LMFDB - Embedded newform 9025.2.a.cc.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9025,2,Mod(1,9025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9025.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,-6,-9,6,0,12,0,-6,6,0,0,-18,-9,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 6x^{7} + 16x^{6} + 12x^{5} - 27x^{4} - 8x^{3} + 15x^{2} - 1 $ x^9 - 3x^8 - 6x^7 + 16x^6 + 12x^5 - 27x^4 - 8x^3 + 15*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.28997$ of defining polynomial
Character	$\chi$	$=$	9025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +7.57362 q^{6} +2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} -0.577601 q^{11} -10.7287 q^{12} +0.670397 q^{13} -6.73045 q^{14} +0.0353277 q^{16} +0.351901 q^{17} -18.1783 q^{18} -9.72050 q^{21} +1.32269 q^{22} +4.12081 q^{23} +9.42123 q^{24} -1.53519 q^{26} -16.3323 q^{27} +9.53431 q^{28} +3.00800 q^{29} +0.297707 q^{31} +5.61633 q^{32} +1.91030 q^{33} -0.805843 q^{34} +25.7513 q^{36} +8.30595 q^{37} -2.21721 q^{39} +2.67214 q^{41} +22.2596 q^{42} +6.59830 q^{43} -1.87371 q^{44} -9.43652 q^{46} -11.0325 q^{47} -0.116839 q^{48} +1.63832 q^{49} -1.16384 q^{51} +2.17474 q^{52} +4.10660 q^{53} +37.4004 q^{54} -8.37237 q^{56} -6.88822 q^{58} +0.610572 q^{59} +1.02693 q^{61} -0.681739 q^{62} +23.3313 q^{63} -12.9319 q^{64} -4.37452 q^{66} +3.33593 q^{67} +1.14155 q^{68} -13.6288 q^{69} -13.2247 q^{71} -22.6130 q^{72} -7.13879 q^{73} -19.0204 q^{74} -1.69763 q^{77} +5.07733 q^{78} +1.54232 q^{79} +30.2010 q^{81} -6.11911 q^{82} -13.3186 q^{83} -31.5328 q^{84} -15.1099 q^{86} -9.94837 q^{87} +1.64536 q^{88} -6.57130 q^{89} +1.97037 q^{91} +13.3677 q^{92} -0.984606 q^{93} +25.2640 q^{94} -18.5749 q^{96} -12.1979 q^{97} -3.75170 q^{98} -4.58513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 18 q^{12} - 9 q^{13} + 12 q^{16} + 9 q^{17} - 24 q^{18} + 12 q^{21} - 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} - 24 q^{27} + 15 q^{28}+ \cdots - 36 q^{99}+O(q^{100}) $ 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 18 * q^12 - 9 * q^13 + 12 * q^16 + 9 * q^17 - 24 * q^18 + 12 * q^21 - 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 - 24 * q^27 + 15 * q^28 + 9 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^33 - 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 + 6 * q^41 + 12 * q^43 + 48 * q^44 - 9 * q^46 - 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 - 6 * q^58 + 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 - 60 * q^67 + 51 * q^68 - 15 * q^69 - 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 + 6 * q^78 + 15 * q^79 + 33 * q^81 - 24 * q^82 - 48 * q^84 - 39 * q^86 - 15 * q^87 - 27 * q^88 - 39 * q^89 + 21 * q^91 + 6 * q^92 - 15 * q^93 + 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * 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 $

$2$	−2.28997	−1.61925	−0.809626	−	0.586946i	$-0.800330\pi$
$2$	−2.28997	−1.61925	−0.809626	+	0.586946i	$0.800330\pi$
$3$	−3.30730	−1.90947	−0.954736	−	0.297455i	$-0.903862\pi$
$3$	−3.30730	−1.90947	−0.954736	+	0.297455i	$0.903862\pi$
$4$	3.24395	1.62198
$5$	0	0
$5$	0	0
$6$	7.57362	3.09192
$7$	2.93910	1.11088	0.555438	−	0.831558i	$-0.312551\pi$
$7$	2.93910	1.11088	0.555438	+	0.831558i	$0.312551\pi$
$8$	−2.84861	−1.00714
$9$	7.93825	2.64608
$10$	0	0
$11$	−0.577601	−0.174153	−0.0870766	−	0.996202i	$-0.527752\pi$
$11$	−0.577601	−0.174153	−0.0870766	+	0.996202i	$0.527752\pi$
$12$	−10.7287	−3.09712
$13$	0.670397	0.185935	0.0929673	−	0.995669i	$-0.470365\pi$
$13$	0.670397	0.185935	0.0929673	+	0.995669i	$0.470365\pi$
$14$	−6.73045	−1.79879
$15$	0	0
$16$	0.0353277	0.00883192
$17$	0.351901	0.0853486	0.0426743	−	0.999089i	$-0.486412\pi$
$17$	0.351901	0.0853486	0.0426743	+	0.999089i	$0.486412\pi$
$18$	−18.1783	−4.28467
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−9.72050	−2.12119
$22$	1.32269	0.281998
$23$	4.12081	0.859248	0.429624	−	0.903008i	$-0.358646\pi$
$23$	4.12081	0.859248	0.429624	+	0.903008i	$0.358646\pi$
$24$	9.42123	1.92310
$25$	0	0
$26$	−1.53519	−0.301075
$27$	−16.3323	−3.14315
$28$	9.53431	1.80182
$29$	3.00800	0.558572	0.279286	−	0.960208i	$-0.409902\pi$
$29$	3.00800	0.558572	0.279286	+	0.960208i	$0.409902\pi$
$30$	0	0
$31$	0.297707	0.0534697	0.0267348	−	0.999643i	$-0.491489\pi$
$31$	0.297707	0.0534697	0.0267348	+	0.999643i	$0.491489\pi$
$32$	5.61633	0.992836
$33$	1.91030	0.332540
$34$	−0.805843	−0.138201
$35$	0	0
$36$	25.7513	4.29188
$37$	8.30595	1.36549	0.682745	−	0.730657i	$-0.260786\pi$
$37$	8.30595	1.36549	0.682745	+	0.730657i	$0.260786\pi$
$38$	0	0
$39$	−2.21721	−0.355037
$40$	0	0
$41$	2.67214	0.417318	0.208659	−	0.977988i	$-0.433090\pi$
$41$	2.67214	0.417318	0.208659	+	0.977988i	$0.433090\pi$
$42$	22.2596	3.43474
$43$	6.59830	1.00623	0.503116	−	0.864219i	$-0.332187\pi$
$43$	6.59830	1.00623	0.503116	+	0.864219i	$0.332187\pi$
$44$	−1.87371	−0.282472
$45$	0	0
$46$	−9.43652	−1.39134
$47$	−11.0325	−1.60925	−0.804625	−	0.593784i	$-0.797633\pi$
$47$	−11.0325	−1.60925	−0.804625	+	0.593784i	$0.797633\pi$
$48$	−0.116839	−0.0168643
$49$	1.63832	0.234046
$50$	0	0
$51$	−1.16384	−0.162971
$52$	2.17474	0.301582
$53$	4.10660	0.564085	0.282042	−	0.959402i	$-0.408988\pi$
$53$	4.10660	0.564085	0.282042	+	0.959402i	$0.408988\pi$
$54$	37.4004	5.08955
$55$	0	0
$56$	−8.37237	−1.11880
$57$	0	0
$58$	−6.88822	−0.904468
$59$	0.610572	0.0794897	0.0397448	−	0.999210i	$-0.487345\pi$
$59$	0.610572	0.0794897	0.0397448	+	0.999210i	$0.487345\pi$
$60$	0	0
$61$	1.02693	0.131485	0.0657426	−	0.997837i	$-0.479058\pi$
$61$	1.02693	0.131485	0.0657426	+	0.997837i	$0.479058\pi$
$62$	−0.681739	−0.0865809
$63$	23.3313	2.93947
$64$	−12.9319	−1.61648
$65$	0	0
$66$	−4.37452	−0.538467
$67$	3.33593	0.407548	0.203774	−	0.979018i	$-0.434679\pi$
$67$	3.33593	0.407548	0.203774	+	0.979018i	$0.434679\pi$
$68$	1.14155	0.138433
$69$	−13.6288	−1.64071
$70$	0	0
$71$	−13.2247	−1.56948	−0.784742	−	0.619823i	$-0.787205\pi$
$71$	−13.2247	−1.56948	−0.784742	+	0.619823i	$0.787205\pi$
$72$	−22.6130	−2.66497
$73$	−7.13879	−0.835532	−0.417766	−	0.908555i	$-0.637187\pi$
$73$	−7.13879	−0.835532	−0.417766	+	0.908555i	$0.637187\pi$
$74$	−19.0204	−2.21107
$75$	0	0
$76$	0	0
$77$	−1.69763	−0.193463
$78$	5.07733	0.574894
$79$	1.54232	0.173525	0.0867623	−	0.996229i	$-0.472348\pi$
$79$	1.54232	0.173525	0.0867623	+	0.996229i	$0.472348\pi$
$80$	0	0
$81$	30.2010	3.35567
$82$	−6.11911	−0.675743
$83$	−13.3186	−1.46191	−0.730953	−	0.682428i	$-0.760924\pi$
$83$	−13.3186	−1.46191	−0.730953	+	0.682428i	$0.760924\pi$
$84$	−31.5328	−3.44052
$85$	0	0
$86$	−15.1099	−1.62934
$87$	−9.94837	−1.06658
$88$	1.64536	0.175396
$89$	−6.57130	−0.696556	−0.348278	−	0.937391i	$-0.613234\pi$
$89$	−6.57130	−0.696556	−0.348278	+	0.937391i	$0.613234\pi$
$90$	0	0
$91$	1.97037	0.206550
$92$	13.3677	1.39368
$93$	−0.984606	−0.102099
$94$	25.2640	2.60578
$95$	0	0
$96$	−18.5749	−1.89579
$97$	−12.1979	−1.23851	−0.619255	−	0.785190i	$-0.712565\pi$
$97$	−12.1979	−1.23851	−0.619255	+	0.785190i	$0.712565\pi$
$98$	−3.75170	−0.378979
$99$	−4.58513	−0.460823
$100$	0	0
$101$	−0.580821	−0.0577939	−0.0288969	−	0.999582i	$-0.509199\pi$
$101$	−0.580821	−0.0577939	−0.0288969	+	0.999582i	$0.509199\pi$
$102$	2.66516	0.263891
$103$	6.47111	0.637617	0.318809	−	0.947819i	$-0.396717\pi$
$103$	6.47111	0.637617	0.318809	+	0.947819i	$0.396717\pi$
$104$	−1.90970	−0.187262
$105$	0	0
$106$	−9.40398	−0.913396
$107$	−18.3788	−1.77675	−0.888374	−	0.459120i	$-0.848165\pi$
$107$	−18.3788	−1.77675	−0.888374	+	0.459120i	$0.848165\pi$
$108$	−52.9811	−5.09811
$109$	−2.50969	−0.240385	−0.120192	−	0.992751i	$-0.538351\pi$
$109$	−2.50969	−0.240385	−0.120192	+	0.992751i	$0.538351\pi$
$110$	0	0
$111$	−27.4703	−2.60737
$112$	0.103832	0.00981117
$113$	11.3386	1.06665	0.533325	−	0.845911i	$-0.320942\pi$
$113$	11.3386	1.06665	0.533325	+	0.845911i	$0.320942\pi$
$114$	0	0
$115$	0	0
$116$	9.75781	0.905990
$117$	5.32178	0.491998
$118$	−1.39819	−0.128714
$119$	1.03427	0.0948117
$120$	0	0
$121$	−10.6664	−0.969671
$122$	−2.35164	−0.212908
$123$	−8.83757	−0.796857
$124$	0.965746	0.0867266
$125$	0	0
$126$	−53.4280	−4.75974
$127$	−19.1921	−1.70302	−0.851512	−	0.524336i	$-0.824314\pi$
$127$	−19.1921	−1.70302	−0.851512	+	0.524336i	$0.824314\pi$
$128$	18.3809	1.62466
$129$	−21.8226	−1.92137
$130$	0	0
$131$	−6.85020	−0.598505	−0.299252	−	0.954174i	$-0.596737\pi$
$131$	−6.85020	−0.598505	−0.299252	+	0.954174i	$0.596737\pi$
$132$	6.19692	0.539373
$133$	0	0
$134$	−7.63916	−0.659923
$135$	0	0
$136$	−1.00243	−0.0859577
$137$	−13.2418	−1.13132	−0.565660	−	0.824638i	$-0.691379\pi$
$137$	−13.2418	−1.13132	−0.565660	+	0.824638i	$0.691379\pi$
$138$	31.2094	2.65672
$139$	2.90988	0.246813	0.123406	−	0.992356i	$-0.460618\pi$
$139$	2.90988	0.246813	0.123406	+	0.992356i	$0.460618\pi$
$140$	0	0
$141$	36.4877	3.07282
$142$	30.2842	2.54139
$143$	−0.387222	−0.0323811
$144$	0.280440	0.0233700
$145$	0	0
$146$	16.3476	1.35294
$147$	−5.41842	−0.446904
$148$	26.9441	2.21479
$149$	−8.85659	−0.725560	−0.362780	−	0.931875i	$-0.618172\pi$
$149$	−8.85659	−0.725560	−0.362780	+	0.931875i	$0.618172\pi$
$150$	0	0
$151$	8.37160	0.681271	0.340636	−	0.940195i	$-0.389358\pi$
$151$	8.37160	0.681271	0.340636	+	0.940195i	$0.389358\pi$
$152$	0	0
$153$	2.79348	0.225839
$154$	3.88751	0.313265
$155$	0	0
$156$	−7.19251	−0.575862
$157$	15.8665	1.26629	0.633143	−	0.774035i	$-0.281764\pi$
$157$	15.8665	1.26629	0.633143	+	0.774035i	$0.281764\pi$
$158$	−3.53186	−0.280980
$159$	−13.5818	−1.07710
$160$	0	0
$161$	12.1115	0.954518
$162$	−69.1593	−5.43367
$163$	−9.72260	−0.761533	−0.380766	−	0.924671i	$-0.624340\pi$
$163$	−9.72260	−0.761533	−0.380766	+	0.924671i	$0.624340\pi$
$164$	8.66830	0.676880
$165$	0	0
$166$	30.4991	2.36719
$167$	−0.282149	−0.0218333	−0.0109167	−	0.999940i	$-0.503475\pi$
$167$	−0.282149	−0.0218333	−0.0109167	+	0.999940i	$0.503475\pi$
$168$	27.6899	2.13633
$169$	−12.5506	−0.965428
$170$	0	0
$171$	0	0
$172$	21.4046	1.63208
$173$	−15.1289	−1.15023	−0.575116	−	0.818072i	$-0.695043\pi$
$173$	−15.1289	−1.15023	−0.575116	+	0.818072i	$0.695043\pi$
$174$	22.7814	1.72706
$175$	0	0
$176$	−0.0204053	−0.00153811
$177$	−2.01935	−0.151783
$178$	15.0481	1.12790
$179$	−14.4533	−1.08029	−0.540145	−	0.841572i	$-0.681630\pi$
$179$	−14.4533	−1.08029	−0.540145	+	0.841572i	$0.681630\pi$
$180$	0	0
$181$	−6.96487	−0.517695	−0.258847	−	0.965918i	$-0.583343\pi$
$181$	−6.96487	−0.517695	−0.258847	+	0.965918i	$0.583343\pi$
$182$	−4.51207	−0.334457
$183$	−3.39637	−0.251067
$184$	−11.7386	−0.865380
$185$	0	0
$186$	2.25472	0.165324
$187$	−0.203258	−0.0148637
$188$	−35.7888	−2.61016
$189$	−48.0022	−3.49165
$190$	0	0
$191$	5.49050	0.397279	0.198639	−	0.980073i	$-0.436348\pi$
$191$	5.49050	0.397279	0.198639	+	0.980073i	$0.436348\pi$
$192$	42.7696	3.08663
$193$	6.47685	0.466214	0.233107	−	0.972451i	$-0.425111\pi$
$193$	6.47685	0.466214	0.233107	+	0.972451i	$0.425111\pi$
$194$	27.9328	2.00546
$195$	0	0
$196$	5.31463	0.379617
$197$	9.29455	0.662209	0.331104	−	0.943594i	$-0.392579\pi$
$197$	9.29455	0.662209	0.331104	+	0.943594i	$0.392579\pi$
$198$	10.4998	0.746189
$199$	−24.3069	−1.72307	−0.861534	−	0.507700i	$-0.830496\pi$
$199$	−24.3069	−1.72307	−0.861534	+	0.507700i	$0.830496\pi$
$200$	0	0
$201$	−11.0329	−0.778202
$202$	1.33006	0.0935828
$203$	8.84082	0.620504
$204$	−3.77545	−0.264335
$205$	0	0
$206$	−14.8186	−1.03246
$207$	32.7120	2.27364
$208$	0.0236836	0.00164216
$209$	0	0
$210$	0	0
$211$	23.9674	1.64999	0.824994	−	0.565142i	$-0.191179\pi$
$211$	23.9674	1.64999	0.824994	+	0.565142i	$0.191179\pi$
$212$	13.3216	0.914933
$213$	43.7381	2.99688
$214$	42.0869	2.87700
$215$	0	0
$216$	46.5243	3.16558
$217$	0.874990	0.0593982
$218$	5.74711	0.389243
$219$	23.6101	1.59542
$220$	0	0
$221$	0.235914	0.0158693
$222$	62.9061	4.22198
$223$	−20.5690	−1.37740	−0.688701	−	0.725045i	$-0.741819\pi$
$223$	−20.5690	−1.37740	−0.688701	+	0.725045i	$0.741819\pi$
$224$	16.5070	1.10292
$225$	0	0
$226$	−25.9651	−1.72717
$227$	−12.6949	−0.842593	−0.421297	−	0.906923i	$-0.638425\pi$
$227$	−12.6949	−0.842593	−0.421297	+	0.906923i	$0.638425\pi$
$228$	0	0
$229$	5.76019	0.380644	0.190322	−	0.981722i	$-0.439047\pi$
$229$	5.76019	0.380644	0.190322	+	0.981722i	$0.439047\pi$
$230$	0	0
$231$	5.61456	0.369411
$232$	−8.56863	−0.562558
$233$	2.77852	0.182027	0.0910135	−	0.995850i	$-0.470989\pi$
$233$	2.77852	0.182027	0.0910135	+	0.995850i	$0.470989\pi$
$234$	−12.1867	−0.796669
$235$	0	0
$236$	1.98067	0.128930
$237$	−5.10092	−0.331340
$238$	−2.36845	−0.153524
$239$	19.4587	1.25868	0.629340	−	0.777130i	$-0.283325\pi$
$239$	19.4587	1.25868	0.629340	+	0.777130i	$0.283325\pi$
$240$	0	0
$241$	−7.23964	−0.466346	−0.233173	−	0.972435i	$-0.574911\pi$
$241$	−7.23964	−0.466346	−0.233173	+	0.972435i	$0.574911\pi$
$242$	24.4257	1.57014
$243$	−50.8870	−3.26441
$244$	3.33132	0.213266
$245$	0	0
$246$	20.2378	1.29031
$247$	0	0
$248$	−0.848051	−0.0538513
$249$	44.0486	2.79147
$250$	0	0
$251$	14.8558	0.937692	0.468846	−	0.883280i	$-0.344670\pi$
$251$	14.8558	0.937692	0.468846	+	0.883280i	$0.344670\pi$
$252$	75.6857	4.76775
$253$	−2.38018	−0.149641
$254$	43.9493	2.75762
$255$	0	0
$256$	−16.2280	−1.01425
$257$	−19.7558	−1.23233	−0.616166	−	0.787616i	$-0.711315\pi$
$257$	−19.7558	−1.23233	−0.616166	+	0.787616i	$0.711315\pi$
$258$	49.9730	3.11118
$259$	24.4120	1.51689
$260$	0	0
$261$	23.8782	1.47803
$262$	15.6867	0.969130
$263$	−11.8513	−0.730780	−0.365390	−	0.930854i	$-0.619064\pi$
$263$	−11.8513	−0.730780	−0.365390	+	0.930854i	$0.619064\pi$
$264$	−5.44171	−0.334914
$265$	0	0
$266$	0	0
$267$	21.7333	1.33005
$268$	10.8216	0.661034
$269$	−10.8758	−0.663111	−0.331555	−	0.943436i	$-0.607573\pi$
$269$	−10.8758	−0.663111	−0.331555	+	0.943436i	$0.607573\pi$
$270$	0	0
$271$	−5.87245	−0.356726	−0.178363	−	0.983965i	$-0.557080\pi$
$271$	−5.87245	−0.356726	−0.178363	+	0.983965i	$0.557080\pi$
$272$	0.0124319	0.000753792 0
$273$	−6.51659	−0.394402
$274$	30.3232	1.83189
$275$	0	0
$276$	−44.2110	−2.66119
$277$	23.8127	1.43077	0.715385	−	0.698731i	$-0.246251\pi$
$277$	23.8127	1.43077	0.715385	+	0.698731i	$0.246251\pi$
$278$	−6.66353	−0.399652
$279$	2.36327	0.141485
$280$	0	0
$281$	−7.13920	−0.425889	−0.212945	−	0.977064i	$-0.568305\pi$
$281$	−7.13920	−0.425889	−0.212945	+	0.977064i	$0.568305\pi$
$282$	−83.5556	−4.97566
$283$	−26.7342	−1.58918	−0.794592	−	0.607144i	$-0.792315\pi$
$283$	−26.7342	−1.58918	−0.794592	+	0.607144i	$0.792315\pi$
$284$	−42.9003	−2.54567
$285$	0	0
$286$	0.886725	0.0524332
$287$	7.85369	0.463589
$288$	44.5838	2.62713
$289$	−16.8762	−0.992716
$290$	0	0
$291$	40.3422	2.36490
$292$	−23.1579	−1.35521
$293$	−1.07337	−0.0627069	−0.0313535	−	0.999508i	$-0.509982\pi$
$293$	−1.07337	−0.0627069	−0.0313535	+	0.999508i	$0.509982\pi$
$294$	12.4080	0.723650
$295$	0	0
$296$	−23.6605	−1.37524
$297$	9.43353	0.547389
$298$	20.2813	1.17486
$299$	2.76258	0.159764
$300$	0	0
$301$	19.3931	1.11780
$302$	−19.1707	−1.10315
$303$	1.92095	0.110356
$304$	0	0
$305$	0	0
$306$	−6.39698	−0.365691
$307$	25.9701	1.48219	0.741097	−	0.671398i	$-0.234306\pi$
$307$	25.9701	1.48219	0.741097	+	0.671398i	$0.234306\pi$
$308$	−5.50702	−0.313792
$309$	−21.4019	−1.21751
$310$	0	0
$311$	19.0509	1.08028	0.540139	−	0.841576i	$-0.318372\pi$
$311$	19.0509	1.08028	0.540139	+	0.841576i	$0.318372\pi$
$312$	6.31596	0.357571
$313$	15.3992	0.870416	0.435208	−	0.900330i	$-0.356675\pi$
$313$	15.3992	0.870416	0.435208	+	0.900330i	$0.356675\pi$
$314$	−36.3338	−2.05044
$315$	0	0
$316$	5.00321	0.281453
$317$	−25.5404	−1.43449	−0.717245	−	0.696821i	$-0.754597\pi$
$317$	−25.5404	−1.43449	−0.717245	+	0.696821i	$0.754597\pi$
$318$	31.1018	1.74410
$319$	−1.73742	−0.0972770
$320$	0	0
$321$	60.7843	3.39265
$322$	−27.7349	−1.54560
$323$	0	0
$324$	97.9707	5.44282
$325$	0	0
$326$	22.2644	1.23311
$327$	8.30030	0.459008
$328$	−7.61189	−0.420297
$329$	−32.4255	−1.78768
$330$	0	0
$331$	4.53178	0.249089	0.124545	−	0.992214i	$-0.460253\pi$
$331$	4.53178	0.249089	0.124545	+	0.992214i	$0.460253\pi$
$332$	−43.2049	−2.37118
$333$	65.9347	3.61320
$334$	0.646112	0.0353537
$335$	0	0
$336$	−0.343403	−0.0187342
$337$	−20.3396	−1.10797	−0.553984	−	0.832527i	$-0.686893\pi$
$337$	−20.3396	−1.10797	−0.553984	+	0.832527i	$0.686893\pi$
$338$	28.7404	1.56327
$339$	−37.5003	−2.03674
$340$	0	0
$341$	−0.171955	−0.00931191
$342$	0	0
$343$	−15.7585	−0.850880
$344$	−18.7960	−1.01341
$345$	0	0
$346$	34.6448	1.86252
$347$	−27.2663	−1.46373	−0.731867	−	0.681448i	$-0.761351\pi$
$347$	−27.2663	−1.46373	−0.731867	+	0.681448i	$0.761351\pi$
$348$	−32.2720	−1.72996
$349$	12.6223	0.675656	0.337828	−	0.941208i	$-0.390308\pi$
$349$	12.6223	0.675656	0.337828	+	0.941208i	$0.390308\pi$
$350$	0	0
$351$	−10.9491	−0.584420
$352$	−3.24399	−0.172905
$353$	−30.7991	−1.63927	−0.819636	−	0.572884i	$-0.805825\pi$
$353$	−30.7991	−1.63927	−0.819636	+	0.572884i	$0.805825\pi$
$354$	4.62424	0.245775
$355$	0	0
$356$	−21.3170	−1.12980
$357$	−3.42066	−0.181040
$358$	33.0976	1.74926
$359$	−17.2365	−0.909708	−0.454854	−	0.890566i	$-0.650309\pi$
$359$	−17.2365	−0.909708	−0.454854	+	0.890566i	$0.650309\pi$
$360$	0	0
$361$	0	0
$362$	15.9493	0.838278
$363$	35.2769	1.85156
$364$	6.39177	0.335020
$365$	0	0
$366$	7.77759	0.406541
$367$	30.0937	1.57088	0.785440	−	0.618938i	$-0.212437\pi$
$367$	30.0937	1.57088	0.785440	+	0.618938i	$0.212437\pi$
$368$	0.145579	0.00758881
$369$	21.2121	1.10426
$370$	0	0
$371$	12.0697	0.626628
$372$	−3.19401	−0.165602
$373$	6.13352	0.317581	0.158791	−	0.987312i	$-0.449240\pi$
$373$	6.13352	0.317581	0.158791	+	0.987312i	$0.449240\pi$
$374$	0.465455	0.0240681
$375$	0	0
$376$	31.4272	1.62073
$377$	2.01655	0.103858
$378$	109.924	5.65386
$379$	30.8958	1.58701	0.793505	−	0.608564i	$-0.208254\pi$
$379$	30.8958	1.58701	0.793505	+	0.608564i	$0.208254\pi$
$380$	0	0
$381$	63.4741	3.25187
$382$	−12.5731	−0.643294
$383$	−4.65116	−0.237663	−0.118831	−	0.992914i	$-0.537915\pi$
$383$	−4.65116	−0.237663	−0.118831	+	0.992914i	$0.537915\pi$
$384$	−60.7912	−3.10224
$385$	0	0
$386$	−14.8318	−0.754918
$387$	52.3790	2.66257
$388$	−39.5694	−2.00883
$389$	−16.1770	−0.820207	−0.410104	−	0.912039i	$-0.634507\pi$
$389$	−16.1770	−0.820207	−0.410104	+	0.912039i	$0.634507\pi$
$390$	0	0
$391$	1.45012	0.0733356
$392$	−4.66694	−0.235716
$393$	22.6557	1.14283
$394$	−21.2842	−1.07228
$395$	0	0
$396$	−14.8740	−0.747445
$397$	9.93505	0.498626	0.249313	−	0.968423i	$-0.419795\pi$
$397$	9.93505	0.498626	0.249313	+	0.968423i	$0.419795\pi$
$398$	55.6619	2.79008
$399$	0	0
$400$	0	0
$401$	−12.9340	−0.645893	−0.322946	−	0.946417i	$-0.604673\pi$
$401$	−12.9340	−0.645893	−0.322946	+	0.946417i	$0.604673\pi$
$402$	25.2650	1.26010
$403$	0.199582	0.00994187
$404$	−1.88416	−0.0937403
$405$	0	0
$406$	−20.2452	−1.00475
$407$	−4.79752	−0.237804
$408$	3.31534	0.164134
$409$	−6.24031	−0.308564	−0.154282	−	0.988027i	$-0.549306\pi$
$409$	−6.24031	−0.308564	−0.154282	+	0.988027i	$0.549306\pi$
$410$	0	0
$411$	43.7945	2.16022
$412$	20.9920	1.03420
$413$	1.79453	0.0883032
$414$	−74.9094	−3.68160
$415$	0	0
$416$	3.76517	0.184603
$417$	−9.62385	−0.471282
$418$	0	0
$419$	−30.5403	−1.49199	−0.745995	−	0.665951i	$-0.768026\pi$
$419$	−30.5403	−1.49199	−0.745995	+	0.665951i	$0.768026\pi$
$420$	0	0
$421$	36.5695	1.78229	0.891144	−	0.453721i	$-0.149904\pi$
$421$	36.5695	1.78229	0.891144	+	0.453721i	$0.149904\pi$
$422$	−54.8847	−2.67174
$423$	−87.5784	−4.25821
$424$	−11.6981	−0.568111
$425$	0	0
$426$	−100.159	−4.85271
$427$	3.01826	0.146064
$428$	−59.6201	−2.88184
$429$	1.28066	0.0618308
$430$	0	0
$431$	23.9033	1.15138	0.575691	−	0.817667i	$-0.304733\pi$
$431$	23.9033	1.15138	0.575691	+	0.817667i	$0.304733\pi$
$432$	−0.576981	−0.0277600
$433$	14.6544	0.704246	0.352123	−	0.935954i	$-0.385460\pi$
$433$	14.6544	0.704246	0.352123	+	0.935954i	$0.385460\pi$
$434$	−2.00370	−0.0961806
$435$	0	0
$436$	−8.14132	−0.389898
$437$	0	0
$438$	−54.0664	−2.58339
$439$	−17.0244	−0.812529	−0.406264	−	0.913756i	$-0.633169\pi$
$439$	−17.0244	−0.812529	−0.406264	+	0.913756i	$0.633169\pi$
$440$	0	0
$441$	13.0054	0.619304
$442$	−0.540234	−0.0256963
$443$	35.9913	1.71000	0.854999	−	0.518630i	$-0.173558\pi$
$443$	35.9913	1.71000	0.854999	+	0.518630i	$0.173558\pi$
$444$	−89.1124	−4.22909
$445$	0	0
$446$	47.1024	2.23036
$447$	29.2914	1.38544
$448$	−38.0081	−1.79571
$449$	3.55766	0.167896	0.0839481	−	0.996470i	$-0.473247\pi$
$449$	3.55766	0.167896	0.0839481	+	0.996470i	$0.473247\pi$
$450$	0	0
$451$	−1.54343	−0.0726772
$452$	36.7820	1.73008
$453$	−27.6874	−1.30087
$454$	29.0710	1.36437
$455$	0	0
$456$	0	0
$457$	4.61695	0.215972	0.107986	−	0.994152i	$-0.465560\pi$
$457$	4.61695	0.215972	0.107986	+	0.994152i	$0.465560\pi$
$458$	−13.1907	−0.616359
$459$	−5.74735	−0.268263
$460$	0	0
$461$	−29.1737	−1.35875	−0.679377	−	0.733790i	$-0.737750\pi$
$461$	−29.1737	−1.35875	−0.679377	+	0.733790i	$0.737750\pi$
$462$	−12.8572	−0.598170
$463$	17.6378	0.819696	0.409848	−	0.912154i	$-0.365582\pi$
$463$	17.6378	0.819696	0.409848	+	0.912154i	$0.365582\pi$
$464$	0.106266	0.00493326
$465$	0	0
$466$	−6.36272	−0.294748
$467$	−16.9435	−0.784052	−0.392026	−	0.919954i	$-0.628226\pi$
$467$	−16.9435	−0.784052	−0.392026	+	0.919954i	$0.628226\pi$
$468$	17.2636	0.798010
$469$	9.80462	0.452735
$470$	0	0
$471$	−52.4754	−2.41794
$472$	−1.73928	−0.0800570
$473$	−3.81118	−0.175238
$474$	11.6809	0.536523
$475$	0	0
$476$	3.35514	0.153782
$477$	32.5992	1.49261
$478$	−44.5599	−2.03812
$479$	−14.4613	−0.660752	−0.330376	−	0.943849i	$-0.607176\pi$
$479$	−14.4613	−0.660752	−0.330376	+	0.943849i	$0.607176\pi$
$480$	0	0
$481$	5.56829	0.253892
$482$	16.5785	0.755132
$483$	−40.0563	−1.82262
$484$	−34.6012	−1.57278
$485$	0	0
$486$	116.530	5.28589
$487$	0.331932	0.0150413	0.00752064	−	0.999972i	$-0.497606\pi$
$487$	0.331932	0.0150413	0.00752064	+	0.999972i	$0.497606\pi$
$488$	−2.92533	−0.132424
$489$	32.1556	1.45413
$490$	0	0
$491$	−3.34188	−0.150817	−0.0754084	−	0.997153i	$-0.524026\pi$
$491$	−3.34188	−0.150817	−0.0754084	+	0.997153i	$0.524026\pi$
$492$	−28.6687	−1.29248
$493$	1.05852	0.0476733
$494$	0	0
$495$	0	0
$496$	0.0105173	0.000472240 0
$497$	−38.8688	−1.74350
$498$	−100.870	−4.52009
$499$	−14.0914	−0.630818	−0.315409	−	0.948956i	$-0.602142\pi$
$499$	−14.0914	−0.630818	−0.315409	+	0.948956i	$0.602142\pi$
$500$	0	0
$501$	0.933152	0.0416902
$502$	−34.0194	−1.51836
$503$	3.70599	0.165242	0.0826210	−	0.996581i	$-0.473671\pi$
$503$	3.70599	0.165242	0.0826210	+	0.996581i	$0.473671\pi$
$504$	−66.4619	−2.96045
$505$	0	0
$506$	5.45054	0.242306
$507$	41.5085	1.84346
$508$	−62.2583	−2.76226
$509$	35.3434	1.56657	0.783284	−	0.621664i	$-0.213543\pi$
$509$	35.3434	1.56657	0.783284	+	0.621664i	$0.213543\pi$
$510$	0	0
$511$	−20.9816	−0.928172
$512$	0.399682	0.0176636
$513$	0	0
$514$	45.2401	1.99546
$515$	0	0
$516$	−70.7915	−3.11642
$517$	6.37235	0.280256
$518$	−55.9028	−2.45623
$519$	50.0360	2.19634
$520$	0	0
$521$	5.04908	0.221204	0.110602	−	0.993865i	$-0.464722\pi$
$521$	5.04908	0.221204	0.110602	+	0.993865i	$0.464722\pi$
$522$	−54.6804	−2.39330
$523$	−23.3660	−1.02172	−0.510862	−	0.859663i	$-0.670674\pi$
$523$	−23.3660	−1.02172	−0.510862	+	0.859663i	$0.670674\pi$
$524$	−22.2217	−0.970761
$525$	0	0
$526$	27.1390	1.18332
$527$	0.104763	0.00456356
$528$	0.0674865	0.00293697
$529$	−6.01894	−0.261693
$530$	0	0
$531$	4.84687	0.210336
$532$	0	0
$533$	1.79139	0.0775939
$534$	−49.7685	−2.15369
$535$	0	0
$536$	−9.50276	−0.410457
$537$	47.8014	2.06278
$538$	24.9053	1.07374
$539$	−0.946294	−0.0407598
$540$	0	0
$541$	31.8509	1.36938	0.684689	−	0.728836i	$-0.259938\pi$
$541$	31.8509	1.36938	0.684689	+	0.728836i	$0.259938\pi$
$542$	13.4477	0.577629
$543$	23.0349	0.988523
$544$	1.97639	0.0847372
$545$	0	0
$546$	14.9228	0.638636
$547$	−29.7080	−1.27022	−0.635112	−	0.772420i	$-0.719046\pi$
$547$	−29.7080	−1.27022	−0.635112	+	0.772420i	$0.719046\pi$
$548$	−42.9557	−1.83498
$549$	8.15204	0.347921
$550$	0	0
$551$	0	0
$552$	38.8231	1.65242
$553$	4.53303	0.192764
$554$	−54.5304	−2.31678
$555$	0	0
$556$	9.43951	0.400324
$557$	21.6442	0.917093	0.458546	−	0.888670i	$-0.348370\pi$
$557$	21.6442	0.917093	0.458546	+	0.888670i	$0.348370\pi$
$558$	−5.41181	−0.229100
$559$	4.42348	0.187093
$560$	0	0
$561$	0.672237	0.0283819
$562$	16.3485	0.689622
$563$	5.92838	0.249852	0.124926	−	0.992166i	$-0.460131\pi$
$563$	5.92838	0.249852	0.124926	+	0.992166i	$0.460131\pi$
$564$	118.364	4.98404
$565$	0	0
$566$	61.2205	2.57329
$567$	88.7638	3.72773
$568$	37.6721	1.58069
$569$	−5.27877	−0.221297	−0.110649	−	0.993860i	$-0.535293\pi$
$569$	−5.27877	−0.221297	−0.110649	+	0.993860i	$0.535293\pi$
$570$	0	0
$571$	16.5322	0.691852	0.345926	−	0.938262i	$-0.387565\pi$
$571$	16.5322	0.691852	0.345926	+	0.938262i	$0.387565\pi$
$572$	−1.25613	−0.0525214
$573$	−18.1587	−0.758592
$574$	−17.9847	−0.750667
$575$	0	0
$576$	−102.656	−4.27735
$577$	−36.2634	−1.50966	−0.754832	−	0.655918i	$-0.772282\pi$
$577$	−36.2634	−1.50966	−0.754832	+	0.655918i	$0.772282\pi$
$578$	38.6459	1.60746
$579$	−21.4209	−0.890223
$580$	0	0
$581$	−39.1447	−1.62400
$582$	−92.3823	−3.82937
$583$	−2.37197	−0.0982371
$584$	20.3356	0.841495
$585$	0	0
$586$	2.45798	0.101538
$587$	26.6519	1.10004	0.550021	−	0.835151i	$-0.314620\pi$
$587$	26.6519	1.10004	0.550021	+	0.835151i	$0.314620\pi$
$588$	−17.5771	−0.724867
$589$	0	0
$590$	0	0
$591$	−30.7399	−1.26447
$592$	0.293430	0.0120599
$593$	27.6836	1.13683	0.568414	−	0.822742i	$-0.307557\pi$
$593$	27.6836	1.13683	0.568414	+	0.822742i	$0.307557\pi$
$594$	−21.6025	−0.886360
$595$	0	0
$596$	−28.7304	−1.17684
$597$	80.3901	3.29015
$598$	−6.32621	−0.258698
$599$	−34.3545	−1.40369	−0.701843	−	0.712331i	$-0.747639\pi$
$599$	−34.3545	−1.40369	−0.701843	+	0.712331i	$0.747639\pi$
$600$	0	0
$601$	16.8903	0.688970	0.344485	−	0.938792i	$-0.388053\pi$
$601$	16.8903	0.688970	0.344485	+	0.938792i	$0.388053\pi$
$602$	−44.4096	−1.81000
$603$	26.4814	1.07841
$604$	27.1571	1.10501
$605$	0	0
$606$	−4.39892	−0.178694
$607$	4.71187	0.191249	0.0956245	−	0.995417i	$-0.469515\pi$
$607$	4.71187	0.191249	0.0956245	+	0.995417i	$0.469515\pi$
$608$	0	0
$609$	−29.2393	−1.18483
$610$	0	0
$611$	−7.39613	−0.299215
$612$	9.06192	0.366306
$613$	41.0465	1.65785	0.828926	−	0.559358i	$-0.188952\pi$
$613$	41.0465	1.65785	0.828926	+	0.559358i	$0.188952\pi$
$614$	−59.4708	−2.40005
$615$	0	0
$616$	4.83588	0.194843
$617$	6.47810	0.260798	0.130399	−	0.991462i	$-0.458374\pi$
$617$	6.47810	0.260798	0.130399	+	0.991462i	$0.458374\pi$
$618$	49.0097	1.97146
$619$	−36.6443	−1.47286	−0.736429	−	0.676514i	$-0.763490\pi$
$619$	−36.6443	−1.47286	−0.736429	+	0.676514i	$0.763490\pi$
$620$	0	0
$621$	−67.3021	−2.70074
$622$	−43.6260	−1.74924
$623$	−19.3137	−0.773788
$624$	−0.0783287	−0.00313566
$625$	0	0
$626$	−35.2637	−1.40942
$627$	0	0
$628$	51.4703	2.05389
$629$	2.92288	0.116543
$630$	0	0
$631$	−15.1190	−0.601878	−0.300939	−	0.953643i	$-0.597300\pi$
$631$	−15.1190	−0.601878	−0.300939	+	0.953643i	$0.597300\pi$
$632$	−4.39347	−0.174763
$633$	−79.2676	−3.15060
$634$	58.4866	2.32280
$635$	0	0
$636$	−44.0586	−1.74704
$637$	1.09832	0.0435172
$638$	3.97864	0.157516
$639$	−104.981	−4.15298
$640$	0	0
$641$	−10.5736	−0.417632	−0.208816	−	0.977955i	$-0.566961\pi$
$641$	−10.5736	−0.417632	−0.208816	+	0.977955i	$0.566961\pi$
$642$	−139.194	−5.49356
$643$	3.49394	0.137788	0.0688938	−	0.997624i	$-0.478053\pi$
$643$	3.49394	0.137788	0.0688938	+	0.997624i	$0.478053\pi$
$644$	39.2891	1.54821
$645$	0	0
$646$	0	0
$647$	−21.5689	−0.847961	−0.423981	−	0.905671i	$-0.639368\pi$
$647$	−21.5689	−0.847961	−0.423981	+	0.905671i	$0.639368\pi$
$648$	−86.0310	−3.37962
$649$	−0.352667	−0.0138434
$650$	0	0
$651$	−2.89386	−0.113419
$652$	−31.5397	−1.23519
$653$	27.9780	1.09486	0.547432	−	0.836850i	$-0.315605\pi$
$653$	27.9780	1.09486	0.547432	+	0.836850i	$0.315605\pi$
$654$	−19.0074	−0.743249
$655$	0	0
$656$	0.0944005	0.00368572
$657$	−56.6694	−2.21089
$658$	74.2534	2.89470
$659$	5.66571	0.220705	0.110352	−	0.993893i	$-0.464802\pi$
$659$	5.66571	0.220705	0.110352	+	0.993893i	$0.464802\pi$
$660$	0	0
$661$	−0.130235	−0.00506555	−0.00253277	−	0.999997i	$-0.500806\pi$
$661$	−0.130235	−0.00506555	−0.00253277	+	0.999997i	$0.500806\pi$
$662$	−10.3776	−0.403338
$663$	−0.780237	−0.0303019
$664$	37.9395	1.47234
$665$	0	0
$666$	−150.988	−5.85068
$667$	12.3954	0.479951
$668$	−0.915278	−0.0354132
$669$	68.0279	2.63011
$670$	0	0
$671$	−0.593157	−0.0228986
$672$	−54.5935	−2.10599
$673$	41.4320	1.59709	0.798543	−	0.601937i	$-0.205604\pi$
$673$	41.4320	1.59709	0.798543	+	0.601937i	$0.205604\pi$
$674$	46.5770	1.79408
$675$	0	0
$676$	−40.7135	−1.56590
$677$	−19.2643	−0.740386	−0.370193	−	0.928955i	$-0.620708\pi$
$677$	−19.2643	−0.740386	−0.370193	+	0.928955i	$0.620708\pi$
$678$	85.8745	3.29799
$679$	−35.8509	−1.37583
$680$	0	0
$681$	41.9860	1.60891
$682$	0.393773	0.0150783
$683$	−14.0647	−0.538170	−0.269085	−	0.963116i	$-0.586721\pi$
$683$	−14.0647	−0.538170	−0.269085	+	0.963116i	$0.586721\pi$
$684$	0	0
$685$	0	0
$686$	36.0865	1.37779
$687$	−19.0507	−0.726829
$688$	0.233103	0.00888696
$689$	2.75305	0.104883
$690$	0	0
$691$	−11.3257	−0.430849	−0.215425	−	0.976520i	$-0.569114\pi$
$691$	−11.3257	−0.430849	−0.215425	+	0.976520i	$0.569114\pi$
$692$	−49.0776	−1.86565
$693$	−13.4762	−0.511918
$694$	62.4390	2.37015
$695$	0	0
$696$	28.3391	1.07419
$697$	0.940329	0.0356175
$698$	−28.9046	−1.09406
$699$	−9.18941	−0.347575
$700$	0	0
$701$	−15.4332	−0.582905	−0.291453	−	0.956585i	$-0.594139\pi$
$701$	−15.4332	−0.582905	−0.291453	+	0.956585i	$0.594139\pi$
$702$	25.0731	0.946323
$703$	0	0
$704$	7.46945	0.281516
$705$	0	0
$706$	70.5290	2.65440
$707$	−1.70709	−0.0642018
$708$	−6.55066	−0.246189
$709$	19.0828	0.716671	0.358335	−	0.933593i	$-0.383344\pi$
$709$	19.0828	0.716671	0.358335	+	0.933593i	$0.383344\pi$
$710$	0	0
$711$	12.2433	0.459160
$712$	18.7191	0.701528
$713$	1.22679	0.0459437
$714$	7.83319	0.293150
$715$	0	0
$716$	−46.8858	−1.75220
$717$	−64.3559	−2.40341
$718$	39.4710	1.47305
$719$	−11.4199	−0.425891	−0.212946	−	0.977064i	$-0.568306\pi$
$719$	−11.4199	−0.425891	−0.212946	+	0.977064i	$0.568306\pi$
$720$	0	0
$721$	19.0192	0.708314
$722$	0	0
$723$	23.9437	0.890475
$724$	−22.5937	−0.839689
$725$	0	0
$726$	−80.7830	−2.99814
$727$	10.9252	0.405192	0.202596	−	0.979262i	$-0.435062\pi$
$727$	10.9252	0.405192	0.202596	+	0.979262i	$0.435062\pi$
$728$	−5.61281	−0.208025
$729$	77.6958	2.87762
$730$	0	0
$731$	2.32195	0.0858805
$732$	−11.0177	−0.407225
$733$	−23.5729	−0.870685	−0.435343	−	0.900265i	$-0.643373\pi$
$733$	−23.5729	−0.870685	−0.435343	+	0.900265i	$0.643373\pi$
$734$	−68.9137	−2.54365
$735$	0	0
$736$	23.1438	0.853092
$737$	−1.92683	−0.0709758
$738$	−48.5750	−1.78807
$739$	−2.24661	−0.0826429	−0.0413214	−	0.999146i	$-0.513157\pi$
$739$	−2.24661	−0.0826429	−0.0413214	+	0.999146i	$0.513157\pi$
$740$	0	0
$741$	0	0
$742$	−27.6393	−1.01467
$743$	26.9188	0.987554	0.493777	−	0.869588i	$-0.335616\pi$
$743$	26.9188	0.987554	0.493777	+	0.869588i	$0.335616\pi$
$744$	2.80476	0.102828
$745$	0	0
$746$	−14.0456	−0.514244
$747$	−105.726	−3.86832
$748$	−0.659361	−0.0241086
$749$	−54.0173	−1.97375
$750$	0	0
$751$	−34.1357	−1.24563	−0.622816	−	0.782369i	$-0.714011\pi$
$751$	−34.1357	−1.24563	−0.622816	+	0.782369i	$0.714011\pi$
$752$	−0.389751	−0.0142128
$753$	−49.1327	−1.79050
$754$	−4.61785	−0.168172
$755$	0	0
$756$	−155.717	−5.66337
$757$	−18.8443	−0.684909	−0.342455	−	0.939534i	$-0.611258\pi$
$757$	−18.8443	−0.684909	−0.342455	+	0.939534i	$0.611258\pi$
$758$	−70.7504	−2.56977
$759$	7.87198	0.285735
$760$	0	0
$761$	−10.8012	−0.391544	−0.195772	−	0.980649i	$-0.562721\pi$
$761$	−10.8012	−0.391544	−0.195772	+	0.980649i	$0.562721\pi$
$762$	−145.354	−5.26560
$763$	−7.37623	−0.267038
$764$	17.8109	0.644377
$765$	0	0
$766$	10.6510	0.384836
$767$	0.409325	0.0147799
$768$	53.6707	1.93668
$769$	48.9272	1.76436	0.882179	−	0.470914i	$-0.156076\pi$
$769$	48.9272	1.76436	0.882179	+	0.470914i	$0.156076\pi$
$770$	0	0
$771$	65.3384	2.35310
$772$	21.0106	0.756188
$773$	26.7556	0.962332	0.481166	−	0.876630i	$-0.340213\pi$
$773$	26.7556	0.962332	0.481166	+	0.876630i	$0.340213\pi$
$774$	−119.946	−4.31138
$775$	0	0
$776$	34.7471	1.24735
$777$	−80.7380	−2.89646
$778$	37.0448	1.32812
$779$	0	0
$780$	0	0
$781$	7.63860	0.273330
$782$	−3.32072	−0.118749
$783$	−49.1275	−1.75567
$784$	0.0578781	0.00206707
$785$	0	0
$786$	−51.8808	−1.85053
$787$	−21.8346	−0.778320	−0.389160	−	0.921170i	$-0.627235\pi$
$787$	−21.8346	−0.778320	−0.389160	+	0.921170i	$0.627235\pi$
$788$	30.1511	1.07409
$789$	39.1957	1.39540
$790$	0	0
$791$	33.3254	1.18492
$792$	13.0613	0.464112
$793$	0.688452	0.0244477
$794$	−22.7509	−0.807401
$795$	0	0
$796$	−78.8503	−2.79478
$797$	13.0244	0.461347	0.230673	−	0.973031i	$-0.425907\pi$
$797$	13.0244	0.461347	0.230673	+	0.973031i	$0.425907\pi$
$798$	0	0
$799$	−3.88234	−0.137347
$800$	0	0
$801$	−52.1646	−1.84315
$802$	29.6184	1.04586
$803$	4.12337	0.145510
$804$	−35.7903	−1.26222
$805$	0	0
$806$	−0.457036	−0.0160984
$807$	35.9696	1.26619
$808$	1.65454	0.0582063
$809$	−9.02269	−0.317221	−0.158610	−	0.987341i	$-0.550701\pi$
$809$	−9.02269	−0.317221	−0.158610	+	0.987341i	$0.550701\pi$
$810$	0	0
$811$	−22.3544	−0.784969	−0.392484	−	0.919759i	$-0.628384\pi$
$811$	−22.3544	−0.784969	−0.392484	+	0.919759i	$0.628384\pi$
$812$	28.6792	1.00644
$813$	19.4220	0.681158
$814$	10.9862	0.385065
$815$	0	0
$816$	−0.0411159	−0.00143934
$817$	0	0
$818$	14.2901	0.499642
$819$	15.6412	0.546549
$820$	0	0
$821$	−34.8750	−1.21715	−0.608573	−	0.793498i	$-0.708258\pi$
$821$	−34.8750	−1.21715	−0.608573	+	0.793498i	$0.708258\pi$
$822$	−100.288	−3.49795
$823$	5.04786	0.175957	0.0879786	−	0.996122i	$-0.471959\pi$
$823$	5.04786	0.175957	0.0879786	+	0.996122i	$0.471959\pi$
$824$	−18.4337	−0.642168
$825$	0	0
$826$	−4.10942	−0.142985
$827$	−50.2402	−1.74702	−0.873512	−	0.486804i	$-0.838163\pi$
$827$	−50.2402	−1.74702	−0.873512	+	0.486804i	$0.838163\pi$
$828$	106.116	3.68779
$829$	16.2711	0.565117	0.282559	−	0.959250i	$-0.408817\pi$
$829$	16.2711	0.565117	0.282559	+	0.959250i	$0.408817\pi$
$830$	0	0
$831$	−78.7559	−2.73201
$832$	−8.66949	−0.300560
$833$	0.576527	0.0199755
$834$	22.0383	0.763124
$835$	0	0
$836$	0	0
$837$	−4.86222	−0.168063
$838$	69.9363	2.41591
$839$	−21.6242	−0.746551	−0.373275	−	0.927721i	$-0.621765\pi$
$839$	−21.6242	−0.746551	−0.373275	+	0.927721i	$0.621765\pi$
$840$	0	0
$841$	−19.9519	−0.687998
$842$	−83.7429	−2.88597
$843$	23.6115	0.813223
$844$	77.7493	2.67624
$845$	0	0
$846$	200.552	6.89511
$847$	−31.3496	−1.07718
$848$	0.145077	0.00498195
$849$	88.4181	3.03450
$850$	0	0
$851$	34.2272	1.17329
$852$	141.884	4.86088
$853$	39.5026	1.35254	0.676271	−	0.736653i	$-0.263595\pi$
$853$	39.5026	1.35254	0.676271	+	0.736653i	$0.263595\pi$
$854$	−6.91172	−0.236514
$855$	0	0
$856$	52.3542	1.78943
$857$	12.4592	0.425599	0.212799	−	0.977096i	$-0.431742\pi$
$857$	12.4592	0.425599	0.212799	+	0.977096i	$0.431742\pi$
$858$	−2.93267	−0.100120
$859$	33.0423	1.12739	0.563694	−	0.825984i	$-0.309380\pi$
$859$	33.0423	1.12739	0.563694	+	0.825984i	$0.309380\pi$
$860$	0	0
$861$	−25.9745	−0.885209
$862$	−54.7378	−1.86438
$863$	8.86619	0.301809	0.150904	−	0.988548i	$-0.451781\pi$
$863$	8.86619	0.301809	0.150904	+	0.988548i	$0.451781\pi$
$864$	−91.7274	−3.12063
$865$	0	0
$866$	−33.5581	−1.14035
$867$	55.8146	1.89556
$868$	2.83843	0.0963425
$869$	−0.890845	−0.0302198
$870$	0	0
$871$	2.23639	0.0757773
$872$	7.14914	0.242100
$873$	−96.8300	−3.27720
$874$	0	0
$875$	0	0
$876$	76.5901	2.58774
$877$	−11.1008	−0.374847	−0.187424	−	0.982279i	$-0.560014\pi$
$877$	−11.1008	−0.374847	−0.187424	+	0.982279i	$0.560014\pi$
$878$	38.9852	1.31569
$879$	3.54996	0.119737
$880$	0	0
$881$	41.9175	1.41224	0.706119	−	0.708094i	$-0.250445\pi$
$881$	41.9175	1.41224	0.706119	+	0.708094i	$0.250445\pi$
$882$	−29.7819	−1.00281
$883$	−26.5966	−0.895047	−0.447524	−	0.894272i	$-0.647694\pi$
$883$	−26.5966	−0.895047	−0.447524	+	0.894272i	$0.647694\pi$
$884$	0.765293	0.0257396
$885$	0	0
$886$	−82.4189	−2.76892
$887$	−20.8117	−0.698788	−0.349394	−	0.936976i	$-0.613613\pi$
$887$	−20.8117	−0.698788	−0.349394	+	0.936976i	$0.613613\pi$
$888$	78.2523	2.62597
$889$	−56.4075	−1.89185
$890$	0	0
$891$	−17.4441	−0.584400
$892$	−66.7249	−2.23412
$893$	0	0
$894$	−67.0764	−2.24337
$895$	0	0
$896$	54.0234	1.80479
$897$	−9.13668	−0.305065
$898$	−8.14692	−0.271866
$899$	0.895502	0.0298666
$900$	0	0
$901$	1.44512	0.0481438
$902$	3.53440	0.117683
$903$	−64.1388	−2.13441
$904$	−32.2994	−1.07426
$905$	0	0
$906$	63.4033	2.10643
$907$	0.805231	0.0267372	0.0133686	−	0.999911i	$-0.495745\pi$
$907$	0.805231	0.0267372	0.0133686	+	0.999911i	$0.495745\pi$
$908$	−41.1818	−1.36667
$909$	−4.61070	−0.152927
$910$	0	0
$911$	33.6958	1.11639	0.558196	−	0.829709i	$-0.311494\pi$
$911$	33.6958	1.11639	0.558196	+	0.829709i	$0.311494\pi$
$912$	0	0
$913$	7.69283	0.254595
$914$	−10.5727	−0.349713
$915$	0	0
$916$	18.6858	0.617396
$917$	−20.1334	−0.664865
$918$	13.1612	0.434386
$919$	−14.2935	−0.471500	−0.235750	−	0.971814i	$-0.575755\pi$
$919$	−14.2935	−0.471500	−0.235750	+	0.971814i	$0.575755\pi$
$920$	0	0
$921$	−85.8911	−2.83021
$922$	66.8068	2.20016
$923$	−8.86580	−0.291821
$924$	18.2134	0.599176
$925$	0	0
$926$	−40.3899	−1.32729
$927$	51.3692	1.68719
$928$	16.8939	0.554570
$929$	14.8180	0.486163	0.243082	−	0.970006i	$-0.421842\pi$
$929$	14.8180	0.486163	0.243082	+	0.970006i	$0.421842\pi$
$930$	0	0
$931$	0	0
$932$	9.01339	0.295244
$933$	−63.0071	−2.06276
$934$	38.8001	1.26958
$935$	0	0
$936$	−15.1597	−0.495510
$937$	48.5601	1.58639	0.793195	−	0.608968i	$-0.208416\pi$
$937$	48.5601	1.58639	0.793195	+	0.608968i	$0.208416\pi$
$938$	−22.4523	−0.733093
$939$	−50.9299	−1.66203
$940$	0	0
$941$	19.0289	0.620323	0.310162	−	0.950684i	$-0.399617\pi$
$941$	19.0289	0.620323	0.310162	+	0.950684i	$0.399617\pi$
$942$	120.167	3.91525
$943$	11.0114	0.358580
$944$	0.0215701	0.000702047 0
$945$	0	0
$946$	8.72749	0.283755
$947$	40.5470	1.31760	0.658801	−	0.752317i	$-0.271064\pi$
$947$	40.5470	1.31760	0.658801	+	0.752317i	$0.271064\pi$
$948$	−16.5471	−0.537426
$949$	−4.78582	−0.155354
$950$	0	0
$951$	84.4697	2.73912
$952$	−2.94625	−0.0954884
$953$	37.8295	1.22542	0.612710	−	0.790308i	$-0.290080\pi$
$953$	37.8295	1.22542	0.612710	+	0.790308i	$0.290080\pi$
$954$	−74.6511	−2.41692
$955$	0	0
$956$	63.1232	2.04155
$957$	5.74618	0.185748
$958$	33.1159	1.06992
$959$	−38.9189	−1.25676
$960$	0	0
$961$	−30.9114	−0.997141
$962$	−12.7512	−0.411115
$963$	−145.896	−4.70142
$964$	−23.4851	−0.756403
$965$	0	0
$966$	91.7276	2.95129
$967$	−28.0754	−0.902843	−0.451421	−	0.892311i	$-0.649083\pi$
$967$	−28.0754	−0.902843	−0.451421	+	0.892311i	$0.649083\pi$
$968$	30.3844	0.976591
$969$	0	0
$970$	0	0
$971$	−35.1868	−1.12920	−0.564599	−	0.825365i	$-0.690969\pi$
$971$	−35.1868	−1.12920	−0.564599	+	0.825365i	$0.690969\pi$
$972$	−165.075	−5.29479
$973$	8.55243	0.274178
$974$	−0.760114	−0.0243556
$975$	0	0
$976$	0.0362791	0.00116127
$977$	−53.3032	−1.70532	−0.852659	−	0.522467i	$-0.825012\pi$
$977$	−53.3032	−1.70532	−0.852659	+	0.522467i	$0.825012\pi$
$978$	−73.6352	−2.35460
$979$	3.79559	0.121307
$980$	0	0
$981$	−19.9225	−0.636077
$982$	7.65279	0.244210
$983$	50.8137	1.62070	0.810352	−	0.585943i	$-0.199276\pi$
$983$	50.8137	1.62070	0.810352	+	0.585943i	$0.199276\pi$
$984$	25.1748	0.802544
$985$	0	0
$986$	−2.42397	−0.0771951
$987$	107.241	3.41352
$988$	0	0
$989$	27.1903	0.864603
$990$	0	0
$991$	−56.2102	−1.78557	−0.892787	−	0.450478i	$-0.851253\pi$
$991$	−56.2102	−1.78557	−0.892787	+	0.450478i	$0.851253\pi$
$992$	1.67202	0.0530866
$993$	−14.9880	−0.475629
$994$	89.0082	2.82317
$995$	0	0
$996$	142.892	4.52769
$997$	−37.4723	−1.18676	−0.593379	−	0.804923i	$-0.702207\pi$
$997$	−37.4723	−1.18676	−0.593379	+	0.804923i	$0.702207\pi$
$998$	32.2689	1.02145
$999$	−135.655	−4.29194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cc.1.2		9
5.4	even	2		1805.2.a.v.1.8		9
19.4	even	9		475.2.l.c.301.1		18
19.5	even	9		475.2.l.c.101.1		18
19.18	odd	2		9025.2.a.cf.1.8		9
95.4	even	18		95.2.k.a.16.3	yes	18
95.23	odd	36		475.2.u.b.149.1		36
95.24	even	18		95.2.k.a.6.3	✓	18
95.42	odd	36		475.2.u.b.149.6		36
95.43	odd	36		475.2.u.b.424.6		36
95.62	odd	36		475.2.u.b.424.1		36
95.94	odd	2		1805.2.a.s.1.2		9
285.119	odd	18		855.2.bs.c.766.1		18
285.194	odd	18		855.2.bs.c.586.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.3	✓	18	95.24	even	18
95.2.k.a.16.3	yes	18	95.4	even	18
475.2.l.c.101.1		18	19.5	even	9
475.2.l.c.301.1		18	19.4	even	9
475.2.u.b.149.1		36	95.23	odd	36
475.2.u.b.149.6		36	95.42	odd	36
475.2.u.b.424.1		36	95.62	odd	36
475.2.u.b.424.6		36	95.43	odd	36
855.2.bs.c.586.1		18	285.194	odd	18
855.2.bs.c.766.1		18	285.119	odd	18
1805.2.a.s.1.2		9	95.94	odd	2
1805.2.a.v.1.8		9	5.4	even	2
9025.2.a.cc.1.2		9	1.1	even	1	trivial
9025.2.a.cf.1.8		9	19.18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28997 q^{2} -3.30730 q^{3} +3.24395 q^{4} +7.57362 q^{6} +2.93910 q^{7} -2.84861 q^{8} +7.93825 q^{9} -0.577601 q^{11} -10.7287 q^{12} +0.670397 q^{13} -6.73045 q^{14} +0.0353277 q^{16} +0.351901 q^{17} -18.1783 q^{18} -9.72050 q^{21} +1.32269 q^{22} +4.12081 q^{23} +9.42123 q^{24} -1.53519 q^{26} -16.3323 q^{27} +9.53431 q^{28} +3.00800 q^{29} +0.297707 q^{31} +5.61633 q^{32} +1.91030 q^{33} -0.805843 q^{34} +25.7513 q^{36} +8.30595 q^{37} -2.21721 q^{39} +2.67214 q^{41} +22.2596 q^{42} +6.59830 q^{43} -1.87371 q^{44} -9.43652 q^{46} -11.0325 q^{47} -0.116839 q^{48} +1.63832 q^{49} -1.16384 q^{51} +2.17474 q^{52} +4.10660 q^{53} +37.4004 q^{54} -8.37237 q^{56} -6.88822 q^{58} +0.610572 q^{59} +1.02693 q^{61} -0.681739 q^{62} +23.3313 q^{63} -12.9319 q^{64} -4.37452 q^{66} +3.33593 q^{67} +1.14155 q^{68} -13.6288 q^{69} -13.2247 q^{71} -22.6130 q^{72} -7.13879 q^{73} -19.0204 q^{74} -1.69763 q^{77} +5.07733 q^{78} +1.54232 q^{79} +30.2010 q^{81} -6.11911 q^{82} -13.3186 q^{83} -31.5328 q^{84} -15.1099 q^{86} -9.94837 q^{87} +1.64536 q^{88} -6.57130 q^{89} +1.97037 q^{91} +13.3677 q^{92} -0.984606 q^{93} +25.2640 q^{94} -18.5749 q^{96} -12.1979 q^{97} -3.75170 q^{98} -4.58513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} - 9 q^{3} + 6 q^{4} + 12 q^{6} - 6 q^{8} + 6 q^{9} - 18 q^{12} - 9 q^{13} + 12 q^{16} + 9 q^{17} - 24 q^{18} + 12 q^{21} - 24 q^{22} + 12 q^{23} + 3 q^{24} - 3 q^{26} - 24 q^{27} + 15 q^{28}+ \cdots - 36 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 - 9 * q^3 + 6 * q^4 + 12 * q^6 - 6 * q^8 + 6 * q^9 - 18 * q^12 - 9 * q^13 + 12 * q^16 + 9 * q^17 - 24 * q^18 + 12 * q^21 - 24 * q^22 + 12 * q^23 + 3 * q^24 - 3 * q^26 - 24 * q^27 + 15 * q^28 + 9 * q^29 + 18 * q^31 - 3 * q^32 + 9 * q^33 - 24 * q^34 + 18 * q^36 - 18 * q^37 + 18 * q^39 + 6 * q^41 + 12 * q^43 + 48 * q^44 - 9 * q^46 - 15 * q^47 + 21 * q^48 - 9 * q^49 - 6 * q^51 - 33 * q^52 - 15 * q^53 + 63 * q^54 - 6 * q^58 + 21 * q^59 - 12 * q^61 + 36 * q^62 - 21 * q^63 - 36 * q^64 + 3 * q^66 - 60 * q^67 + 51 * q^68 - 15 * q^69 - 18 * q^71 - 27 * q^73 + 27 * q^74 + 30 * q^77 + 6 * q^78 + 15 * q^79 + 33 * q^81 - 24 * q^82 - 48 * q^84 - 39 * q^86 - 15 * q^87 - 27 * q^88 - 39 * q^89 + 21 * q^91 + 6 * q^92 - 15 * q^93 + 15 * q^94 - 33 * q^96 - 15 * q^97 + 15 * q^98 - 36 * q^99

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