LMFDB - Embedded newform 9025.2.a.ct.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	9025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37097 q^{2} +2.28512 q^{3} +3.62149 q^{4} -5.41794 q^{6} -1.63677 q^{7} -3.84450 q^{8} +2.22176 q^{9} +O(q^{10})$	\(q-2.37097 q^{2} +2.28512 q^{3} +3.62149 q^{4} -5.41794 q^{6} -1.63677 q^{7} -3.84450 q^{8} +2.22176 q^{9} +2.72748 q^{11} +8.27553 q^{12} +6.19933 q^{13} +3.88073 q^{14} +1.87222 q^{16} +3.12451 q^{17} -5.26771 q^{18} -3.74021 q^{21} -6.46676 q^{22} -7.29904 q^{23} -8.78514 q^{24} -14.6984 q^{26} -1.77838 q^{27} -5.92756 q^{28} -2.22572 q^{29} -4.42666 q^{31} +3.25005 q^{32} +6.23260 q^{33} -7.40811 q^{34} +8.04607 q^{36} -2.04016 q^{37} +14.1662 q^{39} -3.92482 q^{41} +8.86793 q^{42} -0.472856 q^{43} +9.87754 q^{44} +17.3058 q^{46} -2.30160 q^{47} +4.27823 q^{48} -4.32098 q^{49} +7.13986 q^{51} +22.4508 q^{52} -6.36387 q^{53} +4.21648 q^{54} +6.29258 q^{56} +5.27711 q^{58} -12.2661 q^{59} -4.79076 q^{61} +10.4955 q^{62} -3.63651 q^{63} -11.4502 q^{64} -14.7773 q^{66} -0.670960 q^{67} +11.3154 q^{68} -16.6791 q^{69} -2.63494 q^{71} -8.54155 q^{72} +6.51298 q^{73} +4.83714 q^{74} -4.46426 q^{77} -33.5876 q^{78} -4.12016 q^{79} -10.7291 q^{81} +9.30563 q^{82} -6.42396 q^{83} -13.5452 q^{84} +1.12113 q^{86} -5.08603 q^{87} -10.4858 q^{88} -17.3044 q^{89} -10.1469 q^{91} -26.4334 q^{92} -10.1154 q^{93} +5.45702 q^{94} +7.42673 q^{96} -0.129944 q^{97} +10.2449 q^{98} +6.05979 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$	−2.37097	−1.67653	−0.838264	−	0.545265i	$-0.816429\pi$
$2$	−2.37097	−1.67653	−0.838264	+	0.545265i	$0.816429\pi$
$3$	2.28512	1.31931	0.659656	−	0.751567i	$-0.270702\pi$
$3$	2.28512	1.31931	0.659656	+	0.751567i	$0.270702\pi$
$4$	3.62149	1.81075
$5$	0	0
$5$	0	0
$6$	−5.41794	−2.21186
$7$	−1.63677	−0.618642	−0.309321	−	0.950958i	$-0.600102\pi$
$7$	−1.63677	−0.618642	−0.309321	+	0.950958i	$0.600102\pi$
$8$	−3.84450	−1.35924
$9$	2.22176	0.740585
$10$	0	0
$11$	2.72748	0.822365	0.411183	−	0.911553i	$-0.365116\pi$
$11$	2.72748	0.822365	0.411183	+	0.911553i	$0.365116\pi$
$12$	8.27553	2.38894
$13$	6.19933	1.71938	0.859692	−	0.510812i	$-0.170655\pi$
$13$	6.19933	1.71938	0.859692	+	0.510812i	$0.170655\pi$
$14$	3.88073	1.03717
$15$	0	0
$16$	1.87222	0.468054
$17$	3.12451	0.757804	0.378902	−	0.925437i	$-0.376302\pi$
$17$	3.12451	0.757804	0.378902	+	0.925437i	$0.376302\pi$
$18$	−5.26771	−1.24161
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−3.74021	−0.816182
$22$	−6.46676	−1.37872
$23$	−7.29904	−1.52195	−0.760977	−	0.648779i	$-0.775280\pi$
$23$	−7.29904	−1.52195	−0.760977	+	0.648779i	$0.775280\pi$
$24$	−8.78514	−1.79326
$25$	0	0
$26$	−14.6984	−2.88260
$27$	−1.77838	−0.342249
$28$	−5.92756	−1.12020
$29$	−2.22572	−0.413306	−0.206653	−	0.978414i	$-0.566257\pi$
$29$	−2.22572	−0.413306	−0.206653	+	0.978414i	$0.566257\pi$
$30$	0	0
$31$	−4.42666	−0.795051	−0.397526	−	0.917591i	$-0.630131\pi$
$31$	−4.42666	−0.795051	−0.397526	+	0.917591i	$0.630131\pi$
$32$	3.25005	0.574532
$33$	6.23260	1.08496
$34$	−7.40811	−1.27048
$35$	0	0
$36$	8.04607	1.34101
$37$	−2.04016	−0.335400	−0.167700	−	0.985838i	$-0.553634\pi$
$37$	−2.04016	−0.335400	−0.167700	+	0.985838i	$0.553634\pi$
$38$	0	0
$39$	14.1662	2.26841
$40$	0	0
$41$	−3.92482	−0.612954	−0.306477	−	0.951878i	$-0.599150\pi$
$41$	−3.92482	−0.612954	−0.306477	+	0.951878i	$0.599150\pi$
$42$	8.86793	1.36835
$43$	−0.472856	−0.0721099	−0.0360549	−	0.999350i	$-0.511479\pi$
$43$	−0.472856	−0.0721099	−0.0360549	+	0.999350i	$0.511479\pi$
$44$	9.87754	1.48909
$45$	0	0
$46$	17.3058	2.55160
$47$	−2.30160	−0.335723	−0.167862	−	0.985811i	$-0.553686\pi$
$47$	−2.30160	−0.335723	−0.167862	+	0.985811i	$0.553686\pi$
$48$	4.27823	0.617509
$49$	−4.32098	−0.617282
$50$	0	0
$51$	7.13986	0.999781
$52$	22.4508	3.11337
$53$	−6.36387	−0.874145	−0.437072	−	0.899426i	$-0.643985\pi$
$53$	−6.36387	−0.874145	−0.437072	+	0.899426i	$0.643985\pi$
$54$	4.21648	0.573790
$55$	0	0
$56$	6.29258	0.840881
$57$	0	0
$58$	5.27711	0.692919
$59$	−12.2661	−1.59691	−0.798454	−	0.602056i	$-0.794348\pi$
$59$	−12.2661	−1.59691	−0.798454	+	0.602056i	$0.794348\pi$
$60$	0	0
$61$	−4.79076	−0.613393	−0.306697	−	0.951807i	$-0.599224\pi$
$61$	−4.79076	−0.613393	−0.306697	+	0.951807i	$0.599224\pi$
$62$	10.4955	1.33293
$63$	−3.63651	−0.458157
$64$	−11.4502	−1.43127
$65$	0	0
$66$	−14.7773	−1.81896
$67$	−0.670960	−0.0819708	−0.0409854	−	0.999160i	$-0.513050\pi$
$67$	−0.670960	−0.0819708	−0.0409854	+	0.999160i	$0.513050\pi$
$68$	11.3154	1.37219
$69$	−16.6791	−2.00793
$70$	0	0
$71$	−2.63494	−0.312710	−0.156355	−	0.987701i	$-0.549974\pi$
$71$	−2.63494	−0.312710	−0.156355	+	0.987701i	$0.549974\pi$
$72$	−8.54155	−1.00663
$73$	6.51298	0.762287	0.381143	−	0.924516i	$-0.375530\pi$
$73$	6.51298	0.762287	0.381143	+	0.924516i	$0.375530\pi$
$74$	4.83714	0.562307
$75$	0	0
$76$	0	0
$77$	−4.46426	−0.508750
$78$	−33.5876	−3.80305
$79$	−4.12016	−0.463555	−0.231777	−	0.972769i	$-0.574454\pi$
$79$	−4.12016	−0.463555	−0.231777	+	0.972769i	$0.574454\pi$
$80$	0	0
$81$	−10.7291	−1.19212
$82$	9.30563	1.02763
$83$	−6.42396	−0.705121	−0.352560	−	0.935789i	$-0.614689\pi$
$83$	−6.42396	−0.705121	−0.352560	+	0.935789i	$0.614689\pi$
$84$	−13.5452	−1.47790
$85$	0	0
$86$	1.12113	0.120894
$87$	−5.08603	−0.545280
$88$	−10.4858	−1.11779
$89$	−17.3044	−1.83426	−0.917130	−	0.398589i	$-0.869500\pi$
$89$	−17.3044	−1.83426	−0.917130	+	0.398589i	$0.869500\pi$
$90$	0	0
$91$	−10.1469	−1.06368
$92$	−26.4334	−2.75587
$93$	−10.1154	−1.04892
$94$	5.45702	0.562849
$95$	0	0
$96$	7.42673	0.757988
$97$	−0.129944	−0.0131938	−0.00659689	−	0.999978i	$-0.502100\pi$
$97$	−0.129944	−0.0131938	−0.00659689	+	0.999978i	$0.502100\pi$
$98$	10.2449	1.03489
$99$	6.05979	0.609032
$100$	0	0
$101$	3.73547	0.371693	0.185846	−	0.982579i	$-0.440497\pi$
$101$	3.73547	0.371693	0.185846	+	0.982579i	$0.440497\pi$
$102$	−16.9284	−1.67616
$103$	−6.59954	−0.650272	−0.325136	−	0.945667i	$-0.605410\pi$
$103$	−6.59954	−0.650272	−0.325136	+	0.945667i	$0.605410\pi$
$104$	−23.8333	−2.33705
$105$	0	0
$106$	15.0885	1.46553
$107$	−11.7953	−1.14029	−0.570146	−	0.821543i	$-0.693114\pi$
$107$	−11.7953	−1.14029	−0.570146	+	0.821543i	$0.693114\pi$
$108$	−6.44038	−0.619726
$109$	−7.23806	−0.693281	−0.346640	−	0.937998i	$-0.612678\pi$
$109$	−7.23806	−0.693281	−0.346640	+	0.937998i	$0.612678\pi$
$110$	0	0
$111$	−4.66199	−0.442497
$112$	−3.06439	−0.289558
$113$	13.2879	1.25002	0.625010	−	0.780616i	$-0.285095\pi$
$113$	13.2879	1.25002	0.625010	+	0.780616i	$0.285095\pi$
$114$	0	0
$115$	0	0
$116$	−8.06043	−0.748392
$117$	13.7734	1.27335
$118$	29.0825	2.67726
$119$	−5.11411	−0.468809
$120$	0	0
$121$	−3.56087	−0.323715
$122$	11.3587	1.02837
$123$	−8.96867	−0.808678
$124$	−16.0311	−1.43964
$125$	0	0
$126$	8.62205	0.768113
$127$	−8.69369	−0.771440	−0.385720	−	0.922616i	$-0.626047\pi$
$127$	−8.69369	−0.771440	−0.385720	+	0.922616i	$0.626047\pi$
$128$	20.6479	1.82504
$129$	−1.08053	−0.0951355
$130$	0	0
$131$	10.5459	0.921402	0.460701	−	0.887555i	$-0.347598\pi$
$131$	10.5459	0.921402	0.460701	+	0.887555i	$0.347598\pi$
$132$	22.5713	1.96458
$133$	0	0
$134$	1.59083	0.137426
$135$	0	0
$136$	−12.0122	−1.03004
$137$	−0.397219	−0.0339367	−0.0169683	−	0.999856i	$-0.505401\pi$
$137$	−0.397219	−0.0339367	−0.0169683	+	0.999856i	$0.505401\pi$
$138$	39.5457	3.36636
$139$	−7.50543	−0.636602	−0.318301	−	0.947990i	$-0.603112\pi$
$139$	−7.50543	−0.636602	−0.318301	+	0.947990i	$0.603112\pi$
$140$	0	0
$141$	−5.25943	−0.442924
$142$	6.24735	0.524266
$143$	16.9085	1.41396
$144$	4.15961	0.346634
$145$	0	0
$146$	−15.4421	−1.27800
$147$	−9.87393	−0.814388
$148$	−7.38841	−0.607323
$149$	−3.68581	−0.301953	−0.150977	−	0.988537i	$-0.548242\pi$
$149$	−3.68581	−0.301953	−0.150977	+	0.988537i	$0.548242\pi$
$150$	0	0
$151$	4.49051	0.365433	0.182716	−	0.983166i	$-0.441511\pi$
$151$	4.49051	0.365433	0.182716	+	0.983166i	$0.441511\pi$
$152$	0	0
$153$	6.94189	0.561219
$154$	10.5846	0.852933
$155$	0	0
$156$	51.3027	4.10751
$157$	20.2651	1.61733	0.808667	−	0.588266i	$-0.200189\pi$
$157$	20.2651	1.61733	0.808667	+	0.588266i	$0.200189\pi$
$158$	9.76878	0.777162
$159$	−14.5422	−1.15327
$160$	0	0
$161$	11.9469	0.941544
$162$	25.4383	1.99862
$163$	15.6590	1.22651	0.613253	−	0.789887i	$-0.289861\pi$
$163$	15.6590	1.22651	0.613253	+	0.789887i	$0.289861\pi$
$164$	−14.2137	−1.10990
$165$	0	0
$166$	15.2310	1.18215
$167$	−6.04571	−0.467831	−0.233915	−	0.972257i	$-0.575154\pi$
$167$	−6.04571	−0.467831	−0.233915	+	0.972257i	$0.575154\pi$
$168$	14.3793	1.10938
$169$	25.4317	1.95628
$170$	0	0
$171$	0	0
$172$	−1.71244	−0.130573
$173$	−1.64040	−0.124717	−0.0623586	−	0.998054i	$-0.519862\pi$
$173$	−1.64040	−0.124717	−0.0623586	+	0.998054i	$0.519862\pi$
$174$	12.0588	0.914177
$175$	0	0
$176$	5.10642	0.384911
$177$	−28.0294	−2.10682
$178$	41.0281	3.07519
$179$	14.1885	1.06050	0.530248	−	0.847842i	$-0.322099\pi$
$179$	14.1885	1.06050	0.530248	+	0.847842i	$0.322099\pi$
$180$	0	0
$181$	−22.9459	−1.70555	−0.852776	−	0.522277i	$-0.825083\pi$
$181$	−22.9459	−1.70555	−0.852776	+	0.522277i	$0.825083\pi$
$182$	24.0580	1.78329
$183$	−10.9474	−0.809258
$184$	28.0612	2.06870
$185$	0	0
$186$	23.9834	1.75855
$187$	8.52202	0.623192
$188$	−8.33523	−0.607909
$189$	2.91080	0.211729
$190$	0	0
$191$	10.2099	0.738762	0.369381	−	0.929278i	$-0.379570\pi$
$191$	10.2099	0.738762	0.369381	+	0.929278i	$0.379570\pi$
$192$	−26.1650	−1.88830
$193$	11.8312	0.851631	0.425816	−	0.904810i	$-0.359987\pi$
$193$	11.8312	0.851631	0.425816	+	0.904810i	$0.359987\pi$
$194$	0.308092	0.0221197
$195$	0	0
$196$	−15.6484	−1.11774
$197$	2.72674	0.194273	0.0971363	−	0.995271i	$-0.469032\pi$
$197$	2.72674	0.194273	0.0971363	+	0.995271i	$0.469032\pi$
$198$	−14.3676	−1.02106
$199$	4.47838	0.317464	0.158732	−	0.987322i	$-0.449259\pi$
$199$	4.47838	0.317464	0.158732	+	0.987322i	$0.449259\pi$
$200$	0	0
$201$	−1.53322	−0.108145
$202$	−8.85667	−0.623153
$203$	3.64300	0.255688
$204$	25.8569	1.81035
$205$	0	0
$206$	15.6473	1.09020
$207$	−16.2167	−1.12714
$208$	11.6065	0.804764
$209$	0	0
$210$	0	0
$211$	7.34023	0.505322	0.252661	−	0.967555i	$-0.418694\pi$
$211$	7.34023	0.505322	0.252661	+	0.967555i	$0.418694\pi$
$212$	−23.0467	−1.58285
$213$	−6.02114	−0.412562
$214$	27.9662	1.91173
$215$	0	0
$216$	6.83698	0.465197
$217$	7.24543	0.491852
$218$	17.1612	1.16230
$219$	14.8829	1.00569
$220$	0	0
$221$	19.3699	1.30296
$222$	11.0534	0.741858
$223$	−16.5811	−1.11035	−0.555176	−	0.831733i	$-0.687349\pi$
$223$	−16.5811	−1.11035	−0.555176	+	0.831733i	$0.687349\pi$
$224$	−5.31958	−0.355430
$225$	0	0
$226$	−31.5052	−2.09569
$227$	11.7828	0.782052	0.391026	−	0.920380i	$-0.372120\pi$
$227$	11.7828	0.782052	0.391026	+	0.920380i	$0.372120\pi$
$228$	0	0
$229$	−7.82331	−0.516979	−0.258490	−	0.966014i	$-0.583225\pi$
$229$	−7.82331	−0.516979	−0.258490	+	0.966014i	$0.583225\pi$
$230$	0	0
$231$	−10.2014	−0.671200
$232$	8.55679	0.561781
$233$	6.71975	0.440225	0.220113	−	0.975474i	$-0.429358\pi$
$233$	6.71975	0.440225	0.220113	+	0.975474i	$0.429358\pi$
$234$	−32.6563	−2.13481
$235$	0	0
$236$	−44.4215	−2.89159
$237$	−9.41505	−0.611573
$238$	12.1254	0.785972
$239$	−15.9746	−1.03331	−0.516654	−	0.856194i	$-0.672823\pi$
$239$	−15.9746	−1.03331	−0.516654	+	0.856194i	$0.672823\pi$
$240$	0	0
$241$	−10.4554	−0.673493	−0.336747	−	0.941595i	$-0.609327\pi$
$241$	−10.4554	−0.673493	−0.336747	+	0.941595i	$0.609327\pi$
$242$	8.44270	0.542717
$243$	−19.1820	−1.23053
$244$	−17.3497	−1.11070
$245$	0	0
$246$	21.2644	1.35577
$247$	0	0
$248$	17.0183	1.08066
$249$	−14.6795	−0.930275
$250$	0	0
$251$	−11.8661	−0.748984	−0.374492	−	0.927230i	$-0.622183\pi$
$251$	−11.8661	−0.748984	−0.374492	+	0.927230i	$0.622183\pi$
$252$	−13.1696	−0.829606
$253$	−19.9080	−1.25160
$254$	20.6125	1.29334
$255$	0	0
$256$	−26.0552	−1.62845
$257$	3.81629	0.238053	0.119027	−	0.992891i	$-0.462023\pi$
$257$	3.81629	0.238053	0.119027	+	0.992891i	$0.462023\pi$
$258$	2.56191	0.159497
$259$	3.33927	0.207492
$260$	0	0
$261$	−4.94501	−0.306088
$262$	−25.0041	−1.54476
$263$	−2.11957	−0.130699	−0.0653493	−	0.997862i	$-0.520816\pi$
$263$	−2.11957	−0.130699	−0.0653493	+	0.997862i	$0.520816\pi$
$264$	−23.9613	−1.47471
$265$	0	0
$266$	0	0
$267$	−39.5425	−2.41996
$268$	−2.42988	−0.148428
$269$	3.92827	0.239511	0.119755	−	0.992803i	$-0.461789\pi$
$269$	3.92827	0.239511	0.119755	+	0.992803i	$0.461789\pi$
$270$	0	0
$271$	18.9358	1.15027	0.575135	−	0.818058i	$-0.304949\pi$
$271$	18.9358	1.15027	0.575135	+	0.818058i	$0.304949\pi$
$272$	5.84975	0.354693
$273$	−23.1868	−1.40333
$274$	0.941793	0.0568958
$275$	0	0
$276$	−60.4034	−3.63586
$277$	15.0274	0.902909	0.451454	−	0.892294i	$-0.350905\pi$
$277$	15.0274	0.902909	0.451454	+	0.892294i	$0.350905\pi$
$278$	17.7951	1.06728
$279$	−9.83496	−0.588803
$280$	0	0
$281$	−27.4830	−1.63950	−0.819750	−	0.572722i	$-0.805888\pi$
$281$	−27.4830	−1.63950	−0.819750	+	0.572722i	$0.805888\pi$
$282$	12.4699	0.742574
$283$	20.3357	1.20883	0.604415	−	0.796669i	$-0.293407\pi$
$283$	20.3357	1.20883	0.604415	+	0.796669i	$0.293407\pi$
$284$	−9.54240	−0.566237
$285$	0	0
$286$	−40.0896	−2.37055
$287$	6.42404	0.379199
$288$	7.22081	0.425490
$289$	−7.23745	−0.425732
$290$	0	0
$291$	−0.296936	−0.0174067
$292$	23.5867	1.38031
$293$	−4.58659	−0.267951	−0.133976	−	0.990985i	$-0.542774\pi$
$293$	−4.58659	−0.267951	−0.133976	+	0.990985i	$0.542774\pi$
$294$	23.4108	1.36534
$295$	0	0
$296$	7.84339	0.455888
$297$	−4.85048	−0.281454
$298$	8.73893	0.506233
$299$	−45.2491	−2.61682
$300$	0	0
$301$	0.773958	0.0446102
$302$	−10.6469	−0.612658
$303$	8.53597	0.490379
$304$	0	0
$305$	0	0
$306$	−16.4590	−0.940899
$307$	24.3228	1.38818	0.694088	−	0.719890i	$-0.255808\pi$
$307$	24.3228	1.38818	0.694088	+	0.719890i	$0.255808\pi$
$308$	−16.1673	−0.921216
$309$	−15.0807	−0.857911
$310$	0	0
$311$	22.0205	1.24867	0.624334	−	0.781157i	$-0.285370\pi$
$311$	22.0205	1.24867	0.624334	+	0.781157i	$0.285370\pi$
$312$	−54.4620	−3.08330
$313$	−29.4817	−1.66640	−0.833202	−	0.552969i	$-0.813495\pi$
$313$	−29.4817	−1.66640	−0.833202	+	0.552969i	$0.813495\pi$
$314$	−48.0480	−2.71151
$315$	0	0
$316$	−14.9211	−0.839379
$317$	−8.04314	−0.451748	−0.225874	−	0.974157i	$-0.572524\pi$
$317$	−8.04314	−0.451748	−0.225874	+	0.974157i	$0.572524\pi$
$318$	34.4791	1.93349
$319$	−6.07060	−0.339889
$320$	0	0
$321$	−26.9536	−1.50440
$322$	−28.3256	−1.57853
$323$	0	0
$324$	−38.8552	−2.15862
$325$	0	0
$326$	−37.1269	−2.05627
$327$	−16.5398	−0.914654
$328$	15.0890	0.833150
$329$	3.76720	0.207692
$330$	0	0
$331$	−18.2183	−1.00137	−0.500685	−	0.865630i	$-0.666918\pi$
$331$	−18.2183	−1.00137	−0.500685	+	0.865630i	$0.666918\pi$
$332$	−23.2643	−1.27679
$333$	−4.53273	−0.248392
$334$	14.3342	0.784331
$335$	0	0
$336$	−7.00249	−0.382017
$337$	9.60328	0.523124	0.261562	−	0.965187i	$-0.415762\pi$
$337$	9.60328	0.523124	0.261562	+	0.965187i	$0.415762\pi$
$338$	−60.2977	−3.27976
$339$	30.3644	1.64917
$340$	0	0
$341$	−12.0736	−0.653823
$342$	0	0
$343$	18.5299	1.00052
$344$	1.81790	0.0980144
$345$	0	0
$346$	3.88934	0.209092
$347$	−1.26627	−0.0679771	−0.0339885	−	0.999422i	$-0.510821\pi$
$347$	−1.26627	−0.0679771	−0.0339885	+	0.999422i	$0.510821\pi$
$348$	−18.4190	−0.987363
$349$	26.6148	1.42466	0.712330	−	0.701845i	$-0.247640\pi$
$349$	26.6148	1.42466	0.712330	+	0.701845i	$0.247640\pi$
$350$	0	0
$351$	−11.0247	−0.588457
$352$	8.86443	0.472475
$353$	26.8743	1.43037	0.715187	−	0.698934i	$-0.246342\pi$
$353$	26.8743	1.43037	0.715187	+	0.698934i	$0.246342\pi$
$354$	66.4568	3.53214
$355$	0	0
$356$	−62.6676	−3.32138
$357$	−11.6863	−0.618506
$358$	−33.6404	−1.77795
$359$	−21.0567	−1.11133	−0.555664	−	0.831407i	$-0.687536\pi$
$359$	−21.0567	−1.11133	−0.555664	+	0.831407i	$0.687536\pi$
$360$	0	0
$361$	0	0
$362$	54.4039	2.85940
$363$	−8.13699	−0.427081
$364$	−36.7469	−1.92606
$365$	0	0
$366$	25.9560	1.35674
$367$	11.0177	0.575118	0.287559	−	0.957763i	$-0.407156\pi$
$367$	11.0177	0.575118	0.287559	+	0.957763i	$0.407156\pi$
$368$	−13.6654	−0.712356
$369$	−8.72000	−0.453945
$370$	0	0
$371$	10.4162	0.540782
$372$	−36.6329	−1.89933
$373$	4.83309	0.250248	0.125124	−	0.992141i	$-0.460067\pi$
$373$	4.83309	0.250248	0.125124	+	0.992141i	$0.460067\pi$
$374$	−20.2055	−1.04480
$375$	0	0
$376$	8.84852	0.456327
$377$	−13.7980	−0.710632
$378$	−6.90141	−0.354970
$379$	−2.03721	−0.104644	−0.0523221	−	0.998630i	$-0.516662\pi$
$379$	−2.03721	−0.104644	−0.0523221	+	0.998630i	$0.516662\pi$
$380$	0	0
$381$	−19.8661	−1.01777
$382$	−24.2073	−1.23856
$383$	−34.5805	−1.76698	−0.883489	−	0.468451i	$-0.844812\pi$
$383$	−34.5805	−1.76698	−0.883489	+	0.468451i	$0.844812\pi$
$384$	47.1829	2.40779
$385$	0	0
$386$	−28.0515	−1.42778
$387$	−1.05057	−0.0534035
$388$	−0.470590	−0.0238906
$389$	−4.53021	−0.229691	−0.114845	−	0.993383i	$-0.536637\pi$
$389$	−4.53021	−0.229691	−0.114845	+	0.993383i	$0.536637\pi$
$390$	0	0
$391$	−22.8059	−1.15334
$392$	16.6120	0.839033
$393$	24.0987	1.21562
$394$	−6.46503	−0.325703
$395$	0	0
$396$	21.9455	1.10280
$397$	25.1348	1.26148	0.630739	−	0.775995i	$-0.282752\pi$
$397$	25.1348	1.26148	0.630739	+	0.775995i	$0.282752\pi$
$398$	−10.6181	−0.532237
$399$	0	0
$400$	0	0
$401$	−28.9116	−1.44378	−0.721888	−	0.692010i	$-0.756725\pi$
$401$	−28.9116	−1.44378	−0.721888	+	0.692010i	$0.756725\pi$
$402$	3.63522	0.181308
$403$	−27.4423	−1.36700
$404$	13.5280	0.673041
$405$	0	0
$406$	−8.63743	−0.428669
$407$	−5.56448	−0.275821
$408$	−27.4492	−1.35894
$409$	22.9616	1.13538	0.567689	−	0.823243i	$-0.307837\pi$
$409$	22.9616	1.13538	0.567689	+	0.823243i	$0.307837\pi$
$410$	0	0
$411$	−0.907691	−0.0447731
$412$	−23.9002	−1.17748
$413$	20.0768	0.987913
$414$	38.4492	1.88968
$415$	0	0
$416$	20.1481	0.987842
$417$	−17.1508	−0.839877
$418$	0	0
$419$	8.98058	0.438730	0.219365	−	0.975643i	$-0.429601\pi$
$419$	8.98058	0.438730	0.219365	+	0.975643i	$0.429601\pi$
$420$	0	0
$421$	34.0406	1.65904	0.829519	−	0.558478i	$-0.188615\pi$
$421$	34.0406	1.65904	0.829519	+	0.558478i	$0.188615\pi$
$422$	−17.4034	−0.847187
$423$	−5.11360	−0.248632
$424$	24.4659	1.18817
$425$	0	0
$426$	14.2759	0.691671
$427$	7.84138	0.379471
$428$	−42.7165	−2.06478
$429$	38.6380	1.86546
$430$	0	0
$431$	−37.9730	−1.82909	−0.914547	−	0.404480i	$-0.867453\pi$
$431$	−37.9730	−1.82909	−0.914547	+	0.404480i	$0.867453\pi$
$432$	−3.32950	−0.160191
$433$	36.9800	1.77714	0.888572	−	0.458738i	$-0.151698\pi$
$433$	36.9800	1.77714	0.888572	+	0.458738i	$0.151698\pi$
$434$	−17.1787	−0.824603
$435$	0	0
$436$	−26.2126	−1.25535
$437$	0	0
$438$	−35.2869	−1.68607
$439$	−22.1830	−1.05874	−0.529369	−	0.848392i	$-0.677571\pi$
$439$	−22.1830	−1.05874	−0.529369	+	0.848392i	$0.677571\pi$
$440$	0	0
$441$	−9.60016	−0.457150
$442$	−45.9253	−2.18444
$443$	−9.84880	−0.467931	−0.233965	−	0.972245i	$-0.575170\pi$
$443$	−9.84880	−0.467931	−0.233965	+	0.972245i	$0.575170\pi$
$444$	−16.8834	−0.801249
$445$	0	0
$446$	39.3133	1.86154
$447$	−8.42250	−0.398370
$448$	18.7413	0.885445
$449$	37.3039	1.76048	0.880240	−	0.474528i	$-0.157381\pi$
$449$	37.3039	1.76048	0.880240	+	0.474528i	$0.157381\pi$
$450$	0	0
$451$	−10.7049	−0.504072
$452$	48.1220	2.26347
$453$	10.2613	0.482120
$454$	−27.9367	−1.31113
$455$	0	0
$456$	0	0
$457$	14.0343	0.656498	0.328249	−	0.944591i	$-0.393542\pi$
$457$	14.0343	0.656498	0.328249	+	0.944591i	$0.393542\pi$
$458$	18.5488	0.866730
$459$	−5.55655	−0.259358
$460$	0	0
$461$	−10.1359	−0.472077	−0.236039	−	0.971744i	$-0.575849\pi$
$461$	−10.1359	−0.472077	−0.236039	+	0.971744i	$0.575849\pi$
$462$	24.1871	1.12528
$463$	−0.722130	−0.0335602	−0.0167801	−	0.999859i	$-0.505342\pi$
$463$	−0.722130	−0.0335602	−0.0167801	+	0.999859i	$0.505342\pi$
$464$	−4.16703	−0.193449
$465$	0	0
$466$	−15.9323	−0.738050
$467$	−35.0172	−1.62040	−0.810201	−	0.586152i	$-0.800642\pi$
$467$	−35.0172	−1.62040	−0.810201	+	0.586152i	$0.800642\pi$
$468$	49.8802	2.30572
$469$	1.09821	0.0507106
$470$	0	0
$471$	46.3082	2.13377
$472$	47.1570	2.17058
$473$	−1.28970	−0.0593007
$474$	22.3228	1.02532
$475$	0	0
$476$	−18.5207	−0.848895
$477$	−14.1390	−0.647379
$478$	37.8752	1.73237
$479$	−26.9601	−1.23184	−0.615920	−	0.787809i	$-0.711216\pi$
$479$	−26.9601	−1.23184	−0.615920	+	0.787809i	$0.711216\pi$
$480$	0	0
$481$	−12.6476	−0.576681
$482$	24.7895	1.12913
$483$	27.3000	1.24219
$484$	−12.8956	−0.586166
$485$	0	0
$486$	45.4800	2.06301
$487$	−3.06758	−0.139005	−0.0695026	−	0.997582i	$-0.522141\pi$
$487$	−3.06758	−0.139005	−0.0695026	+	0.997582i	$0.522141\pi$
$488$	18.4181	0.833747
$489$	35.7826	1.61814
$490$	0	0
$491$	1.24888	0.0563613	0.0281806	−	0.999603i	$-0.491029\pi$
$491$	1.24888	0.0563613	0.0281806	+	0.999603i	$0.491029\pi$
$492$	−32.4800	−1.46431
$493$	−6.95428	−0.313205
$494$	0	0
$495$	0	0
$496$	−8.28766	−0.372127
$497$	4.31279	0.193455
$498$	34.8046	1.55963
$499$	19.5720	0.876165	0.438083	−	0.898935i	$-0.355658\pi$
$499$	19.5720	0.876165	0.438083	+	0.898935i	$0.355658\pi$
$500$	0	0
$501$	−13.8151	−0.617215
$502$	28.1342	1.25569
$503$	−5.11859	−0.228227	−0.114113	−	0.993468i	$-0.536403\pi$
$503$	−5.11859	−0.228227	−0.114113	+	0.993468i	$0.536403\pi$
$504$	13.9806	0.622744
$505$	0	0
$506$	47.2011	2.09835
$507$	58.1144	2.58095
$508$	−31.4841	−1.39688
$509$	15.8349	0.701871	0.350935	−	0.936400i	$-0.385864\pi$
$509$	15.8349	0.701871	0.350935	+	0.936400i	$0.385864\pi$
$510$	0	0
$511$	−10.6603	−0.471582
$512$	20.4803	0.905108
$513$	0	0
$514$	−9.04830	−0.399103
$515$	0	0
$516$	−3.91313	−0.172266
$517$	−6.27757	−0.276087
$518$	−7.91730	−0.347866
$519$	−3.74850	−0.164541
$520$	0	0
$521$	29.9732	1.31315	0.656575	−	0.754261i	$-0.272004\pi$
$521$	29.9732	1.31315	0.656575	+	0.754261i	$0.272004\pi$
$522$	11.7245	0.513166
$523$	−30.3765	−1.32827	−0.664136	−	0.747611i	$-0.731201\pi$
$523$	−30.3765	−1.32827	−0.664136	+	0.747611i	$0.731201\pi$
$524$	38.1920	1.66843
$525$	0	0
$526$	5.02544	0.219120
$527$	−13.8311	−0.602493
$528$	11.6688	0.507818
$529$	30.2759	1.31635
$530$	0	0
$531$	−27.2522	−1.18265
$532$	0	0
$533$	−24.3313	−1.05390
$534$	93.7540	4.05713
$535$	0	0
$536$	2.57951	0.111418
$537$	32.4223	1.39913
$538$	−9.31380	−0.401546
$539$	−11.7854	−0.507632
$540$	0	0
$541$	−23.8593	−1.02579	−0.512895	−	0.858451i	$-0.671427\pi$
$541$	−23.8593	−1.02579	−0.512895	+	0.858451i	$0.671427\pi$
$542$	−44.8963	−1.92846
$543$	−52.4339	−2.25016
$544$	10.1548	0.435383
$545$	0	0
$546$	54.9752	2.35272
$547$	13.7402	0.587489	0.293745	−	0.955884i	$-0.405098\pi$
$547$	13.7402	0.587489	0.293745	+	0.955884i	$0.405098\pi$
$548$	−1.43852	−0.0614507
$549$	−10.6439	−0.454270
$550$	0	0
$551$	0	0
$552$	64.1230	2.72926
$553$	6.74377	0.286774
$554$	−35.6295	−1.51375
$555$	0	0
$556$	−27.1808	−1.15272
$557$	−27.0314	−1.14536	−0.572679	−	0.819780i	$-0.694096\pi$
$557$	−27.0314	−1.14536	−0.572679	+	0.819780i	$0.694096\pi$
$558$	23.3184	0.987145
$559$	−2.93139	−0.123985
$560$	0	0
$561$	19.4738	0.822185
$562$	65.1614	2.74867
$563$	−38.1678	−1.60858	−0.804290	−	0.594237i	$-0.797454\pi$
$563$	−38.1678	−1.60858	−0.804290	+	0.594237i	$0.797454\pi$
$564$	−19.0470	−0.802022
$565$	0	0
$566$	−48.2153	−2.02664
$567$	17.5610	0.737494
$568$	10.1300	0.425046
$569$	−2.28061	−0.0956082	−0.0478041	−	0.998857i	$-0.515222\pi$
$569$	−2.28061	−0.0956082	−0.0478041	+	0.998857i	$0.515222\pi$
$570$	0	0
$571$	−14.4656	−0.605367	−0.302683	−	0.953091i	$-0.597883\pi$
$571$	−14.4656	−0.605367	−0.302683	+	0.953091i	$0.597883\pi$
$572$	61.2341	2.56033
$573$	23.3308	0.974658
$574$	−15.2312	−0.635738
$575$	0	0
$576$	−25.4395	−1.05998
$577$	8.17830	0.340467	0.170234	−	0.985404i	$-0.445548\pi$
$577$	8.17830	0.340467	0.170234	+	0.985404i	$0.445548\pi$
$578$	17.1598	0.713752
$579$	27.0358	1.12357
$580$	0	0
$581$	10.5146	0.436217
$582$	0.704027	0.0291829
$583$	−17.3573	−0.718867
$584$	−25.0392	−1.03613
$585$	0	0
$586$	10.8746	0.449228
$587$	34.4354	1.42130	0.710651	−	0.703544i	$-0.248400\pi$
$587$	34.4354	1.42130	0.710651	+	0.703544i	$0.248400\pi$
$588$	−35.7584	−1.47465
$589$	0	0
$590$	0	0
$591$	6.23093	0.256306
$592$	−3.81961	−0.156985
$593$	−2.65119	−0.108871	−0.0544357	−	0.998517i	$-0.517336\pi$
$593$	−2.65119	−0.108871	−0.0544357	+	0.998517i	$0.517336\pi$
$594$	11.5003	0.471865
$595$	0	0
$596$	−13.3481	−0.546760
$597$	10.2336	0.418834
$598$	107.284	4.38718
$599$	2.45464	0.100294	0.0501469	−	0.998742i	$-0.484031\pi$
$599$	2.45464	0.100294	0.0501469	+	0.998742i	$0.484031\pi$
$600$	0	0
$601$	−14.9631	−0.610356	−0.305178	−	0.952295i	$-0.598716\pi$
$601$	−14.9631	−0.610356	−0.305178	+	0.952295i	$0.598716\pi$
$602$	−1.83503	−0.0747902
$603$	−1.49071	−0.0607064
$604$	16.2623	0.661705
$605$	0	0
$606$	−20.2385	−0.822134
$607$	−43.0431	−1.74706	−0.873532	−	0.486767i	$-0.838176\pi$
$607$	−43.0431	−1.74706	−0.873532	+	0.486767i	$0.838176\pi$
$608$	0	0
$609$	8.32467	0.337333
$610$	0	0
$611$	−14.2684	−0.577237
$612$	25.1400	1.01622
$613$	39.1922	1.58296	0.791478	−	0.611198i	$-0.209312\pi$
$613$	39.1922	1.58296	0.791478	+	0.611198i	$0.209312\pi$
$614$	−57.6686	−2.32732
$615$	0	0
$616$	17.1629	0.691511
$617$	−27.9028	−1.12332	−0.561662	−	0.827367i	$-0.689838\pi$
$617$	−27.9028	−1.12332	−0.561662	+	0.827367i	$0.689838\pi$
$618$	35.7559	1.43831
$619$	−24.8596	−0.999193	−0.499597	−	0.866258i	$-0.666518\pi$
$619$	−24.8596	−0.999193	−0.499597	+	0.866258i	$0.666518\pi$
$620$	0	0
$621$	12.9804	0.520887
$622$	−52.2099	−2.09343
$623$	28.3233	1.13475
$624$	26.5222	1.06174
$625$	0	0
$626$	69.9001	2.79377
$627$	0	0
$628$	73.3901	2.92858
$629$	−6.37448	−0.254167
$630$	0	0
$631$	44.2670	1.76224	0.881120	−	0.472893i	$-0.156790\pi$
$631$	44.2670	1.76224	0.881120	+	0.472893i	$0.156790\pi$
$632$	15.8400	0.630081
$633$	16.7733	0.666678
$634$	19.0700	0.757368
$635$	0	0
$636$	−52.6644	−2.08828
$637$	−26.7872	−1.06135
$638$	14.3932	0.569833
$639$	−5.85419	−0.231588
$640$	0	0
$641$	−20.3402	−0.803389	−0.401695	−	0.915774i	$-0.631579\pi$
$641$	−20.3402	−0.803389	−0.401695	+	0.915774i	$0.631579\pi$
$642$	63.9061	2.52217
$643$	30.3707	1.19770	0.598852	−	0.800860i	$-0.295624\pi$
$643$	30.3707	1.19770	0.598852	+	0.800860i	$0.295624\pi$
$644$	43.2654	1.70490
$645$	0	0
$646$	0	0
$647$	−48.5913	−1.91032	−0.955161	−	0.296087i	$-0.904318\pi$
$647$	−48.5913	−1.91032	−0.955161	+	0.296087i	$0.904318\pi$
$648$	41.2479	1.62037
$649$	−33.4554	−1.31324
$650$	0	0
$651$	16.5567	0.648906
$652$	56.7088	2.22089
$653$	−19.9555	−0.780918	−0.390459	−	0.920620i	$-0.627684\pi$
$653$	−19.9555	−0.780918	−0.390459	+	0.920620i	$0.627684\pi$
$654$	39.2154	1.53344
$655$	0	0
$656$	−7.34811	−0.286895
$657$	14.4703	0.564539
$658$	−8.93191	−0.348202
$659$	17.0285	0.663335	0.331667	−	0.943396i	$-0.392389\pi$
$659$	17.0285	0.663335	0.331667	+	0.943396i	$0.392389\pi$
$660$	0	0
$661$	27.5335	1.07093	0.535464	−	0.844558i	$-0.320137\pi$
$661$	27.5335	1.07093	0.535464	+	0.844558i	$0.320137\pi$
$662$	43.1951	1.67882
$663$	44.2624	1.71901
$664$	24.6969	0.958427
$665$	0	0
$666$	10.7470	0.416436
$667$	16.2456	0.629033
$668$	−21.8945	−0.847122
$669$	−37.8897	−1.46490
$670$	0	0
$671$	−13.0667	−0.504434
$672$	−12.1559	−0.468923
$673$	37.2560	1.43611	0.718057	−	0.695984i	$-0.245032\pi$
$673$	37.2560	1.43611	0.718057	+	0.695984i	$0.245032\pi$
$674$	−22.7691	−0.877032
$675$	0	0
$676$	92.1006	3.54233
$677$	−22.7880	−0.875815	−0.437907	−	0.899020i	$-0.644280\pi$
$677$	−22.7880	−0.875815	−0.437907	+	0.899020i	$0.644280\pi$
$678$	−71.9930	−2.76488
$679$	0.212688	0.00816223
$680$	0	0
$681$	26.9251	1.03177
$682$	28.6262	1.09615
$683$	4.61408	0.176553	0.0882764	−	0.996096i	$-0.471864\pi$
$683$	4.61408	0.176553	0.0882764	+	0.996096i	$0.471864\pi$
$684$	0	0
$685$	0	0
$686$	−43.9337	−1.67740
$687$	−17.8772	−0.682057
$688$	−0.885288	−0.0337513
$689$	−39.4517	−1.50299
$690$	0	0
$691$	35.7599	1.36037	0.680186	−	0.733040i	$-0.261899\pi$
$691$	35.7599	1.36037	0.680186	+	0.733040i	$0.261899\pi$
$692$	−5.94069	−0.225831
$693$	−9.91850	−0.376773
$694$	3.00229	0.113965
$695$	0	0
$696$	19.5533	0.741165
$697$	−12.2631	−0.464499
$698$	−63.1030	−2.38848
$699$	15.3554	0.580795
$700$	0	0
$701$	32.8766	1.24173	0.620865	−	0.783917i	$-0.286781\pi$
$701$	32.8766	1.24173	0.620865	+	0.783917i	$0.286781\pi$
$702$	26.1393	0.986565
$703$	0	0
$704$	−31.2301	−1.17703
$705$	0	0
$706$	−63.7180	−2.39806
$707$	−6.11411	−0.229945
$708$	−101.508	−3.81491
$709$	44.4229	1.66834	0.834169	−	0.551510i	$-0.185948\pi$
$709$	44.4229	1.66834	0.834169	+	0.551510i	$0.185948\pi$
$710$	0	0
$711$	−9.15400	−0.343302
$712$	66.5267	2.49319
$713$	32.3103	1.21003
$714$	27.7079	1.03694
$715$	0	0
$716$	51.3834	1.92029
$717$	−36.5037	−1.36326
$718$	49.9247	1.86317
$719$	−20.0859	−0.749079	−0.374540	−	0.927211i	$-0.622199\pi$
$719$	−20.0859	−0.749079	−0.374540	+	0.927211i	$0.622199\pi$
$720$	0	0
$721$	10.8019	0.402285
$722$	0	0
$723$	−23.8919	−0.888548
$724$	−83.0982	−3.08832
$725$	0	0
$726$	19.2926	0.716014
$727$	−0.729793	−0.0270665	−0.0135333	−	0.999908i	$-0.504308\pi$
$727$	−0.729793	−0.0270665	−0.0135333	+	0.999908i	$0.504308\pi$
$728$	39.0098	1.44580
$729$	−11.6460	−0.431333
$730$	0	0
$731$	−1.47744	−0.0546452
$732$	−39.6460	−1.46536
$733$	−29.4948	−1.08941	−0.544707	−	0.838626i	$-0.683359\pi$
$733$	−29.4948	−1.08941	−0.544707	+	0.838626i	$0.683359\pi$
$734$	−26.1226	−0.964201
$735$	0	0
$736$	−23.7222	−0.874412
$737$	−1.83003	−0.0674100
$738$	20.6748	0.761051
$739$	−40.4996	−1.48980	−0.744901	−	0.667175i	$-0.767503\pi$
$739$	−40.4996	−1.48980	−0.744901	+	0.667175i	$0.767503\pi$
$740$	0	0
$741$	0	0
$742$	−24.6965	−0.906637
$743$	19.4337	0.712955	0.356477	−	0.934304i	$-0.383978\pi$
$743$	19.4337	0.712955	0.356477	+	0.934304i	$0.383978\pi$
$744$	38.8888	1.42573
$745$	0	0
$746$	−11.4591	−0.419547
$747$	−14.2725	−0.522202
$748$	30.8624	1.12844
$749$	19.3062	0.705433
$750$	0	0
$751$	−5.66378	−0.206674	−0.103337	−	0.994646i	$-0.532952\pi$
$751$	−5.66378	−0.206674	−0.103337	+	0.994646i	$0.532952\pi$
$752$	−4.30909	−0.157136
$753$	−27.1155	−0.988144
$754$	32.7146	1.19139
$755$	0	0
$756$	10.5414	0.383388
$757$	−12.5786	−0.457176	−0.228588	−	0.973523i	$-0.573411\pi$
$757$	−12.5786	−0.457176	−0.228588	+	0.973523i	$0.573411\pi$
$758$	4.83015	0.175439
$759$	−45.4920	−1.65126
$760$	0	0
$761$	50.0335	1.81371	0.906857	−	0.421439i	$-0.138475\pi$
$761$	50.0335	1.81371	0.906857	+	0.421439i	$0.138475\pi$
$762$	47.1019	1.70632
$763$	11.8471	0.428892
$764$	36.9750	1.33771
$765$	0	0
$766$	81.9892	2.96239
$767$	−76.0414	−2.74570
$768$	−59.5392	−2.14844
$769$	−31.7447	−1.14474	−0.572371	−	0.819994i	$-0.693976\pi$
$769$	−31.7447	−1.14474	−0.572371	+	0.819994i	$0.693976\pi$
$770$	0	0
$771$	8.72066	0.314067
$772$	42.8467	1.54209
$773$	11.4374	0.411373	0.205687	−	0.978618i	$-0.434057\pi$
$773$	11.4374	0.411373	0.205687	+	0.978618i	$0.434057\pi$
$774$	2.49087	0.0895325
$775$	0	0
$776$	0.499569	0.0179335
$777$	7.63062	0.273747
$778$	10.7410	0.385083
$779$	0	0
$780$	0	0
$781$	−7.18673	−0.257162
$782$	54.0721	1.93361
$783$	3.95817	0.141453
$784$	−8.08980	−0.288921
$785$	0	0
$786$	−57.1372	−2.03802
$787$	6.64024	0.236699	0.118350	−	0.992972i	$-0.462240\pi$
$787$	6.64024	0.236699	0.118350	+	0.992972i	$0.462240\pi$
$788$	9.87488	0.351778
$789$	−4.84347	−0.172432
$790$	0	0
$791$	−21.7493	−0.773315
$792$	−23.2969	−0.827819
$793$	−29.6995	−1.05466
$794$	−59.5938	−2.11490
$795$	0	0
$796$	16.2184	0.574847
$797$	−0.186468	−0.00660502	−0.00330251	−	0.999995i	$-0.501051\pi$
$797$	−0.186468	−0.00660502	−0.00330251	+	0.999995i	$0.501051\pi$
$798$	0	0
$799$	−7.19137	−0.254412
$800$	0	0
$801$	−38.4461	−1.35843
$802$	68.5485	2.42053
$803$	17.7640	0.626878
$804$	−5.55255	−0.195823
$805$	0	0
$806$	65.0649	2.29181
$807$	8.97655	0.315989
$808$	−14.3610	−0.505219
$809$	1.21997	0.0428918	0.0214459	−	0.999770i	$-0.493173\pi$
$809$	1.21997	0.0428918	0.0214459	+	0.999770i	$0.493173\pi$
$810$	0	0
$811$	19.0938	0.670474	0.335237	−	0.942134i	$-0.391184\pi$
$811$	19.0938	0.670474	0.335237	+	0.942134i	$0.391184\pi$
$812$	13.1931	0.462986
$813$	43.2706	1.51757
$814$	13.1932	0.462422
$815$	0	0
$816$	13.3674	0.467951
$817$	0	0
$818$	−54.4413	−1.90349
$819$	−22.5439	−0.787748
$820$	0	0
$821$	−9.97729	−0.348210	−0.174105	−	0.984727i	$-0.555703\pi$
$821$	−9.97729	−0.348210	−0.174105	+	0.984727i	$0.555703\pi$
$822$	2.15211	0.0750633
$823$	28.2077	0.983260	0.491630	−	0.870804i	$-0.336401\pi$
$823$	28.2077	0.983260	0.491630	+	0.870804i	$0.336401\pi$
$824$	25.3719	0.883873
$825$	0	0
$826$	−47.6014	−1.65626
$827$	8.85297	0.307848	0.153924	−	0.988083i	$-0.450809\pi$
$827$	8.85297	0.307848	0.153924	+	0.988083i	$0.450809\pi$
$828$	−58.7286	−2.04096
$829$	−45.6892	−1.58685	−0.793425	−	0.608668i	$-0.791704\pi$
$829$	−45.6892	−1.58685	−0.793425	+	0.608668i	$0.791704\pi$
$830$	0	0
$831$	34.3393	1.19122
$832$	−70.9835	−2.46091
$833$	−13.5009	−0.467779
$834$	40.6640	1.40808
$835$	0	0
$836$	0	0
$837$	7.87227	0.272105
$838$	−21.2927	−0.735543
$839$	−0.182558	−0.00630259	−0.00315130	−	0.999995i	$-0.501003\pi$
$839$	−0.182558	−0.00630259	−0.00315130	+	0.999995i	$0.501003\pi$
$840$	0	0
$841$	−24.0462	−0.829178
$842$	−80.7092	−2.78142
$843$	−62.8019	−2.16301
$844$	26.5826	0.915010
$845$	0	0
$846$	12.1242	0.416838
$847$	5.82833	0.200264
$848$	−11.9145	−0.409147
$849$	46.4694	1.59483
$850$	0	0
$851$	14.8912	0.510463
$852$	−21.8055	−0.747044
$853$	−49.2184	−1.68520	−0.842602	−	0.538537i	$-0.818977\pi$
$853$	−49.2184	−1.68520	−0.842602	+	0.538537i	$0.818977\pi$
$854$	−18.5917	−0.636193
$855$	0	0
$856$	45.3470	1.54993
$857$	−31.5699	−1.07841	−0.539204	−	0.842175i	$-0.681275\pi$
$857$	−31.5699	−1.07841	−0.539204	+	0.842175i	$0.681275\pi$
$858$	−91.6094	−3.12749
$859$	−10.6896	−0.364723	−0.182362	−	0.983232i	$-0.558374\pi$
$859$	−10.6896	−0.364723	−0.182362	+	0.983232i	$0.558374\pi$
$860$	0	0
$861$	14.6797	0.500282
$862$	90.0327	3.06653
$863$	−25.5826	−0.870841	−0.435420	−	0.900227i	$-0.643400\pi$
$863$	−25.5826	−0.870841	−0.435420	+	0.900227i	$0.643400\pi$
$864$	−5.77981	−0.196633
$865$	0	0
$866$	−87.6783	−2.97943
$867$	−16.5384	−0.561674
$868$	26.2393	0.890619
$869$	−11.2377	−0.381211
$870$	0	0
$871$	−4.15950	−0.140939
$872$	27.8268	0.942333
$873$	−0.288703	−0.00977113
$874$	0	0
$875$	0	0
$876$	53.8984	1.82106
$877$	31.0952	1.05001	0.525005	−	0.851099i	$-0.324063\pi$
$877$	31.0952	1.05001	0.525005	+	0.851099i	$0.324063\pi$
$878$	52.5953	1.77500
$879$	−10.4809	−0.353511
$880$	0	0
$881$	−47.4465	−1.59851	−0.799257	−	0.600990i	$-0.794773\pi$
$881$	−47.4465	−1.59851	−0.799257	+	0.600990i	$0.794773\pi$
$882$	22.7617	0.766425
$883$	14.5332	0.489082	0.244541	−	0.969639i	$-0.421363\pi$
$883$	14.5332	0.489082	0.244541	+	0.969639i	$0.421363\pi$
$884$	70.1477	2.35932
$885$	0	0
$886$	23.3512	0.784498
$887$	37.1270	1.24660	0.623301	−	0.781982i	$-0.285791\pi$
$887$	37.1270	1.24660	0.623301	+	0.781982i	$0.285791\pi$
$888$	17.9230	0.601458
$889$	14.2296	0.477245
$890$	0	0
$891$	−29.2633	−0.980357
$892$	−60.0483	−2.01057
$893$	0	0
$894$	19.9695	0.667879
$895$	0	0
$896$	−33.7960	−1.12904
$897$	−103.400	−3.45241
$898$	−88.4464	−2.95150
$899$	9.85251	0.328600
$900$	0	0
$901$	−19.8840	−0.662431
$902$	25.3809	0.845091
$903$	1.76858	0.0588548
$904$	−51.0854	−1.69907
$905$	0	0
$906$	−24.3293	−0.808287
$907$	−10.8657	−0.360789	−0.180394	−	0.983594i	$-0.557737\pi$
$907$	−10.8657	−0.360789	−0.180394	+	0.983594i	$0.557737\pi$
$908$	42.6713	1.41610
$909$	8.29929	0.275270
$910$	0	0
$911$	39.5522	1.31042	0.655211	−	0.755446i	$-0.272580\pi$
$911$	39.5522	1.31042	0.655211	+	0.755446i	$0.272580\pi$
$912$	0	0
$913$	−17.5212	−0.579867
$914$	−33.2749	−1.10064
$915$	0	0
$916$	−28.3321	−0.936117
$917$	−17.2613	−0.570018
$918$	13.1744	0.434820
$919$	32.1565	1.06074	0.530372	−	0.847765i	$-0.322052\pi$
$919$	32.1565	1.06074	0.530372	+	0.847765i	$0.322052\pi$
$920$	0	0
$921$	55.5805	1.83144
$922$	24.0320	0.791451
$923$	−16.3348	−0.537668
$924$	−36.9441	−1.21537
$925$	0	0
$926$	1.71215	0.0562647
$927$	−14.6626	−0.481582
$928$	−7.23369	−0.237458
$929$	−10.9336	−0.358719	−0.179359	−	0.983784i	$-0.557402\pi$
$929$	−10.9336	−0.358719	−0.179359	+	0.983784i	$0.557402\pi$
$930$	0	0
$931$	0	0
$932$	24.3355	0.797136
$933$	50.3194	1.64738
$934$	83.0247	2.71665
$935$	0	0
$936$	−52.9519	−1.73079
$937$	−45.0301	−1.47107	−0.735535	−	0.677487i	$-0.763069\pi$
$937$	−45.0301	−1.47107	−0.735535	+	0.677487i	$0.763069\pi$
$938$	−2.60382	−0.0850177
$939$	−67.3691	−2.19851
$940$	0	0
$941$	42.6516	1.39040	0.695201	−	0.718816i	$-0.255315\pi$
$941$	42.6516	1.39040	0.695201	+	0.718816i	$0.255315\pi$
$942$	−109.795	−3.57733
$943$	28.6474	0.932888
$944$	−22.9647	−0.747438
$945$	0	0
$946$	3.05785	0.0994192
$947$	−24.7131	−0.803069	−0.401535	−	0.915844i	$-0.631523\pi$
$947$	−24.7131	−0.803069	−0.401535	+	0.915844i	$0.631523\pi$
$948$	−34.0965	−1.10740
$949$	40.3761	1.31066
$950$	0	0
$951$	−18.3795	−0.595996
$952$	19.6612	0.637223
$953$	−15.5170	−0.502646	−0.251323	−	0.967903i	$-0.580866\pi$
$953$	−15.5170	−0.502646	−0.251323	+	0.967903i	$0.580866\pi$
$954$	33.5231	1.08535
$955$	0	0
$956$	−57.8517	−1.87106
$957$	−13.8720	−0.448419
$958$	63.9217	2.06521
$959$	0.650157	0.0209946
$960$	0	0
$961$	−11.4047	−0.367893
$962$	29.9871	0.966821
$963$	−26.2062	−0.844484
$964$	−37.8642	−1.21952
$965$	0	0
$966$	−64.7274	−2.08257
$967$	−16.0510	−0.516166	−0.258083	−	0.966123i	$-0.583091\pi$
$967$	−16.0510	−0.516166	−0.258083	+	0.966123i	$0.583091\pi$
$968$	13.6898	0.440006
$969$	0	0
$970$	0	0
$971$	5.76925	0.185144	0.0925720	−	0.995706i	$-0.470491\pi$
$971$	5.76925	0.185144	0.0925720	+	0.995706i	$0.470491\pi$
$972$	−69.4676	−2.22817
$973$	12.2847	0.393829
$974$	7.27312	0.233046
$975$	0	0
$976$	−8.96933	−0.287101
$977$	46.7724	1.49638	0.748190	−	0.663484i	$-0.230923\pi$
$977$	46.7724	1.49638	0.748190	+	0.663484i	$0.230923\pi$
$978$	−84.8394	−2.71286
$979$	−47.1973	−1.50843
$980$	0	0
$981$	−16.0812	−0.513434
$982$	−2.96106	−0.0944912
$983$	−33.6039	−1.07180	−0.535900	−	0.844282i	$-0.680028\pi$
$983$	−33.6039	−1.07180	−0.535900	+	0.844282i	$0.680028\pi$
$984$	34.4801	1.09919
$985$	0	0
$986$	16.4884	0.525097
$987$	8.60848	0.274011
$988$	0	0
$989$	3.45139	0.109748
$990$	0	0
$991$	45.6040	1.44866	0.724329	−	0.689454i	$-0.242150\pi$
$991$	45.6040	1.44866	0.724329	+	0.689454i	$0.242150\pi$
$992$	−14.3868	−0.456783
$993$	−41.6310	−1.32112
$994$	−10.2255	−0.324333
$995$	0	0
$996$	−53.1616	−1.68449
$997$	−4.80126	−0.152057	−0.0760287	−	0.997106i	$-0.524224\pi$
$997$	−4.80126	−0.152057	−0.0760287	+	0.997106i	$0.524224\pi$
$998$	−46.4047	−1.46892
$999$	3.62817	0.114790

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.2		24
5.2	odd	4		1805.2.b.l.1084.2		24
5.3	odd	4		1805.2.b.l.1084.23		24
5.4	even	2	inner	9025.2.a.ct.1.23		24
19.2	odd	18		475.2.l.f.251.1		48
19.10	odd	18		475.2.l.f.176.1		48
19.18	odd	2		9025.2.a.cu.1.23		24
95.2	even	36		95.2.p.a.4.8	yes	48
95.18	even	4		1805.2.b.k.1084.2		24
95.29	odd	18		475.2.l.f.176.8		48
95.37	even	4		1805.2.b.k.1084.23		24
95.48	even	36		95.2.p.a.24.8	yes	48
95.59	odd	18		475.2.l.f.251.8		48
95.67	even	36		95.2.p.a.24.1	yes	48
95.78	even	36		95.2.p.a.4.1	✓	48
95.94	odd	2		9025.2.a.cu.1.2		24
285.2	odd	36		855.2.da.b.289.1		48
285.143	odd	36		855.2.da.b.784.1		48
285.173	odd	36		855.2.da.b.289.8		48
285.257	odd	36		855.2.da.b.784.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.1	✓	48	95.78	even	36
95.2.p.a.4.8	yes	48	95.2	even	36
95.2.p.a.24.1	yes	48	95.67	even	36
95.2.p.a.24.8	yes	48	95.48	even	36
475.2.l.f.176.1		48	19.10	odd	18
475.2.l.f.176.8		48	95.29	odd	18
475.2.l.f.251.1		48	19.2	odd	18
475.2.l.f.251.8		48	95.59	odd	18
855.2.da.b.289.1		48	285.2	odd	36
855.2.da.b.289.8		48	285.173	odd	36
855.2.da.b.784.1		48	285.143	odd	36
855.2.da.b.784.8		48	285.257	odd	36
1805.2.b.k.1084.2		24	95.18	even	4
1805.2.b.k.1084.23		24	95.37	even	4
1805.2.b.l.1084.2		24	5.2	odd	4
1805.2.b.l.1084.23		24	5.3	odd	4
9025.2.a.ct.1.2		24	1.1	even	1	trivial
9025.2.a.ct.1.23		24	5.4	even	2	inner
9025.2.a.cu.1.2		24	95.94	odd	2
9025.2.a.cu.1.23		24	19.18	odd	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:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37097 q^{2} +2.28512 q^{3} +3.62149 q^{4} -5.41794 q^{6} -1.63677 q^{7} -3.84450 q^{8} +2.22176 q^{9} +O(q^{10})\)	\(q-2.37097 q^{2} +2.28512 q^{3} +3.62149 q^{4} -5.41794 q^{6} -1.63677 q^{7} -3.84450 q^{8} +2.22176 q^{9} +2.72748 q^{11} +8.27553 q^{12} +6.19933 q^{13} +3.88073 q^{14} +1.87222 q^{16} +3.12451 q^{17} -5.26771 q^{18} -3.74021 q^{21} -6.46676 q^{22} -7.29904 q^{23} -8.78514 q^{24} -14.6984 q^{26} -1.77838 q^{27} -5.92756 q^{28} -2.22572 q^{29} -4.42666 q^{31} +3.25005 q^{32} +6.23260 q^{33} -7.40811 q^{34} +8.04607 q^{36} -2.04016 q^{37} +14.1662 q^{39} -3.92482 q^{41} +8.86793 q^{42} -0.472856 q^{43} +9.87754 q^{44} +17.3058 q^{46} -2.30160 q^{47} +4.27823 q^{48} -4.32098 q^{49} +7.13986 q^{51} +22.4508 q^{52} -6.36387 q^{53} +4.21648 q^{54} +6.29258 q^{56} +5.27711 q^{58} -12.2661 q^{59} -4.79076 q^{61} +10.4955 q^{62} -3.63651 q^{63} -11.4502 q^{64} -14.7773 q^{66} -0.670960 q^{67} +11.3154 q^{68} -16.6791 q^{69} -2.63494 q^{71} -8.54155 q^{72} +6.51298 q^{73} +4.83714 q^{74} -4.46426 q^{77} -33.5876 q^{78} -4.12016 q^{79} -10.7291 q^{81} +9.30563 q^{82} -6.42396 q^{83} -13.5452 q^{84} +1.12113 q^{86} -5.08603 q^{87} -10.4858 q^{88} -17.3044 q^{89} -10.1469 q^{91} -26.4334 q^{92} -10.1154 q^{93} +5.45702 q^{94} +7.42673 q^{96} -0.129944 q^{97} +10.2449 q^{98} +6.05979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

Introduction

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