LMFDB - Embedded newform 900.2.n.b.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(181,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("900.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.n (of order $5$, degree $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$1.40799 - 0.132563i$ of defining polynomial
Character	$\chi$	$=$	900.361
Dual form			900.2.n.b.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +O(q^{10})$	$q+(0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +(-4.99517 + 3.62921i) q^{11} +(2.87714 + 2.09036i) q^{13} +(-0.153180 - 0.471439i) q^{17} +(0.0963126 + 0.296420i) q^{19} +(-2.47611 + 1.79900i) q^{23} +(-3.14835 + 3.88431i) q^{25} +(0.0378031 - 0.116346i) q^{29} +(-0.909629 - 2.79955i) q^{31} +(1.44743 + 3.03637i) q^{35} +(3.53298 + 2.56686i) q^{37} +(3.44096 + 2.50001i) q^{41} -3.62663 q^{43} +(-1.63227 + 5.02362i) q^{47} -4.73708 q^{49} +(2.65748 - 8.17888i) q^{53} +(-12.1317 - 6.59054i) q^{55} +(10.4222 + 7.57219i) q^{59} +(9.15882 - 6.65427i) q^{61} +(-1.45094 + 7.81873i) q^{65} +(4.09181 + 12.5933i) q^{67} +(-1.00994 + 3.10827i) q^{71} +(-12.9174 + 9.38504i) q^{73} +(-7.51424 + 5.45941i) q^{77} +(-2.63513 + 8.11010i) q^{79} +(-3.50367 - 10.7832i) q^{83} +(0.804191 - 0.762805i) q^{85} +(11.4335 - 8.30691i) q^{89} +(4.32808 + 3.14453i) q^{91} +(-0.505640 + 0.479617i) q^{95} +(-3.54837 + 10.9208i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{5} + 8 q^{7}+O(q^{10}) $ 8 * q + 5 * q^5 + 8 * q^7	$ 8 q + 5 q^{5} + 8 q^{7} - 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{23} + 5 q^{25} + 3 q^{29} - 3 q^{31} + 10 q^{35} - q^{37} - 10 q^{41} - 12 q^{43} + 33 q^{47} - 8 q^{49} + 19 q^{53} - 15 q^{55} + 38 q^{59} + 46 q^{61} - 25 q^{65} - 8 q^{67} + 25 q^{71} - 26 q^{73} - 23 q^{77} - 16 q^{79} - 8 q^{83} - 30 q^{85} + 30 q^{89} + 25 q^{91} + 25 q^{95} - 14 q^{97}+O(q^{100}) $ 8 * q + 5 * q^5 + 8 * q^7 - 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^23 + 5 * q^25 + 3 * q^29 - 3 * q^31 + 10 * q^35 - q^37 - 10 * q^41 - 12 * q^43 + 33 * q^47 - 8 * q^49 + 19 * q^53 - 15 * q^55 + 38 * q^59 + 46 * q^61 - 25 * q^65 - 8 * q^67 + 25 * q^71 - 26 * q^73 - 23 * q^77 - 16 * q^79 - 8 * q^83 - 30 * q^85 + 30 * q^89 + 25 * q^91 + 25 * q^95 - 14 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.962197	+	2.01846i	0.430308	+	0.902682i
$5$	0.962197	+	2.01846i	0.430308	+	0.902682i
$6$		0			0
$7$	1.50430			0.568572			0.284286	−	0.958740i	$-0.408244\pi$
$7$	1.50430			0.568572			0.284286	+	0.958740i	$0.408244\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.99517	+	3.62921i	−1.50610	+	1.09425i	−0.538231	+	0.842797i	$0.680907\pi$
$11$	−4.99517	+	3.62921i	−1.50610	+	1.09425i	−0.967870	+	0.251450i	$0.919093\pi$
$12$		0			0
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	0.910319	−	0.413906i	$-0.135836\pi$
$13$	2.87714	+	2.09036i	0.797975	+	0.579763i	−0.112344	+	0.993669i	$0.535836\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.153180	−	0.471439i	−0.0371516	−	0.114341i	0.930761	−	0.365629i	$-0.119146\pi$
$17$	−0.153180	−	0.471439i	−0.0371516	−	0.114341i	−0.967912	+	0.251288i	$0.919146\pi$
$18$		0			0
$19$	0.0963126	+	0.296420i	0.0220956	+	0.0680034i	0.961496	−	0.274818i	$-0.0886175\pi$
$19$	0.0963126	+	0.296420i	0.0220956	+	0.0680034i	−0.939401	+	0.342821i	$0.888618\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.47611	+	1.79900i	−0.516305	+	0.375117i	−0.815210	−	0.579165i	$-0.803379\pi$
$23$	−2.47611	+	1.79900i	−0.516305	+	0.375117i	0.298905	+	0.954283i	$0.403379\pi$
$24$		0			0
$25$	−3.14835	+	3.88431i	−0.629671	+	0.776862i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0378031	−	0.116346i	0.00701987	−	0.0216049i	−0.947485	−	0.319800i	$-0.896384\pi$
$29$	0.0378031	−	0.116346i	0.00701987	−	0.0216049i	0.954505	+	0.298195i	$0.0963844\pi$
$30$		0			0
$31$	−0.909629	−	2.79955i	−0.163374	−	0.502814i	0.835539	−	0.549432i	$-0.185156\pi$
$31$	−0.909629	−	2.79955i	−0.163374	−	0.502814i	−0.998913	+	0.0466176i	$0.985156\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.44743	+	3.03637i	0.244661	+	0.513240i
$36$		0			0
$37$	3.53298	+	2.56686i	0.580818	+	0.421989i	0.839019	−	0.544102i	$-0.183130\pi$
$37$	3.53298	+	2.56686i	0.580818	+	0.421989i	−0.258201	+	0.966091i	$0.583130\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.44096	+	2.50001i	0.537388	+	0.390436i	0.823114	−	0.567876i	$-0.192235\pi$
$41$	3.44096	+	2.50001i	0.537388	+	0.390436i	−0.285726	+	0.958311i	$0.592235\pi$
$42$		0			0
$43$	−3.62663			−0.553056			−0.276528	−	0.961006i	$-0.589184\pi$
$43$	−3.62663			−0.553056			−0.276528	+	0.961006i	$0.589184\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.63227	+	5.02362i	−0.238091	+	0.732770i	0.758605	+	0.651551i	$0.225881\pi$
$47$	−1.63227	+	5.02362i	−0.238091	+	0.732770i	−0.996696	+	0.0812191i	$0.974119\pi$
$48$		0			0
$49$	−4.73708			−0.676726
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.65748	−	8.17888i	0.365033	−	1.12346i	−0.584928	−	0.811086i	$-0.698877\pi$
$53$	2.65748	−	8.17888i	0.365033	−	1.12346i	0.949960	−	0.312370i	$-0.101123\pi$
$54$		0			0
$55$	−12.1317	−	6.59054i	−1.63584	−	0.888669i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	10.4222	+	7.57219i	1.35686	+	0.985815i	0.998638	+	0.0521781i	$0.0166164\pi$
$59$	10.4222	+	7.57219i	1.35686	+	0.985815i	0.358220	+	0.933637i	$0.383384\pi$
$60$		0			0
$61$	9.15882	−	6.65427i	1.17267	−	0.851992i	0.181341	−	0.983420i	$-0.441956\pi$
$61$	9.15882	−	6.65427i	1.17267	−	0.851992i	0.991326	+	0.131428i	$0.0419562\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.45094	+	7.81873i	−0.179967	+	0.969794i
$66$		0			0
$67$	4.09181	+	12.5933i	0.499894	+	1.53852i	0.809188	+	0.587550i	$0.199908\pi$
$67$	4.09181	+	12.5933i	0.499894	+	1.53852i	−0.309293	+	0.950967i	$0.600092\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.00994	+	3.10827i	−0.119858	+	0.368884i	−0.992929	−	0.118708i	$-0.962125\pi$
$71$	−1.00994	+	3.10827i	−0.119858	+	0.368884i	0.873071	+	0.487592i	$0.162125\pi$
$72$		0			0
$73$	−12.9174	+	9.38504i	−1.51187	+	1.09844i	−0.546527	+	0.837441i	$0.684050\pi$
$73$	−12.9174	+	9.38504i	−1.51187	+	1.09844i	−0.965340	+	0.260994i	$0.915950\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.51424	+	5.45941i	−0.856327	+	0.622158i
$78$		0			0
$79$	−2.63513	+	8.11010i	−0.296475	+	0.912457i	0.686247	+	0.727369i	$0.259257\pi$
$79$	−2.63513	+	8.11010i	−0.296475	+	0.912457i	−0.982722	+	0.185088i	$0.940743\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.50367	−	10.7832i	−0.384578	−	1.18361i	−0.936786	−	0.349903i	$-0.886215\pi$
$83$	−3.50367	−	10.7832i	−0.384578	−	1.18361i	0.552208	−	0.833706i	$-0.313785\pi$
$84$		0			0
$85$	0.804191	−	0.762805i	0.0872268	−	0.0827378i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	11.4335	−	8.30691i	1.21195	−	0.880531i	0.216541	−	0.976274i	$-0.430523\pi$
$89$	11.4335	−	8.30691i	1.21195	−	0.880531i	0.995406	+	0.0957428i	$0.0305226\pi$
$90$		0			0
$91$	4.32808	+	3.14453i	0.453706	+	0.329637i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.505640	+	0.479617i	−0.0518775	+	0.0492077i
$96$		0			0
$97$	−3.54837	+	10.9208i	−0.360282	+	1.10884i	0.592601	+	0.805497i	$0.298101\pi$
$97$	−3.54837	+	10.9208i	−0.360282	+	1.10884i	−0.952883	+	0.303339i	$0.901899\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.8359			1.47622			0.738111	−	0.674679i	$-0.235718\pi$
$101$	14.8359			1.47622			0.738111	+	0.674679i	$0.235718\pi$
$102$		0			0
$103$	5.95307	−	18.3217i	0.586574	−	1.80529i	−0.00628354	−	0.999980i	$-0.502000\pi$
$103$	5.95307	−	18.3217i	0.586574	−	1.80529i	0.592857	−	0.805308i	$-0.298000\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.63523			−0.834799			−0.417400	−	0.908723i	$-0.637058\pi$
$107$	−8.63523			−0.834799			−0.417400	+	0.908723i	$0.637058\pi$
$108$		0			0
$109$	15.1200	+	10.9853i	1.44823	+	1.05220i	0.986241	+	0.165315i	$0.0528641\pi$
$109$	15.1200	+	10.9853i	1.44823	+	1.05220i	0.461989	+	0.886886i	$0.347136\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.89971	+	3.55985i	0.460926	+	0.334883i	0.793894	−	0.608056i	$-0.208050\pi$
$113$	4.89971	+	3.55985i	0.460926	+	0.334883i	−0.332968	+	0.942938i	$0.608050\pi$
$114$		0			0
$115$	−6.01371	−	3.26694i	−0.560782	−	0.304643i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.230428	−	0.709186i	−0.0211233	−	0.0650109i
$120$		0			0
$121$	8.38144	−	25.7954i	0.761949	−	2.34504i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.8697	−	2.61735i	−0.972212	−	0.234103i
$126$		0			0
$127$	7.47988	−	5.43445i	0.663732	−	0.482230i	−0.204189	−	0.978931i	$-0.565456\pi$
$127$	7.47988	−	5.43445i	0.663732	−	0.482230i	0.867921	+	0.496702i	$0.165456\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.87613	−	18.0849i	−0.513399	−	1.58008i	−0.786175	−	0.618003i	$-0.787942\pi$
$131$	−5.87613	−	18.0849i	−0.513399	−	1.58008i	0.272776	−	0.962078i	$-0.412058\pi$
$132$		0			0
$133$	0.144883	+	0.445904i	0.0125630	+	0.0386648i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.36053	+	4.62120i	0.543417	+	0.394816i	0.825352	−	0.564618i	$-0.190976\pi$
$137$	6.36053	+	4.62120i	0.543417	+	0.394816i	−0.281936	+	0.959433i	$0.590976\pi$
$138$		0			0
$139$	11.1647	−	8.11165i	0.946980	−	0.688021i	−0.00311101	−	0.999995i	$-0.500990\pi$
$139$	11.1647	−	8.11165i	0.946980	−	0.688021i	0.950091	+	0.311974i	$0.100990\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−21.9582			−1.83624
$144$		0			0
$145$	0.271214	−	0.0356438i	0.0225231	−	0.00296005i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.12168			−0.419585			−0.209792	−	0.977746i	$-0.567279\pi$
$149$	−5.12168			−0.419585			−0.209792	+	0.977746i	$0.567279\pi$
$150$		0			0
$151$	−12.9476			−1.05366			−0.526829	−	0.849972i	$-0.676619\pi$
$151$	−12.9476			−1.05366			−0.526829	+	0.849972i	$0.676619\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.77554	−	4.52977i	0.383580	−	0.363840i
$156$		0			0
$157$	−4.02750			−0.321429			−0.160715	−	0.987001i	$-0.551380\pi$
$157$	−4.02750			−0.321429			−0.160715	+	0.987001i	$0.551380\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.72481	+	2.70623i	−0.293556	+	0.213281i
$162$		0			0
$163$	−12.6360	−	9.18062i	−0.989732	−	0.719082i	−0.0298692	−	0.999554i	$-0.509509\pi$
$163$	−12.6360	−	9.18062i	−0.989732	−	0.719082i	−0.959862	+	0.280472i	$0.909509\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.66014	−	11.2647i	−0.283230	−	0.871692i	−0.986924	−	0.161189i	$-0.948467\pi$
$167$	−3.66014	−	11.2647i	−0.283230	−	0.871692i	0.703694	−	0.710503i	$-0.251533\pi$
$168$		0			0
$169$	−0.108909	−	0.335187i	−0.00837761	−	0.0257836i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.9982	−	8.71717i	0.912203	−	0.662754i	−0.0293681	−	0.999569i	$-0.509349\pi$
$173$	11.9982	−	8.71717i	0.912203	−	0.662754i	0.941571	+	0.336814i	$0.109349\pi$
$174$		0			0
$175$	−4.73607	+	5.84317i	−0.358013	+	0.441702i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.295895	−	0.910670i	0.0221162	−	0.0680667i	−0.939389	−	0.342852i	$-0.888607\pi$
$179$	0.295895	−	0.910670i	0.0221162	−	0.0680667i	0.961505	+	0.274786i	$0.0886069\pi$
$180$		0			0
$181$	1.27971	+	3.93855i	0.0951202	+	0.292750i	0.987285	−	0.158960i	$-0.0508141\pi$
$181$	1.27971	+	3.93855i	0.0951202	+	0.292750i	−0.892165	+	0.451710i	$0.850814\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.78168	+	9.60099i	−0.130992	+	0.705879i
$186$		0			0
$187$	2.47611	+	1.79900i	0.181071	+	0.131556i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−14.2634	−	10.3629i	−1.03206	−	0.749836i	−0.0633410	−	0.997992i	$-0.520176\pi$
$191$	−14.2634	−	10.3629i	−1.03206	−	0.749836i	−0.968720	+	0.248156i	$0.920176\pi$
$192$		0			0
$193$	5.25392			0.378185			0.189093	−	0.981959i	$-0.439445\pi$
$193$	5.25392			0.378185			0.189093	+	0.981959i	$0.439445\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.653870	−	2.01240i	0.0465863	−	0.143378i	−0.925058	−	0.379827i	$-0.875984\pi$
$197$	0.653870	−	2.01240i	0.0465863	−	0.143378i	0.971644	+	0.236449i	$0.0759836\pi$
$198$		0			0
$199$	9.07029			0.642976			0.321488	−	0.946914i	$-0.395817\pi$
$199$	9.07029			0.642976			0.321488	+	0.946914i	$0.395817\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.0568672	−	0.175019i	0.00399130	−	0.0122840i
$204$		0			0
$205$	−1.73528	+	9.35095i	−0.121197	+	0.653098i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.55687	−	1.13113i	−0.107691	−	0.0782419i
$210$		0			0
$211$	16.0306	−	11.6469i	1.10359	−	0.801807i	0.121950	−	0.992536i	$-0.461085\pi$
$211$	16.0306	−	11.6469i	1.10359	−	0.801807i	0.981643	+	0.190729i	$0.0610853\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.48953	−	7.32021i	−0.237984	−	0.499234i
$216$		0			0
$217$	−1.36835	−	4.21136i	−0.0928900	−	0.285886i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.544760	−	1.67660i	0.0366445	−	0.112780i
$222$		0			0
$223$	−5.32506	+	3.86888i	−0.356593	+	0.259080i	−0.751629	−	0.659586i	$-0.770732\pi$
$223$	−5.32506	+	3.86888i	−0.356593	+	0.259080i	0.395037	+	0.918665i	$0.370732\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.53193	−	6.92535i	0.632656	−	0.459652i	−0.224663	−	0.974436i	$-0.572128\pi$
$227$	9.53193	−	6.92535i	0.632656	−	0.459652i	0.857319	+	0.514785i	$0.172128\pi$
$228$		0			0
$229$	3.67417	−	11.3079i	0.242796	−	0.747250i	−0.753195	−	0.657798i	$-0.771488\pi$
$229$	3.67417	−	11.3079i	0.242796	−	0.747250i	0.995991	−	0.0894526i	$-0.0285117\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.56054	+	4.80285i	0.102234	+	0.314645i	0.989071	−	0.147437i	$-0.0471025\pi$
$233$	1.56054	+	4.80285i	0.102234	+	0.314645i	−0.886837	+	0.462082i	$0.847102\pi$
$234$		0			0
$235$	−11.7105	+	1.53903i	−0.763911	+	0.100396i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.16762	−	1.57487i	0.140212	−	0.101870i	−0.515468	−	0.856909i	$-0.672382\pi$
$239$	2.16762	−	1.57487i	0.140212	−	0.101870i	0.655680	+	0.755039i	$0.272382\pi$
$240$		0			0
$241$	−10.2390	−	7.43906i	−0.659551	−	0.479192i	0.206960	−	0.978349i	$-0.433643\pi$
$241$	−10.2390	−	7.43906i	−0.659551	−	0.479192i	−0.866511	+	0.499157i	$0.833643\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.55801	−	9.56161i	−0.291200	−	0.610869i
$246$		0			0
$247$	−0.342521	+	1.05417i	−0.0217941	+	0.0670752i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	22.9068			1.44586			0.722932	−	0.690919i	$-0.242794\pi$
$251$	22.9068			1.44586			0.722932	+	0.690919i	$0.242794\pi$
$252$		0			0
$253$	5.83966	−	17.9726i	0.367136	−	1.12993i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	27.7764			1.73264			0.866322	−	0.499486i	$-0.166478\pi$
$257$	27.7764			1.73264			0.866322	+	0.499486i	$0.166478\pi$
$258$		0			0
$259$	5.31466	+	3.86132i	0.330237	+	0.239931i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.47479	+	6.88384i	0.584241	+	0.424476i	0.840250	−	0.542198i	$-0.182408\pi$
$263$	9.47479	+	6.88384i	0.584241	+	0.424476i	−0.256010	+	0.966674i	$0.582408\pi$
$264$		0			0
$265$	19.0658	−	2.50568i	1.17120	−	0.153923i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.29979	−	4.00034i	−0.0792496	−	0.243905i	0.903580	−	0.428419i	$-0.140929\pi$
$269$	−1.29979	−	4.00034i	−0.0792496	−	0.243905i	−0.982830	+	0.184513i	$0.940929\pi$
$270$		0			0
$271$	−3.88308	+	11.9509i	−0.235880	+	0.725965i	0.761123	+	0.648608i	$0.224648\pi$
$271$	−3.88308	+	11.9509i	−0.235880	+	0.725965i	−0.997003	+	0.0773578i	$0.975352\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.62962	−	30.8288i	0.0982695	−	1.85905i
$276$		0			0
$277$	−25.7795	+	18.7299i	−1.54894	+	1.12537i	−0.604543	+	0.796573i	$0.706644\pi$
$277$	−25.7795	+	18.7299i	−1.54894	+	1.12537i	−0.944400	+	0.328800i	$0.893356\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.03691	−	15.5020i	−0.300477	−	0.924773i	−0.981326	−	0.192350i	$-0.938389\pi$
$281$	−5.03691	−	15.5020i	−0.300477	−	0.924773i	0.680849	−	0.732423i	$-0.261611\pi$
$282$		0			0
$283$	−4.21205	−	12.9634i	−0.250381	−	0.770592i	−0.994705	−	0.102774i	$-0.967228\pi$
$283$	−4.21205	−	12.9634i	−0.250381	−	0.770592i	0.744324	−	0.667819i	$-0.232772\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.17624	+	3.76076i	0.305544	+	0.221991i
$288$		0			0
$289$	13.5545	−	9.84792i	0.797323	−	0.579289i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−25.2652			−1.47601			−0.738004	−	0.674796i	$-0.764232\pi$
$293$	−25.2652			−1.47601			−0.738004	+	0.674796i	$0.764232\pi$
$294$		0			0
$295$	−5.25592	+	28.3228i	−0.306012	+	1.64902i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.8847			−0.629477
$300$		0			0
$301$	−5.45554			−0.314452
$302$		0			0
$303$		0			0
$304$		0			0
$305$	22.2440	+	12.0840i	1.27369	+	0.691927i
$306$		0			0
$307$	−7.01023			−0.400095			−0.200047	−	0.979786i	$-0.564110\pi$
$307$	−7.01023			−0.400095			−0.200047	+	0.979786i	$0.564110\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.7403	−	8.52985i	0.665733	−	0.483683i	−0.202861	−	0.979208i	$-0.565024\pi$
$311$	11.7403	−	8.52985i	0.665733	−	0.483683i	0.868594	+	0.495524i	$0.165024\pi$
$312$		0			0
$313$	−17.7334	−	12.8841i	−1.00235	−	0.728250i	−0.0397589	−	0.999209i	$-0.512659\pi$
$313$	−17.7334	−	12.8841i	−1.00235	−	0.728250i	−0.962591	+	0.270960i	$0.912659\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.4194	+	32.0675i	0.585210	+	1.80109i	0.598426	+	0.801178i	$0.295793\pi$
$317$	10.4194	+	32.0675i	0.585210	+	1.80109i	−0.0132156	+	0.999913i	$0.504207\pi$
$318$		0			0
$319$	0.233411	+	0.718364i	0.0130685	+	0.0402207i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.124991	−	0.0908111i	0.00695467	−	0.00505286i
$324$		0			0
$325$	−17.1779	+	4.59450i	−0.952858	+	0.254857i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.45543	+	7.55703i	−0.135372	+	0.416632i
$330$		0			0
$331$	10.3814	+	31.9508i	0.570616	+	1.75617i	0.650645	+	0.759382i	$0.274498\pi$
$331$	10.3814	+	31.9508i	0.570616	+	1.75617i	−0.0800299	+	0.996792i	$0.525502\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−21.4819	+	20.3764i	−1.17368	+	1.11328i
$336$		0			0
$337$	−2.49603	−	1.81347i	−0.135967	−	0.0987859i	0.517723	−	0.855548i	$-0.326780\pi$
$337$	−2.49603	−	1.81347i	−0.135967	−	0.0987859i	−0.653690	+	0.756763i	$0.726780\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	14.7039	+	10.6830i	0.796261	+	0.578518i
$342$		0			0
$343$	−17.6561			−0.953339
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.88556	+	11.9585i	−0.208588	+	0.641967i	0.790959	+	0.611869i	$0.209582\pi$
$347$	−3.88556	+	11.9585i	−0.208588	+	0.641967i	−0.999547	+	0.0300984i	$0.990418\pi$
$348$		0			0
$349$	13.3100			0.712466			0.356233	−	0.934397i	$-0.384061\pi$
$349$	13.3100			0.712466			0.356233	+	0.934397i	$0.384061\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.48923	−	10.7388i	0.185713	−	0.571566i	−0.814247	−	0.580519i	$-0.802850\pi$
$353$	3.48923	−	10.7388i	0.185713	−	0.571566i	0.999960	+	0.00895265i	$0.00284975\pi$
$354$		0			0
$355$	−7.24568	+	0.952250i	−0.384561	+	0.0505402i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.7007	+	11.4072i	0.828652	+	0.602051i	0.919178	−	0.393843i	$-0.128855\pi$
$359$	15.7007	+	11.4072i	0.828652	+	0.602051i	−0.0905254	+	0.995894i	$0.528855\pi$
$360$		0			0
$361$	15.2927	−	11.1108i	0.804881	−	0.584780i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−31.3724	−	17.0430i	−1.64211	−	0.892071i
$366$		0			0
$367$	5.42951	+	16.7103i	0.283418	+	0.872271i	0.986868	+	0.161526i	$0.0516417\pi$
$367$	5.42951	+	16.7103i	0.283418	+	0.872271i	−0.703450	+	0.710744i	$0.748358\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.99764	−	12.3035i	0.207547	−	0.638765i
$372$		0			0
$373$	22.8195	−	16.5793i	1.18155	−	0.858446i	0.189204	−	0.981938i	$-0.439409\pi$
$373$	22.8195	−	16.5793i	1.18155	−	0.858446i	0.992346	+	0.123492i	$0.0394093\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.351971	−	0.255722i	0.0181274	−	0.0131703i
$378$		0			0
$379$	1.12118	−	3.45064i	0.0575912	−	0.177247i	−0.918123	−	0.396296i	$-0.870295\pi$
$379$	1.12118	−	3.45064i	0.0575912	−	0.177247i	0.975714	+	0.219049i	$0.0702954\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.27519	+	13.1577i	0.218452	+	0.672326i	0.998890	+	0.0470934i	$0.0149958\pi$
$383$	4.27519	+	13.1577i	0.218452	+	0.672326i	−0.780439	+	0.625232i	$0.785004\pi$
$384$		0			0
$385$	−18.2498	−	9.91415i	−0.930095	−	0.505272i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.9096	+	12.2855i	−0.857348	+	0.622900i	−0.927162	−	0.374660i	$-0.877759\pi$
$389$	−16.9096	+	12.2855i	−0.857348	+	0.622900i	0.0698138	+	0.997560i	$0.477759\pi$
$390$		0			0
$391$	1.22741	+	0.891765i	0.0620727	+	0.0450985i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.9054	+	2.48461i	−0.951235	+	0.125014i
$396$		0			0
$397$	−4.77499	+	14.6959i	−0.239650	+	0.737566i	0.756821	+	0.653622i	$0.226752\pi$
$397$	−4.77499	+	14.6959i	−0.239650	+	0.737566i	−0.996471	+	0.0839436i	$0.973248\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.25590			−0.112654			−0.0563271	−	0.998412i	$-0.517939\pi$
$401$	−2.25590			−0.112654			−0.0563271	+	0.998412i	$0.517939\pi$
$402$		0			0
$403$	3.23495	−	9.95616i	0.161144	−	0.495952i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−26.9635			−1.33653
$408$		0			0
$409$	1.88712	+	1.37107i	0.0933119	+	0.0677951i	0.633463	−	0.773773i	$-0.281633\pi$
$409$	1.88712	+	1.37107i	0.0933119	+	0.0677951i	−0.540151	+	0.841568i	$0.681633\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	15.6781	+	11.3908i	0.771471	+	0.560507i
$414$		0			0
$415$	18.3942	−	17.4476i	0.902936	−	0.856468i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.55768	+	4.79405i	0.0760977	+	0.234205i	0.981869	−	0.189563i	$-0.0607072\pi$
$419$	1.55768	+	4.79405i	0.0760977	+	0.234205i	−0.905771	+	0.423768i	$0.860707\pi$
$420$		0			0
$421$	3.99823	−	12.3053i	0.194862	−	0.599724i	−0.805116	−	0.593117i	$-0.797897\pi$
$421$	3.99823	−	12.3053i	0.194862	−	0.599724i	0.999978	−	0.00660640i	$-0.00210290\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.31348	+	0.889259i	0.112220	+	0.0431354i
$426$		0			0
$427$	13.7776	−	10.0100i	0.666745	−	0.484419i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.483616	−	1.48842i	−0.0232950	−	0.0716945i	0.938733	−	0.344645i	$-0.112001\pi$
$431$	−0.483616	−	1.48842i	−0.0232950	−	0.0716945i	−0.962028	+	0.272950i	$0.912001\pi$
$432$		0			0
$433$	7.99517	+	24.6066i	0.384224	+	1.18252i	0.937042	+	0.349217i	$0.113552\pi$
$433$	7.99517	+	24.6066i	0.384224	+	1.18252i	−0.552818	+	0.833302i	$0.686448\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.771740	−	0.560702i	−0.0369173	−	0.0268220i
$438$		0			0
$439$	−13.2446	+	9.62279i	−0.632132	+	0.459271i	−0.857138	−	0.515087i	$-0.827760\pi$
$439$	−13.2446	+	9.62279i	−0.632132	+	0.459271i	0.225006	+	0.974357i	$0.427760\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−28.1180			−1.33593			−0.667963	−	0.744194i	$-0.732834\pi$
$443$	−28.1180			−1.33593			−0.667963	+	0.744194i	$0.732834\pi$
$444$		0			0
$445$	27.7684	+	15.0851i	1.31635	+	0.715104i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	2.65681			0.125383			0.0626914	−	0.998033i	$-0.480032\pi$
$449$	2.65681			0.125383			0.0626914	+	0.998033i	$0.480032\pi$
$450$		0			0
$451$	−26.2613			−1.23659
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.18265	+	11.7617i	−0.102324	+	0.551398i
$456$		0			0
$457$	−0.321574			−0.0150426			−0.00752129	−	0.999972i	$-0.502394\pi$
$457$	−0.321574			−0.0150426			−0.00752129	+	0.999972i	$0.502394\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−6.21780	+	4.51749i	−0.289592	+	0.210401i	−0.723090	−	0.690754i	$-0.757279\pi$
$461$	−6.21780	+	4.51749i	−0.289592	+	0.210401i	0.433499	+	0.901154i	$0.357279\pi$
$462$		0			0
$463$	−15.4555	−	11.2291i	−0.718279	−	0.521860i	0.167555	−	0.985863i	$-0.446413\pi$
$463$	−15.4555	−	11.2291i	−0.718279	−	0.521860i	−0.885834	+	0.464002i	$0.846413\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.98372	+	6.10525i	0.0917955	+	0.282517i	0.986405	−	0.164331i	$-0.0525464\pi$
$467$	1.98372	+	6.10525i	0.0917955	+	0.282517i	−0.894610	+	0.446848i	$0.852546\pi$
$468$		0			0
$469$	6.15531	+	18.9441i	0.284226	+	0.874757i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	18.1157	−	13.1618i	0.832959	−	0.605180i
$474$		0			0
$475$	−1.45461	−	0.559126i	−0.0667422	−	0.0256545i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.3709	+	31.9183i	−0.473858	+	1.45839i	0.373633	+	0.927577i	$0.378112\pi$
$479$	−10.3709	+	31.9183i	−0.473858	+	1.45839i	−0.847491	+	0.530810i	$0.821888\pi$
$480$		0			0
$481$	4.79920	+	14.7704i	0.218825	+	0.673473i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−25.4573	+	3.34568i	−1.15596	+	0.151920i
$486$		0			0
$487$	9.63578	+	7.00080i	0.436639	+	0.317237i	0.784298	−	0.620384i	$-0.213023\pi$
$487$	9.63578	+	7.00080i	0.436639	+	0.317237i	−0.347659	+	0.937621i	$0.613023\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	12.6312	+	9.17712i	0.570039	+	0.414158i	0.835119	−	0.550069i	$-0.185398\pi$
$491$	12.6312	+	9.17712i	0.570039	+	0.414158i	−0.265080	+	0.964226i	$0.585398\pi$
$492$		0			0
$493$	−0.0606408			−0.00273112
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.51925	+	4.67577i	−0.0681477	+	0.209737i
$498$		0			0
$499$	30.9130			1.38386			0.691929	−	0.721966i	$-0.256761\pi$
$499$	30.9130			1.38386			0.691929	+	0.721966i	$0.256761\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.59178	+	29.5204i	−0.427676	+	1.31625i	0.472732	+	0.881206i	$0.343268\pi$
$503$	−9.59178	+	29.5204i	−0.427676	+	1.31625i	−0.900408	+	0.435046i	$0.856732\pi$
$504$		0			0
$505$	14.2750	+	29.9456i	0.635230	+	1.33256i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.7945	−	7.84269i	−0.478460	−	0.347621i	0.322269	−	0.946648i	$-0.395554\pi$
$509$	−10.7945	−	7.84269i	−0.478460	−	0.347621i	−0.800729	+	0.599027i	$0.795554\pi$
$510$		0			0
$511$	−19.4316	+	14.1179i	−0.859605	+	0.624540i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	42.7096	−	5.61302i	1.88201	−	0.247339i
$516$		0			0
$517$	−10.0783	−	31.0177i	−0.443242	−	1.36416i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−8.19439	+	25.2197i	−0.359003	+	1.10490i	0.594649	+	0.803985i	$0.297291\pi$
$521$	−8.19439	+	25.2197i	−0.359003	+	1.10490i	−0.953652	+	0.300912i	$0.902709\pi$
$522$		0			0
$523$	14.0888	−	10.2361i	0.616060	−	0.447594i	−0.235483	−	0.971878i	$-0.575667\pi$
$523$	14.0888	−	10.2361i	0.616060	−	0.447594i	0.851543	+	0.524285i	$0.175667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.18048	+	0.857670i	−0.0514226	+	0.0373607i
$528$		0			0
$529$	−4.21267	+	12.9653i	−0.183159	+	0.563707i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.67421	+	14.3857i	0.202463	+	0.623116i
$534$		0			0
$535$	−8.30879	−	17.4299i	−0.359220	−	0.753559i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	23.6626	−	17.1919i	1.01922	−	0.740506i
$540$		0			0
$541$	−4.42275	−	3.21332i	−0.190149	−	0.138151i	0.488638	−	0.872487i	$-0.337494\pi$
$541$	−4.42275	−	3.21332i	−0.190149	−	0.138151i	−0.678787	+	0.734335i	$0.737494\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.62499	+	41.0890i	−0.326619	+	1.76006i
$546$		0			0
$547$	6.68894	−	20.5864i	0.285998	−	0.880212i	−0.700099	−	0.714046i	$-0.746861\pi$
$547$	6.68894	−	20.5864i	0.285998	−	0.880212i	0.986098	−	0.166167i	$-0.0531391\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.0381282			0.00162432
$552$		0			0
$553$	−3.96403	+	12.2000i	−0.168568	+	0.518798i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	2.58830			0.109670			0.0548349	−	0.998495i	$-0.482537\pi$
$557$	2.58830			0.109670			0.0548349	+	0.998495i	$0.482537\pi$
$558$		0			0
$559$	−10.4343	−	7.58099i	−0.441325	−	0.320642i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.0945	+	11.6933i	0.678301	+	0.492815i	0.872794	−	0.488089i	$-0.162306\pi$
$563$	16.0945	+	11.6933i	0.678301	+	0.492815i	−0.194493	+	0.980904i	$0.562306\pi$
$564$		0			0
$565$	−2.47092	+	13.3151i	−0.103953	+	0.560172i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−10.0215	−	30.8431i	−0.420124	−	1.29301i	−0.907587	−	0.419865i	$-0.862077\pi$
$569$	−10.0215	−	30.8431i	−0.420124	−	1.29301i	0.487463	−	0.873144i	$-0.337923\pi$
$570$		0			0
$571$	4.23915	−	13.0468i	0.177403	−	0.545990i	−0.822332	−	0.569008i	$-0.807327\pi$
$571$	4.23915	−	13.0468i	0.177403	−	0.545990i	0.999735	+	0.0230176i	$0.00732739\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.807801	−	15.2819i	0.0336876	−	0.637298i
$576$		0			0
$577$	−19.9368	+	14.4849i	−0.829979	+	0.603015i	−0.919553	−	0.392965i	$-0.871449\pi$
$577$	−19.9368	+	14.4849i	−0.829979	+	0.603015i	0.0895741	+	0.995980i	$0.471449\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.27057	−	16.2212i	−0.218660	−	0.672967i
$582$		0			0
$583$	16.4083	+	50.4995i	0.679561	+	2.09147i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.73236	+	4.89134i	0.277874	+	0.201887i	0.717990	−	0.696054i	$-0.245062\pi$
$587$	6.73236	+	4.89134i	0.277874	+	0.201887i	−0.440115	+	0.897941i	$0.645062\pi$
$588$		0			0
$589$	0.742234	−	0.539264i	0.0305832	−	0.0222200i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−21.7904			−0.894826			−0.447413	−	0.894328i	$-0.647654\pi$
$593$	−21.7904			−0.894826			−0.447413	+	0.894328i	$0.647654\pi$
$594$		0			0
$595$	1.20974	−	1.14749i	0.0495947	−	0.0470424i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−10.6482			−0.435074			−0.217537	−	0.976052i	$-0.569802\pi$
$599$	−10.6482			−0.435074			−0.217537	+	0.976052i	$0.569802\pi$
$600$		0			0
$601$	2.60740			0.106358			0.0531791	−	0.998585i	$-0.483065\pi$
$601$	2.60740			0.106358			0.0531791	+	0.998585i	$0.483065\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	60.1316	−	7.90268i	2.44470	−	0.321290i
$606$		0			0
$607$	32.9820			1.33870			0.669349	−	0.742948i	$-0.266573\pi$
$607$	32.9820			1.33870			0.669349	+	0.742948i	$0.266573\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−15.1975	+	11.0416i	−0.614824	+	0.446696i
$612$		0			0
$613$	15.2007	+	11.0440i	0.613951	+	0.446062i	0.850804	−	0.525484i	$-0.176116\pi$
$613$	15.2007	+	11.0440i	0.613951	+	0.446062i	−0.236852	+	0.971546i	$0.576116\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.1530	−	37.4030i	−0.489260	−	1.50579i	−0.825715	−	0.564087i	$-0.809228\pi$
$617$	−12.1530	−	37.4030i	−0.489260	−	1.50579i	0.336456	−	0.941699i	$-0.390772\pi$
$618$		0			0
$619$	−4.95554	−	15.2516i	−0.199180	−	0.613013i	−0.999902	−	0.0139774i	$-0.995551\pi$
$619$	−4.95554	−	15.2516i	−0.199180	−	0.613013i	0.800722	−	0.599036i	$-0.204449\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	17.1994	−	12.4961i	0.689079	−	0.500645i
$624$		0			0
$625$	−5.17573	−	24.4584i	−0.207029	−	0.978335i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.668937	−	2.05878i	0.0266722	−	0.0820887i
$630$		0			0
$631$	1.49158	+	4.59061i	0.0593788	+	0.182749i	0.976346	−	0.216213i	$-0.0693705\pi$
$631$	1.49158	+	4.59061i	0.0593788	+	0.182749i	−0.916967	+	0.398962i	$0.869371\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.1663	+	9.86883i	0.720909	+	0.391632i
$636$		0			0
$637$	−13.6293	−	9.90223i	−0.540011	−	0.392341i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−29.5813	−	21.4921i	−1.16839	−	0.848887i	−0.177577	−	0.984107i	$-0.556826\pi$
$641$	−29.5813	−	21.4921i	−1.16839	−	0.848887i	−0.990816	+	0.135220i	$0.956826\pi$
$642$		0			0
$643$	−18.3769			−0.724714			−0.362357	−	0.932039i	$-0.618028\pi$
$643$	−18.3769			−0.724714			−0.362357	+	0.932039i	$0.618028\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	12.7110	−	39.1206i	0.499723	−	1.53799i	−0.309743	−	0.950820i	$-0.600243\pi$
$647$	12.7110	−	39.1206i	0.499723	−	1.53799i	0.809465	−	0.587167i	$-0.199757\pi$
$648$		0			0
$649$	−79.5419			−3.12229
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.78128	−	20.8706i	0.265372	−	0.816731i	−0.726236	−	0.687446i	$-0.758732\pi$
$653$	6.78128	−	20.8706i	0.265372	−	0.816731i	0.991608	−	0.129285i	$-0.0412681\pi$
$654$		0			0
$655$	30.8496	−	29.2619i	1.20539	−	1.14336i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17.1550	+	12.4638i	0.668264	+	0.485522i	0.869444	−	0.494032i	$-0.164477\pi$
$659$	17.1550	+	12.4638i	0.668264	+	0.485522i	−0.201179	+	0.979554i	$0.564477\pi$
$660$		0			0
$661$	−14.5172	+	10.5473i	−0.564652	+	0.410244i	−0.833159	−	0.553034i	$-0.813470\pi$
$661$	−14.5172	+	10.5473i	−0.564652	+	0.410244i	0.268507	+	0.963278i	$0.413470\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.760633	+	0.721488i	−0.0294961	+	0.0279781i
$666$		0			0
$667$	0.115702	+	0.356094i	0.00447999	+	0.0137880i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−21.6002	+	66.4785i	−0.833865	+	2.56637i
$672$		0			0
$673$	−27.7504	+	20.1619i	−1.06970	+	0.777183i	−0.975858	−	0.218404i	$-0.929915\pi$
$673$	−27.7504	+	20.1619i	−1.06970	+	0.777183i	−0.0938421	+	0.995587i	$0.529915\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.35495	+	2.43752i	−0.128941	+	0.0936814i	−0.650387	−	0.759603i	$-0.725393\pi$
$677$	−3.35495	+	2.43752i	−0.128941	+	0.0936814i	0.521445	+	0.853285i	$0.325393\pi$
$678$		0			0
$679$	−5.33781	+	16.4281i	−0.204846	+	0.630452i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.654621	−	2.01472i	−0.0250484	−	0.0770910i	0.937751	−	0.347309i	$-0.112904\pi$
$683$	−0.654621	−	2.01472i	−0.0250484	−	0.0770910i	−0.962799	+	0.270218i	$0.912904\pi$
$684$		0			0
$685$	−3.20761	+	17.2850i	−0.122557	+	0.660425i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	24.7428	−	17.9767i	0.942625	−	0.684857i
$690$		0			0
$691$	3.21546	+	2.33617i	0.122322	+	0.0888721i	0.647264	−	0.762266i	$-0.275913\pi$
$691$	3.21546	+	2.33617i	0.122322	+	0.0888721i	−0.524942	+	0.851138i	$0.675913\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	27.1157	+	14.7305i	1.02856	+	0.558761i
$696$		0			0
$697$	0.651515	−	2.00516i	0.0246779	−	0.0759507i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	10.1954			0.385076			0.192538	−	0.981289i	$-0.438328\pi$
$701$	10.1954			0.385076			0.192538	+	0.981289i	$0.438328\pi$
$702$		0			0
$703$	−0.420597	+	1.29447i	−0.0158631	+	0.0488217i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.3176			0.839338
$708$		0			0
$709$	−24.1421	−	17.5403i	−0.906676	−	0.658739i	0.0334959	−	0.999439i	$-0.489336\pi$
$709$	−24.1421	−	17.5403i	−0.906676	−	0.658739i	−0.940172	+	0.340700i	$0.889336\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	7.28873	+	5.29557i	0.272965	+	0.198321i
$714$		0			0
$715$	−21.1281	−	44.3217i	−0.790146	−	1.65754i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.29734	−	7.07047i	−0.0856762	−	0.263684i	0.899036	−	0.437875i	$-0.144269\pi$
$719$	−2.29734	−	7.07047i	−0.0856762	−	0.263684i	−0.984712	+	0.174191i	$0.944269\pi$
$720$		0			0
$721$	8.95520	−	27.5613i	0.333509	−	1.02644i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.332907	+	0.513138i	0.0123638	+	0.0190575i
$726$		0			0
$727$	12.8791	−	9.35722i	0.477660	−	0.347040i	−0.322759	−	0.946481i	$-0.604610\pi$
$727$	12.8791	−	9.35722i	0.477660	−	0.347040i	0.800419	+	0.599441i	$0.204610\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.555527	+	1.70974i	0.0205469	+	0.0632369i
$732$		0			0
$733$	9.45910	+	29.1121i	0.349380	+	1.07528i	0.959197	+	0.282738i	$0.0912428\pi$
$733$	9.45910	+	29.1121i	0.349380	+	1.07528i	−0.609817	+	0.792542i	$0.708757\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−66.1430	−	48.0557i	−2.43641	−	1.77015i
$738$		0			0
$739$	−20.9842	+	15.2459i	−0.771917	+	0.560830i	−0.902542	−	0.430602i	$-0.858301\pi$
$739$	−20.9842	+	15.2459i	−0.771917	+	0.560830i	0.130626	+	0.991432i	$0.458301\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−17.2136			−0.631504			−0.315752	−	0.948842i	$-0.602257\pi$
$743$	−17.2136			−0.631504			−0.315752	+	0.948842i	$0.602257\pi$
$744$		0			0
$745$	−4.92807	−	10.3379i	−0.180550	−	0.378752i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12.9900			−0.474643
$750$		0			0
$751$	10.4020			0.379576			0.189788	−	0.981825i	$-0.439220\pi$
$751$	10.4020			0.379576			0.189788	+	0.981825i	$0.439220\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.4581	−	26.1341i	−0.453397	−	0.951118i
$756$		0			0
$757$	−16.9118			−0.614669			−0.307335	−	0.951601i	$-0.599437\pi$
$757$	−16.9118			−0.614669			−0.307335	+	0.951601i	$0.599437\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	0.422588	−	0.307028i	0.0153188	−	0.0111297i	−0.580100	−	0.814546i	$-0.696986\pi$
$761$	0.422588	−	0.307028i	0.0153188	−	0.0111297i	0.595418	+	0.803416i	$0.296986\pi$
$762$		0			0
$763$	22.7450	+	16.5252i	0.823423	+	0.598252i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.1576	+	43.5725i	0.511200	+	1.57331i
$768$		0			0
$769$	−11.7671	−	36.2154i	−0.424333	−	1.30596i	−0.903632	−	0.428310i	$-0.859109\pi$
$769$	−11.7671	−	36.2154i	−0.424333	−	1.30596i	0.479299	−	0.877651i	$-0.340891\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−18.3577	+	13.3376i	−0.660280	+	0.479721i	−0.866757	−	0.498730i	$-0.833800\pi$
$773$	−18.3577	+	13.3376i	−0.660280	+	0.479721i	0.206478	+	0.978451i	$0.433800\pi$
$774$		0			0
$775$	13.7382	+	5.28070i	0.493489	+	0.189688i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.409643	+	1.26075i	−0.0146770	+	0.0451711i
$780$		0			0
$781$	−6.23574	−	19.1916i	−0.223132	−	0.686731i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.87525	−	8.12934i	−0.138314	−	0.290149i
$786$		0			0
$787$	−1.84384	−	1.33963i	−0.0657257	−	0.0477525i	0.554437	−	0.832226i	$-0.312934\pi$
$787$	−1.84384	−	1.33963i	−0.0657257	−	0.0477525i	−0.620163	+	0.784473i	$0.712934\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	7.37064	+	5.35508i	0.262070	+	0.190405i
$792$		0			0
$793$	40.2611			1.42971
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.06936	+	18.6796i	−0.214988	+	0.661665i	0.784167	+	0.620550i	$0.213091\pi$
$797$	−6.06936	+	18.6796i	−0.214988	+	0.661665i	−0.999154	+	0.0411143i	$0.986909\pi$
$798$		0			0
$799$	2.61836			0.0926310
$800$		0			0
$801$		0			0
$802$		0			0
$803$	30.4644	−	93.7598i	1.07507	−	3.30871i
$804$		0			0
$805$	−9.04643	−	4.91445i	−0.318845	−	0.173212i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.05703	+	6.58032i	0.318428	+	0.231352i	0.735504	−	0.677520i	$-0.236945\pi$
$809$	9.05703	+	6.58032i	0.318428	+	0.231352i	−0.417076	+	0.908871i	$0.636945\pi$
$810$		0			0
$811$	15.6132	−	11.3436i	0.548253	−	0.398329i	−0.278888	−	0.960324i	$-0.589966\pi$
$811$	15.6132	−	11.3436i	0.548253	−	0.398329i	0.827141	+	0.561995i	$0.189966\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.37235	−	34.3389i	0.223214	−	1.20284i
$816$		0			0
$817$	−0.349291	−	1.07501i	−0.0122201	−	0.0376097i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	14.8716	−	45.7701i	0.519023	−	1.59739i	−0.256818	−	0.966460i	$-0.582674\pi$
$821$	14.8716	−	45.7701i	0.519023	−	1.59739i	0.775841	−	0.630928i	$-0.217326\pi$
$822$		0			0
$823$	−28.2356	+	20.5144i	−0.984232	+	0.715087i	−0.958650	−	0.284586i	$-0.908144\pi$
$823$	−28.2356	+	20.5144i	−0.984232	+	0.715087i	−0.0255817	+	0.999673i	$0.508144\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.7401	−	13.6155i	0.651656	−	0.473456i	−0.212179	−	0.977231i	$-0.568056\pi$
$827$	18.7401	−	13.6155i	0.651656	−	0.473456i	0.863835	+	0.503775i	$0.168056\pi$
$828$		0			0
$829$	6.70966	−	20.6502i	0.233036	−	0.717211i	−0.764340	−	0.644814i	$-0.776935\pi$
$829$	6.70966	−	20.6502i	0.233036	−	0.717211i	0.997376	−	0.0723976i	$-0.0230651\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.725626	+	2.23325i	0.0251414	+	0.0773774i
$834$		0			0
$835$	19.2156	−	18.2267i	0.664985	−	0.630762i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.40486	−	6.10649i	0.290168	−	0.210819i	−0.433172	−	0.901311i	$-0.642606\pi$
$839$	8.40486	−	6.10649i	0.290168	−	0.210819i	0.723340	+	0.690492i	$0.242606\pi$
$840$		0			0
$841$	23.4494	+	17.0370i	0.808600	+	0.587482i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.571770	−	0.542345i	0.0196695	−	0.0186572i
$846$		0			0
$847$	12.6082	−	38.8040i	0.433223	−	1.33332i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.3658			−0.458174
$852$		0			0
$853$	10.3861	−	31.9651i	0.355613	−	1.09447i	−0.600039	−	0.799970i	$-0.704848\pi$
$853$	10.3861	−	31.9651i	0.355613	−	1.09447i	0.955653	−	0.294495i	$-0.0951515\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−46.0078			−1.57160			−0.785799	−	0.618482i	$-0.787748\pi$
$857$	−46.0078			−1.57160			−0.785799	+	0.618482i	$0.787748\pi$
$858$		0			0
$859$	24.5549	+	17.8402i	0.837803	+	0.608700i	0.921756	−	0.387770i	$-0.126755\pi$
$859$	24.5549	+	17.8402i	0.837803	+	0.608700i	−0.0839529	+	0.996470i	$0.526755\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.92243	−	4.30289i	−0.201602	−	0.146472i	0.482404	−	0.875949i	$-0.339764\pi$
$863$	−5.92243	−	4.30289i	−0.201602	−	0.146472i	−0.684006	+	0.729477i	$0.739764\pi$
$864$		0			0
$865$	29.1398	+	15.8302i	0.990784	+	0.538241i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.2703	−	50.0748i	−0.551932	−	1.69867i
$870$		0			0
$871$	−14.5519	+	44.7861i	−0.493072	+	1.51752i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.3512	−	3.93728i	−0.552772	−	0.133104i
$876$		0			0
$877$	37.6546	−	27.3577i	1.27151	−	0.923803i	0.272244	−	0.962228i	$-0.412234\pi$
$877$	37.6546	−	27.3577i	1.27151	−	0.923803i	0.999261	+	0.0384252i	$0.0122341\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4.62663	+	14.2393i	0.155875	+	0.479735i	0.998249	−	0.0591598i	$-0.0188422\pi$
$881$	4.62663	+	14.2393i	0.155875	+	0.479735i	−0.842373	+	0.538894i	$0.818842\pi$
$882$		0			0
$883$	−2.70155	−	8.31451i	−0.0909144	−	0.279806i	0.895253	−	0.445558i	$-0.146995\pi$
$883$	−2.70155	−	8.31451i	−0.0909144	−	0.279806i	−0.986167	+	0.165752i	$0.946995\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.3379	+	9.69054i	0.447842	+	0.325376i	0.788743	−	0.614723i	$-0.210732\pi$
$887$	13.3379	+	9.69054i	0.447842	+	0.325376i	−0.340901	+	0.940099i	$0.610732\pi$
$888$		0			0
$889$	11.2520	−	8.17505i	0.377379	−	0.274182i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.64631			−0.0550916
$894$		0			0
$895$	2.12286	−	0.278993i	0.0709594	−	0.00932570i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.360104			−0.0120101
$900$		0			0
$901$	−4.26292			−0.142018
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.71846	+	6.37270i	−0.223329	+	0.211836i
$906$		0			0
$907$	26.0243			0.864124			0.432062	−	0.901844i	$-0.357786\pi$
$907$	26.0243			0.864124			0.432062	+	0.901844i	$0.357786\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−41.7815	+	30.3560i	−1.38428	+	1.00574i	−0.387816	+	0.921737i	$0.626771\pi$
$911$	−41.7815	+	30.3560i	−1.38428	+	1.00574i	−0.996466	+	0.0840029i	$0.973229\pi$
$912$		0			0
$913$	56.6359	+	41.1484i	1.87437	+	1.36181i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.83945	−	27.2050i	−0.291904	−	0.898390i
$918$		0			0
$919$	−8.53835	−	26.2784i	−0.281654	−	0.866843i	−0.987382	−	0.158359i	$-0.949380\pi$
$919$	−8.53835	−	26.2784i	−0.281654	−	0.866843i	0.705727	−	0.708484i	$-0.250620\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.40316	+	6.83180i	−0.309509	+	0.224871i
$924$		0			0
$925$	−21.0935	+	5.64180i	−0.693551	+	0.185501i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.5946	+	51.0728i	−0.544450	+	1.67565i	0.177843	+	0.984059i	$0.443088\pi$
$929$	−16.5946	+	51.0728i	−0.544450	+	1.67565i	−0.722294	+	0.691587i	$0.756912\pi$
$930$		0			0
$931$	−0.456241	−	1.40417i	−0.0149527	−	0.0460197i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.24870	+	6.72892i	−0.0408369	+	0.220059i
$936$		0			0
$937$	24.5304	+	17.8224i	0.801373	+	0.582232i	0.911317	−	0.411706i	$-0.135067\pi$
$937$	24.5304	+	17.8224i	0.801373	+	0.582232i	−0.109943	+	0.993938i	$0.535067\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	38.3217	+	27.8423i	1.24925	+	0.907635i	0.998178	−	0.0603335i	$-0.0192164\pi$
$941$	38.3217	+	27.8423i	1.24925	+	0.907635i	0.251073	+	0.967968i	$0.419216\pi$
$942$		0			0
$943$	−13.0177			−0.423915
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.68770	−	20.5826i	0.217321	−	0.668845i	−0.781660	−	0.623705i	$-0.785627\pi$
$947$	6.68770	−	20.5826i	0.217321	−	0.668845i	0.998981	−	0.0451402i	$-0.0143734\pi$
$948$		0			0
$949$	−56.7833			−1.84327
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.1813	−	43.6456i	0.459378	−	1.41382i	−0.406540	−	0.913633i	$-0.633265\pi$
$953$	14.1813	−	43.6456i	0.459378	−	1.41382i	0.865918	−	0.500187i	$-0.166735\pi$
$954$		0			0
$955$	7.19301	−	38.7612i	0.232760	−	1.25428i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.56815	+	6.95167i	0.308972	+	0.224481i
$960$		0			0
$961$	18.0695	−	13.1282i	0.582886	−	0.423492i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.05530	+	10.6048i	0.162736	+	0.341381i
$966$		0			0
$967$	−4.62587	−	14.2370i	−0.148758	−	0.457830i	0.848717	−	0.528847i	$-0.177375\pi$
$967$	−4.62587	−	14.2370i	−0.148758	−	0.457830i	−0.997475	+	0.0710173i	$0.977375\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.91563	−	21.2841i	0.221933	−	0.683040i	−0.776655	−	0.629926i	$-0.783085\pi$
$971$	6.91563	−	21.2841i	0.221933	−	0.683040i	0.998588	−	0.0531143i	$-0.0169148\pi$
$972$		0			0
$973$	16.7951	−	12.2023i	0.538426	−	0.391189i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−32.6588	+	23.7280i	−1.04485	+	0.759127i	−0.971226	−	0.238159i	$-0.923456\pi$
$977$	−32.6588	+	23.7280i	−1.04485	+	0.759127i	−0.0736229	+	0.997286i	$0.523456\pi$
$978$		0			0
$979$	−26.9647	+	82.9889i	−0.861797	+	2.65234i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.22264	+	22.2290i	0.230367	+	0.708995i	0.997702	+	0.0677498i	$0.0215820\pi$
$983$	7.22264	+	22.2290i	0.230367	+	0.708995i	−0.767336	+	0.641245i	$0.778418\pi$
$984$		0			0
$985$	4.69111	−	0.616520i	0.149471	−	0.0196439i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.97994	−	6.52431i	0.285546	−	0.207461i
$990$		0			0
$991$	−27.3815	−	19.8938i	−0.869803	−	0.631949i	0.0607312	−	0.998154i	$-0.480657\pi$
$991$	−27.3815	−	19.8938i	−0.869803	−	0.631949i	−0.930534	+	0.366205i	$0.880657\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.72741	+	18.3080i	0.276677	+	0.580403i
$996$		0			0
$997$	1.71351	−	5.27364i	0.0542674	−	0.167018i	−0.920249	−	0.391332i	$-0.872014\pi$
$997$	1.71351	−	5.27364i	0.0542674	−	0.167018i	0.974517	+	0.224314i	$0.0720143\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.n.b.361.1		8
3.2	odd	2		300.2.m.b.61.2	✓	8
15.2	even	4		1500.2.o.b.949.4		16
15.8	even	4		1500.2.o.b.949.1		16
15.14	odd	2		1500.2.m.a.301.1		8
25.16	even	5	inner	900.2.n.b.541.1		8
75.29	odd	10		7500.2.a.f.1.2		4
75.38	even	20		1500.2.o.b.49.3		16
75.41	odd	10		300.2.m.b.241.2	yes	8
75.47	even	20		7500.2.d.c.1249.7		8
75.53	even	20		7500.2.d.c.1249.2		8
75.59	odd	10		1500.2.m.a.1201.1		8
75.62	even	20		1500.2.o.b.49.2		16
75.71	odd	10		7500.2.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.m.b.61.2	✓	8	3.2	odd	2
300.2.m.b.241.2	yes	8	75.41	odd	10
900.2.n.b.361.1		8	1.1	even	1	trivial
900.2.n.b.541.1		8	25.16	even	5	inner
1500.2.m.a.301.1		8	15.14	odd	2
1500.2.m.a.1201.1		8	75.59	odd	10
1500.2.o.b.49.2		16	75.62	even	20
1500.2.o.b.49.3		16	75.38	even	20
1500.2.o.b.949.1		16	15.8	even	4
1500.2.o.b.949.4		16	15.2	even	4
7500.2.a.e.1.3		4	75.71	odd	10
7500.2.a.f.1.2		4	75.29	odd	10
7500.2.d.c.1249.2		8	75.53	even	20
7500.2.d.c.1249.7		8	75.47	even	20

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +O(q^{10})\)	\(q+(0.962197 + 2.01846i) q^{5} +1.50430 q^{7} +(-4.99517 + 3.62921i) q^{11} +(2.87714 + 2.09036i) q^{13} +(-0.153180 - 0.471439i) q^{17} +(0.0963126 + 0.296420i) q^{19} +(-2.47611 + 1.79900i) q^{23} +(-3.14835 + 3.88431i) q^{25} +(0.0378031 - 0.116346i) q^{29} +(-0.909629 - 2.79955i) q^{31} +(1.44743 + 3.03637i) q^{35} +(3.53298 + 2.56686i) q^{37} +(3.44096 + 2.50001i) q^{41} -3.62663 q^{43} +(-1.63227 + 5.02362i) q^{47} -4.73708 q^{49} +(2.65748 - 8.17888i) q^{53} +(-12.1317 - 6.59054i) q^{55} +(10.4222 + 7.57219i) q^{59} +(9.15882 - 6.65427i) q^{61} +(-1.45094 + 7.81873i) q^{65} +(4.09181 + 12.5933i) q^{67} +(-1.00994 + 3.10827i) q^{71} +(-12.9174 + 9.38504i) q^{73} +(-7.51424 + 5.45941i) q^{77} +(-2.63513 + 8.11010i) q^{79} +(-3.50367 - 10.7832i) q^{83} +(0.804191 - 0.762805i) q^{85} +(11.4335 - 8.30691i) q^{89} +(4.32808 + 3.14453i) q^{91} +(-0.505640 + 0.479617i) q^{95} +(-3.54837 + 10.9208i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{5} + 8 q^{7}+O(q^{10}) \) 8 * q + 5 * q^5 + 8 * q^7	\( 8 q + 5 q^{5} + 8 q^{7} - 8 q^{11} - 3 q^{17} + 5 q^{19} + 7 q^{23} + 5 q^{25} + 3 q^{29} - 3 q^{31} + 10 q^{35} - q^{37} - 10 q^{41} - 12 q^{43} + 33 q^{47} - 8 q^{49} + 19 q^{53} - 15 q^{55} + 38 q^{59} + 46 q^{61} - 25 q^{65} - 8 q^{67} + 25 q^{71} - 26 q^{73} - 23 q^{77} - 16 q^{79} - 8 q^{83} - 30 q^{85} + 30 q^{89} + 25 q^{91} + 25 q^{95} - 14 q^{97}+O(q^{100}) \) 8 * q + 5 * q^5 + 8 * q^7 - 8 * q^11 - 3 * q^17 + 5 * q^19 + 7 * q^23 + 5 * q^25 + 3 * q^29 - 3 * q^31 + 10 * q^35 - q^37 - 10 * q^41 - 12 * q^43 + 33 * q^47 - 8 * q^49 + 19 * q^53 - 15 * q^55 + 38 * q^59 + 46 * q^61 - 25 * q^65 - 8 * q^67 + 25 * q^71 - 26 * q^73 - 23 * q^77 - 16 * q^79 - 8 * q^83 - 30 * q^85 + 30 * q^89 + 25 * q^91 + 25 * q^95 - 14 * q^97

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