LMFDB - Embedded newform 2601.2.a.bi.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2601,2,Mod(1,2601)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2601, 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("2601.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2601 = 3^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2601.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:	$20.7690895657$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.3418281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - 4x^{3} + 18x^{2} + 12x - 1 $ x^6 - 9x^4 - 4x^3 + 18x^2 + 12x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 867)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.0750494$ of defining polynomial
Character	$\chi$	$=$	2601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09548 q^{2} +2.39104 q^{4} +1.55815 q^{5} +4.13541 q^{7} +0.819422 q^{8} +O(q^{10})$	$q+2.09548 q^{2} +2.39104 q^{4} +1.55815 q^{5} +4.13541 q^{7} +0.819422 q^{8} +3.26508 q^{10} -4.43191 q^{11} +3.67837 q^{13} +8.66568 q^{14} -3.06500 q^{16} +0.406521 q^{19} +3.72561 q^{20} -9.28698 q^{22} +6.47554 q^{23} -2.57216 q^{25} +7.70797 q^{26} +9.88795 q^{28} +4.48652 q^{29} +10.7981 q^{31} -8.06150 q^{32} +6.44361 q^{35} +0.713491 q^{37} +0.851857 q^{38} +1.27678 q^{40} +2.00717 q^{41} -4.13206 q^{43} -10.5969 q^{44} +13.5694 q^{46} -8.22412 q^{47} +10.1017 q^{49} -5.38991 q^{50} +8.79515 q^{52} +4.08803 q^{53} -6.90559 q^{55} +3.38865 q^{56} +9.40143 q^{58} -6.11738 q^{59} -5.33162 q^{61} +22.6272 q^{62} -10.7627 q^{64} +5.73147 q^{65} +6.53830 q^{67} +13.5025 q^{70} +1.63423 q^{71} -4.72766 q^{73} +1.49511 q^{74} +0.972009 q^{76} -18.3278 q^{77} -5.65089 q^{79} -4.77574 q^{80} +4.20598 q^{82} -11.9505 q^{83} -8.65866 q^{86} -3.63160 q^{88} -9.33759 q^{89} +15.2116 q^{91} +15.4833 q^{92} -17.2335 q^{94} +0.633422 q^{95} -13.1311 q^{97} +21.1678 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8	$ 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8} + 12 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} + 15 q^{16} + 9 q^{19} - 6 q^{20} - 18 q^{22} + 9 q^{23} + 15 q^{25} + 12 q^{26} - 15 q^{28} + 6 q^{29} + 24 q^{31} - 42 q^{32} - 3 q^{37} + 6 q^{38} - 3 q^{40} + 18 q^{41} + 3 q^{44} + 15 q^{46} - 24 q^{47} + 21 q^{49} - 12 q^{50} - 18 q^{52} - 24 q^{53} - 24 q^{55} + 54 q^{56} + 3 q^{58} + 9 q^{59} + 21 q^{61} + 30 q^{62} + 24 q^{64} - 9 q^{65} - 6 q^{67} - 3 q^{70} + 27 q^{71} + 18 q^{73} + 36 q^{74} - 3 q^{76} - 33 q^{77} + 24 q^{79} + 3 q^{80} - 15 q^{82} - 6 q^{83} - 6 q^{86} - 24 q^{88} + 39 q^{91} - 15 q^{94} + 42 q^{95} - 33 q^{97} + 57 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8 + 12 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 + 15 * q^16 + 9 * q^19 - 6 * q^20 - 18 * q^22 + 9 * q^23 + 15 * q^25 + 12 * q^26 - 15 * q^28 + 6 * q^29 + 24 * q^31 - 42 * q^32 - 3 * q^37 + 6 * q^38 - 3 * q^40 + 18 * q^41 + 3 * q^44 + 15 * q^46 - 24 * q^47 + 21 * q^49 - 12 * q^50 - 18 * q^52 - 24 * q^53 - 24 * q^55 + 54 * q^56 + 3 * q^58 + 9 * q^59 + 21 * q^61 + 30 * q^62 + 24 * q^64 - 9 * q^65 - 6 * q^67 - 3 * q^70 + 27 * q^71 + 18 * q^73 + 36 * q^74 - 3 * q^76 - 33 * q^77 + 24 * q^79 + 3 * q^80 - 15 * q^82 - 6 * q^83 - 6 * q^86 - 24 * q^88 + 39 * q^91 - 15 * q^94 + 42 * q^95 - 33 * 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 $

$2$	2.09548	1.48173	0.740865	−	0.671654i	$-0.234416\pi$
$2$	2.09548	1.48173	0.740865	+	0.671654i	$0.234416\pi$
$3$	0	0
$3$	0	0
$4$	2.39104	1.19552
$5$	1.55815	0.696827	0.348414	−	0.937341i	$-0.386720\pi$
$5$	1.55815	0.696827	0.348414	+	0.937341i	$0.386720\pi$
$6$	0	0
$7$	4.13541	1.56304	0.781520	−	0.623880i	$-0.214445\pi$
$7$	4.13541	1.56304	0.781520	+	0.623880i	$0.214445\pi$
$8$	0.819422	0.289709
$9$	0	0
$10$	3.26508	1.03251
$11$	−4.43191	−1.33627	−0.668135	−	0.744040i	$-0.732907\pi$
$11$	−4.43191	−1.33627	−0.668135	+	0.744040i	$0.732907\pi$
$12$	0	0
$13$	3.67837	1.02020	0.510099	−	0.860116i	$-0.329609\pi$
$13$	3.67837	1.02020	0.510099	+	0.860116i	$0.329609\pi$
$14$	8.66568	2.31600
$15$	0	0
$16$	−3.06500	−0.766250
$17$	0	0
$17$	0	0
$18$	0	0
$19$	0.406521	0.0932623	0.0466312	−	0.998912i	$-0.485151\pi$
$19$	0.406521	0.0932623	0.0466312	+	0.998912i	$0.485151\pi$
$20$	3.72561	0.833072
$21$	0	0
$22$	−9.28698	−1.97999
$23$	6.47554	1.35024	0.675122	−	0.737706i	$-0.264091\pi$
$23$	6.47554	1.35024	0.675122	+	0.737706i	$0.264091\pi$
$24$	0	0
$25$	−2.57216	−0.514432
$26$	7.70797	1.51166
$27$	0	0
$28$	9.88795	1.86865
$29$	4.48652	0.833127	0.416563	−	0.909107i	$-0.363234\pi$
$29$	4.48652	0.833127	0.416563	+	0.909107i	$0.363234\pi$
$30$	0	0
$31$	10.7981	1.93940	0.969698	−	0.244306i	$-0.0785603\pi$
$31$	10.7981	1.93940	0.969698	+	0.244306i	$0.0785603\pi$
$32$	−8.06150	−1.42508
$33$	0	0
$34$	0	0
$35$	6.44361	1.08917
$36$	0	0
$37$	0.713491	0.117297	0.0586486	−	0.998279i	$-0.481321\pi$
$37$	0.713491	0.117297	0.0586486	+	0.998279i	$0.481321\pi$
$38$	0.851857	0.138190
$39$	0	0
$40$	1.27678	0.201877
$41$	2.00717	0.313467	0.156733	−	0.987641i	$-0.449904\pi$
$41$	2.00717	0.313467	0.156733	+	0.987641i	$0.449904\pi$
$42$	0	0
$43$	−4.13206	−0.630133	−0.315067	−	0.949070i	$-0.602027\pi$
$43$	−4.13206	−0.630133	−0.315067	+	0.949070i	$0.602027\pi$
$44$	−10.5969	−1.59754
$45$	0	0
$46$	13.5694	2.00070
$47$	−8.22412	−1.19961	−0.599806	−	0.800146i	$-0.704756\pi$
$47$	−8.22412	−1.19961	−0.599806	+	0.800146i	$0.704756\pi$
$48$	0	0
$49$	10.1017	1.44309
$50$	−5.38991	−0.762248
$51$	0	0
$52$	8.79515	1.21967
$53$	4.08803	0.561534	0.280767	−	0.959776i	$-0.409411\pi$
$53$	4.08803	0.561534	0.280767	+	0.959776i	$0.409411\pi$
$54$	0	0
$55$	−6.90559	−0.931149
$56$	3.38865	0.452827
$57$	0	0
$58$	9.40143	1.23447
$59$	−6.11738	−0.796415	−0.398207	−	0.917295i	$-0.630368\pi$
$59$	−6.11738	−0.796415	−0.398207	+	0.917295i	$0.630368\pi$
$60$	0	0
$61$	−5.33162	−0.682644	−0.341322	−	0.939947i	$-0.610875\pi$
$61$	−5.33162	−0.682644	−0.341322	+	0.939947i	$0.610875\pi$
$62$	22.6272	2.87366
$63$	0	0
$64$	−10.7627	−1.34534
$65$	5.73147	0.710902
$66$	0	0
$67$	6.53830	0.798780	0.399390	−	0.916781i	$-0.369222\pi$
$67$	6.53830	0.798780	0.399390	+	0.916781i	$0.369222\pi$
$68$	0	0
$69$	0	0
$70$	13.5025	1.61385
$71$	1.63423	0.193947	0.0969736	−	0.995287i	$-0.469084\pi$
$71$	1.63423	0.193947	0.0969736	+	0.995287i	$0.469084\pi$
$72$	0	0
$73$	−4.72766	−0.553331	−0.276665	−	0.960966i	$-0.589229\pi$
$73$	−4.72766	−0.553331	−0.276665	+	0.960966i	$0.589229\pi$
$74$	1.49511	0.173803
$75$	0	0
$76$	0.972009	0.111497
$77$	−18.3278	−2.08864
$78$	0	0
$79$	−5.65089	−0.635775	−0.317888	−	0.948128i	$-0.602973\pi$
$79$	−5.65089	−0.635775	−0.317888	+	0.948128i	$0.602973\pi$
$80$	−4.77574	−0.533944
$81$	0	0
$82$	4.20598	0.464473
$83$	−11.9505	−1.31173	−0.655867	−	0.754877i	$-0.727697\pi$
$83$	−11.9505	−1.31173	−0.655867	+	0.754877i	$0.727697\pi$
$84$	0	0
$85$	0	0
$86$	−8.65866	−0.933687
$87$	0	0
$88$	−3.63160	−0.387130
$89$	−9.33759	−0.989783	−0.494892	−	0.868955i	$-0.664792\pi$
$89$	−9.33759	−0.989783	−0.494892	+	0.868955i	$0.664792\pi$
$90$	0	0
$91$	15.2116	1.59461
$92$	15.4833	1.61425
$93$	0	0
$94$	−17.2335	−1.77750
$95$	0.633422	0.0649877
$96$	0	0
$97$	−13.1311	−1.33326	−0.666631	−	0.745388i	$-0.732264\pi$
$97$	−13.1311	−1.33326	−0.666631	+	0.745388i	$0.732264\pi$
$98$	21.1678	2.13827
$99$	0	0
$100$	−6.15014	−0.615014
$101$	−2.75389	−0.274022	−0.137011	−	0.990570i	$-0.543750\pi$
$101$	−2.75389	−0.274022	−0.137011	+	0.990570i	$0.543750\pi$
$102$	0	0
$103$	10.7754	1.06173	0.530865	−	0.847456i	$-0.321867\pi$
$103$	10.7754	1.06173	0.530865	+	0.847456i	$0.321867\pi$
$104$	3.01414	0.295561
$105$	0	0
$106$	8.56639	0.832041
$107$	3.14199	0.303748	0.151874	−	0.988400i	$-0.451469\pi$
$107$	3.14199	0.303748	0.151874	+	0.988400i	$0.451469\pi$
$108$	0	0
$109$	2.01747	0.193239	0.0966194	−	0.995321i	$-0.469197\pi$
$109$	2.01747	0.193239	0.0966194	+	0.995321i	$0.469197\pi$
$110$	−14.4705	−1.37971
$111$	0	0
$112$	−12.6751	−1.19768
$113$	7.86808	0.740167	0.370084	−	0.928998i	$-0.379329\pi$
$113$	7.86808	0.740167	0.370084	+	0.928998i	$0.379329\pi$
$114$	0	0
$115$	10.0899	0.940887
$116$	10.7275	0.996020
$117$	0	0
$118$	−12.8188	−1.18007
$119$	0	0
$120$	0	0
$121$	8.64179	0.785617
$122$	−11.1723	−1.01149
$123$	0	0
$124$	25.8187	2.31859
$125$	−11.7986	−1.05530
$126$	0	0
$127$	20.0735	1.78123	0.890617	−	0.454755i	$-0.150273\pi$
$127$	20.0735	1.78123	0.890617	+	0.454755i	$0.150273\pi$
$128$	−6.43007	−0.568343
$129$	0	0
$130$	12.0102	1.05336
$131$	0.439032	0.0383584	0.0191792	−	0.999816i	$-0.493895\pi$
$131$	0.439032	0.0383584	0.0191792	+	0.999816i	$0.493895\pi$
$132$	0	0
$133$	1.68113	0.145773
$134$	13.7009	1.18358
$135$	0	0
$136$	0	0
$137$	−2.64760	−0.226200	−0.113100	−	0.993584i	$-0.536078\pi$
$137$	−2.64760	−0.226200	−0.113100	+	0.993584i	$0.536078\pi$
$138$	0	0
$139$	9.38375	0.795919	0.397959	−	0.917403i	$-0.369718\pi$
$139$	9.38375	0.795919	0.397959	+	0.917403i	$0.369718\pi$
$140$	15.4069	1.30212
$141$	0	0
$142$	3.42449	0.287377
$143$	−16.3022	−1.36326
$144$	0	0
$145$	6.99069	0.580545
$146$	−9.90672	−0.819886
$147$	0	0
$148$	1.70599	0.140231
$149$	7.90923	0.647950	0.323975	−	0.946066i	$-0.394981\pi$
$149$	7.90923	0.647950	0.323975	+	0.946066i	$0.394981\pi$
$150$	0	0
$151$	−13.9013	−1.13127	−0.565636	−	0.824655i	$-0.691369\pi$
$151$	−13.9013	−1.13127	−0.565636	+	0.824655i	$0.691369\pi$
$152$	0.333112	0.0270190
$153$	0	0
$154$	−38.4055	−3.09480
$155$	16.8251	1.35142
$156$	0	0
$157$	−2.42647	−0.193653	−0.0968265	−	0.995301i	$-0.530869\pi$
$157$	−2.42647	−0.193653	−0.0968265	+	0.995301i	$0.530869\pi$
$158$	−11.8413	−0.942046
$159$	0	0
$160$	−12.5610	−0.993038
$161$	26.7791	2.11049
$162$	0	0
$163$	−0.565279	−0.0442760	−0.0221380	−	0.999755i	$-0.507047\pi$
$163$	−0.565279	−0.0442760	−0.0221380	+	0.999755i	$0.507047\pi$
$164$	4.79922	0.374756
$165$	0	0
$166$	−25.0420	−1.94363
$167$	−12.1555	−0.940620	−0.470310	−	0.882501i	$-0.655858\pi$
$167$	−12.1555	−0.940620	−0.470310	+	0.882501i	$0.655858\pi$
$168$	0	0
$169$	0.530441	0.0408032
$170$	0	0
$171$	0	0
$172$	−9.87993	−0.753338
$173$	14.7127	1.11858	0.559292	−	0.828971i	$-0.311073\pi$
$173$	14.7127	1.11858	0.559292	+	0.828971i	$0.311073\pi$
$174$	0	0
$175$	−10.6369	−0.804077
$176$	13.5838	1.02392
$177$	0	0
$178$	−19.5668	−1.46659
$179$	−21.1759	−1.58276	−0.791382	−	0.611322i	$-0.790638\pi$
$179$	−21.1759	−1.58276	−0.791382	+	0.611322i	$0.790638\pi$
$180$	0	0
$181$	−3.90645	−0.290364	−0.145182	−	0.989405i	$-0.546377\pi$
$181$	−3.90645	−0.290364	−0.145182	+	0.989405i	$0.546377\pi$
$182$	31.8756	2.36278
$183$	0	0
$184$	5.30620	0.391178
$185$	1.11173	0.0817359
$186$	0	0
$187$	0	0
$188$	−19.6642	−1.43416
$189$	0	0
$190$	1.32732	0.0962942
$191$	13.4653	0.974316	0.487158	−	0.873314i	$-0.338034\pi$
$191$	13.4653	0.974316	0.487158	+	0.873314i	$0.338034\pi$
$192$	0	0
$193$	−24.1986	−1.74186	−0.870928	−	0.491411i	$-0.836481\pi$
$193$	−24.1986	−1.74186	−0.870928	+	0.491411i	$0.836481\pi$
$194$	−27.5160	−1.97553
$195$	0	0
$196$	24.1535	1.72525
$197$	−0.0500785	−0.00356795	−0.00178397	−	0.999998i	$-0.500568\pi$
$197$	−0.0500785	−0.00356795	−0.00178397	+	0.999998i	$0.500568\pi$
$198$	0	0
$199$	8.19228	0.580735	0.290368	−	0.956915i	$-0.406222\pi$
$199$	8.19228	0.580735	0.290368	+	0.956915i	$0.406222\pi$
$200$	−2.10768	−0.149036
$201$	0	0
$202$	−5.77072	−0.406026
$203$	18.5536	1.30221
$204$	0	0
$205$	3.12747	0.218432
$206$	22.5796	1.57320
$207$	0	0
$208$	−11.2742	−0.781727
$209$	−1.80166	−0.124624
$210$	0	0
$211$	−27.3624	−1.88371	−0.941853	−	0.336024i	$-0.890918\pi$
$211$	−27.3624	−1.88371	−0.941853	+	0.336024i	$0.890918\pi$
$212$	9.77465	0.671326
$213$	0	0
$214$	6.58399	0.450072
$215$	−6.43838	−0.439094
$216$	0	0
$217$	44.6546	3.03135
$218$	4.22758	0.286328
$219$	0	0
$220$	−16.5116	−1.11321
$221$	0	0
$222$	0	0
$223$	−10.3368	−0.692201	−0.346101	−	0.938197i	$-0.612494\pi$
$223$	−10.3368	−0.692201	−0.346101	+	0.938197i	$0.612494\pi$
$224$	−33.3376	−2.22746
$225$	0	0
$226$	16.4874	1.09673
$227$	−10.5735	−0.701789	−0.350894	−	0.936415i	$-0.614122\pi$
$227$	−10.5735	−0.701789	−0.350894	+	0.936415i	$0.614122\pi$
$228$	0	0
$229$	−21.6221	−1.42883	−0.714414	−	0.699724i	$-0.753307\pi$
$229$	−21.6221	−1.42883	−0.714414	+	0.699724i	$0.753307\pi$
$230$	21.1432	1.39414
$231$	0	0
$232$	3.67635	0.241364
$233$	−6.55641	−0.429525	−0.214762	−	0.976666i	$-0.568898\pi$
$233$	−6.55641	−0.429525	−0.214762	+	0.976666i	$0.568898\pi$
$234$	0	0
$235$	−12.8144	−0.835922
$236$	−14.6269	−0.952130
$237$	0	0
$238$	0	0
$239$	20.4618	1.32356	0.661781	−	0.749697i	$-0.269801\pi$
$239$	20.4618	1.32356	0.661781	+	0.749697i	$0.269801\pi$
$240$	0	0
$241$	−6.61849	−0.426334	−0.213167	−	0.977016i	$-0.568378\pi$
$241$	−6.61849	−0.426334	−0.213167	+	0.977016i	$0.568378\pi$
$242$	18.1087	1.16407
$243$	0	0
$244$	−12.7481	−0.816115
$245$	15.7399	1.00559
$246$	0	0
$247$	1.49534	0.0951460
$248$	8.84820	0.561861
$249$	0	0
$250$	−24.7237	−1.56366
$251$	6.15242	0.388337	0.194169	−	0.980968i	$-0.437799\pi$
$251$	6.15242	0.388337	0.194169	+	0.980968i	$0.437799\pi$
$252$	0	0
$253$	−28.6990	−1.80429
$254$	42.0636	2.63931
$255$	0	0
$256$	8.05133	0.503208
$257$	−1.34946	−0.0841769	−0.0420885	−	0.999114i	$-0.513401\pi$
$257$	−1.34946	−0.0841769	−0.0420885	+	0.999114i	$0.513401\pi$
$258$	0	0
$259$	2.95058	0.183340
$260$	13.7042	0.849898
$261$	0	0
$262$	0.919982	0.0568367
$263$	−27.4085	−1.69008	−0.845041	−	0.534702i	$-0.820424\pi$
$263$	−27.4085	−1.69008	−0.845041	+	0.534702i	$0.820424\pi$
$264$	0	0
$265$	6.36978	0.391292
$266$	3.52278	0.215996
$267$	0	0
$268$	15.6333	0.954958
$269$	0.878957	0.0535910	0.0267955	−	0.999641i	$-0.491470\pi$
$269$	0.878957	0.0535910	0.0267955	+	0.999641i	$0.491470\pi$
$270$	0	0
$271$	14.8751	0.903595	0.451798	−	0.892120i	$-0.350783\pi$
$271$	14.8751	0.903595	0.451798	+	0.892120i	$0.350783\pi$
$272$	0	0
$273$	0	0
$274$	−5.54800	−0.335167
$275$	11.3996	0.687420
$276$	0	0
$277$	16.3192	0.980524	0.490262	−	0.871575i	$-0.336901\pi$
$277$	16.3192	0.980524	0.490262	+	0.871575i	$0.336901\pi$
$278$	19.6635	1.17934
$279$	0	0
$280$	5.28003	0.315542
$281$	30.5077	1.81994	0.909969	−	0.414676i	$-0.136105\pi$
$281$	30.5077	1.81994	0.909969	+	0.414676i	$0.136105\pi$
$282$	0	0
$283$	−0.235610	−0.0140056	−0.00700278	−	0.999975i	$-0.502229\pi$
$283$	−0.235610	−0.0140056	−0.00700278	+	0.999975i	$0.502229\pi$
$284$	3.90751	0.231868
$285$	0	0
$286$	−34.1610	−2.01998
$287$	8.30046	0.489961
$288$	0	0
$289$	0	0
$290$	14.6489	0.860211
$291$	0	0
$292$	−11.3040	−0.661518
$293$	−24.7566	−1.44630	−0.723149	−	0.690692i	$-0.757306\pi$
$293$	−24.7566	−1.44630	−0.723149	+	0.690692i	$0.757306\pi$
$294$	0	0
$295$	−9.53181	−0.554963
$296$	0.584650	0.0339821
$297$	0	0
$298$	16.5737	0.960086
$299$	23.8195	1.37752
$300$	0	0
$301$	−17.0878	−0.984924
$302$	−29.1299	−1.67624
$303$	0	0
$304$	−1.24599	−0.0714623
$305$	−8.30748	−0.475685
$306$	0	0
$307$	4.52959	0.258517	0.129259	−	0.991611i	$-0.458740\pi$
$307$	4.52959	0.258517	0.129259	+	0.991611i	$0.458740\pi$
$308$	−43.8225	−2.49702
$309$	0	0
$310$	35.2567	2.00244
$311$	28.1271	1.59494	0.797470	−	0.603359i	$-0.206171\pi$
$311$	28.1271	1.59494	0.797470	+	0.603359i	$0.206171\pi$
$312$	0	0
$313$	−12.5047	−0.706806	−0.353403	−	0.935471i	$-0.614976\pi$
$313$	−12.5047	−0.706806	−0.353403	+	0.935471i	$0.614976\pi$
$314$	−5.08461	−0.286941
$315$	0	0
$316$	−13.5115	−0.760082
$317$	−30.7407	−1.72657	−0.863284	−	0.504718i	$-0.831597\pi$
$317$	−30.7407	−1.72657	−0.863284	+	0.504718i	$0.831597\pi$
$318$	0	0
$319$	−19.8839	−1.11328
$320$	−16.7700	−0.937469
$321$	0	0
$322$	56.1150	3.12717
$323$	0	0
$324$	0	0
$325$	−9.46136	−0.524822
$326$	−1.18453	−0.0656051
$327$	0	0
$328$	1.64471	0.0908142
$329$	−34.0102	−1.87504
$330$	0	0
$331$	−11.8693	−0.652396	−0.326198	−	0.945301i	$-0.605768\pi$
$331$	−11.8693	−0.652396	−0.326198	+	0.945301i	$0.605768\pi$
$332$	−28.5740	−1.56820
$333$	0	0
$334$	−25.4716	−1.39374
$335$	10.1877	0.556612
$336$	0	0
$337$	27.5318	1.49975	0.749877	−	0.661578i	$-0.230113\pi$
$337$	27.5318	1.49975	0.749877	+	0.661578i	$0.230113\pi$
$338$	1.11153	0.0604593
$339$	0	0
$340$	0	0
$341$	−47.8562	−2.59156
$342$	0	0
$343$	12.8266	0.692572
$344$	−3.38590	−0.182556
$345$	0	0
$346$	30.8301	1.65744
$347$	14.7510	0.791874	0.395937	−	0.918278i	$-0.370420\pi$
$347$	14.7510	0.791874	0.395937	+	0.918278i	$0.370420\pi$
$348$	0	0
$349$	−25.9305	−1.38803	−0.694013	−	0.719962i	$-0.744159\pi$
$349$	−25.9305	−1.38803	−0.694013	+	0.719962i	$0.744159\pi$
$350$	−22.2895	−1.19142
$351$	0	0
$352$	35.7278	1.90430
$353$	21.2680	1.13198	0.565991	−	0.824411i	$-0.308494\pi$
$353$	21.2680	1.13198	0.565991	+	0.824411i	$0.308494\pi$
$354$	0	0
$355$	2.54638	0.135148
$356$	−22.3266	−1.18331
$357$	0	0
$358$	−44.3738	−2.34523
$359$	−34.8709	−1.84042	−0.920208	−	0.391430i	$-0.871981\pi$
$359$	−34.8709	−1.84042	−0.920208	+	0.391430i	$0.871981\pi$
$360$	0	0
$361$	−18.8347	−0.991302
$362$	−8.18589	−0.430241
$363$	0	0
$364$	36.3716	1.90639
$365$	−7.36642	−0.385576
$366$	0	0
$367$	9.71161	0.506942	0.253471	−	0.967343i	$-0.418428\pi$
$367$	9.71161	0.506942	0.253471	+	0.967343i	$0.418428\pi$
$368$	−19.8476	−1.03463
$369$	0	0
$370$	2.32961	0.121110
$371$	16.9057	0.877700
$372$	0	0
$373$	14.4620	0.748813	0.374407	−	0.927265i	$-0.377846\pi$
$373$	14.4620	0.748813	0.374407	+	0.927265i	$0.377846\pi$
$374$	0	0
$375$	0	0
$376$	−6.73902	−0.347539
$377$	16.5031	0.849954
$378$	0	0
$379$	−16.7515	−0.860465	−0.430233	−	0.902718i	$-0.641568\pi$
$379$	−16.7515	−0.860465	−0.430233	+	0.902718i	$0.641568\pi$
$380$	1.51454	0.0776942
$381$	0	0
$382$	28.2163	1.44367
$383$	−12.4070	−0.633968	−0.316984	−	0.948431i	$-0.602670\pi$
$383$	−12.4070	−0.633968	−0.316984	+	0.948431i	$0.602670\pi$
$384$	0	0
$385$	−28.5575	−1.45542
$386$	−50.7078	−2.58096
$387$	0	0
$388$	−31.3970	−1.59394
$389$	−18.0977	−0.917589	−0.458794	−	0.888542i	$-0.651719\pi$
$389$	−18.0977	−0.917589	−0.458794	+	0.888542i	$0.651719\pi$
$390$	0	0
$391$	0	0
$392$	8.27751	0.418077
$393$	0	0
$394$	−0.104939	−0.00528673
$395$	−8.80496	−0.443025
$396$	0	0
$397$	7.05161	0.353910	0.176955	−	0.984219i	$-0.443375\pi$
$397$	7.05161	0.353910	0.176955	+	0.984219i	$0.443375\pi$
$398$	17.1668	0.860493
$399$	0	0
$400$	7.88367	0.394183
$401$	−23.4901	−1.17304	−0.586520	−	0.809935i	$-0.699502\pi$
$401$	−23.4901	−1.17304	−0.586520	+	0.809935i	$0.699502\pi$
$402$	0	0
$403$	39.7195	1.97857
$404$	−6.58466	−0.327599
$405$	0	0
$406$	38.8788	1.92952
$407$	−3.16213	−0.156741
$408$	0	0
$409$	4.90401	0.242488	0.121244	−	0.992623i	$-0.461312\pi$
$409$	4.90401	0.242488	0.121244	+	0.992623i	$0.461312\pi$
$410$	6.55356	0.323657
$411$	0	0
$412$	25.7644	1.26932
$413$	−25.2979	−1.24483
$414$	0	0
$415$	−18.6206	−0.914052
$416$	−29.6532	−1.45387
$417$	0	0
$418$	−3.77535	−0.184658
$419$	29.9410	1.46271	0.731356	−	0.681996i	$-0.238888\pi$
$419$	29.9410	1.46271	0.731356	+	0.681996i	$0.238888\pi$
$420$	0	0
$421$	−27.0945	−1.32051	−0.660254	−	0.751043i	$-0.729551\pi$
$421$	−27.0945	−1.32051	−0.660254	+	0.751043i	$0.729551\pi$
$422$	−57.3374	−2.79114
$423$	0	0
$424$	3.34982	0.162682
$425$	0	0
$426$	0	0
$427$	−22.0484	−1.06700
$428$	7.51264	0.363137
$429$	0	0
$430$	−13.4915	−0.650619
$431$	4.79840	0.231131	0.115566	−	0.993300i	$-0.463132\pi$
$431$	4.79840	0.231131	0.115566	+	0.993300i	$0.463132\pi$
$432$	0	0
$433$	−0.887773	−0.0426637	−0.0213318	−	0.999772i	$-0.506791\pi$
$433$	−0.887773	−0.0426637	−0.0213318	+	0.999772i	$0.506791\pi$
$434$	93.5729	4.49164
$435$	0	0
$436$	4.82386	0.231021
$437$	2.63245	0.125927
$438$	0	0
$439$	−17.8229	−0.850640	−0.425320	−	0.905043i	$-0.639838\pi$
$439$	−17.8229	−0.850640	−0.425320	+	0.905043i	$0.639838\pi$
$440$	−5.65859	−0.269763
$441$	0	0
$442$	0	0
$443$	28.0844	1.33433	0.667164	−	0.744911i	$-0.267508\pi$
$443$	28.0844	1.33433	0.667164	+	0.744911i	$0.267508\pi$
$444$	0	0
$445$	−14.5494	−0.689708
$446$	−21.6605	−1.02565
$447$	0	0
$448$	−44.5083	−2.10282
$449$	−6.27581	−0.296174	−0.148087	−	0.988974i	$-0.547312\pi$
$449$	−6.27581	−0.296174	−0.148087	+	0.988974i	$0.547312\pi$
$450$	0	0
$451$	−8.89557	−0.418876
$452$	18.8129	0.884885
$453$	0	0
$454$	−22.1566	−1.03986
$455$	23.7020	1.11117
$456$	0	0
$457$	19.6303	0.918267	0.459134	−	0.888367i	$-0.348160\pi$
$457$	19.6303	0.918267	0.459134	+	0.888367i	$0.348160\pi$
$458$	−45.3087	−2.11714
$459$	0	0
$460$	24.1254	1.12485
$461$	−34.1602	−1.59100	−0.795499	−	0.605955i	$-0.792791\pi$
$461$	−34.1602	−1.59100	−0.795499	+	0.605955i	$0.792791\pi$
$462$	0	0
$463$	−32.4372	−1.50748	−0.753742	−	0.657170i	$-0.771753\pi$
$463$	−32.4372	−1.50748	−0.753742	+	0.657170i	$0.771753\pi$
$464$	−13.7512	−0.638384
$465$	0	0
$466$	−13.7388	−0.636439
$467$	35.9553	1.66381	0.831907	−	0.554915i	$-0.187249\pi$
$467$	35.9553	1.66381	0.831907	+	0.554915i	$0.187249\pi$
$468$	0	0
$469$	27.0386	1.24852
$470$	−26.8524	−1.23861
$471$	0	0
$472$	−5.01271	−0.230729
$473$	18.3129	0.842028
$474$	0	0
$475$	−1.04564	−0.0479771
$476$	0	0
$477$	0	0
$478$	42.8773	1.96116
$479$	28.9547	1.32297	0.661487	−	0.749956i	$-0.269926\pi$
$479$	28.9547	1.32297	0.661487	+	0.749956i	$0.269926\pi$
$480$	0	0
$481$	2.62449	0.119666
$482$	−13.8689	−0.631712
$483$	0	0
$484$	20.6629	0.939222
$485$	−20.4603	−0.929053
$486$	0	0
$487$	13.9912	0.634002	0.317001	−	0.948425i	$-0.397324\pi$
$487$	13.9912	0.634002	0.317001	+	0.948425i	$0.397324\pi$
$488$	−4.36884	−0.197768
$489$	0	0
$490$	32.9827	1.49001
$491$	0.159542	0.00720003	0.00360001	−	0.999994i	$-0.498854\pi$
$491$	0.159542	0.00720003	0.00360001	+	0.999994i	$0.498854\pi$
$492$	0	0
$493$	0	0
$494$	3.13345	0.140981
$495$	0	0
$496$	−33.0962	−1.48606
$497$	6.75821	0.303147
$498$	0	0
$499$	6.37135	0.285221	0.142610	−	0.989779i	$-0.454450\pi$
$499$	6.37135	0.285221	0.142610	+	0.989779i	$0.454450\pi$
$500$	−28.2109	−1.26163
$501$	0	0
$502$	12.8923	0.575411
$503$	23.9766	1.06906	0.534532	−	0.845148i	$-0.320488\pi$
$503$	23.9766	1.06906	0.534532	+	0.845148i	$0.320488\pi$
$504$	0	0
$505$	−4.29098	−0.190946
$506$	−60.1382	−2.67347
$507$	0	0
$508$	47.9965	2.12950
$509$	5.68783	0.252108	0.126054	−	0.992023i	$-0.459769\pi$
$509$	5.68783	0.252108	0.126054	+	0.992023i	$0.459769\pi$
$510$	0	0
$511$	−19.5508	−0.864878
$512$	29.7316	1.31396
$513$	0	0
$514$	−2.82777	−0.124727
$515$	16.7897	0.739843
$516$	0	0
$517$	36.4485	1.60301
$518$	6.18289	0.271661
$519$	0	0
$520$	4.69649	0.205955
$521$	6.93674	0.303904	0.151952	−	0.988388i	$-0.451444\pi$
$521$	6.93674	0.303904	0.151952	+	0.988388i	$0.451444\pi$
$522$	0	0
$523$	−2.86550	−0.125299	−0.0626497	−	0.998036i	$-0.519955\pi$
$523$	−2.86550	−0.125299	−0.0626497	+	0.998036i	$0.519955\pi$
$524$	1.04974	0.0458582
$525$	0	0
$526$	−57.4340	−2.50424
$527$	0	0
$528$	0	0
$529$	18.9327	0.823160
$530$	13.3477	0.579789
$531$	0	0
$532$	4.01966	0.174274
$533$	7.38311	0.319798
$534$	0	0
$535$	4.89571	0.211660
$536$	5.35762	0.231414
$537$	0	0
$538$	1.84184	0.0794073
$539$	−44.7696	−1.92836
$540$	0	0
$541$	−29.8884	−1.28500	−0.642502	−	0.766284i	$-0.722104\pi$
$541$	−29.8884	−1.28500	−0.642502	+	0.766284i	$0.722104\pi$
$542$	31.1704	1.33888
$543$	0	0
$544$	0	0
$545$	3.14353	0.134654
$546$	0	0
$547$	11.9209	0.509699	0.254849	−	0.966981i	$-0.417974\pi$
$547$	11.9209	0.509699	0.254849	+	0.966981i	$0.417974\pi$
$548$	−6.33053	−0.270427
$549$	0	0
$550$	23.8876	1.01857
$551$	1.82387	0.0776993
$552$	0	0
$553$	−23.3688	−0.993742
$554$	34.1965	1.45287
$555$	0	0
$556$	22.4369	0.951538
$557$	−21.2677	−0.901142	−0.450571	−	0.892741i	$-0.648780\pi$
$557$	−21.2677	−0.901142	−0.450571	+	0.892741i	$0.648780\pi$
$558$	0	0
$559$	−15.1993	−0.642861
$560$	−19.7497	−0.834576
$561$	0	0
$562$	63.9284	2.69665
$563$	19.8348	0.835935	0.417968	−	0.908462i	$-0.362743\pi$
$563$	19.8348	0.835935	0.417968	+	0.908462i	$0.362743\pi$
$564$	0	0
$565$	12.2597	0.515769
$566$	−0.493716	−0.0207524
$567$	0	0
$568$	1.33912	0.0561883
$569$	36.5103	1.53059	0.765296	−	0.643679i	$-0.222593\pi$
$569$	36.5103	1.53059	0.765296	+	0.643679i	$0.222593\pi$
$570$	0	0
$571$	−16.2502	−0.680049	−0.340025	−	0.940417i	$-0.610435\pi$
$571$	−16.2502	−0.680049	−0.340025	+	0.940417i	$0.610435\pi$
$572$	−38.9793	−1.62981
$573$	0	0
$574$	17.3935	0.725989
$575$	−16.6561	−0.694609
$576$	0	0
$577$	−12.9656	−0.539764	−0.269882	−	0.962893i	$-0.586985\pi$
$577$	−12.9656	−0.539764	−0.269882	+	0.962893i	$0.586985\pi$
$578$	0	0
$579$	0	0
$580$	16.7150	0.694054
$581$	−49.4201	−2.05029
$582$	0	0
$583$	−18.1178	−0.750361
$584$	−3.87395	−0.160305
$585$	0	0
$586$	−51.8771	−2.14302
$587$	−23.8973	−0.986347	−0.493174	−	0.869931i	$-0.664163\pi$
$587$	−23.8973	−0.986347	−0.493174	+	0.869931i	$0.664163\pi$
$588$	0	0
$589$	4.38966	0.180873
$590$	−19.9737	−0.822306
$591$	0	0
$592$	−2.18685	−0.0898791
$593$	21.3745	0.877744	0.438872	−	0.898550i	$-0.355378\pi$
$593$	21.3745	0.877744	0.438872	+	0.898550i	$0.355378\pi$
$594$	0	0
$595$	0	0
$596$	18.9113	0.774637
$597$	0	0
$598$	49.9133	2.04111
$599$	2.23714	0.0914070	0.0457035	−	0.998955i	$-0.485447\pi$
$599$	2.23714	0.0914070	0.0457035	+	0.998955i	$0.485447\pi$
$600$	0	0
$601$	−11.3456	−0.462797	−0.231398	−	0.972859i	$-0.574330\pi$
$601$	−11.3456	−0.462797	−0.231398	+	0.972859i	$0.574330\pi$
$602$	−35.8071	−1.45939
$603$	0	0
$604$	−33.2386	−1.35246
$605$	13.4652	0.547440
$606$	0	0
$607$	−19.2785	−0.782489	−0.391244	−	0.920287i	$-0.627955\pi$
$607$	−19.2785	−0.782489	−0.391244	+	0.920287i	$0.627955\pi$
$608$	−3.27717	−0.132907
$609$	0	0
$610$	−17.4082	−0.704836
$611$	−30.2514	−1.22384
$612$	0	0
$613$	35.8715	1.44884	0.724418	−	0.689361i	$-0.242109\pi$
$613$	35.8715	1.44884	0.724418	+	0.689361i	$0.242109\pi$
$614$	9.49167	0.383053
$615$	0	0
$616$	−15.0182	−0.605099
$617$	8.69729	0.350140	0.175070	−	0.984556i	$-0.443985\pi$
$617$	8.69729	0.350140	0.175070	+	0.984556i	$0.443985\pi$
$618$	0	0
$619$	2.18274	0.0877319	0.0438659	−	0.999037i	$-0.486033\pi$
$619$	2.18274	0.0877319	0.0438659	+	0.999037i	$0.486033\pi$
$620$	40.2295	1.61566
$621$	0	0
$622$	58.9397	2.36327
$623$	−38.6148	−1.54707
$624$	0	0
$625$	−5.52321	−0.220928
$626$	−26.2033	−1.04730
$627$	0	0
$628$	−5.80178	−0.231516
$629$	0	0
$630$	0	0
$631$	−4.20601	−0.167439	−0.0837193	−	0.996489i	$-0.526680\pi$
$631$	−4.20601	−0.167439	−0.0837193	+	0.996489i	$0.526680\pi$
$632$	−4.63046	−0.184190
$633$	0	0
$634$	−64.4165	−2.55831
$635$	31.2776	1.24121
$636$	0	0
$637$	37.1577	1.47224
$638$	−41.6662	−1.64958
$639$	0	0
$640$	−10.0190	−0.396037
$641$	25.3289	1.00043	0.500216	−	0.865901i	$-0.333254\pi$
$641$	25.3289	1.00043	0.500216	+	0.865901i	$0.333254\pi$
$642$	0	0
$643$	20.9322	0.825486	0.412743	−	0.910847i	$-0.364571\pi$
$643$	20.9322	0.825486	0.412743	+	0.910847i	$0.364571\pi$
$644$	64.0299	2.52313
$645$	0	0
$646$	0	0
$647$	36.9349	1.45206	0.726030	−	0.687663i	$-0.241364\pi$
$647$	36.9349	1.45206	0.726030	+	0.687663i	$0.241364\pi$
$648$	0	0
$649$	27.1116	1.06422
$650$	−19.8261	−0.777644
$651$	0	0
$652$	−1.35161	−0.0529329
$653$	−5.77925	−0.226160	−0.113080	−	0.993586i	$-0.536072\pi$
$653$	−5.77925	−0.226160	−0.113080	+	0.993586i	$0.536072\pi$
$654$	0	0
$655$	0.684078	0.0267292
$656$	−6.15197	−0.240194
$657$	0	0
$658$	−71.2676	−2.77830
$659$	1.17066	0.0456024	0.0228012	−	0.999740i	$-0.492742\pi$
$659$	1.17066	0.0456024	0.0228012	+	0.999740i	$0.492742\pi$
$660$	0	0
$661$	15.5313	0.604097	0.302049	−	0.953293i	$-0.402330\pi$
$661$	15.5313	0.604097	0.302049	+	0.953293i	$0.402330\pi$
$662$	−24.8719	−0.966675
$663$	0	0
$664$	−9.79246	−0.380021
$665$	2.61946	0.101578
$666$	0	0
$667$	29.0527	1.12492
$668$	−29.0643	−1.12453
$669$	0	0
$670$	21.3481	0.824748
$671$	23.6292	0.912196
$672$	0	0
$673$	−10.7959	−0.416150	−0.208075	−	0.978113i	$-0.566720\pi$
$673$	−10.7959	−0.416150	−0.208075	+	0.978113i	$0.566720\pi$
$674$	57.6924	2.22223
$675$	0	0
$676$	1.26831	0.0487811
$677$	44.4350	1.70778	0.853888	−	0.520456i	$-0.174238\pi$
$677$	44.4350	1.70778	0.853888	+	0.520456i	$0.174238\pi$
$678$	0	0
$679$	−54.3026	−2.08394
$680$	0	0
$681$	0	0
$682$	−100.282	−3.83999
$683$	−41.6993	−1.59558	−0.797790	−	0.602935i	$-0.793998\pi$
$683$	−41.6993	−1.59558	−0.797790	+	0.602935i	$0.793998\pi$
$684$	0	0
$685$	−4.12537	−0.157622
$686$	26.8779	1.02620
$687$	0	0
$688$	12.6648	0.482840
$689$	15.0373	0.572876
$690$	0	0
$691$	46.4110	1.76556	0.882779	−	0.469789i	$-0.155670\pi$
$691$	46.4110	1.76556	0.882779	+	0.469789i	$0.155670\pi$
$692$	35.1786	1.33729
$693$	0	0
$694$	30.9104	1.17334
$695$	14.6213	0.554618
$696$	0	0
$697$	0	0
$698$	−54.3368	−2.05668
$699$	0	0
$700$	−25.4334	−0.961291
$701$	−14.9568	−0.564910	−0.282455	−	0.959280i	$-0.591149\pi$
$701$	−14.9568	−0.564910	−0.282455	+	0.959280i	$0.591149\pi$
$702$	0	0
$703$	0.290049	0.0109394
$704$	47.6993	1.79774
$705$	0	0
$706$	44.5667	1.67729
$707$	−11.3885	−0.428307
$708$	0	0
$709$	−6.33313	−0.237846	−0.118923	−	0.992903i	$-0.537944\pi$
$709$	−6.33313	−0.237846	−0.118923	+	0.992903i	$0.537944\pi$
$710$	5.33589	0.200252
$711$	0	0
$712$	−7.65143	−0.286749
$713$	69.9236	2.61866
$714$	0	0
$715$	−25.4013	−0.949956
$716$	−50.6326	−1.89223
$717$	0	0
$718$	−73.0713	−2.72700
$719$	5.01618	0.187072	0.0935359	−	0.995616i	$-0.470183\pi$
$719$	5.01618	0.187072	0.0935359	+	0.995616i	$0.470183\pi$
$720$	0	0
$721$	44.5607	1.65953
$722$	−39.4678	−1.46884
$723$	0	0
$724$	−9.34048	−0.347136
$725$	−11.5400	−0.428587
$726$	0	0
$727$	−5.81340	−0.215607	−0.107804	−	0.994172i	$-0.534382\pi$
$727$	−5.81340	−0.215607	−0.107804	+	0.994172i	$0.534382\pi$
$728$	12.4647	0.461973
$729$	0	0
$730$	−15.4362	−0.571319
$731$	0	0
$732$	0	0
$733$	43.5260	1.60767	0.803835	−	0.594853i	$-0.202790\pi$
$733$	43.5260	1.60767	0.803835	+	0.594853i	$0.202790\pi$
$734$	20.3505	0.751151
$735$	0	0
$736$	−52.2026	−1.92421
$737$	−28.9771	−1.06739
$738$	0	0
$739$	31.7968	1.16967	0.584833	−	0.811154i	$-0.301160\pi$
$739$	31.7968	1.16967	0.584833	+	0.811154i	$0.301160\pi$
$740$	2.65819	0.0977170
$741$	0	0
$742$	35.4256	1.30051
$743$	−35.2325	−1.29256	−0.646278	−	0.763102i	$-0.723675\pi$
$743$	−35.2325	−1.29256	−0.646278	+	0.763102i	$0.723675\pi$
$744$	0	0
$745$	12.3238	0.451509
$746$	30.3048	1.10954
$747$	0	0
$748$	0	0
$749$	12.9935	0.474770
$750$	0	0
$751$	21.8717	0.798110	0.399055	−	0.916927i	$-0.369338\pi$
$751$	21.8717	0.798110	0.399055	+	0.916927i	$0.369338\pi$
$752$	25.2070	0.919203
$753$	0	0
$754$	34.5820	1.25940
$755$	−21.6604	−0.788302
$756$	0	0
$757$	10.2908	0.374025	0.187012	−	0.982358i	$-0.440120\pi$
$757$	10.2908	0.374025	0.187012	+	0.982358i	$0.440120\pi$
$758$	−35.1024	−1.27498
$759$	0	0
$760$	0.519040	0.0188276
$761$	−41.0310	−1.48737	−0.743687	−	0.668528i	$-0.766925\pi$
$761$	−41.0310	−1.48737	−0.743687	+	0.668528i	$0.766925\pi$
$762$	0	0
$763$	8.34308	0.302040
$764$	32.1961	1.16482
$765$	0	0
$766$	−25.9986	−0.939369
$767$	−22.5020	−0.812500
$768$	0	0
$769$	−19.1855	−0.691847	−0.345924	−	0.938263i	$-0.612434\pi$
$769$	−19.1855	−0.691847	−0.345924	+	0.938263i	$0.612434\pi$
$770$	−59.8416	−2.15654
$771$	0	0
$772$	−57.8600	−2.08243
$773$	22.6539	0.814802	0.407401	−	0.913249i	$-0.366435\pi$
$773$	22.6539	0.814802	0.407401	+	0.913249i	$0.366435\pi$
$774$	0	0
$775$	−27.7744	−0.997687
$776$	−10.7599	−0.386258
$777$	0	0
$778$	−37.9234	−1.35962
$779$	0.815955	0.0292346
$780$	0	0
$781$	−7.24274	−0.259166
$782$	0	0
$783$	0	0
$784$	−30.9616	−1.10577
$785$	−3.78081	−0.134943
$786$	0	0
$787$	32.1438	1.14580	0.572900	−	0.819625i	$-0.305818\pi$
$787$	32.1438	1.14580	0.572900	+	0.819625i	$0.305818\pi$
$788$	−0.119740	−0.00426555
$789$	0	0
$790$	−18.4506	−0.656444
$791$	32.5378	1.15691
$792$	0	0
$793$	−19.6117	−0.696431
$794$	14.7765	0.524399
$795$	0	0
$796$	19.5881	0.694281
$797$	−38.1275	−1.35055	−0.675273	−	0.737568i	$-0.735974\pi$
$797$	−38.1275	−1.35055	−0.675273	+	0.737568i	$0.735974\pi$
$798$	0	0
$799$	0	0
$800$	20.7354	0.733109
$801$	0	0
$802$	−49.2231	−1.73813
$803$	20.9525	0.739399
$804$	0	0
$805$	41.7259	1.47064
$806$	83.2314	2.93170
$807$	0	0
$808$	−2.25659	−0.0793867
$809$	26.2034	0.921263	0.460631	−	0.887592i	$-0.347623\pi$
$809$	26.2034	0.921263	0.460631	+	0.887592i	$0.347623\pi$
$810$	0	0
$811$	−23.7838	−0.835161	−0.417580	−	0.908640i	$-0.637122\pi$
$811$	−23.7838	−0.835161	−0.417580	+	0.908640i	$0.637122\pi$
$812$	44.3625	1.55682
$813$	0	0
$814$	−6.62618	−0.232247
$815$	−0.880791	−0.0308528
$816$	0	0
$817$	−1.67977	−0.0587677
$818$	10.2763	0.359301
$819$	0	0
$820$	7.47792	0.261140
$821$	−28.7036	−1.00176	−0.500881	−	0.865516i	$-0.666991\pi$
$821$	−28.7036	−1.00176	−0.500881	+	0.865516i	$0.666991\pi$
$822$	0	0
$823$	27.6060	0.962286	0.481143	−	0.876642i	$-0.340222\pi$
$823$	27.6060	0.962286	0.481143	+	0.876642i	$0.340222\pi$
$824$	8.82959	0.307593
$825$	0	0
$826$	−53.0113	−1.84450
$827$	25.0159	0.869889	0.434945	−	0.900457i	$-0.356768\pi$
$827$	25.0159	0.869889	0.434945	+	0.900457i	$0.356768\pi$
$828$	0	0
$829$	−26.6547	−0.925757	−0.462878	−	0.886422i	$-0.653183\pi$
$829$	−26.6547	−0.925757	−0.462878	+	0.886422i	$0.653183\pi$
$830$	−39.0192	−1.35438
$831$	0	0
$832$	−39.5893	−1.37251
$833$	0	0
$834$	0	0
$835$	−18.9401	−0.655450
$836$	−4.30785	−0.148990
$837$	0	0
$838$	62.7408	2.16734
$839$	24.1650	0.834268	0.417134	−	0.908845i	$-0.363035\pi$
$839$	24.1650	0.834268	0.417134	+	0.908845i	$0.363035\pi$
$840$	0	0
$841$	−8.87111	−0.305900
$842$	−56.7761	−1.95663
$843$	0	0
$844$	−65.4247	−2.25201
$845$	0.826509	0.0284328
$846$	0	0
$847$	35.7374	1.22795
$848$	−12.5298	−0.430276
$849$	0	0
$850$	0	0
$851$	4.62024	0.158380
$852$	0	0
$853$	−14.3832	−0.492472	−0.246236	−	0.969210i	$-0.579194\pi$
$853$	−14.3832	−0.492472	−0.246236	+	0.969210i	$0.579194\pi$
$854$	−46.2021	−1.58100
$855$	0	0
$856$	2.57462	0.0879986
$857$	44.3906	1.51635	0.758177	−	0.652049i	$-0.226090\pi$
$857$	44.3906	1.51635	0.758177	+	0.652049i	$0.226090\pi$
$858$	0	0
$859$	−29.6126	−1.01037	−0.505184	−	0.863012i	$-0.668575\pi$
$859$	−29.6126	−1.01037	−0.505184	+	0.863012i	$0.668575\pi$
$860$	−15.3944	−0.524946
$861$	0	0
$862$	10.0550	0.342474
$863$	17.1407	0.583477	0.291739	−	0.956498i	$-0.405766\pi$
$863$	17.1407	0.583477	0.291739	+	0.956498i	$0.405766\pi$
$864$	0	0
$865$	22.9246	0.779460
$866$	−1.86031	−0.0632160
$867$	0	0
$868$	106.771	3.62405
$869$	25.0442	0.849567
$870$	0	0
$871$	24.0503	0.814913
$872$	1.65316	0.0559831
$873$	0	0
$874$	5.51624	0.186590
$875$	−48.7920	−1.64947
$876$	0	0
$877$	35.7976	1.20880	0.604400	−	0.796681i	$-0.293413\pi$
$877$	35.7976	1.20880	0.604400	+	0.796681i	$0.293413\pi$
$878$	−37.3475	−1.26042
$879$	0	0
$880$	21.1656	0.713494
$881$	−43.1096	−1.45240	−0.726200	−	0.687484i	$-0.758715\pi$
$881$	−43.1096	−1.45240	−0.726200	+	0.687484i	$0.758715\pi$
$882$	0	0
$883$	40.9100	1.37673	0.688366	−	0.725363i	$-0.258328\pi$
$883$	40.9100	1.37673	0.688366	+	0.725363i	$0.258328\pi$
$884$	0	0
$885$	0	0
$886$	58.8502	1.97711
$887$	23.6351	0.793587	0.396794	−	0.917908i	$-0.370123\pi$
$887$	23.6351	0.793587	0.396794	+	0.917908i	$0.370123\pi$
$888$	0	0
$889$	83.0122	2.78414
$890$	−30.4880	−1.02196
$891$	0	0
$892$	−24.7157	−0.827541
$893$	−3.34328	−0.111879
$894$	0	0
$895$	−32.9954	−1.10291
$896$	−26.5910	−0.888343
$897$	0	0
$898$	−13.1509	−0.438850
$899$	48.4459	1.61576
$900$	0	0
$901$	0	0
$902$	−18.6405	−0.620661
$903$	0	0
$904$	6.44728	0.214433
$905$	−6.08684	−0.202334
$906$	0	0
$907$	−51.7336	−1.71779	−0.858894	−	0.512154i	$-0.828848\pi$
$907$	−51.7336	−1.71779	−0.858894	+	0.512154i	$0.828848\pi$
$908$	−25.2817	−0.839003
$909$	0	0
$910$	49.6671	1.64645
$911$	33.1280	1.09758	0.548790	−	0.835960i	$-0.315089\pi$
$911$	33.1280	1.09758	0.548790	+	0.835960i	$0.315089\pi$
$912$	0	0
$913$	52.9633	1.75283
$914$	41.1349	1.36062
$915$	0	0
$916$	−51.6993	−1.70819
$917$	1.81558	0.0599556
$918$	0	0
$919$	11.3691	0.375033	0.187517	−	0.982261i	$-0.439956\pi$
$919$	11.3691	0.375033	0.187517	+	0.982261i	$0.439956\pi$
$920$	8.26787	0.272584
$921$	0	0
$922$	−71.5820	−2.35743
$923$	6.01130	0.197864
$924$	0	0
$925$	−1.83521	−0.0603414
$926$	−67.9716	−2.23368
$927$	0	0
$928$	−36.1681	−1.18728
$929$	51.5765	1.69217	0.846086	−	0.533047i	$-0.178953\pi$
$929$	51.5765	1.69217	0.846086	+	0.533047i	$0.178953\pi$
$930$	0	0
$931$	4.10653	0.134586
$932$	−15.6766	−0.513506
$933$	0	0
$934$	75.3437	2.46532
$935$	0	0
$936$	0	0
$937$	46.4413	1.51717	0.758586	−	0.651573i	$-0.225891\pi$
$937$	46.4413	1.51717	0.758586	+	0.651573i	$0.225891\pi$
$938$	56.6588	1.84998
$939$	0	0
$940$	−30.6399	−0.999363
$941$	−0.808546	−0.0263578	−0.0131789	−	0.999913i	$-0.504195\pi$
$941$	−0.808546	−0.0263578	−0.0131789	+	0.999913i	$0.504195\pi$
$942$	0	0
$943$	12.9975	0.423257
$944$	18.7498	0.610253
$945$	0	0
$946$	38.3744	1.24766
$947$	52.2770	1.69878	0.849388	−	0.527769i	$-0.176971\pi$
$947$	52.2770	1.69878	0.849388	+	0.527769i	$0.176971\pi$
$948$	0	0
$949$	−17.3901	−0.564507
$950$	−2.19111	−0.0710891
$951$	0	0
$952$	0	0
$953$	48.1209	1.55879	0.779395	−	0.626533i	$-0.215527\pi$
$953$	48.1209	1.55879	0.779395	+	0.626533i	$0.215527\pi$
$954$	0	0
$955$	20.9810	0.678930
$956$	48.9250	1.58235
$957$	0	0
$958$	60.6741	1.96029
$959$	−10.9489	−0.353559
$960$	0	0
$961$	85.5990	2.76126
$962$	5.49957	0.177313
$963$	0	0
$964$	−15.8251	−0.509691
$965$	−37.7052	−1.21377
$966$	0	0
$967$	12.8134	0.412052	0.206026	−	0.978546i	$-0.433947\pi$
$967$	12.8134	0.412052	0.206026	+	0.978546i	$0.433947\pi$
$968$	7.08127	0.227601
$969$	0	0
$970$	−42.8741	−1.37661
$971$	−18.9275	−0.607414	−0.303707	−	0.952765i	$-0.598224\pi$
$971$	−18.9275	−0.607414	−0.303707	+	0.952765i	$0.598224\pi$
$972$	0	0
$973$	38.8057	1.24405
$974$	29.3183	0.939418
$975$	0	0
$976$	16.3414	0.523076
$977$	4.79457	0.153392	0.0766959	−	0.997055i	$-0.475563\pi$
$977$	4.79457	0.153392	0.0766959	+	0.997055i	$0.475563\pi$
$978$	0	0
$979$	41.3833	1.32262
$980$	37.6348	1.20220
$981$	0	0
$982$	0.334317	0.0106685
$983$	14.8140	0.472493	0.236246	−	0.971693i	$-0.424083\pi$
$983$	14.8140	0.472493	0.236246	+	0.971693i	$0.424083\pi$
$984$	0	0
$985$	−0.0780300	−0.00248624
$986$	0	0
$987$	0	0
$988$	3.57541	0.113749
$989$	−26.7573	−0.850834
$990$	0	0
$991$	15.3311	0.487007	0.243504	−	0.969900i	$-0.421703\pi$
$991$	15.3311	0.487007	0.243504	+	0.969900i	$0.421703\pi$
$992$	−87.0489	−2.76380
$993$	0	0
$994$	14.1617	0.449182
$995$	12.7648	0.404672
$996$	0	0
$997$	−1.92074	−0.0608306	−0.0304153	−	0.999537i	$-0.509683\pi$
$997$	−1.92074	−0.0608306	−0.0304153	+	0.999537i	$0.509683\pi$
$998$	13.3511	0.422620
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2601.2.a.bi.1.6		6
3.2	odd	2		867.2.a.p.1.1	yes	6
17.16	even	2		2601.2.a.bh.1.6		6
51.2	odd	8		867.2.e.k.616.2		24
51.5	even	16		867.2.h.m.688.11		48
51.8	odd	8		867.2.e.k.829.11		24
51.11	even	16		867.2.h.m.733.1		48
51.14	even	16		867.2.h.m.757.1		48
51.20	even	16		867.2.h.m.757.2		48
51.23	even	16		867.2.h.m.733.2		48
51.26	odd	8		867.2.e.k.829.12		24
51.29	even	16		867.2.h.m.688.12		48
51.32	odd	8		867.2.e.k.616.1		24
51.38	odd	4		867.2.d.g.577.11		12
51.41	even	16		867.2.h.m.712.11		48
51.44	even	16		867.2.h.m.712.12		48
51.47	odd	4		867.2.d.g.577.12		12
51.50	odd	2		867.2.a.o.1.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
867.2.a.o.1.1	✓	6	51.50	odd	2
867.2.a.p.1.1	yes	6	3.2	odd	2
867.2.d.g.577.11		12	51.38	odd	4
867.2.d.g.577.12		12	51.47	odd	4
867.2.e.k.616.1		24	51.32	odd	8
867.2.e.k.616.2		24	51.2	odd	8
867.2.e.k.829.11		24	51.8	odd	8
867.2.e.k.829.12		24	51.26	odd	8
867.2.h.m.688.11		48	51.5	even	16
867.2.h.m.688.12		48	51.29	even	16
867.2.h.m.712.11		48	51.41	even	16
867.2.h.m.712.12		48	51.44	even	16
867.2.h.m.733.1		48	51.11	even	16
867.2.h.m.733.2		48	51.23	even	16
867.2.h.m.757.1		48	51.14	even	16
867.2.h.m.757.2		48	51.20	even	16
2601.2.a.bh.1.6		6	17.16	even	2
2601.2.a.bi.1.6		6	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:	\( N \)	\(=\)	\( 2601 = 3^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2601.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09548 q^{2} +2.39104 q^{4} +1.55815 q^{5} +4.13541 q^{7} +0.819422 q^{8} +O(q^{10})\)	\(q+2.09548 q^{2} +2.39104 q^{4} +1.55815 q^{5} +4.13541 q^{7} +0.819422 q^{8} +3.26508 q^{10} -4.43191 q^{11} +3.67837 q^{13} +8.66568 q^{14} -3.06500 q^{16} +0.406521 q^{19} +3.72561 q^{20} -9.28698 q^{22} +6.47554 q^{23} -2.57216 q^{25} +7.70797 q^{26} +9.88795 q^{28} +4.48652 q^{29} +10.7981 q^{31} -8.06150 q^{32} +6.44361 q^{35} +0.713491 q^{37} +0.851857 q^{38} +1.27678 q^{40} +2.00717 q^{41} -4.13206 q^{43} -10.5969 q^{44} +13.5694 q^{46} -8.22412 q^{47} +10.1017 q^{49} -5.38991 q^{50} +8.79515 q^{52} +4.08803 q^{53} -6.90559 q^{55} +3.38865 q^{56} +9.40143 q^{58} -6.11738 q^{59} -5.33162 q^{61} +22.6272 q^{62} -10.7627 q^{64} +5.73147 q^{65} +6.53830 q^{67} +13.5025 q^{70} +1.63423 q^{71} -4.72766 q^{73} +1.49511 q^{74} +0.972009 q^{76} -18.3278 q^{77} -5.65089 q^{79} -4.77574 q^{80} +4.20598 q^{82} -11.9505 q^{83} -8.65866 q^{86} -3.63160 q^{88} -9.33759 q^{89} +15.2116 q^{91} +15.4833 q^{92} -17.2335 q^{94} +0.633422 q^{95} -13.1311 q^{97} +21.1678 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8	\( 6 q - 3 q^{2} + 9 q^{4} + 3 q^{5} + 3 q^{7} - 12 q^{8} + 12 q^{10} + 9 q^{11} + 9 q^{13} + 6 q^{14} + 15 q^{16} + 9 q^{19} - 6 q^{20} - 18 q^{22} + 9 q^{23} + 15 q^{25} + 12 q^{26} - 15 q^{28} + 6 q^{29} + 24 q^{31} - 42 q^{32} - 3 q^{37} + 6 q^{38} - 3 q^{40} + 18 q^{41} + 3 q^{44} + 15 q^{46} - 24 q^{47} + 21 q^{49} - 12 q^{50} - 18 q^{52} - 24 q^{53} - 24 q^{55} + 54 q^{56} + 3 q^{58} + 9 q^{59} + 21 q^{61} + 30 q^{62} + 24 q^{64} - 9 q^{65} - 6 q^{67} - 3 q^{70} + 27 q^{71} + 18 q^{73} + 36 q^{74} - 3 q^{76} - 33 q^{77} + 24 q^{79} + 3 q^{80} - 15 q^{82} - 6 q^{83} - 6 q^{86} - 24 q^{88} + 39 q^{91} - 15 q^{94} + 42 q^{95} - 33 q^{97} + 57 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 9 * q^4 + 3 * q^5 + 3 * q^7 - 12 * q^8 + 12 * q^10 + 9 * q^11 + 9 * q^13 + 6 * q^14 + 15 * q^16 + 9 * q^19 - 6 * q^20 - 18 * q^22 + 9 * q^23 + 15 * q^25 + 12 * q^26 - 15 * q^28 + 6 * q^29 + 24 * q^31 - 42 * q^32 - 3 * q^37 + 6 * q^38 - 3 * q^40 + 18 * q^41 + 3 * q^44 + 15 * q^46 - 24 * q^47 + 21 * q^49 - 12 * q^50 - 18 * q^52 - 24 * q^53 - 24 * q^55 + 54 * q^56 + 3 * q^58 + 9 * q^59 + 21 * q^61 + 30 * q^62 + 24 * q^64 - 9 * q^65 - 6 * q^67 - 3 * q^70 + 27 * q^71 + 18 * q^73 + 36 * q^74 - 3 * q^76 - 33 * q^77 + 24 * q^79 + 3 * q^80 - 15 * q^82 - 6 * q^83 - 6 * q^86 - 24 * q^88 + 39 * q^91 - 15 * q^94 + 42 * q^95 - 33 * q^97 + 57 * q^98

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