LMFDB - Embedded newform 9025.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 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			1.1
Root			$-1.48119$ 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)

$f(q)$	$=$	$q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -3.35026 q^{7} +2.67513 q^{8} -2.35026 q^{9} +O(q^{10})$	\(q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -3.35026 q^{7} +2.67513 q^{8} -2.35026 q^{9} +0.962389 q^{11} +0.156325 q^{12} +6.15633 q^{13} +4.96239 q^{14} -4.35026 q^{16} +6.31265 q^{17} +3.48119 q^{18} -2.70052 q^{21} -1.42548 q^{22} +4.96239 q^{23} +2.15633 q^{24} -9.11871 q^{26} -4.31265 q^{27} -0.649738 q^{28} +3.61213 q^{29} +5.92478 q^{31} +1.09332 q^{32} +0.775746 q^{33} -9.35026 q^{34} -0.455802 q^{36} +10.1563 q^{37} +4.96239 q^{39} -6.31265 q^{41} +4.00000 q^{42} +4.12601 q^{43} +0.186642 q^{44} -7.35026 q^{46} -3.35026 q^{47} -3.50659 q^{48} +4.22425 q^{49} +5.08840 q^{51} +1.19394 q^{52} +1.84367 q^{53} +6.38787 q^{54} -8.96239 q^{56} -5.35026 q^{58} +6.38787 q^{59} -11.2750 q^{61} -8.77575 q^{62} +7.87399 q^{63} +7.08110 q^{64} -1.14903 q^{66} -6.73084 q^{67} +1.22425 q^{68} +4.00000 q^{69} +0.775746 q^{71} -6.28726 q^{72} -0.387873 q^{73} -15.0435 q^{74} -3.22425 q^{77} -7.35026 q^{78} +0.836381 q^{79} +3.57452 q^{81} +9.35026 q^{82} +7.03761 q^{83} -0.523730 q^{84} -6.11142 q^{86} +2.91160 q^{87} +2.57452 q^{88} -7.08840 q^{89} -20.6253 q^{91} +0.962389 q^{92} +4.77575 q^{93} +4.96239 q^{94} +0.881286 q^{96} +10.9927 q^{97} -6.25694 q^{98} -2.26187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 2 q^{3} + q^{4} - 4 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 2 * q^3 + q^4 - 4 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 2 q^{3} + q^{4} - 4 q^{6} + 3 q^{8} + 3 q^{9} - 8 q^{11} - 10 q^{12} + 8 q^{13} + 4 q^{14} - 3 q^{16} - 2 q^{17} + 5 q^{18} + 12 q^{21} - 16 q^{22} + 4 q^{23} - 4 q^{24} - 6 q^{26} + 8 q^{27} - 12 q^{28} + 10 q^{29} - 4 q^{31} - 3 q^{32} + 4 q^{33} - 18 q^{34} - 11 q^{36} + 20 q^{37} + 4 q^{39} + 2 q^{41} + 12 q^{42} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 10 q^{48} + 11 q^{49} - 4 q^{51} + 4 q^{52} + 16 q^{53} + 20 q^{54} - 16 q^{56} - 6 q^{58} + 20 q^{59} - 2 q^{61} - 28 q^{62} + 32 q^{63} - 11 q^{64} + 20 q^{66} + 2 q^{67} + 2 q^{68} + 12 q^{69} + 4 q^{71} - 13 q^{72} - 2 q^{73} - 2 q^{74} - 8 q^{77} - 12 q^{78} - q^{81} + 18 q^{82} + 32 q^{83} - 20 q^{84} + 16 q^{86} + 28 q^{87} - 4 q^{88} - 2 q^{89} - 20 q^{91} - 8 q^{92} + 16 q^{93} + 4 q^{94} + 24 q^{96} + 20 q^{97} - 15 q^{98} - 16 q^{99}+O(q^{100}) $ 3 * q + q^2 + 2 * q^3 + q^4 - 4 * q^6 + 3 * q^8 + 3 * q^9 - 8 * q^11 - 10 * q^12 + 8 * q^13 + 4 * q^14 - 3 * q^16 - 2 * q^17 + 5 * q^18 + 12 * q^21 - 16 * q^22 + 4 * q^23 - 4 * q^24 - 6 * q^26 + 8 * q^27 - 12 * q^28 + 10 * q^29 - 4 * q^31 - 3 * q^32 + 4 * q^33 - 18 * q^34 - 11 * q^36 + 20 * q^37 + 4 * q^39 + 2 * q^41 + 12 * q^42 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 10 * q^48 + 11 * q^49 - 4 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 - 16 * q^56 - 6 * q^58 + 20 * q^59 - 2 * q^61 - 28 * q^62 + 32 * q^63 - 11 * q^64 + 20 * q^66 + 2 * q^67 + 2 * q^68 + 12 * q^69 + 4 * q^71 - 13 * q^72 - 2 * q^73 - 2 * q^74 - 8 * q^77 - 12 * q^78 - q^81 + 18 * q^82 + 32 * q^83 - 20 * q^84 + 16 * q^86 + 28 * q^87 - 4 * q^88 - 2 * q^89 - 20 * q^91 - 8 * q^92 + 16 * q^93 + 4 * q^94 + 24 * q^96 + 20 * q^97 - 15 * q^98 - 16 * q^99

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 $

$2$	−1.48119	−1.04736	−0.523681	−	0.851914i	$-0.675442\pi$
$2$	−1.48119	−1.04736	−0.523681	+	0.851914i	$0.675442\pi$
$3$	0.806063	0.465381	0.232690	−	0.972551i	$-0.425247\pi$
$3$	0.806063	0.465381	0.232690	+	0.972551i	$0.425247\pi$
$4$	0.193937	0.0969683
$5$	0	0
$5$	0	0
$6$	−1.19394	−0.487423
$7$	−3.35026	−1.26628	−0.633140	−	0.774037i	$-0.718234\pi$
$7$	−3.35026	−1.26628	−0.633140	+	0.774037i	$0.718234\pi$
$8$	2.67513	0.945802
$9$	−2.35026	−0.783421
$10$	0	0
$11$	0.962389	0.290171	0.145086	−	0.989419i	$-0.453654\pi$
$11$	0.962389	0.290171	0.145086	+	0.989419i	$0.453654\pi$
$12$	0.156325	0.0451272
$13$	6.15633	1.70746	0.853729	−	0.520718i	$-0.174336\pi$
$13$	6.15633	1.70746	0.853729	+	0.520718i	$0.174336\pi$
$14$	4.96239	1.32625
$15$	0	0
$16$	−4.35026	−1.08757
$17$	6.31265	1.53104	0.765521	−	0.643411i	$-0.222481\pi$
$17$	6.31265	1.53104	0.765521	+	0.643411i	$0.222481\pi$
$18$	3.48119	0.820525
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−2.70052	−0.589303
$22$	−1.42548	−0.303914
$23$	4.96239	1.03473	0.517365	−	0.855765i	$-0.326913\pi$
$23$	4.96239	1.03473	0.517365	+	0.855765i	$0.326913\pi$
$24$	2.15633	0.440158
$25$	0	0
$26$	−9.11871	−1.78833
$27$	−4.31265	−0.829970
$28$	−0.649738	−0.122789
$29$	3.61213	0.670755	0.335378	−	0.942084i	$-0.391136\pi$
$29$	3.61213	0.670755	0.335378	+	0.942084i	$0.391136\pi$
$30$	0	0
$31$	5.92478	1.06412	0.532061	−	0.846706i	$-0.321418\pi$
$31$	5.92478	1.06412	0.532061	+	0.846706i	$0.321418\pi$
$32$	1.09332	0.193274
$33$	0.775746	0.135040
$34$	−9.35026	−1.60356
$35$	0	0
$36$	−0.455802	−0.0759669
$37$	10.1563	1.66969	0.834845	−	0.550485i	$-0.185557\pi$
$37$	10.1563	1.66969	0.834845	+	0.550485i	$0.185557\pi$
$38$	0	0
$39$	4.96239	0.794618
$40$	0	0
$41$	−6.31265	−0.985870	−0.492935	−	0.870066i	$-0.664076\pi$
$41$	−6.31265	−0.985870	−0.492935	+	0.870066i	$0.664076\pi$
$42$	4.00000	0.617213
$43$	4.12601	0.629210	0.314605	−	0.949223i	$-0.398128\pi$
$43$	4.12601	0.629210	0.314605	+	0.949223i	$0.398128\pi$
$44$	0.186642	0.0281374
$45$	0	0
$46$	−7.35026	−1.08374
$47$	−3.35026	−0.488686	−0.244343	−	0.969689i	$-0.578572\pi$
$47$	−3.35026	−0.488686	−0.244343	+	0.969689i	$0.578572\pi$
$48$	−3.50659	−0.506132
$49$	4.22425	0.603465
$50$	0	0
$51$	5.08840	0.712518
$52$	1.19394	0.165569
$53$	1.84367	0.253248	0.126624	−	0.991951i	$-0.459586\pi$
$53$	1.84367	0.253248	0.126624	+	0.991951i	$0.459586\pi$
$54$	6.38787	0.869279
$55$	0	0
$56$	−8.96239	−1.19765
$57$	0	0
$58$	−5.35026	−0.702524
$59$	6.38787	0.831630	0.415815	−	0.909449i	$-0.363496\pi$
$59$	6.38787	0.831630	0.415815	+	0.909449i	$0.363496\pi$
$60$	0	0
$61$	−11.2750	−1.44362	−0.721810	−	0.692091i	$-0.756690\pi$
$61$	−11.2750	−1.44362	−0.721810	+	0.692091i	$0.756690\pi$
$62$	−8.77575	−1.11452
$63$	7.87399	0.992030
$64$	7.08110	0.885138
$65$	0	0
$66$	−1.14903	−0.141436
$67$	−6.73084	−0.822303	−0.411152	−	0.911567i	$-0.634873\pi$
$67$	−6.73084	−0.822303	−0.411152	+	0.911567i	$0.634873\pi$
$68$	1.22425	0.148463
$69$	4.00000	0.481543
$70$	0	0
$71$	0.775746	0.0920641	0.0460321	−	0.998940i	$-0.485342\pi$
$71$	0.775746	0.0920641	0.0460321	+	0.998940i	$0.485342\pi$
$72$	−6.28726	−0.740960
$73$	−0.387873	−0.0453971	−0.0226986	−	0.999742i	$-0.507226\pi$
$73$	−0.387873	−0.0453971	−0.0226986	+	0.999742i	$0.507226\pi$
$74$	−15.0435	−1.74877
$75$	0	0
$76$	0	0
$77$	−3.22425	−0.367438
$78$	−7.35026	−0.832253
$79$	0.836381	0.0941002	0.0470501	−	0.998893i	$-0.485018\pi$
$79$	0.836381	0.0941002	0.0470501	+	0.998893i	$0.485018\pi$
$80$	0	0
$81$	3.57452	0.397168
$82$	9.35026	1.03256
$83$	7.03761	0.772478	0.386239	−	0.922399i	$-0.373774\pi$
$83$	7.03761	0.772478	0.386239	+	0.922399i	$0.373774\pi$
$84$	−0.523730	−0.0571437
$85$	0	0
$86$	−6.11142	−0.659011
$87$	2.91160	0.312157
$88$	2.57452	0.274444
$89$	−7.08840	−0.751369	−0.375684	−	0.926748i	$-0.622592\pi$
$89$	−7.08840	−0.751369	−0.375684	+	0.926748i	$0.622592\pi$
$90$	0	0
$91$	−20.6253	−2.16212
$92$	0.962389	0.100336
$93$	4.77575	0.495222
$94$	4.96239	0.511831
$95$	0	0
$96$	0.881286	0.0899459
$97$	10.9927	1.11614	0.558070	−	0.829794i	$-0.311542\pi$
$97$	10.9927	1.11614	0.558070	+	0.829794i	$0.311542\pi$
$98$	−6.25694	−0.632046
$99$	−2.26187	−0.227326
$100$	0	0
$101$	−2.64974	−0.263659	−0.131829	−	0.991272i	$-0.542085\pi$
$101$	−2.64974	−0.263659	−0.131829	+	0.991272i	$0.542085\pi$
$102$	−7.53690	−0.746265
$103$	−10.7308	−1.05734	−0.528671	−	0.848827i	$-0.677309\pi$
$103$	−10.7308	−1.05734	−0.528671	+	0.848827i	$0.677309\pi$
$104$	16.4690	1.61492
$105$	0	0
$106$	−2.73084	−0.265243
$107$	4.80606	0.464620	0.232310	−	0.972642i	$-0.425372\pi$
$107$	4.80606	0.464620	0.232310	+	0.972642i	$0.425372\pi$
$108$	−0.836381	−0.0804808
$109$	2.77575	0.265868	0.132934	−	0.991125i	$-0.457560\pi$
$109$	2.77575	0.265868	0.132934	+	0.991125i	$0.457560\pi$
$110$	0	0
$111$	8.18664	0.777042
$112$	14.5745	1.37716
$113$	6.99271	0.657818	0.328909	−	0.944362i	$-0.393319\pi$
$113$	6.99271	0.657818	0.328909	+	0.944362i	$0.393319\pi$
$114$	0	0
$115$	0	0
$116$	0.700523	0.0650420
$117$	−14.4690	−1.33766
$118$	−9.46168	−0.871018
$119$	−21.1490	−1.93873
$120$	0	0
$121$	−10.0738	−0.915801
$122$	16.7005	1.51199
$123$	−5.08840	−0.458805
$124$	1.14903	0.103186
$125$	0	0
$126$	−11.6629	−1.03901
$127$	13.4314	1.19184	0.595920	−	0.803043i	$-0.296787\pi$
$127$	13.4314	1.19184	0.595920	+	0.803043i	$0.296787\pi$
$128$	−12.6751	−1.12033
$129$	3.32582	0.292822
$130$	0	0
$131$	20.6253	1.80204	0.901020	−	0.433777i	$-0.142819\pi$
$131$	20.6253	1.80204	0.901020	+	0.433777i	$0.142819\pi$
$132$	0.150446	0.0130946
$133$	0	0
$134$	9.96968	0.861249
$135$	0	0
$136$	16.8872	1.44806
$137$	−20.2374	−1.72900	−0.864500	−	0.502633i	$-0.832365\pi$
$137$	−20.2374	−1.72900	−0.864500	+	0.502633i	$0.832365\pi$
$138$	−5.92478	−0.504351
$139$	−17.5877	−1.49177	−0.745884	−	0.666076i	$-0.767973\pi$
$139$	−17.5877	−1.49177	−0.745884	+	0.666076i	$0.767973\pi$
$140$	0	0
$141$	−2.70052	−0.227425
$142$	−1.14903	−0.0964245
$143$	5.92478	0.495455
$144$	10.2243	0.852021
$145$	0	0
$146$	0.574515	0.0475472
$147$	3.40502	0.280841
$148$	1.96968	0.161907
$149$	−7.42548	−0.608319	−0.304160	−	0.952621i	$-0.598376\pi$
$149$	−7.42548	−0.608319	−0.304160	+	0.952621i	$0.598376\pi$
$150$	0	0
$151$	1.61213	0.131193	0.0655965	−	0.997846i	$-0.479105\pi$
$151$	1.61213	0.131193	0.0655965	+	0.997846i	$0.479105\pi$
$152$	0	0
$153$	−14.8364	−1.19945
$154$	4.77575	0.384841
$155$	0	0
$156$	0.962389	0.0770528
$157$	−4.38787	−0.350190	−0.175095	−	0.984552i	$-0.556023\pi$
$157$	−4.38787	−0.350190	−0.175095	+	0.984552i	$0.556023\pi$
$158$	−1.23884	−0.0985570
$159$	1.48612	0.117857
$160$	0	0
$161$	−16.6253	−1.31026
$162$	−5.29455	−0.415979
$163$	0.649738	0.0508914	0.0254457	−	0.999676i	$-0.491900\pi$
$163$	0.649738	0.0508914	0.0254457	+	0.999676i	$0.491900\pi$
$164$	−1.22425	−0.0955982
$165$	0	0
$166$	−10.4241	−0.809065
$167$	−15.3561	−1.18829	−0.594147	−	0.804357i	$-0.702510\pi$
$167$	−15.3561	−1.18829	−0.594147	+	0.804357i	$0.702510\pi$
$168$	−7.22425	−0.557363
$169$	24.9003	1.91541
$170$	0	0
$171$	0	0
$172$	0.800184	0.0610134
$173$	3.24472	0.246692	0.123346	−	0.992364i	$-0.460638\pi$
$173$	3.24472	0.246692	0.123346	+	0.992364i	$0.460638\pi$
$174$	−4.31265	−0.326941
$175$	0	0
$176$	−4.18664	−0.315580
$177$	5.14903	0.387025
$178$	10.4993	0.786955
$179$	−15.0132	−1.12214	−0.561069	−	0.827769i	$-0.689610\pi$
$179$	−15.0132	−1.12214	−0.561069	+	0.827769i	$0.689610\pi$
$180$	0	0
$181$	−9.22425	−0.685633	−0.342817	−	0.939402i	$-0.611381\pi$
$181$	−9.22425	−0.685633	−0.342817	+	0.939402i	$0.611381\pi$
$182$	30.5501	2.26452
$183$	−9.08840	−0.671834
$184$	13.2750	0.978649
$185$	0	0
$186$	−7.07381	−0.518677
$187$	6.07522	0.444264
$188$	−0.649738	−0.0473870
$189$	14.4485	1.05097
$190$	0	0
$191$	−21.7743	−1.57554	−0.787768	−	0.615972i	$-0.788763\pi$
$191$	−21.7743	−1.57554	−0.787768	+	0.615972i	$0.788763\pi$
$192$	5.70782	0.411926
$193$	12.5442	0.902951	0.451476	−	0.892283i	$-0.350898\pi$
$193$	12.5442	0.902951	0.451476	+	0.892283i	$0.350898\pi$
$194$	−16.2823	−1.16900
$195$	0	0
$196$	0.819237	0.0585169
$197$	−24.5501	−1.74912	−0.874560	−	0.484917i	$-0.838850\pi$
$197$	−24.5501	−1.74912	−0.874560	+	0.484917i	$0.838850\pi$
$198$	3.35026	0.238093
$199$	23.0738	1.63566	0.817829	−	0.575461i	$-0.195177\pi$
$199$	23.0738	1.63566	0.817829	+	0.575461i	$0.195177\pi$
$200$	0	0
$201$	−5.42548	−0.382684
$202$	3.92478	0.276146
$203$	−12.1016	−0.849364
$204$	0.986826	0.0690917
$205$	0	0
$206$	15.8945	1.10742
$207$	−11.6629	−0.810628
$208$	−26.7816	−1.85697
$209$	0	0
$210$	0	0
$211$	20.9380	1.44143	0.720714	−	0.693233i	$-0.243814\pi$
$211$	20.9380	1.44143	0.720714	+	0.693233i	$0.243814\pi$
$212$	0.357556	0.0245570
$213$	0.625301	0.0428449
$214$	−7.11871	−0.486625
$215$	0	0
$216$	−11.5369	−0.784987
$217$	−19.8496	−1.34748
$218$	−4.11142	−0.278460
$219$	−0.312650	−0.0211270
$220$	0	0
$221$	38.8627	2.61419
$222$	−12.1260	−0.813844
$223$	−0.0303172	−0.00203019	−0.00101509	−	0.999999i	$-0.500323\pi$
$223$	−0.0303172	−0.00203019	−0.00101509	+	0.999999i	$0.500323\pi$
$224$	−3.66291	−0.244739
$225$	0	0
$226$	−10.3576	−0.688974
$227$	4.80606	0.318990	0.159495	−	0.987199i	$-0.449013\pi$
$227$	4.80606	0.318990	0.159495	+	0.987199i	$0.449013\pi$
$228$	0	0
$229$	1.87399	0.123837	0.0619184	−	0.998081i	$-0.480278\pi$
$229$	1.87399	0.123837	0.0619184	+	0.998081i	$0.480278\pi$
$230$	0	0
$231$	−2.59895	−0.170999
$232$	9.66291	0.634401
$233$	11.1490	0.730397	0.365199	−	0.930930i	$-0.381001\pi$
$233$	11.1490	0.730397	0.365199	+	0.930930i	$0.381001\pi$
$234$	21.4314	1.40101
$235$	0	0
$236$	1.23884	0.0806418
$237$	0.674176	0.0437924
$238$	31.3258	2.03055
$239$	9.29948	0.601533	0.300767	−	0.953698i	$-0.402757\pi$
$239$	9.29948	0.601533	0.300767	+	0.953698i	$0.402757\pi$
$240$	0	0
$241$	2.31265	0.148971	0.0744855	−	0.997222i	$-0.476269\pi$
$241$	2.31265	0.148971	0.0744855	+	0.997222i	$0.476269\pi$
$242$	14.9213	0.959175
$243$	15.8192	1.01480
$244$	−2.18664	−0.139985
$245$	0	0
$246$	7.53690	0.480535
$247$	0	0
$248$	15.8496	1.00645
$249$	5.67276	0.359497
$250$	0	0
$251$	24.1016	1.52128	0.760639	−	0.649175i	$-0.224886\pi$
$251$	24.1016	1.52128	0.760639	+	0.649175i	$0.224886\pi$
$252$	1.52705	0.0961954
$253$	4.77575	0.300249
$254$	−19.8945	−1.24829
$255$	0	0
$256$	4.61213	0.288258
$257$	−13.3199	−0.830875	−0.415438	−	0.909622i	$-0.636372\pi$
$257$	−13.3199	−0.830875	−0.415438	+	0.909622i	$0.636372\pi$
$258$	−4.92619	−0.306691
$259$	−34.0263	−2.11429
$260$	0	0
$261$	−8.48944	−0.525483
$262$	−30.5501	−1.88739
$263$	−12.9624	−0.799295	−0.399648	−	0.916669i	$-0.630867\pi$
$263$	−12.9624	−0.799295	−0.399648	+	0.916669i	$0.630867\pi$
$264$	2.07522	0.127721
$265$	0	0
$266$	0	0
$267$	−5.71370	−0.349673
$268$	−1.30536	−0.0797373
$269$	11.4010	0.695134	0.347567	−	0.937655i	$-0.387008\pi$
$269$	11.4010	0.695134	0.347567	+	0.937655i	$0.387008\pi$
$270$	0	0
$271$	16.8119	1.02125	0.510626	−	0.859803i	$-0.329414\pi$
$271$	16.8119	1.02125	0.510626	+	0.859803i	$0.329414\pi$
$272$	−27.4617	−1.66511
$273$	−16.6253	−1.00621
$274$	29.9756	1.81089
$275$	0	0
$276$	0.775746	0.0466944
$277$	29.7889	1.78984	0.894921	−	0.446224i	$-0.147231\pi$
$277$	29.7889	1.78984	0.894921	+	0.446224i	$0.147231\pi$
$278$	26.0508	1.56242
$279$	−13.9248	−0.833655
$280$	0	0
$281$	11.6121	0.692721	0.346361	−	0.938101i	$-0.387417\pi$
$281$	11.6121	0.692721	0.346361	+	0.938101i	$0.387417\pi$
$282$	4.00000	0.238197
$283$	−2.26187	−0.134454	−0.0672270	−	0.997738i	$-0.521415\pi$
$283$	−2.26187	−0.134454	−0.0672270	+	0.997738i	$0.521415\pi$
$284$	0.150446	0.00892730
$285$	0	0
$286$	−8.77575	−0.518921
$287$	21.1490	1.24839
$288$	−2.56959	−0.151415
$289$	22.8496	1.34409
$290$	0	0
$291$	8.86082	0.519430
$292$	−0.0752228	−0.00440208
$293$	1.84367	0.107709	0.0538543	−	0.998549i	$-0.482849\pi$
$293$	1.84367	0.107709	0.0538543	+	0.998549i	$0.482849\pi$
$294$	−5.04349	−0.294142
$295$	0	0
$296$	27.1695	1.57920
$297$	−4.15045	−0.240833
$298$	10.9986	0.637131
$299$	30.5501	1.76676
$300$	0	0
$301$	−13.8232	−0.796756
$302$	−2.38787	−0.137407
$303$	−2.13586	−0.122702
$304$	0	0
$305$	0	0
$306$	21.9756	1.25626
$307$	26.2071	1.49572	0.747859	−	0.663857i	$-0.231082\pi$
$307$	26.2071	1.49572	0.747859	+	0.663857i	$0.231082\pi$
$308$	−0.625301	−0.0356298
$309$	−8.64974	−0.492066
$310$	0	0
$311$	6.51388	0.369368	0.184684	−	0.982798i	$-0.440874\pi$
$311$	6.51388	0.369368	0.184684	+	0.982798i	$0.440874\pi$
$312$	13.2750	0.751551
$313$	−16.0752	−0.908625	−0.454313	−	0.890842i	$-0.650115\pi$
$313$	−16.0752	−0.908625	−0.454313	+	0.890842i	$0.650115\pi$
$314$	6.49929	0.366776
$315$	0	0
$316$	0.162205	0.00912473
$317$	−5.69323	−0.319764	−0.159882	−	0.987136i	$-0.551111\pi$
$317$	−5.69323	−0.319764	−0.159882	+	0.987136i	$0.551111\pi$
$318$	−2.20123	−0.123439
$319$	3.47627	0.194634
$320$	0	0
$321$	3.87399	0.216225
$322$	24.6253	1.37231
$323$	0	0
$324$	0.693229	0.0385127
$325$	0	0
$326$	−0.962389	−0.0533018
$327$	2.23743	0.123730
$328$	−16.8872	−0.932438
$329$	11.2243	0.618813
$330$	0	0
$331$	12.3127	0.676764	0.338382	−	0.941009i	$-0.390120\pi$
$331$	12.3127	0.676764	0.338382	+	0.941009i	$0.390120\pi$
$332$	1.36485	0.0749059
$333$	−23.8700	−1.30807
$334$	22.7454	1.24457
$335$	0	0
$336$	11.7480	0.640905
$337$	3.76845	0.205281	0.102640	−	0.994719i	$-0.467271\pi$
$337$	3.76845	0.205281	0.102640	+	0.994719i	$0.467271\pi$
$338$	−36.8822	−2.00613
$339$	5.63656	0.306136
$340$	0	0
$341$	5.70194	0.308777
$342$	0	0
$343$	9.29948	0.502125
$344$	11.0376	0.595108
$345$	0	0
$346$	−4.80606	−0.258376
$347$	22.3634	1.20053	0.600266	−	0.799800i	$-0.295061\pi$
$347$	22.3634	1.20053	0.600266	+	0.799800i	$0.295061\pi$
$348$	0.564666	0.0302693
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	0	0
$351$	−26.5501	−1.41714
$352$	1.05220	0.0560824
$353$	−5.53690	−0.294700	−0.147350	−	0.989084i	$-0.547074\pi$
$353$	−5.53690	−0.294700	−0.147350	+	0.989084i	$0.547074\pi$
$354$	−7.62672	−0.405355
$355$	0	0
$356$	−1.37470	−0.0728589
$357$	−17.0475	−0.902247
$358$	22.2374	1.17528
$359$	−10.3634	−0.546961	−0.273481	−	0.961878i	$-0.588175\pi$
$359$	−10.3634	−0.546961	−0.273481	+	0.961878i	$0.588175\pi$
$360$	0	0
$361$	0	0
$362$	13.6629	0.718107
$363$	−8.12013	−0.426196
$364$	−4.00000	−0.209657
$365$	0	0
$366$	13.4617	0.703653
$367$	−3.35026	−0.174882	−0.0874411	−	0.996170i	$-0.527869\pi$
$367$	−3.35026	−0.174882	−0.0874411	+	0.996170i	$0.527869\pi$
$368$	−21.5877	−1.12534
$369$	14.8364	0.772351
$370$	0	0
$371$	−6.17679	−0.320683
$372$	0.926192	0.0480208
$373$	−12.6048	−0.652653	−0.326327	−	0.945257i	$-0.605811\pi$
$373$	−12.6048	−0.652653	−0.326327	+	0.945257i	$0.605811\pi$
$374$	−8.99859	−0.465306
$375$	0	0
$376$	−8.96239	−0.462200
$377$	22.2374	1.14529
$378$	−21.4010	−1.10075
$379$	37.2506	1.91343	0.956717	−	0.291018i	$-0.0939941\pi$
$379$	37.2506	1.91343	0.956717	+	0.291018i	$0.0939941\pi$
$380$	0	0
$381$	10.8265	0.554660
$382$	32.2520	1.65016
$383$	30.8324	1.57546	0.787731	−	0.616019i	$-0.211256\pi$
$383$	30.8324	1.57546	0.787731	+	0.616019i	$0.211256\pi$
$384$	−10.2170	−0.521382
$385$	0	0
$386$	−18.5804	−0.945717
$387$	−9.69720	−0.492936
$388$	2.13189	0.108230
$389$	−1.37470	−0.0697000	−0.0348500	−	0.999393i	$-0.511095\pi$
$389$	−1.37470	−0.0697000	−0.0348500	+	0.999393i	$0.511095\pi$
$390$	0	0
$391$	31.3258	1.58422
$392$	11.3004	0.570758
$393$	16.6253	0.838635
$394$	36.3634	1.83196
$395$	0	0
$396$	−0.438658	−0.0220434
$397$	9.38646	0.471093	0.235546	−	0.971863i	$-0.424312\pi$
$397$	9.38646	0.471093	0.235546	+	0.971863i	$0.424312\pi$
$398$	−34.1768	−1.71313
$399$	0	0
$400$	0	0
$401$	−14.1016	−0.704199	−0.352099	−	0.935963i	$-0.614532\pi$
$401$	−14.1016	−0.704199	−0.352099	+	0.935963i	$0.614532\pi$
$402$	8.03620	0.400809
$403$	36.4749	1.81694
$404$	−0.513881	−0.0255665
$405$	0	0
$406$	17.9248	0.889592
$407$	9.77433	0.484496
$408$	13.6121	0.673901
$409$	−35.1490	−1.73801	−0.869004	−	0.494805i	$-0.835239\pi$
$409$	−35.1490	−1.73801	−0.869004	+	0.494805i	$0.835239\pi$
$410$	0	0
$411$	−16.3127	−0.804644
$412$	−2.08110	−0.102529
$413$	−21.4010	−1.05308
$414$	17.2750	0.849022
$415$	0	0
$416$	6.73084	0.330007
$417$	−14.1768	−0.694241
$418$	0	0
$419$	9.02776	0.441035	0.220518	−	0.975383i	$-0.429225\pi$
$419$	9.02776	0.441035	0.220518	+	0.975383i	$0.429225\pi$
$420$	0	0
$421$	−15.2097	−0.741274	−0.370637	−	0.928778i	$-0.620861\pi$
$421$	−15.2097	−0.741274	−0.370637	+	0.928778i	$0.620861\pi$
$422$	−31.0132	−1.50970
$423$	7.87399	0.382847
$424$	4.93207	0.239523
$425$	0	0
$426$	−0.926192	−0.0448741
$427$	37.7743	1.82803
$428$	0.932071	0.0450534
$429$	4.77575	0.230575
$430$	0	0
$431$	−16.3127	−0.785753	−0.392876	−	0.919591i	$-0.628520\pi$
$431$	−16.3127	−0.785753	−0.392876	+	0.919591i	$0.628520\pi$
$432$	18.7612	0.902647
$433$	11.1432	0.535506	0.267753	−	0.963488i	$-0.413719\pi$
$433$	11.1432	0.535506	0.267753	+	0.963488i	$0.413719\pi$
$434$	29.4010	1.41130
$435$	0	0
$436$	0.538319	0.0257808
$437$	0	0
$438$	0.463096	0.0221276
$439$	−27.3865	−1.30708	−0.653542	−	0.756890i	$-0.726718\pi$
$439$	−27.3865	−1.30708	−0.653542	+	0.756890i	$0.726718\pi$
$440$	0	0
$441$	−9.92810	−0.472767
$442$	−57.5633	−2.73800
$443$	−19.5125	−0.927065	−0.463533	−	0.886080i	$-0.653418\pi$
$443$	−19.5125	−0.927065	−0.463533	+	0.886080i	$0.653418\pi$
$444$	1.58769	0.0753484
$445$	0	0
$446$	0.0449056	0.00212634
$447$	−5.98541	−0.283100
$448$	−23.7235	−1.12083
$449$	22.1016	1.04304	0.521519	−	0.853240i	$-0.325366\pi$
$449$	22.1016	1.04304	0.521519	+	0.853240i	$0.325366\pi$
$450$	0	0
$451$	−6.07522	−0.286071
$452$	1.35614	0.0637875
$453$	1.29948	0.0610547
$454$	−7.11871	−0.334098
$455$	0	0
$456$	0	0
$457$	17.8496	0.834967	0.417483	−	0.908685i	$-0.362912\pi$
$457$	17.8496	0.834967	0.417483	+	0.908685i	$0.362912\pi$
$458$	−2.77575	−0.129702
$459$	−27.2243	−1.27072
$460$	0	0
$461$	−35.2506	−1.64178	−0.820892	−	0.571083i	$-0.806523\pi$
$461$	−35.2506	−1.64178	−0.820892	+	0.571083i	$0.806523\pi$
$462$	3.84955	0.179097
$463$	26.3634	1.22521	0.612606	−	0.790388i	$-0.290121\pi$
$463$	26.3634	1.22521	0.612606	+	0.790388i	$0.290121\pi$
$464$	−15.7137	−0.729490
$465$	0	0
$466$	−16.5139	−0.764991
$467$	6.78560	0.314000	0.157000	−	0.987599i	$-0.449818\pi$
$467$	6.78560	0.314000	0.157000	+	0.987599i	$0.449818\pi$
$468$	−2.80606	−0.129710
$469$	22.5501	1.04127
$470$	0	0
$471$	−3.53690	−0.162972
$472$	17.0884	0.786557
$473$	3.97082	0.182579
$474$	−0.998585	−0.0458665
$475$	0	0
$476$	−4.10157	−0.187995
$477$	−4.33312	−0.198400
$478$	−13.7743	−0.630023
$479$	12.7104	0.580752	0.290376	−	0.956913i	$-0.406220\pi$
$479$	12.7104	0.580752	0.290376	+	0.956913i	$0.406220\pi$
$480$	0	0
$481$	62.5256	2.85092
$482$	−3.42548	−0.156027
$483$	−13.4010	−0.609769
$484$	−1.95368	−0.0888036
$485$	0	0
$486$	−23.4314	−1.06287
$487$	−15.7586	−0.714090	−0.357045	−	0.934087i	$-0.616216\pi$
$487$	−15.7586	−0.714090	−0.357045	+	0.934087i	$0.616216\pi$
$488$	−30.1622	−1.36538
$489$	0.523730	0.0236839
$490$	0	0
$491$	−14.5501	−0.656636	−0.328318	−	0.944567i	$-0.606482\pi$
$491$	−14.5501	−0.656636	−0.328318	+	0.944567i	$0.606482\pi$
$492$	−0.986826	−0.0444896
$493$	22.8021	1.02695
$494$	0	0
$495$	0	0
$496$	−25.7743	−1.15730
$497$	−2.59895	−0.116579
$498$	−8.40246	−0.376523
$499$	−5.48612	−0.245592	−0.122796	−	0.992432i	$-0.539186\pi$
$499$	−5.48612	−0.245592	−0.122796	+	0.992432i	$0.539186\pi$
$500$	0	0
$501$	−12.3780	−0.553009
$502$	−35.6991	−1.59333
$503$	36.6615	1.63466	0.817328	−	0.576173i	$-0.195455\pi$
$503$	36.6615	1.63466	0.817328	+	0.576173i	$0.195455\pi$
$504$	21.0640	0.938263
$505$	0	0
$506$	−7.07381	−0.314469
$507$	20.0713	0.891396
$508$	2.60483	0.115571
$509$	−39.1900	−1.73706	−0.868532	−	0.495632i	$-0.834936\pi$
$509$	−39.1900	−1.73706	−0.868532	+	0.495632i	$0.834936\pi$
$510$	0	0
$511$	1.29948	0.0574855
$512$	18.5188	0.818423
$513$	0	0
$514$	19.7294	0.870228
$515$	0	0
$516$	0.644999	0.0283945
$517$	−3.22425	−0.141803
$518$	50.3996	2.21443
$519$	2.61545	0.114806
$520$	0	0
$521$	17.7283	0.776690	0.388345	−	0.921514i	$-0.373047\pi$
$521$	17.7283	0.776690	0.388345	+	0.921514i	$0.373047\pi$
$522$	12.5745	0.550372
$523$	−40.7572	−1.78219	−0.891094	−	0.453819i	$-0.850061\pi$
$523$	−40.7572	−1.78219	−0.891094	+	0.453819i	$0.850061\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	19.1998	0.837152
$527$	37.4010	1.62922
$528$	−3.37470	−0.146865
$529$	1.62530	0.0706652
$530$	0	0
$531$	−15.0132	−0.651516
$532$	0	0
$533$	−38.8627	−1.68333
$534$	8.46310	0.366234
$535$	0	0
$536$	−18.0059	−0.777736
$537$	−12.1016	−0.522221
$538$	−16.8872	−0.728057
$539$	4.06537	0.175108
$540$	0	0
$541$	23.9003	1.02756	0.513778	−	0.857923i	$-0.328246\pi$
$541$	23.9003	1.02756	0.513778	+	0.857923i	$0.328246\pi$
$542$	−24.9018	−1.06962
$543$	−7.43533	−0.319081
$544$	6.90175	0.295910
$545$	0	0
$546$	24.6253	1.05387
$547$	8.55405	0.365745	0.182872	−	0.983137i	$-0.441461\pi$
$547$	8.55405	0.365745	0.182872	+	0.983137i	$0.441461\pi$
$548$	−3.92478	−0.167658
$549$	26.4993	1.13096
$550$	0	0
$551$	0	0
$552$	10.7005	0.455445
$553$	−2.80209	−0.119157
$554$	−44.1232	−1.87461
$555$	0	0
$556$	−3.41090	−0.144654
$557$	4.23743	0.179546	0.0897728	−	0.995962i	$-0.471386\pi$
$557$	4.23743	0.179546	0.0897728	+	0.995962i	$0.471386\pi$
$558$	20.6253	0.873139
$559$	25.4010	1.07435
$560$	0	0
$561$	4.89701	0.206752
$562$	−17.1998	−0.725530
$563$	16.4934	0.695114	0.347557	−	0.937659i	$-0.387011\pi$
$563$	16.4934	0.695114	0.347557	+	0.937659i	$0.387011\pi$
$564$	−0.523730	−0.0220530
$565$	0	0
$566$	3.35026	0.140822
$567$	−11.9756	−0.502926
$568$	2.07522	0.0870744
$569$	10.0000	0.419222	0.209611	−	0.977785i	$-0.432780\pi$
$569$	10.0000	0.419222	0.209611	+	0.977785i	$0.432780\pi$
$570$	0	0
$571$	−26.2619	−1.09902	−0.549512	−	0.835486i	$-0.685186\pi$
$571$	−26.2619	−1.09902	−0.549512	+	0.835486i	$0.685186\pi$
$572$	1.14903	0.0480434
$573$	−17.5515	−0.733224
$574$	−31.3258	−1.30751
$575$	0	0
$576$	−16.6424	−0.693435
$577$	−30.1016	−1.25314	−0.626572	−	0.779363i	$-0.715543\pi$
$577$	−30.1016	−1.25314	−0.626572	+	0.779363i	$0.715543\pi$
$578$	−33.8446	−1.40775
$579$	10.1114	0.420216
$580$	0	0
$581$	−23.5778	−0.978174
$582$	−13.1246	−0.544032
$583$	1.77433	0.0734853
$584$	−1.03761	−0.0429367
$585$	0	0
$586$	−2.73084	−0.112810
$587$	35.1392	1.45035	0.725175	−	0.688565i	$-0.241759\pi$
$587$	35.1392	1.45035	0.725175	+	0.688565i	$0.241759\pi$
$588$	0.660357	0.0272327
$589$	0	0
$590$	0	0
$591$	−19.7889	−0.814007
$592$	−44.1827	−1.81590
$593$	−34.3244	−1.40953	−0.704767	−	0.709439i	$-0.748949\pi$
$593$	−34.3244	−1.40953	−0.704767	+	0.709439i	$0.748949\pi$
$594$	6.14762	0.252240
$595$	0	0
$596$	−1.44007	−0.0589877
$597$	18.5990	0.761204
$598$	−45.2506	−1.85043
$599$	−14.6107	−0.596978	−0.298489	−	0.954413i	$-0.596483\pi$
$599$	−14.6107	−0.596978	−0.298489	+	0.954413i	$0.596483\pi$
$600$	0	0
$601$	−23.5633	−0.961165	−0.480583	−	0.876949i	$-0.659575\pi$
$601$	−23.5633	−0.961165	−0.480583	+	0.876949i	$0.659575\pi$
$602$	20.4749	0.834493
$603$	15.8192	0.644209
$604$	0.312650	0.0127216
$605$	0	0
$606$	3.16362	0.128513
$607$	−8.80606	−0.357427	−0.178714	−	0.983901i	$-0.557194\pi$
$607$	−8.80606	−0.357427	−0.178714	+	0.983901i	$0.557194\pi$
$608$	0	0
$609$	−9.75463	−0.395278
$610$	0	0
$611$	−20.6253	−0.834410
$612$	−2.87732	−0.116309
$613$	−10.4142	−0.420626	−0.210313	−	0.977634i	$-0.567448\pi$
$613$	−10.4142	−0.420626	−0.210313	+	0.977634i	$0.567448\pi$
$614$	−38.8178	−1.56656
$615$	0	0
$616$	−8.62530	−0.347523
$617$	17.2849	0.695863	0.347932	−	0.937520i	$-0.386884\pi$
$617$	17.2849	0.695863	0.347932	+	0.937520i	$0.386884\pi$
$618$	12.8119	0.515372
$619$	−10.6351	−0.427463	−0.213731	−	0.976892i	$-0.568562\pi$
$619$	−10.6351	−0.427463	−0.213731	+	0.976892i	$0.568562\pi$
$620$	0	0
$621$	−21.4010	−0.858794
$622$	−9.64832	−0.386863
$623$	23.7480	0.951443
$624$	−21.5877	−0.864199
$625$	0	0
$626$	23.8105	0.951660
$627$	0	0
$628$	−0.850969	−0.0339574
$629$	64.1133	2.55637
$630$	0	0
$631$	−16.5599	−0.659240	−0.329620	−	0.944114i	$-0.606921\pi$
$631$	−16.5599	−0.659240	−0.329620	+	0.944114i	$0.606921\pi$
$632$	2.23743	0.0890001
$633$	16.8773	0.670813
$634$	8.43278	0.334908
$635$	0	0
$636$	0.288213	0.0114284
$637$	26.0059	1.03039
$638$	−5.14903	−0.203852
$639$	−1.82321	−0.0721249
$640$	0	0
$641$	16.7612	0.662026	0.331013	−	0.943626i	$-0.392610\pi$
$641$	16.7612	0.662026	0.331013	+	0.943626i	$0.392610\pi$
$642$	−5.73813	−0.226466
$643$	−5.73813	−0.226290	−0.113145	−	0.993578i	$-0.536092\pi$
$643$	−5.73813	−0.226290	−0.113145	+	0.993578i	$0.536092\pi$
$644$	−3.22425	−0.127053
$645$	0	0
$646$	0	0
$647$	37.2144	1.46305	0.731525	−	0.681815i	$-0.238809\pi$
$647$	37.2144	1.46305	0.731525	+	0.681815i	$0.238809\pi$
$648$	9.56230	0.375642
$649$	6.14762	0.241315
$650$	0	0
$651$	−16.0000	−0.627089
$652$	0.126008	0.00493485
$653$	−11.7626	−0.460305	−0.230153	−	0.973155i	$-0.573923\pi$
$653$	−11.7626	−0.460305	−0.230153	+	0.973155i	$0.573923\pi$
$654$	−3.31406	−0.129590
$655$	0	0
$656$	27.4617	1.07220
$657$	0.911603	0.0355650
$658$	−16.6253	−0.648122
$659$	−1.23884	−0.0482584	−0.0241292	−	0.999709i	$-0.507681\pi$
$659$	−1.23884	−0.0482584	−0.0241292	+	0.999709i	$0.507681\pi$
$660$	0	0
$661$	9.53690	0.370943	0.185471	−	0.982650i	$-0.440619\pi$
$661$	9.53690	0.370943	0.185471	+	0.982650i	$0.440619\pi$
$662$	−18.2374	−0.708818
$663$	31.3258	1.21659
$664$	18.8265	0.730611
$665$	0	0
$666$	35.3561	1.37002
$667$	17.9248	0.694050
$668$	−2.97812	−0.115227
$669$	−0.0244376	−0.000944811 0
$670$	0	0
$671$	−10.8510	−0.418897
$672$	−2.95254	−0.113897
$673$	39.9307	1.53921	0.769607	−	0.638518i	$-0.220452\pi$
$673$	39.9307	1.53921	0.769607	+	0.638518i	$0.220452\pi$
$674$	−5.58181	−0.215003
$675$	0	0
$676$	4.82909	0.185734
$677$	−3.05334	−0.117349	−0.0586747	−	0.998277i	$-0.518687\pi$
$677$	−3.05334	−0.117349	−0.0586747	+	0.998277i	$0.518687\pi$
$678$	−8.34885	−0.320636
$679$	−36.8284	−1.41335
$680$	0	0
$681$	3.87399	0.148452
$682$	−8.44568	−0.323402
$683$	29.2692	1.11995	0.559977	−	0.828508i	$-0.310810\pi$
$683$	29.2692	1.11995	0.559977	+	0.828508i	$0.310810\pi$
$684$	0	0
$685$	0	0
$686$	−13.7743	−0.525906
$687$	1.51056	0.0576313
$688$	−17.9492	−0.684307
$689$	11.3503	0.432411
$690$	0	0
$691$	2.63515	0.100246	0.0501229	−	0.998743i	$-0.484039\pi$
$691$	2.63515	0.100246	0.0501229	+	0.998743i	$0.484039\pi$
$692$	0.629270	0.0239213
$693$	7.57784	0.287858
$694$	−33.1246	−1.25739
$695$	0	0
$696$	7.78892	0.295238
$697$	−39.8496	−1.50941
$698$	14.8119	0.560640
$699$	8.98683	0.339913
$700$	0	0
$701$	−25.0494	−0.946102	−0.473051	−	0.881035i	$-0.656847\pi$
$701$	−25.0494	−0.946102	−0.473051	+	0.881035i	$0.656847\pi$
$702$	39.3258	1.48426
$703$	0	0
$704$	6.81477	0.256841
$705$	0	0
$706$	8.20123	0.308657
$707$	8.87732	0.333866
$708$	0.998585	0.0375291
$709$	−41.6991	−1.56604	−0.783021	−	0.621995i	$-0.786323\pi$
$709$	−41.6991	−1.56604	−0.783021	+	0.621995i	$0.786323\pi$
$710$	0	0
$711$	−1.96571	−0.0737200
$712$	−18.9624	−0.710646
$713$	29.4010	1.10108
$714$	25.2506	0.944980
$715$	0	0
$716$	−2.91160	−0.108812
$717$	7.49597	0.279942
$718$	15.3503	0.572867
$719$	30.6351	1.14250	0.571249	−	0.820777i	$-0.306459\pi$
$719$	30.6351	1.14250	0.571249	+	0.820777i	$0.306459\pi$
$720$	0	0
$721$	35.9511	1.33889
$722$	0	0
$723$	1.86414	0.0693282
$724$	−1.78892	−0.0664847
$725$	0	0
$726$	12.0275	0.446382
$727$	−7.50071	−0.278186	−0.139093	−	0.990279i	$-0.544419\pi$
$727$	−7.50071	−0.278186	−0.139093	+	0.990279i	$0.544419\pi$
$728$	−55.1754	−2.04494
$729$	2.02776	0.0751023
$730$	0	0
$731$	26.0460	0.963348
$732$	−1.76257	−0.0651466
$733$	−9.84955	−0.363802	−0.181901	−	0.983317i	$-0.558225\pi$
$733$	−9.84955	−0.363802	−0.181901	+	0.983317i	$0.558225\pi$
$734$	4.96239	0.183165
$735$	0	0
$736$	5.42548	0.199986
$737$	−6.47768	−0.238609
$738$	−21.9756	−0.808932
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	0	0
$741$	0	0
$742$	9.14903	0.335871
$743$	−15.7177	−0.576625	−0.288313	−	0.957536i	$-0.593094\pi$
$743$	−15.7177	−0.576625	−0.288313	+	0.957536i	$0.593094\pi$
$744$	12.7757	0.468382
$745$	0	0
$746$	18.6702	0.683565
$747$	−16.5402	−0.605175
$748$	1.17821	0.0430795
$749$	−16.1016	−0.588339
$750$	0	0
$751$	43.7400	1.59610	0.798048	−	0.602593i	$-0.205866\pi$
$751$	43.7400	1.59610	0.798048	+	0.602593i	$0.205866\pi$
$752$	14.5745	0.531478
$753$	19.4274	0.707974
$754$	−32.9380	−1.19953
$755$	0	0
$756$	2.80209	0.101911
$757$	15.7743	0.573328	0.286664	−	0.958031i	$-0.407454\pi$
$757$	15.7743	0.573328	0.286664	+	0.958031i	$0.407454\pi$
$758$	−55.1754	−2.00406
$759$	3.84955	0.139730
$760$	0	0
$761$	43.2262	1.56695	0.783474	−	0.621425i	$-0.213446\pi$
$761$	43.2262	1.56695	0.783474	+	0.621425i	$0.213446\pi$
$762$	−16.0362	−0.580930
$763$	−9.29948	−0.336664
$764$	−4.22284	−0.152777
$765$	0	0
$766$	−45.6688	−1.65008
$767$	39.3258	1.41997
$768$	3.71767	0.134150
$769$	−19.1246	−0.689650	−0.344825	−	0.938667i	$-0.612062\pi$
$769$	−19.1246	−0.689650	−0.344825	+	0.938667i	$0.612062\pi$
$770$	0	0
$771$	−10.7367	−0.386674
$772$	2.43278	0.0875576
$773$	25.8846	0.931005	0.465502	−	0.885047i	$-0.345874\pi$
$773$	25.8846	0.931005	0.465502	+	0.885047i	$0.345874\pi$
$774$	14.3634	0.516283
$775$	0	0
$776$	29.4069	1.05565
$777$	−27.4274	−0.983952
$778$	2.03620	0.0730012
$779$	0	0
$780$	0	0
$781$	0.746569	0.0267144
$782$	−46.3996	−1.65925
$783$	−15.5778	−0.556707
$784$	−18.3766	−0.656307
$785$	0	0
$786$	−24.6253	−0.878355
$787$	19.9814	0.712261	0.356131	−	0.934436i	$-0.384096\pi$
$787$	19.9814	0.712261	0.356131	+	0.934436i	$0.384096\pi$
$788$	−4.76116	−0.169609
$789$	−10.4485	−0.371977
$790$	0	0
$791$	−23.4274	−0.832982
$792$	−6.05079	−0.215005
$793$	−69.4128	−2.46492
$794$	−13.9032	−0.493405
$795$	0	0
$796$	4.47486	0.158607
$797$	28.6458	1.01469	0.507343	−	0.861744i	$-0.330628\pi$
$797$	28.6458	1.01469	0.507343	+	0.861744i	$0.330628\pi$
$798$	0	0
$799$	−21.1490	−0.748199
$800$	0	0
$801$	16.6596	0.588638
$802$	20.8872	0.737551
$803$	−0.373285	−0.0131729
$804$	−1.05220	−0.0371082
$805$	0	0
$806$	−54.0263	−1.90300
$807$	9.18997	0.323502
$808$	−7.08840	−0.249369
$809$	−17.2243	−0.605573	−0.302786	−	0.953058i	$-0.597917\pi$
$809$	−17.2243	−0.605573	−0.302786	+	0.953058i	$0.597917\pi$
$810$	0	0
$811$	15.6267	0.548728	0.274364	−	0.961626i	$-0.411533\pi$
$811$	15.6267	0.548728	0.274364	+	0.961626i	$0.411533\pi$
$812$	−2.34694	−0.0823613
$813$	13.5515	0.475272
$814$	−14.4777	−0.507443
$815$	0	0
$816$	−22.1359	−0.774910
$817$	0	0
$818$	52.0625	1.82032
$819$	48.4749	1.69385
$820$	0	0
$821$	39.2506	1.36986	0.684928	−	0.728611i	$-0.259834\pi$
$821$	39.2506	1.36986	0.684928	+	0.728611i	$0.259834\pi$
$822$	24.1622	0.842754
$823$	45.5271	1.58697	0.793487	−	0.608588i	$-0.208264\pi$
$823$	45.5271	1.58697	0.793487	+	0.608588i	$0.208264\pi$
$824$	−28.7064	−1.00003
$825$	0	0
$826$	31.6991	1.10295
$827$	17.0698	0.593576	0.296788	−	0.954943i	$-0.404084\pi$
$827$	17.0698	0.593576	0.296788	+	0.954943i	$0.404084\pi$
$828$	−2.26187	−0.0786052
$829$	−1.69911	−0.0590125	−0.0295062	−	0.999565i	$-0.509393\pi$
$829$	−1.69911	−0.0590125	−0.0295062	+	0.999565i	$0.509393\pi$
$830$	0	0
$831$	24.0118	0.832959
$832$	43.5936	1.51134
$833$	26.6662	0.923930
$834$	20.9986	0.727122
$835$	0	0
$836$	0	0
$837$	−25.5515	−0.883189
$838$	−13.3719	−0.461924
$839$	50.5910	1.74660	0.873298	−	0.487187i	$-0.161977\pi$
$839$	50.5910	1.74660	0.873298	+	0.487187i	$0.161977\pi$
$840$	0	0
$841$	−15.9525	−0.550088
$842$	22.5285	0.776382
$843$	9.36011	0.322379
$844$	4.06063	0.139773
$845$	0	0
$846$	−11.6629	−0.400979
$847$	33.7499	1.15966
$848$	−8.02047	−0.275424
$849$	−1.82321	−0.0625723
$850$	0	0
$851$	50.3996	1.72768
$852$	0.121269	0.00415460
$853$	22.5237	0.771198	0.385599	−	0.922667i	$-0.373995\pi$
$853$	22.5237	0.771198	0.385599	+	0.922667i	$0.373995\pi$
$854$	−55.9511	−1.91461
$855$	0	0
$856$	12.8568	0.439438
$857$	−23.6180	−0.806776	−0.403388	−	0.915029i	$-0.632167\pi$
$857$	−23.6180	−0.806776	−0.403388	+	0.915029i	$0.632167\pi$
$858$	−7.07381	−0.241496
$859$	15.1754	0.517777	0.258889	−	0.965907i	$-0.416644\pi$
$859$	15.1754	0.517777	0.258889	+	0.965907i	$0.416644\pi$
$860$	0	0
$861$	17.0475	0.580976
$862$	24.1622	0.822968
$863$	30.1055	1.02480	0.512402	−	0.858746i	$-0.328756\pi$
$863$	30.1055	1.02480	0.512402	+	0.858746i	$0.328756\pi$
$864$	−4.71511	−0.160411
$865$	0	0
$866$	−16.5052	−0.560869
$867$	18.4182	0.625515
$868$	−3.84955	−0.130662
$869$	0.804923	0.0273051
$870$	0	0
$871$	−41.4372	−1.40405
$872$	7.42548	0.251459
$873$	−25.8357	−0.874407
$874$	0	0
$875$	0	0
$876$	−0.0606343	−0.00204864
$877$	−5.53102	−0.186769	−0.0933847	−	0.995630i	$-0.529769\pi$
$877$	−5.53102	−0.186769	−0.0933847	+	0.995630i	$0.529769\pi$
$878$	40.5647	1.36899
$879$	1.48612	0.0501255
$880$	0	0
$881$	20.8265	0.701664	0.350832	−	0.936438i	$-0.385899\pi$
$881$	20.8265	0.701664	0.350832	+	0.936438i	$0.385899\pi$
$882$	14.7054	0.495158
$883$	−43.1509	−1.45214	−0.726072	−	0.687618i	$-0.758656\pi$
$883$	−43.1509	−1.45214	−0.726072	+	0.687618i	$0.758656\pi$
$884$	7.53690	0.253494
$885$	0	0
$886$	28.9018	0.970973
$887$	−44.5461	−1.49571	−0.747856	−	0.663861i	$-0.768917\pi$
$887$	−44.5461	−1.49571	−0.747856	+	0.663861i	$0.768917\pi$
$888$	21.9003	0.734927
$889$	−44.9986	−1.50920
$890$	0	0
$891$	3.44007	0.115247
$892$	−0.00587961	−0.000196864 0
$893$	0	0
$894$	8.86556	0.296509
$895$	0	0
$896$	42.4650	1.41866
$897$	24.6253	0.822215
$898$	−32.7367	−1.09244
$899$	21.4010	0.713765
$900$	0	0
$901$	11.6385	0.387734
$902$	8.99859	0.299620
$903$	−11.1424	−0.370795
$904$	18.7064	0.622166
$905$	0	0
$906$	−1.92478	−0.0639464
$907$	53.7558	1.78493	0.892466	−	0.451115i	$-0.148974\pi$
$907$	53.7558	1.78493	0.892466	+	0.451115i	$0.148974\pi$
$908$	0.932071	0.0309319
$909$	6.22758	0.206556
$910$	0	0
$911$	2.28630	0.0757486	0.0378743	−	0.999283i	$-0.487941\pi$
$911$	2.28630	0.0757486	0.0378743	+	0.999283i	$0.487941\pi$
$912$	0	0
$913$	6.77292	0.224151
$914$	−26.4387	−0.874513
$915$	0	0
$916$	0.363436	0.0120082
$917$	−69.1002	−2.28189
$918$	40.3244	1.33090
$919$	−34.8510	−1.14963	−0.574814	−	0.818284i	$-0.694925\pi$
$919$	−34.8510	−1.14963	−0.574814	+	0.818284i	$0.694925\pi$
$920$	0	0
$921$	21.1246	0.696079
$922$	52.2130	1.71954
$923$	4.77575	0.157196
$924$	−0.504032	−0.0165814
$925$	0	0
$926$	−39.0494	−1.28324
$927$	25.2203	0.828343
$928$	3.94921	0.129639
$929$	41.6991	1.36810	0.684052	−	0.729434i	$-0.260216\pi$
$929$	41.6991	1.36810	0.684052	+	0.729434i	$0.260216\pi$
$930$	0	0
$931$	0	0
$932$	2.16220	0.0708254
$933$	5.25060	0.171897
$934$	−10.0508	−0.328872
$935$	0	0
$936$	−38.7064	−1.26516
$937$	−21.9102	−0.715775	−0.357887	−	0.933765i	$-0.616503\pi$
$937$	−21.9102	−0.715775	−0.357887	+	0.933765i	$0.616503\pi$
$938$	−33.4010	−1.09058
$939$	−12.9576	−0.422857
$940$	0	0
$941$	3.55149	0.115775	0.0578877	−	0.998323i	$-0.481563\pi$
$941$	3.55149	0.115775	0.0578877	+	0.998323i	$0.481563\pi$
$942$	5.23884	0.170691
$943$	−31.3258	−1.02011
$944$	−27.7889	−0.904452
$945$	0	0
$946$	−5.88156	−0.191226
$947$	−38.3634	−1.24664	−0.623322	−	0.781965i	$-0.714217\pi$
$947$	−38.3634	−1.24664	−0.623322	+	0.781965i	$0.714217\pi$
$948$	0.130747	0.00424648
$949$	−2.38787	−0.0775136
$950$	0	0
$951$	−4.58910	−0.148812
$952$	−56.5764	−1.83365
$953$	−22.8714	−0.740879	−0.370439	−	0.928857i	$-0.620793\pi$
$953$	−22.8714	−0.740879	−0.370439	+	0.928857i	$0.620793\pi$
$954$	6.41819	0.207797
$955$	0	0
$956$	1.80351	0.0583296
$957$	2.80209	0.0905788
$958$	−18.8265	−0.608258
$959$	67.8007	2.18940
$960$	0	0
$961$	4.10299	0.132354
$962$	−92.6126	−2.98595
$963$	−11.2955	−0.363993
$964$	0.448507	0.0144455
$965$	0	0
$966$	19.8496	0.638649
$967$	−27.6629	−0.889579	−0.444790	−	0.895635i	$-0.646722\pi$
$967$	−27.6629	−0.889579	−0.444790	+	0.895635i	$0.646722\pi$
$968$	−26.9488	−0.866166
$969$	0	0
$970$	0	0
$971$	42.1768	1.35352	0.676759	−	0.736205i	$-0.263384\pi$
$971$	42.1768	1.35352	0.676759	+	0.736205i	$0.263384\pi$
$972$	3.06793	0.0984039
$973$	58.9234	1.88900
$974$	23.3416	0.747912
$975$	0	0
$976$	49.0494	1.57003
$977$	0.856849	0.0274130	0.0137065	−	0.999906i	$-0.495637\pi$
$977$	0.856849	0.0274130	0.0137065	+	0.999906i	$0.495637\pi$
$978$	−0.775746	−0.0248056
$979$	−6.82179	−0.218025
$980$	0	0
$981$	−6.52373	−0.208287
$982$	21.5515	0.687736
$983$	45.2809	1.44424	0.722119	−	0.691769i	$-0.243169\pi$
$983$	45.2809	1.44424	0.722119	+	0.691769i	$0.243169\pi$
$984$	−13.6121	−0.433939
$985$	0	0
$986$	−33.7743	−1.07559
$987$	9.04746	0.287984
$988$	0	0
$989$	20.4749	0.651063
$990$	0	0
$991$	−47.0132	−1.49342	−0.746711	−	0.665148i	$-0.768368\pi$
$991$	−47.0132	−1.49342	−0.746711	+	0.665148i	$0.768368\pi$
$992$	6.47768	0.205667
$993$	9.92478	0.314953
$994$	3.84955	0.122100
$995$	0	0
$996$	1.10016	0.0348598
$997$	−13.6873	−0.433483	−0.216741	−	0.976229i	$-0.569543\pi$
$997$	−13.6873	−0.433483	−0.216741	+	0.976229i	$0.569543\pi$
$998$	8.12601	0.257224
$999$	−43.8007	−1.38579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.bb.1.1		3
5.4	even	2		1805.2.a.f.1.3		3
19.18	odd	2		475.2.a.f.1.3		3
57.56	even	2		4275.2.a.bk.1.1		3
76.75	even	2		7600.2.a.bx.1.2		3
95.18	even	4		475.2.b.d.324.2		6
95.37	even	4		475.2.b.d.324.5		6
95.94	odd	2		95.2.a.a.1.1	✓	3
285.284	even	2		855.2.a.i.1.3		3
380.379	even	2		1520.2.a.p.1.2		3
665.664	even	2		4655.2.a.u.1.1		3
760.189	odd	2		6080.2.a.bo.1.2		3
760.379	even	2		6080.2.a.by.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.a.1.1	✓	3	95.94	odd	2
475.2.a.f.1.3		3	19.18	odd	2
475.2.b.d.324.2		6	95.18	even	4
475.2.b.d.324.5		6	95.37	even	4
855.2.a.i.1.3		3	285.284	even	2
1520.2.a.p.1.2		3	380.379	even	2
1805.2.a.f.1.3		3	5.4	even	2
4275.2.a.bk.1.1		3	57.56	even	2
4655.2.a.u.1.1		3	665.664	even	2
6080.2.a.bo.1.2		3	760.189	odd	2
6080.2.a.by.1.2		3	760.379	even	2
7600.2.a.bx.1.2		3	76.75	even	2
9025.2.a.bb.1.1		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -3.35026 q^{7} +2.67513 q^{8} -2.35026 q^{9} +O(q^{10})\)	\(q-1.48119 q^{2} +0.806063 q^{3} +0.193937 q^{4} -1.19394 q^{6} -3.35026 q^{7} +2.67513 q^{8} -2.35026 q^{9} +0.962389 q^{11} +0.156325 q^{12} +6.15633 q^{13} +4.96239 q^{14} -4.35026 q^{16} +6.31265 q^{17} +3.48119 q^{18} -2.70052 q^{21} -1.42548 q^{22} +4.96239 q^{23} +2.15633 q^{24} -9.11871 q^{26} -4.31265 q^{27} -0.649738 q^{28} +3.61213 q^{29} +5.92478 q^{31} +1.09332 q^{32} +0.775746 q^{33} -9.35026 q^{34} -0.455802 q^{36} +10.1563 q^{37} +4.96239 q^{39} -6.31265 q^{41} +4.00000 q^{42} +4.12601 q^{43} +0.186642 q^{44} -7.35026 q^{46} -3.35026 q^{47} -3.50659 q^{48} +4.22425 q^{49} +5.08840 q^{51} +1.19394 q^{52} +1.84367 q^{53} +6.38787 q^{54} -8.96239 q^{56} -5.35026 q^{58} +6.38787 q^{59} -11.2750 q^{61} -8.77575 q^{62} +7.87399 q^{63} +7.08110 q^{64} -1.14903 q^{66} -6.73084 q^{67} +1.22425 q^{68} +4.00000 q^{69} +0.775746 q^{71} -6.28726 q^{72} -0.387873 q^{73} -15.0435 q^{74} -3.22425 q^{77} -7.35026 q^{78} +0.836381 q^{79} +3.57452 q^{81} +9.35026 q^{82} +7.03761 q^{83} -0.523730 q^{84} -6.11142 q^{86} +2.91160 q^{87} +2.57452 q^{88} -7.08840 q^{89} -20.6253 q^{91} +0.962389 q^{92} +4.77575 q^{93} +4.96239 q^{94} +0.881286 q^{96} +10.9927 q^{97} -6.25694 q^{98} -2.26187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 2 q^{3} + q^{4} - 4 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 2 * q^3 + q^4 - 4 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 2 q^{3} + q^{4} - 4 q^{6} + 3 q^{8} + 3 q^{9} - 8 q^{11} - 10 q^{12} + 8 q^{13} + 4 q^{14} - 3 q^{16} - 2 q^{17} + 5 q^{18} + 12 q^{21} - 16 q^{22} + 4 q^{23} - 4 q^{24} - 6 q^{26} + 8 q^{27} - 12 q^{28} + 10 q^{29} - 4 q^{31} - 3 q^{32} + 4 q^{33} - 18 q^{34} - 11 q^{36} + 20 q^{37} + 4 q^{39} + 2 q^{41} + 12 q^{42} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 10 q^{48} + 11 q^{49} - 4 q^{51} + 4 q^{52} + 16 q^{53} + 20 q^{54} - 16 q^{56} - 6 q^{58} + 20 q^{59} - 2 q^{61} - 28 q^{62} + 32 q^{63} - 11 q^{64} + 20 q^{66} + 2 q^{67} + 2 q^{68} + 12 q^{69} + 4 q^{71} - 13 q^{72} - 2 q^{73} - 2 q^{74} - 8 q^{77} - 12 q^{78} - q^{81} + 18 q^{82} + 32 q^{83} - 20 q^{84} + 16 q^{86} + 28 q^{87} - 4 q^{88} - 2 q^{89} - 20 q^{91} - 8 q^{92} + 16 q^{93} + 4 q^{94} + 24 q^{96} + 20 q^{97} - 15 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + q^2 + 2 * q^3 + q^4 - 4 * q^6 + 3 * q^8 + 3 * q^9 - 8 * q^11 - 10 * q^12 + 8 * q^13 + 4 * q^14 - 3 * q^16 - 2 * q^17 + 5 * q^18 + 12 * q^21 - 16 * q^22 + 4 * q^23 - 4 * q^24 - 6 * q^26 + 8 * q^27 - 12 * q^28 + 10 * q^29 - 4 * q^31 - 3 * q^32 + 4 * q^33 - 18 * q^34 - 11 * q^36 + 20 * q^37 + 4 * q^39 + 2 * q^41 + 12 * q^42 + 4 * q^43 - 12 * q^44 - 12 * q^46 + 10 * q^48 + 11 * q^49 - 4 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 - 16 * q^56 - 6 * q^58 + 20 * q^59 - 2 * q^61 - 28 * q^62 + 32 * q^63 - 11 * q^64 + 20 * q^66 + 2 * q^67 + 2 * q^68 + 12 * q^69 + 4 * q^71 - 13 * q^72 - 2 * q^73 - 2 * q^74 - 8 * q^77 - 12 * q^78 - q^81 + 18 * q^82 + 32 * q^83 - 20 * q^84 + 16 * q^86 + 28 * q^87 - 4 * q^88 - 2 * q^89 - 20 * q^91 - 8 * q^92 + 16 * q^93 + 4 * q^94 + 24 * q^96 + 20 * q^97 - 15 * q^98 - 16 * q^99

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