LMFDB - Embedded newform 9075.2.a.dp.1.1

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:	$6$
Coefficient field:	6.6.860280160.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 9x^{3} + 23x^{2} - 22x - 2 $ x^6 - x^5 - 10x^4 + 9x^3 + 23x^2 - 22x - 2
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			1.1
Root			$2.73519$ 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)

$f(q)$	$=$	$q-2.73519 q^{2} +1.00000 q^{3} +5.48125 q^{4} -2.73519 q^{6} +4.20410 q^{7} -9.52186 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.73519 q^{2} +1.00000 q^{3} +5.48125 q^{4} -2.73519 q^{6} +4.20410 q^{7} -9.52186 q^{8} +1.00000 q^{9} +5.48125 q^{12} -0.0784689 q^{13} -11.4990 q^{14} +15.0816 q^{16} -0.0228569 q^{17} -2.73519 q^{18} -1.26627 q^{19} +4.20410 q^{21} +6.12996 q^{23} -9.52186 q^{24} +0.214627 q^{26} +1.00000 q^{27} +23.0437 q^{28} -5.85972 q^{29} -3.23929 q^{31} -22.2072 q^{32} +0.0625180 q^{34} +5.48125 q^{36} +8.67992 q^{37} +3.46349 q^{38} -0.0784689 q^{39} -3.84194 q^{41} -11.4990 q^{42} -0.859518 q^{43} -16.7666 q^{46} +1.89867 q^{47} +15.0816 q^{48} +10.6745 q^{49} -0.0228569 q^{51} -0.430108 q^{52} +4.55937 q^{53} -2.73519 q^{54} -40.0309 q^{56} -1.26627 q^{57} +16.0274 q^{58} -3.44174 q^{59} +8.13141 q^{61} +8.86007 q^{62} +4.20410 q^{63} +30.5777 q^{64} -0.406754 q^{67} -0.125285 q^{68} +6.12996 q^{69} +8.40424 q^{71} -9.52186 q^{72} +15.1913 q^{73} -23.7412 q^{74} -6.94075 q^{76} +0.214627 q^{78} -13.2182 q^{79} +1.00000 q^{81} +10.5084 q^{82} -14.4615 q^{83} +23.0437 q^{84} +2.35094 q^{86} -5.85972 q^{87} -8.19755 q^{89} -0.329891 q^{91} +33.5998 q^{92} -3.23929 q^{93} -5.19323 q^{94} -22.2072 q^{96} +1.64997 q^{97} -29.1967 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 6 q^{3} + 9 q^{4} - q^{6} + 4 q^{7} + 6 q^{9}+O(q^{10}) $ 6 * q - q^2 + 6 * q^3 + 9 * q^4 - q^6 + 4 * q^7 + 6 * q^9	$ 6 q - q^{2} + 6 q^{3} + 9 q^{4} - q^{6} + 4 q^{7} + 6 q^{9} + 9 q^{12} - 2 q^{13} - 10 q^{14} + 11 q^{16} - 2 q^{17} - q^{18} + 2 q^{19} + 4 q^{21} + 12 q^{23} + 6 q^{27} + 24 q^{28} - 12 q^{29} + 18 q^{31} - 31 q^{32} - q^{34} + 9 q^{36} + 24 q^{37} + 32 q^{38} - 2 q^{39} + 6 q^{41} - 10 q^{42} - 10 q^{43} + 11 q^{46} + 8 q^{47} + 11 q^{48} + 12 q^{49} - 2 q^{51} + 8 q^{52} + 18 q^{53} - q^{54} - 42 q^{56} + 2 q^{57} - 8 q^{58} - 18 q^{59} - 4 q^{61} + 17 q^{62} + 4 q^{63} + 22 q^{64} + 12 q^{67} + 9 q^{68} + 12 q^{69} - 14 q^{73} + 4 q^{74} + 20 q^{76} - 2 q^{79} + 6 q^{81} + 36 q^{82} + 20 q^{83} + 24 q^{84} + 28 q^{86} - 12 q^{87} - 16 q^{89} + 24 q^{91} + 41 q^{92} + 18 q^{93} - 3 q^{94} - 31 q^{96} + 12 q^{97} - 53 q^{98}+O(q^{100}) $ 6 * q - q^2 + 6 * q^3 + 9 * q^4 - q^6 + 4 * q^7 + 6 * q^9 + 9 * q^12 - 2 * q^13 - 10 * q^14 + 11 * q^16 - 2 * q^17 - q^18 + 2 * q^19 + 4 * q^21 + 12 * q^23 + 6 * q^27 + 24 * q^28 - 12 * q^29 + 18 * q^31 - 31 * q^32 - q^34 + 9 * q^36 + 24 * q^37 + 32 * q^38 - 2 * q^39 + 6 * q^41 - 10 * q^42 - 10 * q^43 + 11 * q^46 + 8 * q^47 + 11 * q^48 + 12 * q^49 - 2 * q^51 + 8 * q^52 + 18 * q^53 - q^54 - 42 * q^56 + 2 * q^57 - 8 * q^58 - 18 * q^59 - 4 * q^61 + 17 * q^62 + 4 * q^63 + 22 * q^64 + 12 * q^67 + 9 * q^68 + 12 * q^69 - 14 * q^73 + 4 * q^74 + 20 * q^76 - 2 * q^79 + 6 * q^81 + 36 * q^82 + 20 * q^83 + 24 * q^84 + 28 * q^86 - 12 * q^87 - 16 * q^89 + 24 * q^91 + 41 * q^92 + 18 * q^93 - 3 * q^94 - 31 * q^96 + 12 * q^97 - 53 * 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 $

$2$	−2.73519	−1.93407	−0.967035	−	0.254645i	$-0.918041\pi$
$2$	−2.73519	−1.93407	−0.967035	+	0.254645i	$0.918041\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.48125	2.74062
$5$	0	0
$5$	0	0
$6$	−2.73519	−1.11664
$7$	4.20410	1.58900	0.794501	−	0.607263i	$-0.207733\pi$
$7$	4.20410	1.58900	0.794501	+	0.607263i	$0.207733\pi$
$8$	−9.52186	−3.36649
$9$	1.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	5.48125	1.58230
$13$	−0.0784689	−0.0217634	−0.0108817	−	0.999941i	$-0.503464\pi$
$13$	−0.0784689	−0.0217634	−0.0108817	+	0.999941i	$0.503464\pi$
$14$	−11.4990	−3.07324
$15$	0	0
$16$	15.0816	3.77039
$17$	−0.0228569	−0.00554362	−0.00277181	−	0.999996i	$-0.500882\pi$
$17$	−0.0228569	−0.00554362	−0.00277181	+	0.999996i	$0.500882\pi$
$18$	−2.73519	−0.644690
$19$	−1.26627	−0.290503	−0.145251	−	0.989395i	$-0.546399\pi$
$19$	−1.26627	−0.290503	−0.145251	+	0.989395i	$0.546399\pi$
$20$	0	0
$21$	4.20410	0.917410
$22$	0	0
$23$	6.12996	1.27818	0.639092	−	0.769130i	$-0.279310\pi$
$23$	6.12996	1.27818	0.639092	+	0.769130i	$0.279310\pi$
$24$	−9.52186	−1.94364
$25$	0	0
$26$	0.214627	0.0420918
$27$	1.00000	0.192450
$28$	23.0437	4.35485
$29$	−5.85972	−1.08812	−0.544061	−	0.839046i	$-0.683114\pi$
$29$	−5.85972	−1.08812	−0.544061	+	0.839046i	$0.683114\pi$
$30$	0	0
$31$	−3.23929	−0.581794	−0.290897	−	0.956754i	$-0.593954\pi$
$31$	−3.23929	−0.581794	−0.290897	+	0.956754i	$0.593954\pi$
$32$	−22.2072	−3.92572
$33$	0	0
$34$	0.0625180	0.0107218
$35$	0	0
$36$	5.48125	0.913541
$37$	8.67992	1.42697	0.713485	−	0.700670i	$-0.247116\pi$
$37$	8.67992	1.42697	0.713485	+	0.700670i	$0.247116\pi$
$38$	3.46349	0.561852
$39$	−0.0784689	−0.0125651
$40$	0	0
$41$	−3.84194	−0.600010	−0.300005	−	0.953938i	$-0.596988\pi$
$41$	−3.84194	−0.600010	−0.300005	+	0.953938i	$0.596988\pi$
$42$	−11.4990	−1.77434
$43$	−0.859518	−0.131075	−0.0655376	−	0.997850i	$-0.520876\pi$
$43$	−0.859518	−0.131075	−0.0655376	+	0.997850i	$0.520876\pi$
$44$	0	0
$45$	0	0
$46$	−16.7666	−2.47210
$47$	1.89867	0.276950	0.138475	−	0.990366i	$-0.455780\pi$
$47$	1.89867	0.276950	0.138475	+	0.990366i	$0.455780\pi$
$48$	15.0816	2.17684
$49$	10.6745	1.52493
$50$	0	0
$51$	−0.0228569	−0.00320061
$52$	−0.430108	−0.0596452
$53$	4.55937	0.626277	0.313139	−	0.949707i	$-0.398620\pi$
$53$	4.55937	0.626277	0.313139	+	0.949707i	$0.398620\pi$
$54$	−2.73519	−0.372212
$55$	0	0
$56$	−40.0309	−5.34935
$57$	−1.26627	−0.167722
$58$	16.0274	2.10450
$59$	−3.44174	−0.448077	−0.224038	−	0.974580i	$-0.571924\pi$
$59$	−3.44174	−0.448077	−0.224038	+	0.974580i	$0.571924\pi$
$60$	0	0
$61$	8.13141	1.04112	0.520560	−	0.853825i	$-0.325723\pi$
$61$	8.13141	1.04112	0.520560	+	0.853825i	$0.325723\pi$
$62$	8.86007	1.12523
$63$	4.20410	0.529667
$64$	30.5777	3.82221
$65$	0	0
$66$	0	0
$67$	−0.406754	−0.0496929	−0.0248465	−	0.999691i	$-0.507910\pi$
$67$	−0.406754	−0.0496929	−0.0248465	+	0.999691i	$0.507910\pi$
$68$	−0.125285	−0.0151930
$69$	6.12996	0.737960
$70$	0	0
$71$	8.40424	0.997399	0.498700	−	0.866775i	$-0.333811\pi$
$71$	8.40424	0.997399	0.498700	+	0.866775i	$0.333811\pi$
$72$	−9.52186	−1.12216
$73$	15.1913	1.77800	0.889001	−	0.457905i	$-0.151400\pi$
$73$	15.1913	1.77800	0.889001	+	0.457905i	$0.151400\pi$
$74$	−23.7412	−2.75986
$75$	0	0
$76$	−6.94075	−0.796158
$77$	0	0
$78$	0.214627	0.0243017
$79$	−13.2182	−1.48717	−0.743584	−	0.668642i	$-0.766876\pi$
$79$	−13.2182	−1.48717	−0.743584	+	0.668642i	$0.766876\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	10.5084	1.16046
$83$	−14.4615	−1.58736	−0.793678	−	0.608338i	$-0.791836\pi$
$83$	−14.4615	−1.58736	−0.793678	+	0.608338i	$0.791836\pi$
$84$	23.0437	2.51428
$85$	0	0
$86$	2.35094	0.253508
$87$	−5.85972	−0.628228
$88$	0	0
$89$	−8.19755	−0.868938	−0.434469	−	0.900687i	$-0.643064\pi$
$89$	−8.19755	−0.868938	−0.434469	+	0.900687i	$0.643064\pi$
$90$	0	0
$91$	−0.329891	−0.0345820
$92$	33.5998	3.50302
$93$	−3.23929	−0.335899
$94$	−5.19323	−0.535641
$95$	0	0
$96$	−22.2072	−2.26651
$97$	1.64997	0.167529	0.0837644	−	0.996486i	$-0.473306\pi$
$97$	1.64997	0.167529	0.0837644	+	0.996486i	$0.473306\pi$
$98$	−29.1967	−2.94931
$99$	0	0
$100$	0	0
$101$	16.0533	1.59736	0.798681	−	0.601754i	$-0.205531\pi$
$101$	16.0533	1.59736	0.798681	+	0.601754i	$0.205531\pi$
$102$	0.0625180	0.00619021
$103$	−16.3100	−1.60707	−0.803536	−	0.595256i	$-0.797051\pi$
$103$	−16.3100	−1.60707	−0.803536	+	0.595256i	$0.797051\pi$
$104$	0.747170	0.0732661
$105$	0	0
$106$	−12.4707	−1.21126
$107$	−1.74174	−0.168380	−0.0841900	−	0.996450i	$-0.526830\pi$
$107$	−1.74174	−0.168380	−0.0841900	+	0.996450i	$0.526830\pi$
$108$	5.48125	0.527433
$109$	5.52731	0.529420	0.264710	−	0.964328i	$-0.414724\pi$
$109$	5.52731	0.529420	0.264710	+	0.964328i	$0.414724\pi$
$110$	0	0
$111$	8.67992	0.823862
$112$	63.4045	5.99116
$113$	8.38535	0.788827	0.394414	−	0.918933i	$-0.370948\pi$
$113$	8.38535	0.788827	0.394414	+	0.918933i	$0.370948\pi$
$114$	3.46349	0.324385
$115$	0	0
$116$	−32.1186	−2.98213
$117$	−0.0784689	−0.00725445
$118$	9.41381	0.866611
$119$	−0.0960930	−0.00880883
$120$	0	0
$121$	0	0
$122$	−22.2409	−2.01360
$123$	−3.84194	−0.346416
$124$	−17.7554	−1.59448
$125$	0	0
$126$	−11.4990	−1.02441
$127$	−1.82850	−0.162253	−0.0811264	−	0.996704i	$-0.525852\pi$
$127$	−1.82850	−0.162253	−0.0811264	+	0.996704i	$0.525852\pi$
$128$	−39.2214	−3.46671
$129$	−0.859518	−0.0756763
$130$	0	0
$131$	1.09407	0.0955894	0.0477947	−	0.998857i	$-0.484781\pi$
$131$	1.09407	0.0955894	0.0477947	+	0.998857i	$0.484781\pi$
$132$	0	0
$133$	−5.32354	−0.461609
$134$	1.11255	0.0961095
$135$	0	0
$136$	0.217641	0.0186625
$137$	17.0599	1.45752	0.728761	−	0.684768i	$-0.240097\pi$
$137$	17.0599	1.45752	0.728761	+	0.684768i	$0.240097\pi$
$138$	−16.7666	−1.42727
$139$	14.3029	1.21316	0.606579	−	0.795024i	$-0.292542\pi$
$139$	14.3029	1.21316	0.606579	+	0.795024i	$0.292542\pi$
$140$	0	0
$141$	1.89867	0.159897
$142$	−22.9872	−1.92904
$143$	0	0
$144$	15.0816	1.25680
$145$	0	0
$146$	−41.5509	−3.43878
$147$	10.6745	0.880416
$148$	47.5768	3.91079
$149$	−16.6189	−1.36147	−0.680735	−	0.732530i	$-0.738340\pi$
$149$	−16.6189	−1.36147	−0.680735	+	0.732530i	$0.738340\pi$
$150$	0	0
$151$	6.89775	0.561331	0.280666	−	0.959806i	$-0.409445\pi$
$151$	6.89775	0.561331	0.280666	+	0.959806i	$0.409445\pi$
$152$	12.0573	0.977973
$153$	−0.0228569	−0.00184787
$154$	0	0
$155$	0	0
$156$	−0.430108	−0.0344362
$157$	16.3071	1.30145	0.650723	−	0.759315i	$-0.274466\pi$
$157$	16.3071	1.30145	0.650723	+	0.759315i	$0.274466\pi$
$158$	36.1544	2.87629
$159$	4.55937	0.361581
$160$	0	0
$161$	25.7710	2.03104
$162$	−2.73519	−0.214897
$163$	14.7366	1.15426	0.577132	−	0.816651i	$-0.304172\pi$
$163$	14.7366	1.15426	0.577132	+	0.816651i	$0.304172\pi$
$164$	−21.0586	−1.64440
$165$	0	0
$166$	39.5549	3.07006
$167$	−0.810790	−0.0627408	−0.0313704	−	0.999508i	$-0.509987\pi$
$167$	−0.810790	−0.0627408	−0.0313704	+	0.999508i	$0.509987\pi$
$168$	−40.0309	−3.08845
$169$	−12.9938	−0.999526
$170$	0	0
$171$	−1.26627	−0.0968342
$172$	−4.71123	−0.359228
$173$	17.1474	1.30369	0.651845	−	0.758352i	$-0.273995\pi$
$173$	17.1474	1.30369	0.651845	+	0.758352i	$0.273995\pi$
$174$	16.0274	1.21504
$175$	0	0
$176$	0	0
$177$	−3.44174	−0.258697
$178$	22.4218	1.68059
$179$	−3.77163	−0.281905	−0.140953	−	0.990016i	$-0.545017\pi$
$179$	−3.77163	−0.281905	−0.140953	+	0.990016i	$0.545017\pi$
$180$	0	0
$181$	−5.17637	−0.384756	−0.192378	−	0.981321i	$-0.561620\pi$
$181$	−5.17637	−0.384756	−0.192378	+	0.981321i	$0.561620\pi$
$182$	0.902314	0.0668840
$183$	8.13141	0.601091
$184$	−58.3686	−4.30299
$185$	0	0
$186$	8.86007	0.649652
$187$	0	0
$188$	10.4071	0.759016
$189$	4.20410	0.305803
$190$	0	0
$191$	−26.1298	−1.89069	−0.945345	−	0.326073i	$-0.894275\pi$
$191$	−26.1298	−1.89069	−0.945345	+	0.326073i	$0.894275\pi$
$192$	30.5777	2.20676
$193$	12.3391	0.888191	0.444095	−	0.895980i	$-0.353525\pi$
$193$	12.3391	0.888191	0.444095	+	0.895980i	$0.353525\pi$
$194$	−4.51297	−0.324012
$195$	0	0
$196$	58.5094	4.17925
$197$	5.16530	0.368013	0.184006	−	0.982925i	$-0.441093\pi$
$197$	5.16530	0.368013	0.184006	+	0.982925i	$0.441093\pi$
$198$	0	0
$199$	7.92806	0.562005	0.281003	−	0.959707i	$-0.409333\pi$
$199$	7.92806	0.562005	0.281003	+	0.959707i	$0.409333\pi$
$200$	0	0
$201$	−0.406754	−0.0286902
$202$	−43.9088	−3.08941
$203$	−24.6349	−1.72903
$204$	−0.125285	−0.00877168
$205$	0	0
$206$	44.6109	3.10819
$207$	6.12996	0.426062
$208$	−1.18344	−0.0820565
$209$	0	0
$210$	0	0
$211$	20.5882	1.41735	0.708677	−	0.705533i	$-0.249293\pi$
$211$	20.5882	1.41735	0.708677	+	0.705533i	$0.249293\pi$
$212$	24.9910	1.71639
$213$	8.40424	0.575849
$214$	4.76397	0.325659
$215$	0	0
$216$	−9.52186	−0.647881
$217$	−13.6183	−0.924471
$218$	−15.1182	−1.02394
$219$	15.1913	1.02653
$220$	0	0
$221$	0.00179356	0.000120648 0
$222$	−23.7412	−1.59341
$223$	6.43212	0.430726	0.215363	−	0.976534i	$-0.430906\pi$
$223$	6.43212	0.430726	0.215363	+	0.976534i	$0.430906\pi$
$224$	−93.3614	−6.23797
$225$	0	0
$226$	−22.9355	−1.52565
$227$	14.5875	0.968206	0.484103	−	0.875011i	$-0.339146\pi$
$227$	14.5875	0.968206	0.484103	+	0.875011i	$0.339146\pi$
$228$	−6.94075	−0.459662
$229$	−16.1992	−1.07047	−0.535237	−	0.844702i	$-0.679778\pi$
$229$	−16.1992	−1.07047	−0.535237	+	0.844702i	$0.679778\pi$
$230$	0	0
$231$	0	0
$232$	55.7954	3.66315
$233$	−8.58800	−0.562619	−0.281309	−	0.959617i	$-0.590769\pi$
$233$	−8.58800	−0.562619	−0.281309	+	0.959617i	$0.590769\pi$
$234$	0.214627	0.0140306
$235$	0	0
$236$	−18.8650	−1.22801
$237$	−13.2182	−0.858617
$238$	0.262832	0.0170369
$239$	6.29874	0.407432	0.203716	−	0.979030i	$-0.434698\pi$
$239$	6.29874	0.407432	0.203716	+	0.979030i	$0.434698\pi$
$240$	0	0
$241$	1.13776	0.0732899	0.0366449	−	0.999328i	$-0.488333\pi$
$241$	1.13776	0.0732899	0.0366449	+	0.999328i	$0.488333\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	44.5703	2.85332
$245$	0	0
$246$	10.5084	0.669992
$247$	0.0993630	0.00632231
$248$	30.8441	1.95860
$249$	−14.4615	−0.916460
$250$	0	0
$251$	3.82996	0.241745	0.120873	−	0.992668i	$-0.461431\pi$
$251$	3.82996	0.241745	0.120873	+	0.992668i	$0.461431\pi$
$252$	23.0437	1.45162
$253$	0	0
$254$	5.00128	0.313808
$255$	0	0
$256$	46.1223	2.88264
$257$	9.67810	0.603703	0.301852	−	0.953355i	$-0.402395\pi$
$257$	9.67810	0.603703	0.301852	+	0.953355i	$0.402395\pi$
$258$	2.35094	0.146363
$259$	36.4913	2.26746
$260$	0	0
$261$	−5.85972	−0.362707
$262$	−2.99249	−0.184877
$263$	19.0954	1.17747	0.588735	−	0.808326i	$-0.299626\pi$
$263$	19.0954	1.17747	0.588735	+	0.808326i	$0.299626\pi$
$264$	0	0
$265$	0	0
$266$	14.5609	0.892784
$267$	−8.19755	−0.501682
$268$	−2.22952	−0.136190
$269$	17.4899	1.06638	0.533190	−	0.845996i	$-0.320993\pi$
$269$	17.4899	1.06638	0.533190	+	0.845996i	$0.320993\pi$
$270$	0	0
$271$	23.8385	1.44809	0.724043	−	0.689755i	$-0.242282\pi$
$271$	23.8385	1.44809	0.724043	+	0.689755i	$0.242282\pi$
$272$	−0.344719	−0.0209017
$273$	−0.329891	−0.0199659
$274$	−46.6619	−2.81895
$275$	0	0
$276$	33.5998	2.02247
$277$	−4.93692	−0.296631	−0.148315	−	0.988940i	$-0.547385\pi$
$277$	−4.93692	−0.296631	−0.148315	+	0.988940i	$0.547385\pi$
$278$	−39.1211	−2.34633
$279$	−3.23929	−0.193931
$280$	0	0
$281$	2.13091	0.127120	0.0635598	−	0.997978i	$-0.479755\pi$
$281$	2.13091	0.127120	0.0635598	+	0.997978i	$0.479755\pi$
$282$	−5.19323	−0.309252
$283$	−17.2239	−1.02385	−0.511926	−	0.859029i	$-0.671068\pi$
$283$	−17.2239	−1.02385	−0.511926	+	0.859029i	$0.671068\pi$
$284$	46.0657	2.73350
$285$	0	0
$286$	0	0
$287$	−16.1519	−0.953417
$288$	−22.2072	−1.30857
$289$	−16.9995	−0.999969
$290$	0	0
$291$	1.64997	0.0967228
$292$	83.2671	4.87284
$293$	−19.1742	−1.12017	−0.560084	−	0.828436i	$-0.689231\pi$
$293$	−19.1742	−1.12017	−0.560084	+	0.828436i	$0.689231\pi$
$294$	−29.1967	−1.70279
$295$	0	0
$296$	−82.6490	−4.80388
$297$	0	0
$298$	45.4557	2.63318
$299$	−0.481011	−0.0278176
$300$	0	0
$301$	−3.61350	−0.208279
$302$	−18.8666	−1.08565
$303$	16.0533	0.922238
$304$	−19.0974	−1.09531
$305$	0	0
$306$	0.0625180	0.00357392
$307$	12.0936	0.690217	0.345108	−	0.938563i	$-0.387842\pi$
$307$	12.0936	0.690217	0.345108	+	0.938563i	$0.387842\pi$
$308$	0	0
$309$	−16.3100	−0.927843
$310$	0	0
$311$	10.5043	0.595644	0.297822	−	0.954621i	$-0.403740\pi$
$311$	10.5043	0.595644	0.297822	+	0.954621i	$0.403740\pi$
$312$	0.747170	0.0423002
$313$	0.223857	0.0126532	0.00632658	−	0.999980i	$-0.497986\pi$
$313$	0.223857	0.0126532	0.00632658	+	0.999980i	$0.497986\pi$
$314$	−44.6029	−2.51709
$315$	0	0
$316$	−72.4525	−4.07577
$317$	−11.0776	−0.622179	−0.311090	−	0.950381i	$-0.600694\pi$
$317$	−11.0776	−0.622179	−0.311090	+	0.950381i	$0.600694\pi$
$318$	−12.4707	−0.699323
$319$	0	0
$320$	0	0
$321$	−1.74174	−0.0972142
$322$	−70.4884	−3.92817
$323$	0.0289431	0.00161044
$324$	5.48125	0.304514
$325$	0	0
$326$	−40.3075	−2.23242
$327$	5.52731	0.305661
$328$	36.5824	2.01993
$329$	7.98222	0.440074
$330$	0	0
$331$	27.0860	1.48878	0.744390	−	0.667745i	$-0.232741\pi$
$331$	27.0860	1.48878	0.744390	+	0.667745i	$0.232741\pi$
$332$	−79.2671	−4.35035
$333$	8.67992	0.475657
$334$	2.21766	0.121345
$335$	0	0
$336$	63.4045	3.45900
$337$	20.9072	1.13889	0.569444	−	0.822030i	$-0.307159\pi$
$337$	20.9072	1.13889	0.569444	+	0.822030i	$0.307159\pi$
$338$	35.5406	1.93315
$339$	8.38535	0.455430
$340$	0	0
$341$	0	0
$342$	3.46349	0.187284
$343$	15.4479	0.834107
$344$	8.18421	0.441263
$345$	0	0
$346$	−46.9013	−2.52143
$347$	15.3060	0.821667	0.410833	−	0.911710i	$-0.365238\pi$
$347$	15.3060	0.821667	0.410833	+	0.911710i	$0.365238\pi$
$348$	−32.1186	−1.72174
$349$	−0.634549	−0.0339666	−0.0169833	−	0.999856i	$-0.505406\pi$
$349$	−0.634549	−0.0339666	−0.0169833	+	0.999856i	$0.505406\pi$
$350$	0	0
$351$	−0.0784689	−0.00418836
$352$	0	0
$353$	18.5583	0.987759	0.493879	−	0.869530i	$-0.335578\pi$
$353$	18.5583	0.987759	0.493879	+	0.869530i	$0.335578\pi$
$354$	9.41381	0.500338
$355$	0	0
$356$	−44.9328	−2.38143
$357$	−0.0960930	−0.00508578
$358$	10.3161	0.545224
$359$	16.8668	0.890196	0.445098	−	0.895482i	$-0.353169\pi$
$359$	16.8668	0.890196	0.445098	+	0.895482i	$0.353169\pi$
$360$	0	0
$361$	−17.3966	−0.915608
$362$	14.1583	0.744146
$363$	0	0
$364$	−1.80822	−0.0947763
$365$	0	0
$366$	−22.2409	−1.16255
$367$	12.3622	0.645301	0.322651	−	0.946518i	$-0.395426\pi$
$367$	12.3622	0.645301	0.322651	+	0.946518i	$0.395426\pi$
$368$	92.4494	4.81926
$369$	−3.84194	−0.200003
$370$	0	0
$371$	19.1680	0.995155
$372$	−17.7554	−0.920572
$373$	13.0097	0.673615	0.336807	−	0.941574i	$-0.390653\pi$
$373$	13.0097	0.673615	0.336807	+	0.941574i	$0.390653\pi$
$374$	0	0
$375$	0	0
$376$	−18.0789	−0.932349
$377$	0.459806	0.0236812
$378$	−11.4990	−0.591445
$379$	−27.2309	−1.39876	−0.699380	−	0.714750i	$-0.746540\pi$
$379$	−27.2309	−1.39876	−0.699380	+	0.714750i	$0.746540\pi$
$380$	0	0
$381$	−1.82850	−0.0936767
$382$	71.4700	3.65672
$383$	−11.5059	−0.587924	−0.293962	−	0.955817i	$-0.594974\pi$
$383$	−11.5059	−0.587924	−0.293962	+	0.955817i	$0.594974\pi$
$384$	−39.2214	−2.00151
$385$	0	0
$386$	−33.7498	−1.71782
$387$	−0.859518	−0.0436917
$388$	9.04388	0.459133
$389$	23.0264	1.16749	0.583743	−	0.811939i	$-0.301588\pi$
$389$	23.0264	1.16749	0.583743	+	0.811939i	$0.301588\pi$
$390$	0	0
$391$	−0.140112	−0.00708577
$392$	−101.641	−5.13364
$393$	1.09407	0.0551886
$394$	−14.1281	−0.711762
$395$	0	0
$396$	0	0
$397$	−8.37468	−0.420313	−0.210157	−	0.977668i	$-0.567397\pi$
$397$	−8.37468	−0.420313	−0.210157	+	0.977668i	$0.567397\pi$
$398$	−21.6847	−1.08696
$399$	−5.32354	−0.266510
$400$	0	0
$401$	38.3767	1.91644	0.958221	−	0.286029i	$-0.0923354\pi$
$401$	38.3767	1.91644	0.958221	+	0.286029i	$0.0923354\pi$
$402$	1.11255	0.0554889
$403$	0.254184	0.0126618
$404$	87.9921	4.37777
$405$	0	0
$406$	67.3809	3.34406
$407$	0	0
$408$	0.217641	0.0107748
$409$	−35.6631	−1.76343	−0.881713	−	0.471786i	$-0.843609\pi$
$409$	−35.6631	−1.76343	−0.881713	+	0.471786i	$0.843609\pi$
$410$	0	0
$411$	17.0599	0.841501
$412$	−89.3991	−4.40438
$413$	−14.4694	−0.711994
$414$	−16.7666	−0.824032
$415$	0	0
$416$	1.74258	0.0854368
$417$	14.3029	0.700417
$418$	0	0
$419$	28.0750	1.37155	0.685777	−	0.727812i	$-0.259463\pi$
$419$	28.0750	1.37155	0.685777	+	0.727812i	$0.259463\pi$
$420$	0	0
$421$	−40.2965	−1.96393	−0.981965	−	0.189065i	$-0.939454\pi$
$421$	−40.2965	−1.96393	−0.981965	+	0.189065i	$0.939454\pi$
$422$	−56.3127	−2.74126
$423$	1.89867	0.0923167
$424$	−43.4137	−2.10835
$425$	0	0
$426$	−22.9872	−1.11373
$427$	34.1853	1.65434
$428$	−9.54689	−0.461466
$429$	0	0
$430$	0	0
$431$	17.2384	0.830346	0.415173	−	0.909743i	$-0.363721\pi$
$431$	17.2384	0.830346	0.415173	+	0.909743i	$0.363721\pi$
$432$	15.0816	0.725613
$433$	−17.0888	−0.821237	−0.410619	−	0.911807i	$-0.634687\pi$
$433$	−17.0888	−0.821237	−0.410619	+	0.911807i	$0.634687\pi$
$434$	37.2486	1.78799
$435$	0	0
$436$	30.2966	1.45094
$437$	−7.76219	−0.371316
$438$	−41.5509	−1.98538
$439$	1.97449	0.0942371	0.0471185	−	0.998889i	$-0.484996\pi$
$439$	1.97449	0.0942371	0.0471185	+	0.998889i	$0.484996\pi$
$440$	0	0
$441$	10.6745	0.508308
$442$	−0.00490572	−0.000233341 0
$443$	−26.2675	−1.24801	−0.624003	−	0.781422i	$-0.714495\pi$
$443$	−26.2675	−1.24801	−0.624003	+	0.781422i	$0.714495\pi$
$444$	47.5768	2.25790
$445$	0	0
$446$	−17.5930	−0.833055
$447$	−16.6189	−0.786045
$448$	128.552	6.07350
$449$	6.76495	0.319258	0.159629	−	0.987177i	$-0.448970\pi$
$449$	6.76495	0.319258	0.159629	+	0.987177i	$0.448970\pi$
$450$	0	0
$451$	0	0
$452$	45.9622	2.16188
$453$	6.89775	0.324085
$454$	−39.8995	−1.87258
$455$	0	0
$456$	12.0573	0.564633
$457$	−25.1897	−1.17832	−0.589161	−	0.808016i	$-0.700542\pi$
$457$	−25.1897	−1.17832	−0.589161	+	0.808016i	$0.700542\pi$
$458$	44.3078	2.07037
$459$	−0.0228569	−0.00106687
$460$	0	0
$461$	39.8293	1.85504	0.927518	−	0.373778i	$-0.121938\pi$
$461$	39.8293	1.85504	0.927518	+	0.373778i	$0.121938\pi$
$462$	0	0
$463$	−38.6388	−1.79570	−0.897849	−	0.440303i	$-0.854871\pi$
$463$	−38.6388	−1.79570	−0.897849	+	0.440303i	$0.854871\pi$
$464$	−88.3738	−4.10265
$465$	0	0
$466$	23.4898	1.08814
$467$	10.6309	0.491940	0.245970	−	0.969277i	$-0.420894\pi$
$467$	10.6309	0.491940	0.245970	+	0.969277i	$0.420894\pi$
$468$	−0.430108	−0.0198817
$469$	−1.71004	−0.0789621
$470$	0	0
$471$	16.3071	0.751391
$472$	32.7718	1.50844
$473$	0	0
$474$	36.1544	1.66062
$475$	0	0
$476$	−0.526709	−0.0241417
$477$	4.55937	0.208759
$478$	−17.2282	−0.788002
$479$	−37.6760	−1.72146	−0.860730	−	0.509062i	$-0.829992\pi$
$479$	−37.6760	−1.72146	−0.860730	+	0.509062i	$0.829992\pi$
$480$	0	0
$481$	−0.681104	−0.0310557
$482$	−3.11200	−0.141748
$483$	25.7710	1.17262
$484$	0	0
$485$	0	0
$486$	−2.73519	−0.124071
$487$	−33.8739	−1.53498	−0.767488	−	0.641064i	$-0.778493\pi$
$487$	−33.8739	−1.53498	−0.767488	+	0.641064i	$0.778493\pi$
$488$	−77.4262	−3.50492
$489$	14.7366	0.666414
$490$	0	0
$491$	4.46216	0.201375	0.100687	−	0.994918i	$-0.467896\pi$
$491$	4.46216	0.201375	0.100687	+	0.994918i	$0.467896\pi$
$492$	−21.0586	−0.949396
$493$	0.133935	0.00603214
$494$	−0.271776	−0.0122278
$495$	0	0
$496$	−48.8536	−2.19359
$497$	35.3323	1.58487
$498$	39.5549	1.77250
$499$	−30.5968	−1.36970	−0.684851	−	0.728683i	$-0.740133\pi$
$499$	−30.5968	−1.36970	−0.684851	+	0.728683i	$0.740133\pi$
$500$	0	0
$501$	−0.810790	−0.0362234
$502$	−10.4757	−0.467552
$503$	−33.2223	−1.48131	−0.740655	−	0.671886i	$-0.765484\pi$
$503$	−33.2223	−1.48131	−0.740655	+	0.671886i	$0.765484\pi$
$504$	−40.0309	−1.78312
$505$	0	0
$506$	0	0
$507$	−12.9938	−0.577077
$508$	−10.0224	−0.444674
$509$	1.42863	0.0633228	0.0316614	−	0.999499i	$-0.489920\pi$
$509$	1.42863	0.0633228	0.0316614	+	0.999499i	$0.489920\pi$
$510$	0	0
$511$	63.8656	2.82525
$512$	−47.7104	−2.10852
$513$	−1.26627	−0.0559073
$514$	−26.4714	−1.16760
$515$	0	0
$516$	−4.71123	−0.207400
$517$	0	0
$518$	−99.8105	−4.38542
$519$	17.1474	0.752686
$520$	0	0
$521$	11.4588	0.502020	0.251010	−	0.967985i	$-0.419237\pi$
$521$	11.4588	0.502020	0.251010	+	0.967985i	$0.419237\pi$
$522$	16.0274	0.701501
$523$	−29.5781	−1.29336	−0.646680	−	0.762761i	$-0.723843\pi$
$523$	−29.5781	−1.29336	−0.646680	+	0.762761i	$0.723843\pi$
$524$	5.99687	0.261975
$525$	0	0
$526$	−52.2294	−2.27731
$527$	0.0740403	0.00322525
$528$	0	0
$529$	14.5764	0.633756
$530$	0	0
$531$	−3.44174	−0.149359
$532$	−29.1796	−1.26510
$533$	0.301473	0.0130582
$534$	22.4218	0.970287
$535$	0	0
$536$	3.87306	0.167291
$537$	−3.77163	−0.162758
$538$	−47.8382	−2.06245
$539$	0	0
$540$	0	0
$541$	−25.4976	−1.09623	−0.548115	−	0.836403i	$-0.684654\pi$
$541$	−25.4976	−1.09623	−0.548115	+	0.836403i	$0.684654\pi$
$542$	−65.2028	−2.80070
$543$	−5.17637	−0.222139
$544$	0.507589	0.0217627
$545$	0	0
$546$	0.902314	0.0386155
$547$	6.72363	0.287482	0.143741	−	0.989615i	$-0.454087\pi$
$547$	6.72363	0.287482	0.143741	+	0.989615i	$0.454087\pi$
$548$	93.5093	3.99452
$549$	8.13141	0.347040
$550$	0	0
$551$	7.41999	0.316102
$552$	−58.3686	−2.48433
$553$	−55.5708	−2.36311
$554$	13.5034	0.573705
$555$	0	0
$556$	78.3978	3.32481
$557$	−18.7697	−0.795299	−0.397650	−	0.917537i	$-0.630174\pi$
$557$	−18.7697	−0.795299	−0.397650	+	0.917537i	$0.630174\pi$
$558$	8.86007	0.375077
$559$	0.0674454	0.00285264
$560$	0	0
$561$	0	0
$562$	−5.82844	−0.245858
$563$	10.7917	0.454818	0.227409	−	0.973799i	$-0.426975\pi$
$563$	10.7917	0.454818	0.227409	+	0.973799i	$0.426975\pi$
$564$	10.4071	0.438218
$565$	0	0
$566$	47.1105	1.98020
$567$	4.20410	0.176556
$568$	−80.0240	−3.35773
$569$	14.1026	0.591211	0.295606	−	0.955310i	$-0.404479\pi$
$569$	14.1026	0.591211	0.295606	+	0.955310i	$0.404479\pi$
$570$	0	0
$571$	22.1590	0.927325	0.463662	−	0.886012i	$-0.346535\pi$
$571$	22.1590	0.927325	0.463662	+	0.886012i	$0.346535\pi$
$572$	0	0
$573$	−26.1298	−1.09159
$574$	44.1785	1.84397
$575$	0	0
$576$	30.5777	1.27407
$577$	−31.5239	−1.31236	−0.656179	−	0.754605i	$-0.727828\pi$
$577$	−31.5239	−1.31236	−0.656179	+	0.754605i	$0.727828\pi$
$578$	46.4967	1.93401
$579$	12.3391	0.512797
$580$	0	0
$581$	−60.7976	−2.52231
$582$	−4.51297	−0.187069
$583$	0	0
$584$	−144.649	−5.98562
$585$	0	0
$586$	52.4450	2.16648
$587$	−31.2905	−1.29150	−0.645748	−	0.763551i	$-0.723454\pi$
$587$	−31.2905	−1.29150	−0.645748	+	0.763551i	$0.723454\pi$
$588$	58.5094	2.41289
$589$	4.10182	0.169013
$590$	0	0
$591$	5.16530	0.212472
$592$	130.907	5.38024
$593$	−10.6328	−0.436635	−0.218318	−	0.975878i	$-0.570057\pi$
$593$	−10.6328	−0.436635	−0.218318	+	0.975878i	$0.570057\pi$
$594$	0	0
$595$	0	0
$596$	−91.0921	−3.73128
$597$	7.92806	0.324474
$598$	1.31566	0.0538011
$599$	−33.0858	−1.35185	−0.675924	−	0.736971i	$-0.736255\pi$
$599$	−33.0858	−1.35185	−0.675924	+	0.736971i	$0.736255\pi$
$600$	0	0
$601$	−0.0517727	−0.00211185	−0.00105593	−	0.999999i	$-0.500336\pi$
$601$	−0.0517727	−0.00211185	−0.00105593	+	0.999999i	$0.500336\pi$
$602$	9.88360	0.402825
$603$	−0.406754	−0.0165643
$604$	37.8083	1.53840
$605$	0	0
$606$	−43.9088	−1.78367
$607$	10.7914	0.438008	0.219004	−	0.975724i	$-0.429719\pi$
$607$	10.7914	0.438008	0.219004	+	0.975724i	$0.429719\pi$
$608$	28.1204	1.14043
$609$	−24.6349	−0.998255
$610$	0	0
$611$	−0.148987	−0.00602736
$612$	−0.125285	−0.00506433
$613$	6.69877	0.270561	0.135280	−	0.990807i	$-0.456806\pi$
$613$	6.69877	0.270561	0.135280	+	0.990807i	$0.456806\pi$
$614$	−33.0782	−1.33493
$615$	0	0
$616$	0	0
$617$	−17.4561	−0.702755	−0.351377	−	0.936234i	$-0.614287\pi$
$617$	−17.4561	−0.702755	−0.351377	+	0.936234i	$0.614287\pi$
$618$	44.6109	1.79451
$619$	31.1598	1.25242	0.626209	−	0.779655i	$-0.284606\pi$
$619$	31.1598	1.25242	0.626209	+	0.779655i	$0.284606\pi$
$620$	0	0
$621$	6.12996	0.245987
$622$	−28.7312	−1.15202
$623$	−34.4633	−1.38074
$624$	−1.18344	−0.0473753
$625$	0	0
$626$	−0.612291	−0.0244721
$627$	0	0
$628$	89.3831	3.56678
$629$	−0.198397	−0.00791059
$630$	0	0
$631$	6.55952	0.261130	0.130565	−	0.991440i	$-0.458321\pi$
$631$	6.55952	0.261130	0.130565	+	0.991440i	$0.458321\pi$
$632$	125.862	5.00653
$633$	20.5882	0.818309
$634$	30.2993	1.20334
$635$	0	0
$636$	24.9910	0.990958
$637$	−0.837615	−0.0331875
$638$	0	0
$639$	8.40424	0.332466
$640$	0	0
$641$	9.17095	0.362231	0.181115	−	0.983462i	$-0.442029\pi$
$641$	9.17095	0.362231	0.181115	+	0.983462i	$0.442029\pi$
$642$	4.76397	0.188019
$643$	−10.8962	−0.429704	−0.214852	−	0.976647i	$-0.568927\pi$
$643$	−10.8962	−0.429704	−0.214852	+	0.976647i	$0.568927\pi$
$644$	141.257	5.56631
$645$	0	0
$646$	−0.0791648	−0.00311470
$647$	2.47728	0.0973921	0.0486960	−	0.998814i	$-0.484493\pi$
$647$	2.47728	0.0973921	0.0486960	+	0.998814i	$0.484493\pi$
$648$	−9.52186	−0.374054
$649$	0	0
$650$	0	0
$651$	−13.6183	−0.533744
$652$	80.7752	3.16340
$653$	27.9010	1.09185	0.545926	−	0.837833i	$-0.316178\pi$
$653$	27.9010	1.09185	0.545926	+	0.837833i	$0.316178\pi$
$654$	−15.1182	−0.591169
$655$	0	0
$656$	−57.9425	−2.26227
$657$	15.1913	0.592668
$658$	−21.8329	−0.851134
$659$	3.19475	0.124450	0.0622250	−	0.998062i	$-0.480180\pi$
$659$	3.19475	0.124450	0.0622250	+	0.998062i	$0.480180\pi$
$660$	0	0
$661$	−14.8273	−0.576717	−0.288358	−	0.957523i	$-0.593109\pi$
$661$	−14.8273	−0.576717	−0.288358	+	0.957523i	$0.593109\pi$
$662$	−74.0852	−2.87940
$663$	0.00179356	6.96561e−5 0
$664$	137.700	5.34381
$665$	0	0
$666$	−23.7412	−0.919953
$667$	−35.9198	−1.39082
$668$	−4.44414	−0.171949
$669$	6.43212	0.248680
$670$	0	0
$671$	0	0
$672$	−93.3614	−3.60149
$673$	−22.7828	−0.878211	−0.439105	−	0.898436i	$-0.644705\pi$
$673$	−22.7828	−0.878211	−0.439105	+	0.898436i	$0.644705\pi$
$674$	−57.1851	−2.20269
$675$	0	0
$676$	−71.2225	−2.73933
$677$	−18.8485	−0.724405	−0.362203	−	0.932099i	$-0.617975\pi$
$677$	−18.8485	−0.724405	−0.362203	+	0.932099i	$0.617975\pi$
$678$	−22.9355	−0.880832
$679$	6.93663	0.266204
$680$	0	0
$681$	14.5875	0.558994
$682$	0	0
$683$	−18.3894	−0.703650	−0.351825	−	0.936066i	$-0.614439\pi$
$683$	−18.3894	−0.703650	−0.351825	+	0.936066i	$0.614439\pi$
$684$	−6.94075	−0.265386
$685$	0	0
$686$	−42.2528	−1.61322
$687$	−16.1992	−0.618038
$688$	−12.9629	−0.494205
$689$	−0.357769	−0.0136299
$690$	0	0
$691$	−18.0662	−0.687269	−0.343635	−	0.939103i	$-0.611658\pi$
$691$	−18.0662	−0.687269	−0.343635	+	0.939103i	$0.611658\pi$
$692$	93.9890	3.57292
$693$	0	0
$694$	−41.8647	−1.58916
$695$	0	0
$696$	55.7954	2.11492
$697$	0.0878150	0.00332623
$698$	1.73561	0.0656938
$699$	−8.58800	−0.324828
$700$	0	0
$701$	−22.5834	−0.852963	−0.426481	−	0.904496i	$-0.640247\pi$
$701$	−22.5834	−0.852963	−0.426481	+	0.904496i	$0.640247\pi$
$702$	0.214627	0.00810058
$703$	−10.9911	−0.414539
$704$	0	0
$705$	0	0
$706$	−50.7604	−1.91039
$707$	67.4897	2.53821
$708$	−18.8650	−0.708992
$709$	39.7417	1.49253	0.746266	−	0.665648i	$-0.231845\pi$
$709$	39.7417	1.49253	0.746266	+	0.665648i	$0.231845\pi$
$710$	0	0
$711$	−13.2182	−0.495723
$712$	78.0559	2.92527
$713$	−19.8567	−0.743640
$714$	0.262832	0.00983625
$715$	0	0
$716$	−20.6733	−0.772596
$717$	6.29874	0.235231
$718$	−46.1339	−1.72170
$719$	−13.2796	−0.495247	−0.247624	−	0.968856i	$-0.579650\pi$
$719$	−13.2796	−0.495247	−0.247624	+	0.968856i	$0.579650\pi$
$720$	0	0
$721$	−68.5689	−2.55364
$722$	47.5828	1.77085
$723$	1.13776	0.0423139
$724$	−28.3730	−1.05447
$725$	0	0
$726$	0	0
$727$	40.1610	1.48949	0.744745	−	0.667349i	$-0.232571\pi$
$727$	40.1610	1.48949	0.744745	+	0.667349i	$0.232571\pi$
$728$	3.14118	0.116420
$729$	1.00000	0.0370370
$730$	0	0
$731$	0.0196459	0.000726632 0
$732$	44.5703	1.64736
$733$	−16.6840	−0.616237	−0.308119	−	0.951348i	$-0.599699\pi$
$733$	−16.6840	−0.616237	−0.308119	+	0.951348i	$0.599699\pi$
$734$	−33.8129	−1.24806
$735$	0	0
$736$	−136.129	−5.01779
$737$	0	0
$738$	10.5084	0.386820
$739$	30.0698	1.10614	0.553068	−	0.833136i	$-0.313457\pi$
$739$	30.0698	1.10614	0.553068	+	0.833136i	$0.313457\pi$
$740$	0	0
$741$	0.0993630	0.00365019
$742$	−52.4282	−1.92470
$743$	8.68420	0.318593	0.159296	−	0.987231i	$-0.449077\pi$
$743$	8.68420	0.318593	0.159296	+	0.987231i	$0.449077\pi$
$744$	30.8441	1.13080
$745$	0	0
$746$	−35.5839	−1.30282
$747$	−14.4615	−0.529119
$748$	0	0
$749$	−7.32244	−0.267556
$750$	0	0
$751$	−34.1267	−1.24530	−0.622651	−	0.782500i	$-0.713944\pi$
$751$	−34.1267	−1.24530	−0.622651	+	0.782500i	$0.713944\pi$
$752$	28.6350	1.04421
$753$	3.82996	0.139572
$754$	−1.25765	−0.0458011
$755$	0	0
$756$	23.0437	0.838092
$757$	36.1782	1.31492	0.657459	−	0.753490i	$-0.271631\pi$
$757$	36.1782	1.31492	0.657459	+	0.753490i	$0.271631\pi$
$758$	74.4817	2.70530
$759$	0	0
$760$	0	0
$761$	22.4924	0.815350	0.407675	−	0.913127i	$-0.366340\pi$
$761$	22.4924	0.815350	0.407675	+	0.913127i	$0.366340\pi$
$762$	5.00128	0.181177
$763$	23.2374	0.841250
$764$	−143.224	−5.18167
$765$	0	0
$766$	31.4708	1.13708
$767$	0.270070	0.00975165
$768$	46.1223	1.66429
$769$	12.2384	0.441327	0.220664	−	0.975350i	$-0.429178\pi$
$769$	12.2384	0.441327	0.220664	+	0.975350i	$0.429178\pi$
$770$	0	0
$771$	9.67810	0.348548
$772$	67.6339	2.43420
$773$	41.3335	1.48666	0.743332	−	0.668923i	$-0.233244\pi$
$773$	41.3335	1.48666	0.743332	+	0.668923i	$0.233244\pi$
$774$	2.35094	0.0845028
$775$	0	0
$776$	−15.7108	−0.563984
$777$	36.4913	1.30912
$778$	−62.9815	−2.25800
$779$	4.86494	0.174304
$780$	0	0
$781$	0	0
$782$	0.383233	0.0137044
$783$	−5.85972	−0.209409
$784$	160.988	5.74957
$785$	0	0
$786$	−2.99249	−0.106739
$787$	−9.26481	−0.330255	−0.165127	−	0.986272i	$-0.552804\pi$
$787$	−9.26481	−0.330255	−0.165127	+	0.986272i	$0.552804\pi$
$788$	28.3123	1.00858
$789$	19.0954	0.679813
$790$	0	0
$791$	35.2529	1.25345
$792$	0	0
$793$	−0.638063	−0.0226583
$794$	22.9063	0.812915
$795$	0	0
$796$	43.4557	1.54024
$797$	−46.0523	−1.63126	−0.815628	−	0.578577i	$-0.803608\pi$
$797$	−46.0523	−1.63126	−0.815628	+	0.578577i	$0.803608\pi$
$798$	14.5609	0.515449
$799$	−0.0433979	−0.00153531
$800$	0	0
$801$	−8.19755	−0.289646
$802$	−104.967	−3.70653
$803$	0	0
$804$	−2.22952	−0.0786291
$805$	0	0
$806$	−0.695240	−0.0244888
$807$	17.4899	0.615675
$808$	−152.857	−5.37750
$809$	−2.69777	−0.0948485	−0.0474243	−	0.998875i	$-0.515101\pi$
$809$	−2.69777	−0.0948485	−0.0474243	+	0.998875i	$0.515101\pi$
$810$	0	0
$811$	25.1697	0.883828	0.441914	−	0.897057i	$-0.354300\pi$
$811$	25.1697	0.883828	0.441914	+	0.897057i	$0.354300\pi$
$812$	−135.030	−4.73862
$813$	23.8385	0.836053
$814$	0	0
$815$	0	0
$816$	−0.344719	−0.0120676
$817$	1.08838	0.0380777
$818$	97.5452	3.41059
$819$	−0.329891	−0.0115273
$820$	0	0
$821$	16.3843	0.571814	0.285907	−	0.958257i	$-0.407705\pi$
$821$	16.3843	0.571814	0.285907	+	0.958257i	$0.407705\pi$
$822$	−46.6619	−1.62752
$823$	37.9024	1.32120	0.660598	−	0.750740i	$-0.270303\pi$
$823$	37.9024	1.32120	0.660598	+	0.750740i	$0.270303\pi$
$824$	155.302	5.41019
$825$	0	0
$826$	39.5766	1.37705
$827$	38.4533	1.33715	0.668575	−	0.743644i	$-0.266904\pi$
$827$	38.4533	1.33715	0.668575	+	0.743644i	$0.266904\pi$
$828$	33.5998	1.16767
$829$	31.9916	1.11111	0.555557	−	0.831479i	$-0.312505\pi$
$829$	31.9916	1.11111	0.555557	+	0.831479i	$0.312505\pi$
$830$	0	0
$831$	−4.93692	−0.171260
$832$	−2.39940	−0.0831842
$833$	−0.243986	−0.00845361
$834$	−39.1211	−1.35465
$835$	0	0
$836$	0	0
$837$	−3.23929	−0.111966
$838$	−76.7904	−2.65268
$839$	−28.5217	−0.984680	−0.492340	−	0.870403i	$-0.663858\pi$
$839$	−28.5217	−0.984680	−0.492340	+	0.870403i	$0.663858\pi$
$840$	0	0
$841$	5.33630	0.184010
$842$	110.218	3.79838
$843$	2.13091	0.0733925
$844$	112.849	3.88443
$845$	0	0
$846$	−5.19323	−0.178547
$847$	0	0
$848$	68.7625	2.36131
$849$	−17.2239	−0.591121
$850$	0	0
$851$	53.2076	1.82393
$852$	46.0657	1.57818
$853$	−15.4094	−0.527607	−0.263804	−	0.964576i	$-0.584977\pi$
$853$	−15.4094	−0.527607	−0.263804	+	0.964576i	$0.584977\pi$
$854$	−93.5031	−3.19961
$855$	0	0
$856$	16.5846	0.566849
$857$	33.8611	1.15667	0.578336	−	0.815798i	$-0.303702\pi$
$857$	33.8611	1.15667	0.578336	+	0.815798i	$0.303702\pi$
$858$	0	0
$859$	44.0831	1.50410	0.752048	−	0.659109i	$-0.229066\pi$
$859$	44.0831	1.50410	0.752048	+	0.659109i	$0.229066\pi$
$860$	0	0
$861$	−16.1519	−0.550455
$862$	−47.1503	−1.60595
$863$	−9.86583	−0.335837	−0.167918	−	0.985801i	$-0.553705\pi$
$863$	−9.86583	−0.335837	−0.167918	+	0.985801i	$0.553705\pi$
$864$	−22.2072	−0.755505
$865$	0	0
$866$	46.7412	1.58833
$867$	−16.9995	−0.577333
$868$	−74.6453	−2.53363
$869$	0	0
$870$	0	0
$871$	0.0319175	0.00108148
$872$	−52.6303	−1.78229
$873$	1.64997	0.0558429
$874$	21.2310	0.718151
$875$	0	0
$876$	83.2671	2.81333
$877$	−33.4906	−1.13090	−0.565449	−	0.824784i	$-0.691297\pi$
$877$	−33.4906	−1.13090	−0.565449	+	0.824784i	$0.691297\pi$
$878$	−5.40059	−0.182261
$879$	−19.1742	−0.646729
$880$	0	0
$881$	0.0156474	0.000527176 0	0.000263588	−	1.00000i	$-0.499916\pi$
$881$	0.0156474	0.000527176 0	0.000263588		1.00000i	$0.499916\pi$
$882$	−29.1967	−0.983104
$883$	−10.5718	−0.355768	−0.177884	−	0.984051i	$-0.556925\pi$
$883$	−10.5718	−0.355768	−0.177884	+	0.984051i	$0.556925\pi$
$884$	0.00983095	0.000330651 0
$885$	0	0
$886$	71.8465	2.41373
$887$	−38.9927	−1.30925	−0.654623	−	0.755955i	$-0.727173\pi$
$887$	−38.9927	−1.30925	−0.654623	+	0.755955i	$0.727173\pi$
$888$	−82.6490	−2.77352
$889$	−7.68719	−0.257820
$890$	0	0
$891$	0	0
$892$	35.2560	1.18046
$893$	−2.40424	−0.0804547
$894$	45.4557	1.52027
$895$	0	0
$896$	−164.891	−5.50861
$897$	−0.481011	−0.0160605
$898$	−18.5034	−0.617467
$899$	18.9813	0.633063
$900$	0	0
$901$	−0.104213	−0.00347185
$902$	0	0
$903$	−3.61350	−0.120250
$904$	−79.8441	−2.65558
$905$	0	0
$906$	−18.8666	−0.626802
$907$	28.0569	0.931614	0.465807	−	0.884886i	$-0.345764\pi$
$907$	28.0569	0.931614	0.465807	+	0.884886i	$0.345764\pi$
$908$	79.9576	2.65349
$909$	16.0533	0.532454
$910$	0	0
$911$	19.9816	0.662018	0.331009	−	0.943628i	$-0.392611\pi$
$911$	19.9816	0.662018	0.331009	+	0.943628i	$0.392611\pi$
$912$	−19.0974	−0.632377
$913$	0	0
$914$	68.8984	2.27896
$915$	0	0
$916$	−88.7918	−2.93376
$917$	4.59959	0.151892
$918$	0.0625180	0.00206340
$919$	−29.0321	−0.957681	−0.478840	−	0.877902i	$-0.658943\pi$
$919$	−29.0321	−0.957681	−0.478840	+	0.877902i	$0.658943\pi$
$920$	0	0
$921$	12.0936	0.398497
$922$	−108.941	−3.58777
$923$	−0.659471	−0.0217068
$924$	0	0
$925$	0	0
$926$	105.684	3.47301
$927$	−16.3100	−0.535691
$928$	130.128	4.27166
$929$	10.8422	0.355721	0.177860	−	0.984056i	$-0.443082\pi$
$929$	10.8422	0.355721	0.177860	+	0.984056i	$0.443082\pi$
$930$	0	0
$931$	−13.5168	−0.442995
$932$	−47.0729	−1.54193
$933$	10.5043	0.343895
$934$	−29.0775	−0.951446
$935$	0	0
$936$	0.747170	0.0244220
$937$	37.2335	1.21637	0.608183	−	0.793797i	$-0.291899\pi$
$937$	37.2335	1.21637	0.608183	+	0.793797i	$0.291899\pi$
$938$	4.67727	0.152718
$939$	0.223857	0.00730530
$940$	0	0
$941$	−27.3449	−0.891419	−0.445709	−	0.895178i	$-0.647049\pi$
$941$	−27.3449	−0.891419	−0.445709	+	0.895178i	$0.647049\pi$
$942$	−44.6029	−1.45324
$943$	−23.5509	−0.766924
$944$	−51.9069	−1.68943
$945$	0	0
$946$	0	0
$947$	10.7746	0.350126	0.175063	−	0.984557i	$-0.443987\pi$
$947$	10.7746	0.350126	0.175063	+	0.984557i	$0.443987\pi$
$948$	−72.4525	−2.35315
$949$	−1.19204	−0.0386953
$950$	0	0
$951$	−11.0776	−0.359215
$952$	0.914984	0.0296548
$953$	−0.814050	−0.0263697	−0.0131848	−	0.999913i	$-0.504197\pi$
$953$	−0.814050	−0.0263697	−0.0131848	+	0.999913i	$0.504197\pi$
$954$	−12.4707	−0.403755
$955$	0	0
$956$	34.5250	1.11662
$957$	0	0
$958$	103.051	3.32942
$959$	71.7214	2.31600
$960$	0	0
$961$	−20.5070	−0.661516
$962$	1.86295	0.0600638
$963$	−1.74174	−0.0561267
$964$	6.23637	0.200860
$965$	0	0
$966$	−70.4884	−2.26793
$967$	−3.35764	−0.107974	−0.0539872	−	0.998542i	$-0.517193\pi$
$967$	−3.35764	−0.107974	−0.0539872	+	0.998542i	$0.517193\pi$
$968$	0	0
$969$	0.0289431	0.000929786 0
$970$	0	0
$971$	−56.1483	−1.80189	−0.900943	−	0.433937i	$-0.857124\pi$
$971$	−56.1483	−1.80189	−0.900943	+	0.433937i	$0.857124\pi$
$972$	5.48125	0.175811
$973$	60.1309	1.92771
$974$	92.6516	2.96875
$975$	0	0
$976$	122.634	3.92543
$977$	48.9637	1.56649	0.783243	−	0.621716i	$-0.213564\pi$
$977$	48.9637	1.56649	0.783243	+	0.621716i	$0.213564\pi$
$978$	−40.3075	−1.28889
$979$	0	0
$980$	0	0
$981$	5.52731	0.176473
$982$	−12.2049	−0.389473
$983$	−1.28160	−0.0408768	−0.0204384	−	0.999791i	$-0.506506\pi$
$983$	−1.28160	−0.0408768	−0.0204384	+	0.999791i	$0.506506\pi$
$984$	36.5824	1.16620
$985$	0	0
$986$	−0.366338	−0.0116666
$987$	7.98222	0.254077
$988$	0.544633	0.0173271
$989$	−5.26881	−0.167538
$990$	0	0
$991$	21.4347	0.680896	0.340448	−	0.940263i	$-0.389421\pi$
$991$	21.4347	0.680896	0.340448	+	0.940263i	$0.389421\pi$
$992$	71.9356	2.28396
$993$	27.0860	0.859547
$994$	−96.6404	−3.06525
$995$	0	0
$996$	−79.2671	−2.51167
$997$	43.1737	1.36732	0.683662	−	0.729799i	$-0.260386\pi$
$997$	43.1737	1.36732	0.683662	+	0.729799i	$0.260386\pi$
$998$	83.6880	2.64910
$999$	8.67992	0.274621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9075.2.a.dp.1.1		6
5.2	odd	4		1815.2.c.h.364.1	✓	12
5.3	odd	4		1815.2.c.h.364.12	yes	12
5.4	even	2		9075.2.a.dr.1.6		6
11.10	odd	2		9075.2.a.ds.1.6		6
55.32	even	4		1815.2.c.i.364.12	yes	12
55.43	even	4		1815.2.c.i.364.1	yes	12
55.54	odd	2		9075.2.a.do.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1815.2.c.h.364.1	✓	12	5.2	odd	4
1815.2.c.h.364.12	yes	12	5.3	odd	4
1815.2.c.i.364.1	yes	12	55.43	even	4
1815.2.c.i.364.12	yes	12	55.32	even	4
9075.2.a.do.1.1		6	55.54	odd	2
9075.2.a.dp.1.1		6	1.1	even	1	trivial
9075.2.a.dr.1.6		6	5.4	even	2
9075.2.a.ds.1.6		6	11.10	odd	2

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-2.73519 q^{2} +1.00000 q^{3} +5.48125 q^{4} -2.73519 q^{6} +4.20410 q^{7} -9.52186 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.73519 q^{2} +1.00000 q^{3} +5.48125 q^{4} -2.73519 q^{6} +4.20410 q^{7} -9.52186 q^{8} +1.00000 q^{9} +5.48125 q^{12} -0.0784689 q^{13} -11.4990 q^{14} +15.0816 q^{16} -0.0228569 q^{17} -2.73519 q^{18} -1.26627 q^{19} +4.20410 q^{21} +6.12996 q^{23} -9.52186 q^{24} +0.214627 q^{26} +1.00000 q^{27} +23.0437 q^{28} -5.85972 q^{29} -3.23929 q^{31} -22.2072 q^{32} +0.0625180 q^{34} +5.48125 q^{36} +8.67992 q^{37} +3.46349 q^{38} -0.0784689 q^{39} -3.84194 q^{41} -11.4990 q^{42} -0.859518 q^{43} -16.7666 q^{46} +1.89867 q^{47} +15.0816 q^{48} +10.6745 q^{49} -0.0228569 q^{51} -0.430108 q^{52} +4.55937 q^{53} -2.73519 q^{54} -40.0309 q^{56} -1.26627 q^{57} +16.0274 q^{58} -3.44174 q^{59} +8.13141 q^{61} +8.86007 q^{62} +4.20410 q^{63} +30.5777 q^{64} -0.406754 q^{67} -0.125285 q^{68} +6.12996 q^{69} +8.40424 q^{71} -9.52186 q^{72} +15.1913 q^{73} -23.7412 q^{74} -6.94075 q^{76} +0.214627 q^{78} -13.2182 q^{79} +1.00000 q^{81} +10.5084 q^{82} -14.4615 q^{83} +23.0437 q^{84} +2.35094 q^{86} -5.85972 q^{87} -8.19755 q^{89} -0.329891 q^{91} +33.5998 q^{92} -3.23929 q^{93} -5.19323 q^{94} -22.2072 q^{96} +1.64997 q^{97} -29.1967 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 6 q^{3} + 9 q^{4} - q^{6} + 4 q^{7} + 6 q^{9}+O(q^{10}) \) 6 * q - q^2 + 6 * q^3 + 9 * q^4 - q^6 + 4 * q^7 + 6 * q^9	\( 6 q - q^{2} + 6 q^{3} + 9 q^{4} - q^{6} + 4 q^{7} + 6 q^{9} + 9 q^{12} - 2 q^{13} - 10 q^{14} + 11 q^{16} - 2 q^{17} - q^{18} + 2 q^{19} + 4 q^{21} + 12 q^{23} + 6 q^{27} + 24 q^{28} - 12 q^{29} + 18 q^{31} - 31 q^{32} - q^{34} + 9 q^{36} + 24 q^{37} + 32 q^{38} - 2 q^{39} + 6 q^{41} - 10 q^{42} - 10 q^{43} + 11 q^{46} + 8 q^{47} + 11 q^{48} + 12 q^{49} - 2 q^{51} + 8 q^{52} + 18 q^{53} - q^{54} - 42 q^{56} + 2 q^{57} - 8 q^{58} - 18 q^{59} - 4 q^{61} + 17 q^{62} + 4 q^{63} + 22 q^{64} + 12 q^{67} + 9 q^{68} + 12 q^{69} - 14 q^{73} + 4 q^{74} + 20 q^{76} - 2 q^{79} + 6 q^{81} + 36 q^{82} + 20 q^{83} + 24 q^{84} + 28 q^{86} - 12 q^{87} - 16 q^{89} + 24 q^{91} + 41 q^{92} + 18 q^{93} - 3 q^{94} - 31 q^{96} + 12 q^{97} - 53 q^{98}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + 9 * q^4 - q^6 + 4 * q^7 + 6 * q^9 + 9 * q^12 - 2 * q^13 - 10 * q^14 + 11 * q^16 - 2 * q^17 - q^18 + 2 * q^19 + 4 * q^21 + 12 * q^23 + 6 * q^27 + 24 * q^28 - 12 * q^29 + 18 * q^31 - 31 * q^32 - q^34 + 9 * q^36 + 24 * q^37 + 32 * q^38 - 2 * q^39 + 6 * q^41 - 10 * q^42 - 10 * q^43 + 11 * q^46 + 8 * q^47 + 11 * q^48 + 12 * q^49 - 2 * q^51 + 8 * q^52 + 18 * q^53 - q^54 - 42 * q^56 + 2 * q^57 - 8 * q^58 - 18 * q^59 - 4 * q^61 + 17 * q^62 + 4 * q^63 + 22 * q^64 + 12 * q^67 + 9 * q^68 + 12 * q^69 - 14 * q^73 + 4 * q^74 + 20 * q^76 - 2 * q^79 + 6 * q^81 + 36 * q^82 + 20 * q^83 + 24 * q^84 + 28 * q^86 - 12 * q^87 - 16 * q^89 + 24 * q^91 + 41 * q^92 + 18 * q^93 - 3 * q^94 - 31 * q^96 + 12 * q^97 - 53 * q^98

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