LMFDB - Embedded newform 7605.2.a.bz.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7605,2,Mod(1,7605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7605, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.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:	$60.7262307372$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2535)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	7605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.24698 q^{2} -0.445042 q^{4} -1.00000 q^{5} +2.24698 q^{7} +3.04892 q^{8} +O(q^{10})$	$q-1.24698 q^{2} -0.445042 q^{4} -1.00000 q^{5} +2.24698 q^{7} +3.04892 q^{8} +1.24698 q^{10} +1.00000 q^{11} -2.80194 q^{14} -2.91185 q^{16} +6.49396 q^{17} -2.33513 q^{19} +0.445042 q^{20} -1.24698 q^{22} -0.198062 q^{23} +1.00000 q^{25} -1.00000 q^{28} -3.82908 q^{29} -1.71379 q^{31} -2.46681 q^{32} -8.09783 q^{34} -2.24698 q^{35} -4.54288 q^{37} +2.91185 q^{38} -3.04892 q^{40} +5.75302 q^{41} -3.75302 q^{43} -0.445042 q^{44} +0.246980 q^{46} -1.97285 q^{47} -1.95108 q^{49} -1.24698 q^{50} -12.0586 q^{53} -1.00000 q^{55} +6.85086 q^{56} +4.77479 q^{58} +9.83877 q^{59} -13.6136 q^{61} +2.13706 q^{62} +8.89977 q^{64} -7.91185 q^{67} -2.89008 q^{68} +2.80194 q^{70} +7.14675 q^{71} -14.3545 q^{73} +5.66487 q^{74} +1.03923 q^{76} +2.24698 q^{77} +10.6189 q^{79} +2.91185 q^{80} -7.17390 q^{82} -12.7192 q^{83} -6.49396 q^{85} +4.67994 q^{86} +3.04892 q^{88} -6.87263 q^{89} +0.0881460 q^{92} +2.46011 q^{94} +2.33513 q^{95} +11.1414 q^{97} +2.43296 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - q^{4} - 3 q^{5} + 2 q^{7}+O(q^{10}) $ 3 * q + q^2 - q^4 - 3 * q^5 + 2 * q^7	$ 3 q + q^{2} - q^{4} - 3 q^{5} + 2 q^{7} - q^{10} + 3 q^{11} - 4 q^{14} - 5 q^{16} + 10 q^{17} - 6 q^{19} + q^{20} + q^{22} - 5 q^{23} + 3 q^{25} - 3 q^{28} - q^{29} + 3 q^{31} - 4 q^{32} - 6 q^{34} - 2 q^{35} + 5 q^{37} + 5 q^{38} + 22 q^{41} - 16 q^{43} - q^{44} - 4 q^{46} - 12 q^{47} - 15 q^{49} + q^{50} - 5 q^{53} - 3 q^{55} + 7 q^{56} + 16 q^{58} - 3 q^{59} - 10 q^{61} + q^{62} + 4 q^{64} - 20 q^{67} - 8 q^{68} + 4 q^{70} - 6 q^{71} + 2 q^{73} + 18 q^{74} + 16 q^{76} + 2 q^{77} - 2 q^{79} + 5 q^{80} + 12 q^{82} - 27 q^{83} - 10 q^{85} - 10 q^{86} - 4 q^{89} + 4 q^{92} - 18 q^{94} + 6 q^{95} + 9 q^{97} - 12 q^{98}+O(q^{100}) $ 3 * q + q^2 - q^4 - 3 * q^5 + 2 * q^7 - q^10 + 3 * q^11 - 4 * q^14 - 5 * q^16 + 10 * q^17 - 6 * q^19 + q^20 + q^22 - 5 * q^23 + 3 * q^25 - 3 * q^28 - q^29 + 3 * q^31 - 4 * q^32 - 6 * q^34 - 2 * q^35 + 5 * q^37 + 5 * q^38 + 22 * q^41 - 16 * q^43 - q^44 - 4 * q^46 - 12 * q^47 - 15 * q^49 + q^50 - 5 * q^53 - 3 * q^55 + 7 * q^56 + 16 * q^58 - 3 * q^59 - 10 * q^61 + q^62 + 4 * q^64 - 20 * q^67 - 8 * q^68 + 4 * q^70 - 6 * q^71 + 2 * q^73 + 18 * q^74 + 16 * q^76 + 2 * q^77 - 2 * q^79 + 5 * q^80 + 12 * q^82 - 27 * q^83 - 10 * q^85 - 10 * q^86 - 4 * q^89 + 4 * q^92 - 18 * q^94 + 6 * q^95 + 9 * q^97 - 12 * 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 $

$2$	−1.24698	−0.881748	−0.440874	−	0.897569i	$-0.645331\pi$
$2$	−1.24698	−0.881748	−0.440874	+	0.897569i	$0.645331\pi$
$3$	0	0
$3$	0	0
$4$	−0.445042	−0.222521
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	2.24698	0.849278	0.424639	−	0.905363i	$-0.360401\pi$
$7$	2.24698	0.849278	0.424639	+	0.905363i	$0.360401\pi$
$8$	3.04892	1.07796
$9$	0	0
$10$	1.24698	0.394330
$11$	1.00000	0.301511	0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000	0.301511	0.150756	+	0.988571i	$0.451829\pi$
$12$	0	0
$13$	0	0
$13$	0	0
$14$	−2.80194	−0.748849
$15$	0	0
$16$	−2.91185	−0.727963
$17$	6.49396	1.57502	0.787508	−	0.616304i	$-0.211371\pi$
$17$	6.49396	1.57502	0.787508	+	0.616304i	$0.211371\pi$
$18$	0	0
$19$	−2.33513	−0.535715	−0.267857	−	0.963459i	$-0.586316\pi$
$19$	−2.33513	−0.535715	−0.267857	+	0.963459i	$0.586316\pi$
$20$	0.445042	0.0995144
$21$	0	0
$22$	−1.24698	−0.265857
$23$	−0.198062	−0.0412988	−0.0206494	−	0.999787i	$-0.506573\pi$
$23$	−0.198062	−0.0412988	−0.0206494	+	0.999787i	$0.506573\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−3.82908	−0.711043	−0.355522	−	0.934668i	$-0.615697\pi$
$29$	−3.82908	−0.711043	−0.355522	+	0.934668i	$0.615697\pi$
$30$	0	0
$31$	−1.71379	−0.307806	−0.153903	−	0.988086i	$-0.549184\pi$
$31$	−1.71379	−0.307806	−0.153903	+	0.988086i	$0.549184\pi$
$32$	−2.46681	−0.436075
$33$	0	0
$34$	−8.09783	−1.38877
$35$	−2.24698	−0.379809
$36$	0	0
$37$	−4.54288	−0.746844	−0.373422	−	0.927662i	$-0.621816\pi$
$37$	−4.54288	−0.746844	−0.373422	+	0.927662i	$0.621816\pi$
$38$	2.91185	0.472365
$39$	0	0
$40$	−3.04892	−0.482076
$41$	5.75302	0.898471	0.449235	−	0.893413i	$-0.351696\pi$
$41$	5.75302	0.898471	0.449235	+	0.893413i	$0.351696\pi$
$42$	0	0
$43$	−3.75302	−0.572330	−0.286165	−	0.958180i	$-0.592381\pi$
$43$	−3.75302	−0.572330	−0.286165	+	0.958180i	$0.592381\pi$
$44$	−0.445042	−0.0670926
$45$	0	0
$46$	0.246980	0.0364152
$47$	−1.97285	−0.287770	−0.143885	−	0.989594i	$-0.545960\pi$
$47$	−1.97285	−0.287770	−0.143885	+	0.989594i	$0.545960\pi$
$48$	0	0
$49$	−1.95108	−0.278726
$50$	−1.24698	−0.176350
$51$	0	0
$52$	0	0
$53$	−12.0586	−1.65638	−0.828188	−	0.560450i	$-0.810628\pi$
$53$	−12.0586	−1.65638	−0.828188	+	0.560450i	$0.810628\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	6.85086	0.915484
$57$	0	0
$58$	4.77479	0.626961
$59$	9.83877	1.28090	0.640450	−	0.768000i	$-0.278748\pi$
$59$	9.83877	1.28090	0.640450	+	0.768000i	$0.278748\pi$
$60$	0	0
$61$	−13.6136	−1.74304	−0.871519	−	0.490361i	$-0.836865\pi$
$61$	−13.6136	−1.74304	−0.871519	+	0.490361i	$0.836865\pi$
$62$	2.13706	0.271407
$63$	0	0
$64$	8.89977	1.11247
$65$	0	0
$66$	0	0
$67$	−7.91185	−0.966587	−0.483293	−	0.875458i	$-0.660560\pi$
$67$	−7.91185	−0.966587	−0.483293	+	0.875458i	$0.660560\pi$
$68$	−2.89008	−0.350474
$69$	0	0
$70$	2.80194	0.334896
$71$	7.14675	0.848163	0.424082	−	0.905624i	$-0.360597\pi$
$71$	7.14675	0.848163	0.424082	+	0.905624i	$0.360597\pi$
$72$	0	0
$73$	−14.3545	−1.68007	−0.840034	−	0.542534i	$-0.817465\pi$
$73$	−14.3545	−1.68007	−0.840034	+	0.542534i	$0.817465\pi$
$74$	5.66487	0.658528
$75$	0	0
$76$	1.03923	0.119208
$77$	2.24698	0.256067
$78$	0	0
$79$	10.6189	1.19472	0.597362	−	0.801972i	$-0.296216\pi$
$79$	10.6189	1.19472	0.597362	+	0.801972i	$0.296216\pi$
$80$	2.91185	0.325555
$81$	0	0
$82$	−7.17390	−0.792225
$83$	−12.7192	−1.39611	−0.698055	−	0.716044i	$-0.745951\pi$
$83$	−12.7192	−1.39611	−0.698055	+	0.716044i	$0.745951\pi$
$84$	0	0
$85$	−6.49396	−0.704369
$86$	4.67994	0.504651
$87$	0	0
$88$	3.04892	0.325016
$89$	−6.87263	−0.728497	−0.364248	−	0.931302i	$-0.618674\pi$
$89$	−6.87263	−0.728497	−0.364248	+	0.931302i	$0.618674\pi$
$90$	0	0
$91$	0	0
$92$	0.0881460	0.00918986
$93$	0	0
$94$	2.46011	0.253741
$95$	2.33513	0.239579
$96$	0	0
$97$	11.1414	1.13124	0.565618	−	0.824668i	$-0.308638\pi$
$97$	11.1414	1.13124	0.565618	+	0.824668i	$0.308638\pi$
$98$	2.43296	0.245766
$99$	0	0
$100$	−0.445042	−0.0445042
$101$	8.19136	0.815071	0.407535	−	0.913189i	$-0.366388\pi$
$101$	8.19136	0.815071	0.407535	+	0.913189i	$0.366388\pi$
$102$	0	0
$103$	−9.52111	−0.938142	−0.469071	−	0.883160i	$-0.655411\pi$
$103$	−9.52111	−0.938142	−0.469071	+	0.883160i	$0.655411\pi$
$104$	0	0
$105$	0	0
$106$	15.0368	1.46051
$107$	14.1836	1.37118	0.685590	−	0.727988i	$-0.259544\pi$
$107$	14.1836	1.37118	0.685590	+	0.727988i	$0.259544\pi$
$108$	0	0
$109$	10.1957	0.976568	0.488284	−	0.872685i	$-0.337623\pi$
$109$	10.1957	0.976568	0.488284	+	0.872685i	$0.337623\pi$
$110$	1.24698	0.118895
$111$	0	0
$112$	−6.54288	−0.618244
$113$	−6.88769	−0.647939	−0.323970	−	0.946067i	$-0.605018\pi$
$113$	−6.88769	−0.647939	−0.323970	+	0.946067i	$0.605018\pi$
$114$	0	0
$115$	0.198062	0.0184694
$116$	1.70410	0.158222
$117$	0	0
$118$	−12.2687	−1.12943
$119$	14.5918	1.33763
$120$	0	0
$121$	−10.0000	−0.909091
$122$	16.9758	1.53692
$123$	0	0
$124$	0.762709	0.0684933
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−18.4547	−1.63759	−0.818796	−	0.574084i	$-0.805358\pi$
$127$	−18.4547	−1.63759	−0.818796	+	0.574084i	$0.805358\pi$
$128$	−6.16421	−0.544844
$129$	0	0
$130$	0	0
$131$	−8.11960	−0.709413	−0.354707	−	0.934978i	$-0.615419\pi$
$131$	−8.11960	−0.709413	−0.354707	+	0.934978i	$0.615419\pi$
$132$	0	0
$133$	−5.24698	−0.454971
$134$	9.86592	0.852286
$135$	0	0
$136$	19.7995	1.69780
$137$	21.7778	1.86060	0.930300	−	0.366798i	$-0.119546\pi$
$137$	21.7778	1.86060	0.930300	+	0.366798i	$0.119546\pi$
$138$	0	0
$139$	−19.4058	−1.64598	−0.822990	−	0.568056i	$-0.807696\pi$
$139$	−19.4058	−1.64598	−0.822990	+	0.568056i	$0.807696\pi$
$140$	1.00000	0.0845154
$141$	0	0
$142$	−8.91185	−0.747866
$143$	0	0
$144$	0	0
$145$	3.82908	0.317988
$146$	17.8998	1.48140
$147$	0	0
$148$	2.02177	0.166188
$149$	11.4668	0.939398	0.469699	−	0.882827i	$-0.344362\pi$
$149$	11.4668	0.939398	0.469699	+	0.882827i	$0.344362\pi$
$150$	0	0
$151$	−6.17092	−0.502182	−0.251091	−	0.967963i	$-0.580789\pi$
$151$	−6.17092	−0.502182	−0.251091	+	0.967963i	$0.580789\pi$
$152$	−7.11960	−0.577476
$153$	0	0
$154$	−2.80194	−0.225787
$155$	1.71379	0.137655
$156$	0	0
$157$	−15.3080	−1.22171	−0.610855	−	0.791743i	$-0.709174\pi$
$157$	−15.3080	−1.22171	−0.610855	+	0.791743i	$0.709174\pi$
$158$	−13.2416	−1.05345
$159$	0	0
$160$	2.46681	0.195019
$161$	−0.445042	−0.0350742
$162$	0	0
$163$	19.5918	1.53455	0.767274	−	0.641320i	$-0.221613\pi$
$163$	19.5918	1.53455	0.767274	+	0.641320i	$0.221613\pi$
$164$	−2.56033	−0.199929
$165$	0	0
$166$	15.8605	1.23102
$167$	9.05429	0.700642	0.350321	−	0.936630i	$-0.386072\pi$
$167$	9.05429	0.700642	0.350321	+	0.936630i	$0.386072\pi$
$168$	0	0
$169$	0	0
$170$	8.09783	0.621076
$171$	0	0
$172$	1.67025	0.127355
$173$	13.4547	1.02294	0.511472	−	0.859300i	$-0.329100\pi$
$173$	13.4547	1.02294	0.511472	+	0.859300i	$0.329100\pi$
$174$	0	0
$175$	2.24698	0.169856
$176$	−2.91185	−0.219489
$177$	0	0
$178$	8.57002	0.642350
$179$	−21.3980	−1.59936	−0.799682	−	0.600423i	$-0.794999\pi$
$179$	−21.3980	−1.59936	−0.799682	+	0.600423i	$0.794999\pi$
$180$	0	0
$181$	−14.1032	−1.04828	−0.524142	−	0.851631i	$-0.675614\pi$
$181$	−14.1032	−1.04828	−0.524142	+	0.851631i	$0.675614\pi$
$182$	0	0
$183$	0	0
$184$	−0.603875	−0.0445183
$185$	4.54288	0.333999
$186$	0	0
$187$	6.49396	0.474885
$188$	0.878002	0.0640349
$189$	0	0
$190$	−2.91185	−0.211248
$191$	−7.19136	−0.520348	−0.260174	−	0.965562i	$-0.583780\pi$
$191$	−7.19136	−0.520348	−0.260174	+	0.965562i	$0.583780\pi$
$192$	0	0
$193$	11.3013	0.813483	0.406742	−	0.913543i	$-0.366665\pi$
$193$	11.3013	0.813483	0.406742	+	0.913543i	$0.366665\pi$
$194$	−13.8931	−0.997464
$195$	0	0
$196$	0.868313	0.0620224
$197$	−20.5066	−1.46104	−0.730519	−	0.682893i	$-0.760722\pi$
$197$	−20.5066	−1.46104	−0.730519	+	0.682893i	$0.760722\pi$
$198$	0	0
$199$	19.9681	1.41550	0.707749	−	0.706464i	$-0.249711\pi$
$199$	19.9681	1.41550	0.707749	+	0.706464i	$0.249711\pi$
$200$	3.04892	0.215591
$201$	0	0
$202$	−10.2145	−0.718687
$203$	−8.60388	−0.603874
$204$	0	0
$205$	−5.75302	−0.401808
$206$	11.8726	0.827205
$207$	0	0
$208$	0	0
$209$	−2.33513	−0.161524
$210$	0	0
$211$	−9.74632	−0.670964	−0.335482	−	0.942047i	$-0.608899\pi$
$211$	−9.74632	−0.670964	−0.335482	+	0.942047i	$0.608899\pi$
$212$	5.36658	0.368579
$213$	0	0
$214$	−17.6866	−1.20903
$215$	3.75302	0.255954
$216$	0	0
$217$	−3.85086	−0.261413
$218$	−12.7138	−0.861087
$219$	0	0
$220$	0.445042	0.0300047
$221$	0	0
$222$	0	0
$223$	24.5351	1.64299	0.821496	−	0.570214i	$-0.193140\pi$
$223$	24.5351	1.64299	0.821496	+	0.570214i	$0.193140\pi$
$224$	−5.54288	−0.370349
$225$	0	0
$226$	8.58881	0.571319
$227$	0.0217703	0.00144494	0.000722472	−	1.00000i	$-0.499770\pi$
$227$	0.0217703	0.00144494	0.000722472		1.00000i	$0.499770\pi$
$228$	0	0
$229$	−7.36898	−0.486956	−0.243478	−	0.969906i	$-0.578288\pi$
$229$	−7.36898	−0.486956	−0.243478	+	0.969906i	$0.578288\pi$
$230$	−0.246980	−0.0162854
$231$	0	0
$232$	−11.6746	−0.766473
$233$	8.10992	0.531298	0.265649	−	0.964070i	$-0.414414\pi$
$233$	8.10992	0.531298	0.265649	+	0.964070i	$0.414414\pi$
$234$	0	0
$235$	1.97285	0.128695
$236$	−4.37867	−0.285027
$237$	0	0
$238$	−18.1957	−1.17945
$239$	−6.38165	−0.412795	−0.206397	−	0.978468i	$-0.566174\pi$
$239$	−6.38165	−0.412795	−0.206397	+	0.978468i	$0.566174\pi$
$240$	0	0
$241$	1.30127	0.0838224	0.0419112	−	0.999121i	$-0.486655\pi$
$241$	1.30127	0.0838224	0.0419112	+	0.999121i	$0.486655\pi$
$242$	12.4698	0.801589
$243$	0	0
$244$	6.05861	0.387863
$245$	1.95108	0.124650
$246$	0	0
$247$	0	0
$248$	−5.22521	−0.331801
$249$	0	0
$250$	1.24698	0.0788659
$251$	−9.51142	−0.600355	−0.300178	−	0.953883i	$-0.597046\pi$
$251$	−9.51142	−0.600355	−0.300178	+	0.953883i	$0.597046\pi$
$252$	0	0
$253$	−0.198062	−0.0124521
$254$	23.0127	1.44394
$255$	0	0
$256$	−10.1129	−0.632056
$257$	−7.38942	−0.460939	−0.230470	−	0.973080i	$-0.574026\pi$
$257$	−7.38942	−0.460939	−0.230470	+	0.973080i	$0.574026\pi$
$258$	0	0
$259$	−10.2078	−0.634279
$260$	0	0
$261$	0	0
$262$	10.1250	0.625523
$263$	3.06398	0.188933	0.0944666	−	0.995528i	$-0.469885\pi$
$263$	3.06398	0.188933	0.0944666	+	0.995528i	$0.469885\pi$
$264$	0	0
$265$	12.0586	0.740754
$266$	6.54288	0.401170
$267$	0	0
$268$	3.52111	0.215086
$269$	18.2687	1.11387	0.556933	−	0.830558i	$-0.311978\pi$
$269$	18.2687	1.11387	0.556933	+	0.830558i	$0.311978\pi$
$270$	0	0
$271$	4.04892	0.245954	0.122977	−	0.992410i	$-0.460756\pi$
$271$	4.04892	0.245954	0.122977	+	0.992410i	$0.460756\pi$
$272$	−18.9095	−1.14655
$273$	0	0
$274$	−27.1564	−1.64058
$275$	1.00000	0.0603023
$276$	0	0
$277$	28.1608	1.69202	0.846008	−	0.533170i	$-0.179000\pi$
$277$	28.1608	1.69202	0.846008	+	0.533170i	$0.179000\pi$
$278$	24.1987	1.45134
$279$	0	0
$280$	−6.85086	−0.409417
$281$	−24.3937	−1.45521	−0.727604	−	0.685997i	$-0.759366\pi$
$281$	−24.3937	−1.45521	−0.727604	+	0.685997i	$0.759366\pi$
$282$	0	0
$283$	−7.16315	−0.425805	−0.212902	−	0.977073i	$-0.568292\pi$
$283$	−7.16315	−0.425805	−0.212902	+	0.977073i	$0.568292\pi$
$284$	−3.18060	−0.188734
$285$	0	0
$286$	0	0
$287$	12.9269	0.763052
$288$	0	0
$289$	25.1715	1.48068
$290$	−4.77479	−0.280385
$291$	0	0
$292$	6.38835	0.373850
$293$	−5.01075	−0.292731	−0.146366	−	0.989231i	$-0.546758\pi$
$293$	−5.01075	−0.292731	−0.146366	+	0.989231i	$0.546758\pi$
$294$	0	0
$295$	−9.83877	−0.572836
$296$	−13.8509	−0.805065
$297$	0	0
$298$	−14.2989	−0.828312
$299$	0	0
$300$	0	0
$301$	−8.43296	−0.486068
$302$	7.69501	0.442798
$303$	0	0
$304$	6.79954	0.389981
$305$	13.6136	0.779510
$306$	0	0
$307$	29.8213	1.70199	0.850996	−	0.525172i	$-0.175999\pi$
$307$	29.8213	1.70199	0.850996	+	0.525172i	$0.175999\pi$
$308$	−1.00000	−0.0569803
$309$	0	0
$310$	−2.13706	−0.121377
$311$	6.22952	0.353244	0.176622	−	0.984279i	$-0.443483\pi$
$311$	6.22952	0.353244	0.176622	+	0.984279i	$0.443483\pi$
$312$	0	0
$313$	8.22713	0.465025	0.232512	−	0.972593i	$-0.425305\pi$
$313$	8.22713	0.465025	0.232512	+	0.972593i	$0.425305\pi$
$314$	19.0887	1.07724
$315$	0	0
$316$	−4.72587	−0.265851
$317$	−20.2010	−1.13460	−0.567302	−	0.823510i	$-0.692013\pi$
$317$	−20.2010	−1.13460	−0.567302	+	0.823510i	$0.692013\pi$
$318$	0	0
$319$	−3.82908	−0.214388
$320$	−8.89977	−0.497512
$321$	0	0
$322$	0.554958	0.0309266
$323$	−15.1642	−0.843759
$324$	0	0
$325$	0	0
$326$	−24.4306	−1.35308
$327$	0	0
$328$	17.5405	0.968511
$329$	−4.43296	−0.244397
$330$	0	0
$331$	11.2771	0.619846	0.309923	−	0.950762i	$-0.399697\pi$
$331$	11.2771	0.619846	0.309923	+	0.950762i	$0.399697\pi$
$332$	5.66056	0.310664
$333$	0	0
$334$	−11.2905	−0.617790
$335$	7.91185	0.432271
$336$	0	0
$337$	−21.1075	−1.14980	−0.574900	−	0.818224i	$-0.694959\pi$
$337$	−21.1075	−1.14980	−0.574900	+	0.818224i	$0.694959\pi$
$338$	0	0
$339$	0	0
$340$	2.89008	0.156737
$341$	−1.71379	−0.0928070
$342$	0	0
$343$	−20.1129	−1.08599
$344$	−11.4426	−0.616946
$345$	0	0
$346$	−16.7778	−0.901979
$347$	−21.3744	−1.14744	−0.573718	−	0.819053i	$-0.694499\pi$
$347$	−21.3744	−1.14744	−0.573718	+	0.819053i	$0.694499\pi$
$348$	0	0
$349$	4.31527	0.230991	0.115496	−	0.993308i	$-0.463154\pi$
$349$	4.31527	0.230991	0.115496	+	0.993308i	$0.463154\pi$
$350$	−2.80194	−0.149770
$351$	0	0
$352$	−2.46681	−0.131482
$353$	−10.2198	−0.543947	−0.271973	−	0.962305i	$-0.587676\pi$
$353$	−10.2198	−0.543947	−0.271973	+	0.962305i	$0.587676\pi$
$354$	0	0
$355$	−7.14675	−0.379310
$356$	3.05861	0.162106
$357$	0	0
$358$	26.6829	1.41024
$359$	−8.71678	−0.460054	−0.230027	−	0.973184i	$-0.573881\pi$
$359$	−8.71678	−0.460054	−0.230027	+	0.973184i	$0.573881\pi$
$360$	0	0
$361$	−13.5472	−0.713010
$362$	17.5864	0.924322
$363$	0	0
$364$	0	0
$365$	14.3545	0.751349
$366$	0	0
$367$	−5.37973	−0.280820	−0.140410	−	0.990093i	$-0.544842\pi$
$367$	−5.37973	−0.280820	−0.140410	+	0.990093i	$0.544842\pi$
$368$	0.576728	0.0300640
$369$	0	0
$370$	−5.66487	−0.294503
$371$	−27.0954	−1.40673
$372$	0	0
$373$	−12.6843	−0.656766	−0.328383	−	0.944545i	$-0.606504\pi$
$373$	−12.6843	−0.656766	−0.328383	+	0.944545i	$0.606504\pi$
$374$	−8.09783	−0.418729
$375$	0	0
$376$	−6.01507	−0.310203
$377$	0	0
$378$	0	0
$379$	−7.99223	−0.410533	−0.205267	−	0.978706i	$-0.565806\pi$
$379$	−7.99223	−0.410533	−0.205267	+	0.978706i	$0.565806\pi$
$380$	−1.03923	−0.0533113
$381$	0	0
$382$	8.96748	0.458816
$383$	−0.763774	−0.0390270	−0.0195135	−	0.999810i	$-0.506212\pi$
$383$	−0.763774	−0.0390270	−0.0195135	+	0.999810i	$0.506212\pi$
$384$	0	0
$385$	−2.24698	−0.114517
$386$	−14.0925	−0.717287
$387$	0	0
$388$	−4.95838	−0.251724
$389$	28.8799	1.46427	0.732135	−	0.681159i	$-0.238524\pi$
$389$	28.8799	1.46427	0.732135	+	0.681159i	$0.238524\pi$
$390$	0	0
$391$	−1.28621	−0.0650463
$392$	−5.94869	−0.300454
$393$	0	0
$394$	25.5714	1.28827
$395$	−10.6189	−0.534297
$396$	0	0
$397$	33.1347	1.66298	0.831491	−	0.555539i	$-0.187488\pi$
$397$	33.1347	1.66298	0.831491	+	0.555539i	$0.187488\pi$
$398$	−24.8998	−1.24811
$399$	0	0
$400$	−2.91185	−0.145593
$401$	−11.0435	−0.551488	−0.275744	−	0.961231i	$-0.588924\pi$
$401$	−11.0435	−0.551488	−0.275744	+	0.961231i	$0.588924\pi$
$402$	0	0
$403$	0	0
$404$	−3.64550	−0.181370
$405$	0	0
$406$	10.7289	0.532464
$407$	−4.54288	−0.225182
$408$	0	0
$409$	−33.3424	−1.64868	−0.824338	−	0.566097i	$-0.808453\pi$
$409$	−33.3424	−1.64868	−0.824338	+	0.566097i	$0.808453\pi$
$410$	7.17390	0.354294
$411$	0	0
$412$	4.23729	0.208756
$413$	22.1075	1.08784
$414$	0	0
$415$	12.7192	0.624359
$416$	0	0
$417$	0	0
$418$	2.91185	0.142423
$419$	−39.9071	−1.94959	−0.974794	−	0.223107i	$-0.928380\pi$
$419$	−39.9071	−1.94959	−0.974794	+	0.223107i	$0.928380\pi$
$420$	0	0
$421$	−9.41657	−0.458935	−0.229468	−	0.973316i	$-0.573699\pi$
$421$	−9.41657	−0.458935	−0.229468	+	0.973316i	$0.573699\pi$
$422$	12.1535	0.591621
$423$	0	0
$424$	−36.7657	−1.78550
$425$	6.49396	0.315003
$426$	0	0
$427$	−30.5894	−1.48032
$428$	−6.31229	−0.305116
$429$	0	0
$430$	−4.67994	−0.225687
$431$	25.9976	1.25226	0.626130	−	0.779718i	$-0.284638\pi$
$431$	25.9976	1.25226	0.626130	+	0.779718i	$0.284638\pi$
$432$	0	0
$433$	6.93661	0.333352	0.166676	−	0.986012i	$-0.446697\pi$
$433$	6.93661	0.333352	0.166676	+	0.986012i	$0.446697\pi$
$434$	4.80194	0.230500
$435$	0	0
$436$	−4.53750	−0.217307
$437$	0.462500	0.0221244
$438$	0	0
$439$	18.6775	0.891431	0.445715	−	0.895175i	$-0.352949\pi$
$439$	18.6775	0.891431	0.445715	+	0.895175i	$0.352949\pi$
$440$	−3.04892	−0.145351
$441$	0	0
$442$	0	0
$443$	−36.9245	−1.75434	−0.877169	−	0.480183i	$-0.840570\pi$
$443$	−36.9245	−1.75434	−0.877169	+	0.480183i	$0.840570\pi$
$444$	0	0
$445$	6.87263	0.325794
$446$	−30.5948	−1.44870
$447$	0	0
$448$	19.9976	0.944798
$449$	−15.3884	−0.726221	−0.363111	−	0.931746i	$-0.618285\pi$
$449$	−15.3884	−0.726221	−0.363111	+	0.931746i	$0.618285\pi$
$450$	0	0
$451$	5.75302	0.270899
$452$	3.06531	0.144180
$453$	0	0
$454$	−0.0271471	−0.00127408
$455$	0	0
$456$	0	0
$457$	25.2946	1.18323	0.591615	−	0.806221i	$-0.298491\pi$
$457$	25.2946	1.18323	0.591615	+	0.806221i	$0.298491\pi$
$458$	9.18896	0.429372
$459$	0	0
$460$	−0.0881460	−0.00410983
$461$	−8.68664	−0.404577	−0.202289	−	0.979326i	$-0.564838\pi$
$461$	−8.68664	−0.404577	−0.202289	+	0.979326i	$0.564838\pi$
$462$	0	0
$463$	−1.73663	−0.0807079	−0.0403539	−	0.999185i	$-0.512849\pi$
$463$	−1.73663	−0.0807079	−0.0403539	+	0.999185i	$0.512849\pi$
$464$	11.1497	0.517613
$465$	0	0
$466$	−10.1129	−0.468471
$467$	−22.3177	−1.03274	−0.516369	−	0.856366i	$-0.672717\pi$
$467$	−22.3177	−1.03274	−0.516369	+	0.856366i	$0.672717\pi$
$468$	0	0
$469$	−17.7778	−0.820901
$470$	−2.46011	−0.113476
$471$	0	0
$472$	29.9976	1.38075
$473$	−3.75302	−0.172564
$474$	0	0
$475$	−2.33513	−0.107143
$476$	−6.49396	−0.297650
$477$	0	0
$478$	7.95779	0.363981
$479$	−26.6765	−1.21888	−0.609440	−	0.792832i	$-0.708606\pi$
$479$	−26.6765	−1.21888	−0.609440	+	0.792832i	$0.708606\pi$
$480$	0	0
$481$	0	0
$482$	−1.62266	−0.0739102
$483$	0	0
$484$	4.45042	0.202292
$485$	−11.1414	−0.505904
$486$	0	0
$487$	−8.61655	−0.390453	−0.195227	−	0.980758i	$-0.562544\pi$
$487$	−8.61655	−0.390453	−0.195227	+	0.980758i	$0.562544\pi$
$488$	−41.5066	−1.87892
$489$	0	0
$490$	−2.43296	−0.109910
$491$	0.992230	0.0447787	0.0223894	−	0.999749i	$-0.492873\pi$
$491$	0.992230	0.0447787	0.0223894	+	0.999749i	$0.492873\pi$
$492$	0	0
$493$	−24.8659	−1.11990
$494$	0	0
$495$	0	0
$496$	4.99031	0.224072
$497$	16.0586	0.720327
$498$	0	0
$499$	−16.7138	−0.748212	−0.374106	−	0.927386i	$-0.622050\pi$
$499$	−16.7138	−0.748212	−0.374106	+	0.927386i	$0.622050\pi$
$500$	0.445042	0.0199029
$501$	0	0
$502$	11.8605	0.529362
$503$	−30.6547	−1.36683	−0.683413	−	0.730032i	$-0.739505\pi$
$503$	−30.6547	−1.36683	−0.683413	+	0.730032i	$0.739505\pi$
$504$	0	0
$505$	−8.19136	−0.364511
$506$	0.246980	0.0109796
$507$	0	0
$508$	8.21313	0.364399
$509$	25.9506	1.15024	0.575120	−	0.818069i	$-0.304955\pi$
$509$	25.9506	1.15024	0.575120	+	0.818069i	$0.304955\pi$
$510$	0	0
$511$	−32.2543	−1.42685
$512$	24.9390	1.10216
$513$	0	0
$514$	9.21446	0.406432
$515$	9.52111	0.419550
$516$	0	0
$517$	−1.97285	−0.0867660
$518$	12.7289	0.559274
$519$	0	0
$520$	0	0
$521$	12.3375	0.540516	0.270258	−	0.962788i	$-0.412891\pi$
$521$	12.3375	0.540516	0.270258	+	0.962788i	$0.412891\pi$
$522$	0	0
$523$	−20.7748	−0.908418	−0.454209	−	0.890895i	$-0.650078\pi$
$523$	−20.7748	−0.908418	−0.454209	+	0.890895i	$0.650078\pi$
$524$	3.61356	0.157859
$525$	0	0
$526$	−3.82072	−0.166591
$527$	−11.1293	−0.484800
$528$	0	0
$529$	−22.9608	−0.998294
$530$	−15.0368	−0.653158
$531$	0	0
$532$	2.33513	0.101241
$533$	0	0
$534$	0	0
$535$	−14.1836	−0.613210
$536$	−24.1226	−1.04194
$537$	0	0
$538$	−22.7808	−0.982148
$539$	−1.95108	−0.0840391
$540$	0	0
$541$	−45.5797	−1.95962	−0.979812	−	0.199919i	$-0.935932\pi$
$541$	−45.5797	−1.95962	−0.979812	+	0.199919i	$0.935932\pi$
$542$	−5.04892	−0.216870
$543$	0	0
$544$	−16.0194	−0.686825
$545$	−10.1957	−0.436734
$546$	0	0
$547$	−14.0194	−0.599425	−0.299713	−	0.954030i	$-0.596891\pi$
$547$	−14.0194	−0.599425	−0.299713	+	0.954030i	$0.596891\pi$
$548$	−9.69202	−0.414023
$549$	0	0
$550$	−1.24698	−0.0531714
$551$	8.94139	0.380916
$552$	0	0
$553$	23.8605	1.01465
$554$	−35.1159	−1.49193
$555$	0	0
$556$	8.63640	0.366265
$557$	−21.2591	−0.900775	−0.450388	−	0.892833i	$-0.648714\pi$
$557$	−21.2591	−0.900775	−0.450388	+	0.892833i	$0.648714\pi$
$558$	0	0
$559$	0	0
$560$	6.54288	0.276487
$561$	0	0
$562$	30.4185	1.28313
$563$	−13.5198	−0.569791	−0.284895	−	0.958559i	$-0.591959\pi$
$563$	−13.5198	−0.569791	−0.284895	+	0.958559i	$0.591959\pi$
$564$	0	0
$565$	6.88769	0.289767
$566$	8.93230	0.375452
$567$	0	0
$568$	21.7899	0.914282
$569$	30.9202	1.29624	0.648121	−	0.761537i	$-0.275555\pi$
$569$	30.9202	1.29624	0.648121	+	0.761537i	$0.275555\pi$
$570$	0	0
$571$	5.33645	0.223324	0.111662	−	0.993746i	$-0.464383\pi$
$571$	5.33645	0.223324	0.111662	+	0.993746i	$0.464383\pi$
$572$	0	0
$573$	0	0
$574$	−16.1196	−0.672819
$575$	−0.198062	−0.00825977
$576$	0	0
$577$	−17.3889	−0.723911	−0.361956	−	0.932195i	$-0.617891\pi$
$577$	−17.3889	−0.723911	−0.361956	+	0.932195i	$0.617891\pi$
$578$	−31.3884	−1.30558
$579$	0	0
$580$	−1.70410	−0.0707590
$581$	−28.5797	−1.18569
$582$	0	0
$583$	−12.0586	−0.499416
$584$	−43.7657	−1.81104
$585$	0	0
$586$	6.24831	0.258115
$587$	21.4668	0.886030	0.443015	−	0.896514i	$-0.353909\pi$
$587$	21.4668	0.886030	0.443015	+	0.896514i	$0.353909\pi$
$588$	0	0
$589$	4.00192	0.164896
$590$	12.2687	0.505096
$591$	0	0
$592$	13.2282	0.543675
$593$	−4.27605	−0.175596	−0.0877981	−	0.996138i	$-0.527983\pi$
$593$	−4.27605	−0.175596	−0.0877981	+	0.996138i	$0.527983\pi$
$594$	0	0
$595$	−14.5918	−0.598205
$596$	−5.10321	−0.209036
$597$	0	0
$598$	0	0
$599$	23.2180	0.948663	0.474332	−	0.880346i	$-0.342690\pi$
$599$	23.2180	0.948663	0.474332	+	0.880346i	$0.342690\pi$
$600$	0	0
$601$	−32.2704	−1.31634	−0.658169	−	0.752871i	$-0.728669\pi$
$601$	−32.2704	−1.31634	−0.658169	+	0.752871i	$0.728669\pi$
$602$	10.5157	0.428589
$603$	0	0
$604$	2.74632	0.111746
$605$	10.0000	0.406558
$606$	0	0
$607$	13.8920	0.563859	0.281929	−	0.959435i	$-0.409026\pi$
$607$	13.8920	0.563859	0.281929	+	0.959435i	$0.409026\pi$
$608$	5.76032	0.233612
$609$	0	0
$610$	−16.9758	−0.687332
$611$	0	0
$612$	0	0
$613$	−27.6668	−1.11745	−0.558726	−	0.829353i	$-0.688710\pi$
$613$	−27.6668	−1.11745	−0.558726	+	0.829353i	$0.688710\pi$
$614$	−37.1866	−1.50073
$615$	0	0
$616$	6.85086	0.276029
$617$	10.3709	0.417517	0.208758	−	0.977967i	$-0.433058\pi$
$617$	10.3709	0.417517	0.208758	+	0.977967i	$0.433058\pi$
$618$	0	0
$619$	43.1473	1.73424	0.867119	−	0.498101i	$-0.165969\pi$
$619$	43.1473	1.73424	0.867119	+	0.498101i	$0.165969\pi$
$620$	−0.762709	−0.0306311
$621$	0	0
$622$	−7.76809	−0.311472
$623$	−15.4426	−0.618697
$624$	0	0
$625$	1.00000	0.0400000
$626$	−10.2591	−0.410035
$627$	0	0
$628$	6.81269	0.271856
$629$	−29.5013	−1.17629
$630$	0	0
$631$	22.6987	0.903622	0.451811	−	0.892114i	$-0.350778\pi$
$631$	22.6987	0.903622	0.451811	+	0.892114i	$0.350778\pi$
$632$	32.3763	1.28786
$633$	0	0
$634$	25.1903	1.00043
$635$	18.4547	0.732354
$636$	0	0
$637$	0	0
$638$	4.77479	0.189036
$639$	0	0
$640$	6.16421	0.243662
$641$	16.1075	0.636209	0.318104	−	0.948056i	$-0.396954\pi$
$641$	16.1075	0.636209	0.318104	+	0.948056i	$0.396954\pi$
$642$	0	0
$643$	−32.8732	−1.29639	−0.648197	−	0.761473i	$-0.724476\pi$
$643$	−32.8732	−1.29639	−0.648197	+	0.761473i	$0.724476\pi$
$644$	0.198062	0.00780475
$645$	0	0
$646$	18.9095	0.743983
$647$	10.2814	0.404204	0.202102	−	0.979364i	$-0.435223\pi$
$647$	10.2814	0.404204	0.202102	+	0.979364i	$0.435223\pi$
$648$	0	0
$649$	9.83877	0.386206
$650$	0	0
$651$	0	0
$652$	−8.71917	−0.341469
$653$	−14.3575	−0.561852	−0.280926	−	0.959729i	$-0.590642\pi$
$653$	−14.3575	−0.561852	−0.280926	+	0.959729i	$0.590642\pi$
$654$	0	0
$655$	8.11960	0.317259
$656$	−16.7520	−0.654054
$657$	0	0
$658$	5.52781	0.215497
$659$	16.0258	0.624277	0.312139	−	0.950037i	$-0.398955\pi$
$659$	16.0258	0.624277	0.312139	+	0.950037i	$0.398955\pi$
$660$	0	0
$661$	−27.4282	−1.06683	−0.533416	−	0.845853i	$-0.679092\pi$
$661$	−27.4282	−1.06683	−0.533416	+	0.845853i	$0.679092\pi$
$662$	−14.0623	−0.546548
$663$	0	0
$664$	−38.7797	−1.50494
$665$	5.24698	0.203469
$666$	0	0
$667$	0.758397	0.0293653
$668$	−4.02954	−0.155908
$669$	0	0
$670$	−9.86592	−0.381154
$671$	−13.6136	−0.525546
$672$	0	0
$673$	1.10321	0.0425257	0.0212628	−	0.999774i	$-0.493231\pi$
$673$	1.10321	0.0425257	0.0212628	+	0.999774i	$0.493231\pi$
$674$	26.3207	1.01383
$675$	0	0
$676$	0	0
$677$	31.7754	1.22123	0.610614	−	0.791929i	$-0.290923\pi$
$677$	31.7754	1.22123	0.610614	+	0.791929i	$0.290923\pi$
$678$	0	0
$679$	25.0344	0.960734
$680$	−19.7995	−0.759278
$681$	0	0
$682$	2.13706	0.0818324
$683$	4.45606	0.170506	0.0852532	−	0.996359i	$-0.472830\pi$
$683$	4.45606	0.170506	0.0852532	+	0.996359i	$0.472830\pi$
$684$	0	0
$685$	−21.7778	−0.832086
$686$	25.0804	0.957573
$687$	0	0
$688$	10.9282	0.416636
$689$	0	0
$690$	0	0
$691$	14.1438	0.538054	0.269027	−	0.963133i	$-0.413298\pi$
$691$	14.1438	0.538054	0.269027	+	0.963133i	$0.413298\pi$
$692$	−5.98792	−0.227627
$693$	0	0
$694$	26.6534	1.01175
$695$	19.4058	0.736104
$696$	0	0
$697$	37.3599	1.41511
$698$	−5.38106	−0.203676
$699$	0	0
$700$	−1.00000	−0.0377964
$701$	4.74632	0.179266	0.0896329	−	0.995975i	$-0.471431\pi$
$701$	4.74632	0.179266	0.0896329	+	0.995975i	$0.471431\pi$
$702$	0	0
$703$	10.6082	0.400095
$704$	8.89977	0.335423
$705$	0	0
$706$	12.7439	0.479624
$707$	18.4058	0.692222
$708$	0	0
$709$	−15.4112	−0.578779	−0.289390	−	0.957211i	$-0.593452\pi$
$709$	−15.4112	−0.578779	−0.289390	+	0.957211i	$0.593452\pi$
$710$	8.91185	0.334456
$711$	0	0
$712$	−20.9541	−0.785287
$713$	0.339437	0.0127120
$714$	0	0
$715$	0	0
$716$	9.52303	0.355892
$717$	0	0
$718$	10.8696	0.405651
$719$	−11.8194	−0.440789	−0.220395	−	0.975411i	$-0.570734\pi$
$719$	−11.8194	−0.440789	−0.220395	+	0.975411i	$0.570734\pi$
$720$	0	0
$721$	−21.3937	−0.796744
$722$	16.8931	0.628695
$723$	0	0
$724$	6.27652	0.233265
$725$	−3.82908	−0.142209
$726$	0	0
$727$	−21.9675	−0.814729	−0.407364	−	0.913266i	$-0.633552\pi$
$727$	−21.9675	−0.814729	−0.407364	+	0.913266i	$0.633552\pi$
$728$	0	0
$729$	0	0
$730$	−17.8998	−0.662500
$731$	−24.3720	−0.901430
$732$	0	0
$733$	36.0586	1.33186	0.665928	−	0.746016i	$-0.268036\pi$
$733$	36.0586	1.33186	0.665928	+	0.746016i	$0.268036\pi$
$734$	6.70841	0.247612
$735$	0	0
$736$	0.488582	0.0180094
$737$	−7.91185	−0.291437
$738$	0	0
$739$	−36.9842	−1.36049	−0.680243	−	0.732987i	$-0.738126\pi$
$739$	−36.9842	−1.36049	−0.680243	+	0.732987i	$0.738126\pi$
$740$	−2.02177	−0.0743218
$741$	0	0
$742$	33.7875	1.24038
$743$	1.42865	0.0524120	0.0262060	−	0.999657i	$-0.491657\pi$
$743$	1.42865	0.0524120	0.0262060	+	0.999657i	$0.491657\pi$
$744$	0	0
$745$	−11.4668	−0.420111
$746$	15.8170	0.579102
$747$	0	0
$748$	−2.89008	−0.105672
$749$	31.8702	1.16451
$750$	0	0
$751$	−37.9874	−1.38618	−0.693091	−	0.720850i	$-0.743752\pi$
$751$	−37.9874	−1.38618	−0.693091	+	0.720850i	$0.743752\pi$
$752$	5.74466	0.209486
$753$	0	0
$754$	0	0
$755$	6.17092	0.224583
$756$	0	0
$757$	30.6805	1.11510	0.557551	−	0.830142i	$-0.311741\pi$
$757$	30.6805	1.11510	0.557551	+	0.830142i	$0.311741\pi$
$758$	9.96615	0.361987
$759$	0	0
$760$	7.11960	0.258255
$761$	−52.1213	−1.88939	−0.944697	−	0.327944i	$-0.893644\pi$
$761$	−52.1213	−1.88939	−0.944697	+	0.327944i	$0.893644\pi$
$762$	0	0
$763$	22.9095	0.829378
$764$	3.20046	0.115788
$765$	0	0
$766$	0.952411	0.0344120
$767$	0	0
$768$	0	0
$769$	−30.4222	−1.09705	−0.548526	−	0.836133i	$-0.684811\pi$
$769$	−30.4222	−1.09705	−0.548526	+	0.836133i	$0.684811\pi$
$770$	2.80194	0.100975
$771$	0	0
$772$	−5.02954	−0.181017
$773$	−23.1118	−0.831275	−0.415637	−	0.909530i	$-0.636441\pi$
$773$	−23.1118	−0.831275	−0.415637	+	0.909530i	$0.636441\pi$
$774$	0	0
$775$	−1.71379	−0.0615612
$776$	33.9691	1.21942
$777$	0	0
$778$	−36.0127	−1.29112
$779$	−13.4340	−0.481324
$780$	0	0
$781$	7.14675	0.255731
$782$	1.60388	0.0573545
$783$	0	0
$784$	5.68127	0.202902
$785$	15.3080	0.546365
$786$	0	0
$787$	16.2929	0.580780	0.290390	−	0.956908i	$-0.406215\pi$
$787$	16.2929	0.580780	0.290390	+	0.956908i	$0.406215\pi$
$788$	9.12631	0.325111
$789$	0	0
$790$	13.2416	0.471115
$791$	−15.4765	−0.550281
$792$	0	0
$793$	0	0
$794$	−41.3183	−1.46633
$795$	0	0
$796$	−8.88663	−0.314978
$797$	−18.2573	−0.646705	−0.323353	−	0.946279i	$-0.604810\pi$
$797$	−18.2573	−0.646705	−0.323353	+	0.946279i	$0.604810\pi$
$798$	0	0
$799$	−12.8116	−0.453243
$800$	−2.46681	−0.0872150
$801$	0	0
$802$	13.7711	0.486273
$803$	−14.3545	−0.506559
$804$	0	0
$805$	0.445042	0.0156857
$806$	0	0
$807$	0	0
$808$	24.9748	0.878609
$809$	24.7259	0.869315	0.434658	−	0.900596i	$-0.356869\pi$
$809$	24.7259	0.869315	0.434658	+	0.900596i	$0.356869\pi$
$810$	0	0
$811$	−3.05429	−0.107251	−0.0536254	−	0.998561i	$-0.517078\pi$
$811$	−3.05429	−0.107251	−0.0536254	+	0.998561i	$0.517078\pi$
$812$	3.82908	0.134375
$813$	0	0
$814$	5.66487	0.198554
$815$	−19.5918	−0.686271
$816$	0	0
$817$	8.76377	0.306606
$818$	41.5773	1.45372
$819$	0	0
$820$	2.56033	0.0894108
$821$	−17.7646	−0.619990	−0.309995	−	0.950738i	$-0.600327\pi$
$821$	−17.7646	−0.619990	−0.309995	+	0.950738i	$0.600327\pi$
$822$	0	0
$823$	32.1333	1.12010	0.560049	−	0.828460i	$-0.310782\pi$
$823$	32.1333	1.12010	0.560049	+	0.828460i	$0.310782\pi$
$824$	−29.0291	−1.01128
$825$	0	0
$826$	−27.5676	−0.959201
$827$	24.5724	0.854467	0.427233	−	0.904141i	$-0.359488\pi$
$827$	24.5724	0.854467	0.427233	+	0.904141i	$0.359488\pi$
$828$	0	0
$829$	−9.57135	−0.332427	−0.166213	−	0.986090i	$-0.553154\pi$
$829$	−9.57135	−0.332427	−0.166213	+	0.986090i	$0.553154\pi$
$830$	−15.8605	−0.550528
$831$	0	0
$832$	0	0
$833$	−12.6703	−0.438998
$834$	0	0
$835$	−9.05429	−0.313337
$836$	1.03923	0.0359425
$837$	0	0
$838$	49.7633	1.71904
$839$	48.3510	1.66926	0.834632	−	0.550808i	$-0.185680\pi$
$839$	48.3510	1.66926	0.834632	+	0.550808i	$0.185680\pi$
$840$	0	0
$841$	−14.3381	−0.494418
$842$	11.7423	0.404665
$843$	0	0
$844$	4.33752	0.149304
$845$	0	0
$846$	0	0
$847$	−22.4698	−0.772071
$848$	35.1129	1.20578
$849$	0	0
$850$	−8.09783	−0.277753
$851$	0.899772	0.0308438
$852$	0	0
$853$	−0.524090	−0.0179445	−0.00897225	−	0.999960i	$-0.502856\pi$
$853$	−0.524090	−0.0179445	−0.00897225	+	0.999960i	$0.502856\pi$
$854$	38.1444	1.30527
$855$	0	0
$856$	43.2446	1.47807
$857$	19.9377	0.681058	0.340529	−	0.940234i	$-0.389394\pi$
$857$	19.9377	0.681058	0.340529	+	0.940234i	$0.389394\pi$
$858$	0	0
$859$	−34.8437	−1.18885	−0.594425	−	0.804151i	$-0.702620\pi$
$859$	−34.8437	−1.18885	−0.594425	+	0.804151i	$0.702620\pi$
$860$	−1.67025	−0.0569551
$861$	0	0
$862$	−32.4185	−1.10418
$863$	15.4416	0.525638	0.262819	−	0.964845i	$-0.415348\pi$
$863$	15.4416	0.525638	0.262819	+	0.964845i	$0.415348\pi$
$864$	0	0
$865$	−13.4547	−0.457475
$866$	−8.64981	−0.293932
$867$	0	0
$868$	1.71379	0.0581699
$869$	10.6189	0.360223
$870$	0	0
$871$	0	0
$872$	31.0858	1.05270
$873$	0	0
$874$	−0.576728	−0.0195081
$875$	−2.24698	−0.0759618
$876$	0	0
$877$	−7.15751	−0.241692	−0.120846	−	0.992671i	$-0.538561\pi$
$877$	−7.15751	−0.241692	−0.120846	+	0.992671i	$0.538561\pi$
$878$	−23.2905	−0.786017
$879$	0	0
$880$	2.91185	0.0981586
$881$	29.9420	1.00877	0.504386	−	0.863479i	$-0.331719\pi$
$881$	29.9420	1.00877	0.504386	+	0.863479i	$0.331719\pi$
$882$	0	0
$883$	18.5139	0.623043	0.311522	−	0.950239i	$-0.399161\pi$
$883$	18.5139	0.623043	0.311522	+	0.950239i	$0.399161\pi$
$884$	0	0
$885$	0	0
$886$	46.0441	1.54688
$887$	46.5991	1.56464	0.782322	−	0.622874i	$-0.214035\pi$
$887$	46.5991	1.56464	0.782322	+	0.622874i	$0.214035\pi$
$888$	0	0
$889$	−41.4674	−1.39077
$890$	−8.57002	−0.287268
$891$	0	0
$892$	−10.9191	−0.365600
$893$	4.60686	0.154163
$894$	0	0
$895$	21.3980	0.715258
$896$	−13.8509	−0.462725
$897$	0	0
$898$	19.1890	0.640344
$899$	6.56225	0.218863
$900$	0	0
$901$	−78.3081	−2.60882
$902$	−7.17390	−0.238865
$903$	0	0
$904$	−21.0000	−0.698450
$905$	14.1032	0.468807
$906$	0	0
$907$	25.6004	0.850048	0.425024	−	0.905182i	$-0.360266\pi$
$907$	25.6004	0.850048	0.425024	+	0.905182i	$0.360266\pi$
$908$	−0.00968868	−0.000321530 0
$909$	0	0
$910$	0	0
$911$	24.9782	0.827566	0.413783	−	0.910376i	$-0.364207\pi$
$911$	24.9782	0.827566	0.413783	+	0.910376i	$0.364207\pi$
$912$	0	0
$913$	−12.7192	−0.420943
$914$	−31.5418	−1.04331
$915$	0	0
$916$	3.27950	0.108358
$917$	−18.2446	−0.602489
$918$	0	0
$919$	38.5338	1.27111	0.635556	−	0.772055i	$-0.280771\pi$
$919$	38.5338	1.27111	0.635556	+	0.772055i	$0.280771\pi$
$920$	0.603875	0.0199092
$921$	0	0
$922$	10.8321	0.356735
$923$	0	0
$924$	0	0
$925$	−4.54288	−0.149369
$926$	2.16554	0.0711640
$927$	0	0
$928$	9.44563	0.310068
$929$	−36.7840	−1.20684	−0.603422	−	0.797422i	$-0.706197\pi$
$929$	−36.7840	−1.20684	−0.603422	+	0.797422i	$0.706197\pi$
$930$	0	0
$931$	4.55602	0.149318
$932$	−3.60925	−0.118225
$933$	0	0
$934$	27.8297	0.910615
$935$	−6.49396	−0.212375
$936$	0	0
$937$	−10.3244	−0.337283	−0.168641	−	0.985677i	$-0.553938\pi$
$937$	−10.3244	−0.337283	−0.168641	+	0.985677i	$0.553938\pi$
$938$	22.1685	0.723828
$939$	0	0
$940$	−0.878002	−0.0286373
$941$	21.8170	0.711214	0.355607	−	0.934636i	$-0.384274\pi$
$941$	21.8170	0.711214	0.355607	+	0.934636i	$0.384274\pi$
$942$	0	0
$943$	−1.13946	−0.0371058
$944$	−28.6491	−0.932448
$945$	0	0
$946$	4.67994	0.152158
$947$	−59.4476	−1.93179	−0.965893	−	0.258942i	$-0.916626\pi$
$947$	−59.4476	−1.93179	−0.965893	+	0.258942i	$0.916626\pi$
$948$	0	0
$949$	0	0
$950$	2.91185	0.0944730
$951$	0	0
$952$	44.4892	1.44190
$953$	−21.4601	−0.695161	−0.347581	−	0.937650i	$-0.612997\pi$
$953$	−21.4601	−0.695161	−0.347581	+	0.937650i	$0.612997\pi$
$954$	0	0
$955$	7.19136	0.232707
$956$	2.84010	0.0918554
$957$	0	0
$958$	33.2650	1.07474
$959$	48.9342	1.58017
$960$	0	0
$961$	−28.0629	−0.905255
$962$	0	0
$963$	0	0
$964$	−0.579121	−0.0186522
$965$	−11.3013	−0.363801
$966$	0	0
$967$	−8.09379	−0.260279	−0.130139	−	0.991496i	$-0.541542\pi$
$967$	−8.09379	−0.260279	−0.130139	+	0.991496i	$0.541542\pi$
$968$	−30.4892	−0.979959
$969$	0	0
$970$	13.8931	0.446080
$971$	−55.6238	−1.78505	−0.892527	−	0.450994i	$-0.851070\pi$
$971$	−55.6238	−1.78505	−0.892527	+	0.450994i	$0.851070\pi$
$972$	0	0
$973$	−43.6045	−1.39790
$974$	10.7447	0.344281
$975$	0	0
$976$	39.6407	1.26887
$977$	−38.0847	−1.21844	−0.609219	−	0.793002i	$-0.708517\pi$
$977$	−38.0847	−1.21844	−0.609219	+	0.793002i	$0.708517\pi$
$978$	0	0
$979$	−6.87263	−0.219650
$980$	−0.868313	−0.0277373
$981$	0	0
$982$	−1.23729	−0.0394835
$983$	7.66786	0.244567	0.122283	−	0.992495i	$-0.460978\pi$
$983$	7.66786	0.244567	0.122283	+	0.992495i	$0.460978\pi$
$984$	0	0
$985$	20.5066	0.653396
$986$	31.0073	0.987473
$987$	0	0
$988$	0	0
$989$	0.743332	0.0236366
$990$	0	0
$991$	−34.7784	−1.10477	−0.552386	−	0.833589i	$-0.686282\pi$
$991$	−34.7784	−1.10477	−0.552386	+	0.833589i	$0.686282\pi$
$992$	4.22760	0.134227
$993$	0	0
$994$	−20.0248	−0.635147
$995$	−19.9681	−0.633030
$996$	0	0
$997$	−59.5220	−1.88508	−0.942540	−	0.334094i	$-0.891570\pi$
$997$	−59.5220	−1.88508	−0.942540	+	0.334094i	$0.891570\pi$
$998$	20.8418	0.659734
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7605.2.a.bz.1.1		3
3.2	odd	2		2535.2.a.v.1.3	✓	3
13.12	even	2		7605.2.a.bq.1.3		3
39.38	odd	2		2535.2.a.bd.1.1	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.2.a.v.1.3	✓	3	3.2	odd	2
2535.2.a.bd.1.1	yes	3	39.38	odd	2
7605.2.a.bq.1.3		3	13.12	even	2
7605.2.a.bz.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:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)

\(f(q)\)	\(=\)	\(q-1.24698 q^{2} -0.445042 q^{4} -1.00000 q^{5} +2.24698 q^{7} +3.04892 q^{8} +O(q^{10})\)	\(q-1.24698 q^{2} -0.445042 q^{4} -1.00000 q^{5} +2.24698 q^{7} +3.04892 q^{8} +1.24698 q^{10} +1.00000 q^{11} -2.80194 q^{14} -2.91185 q^{16} +6.49396 q^{17} -2.33513 q^{19} +0.445042 q^{20} -1.24698 q^{22} -0.198062 q^{23} +1.00000 q^{25} -1.00000 q^{28} -3.82908 q^{29} -1.71379 q^{31} -2.46681 q^{32} -8.09783 q^{34} -2.24698 q^{35} -4.54288 q^{37} +2.91185 q^{38} -3.04892 q^{40} +5.75302 q^{41} -3.75302 q^{43} -0.445042 q^{44} +0.246980 q^{46} -1.97285 q^{47} -1.95108 q^{49} -1.24698 q^{50} -12.0586 q^{53} -1.00000 q^{55} +6.85086 q^{56} +4.77479 q^{58} +9.83877 q^{59} -13.6136 q^{61} +2.13706 q^{62} +8.89977 q^{64} -7.91185 q^{67} -2.89008 q^{68} +2.80194 q^{70} +7.14675 q^{71} -14.3545 q^{73} +5.66487 q^{74} +1.03923 q^{76} +2.24698 q^{77} +10.6189 q^{79} +2.91185 q^{80} -7.17390 q^{82} -12.7192 q^{83} -6.49396 q^{85} +4.67994 q^{86} +3.04892 q^{88} -6.87263 q^{89} +0.0881460 q^{92} +2.46011 q^{94} +2.33513 q^{95} +11.1414 q^{97} +2.43296 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - q^{4} - 3 q^{5} + 2 q^{7}+O(q^{10}) \) 3 * q + q^2 - q^4 - 3 * q^5 + 2 * q^7	\( 3 q + q^{2} - q^{4} - 3 q^{5} + 2 q^{7} - q^{10} + 3 q^{11} - 4 q^{14} - 5 q^{16} + 10 q^{17} - 6 q^{19} + q^{20} + q^{22} - 5 q^{23} + 3 q^{25} - 3 q^{28} - q^{29} + 3 q^{31} - 4 q^{32} - 6 q^{34} - 2 q^{35} + 5 q^{37} + 5 q^{38} + 22 q^{41} - 16 q^{43} - q^{44} - 4 q^{46} - 12 q^{47} - 15 q^{49} + q^{50} - 5 q^{53} - 3 q^{55} + 7 q^{56} + 16 q^{58} - 3 q^{59} - 10 q^{61} + q^{62} + 4 q^{64} - 20 q^{67} - 8 q^{68} + 4 q^{70} - 6 q^{71} + 2 q^{73} + 18 q^{74} + 16 q^{76} + 2 q^{77} - 2 q^{79} + 5 q^{80} + 12 q^{82} - 27 q^{83} - 10 q^{85} - 10 q^{86} - 4 q^{89} + 4 q^{92} - 18 q^{94} + 6 q^{95} + 9 q^{97} - 12 q^{98}+O(q^{100}) \) 3 * q + q^2 - q^4 - 3 * q^5 + 2 * q^7 - q^10 + 3 * q^11 - 4 * q^14 - 5 * q^16 + 10 * q^17 - 6 * q^19 + q^20 + q^22 - 5 * q^23 + 3 * q^25 - 3 * q^28 - q^29 + 3 * q^31 - 4 * q^32 - 6 * q^34 - 2 * q^35 + 5 * q^37 + 5 * q^38 + 22 * q^41 - 16 * q^43 - q^44 - 4 * q^46 - 12 * q^47 - 15 * q^49 + q^50 - 5 * q^53 - 3 * q^55 + 7 * q^56 + 16 * q^58 - 3 * q^59 - 10 * q^61 + q^62 + 4 * q^64 - 20 * q^67 - 8 * q^68 + 4 * q^70 - 6 * q^71 + 2 * q^73 + 18 * q^74 + 16 * q^76 + 2 * q^77 - 2 * q^79 + 5 * q^80 + 12 * q^82 - 27 * q^83 - 10 * q^85 - 10 * q^86 - 4 * q^89 + 4 * q^92 - 18 * q^94 + 6 * q^95 + 9 * q^97 - 12 * q^98

Introduction

L-functions

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Database

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