LMFDB - Embedded newform 1150.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(1,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.43163$ of defining polynomial
Character	$\chi$	$=$	1150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.43163 q^{3} +1.00000 q^{4} +1.43163 q^{6} -3.08719 q^{7} -1.00000 q^{8} -0.950444 q^{9} -6.46926 q^{11} -1.43163 q^{12} -3.95044 q^{13} +3.08719 q^{14} +1.00000 q^{16} +3.43163 q^{17} +0.950444 q^{18} +3.08719 q^{19} +4.41970 q^{21} +6.46926 q^{22} +1.00000 q^{23} +1.43163 q^{24} +3.95044 q^{26} +5.65556 q^{27} -3.08719 q^{28} +0.863254 q^{29} -5.95044 q^{31} -1.00000 q^{32} +9.26157 q^{33} -3.43163 q^{34} -0.950444 q^{36} +7.03763 q^{37} -3.08719 q^{38} +5.65556 q^{39} +5.60601 q^{41} -4.41970 q^{42} -8.00000 q^{43} -6.46926 q^{44} -1.00000 q^{46} -3.90089 q^{47} -1.43163 q^{48} +2.53074 q^{49} -4.91281 q^{51} -3.95044 q^{52} +6.00000 q^{53} -5.65556 q^{54} +3.08719 q^{56} -4.41970 q^{57} -0.863254 q^{58} +6.86325 q^{59} -13.5069 q^{61} +5.95044 q^{62} +2.93420 q^{63} +1.00000 q^{64} -9.26157 q^{66} +10.0753 q^{67} +3.43163 q^{68} -1.43163 q^{69} +2.56837 q^{71} +0.950444 q^{72} -5.90089 q^{73} -7.03763 q^{74} +3.08719 q^{76} +19.9718 q^{77} -5.65556 q^{78} +15.8018 q^{79} -5.24533 q^{81} -5.60601 q^{82} -9.03763 q^{83} +4.41970 q^{84} +8.00000 q^{86} -1.23586 q^{87} +6.46926 q^{88} +16.7641 q^{89} +12.1958 q^{91} +1.00000 q^{92} +8.51882 q^{93} +3.90089 q^{94} +1.43163 q^{96} +14.2949 q^{97} -2.53074 q^{98} +6.14867 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9} + 3 q^{11} - q^{12} + q^{13} + 3 q^{14} + 3 q^{16} + 7 q^{17} - 10 q^{18} + 3 q^{19} - 22 q^{21} - 3 q^{22} + 3 q^{23} + q^{24}+ \cdots + 57 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9 + 3 * q^11 - q^12 + q^13 + 3 * q^14 + 3 * q^16 + 7 * q^17 - 10 * q^18 + 3 * q^19 - 22 * q^21 - 3 * q^22 + 3 * q^23 + q^24 - q^26 + 14 * q^27 - 3 * q^28 - 4 * q^29 - 5 * q^31 - 3 * q^32 + 9 * q^33 - 7 * q^34 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + q^41 + 22 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^46 + 14 * q^47 - q^48 + 30 * q^49 - 21 * q^51 + q^52 + 18 * q^53 - 14 * q^54 + 3 * q^56 + 22 * q^57 + 4 * q^58 + 14 * q^59 + q^61 + 5 * q^62 - 8 * q^63 + 3 * q^64 - 9 * q^66 - 8 * q^67 + 7 * q^68 - q^69 + 11 * q^71 - 10 * q^72 + 8 * q^73 - 2 * q^74 + 3 * q^76 + 24 * q^77 - 14 * q^78 - 4 * q^79 + 7 * q^81 - q^82 - 8 * q^83 - 22 * q^84 + 24 * q^86 - 36 * q^87 - 3 * q^88 + 18 * q^89 + q^91 + 3 * q^92 + 16 * q^93 - 14 * q^94 + q^96 + 33 * q^97 - 30 * q^98 + 57 * q^99

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.43163	−0.826550	−0.413275	−	0.910606i	$-0.635615\pi$
$3$	−1.43163	−0.826550	−0.413275	+	0.910606i	$0.635615\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	1.43163	0.584459
$7$	−3.08719	−1.16685	−0.583424	−	0.812168i	$-0.698287\pi$
$7$	−3.08719	−1.16685	−0.583424	+	0.812168i	$0.698287\pi$
$8$	−1.00000	−0.353553
$9$	−0.950444	−0.316815
$10$	0	0
$11$	−6.46926	−1.95056	−0.975278	−	0.220983i	$-0.929074\pi$
$11$	−6.46926	−1.95056	−0.975278	+	0.220983i	$0.929074\pi$
$12$	−1.43163	−0.413275
$13$	−3.95044	−1.09566	−0.547828	−	0.836591i	$-0.684545\pi$
$13$	−3.95044	−1.09566	−0.547828	+	0.836591i	$0.684545\pi$
$14$	3.08719	0.825086
$15$	0	0
$16$	1.00000	0.250000
$17$	3.43163	0.832292	0.416146	−	0.909298i	$-0.363381\pi$
$17$	3.43163	0.832292	0.416146	+	0.909298i	$0.363381\pi$
$18$	0.950444	0.224022
$19$	3.08719	0.708250	0.354125	−	0.935198i	$-0.384779\pi$
$19$	3.08719	0.708250	0.354125	+	0.935198i	$0.384779\pi$
$20$	0	0
$21$	4.41970	0.964459
$22$	6.46926	1.37925
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.43163	0.292230
$25$	0	0
$26$	3.95044	0.774746
$27$	5.65556	1.08841
$28$	−3.08719	−0.583424
$29$	0.863254	0.160302	0.0801511	−	0.996783i	$-0.474460\pi$
$29$	0.863254	0.160302	0.0801511	+	0.996783i	$0.474460\pi$
$30$	0	0
$31$	−5.95044	−1.06873	−0.534366	−	0.845253i	$-0.679449\pi$
$31$	−5.95044	−1.06873	−0.534366	+	0.845253i	$0.679449\pi$
$32$	−1.00000	−0.176777
$33$	9.26157	1.61223
$34$	−3.43163	−0.588519
$35$	0	0
$36$	−0.950444	−0.158407
$37$	7.03763	1.15698	0.578490	−	0.815690i	$-0.303642\pi$
$37$	7.03763	1.15698	0.578490	+	0.815690i	$0.303642\pi$
$38$	−3.08719	−0.500808
$39$	5.65556	0.905615
$40$	0	0
$41$	5.60601	0.875511	0.437756	−	0.899094i	$-0.355774\pi$
$41$	5.60601	0.875511	0.437756	+	0.899094i	$0.355774\pi$
$42$	−4.41970	−0.681975
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−6.46926	−0.975278
$45$	0	0
$46$	−1.00000	−0.147442
$47$	−3.90089	−0.569003	−0.284501	−	0.958676i	$-0.591828\pi$
$47$	−3.90089	−0.569003	−0.284501	+	0.958676i	$0.591828\pi$
$48$	−1.43163	−0.206638
$49$	2.53074	0.361534
$50$	0	0
$51$	−4.91281	−0.687931
$52$	−3.95044	−0.547828
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−5.65556	−0.769625
$55$	0	0
$56$	3.08719	0.412543
$57$	−4.41970	−0.585404
$58$	−0.863254	−0.113351
$59$	6.86325	0.893520	0.446760	−	0.894654i	$-0.352578\pi$
$59$	6.86325	0.893520	0.446760	+	0.894654i	$0.352578\pi$
$60$	0	0
$61$	−13.5069	−1.72938	−0.864690	−	0.502305i	$-0.832485\pi$
$61$	−13.5069	−1.72938	−0.864690	+	0.502305i	$0.832485\pi$
$62$	5.95044	0.755707
$63$	2.93420	0.369674
$64$	1.00000	0.125000
$65$	0	0
$66$	−9.26157	−1.14002
$67$	10.0753	1.23089	0.615445	−	0.788180i	$-0.288976\pi$
$67$	10.0753	1.23089	0.615445	+	0.788180i	$0.288976\pi$
$68$	3.43163	0.416146
$69$	−1.43163	−0.172348
$70$	0	0
$71$	2.56837	0.304810	0.152405	−	0.988318i	$-0.451298\pi$
$71$	2.56837	0.304810	0.152405	+	0.988318i	$0.451298\pi$
$72$	0.950444	0.112011
$73$	−5.90089	−0.690647	−0.345323	−	0.938484i	$-0.612231\pi$
$73$	−5.90089	−0.690647	−0.345323	+	0.938484i	$0.612231\pi$
$74$	−7.03763	−0.818108
$75$	0	0
$76$	3.08719	0.354125
$77$	19.9718	2.27600
$78$	−5.65556	−0.640366
$79$	15.8018	1.77784	0.888919	−	0.458064i	$-0.151457\pi$
$79$	15.8018	1.77784	0.888919	+	0.458064i	$0.151457\pi$
$80$	0	0
$81$	−5.24533	−0.582814
$82$	−5.60601	−0.619080
$83$	−9.03763	−0.992009	−0.496005	−	0.868320i	$-0.665200\pi$
$83$	−9.03763	−0.992009	−0.496005	+	0.868320i	$0.665200\pi$
$84$	4.41970	0.482229
$85$	0	0
$86$	8.00000	0.862662
$87$	−1.23586	−0.132498
$88$	6.46926	0.689625
$89$	16.7641	1.77700	0.888498	−	0.458881i	$-0.151750\pi$
$89$	16.7641	1.77700	0.888498	+	0.458881i	$0.151750\pi$
$90$	0	0
$91$	12.1958	1.27846
$92$	1.00000	0.104257
$93$	8.51882	0.883360
$94$	3.90089	0.402346
$95$	0	0
$96$	1.43163	0.146115
$97$	14.2949	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$97$	14.2949	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$98$	−2.53074	−0.255643
$99$	6.14867	0.617964
$100$	0	0
$101$	0.863254	0.0858970	0.0429485	−	0.999077i	$-0.486325\pi$
$101$	0.863254	0.0858970	0.0429485	+	0.999077i	$0.486325\pi$
$102$	4.91281	0.486441
$103$	−1.53074	−0.150828	−0.0754141	−	0.997152i	$-0.524028\pi$
$103$	−1.53074	−0.150828	−0.0754141	+	0.997152i	$0.524028\pi$
$104$	3.95044	0.387373
$105$	0	0
$106$	−6.00000	−0.582772
$107$	−17.6274	−1.70410	−0.852052	−	0.523457i	$-0.824642\pi$
$107$	−17.6274	−1.70410	−0.852052	+	0.523457i	$0.824642\pi$
$108$	5.65556	0.544207
$109$	−2.91281	−0.278997	−0.139498	−	0.990222i	$-0.544549\pi$
$109$	−2.91281	−0.278997	−0.139498	+	0.990222i	$0.544549\pi$
$110$	0	0
$111$	−10.0753	−0.956302
$112$	−3.08719	−0.291712
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	4.41970	0.413943
$115$	0	0
$116$	0.863254	0.0801511
$117$	3.75467	0.347120
$118$	−6.86325	−0.631814
$119$	−10.5941	−0.971158
$120$	0	0
$121$	30.8513	2.80467
$122$	13.5069	1.22286
$123$	−8.02571	−0.723654
$124$	−5.95044	−0.534366
$125$	0	0
$126$	−2.93420	−0.261399
$127$	−20.9385	−1.85799	−0.928997	−	0.370088i	$-0.879327\pi$
$127$	−20.9385	−1.85799	−0.928997	+	0.370088i	$0.879327\pi$
$128$	−1.00000	−0.0883883
$129$	11.4530	1.00838
$130$	0	0
$131$	10.7641	0.940467	0.470234	−	0.882542i	$-0.344170\pi$
$131$	10.7641	0.940467	0.470234	+	0.882542i	$0.344170\pi$
$132$	9.26157	0.806116
$133$	−9.53074	−0.826420
$134$	−10.0753	−0.870370
$135$	0	0
$136$	−3.43163	−0.294260
$137$	−3.26157	−0.278655	−0.139327	−	0.990246i	$-0.544494\pi$
$137$	−3.26157	−0.278655	−0.139327	+	0.990246i	$0.544494\pi$
$138$	1.43163	0.121868
$139$	−16.9385	−1.43671	−0.718353	−	0.695678i	$-0.755104\pi$
$139$	−16.9385	−1.43671	−0.718353	+	0.695678i	$0.755104\pi$
$140$	0	0
$141$	5.58462	0.470310
$142$	−2.56837	−0.215533
$143$	25.5565	2.13714
$144$	−0.950444	−0.0792037
$145$	0	0
$146$	5.90089	0.488361
$147$	−3.62308	−0.298826
$148$	7.03763	0.578490
$149$	3.26157	0.267198	0.133599	−	0.991035i	$-0.457347\pi$
$149$	3.26157	0.267198	0.133599	+	0.991035i	$0.457347\pi$
$150$	0	0
$151$	0.294881	0.0239971	0.0119986	−	0.999928i	$-0.496181\pi$
$151$	0.294881	0.0239971	0.0119986	+	0.999928i	$0.496181\pi$
$152$	−3.08719	−0.250404
$153$	−3.26157	−0.263682
$154$	−19.9718	−1.60938
$155$	0	0
$156$	5.65556	0.452807
$157$	−7.13675	−0.569574	−0.284787	−	0.958591i	$-0.591923\pi$
$157$	−7.13675	−0.569574	−0.284787	+	0.958591i	$0.591923\pi$
$158$	−15.8018	−1.25712
$159$	−8.58976	−0.681212
$160$	0	0
$161$	−3.08719	−0.243305
$162$	5.24533	0.412112
$163$	8.12482	0.636385	0.318193	−	0.948026i	$-0.396924\pi$
$163$	8.12482	0.636385	0.318193	+	0.948026i	$0.396924\pi$
$164$	5.60601	0.437756
$165$	0	0
$166$	9.03763	0.701456
$167$	7.80178	0.603719	0.301860	−	0.953352i	$-0.402393\pi$
$167$	7.80178	0.603719	0.301860	+	0.953352i	$0.402393\pi$
$168$	−4.41970	−0.340988
$169$	2.60601	0.200462
$170$	0	0
$171$	−2.93420	−0.224384
$172$	−8.00000	−0.609994
$173$	19.3325	1.46982	0.734912	−	0.678163i	$-0.237223\pi$
$173$	19.3325	1.46982	0.734912	+	0.678163i	$0.237223\pi$
$174$	1.23586	0.0936902
$175$	0	0
$176$	−6.46926	−0.487639
$177$	−9.82562	−0.738539
$178$	−16.7641	−1.25653
$179$	2.17438	0.162521	0.0812604	−	0.996693i	$-0.474105\pi$
$179$	2.17438	0.162521	0.0812604	+	0.996693i	$0.474105\pi$
$180$	0	0
$181$	−7.26157	−0.539748	−0.269874	−	0.962896i	$-0.586982\pi$
$181$	−7.26157	−0.539748	−0.269874	+	0.962896i	$0.586982\pi$
$182$	−12.1958	−0.904011
$183$	19.3368	1.42942
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−8.51882	−0.624630
$187$	−22.2001	−1.62343
$188$	−3.90089	−0.284501
$189$	−17.4598	−1.27001
$190$	0	0
$191$	8.58976	0.621533	0.310767	−	0.950486i	$-0.399414\pi$
$191$	8.58976	0.621533	0.310767	+	0.950486i	$0.399414\pi$
$192$	−1.43163	−0.103319
$193$	−2.44787	−0.176202	−0.0881008	−	0.996112i	$-0.528080\pi$
$193$	−2.44787	−0.176202	−0.0881008	+	0.996112i	$0.528080\pi$
$194$	−14.2949	−1.02631
$195$	0	0
$196$	2.53074	0.180767
$197$	10.7428	0.765389	0.382695	−	0.923875i	$-0.374996\pi$
$197$	10.7428	0.765389	0.382695	+	0.923875i	$0.374996\pi$
$198$	−6.14867	−0.436967
$199$	−11.3111	−0.801824	−0.400912	−	0.916116i	$-0.631307\pi$
$199$	−11.3111	−0.801824	−0.400912	+	0.916116i	$0.631307\pi$
$200$	0	0
$201$	−14.4240	−1.01739
$202$	−0.863254	−0.0607384
$203$	−2.66503	−0.187048
$204$	−4.91281	−0.343966
$205$	0	0
$206$	1.53074	0.106652
$207$	−0.950444	−0.0660604
$208$	−3.95044	−0.273914
$209$	−19.9718	−1.38148
$210$	0	0
$211$	23.1129	1.59116	0.795579	−	0.605850i	$-0.207167\pi$
$211$	23.1129	1.59116	0.795579	+	0.605850i	$0.207167\pi$
$212$	6.00000	0.412082
$213$	−3.67695	−0.251941
$214$	17.6274	1.20498
$215$	0	0
$216$	−5.65556	−0.384812
$217$	18.3701	1.24705
$218$	2.91281	0.197280
$219$	8.44787	0.570854
$220$	0	0
$221$	−13.5565	−0.911906
$222$	10.0753	0.676208
$223$	5.72651	0.383475	0.191738	−	0.981446i	$-0.438588\pi$
$223$	5.72651	0.383475	0.191738	+	0.981446i	$0.438588\pi$
$224$	3.08719	0.206272
$225$	0	0
$226$	−6.00000	−0.399114
$227$	17.6274	1.16997	0.584986	−	0.811044i	$-0.301100\pi$
$227$	17.6274	1.16997	0.584986	+	0.811044i	$0.301100\pi$
$228$	−4.41970	−0.292702
$229$	−16.0753	−1.06228	−0.531142	−	0.847283i	$-0.678237\pi$
$229$	−16.0753	−1.06228	−0.531142	+	0.847283i	$0.678237\pi$
$230$	0	0
$231$	−28.5922	−1.88123
$232$	−0.863254	−0.0566754
$233$	6.44787	0.422414	0.211207	−	0.977441i	$-0.432261\pi$
$233$	6.44787	0.422414	0.211207	+	0.977441i	$0.432261\pi$
$234$	−3.75467	−0.245451
$235$	0	0
$236$	6.86325	0.446760
$237$	−22.6222	−1.46947
$238$	10.5941	0.686712
$239$	4.34876	0.281298	0.140649	−	0.990060i	$-0.455081\pi$
$239$	4.34876	0.281298	0.140649	+	0.990060i	$0.455081\pi$
$240$	0	0
$241$	0.764142	0.0492227	0.0246114	−	0.999697i	$-0.492165\pi$
$241$	0.764142	0.0492227	0.0246114	+	0.999697i	$0.492165\pi$
$242$	−30.8513	−1.98320
$243$	−9.45734	−0.606688
$244$	−13.5069	−0.864690
$245$	0	0
$246$	8.02571	0.511701
$247$	−12.1958	−0.775998
$248$	5.95044	0.377854
$249$	12.9385	0.819945
$250$	0	0
$251$	−22.5402	−1.42273	−0.711363	−	0.702825i	$-0.751922\pi$
$251$	−22.5402	−1.42273	−0.711363	+	0.702825i	$0.751922\pi$
$252$	2.93420	0.184837
$253$	−6.46926	−0.406719
$254$	20.9385	1.31380
$255$	0	0
$256$	1.00000	0.0625000
$257$	9.90089	0.617600	0.308800	−	0.951127i	$-0.400073\pi$
$257$	9.90089	0.617600	0.308800	+	0.951127i	$0.400073\pi$
$258$	−11.4530	−0.713034
$259$	−21.7265	−1.35002
$260$	0	0
$261$	−0.820475	−0.0507861
$262$	−10.7641	−0.665011
$263$	7.25725	0.447501	0.223751	−	0.974646i	$-0.428170\pi$
$263$	7.25725	0.447501	0.223751	+	0.974646i	$0.428170\pi$
$264$	−9.26157	−0.570010
$265$	0	0
$266$	9.53074	0.584367
$267$	−24.0000	−1.46878
$268$	10.0753	0.615445
$269$	−6.93852	−0.423049	−0.211525	−	0.977373i	$-0.567843\pi$
$269$	−6.93852	−0.423049	−0.211525	+	0.977373i	$0.567843\pi$
$270$	0	0
$271$	−10.2992	−0.625632	−0.312816	−	0.949814i	$-0.601272\pi$
$271$	−10.2992	−0.625632	−0.312816	+	0.949814i	$0.601272\pi$
$272$	3.43163	0.208073
$273$	−17.4598	−1.05671
$274$	3.26157	0.197039
$275$	0	0
$276$	−1.43163	−0.0861738
$277$	17.8018	1.06961	0.534803	−	0.844977i	$-0.320386\pi$
$277$	17.8018	1.06961	0.534803	+	0.844977i	$0.320386\pi$
$278$	16.9385	1.01590
$279$	5.65556	0.338590
$280$	0	0
$281$	−18.9385	−1.12978	−0.564889	−	0.825167i	$-0.691081\pi$
$281$	−18.9385	−1.12978	−0.564889	+	0.825167i	$0.691081\pi$
$282$	−5.58462	−0.332559
$283$	−12.6889	−0.754275	−0.377138	−	0.926157i	$-0.623092\pi$
$283$	−12.6889	−0.754275	−0.377138	+	0.926157i	$0.623092\pi$
$284$	2.56837	0.152405
$285$	0	0
$286$	−25.5565	−1.51118
$287$	−17.3068	−1.02159
$288$	0.950444	0.0560054
$289$	−5.22394	−0.307290
$290$	0	0
$291$	−20.4649	−1.19968
$292$	−5.90089	−0.345323
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	3.62308	0.211302
$295$	0	0
$296$	−7.03763	−0.409054
$297$	−36.5873	−2.12301
$298$	−3.26157	−0.188938
$299$	−3.95044	−0.228460
$300$	0	0
$301$	24.6975	1.42354
$302$	−0.294881	−0.0169685
$303$	−1.23586	−0.0709982
$304$	3.08719	0.177062
$305$	0	0
$306$	3.26157	0.186451
$307$	22.9599	1.31039	0.655196	−	0.755459i	$-0.272586\pi$
$307$	22.9599	1.31039	0.655196	+	0.755459i	$0.272586\pi$
$308$	19.9718	1.13800
$309$	2.19145	0.124667
$310$	0	0
$311$	18.0753	1.02495	0.512477	−	0.858701i	$-0.328728\pi$
$311$	18.0753	1.02495	0.512477	+	0.858701i	$0.328728\pi$
$312$	−5.65556	−0.320183
$313$	−15.1625	−0.857033	−0.428516	−	0.903534i	$-0.640964\pi$
$313$	−15.1625	−0.857033	−0.428516	+	0.903534i	$0.640964\pi$
$314$	7.13675	0.402750
$315$	0	0
$316$	15.8018	0.888919
$317$	−14.0257	−0.787762	−0.393881	−	0.919161i	$-0.628868\pi$
$317$	−14.0257	−0.787762	−0.393881	+	0.919161i	$0.628868\pi$
$318$	8.58976	0.481690
$319$	−5.58462	−0.312678
$320$	0	0
$321$	25.2359	1.40853
$322$	3.08719	0.172042
$323$	10.5941	0.589471
$324$	−5.24533	−0.291407
$325$	0	0
$326$	−8.12482	−0.449992
$327$	4.17006	0.230605
$328$	−5.60601	−0.309540
$329$	12.0428	0.663940
$330$	0	0
$331$	−24.7403	−1.35985	−0.679925	−	0.733282i	$-0.737988\pi$
$331$	−24.7403	−1.35985	−0.679925	+	0.733282i	$0.737988\pi$
$332$	−9.03763	−0.496005
$333$	−6.68888	−0.366548
$334$	−7.80178	−0.426894
$335$	0	0
$336$	4.41970	0.241115
$337$	−14.7146	−0.801555	−0.400777	−	0.916176i	$-0.631260\pi$
$337$	−14.7146	−0.801555	−0.400777	+	0.916176i	$0.631260\pi$
$338$	−2.60601	−0.141748
$339$	−8.58976	−0.466532
$340$	0	0
$341$	38.4950	2.08462
$342$	2.93420	0.158663
$343$	13.7975	0.744993
$344$	8.00000	0.431331
$345$	0	0
$346$	−19.3325	−1.03932
$347$	−9.43163	−0.506316	−0.253158	−	0.967425i	$-0.581469\pi$
$347$	−9.43163	−0.506316	−0.253158	+	0.967425i	$0.581469\pi$
$348$	−1.23586	−0.0662490
$349$	18.3488	0.982187	0.491093	−	0.871107i	$-0.336597\pi$
$349$	18.3488	0.982187	0.491093	+	0.871107i	$0.336597\pi$
$350$	0	0
$351$	−22.3420	−1.19253
$352$	6.46926	0.344813
$353$	33.1129	1.76242	0.881211	−	0.472723i	$-0.156729\pi$
$353$	33.1129	1.76242	0.881211	+	0.472723i	$0.156729\pi$
$354$	9.82562	0.522226
$355$	0	0
$356$	16.7641	0.888498
$357$	15.1668	0.802711
$358$	−2.17438	−0.114920
$359$	33.0376	1.74366	0.871830	−	0.489809i	$-0.162933\pi$
$359$	33.0376	1.74366	0.871830	+	0.489809i	$0.162933\pi$
$360$	0	0
$361$	−9.46926	−0.498382
$362$	7.26157	0.381660
$363$	−44.1676	−2.31820
$364$	12.1958	0.639232
$365$	0	0
$366$	−19.3368	−1.01075
$367$	2.27349	0.118675	0.0593376	−	0.998238i	$-0.481101\pi$
$367$	2.27349	0.118675	0.0593376	+	0.998238i	$0.481101\pi$
$368$	1.00000	0.0521286
$369$	−5.32819	−0.277375
$370$	0	0
$371$	−18.5231	−0.961673
$372$	8.51882	0.441680
$373$	−23.9762	−1.24144	−0.620719	−	0.784033i	$-0.713159\pi$
$373$	−23.9762	−1.24144	−0.620719	+	0.784033i	$0.713159\pi$
$374$	22.2001	1.14794
$375$	0	0
$376$	3.90089	0.201173
$377$	−3.41024	−0.175636
$378$	17.4598	0.898035
$379$	−13.8795	−0.712942	−0.356471	−	0.934306i	$-0.616020\pi$
$379$	−13.8795	−0.712942	−0.356471	+	0.934306i	$0.616020\pi$
$380$	0	0
$381$	29.9762	1.53572
$382$	−8.58976	−0.439490
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	1.43163	0.0730574
$385$	0	0
$386$	2.44787	0.124593
$387$	7.60355	0.386510
$388$	14.2949	0.725713
$389$	−26.6436	−1.35089	−0.675443	−	0.737412i	$-0.736048\pi$
$389$	−26.6436	−1.35089	−0.675443	+	0.737412i	$0.736048\pi$
$390$	0	0
$391$	3.43163	0.173545
$392$	−2.53074	−0.127822
$393$	−15.4102	−0.777344
$394$	−10.7428	−0.541212
$395$	0	0
$396$	6.14867	0.308982
$397$	8.66749	0.435009	0.217504	−	0.976059i	$-0.430208\pi$
$397$	8.66749	0.435009	0.217504	+	0.976059i	$0.430208\pi$
$398$	11.3111	0.566975
$399$	13.6445	0.683078
$400$	0	0
$401$	39.9762	1.99631	0.998157	−	0.0606854i	$-0.0193286\pi$
$401$	39.9762	1.99631	0.998157	+	0.0606854i	$0.0193286\pi$
$402$	14.4240	0.719405
$403$	23.5069	1.17096
$404$	0.863254	0.0429485
$405$	0	0
$406$	2.66503	0.132263
$407$	−45.5283	−2.25675
$408$	4.91281	0.243220
$409$	30.1248	1.48958	0.744788	−	0.667301i	$-0.232550\pi$
$409$	30.1248	1.48958	0.744788	+	0.667301i	$0.232550\pi$
$410$	0	0
$411$	4.66935	0.230322
$412$	−1.53074	−0.0754141
$413$	−21.1882	−1.04260
$414$	0.950444	0.0467118
$415$	0	0
$416$	3.95044	0.193686
$417$	24.2496	1.18751
$418$	19.9718	0.976854
$419$	25.8770	1.26418	0.632088	−	0.774897i	$-0.282198\pi$
$419$	25.8770	1.26418	0.632088	+	0.774897i	$0.282198\pi$
$420$	0	0
$421$	−10.7146	−0.522197	−0.261098	−	0.965312i	$-0.584085\pi$
$421$	−10.7146	−0.522197	−0.261098	+	0.965312i	$0.584085\pi$
$422$	−23.1129	−1.12512
$423$	3.70757	0.180268
$424$	−6.00000	−0.291386
$425$	0	0
$426$	3.67695	0.178149
$427$	41.6983	2.01792
$428$	−17.6274	−0.852052
$429$	−36.5873	−1.76645
$430$	0	0
$431$	32.2496	1.55341	0.776705	−	0.629864i	$-0.216889\pi$
$431$	32.2496	1.55341	0.776705	+	0.629864i	$0.216889\pi$
$432$	5.65556	0.272103
$433$	−20.6393	−0.991862	−0.495931	−	0.868362i	$-0.665173\pi$
$433$	−20.6393	−0.991862	−0.495931	+	0.868362i	$0.665173\pi$
$434$	−18.3701	−0.881795
$435$	0	0
$436$	−2.91281	−0.139498
$437$	3.08719	0.147680
$438$	−8.44787	−0.403655
$439$	−16.2239	−0.774326	−0.387163	−	0.922011i	$-0.626545\pi$
$439$	−16.2239	−0.774326	−0.387163	+	0.922011i	$0.626545\pi$
$440$	0	0
$441$	−2.40533	−0.114539
$442$	13.5565	0.644815
$443$	15.6770	0.744834	0.372417	−	0.928065i	$-0.378529\pi$
$443$	15.6770	0.744834	0.372417	+	0.928065i	$0.378529\pi$
$444$	−10.0753	−0.478151
$445$	0	0
$446$	−5.72651	−0.271158
$447$	−4.66935	−0.220853
$448$	−3.08719	−0.145856
$449$	22.5727	1.06527	0.532636	−	0.846345i	$-0.321202\pi$
$449$	22.5727	1.06527	0.532636	+	0.846345i	$0.321202\pi$
$450$	0	0
$451$	−36.2667	−1.70773
$452$	6.00000	0.282216
$453$	−0.422160	−0.0198348
$454$	−17.6274	−0.827295
$455$	0	0
$456$	4.41970	0.206972
$457$	1.45302	0.0679693	0.0339846	−	0.999422i	$-0.489180\pi$
$457$	1.45302	0.0679693	0.0339846	+	0.999422i	$0.489180\pi$
$458$	16.0753	0.751148
$459$	19.4078	0.905878
$460$	0	0
$461$	−29.7027	−1.38339	−0.691695	−	0.722189i	$-0.743136\pi$
$461$	−29.7027	−1.38339	−0.691695	+	0.722189i	$0.743136\pi$
$462$	28.5922	1.33023
$463$	−22.9624	−1.06715	−0.533576	−	0.845752i	$-0.679152\pi$
$463$	−22.9624	−1.06715	−0.533576	+	0.845752i	$0.679152\pi$
$464$	0.863254	0.0400756
$465$	0	0
$466$	−6.44787	−0.298692
$467$	−9.48550	−0.438937	−0.219468	−	0.975620i	$-0.570432\pi$
$467$	−9.48550	−0.438937	−0.219468	+	0.975620i	$0.570432\pi$
$468$	3.75467	0.173560
$469$	−31.1043	−1.43626
$470$	0	0
$471$	10.2172	0.470782
$472$	−6.86325	−0.315907
$473$	51.7541	2.37966
$474$	22.6222	1.03907
$475$	0	0
$476$	−10.5941	−0.485579
$477$	−5.70266	−0.261107
$478$	−4.34876	−0.198908
$479$	−30.5659	−1.39659	−0.698296	−	0.715809i	$-0.746058\pi$
$479$	−30.5659	−1.39659	−0.698296	+	0.715809i	$0.746058\pi$
$480$	0	0
$481$	−27.8018	−1.26765
$482$	−0.764142	−0.0348057
$483$	4.41970	0.201104
$484$	30.8513	1.40233
$485$	0	0
$486$	9.45734	0.428994
$487$	21.1367	0.957797	0.478899	−	0.877870i	$-0.341036\pi$
$487$	21.1367	0.957797	0.478899	+	0.877870i	$0.341036\pi$
$488$	13.5069	0.611428
$489$	−11.6317	−0.526004
$490$	0	0
$491$	−28.0514	−1.26594	−0.632971	−	0.774175i	$-0.718165\pi$
$491$	−28.0514	−1.26594	−0.632971	+	0.774175i	$0.718165\pi$
$492$	−8.02571	−0.361827
$493$	2.96237	0.133418
$494$	12.1958	0.548714
$495$	0	0
$496$	−5.95044	−0.267183
$497$	−7.92905	−0.355667
$498$	−12.9385	−0.579789
$499$	3.80178	0.170191	0.0850954	−	0.996373i	$-0.472880\pi$
$499$	3.80178	0.170191	0.0850954	+	0.996373i	$0.472880\pi$
$500$	0	0
$501$	−11.1692	−0.499005
$502$	22.5402	1.00602
$503$	−19.0872	−0.851056	−0.425528	−	0.904945i	$-0.639912\pi$
$503$	−19.0872	−0.851056	−0.425528	+	0.904945i	$0.639912\pi$
$504$	−2.93420	−0.130700
$505$	0	0
$506$	6.46926	0.287594
$507$	−3.73083	−0.165692
$508$	−20.9385	−0.928997
$509$	−9.41024	−0.417101	−0.208551	−	0.978012i	$-0.566875\pi$
$509$	−9.41024	−0.417101	−0.208551	+	0.978012i	$0.566875\pi$
$510$	0	0
$511$	18.2172	0.805880
$512$	−1.00000	−0.0441942
$513$	17.4598	0.770869
$514$	−9.90089	−0.436709
$515$	0	0
$516$	11.4530	0.504191
$517$	25.2359	1.10987
$518$	21.7265	0.954608
$519$	−27.6770	−1.21488
$520$	0	0
$521$	25.8018	1.13040	0.565198	−	0.824955i	$-0.308800\pi$
$521$	25.8018	1.13040	0.565198	+	0.824955i	$0.308800\pi$
$522$	0.820475	0.0359112
$523$	19.1129	0.835749	0.417874	−	0.908505i	$-0.362775\pi$
$523$	19.1129	0.835749	0.417874	+	0.908505i	$0.362775\pi$
$524$	10.7641	0.470234
$525$	0	0
$526$	−7.25725	−0.316431
$527$	−20.4197	−0.889496
$528$	9.26157	0.403058
$529$	1.00000	0.0434783
$530$	0	0
$531$	−6.52314	−0.283080
$532$	−9.53074	−0.413210
$533$	−22.1462	−0.959259
$534$	24.0000	1.03858
$535$	0	0
$536$	−10.0753	−0.435185
$537$	−3.11290	−0.134332
$538$	6.93852	0.299141
$539$	−16.3720	−0.705193
$540$	0	0
$541$	30.8394	1.32589	0.662945	−	0.748668i	$-0.269306\pi$
$541$	30.8394	1.32589	0.662945	+	0.748668i	$0.269306\pi$
$542$	10.2992	0.442389
$543$	10.3959	0.446129
$544$	−3.43163	−0.147130
$545$	0	0
$546$	17.4598	0.747210
$547$	−13.8513	−0.592240	−0.296120	−	0.955151i	$-0.595693\pi$
$547$	−13.8513	−0.592240	−0.296120	+	0.955151i	$0.595693\pi$
$548$	−3.26157	−0.139327
$549$	12.8375	0.547893
$550$	0	0
$551$	2.66503	0.113534
$552$	1.43163	0.0609341
$553$	−48.7831	−2.07447
$554$	−17.8018	−0.756325
$555$	0	0
$556$	−16.9385	−0.718353
$557$	28.7641	1.21878	0.609388	−	0.792872i	$-0.291415\pi$
$557$	28.7641	1.21878	0.609388	+	0.792872i	$0.291415\pi$
$558$	−5.65556	−0.239419
$559$	31.6036	1.33669
$560$	0	0
$561$	31.7823	1.34185
$562$	18.9385	0.798873
$563$	−36.1505	−1.52356	−0.761782	−	0.647834i	$-0.775675\pi$
$563$	−36.1505	−1.52356	−0.761782	+	0.647834i	$0.775675\pi$
$564$	5.58462	0.235155
$565$	0	0
$566$	12.6889	0.533353
$567$	16.1933	0.680055
$568$	−2.56837	−0.107767
$569$	−10.3488	−0.433843	−0.216921	−	0.976189i	$-0.569601\pi$
$569$	−10.3488	−0.433843	−0.216921	+	0.976189i	$0.569601\pi$
$570$	0	0
$571$	19.6060	0.820486	0.410243	−	0.911976i	$-0.365444\pi$
$571$	19.6060	0.820486	0.410243	+	0.911976i	$0.365444\pi$
$572$	25.5565	1.06857
$573$	−12.2973	−0.513729
$574$	17.3068	0.722372
$575$	0	0
$576$	−0.950444	−0.0396018
$577$	34.1505	1.42171	0.710853	−	0.703341i	$-0.248309\pi$
$577$	34.1505	1.42171	0.710853	+	0.703341i	$0.248309\pi$
$578$	5.22394	0.217287
$579$	3.50444	0.145639
$580$	0	0
$581$	27.9009	1.15752
$582$	20.4649	0.848299
$583$	−38.8156	−1.60758
$584$	5.90089	0.244180
$585$	0	0
$586$	−6.00000	−0.247858
$587$	5.19062	0.214240	0.107120	−	0.994246i	$-0.465837\pi$
$587$	5.19062	0.214240	0.107120	+	0.994246i	$0.465837\pi$
$588$	−3.62308	−0.149413
$589$	−18.3701	−0.756929
$590$	0	0
$591$	−15.3796	−0.632633
$592$	7.03763	0.289245
$593$	2.09911	0.0862002	0.0431001	−	0.999071i	$-0.486277\pi$
$593$	2.09911	0.0862002	0.0431001	+	0.999071i	$0.486277\pi$
$594$	36.5873	1.50120
$595$	0	0
$596$	3.26157	0.133599
$597$	16.1933	0.662748
$598$	3.95044	0.161546
$599$	11.1581	0.455909	0.227955	−	0.973672i	$-0.426796\pi$
$599$	11.1581	0.455909	0.227955	+	0.973672i	$0.426796\pi$
$600$	0	0
$601$	9.57784	0.390688	0.195344	−	0.980735i	$-0.437418\pi$
$601$	9.57784	0.390688	0.195344	+	0.980735i	$0.437418\pi$
$602$	−24.6975	−1.00660
$603$	−9.57597	−0.389964
$604$	0.294881	0.0119986
$605$	0	0
$606$	1.23586	0.0502033
$607$	24.6975	1.00244	0.501221	−	0.865320i	$-0.332885\pi$
$607$	24.6975	1.00244	0.501221	+	0.865320i	$0.332885\pi$
$608$	−3.08719	−0.125202
$609$	3.81533	0.154605
$610$	0	0
$611$	15.4102	0.623431
$612$	−3.26157	−0.131841
$613$	26.3488	1.06422	0.532108	−	0.846676i	$-0.321400\pi$
$613$	26.3488	1.06422	0.532108	+	0.846676i	$0.321400\pi$
$614$	−22.9599	−0.926587
$615$	0	0
$616$	−19.9718	−0.804688
$617$	−5.94612	−0.239382	−0.119691	−	0.992811i	$-0.538190\pi$
$617$	−5.94612	−0.239382	−0.119691	+	0.992811i	$0.538190\pi$
$618$	−2.19145	−0.0881530
$619$	39.6856	1.59510	0.797549	−	0.603254i	$-0.206129\pi$
$619$	39.6856	1.59510	0.797549	+	0.603254i	$0.206129\pi$
$620$	0	0
$621$	5.65556	0.226950
$622$	−18.0753	−0.724752
$623$	−51.7541	−2.07348
$624$	5.65556	0.226404
$625$	0	0
$626$	15.1625	0.606014
$627$	28.5922	1.14186
$628$	−7.13675	−0.284787
$629$	24.1505	0.962945
$630$	0	0
$631$	−23.0138	−0.916164	−0.458082	−	0.888910i	$-0.651463\pi$
$631$	−23.0138	−0.916164	−0.458082	+	0.888910i	$0.651463\pi$
$632$	−15.8018	−0.628561
$633$	−33.0891	−1.31517
$634$	14.0257	0.557032
$635$	0	0
$636$	−8.58976	−0.340606
$637$	−9.99754	−0.396117
$638$	5.58462	0.221097
$639$	−2.44109	−0.0965682
$640$	0	0
$641$	25.4617	1.00568	0.502838	−	0.864381i	$-0.332289\pi$
$641$	25.4617	1.00568	0.502838	+	0.864381i	$0.332289\pi$
$642$	−25.2359	−0.995980
$643$	16.4479	0.648641	0.324320	−	0.945947i	$-0.394864\pi$
$643$	16.4479	0.648641	0.324320	+	0.945947i	$0.394864\pi$
$644$	−3.08719	−0.121652
$645$	0	0
$646$	−10.5941	−0.416819
$647$	34.9147	1.37264	0.686319	−	0.727301i	$-0.259226\pi$
$647$	34.9147	1.37264	0.686319	+	0.727301i	$0.259226\pi$
$648$	5.24533	0.206056
$649$	−44.4002	−1.74286
$650$	0	0
$651$	−26.2992	−1.03075
$652$	8.12482	0.318193
$653$	34.2754	1.34130	0.670649	−	0.741775i	$-0.266016\pi$
$653$	34.2754	1.34130	0.670649	+	0.741775i	$0.266016\pi$
$654$	−4.17006	−0.163062
$655$	0	0
$656$	5.60601	0.218878
$657$	5.60846	0.218807
$658$	−12.0428	−0.469476
$659$	35.2548	1.37333	0.686666	−	0.726973i	$-0.259074\pi$
$659$	35.2548	1.37333	0.686666	+	0.726973i	$0.259074\pi$
$660$	0	0
$661$	28.5684	1.11118	0.555590	−	0.831456i	$-0.312492\pi$
$661$	28.5684	1.11118	0.555590	+	0.831456i	$0.312492\pi$
$662$	24.7403	0.961559
$663$	19.4078	0.753736
$664$	9.03763	0.350728
$665$	0	0
$666$	6.68888	0.259189
$667$	0.863254	0.0334253
$668$	7.80178	0.301860
$669$	−8.19822	−0.316962
$670$	0	0
$671$	87.3796	3.37325
$672$	−4.41970	−0.170494
$673$	23.8770	0.920392	0.460196	−	0.887817i	$-0.347779\pi$
$673$	23.8770	0.920392	0.460196	+	0.887817i	$0.347779\pi$
$674$	14.7146	0.566785
$675$	0	0
$676$	2.60601	0.100231
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	8.58976	0.329888
$679$	−44.1310	−1.69359
$680$	0	0
$681$	−25.2359	−0.967040
$682$	−38.4950	−1.47405
$683$	−34.6480	−1.32577	−0.662884	−	0.748722i	$-0.730668\pi$
$683$	−34.6480	−1.32577	−0.662884	+	0.748722i	$0.730668\pi$
$684$	−2.93420	−0.112192
$685$	0	0
$686$	−13.7975	−0.526789
$687$	23.0138	0.878031
$688$	−8.00000	−0.304997
$689$	−23.7027	−0.903000
$690$	0	0
$691$	−18.1744	−0.691386	−0.345693	−	0.938348i	$-0.612356\pi$
$691$	−18.1744	−0.691386	−0.345693	+	0.938348i	$0.612356\pi$
$692$	19.3325	0.734912
$693$	−18.9821	−0.721071
$694$	9.43163	0.358020
$695$	0	0
$696$	1.23586	0.0468451
$697$	19.2377	0.728681
$698$	−18.3488	−0.694511
$699$	−9.23095	−0.349146
$700$	0	0
$701$	−40.6907	−1.53687	−0.768434	−	0.639929i	$-0.778964\pi$
$701$	−40.6907	−1.53687	−0.768434	+	0.639929i	$0.778964\pi$
$702$	22.3420	0.843244
$703$	21.7265	0.819431
$704$	−6.46926	−0.243819
$705$	0	0
$706$	−33.1129	−1.24622
$707$	−2.66503	−0.100229
$708$	−9.82562	−0.369269
$709$	−26.4454	−0.993178	−0.496589	−	0.867986i	$-0.665414\pi$
$709$	−26.4454	−0.993178	−0.496589	+	0.867986i	$0.665414\pi$
$710$	0	0
$711$	−15.0187	−0.563245
$712$	−16.7641	−0.628263
$713$	−5.95044	−0.222846
$714$	−15.1668	−0.567602
$715$	0	0
$716$	2.17438	0.0812604
$717$	−6.22580	−0.232507
$718$	−33.0376	−1.23295
$719$	−2.24778	−0.0838281	−0.0419140	−	0.999121i	$-0.513346\pi$
$719$	−2.24778	−0.0838281	−0.0419140	+	0.999121i	$0.513346\pi$
$720$	0	0
$721$	4.72568	0.175994
$722$	9.46926	0.352409
$723$	−1.09397	−0.0406850
$724$	−7.26157	−0.269874
$725$	0	0
$726$	44.1676	1.63921
$727$	−21.4830	−0.796762	−0.398381	−	0.917220i	$-0.630428\pi$
$727$	−21.4830	−0.796762	−0.398381	+	0.917220i	$0.630428\pi$
$728$	−12.1958	−0.452005
$729$	29.2754	1.08427
$730$	0	0
$731$	−27.4530	−1.01539
$732$	19.3368	0.714710
$733$	−11.3778	−0.420247	−0.210123	−	0.977675i	$-0.567387\pi$
$733$	−11.3778	−0.420247	−0.210123	+	0.977675i	$0.567387\pi$
$734$	−2.27349	−0.0839161
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−65.1795	−2.40092
$738$	5.32819	0.196134
$739$	21.8770	0.804760	0.402380	−	0.915473i	$-0.368183\pi$
$739$	21.8770	0.804760	0.402380	+	0.915473i	$0.368183\pi$
$740$	0	0
$741$	17.4598	0.641402
$742$	18.5231	0.680006
$743$	−5.36068	−0.196664	−0.0983322	−	0.995154i	$-0.531351\pi$
$743$	−5.36068	−0.196664	−0.0983322	+	0.995154i	$0.531351\pi$
$744$	−8.51882	−0.312315
$745$	0	0
$746$	23.9762	0.877829
$747$	8.58976	0.314283
$748$	−22.2001	−0.811716
$749$	54.4191	1.98843
$750$	0	0
$751$	24.3915	0.890060	0.445030	−	0.895516i	$-0.353193\pi$
$751$	24.3915	0.890060	0.445030	+	0.895516i	$0.353193\pi$
$752$	−3.90089	−0.142251
$753$	32.2692	1.17595
$754$	3.41024	0.124194
$755$	0	0
$756$	−17.4598	−0.635007
$757$	−41.9437	−1.52447	−0.762234	−	0.647301i	$-0.775898\pi$
$757$	−41.9437	−1.52447	−0.762234	+	0.647301i	$0.775898\pi$
$758$	13.8795	0.504126
$759$	9.26157	0.336174
$760$	0	0
$761$	−18.3745	−0.666074	−0.333037	−	0.942914i	$-0.608073\pi$
$761$	−18.3745	−0.666074	−0.333037	+	0.942914i	$0.608073\pi$
$762$	−29.9762	−1.08592
$763$	8.99240	0.325547
$764$	8.58976	0.310767
$765$	0	0
$766$	0	0
$767$	−27.1129	−0.978990
$768$	−1.43163	−0.0516594
$769$	42.4993	1.53256	0.766282	−	0.642505i	$-0.222105\pi$
$769$	42.4993	1.53256	0.766282	+	0.642505i	$0.222105\pi$
$770$	0	0
$771$	−14.1744	−0.510478
$772$	−2.44787	−0.0881008
$773$	15.0376	0.540866	0.270433	−	0.962739i	$-0.412833\pi$
$773$	15.0376	0.540866	0.270433	+	0.962739i	$0.412833\pi$
$774$	−7.60355	−0.273304
$775$	0	0
$776$	−14.2949	−0.513156
$777$	31.1043	1.11586
$778$	26.6436	0.955221
$779$	17.3068	0.620081
$780$	0	0
$781$	−16.6155	−0.594548
$782$	−3.43163	−0.122715
$783$	4.88219	0.174475
$784$	2.53074	0.0903836
$785$	0	0
$786$	15.4102	0.549665
$787$	8.39154	0.299126	0.149563	−	0.988752i	$-0.452213\pi$
$787$	8.39154	0.299126	0.149563	+	0.988752i	$0.452213\pi$
$788$	10.7428	0.382695
$789$	−10.3897	−0.369882
$790$	0	0
$791$	−18.5231	−0.658607
$792$	−6.14867	−0.218483
$793$	53.3582	1.89481
$794$	−8.66749	−0.307598
$795$	0	0
$796$	−11.3111	−0.400912
$797$	22.0514	0.781101	0.390551	−	0.920581i	$-0.372285\pi$
$797$	22.0514	0.781101	0.390551	+	0.920581i	$0.372285\pi$
$798$	−13.6445	−0.483009
$799$	−13.3864	−0.473576
$800$	0	0
$801$	−15.9334	−0.562978
$802$	−39.9762	−1.41161
$803$	38.1744	1.34714
$804$	−14.4240	−0.508696
$805$	0	0
$806$	−23.5069	−0.827995
$807$	9.93337	0.349671
$808$	−0.863254	−0.0303692
$809$	2.04524	0.0719066	0.0359533	−	0.999353i	$-0.488553\pi$
$809$	2.04524	0.0719066	0.0359533	+	0.999353i	$0.488553\pi$
$810$	0	0
$811$	4.24965	0.149225	0.0746126	−	0.997213i	$-0.476228\pi$
$811$	4.24965	0.149225	0.0746126	+	0.997213i	$0.476228\pi$
$812$	−2.66503	−0.0935242
$813$	14.7446	0.517116
$814$	45.5283	1.59577
$815$	0	0
$816$	−4.91281	−0.171983
$817$	−24.6975	−0.864057
$818$	−30.1248	−1.05329
$819$	−11.5914	−0.405036
$820$	0	0
$821$	−29.2548	−1.02100	−0.510500	−	0.859878i	$-0.670540\pi$
$821$	−29.2548	−1.02100	−0.510500	+	0.859878i	$0.670540\pi$
$822$	−4.66935	−0.162862
$823$	−13.5846	−0.473530	−0.236765	−	0.971567i	$-0.576087\pi$
$823$	−13.5846	−0.473530	−0.236765	+	0.971567i	$0.576087\pi$
$824$	1.53074	0.0533258
$825$	0	0
$826$	21.1882	0.737231
$827$	−24.7880	−0.861963	−0.430981	−	0.902361i	$-0.641833\pi$
$827$	−24.7880	−0.861963	−0.430981	+	0.902361i	$0.641833\pi$
$828$	−0.950444	−0.0330302
$829$	26.1505	0.908246	0.454123	−	0.890939i	$-0.349953\pi$
$829$	26.1505	0.908246	0.454123	+	0.890939i	$0.349953\pi$
$830$	0	0
$831$	−25.4855	−0.884082
$832$	−3.95044	−0.136957
$833$	8.68455	0.300902
$834$	−24.2496	−0.839697
$835$	0	0
$836$	−19.9718	−0.690740
$837$	−33.6531	−1.16322
$838$	−25.8770	−0.893908
$839$	6.37260	0.220007	0.110003	−	0.993931i	$-0.464914\pi$
$839$	6.37260	0.220007	0.110003	+	0.993931i	$0.464914\pi$
$840$	0	0
$841$	−28.2548	−0.974303
$842$	10.7146	0.369249
$843$	27.1129	0.933818
$844$	23.1129	0.795579
$845$	0	0
$846$	−3.70757	−0.127469
$847$	−95.2439	−3.27262
$848$	6.00000	0.206041
$849$	18.1657	0.623447
$850$	0	0
$851$	7.03763	0.241247
$852$	−3.67695	−0.125970
$853$	33.6293	1.15144	0.575722	−	0.817646i	$-0.304721\pi$
$853$	33.6293	1.15144	0.575722	+	0.817646i	$0.304721\pi$
$854$	−41.6983	−1.42689
$855$	0	0
$856$	17.6274	0.602492
$857$	−11.1795	−0.381885	−0.190943	−	0.981601i	$-0.561154\pi$
$857$	−11.1795	−0.381885	−0.190943	+	0.981601i	$0.561154\pi$
$858$	36.5873	1.24907
$859$	47.9009	1.63436	0.817179	−	0.576385i	$-0.195537\pi$
$859$	47.9009	1.63436	0.817179	+	0.576385i	$0.195537\pi$
$860$	0	0
$861$	24.7769	0.844394
$862$	−32.2496	−1.09843
$863$	30.1180	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$863$	30.1180	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$864$	−5.65556	−0.192406
$865$	0	0
$866$	20.6393	0.701353
$867$	7.47873	0.253991
$868$	18.3701	0.623523
$869$	−102.226	−3.46777
$870$	0	0
$871$	−39.8018	−1.34863
$872$	2.91281	0.0986402
$873$	−13.5865	−0.459833
$874$	−3.08719	−0.104426
$875$	0	0
$876$	8.44787	0.285427
$877$	22.3940	0.756191	0.378096	−	0.925767i	$-0.376579\pi$
$877$	22.3940	0.756191	0.378096	+	0.925767i	$0.376579\pi$
$878$	16.2239	0.547531
$879$	−8.58976	−0.289726
$880$	0	0
$881$	21.1129	0.711312	0.355656	−	0.934617i	$-0.384258\pi$
$881$	21.1129	0.711312	0.355656	+	0.934617i	$0.384258\pi$
$882$	2.40533	0.0809915
$883$	−49.1061	−1.65255	−0.826276	−	0.563265i	$-0.809545\pi$
$883$	−49.1061	−1.65255	−0.826276	+	0.563265i	$0.809545\pi$
$884$	−13.5565	−0.455953
$885$	0	0
$886$	−15.6770	−0.526678
$887$	43.0566	1.44570	0.722849	−	0.691006i	$-0.242832\pi$
$887$	43.0566	1.44570	0.722849	+	0.691006i	$0.242832\pi$
$888$	10.0753	0.338104
$889$	64.6412	2.16800
$890$	0	0
$891$	33.9334	1.13681
$892$	5.72651	0.191738
$893$	−12.0428	−0.402996
$894$	4.66935	0.156166
$895$	0	0
$896$	3.08719	0.103136
$897$	5.65556	0.188834
$898$	−22.5727	−0.753261
$899$	−5.13675	−0.171320
$900$	0	0
$901$	20.5898	0.685944
$902$	36.2667	1.20755
$903$	−35.3576	−1.17663
$904$	−6.00000	−0.199557
$905$	0	0
$906$	0.422160	0.0140253
$907$	37.9762	1.26098	0.630489	−	0.776198i	$-0.282854\pi$
$907$	37.9762	1.26098	0.630489	+	0.776198i	$0.282854\pi$
$908$	17.6274	0.584986
$909$	−0.820475	−0.0272134
$910$	0	0
$911$	−15.7504	−0.521833	−0.260916	−	0.965361i	$-0.584025\pi$
$911$	−15.7504	−0.521833	−0.260916	+	0.965361i	$0.584025\pi$
$912$	−4.41970	−0.146351
$913$	58.4668	1.93497
$914$	−1.45302	−0.0480615
$915$	0	0
$916$	−16.0753	−0.531142
$917$	−33.2309	−1.09738
$918$	−19.4078	−0.640552
$919$	30.4240	1.00360	0.501798	−	0.864985i	$-0.332672\pi$
$919$	30.4240	1.00360	0.501798	+	0.864985i	$0.332672\pi$
$920$	0	0
$921$	−32.8700	−1.08310
$922$	29.7027	0.978205
$923$	−10.1462	−0.333967
$924$	−28.5922	−0.940615
$925$	0	0
$926$	22.9624	0.754590
$927$	1.45488	0.0477846
$928$	−0.863254	−0.0283377
$929$	−37.8018	−1.24024	−0.620118	−	0.784509i	$-0.712915\pi$
$929$	−37.8018	−1.24024	−0.620118	+	0.784509i	$0.712915\pi$
$930$	0	0
$931$	7.81287	0.256057
$932$	6.44787	0.211207
$933$	−25.8770	−0.847176
$934$	9.48550	0.310375
$935$	0	0
$936$	−3.75467	−0.122725
$937$	32.6907	1.06796	0.533980	−	0.845497i	$-0.320696\pi$
$937$	32.6907	1.06796	0.533980	+	0.845497i	$0.320696\pi$
$938$	31.1043	1.01559
$939$	21.7070	0.708381
$940$	0	0
$941$	−46.4882	−1.51547	−0.757736	−	0.652561i	$-0.773694\pi$
$941$	−46.4882	−1.51547	−0.757736	+	0.652561i	$0.773694\pi$
$942$	−10.2172	−0.332893
$943$	5.60601	0.182557
$944$	6.86325	0.223380
$945$	0	0
$946$	−51.7541	−1.68267
$947$	37.2052	1.20901	0.604504	−	0.796602i	$-0.293371\pi$
$947$	37.2052	1.20901	0.604504	+	0.796602i	$0.293371\pi$
$948$	−22.6222	−0.734737
$949$	23.3111	0.756711
$950$	0	0
$951$	20.0796	0.651125
$952$	10.5941	0.343356
$953$	−49.1104	−1.59084	−0.795422	−	0.606056i	$-0.792751\pi$
$953$	−49.1104	−1.59084	−0.795422	+	0.606056i	$0.792751\pi$
$954$	5.70266	0.184631
$955$	0	0
$956$	4.34876	0.140649
$957$	7.99509	0.258445
$958$	30.5659	0.987540
$959$	10.0691	0.325148
$960$	0	0
$961$	4.40778	0.142187
$962$	27.8018	0.896365
$963$	16.7538	0.539885
$964$	0.764142	0.0246114
$965$	0	0
$966$	−4.41970	−0.142202
$967$	−1.96751	−0.0632709	−0.0316355	−	0.999499i	$-0.510072\pi$
$967$	−1.96751	−0.0632709	−0.0316355	+	0.999499i	$0.510072\pi$
$968$	−30.8513	−0.991599
$969$	−15.1668	−0.487227
$970$	0	0
$971$	26.1205	0.838247	0.419123	−	0.907929i	$-0.362337\pi$
$971$	26.1205	0.838247	0.419123	+	0.907929i	$0.362337\pi$
$972$	−9.45734	−0.303344
$973$	52.2924	1.67642
$974$	−21.1367	−0.677265
$975$	0	0
$976$	−13.5069	−0.432345
$977$	0.639319	0.0204536	0.0102268	−	0.999948i	$-0.496745\pi$
$977$	0.639319	0.0204536	0.0102268	+	0.999948i	$0.496745\pi$
$978$	11.6317	0.371941
$979$	−108.452	−3.46613
$980$	0	0
$981$	2.76846	0.0883902
$982$	28.0514	0.895157
$983$	6.46926	0.206337	0.103169	−	0.994664i	$-0.467102\pi$
$983$	6.46926	0.206337	0.103169	+	0.994664i	$0.467102\pi$
$984$	8.02571	0.255850
$985$	0	0
$986$	−2.96237	−0.0943410
$987$	−17.2408	−0.548780
$988$	−12.1958	−0.387999
$989$	−8.00000	−0.254385
$990$	0	0
$991$	37.2334	1.18276	0.591379	−	0.806394i	$-0.298584\pi$
$991$	37.2334	1.18276	0.591379	+	0.806394i	$0.298584\pi$
$992$	5.95044	0.188927
$993$	35.4189	1.12398
$994$	7.92905	0.251494
$995$	0	0
$996$	12.9385	0.409973
$997$	−9.65124	−0.305658	−0.152829	−	0.988253i	$-0.548838\pi$
$997$	−9.65124	−0.305658	−0.152829	+	0.988253i	$0.548838\pi$
$998$	−3.80178	−0.120343
$999$	39.8018	1.25927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.a.q.1.2		3
4.3	odd	2		9200.2.a.cf.1.2		3
5.2	odd	4		1150.2.b.j.599.2		6
5.3	odd	4		1150.2.b.j.599.5		6
5.4	even	2		230.2.a.d.1.2	✓	3
15.14	odd	2		2070.2.a.z.1.2		3
20.19	odd	2		1840.2.a.r.1.2		3
40.19	odd	2		7360.2.a.ce.1.2		3
40.29	even	2		7360.2.a.bz.1.2		3
115.114	odd	2		5290.2.a.r.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.2	✓	3	5.4	even	2
1150.2.a.q.1.2		3	1.1	even	1	trivial
1150.2.b.j.599.2		6	5.2	odd	4
1150.2.b.j.599.5		6	5.3	odd	4
1840.2.a.r.1.2		3	20.19	odd	2
2070.2.a.z.1.2		3	15.14	odd	2
5290.2.a.r.1.2		3	115.114	odd	2
7360.2.a.bz.1.2		3	40.29	even	2
7360.2.a.ce.1.2		3	40.19	odd	2
9200.2.a.cf.1.2		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.43163 q^{3} +1.00000 q^{4} +1.43163 q^{6} -3.08719 q^{7} -1.00000 q^{8} -0.950444 q^{9} -6.46926 q^{11} -1.43163 q^{12} -3.95044 q^{13} +3.08719 q^{14} +1.00000 q^{16} +3.43163 q^{17} +0.950444 q^{18} +3.08719 q^{19} +4.41970 q^{21} +6.46926 q^{22} +1.00000 q^{23} +1.43163 q^{24} +3.95044 q^{26} +5.65556 q^{27} -3.08719 q^{28} +0.863254 q^{29} -5.95044 q^{31} -1.00000 q^{32} +9.26157 q^{33} -3.43163 q^{34} -0.950444 q^{36} +7.03763 q^{37} -3.08719 q^{38} +5.65556 q^{39} +5.60601 q^{41} -4.41970 q^{42} -8.00000 q^{43} -6.46926 q^{44} -1.00000 q^{46} -3.90089 q^{47} -1.43163 q^{48} +2.53074 q^{49} -4.91281 q^{51} -3.95044 q^{52} +6.00000 q^{53} -5.65556 q^{54} +3.08719 q^{56} -4.41970 q^{57} -0.863254 q^{58} +6.86325 q^{59} -13.5069 q^{61} +5.95044 q^{62} +2.93420 q^{63} +1.00000 q^{64} -9.26157 q^{66} +10.0753 q^{67} +3.43163 q^{68} -1.43163 q^{69} +2.56837 q^{71} +0.950444 q^{72} -5.90089 q^{73} -7.03763 q^{74} +3.08719 q^{76} +19.9718 q^{77} -5.65556 q^{78} +15.8018 q^{79} -5.24533 q^{81} -5.60601 q^{82} -9.03763 q^{83} +4.41970 q^{84} +8.00000 q^{86} -1.23586 q^{87} +6.46926 q^{88} +16.7641 q^{89} +12.1958 q^{91} +1.00000 q^{92} +8.51882 q^{93} +3.90089 q^{94} +1.43163 q^{96} +14.2949 q^{97} -2.53074 q^{98} +6.14867 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{7} - 3 q^{8} + 10 q^{9} + 3 q^{11} - q^{12} + q^{13} + 3 q^{14} + 3 q^{16} + 7 q^{17} - 10 q^{18} + 3 q^{19} - 22 q^{21} - 3 q^{22} + 3 q^{23} + q^{24}+ \cdots + 57 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - q^3 + 3 * q^4 + q^6 - 3 * q^7 - 3 * q^8 + 10 * q^9 + 3 * q^11 - q^12 + q^13 + 3 * q^14 + 3 * q^16 + 7 * q^17 - 10 * q^18 + 3 * q^19 - 22 * q^21 - 3 * q^22 + 3 * q^23 + q^24 - q^26 + 14 * q^27 - 3 * q^28 - 4 * q^29 - 5 * q^31 - 3 * q^32 + 9 * q^33 - 7 * q^34 + 10 * q^36 + 2 * q^37 - 3 * q^38 + 14 * q^39 + q^41 + 22 * q^42 - 24 * q^43 + 3 * q^44 - 3 * q^46 + 14 * q^47 - q^48 + 30 * q^49 - 21 * q^51 + q^52 + 18 * q^53 - 14 * q^54 + 3 * q^56 + 22 * q^57 + 4 * q^58 + 14 * q^59 + q^61 + 5 * q^62 - 8 * q^63 + 3 * q^64 - 9 * q^66 - 8 * q^67 + 7 * q^68 - q^69 + 11 * q^71 - 10 * q^72 + 8 * q^73 - 2 * q^74 + 3 * q^76 + 24 * q^77 - 14 * q^78 - 4 * q^79 + 7 * q^81 - q^82 - 8 * q^83 - 22 * q^84 + 24 * q^86 - 36 * q^87 - 3 * q^88 + 18 * q^89 + q^91 + 3 * q^92 + 16 * q^93 - 14 * q^94 + q^96 + 33 * q^97 - 30 * q^98 + 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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