LMFDB - Embedded newform 7225.2.a.bx.1.11

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			1.11
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)

$f(q)$	$=$	$q-0.903848 q^{2} -2.88161 q^{3} -1.18306 q^{4} +2.60454 q^{6} -0.726991 q^{7} +2.87700 q^{8} +5.30368 q^{9} +O(q^{10})$	\(q-0.903848 q^{2} -2.88161 q^{3} -1.18306 q^{4} +2.60454 q^{6} -0.726991 q^{7} +2.87700 q^{8} +5.30368 q^{9} -2.50358 q^{11} +3.40912 q^{12} -6.29663 q^{13} +0.657089 q^{14} -0.234252 q^{16} -4.79372 q^{18} +0.202859 q^{19} +2.09490 q^{21} +2.26286 q^{22} +0.666914 q^{23} -8.29040 q^{24} +5.69120 q^{26} -6.63830 q^{27} +0.860073 q^{28} +7.93568 q^{29} -5.56241 q^{31} -5.54227 q^{32} +7.21436 q^{33} -6.27457 q^{36} +7.94487 q^{37} -0.183354 q^{38} +18.1444 q^{39} +5.12655 q^{41} -1.89347 q^{42} -11.9561 q^{43} +2.96189 q^{44} -0.602789 q^{46} -10.9207 q^{47} +0.675023 q^{48} -6.47148 q^{49} +7.44929 q^{52} +3.87580 q^{53} +6.00002 q^{54} -2.09155 q^{56} -0.584562 q^{57} -7.17264 q^{58} -3.37248 q^{59} -1.13465 q^{61} +5.02757 q^{62} -3.85573 q^{63} +5.47788 q^{64} -6.52068 q^{66} -5.61946 q^{67} -1.92179 q^{69} +3.96368 q^{71} +15.2587 q^{72} -5.18908 q^{73} -7.18095 q^{74} -0.239995 q^{76} +1.82008 q^{77} -16.3998 q^{78} +14.0406 q^{79} +3.21797 q^{81} -4.63362 q^{82} +12.3494 q^{83} -2.47840 q^{84} +10.8065 q^{86} -22.8675 q^{87} -7.20282 q^{88} +13.0419 q^{89} +4.57759 q^{91} -0.788999 q^{92} +16.0287 q^{93} +9.87063 q^{94} +15.9707 q^{96} -11.9245 q^{97} +5.84924 q^{98} -13.2782 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.903848	−0.639117	−0.319558	−	0.947567i	$-0.603535\pi$
$2$	−0.903848	−0.639117	−0.319558	+	0.947567i	$0.603535\pi$
$3$	−2.88161	−1.66370	−0.831849	−	0.555002i	$-0.812718\pi$
$3$	−2.88161	−1.66370	−0.831849	+	0.555002i	$0.812718\pi$
$4$	−1.18306	−0.591530
$5$	0	0
$5$	0	0
$6$	2.60454	1.06330
$7$	−0.726991	−0.274777	−0.137388	−	0.990517i	$-0.543871\pi$
$7$	−0.726991	−0.274777	−0.137388	+	0.990517i	$0.543871\pi$
$8$	2.87700	1.01717
$9$	5.30368	1.76789
$10$	0	0
$11$	−2.50358	−0.754859	−0.377430	−	0.926038i	$-0.623192\pi$
$11$	−2.50358	−0.754859	−0.377430	+	0.926038i	$0.623192\pi$
$12$	3.40912	0.984127
$13$	−6.29663	−1.74637	−0.873186	−	0.487388i	$-0.837950\pi$
$13$	−6.29663	−1.74637	−0.873186	+	0.487388i	$0.837950\pi$
$14$	0.657089	0.175614
$15$	0	0
$16$	−0.234252	−0.0585630
$17$	0	0
$17$	0	0
$18$	−4.79372	−1.12989
$19$	0.202859	0.0465391	0.0232696	−	0.999729i	$-0.492592\pi$
$19$	0.202859	0.0465391	0.0232696	+	0.999729i	$0.492592\pi$
$20$	0	0
$21$	2.09490	0.457146
$22$	2.26286	0.482443
$23$	0.666914	0.139061	0.0695306	−	0.997580i	$-0.477850\pi$
$23$	0.666914	0.139061	0.0695306	+	0.997580i	$0.477850\pi$
$24$	−8.29040	−1.69227
$25$	0	0
$26$	5.69120	1.11614
$27$	−6.63830	−1.27754
$28$	0.860073	0.162539
$29$	7.93568	1.47362	0.736809	−	0.676101i	$-0.236332\pi$
$29$	7.93568	1.47362	0.736809	+	0.676101i	$0.236332\pi$
$30$	0	0
$31$	−5.56241	−0.999038	−0.499519	−	0.866303i	$-0.666490\pi$
$31$	−5.56241	−0.999038	−0.499519	+	0.866303i	$0.666490\pi$
$32$	−5.54227	−0.979745
$33$	7.21436	1.25586
$34$	0	0
$35$	0	0
$36$	−6.27457	−1.04576
$37$	7.94487	1.30613	0.653064	−	0.757303i	$-0.273483\pi$
$37$	7.94487	1.30613	0.653064	+	0.757303i	$0.273483\pi$
$38$	−0.183354	−0.0297439
$39$	18.1444	2.90544
$40$	0	0
$41$	5.12655	0.800633	0.400316	−	0.916377i	$-0.368900\pi$
$41$	5.12655	0.800633	0.400316	+	0.916377i	$0.368900\pi$
$42$	−1.89347	−0.292169
$43$	−11.9561	−1.82329	−0.911647	−	0.410975i	$-0.865188\pi$
$43$	−11.9561	−1.82329	−0.911647	+	0.410975i	$0.865188\pi$
$44$	2.96189	0.446522
$45$	0	0
$46$	−0.602789	−0.0888763
$47$	−10.9207	−1.59294	−0.796472	−	0.604675i	$-0.793303\pi$
$47$	−10.9207	−1.59294	−0.796472	+	0.604675i	$0.793303\pi$
$48$	0.675023	0.0974312
$49$	−6.47148	−0.924498
$50$	0	0
$51$	0	0
$52$	7.44929	1.03303
$53$	3.87580	0.532383	0.266191	−	0.963920i	$-0.414235\pi$
$53$	3.87580	0.532383	0.266191	+	0.963920i	$0.414235\pi$
$54$	6.00002	0.816499
$55$	0	0
$56$	−2.09155	−0.279496
$57$	−0.584562	−0.0774271
$58$	−7.17264	−0.941814
$59$	−3.37248	−0.439060	−0.219530	−	0.975606i	$-0.570452\pi$
$59$	−3.37248	−0.439060	−0.219530	+	0.975606i	$0.570452\pi$
$60$	0	0
$61$	−1.13465	−0.145277	−0.0726386	−	0.997358i	$-0.523142\pi$
$61$	−1.13465	−0.145277	−0.0726386	+	0.997358i	$0.523142\pi$
$62$	5.02757	0.638502
$63$	−3.85573	−0.485776
$64$	5.47788	0.684734
$65$	0	0
$66$	−6.52068	−0.802640
$67$	−5.61946	−0.686526	−0.343263	−	0.939239i	$-0.611532\pi$
$67$	−5.61946	−0.686526	−0.343263	+	0.939239i	$0.611532\pi$
$68$	0	0
$69$	−1.92179	−0.231356
$70$	0	0
$71$	3.96368	0.470402	0.235201	−	0.971947i	$-0.424425\pi$
$71$	3.96368	0.470402	0.235201	+	0.971947i	$0.424425\pi$
$72$	15.2587	1.79825
$73$	−5.18908	−0.607336	−0.303668	−	0.952778i	$-0.598211\pi$
$73$	−5.18908	−0.607336	−0.303668	+	0.952778i	$0.598211\pi$
$74$	−7.18095	−0.834768
$75$	0	0
$76$	−0.239995	−0.0275293
$77$	1.82008	0.207418
$78$	−16.3998	−1.85691
$79$	14.0406	1.57969	0.789847	−	0.613304i	$-0.210160\pi$
$79$	14.0406	1.57969	0.789847	+	0.613304i	$0.210160\pi$
$80$	0	0
$81$	3.21797	0.357552
$82$	−4.63362	−0.511698
$83$	12.3494	1.35552	0.677762	−	0.735282i	$-0.262950\pi$
$83$	12.3494	1.35552	0.677762	+	0.735282i	$0.262950\pi$
$84$	−2.47840	−0.270415
$85$	0	0
$86$	10.8065	1.16530
$87$	−22.8675	−2.45166
$88$	−7.20282	−0.767823
$89$	13.0419	1.38244	0.691221	−	0.722644i	$-0.257073\pi$
$89$	13.0419	1.38244	0.691221	+	0.722644i	$0.257073\pi$
$90$	0	0
$91$	4.57759	0.479862
$92$	−0.788999	−0.0822588
$93$	16.0287	1.66210
$94$	9.87063	1.01808
$95$	0	0
$96$	15.9707	1.63000
$97$	−11.9245	−1.21075	−0.605374	−	0.795942i	$-0.706976\pi$
$97$	−11.9245	−1.21075	−0.605374	+	0.795942i	$0.706976\pi$
$98$	5.84924	0.590862
$99$	−13.2782	−1.33451
$100$	0	0
$101$	10.0642	1.00143	0.500713	−	0.865613i	$-0.333071\pi$
$101$	10.0642	1.00143	0.500713	+	0.865613i	$0.333071\pi$
$102$	0	0
$103$	9.80719	0.966331	0.483166	−	0.875529i	$-0.339487\pi$
$103$	9.80719	0.966331	0.483166	+	0.875529i	$0.339487\pi$
$104$	−18.1154	−1.77636
$105$	0	0
$106$	−3.50314	−0.340255
$107$	3.81498	0.368808	0.184404	−	0.982851i	$-0.440965\pi$
$107$	3.81498	0.368808	0.184404	+	0.982851i	$0.440965\pi$
$108$	7.85351	0.755704
$109$	3.20733	0.307207	0.153603	−	0.988133i	$-0.450912\pi$
$109$	3.20733	0.307207	0.153603	+	0.988133i	$0.450912\pi$
$110$	0	0
$111$	−22.8940	−2.17300
$112$	0.170299	0.0160918
$113$	−0.403282	−0.0379376	−0.0189688	−	0.999820i	$-0.506038\pi$
$113$	−0.403282	−0.0379376	−0.0189688	+	0.999820i	$0.506038\pi$
$114$	0.528355	0.0494850
$115$	0	0
$116$	−9.38838	−0.871689
$117$	−33.3953	−3.08740
$118$	3.04821	0.280610
$119$	0	0
$120$	0	0
$121$	−4.73206	−0.430187
$122$	1.02555	0.0928491
$123$	−14.7727	−1.33201
$124$	6.58066	0.590961
$125$	0	0
$126$	3.48499	0.310467
$127$	2.16112	0.191769	0.0958844	−	0.995392i	$-0.469432\pi$
$127$	2.16112	0.191769	0.0958844	+	0.995392i	$0.469432\pi$
$128$	6.13338	0.542119
$129$	34.4529	3.03341
$130$	0	0
$131$	−8.04478	−0.702876	−0.351438	−	0.936211i	$-0.614307\pi$
$131$	−8.04478	−0.702876	−0.351438	+	0.936211i	$0.614307\pi$
$132$	−8.53501	−0.742877
$133$	−0.147477	−0.0127879
$134$	5.07913	0.438770
$135$	0	0
$136$	0	0
$137$	−7.87082	−0.672450	−0.336225	−	0.941782i	$-0.609150\pi$
$137$	−7.87082	−0.672450	−0.336225	+	0.941782i	$0.609150\pi$
$138$	1.73700	0.147863
$139$	17.4627	1.48117	0.740583	−	0.671965i	$-0.234549\pi$
$139$	17.4627	1.48117	0.740583	+	0.671965i	$0.234549\pi$
$140$	0	0
$141$	31.4691	2.65018
$142$	−3.58256	−0.300642
$143$	15.7642	1.31826
$144$	−1.24240	−0.103533
$145$	0	0
$146$	4.69014	0.388159
$147$	18.6483	1.53809
$148$	−9.39925	−0.772613
$149$	7.42906	0.608613	0.304306	−	0.952574i	$-0.401575\pi$
$149$	7.42906	0.608613	0.304306	+	0.952574i	$0.401575\pi$
$150$	0	0
$151$	−13.5132	−1.09969	−0.549844	−	0.835267i	$-0.685313\pi$
$151$	−13.5132	−1.09969	−0.549844	+	0.835267i	$0.685313\pi$
$152$	0.583627	0.0473384
$153$	0	0
$154$	−1.64508	−0.132564
$155$	0	0
$156$	−21.4659	−1.71865
$157$	2.75786	0.220101	0.110051	−	0.993926i	$-0.464899\pi$
$157$	2.75786	0.220101	0.110051	+	0.993926i	$0.464899\pi$
$158$	−12.6906	−1.00961
$159$	−11.1686	−0.885724
$160$	0	0
$161$	−0.484840	−0.0382108
$162$	−2.90856	−0.228518
$163$	−1.38371	−0.108381	−0.0541905	−	0.998531i	$-0.517258\pi$
$163$	−1.38371	−0.108381	−0.0541905	+	0.998531i	$0.517258\pi$
$164$	−6.06501	−0.473598
$165$	0	0
$166$	−11.1620	−0.866338
$167$	14.6843	1.13630	0.568151	−	0.822924i	$-0.307659\pi$
$167$	14.6843	1.13630	0.568151	+	0.822924i	$0.307659\pi$
$168$	6.02704	0.464996
$169$	26.6476	2.04981
$170$	0	0
$171$	1.07590	0.0822762
$172$	14.1448	1.07853
$173$	14.7492	1.12136	0.560681	−	0.828032i	$-0.310539\pi$
$173$	14.7492	1.12136	0.560681	+	0.828032i	$0.310539\pi$
$174$	20.6688	1.56689
$175$	0	0
$176$	0.586470	0.0442068
$177$	9.71818	0.730463
$178$	−11.7879	−0.883542
$179$	14.2764	1.06707	0.533534	−	0.845779i	$-0.320864\pi$
$179$	14.2764	1.06707	0.533534	+	0.845779i	$0.320864\pi$
$180$	0	0
$181$	6.02407	0.447766	0.223883	−	0.974616i	$-0.428127\pi$
$181$	6.02407	0.447766	0.223883	+	0.974616i	$0.428127\pi$
$182$	−4.13745	−0.306688
$183$	3.26962	0.241698
$184$	1.91871	0.141449
$185$	0	0
$186$	−14.4875	−1.06227
$187$	0	0
$188$	12.9198	0.942274
$189$	4.82599	0.351039
$190$	0	0
$191$	14.1379	1.02298	0.511492	−	0.859288i	$-0.329093\pi$
$191$	14.1379	1.02298	0.511492	+	0.859288i	$0.329093\pi$
$192$	−15.7851	−1.13919
$193$	23.2770	1.67552	0.837758	−	0.546042i	$-0.183866\pi$
$193$	23.2770	1.67552	0.837758	+	0.546042i	$0.183866\pi$
$194$	10.7779	0.773809
$195$	0	0
$196$	7.65615	0.546868
$197$	9.29796	0.662452	0.331226	−	0.943551i	$-0.392538\pi$
$197$	9.29796	0.662452	0.331226	+	0.943551i	$0.392538\pi$
$198$	12.0015	0.852908
$199$	7.56226	0.536075	0.268037	−	0.963409i	$-0.413625\pi$
$199$	7.56226	0.536075	0.268037	+	0.963409i	$0.413625\pi$
$200$	0	0
$201$	16.1931	1.14217
$202$	−9.09652	−0.640029
$203$	−5.76916	−0.404916
$204$	0	0
$205$	0	0
$206$	−8.86421	−0.617598
$207$	3.53710	0.245845
$208$	1.47500	0.102273
$209$	−0.507876	−0.0351305
$210$	0	0
$211$	−24.9647	−1.71864	−0.859322	−	0.511435i	$-0.829114\pi$
$211$	−24.9647	−1.71864	−0.859322	+	0.511435i	$0.829114\pi$
$212$	−4.58531	−0.314920
$213$	−11.4218	−0.782607
$214$	−3.44816	−0.235711
$215$	0	0
$216$	−19.0984	−1.29948
$217$	4.04382	0.274512
$218$	−2.89894	−0.196341
$219$	14.9529	1.01042
$220$	0	0
$221$	0	0
$222$	20.6927	1.38880
$223$	−12.1685	−0.814860	−0.407430	−	0.913236i	$-0.633575\pi$
$223$	−12.1685	−0.814860	−0.407430	+	0.913236i	$0.633575\pi$
$224$	4.02918	0.269211
$225$	0	0
$226$	0.364506	0.0242466
$227$	1.98651	0.131850	0.0659248	−	0.997825i	$-0.479000\pi$
$227$	1.98651	0.131850	0.0659248	+	0.997825i	$0.479000\pi$
$228$	0.691571	0.0458004
$229$	2.29201	0.151460	0.0757302	−	0.997128i	$-0.475871\pi$
$229$	2.29201	0.151460	0.0757302	+	0.997128i	$0.475871\pi$
$230$	0	0
$231$	−5.24477	−0.345081
$232$	22.8309	1.49893
$233$	−22.7030	−1.48732	−0.743662	−	0.668555i	$-0.766913\pi$
$233$	−22.7030	−1.48732	−0.743662	+	0.668555i	$0.766913\pi$
$234$	30.1843	1.97321
$235$	0	0
$236$	3.98984	0.259717
$237$	−40.4596	−2.62813
$238$	0	0
$239$	13.2285	0.855683	0.427841	−	0.903854i	$-0.359274\pi$
$239$	13.2285	0.855683	0.427841	+	0.903854i	$0.359274\pi$
$240$	0	0
$241$	−2.89925	−0.186757	−0.0933787	−	0.995631i	$-0.529767\pi$
$241$	−2.89925	−0.186757	−0.0933787	+	0.995631i	$0.529767\pi$
$242$	4.27706	0.274940
$243$	10.6420	0.682683
$244$	1.34236	0.0859358
$245$	0	0
$246$	13.3523	0.851311
$247$	−1.27733	−0.0812746
$248$	−16.0031	−1.01619
$249$	−35.5862	−2.25518
$250$	0	0
$251$	9.85445	0.622008	0.311004	−	0.950409i	$-0.399335\pi$
$251$	9.85445	0.622008	0.311004	+	0.950409i	$0.399335\pi$
$252$	4.56155	0.287351
$253$	−1.66968	−0.104972
$254$	−1.95333	−0.122563
$255$	0	0
$256$	−16.4994	−1.03121
$257$	5.28936	0.329941	0.164970	−	0.986299i	$-0.447247\pi$
$257$	5.28936	0.329941	0.164970	+	0.986299i	$0.447247\pi$
$258$	−31.1402	−1.93870
$259$	−5.77584	−0.358893
$260$	0	0
$261$	42.0883	2.60520
$262$	7.27126	0.449220
$263$	−12.5802	−0.775726	−0.387863	−	0.921717i	$-0.626787\pi$
$263$	−12.5802	−0.775726	−0.387863	+	0.921717i	$0.626787\pi$
$264$	20.7557	1.27743
$265$	0	0
$266$	0.133297	0.00817294
$267$	−37.5817	−2.29997
$268$	6.64815	0.406101
$269$	9.20257	0.561091	0.280545	−	0.959841i	$-0.409485\pi$
$269$	9.20257	0.561091	0.280545	+	0.959841i	$0.409485\pi$
$270$	0	0
$271$	14.6023	0.887028	0.443514	−	0.896267i	$-0.353732\pi$
$271$	14.6023	0.887028	0.443514	+	0.896267i	$0.353732\pi$
$272$	0	0
$273$	−13.1908	−0.798346
$274$	7.11403	0.429774
$275$	0	0
$276$	2.27359	0.136854
$277$	13.0658	0.785050	0.392525	−	0.919741i	$-0.371602\pi$
$277$	13.0658	0.785050	0.392525	+	0.919741i	$0.371602\pi$
$278$	−15.7836	−0.946638
$279$	−29.5012	−1.76619
$280$	0	0
$281$	−7.56115	−0.451060	−0.225530	−	0.974236i	$-0.572411\pi$
$281$	−7.56115	−0.451060	−0.225530	+	0.974236i	$0.572411\pi$
$282$	−28.4433	−1.69377
$283$	−4.11802	−0.244791	−0.122396	−	0.992481i	$-0.539058\pi$
$283$	−4.11802	−0.244791	−0.122396	+	0.992481i	$0.539058\pi$
$284$	−4.68927	−0.278257
$285$	0	0
$286$	−14.2484	−0.842525
$287$	−3.72696	−0.219995
$288$	−29.3944	−1.73208
$289$	0	0
$290$	0	0
$291$	34.3617	2.01432
$292$	6.13899	0.359257
$293$	18.5803	1.08547	0.542736	−	0.839903i	$-0.317388\pi$
$293$	18.5803	1.08547	0.542736	+	0.839903i	$0.317388\pi$
$294$	−16.8552	−0.983016
$295$	0	0
$296$	22.8574	1.32856
$297$	16.6196	0.964365
$298$	−6.71474	−0.388975
$299$	−4.19931	−0.242852
$300$	0	0
$301$	8.69200	0.500998
$302$	12.2139	0.702829
$303$	−29.0011	−1.66607
$304$	−0.0475202	−0.00272547
$305$	0	0
$306$	0	0
$307$	−9.82624	−0.560813	−0.280407	−	0.959881i	$-0.590469\pi$
$307$	−9.82624	−0.560813	−0.280407	+	0.959881i	$0.590469\pi$
$308$	−2.15327	−0.122694
$309$	−28.2605	−1.60768
$310$	0	0
$311$	−28.6883	−1.62676	−0.813382	−	0.581729i	$-0.802376\pi$
$311$	−28.6883	−1.62676	−0.813382	+	0.581729i	$0.802376\pi$
$312$	52.2016	2.95533
$313$	−0.968645	−0.0547511	−0.0273755	−	0.999625i	$-0.508715\pi$
$313$	−0.968645	−0.0547511	−0.0273755	+	0.999625i	$0.508715\pi$
$314$	−2.49268	−0.140670
$315$	0	0
$316$	−16.6109	−0.934436
$317$	26.5248	1.48978	0.744892	−	0.667185i	$-0.232501\pi$
$317$	26.5248	1.48978	0.744892	+	0.667185i	$0.232501\pi$
$318$	10.0947	0.566081
$319$	−19.8676	−1.11237
$320$	0	0
$321$	−10.9933	−0.613585
$322$	0.438222	0.0244211
$323$	0	0
$324$	−3.80705	−0.211503
$325$	0	0
$326$	1.25067	0.0692681
$327$	−9.24228	−0.511099
$328$	14.7491	0.814383
$329$	7.93923	0.437704
$330$	0	0
$331$	6.12601	0.336716	0.168358	−	0.985726i	$-0.446154\pi$
$331$	6.12601	0.336716	0.168358	+	0.985726i	$0.446154\pi$
$332$	−14.6101	−0.801832
$333$	42.1370	2.30909
$334$	−13.2723	−0.726230
$335$	0	0
$336$	−0.490736	−0.0267718
$337$	15.8752	0.864777	0.432388	−	0.901687i	$-0.357671\pi$
$337$	15.8752	0.864777	0.432388	+	0.901687i	$0.357671\pi$
$338$	−24.0853	−1.31007
$339$	1.16210	0.0631167
$340$	0	0
$341$	13.9260	0.754133
$342$	−0.972451	−0.0525841
$343$	9.79364	0.528807
$344$	−34.3978	−1.85461
$345$	0	0
$346$	−13.3310	−0.716681
$347$	−1.70339	−0.0914428	−0.0457214	−	0.998954i	$-0.514559\pi$
$347$	−1.70339	−0.0914428	−0.0457214	+	0.998954i	$0.514559\pi$
$348$	27.0536	1.45023
$349$	−35.2541	−1.88711	−0.943553	−	0.331221i	$-0.892540\pi$
$349$	−35.2541	−1.88711	−0.943553	+	0.331221i	$0.892540\pi$
$350$	0	0
$351$	41.7990	2.23106
$352$	13.8756	0.739569
$353$	−22.4928	−1.19717	−0.598586	−	0.801059i	$-0.704270\pi$
$353$	−22.4928	−1.19717	−0.598586	+	0.801059i	$0.704270\pi$
$354$	−8.78375	−0.466851
$355$	0	0
$356$	−15.4294	−0.817755
$357$	0	0
$358$	−12.9037	−0.681981
$359$	18.0039	0.950208	0.475104	−	0.879930i	$-0.342410\pi$
$359$	18.0039	0.950208	0.475104	+	0.879930i	$0.342410\pi$
$360$	0	0
$361$	−18.9588	−0.997834
$362$	−5.44485	−0.286175
$363$	13.6360	0.715702
$364$	−5.41556	−0.283853
$365$	0	0
$366$	−2.95524	−0.154473
$367$	−31.2820	−1.63291	−0.816454	−	0.577411i	$-0.804063\pi$
$367$	−31.2820	−1.63291	−0.816454	+	0.577411i	$0.804063\pi$
$368$	−0.156226	−0.00814384
$369$	27.1896	1.41543
$370$	0	0
$371$	−2.81767	−0.146286
$372$	−18.9629	−0.983180
$373$	24.3521	1.26091	0.630453	−	0.776228i	$-0.282869\pi$
$373$	24.3521	1.26091	0.630453	+	0.776228i	$0.282869\pi$
$374$	0	0
$375$	0	0
$376$	−31.4188	−1.62030
$377$	−49.9680	−2.57348
$378$	−4.36196	−0.224355
$379$	−6.54787	−0.336341	−0.168171	−	0.985758i	$-0.553786\pi$
$379$	−6.54787	−0.336341	−0.168171	+	0.985758i	$0.553786\pi$
$380$	0	0
$381$	−6.22752	−0.319045
$382$	−12.7785	−0.653806
$383$	−18.3898	−0.939675	−0.469838	−	0.882753i	$-0.655688\pi$
$383$	−18.3898	−0.939675	−0.469838	+	0.882753i	$0.655688\pi$
$384$	−17.6740	−0.901923
$385$	0	0
$386$	−21.0389	−1.07085
$387$	−63.4115	−3.22339
$388$	14.1074	0.716193
$389$	2.15031	0.109025	0.0545124	−	0.998513i	$-0.482640\pi$
$389$	2.15031	0.109025	0.0545124	+	0.998513i	$0.482640\pi$
$390$	0	0
$391$	0	0
$392$	−18.6185	−0.940375
$393$	23.1819	1.16937
$394$	−8.40394	−0.423384
$395$	0	0
$396$	15.7089	0.789402
$397$	−0.387651	−0.0194556	−0.00972782	−	0.999953i	$-0.503097\pi$
$397$	−0.387651	−0.0194556	−0.00972782	+	0.999953i	$0.503097\pi$
$398$	−6.83513	−0.342614
$399$	0.424971	0.0212752
$400$	0	0
$401$	−16.7192	−0.834917	−0.417458	−	0.908696i	$-0.637079\pi$
$401$	−16.7192	−0.834917	−0.417458	+	0.908696i	$0.637079\pi$
$402$	−14.6361	−0.729982
$403$	35.0244	1.74469
$404$	−11.9066	−0.592374
$405$	0	0
$406$	5.21444	0.258789
$407$	−19.8906	−0.985943
$408$	0	0
$409$	−15.7306	−0.777828	−0.388914	−	0.921274i	$-0.627150\pi$
$409$	−15.7306	−0.777828	−0.388914	+	0.921274i	$0.627150\pi$
$410$	0	0
$411$	22.6807	1.11875
$412$	−11.6025	−0.571613
$413$	2.45176	0.120643
$414$	−3.19700	−0.157124
$415$	0	0
$416$	34.8977	1.71100
$417$	−50.3207	−2.46421
$418$	0.459042	0.0224525
$419$	−10.6214	−0.518888	−0.259444	−	0.965758i	$-0.583539\pi$
$419$	−10.6214	−0.518888	−0.259444	+	0.965758i	$0.583539\pi$
$420$	0	0
$421$	−17.0231	−0.829656	−0.414828	−	0.909900i	$-0.636158\pi$
$421$	−17.0231	−0.829656	−0.414828	+	0.909900i	$0.636158\pi$
$422$	22.5643	1.09841
$423$	−57.9198	−2.81615
$424$	11.1507	0.541526
$425$	0	0
$426$	10.3235	0.500178
$427$	0.824881	0.0399188
$428$	−4.51334	−0.218161
$429$	−45.4261	−2.19320
$430$	0	0
$431$	19.6907	0.948467	0.474234	−	0.880399i	$-0.342725\pi$
$431$	19.6907	0.948467	0.474234	+	0.880399i	$0.342725\pi$
$432$	1.55504	0.0748167
$433$	−21.9579	−1.05523	−0.527614	−	0.849484i	$-0.676913\pi$
$433$	−21.9579	−1.05523	−0.527614	+	0.849484i	$0.676913\pi$
$434$	−3.65500	−0.175445
$435$	0	0
$436$	−3.79446	−0.181722
$437$	0.135290	0.00647179
$438$	−13.5152	−0.645779
$439$	−8.49879	−0.405625	−0.202813	−	0.979218i	$-0.565008\pi$
$439$	−8.49879	−0.405625	−0.202813	+	0.979218i	$0.565008\pi$
$440$	0	0
$441$	−34.3227	−1.63441
$442$	0	0
$443$	4.70952	0.223756	0.111878	−	0.993722i	$-0.464313\pi$
$443$	4.70952	0.223756	0.111878	+	0.993722i	$0.464313\pi$
$444$	27.0850	1.28540
$445$	0	0
$446$	10.9984	0.520791
$447$	−21.4077	−1.01255
$448$	−3.98236	−0.188149
$449$	26.2370	1.23820	0.619101	−	0.785311i	$-0.287497\pi$
$449$	26.2370	1.23820	0.619101	+	0.785311i	$0.287497\pi$
$450$	0	0
$451$	−12.8348	−0.604365
$452$	0.477107	0.0224412
$453$	38.9398	1.82955
$454$	−1.79551	−0.0842673
$455$	0	0
$456$	−1.68178	−0.0787568
$457$	20.6825	0.967485	0.483743	−	0.875210i	$-0.339277\pi$
$457$	20.6825	0.967485	0.483743	+	0.875210i	$0.339277\pi$
$458$	−2.07163	−0.0968009
$459$	0	0
$460$	0	0
$461$	1.94101	0.0904020	0.0452010	−	0.998978i	$-0.485607\pi$
$461$	1.94101	0.0904020	0.0452010	+	0.998978i	$0.485607\pi$
$462$	4.74047	0.220547
$463$	−10.6872	−0.496676	−0.248338	−	0.968673i	$-0.579884\pi$
$463$	−10.6872	−0.496676	−0.248338	+	0.968673i	$0.579884\pi$
$464$	−1.85895	−0.0862995
$465$	0	0
$466$	20.5201	0.950574
$467$	4.85368	0.224602	0.112301	−	0.993674i	$-0.464178\pi$
$467$	4.85368	0.224602	0.112301	+	0.993674i	$0.464178\pi$
$468$	39.5086	1.82629
$469$	4.08529	0.188641
$470$	0	0
$471$	−7.94707	−0.366182
$472$	−9.70263	−0.446600
$473$	29.9332	1.37633
$474$	36.5693	1.67969
$475$	0	0
$476$	0	0
$477$	20.5560	0.941196
$478$	−11.9566	−0.546881
$479$	−7.60904	−0.347666	−0.173833	−	0.984775i	$-0.555615\pi$
$479$	−7.60904	−0.347666	−0.173833	+	0.984775i	$0.555615\pi$
$480$	0	0
$481$	−50.0259	−2.28098
$482$	2.62048	0.119360
$483$	1.39712	0.0635712
$484$	5.59831	0.254469
$485$	0	0
$486$	−9.61872	−0.436314
$487$	−0.425586	−0.0192851	−0.00964257	−	0.999954i	$-0.503069\pi$
$487$	−0.425586	−0.0192851	−0.00964257	+	0.999954i	$0.503069\pi$
$488$	−3.26439	−0.147772
$489$	3.98733	0.180313
$490$	0	0
$491$	0.279220	0.0126010	0.00630052	−	0.999980i	$-0.497994\pi$
$491$	0.279220	0.0126010	0.00630052	+	0.999980i	$0.497994\pi$
$492$	17.4770	0.787924
$493$	0	0
$494$	1.15451	0.0519440
$495$	0	0
$496$	1.30301	0.0585067
$497$	−2.88156	−0.129256
$498$	32.1645	1.44132
$499$	−18.5254	−0.829311	−0.414655	−	0.909979i	$-0.636098\pi$
$499$	−18.5254	−0.829311	−0.414655	+	0.909979i	$0.636098\pi$
$500$	0	0
$501$	−42.3143	−1.89046
$502$	−8.90693	−0.397536
$503$	−8.12470	−0.362262	−0.181131	−	0.983459i	$-0.557976\pi$
$503$	−8.12470	−0.362262	−0.181131	+	0.983459i	$0.557976\pi$
$504$	−11.0929	−0.494118
$505$	0	0
$506$	1.50913	0.0670891
$507$	−76.7879	−3.41027
$508$	−2.55674	−0.113437
$509$	−15.1877	−0.673181	−0.336590	−	0.941651i	$-0.609274\pi$
$509$	−15.1877	−0.673181	−0.336590	+	0.941651i	$0.609274\pi$
$510$	0	0
$511$	3.77241	0.166882
$512$	2.64618	0.116946
$513$	−1.34664	−0.0594557
$514$	−4.78077	−0.210871
$515$	0	0
$516$	−40.7598	−1.79435
$517$	27.3408	1.20245
$518$	5.22048	0.229375
$519$	−42.5015	−1.86561
$520$	0	0
$521$	−37.3496	−1.63631	−0.818157	−	0.574995i	$-0.805004\pi$
$521$	−37.3496	−1.63631	−0.818157	+	0.574995i	$0.805004\pi$
$522$	−38.0414	−1.66503
$523$	8.03541	0.351364	0.175682	−	0.984447i	$-0.443787\pi$
$523$	8.03541	0.351364	0.175682	+	0.984447i	$0.443787\pi$
$524$	9.51745	0.415772
$525$	0	0
$526$	11.3706	0.495780
$527$	0	0
$528$	−1.68998	−0.0735469
$529$	−22.5552	−0.980662
$530$	0	0
$531$	−17.8866	−0.776210
$532$	0.174474	0.00756440
$533$	−32.2800	−1.39820
$534$	33.9682	1.46995
$535$	0	0
$536$	−16.1672	−0.698316
$537$	−41.1390	−1.77528
$538$	−8.31772	−0.358603
$539$	16.2019	0.697866
$540$	0	0
$541$	16.3264	0.701929	0.350964	−	0.936389i	$-0.385854\pi$
$541$	16.3264	0.701929	0.350964	+	0.936389i	$0.385854\pi$
$542$	−13.1983	−0.566915
$543$	−17.3590	−0.744947
$544$	0	0
$545$	0	0
$546$	11.9225	0.510236
$547$	−28.8042	−1.23158	−0.615789	−	0.787911i	$-0.711162\pi$
$547$	−28.8042	−1.23158	−0.615789	+	0.787911i	$0.711162\pi$
$548$	9.31165	0.397774
$549$	−6.01783	−0.256835
$550$	0	0
$551$	1.60983	0.0685809
$552$	−5.52898	−0.235329
$553$	−10.2074	−0.434063
$554$	−11.8095	−0.501738
$555$	0	0
$556$	−20.6594	−0.876154
$557$	7.64838	0.324072	0.162036	−	0.986785i	$-0.448194\pi$
$557$	7.64838	0.324072	0.162036	+	0.986785i	$0.448194\pi$
$558$	26.6646	1.12880
$559$	75.2834	3.18415
$560$	0	0
$561$	0	0
$562$	6.83413	0.288280
$563$	−42.3891	−1.78649	−0.893244	−	0.449572i	$-0.851577\pi$
$563$	−42.3891	−1.78649	−0.893244	+	0.449572i	$0.851577\pi$
$564$	−37.2298	−1.56766
$565$	0	0
$566$	3.72207	0.156450
$567$	−2.33944	−0.0982471
$568$	11.4035	0.478481
$569$	−30.8191	−1.29200	−0.646001	−	0.763336i	$-0.723560\pi$
$569$	−30.8191	−1.29200	−0.646001	+	0.763336i	$0.723560\pi$
$570$	0	0
$571$	−22.0459	−0.922594	−0.461297	−	0.887246i	$-0.652616\pi$
$571$	−22.0459	−0.922594	−0.461297	+	0.887246i	$0.652616\pi$
$572$	−18.6499	−0.779793
$573$	−40.7400	−1.70194
$574$	3.36860	0.140603
$575$	0	0
$576$	29.0529	1.21054
$577$	20.2437	0.842755	0.421378	−	0.906885i	$-0.361547\pi$
$577$	20.2437	0.842755	0.421378	+	0.906885i	$0.361547\pi$
$578$	0	0
$579$	−67.0753	−2.78755
$580$	0	0
$581$	−8.97790	−0.372466
$582$	−31.0577	−1.28738
$583$	−9.70341	−0.401874
$584$	−14.9290	−0.617766
$585$	0	0
$586$	−16.7938	−0.693744
$587$	−12.7637	−0.526812	−0.263406	−	0.964685i	$-0.584846\pi$
$587$	−12.7637	−0.526812	−0.263406	+	0.964685i	$0.584846\pi$
$588$	−22.0620	−0.909823
$589$	−1.12839	−0.0464944
$590$	0	0
$591$	−26.7931	−1.10212
$592$	−1.86110	−0.0764908
$593$	−2.87908	−0.118230	−0.0591148	−	0.998251i	$-0.518828\pi$
$593$	−2.87908	−0.118230	−0.0591148	+	0.998251i	$0.518828\pi$
$594$	−15.0216	−0.616342
$595$	0	0
$596$	−8.78902	−0.360012
$597$	−21.7915	−0.891867
$598$	3.79554	0.155211
$599$	−12.6720	−0.517762	−0.258881	−	0.965909i	$-0.583354\pi$
$599$	−12.6720	−0.517762	−0.258881	+	0.965909i	$0.583354\pi$
$600$	0	0
$601$	13.7248	0.559846	0.279923	−	0.960022i	$-0.409691\pi$
$601$	13.7248	0.559846	0.279923	+	0.960022i	$0.409691\pi$
$602$	−7.85624	−0.320197
$603$	−29.8038	−1.21370
$604$	15.9869	0.650498
$605$	0	0
$606$	26.2126	1.06481
$607$	7.80403	0.316756	0.158378	−	0.987379i	$-0.449374\pi$
$607$	7.80403	0.316756	0.158378	+	0.987379i	$0.449374\pi$
$608$	−1.12430	−0.0455965
$609$	16.6245	0.673658
$610$	0	0
$611$	68.7635	2.78187
$612$	0	0
$613$	44.7999	1.80945	0.904726	−	0.425994i	$-0.140076\pi$
$613$	44.7999	1.80945	0.904726	+	0.425994i	$0.140076\pi$
$614$	8.88142	0.358425
$615$	0	0
$616$	5.23638	0.210980
$617$	−21.5816	−0.868843	−0.434422	−	0.900710i	$-0.643047\pi$
$617$	−21.5816	−0.868843	−0.434422	+	0.900710i	$0.643047\pi$
$618$	25.5432	1.02750
$619$	−38.5766	−1.55052	−0.775262	−	0.631640i	$-0.782382\pi$
$619$	−38.5766	−1.55052	−0.775262	+	0.631640i	$0.782382\pi$
$620$	0	0
$621$	−4.42718	−0.177657
$622$	25.9299	1.03969
$623$	−9.48136	−0.379863
$624$	−4.25037	−0.170151
$625$	0	0
$626$	0.875508	0.0349923
$627$	1.46350	0.0584466
$628$	−3.26271	−0.130196
$629$	0	0
$630$	0	0
$631$	−24.2230	−0.964304	−0.482152	−	0.876088i	$-0.660145\pi$
$631$	−24.2230	−0.964304	−0.482152	+	0.876088i	$0.660145\pi$
$632$	40.3949	1.60682
$633$	71.9387	2.85931
$634$	−23.9744	−0.952146
$635$	0	0
$636$	13.2131	0.523932
$637$	40.7486	1.61452
$638$	17.9573	0.710937
$639$	21.0221	0.831621
$640$	0	0
$641$	43.4317	1.71545	0.857725	−	0.514108i	$-0.171877\pi$
$641$	43.4317	1.71545	0.857725	+	0.514108i	$0.171877\pi$
$642$	9.93625	0.392152
$643$	−35.4825	−1.39929	−0.699646	−	0.714490i	$-0.746659\pi$
$643$	−35.4825	−1.39929	−0.699646	+	0.714490i	$0.746659\pi$
$644$	0.573595	0.0226028
$645$	0	0
$646$	0	0
$647$	28.2269	1.10971	0.554857	−	0.831946i	$-0.312773\pi$
$647$	28.2269	1.10971	0.554857	+	0.831946i	$0.312773\pi$
$648$	9.25811	0.363693
$649$	8.44329	0.331428
$650$	0	0
$651$	−11.6527	−0.456706
$652$	1.63702	0.0641105
$653$	3.72898	0.145926	0.0729632	−	0.997335i	$-0.476754\pi$
$653$	3.72898	0.145926	0.0729632	+	0.997335i	$0.476754\pi$
$654$	8.35361	0.326652
$655$	0	0
$656$	−1.20091	−0.0468875
$657$	−27.5212	−1.07371
$658$	−7.17585	−0.279744
$659$	−16.0238	−0.624200	−0.312100	−	0.950049i	$-0.601032\pi$
$659$	−16.0238	−0.624200	−0.312100	+	0.950049i	$0.601032\pi$
$660$	0	0
$661$	−27.5405	−1.07120	−0.535601	−	0.844471i	$-0.679915\pi$
$661$	−27.5405	−1.07120	−0.535601	+	0.844471i	$0.679915\pi$
$662$	−5.53698	−0.215201
$663$	0	0
$664$	35.5292	1.37880
$665$	0	0
$666$	−38.0854	−1.47578
$667$	5.29241	0.204923
$668$	−17.3723	−0.672156
$669$	35.0648	1.35568
$670$	0	0
$671$	2.84070	0.109664
$672$	−11.6105	−0.447886
$673$	18.9406	0.730106	0.365053	−	0.930987i	$-0.381051\pi$
$673$	18.9406	0.730106	0.365053	+	0.930987i	$0.381051\pi$
$674$	−14.3488	−0.552693
$675$	0	0
$676$	−31.5257	−1.21253
$677$	10.5909	0.407042	0.203521	−	0.979071i	$-0.434762\pi$
$677$	10.5909	0.407042	0.203521	+	0.979071i	$0.434762\pi$
$678$	−1.05036	−0.0403390
$679$	8.66898	0.332685
$680$	0	0
$681$	−5.72436	−0.219358
$682$	−12.5869	−0.481979
$683$	45.0651	1.72437	0.862184	−	0.506596i	$-0.169096\pi$
$683$	45.0651	1.72437	0.862184	+	0.506596i	$0.169096\pi$
$684$	−1.27285	−0.0486688
$685$	0	0
$686$	−8.85196	−0.337970
$687$	−6.60469	−0.251985
$688$	2.80075	0.106778
$689$	−24.4045	−0.929738
$690$	0	0
$691$	−13.0470	−0.496332	−0.248166	−	0.968718i	$-0.579828\pi$
$691$	−13.0470	−0.496332	−0.248166	+	0.968718i	$0.579828\pi$
$692$	−17.4492	−0.663319
$693$	9.65314	0.366692
$694$	1.53961	0.0584426
$695$	0	0
$696$	−65.7899	−2.49376
$697$	0	0
$698$	31.8643	1.20608
$699$	65.4213	2.47446
$700$	0	0
$701$	4.42228	0.167027	0.0835136	−	0.996507i	$-0.473386\pi$
$701$	4.42228	0.167027	0.0835136	+	0.996507i	$0.473386\pi$
$702$	−37.7799	−1.42591
$703$	1.61169	0.0607861
$704$	−13.7143	−0.516878
$705$	0	0
$706$	20.3301	0.765132
$707$	−7.31659	−0.275169
$708$	−11.4972	−0.432090
$709$	−32.0483	−1.20360	−0.601800	−	0.798647i	$-0.705549\pi$
$709$	−32.0483	−1.20360	−0.601800	+	0.798647i	$0.705549\pi$
$710$	0	0
$711$	74.4670	2.79273
$712$	37.5216	1.40618
$713$	−3.70965	−0.138927
$714$	0	0
$715$	0	0
$716$	−16.8898	−0.631202
$717$	−38.1195	−1.42360
$718$	−16.2728	−0.607294
$719$	−27.7269	−1.03404	−0.517020	−	0.855973i	$-0.672959\pi$
$719$	−27.7269	−1.03404	−0.517020	+	0.855973i	$0.672959\pi$
$720$	0	0
$721$	−7.12973	−0.265525
$722$	17.1359	0.637733
$723$	8.35452	0.310708
$724$	−7.12684	−0.264867
$725$	0	0
$726$	−12.3248	−0.457417
$727$	10.5407	0.390934	0.195467	−	0.980710i	$-0.437378\pi$
$727$	10.5407	0.390934	0.195467	+	0.980710i	$0.437378\pi$
$728$	13.1697	0.488103
$729$	−40.3199	−1.49333
$730$	0	0
$731$	0	0
$732$	−3.86816	−0.142971
$733$	−16.4227	−0.606585	−0.303293	−	0.952898i	$-0.598086\pi$
$733$	−16.4227	−0.606585	−0.303293	+	0.952898i	$0.598086\pi$
$734$	28.2742	1.04362
$735$	0	0
$736$	−3.69622	−0.136244
$737$	14.0688	0.518231
$738$	−24.5752	−0.904627
$739$	1.80904	0.0665467	0.0332733	−	0.999446i	$-0.489407\pi$
$739$	1.80904	0.0665467	0.0332733	+	0.999446i	$0.489407\pi$
$740$	0	0
$741$	3.68077	0.135216
$742$	2.54675	0.0934941
$743$	43.1045	1.58135	0.790676	−	0.612235i	$-0.209729\pi$
$743$	43.1045	1.58135	0.790676	+	0.612235i	$0.209729\pi$
$744$	46.1146	1.69064
$745$	0	0
$746$	−22.0106	−0.805866
$747$	65.4973	2.39642
$748$	0	0
$749$	−2.77345	−0.101340
$750$	0	0
$751$	29.3004	1.06919	0.534593	−	0.845110i	$-0.320465\pi$
$751$	29.3004	1.06919	0.534593	+	0.845110i	$0.320465\pi$
$752$	2.55819	0.0932876
$753$	−28.3967	−1.03483
$754$	45.1635	1.64476
$755$	0	0
$756$	−5.70943	−0.207650
$757$	10.3516	0.376234	0.188117	−	0.982147i	$-0.439762\pi$
$757$	10.3516	0.376234	0.188117	+	0.982147i	$0.439762\pi$
$758$	5.91828	0.214961
$759$	4.81136	0.174641
$760$	0	0
$761$	−40.0677	−1.45245	−0.726227	−	0.687455i	$-0.758728\pi$
$761$	−40.0677	−1.45245	−0.726227	+	0.687455i	$0.758728\pi$
$762$	5.62873	0.203907
$763$	−2.33170	−0.0844132
$764$	−16.7260	−0.605125
$765$	0	0
$766$	16.6216	0.600562
$767$	21.2353	0.766761
$768$	47.5448	1.71563
$769$	40.8532	1.47320	0.736602	−	0.676327i	$-0.236429\pi$
$769$	40.8532	1.47320	0.736602	+	0.676327i	$0.236429\pi$
$770$	0	0
$771$	−15.2419	−0.548922
$772$	−27.5381	−0.991117
$773$	−17.1111	−0.615442	−0.307721	−	0.951477i	$-0.599566\pi$
$773$	−17.1111	−0.615442	−0.307721	+	0.951477i	$0.599566\pi$
$774$	57.3143	2.06012
$775$	0	0
$776$	−34.3067	−1.23154
$777$	16.6437	0.597091
$778$	−1.94355	−0.0696796
$779$	1.03997	0.0372608
$780$	0	0
$781$	−9.92341	−0.355087
$782$	0	0
$783$	−52.6794	−1.88261
$784$	1.51596	0.0541414
$785$	0	0
$786$	−20.9529	−0.747366
$787$	18.4210	0.656639	0.328320	−	0.944567i	$-0.393518\pi$
$787$	18.4210	0.656639	0.328320	+	0.944567i	$0.393518\pi$
$788$	−11.0000	−0.391860
$789$	36.2511	1.29057
$790$	0	0
$791$	0.293182	0.0104244
$792$	−38.2014	−1.35743
$793$	7.14448	0.253708
$794$	0.350377	0.0124344
$795$	0	0
$796$	−8.94661	−0.317104
$797$	−28.5994	−1.01304	−0.506521	−	0.862228i	$-0.669069\pi$
$797$	−28.5994	−1.01304	−0.506521	+	0.862228i	$0.669069\pi$
$798$	−0.384109	−0.0135973
$799$	0	0
$800$	0	0
$801$	69.1702	2.44401
$802$	15.1116	0.533609
$803$	12.9913	0.458453
$804$	−19.1574	−0.675629
$805$	0	0
$806$	−31.6568	−1.11506
$807$	−26.5182	−0.933486
$808$	28.9547	1.01862
$809$	−27.1783	−0.955537	−0.477769	−	0.878486i	$-0.658554\pi$
$809$	−27.1783	−0.955537	−0.477769	+	0.878486i	$0.658554\pi$
$810$	0	0
$811$	19.0265	0.668111	0.334055	−	0.942553i	$-0.391583\pi$
$811$	19.0265	0.668111	0.334055	+	0.942553i	$0.391583\pi$
$812$	6.82526	0.239520
$813$	−42.0782	−1.47575
$814$	17.9781	0.630133
$815$	0	0
$816$	0	0
$817$	−2.42541	−0.0848545
$818$	14.2181	0.497123
$819$	24.2781	0.848345
$820$	0	0
$821$	28.8147	1.00564	0.502819	−	0.864392i	$-0.332296\pi$
$821$	28.8147	1.00564	0.502819	+	0.864392i	$0.332296\pi$
$822$	−20.4999	−0.715015
$823$	41.7187	1.45422	0.727112	−	0.686519i	$-0.240862\pi$
$823$	41.7187	1.45422	0.727112	+	0.686519i	$0.240862\pi$
$824$	28.2153	0.982926
$825$	0	0
$826$	−2.21602	−0.0771052
$827$	27.0696	0.941302	0.470651	−	0.882319i	$-0.344019\pi$
$827$	27.0696	0.941302	0.470651	+	0.882319i	$0.344019\pi$
$828$	−4.18460	−0.145425
$829$	21.8341	0.758331	0.379165	−	0.925329i	$-0.376211\pi$
$829$	21.8341	0.758331	0.379165	+	0.925329i	$0.376211\pi$
$830$	0	0
$831$	−37.6506	−1.30609
$832$	−34.4922	−1.19580
$833$	0	0
$834$	45.4822	1.57492
$835$	0	0
$836$	0.600847	0.0207807
$837$	36.9250	1.27631
$838$	9.60010	0.331630
$839$	−45.6890	−1.57736	−0.788680	−	0.614805i	$-0.789235\pi$
$839$	−45.6890	−1.57736	−0.788680	+	0.614805i	$0.789235\pi$
$840$	0	0
$841$	33.9750	1.17155
$842$	15.3863	0.530247
$843$	21.7883	0.750428
$844$	29.5348	1.01663
$845$	0	0
$846$	52.3506	1.79985
$847$	3.44017	0.118205
$848$	−0.907915	−0.0311779
$849$	11.8665	0.407259
$850$	0	0
$851$	5.29854	0.181632
$852$	13.5126	0.462935
$853$	−0.0970449	−0.00332276	−0.00166138	−	0.999999i	$-0.500529\pi$
$853$	−0.0970449	−0.00332276	−0.00166138	+	0.999999i	$0.500529\pi$
$854$	−0.745567	−0.0255128
$855$	0	0
$856$	10.9757	0.375141
$857$	46.7682	1.59757	0.798786	−	0.601616i	$-0.205476\pi$
$857$	46.7682	1.59757	0.798786	+	0.601616i	$0.205476\pi$
$858$	41.0583	1.40171
$859$	26.3135	0.897806	0.448903	−	0.893580i	$-0.351815\pi$
$859$	26.3135	0.897806	0.448903	+	0.893580i	$0.351815\pi$
$860$	0	0
$861$	10.7396	0.366006
$862$	−17.7974	−0.606182
$863$	−33.5202	−1.14104	−0.570520	−	0.821284i	$-0.693258\pi$
$863$	−33.5202	−1.14104	−0.570520	+	0.821284i	$0.693258\pi$
$864$	36.7913	1.25167
$865$	0	0
$866$	19.8466	0.674414
$867$	0	0
$868$	−4.78408	−0.162382
$869$	−35.1519	−1.19245
$870$	0	0
$871$	35.3837	1.19893
$872$	9.22749	0.312482
$873$	−63.2436	−2.14047
$874$	−0.122281	−0.00413623
$875$	0	0
$876$	−17.6902	−0.597696
$877$	3.96792	0.133987	0.0669936	−	0.997753i	$-0.478659\pi$
$877$	3.96792	0.133987	0.0669936	+	0.997753i	$0.478659\pi$
$878$	7.68162	0.259242
$879$	−53.5412	−1.80590
$880$	0	0
$881$	−44.7632	−1.50811	−0.754056	−	0.656811i	$-0.771905\pi$
$881$	−44.7632	−1.50811	−0.754056	+	0.656811i	$0.771905\pi$
$882$	31.0225	1.04458
$883$	6.22372	0.209445	0.104722	−	0.994501i	$-0.466605\pi$
$883$	6.22372	0.209445	0.104722	+	0.994501i	$0.466605\pi$
$884$	0	0
$885$	0	0
$886$	−4.25669	−0.143006
$887$	16.8428	0.565526	0.282763	−	0.959190i	$-0.408749\pi$
$887$	16.8428	0.565526	0.282763	+	0.959190i	$0.408749\pi$
$888$	−65.8661	−2.21032
$889$	−1.57112	−0.0526936
$890$	0	0
$891$	−8.05647	−0.269902
$892$	14.3960	0.482014
$893$	−2.21536	−0.0741342
$894$	19.3493	0.647136
$895$	0	0
$896$	−4.45891	−0.148962
$897$	12.1008	0.404033
$898$	−23.7143	−0.791356
$899$	−44.1415	−1.47220
$900$	0	0
$901$	0	0
$902$	11.6007	0.386260
$903$	−25.0469	−0.833510
$904$	−1.16024	−0.0385891
$905$	0	0
$906$	−35.1956	−1.16930
$907$	28.9372	0.960845	0.480422	−	0.877037i	$-0.340483\pi$
$907$	28.9372	0.960845	0.480422	+	0.877037i	$0.340483\pi$
$908$	−2.35016	−0.0779929
$909$	53.3774	1.77041
$910$	0	0
$911$	15.3748	0.509389	0.254694	−	0.967022i	$-0.418025\pi$
$911$	15.3748	0.509389	0.254694	+	0.967022i	$0.418025\pi$
$912$	0.136935	0.00453436
$913$	−30.9178	−1.02323
$914$	−18.6938	−0.618336
$915$	0	0
$916$	−2.71159	−0.0895933
$917$	5.84848	0.193134
$918$	0	0
$919$	9.89298	0.326339	0.163170	−	0.986598i	$-0.447828\pi$
$919$	9.89298	0.326339	0.163170	+	0.986598i	$0.447828\pi$
$920$	0	0
$921$	28.3154	0.933024
$922$	−1.75438	−0.0577774
$923$	−24.9578	−0.821497
$924$	6.20487	0.204125
$925$	0	0
$926$	9.65959	0.317434
$927$	52.0142	1.70837
$928$	−43.9817	−1.44377
$929$	−7.21578	−0.236742	−0.118371	−	0.992969i	$-0.537767\pi$
$929$	−7.21578	−0.236742	−0.118371	+	0.992969i	$0.537767\pi$
$930$	0	0
$931$	−1.31280	−0.0430253
$932$	26.8590	0.879797
$933$	82.6685	2.70645
$934$	−4.38699	−0.143547
$935$	0	0
$936$	−96.0783	−3.14042
$937$	4.90678	0.160298	0.0801488	−	0.996783i	$-0.474460\pi$
$937$	4.90678	0.160298	0.0801488	+	0.996783i	$0.474460\pi$
$938$	−3.69248	−0.120564
$939$	2.79126	0.0910892
$940$	0	0
$941$	−26.2958	−0.857218	−0.428609	−	0.903490i	$-0.640996\pi$
$941$	−26.2958	−0.857218	−0.428609	+	0.903490i	$0.640996\pi$
$942$	7.18294	0.234033
$943$	3.41897	0.111337
$944$	0.790011	0.0257127
$945$	0	0
$946$	−27.0550	−0.879636
$947$	−33.0347	−1.07348	−0.536742	−	0.843746i	$-0.680345\pi$
$947$	−33.0347	−1.07348	−0.536742	+	0.843746i	$0.680345\pi$
$948$	47.8661	1.55462
$949$	32.6737	1.06063
$950$	0	0
$951$	−76.4343	−2.47855
$952$	0	0
$953$	−51.4399	−1.66630	−0.833151	−	0.553046i	$-0.813465\pi$
$953$	−51.4399	−1.66630	−0.833151	+	0.553046i	$0.813465\pi$
$954$	−18.5795	−0.601534
$955$	0	0
$956$	−15.6501	−0.506162
$957$	57.2508	1.85066
$958$	6.87741	0.222199
$959$	5.72202	0.184774
$960$	0	0
$961$	−0.0596155	−0.00192308
$962$	45.2158	1.45782
$963$	20.2334	0.652013
$964$	3.42999	0.110472
$965$	0	0
$966$	−1.26278	−0.0406294
$967$	30.2986	0.974337	0.487169	−	0.873308i	$-0.338030\pi$
$967$	30.2986	0.974337	0.487169	+	0.873308i	$0.338030\pi$
$968$	−13.6141	−0.437575
$969$	0	0
$970$	0	0
$971$	34.8251	1.11759	0.558796	−	0.829305i	$-0.311264\pi$
$971$	34.8251	1.11759	0.558796	+	0.829305i	$0.311264\pi$
$972$	−12.5901	−0.403827
$973$	−12.6952	−0.406990
$974$	0.384665	0.0123255
$975$	0	0
$976$	0.265795	0.00850788
$977$	−20.6989	−0.662215	−0.331108	−	0.943593i	$-0.607422\pi$
$977$	−20.6989	−0.662215	−0.331108	+	0.943593i	$0.607422\pi$
$978$	−3.60394	−0.115241
$979$	−32.6516	−1.04355
$980$	0	0
$981$	17.0106	0.543108
$982$	−0.252373	−0.00805354
$983$	44.3237	1.41371	0.706853	−	0.707360i	$-0.250114\pi$
$983$	44.3237	1.41371	0.706853	+	0.707360i	$0.250114\pi$
$984$	−42.5011	−1.35489
$985$	0	0
$986$	0	0
$987$	−22.8778	−0.728207
$988$	1.51116	0.0480763
$989$	−7.97371	−0.253549
$990$	0	0
$991$	−26.1318	−0.830103	−0.415051	−	0.909798i	$-0.636236\pi$
$991$	−26.1318	−0.830103	−0.415051	+	0.909798i	$0.636236\pi$
$992$	30.8284	0.978802
$993$	−17.6528	−0.560193
$994$	2.60449	0.0826094
$995$	0	0
$996$	42.1005	1.33401
$997$	26.2757	0.832160	0.416080	−	0.909328i	$-0.363404\pi$
$997$	26.2757	0.832160	0.416080	+	0.909328i	$0.363404\pi$
$998$	16.7441	0.530026
$999$	−52.7404	−1.66863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bx.1.11		24
5.4	even	2		7225.2.a.cb.1.14		24
17.5	odd	16		425.2.m.c.76.4	✓	24
17.7	odd	16		425.2.m.c.151.4	yes	24
17.16	even	2	inner	7225.2.a.bx.1.12		24
85.7	even	16		425.2.n.e.49.3		24
85.22	even	16		425.2.n.d.399.4		24
85.24	odd	16		425.2.m.d.151.3	yes	24
85.39	odd	16		425.2.m.d.76.3	yes	24
85.58	even	16		425.2.n.d.49.4		24
85.73	even	16		425.2.n.e.399.3		24
85.84	even	2		7225.2.a.cb.1.13		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.4	✓	24	17.5	odd	16
425.2.m.c.151.4	yes	24	17.7	odd	16
425.2.m.d.76.3	yes	24	85.39	odd	16
425.2.m.d.151.3	yes	24	85.24	odd	16
425.2.n.d.49.4		24	85.58	even	16
425.2.n.d.399.4		24	85.22	even	16
425.2.n.e.49.3		24	85.7	even	16
425.2.n.e.399.3		24	85.73	even	16
7225.2.a.bx.1.11		24	1.1	even	1	trivial
7225.2.a.bx.1.12		24	17.16	even	2	inner
7225.2.a.cb.1.13		24	85.84	even	2
7225.2.a.cb.1.14		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)

\(f(q)\)	\(=\)	\(q-0.903848 q^{2} -2.88161 q^{3} -1.18306 q^{4} +2.60454 q^{6} -0.726991 q^{7} +2.87700 q^{8} +5.30368 q^{9} +O(q^{10})\)	\(q-0.903848 q^{2} -2.88161 q^{3} -1.18306 q^{4} +2.60454 q^{6} -0.726991 q^{7} +2.87700 q^{8} +5.30368 q^{9} -2.50358 q^{11} +3.40912 q^{12} -6.29663 q^{13} +0.657089 q^{14} -0.234252 q^{16} -4.79372 q^{18} +0.202859 q^{19} +2.09490 q^{21} +2.26286 q^{22} +0.666914 q^{23} -8.29040 q^{24} +5.69120 q^{26} -6.63830 q^{27} +0.860073 q^{28} +7.93568 q^{29} -5.56241 q^{31} -5.54227 q^{32} +7.21436 q^{33} -6.27457 q^{36} +7.94487 q^{37} -0.183354 q^{38} +18.1444 q^{39} +5.12655 q^{41} -1.89347 q^{42} -11.9561 q^{43} +2.96189 q^{44} -0.602789 q^{46} -10.9207 q^{47} +0.675023 q^{48} -6.47148 q^{49} +7.44929 q^{52} +3.87580 q^{53} +6.00002 q^{54} -2.09155 q^{56} -0.584562 q^{57} -7.17264 q^{58} -3.37248 q^{59} -1.13465 q^{61} +5.02757 q^{62} -3.85573 q^{63} +5.47788 q^{64} -6.52068 q^{66} -5.61946 q^{67} -1.92179 q^{69} +3.96368 q^{71} +15.2587 q^{72} -5.18908 q^{73} -7.18095 q^{74} -0.239995 q^{76} +1.82008 q^{77} -16.3998 q^{78} +14.0406 q^{79} +3.21797 q^{81} -4.63362 q^{82} +12.3494 q^{83} -2.47840 q^{84} +10.8065 q^{86} -22.8675 q^{87} -7.20282 q^{88} +13.0419 q^{89} +4.57759 q^{91} -0.788999 q^{92} +16.0287 q^{93} +9.87063 q^{94} +15.9707 q^{96} -11.9245 q^{97} +5.84924 q^{98} -13.2782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} + 24 q^{9}+O(q^{10}) \) 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

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