LMFDB - Embedded newform 9075.2.a.ci.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9075,2,Mod(1,9075)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9075, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9075.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9075 = 3 \cdot 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9075.a (trivial)

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:	yes
Analytic conductor:	$72.4642398343$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1815)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.772866$ of defining polynomial
Character	$\chi$	$=$	9075.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.772866 q^{2} -1.00000 q^{3} -1.40268 q^{4} -0.772866 q^{6} -1.62981 q^{7} -2.62981 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.772866 q^{2} -1.00000 q^{3} -1.40268 q^{4} -0.772866 q^{6} -1.62981 q^{7} -2.62981 q^{8} +1.00000 q^{9} +1.40268 q^{12} +4.80536 q^{13} -1.25963 q^{14} +0.772866 q^{16} +2.17554 q^{17} +0.772866 q^{18} +5.17554 q^{19} +1.62981 q^{21} -4.62981 q^{23} +2.62981 q^{24} +3.71390 q^{26} -1.00000 q^{27} +2.28610 q^{28} -2.45427 q^{29} +5.80536 q^{31} +5.85695 q^{32} +1.68140 q^{34} -1.40268 q^{36} -8.88944 q^{37} +4.00000 q^{38} -4.80536 q^{39} +5.09146 q^{41} +1.25963 q^{42} +1.54573 q^{43} -3.57822 q^{46} -9.72128 q^{47} -0.772866 q^{48} -4.34371 q^{49} -2.17554 q^{51} -6.74037 q^{52} +5.26701 q^{53} -0.772866 q^{54} +4.28610 q^{56} -5.17554 q^{57} -1.89682 q^{58} -7.15645 q^{59} -14.2596 q^{61} +4.48676 q^{62} -1.62981 q^{63} +2.98090 q^{64} +4.72128 q^{67} -3.05159 q^{68} +4.62981 q^{69} +13.4426 q^{71} -2.62981 q^{72} +1.17554 q^{73} -6.87034 q^{74} -7.25963 q^{76} -3.71390 q^{78} +4.89682 q^{79} +1.00000 q^{81} +3.93502 q^{82} +4.00000 q^{83} -2.28610 q^{84} +1.19464 q^{86} +2.45427 q^{87} +11.5457 q^{89} -7.83184 q^{91} +6.49414 q^{92} -5.80536 q^{93} -7.51324 q^{94} -5.85695 q^{96} -4.72128 q^{97} -3.35710 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 - 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 + 3 * q^9	$ 3 q + q^{2} - 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} + 3 q^{9} - 5 q^{12} - 4 q^{13} + 12 q^{14} + q^{16} - 4 q^{17} + q^{18} + 5 q^{19} - 3 q^{21} - 6 q^{23} - 2 q^{26} - 3 q^{27} + 20 q^{28} - 10 q^{29} - q^{31} + 11 q^{32} + 9 q^{34} + 5 q^{36} - 3 q^{37} + 12 q^{38} + 4 q^{39} + 10 q^{41} - 12 q^{42} + 2 q^{43} + 9 q^{46} - 16 q^{47} - q^{48} + 8 q^{49} + 4 q^{51} - 36 q^{52} - q^{54} + 26 q^{56} - 5 q^{57} + 18 q^{58} + 18 q^{59} - 27 q^{61} - q^{62} + 3 q^{63} - 20 q^{64} + q^{67} - 21 q^{68} + 6 q^{69} + 14 q^{71} - 7 q^{73} + 32 q^{74} - 6 q^{76} + 2 q^{78} - 9 q^{79} + 3 q^{81} + 46 q^{82} + 12 q^{83} - 20 q^{84} + 22 q^{86} + 10 q^{87} + 32 q^{89} - 34 q^{91} + 5 q^{92} + q^{93} - 37 q^{94} - 11 q^{96} - q^{97} + 57 q^{98}+O(q^{100}) $ 3 * q + q^2 - 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 + 3 * q^9 - 5 * q^12 - 4 * q^13 + 12 * q^14 + q^16 - 4 * q^17 + q^18 + 5 * q^19 - 3 * q^21 - 6 * q^23 - 2 * q^26 - 3 * q^27 + 20 * q^28 - 10 * q^29 - q^31 + 11 * q^32 + 9 * q^34 + 5 * q^36 - 3 * q^37 + 12 * q^38 + 4 * q^39 + 10 * q^41 - 12 * q^42 + 2 * q^43 + 9 * q^46 - 16 * q^47 - q^48 + 8 * q^49 + 4 * q^51 - 36 * q^52 - q^54 + 26 * q^56 - 5 * q^57 + 18 * q^58 + 18 * q^59 - 27 * q^61 - q^62 + 3 * q^63 - 20 * q^64 + q^67 - 21 * q^68 + 6 * q^69 + 14 * q^71 - 7 * q^73 + 32 * q^74 - 6 * q^76 + 2 * q^78 - 9 * q^79 + 3 * q^81 + 46 * q^82 + 12 * q^83 - 20 * q^84 + 22 * q^86 + 10 * q^87 + 32 * q^89 - 34 * q^91 + 5 * q^92 + q^93 - 37 * q^94 - 11 * q^96 - q^97 + 57 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	0.772866	0.546498	0.273249	−	0.961943i	$-0.411902\pi$
$2$	0.772866	0.546498	0.273249	+	0.961943i	$0.411902\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.40268	−0.701339
$5$	0	0
$5$	0	0
$6$	−0.772866	−0.315521
$7$	−1.62981	−0.616012	−0.308006	−	0.951384i	$-0.599662\pi$
$7$	−1.62981	−0.616012	−0.308006	+	0.951384i	$0.599662\pi$
$8$	−2.62981	−0.929779
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	1.40268	0.404918
$13$	4.80536	1.33277	0.666383	−	0.745609i	$-0.267842\pi$
$13$	4.80536	1.33277	0.666383	+	0.745609i	$0.267842\pi$
$14$	−1.25963	−0.336649
$15$	0	0
$16$	0.772866	0.193216
$17$	2.17554	0.527647	0.263824	−	0.964571i	$-0.415016\pi$
$17$	2.17554	0.527647	0.263824	+	0.964571i	$0.415016\pi$
$18$	0.772866	0.182166
$19$	5.17554	1.18735	0.593676	−	0.804704i	$-0.297676\pi$
$19$	5.17554	1.18735	0.593676	+	0.804704i	$0.297676\pi$
$20$	0	0
$21$	1.62981	0.355654
$22$	0	0
$23$	−4.62981	−0.965383	−0.482691	−	0.875791i	$-0.660341\pi$
$23$	−4.62981	−0.965383	−0.482691	+	0.875791i	$0.660341\pi$
$24$	2.62981	0.536808
$25$	0	0
$26$	3.71390	0.728355
$27$	−1.00000	−0.192450
$28$	2.28610	0.432033
$29$	−2.45427	−0.455746	−0.227873	−	0.973691i	$-0.573177\pi$
$29$	−2.45427	−0.455746	−0.227873	+	0.973691i	$0.573177\pi$
$30$	0	0
$31$	5.80536	1.04267	0.521337	−	0.853351i	$-0.325434\pi$
$31$	5.80536	1.04267	0.521337	+	0.853351i	$0.325434\pi$
$32$	5.85695	1.03537
$33$	0	0
$34$	1.68140	0.288358
$35$	0	0
$36$	−1.40268	−0.233780
$37$	−8.88944	−1.46141	−0.730707	−	0.682691i	$-0.760810\pi$
$37$	−8.88944	−1.46141	−0.730707	+	0.682691i	$0.760810\pi$
$38$	4.00000	0.648886
$39$	−4.80536	−0.769473
$40$	0	0
$41$	5.09146	0.795153	0.397576	−	0.917569i	$-0.369851\pi$
$41$	5.09146	0.795153	0.397576	+	0.917569i	$0.369851\pi$
$42$	1.25963	0.194365
$43$	1.54573	0.235722	0.117861	−	0.993030i	$-0.462396\pi$
$43$	1.54573	0.235722	0.117861	+	0.993030i	$0.462396\pi$
$44$	0	0
$45$	0	0
$46$	−3.57822	−0.527580
$47$	−9.72128	−1.41799	−0.708997	−	0.705212i	$-0.750852\pi$
$47$	−9.72128	−1.41799	−0.708997	+	0.705212i	$0.750852\pi$
$48$	−0.772866	−0.111554
$49$	−4.34371	−0.620530
$50$	0	0
$51$	−2.17554	−0.304637
$52$	−6.74037	−0.934722
$53$	5.26701	0.723479	0.361739	−	0.932279i	$-0.382183\pi$
$53$	5.26701	0.723479	0.361739	+	0.932279i	$0.382183\pi$
$54$	−0.772866	−0.105174
$55$	0	0
$56$	4.28610	0.572755
$57$	−5.17554	−0.685518
$58$	−1.89682	−0.249065
$59$	−7.15645	−0.931690	−0.465845	−	0.884866i	$-0.654250\pi$
$59$	−7.15645	−0.931690	−0.465845	+	0.884866i	$0.654250\pi$
$60$	0	0
$61$	−14.2596	−1.82576	−0.912879	−	0.408230i	$-0.866146\pi$
$61$	−14.2596	−1.82576	−0.912879	+	0.408230i	$0.866146\pi$
$62$	4.48676	0.569819
$63$	−1.62981	−0.205337
$64$	2.98090	0.372613
$65$	0	0
$66$	0	0
$67$	4.72128	0.576796	0.288398	−	0.957511i	$-0.406877\pi$
$67$	4.72128	0.576796	0.288398	+	0.957511i	$0.406877\pi$
$68$	−3.05159	−0.370060
$69$	4.62981	0.557364
$70$	0	0
$71$	13.4426	1.59534	0.797669	−	0.603096i	$-0.206066\pi$
$71$	13.4426	1.59534	0.797669	+	0.603096i	$0.206066\pi$
$72$	−2.62981	−0.309926
$73$	1.17554	0.137587	0.0687935	−	0.997631i	$-0.478085\pi$
$73$	1.17554	0.137587	0.0687935	+	0.997631i	$0.478085\pi$
$74$	−6.87034	−0.798661
$75$	0	0
$76$	−7.25963	−0.832736
$77$	0	0
$78$	−3.71390	−0.420516
$79$	4.89682	0.550935	0.275468	−	0.961310i	$-0.411167\pi$
$79$	4.89682	0.550935	0.275468	+	0.961310i	$0.411167\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	3.93502	0.434550
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−2.28610	−0.249434
$85$	0	0
$86$	1.19464	0.128822
$87$	2.45427	0.263125
$88$	0	0
$89$	11.5457	1.22385	0.611923	−	0.790918i	$-0.290396\pi$
$89$	11.5457	1.22385	0.611923	+	0.790918i	$0.290396\pi$
$90$	0	0
$91$	−7.83184	−0.820999
$92$	6.49414	0.677061
$93$	−5.80536	−0.601988
$94$	−7.51324	−0.774931
$95$	0	0
$96$	−5.85695	−0.597772
$97$	−4.72128	−0.479373	−0.239686	−	0.970850i	$-0.577045\pi$
$97$	−4.72128	−0.479373	−0.239686	+	0.970850i	$0.577045\pi$
$98$	−3.35710	−0.339119
$99$	0	0
$100$	0	0
$101$	13.6107	1.35432	0.677158	−	0.735837i	$-0.263211\pi$
$101$	13.6107	1.35432	0.677158	+	0.735837i	$0.263211\pi$
$102$	−1.68140	−0.166484
$103$	−14.6181	−1.44036	−0.720182	−	0.693785i	$-0.755942\pi$
$103$	−14.6181	−1.44036	−0.720182	+	0.693785i	$0.755942\pi$
$104$	−12.6372	−1.23918
$105$	0	0
$106$	4.07069	0.395380
$107$	−19.3320	−1.86889	−0.934447	−	0.356102i	$-0.884106\pi$
$107$	−19.3320	−1.86889	−0.934447	+	0.356102i	$0.884106\pi$
$108$	1.40268	0.134973
$109$	−8.78626	−0.841571	−0.420786	−	0.907160i	$-0.638246\pi$
$109$	−8.78626	−0.841571	−0.420786	+	0.907160i	$0.638246\pi$
$110$	0	0
$111$	8.88944	0.843748
$112$	−1.25963	−0.119024
$113$	−12.5266	−1.17841	−0.589203	−	0.807985i	$-0.700558\pi$
$113$	−12.5266	−1.17841	−0.589203	+	0.807985i	$0.700558\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	3.44255	0.319633
$117$	4.80536	0.444255
$118$	−5.53097	−0.509167
$119$	−3.54573	−0.325037
$120$	0	0
$121$	0	0
$122$	−11.0208	−0.997774
$123$	−5.09146	−0.459082
$124$	−8.14305	−0.731268
$125$	0	0
$126$	−1.25963	−0.112216
$127$	−17.2405	−1.52985	−0.764925	−	0.644120i	$-0.777224\pi$
$127$	−17.2405	−1.52985	−0.764925	+	0.644120i	$0.777224\pi$
$128$	−9.41006	−0.831740
$129$	−1.54573	−0.136094
$130$	0	0
$131$	15.6107	1.36391	0.681957	−	0.731392i	$-0.261129\pi$
$131$	15.6107	1.36391	0.681957	+	0.731392i	$0.261129\pi$
$132$	0	0
$133$	−8.43517	−0.731422
$134$	3.64891	0.315218
$135$	0	0
$136$	−5.72128	−0.490595
$137$	10.6948	0.913718	0.456859	−	0.889539i	$-0.348974\pi$
$137$	10.6948	0.913718	0.456859	+	0.889539i	$0.348974\pi$
$138$	3.57822	0.304599
$139$	6.98090	0.592112	0.296056	−	0.955171i	$-0.404328\pi$
$139$	6.98090	0.592112	0.296056	+	0.955171i	$0.404328\pi$
$140$	0	0
$141$	9.72128	0.818679
$142$	10.3893	0.871849
$143$	0	0
$144$	0.772866	0.0644055
$145$	0	0
$146$	0.908538	0.0751911
$147$	4.34371	0.358263
$148$	12.4690	1.02495
$149$	3.89682	0.319240	0.159620	−	0.987179i	$-0.448973\pi$
$149$	3.89682	0.319240	0.159620	+	0.987179i	$0.448973\pi$
$150$	0	0
$151$	5.72128	0.465591	0.232795	−	0.972526i	$-0.425213\pi$
$151$	5.72128	0.465591	0.232795	+	0.972526i	$0.425213\pi$
$152$	−13.6107	−1.10397
$153$	2.17554	0.175882
$154$	0	0
$155$	0	0
$156$	6.74037	0.539662
$157$	15.2405	1.21633	0.608163	−	0.793812i	$-0.291907\pi$
$157$	15.2405	1.21633	0.608163	+	0.793812i	$0.291907\pi$
$158$	3.78458	0.301085
$159$	−5.26701	−0.417701
$160$	0	0
$161$	7.54573	0.594687
$162$	0.772866	0.0607221
$163$	17.2405	1.35038	0.675191	−	0.737643i	$-0.264061\pi$
$163$	17.2405	1.35038	0.675191	+	0.737643i	$0.264061\pi$
$164$	−7.14169	−0.557672
$165$	0	0
$166$	3.09146	0.239944
$167$	5.53835	0.428570	0.214285	−	0.976771i	$-0.431258\pi$
$167$	5.53835	0.428570	0.214285	+	0.976771i	$0.431258\pi$
$168$	−4.28610	−0.330680
$169$	10.0915	0.776266
$170$	0	0
$171$	5.17554	0.395784
$172$	−2.16816	−0.165321
$173$	18.7022	1.42190	0.710950	−	0.703242i	$-0.248265\pi$
$173$	18.7022	1.42190	0.710950	+	0.703242i	$0.248265\pi$
$174$	1.89682	0.143798
$175$	0	0
$176$	0	0
$177$	7.15645	0.537911
$178$	8.92330	0.668829
$179$	1.19464	0.0892918	0.0446459	−	0.999003i	$-0.485784\pi$
$179$	1.19464	0.0892918	0.0446459	+	0.999003i	$0.485784\pi$
$180$	0	0
$181$	15.3437	1.14049	0.570244	−	0.821475i	$-0.306848\pi$
$181$	15.3437	1.14049	0.570244	+	0.821475i	$0.306848\pi$
$182$	−6.05296	−0.448675
$183$	14.2596	1.05410
$184$	12.1755	0.897593
$185$	0	0
$186$	−4.48676	−0.328985
$187$	0	0
$188$	13.6358	0.994495
$189$	1.62981	0.118551
$190$	0	0
$191$	15.7139	1.13702	0.568509	−	0.822677i	$-0.307521\pi$
$191$	15.7139	1.13702	0.568509	+	0.822677i	$0.307521\pi$
$192$	−2.98090	−0.215128
$193$	11.2405	0.809111	0.404555	−	0.914513i	$-0.367426\pi$
$193$	11.2405	0.809111	0.404555	+	0.914513i	$0.367426\pi$
$194$	−3.64891	−0.261977
$195$	0	0
$196$	6.09283	0.435202
$197$	−2.74037	−0.195244	−0.0976218	−	0.995224i	$-0.531124\pi$
$197$	−2.74037	−0.195244	−0.0976218	+	0.995224i	$0.531124\pi$
$198$	0	0
$199$	−25.0650	−1.77681	−0.888405	−	0.459061i	$-0.848186\pi$
$199$	−25.0650	−1.77681	−0.888405	+	0.459061i	$0.848186\pi$
$200$	0	0
$201$	−4.72128	−0.333013
$202$	10.5193	0.740132
$203$	4.00000	0.280745
$204$	3.05159	0.213654
$205$	0	0
$206$	−11.2978	−0.787157
$207$	−4.62981	−0.321794
$208$	3.71390	0.257512
$209$	0	0
$210$	0	0
$211$	−17.9735	−1.23735	−0.618674	−	0.785648i	$-0.712330\pi$
$211$	−17.9735	−1.23735	−0.618674	+	0.785648i	$0.712330\pi$
$212$	−7.38792	−0.507404
$213$	−13.4426	−0.921068
$214$	−14.9410	−1.02135
$215$	0	0
$216$	2.62981	0.178936
$217$	−9.46165	−0.642299
$218$	−6.79060	−0.459917
$219$	−1.17554	−0.0794359
$220$	0	0
$221$	10.4543	0.703230
$222$	6.87034	0.461107
$223$	12.7863	0.856231	0.428116	−	0.903724i	$-0.359178\pi$
$223$	12.7863	0.856231	0.428116	+	0.903724i	$0.359178\pi$
$224$	−9.54573	−0.637801
$225$	0	0
$226$	−9.68140	−0.643997
$227$	14.2787	0.947712	0.473856	−	0.880602i	$-0.342862\pi$
$227$	14.2787	0.947712	0.473856	+	0.880602i	$0.342862\pi$
$228$	7.25963	0.480781
$229$	−25.9692	−1.71609	−0.858046	−	0.513573i	$-0.828322\pi$
$229$	−25.9692	−1.71609	−0.858046	+	0.513573i	$0.828322\pi$
$230$	0	0
$231$	0	0
$232$	6.45427	0.423744
$233$	−10.5648	−0.692125	−0.346062	−	0.938211i	$-0.612481\pi$
$233$	−10.5648	−0.692125	−0.346062	+	0.938211i	$0.612481\pi$
$234$	3.71390	0.242785
$235$	0	0
$236$	10.0382	0.653431
$237$	−4.89682	−0.318083
$238$	−2.74037	−0.177632
$239$	6.45427	0.417492	0.208746	−	0.977970i	$-0.433062\pi$
$239$	6.45427	0.417492	0.208746	+	0.977970i	$0.433062\pi$
$240$	0	0
$241$	25.6181	1.65021	0.825103	−	0.564982i	$-0.191117\pi$
$241$	25.6181	1.65021	0.825103	+	0.564982i	$0.191117\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	20.0017	1.28048
$245$	0	0
$246$	−3.93502	−0.250887
$247$	24.8703	1.58246
$248$	−15.2670	−0.969456
$249$	−4.00000	−0.253490
$250$	0	0
$251$	4.80536	0.303311	0.151656	−	0.988433i	$-0.451539\pi$
$251$	4.80536	0.303311	0.151656	+	0.988433i	$0.451539\pi$
$252$	2.28610	0.144011
$253$	0	0
$254$	−13.3246	−0.836060
$255$	0	0
$256$	−13.2345	−0.827157
$257$	−11.7863	−0.735207	−0.367603	−	0.929983i	$-0.619822\pi$
$257$	−11.7863	−0.735207	−0.367603	+	0.929983i	$0.619822\pi$
$258$	−1.19464	−0.0743752
$259$	14.4881	0.900248
$260$	0	0
$261$	−2.45427	−0.151915
$262$	12.0650	0.745377
$263$	12.4235	0.766063	0.383031	−	0.923735i	$-0.374880\pi$
$263$	12.4235	0.766063	0.383031	+	0.923735i	$0.374880\pi$
$264$	0	0
$265$	0	0
$266$	−6.51925	−0.399721
$267$	−11.5457	−0.706587
$268$	−6.62243	−0.404529
$269$	31.2214	1.90360	0.951802	−	0.306713i	$-0.0992291\pi$
$269$	31.2214	1.90360	0.951802	+	0.306713i	$0.0992291\pi$
$270$	0	0
$271$	25.5002	1.54902	0.774512	−	0.632559i	$-0.217995\pi$
$271$	25.5002	1.54902	0.774512	+	0.632559i	$0.217995\pi$
$272$	1.68140	0.101950
$273$	7.83184	0.474004
$274$	8.26564	0.499346
$275$	0	0
$276$	−6.49414	−0.390901
$277$	24.6033	1.47827	0.739136	−	0.673557i	$-0.235234\pi$
$277$	24.6033	1.47827	0.739136	+	0.673557i	$0.235234\pi$
$278$	5.39530	0.323589
$279$	5.80536	0.347558
$280$	0	0
$281$	−11.5457	−0.688761	−0.344380	−	0.938830i	$-0.611911\pi$
$281$	−11.5457	−0.688761	−0.344380	+	0.938830i	$0.611911\pi$
$282$	7.51324	0.447407
$283$	6.09884	0.362539	0.181269	−	0.983434i	$-0.441979\pi$
$283$	6.09884	0.362539	0.181269	+	0.983434i	$0.441979\pi$
$284$	−18.8556	−1.11887
$285$	0	0
$286$	0	0
$287$	−8.29813	−0.489823
$288$	5.85695	0.345124
$289$	−12.2670	−0.721589
$290$	0	0
$291$	4.72128	0.276766
$292$	−1.64891	−0.0964952
$293$	5.82446	0.340268	0.170134	−	0.985421i	$-0.445580\pi$
$293$	5.82446	0.340268	0.170134	+	0.985421i	$0.445580\pi$
$294$	3.35710	0.195790
$295$	0	0
$296$	23.3776	1.35879
$297$	0	0
$298$	3.01172	0.174464
$299$	−22.2479	−1.28663
$300$	0	0
$301$	−2.51925	−0.145207
$302$	4.42178	0.254445
$303$	−13.6107	−0.781915
$304$	4.00000	0.229416
$305$	0	0
$306$	1.68140	0.0961194
$307$	−10.2670	−0.585969	−0.292985	−	0.956117i	$-0.594648\pi$
$307$	−10.2670	−0.585969	−0.292985	+	0.956117i	$0.594648\pi$
$308$	0	0
$309$	14.6181	0.831594
$310$	0	0
$311$	−0.454269	−0.0257592	−0.0128796	−	0.999917i	$-0.504100\pi$
$311$	−0.454269	−0.0257592	−0.0128796	+	0.999917i	$0.504100\pi$
$312$	12.6372	0.715440
$313$	−0.103180	−0.00583208	−0.00291604	−	0.999996i	$-0.500928\pi$
$313$	−0.103180	−0.00583208	−0.00291604	+	0.999996i	$0.500928\pi$
$314$	11.7789	0.664721
$315$	0	0
$316$	−6.86867	−0.386393
$317$	19.0841	1.07187	0.535934	−	0.844260i	$-0.319959\pi$
$317$	19.0841	1.07187	0.535934	+	0.844260i	$0.319959\pi$
$318$	−4.07069	−0.228273
$319$	0	0
$320$	0	0
$321$	19.3320	1.07901
$322$	5.83184	0.324995
$323$	11.2596	0.626502
$324$	−1.40268	−0.0779266
$325$	0	0
$326$	13.3246	0.737982
$327$	8.78626	0.485881
$328$	−13.3896	−0.739317
$329$	15.8439	0.873500
$330$	0	0
$331$	−9.45427	−0.519654	−0.259827	−	0.965655i	$-0.583665\pi$
$331$	−9.45427	−0.519654	−0.259827	+	0.965655i	$0.583665\pi$
$332$	−5.61072	−0.307928
$333$	−8.88944	−0.487138
$334$	4.28040	0.234213
$335$	0	0
$336$	1.25963	0.0687183
$337$	16.9544	0.923566	0.461783	−	0.886993i	$-0.347210\pi$
$337$	16.9544	0.923566	0.461783	+	0.886993i	$0.347210\pi$
$338$	7.79934	0.424228
$339$	12.5266	0.680353
$340$	0	0
$341$	0	0
$342$	4.00000	0.216295
$343$	18.4881	0.998265
$344$	−4.06498	−0.219169
$345$	0	0
$346$	14.4543	0.777066
$347$	−28.0576	−1.50621	−0.753106	−	0.657900i	$-0.771445\pi$
$347$	−28.0576	−1.50621	−0.753106	+	0.657900i	$0.771445\pi$
$348$	−3.44255	−0.184540
$349$	17.5340	0.938574	0.469287	−	0.883046i	$-0.344511\pi$
$349$	17.5340	0.938574	0.469287	+	0.883046i	$0.344511\pi$
$350$	0	0
$351$	−4.80536	−0.256491
$352$	0	0
$353$	20.4884	1.09049	0.545245	−	0.838277i	$-0.316437\pi$
$353$	20.4884	1.09049	0.545245	+	0.838277i	$0.316437\pi$
$354$	5.53097	0.293968
$355$	0	0
$356$	−16.1950	−0.858331
$357$	3.54573	0.187660
$358$	0.923298	0.0487978
$359$	−28.6640	−1.51283	−0.756414	−	0.654094i	$-0.773050\pi$
$359$	−28.6640	−1.51283	−0.756414	+	0.654094i	$0.773050\pi$
$360$	0	0
$361$	7.78626	0.409803
$362$	11.8586	0.623275
$363$	0	0
$364$	10.9856	0.575799
$365$	0	0
$366$	11.0208	0.576065
$367$	22.5990	1.17966	0.589829	−	0.807528i	$-0.299195\pi$
$367$	22.5990	1.17966	0.589829	+	0.807528i	$0.299195\pi$
$368$	−3.57822	−0.186528
$369$	5.09146	0.265051
$370$	0	0
$371$	−8.58424	−0.445671
$372$	8.14305	0.422198
$373$	−26.0841	−1.35058	−0.675291	−	0.737551i	$-0.735982\pi$
$373$	−26.0841	−1.35058	−0.675291	+	0.737551i	$0.735982\pi$
$374$	0	0
$375$	0	0
$376$	25.5651	1.31842
$377$	−11.7936	−0.607403
$378$	1.25963	0.0647882
$379$	9.16383	0.470714	0.235357	−	0.971909i	$-0.424374\pi$
$379$	9.16383	0.470714	0.235357	+	0.971909i	$0.424374\pi$
$380$	0	0
$381$	17.2405	0.883259
$382$	12.1447	0.621378
$383$	18.3511	0.937697	0.468848	−	0.883279i	$-0.344669\pi$
$383$	18.3511	0.937697	0.468848	+	0.883279i	$0.344669\pi$
$384$	9.41006	0.480205
$385$	0	0
$386$	8.68742	0.442178
$387$	1.54573	0.0785739
$388$	6.62243	0.336203
$389$	−12.5990	−0.638795	−0.319397	−	0.947621i	$-0.603480\pi$
$389$	−12.5990	−0.638795	−0.319397	+	0.947621i	$0.603480\pi$
$390$	0	0
$391$	−10.0724	−0.509381
$392$	11.4231	0.576956
$393$	−15.6107	−0.787456
$394$	−2.11794	−0.106700
$395$	0	0
$396$	0	0
$397$	29.6948	1.49034	0.745170	−	0.666875i	$-0.232369\pi$
$397$	29.6948	1.49034	0.745170	+	0.666875i	$0.232369\pi$
$398$	−19.3719	−0.971024
$399$	8.43517	0.422287
$400$	0	0
$401$	39.0533	1.95023	0.975114	−	0.221706i	$-0.0711626\pi$
$401$	39.0533	1.95023	0.975114	+	0.221706i	$0.0711626\pi$
$402$	−3.64891	−0.181991
$403$	27.8968	1.38964
$404$	−19.0915	−0.949836
$405$	0	0
$406$	3.09146	0.153427
$407$	0	0
$408$	5.72128	0.283245
$409$	−29.5193	−1.45963	−0.729817	−	0.683643i	$-0.760395\pi$
$409$	−29.5193	−1.45963	−0.729817	+	0.683643i	$0.760395\pi$
$410$	0	0
$411$	−10.6948	−0.527535
$412$	20.5045	1.01018
$413$	11.6637	0.573932
$414$	−3.57822	−0.175860
$415$	0	0
$416$	28.1447	1.37991
$417$	−6.98090	−0.341856
$418$	0	0
$419$	−22.8703	−1.11729	−0.558645	−	0.829407i	$-0.688678\pi$
$419$	−22.8703	−1.11729	−0.558645	+	0.829407i	$0.688678\pi$
$420$	0	0
$421$	−21.6033	−1.05288	−0.526441	−	0.850212i	$-0.676474\pi$
$421$	−21.6033	−1.05288	−0.526441	+	0.850212i	$0.676474\pi$
$422$	−13.8911	−0.676209
$423$	−9.72128	−0.472665
$424$	−13.8512	−0.672676
$425$	0	0
$426$	−10.3893	−0.503362
$427$	23.2405	1.12469
$428$	27.1166	1.31073
$429$	0	0
$430$	0	0
$431$	−34.4161	−1.65776	−0.828882	−	0.559424i	$-0.811023\pi$
$431$	−34.4161	−1.65776	−0.828882	+	0.559424i	$0.811023\pi$
$432$	−0.772866	−0.0371845
$433$	20.2938	0.975258	0.487629	−	0.873051i	$-0.337862\pi$
$433$	20.2938	0.975258	0.487629	+	0.873051i	$0.337862\pi$
$434$	−7.31258	−0.351015
$435$	0	0
$436$	12.3243	0.590227
$437$	−23.9618	−1.14625
$438$	−0.908538	−0.0434116
$439$	−7.28610	−0.347747	−0.173873	−	0.984768i	$-0.555628\pi$
$439$	−7.28610	−0.347747	−0.173873	+	0.984768i	$0.555628\pi$
$440$	0	0
$441$	−4.34371	−0.206843
$442$	8.07974	0.384314
$443$	−7.25963	−0.344915	−0.172458	−	0.985017i	$-0.555171\pi$
$443$	−7.25963	−0.344915	−0.172458	+	0.985017i	$0.555171\pi$
$444$	−12.4690	−0.591754
$445$	0	0
$446$	9.88206	0.467929
$447$	−3.89682	−0.184313
$448$	−4.85831	−0.229534
$449$	22.0000	1.03824	0.519122	−	0.854700i	$-0.326259\pi$
$449$	22.0000	1.03824	0.519122	+	0.854700i	$0.326259\pi$
$450$	0	0
$451$	0	0
$452$	17.5708	0.826463
$453$	−5.72128	−0.268809
$454$	11.0355	0.517923
$455$	0	0
$456$	13.6107	0.637380
$457$	−3.61072	−0.168902	−0.0844511	−	0.996428i	$-0.526914\pi$
$457$	−3.61072	−0.168902	−0.0844511	+	0.996428i	$0.526914\pi$
$458$	−20.0707	−0.937842
$459$	−2.17554	−0.101546
$460$	0	0
$461$	20.1032	0.936298	0.468149	−	0.883649i	$-0.344921\pi$
$461$	20.1032	0.936298	0.468149	+	0.883649i	$0.344921\pi$
$462$	0	0
$463$	20.6874	0.961426	0.480713	−	0.876878i	$-0.340378\pi$
$463$	20.6874	0.961426	0.480713	+	0.876878i	$0.340378\pi$
$464$	−1.89682	−0.0880577
$465$	0	0
$466$	−8.16519	−0.378245
$467$	0.850934	0.0393765	0.0196883	−	0.999806i	$-0.493733\pi$
$467$	0.850934	0.0393765	0.0196883	+	0.999806i	$0.493733\pi$
$468$	−6.74037	−0.311574
$469$	−7.69480	−0.355313
$470$	0	0
$471$	−15.2405	−0.702246
$472$	18.8201	0.866266
$473$	0	0
$474$	−3.78458	−0.173832
$475$	0	0
$476$	4.97352	0.227961
$477$	5.26701	0.241160
$478$	4.98828	0.228159
$479$	28.4013	1.29769	0.648845	−	0.760921i	$-0.275253\pi$
$479$	28.4013	1.29769	0.648845	+	0.760921i	$0.275253\pi$
$480$	0	0
$481$	−42.7169	−1.94772
$482$	19.7993	0.901835
$483$	−7.54573	−0.343343
$484$	0	0
$485$	0	0
$486$	−0.772866	−0.0350579
$487$	−4.06498	−0.184202	−0.0921010	−	0.995750i	$-0.529358\pi$
$487$	−4.06498	−0.184202	−0.0921010	+	0.995750i	$0.529358\pi$
$488$	37.5002	1.69755
$489$	−17.2405	−0.779644
$490$	0	0
$491$	−27.9618	−1.26190	−0.630949	−	0.775824i	$-0.717334\pi$
$491$	−27.9618	−1.26190	−0.630949	+	0.775824i	$0.717334\pi$
$492$	7.14169	0.321972
$493$	−5.33937	−0.240473
$494$	19.2214	0.864813
$495$	0	0
$496$	4.48676	0.201462
$497$	−21.9088	−0.982746
$498$	−3.09146	−0.138532
$499$	1.13735	0.0509147	0.0254574	−	0.999676i	$-0.491896\pi$
$499$	1.13735	0.0509147	0.0254574	+	0.999676i	$0.491896\pi$
$500$	0	0
$501$	−5.53835	−0.247435
$502$	3.71390	0.165759
$503$	21.8512	0.974299	0.487149	−	0.873319i	$-0.338037\pi$
$503$	21.8512	0.974299	0.487149	+	0.873319i	$0.338037\pi$
$504$	4.28610	0.190918
$505$	0	0
$506$	0	0
$507$	−10.0915	−0.448178
$508$	24.1829	1.07294
$509$	18.2331	0.808170	0.404085	−	0.914721i	$-0.367590\pi$
$509$	18.2331	0.808170	0.404085	+	0.914721i	$0.367590\pi$
$510$	0	0
$511$	−1.91592	−0.0847552
$512$	8.59162	0.379699
$513$	−5.17554	−0.228506
$514$	−9.10919	−0.401789
$515$	0	0
$516$	2.16816	0.0954481
$517$	0	0
$518$	11.1974	0.491984
$519$	−18.7022	−0.820934
$520$	0	0
$521$	37.1035	1.62553	0.812767	−	0.582589i	$-0.197960\pi$
$521$	37.1035	1.62553	0.812767	+	0.582589i	$0.197960\pi$
$522$	−1.89682	−0.0830216
$523$	−15.1106	−0.660739	−0.330369	−	0.943852i	$-0.607173\pi$
$523$	−15.1106	−0.660739	−0.330369	+	0.943852i	$0.607173\pi$
$524$	−21.8968	−0.956567
$525$	0	0
$526$	9.60166	0.418652
$527$	12.6298	0.550163
$528$	0	0
$529$	−1.56483	−0.0680360
$530$	0	0
$531$	−7.15645	−0.310563
$532$	11.8318	0.512975
$533$	24.4663	1.05975
$534$	−8.92330	−0.386149
$535$	0	0
$536$	−12.4161	−0.536293
$537$	−1.19464	−0.0515526
$538$	24.1300	1.04032
$539$	0	0
$540$	0	0
$541$	−3.27439	−0.140777	−0.0703884	−	0.997520i	$-0.522424\pi$
$541$	−3.27439	−0.140777	−0.0703884	+	0.997520i	$0.522424\pi$
$542$	19.7082	0.846539
$543$	−15.3437	−0.658462
$544$	12.7420	0.546311
$545$	0	0
$546$	6.05296	0.259043
$547$	−18.2479	−0.780224	−0.390112	−	0.920767i	$-0.627564\pi$
$547$	−18.2479	−0.780224	−0.390112	+	0.920767i	$0.627564\pi$
$548$	−15.0014	−0.640827
$549$	−14.2596	−0.608586
$550$	0	0
$551$	−12.7022	−0.541131
$552$	−12.1755	−0.518226
$553$	−7.98090	−0.339382
$554$	19.0151	0.807873
$555$	0	0
$556$	−9.79196	−0.415272
$557$	16.3585	0.693131	0.346565	−	0.938026i	$-0.387348\pi$
$557$	16.3585	0.693131	0.346565	+	0.938026i	$0.387348\pi$
$558$	4.48676	0.189940
$559$	7.42779	0.314162
$560$	0	0
$561$	0	0
$562$	−8.92330	−0.376407
$563$	−31.2214	−1.31583	−0.657913	−	0.753094i	$-0.728561\pi$
$563$	−31.2214	−1.31583	−0.657913	+	0.753094i	$0.728561\pi$
$564$	−13.6358	−0.574172
$565$	0	0
$566$	4.71359	0.198127
$567$	−1.62981	−0.0684457
$568$	−35.3514	−1.48331
$569$	8.97352	0.376190	0.188095	−	0.982151i	$-0.439769\pi$
$569$	8.97352	0.376190	0.188095	+	0.982151i	$0.439769\pi$
$570$	0	0
$571$	−19.5990	−0.820193	−0.410096	−	0.912042i	$-0.634505\pi$
$571$	−19.5990	−0.820193	−0.410096	+	0.912042i	$0.634505\pi$
$572$	0	0
$573$	−15.7139	−0.656457
$574$	−6.41334	−0.267688
$575$	0	0
$576$	2.98090	0.124204
$577$	−10.4204	−0.433807	−0.216904	−	0.976193i	$-0.569596\pi$
$577$	−10.4204	−0.433807	−0.216904	+	0.976193i	$0.569596\pi$
$578$	−9.48075	−0.394347
$579$	−11.2405	−0.467140
$580$	0	0
$581$	−6.51925	−0.270464
$582$	3.64891	0.151252
$583$	0	0
$584$	−3.09146	−0.127926
$585$	0	0
$586$	4.50152	0.185956
$587$	4.59162	0.189516	0.0947582	−	0.995500i	$-0.469792\pi$
$587$	4.59162	0.189516	0.0947582	+	0.995500i	$0.469792\pi$
$588$	−6.09283	−0.251264
$589$	30.0459	1.23802
$590$	0	0
$591$	2.74037	0.112724
$592$	−6.87034	−0.282369
$593$	16.1829	0.664553	0.332277	−	0.943182i	$-0.392183\pi$
$593$	16.1829	0.664553	0.332277	+	0.943182i	$0.392183\pi$
$594$	0	0
$595$	0	0
$596$	−5.46599	−0.223896
$597$	25.0650	1.02584
$598$	−17.1946	−0.703141
$599$	−40.0120	−1.63485	−0.817424	−	0.576037i	$-0.804598\pi$
$599$	−40.0120	−1.63485	−0.817424	+	0.576037i	$0.804598\pi$
$600$	0	0
$601$	36.9162	1.50584	0.752922	−	0.658110i	$-0.228644\pi$
$601$	36.9162	1.50584	0.752922	+	0.658110i	$0.228644\pi$
$602$	−1.94704	−0.0793556
$603$	4.72128	0.192265
$604$	−8.02511	−0.326537
$605$	0	0
$606$	−10.5193	−0.427315
$607$	−19.7139	−0.800162	−0.400081	−	0.916480i	$-0.631018\pi$
$607$	−19.7139	−0.800162	−0.400081	+	0.916480i	$0.631018\pi$
$608$	30.3129	1.22935
$609$	−4.00000	−0.162088
$610$	0	0
$611$	−46.7142	−1.88985
$612$	−3.05159	−0.123353
$613$	3.73299	0.150774	0.0753871	−	0.997154i	$-0.475981\pi$
$613$	3.73299	0.150774	0.0753871	+	0.997154i	$0.475981\pi$
$614$	−7.93502	−0.320231
$615$	0	0
$616$	0	0
$617$	24.8851	1.00184	0.500918	−	0.865495i	$-0.332996\pi$
$617$	24.8851	1.00184	0.500918	+	0.865495i	$0.332996\pi$
$618$	11.2978	0.454465
$619$	29.9470	1.20367	0.601837	−	0.798619i	$-0.294436\pi$
$619$	29.9470	1.20367	0.601837	+	0.798619i	$0.294436\pi$
$620$	0	0
$621$	4.62981	0.185788
$622$	−0.351089	−0.0140774
$623$	−18.8174	−0.753903
$624$	−3.71390	−0.148675
$625$	0	0
$626$	−0.0797444	−0.00318723
$627$	0	0
$628$	−21.3776	−0.853058
$629$	−19.3394	−0.771111
$630$	0	0
$631$	−10.2787	−0.409190	−0.204595	−	0.978847i	$-0.565588\pi$
$631$	−10.2787	−0.409190	−0.204595	+	0.978847i	$0.565588\pi$
$632$	−12.8777	−0.512248
$633$	17.9735	0.714383
$634$	14.7494	0.585775
$635$	0	0
$636$	7.38792	0.292950
$637$	−20.8731	−0.827021
$638$	0	0
$639$	13.4426	0.531779
$640$	0	0
$641$	−13.8586	−0.547383	−0.273691	−	0.961818i	$-0.588245\pi$
$641$	−13.8586	−0.547383	−0.273691	+	0.961818i	$0.588245\pi$
$642$	14.9410	0.589675
$643$	16.4499	0.648722	0.324361	−	0.945933i	$-0.394851\pi$
$643$	16.4499	0.648722	0.324361	+	0.945933i	$0.394851\pi$
$644$	−10.5842	−0.417077
$645$	0	0
$646$	8.70218	0.342383
$647$	15.3172	0.602182	0.301091	−	0.953595i	$-0.402649\pi$
$647$	15.3172	0.602182	0.301091	+	0.953595i	$0.402649\pi$
$648$	−2.62981	−0.103309
$649$	0	0
$650$	0	0
$651$	9.46165	0.370831
$652$	−24.1829	−0.947076
$653$	37.2214	1.45659	0.728294	−	0.685265i	$-0.240314\pi$
$653$	37.2214	1.45659	0.728294	+	0.685265i	$0.240314\pi$
$654$	6.79060	0.265533
$655$	0	0
$656$	3.93502	0.153637
$657$	1.17554	0.0458624
$658$	12.2452	0.477367
$659$	−33.1564	−1.29159	−0.645796	−	0.763510i	$-0.723474\pi$
$659$	−33.1564	−1.29159	−0.645796	+	0.763510i	$0.723474\pi$
$660$	0	0
$661$	14.2670	0.554922	0.277461	−	0.960737i	$-0.410507\pi$
$661$	14.2670	0.554922	0.277461	+	0.960737i	$0.410507\pi$
$662$	−7.30688	−0.283990
$663$	−10.4543	−0.406010
$664$	−10.5193	−0.408226
$665$	0	0
$666$	−6.87034	−0.266220
$667$	11.3628	0.439970
$668$	−7.76853	−0.300573
$669$	−12.7863	−0.494345
$670$	0	0
$671$	0	0
$672$	9.54573	0.368235
$673$	19.9427	0.768735	0.384367	−	0.923180i	$-0.374420\pi$
$673$	19.9427	0.768735	0.384367	+	0.923180i	$0.374420\pi$
$674$	13.1035	0.504728
$675$	0	0
$676$	−14.1551	−0.544426
$677$	25.6255	0.984867	0.492434	−	0.870350i	$-0.336107\pi$
$677$	25.6255	0.984867	0.492434	+	0.870350i	$0.336107\pi$
$678$	9.68140	0.371812
$679$	7.69480	0.295299
$680$	0	0
$681$	−14.2787	−0.547162
$682$	0	0
$683$	0.870342	0.0333027	0.0166514	−	0.999861i	$-0.494699\pi$
$683$	0.870342	0.0333027	0.0166514	+	0.999861i	$0.494699\pi$
$684$	−7.25963	−0.277579
$685$	0	0
$686$	14.2888	0.545550
$687$	25.9692	0.990786
$688$	1.19464	0.0455453
$689$	25.3099	0.964229
$690$	0	0
$691$	4.32461	0.164516	0.0822580	−	0.996611i	$-0.473787\pi$
$691$	4.32461	0.164516	0.0822580	+	0.996611i	$0.473787\pi$
$692$	−26.2331	−0.997235
$693$	0	0
$694$	−21.6848	−0.823142
$695$	0	0
$696$	−6.45427	−0.244648
$697$	11.0767	0.419560
$698$	13.5514	0.512929
$699$	10.5648	0.399599
$700$	0	0
$701$	−5.02648	−0.189847	−0.0949237	−	0.995485i	$-0.530261\pi$
$701$	−5.02648	−0.189847	−0.0949237	+	0.995485i	$0.530261\pi$
$702$	−3.71390	−0.140172
$703$	−46.0077	−1.73521
$704$	0	0
$705$	0	0
$706$	15.8348	0.595951
$707$	−22.1829	−0.834275
$708$	−10.0382	−0.377259
$709$	32.1373	1.20694	0.603472	−	0.797384i	$-0.293784\pi$
$709$	32.1373	1.20694	0.603472	+	0.797384i	$0.293784\pi$
$710$	0	0
$711$	4.89682	0.183645
$712$	−30.3631	−1.13791
$713$	−26.8777	−1.00658
$714$	2.74037	0.102556
$715$	0	0
$716$	−1.67570	−0.0626238
$717$	−6.45427	−0.241039
$718$	−22.1534	−0.826758
$719$	42.6640	1.59110	0.795549	−	0.605889i	$-0.207183\pi$
$719$	42.6640	1.59110	0.795549	+	0.605889i	$0.207183\pi$
$720$	0	0
$721$	23.8248	0.887281
$722$	6.01773	0.223957
$723$	−25.6181	−0.952747
$724$	−21.5223	−0.799870
$725$	0	0
$726$	0	0
$727$	0.351089	0.0130212	0.00651058	−	0.999979i	$-0.497928\pi$
$727$	0.351089	0.0130212	0.00651058	+	0.999979i	$0.497928\pi$
$728$	20.5963	0.763348
$729$	1.00000	0.0370370
$730$	0	0
$731$	3.36281	0.124378
$732$	−20.0017	−0.739283
$733$	22.0000	0.812589	0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000	0.812589	0.406294	+	0.913742i	$0.366821\pi$
$734$	17.4660	0.644681
$735$	0	0
$736$	−27.1166	−0.999530
$737$	0	0
$738$	3.93502	0.144850
$739$	15.2479	0.560903	0.280452	−	0.959868i	$-0.409516\pi$
$739$	15.2479	0.560903	0.280452	+	0.959868i	$0.409516\pi$
$740$	0	0
$741$	−24.8703	−0.913635
$742$	−6.63446	−0.243559
$743$	−4.11056	−0.150802	−0.0754009	−	0.997153i	$-0.524024\pi$
$743$	−4.11056	−0.150802	−0.0754009	+	0.997153i	$0.524024\pi$
$744$	15.2670	0.559716
$745$	0	0
$746$	−20.1595	−0.738091
$747$	4.00000	0.146352
$748$	0	0
$749$	31.5075	1.15126
$750$	0	0
$751$	−24.4928	−0.893754	−0.446877	−	0.894595i	$-0.647464\pi$
$751$	−24.4928	−0.893754	−0.446877	+	0.894595i	$0.647464\pi$
$752$	−7.51324	−0.273980
$753$	−4.80536	−0.175117
$754$	−9.11490	−0.331945
$755$	0	0
$756$	−2.28610	−0.0831448
$757$	1.03082	0.0374656	0.0187328	−	0.999825i	$-0.494037\pi$
$757$	1.03082	0.0374656	0.0187328	+	0.999825i	$0.494037\pi$
$758$	7.08241	0.257245
$759$	0	0
$760$	0	0
$761$	−14.4161	−0.522582	−0.261291	−	0.965260i	$-0.584148\pi$
$761$	−14.4161	−0.522582	−0.261291	+	0.965260i	$0.584148\pi$
$762$	13.3246	0.482700
$763$	14.3200	0.518417
$764$	−22.0415	−0.797435
$765$	0	0
$766$	14.1829	0.512450
$767$	−34.3893	−1.24173
$768$	13.2345	0.477559
$769$	−29.1447	−1.05099	−0.525493	−	0.850798i	$-0.676119\pi$
$769$	−29.1447	−1.05099	−0.525493	+	0.850798i	$0.676119\pi$
$770$	0	0
$771$	11.7863	0.424472
$772$	−15.7669	−0.567461
$773$	44.3203	1.59409	0.797045	−	0.603920i	$-0.206395\pi$
$773$	44.3203	1.59409	0.797045	+	0.603920i	$0.206395\pi$
$774$	1.19464	0.0429405
$775$	0	0
$776$	12.4161	0.445711
$777$	−14.4881	−0.519759
$778$	−9.73733	−0.349100
$779$	26.3511	0.944126
$780$	0	0
$781$	0	0
$782$	−7.78458	−0.278376
$783$	2.45427	0.0877084
$784$	−3.35710	−0.119897
$785$	0	0
$786$	−12.0650	−0.430344
$787$	9.03851	0.322188	0.161094	−	0.986939i	$-0.448498\pi$
$787$	9.03851	0.322188	0.161094	+	0.986939i	$0.448498\pi$
$788$	3.84386	0.136932
$789$	−12.4235	−0.442287
$790$	0	0
$791$	20.4161	0.725912
$792$	0	0
$793$	−68.5226	−2.43331
$794$	22.9501	0.814468
$795$	0	0
$796$	35.1581	1.24615
$797$	53.5873	1.89816	0.949079	−	0.315037i	$-0.102017\pi$
$797$	53.5873	1.89816	0.949079	+	0.315037i	$0.102017\pi$
$798$	6.51925	0.230779
$799$	−21.1491	−0.748200
$800$	0	0
$801$	11.5457	0.407948
$802$	30.1829	1.06580
$803$	0	0
$804$	6.62243	0.233555
$805$	0	0
$806$	21.5605	0.759436
$807$	−31.2214	−1.09905
$808$	−35.7936	−1.25922
$809$	−24.8703	−0.874395	−0.437197	−	0.899366i	$-0.644029\pi$
$809$	−24.8703	−0.874395	−0.437197	+	0.899366i	$0.644029\pi$
$810$	0	0
$811$	−35.0415	−1.23048	−0.615238	−	0.788342i	$-0.710940\pi$
$811$	−35.0415	−1.23048	−0.615238	+	0.788342i	$0.710940\pi$
$812$	−5.61072	−0.196898
$813$	−25.5002	−0.894329
$814$	0	0
$815$	0	0
$816$	−1.68140	−0.0588609
$817$	8.00000	0.279885
$818$	−22.8144	−0.797687
$819$	−7.83184	−0.273666
$820$	0	0
$821$	−35.4044	−1.23562	−0.617810	−	0.786327i	$-0.711980\pi$
$821$	−35.4044	−1.23562	−0.617810	+	0.786327i	$0.711980\pi$
$822$	−8.26564	−0.288297
$823$	−27.4502	−0.956855	−0.478428	−	0.878127i	$-0.658793\pi$
$823$	−27.4502	−0.956855	−0.478428	+	0.878127i	$0.658793\pi$
$824$	38.4429	1.33922
$825$	0	0
$826$	9.01445	0.313653
$827$	21.7407	0.755998	0.377999	−	0.925806i	$-0.376612\pi$
$827$	21.7407	0.755998	0.377999	+	0.925806i	$0.376612\pi$
$828$	6.49414	0.225687
$829$	35.5193	1.23363	0.616817	−	0.787106i	$-0.288422\pi$
$829$	35.5193	1.23363	0.616817	+	0.787106i	$0.288422\pi$
$830$	0	0
$831$	−24.6033	−0.853480
$832$	14.3243	0.496606
$833$	−9.44993	−0.327421
$834$	−5.39530	−0.186824
$835$	0	0
$836$	0	0
$837$	−5.80536	−0.200663
$838$	−17.6757	−0.610597
$839$	−18.6492	−0.643843	−0.321921	−	0.946766i	$-0.604329\pi$
$839$	−18.6492	−0.643843	−0.321921	+	0.946766i	$0.604329\pi$
$840$	0	0
$841$	−22.9766	−0.792295
$842$	−16.6965	−0.575398
$843$	11.5457	0.397656
$844$	25.2111	0.867801
$845$	0	0
$846$	−7.51324	−0.258310
$847$	0	0
$848$	4.07069	0.139788
$849$	−6.09884	−0.209312
$850$	0	0
$851$	41.1564	1.41082
$852$	18.8556	0.645982
$853$	−5.32027	−0.182163	−0.0910813	−	0.995843i	$-0.529032\pi$
$853$	−5.32027	−0.182163	−0.0910813	+	0.995843i	$0.529032\pi$
$854$	17.9618	0.614640
$855$	0	0
$856$	50.8395	1.73766
$857$	−17.6181	−0.601823	−0.300911	−	0.953652i	$-0.597291\pi$
$857$	−17.6181	−0.601823	−0.300911	+	0.953652i	$0.597291\pi$
$858$	0	0
$859$	−11.9012	−0.406062	−0.203031	−	0.979172i	$-0.565079\pi$
$859$	−11.9012	−0.406062	−0.203031	+	0.979172i	$0.565079\pi$
$860$	0	0
$861$	8.29813	0.282800
$862$	−26.5990	−0.905965
$863$	−21.7407	−0.740061	−0.370031	−	0.929020i	$-0.620653\pi$
$863$	−21.7407	−0.740061	−0.370031	+	0.929020i	$0.620653\pi$
$864$	−5.85695	−0.199257
$865$	0	0
$866$	15.6844	0.532977
$867$	12.2670	0.416609
$868$	13.2717	0.450469
$869$	0	0
$870$	0	0
$871$	22.6874	0.768734
$872$	23.1062	0.782475
$873$	−4.72128	−0.159791
$874$	−18.5193	−0.626423
$875$	0	0
$876$	1.64891	0.0557115
$877$	39.8777	1.34657	0.673287	−	0.739381i	$-0.264882\pi$
$877$	39.8777	1.34657	0.673287	+	0.739381i	$0.264882\pi$
$878$	−5.63118	−0.190043
$879$	−5.82446	−0.196454
$880$	0	0
$881$	51.5873	1.73802	0.869010	−	0.494795i	$-0.164757\pi$
$881$	51.5873	1.73802	0.869010	+	0.494795i	$0.164757\pi$
$882$	−3.35710	−0.113040
$883$	−24.1343	−0.812184	−0.406092	−	0.913832i	$-0.633109\pi$
$883$	−24.1343	−0.812184	−0.406092	+	0.913832i	$0.633109\pi$
$884$	−14.6640	−0.493203
$885$	0	0
$886$	−5.61072	−0.188496
$887$	43.3896	1.45688	0.728440	−	0.685110i	$-0.240246\pi$
$887$	43.3896	1.45688	0.728440	+	0.685110i	$0.240246\pi$
$888$	−23.3776	−0.784500
$889$	28.0988	0.942405
$890$	0	0
$891$	0	0
$892$	−17.9350	−0.600509
$893$	−50.3129	−1.68366
$894$	−3.01172	−0.100727
$895$	0	0
$896$	15.3366	0.512361
$897$	22.2479	0.742836
$898$	17.0030	0.567399
$899$	−14.2479	−0.475194
$900$	0	0
$901$	11.4586	0.381742
$902$	0	0
$903$	2.51925	0.0838355
$904$	32.9427	1.09566
$905$	0	0
$906$	−4.42178	−0.146904
$907$	28.6181	0.950248	0.475124	−	0.879919i	$-0.342403\pi$
$907$	28.6181	0.950248	0.475124	+	0.879919i	$0.342403\pi$
$908$	−20.0285	−0.664668
$909$	13.6107	0.451439
$910$	0	0
$911$	−19.3776	−0.642007	−0.321004	−	0.947078i	$-0.604020\pi$
$911$	−19.3776	−0.642007	−0.321004	+	0.947078i	$0.604020\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	−2.79060	−0.0923048
$915$	0	0
$916$	36.4264	1.20356
$917$	−25.4426	−0.840187
$918$	−1.68140	−0.0554946
$919$	29.7096	0.980028	0.490014	−	0.871715i	$-0.336992\pi$
$919$	29.7096	0.980028	0.490014	+	0.871715i	$0.336992\pi$
$920$	0	0
$921$	10.2670	0.338309
$922$	15.5371	0.511686
$923$	64.5963	2.12621
$924$	0	0
$925$	0	0
$926$	15.9886	0.525418
$927$	−14.6181	−0.480121
$928$	−14.3745	−0.471867
$929$	7.11490	0.233432	0.116716	−	0.993165i	$-0.462763\pi$
$929$	7.11490	0.233432	0.116716	+	0.993165i	$0.462763\pi$
$930$	0	0
$931$	−22.4811	−0.736787
$932$	14.8191	0.485415
$933$	0.454269	0.0148721
$934$	0.657657	0.0215192
$935$	0	0
$936$	−12.6372	−0.413060
$937$	−8.68308	−0.283664	−0.141832	−	0.989891i	$-0.545299\pi$
$937$	−8.68308	−0.283664	−0.141832	+	0.989891i	$0.545299\pi$
$938$	−5.94704	−0.194178
$939$	0.103180	0.00336716
$940$	0	0
$941$	−14.2861	−0.465714	−0.232857	−	0.972511i	$-0.574807\pi$
$941$	−14.2861	−0.465714	−0.232857	+	0.972511i	$0.574807\pi$
$942$	−11.7789	−0.383777
$943$	−23.5725	−0.767627
$944$	−5.53097	−0.180018
$945$	0	0
$946$	0	0
$947$	−48.5916	−1.57902	−0.789508	−	0.613741i	$-0.789664\pi$
$947$	−48.5916	−1.57902	−0.789508	+	0.613741i	$0.789664\pi$
$948$	6.86867	0.223084
$949$	5.64891	0.183371
$950$	0	0
$951$	−19.0841	−0.618844
$952$	9.32461	0.302212
$953$	−50.0000	−1.61966	−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000	−1.61966	−0.809829	+	0.586665i	$0.800440\pi$
$954$	4.07069	0.131793
$955$	0	0
$956$	−9.05327	−0.292804
$957$	0	0
$958$	21.9504	0.709185
$959$	−17.4305	−0.562861
$960$	0	0
$961$	2.70218	0.0871670
$962$	−33.0144	−1.06443
$963$	−19.3320	−0.622965
$964$	−35.9340	−1.15735
$965$	0	0
$966$	−5.83184	−0.187636
$967$	17.3819	0.558964	0.279482	−	0.960151i	$-0.409837\pi$
$967$	17.3819	0.558964	0.279482	+	0.960151i	$0.409837\pi$
$968$	0	0
$969$	−11.2596	−0.361711
$970$	0	0
$971$	7.69046	0.246799	0.123399	−	0.992357i	$-0.460620\pi$
$971$	7.69046	0.246799	0.123399	+	0.992357i	$0.460620\pi$
$972$	1.40268	0.0449909
$973$	−11.3776	−0.364748
$974$	−3.14169	−0.100666
$975$	0	0
$976$	−11.0208	−0.352766
$977$	3.78626	0.121133	0.0605666	−	0.998164i	$-0.480709\pi$
$977$	3.78626	0.121133	0.0605666	+	0.998164i	$0.480709\pi$
$978$	−13.3246	−0.426074
$979$	0	0
$980$	0	0
$981$	−8.78626	−0.280524
$982$	−21.6107	−0.689626
$983$	20.6446	0.658460	0.329230	−	0.944250i	$-0.393211\pi$
$983$	20.6446	0.658460	0.329230	+	0.944250i	$0.393211\pi$
$984$	13.3896	0.426845
$985$	0	0
$986$	−4.12662	−0.131418
$987$	−15.8439	−0.504316
$988$	−34.8851	−1.10984
$989$	−7.15645	−0.227562
$990$	0	0
$991$	27.8130	0.883511	0.441755	−	0.897136i	$-0.354356\pi$
$991$	27.8130	0.883511	0.441755	+	0.897136i	$0.354356\pi$
$992$	34.0017	1.07955
$993$	9.45427	0.300022
$994$	−16.9326	−0.537069
$995$	0	0
$996$	5.61072	0.177782
$997$	−30.7213	−0.972953	−0.486476	−	0.873694i	$-0.661718\pi$
$997$	−30.7213	−0.972953	−0.486476	+	0.873694i	$0.661718\pi$
$998$	0.879017	0.0278248
$999$	8.88944	0.281249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9075.2.a.ci.1.2		3
5.4	even	2		1815.2.a.l.1.2	✓	3
11.10	odd	2		9075.2.a.ce.1.2		3
15.14	odd	2		5445.2.a.bc.1.2		3
55.54	odd	2		1815.2.a.n.1.2	yes	3
165.164	even	2		5445.2.a.ba.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.a.l.1.2	✓	3	5.4	even	2
1815.2.a.n.1.2	yes	3	55.54	odd	2
5445.2.a.ba.1.2		3	165.164	even	2
5445.2.a.bc.1.2		3	15.14	odd	2
9075.2.a.ce.1.2		3	11.10	odd	2
9075.2.a.ci.1.2		3	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9075.a (trivial)

\(f(q)\)	\(=\)	\(q+0.772866 q^{2} -1.00000 q^{3} -1.40268 q^{4} -0.772866 q^{6} -1.62981 q^{7} -2.62981 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.772866 q^{2} -1.00000 q^{3} -1.40268 q^{4} -0.772866 q^{6} -1.62981 q^{7} -2.62981 q^{8} +1.00000 q^{9} +1.40268 q^{12} +4.80536 q^{13} -1.25963 q^{14} +0.772866 q^{16} +2.17554 q^{17} +0.772866 q^{18} +5.17554 q^{19} +1.62981 q^{21} -4.62981 q^{23} +2.62981 q^{24} +3.71390 q^{26} -1.00000 q^{27} +2.28610 q^{28} -2.45427 q^{29} +5.80536 q^{31} +5.85695 q^{32} +1.68140 q^{34} -1.40268 q^{36} -8.88944 q^{37} +4.00000 q^{38} -4.80536 q^{39} +5.09146 q^{41} +1.25963 q^{42} +1.54573 q^{43} -3.57822 q^{46} -9.72128 q^{47} -0.772866 q^{48} -4.34371 q^{49} -2.17554 q^{51} -6.74037 q^{52} +5.26701 q^{53} -0.772866 q^{54} +4.28610 q^{56} -5.17554 q^{57} -1.89682 q^{58} -7.15645 q^{59} -14.2596 q^{61} +4.48676 q^{62} -1.62981 q^{63} +2.98090 q^{64} +4.72128 q^{67} -3.05159 q^{68} +4.62981 q^{69} +13.4426 q^{71} -2.62981 q^{72} +1.17554 q^{73} -6.87034 q^{74} -7.25963 q^{76} -3.71390 q^{78} +4.89682 q^{79} +1.00000 q^{81} +3.93502 q^{82} +4.00000 q^{83} -2.28610 q^{84} +1.19464 q^{86} +2.45427 q^{87} +11.5457 q^{89} -7.83184 q^{91} +6.49414 q^{92} -5.80536 q^{93} -7.51324 q^{94} -5.85695 q^{96} -4.72128 q^{97} -3.35710 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 - 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 + 3 * q^9	\( 3 q + q^{2} - 3 q^{3} + 5 q^{4} - q^{6} + 3 q^{7} + 3 q^{9} - 5 q^{12} - 4 q^{13} + 12 q^{14} + q^{16} - 4 q^{17} + q^{18} + 5 q^{19} - 3 q^{21} - 6 q^{23} - 2 q^{26} - 3 q^{27} + 20 q^{28} - 10 q^{29} - q^{31} + 11 q^{32} + 9 q^{34} + 5 q^{36} - 3 q^{37} + 12 q^{38} + 4 q^{39} + 10 q^{41} - 12 q^{42} + 2 q^{43} + 9 q^{46} - 16 q^{47} - q^{48} + 8 q^{49} + 4 q^{51} - 36 q^{52} - q^{54} + 26 q^{56} - 5 q^{57} + 18 q^{58} + 18 q^{59} - 27 q^{61} - q^{62} + 3 q^{63} - 20 q^{64} + q^{67} - 21 q^{68} + 6 q^{69} + 14 q^{71} - 7 q^{73} + 32 q^{74} - 6 q^{76} + 2 q^{78} - 9 q^{79} + 3 q^{81} + 46 q^{82} + 12 q^{83} - 20 q^{84} + 22 q^{86} + 10 q^{87} + 32 q^{89} - 34 q^{91} + 5 q^{92} + q^{93} - 37 q^{94} - 11 q^{96} - q^{97} + 57 q^{98}+O(q^{100}) \) 3 * q + q^2 - 3 * q^3 + 5 * q^4 - q^6 + 3 * q^7 + 3 * q^9 - 5 * q^12 - 4 * q^13 + 12 * q^14 + q^16 - 4 * q^17 + q^18 + 5 * q^19 - 3 * q^21 - 6 * q^23 - 2 * q^26 - 3 * q^27 + 20 * q^28 - 10 * q^29 - q^31 + 11 * q^32 + 9 * q^34 + 5 * q^36 - 3 * q^37 + 12 * q^38 + 4 * q^39 + 10 * q^41 - 12 * q^42 + 2 * q^43 + 9 * q^46 - 16 * q^47 - q^48 + 8 * q^49 + 4 * q^51 - 36 * q^52 - q^54 + 26 * q^56 - 5 * q^57 + 18 * q^58 + 18 * q^59 - 27 * q^61 - q^62 + 3 * q^63 - 20 * q^64 + q^67 - 21 * q^68 + 6 * q^69 + 14 * q^71 - 7 * q^73 + 32 * q^74 - 6 * q^76 + 2 * q^78 - 9 * q^79 + 3 * q^81 + 46 * q^82 + 12 * q^83 - 20 * q^84 + 22 * q^86 + 10 * q^87 + 32 * q^89 - 34 * q^91 + 5 * q^92 + q^93 - 37 * q^94 - 11 * q^96 - q^97 + 57 * q^98

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