LMFDB - Embedded newform 7225.2.a.bx.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7225,2,Mod(1,7225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7225, 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("7225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7225 = 5^{2} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7225.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:	$57.6919154604$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 425)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	7225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.38987 q^{2} -0.110824 q^{3} -0.0682683 q^{4} +0.154031 q^{6} -1.71589 q^{7} +2.87462 q^{8} -2.98772 q^{9} +O(q^{10})$	\(q-1.38987 q^{2} -0.110824 q^{3} -0.0682683 q^{4} +0.154031 q^{6} -1.71589 q^{7} +2.87462 q^{8} -2.98772 q^{9} +5.80080 q^{11} +0.00756580 q^{12} -1.25411 q^{13} +2.38486 q^{14} -3.85880 q^{16} +4.15253 q^{18} +2.82534 q^{19} +0.190162 q^{21} -8.06234 q^{22} -2.05243 q^{23} -0.318578 q^{24} +1.74304 q^{26} +0.663586 q^{27} +0.117141 q^{28} +5.20588 q^{29} -2.86221 q^{31} -0.386013 q^{32} -0.642871 q^{33} +0.203966 q^{36} -6.30922 q^{37} -3.92685 q^{38} +0.138986 q^{39} -9.45135 q^{41} -0.264300 q^{42} +7.43371 q^{43} -0.396010 q^{44} +2.85261 q^{46} -7.63491 q^{47} +0.427650 q^{48} -4.05573 q^{49} +0.0856157 q^{52} +7.20735 q^{53} -0.922296 q^{54} -4.93252 q^{56} -0.313117 q^{57} -7.23549 q^{58} +2.18242 q^{59} -5.73807 q^{61} +3.97809 q^{62} +5.12659 q^{63} +8.25411 q^{64} +0.893505 q^{66} -2.46660 q^{67} +0.227460 q^{69} +13.4782 q^{71} -8.58855 q^{72} -5.83755 q^{73} +8.76898 q^{74} -0.192881 q^{76} -9.95351 q^{77} -0.193172 q^{78} -3.92217 q^{79} +8.88961 q^{81} +13.1361 q^{82} +8.90908 q^{83} -0.0129821 q^{84} -10.3319 q^{86} -0.576939 q^{87} +16.6751 q^{88} +14.3079 q^{89} +2.15190 q^{91} +0.140116 q^{92} +0.317203 q^{93} +10.6115 q^{94} +0.0427797 q^{96} -8.49352 q^{97} +5.63693 q^{98} -17.3311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9} - 16 q^{13} + 24 q^{16} - 40 q^{18} - 16 q^{21} - 16 q^{26} - 56 q^{32} - 48 q^{33} + 24 q^{36} - 48 q^{38} - 32 q^{43} - 88 q^{47} + 16 q^{49} - 48 q^{52} - 48 q^{53} - 8 q^{59} + 72 q^{64} + 32 q^{66} - 40 q^{67} - 48 q^{69} - 120 q^{72} + 32 q^{76} - 120 q^{77} - 24 q^{81} - 104 q^{83} + 40 q^{84} - 16 q^{86} - 64 q^{87} + 16 q^{89} + 72 q^{93} + 112 q^{94} - 48 q^{98}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9 - 16 * q^13 + 24 * q^16 - 40 * q^18 - 16 * q^21 - 16 * q^26 - 56 * q^32 - 48 * q^33 + 24 * q^36 - 48 * q^38 - 32 * q^43 - 88 * q^47 + 16 * q^49 - 48 * q^52 - 48 * q^53 - 8 * q^59 + 72 * q^64 + 32 * q^66 - 40 * q^67 - 48 * q^69 - 120 * q^72 + 32 * q^76 - 120 * q^77 - 24 * q^81 - 104 * q^83 + 40 * q^84 - 16 * q^86 - 64 * q^87 + 16 * q^89 + 72 * q^93 + 112 * q^94 - 48 * 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 $

$2$	−1.38987	−0.982785	−0.491392	−	0.870938i	$-0.663512\pi$
$2$	−1.38987	−0.982785	−0.491392	+	0.870938i	$0.663512\pi$
$3$	−0.110824	−0.0639845	−0.0319923	−	0.999488i	$-0.510185\pi$
$3$	−0.110824	−0.0639845	−0.0319923	+	0.999488i	$0.510185\pi$
$4$	−0.0682683	−0.0341341
$5$	0	0
$5$	0	0
$6$	0.154031	0.0628830
$7$	−1.71589	−0.648544	−0.324272	−	0.945964i	$-0.605119\pi$
$7$	−1.71589	−0.648544	−0.324272	+	0.945964i	$0.605119\pi$
$8$	2.87462	1.01633
$9$	−2.98772	−0.995906
$10$	0	0
$11$	5.80080	1.74901	0.874503	−	0.485020i	$-0.161188\pi$
$11$	5.80080	1.74901	0.874503	+	0.485020i	$0.161188\pi$
$12$	0.00756580	0.00218406
$13$	−1.25411	−0.347827	−0.173913	−	0.984761i	$-0.555641\pi$
$13$	−1.25411	−0.347827	−0.173913	+	0.984761i	$0.555641\pi$
$14$	2.38486	0.637379
$15$	0	0
$16$	−3.85880	−0.964701
$17$	0	0
$17$	0	0
$18$	4.15253	0.978761
$19$	2.82534	0.648178	0.324089	−	0.946027i	$-0.394942\pi$
$19$	2.82534	0.648178	0.324089	+	0.946027i	$0.394942\pi$
$20$	0	0
$21$	0.190162	0.0414968
$22$	−8.06234	−1.71890
$23$	−2.05243	−0.427961	−0.213981	−	0.976838i	$-0.568643\pi$
$23$	−2.05243	−0.427961	−0.213981	+	0.976838i	$0.568643\pi$
$24$	−0.318578	−0.0650295
$25$	0	0
$26$	1.74304	0.341839
$27$	0.663586	0.127707
$28$	0.117141	0.0221375
$29$	5.20588	0.966708	0.483354	−	0.875425i	$-0.339418\pi$
$29$	5.20588	0.966708	0.483354	+	0.875425i	$0.339418\pi$
$30$	0	0
$31$	−2.86221	−0.514068	−0.257034	−	0.966402i	$-0.582745\pi$
$31$	−2.86221	−0.514068	−0.257034	+	0.966402i	$0.582745\pi$
$32$	−0.386013	−0.0682381
$33$	−0.642871	−0.111909
$34$	0	0
$35$	0	0
$36$	0.203966	0.0339944
$37$	−6.30922	−1.03723	−0.518615	−	0.855008i	$-0.673552\pi$
$37$	−6.30922	−1.03723	−0.518615	+	0.855008i	$0.673552\pi$
$38$	−3.92685	−0.637019
$39$	0.138986	0.0222555
$40$	0	0
$41$	−9.45135	−1.47605	−0.738027	−	0.674772i	$-0.764242\pi$
$41$	−9.45135	−1.47605	−0.738027	+	0.674772i	$0.764242\pi$
$42$	−0.264300	−0.0407824
$43$	7.43371	1.13363	0.566815	−	0.823845i	$-0.308175\pi$
$43$	7.43371	1.13363	0.566815	+	0.823845i	$0.308175\pi$
$44$	−0.396010	−0.0597008
$45$	0	0
$46$	2.85261	0.420594
$47$	−7.63491	−1.11367	−0.556833	−	0.830624i	$-0.687984\pi$
$47$	−7.63491	−1.11367	−0.556833	+	0.830624i	$0.687984\pi$
$48$	0.427650	0.0617259
$49$	−4.05573	−0.579390
$50$	0	0
$51$	0	0
$52$	0.0856157	0.0118728
$53$	7.20735	0.990006	0.495003	−	0.868891i	$-0.335167\pi$
$53$	7.20735	0.990006	0.495003	+	0.868891i	$0.335167\pi$
$54$	−0.922296	−0.125509
$55$	0	0
$56$	−4.93252	−0.659136
$57$	−0.313117	−0.0414734
$58$	−7.23549	−0.950066
$59$	2.18242	0.284128	0.142064	−	0.989858i	$-0.454626\pi$
$59$	2.18242	0.284128	0.142064	+	0.989858i	$0.454626\pi$
$60$	0	0
$61$	−5.73807	−0.734684	−0.367342	−	0.930086i	$-0.619732\pi$
$61$	−5.73807	−0.734684	−0.367342	+	0.930086i	$0.619732\pi$
$62$	3.97809	0.505218
$63$	5.12659	0.645889
$64$	8.25411	1.03176
$65$	0	0
$66$	0.893505	0.109983
$67$	−2.46660	−0.301343	−0.150672	−	0.988584i	$-0.548144\pi$
$67$	−2.46660	−0.301343	−0.150672	+	0.988584i	$0.548144\pi$
$68$	0	0
$69$	0.227460	0.0273829
$70$	0	0
$71$	13.4782	1.59956	0.799781	−	0.600291i	$-0.204949\pi$
$71$	13.4782	1.59956	0.799781	+	0.600291i	$0.204949\pi$
$72$	−8.58855	−1.01217
$73$	−5.83755	−0.683233	−0.341617	−	0.939839i	$-0.610974\pi$
$73$	−5.83755	−0.683233	−0.341617	+	0.939839i	$0.610974\pi$
$74$	8.76898	1.01937
$75$	0	0
$76$	−0.192881	−0.0221250
$77$	−9.95351	−1.13431
$78$	−0.193172	−0.0218724
$79$	−3.92217	−0.441278	−0.220639	−	0.975356i	$-0.570814\pi$
$79$	−3.92217	−0.441278	−0.220639	+	0.975356i	$0.570814\pi$
$80$	0	0
$81$	8.88961	0.987735
$82$	13.1361	1.45064
$83$	8.90908	0.977898	0.488949	−	0.872312i	$-0.337380\pi$
$83$	8.90908	0.977898	0.488949	+	0.872312i	$0.337380\pi$
$84$	−0.0129821	−0.00141646
$85$	0	0
$86$	−10.3319	−1.11411
$87$	−0.576939	−0.0618544
$88$	16.6751	1.77757
$89$	14.3079	1.51664	0.758318	−	0.651885i	$-0.226022\pi$
$89$	14.3079	1.51664	0.758318	+	0.651885i	$0.226022\pi$
$90$	0	0
$91$	2.15190	0.225581
$92$	0.140116	0.0146081
$93$	0.317203	0.0328924
$94$	10.6115	1.09449
$95$	0	0
$96$	0.0427797	0.00436618
$97$	−8.49352	−0.862386	−0.431193	−	0.902260i	$-0.641907\pi$
$97$	−8.49352	−0.862386	−0.431193	+	0.902260i	$0.641907\pi$
$98$	5.63693	0.569416
$99$	−17.3311	−1.74185
$100$	0	0
$101$	−2.53832	−0.252572	−0.126286	−	0.991994i	$-0.540306\pi$
$101$	−2.53832	−0.252572	−0.126286	+	0.991994i	$0.540306\pi$
$102$	0	0
$103$	−16.6715	−1.64269	−0.821347	−	0.570429i	$-0.806777\pi$
$103$	−16.6715	−1.64269	−0.821347	+	0.570429i	$0.806777\pi$
$104$	−3.60508	−0.353507
$105$	0	0
$106$	−10.0173	−0.972962
$107$	9.09572	0.879316	0.439658	−	0.898165i	$-0.355100\pi$
$107$	9.09572	0.879316	0.439658	+	0.898165i	$0.355100\pi$
$108$	−0.0453019	−0.00435917
$109$	0.743718	0.0712352	0.0356176	−	0.999365i	$-0.488660\pi$
$109$	0.743718	0.0712352	0.0356176	+	0.999365i	$0.488660\pi$
$110$	0	0
$111$	0.699216	0.0663667
$112$	6.62127	0.625651
$113$	9.03685	0.850115	0.425058	−	0.905166i	$-0.360254\pi$
$113$	9.03685	0.850115	0.425058	+	0.905166i	$0.360254\pi$
$114$	0.435191	0.0407594
$115$	0	0
$116$	−0.355397	−0.0329977
$117$	3.74692	0.346403
$118$	−3.03328	−0.279236
$119$	0	0
$120$	0	0
$121$	22.6493	2.05902
$122$	7.97515	0.722037
$123$	1.04744	0.0944446
$124$	0.195398	0.0175473
$125$	0	0
$126$	−7.12528	−0.634770
$127$	−14.4995	−1.28662	−0.643311	−	0.765605i	$-0.722440\pi$
$127$	−14.4995	−1.28662	−0.643311	+	0.765605i	$0.722440\pi$
$128$	−10.7001	−0.945764
$129$	−0.823837	−0.0725348
$130$	0	0
$131$	16.8481	1.47203	0.736014	−	0.676966i	$-0.236706\pi$
$131$	16.8481	1.47203	0.736014	+	0.676966i	$0.236706\pi$
$132$	0.0438877	0.00381993
$133$	−4.84797	−0.420372
$134$	3.42825	0.296156
$135$	0	0
$136$	0	0
$137$	−20.2283	−1.72822	−0.864111	−	0.503300i	$-0.832119\pi$
$137$	−20.2283	−1.72822	−0.864111	+	0.503300i	$0.832119\pi$
$138$	−0.316139	−0.0269115
$139$	4.25696	0.361071	0.180535	−	0.983569i	$-0.442217\pi$
$139$	4.25696	0.361071	0.180535	+	0.983569i	$0.442217\pi$
$140$	0	0
$141$	0.846135	0.0712575
$142$	−18.7328	−1.57203
$143$	−7.27482	−0.608351
$144$	11.5290	0.960751
$145$	0	0
$146$	8.11341	0.671471
$147$	0.449474	0.0370720
$148$	0.430720	0.0354049
$149$	−4.32633	−0.354427	−0.177213	−	0.984172i	$-0.556708\pi$
$149$	−4.32633	−0.354427	−0.177213	+	0.984172i	$0.556708\pi$
$150$	0	0
$151$	20.0611	1.63255	0.816276	−	0.577662i	$-0.196035\pi$
$151$	20.0611	1.63255	0.816276	+	0.577662i	$0.196035\pi$
$152$	8.12178	0.658763
$153$	0	0
$154$	13.8341	1.11478
$155$	0	0
$156$	−0.00948831	−0.000759673 0
$157$	−21.7028	−1.73207	−0.866035	−	0.499983i	$-0.833339\pi$
$157$	−21.7028	−1.73207	−0.866035	+	0.499983i	$0.833339\pi$
$158$	5.45129	0.433681
$159$	−0.798751	−0.0633451
$160$	0	0
$161$	3.52174	0.277552
$162$	−12.3554	−0.970731
$163$	−1.32611	−0.103869	−0.0519344	−	0.998650i	$-0.516539\pi$
$163$	−1.32611	−0.103869	−0.0519344	+	0.998650i	$0.516539\pi$
$164$	0.645227	0.0503838
$165$	0	0
$166$	−12.3824	−0.961063
$167$	24.9911	1.93387	0.966933	−	0.255031i	$-0.0820858\pi$
$167$	24.9911	1.93387	0.966933	+	0.255031i	$0.0820858\pi$
$168$	0.546644	0.0421745
$169$	−11.4272	−0.879017
$170$	0	0
$171$	−8.44132	−0.645524
$172$	−0.507486	−0.0386955
$173$	−15.9603	−1.21344	−0.606721	−	0.794915i	$-0.707516\pi$
$173$	−15.9603	−1.21344	−0.606721	+	0.794915i	$0.707516\pi$
$174$	0.801869	0.0607895
$175$	0	0
$176$	−22.3841	−1.68727
$177$	−0.241866	−0.0181798
$178$	−19.8861	−1.49053
$179$	14.9549	1.11778	0.558890	−	0.829242i	$-0.311228\pi$
$179$	14.9549	1.11778	0.558890	+	0.829242i	$0.311228\pi$
$180$	0	0
$181$	24.4922	1.82049	0.910245	−	0.414071i	$-0.135893\pi$
$181$	24.4922	1.82049	0.910245	+	0.414071i	$0.135893\pi$
$182$	−2.99086	−0.221697
$183$	0.635918	0.0470084
$184$	−5.89996	−0.434951
$185$	0	0
$186$	−0.440870	−0.0323262
$187$	0	0
$188$	0.521222	0.0380140
$189$	−1.13864	−0.0828237
$190$	0	0
$191$	−0.254656	−0.0184263	−0.00921313	−	0.999958i	$-0.502933\pi$
$191$	−0.254656	−0.0184263	−0.00921313	+	0.999958i	$0.502933\pi$
$192$	−0.914758	−0.0660170
$193$	−2.96901	−0.213714	−0.106857	−	0.994274i	$-0.534079\pi$
$193$	−2.96901	−0.213714	−0.106857	+	0.994274i	$0.534079\pi$
$194$	11.8049	0.847540
$195$	0	0
$196$	0.276878	0.0197770
$197$	6.08116	0.433265	0.216632	−	0.976253i	$-0.430493\pi$
$197$	6.08116	0.433265	0.216632	+	0.976253i	$0.430493\pi$
$198$	24.0880	1.71186
$199$	−12.5632	−0.890581	−0.445290	−	0.895386i	$-0.646900\pi$
$199$	−12.5632	−0.890581	−0.445290	+	0.895386i	$0.646900\pi$
$200$	0	0
$201$	0.273360	0.0192813
$202$	3.52793	0.248224
$203$	−8.93271	−0.626953
$204$	0	0
$205$	0	0
$206$	23.1712	1.61441
$207$	6.13208	0.426209
$208$	4.83935	0.335549
$209$	16.3892	1.13367
$210$	0	0
$211$	−12.0459	−0.829277	−0.414639	−	0.909986i	$-0.636092\pi$
$211$	−12.0459	−0.829277	−0.414639	+	0.909986i	$0.636092\pi$
$212$	−0.492033	−0.0337930
$213$	−1.49371	−0.102347
$214$	−12.6418	−0.864179
$215$	0	0
$216$	1.90756	0.129793
$217$	4.91123	0.333396
$218$	−1.03367	−0.0700089
$219$	0.646943	0.0437164
$220$	0	0
$221$	0	0
$222$	−0.971818	−0.0652242
$223$	17.7704	1.18999	0.594997	−	0.803728i	$-0.297153\pi$
$223$	17.7704	1.18999	0.594997	+	0.803728i	$0.297153\pi$
$224$	0.662355	0.0442554
$225$	0	0
$226$	−12.5600	−0.835480
$227$	−11.1731	−0.741583	−0.370791	−	0.928716i	$-0.620914\pi$
$227$	−11.1731	−0.741583	−0.370791	+	0.928716i	$0.620914\pi$
$228$	0.0213760	0.00141566
$229$	−21.3463	−1.41060	−0.705300	−	0.708909i	$-0.749188\pi$
$229$	−21.3463	−1.41060	−0.705300	+	0.708909i	$0.749188\pi$
$230$	0	0
$231$	1.10309	0.0725782
$232$	14.9649	0.982496
$233$	8.30552	0.544113	0.272056	−	0.962281i	$-0.412296\pi$
$233$	8.30552	0.544113	0.272056	+	0.962281i	$0.412296\pi$
$234$	−5.20772	−0.340439
$235$	0	0
$236$	−0.148990	−0.00969845
$237$	0.434672	0.0282350
$238$	0	0
$239$	−3.42382	−0.221468	−0.110734	−	0.993850i	$-0.535320\pi$
$239$	−3.42382	−0.221468	−0.110734	+	0.993850i	$0.535320\pi$
$240$	0	0
$241$	6.34827	0.408928	0.204464	−	0.978874i	$-0.434455\pi$
$241$	6.34827	0.408928	0.204464	+	0.978874i	$0.434455\pi$
$242$	−31.4795	−2.02358
$243$	−2.97594	−0.190907
$244$	0.391728	0.0250778
$245$	0	0
$246$	−1.45580	−0.0928187
$247$	−3.54328	−0.225453
$248$	−8.22776	−0.522463
$249$	−0.987344	−0.0625704
$250$	0	0
$251$	5.06308	0.319579	0.159789	−	0.987151i	$-0.448919\pi$
$251$	5.06308	0.319579	0.159789	+	0.987151i	$0.448919\pi$
$252$	−0.349983	−0.0220469
$253$	−11.9057	−0.748507
$254$	20.1524	1.26447
$255$	0	0
$256$	−1.63651	−0.102282
$257$	−17.8268	−1.11200	−0.556001	−	0.831181i	$-0.687665\pi$
$257$	−17.8268	−1.11200	−0.556001	+	0.831181i	$0.687665\pi$
$258$	1.14502	0.0712861
$259$	10.8259	0.672689
$260$	0	0
$261$	−15.5537	−0.962750
$262$	−23.4167	−1.44669
$263$	9.10776	0.561609	0.280804	−	0.959765i	$-0.409399\pi$
$263$	9.10776	0.561609	0.280804	+	0.959765i	$0.409399\pi$
$264$	−1.84801	−0.113737
$265$	0	0
$266$	6.73803	0.413135
$267$	−1.58567	−0.0970412
$268$	0.168391	0.0102861
$269$	−12.7642	−0.778249	−0.389125	−	0.921185i	$-0.627222\pi$
$269$	−12.7642	−0.778249	−0.389125	+	0.921185i	$0.627222\pi$
$270$	0	0
$271$	−16.4128	−0.997004	−0.498502	−	0.866889i	$-0.666116\pi$
$271$	−16.4128	−0.997004	−0.498502	+	0.866889i	$0.666116\pi$
$272$	0	0
$273$	−0.238484	−0.0144337
$274$	28.1147	1.69847
$275$	0	0
$276$	−0.0155283	−0.000934692 0
$277$	−18.4447	−1.10824	−0.554119	−	0.832438i	$-0.686945\pi$
$277$	−18.4447	−1.10824	−0.554119	+	0.832438i	$0.686945\pi$
$278$	−5.91661	−0.354855
$279$	8.55147	0.511963
$280$	0	0
$281$	18.7463	1.11831	0.559156	−	0.829062i	$-0.311125\pi$
$281$	18.7463	1.11831	0.559156	+	0.829062i	$0.311125\pi$
$282$	−1.17602	−0.0700307
$283$	−19.7902	−1.17640	−0.588202	−	0.808714i	$-0.700164\pi$
$283$	−19.7902	−1.17640	−0.588202	+	0.808714i	$0.700164\pi$
$284$	−0.920130	−0.0545997
$285$	0	0
$286$	10.1110	0.597878
$287$	16.2175	0.957286
$288$	1.15330	0.0679587
$289$	0	0
$290$	0	0
$291$	0.941290	0.0551794
$292$	0.398519	0.0233216
$293$	−14.0051	−0.818189	−0.409094	−	0.912492i	$-0.634155\pi$
$293$	−14.0051	−0.818189	−0.409094	+	0.912492i	$0.634155\pi$
$294$	−0.624710	−0.0364338
$295$	0	0
$296$	−18.1366	−1.05417
$297$	3.84933	0.223361
$298$	6.01303	0.348325
$299$	2.57397	0.148856
$300$	0	0
$301$	−12.7554	−0.735209
$302$	−27.8823	−1.60445
$303$	0.281308	0.0161607
$304$	−10.9024	−0.625298
$305$	0	0
$306$	0	0
$307$	13.2813	0.758001	0.379001	−	0.925396i	$-0.376268\pi$
$307$	13.2813	0.758001	0.379001	+	0.925396i	$0.376268\pi$
$308$	0.679509	0.0387186
$309$	1.84761	0.105107
$310$	0	0
$311$	−23.5552	−1.33569	−0.667846	−	0.744300i	$-0.732783\pi$
$311$	−23.5552	−1.33569	−0.667846	+	0.744300i	$0.732783\pi$
$312$	0.399531	0.0226190
$313$	−32.6572	−1.84590	−0.922948	−	0.384924i	$-0.874228\pi$
$313$	−32.6572	−1.84590	−0.922948	+	0.384924i	$0.874228\pi$
$314$	30.1640	1.70225
$315$	0	0
$316$	0.267760	0.0150627
$317$	25.4010	1.42666	0.713331	−	0.700828i	$-0.247186\pi$
$317$	25.4010	1.42666	0.713331	+	0.700828i	$0.247186\pi$
$318$	1.11016	0.0622546
$319$	30.1983	1.69078
$320$	0	0
$321$	−1.00803	−0.0562627
$322$	−4.89475	−0.272774
$323$	0	0
$324$	−0.606878	−0.0337155
$325$	0	0
$326$	1.84312	0.102081
$327$	−0.0824221	−0.00455795
$328$	−27.1690	−1.50016
$329$	13.1006	0.722262
$330$	0	0
$331$	−18.4380	−1.01344	−0.506722	−	0.862109i	$-0.669143\pi$
$331$	−18.4380	−1.01344	−0.506722	+	0.862109i	$0.669143\pi$
$332$	−0.608207	−0.0333797
$333$	18.8502	1.03298
$334$	−34.7342	−1.90057
$335$	0	0
$336$	−0.733799	−0.0400320
$337$	6.60735	0.359925	0.179963	−	0.983673i	$-0.442402\pi$
$337$	6.60735	0.359925	0.179963	+	0.983673i	$0.442402\pi$
$338$	15.8823	0.863884
$339$	−1.00150	−0.0543942
$340$	0	0
$341$	−16.6031	−0.899108
$342$	11.7323	0.634411
$343$	18.9704	1.02430
$344$	21.3691	1.15214
$345$	0	0
$346$	22.1828	1.19255
$347$	−9.61510	−0.516165	−0.258083	−	0.966123i	$-0.583091\pi$
$347$	−9.61510	−0.516165	−0.258083	+	0.966123i	$0.583091\pi$
$348$	0.0393866	0.00211135
$349$	−0.688051	−0.0368305	−0.0184153	−	0.999830i	$-0.505862\pi$
$349$	−0.688051	−0.0368305	−0.0184153	+	0.999830i	$0.505862\pi$
$350$	0	0
$351$	−0.832207	−0.0444199
$352$	−2.23918	−0.119349
$353$	−15.3590	−0.817475	−0.408737	−	0.912652i	$-0.634031\pi$
$353$	−15.3590	−0.817475	−0.408737	+	0.912652i	$0.634031\pi$
$354$	0.336162	0.0178668
$355$	0	0
$356$	−0.976776	−0.0517690
$357$	0	0
$358$	−20.7853	−1.09854
$359$	−25.5542	−1.34870	−0.674351	−	0.738411i	$-0.735576\pi$
$359$	−25.5542	−1.34870	−0.674351	+	0.738411i	$0.735576\pi$
$360$	0	0
$361$	−11.0174	−0.579866
$362$	−34.0409	−1.78915
$363$	−2.51009	−0.131746
$364$	−0.146907	−0.00770001
$365$	0	0
$366$	−0.883842	−0.0461992
$367$	−1.15721	−0.0604057	−0.0302029	−	0.999544i	$-0.509615\pi$
$367$	−1.15721	−0.0604057	−0.0302029	+	0.999544i	$0.509615\pi$
$368$	7.91993	0.412855
$369$	28.2380	1.47001
$370$	0	0
$371$	−12.3670	−0.642063
$372$	−0.0216549	−0.00112275
$373$	−15.1464	−0.784251	−0.392126	−	0.919912i	$-0.628260\pi$
$373$	−15.1464	−0.784251	−0.392126	+	0.919912i	$0.628260\pi$
$374$	0	0
$375$	0	0
$376$	−21.9475	−1.13185
$377$	−6.52873	−0.336247
$378$	1.58256	0.0813979
$379$	15.6402	0.803384	0.401692	−	0.915775i	$-0.368422\pi$
$379$	15.6402	0.803384	0.401692	+	0.915775i	$0.368422\pi$
$380$	0	0
$381$	1.60690	0.0823239
$382$	0.353938	0.0181090
$383$	4.62293	0.236221	0.118110	−	0.993000i	$-0.462316\pi$
$383$	4.62293	0.236221	0.118110	+	0.993000i	$0.462316\pi$
$384$	1.18583	0.0605143
$385$	0	0
$386$	4.12653	0.210035
$387$	−22.2098	−1.12899
$388$	0.579838	0.0294368
$389$	−6.33834	−0.321367	−0.160683	−	0.987006i	$-0.551370\pi$
$389$	−6.33834	−0.321367	−0.160683	+	0.987006i	$0.551370\pi$
$390$	0	0
$391$	0	0
$392$	−11.6587	−0.588852
$393$	−1.86719	−0.0941870
$394$	−8.45201	−0.425806
$395$	0	0
$396$	1.18317	0.0594564
$397$	−3.24553	−0.162889	−0.0814444	−	0.996678i	$-0.525953\pi$
$397$	−3.24553	−0.162889	−0.0814444	+	0.996678i	$0.525953\pi$
$398$	17.4612	0.875249
$399$	0.537273	0.0268973
$400$	0	0
$401$	−12.4948	−0.623958	−0.311979	−	0.950089i	$-0.600992\pi$
$401$	−12.4948	−0.623958	−0.311979	+	0.950089i	$0.600992\pi$
$402$	−0.379934	−0.0189494
$403$	3.58951	0.178806
$404$	0.173287	0.00862133
$405$	0	0
$406$	12.4153	0.616160
$407$	−36.5985	−1.81412
$408$	0	0
$409$	11.7076	0.578904	0.289452	−	0.957192i	$-0.406527\pi$
$409$	11.7076	0.578904	0.289452	+	0.957192i	$0.406527\pi$
$410$	0	0
$411$	2.24179	0.110580
$412$	1.13814	0.0560719
$413$	−3.74479	−0.184269
$414$	−8.52278	−0.418872
$415$	0	0
$416$	0.484101	0.0237350
$417$	−0.471775	−0.0231029
$418$	−22.7789	−1.11415
$419$	0.544535	0.0266023	0.0133011	−	0.999912i	$-0.495766\pi$
$419$	0.544535	0.0266023	0.0133011	+	0.999912i	$0.495766\pi$
$420$	0	0
$421$	−24.3097	−1.18478	−0.592391	−	0.805651i	$-0.701816\pi$
$421$	−24.3097	−1.18478	−0.592391	+	0.805651i	$0.701816\pi$
$422$	16.7423	0.815001
$423$	22.8110	1.10911
$424$	20.7184	1.00617
$425$	0	0
$426$	2.07606	0.100585
$427$	9.84588	0.476475
$428$	−0.620949	−0.0300147
$429$	0.806228	0.0389251
$430$	0	0
$431$	4.24444	0.204448	0.102224	−	0.994761i	$-0.467404\pi$
$431$	4.24444	0.204448	0.102224	+	0.994761i	$0.467404\pi$
$432$	−2.56065	−0.123199
$433$	25.7042	1.23527	0.617633	−	0.786467i	$-0.288092\pi$
$433$	25.7042	1.23527	0.617633	+	0.786467i	$0.288092\pi$
$434$	−6.82595	−0.327656
$435$	0	0
$436$	−0.0507723	−0.00243155
$437$	−5.79882	−0.277395
$438$	−0.899165	−0.0429638
$439$	3.10010	0.147960	0.0739798	−	0.997260i	$-0.476430\pi$
$439$	3.10010	0.147960	0.0739798	+	0.997260i	$0.476430\pi$
$440$	0	0
$441$	12.1174	0.577018
$442$	0	0
$443$	26.3141	1.25022	0.625109	−	0.780537i	$-0.285054\pi$
$443$	26.3141	1.25022	0.625109	+	0.780537i	$0.285054\pi$
$444$	−0.0477343	−0.00226537
$445$	0	0
$446$	−24.6985	−1.16951
$447$	0.479464	0.0226778
$448$	−14.1631	−0.669145
$449$	14.7052	0.693982	0.346991	−	0.937868i	$-0.387203\pi$
$449$	14.7052	0.693982	0.346991	+	0.937868i	$0.387203\pi$
$450$	0	0
$451$	−54.8254	−2.58163
$452$	−0.616930	−0.0290179
$453$	−2.22326	−0.104458
$454$	15.5291	0.728816
$455$	0	0
$456$	−0.900092	−0.0421507
$457$	−10.5823	−0.495018	−0.247509	−	0.968886i	$-0.579612\pi$
$457$	−10.5823	−0.495018	−0.247509	+	0.968886i	$0.579612\pi$
$458$	29.6685	1.38632
$459$	0	0
$460$	0	0
$461$	−18.5051	−0.861868	−0.430934	−	0.902383i	$-0.641816\pi$
$461$	−18.5051	−0.861868	−0.430934	+	0.902383i	$0.641816\pi$
$462$	−1.53315	−0.0713287
$463$	−37.7389	−1.75387	−0.876937	−	0.480605i	$-0.840417\pi$
$463$	−37.7389	−1.75387	−0.876937	+	0.480605i	$0.840417\pi$
$464$	−20.0885	−0.932584
$465$	0	0
$466$	−11.5436	−0.534746
$467$	−30.2388	−1.39929	−0.699643	−	0.714493i	$-0.746657\pi$
$467$	−30.2388	−1.39929	−0.699643	+	0.714493i	$0.746657\pi$
$468$	−0.255795	−0.0118242
$469$	4.23241	0.195434
$470$	0	0
$471$	2.40520	0.110826
$472$	6.27364	0.288768
$473$	43.1214	1.98273
$474$	−0.604137	−0.0277489
$475$	0	0
$476$	0	0
$477$	−21.5335	−0.985953
$478$	4.75865	0.217656
$479$	−26.9575	−1.23172	−0.615859	−	0.787857i	$-0.711191\pi$
$479$	−26.9575	−1.23172	−0.615859	+	0.787857i	$0.711191\pi$
$480$	0	0
$481$	7.91244	0.360776
$482$	−8.82326	−0.401888
$483$	−0.390295	−0.0177590
$484$	−1.54623	−0.0702830
$485$	0	0
$486$	4.13617	0.187620
$487$	3.83241	0.173663	0.0868316	−	0.996223i	$-0.472326\pi$
$487$	3.83241	0.173663	0.0868316	+	0.996223i	$0.472326\pi$
$488$	−16.4948	−0.746683
$489$	0.146965	0.00664600
$490$	0	0
$491$	5.90130	0.266322	0.133161	−	0.991094i	$-0.457487\pi$
$491$	5.90130	0.266322	0.133161	+	0.991094i	$0.457487\pi$
$492$	−0.0715070	−0.00322378
$493$	0	0
$494$	4.92469	0.221572
$495$	0	0
$496$	11.0447	0.495922
$497$	−23.1270	−1.03739
$498$	1.37228	0.0614932
$499$	44.0907	1.97377	0.986884	−	0.161428i	$-0.0516101\pi$
$499$	44.0907	1.97377	0.986884	+	0.161428i	$0.0516101\pi$
$500$	0	0
$501$	−2.76962	−0.123738
$502$	−7.03701	−0.314077
$503$	35.5344	1.58440	0.792201	−	0.610260i	$-0.208935\pi$
$503$	35.5344	1.58440	0.792201	+	0.610260i	$0.208935\pi$
$504$	14.7370	0.656437
$505$	0	0
$506$	16.5474	0.735621
$507$	1.26642	0.0562435
$508$	0.989855	0.0439177
$509$	−32.9351	−1.45982	−0.729911	−	0.683542i	$-0.760438\pi$
$509$	−32.9351	−1.45982	−0.729911	+	0.683542i	$0.760438\pi$
$510$	0	0
$511$	10.0166	0.443107
$512$	23.6747	1.04628
$513$	1.87486	0.0827769
$514$	24.7768	1.09286
$515$	0	0
$516$	0.0562419	0.00247591
$517$	−44.2886	−1.94781
$518$	−15.0466	−0.661109
$519$	1.76880	0.0776416
$520$	0	0
$521$	24.4834	1.07264	0.536318	−	0.844016i	$-0.319815\pi$
$521$	24.4834	1.07264	0.536318	+	0.844016i	$0.319815\pi$
$522$	21.6176	0.946176
$523$	−9.59229	−0.419442	−0.209721	−	0.977761i	$-0.567256\pi$
$523$	−9.59229	−0.419442	−0.209721	+	0.977761i	$0.567256\pi$
$524$	−1.15019	−0.0502464
$525$	0	0
$526$	−12.6586	−0.551940
$527$	0	0
$528$	2.48071	0.107959
$529$	−18.7875	−0.816849
$530$	0	0
$531$	−6.52047	−0.282964
$532$	0.330962	0.0143490
$533$	11.8530	0.513410
$534$	2.20387	0.0953706
$535$	0	0
$536$	−7.09054	−0.306265
$537$	−1.65737	−0.0715206
$538$	17.7406	0.764851
$539$	−23.5265	−1.01336
$540$	0	0
$541$	37.8277	1.62634	0.813170	−	0.582027i	$-0.197740\pi$
$541$	37.8277	1.62634	0.813170	+	0.582027i	$0.197740\pi$
$542$	22.8116	0.979840
$543$	−2.71433	−0.116483
$544$	0	0
$545$	0	0
$546$	0.331461	0.0141852
$547$	24.3150	1.03964	0.519818	−	0.854277i	$-0.326000\pi$
$547$	24.3150	1.03964	0.519818	+	0.854277i	$0.326000\pi$
$548$	1.38095	0.0589914
$549$	17.1437	0.731677
$550$	0	0
$551$	14.7084	0.626599
$552$	0.653860	0.0278301
$553$	6.72999	0.286188
$554$	25.6358	1.08916
$555$	0	0
$556$	−0.290615	−0.0123248
$557$	26.8276	1.13672	0.568360	−	0.822780i	$-0.307578\pi$
$557$	26.8276	1.13672	0.568360	+	0.822780i	$0.307578\pi$
$558$	−11.8854	−0.503150
$559$	−9.32266	−0.394307
$560$	0	0
$561$	0	0
$562$	−26.0549	−1.09906
$563$	−39.2776	−1.65536	−0.827678	−	0.561204i	$-0.810338\pi$
$563$	−39.2776	−1.65536	−0.827678	+	0.561204i	$0.810338\pi$
$564$	−0.0577642	−0.00243231
$565$	0	0
$566$	27.5057	1.15615
$567$	−15.2536	−0.640590
$568$	38.7446	1.62569
$569$	−9.94230	−0.416803	−0.208402	−	0.978043i	$-0.566826\pi$
$569$	−9.94230	−0.416803	−0.208402	+	0.978043i	$0.566826\pi$
$570$	0	0
$571$	−0.453488	−0.0189779	−0.00948893	−	0.999955i	$-0.503020\pi$
$571$	−0.453488	−0.0189779	−0.00948893	+	0.999955i	$0.503020\pi$
$572$	0.496639	0.0207655
$573$	0.0282221	0.00117900
$574$	−22.5401	−0.940806
$575$	0	0
$576$	−24.6610	−1.02754
$577$	28.8048	1.19916	0.599579	−	0.800316i	$-0.295335\pi$
$577$	28.8048	1.19916	0.599579	+	0.800316i	$0.295335\pi$
$578$	0	0
$579$	0.329039	0.0136744
$580$	0	0
$581$	−15.2870	−0.634210
$582$	−1.30827	−0.0542295
$583$	41.8084	1.73153
$584$	−16.7807	−0.694391
$585$	0	0
$586$	19.4653	0.804104
$587$	−21.1020	−0.870973	−0.435486	−	0.900195i	$-0.643424\pi$
$587$	−21.1020	−0.870973	−0.435486	+	0.900195i	$0.643424\pi$
$588$	−0.0306848	−0.00126542
$589$	−8.08672	−0.333207
$590$	0	0
$591$	−0.673942	−0.0277223
$592$	24.3460	1.00062
$593$	−38.1229	−1.56552	−0.782760	−	0.622324i	$-0.786189\pi$
$593$	−38.1229	−1.56552	−0.782760	+	0.622324i	$0.786189\pi$
$594$	−5.35005	−0.219515
$595$	0	0
$596$	0.295351	0.0120981
$597$	1.39231	0.0569834
$598$	−3.57747	−0.146294
$599$	−35.4595	−1.44884	−0.724418	−	0.689360i	$-0.757892\pi$
$599$	−35.4595	−1.44884	−0.724418	+	0.689360i	$0.757892\pi$
$600$	0	0
$601$	−26.4764	−1.07999	−0.539997	−	0.841667i	$-0.681575\pi$
$601$	−26.4764	−1.07999	−0.539997	+	0.841667i	$0.681575\pi$
$602$	17.7283	0.722552
$603$	7.36951	0.300110
$604$	−1.36954	−0.0557257
$605$	0	0
$606$	−0.390981	−0.0158825
$607$	24.4832	0.993743	0.496872	−	0.867824i	$-0.334482\pi$
$607$	24.4832	0.993743	0.496872	+	0.867824i	$0.334482\pi$
$608$	−1.09062	−0.0442304
$609$	0.989962	0.0401153
$610$	0	0
$611$	9.57499	0.387363
$612$	0	0
$613$	−13.6998	−0.553329	−0.276665	−	0.960967i	$-0.589229\pi$
$613$	−13.6998	−0.553329	−0.276665	+	0.960967i	$0.589229\pi$
$614$	−18.4592	−0.744952
$615$	0	0
$616$	−28.6126	−1.15283
$617$	7.69707	0.309872	0.154936	−	0.987924i	$-0.450483\pi$
$617$	7.69707	0.309872	0.154936	+	0.987924i	$0.450483\pi$
$618$	−2.56794	−0.103298
$619$	−43.3404	−1.74200	−0.870999	−	0.491284i	$-0.836528\pi$
$619$	−43.3404	−1.74200	−0.870999	+	0.491284i	$0.836528\pi$
$620$	0	0
$621$	−1.36196	−0.0546537
$622$	32.7386	1.31270
$623$	−24.5508	−0.983605
$624$	−0.536318	−0.0214699
$625$	0	0
$626$	45.3892	1.81412
$627$	−1.81633	−0.0725372
$628$	1.48161	0.0591227
$629$	0	0
$630$	0	0
$631$	0.733705	0.0292083	0.0146042	−	0.999893i	$-0.495351\pi$
$631$	0.733705	0.0292083	0.0146042	+	0.999893i	$0.495351\pi$
$632$	−11.2747	−0.448485
$633$	1.33499	0.0530609
$634$	−35.3040	−1.40210
$635$	0	0
$636$	0.0545293	0.00216223
$637$	5.08632	0.201527
$638$	−41.9716	−1.66167
$639$	−40.2689	−1.59301
$640$	0	0
$641$	−28.1753	−1.11286	−0.556429	−	0.830895i	$-0.687829\pi$
$641$	−28.1753	−1.11286	−0.556429	+	0.830895i	$0.687829\pi$
$642$	1.40103	0.0552941
$643$	9.47225	0.373549	0.186775	−	0.982403i	$-0.440197\pi$
$643$	9.47225	0.373549	0.186775	+	0.982403i	$0.440197\pi$
$644$	−0.240423	−0.00947399
$645$	0	0
$646$	0	0
$647$	−24.3690	−0.958044	−0.479022	−	0.877803i	$-0.659009\pi$
$647$	−24.3690	−0.958044	−0.479022	+	0.877803i	$0.659009\pi$
$648$	25.5542	1.00387
$649$	12.6598	0.496941
$650$	0	0
$651$	−0.544284	−0.0213322
$652$	0.0905312	0.00354547
$653$	−5.04532	−0.197439	−0.0987194	−	0.995115i	$-0.531475\pi$
$653$	−5.04532	−0.197439	−0.0987194	+	0.995115i	$0.531475\pi$
$654$	0.114556	0.00447949
$655$	0	0
$656$	36.4709	1.42395
$657$	17.4409	0.680436
$658$	−18.2082	−0.709828
$659$	−8.17372	−0.318403	−0.159201	−	0.987246i	$-0.550892\pi$
$659$	−8.17372	−0.318403	−0.159201	+	0.987246i	$0.550892\pi$
$660$	0	0
$661$	−30.6451	−1.19195	−0.595977	−	0.803001i	$-0.703235\pi$
$661$	−30.6451	−1.19195	−0.595977	+	0.803001i	$0.703235\pi$
$662$	25.6264	0.995998
$663$	0	0
$664$	25.6102	0.993869
$665$	0	0
$666$	−26.1992	−1.01520
$667$	−10.6847	−0.413714
$668$	−1.70610	−0.0660108
$669$	−1.96940	−0.0761412
$670$	0	0
$671$	−33.2854	−1.28497
$672$	−0.0734051	−0.00283166
$673$	−6.61817	−0.255112	−0.127556	−	0.991831i	$-0.540713\pi$
$673$	−6.61817	−0.255112	−0.127556	+	0.991831i	$0.540713\pi$
$674$	−9.18334	−0.353729
$675$	0	0
$676$	0.780116	0.0300045
$677$	−41.2772	−1.58641	−0.793207	−	0.608953i	$-0.791590\pi$
$677$	−41.2772	−1.58641	−0.793207	+	0.608953i	$0.791590\pi$
$678$	1.39196	0.0534578
$679$	14.5739	0.559296
$680$	0	0
$681$	1.23825	0.0474498
$682$	23.0761	0.883630
$683$	−13.2289	−0.506191	−0.253095	−	0.967441i	$-0.581449\pi$
$683$	−13.2289	−0.506191	−0.253095	+	0.967441i	$0.581449\pi$
$684$	0.576275	0.0220344
$685$	0	0
$686$	−26.3663	−1.00667
$687$	2.36569	0.0902566
$688$	−28.6852	−1.09361
$689$	−9.03878	−0.344350
$690$	0	0
$691$	−34.6103	−1.31664	−0.658320	−	0.752739i	$-0.728732\pi$
$691$	−34.6103	−1.31664	−0.658320	+	0.752739i	$0.728732\pi$
$692$	1.08959	0.0414198
$693$	29.7383	1.12966
$694$	13.3637	0.507280
$695$	0	0
$696$	−1.65848	−0.0628645
$697$	0	0
$698$	0.956299	0.0361965
$699$	−0.920455	−0.0348148
$700$	0	0
$701$	15.6045	0.589373	0.294687	−	0.955594i	$-0.404785\pi$
$701$	15.6045	0.589373	0.294687	+	0.955594i	$0.404785\pi$
$702$	1.15666	0.0436552
$703$	−17.8257	−0.672309
$704$	47.8804	1.80456
$705$	0	0
$706$	21.3469	0.803402
$707$	4.35547	0.163804
$708$	0.0165118	0.000620551 0
$709$	−46.9998	−1.76511	−0.882557	−	0.470205i	$-0.844180\pi$
$709$	−46.9998	−1.76511	−0.882557	+	0.470205i	$0.844180\pi$
$710$	0	0
$711$	11.7183	0.439472
$712$	41.1298	1.54140
$713$	5.87449	0.220001
$714$	0	0
$715$	0	0
$716$	−1.02094	−0.0381544
$717$	0.379443	0.0141705
$718$	35.5170	1.32548
$719$	37.8943	1.41322	0.706609	−	0.707605i	$-0.250224\pi$
$719$	37.8943	1.41322	0.706609	+	0.707605i	$0.250224\pi$
$720$	0	0
$721$	28.6065	1.06536
$722$	15.3128	0.569883
$723$	−0.703544	−0.0261651
$724$	−1.67204	−0.0621408
$725$	0	0
$726$	3.48870	0.129478
$727$	20.6445	0.765664	0.382832	−	0.923818i	$-0.374949\pi$
$727$	20.6445	0.765664	0.382832	+	0.923818i	$0.374949\pi$
$728$	6.18591	0.229265
$729$	−26.3390	−0.975520
$730$	0	0
$731$	0	0
$732$	−0.0434131	−0.00160459
$733$	−34.3748	−1.26966	−0.634830	−	0.772652i	$-0.718930\pi$
$733$	−34.3748	−1.26966	−0.634830	+	0.772652i	$0.718930\pi$
$734$	1.60836	0.0593658
$735$	0	0
$736$	0.792265	0.0292033
$737$	−14.3083	−0.527051
$738$	−39.2470	−1.44470
$739$	17.4672	0.642543	0.321272	−	0.946987i	$-0.395890\pi$
$739$	17.4672	0.642543	0.321272	+	0.946987i	$0.395890\pi$
$740$	0	0
$741$	0.392682	0.0144255
$742$	17.1885	0.631009
$743$	−18.4036	−0.675161	−0.337581	−	0.941297i	$-0.609609\pi$
$743$	−18.4036	−0.675161	−0.337581	+	0.941297i	$0.609609\pi$
$744$	0.911837	0.0334296
$745$	0	0
$746$	21.0515	0.770750
$747$	−26.6178	−0.973895
$748$	0	0
$749$	−15.6072	−0.570276
$750$	0	0
$751$	−3.02639	−0.110435	−0.0552173	−	0.998474i	$-0.517585\pi$
$751$	−3.02639	−0.110435	−0.0552173	+	0.998474i	$0.517585\pi$
$752$	29.4616	1.07436
$753$	−0.561113	−0.0204481
$754$	9.07407	0.330458
$755$	0	0
$756$	0.0777329	0.00282712
$757$	11.6719	0.424222	0.212111	−	0.977246i	$-0.431966\pi$
$757$	11.6719	0.424222	0.212111	+	0.977246i	$0.431966\pi$
$758$	−21.7378	−0.789553
$759$	1.31945	0.0478929
$760$	0	0
$761$	−1.13354	−0.0410908	−0.0205454	−	0.999789i	$-0.506540\pi$
$761$	−1.13354	−0.0410908	−0.0205454	+	0.999789i	$0.506540\pi$
$762$	−2.23338	−0.0809067
$763$	−1.27614	−0.0461992
$764$	0.0173849	0.000628964 0
$765$	0	0
$766$	−6.42526	−0.232154
$767$	−2.73699	−0.0988271
$768$	0.181365	0.00654445
$769$	14.6207	0.527235	0.263617	−	0.964627i	$-0.415084\pi$
$769$	14.6207	0.527235	0.263617	+	0.964627i	$0.415084\pi$
$770$	0	0
$771$	1.97564	0.0711510
$772$	0.202689	0.00729494
$773$	−24.8748	−0.894683	−0.447342	−	0.894363i	$-0.647629\pi$
$773$	−24.8748	−0.894683	−0.447342	+	0.894363i	$0.647629\pi$
$774$	30.8687	1.10955
$775$	0	0
$776$	−24.4156	−0.876470
$777$	−1.19978	−0.0430417
$778$	8.80946	0.315834
$779$	−26.7033	−0.956745
$780$	0	0
$781$	78.1841	2.79765
$782$	0	0
$783$	3.45455	0.123456
$784$	15.6503	0.558938
$785$	0	0
$786$	2.59514	0.0925656
$787$	23.5543	0.839622	0.419811	−	0.907612i	$-0.362096\pi$
$787$	23.5543	0.839622	0.419811	+	0.907612i	$0.362096\pi$
$788$	−0.415150	−0.0147891
$789$	−1.00936	−0.0359343
$790$	0	0
$791$	−15.5062	−0.551337
$792$	−49.8204	−1.77029
$793$	7.19615	0.255543
$794$	4.51086	0.160085
$795$	0	0
$796$	0.857667	0.0303992
$797$	−31.8025	−1.12650	−0.563251	−	0.826286i	$-0.690450\pi$
$797$	−31.8025	−1.12650	−0.563251	+	0.826286i	$0.690450\pi$
$798$	−0.746739	−0.0264343
$799$	0	0
$800$	0	0
$801$	−42.7480	−1.51043
$802$	17.3660	0.613217
$803$	−33.8624	−1.19498
$804$	−0.0186618	−0.000658151 0
$805$	0	0
$806$	−4.98895	−0.175728
$807$	1.41459	0.0497959
$808$	−7.29670	−0.256697
$809$	−16.7285	−0.588142	−0.294071	−	0.955784i	$-0.595010\pi$
$809$	−16.7285	−0.588142	−0.294071	+	0.955784i	$0.595010\pi$
$810$	0	0
$811$	−49.7836	−1.74814	−0.874069	−	0.485802i	$-0.838528\pi$
$811$	−49.7836	−1.74814	−0.874069	+	0.485802i	$0.838528\pi$
$812$	0.609820	0.0214005
$813$	1.81894	0.0637928
$814$	50.8671	1.78289
$815$	0	0
$816$	0	0
$817$	21.0028	0.734794
$818$	−16.2720	−0.568938
$819$	−6.42928	−0.224657
$820$	0	0
$821$	−16.0267	−0.559337	−0.279669	−	0.960097i	$-0.590225\pi$
$821$	−16.0267	−0.559337	−0.279669	+	0.960097i	$0.590225\pi$
$822$	−3.11580	−0.108676
$823$	32.0783	1.11818	0.559090	−	0.829107i	$-0.311151\pi$
$823$	32.0783	1.11818	0.559090	+	0.829107i	$0.311151\pi$
$824$	−47.9243	−1.66952
$825$	0	0
$826$	5.20477	0.181097
$827$	−3.82792	−0.133110	−0.0665549	−	0.997783i	$-0.521201\pi$
$827$	−3.82792	−0.133110	−0.0665549	+	0.997783i	$0.521201\pi$
$828$	−0.418627	−0.0145483
$829$	4.09989	0.142395	0.0711976	−	0.997462i	$-0.477318\pi$
$829$	4.09989	0.142395	0.0711976	+	0.997462i	$0.477318\pi$
$830$	0	0
$831$	2.04413	0.0709101
$832$	−10.3515	−0.358875
$833$	0	0
$834$	0.655705	0.0227052
$835$	0	0
$836$	−1.11886	−0.0386967
$837$	−1.89932	−0.0656501
$838$	−0.756832	−0.0261443
$839$	−46.5840	−1.60826	−0.804128	−	0.594456i	$-0.797368\pi$
$839$	−46.5840	−1.60826	−0.804128	+	0.594456i	$0.797368\pi$
$840$	0	0
$841$	−1.89879	−0.0654756
$842$	33.7872	1.16439
$843$	−2.07755	−0.0715547
$844$	0.822356	0.0283067
$845$	0	0
$846$	−31.7042	−1.09001
$847$	−38.8636	−1.33537
$848$	−27.8117	−0.955059
$849$	2.19324	0.0752717
$850$	0	0
$851$	12.9492	0.443894
$852$	0.101973	0.00349354
$853$	−35.3818	−1.21145	−0.605725	−	0.795674i	$-0.707117\pi$
$853$	−35.3818	−1.21145	−0.605725	+	0.795674i	$0.707117\pi$
$854$	−13.6845	−0.468273
$855$	0	0
$856$	26.1467	0.893677
$857$	−9.21209	−0.314679	−0.157339	−	0.987545i	$-0.550292\pi$
$857$	−9.21209	−0.314679	−0.157339	+	0.987545i	$0.550292\pi$
$858$	−1.12055	−0.0382550
$859$	−16.7755	−0.572374	−0.286187	−	0.958174i	$-0.592388\pi$
$859$	−16.7755	−0.572374	−0.286187	+	0.958174i	$0.592388\pi$
$860$	0	0
$861$	−1.79729	−0.0612515
$862$	−5.89921	−0.200928
$863$	−34.1729	−1.16326	−0.581630	−	0.813454i	$-0.697585\pi$
$863$	−34.1729	−1.16326	−0.581630	+	0.813454i	$0.697585\pi$
$864$	−0.256153	−0.00871449
$865$	0	0
$866$	−35.7254	−1.21400
$867$	0	0
$868$	−0.335281	−0.0113802
$869$	−22.7517	−0.771798
$870$	0	0
$871$	3.09338	0.104815
$872$	2.13790	0.0723986
$873$	25.3762	0.858856
$874$	8.05959	0.272620
$875$	0	0
$876$	−0.0441657	−0.00149222
$877$	−13.1872	−0.445300	−0.222650	−	0.974898i	$-0.571471\pi$
$877$	−13.1872	−0.445300	−0.222650	+	0.974898i	$0.571471\pi$
$878$	−4.30873	−0.145413
$879$	1.55211	0.0523514
$880$	0	0
$881$	−31.9932	−1.07788	−0.538939	−	0.842345i	$-0.681175\pi$
$881$	−31.9932	−1.07788	−0.538939	+	0.842345i	$0.681175\pi$
$882$	−16.8416	−0.567085
$883$	−48.1807	−1.62141	−0.810704	−	0.585456i	$-0.800915\pi$
$883$	−48.1807	−1.62141	−0.810704	+	0.585456i	$0.800915\pi$
$884$	0	0
$885$	0	0
$886$	−36.5731	−1.22870
$887$	41.0024	1.37672	0.688362	−	0.725367i	$-0.258330\pi$
$887$	41.0024	1.37672	0.688362	+	0.725367i	$0.258330\pi$
$888$	2.00998	0.0674505
$889$	24.8795	0.834431
$890$	0	0
$891$	51.5668	1.72755
$892$	−1.21315	−0.0406194
$893$	−21.5712	−0.721854
$894$	−0.666391	−0.0222874
$895$	0	0
$896$	18.3602	0.613370
$897$	−0.285259	−0.00952450
$898$	−20.4383	−0.682035
$899$	−14.9003	−0.496954
$900$	0	0
$901$	0	0
$902$	76.2000	2.53718
$903$	1.41361	0.0470420
$904$	25.9775	0.863999
$905$	0	0
$906$	3.09004	0.102660
$907$	55.6557	1.84802	0.924008	−	0.382373i	$-0.124893\pi$
$907$	55.6557	1.84802	0.924008	+	0.382373i	$0.124893\pi$
$908$	0.762766	0.0253133
$909$	7.58378	0.251538
$910$	0	0
$911$	−14.6619	−0.485771	−0.242886	−	0.970055i	$-0.578094\pi$
$911$	−14.6619	−0.485771	−0.242886	+	0.970055i	$0.578094\pi$
$912$	1.20826	0.0400094
$913$	51.6798	1.71035
$914$	14.7080	0.486496
$915$	0	0
$916$	1.45727	0.0481496
$917$	−28.9095	−0.954675
$918$	0	0
$919$	1.54175	0.0508578	0.0254289	−	0.999677i	$-0.491905\pi$
$919$	1.54175	0.0508578	0.0254289	+	0.999677i	$0.491905\pi$
$920$	0	0
$921$	−1.47189	−0.0485004
$922$	25.7196	0.847031
$923$	−16.9030	−0.556370
$924$	−0.0753063	−0.00247739
$925$	0	0
$926$	52.4521	1.72368
$927$	49.8098	1.63597
$928$	−2.00954	−0.0659663
$929$	−13.5951	−0.446041	−0.223020	−	0.974814i	$-0.571592\pi$
$929$	−13.5951	−0.446041	−0.223020	+	0.974814i	$0.571592\pi$
$930$	0	0
$931$	−11.4588	−0.375548
$932$	−0.567004	−0.0185728
$933$	2.61049	0.0854636
$934$	42.0279	1.37520
$935$	0	0
$936$	10.7710	0.352060
$937$	15.7062	0.513098	0.256549	−	0.966531i	$-0.417414\pi$
$937$	15.7062	0.513098	0.256549	+	0.966531i	$0.417414\pi$
$938$	−5.88249	−0.192070
$939$	3.61922	0.118109
$940$	0	0
$941$	43.2767	1.41078	0.705389	−	0.708820i	$-0.250772\pi$
$941$	43.2767	1.41078	0.705389	+	0.708820i	$0.250772\pi$
$942$	−3.34291	−0.108918
$943$	19.3982	0.631694
$944$	−8.42155	−0.274098
$945$	0	0
$946$	−59.9331	−1.94859
$947$	−20.5069	−0.666385	−0.333192	−	0.942859i	$-0.608126\pi$
$947$	−20.5069	−0.666385	−0.333192	+	0.942859i	$0.608126\pi$
$948$	−0.0296743	−0.000963777 0
$949$	7.32090	0.237647
$950$	0	0
$951$	−2.81505	−0.0912843
$952$	0	0
$953$	−5.27570	−0.170897	−0.0854483	−	0.996343i	$-0.527232\pi$
$953$	−5.27570	−0.170897	−0.0854483	+	0.996343i	$0.527232\pi$
$954$	29.9288	0.968979
$955$	0	0
$956$	0.233738	0.00755963
$957$	−3.34671	−0.108184
$958$	37.4673	1.21051
$959$	34.7095	1.12083
$960$	0	0
$961$	−22.8078	−0.735734
$962$	−10.9972	−0.354565
$963$	−27.1754	−0.875717
$964$	−0.433386	−0.0139584
$965$	0	0
$966$	0.542458	0.0174533
$967$	5.90267	0.189817	0.0949086	−	0.995486i	$-0.469744\pi$
$967$	5.90267	0.189817	0.0949086	+	0.995486i	$0.469744\pi$
$968$	65.1080	2.09265
$969$	0	0
$970$	0	0
$971$	1.80541	0.0579384	0.0289692	−	0.999580i	$-0.490778\pi$
$971$	1.80541	0.0579384	0.0289692	+	0.999580i	$0.490778\pi$
$972$	0.203163	0.00651644
$973$	−7.30446	−0.234170
$974$	−5.32655	−0.170674
$975$	0	0
$976$	22.1421	0.708751
$977$	9.75480	0.312084	0.156042	−	0.987750i	$-0.450127\pi$
$977$	9.75480	0.312084	0.156042	+	0.987750i	$0.450127\pi$
$978$	−0.204262	−0.00653159
$979$	82.9973	2.65260
$980$	0	0
$981$	−2.22202	−0.0709436
$982$	−8.20202	−0.261737
$983$	−4.01890	−0.128183	−0.0640916	−	0.997944i	$-0.520415\pi$
$983$	−4.01890	−0.128183	−0.0640916	+	0.997944i	$0.520415\pi$
$984$	3.01099	0.0959870
$985$	0	0
$986$	0	0
$987$	−1.45187	−0.0462136
$988$	0.241894	0.00769566
$989$	−15.2572	−0.485150
$990$	0	0
$991$	−13.8927	−0.441317	−0.220659	−	0.975351i	$-0.570821\pi$
$991$	−13.8927	−0.441317	−0.220659	+	0.975351i	$0.570821\pi$
$992$	1.10485	0.0350790
$993$	2.04338	0.0648448
$994$	32.1435	1.01953
$995$	0	0
$996$	0.0674043	0.00213579
$997$	−16.0690	−0.508910	−0.254455	−	0.967085i	$-0.581896\pi$
$997$	−16.0690	−0.508910	−0.254455	+	0.967085i	$0.581896\pi$
$998$	−61.2802	−1.93979
$999$	−4.18671	−0.132462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bx.1.7		24
5.4	even	2		7225.2.a.cb.1.18		24
17.11	odd	16		425.2.m.c.376.3	yes	24
17.14	odd	16		425.2.m.c.26.3	✓	24
17.16	even	2	inner	7225.2.a.bx.1.8		24
85.14	odd	16		425.2.m.d.26.4	yes	24
85.28	even	16		425.2.n.d.274.3		24
85.48	even	16		425.2.n.e.349.4		24
85.62	even	16		425.2.n.e.274.4		24
85.79	odd	16		425.2.m.d.376.4	yes	24
85.82	even	16		425.2.n.d.349.3		24
85.84	even	2		7225.2.a.cb.1.17		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.3	✓	24	17.14	odd	16
425.2.m.c.376.3	yes	24	17.11	odd	16
425.2.m.d.26.4	yes	24	85.14	odd	16
425.2.m.d.376.4	yes	24	85.79	odd	16
425.2.n.d.274.3		24	85.28	even	16
425.2.n.d.349.3		24	85.82	even	16
425.2.n.e.274.4		24	85.62	even	16
425.2.n.e.349.4		24	85.48	even	16
7225.2.a.bx.1.7		24	1.1	even	1	trivial
7225.2.a.bx.1.8		24	17.16	even	2	inner
7225.2.a.cb.1.17		24	85.84	even	2
7225.2.a.cb.1.18		24	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7225 = 5^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7225.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38987 q^{2} -0.110824 q^{3} -0.0682683 q^{4} +0.154031 q^{6} -1.71589 q^{7} +2.87462 q^{8} -2.98772 q^{9} +O(q^{10})\)	\(q-1.38987 q^{2} -0.110824 q^{3} -0.0682683 q^{4} +0.154031 q^{6} -1.71589 q^{7} +2.87462 q^{8} -2.98772 q^{9} +5.80080 q^{11} +0.00756580 q^{12} -1.25411 q^{13} +2.38486 q^{14} -3.85880 q^{16} +4.15253 q^{18} +2.82534 q^{19} +0.190162 q^{21} -8.06234 q^{22} -2.05243 q^{23} -0.318578 q^{24} +1.74304 q^{26} +0.663586 q^{27} +0.117141 q^{28} +5.20588 q^{29} -2.86221 q^{31} -0.386013 q^{32} -0.642871 q^{33} +0.203966 q^{36} -6.30922 q^{37} -3.92685 q^{38} +0.138986 q^{39} -9.45135 q^{41} -0.264300 q^{42} +7.43371 q^{43} -0.396010 q^{44} +2.85261 q^{46} -7.63491 q^{47} +0.427650 q^{48} -4.05573 q^{49} +0.0856157 q^{52} +7.20735 q^{53} -0.922296 q^{54} -4.93252 q^{56} -0.313117 q^{57} -7.23549 q^{58} +2.18242 q^{59} -5.73807 q^{61} +3.97809 q^{62} +5.12659 q^{63} +8.25411 q^{64} +0.893505 q^{66} -2.46660 q^{67} +0.227460 q^{69} +13.4782 q^{71} -8.58855 q^{72} -5.83755 q^{73} +8.76898 q^{74} -0.192881 q^{76} -9.95351 q^{77} -0.193172 q^{78} -3.92217 q^{79} +8.88961 q^{81} +13.1361 q^{82} +8.90908 q^{83} -0.0129821 q^{84} -10.3319 q^{86} -0.576939 q^{87} +16.6751 q^{88} +14.3079 q^{89} +2.15190 q^{91} +0.140116 q^{92} +0.317203 q^{93} +10.6115 q^{94} +0.0427797 q^{96} -8.49352 q^{97} +5.63693 q^{98} -17.3311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9} - 16 q^{13} + 24 q^{16} - 40 q^{18} - 16 q^{21} - 16 q^{26} - 56 q^{32} - 48 q^{33} + 24 q^{36} - 48 q^{38} - 32 q^{43} - 88 q^{47} + 16 q^{49} - 48 q^{52} - 48 q^{53} - 8 q^{59} + 72 q^{64} + 32 q^{66} - 40 q^{67} - 48 q^{69} - 120 q^{72} + 32 q^{76} - 120 q^{77} - 24 q^{81} - 104 q^{83} + 40 q^{84} - 16 q^{86} - 64 q^{87} + 16 q^{89} + 72 q^{93} + 112 q^{94} - 48 q^{98}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 + 24 * q^9 - 16 * q^13 + 24 * q^16 - 40 * q^18 - 16 * q^21 - 16 * q^26 - 56 * q^32 - 48 * q^33 + 24 * q^36 - 48 * q^38 - 32 * q^43 - 88 * q^47 + 16 * q^49 - 48 * q^52 - 48 * q^53 - 8 * q^59 + 72 * q^64 + 32 * q^66 - 40 * q^67 - 48 * q^69 - 120 * q^72 + 32 * q^76 - 120 * q^77 - 24 * q^81 - 104 * q^83 + 40 * q^84 - 16 * q^86 - 64 * q^87 + 16 * q^89 + 72 * q^93 + 112 * q^94 - 48 * q^98

Introduction

L-functions

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