LMFDB - Embedded newform 7225.2.a.bg.1.1

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:	$0$
Dimension:	$6$
Coefficient field:	6.6.93924352.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 17x^{4} + 73x^{2} - 67 $ x^6 - 17x^4 + 73x^2 - 67
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 425)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.29112$ of defining polynomial
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)

$f(q)$	$=$	$q-1.48119 q^{2} -3.29112 q^{3} +0.193937 q^{4} +4.87478 q^{6} +2.22194 q^{7} +2.67513 q^{8} +7.83146 q^{9} +O(q^{10})$	\(q-1.48119 q^{2} -3.29112 q^{3} +0.193937 q^{4} +4.87478 q^{6} +2.22194 q^{7} +2.67513 q^{8} +7.83146 q^{9} -2.86020 q^{11} -0.638268 q^{12} +2.28726 q^{13} -3.29112 q^{14} -4.35026 q^{16} -11.5999 q^{18} -5.76845 q^{19} -7.31265 q^{21} +4.23652 q^{22} +1.58367 q^{23} -8.80417 q^{24} -3.38787 q^{26} -15.9009 q^{27} +0.430914 q^{28} -9.23509 q^{29} +1.15275 q^{31} +1.09332 q^{32} +9.41327 q^{33} +1.51881 q^{36} -0.514485 q^{37} +8.54420 q^{38} -7.52763 q^{39} +7.09672 q^{41} +10.8315 q^{42} +7.89446 q^{43} -0.554698 q^{44} -2.34572 q^{46} +3.03761 q^{47} +14.3172 q^{48} -2.06300 q^{49} +0.443583 q^{52} -5.73084 q^{53} +23.5523 q^{54} +5.94397 q^{56} +18.9847 q^{57} +13.6790 q^{58} +7.50659 q^{59} -11.8879 q^{61} -1.70745 q^{62} +17.4010 q^{63} +7.08110 q^{64} -13.9429 q^{66} +7.35026 q^{67} -5.21203 q^{69} +8.80417 q^{71} +20.9502 q^{72} +2.65285 q^{73} +0.762052 q^{74} -1.11871 q^{76} -6.35519 q^{77} +11.1499 q^{78} -11.4570 q^{79} +28.8373 q^{81} -10.5116 q^{82} -3.08840 q^{83} -1.41819 q^{84} -11.6932 q^{86} +30.3938 q^{87} -7.65142 q^{88} +2.15633 q^{89} +5.08214 q^{91} +0.307131 q^{92} -3.79384 q^{93} -4.49929 q^{94} -3.59825 q^{96} -8.72060 q^{97} +3.05571 q^{98} -22.3996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} + 16 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 + 16 * q^9	$ 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} + 16 q^{9} + 2 q^{13} - 6 q^{16} - 16 q^{18} - 12 q^{19} - 2 q^{21} - 22 q^{26} - 6 q^{32} + 28 q^{33} + 20 q^{36} + 32 q^{38} + 34 q^{42} + 8 q^{43} + 40 q^{47} - 4 q^{49} - 30 q^{52} + 10 q^{53} + 4 q^{59} - 22 q^{64} + 16 q^{66} + 24 q^{67} + 24 q^{69} + 52 q^{72} + 36 q^{76} - 44 q^{77} + 34 q^{81} + 20 q^{83} - 6 q^{84} - 4 q^{86} + 76 q^{87} - 8 q^{89} + 30 q^{93} + 40 q^{94} - 16 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 + 16 * q^9 + 2 * q^13 - 6 * q^16 - 16 * q^18 - 12 * q^19 - 2 * q^21 - 22 * q^26 - 6 * q^32 + 28 * q^33 + 20 * q^36 + 32 * q^38 + 34 * q^42 + 8 * q^43 + 40 * q^47 - 4 * q^49 - 30 * q^52 + 10 * q^53 + 4 * q^59 - 22 * q^64 + 16 * q^66 + 24 * q^67 + 24 * q^69 + 52 * q^72 + 36 * q^76 - 44 * q^77 + 34 * q^81 + 20 * q^83 - 6 * q^84 - 4 * q^86 + 76 * q^87 - 8 * q^89 + 30 * q^93 + 40 * q^94 - 16 * 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 $

$2$	−1.48119	−1.04736	−0.523681	−	0.851914i	$-0.675442\pi$
$2$	−1.48119	−1.04736	−0.523681	+	0.851914i	$0.675442\pi$
$3$	−3.29112	−1.90013	−0.950064	−	0.312056i	$-0.898982\pi$
$3$	−3.29112	−1.90013	−0.950064	+	0.312056i	$0.898982\pi$
$4$	0.193937	0.0969683
$5$	0	0
$5$	0	0
$6$	4.87478	1.99012
$7$	2.22194	0.839813	0.419906	−	0.907567i	$-0.362063\pi$
$7$	2.22194	0.839813	0.419906	+	0.907567i	$0.362063\pi$
$8$	2.67513	0.945802
$9$	7.83146	2.61049
$10$	0	0
$11$	−2.86020	−0.862384	−0.431192	−	0.902260i	$-0.641907\pi$
$11$	−2.86020	−0.862384	−0.431192	+	0.902260i	$0.641907\pi$
$12$	−0.638268	−0.184252
$13$	2.28726	0.634371	0.317186	−	0.948363i	$-0.397262\pi$
$13$	2.28726	0.634371	0.317186	+	0.948363i	$0.397262\pi$
$14$	−3.29112	−0.879588
$15$	0	0
$16$	−4.35026	−1.08757
$17$	0	0
$17$	0	0
$18$	−11.5999	−2.73412
$19$	−5.76845	−1.32337	−0.661687	−	0.749780i	$-0.730159\pi$
$19$	−5.76845	−1.32337	−0.661687	+	0.749780i	$0.730159\pi$
$20$	0	0
$21$	−7.31265	−1.59575
$22$	4.23652	0.903228
$23$	1.58367	0.330217	0.165109	−	0.986275i	$-0.447203\pi$
$23$	1.58367	0.330217	0.165109	+	0.986275i	$0.447203\pi$
$24$	−8.80417	−1.79714
$25$	0	0
$26$	−3.38787	−0.664417
$27$	−15.9009	−3.06013
$28$	0.430914	0.0814352
$29$	−9.23509	−1.71491	−0.857456	−	0.514557i	$-0.827956\pi$
$29$	−9.23509	−1.71491	−0.857456	+	0.514557i	$0.827956\pi$
$30$	0	0
$31$	1.15275	0.207040	0.103520	−	0.994627i	$-0.466989\pi$
$31$	1.15275	0.207040	0.103520	+	0.994627i	$0.466989\pi$
$32$	1.09332	0.193274
$33$	9.41327	1.63864
$34$	0	0
$35$	0	0
$36$	1.51881	0.253134
$37$	−0.514485	−0.0845807	−0.0422904	−	0.999105i	$-0.513465\pi$
$37$	−0.514485	−0.0845807	−0.0422904	+	0.999105i	$0.513465\pi$
$38$	8.54420	1.38605
$39$	−7.52763	−1.20539
$40$	0	0
$41$	7.09672	1.10832	0.554161	−	0.832410i	$-0.313039\pi$
$41$	7.09672	1.10832	0.554161	+	0.832410i	$0.313039\pi$
$42$	10.8315	1.67133
$43$	7.89446	1.20389	0.601947	−	0.798536i	$-0.294392\pi$
$43$	7.89446	1.20389	0.601947	+	0.798536i	$0.294392\pi$
$44$	−0.554698	−0.0836239
$45$	0	0
$46$	−2.34572	−0.345857
$47$	3.03761	0.443081	0.221541	−	0.975151i	$-0.428891\pi$
$47$	3.03761	0.443081	0.221541	+	0.975151i	$0.428891\pi$
$48$	14.3172	2.06651
$49$	−2.06300	−0.294715
$50$	0	0
$51$	0	0
$52$	0.443583	0.0615139
$53$	−5.73084	−0.787192	−0.393596	−	0.919284i	$-0.628769\pi$
$53$	−5.73084	−0.787192	−0.393596	+	0.919284i	$0.628769\pi$
$54$	23.5523	3.20506
$55$	0	0
$56$	5.94397	0.794296
$57$	18.9847	2.51458
$58$	13.6790	1.79613
$59$	7.50659	0.977274	0.488637	−	0.872487i	$-0.337494\pi$
$59$	7.50659	0.977274	0.488637	+	0.872487i	$0.337494\pi$
$60$	0	0
$61$	−11.8879	−1.52209	−0.761047	−	0.648697i	$-0.775314\pi$
$61$	−11.8879	−1.52209	−0.761047	+	0.648697i	$0.775314\pi$
$62$	−1.70745	−0.216846
$63$	17.4010	2.19232
$64$	7.08110	0.885138
$65$	0	0
$66$	−13.9429	−1.71625
$67$	7.35026	0.897977	0.448989	−	0.893537i	$-0.351784\pi$
$67$	7.35026	0.897977	0.448989	+	0.893537i	$0.351784\pi$
$68$	0	0
$69$	−5.21203	−0.627455
$70$	0	0
$71$	8.80417	1.04486	0.522431	−	0.852681i	$-0.325025\pi$
$71$	8.80417	1.04486	0.522431	+	0.852681i	$0.325025\pi$
$72$	20.9502	2.46900
$73$	2.65285	0.310493	0.155246	−	0.987876i	$-0.450383\pi$
$73$	2.65285	0.310493	0.155246	+	0.987876i	$0.450383\pi$
$74$	0.762052	0.0885867
$75$	0	0
$76$	−1.11871	−0.128325
$77$	−6.35519	−0.724241
$78$	11.1499	1.26248
$79$	−11.4570	−1.28902	−0.644508	−	0.764598i	$-0.722938\pi$
$79$	−11.4570	−1.28902	−0.644508	+	0.764598i	$0.722938\pi$
$80$	0	0
$81$	28.8373	3.20415
$82$	−10.5116	−1.16081
$83$	−3.08840	−0.338996	−0.169498	−	0.985531i	$-0.554215\pi$
$83$	−3.08840	−0.338996	−0.169498	+	0.985531i	$0.554215\pi$
$84$	−1.41819	−0.154737
$85$	0	0
$86$	−11.6932	−1.26091
$87$	30.3938	3.25855
$88$	−7.65142	−0.815644
$89$	2.15633	0.228570	0.114285	−	0.993448i	$-0.463542\pi$
$89$	2.15633	0.228570	0.114285	+	0.993448i	$0.463542\pi$
$90$	0	0
$91$	5.08214	0.532753
$92$	0.307131	0.0320206
$93$	−3.79384	−0.393403
$94$	−4.49929	−0.464067
$95$	0	0
$96$	−3.59825	−0.367245
$97$	−8.72060	−0.885443	−0.442721	−	0.896659i	$-0.645987\pi$
$97$	−8.72060	−0.885443	−0.442721	+	0.896659i	$0.645987\pi$
$98$	3.05571	0.308673
$99$	−22.3996	−2.25124
$100$	0	0
$101$	7.24965	0.721367	0.360683	−	0.932688i	$-0.382543\pi$
$101$	7.24965	0.721367	0.360683	+	0.932688i	$0.382543\pi$
$102$	0	0
$103$	7.73813	0.762461	0.381231	−	0.924480i	$-0.375500\pi$
$103$	7.73813	0.762461	0.381231	+	0.924480i	$0.375500\pi$
$104$	6.11871	0.599989
$105$	0	0
$106$	8.48849	0.824475
$107$	10.5952	1.02428	0.512138	−	0.858903i	$-0.328854\pi$
$107$	10.5952	1.02428	0.512138	+	0.858903i	$0.328854\pi$
$108$	−3.08376	−0.296735
$109$	−14.5408	−1.39275	−0.696377	−	0.717676i	$-0.745206\pi$
$109$	−14.5408	−1.39275	−0.696377	+	0.717676i	$0.745206\pi$
$110$	0	0
$111$	1.69323	0.160714
$112$	−9.66600	−0.913351
$113$	−4.02916	−0.379032	−0.189516	−	0.981878i	$-0.560692\pi$
$113$	−4.02916	−0.379032	−0.189516	+	0.981878i	$0.560692\pi$
$114$	−28.1200	−2.63368
$115$	0	0
$116$	−1.79102	−0.166292
$117$	17.9126	1.65602
$118$	−11.1187	−1.02356
$119$	0	0
$120$	0	0
$121$	−2.81924	−0.256294
$122$	17.6083	1.59418
$123$	−23.3561	−2.10595
$124$	0.223561	0.0200764
$125$	0	0
$126$	−25.7742	−2.29615
$127$	3.06793	0.272235	0.136117	−	0.990693i	$-0.456538\pi$
$127$	3.06793	0.272235	0.136117	+	0.990693i	$0.456538\pi$
$128$	−12.6751	−1.12033
$129$	−25.9816	−2.28755
$130$	0	0
$131$	7.42786	0.648975	0.324487	−	0.945890i	$-0.394808\pi$
$131$	7.42786	0.648975	0.324487	+	0.945890i	$0.394808\pi$
$132$	1.82558	0.158896
$133$	−12.8171	−1.11139
$134$	−10.8872	−0.940508
$135$	0	0
$136$	0	0
$137$	5.37565	0.459273	0.229637	−	0.973276i	$-0.426246\pi$
$137$	5.37565	0.459273	0.229637	+	0.973276i	$0.426246\pi$
$138$	7.72004	0.657173
$139$	4.91500	0.416885	0.208442	−	0.978035i	$-0.433161\pi$
$139$	4.91500	0.416885	0.208442	+	0.978035i	$0.433161\pi$
$140$	0	0
$141$	−9.99714	−0.841911
$142$	−13.0407	−1.09435
$143$	−6.54202	−0.547071
$144$	−34.0689	−2.83907
$145$	0	0
$146$	−3.92939	−0.325198
$147$	6.78959	0.559996
$148$	−0.0997774	−0.00820165
$149$	−16.7381	−1.37124	−0.685621	−	0.727959i	$-0.740469\pi$
$149$	−16.7381	−1.37124	−0.685621	+	0.727959i	$0.740469\pi$
$150$	0	0
$151$	1.81336	0.147569	0.0737845	−	0.997274i	$-0.476492\pi$
$151$	1.81336	0.147569	0.0737845	+	0.997274i	$0.476492\pi$
$152$	−15.4314	−1.25165
$153$	0	0
$154$	9.41327	0.758543
$155$	0	0
$156$	−1.45988	−0.116884
$157$	−4.31994	−0.344769	−0.172385	−	0.985030i	$-0.555147\pi$
$157$	−4.31994	−0.344769	−0.172385	+	0.985030i	$0.555147\pi$
$158$	16.9701	1.35007
$159$	18.8609	1.49576
$160$	0	0
$161$	3.51881	0.277321
$162$	−42.7137	−3.35591
$163$	4.66743	0.365581	0.182791	−	0.983152i	$-0.441487\pi$
$163$	4.66743	0.365581	0.182791	+	0.983152i	$0.441487\pi$
$164$	1.37631	0.107472
$165$	0	0
$166$	4.57452	0.355051
$167$	−8.16590	−0.631897	−0.315948	−	0.948776i	$-0.602323\pi$
$167$	−8.16590	−0.631897	−0.315948	+	0.948776i	$0.602323\pi$
$168$	−19.5623	−1.50926
$169$	−7.76845	−0.597573
$170$	0	0
$171$	−45.1754	−3.45465
$172$	1.53102	0.116740
$173$	−23.4285	−1.78124	−0.890619	−	0.454750i	$-0.849728\pi$
$173$	−23.4285	−1.78124	−0.890619	+	0.454750i	$0.849728\pi$
$174$	−45.0191	−3.41289
$175$	0	0
$176$	12.4426	0.937899
$177$	−24.7051	−1.85695
$178$	−3.19394	−0.239396
$179$	14.5296	1.08599	0.542997	−	0.839735i	$-0.317289\pi$
$179$	14.5296	1.08599	0.542997	+	0.839735i	$0.317289\pi$
$180$	0	0
$181$	9.40223	0.698862	0.349431	−	0.936962i	$-0.386375\pi$
$181$	9.40223	0.698862	0.349431	+	0.936962i	$0.386375\pi$
$182$	−7.52763	−0.557985
$183$	39.1246	2.89217
$184$	4.23652	0.312320
$185$	0	0
$186$	5.61942	0.412036
$187$	0	0
$188$	0.589104	0.0429648
$189$	−35.3307	−2.56993
$190$	0	0
$191$	−6.20711	−0.449131	−0.224565	−	0.974459i	$-0.572096\pi$
$191$	−6.20711	−0.449131	−0.224565	+	0.974459i	$0.572096\pi$
$192$	−23.3047	−1.68187
$193$	−14.0937	−1.01448	−0.507242	−	0.861804i	$-0.669335\pi$
$193$	−14.0937	−1.01448	−0.507242	+	0.861804i	$0.669335\pi$
$194$	12.9169	0.927380
$195$	0	0
$196$	−0.400092	−0.0285780
$197$	25.2195	1.79682	0.898409	−	0.439159i	$-0.144724\pi$
$197$	25.2195	1.79682	0.898409	+	0.439159i	$0.144724\pi$
$198$	33.1781	2.35786
$199$	12.6098	0.893883	0.446942	−	0.894563i	$-0.352513\pi$
$199$	12.6098	0.893883	0.446942	+	0.894563i	$0.352513\pi$
$200$	0	0
$201$	−24.1906	−1.70627
$202$	−10.7381	−0.755533
$203$	−20.5198	−1.44020
$204$	0	0
$205$	0	0
$206$	−11.4617	−0.798573
$207$	12.4024	0.862028
$208$	−9.95017	−0.689920
$209$	16.4989	1.14126
$210$	0	0
$211$	13.5954	0.935945	0.467972	−	0.883743i	$-0.344985\pi$
$211$	13.5954	0.935945	0.467972	+	0.883743i	$0.344985\pi$
$212$	−1.11142	−0.0763326
$213$	−28.9756	−1.98537
$214$	−15.6935	−1.07279
$215$	0	0
$216$	−42.5370	−2.89427
$217$	2.56134	0.173875
$218$	21.5377	1.45872
$219$	−8.73084	−0.589976
$220$	0	0
$221$	0	0
$222$	−2.50800	−0.168326
$223$	18.8119	1.25974	0.629870	−	0.776700i	$-0.283108\pi$
$223$	18.8119	1.25974	0.629870	+	0.776700i	$0.283108\pi$
$224$	2.42929	0.162314
$225$	0	0
$226$	5.96797	0.396984
$227$	−3.39090	−0.225062	−0.112531	−	0.993648i	$-0.535896\pi$
$227$	−3.39090	−0.225062	−0.112531	+	0.993648i	$0.535896\pi$
$228$	3.68182	0.243834
$229$	−20.1817	−1.33365	−0.666823	−	0.745216i	$-0.732346\pi$
$229$	−20.1817	−1.33365	−0.666823	+	0.745216i	$0.732346\pi$
$230$	0	0
$231$	20.9157	1.37615
$232$	−24.7051	−1.62197
$233$	0.347344	0.0227553	0.0113776	−	0.999935i	$-0.496378\pi$
$233$	0.347344	0.0227553	0.0113776	+	0.999935i	$0.496378\pi$
$234$	−26.5320	−1.73445
$235$	0	0
$236$	1.45580	0.0947646
$237$	37.7064	2.44929
$238$	0	0
$239$	3.94921	0.255453	0.127727	−	0.991809i	$-0.459232\pi$
$239$	3.94921	0.255453	0.127727	+	0.991809i	$0.459232\pi$
$240$	0	0
$241$	8.47303	0.545796	0.272898	−	0.962043i	$-0.412018\pi$
$241$	8.47303	0.545796	0.272898	+	0.962043i	$0.412018\pi$
$242$	4.17584	0.268433
$243$	−47.2044	−3.02816
$244$	−2.30551	−0.147595
$245$	0	0
$246$	34.5950	2.20570
$247$	−13.1939	−0.839510
$248$	3.08376	0.195819
$249$	10.1643	0.644135
$250$	0	0
$251$	9.22425	0.582230	0.291115	−	0.956688i	$-0.405974\pi$
$251$	9.22425	0.582230	0.291115	+	0.956688i	$0.405974\pi$
$252$	3.37469	0.212585
$253$	−4.52961	−0.284774
$254$	−4.54420	−0.285128
$255$	0	0
$256$	4.61213	0.288258
$257$	6.78067	0.422967	0.211483	−	0.977382i	$-0.432171\pi$
$257$	6.78067	0.422967	0.211483	+	0.977382i	$0.432171\pi$
$258$	38.4838	2.39590
$259$	−1.14315	−0.0710320
$260$	0	0
$261$	−72.3242	−4.47675
$262$	−11.0021	−0.679712
$263$	16.7757	1.03444	0.517218	−	0.855853i	$-0.326967\pi$
$263$	16.7757	1.03444	0.517218	+	0.855853i	$0.326967\pi$
$264$	25.1817	1.54983
$265$	0	0
$266$	18.9847	1.16402
$267$	−7.09672	−0.434312
$268$	1.42548	0.0870753
$269$	−1.02897	−0.0627374	−0.0313687	−	0.999508i	$-0.509987\pi$
$269$	−1.02897	−0.0627374	−0.0313687	+	0.999508i	$0.509987\pi$
$270$	0	0
$271$	6.93207	0.421093	0.210547	−	0.977584i	$-0.432476\pi$
$271$	6.93207	0.421093	0.210547	+	0.977584i	$0.432476\pi$
$272$	0	0
$273$	−16.7259	−1.01230
$274$	−7.96239	−0.481025
$275$	0	0
$276$	−1.01080	−0.0608433
$277$	−23.8432	−1.43260	−0.716300	−	0.697792i	$-0.754166\pi$
$277$	−23.8432	−1.43260	−0.716300	+	0.697792i	$0.754166\pi$
$278$	−7.28007	−0.436629
$279$	9.02773	0.540476
$280$	0	0
$281$	9.75131	0.581714	0.290857	−	0.956766i	$-0.406060\pi$
$281$	9.75131	0.581714	0.290857	+	0.956766i	$0.406060\pi$
$282$	14.8077	0.881786
$283$	−30.2181	−1.79628	−0.898140	−	0.439709i	$-0.855082\pi$
$283$	−30.2181	−1.79628	−0.898140	+	0.439709i	$0.855082\pi$
$284$	1.70745	0.101319
$285$	0	0
$286$	9.69001	0.572982
$287$	15.7685	0.930782
$288$	8.56230	0.504538
$289$	0	0
$290$	0	0
$291$	28.7005	1.68245
$292$	0.514485	0.0301079
$293$	4.26187	0.248981	0.124490	−	0.992221i	$-0.460270\pi$
$293$	4.26187	0.248981	0.124490	+	0.992221i	$0.460270\pi$
$294$	−10.0567	−0.586519
$295$	0	0
$296$	−1.37631	−0.0799966
$297$	45.4798	2.63900
$298$	24.7924	1.43619
$299$	3.62225	0.209480
$300$	0	0
$301$	17.5410	1.01105
$302$	−2.68594	−0.154558
$303$	−23.8594	−1.37069
$304$	25.0943	1.43926
$305$	0	0
$306$	0	0
$307$	−6.96239	−0.397365	−0.198682	−	0.980064i	$-0.563666\pi$
$307$	−6.96239	−0.397365	−0.198682	+	0.980064i	$0.563666\pi$
$308$	−1.23250	−0.0702284
$309$	−25.4671	−1.44877
$310$	0	0
$311$	−14.4170	−0.817513	−0.408757	−	0.912643i	$-0.634037\pi$
$311$	−14.4170	−0.817513	−0.408757	+	0.912643i	$0.634037\pi$
$312$	−20.1374	−1.14006
$313$	−11.1259	−0.628872	−0.314436	−	0.949279i	$-0.601815\pi$
$313$	−11.1259	−0.628872	−0.314436	+	0.949279i	$0.601815\pi$
$314$	6.39868	0.361098
$315$	0	0
$316$	−2.22194	−0.124994
$317$	−4.09653	−0.230084	−0.115042	−	0.993361i	$-0.536700\pi$
$317$	−4.09653	−0.230084	−0.115042	+	0.993361i	$0.536700\pi$
$318$	−27.9366	−1.56661
$319$	26.4142	1.47891
$320$	0	0
$321$	−34.8700	−1.94625
$322$	−5.21203	−0.290455
$323$	0	0
$324$	5.59261	0.310701
$325$	0	0
$326$	−6.91337	−0.382896
$327$	47.8554	2.64641
$328$	18.9847	1.04825
$329$	6.74938	0.372105
$330$	0	0
$331$	−30.4894	−1.67585	−0.837926	−	0.545784i	$-0.816232\pi$
$331$	−30.4894	−1.67585	−0.837926	+	0.545784i	$0.816232\pi$
$332$	−0.598953	−0.0328718
$333$	−4.02916	−0.220797
$334$	12.0953	0.661825
$335$	0	0
$336$	31.8119	1.73548
$337$	27.6055	1.50377	0.751883	−	0.659296i	$-0.229146\pi$
$337$	27.6055	1.50377	0.751883	+	0.659296i	$0.229146\pi$
$338$	11.5066	0.625876
$339$	13.2605	0.720209
$340$	0	0
$341$	−3.29711	−0.178548
$342$	66.9135	3.61827
$343$	−20.1374	−1.08732
$344$	21.1187	1.13864
$345$	0	0
$346$	34.7022	1.86560
$347$	1.77481	0.0952770	0.0476385	−	0.998865i	$-0.484830\pi$
$347$	1.77481	0.0952770	0.0476385	+	0.998865i	$0.484830\pi$
$348$	5.89446	0.315976
$349$	−11.1319	−0.595876	−0.297938	−	0.954585i	$-0.596299\pi$
$349$	−11.1319	−0.595876	−0.297938	+	0.954585i	$0.596299\pi$
$350$	0	0
$351$	−36.3694	−1.94126
$352$	−3.12712	−0.166676
$353$	−27.4241	−1.45964	−0.729818	−	0.683642i	$-0.760395\pi$
$353$	−27.4241	−1.45964	−0.729818	+	0.683642i	$0.760395\pi$
$354$	36.5930	1.94490
$355$	0	0
$356$	0.418190	0.0221640
$357$	0	0
$358$	−21.5212	−1.13743
$359$	−1.65703	−0.0874548	−0.0437274	−	0.999043i	$-0.513923\pi$
$359$	−1.65703	−0.0874548	−0.0437274	+	0.999043i	$0.513923\pi$
$360$	0	0
$361$	14.2750	0.751318
$362$	−13.9265	−0.731962
$363$	9.27844	0.486992
$364$	0.985612	0.0516601
$365$	0	0
$366$	−57.9511	−3.02915
$367$	20.8321	1.08743	0.543713	−	0.839271i	$-0.317018\pi$
$367$	20.8321	1.08743	0.543713	+	0.839271i	$0.317018\pi$
$368$	−6.88937	−0.359133
$369$	55.5777	2.89326
$370$	0	0
$371$	−12.7336	−0.661093
$372$	−0.735765	−0.0381476
$373$	36.6810	1.89927	0.949635	−	0.313357i	$-0.101454\pi$
$373$	36.6810	1.89927	0.949635	+	0.313357i	$0.101454\pi$
$374$	0	0
$375$	0	0
$376$	8.12601	0.419067
$377$	−21.1230	−1.08789
$378$	52.3317	2.69165
$379$	17.6245	0.905312	0.452656	−	0.891685i	$-0.350477\pi$
$379$	17.6245	0.905312	0.452656	+	0.891685i	$0.350477\pi$
$380$	0	0
$381$	−10.0969	−0.517281
$382$	9.19394	0.470403
$383$	11.5066	0.587959	0.293980	−	0.955812i	$-0.405020\pi$
$383$	11.5066	0.587959	0.293980	+	0.955812i	$0.405020\pi$
$384$	41.7153	2.12878
$385$	0	0
$386$	20.8755	1.06253
$387$	61.8251	3.14275
$388$	−1.69124	−0.0858599
$389$	10.6194	0.538426	0.269213	−	0.963081i	$-0.413236\pi$
$389$	10.6194	0.538426	0.269213	+	0.963081i	$0.413236\pi$
$390$	0	0
$391$	0	0
$392$	−5.51881	−0.278742
$393$	−24.4460	−1.23314
$394$	−37.3550	−1.88192
$395$	0	0
$396$	−4.34409	−0.218299
$397$	−12.3026	−0.617452	−0.308726	−	0.951151i	$-0.599903\pi$
$397$	−12.3026	−0.617452	−0.308726	+	0.951151i	$0.599903\pi$
$398$	−18.6775	−0.936220
$399$	42.1827	2.11178
$400$	0	0
$401$	−16.6791	−0.832917	−0.416458	−	0.909155i	$-0.636729\pi$
$401$	−16.6791	−0.832917	−0.416458	+	0.909155i	$0.636729\pi$
$402$	35.8309	1.78709
$403$	2.63664	0.131341
$404$	1.40597	0.0699497
$405$	0	0
$406$	30.3938	1.50842
$407$	1.47153	0.0729411
$408$	0	0
$409$	−35.9438	−1.77731	−0.888654	−	0.458578i	$-0.848359\pi$
$409$	−35.9438	−1.77731	−0.888654	+	0.458578i	$0.848359\pi$
$410$	0	0
$411$	−17.6919	−0.872678
$412$	1.50071	0.0739345
$413$	16.6791	0.820727
$414$	−18.3704	−0.902856
$415$	0	0
$416$	2.50071	0.122607
$417$	−16.1758	−0.792134
$418$	−24.4381	−1.19531
$419$	−26.8032	−1.30942	−0.654711	−	0.755879i	$-0.727210\pi$
$419$	−26.8032	−1.30942	−0.654711	+	0.755879i	$0.727210\pi$
$420$	0	0
$421$	7.24965	0.353326	0.176663	−	0.984271i	$-0.443470\pi$
$421$	7.24965	0.353326	0.176663	+	0.984271i	$0.443470\pi$
$422$	−20.1374	−0.980274
$423$	23.7889	1.15666
$424$	−15.3307	−0.744527
$425$	0	0
$426$	42.9184	2.07941
$427$	−26.4142	−1.27827
$428$	2.05480	0.0993223
$429$	21.5306	1.03951
$430$	0	0
$431$	17.6517	0.850252	0.425126	−	0.905134i	$-0.360230\pi$
$431$	17.6517	0.850252	0.425126	+	0.905134i	$0.360230\pi$
$432$	69.1730	3.32809
$433$	−3.37073	−0.161987	−0.0809935	−	0.996715i	$-0.525809\pi$
$433$	−3.37073	−0.161987	−0.0809935	+	0.996715i	$0.525809\pi$
$434$	−3.79384	−0.182110
$435$	0	0
$436$	−2.81999	−0.135053
$437$	−9.13531	−0.437001
$438$	12.9321	0.617918
$439$	0.945399	0.0451214	0.0225607	−	0.999745i	$-0.492818\pi$
$439$	0.945399	0.0451214	0.0225607	+	0.999745i	$0.492818\pi$
$440$	0	0
$441$	−16.1563	−0.769349
$442$	0	0
$443$	5.71767	0.271655	0.135827	−	0.990733i	$-0.456631\pi$
$443$	5.71767	0.271655	0.135827	+	0.990733i	$0.456631\pi$
$444$	0.328379	0.0155842
$445$	0	0
$446$	−27.8641	−1.31941
$447$	55.0872	2.60553
$448$	15.7338	0.743350
$449$	20.6759	0.975756	0.487878	−	0.872912i	$-0.337771\pi$
$449$	20.6759	0.975756	0.487878	+	0.872912i	$0.337771\pi$
$450$	0	0
$451$	−20.2981	−0.955798
$452$	−0.781402	−0.0367541
$453$	−5.96797	−0.280400
$454$	5.02257	0.235721
$455$	0	0
$456$	50.7864	2.37829
$457$	15.0689	0.704893	0.352446	−	0.935832i	$-0.385350\pi$
$457$	15.0689	0.704893	0.352446	+	0.935832i	$0.385350\pi$
$458$	29.8930	1.39681
$459$	0	0
$460$	0	0
$461$	22.3127	1.03920	0.519602	−	0.854409i	$-0.326080\pi$
$461$	22.3127	1.03920	0.519602	+	0.854409i	$0.326080\pi$
$462$	−30.9802	−1.44133
$463$	19.5574	0.908908	0.454454	−	0.890770i	$-0.349834\pi$
$463$	19.5574	0.908908	0.454454	+	0.890770i	$0.349834\pi$
$464$	40.1750	1.86508
$465$	0	0
$466$	−0.514485	−0.0238330
$467$	16.1260	0.746223	0.373111	−	0.927787i	$-0.378291\pi$
$467$	16.1260	0.746223	0.373111	+	0.927787i	$0.378291\pi$
$468$	3.47390	0.160581
$469$	16.3318	0.754133
$470$	0	0
$471$	14.2174	0.655105
$472$	20.0811	0.924308
$473$	−22.5798	−1.03822
$474$	−55.8505	−2.56530
$475$	0	0
$476$	0	0
$477$	−44.8808	−2.05495
$478$	−5.84955	−0.267552
$479$	−5.44569	−0.248820	−0.124410	−	0.992231i	$-0.539704\pi$
$479$	−5.44569	−0.248820	−0.124410	+	0.992231i	$0.539704\pi$
$480$	0	0
$481$	−1.17676	−0.0536556
$482$	−12.5502	−0.571646
$483$	−11.5808	−0.526945
$484$	−0.546753	−0.0248524
$485$	0	0
$486$	69.9189	3.17158
$487$	−1.41653	−0.0641890	−0.0320945	−	0.999485i	$-0.510218\pi$
$487$	−1.41653	−0.0641890	−0.0320945	+	0.999485i	$0.510218\pi$
$488$	−31.8018	−1.43960
$489$	−15.3611	−0.694651
$490$	0	0
$491$	−21.1636	−0.955101	−0.477550	−	0.878604i	$-0.658475\pi$
$491$	−21.1636	−0.955101	−0.477550	+	0.878604i	$0.658475\pi$
$492$	−4.52961	−0.204211
$493$	0	0
$494$	19.5428	0.879271
$495$	0	0
$496$	−5.01478	−0.225170
$497$	19.5623	0.877489
$498$	−15.0553	−0.674643
$499$	−34.6782	−1.55241	−0.776205	−	0.630481i	$-0.782858\pi$
$499$	−34.6782	−1.55241	−0.776205	+	0.630481i	$0.782858\pi$
$500$	0	0
$501$	26.8749	1.20068
$502$	−13.6629	−0.609806
$503$	−25.6071	−1.14176	−0.570882	−	0.821032i	$-0.693399\pi$
$503$	−25.6071	−1.14176	−0.570882	+	0.821032i	$0.693399\pi$
$504$	46.5499	2.07350
$505$	0	0
$506$	6.70923	0.298262
$507$	25.5669	1.13547
$508$	0.594984	0.0263981
$509$	39.3390	1.74367	0.871835	−	0.489799i	$-0.162930\pi$
$509$	39.3390	1.74367	0.871835	+	0.489799i	$0.162930\pi$
$510$	0	0
$511$	5.89446	0.260756
$512$	18.5188	0.818423
$513$	91.7235	4.04969
$514$	−10.0435	−0.442999
$515$	0	0
$516$	−5.03878	−0.221820
$517$	−8.68819	−0.382106
$518$	1.69323	0.0743962
$519$	77.1060	3.38458
$520$	0	0
$521$	5.72041	0.250616	0.125308	−	0.992118i	$-0.460008\pi$
$521$	5.72041	0.250616	0.125308	+	0.992118i	$0.460008\pi$
$522$	107.126	4.68878
$523$	21.6873	0.948322	0.474161	−	0.880438i	$-0.342752\pi$
$523$	21.6873	0.948322	0.474161	+	0.880438i	$0.342752\pi$
$524$	1.44053	0.0629300
$525$	0	0
$526$	−24.8481	−1.08343
$527$	0	0
$528$	−40.9502	−1.78213
$529$	−20.4920	−0.890956
$530$	0	0
$531$	58.7875	2.55116
$532$	−2.48571	−0.107769
$533$	16.2320	0.703087
$534$	10.5116	0.454882
$535$	0	0
$536$	19.6629	0.849308
$537$	−47.8187	−2.06353
$538$	1.52410	0.0657088
$539$	5.90061	0.254157
$540$	0	0
$541$	35.4836	1.52556	0.762780	−	0.646659i	$-0.223834\pi$
$541$	35.4836	1.52556	0.762780	+	0.646659i	$0.223834\pi$
$542$	−10.2677	−0.441037
$543$	−30.9438	−1.32793
$544$	0	0
$545$	0	0
$546$	24.7743	1.06024
$547$	−23.5121	−1.00530	−0.502652	−	0.864489i	$-0.667642\pi$
$547$	−23.5121	−1.00530	−0.502652	+	0.864489i	$0.667642\pi$
$548$	1.04254	0.0445349
$549$	−93.0998	−3.97340
$550$	0	0
$551$	53.2721	2.26947
$552$	−13.9429	−0.593448
$553$	−25.4568	−1.08253
$554$	35.3165	1.50045
$555$	0	0
$556$	0.953198	0.0404246
$557$	−22.2120	−0.941154	−0.470577	−	0.882359i	$-0.655954\pi$
$557$	−22.2120	−0.941154	−0.470577	+	0.882359i	$0.655954\pi$
$558$	−13.3718	−0.566074
$559$	18.0567	0.763716
$560$	0	0
$561$	0	0
$562$	−14.4436	−0.609266
$563$	6.85685	0.288982	0.144491	−	0.989506i	$-0.453846\pi$
$563$	6.85685	0.288982	0.144491	+	0.989506i	$0.453846\pi$
$564$	−1.93881	−0.0816386
$565$	0	0
$566$	44.7589	1.88136
$567$	64.0747	2.69088
$568$	23.5523	0.988233
$569$	−26.7513	−1.12147	−0.560737	−	0.827994i	$-0.689482\pi$
$569$	−26.7513	−1.12147	−0.560737	+	0.827994i	$0.689482\pi$
$570$	0	0
$571$	−34.0639	−1.42553	−0.712766	−	0.701402i	$-0.752558\pi$
$571$	−34.0639	−1.42553	−0.712766	+	0.701402i	$0.752558\pi$
$572$	−1.26874	−0.0530486
$573$	20.4283	0.853406
$574$	−23.3561	−0.974867
$575$	0	0
$576$	55.4553	2.31064
$577$	−29.0797	−1.21060	−0.605302	−	0.795996i	$-0.706947\pi$
$577$	−29.0797	−1.21060	−0.605302	+	0.795996i	$0.706947\pi$
$578$	0	0
$579$	46.3839	1.92765
$580$	0	0
$581$	−6.86222	−0.284693
$582$	−42.5111	−1.76214
$583$	16.3914	0.678861
$584$	7.09672	0.293664
$585$	0	0
$586$	−6.31265	−0.260773
$587$	35.2506	1.45495	0.727474	−	0.686135i	$-0.240694\pi$
$587$	35.2506	1.45495	0.727474	+	0.686135i	$0.240694\pi$
$588$	1.31675	0.0543018
$589$	−6.64960	−0.273992
$590$	0	0
$591$	−83.0005	−3.41418
$592$	2.23814	0.0919871
$593$	29.0811	1.19422	0.597109	−	0.802160i	$-0.296316\pi$
$593$	29.0811	1.19422	0.597109	+	0.802160i	$0.296316\pi$
$594$	−67.3644	−2.76399
$595$	0	0
$596$	−3.24614	−0.132967
$597$	−41.5002	−1.69849
$598$	−5.36526	−0.219402
$599$	−30.2823	−1.23730	−0.618651	−	0.785666i	$-0.712321\pi$
$599$	−30.2823	−1.23730	−0.618651	+	0.785666i	$0.712321\pi$
$600$	0	0
$601$	6.16753	0.251579	0.125789	−	0.992057i	$-0.459854\pi$
$601$	6.16753	0.251579	0.125789	+	0.992057i	$0.459854\pi$
$602$	−25.9816	−1.05893
$603$	57.5633	2.34416
$604$	0.351676	0.0143095
$605$	0	0
$606$	35.3405	1.43561
$607$	10.0405	0.407531	0.203766	−	0.979020i	$-0.434682\pi$
$607$	10.0405	0.407531	0.203766	+	0.979020i	$0.434682\pi$
$608$	−6.30677	−0.255773
$609$	67.5329	2.73657
$610$	0	0
$611$	6.94780	0.281078
$612$	0	0
$613$	28.0494	1.13290	0.566452	−	0.824095i	$-0.308316\pi$
$613$	28.0494	1.13290	0.566452	+	0.824095i	$0.308316\pi$
$614$	10.3127	0.416185
$615$	0	0
$616$	−17.0010	−0.684988
$617$	24.4575	0.984622	0.492311	−	0.870419i	$-0.336152\pi$
$617$	24.4575	0.984622	0.492311	+	0.870419i	$0.336152\pi$
$618$	37.7217	1.51739
$619$	35.6042	1.43106	0.715528	−	0.698584i	$-0.246186\pi$
$619$	35.6042	1.43106	0.715528	+	0.698584i	$0.246186\pi$
$620$	0	0
$621$	−25.1817	−1.01051
$622$	21.3544	0.856233
$623$	4.79121	0.191956
$624$	32.7472	1.31094
$625$	0	0
$626$	16.4796	0.658657
$627$	−54.3000	−2.16853
$628$	−0.837795	−0.0334317
$629$	0	0
$630$	0	0
$631$	−8.67021	−0.345155	−0.172578	−	0.984996i	$-0.555210\pi$
$631$	−8.67021	−0.345155	−0.172578	+	0.984996i	$0.555210\pi$
$632$	−30.6490	−1.21915
$633$	−44.7440	−1.77841
$634$	6.06775	0.240981
$635$	0	0
$636$	3.65781	0.145042
$637$	−4.71862	−0.186959
$638$	−39.1246	−1.54896
$639$	68.9495	2.72760
$640$	0	0
$641$	40.0079	1.58022	0.790108	−	0.612967i	$-0.210024\pi$
$641$	40.0079	1.58022	0.790108	+	0.612967i	$0.210024\pi$
$642$	51.6493	2.03843
$643$	20.5923	0.812082	0.406041	−	0.913855i	$-0.366909\pi$
$643$	20.5923	0.812082	0.406041	+	0.913855i	$0.366909\pi$
$644$	0.682425	0.0268913
$645$	0	0
$646$	0	0
$647$	34.0205	1.33748	0.668741	−	0.743495i	$-0.266833\pi$
$647$	34.0205	1.33748	0.668741	+	0.743495i	$0.266833\pi$
$648$	77.1436	3.03049
$649$	−21.4704	−0.842786
$650$	0	0
$651$	−8.42968	−0.330385
$652$	0.905186	0.0354498
$653$	43.7895	1.71362	0.856808	−	0.515636i	$-0.172444\pi$
$653$	43.7895	1.71362	0.856808	+	0.515636i	$0.172444\pi$
$654$	−70.8832	−2.77175
$655$	0	0
$656$	−30.8726	−1.20537
$657$	20.7757	0.810536
$658$	−9.99714	−0.389729
$659$	−21.8192	−0.849957	−0.424978	−	0.905203i	$-0.639718\pi$
$659$	−21.8192	−0.849957	−0.424978	+	0.905203i	$0.639718\pi$
$660$	0	0
$661$	36.1002	1.40413	0.702067	−	0.712111i	$-0.252261\pi$
$661$	36.1002	1.40413	0.702067	+	0.712111i	$0.252261\pi$
$662$	45.1608	1.75522
$663$	0	0
$664$	−8.26187	−0.320623
$665$	0	0
$666$	5.96797	0.231254
$667$	−14.6253	−0.566294
$668$	−1.58367	−0.0612739
$669$	−61.9123	−2.39367
$670$	0	0
$671$	34.0019	1.31263
$672$	−7.99508	−0.308417
$673$	15.8847	0.612310	0.306155	−	0.951982i	$-0.400957\pi$
$673$	15.8847	0.612310	0.306155	+	0.951982i	$0.400957\pi$
$674$	−40.8891	−1.57499
$675$	0	0
$676$	−1.50659	−0.0579457
$677$	22.3322	0.858296	0.429148	−	0.903234i	$-0.358814\pi$
$677$	22.3322	0.858296	0.429148	+	0.903234i	$0.358814\pi$
$678$	−19.6413	−0.754320
$679$	−19.3766	−0.743606
$680$	0	0
$681$	11.1598	0.427646
$682$	4.88366	0.187005
$683$	−35.6476	−1.36402	−0.682009	−	0.731344i	$-0.738893\pi$
$683$	−35.6476	−1.36402	−0.682009	+	0.731344i	$0.738893\pi$
$684$	−8.76116	−0.334991
$685$	0	0
$686$	29.8274	1.13882
$687$	66.4204	2.53410
$688$	−34.3430	−1.30931
$689$	−13.1079	−0.499372
$690$	0	0
$691$	8.80417	0.334926	0.167463	−	0.985878i	$-0.446442\pi$
$691$	8.80417	0.334926	0.167463	+	0.985878i	$0.446442\pi$
$692$	−4.54365	−0.172724
$693$	−49.7704	−1.89062
$694$	−2.62884	−0.0997895
$695$	0	0
$696$	81.3073	3.08194
$697$	0	0
$698$	16.4885	0.624098
$699$	−1.14315	−0.0432380
$700$	0	0
$701$	34.8832	1.31752	0.658760	−	0.752353i	$-0.271081\pi$
$701$	34.8832	1.31752	0.658760	+	0.752353i	$0.271081\pi$
$702$	53.8702	2.03320
$703$	2.96778	0.111932
$704$	−20.2534	−0.763328
$705$	0	0
$706$	40.6204	1.52877
$707$	16.1082	0.605813
$708$	−4.79121	−0.180065
$709$	−41.3038	−1.55120	−0.775598	−	0.631227i	$-0.782552\pi$
$709$	−41.3038	−1.55120	−0.775598	+	0.631227i	$0.782552\pi$
$710$	0	0
$711$	−89.7252	−3.36496
$712$	5.76845	0.216182
$713$	1.82558	0.0683684
$714$	0	0
$715$	0	0
$716$	2.81782	0.105307
$717$	−12.9973	−0.485394
$718$	2.45439	0.0915969
$719$	8.32990	0.310653	0.155326	−	0.987863i	$-0.450357\pi$
$719$	8.32990	0.310653	0.155326	+	0.987863i	$0.450357\pi$
$720$	0	0
$721$	17.1936	0.640324
$722$	−21.1441	−0.786902
$723$	−27.8858	−1.03708
$724$	1.82344	0.0677674
$725$	0	0
$726$	−13.7432	−0.510057
$727$	−28.8470	−1.06988	−0.534938	−	0.844891i	$-0.679665\pi$
$727$	−28.8470	−1.06988	−0.534938	+	0.844891i	$0.679665\pi$
$728$	13.5954	0.503879
$729$	68.8432	2.54975
$730$	0	0
$731$	0	0
$732$	7.58769	0.280449
$733$	−14.1128	−0.521269	−0.260635	−	0.965437i	$-0.583932\pi$
$733$	−14.1128	−0.521269	−0.260635	+	0.965437i	$0.583932\pi$
$734$	−30.8564	−1.13893
$735$	0	0
$736$	1.73146	0.0638223
$737$	−21.0232	−0.774401
$738$	−82.3213	−3.03029
$739$	30.2981	1.11453	0.557266	−	0.830334i	$-0.311850\pi$
$739$	30.2981	1.11453	0.557266	+	0.830334i	$0.311850\pi$
$740$	0	0
$741$	43.4228	1.59518
$742$	18.8609	0.692404
$743$	−9.45865	−0.347004	−0.173502	−	0.984834i	$-0.555508\pi$
$743$	−9.45865	−0.347004	−0.173502	+	0.984834i	$0.555508\pi$
$744$	−10.1490	−0.372082
$745$	0	0
$746$	−54.3317	−1.98923
$747$	−24.1866	−0.884943
$748$	0	0
$749$	23.5418	0.860200
$750$	0	0
$751$	−42.6879	−1.55770	−0.778852	−	0.627208i	$-0.784198\pi$
$751$	−42.6879	−1.55770	−0.778852	+	0.627208i	$0.784198\pi$
$752$	−13.2144	−0.481880
$753$	−30.3581	−1.10631
$754$	31.2873	1.13942
$755$	0	0
$756$	−6.85192	−0.249202
$757$	−36.3938	−1.32275	−0.661377	−	0.750054i	$-0.730028\pi$
$757$	−36.3938	−1.32275	−0.661377	+	0.750054i	$0.730028\pi$
$758$	−26.1054	−0.948190
$759$	14.9075	0.541107
$760$	0	0
$761$	−0.555002	−0.0201188	−0.0100594	−	0.999949i	$-0.503202\pi$
$761$	−0.555002	−0.0201188	−0.0100594	+	0.999949i	$0.503202\pi$
$762$	14.9555	0.541780
$763$	−32.3087	−1.16965
$764$	−1.20379	−0.0435514
$765$	0	0
$766$	−17.0435	−0.615806
$767$	17.1695	0.619955
$768$	−15.1791	−0.547727
$769$	−6.56959	−0.236906	−0.118453	−	0.992960i	$-0.537793\pi$
$769$	−6.56959	−0.236906	−0.118453	+	0.992960i	$0.537793\pi$
$770$	0	0
$771$	−22.3160	−0.803691
$772$	−2.73328	−0.0983728
$773$	−28.9995	−1.04304	−0.521520	−	0.853239i	$-0.674635\pi$
$773$	−28.9995	−1.04304	−0.521520	+	0.853239i	$0.674635\pi$
$774$	−91.5750	−3.29160
$775$	0	0
$776$	−23.3287	−0.837453
$777$	3.76225	0.134970
$778$	−15.7294	−0.563927
$779$	−40.9371	−1.46672
$780$	0	0
$781$	−25.1817	−0.901073
$782$	0	0
$783$	146.846	5.24785
$784$	8.97461	0.320522
$785$	0	0
$786$	36.2092	1.29154
$787$	−5.08214	−0.181159	−0.0905793	−	0.995889i	$-0.528872\pi$
$787$	−5.08214	−0.181159	−0.0905793	+	0.995889i	$0.528872\pi$
$788$	4.89099	0.174234
$789$	−55.2110	−1.96556
$790$	0	0
$791$	−8.95254	−0.318316
$792$	−59.9217	−2.12923
$793$	−27.1908	−0.965573
$794$	18.2226	0.646696
$795$	0	0
$796$	2.44550	0.0866783
$797$	−44.1147	−1.56262	−0.781312	−	0.624140i	$-0.785449\pi$
$797$	−44.1147	−1.56262	−0.781312	+	0.624140i	$0.785449\pi$
$798$	−62.4807	−2.21179
$799$	0	0
$800$	0	0
$801$	16.8872	0.596679
$802$	24.7051	0.872366
$803$	−7.58769	−0.267764
$804$	−4.69144	−0.165454
$805$	0	0
$806$	−3.90538	−0.137561
$807$	3.38646	0.119209
$808$	19.3938	0.682270
$809$	−26.1618	−0.919800	−0.459900	−	0.887971i	$-0.652115\pi$
$809$	−26.1618	−0.919800	−0.459900	+	0.887971i	$0.652115\pi$
$810$	0	0
$811$	52.3863	1.83953	0.919766	−	0.392467i	$-0.128378\pi$
$811$	52.3863	1.83953	0.919766	+	0.392467i	$0.128378\pi$
$812$	−3.97953	−0.139654
$813$	−22.8143	−0.800131
$814$	−2.17962	−0.0763957
$815$	0	0
$816$	0	0
$817$	−45.5388	−1.59320
$818$	53.2398	1.86149
$819$	39.8005	1.39074
$820$	0	0
$821$	−10.7785	−0.376174	−0.188087	−	0.982152i	$-0.560229\pi$
$821$	−10.7785	−0.376174	−0.188087	+	0.982152i	$0.560229\pi$
$822$	26.2052	0.914010
$823$	−12.5664	−0.438038	−0.219019	−	0.975721i	$-0.570286\pi$
$823$	−12.5664	−0.438038	−0.219019	+	0.975721i	$0.570286\pi$
$824$	20.7005	0.721137
$825$	0	0
$826$	−24.7051	−0.859599
$827$	0.139991	0.00486796	0.00243398	−	0.999997i	$-0.499225\pi$
$827$	0.139991	0.00486796	0.00243398	+	0.999997i	$0.499225\pi$
$828$	2.40528	0.0835893
$829$	28.8291	1.00128	0.500638	−	0.865657i	$-0.333099\pi$
$829$	28.8291	1.00128	0.500638	+	0.865657i	$0.333099\pi$
$830$	0	0
$831$	78.4709	2.72212
$832$	16.1963	0.561506
$833$	0	0
$834$	23.9596	0.829652
$835$	0	0
$836$	3.19975	0.110666
$837$	−18.3298	−0.633570
$838$	39.7008	1.37144
$839$	−3.35848	−0.115948	−0.0579738	−	0.998318i	$-0.518464\pi$
$839$	−3.35848	−0.115948	−0.0579738	+	0.998318i	$0.518464\pi$
$840$	0	0
$841$	56.2868	1.94092
$842$	−10.7381	−0.370061
$843$	−32.0927	−1.10533
$844$	2.63664	0.0907570
$845$	0	0
$846$	−35.2360	−1.21144
$847$	−6.26416	−0.215239
$848$	24.9307	0.856122
$849$	99.4514	3.41316
$850$	0	0
$851$	−0.814772	−0.0279300
$852$	−5.61942	−0.192518
$853$	−0.314930	−0.0107830	−0.00539150	−	0.999985i	$-0.501716\pi$
$853$	−0.314930	−0.0107830	−0.00539150	+	0.999985i	$0.501716\pi$
$854$	39.1246	1.33882
$855$	0	0
$856$	28.3435	0.968762
$857$	−13.6790	−0.467264	−0.233632	−	0.972325i	$-0.575061\pi$
$857$	−13.6790	−0.467264	−0.233632	+	0.972325i	$0.575061\pi$
$858$	−31.8910	−1.08874
$859$	−49.4227	−1.68628	−0.843140	−	0.537695i	$-0.819295\pi$
$859$	−49.4227	−1.68628	−0.843140	+	0.537695i	$0.819295\pi$
$860$	0	0
$861$	−51.8958	−1.76861
$862$	−26.1456	−0.890522
$863$	−16.5091	−0.561978	−0.280989	−	0.959711i	$-0.590662\pi$
$863$	−16.5091	−0.561978	−0.280989	+	0.959711i	$0.590662\pi$
$864$	−17.3848	−0.591442
$865$	0	0
$866$	4.99271	0.169659
$867$	0	0
$868$	0.496738	0.0168604
$869$	32.7694	1.11163
$870$	0	0
$871$	16.8119	0.569651
$872$	−38.8985	−1.31727
$873$	−68.2950	−2.31144
$874$	13.5312	0.457699
$875$	0	0
$876$	−1.69323	−0.0572089
$877$	32.7634	1.10634	0.553170	−	0.833068i	$-0.313418\pi$
$877$	32.7634	1.10634	0.553170	+	0.833068i	$0.313418\pi$
$878$	−1.40032	−0.0472585
$879$	−14.0263	−0.473095
$880$	0	0
$881$	42.7605	1.44064	0.720319	−	0.693643i	$-0.243995\pi$
$881$	42.7605	1.44064	0.720319	+	0.693643i	$0.243995\pi$
$882$	23.9307	0.805787
$883$	−15.4558	−0.520129	−0.260065	−	0.965591i	$-0.583744\pi$
$883$	−15.4558	−0.520129	−0.260065	+	0.965591i	$0.583744\pi$
$884$	0	0
$885$	0	0
$886$	−8.46898	−0.284521
$887$	46.3666	1.55684	0.778419	−	0.627746i	$-0.216022\pi$
$887$	46.3666	1.55684	0.778419	+	0.627746i	$0.216022\pi$
$888$	4.52961	0.152004
$889$	6.81674	0.228626
$890$	0	0
$891$	−82.4806	−2.76321
$892$	3.64832	0.122155
$893$	−17.5223	−0.586362
$894$	−81.5948	−2.72894
$895$	0	0
$896$	−28.1633	−0.940870
$897$	−11.9213	−0.398040
$898$	−30.6250	−1.02197
$899$	−10.6458	−0.355056
$900$	0	0
$901$	0	0
$902$	30.0654	1.00107
$903$	−57.7294	−1.92112
$904$	−10.7785	−0.358489
$905$	0	0
$906$	8.83973	0.293680
$907$	−28.6940	−0.952769	−0.476385	−	0.879237i	$-0.658053\pi$
$907$	−28.6940	−0.952769	−0.476385	+	0.879237i	$0.658053\pi$
$908$	−0.657619	−0.0218238
$909$	56.7753	1.88312
$910$	0	0
$911$	−28.7180	−0.951470	−0.475735	−	0.879589i	$-0.657818\pi$
$911$	−28.7180	−0.951470	−0.475735	+	0.879589i	$0.657818\pi$
$912$	−82.5882	−2.73477
$913$	8.83344	0.292344
$914$	−22.3199	−0.738278
$915$	0	0
$916$	−3.91397	−0.129321
$917$	16.5042	0.545017
$918$	0	0
$919$	−31.0797	−1.02522	−0.512612	−	0.858620i	$-0.671322\pi$
$919$	−31.0797	−1.02522	−0.512612	+	0.858620i	$0.671322\pi$
$920$	0	0
$921$	22.9140	0.755043
$922$	−33.0494	−1.08842
$923$	20.1374	0.662831
$924$	4.05631	0.133443
$925$	0	0
$926$	−28.9683	−0.951956
$927$	60.6009	1.99039
$928$	−10.0969	−0.331447
$929$	58.1981	1.90942	0.954709	−	0.297542i	$-0.0961669\pi$
$929$	58.1981	1.90942	0.954709	+	0.297542i	$0.0961669\pi$
$930$	0	0
$931$	11.9003	0.390018
$932$	0.0673628	0.00220654
$933$	47.4480	1.55338
$934$	−23.8858	−0.781566
$935$	0	0
$936$	47.9184	1.56626
$937$	−12.9043	−0.421565	−0.210783	−	0.977533i	$-0.567601\pi$
$937$	−12.9043	−0.421565	−0.210783	+	0.977533i	$0.567601\pi$
$938$	−24.1906	−0.789850
$939$	36.6166	1.19494
$940$	0	0
$941$	17.1263	0.558300	0.279150	−	0.960247i	$-0.409947\pi$
$941$	17.1263	0.558300	0.279150	+	0.960247i	$0.409947\pi$
$942$	−21.0588	−0.686133
$943$	11.2388	0.365987
$944$	−32.6556	−1.06285
$945$	0	0
$946$	33.4450	1.08739
$947$	−8.16590	−0.265356	−0.132678	−	0.991159i	$-0.542358\pi$
$947$	−8.16590	−0.265356	−0.132678	+	0.991159i	$0.542358\pi$
$948$	7.31265	0.237504
$949$	6.06775	0.196968
$950$	0	0
$951$	13.4821	0.437189
$952$	0	0
$953$	38.0557	1.23275	0.616373	−	0.787455i	$-0.288602\pi$
$953$	38.0557	1.23275	0.616373	+	0.787455i	$0.288602\pi$
$954$	66.4772	2.15228
$955$	0	0
$956$	0.765897	0.0247709
$957$	−86.9323	−2.81012
$958$	8.06613	0.260605
$959$	11.9444	0.385703
$960$	0	0
$961$	−29.6712	−0.957134
$962$	1.74301	0.0561968
$963$	82.9758	2.67386
$964$	1.64323	0.0529249
$965$	0	0
$966$	17.1534	0.551902
$967$	56.0322	1.80187	0.900937	−	0.433949i	$-0.142880\pi$
$967$	56.0322	1.80187	0.900937	+	0.433949i	$0.142880\pi$
$968$	−7.54183	−0.242404
$969$	0	0
$970$	0	0
$971$	−30.4894	−0.978453	−0.489226	−	0.872157i	$-0.662721\pi$
$971$	−30.4894	−0.978453	−0.489226	+	0.872157i	$0.662721\pi$
$972$	−9.15466	−0.293636
$973$	10.9208	0.350105
$974$	2.09815	0.0672291
$975$	0	0
$976$	51.7156	1.65538
$977$	−10.1549	−0.324884	−0.162442	−	0.986718i	$-0.551937\pi$
$977$	−10.1549	−0.324884	−0.162442	+	0.986718i	$0.551937\pi$
$978$	22.7527	0.727552
$979$	−6.16753	−0.197115
$980$	0	0
$981$	−113.876	−3.63577
$982$	31.3474	1.00034
$983$	58.0796	1.85245	0.926225	−	0.376971i	$-0.123034\pi$
$983$	58.0796	1.85245	0.926225	+	0.376971i	$0.123034\pi$
$984$	−62.4807	−1.99181
$985$	0	0
$986$	0	0
$987$	−22.2130	−0.707047
$988$	−2.55879	−0.0814059
$989$	12.5022	0.397547
$990$	0	0
$991$	33.1347	1.05256	0.526280	−	0.850311i	$-0.323586\pi$
$991$	33.1347	1.05256	0.526280	+	0.850311i	$0.323586\pi$
$992$	1.26033	0.0400155
$993$	100.344	3.18433
$994$	−28.9756	−0.919049
$995$	0	0
$996$	1.97122	0.0624607
$997$	51.2142	1.62197	0.810985	−	0.585067i	$-0.198932\pi$
$997$	51.2142	1.62197	0.810985	+	0.585067i	$0.198932\pi$
$998$	51.3651	1.62594
$999$	8.18076	0.258828

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7225.2.a.bg.1.1		6
5.4	even	2		7225.2.a.ba.1.6		6
17.4	even	4		425.2.d.a.101.6	yes	6
17.13	even	4		425.2.d.a.101.5	✓	6
17.16	even	2	inner	7225.2.a.bg.1.2		6
85.4	even	4		425.2.d.b.101.1	yes	6
85.13	odd	4		425.2.c.c.424.4		12
85.38	odd	4		425.2.c.c.424.3		12
85.47	odd	4		425.2.c.c.424.9		12
85.64	even	4		425.2.d.b.101.2	yes	6
85.72	odd	4		425.2.c.c.424.10		12
85.84	even	2		7225.2.a.ba.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.c.c.424.3		12	85.38	odd	4
425.2.c.c.424.4		12	85.13	odd	4
425.2.c.c.424.9		12	85.47	odd	4
425.2.c.c.424.10		12	85.72	odd	4
425.2.d.a.101.5	✓	6	17.13	even	4
425.2.d.a.101.6	yes	6	17.4	even	4
425.2.d.b.101.1	yes	6	85.4	even	4
425.2.d.b.101.2	yes	6	85.64	even	4
7225.2.a.ba.1.5		6	85.84	even	2
7225.2.a.ba.1.6		6	5.4	even	2
7225.2.a.bg.1.1		6	1.1	even	1	trivial
7225.2.a.bg.1.2		6	17.16	even	2	inner

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)

\(f(q)\)	\(=\)	\(q-1.48119 q^{2} -3.29112 q^{3} +0.193937 q^{4} +4.87478 q^{6} +2.22194 q^{7} +2.67513 q^{8} +7.83146 q^{9} +O(q^{10})\)	\(q-1.48119 q^{2} -3.29112 q^{3} +0.193937 q^{4} +4.87478 q^{6} +2.22194 q^{7} +2.67513 q^{8} +7.83146 q^{9} -2.86020 q^{11} -0.638268 q^{12} +2.28726 q^{13} -3.29112 q^{14} -4.35026 q^{16} -11.5999 q^{18} -5.76845 q^{19} -7.31265 q^{21} +4.23652 q^{22} +1.58367 q^{23} -8.80417 q^{24} -3.38787 q^{26} -15.9009 q^{27} +0.430914 q^{28} -9.23509 q^{29} +1.15275 q^{31} +1.09332 q^{32} +9.41327 q^{33} +1.51881 q^{36} -0.514485 q^{37} +8.54420 q^{38} -7.52763 q^{39} +7.09672 q^{41} +10.8315 q^{42} +7.89446 q^{43} -0.554698 q^{44} -2.34572 q^{46} +3.03761 q^{47} +14.3172 q^{48} -2.06300 q^{49} +0.443583 q^{52} -5.73084 q^{53} +23.5523 q^{54} +5.94397 q^{56} +18.9847 q^{57} +13.6790 q^{58} +7.50659 q^{59} -11.8879 q^{61} -1.70745 q^{62} +17.4010 q^{63} +7.08110 q^{64} -13.9429 q^{66} +7.35026 q^{67} -5.21203 q^{69} +8.80417 q^{71} +20.9502 q^{72} +2.65285 q^{73} +0.762052 q^{74} -1.11871 q^{76} -6.35519 q^{77} +11.1499 q^{78} -11.4570 q^{79} +28.8373 q^{81} -10.5116 q^{82} -3.08840 q^{83} -1.41819 q^{84} -11.6932 q^{86} +30.3938 q^{87} -7.65142 q^{88} +2.15633 q^{89} +5.08214 q^{91} +0.307131 q^{92} -3.79384 q^{93} -4.49929 q^{94} -3.59825 q^{96} -8.72060 q^{97} +3.05571 q^{98} -22.3996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} + 16 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 + 16 * q^9	\( 6 q + 2 q^{2} + 2 q^{4} + 6 q^{8} + 16 q^{9} + 2 q^{13} - 6 q^{16} - 16 q^{18} - 12 q^{19} - 2 q^{21} - 22 q^{26} - 6 q^{32} + 28 q^{33} + 20 q^{36} + 32 q^{38} + 34 q^{42} + 8 q^{43} + 40 q^{47} - 4 q^{49} - 30 q^{52} + 10 q^{53} + 4 q^{59} - 22 q^{64} + 16 q^{66} + 24 q^{67} + 24 q^{69} + 52 q^{72} + 36 q^{76} - 44 q^{77} + 34 q^{81} + 20 q^{83} - 6 q^{84} - 4 q^{86} + 76 q^{87} - 8 q^{89} + 30 q^{93} + 40 q^{94} - 16 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 2 * q^4 + 6 * q^8 + 16 * q^9 + 2 * q^13 - 6 * q^16 - 16 * q^18 - 12 * q^19 - 2 * q^21 - 22 * q^26 - 6 * q^32 + 28 * q^33 + 20 * q^36 + 32 * q^38 + 34 * q^42 + 8 * q^43 + 40 * q^47 - 4 * q^49 - 30 * q^52 + 10 * q^53 + 4 * q^59 - 22 * q^64 + 16 * q^66 + 24 * q^67 + 24 * q^69 + 52 * q^72 + 36 * q^76 - 44 * q^77 + 34 * q^81 + 20 * q^83 - 6 * q^84 - 4 * q^86 + 76 * q^87 - 8 * q^89 + 30 * q^93 + 40 * q^94 - 16 * q^98

Introduction

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