	1.00603i	0.995381	−	0.0960045i	$-0.0306063\pi$
$564$		0			0
$565$		0			0
$566$	8.66025			0.364018
$567$		0			0
$568$	1.96902			0.0826181
$569$	−2.66025	−	4.60770i	−0.111524	−	0.193165i	0.804861	−	0.593463i	$-0.202240\pi$
$569$	−2.66025	−	4.60770i	−0.111524	−	0.193165i	−0.916385	+	0.400299i	$0.868906\pi$
$570$		0			0
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	−0.917513	−	0.397706i	$-0.869806\pi$
$571$	−2.73205	+	4.73205i	−0.114333	+	0.198030i	0.803180	+	0.595736i	$0.203140\pi$
$572$	−10.0382	+	17.3867i	−0.419718	+	0.726973i
$573$		0			0
$574$	−3.69615	−	6.40192i	−0.154274	−	0.267211i
$575$		0			0
$576$		0			0
$577$	−28.5617			−1.18904			−0.594519	−	0.804082i	$-0.702657\pi$
$577$	−28.5617			−1.18904			−0.594519	+	0.804082i	$0.702657\pi$
$578$	16.2820	+	28.2013i	0.677244	+	1.17302i
$579$		0			0
$580$		0			0
$581$	−4.66987	+	8.08846i	−0.193739	+	0.335566i
$582$		0			0
$583$	9.14162	+	15.8338i	0.378607	+	0.655767i
$584$	4.39230			0.181755
$585$		0			0
$586$	−17.1244			−0.707401
$587$	−11.0041	−	19.0597i	−0.454189	−	0.786678i	0.544452	−	0.838792i	$-0.316737\pi$
$587$	−11.0041	−	19.0597i	−0.454189	−	0.786678i	−0.998641	+	0.0521138i	$0.983404\pi$
$588$		0			0
$589$	3.73205	−	6.46410i	0.153776	−	0.266349i
$590$		0			0
$591$		0			0
$592$	9.46979	+	16.4022i	0.389206	+	0.674124i
$593$	−28.9406			−1.18845			−0.594224	−	0.804299i	$-0.702541\pi$
$593$	−28.9406			−1.18845			−0.594224	+	0.804299i	$0.702541\pi$
$594$		0			0
$595$		0			0
$596$	6.69615	+	11.5981i	0.274285	+	0.475076i
$597$		0			0
$598$	−4.57081	+	7.91688i	−0.186914	+	0.323745i
$599$	16.8564	−	29.1962i	0.688734	−	1.19292i	−0.283514	−	0.958968i	$-0.591500\pi$
$599$	16.8564	−	29.1962i	0.688734	−	1.19292i	0.972248	−	0.233954i	$-0.0751666\pi$
$600$		0			0
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	0.985401	−	0.170252i	$-0.0544581\pi$
$601$	8.46410	+	14.6603i	0.345258	+	0.598004i	−0.640143	+	0.768256i	$0.721125\pi$
$602$	15.8338			0.645335
$603$		0			0
$604$	−39.1244			−1.59195
$605$		0			0
$606$		0			0
$607$	4.36276	−	7.55652i	0.177079	−	0.306710i	−0.763800	−	0.645453i	$-0.776669\pi$
$607$	4.36276	−	7.55652i	0.177079	−	0.306710i	0.940879	+	0.338743i	$0.110002\pi$
$608$	10.3664	−	17.9551i	0.420412	−	0.728174i
$609$		0			0
$610$		0			0
$611$	−10.7321			−0.434172
$612$		0			0
$613$	24.3190			0.982236			0.491118	−	0.871093i	$-0.336588\pi$
$613$	24.3190			0.982236			0.491118	+	0.871093i	$0.336588\pi$
$614$	−24.9904	−	43.2846i	−1.00853	−	1.74682i
$615$		0			0
$616$	1.09808	−	1.90192i	0.0442428	−	0.0766307i
$617$	−6.55343	+	11.3509i	−0.263831	+	0.456969i	−0.967257	−	0.253800i	$-0.918320\pi$
$617$	−6.55343	+	11.3509i	−0.263831	+	0.456969i	0.703426	+	0.710769i	$0.251653\pi$
$618$		0			0
$619$	−9.90192	−	17.1506i	−0.397992	−	0.689342i	0.595486	−	0.803366i	$-0.296959\pi$
$619$	−9.90192	−	17.1506i	−0.397992	−	0.689342i	−0.993478	+	0.114023i	$0.963626\pi$
$620$		0			0
$621$		0			0
$622$	−54.1934			−2.17296
$623$	3.31388	+	5.73981i	0.132768	+	0.229961i
$624$		0			0
$625$		0			0
$626$	−5.36603	+	9.29423i	−0.214470	+	0.371472i
$627$		0			0
$628$	−18.5235	−	32.0836i	−0.739167	−	1.28028i
$629$	1.60770			0.0641030
$630$		0			0
$631$	−33.3205			−1.32647			−0.663234	−	0.748412i	$-0.730817\pi$
$631$	−33.3205			−1.32647			−0.663234	+	0.748412i	$0.730817\pi$
$632$	0.138701	+	0.240237i	0.00551722	+	0.00955610i
$633$		0			0
$634$	−33.9545	+	58.8109i	−1.34850	+	2.33568i
$635$		0			0
$636$		0			0
$637$	−7.58871	−	13.1440i	−0.300675	−	0.520785i
$638$	59.0924			2.33949
$639$		0			0
$640$		0			0
$641$	−12.5263	−	21.6962i	−0.494758	−	0.856946i	0.505223	−	0.862989i	$-0.331410\pi$
$641$	−12.5263	−	21.6962i	−0.494758	−	0.856946i	−0.999982	+	0.00604207i	$0.998077\pi$
$642$		0			0
$643$	12.6078	−	21.8374i	0.497203	−	0.861181i	−0.502792	−	0.864408i	$-0.667694\pi$
$643$	12.6078	−	21.8374i	0.497203	−	0.861181i	0.999995	+	0.00322641i	$0.00102700\pi$
$644$	−1.50000	+	2.59808i	−0.0591083	+	0.102379i
$645$		0			0
$646$	−1.00000	−	1.73205i	−0.0393445	−	0.0681466i
$647$	12.3861			0.486950			0.243475	−	0.969907i	$-0.421713\pi$
$647$	12.3861			0.486950			0.243475	+	0.969907i	$0.421713\pi$
$648$		0			0
$649$	12.0000			0.471041
$650$		0			0
$651$		0			0
$652$	−16.4022	+	28.4094i	−0.642358	+	1.11260i
$653$	−0.226633	+	0.392541i	−0.00886885	+	0.0153613i	−0.870426	−	0.492300i	$-0.836156\pi$
$653$	−0.226633	+	0.392541i	−0.00886885	+	0.0153613i	0.861557	+	0.507661i	$0.169490\pi$
$654$		0			0
$655$		0			0
$656$	19.0526			0.743877
$657$		0			0
$658$	−7.58871			−0.295839
$659$	18.1244	+	31.3923i	0.706025	+	1.22287i	0.966320	+	0.257342i	$0.0828466\pi$
$659$	18.1244	+	31.3923i	0.706025	+	1.22287i	−0.260296	+	0.965529i	$0.583820\pi$
$660$		0			0
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	−0.394323	−	0.918972i	$-0.629021\pi$
$661$	15.3923	−	26.6603i	0.598691	−	1.03696i	0.993015	−	0.117992i	$-0.0376457\pi$
$662$	−11.9700	+	20.7327i	−0.465229	+	0.805800i
$663$		0			0
$664$	−2.69615	−	4.66987i	−0.104631	−	0.181226i
$665$		0			0
$666$		0			0
$667$	12.4877			0.483525
$668$	14.7291	+	25.5116i	0.569887	+	0.987073i
$669$		0			0
$670$		0			0
$671$	25.2224	−	43.6865i	0.973701	−	1.68650i
$672$		0			0
$673$	−0.808643	−	1.40061i	−0.0311709	−	0.0539896i	0.850019	−	0.526752i	$-0.176590\pi$
$673$	−0.808643	−	1.40061i	−0.0311709	−	0.0539896i	−0.881190	+	0.472762i	$0.843257\pi$
$674$	−3.46410			−0.133432
$675$		0			0
$676$	−12.1244			−0.466321
$677$	16.5409	+	28.6496i	0.635717	+	1.10109i	0.986363	+	0.164586i	$0.0526287\pi$
$677$	16.5409	+	28.6496i	0.635717	+	1.10109i	−0.350646	+	0.936508i	$0.614038\pi$
$678$		0			0
$679$	4.60770	−	7.98076i	0.176827	−	0.306274i
$680$		0			0
$681$		0			0
$682$	−12.4877	−	21.6293i	−0.478178	−	0.828229i
$683$	19.6975			0.753702			0.376851	−	0.926274i	$-0.377007\pi$
$683$	19.6975			0.753702			0.376851	+	0.926274i	$0.377007\pi$
$684$		0			0
$685$		0			0
$686$	−11.4282	−	19.7942i	−0.436331	−	0.755747i
$687$		0			0
$688$	−20.4046	+	35.3417i	−0.777917	+	1.34739i
$689$	4.73205	−	8.19615i	0.180277	−	0.312249i
$690$		0			0
$691$	−10.1244	−	17.5359i	−0.385149	−	0.667097i	0.606641	−	0.794976i	$-0.292516\pi$
$691$	−10.1244	−	17.5359i	−0.385149	−	0.667097i	−0.991790	+	0.127879i	$0.959183\pi$
$692$	1.31268			0.0499005
$693$		0			0
$694$	−19.1244			−0.725951
$695$		0			0
$696$		0			0
$697$	0.808643	−	1.40061i	0.0306295	−	0.0530519i
$698$	−20.8021	+	36.0303i	−0.787370	+	1.36377i
$699$		0			0
$700$		0			0
$701$	23.1962			0.876107			0.438053	−	0.898949i	$-0.355668\pi$
$701$	23.1962			0.876107			0.438053	+	0.898949i	$0.355668\pi$
$702$		0			0
$703$	11.5911			0.437167
$704$	−13.5622	−	23.4904i	−0.511144	−	0.885327i
$705$		0			0
$706$	8.73205	−	15.1244i	0.328635	−	0.569213i
$707$	−1.13681	+	1.96902i	−0.0427542	+	0.0740525i
$708$		0			0
$709$	15.8923	+	27.5263i	0.596848	+	1.03377i	0.993283	+	0.115708i	$0.0369138\pi$
$709$	15.8923	+	27.5263i	0.596848	+	1.03377i	−0.396435	+	0.918063i	$0.629753\pi$
$710$		0			0
$711$		0			0
$712$	−3.82654			−0.143406
$713$	−2.63896	−	4.57081i	−0.0988298	−	0.171178i
$714$		0			0
$715$		0			0
$716$	21.2942	−	36.8827i	0.795803	−	1.37837i
$717$		0			0
$718$	9.46979	+	16.4022i	0.353409	+	0.612123i
$719$	−19.6077			−0.731244			−0.365622	−	0.930763i	$-0.619144\pi$
$719$	−19.6077			−0.731244			−0.365622	+	0.930763i	$0.619144\pi$
$720$		0			0
$721$	−8.19615			−0.305241
$722$	11.1428	+	19.2999i	0.414693	+	0.718269i
$723$		0			0
$724$	−7.33013	+	12.6962i	−0.272422	+	0.471849i
$725$		0			0
$726$		0			0
$727$	14.1607	+	24.5271i	0.525192	+	0.909659i	0.999570	+	0.0293377i	$0.00933982\pi$
$727$	14.1607	+	24.5271i	0.525192	+	0.909659i	−0.474378	+	0.880321i	$0.657327\pi$
$728$	−1.13681			−0.0421331
$729$		0			0
$730$		0			0
$731$	1.73205	+	3.00000i	0.0640622	+	0.110959i
$732$		0			0
$733$	20.7327	−	35.9101i	0.765781	−	1.32637i	−0.174052	−	0.984736i	$-0.555686\pi$
$733$	20.7327	−	35.9101i	0.765781	−	1.32637i	0.939833	−	0.341635i	$-0.110981\pi$
$734$	23.9545	−	41.4904i	0.884176	−	1.53144i
$735$		0			0
$736$	−7.33013	−	12.6962i	−0.270192	−	0.467986i
$737$	−24.3190			−0.895803
$738$		0			0
$739$	−45.8564			−1.68686			−0.843428	−	0.537243i	$-0.819466\pi$
$739$	−45.8564			−1.68686			−0.843428	+	0.537243i	$0.819466\pi$
$740$		0			0
$741$		0			0
$742$	3.34607	−	5.79555i	0.122838	−	0.212762i
$743$	−12.6586	+	21.9253i	−0.464398	+	0.804361i	−0.999174	−	0.0406329i	$-0.987063\pi$
$743$	−12.6586	+	21.9253i	−0.464398	+	0.804361i	0.534776	+	0.844994i	$0.320396\pi$
$744$		0			0
$745$		0			0
$746$	−62.1051			−2.27383
$747$		0			0
$748$	−3.10583			−0.113560
$749$	5.25833	+	9.10770i	0.192135	+	0.332788i
$750$		0			0
$751$	−17.2224	+	29.8301i	−0.628455	+	1.08852i	0.359406	+	0.933181i	$0.382979\pi$
$751$	−17.2224	+	29.8301i	−0.628455	+	1.08852i	−0.987862	+	0.155336i	$0.950354\pi$
$752$	9.77938	−	16.9384i	0.356617	−	0.617679i
$753$		0			0
$754$	−15.2942	−	26.4904i	−0.556983	−	0.964723i
$755$		0			0
$756$		0			0
$757$	−7.34847			−0.267085			−0.133542	−	0.991043i	$-0.542635\pi$
$757$	−7.34847			−0.267085			−0.133542	+	0.991043i	$0.542635\pi$
$758$	−12.1087	−	20.9730i	−0.439810	−	0.761772i
$759$		0			0
$760$		0			0
$761$	1.03590	−	1.79423i	0.0375513	−	0.0650407i	−0.846639	−	0.532168i	$-0.821378\pi$
$761$	1.03590	−	1.79423i	0.0375513	−	0.0650407i	0.884190	+	0.467127i	$0.154711\pi$
$762$		0			0
$763$	−2.08913	−	3.61849i	−0.0756318	−	0.130998i
$764$	−0.588457			−0.0212896
$765$		0			0
$766$	−39.5167			−1.42779
$767$	−3.10583	−	5.37945i	−0.112145	−	0.194241i
$768$		0			0
$769$	13.8205	−	23.9378i	0.498380	−	0.863220i	−0.501618	−	0.865089i	$-0.667262\pi$
$769$	13.8205	−	23.9378i	0.498380	−	0.863220i	0.999998	+	0.00186930i	$0.000595016\pi$
$770$		0			0
$771$		0			0
$772$	−17.9551	−	31.0991i	−0.646217	−	1.11928i
$773$	−7.72741			−0.277935			−0.138968	−	0.990297i	$-0.544378\pi$
$773$	−7.72741			−0.277935			−0.138968	+	0.990297i	$0.544378\pi$
$774$		0			0
$775$		0			0
$776$	2.66025	+	4.60770i	0.0954976	+	0.165407i
$777$		0			0
$778$	−23.3023	+	40.3608i	−0.835429	+	1.44701i
$779$	5.83013	−	10.0981i	0.208886	−	0.361801i
$780$		0			0
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	−1.41421			−0.0505722
$783$		0			0
$784$	27.6603			0.987866
$785$		0			0
$786$		0			0
$787$	−8.15711	+	14.1285i	−0.290770	+	0.503628i	−0.973992	−	0.226583i	$-0.927245\pi$
$787$	−8.15711	+	14.1285i	−0.290770	+	0.503628i	0.683222	+	0.730210i	$0.260578\pi$
$788$	18.0430	−	31.2514i	0.642755	−	1.11328i
$789$		0			0
$790$		0			0
$791$	−2.28719			−0.0813230
$792$		0			0
$793$	−26.1122			−0.927271
$794$	28.3923	+	49.1769i	1.00761	+	1.74522i
$795$		0			0
$796$	−3.97372	+	6.88269i	−0.140845	+	0.243950i
$797$	−7.95404	+	13.7768i	−0.281747	+	0.487999i	−0.971815	−	0.235745i	$-0.924247\pi$
$797$	−7.95404	+	13.7768i	−0.281747	+	0.487999i	0.690068	+	0.723744i	$0.257580\pi$
$798$		0			0
$799$	−0.830127	−	1.43782i	−0.0293678	−	0.0508665i
$800$		0			0
$801$		0			0
$802$	59.7487			2.10980
$803$	−20.0764	−	34.7733i	−0.708480	−	1.22712i
$804$		0			0
$805$		0			0
$806$	−6.46410	+	11.1962i	−0.227688	+	0.394368i
$807$		0			0
$808$	−0.656339	−	1.13681i	−0.0230899	−	0.0399929i
$809$	−37.1769			−1.30707			−0.653535	−	0.756896i	$-0.726715\pi$
$809$	−37.1769			−1.30707			−0.653535	+	0.756896i	$0.726715\pi$
$810$		0			0
$811$	43.5692			1.52992			0.764961	−	0.644076i	$-0.222758\pi$
$811$	43.5692			1.52992			0.764961	+	0.644076i	$0.222758\pi$
$812$	−5.01910	−	8.69333i	−0.176136	−	0.305076i
$813$		0			0
$814$	19.3923	−	33.5885i	0.679700	−	1.17727i
$815$		0			0
$816$		0			0
$817$	12.4877	+	21.6293i	0.436889	+	0.756714i
$818$	−45.3292			−1.58490
$819$		0			0
$820$		0			0
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	−0.999872	−	0.0160280i	$-0.994898\pi$
$821$	−14.7224	−	25.5000i	−0.513816	−	0.889956i	0.486055	−	0.873928i	$-0.338435\pi$
$822$		0			0
$823$	1.01669	−	1.76097i	0.0354397	−	0.0613834i	−0.847762	−	0.530378i	$-0.822050\pi$
$823$	1.01669	−	1.76097i	0.0354397	−	0.0613834i	0.883201	+	0.468994i	$0.155383\pi$
$824$	2.36603	−	4.09808i	0.0824244	−	0.142763i
$825$		0			0
$826$	−2.19615	−	3.80385i	−0.0764139	−	0.132353i
$827$	11.5539			0.401770			0.200885	−	0.979615i	$-0.435618\pi$
$827$	11.5539			0.401770			0.200885	+	0.979615i	$0.435618\pi$
$828$		0			0
$829$	31.5885			1.09711			0.548556	−	0.836114i	$-0.315178\pi$
$829$	31.5885			1.09711			0.548556	+	0.836114i	$0.315178\pi$
$830$		0			0
$831$		0			0
$832$	−7.02030	+	12.1595i	−0.243385	+	0.421555i
$833$	1.17398	−	2.03339i	0.0406759	−	0.0704527i
$834$		0			0
$835$		0			0
$836$	−22.3923			−0.774454
$837$		0			0
$838$	31.0112			1.07126
$839$	0.633975	+	1.09808i	0.0218872	+	0.0379098i	0.876762	−	0.480925i	$-0.159699\pi$
$839$	0.633975	+	1.09808i	0.0218872	+	0.0379098i	−0.854874	+	0.518835i	$0.826366\pi$
$840$		0			0
$841$	−6.39230	+	11.0718i	−0.220424	+	0.381786i
$842$	12.1087	−	20.9730i	0.417295	−	0.722776i
$843$		0			0
$844$	11.3660	+	19.6865i	0.391235	+	0.677638i
$845$		0			0
$846$		0			0
$847$	−10.2141			−0.350959
$848$	8.62398	+	14.9372i	0.296149	+	0.512945i
$849$		0			0
$850$		0			0
$851$	4.09808	−	7.09808i	0.140480	−	0.243319i
$852$		0			0
$853$	−17.4746	−	30.2669i	−0.598319	−	1.03632i	−0.993069	−	0.117530i	$-0.962502\pi$
$853$	−17.4746	−	30.2669i	−0.598319	−	1.03632i	0.394750	−	0.918788i	$-0.370831\pi$
$854$	−18.4641			−0.631829
$855$		0			0
$856$	−6.07180			−0.207530
$857$	−4.43211	−	7.67664i	−0.151398	−	0.262229i	0.780344	−	0.625351i	$-0.215044\pi$
$857$	−4.43211	−	7.67664i	−0.151398	−	0.262229i	−0.931742	+	0.363122i	$0.881711\pi$
$858$		0			0
$859$	11.2224	−	19.4378i	0.382904	−	0.663210i	−0.608572	−	0.793499i	$-0.708257\pi$
$859$	11.2224	−	19.4378i	0.382904	−	0.663210i	0.991476	+	0.130289i	$0.0415905\pi$
$860$		0			0
$861$		0			0
$862$	−5.79555	−	10.0382i	−0.197397	−	0.341902i
$863$	13.0697			0.444898			0.222449	−	0.974944i	$-0.428595\pi$
$863$	13.0697			0.444898			0.222449	+	0.974944i	$0.428595\pi$
$864$		0			0
$865$		0			0
$866$	29.4904	+	51.0788i	1.00212	+	1.73573i
$867$		0			0
$868$	−2.12132	+	3.67423i	−0.0720023	+	0.124712i
$869$	1.26795	−	2.19615i	0.0430122	−	0.0744994i
$870$		0			0
$871$	6.29423	+	10.9019i	0.213272	+	0.369398i
$872$	2.41233			0.0816916
$873$		0			0
$874$	−10.1962			−0.344890
$875$		0			0
$876$		0			0
$877$	−2.36156	+	4.09034i	−0.0797441	+	0.138121i	−0.903139	−	0.429347i	$-0.858744\pi$
$877$	−2.36156	+	4.09034i	−0.0797441	+	0.138121i	0.823395	+	0.567468i	$0.192077\pi$
$878$	−9.00292	+	15.5935i	−0.303834	+	0.526256i
$879$		0			0
$880$		0			0
$881$	8.41154			0.283392			0.141696	−	0.989910i	$-0.454744\pi$
$881$	8.41154			0.283392			0.141696	+	0.989910i	$0.454744\pi$
$882$		0			0
$883$	−17.6913			−0.595359			−0.297679	−	0.954666i	$-0.596213\pi$
$883$	−17.6913			−0.595359			−0.297679	+	0.954666i	$0.596213\pi$
$884$	0.803848	+	1.39230i	0.0270363	+	0.0468283i
$885$		0			0
$886$	−13.4282	+	23.2583i	−0.451129	+	0.781379i
$887$	14.0914	−	24.4070i	0.473142	−	0.819506i	−0.526386	−	0.850246i	$-0.676453\pi$
$887$	14.0914	−	24.4070i	0.473142	−	0.819506i	0.999527	+	0.0307403i	$0.00978648\pi$
$888$		0			0
$889$	2.08846	+	3.61731i	0.0700446	+	0.121321i
$890$		0			0
$891$		0			0
$892$	28.9778			0.970248
$893$	−5.98502	−	10.3664i	−0.200281	−	0.346897i
$894$		0			0
$895$		0			0
$896$	1.83975	−	3.18653i	0.0614616	−	0.106455i
$897$		0			0
$898$	−11.5911	−	20.0764i	−0.386800	−	0.669958i
$899$	17.6603			0.589002
$900$		0			0
$901$	1.46410			0.0487763
$902$	−19.5080	−	33.7888i	−0.649545	−	1.12504i
$903$		0			0
$904$	0.660254	−	1.14359i	0.0219597	−	0.0380354i
$905$		0			0
$906$		0			0
$907$	−24.8553	−	43.0506i	−0.825305	−	1.42947i	−0.901686	−	0.432392i	$-0.857670\pi$
$907$	−24.8553	−	43.0506i	−0.825305	−	1.42947i	0.0763808	−	0.997079i	$-0.475664\pi$
$908$	−3.28169			−0.108907
$909$		0			0
$910$		0			0
$911$	11.0718	+	19.1769i	0.366825	+	0.635360i	0.989067	−	0.147465i	$-0.0471114\pi$
$911$	11.0718	+	19.1769i	0.366825	+	0.635360i	−0.622242	+	0.782825i	$0.713778\pi$
$912$		0			0
$913$	−24.6472	+	42.6902i	−0.815703	+	1.41284i
$914$	−33.4186	+	57.8827i	−1.10539	+	1.91459i
$915$		0			0
$916$	−17.2583	−	29.8923i	−0.570231	−	0.987670i
$917$	−0.832204			−0.0274818
$918$		0			0
$919$	−15.1769			−0.500640			−0.250320	−	0.968163i	$-0.580536\pi$
$919$	−15.1769			−0.500640			−0.250320	+	0.968163i	$0.580536\pi$
$920$		0			0
$921$		0			0
$922$	18.0752	−	31.3071i	0.595275	−	1.03105i
$923$	−4.65874	+	8.06918i	−0.153344	+	0.265600i
$924$		0			0
$925$		0			0
$926$	−0.339746			−0.0111647
$927$		0			0
$928$	49.0542			1.61028
$929$	1.73205	+	3.00000i	0.0568267	+	0.0984268i	0.893039	−	0.449979i	$-0.148568\pi$
$929$	1.73205	+	3.00000i	0.0568267	+	0.0984268i	−0.836213	+	0.548405i	$0.815235\pi$
$930$		0			0
$931$	8.46410	−	14.6603i	0.277400	−	0.480470i
$932$	6.12372	−	10.6066i	0.200589	−	0.347431i
$933$		0			0
$934$	−5.56218	−	9.63397i	−0.182000	−	0.315233i
$935$		0			0
$936$		0			0
$937$	13.8647			0.452941			0.226471	−	0.974018i	$-0.427281\pi$
$937$	13.8647			0.452941			0.226471	+	0.974018i	$0.427281\pi$
$938$	4.45069	+	7.70882i	0.145320	+	0.251702i
$939$		0			0
$940$		0			0
$941$	−4.16025	+	7.20577i	−0.135620	+	0.234901i	−0.925834	−	0.377930i	$-0.876636\pi$
$941$	−4.16025	+	7.20577i	−0.135620	+	0.234901i	0.790214	+	0.612831i	$0.209969\pi$
$942$		0			0
$943$	−4.12252	−	7.14042i	−0.134248	−	0.232524i
$944$	11.3205			0.368451
$945$		0			0
$946$	83.5692			2.71707
$947$	1.15539	+	2.00120i	0.0375453	+	0.0650303i	0.884187	−	0.467132i	$-0.154713\pi$
$947$	1.15539	+	2.00120i	0.0375453	+	0.0650303i	−0.846642	+	0.532163i	$0.821379\pi$
$948$		0			0
$949$	−10.3923	+	18.0000i	−0.337348	+	0.584305i
$950$		0			0
$951$		0			0
$952$	−0.0879327	−	0.152304i	−0.00284992	−	0.00493620i
$953$	37.0197			1.19919			0.599594	−	0.800305i	$-0.295329\pi$
$953$	37.0197			1.19919			0.599594	+	0.800305i	$0.295329\pi$
$954$		0			0
$955$		0			0
$956$	11.1962	+	19.3923i	0.362109	+	0.627192i
$957$		0			0
$958$	30.7709	−	53.2968i	0.994163	−	1.72194i
$959$	−8.32051	+	14.4115i	−0.268683	+	0.465373i
$960$		0			0
$961$	11.7679	+	20.3827i	0.379611	+	0.657506i
$962$	−20.0764			−0.647289
$963$		0			0
$964$	10.8564			0.349661
$965$		0			0
$966$		0			0
$967$	17.3545	−	30.0588i	0.558082	−	0.966627i	−0.439574	−	0.898206i	$-0.644871\pi$
$967$	17.3545	−	30.0588i	0.558082	−	0.966627i	0.997657	−	0.0684208i	$-0.0217960\pi$
$968$	2.94855	−	5.10703i	0.0947698	−	0.164146i
$969$		0			0
$970$		0			0
$971$	−27.8038			−0.892268			−0.446134	−	0.894966i	$-0.647200\pi$
$971$	−27.8038			−0.892268			−0.446134	+	0.894966i	$0.647200\pi$
$972$		0			0
$973$	7.17260			0.229943
$974$	1.09808	+	1.90192i	0.0351846	+	0.0609416i
$975$		0			0
$976$	23.7942	−	41.2128i	0.761635	−	1.31919i
$977$	−7.77817	+	13.4722i	−0.248846	+	0.431014i	−0.963206	−	0.268765i	$-0.913385\pi$
$977$	−7.77817	+	13.4722i	−0.248846	+	0.431014i	0.714360	+	0.699778i	$0.246718\pi$
$978$		0			0
$979$	17.4904	+	30.2942i	0.558995	+	0.968208i
$980$		0			0
$981$		0			0
$982$	41.9459			1.33855
$983$	17.9365	+	31.0669i	0.572085	+	0.990881i	0.996352	+	0.0853431i	$0.0271987\pi$
$983$	17.9365	+	31.0669i	0.572085	+	0.990881i	−0.424266	+	0.905537i	$0.639468\pi$
$984$		0			0
$985$		0			0
$986$	2.36603	−	4.09808i	0.0753496	−	0.130509i
$987$		0			0
$988$	5.79555	+	10.0382i	0.184381	+	0.319358i
$989$	17.6603			0.561563
$990$		0			0
$991$	25.0718			0.796432			0.398216	−	0.917292i	$-0.369629\pi$
$991$	25.0718			0.796432			0.398216	+	0.917292i	$0.369629\pi$
$992$	−10.3664	−	17.9551i	−0.329132	−	0.570074i
$993$		0			0
$994$	−3.29423	+	5.70577i	−0.104487	+	0.180976i
$995$		0			0
$996$		0			0
$997$	7.58871	+	13.1440i	0.240337	+	0.416275i	0.960810	−	0.277207i	$-0.0894088\pi$
$997$	7.58871	+	13.1440i	0.240337	+	0.416275i	−0.720473	+	0.693483i	$0.756075\pi$
$998$	−7.45001			−0.235826
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.e.d.226.1		8
3.2	odd	2		225.2.e.d.76.4		8
5.2	odd	4		135.2.j.a.64.4		8
5.3	odd	4		135.2.j.a.64.1		8
5.4	even	2	inner	675.2.e.d.226.4		8
9.2	odd	6		225.2.e.d.151.4		8
9.4	even	3		2025.2.a.r.1.4		4
9.5	odd	6		2025.2.a.t.1.1		4
9.7	even	3	inner	675.2.e.d.451.1		8
15.2	even	4		45.2.j.a.4.1	✓	8
15.8	even	4		45.2.j.a.4.4	yes	8
15.14	odd	2		225.2.e.d.76.1		8
20.3	even	4		2160.2.by.c.1009.4		8
20.7	even	4		2160.2.by.c.1009.2		8
45.2	even	12		45.2.j.a.34.4	yes	8
45.4	even	6		2025.2.a.r.1.1		4
45.7	odd	12		135.2.j.a.19.1		8
45.13	odd	12		405.2.b.c.244.1		4
45.14	odd	6		2025.2.a.t.1.4		4
45.22	odd	12		405.2.b.c.244.4		4
45.23	even	12		405.2.b.d.244.4		4
45.29	odd	6		225.2.e.d.151.1		8
45.32	even	12		405.2.b.d.244.1		4
45.34	even	6	inner	675.2.e.d.451.4		8
45.38	even	12		45.2.j.a.34.1	yes	8
45.43	odd	12		135.2.j.a.19.4		8
60.23	odd	4		720.2.by.d.49.4		8
60.47	odd	4		720.2.by.d.49.1		8
180.7	even	12		2160.2.by.c.289.4		8
180.43	even	12		2160.2.by.c.289.2		8
180.47	odd	12		720.2.by.d.529.4		8
180.83	odd	12		720.2.by.d.529.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.j.a.4.1	✓	8	15.2	even	4
45.2.j.a.4.4	yes	8	15.8	even	4
45.2.j.a.34.1	yes	8	45.38	even	12
45.2.j.a.34.4	yes	8	45.2	even	12
135.2.j.a.19.1		8	45.7	odd	12
135.2.j.a.19.4		8	45.43	odd	12
135.2.j.a.64.1		8	5.3	odd	4
135.2.j.a.64.4		8	5.2	odd	4
225.2.e.d.76.1		8	15.14	odd	2
225.2.e.d.76.4		8	3.2	odd	2
225.2.e.d.151.1		8	45.29	odd	6
225.2.e.d.151.4		8	9.2	odd	6
405.2.b.c.244.1		4	45.13	odd	12
405.2.b.c.244.4		4	45.22	odd	12
405.2.b.d.244.1		4	45.32	even	12
405.2.b.d.244.4		4	45.23	even	12
675.2.e.d.226.1		8	1.1	even	1	trivial
675.2.e.d.226.4		8	5.4	even	2	inner
675.2.e.d.451.1		8	9.7	even	3	inner
675.2.e.d.451.4		8	45.34	even	6	inner
720.2.by.d.49.1		8	60.47	odd	4
720.2.by.d.49.4		8	60.23	odd	4
720.2.by.d.529.1		8	180.83	odd	12
720.2.by.d.529.4		8	180.47	odd	12
2025.2.a.r.1.1		4	45.4	even	6
2025.2.a.r.1.4		4	9.4	even	3
2025.2.a.t.1.1		4	9.5	odd	6
2025.2.a.t.1.4		4	45.14	odd	6
2160.2.by.c.289.2		8	180.43	even	12
2160.2.by.c.289.4		8	180.7	even	12
2160.2.by.c.1009.2		8	20.7	even	4
2160.2.by.c.1009.4		8	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 1.67303i) q^{2} +(-0.866025 + 1.50000i) q^{4} +(0.448288 + 0.776457i) q^{7} -0.517638 q^{8} +O(q^{10})\)	\(q+(-0.965926 - 1.67303i) q^{2} +(-0.866025 + 1.50000i) q^{4} +(0.448288 + 0.776457i) q^{7} -0.517638 q^{8} +(2.36603 + 4.09808i) q^{11} +(1.22474 - 2.12132i) q^{13} +(0.866025 - 1.50000i) q^{14} +(2.23205 + 3.86603i) q^{16} +0.378937 q^{17} +2.73205 q^{19} +(4.57081 - 7.91688i) q^{22} +(0.965926 - 1.67303i) q^{23} -4.73205 q^{26} -1.55291 q^{28} +(3.23205 + 5.59808i) q^{29} +(1.36603 - 2.36603i) q^{31} +(3.79435 - 6.57201i) q^{32} +(-0.366025 - 0.633975i) q^{34} +4.24264 q^{37} +(-2.63896 - 4.57081i) q^{38} +(2.13397 - 3.69615i) q^{41} +(4.57081 + 7.91688i) q^{43} -8.19615 q^{44} -3.73205 q^{46} +(-2.19067 - 3.79435i) q^{47} +(3.09808 - 5.36603i) q^{49} +(2.12132 + 3.67423i) q^{52} +3.86370 q^{53} +(-0.232051 - 0.401924i) q^{56} +(6.24384 - 10.8147i) q^{58} +(1.26795 - 2.19615i) q^{59} +(-5.33013 - 9.23205i) q^{61} -5.27792 q^{62} -5.73205 q^{64} +(-2.56961 + 4.45069i) q^{67} +(-0.328169 + 0.568406i) q^{68} -3.80385 q^{71} -8.48528 q^{73} +(-4.09808 - 7.09808i) q^{74} +(-2.36603 + 4.09808i) q^{76} +(-2.12132 + 3.67423i) q^{77} +(-0.267949 - 0.464102i) q^{79} -8.24504 q^{82} +(5.20857 + 9.02150i) q^{83} +(8.83013 - 15.2942i) q^{86} +(-1.22474 - 2.12132i) q^{88} +7.39230 q^{89} +2.19615 q^{91} +(1.67303 + 2.89778i) q^{92} +(-4.23205 + 7.33013i) q^{94} +(-5.13922 - 8.90138i) q^{97} -11.9700 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q + 12 q^{11} + 4 q^{16} + 8 q^{19} - 24 q^{26} + 12 q^{29} + 4 q^{31} + 4 q^{34} + 24 q^{41} - 24 q^{44} - 16 q^{46} + 4 q^{49} + 12 q^{56} + 24 q^{59} - 8 q^{61} - 32 q^{64} - 72 q^{71} - 12 q^{74} - 12 q^{76} - 16 q^{79} + 36 q^{86} - 24 q^{89} - 24 q^{91} - 20 q^{94}+O(q^{100}) \) 8 * q + 12 * q^11 + 4 * q^16 + 8 * q^19 - 24 * q^26 + 12 * q^29 + 4 * q^31 + 4 * q^34 + 24 * q^41 - 24 * q^44 - 16 * q^46 + 4 * q^49 + 12 * q^56 + 24 * q^59 - 8 * q^61 - 32 * q^64 - 72 * q^71 - 12 * q^74 - 12 * q^76 - 16 * q^79 + 36 * q^86 - 24 * q^89 - 24 * q^91 - 20 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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